Answers
The graph of y=|x| would look like graph A
The reflected graph (mirrored image) would be graph D
Related Questions
what is the midpoint of the line segment
Answers
Answer:
The answer to your question is (-1, -1)
Step-by-step explanation:
Data
A (1, -6)
B (-3, 4)
Formula
Xm = [tex]\frac{x1 + x2}{2}[/tex]
Ym = [tex]\frac{y1 + y2}{2}[/tex]
Process
1.- Substitute the values in the formula
x1 = 1 x2 = -3
Xm = [tex]\frac{1 - 3}{2} = \frac{-2}{2} = -1[/tex]
y1 = -6 y2 = 4
Ym = [tex]\frac{-6 + 4}{2} = \frac{-2}{2} = -1[/tex]
2.- The midpoint is (-1, -1)
An aquarium is to be drained. The aquarium is shaped like a rectangular prism with length 33 in , width 26 in , and height 12 in . Suppose water is pumped out of the aquarium at a rate of 396 in^3 per minute. If the aquarium starts completely full, how many minutes does it take to empty the aquarium?
Answers
Answer:
To empty the aquarium it takes 26 minutes
Step-by-step explanation:
step 1
Find the volume of the aquarium
The volume of rectangular prism is
[tex]V=LWH[/tex]
we have
[tex]L=33\ in\\W=26\ in\\H=12\ in[/tex]
substitute the given values
[tex]V=(33)(26)(12)=10,296\ in^3[/tex]
step 2
Divide the volume by the rate of 396 in^3 per minute
[tex]10,296/(396)=26\ minutes[/tex]
therefore
To empty the aquarium it takes 26 minutes
When planning his crops, Farmer Joe knows that his 5 acres can support corn and strawberries. He wants to make $5,500 from his crops. He can make $1,000 per acre of corn (the variable c) and $1,500 per acre of strawberries (the variable s). Which equation below would be a constraint in his system of equations?a. c + s = 5.
b. c − s = 5.c. 1,500c + 1,000s = 5,500.d. 1,500s − 1,000c = 5,500.
Answers
Answer:
Option a) c + s = 5.
Step-by-step explanation:
Let variable c represent acre of corn crop and variable s represent acre of strawberries crop.
5 acres can support corn and strawberries.
Thus, this can be expressed with the help of equation.
[tex]c + s = 5[/tex]
Farmer wants to make $5,500 from his crops.
He can make $1,000 per acre of corn and $1,500 per acre of strawberries.
This can be written as:
[tex]1000c + 1500s = 5500[/tex]
We have to find the constraint for the given system.
A constraint is something that limits or controls what we want to do. Here, the amount of land is limited and act as a constraint for the given situation.
Thus, the constraint for the given system is
Option a) c + s = 5.
In a psychology class, 32 students have a mean score of 93.2 on a test. Then 16 more students take the test and their mean score is 63.4.What is the mean score of all of these students together? Round to one decimal place.mean of the scores of all the students =
Answers
The mean score of all the students together, after calculating the combined total score and dividing by the total number of students, is 83.1.
Explanation:The subject of this question is the computation of the mean score of all students. The first step is to find the total score of both sets of students. For the first group, the total score is the mean score multiplied by the number of students, which is 93.2 * 32 = 2974.4. For the second group, total score is 63.4 * 16 = 1014.4. The combined total score is 2974.4 + 1014.4 = 3988.8. Since there are 32 + 16 = 48 students in total, the mean score of all students is calculated by dividing the combined score by the total number of students. So, the mean score of all the students together is 3988.8 / 48 = 83.1 (rounded to one decimal place).
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There are 360 students in front of the school waiting for buses to transport them to a museum each bus can transport no more than 42 students what is the minimum number of buses needed to transport all of the students to the museum
Answers
But you can’t have half a coach so you will need 9 coaches
Answer:
the answer is a
Step-by-step explanation:
Which of the following is a polynomial function in factored form with zeros at –6, –2, and 3? a.f(x) = (x + 6)(x + 2)(x – 3) b.f(x) = x3 + 5x2 – 12x – 36 c.f(x) = (x – 6)(x – 2)(x + 3) d.f(x) = x3 – 5x2 – 12x + 36
Answers
Answer:
a) f(x) = (x + 6)(x + 2)(x – 3)
b) [tex]f(x) = x^3 + 5x^2 - 12x - 36[/tex]
Step-by-step explanation:
We have to find the polynomial with zeroes as -6, -2, and 3.
Roots are those values of x for which the polynomial is zero.
a) f(x) = (x + 6)(x + 2)(x – 3)
[tex]f(x) = (x + 6)(x + 2)(x -3)=0\\\Rightarrow x+6 = 0, x+2 = 0, x-3 = 0\\\Rightarrow x = -6,x = -2, x = 3[/tex]
b)
[tex]f(x) = x^3 + 5x^2 - 12x - 36 \\\text{It can be factored as}\\f(x) = (x+6)(x-3)(x+2) = 0\\\Rightarrow (x+6)=0,(x-3)=0,(x+2)=0\\\Rightarrow x = -6, x = 3, x = -2[/tex]
c) f(x) = (x – 6)(x – 2)(x + 3)
[tex]f(x) = (x - 6)(x - 2)(x + 3) =0\\\Rightarrow (x -6)(x -2)(x + 3) = 0\\\Rightarrow (x -6)=0,(x -2)=0,(x + 3)=0\\\Rightarrow x = 6, x = 2, x = -3[/tex]
d)
[tex]f(x) = x^3 - 5x^2 - 12x + 36\\f(x) = (x-2)(x+3)(x-6)=0\\\Rightarrow (x-2) = 0, (x+3)=0,(x-6)=0\\\Rightarrow x =2, x = -3, x = 6[/tex]
There are 950 students at Hanover High School. The ratio of the number of freshmen to all students is 3:10. The ratio of the number of sophomores to all students is 1:2. What is the ratio of the number of freshmen to sophomores?
Answers
Hi there! Since the ratios of students at Hanover High School are in different scales, we need to scale them up! First, let's take the ratio 1:2. This can be scaled up to 5:10. Now, combine the two ratios to find the ratio of freshmen to sophomores. 3:10 + 5:10 = 8:10. The remaining number is 2, since 8 + 2 = 10, so the ratio of freshmen to sophomores is 2:10!
Hope this was helpful!
Use the position function s(t) = −16t² + 400, which gives the height (in feet) of an object that has fallen for t seconds from a height of 400 feet. The velocity at time t = a seconds is given by [tex]\underset{(t \rightarrow a)}{lim} \frac{s(a) - s(t)}{a-t}[/tex]. A construction worker drops a full paint can from a height of 500 feet. When will the paint can hit the ground? At what velocity will the paint can impact the ground?
Answers
Answer:
160m/s
Step-by-step explanation:
The object can hit the ground when t = a; meaning that s(a) = s(t) = 0
So, 0 = -16a² + 400
16a² = 400
a² = 25
a = √25
a = 5 (positive 5 only because that's the only physical solution)
The instantaneous velocity is
v(a) = lim(t->a) [s(t) - s(a)]/[t-a)
Where s(t) = -16t² + 400
and s(a) = -16a² + 400
v(a) = Lim(t->a) [-16t² + 400 + 16a² - 400]/(t-a)
v(a) = Lim(t->a) (-16t² + 16a²)/(t-a)
v(a) = lim (t->a) -16(t² - a²)(t-a)
v(a) = -16lim t->a (t²-a²)(t-a)
v(a) = -16lim t->a (t-a)(t+a)/(t-a)
v(a) = -16lim t->a (t+a)
But a = t
So, we have
v(a) = -16lim t->a 2a
v(a) = -32lim t->a (a)
v(a) = -32 * 5
v(a) = -160
Velocity = 160m/s
Using movement concepts, it is found that:
The object hits the ground after 5.59 seconds.The object hits the ground at a velocity of -178.88 feet per second.----------------------------------
The height of the object after t seconds, dropped from a height of 500 feet, is given by:
[tex]h(t) = -16t^2 + 500[/tex]
----------------------------------
It hits the ground when [tex]h(t) = 0[/tex], thus:
[tex]h(t) = 0[/tex]
[tex]-16t^2 + 500 = 0[/tex]
[tex]16t^2 = 500[/tex]
[tex]t^2 = \frac{500}{16}[/tex]
[tex]t = \sqrt{\frac{500}{16}}[/tex]
[tex]t = 5.59[/tex]
The object hits the ground after 5.59 seconds.
----------------------------------
The velocity is the derivative of the position, thus:
[tex]v(t) = h^{\prime}(t) = -32t[/tex]
The velocity when it impacts the ground is v(5.59), thus:
[tex]v(5.59) = -32(5.59) = -178.88[/tex]
The object hits the ground at a velocity of -178.88 feet per second.
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The vector product of vectors A and B has magnitude 12.0 m² and is in the +z-direction. Vector A has magnitude 8.0 m and is in the −x-direction. Vector B has no x-component.
Part A: What is the magnitude of vector B?
Part B: What is the direction angle θ of vector B measured from the +y-direction to the +z-direction?
Answers
Final answer:
The magnitude of vector B is 1. There is no valid direction angle theta for vector B.
Explanation:
Part A:
The magnitude of vector B can be found using the formula for the magnitude of the vector product:
|A x B| = |A||B|sin(theta)
Given |A x B| = 12, |A| = 8, and |B| = ?
Using the formula above, we can solve for |B|:
12 = 8 * |B| * sin(theta)
sin(theta) = 12 / (8 * |B|) = 1.5 / |B|
Sine of any angle lies between -1 and 1, therefore 1.5 / |B| should lie in this range
|-1| <= 1.5 / |B| <= |1|
1 <= 1.5 / |B| <= 1
1.5 <= |B| <= 1
The magnitude of vector B is 1.
Part B:
The direction angle theta can be found using the formula:
cos(theta) = Bz / |B|
Given Bz = |B| and sin(theta) = 1.5 / |B|
1.5 / |B| = sqrt(1 - sin^2(theta)) = sqrt(1 - 1) = sqrt(0) = 0
This implies that sin(theta) = 1.5 / |B| = 0, which is not possible
Hence, there is no valid direction angle theta for vector B.
Final answer:
The magnitude of vector B is 1.5 m. The direction angle θ of vector B measured from the +y-direction to the +z-direction is 90°.
Explanation:
Part A: To find the magnitude of vector B, we need to use the relationship between the magnitude of the vector product A x B and the magnitudes of vectors A and B. According to the given information, the magnitude of the vector product A x B is 12.0 m². Since the vector product is in the +z-direction, we can conclude that the magnitudes of vectors A and B multiplied by the sine of the angle between them equals 12.0 m².
Let's use this information to find the magnitude of vector B:
|A x B| = |A||B|sin(θ)
12.0 m² = 8.0 m * |B| * sin(90°)
|B| = 12.0 m² / (8.0 m * sin(90°))
|B| = 12.0 m² / 8.0 m = 1.5 m
Therefore, the magnitude of vector B is 1.5 m.
Part B: To find the direction angle θ of vector B measured from the +y-direction to the +z-direction, we can use the relationship between the components of vectors A and B and the direction angle θ:
tan(θ) = By / Bz
Substituting the given information into the equation:
tan(θ) = 0 / Bz
Since vector B has no x-component, we know that Bx = 0. Therefore, we only need to find the value of Bz to determine the direction angle θ.
Recall that |B| = 1.5 m. Using the Pythagorean theorem, we can find the value of Bz:
|B|² = Bx² + By² + Bz²
(1.5 m)² = (0)² + (0)² + Bz²
Bz² = (1.5 m)²
Bz = 1.5 m
Since Bz > 0, we know that the direction angle θ is in the positive range. In this case, the direction angle θ is 90° measured from the +y-direction to the +z-direction.
The problems about the Exeter spring and the Canadian plains contain relationships that are called direct variations. In your own words, describe what it means for one quantity to vary directly with another. Which of the following describe direct variations? (a) The gallons of water in a tub and the number of minutes since the tap was opened. (b) The height of a ball and the number of seconds since it was thrown. (c) The length of a side of a square and the perimeter of the square. (d) The length of a side of a square and the area of the square.
Answers
Answer:
(a) The gallons of water in a tub and the number of minutes since the tap was opened.
(c) The length of a side of a square and the perimeter of the square.
(d) The length of a side of a square and the area of the square.
Step-by-step explanation:
Direct variation:
When one quantity increases with the another quantity , they are said to be in direct proportion.An increase in one quantity leads to a proportional increase in another quantity, then, the quantity is said to vary directly with another.Mathematically, it can be expressed as:[tex]\text{If y varies directly with x}\\y = kx\\\text{where k is a proportionality constant.}[/tex]
(a) The gallons of water in a tub and the number of minutes since the tap was opened.
As the minutes for which the tap is opened increases, there is an increase in the amount of water in tub.
Thus, there is a direct variation between the gallons of water in a tub and the number of minutes since the tap was opened.
(b) The height of a ball and the number of seconds since it was thrown.
As the time increases after the ball was thrown, its height increases. But after some time the height decreases and becomes zero.
Thus, this not an example of direct variation.
(c) The length of a side of a square and the perimeter of the square.
As the side of square increases the perimeter increases.
Thus, there is a direct variation between length of a side of a square and the perimeter of the square.
(d) The length of a side of a square and the area of the square.
As the side of square increases the area increases.
Thus, there is a direct variation between length of a side of a square and the area of the square.
Given the functions f(x)=x-7 and g(x)=x^2+1, evaluate (f*g)(-1).
I keep getting -16, but that's not an answer choice...?
Answers
For this case we have the following functions:
[tex]f (x) = x-7\\g (x) = x ^ 2 + 1[/tex]
We must find [tex](f * g) (x)[/tex]. By definition we have to:
[tex](f * g) (x) = f (x) * g (x)[/tex]
So:
[tex](f*g)(x)=(x-7)(x^2+1)[/tex]
We apply distributive property:
[tex](f * g) (x) = x ^ 3 + x-7x ^ 2-7\\(f * g) (x) = x ^ 3-7x ^ 2 + x-7[/tex]
We evaluate at [tex]x = -1:[/tex]
[tex](f * g) (- 1) = (- 1) ^ 3-7 (-1) ^ 2 + (- 1) -7\\(f * g) (- 1) = - 1-7 (1) -1-7\\(f * g) (- 1) = - 1-7-1-7[/tex]
Equal signs are added and the same sign is placed:
[tex](f * g) (- 1) = - 16[/tex]
Answer:
[tex](f * g) (- 1) = - 16[/tex]
In an analysis of the environmental impact of a community's motor vehicle use, which of the following is best represented by "a" in the I = P x A x T equation?
a) energy efficiency of motor vehicles.
b) the number of cars owned by each household.
c) average family size.
d) the average daily commute by motor vehicles.
Answers
Answer:
The answer is B.
Step-by-step explanation:
The variable A in the I=PAT equation stands for affluence. It represents the average consumption of each person in the population. As the consumption of each person increases, the total environmental impact increases as well. The choice B is the best choice that represents average consumption of each person in the population.
The sum of frequencies for all classes will always equal Question 1 options: the sample size a value between 0 and 100 the number of classes 1?
Answers
Answer: 100
Step-by-step explanation:
The sum of frequencies for all classes will always equal to the number of element in a data set.
Between 0-100 there will be 100 numbers.
So that it's 100
In the field of statistics, when you group data into classes, the sum of the frequencies always equates to the sample size. The reason is that every element or member of your sample belongs to only one class.
Explanation:In statistics, the term frequency is related to the times a data value occurs. When dealing with numerical datasets grouped into classes for data analysis, the sum of frequencies for all classes always equals the total sample size. This is because every member of the sample belongs to one and only one class. For example, if you conducted a survey on the favorite fruits of 100 people (your sample size), and you grouped the responses into classes - apples, bananas, oranges, etc., the sum of the frequencies (i.e., the total number of people that prefer each fruit) should add up to 100 (the sample size).
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Find an equation of the line that (a) has y-intercept of 7 and (b) is parallel to the line -5x-6y=1
Write your answer in the form y=mx+b
Answers
Answer:
The answer to your question is 5x + 6y - 42 = 0
Step-by-step explanation:
Data
y-intercept = 7
parallel to -5x - 6y = 1
Process
1.- Find the slope
- 6y = 5x + 1
y = -5/6 x - 1/6
As the lines are parallels, the slope is the same in both lines
m = -5/6
2.- Find the equation of the new line
If the line has a y-intercept of 7, it means that the point is (0, 7)
y - y1 = m(x - x1)
Substitution
y - 7 = -5/6 (x - 0)
Simplification
y - 7 = -5/6x
Equal to zero
5/6x + y - 7 = 0
Multiply by 6
5x + 6y - 42 = 0 This is the equation of the line
Answer:
6y = -5x + 42
Step-by-step explanation:
-5x - 6y = 1
-6y = 5x + 1---------------------(i)
y = -5x/6 - 1/6
comparing the equation above with y = mx + c, we have;
m = -5/6
for condition of parallelism
the gradient of the new line = -5/6
Using the formula
y = mx + c
y = -5x/6 + 7
6y = -5x + 42
Please help!
Find the solutions of each equation on the interval [0,2pi).
(SHOW WORK)
Picture below.
Answers
Answer:
x = 0
Step-by-step explanation:
The argument x+3π/2 shifts the sine function 3π/2 to the left, making it equivalent to -cos(x). Then the equation becomes ...
-2cos(x) = -2
cos(x) = 1
On the interval [0, 2π), cos(x) is only 1 at x=0.
James Smith and Bill Ross purchased a property together for their business venture with stated proportionate interest of 1/3 and 2/3 respectively without the right of survivorship. Each of them wants his share to be inherited by his wife. They are a partnership and not a corporation. James and Bill most likely took title as:_________
A) joint tenants.
B) tenants in common.
C) in severalty.
D) a general partnership.
Answers
Answer:
B) tenants in common.
Explanation:
There were two men, first was James Smith, and second was Bill Ross who bought a property mutually for their business venture by declared proportionate interest of 1/3 as well as 2/3 sequentially without the right regarding survivorship. Both of them want their shares to be acquired by their spouses'. Both hold a partnership but not a company. James, as well as Bill, most likely took the title as tenants in common. Because tenants in common possess versatility in whence they divide control as well as assign the rights concerning survivorship. Joint tenants, on the different hand, keep the property in similar shares while a common partnership is a business unit serving separate sharers. Severalty, as asserted beforehand, is individual ownership.
Write an expression for the rate of change of the height of the dough with respect to the radius of the dough in terms of height h and radius r.
Answers
Answer:
[tex]h'=\frac{dh}{dr}=-\frac{2}{r^3\pi}[/tex]
Step-by-step explanation:
Assuming the dough is of cylindrical shape and that the volume must stay the same the equation for the volume of the cylinder is the following:
[tex]V=r^2\pi h[/tex]
where V is the volume, r the radius and h the height of the cylinder. If you get h to the left hand side you get the following equation:
[tex]h=\frac{V}{r^2\pi}[/tex]
To find the rate of change of the height you need to derive the above equation with respect to r:
[tex]h'=-\frac{2}{r^3\pi}[/tex]
Rate of change is simply how much a quantity changes, over another.
The expression for the rate of change of the dough in terms of height h and radius r is [tex]\mathbf{h' = \frac{-2}{\pi r^3}}[/tex]
From the complete question, we have:
[tex]\mathbf{V = \pi r^2h}[/tex]
Next, we make h the subject
[tex]\mathbf{h = \frac{V}{\pi r^2}}[/tex]
Rewrite as:
[tex]\mathbf{h = \frac{V}{\pi}r^{-2}}[/tex]
Differentiate with respect to r
[tex]\mathbf{h' = -2\times \frac{V}{\pi}r^{-2-1}}[/tex]
[tex]\mathbf{h' = -2\times \frac{V}{\pi}r^{-3}}[/tex]
Rewrite as:
[tex]\mathbf{h' = \frac{-2V}{\pi r^3}}[/tex]
Remove V, to leave the answer in terms of r and h
[tex]\mathbf{h' = \frac{-2}{\pi r^3}}[/tex]
Hence, the expression for the rate of change of the dough in terms of height h and radius r is [tex]\mathbf{h' = \frac{-2}{\pi r^3}}[/tex]
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A salesperson at an electronic store is given a choice of two different compensation plans. Plan A pays him a weekly salary of $250 plus a commission of $25 for each stereo sold. Plan B offers no salary but pays $50 commission on each stereo sold. How many stereos must the salesperson sell to make the same amount of money with both plans?
Answers
Answer:
10 stereos must the salesperson sell to make the same amount of money with both plans.
Step-by-step explanation:
Let the Number of stereo sold = x
According to Plan A
250 + 25X
According to Plan B
50X
According to given condition
250 + 25X = 50X
250 = 50X - 25X
250 = 25X
X = 250/25
X= 10
In a collection of toys, 1/2 are red, 1/2 are waterproof, and 1/3 are cool. 1/4 are red and waterproof. 1/6 are red and cool. 1/6 are waterproof and cool. 1/6 are neither red, waterproof, nor cool. Each toy has an equal chance of being selected.Draw an area diagram to represent these events.
Answers
Answer:
only red = 1/12, only water proof = 1/12 , only cool = nil we assume nil for toys with three collections( cool, red, waterproof) as it was not stated.
11/6 are neither red, water proof and cool.
Step-by-step explanation:
outside the circles contain probability of neither red, cool and water proof. where the circles intersect shows probability of both either red and cool, water proof and cool and water proof and red etc. where all the circles intersect if for the three combinations which is nill. Attached is the diagram
Answer:
The answer representation is attached below
Step-by-step explanation:
This is a representation on a diagram.
n(R) = Number of red toys
n(WP) Number of water proof toys
n(C) = Number of cool toys
n(R∩WP) = Number of red and waterproof
n(R∩C) = Number of red and cool
n(WP∩C) = Number of waterproof and cool
n(R'∩WP∩C) = Neither red, waterproof nor cool
From the image as depicted on a venn diagram, each part is represented and filled ont the diagram, the small circle space filled represent the information given in the question.
A veterinarian's office recorded one particular week that they had 50 patients. The following table shows the recorded number of dogs.
Monday Tuesday Wednesday Thursday Friday
7 4 5 5 2
The formula for standard error is given below, where represents the sample proportion, and n is the total number of elements in the sample.
Use the given data to complete the table below.
Percentage of patients that were dogs [23%; 42%; 22%; 46%]
Standard error [.07; .09; .05; .16]
Margin of error 90% confidence interval [(32%, 60%)(34%,58%)(6%, 23%)(5%,21%)]
Margin of error 95% confidence interval [(32%, 60%)(34%,58%)(6%, 23%)(5%,21%)]
Answers
Answer:
1. The correct answer is 46%
2. The correct answer is .07
3. The correct answer is (34%,58%)
4. The correct answer is (32%,60%)
Step-by-step explanation:
1. Let's calculate the percentage or proportion of patients that were dogs:
p = (7 + 4 + 5 + 5 + 2)/50 = 23/50 = 0.46
The correct answer is 46%
2. Let's estimate the standard error, using the given formula, this way:
S.e = √ (0.46 * 0.54)/50 = √0.049 = 0.07
The correct answer is .07
3. Let's calculate the confidence limits of the 90% confidence interval, this way:
Confidence limits = proportion +/- 1.645 * standard error
Confidence limits = 0.46 +/- 1.645 * 0.07
Confidence limits = 0.46 +/- 0.12
Confidence limits = 0.34, 0.58
The correct answer is (34%,58%)
4. Let's calculate the confidence limits of the 95% confidence interval, this way:
Confidence limits = proportion +/- 1.96 * standard error
Confidence limits = 0.46 +/- 1.96 * 0.07
Confidence limits = 0.46 +/- 0.14
Confidence limits = 0.32, 0.60
The correct answer is (32%,60%)
Answer:
46%
0.07
(34%,58%)
(32%,60%)
Step-by-step explanation:
i got it right
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What is the slope of the line that contains the points (-1 , 8) and (5, -4)?
A -1/2
B -2
C 1/2
D 2
Answers
Answer:
B ) -2
Step-by-step explanation:
slope of given points
slope [tex]m= \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
The given points are
[tex]m = \frac{-4-8}{5-(-1)}[/tex]
[tex]m=\frac{-12}{6}[/tex]
[tex]m=-2[/tex]
final answer :-
slope of the line is m=-2
The line y = 5x/3 + b goes through the point (7, –1). What is the value of b?
(A) 3
(B) –5/3
(C) –7/5
(D) 16/3
(E) –38/3
Answers
Answer:
[tex]y=\frac{5}{3} x-\frac{38}{3}[/tex]
the value of b is -38/3
Step-by-step explanation:
[tex]y=\frac{5}{3} x+b[/tex] goes through the point (7,-1)
we need to find out b for the given equation using (7,-1)
Plug in 7 for x and -1 for y
[tex]y=\frac{5}{3} x+b[/tex]
[tex]-1=\frac{5}{3} (7)+b[/tex]
[tex]-1=\frac{35}{3}+b[/tex]
subtract 35/3 from both sides
[tex]-1 -\frac{35}{3} =b[/tex]
[tex]\frac{-38}{3} =b[/tex]
Replace it in the original equation
[tex]y=\frac{5}{3} x-\frac{38}{3}[/tex]
A small radio transmitter broadcasts in a 44 mile radius. If you drive along a straight line from a city 56 miles south of the transmitter to a second city 53 miles west of the transmitter, during how much of the drive will you pick up a signal from the transmitter? (Hint: you will need to find the equations of the circle and line, the intersection and the differnence of the distances.) Please also show work for finding the points of intersection.
Answers
Answer:
the transmitter signal is picked up for 42.63m of the drive.
Ans = 42.63m
Step-by-step explanation:
Solution
Let triangle ABC formed by line from 56 miles south of transmitter, to the transmitter itself then to 53 miles west of the transmitter with sides
AB BC AC
Where AB = 56 miles
and BC = 53 miles
Therefore AC = Sqr((56m)^2 +(53m)^2) = 77.10m
The point of intersection of the radius of the radio transmitter signal and the triangle formed by the path of travel of the traveller and the lines AB and AC
To find the perpendicular line that can be drawn from C to AB we have from trigonometric relations
56 × sin(t) = 53 × sin (90 - t) because the traveller moves from directly south of the transmitter to directly west of the transmitter
Hence we have
56×sin(t) = 53×cos(t) because sin(90-t) = cos(t)
Rearranging 56×sin(t) = 53×cos(t) we have
1=(56×sin(t))/ (53×cos(t))
or (sin(t)/ cos(t))=1/(56/53)=53/56
That is tan(t)=53/56 and ACTAN(t) = 43.42°
Angle (t)
Drawing a perpendicular line from the point of the radio transmitter C to the travel path of the traveller AB and calling the point of Intersection E we have EC = 53×sin(43.42)=38.49m
It is seen that the distance from the point of intersection of the radius of the radio transmitter and intersection of the line CE and AB is EI1 where I1 is the first point of intersection of the radius of the radio transmitter and the line AB
EI1=Sqr((44m)^2-(38.49m)^2)
= 21.31m
Also since the triangles CEI1 and CEI2 are identical, it follows that EI1 = EI2 = 21.32m
The distance over which the traveller will be able to receive the signal from the radio transmitter while travelling from point A to point B is the distance I1 to I2 which is equal to 2*I
=2×21.31=42.63m
Ans = 42.63m
The signal will be picked up for approximately 3.015 miles of the drive.
To solve this, first, find the equations of the circle and the line representing the transmitter's broadcast range and the path of the drive, respectively.
Then, find the intersection points. Calculate the distances from these points to the transmitter.
Determine the portion of the drive where the distance is within the broadcast range (44 miles).
It turns out the signal is picked up only for a short portion of the drive near one of the intersection points.
1. Equation of the Circle:The equation of a circle with center (h, k) and radius r is:
(x - h) ²+ (y - k)² = r²
Given that the transmitter broadcasts in a 44-mile radius and assuming the center of the circle is at the origin (0,0) the equation of the circle is:
x² + y² = 44²
2. Equation of the Line:The equation of a straight line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Given that the drive is along a straight line from a city 56 miles south of the transmitter to a second city 53 miles west of the transmitter, the line can be represented as:
y = - 56/53 * x + 56
Next, we'll find the points of intersection between the circle and the line, which is step 3.
Substitute y = - 56/53 * x + 56 into x² + y² = 44² to solve for the x-coordinates of the intersection points. Then, use these x-coordinates to find the corresponding y-coordinates.
x² + (- 56/53 * x + 56)² = 44²
Expanding and simplifying this equation will give us a quadratic equation in x, which we can solve to find the x-coordinates of the intersection points.
x² + (3136/2809 * x² - 5376/53 * x + 3136) = 44²
x² + 3136/2809 * x² - 5876/53 * x + 3136 - 44² = 0
59345/2809 * x² - 5376/53 * x + 3136 - 44² = 0
345x² - 150992x + 17424 - 44² * 2809 = 0
59345x² - 150992x + 0 = 0
3. Now, let's solve this quadratic equation. We can use the quadratic formula:x = (-b±√b-4ac)/2a
Where a = 59345, b = -150992, and c = 0
x= [150992±√(-150992)2-4(59345)(0)] / 2(59345)
x= (150992±√22793455664) / 118690
x₁= (150992±151034) / 118690
x₁ = 302026 / 118690 = 2.545
x₂ = (150992-151034) / 118690
x₂ = -42 / 118690
≈ -0.00035
Now, we'll find the corresponding y-coordinates by substituting these x-values into
the equation of the line y = - 56/53 * x + 56
For x =2.545:
y₁ = - 56/53 * 2.545 + 56
y₁ ≈ 1.615
For x ≈ -0.00035:
y₂ = - 56/53 * (- 0.00035) + 56
y₂ ≈ 56
So, the two points of intersection are approximately (2.545, 1.615) and (-0.00035, 56).
4. Determine the distances from these intersection points to the transmitter.The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √(x₂-x₁)² + (y₂ - y₁)²
Let's calculate the distances from these intersection points to the origin (transmitter),
which is (0,0).
For point (2.545, 1.615) :
[tex]d_1 = \sqrt{(2.545 - 0)^2 + (1.615 - 0)^2}[/tex]
d[tex]d_1 = \sqrt{2.545^2 + 1.615^2}[/tex]
[tex]d_1 \approx \sqrt{6.475 + 2.61}[/tex]
[tex]d_1 \approx \sqrt{9.085}[/tex]
[tex]d_1 \approx 3.015[/tex]
For point (-0.00035, 56):
[tex]d_2 = \sqrt{(-0.00035 - 0)^2 + (56 - 0)^2}[/tex]
[tex]d_2 = \sqrt{(-0.00035)^2 + 56^2}[/tex]
[tex]d_2 \approx \sqrt{0 + 3136}[/tex]
[tex]d_2 \approx \sqrt{3136}[/tex]
[tex]d_2 = 56[/tex]
5. Calculate the portion of the drive during which the signal will be picked up.Since the signal from the transmitter can be picked up within a 44-mile radius, we need to determine at what points along the path the distances to the transmitter are less than or equal to 44 miles.
From our calculations, we see that d₁ ≈ 3.015 miles and d₂ = 56 miles.
Thus, the signal will be picked up during the portion of the drive where
d₁ ≤ 44 miles.
Therefore, the signal will be picked up for approximately 3.015 miles of the drive.
Which expressions are equivalent to this expression?
3y+3z
3(y+z) 3y+z 10y+2z+y+z 6+y+3z
Answers
Only option 1: 3y+3z is equivalent to given expression
Step-by-step explanation:
In order to find the equivalent expression to given expression, we have to simplify each of the options to compare with the given expression
Given expression is:
[tex]3y+3z[/tex]
Option 1:
[tex]3(y+z)\\= 3y+3z[/tex]
Option 2:
[tex]3y+z[/tex]
Option 3:
[tex]10y+2z+y+z\\= 10y+y+2z+z\\= 11y+3z[/tex]
Option 4:
[tex]6+y+3z[/tex]
Hence,
Only option 1: 3(y+z) is equivalent to given expression
Keywords: Polynomials, expressions
Learn more about polynomials at:
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Using drt what is the Answer to this question a car in a bus set out at 2 PM find the same point headed in the same direction. The average speed of the car is 30 mph slower than twice the speed of the bus. In two hours the car is 20 miles ahead of the bus. Find the rate of the car
Answers
Answer: the rate of the car is 50mph
Step-by-step explanation:
Let x represent the average speed of the bus.
Let y represent the distance travelled by the bus.
The average speed of the car is 30 mph slower than twice the speed of the bus. This means that the average speed of the car would be
2x - 30
Distance = speed × time
Time = distance/speed
Therefore, In 2 hours time,
2 = y/x
2x = y
In two hours the car is 20 miles ahead of the bus. Therefore
2 = (y + 20)/(2x - 30)
2(2x - 30) = y + 20
4x - 60 = y + 20 - - - - - - - - -1
Substituting y = 2x into equation 1, it becomes
4x - 60 = 2x + 20
4x - 2x = 20 + 60
2x = 80
x = 80/2 = 40
The speed of the car would be
2x - 30 = 2 × 40 - 30
= 80 - 30 = 50 mph
A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?
a 3
b 4
c 6
d 7
Answers
Answer: A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?
a 3
b 4
c 6
d 7
Step-by-step explanation:
3lbs of Cashews
Answer:
Step-by-step explanation:
4x+(10-x)*6.5 =4.75*10
4x+65-6.5x=47.5
6.5 x-4 x=65-47.5
2.5 x=17.5
x=7
peanuts=7 -pound
cashews=10-7=3 -pound
Find the product of all constants t such that the quadratic x^2 tx - 9 can be factored in the form (x a)(x b), where a and b are integers.
Answers
Answer:
product of the constants P will be
P = 12
Step-by-step explanation:
the quadratic equation
F= x² + t*x - 9
has as solution
a and b= [-t ± √( t² - 4*1*(-9)) ] /2]
then
a - b = -t/2
a= b - t/2
since b is an integer , then t/2 should be an integer , then t=2*n , where n is any integer
also
a and b= [-t ± √( t² - 4*1*(-9)) ] /2] = [-2*n ± √(4*n²+36 )] /2 = -n ± n √ (1+9/ n²]
since n are integers , then √ (1+9/ n²] should be and integer and therefore
9/ n² should be an integer. Then the possible values of n are
n=1 and n=3
therefore the possible values of t are
t₁=2*1 = 2
t₂=2*3 = 6
the product of the constants P will be
P=t₁*t₂ = 12
Answer:
729
Step-by-step explanation:
Important Characteristics Quiz The probability of success in each of the 58 identical engine tests is p = 0.92. What is the mean of this binomial distribution?
Answers
Answer: The mean of this binomial distribution is 53.36.
Step-by-step explanation:
We know that , the mean of this binomial distribution is given by :_
[tex]\mu = np[/tex]
, where n = sample size or the number of possible trials .
p = probability of getting success in each trial.
We are given that , the probability of success in each of the 58 identical engine tests is p = 0.92.
i.e. n= 58
p=0.92
Then, the mean of this binomial distribution = [tex]58\times0.92=53.36[/tex]
Hence , the mean of this binomial distribution is 53.36.
The reaction time of a driver to visual stimulus is normally distributed with a mean of 0.4 seconds and a standard deviation of 0.05 seconds.(a) What is the probability that a reaction requires more than 0.5 second? (b) What is the probability that a reaction requires between 0.4 and 0.5 second? (c) What is the reaction time that is exceeded 90% of the time?
Answers
Answer:
a) [tex]P(X>0.5)=P(\frac{X-\mu}{\sigma}>\frac{0.5-\mu}{\sigma})=P(Z>\frac{0.5-0.4}{0.05})=P(z>2)[/tex]
[tex]P(z>2)=1-P(z<2)[/tex]
[tex]P(Z>2) = 1-P(Z<2)= 1- 0.97725=0.02275[/tex]
b)[tex]P(0.4<X<0.5)=P(\frac{0.4-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{0.5-\mu}{\sigma})=P(\frac{0.4-0.4}{0.05}<Z<\frac{0.5-0.4}{0.05})=P(0<z<2)[/tex]
[tex]P(0<z<2)=P(z<2)-P(z<0)[/tex]
[tex]P(0<z<2)=P(z<2)-P(z<0)=0.97725-0.5=0.47725[/tex]
c) [tex]a=0.4 +1.28*0.05=0.464[/tex]
So the value of height that separates the bottom 90% of data from the top 10% is 0.464.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
Let X the random variable that represent the reaction time of a driver to visual stimulus of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(0.4,0.05)[/tex]
Where [tex]\mu=0.4[/tex] and [tex]\sigma=0.05[/tex]
We are interested on this probability
[tex]P(X>0.5)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X>0.5)=P(\frac{X-\mu}{\sigma}>\frac{0.5-\mu}{\sigma})=P(Z>\frac{0.5-0.4}{0.05})=P(z>2)[/tex]
And we can find this probability using the complement rule:
[tex]P(z>2)=1-P(z<2)[/tex]
And using the normal standard table or excel we have this:
[tex]P(Z>2) = 1-P(Z<2)= 1- 0.97725=0.02275[/tex]
Part b
[tex]P(0.4<X<0.5)=P(\frac{0.4-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{0.5-\mu}{\sigma})=P(\frac{0.4-0.4}{0.05}<Z<\frac{0.5-0.4}{0.05})=P(0<z<2)[/tex]
And we can find this probability on this way:
[tex]P(0<z<2)=P(z<2)-P(z<0)[/tex]
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
[tex]P(0<z<2)=P(z<2)-P(z<0)=0.97725-0.5=0.47725[/tex]
Part c
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.10[/tex] (a)
[tex]P(X<a)=0.90[/tex] (b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.90 of the area on the left and 0.10 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.90 and P(z>1.28)=0.1
If we use condition (b) from previous we have this:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.9[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.9[/tex]
But we know which value of z satisfy the previous equation so then we can do this:
[tex]z=1.28=\frac{a-0.4}{0.05}[/tex]
And if we solve for a we got
[tex]a=0.4 +1.28*0.05=0.464[/tex]
So the value of height that separates the bottom 90% of data from the top 10% is 0.464.
Answer:
a) 0.0228
b) 0.4772
c) 0.336
Step-by-step explanation:
Mean(μ) = 0.4 seconds
Standard deviation (σ) = 0.05 seconds
From normal distribution,
Z= (x - μ) / σ
a) P(x > 0.5)
Let x be the random variable for the required seconds
When x= 0.5
Z = (0.5 - 0.4)/0.05
Z = 2
From the normal distribution table, 2= 0.4772
φ(Z) = 0.4772
Recall that when Z is positive,
P(x >a) = 0.5 - φ(Z)
P(x > 0.5) = 0.5 - 0.4772
= 0.0228
b) For x = 0.4
Z= (x - μ) / σ
= (0.4 - 0.4) / 0.05
= 0
For x= 0.5
Z= (x - μ) / σ
= (0.5 - 0.4) / 0.05
= 2
From the table, P(0.4 < x < 0.5) = P(0 < Z < 2)
So we have
P(Z < 2) - P(Z<0)
From the table, 2 = 0.4772 and 0 = 0
We then have
0.4772 - 0
= 0.4772
c) we are looking for x such that 90% of the values lie above it or 10% of the value lie below it.
From the table , 10% probability gives a z value of -1.28
x = μ + Zσ
x = 0.4 + (-1.28*0.05)
x = 0.4 - (1.28*0.05)
= 0.336
A line is a set of all points that:
Answers
A line is a set of all points that : C. are the same distance from two points.
Step-by-step explanation:
A line is defined as a set of all points that are the same distance from two given points. For a line to form, you must connect points, thus its correct to say a line is formed when you draw a locus of a given point.
Learn More
Definition of a line:https://brainly.com/question/1592203
Keywords: line, set , points
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