Sarah is setting up a garden plot in the shape of a right triangle. One leg of the triangle will be 7 feet longer than the other and the hypotenuse will be 1 foot longer than the longest leg. Find the length of each side of the garden plot. As a part of your work, include a sketch with the sides labeled. Show your work algebraically and be sure to use proper units in your answer.

We can use the formula for the volume of a pentagonal pyramid to solve this problem:

Volume = (1/3) × Base Area × Height

We know that the base area is 12 cm² and the volume is 48 cubic centimeters. We can substitute these values into the formula and solve for the height:

48 = (1/3) × 12 × Height

Multiplying both sides by 3 gives:

144 = 12 × Height

Dividing both sides by 12 gives:

Height = 12

Therefore, the height of the pentagonal pyramid is 12 centimeters.

You are approximately 3.4 miles from your starting point.

We  have,

To solve this problem, we need to use the Pythagorean theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse.

 |\

8 | \

 |  \

 |___\

    3

We can see that the three blocks north and 10 blocks south cancel each other out, so we only need to consider the 8 blocks west.

Using the distance formula, we can find that the distance traveled west is:

8 blocks × 2/10 mile per block = 1.6 miles

Now we can use the Pythagorean theorem to find the distance from the starting point:

distance = √(3² + 1.6²)

distance ≈ 3.4 miles

Therefore,

You are approximately 3.4 miles from your starting point.

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Answer: 0

Step-by-step explanation:

Put 0 in the front box.

this is because you cant divide 11 apples equally into 6 people; 11 isn't a multiple of 6

The reference angle of 13π/8 is 3π/8 and the sketch of the angle is attached

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

Angle = 13π/8

Rewrite as

θ = 13π/8

The above angle is in the fourth quadrant

So, we subtract it from 2π to calculate the reference angle

Using the above as a guide, we have the following:

Reference angle = 2π - 13π/8

Evaluate the difference

Reference angle = 3π/8

Hence, the reference angle is 3π/8 and the sketch of the angle is added as an attachment

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Answer:

23.35 minutes

Step-by-step explanation:

Brendan finished in 22.5 minutes. Tobias finished 85 seconds after. Just add 85 seconds to 22.5 minutes. There are 100 second in 1 minute. Since Brendan is already at 22.5, there is only 0.5 left to get to 23. 0.5 in this case means 50 seconds. You do 85 - 50 = 35. Now, you are at 23 minutes. Add 35 seconds to that to get to 23.25 minutes.

Answer:

ellipses

a pair of parallel straight

Step-by-step explanation:

The median total of amount Franky earned is A = $81.67 per day.

Given data ,

For the first five days: $(100 + x) per day

For the next two days: $(175 + 2x) per day

For the final three days: $(75 + 2x) per day

Now , the average amount she earns is $80 per day

So , Average earnings = Total earnings / Total number of days

Average earnings = [(100 + x) * 5 + (175 + 2x) * 2 + (75 + 2x) * 3] / 10

Simplifying the equation:

80 = [500 + 5x + 350 + 4x + 225 + 6x] / 10

Multiplying both sides by 10:

800 = 1075 + 15x

Subtracting 1075 from both sides:

15x = -275

Dividing both sides by 15:

x = -18.33

For the first five days: $(100 - 18.33) = $81.67 per day

For the next two days: $(175 + 2*(-18.33)) = $138.34 per day

For the final three days: $(75 + 2*(-18.33)) = $38.34 per day

Arranging the earnings in ascending order: $38.34, $38.34, $38.34, $81.67, $81.67, $81.67, $81.67, $138.34, $138.34

The median is the middle value when the earnings are arranged in ascending order. In this case, the middle value is $81.67

Hence , the median is $81.67

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62. The slope of the line is 1/8. the equation of line is y = 1/8x - 3/8

63. It has an infinite slope.  The equation of line is x = 3

64. The slope of the line is -5. The slope of the new line is 1/5. The equation of line is  y = 1/5x - 1

65. The slope of the line is 2/9. The slope of the new line is -9/2. The equation of line is y = -9/2x - 4

62) through: (3,0), parallel to y = 1/8x - 3. If a line is parallel to another, they have the same slope. Therefore the slope is 1/8.

For line equation⇒ (y - y1 = m(x - x1))

Substituting (3,0) and slope 1/8 gives us:

(y = mx + b) ⇒ y - 0 = 1/8 × (x - 3)

First, substitute the point and the slope into the equation: 0 = 1/8×3 + b

Then solve for b, the y-intercept: b = -3/8

⇒ y = 1/8x - 3/8

63) through: (3,-1), parallel to x = 0. A line parallel to x = 0 is a vertical line. A vertical line has the equation x = a, where a is the x-coordinate of any point on the line. A line through (3, -1) and parallel to x = 0 would simply be x = 3 or y = -1

64) through: (5, 0), perp. to y= -5x - 4. If a line is perpendicular to another, their slopes are negative reciprocals. The slope of y = -5x - 4 is -5, so the slope of the line we are looking for is -1/(-5) = 1/5

65) through: (-2, 5), perp. to y=2/9x - 1.  perpendicular  line to y = 2/9x - 1 has the slope that is the negative reciprocal of 2/9, which is -9/2. y = -9/2x - 4.

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The simplified expression of (3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) is (b) -a³b - 8ab²

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

(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab)

Open the bracket

So, we have

(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) = 3a³b - 4ab² + 5ab -4a³b - 4ab² - 5ab

Evaluate the like terms

So, we have

(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) = -a³b - 8ab²

Hence, the simplified expression is (b) -a³b - 8ab²

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To find the length of arc LM, we need to use the formula for the circumference of a circle:

C = 2πr

In this case, the arc LM is a portion of the circumference of the circle. To find the length of the arc, we need to determine the angle at the center of the circle that corresponds to the arc.

Looking at the image you provided, we can see that angle LOM is a right angle (90 degrees). The angle at the center of the circle, LOCM, is half of the right angle, which is 45 degrees.

To calculate the length of arc LM, we need to find the fraction of the total circumference represented by the central angle LOCM. The fraction is given by:

Fraction of circumference = Angle at center / 360 degrees

Fraction of circumference = 45 degrees / 360 degrees

Fraction of circumference = 1/8

Now, we can calculate the length of arc LM:

Length of arc LM = Fraction of circumference * Circumference

Length of arc LM = (1/8) * (2πr)

Since the radius (r) is not given in the image, we cannot calculate the exact length of arc LM. However, we can provide the formula for the length of arc LM in terms of the radius:

Length of arc LM = (1/8) * (2πr) = πr/4

So, the length of arc LM is πr/4, where r is the radius of the circle.

If you have the value of the radius, you can substitute it into the formula to find the specific length of arc LM.

In triangle ABC, side BC (a) is 15 cm, side AC (b) is 13.30 cm, and side AB (c) is 12.23 cm. Also angle A is 70°, B is 50°, and C is 60°

Using the Law of Sines and the fact that the sum of the angles in a triangle is 180 degrees.

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. Using this, we can find the lengths of the other sides of triangle ABC.

Let's denote side AB as c, BC as a, side AC as b, and angle C as ∠C.

Using the Law of Sines, we have:

sin(∠A) / a = sin(∠B) / b

Substitute in the known values, we get:

sin(70°) / 15 = sin(50°) / b

Make b the subject of the formula:

b = (15 * sin(50°)) / sin(70°)

Using a calculator, we can find the value of b:

b = (15 * 0.766) / 0.9397

  = 12.23 cm

Therefore side AC = b = 12.23 cm

Now, to find side AB (c), we can use the Law of Sines again:

sin(∠B) / b = sin(∠C) / c

But ∠C is unknown. To find ∠C, we apply the sum of angle in a triangle rule

∠A + ∠B + ∠C = 180

70 + 50 + ∠C = 180

∠C = 180 - 70 - 50

∠C = 60°

Substitute the values in the Sine rule equation

sin(50°) / 12.233 = sin(60) / c

Make c the subject of the formula

c = (12.233 * sin(60)) / sin(50°)

c = (12.233 * sin(60°)) / sin(50°)

  = 13.30 cm

Therefore, the lengths of the sides of triangle ABC are:

Side AB = c = 12.23 cm

Side BC = a = 15 cm

Side AC = b = 13.30 cm

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The closest length to the arc from point C to point D is 16.34 ft (option c).

To find the length of the arc from point C to point D, we need to calculate the circumference of the circle and then find the fraction of the circumference represented by the central angle.

The circumference of a circle can be calculated using the formula:

Circumference = 2 × π × radius

Given the radius of 18 feet, the circumference is:

Circumference = 2 × π × 18 = 36π feet

To find the length of the arc, we need to find the fraction of the circumference represented by the central angle of 52°. The fraction is calculated by dividing the central angle by 360° and then multiplying it by the circumference.

Length of the arc = (Central angle / 360°) * Circumference

Length of the arc = (52° / 360°) × 36π

Length of the arc = (13/90) × 36π

Length of the arc = 468π / 90

Length of the arc ≈ 16.41 ft

Among the given options, the closest length to the arc from point C to point D is 16.34 ft (option c).

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Out of the following 30 samples, you may expect that about 12 will be portions of vanilla cake.

To solve this problem, use the concept of probability and make a prediction based on the past data.

In this case, out of the 10 pieces of cake that have been taken, 4 are vanilla and 6 are coconut.

Therefore, the probability of selecting a piece of vanilla cake from the tray is 4/10, or 2/5.

To predict how many of the next 30 samples will be pieces of vanilla cake, multiply the probability of selecting a vanilla cake by the total number of samples:

(2/5) x 30 = 12

So expect that out of the next 30 samples taken, approximately 12 of them will be pieces of vanilla cake.

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The options 2nd and 3rd are the monomials with degree 2.

Given are the expressions we need to find the monomials with degree 2.

So,

The general form of a monomial with degree 2 is:

ax²

The highest exponent of a polynomial's variable(s) in any of its terms is referred to as the polynomial's degree in mathematics.

It controls the polynomial's behavior and complexity.

A non-negative integer is used to represent the degree.

And,

A monomial is a mathematical expression consisting of a single term. It is composed of a coefficient multiplied by one or more variables raised to non-negative integer exponents.

Here, the monomials can be 2x² and x²

Hence the options 2nd and 3rd are the monomials with degree 2.

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The measure of angle BGF from the given parallel lines is 108°.

Given that, measure of angle BGF=4x+28 and the measure of angle EHD = 2x+32.

1) From the given figure, angle BGF and angle EHC are interior alternate angles.

Angle FHC and angle EGA are corresponding angles.

Angle FHC and angle EGA are exterior alternate angles.

2) angle BGF+angle EHD=180°

3) 4x+28+2x+32=180°

6x+60=180

6x=120

x=20

Angle BGF=4x+28=108 °

Angle EHD = 2x+32

= 112°

Angle FHD=180-112=68°

Angle EGB=180-108=72°

Therefore, the measure of angle BGF from the given parallel lines is 108°.

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The surface area of the prism is 248.88 cm²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of a prism is expressed as;

SA = 2B + ph

where h is the height of the prism, B is the base area of the prism and P is the perimeter of the base.

Base area = 61.94 cm²

height = 5cm

perimeter = 5 × 5 = 25cm

SA = 2 × 61.94 + 25 × 5

SA = 123.88+ 125

SA = 248.88 cm²

Therefore the surface area of the prism is 258.88 cm²

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The equivalent sine and cosine values are as follows:

The relationship between sine and cosine angles is:

sinθ = cos(90 - θ)

This equation is known as the complementary angle identity for sine and cosine. It states that the sine of an angle is equal to the cosine of its complementary angle (90 degrees minus the original angle).

For example, if we have an angle theta = 30 degrees, its complementary angle would be 90 - 30 = 60 degrees.

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Answer:

8% of $15,000 = .08 × $15,000 = $1,200

The answers to all parts are shown below.

The law of uninhibited decay is a first-order chemical reaction, which means that the rate of the reaction is proportional to the concentration of compound A.

The rate law can be written as:

rate = k[A]

where k is the rate constant and [A] is the concentration of compound A.

From the given data, we can use the following equation to determine the rate constant:

ln([A]t/[A]0) = -kt

where [A]t is the concentration of compound A at time t, [A]0 is the initial concentration of compound A, k is the rate constant, and t is the time.

Using the given data:

[A]t = 0.37 M

[A]0 = 0.40 M

t = 30 minutes = 0.5 hours

ln(0.37/0.40) = -k(0.5)

k = 0.0486 h⁻¹

(a) How much of compound A will remain after 2 hours?

Using the same equation and substituting the known values:

ln([A]t/[A]0) = -kt

ln([A]t/0.40) = -0.0486 x 2

[A]t/0.40 = e⁻(⁹⁷² /¹⁰⁰⁰⁰)

[A]t = 0.25 M

Therefore, after 2 hours, 0.25 M of compound A will remain.

(b) How long will it take until 0.10 M of compound A remains?

Substituting the known values into the equation again:

ln([A]t/[A]0) = -kt

ln(0.10/0.40) = -0.0486t

t = 4.26 hours

Therefore, it will take approximately 4.26 hours until 0.10 M of compound A remains.

(c) After 2 hours, the amount of compound A remaining will be 0.25 M.

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Answer:

The answer is B:14

Step-by-step explanation:

When you simply multiply 5% by 14, you get 0.7. So you know that 5% of 14 is 7.

Answer:

A

Step-by-step explanation:

i do this all the time math is my thing

Based on the given data, we can estimate that approximately 36 out of the next 100 books that come down the chute will be nonfiction.

To estimate the number of nonfiction books out of the next 100, we can use the ratio of nonfiction to the total number of books that came down the chute so far today.

The total number of books that came down the chute so far is:

41 (fiction) + 23 (nonfiction) = 64

The ratio of nonfiction books to the total number of books in library is:

[tex]23/64[/tex]

To estimate the number of nonfiction books out of the next 100, we can multiply the ratio by 100:

[tex](23/64)*100=35.9375[/tex]

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If two sides of the triangle measure: x + 7 and x – 7, the measurement of the hypotenuse is 2x + 3.

In a right triangle, the hypotenuse is the side opposite the right angle and it is the longest side. We can use the Pythagorean theorem to relate the sides of the right triangle:

a² + b² = c²

where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse.

We are given that the perimeter of the triangle is 4x + 3. The perimeter of a triangle is the sum of the lengths of its sides, so we can write:

a + b + c = 4x + 3

Substituting the given side lengths, we get:

(x + 7) + (x - 7) + c = 4x + 3

Simplifying, we get:

2x + c = 4x + 3 - 7 + 7

2x + c = 4x + 3

Solving for c, we get:

c = 2x + 3

We did not need to use the Pythagorean theorem in this problem, as we were only asked for the measurement of the hypotenuse in terms of x.

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Step-by-step explanation:

(35-24.8) / 6.2  = z-score of  + 1.645  corresponding to   .9495  =

           ~ 95th percentile

The number of weeks that the puppies weigh the same amount will be A. 6 weeks.

The equation that has no solution is A. 13 - 7x = -7x + 13.

The option determined from the graph is B. The ordered pair (25, 6) is a solution to y = x + 40 and y = 3x + 15.

Puppy A weighs 4 1/5 pounds at birth and gains 3/4 pound each week. Puppy B weighs 5 2/3pounds at birth and gains 1/2 pound each week.

After how many weeks will the puppies weigh the same amount will be calculated thus:

4 1/5 + 3/4x = 5 2/3 + 1/2x

4.2 + 0 75x = 5.67 + 0.5x

Collect the like terms

5.67 - 4.2 = 0.25x

Divide

x = 1.47 / 0.25

x = 6

Hence ,the number of weeks that the puppies weigh the same amount will be A. 6 weeks.

It should be noted that the equation that has no solution is A. 13 - 7x = -7x + 13. This is because the values gives 0 all through.

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Diego is correct as the number of groups result to 6/5 or 1 1/5.

We have to find the number of groups of 5/6 in 1.

So, we need to perform the division as

= 1/ (5/6)

= 1 x 6/5

= 6/5

= 1 1/5

Thus, Diego is correct as the number of groups result to 6/5 or 1 1/5.

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The sample size needed to be 99​% confident that the sample proportion will not differ from the true proportion by more than ​4% is given as follows:

n = 1037.

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 margin of error is given as follows:

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

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

As we have no estimate, the parameter is given as follows:

[tex]\pi = 0.5[/tex]

Then the sample size for M = 0.04 is obtained as follows:

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

[tex]0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.04\sqrt{n} = 2.575 \times 0.5[/tex]

[tex]\sqrt{n} = \frac{2.575 \times 0.5}{0.04}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2[/tex]

n = 1037.

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Answer:

4x = 100, so x = 25

The correct answer is C.