A group of students interning at WDHS are wanting to reward their loyal listeners with free ice cream. To make it easier on their listeners they rent 6 ice cream trucks to space evenly throughout their coverage area.

a) The 90% confidence interval for the proportion of adults that have blue eyes is given as follows: (0.087, 0.133).

b) As the interval does not contain 0.08, the belief that 8% of people have blue eyes is misguided.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 9%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

The parameters for this problem are given as follows:

[tex]n = 500, \pi = \frac{55}{500} = 0.11[/tex]

The lower bound of the interval is given as follows:

0.11 - 1.645 x sqrt(0.11 x 0.89/500) = 0.087.

The upper bound of the interval is given as follows:

0.11 + 1.645 x sqrt(0.11 x 0.89/500) = 0.133.

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Answer:

A=40.8 B=8

Step-by-step explanation:

A Explanation

£7.20*3=£21.6

£9.60*2=£19.2

19.2+21.6=40.8

B Explanation

£9.60*3=£28.8

86.40-28.8=57.6

57.6/7.20=8

The total number of beds in Shelter B is 10.2. This is because the ratio of the occupancy of Shelter A to Shelter B is 14:25, meaning that if Shelter A is 70% occupied, then Shelter B must be 50% occupied.

Occupancy is used to measure the efficiency of a business or facility by determining how often a space is used, how long people stay in the space, and whether or not the space is being used to its full potential.

To calculate the number of beds in Shelter B, we need to first calculate the total number of beds in Shelter A. Since Shelter A is 70% occupied, we can use the following equation to calculate the total number of beds in Shelter A:

Total beds in Shelter A = (Occupied beds in Shelter A ÷ 70%) x 100%

Total beds in Shelter A = (400 ÷ 70%) x 100%

Total beds in Shelter A = 571.43

Since the ratio of the occupancy of Shelter A to Shelter B is 14:25, we can use the following equation to calculate the total number of beds in Shelter B:

Total beds in Shelter B = (Total beds in Shelter A x 25%) ÷ 14

Total beds in Shelter B = (571.43 x 25%) ÷ 14

Total beds in Shelter B = 10.2

Therefore, the total number of beds in Shelter B is 10.2. This is because the ratio of the occupancy of Shelter A to Shelter B is 14:25, meaning that if Shelter A is 70% occupied, then Shelter B must be 50% occupied. As a result, the total number of beds in Shelter B is 10.2.

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Answer:

First, we need to figure out how many socks are in the drawer.

5 black socks + 5 striped socks + 9 polka dot socks + 11 white socks + 5 blue socks + 1 sock with photos of small socks = 36 socks

Pay attention to the polka dot socks now. There are 9 polka dot socks in the drawer; the odds of picking one on the first draw are 9/36 socks.

If we don't replace the first sock and draw again, there will be 8 polka dot socks remaining out of a total of 35 socks in the drawer.

As a result, the likelihood of picking a second polka dot sock after selecting the first is 8/35.

To calculate the likelihood of picking a pair of polka dot socks, multiply the odds of selecting a polka dot sock on the first draw by the probability of selecting another polka dot sock on the second draw.

The probability of choosing a pair of polka dot socks is (9/36) x (8/35) = 0.0571, or approximately 5.71%.

On average, it will take us two to three inquiries to discover a kid who enjoys a salad for lunch.

The idea of probability is used to determine the likelihood or probability that a given occurrence will take place.

It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that it is guaranteed to happen.

Probabilities can be expressed using percentages, decimals, or fractions.

The likelihood that any particular student will choose a salad is 20%, or 0.2, assuming that each student's taste for lunch is independent of the preferences of the others.

There is a 0.2 chance that the first student you question will say they prefer a salad. You go on to the next kid if they don't want a salad.

Given that the first student didn't like a salad, there is a 0.2 chance that the second student will as well. None of the first two pupils had a (1-0.2) (1-0.2) = 0.64 chance of preferring a salad.

Given that none of the n-1 students before them did, the likelihood that the nth student would prefer a salad is similarly 0.2. (1-0.2)n-1 is the likelihood that none of the first n-1 students will choose a salad.

In order to identify a student who prefers a salad, you must thus question an anticipated number of students: E(x) = 1(0.2) + 2(1-0.2)(0.2) + 3(1-0.2)2(0.2) +...

Although this is an infinite series, by truncating it after a predetermined number of words, we may approximate it. Say we decide to quit after ten terms:

E(x) ≈ 1×(0.2) + 2×(1-0.2)(0.2) + 3(1-0.2)²×(0.2) + ... + 10×(1-0.2)⁹ × (0.2) E(x) ≈ 2.48

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As a result, the total number of pupils i Ms. Morales' class is 10x = 10(3) = 30.

30 pupils is the right response.

In math, a mean is the average of a data collection, which is calculated by adding all of the numbers together and then dividing the total of the numbers by the number of numbers.

If the boy-to-girl ratio in Ms. Morales' class is 3:7, the class may be divided into 10 equal portions, with three males and seven girls.

If x equals the number of guys in the class, then the number of girls in the class is 7x.

The total number of pupils in the class is the sum of the male and female students:

Total number of pupils = 3 times + 7 times = 10 times

To get the value of x, we must first determine the total number of pupils in the class. Ms. Morales's school has class sizes ranging from 22 to 34 pupils each class. Because 10x is the total number of pupils in the class, we must find an x value that gives us a total number of students between 22 and 34.

Let's see whether x = 2 works. If x equals 2, the total number of pupils in the class is 10x = 20, which is insufficient.

Let's see whether x = 3 works. If x = 3, the total number of pupils in the class is 10x = 30, which is between 22 and 34.

As a result, the total number of pupils in Ms. Morales' class is 10x = 10(3) = 30.

30 pupils is the right response.

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The total number of students in Ms. Morales's class is 84.

None of the given options is correct. The correct answer is 84.

What are proportions?

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other.

Let's first assume that the total number of students in Ms. Morales's class is x.

According to the problem statement, the ratio of boys to girls is 3:7. This means that out of every 3 + 7 = 10 students, 3 are boys and 7 are girls. Therefore, we can write:

Number of boys = (3/10)*x

Number of girls = (7/10)*x

The problem statement also tells us that the class sizes range from 22 to 34 students. This means that the total number of students x must be a multiple of both 3 and 7, and it must also be between 22 and 34 inclusive.

To find the possible values of x, we can list the multiples of 3 and 7 that are between 22 and 34:

Multiples of 3: 24, 27, 30, 33

Multiples of 7: 28

We can see that the only multiple of both 3 and 7 that is between 22 and 34 is 21*4 = 84. Therefore, the total number of students in Ms. Morales's class is 84.

Answer: None of the given options is correct. The correct answer is 84.

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The probability for each colour of the block is removed from the box is as follows:

Blue: 9/40

Red: 15/40

Yellow: 11/40

Orange: 5/40

Explain the term probability

Probability is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1. It is used to model uncertainty and randomness in various fields, such as statistics, science, engineering, and economics. Probability theory provides a framework for analyzing and predicting the outcomes of random experiments, and it has applications in many real-world situations, such as gambling, insurance, and quality control.

According to the given information

The probability of drawing a block of a certain colour from the box can be calculated by dividing the number of blocks of that colour by the total number of blocks in box 1. Based on the experimental results, the probability for each color of block being removed from the box is as follows:

The probability of drawing Blue: 9/40

The probability of drawing Red: 15/40

The probability of drawing Yellow: 11/40

The probability of drawing Orange: 5/40

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The missing fourth vertex needed to create a rectangle is (25, 3) option D.

Vertices (singular: vertex) are the corners or points where two or more lines, edges, or curves intersect and form an angle.

Here, the width of one side of the rectangle;

⇒ +3 - (-6) = 9 unit                (left side y-coordinates)

Similarly the length of the rectangle;

⇒ 25 - (-15) = 40 unit             (up-side x-coordinates)

Since a rectangular shape has two sets of equal sides of equivalent width (y-coordinates) and length (x-coordinates), we realize that the missing fourth vertex should be 9 units and 40 units over the point (25, -6). and (-15, 3)

So, we add 9 to the y-coordinate of (25, -6) and add 40 to the x-coordinate of (-15, 3) to get the missing vertex:

⇒ (25, -6+9) = (25, 3)

⇒ (-15+40, 3) = (25, 3)

Therefore, the missing fourth vertex is (25, 3)

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Answer:

68°

Step-by-step explanation:

Total angle in a quadrant = 90°

x + 22° = 90°

x = 90 - 22

x = 68°

The correct answer is option A. 2.5.

What is a number line?

A number line is a visual representation of a line where the points are the real numbers. The line is usually drawn horizontally, with zero in the center and positive numbers to the right and negative numbers to the left. The numbers on the number line are evenly spaced and correspond to points on the line. A number line is a useful tool for understanding the relationships between numbers and for performing operations such as addition and subtraction. It is also used to represent measurements, such as distances and time intervals.

To find the midpoint of a line segment, we add the coordinates of the two endpoints and divide by 2. In this case, the coordinates of point S are -2 and the coordinates of point T are 7.

So the coordinate of the midpoint, point R, is:

R = (S + T)/2 = (-2 + 7)/2 = 5/2 = 2.5

Therefore, point R lies at 2.5 on the number line.

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Answer:

We can use the Pythagorean theorem to determine if the triangle is a right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's label the sides of the triangle as a = 18 mm, b = 25 mm, and c = 15 mm. We want to see if a right angle exists between sides a and b, so we will check if c² = a² + b².

a² + b² = 18² + 25² = 324 + 625 = 949

c² = 15² = 225

Since c² is not equal to a² + b², the triangle is not a right triangle.

Therefore, the answer is no, the triangle is not a right triangle.

To solve for x, we need to isolate the variable (x) on one side of the equation. We can do that by first subtracting 3 from both sides of the equation to get:

11 - 3 = 4x

Simplifying the left side gives:

8 = 4x

Finally, dividing both sides by 4 gives:

x = 2

Therefore, the solution to the equation 11=3+4x is x=2.

the solution to the equation [tex]11=3+4x[/tex] 11=3+4x is [tex]x = 2[/tex] X = 2.

The equation [tex]11=3+4x[/tex] 11=3+4x is a linear equation in one variable [tex](x)[/tex](x) with coefficients and constants that are real numbers.

It can be simplified by performing basic algebraic operations, such as isolating the variable term [tex](4x)[/tex] (4x) and solving for the value of [tex]x[/tex] x.

to solve for x in the equation  [tex]11=3+4x[/tex] 11=3+4x, we will follow the steps of algebraic manipulation:

First, we will isolate the variable term [tex](4x)[/tex] (4x)  by subtracting 3 from both sides of the equation:

[tex]11 - 3 = 4x[/tex] 11 - 3 = 4x

[tex]8 = 4x[/tex] 8 = 4x

Next, we will isolate x by dividing both sides by 4:

 [tex]8/4 = x[/tex] 8/4 = x

   [tex]2 = x[/tex] 2 = x

Therefore, the solution to the equation [tex]11=3+4x[/tex] 11=3+4x is [tex]x=2[/tex] x=2.

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Answer:

1/5

Step-by-step explanation:

-2/5 - (-9/15) make like denominators

-6/15 - (-9/15) negative and negative make positive

-6/15 + 9/15 solve

3/15 simplify

1/5

From the given dimensions, it seems like the figure is a trapezoid.Therefore, the surface area of the figure is 300 square feet.

Surface area is the measure of the total area that the surface of an object occupies. It is calculated by adding the area of all the faces or surfaces of the object.

A trapezoid is a four-sided geometric shape that has one pair of parallel sides. It is also called a trapezium. The parallel sides are called bases and the non-parallel sides are called legs.

According to the given information:

To calculate the surface area of the figure, we need to split it into smaller shapes and then calculate their individual areas. From the given dimensions, it seems like the figure is a trapezoid.

The formula for the surface area of a trapezoid is (1/2) × (a + b) × h, where a and b are the lengths of the two parallel sides and h is the height.

Using this formula, we can calculate the surface area of the trapezoid:

Surface Area = (1/2) × (15 + 9) × 15 + 2 × 15 × 4

= (1/2) × 24 × 15 + 2 × 15 × 4

= 180 + 120

= 300ft²

Therefore, the surface area of the figure is 300 square feet.

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Applying the intersecting secants theorem, the length of segment KL is approximately, 45.8.

According to the intersecting secants theorem, if two lines from a point outside a circle intersect the circle, then the product of the length of one line segment and its portion outside the circle is equal to the product of the length of the other line segment and its portion outside the circle.

Using the theorem, we have:

MN * MO = ML * MK

Substitute:

21 * 48 = 22 * KL

1,008 = 22KL

1,008/22 = KL

KL = 45.8 (nearest tenth)

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Answer:

[tex]y =\frac{x}{4}[/tex]

Step-by-step explanation:

We are given several functions, and we want to figure out which one is linear.

A linear function has both of its variables (x and y) with a power of 1. Variables with other powers do not mean that the function is linear.

Let's go through the list.

Starting with [tex]y=\frac{3}{x} -7[/tex], we can see that x is in the denominator. If this is the case, it means that the power of x is -1.

Even though y has a power of 1, this is NOT linear, because x has a power of -1.

Now, with y=√x-2, this is also not linear. This is because √x = [tex]x^\frac{1}{2}[/tex], even though y has a power of 1.

For x² - 1 = y, we can clearly see that x has a power of 2, while y has a power of 1. This means that the function is not linear.

This leaves us with [tex]y = \frac{x}{4}[/tex]. x is in a fraction, however it is not in the denominator. This means that the power of x in this function is 1. We can also see that the power of y in this function is 1.

This means that [tex]y=\frac{x}{4}[/tex] is linear.

Answer:

if we substitute x = 3 in the given function f(x) = r + 7, we get:

f(3) = r + 7 (where x = 3)

Therefore, the value of f(3) is r + 7.

The equation of g ( x ), given that it is a vertical stretch, would be (4/5)x² - 4.

The output (dependent variable) of f(x) must be multiplied by the stretching factor in order to obtain the equation of g(x), which is a vertical stretching of f(x) by a factor of 2.

The function can be shown as:
f(x) = Ay² + B

g(x) = 2(Ay² + B)

g(x) = 2((2/5)x² - 2)

g(x) = (4/5)x² - 4

So, the equation of g(x) is g(x) = (4/5)x² - 4.

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The percentage increase in the number of archers is 77%.

A value's percentage growth is a way to represent how much it has grown in comparison to its starting point. It is calculated by subtracting the original value from the new value, multiplying the result by 100, and then subtracting the difference between the two values.

The following formula is used to determine the percentage increase:

(New Value - Original Value) / Original Value * 100 is the formula for percentage increase.

The percentage increase is given by the formula:

Percentage Increase = (New Value - Original Value) / Original Value * 100

Now, given that there were 1158 more archers in 2012 and 2013 and from the table we have the archers in 2012-13 = 2645 the archers in 2011-12 is:

2645- 1158 = 1487

Thus,

percentage increase = 1158/ 1487 (100) = 77%

Hence, the percentage increase in the number of archers is 77%.

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Answer:

To perform these operations, we need to ensure that the dimensions of the matrices match. Since k is a row matrix with 1 row and 4 columns, and L is a column matrix with 4 rows and 1 column, we need to transpose one of them to match the dimensions. Let's transpose k to get a column matrix with 4 rows and 1 column:

k^T = 2

3

4

3

Now we can perform the matrix operations:

1. k + L:

2 + 7 = 9 3 + 10 = 13 4 + 5 = 9 3 + 11 = 14

9 + 1 = 10 13 + 6 = 19 5 + 9 = 14 11 + 4 = 15

10 + 11 = 21 4 + 7 = 11 7 + 10 = 17 3 + 7 = 10

= 9 13 9 14

10 19 14 15

21 11 17 10

2. K - L:

2 - 7 = -5 3 - 10 = -7 4 - 5 = -1 3 - 11 = -8

9 - 1 = 8 13 - 6 = 7 5 - 9 = -4 11 - 4 = 7

10 - 11 = -1 4 - 7 = -3 7 - 10 = -3 3 - 7 = -4

= -5 -7 -1 -8

8 7 -4 7

-1 -3 -3 -4

3. 2k + 3L:

2(2) + 3(7) = 20 2(3) + 3(10) = 36 2(4) + 3(5) = 22 2(3) + 3(11) = 37

2(9) + 3(1) = 21 2(13) + 3(6) = 44 2(5) + 3(9) = 23 2(11) + 3(4) = 29

2(10) + 3(11) = 42 2(4) + 3(7) = 29 2(7) + 3(10) = 34 2(3) + 3(7) = 23

= 20 36 22 37

21 44 23 29

42 29 34 23

4. 3L - 2K:

3(7) - 2(2) = 17 3(10) - 2(3) = 27 3(5) - 2(4) = 7 3(11) - 2(3) = 29

3(1) - 2(9) = -15 3(6) - 2(13) = -11 3(9) - 2(5) = 17 3(4) - 2(11) = -14

3(11) - 2(10) = 13 3(7) - 2(4) = 14 3(10) - 2(7) = 16 3(7) - 2(3) = 15

= 17 27 7 29

-15 -11 17 -14

13 14 16 15

The z score that corresponds to P4 is = -1.75

let the z score corresponding to the 4th percentile be a.

according to the problem:-

[tex]P(Z\leq a)=P_{4}=0.04[/tex]

[tex]\Rightarrow \Phi(a)=0.04[/tex]

[tex]\Rightarrow a=\Phi^{-1}(0.04)[/tex]

[tex]\Rightarrow \mathbf{a\approx -1.75} [ excel function : =NORMSINV(0.04) ][/tex]

the z score that corresponds to P4 is = -1.75

A Z-table, also referred to as a standard normal table, is an essential reference tool in statistical analysis. Its primary functions include calculating areas and probabilities under the standard normal distribution curve based on given values of z-scores.

In most cases, it provides cumulative probabilities for z- scores between -3.49 and 3.49, approximated to two decimal places.

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Answer:

Step-by-step explanation:

7 + 3 ( v - 2u )/u + 1

u = 2 and v = 5

7 + 3(v - 2u)/u + 1

7 + 3 ((5) - 2(2)) / (2) + 1

→ 7+3 ((5) -2 (2)) = 10

→ (2) + 1  = 3

10/3

Answer:

10/3

Step-by-step explanation:

u = 2

v = 5

7 + 3(v - 2u)

= 7 + 3(5 - 2*2)

= 7 + 3(5 - 4)

= 7 + 3(1)

= 7 + 3

= 10

u + 1

= 2 + 1

= 3

7 + 3(v - 2u)/u + 1

= 10/3

Answer: AC = 4.50

Step-by-step explanation:

sin 40 = x/7

x = sin 40 (7)

x = 4.50

Answer:

Total Charge = Initial Charge + Daily Charge x Number of Days

Step-by-step explanation:

Let's assume that x is the number of days that Frank rented the car.

The initial charge for the rental is $40, which is a one-time charge, so it does not depend on the number of days.

The daily charge for x days is $35 per day. Therefore, the total charge for x days can be calculated as:

Total Charge = Initial Charge + Daily Charge x Number of Days

Total Charge = $40 + $35x

We know that Frank was charged $180, so we can set the total charge equal to $180 and solve for x:

$40 + $35x = $180

Subtracting $40 from both sides gives:

$35x = $140

Dividing both sides by $35 gives:

x = 4

Therefore, Frank rented the car for 4 days.

Step-by-step explanation:

there are many possibilities, 4 of them really easy.

the endpoint of a diameter is simply a point on the circle arc.

the easy options are to assume that the center of the circle is on the x- or the y-axis.

let's go with the x-axis (we only need 2 circles : one with the center left, and one with the center right of the origin).

we know the radius is 3.

so, the center of either circle is 3 units away from the origin.

so, center of circle1 = (-3, 0), center of circle2 = (3, 0).

the equation for a circle is

(x - h)² + (y - k)² = r²

r is the radius, (h, k) is the center point.

equation for circle1 :

(x - -3)² + (y - 0)² = 3²

(x + 3)² + y² = 9

equation for circle2 :

(x - 3)² + (y - 0)² = 3²

(x - 3)² + y² = 9

you see ?

the other 2 easy options would be to put the centers on the y-axis : (0, -3) and (0, 3)

Answer:

57° + 124° + 140° = 321°

360° - 321° = 39° (measure of missing interior angle)

39° + c = 180°, so c = 141°.

Answer:

c=141

Step-by-step explanation:

140+57+124=321

360-321=39

180-39=141

Answer:

Step-by-step explanation:

f(x) = 2x2 − 12x + 24

      = 2(x^2 - 6x) + 24

      = 2[(x - 3)^2 - 9) + 24

      = 2(x - 3)^2 - 18 + 24

      = 2(x - 3)^2 + 6

- so the minimum cost is 6

Check the picture below.

Answer:

To write the ratio 3.0 to 1.2 in lowest terms using a colon, we need to divide both numbers by their greatest common factor (GCF).

The GCF of 3.0 and 1.2 is 0.6, since:

3.0 = 5(0.6)

1.2 = 2(0.6)

Dividing both numbers by 0.6, we get:

3.0/0.6 = 5

1.2/0.6 = 2

Therefore, the ratio 3.0 to 1.2 in lowest terms using a colon is:

5:2