x + 6y = -7
2x + 12y = -14

The approximate mean age is [tex]\(45.15\)[/tex] years, and the approximate standard deviation for age is [tex]\(9.22\)[/tex] years, both rounded to two decimal places.

To approximate the mean and standard deviation for the age groups provided, we can calculate the weighted average based on the midpoint of each age group and use the formula for the standard deviation of a weighted dataset.

First, calculate the midpoints of the age groups:

- For 25-34 years: midpoint = (25 + 34) / 2 = 29.5

- For 35-44 years: midpoint = (35 + 44) / 2 = 39.5

- For 45-54 years: midpoint = (45 + 54) / 2 = 49.5

- For 55-64 years: midpoint = (55 + 64) / 2 = 59.5

Next, calculate the weighted mean using the formula:

[tex]\[ \text{Weighted Mean} = \frac{\sum (\text{Midpoint} \times \text{Number of People})}{\sum \text{Number of People}} \][/tex]

[tex]\[ \text{Weighted Mean} = \frac{(29.5 \times 22.1) + (39.5 \times 31.5) + (49.5 \times 37.7) + (59.5 \times 25.3)}{22.1 + 31.5 + 37.7 + 25.3} \][/tex]

[tex]\[ \text{Weighted Mean} \approx \frac{651.45 + 1244.25 + 1867.35 + 1503.35}{116.6} \][/tex]

[tex]\[ \text{Weighted Mean} \approx \frac{5266.4}{116.6} \][/tex]

[tex]\[ \text{Weighted Mean} \approx 45.15 \text{ years (approx)} \][/tex]

Now, calculate the standard deviation using the formula:

[tex]\[ \text{Weighted SD} = \sqrt{\frac{\sum (\text{Number of People} \times (\text{Midpoint} - \text{Weighted Mean})^2)}{\sum \text{Number of People}}} \][/tex]

[tex]\[ \text{Weighted SD} = \sqrt{\frac{(22.1 \times (29.5 - 45.15)^2) + (31.5 \times (39.5 - 45.15)^2) + (37.7 \times (49.5 - 45.15)^2) + (25.3 \times (59.5 - 45.15)^2)}{116.6}} \][/tex]

[tex]\[ \text{Weighted SD} \approx \sqrt{\frac{9919.575}{116.6}} \][/tex]

[tex]\[ \text{Weighted SD} \approx \sqrt{85.004} \][/tex]

[tex]\[ \text{Weighted SD} \approx 9.22 \text{ years (approx)} \][/tex]

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Answer y = 0.15x + 100

Step-by-step explanation:

Answer:

Step-by-step explanation: so, u would do 80 times 30 which equals 2400. Then u would divide 2,400 by 4 which gives u ur answer which is 60ft long! :)

Answer:

if im right its 110ft

Step-by-step explanation:

Step-by-step explanation:

We have,

[tex]\dfrac{x+16}{3}=3x[/tex]

To find, the value of x in the given equation = ?

∴ [tex]\dfrac{x+16}{3}=3x[/tex]

By crossmultiplication, we get

3(3x) = x + 16

⇒ 9x = x + 16

⇒  9x - x = 16

⇒  8x = 16

⇒  x = [tex]\dfrac{16}{8}[/tex]

⇒  x = 2

∴ The value of x = 2

Thus, the required value of x is equal to 2.

It will take Luis 12240 seconds to complete the project.

12240 seconds are 204 minutes when converted.

Step-by-step explanation:

Given,

Time taken to paint 1 square foot = 45 seconds

Time taken for 272 square feet = 45*272

Time taken for 272 square feet = 12240 seconds

We know that;

60 seconds = 1 minute

Therefore;

We will divide the total seconds by 60 to convert them into minutes.

12240 seconds = [tex]\frac{12240}{60} = 204\ minutes[/tex]

It will take Luis 12240 seconds to complete the project.

12240 seconds are 204 minutes when converted.

Keywords: conversion, multiplication

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Final answer:

The negative solution to the equation x² - 3x - 4 = 0 is x = -1.

Explanation:

The difference of the square of a number and 4 is equal to 3 times that number. To find the negative solution, let's represent the number as x.

The equation becomes x2 - 4 = 3x.

Rearranging the equation, we get x2 - 3x - 4 = 0.

To find the negative solution, we can use the quadratic formula: x = (-b - √(b2 - 4ac)) / (2a).

For our equation, a = 1, b = -3, and c = -4. Plugging these values into the quadratic formula, we get x = (-(-3) - √((-3)2 - 4(1)(-4))) / (2(1)).

Simplifying further, we get x = (3 - √(9 + 16)) / 2, which simplifies to x = (3 - √25) / 2.

The square root of 25 is 5, so x = (3 - 5) / 2, which equals -1.

Therefore, the negative solution to the equation is x = -1.

The question cannot be fully answered as provided since only two dimensions of the ice block are given. To determine the amount of reflective material, all three dimensions (length, width, height) of the block are needed to calculate the total surface area. Without the third dimension, the exact surface area cannot be calculated.

The question asks how much reflective material would be needed to cover a block of ice with given dimensions completely for an ice carving competition. Since only two dimensions are provided, let's assume the block has a third dimension making it a rectangular prism. To find the surface area of the block (which is the amount of reflective material needed), we calculate the area of each face and sum them up. A rectangular prism has six faces: the front and back, the top and bottom, and the two sides. If we denote the dimensions of the block as length (l), width (w), and height (h), the areas of the respective faces are:

Assuming the dimensions provided are the length and height (l = 3 ft and h = 4 ft), and an unknown width (w), we cannot calculate the exact surface area without the third dimension. Ideally, the width would be provided to complete the calculation.

Answer:

Restrictions: x ≠ 0, 3

The value of x is equal to 5.

General Formulas and Concepts:

Pre-Algebra

Algebra I

Equality Properties

Terms/Coefficients

Domain

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle \frac{2}{x - 3} = \frac{5}{x}[/tex]

Step 2: Examine

Since we have an x - 3 and x in the denominator, we must make sure the denominator cannot equal 0, or that would get us an undefined answer. Therefore, our restrictions are that x ≠ 0, 3.

Step 3: Solve for x

Since 5 is not equal to 0 or 3, it can be our solution.

∴ we have found the value of x from the given rational function.

---

Topic: Algebra I

Answer:

[tex]2(x - 3)\: >\: \frac{1}{14}[/tex]

Step-by-step explanation:

The difference of x and 3 is given as:

x-3

Twice the difference of x and 3 becomes:

2(x-3)

The reciprocal of 14 is

[tex] \frac{1}{14} [/tex]

Twice the difference of x and 3 is greater than the reciprocal of 14 then becomes

[tex]2(x - 3)\: >\: \frac{1}{14} [/tex]

Answer:

p=17

The drawing will help

Answer: p = 16

Step-by-step explanation: To solve for p in this equation, our first step is to simplify the left by distributing the 5 through both terms inside the parentheses.

When we do that,

we get 5 times 9 which is 45 and 5 times p which is 5p.

So we have 45 + 5p = 125.

Our next step is to isolate the p term by subtracting 45 from both sides of the equation. On the left side of the equation, 45 - 45 cancels and we're left with 5p.

On the right side of the equation, 125 - 45 simplifies to 80.

So we have 5p = 80.

We want to solve our equation for p so we want to get p by itself on the left side of the equation. Since p is being multiplied by 5, we need to divide both sides of the equation by 5. On the left side of the equation.notice that the 5 and 5 cancel each other out so we're just left with p and on the right side, 80 divided by 5 is 16 so we have p = 16.

Answer: The height/width has to be less than 9 for the area to be less than 36

Step-by-step explanation:

Pennant's are triangle.

Triangle area = bh(1/2)

the base is 8in

(8 * h)/2 = 36

*2

8 * h = 72

/8

h = 9

The height/width has to be less than 9

Final answer:

Min will need a total of 700 bookmarks for the pages where the digits in the thousands and units places add up to 7, since there are 700 four-digit page numbers meeting the criteria.

Explanation:

To determine the number of bookmarks Min needs for the pages where the digits in the thousands and units place add up to 7, we will consider all four-digit numbers that meet this criterion. This involves taking the sum of the thousands and units digits, which can equal 7 in the following ways: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1, and 7+0. Considering that for every combination of thousands and units digits, there are 10 possibilities for the hundreds digit and 10 possibilities for the tens digit, we can calculate the total number of eligible page numbers.

For 1+6 or 6+1, the number of possibilities is 2 (the two combinations) multiplied by 100 (since there are 10 choices for each of the two remaining digits), giving us 200 options.

For 2+5 or 5+2, we have another 200 options.

For 3+4 or 4+3, we get another 200 options.

For 7+0, we would only have 100 options, as there is only one combination.

Summing these up, we find Min will need 700 bookmarks: 200 + 200 + 200 + 100 = 700.

Answer:

look at picture shown please

Answer:

1) a = 3189 b = 5

2) a = 53 b = -5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Final answer:

The remainder when the function f(x) = 4x² + 5x + 2 is divided by x + 7 is found using the remainder theorem, which gives us a result of 163.

Explanation:

To find the remainder when the function f(x) = 4x² + 5x + 2 is divided by x + 7, we can use the remainder theorem. The remainder theorem states that if a polynomial f(x) is divided by a linear divisor of the form x - r, the remainder is f(r). Here, our linear divisor is x + 7, which we can rewrite as x - (-7). So, we substitute x = -7 into the polynomial to get the remainder.

Substituting x = -7 into the function gives us:
f(-7) = 4(-7)² + 5(-7) + 2 = 4(49) - 35 + 2 = 196 - 35 + 2 = 163.

Therefore, the remainder when f(x) is divided by x + 7 is 163.

Answer:

5/2 or 2 1/2

Step-by-step explanation:

Answer:

The measure of each interior angle of the dodecagon is 150 degrees.

Step-by-step explanation:

(n - 2) x 180 = 1800       Use the equation to find the number of sides

n - 2 = 10                        Divide by 180 on both sides

  + 2  + 2                        Add 2 to both sides

n = 12

Take the sum of the interior angles divided by the number of sides to find the measure of each angle

1800/12 = 150 degrees for each angles of the dodecagon.

Answer:

1, 2, 3

Step-by-step explanation:

The range includes only the y-axis. On this graph, the line only passes by the 1,2, and 3 on the y-axis.

Answer:

  [tex]10+\dfrac{x}{6}[/tex]

Step-by-step explanation:

The wording, "the sum of A and B" translates to the math formula A+B.

The wording, "the quotient of A and B" translates to the math formula A/B.

Then "the sum of 10 and the quotient of x and 6" will translate to the math formula ...

  [tex]\boxed{10+\dfrac{x}{6}}[/tex]

Answer:

6 combinations

Step-by-step explanation:

Pants options: Navy Blue, Khaki

Shirt options: Red, white, blue

Possible combinations:

Navy Blue with:       Khaki with:

Red                           Red

White                        White

Blue                           Blue

There are 6 outfit possibilities

Hope this helps and let me know if you have any questions about my answer :)

[tex]\frac{\text{Distance of melkon}}{\text{Distance of tamar}} = \frac{45}{4}\\\\\frac{\text{Distance of tamar}}{\text{Distance of melkon}} = \frac{4}{45}[/tex]

Solution:

Given that,

Tamar travels 8/9 miles to the grocery store

Melkon travels 10 miles to the grocery store

Therefore,

[tex]Tamar = \frac{8}{9}\ miles\\\\Melkon = 10\ miles[/tex]

[tex]\text{ Distance of melkon : Distance of tamar } = 10 : \frac{8}{9}\\\\\text{ Distance of melkon : Distance of tamar } = \frac{10 \times 9}{1 \times 9} : \frac{8}{9}\\\\\text{ Distance of melkon : Distance of tamar } = \frac{90}{9} : \frac{8}{9}\\\\\text{ Distance of melkon : Distance of tamar } =90 : 8\\\\In\ fraction\ form\\\\\frac{\text{Distance of melkon}}{\text{Distance of tamar}} = \frac{90}{8}\\\\In\ simplest\ form\\\\\frac{\text{Distance of melkon}}{\text{Distance of tamar}} = \frac{45}{4}[/tex]

[tex]\text{ Distance of tamar : Distance of melkon } = \frac{8}{9} : 10\\\\\text{ Distance of tamar : Distance of melkon } = \frac{8}{9} : \frac{10 \times 9}{1 \times 9}\\\\\text{ Distance of tamar : Distance of melkon } = \frac{8}{9} : \frac{90}{9}\\\\\text{ Distance of tamar : Distance of melkon } = 8 : 90\\\\In\ fraction\ form\\\\\frac{\text{Distance of tamar}}{\text{distance of melkon}} = \frac{8}{90}\\\\\frac{\text{Distance of tamar}}{\text{distance of melkon}} = \frac{4}{45}[/tex]

Thus the required are found

Answer:

.97 cents

Step-by-step explanation:

3.88 divided by 4 = .97

Answer:

97¢

Step-by-step explanation:

If 4 liters cost $3.88, then divide 4 into 3.88

Option A: 7/16 of a foot is the right answer

Step-by-step explanation:

Given

Length of Braden's Jump = [tex]9\frac{5}{16} = \frac{149}{16}[/tex] feet

Length of Jordan's Jump = [tex]8\frac{7}{8} = \frac{71}{8}[/tex]

In order to find how much farther Braden jumped than Jordan

[tex]=\frac{149}{16} - \frac{71}{8}\\=\frac{149-142}{16}\\=\frac{7}{16}[/tex]

Braden jumped 7/16 feet farther than Jordan

Hence,

Option A: 7/16 of a foot is the right answer

Keywords: Fractions, measurements

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Final answer:

By converting Jordan's jump to sixteenths and subtracting it from Braden's, we determine that Braden jumped 9/16 of a foot farther than Jordan. The correct answer is option B.

Explanation:

The question involves finding out how much farther Braden jumped than Jordan. To solve this, we subtract Jordan's jump length from Braden's jump length. Braden jumped 9 5/16 feet, and Jordan jumped 8 7/8 feet.

First, we need to find a common denominator to subtract the fractions. The common denominator for 16 and 8 is 16. Convert Jordan's jump to sixteenths: 8 7/8 equals 8 14/16.

Now, subtract Jordan's jump from Braden's: 9 5/16 - 8 14/16 = 1 - 9/16. Braden jumped 9/16 of a foot farther than Jordan.

So the correct answer is option B. 9/16 of a foot.

Check the picture below.

The measure of arc CD of circle A will be 90°. Then the correct option is A.

Let r be the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/2π) 2πr

In circle A, arc CD is congruent to arc BD. And we know that the Line segment CAD is the diameter of the circle. Then the equation is given as,

arc CD = arc BD                           ....1

arc CD + arc BD = 180°                ....2

From equations 1 and 2, then we have

arc CD + arc CD = 180°

2 arc CD = 180°

arc CD = 90°

The measure of arc CD of circle A will be 90°. Then the correct option is A.

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A number line can be defined as a horizontal line that can be extended and have numbers on it. The distance between -2/3 and 4/3 on a number line is 3 units.

A number line can be defined as a horizontal line that can be extended in any direction indefinitely and has all the integers over it. As one walks from left to right on the number line, the numbers grow, and as one proceeds from right to left, the numbers decrease.

The distance between the two can be found by deducting -2/3  from 4/3. Therefore, the distance between the two can be written as,

[tex]\rm Distance = \dfrac{4}{3}-(- \dfrac{2}{3}) = \dfrac{4}{3}+\dfrac{2}{3} = \dfrac{4+2}{3} = \dfrac{6}{3} = 2[/tex]

Thus, the distance between -2/3 and 4/3 on a number line is 3 units.

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Answer:

  they have the same value (0)

Step-by-step explanation:

Cosine is an even function, meaning that cos(x) = cos(-x). When x=90°, we have ...

  cos(90°) = cos(-90°)

Both values happen to be zero.

The relationship between cos(90°) and cos(-90°) is that they both equal 0.

The relationship between cos(90°) and cos(-90°) can be explained using the unit circle. In the unit circle, the cosine function represents the x-coordinate of the point on the circle corresponding to the given angle.

For cos(90°), the x-coordinate is 0, which means the cosine value is 0.

For cos(-90°), the x-coordinate is also 0, so the cosine value is also 0. Therefore, cos(90°) = cos(-90°) = 0.

To calculate a 20% tip and round up, multiply the bill by 0.2, then round to the nearest 10 cents.

To calculate a 20% tip, first, determine the total bill amount. Then, multiply the bill amount by 0.2 to find 20% of the bill. Finally, round up to the nearest multiple of 5 or 10 cents. Since Kadisha always rounds up, she should round up to the nearest 10 cents.

If the total bill is $50, to calculate a 20% tip, we multiply $50 by 0.2 to get $10, which is 20% of the bill. Then, we round up to the nearest 10 cents, making the tip $10.00.

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Answer:

Step-by-step explanation:

The function that will have the domain [tex](\infty, \infty)[/tex] and a range of [tex](-3, \infty)[/tex] is the

function in option d.) [tex]f(x) = e^x - 3[/tex]

Answer:

$63

Step-by-step explanation:

30% of 90 is 27

90-27=63