Solve for the missing side in each triangle

In light of this, the 95% confidence interval for is (100.67, 111.33) as s is the sample standard deviation, n is the sample size.

A collection of information's values' standard deviation serves as a gauge for how much variance or dispersion there is. It is a statistical word used to describe the degree to which the individual data points depart as from mean or average value that is contained in the data set. By taking taking square root of the variance—the sum of the squared deviations amongst each point in the data and the mean—we can determine the standard deviation. While a high standard deviation suggests that the data points are widely dispersed, a modest standard deviation suggests that the statistics are close to the mean.

given

(a) When the sample size, n, is 16, we can apply the following formula to create a 95% confidence interval regarding the population mean, :

x ± tα/2 * (s/√n)

where t/2 is the crucial value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%, and x is the sample mean, s is the sample standard deviation, n is the sample size.

We determine that t0.025,15 = 2.131 using a t-distribution table or calculator.

When we enter the values, we obtain:

106 ± 2.131 * (10/√16)

which is equivalent to:

106 ± 5.33

In light of this, the 95% confidence interval for is (100.67, 111.33) as s is the sample standard deviation, n is the sample size.

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Answer:

The linear function is y = (1/3)x - 4.

Step-by-step explanation:

The y-intercept is -4. Starting at (0, -4), go up 1 unit and then right 3 units. You will end at (3, -1). So the slope of this line is 1/3, and it follows that the function is

y = (1/3)x - 4.

The amount of water in the basement is V = 22,500 gallons

Given data ,

To calculate the amount of water in the basement, we need to determine the volume of water in cubic feet and then convert it to the most appropriate units to describe the amount of water.

First, we need to convert the dimensions of the basement to feet, since the depth of the water is given in inches. 18 inches is equal to 1.5 feet, so the volume of water in cubic feet can be calculated as:

50 feet x 40 feet x 1.5 feet = 3,000 cubic feet

There are 7.5 gallons in 1 cubic foot of water, so the amount of water in the basement in gallons can be calculated as:

3,000 cubic feet x 7.5 gallons per cubic foot = 22,500 gallons

Hence , there are 22,500 gallons of water in the basement

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The given line AB is having endpoints A(-3,5) & B(1,-1).

To find the equation of line AB it can be written as[tex]y-y_1=(x-x_1){(y_2-y_1)/(x_2-x_1)}\\[/tex]

Substituting the given points

[tex]y-(-1)=(x-1){(5-(-1))/(-3-1)}\\[/tex]

y=-(3/2)x+1/2

For two perpendicular lines [tex]m_1*m_2=-1[/tex]

Therefore, (-3/2)*[tex]m_2[/tex]=-1

or [tex]m_2[/tex] = 2/3

Also, the midpoint of AB will be [tex]{1-(-3)}/2, {5-(-1)}/2[/tex] = (2,3).

The line passing through (2,3) & perpendicular to y=-3/2x+1/2 will be given as follows

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

3y-9=2x-4

3y=2x+5 is the required equation of the line.

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The statistical questions are:

A statistical question is a question that can be answered by collecting and analyzing data. It is a question that expects a variability in the response, meaning different individuals may give different answers. Statistical questions usually ask about a population, a group of individuals or objects that share a common characteristic or feature, and seek to understand a pattern or trend within that population.

In general, a statistical question is open-ended, does not have a single correct answer, and requires data analysis to arrive at a reasonable conclusion.

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Answer:

30%

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

not good at explaining this concept but keep the signal its X|X and its near the square root so tadaaa

The function g(x) is defined as follows:

D. g(x) = f(x) + 4.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The y-intercept for each function is given as follows:

Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:

g(x) = f(x) + 4.

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Answer: D

Step-by-step explanation:

The function g(x) is defined as follows:

D. g(x) = f(x) + 4.

What is a translation?

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

Translation left a units: f(x + a).

Translation right a units: f(x - a).

Translation up a units: f(x) + a.

Translation down a units: f(x) - a.

The y-intercept for each function is given as follows:

f(x): y = -5.

g(x): y = -1.

Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:

g(x) = f(x) + 4.

Answer:

gain of 700 or 700

Step-by-step explanation:

A loss of 700 would be -700 and the opposite of that is 700.

Helping in the name of Jesus.

The system of equations where the combination of the candies gives you a total of 22 points are:

x + y = 9

2x + 3y = 22

To create the equations, we shall first define the variables:

x = the number of purple candies

y = the number of yellow candies

Next, we shall use the given information that purple candies are worth 2 points and yellow candies are worth 3 points.

Then, we would make sure that the total number of candies selected is 9.

The first equation represents the total number of candies selected:

x + y = 9

The second equation represents the total number of points obtained:

2x + 3y = 22

Therefore, the system of equations is:

x + y = 9

2x + 3y = 22

This is a system of linear equations.

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Answer:

No

Step-by-step explanation:

In order for a triangle to be a right angle, the sum of the squares of the two legs (a and b) must be equal the square of the longest side, known as the hypotenuse (c):

[tex]a^2+b^2=c^2[/tex]

The square root of 155 is the longest side as it is approximately 12.45.  Thus, if the triangle is a right triangle, the square root of 155 must be the hypotenuse.

We can now check to see whether the sum of the squares of 7 and 9 equal the square of the square root of 155:

[tex]7^2+9^2=(\sqrt{155})^2\\ 49+81=155\\130=155[/tex]

The equation is not true since 130 is less than and not equal to 155.  Therefore, a triangle with side lengths 7, 9, and the square root of 155 cannot be a right triangle.

Answer: Cut 3 inch per person

Step-by-step explanation:

there is a 4 foot sub you take the quadrilatiral and divide it by 10 and you get 3 inches per person remember to multiply the reciprocal by 12 as there are 12 inches in a foot and you have 4 foot so the product of that reciprocal will be equal to 4 divided by your sum from adding the recriptorcal into the quadrilateral remember a quadrilateral not a duolateral or a triolatiral as there is 4 feet in the sub. >:)

Answer:

7 Cuts

Step-by-step explanation:

This is because if you do 48 inches / 6 inches = 8 sections Since each cut will create two sections, you need to make 7 cuts (one fewer than the number of sections) to get 8 equal portions.

Step-by-step explanation:

X component  = 4.5 - 2.1  =   2.4

Y component  = 7.8 - 2.1  =    5.7

Find magnitude using Pythagorean theorem

  m^2 = 2.4^2 + 5.7^2

    magnitude  = 6.18    units

Remember for a right triangle   tangent Φ = opposite leg / adjacent leg

    angle = arctan ( 5.7 / 2.4 )   = 67.2 degrees

The trigonometry functions when evaluated are shown below

In trigonometry, sine (sin), cosine (cos), and tangent (tan) are three basic functions that relate angles to the sides of a right triangle.

They are defined as follows:

sin A = opposite side/hypotenuse.

cos A = adjacent side/hypotenuse.

tan A = opposite side/adjacent side.

So, we have

Figure 1

Figure 2

Figure 3

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Based on the data given in the table, B. Median for both coffee shops because the data distribution is not symmetric

It is better to describe the centers of distribution in terms of the median rather than the mean for both coffee shops because the data distribution is not symmetric.

The median is a better measure of central tendency in this case because it is not influenced by outliers or extreme values, which may exist in the data.

The mean, on the other hand, is sensitive to outliers and may not provide an accurate representation of the data distribution.

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A.15/22 is the correct answer.

The correct answer is:

A. 15/22, represents a proper fraction.

Here, we have,

A proper fraction is a fraction where the numerator (the top number) is smaller than the denominator (the bottom number).

Out of the given options, only option A,

15/22, represents a proper fraction because 15 is smaller than 22.

Therefore, the correct answer is:

A. 15/22, represents a proper fraction.

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Answer:

90.95%

Step-by-step explanation:

85 * 0.07 = 5.95 5.95 + 85= 90.95

Answer:

The answer to your problem is, 90.95%

Step-by-step explanation:

Calculation:

In order to find the answer we need to

= Old score + New Score

= 85 + 7% of 85

= 85 + ( [tex]\frac{7}{100}[/tex] x 85 )

= 85 + ( 0.07 x 85 )

= 85 + 5.95

= 90.95

Which 90.95% is our answer.

Thus the answer to your problem is, 90.95%

The numerical expression that represents the sum of eight squared and thirty two will be 96.

A numerical expression is a mathematical expression that consists of numbers and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.

The numerical expression that represents the sum of eight squared and thirty two is

= 8² + 32

= 64 + 32

= 96.

The question is incomplete and the complete question is '' What is the numerical expression that represents the sum of eight squared and thirty two''.

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Step-by-step explanation:

Only ONE .....there are three sides to a triangle and you supplied 3 sides.

Caroline needs to fill the 1-quart pitcher four and a half times in order to fill all 3 pint glasses.

Since Caroline has 3 pint glasses to fill, she needs to use the 1-quart pitcher multiple times. Each time she fills the pitcher, she can pour it into 2 pint glasses

From this, we can say that Caroline needs to pour a total of 3 x 1.5 = 4.5 quarts of juice.

What is a Pitcher

Pitcher is a container with a spout and handle, used for holding and pouring liquids. It is typically used for serving beverages such as water, juice, milk, or iced tea. Pitchers can be made from a variety of materials, including glass, ceramic, metal, or plastic.

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There would be 35 more defective bean seeds than pumpkin seeds in the shipment.

Calculate the number of defective bean seeds:

Defective bean seeds = Total bean seeds * Defect rate for bean seeds

Defective bean seeds = 1,750 * 0.05 = 87.5

Since we can't have half a seed, we'll round it up to the nearest whole number.

Defective bean seeds = 88

Calculate the number of defective pumpkin seeds:

Defective pumpkin seeds = Total pumpkin seeds * Defect rate for pumpkin seeds

Defective pumpkin seeds = 1,750 * 0.03 = 52.5

Similarly, we'll round it up to the nearest whole number.

Defective pumpkin seeds = 53

Calculate the difference in defective seeds:

Difference in defective seeds = Defective bean seeds - Defective pumpkin seeds

Difference in defective seeds = 88 - 53 = 35

So, there would be 35 more defective bean seeds than pumpkin seeds in the shipment.

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In a shipment of 1,750 seeds of each type, with a defect rate of 5% for bean seeds and 3% for pumpkin seeds, how many more defective bean seeds would be expected than pumpkin seeds?

Answer:

Step-by-step explanation:

Answer:

f(-1) = 16

Step-by-step explanation:

"output" and the f(x) setup just means to plug in -1 in place of x and calculate.

For the function f(x) = 12(3/4)ˣ you have to already know that once you put that -1 in place of x that the -1 power only goes to the 3/4, not the 12 and also what to do with a negative exponent.

Exponent rules are just shortcuts. The shortcut to know here is that the -1 exponent will flip the 3/4 over and make it 4/3 (there are math reasons for this, it's not random. But that's how it works)

So now you have

f(-1) = 12(3/4)⁻¹ which becomes

f(-1) = 12(4/3)

Now you need to know how to multiply with fractions. Here you have a whole, big number times a fraction, which is:

"big num×top all over bottom"

So multiply the 12 times the 4 and put it over the 3

f(-1) = 48/3 = 16

(or you can "cancel" the 12 with the 3 and get 4×4, which is 16, so it comes out the same)

[SKIP TO HERE IF YOU DON'T CARE WHY]

f(x) = 12(3/4)ˣ

f(-1) = 12(3/4)⁻¹

f(-1) = 12(4/3)

f(-1) = 16

If cos(x) = -5/6, and x lies in quadrant"II", then exact values are:

sin(2x) = (-5√11)/(18);

cos(2x) = 7/18;

tan (2x) = -5√11/7.

We know that, Cos(x) = -5/6 and "x" is in quadrant II, so, we can use the Pythagorean identity to find sin(x):

sin(x) = √(1 - cos²(x)) = √(1 - (-5/6)²) = √(1 - 25/36) = √(11/36) = √11/6

Using the double angle trigonometry identities for sine and cosine, we find sin(2x) and cos(2x):

Substituting the value of Sin(x) and Cos(x),

We get,

sin(2x) = 2sin(x)cos(x) = 2(√11/6)(-5/6) = (-5√11)/(18);

cos(2x) = cos²(x) - sin²(x) = (-5/6)² - (11/6) = 25/36 - 11/36 = 14/36 = 7/18;

Finally, we find tan(2x) by using the identity:

tan(2x) = sin(2x)/cos(2x) = (-5√11/18) / (7/18) = -5√11/7.

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To find the probability of winning the lottery game, we can use the formula for combinations:

nCk = n! / (k! * (n - k)!)

where n is the total number of choices (22 in this case) and k is the number of choices we make (6 in this case).

So, the number of possible combinations of six numbers from 22 is:

22C6 = 22! / (6! * 16!) = 13,983,816

Therefore, the probability of winning the lottery game is 1 in 13,983,816.

The expected value of playing the lottery game can be calculated as follows:

Expected value = (Probability of winning * Amount won) - (Probability of losing * Amount lost)

Expected value = (1/13,983,816 * $40,000) - (13,983,815/13,983,816 * $1)

Expected value = $0.5709

This means that on average, the player can expect to win about 57 cents per game played. However, it is important to note that this is just an average and the actual outcome of any single game can vary widely.

The inverse statement of M implies N is a negation of both the conclusion and the hypothesis.

An inverse statement is one in which both the hypothesis and the conclusion are negated. Let us assume a statement with the hypothesis and conclusion as follows: If they annul the law, we will drive carelessly.

The inverse of this statement will be: If they do not annul the law, we will not drive carelessly. So, both the hypothesis and the conclusion are rewritten in negative terms.

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