How many square feet of outdoor carpet will we need for this hole? 72 ft 9 ft 3 ft 6 ft 6 ft 12 ft

Answer: We know that the center of the ellipse is the midpoint of the line segment joining the foci. So, the center is ((15+3)/2, (-2-2)/2) = (9, -2).

The distance between the foci is 2c, where c is the distance between the center and each focus. So, 2c = 15 - 3 = 12, which means c = 6.

The distance between the center and each co-vertex is b. So, b = 10 - (-2) = 12.

The semi-major axis is a, which is the distance from the center to a vertex. Since we have the co-vertices, we can use the Pythagorean theorem to find a:

a^2 = b^2 - c^2

a^2 = 12^2 - 6^2

a^2 = 108

a = sqrt(108) = 6*sqrt(3)

Therefore, the equation of the ellipse is:

(x - 9)^2 / (6*sqrt(3))^2 + (y + 2)^2 / 12^2 = 1

Simplifying, we get:

(x - 9)^2 / 72 + (y + 2)^2 / 144 = 1

So, the equation of the ellipse is (x - 9)^2 / 72 + (y + 2)^2 / 144 = 1.

Enjoy!!!!!!!!!!!!!!!!!!!!!!

For the computation of confidence interval for the difference in two population proportions following are negative,

p₁(cap) - p₂(cap)

Lower bound of the confidence interval

Upper bound of the confidence interval

For the computation of confidence interval,

The difference in two population proportions,

p₁ - p₂, can be negative or positive.

This implies,

The sample estimate of the difference in proportions,

p₁(cap) - p₂(cap), can also be negative or positive.

The standard error and critical value are always positive values and cannot be negative.

The lower and upper bounds of the confidence interval can be negative or positive.

Depending on the sample estimate and the margin of error.

So, both the lower and upper bounds can be negative.

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The above question is incomplete, the complete question is:

You are computing a confidence interval for the difference in 2 population proportions. which of the following could be negative?

Select all.

a. p₁

b. p₁(cap) - p₂(cap)

c. Standard error

d. Critical value

e. Lower bound of the confidence interval

f. Upper bound of the confidence interval

answer: 175

Step-by-step explanation:

Answer:

71.9 degrees

Step-by-step explanation:

The find the value of x on the given diagram, we must first find the included angle between the two line segments labelled 94 mi and 119 mi in the triangle. To do this, we can use the Law of Cosines.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]

The values to substitute into the formula are:

Solving for the angle C:

[tex]\begin{aligned}173^2&=119^2+94^2-2(119)(94)\cos C\\\\29929&=14161+8836-22372\cos C\\\\29929&=22997-22372\cos C\\\\6932&=-22372\cos C\\\\-\dfrac{6932}{22372}&=\cos C\\\\C&=\cos^{-1}\left(-\dfrac{6932}{22372}\right)\\\\C&=108.0502874...^{\circ}\end{aligned}[/tex]

As angles on a straight line sum to 180°, the value of x can be calculated by subtracting the found value of C from 180°:

[tex]x=180^{\circ}-108.0502874...^{\circ}[/tex]

[tex]x=71.9497125...^{\circ}[/tex]

[tex]x=71.9^{\circ}\; \sf (nearest\;tenth)[/tex]

Therefore, the ship turned 71.9 degrees north of west when it changed direction.

Answer:

The answer is brand B

Step-by-step explanation:

You divide $14.88 by 24 which equals 68 cents per item.

Then brand B is 60 cents per item which is the better buy!

By answering the presented question, we may conclude that so by SAS congruency property we have said that all these triangles are similar.

A triangle is a closed, a double geometric shape made up of three line segments known as sides that connect at three parameters known as vertices.

Triangles are differentiated by their angles and their sides. Triangles can be collinear (all sides equal), angles, or scalene dependent on their sides.

Triangles are classed as acute (all angles just under 90 degrees), right (one angle of approximately to 90 degrees), or ambiguous (all angles greater than 90 degrees).

The area of a triangle may be determined with the formula A = (1/2)bh, where A is the surface, b is really the right triangle base, and h is the triangle's height

here, from the figure, we have

Two sides of the triangle are equal.

And also all angles are also same.

Therefore, so by SAS congruency property we have say that all these triangles are similar.

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value of variable x in the triangle is 8.

The Triangle Proportionality Theorem, also known as the Side-Splitter Theorem, states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. In other words, if a line is drawn parallel to one side of a triangle, and intersects the other two sides, then the ratio of the lengths of the line segments it creates on those sides is equal.

More formally, let ABC be a triangle, and let D be a point on the line segment BC that is between B and C. If the line through D parallel to AB intersects AC at point E, then BD/DC = AE/EC. This theorem is useful in many geometrical proofs and can be used to solve problems involving similar triangles.

According to Triangle Proportionality Theorem

4x-7/5=20/4

4x-7=5×5

4x=32

x=8

Hence, value of variable x in the triangle is 8.

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Answer:

The number must be at most 10.

If the number is doubled and then decreased by 9, the result is 2x - 9.

2x - 9 ≤ 19

2x ≤ 28

x ≤ 14

Therefore, the range of values of the number is 0 to 10.

Answer: We are given that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C.

To find the probability of obtaining a reading between 0°C and 1.08°C, we need to calculate the z-scores for these values using the formula:

z = (x - mu) / sigma

where x is the value we are interested in, mu is the mean, and sigma is the standard deviation.

For x = 0°C, we have:

z1 = (0 - 0) / 1.00 = 0

For x = 1.08°C, we have:

z2 = (1.08 - 0) / 1.00 = 1.08

Using a standard normal table or a calculator, we can find the probability of obtaining a z-score between 0 and 1.08.

Using a standard normal table or a calculator, we find that the probability of obtaining a z-score between 0 and 1.08 is 0.3583.

Therefore, the probability of obtaining a reading between 0°C and 1.08°C is 0.3583, rounded to 4 decimal places.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Section 1

1: 2x + 20

2. 8x - 49
3: 7x + 21

4.8x - 4

5. 15x + 5

6. 12x + 15

7. 20x - 50

8. 21x + 14

9. 24x - 6

10. 45x - 18

11. 18x - 8

12. 30x + 9

13. 24x + 36

14. 25x - 20

15. 14x - 63

16. 32x + 20

17. 24x - 10

18. 42x - 18

19. 24x - 80

20. 48x - 32

Answer: 90 feet

Step-by-step explanation:

Since the baseball diamond is shaped like a square, all sides are equal in length.

Let's denote the length of each side by x.

The perimeter of a square is the sum of the lengths of all four sides, so we can write:

4x = 360

Dividing both sides by 4, we get:

x = 90

Therefore, each side of the baseball diamond is 90 feet long.

Answer:

The perimeter of a circle is also known as the circumference. The formula for the circumference of a circle is:

C = 2πr

where C is the circumference, π is a constant approximately equal to 3.14, and r is the radius of the circle.

Substituting the given value, we get:

C = 2 x 3.14 x 10

C = 62.8 cm

Therefore, the perimeter of the circle is 62.8 cm.

Answer:

Step-by-step explanation:

We can use the formula distance = rate x time to solve the problem.

The rate is 15 miles per hour and the time is 3 1/3 hours.

To work with the time, we need to convert it to an improper fraction:

3 1/3 = (3 x 3 + 1)/3 = 10/3

Now we can plug in the values:

distance = 15 x 10/3

distance = 50 miles (rounded to the nearest mile)

Therefore, Jaq rode 50 miles.

Answer:

(f - g)(x) = -4x² + x - 8

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

            = x - 8 - (4x²)

            = -4x² + x - 8

Answer:

Step-by-step explanation:

If the zeros and their multiplicities are given, we can write the polynomial as the product of linear factors corresponding to each zero.

For this problem, the polynomial has zeros of -9 (multiplicity 1) and -1 (multiplicity 2), so the linear factors are:

(x + 9) and (x + 1)^2

To find the third factor, we use the fact that the degree of the polynomial is 3. We can multiply the linear factors together and then simplify:

(x + 9)(x + 1)^2 = (x^2 + 10x + 9)(x + 1)

= x^3 + 11x^2 + 19x + 9

Therefore, the polynomial with zeros of -9 (multiplicity 1), -1 (multiplicity 2), and degree 3 is:

f(x) = x^3 + 11x^2 + 19x + 9

Answer:

Answer: B. Symmetric.

Explanation:

In a symmetric distribution, the data is evenly distributed around the mean or median, creating a mirror image on both sides of the center. In this histogram, the median and mean are very close together at 55 and the bars on both sides of the center are roughly equal in height, indicating a fairly even distribution. Therefore, the histogram is symmetric.

Using compounding we know that the additional amount Jason has more than Kayden is $249.48.

Calculating interest on the principal borrowed as well as any prior interest.

In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one.

So, the amount of Jason after 8 years:

Amount: $5500

Interest: 1.875%

Compounded: Quarterly

Using a compounding calculator:

Amount after 8 years: $6,387.85

The amount of Kayden:

Amount: $5500

Interest: 1.375%

Compounded: Quarterly

Using a compounding calculator:

Amount after 8 years: $6,138.37

The additional amount Jason got: 6,387.85 - 6,138.37 = $249.48

Therefore, using compounding we know that the additional amount Jason has more than Kayden is $249.48.

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Answer:253

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex](3x+5)+(x-25)=180 \text{ \ (angles on a straight line are supplementary)}[/tex]

                 [tex]4x-20=180[/tex]

                         [tex]4x=200[/tex]         (+20 both sides)

                           [tex]x=50[/tex]           (÷4 both sides)

Part A: The probability of rolling a 5 is 1/6 or approximately 0.167. Part B: the probability of rolling an even number is 3/6 or 1/2 or 0.5.

Probability is a branch of mathematics concerned with measuring the likelihood or chance of an event occurring. It is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. Probability is expressed as a number between 0 and 1, where 0 means that the event will not occur and 1 means that the event will definitely occur. For example, if the probability of an event is 0.5, it means that the event has an equal chance of occurring or not occurring. Probability is used in various fields, such as science, engineering, finance, and statistics, to make predictions and make decisions based on uncertain events.

Part A:

The number cube has six faces, and each face has an equal chance of landing face-up. Therefore, the probability of rolling a 5 is 1/6 or approximately 0.167.

Part B:

The even numbers on a number cube are 2, 4, and 6. There are three even numbers out of a total of six possible outcomes. Therefore, the probability of rolling an even number is 3/6 or 1/2 or 0.5.

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There is no second place winner. all three competitors picked the same amount of strawberries, so there is a tie for first place.

Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.

The problem states that each of the three competitors picked 1 pound of strawberries. Since all of them picked the same amount, there is no way to determine who came in second. All three competitors can be considered tied for first place. If the problem had given different weights of strawberries picked by each competitor, then we could have compared the weights and determined who picked the second greatest amount of strawberries. But since all three competitors picked the same amount, there is no way to determine a second place winner.

Therefore,  there is no second place winner. all three competitors picked the same amount of strawberries, so there is a tie for first place.

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The argument  using the components of the non zero vectors which are not parallel are as follow, sa1 + tb1 = c1

sa2 + tb2 = c2

sa3 + tb3 = c3

Geometric argument,

a and b are nonzero vectors that are not parallel.

A plane in three-dimensional space.

Any vector in this plane can be written as a linear combination of a and b.

Let c be any vector in this plane.

Construct a parallelogram with sides a and b, and the diagonal of the parallelogram passing through the point c.

This diagonal is the vector c written as a linear combination of a and b, say c = sa + tb for some scalars s and t.

Diagonal of a parallelogram bisects and is bisected by its opposite sides.

c lies on the line passing through the midpoints of a and b.

c can be expressed as a linear combination of a and b.

Argument using components,

a and b are nonzero vectors that are not parallel, they are linearly independent.

Any vector in the plane determined by a and b can be expressed as a linear combination of a and b.

Let c = (c1, c2, c3) be any vector in this plane.

Now, c as c = sa + tb, where s and t are scalars to be determined.

Writing a and b in terms of their components, we have,

a = (a1, a2, a3) and b = (b1, b2, b3)

Then, we can write c as,

c = (s a1 + t b1, s a2 + t b2, s a3 + t b3)

Values of s and t such that c has the components (c1, c2, c3).

Equating the components of c with those of (c1, c2, c3), to get the system of equations,

sa1 + tb1 = c1

sa2 + tb2 = c2

sa3 + tb3 = c3

Therefore, solution of the argument of non zero vectors solved using standard techniques such as Gaussian elimination or Cramer's rule.

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The above question is incomplete, I answer the question in general according to my knowledge:

Suppose that a and b are nonzero vectors that are not parallel and c is any vector in the plane determined by a and b. Give a geometric argument to show that c can be written as c=sa +tb for suitable scalars s and t. Then give an argument using components.

Answer:

2 1/2

Step-by-step explanation:

20/8=2r4

2r4= 2 4/8

2 4/8 = 2 1/2

Answer:

2 1/2

Step-by-step explanation:

Step 1:

We first want to find the whole number, and to do this we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.

20/8= 2.5 = 2

Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.

Step 2: Get the new numerator

To work this out we'll use the whole number we calculated in step one (2) and multiply it by the original denominator (8). The result of that multiplication is then subtracted from the original numerator:

20 - (8 x 2) = 4

Step 3: Our mixed fraction

We've now simplified 20/8 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:

2 4/8

Step four: Convert it by simplifying

2 4/8 = 2 1/2

The chance that both numbers drawn are even numbers is 8/21.

The probability refers to the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.

There are 4 even numbers and 3 odd numbers in the first box, and 2 even numbers and 1 odd number in the second box.

The probability of drawing an even number from the first box is 4/7, and the probability of drawing an even number from the second box is 2/3.

By the multiplication rule of probability, the probability of drawing an even number from both boxes is

(4/7) × (2/3) = 8/21

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Answer:

gdiduusuehfuehvv

Step-by-step explanation:

bbzbhshxhdhhd are the best and my mom I WINNNNNN you want it to be over with you guys to come in and your mom are doing ghhdhhsuwuwhsh and your family are doing well and your family are doing well and your family are doing well and your family are doing well and your family and my wife was the best and I WINNNNNN and my mom are doing ghhdhhsuwuwhsh and what is the only ones I WINNNNNN with the kids I WINNNNNN and I will be over and I can do i and eat early for you and Darshanie and I WINNNNNN and my friend and your mom and my mom ever had a great day I love ever and your mom are the kids I will get you a great mom and I will send you a link and I WINNNNNN with the only ones I WINNNNNN with you don't need me I can get it and I will be over and your mom and your mom I will send it out tomorrow night I will send it out tomorrow night with you guys and I can send the best ones that have to do i I will send you and Darshanie and your mom I will send it and your family and I WINNNNNN and my friend are doing errands to run out to do i you guys and I WINNNNNN you want me I will send you and Darshanie is done now we have a great day for a great mom I will be over there and I WINNNNNN you and everyone and my friend and my friend and what time do the kids have a whole new world we live together I will be home tomorrow night with the only one that has to wait until the way home tomorrow morning to run out of wo you guys to run out with the best ones that w with the kids I will get you guys want me when we good day for you it

Answer:

We can use the formula |a × b| = |a| |b| sin θ to solve for the magnitude of the cross product |a × b|, where θ is the angle between vectors a and b. In this case, we have |a × b| = 1 and θ = π/4, so we can write:

1 = |a| |b| sin(π/4)

Simplifying, we have:

|a| |b| = √2

Now, we need to find the dot product a · b. We know that:

a · b = |a| |b| cos θ

where θ is the angle between vectors a and b. Since we're given the angle between a and b, we can substitute θ = π/4 and use the value we found for |a| |b|:

a · b = (√2) cos(π/4) = (√2)/2

Therefore, a · b is equal to (√2)/2.

Step-by-step explanation:

Answer:

15 people at each table

Step-by-step explanation:

1) divide total number of people by number of tables

240/16

2) solve

15 people at each table

Answer:

D

Step-by-step explanation:

First, let's calculate the initial monthly payment without purchasing any points.

The amount of the mortgage after the 20% down payment is:

$125,000 x 0.8 = $100,000

To calculate the monthly payment, we can use the formula:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Where:

M = Monthly payment

P = Principal (loan amount)

i = Interest rate (per month) = 4.75% / 12 = 0.0039583

n = Number of payments = 30 years x 12 months per year = 360

So, plugging in the values:

M = $100,000 [ 0.0039583(1 + 0.0039583)^360 ] / [ (1 + 0.0039583)^360 – 1]

M = $522.12 (rounded to the nearest cent)

Now, let's calculate the new monthly payment if Ashlee purchases 2 points. Each point costs 1% of the loan amount, so for a $100,000 loan, each point is $1,000.

By purchasing 2 points, Ashlee would pay an additional $2,000 upfront (2 x $1,000). This will lower the interest rate on the loan by 0.5%, from 4.75% to 4.25%.

Using the same formula as before, but with the new interest rate of 4.25% / 12 = 0.0035417, we get:

M = $100,000 [ 0.0035417(1 + 0.0035417)^360 ] / [ (1 + 0.0035417)^360 – 1]

M = $505.16 (rounded to the nearest cent)

The difference in monthly payments is:

$522.12 - $505.16 = $16.96

Rounding to the nearest cent, the answer is option D, $14.96.

Answer:

7x² - 2x + 4

Explanation:

(5x² + 2x + 11) − (7 + 4x - 2x²) ​

= 5x² + 2x + 11 - 7 - 4x + 2x²

= 7x² + 2x + 11 - 7 - 4x

= 7x² - 2x + 11 - 7

= 7x² - 2x + 4

So, the answer is 7x² - 2x + 4

Answer:

102 and 87

Step-by-step explanation:

Let the two numbers be x and y.

x+y = 189

x-y =15

Add the two equations together.

x+y = 189

x-y =15

-------------------

2x =204

2x/2 = 204/2

x = 102

Now we can find y.

x+y = 189

102+y =189

y = 189-102

y =87

Answer:  Choice D)  [tex]2a^3b[/tex]

Work Shown:

[tex]\frac{18a^6b^2}{9a^3b}=\frac{18a^6b^2}{9a^3b}\\\\\frac{18a^6b^2}{9a^3b}=\frac{18}{9}*\frac{a^6}{a^3}*\frac{b^2}{b}\\\\\frac{18a^6b^2}{9a^3b}=2a^{6-3}b^{2-1}\\\\\frac{18a^6b^2}{9a^3b}=2a^3b\\\\[/tex]

The formula used on the 3rd line was (a^b)/(a^c) = a^(b-c). We subtract the exponents when dividing exponential expressions with the same base.