Deborah spends 1/5 of her consulting time writing grant proposa
her consulting time writing grant proposals. If she spends 48 hours per month
writing grant proposals, how much time does she spend on consulting work?

Answer:

Step-by-step explanation:

We know:

1min = 60s → 3min = (3)(60s) = 180s

40s : 3min = 40s : 180s = (40/20) : (180/20) = 2 : 9

$1 = ¢100 → $3 = (3)(¢100) = ¢300

$3 : ¢65 = ¢300 : ¢65 = (300/5) : (65/5) = 60 : 13

Answer:

Step-by-step explanation:

[tex]-38=7v+17-12v\qquad\text{subtract 17 from both sides}\\\\-38-17=7v+17-17-12v\qquad\text{combine like terms}\\\\-55=-5v\qquad\text{divide both sides by (-5)}\\\\\dfrac{-55}{-5}=\dfrac{-5v}{-5}\\\\11=v\to v=11[/tex]

Answer:

communicative property  of addition

Step-by-step explanation:

communicative property  of addition:  The order in which numbers are added doesn't change the sum of the numbers .

For any number a & b,

a + b = b + a

similarly,

3 +4 = 4 +3

The property demonstrated in statement 3 + 4 = 4 + 3 is known as the commutative property of addition.

According to the commutative property of addition, altering the order of addends has no impact on the sum.

The given statement is 3 + 4 = 4 + 3.

The value of the R.H.S and L.H.S are the same i.e. 7. Clearly if we alter the addends 3 and 4, we can get the same result. So, it can be concluded that this property is the commutative property of addition.

Therefore the property demonstrated in statement 3 + 4 = 4 + 3 is known as the commutative property of addition.

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Answer:

The cost of each notebook is $5

The cost of each thumb drive is $18

Step-by-step explanation:

We solve this problem by the system of equations

Equation for Troy and equation for Lisa and then solve the two

equations simultaneous using the elimination method

Assume that the price of one notebook is $x and the price of one

thumb drive is $y

Troy bought 4 notebooks and 13 thumb drives for $254

∴ 4 x + 13 y = 254 ⇒ (1)

Lisa bought 5 notebooks and 8 thumb drives for $169

∴ 5 x + 8 y = 169 ⇒ (2)

To solve the equation multiply equation (1) by 5 and equation (2) by -4

to eliminate x

∵ 20 x + 65 y = 1270 ⇒ (3)

∵ -20 x - 32 y = -676 ⇒ (4)

Add equations (3) and (4)

∴ 33 y = 594

Divide both sides by 33

∴ y = 18

Substitute the value of y in equation (1) or (2) to find x

∴ 4 x + 13(18) = 254

∴ 4 x + 234 = 254

Subtract 234 from both sides

∴ 4 x = 20

Divide both sides by 4

∴ x = 5

x represents the cost per notebook and y represents the cost per

thumb drive

The cost of each notebook is $5

The cost of each thumb drive is $18

Answer: n=4, d=20

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

because eight is 50% of 16

Answer: She will be 16

Step-by-step explanation:

Answer:

B. 2 m

Step-by-step explanation:

cm are centimeters and mm means millimeters and these a both smaller than an inch, and km kilometers is a distance like miles. Whilst m stands for meters.

Answer:

0

Step-by-step explanation:

-y₁ + y₂\-x₁ + x₂ = m

[tex] \frac{ - 2 + 2}{9 + 7} = \frac{0}{16} = 0[/tex]

I am joyous to assist you anytime.

Answer:

#4: 2/45 (0.044444...)

#11: 39/250 (0.156)

#12: 2/15 (0.133333)

Answer:

173,482-5.5=173,476.5

Answer:

$9,541.51

Step-by-step explanation:

Final answer:

4.17 can be written as 4 17/100.

Explanation:

The number 4.17 can be written as a whole number with a fraction by separating it into the whole number part and the fractional part.

Thus, 4.17 can be written as 4 17/100.

Answer:

B. No solutions.

Step-by-step explanation:

Let's try solving it:

3(x + 8) = 3x + 4

3x + 8 = 3x + 4.

There are no solutions  because if we simplify we get an absurd result. Subtract 3x from both sides of the equation:

3x - 3x + 8 = 3x - 3x + 4

8 = 4.

There are no solutions for x in this equation.

To solve this equation, we need to combine like terms and isolate the variable. Here are the steps:

Since 23 does not equal 4, these two sides are not equal. Therefore, there are no solutions for x in this equation.

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Answer:

'(3, -4), '(1, 0), '(4, 0)

Step-by-step explanation:

According to the 180°-rotation rule, you take the OPPOSITE of both the x-coordinate and y-coordinate:

(-3, 4) → (3, -4)

(-1, 0) → (1, 0)

(-4, 0) → (4, 0)

I am joyous to assist you anytime.

The coordinates of the vertices after rotated 180° about the origin are;

( 3, -4 ), ( 1, 0 ) and ( 4, 0 ).

Here,

Given that;

A triangle has vertices at (-3, 4), (-1,0), and (-4,0).

We have to find the value of the coordinates of the vertices after rotated 180° about the origin.

What is Rotation 180 degree about the origin?

The rule for a rotation by 180° about the origin is (x, y) → (−x,−y).

Now,

A triangle has vertices at (-3, 4), (-1,0), and (-4,0).

Hence the coordinates of the vertices after rotated 180° about the origin are,

(-3, 4) ⇒ (3, -4)

(-1, 0) ⇒  (1, 0)

(-4,0) ⇒ (4, 0)

So, The coordinates of the vertices after rotated 180° about the origin are;

( 3, -4 ), ( 1, 0 ) and ( 4, 0 ).

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Answer:

x = 3.65

Step-by-step explanation:

7.4x + 5 = 32

-5              -5

7.4x = 27

-----    -----

7.4     7.4

x = 3.64864865

This rounds to 3.65

x = 3.65

Answer:

The change in price is $0

Step-by-step explanation:

dropped $3 means "-3", increased $6 means "+6"

the price dropped twice so 2(-3) and increased once by 6

so, 2(-3) + 6 = 0

The price of the online movie stayed the same from Monday morning to the following Monday morning. It dropped $6 on the first day and increased $6 on the next Monday, so the decrease and increase balanced each other out.

This problem belongs to the field of basic mathematics, specifically, arithmetic operations. To solve this, we'll follow the changes day by day. On Monday morning, the price of the online movie dropped $3 and then another $3 in the afternoon. That's a total drop of $3 + $3 = $6. The following Monday morning, the price increased by $6. So overall, the movie price just returned to its original price because the total amount of decrease, which is $6, and the total amount of increase, which is also $6, balanced each other out. So, the price of the online movie when its changed from Monday morning to the following Monday morning remained the same.

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The classification of the numbers into rational and irrational are:

1. Pi is irrational

2. 7 squared is irrational

3. 7.1234... is irrational

1) π is a mathematical expression whose approximate value is 3.14159365…

The given value of π is expressed in decimal which is non-terminating and non-repeating. As the value is non-terminating it shows the nature of irrational numbers. Hence, π is not a rational number

2) 7 squared is not a perfect square and as such it will have non-terminating and non-repeating decimal and so it is irrational.

3) 7.1234... is an irrational number because it is non-terminating and non-repeating decimal.

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Answer:

0.55 or 55/100 or 11/20

Step-by-step explanation:

Hey there!

3/10 + 1/4

≈ 6/20 + 5/20

= 6 + 5 / 20 - 0

= 11 / 20

Thus, your answer is: 11/20

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

The mean (or average) of a set of numbers can be found with the following formula:

[tex]Mean = \frac{A_{1} + A_{2} + ... + A_{N}}{N}[/tex]

For this problem, we have five numbers, so we add them together and divide by 5:

[tex]Mean = \frac{92 + 85 + 78 + 97 + 88}{5}[/tex]

[tex]Mean = \frac{440}{5}[/tex]

[tex]Mean = 88[/tex]

Answer:

88%

Step-by-step explanation:

Emma took tests of her 5 chapters throughout the year.

She received  the score on the five tests

92%, 85%, 78%, 97% and 88%

We have to calculate the average (mean) of her final grade.

average =  [tex]\frac{\text{addition of all grades}}{\text{total number of tests}}[/tex]

=  [tex]\frac{92+85+78+97+88}{5}[/tex]

=  [tex]\frac{440}{5}[/tex]

= 88%

Her final grade would be 88%.

Answer:

A. 1/36 B. 1

Step-by-step explanation:

A. if (6^2)x=1; 6^2=36

36x=1

x=1/36

B. If (6^0)x=1; 6^0=1

(1)x=1

x=1

Answer:

Step-by-step explanation:

median- 23447

mode- 2579

range-1109766

Answer:

[tex](34)[/tex]

Step-by-step explanation:

We are looking for what number times .50 makes the equation true.

So, just do backwards equation:

[tex]52 - 35[/tex]

[tex]==> 17[/tex]

Thus, meaning that what multiplied by 0.50 is equal to 17?

[tex]0.50 * 34[tex]

[tex]==> 17[tex]

Put any Variable in between the parentheses, for example x.

Step-by-step explanation:

1. Move the Constant 35 to the other side of the problem, and flip it's sign.

0.5(×)=52-35

2. Subtract the numbers

0.5×=17

3. Divide both sides of the equation by 0.5

×=34

Answer:

Dave should stop at Springfield.

Step-by-step explanation:

As shown, Gilmore is 26 miles away.

And Dave is driving to Gilmore but he wants to stop for lunch when he is about halfway there.

That means he wants to stop around [tex]\frac{26}{2}=13[/tex] miles.

And Springfield is 15 miles away that is nearest to 13 miles.

Hence, Dave should stop at Springfield.

Answer:

Step-by-step explanation:

(−4.46)(11)=−49.06

Check the picture below.

The measure of m∠EBC if m∠EBD = 36° and m∠DBC = 108° is 144degrees

The point where two lines intersect is known as the angle.

From the diagram shown:

m∠EBC = m∠EBD + m∠DBC

Given the following:

m∠EBD = 36degrees

m∠DBC = 108degrees

Substitute the given values into the expression as shown:

m∠EBC = 36 + 108

m∠EBC = 144degrees

Hence the measure of m∠EBC is 144degrees

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In the number 861, the value of the digit 6 is 60 because it falls in the tens place.

The value of the 6 in 861 is in the tens place. This means that it's value is not simply 6, but 60. In other words, the value of a digit depends on its position or place value in the number. In this case, because 6 falls in the tens place, it represents 60 rather than 6.

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Answer: [tex]h=\dfrac{E}{mg}[/tex], where E = gravitational potential energy, m = mass, g = gravity, and h = height.

Step-by-step explanation:

Given : The formula [tex]E= mgh[/tex] , where E = gravitational potential energy, m = mass, g = gravity, and h = height, is used to calculate gravitational potential energy.

To find the formula for h (height), we need to divide mg on both the sides , we get

[tex]h=\dfrac{E}{mg}[/tex]

Hence, the formula for h will be [tex]h=\dfrac{E}{mg}[/tex], where E = gravitational potential energy, m = mass, g = gravity, and h = height.

For the formula  E= mgh, when we solve for h, we would get : Option B. h equals E over m times g

To solve the formula E = mgh for h,

we need to isolate the variable h on one side of the equation.

Here's the step-by-step process:

equation: E = mgh.

Divide both sides of the equation by mg to make h the formula of the equation

E/(mg) = h

Therefore, the formula E = mgh, when solved for h, becomes h = E/(mg). Option B is correct.

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Answer: 17

Step-by-step explanation:

Gabby's savings over 'b' weeks can be written as an inequality 50 + 20b > 400. Simplifying this, we find that Gabby has to save up for at least 18 weeks to save more than $400.

Gabby's savings can be represented as 50 + 20b, with 'b' being the number of weeks. For her to save more than $400, we can write this inequality 50 + 20b > 400. Subtract 50 from both sides to simplify the inequality and we get 20b > 350. To find the least number of weeks, divide both sides by 20 to solve for b and we get b > 17.5. However, since 'b' must be a whole number (because you can't have half a week), the least number of weeks Gabby must save is 18 weeks.

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Answer:

Step-by-step explanation:

11. I can't see the full problem statement, so I'm unable to answer the question.

12. Answer below:

"one half" = [tex]\frac{1}{2}[/tex]

"negative five eighths" = [tex]\frac{-5}{8}[/tex]

To evaluate the expression, you multiply the two numbers together:

[tex]\frac{1}{2} * \frac{-5}{8} = \frac{1 * -5}{2 * 8} = \frac{-5}{16}[/tex]

13. Answer below:

"one third" = [tex]\frac{1}{3}[/tex]

"eleven sixteenths" = [tex]\frac{11}{16}[/tex]

To evaluate the expression, you multiply the two numbers together

[tex]\frac{1}{3} * \frac{11}{16} = \frac{1 * 11}{3 * 16} = \frac{11}{48}[/tex]

Answer:

Step-by-step explanation:

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Hey!

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

Find the zero term:

Plug in 0 for n.

a = 8 + 3(0 - 1)

a = 8 + 3(-1)

a = 8 + (-3)

a = 5

Answer: 5

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

Find the first term:

Plug in 1 for n.

a = 8 + 3(1 - 1)

a = 8 + 3(0)

a = 8 + 0

a = 8

Answer: 8

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

Find the 40th term:

Plug in 40 for n.

a = 8 + 3(40 - 1)

a = 8 + 3(39)

a = 8 + 117

a = 125

Answer: 125

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

Hope This Helped! Good Luck!

Final answer:

To create a 35% saline solution by mixing a 50% and a 30% solution, the nurse needs to use 6000cc of the 30% solution.

Explanation:

The question asks how much of a 30% saline solution a nurse needs to mix with 60cc of a 50% saline solution to achieve a final solution concentration of 35%. To solve this problem, let's denote the volume of the 30% solution needed as x cc. Using the concept of weighted averages for concentrations, we can set up the following equation:

(60cc × 50%) + (x cc × 30%) = (60cc + x cc) × 35%

Solving this equation, we get:

3000 + 0.3x = 0.35(60 + x)

3000 + 0.3x = 21 + 0.35x

Subtracting 0.3x from both sides:

3000 = 21 + 0.05x

Subtracting 21 from both sides and dividing by 0.05:

x = 6000 cc

Therefore, the nurse should use 6000cc of the 30% saline solution to achieve the desired concentration.