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The measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

The dilation if the triangle ABC implies it is bigger than the triangle A'B'C' with a scale factor 1/2 since AC = 10 and A'C' = 5

side A'B' = 8 × 1/2

side A'B' = 4

Therefore, the measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.

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Answer:

the answer is B, 4. :)

Step 1: Calculate the initial number of hospitals. In 2000, there were 5,727 hospitals, so the initial number of hospitals (H0) is 5,727.

Step 2: Calculate the rate of change. From 2014 to 2017, the number of hospitals decreased by 156. Therefore, the rate of change (r) is -156.

Step 3: Calculate the equation. The equation for the number of hospitals H in this country t years since 2000 is H = H0 + rt. Substituting in the values from Steps 1 and 2, this gives us H = 5,727 – 156t.

Therefore, the equation for the number of hospitals H in this country t years since 2000 is H = 5,727 – 156t.

First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). More than one variable may be present in a linear equation.

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Answer:

Step-by-step explanation:

Substitute for r.

1/5(1/4) + 9/20  ->  1/20 + 9/20 = 10/20.

Simplify the final answer.

10/20 = 1/2

Answer: 20 units

Step-by-step explanation: Set the two half diagonal values equal to each other. When you solve for x, the value is 3. Substitute it back in and the half diagonals equal 10. Multiply it by two and the dial length is 20. You can use this length for TE because it is a diagonal. Hope this helps!

The Frequency table for grouped data using four classes are given in the table below.

The frequency table is to represent the data in the table form in which larger data are arranged according to their characteristics. In which frequency is the number which represents how many times the particular data occurs in it.

Here, there are 20 hours for each employee is given, we have to group into four classes.

Let us split the hours as,

0 - 5 ----this includes- 1,1,2,2,3,3,5(7 hours)

5 - 10---this includes - 8,10(2 hours)

10 - 15--this includes - 12,13,15,15(4 hours)

15 - 20-this includes - 17,18,18,19,19,20,20(7 hours)

(Note:This is exclusive classes i.e., upperlimit is not included)

Using this data the frequency table is constructed as shown below:

No. of hours              Frequency

     0 - 5                               7

     5 - 10                              2

    10 - 15                              4

    15 - 20                             7

Hence, the frequency table for the given data are grouped using four classes.

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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.

The probability of drawing a green ball in one draw is 8/14 = 4/7. Since the balls are replaced after each draw, each draw is independent of the others. Therefore, the probability of getting 6 green balls in a row is (4/7)^6 ≈ 0.066.

Rounding to three decimal places, the probability is approximately 0.066.

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

The equation for this problem is this:

First, we need to find a common denominator between  [tex]\frac{5}{3}[/tex] and [tex]\frac{2}{9}[/tex].

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

To find the common denominator, we can multiply the denominators, 3 and 9.

Now we know that the two new fractions are going to have a denominator of 27.

Now, we can use these equations to solve for the numerator.

Now, the fractions look like this:

To add them together, we can use this equation:

Now, we need to convert [tex]1 \frac{9}{8}[/tex] into an improper fraction.

An improper fraction is a fraction that has a numerator that is greater than the denominator. For example, [tex]\frac{3}{2}[/tex] is a improper fraction.

To convert [tex]\frac{51}{27}[/tex] and [tex]\frac{17}{8}[/tex] into common denominators, we need to multiply the denominators, like we did above.

The new fractions will look like this:

To solve for the numerators, we can use these equations:

The fractions now look like this:

Now, convert them to mixed numbers.

Therefore, 5 thirds + 2 ninths < 1 9/8.

The cost of the athletic shoe is $20 meanwhile the cost of the casual shoe is $35.

A system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by substitution or adding methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

Firstly, you should extract the main information of the question.

Next,  you should convert the given text information into equations. See below.

20A+10C=750 (1)

25A+20C=1200 (2)

From the substitution method, you can solve this question by following the steps below:

1) Multiply equation 1 by the number -2. Then, you have:

-40A-20C= -1500 (1)

25A+20C=1200 (2)

2) Sum the previous equations presented in step 1.

-15A=-300

15A=300

A=300/15

A=20

3) Find the variable C from equation 2. In step 2, you find  A=20, thus.

25A+20C=1200 (2)

25*20+20C=1200

500+20C=1200

20C=1200-500

20C=700

C=700/20

C=35

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The solution for the equation is x = 65.

Equation is a physical and mathematical statement that describing physical sonoma nadigai the relationship between different physical quantity typically consist of pramod variable richard simple representing physical quantity and then it personal variable maybe point it such as  that your energy.

This can be determined by solving the equation for x one step at a time.

First, 3 = 5 can be solved by subtracting 3 from both sides,

thus yielding

x = 2.

Then,

5 = 13 can be solved by subtracting 5 from both sides,

thus yielding

x = 8.

Finally,

13 = 65 can be solved by subtracting 13 from both sides,

thus yielding

x = 65. This is the final answer to the equation.

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Answer:

its x=3



Step-by-step explanation:

first x 2/3 to both sides than solve for x

Answer: Let's denote the original number of pages Mark planned to read as "P".

From the first statement, we know that P - 18 pages will take 5 more days, which means P pages will take 5 days less, or 5 - 5 = 0 days.

From the second statement, we know that P - 24 pages will take 8 more days, which means P pages will take 8 days less, or 8 - 8 = 0 days.

So, we have two equations:

P - 18 = 5 * X

P - 24 = 8 * Y

Where X and Y are the number of pages Mark reads per day.

Since X and Y are equal, we can substitute one of them for the other:

P - 18 = 5 * (P - 24) / 8

Expanding the right side and solving for P, we find that P = 288 pages.

Step-by-step explanation:

The volume of the conical hole will be 154 cubic feet.

The area a cone takes up in a three-dimensional plane is known as its volume. A cone's base is circular, so it is made of a radius and a diameter.

Given that a cone-shaped hole is 3 feet deep and the circumference of the base of the hole is 44 feet,

The volume of the cone will be calculated as:-

Volume = (1/3)πr²h

The circumference of the cone is,

2πr = 44

2 x ( 22 / 7 ) x r =  44

r = 7 feet

The volume of the cone will be calculated as:-

Volume = (1/3)πr²h

Volume = ( 1 / 3 )  x ( 22 / 7 ) x 7 x 7 x 3

Volume = 22 x 7

Volume = 154 cubic feet

Therefore, the volume will be 154 cubic feet.

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If the rates are the same ones, the tank will be filled in 15 minutes.

Let's define R as the rate at which we fill the tank, we know that we can fill a volume V in 6 minutes, then:

R*6 min = V

R = V/6min

Then r is the rate at which we empty the tank, we know that a volume V is emptied in 10 minutes, then:

r*10 min = V

r = V/10min

If both valves are open, the rate at which we will fill the tank is:

R - r

Now we need to find the value of time T such that:

(R - r)*T = V

(V/6min - V/10min)*T = V

(1/6min - 1/10min)*T = 1

(5/30min - 3/30min)*T = 1

(2/30 min)*T = 1

T = (30min/2)

T = 15 minutes.

The tank will be filled in 15 minutes.

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The skid marks would be approximately 1.9 ft in length to the nearest foot.

The drag factor of the road is given as 0.97 and the braking efficiency as 90%. To calculate the skid marks, we need to use the coefficient of friction (μ) between the tires and the road surface. The formula for calculating this is: μ = (2 x Drag Factor x Efficiency) / 100.

Therefore, μ = (2 x 0.97 x 0.9) / 100 = 0.0174

Once we have the coefficient of friction, we can use the following equation to calculate the skid marks: Skid Length = Initial Speed x Reaction Time x 0.5 x μ.

Since the speed is given as 35 mi/h and the reaction time is assumed to be 0.75 seconds, the skid marks will be: Skid Length = 35 mi/h x 0.75 s x 0.5 x 0.0174 = 1.9 ft

Therefore, the skid marks would be approximately 1.9 ft in length to the nearest foot.

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The one-digit integers that satisfy the inequality k≥0 are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

The given inequality is k≥0, k greater than or equal to zero.

The negative values on the number line are -1, -2, -3...-9 while the value greater than or equal to zero are 1, 2, 3, 4,...9

Hence, the one-digit integers that satisfy the inequality k≥0 are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

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Answer:

the answer of the equation is b

There are 31 bags of  [tex]$\frac{1}{3}[/tex] pound bags of trail mix he can make.

As per the data given:
Diego is making a trail mix for him and his friends to take with them on a hike next week.

He mixes [tex]$4\frac{2}{6}[/tex] pounds of nuts, [tex]$3\frac{3}{6}[/tex] pounds of raisins, and [tex]$2\frac{3}{6}[/tex] pounds of chocolate chips.

Here we have to determine how many [tex]$\frac{1}{3}[/tex] pound bags of trail mix can he make.

First, we have to convert all the mixed fractions to improper fractions.

[tex]$4\frac{2}{6} = \frac{26}{6}[/tex]

[tex]$3\frac{3}{6} = \frac{21}{6}[/tex]

[tex]$2\frac{3}{6} = \frac{15}{6}[/tex]

The total number of pounds he mixed with nuts, peanuts, and chocolate chips.

Add up all the improper fractions.

[tex]$=\frac{26}{6}+ \frac{21}{6} +\frac{15}{6}[/tex]

As all the denominators have the same value we can add all the fractions directly.

[tex]$=\frac{26+21+15}{6}[/tex]

[tex]$=\frac{63}{6}[/tex]

[tex]$=\frac{31}{3}[/tex]

To see how many [tex]$\frac{1}{3}[/tex] bag he can have, we have to divide the total by [tex]$\frac{1}{3}[/tex].

So we have:

[tex]$=\frac{\frac{31}{3} }{\frac{1}{3} }[/tex]

= 31

Therefore the answer is 31.

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Answer:

195m^3

Step-by-step explanation:

Volume of a rectangle = Length x Width x Height

L = 5m

W = 3m

H = 13m

V = 5m x 3m x 13m

V = 195m^3

As per the figure, the angle equation p + q + r = 180 is proved.

In geometry, an angle is defined as the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. When two lines are parallel, the angles opposite to each other are called corresponding angles.

In the given figure AB || CD, we are asked to prove that the sum of angles p, q, and r is equal to 180 degrees. This can be proven using the concept of corresponding angles.

Since lines AB and CD are parallel, the angles opposite to each other are equal, i.e., p = r. Therefore, the sum of angles p and r can be represented as 2p.

Furthermore, since lines AB and CD are parallel, the alternate interior angles are equal. This means that angle q is equal to angle p.

Therefore, the sum of all three angles, p, q, and r, can be represented as 2p + q.

And since we know that p = q, we can simplify this to 3p.

Finally, since the sum of angles in a triangle is always 180 degrees, we know that

=> 3p = 180 degrees.

Solving for p, we find that p = 60 degrees.

Therefore, the sum of angles p, q, and r is equal to

=> 2p + q = 2 * 60 + 60 = 180 degrees,

which proves the statement p + q + r = 180 degrees.

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Domain of function =  {-3 , -4}

Range of function =  {4 , -1 , -4}

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

Given,

points on graph of a function are

(-3 , 4) , (-3 , -1) , (-4 , -4)

Range is set of y-values,

Range = {4 , -1 , -4}

Domain is set of x - values

Domain = {-3 , -4}

Hence, Domain and range of function are {-3 , -4} and {4 , -1, -4} respectively.

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[tex]-1+6x < 5[/tex]

Simplify:

[tex]6x-1 < 5[/tex]

Add 1 to both sides:

[tex]6x-1+1 < 5+1[/tex]

[tex]6x < 6[/tex]

Divide both sides by 6:
[tex]\dfrac{6x}{6} < \dfrac{6}{6}[/tex]

[tex]\boxed{x < 1}[/tex]

D. $128.94. is the total amount of money Nate will earn after taxes when he buys a CD for $1000  The formula for compound interest is:

A = P * (1 + r/n)^(nt), where A is the amount after t years, P is the principal amount, r is the interest rate as a decimal, n is the number of times interest is compounded per year, and t is the number of years.

We can use this formula to calculate the amount of money Nate will have after 5 years:

A = 1000 * (1 + 0.03/4)^(4 * 5) = 1000 * (1 + 0.0075)^20 = 1000 * 1.1629 = 1162.9

The interest earned is 1162.9 - 1000 = $162.9.

And the amount of interest taxed is 20% of $162.9, which is 20% * $162.9 = $32.58.

So, the total amount of interest earned after taxes is $162.9 - $32.58 = $130.32.

Therefore, the correct answer is D. $128.94.

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Step-by-step explanation:

the function is

d(n) = sqrt(1.49×n)

so,

85 = sqrt(1.49×n)

85² = 1.49×n

n = 85²/1.49 = 7225/1.49 = 4,848.993289... ft

≈ 4,849 ft

The value of P(Greater than 2) is 0.75

From the question, we have the following parameters that can be used in our computation:

Spinner = 6 5 7 2

Using the above as a guide, we have the following:

Greater than 2 = 3

Total = 4

The probability is

P = Greater than 2/Total

Substitute the known values in the above equation, so, we have the following representation

P(Greater than 2) = 3/4

Evaluate

P(Greater than 2) = 0.75

Hence, the solution is 0.75

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1.511; 1.512 ;1.5113

Step-by-step explanation:

we know that there are infinite numbers.

and every decimal number is a rational number

now, extend the number upto 3 decimal or 2 decimal .

then it will become 1.500

there are numbers upto 1.599

like this we can extend upto infinite values

you can write infinite numbers, but question is asked for only 3

Answer:

-60, +1180

Step-by-step explanation:

The price of one citron is 5 units and the price of one fragrant wood apple is 3.5 units." Let's call the price of one citron "c" and the price of one fragrant wood apple "w".

Using the information from the first equation:

4c + 3w = 34

Using the information from the second equation:

3c + 4w = 29

We can now solve the system of equations to find the value of "c" and "w".

Subtracting the second equation from the first:

4c + 3w - (3c + 4w) = 34 - 29

c = 5

Substituting the value of c back into one of the original equations:

3c + 4w = 29

3 * 5 + 4w = 29

15 + 4w = 29

4w = 14

w = 3.5

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Using simultaneous equations, the child ticket costs $18.

Simultaneous equations are two or more equations solved concurrently or at the same time.

Simultaneous equations are also known as a system of equations.

                Family A     Family B      Total Cost

Adults            2                  2                $62

Children         1                  4                 $70

Let the ticket cost per child = x

Let the ticket cost per adult = y

2x + 2y = 62 ... Equation 1

x + 4y = 70 ... Equation 2

Multiply Equation 1 by 2

4x + 4y = 124 ... Equation 3

Subtract Equation 2 from Equation 3:

4x + 4y = 124

-

x + 4y = 70

3x = 54

x = 18

= $18

From Equation 2, Substitute x = 18:

x + 4y = 70

18 + 4y = 70

4y = 52

y = 13

= $13

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Another family of one adult and four children pays $70.

Answer:

1 harmful

Step-by-step explanation:

2 they will be not use if you not use