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The hypotenuse of a right triangle is 13 cm long. The length of one leg is 7 cm longer than the other. Find the lengths of the legs.

The appropriate null hypothesis for the company to test depends on the specific study or experiment being conducted.

However, in the given options, option C is the appropriate null hypothesis for the company to test. This hypothesis states that the proportion of people in the population who trust each brand is the same for all five brands. This hypothesis can be tested using statistical methods to determine if there is a significant difference in trust levels between the five brands. Options A and B are not appropriate null hypotheses as they do not make a specific statement about the relationship between the variables being studied. Option D is an alternative hypothesis, which suggests that there is a difference in trust levels between at least one of the brands and the other four.

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To find the product of the mode and median of the set 8,3,1,7,3,4,8,3,4,9,5, we first need to find the mode and median of the set.

The mode is the number that appears most frequently in a data set. In this case, the number 3 appears three times in the set, which is more than any other number. So the mode of this set is 3.

The median is the middle value when a data set is ordered from least to greatest. To find the median, we first need to put the numbers in order: 1,3,3,3,4,4,5,7,8,8,9. Since there are an odd number of numbers in the set (11), the median is the middle number. In this case, the median is 4.

So the product of the mode and median of this set is 3 * 4 = 12.

Answer:

med = 3

mode = 4

product of mode and median = 12

Step-by-step explanation:

1) Rearrange terms 1,3,3,3,4,4,5,7,8,9

2) Multiply terms 4 x 3 = 12

John needs to make an annual beginning-of-the-year payment of approximately $369,238.68 to fund the estimated college costs of $196,000 in 10 years, given the after-tax rate of return of 8.65% compounded annually.

To compute the annual beginning-of-the-year payment necessary to fund the estimated college costs, we can use the present value of an annuity formula.

The present value of an annuity formula is given by:

P = A * [(1 - (1 + r)^(-n)) / r],

where P is the present value, A is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, John wants to accumulate $196,000 in 10 years, and the interest rate he can earn is 8.65% compounded annually. Therefore, we can substitute the given values into the formula and solve for A:

196,000 = A * [(1 - (1 + 0.0865)^(-10)) / 0.0865].

Simplifying the expression inside the brackets:

196,000 = A * (1 - 0.469091).

196,000 = A * 0.530909.

Dividing both sides by 0.530909:

A = 196,000 / 0.530909.

A ≈ 369,238.68.

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The correct answer is row number 16 since the sum is 65536 in

pascal's triangle which equals to the 2 power of 16 , that is 4th option.

Pascal's triangle, in algebra, a triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression, such as (x + y)n. This triangle is the triangular array of numbers that begins with 1 on the top and with 1's running down the two sides of a triangle. In any row of Pascal's triangle, the sum of the first, third, fifth, … numbers is equal to the sum of the second, fourth, sixth numbers.

(1+x)n=(n0)+(n1)x+(n2)x2+⋯+(nr)xr+⋯+(nn−1)xn−1+(nn)xn.

We know that , 2^16 = 65536

Therefore, the numbers come from the row number.16

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The correct answer is option C. At the point (2,1) on the curve x² - xy + y²= 3, the derivative dy/dx exists, and the tangent line at that point is neither horizontal nor vertical.

To determine the correct option, we need to analyze the properties of the curve x² - xy + y² = 3 at the point (2,1). First, let's find the derivative dy/dx. Taking the derivative of the given equation implicitly with respect to x, we get:

2x - y - x(dy/dx) + 2y(dy/dx) = 0

Rearranging the terms, we have:

dy/dx = (2x - y) / (x - 2y)

Now, substituting the values x = 2 and y = 1 into the expression for dy/dx, we can determine its value at the point (2,1):

dy/dx = (2(2) - 1) / (2 - 2(1)) = 3 / 0

Since the denominator is zero, dy/dx is undefined at (2,1). Therefore, option D, stating that dy/dx does not exist at (2,1) and the tangent line at that point is vertical, is incorrect.

However, we can still determine the nature of the tangent line at (2,1). Although the derivative is undefined, it is still possible for the tangent line to exist and have a defined slope. In this case, the tangent line would be neither horizontal nor vertical. Therefore, option C, which states that dy/dx exists at (2,1) and the tangent line at that point is neither horizontal nor vertical, is the correct answer.

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Answer:

The intercept form of the equation of a line is x/a + y/b = 1. This is one of the important forms of equations of a line.

Step-by-step explanation:

The percentage of all patients who took the test had a true negative result is given as follows:

18%.

Two parameters are used to calculate a percentage, as follows:

The proportion is given by the number of desired outcomes divided by the number of total outcomes, while the percentage is the proportion multiplied by 100%.

For the true negative tests, we have those are the people that tested negative and did not have the disease, hence the percentage is given as follows:

18%.

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They rented out 5 self-propelled mowers and 20 riding mowers.

Data;

To solve this problem, we have to write a system of equations to represent the problem.

since we have

Let's write equations with these variables.

\(x+y = 25...equation (i)\\20x+40y = 900...equation(ii)\)

From equation (i)

\(x+y= 25\\x = 25 - y...equation(iii)\)

Put equation (iii) into equation (ii)

\(20x+40y=900\\x = 25-y\\20(25-y)+40y=900\\\\500-20y+40y=900\\500+20y=900\\20y=900-500\\20y=400\\\frac{20y}{20}=\frac{400}{20}\\ y=20\)

Let's substitute the value of y into equation(i)

\(x+y =25\\x+20 = 25\\x = 25 - 20\\x = 5\)

From the calculations above, they rented 5 self-propelled mowers and 20 riding mowers.

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The acceleration produced by a car will decrease as its mass rises. Less acceleration will be recorded by the computer system, which will cause a drop in the acceleration value on the graph.

Graph:

An organized visual representation of any data in mathematics is called a graph. The graph shows the correlation between the variable values. In graph theory, a graph is used to represent the collection of objects that are somehow connected to one another. In essence, the objects' vertices or nodes are mathematical concepts, and the connections between the nodes are represented by the edges. Different types of graphs are used in mathematics and statistics to visually display data. The discipline of graph theory is the study of points and lines. It is a field of mathematics that specializes in the study of graphs. This image visually illustrates the mathematical truth. The graph theory is used to study relationships.

Complete question:

Use the image to answer the question. Students are using the experimental setup shown in the image in which the two ends of a string are attached to a car and to a hanger. The students conduct three trials in which they place metal discs on the hanger to manipulate the force applied to the car. As a result, the car accelerates along the table while two photogate probes collect motion data. On the fourth trial of this experiment, a student places some discs on the car by mistake. In 1-2 sentences, explain how this mistake will affect the graphs produced by the computer.

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It will take 5 minutes to print a batch of newspapers if 20 printers are used.

What is proportionality?

Proportionality is a mathematical relationship between two variables, where one variable is a constant multiple of the other. In other words, two quantities are proportional if they maintain a constant ratio to each other, meaning that as one quantity increases or decreases, the other quantity changes in the same proportion.

We are given that the time it takes to print a batch of newspapers, m, is inversely proportional to the number of printers used, n, and the equation of proportionality is:

m = k/n

where k is a constant of proportionality. We are also given that when k = 100, the equation is satisfied. So we can substitute k = 100 into the equation to get:

m = 100/n

To find the time it will take to print a batch of newspapers if 20 printers are used, we can substitute n = 20 into the equation:

m = 100/20 = 5

So it will take 5 minutes to print a batch of newspapers if 20 printers are used. Rounded to 1 decimal place, the answer is 5.0 minutes.

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Answer:

04x=24

Step-by-step explanation:

04x=24

divide both sides by 4 to let x stand alone

04x÷4=24÷4

x=6

To find the dimensions of a similar triangular prism, we need to consider the proportional relationship between the corresponding sides of the two prisms.

A similar triangular prism maintains the same shape as the original prism but can have different dimensions. The key is that the ratios between corresponding sides remain constant.

Let's assume the dimensions of the similar triangular prism are represented by the variables "x," "y," and "z" for length, width, and height, respectively.

To determine the dimensions, we can set up the following ratios based on the given prism:

Length ratio: x/16 = y/10 = z/6

Width ratio: x/16 = y/10 = z/6

Height ratio: x/16 = y/10 = z/6

Now, we can solve for "x," "y," and "z" by cross-multiplying and simplifying:

x/16 = y/10 = z/6

Simplifying the ratios, we have:

10x = 16y

6x = 16z

To find a set of dimensions that satisfies these equations, we can choose any values for "x," "y," and "z" that maintain this ratio relationship. For example, we can let x = 8, y = 5, and z = 3, which satisfies the equations.

Therefore, a similar triangular prism would have dimensions of 8 cm for length, 5 cm for width, and 3 cm for height.

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The value of 7 in the product of 279×10 is,

⇒ 700

We have to given that;

To find value of 7 in the product of 279×10 .

Now, WE can find the product as;

⇒ 279 x 10

⇒ 2790

Hence, By place value we get;

The value of 7 in the product of 279×10 is,

⇒ 700

Thus, The value of 7 in the product of 279×10 is,

⇒ 700

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The penny will fall from distance of 232 feet during the 8th second only, as it falls 960 feet in the first 8 seconds, but 728 feet in the first 8 seconds.

The distance the penny falls each second is increasing by 32 feet (16 feet + 32 feet = 48 feet, 48 feet + 32 feet = 80 feet, and so on). Therefore, during the 8th second, the distance it will fall is:

16 + 48 + 80 + ... + (8 - 1) * 32 feet

Using the formula for the sum of an arithmetic sequence, we get:

(8 / 2) * (16 + (8 - 1) * 32) feet

= 4 * (16 + 7 * 32) feet

= 4 * 240 feet

= 960 feet

So the penny will fall 960 feet during the first 8 seconds. However, we need to subtract the distance it fell during the first 7 seconds to find the distance it fell during the 8th second only. The total distance it fell during the first 7 seconds is:

16 + 48 + 80 + ... + (7 - 1) * 32 feet

= (7 / 2) * (16 + (7 - 1) * 32) feet

= 3.5 * (16 + 6 * 32) feet

= 3.5 * 208 feet

= 728 feet

Therefore, the penny will fall 960 - 728 = 232 feet during the 8th second only.

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Answer:

<stv and <stq

Step-by-step explanation:

adjacent angles have the same vertex and are side by side.

We substitute the values into the formula. Let's calculate one of them as an example, P(X=8) = (12 choose 8) * (0.596⁸) * (1-0.596)¹²⁻⁸.

The binomial distribution can be used to calculate the probability of getting a certain number of successes in a fixed number of independent trials, where each trial has the same probability of success. In this case, we have a weighted coin with a 0.596 probability of landing on heads. We want to find the probability of getting more than 7 heads when the coin is tossed 12 times.

To calculate this probability, we can use the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

Where:
- P(X=k) is the probability of getting exactly k successes
- n is the number of trials (12 tosses in this case)
- k is the number of successes (more than 7 heads in this case)
- p is the probability of success on each trial (0.596)
- (n choose k) represents the number of combinations of n items taken k at a time

In this case, we need to find the probability of getting more than 7 heads, so we sum up the probabilities of getting 8, 9, 10, 11, and 12 heads:

P(X>7) = P(X=8) + P(X=9) + P(X=10) + P(X=11) + P(X=12)

To calculate each individual probability, we substitute the values into the formula. Let's calculate one of them as an example:

P(X=8) = (12 choose 8) * (0.596⁸) * (1-0.596)¹²⁻⁸

We repeat this calculation for each value of k, and then sum up the probabilities. Finally, we round the answer to 3 decimal places, if necessary.

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Answer:0.427

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

Because 3x4 = 12, and 12 is the number on the other side of the triangle because the sides are equal.

Hope this helps! :)

The equation represents a circle that has a diameter of 12 units will be x² + (y - 3)² = 36. Hence, option A is correct.

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

As per the provided information in the question,

Use the equation of a circle,

(x -a)² + (y - b)² = r²

Here, a and b represent the center of the circle and r is the radius of the circle.

A center can be anywhere along the y-axis if it is (0, 3).

(x -0)² + (y - 3)² = 6²

x² + (y - 3)² = 36

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The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .

In the question ,

it is given that ,

The random variable X is said to be normally distributed  ,

the mean is given as , μ = 70 , and

standard deviation of normal distribution is  (σ) = 10

probability that X is between 72 and 84 is written as P(72 < X < 84)

= P((72 - 70)/10 \(<\) Z \(<\) (84 - 70)/10)

= P(0.2 < Z < 1.4)

= P(0 \(<\) Z \(<\) 1.4) – P(0 \(<\) Z \(<\) 0.2)

From the z table , we get the values as

= 0.4192 – 0.0793

= 0.3399

≈ 0.340

Therefore , The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .

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Answer: It's A

Step-by-step explanation:

Answer:

hmm..

Step-by-step explanation:

There are various techniques to simplify algebraic expressions, including:

1. Combining like terms: In an algebraic expression, like terms are terms that have the same variable raised to the same power. To simplify the expression, we can combine these like terms. For example, in the expression 3x + 2y + 5x - 4y, we can combine the x terms and the y terms to get 8x - 2y.

2. Distributing: When a number or variable is outside a set of parentheses and is being multiplied by a sum or difference inside the parentheses, the number or variable can be distributed to each term inside the parentheses. For example, in the expression 3(x + 2), the 3 can be distributed to both x and 2, resulting in the simplified expression 3x + 6.

3. Simplifying exponents: When an expression contains exponents, rules of exponentiation can be used to simplify the expression. For example, in the expression x^2 * x^3, the exponents can be added to give x^(2+3) = x^5.

4. Factoring: When an expression contains common factors, those factors can be factored out. For example, in the expression 2x^2 + 4x, both terms have a factor of 2 and a factor of x, so these factors can be factored out to give 2x(x + 2).

Answer:

QT. . . . . . . . . . . . . . . I think

Answer:

1}6 times

Step-by-step explanation:

2}Yes.New York and Mast has the same number of president which is four

3}Yes,this can be done using piechart.

4}I am still working on this question

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\(y + 1 = \frac{8}{9} (x + 4) \\ \)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Thus the correct answer is the second one.

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

The probability of drawing two orange balls, given that at least one ball is orange, is 1/5.

There are a total of 6 possible outcomes when selecting 2 balls from the urn without replacement: (O,O), (O,B), (B,O), (B,B), (O,B), (B,O).

The event that at least one of the balls selected is orange corresponds to the outcomes (O,O), (O,B), and (B,O). The probability of this event is the sum of the probabilities of the individual outcomes:

P(at least one orange) = P(O,O) + P(O,B) + P(B,O)

To calculate the individual probabilities, we can use the formula for the number of combinations of n items taken k at a time:

C(n,k) = n! / (k! (n-k)!).

The probability of each outcome is the number of ways it can occur divided by the total number of possible outcomes:

P(O,O) = C(2,2) / C(4,2)

= 2! / (2! (2!)) / (4! / (2! (2!)))

= 1/6

P(O,B) = C(2,1) * C(2,1) / C(4,2)

= 2 * 2! / (1! (2!)) / (4! / (2! (2!)))

= 2/6

P(B,O) = P(O,B) = 2/6

So,

P(at least one orange) = 1/6 + 2/6 + 2/6

=> 5/6

And the probability that both balls are orange is:

P(both orange) = P(O,O) = 1/6.

So, the probability of drawing two orange balls, given that at least one ball is orange, is 1/5.

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Answer:

The y-intercept is 3

Gradient: 4

11-3= 8

2-0= 2

8/2= 4

Hope this helped!