Henry walks to and from school each day. after 100 days of school, he has walked 125 miles. How many miles does Henry walk to and from school?

557,568 inch³ of refrigerant can be held by the tubing.

Here we have to find how much a refrigerant can hold.

Data given:

outer diameter (d) = 78inch

outer radius(r) = 39 inch

inner diameter (d') = 34 inch

inner radius (r') = 17inch

Height (h) = 12 feet

= 12 × 12

= 144 inch

the formula to find the volume of the cylinder:

volume= пr²h

So here we get

Refrigerant hold = Volume of the outer cylinder - the volume of the inner cylinder

= πr²h - πr'²h

= πh(r² - r'²)

= π ×144 ( 39² - 17²)

= π × 144 ×56 × 22

= 22/7 × 144 × 56 × 22

= 557,568 inch³

Therefore the refrigerant can hold 557,568 inch³.

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By using the concept of unitary method, ratio and percentage, it can be calculated that-

7) Option D is correct

6) Option C is correct

8) Option D is correct

What is Unitary method, ratio and percentage?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Ratio is used to determine how much one quantity is bigger  as compared to another. The first part of the ratio is called antecedant and the second part of the ratio is called consequent.

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

Here, unitary method, ratio and percentage will be used.
7) The scale on a map reads [tex]\frac{1}{2} \ inch = 30 \ miles\\[/tex]

1 inch = [tex]30 \div \frac{1}{2} \ miles[/tex] = 60  miles

[tex]\frac{23}{4} \ inches[/tex] = [tex]\frac{23}{4} \times 60 \ miles[/tex] = 345 miles

Option D is correct

6) Let the number of empty seats be 3x and the number of full seats be 7x

Total number of seats = 3x + 7x = 10x

By the problem,

7x  = 203

x = [tex]\frac{203}{7}[/tex]

x = 29

Total number of seats = [tex]29 \times 10[/tex] = 290

Option C is correct

8) Let the number of students be x

Percentage of students in the band = [tex]\frac{37.5}{100} \times x[/tex]

By the problem,

[tex]\frac{37.5}{100} \times x =42\\x = \frac{42 \times 100}{37.5}\\x = 112[/tex]

Option D is correct

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Answer: 3:2

Step-by-step explanation:

We know that every 3 child tickets were sold for every 2 adults tickets sold

So the ratio is 3:2

Answer: C. 20

Step-by-step explanation:

Ley y be the duck mass, and x be the number of weeks

Our equation will be

y = 0.042x + 0.05

Then we plug 0.89 in the y

0.89 = 0.042x + 0.05

0.84 = 0.042x

x = 20 Weeks

So the answer is C. 20 weeks

Answer:

150%

Step-by-step explanation:

2 x 2 = 4

Remainder=1

50% OR 0.5 x 2 = 1

The statement that "close to 60 country songs" but probably not exactly 60 country songs is, best prediction to complete the given statement .

So, the correct option is option (B).

Mekala has MP3 player Jumble has 4 techno songs, 2 country songs, and 3 jazz songs on it.

firstly, we represent this songs in ratio format :

Now, the ratio of techno songs to country songs to jazz songs = 4 : 2 : 3

Let the total number of songs which is unknowns be" x". So,

Total number of techno songs = 4x

Total number of country songs = 2x

Total number of jazz songs = 3x

Total number of songs that Mekala plans to Listen = 270

Then, 4 x + 2 x + 3 x = 270

=> 9 x = 270

Dividing both sides by 9, we get

=> x = 30

So, Number of techno songs = 4 × 30

= 120

Number of country songs = 2×30 = 60

Number of jazz songs = 3 × 30 = 90

but all this is based on prediction only.

Hence, the total country songs are close to 60 but not exactly 60.

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Complete question:

Mekala has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Mekala's Jumble has 4 techno songs, 2 country songs, and3 jazz songs on it. Mekala plans to listen to 270 songs.

Complete the following statement with the best prediction.

Mekala will listen to...

Please choose from one of the following options.

a) Exactly 60 country songs

b) Close to 60 country songs but probably not exactly 60country songs

c)Exactly 210 country songs

d)Close to 210 country songs but probably not exactly 210 country songs

Answer:

x = 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 8[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 4[tex]\sqrt{3}[/tex]

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

Explanation:

Segments JK, KL, and JL are tangent to the circle.

We can break those segments into smaller pieces and notice we have these 3 pairs of congruent tangents:

Let's use the first equation to solve for x.

MJ = NJ

5x-8 = 8x-35

5x-8x = -35+8

-3x = -27

x = -27/(-3)

x = 9

Use the same idea to find y.

KN = KO

7y-9 = 2y+11

7y-2y = 11+9

5y = 20

y = 20/5

y = 4

Now compute the length of segment KO.

KO = 2y+11 = 2*4+11 = 19 units

Subtract this from LK to find LO

LO = LK - KO

LO = 32 - 19

LO = 13

This makes segment LM to be also 13 units long.

Now use the value of x to find sides MJ and NJ

MJ = 5x-8 = 5*9-13 = 32

NJ = 32 as well

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

We have these pieces:

which give us

Therefore, the perimeter of triangle JLK is:

JK+KL+JL = 51+32+45 = 128 units

If the sample mean is 12.8, sample standard deviation is 2 and sample size is 20, then the student's t-distribution should be use to perform the hypothesis test

The population mean = 13

The sample mean = 12.8

The standard deviation = 2

The sample size of the population = 20

The given condition is the underlying population is normal.

Here population standard deviation is missing in the given data. So to perform a hypothesis test when the population standard deviation is missing then we have to use the student t-distribution

Therefore, the student's t-distribution should be use to perform the hypothesis test

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To find the slope of a line given an equation in the form of ax + by = c .The slope of 7x + y = -4 is 7.

To find the slope of a line given an equation in the form of ax + by = c, you first need to put the equation into slope-intercept form, which is y = mx + b. To do this, start by subtracting ax from both sides of the equation, leaving you with by = c - ax. Then divide both sides by b, giving you y = (c - ax) / b. This is the equation in slope-intercept form, with m being the slope, which in this case is 7.

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The unknown wavelength of a light with m= 4 bright fring overlaps m = 3 bright orange fringe and used in a double slit is 450 nm.

Double Slit experiment:

In modern physics, the double-slit experiment shows that light and matter can exhibit properties of both classically defined waves and particles.

Furthermore, it demonstrates the fundamental stochastic nature of quantum mechanical phenomena.

Formula ,

λ = x.d/n.L

where , λ = wavelength of light used (nm)

x = distance from central fringe (m)

d = distance between the slits (m)

n = the order of the fringe

L = length from slits to the viewing screen (m)

thus, taking ratios for the two waves: let w = unknown wavelength

600/w = 4/3 (as other factors are same for both)

thus, w = 450 nm

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Complete questions :

A double slit is illuminated simultaneously with light of wavelength 700 nm and light of an unknown wavelength. The m = 4 bright fringe of the unknown wavelength overlaps the m = 3 bright orange fringe What is the unknown wavelength? Express your answer to three significant figures and include the appropriate units.

Answer: Area=35km^2

Step-by-step explanation:

You need to find the areas of the rectangle and then the triangle.

First, you start with splitting up the figure to a rectangle and a triangle.

Secondly 6*5= 30 so the area of the rectangle is 30 km.

Thirdly, you add that to the area of the triangle, which you figure out because the opposite side of the figure is 6 km so the remaining length is going to be 2km. The area of a triangle is (1/2)(Base)(Height), so (1/2)(5)(2)= 5.

Add the 30 with the 5 and you get a total of 35 km for the area.

Answer:

i think the answer is 240km cuz you multiply 8x5x6. hope this helps, boo!

Step-by-step explanation:

Initial value of the linear function through A and B is 3.

The starting output value, or the y-value when x = 0, is the initial value. The rate of change is the rate at which the input or, in the case of a graph, the rate at which y changes in relation to x. A function's starting value in mathematics denotes the function's y-intercept. The constant in an equation can also be used to determine initial values. In graph functions, understanding the y-intercept is beneficial. By substituting 0 0 for x x and finding y y, you may verify the starting value.

Given,

Points

A (1,3)

B (6,13)

Linear function,

f(x) = ax + b

Equating,

f(x) = x + 3

Let x = 0

f(x) = 3

As we know,

The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

Initial value of the linear function through A and B is 3.

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Answer:

a = −1 / 2 b^3 + 1 / 2 bh

Step-by-step explanation:

1 )

h = 2a / b^1 + b^2

2 ) Multiply both sides by b.

bh = b^3 + 2a

3 ) Flip the equation.

b^3 + 2a = bh

4 ) Add -b^3 to both sides.

b^3 + 2a + −b^3 = bh + −b^3

2a = −b^3 + bh

5 ) Divide both sides by 2.

2a / 2 = −b^3 + bh / 2

a = −1 / 2 b^3 + 1 / 2 bh

Hope this helps! :)

Answer: ( -9, -8)

Step-by-step explanation:

When reflected across the y-axis, the y-coordinate will be the opposite!

So the answer is (-9, -8)

Answer:

A strong positive association

Step-by-step explanation:

A perfect fit for a positive line would be 1.  A perfect fit for a negative line would be -1.

The scale goes from 1 tp -1.  

.86 is pretty close to 1.

Answer:

3/2*2/3=1

Step-by-step explanation:

3/2*2/3. Everything cancels out, and you are left with 1.

3/2*2/3=6/6=1

Answer:

=1

Using the given fractions,

3/2×2/3

Applying the fractions formula for multiplication,

=3×2/2×3

=6/6

Simplifying 6/6, the answer is

=1

It is true that a multiple linear regression model interprets the slope differently than a simple linear regression model.

The link between two variables is determined through simple linear regression. The slope of a straight line used to represent linear regression indicates how changing one variable impacts another variable.

For the complex relationships between data, multiple linear regression is used. More than one variable may contribute to the explanation of this relationship.

One y-intercept and numerous slopes (one for each variable) make up a multiple regression formula. The formula is understood in the same way as a simple linear regression formula, however more than one variable influences the relationship's slope.

Therefore, the statement is true.

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The equation relating C and S is given as follows:

C(S) = 5000 + 200S.

The graph of the equation is then given by the image shown at the end of the answer.

The first step in defining the function is verifying the input and the output variables, as follows:

Then from these variables, we identify the type of function, which is linear, as for each additional ton of sugar, the cost increases by a fixed amount.

This fixed amount is of $200, hence it represents the slope of the function. The fixed fee of $5,000 to rent trucks is the intercept, hence the equation is defined as follows:

C(S) = 5000 + 200S.

And then the graph starting at (0,5000) and connecting point (10, 7000) is given at the end of the answer.

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the average rate of change of the function on the interval from x = 0 to x = 5 is 580.8

Average rate of change of a function f(x) between x-values x1 and x2 = (f(x2) -f(x1)/ (x2 -x1)

For this given function f(x)=12(3)x then it will mean that

f(x) = 12.3^x and x-values 0 and 5, the average rate of change is

the average rate of change = (f(5) -f(0))/(5 -0) = (2916 -12)/5 = 580.8

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Answer:

1503

Step-by-step explanation:

1803 - 300

The required type ii error probability of the test using is 0.085.

It is determined by duplicating the pretest chances by the probability of a positive or negative test (as we will show). Post-test  probability  is characterized, as the likelihood of the objective problem after a symptomatic experimental outcome is known.

We have,

standard deviation = 7, mean = 6, size of the sample = 23.

P(type II error) = P(Xbar >=8 given mean =6)

=P(Z>(8-6)×√(23)/7) =P(Z>1.37)=1-P(Z<1.37)

=1-0.9147=0.0853 =0.085

Thus, required probability is 0.085

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1) The line's equation is y = 4 because it passes through the coordinates (-5,4).

2)  The equation of the line is y= 2x + 4

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

1) A line with a slope of 0 is considered to be horizontal.

The equation is y=4 because along a horizontal line, the y-values remain constant.

The line's equation is y=4 because it passes through the coordinates (-5,4).

2) (x1,y1) = (-2,0) , m=2

y-y1=m(x-x1)

y-0 = 2 (x-(-2))

y=2(x+2)

y= 2x + 4

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The solution is 16 units

The length of the line segment is 16 units

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:  y=f(x+c) (same output, but c units earlier)

Right shift by c units:  y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the length of the line segment be = A

Now , the initial length of the line segment = 16 units

The line is reflected across the y-axis

So , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y)

And , the resulting line is translated 5 units down

But , the line segment does not change in dimension at all

So , the reflection and a translation does not affect the length of the line segment

Hence , the length of the line segment is 16 units

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Therefore lifetime value is such that   the total lifetime of all batteries in a package exceeds that value for only 5% of all packages is 13.548 hours

In statistics, the standard deviation measures how widely distributed or how much a bunch of values can vary. While a big standard deviation shows that values are scattered throughout a wider range, a low standard deviation suggests that values are frequently close to the set's mean.

Here,

given that the  lifetime of a certain type of battery is normally distributed with mean value 13 hours and standard deviation 1 hour.

Sample size=n =9

Sample mean =X' N is(13,1/3)

If c is the lifetime value, then only 5% of all packages will have a total battery lifetime that is longer than that amount.

Then we have P(X>c) =0.05

Convert into Z score to get

P(x-13/(1/3) > z) = 0.05

z =1.645 from std normal distribution table

Hence x = 13 + 1.645/3

x=13.548

Therefore lifetime value is such that   the total lifetime of all batteries in a package exceeds that value for only 5% of all packages is 13.548 hours.

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The value of the larger of the two numbers is 5.73.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Two numbers = M and N

M + N = 8 _____(1)

M = 8 - N _____(2)

MN = 13 _____(3)

Putting (2) in (3) we get,

(8 - N)N = 13

8N - N² = 13

N² - 8N + 13 = 0

This is in the form of ax² + bx + c = 0

a = 1, b = -8 and c = 13

Using the determinant we have,

N = -b ± √(b² - 4ac) / 2a

N = 8 ± √(64 - 52) / 2

N = 8 ± √12 / 2

N = 8 ± 2√3 / 2

N = 4 ± √3

N = 4 + √3 and N = 4 - √3

[√3 = 1.73]

N = 5.73

N = 2.27

Now,

When N = 5.73, M = 8 - 5.73 = 2.27

When N = 2.27, M = 8 - 2.27 = 5.73

Now,

The two numbers are 5.73 and 2.27

Thus,

The larger of the two numbers is 5.73.

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constructing cones a right triangle whose hypotenuse is 23 m long is revolved about one of its legs to generate a right circular cone. radius: 11.5 m height: 23 m volume: 1650.6 m³

The hypotenuse of the triangle is 23 m. This means that the two sides are 11.5 m and 11.5 m. This gives us the radius of the cone.

The height of the cone is the same as the hypotenuse, so the height is 23 m.

The volume of a right circular cone can be calculated using the following formula: V = (πr²h)/3. In this case, the radius is 11.5 m, the height is 23 m, and π = 3.14. Plugging these values into the formula, we get a volume of 1650.6 m³.

V = (πr²h)/3

V = (3.14 × 11.5² × 23)/3

V = 1650.6 m³

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Answer: 34

Step-by-step explanation:

Synthetic division is a yet another way to divide a polynomial by the factor, where k is a constant.

What is a synthetic division?

Synthetic division is usually used to find factors of polynomials of degree 3 that cannot be factored by grouping the polynomial.

Synthetic division is also used to find factor polynomials of degree 4 or higher.

We use synthetic division if and only if no other methods will work since there is a trial and error aspect to using it.

Taking an example:

We have to find the roots of the polynomial, [tex]f(x)= x^3+3x^2-4[/tex]

Substituting x=1 in the above equation, we get,

f(1)= [tex]1^3+3-4[/tex]=0

Thus, (x-1) is a root of the above polynomial.

Dividing the given function by (x-1)

[tex]x^3+3x^2-4/x-1\\=x^2+4x+4\\=(x+2)^2[/tex]

Thus, the roots of the given polynomial are given as, (x-1) and [tex](x+2)^2[/tex].

Hence, this is the synthetic division to find out the roots of the polynomial.

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