What is there area to this?​

Step-by-step explanation:

8x² − 8x + 2

2 (4x² − 4x + 1)

2 (2x − 1)²

Answer:

c

Step-by-step explanation:

cuzz im right

We have been given a function [tex]h(x)=\frac{1}{8}x^3-x^2[/tex]. We are asked to find the average rate of change of our given function over the interval [tex]-2\leq x\leq 2[/tex].

We will use average rate of change formula to solve our given problem.

[tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]

[tex]\text{Average rate of change}=\frac{h(2)-h(-2)}{2-(-2)}[/tex]

[tex]\text{Average rate of change}=\frac{\frac{1}{8}(2)^3-2^2-(\frac{1}{8}(-2)^3-(-2)^2)}{2+2}[/tex]

[tex]\text{Average rate of change}=\frac{\frac{1}{8}(8)-4-(\frac{1}{8}(-8)-(4))}{4}[/tex]

[tex]\text{Average rate of change}=\frac{1-4-(-1-4)}{4}[/tex]

[tex]\text{Average rate of change}=\frac{-3-(-5)}{4}[/tex]

[tex]\text{Average rate of change}=\frac{-3+5}{4}[/tex]

[tex]\text{Average rate of change}=\frac{2}{4}[/tex]

[tex]\text{Average rate of change}=\frac{1}{2}[/tex]

Therefore, the average rate of change over the interval [tex]-2\leq x\leq 2[/tex] is [tex]\frac{1}{2}[/tex].

The average rate of change of h over the interval -2 ≤ x ≤ 2 in the equation h(x)=1/8x³-x² is 3/8.

To find the average rate of change of h over the interval -2 ≤ x ≤ 2, we need to calculate the difference in the values of h at the endpoints of the interval and divide it by the change in x.

First, let's find the value of h at x = -2: h(-2) = (1/8) * (-2)^3 - (-2)^2 = -(1/2).

Next, let's find the value of h at x = 2: h(2) = (1/8) * (2)^3 - (2)^2 = 1.

The change in x is 2 - (-2) = 4. So, the average rate of change of h over the interval -2 ≤ x ≤ 2 is (1 - (-1/2))/4 = 3/8.

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Answer:

A = $100(1.12)^2

Step-by-step explanation:

The standard formula for compound interest is given as;

A = P(1+r/n)^(nt) .....1

Where;

A = final amount/value

P = initial amount/value (principal)

r = rate yearly

n = number of times compounded yearly.

t = time of investment in years

For this case;

P = $100

t = 2years

n = 1

r = 12% = 0.12

Substituting the values, we have;

A = $100(1+0.12)^(2)

A = $100(1.12)^2

Answer:

0.9552

Step-by-step explanation:

Probability of making home can be made by either of the options :-

So, probability of making out at home : Reach through flight or car =  0.72 + 0.2352 = 9.9552

Final answer:

The probability of making it home for the holidays can be calculated using conditional probability. The probability of the flight being canceled is 28 percent, and the probability of Walter having a seat in his car is 84 percent. The probability of making it home is approximately 60.48 percent.

Explanation:

The probability of making it home for the holidays can be calculated using the concept of conditional probability. The probability of the flight being canceled is given as 28 percent, which means there is a 72 percent chance that the flight is not canceled. The probability of Walter having a seat in his car is given as 84 percent. To calculate the probability of making it home, we need to calculate the probability of both events happening.

The probability of the flight not being canceled is 72 percent (0.72) and the probability of Walter having a seat is 84 percent (0.84). To find the probability of both events happening, we multiply the probabilities: 0.72 * 0.84 = 0.6048 or approximately 60.48 percent. So, there is a 60.48 percent probability of making it home for the holidays.

Answer:

The volume of the sphere is 678.24 u³  

V = ⁴⁄₃ * π * (6u)³

Step-by-step explanation:

To calculate the volume of a sphere we have to use the following formula:

V = volume

r = radius  = 6 units

π = 3.14

V = ⁴⁄₃πr³

we replace with the known values

V = ⁴⁄₃ * 3.14 * (6u)³

V = 4.187 * 216 u³

V = 678.24 u³

The volume of the sphere is 678.24 u³

Answer:

A

C

D

Step-by-step explanation:

Answer:

  299

Step-by-step explanation:

On average, it travels 52 miles in each hour. In 5 3/4 hours, it travels 5 3/4 times 52 miles.

  (5 3/4)(52 miles) = 299 miles

It travels 299 miles in the given time.

Answer:

The car will travel 195 miles.

Step-by-step explanation:

(3.75 hrs)(52 mph)=195 miles

Answer:

The second one is the correct answer

Step-by-step explanation:

The third one is incorrect as she stated, I tried it and got it wrong when I did the retry I put the second one and I got it correct.

Answer:

a) 99.73% probability that a randomly selected person does not have a birthday on March 14.

b) 96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.

c) 98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.

d) 92.33% probability that a randomly selected person was not born in February.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

A non-leap year has 365 days.

​(a) Compute the probability that a randomly selected person does not have a birthday on March 14.

There are 365-1 = 364 days that are not March 14. So

364/365 = 0.9973

99.73% probability that a randomly selected person does not have a birthday on March 14.

​(b) Compute the probability that a randomly selected person does not have a birthday on the 2 nd day of a month.

There are 12 months, so there are 12 2nds of a month.

So

(365-12)/365 = 0.9671

96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.

​(c) Compute the probability that a randomly selected person does not have a birthday on the 31 st day of a month.

The following months have 31 days: January, March, May, July, August, October, December.

So there are 7 31st days of a month during a year.

Then

(365-7)/365 = 0.9808

98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.

(d) Compute the probability that a randomly selected person was not born in February.

During a non-leap year, February has 28 days. So

(365-28)/365 = 0.9233

92.33% probability that a randomly selected person was not born in February.

The probability that a person does not have a birthday on March 14, on the 2nd day of a month, on the 31st day of a month, or is not born in February is approximately 0.9973, 0.9671, 0.9808, and 0.9233 respectively. These probabilities were computed by subtracting the fraction of the year representing the specific days or month from 1. These solutions are based on a standard non-leap year of 365 days.

To solve the probability questions, we will assume a non-leap year with 365 days.

(a) Probability that a randomly selected person does not have a birthday on March 14:

There is only one day out of the year that is March 14. Therefore, the probability that a person does have a birthday on March 14 is:

P(March 14) = 1/365

Consequently, the probability that a person does not have a birthday on March 14 is:

P(Not March 14) = 1 - 1/365 = 364/365 ≈ 0.9973

(b) Probability that a randomly selected person does not have a birthday on the 2nd day of a month:

Since there are 12 months in a year, there are 12 days which fall on the 2nd day of each month.

P(2nd day) = 12/365

Therefore, the probability that a person does not have a birthday on the 2nd day of any month is:

P(Not 2nd day) = 1 - 12/365 = 353/365 ≈ 0.9671
(c) Probability that a randomly selected person does not have a birthday on the 31st day of a month:

There are only 7 months with 31 days (January, March, May, July, August, October, December).

P(31st day) = 7/365

Therefore, the probability that a person does not have a birthday on the 31st day of any month is:

P(Not 31st day) = 1 - 7/365 = 358/365 ≈ 0.9808
(d) Probability that a randomly selected person was not born in February:

February has 28 days out of the year.

P(February birthday) = 28/365

Therefore, the probability that a person was not born in February is:

P(Not February) = 1 - 28/365 = 337/365 ≈ 0.9233

The independent variable which will on on the x-axis is the price of a t-shirt.

The dependent variable which will on on the x-axis is the number of t-shirts sold.

The independent variable can be described as the variable that is used to determine the dependent variable. It is the variable that the researcher manipulates in the experiment.  

The dependent variable is the variable whose value is determined in the experiment. The value of the dependent variable depends on the independent variable.  

For example, assume that if the price of a shirt is $1. A person purchases 10 t shirts. If the price increases to $10, only one shirt would be sold. This means that the amount of shirts bought is dependent on the price of the t-shirt. The price of the shirt is the independent variable while the amount of shirts bought is the dependent variable.

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The equation of parabola which represents the graph is f(x) = -3 (x + 1)² + 2.

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.

Here, general equation of parabola in downward direction is

(y-y₁) = -4a(x-x₁)²

vertex of parabola (-1, 2)

(y-2) = -4a(x-(-1))²

(y - 2) = -4a(x + 1)²

put the value of x = 0 and y = -1

so we get, a = 3/4

put in equation of parabola

( y - 2 ) = -3 ( x + 1 ) ²

y = -3 (x + 1)² + 2

f(x) = -3 (x + 1)² + 2

Thus, the equation of parabola which represents the graph is f(x) = -3 (x + 1)² + 2.

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Answer:

The model for the pollutant levels in the soil t years from the first measurement is:

[tex]Y(t)=65e^{0.044}[/tex]

Step-by-step explanation:

We have a first measurement of 65 parts per million (ppm) of pollutant.

We also know that the pollutant levels were growing exponentially at a rate of 4.5% a year.

We can model this as:

[tex]Y(t)=Y_0e^{kt}[/tex]

The value of Y0 is the first measurement, that correspond to t=0.

[tex]Y_0=65[/tex]

The ratio for the pollutant levels for two consecutive years is 1+0.045=1.045. This can be expressed as the division between Y(t+1) and Y(t), and gives us this equation:

[tex]\dfrac{Y(t+1)}{Y(t)}=\dfrac{Y_0e^{k(t+1)}}{Y_0e^{kt}} =\dfrac{e^{k(t+1)}}{e^{kt}}=e^{k(t+1-t)}=e^k=1.045\\\\\\k=ln(1.045)\approx 0.044[/tex]

Then, we have the model for the pollutant levels in the soil t years from the first measurement:

[tex]Y(t)=65e^{0.044}[/tex]

Answer:

6

Step-by-step explanation:

The mode is the number which appears most often in a set of numbers in this case that would be 6 because it appears twice

The mode of a set of values is the one that appears most frequently. In your list: 9, 10, 6, 5, 6 - the number 6 appears twice, more than any other number, making 6 the mode.

In statistics, the mode of a set of values is the value that appears most frequently. An easy way to find the mode is to count the frequency of each number. Looking at your list of numbers: 9, 10, 6, 5, 6. The number 6 is the only number that appears more than once.

So, the mode of the given set of numbers is 6 because it appears more frequently than the other numbers.

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Answer:

Laurens dog: 8 feet

Cheyenne's dog: 2 feet

Step-by-step explanation:

The first step is to evaluate the question, we know that you need to find the height each dog jumped, given the sum of both combined

next, you do simple math:

4x2= 8

10-8= 2

hope this helps

stay safe :))))

brainliest is apprceiated:))))

Answer:

We conclude that the commuting times are same in the winter.

Step-by-step explanation:

We are given that the Census Bureau reports the average commute time for citizens of Cleveland, Ohio is 33 minutes. To see if the commute time is different in the winter, a random sample of 40 drivers were surveyed.

The average commute time for the month of January was calculated to be 34.2 minutes and the population standard deviation is assumed to be 7.5 minutes.

Let [tex]\mu[/tex] = average commute time in winter.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 33 minutes      {means that the commuting times are same in the winter}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 33 minutes      {means that the commuting times are different in the winter}

The test statistics that would be used here One-sample z test statistics as we know about population standard deviation;

                    T.S. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean commute time for the month of January = 34.2

            [tex]\sigma[/tex] = population standard deviation = 7.5 minutes

            n = sample of drivers = 40

So, test statistics  =  [tex]\frac{34.2-33}{\frac{7.5}{\sqrt{40}}}[/tex]  

                              =  1.012

The value of z test statistics is 1.012.

Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test. Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the commuting times are same in the winter.

Also, P-value of the test statistics is given by;

         P-value = P(Z > 1.012) = 1 - P(Z [tex]\leq[/tex] 1.012)

                       = 1 - 0.84423 = 0.1558

3Answer:

Step-by-step explanation:

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images for the step by step explanation to the question

Answer

it is 0

Step-by-step explanation: you have to add 6 yto negative six so it is zero

Answer:

its is the option that shows the first line at six then 0

Answer:

speed = 25 m/s

Step-by-step explanation:

Driving at a speed of 90 km / hour . what is the speed in meters per seconds.

converting from km to meter one have to multiply by 1000. This means 1 km is equal to 1000 meter. Converting 90 km to meter we have to multiply 90 by 1000.

90 × 1000 = 90000 meters

The time is in hours so we have to convert to seconds as required by the question.  

60 minutes = 1 hour

Therefore,

1 minutes = 60 seconds

60 minutes = 3600 seconds

This means 1 hour = 3600 seconds

speed = 90000/3600

speed = 25 m/s

Answer:

mArc A B = 120° (C)

Step-by-step explanation:

Question:

In circle O, AC and BD are diameters.

Circle O is shown. Line segments B D and A C are diameters. A radius is drawn to cut angle D O C into 2 equal angle measures of x. Angles A O D and B O C also have angle measure x.

What is mArc A B?

a)72°

b) 108°

c) 120°

d) 144°

Solution:

Find attached the diagram of the question.

Let P be the radius drawn to cut angle D O C into 2 equal angle measures of x

From the diagram,

m Arc AOC = 180° (sum of angle in a semicircle)

∠AOD + ∠DOP + ∠COP = 180° (sum of angles on a straight line)

x° +x° + x° =180°

3x = 180

x = 180/3

x = 60°

m Arc DOB = 180° (sum of angle in a semicircle)

∠AOB + ∠AOD = 180° (sum of angles on a straight line)

∠AOB + x° = 180

∠AOB + 60° = 180°

∠AOB = 180°-60°

∠AOB = 120°

mArc A B = 120°

Answer:

c

Step-by-step explanation:

Answer:

3.8 percent

Step-by-step explanation:

To find his average return over n years, we sum all of his returns, and divide by n.

In this problem:

5 years.

The sum is (12 + 15 - 15 + 19 - 12) = 19

19/5 = 3.8

So the correct answer is:

3.8 percent

Answer:

The answer is 3.82

Step-by-step explanation:

(12 + 15− 15− 12 + 19)/5 = 3.8 3.

We have been given that a huge ice glacier in the Himalayas initially covered an area of 45 square kilo-meters. The relationship between A, the area of the glacier in square kilo-meters, and t, the number of years the glacier has been melting, is modeled by the equation [tex]A=45e^{-0.05t}[/tex].

To find the time it will take for the area of the glacier to decrease to 15 square kilo-meters, we will equate [tex]A=15[/tex] and solve for t as:

[tex]15=45e^{-0.05t}[/tex]

[tex]\frac{15}{45}=\frac{45e^{-0.05t}}{45}[/tex]

[tex]\frac{1}{3}=e^{-0.05t}[/tex]

Now we will switch sides:

[tex]e^{-0.05t}=\frac{1}{3}[/tex]

Let us take natural log on both sides of equation.

[tex]\text{ln}(e^{-0.05t})=\text{ln}(\frac{1}{3})[/tex]

Using natural log property [tex]\text{ln}(a^b)=b\cdot \text{ln}(a)[/tex], we will get:

[tex]-0.05t\cdot \text{ln}(e)=\text{ln}(\frac{1}{3})[/tex]

[tex]-0.05t\cdot (1)=\text{ln}(\frac{1}{3})[/tex]

[tex]-0.05t=\text{ln}(\frac{1}{3})[/tex]

[tex]t=\frac{\text{ln}(\frac{1}{3})}{-0.05}[/tex]

[tex]t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-0.05\cdot 100}[/tex]

[tex]t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-5}[/tex]

[tex]t=-\text{ln}(\frac{1}{3})\cdot 20[/tex]

[tex]t=-(\text{ln}(1)-\text{ln}(3))\cdot 20[/tex]

[tex]t=-(0-\text{ln}(3))\cdot 20[/tex]

[tex]t=20\text{ln}(3)[/tex]

Therefore, it will take [tex]20\text{ln}(3)[/tex] years for area of the glacier to decrease to 15 square kilo-meters.

Answer:

The answer would be 2924. 82

Answer:

V = 1001

Step-by-step explanation:

This is rather simple question, but I can understand not knowing how to find volume.

The volume of a rectangular prism(as specified by the way the dimensions were given) is whl, when w is width, h is height, and l is length. It does not actually matter the order, due to the Commutative Property of Multiplication, which states that is does not matter what order you multiply things.

Plugging in the numbers, we end up with 1001.

Hope this helps!

Answer:

yes

Step-by-step explanation:

By definition, all sides are the same length, so the perimeter is simply the length of a side times the number of sides.

Since it is true that the distance between sides of a polygon are always the same.

A polygon is defined as a closed figure made up of three or more line segments connected end to end

For a regular polygon of any number of sides, then the sum of its exterior angle is 360° .

Exterior angle is an measure of rotation between one extended side of the polygon with its adjacent side which is not extended. Also, regular having 'n' sides, all the exterior angles are of same measure, and therefore, their measure is (360/n)°.

When a polygon is four sided (a quadrilateral), the sum of its angles is 360°

Based on the definition, all sides are the same length, thus the perimeter is simply the length of a side times the number of sides.

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Answer:

easy peasy lemon squeezy

Step-by-step explanation:

Answer:

Angle A equals Angle B so 6x-2=4x+48 ---> 2x=50 ---> x=25. From this we find that both Angles A and B are equal to 148 degrees. :)

Answer:

[tex]z=\frac{0.47-0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=-1.897[/tex]  

We have aleft tailed test the p value would be:  

[tex]p_v =P(z<-1.897)=0.0289[/tex]  

The p value obtained is less compared to the significance level so then we have enough evidence to conclude that the true proportion is significantly lower than 0.5.

Step-by-step explanation:

Information given

n=1000 represent the random sample selected

X=470 represent the number of people who felt political news was reported fairly

[tex]\hat p=\frac{470}{1000}=0.470[/tex] estimated proportion of people who felt political news was reported fairly

[tex]p_o=0.5[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

z would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

For this case we want to test if proportion for the U.S. is below .50 so then the system of hypothesis for this case are:

Null hypothesis:[tex]p \geq 0.5[/tex]  

Alternative hypothesis:[tex]p < 0.5[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info provided we got:

[tex]z=\frac{0.47-0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=-1.897[/tex]  

We have aleft tailed test the p value would be:  

[tex]p_v =P(z<-1.897)=0.0289[/tex]  

The p value obtained is less compared to the significance level so then we have enough evidence to conclude that the true proportion is significantly lower than 0.5.