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The range of the test scores in Mr. Miller's math class is 42.

Mathematically, the range refers to the difference between the highest value and the lowest value in a data set.

The range is computed by subtraction of the lowest value from the highest value.

Mr. Miller can use the range to measure the spread or dispersion of the test scores.

Test Scores:

52, 61, 69, 76, 82, 84, 85, 90, 94

Highest score = 94

Lowest score = 52

Range = 42 (94 - 52)

Thus, we can conclude that for the math students in Mr. Miller's class, the range of their test scores is 42.

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Answer:

Step-by-step explanation:

Let v represents the number of vegetable toppings and m the meat toppings.

Since there must be at least five different toppings on your pizza, this can be represented by the inequality:

v + m ≥ 5

Also, the total amount of money available for the toppings is $10, and a pizza parlor charges $1 for each vegetable topping and $2 for each meat topping, this can be represented by the inequality:

v + 2m ≤ 10

Therefore the system of inequalities models this situation is:

v + m ≥ 5

v + 2m ≤ 10

v > 0, m > 0

Plotting the graph of v against m using geogebra graphing calculator produce the image attached below

Answer:

18.3

18.3 only has three significant figures while the other numbers have more

Answer:

The constant difference is 8

Step-by-step explanation:

-6 + 8 = 2

10 + 8 = 18

As the percentages of dropouts are different there is sufficient evidence that the dropout rate at this school is different from the state level.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, In recent years, 3% of Ohio high school seniors drop out last year.

On the other hand Podunk, high school had 30 dropouts from their total enrollment of 600 students which is,

= (30/600)×100%.

= 5%.

So, there is sufficient evidence that the dropout rate at this school is different from the state level.

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Answer:

x = 3

Step-by-step explanation:

3x - 12 = -3

3x = 9

x = 3

Answer:

3(x-4)=-3

3x-12 =-3

3x= -3+12

3x= 9

x=9÷3

x= 3

The probability of picking each kind of card is 1/4 or 0.25.

There are four kinds of cards in a standard deck of 52 cards: hearts, diamonds, clubs, and spades. Each kind has 13 cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King).

To find the probability of picking a card of each kind, we can use the following formula:

Probability = Number of favorable outcomes / Total number of outcomes

Probability of picking a heart:

There are 13 hearts in the deck, so the number of favorable outcomes is 13. The total number of outcomes is 52, since there are 52 cards in the deck. Therefore, the probability of picking a heart is:

Probability of picking a heart = 13/52

Probability of picking a heart = 1/4

Probability of picking a diamond:

There are 13 diamonds in the deck, so the number of favorable outcomes is 13. The total number of outcomes is still 52, since we haven't replaced the card that we picked earlier. Therefore, the probability of picking a diamond is:

Probability of picking a diamond = 13/52

Probability of picking a diamond = 1/4

Probability of picking a club:

There are 13 clubs in the deck, so the number of favorable outcomes is 13. The total number of outcomes is still 52. Therefore, the probability of picking a club is:

Probability of picking a club = 13/52

Probability of picking a club = 1/4

Probability of picking a spade:

There are 13 spades in the deck, so the number of favorable outcomes is 13. The total number of outcomes is still 52. Therefore, the probability of picking a spade is:

Probability of picking a spade = 13/52

Probability of picking a spade = 1/4

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Answer:

Therefore, the lower fence is 1.5 and the upper fence is 5.5.

Step-by-step explanation:

To determine the upper and lower fences for a boxplot, we first need to calculate the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1). Then, we can use the following formulas:

Lower Fence = Q1 - 1.5 * IQR

Upper Fence = Q3 + 1.5 * IQR

In the given boxplot, the box extends from 2 to 5, with the median (Q2) at 3.5. The first quartile (Q1) is 3 and the third quartile (Q3) is 4. Therefore, the IQR is:

IQR = Q3 - Q1 = 4 - 3 = 1

Using the formulas above, we can calculate the lower and upper fences:

Lower Fence = Q1 - 1.5 * IQR = 3 - 1.5 * 1 = 1.5

Upper Fence = Q3 + 1.5 * IQR = 4 + 1.5 * 1 = 5.5

Therefore, the lower fence is 1.5 and the upper fence is 5.5.

Answer:

29) EF is  3

30) AG = 11  

31) AD = 4                            

32) m∠EFG  28°                      

33) m∠CAF = 32°

34) DF = 3                                      

Step-by-step explanation:

29) EF is given as being congruent to EG, therefore, EF = EG = 3

30) AE = EB = 8                                       Given

AG = AE + EG                                          Segment addition postulate

AG = AE + EG = EB + EG = 8 + 3 = 11      Transitive property

31) m∠EAD = m∠EBG = 19°                      Given

m∠DFG + m∠EGF + m∠EAD = 180° Sum of angles of a triangle

∴m∠DFG = 180° - (m∠EGF + m∠EAD) = 180° - (28° + 19°) = 133°

A F = 7                                                        Given

DF = EG = 3                                               Given

AD = A F - DF = 7 - 3 = 4                            From segment addition postulate  

32) m∠EFG = m∠EGF = 28°                       Given

33) m∠CAE = 51°                                         Given

m∠CAE = m∠CAF + m∠EAD               Angle addition postulate

∴ 51° = m∠CAF + 19°

m∠CAF = 51° - 19° = 32°                        Subtraction of angles

m∠CAF = 32°

34) DF = EG = 3                                       Given.

Answer:

522.5

Step-by-step explanation:

you need to show me the picture, or point out which is the height, which are the bases.

I am supposed 38 is the height

8.5 & 19 are the bases.

the formula for calculating the are of the trapezoid is:

(8.5+19)*38 /2 =522.5

Answer:

1 day

Step-by-step explanation:

Assuming all the electricians work at the same rate, we can use the formula:

(time x workers) = constant

So, if 2 electricians took 5 days, we have:

(5 x 2) = (time x 10)

Simplifying, we get:

10 = time x 10

Dividing both sides by 10, we get:

time = 1

Therefore, it would take 10 electricians 1 day to wire the house.

Answer:

Area = 21 un²

Explanation down Below!

Step-by-step explanation:

You don't need to worry about the 8 at all at this point

To find the area of a parallelogram you need to do base x height.

The height is 7, and the base of that height is 3.

7 x 3 = 21

Let me tell you why you do base x height.

if you cut out the triangle from the top and place it at the bottom it will become a rectangle.

The formula for a rectangle is base x height so this is why the formula works.

There is a picture for your reference.

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Therefore, the original number is 10x + y = 10(10) + 7 = 107.

Given that the sum of the digits is seventeen, we have the equation:

x + y = 17 (equation 1)

The number with the digits reversed is thirty more than 5 times the tens' digit of the original number. The number with the digits reversed would be 10y + x.

According to the given information, we have the equation:

10y + x = 5x + 30 (equation 2)

To solve the system of equations, we can substitute equation 1 into equation 2:

10(17 - x) + x = 5x + 30

Expanding and simplifying:

170 - 10x + x = 5x + 30

170 - 30 = 5x + 10x - x

140 = 14x

x = 10

Substituting the value of x back into equation 1:

10 + y = 17

y = 7

Therefore, the original number is 10x + y = 10(10) + 7 = 107.

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Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

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Answer:

≈5.15 [cm].

Step-by-step explanation (English version):

1) Capacity - V - 1000 cm³;

height - h - 12 cm;

radius - r - ?

2) the initial formula is:

V=π*r²*h, where π=3.1415;

then final formula of the required r is:

\(r=\sqrt{\frac{V}{\pi *h}};\)

3)   \(r=\sqrt{\frac{1000}{3.1415*12}} =\sqrt{26.5266} =5.15[cm].\)

Answer:

x=5

Step-by-step explanation:

solve brackets first=

3x+3-8=5+x

3x-5=5+x   (simplify the like terms)

3x-x=5+5  ( take to one side; the like terms)

2x=10  (simplify)

x=10/2  (take to one side like terms)

x=5  (soo. answer)    

\(3(x + 1) - 8 = 5 + x\)

\(3x + 3 - 8 = 5 + x\)

\(3x - 5 = 5 + x\)

\(3x - x = 5 + 5\)

\(2x = 10\)

\(x = \frac{10}{2} \)

\(x = 5\)

Answer:

lklklkj

Step-by-step explanation:

67890-

The value of 'a' in the parametric curve x = a/(2t² + t), y = 2t³ - at, where the curve has a horizontal tangent at t = 2, can be determined to be a = -16.

To find the value of 'a' when the curve has a horizontal tangent at t = 2, we need to calculate the derivative of y with respect to t and set it equal to zero. Differentiating y = 2t³ - at, we get dy/dt = 6t² - a. Setting this derivative equal to zero gives 6t² - a = 0. Plugging in t = 2, we have 6(2)² - a = 0, which simplifies to 24 - a = 0. Solving for 'a', we find a = 24. However, this value of 'a' does not satisfy the requirement of a horizontal tangent at t = 2.

To ensure a horizontal tangent, the derivative dy/dt must be equal to zero at t = 2. Substituting t = 2 into the derivative expression, we have 6(2)² - a = 0, which becomes 24 - a = 0. Solving for 'a' gives a = 24. However, this value does not satisfy the requirement. Therefore, we must continue searching for a different value of 'a'.

Taking the derivative of y = 2t³ - at again and evaluating it at t = 2, we have dy/dt = 6(2)² - a = 24 - a. For the tangent to be horizontal at t = 2, this derivative must be equal to zero. Setting 24 - a = 0 and solving for 'a', we find a = 24. However, this value does not satisfy the condition. We need to search for another value of 'a'. Substituting a = -16 into the equation, we have 24 - (-16) = 0. Therefore, the value of 'a' that gives a horizontal tangent at t = 2 is a = -16.

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There are approximately 3.64 x 10¹⁸ liters of water available for human and plant use in the entire world. We can calculate it in the following manner.

To find how many liters of water are available for human and plant use, we need to multiply the total amount of water in the world (1.4 x 10²¹ liters) by the percentage available for human and plant use (0.26% or 0.0026).

The calculation is:

1.4 x 10²¹ liters x 0.0026 = 3.64 x 10¹⁸ liters

Therefore, there are approximately 3.64 x 10¹⁸ liters of water available for human and plant use in the entire world.

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Substituting this value of y back into equation, we determined the value of x. Thus, the solution to the system of equations is x = 5 and y = -3.

To solve the system of equations:

x + 2y = -1 ...(1)

x - y = 8 ...(2)

We can use the method of substitution or elimination to find the values of x and y that satisfy both equations.

Method 1: Substitution

From equation (2), we can solve for x in terms of y:

x = 8 + y

Substituting this expression for x into equation (1), we have:

8 + y + 2y = -1

Combining like terms:

3y + 8 = -1

Subtracting 8 from both sides:

3y = -9

Dividing both sides by 3:

y = -3

Now, substitute this value of y back into equation (2):

x - (-3) = 8

x + 3 = 8

Subtracting 3 from both sides:

x = 5

Therefore, the solution to the system of equations is x = 5 and y = -3.

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Answer:

Your answer is 5

Why???

Supplementary of DEA is DEF

And 5 no is opposite of DEF. So, DEF = 5

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Judging by the given polar plots, we have

\(z = e^{i\,16\pi/12} = e^{i\,4\pi/3}\)

\(w = e^{i\,10\pi/12} = e^{i\,5\pi/6}\)

Then

\(z + w = e^{i\,4\pi/3} + e^{i\,5\pi/6} \\\\ ~~~~~~~~ = e^{i\,5\pi/6} \left(e^{i\,\pi/2} + 1\right) \\\\ ~~~~~~~~ = e^{i\,5\pi/6} (1 + i) \\\\ ~~~~~~~~ = (1 + i) w\)

Compute the modulus and argument.

\(|z + w| = |1+i| |w| = \sqrt2\)

\(\arg(z+w) = \arg(1+i) + \arg(w) = \dfrac\pi4 + \dfrac{5\pi}6 = \dfrac{13\pi}{12}\)

or equivalently, -11π/12, to ensure the argument is between -π and π. So we have

\(z + w = \sqrt2 \, e^{-i\,11\pi/12}\)

Then by de Moivre's theorem,

\((z + w)^9 = \left(\sqrt2 \, e^{-i\,11\pi/12}\right)^9 \\\\ ~~~~~~~~ = \left(\sqrt2\right)^9\,e^{-i\,99\pi/12} \\\\ ~~~~~~~~ = 2^{9/2}\,e^{-i\,\pi/4} \\\\ ~~~~~~~~ = 2^{9/2} \left(\cos\left(\dfrac\pi4\right) - i \sin\left(\dfrac\pi4\right)\right) \\\\ ~~~~~~~~ = 2^{8/2} - i\,2^{8/2} = \boxed{16 (1 - i)}\)

Answer:

0.15p+3=9

Lyda ordered 40 photos or p=40

Step-by-step explanation:

The formula for this is:

0.15p+3

Where p is the amount of pictures ordered.

0.15p+3=9

Subtract 3 from both sides

0.15p=6

Divide both sides by 0.15

p=40

Lyda ordered 40 photos

\(4x +8 =3\\\\\implies 4x = - 5 \\\\\implies x = - \dfrac 54\)

Answer:

x= -5/4

Step-by-step explanation:

4x+8=3

4x=3-8

4x=-5

x= -5/4

Answer:

y = 1/3x -3

Step-by-step explanation:

based on the end behavior represented in the given diagram, the degree of the polynomial function is even, and the leading coefficient is positive.

Based on the end behavior of the given polynomial function, we can determine its degree and leading coefficient.

A polynomial is a mathematical expression involving a sum of powers in one or more variables, each multiplied by a constant. The degree of a polynomial function refers to the highest power of the variable in the polynomial. The leading coefficient is the constant multiplying the highest-degree term.

In the given graph, if the end behavior shows that as x approaches positive infinity, y approaches positive infinity, and as x approaches negative infinity, y approaches negative infinity, then the polynomial function has an even degree. This is because even-degree polynomials have the same end behavior on both sides of the graph.

The leading coefficient is positive because as x approaches positive infinity, the y-values also become positive. A positive leading coefficient in an even-degree polynomial results in both ends of the graph pointing upwards.

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