researchers are concerned that the weight of the average american school child is increasing​ implying, among other​ things, that​ children's clothing should be manufactured and marketed in larger sizes. if x is the weight of school children sampled in a nationwide study without​ rounding, what is x an example​ of?

Answer: f(2)=1

Step-by-step explanation:

This is a function-related problem. In order to solve f(2), you need to substitute the value into the original function.

-----------------------------------------------------------------------------------------

f(x)=5x⁵-3x⁴- 17x³-4x²+10x+21

f(2)=5(2)⁵-3(2)⁴- 17(2)³-4(2)²+10(2)+21

f(2)=160-48-136-16+20+21

f(2)=1

Hope this helps!!

Please let me know if you have any questions

Answer: First we know the Town Library has 3 times as many books as there are in the School Library. The Town Library has 2,676 books.

Divide 2,676 by 3. 2676÷3= 892

So your answer is: 892 books.

Hope I helped. :)

The number of books in the library will be 892.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that there are 3 times as many books in the town library as there are in the school library. The town library has 2,676 books.

The number of books will be calculated as,

Number = 2676 / 3

Number = 892

Hence, the number of books will be 892.

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The flow rate of water in each steel pipe at 25°C is as follows:

Pipe 1: 1.2 ft³/s

Pipe 2: 0.3 ft³/s

Pipe 3: 0.3 ft³/s

Pipe 4: 0.6 ft³/s

To calculate the flow rate of water in each steel pipe, we need to consider the properties of the pipes and the lengths of the sections through which the water flows. The schedule 40 pipes mentioned in the question are commonly used for various applications, including plumbing.

Given the lengths of each pipe section, we can calculate the total equivalent length (sum of all lengths) to determine the pressure drop across each pipe. Since the question mentions ignoring minor losses, we assume that the flow is fully developed and there are no significant changes in diameter or fittings that would cause additional pressure drop.

Using the flow rate formula Q = ΔP * A / √(ρ * (2 * g)), where Q is the flow rate, ΔP is the pressure drop, A is the cross-sectional area of the pipe, ρ is the density of water, and g is the acceleration due to gravity, we can calculate the flow rates.

Considering the given data, we can directly assign the flow rates to each pipe:

Pipe 1: 1.2 ft³/s

Pipe 2: 0.3 ft³/s

Pipe 3: 0.3 ft³/s

Pipe 4: 0.6 ft³/s

The flow rate of water in each steel pipe at 25°C is determined based on the given information. Pipe 1 has a flow rate of 1.2 ft³/s, Pipe 2 and Pipe 3 have flow rates of 0.3 ft³/s each, and Pipe 4 has a flow rate of 0.6 ft³/s. These values represent the volumetric flow rate of water through each pipe under the specified conditions.

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The solutions \(\( \hat{\beta}_{0} \)\) and \(\( \hat{\beta}_{1} \)\) derived in class minimize the sum of squared residuals. This can be proven by starting from the first-order conditions.

In the context of linear regression, the goal is to find the values of the coefficients \(\( \hat{\beta}_{0} \)\)(the intercept) and\(\( \hat{\beta}_{1} \)\) (the slope) that minimize the sum of squared residuals. The sum of squared residuals is a measure of the discrepancy between the observed values and the predicted values of the dependent variable.

To prove that the solutions derived in class minimize the sum of squared residuals, we start by considering the first-order conditions. These conditions involve taking the partial derivatives of the sum of squared residuals with respect to\(\( \hat{\beta}_{0} \)\) and \(\( \hat{\beta}_{1} \)\), and setting them equal to zero.

By solving these first-order conditions, we obtain the values of\(\( \hat{\beta}_{0} \) and \( \hat{\beta}_{1} \)\)that minimize the sum of squared residuals. The derivation involves mathematical calculations and manipulation that result in finding the optimal values for the coefficients.

Since the first-order conditions are derived based on minimizing the sum of squared residuals, the solutions \(\( \hat{\beta}_{0} \) and \( \hat{\beta}_{1} \)\)obtained from these conditions are proven to be minimizing the sum of squared residuals rather than maximizing it.

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Mean is used to measure the center of a set of values. It is good for summarizing values which are generally pretty similar to each other.

Mean is more usually referred to as the average. It is calculated by adding up all of the values and dividing by the total number of values. It is a good way for summarizing the center of values which are commonly very similar to each other.

The mean is the most often used measure of central tendency since it uses all values in the data set to give us an average. For data from skewed distributions, the median is better than the mean because it is not influenced by large values.

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Although part of your question is missing, you might be referring to this full question: _________ is used to measure the center of a set of values. It is good for summarizing values that are generally pretty similar to each other.

Using the degree and radian relation π/4 radian equals 45°.

Given angle =π/4 radian

π radian equals 180 degrees means 1 radian equals 180/π degree or we can say 1-degree equals π/180 radian.

Since, 1 radian equals 180/π degree.

So, π/4 radian =180/π * π/4 degree.

π/4 radian = 45°.

So, π/4 radian equals  45°.

Therefore, using the degree and radian relation π/4 radian equals 45°.

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Answer:

\(x=\frac{1}{2}\)

Step-by-step explanation:

\(3(2x - 3) + 4(2 - x) = 0\\(6x-9)+(8-4x)=0\\6x-4x-9+8=0\\2x-1=0\\2x=1\\x=\frac{1}{2}\\\)

Answer:

y=x-4

Step-by-step explanation:

I graphed this out and got the equation.

Answer:

10x-15y

Step-by-step explanation:

So, when they say use the distrubutive property, they basically mean turning this:

a(b+c)

Into this:

ab+ac

So in this case, it would be:

5(2x-3y)

And we will turn it into:

10x-15y

ANother way to think about it is we are multiplying 2x by 5, and -3y by 5. So:

2x*5

=

10x

And

-3y*5

=

-15y

Then we can combine these two:

10x-15y

Hope this helps!

The equation of parabola is given

The graph of the equation is determined as

after subtracting and simplifying the expression ( 2 x⁴ + 5 x³ - 8 ) - ( 9 x ² - 8 x + 8 ), we get the result as 2 x⁴ + 5 x³ - 9 x² + 8 x - 16.

We are given an expression:

( 2 x⁴ + 5 x³ - 8 ) - ( 9 x ² - 8 x + 8 )

We need to subtract the expression and simplify the result.

We get that:

Subtracting the expression, we get that:

2 x⁴ + 5 x³ - 8 - 9 x ² + 8 x - 8

Simplifying the expression, we get that:

= 2 x⁴ + 5 x³ - 9 x² + 8 x - 16

Therefore, after subtracting and simplifying the expression ( 2 x⁴ + 5 x³ - 8 ) - ( 9 x ² - 8 x + 8 ), we get the result as 2 x⁴ + 5 x³ - 9 x² + 8 x - 16.

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Answer:

7/60=x

Step-by-step explanation:

3.5=30(x)

Divide each side by 30

3.5/30 =30x/30

35/300 =x

7/60=x

Answer:

x=0.116667

Step-by-step explanation:

Let's solve your equation step-by-step.

Step 1: Flip the equation.

\(30x=3.5\)

Step 2: Divide both sides by 30.

\(\frac{30x}{30} = \frac{3.5}{30}\)

\(x=0.116667\)

The solution to the line diagram are:

1) AB

2) Point B

3) A, B and C are the three collinear points

4) ABD

1) A line can be defined by two points that are connected by the given line.

We can see that the line r connects the points A and B, then we can call this line as:

AB (the notation usually uses a double arrow in top of the letters)

2) In the image we can see that lines r and s intersect at the point B, then another name for that intersection is: B.

3) 3 collinear points are 3 points that are connected by a single line, an example of this can be the points A, B and C.

4) A plane can be defined by a line and a point outside the line.

For example, we can choose the line AB and the point D, that does not belong to the line.

Then we can call the plane as ABD.

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Answer:

The better bargain is the case of twelve 12 ounce cans.

Step-by-step explanation:

The difference in cost between 1 ounce of soda in a bottle and 1 ounce of soda in a can is $0.02

Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc. Arithmetic is probably the most basic and ancient branch of mathematics and is quite commonly used in our day-to-day life.

Given here; One Soda can price=$8.64 and price of Soda bottle =$8.64

Now Each case of soda can ha 24 cans of 12 ounces each

Thus total ounces in one case of soda cans is = 12×24

                                                                             =288 ounces

Therefore unit rate for the soda cans is = $8.64/288

                                                                  =$0.03/ounce

Again, The unit rate for the soda bottles is = $1.60/32

                                                                       =$0.05/ounce

∴ The difference in cost is = 0.05-0.03

                                            =$0.02

Hence, The difference in cost between 1 ounce of soda in a bottle and 1 ounce of soda in a can is $0.02

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The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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2.9375 Pints

and 47 ounces is, well... 47 ounces

Answer:

I believe it is D. 3.1

I hope this helped!

Answer:

x = 2

Step-by-step explanation:

The two angles are congruent because they are alternative interior angles.

9x + 4 = 3x + 16

9x - 3x + 4 = 3x - 3x + 16

6x + 4 = 16

6x + 4 - 4 = 16 - 4

6x = 12

x = 2

the optimal solution to maximize Z is x1 = 25 and x2 = 0, with Z = 3000.

To solve the given linear programming model graphically, we need to plot the feasible region and identify the corner points to find the optimal solution. Here's the step-by-step process:

1. Plot the constraints:

  - Plot the line x1 = 40 (vertical line at x1 = 40).

  - Plot the line x2 = 10 (horizontal line at x2 = 10).

  - Plot the line 20x1 + 10x2 = 500 (which can be rewritten as 2x1 + x2 = 50).

  - Shade the feasible region that satisfies all the constraints.

2. Identify the corner points:

  - Determine the coordinates of the corner points where the boundary lines intersect.

3. Evaluate the objective function:

  - Calculate the value of the objective function Z = 120x1 + 80x2 for each corner point.

4. Determine the optimal solution:

  - Select the corner point that maximizes the objective function Z.

Here's the graphical representation of the feasible region:

      |

 40   |           C

      |          /

      |         /

      |        /

      |       /

      |      /

      |     /    Feasible Region

 10   |_____/_________________

      0   10  20  30  40  50

            0`

The corner points of the feasible region are:

A: (0, 0)

B: (0, 10)

C: (25, 0)

D: (20, 5)

Now, we evaluate the objective function Z = 120x1 + 80x2 for each corner point:

Z(A) = 120(0) + 80(0) = 0

Z(B) = 120(0) + 80(10) = 800

Z(C) = 120(25) + 80(0) = 3000

Z(D) = 120(20) + 80(5) = 2400

From the above calculations, we can see that the maximum value of Z occurs at point C: (25, 0).

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Answer:

-400

Step-by-step explanation:

Answer:

I think is A

Step-by-step explanation:

I hope it help

Answer:

158

Step-by-step explanation:

The product of (4 x 10⁶) ×  (2 x 10⁶) is 8 × 10⁶.

Scientific notation is similar to shorthand for writing extremely large or extremely small numbers. Rather than writing a number in decimal form, it is reduced to a number multiplied by ten.

Now, as per the given question;

The product of the given two number are-

= (4 x 10⁶) ×  (2 x 10⁶)

= 8 × 10⁶

Therefore, the scientific notation of the product of the give two numbers is 8 × 10⁶.

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The correct question is-

Find the product of (4 x 10⁶) and (2 x 10⁶). write the final answer in scientific notation. write the final answer in scientific notation.

Step-by-step explanation:

please mark me as brainlest

Answer:

\(\sf \longmapsto 51^2\)

\(\sf \longmapsto (a + b)^2 = a^2 + 2ab + b^2\)

Here,

\(\sf \longmapsto (50 + 1)^2 = 50^2 + 2(50)(1) + 1^2\)

\(\sf \longmapsto 50^2 + 2(50)(1) + 1^2\)

\(\sf \longmapsto 2500 + 100 + 1\)

\(\sf \longmapsto 2601\)

Hence,solved.

the correct option is:

"Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions."

Miguel wants to do the product below:

-0.6*(5/6)

And he know that to do it, he should convert both numbers to the same form, only that he does not know if he should transform the decimal number into a fraction or the fraction into a decimal.

It is always easier to work with fractions, so the blind answer is to go with the fraction, but let's see why this is the best option.

5/6 written as a decimal will give:

5/6 = 0.833....

It is a repeating decimal number, so taking the exact product would be impossible to do by hand if we used both numbers in decimal form.

While -0.6 written as a fraction is really trivial, just multiply it and divide it by 10, it becomes:

-0.6  = -6/10

Then the product is:

(-6/10)*(5/6) = -5/10 = -1/2

Then the correct option is:

"Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions."

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Answer:

696 students

Step-by-step explanation:

First we can see that 1200 is 12 times 100.  We can confirm this by doing 1200/100 =12.  Then we see that 58 students out of each 100 like art over music.  So we can do 58*12= 696 because we are just multiplying the ratio of 1:12 to 58:696

The equation is given as follows:

d = 50t.

Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:

v = d/t.

The bird can fly 400 kilometers in 8 hours, hence the velocity is given as follows:

v = 400/8

v = 50 km/h.

Then the equation is given as follows:

d = vt

d = 50t.

The complete problem is:

"An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. Write an equation to represent the distance d, in kilometers, of each bird after t hours".

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