ID: A
17. N.Q.1-2 ULHS has a student that can run 100 yds in 15 seconds. Mrs. Duke's class converted his speed to
miles per hour below and determined he can run 4.55 miles per hour. Is the conversion correct? If not, explain
what the class did wrong and then work it out using dimensional analysis. You MUST Show all work.
100 yds
60 sec
60 min 1 mile
= 4.55 mph
15 sec
1 min 1 hr 5280 yds

Answer:  x=8

Step-by-step explanation:

3x - 5= 2.5x + 3 -(x-4)   apply the distributive property

3x -5 = 2.5x + 3 - x + 4     combine like terms  on the right side

3x - 5 = 1.5x + 7            Add 5 to both sides

    +5             +5

3x = 1.5x + 12      subtract 1.5x from both sides

-1.5x  -15.x

1.5x = 12       Now divide both sides by 1.5

x = 8

Answer:

4 : 9

Step-by-step explanation:

Step 1: Find total amount of shapes

16 circles + 20 squares = 36 total shapes

Step 2: Write out ratio of circles to total shapes

16 : 36

Step 3: Simplify by dividing both numbers by 4

16/4 : 36/4

4 : 9

Answer:

A

Step-by-step explanation:

So we have the piecewise function:

[tex]f(x)= \begin{cases}\sqrt{2x} & \text{if }x<3 \\2x+10 & \text{if }3\leq x<8\\42&\text{if } x\geq 8\end{cases}[/tex]

And we want to find f(8).

Since our input value is 8, choose the equation that fits our input.

The first equation demand x to be less than 3. 8 is not less than 3, so we won't use that.

The second equation demand x to e greater than or equal to 3 and less than 8. 8 is not less than 8. So, we won't use that.

The third equation demands x to be greater than or equal to 8. 8 is greater than or equal to 8, so we'll use the third equation.

So:

[tex]f(x)=42\text{ if }x\geq 8[/tex]

[tex]f(8)=42[/tex]

There're nothing more to do, we're done :)

The answer is A.

Edit: Improved Format

Answer:

Ok, the straightforward thing you can do, when you have a number line like in this situation, you can just "count" the number of units that are between A and B.

Now, a more correct way:

First, A is located at the value -3, then we can write:

A = -3.

And B is located at the value 5, then:

B = 5.

Now, the distance between A and B is equivalent to the difference between A and B:

D = B - A = 5 - (-3) = 8

The distance between A and B is 8 units.

Answer:

14.2

Step-by-step explanation:

= AB+BC+CD+DA

= 2.2+4.5+6.1+1.4

= 14.2

​  

Answer: 14.2

Step-by-step explanation:

Khan Academy

Your answer is 6% of x.

We can write the given information as equations to find the answer:

Another way to write "20% of x" is to write 0.2x, so therefore 0.2x = y

You can also write "30% of y" as 0.3y, so 0.3y = z

Now we can substitute in the first equation to the second equation, as we know what y equals in terms of x:

0.3(0.2x) = z

Multiplying out we get:

0.06x = z, and 0.06 as a percentage is 6%

I hope this helps!

Answer:

9x² - 9y + 9

Step-by-step explanation:

Step 1: Write out expression

3 - 2y - 1 + 5x² - 7y + 7 + 4x²

Step 2: Combine like terms (x²)

9x² + 3 - 2y - 1 - 7y + 7

Step 3: Combine like terms (y)

9x² - 9y + 3 - 1 + 7

Step 4: Combine like terms (constants)

9x² - 9y + 9

Answer: the distance is 9,

Step-by-step explanation: If you count the blocks you will see it's nine! Hope this helped you!

Answer:

t = 32/5

Step-by-step explanation:

7 - (5t - 13) = -12

7 - (5t - (-13) = -12

7 - 5t + 13 = -12

-5t = -12 - 13 - 7

-5t = -32

t = -32 / -5

t = 32/5

Answer:

the answer is 19-2v combine like terms if not that then try this....

19-2y=0

-2y=-19

Then divide by -2

y=-19/-2

=9.5

Answer:

x = -18

I hope this helps!

Answer:

X- (-18)

Step-by-step explanation:

Hope this helps:)

Answer:

y = 4(x + 11)² - 484

Step-by-step explanation:

y = 4x² + 88x

factor the expression

y = 4(x² + 22x)

complete the square

y + ? = 4(x² + 22x + ?)

y + ? = 4(x² + 22x + 121)

add 4 • 121 to the left side

y + 4 • 121 = 4(x² + 22x + 121)

multiply

y + 484 = 4(x² + 22x + 121)

y + 484 = 4(x + 11)²

subtract both sides by 484

y = 4(x + 11)² - 484

Answer:

y = 4(x + 11)² - 484

Step-by-step explanation:

Answer:

Complementary

Step-by-step explanation:

Complementary Angles add up to 90°

Supplementary Angles add up to 180°

60 + 30 = 90

Answer:

the answer is A.

Step-by-step explanation:

Answer:

length = 19 units

Step-by-step explanation:

width = x

length = 2x-3

width = 11 units

length = 2(11)-3

length = 22-3

length = 19 units

perimeter = 11 + 11 + 19 + 19 = 60 units

The perimeter of a shape is the sum of the side lengths of the shape. The length of the rectangle is 19 units.

Given that:

[tex]Perimeter = 60[/tex]

[tex]Length = 2 \times Width -3[/tex]

The perimeter of a rectangle is:

[tex]Perimeter = 2 \times (Length + Width)[/tex]

So, we have:

[tex]60= 2 \times (2\times Width - 3+ Width)[/tex]

Divide both sides by 2

[tex]30= 2\times Width - 3+ Width[/tex]

Collect like terms

[tex]3 + 30= 2\times Width + Width[/tex]

[tex]33= 3Width[/tex]

Divide both sides by 3

[tex]11= Width[/tex]

Rewrite as:

[tex]Width = 11[/tex]

Recall that: [tex]Length = 2 \times Width -3[/tex]

[tex]Length = 2 \times 11 - 3[/tex]

[tex]Length = 22- 3[/tex]

[tex]Length = 19[/tex]

Hence, the length of the rectangle is 19 units.

Read more about perimeters at:

https://brainly.com/question/6465134

Answer:

a. F=GMm/r^2; a. M =

[tex]M = \frac{Fr^{2} }{Gm}[/tex]

a.  F=GMm/r^2; b. r =

[tex]r = \sqrt{\frac{GMm}{F} \\}[/tex]

b. M=kxa^3/p^2; a. P =

[tex]p = \sqrt{\frac{kxa^{3}}{M}}[/tex]

b. M=kxa^3/p^2; b. a =

[tex]a = \sqrt[3]{\frac{Mp^{2}}{kx} }[/tex]

Step-by-step explanation:

For a.  F=GMm/r^2; a. M =

To solve for M, we will rearrange the given equation F=GMm/r^2 such that M is the subject of the formula

From

F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

First, Cross multiplication, we then get

[tex]Fr^{2} = GMm[/tex]

Now, divide both sides by [tex]Gm[/tex]

[tex]\frac{Fr^{2} }{Gm} = \frac{GMm}{Gm} \\[/tex]

The equation becomes

[tex]\frac{Fr^{2} }{Gm} = M[/tex]

∴ [tex]M = \frac{Fr^{2} }{Gm}[/tex]

For a.  F=GMm/r^2; b. r =

Also, to solve for r, we will rearrange the given equation F=GMm/r^2 such that r is the subject of the formula

From

F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

First, Cross multiplication, we then get

[tex]Fr^{2} = GMm[/tex]

Now, divide both sides by [tex]F[/tex], Such that we have

[tex]\frac{Fr^{2} }{F} = \frac{GMm}{F} \\[/tex]

Then, [tex]r^{2} = \frac{GMm}{F} \\[/tex]

∴ [tex]r = \sqrt{\frac{GMm}{F} \\}[/tex]

For b. M=kxa^3/p^2; a. P =

To solve for P, we will rearrange the given equation M=kxa^3/p^2 such that P becomes the subject of the formula

From

M=kxa^3/p^2

[tex]M = \frac{kxa^{3}}{p^{2} } \\[/tex]

First, Cross multiply, we then get

[tex]Mp^{2} = kxa^{3}[/tex]

Divide both sides by [tex]M[/tex], such that the equation becomes

[tex]\frac{Mp^{2} }{M} = \frac{kxa^{3}}{M}[/tex]

Then, [tex]p^{2} = \frac{kxa^{3}}{M}[/tex]

∴ [tex]p = \sqrt{\frac{kxa^{3}}{M}}[/tex]

For b. M=kxa^3/p^2; b. a =

To solve for a, we will rearrange the given equation M=kxa^3/p^2 such that a becomes the subject of the formula

From

M=kxa^3/p^2

[tex]M = \frac{kxa^{3}}{p^{2} } \\[/tex]

First, Cross multiply, we then get

[tex]Mp^{2} = kxa^{3}[/tex]

Now, Divide both sides by [tex]kx[/tex], such that the equation gives

[tex]\frac{Mp^{2}}{kx} = \frac{ kxa^{3}}{kx}[/tex]

Then, [tex]\frac{Mp^{2}}{kx} = a^{3}[/tex]

[tex]a^{3} = \frac{Mp^{2}}{kx}[/tex]

∴ [tex]a = \sqrt[3]{\frac{Mp^{2}}{kx} }[/tex]

Answer:

50 square units

Step-by-step explanation:

Using the formula provided, [tex]a = \frac{1}{2}h(b_1+b_2)[/tex], substituting the height (5), b1 (8) and b2 (12), we can solve for the formula.

[tex]a = \frac{1}{2}\cdot5(8+12)\\\\a = \frac{1}{2}\cdot5(20)\\\\a = \frac{1}{2}100\\\\a = 50[/tex]

Hope this helped!

Answer:

50 units²

Step-by-step explanation:

The area of a trapezoid can be found using the following formula.

[tex]A=\frac{1}{2}h(b_{1} +b_{2} )[/tex]

The height of the trapezoid is 5 units. The bases are 8 units and 12 units.

[tex]h= 5 \\b_{1} = 8\\b_{2} = 12[/tex]

Substitute the values into the formula.

[tex]A=\frac{1}{2}*5(8+12)[/tex]

Solve inside the parentheses. Add 8 and 12.

8+12=20

[tex]A=\frac{1}{2}*5(20)[/tex]

Multiply 5 and 20.

5*20= 100

[tex]A=\frac{1}{2}*100[/tex]

Multiply 1/2 and 100 or divide 100 by 2.

100 * 1/2= 50     or      100/2= 50

[tex]A= 50[/tex]

Add appropriate units. For this problem, the units are units².

[tex]A= 50 units^2[/tex]

The area of the trapezoid is 50 square units.

Answer:

No solution (because the n's cancel out!)

Step-by-step explanation:

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

8

2

=

6

n

+4

Multiply all terms by n and cancel:

8n

2

=6+4n

4n=4n+6(Simplify both sides of the equation)

4n−4n=4n+6−4n(Subtract 4n from both sides)

0=6

Answer:

No solutions.

Don't quite understand the question so I'm gonna provide 2 answers

The simplest one being 3

If you're making combinations then 7

hand-tossed(1), thin(2), pan(3), hand-tossed and thin(4), hand-tossed and pan(5), thin and pan(6), all 3(7)

Answer:

a. Types of computer software used in a database management system. =Qualitative

b. Life-lengths of laser printers =Quantitative

c. Brands of calculators used by 100 engineering students on campus =Qualitative

d. Mileage attained by 12 automobiles powered by alcohol= Quantitative

Step-by-step explanation:

Data is described as quantitative when it deals with numeric values whereas qualitative data is categorical in nature. Quantitative data tells us how much, how many, or the frequency of occurrence of certain variables. Qualitative data provides answers to the what, why, which, and where questions.

1. Types of computer software are not numeric variables as they answer the 'what' question.

2. Length deals with numbers, so the life-lengths of laser printers is a quantitative variable.

3. Brands of calculators are categorical data and are thus qualitative.

4. Mileage is a numerical variable and is thus quantitative.

children

25.5 %

so 25.5% of 100

495

Answer:

8 cubic units

Step-by-step explanation:

Let he vertices of the parallelepiped be A = (4,2,4), B= (6,3,8), C = (6,1,10) and D =  (0,6,3)

The edges of the parallelepiped are

AB = (6,3,8)  - (4,2,4) = (2,1,4)

AC = (6,1,10) - (4,2,4) = (2,-1,6)

AD = (0,6,3) - (4,2,4) = (-4,4,-1)

Therefore the volume of the parallelopiped is = |[AB,AC,AD]|

=  [tex]$ \begin{vmatrix}\ 2\ \ \ 1\ \ \ \ 4\ \\2\ -1\ \ \ 6 \\-4\ \ \ 4\ -1 \end{vmatrix}$[/tex]

= |2(1-24)+1(-2+24)+4(8-4)|

= |2(-23) + 1(22) + 4(4)|

= |8|

=8 cubic units

Answer:

384 inches per second.

Step-by-step explanation:

We are given that the acceleration of an object due to gravity is 32 feet per second.

And we want to find the acceleration in inches per second.

The acceleration can be represented as a ratio of 32 feet : second. This can be written as a fraction:

[tex]\displaystyle \frac{32\text{ feet}}{\text{second}}[/tex]

Use dimensional analysis. It is known that there is 12 inches in a feet. So, multiply by 12in/feet:

[tex]\displaystyle = \frac{32\text{ feet}}{\text{second}}\cdot\frac{12\text{ inches}}{\text{feet}}[/tex]

Cancel like units:

[tex]\displaystyle =\frac{32\cdot 12\text{ inches}}{\text{second}}[/tex]

Multiply:

[tex]\displaystyle =\frac{384\text{ inches}}{\text{second}}[/tex]

In conclusion, our answer is 384 inches per second.

Answer:

1) 78

2) 28

3) 74

4) 28

5) 74

6) 106

7) 74

8) 74

9) 78

10) 78

Answer:

Step-by-step explanation:

Answer:

obtuse , 90 , 180 .

Step-by-step explanation:

Answer:

Five billion, six-hundred and eight million, nine-hundred and twelve thousand, and thirteen.

Hope this helps!

Answer:

Hey there!

8(2)+8(6)

16+48=64

The total price is 64 dollars.

Let me know if this helps :)