What kind of sequence is this? –38, –44, –50, –56

Mean =  (sum of all observations in given data set) ÷ (total number of observations)

In an odd-numbered set, the median will be the number in the very middle of the list. In an even-numbered set, the average of the two middle numbers will be mode.

The mode is the most frequent number.

Mean:

Using two straightforward procedures, we can determine the mean, or average, of a data set:

(1) Add up all of the values to find the sum.

(2) Divide the sum by the number of values in the data set

Mean = (sum of all observations in given data set) ÷ (total number of observations)

Median:

The middle score in the group is known as the median. To find the median, start by arranging all of the data points from smallest to largest. Means arrange the data either in ascending order or in the descending order. In an odd-numbered set, the median will be the number in the very middle of the list. In an even-numbered set, you will need to calculate the average of the two middle numbers.

Mode:

To quickly determine the mode, arrange the numbers in ascending order by least to greatest, then tally the frequency of each number. The mode is the most frequent number.

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The event for which the probability can be calculated from the two events given is event B.

Given that:

Mean = 2.5 children per family

Standard deviation = 1.3 children per family

Here, for event B, the sample size is going to take 40.

So, the distribution can be formulated to be approximately normal distribution since the sample size is 40 which is greater than 30.

So, the mean is the same which is 2.5.

The standard deviation can be calculated as 1.3/√40.

So, event B can be calculated for the probability.

Hence the event is event B.

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The complete question is given below:

The distribution of the number of children per family in the United States is strongly skewed right with a mean of 2.5 children per family and a standard deviation of 1.3 children per family.

Event A: Randomly selecting a family from the United States that has 3 or more children.

Event B: Randomly selecting 40 families from the United States and finding an average of 3 or more children.

The probability of one of the two events can be calculated even though the distribution of the population is strongly skewed right. For which event can the probability be calculated?

When comparing the data to determine the location with the most consistent temperature, the measure of variability that should be used for both sets of data is the IQR (Interquartile Range).

This is because the IQR is a robust measure of variability that is not influenced by extreme values or outliers. Therefore, it is suitable for both symmetric and skewed distributions. Therefore, the answer is iqr, because sunny town is symmetric and iqr, because beach town is skewed.

When comparing the data to determine the location with the most consistent temperature, you should use the IQR (interquartile range) because it is a robust measure of variability that is not affected by extreme values or skewness. In this case, you should use IQR for both Sunny Town and Beach Town, regardless of their symmetry or skewness, to get a reliable comparison of their temperature consistency.

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In the trapezoid ABCD, the midpoints S and T divide the legs into equal segments. By setting up equations based on the fact that S and T are midpoints, we can solve for the value of x. We find that x equals 0, which means that the legs of the trapezoid have equal lengths.

To find the value of x in the trapezoid ABCD, we need to use the fact that S and T are midpoints of the legs.

First, let's label the points:
- A is one endpoint of the shorter base
- B is the other endpoint of the shorter base
- C is one endpoint of the longer base
- D is the other endpoint of the longer base
- S is the midpoint of AB
- T is the midpoint of CD

Given that AB = 3x, ST = 15, and CD = 9x, we can set up an equation based on the fact that S and T are midpoints.
Since S and T are midpoints, the lengths of AS and SB must be equal, and the lengths of CT and TD must also be equal.
Therefore, AS = SB and CT = TD.

From this information, we can set up the following equation:
AS + ST + TB = AB

Since ST = 15, AS = SB, and AB = 3x, the equation becomes:
AS + 15 + SB = 3x
Since AS = SB, we can rewrite the equation as:
2AS + 15 = 3x
Similarly, we can set up an equation for CT and TD:
CT + ST + TD = CD

Since ST = 15, CT = TD, and CD = 9x, the equation becomes:
CT + 15 + TD = 9x

Since CT = TD, we can rewrite the equation as:
2CT + 15 = 9x

Now we have two equations:
2AS + 15 = 3x
2CT + 15 = 9x

To find the value of x, we can solve this system of equations. Subtracting the first equation from the second equation gives us:
2CT + 15 - (2AS + 15) = 9x - 3x

Simplifying both sides gives us:
2CT - 2AS = 6x

Now we can substitute AS and CT with their respective values:
2(TD) - 2(SB) = 6x
Since TD = CT and SB = AS, we have:
2TD - 2SB = 6x
Since we know that SB = AS and TD = CT, we can rewrite the equation as:
2(TD) - 2(AS) = 6x
Simplifying gives us:
2TD - 2AS = 6x

Since TD = CT and AS = SB, we have:
2CT - 2SB = 6x
Substituting the values of CT and SB gives us:
2(9x) - 2(3x) = 6x
Simplifying gives us:
18x - 6x = 6x
Combining like terms gives us:
12x = 6x
Dividing both sides by 6 gives us:
x = 0

Therefore, the value of x in the trapezoid ABCD is 0.

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Answer:

No asymptotes

Step-by-step explanation:

There are no asymptotes because it's not a rational expression. It's a linear expression rather.

Answer:

y=6

Step-by-step explanation:

took the test

Answer: 1/18

Step-by-step explanation:

-4/9 is equivalent to -8/18. (-7/18) - (-8/18) = 1/18

Step-by-step explanation:

(-4/9) - (-7/18)

First we have to find the LCM (Least Common Multiple) between the two denominators.

9, 18

18

As you can see from above, 18 is the LCM of 9 and 18. Now we multiply the numerators with the amount of times you had to list the multiples. For 9 it's 2 times (9, 18), and for 18 it's 1 time (18).

So 4x2=8 and 7x1=7

We can now rewrite the fractions as so:

(-8/18) - (-7/18)

Since they're both negatives we change the second fraction to a positive

(-8/18) - (+7/18)

And if we subtract both we end up with

-1/18

I hope this helps, I tried to explain this in the most simplest way I can

Answer:

they will have the same aboulsute value.

Step-by-step explanation:

because the abouslute value can not be negitive

Starting from an initial altitude of 0 feet, the drone ascended 2023 feet, descended 734 feet, and then ascended 534 feet. Evaluating the expression, we find that the drone's current altitude is 1823 feet.

To determine the drone's current altitude, we can use an addition expression to combine the changes in altitude. Given that the drone ascended 2023 feet, then descended 734 feet, and finally ascended 534 feet, we can write the addition expression as follows:

Current Altitude = Initial Altitude + Ascend 1 - Descend - Ascend 2

Let's evaluate this expression step by step:

Initial Altitude: The drone starts at an initial altitude of 0 feet.

Ascend 1: The drone ascends 2023 feet. Adding this to the initial altitude, we get 0 + 2023 = 2023 feet.

Descend: The drone descends 734 feet. Subtracting this from the current altitude, we have 2023 - 734 = 1289 feet.

Ascend 2: The drone ascends an additional 534 feet. Adding this to the current altitude, we get 1289 + 534 = 1823 feet.

Therefore, the drone's current altitude is 1823 feet.

To determine the drone's current altitude, we need to account for the changes in altitude as it ascends and descends. By using an addition expression, we can combine these changes to find the final altitude.

Starting with an initial altitude of 0 feet, we add the ascent of 2023 feet to find the altitude after the first ascent. Then, we subtract the descent of 734 feet to adjust the altitude downward. Finally, we add the second ascent of 534 feet to determine the drone's current altitude.

In the evaluation of the expression, we perform the addition and subtraction operations step by step to get the final result of 1823 feet as the drone's current altitude.

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Answer:

1500+337.50 = $1,837.5

Step-by-step explanation:

You want to calculate the interest on $1500 at 4.5% interest per year after 5 year(s).

The formula we'll use for this is the simple interest formula, or:

I = P x r x t

Where:

P is the principal amount, $1500.00.

r is the interest rate, 4.5% per year, or in decimal form, 4.5/100=0.045.

t is the time involved, 5....year(s) time periods.

So, t is 5....year time periods.

To find the simple interest, we multiply 1500 × 0.045 × 5 to get that:

The interest is: $337.50

If we want to find the value of f(x) at x = -2, we simply put "-2" into the given function. Shown below:

Answer:

the equation of A⁢B↔ is y = 0.5x + 0.5.

Step-by-step explanation:

Answers will vary based on the method used, but the final slope-intercept form of the equation of A⁢B↔ will be the same.

Let the equation of A⁢B↔ in slope-intercept form be y=m⁢x+d, where m is the slope and d is the y-intercept.

The coordinates of points A and B are (1, 1) and (5, 3), respectively, so the slope of A⁢B↔ is

m=yB−yA/xB−xA=24=0.5.

Substitute the value of m back in the equation:

y = 0.5x + d.

Substitute the coordinate of point A (1, 1) in the equation above, and solve for d:

1 = 0.5 + d

d = 0.5.

Therefore, the equation of A⁢B↔ is y = 0.5x + 0.5.

To check whether C lies on A⁢B↔ substitute the x-coordinate of C into the right side of the equation: 0.5 (2.6) + 0.5 = 1.8.

The result is equal to the y-coordinate of C. Thus, C satisfies the equation of A⁢B↔ which means that C lies on A⁢B↔.

Answer:

6\(\sqrt{3} \\\)

Step-by-step explanation:

Because they give you a 60 degree angle and a right angle, we know this is a 30 60 90 triangle. Because of the properties of a 30 60 90 triangle, we know that if the shortest side (the bottom) is referred to as b, the hypotenuse will be 2 times the value of b (2b) and the side x would be b times the square root of 3. To solve this you would divide 12 by 2 to get b, which would be 6. To get the side you're solving for, x, you would then multiply 6 by the square root of 3. this is your answer.

Answer:

6√3

Step-by-step explanation:

it's a 30,60,90 triangle

the other side is 12/2 = 6

so x = 6√3

The slope of the secant line PQ is -2.5.

To find the slope of the secant line PQ, we first need to find the coordinates of point Q. Since Q has an x-coordinate of 1.5, we can plug this value into the given equation y = 2x + x^2 to find the y-coordinate.

y = 2(1.5) + (1.5)^2
y = 3 + 2.25
y = 5.25

So, Q has coordinates (1.5, 5.25). Now we can find the slope of the secant line PQ using the formula:

slope = (y2 - y1) / (x2 - x1)

where P is (x1, y1) and Q is (x2, y2). Plugging in the coordinates:

slope = (5.25 - 4) / (1.5 - 2)
slope = 1.25 / (-0.5)
slope = -2.5

The slope of the secant line PQ is -2.5.

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Answer: See explanation

Step-by-step explanation:

By the Triangle Inequality Theorem, the length of the side must be greater than 1 ft because the sum of two side lengths must be greater than the length of the third side. The third side must be less than 7 ft but greater than 1 ft.

Triangle inequality: 1 < x < 7

Hope that helped!

Answer:

Perpendicular bisector - A line that bisects another line into two equal halves so that four right angles are created.

Cylinder - A 3D solid with circles as its bases.

Plane - A flat, 2D surface that extends infinitely.  

Regular Polygon -  A polygon where all angles and all sides are equal  (ex. square, pentagon, triangle).

To convert infix notation to postfix notation, we use a set of steps involving scanning the infix expression and creating a stack and list. The resulting postfix expression can be evaluated using a stack-based algorithm.

The postfix expression for the given infix expression is:

a 7 b c / * 2 d * -

To convert an infix expression to postfix notation, we use the following steps:

1. Create an empty stack and a list to hold the postfix expression.

2. Scan the infix expression from left to right.

3. If the token is an operand (such as a variable or a number), add it to the postfix expression list.

4. If the token is a left parenthesis, push it onto the stack.

5. If the token is a right parenthesis, pop tokens from the stack and add them to the postfix expression list until a left parenthesis is encountered. Discard the left and right parentheses.

6. If the token is an operator, pop operators from the stack and add them to the postfix expression list if they have higher precedence than the current operator. Then push the current operator onto the stack.

7. After all tokens have been processed, pop any remaining operators from the stack and add them to the postfix expression list.

Using these steps on the given infix expression, we obtain the postfix expression:

a 7 b c / * 2 d * -

This postfix expression can be evaluated using a stack-based algorithm to compute the final result.

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Answer:

x = 60⁰

y = 60⁰

Step-by-step explanation:

Parallel angles will always have the same degree so if the parallel of x is 60⁰ then x is also 60⁰

To solve for y the angle we need to know the angle parallel to it and since the adjacent angle of 60⁰ is supplementary then the other angle is 120⁰. The angle below the 120⁰ is also supplementary to is meaning that angle is 60⁰. The 60⁰ angle is parallel to y wich means tha y is equal to 60⁰ as well.

These three expressions

6x ÷ 6 = 20 ÷ 6

6x + 5 = 20 + 5

6x − 1 = 20 − 1

will be equal to the given expression.

Operators, constants, and variables all come together to form an expression. A value can be produced by an expression using one or more operands and zero or more operators.

We have to check which equation will be equal to 6x = 20

6x ÷ 6 = 20 ÷ 6

After Multiplying both sides by 6.

We get, 6x = 20

6x ÷ 6 = 20 ÷ 20

After simplifying we get,

x = 1

Multiplying both sides by 6

6x = 6, Hence it doesn't satisfy.

6x + 5 = 20 + 5

Subtract 5 both sides of the equation

We get, 6x = 20

6x − 1 = 20 − 1

Adding 1 both sides of the equation,

We get, 6x = 20

6x × 6 = 20 × 20

After simplifying, we get

36x = 400

Hence, only

6x ÷ 6 = 20 ÷ 6

6x + 5 = 20 + 5

6x − 1 = 20 − 1

will be equal to the given expression.

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If Two planes are parallel and each plane contains a line, the two lines are  not skew because In the event that any two lines fall on a single plane, they will either intersect or be parallel to one another. Both instances violate the concept of a skew line because the skew lines are neither parallel nor intersect.

Infinitely many lines cross through, yet only one of them is parallel to. Lines that never intersect and are in distinct planes are known as skew lines. Parallel lines and skew lines are distinguished by the fact that they both reside in the same plane, whereas skew lines do not.

The two lines would overlap at some point if the two planes on which they are located weren't parallel, which again defies the definition of skew lines.

Therefore, The skew lines are thus present if and only if both lines fall on a pair of parallel planes.

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Answer:7/8

Step-by-step explanation:your mom

Answer:

0.0274

Step-by-step explanation:

A z-score measures exactly how many standard deviations above or below the mean a data point is.

The z-score for a normal distribution is given by the formula
\(z = \dfrac{X - \mu}{\sigma}\\where\\\\X = data \;point}\\\mu = mean\\\sigma = standard\; deviation\)

Plugging in values:
X = 125
μ = 100
σ = 13

z = (125-100)/13 = 1.92308

We are asked to find the probability that the score exceeds 125

This is the same as P(z > 1.92308) which is the area to the right of z = 1.92308

P(z > 1.92308) = 0.0274 (from either the tables or calculator)

The total amount the mechanic will need in retirement savings to meet their retirement income goal is $880,000.

Option A.

The total amount the mechanic will need in retirement savings to meet their retirement income goal is calculated as follows;

80% of  $44,000 = ?

= 0.8 x  $44,000

= $35,200

The amount needed to generate $35,200 annually at a 4% withdrawal rate is calculated as follows;

Let the amount = x

0.04x = $35,200

x = $35,200/0.04

x = $880,000

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Answer:

840.32

Step-by-step explanation:

Answer:

If the dimensions of the scaled painting are 8 times smaller than the actual painting, then the actual dimensions can be found by multiplying the scaled dimensions by 8.

So, the actual dimensions of the painting are:

12 inches x 8 = 96 inches (width)

16 inches x 8 = 128 inches (height)

μx = 752 hours, σx ≈ 8.21 hours

The shape of the sampling distribution is approximately normal.

To find the mean (μx) and standard deviation (σx) of the sampling distribution of x, we can use the following formulas:

μx = μ (mean of the population)

σx = σ / √n (standard deviation of the population divided by the square root of the sample size)

Given:

- Mean of the population (μ) = 752 hours

- Standard deviation of the population (σ) = 45 hours

- Sample size (n) = 30

Substituting the values into the formulas, we have:

μx = 752 hours

σx = 45 hours / √30 ≈ 8.21 hours (rounded to one decimal place)

Therefore:

μx = 752 hours

σx ≈ 8.21 hours

The shape of the sampling distribution of x, assuming that the sample size is sufficiently large (n ≥ 30) and the population distribution is approximately normal, follows an approximately normal distribution. The Central Limit Theorem states that regardless of the shape of the population distribution, the sampling distribution of the sample mean tends to be approximately normal.

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Answer: the inner semi circle

Step-by-step explanation:

It Depends, but I think the outer semi circle is easier to use.

The point that is located at the ordered pair (4, -2) is given as follows:

Point B.

The general format of an ordered pair is given as follows:

(x,y).

In which the coordinates are given as follows:

On the coordinate plane, we have that:

Hence the coordinates for this problem are given as follows:

A(-2, 4), B(4, -2), C(-4, 2) and D(2, -4).

The graph is given by the image presented at the end of the answer.

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Answer:

14.01m

Step-by-step explanation:

Perimeter of the rectangular wire = circumference of the circle

Perimeter of the rectangular wire = 2(L+W)

Perimeter if the rectangular wire = 2(12+10)

Perimeter if the rectangular wire = 2(22)

Perimeter if the rectangular wire = 44m²

Circumference of the circle = πd

44 = πd

d = 44/3.14

d = 14.01m

Hence the circumference of the circle is 14.01m

The null hypothesis assumes that the proportion of patients needing a root canal is 20% or less, while the alternative hypothesis suggests that the proportion is greater than 20%.

The null and alternative hypotheses in this case can be stated as follows:

Null Hypothesis (H0): The proportion of patients that need a root canal (p) is equal to or less than 20%.

Alternative Hypothesis (Ha): The proportion of patients that need a root canal (p) is more than 20%.

Symbolically, we can represent the hypotheses as:

H0: p ≤ 0.20

Ha: p > 0.20

The dental assistant will collect data and perform a statistical test to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

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