I was able to simplify to the final form of x+4/2x-6 but am unsure what the limits are. For example x cannot equal ….

The standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

\(\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{N}\)

SD is the standard deviation

xi is each value from the data set

X is the mean of the data set

N is the number of observations in the data set.

It is given that:

The data set:

45, 76, 30, 22, 51, 40, 63, 66, 41

From the formula:

∑(x(i) - X)² = 2463.55

N = 9

SD = √(2463.55/9)

SD = 16.54

Thus, the standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.

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Answer:

You did it correctly what answer you want ??

Answer:

Standardized z score = 2.06

His house rent is not an outlier

Step-by-step explanation:

The mean monthly rent of students at Oxnard university is 970 with a standard deviation of 204. John`s rent is 1390. What is his standardized z-score? Is john`s rent an outlier? How high would the rent have to be to qualify as an outlier

We solve using z score formula

= z = (x-μ)/σ, where

x is the raw score = 1390

μ is the population mean = 970

σ is the population standard deviation = 204

His z score is calculated as:

z = 1390 - 970/204

z = 2.06

No his house rent is not an outlier

Answer:

it is up and down

Step-by-step explanation:

Hope this helps.

Answer:

The third number can be any number less than 30.

Step-by-step explanation:

If the arithmetic mean of three numbers is less than 20, then their sum must be less than 20 * 3, or 60. We know that two of the numbers are 5 and 25, which add up to 30. In order for the arithmetic mean of the three numbers to be less than 20, the unknown number must be less than (60 - 30), or in order words, less than 30. So the third number can be any number less than 30.

The boundary line of the inequality y < (1/3)x + 1 is the equation y = (1/3)x + 1 with a dashed line because the inequality does not include the line itself.

To graph this line, we can start by plotting the y-intercept, which is the point (0, 1). From there, we can use the slope of 1/3 to find additional points on the line. For example, if we move 3 units to the right (increasing x by 3), we move up 1 unit (increasing y by 1), so we can plot the point (3, 2). Similarly, if we move 3 units to the left (decreasing x by 3), we move down 1 unit (decreasing y by 1), so we can plot the point (-3, 0).

Using these points, we can draw a dashed line through them to represent the boundary line of the inequality:

      |

   3  |         *

       |      *    

   2  |   *

       |*      

   1  |  

       |

   0  | *    

       |

       ---------------

          -3   0   3   6   x

The correct graph showing the boundary line of y < (1/3)x + 1 is the one with a dashed line passing through the points (0, 1), (3, 2), and (-3, 0), as shown above.

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The missing numbers for the respective rows are:

row 1: 4/5

row 2: -4/5 and -2/5

row 3: -3/5 and 6/5

Missing number for row 1(top row):

1 - 1/5 = 4/5

Missing number for row 2 (2nd number for last column):

3/5 - 1 = -2/5

Missing number for row 2 (1st number for first column):

-2/5 - 2/5 = -4/5

Missing number for row 3 (1st number for first column):

1/5 + (-4/5) = -3/5

Missing number for row 3 (2nd number for second column):

4/5 + 2/5 = 6/5

Therefore, row 1 have the missing number; 4/5. Row 2 missing numbers from left; -4/5 and -2/5. Row 3 missing number from left; -3/5 and 6/5

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Possible question:

If the sum of the first two numbers in row 1 is equal to 1 and the sum of the first two in last column to the right is equal to 3/5. Find the missing numbers.

30 people are homozygous for the rarer allele, founded by using frequency property.

What is frequency?

The frequency is the number of times a repeated event occurs in a certain amount of time. It is also sometimes referred to as temporal frequency to underline the contrast to spatial frequency and ordinary frequency to stress the contrast to angular frequency.

According to the Hardy-Weinberg principle, alleles act with a frequency of (p + q) squared, where p is 0.8 and q is 0.2 .

Now, homozygous for the less frequent allele is being requested; the frequency will be 0.2*0.2 = 0.04

Finding the total number of members—which is

0.04*750

=30 —is now necessary.

Therefore, 30 people are homozygous for the rarer allele.

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Answer: CD=7

Step-by-step explanation:

CD+DE=CE

x+7=2x

x=7

CD=x

CD=7

Answer: False

Step-by-step explanation:

-7 + 9 = 2

-9 + 7 = -2

=> -7 + 9 > (not equal sign) -9 + 7

Answer:

No.

Step-by-step explanation:

25x + 20y = 5x(5 + 4y)

Distribute the 5x inside the (5 + 4y).

5x * 5 = 25x

5x * 4y = 20xy

25x + 20y ≠ 25 + 20xy, so the two expressions below are not equal.

Answer:

13

Step-by-step explanation:

The gravitational potential energy of the stone-Earth system can be calculated before the stone is released, after it reaches the bottom of the well, and the change in gravitational potential energy during the process.

Gravitational potential energy is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.

(a) Before the stone is released, it is held 11 m above the top edge of the well. The mass of the stone is 0.25 kg, and the acceleration due to gravity is approximately 9.8 m/s². Using the formula, the gravitational potential energy is calculated as PE = (0.25 kg)(9.8 m/s²)(11 m).

(b) After the stone reaches the bottom of the well, its height is 7.3 m. Using the same formula, the gravitational potential energy at this point is given by PE = (0.25 kg)(9.8 m/s²)(7.3 m).

(c) The change in gravitational potential energy can be determined by subtracting the initial potential energy from the final potential energy. The change in gravitational potential energy is equal to the gravitational potential energy after reaching the bottom of the well minus the gravitational potential energy before the stone was released.

By calculating these values, we can determine the specific numerical values for (a), (b), and (c) based on the given data.

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A zero solution, also known as the trivial solution, refers to a solution of a system of equations in which all variables are equal to zero.

This type of solution occurs when the coefficients in the system of equations are set up in such a way that the only solution to the system is for all the variables to be equal to zero.

A zero solution is the answer to a system of equations where all the variables are equal to zero. This happens when the coefficients in the equations are set up such that the only solution is for all the variables to be equal to zero. This type of solution is also known as the trivial solution. A trivial solution can be thought of as a “placeholder” for when there is no other meaningful solution to a system of equations.

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The area of the entire circle is approximately 45.19 square inches.

To solve this problem, we can use the formula for the area of a sector of a circle:

Area of sector = (central angle / 360°) x π\(r^2\)

where r denotes the circle's radius.

We are given that the central angle measure of the sector is 120° and its area is 15 square inches. We can substitute these values into the formula:

15 = (120/360) x π\(r^2\)

Simplifying this equation, we get:

15 = (1/3)π\(r^2\)

Multiplying both sides by 3, we get:

45 = π\(r^2\)

Dividing both sides by π and taking the square root, we get:

r = √(45/π) ≈ 3.79 inches (rounded to two decimal places)

Now that we know the radius of the circle, we can use the formula for the area of a circle to find its area:

Area of circle = π\(r^2\)

Substituting r ≈ 3.79 inches into this formula, we get:

Area of circle ≈ π(3.79\()^2\) ≈ 45.19 square inches

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The inequality in vertex form that represents the region less than or equal to the quadratic function with the given vertex (-6, 12) and includes the point (-9, 15) on the boundary is:

(1/3)(x + 6)² + 12 ≤ 0

To determine the inequality in vertex form that represents the region less than or equal to the quadratic function with the given vertex and includes the point on the boundary can use the vertex form of a quadratic equation:

Vertex form:

f(x) = a(x - h)² + k

(h, k) represents the vertex of the parabola.

Given that the vertex is (-6, 12), we have h = -6 and k = 12.

Substituting these values into the vertex form equation, we get:

f(x) = a(x + 6)² + 12

Now, we need to find the value of 'a' to include the point (-9, 15) on the boundary.

Substituting x = -9 and y = 15 into the equation, we have:

15 = a(-9 + 6)² + 12

15 = a(-3)² + 12

15 = 9a + 12

3 = 9a

a = 3/9

a = 1/3

Substituting this value of 'a' back into the equation, we get the final inequality:

f(x) = (1/3)(x + 6)² + 12 ≤ 0

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True. The p-value is defined as the probability of obtaining a statistic as extreme as (or more extreme than) the observed sample, assuming that the null hypothesis is true.

It is essentially a measure of evidence against the null hypothesis and is used to assess the significance of a particular statistical result. The p-value is typically compared to a predetermined level of significance, known as the alpha level, to determine whether to reject or fail to reject the null hypothesis.

It is important to note that the p-value is not the same as the proportion of samples that would give a statistic as extreme as the observed sample. Rather, it is the probability of obtaining such a statistic, given that the null hypothesis is true. The proportion of samples that would give a similar statistic is known as the sampling distribution, which is a theoretical distribution that describes the range of possible values for a statistic, assuming that the null hypothesis is true.

In summary, the p-value provides a measure of the strength of evidence against the null hypothesis, while the sampling distribution describes the range of possible values for a statistic under the null hypothesis. Together, these concepts form the basis of hypothesis testing and are essential for making informed decisions based on statistical data.

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Answer:

c. 80 cm

Step-by-step explanation:

Area of a parallelogram = base × height

A = 16 cm × 5 cm

A = 80 cm

Answer:

Step-by-step explanation:

\(Base =16\\Height =5\\Area = Base\times Height\\= 16 \times 5\\= 80cm\)

(a) There are 2²⁸ = 268,435,456 ways to place testing dummies into the rollercoaster

(b) There are 15 × 2²⁴ = 402,653,184 ways to place dummies into the rollercoaster if the front car must have 3 or fewer testing dummies.

(c) There is only 1 × 2²⁴ = 16,777,216 way to place dummies into the rollercoaster if the back car must be empty.

(d) There are 15 × 2²⁰ = 15,728,640 ways to place dummies into the rollercoaster if neither the front nor the back car can be full.

a) There are 7 cars and each car has 4 seats, there are a total of 7 × 4 = 28 seats. Each seat can either be occupied by a testing dummy or left empty.

For each seat, there are two possibilities (dummy or empty). Since each seat can be treated independently, the total number of ways to place the testing dummies is 2²⁸.

2²⁸ = 268,435,456

b) If the front car must have 3 or fewer testing dummies,

The front car can have 0, 1, 2, or 3 testing dummies.

There are C(4, 0) + C(4, 1) + C(4, 2) + C(4, 3) = 1 + 4 + 6 + 4 = 15 ways to select the number of dummies for the front car.

The remaining 6 cars can have any number of dummies between 0 and 4. Each car has 4 seats, and each seat can be occupied by a dummy or left empty. So, there are 2⁴ possibilities for each of the 6 remaining cars.

Total number of ways = 15 × (2⁴)⁶ = 15 × 2²⁴.

15 × 2²⁴ = 402,653,184

c) If the back car must be empty, we can calculate the number of arrangements by considering the possibilities for the back car and then multiplying it by the remaining possibilities for the other cars.

The back car can have 0 dummies. There is only 1 possibility for the back car.

The remaining 6 cars can have any number of dummies between 0 and 4. Each car has 4 seats, and each seat can be occupied by a dummy or left empty. So, there are 2^4 possibilities for each of the 6 remaining cars.

Total number of ways = 1 × (2⁴)⁶ = 1 × 224.

1 × 2²⁴ = 16,777,216

d) If neither the front nor back car can be full, we can calculate the number of arrangements by considering the possibilities for both the front and back cars and then multiplying it by the remaining possibilities for the other cars.

The front car can have 0, 1, 2, or 3 testing dummies. There are C(4, 0) + C(4, 1) + C(4, 2) + C(4, 3) = 1 + 4 + 6 + 4 = 15 ways to select the number of dummies for the front car.

The back car can have 0 dummies. There is only 1 possibility for the back car.

The remaining 5 cars (excluding the front and back cars) can have any number of dummies between 0 and 4. Each car has 4 seats, and each seat can be occupied by a dummy or left empty. So, there are 2^4 possibilities for each of the 5 remaining cars.

Total number of ways = 15 × 1 × (2⁴)⁵ = 15 × 2²⁰.

15 × 2²⁰ = 15,728,640

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The question is incomplete the complete question is :

an amusement park is testing a roller coaster ride for safety. the roller coaster has 7 distinguishable cars, each of which contains 4 distinguishable seats. each seat can either be occupied by a testing dummy or left empty. the dummies are indistinguishable from one another, and there are enough to fill every car. for all sub-problems below, you are allowed to leave the entire ride empty, fill every seat in the ride, or anything in between. (update 2/17/23: the cars cannot be rearranged. they are fixed in one order.) a.) how many ways are there to place testing dummies into the rollercoaster? b.) how many ways are there to place dummies into the roller coaster if the front car must have 3 or fewer testing dummies in it? c.) how many ways are there to place dummies into the roller coaster if the back car must be empty? d.) how many ways are there to place dummies into the roller coaster if the neither the front or back car can be full?

Answer:

B is the answer

Step-by-step explanation:

Though I am not so sure

Answer:

25

Step-by-step explanation:

divide the length value by 100.

Solution :-

Multiplying them,

>> 4 × (4 - w) = 3 (2w + 2)

Transposing terms from R.H.S. to L.H.S.,

>> 16 - 4w = 6w + 6

Solving them now,

>> -6w - 4w = -16 + 6

>> -10w = -10

>> 10w = 10

>> w = 1

To determine the degree of a polynomial function given in factored form, a good first step is to count the highest power of the variable in the factored expression.

In factored form, a polynomial function is expressed as the product of linear factors or irreducible quadratic factors.

Each factor represents a root or zero of the function.

The degree of a polynomial is determined by the highest power of the variable in the expression.

To find the degree of the function, examine each factor in the factored form.

For linear factors, the degree is 1 since the highest power of the variable is 1.

For irreducible quadratic factors, the degree is 2 since the highest power of the variable is 2.

By observing the highest power in the factored expression, you can determine the degree of the polynomial function.

If the highest power is 1, the polynomial has a degree of 1 (linear function). If the highest power is 2, the polynomial has a degree of 2 (quadratic function). And so on.

It's important to note that the degree of a polynomial corresponds to the highest power of the variable in the expression and not the number of factors.

The number of factors indicates the number of roots or zeros of the polynomial, but it doesn't determine the degree.

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We have the following equation given:

And we need to solve for m. So we can start aggrupating the terms like this:

Now we can subtract 5m from both sides of the equation and we got:

And now we can add 5 in both sides of the equation and we got:

And dividing by 3 got this:

At a significance level of 0.01, we can confidently state that the student's claim is true.

The hypothesis in this question can be stated as follows:

Null Hypothesis: H0: μ1 = μ2 (There is no difference between the mean of four-year college enrollment and two-year college enrollment.)

Alternative Hypothesis: H1: μ1 > μ2 (Mean enrollment of four-year colleges is greater than the mean enrollment of two-year colleges in the United States.)

The significance level (α) is given as 0.01, which represents the probability of rejecting the null hypothesis when it is actually true.

To calculate the test statistic, we can use the formula:

z = ((X1 - X2) - (μ1 - μ2)) / √((σ1² / n1) + (σ2²  / n2))

Substituting the given values:

z = ((6193 - 4305) - (0)) / √((598²  / 35) + (572²  / 35))

z = 10.33

Since this is a right-tailed test, we need to compare the test statistic with the critical value. At a significance level of 0.01, the critical value is 2.33.

The calculated test statistic (10.33) is greater than the critical value (2.33). Therefore, we reject the null hypothesis and conclude that there is enough evidence to support the claim that the mean enrollment at four-year colleges is higher than at two-year colleges in the United States.

In conclusion, at a significance level of 0.01, we can confidently state that the student's claim is true. The mean enrollment at four-year colleges is higher than at two-year colleges in the United States.

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Evaluate the integral. (use symbolic notation and fractions where needed. use for the arbitrary constant. absorb into as muсh as possible.) ∫70( 1)(2 9)2= ∫70(1)(29)^2 dx = 58,870x + C, where C is the arbitrary constant of integration.

To evaluate the integral, we first need to simplify the integrand:
70(1)(29)^2 = 70(1)(841) = 58,870

So the integral becomes:
∫58,870 dx

Since the indefinite integral of a constant is equal to that constant times the variable, we have:
∫58,870 dx = 58,870x + C

where C is the arbitrary constant of integration.

Therefore, the final answer is:
∫70(1)(29)^2 dx = 58,870x + C, where C is the arbitrary constant of integration.

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The value of Sin(P) = Sin(30°) = 1/2

It is a triangle with constant angles of 30, 60, and 90. This triangle is always a right triangle, as one of the angles is 90 degrees. Thus, a right-angled triangle is formed by these angles. Additionally, the right angle is equal to the sum of two acute angles, which will have a 1: 2 or 2: 1 ratio.

Triangle PQR is given.

Angle QRP is a right angle.

∠QRP = 90°

And the other two angle measures are,

∠RPQ = 30°, and ∠PQR = 60°.

The value of Sin(P) = Sin(30°) = 1/2

Therefore, SinP = 1/2.

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