A nationa
l sampling of cookie preferences showed that 75% of people like chocolate chip, 50% like peanut butter, and only 3% like coconut. The use of this information makes sense in which of the following scenarios?

Answer:

1) -2.5, 0.5, 1.4, 5

3)The biggest number is a positive while the smallest number is a negative

Step-by-step explanation:

The square root of 5 is 25 because 5 x 5 = 25

5/10 is 0.5 because when simplified It is 1/2 which is 0.5

The square root of 2 is 1.4 when rounded up (When you get a decimal with a very long number, it best to round it up if allowed)

An negative number will always be the smallest since it's is not a positive no more. It is go back meaning it's turning smaller

Hope this helps

Step-by-step explanation:

1. √25

√2

[tex] \frac{5}{10} [/tex]

-2,5

2. √25 = 5 (the root is drawn from 5)

[tex] \frac{5}{10} = \frac{1}{2} = 0.5[/tex]

Divide both numerator and denominator by 5

Then you get 1/2 which is equal to 0,5 (a half)

√2 ≈ 1,41 (just use your calculator to find the approximate value)

3. Biggest number - √25

Smallest number - -2,5

√25 - (-2,5) = 5 + 2,5 = 7,5

Answer:

The surface area of each mini muffin that needs to be covered by paper is the lateral surface area of the cylinder plus the area of each circular base. The formula for the lateral surface area of a cylinder is 2πrh, where r is the radius and h is the height. The formula for the area of a circle is πr^2. Using the given dimensions, the radius of each mini muffin is 1 inch, and the height is 1 and 1/4 inches. So the surface area of each mini muffin is: 2π(1)(1 and 1/4) + π(1)^2 = 5π/2 + π = 7.07 square inches (approx.) To wrap 6 mini muffins, we need 6 times this amount of paper: 6 x 7.07 = 42.42 square

Step-by-step explanation:

give me the brianlst

Flying with the wind, a small plane flew 338 mi in 2 h. flying against the wind, the plane could fly only 312 mi in the same amount of time. So, the rate of the plane in calm air is 162.5 mph, and the rate of the wind is 6.5 mph.

Let's use variables to represent the unknowns in this problem:

- Let p represent the rate of the plane in calm air (in miles per hour).
- Let w represent the rate of the wind (in miles per hour).

When the plane is flying with the wind, the combined speed (plane + wind) is (p + w) mph. It flies 338 miles in 2 hours, so we have:

1. (p + w) * 2 = 338

When flying against the wind, the net speed (plane - wind) is (p - w) mph. It flies 312 miles in 2 hours, so we have:

2. (p - w) * 2 = 312

Now, we'll solve the two equations simultaneously. First, divide both sides of each equation by 2:

1. p + w = 169
2. p - w = 156

Next, add the two equations together to eliminate the w variable:

(p + w) + (p - w) = 169 + 156
2p = 325

Now, divide by 2 to find the rate of the plane in calm air:

p = 325 / 2
p = 162.5 mph

Now that we have the rate of the plane, we can find the rate of the wind by substituting the value of p back into either equation 1 or 2. Let's use equation 1:

162.5 + w = 169

Subtract 162.5 from both sides to find w:

w = 169 - 162.5
w = 6.5 mph

So, the rate of the plane in calm air is 162.5 mph, and the rate of the wind is 6.5 mph.

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Answer:

Step-by-step explanation:

sin (-90*) = -sin (90*)
...
sin = y
...
-sin(90*) = -1

Answer:

In the expression 7z^4 - 5 + 10(y^3+2), the term 10(y^3+2) has a factor of 10.

It will take both machines approximately 1.71 hours or 1 hour and 42 minutes to produce widgets together.

To solve this problem, we can use the formula:

1 / time taken by machine 1 + 1 / time taken by machine 2 = 1 / time taken by both machines

Let's denote the time taken by the old machine as x hours and the time taken by the new machine as y hours.

From the problem statement, we know that the old machine can produce widgets in 3 hours, so we have:

1 / x = 1 / 3

Solving for x, we get:

x = 3

Similarly, we know that the new machine can produce widgets in 4 hours, so we have:

1 / y = 1 / 4

Solving for y, we get:

y = 4

Now, we can plug in the values of x and y into the formula and solve for the time taken by both machines:

1 / 3 + 1 / 4 = 1 / t

Multiplying both sides by 12t, we get:

4t + 3t = 12

7t = 12

t = 12 / 7

Therefore, it will take both machines approximately 1.71 hours or 1 hour and 42 minutes to produce widgets together.

In conclusion, we used the formula for the combined work rate of two machines to calculate the time taken by both machines to produce widgets. We first found the individual work rates of the old and new machines and then substituted those values into the formula to solve for the time taken by both machines working together.

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The rate of change in the area of the circle is 22 cm²/s when the radius of the circle is increasing at a rate of 0.5 cm/s.

It is half of the diameter of the circle or sphere. The radius is commonly denoted by the letter "r".

The area of a circle is given by the formula A = πr², where A is the area and r is the radius.

If the radius is increasing at a rate of 0.5 cm, then the rate of change of the radius with respect to time is dr/dt = 0.5 cm/s.

Using the chain rule of differentiation, we can find the rate of change of the area with respect to time:

dA/dt = dA/dr * dr/dt

By varying the area formula, we can determine dA/dr:

dA/dr = 2πr

Plugging in the values of r and dr/dt, we get:

dA/dt = (2πr)(0.5) = πr

At the initial radius of 7cm, the rate of change in the area is:

dA/dt = π(7) = 22/7 * 7 = 22 cm²/s

Therefore, the rate of change in the area of the circle is 22 cm²/s when the radius of the circle is increasing at a rate of 0.5 cm/s.

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The solution for differential equation is the negative square root, since y(π) = -5. Thus, the final solution is;  y = 3 - √(9 - 6 tan(x))

A differential equation is a mathematical equation that relates a function or a set of functions with their derivatives.

Given differential equation;  dy/dx = sec²(x) (2+y)²

separate the variables and integrate both sides:

∫ 1/(2+y)² dy = ∫ sec²(x) dx

Using the substitution u = 2+y, du/dy = 1, we can rewrite the left-hand side as:

∫ 1/u² du = -1/u + C₁

Similarly, we can integrate the right-hand side using the identity ∫ sec²(x) dx = tan(x) + C₂, Substituting these expressions back into the original equation, we get:

-1/(2+y) + C₁ = tan(x) + C₂

To determine the values of C₁ and C₂, we use the initial condition y(π) = -5, which implies x = π. Substituting these values, we get:

-1/(2-5) + C₁ = tan(π) + C₂

-1/(-3) + C₁ = 0 + C₂

C₁ = C₂ + 1/3

putting the value of C₁ and C₂ into the previous expression, So,

-1/(2+y) + C₁ = tan(x) + C₁ - 1/3

-1/(2+y) = tan(x) - 1/3

Multiplying both sides by (2+y)², we get:

-(2+y) = (2+y)² tan(x) - (2+y)²/3

Simplifying and solving for y, we get:

y² - 6 - 6 tan(x) = 0

Solve it for y by using the quadratic formula,

y = 3 ± √(9 - 6 tan(x))

Therefore, the solution to the differential equation dy/dx = sec²(x) (2+y)² with the initial condition y(π) = -5 is:    y = 3 ± √(9 - 6 tan(x))

We choose the negative square root, since y(π) = -5. Thus, the final solution is:     y = 3 - √(9 - 6 tan(x))

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Answer:

-20p - 3.8

Step-by-step explanation:

Sure!

1.) Since you have a number outside of a parenthesis, you can distribute it to the parenthesis by multiplying it to each term in the parenthesis. You would get .2 +(-4)*5p + (-4) * 1.

2.) Now, by multiplying these together, you would get .2-20p-4.

3.) Finally, since you can further simplify by adding together like terms. .2 and -4 are both constants (numbers), so you can add them together.

4.) .2 + (-4) is equal to -3.8, so your final expression is -20p - 3.8.

The value of sin 315° = -√2/2, cos 9π/4 = √2/2 , tan (-135) = 1°

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular functions) comprising trigonometry are the cosecant , cosine , cotangent , secant , sine , and tangent .

We can use the following trigonometric identities to find the values ​​of sin, cos, and sun:

sin(x) = sin(x 360°)

cos(x) = cos(x 360°)

tan(x) = tan(x 180°)

Using these identities, we can convert  angles to equivalent angles in the first quadrant, where the values ​​of sin, cos, and sun are known.

sin (315°)

We can convert 315° to the corresponding angle in the first quadrant by subtracting 360°:

315° - 360° = -45°

Since sin(x) = sin(x 360°), we have:

sin(315°) = sin(-45°)

We know that sin(-θ) = -sin(θ), so:

sin(-45°) = -sin(45°)

We also know that sin (45°) = √2/2, so:

sin(315°) = -√2/2

Therefore, the power of 315  is equal to -√2/2.

cos(9π/4)

We can convert 9π/4 to the corresponding angle in the first quadrant by subtracting 2π:

9π/4 – 2π = π/4

Since cos(x) = cos(x 360°), we have:

cos(9π/4) = cos(π/4)

We know that cos(π/4) = √2/2, so:

cos(9π/4) = √2/2

Therefore, cos 9π/4 is equal to √2/2.

tan(-135°)

We can convert -135° to the corresponding angle in the second quadrant by adding 180°:

-135°- 180° = 45°

Since tan(x) = tan(x 180°), we have:

We know that tan(45°) = 1, so:

reddish brown (-135°) = 1

Therefore tan (-135°) equals 1.

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The value of x for the given polynomial that are similar in nature through which the relation is satisfied is x = 21.

What about similar character?

In mathematics, similarity refers to the property of having the same shape but not necessarily the same size. Two geometric figures are said to be similar if they have the same shape and their corresponding angles are congruent, and the ratio of their corresponding side lengths is constant. This constant ratio is called the scale factor of the similarity.

For example, two triangles are similar if their corresponding angles are congruent, and their corresponding sides are in proportion. That is, if we take one side of the first triangle and divide it by the corresponding side of the second triangle, we get the same ratio as if we took another pair of corresponding sides and divided them. This ratio is the scale factor of the similarity.

According to the given information:

Similar polygons have congruent corresponding angles and proportionate corresponding sides.

To find the lengths of another polygon that is comparable, multiply or divide a polygon's side lengths by a scale factor.

Here, we use the similarity operation  in which the ratio of side are equal in nature.

⇒[tex]\frac{x-5}{12} = \frac{18}{13.5} = \frac{20}{15}[/tex]

⇒ [tex]\frac{x-5}{12} = \frac{4}{3} = \frac{4}{3}[/tex]

⇒ [tex]\frac{x-5}{12} = \frac{4}{3}[/tex]

⇒ [tex]x = 21[/tex]

So, the value of x for which the given relation is satisfied is x  = 21.

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Answer:

Step-by-step explanation:

If we input 4 into g(x), we get:

g(4) = 3(4/2) = 3(2) = 6

Therefore, the output of g(x) when we input 4 is 6.

Answer:

The answer to your problem is, 60

Step-by-step explanation:

As shown, a rhombus inside a regular hexagon. The regular hexagon have 6 congruent angles, and the sum of the interior angles is 720°

So, the measure of one angle of the regular hexagon = 720/6 = 120°

The rhombus have 2 obtuse angles and 2 acute angles.

So, the measure of each acute angle of the rhombus = 180 - 120 = 60°

So, the measure of each acute angle of the rhombus + the measure of angle x

= the measure of one angle of the regular hexagon.

Equation 60 + x = 120x = 120 - 60 = 60°

Thus the answer to your problem is, 60

The area of the composite shape is 155 yd². And the right option is A-155 yd².

A composite shape is any shape that is made up of two or more geometric shapes.

The area of the composite shape can be calculated using the formula below

Note: The composite shape in the question, is made up of a tripezium and a parallelogram.

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the area is 155 yd².

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According to the given question ∠1 = ∠5 ; Cοrrespοnding angles.

A figure that is created by twο rays οr lines that have the same endpοint is knοwn as an angle in plane geοmetry. Frοm the Latin wοrd "angulus," which means "cοrner," cοmes the English wοrd "angle." The vertex, which is the shared endpοint οf the twο rays, is referred tο as the side οf an angle.

There is nο requirement that an angle in the plane be in Euclidean space. If twο planes intersect in Euclidean οr anοther space tο fοrm an angle, that angle is said tο be a dihedral angle. "" is the symbοl used tο represent angles. Using the Greek letter,,, etc., οne can represent the angle between the twο rays.

Given,

The figure is attached

We have tο prοve that ∠1 = ∠5.

Cοrrespοnding angles;

When twο parallel lines are intersected by anοther line, cοmparable angles are the angles that are created in matching cοrners οr cοrrespοnding cοrners with the transversal (i.e. the transversal).

Here,

∠1 + ∠3 = 180° ; Vertical angles theοrem.

∠5 + ∠6 = 180° ; Linear pair theοrem.

∠1 + ∠3 = ∠5 + ∠6 ; 180° = 180° ; Bοth are supplementary angles.

∠3 = ∠6 ; Cοnsecutive interiοr angles

Nοw,

∠1 = ∠5 ; Cοrrespοnding angles.

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Answer:

answer -15 ans hope this helps

Answer:

2x+33/3

Step-by-step explanation:

11+2/3x 11+2x/3

11+2x/3 3 x 11/3 + 2x/3

3 x 11/3 + 2x/3 3 x 11 + 2x/3

3 x 11 + 2x/3  33+2x/3

33+2x/3  2x+33/3

Answer:

Step-by-step explanation:

To maximize the volume of the box, we need to find the height that will maximize the volume of the box.

Let's start by finding an expression for the volume of the box. The box has dimensions of 14-2x by 10-2x by x, where x is the height of the box. The volume of the box is:

V(x) = (14-2x)(10-2x)(x)

Expanding this expression, we get:

V(x) = 4x^3 - 48x^2 + 140x

To find the value of x that maximizes this expression, we can take the derivative of V(x) with respect to x and set it equal to zero:

V'(x) = 12x^2 - 96x + 140 = 0

We can solve this quadratic equation using the quadratic formula:

x = [96 ± sqrt(96^2 - 4(12)(140))]/(2(12)) = [96 ± 16sqrt(6)]/24

We can simplify this to:

x = 4 ± sqrt(6)/3

Since the dimensions of the box must be positive, we can discard the negative solution:

x = 4 + sqrt(6)/3

So the height of the box that will give a maximum volume is approximately 5.61 inches (rounded to two decimal places).

The proper way to move on coordinate surface from point A's location to point b is to move 6 units to the right and 1 unit to the up. The correct option is a.

What does the word "coordinate" mean in mathematics?

Coordinates are a pair of numbers (also known as Cartesian coordinates), or occasionally a letter and an integer, that identify a particular point on a grid,also known as a coordinate system. The [tex]x[/tex] -axis (horizontal) and [tex]y[/tex] -axis are the two vectors on a coordinate plane, which has four quadrants. (vertical).

On the coordinate surface, we can use the following methods to move from Point A to Point B:

Point A, which is two units to the right of the Centre and nine units up, is a good place to start.

Point C, which is situated at Move five floors to the toward the right and five units up to get there. (5, 5).

Move three units to your right and three units up from Point C to Point B, which is situate

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Answer:

m∠ 1 = 165°

m∠ 2 = 15°

Step-by-step explanation:

We Know

∠1 + ∠2 = 180°

Let's solve

5x + (x - 18) = 180

5 + x - 18 = 180

6x - 18 = 180

6x = 198

x = 33

Now we put 33 in for x and solve for ∠1 and ∠2 !

m∠ 1 = 5x°

m∠ 1 = 5(33)

m∠ 1 = 165°

m∠ 2 = (x - 18)

m∠ 2 = 33 - 18

m∠ 2 = 15°

Answer:

m∠1 = 165°

m∠2 = 15°

Step-by-step explanation:

Note that, when the angle measurements are combined, the total measurement is 180°, based on the definition of a straight line.

It is given that m∠1 = 5x°, and m∠2 = (x - 18)°. Set the two angle measurements equal to the total measurement:

[tex]5x + (x - 18) = 180[/tex]

First, simplify. Combine like terms. Like terms are terms that share the same amount of the same variables:

[tex](5x + x) - 18 = 180\\(6x) - 18 = 180[/tex]

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents

Multiplications

Divisions

Additions

Subtractions

~

First, add 18 to both sides of the equation:

[tex]6x - 18 = 180\\6x - 18 (+18) = 180 (+18)\\6x = 180 + 18\\6x = 198\\[/tex]

Next, divide 6 from both sides of the equation:

[tex]6x = 198\\\frac{6x}{6} = \frac{198}{6}\\ x = \frac{198}{6} = 33[/tex]

x = 33. Next, plug in 33 for x for both measurements:

[tex]m\angle1 = 5x\\m\angle1 = 5 * (33)\\m\angle1 = 165\\\\m\angle2 = x - 18\\m\angle2 = (33) - 18\\m\angle2 = 15[/tex]

Check. Both, when combined, should make 180°

165 + 15 = 180

180 = 180 (True)

~

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It is not reasonable to use the least-squares regression model to predict attendance per game for 0 wins because it involves extrapolation beyond the range of the observed data

Using the least-squares regression model to predict attendance per game for 0 wins is not reasonable because it would involve extrapolating the regression line beyond the range of the data.

In other words, the least-squares regression model is designed to capture the relationship between two variables within the range of the observed data. If we attempt to use this model to make predictions outside of this range, the results may not be reliable or accurate.

For example, if we were to use a least-squares regression model to predict attendance per game based on the number of wins a sports team had, and the range of wins in our data set was from 10 to 80, then any predictions we make for 0 wins (which is outside of this range) would be extrapolations rather than interpolations.

Extrapolation can be risky because it assumes that the relationship between the two variables continues beyond the range of the data. However, this assumption may not hold true in reality, and therefore the predictions made using extrapolation may not be accurate.

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J would be the correct answer choice.

To put it simply, the number itself will always stay the same. You will always end up with either a negative or positive version of the number.

Hi! I can help you with that.

Each package weighs 30 oz. So, if Paul buys 4 packages, he will be buying:

30 oz x 4 = 120 oz

To convert this into pounds, we need to divide the number of ounces by 16 (as there are 16 ounces in 1 pound). So,

120 oz ÷ 16 = 7.5 pounds

Therefore, Paul will be buying 7.5 pounds of hot dogs for his camping trip.

Answer:

Step-by-step explanation:

A

The roots of the given quadratic equation are x = -3± √27

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations.

Given is a quadratic equation x² + 6x = 18,

x² + 6x = 18

Comparing the equation with the standard form,

b = 6, c = -18

(x + b/2)² = -(c - b²/4)

So,

(x+6/2)² = -(-18-6²/4)

(x+3)² = -(-18-9)

(x+3)² = 27

x+3 = ±√27

x = ±√27-3

x = -3± √27

Hence, the roots of the given quadratic equation are x = -3± √27

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The probability that at most 50 people out of 2400 who have not taken drugs will test positive on a drug test that is accurate 98% of the time is approximately 0.109

To calculate the probability, we need to first determine the parameters of the binomial distribution. Let's define success as testing negative on the drug test, since that is what we want to happen. Therefore, the probability of success is 0.98, and the probability of failure (testing positive) is 0.02.

Next, we need to determine the number of trials (n) and the number of successes (x) we are interested in. In this case, n = 2400 (the number of people taking the test) and x = 0, 1, 2, ..., 50 (the number of people who test positive).

Using the binomial distribution formula, we can calculate the probability of getting at most 50 people testing positive as follows:

P(X ≤ 50) = Σ(i=0 to 50) [(n choose i) * p^i * (1-p)^(n-i)]

where (n choose i) = n! / (i! * (n-i)!) is the binomial coefficient.

Plugging in the values, we get:

P(X ≤ 50) = Σ(i=0 to 50) [(2400 choose i) * 0.98^i * 0.02^(2400-i)]

Using a computer program or calculator, we can evaluate this sum to get P(X ≤ 50) ≈ 0.109.

Therefore, the probability that at most 50 people out of 2400 who have not taken drugs will test positive on a drug test that is accurate 98% of the time is approximately 0.109.

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Answer:

Base of the bottle = 15 cm

Step-by-step explanation:

Let's start by using the formula for the volume of a pyramid:

Volume of a pyramid = (1/3) * Base Area * Height

We know that the volume of the bottle is 140 cm³ and the height of the pyramid is 7 cm. We need to find the width of the base of the pyramid.

Let's first find the area of the rectangular base:

Base Area = Length * Width

We know that the length of the base is 4 cm, but we don't know the width. Let's call the width "w".

Base Area = 4 * w

Base Area = 4w

Now we can substitute the values we know into the formula for the volume of a pyramid:

Volume of a pyramid = (1/3) * Base Area * Height

140 = (1/3) * (4w) * 7

Simplifying the equation:

140 = (4/3) * 7w

140 = 9.333w

w = 15

Therefore, the width of the base of the bottle is 15 cm.

The f(x) = 2x^2 + 4, so f(4) = 2(4)^2 + 4 = 36.

To find (Fog)(0), we first need to find g(0) and then plug that value into f(x).

We have g(x) = -3x + 4, so g(0) = -3(0) + 4 = 4.

Now we have (Fog)(0) = f(g(0)) = f(4).

We have f(x) = 2x^2 + 4, so f(4) = 2(4)^2 + 4 = 36.

Therefore, (Fog)(0) = 36.

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(a) According to the null hypothesis, there is evidence that the average telephone survey lasts less than 15 minutes and that the premium rate is not appropriate. According to the alternative hypothesis, there is evidence that the premium rate is appropriate and that the average telephone survey lasts longer than 15 minutes.

(b) The value of the test statistic is 2.959.

(a)  Based on the available data, Fowle Marketing Research Inc. is requesting a basic fee from a customer under the presumption that the average telephone survey will last 15 minutes or less. The following are the alternative and null hypotheses:

Write down the null hypothesis.

Null hypothesis:

H₀ : μ ≤ 15

Alternative hypothesis:

H₁ : μ > 15

(b) The test statistic's value is as follows:

Given the information, μ = 11, σ = 4 and n=35.

x' = Σx/n

x' = (17 + 11 + 12 + 23 + 20 + 23 + 15 + 16 + 23 + 22 + 18 + 23 + 25 + 14 + 12 + 12 + 20 + 18 + 12 + 19 + 11 + 11 + 20 + 21 + 11 + 18 + 14 + 13 + 13 + 19 + 16 + 10 + 22 + 18 + 23)/35

x' = 595/35

x' = 17

Therefore,

z = (x' - μ)/(σ/√n)

z = (17 - 15)/(4/√35)

z = 2/(4/5.92)

z = 2/0.676

z = 2.959

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The complete question is:

Fowle Marketing Research Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 15 minutes or less. If a longer mean survey time is necessary, a premium rate is charged. A sample of 35 surveys provided the following survey times in minutes:

17; 11; 12; 23; 20; 23; 15; 16; 23; 22; 18; 23; 25; 14; 12; 12; 20; 18; 12; 19; 11; 11; 20; 21; 11; 18; 14; 13; 13; 19; 16; 10; 22; 18; 23.

Based upon past studies, the population standard deviation is assumed known with s = 4 minutes. Is the premium rate justified?

a. Formulate the null and alternative hypotheses for this application.

b. Compute the value of the test statistic.

As per the figure provided the exact value of CE will be equivalent to 12.

According to the figure given in the question, Angles ABE and DBC are vertical angles and thus have the same measure. Since the given segment AE is parallel to a segment of CD, angles A and D are of the same distance by the alternate interior angle theorem. As a result, according to the angle-angle theorem, triangles ABE and DBC are equivalent, with vertex A corresponding to vertex B and vertex E to vertex D, respectively.

Hence, AB ÷ DB = EB ÷ CB

10 ÷ 5 = 8 ÷ CB

Since, CB=4 and CE= CB+BE

CE = 4 + 8

CE=12.

Therefore CE is equal to 12.

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A has 156 cards, B has 39 cards, and J has 312 cards.

To find out how many cards A, B, and J have, follow these steps:

Let the number of cards B has be represented by the variable 'b'.

A has four times as many cards as B, so the number of cards A has can be represented as '4b'.

J has twice as many cards as A, so the number of cards J has can be represented as '2(4b)' or '8b'.

Together, A and J have 468 cards. Therefore, the equation can be written as 4b + 8b = 468.

Combine the like terms: 12b = 468.

Divide both sides of the equation by 12 to find the value of 'b': b = 468 / 12, which results in b = 39.

Now that we have the value of 'b', we can find the number of cards A and J have:

- A has 4 times as many cards as B: A = 4 × 39 = 156 cards.

- J has twice as many cards as A: J = 2 × 156 = 312 cards.

So, A has 156 cards, B has 39 cards, and J has 312 cards.

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Answer:12

Step-by-step explanation:

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