Ryan and Khalil each have their own savings. Together, they borrowed $72 from a friend to buy a gift for their coach. Each has to pay back an equal amount to their friend. Ryan also owes the friend $12. Which explains whether the equation below represents the debt that Ryan owes his friend?

StartFraction negative 72 over 2 EndFraction minus (positive 12) = negative 48
It represents the debt because each one owes $36, and Ryan owes an additional $12.
It represents the debt because Ryan has to pay back $36 and he will get back $12.
It does not represent the debt because paying back $12 means that –12 is added, so the result is not –48.
It does not represent the debt because the result should be a positive number since a dollar amount cannot be negative.

The coordinates of the point that corresponds to -π/3 on the unit circle are (x, y) = (1/2, √3/2)

A unit circle is a circle in which the value of the radius is equal to 1 unit.

The coordinates of a point with angle Ф on a unit circle are given by

To find the coordinates of the point that corresponds to -π/3 on the unit circle, since we have the coordinates of a point on a unit circle as

substituting Ф = -π/3 into both equations, we have that the x - coordinate is

Also, we have that the y - coordinate is

So, the coordinates of the point are (x, y) = (1/2, √3/2)

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Answer:

\({x,y} = {2,-3}\)

Step-by-step explanation:

\(x - y = 5 \\\\[2] 3x - 2y = 12\)    <----------- Linear equations given

Graphic Representation of the Equations: PICTURE

\(y + x = 5 \\-2y + 3x = 12\)
Solve by Substitution :

// Solve equation [1] for the variable  \(x\)

\([1] x = y + 5\)

// Plug this in for variable  \(x\)  in equation\([2]\)

\([2] 3*(y +5) - 2y = 12 \\ [2] y = -3\)

// Solve equation \([2]\) for the variable \(y\)

\([2] y = - 3\)

// By now we know this much :

\(x = y+5 \\ y = -3\)

// Use the  y  value to solve for  \(x\)

\(x = (-3)+5 = 2\)

Solution :

\({x,y} = {2,-3}\)

Explanation

We are given the measure of arc PR = 118°.

We are required to find m∠PQR.

We know that an arc measure is an angle the arc makes at the center of a circle. Therefore, we have:

Hence, the answer is:

But since Q is the measure of the angle, then the final answer is 118°.

Answer:

Step-by-step explanation:

A - Growth (25%)

B- Growth (75%)

C - Growth

D - Growth (100%)

E - Growth (99%)

An rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay.

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

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Answer:

x < ( -2b+8)/-a

Step-by-step explanation:

-ax + 2b > 8

Subtract 2b from each side

-ax + 2b-2b >-2b+ 8

-ax > -2b+8

Divide each side by -a, remembering to flip the inequality

-ax /-a < (-2b+8)/ -a

x < ( -2b+8)/-a

Answer:

y=2x-1

Step-by-step explanation:

Remeber to put no spaces on the test

and it is this answer bc he owes one dollar evryday and owing is negative

Answer:

the last one

Step-by-step explanation:

Answer:

last one

Step-by-step explanation:

(g o f)(0) cannot be evaluated due to the undefined nature of f(x) at x = 0.

To evaluate (g o f)(0), we need to substitute 0 into the composite function (g o f)(x) = g(f(x)). However, we encounter an issue when considering the function f(x) = 1/x.

The function f(x) has a vertical asymptote at x = 0, which means the function approaches infinity as x approaches 0 from the left or right. This implies that f(x) is undefined at x = 0. Since f(x) is undefined at 0, we cannot evaluate (g o f)(0) since it requires the input of f(x) at x = 0.

In other words, we cannot substitute 0 into f(x) to obtain a valid value to use in the function g(x) = x - 4.

Therefore, (g o f)(0) cannot be evaluated due to the undefined nature of f(x) at x = 0.

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Answer:

( fraction negative 1 over 4, fraction 1 and 3 over 4 )

Step-by-step explanation:

Answer:

1st one will be it!

Step-by-step explanation:

Answer:

34 inches

Step-by-step explanation :

54/360 X 20

Answer:

330

Step-by-step explanation:

substitute x for 40 because that is how much you have in your account.

y= 70 - 10(40)

y = 70 - 400

y = 330

Therefore you bought 330 video games!!

Hope this helps, please tell me if I am wrong, I love learning from my mistakes:)

Answer:

0.7

Step-by-step explanation:

zero and seven TENths. the place value of the 7 is tenths so on the bottom of the fraction will be 10. i'm bad at explaining so sorry.

the decimal equivalent of 7 / 10 is 0.7.

To find the decimal equivalent of 7 / 10, we divide the numerator ( 7) by the denominator ( 10).

When we perform the division, 7 ÷ 10, we get 0.7.

Therefore, the decimal equivalent of 7 / 10 is 0.7.

In decimal form, the number 0.7 represents 7 tenths or 7 parts out of 10. It indicates that the numerator ( 7) is 7 / 10th of the denominator ( 10). This decimal representation makes it easier to compare the fraction with other decimal numbers and perform arithmetic operations using decimals.

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Answer:

A and C.

Step-by-step explanation:

A. 4/18 = 6/27     2/9 = 2/9 (Correct)

B. 4/6 = 16/36     2/3 = 4/9 (Unequal)

C. 3/4 = 9/12     3/4 = 3/4 (Correct)

D. 5/9 = 8/12     5/9 = 2/3 (Unequal)

The solution to the given system is (3,8).

Step-by-step explanation:

To draw a graph system for a linear equation,

Step 1: Consider two x values and draw a line joining the new points.

y = x + 5  ⇒1

y = 2x + 2  ⇒2

For both equations substitute two random values for x.

Let us Consider x=0 and x=10.

For equation 1,

y=x+5.                           y=x+5

y=0+5.                           y=10+5

y=5                                y=15

The new points for equation 1 are (0,5) and (10,15).

Draw a big straight line passing through these two points.

For equation 2,

y=2x+2.                         y=2x+2

y=0+2.                           y=20+2

y=2                                y=22.

The new points for equation 1 are (0,2) and (10,22).

Again, draw a big straight line passing through these two points.

Step 2: Mark the intercepting point and that will be the solution for the given system.

For this system, the solution is (3,8).

To check this answer equates both equations,

x+5=2x+2.

2x-x=5-2.

x=3.

Substitute the x value in any of the equations,

y=3+5.

y=8.

Solution:

Given:

Population of the world in 1987 = 5 billion

Annual growth rate = 1.2% per year.

We want to determine the projected world population in 2019.

An exponential growth can be modelled by the function

For the question before us,

r=1.2% = 0.012

x = 2019 -1987 = 32

a = 5,000,000,000

Thus,

The projected world population in 2019 is 7,323,967,432.5

Answer: The number of sets contain any 4 numbers = 210

Step-by-step explanation:

Given: Universal set = {0,1,2,3,4,5,6,7,8,9}.

i.e. Total choices = Numbers in set = 10

By combinations, the number of sets contain any 4 numbers =\(^{10}C_4\)

\(=\dfrac{10!}{4!6!}\ \ \ \ \ [^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{10\times9\times8\times7\times6!}{4\times3\times2\times1 \times6!}\\\\=210\)

Hence, the number of sets contain any 4 numbers = 210

i) P(A|B) = 1/5

ii) P(B|A) = 1/2

iii) P(A∩B) = 0.1

iv) P(A∪B) = 0.6

i) Probability of A given B can be obtained by using the following formula.P(A|B) = P(A∩B) / P(B)The probability of A∩B can be found as follows.P(A∩B) = P(A) × P(B) [As A and B are independent events.]P(A∩B) = 0.2 × 0.5 = 0.1

Now, substitute this value of P(A∩B) into the above formula to get the probability of A given B.P(A|B) = P(A∩B) / P(B) = 0.1 / 0.5 = 1/5

ii) Similarly, probability of B given A can be obtained as:P(B|A) = P(A∩B) / P(A)Substituting the values of P(A∩B) and P(A), we get,P(B|A) = P(A∩B) / P(A) = 0.1 / 0.2 = 1/2

iii) Probability of A∩B is already calculated in part i, and its value is 0.1.

iv) Probability of A∪B can be found as follows. P(A∪B) = P(A) + P(B) - P(A∩B)As calculated P(A∩B) in part i, use that value. Substituting the given values, :P(A∪B) = 0.2 + 0.5 - 0.1 = 0.6

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Answer: A good way to get a small standard error is to use a large sample.

Step-by-step explanation:

In order to find the small standard error, there is always need of a complete set which is called the large sample.

If tried to do a small or repeating sample, you will most likely not get an error and you could get a repetition. If you do a population sample, you wont get accurate results at all.

Therefore, a good way to get a small standard error is to use a large sample. Hope this helps!

-From a 5th Grade Honors Student

Using the concept of even and odd functions, it is found that, considering the function has a local max at (-1,3):

For a function increasing on [2,5], we have that:

Hence, considering the function has a local max at (-1,3):

For a function increasing on [2,5], we have that:

For even functions it will decrease because we have that f(4) > f(3), for example, hence f(-4) > f(-3).

For the odd function it will increase because if f(4) > f(3), then f(-3) > f(-4) due to the negative signal.

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Answer:

  234 square millimeters

Step-by-step explanation:

You want the area of the irregular polygon shown.

There are always several ways you can find the area of a figure like this. In the attachment we have shown extensions of the vertical and horizontal lines that will divide the figure into a triangle and two rectangles.

The triangle has a base of 12 mm and a height of 13 mm. Its area is ...

  A = 1/2bh

  A = 1/2(12 mm)(13 mm) = 78 mm²

The upper rectangle has a width of 8 mm and a length of 14 mm. Its area is ...

  A = LW

  A = (14 mm)(8 mm) = 112 mm²

The lower rectangle has a width of 4 mm and a length of 11 mm. Its area is ...

  A = (4 mm)(11 mm) = 44 mm²

The area of the figure is the sum of the areas of its parts:

  total area = triangle area + upper rectangle + lower rectangle

  total area = 78 mm² + 112 mm² + 44 mm² = 234 mm²

The area of the figure is 234 square millimeters.

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To solve this problem, we can use the M/M/1 queueing model, where "M" stands for Poisson arrivals and "M" stands for exponential service time, and "1" means there is one server.

From the problem, we know that the arrival rate, λ, is 1/7 customers per minute, and the service rate, μ, is 1/15 customers per minute. The utilization factor, ρ, is given by ρ = λ/μ = (1/7)/(1/15) = 15/7. Since ρ > 1, the system is not stable, and the average customer waiting time is infinite.

To limit the average customer waiting time to 2 minutes, we need to reduce the utilization factor. One way to do this is to increase the number of servers. Let's assume the call center has "k" servers. The average customer waiting time, W, can be approximated by the following formula:

W = (ρ^k / kμ) / (1 - ρ)

We want to find the minimum value of "k" such that W ≤ 2. Rearranging the formula, we get:

k ≥ (ρ/(1-ρ)) * (ρ^(k-1)) * (1/(2μ))

We can use trial and error or numerical methods to find the smallest integer value of "k" that satisfies this inequality. For example, starting with k = 1, we can calculate the right-hand side of the inequality and check if it is greater than or equal to 1. If it is not, we can increase k by 1 and repeat the calculation until we find the smallest integer value of "k" that satisfies the inequality.

Alternatively, we can use a formula for the Erlang C model, which is a generalization of the M/M/k model for multiple servers. The formula gives the probability that a customer has to wait for service, given the arrival rate, service rate, and number of servers. We can then use this probability to calculate the average customer waiting time using Little's law.

The minimum number of customer services needed to achieve the goal of limiting the average customer waiting time to 2 minutes is the smallest integer value of "k" that satisfies the inequality.

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The marginal-demand function of a company that identifies the rate at which the quantity of a product that consumers demand changes with respect to price is represented by the equation \(2000 D'(x) = −x²,\) where x is the price per unit in dollars.

Let's assume that D(x) is the demand function that corresponds to the marginal-demand function \(2000 D'(x) = −x².\)

Therefore, integrating the marginal-demand function 2000 D'(x) = −x² with respect to x yields the demand function D(x) as follows:\(∫2000 D'(x) dx = ∫(−x²) dx2000 D(x) + C = −(x³/3) + K,\) where C and K are constants of integration\(2000 D(x) = −(x³/3) + K₁D(x) = (−x³/6000) + K₂, where K₂ = K₁/2000\)

Thus, the demand function that corresponds to the marginal-demand function \(2000 D'(x) = −x² is D(x) = (−x³/6000) + K₂.\)The demand function is determined by a value of D(x) and the corresponding value of x. When\(x = 2, D(x) = 1004.\) Thus,\(1004 = (−2³/6000) + K₂, which gives K₂ = 1004.5\)

Therefore, the demand function is given by \(D(x) = (−x³/6000) + 1004.5.\)

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The point estimate is 0.942 gallons.

The standard error is 0.00424.

The critical value is 2.009.

The margin of error is 0.0085.

We are 95% confident that the true mean amount of water included in a 1-gallon bottle is between 0.9335 and 0.9505 gallons.

Based on these results, we cannot say for sure whether the distributor has a right to complain to the water bottling company.

To construct a 95% confidence interval for the population mean amount of water included in a 1-gallon bottle, we need to use the following formula:

Confidence interval = sample mean ± (critical value x standard error)

The point estimate is the sample mean amount of water per 1-gallon bottle, which is 0.942 gallons.

The standard error is calculated using the formula:

Standard error = standard deviation / √(sample size)

In this case, the standard deviation is 0.03 gallons and the sample size is 50. Therefore:

Standard error = 0.03 / √(50) ≈ 0.00424

The critical value is obtained from a t-distribution table with a degrees of freedom of 49 and a confidence level of 95%, which gives a value of 2.009.

The margin of error is calculated by multiplying the critical value by the standard error, which gives:

Margin of error = 2.009 x 0.00424 ≈ 0.0085

Therefore, the 95% confidence interval is:

0.942 - 0.0085 = 0.9335

0.942 + 0.0085 = 0.9505

The confidence interval tells us that the population mean could be between 0.9335 and 0.9505 gallons, but we don't know what the true value actually is. If the distributor's expectations fall within this range, they may not have a legitimate complaint.

However, if the actual mean amount of water is significantly lower than the lower end of the confidence interval, the distributor may have a valid complaint.

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Answer:

B

Step-by-step explanation:

The answer is B because we can estimate by seeing that: 3 x 3 = 9, so henceforth the answer must be between 3 and 4, so it must be B.

Length in the International System of Units (SI) equaling 1×10^−6 meter (SI standard prefix "micro-" = 10^−6).

The micrometer (international spelling as used by the International Bureau of Weights and Measures; SI symbol: μm) or micrometer (American spelling), also commonly known as a micron, is a unit of length in the International System of Units (SI) equaling 1×10^−6 meter (SI standard prefix "micro-" = 10^−6).

To convert a micrometer measurement to a meter measurement, divide the length by the conversion ratio.

Since one meter is equal to 1,000,000 micrometers, you can use this simple formula to convert:

meters = micrometers ÷ 1,000,000

The length in meters is equal to the micrometers divided by 1,000,000.

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The crucial element missing in this design is the control group. In order to effectively study the effect of weather on college students' study habits, it is important to have a control group.

A control group serves as a baseline for comparison and helps to isolate the effect of the independent variable, which in this case is the weather. By having a control group, the researcher can compare the study habits of students on sunny days (the experimental group) with those on other types of weather conditions or non-sunny days (the control group). This allows the researcher to determine whether the weather itself has a significant impact on the study habits of college students.

Without a control group, it becomes difficult to attribute any differences in study habits solely to the weather, as there may be other factors at play that could influence the students' behavior. Therefore, including a control group is crucial for a more rigorous and valid study design in this case.

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The crucial element missing in this design is the control group. In order to effectively study the effect of weather on college students' study habits, it is important to have a control group.

A control group serves as a baseline for comparison and helps to isolate the effect of the independent variable, which in this case is the weather. By having a control group, the researcher can compare the study habits of students on sunny days (the experimental group) with those on other types of weather conditions or non-sunny days (the control group). This allows the researcher to determine whether the weather itself has a significant impact on the study habits of college students.

Without a control group, it becomes difficult to attribute any differences in study habits solely to the weather, as there may be other factors at play that could influence the students' behavior. Therefore, including a control group is crucial for a more rigorous and valid study design in this case.

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Judith bought 6 cookie kits and 4 house kits.

Let y represent the number of house kits and x represent the number of cookie kits.

If Judith bought a combination of  10 gingerbread house and cookie kits, hence:

x + y = 10     (1)

Also, number of house kits was one more than half the  number of cookie kits, hence:

y = (1/2)x + 1   (2)

From the graph, the solution is at (6, 4)

Hence, Judith bought 6 cookie kits and 4 house kits.

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