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2. A store sells two shades of purple paint. The tables show the number of gallons of blue paint and the number of gallons of red paint used to make each shade of purple paint.

Shade A
Number of Gallons of Blue Paint
8
12
16
24

Number of Gallons of Red Paint for shade A
12
18
24
36

Shade B
Number of Gallons of Blue Paint
5
7
9
12


Number of Gallons of Red Paint
10
14
18
24

Based on the tables, which statements are true? Choose all that apply.

A. The ratio of the number of gallons of red paint to the number of gallons of blue paint in
shade B is 2:1.

B. Shade B should be redder than shade A because shade B has 2 gallons of red paint for every 1 gallon of blue paint. Shade A has 13 gallons of red paint for every 1 gallon of blue paint.

C. Shade A should be bluer than shade B because shade A has 1 gallon of blue paint for every 2 gallons of red paint. Shade B has 1 gallon of blue paint for every 1/2 gallons of red paint.

D. Shade A should be bluer than shade B because shade A has gallons of blue paint for every 1 gallon of red paint. Shade B has gallon of blue paint for every 1 gallon of red paint.

E. If the store owner adds 1 gallon of blue paint to 20 gallons of shade A, she creates 21 gallons
of shade B.

G is the matrix representation of the four colored graph.

According to the statement

we have given that a graph is colored with one of the four colors red, blue, yellow, or green.

And we have to represent the edges of this graph using a variation of the adjacency matrix structure

So, Adjacency Matrix Structure is a way of representing a graph as a matrix of booleans (0's and 1's). A finite graph can be represented in the form of a square matrix on a computer, where the boolean value of the matrix indicates if there is a direct path between two vertices.

And in this graph representation the Adjacency Matrix Structure denoted by a matrix G.

so, there are a four colors used that's why there are 4 into 4 matrix is formed to represent the edges.

G =  [tex]\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right][/tex]

And this is the matrix representation of the graph which is colored with four graphs.

So, G is the matrix representation of the four colored graph.

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Answer:

second option : π/2 or pi/2

Step-by-step explanation:

sinθ = 1 = 90

π = 180

π/2 = 90

https://www.mathsisfun.com/geometry/radians.html

Answer:

(8 , 5)

Step-by-step explanation:

• Marty would get the best view ,if he stood at the midpoint

of the line that connect the park to the high school .

• On the coordinates plane ,the park is located at (-4 , -11)

and the high school is located at (20 , 21) .

•• Calculating the midpoint (best position) :

Let M(x , y) be the midpoint.

[tex]x=\frac{-4+20}{2} =8[/tex]

[tex]y=\frac{-11+21}{2} =5[/tex]

Answer:

(8, 5)

Step-by-step explanation:

Given points:

To find the point that is between and equidistant from the High School and the park, use the formula for midpoint between two points.

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]

Define the endpoints:

[tex]\textsf{Let }(x_1,y_1)=(20,21)[/tex]

[tex]\textsf{Let }(x_2,y_2)=(-4,-11)[/tex]

Substitute the endpoints into the formula:

[tex]\implies \textsf{Midpoint} =\left(\dfrac{-4+20}{2},\dfrac{-11+21}{2}\right) = (8,5)\end{aligned}[/tex]

Therefore, the point at which Marty would get the best view is (8, 5).

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Answer:

98, 27

Step-by-step explanation:

In the first figure, the two angles are supplementary, meaning that their sum would equal 180 degrees, giving the equation: b+82 = 180 --> b=98

In the second figure, the two angles are complementary, meaning that they add up to 90 degrees, giving the equation: b+63 = 90 --> b=27

The length of the segment [tex]pt[/tex]is [tex]10[/tex] if the coordinates of [tex]p[/tex] and [tex]t[/tex] is [tex](-6 )and( 4)[/tex]

How can find the length of the segment ?

The coordinate of [tex]p=-6[/tex]

The coordinate of [tex]t=4[/tex]

We can assume only [tex]x[/tex] coordinates given and [tex]y[/tex] coordinates is [tex]0[/tex]

so coordinate of [tex]p=(-6,0)\\[/tex]

And coordinate of [tex]t=(4,0)[/tex]

So the length of the segment

[tex]pt=x_{2} -x_{1} \\pt=4-(-6)\\pt=4+6\\pt=10[/tex]

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Answer:

See below

Step-by-step explanation:

Slope, m of given line = - 1/2

perpendicular slope is = -1/m = -1 / (-1/2) = +2

Point (6,9)  slope form of line

y -9 = 2(x-6)    expand and simplify

y - 9 = 2x -12

y = 2x -3

Answer:

Perimeter = 36

Area = 81

Step-by-step explanation:

Perimeter of a square is side length * 4.

9*4 = 36

Area of a square is L*L,

9*9 = 81

Answer:

Step-by-step explanation:

You have 2 x's.  I think the first one is for multiplication and the second one is a variable.

2x2 -1 = 7x  

4-1 = 7x (first multiple 2x2)

3=7x  (second 4-1)

0.428571429 = x (Divide both sides by 7.  On the left side, 3/7 is 0.428571429 and 7x/7 is just x because the 7s cancel out.

Since the answer needs to be to two decimal places, I have to decide if 0.428571429 is closer to 0.42 or 0.43 Since the digit after the 2 in the answer is 8, that makes the number closer to 0.43 than 0.42.  So, the final answer is 0.43

Se calcula que la aceleración es - 8,35 m/s.

Ahora sabemos lo siguiente de la pregunta;

Velocidad inicial (u) = 60 km/h o 16,7 m/s

Tiempo empleado (t) = 2 s

Dado que;

v = tu + en

v = 0 m/s porque el carro se detenía

tu = -en

a = -(u/t)

 a= -1(6,7 m/s/2 s)

a =- 8,35 m/s

La aceleración es negativa porque la velocidad disminuye con el tiempo.

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The inequality that represents the height that is displayed by the graph is: 10 ≤ h ≥ 50.

In an inequality graph, we the small circle at any end is shaded or full, the inequality sign used is either "less than or equal to" or "greater than or equal to" ("≤" or "≥"). If the circle is empty or not shaded, we use "less than" or "greater than" ("<" or ">").

In the graph showing Jeremy’s height above the ground at any time during the ride, we have a full circle (shaded) starting from 10, and another on the right at 50.

This implies that the range of height is from 10 to 50. Since the circle is full (shaded), then we would use "less than or equal to" and "greater than or equal to" ("≤" and "≥") in writing the inequality that represents the height.

Thus, where h is the height, the inequality would be: 10 ≤ h ≥ 50.

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The group that have the longer average forearm length is group Y, because six children have a forearm length longer than 12 inches.

A dot plot is a graph that shows the frequency of a number using dots. The greater the number of dots above a number, the greater its frequency.

In group X, the highest arm length is 12 while in group Y, it is 13. This means that group Y would have longer arm lengths.

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The equation of the new graph g(x) is expressed as g(x) = 4^x + 6

The standard exponential equation is expressed as y = ab^x. Exponential equation is inverse of logarithmic equation.

Translations is a transformation technique that changes the position of an object from one point on the plane to another.

Given the function f(x) = 4^x

If the function is shifted 6 units up, the function g(x) is derived by adding 4 to the function f(x). The resulting function is given as;

g(x) = f(x) + 6

g(x) = 4^x + 6

Hence the equation of the new graph g(x) is expressed as g(x) = 4^x + 6

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Haven worked on an externship in a prosecutor’s office, the legal support position which you would be best suited for is: paralegal.

Paralegal can be defined as a person who has been trained in subsidiary legal matters (issues), but not fully qualified to act as an attorney or lawyer.

In this context, we can infer and logically deduce that paralegal is a legal support position which you would be best suited for a person who has worked on an externship in a prosecutor’s office.

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Complete Question:

If you had worked on an externship in a prosecutor’s office, and then you moved to another state, which of these legal support positions would be best suited for?

mediator

paralegal

legal secretary

court reporter

Answer:

Length= 50

Width=17

Step-by-step explanation:

length= n+8

Since n= 42, Just plug it in. So it would be 42+8 which is 50 for the length

Widith: 1/2n-4

basically since N is given for 42, you do 1/2 multipied by 42 which is 21.

Since you also have to subtract 4 inches it would be 17 for the length

The confidence interval is from 3.44 to 4.06 minutes.

According to the statement

we have given that the mean length of songs is 3.75 minutes and standard deviation 0.5 minutes and the sample size n is 7. and the confidence interval is 90%

and we have to find the mean interval.

So, We know that the

A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.

And A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.

We know that the z value for 90% confidence interval is 1.64.

so, The formula to calculate margin of error is

MOE = Z*standard deviation/ (n)^1/2

put the values in it

MOE = Z*standard deviation/ (n)^1/2

MOE = 1.64*0.5/ (7)^1/2

MOE = 1.64*0.189

MOE = 0.310

And to find the interval the formula is

Confidence interval = sample mean ± margin of error

Confidence interval = 3.75 ± 0.310

Confidence interval = (4.06,3.44)

So, The confidence interval is from 3.44 to 4.06 minutes.

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Her gross pay is $421.38

First, we know that she gets $16 per hour, and she worked 20 hours, then she gets:

20*$16 = $320

Now we also know that she receives a percentage of 8% of the gratuities, and the gratuities totaled $1,267.28

The 8% of $1,267.28 is:

$1,267.28*(8%/100%) = $1,267.28*0.08 = $101.38

Her gross pay is:

P = $101.38 + $320 = $421.38

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Answer:

too small

Step-by-step explanation:

The standard deviation of the sampling distribution of the sample mean is also called standard error of the mean.

For the given question,

Standard error is a mathematical tool used in statistics to measure variability. The standard error of the mean (SEM) measures how much discrepancy is likely in a sample's mean compared with the population mean.The SEM takes the SD and divides it by the square root of the sample size. The SEM will always be smaller than the SD.

The standard error of the mean indicates how different the population mean is likely to be from a sample mean. You can decrease the standard error by increasing the sample size.

Standard error of the mean and standard deviation are both measures of variability used to summarize sets of data.  It helps you estimate how well your sample data represents the whole population by measuring the accuracy with which the sample data represents a population using standard deviation.

Hence we can conclude that the standard deviation of the sampling distribution of the sample mean is also called standard error of the mean.

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The net Change in latitude and longitude of the helicopter are; 28.47 and 7.35 respectively.

The net change in latitude of the helicopter can be evaluated as follows;

x = |-6.20° - 22.27°| = |-28.47°|

x = 28.47°

The net change in longitude of the helicopter can be evaluated similarly as follows;

y = |106.80° - 114.15°| = |-7.35°|

x= 7.35°

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The value of x from the given expression is [tex]\frac{5+\sqrt{29}}{2log2} \\[/tex]

Given the algebraic expression below;

2^x + 2^-x = 5

This can also be expressed as:

1/2^x+ 1/2^x = 5

Let P = 2^x, such that;

P + 1/P = 5

P²-1/P = 5

P²-1 = 5P

P²-5P-1=0

On factrorizing, then;

P = [tex]\frac{5+\sqrt{29}}{2} \\[/tex]

Since 2^x = P, then;

[tex]2^x=\frac{5+\sqrt{29}}{2} \\\\xlog2=\frac{5+\sqrt{29}}{2} \\\\x=\frac{5+\sqrt{29}}{2log2} \\[/tex]

Hence the value of x from the given expression is [tex]\frac{5+\sqrt{29}}{2log2} \\[/tex]

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There are 17 hops in a hop, a skip, and a jump.

We have the relations:

How many hops are in a hop, a skip and a jump?

So we have:

1 hop + 1 skip + 1 jump.

First, using the second relation we rewrite:

1 hop + 1 skip + 3 skips = 1 hop + 4 skips.

Now, using the first relation:

1 hop + 4 skips = 1 hop + 4*(4 hops) = 1 hop + 16 hops = 17 hops.

There are 17 hops in a hop, a skip, and a jump.

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Answer: 113.1 ft^3

Step-by-step explanation:

We know the radius is 3 so substitute it in the formula like this...

V = 4/3 π (3)^3

Solve for (3)^3 which is 27.

Next multiply 4/3 by π. Which equals 4.1887....

Then multiply that answer by 27.

And your answer is 113.1 ft^3.

Answer:

[tex]V=108ft^{3}[/tex]

Step-by-step explanation:

[tex]V=\frac{4}{3}(3)(3)^{3}[/tex]

[tex]V=\frac{4}{3}(3)(27)[/tex]

[tex]V=\frac{4}{3} (81)=\frac{324}{3}[/tex]

[tex]V=108[/tex]

Hope this helps

Answer:

17.5 hours

I hope this helps and you can give a brainliest!

Step-by-step explanation:

Given: time spent per day follows the arithmetic sequence 1,1.5,2... (for 7 terms) with first term 1 and common difference 0.5 (in hours)

Concept used: the total study time is the partial sum S7of the given arithmetic series.

Calculation: As the number of terms is small, it can be calculated by hand.

S7 = 1+1.5+2+2.5+3+3.5+4

S7= 17.5 hours

Conclusion: Total time spent after one week is 17.5 hours

Answer:

17 and 1/2 hours.

Step-by-step explanation:

this is an arithmetic series  with common difference 0.5 hours.

Number of hours after 7 days

= (n/2)[2a + (n -1)d]

= (7/2)(2*1 + (7-1)0.5)

= 3.5 * 5

= 17.5 hours

The domain of the graph is the set of all real values

The domain is the set of x values of the graph

From the graph, the x values extend in both directions without end

This means that the x values can accommodate all real values

Hence, the domain of the graph is the set of all real values

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With the given rate Mamadou will take 6 hours to travel 126 miles.

In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.

Given that,

The distance travelled in 8 hours is 168 miles.

In order to calculate time for 126 miles, unitary method can be used as,

The time for 168 miles is 8 hours.

Then, the time for 1 mile is 8/168 hours.

Thus, the time for 126 mile is 8/168 × 126 = 6 hours.

Hence, the time taken by Mamadou to travel 126 miles is 6 hours.

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The values of x and y from the given diagram are 47 ad 86 degrees respectively

From the given circle, the triangle HJL is a right triangle.

Determine the value of y

43 = 1/2 <y

<y = 43 * 2

<y = 86 degrees

Since the sum of angle on a straight line is 180 degrees, such that;

x+90+43 = 180

x + 133 = 180

x = 47 degrees

Hence the values of x and y from the given diagram are 47 ad 86 degrees respectively

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The probability of drawing two blue marbles if the first marble is not replaced is 1/5

The probability of tossing a head and drawing a red marble

The given parameters are:

White = 1

Blue =3

Red = 2

Total = 6

The probability of a head is

P(Head)= 1/2

The probability of drawing a red marble is

P(Red)= 2/6 = 1/3

The required probability is

P = P(Head) * P(Red)

This gives

P = 1/2 * 1/3

P =1/6

The probability of drawing two blue marbles if the first marble is not replaced.

Here, we have:

P(B1) = 3/6 = 1/2

P(B2) = 2/5

The required probability is

P = P(B1) * P(B2)

This gives

P = 1/2 * 2/5

P =1/5

Hence, the probability of drawing two blue marbles if the first marble is not replaced is 1/5

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A state license plate consists of three letters followed by three digits. If repetition is allowed, the number of different ways in which license plates are possible is 17,576,000.

An arrangement of items in a specific order is referred to as a permutation. When the order of the arrangements counts, it is a mathematical technique that establishes the total number of alternative arrangements in a collection.

Calculation for the permutation -

Three letters are followed by three digits on a state license plate.

26 letters from a to z and 10 numbers from 0 to 9 make up the alphabet.

The potential of arrangements is due to the license plate's composition of three letters and three numerals.

Total ways = 26×26×26×10×10×10

                  = 17,576,000

Therefore, the number of different ways in which license plates are possible is 17,576,000.

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Answer:

4 (5a + 7b)

Don't worry I helped my brother with this.