what are the solutions to the following system of equations?x y = 3y = x2 − 9 (3, 0) and (1, 2) (−3, 0) and (1, 2) (3, 0) and (−4, 7) (−3, 0) and (−4, 7)

It is FALSE to state that if a researcher is interested determining if there is a relationship betweenethnicity and job type, then a Chi- Square Goodness of Fit test can be   used.

A Chi-Square Goodness of Fit test is not   appropriate for determining the relationship between ethnicity and job type.

This test is used to assess thedistribution of categorical variables within a single population or sample,   comparing observed frequencies with expected frequencies.

To examine the relationship between ethnicity and job type, a Chi-Square test of independence   or another suitable statistical test, such as logistic regression,would be more appropriate.

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In the given problem, we calculated the price of a bond with a $1,000 face value, a $50 annual coupon, and six years to maturity when the interest rate is 4%. The price of the bond was found to be $1,160.79.

The calculation of the price of the bond can be done using the following formula:

Price = (Annual Coupon Payment / Interest Rate) x (1 - 1 / (1 + Interest Rate) ^ Years to Maturity) + Face Value / (1 + Interest Rate) ^ Years to Maturity.

The annual coupon payment is $50, the interest rate is 4% or 0.040 and the face value is $1,000. Therefore, the price of the bond is given as:Price = ($50 / 0.040) x (1 - 1 / (1 + 0.040) ^ 6) + $1,000 / (1 + 0.040) ^ 6Price = ($1,250) x (1 - 1 / 1.281) + $747.26Price = $1,160.79.

Therefore, the price of the bond is $1,160.79. The bond offers an annual coupon of $50 and has a face value of $1,000. It has six years to maturity and the interest rate is 4%.

Using the bond pricing formula, we can calculate that the price of the bond is $1,160.79.

In finance, a bond is a type of debt security in which the issuer owes the holders a debt and is obliged to pay interest or repay the principal at a later date, known as maturity.

A bond can be issued by a company, municipality, or government entity as a means of raising capital. The price of a bond is determined by several factors, including its face value, coupon rate, and interest rate.

In the given problem, we are asked to calculate the price of a bond with a $1,000 face value, a $50 annual coupon, and six years to maturity when the interest rate is 4%.

Using the bond pricing formula, we found that the price of the bond is $1,160.79.

This means that if an investor were to buy the bond for this price, they would receive the annual coupon payments of $50 for the next six years and then receive the face value of $1,000 at maturity.

In conclusion, the price of a bond can be calculated using the bond pricing formula. The price of a bond depends on several factors, including its face value, coupon rate, and interest rate. In the given problem, we calculated the price of a bond with a $1,000 face value, a $50 annual coupon, and six years to maturity when the interest rate is 4%. The price of the bond was found to be $1,160.79.

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This question basically asks:

4 is 20% of what

So, just multiply everything by five so you turn that into

100% is 20

4 is indeed 20% of 20

Answer:

There is 20 total

Step-by-step explanation:

every 20% is 4, so you add 4 till you get 100%

Alessia spent $5,408 on entertainment in 2021.

To determine how much Alessia spent on entertainment in 2021, we need to work backward from the given information about her salary in 2022.

Let's assume Alessia's salary in 2021 was the same as in 2022, which is $26,000 after tax.

Since Alessia spends 35% of her after-tax salary on rent, we can calculate her rent expenditure:

Rent = 35% × $26,000

= $9,100

The remaining amount is split between food, petrol, and entertainment in the ratio 6:11:8.

To determine the ratio's total parts, we sum the individual parts:

Total parts = 6 + 11 + 8 = 25

Next, we calculate the value of one part of the ratio:

One part = ($26,000 - $9,100) / 25

= $16,900 / 25

= $676

Now, we can calculate how much Alessia spent on entertainment in 2021, which is 8 parts of the ratio:

Entertainment expenditure = 8 × $676

= $5,408

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Answer:

i would say the first one

Step-by-step explanation:

In the first month's payment for a $180,000 mortgage with a 5.5 percent, 30-year loan, a portion will go towards the principal. The exact amount can be determined using an amortization schedule.

To calculate how much of the first month's payment goes towards the principal, we can follow these steps:

Step 1: Determine the monthly interest rate: Divide the annual interest rate by 12 to obtain the monthly interest rate. In this case, 5.5 percent divided by 12 equals 0.004583 (approx).

Step 2: Calculate the monthly payment: Use a loan payment formula or a mortgage calculator to determine the monthly payment amount. For a $180,000 mortgage with a 30-year loan term and a 5.5 percent interest rate, the monthly payment would be approximately $1,019.32 (approx).

Step 3: Create an amortization schedule: An amortization schedule shows the breakdown of each monthly payment, indicating the amount allocated to interest and principal. Using the loan details, create an amortization schedule or use an online tool to generate one.

Step 4: Locate the first month on the schedule: Find the first month's entry on the amortization schedule to determine the amount allocated to principal. This amount will vary depending on the specific terms of the loan. Locate the principal portion of the payment, which represents the reduction of the loan balance.

By following these steps and referencing the amortization schedule, you can determine the exact amount of the first month's payment that goes towards the principal of the $180,000 mortgage.

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If the null hypothesis is true in a chi-squared test, then we expect the test statistic to be approximately equal to its expected value.

In a chi-squared test, the null hypothesis is the statement that there is no significant association between two variables. If the null hypothesis is true, then we expect the test statistic to be approximately equal to its expected value. The expected value is calculated using the degrees of freedom and the expected frequency of each category in the contingency table.

The chi-squared test statistic is calculated by subtracting the observed frequency from the expected frequency for each category and then squaring the result. These squared differences are then summed across all categories to calculate the chi-squared test statistic.

If the null hypothesis is true, we expect the test statistic to be close to its expected value. This is because when the null hypothesis is true, the observed frequencies should be close to the expected frequencies. Therefore, the squared differences should be small, resulting in a small test statistic.

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Answer:

He had $20 before he bought the game, you can use subtraction to find out how much Ken had

$32 - $12 = $20

Answer: 7

Step-by-step explanation:

\(g(3)=5 \implies f(g(3))=f(5)=2(5)-3=7\)

A ratio in mathematics displays how often one number occurs in another and the given situation's specific heat ratio is 1.24.

In mathematics, a ratio shows how frequently one number appears in another.

For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.

Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.

So, e are informed that the volume is halved, and the pressure increases by a factor of 2.5.

We shall therefore have:

PVγ = 2.5P(0.5V)γ

We'll condense this to:

(1/0.5)γ = 2.5

γ = In2.5/In2

γ = 1.32

The volume temperature relation is written as follows if the volume expands in an adiabatic process:

T1V1∧γ-1 = T2V2∧γ-1

T1V1∧1.32-1 = T2(0.5V1)∧1.32-1

Condensing this results in:

T₁ = 1.24T₂

Therefore, a ratio in mathematics displays how often one number occurs in another and the given situation's specific heat ratio is 1.24.

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The distribution of the total resistance of the two components in series for a randomly selected toaster is also normal, with a mean equal to the sum of the means of the two components, and a standard deviation equal to the square root of the sum of the variances of the two components.

Let's accept that the resistance of each component is regularly conveyed, with implies of μ1 and μ2, and standard deviations of σ1 and σ2, separately. We also assume that the two components are free of each other.

Add up to resistance = R1 + R2

where R1 and R2 are the resistances of the two components.

Concurring to the properties of ordinary dispersions, the entirety of two autonomous ordinary factors is additionally regularly dispersed, with a cruel rise to the entirety of the implies and a change rise to the whole of the changes. Hence, the cruelty of the overall resistance is:

Cruel = μ1 + μ2

and the change is:

Fluctuation = σ1\(^{2}\)+ σ2\(^{2}\)

The standard deviation of the full resistance is at that point the square root of the change:

Standard deviation = sqrt(σ1\(^{2}\) + σ2\(^{2}\))

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Answer:

92 over 100

Step-by-step explanation:

Answer: USE the forumla

Step-by-step explanation:

Consider a frustum of radii 'R' and 'r', and height 'H' which is formed by a cone of base radius 'R' and height 'H + h'. Its volume (V) can be calculated by using: V = πh/3 [ (R3 - r3) / r ] (OR) V = πH/3 (R2 + Rr + r2)

Answer: i think c and a

Step-by-step explanation:

To calculate the sample size needed to provide a margin of error of 3 or less with a 0.95 probability, we can use the formula:

n = (Z * σ / E)^2

Where:
n = sample size
Z = z-score corresponding to the desired confidence level (in this case, 0.95)
σ = population standard deviation
E = margin of error

Given that the population standard deviation (σ) equals 17 and the margin of error (E) is 3, we can substitute these values into the formula:

n = (Z * σ / E)^2
n = (1.96 * 17 / 3)^2
n = (33.32 / 3)^2
n = 11.107^2
n ≈ 123.29

Since the sample size cannot be a decimal, we need to round it up to the nearest whole number. Therefore, the sample size needed to provide a margin of error of 3 or less with a 0.95 probability when the population standard deviation equals 17 is 124.

In conclusion, a sample size of at least 124 is needed to achieve a margin of error of 3 or less with a 0.95 probability, assuming a population standard deviation of 17.

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Trevor and Kim will be situated 21 kilometers apart from each other at 1:30 PM. They will be separated by a distance of 21 km when the clock strikes 1:30 in the afternoon.

To determine at what time Trevor and Kim will be 21 km apart, we can set up a distance-time equation based on their relative speeds and distances.

Let's assume that t represents the time elapsed in hours since noon. At time t, Trevor would have traveled a distance of 8t km, while Kim would have traveled a distance of 6t km in the opposite direction.

Since they are running in opposite directions, the total distance between them is the sum of the distances they have traveled:

Total distance = 8t + 6t

We want to find the time when this total distance equals 21 km:

8t + 6t = 21

Combining like terms, we have:

14t = 21

To solve for t, we divide both sides of the equation by 14:

t = 21 / 14

Simplifying, we find:

t = 3 / 2

So, they will be 21 km apart after 3/2 hours, which is equivalent to 1 hour and 30 minutes.

Therefore, Trevor and Kim will be 21 km apart at 1:30 PM.

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For the first part, the number of license plates is: 65,780,800 and for the second part, the number of license plates with 3 consecutive digits is: 16,524,288.

If there are no restrictions on where the digits and letters are placed, the number of 8-place license plates consisting of 5 letters and 3 digits with no repetitions allowed can be found using the permutation formula:

nPr = n! / (n-r)!

where n is the number of available characters (26 letters and 10 digits) and r is the number of characters needed for the license plate (8).

Therefore, the number of license plates is:

(26 P 5) x (10 P 3) = (26!/21!) x (10!/7!) = 65,780,800

If the 3 digits must be consecutive, there are 8 possible positions for the block of digits (either the first 3, second 3, or last 3). Once the position of the block is chosen, the number of license plates can be found by counting the number of ways to arrange the letters and the block of digits. The number of ways to arrange the letters is 26 P 5, and the number of ways to arrange the block of digits is 10 (since there are only 10 possible sets of consecutive digits).

Therefore, the number of license plates with 3 consecutive digits is:

8 x (26 P 5) x 10 = 16,524,288

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The complete question goes thus:

If there are no restrictions on where the digits and letters are placed, how many 8

-place license plates consisting of 5

letters and 3

digits are possible if no repetitions of letters or digits are allowed? What if the 3

digits must be consecutive?

Answer

17/50, which is 34%.

Step-by-step explanation:

1. Add together all the numbers. They add up to 50.

2. Add together the times 1 and 3 were spun. This adds up to 17.

3. Divide 17 by 50 to get the probability.

4. 17/50 equals .34, or 34%. The probability is 34 percent.

Hope this helps!

The probability helps us to know the chances of an event occurring. The probability of the spinner landing on 1 or 3 is 0.34.

The probability helps us to know the chances of an event occurring.

\(\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)

The total number of outcomes is 50(8+6+9+11+9+7). And the outcomes that land on 1 or 3 are 17(8+9).

Therefore, the probability of the spinner landing on 1 or 3 can be written as,

\(\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\\\\\\Probability=\dfrac{\text{Number of outcome that lands on 1 or 3}}{\text{Number of total outcomes}}\\\\\\\Probability = \dfrac{17}{50} = 0.34=34\%\)

Hence, the probability of the spinner landing on 1 or 3 is 0.34.

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Chenelle can travel at most 239.31 miles without exceeding her spending limit of $300.

To figure out the maximum number of miles Chenelle can travel without exceeding her spending limit, we need to use algebra. Let's start by setting up the equation:

19.95 + 1.17x ≤ 300

In this equation, x represents the number of miles Chenelle can travel. We want to solve for x, so we need to isolate it on one side of the inequality. First, we'll subtract 19.95 from both sides:

1.17x ≤ 280.05

Next, we'll divide both sides by 1.17:

x ≤ 239.31

So Chenelle can travel at most 239.31 miles without exceeding her spending limit of $300.

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The given statement, "Andrew is studying mathematics and studying about the coordinate system. in this system, the coordinates of a point are dependent on the distance of the point from the origin, and the angle the point subtends at the origin." is False.

In the coordinate system, the coordinates of a point are not dependent on the distance of the point from the origin and the angle the point subtends at the origin. The coordinates of a point in the Cartesian coordinate system (most commonly used) are determined by the distances of the point along each of the coordinate axes (usually denoted as x and y).

The x-coordinate represents the horizontal distance of the point from the origin, and the y-coordinate represents the vertical distance of the point from the origin. The coordinates of a point are usually written as (x, y).

The distance of a point from the origin can be calculated using the Pythagorean theorem as the square root of the sum of the squares of the x-coordinate and y-coordinate. However, the distance from the origin is not a factor in determining the coordinates of a point.

The angle that a point subtends at the origin is typically referred to as the polar angle or the angle in polar coordinates. Polar coordinates are an alternative coordinate system that uses the distance from the origin and the angle to represent a point. However, in the Cartesian coordinate system, the coordinates of a point are not directly dependent on the angle it subtends at the origin.

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The probability that the sum of two fair, six-sided dice is between 3 and 11 (inclusive) is approximately 0.7222 or 72.22%. The total number of favorable outcomes is 31 + 15 = 46.

To find the probability that the sum of two fair, six-sided dice is between 3 and 11 (inclusive), we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.

The possible outcomes for rolling two dice can be represented by a sample space of 36 equally likely outcomes, as each die has 6 possible outcomes (1, 2, 3, 4, 5, 6).

We can calculate the favorable outcomes by considering the combinations of two numbers that sum to a value between 3 and 11.

To simplify the calculation, we can break down the favorable outcomes into two cases:

1. The sum is between 3 and 7 (inclusive): In this case, we have the following favorable outcomes:

  - (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

  - (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

  - (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

  - (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

  - (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

  - (6, 1), (6, 2), (6, 3), (6, 4), (6, 5)

  The total number of favorable outcomes in this case is 31.

2. The sum is between 8 and 11 (inclusive): In this case, we have the following favorable outcomes:

  - (2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6)

  - (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3)

  - (6, 4), (6, 5), (6, 6)

  The total number of favorable outcomes in this case is 15.

Therefore, the total number of favorable outcomes is 31 + 15 = 46.

Since there are 36 possible outcomes in the sample space, the probability of the sum of two dice being between 3 and 11 (inclusive) is given by:

P(sum between 3 and 11) = favorable outcomes / total outcomes = 46 / 36 = 23 / 18 ≈ 0.7222.

Hence, the probability that the sum of the two numbers showing is between 3 and 11 (inclusive) is approximately 0.7222, or 72.22%.

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Answer:

It should 3/10

Step-by-step explanation:

The equations we can use to find the lengths of the legs of the given triangle are:

100 = (x + 2)² + x²; 24 = 0.5 × (x + 2)(x); and x² + 2x - 48 = 0

To determine the lengths of the legs of a right triangle, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Thus, for the given right triangle, we can use the equation:

10² = (x + 2)² + x²

Simplifying, we get:

100 = (x + 2)² + x²

To find the area of the triangle, we use the formula:

Area of triangle = 1/2 × base × height

where the base is one of the legs of the triangle, and the height is the perpendicular distance from that leg to the opposite vertex. In this case, the two legs have lengths x and x+2, so the area is:

Area of triangle = 1/2 × (x + 2)(x)

Simplifying, we get:

24 = 0.5 × (x + 2)(x)

Expanding the right-hand side and simplifying, we get:

24 = x² + 2x / 2

Multiplying both sides by 2, we get:

48 = x² + 2x

Rearranging, we get:

x² + 2x - 48 = 0

So, to find the length of the legs of the right triangle, we need to solve the quadratic equation x² + 2x - 48 = 0.

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The value of the 2.6 pounds of steak cost $27.06 in the neighborhood grocery.

For the given question;

44 pounds of steak cost $45.80.

Let 'x' be the amount for the 2.6 pounds of steak.

Then, ratio of the quantity becomes,

44/45.80 = 26/x

On simplification,

x = (26 x 45.80)/44

x  = $27.06

Thus, the value of the 2.6 pounds of steak cost $27.06 in the  neighborhood grocery.

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The correct question is-

At the neighborhood grocery, 44 pounds of steak cost $45.80. How much would it cost to buy 2.6 pounds of steak?

An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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Answer:

17 is your answer

Step-by-step explanation:

The measure of angle KJM in the parallelogram is given as follows:

m < KJM = 129º.

In a parallelogram, the angle measures are obtained as follows:

Angle KJM is opposite to angle MLK, hence:

m < KJM = m < MLK.

By the angle addition postulate, the measure of angle MLK is given as follows:

m < MLK = m < KLO + m < MLO = 68º + 61º = 129º.

Hence the measure of angle KJM is obtained as follows:

m < KJM = m < MLK = 129º.

The problem is given by the image shown at the end of the answer.

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