Yesterday, a movie theater sold 299 bags of popcorn. A large bag of popcorn costs $4. A small bag of popcorn costs $1. In all, the movie theater made $662 from popcorn sales. Write and solve a system of equations to find how many bags of each size of popcorn were sold.

Answer:

Yes. At this significance level, there is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

Step-by-step explanation:

The question is incomplete:

The significance level is 0.05.

The data is:

Brand X: 91, 100, 88, 89

Brand Y: 99, 96, 94, 99

Brand Z: 83, 88, 89, 76

We have to check if there is a significant difference between the absorbency rating of each brand.

Null hypothesis: all means are equal

[tex]H_0:\mu_x=\mu_y=\mu_z[/tex]

Alternative hypothesis: the means are not equal

[tex]H_a: \mu_x\neq\mu_y\neq\mu_z[/tex]

We have to apply a one-way ANOVA

We start by calculating the standard deviation for each brand:

[tex]s_x^2=30,\,\,s_y^2=6,\,\,s_z^2=35.33[/tex]

Then, we calculate the mean standard error (MSE):

[tex]MSE=(\sum s_i^2)/a=(30+6+35.33)/3=71.33/3=23.78[/tex]

Now, we calculate the mean square between (MSB), but we previously have to know the sample means and the mean of the sample means:

[tex]M_x=92,\,\,M_y=97,\,\,M_z=84\\\\M=(92+97+84)/3=91[/tex]

The MSB is then:

[tex]s^2=\dfrac{\sum(M_i-M)^2}{N-1}\\\\\\s^2=\dfrac{(92-91)^2+(97-91)^2+(84-91)^2}{3-1}\\\\\\s^2=\dfrac{1+36+49}{2}=\dfrac{86}{2}=43\\\\\\\\MSB=ns^2=4*43=172[/tex]

Now we calculate the F statistic as:

[tex]F=MSB/MSE=172/23.78=7.23[/tex]

The degrees of freedom of the numerator are:

[tex]dfn=a-1=3-1=2[/tex]

The degrees of freedom of the denominator are:

[tex]dfd=N-a=3*4-3=12-3=9[/tex]

The P-value of F=7.23, dfn=2 and dfd=9 is:

[tex]P-value=P(F>7.23)=0.01342[/tex]

As the P-value (0.013) is smaller than the significance level (0.05), the null hypothesis is rejected.

There is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

Answer:

173

Step-by-step explanation:

Same thing as last time, just instead of 90, it's 180.

Answer: B. You may use the t procedure, provided your sample size is large, say, at least 30.

Step-by-step explanation: To use a T test hypothesis, the following steps is considered;

1. Add the test hypothesis when using a T test module in the experiment

2. Add the date set that contains the columns that is to be analyzed

3. Decide which kind of T test is appropriated for the data

4. If single sample is been used, the adequate parameters should be used.

The correct statement in this case is "You may use the t procedure, provided your sample size is large, say, at least 30."

Answer:

The x-intercept is -6.

Step-by-step explanation:

You could use a graphing calculator, which would make it so much easier to find, but under the circumstances you aren't allowed to do so, you should:

1) Start from the y-intercept. In your case, it is -2. Since the y-intercept is negative, you want to apply the slope in a certain way.

The line will remain the same if your slope is -1/3 or if it is 1/-3. In your case, since your y-intercept is -2, you want to apply the slope 1/-3.

2) Move the point (0,-2) up 1, then left 3. This will get you the point (-3,-1). Your final answer should be in the format (x,0).

3) Now, move the point (-3,-1) up 1, then left 3. This will result in your point being (-6,0). Notice how the y-value is 0, so this is your final answer.

Keep in mind that this technique will not always be so easy to use. This particular problem is fine, though.

Answer:x-2y

Step-by-step explanation:

-1/2(-2x+4y)

Open the brackets

2x/2 - 4y/2

x - 2y

Answer:

[tex]P(x\geq 17)=0.00128[/tex]

Step-by-step explanation:

The probability that the man gets x out of 20 correct follows a Binomial distribution, so the probability is calculated as:

[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}[/tex]

Where n is the number of identical experiments and p is the probability of success. In this case n is 20.

Additionally, if he has no ESP the probability that he predict correctly is 0.5, because he is only guessing.

Then, the probability that he gets x out of 20 correct is equal to:

[tex]P(x)=\frac{20!}{x!(20-x)!}*0.5^{x}*(1-0.5)^{20-x}[/tex]

Therefore the probability that he would have done at least 17 out of 20 well if he had no ESP is:

[tex]P(x\geq 17)=P(17)+P(18)+P(19)+P(20)\\[/tex]

Where:

[tex]P(17)=\frac{20!}{17!(20-17)!}*0.5^{17}*(1-0.5)^{20-17}=0.00108719\\P(18)=\frac{20!}{18!(20-18)!}*0.5^{18}*(1-0.5)^{20-18}=0.00018119\\P(19)=\frac{20!}{19!(20-19)!}*0.5^{19}*(1-0.5)^{20-19}=0.00001907\\P(20)=\frac{20!}{20!(20-20)!}*0.5^{20}*(1-0.5)^{20-20}=0.00000095[/tex]

So, [tex]P(x\geq 17)[/tex] is equal to:

[tex]P(x\geq 17)=0.00108719+0.00018119+0.00001907+0.00000095\\P(x\geq 17)=0.00128[/tex]

The probability that he would have done at least 17 out of 20 if he had no ESP is 0.00128 and this can be determined by using the binomial distribution formula.

Given :

A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 20 times, and the man is asked to predict the outcome in advance. He gets 17 out of 20 correct.

The formula of the binomial distribution is given by:

[tex]\rm P(x)=\dfrac{n!}{x!(n-x)!}\times p^x \times (1-p)^{n-x}[/tex]

Now, put all the known terms in the above formula.

[tex]\rm P(x)=\dfrac{20!}{x!(20-x)!}\times 0.5^x \times (1-05)^{20-x}[/tex]

Now, the probability that he would have done at least 17 out of 20 if he had no ESP:

[tex]\rm P(x\geq 17) = P(17)+P(18)+P(19)+P(20)[/tex]

where:

[tex]\rm P(17)=\dfrac{20!}{(20-17!)}\times 0.5^{17}\times 0.5^{20-17}=0.00108719[/tex]

[tex]\rm P(18)=\dfrac{20!}{(20-18!)}\times 0.5^{18}\times 0.5^{20-18}=0.00018119[/tex]

[tex]\rm P(19)=\dfrac{20!}{(20-19!)}\times 0.5^{19}\times 0.5^{20-19}=0.00001907[/tex]

[tex]\rm P(20)=\dfrac{20!}{(20-20!)}\times 0.5^{20}\times 0.5^{20-20}=0.00000095[/tex]

So, the value of P(x [tex]\geq[/tex] 17) is:

[tex]\rm P(x\geq 17)= 0.00108719+0.00018119+0.00001907+0.00000095[/tex]

[tex]\rm P(x\geq 17)= 0.00128[/tex]

For more information, refer to the link given below:

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Answer:

39

Step-by-step explanation:

We notice this is an arithmetic sequence.

14, 9,  4.

common difference = d = 14 - 9 = 5

first term a_1 = 14

Find 6th term a_6

a_n = (n -1)*d + a_1

a_6 = (6 -1)*5 + 14

a_6 = 5*5 + 14 = 25 + 14 = 39

Answer: as the x values increase the y values decrease

Step-by-step explanation:

Took the teat

Answer:

38 bananas

Step-by-step explanation:

6(7)=42 bananas 42-4=38 bananas

We have been given that Layana’s house is located at [tex](2\frac{2}{3}, 7\frac{1}{3})[/tex] on a map. The store where she works is located at [tex](-1\frac{1}{3}, 7\frac{1}{3})[/tex].

We are asked to find the distance from Layana’s home to the store

We will use distance formula to solve our given problem.

Let us convert our given coordinates in improper fractions.

[tex]2\frac{2}{3}\Rightarrow \frac{8}{3}[/tex]

[tex]7\frac{1}{3}\Rightarrow \frac{22}{3}[/tex]

[tex]-1\frac{1}{3}\Rightarrow -\frac{4}{3}[/tex]

Now we will use distance formula to solve our given problem.

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Upon substituting coordinates of our given point in above formula, we will get:

[tex]D=\sqrt{(\frac{22}{3}-\frac{22}{3})^2+(\frac{8}{3}-(-\frac{4}{3}))^2}[/tex]

[tex]D=\sqrt{(0)^2+(\frac{8}{3}+\frac{4}{3})^2}[/tex]

[tex]D=\sqrt{0+(\frac{8+4}{3})^2}[/tex]

[tex]D=\sqrt{(\frac{12}{3})^2}[/tex]

[tex]D=\sqrt{(4)^2}[/tex]

[tex]D=4[/tex]

Therefore, the distance from Layana's home to the store is 4 units and option A is the correct choice.

Answer:

its A ^3^

Step-by-step explanation:

Answer:

y = 41/6

Step-by-step explanation:

This means that  y = kx.    k is a constant.

6 = k*72

and.

y = k*82 ...

k = 6/72 = 1/12

y = 82/12

y = 41/6

Answer:

The difference between mistrust and distrust comes down to nuances in meaning. Distrust is a withholding of trust based on evidence or informed opinion. Many people distrust salespeople working on commission, for instance, knowing that these salespeople personally benefit from their purchases.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The volume of a cube is the cube of the edge dimension. Here, that dimension is 5/8 in, so the volume is ...

  V = s³ = (5/8 in)³ = 125/512 in³ . . . volume of the cube

The volume of a cube 1/8 inch on a side is ...

  V = (1/8 in)³ = 1/512 in³

Clearly, a volume that is 125/512 in³ will require 125 of the cubes of size 1/512 in³ to fill it.

  125 of the smaller cubes will fit inside.

_____

Alternate solution

You can also determine the number of smaller cubes by considering it takes 5 of them in each direction to make 5/8 inch. Then the volume is 5³ = 125 of the smaller cubes.

Answer:

5

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Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below for the full explanation to the above question.

The final expression for the triple integral in spherical coordinates is:

[tex]\int\limits^{2\pi}_0\int\limits^{\pi /2}_0 \int\limits^1_0[/tex]ρ⁴ sin(φ) dρ dφ dθ

To evaluate the given integral efficiently in spherical coordinates, we'll set up the triple integral over the unit ball centered at the origin. The integral represents the volume element for a sphere, which we can express in spherical coordinates as follows:

∭D (x² + y² + z²)^(3/2) dV

In spherical coordinates, the volume element dV is given by:

dV = ρ² sin(φ) dρ dφ dθ

Here, ρ represents the radial distance from the origin, φ represents the polar angle (measured from the positive z-axis), and θ represents the azimuthal angle (measured from the positive x-axis in the xy-plane).

The limits of integration for the triple integral in spherical coordinates can be set as follows:

ρ: 0 to 1 (since D is the unit ball, ρ ranges from 0 to the radius of the sphere, which is 1)

φ: 0 to π/2 (since we only need to consider the upper half of the sphere)

θ: 0 to 2π (covering a full revolution around the z-axis)

Now, we can express the integral using these limits and the volume element:

∭D (x² + y² + z²)[tex]^{(3/2)[/tex] dV

= ∫[0 to 2π] ∫[0 to π/2] ∫[0 to 1] (ρ²)[tex]^{(3/2)[/tex] (ρ² sin(φ)) dρ dφ dθ

Simplifying the integrand:

(ρ²)[tex]^{(3/2)[/tex] (ρ² sin(φ)) = ρ³ ρ sin(φ) = ρ⁴ sin(φ)

Therefore, the final expression for the triple integral in spherical coordinates is:

[tex]\int\limits^{2\pi}_0\int\limits^{\pi /2}_0 \int\limits^1_0[/tex]ρ⁴ sin(φ) dρ dφ dθ

Learn more about triple integral click;

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Answer:

The largest value is -2 from -16/ 8

The largest absolute value is -108  from -16*8

Step-by-step explanation:

Are you asking for the greatest value?

The largest number?

-16 * 8 =   - 108

-16 / 8 = -2

-16 + 8 = -8

-16 - 8 = -24

The largest value is -2 from -16/ 8

The largest absolute value is -108  from -16*8

Answer:

a. Gwen expect to make 3.75 sets

b. The variance for the number of sets Gwen will make is 0.9375

c. Gwen expect to make 2 shots

Step-by-step explanation:

a. According to the given data we have the following:

Here this follows negative binomial distribution with parameter r =3 and p=0.8

To calculate how many sets does Gwen expect to make we have to calculate the following formula:

expected number of sets =r/p

expected number of sets =3/0.8=3.75

Gwen expect to make 3.75 sets.

b. In order to calculate the variance for the number of sets Gwen will make we have to use the following formula:

variance for the number of sets=σ∧2=r(1-p)/p∧2

variance for the number of sets=3*(1-0.8)/0.8^2

variance for the number of sets=0.9375

The variance for the number of sets Gwen will make is 0.9375

c. To calculate how many shots does Gwen expect to make, we have to calculate first the probability she shoots all the three in the set as follows:

probability she shoots all the three in the set=0.8∧3=0.512

if E(X)=1/p, therefore, 1/p=1/0.512=1.95

Gwen expect to make 2 shots

Answer:

a) A 95% confidence interval for μ is 25.5 ±2.2284 3.01

The 95% of confidence intervals for mean μ is determined by

(23.478 , 27.522)

Step-by-step explanation:

Step( i ) :-

Given sample size 'n' =11

The mean of the sample x⁻ = 25.5

The standard deviation of the sample 'S' = 3.01

95% of confidence intervals:

The 95% of confidence intervals for mean μ is determined by

[tex]( x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]

Step(ii):-

The critical value ∝ =0.05

[tex]t_{\frac{\alpha }{2} } = 2.228[/tex]

The degrees of freedom ν=n-1 = 11-1 =10

[tex]( 25.5 - 2.228 \frac{3.01}{\sqrt{11} } , 25.5 + 2.228 \frac{3.01}{\sqrt{11} } )[/tex]

(25.5-2.0220, 25.5 + 2.0220)

(23.478 , 27.522)

Final answer:-

The 95% of confidence intervals for mean μ is determined by

(23.478 , 27.522)

Final answer:

The correct statement is: a. A 95% confidence interval for μ is 25.5 ±2.2284 3.01. To calculate the confidence interval for the population mean, we use the formula: sample mean ± (critical value) × (standard deviation / square root of sample size).

Explanation:

The correct statement is:

a. A 95% confidence interval for μ is 25.5 ±2.2284 3.01

To calculate the confidence interval for the population mean, we use the formula: sample mean ± (critical value) × (standard deviation / square root of sample size).

In this case, with a sample mean of 25.5, standard deviation of 3.01, and a sample size of 11, the critical value for a 95% confidence level is 2.2284. Therefore, the correct confidence interval is 25.5 ± 2.2284 × 3.01.

Answer:

The answer is A. True

Step-by-step explanation:

The range of Fx) = 7*4^x is all positive real numbers.

hope this helps : )

Answer:

It's D.

Step-by-step explanation:

Answer:

3(x - 2)(x - 5)

Step-by-step explanation:

Factor 3 from all terms within the trinomial:

(3x² - 21x + 30)/3 = x² - 7x + 10

3(x² - 7x + 10)

Simplify.

(x² - 7x + 10)

x               -5

x               -2

3(x - 2)(x - 5)* is your answer.

* remember to bring the 3 that you factored out in the beginning and stick it to the front.

~

Answer:

The fraction that represents the proportion of students that go make their homework is 1/6

Step-by-step explanation:

The sum of the percentage of students is 100% = 1.

In this problem, we have that:

1/3 said they watch television

1/2 said they go to sports practice

x said they do homework.

This is a sum of fractions, and the lesser common multiple of 3 and 2 is 6.

So

[tex]\frac{1}{3} + \frac{1}{2} + x = 1[/tex]

[tex]\frac{2 + 3 + 6x}{6} = 1[/tex]

[tex]5 + 6x = 6[/tex]

[tex]6x = 1[/tex]

[tex]x = \frac{1}{6}[/tex]

The fraction that represents the proportion of students that go make their homework is 1/6

Answer:

Use order of operation

Step-by-step explanation:

Answer:

2(x+8)(x-7)

Step-by-step explanation:

If the question is asking 2x^2+2x-112, then the answer is 2(x+8)(x-7).

First, you factor out the two: 2(x^2+x-56)

Next, you find something that adds to x and multiplies to -56: 8 and -7

After, you get 2(x+8)(x-7)

Answer:

x = 2

Step-by-step explanation:

the 2 given angles are vertical angles, meaning they are equal.

38x-1 = 75

solve the above equation, and x = 2

Answer:

2

Step-by-step explanation:

Those two angles are equal:

75 = 38x - 1

so, add 1 to both

76 = 38x

divide by 38

2 = x

Answer:

P(1) = 0.2857

P(2) = 0.1428

P(3) = 0.1428

P(4) = 0.1428

P(5) = 0.1428

P(6) = 0.1428

Step-by-step explanation:

From the question, we know that Rolling a 1 with the red die is twice as likely as rolling each of the other five numbers, so we can write the following equation:

P(1) = 2X        

Where X is the probability of rolling each of the other five numbers or:

P(2) = P(3) = P(4) = P(5) = P(6) = X  

Additionally, the sum of all the probabilities is 1, so:

P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

Now, we can replace P(1) by 2X and P(2), P(3), P(4), P(5) and P(6) by X, as:

P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

2X  +   X   +    X   +   X  +   X   +   X  = 1

Finally, solving for X, we get:

7X = 1

X = 1/7

X = 0.1428

So, the probability of rolling a 1 is equal to:

P(1) = 2X  = 2*(0.1428) = 0.2857

And the probability of rolling each of the other five numbers is:

P(2) = P(3) = P(4) = P(5) = P(6) = X  

P(2) = P(3) = P(4) = P(5) = P(6) = 0.1428

Answer:

99% confidence interval for the proportion of people who disagree with the statement is [0.667 , 0.713].

Step-by-step explanation:

We are given that a survey that asked whether people agree or disagree with the statement ‘‘There is only one true love for each person." has been conducted. The result is that 735 of the 2625 respondents agreed, 1812 disagreed, and 78 answered ‘‘don’t know."

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

                                 P.Q. =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of people who disagree with the statement = [tex]\frac{1812}{2625}[/tex] = 0.69

           n = sample of respondents = 2625

           p = population proportion of people who disagree with statement

Here for constructing 99% confidence interval we have used One-sample z proportion statistics.

So, 99% confidence interval for the population proportion, p is ;

P(-2.58 < N(0,1) < 2.58) = 0.99  {As the critical value of z at 0.5% level

                                                   of significance are -2.58 & 2.58}  

P(-2.58 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.58) = 0.99

P( [tex]-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

P( [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

99% confidence interval for p = [ [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

= [ [tex]0.69-2.58 \times {\sqrt{\frac{0.69(1-0.69)}{2625} } }[/tex] , [tex]0.69+2.58 \times {\sqrt{\frac{0.69(1-0.69)}{2625} } }[/tex] ]

 = [0.667 , 0.713]

Therefore, 99% confidence interval for the proportion of people who disagree with the statement is [0.667 , 0.713].

Answer:

the answer is 262 days

Step-by-step explanation:

To find the second time after the hottest day of the year that the daily high temperature is 20 degrees Celsius, you need to solve the equation T(t) = 20. This involves finding the inverse cosine of a specific value, setting up an equation, and adding one year to the solution. After performing these steps, you can find the value of t that corresponds to the second time.

To find the second time after the hottest day of the year that the daily high temperature is 20 degrees Celsius, we need to solve the equation T(t) = 20. We can rewrite this equation as 7.5cos(2π/365t) + 21.5 = 20. Subtracting 21.5 from both sides gives us 7.5cos(2π/365t) = -1.5. Dividing both sides by 7.5 and simplifying further, we have cos(2π/365t) = -0.2. To find the second time, we need to find the value of t that satisfies this equation.

To find the value of t, we need to use the inverse cosine function (also known as arccosine). The inverse cosine function (cos^(-1)) gives us the angle whose cosine is a specific value. In this case, we want to find t such that cos(2π/365t) = -0.2. We can use a calculator or math software to find the inverse cosine of -0.2. Let's assume the inverse cosine of -0.2 is x.

Now we can set up an equation: 2π/365t = x. Solving for t, we get t = (365x)/(2π). However, we need to find the second time after the hottest day, so we need to find the value of t that satisfies the equation after adding one year (365 days) to the original value. Therefore, the second time after the hottest day of the year that the daily high temperature is 20 degrees Celsius is t = (365x)/(2π) + 365.

Answer:

Step-by-step explanation:

+ You click on -15 for a point.

+ Then you move the mouse to the left.

+ Because x<-15, that means you do not take -15, you click on the -15 one more.

That is all.

Hope you understand.

Answer:

1.) You click on -15 for a point.

2.) Then you move the mouse to the left.

3.) Because x<-15, that means you do not take -15, you click on the -15 one more.

Answer:

[tex] 12 +18 + x+y + z +w[/tex]

In this special case we know that [tex] x+y =12[/tex] and [tex] z+w =18[/tex]  and for this case we can add all the values 12+18 +12+18=60 and that represent the perimeter  

Step-by-step explanation:

For this case we know that the perimeter is given by:

[tex] 12 +18 + x+y + z +w[/tex]

In this special case we know that [tex] x+y =12[/tex] and [tex] z+w =18[/tex]  and for this case we can add all the values 12+18 +12+18=60 and that represent the perimeter