Meghan is spending money at a constant rate. Suppose she initially has $1100, and after 4 months, she has $720.

Express the rate at which Meghan's amount of money is changing.

The equation of the hyperbola with center (-10, 5), a focus at (-10, 15),

and a co-vertex at (-18,5) is:

[(y - 5)² / 36] - [(x + 10)² / 64] = 1

From the question, we are to determine the equation of the hyperbola with the given center, focus and co-vertex.

The equation of a hyperbola with center (h, k), a focus at (h, k + c), and a co-vertex at (h + b, k) is given by

[(y - k)² / a²] - [(x - h)² / b²] = 1

Where a² = c² - b²

From the given information,

The center of the hyperbola is (-10, 5)

Thus,

h = -10, k = 5

The focus is at (-10, 15)

By comparison with (h, k + c)

k + c = 15

5 + c = 15

c = 15 - 5

c = 10

The co-vertex is at (-18, 5)

By comparing with (h + b, k)

h + b = -18

-10 + b = -18

b = -18 + 10

b = -8

From the formula a² = c² - b²

Then,

a² = c² - b²

a² = 10² - 8²

a² = 100 - 64

a² = 36

Now,

We can write the equation of the hyperbola

[(y - k)² / a²] - [(x - h)² / b²] = 1

Substitute the values

[(y - (5))² / (36)] - [(x - (-10))² / (-8)²] = 1

[(y - 5)² / 36] - [(x + 10)² / 64] = 1

Hence,

The equation of the hyperbola is:

[(y - 5)² / 36] - [(x + 10)² / 64] = 1

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The value of collinear point mLP = 13x - 34.

Three or more points on the same line are referred to as collinear points. The Latin terms "col" and "linear," which signify together and in the same line, are the source of the English word "collinear."

Since L, M, and P are collinear points, we have:

mLM + mMP = mLP

Substituting the given values, we get:

(8x - 56) + mNP = mLP

(8x - 56) + (5x + 22) = mLP

13x - 34 = mLP

Therefore, mLP = 13x - 34.

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The complete question is:

If mLM = (8x - 56) and mNP = (5x + 22), find mLP.

In this case, the given sample mean of 25.3 is only slightly higher than the population mean of 25, and is well within one standard deviation from the population mean. Therefore, the probability of a sample mean being less than 25.3 is 0.9582.

In statistics, the mean is a measure of central tendency that represents the sum of all values in a dataset divided by the total number of values in that dataset. It is also commonly referred to as the average.

Here,

To find the required probability, we need to calculate the z-score first:

z = (x - μ) / (σ / √n)

z = (25.3 - 25) / (1.3 / √68)

z = 1.73

Looking at the standard normal table, the probability of a z-score being less than 1.73 is 0.9582.

To determine whether the given sample mean would be considered unusual, we need to compare it to the population mean and standard deviation. A sample mean is considered unusual if it falls outside the range of values that are expected to occur with a high probability based on the population mean and standard deviation.

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The minimum amount the student needs to earn per month to save enough money to pay the remaining cost is $500.

The total annual cost to attend community college is $5,000. The college offered a high school senior a scholarship for $1,800 and the student can get a loan for $1,200. To find the minimum amount the student needs to earn per month to save enough money to pay the remaining cost, follow these steps:

1. Subtract the scholarship and loan amounts from the total cost: $5,000 - $1,800 - $1,200 = $2,000.

2. Divide the remaining cost by the number of months (4) until the cost must be paid: $2,000 / 4 = $500.

Therefore, the minimum amount the student needs to earn per month to save enough money to pay the remaining cost is $500.

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The two lengths of the chords of circle are solved and x = 5 units

Given data ,

Let the length of the two chords be represented as AB and CD

Now , AB = 21 and CD = 3x

where E is the extended point of the two chords which intersect at point E

Now , from the intersection of chords outside the circle ,

BE ( AE ) = DE ( CE )

On simplifying , we get

4 ( 25 ) = x ( 4x )

100 = 4x²

Divide by 4 on both sides , we get

x² = 25

Taking square roots on both sides , we get

x = 5 units

Hence , the chords are solved and x = 5 units

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Answer:

Step-by-step explanation:

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Answer:

XY = 7.5 cm

Area = 105 cm²

Step-by-step explanation:

First, let us use the sin Θ to find the value of XY.

Sin Θ = Opposite ÷ Hypotenuse

Sin 43 = XY ÷ 11

0.6819 = XY ÷ 11

0.6819 × 11 = XY

7.5 cm = XY

The formula to find the area of the triangle is:

[tex]\sf Area=\frac{1}{2}*base*height\\\\\sf Area=\frac{1}{2}*28\:cm\:*7.5\\\\Area=105\:cm^2[/tex]

The angle between the two kayakers is given as follows:

83º.

The cosine of the angle between two vectors a and b is obtained according to the equation presented as follows:

[tex]\cos{\theta} = \frac{ab}{|a||b|}[/tex]

In which:

The dot product of the two vectors in this problem is given as follows:

190 x 128 - 160 x 121 = 4960.

The norm of each vector is given as follows:

Hence the angle is obtained as follows:

cos(x) = 4960/(248.4 x 176.1)

cos(x) = 0.1134

x = arccos(0.1134)

x = 83º.

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The dot in the graph of the inequality, x > 5, will be opened

From the question, we are to determine if the dot in the graph of the given inequality will be opened or closed

The given inequality is x > 5

If the sign of an inequality has the equals sign included, that is greater than or equal to (≥) OR less than or equal to (≤), the dot in the graph will be closed.

But if the inequality is less than or greater than (< or >), the dot in the graph will be opened.

Hence,

The dot in the graph of x > 5 will be opened since the inequality sign is not greater than or equal to (≥) OR less than or equal to (≤).

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Answer:

140° + 90° + 90° + k = 360°

320° + k = 360°

k = 40°

Therefore , the solution of the given problem of angles comes out to be k has a value of 40 degrees.

The largest and smallest walls of a skew are found at the intersection of the pathways connecting its ends. Two pathways could meet at a crossroads. Another result of two entities interacting is an angle. More than anything else, they resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their endpoints to produce a two-dimensional curve.

Here,

According to the information provided, it seems that there is a 140° angle followed by an angle designated as "k". These two angles appear to be adjacent, and since the sum of all angles on a straight line is 180 degrees, we may construct the following equation:

=> 140° + k = 180°

We can now calculate the value of k as follows:

=> k = 180° - 140°

=> k = 40°

So, "k" has a value of 40 degrees.

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Answer: >$15

Step-by-step explanation: She needs at least $15, so, we use the greater then symbol, because she’ll be fine if she has more than $15(>15) but she won’t be able to buy the ticket if she has under $15(<15)

The equation of the asymptotes for the given function y = 8/x are x = 0 and y = 0.

What is an asymptote?

an asymptote is a straight line or a curve that a function approaches but never touches as the independent variable (usually denoted by "x") approaches a certain value or becomes very large or small.

In the case of a straight line asymptote, the function approaches the line as x approaches positive or negative infinity. If the line is horizontal, then the function approaches a horizontal asymptote, and if the line is vertical, then the function approaches a vertical asymptote. For example, the function y = 1/x has a vertical asymptote at x = 0, because as x approaches 0, the function approaches infinity (or negative infinity) and never touches the vertical line x = 0.

The given equation y = 8/x represents a hyperbolic function. The graph of this function has two asymptotes, one in the x-axis (y = 0) and the other in the y-axis (x = 0).

To find the equation of the asymptotes, we can use the fact that as x becomes very large or very small, the function approaches the asymptotes. The equation of the vertical asymptote, which is x = 0, can be obtained by taking the limit of the function as x approaches 0 from both the positive and negative sides. We get:

lim x→0+ 8/x = +∞

lim x→0- 8/x = -∞

So the vertical asymptote is x = 0.

The equation of the horizontal asymptote, which is y = 0, can be obtained by taking the limit of the function as x becomes very large. We get:

lim x→±∞ 8/x = 0

So the horizontal asymptote is y = 0.

Therefore, the equation of the asymptotes for the given function y = 8/x are x = 0 and y = 0.

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Answer: 1134.11

A=3.14*r^2

Step-by-step explanation:

Answer:

a ≈ 1134.11 cm2

Step-by-step explanation:

The formula:

[tex]a=\pi r^{2}[/tex]

[tex]a=\pi (19)^{2} =361\pi[/tex]

[tex]a=1134.11cm^{2}[/tex]

Hope this helps

Answer:

40°

Step-by-step explanation:

360-240=120

120÷3=40°

Answer

40°

Add of all angles would be 360° .

so equation would be

360° - 240° = 3x

360 - 240 is 120

so

120 = 3x

Dive the both sides of equation by 3 (*just to make it simple and clear. you cam just move 3 to other side of equation . since its multiplied in its side, it would change to division*)

120/3 = 3x/3

40° = x

all the X angle would be 40°

240 + 40 + 40 + 40 = 360°

Answer:

N(0)=10000/(5+1245)

Step-by-step explanation:

substitute zero in for t. Anything to the zero power equals 1.

Answer:

8 people

Step-by-step explanation:

N(0)=10000/(5+1245e^-0.97(0))

N(0) = 10000/(5+1245e^0)

e^0 = 1

= 10000/5+1245(1)

= 10000/5+1245

= 10000/1250

= 8

substitute zero in for t. Anything to the zero power equals 1.

Answer:

3 1/2 is located between 3 and 4 on the number line.

Answer:

2.8

Step-by-step explanation:

The formula for calculating simple interest is:

I = Prt

Where I is the interest earned, P is the principal amount, r is the interest rate per year, and t is the time period in years.

In this case, we know that Nick invested $1,000 and earned $112 in interest over a period of 4 years. We can use this information to calculate the interest rate:

112 = 1000 * r * 4

Simplifying the equation, we get:

r = 112 / (1000 * 4)r = 0.028

Multiplying by 100 to convert to a percentage, we get:r = 2.8%

Therefore, Nick's interest rate was 2.8% to the nearest tenth.

Answer:

Let's say that the total cost of the classes is C and the number of classes is n. We can assume that each class costs the same amount, which we'll call p.

Then, the total cost of the classes can be expressed as:

C = np

However, Gregory charges a one-time processing fee of $3.00, so the total cost of the classes (including the processing fee) can be expressed as:

C = np + 3

Therefore, the equation that represents the relationship between the total cost of the classes (including the processing fee) and the number of classes is:

C = np + 3

Answer: D (t−3)(t−5)(t+4)

Step-by-step explanation:

Hope this helps! :)

the discount on the dog food is $0.27, and the discounted price is $1.08.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

If the original price of the dog food is $1.35 and it is on sale for 20% off, the discount would be:

Discount = 20% of $1.35

Discount = 0.20 x $1.35

Discount = $0.27

Therefore, the discounted price of the dog food would be:

Discounted price = Original price - Discount

Discounted price = $1.35 - $0.27

Discounted price = $1.08

So the discount on the dog food is $0.27, and the discounted price is $1.08.

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The total measurements of the roof in square feet as required to be determined in the task content is; 2649 ft².

It follows from the task content that the total area of the roof as given in the task content is to be determined.

On this note, the area of the roof is the total area of the 71ft by 39 ft rectangle minus the area of the shaded region with dimensions 15 ft by 8 ft.

Therefore;

Area = (71 × 39) - (15 × 8)

= 2649 ft².

Ultimately, the total area measure of the roof in square feet is; 2649 square feet.

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Answer:

There seems to be a mistake in the provided function for the population size. The function should include the variable t, which represents the number of years from the time the species was added to the lake. Without the variable t, we cannot determine the initial population size or the population size after 7 years.

Assuming that the correct function for the population size is:

P(t) = -2000/(1 + 6e^(-0.42t))

We can find the initial population size by setting t = 0:

P(0) = -2000/(1 + 6e^0) ≈ -480

Rounding to the nearest whole number, the initial population size is -480.

To find the population size after 7 years, we can substitute t = 7 into the function:

P(7) = -2000/(1 + 6e^(-0.42*7)) ≈ 838

Rounding to the nearest whole number, the population size after 7 years is 838.

The length of arc AB is 37.71 cm (rounded to the nearest hundredth).

The measure of arc AB is 135°, say Ф = 135°

The radius of the circle is 16 centimeters, say r = 16 cm

The length of an arc can be calculated by the formula as,

Length of Arc = (Ф / 360°)* 2πr            in units

⇒ Length of Arc AB = ( 135° / 360°)* 2π (16)   in cm

Let us consider π = 22/7

⇒ Length of Arc AB  = [tex]\frac{(135) (22/7)(2)(16)}{360}[/tex] in cm

= [tex]\frac{(135)(22)(2)(16)}{(360)(7)}[/tex]  in cm

= [tex]\frac{95040}{2520}[/tex]  in cm

=  37.7142857143 cm

= 37.71 cm (rounded to the nearest hundredth)

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Answer:

To find the inverse of the function f(x) = (x - 12)^2 on the domain [12, infinity), we can follow the steps below:

Step 1: Replace f(x) with y.

y = (x - 12)^2

Step 2: Swap the positions of x and y.

x = (y - 12)^2

Step 3: Solve for y.

Taking the square root of both sides, we get:

y - 12 = ±√x

Adding 12 to both sides, we get:

y = 12 ± √x

However, we are given that the domain of the inverse function is [12, infinity). Since the expression 12 - √x is negative for x > 144, we must choose the positive square root to satisfy the given domain. Therefore, the inverse function is:

f^-1(x) = 12 + √x, x ≥ 144

Note that we have restricted the domain of the inverse function to [144, infinity) to ensure that the function is one-to-one and has a unique inverse.

Answer: - 7.5

Step-by-step explanation:

The next step to take in copying the angle is:  place the compass at point C and open the compass to the distance between B and C.

The steps that we take in copying an angle are:

1). Draw a working line with the help of a straightedge.

2). Now we put a point A as the vertex of the angle.

3). Construct an arc with a radius 'r' (any length ) from vertex A which intersects the working line say at C.

4). With the same radius we draw an arc from point E which intersects the line ED and EF at G and H respectively.

5). Mark an arc from point G which intersects line EF at I.

6). Measure the distance between points G and I with compass and mark an arc from point C which intersects the previous arc say at U.

7). Now join the points S and U.

Hence we copy any angle.

Thus, looking at the given image, the next step is to place the compass at point C and open the compass to the distance between B and C.

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Answer: B: [tex]f(x) = x^2 - 4x-5[/tex]

Step-by-step explanation:

Lets write this first in vertex form:

We know the vertex of this function is at (2, -9)

this gives us h,k values. Since there is no stretch or compression, and no negative coefficient we can simply plug in:

f(x) = [tex](x-2)^2 - 9[/tex]

Expanding this, we get answer B.

Answer:

3 and 4

Step-by-step explanation:

- 2 < x < 5

has solutions x = - 1, 0, 1, 2, 3, 4

x > 2

has solutions

x = 3, 4, 5, 6, ...........

the integer values that satisfy both are x = 3, 4

Answer:

multiple of 3

Step-by-step explanation:

I think that it will least likely land on a multiple of 3 because none of them are multiples of 3.

Kareem drove the truck for 144 miles.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

The additional charge for each mile driven is $0.78, so the total cost of driving "x" miles is:

0.78x

In addition to the cost per mile, Kareem also had to pay a base fee of $15.99. So the total cost of renting the truck for "x" miles is:

0.78x + 15.99

We know that Kareem paid $128.31 in total, so we can set up the equation:

0.78x + 15.99 = 128.31

Solving for "x", we get:

0.78x = 112.32

x = 144

Therefore, Kareem drove the truck for 144 miles.

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