Simplify. 2x + 6x^2 - 10 + 4x^2 - 3X + (-6) =

To word his guarantee for free replacement of tires, the mechanic needs to determine the minimum life expectancy that the tires must meet in order to replace approximately 10% of them.

Since the life expectancy of the tires is normally distributed, we can use the standard normal distribution and the z-score formula to determine the minimum life expectancy that corresponds to a probability of 10%:

z = (x - μ) / σ

where z is the z-score, x is the minimum life expectancy, μ is the mean life expectancy of 24,000 miles, and σ is the standard deviation of 2700 miles.

Solving for x, we get:

x = zσ + μ

Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to a probability of 10%, which is approximately -1.28. Plugging this into the formula, we get:

x = (-1.28) * 2700 + 24000

x ≈ 20,856 miles

Therefore, the mechanic should guarantee free replacement of tires that wear out before reaching a mileage of approximately 20,856 miles, in order to replace approximately 10% of the tires.

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If the class has 50 students, and 10 of them are math majors There are a total of 50! (50 factorial) ways to line up the 50 students.

          To ensure that all the 10 math majors are in the front half of the line, the first 10 positions in the line must be filled by the math majors, leaving 40 positions in the second half to be filled by the remaining 40 students.

       Thus, there are 10! (10 factorial) ways to fill the first 10 positions and 40! (40 factorial) ways to fill the second half.

       Therefore, the total number of ways to line up the students so that all the math majors are in the front half of the line is

          10! × 40! = 30,240,000.

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Answer:

Step-by-step explanation:

250

The test static for sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago is 0.2377.

A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data fit the distribution predicted by the statistical test's null hypothesis.

In order to determine whether to accept or reject your null hypothesis, the test statistic is utilised to calculate the p value of your findings.

In a sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago.

In a sample of 50 women, 48 women said that they had less leisure time than they

had 10 years ago.

p-hat men:: 44/50 = 0.22

p-hat women:: 48/50 = 0.24

Test Stat:

z(0.24-0.22) =[tex]\frac{0.02}{\sqrt{[(0.22*0.78/50)+(0.24*0.76/50)]} }[/tex] = 0.2377

At [tex]\alpha[/tex] = .05, is there a difference in the proportions between the men and women

[tex]p-value = 2*P(z > 0.2377) = 0.8121[/tex]

Since the p-value is greater than 5%, fail to reject H.

H: p(men)-p(women) = 0

Ha: p(men)-p(women) # 0 = .05, is there a difference in the proportions between the men and women

p-value = 2*P(z > 0.2377) = 0.8121

Since the p-value is greater than 5%, fail to reject H.

H: p(men)-p(women) = 0

Ha: p(men)-p(women) # 0

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Complete question:

In a sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago. In a sample of 50 women, 48 women said that they had less leisure time than they had 10 years ago. What is the test statistic? At  [tex]\alpha[/tex] = .05, is there a difference in the proportions between the men and women?

The slope-intercept definition of the linear function is given as follows:

y = -2x - 3.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

For this problem, the slope and the intercept are given as follows:

Hence the function is defined as follows:

y = -2x - 3.

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The value of y when x = 25 is 30

What are direct variations ?

One quantity directly changes in response to a change in another quantity, which is referred to as direct variation. This suggests that if one quantity increases, the other will follow suit and rise in proportion. In a similar manner, if one quantity declines, the other amount also declines.

given y is directly proportional to x then the equation connecting them is

y = kx ← k is the constant of proportionality

To find k use the condition y = 36 when x = 30

So, 36=k(30)

=> k = 36/30 = 1.2

equation of proportionality:

y=1.2x

When x = 25 then

y=1.2(25) = 30

The value of y when x = 25 is 30

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As a result, (x, y) = is the answer to a set of equations. (-17, -3). There aren't an endless number of answers because there is a single one.

The meaning of an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.

The statements that are true about this system of equations are:

The x-variable will be eliminated when adding the system of equations.

There are infinitely many solutions to the system of equations.

To eliminate the x-variable, we can add the two equations as follows:

(2x - 7y) + (-2x + 11y) = -13 + 1

Simplifying the left-hand side and the right-hand side gives:

4y = -12

Dividing both sides by 4 yields:

y = -3

Substituting y = -3 into either of the original equations gives:

2x - 7(-3) = -13

Simplifying this equation yields:

2x + 21 = -13

Subtracting 21 from both sides yields:

2x = -34

Dividing both sides by 2 yields:

x = -17

Therefore, the solution to the system of equations is (x, y) = (-17, -3). Since there is a unique solution, there are not infinitely many solutions.

The statement "The sum of the system of equations is 4y = -12" is false since the sum of the equations does not simplify to that expression.

The statement "x = 17" is false since the correct solution is x = -17.

The statement "The y-variable will be eliminated when adding the system of equations" is false since adding the equations only eliminated the x-variable.

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Answer:

16

Step-by-step explanation:

a^2 + b^2 = c^2

a^2= 3^2 = 9

c^2=5^2 = 25

25-9= b^2

25-9=16

b^2 = 16

The point that partitions segment AB in a 1:4 ratio is (-1, -0.4).

In this scenario, line ratio would be used to determine the coordinates of the point Q on the directed line segment AB that partitions the segment into a ratio of 1 to 4.

In Mathematics, line ratio can be used to determine the coordinates of Q and this is modeled by the following mathematical expression:

Q(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Substituting the given parameters into the line ratio formula, we have;

Q(x, y) = [(1(7) + 4(-3))/(1 + 4)],  [(1(-10) + 4(2))/(1 + 4)]

Q(x, y) = [(7 - 12)/(5)],  [(-10 + 8)/5]

Q(x, y) = [-5/5],  [(-2)/(5)]

Q(x, y) = [-1, -2/5]

Q(x, y) = [-1, -0.4]

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I have no idea, good luck though pal

Step-by-step explanation:

You

Got

This

<3

Answer: Gloria must but at least one ticket in order for the first plan to be the better plan

What are linear and non-linear functions?

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.

Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.

An example of a non-linear function is a quadratic function.

Given, A sports ticketing company offers two ticket plans. One costs $11 plus $25 per ticket and the other plan costs$40 per ticket.

Let, The number of tickets be 'x'.

Therefore, The number of tickets Gloria should buy so that the first plan is a better plan is,

11x + 25 < 40x.

11x - 40x < - 25.

- 29x < - 25.

29x > 25.

x > 25/29.

x > 0.86.

So, Gloria must buy at least 1 ticket.

Step-by-step explanation:

If a multiplies an n x p matrix b then the total number of multiplications involved is m x p. And is given by Dimensional vector.

For explanation, There are two separate cases to consider when multiplying an m-by-n matrix and an n-dimensional vector, or an m-by-n matrix and an n-by-p matrix.

When an m-by-n matrix, A, multiplies an n-dimensional vector, x, the number of separate multiplications involved is m. This is because in order to compute the dot product of A and x, each row of A needs to be multiplied by the vector x, resulting in m separate multiplications.

On the other hand, when A multiplies an n-by-p matrix, B, the number of separate multiplications involved is m x p. This is because in order to multiply A and B, each row of A must be multiplied by each column of B, resulting in m x p separate multiplications.

Therefore, the number of separate multiplications involved when multiplying an m-by-n matrix and an n-dimensional vector is m, and the number of separate multiplications involved when multiplying an m x n matrix and an n x p matrix is m x p.

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Answer: 12 cupcakes

Step-by-step explanation:

24/8 = 3

3x4=12

Answer:

The answer to your problem is, 12

Step-by-step explanation:

First, we want to know the problem:

24 ÷ 8 = ?

? = 3

Next, we can do some easy multiplication such as the following:

3 x 4 = ?

? = 12.

Thus, the answer to your problem is, 12

Answer:

1. 48

2. 103

3. 47

4. 60

hope this helps

The length of segment AB, is calculated using the formulae velow

Information from the question

a figure of right triangle

The length of AB is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The length of AB is solved using sin, cos and tan as follows

Sin = opposite / hypotenuse - SOH

sin C = AB / 10

AB = 10 Sin C

Cos = adjacent / hypotenuse - CAH

cos A = AB / 10

AB = 10 cos A

Tan = opposite / adjacent - TOA

tan C = AB / 8

AB = 8 tan C

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The probability that at least 4 buyers would prefer green among the 16 selected is approximately 0.1031.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

This problem can be modeled as a binomial distribution with n = 16 trials and p = 0.3 probability of success (preferring green).

Let X be the number of buyers who prefer green among the 16 selected. We need to find P(X ≥ 4).

Using a binomial probability table or calculator, we can find:

P(X ≥ 4) = 1 - P(X < 4)

= 1 - P(X ≤ 3)

= 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

= 1 - [0.1233 + 0.2854 + 0.3028 + 0.1854]

= 0.1031 (rounded to 4 decimal places)

Therefore, the probability that at least 4 buyers would prefer green among the 16 selected is approximately 0.1031.

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The false statement regarding the normal distribution is given as follows:

99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The percentage of scores within 1 standard deviation of the mean is obtained considering that:

Hence the percentage is given as follows:

84.13 - 15.87 = 68.26%, which is different of 99.72%.

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The correct answer is that all of the following are characteristics of the normal probability distribution as given below.

A subfield of statistics known as probability studies random events and their likelihood of happening.

The statement "99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean" is actually a characteristic of the normal probability distribution.

The correct answer is that all of the following are characteristics of the normal probability distribution:

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The probability that exactly 7 employees out of 23 sent complete the program is 0.217 or 21.7%.

In this case, the number of trials is 23, and the probability of success is 0.4 (since, on average, 40% of those sent complete the program). We want to find the probability of exactly 7 successes.

The binomial probability formula is:

P(X=k) = [tex](^n_k) \times p^k \times (1-p)^{(n-k)}[/tex]

Where P(X=k) is the probability of k successes, n is the total number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials.

Using this formula, we can calculate the probability of exactly 7 employees completing the program as follows:

P(X=7) = [tex](^{23} _7) \times 0.4^7 \times (1-0.4)^{(23-7)}[/tex]

= 0.217 or 21.7%

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Therefore, sin(A) is approximately 0.6708 (rounded to four decimal places).

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems related to geometry, physics, engineering, and many other fields. Trigonometry is based on the study of the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios of the lengths of the sides of a right triangle, and can be used to calculate the unknown side lengths or angles of a triangle. Trigonometry is also useful for working with periodic functions, such as waves and oscillations. The trigonometric functions can be used to model and analyze these periodic phenomena, and to predict future behavior based on past observations. Applications of trigonometry can be found in many areas of science, engineering, and technology, including astronomy, navigation, architecture, surveying, and electronics.

Here,

To find sin(A), we need to use the trigonometric ratios of the sides of the right triangle ABC, where angle A is opposite to side a, angle B is opposite to side b and angle C is opposite to side c. We have sides of the triangle as follows:

a = 72

b = 65

c = 97

To find sin(A), we can use the following formula:

sin(A) = opposite/hypotenuse

In this case, the opposite side of angle A is b and the hypotenuse is c, so we have:

sin(A) = b/c

sin(A) = 65/97

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Complete question:

Find sin(A) when we have sides of the triangle as follows:

a = 72

b = 65

c = 97

Answer:

To find how much greater 4/5 is than 3/4 we can turn them into decimal values:

4/5 = 0.8

3/4 = 0.75

0.8 - 0.75 = 0.05

4/5 is 0.05 or 1/20 greater than 3/4

We can see here that the figures that have the same area are: A. Figures I and II.

Area is a measure of the size of a two-dimensional surface or shape. It refers to the amount of space inside the boundaries of a flat object, such as a rectangle, triangle, or circle. Area is typically measured in square units, such as square meters, square feet, or square centimeters.

The area of Figure I which is a rectangle is = l × b = 2cm × 5.8cm = 11.6cm².

The area of Figure II which is a parallelogram is = b × h = 4cm × 2.9cm = 11.6cm².

Thus, Figures I and II have the same area.

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Answer:

Step-by-step explanation:

Y

The circumference of a gazebo is 47.1 ft

To calculate the circumference, you can use the formula C=2πr. This formula states that the circumference of a circle is equal to two times the constant π (approximated as 6.28) multiplied by the radius of the circle. The radius of a circle is equal to half of the diameter, so in this case the radius would be 7.5 ft (half of 15 ft).

Therefore, to calculate the circumference of a gazebo with a diameter of 15 ft, you can use the formula C=2πr. Plugging in the radius of 7.5 ft, the equation would become C=2π(7.5) which results in a circumference of 47.12 ft. To round this answer to one decimal place, the final answer is 47.1 ft

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Answer:

To solve the problem, we need to first determine the value of the quarters Anna has. Since there are 5 quarters, we have:

5 quarters = 5 x $0.25 = $1.25

Thus, Anna has $2.00 - $1.25 = $0.75 left. We can find the maximum number of dimes she can have by dividing this amount by the value of a dime, which is $0.10. Therefore:

$0.75 ÷ $0.10 = 7.5

Since Anna cannot have a fraction of a dime, we round down to the nearest whole number to get a maximum of 7 dimes. Therefore, the answer is option B, 5.

answer for number 14 is 1115

you mutliply 27 into 1 ×45 into 100

it is 100 because we are dealing with percentage

so you say (write in fraction form)

27÷1×45÷100

=1215÷100

you get the answer of 1115

so there were 1115 female butterflies

we can subtract the answer from the original number to get the number of male butterflies

1215-1115 =100 male butterflies

Answer:

Step-by-step explanation:

Let's use algebra to solve this problem.

Let's start by assigning variables to the unknown quantities. Let G be the initial number of green beads and Y be the initial number of yellow beads.

We know that the number of green beads is 1/3 the number of yellow beads:

G = (1/3)Y

After giving away some beads, he had 42 green beads and 270 yellow beads left. So we can set up two equations using this information:

G - 2f = 42

Y - 3f = 270

where f is the number of friends he gave the beads to.

Now we can substitute G = (1/3)Y into the first equation:

(1/3)Y - 2f = 42

Multiplying both sides by 3, we get:

Y - 6f = 126

Now we have two equations that we can solve simultaneously:

Y - 3f = 270

Y - 6f = 126

Subtracting the first equation from the second, we get:

3f = 144

So f = 48. He gave the beads to 48 friends.

To find the total number of beads he had at first, we can use the equation G = (1/3)Y:

G + Y = (4/3)Y = (4/3)(270) = 360

So he had a total of 360 beads at first.

The correct option is the second one, your supervisor did not divide by the total number of bags.

Here we can see a table with the size of each bag (in grams) and the number of sold bags.

Now, remember that for a set of N numbers {x₁, ..., xₙ} the mean is:

M = (x₁ + x₂ + ...)/N

So the denominator is the amount of elements in the set.

Then here in the denominator we should see the total number of bags sold, which is:

25 + 32 + 40 + 18 = 115

That number should be in the denominator instead of the sum of the masses.

Then the correct option is the second one.

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