Please write legibly.
4. There are 12 products randomly tested in a factory floor for quality control (faulty or not). a. Which distribution it may fit into? (5pt) b. What is the mean and standard deviation of this distrib

The side lengths of the triangle are CA = 42.0 and BC = 36.4

From the question, we have the following parameters that can be used in our computation:

The triangle

Using the tangent rratio, we have

tan(60) = BC/21

So, we have

BC = 21 * tan(60)

Evaluate

BC = 36.4

Next, we have

CA = √[36.4^2 + 21^2] -- pythagoras theorem

Evaluate

CA = 42.0

Hence, the side lengths are CA = 42.0 and BC = 36.4

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The complete table is

                Dog         Not Dog         Total

Cat            31              10                     41

Not cat     24              7                       31

Total         55              17                      72

Given a venn diagram represents the results of a survey that asked participants whether they would want a dog or a cat as a pet as shown in figure which is attached below.

In the figure cat and dog are overlapping which means 31 people like both.

The people that like only dog but not cat are 24 and the people that like only car but not dog is 10.

The people that like not cat not dog is 31-24=7.

The total people that like cats are 31+10=41 and the total people that dont like cat is 24+7=31

The total people that like dogs are 31+24=55 and the people that didn't like dogs are 31+10-24=17 and the total people that like both dog and not dog and also like cat and not cat is 55+17=41+31=72.

Hence, the complete table is shown in attached figure for the given venn diagram.

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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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Step-by-step explanation:

plug in y

6=1/3x+11/15

multiply both sides by 15 to get rid of the fraction

90 = 5x +11

move terms to make them like terms

-5x =11- 90

-5x = -79

divide both sides by -5

evaluate for x

The test-statistic (z-score) is 1.19984.

To find the test statistic (z-score) using the p-value, you will need to use the inverse of the standard normal cumulative distribution function (CDF), also known as the inverse normal function or the "normal inverse function." This function can be found using a calculator or a spreadsheet program with built-in functions, or you can use a table of standard normal probabilities to find the corresponding z-score for a given p-value.

For example, if the p-value is 0.05, you would look up the corresponding z-score in a table of standard normal probabilities and find that it is approximately 1.645. This means that the test statistic (z-score) for a p-value of 0.05 is 1.645.

It's important to note that this method only works for a one-tailed test, for a two-tailed test you need to divide your p-value by 2 and then use the inverse normal function.

so, the p-value is 0.1151, you would look up the corresponding z-score in a table of standard normal probabilities and find that it is approximately 1.19984.

Therefore, the test-statistic (z-score) is 1.19984.

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The given case of Gallup asking the same 50 people how many hours had they worked at a job in the past 7 days. is an example of dependent sample.

The measured values in relation in a dependent sample (also called a paired sample).

Some characteristics of dependent sample are-

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Answer:

c. 17/2

Step-by-step explanation:

y(1/2 + z) + 6

2 (1/2 + 3/4) + 6

1 + 6/4 + 6

find common denominator

4/4 + 6/4 + 24/4 = 34/4 reduced to 17/2

Answer:

x=0

Step-by-step explanation:

8x +9-3x=8+5x+1

5x+9=9+5x

5x -5x = 9-9

0=0

Answer:

4

Step-by-step explanation:

By the triangle midsegment theorem, 2(YW)=VZ.

This means 2(7s)=s+52, and thus s=4.

Answer:

It would be 8p+4

Step-by-step explanation:

dividing (48p + 24) by 6 involves factoring and simplifying the expression to obtain the result of 8p + 4

To divide (48p + 24) by 6, you first factor out the common factor of 6 from the expression, which yields

(48p + 24) = 6(8p + 4).

Then, you can further simplify by dividing each term by 6.

The result is 8p + 4.

This process of division distributes the division operation across all terms in the expression, and as a result, each term's coefficient is divided by 6.

In this case, it simplifies the original expression to 8p + 4.

In summary, dividing (48p + 24) by 6 involves factoring and simplifying the expression to obtain the result of 8p + 4

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Answer:

I can't see what the options are, but any fraction equal to 1/2 will be equal to 3:6.

Step-by-step explanation:

Treat a ratio like a fraction. In this case, 3 is the numerator and 6 is the denominator. If you reduce 3/6, you get 1/2. Fractions/ratios also equal to 1/2 or 3/6 are:

2:4

4:8

5:10

6:12

7:14

8:16

9:18

10:20

If any of these ratios are not one of the options, comment below with the choices and I will help you narrow it down.

Answer:

6:12,

Step-by-step explanation:

equivalent ratios are when all numbers in a ratio can be divided or multiplied to get a whole number. for example, 3:6. the 3 can be multiplied by 2 to get 6, and the 6 can be multiplied by 2 to get 12.

anyways bye taniya from concord

Answer:

y = x + 4

Step-by-step explanation:

We want to form an equation to represent the table. I will form an equation in standard y-intercept form. I can either calculate the slope mathematically, or look at the table and see that as x increases by 1, so does the respective value of y.

y = mx + b

m is slope and b is the y-intecept.

\(m = \frac{-2 - (-3)}{2-1} \\m = \frac{-2 + 3}{2 - 1}\\m = \frac{1}{1} \\m = 1\)

So now we have the slope of our equation.

y = x + b

We can find the y-intecept two ways, use the table, or plug in a point from the table in calculate b from our equation. Should we choose to use the table, remember that y-intercept means that at that point x = 0. Following the pattern from the table, we can infer that when x = 0, y = -4. So the y-intercept of the function is -4.

y = x + b

Substitute the point (4, 0) into the equation to calculate b.

0 = 4 + b

b = -4

So our equation of the function is y = x + 4.

You can check this by substituting any point from the table into our equation.

Answer:

106 items

Step-by-step explanation:

We are actually finding the "break even" point, where revenue = costs.

Set the revenue 7.5x - 100 equal to the costs 79.86 + 5.8x:

7.5x - 100 = 79.86 + 5.8x

Group the x terms together:    

1.7x  - 100  =  79.86

and then group the constants together on the right side:

  1.7x = 179.86

Solving for x, we get 105.8 (items)

Round this up:  106 items

The company will begin making a profit as production passes 106 items.

Answer:

first one : 7.5x -100 > 79.86 + 5.8x

second one : x > 105.8

last one : 106

Step-by-step explanation:

Answer:

y=3x+8

Step-by-step explanation:

m=3

y-(-1)=3(x-(-3))

y+1=3x+9

y=3x+8

The equation of the line passes through the point  (-3, -1)(and (-4, -4) is y=3x+8.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that line passes through the points (-3, -1)(and (-4, -4)

The slope will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -4 + 1 ) / ( -4 + 3 )

Slope = 3

The y-intercept is calculated as,

y = 3x + c

-1 = 3 x -3 + c

c = 8

The equation of the line will be,

y=3x+8

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Answer:

Step-by-step explanation:

Since 4e cancels out itself, the answer remains 2f.

*Note: I am not entirely sure this is correct, sorry if it isn't *

The height of the cell tower is 324 feet.

Let h be the height of the cell tower in feet. From the given information, we can set up the following two proportions:

\(\frac {72}h= \frac {length of tower shadow} {height of tower}\)

\(\frac {6}{27}= \frac{length of tree shadow}{height of tree}\)

We can simplify the second proportion:

\(\frac{6}{27}= \frac2{9}= \frac{length of tree shadow}{height of tree}\)

Now we can use the first proportion to solve for the height of the tower:

\(\frac{h}{72}= \frac9{2}\)

Cross-multiplying, we get:

\(2h=72\times9=6482\)

Dividing both sides by 2, we get:\(h=6482=324\)

Therefore, the height of the cell tower is 324 feet.

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Answer:

In math, the initial value of a function means that it is the y-intercept of the function. For instance, if the function is f(x)=2x+3 f (x) = 2x + 3 , the y intercept, (initial value) is 3 . This value is graphed on the y axis.

Step-by-step explanation:

Answer:

In math, an initial value of a function means that it is the y-intercept of the function. Knowing the y-intercept will help in graph functions. For instance, if the function is f(x)=2x+3 f ( x ) = 2 x + 3 , the y intercept, (initial value) is 3 . This value is graphed on the y axis.

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

The two triangles at the left have the same angles and share a side, so they are congruent.  Therefore, the vertical side is also 6x−2.

Using the same logic, the two triangles on the right have the same angles and share a side, so they are congruent.  Therefore, the vertical side is also 9x−11.

So:

6x − 2 = 9x − 11

9 = 3x

x = 3

Answer:

the answer is b

To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.

1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.

2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.

3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.

4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.

If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.

It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.

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Answer:

y = 104

Step-by-step explanation:

Angles 2 and 3 are a linear pair and angle 3 is 76.

y + 76 = 180

y = 104

Answer: \(y=\frac{3}{5}-\frac{2}{5}x\)

Step-by-step explanation:

Move the variables to the right:

\(2x+5y=3\)

\(5y=3-2x\)

Divide both sides:

\(5y=3-2x\)

\(y=\frac{3}{5}-\frac{2}{5} x\)

Solution:

\(y=\frac{3}{5}-\frac{2}{5} x\)

The correct answer is Yes, past age 85 years of age, for every 100 men, there are 200 women.

Given,

In the question:

Your grandmother is 87 years old and she has remarked to you that nearly all of her friends are women. She told you that it is rare to see a man older than age 85. She is correct because, after age 85, for every 100 men, there are __________.

Now, According to the question:

Your grandmother is 87 years old and she told you that all of her friends are women. There is no single man in her circle of friends. She also told that it is rare to see a man over the age of 85. It is because of the fact that women are more in number than man above the age of 85 and this ratio is like 100 men per 200 women, which means the chances of getting a male friend is almost half after the age of 85. So women are more in number than men.

Hence, The correct answer is Yes, past age 85 years of age, for every 100 men, there are 200 women.

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Answer:

New avg = 103

Step-by-step explanation:

(5 x 100 + 118) / 6 = 103 average

Answer:

\(I=\frac{P}{V}\)

Step-by-step explanation:

We are given the equation \(P=I*V\), and we need to solve the equation for \(I\). Solving an equation for a variable means that we manipulate the equation so it is in the form (variable being solved for) = ?, where the ? is any expression.

To solve for \(I\), we need to isolate the variable. This is the process of getting the equation into the form mentioned above by essentially getting all \(I\) terms on one side and all \(\text non-I\) terms on the other side.

In this case, we need to "get rid" of the \(V\) from the right-hand side (RHS). Notice that it is being multiplied by the variable we are solving for. Therefore, to remove it from the RHS, we will need to perform the opposite operation, which is division. We will use what's called the Division Property of Equality to do this, which states that in order to maintain equality, you need to divide both sides of an equation by the same number.

Dividing both sides by \(V\), we get:

\(P=I*V\)

\(\frac{P}{V}=\frac{I*V}{V}\)

\(\frac{P}{V} = I\) (simplify RHS)

\(\bf I=\frac{P}{V}\) (this uses the Symmetric Property of Equality - if a = b then b = a)

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Based on this analysis, we can determine which statements are true:

The radius of the circle is 3 units.

The center of the circle lies on the x-axis.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

A mathematical statement proving the equality of two expressions is known as an equation. It consists of an equal sign placed between two expressions, referred to as the equation's left-hand side (LHS) and right-hand side (RHS). The equal sign indicates that the values on the two sides of the equation are equal.

Here,

x² + y² – 2x – 8 = 0

We can complete the square for the x terms by adding (–2/2)² = 1 to both sides:

x² – 2x + 1 + y² – 8 = 1

(x – 1)² + y² = 9

Comparing this equation to the standard form of a circle, (x – h)² + (y – k)² = r², we see that the center of this circle is (h, k) = (1, 0), and the radius = 3.

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Answer:

Yes, 60,120,180

Answer:its d) 60,120,180

Step-by-step explanation:

Step-by-step explanation:

F(x) = 4x^3 - 3x^2 + 5 neither

F(x) = -7x^2+1 even

y = cos (-x) even

y = csc x odd

y = sin x/cos x odd