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Answer:

Is the relation a function?

no

Step-by-step explanation:

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hello

the answer to the question is:

Tan (x) = 6.7/4.9 = 1.3673 ----> x = 53.81° or 54°

Sure. Here are the steps on how to solve the equation 3|x + 1| ≥-6:

Divide both sides of the equation by 3.

Simplify both sides of the equation.

Isolate x on the left-hand side of the equation.

Test each solution in the original equation to make sure it makes the equation true.

Write the solution in interval notation.

Here are the detailed steps:

Divide both sides of the equation by 3:

3|x + 1| ≥-6

|x + 1| ≥ -2

Simplify both sides of the equation:

|x + 1| ≥ -2

x + 1 ≥ -2 or x + 1 ≤ -2

Isolate x on the left-hand side of the equation:

x + 1 ≥ -2

x ≥ -2 - 1

x ≥ -3

x + 1 ≤ -2

x ≤ -2 - 1

x ≤ -3

Test each solution in the original equation to make sure it makes the equation true.

Test x = -3 in the original equation:

3|-3 + 1| ≥-6

3|-2| ≥-6

3(2) ≥-6

6 ≥-6

True

Test x = -4 in the original equation:

The number of ways of selecting a committee of 4 women and 3 men from  8 women and 5 men is 700 ways

First, we shall obtain the number of ways to choosing a committee of 4 women from 8 women. This is given below:

C(n, r) = n! / [r!(n - r)!]

C(8, 4) = 8! / [4!(8 - 4)!]

C(8, 4) = 70 ways

Next, we shall obtain the number of ways to choosing a committee of 3 men from 5 men. This is given below:

C(n, r) = n! / [r!(n - r)!]

C(5, 3) = 5! / [3!(5 - 3)!]

C(5, 3) = 10 ways

Finally, we shall determine the Total ways of selecting the committee. Details below:

Total ways of selecting = [C(8, 4)] × C(5, 3)]

Total ways of selecting = 70 × 10

Total ways of selecting = 700 ways

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It should be noted that when b = 8, the expression b/2 - 3 evaluates to 1.

In order to evaluate the expression b/2 - 3 when b = 8, we substitute the value of b into the expression and perform the calculations.

Given that b = 8, we have:

8/2 - 3

Now we simplify the expression:

8/2 is equal to 4, so we have:

4 - 3

Finally, subtracting 3 from 4 gives us the result:

4 - 3 = 1

Therefore, when b = 8, the expression b/2 - 3 evaluates to 1.

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b/2-3 Evaluate the expression you got in part d for b = 8

Hello !

100% - 60% = 40%

=> 40% of police officers have ride-alongs

                                                                      total

number of policier            258          ?           ??

frequency in %                  60%        40%      100%

3.1 Calculate the number of of the police officers have ride-alongs with teenagers who want to join the police force

? = 258 x 40 ÷ 60 = 172

3.2 Calculate the total

?? = 258 + 172 = 430

In total there are 430 police officers.

Have a good day !

The data set with the greater range is greater for girls. The median is greater for girls.

The range of a dataset is the difference between the maximum and minimum values in the set.

The median is the middle value in a sorted dataset, or the average of the two middle values if the set has an even number of elements.

To determine which dataset has a greater range, you need to compare the difference between the highest and lowest values of the two datasets.

To determine which dataset has a larger median, you need to sort the datasets and find the middle value(s).

The range for boys is 60 as for girls the range is 80. The median for boys is 90 and for girl 110.

Hence, the data set with the greater range is greater for girls. The median is greater for girls.

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Answer:

FE = 12

DE = 20

Step-by-step explanation:

Part A

We can solve for FE by equating the ratios of the triangles' sides. Remember we can only do this because the triangles are similar, so the scale factor between the side lengths is the same.

[tex]HE : GH = FE : DF[/tex]

↓ plugging in the given values

[tex]9 : 12 = FE : 16[/tex]

↓ representing as fractions

[tex]\dfrac{9}{12} = \dfrac{FE}{16}[/tex]

↓ multiplying both sides by 16

[tex]\boxed{FE = 12}[/tex]

Part B

We can solve for DE using the same technique.

[tex]GE : GH = DE : DF[/tex]

↓ plugging in the given values

[tex]15 : 12 = DE : 16[/tex]

↓ representing as fractions

[tex]\dfrac{15}{12}= \dfrac{DE}{16}[/tex]

↓ multiplying both sides by 16

[tex]\boxed{DE = 20}[/tex]

Answer:

Unknown but formula (Check step by step solution)

Step-by-step explanation:

Without the image of the base of the crayon, I cannot determine the exact dimensions of the triangular prism or calculate the volume of a single crayon. However, I can give you a general formula for calculating the volume of a triangular prism and use it to find the total volume of wax needed to make a box of 8 crayons.

The formula for the volume of a triangular prism is:

Volume = (1/2) x base x height x length

where base is the area of the base of the triangular prism, height is the height of the triangular prism, and length is the length of the triangular prism.

Assuming all the crayons in the box have the same dimensions, let's say the base of the triangular prism has a length of L and a width of W. We can calculate the area of the base of one crayon as:

Base area = (1/2) x L x W

Since the crayon is 90 millimeters long, its height is 90 millimeters. Therefore, the volume of one crayon is:

Volume of one crayon = (1/2) x L x W x 90

To find the total volume of wax used to make a box of 8 crayons, we can multiply the volume of one crayon by the number of crayons:

Total volume of wax = Volume of one crayon x 8

Total volume of wax = (1/2) x L x W x 90 x 8

Total volume of wax = 360 x L x W

Again, without knowing the exact dimensions of the triangular prism, I cannot calculate the total volume of wax used to make a box of 8 crayons. But you can use the formula above and substitute the values of L and W based on the dimensions of the base of the crayon to find the answer.

Answer:

9 + x ≥ -23

Step-by-step explanation:

'At least' here means the lowest possibility of the sum 9 + x can equal -23, which means 9 + x can also be greater than -23. So the sum is either equal to -23 or greater than -23.

The rate of change of y with respect to x for the given linear relationship is 10.

To determine the rate of change of y with respect to x, we can calculate the slope of the linear relationship between x and y using the formula:

slope = (change in y) / (change in x)

Given the values in the table:

x: -8.5, -6.5, -2.5, -1

y: -92, -72, -32, -17

We can calculate the change in y and change in x between any two points.

For example, between the first two points (-8.5, -92) and (-6.5, -72), the change in y is:

change in y = -72 - (-92) = -72 + 92 = 20

And the change in x is

change in x = -6.5 - (-8.5) = -6.5 + 8.5 = 2

Using the formula for slope:

slope = (change in y) / (change in x) = 20 / 2 = 10.

Therefore, the rate of change of y with respect to x is 10.

This means that for every unit increase in x, y increases by 10 units.

We can perform the same calculations for the other points in the table and observe that the rate of change of y with respect to x remains constant at 10.

Hence, the rate of change of y with respect to x for the given linear relationship is 10.

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Note that the   curvature of the curve defined by the function y = 3x² - 2x +4   at point x = 2 is approximately 0.0002.

To find the curvature   of the curve defined by the function, we need to first find the second derivative of the function.

y = 3x² - 2x + 4

Taking the first derivative of y with respect to x

y' = 6x - 2

Taking the second derivative of y with respect to x:

y'' = 6

So the second derivative of y is a constant 6.

To find the curvature of the curve at point x = 2, we need to evaluate the following formula:

k = |y''| / [1 + (y')²][tex]^{(3/2)}[/tex]

Substituting x = 2 and y'' = 6, we get:

k = |6| / [1 + (6x2 - 2)²][tex]^{(3/2)}[/tex]

= 6 / [1 + (22)²][tex]^{(3/2)}[/tex]

= 6 / [1 + 484][tex]^{(3/2)}[/tex]

= 6 / 485[tex]^{(3/2)}[/tex]

k ≈ 0.0002

Hence,  the curvature of the curve defined by the function y = 3x² - 2x + 4 at point x = 2 is approximately 0.0002.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Find the curvature of the curve defined by the function

y=3x^2 -2x + 4

at point x =2

The scale factor used to create the image is given as follows:

4.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

In the context of this problem, we have that each vertex of A'B'C'D' is obtained with the multiplication of each of the coordinates of ABCD by four.

For example, we have that vertex A has the coordinates A(1, -2), while the equivalent vertex A' has the coordinates of A'(4, -8).

Hence the scale factor used to create the image is given as follows:

4.

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The required sign that makes the statement true is "||".

The given options are 7, 22, 64, and V.

To express a percentage in mathematical notation, we divide the number by 100. In this case, 67.18% can be written as 0.6718.

Using the "||" symbol, we can write the equation as: 0.6718 || 7 = 22.

This equation represents the statement "0.6718 is to 7 as 22 is to 100." The vertical bar "||" signifies the ratio or proportion between the numbers. The double vertical bars "||" typically represent the symbol for "is equivalent to" or "is parallel to" in various contexts.

Therefore, the sign "||" makes the statement true.

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The probability P(G|N) value is 0.585 when P(G∩N)=0.24, P(G)=0.37, and P(N)=0.41.

To find P(G|N), which represents the probability of event G given event N, we can use the formula:

P(G|N) = P(G∩N) / P(N)

Given that P(G∩N) = 0.24 and P(N) = 0.41

we can substitute these values into the formula:

P(G|N) = 0.24 / 0.41

Calculating the division:

P(G|N) = 0.585

Therefore, the value of P(G|N) is 0.585.

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The coordinates in the solution to the systems of inequalities graphically is (-5, 1)

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

y < 1/2x + 5

y ≤ -3x - 2

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (-5, 1)

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Answer:

(-5, -5)

Step-by-step explanation:

Given system of linear inequalities:

[tex]\begin{cases}y < \dfrac{1}{2}x+5\\\\y\leq-3x-2\end{case}[/tex]

When graphing inequalities:

To graph linear inequalities, treat them as equations (swap the inequality sign for an "equals" sign). Plug in two values of x to find two points on the line to help draw the lines.  

Substitute x = 0 and x = 6 into the equation of the inequality to find two points on the line.

[tex]\begin{aligned}x=0 \implies y&=\dfrac{1}{2}(0)+5\\y&=5\end{aligned}[/tex]               [tex]\begin{aligned}x=6 \implies y&=\dfrac{1}{2}(6)+5\\y&=8\end{aligned}[/tex]

Plots points (0, 5) and (6, 8).

As the inequality sign is <, draw a dashed line through the plotted points and shade below the line.

Substitute x = 0 and x = 2 into the equation of the inequality to find two points on the line.

[tex]\begin{aligned}x=0 \implies y&=-3(0)-2\\y&=-2\end{aligned}[/tex]               [tex]\begin{aligned}x=2 \implies y&=-3(2)-2\\y&=-8\end{aligned}[/tex]

Plots points (0, -2) and (2, -8).

As the inequality sign is ≤, draw a solid line through the plotted points and shade below the line.

The solution set is the set of points contained within the overlapping shaded region and on the solid line.

Therefore, a point in the solution set is (-5, -5).

Michelle pays $1365 in total.

Option D is the correct answer.

We have,

To calculate the total amount Michelle pays for the T-shirts, we need to consider the cost per shirt and the shipping fee.

The cost per shirt is $6.50, and she ordered 200 shirts, so the cost of the shirts alone is:

= $6.50 x 200

= $1300

The shipping fee is 5% of the total order, which is:

= 5% x $1300

= $65

To find the total amount Michelle pays, we add the cost of the shirts and the shipping fee:

= $1300 + $65 = $1365

Therefore,

Michelle pays $1365 in total.

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The equation for the parabola in the graph is the one in option C:

y = (-1/4)x² -2x - 7

Remember that a parabola with leading coefficient a and a vertex (h, k) can be written as:

y = a*(x - h)² + k

Here the vertx is at (-4, -3), then:

y = a*(x + 4)² - 3

And we can see that it passes through the point (0, -7), replacing that we will get:

-7 = a*(0 + 4)² - 3

-7 = a*16 - 3

-7 + 3 = a*16

-4 = a*16

-4/16 = a

-1/4 = a

The quadratic is:

y = (-1/4)*(x + 4)² - 3

Expanding that, we will get:

y = (-1/4)x² -2x - 4 - 3

y = (-1/4)x² -2x - 7

The correct option is C.

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The area of triangle ABC is given as follows:

A = 5.5 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The base AB has the length given as follows:

[tex]AB = \sqrt{(-4  - (-8))^2 + (-7 - (-8))^2}[/tex]

b = 4.12.

The midpoint of the base AB is given by the mean of the coordinates, hence:

M = (-6, -7.5).

The height is given by the distance MC, as follows:

[tex]h = \sqrt{(-6 - (-5))^2 + (-7.5 - (-5))^2}[/tex]

h = 2.69.

Hence the area of the triangle is given as follows:

A = 0.5 x 4.12 x 2.69

A = 5.5 square units.

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The revenue function for the cakes can be shown as: R(x1, x2, x3, x4, x5) = $9x1 + $12x2 + $4x3 + $5x4 + $8x5

The revenue function is described as  the total amount of money earned from selling a certain quantity of cakes.

We make the following  

Cake 1 sold =  x1

Cake 2 =  x2

Cake 3 = x3,

Cake 4 =  x4,

Cake 5=  x5.

The revenue generated from selling each cake is:

Revenue1 = $9 * x1

Revenue2 = $12 * x2

Revenue3 = $4 * x3

Revenue4 = $5 * x4

Revenue5 = $8 * x5

Total revenue = Revenue1 + Revenue2 + Revenue3 + Revenue4 + Revenue5

Total revenue = $9 * x1 + $12 * x2 + $4 * x3 + $5 * x4 + $8 * x5

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They are similar because AB is four more than ED, AC is three more than DF, and BC is three more than EF.

To determine if two triangles are similar, we need to compare the ratios of the corresponding sides.

In this case, the given information allows us to compare the lengths of the corresponding sides of triangle ABC and triangle DEF.

We have:

AB = 16 and ED = 12 (AB is four more than ED)

AC = 12 and DF = 9 (AC is three more than DF)

BC = 1 and EF = 9 (BC is three more than EF)

The corresponding sides are proportional because the ratios of the lengths are consistent:

AB/ED = 16/12 = 4/3

AC/DF = 12/9 = 4/3

BC/EF = 1/9

Since the ratios of the corresponding sides are the same, we can conclude that triangle ABC and triangle DEF are similar

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Answer:

  f(x)=40(2.25)^x

Step-by-step explanation:

You want the equation of the exponential function that goes through points (0, 40) and (1, 90).

The exponential function can be written ...

  f(x) = a·b^x

When x = 0, this is ...

  f(0) = a·b^0 = a·1 = a

Using the given point, we have a = 40.

When x = 1, this is ...

  f(1) = 40·b^1 = 40b

Using the given point, we have ...

  90 = 40b

  b = 90/40 = 2.25

The function equation is ...

  f(x) = 40(2.25^x)

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Since AC is the angle bisector of ∠BAD, the flowchart proof should be completed as follows;

Statement                                 Reason

AC bisects ∠BAD                      Given

∠BAC ≅ ∠DAC                         Definition of an angle bisector.

∠BCA ≅ ∠DCA                         Congruent angles of a triangle (SAS).

AC ≅ AC                                   Reflexive property

ΔABC ≅ ΔADC                         AAS postulate

In Mathematics and Geometry, an angle bisector can be defined as a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.

By applying the angle bisector theorem to the given triangle, the variable y can be calculated by using the following mathematical equation (formula):

AC bisects ∠BAD       Given

∠BAC ≅ ∠DAC           Definition of an angle bisector.

Based on side, angle, side (SA) and congruent angles of a triangle (SAS), we can logically deduce that ∠BCA is congruent to ∠DCA

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Answer: I think question two is Adjacent angles and complimentary angles.

Step-by-step explanation: Complementary angles are two acute angles that add to form a right angle.
Adjacent angles are two angles that share a common side.

Answer:

30% increase

Step-by-step explanation:

percentage increase is calculated as

[tex]\frac{increase}{original}[/tex] × 100%

increase = $35.10 - $27 = $8.10 , then

percentage increase = [tex]\frac{8.10}{27}[/tex] × 100% = 0.3 × 100% = 30%

Answer:

Step-by-step explanation:

step 1:       35.10-27 =8.1

step 2:       8.1/27 x 100 = 30%

so therefore = 30% increase

As it only told interest i asume its simple interest for compound interest the answer would be different

Answer: B   =[tex]x^{\frac{4}{5} }[/tex]

Step-by-step explanation:

Rules needed:

When you have a root, you can write it in exponented form.  It becomes a fraction.

             EX.

                          [tex]\sqrt[5]{x} =x^{\frac{1}{5} }[/tex]

When you have a number that is multiplied to another number both have exponents and same bases, you can combine the two by adding the exponents

            EX.

                       [tex]x^{\frac{1}{5} } *x^{\frac{1}{5} } = x^{\frac{2}{5} }[/tex]

Your problem:

[tex]\sqrt[5]{x}* \sqrt[5]{x}* \sqrt[5]{x}* \sqrt[5]{x}[/tex]              >convert to exponent form

=[tex]x^{\frac{1}{5} } *x^{\frac{1}{5} } *x^{\frac{1}{5} } *x^{\frac{1}{5} }[/tex]                >add all exponents [tex](\frac{1}{5} +\frac{1}{5} +\frac{1}{5}+\frac{1}{5})[/tex]

=[tex]x^{\frac{4}{5} }[/tex]

B

Answer:  d. Y=2

Step-by-step explanation:

Solving a system of equations we can see that:

We can use the variables:

x = mass of the 60% solution.

y = mass of the 85% solution.

We can write a system of equations.

x + y = 70

x*0.6 + y*0.85 = 70*0.8

We can isolate x on the first equation to get:

x = 70 - y

Replace that in the other one:

(70 - y)*0.6 + y*0.85 = 70*0.8

Now we can solve this for y.

y*0.25 = 70*0.8 - 70*0.6

y = 14/0.25 = 56

Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.

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