Match each
Match each investment characteristic to the level of risk involved.
growth
savings
speculation
high risk because returns are not guaranteed, but time frames are set
moderate risk because expectations of returns are reasonable and average
low risk because of steady interest without fluctuation in value

Answer:

a) - The population consists of all of Danielle's colleagues that could have been one of the randomly surveyed 50.

- The sample is Danielle's 50 colleagues that she ramdomly sampled.

b) From the statistical test performed, there is significant evidence to conclude that Danielle is truly overpaying for her auto insurance compared to her colleagues.

c) Check Explanation

Step-by-step explanation:

The full complete, correct question is attached to the solution of this question.

a) The population is normally the extended distribution where every selected random sample is extracted from. So, for this question, the population will be all of Danielle's colleagues.

The sample is the subset distribution obtained from the population. In the question, it is stated explicitly that Danielle randomly picked 50 of her colleagues to participate in the survey. Hence, the sample is Danielle's 50 colleagues that she ramdomly sampled.

b) The appropriate statistical inference for this question is to carry out the t-test hypothesis test.

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, Danielle wants to prove that she is overpaying for her auto insurance compared to her colleagues.

So, the null hypothesis is that there is no significant evidence to conclude that Danielle is overpaying for her auto insurance compared to her colleagues.

That is, Danielle isn't overpaying for her auto insurance compared to her colleagues or better stated that her colleagues are paying more than or just about the same for auto insurance compared to her.

While, the alternative hypothesis is that there is significant evidence to conclude that Danielle is overpaying for her auto insurance compared to her colleagues.

Let μ be the mean Danielle's colleagues' auto insurance fees.

Mathematically,

The null hypothesis is represented as

H₀: μ ≥ 476

The alternative hypothesis is given as

Hₐ: μ < 476

To do this test, we will use the t-distribution because no information on the population standard deviation is known

So, we compute the t-test statistic

t = (x - μ₀)/σₓ

x = sample mean = $447

μ₀ = Danielle's auto insurance bill that we're comparing the sample against = $476

σₓ = standard error = [σ/√n]

σ = Sample standard deviation = $75

n = Sample size = 30 (30 colleagues got back to Danielle)

σₓ = [75/√30] = $13.693

t = (447 - 476) ÷ 13.693

t = -2.117 = -2.12

checking the tables for the p-value of this t-statistic

Degree of freedom = df = n - 1 = 30 - 1 = 29

Significance level = 0.05 (Most hypothesis tests are carried out at this level of significance)

The hypothesis test uses a one-tailed condition because we're testing only in one direction. (Checking whether Danielle is overpaying or that the mean is of her colleagues' auto insurance fees is less than Danielle's)

p-value (for t = -2.12, at 0.05 significance level, df = 29, with a one tailed condition) = 0.021342

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.021342

0.021342 < 0.10

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that Danielle is truly overpaying for her auto insurance compared to her colleagues.

c) The two type of errors associated with this test include the Type I and Type II errors.

In Hypothesis testing, A type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true.

A type II error involves failing to reject the null hypothesis when in reality it should have been rejected. It entails not rejecting the null hypothesis and making conclusions based on the null hypothesis, when in reality, the alternative hypothesis should have been accepted together with its conclusion.

For this question, a type I error entails obtaining from the statistical test that Danielle is overpaying when she isn't overpaying for her auto insurance compared to her colleagues in reality.

A type II error would be obtaining from the statistical test that Danielle isn't overpaying when she is truly overpaying for her auto insurance compared to her colleagues, in reality.

Hope this Helps!!!

Answer:

8 to 20 1 to 4 4 to 10

Step-by-step explanation:

it was easy

Answer:

7

Step-by-step explanation:

67ururiierururf8fucicififfifig

Answer:

25 miles per gallon x 7 gallons used=175 miles driven

175/7=25

NOTE: THIS IS AN EXAMPLE

Answer:

14%

Step-by-step explanation:

you divide 35 by 245 to get 0.14285714285 than you round

The student asked about the simple interest earned on an investment. The simple interest can be calculated using the formula I = PRT. For a principal of $21,500 at a 9% APR for 16 years, the interest earned is $30,960.

To calculate simple interest, you can use the formula I = PRT, where I is the interest, P is the principal amount (the initial amount of money), R is the rate of interest per period, and T is the time the money is invested for.

In this case, we have:

Plugging these values into the formula, we get:

I = PRT

I = $21,500 × 0.09 × 16

I = $30,960

The simple interest earned after 16 years is $30,960.

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Final answer:

The simple interest on $21,500 at 9% APR over 16 years is calculated using the formula I = PRT, which gives us a total interest of $30,960.

Explanation:

To calculate the simple interest earned on a sum of money, we can use the formula I = PRT, where I stands for interest, P for principal amount, R for the annual interest rate (in decimal form), and T for the time in years. In this case, the student wants to determine the interest earned on $21,500 at 9% APR for 16 years.

First, convert the interest rate from a percentage to a decimal by dividing by 100:

R = 9% / 100 = 0.09

Next, apply the values to the simple interest formula:

I = PRT

I = $21,500 × 0.09 × 16

I = $30,960

Therefore, the total simple interest earned after 16 years is $30,960.

Answer:

(a) The expected value of the prize for one play of Instant Lotto is $3.50.

(b) The probability that the visitor wins some prize at least twice in the 20 free plays is 0.2641.

(c) The probability that a randomly selected day has at least 1000 people play Instant Lotto is 0.2579.

Step-by-step explanation:

(a)

The probability distribution of the monetary prizes that can be won at the game called Instant Lotto is:

X         P (X = x)

$10        0.05

$15        0.04

$30       0.03

$50       0.01

$1000   0.001

$0         0.869

___________

Total =   1.000

Compute the expected value of the prize for one play of Instant Lotto as follows:

[tex]E(X)=\sum x\cdot P (X=x)[/tex]

         [tex]=(10\times 0.05)+(15\times 0.04)+(30\times 0.03) \\+ (50\times 0.01)+(1000\times 0.001)+(0\times 0.869)\\=0.5+0.6+0.9+0.5+1+0\\=3.5[/tex]          

Thus, the expected value of the prize for one play of Instant Lotto is $3.50.

(b)

Let X = number of times a visitor wins some prize.

A visitor to the casino is given n = 20 free plays of Instant Lotto.

The probability that a visitor wins at any of the 20 free plays is, p = 1/20 = 0.05.

The event of a visitor winning at a random free play is independent of the others.

The random variable X follows Binomial distribution with parameters n = 20 and p = 0.05.

Compute the probability that the visitor wins some prize at least twice in the 20 free plays as follows:

P (X ≥ 2) = 1 - P (X < 2)

              = 1 - P (X = 0) - P (X = 1)

              [tex]=1-[{20\choose 0}0.05^{0}(1-0.05)^{20-0}]-[{20\choose 1}0.05^{1}(1-0.05)^{20-1}]\\=1-0.3585-0.3774\\=0.2641[/tex]

Thus, the probability that the visitor wins some prize at least twice in the 20 free plays is 0.2641.

(c)

Let X = number of people who play Instant Lotto each day.

The random variable X is normally distributed with a mean, μ = 800 people and a standard deviation, μ = 310 people.

Compute the probability that a randomly selected day has at least 1000 people play Instant Lotto as follows:

Apply continuity correction:

P (X ≥ 1000) = P (X > 1000 + 0.50)

                    = P (X > 1000.50)

                    [tex]=P(\frac{X-\mu}{\sigma}>\frac{1000.50-800}{310})[/tex]

                    [tex]=P(Z>0.65)\\=1-P(Z<0.65)\\=1-0.74215\\=0.25785\\\approx0.2579[/tex]

Thus, the probability that a randomly selected day has at least 1000 people play Instant Lotto is 0.2579.

Angle: [tex]\( 60^\circ \)[/tex], complementary angle: [tex]\( 30^\circ \)[/tex]. Angle is 30° more than its complementary angle.

Let's denote the measure of the angle as [tex]\( x \)[/tex] degrees.

The complementary angle would be [tex]\( 90^\circ - x \)[/tex] degrees.

Given that the angle measures 30° more than its complementary angle, we can write the equation:

[tex]\[ x = (90^\circ - x) + 30^\circ \][/tex]

Now, let's solve for [tex]\( x \)[/tex]:

[tex]\[ x = 90^\circ - x + 30^\circ \][/tex]

[tex]\[ 2x = 90^\circ + 30^\circ \][/tex]

[tex]\[ 2x = 120^\circ \][/tex]

Dividing both sides by 2:

[tex]\[ x = \frac{120^\circ}{2} \][/tex]

[tex]\[ x = 60^\circ \][/tex]

So, the angle measures [tex]\( 60^\circ \)[/tex] and its complementary angle measures:

[tex]\[ 90^\circ - 60^\circ = 30^\circ \][/tex]

Therefore, the measure of the angle is [tex]\( 60^\circ \)[/tex] and the measure of its complementary angle is [tex]\( 30^\circ \)[/tex].

Answer:

-1

Step-by-step explanation:

The weight of the cell phone is given by:

[tex]W=2.8*10^n[/tex]

The options provided for 'n' are:

a. -3

b. -1

c. 0

d. 1

Applying the possible values:

[tex]W_a=2.8*10^{-3}\\W_a = 0.0028\ pounds\\\\W_b=2.8*10^{-1}\\W_b = 0.28\ pounds\\\\W_c=2.8*10^{0}\\W_c = 2.8\ pounds\\\\W_d=2.8*10^{1}\\W_d = 28\ pounds[/tex]

A cellphone could not possibly weigh as little as 0.0028 or as much as 2.8 or 28 pounds. Therefore, the most reasonable value for n is -1.

Answer:

(B)-1

Step-by-step explanation:

Let us plug in the given values into [tex]2.8X10^n[/tex][tex]2.8X10^{-3}=2.8X 0.001=0.0028\:Pounds\\2.8X10^{-1}=2.8X 0.1=0.28\:Pounds\\2.8X10^{0}=2.8X 1=2.8\:Pounds\\2.8X10^{1}=2.8X 10=28\:Pounds[/tex]

A reasonable value for the weight of a cell phone will be 0.28 Pounds.

Therefore, n=-1

Answer:

Bruh i got correlation hw that i posted on here too and nobody helped lol.

Step-by-step explanation:

Answer:

It should go exponents, multiplication and division, then addition and subtraction

Step-by-step explanation:

By using PEMDAS, for order of operations, it's easier to remember which set comes first. (parentheses, exponents, multiplication, division, addition, subtraction)

Answer:

114 square meters

Step-by-step explanation:

formula:1/2×h(a+b)

1/2×12{(12+5)+12}

1/2×12(17+12)

=6×19

=114m^2

Answer:

-0.71828

Step-by-step explanation:

2 + e(6-7)

2 + e(-1)

2 -e

e is approximately 2.718281828459045235360287471352662497757247093699959574966

2 - 2.71828.....

-0.71828

Answer:

2.37 (3 sf)

Step-by-step explanation:

2 + e^(6-7)

2 + e^(-1)

2 + 1/e (exact)

Roughly, 2.367879441

Answer:

(D) 180 degrees

Step-by-step explanation:

There are 12 hours on the clock.

For each 1 hour, the hour hand rotates = [tex]360^0 \div 12=30^0[/tex]

From 8 o'clock in the morning to 2 o'clock in the afternoon= 6 Hours

Therefore:

Number of degrees rotated by the hour hand = [tex]6 X 30^0 =180^0[/tex]

Answer:

=BINOMDIST(10,25,70%,FALSE) -BINOMDIST(5,25,70%,FALSE)

0.001324586

Step-by-step explanation:

The success probability is p = 70% = 0.70

The number of trials are n = 25

The Excel formula for the binomial distribution is given by

BINOMDIST(Number_s, Trial_s, Probability_s, Cumulative)

Where

Numbers = 5 and 10

Trials = 25

Probability = 70%

Cumulative = FALSE

The probability of between 5 and 10 customers is then

=BINOMDIST(10,25,70%,FALSE) -BINOMDIST(5,25,70%,FALSE)

0.001324586

Note: FALSE option provides the probability of exactly 10 and 5 where TRUE option gives cumulative results (0 to 5 or 0 to 10) that would be wrong in this case.

Using the binomial distribution, it is found that the Excel statement that will find the probability of between 5 and 10 customers is:

BINON.DIST.RANGE(25, 0.75, 5, 10)

For each customer, there are only two possible outcomes, either they purchase a pair of running shoes, or they do not. Customers' purchases are independent, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Using Excel, the probability of the number of successes being between a and b, inclusive, is given by:

BINOM.DIST.RANGE(n, p, a, b)

In this problem:

Then, the Excel statement is:

BINON.DIST.RANGE(25, 0.75, 5, 10)

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Answer:

[tex]P(49.5<X<67.2)=P(\frac{49.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{67.2-\mu}{\sigma})=P(\frac{49.5-55.7}{5.2}<Z<\frac{67.2-55.7}{5.2})=P(-1.192<z<2.212)[/tex]

[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)[/tex]

[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)=0.987-0.117=0.870[/tex]

Step-by-step explanation:

We define X the random variable that represent the heights of a population for ten year old children, and for this case we know the distribution for X is given by:

[tex]X \sim N(55.7,5.2)[/tex]  

Where [tex]\mu=55.7[/tex] and [tex]\sigma=5.2[/tex]

We want to find this probability:

[tex]P(49.5<X<67.2)[/tex]

We can use the z score formula to solve this problem given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula we have:

[tex]P(49.5<X<67.2)=P(\frac{49.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{67.2-\mu}{\sigma})=P(\frac{49.5-55.7}{5.2}<Z<\frac{67.2-55.7}{5.2})=P(-1.192<z<2.212)[/tex]

And we can find this probability with this difference

[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)[/tex]

We can use tables for the normal standard distribution, excel or a calculator and we got this

[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)=0.987-0.117=0.870[/tex]

Answer:

The expected number of tickets a customer will get is 4.75.

Step-by-step explanation:

The probability distribution of the number of ticket a wheel at a shopping center is arranged to give is as follows:

X           Probability (p)

2                  0.50

5                  0.25

10                  0.23

10                  0.02

The formula to compute the expected value of a random variable is:

[tex]E(X)=\sum x\cdot P (X=x)[/tex]

Compute the expected number of tickets a customer will get as follows:

[tex]E(X)=\sum x\cdot P (X=x)[/tex]

         [tex]=(2\times 0.50)+(5\times 0.25)+(10\times 0.23)+(10\times 0.02)\\=1+1.25+2.3+0.2\\=4.75[/tex]

Thus, the expected number of tickets a customer will get is 4.75.

Under a normal distribution with a mean of 16 ounces and a standard deviation of 0.5 ounce, there's a 15.87% probability that a randomly selected can will have less than 15.5 ounces of soda.

This question is related to probability within the field of statistics. Particularly, it's about the normal distribution, a common statistical distribution that shows the spread of data around the mean. In this specific case, the amount of soda in a 16-ounce can is normally distributed with a mean (µ) of 16 ounces and a standard deviation (σ) of 0.5 ounce.

We're asked to calculate the probability that a randomly selected can will have less than 15.5 ounces. This requires us to standardize the score of 15.5, meaning we use the formula (X - µ) / σ, where X is the value we are assessing. So, (15.5 - 16) / 0.5 equals -1.

This standardized score is known as a z-score, and tells us how many standard deviations a value is from the mean. In this case, 15.5 is one standard deviation below the mean. We then look up this z-score in a z-table, which gives us the probability associated with this z-score. For a z-score of -1, the probability is 0.1587, or 15.87%.

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The probability that a randomly selected can will have less than 15.5 ounces is approximately 0.1587.

To find the probability that a randomly selected can will have less than 15.5 ounces, we can use the standard normal distribution.

First, we need to calculate the z-score for 15.5 ounces using the formula:

where:

Plugging in the values:

Next, we look up the z-score of -1 in the standard normal distribution table to find the probability. The probability that a randomly selected can will have less than 15.5 ounces is the area to the left of the z-score of -1.

Using the standard normal distribution table, the area to the left of -1 is approximately 0.1587.

Therefore, the probability that a randomly selected can will have less than 15.5 ounces is approximately 0.1587.

Answer:

The graphs of the equations intersect each other at two places.

The correct answer is the graphs of the equations intersect each other at two places.

A quadratic expression can be written as the product of two linear factors and each factor can be equated to zero, So there exist two solutions.

Each shows two lines that make up a system of equations. If the graphs of the equations intersect, then there is one solution that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.

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The type of triangle is,

⇒ A scalene triangle

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The angle measures in a triangle are 25°, 135°, and 20°.

Now, We have alL angles are different to each other.

Hence, By definition of a scalene triangle,

The type of triangle is,

⇒ A scalene triangle

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Answer:

(5 x 15) + (3 x 15) = 120

Step-by-step explanation:

5 x 15 = 75

3 x 15 = 45

75 + 45 = 120

Hope this helps :)

Answer:

5 * 15 = 75

3 * 15 = 45

45 + 75 = 120

Step-by-step explanation:

When you have a equation like that, you need to multiply. It is a faster way to solve the problem.

You had 15 five times.

15+15+15+15+15= 75 It equals the same thing because it is the same as 5 * 15

Same for the three fifteens.

15+15+15= 45.

The sum of the whole equation is 120 because you add 75 and 45.

Hope this helps, have a good day/night. Stay safe and healthy!

The length of the L of the ramp, which the builder makes with a base to height ratio of 12 to 1 is 9.63 meter.

Pythagoras theorem states that, right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

A builder makes all the ramps with a base to height ratio of 12 to 1 to be wheelchair accessible.

Let p is the factor of ratio. Thus, the height and base is,

h = p

b = 12p

According to Pythagoras theorem,

unknown side (say l) is hypotenuse

l² = (12p)² + p²

[tex]l^2=144p+p^2[/tex]

[tex]l = \sqrt{144p+p^2}[/tex]

[tex]l = \sqrt{145} p[/tex]

A ramp needs to cover a height of 0.8 m. Height is equal to the factor p.

Thus, the value of p is,

p = h

p = 0.80

Thus, the length of the l is,

[tex]l = \sqrt{145} p[/tex]

[tex]l = \sqrt{145} {(0.8)}[/tex]

[tex]l=(12.041)(0.8)[/tex]

[tex]l=9.63m[/tex]

Hence, the length of the L of the ramp, which the builder makes with a base to height ratio of 12 to 1 is 9.63 meter.

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The correct question has in the image below

Answer:

7

Step-by-step explanation:

The comparison of the slopes is accurate: the slope of the line for Car 1 is greater than the slope of the line for Car 2.

Step 1:

The comparison of the slopes of the two lines can be made by calculating the slope of each line. Let's calculate the slopes:

For Car 1:

The coordinates are (2, 50) and (4, 100).

Using the slope formula [tex]\( m = \frac{y_2 - y_1}{x_2 - x_1} \)[/tex]:

[tex]\[ m = \frac{100 - 50}{4 - 2} = \frac{50}{2} = 25 \][/tex]

For Car 2:

The coordinates are (2, 40) and (4, 80).

Using the slope formula:

[tex]\[ m = \frac{80 - 40}{4 - 2} = \frac{40}{2} = 20 \][/tex]

Step 2:

Comparing the slopes:

- The slope of the line for Car 1 is 25.

- The slope of the line for Car 2 is 20.

Therefore, the comparison of the slopes is accurate: the slope of the line for Car 1 is greater than the slope of the line for Car 2.

Answer:

Point Estimate for different between population means = - 0.99

Step-by-step explanation:

We are given data of two samples and we have to find the best point estimate of the true difference between two population means. Remember that in absence of data about population the best estimator is the sample data. So, we will find the means of both sample data and find the difference of that means. This difference between the means of sample data will be the best point estimate for the true difference between the population means.

Formula to calculate the mean is:

[tex]Mean=\frac{\text{Sum of Values}}{\text{Number of Values}}[/tex]

Mean of Sample 1:

[tex]Mean=\frac{1414}{11}=128.55[/tex]

Mean of Sample 2:

[tex]Mean=\frac{1684}{13}=129.54[/tex]

Therefore the best point estimate for difference between two population means would be = Mean of Sample 1 - Mean of Sample 2

= 128.55 - 129.54

= - 0.99

Final answer:

The point estimate for the true difference between the given population means is -1.028.

Explanation:

The point estimate for the true difference between the given population means can be found by subtracting one sample mean from the other. Let's calculate it:

Sample 1: 129, 127, 129, 129, 128, 130, 127, 129, 128, 131, 127
Sample 2: 131, 126, 132, 129, 128, 131, 131, 130, 128, 129, 126, 132, 131

Sample mean of Sample 1 = (129+127+129+129+128+130+127+129+128+131+127)/11 = 128.818

Sample mean of Sample 2 = (131+126+132+129+128+131+131+130+128+129+126+132+131)/13 = 129.846

Point estimate for the difference = Sample mean of Sample 1 - Sample mean of Sample 2 = 128.818 - 129.846 = -1.028

Answer:

The y-intercept is y = 2

Step-by-step explanation:

A linear function has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept, which is the value of y when x = 0.

We are given these three points:

(-28, -54)

(-21, -40)

(-14, -26)

We use two of them to build a system, to find values for m and b.

(-28, -54)

This means that when [tex]x = -28, y = -54[/tex]

So

[tex]y = mx + b[/tex]

[tex]-54 = -28m + b[/tex]

[tex]28m = b + 54[/tex]

[tex]m = \frac{b + 54}{28}[/tex]

(-21, -40)

This means that when [tex]x = -21, y = -40[/tex]

So

[tex]y = mx + b[/tex]

[tex]-40 = -21m + b[/tex]

[tex]-40 = -21\frac{b + 54}{28} + b[/tex]

[tex]-40 = \frac{-21b - 1134 + 28b}{28}[/tex]

[tex]7b - 1134 = -40*28[/tex]

[tex]7b = 14[/tex]

[tex]b = \frac{14}{7}[/tex]

[tex]b = 2[/tex]

The y-intercept is y = 2

Answer:

y = (0,2)

Step-by-step explanation:

Answer:

[tex]a. \ H_o:p=0.45, \ \ \ \ H_a:p\neq 0.45\\\\b.\ \hat p=0.2209\\\\c. \ Yes\ (-4.2706<-1.96)[/tex]

Step-by-step explanation:

a. The professor's claim is that 45% first-timers fail his test. The null hypothesis is therefore stated as:

[tex]H_o:p=0.45[/tex]

-The alternative hypothesis is that more or less people fail the test as opposed to the professor's exact claim, hence:

[tex]H_a:p\neq 0.45[/tex]

b. To compute the P-value we use the z-value for a 95% confidence level:

[tex]z_{\alpha/2}=z_{0.025}=1.96[/tex]

#The proportion of failures in the sample of 86 is 19:

[tex]\hat p=\frac{19}{86}\\\\=0.2209[/tex]

The z-value is calculated as:

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

[tex]=\frac{0.2209-0.45}{\sqrt{\frac{0.45(1-0.45)}{86}}}\\\\\\=-4.2706[/tex]

-4.2706 is less than the stated confidence level for the given 45% proportion and greatly differs from it.

- Reject the null hypothesis as there is enough evidence to reject the claim.

-Hence,Yes, Professor Brown can conclude that percentage  of failures differs from 45%.

Answer:

840cm³

Step-by-step explanation:

devide them into 2 shapes.

a×b×h

a×b×h

V=720cm³+120cm³=840cm³

Answer:

840 cm^3

Step-by-step explanation:

L x W x H = V

Split the prism into 2 different prisms.

6 is constant throughout the figure, so all we have to do is find the L and H of the two prisms and multiply them by 6.

15 x 8 = 120

The height of the higher prism can be determined by subtracting the bottom height from the total height.

12 - 8 = 4

5 x 4 = 20

Add the two side areas together.

20 + 120 = 140

Multiply by the width, 6.

140 x 6 = 840

Answer:

Check the explanation

Step-by-step explanation:

b ) [tex]P(s^2<p\sigma^2)=0.05[/tex]

or , [tex]P\left (\frac{(n-1)s^2}{\sigma^2}<(n-1)p \right )=0.05[/tex]

or , [tex]P\left (\chi^2_5<5p \right )=0.05=P(\chi^2_5< 1.145476 )[/tex]

or , 5p =1.145476

or , [tex]p =\frac{1.145476}{5}= 0.2290952[/tex]

Required percentage = 22.91