Answer:
A. slope = -2; point = (8, -3)
Step-by-step explanation:
Compare to the point-slope form for slope m and point (h, k).
y -k = m(x -h)
You see that k = -3, m = -2, h = 8, so ...
the slope is -2the point is (h, k) = (8, -3)Average speed of automobile = 35 mph.
Time of travel = 2.5 hrs.
Distance traveled = _____.
14
32.5
37.5
87.5
Answer:
87.5
Step-by-step explanation:
35*2.5= 87.5
since you are finding distance you have to multiply speed and time
hope this helps :)
3. A power line extends from a light pole 43 meters to the ground and makes an angle of 60 degrees with the ground. To the nearest tenth of a meter, how tall is the light pole? (2 points)
Answer:
[tex]37.2\ m[/tex]
Step-by-step explanation:
Let
h-----> the height of the light pole
we know that
In the right triangle of the figure
[tex]sin(60\°)=\frac{h}{43}[/tex]
[tex]h=sin(60\°)(43)=37.2\ m[/tex]
A flower is 9 3/4 inches tall.In one week,it grew 1 1/8 inches.How tall is the flower at the end of the week?
Answer:
the length of flower at the end of week is 10 7/8 inches.
Step-by-step explanation:
Original height = 9 3/4 inches
=> 39/4 inches
Growth in one week = 1 1/8 inches
=> 9/8 inches
The height by the end of week = Original height + growth
=> 39/4 + 9/8
=> (39*2)/4*2 + 9/8
=> 78/8 + 9/8
=> 87/8 inches
=> 10 7/8 inches
Therefore, the length of flower at the end of week is 10 7/8 inches.
Final answer:
To find the height of the flower at the end of the week, add the initial height of 9 3/4 inches to the growth of 1 1/8 inches, resulting in a new height of 10 7/8 inches.
Explanation:
The question asks how tall the flower will be at the end of the week after growing an additional 1 1/8 inches from its original height of 9 3/4 inches. To find the answer, you simply add these two measurements.
First, convert the mixed numbers to improper fractions to make them easier to add:
9 3/4 inches is the same as (9 × 4 + 3)/4 = 39/4 inches.1 1/8 inches is the same as (1 × 8 + 1)/8 = 9/8 inches.Now, add the two improper fractions together:
(39/4) + (9/8) = (39/4) × (2/2) + (9/8) = (78/8) + (9/8) = 87/8
Convert 87/8 back to a mixed number:
87 divided by 8 is 10 with a remainder of 7, so the mixed number is 10 7/8 inches.
So, the flower will be 10 7/8 inches tall at the end of the week.
Solve the equation. Round to the nearest hundredth. Show work.
[tex]2.8[/tex] · [tex]13^{4x} +4.8 = 19.3[/tex]
Answer:
Final answer is approx x=0.16.
Step-by-step explanation:
Given equation is [tex]2.8\times 13^{4x} +4.8 = 19.3[/tex]
Now we need to solve equation [tex]2.8\times 13^{4x} +4.8 = 19.3[/tex] and round to the nearest hundredth.
[tex]2.8\times 13^{4x} +4.8 = 19.3[/tex]
[tex]2.8\times 13^{4x} = 19.3-4.8 [/tex]
[tex]2.8\times 13^{4x} = 14.5 [/tex]
[tex]13^{4x} = \frac{14.5}{2.8} [/tex]
[tex]13^{4x} = 5.17857142857 [/tex]
[tex]\log(13^{4x}) = \log(5.17857142857) [/tex]
[tex]4x \log(13) = \log(5.17857142857) [/tex]
[tex]4x = \frac{\log(5.17857142857)}{\log\left(13\right)} [/tex]
[tex]4x = 0.641154659628 [/tex]
[tex]x = \frac{0.641154659628}{4} [/tex]
[tex]x = 0.160288664907 [/tex]
Round to the nearest hundredth.
Hence final answer is approx x=0.16.
Factor the expression below.
[tex]x^{2} - 10x + 25[/tex]
A. (x - 5)(x - 5)
B. (x + 5)(x + 5)
C. (x - 5)(x + 5)
D. 5(x2 - x + 5)
Answer:
A. (x - 5)(x - 5)
Step-by-step explanation:
We will do this the old fashioned way...just plain old factoring.
This polynomial is of the form
[tex]y=ax^2+bx+c[/tex]
The product of a and c have to add up to equal the "middle" term, -10.
a = 1, b = -10, c = 25
a * c = 1 * 25 = 25
Now we need the factors of 25 to find the combination of factors that will result in a -10. The factors of 25 are: 1, 25 and 5, 5
5 and 5 add up to be 10, but since we need a -10, we will use -5 and -5. The product of -5 * -5 = 25, so we are not messing anything up by using the negative 5.
Putting them in order in standard form we have
[tex]x^2-5x-5x+25[/tex]
Factor by grouping:
[tex](x^2-5x)-(5x+25)[/tex]
There is an x common to both terms in the first set of parenthesis, so we will factor that out; there is a 5 common to both terms in the second set of parenthesis, so we will factor that out:
x(x - 5) - 5(x - 5)
NOW what's common in both terms is the (x - 5) so we factor THAT out, and what's left gets grouped together:
(x - 5)(x - 5)
What is the inverse of the following statement? If two triangles are congruent, then their corresponding angles are congruent. If two triangles are congruent, then their corresponding angles are congruent. If the corresponding angles of two triangles are congruent, then the triangles are congruent. If two triangles are not congruent, then their corresponding angles are not congruent. If the corresponding angles of two triangles are not congruent, then the triangles are not congruent.
Answer:
The two triangles may be congruent, but additional information is needed about the third angle in each triangle
Answer:
If the corresponding angles of two triangles are not congruent, then the triangles are not congruent.
Step-by-step explanation:
What is the inverse of the following statement? If two triangles are congruent, then their corresponding angles are congruent.
Inverse of a statement means its opposite or negating both the hypothesis and conclusion of a conditional statement.
So, the inverse of the given statement will be :
If the corresponding angles of two triangles are not congruent, then the triangles are not congruent.
The price of a book increased from $20 to $25. What is the markup rate?
20%
25%
3%
5%
Answer: The price of a book increased from $20 to $25. What is the markup rate?
The area of a rectangular room is 120 square feet. The width is 10 feet. What is the length?
The length of the rectangular room is 12 ft
To find the length of the rectangular room by using the formula for the area of a rectangle:
Area = Length * Width
Given that Area of a rectangular room = 120 [tex]ft^{2}[/tex]
Width = 10 ft
Length = ?
To calculate the length of the rectangular room,
Length = Area/Width
Length = 120/10
Length = 12 ft
Therefore, the length of the rectangular room is 12 ft
1. Preliminaries We (the RAF in World War II) want to know the number of warplanes fielded by the Germans. That number is N. The warplanes have serial numbers from 1 to N, so N is also equal to the largest serial number on any of the warplanes. We only see a small number of serial numbers (assumed to be a random sample with replacement from among all the serial numbers), so we have to use estimation. Question 1.1 Is N a population parameter or a statistic? If we use our random sample to compute a number that is an estimate of N, is that a population parameter or a statistic? Write your answer here, replacing this text. Check your answer with a neighbor or a TA. To make the situation realistic, we're going to hide the true number of warplanes from you. You'll have access only to this random sample:
Answer:
N is a population parameter; the estimate of N is a statistic.
Step-by-step explanation:
A measure of a population is called a parameter. The population is the entire set we are measuring. In this problem, N is the total number of warplanes fielded by the Germans. Since it is the total, it is a population, making it a parameter.
A measure of a sample is a statistic. This means an estimate of N based on a sample would be a statistic.
In the context of the RAF's scenario, N is a population parameter representing the number of German warplanes in World War II. However, using the observed serial numbers to estimate N would produce a statistic, which may not be accurate as it corresponds to a sample rather than the total population.
Explanation:In the given scenario, N is a population parameter. It represents the total number of warplanes built by Germany. A parameter represents a factual characteristic about a population. Estimating N from the observed serial numbers on the warplanes is a statistic. A statistic is derived from a sample, and it is used to estimate a population parameter when we don't have access to the full population.
For instance, suppose the RAF captures some German warplanes, and the highest observed serial number is 5000. They might then estimate that the Germans produced around 5000 planes (which would be a statistic). But this estimate could be incorrect since they're basing it on a sample rather than the total population of German warplanes (i.e., all the planes built by Germany).
This method for estimating N is similar to a technique called mark and recapture in biology, where scientists mark a number of individuals in a population, release them back into their natural environment, and later recapture a number of individuals. Using the ratio of marked to unmarked individuals in the recaptured sample, scientists can estimate the total population size.
Learn more about Estimating Population from Sample here:https://brainly.com/question/35639662
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Jim wants to collect at least 25 coins for his coin collection. He has already collected 5 coins. The inequality shown can be used to find n, the number of coins Jim still needs to collect. N + 5 ? 25 Which inequality represents the solution set for this situation? A) n ? 20 B) n ? 20 Eliminate C) n ? 30 D) n ? 30
Answer:
The answer is A for sure
Step-by-step explanation:
And this is why
n ≥ 20
n + 5 ≥ 25
n + 5 − 5 ≥ 25 − 5
n ≥ 20
Inequality shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
The inequality that represents the solutions set is
n ≥ 20.
Option A is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Jim wants to collect at least 25 coins for his coin collection. He has already collected 5 coins.
The inequality shows the above situation.
n + 5 ≥ 25
Subtract 5 on both sides.
n ≥ 25 - 5
n ≥ 20
Thus,
The inequality that represents the solutions set is
n ≥ 20.
Option A is the correct answer.
Learn more about inequalities here:
https://brainly.com/question/20383699
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Which dilation shows an enlargement?
SEE attached IMAGE!
The last one does
in the first for the image (the letters with ') are on the smaller shape where as on the last one it is on the bigger shape meaning it is the enlargement of TYO
Answer:
the last one
Step-by-step explanation:
I did this assignment.
Help, please with this question!! I don't understand!!
Answer:
this is basic math area and primeemator
so take the triangles and put them together then add it up so it would look like this 9+9+11.75+11.75 = 41.5 them times 41.5 times the price per foot like this
41.5 X 4.25 = 176.38 thats how mush he would have to pay
Answer: $449.44
Step-by-step explanation: please see images below!
Find sin and tan (Picture provided)
Answer:
The correct option is
Option d. Sin θ = -√65/9 and Tan θ = -√65/4
Step-by-step explanation:
Points to remeber
Sin θ = Opposit side/ Hypotenuse
Cos θ = Adjacent side/Hypotenuse
Tan θ= Opposite side /Adjacent side
To find opposite side
It is given that,
Cos θ = -4/9 = Adjacent side/Hypotenuse
We can find opposite side of angle θ
opposit side ² = Hypotenuse² - adjacent side² = 9² - 4²
= 81 - 16 = 65
Opposite side = √65
To find sinθ and tanθ
Sin θ = Opposit side/ Hypotenuse = -√65/9
Tan θ = Opposite side /Adjacent side = -√65/4
Therefore the correct option is
Option d. Sin θ = -√65/9 and Tan θ = -√65/4
The sum of two numbers is 9 and there difference is 1.What are those two numbers
Final answer:
To find the two numbers where their sum is 9 and their difference is 1, set up two equations x + y = 9 and x - y = 1. Solve these equations simultaneously to get the numbers 5 and 4.
Explanation:
The question asks to find two numbers where their sum is 9 and their difference is 1. The solution involves setting up two equations based on the information given:
Let the first number be x and the second number be y.
The sum of the two numbers is 9, so we have the equation x + y = 9.
The difference between the two numbers is 1, leading to the equation x - y = 1.
We can solve these two equations simultaneously to find the values of x and y. Adding the two equations together leads to 2x = 10, which simplifies to x = 5. Substituting x back into one of the original equations, for example, x + y = 9, we get 5 + y = 9, which simplifies to y = 4.
Therefore, the two numbers are 5 and 4.
If you were to round off the measurement 2.33501 grams to three digits, you would get
Answer:
2.34 grams
Step-by-step explanation:
The first 3 digits of the number are 2, 3, 3. The next digit is 5, which is more than 4, so 1 is added to the digit to its left and all digits to the right of the first three are dropped.
2.33 becomes 2.34 because of the 5 in the thousandths place.
Your rounded measurement is 2.34 grams.
What is COS A?
3/4
4/3
3/5
4/5
Answer: third option
Step-by-step explanation:
As you can see in the figure attached, the triangle is a right triangle.
Then, you can calculate cosA as it is shown below:
- You need to remember the following:
[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]
- Now, you must substitute values. Based on the figure:
[tex]adjacent=3\\ hyppotenuse=5[/tex]
[tex]\alpha=A[/tex]
Therefore, you obtain that cosA is:
[tex]cosA=\frac{3}{5}[/tex]
Answer:
Cos A = 3/5
Step-by-step explanation:
We are given a right angled triangle, ΔBCD, with all three side lengths known and we are to find the value of Cos A.
We Cos is the ratio of the base of the triangle to its hypotenuse, with respect to the angle (here angle A).
Considering the angle A, our perpendicular is CD, base is BC and hypotenuse BD.
Therefore, Cos A = BC/BD = 3/5
What is the domain of the function
y=In(x+2)
Answer:The domain: x > -2\to x\in(-2;\ \infty)
Step-by-step explanation:
y = ln(x + 2)
D:
x + 2 > 0 |subtract 2 from both sides
x > -2
Answer: The domain: x > -2\to x\in(-2;\ \infty)
Answer:
[tex]\large\boxed{x>-2\to x\in(-2,\ \infty)}[/tex]
Step-by-step explanation:
[tex]\text{The domain of}\ \log_ax:\\\\a>0\ \wedge\ a\neq1\ \vedge\ x>0\\=========================\\\\y=\ln(x+2)\\\\\text{The domain:}\\\\x+2>0\qquad\text{subtract 2 from both sides}\\\\x+2-2>0-2\\\\x>-2\to x\in(-2,\ \infty)[/tex]
(6Q) Find the log .
Answer:
c. 4.9713
That's the answer
In a school,3/5 of the pupils were boys and there were 240 girls. How many boys were in the school.
Answer:
If 2/5 is 240 then 1/5 is 120..multiply 120 by 5 which is 600 so...
600=total
Then..multiply 120 by 3 which will give the 3/5 boys which is 360 so...
360 boys
Step-by-step explanation:
A rational function is a function whose equation contains a rational expression.A.Trueb.False
The answer is true because false would mean that it’s another crazy definition. But yes it is true
A rational function is a fractional expression in the form f(x) = p(x)/q(x), where q(x) cannot be zero.
Example: f(x) = 3x/(4x - 2).
True is the answer.
Each of the four lines shown here has equation y = mx + b. For which line is it true that
m > 0 and b < 0?
Step-by-step explanation: usatestprep approved
The graph of the linear equation with m > 0 and b < 0 is in the image at the end.
For which line is it true that m > 0 and b < 0?
A general linear equation is written as:
y = mx + b
Where m is the slope and b is the y-intercept.
When m > 0, we will see a line that goes upwards.When b < 0, we will see that the line intercepts the vertical axis below the horizontal axis.With this we can see that the correct option from the given ones is the second graph. You can see the image below.
What is the volume of a cylinder with a height of 5cm and diameter of 9cm?
(Use 3.14 for π.)
317.9 cm3
343.8 cm3
1271.4 cm3
2543.4 cm3
The equation is V = PI x r^2 x h
r = 1/2 the diameter = 4.5
Volume = 3.14 x 4.5^2 x 5
Volume = 317.9 cm^3
Expand the following log:
[tex]log_{b} (\frac{x^{3} }{y^{2} })[/tex]
SHOW ALL WORK.
Answer:
[tex]\log_b(\frac{x^3}{y^2} )=3\log_b(x)-2\log_b(y)[/tex]
Step-by-step explanation:
The given logarithmic expression is
[tex]\log_b(\frac{x^3}{y^2} )[/tex]
Recall and use the quotient rule of logarithms;
[tex]\log_b(MN)=\log_b(M)-\log_b(N)[/tex];
We apply this property to obtain;
[tex]\log_b(\frac{x^3}{y^2} )=\log_b(x^3)-\log_b(y^2)[/tex]
Recall again that;
[tex]\log_b(M^n)=n\log_b(M)[/tex]
We apply this property also to obtain;
[tex]\log_b(\frac{x^3}{y^2} )=3\log_b(x)-2\log_b(y)[/tex]
A girl makes 12 foul shots for every 8 that she misses.How many shots did she make if she shot 125 foul shots
Answer: There are 208 shots she make if she shot 125 foul shots.
Step-by-step explanation:
Since we have given that
Number of foul shots = 12
Number of shots she misses = 8
Total number of shots = 12+8=20
So, if the number of foul shots = 125
We need to find the number of shots she make.
According to question, we get that
[tex]\dfrac{12}{20}=\dfrac{125}{x}\\\\12x=125\times 20\\\\12x=2500\\\\x=\dfrac{2500}{12}\\\\x=208.33\\\\x\approx 208[/tex]
Hence, there are 208 shots she make if she shot 125 foul shots.
Identify the type of transformation in the following graphic and describe the change.
Answer: transformation 5 units right
Step-by-step explanation: the preimage mapped to the image is moved 5 units to the right.
the algebraic expression is (x,y)-->(x+5,y)
Answer: M.A.T.H was translated (-5, 0) units; or five units to the left
Step-by-step explanation:
Point A is moved to the left to become A'.
Similarly, Points M, H, and T have moved to the left to become M', H', and T', respectively.
This type of transformation, in which all the points in a figure move in the same direction and by the same amount, is called a translation (moving sideways).
Each point has moved five units to the left.
1 Geometry question!
First find the value of the two vertical angles which have x in them.
Vertical angles are the same so you have:
4x = x +36
subtract 1x from each side:
3x = 36
Divide both sides by 3:
x = 36/3
x = 12
Now replace x with 12 to solve for the angles:
4x = 4(12) = 48 degrees.
All 4 angles need to equal 360 degrees, so now subtract 48 +48 from 360:
360 - 96 = 264
Y and the angle above it are vertical angles, so you can divide 264 by 2 to find y:
Y = 264 /2
Y = 132 degrees.
Find x of this triangle.
Answer:
x=18
Step-by-step explanation:
First, using the Pythagorean theorem, you can make the equation 10^2+y^2=26^2. You can solve this to get y=24. Another way to solve for the value of y is to use your Pythagorean triples! (in this case, all the values are double the values of the Pythagorean triple 5, 12, 13).
Next, you can use the Pythagorean theorem again to get the equation 24^2+x^2=30^2. Solving it, you would get x=18.
Hope this helps!
If you buy 8 kilograms of apples and 2.5 kilograms of pears how many more grams of apples are there
Answer:
[tex]5,500\ g[/tex]
Step-by-step explanation:
we know that
[tex]1\ kg=1,000\ g[/tex]
step 1
Find the difference between the kilograms of apples and the kilograms of pears
[tex]8-2.5=5.5\ kg[/tex]
step 2
Convert to grams
[tex]5.5\ kg=5.5*1,000=5,500\ g[/tex]
I believe the answer is A. I and III only, however, I am not 100% sure.
Answer:
correct
Step-by-step explanation:
The asymptotes of the cotangent function are at multiples of π. The cosine function has no asymptotes.
sec(x)² = 1 + tan(x)² so both functions have their vertical asymptotes in the same places.
Claim amounts for wind damage to insured homes are independent random variables with common density f(x) = ( 3 x4 , x > 1 0 , otherwise where x is amount of claim in thousands. (a) find the probability that a claim is below average? [19/27] (b) suppose 3 claims will be made. what is the expected value of the largest of the three claims? [2.025] (c) suppose 3 claims will be made. what is the expected value of smallest of the three claims?[1.125]
Final answer:
The random variable X represents claim amounts for wind damage to insured homes. The probability that a claim is below average is 19/27. The expected value of the largest claim is 2.025 and the expected value of the smallest claim is 1.125.
Explanation:
a. The random variable X represents the claim amounts for wind damage to insured homes.
b. To find the probability that a claim is below average, we first need to calculate the average claim amount. We can do this by finding the expected value of X, which is given by E(X) = ∫[10,∞]x * f(x) dx, where f(x) is the density function of X. Evaluating this integral, we get E(X) = 19/27. Therefore, the probability that a claim is below average is P(X < E(X)) = P(X < 19/27) = 19/27.
c. The expected value of the largest of the three claims can be calculated by finding the maximum of three independent random variables with density f(x). Since the density is continuous, the probability that the maximum claim amount is less than or equal to x is given by P(X₁ ≤ x, X₂ ≤ x, X₃ ≤ x) = [F(x)]³, where F(x) is the cumulative distribution function of X. To find the expected value, we need to find the maximum amount x such that [F(x)]³ = 1/2. Solving this equation, we get x ≈ 2.025.
d. Similarly, the expected value of the smallest of the three claims can be calculated by finding the minimum of three independent random variables with density f(x). The probability that the minimum claim amount is greater than or equal to x is given by P(X₁ ≥ x, X₂ ≥ x, X₃ ≥ x) = [1 - F(x)]³. To find the expected value, we need to find the minimum amount x such that [1 - F(x)]³ = 1/2. Solving this equation, we get x ≈ 1.125.