which of the following is the equation of a line given the following
slope:5 and y-intercept: -3

a. y = -3x - 5
b. y = 5 + 3x
c. y = 5x - 3
d. y = -3x + 5​

Answer:

yes

Step-by-step explanation:

if there's more it will make a graph and lead to a linear equation that you have to solve then

a) Fiscal policy: Increase government spending or reduce taxes to boost aggregate demand (AD). Monetary policy: Lower interest rates or increase money supply to stimulate AD.

b) Impact depends on SRAS slope. Output ↑, unemployment ↓ in short run. Inflation ↑ if SRAS is steep.

c) Higher inflation expectations from persistent expansionary policies can lead to increased wages and prices, resulting in higher inflation in the long run.

d) Expansionary fiscal policy can lead to budget deficits, crowding out private investment, higher government debt, future tax burdens, and dependency on government intervention.

a) Fiscal policy involves using government spending and taxation to influence aggregate demand (AD) and stabilize the economy. To minimize the unemployment rate, the prime minister could implement expansionary fiscal policy by increasing government spending or reducing taxes. This would lead to an increase in AD, stimulating economic activity, and potentially reducing unemployment. Monetary policy, on the other hand, involves actions taken by the central bank to influence the money supply and interest rates. The prime minister could work with the central bank to implement expansionary monetary policy, such as lowering interest rates or conducting open market operations to increase the money supply. This would encourage borrowing and spending, boosting AD and potentially reducing unemployment.

b) If the central bank helps the prime minister achieve the goal of minimizing the unemployment rate, it can have short-run effects on both the unemployment rate and the inflation rate. Expansionary fiscal and monetary policies can increase AD, leading to increased output and potentially reducing unemployment in the short run. However, the impact on inflation will depend on the slope of the short-run aggregate supply (SRAS) curve. If the SRAS is relatively flat, the increase in output will have a larger impact on reducing unemployment without significantly increasing inflation. Conversely, if the SRAS is steep, the increase in output may lead to a significant increase in inflation with only a modest reduction in unemployment.

c) The opposition leader's argument is related to the long-run implications of the prime minister and central bank's agreement on inflation expectations. According to the AD-AS model, in the long run, the economy will reach the natural rate of unemployment (NRU) where the SRAS curve intersects the long-run aggregate supply (LRAS) curve. If expansionary fiscal and monetary policies are used persistently to reduce the unemployment rate below the NRU, it can create inflationary pressures. This may result in higher inflation expectations among households and businesses, leading to higher wage demands and increased prices.

d) If the prime minister chooses to use fiscal policy to minimize the unemployment rate, the opposition leader argues that it will also be costly in the long run. This is because expansionary fiscal policy, such as increasing government spending or reducing taxes, can lead to budget deficits. Persistent budget deficits can increase government debt and require borrowing, which may lead to higher interest rates and crowding out private investment. Higher government debt can also result in future tax burdens or reduced government spending on other essential areas, impacting long-term economic growth.

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The length of the sides of the square are 8 centimetres and 12 centimetres respectively

area = l²

where

Therefore,

x² + y² = 208

perimeter = 4l

4x + 4y = 80 cm

x + y = 20

x = 20 - y

(20 - y)² + y² = 208

y² - 40y + 400 + y² = 208

2y² - 40y + 192

y² - 20y + 96

(y - 12)(y - 8)

Therefore, y  = 12 and y = 8

when y = 8

x + 8 = 20

x = 12

when y = 12

x + 12 = 20

x = 8

Therefore, the length of the sides of the square are 12 cm and 8 cm.

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Answer:

1/4

or 25%

or 0.25

Step-by-step explanation:

With a question like this, you have to multiply.

1/2 * 1/2 = 1/4

or

0.5 * 0.5 = 0.25

If someone wants the product of two line segments to be represented as another line segment, they can make use of similar triangles

The correlation between the lengths of line segments can be established by creating a geometric shape comprising of two triangles that are identical and share one side.

If the legs of the triangles are used to represent the two line segments and their shared side represents the resulting line segment, it is possible for the lengths to be proportional through the similarity of the triangles.

To represent the product of the two original line segments, it is necessary to ensure that they and the resulting line segment are a collection of similar triangles. This is because the length of the resulting line segment can represent the product of the initial segments.

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Answer:

A, B,

Step-by-step explanation:

\(\it tan60^o=\dfrac{AB}{BC} \Rightarrow \sqrt3=\dfrac{AB}{50} \Rightarrow AB=50\sqrt3\approx50\cdot1,732\approx87\ m\)

Answer:

84%

Step-by-step explanation:

21/25=?/100  ==> decimal value is dividing a number by 100

100 * 21/25=100 * ?/100  ==> percent value is multiplying a decimal by 100

2100/25 = ? ==> solve for ?

? = 84%

Answer:

21 is 84% of 25

please mark brilliant

Answer: c

Step-by-step explanation:

i did the test

The investment account would have $9,522.80 after 34 years.

To calculate the amount the investment account would have after 34 years, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A is the final amount in the account,
P is the initial amount invested,
r is the annual interest rate (expressed as a decimal),
n is the number of times the interest is compounded per year, and
t is the number of years.

In this case, the initial amount invested is the money saved from not buying mocha lattes each day, which is $46 multiplied by 30 (days in a month), giving us $1,380 per month. Since the money is invested at the end of the month, we can consider it as being invested annually. Therefore, n = 1.

The annual interest rate is given as 7.03%, which, when converted to a decimal, is 0.0703. So, r = 0.0703.

The number of years is 34, so t = 34.

Now, we can substitute these values into the formula:

A = $1,380(1 + 0.0703/1)^(1*34)

Calculating the exponent first:

(1 + 0.0703/1)^(1*34) = (1.0703)^34 ≈ 6.9011

Now, we can calculate the final amount:

A = $1,380 * 6.9011 ≈ $9,522.80

Therefore, the investment account would have approximately $9,522.80 after 34 years.

It's important to note that this calculation assumes that no additional contributions are made to the investment account over the 34-year period. Additionally, the effective annual rate of 7.03% is assumed to remain constant throughout the entire period.

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Answer:

Step-by-step explanation:

$18 spent on parking. 100-18=82

$42.50 on admission 80- 42.50= 39.5

20 percent of 100 is 20 so 39.5-20=19.5

12.75 so 19.4-12.75=6.65

1.75x=6.65

x=3.8 so basically henry played 3 games

To find the z-score for the amount spent yesterday by a customer which made a purchase of $32.25, we first need to calculate the standard deviation of the sampling distribution of the means.

We can use the formula:
Standard Deviation = standard deviation of population / square root of sample size
Since we don't know the sample size, we will assume that it is large enough (more than 30) and use the central limit theorem to estimate the standard deviation of the sampling distribution of the means.
The standard deviation of the sampling distribution of the means is:
Standard Deviation = 2.50 / sqrt(n)
Assuming n is large enough, we can estimate the standard deviation to be approximately:
Standard Deviation ≈ 2.50 / sqrt(30) ≈ 0.456
Now we can calculate the z-score using the formula:
z-score = (x - μ) / σ
Where:
x = $32.25 (amount spent by the customer)
μ = $28.50 (mean amount spent by a typical customer)
σ = 0.456 (estimated standard deviation of the sampling distribution of the means)
z-score = (32.25 - 28.50) / 0.456 ≈ 8.24
Therefore, the z-score for the amount spent yesterday by a customer which made a purchase of $32.25 is approximately 8.24. This suggests that the amount spent by this customer is quite unusual, as it is more than 8 standard deviations above the mean.

To calculate the z-score for a customer's purchase of $32.25 at a convenience store chain, where the mean amount spent by a typical customer is $28.50 and the standard deviation is $2.50, you can follow these steps:
1. Determine the mean (μ) and the standard deviation (σ). In this case, μ = $28.50 and σ = $2.50.
2. Identify the individual data point (x) for which you want to calculate the z-score. Here, x = $32.25.
3. Use the z-score formula: z = (x - μ) / σ.
4. Plug in the values: z = ($32.25 - $28.50) / $2.50 = $3.75 / $2.50 = 1.5.
So, the z-score for the amount spent yesterday by the customer who made a purchase of $32.25 is 1.5.

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The probability of given data is that it is actually going to rain in Seattle with value of  0.4706 approximately.

Firstly, denote the variables to the events: R: It is actually raining in Seattle. U: Your umbrella is with you. F1: Your first friend says it is raining. F2: Your second friend says it is raining. F3: Your third friend says it is raining.

We want to find the probability of R given that F1, F2, and F3 all say it is raining. Using Bayes' theorem, we have:

P(R | F1F2F3) = P(F1F2F3 | R) * P(R) / P(F1F2F3)

The denominator, P(F1F2F3), can be calculated using the law of total probability as follows:

P(F1F2F3) = P(F1F2F3 | R) * P(R) + P(F1F2F3 | R') * P(R')

where R' represents the event that it is not raining in Seattle. Since the probability of raining in Seattle is 0.1,

we have P(R) = 0.1 and P(R') = 0.9.

To calculate the probabilities of the events involving your friends' responses, we can use the following table:

Event Probability

F1         2/3 if R, 1/3 if R'

F2         2/3 if R, 1/3 if R'

F3         2/3 if R, 1/3 if R'

If it is raining, each friend will tell you the truth with probability 2/3, and if it is not raining, they will lie with probability 2/3. Therefore, we have:

P(F1F2F3 | R) = (2/3)^3 = 8/27

P(F1F2F3 | R') = (1/3)^3 = 1/27

Substituting these values into the equation, we get:

P(R | F1F2F3) = (8/27 * 0.1) / [(8/27 * 0.1) + (1/27 * 0.9)]

= 8/17

≈ 0.4706

Therefore, given that all three of your friends say it is raining, the probability that it is actually raining in Seattle is approximately 0.4706 or 47.06%. This means it is better to bring an umbrella to be safe.

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Answer:

The answer is option D

Step-by-step explanation:

f (n)=-2. (-5)^n-1. Jesus loves you

Answer:

36.45

Step-by-step explanation:

5.50 × 3 = 16.5

16.5 + 19.95 = 36.45

sorry if wrong.

hope it helps.

\(3\)

According to the Remainder Theorem, if we divide a polynomial, \(P(x)\), by \(x -\blue a\), the remainder is \(P(\blue a)\).

If we let \(P(x) = x^2 -1\), the remainder when we divide \(P(x)\) by \(x -\blue 2\) is \(P(\blue 2)\).

The last thing we need to do now is to evaluate \(P(\blue 2)\).

\(&P(\blue 2) &= &(\blue 2)^2 -1 \\ &P(\blue 2) &= &4 -1 \\ &P(\blue 2) &= &3\)

The length and width of rectangle is 160 feet and 100 feet.

The perimeter of the rectangle is calculated by the formula -

Perimeter = 2 × (length + width)

As per the given information, length = (60 + width)

Keep the values in formula to find the breadth of rectangle.

520 = 2 × (60 + width + width)

520 = 2 × (60 + 2 × width)

(60 + 2 × width) = \(\frac{520}{2}\)

(60 + 2 × width) = 260

2 × width = 260 - 60

2 × width = 200

Width = \(\frac{200}{2}\)

Width = 100 feet

Keep the value in formula to find the length of perimeter

520 =  2 × (length + width)

Length + 100 = \(\frac{520}{2}\)

Length = 260 - 100

Length =  160 feet

Hence, the length and width of rectangle is 160 feet and 100 feet.

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The classification of each pair of angles is given below.

What is an angle?

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together.

The Latin word "angulus," which means "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

Corresponding angle = figure 3 and figure 5

Alternate interior angle = figure 4

Alternate exterior angle = figure 1

None of these = figure 2

Hence, these are the required answer.

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Answer:

j : k : m = 4 : 12 : 15

Step-by-step explanation:

Given

j : k = 1 : 3 , then k = 3j

Given

k : m = 4 : 5

then expressing in fractional terms

\(\frac{k}{m}\) = \(\frac{4}{5}\) ( substitute k = 3j )

\(\frac{3j}{m}\) = \(\frac{4}{5}\) ( cross- multiply )

4m = 15j ( divide both sides by 4 )

m = \(\frac{15}{4}\) j , so

j : k : m = 1 : 3 : \(\frac{15}{4}\) ( multiply each part by 4 to clear the fraction )

            = 4 : 12 : 15

The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z=\dfrac{X-\mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

\(Z=\dfrac{X-\mu}{\sigma}\)

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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Answer:

$170 + $35n

Step-by-step explanation:

Given that:

First day:

Transport fare = $70

Fee per ticket = $19

2nd day:

Transport fare = $100

Fee per ticket = $16

Total cost in dollars for the two days for n members

Number of members = n

First day:

70 + 19n

Second day :

100 + 16n

Totak cost :

(70 + 19n) + (100 + 16n)

70 + 100 + 19n + 16n

170 + 35n

$170 + $35n

The calculated measure of angle y is 60 degrees

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

The figure

From the figure, we can see that

The shape can be divided into two triangles such that

Each triangle is an equilateral triangle

The measure of an angle in an equilateral triangle is 60 degrees

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

y = 60

Hence, the value of y is 60 degrees

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Answer:

18

Step-by-step explanation:

9+(-15)+4+20

9-15+4+20

18 ans

Using the normal distribution, the probability that a single randomly selected value is less than 971 dollars is 0.2123.

In the given question,

CNNBC recently reported that the mean annual cost of auto insurance is 1007 dollars.

The standard deviation is 241 dollars.

We take a simple random sample of 99 auto insurance policies.

We have to find the probability that a single randomly selected value is less than 971 dollars.

From the question,

Mean = 1107 dollars

Standard Deviation = 241 dollars

So the probability that a single randomly selected value is less than 971 dollars.

Using the normal distribution

z = (x−mean)/Standard Deviation

P(x<971) = P(z<(973−1107)/241)

Simplifying

P(x<971) = P(z<(−134)/241)

P(x<971) = P(z<−0.56)

P(x<971) = 0.2123

Hence, the probability that a single randomly selected value is less than 971 dollars is 0.2123.

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Option second \(\rm (w-2.5)(w+2.5)\) and option fourth  \(\rm (-4v-9)(-4v+9)\)  are the products that result in a difference in squares.

It is required to identify which products result in a difference in squares.

Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.

We know that:

\(\rm (a^2-b^2)=(a+b)(a-b)\)

In option first:

\(\rm = (5z+3)(-5z-3)\\\rm = -(5z+3)(5z+3)\\\rm = -(5z+ 3)^2\)

Which is not the difference between squares.

In option second:

\(\rm=(w-2.5)(w+2.5)\\\rm =(w^2-2.5^2)\)By using \(\rm (a^2-b^2)=(a+b)(a-b)\)

It is the difference between squares.

Similarly, in option third:

\(\rm =(8g+1)(8g+1)\\\rm =(8g+1)^2\)

It is not the difference between squares.

Similarly, in option forth:

\(\rm = (-4v-9)(-4v+9)\\\rm = (4v+9)(4v-9)\\\rm = (4v)^2-9^2\)

It is the difference between squares.

Similarly, in option fifth:

\(\rm = (6y+7)(7y-6)\\\rm = 42y^2+13y-42\)

It is not the difference between squares.

Similarly, in option sixth:

\(\rm =(p-5)(p-5)\\\rm =(p-5)^2\)

It is also not the difference between squares.

Thus, option second and option fourth are correct.

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Answer:

Terrence made $30 more than Teresa.

Step-by-step explanation:

Giving the following information:

Terrence earns $450 per week.

Teresa earns $300 per week plus a 6% commission on the total sales of books she sells.

First, we need to structure the total income formula for each:

Terrence= 450

Teresa= 300 + 0.06*x

x= sales

Now, for $2,000 sales of books:

Terrence= $450

Teresa= 300 + 0.06*2,000= $420

The average height above the x-axis of a point in the region \(0\leq y\leq x^2\), for 0≤x≤25 using definite integral is 208.33 units.

To calculate the average height above the x-axis of a point in the region \(0\leq y\leq x^2\), for 0 ≤ x ≤ 25, we need to find the average value of y over this range.

The equation y = x² represents a parabola that opens upwards. To find the average height, we need to integrate the function y = x² over the given range and then divide by the length of the range.

Let's calculate it step by step:

Calculate the definite integral of y = x² with respect to x over the range 0 to 25:

∫[0,25] \(x^{2}\) dx = \([x^3/3]\) evaluated from 0 to 25

\(= (25^3/3) - (0^3/3)\\= (25^3/3)\\= 16666.67\)

Calculate the length of the range:

Length = 25 - 0 = 25

Divide the definite integral by the length of the range to find the average height:

\(Average height = (25^3/3) / 25\\= (25^2/3)\\= 208.33\)

Therefore, the average height above the x-axis of a point in the region \(0\leq y\leq x^2\), for 0 ≤ x ≤ 25, is approximately 208.33 units.

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What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation?

It's 2 (to get - 4x & 4x + - 4x = 0)

What number would you multiply the second equation by in order to eliminate the y-terms when adding to the first equation?

It's 3 (to get 9y & - 9y + + 9y =0)

Hope this helps!

Answer:

A=5.375

Step-by-step explanation:

46.28-3.28= 43

43÷8= 5.375

I hope this helps