a surveyor measures the distance across a straight river by the following method: starting directly across from a tree on the opposite bank, she walks along the riverbank to cstablish a basclinc. then she sights across to the tree. the angle from her bascline to the tree is how wide is the river?

The triangles in the questions 15,18 and 20 are right triangles , remaining are not.

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

In a right triangle,

Square of the longest side = sum of the squares of other two sides

The triangles in the questions 15,18 and 20 follow this rule

So, the triangles in the questions 15,18 and 20 are right triangles , remaining are not.

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The length of the shorter leg is 16 units which was found using the given data.

A quadratic equation is a second-degree algebraic equation in x. In its usual form, the quadratic equation is ax² + bx + c = 0.

Given: The larger leg of a right triangle is twice more than three times the shorter leg, and the triangle's area is 400.

We know that,

Area of triangle = 1/2(larger leg)(shorter leg)

                  400=1/2(larger leg)(shorter leg)   Equation(1)

larger leg = 2 + 3(shorter leg)

We need to substitute this in Equation(1)

400 = 1/2[2+3(shorter leg)](shorter leg)

800 = 2(shorter leg) + 3(shorter leg)²

3(shorter leg)² + 2(shorter leg) - 800 = 0

Solving this quadratic equation,

we get, shorter leg = - 16 or +16

Thus, we found that the length of the shorter leg is 16 units as -16 cannot be the length because it is negative.

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Answer:

What is 12.5 percent of 350? = 43.75.

Answer:

The correct value for n is 2800.

Step-by-step explanation:

We need to find the value of n.  According to the given information, 12.5% of n is 350.  Here the percentagle 12.5% must be converted to the equivalent 0.125.  

Then the equation to be solved is 0.125n = 350, so that

       350

n = --------- = 2800

      0.125

The correct value for n is 2800.

Answer:

1

Step-by-step explanation:

An equilateral triangle is a triangle with all three sides of equal length, so there's only one option, a triangle with all three sides 7 centimeters.

Answer:

use long divison  ike this

      16

  -------

8 | 132

    8

  -----

    52

    48

  -----

     4

Step-by-step explanation:

Answer:

Step-by-step explanation:

                                         132/8 = 16 with 4 leftover

                                             32 divided by 8 is 4, 96 divided by 8 is 12, the                                                                  

                                                  extra 4 left over

The board of directors for Procter and Gamble is concerned that only

19% of the people who use toothpaste buy Crest toothpaste. A marketing

director suggests that the company invest in a new marketing campaign

which will include advertisements and new labeling for the toothpaste.

The research department conducts product trials in test markets for one

month to determine if the market share increases with new labels.

PROCTOR and GAMBLE had only 19% of the people who use toothpaste

buy Crest toothpaste. Hence, it was worried about the market share of

the toothpaste it had been producing. The marketing director suggested

that the company invest in a new marketing campaign which will include

advertisements and new labeling for the toothpaste. The research

department conducted product trials in test markets for one month to

determine if the market share increases with new labels. This is an

effective approach because new labels attract customers easily. By

changing or improving the way that a product is labeled or packaged,

companies can influence the likelihood of a purchase by making the

product look more appealing or professional. Therefore, after changing

the labeling, the market share of Crest Toothpaste will increase.

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In 10,000 independent tosses of a coin and the coin landed on heads 5800 times, is it reasonable to assume that the coin is not fair and may be biased towards heads.

In order to determine if the coin is fair or not, we need to calculate the probability of getting 5800 or more heads in 10,000 tosses assuming the coin is fair.

The probability of getting a head on any one toss of a fair coin is 0.5. The number of heads in 10,000 tosses is a binomial random variable with parameters n=10,000 and p=0.5. We can use the normal approximation to the binomial distribution to calculate the probability of getting 5800 or more heads.

The mean of the binomial distribution is np = 5000 and the standard deviation is sqrt(np(1-p)) = 50.

We can standardize the variable X = number of heads in 10,000 tosses by subtracting the mean and dividing by the standard deviation:

Z = (X - 5000) / 50

The probability of getting 5800 or more heads can be calculated as:

P(X >= 5800) = P(Z >= (5800-5000)/50)

Using a standard normal table or calculator, we find that P(Z >= 1.6) = 0.0548.

This means that the probability of getting 5800 or more heads in 10,000 tosses assuming the coin is fair is only 0.0548, which is quite low.

Therefore, it is reasonable to conclude that the coin is not fair and may be biased towards heads.

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Answer:

number 1

k=12

Step-by-step explanation:

Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

The exact value of side lengths of triangle are d= \(\frac{8}{\sqrt{3} }\) and h=\(\frac{5\sqrt{2} }{2}\)

A triangle is a closed, two-dimensional shape that consists of three straight sides and three angles. It is one of the basic shapes in geometry and is often used in various mathematical and scientific contexts.

The three sides of a triangle are usually named using lowercase letters a, b, and c, and the three angles are named using uppercase letters A, B, and C, with the opposite angles and sides having the same letter. The sum of the angles in a triangle is always 180 degrees, and this property is known as the Angle Sum Theorem.

Triangles can be classified based on their side lengths and angles. Based on the side lengths, triangles can be classified as:

Scalene triangle: A triangle in which all three sides have different lengths.

Isosceles triangle: A triangle in which two sides have the same length, and the third side has a different length.

Equilateral triangle: A triangle in which all three sides have the same length.

Let's start with the first triangle. We can use the trigonometric ratios for a 30-60-90 triangle:

sin(60) = opposite / hypotenuse = d / (2d) = \(\frac{1}{2}\)

cos(60) = adjacent / hypotenuse = 4 / (2d) = \(\frac{1}{2\sqrt{3} }\)

Solving for d:

d = 2 * sin(60) = 2 *\(\frac{1}{2}\)  = 1

2d = 4 / cos(60) = \(\frac{4}{\frac{1}{2\sqrt{3} }}\) = \(\frac{8}{\sqrt{3} }\)

So d = 1 and 2d = \(\frac{8}{\sqrt{3} }\) in the first triangle.

For the second triangle, we can use the trigonometric ratios for a 45-45-90 triangle:

sin(45) = opposite / hypotenuse = \(\frac{h}{5}\)

cos(45) = adjacent / hypotenuse = \(\frac{h}{5}\)

Since sin(45) = cos(45) = \(\frac{1}{\sqrt{2} }\), we can solve for h:

h = 5 * sin(45) = 5 * \(\frac{1}{\sqrt{2} }\) = \(\frac{5\sqrt{2} }{2}\)

So h =  \(\frac{5\sqrt{2} }{2}\) in the second triangle.

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B. 5/3 is the evaluation of \(log_{8} 32\) using the base conversion method.

using the base conversion - \(log_{a} p= \frac{log_{b} p}{log_{b} a}\)

convert the base 8 into the base 2 algorithm

\(\frac{log_{2} 32}{log_{2} 8}\)

since 32=\(2^{5}\)

then, \(log_{2}(32)=5\)

similarly, since \(8=2^{3}\)

then, \(log_{2} (8)=3\)

this makes our expression 5/3.

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Answer:

5/3

Step-by-step explanation:

The change of base formula says logb b a = [logc c a] / [logc c b].

To evaluate log8 32, you need to use the following equation: log8 32 = x, where x is the unknown value.

This can be rewritten as 8^x = 32.

Solving for x gives x = 5/3.

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The largest subset S on which the vector-valued function F is continuous is the interval (-3, ∞).

To find the largest subset S on which the given vector-valued function is continuous, we need to examine the individual component functions and identify any restrictions or conditions that could cause discontinuities.

Component 1: f1(t) = t/(9 + t^4)

This function is a rational function. It will be continuous for all real values of t except where the denominator equals zero: 9 + t^4 = 0. However, there are no real values of t that satisfy this equation, so f1(t) is continuous for all real values of t.

Component 2: f2(t) = 7t^2 - 7t + 1

This function is a polynomial function, and polynomial functions are continuous for all real values of t. Therefore, f2(t) is continuous for all real values of t.

Component 3: f3(t) = ln(t + 3)

The natural logarithm function is defined for the positive values of its argument. Therefore, t + 3 > 0, which implies t > -3. Hence, the function f3(t) is continuous for t > -3.

Taking all these considerations into account.The function is continuous for all values of t greater than -3.

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The average value of the function on the closed interval 1≤x≤3 is approximately 0.281.

1. Determine the length of the closed interval. The interval is from x=1 to x=3, so the length is (3-1) = 2.

2. Integrate the function over the closed interval. To do this, you need to find the integral of sin(2x)cos(x) with respect to x from 1 to 3:
∫[1,3] sin(2x)cos(x) dx

3. Divide the result of the integration by the length of the closed interval to find the average value:
(1/2) * ∫[1,3] sin(2x)cos(x) dx

Now, let's calculate the integral:

∫ sin(2x)cos(x) dx = (1/4) * sin^2(x) + C (using integration by parts)

Now, we evaluate the definite integral from 1 to 3:

[(1/4) * sin^2(3)] - [(1/4) * sin^2(1)]

Finally, divide the result by 2 to find the average value:

(1/2) * {[(1/4) * sin^2(3)] - [(1/4) * sin^2(1)]}

After calculating the values, the average value of the function on the closed interval 1≤x≤3 is approximately 0.281.

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The probability of a card being black given it is a queen is P(A|B) = P(A ∩ B) / P(B) = (4/52) / (4/52) = 1. This means that if you draw a queen from a standard deck of 52 cards, it will be black with a probability of 100%.

The probability of a card being black given it is a queen can be determined using the formula P(A|B) = P(A ∩ B) / P(B). Where P(A) is the probability of a card being black and P(B) is the probability of a card being a queen.

To calculate this, we first need to calculate the probability of a card being a queen, which is 4/52 (there are 4 queens in a standard deck of 52 cards). The probability of a card being black is 26/52 (there are 26 black cards in a standard deck of 52 cards).

Using the formula, the probability of a card being black given it is a queen is P(A|B) = P(A ∩ B) / P(B) = (4/52) / (4/52) = 1. This means that if you draw a queen from a standard deck of 52 cards, it will be black with a probability of 100%.

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I would say D, 2 square inches.

Answer:

198 on edge

Step-by-step explanation

jus took the test, bouta make sum waffles rn ngl

The amount of juice the cup can hold given that the cup has diameter of 8 centimeters and a height of 12 centimeters is 602.88 cm³

To know the amount of juice the cup can hold, we shall obtain the volume of the cup.

We shall use the formula for obtaining volume of cylinder to obtain the volume of the cup. Details below:

Volume = πr²h

Volume = 3.14 × 4² × 12

Volume = 3.14 × 16 × 12

Volume = 602.88 cm³

Thus, we can conclude from the above calculation that the amount of juice the cup can hold is 602.88 cm³

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When the company asked its customers to describe how satisfied they were with the latest product, it's a discrete data.

It should be noted that the main distinction between continuous and discrete data is that the former has a finite value that can be counted while the latter has an endless number of possible values that can be measured.

A count involving integers is referred to as discrete data because there are a finite number of possible values. This kind of data cannot be separated into separate components. Discrete data consists of discrete variables that are non-negative, countable, and finite.

In this case, it should be noted that the measurement was taken based on their satisfaction. Therefore, it's a discrete variable.

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Answer:

A. 7

Step-by-step explanation:

Answer:

y= -1+5x

Step-by-step explanation:

Answer:

D. 7

Step-by-step explanation:

Answer:

kakaakasksjnxznxccchjvgv

Step-by-step explanation:

Slope of the line for the similar triangles is same passing through the the points are as follow:

Passing through points A(0, 3) and B (2,8) is 2.5.

Passing through the point C (2,8) and D(6,18) is 2.5.

As given in the question,

Two similar triangles ,

To prove: Slope of the line passing through the points A(0, 3) and B (2,8) and C (2,8) and D(6,18) is same.

Slope of the passing through the points A(0,3) and B(2,8) is equal to

= ( y₂ - y₁) / (x₂ -x₁)

= ( 8 -3 ) / (2-0)

= 2.5

Slope of the passing through the points C(2,8) and D(6,18) is equal to

= ( y₂ - y₁) / (x₂ -x₁)

= ( 18 -8 ) / (6-2)

= 2.5

Therefore, slope of the line for the similar triangles is same passing through the the points are as follow:

Passing through points A(0, 3) and B (2,8) is 2.5.

Passing through the point C (2,8) and D(6,18) is 2.5.

The complete question is:

Explain how similar triangles can be used to prove the slope of the line is the same through Points A(0, 3) and B(2, 8) as through C(2, 8) and

D(6, 18).

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The determinants for solving the linear system is given as follows:

The system of equations for this problem is defined as follows:

The matrix A is composed by the coefficients of x and y, hence:

A = [5 3]

  = [-8 -3]

The determinant of a 2 x 2 matrix is the multiplication of the principal diagonal subtracted by the multiplication of the secondary diagonal, hence:

|A| = 5 x (-3) - 3 x (-8)

|A| = -15 + 24

|A| = 9.

For the matrix Ax, the coefficients of x are replaced by the results of the equalities, hence:

Ax = [17 3]

    = [9 - 3]

|Ax| = 17 x (-3) - 3 x 9

|Ax| = -51 - 27

|Ax| = -78.

For the matrix Ay, the coefficients of y are replaced by the results of the equalities, hence:

Ax = [5 17]

    = [-8 -9]

|Ay| = 5 x (-9) + 17 x 8

|Ay| = 91.

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Yes. \(f(x)\) is a PDF if

• \(f(x) \ge 0\) for all \(x\) in the support; this is true, since \(e^{-x}>0\) for all \(x\), and multiplying a positive number \(x\) doesn't change this fact;

• the integral of \(f(x)\) over its support is 1; this is also true, since

\(\displaystyle \int_{-\infty}^\infty f(x) \, dx = \int_0^\infty xe^{-x} \, dx = 1\)

which can be computed by parts.

Answer: i took a screen shot hope it helps

Step-by-step explanation:

Answer:

this is a finance and it is an

Option A is the correct Answer a<b.

                angle a= 180-(75+75)=30°

         to confirm that a<b.

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Answer:

x(5x²-7)

Step-by-step explanation:

5x³-7x

=x(5x²-7)

To prove your answer,let's multiply x by each term in the bracket

=x X 5x²=5x³

x X -7 =-7x

A debt is a required amount a debtor owes a creditor

The best correct option is the option;

It does not represent the debt because the result should be a positive number since a dollar amount cannot be negative

Reason:

The  given equation is presented as follows;

\(-\dfrac{72}{2} -12= -48\)

The given equation represents the debt because Ryan owes \(\dfrac{72}{2}\), and Khalil owes \(\dfrac{72}{2}\) , while Ryan, also owes 12 dollars

However the amount Ryan owes is a positive number and not a negative number

Therefore, the correct option is it does not represent the debt because the result should be a positive number since a dollar amount cannot be negative

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