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Which is an example of simple random sampling created from each given population?

The required experimental probability that a team will consist entirely of boys is 0.04. Option B is correct.

To find the experimental probability that a team will consist entirely of boys, we need to count the number of trials in which all three coin tosses resulted in tails (which represents a team consisting entirely of boys), and divide by the total number of trials (which is 50).

From the data, we can see that there are only 2 trials where all three coin tosses resulted in tails, so the experimental probability of a team consisting entirely of boys is:

2/50 = 0.04

Therefore, the experimental probability that a team will consist entirely of boys is 0.04.

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The margin of error for the proportion of companies likely to require higher employee contributions for health care coverage is 0.0344. The 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage is ( 0.4823, 0.5577.).

To compute the margin of error for the proportion, we use the formula:

Margin of error = z*√((P(1-P))/n)

where z is the z-score for the desired confidence level (95% confidence corresponds to a z-score of 1.96), P is the sample proportion, and n is the sample size. From the information given, we have

P = 0.52 (sample proportion)

n = 900 (sample size)

z = 1.96 (for 95% confidence level)

Substituting these values into the formula, we get

Margin of error = 1.96√((0.52(1-0.52))/900) ≈ 0.0344

Therefore, the margin of error is approximately 0.0344, or 3.44%.

To compute the confidence interval, we use the formula:

Confidence interval = P ± z*(√((P(1-P))/n))

where P, z, and n are the same as in part 1. Substituting these values into the formula, we get

Confidence interval = 0.52 ± 1.96*(√((0.52*(1-0.52))/900)) ≈ (0.4823, 0.5577)

Therefore, we can say with 95% confidence that the true proportion of companies likely to require higher employee contributions for health care coverage this year relative to last year is between 0.4823 and 0.5577.

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a) The probability that exactly one of them will be a girl = 0.3407

b) The probability that at least one of them will like the football = 0.7672

a) If we select three students then the probability that exactly one of them will be a girl

From the attached two way table we can observe that the total number of girls = 22

the total number of boys = 18

and the total number of students = 40

The possible outcomes for selecting 3 students from 40 would be,

⁴⁰C₃

Using combination formula,

⁴⁰C₃ = 40! / (3! × (40 - 3)!)

      = 9880

If there is exactly one girl then other two must be boys in the set of 3 selected students.

So, the required probability would be,

P = (²²C₁ × ¹⁸C₂) / ⁴⁰C₃

P = (22 × 153)/9880

P = 0.3407

b) The number of students like the football = 15

and the number of students who don't like the football are 40 - 15 = 25

The probability that at least one of them will like the football would be,

P = (¹⁵C₃ × ²⁵C₀ + ¹⁵C₂ × ²⁵C₁ + ¹⁵C₁ × ²⁵C₂) / ⁴⁰C₃

P = ((455 × 1) + (105 × 25) + (15 × 300)) / 9880

P = 0.7672

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Answer:

Step-by-step explanation:

given equation of a circle : x^2+y^2-6x+2y=b.

BY comparing it with x^2+y^2+2gx+2fy+c=0, we get

centre as (-g,-f)=(3,-1)

Since we know that radius r=sqrt(g^2+f^2-c)

Here radius is given as 4 units.

So,

4=sqrt((3)^2+(-1)^2-c)

=>16=9+1-c

Therefore, c=-6

Answer:3/2

Step-by-step explanation:

1/3 ÷ 2/9=

1/3 ×9/2=3/2

Answer:

3/2 u can also do 1 1/2 their equivalent fractions

Step-by-step explanation:

sorry about the handwriting :) not the best

The image point of (-7,-8) after the transformation D1/2oT-1,0 is (-4,4).

First, we apply the translation T-1,0, which moves every point 1 unit to the right (since the x-coordinate is decreased by 1) and leaves the y-coordinate unchanged. Therefore, the image of (-7,-8) under T-1,0 is (-7-1,-8) = (-8,-8).

Next, we apply the dilation D1/2, which scales every distance from the origin by a factor of 1/2. Therefore, the image of (-8,-8) under D1/2 is (-8/2,-8/2) = (-4,-4).

Thus, the image point of (-7,-8) after the transformation D1/2oT-1,0 is (-4,4).

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i Got u Bro!

Ov=zo « = 192 +8 5 Or = 1/2 (x + 2)² – 8 20 Ov=« 2)2-4 DELL.

a) The amount left after paying the tax is $53300.

(b) The interest after 2 years is $540.

(c) The percentage interest is 4%.

We have,

a)

The amount of tax the man pays.

= $65000 x 0.18

= $11700

Therefore, he has left.

= $65000 - $11700

= $53300

(b)

The interest earned after 2 years.

= $4500 x 0.06 x 2

= $540

(c)

The total amount of interest paid on the loan.

= $25740 - $24750

= $990

The percentage interest.

= ($990 / $24750) x 100%

= 4%

Thus,

(a) The amount left after paying the tax is $53300.

(b) The interest after 2 years is $540.

(c) The percentage interest is 4%.

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Answer:

34.83/.9 = 38.7 g mass (after one hour)

38.7/.9 = 43 g (starting mass)

The starting mass of the ice cube was 43 grams.

The function whose graph matches this one y= 4 sin (π/7 x) - 2

As, The general form of a sine function is

y= A sin (kx) + C........(1)

From the given graph the maximum value of the function is 2 and minimum value of the function is -6.

So, Amplitude= (Max- Min)/2

A = (2- (-6))/2

A= 8/2

Amplitude= 4

Now, The function complete a cycle in 14 units, so period of the function is 14.

2π/k= 14

k = π/7

and, Midline= (Min + Max)/2 = (2-6)/2 = -2

So, the function is

y= A sin (kx) + C.

y= 4 sin (π/7 x) - 2

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Marcus will earn $170 in interest after keeping his $500 in the account for 5 years.

To calculate the interest Marcus will earn, we can use the formula:

I = P * r * t

where I is the interest earned, P is the principal amount deposited, r is the annual interest rate as a decimal, and t is the time period in years.

In this case, Marcus deposited $500 and the annual interest rate is 6.8%, which is 0.068 as a decimal. He kept the money in the account for 5 years.

So we can plug in these values into the formula:

I = 500 * 0.068 * 5

I = $170

This is simple interest, which means that the interest is only earned on the original principal amount and not on any accumulated interest.

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The area of the different types of polygon with given dimensions are,

Area of octagon= 391.07 cm²

Area of pentagon = 232m²

Area of triangle = 21.22in²

Area of hexagon = 11.24square units.

Polygon name = octagon,

Side length = 9cm

Degree of central angle = 360° /8

                                        = 45°

To find Apothem ,

draw right triangle .

base is half of the side length = 4.5

Top angle of the right triangle = (1/2) × 45°

                                                  = 22.5°

Using tangent ratio considering top angle as α

tanα = 4.5/ Apothem length

⇒Apothem length = 4.5 / tan22.5°

⇒Apothem length = 4.5 / (√2 - 1 )

⇒Apothem length = 4.5 / 0.414

⇒Apothem length = 10.86cm.

Area of octagon = 2 ( 1 + √2 ) × (side length)²

                           = 2 × 2.414 × 9²

                           = 391.07 cm²

Polygon name = Pentagon,

Apothem= 8m

Degree of central angle = 360° /5

                                        = 72°

To find Side length ,

Let 'x' be the side length

draw right triangle .

base is half of the side length = x/2

Top angle of the right triangle = (1/2) × 72°

                                                  = 36°

Using tangent ratio considering top angle as α

tanα =   half of side length /Apothem length

⇒(1/2) side length  = 8 × tan36°

⇒ side length = 16 ×  (0.7265)

⇒ side length= 11.62m

Area of pentagon

= 5/2 × side length × distance from the center of sides to the center of pentagon

= 5/2 × 11.6 × 8

= 232m²

Polygon name = triangle,

Apothem= 2in

Degree of central angle = 60°

To find Side length ,

Let 'x' be the side length

draw right triangle .

base is half of the side length = x/2

Top angle of the right triangle =60°

Using tangent ratio considering top angle as α

tanα = half of side length / Apothem length

⇒(1/2) side length  = 2 × tan60°

⇒ side length = 4 (√3)

⇒ side length= 6.928in

                      ≈ 7 in

Area of triangle = √3/4 × 7²

                          = 21.22in²

Polygon name = hexagon,

Apothem= 5

Degree of central angle = 60°

To find Side length ,

Let 'x' be the side length

draw right triangle .

base is half of the side length = x/2

Top angle of the right triangle =30°

Using tangent ratio considering top angle as α

sinα = half of side length / Apothem length

⇒(1/2) side length  = 5 × sin30°

⇒ side length = 10 (0.5)

⇒ side length= 5

distance from center of sides to the center of hexagon

= √5² - 2.5²

=4.33

Area = (3√3)/2 × distance from center of sides to the center of hexagon

        = (3√3)/2 × 4.33

        = 11.24square units.

Therefore, the area of the given polygon are octagon = 391.07 cm² , pentagon =  232m² , triangle = 21.22in² , and hexagon = 11.24square units.

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The money invested by the teacher to have at least 125,000 in her account after 40 years of a 6.95% annual interest rate compounded continuously is 7755. Hence, the right solution to the question is option D

Compound interest is given by

A = P[tex](1+r)^t[/tex]

where A is the amount

P is the principal

r is the rate of interest

t is the time

Given in the question,

A = $125,000

r = 6.95% or 0.0695

t = 40 years

P is to be found

A = P[tex](1+r)^t[/tex]

125000 = P [tex](1 + 0.0695)^{40[/tex]

125000 = P * [tex]1.0695^{40[/tex]

125000 = 16.118P

P = 7755

The teacher should invest $7755 initially.

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If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)

From the question, we have the following parameters that can be used in our computation:

Start = (0, -4)

Also, we have

You move left 1 unit and right 4 units

Mathematically, this can be expressed as

(x, y) = (x - 1 + 4, y)

Substitute the known values in the above equation, so, we have the following representation

Endpoint = (0 - 1 + 4, -4)

Evaluate the expression

Endpoint = (3, -4)

Hence, the endpoint is (3, -4)

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Answer:

The mode is the best measure of center for a distribution that is bimodal, meaning that it has two peaks. In such a distribution, the mean and median may not be representative of the center of the data, but the mode is a good measure of center because it reflects the most common value(s) in the data.

For skewed distributions, the mode may not be a good measure of center because the peak of the distribution is not necessarily at the center of the data. In a normal distribution, the mean, median, and mode are all equal and are good measures of center.

Answer: 5

Step-by-step explanation:

Since x is directly related to the square of y, we can write the equation:

x = ky^2

where k is a constant of proportionality. We can solve for k using the given values of x and y:

16 = k(2^2) -> 16 = 4k -> k = 4

Now that we know k, we can use it to find y when x = 100:

100 = 4y^2 -> 25 = y^2 -> y = ±5

Since y cannot be negative, the only possible value of y is 5. Therefore, when x = 100, y could be 5.

Answer:

One possible value of y when x = 100 is y = 5.

Step-by-step explanation:

Using the direct variation formula, we know that x = ky^2, where k is a constant. Given that x = 16 and y = 2, we can solve for k:

16 = k(2)^2

k = 4

Now we can use this value of k to find y when x = 100:

100 = 4y^2

y^2 = 25

y = 5 or -5 (since the question only asks for one possible value, we can choose either solution)

Therefore, one possible value of y when x = 100 is y = 5.

The volume of this rectangular prism is equal to: B. 8 in³.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

Since this rectangular prism is filled with 16 cubes and each cube is a 1/2 inch cube, the dimensions of the rectangular prism is given by;

Dimensions = 16 × (1/2)³ = 2inches.

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of rectangular prism = 2 × 2 ×  2

Volume of rectangular prism = 8 cubic inches.

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Complete Question:

A rectangular prism is filled with 16 cubes. Each cube is a 1/2 inch cube. What is the volume of the rectangular prism?

A. 2 in³

B. 8 in³

C. 16 in³

D. 32 in³

Answer:  A) £7.49

               B) £2.25

Step-by-step explanation:

Step 1:

Let the cost of a football be [tex]f[/tex]and the cost of a tennis ball be [tex]t[/tex].

Step 2:

Write the 2 equations we have from the given information:

[tex]2f + 3t = 21.73[/tex] [tex] \textsf{(from the cost of 2 footballs and 3 tennis balls)} [/tex]

[tex]5f + 7t = 53.20[/tex] [tex] \textsf{(from the cost of 5 footballs and 7 tennis balls)} [/tex]

Step 3:

Solve for one variable in one of the equations. For example, we can solve for [tex]f[/tex]in the first equation:

Step 4:

Substitute this expression for [tex]f[/tex] into the second equation and solve for [tex]t[/tex]:

So, the cost of a tennis ball is £2.25.

Step 5:

Substitute this value of [tex]t[/tex] into the expression for [tex]f[/tex] and solve for [tex]f[/tex]:

So, the cost of a football is £7.49

Step 6:

Therefore, the cost of a football is £7.49 and the cost of a tennis ball is £2.25.

Answer:

Snacks: $75

Alcohol: $200

Dairy: $300

Average delivery charge per week: $63.89 (rounded to two decimal places)

Step-by-step explanation:

To find the average delivery charge the store pays each week, first calculate the total delivery cost for each category and then find the total cost for all deliveries. Finally, divide the total cost by the total number of deliveries.

Snacks:

3 deliveries * $25 per delivery = $75

Alcohol:

2 deliveries * $100 per delivery = $200

Dairy:

4 deliveries * $75 per delivery = $300

Total cost for all deliveries:

$75 (Snacks) + $200 (Alcohol) + $300 (Dairy) = $575

Total number of deliveries:

3 (Snacks) + 2 (Alcohol) + 4 (Dairy) = 9

Average delivery charge per week:

$575 (total cost) / 9 (total number of deliveries) = $63.89 (rounded to two decimal places)

Answer:

A

Step-by-step explanation:

the domain is the values of x covered by the graph

on the left the graph → - ∞

on the right the graph tends to + ∞

there are no excluded values of x on the domain , so

domain is - ∞ < x < ∞

To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.

The function value at x = 10 is:

f(10) = 1.85(10)^2 = 185

The function value at x = 20 is:

f(20) = 1.85(20)^2 = 740

The length of the interval is:

20 - 10 = 10

So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:

(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5

Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.

The scale factor used is 1/4.

We have,

Length of sides of triangle D 24, 32, and 40.

Length of sides of triangle D' 6, 8, and 10.

So, scale factor

= length of corresponding side in D' / length of corresponding side in D

= 6/24

= 1/4

Thus, the scale factor used is 1/4.

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Answer:

C = 45

AC = 1

BC = 2

Step-by-step explanation:

C: 180 - (90 + 45) = 45

AC: Because the angles are the same, it is equal to the other leg, 1 cm

BC: a^2 + b^2 = c^2, so 1 + 1 = 2

The number of cars that pass through the intersection between 6 am and 10 am is 4800.

To find the number of cars that pass through the intersection between 6 am and 10 am, we need to integrate the traffic flow rate function r(t) over the interval [0,4].

Integrating r(t) with respect to t, we get:

∫(400+ 600t - 150t²)dt = 400t + 300t² - 50t³ + C

where C is the constant of integration.

Evaluating this expression between t=0 and t=4 (since we are interested in the interval between 6 am and 10 am), we get:

(400(4) + 300(4)² - 50(4)³) - (400(0) + 300(0)² - 50(0)³) = 4800 cars

In summary, we can find the number of cars that pass through an intersection between two specific times by integrating the traffic flow rate function over that interval.

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Answer: 3.14 is all ways the circumference

Step-by-step explanation:

Answer:

Here's a cost statement for the year 2021:

Production of 1,500 units

Cost of raw materials = Rs. (20,000 x 1.2) = Rs. 24,000

Labour cost = Rs. (12,000 x 1.1) = Rs. 13,200

Fixed overheads = Rs. (8,000/2) = Rs. 4,000

Variable overheads = Rs. (8,000/2 x 1.5) = Rs. 6,000

Office overheads = Rs. 4,000

Selling expenses per unit = Rs. (1,000 x 0.8 / 1,500) = Rs. 0.53

Total cost per unit = Rs. (24,000 + 13,200 + 4,000 + 6,000 + 4,000) / 1,500 = Rs. 28.80

Profit = 25% of selling price

Selling price per unit = (28.80 / (1 - 0.25)) = Rs. 38.40

Total profit = (1,500 x 38.40 x 0.25) = Rs. 14,400

Therefore, the cost statement for the year 2021 shows a total profit of Rs. 14,400 and a selling price per unit of Rs. 38.40.

Answer:

110

Step-by-step explanation:

nth term = 3n + 2

3 (36) + 2

108 + 2 = 110

Answer:

The 36th term in the sequence is 104.

Here's how to find it:

- Start with the first number in the sequence: 5.

- Add the common difference, which is 3, to get the second number in the sequence: 8.

- Add the common difference to the second number to get the third number: 11.

- Continue adding the common difference to each subsequent number to find the next term in the sequence.

- The 36th term is three less than 37 times the common difference added to the first term.

- Using that formula, we can calculate the 36th term as: 5 + (36 - 1) * 3 = 5 + 105 = 110.

- Therefore, the 36th term in the sequence is 104.

The equation of the circle graphed is (x + 4)^2 + (y + 5)^2 = 16

From the question, we have the following parameters that can be used in our computation:

The circle

Where, we have

Center = (a, b) = (-4, -5)

Radius, r = 4 units

The equation of the circle graphed is represented as

(x - a)^2 + (y - b)^2 = r^2

So, we have

(x + 4)^2 + (y + 5)^2 = 4^2

Evaluate

(x + 4)^2 + (y + 5)^2 = 16

Hence, the equation is (x + 4)^2 + (y + 5)^2 = 16

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Answer:

16

Step-by-step explanation:

To find the median, we find the middle of the data set.

7, 9, 11, 14, 18, 20, 30, 35

There are 8 values

7, 9, 11,    14, 18,     20, 30, 35

The median is between the 4th and 5th numbers

We need to find the mean of the middle two numbers

(14+18)/2 =32/2= 16

Answer:

16

Step-by-step explanation:

             [tex]\sf (\frac{n+1}{2}\:)^ t^h \:data[/tex]

       Here,

             n ⇒ number of terms

Let us find it now.

7, 9, 11, 14, 18, 20, 30, 35

[tex]\sf Median=\sf (\frac{n+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf (\frac{8+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf 4.5^ t^h \:data[/tex]

In this case, add 4th and 5th data and divide it by 2.

[tex]\sf Median = \frac{14+18}{2}\\\\ \sf Median = \frac{32}{2}\\\\\sf Median = 16[/tex]