The lengths of the legs of a right triangle are given. Find the hypotenuse.a =8. b = 15The length of the hypotenuse, C, is

Answer:

  c:  8,20,25

Step-by-step explanation:

You want to know which set of side lengths can form a triangle from the sets ...

A set of lengths can form a triangle if and only if the sum of the shorter two exceeds the longest.

In sets a, b, d, the sum of the shorter two is equal to the longest. These lengths will form a line segment, not a triangle.

A triangle can be formed by ...

  c: 8,20,25 . . . . . . 8+20=28 > 25

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The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.

To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:

-5/3 x² + 3x + 11 = -9 + 25/3 x²

First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:

-5x² + 9x + 33 = -27 + 25x²

Next, let's combine like terms:

-5x² - 25x² + 9x + 33 = -27

-30x² + 9x + 33 = -27

Now, let's bring all the terms to one side to have a quadratic equation equal to zero:

-30x² + 9x + 33 + 27 = 0

-30x² + 9x + 60 = 0

Finally, we have the quadratic equation in standard form:

-30x² + 9x + 60 = 0

Dividing each term by 3, we get:

-10x² + 3x + 20 = 0

(-2x + 5)(5x + 4) = -10x² + 3x + 20

So, the factored form of the equation -30x² + 9x + 60 = 0 is:

(-2x + 5)(5x + 4) = 0

Now we can set each factor equal to zero and solve for x:

-2x + 5 = 0 --> x = 5/2

5x + 4 = 0 --> x = -4/5

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Answer:

X > 2

Step-by-step explanation:

Answer:

y = (x/2) + 2

Step-by-step explanation:

Given equation,

→ 2x - 4y = -8

Solving for the value of y,

→ 2x - 4y = -8

→ -4y = -2x - 8

→ 4y = 2x + 8

→ y = (2x + 8)/4

→ [ y = (x/2) + 2 ]

Hence, the value is (x/2) + 2.

By working with fractions, we will see that the amount that Rollie borrowed from his sister is $31.50.

Let's say that Rollie borrowed a quantity x.

The first month, Rollie returns one third of x + $3, so now he owes:

x - x/3 - 3 = (2/3)*x - 3

the second month returns another third of what he owes plus $3, so now he returns:

(1/3)*((2/3)*x - 3) + 3 = (2/9)*x + 2

So no he owes:

(2/3)*x - 3 - (2/9)*x - 2 = (4/9)*x - 5

Finally, on the third month he returns:

(1/3)*((4/9)*x - 5) + 3 = (4/27)*x - 5/3 + 3 = (4/27)*x + 4/3

Now he owes:

(4/9)*x - 5 -  (4/27)*x - 4/3 = (8/27)*x - 19/3

And that is equal to $3, what he owes at the end of the third month, so we need to solve:

(8/27)*x - 19/3 = 3

(8/27)*x = 3 + 19/3 = 28/3

Solving for x, we get:

x = (27/8)*(28/3) = 31.5

So Rollie borrowed $31.5 from his sister.

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To find the mean deviation of a set of numbers, you need to first find the average (mean) of the set, and then for each number in the set, subtract the mean and take the absolute value of the result. The mean deviation is then the average of these absolute values.

For the first 10 even natural numbers (2, 4, 6, 8, 10, 12, 14, 16, 18, 20), the mean is (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20) / 10 = 60/10 = 6.

To find the mean deviation, you would subtract the mean from each number, take the absolute value of the result, and then average those values. The mean deviation of the first 10 even natural numbers is therefore (|6 - 2| + |6 - 4| + |6 - 6| + |6 - 8| + |6 - 10| + |6 - 12| + |6 - 14| + |6 - 16| + |6 - 18| + |6 - 20|) / 10 = (4 + 2 + 0 + 2 + 4 + 6 + 8 + 10 + 12 + 14) / 10 = 5.5.

So the answer is B: 5.5.

Numbers in Nature When counting or organizing objects, the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are utilized. Absolute numbers are integers and zeros. neither a fraction nor a decimal.

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Answer:

D

Step-by-step explanation:

The tangent- tangent angle x is half the difference of the intercepted arcs.

The sum of the 2 arcs on the circle = 360°, thus

lower arc = 360° - 243° = 117°, then

x = \(\frac{1}{2}\) (243 - 117)° = 0.5 × 126° = 63°

The solution to this system of linear equations y - x = 6 and y + x = -10 is (-8, -2).

y - x = 6

⇒y = x + 6

y + x = -10

⇒y = - x - 10

Since both equations are equal to y, equate them.

x + 6 = - x - 10

x + x = - 10 - 6

2x = - 16

Divide both sides by 2

x = -8

Put the value of x in either of the equations

y - x = 6

y - (-8) = 6

y + 8 = 6

y = 6 - 8

y = - 2

Therefore, the solution to the system of linear equations is (-8, -2).

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Answer:

119.4

Step-by-step explanation:

Answer:

x= 119.4

Step-by-step explanation:

Let's solve your equation step-by-step.

x + 5.8= 125.2

Step 1: Subtract 5.8 from both sides.

x + 5.8 − 5.8 = 125.2 − 5.8

x = 119.4

Okay, here we have this:

Considering that a function is one-to-one if there are no two elements in the domain of f they correspond to the same element in the range of f.

According with this we obtain that the correct answer is one-to-one function.

1) The value of P(A∩B) = 0.

2) The value of P(A|B) = 0.

3) P(A|B) is not equal to P(A). A and B are independent events.

4) The statement "Mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent." is not accurate.

5) We can conclude that mutually exclusive events have a probability of intersection of zero and are not independent.

1) Since A and B are mutually exclusive, they cannot occur at the same time, so P(A∩B) = 0.

2) The conditional probability of A given B is defined as the probability of A occurring given that B has occurred. Since A and B are mutually exclusive, if B has occurred, then A cannot occur. Therefore, P(A|B) = 0.

3) No, P(A|B) is not equal to P(A). Since B has occurred, the sample space has been reduced to only those outcomes in which B has occurred. Therefore, the probability of A given that B has occurred can only be determined from the portion of the sample space in which both A and B occur.

However, since A and B are mutually exclusive, this probability is zero. Therefore, P(A|B) ≠ P(A).

4) The statement is not accurate. Mutually exclusive events and independent events are different concepts. Two events are mutually exclusive if they cannot occur at the same time, whereas two events are independent if the occurrence of one event does not affect the probability of the other event.

If two events are mutually exclusive, they are not independent because the occurrence of one event precludes the occurrence of the other event.

5) Mutually exclusive events have a relationship where if one event occurs, the other cannot. In contrast, independent events are events where the occurrence of one event does not affect the probability of the other event occurring.

Therefore, we can conclude that mutually exclusive events and independent events are not the same concept, and we must be careful not to confuse them.

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The four points with y-coordinates half their x-coordinates are (0,0), (2,1), (4,2), and (6,3). These points do lie on a line, as they all satisfy the linear equation y = x/2.

To plot four points whose y-coordinates are half their x-coordinates, we can choose any four values of x and then compute the corresponding values of y using the equation y = x/2. For example

If x = 0, then y = 0/2 = 0, so the first point is (0,0).

If x = 2, then y = 2/2 = 1, so the second point is (2,1).

If x = 4, then y = 4/2 = 2, so the third point is (4,2).

If x = 6, then y = 6/2 = 3, so the fourth point is (6,3).

We can plot these points on a coordinate plane

As we can see from the plot, the four points do lie on a straight line. This is because the equation y = x/2 is the equation of a linear function with slope 1/2 and y-intercept 0. Therefore, any two points on this line will have a constant slope between them, and thus the four points will be collinear.

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a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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Answer:

D. Move each digit of the whole number three places to the left and fill in the blank places with zeros.

Step-by-step explanation:

Take the number 5 for example.

If you multiply this by 1,000 you get 5,000.

You may do this by moving the digit 3 places to the left which will give you

5---, then you replace the empty spaces with zeros.

The XYZ corporation will receive $1500000 for all the shares sold.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Now,

Given: Cost of 1 share = $15

To find: Money received on selling 100000 shares.

Finding:

By unitary method,

Money received on selling 1 share = $15

Money received on selling 100000 shares = 15(100000) = $1500000

Hence, The XYZ corporation will receive $1500000 for all the shares sold.

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Answer:

p = 6

Step-by-step explanation:

$7.00 × p + 3 = 45

Simplify to:

7p + 3 = 45

- 3 - 3

7p = 42

÷7 ÷7

p = 6

Answer:

x + 0.15x = OP

Step-by-step explanation:

OP= Original Price

An answer option which distinguishes the element that needs to be adjusted on the chart in the following scenario is: C. x-axis value.

In an experiment, there are two (2) main types of variables and these include the following:

In Mathematics, an independent variable can be defined as the variable that is being manipulated by an experimenter or researcher. This ultimately implies that, an independent variable is typically considered to be the cause in an experiment and it is represented by the x-axis value on a graph.

In this scenario, we can reasonably infer and logically deduce that the independent variable (x-axis value) represents the element that should be adjusted on Donna's demographic chart on population growth.

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The 95% confidence interval for the true population mean, based on a sample with a sample size (n) of 225, a sample mean (X) of 8.5, and a sample standard deviation (σ) of 45, is (2.62, 14.38).

To calculate the confidence interval, we can use the formula:

Confidence interval = X ± Z * (σ/√n)

where X is the sample mean, Z is the critical value for the desired level of confidence (in this case, 95%), σ is the sample standard deviation, and n is the sample size.

The critical value Z can be obtained from a standard normal distribution table or calculated using statistical software. For a 95% confidence level, the Z-value is approximately 1.96.

Plugging in the values into the formula, we get:

Confidence interval = 8.5 ± 1.96 * (45/√225)

                 = 8.5 ± 1.96 * (45/15)

                 = 8.5 ± 1.96 * 3

Calculating the upper and lower bounds of the confidence interval:

Upper bound = 8.5 + 1.96 * 3

          = 8.5 + 5.88

          = 14.38

Lower bound = 8.5 - 1.96 * 3

          = 8.5 - 5.88

          = 2.62

Therefore, the 95% confidence interval for the true population mean is (2.62, 14.38).

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When booking a show for a future date, it is normal practice for the booking agent to collect a 50% advance fee when the advances are not given for shows. This is to ensure that the performer is fully committed to performing at the event and to cover any expenses that may be incurred in the process.

The advance fee is usually non-refundable and is paid by the promoter or venue operator to the booking agent. This is to show their commitment to the performer and to demonstrate that they are serious about booking them for the event. The remaining balance is then usually paid on the day of the performance or shortly after.

The booking agent should also ensure that all parties involved in the booking are aware of the terms and conditions and have signed a contract or agreement to confirm their agreement.

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Answer:

Plug in a = x, b = 16, c = 20

Step-by-step explanation:

The list price of the gift basket is $65.20. This can be determined by taking the total charge of the gift basket ($45.20) and subtracting the shipping charge of $5.50. The remaining $39.70 is the discounted amount of the gift basket.

Since the gift basket was discounted by 30%, the original list price can be determined by dividing the discounted amount by 70%, which is 0.7. Then, the list price can be calculated by multiplying the discounted amount by 1.43 (the reciprocal of 0.7). Therefore, the list price of the gift basket is $65.20.

This method of calculating the list price of the gift basket is called reverse-discounting. The process of reverse-discounting involves subtracting the discounted amount from the total charge to get the original list price. This method is useful when the discount rate is known and the total charge is given. It allows for the original list price of the item to be determined quickly and accurately.

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The parent function of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)

Parent functions are the basic function that represents the entire family of that function family

The function is given as;

g(x) = 3cos (x + 180°) + 1

As a general rule, the parent function of any function is the basic equation of the function family

The basic equation of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)

Hence, the parent function of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)

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Answer:

Diameter: Line segment BC

Chord: line segment DE

Radius: line segment GA

Step-by-step explanation:

Diameter: all the way across circle, going through center

Radius: half of diameter

Chord: connects two points of circle, not through center (since then it would be diameter)

The result of an average of more than 100% in a survey of tenants on cleaning chores in shared apartments is likely due to social desirability bias.

The average tenant response of more than 100% in a study about cleaning duties in shared apartments is probably the product of social desirability bias. Social desirability bias occurs when respondents give answers that they think are socially acceptable or desirable, rather than their true opinions or behavior.

In this case, tenants may have overstated their contribution to cleaning the apartment, in order to appear more helpful or responsible, leading to an average percentage higher than 100%.

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