A rectangular pen is to be constructed with three equal sections. One side of the pen will be enclosed with the side of the barn. All other sides need to be fenced. If the total amount of fencing available is 510 feet, calculate the dimensions of each rectangular pen that would maximize the fenced area. State the maximum area as well. Show all work.

We must first convert the given information into an equivalent fraction. The answer is 56%.

Equivalent fractions have the same value or represent the same portion of a whole even though they may have different numerators and denominators.

To do this, we must multiply both the numerator (14) and denominator (25) by the same number so that the denominator equals 100.

To do this, we must multiply both 14 and 25 by 4.

This gives us 14*4/25*4 = 56/100.

To convert this fraction to a percent, we can simply divide the numerator by the denominator and multiply the result by 100.

Therefore, 56/100 * 100 = 56%.

This result can also be found by setting up a proportion. We can set up the proportion as follows:

14/25 = x/100.

To solve for x, we must multiply both sides by 100. This gives us 14*100/25 = x.

Hence, x = 56. Therefore, 56% of swimmers finished the race in less than 47 minutes.

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The equation for the sinusoidal function that represents Jane's motion would be d(t) = 25 x sin(π/4 x (t + 4)) - 5

Let d(t) be the distance Jane is from the bank (in feet) at time t (in seconds). Since Jane's motion is sinusoidal, we can express it as:

d(t) = A x sin(B x (t - C)) + D

We need to find the values of A, B, C, and D that satisfy these conditions.

Since the amplitude is half the peak-to-peak amplitude, we have:

A = 50 / 2 = 25

The vertical shift (D) is the average of the maximum and minimum distances:

D = (20 + (-30)) / 2 = -10 / 2 = -5

Since the sine function is -1 at 3π/2 (270 degrees), we have:

π/4 x (2 - C) = 3π/2

2 - C = 6

C = -4

So, the equation of the sinusoidal function representing Jane's motion is:

d(t) = 25 x sin(π/4 x (t + 4)) - 5

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The question is:

Find the sinusoidal function that represents Jane's motion.

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Note that the function that is graphed below is y = x + 7.

The equation y = x + 7 represents a linear function, where x is the independent variable and y is the dependent variable.

It has a slope of 1, which means that for every unit increase in x, y increases by 1. The y-intercept is 7, which is the value of y when x is zero. This equation can be graphed as a straight line on a coordinate plane, with a positive slope and y-intercept of (0, 7).

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Thus, the Area of shaded region for the given sector of circle is found as:

1.14 sq. cm.

Two radii that meet at the centre to form a sector define a circle. The sector is the portion of the circle created by these two radii. Knowing a circle's central angle measurement and radius measurement are both crucial for solving circle-related difficulties.

Given:

Area of shaded region = area of sector - area of triangle

Area of shaded region = Ф/360° * (πr²) - 1/2*base*height

Area of shaded region = 90/360° * (3.14*2²) - 1/2*2*2

Area of shaded region = 1/4*3.14*4 - 2

Area of shaded region = 3.14 - 2

Area of shaded region = 1.14 sq. cm

Thus, the Area of shaded region for the given sector of circle is found as:

1.14 sq. cm.

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The plant is not in the sprinkler's range since the distance between the sprinkler and the plant is greater than the radius of the sprinkler's range.

The distance between the sprinkler and the plant can be calculated using the Pythagorean theorem, which 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.

In this case, the distance between the sprinkler and the plant is the hypotenuse of a right triangle with legs of length 4 feet and 6 feet:

distance = sqrt(4^2 + 6^2)

distance = sqrt(16 + 36)

distance = sqrt(52)

distance ≈ 7.21 feet

Since the distance between the sprinkler and the plant is greater than the radius of the sprinkler's range (8 feet), the plant is not in the sprinkler's range. Therefore, the plant will not receive water from the sprinkler.

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The situation can be represented by the equation 2x + 150 = 5x is"Mary has 2 stamps and buys 150 stamps each week. Nick has no stamps and buys 5 stamps each week. When will they have the same number of stamps?" (option b)

The equation 2x + 150 = 5x means that two expressions, 2x + 150 and 5x, are equal. In other words, whatever value we substitute for x, these two expressions will always have the same value. We can use this equation to solve different situations by finding the value of x that satisfies the equation.

Mary starts with 2 stamps and buys 150 stamps each week, while Nick starts with no stamps and buys 5 stamps each week. To determine when they will have the same number of stamps, we need to use the equation 2x + 150 = 5x. We can rewrite the equation as 150 = 3x, and solve for x by dividing both sides by 3. This gives us x = 50, which means that it will take Mary 50 weeks to have the same number of stamps as Nick.

Hence the correct option is (b).

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The only option that represents an independent event is: Option C: "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".

Independent events are defined as those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.

Looking at the given options, the only one that represents an independent event is "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".

This is because each event does not depend on another one of the events being described.

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Answer:

y = -4

Step-by-step explanation:

13 - y = 17

y = 13 - 17 = -4

Answer:

y = -4

Step-by-step explanation:

Alright so you shift the y to the other side:
13 = 17 + y

Now you shift the 17 to the other side,
y = 13 - 17 = -4

Hence, y = -4

Hope this helps and be sure to mark this as brainliest! :)

Answer: 6 3/7

Step-by-step explanation:

9/1 x 5/7

If we multiply the numerators and denominators, we get 45/7 or 6 3/7 as a mixed number.

Answer:

[tex]\frac{45}{7}[/tex] or 6.4285

Step-by-step explanation:

First, multiply 9 and 5, which gives you 45.

9(5)=45

Then, divide 45 by 7.

45/7=6.4285

That gives  you  [tex]\frac{45}{7}[/tex] or 6.4285

Hope this helps!

Answer:

Table D represents the linear function

y = x + 1.

The number of papers they have left to grade is 39.

What is Subtraction?

Subtraction is a mathematical operation that involves taking away or removing a certain number of items or quantity from a larger group. It is the inverse of addition and is denoted by the minus sign (-).

Let p be the number of papers they have left to grade.

The total number of papers is 87, and Mr. Lewis has already graded 32 and Ms. Yonkers has graded 16, so the number of papers they have left to grade is:

p = 87 - 32 - 16

p = 39

Therefore, they have 39 papers left to grade.

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The height of the parabolic balloon arch for the prom is 12.25 feet.

Using these assumptions, we can find the equation of the parabola that the arch follows as x = a(y-k)² + h, where (h,k) is the vertex and a is a constant that determines the shape of the parabola. We can find the value of a by using one of the points that the arch passes through, say (3,0):

3 = a(0-k)² + h h = 3 - a(k²)

Similarly, using the other point that the arch passes through, say (7,0):

7 = a(0-k)² + h h = 7 - a(k²)

Equating the expressions for h, we get:

3 - a(k²) = 7 - a(k²) a = -1/4

Substituting this value of a into one of the equations for h, say h = 7 - a(k²), we get:

h = 7 + 1/4(k²)

So the vertex of the parabola is at (h,k) = (7,0), and the equation of the parabola is x = -1/4(y² - 28y + 49).

To find the height of the arch, we need to find the y-coordinate of the vertex, which is k = 0. So the height of the arch is given by the distance between the vertex and the lowest point of the arch, which is the x-intercept of the parabola. To find the x-intercept, we set y = 0 in the equation of the parabola:

x = -1/4(0² - 28(0) + 49)

x = -1/4(49) = -12.25

However, since we are dealing with a physical object, the height cannot be negative. Therefore, we take the absolute value of the x-intercept, which gives us:

| -12.25 | = 12.25 feet

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The number of atoms in 8.500 moles of chlorine atoms can be calculated using Avogadro's number, which is approximately 6.022 × 10²³ atoms/mole.

So, the number of atoms in 8.500 moles of chlorine atoms would be:

8.500 moles × 6.022 × 10²³ atoms/mole = 5.12 × 10²⁴ atoms of chlorine.

The molar mass of oxygen is approximately 16.00 g/mol. Therefore, the mass of 15.50 moles of oxygen would be:

15.50 moles × 16.00 g/mol = 248 g of oxygen.

The molar mass of helium is approximately 4.00 g/mol. Therefore, the number of moles of helium in 1.953 x 10^8 g of helium would be:

1.953 x 10^8 g / 4.00 g/mol = 4.88 x 10⁷ moles of helium.

The molar mass of sulfur is approximately 32.06 g/mol. Therefore, the number of moles of sulfur in 147.82 g of sulfur would be:

147.82 g / 32.06 g/mol ≈ 4.61 moles of sulfur.

The molar mass of cobalt (Co) is approximately 58.93 g/mol.

The formula mass of Ca₃(PO₄)₂ can be calculated by adding the molar masses of all the individual atoms in the formula.

The molar mass of calcium (Ca) is approximately 40.08 g/mol, the molar mass of phosphorus (P) is approximately 30.97 g/mol, and the molar mass of oxygen (O) is approximately 16.00 g/mol.

Therefore, the formula mass of Ca₃(PO₄)₂ would be:

3 × 40.08 g/mol (for Ca) + 2 × (2 × 30.97 g/mol + 4 × 16.00 g/mol) (for P and O) = 310.17 g/mol.

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The type of variable for,

a. The number of counties in California: Quantitative discrete.

b. The stages of childhood: Qualitative ordinal.

c. In the scenario above, 23 minutes is a statistic, because 28 students is a sample.

d. Between 6 minutes and 8 minutes: Approximately 68% of the athlete's mile times are expected to be between 6 and 8 minutes, according to the empirical rule.

e. Between 4 minutes and 7 minutes: Approximately 68% of the athlete's mile times are expected to be between 4 and 10 minutes, according to the empirical rule.

f. Less than 9 minutes: Approximately 84% of the athlete's mile times are expected to be less than 9 minutes, according to the empirical rule.

In statistics, variables can be categorized into two types: qualitative and quantitative.

Qualitative variables describe characteristics or qualities that cannot be measured numerically, such as gender or hair color.

Quantitative variables, on the other hand, represent numerical values that can be measured or counted.

There are two types of quantitative variables: continuous and discrete. Continuous variables can take any numerical value within a range, such as age or weight.

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Answer:

Let x be the measure of the angle we are trying to find, in degrees.

The complementary angle to x is 90° - x, since the sum of complementary angles is 90 degrees.

The problem tells us that x is 3.4 degrees less than its complementary angle, so we can set up the following equation:

x = (90 - x) - 3.4

Simplifying and solving for x, we get:

x = 86.6/2

x = 43.3

Therefore, the angle we are trying to find has a measure of 43.3 degrees, and its complementary angle has a measure of 90 - 43.3 = 46.7 degrees.

Answer:

565.486677646 inches squared

Step-by-step explanation:

Let's recall the formula for the surface area of a cylinder:

[tex]A=2\pi rh+2\pi r^2[/tex]

Where r is the radius and h is the height.

We are given that the radius is 6 inches and the height is 9 inches.

Substitute the values and solve the equation, like so:

[tex]A=2\pi (6)(9)+2\pi (6)^2=\\A=2\pi (54) +2\pi(36)=\\A=108\pi +72\pi =\\A=180\pi[/tex]

Thus, in terms of pi, the surface area is equal to [tex]180\pi[/tex].

180 times pi is equal to approximately 565.486677646 inches squared.

The perimeter of the rectangular mural after increasing the dimensions by Hailey is equal to 7826 centimeters.

Measures of rectangular mural are,

length = 890 centimeters

Width = 2891 centimeters

New mural is 66 centimeters longer.

The new dimensions of the  rectangular mural will be,

New  length = 890 cm + 66 cm

                     = 956 cm

New width = 2891 cm + 66 cm

                  = 2957 cm

The perimeter of the new mural can be calculated by adding up the lengths of all four sides,

Perimeter = 2(length + width)

⇒Perimeter = 2(956 cm + 2957 cm)

⇒Perimeter = 2(3913 cm)

⇒ Perimeter = 7826 cm

Therefore, the perimeter of Hailey's new mural will be 7826 centimeters.

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The above question is incomplete , the complete question is:

A rectangular mural measures 890 centimeters by 2891centimeters. Hailey creates a new mural that is 66 centimeters longer. What's is the perimeter of Hailey new mural?

Answer:

below

Step-by-step explanation:

26. yes because a straight line is formed

27. domain - -2 to 2

range -2 to 1

Answer:

Yes, the graph is a linear function.

Domain: x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]

Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]

Step-by-step explanation:

A linear function is an expression that will form a straight line when graphed (or a graph that forms a straight line). These points form a straight line, so the function is linear.

The domain of the function is everything that x can be equal to. We can see here that the ordered points are:

(-2, -1.5), (-1.5, -1), (-1, -0.5), (-0.5, 0), (0, 0.5), (0.5, 1), (1, 1.5), (1.5, 2)

So, the domain of the function is all of the x values of the ordered pairs, or:

x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]

(the symbol next to the x means "belongs to.")

As for the range, it is everything that y can be equal to. Let us look once again at the ordered pairs. The range of the function is equal to the y coordinates of these ordered pairs, or:

Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]

Keep in mind that if the function contains more than one value for x or y, it is listed ONLY ONCE in the domain/range.

Okay, here are the steps to find the minimum value of P:

1) Given: |z|=|w|=1 (z and w are complex numbers with unit modulus)

|z+w|=sqrt(2)

Find z and w such that these conditions are satisfied.

Possible solutions:

z = 1, w = i (or vice versa)

z = i, w = 1 (or vice versa)

2) Substitute into P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|

For the cases:

z = 1, w = i: P = |-1-4+2(1+i)i| = |-5+2i| = sqrt(25+4) = 5

z = i, w = 1: P = |1-\frac{4}{i}+2(1+\frac{1}{i})i| = |-3+2i| = sqrt(9+4) = 5

3) The minimum value of P is 5.

So in summary, the minimum value of

P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|

is 5.

Let me know if you have any other questions!

Based on the definition of the tangent of a circle and the Pythagorean triple of a right triangle, AB is not tangent to circle C in both question 19 and 20.

In geometry, the tangent of a circle is a line that intersects the circle at exactly one point, which is called the point of tangency. This line is perpendicular to the radius of the circle at that point. This means that it forms a right angle at that point.

19. If AB is tangent to circle C, the lengths of the triangle ABC will form a Pythagorean triple. Let's check:

4.8² + 7.2² = 12²

74.88 = 144 [not true} Therefore, AB is not tangent to circle C.

20. Also, we will have the following:

15² + 11.2² = 6.8²

350.44 = 46.24 [not true].

AB is not tangent to circle C.

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The tent occupies 640 cubic feet of space.

Volume is a measurement of the amount of three-dimensional space occupied by an object or substance. It is the measure of the amount of space that an object or substance occupies in three dimensions, typically expressed in cubic units such as cubic meters, cubic centimeters, or cubic feet.

For example, the volume of a cube can be calculated by multiplying its length by its width by its height (or side cubed):

V = l x w x h = [tex]s^3[/tex],

where V is the volume, l is the length, w is the width, h is the height, and s is the length of a side.

Volume is an important measurement in fields such as physics, engineering, architecture, and chemistry, where it is used to calculate quantities such as the amount of fluid that can be held by a container, the amount of material needed to construct a building, or the amount of a substance that can react with another substance in a chemical reaction.

The volume of the tent can be found by calculating the volume of the square pyramid and then adding the volume of the rectangular box formed by the tent's base.

The base of the tent is an 8-ft by 8-ft square, so its area is 8 x 8 = 64 square feet. The height of the pyramid is 3 ft, so its volume is:

V(pyramid) = (1/3) x base area x height

V(pyramid) = (1/3) x 64 x 3

V(pyramid) = 64 cubic feet

The rectangular box formed by the tent's base has dimensions of 8 ft by 8 ft by 9 ft, so its volume is:

V(box) = length x width x height

V(box) = 8 x 8 x 9

V(box) = 576 cubic feet

Therefore, the total volume of space the tent occupies is:

V(total) = V(pyramid) + V(box)

V(total) = 64 + 576

V(total) = 640 cubic feet

So the tent occupies 640 cubic feet of space.

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Sharon's desired percentile rank of 0.78.

To determine the goal Sharon set for herself, we need to understand the relationship between standardized scores and percentile ranks.

In a standardized test, such as Sharon's Statistics final, the standardized score represents how well a student performed relative to the average score of the test-takers.

The percentile rank, on the other hand, indicates the percentage of test-takers that scored below a particular student.

In Sharon's case, she wants her standardized score to be equal to her percentile rank.

Therefore, her goal is to achieve a standardized score of 0.78 (written as a decimal) on her Statistics final.

This means she aims to score better than approximately 78% of her classmates, as indicated by her desired percentile rank of 0.78.

Hence her desired percentile rank of 0.78.

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The point (1,2) is the point of intersection of the two lines.

It should be noted that to verify if the point (1,2) is a solution to the system of linear equations, we need to substitute x=1 and y=2 into both equations and check if they are true.

The equation is true, so (1,2) is a solution to the first equation.

Substituting x=1 and y=2 into the second equation also makes the equation true.

Therefore, the point (1,2) is the point of intersection of the two lines.

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(a) For the null hypothesis, we would use the claim that the average weight of a healthy 3-month-old colt is equal to 60 kg, that is,

H0 : μ = 60 kg.

(b) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is less than 60 kg, that is,

H1: μ < 60 kg.

(c) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is greater than 60 kg, that is, H1: μ > 60 kg.

(d) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is different from 60 kg, that is, H1: μ ≠ 60 kg.

(e) For the test in part (b), the area corresponding to the p-value would be on the left of the mean because the alternate hypothesis is one-tailed and represents a left-tailed test.

For the test in part (c), the area corresponding to the p-value would be on the right of the mean because the alternate hypothesis is one-tailed and represents a right-tailed test.

For the test in part (d), the area corresponding to the p-value would be on both sides of the mean because the alternate hypothesis is two-tailed and represents a two-tailed test.

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Answer: 1 is .4

2. is .6

3 is .5

4 is .375

5 is .18

6 is .71

7 is .16

8 is .66 repeating

9 is .91

and 10 is .25

Step-by-step explanation:

to get all these and fractions to decimals in the future just divide the numerator by the denominator in other words the top number by the bottom number

1): 0.4

2): 0.67 or 0.7

3): 0.5

4): 0.37 or 0.4

5): 0.18

6): 0.42 or 0.5

7): 0.17

8): 0.7

9): 0.97 or 1

10): 0.25

The drive-thru with typically more wait time is Burger Quick, because it has a larger median. The Option A.

The median is a measure of central tendency that represents the middle value of a set of data. In this case, the median wait time at Burger Quick is 15.5 minutes, while the median wait time at Super Fast Food is 12 minutes.

This indicates that, on average, customers at Burger Quick experience a longer wait time compared to customers at Super Fast Food. The larger median at Burger Quick suggests that there may be some longer wait times skewing the data towards the higher end which could be due to various factors such as slower service, or other operational issues at Burger Quick resulting in a longer wait time for customers at their drive-thru.

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The two options that represent circles with diameter 12 units and center on the y-axis are:

x² + (y - 6)² = 36

x² + (y + 6)² = 36

The diameter of a circle is a straight line segment that passes through the center of the circle and connects two points on its circumference. It is twice the length of the circle's radius.

The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:

x² + (y - 6)² = 36

x² + (y + 6)² = 36

Explanation:

For a circle with diameter 12 units, the radius is half of the diameter, which is 6 units.

Since the center of the circle lies on the y-axis, the x-coordinate of the center is 0.

The general equation for a circle with center (h, k) and radius r is (x - h)² + (y - k)² = r².

Using the given information, we substitute h = 0, k = ±6, and r = 6 to get the two equations:

(x - 0)² + (y - 6)² = 6² => x² + (y - 6)² = 36

(x - 0)² + (y + 6)² = 6² => x² + (y + 6)² = 36

Therefore, the two options that represent circles with diameter 12 units and center on the y-axis are:

x² + (y - 6)² = 36

x² + (y + 6)² = 36

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A statistician would reply that in order to determine if the generic drug is less effective than the name-brand drug, a hypothesis test needs to be conducted.

The null hypothesis (H0) would be that there is no difference in the average blood pressure reduction between the two drugs, while the alternative hypothesis (H1) would be that the name-brand drug has a higher average reduction in blood pressure than the generic drug.

To test these hypotheses, a t-test would be appropriate since we have two independent samples (control and treatment groups) with known means, standard deviations, and sample sizes. The t-test will provide a p-value, which can be compared to a chosen significance level (e.g., α = 0.05).

If the p-value is less than the significance level, we reject the null hypothesis and conclude that there is a significant difference in the average blood pressure reduction between the two drugs. If the p-value is greater than the significance level, we fail to reject the null hypothesis, meaning we do not have enough evidence to claim that the name-brand drug is more effective than the generic drug.

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