Learn by DoingHere are the directions, grading rubric, and definition of high-quality feedback for the Learn by Doing discussion board exercises.ContextStudents researching backpack weights gathered data from 45 elementary school children in the 3rd and 5th grades. The variable is "percent of body weight carried in the school backpack." So a child who weighs 60 pounds and carries 9 pounds has a variable value of 15% (9 ÷ 60 = 0.15 = 15%). The American Chiropractic Association (ACA) recommends that children carry no more than 10% of their body weight.PromptWhen we analyze backpack weight as a percentage of body weight, how do 3rd and 5th graders compare? Are children in this study following the ACA recommendation?% of body weight carried in backpack Thirdgraders Fifthgraders0-5% 1 15-10% 6 610-15% 11 415-20% 3 720-25% 0 125-30% 0 230-35% 0 1Totals 21 22Note: Left-hand end-points are included in each bin. So the 2nd bin contains students carrying 5% of their body weight.GradingTo view the grading rubric for this discussion board, click on menu icon (three vertical dots) and then select show rubric. Please note, if viewing the course via the Canvas mobile app the rubric does not appear on this page.Tips for SuccessTo post your initial post, click the "reply" button at the top of the introduction thread below.You are required to reply to two of your peers in this discussion; don't forget to complete this requirement of the activity or you will lose points. Provide high-quality feedback to your peers.

Answer:

x=4

Step-by-step explanation:

2x+17=25

First subtract 17 from both 17 and 25

2x=8

Now to isolate the exponent, divide by two for both the 2x and 8

x=4

Hope this helped!

Answer:

76.5in²

Step-by-step explanation:

First we will find the area of the square. This is done by multiplying the side length (9in) by itself.

\(9 * 9 = \boxed{81}\)

The area of the square is 81in².

Next we will find the area of the triangular hole. We can use the formula \(\frac{1}{2}bh\), where b is the base of the triangle (3) and h is the height of the triangle (3).

\(\frac{1}{2}bh\\\frac{1}{2}(3)(3)\\\frac{9}{2}\\\boxed{4.5}\)

The area of the triangle is 4.5in².

Now we can find the area of the figure by subtracting the area of the square and the area of the triangular hole.

\(81 - 4.5 = \boxed{76.5}\)

The area of the figure is 76.5in².

That is the answer

- Kan Academy Advance

Answer:

9<n<17.

Step-by-step explanation:

Answer:

0.083

Step-by-step explanation:

151 divided by 1800 is 0.083

might be wrong WARNING

The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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"Distance traveled is a function of time." In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.

Distance is a fundamental concept in physics and mathematics that measures the extent or length between two points.

It represents the amount of ground covered or space traveled. When we say that distance is a function of various factors, it means that different variables or parameters can influence the distance traveled.

In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.

The sentence "Distance traveled is a function of time" expresses this relationship, indicating that the distance traveled can be determined or calculated based on the value of time.

Thus, it implies that as time changes, the corresponding distance traveled also changes, establishing a functional relationship between the two variables.

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Answer:

8.8

Explination:

Im not sure how to explian it but that is the right answer

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

The surface area of the given sphere is 764.15 square inches.

Given that, the sphere has diameter = 15.6 inches.

Here, radius = 15.6/2 = 7.8 inches

We know that, surface area of a sphere is 4πr².

Now, surface area = 4×3.14×7.8²

= 764.15 square inches

Therefore, the surface area of the given sphere is 764.15 square inches.

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Answer:

38.4

Explanation:

32% = .32

.32*120

38.4

Answer:

32% of 120=32/100×120=32/10×12=3.2×12=38.4

Answer:

4.8 pounds.. Happy to help! brainliest please

Step-by-step explanation:

The area of the shaded region is 559 ft².

In order to find the area of the shaded region, we will subtract the area of the square from the area of the rectangle. That is:

area of the shaded region = area of rectangle - area of square

area of the shaded region = (32 * 20) - (9 * 9)

area of the shaded region = 640 - 81

area of the shaded region = 559 ft²

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Complete Question

See attached image

Answer:A truncated cone and a sphere

Step-by-step explanation:

I just did it.

The combination of geometric shapes can she use to best estimate the vase's volume is a truncated cone and a sphere.

Sophie needs to determine the amount of water that will fit into her new vase, as shown below.

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

We have to determine the combination of geometric shapes can she use to best estimate the vase's volume.

Therefore the combination of geometric shapes can she use to best estimate the vase's volume is a truncated cone and a sphere.

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Answer:

the value of a - b is 4.

Step-by-step explanation:

We have been given the following two equations:

a + b = 10 ------------(1)

a² - b² = 40 -------(2)

We can factor the left-hand side of equation (2) using the difference of squares identity:

(a + b)(a - b) = 40

Substituting equation (1) into this equation, we get:

10(a - b) = 40

Dividing both sides by 10, we get:

a - b = 4

Therefore, the value of a - b is 4.

Step-by-step explanation:

if I understand this correctly :

a + b = 10

a² - b² = 40

(a² - b²) = (a + b)(a - b) = 40

10(a - b) = 40

(a - b) = 4

The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.

We are given that;

The concrete portion of the patio cost=$3 per square

To construct and the brick portion of the patio cost= $6 per square

Now,

The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:

6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft

Therefore, the area of the concrete portion is:

24 ft x 12 ft = 288 ft^2

The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:

3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft

Therefore, the area of one brick rectangle is:

12 ft x 24 ft = 288 ft^2

Since there are two brick rectangles, the total area of the brick portion is:

2 x 288 ft^2 = 576 ft^2

Now we can multiply the areas by their costs per square foot to get the costs of each portion:

Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456

The total cost of constructing the patio is the sum of the costs of each portion:

Total cost = $864 + $3456 = $4320

Therefore, by area the answer will be $4320.

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Answer:

18 Bowls of Candy

Step-by-step explanation:

Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.

Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.

Now, we can calculate the total number of bowls of candy:

Total bowls of candy = (Number of bags) x (Bowls per bag)

Total bowls of candy = 6 bags x 3 bowls per bag

Total bowls of candy = 18 bowls

Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.

The margin of error would tell how many percentage differs from  Harris County's sample

The range of reasonable means for Harris County's sample is 77.7 to 82.3

The given parameters are:

The range (R) is calculated as:

\(R = \bar x \pm E\)

Substitute known values

\(R = 80 \pm 2.3\)

Expand

\(R = (80 - 2.3,80 + 2.3)\)

Evaluate the difference and sum

\(R = (77.7,82.3)\)

Hence, the range of reasonable means for Harris County's sample is 77.7 to 82.3

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Answer:

x=-6

Step-by-step explanation:

For the rational expression, 6x/(x+6) to be undefined, the denominator need to be 0, so x=-6 is the point at which the function is undefined.

The rational expression 6x / (x + 6) is undefined when x equals -6, and it is defined for all other real numbers.

To find the real numbers for which the rational expression 6x / (x + 6) is undefined, we need to identify the values of x that would make the denominator equal to zero. When the denominator is zero, the expression becomes undefined.

In this case, the denominator is (x + 6). Setting the denominator equal to zero, we have:

x + 6 = 0

Solving for x, we subtract 6 from both sides:

x = -6

Therefore, the rational expression 6x / (x + 6) is undefined when x = -6.

When x is equal to -6, the denominator becomes zero, which causes division by zero. Division by zero is undefined in mathematics. Hence, for x = -6, the rational expression is not defined.

For any other real numbers other than x = -6, the expression is defined and can be simplified or evaluated.

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Answer:

0.7768

Step-by-step explanation:

The function for fine at every speed should be doubled in construction zones is f(n)= -8.75n+637.5.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The coordinate points from the graph are (10, 550) and (30, 200).

Here, slope = (200-550)(30-10)

= -350/20

= -35/2

= -17.5

Substitute m= -17.5 and (x, y)=(10, 550) in y=mx+c, we get

550=-17.5(10)+c

c=550+175

c=725

So, the equation is y= -17.5x+725

Thus, f(n)= -17.5n+725

a) The fine at every speed should go up by $10.

So, the coordinates are (10, 560) and (30, 210)

New slope (m)= (210-560)(30-10)

= -350/20

= -35/2

= -17.5

Substitute m= -17.5 and (x, y)=(10, 560) in y=mx+c, we get

560=-17.5(10)+c

c=550+175

c=735

So, the equation is y= -17.5x+735

Thus, f(n)= -17.5n+735

b) The fine at every speed should be doubled in construction zones.

So, the coordinates are (20, 550) and (60, 200)

New slope (m)= (200-550)(60-20)

= -350/40

= -8.75

Substitute m= -8.75 and (x, y)=(20, 550) in y=mx+c, we get

550=-8.75(10)+c

c=550+87.5

c=637.5

So, the equation is y= -8.75x+637.5

Thus, f(n)= -8.75n+637.5

Therefore, the function for fine at every speed should be doubled in construction zones is f(n)= -8.75n+637.5.

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Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

The respective exterior angles are 155°, 55°, 150°

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°

Given here: The angles of the triangle as 30°, 25°, and 125°

We know that sum of an exterior angle is the sum of the two non-adjacent angles

Thus we have ∠DBC= 30+125=155°

∠ECA=30+25=55°

∠FAD=25+125=150°

Hence, The respective exterior angles are 155°, 55°, 150°

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Answer:

y = 5

Step-by-step explanation:

\(14y-7y=35\\7y=35\\y=5\)

14 minus 7 is 7

7Y is equal to 35

divide both sides by 7 is equal to 5

Answer:

\(f'(x)=36x^2(2x^3-4)^5\)

Step-by-step explanation:

The Chain Rule for Derivatives

Given a function y=f(u) and u=g(x), the derivative dy/dx is computed by using the chain rule:

\(y'=f'(u).u'(x)\)

We have:

\(f(x)=(2x^3-4)^6\)

It can be written as:

\(f(x)=u^6\)

Where:

\(u=2x^3-4\)

Thus:

\(f'(x)=(u^6)'(2x^3-4)'\)

\(f'(x)=6u^5(6x^2)\)

Changing back u:

\(f'(x)=6(2x^3-4)^5(6x^2)\)

Operating:

\(\mathbf{f'(x)=36x^2(2x^3-4)^5}\)

Answer:

398.4

Step-by-step explanation:

i don't know how to explain i asked gogle

Answer:

The answer is A.

Step-by-step explanation:

The ratio is 1 second/2 centimeters, but since they're asking for a unit ratio, you need to divide the top and bottom by 2 which gives you a unit ratio of ½ second/1 centimeter.

Answer:

Perhaps, B or A

Step-by-step explanation:

Can i please get the equation so i can solve it

I will edit this after you put it

Ignore this \/

Under a dilation with center P and scale factor k, A' is the image of A. What is the value of k if PA = 7, and PA' = 28

Under a dilation with center P and scale factor k, A' is the image of A. What is the value of k if PA = 7, and PA' = 28?Under a dilation with center P and scale factor k, A' is the image of A. What is the value of k if PA = 7, and PA' = 28?Under a dilation with center P and scale factor k, A' is the image of A. What is the value of k if PA = 7, and PA' = 28?Under a dilation with center P and scale factor k, A' is the image of A. What is the value of k if PA = 7, and PA' = 28?Under a dilation with center P and scale factor k, A' is the image of A. What is the value of k if PA = 7, and PA' = 28?Under a dilation with center P and scale factor k, A' is the image of A. What is the value of k if PA = 7, and PA' = 28?Under a dilation with center P and scale factor k, A' is the image of A. What is the value of k if PA = 7, and PA' = 28?Under a dilation with center P and scale factor k, A' is the image of A. What is the value of k if PA = 7, and PA' = 28?Under a dilation with center P and scale factor k, A' is the image of A. What is the value of k if PA = 7, and PA' = 28?

Answer:

26 ft

Step-by-step explanation:

A=bh

40= 8h

h=5

P=2(l+w)

P= 2(8+5)

P = 2(13)

P = 26

Answer:

Step-by-step explanation:

Remark

It's a right angle triangle. I feel for 17 points, I should be telling you more.

Surface Area

The two faces are triangles. Their area = 1.5 * 2 / 2= 1.5

What I have you is the area of 1 triangle. There are 2 so 2*2.5 = 3

======================

The height of the prism = 10 meters.

The Area of that face = L * w = 10 * 2.5

Area of that face = 25 m^2

Area of the rectangle containing 1.5 as the width = 1.5 * 10 = 15

Area of the rectangle containing 2 as the width = 2  * 10 = 20

The Total Surface Area = 20 + 15 + 25 + 5 = 65 m^2

Volume

Volume = Area of 1 triangle * height

Volume = 1.5 * 10 = 15 m^3

The total amount to each person end up paying $20.54.

To find the total amount each person will pay, first calculate the 20% tip on the total bill and then divide the sum by the number of people.

To split the bill evenly among Raphael and his four friends, we first need to find the total cost including the 20% tip.

The tip is 20% of the original bill, which is equivalent to 0.20 x $85.60 = $17.12.

Therefore, the total cost of the bill with the tip is $85.60 + $17.12 = $102.72.

To split this evenly among the five people, we divide by 5:

$102.72 ÷ 5 = $20.54

So each person will end up paying $20.54.

20% of $85.60 is ($85.60 * 0.20) = $17.12

Add the tip to the total bill:

$85.60 + $17.12 = $102.72

Divide the total amount by the number of people (5): $102.72 / 5 = $20.54

Therefore, the answer is B. $20.54.

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