A sailboat sail is triangular with a height 3 feet greater than its base. If the sail's area is 90 square feet, find its base
and height.
←
The base of the sail is
and the height is

The radius of the circle is approximately 286.26 meters.

We have,

We can use the formula for the length of an arc of a circle, which is:

s = r x [tex]\alpha[/tex]

where s is the arc length, r is the radius of the circle, and alpha is the central angle in radians.

To use this formula, we need to convert the central angle from degrees to radians.

We know that the circle has a central angle of alpha = 3,

so:

alpha (in radians) = (3/180) x π = 0.0524 radians

where π is the mathematical constant pi (approximately equal to 3.14159).

Now we can solve for the radius, r:

s = r x α

15 = r x 0.0524

r = 15 / 0.0524

r ≈ 286.26 meters

Therefore,

The radius of the circle is approximately 286.26 meters.

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There are 30 different pairs that can be formed from the 6 men and 5 women.

The number of different mixed doubles tennis pairs can be calculated by multiplying the number of choices for the first player by the number of choices for the second player. For the first player, there are 6 men to choose from, and for the second player, there are 5 women to choose from. Therefore, the number of different mixed doubles tennis pairs is:

6 x 5 = 30

Therefore, there are 30 different pairs that can be formed from the 6 men and 5 women.

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To be 90% certain that the projected percentage is off by no more than one percentage point, the epidemiologist must survey at least 968 women.

(a) First, we need to find the critical value of the standard normal distribution that corresponds to a 90% confidence level. We can do this using a standard normal distribution table or a calculator. The critical value is approximately 1.645.

(b) We also need to estimate the proportion of women who give birth. Let's assume that a prior study found this proportion to be 0.6. This will be our point estimate.

(c) Finally, we can use the formula for the margin of error to determine the sample size:

margin of error = critical value * standard error

where the standard error is given by:

standard error = sqrt[(point estimate * (1 - point estimate)) / sample size]

margin of error = 0.01

Plugging in the values we have:

0.01 = 1.645 * sqrt[(0.6 * 0.4) / sample size]

Solving for the sample size:

sample size = (1.645 / 0.01)^2 * 0.6 * 0.4

sample size ≈ 968

Therefore, the epidemiologist needs to survey at least 968 women to be 90% confident that the estimated percentage is in error by no more than one percentage point.

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The {x} - intercept and {y} - intercept for the given line is (-7.5, 0)

and (0, 5.5) respectively.

Given is a straight line plotted on the graph as shown in the image. We can say that {x} - intercept is the coordinate at which the line cuts the {x] - axis. Similarly, {y} - intercept is the coordinate at which the line cuts the {y] - axis.

From the graph given below, we can see that -

{x} intercept : (-7.5, 0)

{y} intercept : (0, 5.5)

Therefore, the {x} - intercept and {y} - intercept for the given line is (-7.5, 0)

and (0, 5.5) respectively.

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Answer:

16

Step-by-step explanation:

let the center be O then OB=12,OG=12

and ΔROG is right angle triangle at G

Applying Pythagoras' theorem in ΔROG,

RO=RB+BO=8+12=20

∴GR²+OG²=RO²

x²+12²=20²

x²=400-144

=256

x=√256

=16

The limit of the given function as x approaches infinity is 0.

To find the limit of the given function as x approaches infinity, we can use L'Hospital's Rule since we have an indeterminate form of type ∞/∞: lim (x → ∞) ln(x)/√x

Step 1: Apply L'Hospital's Rule by taking the derivative of both the numerator and the denominator with respect to x: Derivative of ln(x) = 1/x Derivative of √x = 1/(2√x)

Step 2: Create a new fraction with the derivatives and find the limit: lim (x → ∞) (1/x) / (1/(2√x))

Step 3: Simplify the expression: lim (x → ∞) (1/x) * (2√x) = lim (x → ∞) (2√x) / x

Step 4: Rewrite the expression as: lim (x → ∞) (2/√x)

Step 5: As x approaches infinity, the expression converges to: (2/∞) = 0

So, the limit of the given function as x approaches infinity is 0.

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Answer:

Step-by-step explanation:

To determine the ordered pairs formed from combining a term in Pattern A with its corresponding term in Pattern B, we need to find the terms that have the same position in each pattern.

Pattern A: 1, 4, 7, 10, 13

Pattern B: 5, 13, 17, 17, 13

The ordered pairs formed by combining a term in Pattern A with its corresponding term in Pattern B are:

(1, 5)

(4, 13)

(7, 17)

(10, 17)

(13, 13)

Therefore, the correct answers are:

(10, 17)

(1, 5)

(7, 13)

(4, 13)

(13, 17)

Note that (1, 4) is not a correct answer, since 4 is not the corresponding term in Pattern B for the first term (1) in Pattern A.

The null hypothesis (H0) is that there is no significant difference in productivity between the four programs. The alternative hypothesis (Ha) is that at least one of the programs results in a significantly higher productivity than the others.

Based on the information provided, we can state the null and alternative hypotheses for the Ahmadi Corporation's productivity study:

Null Hypothesis (H0): There is no significant difference in productivity among the four different programs.

Alternative Hypothesis (H1): There is a significant difference in productivity among the four different programs.

In this case, the "sample" refers to the twenty employees who were randomly assigned to one of the four programs. The "null" hypothesis represents the assumption that there is no effect of the programs on productivity, while the "alternative" hypothesis suggests that at least one of the programs has a significant impact on productivity.

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Answer:

5.3

Step-by-step explanation:

The cylinder popcorn container will hold the most popcorn and the cone popcorn container has a better unit rate

For the cone, we have

Radius, r = 6 cm

Height, h = 19 cm

So, the volume is

V = 1/3 * 3.14 * 6^2 * 19

V = 715.92

For the cylinder, we have

Radius, r = 4 cm

Height, h = 15 cm

So, the volume is

V = 3.14 * 4^2 * 15

V = 753.6

The cylinder popcorn container will hold the most popcorn because it has a higher volume

For the cone, we have

Unit rate = 715.92/6.75 = 222222

For the cylinder, we have

Unit rate = 753.6/6.25 = 120.576

The container that has a better unit rate is the cone popcorn container

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The equation of the circle passing through the point (-6, 3) having center at (5, - 4) is (x - 5)² + (y + 4)² = 170

The general equation of a circle with (h, k) representing the circle's center, and {r} represents the length of its radius is

(x – h)² + (y – k)² = r²

We can write the equation of the circle as -

(x – h)² + (y – k)² = r²

(x - 5)² + (y + 4)² = (11)² + (-7)²

(x - 5)² + (y + 4)² = 121 + 49

(x - 5)² + (y + 4)² = 170

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Answer:

The answer for the Perimeter of the semi circle is 15.71cm

Step-by-step explanation:

Perimeter of semi circle =perimeter of circle/2

P=2pir/2

P=pir

r=d/2=10/2

r=5cm

P=pir

P=5pi

P=5×3.142

P=15.71cm

The rate at which the circumference is growing when the water covers 50 ft is found to be at  0.019 ft/s.

The formula for the area of a circle is shown as  :

A = πr^2

where A = area

π = 3.142

r = radius

We will differentiate with respect to time, :

dA/dt = 2πrn xdr/dt

we have that dA/dt = 3 ft²/s

3 = 2π(25) x dr/dt

we calculate for  dr/dt,

dr/dt = 3/(50π) =  0.019 ft/s

In conclusion, if a person is making an ice rink by pouring water out of a hose. If water is spreading in a circular shape and the area covered by water grows with the rate of 3 ft?/sec, the rate at which the circumference is growing when the water covers 50 ft is found to be at  0.019 ft/s.

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Based on the information, it can be inferred that Sofia Carbondale had to pay $25,740 in total.

To calculate how much Sofia Carbondale had to pay, we must carefully look at the information in the graph and establish the value of the payments she must make. In the case of visits to specialists, she must pay the following:

Additionally, we must add the value of hospital charges and her visit to emergencies.

$100 + $24,560 + $1,080 = $25,740

Note: This question is incomplete. Here is the correct and complete information:

Attached images

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Answer:

The correct answer to 999x600+20 is 599,980. The calculation can be broken down as follows:

999 x 600 = 599,400

599,400 + 20 = 599,980 duh

Step-by-step explanation:

gg

Therefore, the only claim that the interval would tend to refute is option E: The population mean is less than 125.

Based on the 90% confidence interval of 135 to 160, we can conclude that the population mean is likely to be within this interval with a 90% degree of confidence.

A. The claim that the population mean is more than 110 is not refuted by the confidence interval since the lower limit of the interval is above 110.

B. The claim that the population mean is less than 150 is not refuted by the confidence interval since the upper limit of the interval is above 150.

C. The claim that the population mean is between 140 and 150 is not refuted by the confidence interval since both values are within the interval.

D. The claim that the population mean is more than 140 is not refuted by the confidence interval since the lower limit of the interval is above 140.

E. The claim that the population mean is less than 125 is refuted by the confidence interval since the lower limit of the interval is above 125.

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Karolina ran 1.66 miles on Wednesday.

It is given that Karolina ran 1.38 miles on Monday.

She ran 2.17 miles on Tuesday.

We have to find how many miles she ran on Wednesday.

Let she ran 'D' miles on Wednesday.

It is also given that Karolina ran total of 5.21 miles on Monday, Tuesday, and Wednesday.

According to information we can form an equation which is,

1.38 + 2.17 + x = 5.21

3.55 + x = 5.21

3.55 + x - 3.55 = 5.21 - 3.55 [Subtracting 3.55 from both sides]

x = 1.66

Hence Karolina ran 1.66 miles on Wednesday.

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The simplest form is defined as the smallest possible equivalent fraction of the number. To simplify a fraction, we should divide the top and bottom by the greatest number. 2 2/3 / 1 4/5 in simplest terms is 11 / 105.

The fraction is said to be in the simplest form, when the numerator and denominator of the fraction does not have any common factor.

2 2/3 / 1 4/ 5 = 8 / 3 × 5 /9 = 40 / 27

Thus 2 2/3 / 1 4/5 in simplest terms is 40 / 27.

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There are 495 different ways in which a committee of 4 people can be formed from a group of 12 people in the baking club.

To solve this problem, we can use the combination method, which is a mathematical technique used to count the number of combinations that can be formed from a set of items. The formula for the combination method is:

ⁿCₓ= n! / (x! * (n-x)!)

Where n is the total number of items in the set, r is the number of items to be selected, and the exclamation mark denotes the factorial function. The factorial of a positive integer n is defined as the product of all positive integers up to and including n.

Now, let's apply the combination method to the problem at hand. We are given that there are 12 people in the baking club, including Mark, and we need to form an executive committee of 4 people. Using the formula above, we can calculate the number of possible committees as follows:

¹²C₄= 12! / (4! * (12-4)!)

= (1211109) / (4321)

= 495

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There are 480 ways to arrange the six people such that the two people do not sit side-by-side.

(a) There are 6 people and they want 2 specific people to sit together, so we can consider them as a single entity. This reduces the problem to arranging 5 entities (the group of 2 people and the remaining 4 individuals) in a row. The number of ways to do this is 5!, or 120 ways.

(b) If two people do not want to sit together, we can consider them as separate entities. This means that we have to arrange 6 entities in a row, but we cannot place the two people next to each other.

To count the number of ways to arrange the six people such that the two people do not sit side-by-side, we can use complementary counting. We first find the total number of ways to arrange the six people, which is 6!, or 720 ways.

Next, we count the number of arrangements where the two people sit side-by-side. We can treat them as a single entity and arrange the remaining 5 entities in a row, which can be done in 5! ways. However, since the two people can swap positions, we need to multiply by 2 to get the total number of arrangements where they sit side-by-side, which is

Finally, we subtract the number of arrangements where the two people sit side-by-side from the total number of arrangements to get the number of arrangements where they do not sit side-by-side:

Therefore, there are 480 ways to arrange the six people such that the two people do not sit side-by-side.

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Answer:

Step-by-step explanation:

To solve this problem, we can use the following formula:

Total amount of money = Amount saved + Amount earned per week * Number of weeks

We want to find the number of weeks, so we can rearrange the formula to solve for Number of weeks:

Number of weeks = (Total amount of money - Amount saved) / Amount earned per week

Substituting the values we have:

Number of weeks = ($250 - $45) / $20

Number of weeks = $205 / $20

Number of weeks = 10.25

Therefore, it will take Wendell 10.25 weeks to have enough money to buy a new tennis racket.

I hope that helps! Let me know if you have any other questions.

Answer:

Length is usually longer than width so the length of the rectangle is 9 inches and the width is 6 inches.

A portable cooler with dimensions 19 inches * 14 inches * 14 inches has a volume of 3724 cubic inches.

A prism is a 3-Dimensional shape that is bound by plane figures on all sides. The ends face of the prism are identical and are called bases. A rectangular prism is known as a cuboid. All the faces of the prism are rectangles and it has 6 faces, two on ends and 6 laterally.

Volume is the measurement of space that is occupied by an object. The volume of the cuboid is calculated by

V = l * b * h

l is the length of the cuboid

b is the breadth of the cuboid

h is the height of the cuboid

Given, l = 19 inches

b = 14 inches

h = 14 inches

V = 19 * 14 * 14

= 3724 cubic inches

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The values of x and y of the given simultaneous equations are:

x = -2

y = 10

There are different methods of solving simultaneous linear equations such as:

Elimination Method

Substitution Method

Graphical Method

We are given the equations as:

-¹/₂x + ¹/₅y = 3  -----(1)

2x + ¹/₃y = -²/₃  -----(2)

Multiply eq 1 by 10 and eq 2 by 6 to get:

-5x + 2y = 30  -----(3)

12x + 2y = -4   ----(4)

Subtract eq 4 from eq 3 to get:

-17x = 34

x = -2

12(-2) + 2y = -4

-24 + 2y = -4

2y = 20

y = 10

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Answer:

Step-by-step explanation:

the options are not all shown.  It's not A   A is g(x)=2f(x)  it's a positive function with a stretch of 2    the answer will be like answer A but flipped along y-axis

Answer: 4 yards

Step-by-step explanation:

      The diameter is equal to the radius times 2.

      We will multiply the given radius by 2 to find the diameter.

                    2 yards * 2 = 4 yards

Answer: 4 yards

Step-by-step explanation: Since the radius is half of the circle, you multiply it by two to get the diameter.

The curved length DE of the given triangle is calculated as: 15.75

Pythagoras Theorem is defined as the way in which you whereby you can find the missing length of a right angled triangle.

The triangle has three sides, namely the hypotenuse (which is always the longest side), Opposite side (which doesn't touch the hypotenuse) and finally, the adjacent side (which is located between the opposite and the hypotenuse).

Pythagoras is in the form of; a² + b² = c²

Applying the Pythagoras theorem to triangle ABC gives:

AB = √(12² + 9²)

AB = √225

AB = 15

We are told that DE is 5% longer than AB. Thus:

DE = 1.05 * 15

DE = 15.75

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Answer:

a=9

Step-by-step explanation:

a= 9/4 =36/4 = 9