Use the digits 5, 3, and 2 only once in each number.
How many different 3-digit numbers can you make?
A. 5
B. 12
C. 8
D. 10
E. 6

Answer:

42

Step-by-step explanation:

Because she is moving from a 65 degree pool into a 107 degree hot tub so there is a 42 degree difference when she moves to the hot tub from the pool.

Answer:

The Proof is given below.

Step-by-step explanation:

Given:

[tex]\overline{HF}[/tex]  bisect ∠ EHG.i.e

∴ ∠EHF ≅ ∠ GHF

[tex]\overline{EH} \cong \overline{GH}[/tex]  

To Prove:

[tex]\overline{EF} \cong \overline{GF}[/tex]  

Proof:

In  Δ EHF and Δ GHF

    EH ≅ GH     ………............{Given}

∠ EHF ≅ ∠ GHF     …………..{EF bisect ∠ EHG as given above}

     HF ≅ HF     ………............{Reflexive Property}

Δ EHF ≅ Δ GHF …................{ By Side-Angle-Side test}

∴ EF ≅ GF........{corresponding parts of congruent triangles (c.p.c.t).}

[tex]\overline{EF} \cong \overline{GF}[/tex]  ....... PROVED

Answer:

The manufacturer should decrease the level of unskilled labor by 2 for the total output to stay the same.

Step-by-step explanation:

Q(x,y) = 60 x^⅓ y^⅔

Take the partial derivatives with respect to x and y.

∂Q/∂x = 20 x^-⅔ y^⅔

∂Q/∂y = 40 x^⅓ y^-⅓

So the total differential is:

dQ = ∂Q/∂x dx + ∂Q/∂y dy

dQ = 20 x^-⅔ y^⅔ dx + 40 x^⅓ y^-⅓ dy

If dQ = 0:

0 = 20 x^-⅔ y^⅔ dx + 40 x^⅓ y^-⅓ dy

If x = 10, y = 40, and dx = 1:

0 = 20 (10)^-⅔ (40)^⅔ (1) + 40 (10)^⅓ (40)^-⅓ dy

0 = 20 (4)^⅔ + 40 (1/4)^⅓ dy

-20 (4)^⅔ = 40 (1/4)^⅓ dy

-20 (4)^⅔ (1/4)^⅔ = 40 (1/4)^⅓ (1/4)^⅔ dy

-20 = 40 (1/4) dy

-20 = 10 dy

dy = -2

The manufacturer should decrease the level of unskilled labor by 2 for the total output to stay the same.

To maintain the same level of production when adding one skilled worker, we use calculus to find the necessary change in the number of unskilled workers based on the manufacturer's production function.

The question deals with partial derivatives and their application in the context of production functions. Using calculus, specifically the concept of partial derivatives, we can estimate the change in the number of unskilled workers required to maintain the same level of production when there is an increase in the number of skilled workers. Given the manufacturer's production function Q(x, y) = 60x1/3y2/3, where x is the number of skilled workers and y is the number of unskilled workers, we first calculate the partial derivative of Q with respect to x, Qx, and then find the partial derivative with respect to y, Qy. We then use these derivatives to form an equation that represents the change in y needed to offset the change in x. With x initially at 10 and increasing by 1, and y initially at 40, we can solve for the change in y that keeps the total output constant.

Answer:

25 can.                            

Step-by-step explanation:

Here is the complete question: You are making juice from concentrate. The directions on the packaging say to mix  1 can of juice with 3 cans of water to make orange juice. How many 12 fluid ounces cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?

Given: Ratio to make juice with concentrate:water is 1:3.

As required we need to prepare 200 6 ounce serving of Orange juice.

∴ [tex]200\times 6= 1200\ ounce[/tex]

Let there be x ounce of concentrate and 3x ounce of water to make 1200 ounce of orange juice.

Now, [tex]x+3x= 1200[/tex]

∴ x= 300 ounce

Next, lets find out how many cans of 12 ounce is required.

[tex]\frac{300}{12} = 25\ cans[/tex]

∴ 25 cans is required to make 1200 ounce of orange juice.

Answer:

6/60 is 1/10

Step-by-step explanation:

i hour is 6o min so 6/60 is 1/10 that is the fraction of the hour

or these would work too:

10% .1 or 1/10

Answer: 0.100

Step-by-step explanation:

So, you start by 1, 6 divided by 0.1 is 60.

I got to one hundred. 60 times 0.100 is 6.

Therefor your answer is 0.100

Answer:

Option C: 0.04 is the correct answer.

Step-by-step explanation:

Given that:

cups of sugar used = 7.5

cookies = 14 dozen

As we know that 1 dozen cookies equal 12 cookies so,

14 dozen cookies = 14* 12 = 168 cookies

Now,

we have to find the rate of cups of sugar per cookie, So:

Rate = cups of sugar / total cookies

By putting values:

Rate = 7.5/ 168

By simplifying we get

Rate = 0.04464

By rounding it off to nearest hundred:

Rate = 0.04

Hence the rate of cups of sugar per cookie is 0.04

i hope it will help you!

Answer: 27

Step-by-step explanation:

2/3x-7=11

2/3x=18

1/3x=9

x=27

Answer:

The value of x is 6 and The value of y is - 4

Step-by-step explanation:

Given as :

The Two linear equation is

- 3 x - 9 y = 18

4 x + 3 y = 12

Now,

4 × ( - 3 x - 9 y ) = 4 × 18

Or, - 12 x - 36 y = 72      ......1

And 3 × ( 4 x + 3 y ) =  3 × 12

or, 12 x + 9 y = 36        .....2

Solving eq 1 and 2

( 12 x + 9 y ) + (  - 12 x - 36 y ) = 72 + 36

Or, 9 y - 36 y = 108

or , 27 y = - 108

∴ y = - [tex]\frac{108}{27}[/tex]

I.e y = - 4

Put the value of y to get x value

So, 12 x + 9 (-4) = 36

Or, 12 x = 36 + 36

or, 12 x = 72

∴  x = [tex]\frac{72}{12}[/tex]

I.e x = 6

Hence The value of x is 6 and The value of y is - 4    Answer

The statement H(30) = H(25) + 5 means that when Amelia was 30 months old, she was 5 centimeters taller than when she was 25 months old.

The function H(t) tells us Amelia's height in centimeters when she was t months old. So H(30) tells us Amelia's height when she was 30 months old, and H(25) tells us Amelia's height when she was 25 months old.

The equation H(30) = H(25) + 5 tells us that these two values are equal, which means that Amelia was 5 centimeters taller when she was 30 months old than when she was 25 months old.

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Answer:

The value of r=[tex]\frac{-106}{47}[/tex]

The value of x=[tex]\frac{83}{32}[/tex]

Step-by-step explanation:

Given that,

A) [tex]\frac{2r-2}{7r+10} = \frac{9}{8}[/tex]

Now,

[tex]\frac{2r-2}{7r+10} = \frac{9}{8}[/tex]

8(2r-2)=9(7r+10)

16r-16=63r+90

-16-90=63r-16r

-(16+90)=47r

-106=47r

r=[tex]\frac{-106}{47}[/tex]

B) [tex]\frac{x+4}{9} = \frac{3(x-2)-1}{5}[/tex]

Now,

[tex]\frac{x+4}{9} = \frac{3(x-2)-1}{5}[/tex]

5(x+5)=9[3(x-2)-1]

5x+25=9[3x-6-1]

5x+25=9[3x-7]

5x+25=27x-63

25+63=27x+5x

83=32x

x=[tex]\frac{83}{32}[/tex]

Final answer:

To find the value of n² + 5 when n = 3, you substitute 3 for n in the expression to get 3² + 5, which simplifies to 9 + 5, resulting in a final value of 14.

Explanation:

To evaluate the expression n² + 5 when n = 3, we simply substitute the value of n into the expression
1. Substitute 3 for n: (3)² + 5
2. Calculate the square of 3: 3² = 9
3. Add 5 to the result: 9 + 5 = 14
Therefore, the evaluated expression n² + 5 when n = 3 is equal to 14.

Answer:

Associative property of addition

Step-by-step explanation:

Answer:

The associative property of addition

Step-by-step explanation:

In an equation with 3 or more number numbers being added the placement of parentheses does not change the answer.

The number 64 can be expressed in the form of base powers as 64=8^2, 64=4^3, and 64=2^6.

The number 64 can be expressed as powers of different bases in several ways. The most common notations are as follows: 64 = 8^2, which means that 8 multiplied by itself results in 64. 64 = 4^3, which means 4 multiplied by itself three times equals to 64, and finally, 64 = 2^6, where 2 is multiplied by itself six times to produce 64. Each of these forms express the number 64 in a different base.

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This would be C. 60$

This is because if she got the bag for 50% off, 30 divided by 2 is 15$, 45 divided by 2 is 22.5, 60 divided by 2 is 30$ so option C. Would be your answer.

Answer:

First one

Step-by-step explanation:

Answer:

If its written as the fourth root of (81^3) the answer is 27.

Answer:

9 bathrooms

Step-by-step explanation:

9 is their greatest common factor.

give each bathroom 1 bar of soap and 2 toilet paper rolls

Step-by-step explanation:

Since has 9 bars of some and 18 rolls of paper then he can fully stock nine because there are more rolls then bars

Answer:

$87

Step-by-step explanation:

to find discounted price, you multiply the original price by the decimal equivalent of the discount. so,

[tex]145 \times .40 = 58[/tex]

so that's 40% of 145 but now you gotta take the 40% off the original price so,

[tex]145 - 58 = 87[/tex]

There are $87 the weed eater cost during the blowout sale.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

This weekend the hardware store is having a blowout sale, where everything is discounted 40%.

And, A weed eater originally sells for $145.

Now, The discounted price is,

⇒ 40% of 145

⇒ 40/100 × 145

⇒ $58

Thus, The weed eater cost during the blowout sale = $145 - $58

                                                                               = $87

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Answer:

The actual speed of the car is either 57 mph or 63 mph

Step-by-step explanation:

Given as :

The measured speed o the car = 60 mph

The percentage error in speedometer = 5 %

Let The actual speed of car = x mph

Now, percentage error = [tex]\dfrac{\textrm actual value - \textrm measured value}{\textrm measured value}[/tex] × 100

So, [tex]\frac{5}{100}[/tex] = [tex]\frac{x - 60}{60}[/tex]

or,  [tex]\frac{5}{100}[/tex] × 60 = x - 60

Or, 3 = x - 60

∴  x = 63 mph

Hence The actual speed of the car is either 57 mph or 63 mph . Answer

The correct statement describing the actual speed of the car is: The actual speed of the car is either 57 mph or 63 mph.

To understand why this is the correct answer, let's calculate the range of possible actual speeds given the percent error of the speedometer.

The speedometer shows a speed of 60 mph with a percent error of 5%. The percent error formula is given by:

[tex]\[ \text{Percent Error} = \left( \frac{\text{Error}}{\text{True Value}} \right) \times 100\% \][/tex]

Here, the true value is the actual speed of the car, and the error is the difference between the measured speed (60 mph) and the true value. We can rearrange the formula to solve for the true value:

[tex]\[ \text{True Value} = \frac{\text{Measured Value}}{1 \pm \text{Percent Error}} \][/tex]

Since the percent error is 5%, we have:

[tex]\[ \text{True Value} = \frac{60 \text{ mph}}{1 \pm 0.05} \][/tex]

Now, we calculate the true value for both the lower and upper bounds of the speedometer reading:

For the lower bound (actual speed could be less than the measured speed):

[tex]\[ \text{True Value}_{\text{lower}} = \frac{60 \text{ mph}}{1 + 0.05} = \frac{60 \text{ mph}}{1.05} \approx 57.14 \text{ mph} \][/tex]

For the upper bound (actual speed could be more than the measured speed):

[tex]\[ \text{True Value}_{\text{upper}} = \frac{60 \text{ mph}}{1 - 0.05} = \frac{60 \text{ mph}}{0.95} \approx 63.16 \text{ mph} \][/tex]

Rounding these values to the nearest whole number, we get:

[tex]\[ \text{True Value}_{\text{lower}} \approx 57 \text{ mph} \][/tex]

[tex]\[ \text{True Value}_{\text{upper}} \approx 63 \text{ mph} \][/tex]

Therefore, the actual speed of the car could be either 57 mph or 63 mph, which corresponds to the third option provided in the question.

Answer:

Part a) [tex]-16t^{2}+35t+1.5=0[/tex]

Part b)

[tex]a=-16\\b=35\\c=1.5[/tex]

Part c) The soccer ball will take 2.23 seconds to reach the ground

Step-by-step explanation:

we have

[tex]h(t)=-16t^{2}+35t+1.5[/tex]

where

t  is the time the ball has been in the air, in seconds

h(t) is the height, in feet, of the  soccer ball

Part a) Write an equation that could be used to determine the time the ball traveled before it hit the ground

we know that

When the ball hit the ground, the value of h(t) is equal to zero

so

For h(t)=0

[tex]-16t^{2}+35t+1.5=0[/tex]

This equation can be used to determine the time the ball traveled before it hit the ground

Part b) Determine the values of a, b, and c

we know that

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]-16t^{2}+35t+1.5=0[/tex]

so

[tex]a=-16\\b=35\\c=1.5[/tex]

Part c)  How long will it take for the soccer ball to reach the ground after it was kicked?

Solve the quadratic equation by the formula

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

we have

[tex]a=-16\\b=35\\c=1.5[/tex]

substitute the values

[tex]x=\frac{-35(+/-)\sqrt{35^{2}-4(-16)(1.5)}} {2(-16)}[/tex]

[tex]x=\frac{-35(+/-)\sqrt{1,321}} {-32}[/tex]

[tex]x_1=\frac{-35(+)\sqrt{1,321}} {-32}=-0.04[/tex]  ---> cannot be a solution (is negative)

[tex]x_2=\frac{-35(-)\sqrt{1,321}} {-32}=2.23[/tex]

therefore

The soccer ball will take 2.23 seconds to reach the ground

Answer:

32 Dollars

Step-by-step explanation:

160 divided by 5 equals 32

Answer:10times

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer:

12%

Step-by-step explanation:

So we know the ratio of left-handed men to men is 3:25. We also know that percent is out of one hundred, so we can do (ratios are essentially fractions) 3/25*4/4+ 12/100. Converting 12/100 to a percent should be simple and you get an answer of 12%

Please let me know if this was correct

Slope intercept form: y = mx + b

m = slope

b = y-intercept

Solve for the y-intercept.

9 = 2(7) + b

9 = 14 + b

9 - 14 = 14 + b - 14

-5 = b

y = 2x - 5

______

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Final answer:

The equation of the line with a slope of 2 that passes through the point (7,9) in slope-intercept form is y = 2x - 5, where 2 is the slope and -5 is the y-intercept.

Explanation:

To find the equation of a line with a slope of 2 that passes through the point (7,9), we can use the point-slope form of a line equation, which is:

[tex]y - y_1 = m(x - x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is the point the line passes through. Plugging in our values we get: y - 9 = 2(x - 7).

To convert this to slope-intercept form (y = mx + b), expand the right side to get y - 9 = 2x - 14 and then add 9 to both sides to isolate y, resulting in y = 2x - 5. Here, the m value is 2 (the slope) and the b value is -5 (the y-intercept).

Answer: c

Step-by-step explanation:

Answer:

The two pyramids have the same volume.

Step-by-step explanation:

What determines the volume of a pyramid is the Base Area, and its height. Since in these two figures, both bases measure the same (congruent) and their respective heights are equal. Then when we compare the volumes of these two solids, the triangular and the Hexagonal pyramid have the same volume, as it follows:

Then:

[tex]\\V=\frac{1}{3}*B*h\\V_{\bigtriangleup \: Triangular\: base}=\frac{1}{3}*15*5\Rightarrow V_{\bigtriangleup \: pyramid}=15 \:in^{3}\\V_{\bigtriangleup \: hexagonal \:base}=\frac{1}{3}*15*5\Rightarrow V_{\bigtriangleup \: hexagonal \:base}=15 \:in^{3}[/tex]

However, each surface area measure differently.

Answer:

See explanation

Step-by-step explanation:

Which situation can be modeled by the inequality [tex]65-8x\ge 9?[/tex]

Suppose you have $65.

Each day you spend $8.

You want to have at least $9 left.

If x is the number of days you are spending money, what is the maximum number of days you can spend money?

Solution:

Let x be the number of days you are spending money, each day you spend $8, so in x days you spend $8x. Initially, you have $65, so after x days, $(65 - 8x). This amount of money must be no less than $9, so

[tex]65-8x\ge 9[/tex]

Answer:

It is the same answer.

Step-by-step explanation:

579.8 X 0.001= 0.5798

579.8/10^3 (or 1000)=0.5798

If you use a calculator it's easy.

Hope this helped. :D

Following are the calculation to the given expression:

Given:

[tex]\bold{579.8 \times 0.001= 579.8 \div 10^3}[/tex]

To find:

Prove=?

Solution:

[tex]\to \bold{579.8 \times 0.001= 579.8 \div 10^3}[/tex]

Solve L.H.S part:

[tex]\to \bold{579.8 \times 0.001}\\\\\to \bold{0.5798}[/tex]

Solve R.H.S part:

[tex]\to \bold{ 579.8 \div 10^3}\\\\\to \bold{ \frac{579.8}{ 10^3}}\\\\\to \bold{ \frac{579.8}{ 1000}}\\\\\to \bold{ 0.5798}\\[/tex]

Therefore, the L.H.S= R.H.S, so, the answer is the same.

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