Find the mean, median, mode, and range for the data set given.

112, 122, 132, 142, 152

Answer:

x=1.9

Step-by-step explanation:

[tex]\frac{x}{4.6} =\frac{4.6}{11}[/tex]

[tex]11x=21.16[/tex]

[tex]X=1.9[/tex]

In response to the stated question, we may state that As a result, the equation proper answer is: B. 16/40 + 15/40 = 31/40

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

We must identify a common denominator for the two fractions in order to solve the formula 2/5 + 3/8. Because 40 is the lowest common multiple of 5 and 8, we can transform both fractions to have a denominator of 40:

2/5 = 16/40

3/8 = 15/40

We can now sum the two fractions:

16/40 + 15/40 = 31/40

As a result, the proper answer is:

B. 16/40 + 15/40 = 31/40

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Answer:

p ≥ 228

Step-by-step explanation:

p ≥ 228

This inequality means the Bowlers have to score at least 228 points to move on.

Hope this helped!

Answer:

  see attached

Step-by-step explanation:

You want the given triangle dilated by a factor of -3 about point A.

To find the image point corresponding to a pre-image point, multiply the pre-image point's distance from A by the dilation factor. The negative sign means the distance to the image point is measured in the opposite direction.

In the attached figure, the chosen point is 4 units up and 5 units right of A. Its image in the dilated figure is 3·4 = 12 units down, and 3·5 = 15 units left of A.

This same process can be used to locate the other vertices of the triangle's image.

     |-----|-----|-----|----|-----|-----|--│--|-----|----|-----|

    -5   -4   -3   -2   -1    0    1   │  2    3    4    5

                                            1 1/2

On this number line, the tick mark labeled "1 1/2" is located halfway between the integer values of 1 and 2.

To represent the number 1 1/2 on a number line, we need to draw a horizontal line with evenly spaced tick marks. Each tick mark represents a specific value on the number line. Since 1 1/2 is a mixed number that includes a whole number (1) and a fraction (1/2), we need to locate it between the integer values of 1 and 2. The tick mark for 1 1/2 should be halfway between these two integers, which means it would be located at the midpoint of the line segment that connects the tick marks for 1 and 2. By placing the tick mark for 1 1/2 in the correct position on the number line, we can accurately represent this number visually.

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Hello,

3m + 5 > 2(m - 7) =

3m + 5 > 2m - 14

3m - 2m > - 14 - 15

x > - 29

Step-by-step explanation:

3m±2m>-14-5

5m>-19

m>-19/5

m>3.8

We need 144 men to build the house in 12 days working 13 hours a day.

Let M be the number of men needed to build the house in 12 days working 13 hours a day.

140 x 10 x 16 = M x 13 x 12

Simplifying the equation, we get:

22400 = 156M

Dividing both sides by 156, we get:

M = 144.1

An equation in mathematics is a statement that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The expressions on either side can be numbers, variables, or combinations of both. The equation expresses that the values of the expressions on both sides are equivalent.

Equations play a fundamental role in many areas of mathematics and are used to model various real-world situations, such as physics, engineering, and finance. They can be solved using various techniques, such as substitution, elimination, or graphing, to find the values of the variables that satisfy the equation.

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Answer:

x = 4

Step-by-step explanation:

6x + 21  =  5x + 25

Then, subtract 5x from both sides:

x + 21  = 25

Then, subtract 21 from both sides.

x = 4

Therefore, x is equal to 4 degrees

Answer:$2.60

Step-by-step explanation:40*0.065

Answer:42.06

Step-by-step explanation:

Answer:

A ,B ,C

Step-by-step explanation:

2+2+2+2 equals 8

4x2 equals 8 and

1x8 equals 8

Answer:

A) 2 + 2 + 2 + 2

B) 4 × 2

C) 1 × 8

Hope this helps!

Step-by-step explanation:

A = 4 + 4 = 8

B = 8

C = 8

D = 16

E = 16

Answer: $1,071.54

Step-by-step explanation:

To find the interest refund, first we need to calculate the total interest charged on the loan. We can do this by multiplying the monthly interest by the number of months in the loan:

Monthly interest = Total interest / Number of months

Monthly interest = $2,802 / 35

Monthly interest = $80.06

Total interest charged on the loan = Monthly interest x Number of months

Total interest charged on the loan = $80.06 x 35

Total interest charged on the loan = $2,802.10

Now we need to calculate the interest that would have been charged for the remaining 13 months of the loan:

Interest for remaining 13 months = Monthly interest x Remaining months

Interest for remaining 13 months = $80.06 x 13

Interest for remaining 13 months = $1,040.78

Finally, we can find the interest refund by subtracting the interest for the remaining 13 months from the total interest charged on the loan:

Interest refund = Total interest charged - Interest for remaining months

Interest refund = $2,802.10 - $1,040.78

Interest refund = $1,074.32

Therefore, the interest refund on the loan is $1,074.30.

Answer: The graph of function g(x) is shifting down by 3 (vertical shift) because the -3 is not part of x but y (the whole graph). Originally there is no y-intercept and the f(x) function crosses the origin, but now there is a y-intercept at (0, -3)

The maximum area of the surfboard correct to 2 places is 0.67 m².

Given that a surfboard is in the shape of a rectangle and a semicircle, and its perimeter is to be 4m. We need to find the maximum area of the surfboard, correct to 2 decimal places.

Let the radius of the semicircle be 'r' and the length and breadth of the rectangle be 'l' and 'b' respectively. Perimeter of the surfboard = [tex]4m => l + 2r + b + 2r = 4 => l + b = 4 - 4r[/tex] -----(1)

Area of surfboard = Area of rectangle + Area of semicircle Area of rectangle = l × b Area of semicircle = πr²/2 + 2r²/2 = (π + 2)r²/2Area of surfboard = l × b + (π + 2)r²/2 -----(2)

We have to maximize the area of the surfboard. So, we have to find the value of 'l', 'b', and 'r' such that the area of the surfboard is maximum .From equation (1), we have l + b = 4 - 4r => l = 4 - 4r - bWe will substitute this value of 'l' in equation (2)

Area of surfboard = l × b + (π + 2)r²/2 = (4 - 4r - b) × b + (π + 2)r²/2 = -2b² + (4 - 4r) b + (π + 2)r²/2Now, we have to maximize the area of the surfboard, that is, we need to find the maximum value of the above equation.

To find the maximum value of the equation, we can differentiate the above equation with respect to 'b' and equate it to zero. d(Area of surfboard)/db = -4b + 4 - 4r = 0 => b = 1 - r Substitute the value of 'b' in equation (1),

we get l = 3r - 3Now, we can substitute the values of 'l' and 'b' in the equation for the area of the surfboard.

Area of surfboard =

[tex]l × b + (π + 2)r²/2 = (3r - 3)(1 - r) + (π + 2)r²/2 = -r³ + (π/2 - 1)r² + 3r - 3[/tex]

[tex]-r³ + (π/2 - 1)r² + 3r - 3 = -0.6685 m² \\[/tex]

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Answer:

Step-by-step explanation:

see diagram

Hi!
Let's write this out.
Her limit is $900, and she's used $450. So, we subtract 450 from 900.
900-450 = 450.

So, she has $450 available credit left.
Hope this helps!
~~~PicklePoppers~~~

Answer: your credit utilization ratio on that card would be 50% but the answer is 450

Step-by-step explanation:

900-450 = 450

Answer:

$109.99

Step-by-step explanation:

The original price of each tire is [tex]\[/tex][tex]109.99[/tex]

Take the amount saved and divide by 4 to find the amount saved on each tire

[tex]96.16\div4 =24.04[/tex]

Add that to the sale price of each tire to find the original price

[tex]85.95+24.04 =109.99[/tex]

Therefore, The original price is $109.99.

The polynomial function modeled by the given diagram is given as follows:

p(x) = 3x² - 7x - 6.

The polynomial function modeled by the given diagram is obtained considering the keys of the problem, which are the terms represented by each figure.

The polynomial is constructed as follows:

Then the expression used to construct the polynomial is given as follows:

p(x) = 3x² + 2x - 9x - 6.

Combining the like terms, the polynomial function is defined as follows:

p(x) = 3x² - 7x - 6.

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Answer:

Let's use the formula for the volume of a right circular cone to solve this problem:

V = (1/3)πr^2h

We are given that the radius is increasing at a rate of 1.4 in/s and the height is decreasing at a rate of 2.6 in/s. We want to find the rate at which the volume is changing when the radius is 144 in. and the height is 138 in. In other words, we want to find dV/dt when r = 144 and h = 138.

Using the chain rule of differentiation, we can express the rate of change of the volume as follows:

dV/dt = (dV/dr) (dr/dt) + (dV/dh) (dh/dt)

To find dV/dr and dV/dh, we differentiate the formula for the volume with respect to r and h, respectively:

dV/dr = (2/3)πrh

dV/dh = (1/3)πr^2

Substituting the given values and their rates of change, we have:

dV/dt = (2/3)π(144)(138)(1.4) + (1/3)π(144)^2(-2.6)

dV/dt = 55,742.4 - 1,994,598.4

dV/dt = -1,938,856 in^3/s

Therefore, when the radius is 144 in. and the height is 138 in., the volume of the cone is decreasing at a rate of approximately 1,938,856 cubic inches per second.

Step-by-step explanation:

Answer: Felipe has walked 25.1 meters.

Step-by-step explanation:

Felipe walks the length of his living room, which is 9.1 meters. He then turns and walks the width of his living room, which is 3.5 meters. Finally, he walks back to the corner he started from, which is another 9.1 meters.

The total distance that Felipe has walked is the sum of the distances he covered in each of these three parts of his walk. So, we need to add up 9.1 meters, 3.5 meters, and 9.1 meters to get the total distance.

9.1 m + 3.5 m + 9.1 m = 21.7 m

Therefore, Felipe has walked 21.7 meters so far. However, he still needs to walk back to the corner he started from. This distance is equal to the diagonal of the rectangle formed by his living room.

We can use the Pythagorean theorem to find the length of this diagonal. The length and width of the rectangle are 9.1 meters and 3.5 meters, respectively. Let d be the length of the diagonal, then:

d² = 9.1² + 3.5²

d² = 83.06

d ≈ 9.11 meters

Therefore, the total distance that Felipe has walked is approximately:

21.7 m + 9.11 m ≈ 25.1 m

So, Felipe has walked about 25.1 meters.

Answer:

Felipe has walked 25.2 meters in total.

Step-by-step explanation:

To find out how far Felipe has walked, we need to calculate the perimeter of his living room. The perimeter is the distance around the outside of a shape.

The formula for the perimeter of a rectangle is:

perimeter = 2(length + width)

Given that the length of Felipe's living room is 9.1 meters and the width is 3.5 meters, we can substitute these values into the formula and get:

perimeter = 2(9.1 + 3.5)

perimeter = 2(12.6)

perimeter = 25.2 meters

The Sale price is C. $260.63.

Selling price is the price at which a product or service is sold by a business or seller to a customer. It is the amount of money that a customer must pay in order to purchase the product or service. The selling price is typically determined by factors such as production costs, competition, supply and demand, and profit margins.

Sale price is the discounted price at which a product or service is sold for a limited period of time. It is usually a lower price than the regular price, and it is offered to customers as an incentive to make a purchase. Sale prices can be determined by applying a discount or markdown to the regular selling price.

In the given question,

To find the sale price, we need to first calculate the amount of the markdown:

Markdown = Regular Price x Markdown Rate

Markdown = $389 x 0.33

Markdown = $128.37

The sale price is then the regular price minus the markdown:

Sale Price = Regular Price - Markdown

Sale Price = $389 - $128.37

Sale Price = $260.63

Therefore, the answer is C. $260.63.

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The correct option is C, A 95% confidence interval for the average starting salary of all attorneys in the city is (91331.94, 113352.06)

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

∝= [tex]\frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a p-value of 1-∝.

So it is z with a value of, so [tex]1-0.025=0.975,Soz= 1.96[/tex]

Now, find M as such

[tex]M= z*\frac{1}{\sqrt{n} } *[/tex]σ

In which is the standard deviation of the population and n is the size of the sample.

[tex]M= 1.96* \frac{21756}{\sqrt{15}} =11010.06[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 102342 - 11010.06 = 91331.94.

The upper end of the interval is the sample mean added to M. So it is 102342 + 11010.06 = 113.352.06.

So the correct answer is:

(91331.94, 113352.06)

Standard deviation is a measure of how much the values in a data set vary from the average or mean value. It is a statistical measure that indicates the extent to which the values are spread out from the mean. A low standard deviation indicates that the values are clustered around the mean, while a high standard deviation indicates that the values are more widely spread out.

Standard deviation is commonly used in statistics and probability theory to measure the uncertainty or risk associated with a particular event or outcome. It is also used in fields such as finance, economics, and engineering to analyze data and make predictions. Standard deviation can provide valuable insights into the distribution of data and help identify trends and patterns in the data set.

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Complete Question:

A random sample of 15 recent college graduates found that starting salaries for attorneys in New York City had a mean of $102,342 and a standard deviation of $21,756. There are no outliers in the sample data set. Construct a 95% confidence interval for the average starting salary of all attorneys in the city. Group of answer choices

A). (89869.82, 114814.18)

B). (90292.73, 114391.27)

C). (91331.94, 113352.06)

D). (90371.37, 114312.63)

The z-score for the 75th percentile of the standard normal distribution is given by 0.67 that is option A.

The most significant continuous probability distribution is the Normal Distribution, often known as the Gaussian Distribution. It is also known as a bell curve. The normal distribution represents a large number of random variables either nearly or exactly.

I found one that shows the following:

Z value Table entry

0.67   0.7486

0.68   0.7517

As a result, the Z value for 0.75 is between 0.67 and 0.68.

Interpolation yields the z value of 0.6745.

If you have a TI-84 calculator, you may calculate the z value as follows:

VARS - 2nd (this will show the DISTR menu)

To select invNorm, press 3.

Enter the value for the area/table (0.75)

If you press enter, it will return the z value.

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Complete question:

what is the z-score for the 75th percentile of the standard normal distribution is:

The instantaneous velocity of the object at t = 6 is 2.

Suppose that s is the position function of an object, given as s(t) = 2t - 7. We compute the instantaneous velocity of the object at t = 6 as follows. Use exact values. First we compute and simplify (6 + h). s(6 + h) = 2(6 + h) - 7 = 12 + 2h - 7 = 2h + 5Then we compute and simplify the average velocity of the object between t = 6 and t = 6 + h.8(6+h) - s(6) h = 8(6 + h) - (2(6) - 7) h= 8h + 56

Then, to rationalize the numerator in the average velocity. (If it applies, simplify again.)$(6 + h) - $(6) h(h(h) + 56)/(h(h)) = (8h + 56)/h The instantaneous velocity of the object att = 6 is the limit of the average velocity as h approaches zero.s(6 + h) – $(6) v(6) lim h -0s(6 + h) – s(6) v(6) lim h -0Using the above calculation, we get:s(6 + h) – s(6) / h lim h -0s(6 + h) = 2(6 + h) - 7 = 2h + 5So,s(6 + h) – s(6) / h lim h -0(2h + 5 - (2(6) - 7)) / h= (2h + 5 - 5) / h = (2h / h) = 2

Therefore, the instantaneous velocity of the object at t = 6 is 2.

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Thus, the following outcomes satisfy the condition:1, 61, 11, 12, 21, 13, 31, 14, 41, 15, 52, 25, 34, and 43Therefore, the probability of the sum being 7 or at least one die being 1 is:P(sum is 7 or at least one die is 1) = 15/36 = 5/12

Hence, P(sum is odd) = 7/36, P(sum is 5) = 1/9, P(sum is 7) = 1/6, P(sum is 7 and at least one die is 1) = 5/18, and P(sum is 7 or at least one die is 1) = 5/12.

In the given experiment of rolling two dice, the following probabilities are to be determined:

P(sum is odd), P(sum is 5), P(sum is 7), P(sum is 7 and at least one of the die is 1), and P(sum is 7 or at least one of the die is 1).The sum of two dice is odd if one die has an odd number and the other has an even number. The possibilities of odd numbers are 1, 3, and 5, while the possibilities of even numbers are 2, 4, and 6. Therefore, the following outcomes satisfy the condition:

1, 22, 24, 36, 42, 44, and 66Thus, the probability of the sum being odd is: P(sum is odd) = 7/36The sum of two dice is 5 if one die has 1 and the other has 4, or one die has 2 and the other has 3. Thus, the following outcomes satisfy the condition:1, 42, 3Therefore, the probability of the sum being 5 is: P(sum is 5) = 4/36 = 1/9The sum of two dice is 7 if the dice show 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, or 6 and 1.

Thus, the following outcomes satisfy the condition:1, 63, 54, 45, 36, and 2Therefore, the probability of the sum being 7 is: P(sum is 7) = 6/36 = 1/6The sum of two dice is 7 and at least one die is 1 if the dice show 1 and 6, 6 and 1, 1 and 1, 1 and 2, 2 and 1, 1 and 3, 3 and 1, 1 and 4, 4 and 1, or 1 and 5. Thus, the following outcomes satisfy the condition:1, 61, 11, 12, 21, 13, 31, 14, 41, and 15

Therefore, the probability of the sum being 7 and at least one die being 1 is:P(sum is 7 and at least one die is 1) = 10/36 = 5/18The sum of two dice is 7 or at least one die is 1 if the dice show 1 and 6, 6 and 1, 1 and 1, 1 and 2, 2 and 1, 1 and 3, 3 and 1, 1 and 4, 4 and 1, 1 and 5, 2 and 5, 5 and 2, 3 and 4, or 4 and 3.

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The confidence interval is calculated by adding and subtracting the product of a constant (usually 1.96), the margin of error, and the mean.

The constant times the margin of error is added and subtracted from the sample mean to obtain the confidence interval range.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.

A low standard deviation means data are clustered around the mean, and a high standard deviation indicates data are more spread out.
The constant is determined by the confidence level of your analysis (typically 95%) and the margin of error is determined by the standard deviation and the size of your sample.

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Answer:

If a quadratic equation has solutions of -3 and -4, then it can be written in factored form as:

(x + 3)(x + 4) = 0

To convert this to standard form, we can multiply out the factors:

x^2 + 7x + 12 = 0

Therefore, the quadratic equation in standard form that has solutions of -3 and -4 is:

x^2 + 7x + 12 = 0

The set of all possible y-values for the function h constitutes its range. The range is therefore [-3, 0].

The collection of all feasible output values (dependent variable) of a function is known as the range in mathematics. It is the totality of all possible numbers that the function can accept as input (an independent variable) and output. On the number line, the range is frequently represented by an interval or group of intervals. For instance, the range can be written as [-3, 3] if the domain of a function f(x) is [-2, 2] and its output numbers fall within [-3, 3].

given

The collection of all x-values for which h(x) is specified is the domain of the function h.

The graph's [-2, 4] domain can be determined by looking at the graph, which shows that it begins at x=-2 and concludes at x=4.

The set of all possible y-values for the function h constitutes its range. Looking at the graph, we can see that it takes all values between y=-3 and y=0, and that it begins at y=-3.

The range is therefore [-3, 0].

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The complete question is :-  The entire graph of the function h is shown in the figure below. Write the domain and range of h as intervals or unions of intervals.

-2

-3-

4-

domain =

range =

By answering the presented question, we may conclude that Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

To simplify the expression,

[tex]a(b+c) = ab + ac\\9(4/3m-5-2/3m+2) = 9(4/3m - 2/3m - 5 + 2)\\= 9(2/3m - 3)\\= 6m - 27[/tex]

Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.

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The number of students that are in the sixth grade is given as follows:

250 students.

The number of students is obtained applying the proportions in the context of the problem.

We know that all students in the sixth grade either purchased their lunch or brought their lunch from home on Monday, and 24% of the students purchased their lunch, hence 76% of the students brought their lunch from home.

190 students brought their lunch from home, which is equivalent to 76% of the number of students, hence the number of students is given as follows:

0.76n = 190

n = 190/0.76

n = 250 students.

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