Which pairs of figures are congruent? Which pairs are similar?

Answer:

the correct answer is B

Step-by-step explanation:

$2.29 is the cost of a notebook.

Here, we have,

given that,

Jack bought 3 pencils and 4 notebooks and paid a total of $10.93. Sara bought 5 pencils and 2 notebooks and paid a total of $7.53.

let, the cost of a notebook = n

the cost of a pencil = p

we would solve this with simultaneous equations,

so if we write it as:

4n + 3p = 10.93

2n + 5p = 7.53

=> we get,

multiplying the equations by 5 and 3, we get,

20n + 15p = 54.65

6n + 15p = 22.59

(subtract)

14n = 32.06

divide both sides by 14,

14n ÷ 14 = 32.06÷ 14

n = 2.29

notebooks = 2.29

So the final answer is notebooks are $2.29.

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The company is deploying chargeback type of IT funding model where the IT department charges her department for actual usage of a SharePoint server, determining how often users log in and how much storage space her department consumes.

A financing model is a planned, institutionalized strategy for creating a steady income stream to sustain an organization's core services and operations. Nonprofits need funding because it enables them to make investments in their operations and increase their overall effect. Securing funding is crucial to keeping your organization operational because nonprofits frequently rely on grants to assist with operational costs. Grants of all kinds are available to nonprofit organizations.

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The probability that it stops working in less than 2 years is 0.40.

Given:

the probability that a new microwave oven will stop working in less than 2 years is 0.05. the probability that a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. the probability that a new microwave oven is damaged during delivery is 0.10.

here

P ( A ∩ B ) = 0.04

P ( A ) = 0.10

we know that,

According to conditional probability:

P ( B / A ) = P ( A ∩ B ) / P ( A )

substitute values

= 0.04 / 0.10

= 004 / 100 / 010/100

= 4 / 100 * 100 / 10

= 4 * 100 / 100 * 10

= 4 * 1 / 10 * 1

= 4 / 10

= 0.40

Therefore the probability that it stops working in less than 2 years is 0.40.

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The probability that no two teams win the same number of games is 742.

The number of powers of 2 in 40! is

= (40/2) + (40/4) + (40/8) + (40/16) + (40/32)

= 20 + 10 + 5 + 2 + 1

= 38.

780-38 = 742.

Hence, the probability that no two teams win the same number of games is 742.

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A spherical snowball is melting and its radius decreases from 7 cm to 6.8 cm. Its approximate change in volume is 123.2 cm³.

The approximated value can be obtained using derivative approach.

The volume of the sphere is given by:

V = 4/3 πr³

dV/dr = 4 . πr²

Suppose the change of the radius is Δr, using the above derivative, the change of volume can be approximated as:

ΔV = 4 . πr² Δr

Parameters given:

r = 7 cm

Δr = 7 - 6.8 = 0.2 cm

Hence,

ΔV = 4 . π7² (0.2)

ΔV = 4 . π7² (0.2)

ΔV = 123.2 cm³

Therefore, the approximate change in volume is 123.2 cm³

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After 1.67 minutes, the Ferris wheel will be higher than 12 meters.

Given,

The Ferris wheel has a 16-meter diameter.

The circumference of a circle with a diameter of 16 meters, which is calculated as follows, is the distance travelled by the Ferris wheel in one rotation; 16π meter

The Ferris wheel makes one revolution in 7 minutes, hence the following is true:

16π meter = 7 minutes

1 meter = (7/16π) minutes

12 meters = (7 ×12)/16π minutes

12 meters = 1.67 minutes

Therefore,

The Ferris wheel will be above 12 meters after 1.67 minutes.

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The given statement is false.

Given that,

The z-statistic can be used as the foundation for statistical inferences about the difference in two population means using two independent random samples if the populations are normally distributed but the population variances are unknown.

If the sample sizes are small, the populations are normally distributed, and the population variances are known, the z statistic can be used as the foundation for statistical inferences about the difference between two population means using two independent random samples.

Therefore, the above given statement can be concluded as false.

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The regression equation is y = 0.9x+ 7.5

given that

xi:  2   6    9    13    20

Yi : 7   18   9    26   23  

from the given data we have:

∑x = 2+6+9+13+20 = 50

∑y = 7+18+9+26+23 = 83

Also, we need to calculate:

∑xy = 2 × 7+ 6 × 18+ 9× 9+ 13 × 26+ 20×23 = 1001

∑[tex]x^{2}[/tex] = [tex]2^{2}[/tex] + [tex]6^{2}[/tex] + [tex]9^{2}[/tex] + [tex]13^{2}[/tex] + [tex]20^{2}[/tex] = 690

∑[tex]y^{2}[/tex]= [tex]7^{2}[/tex] +  [tex]18^{2}[/tex] + [tex]9^{2}[/tex] + [tex]26^{2}[/tex] + [tex]23^{2}[/tex] = 1659

the slope b is calculated:

b = ∑xy - ∑x × ∑y/n ÷ ∑[tex]x^{2}[/tex] - (∑x)^2 /n

now we need to substitute above values in the equation:

b = 1001 - 50×83 /5 ÷ 690 - (50)^2/5

b= 0.9

the y-intercept (a) is :

a = y - bx

where

y = ∑y/n = 83/5 = 16.6

x = ∑x/n = 50/5 = 10

now substitute these values

a = 16.5 - 0.9 × 10

a = 7.5

the regression equation:

y = bx + a

now ,

y = 0.9x+ 7.5

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The probability for given conditions are a) p(4)=0.166, b) p(even)=0.5 and c) p(greater than 3)=0.5

A die is rolled, then the sample space for outcomes is {1,2,3,4,5,6}

Total number of outcomes =6

Thus, the probability for given conditions are a)p(4)=0.166, b)p(even)=0.5 and c)p(greater than 3)=0.5

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The probability that a seat will be available for every person holding a reservation and planning to fly is 0.8980.

What is probability?

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

Given:

The probability that a person who makes reservations on a certain flight and does not show up for the flight is p=0.05.

The probability that a person who makes reservations on a certain flight and does show up for the flight is 1-p=1-0.05=0.95.

The airlines sell 160 tickets for a flight with only 155 seats.

Let X be a random variable that denotes the number of persons who show up for the flight and it follows a binomial distribution with parameters n = 160 and p = 0.95.

Hence, X~ Binom (n = 160, p = 0.95).

Here,

np=160×0.95=152>5

n(1-p)=160×0.05 = 8.1>5

Hence, both np and n(1-p) are greater than 5, the binomial distribution can be approximated to normal distribution.

The probability that a seat will be available for every person holding a reservation and planning to fly is calculated as follows:

P(X ≤ 155) = (P < 155 + 0.5)

                 [tex]=P(x < 155.5)\\\\=P(\frac{X-np}{\sqrt{np(1-p)}} < \frac{155.5 - (160 \times 0.95}{\sqrt{160\times 0.95 \times 0.05}})\\\\=P(Z < \frac{155.5-152}{2.7568})\\\\=P(Z < 1.27)\\\\=0.8980[/tex]

Hence the probability that a seat will be available for every person holding a reservation and planning to fly is 0.8980.

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A 95% confidence interval for the difference in mean revenue at the box office for drama and comedy movies is (7.44, 72.56).

We have given that,

Sample mean of peoples who like drama , x₁-bar = 190

Sample mean of peoples who like comedy,x₂-bar = 150

Sample size for darama sample, n₁ = 17

Sample size for comedy sample, n₂ = 14

Standard deviations, s₁ = 60

Standard deviations, s₂ = 30

Confidence level = 0.95 or 95%

Using Z-table , Z-score for 95% confidence level is 1.96..

We have to calculate a 95% confidence interval for the difference in mean revenue at the box office for drama and comedy movies.

It is given by following Confidence interval formula,

x₁-bar - x₂-bar ± Z ( √(s₁²/n₁ + s₂²/n₂))

= 190 - 150 ± 1.96(√(60²/17 + 30²/14))

= 40 ± 1.96(√3600/17 + 900/14))

= 40 ± 32.56

= (7.44, 72.56)

Hence, the required 95% confidence interval is

(7.44, 72.56) .

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Complete question:

A Hollywood studio believes that a movie that is considered a drama will draw a larger crowd on average than a movie that is considered a comedy. To test this theory. the studio randomy selects several movies that are classified as dramas and several movies that are classified as comedies and determines the box office revenue for. each movie. The results of the survey are as follows. Assurne that the population variances are approximately equal, Calculate a

95%

confidence interval for the difference in mean revenue at the box office for drama and comedy movies: Let dramas be Population-1 and comedies be Population 2. Write your answer using interval notation and round the interval endpoints to two decimal places

20.11 cm3/min is the rate at which the snowball's volume is decreasing.

Given,

The decreasing diameter when the spherical ball is melting = 0.2 cm/min

We have to find the rate in decrease in volume of snowball when diameter is 8 cm.

Here,

Volume of sphere, V = 4/3 π r³ = 4/3 π (D/2)³ = 1/6 π D³

Considering differences according to time,

dV/dt = d/dt (1/6 π D³) = 1/6 π × 3D² dD/dt

dV/dt = 1/2 π D² dD/dt

Substituting

D is 8 cm, and the diameter is changing at a rate of 0.2 cm/min.

dV/dt = 1/2 π D² dD/dt

dV/dt = 1/2 × π × 8² × 0.2 = 20.11 cm³/min

Therefore,

Decreasing snowball volume at a rate of 20.11 cm3/min

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4300 km to miles:

[tex]{ \red{ \tt{2671.896}}}[/tex]

2671.896 in nearest whole number :

[tex]{ \blue{\boxed{ \tt{2672}}}}[/tex]

The percent of increase on the truck was 375%.

The value of n should be greater than -5/2 and less than 3. So the value of n under the interval (-5/2, 3).

In the given question, n is an integer with -5<2n<6.

We have to write the value of integer.

As we know;

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. A common way to represent the set of integers in mathematical terms is z with bold.

To find the value of integer n we firstly divide the whole inequality by 2.

The given inequality is -5<2n<6.

Divide by 2, we get

-5/2<n<3

Now we can say that the value of n should be greater than -5/2 and less than 3. So the value of n under the interval (-5/2, 3).

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The 95% confidence interval for the population proportion who claim they always buckle up is 0.0204.

a) x: 330

b) n: Number of drivers who are surveyed = 430

c) p': proportion of drivers in a sample who claimed to always buckle up = 0.7674

d) normal distribution should be used for this problem.

e) 95% confidence interval for the population proportion who claim they always buckle up.

The error margin is:

1.96 × sqrt(p(1-p) ÷ n)

1.96 × sqrt(0.7674 × 0.2326 ÷ 430) = 0.0204

(0.7674 - 0.0204,0.7674 + 0.0204) = (0.747, 0.7878)

The confidence interval is (0.747, 0.7878).

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The  frequency table formed using tally marks can be analyzed by using the numbers indicated by the tally  marks as follows;

The true statements are as follows;

Tally marks makes use of vertical lines to represent data, in which the fifth count is represented by a diagonal line across four vertical lines;

The data in the table are as follows

The number of students that prefer red = 5 + 1 = 6

The number of students that prefer yellow = 2

The number of students that prefer Blue = 5

The number of students that prefer purple = 3

The number of students that prefer Green = 6

Therefore;

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Yes, this statement is true. Because flux integral of curl vector does not depend on surface, it depends only on the boundary of the surfaces. Till we are integrating in the same boundary limits.

Given:

The image displays a paraboloid's part P, its hemisphere H, and its disk D. Assume F is a vector field on R3 with continuous partial derivatives in each of its components.

we are asked why the statement is true = ?

Yes, this claim is accurate. Because the flux integral of the curl vector is surface-independent, it only depends on the boundaries of the surfaces. till our integration is within the same boundary limitations.

Hence above given expression will hold true.

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Answer:

see solution

Step-by-step explanation:

equation: y = 1 - 3x

when x is -2:
y = 1 -3 * -2  = y = 1+6 = y = 7
coordinates = (x,y) = (-2,7)

when x is -1:
y = 1-3*-1 = y = 1+3 = y = 4
coordinates = (x,y) = (-1,4)

when x is 0:
y = 1 - 3 * 0 = y = 1-0 = y =1
coordinates = (x,y) = (0,1)

when x is 1
y = 1-3*1 = y = 1-3 = y = -2
coordinates = (x,y) = (1,-2)

When x is 2
y = 1-3*2 = y = 1-6 = y = -5
coordinates = (x,y) = (2,-5)

when x is 3
y = 1-3*3 = y = 1-9 = y = -8
coordinates = (x,y) = (3,-8)

Plot these points on the graph and join up the dots to see the line.

bye

Using proportions and ratios, the cost of 1.4lbs is $10.96

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

This is basically the process of comparing two ratios with one another.

In this problem, we will compare the two ratios and solve for the unknown cost of 1.4lbs

0.6 / 4.71 = 1.4 / x

Cross multiply both sides

x = (4.71 * 1.4) / 0.6

x = 10.96

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Answer:

2 1/6 more cups

Step-by-step explanation:

Answer: 2 1/6

Step-by-step explanation:

2 1/6

Answer: Yes, they are proportional

Answer:

No.

Step-by-step explanation:

A proportional relationship shows that each time the amount of money would have increased/decreased in the same amount if she had payed it off constantly and it did not therfore your answer is no.

Answer:

6400

Step-by-step explanation:

-2(12-2(-4))^2

Simplify:

-2(10(-4))^2

-2(-40))^2

80^2

6400

Answer: y=3x-1

Step-by-step explanation:

1st subtract 1 from 16 so 15 then do 15/5 to get 3 seconds

The probability P(DD) of the letters D and D is 4/9

The letters of the alphabets used to generate the word ADD are given as

Sample space (letters) = {A, D, D}

It is assumed that when a card (i.e. letter) is selected, the card is returned to the set

This means that the selection is with replacement

These letters mean that

P(Letter D) = Count of letter D/Number of letters

So, we have the following representation

P(Letter D) = 2/3

Now, the sample space is

Sample space (letters) = {A, D, D}

These letters mean that

P(Letter D2) = 2/3

So, we have the probability equation

P(DD) = P(D) * P(D2)

This gives

P(DD) = 2/3 * 2/3

Evaluate

P(DD) = 4/9

So, the probability is 4/9

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A good half a mile time is totally good, if a half mile is the longest distance you've ever run, try a 3/4 mile run the next time. After a few successful attempts at that distance, increase it to a mile.

In the given question, we have to explain, what is a good half a mile time.

First, some background is required for 5:43 for half a mile. When did you start running? Was that time calculated using a full effort, or was it only the distance covered without walking? Don't worry about if it's good if you're spanking new. Use it as a foundation.

Second, like with most things in life, practise makes perfect, and running performance is no exception. If a half mile is the longest distance you've ever run, try a 3/4 mile run the next time. After a few successful attempts at that distance, increase it to a mile. The goal is to gradually push your boundaries until you consistently cross that threshold and then push your limits even farther.

Your body will be encouraged to adapt to the challenge, grow to it, and become prepared for when the challenge gets harder.

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For the correct statement of the p-value, we would reject the null hypothesis.

There are two main methods for interpreting the statistical significance of a hypothesis test;

1) compare the p-value to the level of significance or

2) compare test statistics to a critical value.

Either method is acceptable, and is chosen by the researcher based upon which one is most typical in their field of research.

Under a hypothesis test we reject the null hypothesis if our p-value is less than the level of significance (p<α), and fail to reject the null hypothesis otherwise. Under the question, we are given a level of significance of 0.05 and a p-value of 0.01, where

p = 0.01 <α = 0.05

hence we would reject the null hypothesis. Thus the statement is TRUE.

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The best guess for the mean score for all the Georgia students would be 1050 number here.

Given that:

The mean score for a random sample of Georgia students is 1050.

Assuming,

1) X-bar = 42; µ = 44; standard deviation (sigma) = 10; N = 64. Calculate the standard error.

1) The standard error is computed as:

[tex]\sigma_{\bar X} = \frac{\sigma}{\sqrt{n}} = \frac{10}{\sqrt{64}} = 1.25[/tex]

2) You know that X-bar = 42, mu = 44, sigma-sub-X = 10, and N = 64, Calculate z-obtained.

2) The Z-value is computed as:

[tex]Z = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{N}}} = \frac{42- 44}{\frac{10}{\sqrt{64}}} = -1.6[/tex]

3) The mean score on most IQ tests is 100 with a standard deviation of 15. If Sally has a score of 110 on an IQ test, what is her z-score.

3) The Z -score here is computed as:

[tex]Z = \frac{X -\mu}{\sigma} = \frac{110-100}{15} = 0.6667[/tex]

The best point estimate for the population mean score is equal to the sample mean which is 1050 in this case. Therefore the best guess for the mean score for all the Georgia students would be 1050 here.

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Answer:

by dividing by 100

Step-by-step explanation:

630 ÷ 100 = 6.3