which relation is not a function?
A) (1,2)(2,10)(4,5)
b) (-3,5)(3,5)(5,6)
c) (3,6)(6,3)(3,2)
d) (1,6)(-1,6)(2,2)​

Answer:

is finding the square root

The inverse operation of squaring a number is finding the square root of that number. The square root of a number "x" is the value that, when squared, gives the original number.

When a number is squared, it is multiplied by itself. For example, squaring the number 4 gives 4^2 = 16.

The inverse operation undoes the effect of squaring and returns you to the original number. In this case, finding the square root of a number is the inverse operation of squaring.

The square root of a number "x" is a value that, when squared, gives the original number. It is denoted by the symbol √x.

For example, if you have the number 25 and you want to find its square root, you calculate:

√25 = 5

5 is the square root of 25 because when you square 5 (5^2), you get 25.

The inverse operation of squaring a number is finding the square root of that number. The square root of a number "x" is the value that, when squared, gives the original number. The concept of square root and squaring are inverse operations that are used in various mathematical calculations and problem-solving.

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Answer:

(-5,2)

Step-by-step explanation:

Answer:

x ≥ −5

Step-by-step explanation:

I'm pretty sure this is the answer.

if it isn't, I'm sorry for disappointing you.

Answer:

x - 27

Step-by-step explanation:

Our goal here is to solve for x.

Start by performing the indicated multiplication:

-5(x+4) + -3x + -9x+-7  =>  -5x - 20 - 3x + 9x - 7

Combine like terms:  x - 27

Answer:

\(-5(x+4) + -3x + -9x+-7\)

\(\longmapsto -5\left(x+4\right)+\left(-3\right)x+\left(-9\right)x+\left(-7\right)\)

\(\longmapsto -5\left(x+4\right)-3x-9x-7\)

\(\longmapsto -5(x+4)=-5x-20\)

\(\longmapsto -5x-20-3x-9x-7\)

\(\longmapsto =-17x-27\)

\(ANSWER:=-17x-27\)

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

hope it helps....

have a great day!!

The maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.

To determine the maximum price Matthew can pay for the car, we need to consider his repayment capability and the terms of the loan.

Matthew can make annual repayments of $35,000. Since the loan term is six years, the total amount he can repay over the loan period is $35,000 multiplied by six, which equals $210,000.

To calculate the maximum price of the car, we need to account for the interest rate of 9.25%. The interest rate represents the cost of borrowing and is applied to the loan amount.

Let's assume the loan amount is denoted by P.

The formula to calculate the future value of a loan with interest is:

FV = P(1 + r)^n

Where:

FV = Future value (total amount repaid)

P = Principal amount (maximum price of the car)

r = Interest rate per period (9.25% or 0.0925)

n = Number of periods (six years)

Since Matthew can repay a total of $210,000 over the loan period, we can set up the equation:

$210,000 = P(1 + 0.0925)^6

Now we can solve for P:

P = $210,000 / (1 + 0.0925)^6

Evaluating this expression, we find:

P ≈ $126,318.29

Therefore, the maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.

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Answer:

Step-by-step explanation:

The probability the mean age at heart attack after using cocaine is greater than 42 is 0.9192. Hence, the correct option is D. 0.9192.

The standard deviation of the age of people who suffered heart attacks soon after using cocaine was 10 years. In a random sample of size 49, what is the probability the mean age at heart attack after using cocaine is greater than 42?We are given the following details:

The mean age of people in the study who suffered heart attacks soon after using cocaine was only 44.

Standard deviation = 10

Sample size = 49

Now we need to find the z-score using the formula:

z = (x - μ) / (σ / √n)

wherez is the z-score

x is the value to be standardized

μ is the mean

σ is the standard deviation

n is the sample size.

Substitute the values in the formula as given,

z = (42 - 44) / (10 / √49)z = -2 / (10/7)

z = -1.4

Probability of z > -1.4 can be found using the standard normal distribution table or calculator.

P(z > -1.4) = 0.9192

Therefore, the probability the mean age at heart attack after using cocaine is greater than 42 is 0.9192. Hence, the correct option is D. 0.9192.

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Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

```

A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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B

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A

```

We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

The sample space of the experiment of rolling three fair coins consists of all possible outcomes when three coins are tossed simultaneously. Therefore, there are 2 x 2 x 2 = 8 possible outcomes in the sample space.

In this experiment, we are rolling three fair coins. To find the number of elementary events in the sample space, we need to consider all possible outcomes.

An elementary event is an individual outcome in the sample space. The sample space is the set of all possible outcomes for an experiment. In this case, each coin can have 2 possible outcomes: heads (H) or tails (T).
Each outcome in the sample space is an elementary event, which is an outcome that cannot be further broken down into simpler outcomes. Therefore, there are 8 elementary events in the sample space of this experiment.

Since there are three coins, we can determine the number of elementary events in the sample space by multiplying the number of outcomes for each coin: 2 (for the first coin) x 2 (for the second coin) x 2 (for the third coin) = 8.

So, there are 8 elementary events in the sample space of this experiment. The correct answer is c. 8.

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Answer:

(16,-2)

Step-by-step explanation:

The equation of the tangent to the curve without eliminating the parameter is \(y - cos^2(1/2) = -2sin(1/2) \times cos(1/2)(x - sin(1/2)).\)

The equations of the tangents to the curve by first eliminating the parameter is \(y - cos^2(1/2) = -1 / (2sin(1/2))(x - sin(1/2))\).

To find the equation of the tangent to the curve without eliminating the parameter, we need to find the derivative of both x and y with respect to t.

Given x = sin(t) and y = cos^2(t), we can find the derivatives as follows:

dx/dt = cos(t)
dy/dt = -2sin(t) * cos(t)

Now, we need to find the values of t for which the tangent is desired. Let's substitute the values t = 2 and t = 1/2 into the derivatives:

When t = 2:
dx/dt = cos(2)
\(dy/dt = -2sin(2) \times cos(2)\)

When t = 1/2:
dx/dt = cos(1/2)
\(dy/dt = -2sin(1/2) \times cos(1/2)\)
Now, we have the slopes of the tangents at the given points. Let's use the point-slope form of a line to find the equations of the tangents.

For t = 2:
y - y1 = m(x - x1), where (x1, y1) is the point \((sin(2),cos^2(2))\)

Substituting the values, we get:
\(y - cos^2(2) = -2sin(2) \times cos(2)(x - sin(2))\)

For t = 1/2:
y - y1 = m(x - x1), where (x1, y1) is the point \((sin(1/2), cos^2(1/2))\)

Substituting the values, we get:
\(y - cos^2(1/2) = -2sin(1/2) \times cos(1/2)(x - sin(1/2))\)
This is the equation of the tangent to the curve without eliminating the parameter.

To find the equation of the tangent by eliminating the parameter, we can solve the given equations to express x in terms of y and then find the derivative of x with respect to y.

From the equation x = sin(t), we can express t in terms of x as t = arcsin(x).

Now, substitute this value of t into the equation y = cos^2(t):
\(y = cos^2(arcsin(x))\)
To eliminate the parameter, we need to find the derivative of x with respect to y:
dx/dy = dx/dt * dt/dy

We already found dx/dt as cos(t), and dt/dy can be found by taking the reciprocal of dy/dt.
So, \(dt/dy = 1 / (dy/dt) = 1 / (-2sin(t) \times cos(t))\)

Substituting the values, we get:
dx/dy = cos(t) / (-2sin(t) * cos(t))

Simplifying further, we get:
dx/dy = -1/(2sin(t))

Now, substitute the values t = 2 and t = 1/2 into the derivative:

When t = 2:
dx/dy = -1/(2sin(2))

When t = 1/2:
dx/dy = -1/(2sin(1/2))

Now, we have the slopes of the tangents at the given points. Let's use the point-slope form of a line to find the equations of the tangents.

For t = 2:
y - y1 = m(x - x1), where (x1, y1) is the point \((sin(2), cos^2(2))\)

Substituting the values, we get:
\(y - cos^2(2) = -1 / (2sin(2))(x - sin(2))\)

For t = 1/2:
y - y1 = m(x - x1), where (x1, y1) is the point \((sin(1/2), cos^2(1/2))\)

Substituting the values, we get:
\(y - cos^2(1/2) = -1 / (2sin(1/2))(x - sin(1/2))\)

These are the equations of the tangents to the curve by first eliminating the parameter.

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The range that is appropriate to use to represent the numerical data is 0.0 to 26.0.

A line graph is a graph that is used to represent numerical data. It shows the changes in the data with the passage of time. There are two axes on a line graph, the vertical axis and the horizontal axis. The range of the vertical axis should start from 0 and end at the largest number of data set.

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Solution

Blue = 21%

Brown = 14 %

green = 18%

orange =21 %

red = 11%

yellow = 15%

Total = 100 %

(1)

The probability that it would be red or blue?

(2) The probability that it wouldn’t be yellow?

(3) The probability that they would both be orange

the time required for an investment of $5000 to grow to $\(7200\) at an interest rate of  \(7.5\) percent per year, compounded quarterly, is approximately  \(3.79\) years.

o find the time required for an investment of $5000 to grow to $7200 at an interest rate of 7.5 percent per year, compounded quarterly, we can use the formula for compound interest:

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

where:

A = the final amount (in this case, $7200)

P = the principal amount (in this case, $5000)

r = the annual interest rate (in decimal form, so 7.5% = 0.075)

n = the number of times the interest is compounded per year (in this case, quarterly, so n = 4)

t = the number of years (which we need to find)

Plugging in the values, we get:

\(7200 = 5000(1 + 0.075/4)^(4t)\)

Now we can solve for t by isolating it on one side of the equation.

Dividing both sides by 5000:

Taking the natural logarithm of both sides:

\(ln(7200/5000) = ln((1 + 0.075/4)^(4t))\)

Using the property of logarithms that ln(a^b) = b * ln(a):

\(ln(7200/5000) = 4t\times ln(1 + 0.075/4)\)

Dividing both sides by \(4 \times ln(1 + 0.075/4):\)

\(t = ln(7200/5000) / (4 * ln(1 + 0.075/4))\)

Using a calculator, we can find the value of t to be approximately 3.79 years (rounded to two decimal places).

Therefore, the time required for an investment of $5000 to grow to $7200 at an interest rate of 7.5 percent per year, compounded quarterly, is approximately 3.79 years.

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Answer:

42x_19x=-28-18

Step-by-step explanation:

23x=10

23x/23=10/23

12 will be the value of x.

Interior angles on the same side of the transversal are also referred to as consecutive interior angles or allied angles or co-interior angles.

∠3 and ∠5 are co-interior angles,

So,

∠3 + ∠5 = 180°

9x-16+7x+4 = 180°

16x -12 = 180°

16x = 192

x = 12

Therefore, the value of x will be 12.

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The APR if the finance terms are $21.99 per week for 52 weeks is 83.48%. Hence option 4 is correct.

The annual percentage rate, or APR, is the interest rate that is charged on a loan balance that is still outstanding. The expected cost of the annual fees connected with a certain sort of borrowing is what the APR conceptually reflects.

APR is a commonly used formula by lenders that enables borrowers to compare various loan choices. The stated interest rate on a loan is typically insufficient on its own to help borrowers choose the best loan option.

A loan with a low stated interest rate could also have significant costs attached that should not be disregarded. The best alternative might be a loan with a smaller fee structure and a higher advertised interest rate. APR is calculated as (Periodic Interest Rate x 365 Days) x 100 i.e.

\($\mathrm{APR=\left(\left(\frac{\frac{Fees+Interest}{Principal}}{n} \right) \times 365 \right) \times 100}\)

​where:

Interest = Total interest paid over life of the loan

Principal = Loan amount

n = Number of days in loan term

Fees = 0

​Interest = 2​Interest = $519.48

Principal = $624.00

n = 52 × 7 = 364 days

Plug the data in the formula:-

\($\mathrm{APR=\left(\left(\frac{\frac{0+519.48}{624}}{364} \right) \times 365 \right) \times 100}\)

APR = 83.48%

Thus, The APR if the finance terms are $21.99 per week for 52 weeks is 83.48%. Hence option 4 is correct.

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Let's solve the problem step by step.According to the given data;Farmer Jones has x sheepFarmer Smith has 100 more sheep than Farmer Jones. Thus, Farmer Smith has x + 100 sheep.Farmer White has twice as many sheep as Farmer Jones. Thus, Farmer White has 2x sheep.The total number of sheep is 2500. So; x + x + 100 + 2x

= 25004x + 100

= 25004x

= 2500 - 1004x

= 2400x

= 2400/4x

= 600

Therefore, Farmer Jones has 600 sheep. Farmer Smith has 600 + 100 = 700 sheep.

Farmer White has 2(600) = 1200 sheep.

Therefore, there are 600 + 700 + 1200 = 2500 sheep.

The content describes the number of sheep owned by three farmers: Farmer Jones, Farmer Smith, and Farmer White. It provides the following information:

1. Farmer Jones has "x" number of sheep. The exact number of sheep owned by Farmer Jones is not specified.

2. Farmer Smith has 100 more sheep than Farmer Jones. This means Farmer Smith's sheep count is "x + 100."

3. Farmer White has twice as many sheep as Farmer Jones. Therefore, Farmer White's sheep count is "2x."

4. The total number of sheep owned by all three farmers combined is 2500.

So, to summarize:

- Farmer Jones: x sheep

- Farmer Smith: x + 100 sheep

- Farmer White: 2x sheep

- Total sheep count: x + (x + 100) + 2x = 2500

From this information, we can solve for the value of "x" and calculate the number of sheep each farmer owns.

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Considering the given information the number of sheep with the farmers will be:

Farmer Jones has 600 sheep.

Farmer Smith has 700 sheep.

Farmer White has 1200 sheep.

Let's suppose that the number of sheep Farmer Jones has is x

.Therefore, Farmer Smith has 100 more sheep than Farmer Jones has.

The number of sheep Farmer Smith has can be given by the equation:

              x + 100

Farmer White has twice as many sheep as Farmer J has.

Hence, the number of sheep Farmer White has is:

                               2 x

Now, the sum of the sheep Farmer Jones, Farmer Smith and Farmer White have is 2500.

Sheep Farmer Jones has = x

Sheep Farmer Smith has = x + 100

Sheep Farmer White has = 2x

Therefore,

x + x + 100 + 2x = 2500

4x + 100 = 2500

4x = 2500 - 100

4x = 2400

x = 2400/4

x = 600

Therefore, Farmer Jones has 600 sheep. Farmer Smith has 600 + 100 = 700 sheep. Farmer White has 2 * 600 = 1200 sheep.

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To show that every amount greater than 17 dollars can be made from a combination of 3-dollar and 10-dollar bills, we can use a technique called "proof by induction."

First, let's check the base case: can we make 18 dollars using only 3-dollar and 10-dollar bills? Yes, we can use two 3-dollar bills and one 10-dollar bill: 3 + 3 + 10 = 16.

Now, let's assume that we can make any amount greater than n dollars using only 3-dollar and 10-dollar bills. We want to prove that we can make any amount greater than n+1 dollars as well.

To do this, we can consider two cases:

1. The amount we want to make includes at least one 10-dollar bill. In this case, we can subtract 10 dollars from the amount and use our induction hypothesis to make the remaining amount using only 3-dollar and 10-dollar bills. Then we add the 10-dollar bill back in, and we have made the original amount.

2. The amount we want to make does not include any 10-dollar bills. In this case, we can use our induction hypothesis to make the amount n-7 using only 3-dollar and 10-dollar bills (since 10 - 3 = 7). Then we add a 10-dollar bill and a 3-dollar bill to get n+3, and we can add another 3-dollar bill to get n+6. Finally, we add one more 3-dollar bill to get n+9, which is greater than n+1.

Therefore, we have shown that any amount greater than 17 dollars can be made from a combination of 3-dollar and 10-dollar bills using proof by induction.

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The number of trees saved by this process is 68trees

A rate is a ratio in which the two terms being compared have different units.For example, *

3 guest to a table. Rates often use the word per. Therefore we can say 3guest per table.

Similarly I tonne of recycled office paper save 17trees.

If 1 tonne = 2000pounds

then 2000pounds save 17trees

therefore 1 pound will save 17/2000 trees

8000 pounds will therefore save 17/2000× 8000

= 17×4= 68 trees

Therefore 8000pounds of recycled office paper will save 68 trees.

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Answer:

18 + √3

Step-by-step explanation:

The product of a surd and its conjugate gives a rational number. Hence;

(18 - √3) (18 + √3)

=324 + 18√3 - 18√3 - 3

=321

A rational number does not contain any surd, hence the answer.

Answer: cube root 1/18 & cube root 12

The correct option is option (A) . Using Scatter plots,

Visulazation by scatter plots show the association and the distribution of Y changes as X changes.

Scatter plots:

A scatterplot plots pairs of numeric data using one variable on each axis to explore the relationship between them. If the variables are correlated, the points are along a straight line or curve.

A correlation exists between two variables if one of them is related to the other in some way. A scatterplot is a great place to start. A scatterplot (or scatterplot) is a graph of paired (x,y) sample data with a horizontal x-axis and a vertical y-axis. Each unique (x,y) pair is represented as one point.

Thus, the Visual examination of a scattergram indicates the existence of an association between variables and change in Y with change in X .

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The graph of the inequality y^2 > 0 represents all real numbers except y = 0.

The graph of the inequality y < 30 represents all real numbers less than 30.

The inequality y^2 > 0 represents all values of y where y squared is greater than 0. Since the square of any nonzero number is always positive, the solution is all real numbers except y = 0, which can be graphed as a number line with an open circle at y = 0.

The inequality y < 30 represents all values of y that are less than 30. This can be graphed as a horizontal line on the y-axis with an open circle at y = 30, indicating that 30 is not included in the solution set.

For the real-world applications, let's solve them step-by-step:

Two numbers add up to 144. One number is half the square of the other number.

Let's assume the two numbers are x and y. We have the following system of equations:

x + y = 144 (Equation 1)

x = (1/2)y^2 (Equation 2)

From Equation 1, we can solve for x in terms of y: x = 144 - y.

Substituting this into Equation 2, we get 144 - y = (1/2)y^2.

Rearranging the equation, we have: (1/2)y^2 + y - 144 = 0.

Now we can solve this quadratic equation for y. Once we find the value(s) of y, we can substitute them back into Equation 1 to find the corresponding values of x.

The squares of two numbers add to 1,156. The second number is the square root of three times the square of the first number.

Let's assume the two numbers are x and y. We have the following system of equations:

x^2 + y^2 = 1156 (Equation 1)

y = √(3x^2) (Equation 2)

Substituting Equation 2 into Equation 1, we get: x^2 + (√(3x^2))^2 = 1156.

Simplifying, we have x^2 + 3x^2 = 1156.

Combining like terms, we get 4x^2 = 1156.

Now we can solve this quadratic equation for x. Once we find the value(s) of x, we can substitute them back into Equation 2 to find the corresponding values of y.

Remember to leave a 1 line space between paragraphs in your answer.

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The best description of the transformation for the image being projected on the retina is A. A dilation with a scale factor between 0 and - 1 and center at the nodal point.

An mage is inverted and reversed as it passes through the lens of the eye, and is then projected upside down and reversed onto the retina. The process of transforming the image is called "rectification."

In mathematical terms, a dilation would have taken place because the object was shrunken by the eyes at the nodal point. When an object shrinks , then the scale factor is between 0 and 1 but because this image is inverted, the scale factor is between 0 and - 1.

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Answer: 42 parcels total.

each parcel contains 6 tins of beans in each parcel, 4 chocolate bars, and 7 packets of soup.

Answer:

The number of packages is 42.

The contents of each package is 4 chocolate bars, 6 tins of beans, 7 packets of soup.

Step-by-step explanation:

We need to find the greatest common factor (GCF) of the three numbers to find the number of packages.

168 = 2³ × 3 × 7

252 = 2² × 3² × 7

294 = 2 × 3 × 7²

GCF = 2 × 3 × 7 = 42

The number of packages is 42.

168/42 = 4

252/42 = 6

294/42 = 7

The contents of each package is 4 chocolate bars, 6 tins of beans, 7 packets of soup.

The solution x = 2 is valid for the original equation.

To solve the rational equation (4/x) = (3x + 2)/x², we can start by multiplying both sides of the equation by x² to eliminate the denominators:

x² * (4/x) = x² * [(3x + 2)/x²]

Simplifying:

4x = 3x + 2

Next, we can isolate the x term by subtracting 3x from both sides:

4x - 3x = 3x + 2 - 3x

x = 2

So, the solution to the rational equation is x = 2.

Now, let's check for extraneous solutions by substituting x = 2 back into the original equation:

(4/2) = (3(2) + 2)/(2²)

2 = (6 + 2)/4

2 = 8/4

2 = 2

Since the equation is true when x = 2, there are no extraneous solutions.

Therefore, for the initial equation, x = 2 is a viable answer.

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Answer:

The 3rd:

f(x) = (x - 1)(x - 1)(x – 6)

Step-by-step explanation:

Its roots are the x-values for which f(x)=0, that are:

x1=1

x2=1

x3=6