if we want to estimate the population mean time for previews at movie theaters with a margin of error of 75 seconds, what sample size should be used? assume 95% confidence.

The point G on AB such that the ratio of AG to GB is 3:2 is; G(4.2, 2)

How to partition a Line segment?

The formula to partition a line segment in the ratio a:b is;

(x, y) = [(bx1 + ax2)/(a + b)], [(by1 + ay2)/(a + b)]

We want to find point G on AB such that the ratio of AG to GB is 3:2.

From the graph, the coordinates of the points A and B are;

A(3, 5) and B(5, 0)

Thus, coordinates of point G that divides the line AB in the ratio of 3:2 is;

G(x, y) = [(2 * 3 + 3 * 5)/(2 + 3)], [(2 * 5 + 3 * 0)/(2 + 3)]

G(x, y) = (21/5, 10/5)

G(x, y) = (4.2, 2)

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Answer:

42,46

Step-by-step explanation:

2n+2n+4=88

4n+4=88

4(n+1)=88

n+1=88/4

n+1=22

n=22-1

n=21

Therefore

2n=2*21=42

2n+4=2*21+4

2n+4 = 42+4 = 46

Yes, it would be possible to use 14C age dating to estimate the age of a dinosaur bone.

Explanation:14C dating is a method used to determine the age of once-living organisms based on the radioactive decay of carbon-14 in their tissues. However, 14C dating is only effective for samples that are less than 50,000 years old. Therefore, it is not possible to use 14C dating to directly date dinosaur bones as they are much older than 50,000 years, and all the carbon-14 would have already decayed.

However, indirect dating methods such as radiometric dating can be used to estimate the age of the rocks in which the dinosaur bones were found. This method is based on the radioactive decay of isotopes in the rocks and can be used to determine the age of the rocks to within a few million years. By association, the age of the dinosaur bones can also be estimated, providing an indirect method of dating them. Therefore, while 14C dating is not useful for directly dating dinosaur bones, it can be used indirectly to estimate their age.

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The perimeter of the triangle is 170 inches.

To solve for the perimeter, we first need to find the length of the perpendicular height. We can do this using the sine function:

sin(35°) = 46/x

x = 46/sin(35°) = 65 inches

Now that we know the length of the perpendicular height, we can find the length of the base of the triangle using the cosine function:

cos(35°) = 65/x

x = 65/cos(35°) = 75 inches

The perimeter of the triangle is the sum of the lengths of the three sides, so the perimeter is:

P = 65 + 75 + 30

= 170 inches

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Answer: 0.72

Step-by-step explanation:

Given:  18 out of every 25 shoppers between the age of 18 and 34 research purchases online before going to a store.

Fraction of shoppers between the age of 18 and 34 research purchases online before going to a store \(=\dfrac{18}{25}\)

In decimal , \(\dfrac{18}{25}=\dfrac{18}{25}\times\dfrac{4}{4}=\dfrac{72}{100}=0.72\)

Hence, this value written as a decimal = 0.72

The cost of 1 pound of radish is $1.65. Hence, the answer is $1.65.

Given that Haseen bought 4 2/5 pounds of radish for $13.20.

We need to find the cost of 1 pound of radish at that rate.

Let's do it step by step.

Solution:

We have, Haseen bought 4 2/5 pounds of radish for $13.20.

Then the cost of 1 pound of radish= Total cost / Total amount bought

= $13.2/ 4 2/5 pounds

$1 = 100 cents

Then $13.20 = 13.20 x 100 cents

= 1320 cents

= (33 x 40 cents)

Therefore,

$13.20 = $1.65 x 8

Now, $1.65 represents the cost of 1 pound of radish as shown above.

So, the cost of 1 pound of radish is $1.65.

Hence, the answer is $1.65.

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Answer:B

Step-by-step explanation:the line touches the graph on the y axis at 3 so the y intercept has to be a positive 3. Then it goes up 1 over 3 each time. Meaning it’s Y=1/3X+3

Answer:

Goku died you I just started watching

Answer:

\(y^7\)

Step-by-step explanation:

If we want to simplify the expression \(y^9 \cdot y^{-2}\), we have to note that exponent rules state that \(x^a \cdot x^b = x^{a+b}\).

This means that if we add the exponents, that will be what we raise y to the power of.

\(9 + -2 = 9-2 = 7\)

So \(y^7\).

Hope this helped!

Answer:

40=(x/6)

40×6=240

x=240?

The value of x is 204 degree.

The point where they meet is called a vertex. When two lines intersect, the opposite (X) angles are equal.

As line UM and FQ is intersecting at point x.

Using Vertical opposite angle,

x/6= 40

x=40*6

x=240

Hence, the vertically opposite angle is 240.

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To construct a nonzero vector v in \(R^{3}\) that is orthogonal to \(u_{1}\) and \(u_{2}\), we can use the cross product of u1 and u2.

The cross product of two vectors, say

\(u_1 = [u_{11}, u_{12}, u_{13}]\)  and \(u_2 = [u_{21}, u_{22}, u_{23}]\) is given by the following formula:

\(v = [u_{12}u_{23} - u_{13}u_{22}, u_{13}u_{21} - u_{11}u_{23}, u_{11}u_{22} - u_{12}u_{21}]\)

Let's calculate the cross product of u1 and u2:

\(u_{1}\) = [-1, 2, 0]

\(u_{2}\) = [1, -1, 1]

v = [2(1) - 0(-1), 0(1) - (-1)(1), (-1)(-1) - 2(1)]

= [2, 1, -1]

Therefore, the nonzero vector v = [2, 1, -1] is orthogonal to both u1 and u2.

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Answer: a) To find the scale factor, we need to find the ratio of the corresponding lengths of the two prisms, since the volumes of two similar prisms are proportional to the cube of the scale factor. Let x be the scale factor.

(volume of larger prism) / (volume of smaller prism) = (x³) = 27/1

x³ = 27

x = 3

Therefore, the scale factor is 3.

b) The ratio of the areas is equal to the square of the scale factor. Let A1 and A2 be the areas of the larger and smaller prisms, respectively.

(A1) / (A2) = (scale factor)²

A2 = A1 / (scale factor)²

A2 = 153 / 9

A2 = 17 cm²

Therefore, the ratio of their areas is 9:1.

c) The ratio of the volumes is equal to the cube of the scale factor.

(volume of larger prism) / (volume of smaller prism) = (scale factor)³

(volume of smaller prism) = (1 cm³) * (scale factor)³

(volume of smaller prism) = 27 cm³

Therefore, the ratio of their volumes is 27:1.

d) To find the surface area of the smaller prism, we can use the same ratio as in part (b) to find that the surface area of the smaller prism is equal to the surface area of the larger prism divided by the square of the scale factor.

(surface area of smaller prism) = (surface area of larger prism) / (scale factor)²

(surface area of smaller prism) = 153 / 9

(surface area of smaller prism) = 17 cm²

Therefore, the surface area of the smaller prism is 17 cm².

Step-by-step explanation:

================================================

Work Shown:

Use the given area A = 28.3 to find the radius r

A = pi*r^2

28.3 = 3.14*r^2

3.14*r^2 = 28.3

r^2 = 28.3/3.14

r^2 = 9.01273885350319 approximately

r = sqrt(9.01273885350319)

r = 3.00212239149292

---------

Which is then used to find the circumference

C = 2*pi*r

C = 2*3.14*3.00212239149292

C = 18.8533286185756

C = 18.9

Answer:

1) x = -5 or 9; 2) x =7 or 0

Step-by-step explanation:

1) \(\frac{a}{b} = \frac{c}{d}; ad = bc\)

So just multiply to get

\(8x + 48 = x^2 + 4x + 3\\0 = x^2 - 4x - 45\\(x + 5)(x - 9) = 0\)

2) Multiply by the LCM, in this case it is 2x - 6 as (x-3)(2) = 2x -6.

You get:

\((2)(x)+(x)\left(x-3\right)=6x\\2x + x^2 -3x -6x = 0\\x^2 - 7x = 0\\take\ out\ the\ x\\x(x-7) = 0\\x = 0 \ or \ x = 7\)

The maximum number of tickets the theater can sell is 39,572.

The maximum number means the greatest amount of something possible.

The theater sale each weekend is 761 tickets.

There are eight weekend days in a month and in case the month starts with a Saturday or a Sunday there can be an additional weekend.

To calculate the maximum number of tickets the theater can sell in 1 year, we can multiply the maximum number of tickets sold per weekend by the number of weekends in a year, which is 52.

So, 761 tickets x 52 weekends = 39,572 tickets

Therefore, the maximum number of tickets the theater can sell in 1 year is 39,572 tickets.

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Answer:

x <24

Step-by-step explanation:

first cancel negative signs

then transfer 2 to right side

Greetings.

The answer is x > 24.

Explanation:

Solving Inequality is almost the same as equation. However, you have to know one thing about solving an Inequality.

That is whenever you move the negative coefficient of the variable, you have to swap the sign of Inequality.

\(-\frac{1}{2}x<-12\)

Reminder that

\(-\frac{1}{2}x=-\frac{x}{2}\)

We use negative x above 2 instead (Easier in solving)

\(-\frac{x}{2}<-12\)

Then we move 2 to divide -12.

\(-x<-12(2)\\-x<-24\)

Because the coefficient for x is in negative. We move -1 to divide -24 as we get 24 (Because negative divide negative = positive)

But remember that "whenever you move the negative coefficient of the variable, you have to swap the sign of Inequality."

So we change from < to > instead.

\(x>24\)

Answer:

D. 13

Step-by-step explanation:

You find the difference of the two temperatures

11-(-2)

11+2

13

Answer:

The correct answer is option B 12cm

Answer:

Options (a), (b), (e)

Step-by-step explanation:

a). \(\frac{5^{10}}{5^{8}}=5^{10-8}\)

          = 5²

    True.

b). (4⁸)³ = \(4^{8}\times 4^8\times 4^8\)

            = \(4^{24}\) [Since, \(x^{a}\times x^{b}\times x^c=x^{a+b+c}\)]

    True.

c). \(10^{-4}=\frac{1}{10^4}\)

    And \(\frac{1}{4^{10}}\neq \frac{1}{10^4}\)

    False.

d). \(15^{6}\times 15^{3}=15^{6+3}\)  [Since, \(x^{a}\times x^{b}=x^{a+b}\)]

                    = 15⁹

    And \(15^{9}\neq 15^{18}\)

    False.

e). \((6^{8})^{0}=1\) [Since, a⁰ = 1]

    True.

The monthly total cost of the owner is given by the equation 1000 + 2Q + 0.01Q^2, where Q represents the number of Shikanji glasses produced each month.

To calculate the number of glasses that should be produced each month, we need to find the value of Q that minimizes the total cost. This can be done by taking the derivative of the total cost equation with respect to Q and setting it equal to zero.

Taking the derivative of 1000 + 2Q + 0.01Q^2 with respect to Q gives us 2 + 0.02Q. Setting this equal to zero, we get 2 + 0.02Q = 0. Solving for Q, we find Q = -100.

Since producing a negative number of glasses is not possible in this context, we can disregard this value.

To find the minimum point of the equation, we can use the second derivative test. Taking the derivative of 2 + 0.02Q with respect to Q gives us 0.02.

Since the second derivative is positive, we can conclude that Q = -100 corresponds to a minimum point. Therefore, the number of glasses that should be produced each month is 100.

To calculate the economic profit earned by the firm each month, we need to subtract the total cost from the total revenue.

The total revenue is equal to the average price of a Shikanji glass multiplied by the number of glasses produced. The average price is given as Rs. 10, and the number of glasses produced is 100. Therefore, the total revenue is 10 * 100 = Rs. 1000.

The total cost is given by the equation 1000 + 2Q + 0.01Q^2, where Q is the number of glasses produced. Substituting Q = 100 into this equation, we get 1000 + 2 * 100 + 0.01 * 100^2 = 1000 + 200 + 100 = Rs. 1300.

Finally, we can calculate the economic profit by subtracting the total cost from the total revenue: 1000 - 1300 = -300.

The negative sign indicates that the firm is incurring an economic loss of Rs. 300 each month.

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Answer:

the total payment need to pay is $525

Step-by-step explanation:

Given that

The amount at promissory note issued is $500

The rate of interest is 10%

And, the time period is 180 days

So, the total payment included is

= $500 + ($500 × 10% × 180 days ÷ 360 days)

= $500 + $25

= $525

hence, the total payment need to pay is $525

Answer:

The profit is $100.56

Step-by-step explanation:

The total cost for the ice cream was 100 * 2.40 = 240

14 1/2 gallons were ruined so there were 100 -14 = 86 half gallons left

They sold these at 3.96 each

86 * 3.96 =340.56

The profit is the money made minus the cost

340.56-240 = 100.56

The profit is $100.56

Answer:

ang. PQR

Step-by-step explanation:

The diameter which subtends an angle to the circumference of the circle is equal to 90 degrees. Hence, either ang. PQR and ang. PSR are both right angles.

Answer:

9

Step-by-step explanation:

Given data

Ride ticket= $2

Admission= $7

Amount= $25

We want to find the greatest number of rides

let the number of rides be x

The expression to describe how she spends the amount is given as

y=7+2x

for y= 25, let us find x

25= 7+2x

25-7= 2x

18=3x

x= 18/2

x= 9

Hence the number of rides is 9

a). The number of ways which the company can choose 4 workers from the list of employees is; 2,730 ways.

b). The number of ways the company can choose the workers if 2 labourers and 3 joiners are on holiday is; 700 ways.

It follows from the task content that the number of ways the company can choose 4 workers in each scenario be determined.

a). Since there are 3 labourers, 13 joiners, 10 electricians, and 7 plumbers.

The number of possible ways to choose 4 workers is; ³C₁ × ¹³C₁ × ¹⁰C₁ × ⁷C₁

= 3 × 13 × 10 × 7

= 2,730 ways.

b). Also, when 2 labourers and 3 joiners are absent, it follows that the selection space is now; 1 labourer, 10 joiners, 10 electricians and 7 plumbers.

The number of possible ways is therefore; ¹C₁ × ¹⁰C₁ × ¹⁰C₁ × ⁷C₁

= 1 × 10 × 10 × 7

= 700 ways.

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The pharmacy should send two pills marked  for the patient to take.

To answer this question, we can use the formula below;

Dosage = (Amount of Drug x Patient's Weight) / Time

Since we don't have any information about the patient's weight or the time, we can't calculate the dosage.

However, we can calculate the number of pills required.

So, let's proceed with the calculation.

Each pill contains 2.5 mg of the pain reliever.

We need to administer a low dose, so let's assume the dose required is 5 mg.

To administer this dose, we need to give two pills, i.e., 2 x 2.5 = 5mg.

However, the question asks us to round the answer to the nearest tenth of a pill.

Since we can't divide a pill into parts, we need to round the answer up or down to the nearest whole pill.

In this case, since we need two pills, the answer is 2 pills.

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Answer:

x is 60°

y is 30°

(would really, reallly appreciate the brainliest)

Step-by-step explanation:

x can be seen as what's needed to do a full 180 ° turn when you already turned 120°

y is 60° bc the sum of all tree angles of a triangle is always 180°

90° are given with the little square, 60 by the similar reasoning as above

Answer:

Step-by-step explanation:

L an M are parallel & P is transversal.

So, 120, x are co-interior angles, ie 180

x +120 = 180

x = 180 - 120

x = 60

The angle  vertically opposite to x, will have the same value of x.

Vertically opposite angles are equal

In triangle, sum of angles = 180

60 + 90 + y = 180

150 + y =180

y =180 -  150

y =30

it is possible to make a triangle with the sides 3, 3 and 9

true

The bicycle manufacturer is studying the reliability of its models and analyzing the probability of defects. They found the probability of a brake defect is 4 percent and the probability of both brake and chain defects is 1 percent.

Given that the probability of a defect with brakes or chain is 6 percent, we can find the probability of a chain defect using the formula: P(A and B) = P(A|B) * P(B), where P(A and B) is the probability of both events A and B occurring, P(A|B) is the probability of event A occurring given that event B has occurred, and P(B) is the probability of event B occurring.

In this case, we want to find the probability of a chain defect given that there is a defect with either the brakes or the chain. Let's use the events: A = brake defect, B = chain defect, From the problem statement, we know that: P(A) = 0.04 (probability of a brake defect), P(A and B) = 0.01 (probability of both a brake defect and a chain defect)
P(A or B) = 0.06 (probability of a defect with the brakes or the chain).

To find P(B|A or B), we can use the formula: P(B|A or B) = P(A and B) / P(A or B) = 0.01 / 0.06, = 1/6, = 0.1667, So the probability of a chain defect given that there is a defect with either the brakes or the chain is 16.67%, or approximately 2/12 or 1/6.

Therefore, the correct answer is option 2: 2%, Solving for the probability of a chain defect, we get: P(chain defect) = 0.06 - 0.04 + 0.01 = 0.03, So, the probability of a chain defect is 3 percent.

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