Answer:
a) 0.54
Step-by-step explanation:
The correlation coefficient can be found by taking square root of R-squared value and the sign of correlation coefficient can be assessed by considering the sign of slope value. So,
r²=28.8%=28.8/100=0.288
r=[tex]\sqrt{r^{2} }[/tex]=[tex]\sqrt{0.288}[/tex]=0.5367
By rounding to two decimal places the correlation coefficient
r=0.54
We can see that slope=0.4845 has positive sign so, the correlation coefficient contains the positive sign.
Hence the correlation coefficient r=0.54.
Bianca and Meredith are sisters. Meredith's height is 23 of Bianca's height plus 32 inches. Meredith is 60 inches tall. A girl is sixty inches tall. Write an equation to find Bianca's height, x, in inches.
Answer:
Bianca's height = 42 inches
Step-by-step explanation:
Let x be the Bianca height.
Given:
Meredith height = 60 inches
We need to find the Bianca height.
Solution:
From the given statement the Meredith's height is [tex]\frac{2}{3}[/tex] of Bianca's height plus 32 inches, so the equation is.
Meredith's height = [tex]\frac{2}{3}(Bianca\ height)+32[/tex]
Substitute Meredith's height in above equation.
[tex]60=\frac{2}{3}x+32[/tex]
Now we solve the above equation for x.
[tex]\frac{2}{3}x=60-32[/tex]
[tex]\frac{2}{3}x=28[/tex]
By cross multiplication.
[tex]x=\frac{3\times 28}{2}[/tex]
28 divided by 2.
[tex]x= 3\times 14[/tex]
[tex]x=42\ in[/tex]
Therefore, the height of the Bianca is 42 inches.
You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0.793. How confident can you be that your predicted value will be reasonably close to the actual value? A. I can’t be confident at all; this is about as close to a random guess as you can get. B. I can be a little confident; it might be close, or it might be way off. C. I can be very confident; it will be close, but it probably won’t be exact. D. I can be certain that my predicted value will match the actual value exactly.
Answer:
The correct option is c.
can be very confident; it will be close, but it probably won’t be exact.
Step-by-step explanation:
Correlation coefficient r lies between -1 and +1 , if r is close to +1 the variables compared are highly positively correlated. If r is close to -1 then the variables compared are highly negatively correlated. If r is close to zero then the correlation between the variables compared is low. If r=0 then the variables compared do not correlate at all.
The closer the correlation coefficient is to +1, the better the prediction.
Therefore since r=0.793 , the correlation coefficient is close to +1 , it means there is a highly positive correlation between variables. Therefore the correct option is c. If r is exactly +1 then we can say without any shadow of doubt that the prediction will be perfect.
Jack decides to grow and sell bean plants. Let P represent the number of plants he will grow and sell. After considering his expenses, the expression -3p(p-10)-6p(p-10) represents his profit.
a. Rewrite and simplify the profit expression by factoring out the greatest common factor.
b. Rewrite the expression in simplest form with no parentheses.
Answer:
b. [tex]\displaystyle 90 - 9p^2[/tex]
a. [tex]\displaystyle -9[-10 + p^2][/tex]
Step-by-step explanation:
b. [tex]\displaystyle 90 - 9p^2 = -3p^2 + 30 - 6p^2 + 60 = -3p(p - 10) - 6p(p - 10)[/tex]
a. [tex]\displaystyle -9[-10 + p^2] = 90 - 9p^2[/tex]
I am joyous to assist you anytime.
Final answer:
The profit expression -3p(p-10)-6p(p-10) simplifies first by factoring out the greatest common factor to -9p(p-10), and then further simplifies to -9p² + 90p by distributing the -9p across the parentheses.
Explanation:
The student is tasked with simplifying the profit expression given by -3p(p-10)-6p(p-10), first by factoring out the greatest common factor, and then by writing the expression in the simplest form without parentheses.
To begin, we notice that both terms in the expression share a common factor of p(p-10), so we can factor this out:
-3p(p-10) - 6p(p-10) = -9p(p-10).
Upon factoring out the common factor, our expression simplifies to -9p(p-10). Next, we simplify this expression by removing the parentheses and multiplying through by the common factor:
-9p(p - 10) = -9p² + 90p.
Therefore, the simplified profit expression with no parentheses is -9p² + 90p.
The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with acceleration of −5.65 m/s2 for 4.00 s, making straight skid marks 62.9 m long, all the way to the tree. With what speed (in m/s) does the car then strike the tree?
Answer: the speed with which the car strikes the tree is 27.025 m/s
Step-by-step explanation:
We would apply Newton's equation of motion. It is expressed as
S = ut + 1/2at²
Where
S represents the distance covered by the car
u represents the initial velocity of the car( the speed with which the car strikes the tree)
t represents the time taken to cover the distance
a represents the deceleration of the car.
From the information given,
S = 62.9 meters
a = - 5.65 m/s2
t = 4 seconds
Therefore
62.9 = u × 4 + 1/2 × - 5.65 × 4²
62.9 = 4u - 45.2
4u = 62.9 + 45.2
4u = 108.1
u = 108.1/4 = 27.025 m/s
Final answer:
The car's speed at the moment it strikes the tree, after decelerating with an acceleration of -5.65 m/s² for 4.00 seconds over a distance of 62.9 m, is calculated to be 22.6 m/s.
Explanation:
The question relates to the final speed of a car after it has been decelerating over a certain distance due to the driver applying the brakes. With an acceleration of −5.65 m/s² over a time period of 4.00 seconds, and the car making skid marks 62.9 m long, we are tasked with determining the speed at which the car eventually hits the tree.
To solve this problem, we first calculate the initial speed of the car before it started to decelerate. We use the kinematic equation: v = u + at, where 'v' is the final velocity (0 m/s, since the car eventually stops), 'u' is the initial velocity, 'a' is the acceleration, and 't' is the time. Rearranging this equation to solve for 'u', we get u = v - at. Substituting the given values, we find that the initial velocity 'u' was 22.6 m/s.
However, to find the speed at which the car hits the tree implies we need to know the speed at a specific point before it comes to a complete stop, specifically at the end of the 62.9 m distance. For this, considering the constant deceleration, the car's speed when it strikes the tree can be considered to be the same as its speed just before deceleration, which is calculated to be 22.6 m/s.
In his coin box , Brian has 12 fewer nickels than dimes. The value of his nickels and dimes is 2.40. Determine the exact number of nickels and dimes Brian has in his possession
Answer:
There are 8 nickels, and 20 dimes.
Brian has 20 dimes and 8 nickels in his coin box.
Explanation:Let's make a system of equations to solve this problem. Let's assume the number of dimes is 'x', then the number of nickels would be 'x - 12' since Brian has 12 fewer nickels than dimes.
The value of dimes in cents is 'x * 10', and the value of nickels in cents is '(x - 12) * 5'. We can write the equation: '10x + 5(x - 12) = 240' since the total value is $2.40 or 240 cents.
Simplifying the equation, we get '10x + 5x - 60 = 240'. Combining like terms, we have '15x - 60 = 240'. Adding 60 to both sides, we get '15x = 300'. Dividing both sides by 15, we get 'x = 20'.
Therefore, Brian has 20 dimes and 20 - 12 = 8 nickels.
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A categorical variable whose values are purely qualitative and unordered is called a _______ variable. Please type the correct answer in the following input field, and then select the submit answer button or press the enter key when finished. Your answer:
Answer: Nominal
Step-by-step explanation:
A categorical variable whose values are purely qualitative and unordered is called a Nominal variable. Nominal variables are qualitative variables that does not have a particular rank, order or value. An example of nominal variables are colour (red,blue etc), gender (male, female), skin and hair colour etc.
If you invested $100 at an interest rate of 5% per year compounded quarterly, how much will the investment be worth at the end of two years? *
50 points
Answer: the investment would be
$110.45
Step-by-step explanation:
Initial amount deposited into the account is $100 This means that the principal is
P = 100
It was compounded quarterly. This means that it was compounded 4 times in a year. So
n = 4
The rate at which the principal was compounded is 5%. So
r = 5/100 = 0.05
It was compounded for 2 years. So
t = 2
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 100 (1+0.05/4)^4×2
A = 100 (1.0125)^8
A = $110.45
To make lemonade, use 1 cup of lemon juice for every 3 cups of water. If you use 12 cups of water, how many cups of lemon juice will you need? Use a double number lineto solve.
Answer:
4 cups of lemon juice is required for 12 cups of water to make lemonade.
Step-by-step explanation:
Given:
To make lemonade 1 cup of lemon juice is required with 3 cups of water.
To find how many cups of lemon juice is required with 12 cups of water.
Solution:
We will construct a double number line of which one represents the cups of lemon juice and the other represents the cups of water.
From the number lines we can see that with 1 cup of lemon juice there are 3 cups of water.
So, ratio of cups of lemon juice to cups of water = 1 : 3
If we require [tex]x[/tex] cups of lemon juice with 12 cups of water then ratio = x : 12
Since ratio will always be equivalent, so we can write it as:
[tex]\frac{x}{12}=\frac{1}{3}[/tex]
Multiplying both sides by 12.
[tex]12.\frac{x}{12}=12\times\frac{1}{3}[/tex]
∴ [tex]x=4[/tex]
Thus, 4 cups of lemon juice is required for 12 cups of water to make lemonade.
1.) Simplify the expression.
sin ( u + π/2 )
a.) tan u
b.) sin u
c.) csc u
d.) cos u
e.) cot u
Answer:
[tex]sin ( u +\frac{\pi}{2} ) = cos (u)[/tex]
Step-by-step explanation:
Let us use the identity
sin(A+B)= cos(A) sin(B)+cos (B) sin(A) to simplify the given expression
Then
[tex]sin(u + \frac{\pi}{2})= \cos \left(u\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(u\right)[/tex]--------------------(1)
Here
[tex]cos (\frac{\pi}{2}) = 0\\[/tex]---------------------(2)
[tex]sin(\frac{\pi}{2})= 1[/tex]---------------------(3)
Substituting the values in (1)
[tex]sin(u + \frac{\pi}{2})= \cos \left(u\right)(1)+(0)\sin \left(u\right)[/tex]
[tex]sin(u + \frac{\pi}{2})= \cos \left(u\right) + 0[/tex]
[tex]sin(u + \frac{\pi}{2})= \cos \left(u\right)[/tex]
The inverse of a cosine function is the
function ___
arcsine
secant
arccosine
cosecant
Answer:
cosecant
Step-by-step explanation:
Inverse Cosine
cos-1
Cos-1
arccos
Arccos
The inverse function of cosine.
Basic idea: To find cos-1 (½), we ask "what angle has cosine equal to ½?" The answer is 60°. As a result we say cos-1 (½) = 60°. In radians this is cos-1 (½) = π/3.
More: There are actually many angles that have cosine equal to ½. We are really asking "what is the simplest, most basic angle that has cosine equal to ½?" As before, the answer is 60°. Thus cos-1 (½) = 60° or cos-1 (½) = π/3.
Details: What is cos-1 (–½)? Do we choose 120°, –120°, 240°, or some other angle? The answer is 120°. With inverse cosine, we select the angle on the top half of the unit circle. Thus cos-1 (–½) = 120° or cos-1 (–½) = 2π/3.
In other words, the range of cos-1 is restricted to [0, 180°] or [0, π].
Note: arccos refers to "arc cosine", or the radian measure of the arc on a circle corresponding to a given value of cosine.
Technical note: Since none of the six trig functions sine, cosine, tangent, cosecant, secant, and cotangent are one-to-one, their inverses are not functions. Each trig function can have its domain restricted, however, in order to make its inverse a function. Some mathematicians write these restricted trig functions and their inverses with an initial capital letter (e.g. Cos or Cos-1). However, most mathematicians do not follow this practice. This website does not distinguish between capitalized and uncapitalized trig functions.

See also
Inverse trigonometry, inverse trig functions, interval notation
which of the following values for x and y satisfy the following system of the equations?
{ x + 4y = 10
{5x + 10y = 20
a. x = 3, y = 2
b. x = 2, y - 3
c. x = -2, y = 3
d. x = 3, y = -2
Answer:
The answer to your question is letter C
Step-by-step explanation:
Equations
x + 4y = 10
5x + 10y = 20
Process
1.- Substitute all the options in both equations and evaluate them
a) x = 3, y = 2 This option is incorrect
(3) + 4(2) = 10 3 + 8 = 10 11 ≠ 10
5(3) + 10(2) = 20 15 + 20 = 20 35 ≠ 20
b) x = 2, y = -3 This option is incorrect
(2) + 4(-3) = 10 2 -12 = 10 -10 ≠ 10
(2) + 10(-3) = 20 2 - 30 = 20 -28 ≠ 20
c) x = -2, y = 3 This is the right answer
(-2) + 4(3) = 10 -2 + 12 = 10 10 = 10
5(-2) + 10(3) = 20 -10 + 30 = 20 20 = 20
d) x = 3, y = -2 This option is incorrect
(3) + 4(-2) = 10 3 - 6 = 10 - 3 ≠ 10
5(3) + 10(-2) = 20 15 - 20 = 20 -10 ≠ 10
Out of 200 people sampled, 110 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.
Answer:
From the sample of n= 200 people,
The proportion of people with kids is:
p'= 110/200= 0.55
The confidence interval for population proportion is given by:
[tex]p' - Z_{\alpha /2} \sqrt[]{\frac{p'(1-p')}{n} } } \leq P\leq p' + Z_{\alpha /2}\sqrt[]{\frac{p'(1-p')}{n} } }[/tex]
[tex]= p' - Z_{\alpha /2} \sqrt[]{\frac{0.55(0.45)}{200} } } \leq P \le p' + Z_{\alpha /2} \sqrt[]{\frac{0.55(0.45)}{200} } }[/tex]
[tex]= p' - Z_{\alpha /2} 0.0352} } } \leq P\le p' + Z_{\alpha /2} 0.0352} }[/tex]
Where P is the population proportion and Z is the critical value at a given level of significance α.
how can you write the statement "obtuse angles have greater measures than acute angles" so that it is a good definition
Since obtuse angles are greater than 90 degrees and acute angles are less than 90 degrees, then obtuse angles have greater measures than acute angles.
Happy to help
Answer:
Step-by-step explanation:
obtuse angles >90
acute angles <90
* ANSWER ASAP PLEASE *
- can anyone answer this question?? you have to find x.
Answer:
The answer is the last one
Step-by-step explanation:
Answer:
Step-by-step explanation:
X= 11/tan17
Where tan17= 3.494
Therefore, X = 3.148
The systematic use of critical reasoning to try to find answers to fundamental questions about reality, morality, and knowledge is called__________
Answer:
Metaphysics
Step-by-step explanation:
Metaphysics is a system of reasoning or process that is often employed to find answers through examining fundamental nature of reality, the relationship between minds and also knowledge.
The systematic use of critical reasoning to try to find answers to fundamental questions about reality, morality, and knowledge is called philosophy.
The systematic use of critical reasoning to try to find answers to fundamental questions about reality, morality, and knowledge is called philosophy.
Philosophy is the discipline that seeks to explore and understand the fundamental aspects of existence, including the nature of reality, the principles of ethics and morality, and the limits of human knowledge. It involves the rigorous examination of concepts, arguments, and ideas to gain deeper insights into the nature of the world and our place in it.
Philosophers engage in critical thinking and analysis to address questions related to the meaning of life, the nature of truth, the basis of ethics, and the foundations of human understanding. Through philosophical inquiry, individuals seek to develop a deeper and more comprehensive understanding of the complex issues that shape our lives and society.
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A certain car costs $11,595 before taxes are added. Taxes are $860 and license tags cost $95. What is the overall tax rate (to the nearest tenth)?
A. 0.8%
B. 7.4%
C. 8.2%
D. 12.1%
Answer:
The answer is B)7.4%
Step-by-step explanation:
Pure cost of the car is 11595$. It is stated that taxes costs 860$ for the car. To find the overall tax rate we need to simply divide tax value to car original cost.
[tex]860/11595=0.074[/tex]
Ronald is calculating the time required to fill the swimming pool at school. He found that it takes 8 minutes to fill the swimming pool with 72 gallons of water. At what rate does the swimming pool fill, in gallons per minute?
Answer:
The rate the swimming pool is filled is 9 gallons of water per minute
Step-by-step explanation:
Let's review the information provided by Ronald to us to help him to find the answer to the question:
Time it takes to fill the swimming pool = 8 minutes
Amount of water the swimming pool can hold = 72 gallons
2. At what rate does the swimming pool fill, in gallons per minute?
Rate the swimming pool is filled = Amount of water the swimming pool can hold /Time it takes to fill the swimming pool
Replacing with the real values, we have:
Rate the swimming pool is filled = 72/8 = 9 gallons of water per minute
Write the expression in radical form. x 1/5
Answer:
[tex]x^{\frac{1}{5} } = \sqrt[5]{x}[/tex]
Step-by-step explanation:
A radical expression is an expression with a variable, number, or combination of both of them under a root symbol.
A radical expression has a general form of [tex]\sqrt[n]{x}[/tex]
For the given expression [tex]x^{\frac{1}{5} }[/tex]
So, [tex]x^{\frac{1}{5} } = \sqrt[5]{x}[/tex]
[tex]x^{1/5}[/tex] in radical form is √5x.
To write the expression [tex]x^{1/5}[/tex] in radical form, we use the property of exponents where a fractional exponent represents a root. Specifically, the exponent 1/5 indicates the fifth root of the base.
Here are the steps:
Identify the base and the fractional exponent: base = x, exponent = 1/5.Rewrite the expression using the radical symbol, where the denominator of the exponent (5) becomes the index of the root.So,[tex]x^{1/5}[/tex] is equivalent to √5x.Therefore, the radical form of [tex]x^{1/5}[/tex] is √5x.
Let A(t) be the area of the region in the first quadrant enclosed by the coordinate axes, the curve y = e −x , and the vertical line x = t, t > 0. Let V (t) be the volume of the solid generated by revolving the region about the x-axis. Find the following limits.
Answer:
I=\frac{t^2}{2}
Step-by-step explanation:
From exercise we have that x=t, t>0. Because A(t) be the area of the region in the first quadrant, we get that x started at 0. The limits for y are the following e-x and e. We get the integral :
I=\int\limits^0_t \int\limits^{e}_{e-x} 1 dy dx
I=\int\limits^0_t [y]_{e-x}^{e} dx
I=\int\limits^0_t (e-e+x) dx
I=\int\limits^0_t {x} \, dx
I=[\frac{x^2}{2} ]_{0}^{t}
I=\frac{t^2}{2}
Two physics students are doing a side competition during a game of bowling, seeing who can toss a ball with the larger momentum. The first bowler throws a 4.5 kg ball at 8.6 m/s. Part A A second bowler throws a 6.4 kg ball. What speed must she beat to win the competition?
Answer:
she should beat a speed of v₂ = 6.04 m/s in order to win the competition
Step-by-step explanation:
Since the momentum p is defined as
p = m*v
where
m= mass of the ball
v= velocity of the ball
denoting 1 and 2 as the first and second bowler , then to reach the momentum of the first bowler
p₂=p₁
therefore
m₁*v₁ = m₂*v₂
v₂ = v₁ * (m₁/m₂)
replacing values
v₂ = v₁ * (m₁/m₂) =8.6 m/s * (4.5 kg/6.4 kg ball) = 6.04 m/s
then since the momentum p = m*v increases with increasing v (at constant m) , she should beat a speed of v₂ = 6.04 m/s in order to win the competition
Condo living room is in the shape of a rectangle has a area of three 60 ft.² the width of the living room is 58 it's what what is the length of the living room
Question is not proper, Proper question is given below;
Consuelo's living room is in the shape of a rectangle and has an area of 360 square feet. The width of the living room is [tex]\frac{5}{8}\ ft[/tex] its length. What is the length of the living room?
Answer:
Length of the living room is 24 feet.
Step-by-step explanation:
Given:
Area of the living room = [tex]360 \ ft^2[/tex]
We need to find the length of the living room.
Solution:
the length of the living room be 'l'.
Given:
Width of the living room [tex]\frac{5}{8}\ ft[/tex] of it length.
width [tex]w= \frac{5}{8}l[/tex]
It has been given that living room is in rectangular format.
So we can say that;
Area of living room is equal to length of the living room times width of the living room.
framing in equation form we get;
[tex]l\times w=360\\\\l\times\frac{5}{8}l=360\\\\\frac{5}{8}l^2=360[/tex]
Now Multiplying both side by [tex]\frac{8}{5}[/tex] we get;
[tex]\frac{5}{8}l^2\times\frac{8}{5}=360\times\frac{8}{5}\\\\l^2= 576[/tex]
Taking square root on both side we get;
[tex]\sqrt{l^2} =\sqrt{576} \\\\l=24 \ ft[/tex]
Hence Length of the living room is 24 feet.
1. Write the equation of the line with a slope of -5 and a y-intercept of (0,3). 2. Write the equation of the line with a slope of -1/3 and passing through the point (6, -4). 3. Write the equation of the line passing through the points (0, -4) and (-2, 2). 4. Write the equation of the line passing through the points (-6,1) and (-4,2). 5. Write the equation of the line with an undefined slope, passing through the point (2, 5). Hint: refer back to lesson 4.04 for help with this one.
Answer:
Step-by-step explanation:
1) The equation of a line is given by y = mx + c, where m = slope or gradient and c is intercept on y - axis. Given in this question, m = -5 and c = 3. Subtituting this in the equation y = mx + c, we have y = -5x + 3, therefore, the equation of the line is y = -5x + 3 or y + 5x = 3
2) The equation of a line is given as y-y1 = m(x-x1), where x1 = 6, y1 = -4 and m = -1/3. The equation of the line is y - -4 = -1/3(x - 6)
y+4 =-1/3(x-6)
3(y+4)= -1(x-6)
3y + 12 = -x+6
x+3y=6-12
x+3y= -6, therefore the equation of the line is x+3y = -6
3) The equation is y-y1=m(x-x1), where m=(y2-y1)/(x2-x1)=
(2- -4)/(-2-0)=6/-2=-3
y- -4= -3(x-0)= -3x
y+4= -3x
y+3x= -4
4) y-y1=m(x-x1)
m=(2-1) /(-4- -6)=1/2
y-1=1/2(x- -6)
y-1=1/2(x+6)
2(y-1) = x+6
2y-2=x+6
2y-x =6+2=8 2y-x=8
5) The equation is with undefined slope passing through (2, 5) is
x-2=0
x=2
When it is 2:00 p.m. in New York City, it is 9:00 PM in Athens. If you leave New York at 7:30 a.m. on Wednesday and fly to Athens over the course of 13 hours and 45 minutes, what time will it be in Athens when you land?a. 2:30 p.m. Wednesdayb. 9:15 p.m. Wednesdayc. 4:15 a.m. Thursdayd. 1:15 p.m. Thursday
Answer:
option (c) 4:15 a.m. Thursday
Step-by-step explanation:
Time difference in New York City and Athens = 7 hours
Now,
The flight leaves at 7:30 a.m on Wednesday i.e 7:30 hrs
Therefore,
the time in Athens at the time of leaving of flight = 7:30 hrs + 7 hours
= 14 : 30 hrs i.e 2 : 30 pm on Wednesday
now,
after the 13 hours and 45 minutes of flight time in Athens i.e
= 14 : 30 + 13 : 45
= 28 : 15 i.e 1 day and 4 : 15 hrs
This means Flight will land at 4 : 15 a.m on Thursday
Hence,
option (c) 4:15 a.m. Thursday
Answer:
C
Step-by-step explanation:
4:15am Thursday
The point of a square pyramid is cut off, making each lateral face of the pyramid a trapezoid with the dimensions shown. What is the area of one trapezoidal face of the figure?
The area of one trapezoidal face of the figure is 2 square inches
How to determine the area?The dimensions of the trapezoid are given as:
Base = 3 inchesHeight = 1 inchTop side length = 1 inch.The area of one trapezoidal face of the figure is the calculated using:
Area = 0.5 * (base + top side) * height
So, we have:
Area = 0.5 * (3 + 1) * 1
Evaluate
Area = 2
Hence, the area of one trapezoidal face of the figure is 2 square inches
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Answer: 2
Step-by-step explanation:
Im in desperate need of help!
Answer:
umm, my regards, how should I help lol
A number is picked randomly in the range [2,8]. If past selection indicates that the numbers picked are less than 5, what is the probability that a number picked will be (a) less than 4 (b) greater than 4. What is the probability that the number picked is 4.5
Answer:
a) P = 2/7
b) P = 4/7
c) P = 1/7
Step-by-step explanation:
In the range of [2,8], we have the following integers which are: 2, 3, 4, 5, 6, 7, 8. So this is a total of 7 integers.
a) We look for the probability that the numbers are less than 4, so we conclude that there are possible numbers 2 and 3 out of possible 7, so the required probability is equal to P = 2/7.
b) We look for the probability that the numbers are greater than 4, so we conclude that there are possible numbers 5, 6, 7, 8 out of possible 7, so the required probability is equal to P = 4/7.
c) Based on the previous two examples, we conclude that the required probability is P = 2/7· 1/2=1/7.
Use the formula for the probability of the complement of an event. A coin is flipped 4 times. What is the probability of getting at least 1 tail?
Answer: 15/16
Step-by-step explanation:
There will be 16 outcomes for 4 coins=2^4
Probability of only head is : P(C)=1/16
P(C) + P(C') = 1
P(C') = 1 - P(C)
P(C') = 1 - 1/16
Take the l.c.m
P(C') = (16-1) / 16
P(C') = 15/16
So the probability of getting at least 1 tail is 15/16
Answer:
D 0.94
Step-by-step explanation:
when solved the answer is 15/16. This equals 0.9375 which rounded to the second decimal = 0.94
The Masterfoods Company says that before the introduction of purple, yellow candies made up 20% of their plain candies, red another 20%, and orange, blue and green each made up 10%. The rest were brown. If you pick a THREE M&Ms in a row (assume with replacement), what is the probability that they are all Brown?
a. 0.09
b. 0.027
c. 0.3
d. 0.6
Answer:
b. 0.027
Step-by-step explanation:
We have been given that the Masterfoods Company says that before the introduction of purple, yellow candies made up 20% of their plain candies, red another 20%, and orange, blue and green each made up 10%.
Probability of a yellow candy would be 0.20 and probability of a red candy would be 0.20.
Probability of orange candy would be 0.10, probability of blue candy would be 0.10 and probability of green candy would be 0.10.
The probability of brown candy would be [tex]1-0.20-0.20-0.10-0.10-0.10=0.30[/tex]
To find the probability that three candies are all Brown, we will use multiplication rule of independent events as:
[tex]0.30\times 0.30\times 0.30=0.027[/tex]
Therefore, the probability that that three candies are Brown would be 0.027 and option 'b' is the correct choice.
The probability that they are all Brown is option b. 0.027.
The calculation is as follows;The probability of brown candy should be
= 1-0.20 -0.20 -0.10 - 0.10-0.10
= 0.30
Now
the probability should be
[tex]= 0.3^3[/tex]
= 0.027
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A ship at position (1, 0) on a nautical chart (with north in the positive y direction) sights a rock at position (7, 4). What is the vector joining the ship to the rock?
Answer:
SR = (6,4)
Step-by-step explanation:
The ship position is (1,0)
The rocks position is (7,4)
SR is the vector line joining ship and rock
Using triangle law of addition
OS + SR = OR
SR = OR - OS
= ( 7 - 1 , 4 - 0)
= (6,4)
The vector line joining Ship and rock is (6,4)
Rick buys and sells antiques via the Internet. So far, he has profited $2,502. Based on his profits to date, he developed the following linear model where x represents time in months, and y represents his total profits, in dollars. Interpret the slope.y = 2,502 + 417x
a. An additional month of buying and selling is associated with an additional $2,919 in profits.
b. An additional month of buying and selling is associated with an additional $2,502 in profits.
c. An additional month of buying and selling is associated with an additional $2,085 in profits.
d. An additional month of buying and selling is associated with an additional $417 in profits.
Answer:
d. An additional month of buying and selling is associated with an additional $417 in profits.
Step-by-step explanation:
We have general form of intercept form of equation:
y = m*x + c ----- (A)
Given equation is : y = 2502 + 417*x
Rewrite equation: y = 417*x + 2502 ------(B)
comparing equation (B) with equation (A), we get
m = 417 (additional benefits per month) because multiplied factor x is the month.
Final answer:
The slope in Rick's linear model represents an additional profit of $417 for each additional month of buying and selling antiques, making option d correct.
Explanation:
Rick's linear model for his profits from buying and selling antiques is given by the equation y = 2,502 + 417x, where x represents time in months and y represents his total profits in dollars. The coefficient of x in this equation, which is 417, represents the slope of the line.
In this context, the slope indicates that for each additional month of buying and selling antiques, Rick's profits are expected to increase by $417. Therefore, the correct interpretation of the slope is that an additional month of buying and selling is associated with an additional $417 in profits, making option d the correct answer.