if we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, what sample size should be used? assume confidence.

Answer:

a=20 because the rate of change is -3

Step-by-step explanation:

26-3 is 23, 23-3 is 20.

An airplane is flying from New York City to Los Angeles. The distance a travels in miles D is related to the time in second T by the equation D equals 0. 15t. The plane is flying at a speed of 792 feet per second.

The distance a travels in miles D is related to the time in second T by the equation D equals 0. 15t. An airplane is flying from New York City to Los Angeles.

The formula relating distance (D), time (T), and speed (S) is given by

D = ST

This means that the speed of the plane is given by:

S = \frac{D}{T}

From the given formula, we have D = 0.15T.

We need to determine the speed S of the plane.

Substituting D, we have:

S = \frac{D}{T}

  = \frac{0.15T}{T}

  = 0.15

Therefore, the plane is flying at a speed of 0.15 miles per second. (Remember that the distance is in miles and time is in seconds)

We know that 1 mile is equivalent to 5280 feet. Therefore, to convert miles per second to feet per second, we multiply by 5280.

Thus, the plane is flying at a speed of 792 feet per second.

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Answer:

y = (x - 2)² - 9    Vertex form

y = x² - 4x - 5   Standard form

Step-by-step explanation:

vertex = (h, k) = (2, -9)

Vertex form

y = a(x - h)² + k

y = a(x - 2)² - 9

find "a" using point (5, 0)

0 = a(5 - 2)² - 9

0 = a(3)² - 9

0 = 9a - 9

9 = 9a

a = 1

y = (x - 2)² - 9

Standard form

y = (x² - 4x + 4)  - 9

y = x² - 4x - 5

The probability of A and B occurring simultaneously (P(A ∩ B)) is c. 0.00.

In this scenario, A and B are stated to be mutually exclusive events. Mutually exclusive events are events that cannot occur at the same time. This means that if event A happens, event B cannot happen, and vice versa.

Given that P(A) = 0.4 and P(B) = 0.5, we can deduce that the probability of A occurring is 0.4 and the probability of B occurring is 0.5. Since A and B are mutually exclusive, their intersection (A ∩ B) would be an empty set, meaning no outcomes can be shared between the two events. Therefore, the probability of A and B occurring simultaneously, P(A ∩ B), would be 0.

To further clarify, let's consider an example: Suppose event A represents flipping a coin and getting heads, and event B represents flipping the same coin and getting tails. Since getting heads and getting tails are mutually exclusive outcomes, the intersection of events A and B would be empty. Therefore, the probability of getting both heads and tails in the same coin flip is 0.

In this case, since events A and B are mutually exclusive, the probability of their intersection, P(A ∩ B), is 0.

Therefore, the correct answer is: c. 0.00

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Answer: 260.16 cm

Step-by-step explanation:

1. The solution for the equation is -16t² + 48t < 0

2. The interval notation for the equation is (0, 3)

Given,

The height of the building = 280 feet

A ball is thrown straight up from the top of the building.

The initial velocity of the ball = 48 feet/second

The height of the object is modeled by, s(t) = -16t² + 48t + 280

1. Solution for the equation:

s(t) < 280

So,

-16t² + 48t + 280 < 280

Add -280 to both sides

ie, -16t² + 48t + 280 - 280 < 280 - 280

We get,

-16t² + 48t < 0

2. Now find the interval notation for the equation:

-16t² + 48t < 0

Here, 48/16 = 3

So,

-16t (t - 3) < 0

Now,

t = 0 and t - 3 = 0  

The interval notation for the equation is (0, 3)

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Answer:

The measure of the angle is 11 and its complement is 79 degrees

Step-by-step explanation:

Mathematically, when two angles are complementary, the sum of the angles equal 90 degrees

so now, if the first angle is x , the second angle which is increased by 68 degrees will be x + 68

So now if we add these two, the value we will get is 90 degrees

Mathematically, we have this as;

x + x + 68 = 90

2x + 68 = 90

2x = 90-68

2x = 22

x = 22/2

x = 11

the measure of the angle is 11 and its complement will be 11 + 68 = 79

The new revised  equation is given as y = (x-1)² - 8

The response from part A is (x – 1)2 = 8, where h = 1 and c = 8.

Set the equation equal to 0  -

0 = (x – 1)2 – 8.

Substitute y for 0 and keep the equation rewritten in the form

y = (x – h)2 – c

⇒  y = (x – 1)2 – 8.

An equation is a mathematical statement that asserts the equality of two expressions.

Equations are used to represent relationships between quantities and solve for unknown values by finding the values that satisfy the equation.

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Answer:

C) (-4, 2)

Step-by-step explanation:

Answer:

The center is ( -4,2) and the radius is 4

Step-by-step explanation:

The equation of a circle can be written as

( x-h) ^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius

(x+4)^2 + (y - 2)^2 = 16

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

The center is ( -4,2) and the radius is 4

Answer:

The answer would be zero. This is due to the fact that the tangent is a line on a point around the circle. These two circles share no common tangents.

Step-by-step explanation:

The number of the common tangent to the concentric circles is zero. Option D is correct.

Two concentric circles are given in the figure, and common tangents to the circles are to be determined.

The circle is the locus of a point whose distance from a fixed point is constant i.e center ( h, k ). The equation of the circle is given by\((x-h)^2 + (y-k)^ = r^2\). where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.

Since the line passes through the circumference of the circle is known as a tangent to the circle and the common tangent of the concentric circle is not possible because the tangent to the inner circle results secant to the outer circle.

Thus, the number of the common tangent to the circles is zero. Option D is correct.

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Answer:

His kinetic energy at the faster speed is 160 J

Step-by-step explanation:

Here in this question, we are interested in calculating the kinetic energy at the faster speed.

Firstly, we need to know the mass of the boy’s body. We can do this by using the kinetic energy formula;

Mathematically;

K.E = 1/2 * m * v^2

From the question;

K.E = 40 Joules

m = ?

v = speed = 2 m/s

Now, plugging these values into the kinetic energy equation, we have;

40 = 1/2 * m * 2^2

40 = 1/2 * m * 4

40 = 4m/2

4m = 40 * 2

4m = 80

m = 80/4

m = 20 kg

Now that we know the mass of the boy’s body, we can proceed to calculate the new K.E

Let’s follow the third statement in the question;

We were told that he doubles his speed upon sighting his friend.

Recall, he was traveling at a speed of 2 m/s.

Now doubling this means the new speed will

be 2 * 2 = 4 m/s

Now, we want to calculate the kinetic energy value at this new speed.

Mathematically, we use the same formula for kinetic energy.

K.E = 1/2 * m * v^2

We know that m is the mass that we calculated as 20kg and our v here is 4 m/s

Plugging these values, we have;

K.E = 1/2 * 20 * 4^2

K.E = (20 * 16)/2

K.E = 320/2

K.E = 160 J

Answer:

A boy weighing 20 kilograms is riding a skateboard. He’s moving at 2 meters/second and has 40 joules of kinetic energy. He doubles his speed when he sees his friends ahead of him. His kinetic energy at the faster speed is 160 joules.

The length of the radius of the circle with a central angle measuring 7pi/6 is 4.9cm

The formula for calculating the legnth of an arc is expressed as:

L = rtheta

r is the radius

Theta is the subtended angle

Given the following

18 = r(7pi/6)
7pi r = 18 * 6

7pi r = 108
r = 108/7pi

r = 4.9cm

Hence the length of the radius of the circle with a central angle measuring 7pi/6 is 4.9cm

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Answer:

B or 4.9cm

Step-by-step explanation:

For the price per acre do 237,000 / 15 = $15800 per acre

Answer:

x=40

Step-by-step explanation:

The 2 angles are opposite each other. Therefore, they are vertical angles. This means the 2 angles are equal. So, we can set them equal to each other.

120=3x

We want to find out what n is. In order to do this, we have to get n by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

x is being multiplied by 3. The opposite of multiplication is division. Divide both sides by 3.

120/3=3x/3

120/3=x

40=x

x is equal to 40.

Answer:

40

Step-by-step explanation:

i had this a while ago

Answer:

no solution

Step-by-step explanation:

Answer:

no solution or ø

Step-by-step explanation:

Distribute: 6x+15=6x+6

Move the 6x to the other side: 15=6

15 does not equal six so it is no solution or ø

Hope this helps

Answer:

a. The 1's are heavier than the x's. There isn't a whole number on top of the x's.

b. The equation would be 2x<9 because the 9 is greater(heavier) than the 2x. To continue to solve you would divide 2 by both sides. That would turn into x<9/2.

Step-by-step explanation:

Answer:

d = 1350 - 60t

Step-by-step explanation:

the slope is for every x how y changes so the x would be represented by t (which is the time in seconds in this case) and y would be the distance from the bottom of the ski slope.

the vertical intercept would define when you are gaining distance or losing distance

In the expression 2*4 + 3y, the coefficient of y is 3. The coefficient is the number next to the variable.

Answer:

t≥-7

Step-by-step explanation:

7−2t≤21

Subtract 7 from each side

7-7−2t≤21-7

−2t≤14

Divide each side by -2, remember to flip the inequality

-2t/-2 ≥14/-2

t≥-7

The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

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The solutions are;

The critical value with a level of significance ‘of 0.10’ and degrees of freedom ‘of 3’ is 1.533.

The critical value with a level of significance ‘of 0.01’ and degrees of freedom ‘of 3’ is 3.747.

The critical value with a level of significance ‘of 0.05’ and degrees of freedom ‘of 3’ is 2.132.

Given;

Let's say you randomly choose n = 4 measurements from a normal distribution. If you were constructing the following confidence intervals, compare the standard normal z values with the appropriate t values.

(a) 80% confidence interval:

The z-value is obtained as shown below:

The level of significance is;

Locate the probability in the z table. Then, the corresponding row value is 1.2 and the column value is 08.

The critical value with a level of significance is 1.28.

α = 1 - 0.80 = 0.20

α/2 = 0.10

The t-value is obtained as shown below;

From the information, the sample size is 4.

df = n - 1 = 4 - 1

              = 3

The critical value with a level of significance ‘of 0.10’ and degrees of freedom ‘of 3’ is 1.533.

(b) 98% confidence interval:

The z-value is obtained as shown below:

The level of significance is;

Locate the probability in the z table. Then, the corresponding row value is 2.3 and the column value is 03.

The critical value with a level of significance is 2.33.

α = 1 - 0.98 = 0.02

α/2 = 0.01

The t-value is obtained as shown below;

From the information, the sample size is 4.

df = n - 1 = 4 - 1

              = 3

The critical value with level of significance ‘0.01’ and degrees of freedom ‘3’ is 3.747

(C) 90% confidence interval:

The z-value is obtained as shown below:

The level of significance is;

Locate the probability in the z table. Then, the corresponding row value is 1.6 and the column value is 04.

The critical value with a level of significance is 1.64.

α = 1 - 0.90 = 0.10

α/2 = 0.05

The t-value is obtained as shown below;

From the information, the sample size is 4.

df = n - 1 = 4 - 1

              = 3

The critical value with a level of significance ‘of 0.05’ and degrees of freedom ‘of 3’ is 2.132.

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Answer

$850.50

I think

Step-by-step explanation:

Answer:

874

Step-by-step explanation:

Couches: 2 × 677 = 1,354

Beds: 4 × 465 = 1,860

Lamps: 3 × 94 = 282

1,354 + 1,860 + 282 = 3496

Four equal payments: 3496 ÷ 4 = 874

Each payment for the franchise rights to open and operate Pepperoni's specialty pizza restaurant is approximately $3,640.04.

To find the amount of each payment, we can use the formula for the present value of an ordinary annuity:

PV = PMT * [(1 - (1 + r)^(-n)) / r],

where PV is the present value (worth) of the franchise rights, PMT is the amount of each payment, r is the interest rate per period, and n is the number of periods.

In this case, the present value (worth) of the franchise rights is $70,000, the interest rate per period is 7.92% or 0.0792, and the number of periods is 12 (payments for two years).

Substituting these values into the formula, we have:

$70,000 = PMT * [(1 - (1 + 0.0792)^(-12)) / 0.0792].

Now, we can solve this equation for PMT. Using a calculator, the amount of each payment is approximately $3,640.04.

Therefore, each payment for the franchise rights to open and operate Pepperoni's specialty pizza restaurant is approximately $3,640.04.

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The given statement " let X be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that X equals 8 will be denoted by P(X=8)" is true. Because In probability theory, P(X=8) denotes the probability that the random variable X takes on the value 8.

Probability is a measure of the likelihood or chance that a certain event or outcome will occur. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

In this case, X represents the number of male births between 1:00am and 3:00am at a hospital in Orange County. So, P(X=8) represents the probability that exactly 8 male births occur during that time period.

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--The given question is incomplete, the complete question is

"True or false let X be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that X equals 8 is denoted by P(X=8)"--

The instantaneous rate of change of f is equal to the average rate for only one value of x in the open interval (0, 1.565), which is x = 0.3925.

To find the values of x where the instantaneous rate of change of f is equal to the average rate, we need to compare the derivative of f with the average rate formula.

The average rate of change of f on the interval (a, b) is given by:

Average rate = (f(b) - f(a))/(b - a)

In this case, the interval is (0, 1.565), so a = 0 and b = 1.565. Substituting these values into the average rate formula, we have:

Average rate = (f(1.565) - f(0))/(1.565 - 0)

To find the instantaneous rate of change, we need to calculate the derivative of f. Taking the derivative of f(x) = (1/4)x², we get:

f'(x) = (1/4) * 2x = (1/2)x

Now we equate the average rate and the derivative:

(1/2)x = (f(1.565) - f(0))/(1.565 - 0)

Simplifying this equation, we have:

(1/2)x = (f(1.565) - f(0))/1.565

To solve for x, we substitute f(x) with its expression:

(1/2)x = ((1/4)(1.565)² - (1/4)(0)²)/1.565

(1/2)x = (1/4)(1.565)²/1.565

Simplifying further:

(1/2)x = (1/4)(1.565)

(1/2)x = 0.19625

Multiplying both sides by 2:

x = 0.3925

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Answer:

3ab + 8

Step-by-step explanation:

10 + 3ab - 2

the only like terms are the numeric values 10 and - 2 , then

= 3ab + 10 - 2

= 3ab + 8

The expression with combining likely terms will be 3ab + 8.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

A mathematical expression serves as proof that two mathematical expressions are equal.

A statement expressing the equality of two mathematical expressions is known as an equation.

Given expression is  10+ 3ab - 2​

Now in this, the likely terms are only numerical values 10 and -2

By combining this

3ab + (10 - 2)

By subtraction

3ab + 8

Hence "The expression with combining likely terms will be 3ab + 8".

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Answer:

Step-by-step explanation:

There are two transformations, one vertical, one horizontal.

The + 9 part outside the absolute value sign moves the graph up 9 units.

Replacing  x  with  x - 1 moves the graph right 1 unit.

Comment:  The horizontal shifts sometimes appear backwards:  x - 1 looks like a shift to the left, but it's not.

Example:  f(4) = |4| = 4.  To get the same output (4) from g(x), you have to use a value for  x  that is 1 unit larger than 4.  g(5) = |5 - 1| = 4.

The volume of the Solid -

V = ∫[-2,2] 4x^2(2x^2 - 1)(12x^2 - 1) dx

What is volume?

Volume is a measure of the amount of three-dimensional space occupied by an object or a region. It quantifies the extent or size of a solid object or a container. In simpler terms, volume is a measure of how much space an object takes up.

What is integral?

In mathematics, an integral is a fundamental concept in calculus that allows us to compute the total accumulation of a quantity over a given interval. It is used to find the area under a curve, the length of a curve, the volume of a solid, and many other applications.

To find the volume of the solid enclosed by the paraboloid z = 3x^2(y - 2)^2 and the planes z = 1, x = -2, x = 2, y = 0, and y = 2, we need to set up a triple integral over the given region.

The limits of integration for x, y, and z are as follows:

x: -2 to 2

y: 0 to 2

z: 1 to 3x^2(y - 2)^2

The volume V can be calculated as follows:

V = ∫∫∫R dz dy dx

where R represents the region defined by the given planes.

V = ∫∫∫R 3x^2(y - 2)^2 dz dy dx

To evaluate this triple integral, we integrate with respect to z first, then y, and finally x, using the given limits of integration:

V = ∫[-2,2] ∫[0,2] ∫[1,3x^2(y-2)^2] 3x^2(y - 2)^2 dz dy dx

Performing the integration:

V = ∫[-2,2] ∫[0,2] [3x^2(y - 2)^2z]∣[1,3x^2(y-2)^2] dy dx

V = ∫[-2,2] ∫[0,2] 3x^2(y - 2)^2[3x^2(y-2)^2 - 1] dy dx

V = ∫[-2,2] [x^2(y - 2)^2(3x^2(y-2)^2 - 1)]∣[0,2] dx

V = ∫[-2,2] 4x^2(2x^2 - 1)(12x^2 - 1) dx

Evaluate this integral using appropriate techniques or numerical methods, such as numerical integration or computer software, to find the volume of the solid enclosed by the paraboloid and the given planes.

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There is no sufficient evidence to conclude that the true variance of the coefficient of thermal expansion for aluminum exceeds 3 at a = 0.05. So the option A is correct.

We may do a hypothesis test to see if there is sufficient evidence to conclude that the standard deviation in this experiment is greater than 3.

Setup of the null and competing hypotheses is as follows:

Null Hypothesis (H0): Aluminum's actual coefficient of thermal expansion has a real variance that is less than or equal to 3.

Alternative Hypothesis (HA): For aluminum, the actual coefficient of thermal expansion variance is greater than 3.

Using the provided data, we can then run a chi-square test and compare the test statistic to the crucial value based on a significance threshold of 0.05.

We must compute the sample variance and contrast it with the value of three because we are testing the variance.

The sample variance is determined using the provided data as follows:

s² = [(22.0 - x')² + (26.0 - x')² + ... + (20.4 - x')²]/(n - 1)

where n is the sample size, and x' is the sample mean.

We apply the algorithm below to determine the test statistic:

x² = (n - 1) × s²/σ²

where σ² is the predicted variance (in this instance, 3).

We may assess if there is sufficient evidence to conclude that the standard deviation is more than 3 by comparing the test statistic to the critical value from the chi-square distribution with (n - 1) degrees of freedom.

Unfortunately, the provided data do not include the population mean (x'). Both the sample variance and the hypothesis test cannot be computed without the value of x'. Therefore, based on the information supplied, we are unable to establish if there is sufficient evidence to infer that the standard deviation is greater than 3.

So the option A is correct.

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The complete question is:

A group of 15 students has performed an experiment, they measured the coefficient of thermal expansion for aluminum. The results are as follows (10⁻⁶ K⁻¹)

22.0, 26.0, 25.6, 23.8, 22.7, 24.8, 24.9, 22.1, 26.1, 24.5, 23.5, 21.0, 21.4, 23.5, 20.4

Is there strong evidence to conclude that the standard deviation in this experiment exceeds 3? Use a = 0.05.

A. There is no sufficient evidence to conclude that the true variance of the coefficient of thermal expansion for aluminum exceeds 3 at a = 0.05.

B. There is sufficient evidence to conclude that the true variance of the coefficient of thermal expansion for aluminum exceeds 3 at a = 0.05.

Answer:

49.95 dollar pizza

Step-by-step explanation:

29.97/3 = 9.99*5 = 49.95

Answer:

$49.95

Step-by-step explanation:

Divided $29.97 by 3, then multiply it by 5.