Use the measurements of the original figure and the scale drawing to calculate the scale factor and missing measures.

What is the scale factor?


What is the length of A?


What is the length of B?

Answer:

We can check this two ways: distributing the -0.5, and plugging in a number for x.

First, we can check this by distributing the -0.5.  Our equation becomes:

-1.5x -2.5 = -1.5x + 2.5

Clearly, this is not true.  We can show this one more time by plugging in a number for x.  I will use 2.

Now, we evaluate both sides and see if they are equal.

-3 - 2.5 = -3 + 2.5

-5.5 = 0.5

Clearly, this is not true.  These expressions are not equivalent.

Step-by-step explanation:

Answer:

Step-by-step explanation:   Using the distributive property to expand the first expression, you would get -1.5x - 2.5. Since the constant term does not have the same sign as the second expression, the two expressions are not equivalent. Also, if you substitute in a value for x and evaluate each expression, the values will not be equal.

Answer:

50 units

Step-by-step explanation:

Find the number of units x that produces the minimum average cost per unit C in the given equation.

C = 0.001x³ + 5x + 250

unit cost f(x) = C/x

= 0.001x³/x + 5x/x+ 250/x

f(x) = 0.001x² + 5 + 250/x

f'(x) = 0.002x - 250/x²

We equate the first derivative to zero

0.002x - 250/x² = 0

0.002x = 250/x²

Cross Multiply

0.002x × x² = 250

0.002x³ = 250

x³ = 250/0.002

x³ = 125000

x = 3√(125000)

x = 50 units

Therefore, the number of units x that produces the minimum average cost per unit C is 50 units.

Answer: 178

Step-by-step explanation:

18x13

234 area of white granite

8x7

56 area of blue granite

234-56 to find the area of the white granite

Answer:

[tex]f = \log_{4}\left(\sqrt{\frac{m\cdot n}{19}}\right)[/tex] is equivalent to  [tex]f = 0.5\cdot \log_{4} m + 0.5\cdot \log_{4}n -0.5\cdot \log_{4}19[/tex].

Step-by-step explanation:

Let be [tex]f = \log_{4}\left(\sqrt{\frac{m\cdot n}{19}}\right)[/tex], we transform this into an equivalent expression with sums and differences of logarithms by applying logarithm properties:

1) [tex]\log_{4}\left(\sqrt{\frac{m\cdot n}{19}}\right)[/tex] Given.

2) [tex]\log_{4}\left[\left(\frac{m\cdot n}{19} \right)^{0.5}\right][/tex] Definition of square root.

3) [tex]0.5\cdot \log_{4}\left(\frac{m\cdot n}{19} \right)[/tex]   [tex]\log_{a} b^{c} = c\cdot \log_{a} b[/tex]

4) [tex]0.5\cdot (\log_{4}m\cdot n -\log_{4} 19)[/tex]   [tex]\log_{a} \frac{b}{c} = \log_{a} b - \log_{a} c[/tex]

5) [tex]0.5\cdot \log_{4} m\cdot n -0.5\cdot \log_{4} 19[/tex] Distributive property.

6) [tex]0.5\cdot (\log_{4}m + \log_{4}n)-0.5\cdot \log_{4}19[/tex]   [tex]\log_{a} b\cdot c = \log_{a}b +\log_{a} c[/tex]

7) [tex]0.5\cdot \log_{4} m + 0.5\cdot \log_{4}n -0.5\cdot \log_{4}19[/tex] Distributive property/Result.

[tex]f = \log_{4}\left(\sqrt{\frac{m\cdot n}{19}}\right)[/tex] is equivalent to  [tex]f = 0.5\cdot \log_{4} m + 0.5\cdot \log_{4}n -0.5\cdot \log_{4}19[/tex].

Answer:

7 hours, 22 minutes

Step-by-step explanation:

17:00 (5:00) - 10:00 = 7 hours apart

43 - 21 = 22 minutes

Answer:

i would say a but i could be wrong

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Because its the most reasonable answer

Answer:

wya

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Put these two numbers on a number line with the correct circles. Now choose from any of the between numbers.

Answer:

The p-value is  [tex]p-value = 0.0039854[/tex]

Step-by-step explanation:

From the question we are told that

   The sample size is  n = 1100

   The population proportion is  p = 0.50

  The sample proportion is  [tex]\^ p = 0.54[/tex]

The null hypothesis is  [tex]H_o : p = 0.50[/tex]

The alternative hypothesis is [tex]H_a : p > 0.50[/tex]

 Generally the test statistics is mathematically represented as

     [tex]z = \frac{\^ p - p }{ \sqrt{\frac{ p(1 - p)}{n} } }[/tex]

=>   [tex]z = \frac{ 0.54 - 0.54 }{ \sqrt{\frac{ 0.50 (1 - 0.50)}{1100} } }[/tex]

=>  [tex]z = 2.6533[/tex]

Generally from the z-table the probability of 2.6533 for a right tailed test is  

         [tex]p-value = 0.0039854[/tex]

Answer:

a

 [tex]E(Z) =  202 [/tex]  

b

[tex]E(Z) = 198[/tex]

c

[tex]E(Z) = -140  [/tex]

Step-by-step explanation:

From the question we are told that

   The mean of X  is [tex] E(X)  =  20[/tex]

   The standard deviation of X is  [tex]s_1 = 5[/tex]

   The mean of Y  is [tex]\= y  =  40[/tex]

    The standard deviation of Y is  [tex]s_2 = 10[/tex]

Considering question a  

Generally the mean of   Z = 2 + 10X. is mathematically  represented

    [tex]E(Z) = E[2 + 10X ][/tex]

=> [tex]E(Z) =  2 +  10 E(X)[/tex]

=>  [tex]E(Z) =  2 +  10 * 20 [/tex]        

=>  [tex]E(Z) =  202 [/tex]          

Considering question b

Generally the mean of   Z = 10X - 2.. is mathematically  represented  

        [tex]E(Z) = E[10X -2 ][/tex]

   => [tex]E(Z) = 10E(X) - 2[/tex]

  =>  [tex]E(Z) = 10* 20  - 2[/tex]

  =>  [tex]E(Z) = 200  - 2[/tex]

 =>  [tex]E(Z) = 198[/tex]

Considering question c

Generally the mean of   -3X - 2Y is mathematically  represented

     [tex]E(Z) = E[-3X -2Y ][/tex]

     [tex]E(Z) = -3 E(X) -2E(Y) [/tex]

=>   [tex]E(Z) = -3 * 20 -2* 40 [/tex]

=> [tex]E(Z) = -140  [/tex]

Answer:

Solving this equation results in the statement 0 = 0. Because this is a true statement, the equation has infinitely many solutions.

Step-by-step explanation:

Answer:

Piecewise functions are functions that behave differently in different regions of the domain.

One example that you may see in your city is the case of the street illumination, such that can be modeled as:

x = time

Suppose that the lights are turned on at a given hour x0 and then turn off at the hour x1, we can define:

f(x) = 0 if x1 < x < x0

f(x) = 1 if x0 ≤ x ≤ x1

Where f(x) represents the intensity of the light at the time x.

Between x1 and x0, the lights are not working, so the illumination that they provide is zero.

Between x0 and x1 the lights are turned on, so the illumination is 1.

Another example can be the accurate description of the velocity of a car as a function of time.

For some pieces, the car will be stopped (maybe in a red light)

For some pieces, the car will be moving slow (maybe there is a lot of traffic)

For some pieces, the car will be moving fast or accelerating (in an empty street).

So we can define this motion as a piecewise function that obviously will depend on how the car moves.

Answer:

Lets take the miles for 6 hours to be x.

Using cross-multiplication, this problem can be solved.

194              4

x                  6

1164 = 4x

x = 291

Therefore, Joe drives 291 miles in 6 hours.

The length of the protein molecule, written in scientific notation, is approximately 2.08 × 10⁻⁷ meters.

Given that a hydrogen atom has about 1.04 × 10⁻¹⁰ meters diameter, whereas a protein molecule has an overall length of 2 × 10³ times the diameter of a hydrogen atom.

We need to find the length of the protein molecule, in meters and in scientific notation.

We must multiply the diameter of a hydrogen atom by the specified factor (2 × 10³), in order to determine the length of the protein molecule in meters.

Let's compute the amount:

Length of protein molecule = Diameter of a hydrogen atom × 2 × 10³

Diameter of a hydrogen atom = 1.04 × 10⁻¹⁰ meters

Length of protein molecule = 1.04 × 10⁻¹⁰ meters × 2 × 10³

To multiply numbers in scientific notation, we add the exponents and multiply the coefficients:

Length of protein molecule = 2.08 × 10⁻⁷ meters

So, the length of the protein molecule, written in scientific notation, is approximately 2.08 × 10⁻⁷ meters.

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The length of the protein molecule, in meters and written in scientific notation, is approximately 2.08 × 10^(-7) meters.

To calculate the length of the protein molecule in meters, we'll start with the given diameter of a hydrogen atom and multiply it by the scaling factor of 2000. Let's perform the calculations:

Diameter of a hydrogen atom = 1.04 × 10^(-10) meters

Length of the protein molecule = 2000 × (Diameter of a hydrogen atom)

Multiplying the diameter by the scaling factor:

Length of the protein molecule = 2000 × (1.04 × 10^(-10))

When multiplying numbers written in scientific notation, we can multiply the coefficients and add the exponents:

Length of the protein molecule = 2000 × 1.04 × 10^(-10)

Calculating the coefficient:

2000 × 1.04 = 2080

Calculating the exponent:

10^(-10)

Putting the coefficient and exponent together:

Length of the protein molecule = 2080 × 10^(-10)

Writing it in scientific notation:

Length of the protein molecule = 2.08 × 10^(-7)

for such more question on length

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Simple answer.

You will have to replace a, with the given numbers.

For the 1st one)

70-25² since a=25. 70-625=-55

2nd)

70-1²=70-1=69

3d)

70-10²=70-100=-30

Hope this helped.

Answer:

1/2 liters

Step-by-step explanation:

Rosanne makes 1 1/2 liters of strawberry lemonade

She pours 1/4 of the lemonade into a thermos

The quantity left is

= 1 1/2 - 1/4

= 3/2 - 1/4

= 5/4

Her brother drinks 2/5 of the remaining lemonade

Therefore the quantity of lemonade that Rosanne brother drinks can be calculated as follows

= 2/5 × 5/4

=1/2

Hence the quantity of lemonade that Rosanne brother drinks is 1/2 liters

Answer:

1/2 liters

Step-by-step explanation: Rosanne makes 1 1/2 liters of strawberry lemonade

She pours 1/4 of the lemonade into a thermos

The quantity left is

= 1 1/2 - 1/4

= 3/2 - 1/4

= 5/4

Her brother drinks 2/5 of the remaining lemonade

Therefore the quantity of lemonade that Rosanne brother drinks can be calculated as follows

= 2/5 × 5/4

=1/2

Answer:

multiply 65 by 5 and divide by 1 fourth

Step-by-step explanation:

Answer:

9.1

Step-by-step explanation:

I think this because it is 9 boxes away from the other points, plus it sloped a bit...

Answer:

9.1

Step-by-step explanation:

Distance=[tex]\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2} }[/tex]

=[tex]\sqrt{(4-3)^{2} +(-5-4)^{2} }[/tex]

=[tex]\sqrt{(1)^{2}+(-9)^{2} }[/tex]

=[tex]\sqrt{1+81}[/tex]

=[tex]\sqrt{82}[/tex]

≈9.1

Answer:

.

Step-by-step explanation:

Answer:

nnnnnnnnnnknbiibbs

Step-by-step explanation:

Answer:

14 f g

Step-by-step explanation:

Multiply  7  by  2 .

Answer:

6

Step-by-step explanation:

A way to answer these questions like I usually do is to subtract the result by the number you already know, like this;    10-4=6, so 6 would be what X equals, or you can just take the long way and keep guessing what the answer would be and keep doing the problems, but that would be very time consuming so I would recommend just doing the subtraction method!

Hope this helps!

Answer:

x = 6

Step-by-step explanation:

x + 4  = 10

=> x = 10 - 4

=> x = 6

Answer:

8

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

because two points on the x value shouldn't have more that one y value

Answer:

288 Miles

Step-by-step explanation:

Solve for x (speed)

5.5x = 264

Divide by 5.5

x = 48

y = 48x

Subsitute 6 hours in for x

y = 48(6)

y = 288

Answer: Allie went 288 miles in 6 hours.

Step-by-step explanation:

First, you must find out how many miles Allie travled in one hour

= 264/5.5

= 48

Next, multiply the quotient by the number of hours to get the answer.

= 48 x 6

= 288

that's the answer. good luck

Step-by-step explanation:

Hope it helps man .................

Answer:

Thank you ☺️

Answer:

One Hundred Sixty

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

We have to find the difference:

We start with 5 yellow counters

Since we have to subtract more yellow counters than we have (5 instead of 8), we add 3 zero-pairs:

We subtract the 8 yellow counters:

We are left with 3 red counters, which means the result is -3