The table shows the results for spinning the spinner 75 times. What is the relative frequency for the event​ "spin a 3​"?

Answer:

18x+24

Step-by-step explanation:

For this, you have to multiply 6 to the numbers inside the parenthesis.

SO, 6 x 3x and 6 x 4

6 x 3x=18x

6 x 4=24

The answer will be 18x+24

Answer:

B. 3 by 12

Step-by-step explanation:

The rectangle is four times as long as it is wide,

(3 times 4=12)

and has an area of 36

(3 times 12=36)

so this is the correct answer.

If the area of the given rectangle is 36 square inches, then the length of rectangle is 12 inches and the breadth of rectangle is 3 inches.

"Area is the quantity that expresses the extent of a region on the plane or on a curved surface."

"A rectangle is a shape with four straight sides and four angles of 90 degrees (right angles)."

Area of rectangle = 36 square inches

Let the width of rectangle be y

Length of rectangle be 4y

Area of rectangle = length × breadth

y×4y = 36

[tex]4y^{2} = 36[/tex]

[tex]y^{2}=9\\y=\sqrt{9}[/tex]

[tex]y=3[/tex]

Hence, the width of the rectangle is 3 inches and the length of the rectangle is 12 inches.

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There is 18.75% probability that it takes 9 or more boxes to get all 3 prizes.

No. of Boxes  |  frequency

        3           |         12

        4           |         4

        5           |         5

        6           |         5

        7           |         0

        8           |         0

        9           |         2

        10          |        2

        11           |        0

        12           |       2

Here 9 or more boxes represent that it is equal to 9 boxes or more than 9 boxes.

P(x ≥ 9) = No. of boxes equal or more than 9 / total no. of boxes

And, The total no. of boxes is 32

From the above data, we have to count the number of boxes equal to or more than 9. (6 times) i.e.

[tex]P(x $\geq$ 9) = 6\div 32\\\\P(x $\leq$ 9) = 3\div 16[/tex]

P(x ≥ 9) = 0.1875

P(x ≥ 9) = 18.75%

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Answer:

See explaination

Step-by-step explanation:

Please kindly check attachment for the step by step solution of the given problem.

Answer:

Reject null hypothesis ([tex]H_0[/tex]) since the​ P-value is less than the significance level.

Step-by-step explanation:

We are given that it has long been stated that the mean temperature of humans is 98.6 degrees F. ​However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6 degrees F.

The sample data resulted in a sample mean of 98.2 degrees F and a sample standard deviation of 0.9 degrees F.

Let [tex]\mu[/tex] = mean temperature of humans.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu\geq[/tex] 98.6°F      {means that the mean temperature of humans is more than or equal to 98.6°F}

Alternate Hypothesis, [tex]H_A[/tex] : p < 98.6°F    {means that the mean temperature of humans is less than 98.6°F}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                        T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean temperature = 98.2°F

            [tex]\sigma[/tex] = sample standard deviation = 0.9°F

            n = sample of healthy adults = 56

So, test statistics  =   [tex]\frac{98.2-98.6}{\frac{0.9}{\sqrt{56} } }[/tex]  ~ [tex]t_5_5[/tex]

                               =  -3.326

The value of t test statistics is -3.326.

Now, P-value of the test statistics is given by following formula;

         P-value = P( [tex]t_5_5[/tex] < -3.326) = 0.00077 or 0.08%

Since, P-value of the test statistics is less than the level of significance as 0.08% < 1%, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean temperature of humans is less than 98.6°F.

To determine if the mean human temperature is less than 98.6°F, we conducted a left-tailed t-test using the provided sample data. We calculated the t-test statistic and then used it to find the p-value. We then used the p-value to make our final decision on whether to reject or fail to reject our null hypothesis.

In this scenario, we are performing a hypothesis test about the average human temperature. Let's formulate our hypothesis first:

We will conduct a left-tailed t-test because we are testing whether the average human temperature is less than a stated value.

Given the data: the sample size n = 250, the sample mean (x_bar) = 98.2 F, and the standard deviation (s) = 0.9 F.

To calculate the t-test statistic, use the formula: t0 = (x_bar - μ) / (s/√n)

For getting the p-value, you would use a statistical table or software with the above t statistic and degree of freedom (which is n-1 in this case).

In the end, if your p-value is less than the significance level (α = 0.01 in this case), we reject the null hypothesis, if not, we fail to reject the null hypothesis.

If the P-value is less than α, we would conclude that the research may be correct, and the average human temperature is indeed lower than 98.6 F (37.0 °C).

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Answer:

a) Null hypothesis:[tex]\mu = 140[/tex]  

Alternative hypothesis:[tex]\mu \neq 140[/tex]  

b) [tex]t=\frac{170-140}{\frac{80}{\sqrt{64}}}=3[/tex]  

c) The degrees of freedom are given by:

[tex]df=n-1=64-1=63[/tex]

Now we can calculate the p value, since we are conducting a two tailed test:

[tex]p_v =2*P(t_{63}>3)=0.0039[/tex]  

Since the p value is lower than the significance level of [tex]\alpha=1-0.95=0.05[/tex] we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes

Step-by-step explanation:

Information provided

[tex]\bar X=170[/tex] represent the sample mean   in minutes

[tex]s=80[/tex] represent the standard deviation

[tex]n=64[/tex] sample size  

[tex]\mu_o =140[/tex] represent the value to verify

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

t would represent the statistic (variable of interest)  

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

Part a

We are interested in determining whether or not the average usage in Soddy-Daisy is significantly different from the U.S. average (140 minutes), the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 140[/tex]  

Alternative hypothesis:[tex]\mu \neq 140[/tex]  

Part b

Since we don't know the population deviation the statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]t=\frac{170-140}{\frac{80}{\sqrt{64}}}=3[/tex]  

Part c

The degrees of freedom are given by:

[tex]df=n-1=64-1=63[/tex]

Now we can calculate the p value, since we are conducting a two tailed test:

[tex]p_v =2*P(t_{63}>3)=0.0039[/tex]  

Since the p value is lower than the significance level of [tex]\alpha=1-0.95=0.05[/tex] we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes

The null hypothesis that the average internet usage in Soddy-Daisy is not significantly different from the U.S. average is rejected based on a computed z-score of 3, which falls outside the critical z-score values for a 95% confidence level. Therefore, the average internet usage in Soddy-Daisy is significantly different from the U.S. average.

This problem pertains to the domain of statistical hypothesis testing. Let's first set up the null and alternative hypotheses:

For the second part, we need to compute the test statistic. The formula for the test statistic (z) in this context is z = (x - μ) / (σ/√n), where x is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.

So, (170-140) / (80/√64) = 30 / (10) = 3. The z score is 3.

For the final part of your question, with 95% confidence, the critical z-score values are -1.96 and +1.96. Since our observed z-score of 3 is outside this range, we reject the null hypothesis. Therefore, we can conclude that the average internet usage in Soddy-Daisy is significantly different from the U.S. average.

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Answer:

153.9 cm

Step-by-step explanation:

A = pi(r²)

= 3.14(7²)

= 3.14(49)

= 153.86

= 153.9 cm

The t-statistic is calculated as: -6.70

What is the test statistic?

The appropriate test to conduct at the alpha equals 0.01 level of significance is a one-tailed t-test.

The null hypothesis is that the mean hippocampal volume of adolescents with alcohol use disorders is equal to 9.02 cm cubed, while the alternative hypothesis is that the mean hippocampal volume is less than 9.02 cm cubed.

Thus:

H₀: μ = 9.02 cm³

Hₐ: μ < 9.02 cm³

The t-statistic is calculated from the formula:

t = (x - μ)/(σ/√n)

t =  (8.02 - 9.02) / (0.7/√(22))

= -6.70.

Therefore, the t-statistic is -6.70

Answer:

The value of w is 11 when c = 2

Step-by-step explanation:

Since c = 2, then we can just plug it into the given equation to find w.

[tex]w=(2)+9[/tex]

[tex]w=11[/tex]

Answer:

95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

Step-by-step explanation:

We are given that the engineers take a random sample of 45 cables and apply weights to each of them until they break. The mean breaking weight for the 45 cables is 768.2 lb. The standard deviation of the breaking weight for the sample is 15.1 lb.

Since, in the question it is not specified that how much confidence interval has be constructed; so we assume to be constructing of 95% confidence interval.

Firstly, the Pivotal quantity for 95% confidence interval for the population mean is given by;

                            P.Q. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean breaking weight = 768.2 lb

            s = sample standard deviation = 15.1 lb

            n = sample of cables = 45

            [tex]\mu[/tex] = population mean breaking strength

Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.02 < [tex]t_4_4[/tex] < 2.02) = 0.95  {As the critical value of t at 44 degree

                                           of freedom are -2.02 & 2.02 with P = 2.5%}  

P(-2.02 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.02) = 0.95

P( [tex]-2.02 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.02 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.02 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.02 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.02 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.02 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                     = [ [tex]768.2-2.02 \times {\frac{15.1}{\sqrt{45} } }[/tex] , [tex]768.2+2.02 \times {\frac{15.1}{\sqrt{45} } }[/tex] ]

                                     = [763.65 lb , 772.75 lb]

Therefore, 95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

Answer:

74.1 or 74

Step-by-step explanation:

Answer:

The s-score corresponding to a score  of 54 is 4.67

Step-by-step explanation:

In a certain normal distribution of scores:

Mean = [tex]\mu = 40[/tex]

Standard deviation = [tex]\sigma = 3[/tex]

We are supposed to find  the z-score corresponding to a score  of 54.

Formula : [tex]Z=\frac{x-\mu}{\sigma}[/tex]

x=54

Substitute the values

So,[tex]Z= \frac{54-40}{3}[/tex]

Z=4.67

So, Option A is true

Hence the s-score corresponding to a score  of 54 is 4.67

Answer:

A quadratic function can have up to two x-intercepts.

An x-intercept of a quadratic function is also called a zero of the function.

Step-by-step explanation:

None needed.

The true statement is

An x-intercept of a quadratic function is also called a zero of the function.

A quadratic function can have up to two x-intercepts.

A quadratic polynomial function has one or more variables and a variable with a maximum exponent of two. It is also known as the polynomial of degree 2 because the second-degree component in a quadratic function is the biggest degree term. A quadratic function must contain at least one term of the second degree. It possesses algebraic qualities.

we have,

The x-intercepts of quadratic functions,

The standard form of quadratic equation is

ax² + bx + c = 0

The zeroes of the quadratic functions are the values of x, which is also known as the x-intercept.

Because the degree of the polynomial is 2, there will be at least two x-intercept values.

The x-intercept is the x position at which the value of y is zero.

Let x = a be an x-intercept, and the function factor is (x - a).

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Answer:

A. 5

Step-by-step explanation:

5 ÷ 1 = 5

10 ÷ 2 = 5

15 ÷ 3 = 5

Answer:

the slope should be 1/5.

Step-by-step explanation:

slope = change in y / change in x

2-1 = 1 = change in Y

10-5 = 5 = change in X

the slope should be 1/5.

apologies in advance if my answer is wrong or I explain badly.

-----------------------------------------------------------------------------------------------

hope this helps! <3

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Edit! someone else answered the question. their answer is probably correct, so please ignore my incorrect answer :'D

Answer:False

Step-by-step explanation:

False

Whenever a stock is sold more money than what is paid for it is termed as Gain or profit

For example if an item is bought for [tex]\$100[/tex] and it is sell for [tex]\$120[/tex]

then there is a profit of

[tex]\Rightarrow \frac{120-100}{100}\times 100[/tex]

[tex]\Rightarrow 20\%[/tex]

or a gain of [tex]\$20[/tex]

Answer: The answer is False, i know this because i took this quiz on edge and it was correct as false <3 hope this helps

Step-by-step explanation: brainliest please :3

The range of g(x) = 3|x-1|-1 is (-∞,∞).

The range is "set of all y-coordinates of the function's graph".

According to the question,

g(x) = 3 |x-1| - 1

To find range of linear polynomial 3|x-1|-1  put any value in right 'x' we can able to get any value 'y' in the set (-∞.∞).

Hence, the range of g(x) = 3|x-1|-1 is (-∞,∞).

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Answer:

5,040

Step-by-step explanation:

Fundamental Counting Principle states that if there are m ways of doing a thing and there are n ways of doing other thing  then there are total m*n ways of doing both things.

Example : If there are 5 path to reach a destination and 3 mode of transport ( bike, car, bicycle) . Then are 5 * 3 ways to reach the destination using the different mode of transport available.

______________________________________

Given no of clarinet players = 7

no of chairs = 7

First player can be seated on seven chairs in seven ways

( for illustration let the seat be a , b, c , d , e , f , g. he can sit on any of the chairs)

since one chair is occupied and 6 chair is available

second player can be seated on 6 chairs in 6 ways

for illustration let the seat be a be occupied then b, c , d , e , f , g are  the chairs on which second player can sit.

\

Similarly 3rd, 4th, 5th, 6th and 7th player can be seat on chairs in

5, 4 , 3, 2, and 1 way respectively.

___________________________________________

now using  fundamental Counting Principle

since 7 players can sit on chair in

7 , 6, 5 , 4, 3 , 2, 1 ways then together they can be seated in

7 *  6 * 5 *  4 * 3 * 2 * 1 ways = 5, 040 ways

Answer:

We conclude that the mean number of thunder days is less than 92.

Step-by-step explanation:

We are given that Historically, a certain region has experienced 92 thunder days annually.

Over the past fifteen years, the mean number of thunder days is 72 with a standard deviation of 38.

Let [tex]\mu[/tex] = mean number of thunder days.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 92 days     {means that the mean number of thunder days is more than or equal to 92}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 92 days     {means that the mean number of thunder days is less than 92}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                       T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean number of thunder days = 72

             s = sample standard deviation = 38

            n = sample of years = 15

So, test statistics  =  [tex]\frac{72-92}{\frac{38}{\sqrt{15} } }[/tex]  ~ [tex]t_1_4[/tex]

                               =  -2.038

The value of z test statistics is -2.038.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of -1.761 at 14 degree of freedom for left-tailed test.

Since our test statistics is less than the critical value of t as -2.038 < -1.761, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean number of thunder days is less than 92.

Data for complete question is attached.

Answers

Therefore .

A. The regression equation is

y = beta0 + beta1+ ∈

B. From the given output regression line

y= 2.478+7.717x

The question addresses using a simple linear regression model to determine the relationship between two variables, and how to interpret the parameters of that model, as well as the significance of the correlation coefficient in the context of a hypothetical student protest situation.

The subject of this question is about linear regression analysis in mathematics, particularly in the context of statistical analysis. The question demonstrates the application of a simple linear regression to decipher the relationship between the duration of student sit-ins (independent variable) and the number of arrests (dependent variable).

A Markov chain is used to model this situation. The transition matrix based on the given probabilities will be [[0.9, 0.1],[0.4, 0.6]]. Also, to calculate the probability of being in a high-volume state two weeks from now given that it is in a high-volume state now, we square the matrix and look at the upper-left entry.

A Markov process, in particular, a Markov chain, is a stochastic process that undergoes transitions from one state to another on a state space following the Markov property, stating that future states depend only on the current state and not on events that occurred before it. The transition matrix in these cases provides the probabilities between state transitions.

Given the data:

Based on these probabilities the transition matrix will be of the form:

[[0.9, 0.1],[0.4, 0.6]].

To find the probability that the volume will be high two weeks from now, we will need to square the matrix as we are considering two steps ahead. The top left element of the resulting matrix will give the desired probability. In general, the i,j-th entry of the square of a transition matrix gives the 2-step transition probability from state i to state j.

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Answer:

c= -10

Step-by-step explanation:

-3(c-1)= 33

-3(c) -3(-1)= 33 (expand)

-3c +3= 33

-3c= 33-3 (-3 on both sides)

-3c= 30 (simplify)

3c= -30 (divide by -1 throughout)

c= -30 ÷3

c= -10

Answer:

-1/4

Step-by-step explanation:

The slope is found by

m = (y2-y1)/(x2-x1)

    = (-1-2)/(7- -5)

    = (-1-2)/(7+5)

     = -3/12

     = -1/4

Answer:

2646/100 or 260  46/100 or 260 23/50

Answer:

1.22 km/min

Step-by-step explanation:

Let Q be baloon height at a time t. Our goal is to determine the speed of the baloon at the moment.

The dy / dt velocity of the baloon when = π/5?  

So we can restate the question as follows:

Owing to the fact d / dt = 0.2 rad / min at some stage = π/5

from fig:

tanθ = y/4

Differentiating w.r.t "t"

sec2 θ * dθ/dt = 1/4(dy/dt)

=> dy/dt = (4/cos2 θ)dθ/dt

At the given moment θ =  and dθ/dt = 0.2 rad/min.

dy/dt = (4/cos2)* (0.2)

= 1.22 km/min

And the velocity of the baloon currently is 1.22 km / min.

Answer:

  4 cm

Step-by-step explanation:

The area of the net is 6 times the area of one square, so one square has an area of ...

  (96 cm^2)/6 = 16 cm^2

The side length (s) is the square root of this value:

  s = √(16 cm^2)

 s = 4 cm

Answer:

The   95.7% confidence interval for the expected amount of garbage per bin for all bins in the city

(48.937 , 50.863)

Step-by-step explanation:

Explanation:-

Given data random sample of 46 bins, the sample mean amount was 49.9 pounds and the sample standard deviation was 3.641

The sample size 'n' =46

mean of the sample x⁻ = 49.9

Standard deviation of the sample S = 3.641

Confidence intervals:-

The   95.7% confidence interval for the expected amount of garbage per bin for all bins in the city

[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,x^{-} + t_{\alpha } \frac{S}{\sqrt{n} })[/tex]

Degrees of freedom = n-1  = 46-1 =45

The tabulated value   t₀.₉₆ =   1.794 ( from t-table)

[tex](49.9 - 1.794 \frac{3.641}{\sqrt{46} } ,49.9+ 1.794 \frac{3.641}{\sqrt{46} })[/tex]

(49.9 -0.9630 , 49.9+0.9630)

(48.937 , 50.863)

Conclusion:-

The   95.7% confidence interval for the expected amount of garbage per bin for all bins in the city

(48.937 , 50.863)

Answer:

x=3, y=5

Step-by-step explanation:

To find x:

Because opposite sides of a parallelogram are congruent, we can set up the equation 2x+5=12x-25. Solving the equation will show that x=3.

To find y:

Using the same method as x, we can find that y=5.

Hope this helped!

Answer:

You have to break apart the shape into individual shapes to find the volume of each one. Then you add.

hope this helped :)

Answer:37.5 %

Step-by-step explanation:

Given

School attendance varies between 200 and 275

Most percentage error arises when attendance of 275 students is expected but only 200 students are present

Percentage error[tex]=\frac{275-200}{200}\times 100=37.5\ \%[/tex]