According to an ice cream store, 70% of their customers prefer chocolate milkshakes over other shakes. (a) If 300 customers of this store are randomly selected, how many would we expect to prefer a chocolate milkshake? (b) Would it be unusual to observe 270 customers of this store who prefer chocolate milkshakes in a random sample of 300 customers? Why? customers to prefer chocolate milkshakes. (a) We would expect about (Type a whole number.) (b) Would it be unusual to observe 270 customers who prefer chocolate milkshakes in a random sample of 300 customers? O A. Yes, because 270 is between u – 20 and + 20. B. No, because 270 is less than u - 20. C. No, because 270 is greater than u + 20. ооо D. No, because 270 is between u-20 and u + 20. E. Yes, because 270 is greater than u + 20.

Answer :  The lifetime of light bulbs is approximately normally distributed with a mean of 850 hours and a standard deviation of 44 hours.

Explanation:

Given that the mean lifetime of light bulbs is 850 hours with a standard deviation of 44 hours and it is normally distributed. We need to test the hypothesis that 850 hours against the alternative.

Therefore, we need to use a hypothesis test for mean. Let us assume a null hypothesis and an alternative hypothesis for the given data.

Null Hypothesis : The null hypothesis H0 states that there is no significant difference between the mean lifetime of light bulbs and the hypothesized value of 850 hours.                                                                                                               Mathematically, it is expressed asH0: μ = 850    

Alternative Hypothesis : The alternative hypothesis Ha states that there is a significant difference between the mean lifetime of light bulbs and the hypothesized value of 850 hours.                                                                                      Mathematically, it is expressed asHa: μ ≠ 850Here, μ represents the population mean and is equal to 850.                                                We know that Z-score is given as, Z = (x - μ)/σwhere x = Sample Mean, μ = Population Mean, σ = Standard Deviation

Now, we need to find the Z-score for the given data. Z = (x - μ)/σZ = (15 - 850)/44Z = -18.75As we know that the area under the curve at 5% level of significance on each tail is 0.025 and the Z-score corresponding to this is ±1.96. The rejection region is in the left tail of the curve and the right tail of the curve.

Hence the critical value of Z at 5% level of significance for a two-tailed test is ±1.96. Z critical value = ±1.96Since the calculated value of Z is less than the critical value of Z, we fail to reject the null hypothesis. Hence, we can conclude that the lifetime of light bulbs is approximately normally distributed with a mean of 850 hours and a standard deviation of 44 hours.

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Answer:

37.8

Step-by-step explanation:

1000 - 300 = 700

I = Prt

I = (700)(1.8%)(3)

I = 37.8

Answer:

Step-by-step explanation:

Answer:

a) yes, because they both increase by the same increments each time. Tis can be represented by the equation y=5x+2

b) y=5x+2

c) The y-intercept represents the amount of units there were initially and the slope represents the amount of units for every worker.

SA= 2 (4)(5) + 2(5)(9) + 2(4)(9)

SA= 202in^2

If the box contains confetti, how much cubic inches of confetti are needed to fill the box?

V= lwh

= 4*5*9

= 180 in^3

Answer:

divide the figure into two parts.

area of square = side²

area of square =12²

area of square =144

area pf trapezium =1/2×(a+b)×h

area of trapezium =1/2×(12+6)×12

area of trapezium =108

area of polygon=144+108=252 unit²

Answer:

see in the picture mark brainliest if correct

Answer:

36+25= 61

61/600 x 100 = 10.1 %

Step-by-step explanation:   Hope This helped!!!!

Answer: -g - 10h

Step-by-step explanation:

(5g - 3h) - (6g + 7h)

= 5g - 3h - 6g - 7h

= 5g - 6g - 3h - 7h

= -g - 10h

Answer:

B.490

Step-by-step explanation:

Correct me if im wrong

Answer: 490

Step-by-step explanation:

Answer:

C. 333.14

Step-by-step explanation:

Both the basketball and baseball has got the shape of a sphere. So that;

volume of a sphere = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

where r is the radius

i. Volume of the baseball = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

                           =  [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](9.25)^{3}[/tex]

                           = 3315.5655

volume of the baseball = 3316.57 cube inches

ii. Volume of the basketball =  [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

                            = [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](9.55)^{3}[/tex]

                            = 3649.8372

Volume of the basketball = 3649.84 cube inches

The required difference = volume of basketball - volume of baseball

                                  = 3649.84 - 3316.57

                                  = 333.27 cube inches

The difference of the volumes of the basketball and baseball is 333.27 cube inches.

The solution to the system of equations is x1 = -(9/7)x4, x2 = (2/7)x4, x3 = -(1/7)x4, and x4 is a free variable.

a) xy + 2x2 + 2x3 = 1 X1 - 2x2 + 2x3 = -3 3x1 - x2 + 5x3 = 7

We can solve the system of equations using both inverse matrix (if possible) and reduced row echelon forms.

We begin by converting the above equations into matrix form as follows:

[xy+2x2+2x3=1] [X1-2x2+2x3=-3] [3x1-x2+5x3=7] = [1] [-3] [7]

We represent the coefficient matrix by A and the variable matrix by X.

Then we have AX = B where B = [1] [-3] [7]

To find the inverse of A.

If the inverse of A exists, we can use it to find X = A^(-1)B.

We can find the inverse of A using the formula A^(-1) = adj(A)/|A| where adj(A) is the adjugate of A and |A| is the determinant of A.

We have: det(A) = |[1,2,2;-1,-2,2;3,-1,5]| = 9adj(A) = [11,6,-4;19,9,-5;-7,-4,3]

Therefore, A^(-1) = adj(A)/|A| = [11/9,2/3,-4/9;19/9,1/3,-5/9;-7/9,-4/3,1/9]

We can use A^(-1) to find X as follows:

X = A^(-1)B = [11/9,2/3,-4/9;19/9,1/3,-5/9;-7/9,-4/3,1/9][1;-3;7] = [-5/3;1/3;2/3]

Therefore, the solution to the system of equations is x = -5/3, y = 1/3, z = 2/3.

We can also solve the system of equations using the reduced row echelon form of the augmented matrix as follows:[1,2,2,1;-1,-2,2,-3;3,-1,5,7] [R2+R1,R3-3R1] [1,2,2,1;-4,-3,4,-2;0,-7,-1,4] [R2/(-4),R3/(-7)] [1,2,2,1;1/4,1,-1,1/2;0,1,1/7,-4/7] [R1-2R2, R3-(1/7)R2] [1,0,3/2,-1/2;0,1,1/7,-4/7;0,0,0,0]

The last row of the above matrix represents the equation 0x1 + 0x2 + 0x3 + 0x4 = 0, which is an identity.

The system of equations is consistent, and we can solve for x, y, and z using the first two rows of the above matrix as follows:

x + (3/2)z = (-1/2)y + (1/7)z = (4/7)

Solving for z, we have: z = 2/3

Substituting z into the first equation, we have:

x + (3/2)(2/3) = (-1/2)x = -5/3

Substituting z into the second equation, we have:

y + (1/7)(2/3) = (4/7)y = 1/3

Therefore, the solution to the system of equations is x = -5/3, y = 1/3, z = 2/3.b) x1 + 2xy + 2x3 + 5x4 = 0 *1 - 2x2 + 2x2 - 4x4 = 0 3x1 - x2 + 5x3 + 2x4 = 0 3x, -2x2 + 6x3 - 3x4 = 0

To solve this system of equations, we begin by converting it into matrix form as follows:[1,2y,2,5;0,-2,2,-4;3,-1,5,2;3,-2,6,-3] [x1;x2;x3;x4] = [0;0;0;0]

We represent the coefficient matrix by A and the variable matrix by X.

Then we have AX = 0. Our task is to find the reduced row echelon form of the augmented matrix [A|0].

We perform the following elementary row operations to the above matrix to obtain the reduced row echelon form:[1,2y,2,5,0;0,-2,2,-4,0;3,-1,5,2,0;3,-2,6,-3,0] [R1-2yR2, R3-3R2, R4-3R2] [1,0,-2y-1,2y+5,0;0,-2,2,-4,0;0,-7,-1,14,0;0,-8,0,9,0] [R3/(-7), R4/(-8)] [1,0,-2y-1,2y+5,0;0,-2,2,-4,0;0,1,1/7,-2/7,0;0,1,0,-9/8,0] [R1+(2y+1)R3] [1,0,0,9/7,0;0,-2,0,-2/7,0;0,1,1/7,-2/7,0;0,0,0,0,0]

The last row of the above matrix represents the equation 0x1 + 0x2 + 0x3 + 0x4 = 0, which is an identity.

The system of equations is consistent, and we can solve for x1, x2, x3, and x4 using the first three rows of the above matrix as follows:

x1 = -(9/7)x4x2 = (2/7)x4x3 = -(1/7)x4

Therefore, the solution to the system of equations is x1 = -(9/7)x4, x2 = (2/7)x4, x3 = -(1/7)x4, and x4 is a free variable.

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Answer:

whats the definition?

Step-by-step explanation:

Answer:

342

Step-by-step explanation:

Given

Shape: Rectangular prism

The missing dimensions are:

[tex]Length = 5 ft[/tex]

[tex]Width = 6 ft[/tex]

[tex]Height = 12 ft[/tex]

Required

Determine the surface area

The surface area is calculated as:

[tex]Area = 2(Length * Width + Length * Height + Width *Height)[/tex]

This gives:

[tex]Area = 2(5ft* 6ft+ 5ft * 12ft+ 6ft*12ft)[/tex]

[tex]Area = 2(30ft^2+ 60ft^2+ 72ft^2)[/tex]

[tex]Area = 324ft^2[/tex]

The conclusions are as follows:

a. We reject the null hypothesis.

b. The p-value for this test is approximately 0.001.

To complete parts a and b, we can follow the steps for hypothesis testing.

a. The z-test statistic can be calculated using the formula:

z = ([tex]\bar{X}[/tex] - μ) / (σ / √n)

Given:

[tex]\bar{X}[/tex] = 49

σ = 11

n = 32

Substituting these values into the formula, we get:

z = (49 - 47) / (11 / √32) ≈ 2.90

The z-test statistic is approximately 2.90 (rounded to two decimal places).

To determine the critical z-score(s), we need to find the z-value that corresponds to the significance level α = 0.10. Since the alternative hypothesis is one-sided (μ > 47), we are performing a right-tailed test.

Using a standard normal distribution table or a calculator, the critical z-score for a right-tailed test at α = 0.10 is approximately 1.28 (rounded to two decimal places).

Because the test statistic z = 2.90 is greater than the critical z-score of 1.28, we reject the null hypothesis.

b. The p-value represents the probability of obtaining a test statistic as extreme as the observed value (or more extreme) assuming the null hypothesis is true. Since the alternative hypothesis is μ > 47, we are looking for the probability in the right tail of the distribution.

Using a standard normal distribution table or a calculator, we can find the p-value corresponding to the z-test statistic z = 2.90. The p-value is the area under the curve to the right of 2.90.

The p-value is approximately 0.001 (rounded to three decimal places).

Therefore, the conclusions are as follows:

a. We reject the null hypothesis.

b. The p-value for this test is approximately 0.001.

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The overall runtime of the algorithm is O(|V|+|E|). The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.Therefore, the algorithm has a total runtime of O(|V|+|E|).

a) Algorithm to determine if a graph has a cycle:The algorithm is implemented using DFS (Depth First Search) traversal, which starts from every vertex in the graph. During the DFS traversal, we maintain a set of vertices on the current path. We continue DFS traversal of each unvisited neighbor vertex, and if a neighbor is already on the path set, then we have found a cycle.

The algorithm to determine if a graph has a cycle is given below -Graph G(V, E)Start DFS from each vertex v in VIf DFS utility detects a cycle, then return true.

Else, return false.Let's take a look at the DFS algorithm below -DFS(vertex u)

1. Mark u as visited.

2. For every unvisited neighbor v of u, doDFS(v)

3. If v is already on the current path, return true to denote the existence of a cycle.

4. If there is no cycle, return false to denote that the graph does not contain a cycle.

The overall runtime of the algorithm is O(|V|+|E|).

The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.

b) Justification of the correctness and runtime of the algorithm:The algorithm provided uses a DFS traversal.

Therefore, the algorithm can detect a cycle in an undirected connected graph. If there is a cycle, then the algorithm will correctly detect it.

Since the algorithm starts DFS from each vertex, it will detect the cycle even if it starts from a vertex other than the one containing the cycle.

Therefore, it's correct.The overall runtime of the algorithm is O(|V|+|E|). The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.

Therefore, the algorithm has a total runtime of O(|V|+|E|).

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Answer: 3 buses

Step-by-step explanation:

Answer:

Simply multiply 21 until you get a number greater than 47. In this case, 3, even though there is only a little remainder of 5 kids on one bus by themselves.

Step-by-step explanation:

The expected value is 0, which means that, on average, you neither gain nor lose points over the long run. This suggests that after playing the game for a long time, we would expect to have a point total close to zero.

To determine whether you would expect to have a positive or negative point total after a long time playing the game, we can calculate the expected value or average point gain/loss per roll.

Let's calculate the expected value for each outcome:

Rolling an even number:

Probability = 3/6 = 1/2,

Point gain/loss = -1

Rolling a 1:

Probability = 1/6,

Point gain/loss = 1

Rolling a 3:

Probability = 1/6,

Point gain/loss = 3

Rolling a 5:

Probability = 1/6,

Point gain/loss = -4

The expected value, we multiply each outcome's point gain/loss by its probability and sum them up

Expected Value = (1/2) × (-1) + (1/6) × 1 + (1/6) × 3 + (1/6) × (-4)

Expected Value = -1/2 + 1/6 + 1/2 - 2/3

Expected Value = 0

The expected value is 0, which means that, on average, you neither gain nor lose points over the long run. This suggests that after playing the game for a long time, you would expect to have a point total close to zero.

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Answer: The estimate is not valid based on the given sample.

Explanation:

The given information can be used to determine if the estimate is valid or not. It is estimated that at a certain college, at most 25% of the students ride bicycles to class, and a random sample of 90 college students is taken. The number of students who ride bicycles to class in the sample is 28.                                                                                            Therefore, to determine if the estimate is valid, the proportion of students who ride bicycles to class in the sample must be calculated.                                                                                                                                                                   The proportion of students who ride bicycles to class in the sample is 28/90 = 0.31 ≈ 31%.The proportion of students who ride bicycles to class in the sample is greater than the estimated proportion of students who ride bicycles to class, which is 25%.

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To find the distance from point Q=(-28, 41) to the line represented by the equation (x, y) = (2, 1) + t(4, 3), we can use the formula for the distance between a point and a line in the coordinate plane. Therefore, the distance from point Q to the line is 233/5.

The distance between a point (x0, y0) and a line Ax + By + C = 0 is given by the formula:

d = |Ax0 + By0 + C| / √(A^2 + B^2)

In this case, we have the line represented parametrically as (x, y) = (2, 1) + t(4, 3), where t is a parameter. To use the formula, we need to convert this parametric representation to the standard form Ax + By + C = 0.

Expanding the parametric equation, we have:

x = 2 + 4t

y = 1 + 3t

From these equations, we can rearrange them to isolate t:

t = (x - 2) / 4

t = (y - 1) / 3

Setting the two expressions for t equal to each other, we get:

(x - 2) / 4 = (y - 1) / 3

Simplifying, we have:

3x - 6 = 4y - 4

4y - 3x = 2

Now we have the equation of the line in standard form. The coefficients A, B, and C are 4, -3, and 2, respectively.

To find the distance between point Q=(-28, 41) and the line, we can substitute the values into the distance formula:

d = |4(-28) + (-3)(41) + 2| / √(4^2 + (-3)^2)

Calculating the numerator and the denominator, we have:

d = |-112 - 123 + 2| / √(16 + 9)

d = |-233| / √25

d = 233 / 5

Therefore, the distance from point Q to the line is 233/5.

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Answer:

the answer is 3,107.21

The answer to that question is that one

Answer:

12/13

Step-by-step explanation:

side² = 13² - 5² = 169 - 25 = 144

side = √144 = 12

sin ∅ = 12/13

Answer: Justin earns a base salary of $1500 per month at

the jewelry shop. He also earns a 3% commission

on all sales. If Just sold $82,975 worth of jewelry

last month, how much would he make for the

month including his base salary and commission?

Step-by-step explanation: $1500 + 3% + $82,975 = 84475. 03 or 84475

The system of linear equations admits an unique solution.

The system of linear equations given by:

-x + 3y = 7   ------------------------(1)

2x + y = 4   ------------------------(2)

We can find whether the system of linear equations admits a unique solution or not by using any one of the methods such as elimination, substitution or matrices.

For this question, we can solve the given system of equations using the substitution method:

From Eq. (2), we get:

y = 4 - 2x   ------------------------(3)

Substituting Eq. (3) into Eq. (1), we get:

-x + 3(4 - 2x) = 7

=> -x + 12 - 6x = 7  

=> -7x = -5  

=> x = 5/7

Substituting the value of x in Eq. (3), we get:

y = 4 - 2(5/7)

=> y = 18/7

Therefore, the unique solution of the given system of linear equations is:x = 5/7 and y = 18/7.

Thus, the given system of linear equations admits a unique solution.

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Answer: y-9=-1/2 x (x+4)

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer:

-21 Feet

Step-by-step explanation:

-336/16

The balloon's elevation during the second minute will be 21 feet.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A sight-seeing balloon pilot starts to land her inflatable. In the main moment the inflatable rise - 336 feet. In the subsequent moment, the inflatable's height changes by 1/16 of that sum.

Then the balloon's elevation during the second minute is given as,

⇒ - 336 x (1/16)

⇒ - 336 / 16

⇒ - 21 feet

The balloon's elevation during the second minute will be 21 feet.

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Answer:

(-2, 4)

Step-by-step explanation:

Hopes this helps!