x varies inversely as y. y = 10 when x = 3.

Find the equation that relates x and y:

Then find x when y = 15:;

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.

b) The inverse function of ƒ(x) is given by: ƒ⁻¹(x) = (1 - x) / x

c) The domain of ƒ⁻¹(x) is all real numbers except for 1.

d) The solutions for (ƒ o g)(x) = 1/8 are x = √5 and x = -√5.

(a) To show that f(x) = 1 / (x + 1), we need to simplify the expression f(x) and demonstrate that it is equivalent to 1 / (x + 1):

f(x) = [2(x - 1) / (x² - 2x - 3)] - (1 / (x - 3))

f(x) = [2(x - 1) / (x - 3)(x + 1)] - (1 / (x - 3))

f(x) = [2(x - 1) - (x + 1)] / (x - 3)(x + 1)

f(x) = [2x - 2 - x - 1] / (x - 3)(x + 1)

f(x) = (x - 3) / (x - 3)(x + 1)

f(x) = 1 / (x + 1)

Therefore, we have shown that f(x) = 1 / (x + 1).

(b) To find the inverse function of ƒ(x), we interchange the roles of x and y and solve for y:

x = 1 / (y + 1)

xy + x = 1

xy = 1 - x

y = (1 - x) / x

Therefore, the inverse function of ƒ(x) is given by:

ƒ⁻¹(x) = (1 - x) / x

(c) The domain of ƒ⁻¹(x) can be determined by looking at the domain of the original function f(x), which is x > 3.

For ƒ(x), the range is all real numbers except for 1 (since f(x) = 1 / (x + 1)).

Therefore, the domain of ƒ⁻¹(x) is all real numbers except for 1.

(d) Given g(x) = 2x² - 3, we are asked to solve (ƒ o g)(x) = 1/8.

(ƒ o g)(x) means we need to substitute g(x) into ƒ(x):

ƒ(g(x)) = 1 / (g(x) + 1)

Substituting g(x) = 2x² - 3:

ƒ(2x² - 3) = 1 / (2x² - 3 + 1)

ƒ(2x² - 3) = 1 / (2x² - 2)

1 / (2x² - 2) = 1 / 8

8 = 2x² - 2

2x² = 10

x² = 5

x = ±√5

Therefore, the solutions for (ƒ o g)(x) = 1/8 are x = √5 and x = -√5.

Learn more about Function here:

https://brainly.com/question/30721594

#SPJ1

Tamika Clark's total travel expense this month is $362.90.

Given that the supervisor for the county is Tamika Clark.

Every month, she makes the trip to the three schools in her district.

Her travel costs for this month include 246 miles at a cost of $0.55 per mile, $180.70 for meals, and $46.10 for other expenses.

We must determine the whole cost of her.

To calculate Tamika Clark's total travel expenses this month, we need to add up her expenses for miles traveled, meals, and miscellaneous items.

Miles traveled:

246 miles x $0.55 per mile = $135.30

Meals: $180.70

Miscellaneous: $46.90

Total travel expenses:

$135.30 (miles traveled) + $180.70 (meals) + $46.90 (miscellaneous) = $362.90

Therefore, Tamika Clark's total travel expense this month is $362.90.

Learn more about expense click;

https://brainly.com/question/29850561

#SPJ1

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.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ1

Answer:

1 calculate the Expected values for opening a sample of 100 cards

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)

Read more about inequalities at

brainly.com/question/30977554

#SPJ1

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).

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.

Learn more about ratios and proportions here:

https://brainly.com/question/26974513

#SPJ1

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

Read more on angle bisector here: brainly.com/question/18714022

#SPJ1

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.

To learn more on Statistics click:

https://brainly.com/question/30218856

#SPJ1

The volume of the figure is 704 cubic centimeters.The correct option is B. 704 cubic centimeters.

The volume of the figure, need to calculate the volumes of the cube and the right triangular prism separately, and then add them together.

Volume of the cube:

The length of each side of the cube is given as 8 cm. The formula for the volume of a cube is V_cube = [tex]side^3.[/tex] Substituting the given value, we have V_cube = [tex]8^3[/tex] = 512 cubic centimeters.

Volume of the right triangular prism:

The base of the right triangular prism is a right triangle with one side measuring 8 cm and the other side measuring 6 cm. The height of the prism is given as 8 cm.

The formula for the volume of a right triangular prism is V_prism = base area * height. The base area of a right triangle is  [tex](1/2) * base * height[/tex]Substituting the given values, we have V_prism = [tex](1/2) * 8 cm * 6 cm * 8[/tex]cm = 192 cubic centimeters.

Add the volumes of the cube and the right triangular prism:

V_figure = V_cube + V_prism = 512 cubic centimeters + 192 cubic centimeters = 704 cubic centimeters.

The volume of the figure is 704 cubic centimeters.

The correct option is B. 704 cubic centimeters.

For more such questions on Volume

https://brainly.com/question/1972490

#SPJ8

Answer:

The graph of g is a reflection over the y-axis.  Let's call the points of a regular function before the reflection is done (x, y).  When a function is reflected over the y-axis, you get the opposite y values as (x, -y).  So with a point like (-2, -3), a reflection over the y-axis would give us (-2, 3), where x stays the same but y becomes the opposite.

There were 172 children and 165 adults admitted to the amusement park.

Given that the admission fee for children is $1.50, so the total amount collected from children is 1.5c.

Similarly, the admission fee for adults is $4, so the total amount collected from adults is 4a.

We are also given that the total number of people admitted to the park is 337, so we can write the following equation based on the number of people:

c + a = 337

The total admission fees collected is $918.

1.5c + 4a = 918

Now we have a system of two equations.

From the first equation, we can express 'c' in terms of 'a':

c = 337 - a

Substituting this value of 'c' into the second equation:

1.5(337 - a) + 4a = 918

505.5 - 1.5a + 4a = 918

2.5a = 918 - 505.5

2.5a = 412.5

a = 412.5 / 2.5

a = 165

Substituting the value of 'a' back into the first equation:

c + 165 = 337

c = 337 - 165

c = 172

Therefore, there were 172 children and 165 adults admitted to the amusement park.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Answer: 6 years

Step-by-step explanation:

75,000*15% = 11,250

11,250*6 = 67,500

75,000-67,500 = 7500

7500 is worth less than 15,000

5 years would have been 18,750; more than 15,000

Answer:

Is the relation a function?

no

Step-by-step explanation:

please make brainlist

The correct options are 1) B, 2) A and 3) D.

1) The table shows the work hour and earned money of Logan we need to build an equation to relate both the variables,

So, let the earned money be y and the hour worked be h,

So,

He worked 45 hours to earn $495,

So, in one hours he earned = $495/45 = $11

Therefore, the equation that relate both the variables is,

y = 11h

2) To represent the amount Mr. Kelly pays per month; we can divide the total rent paid for the year by the number of months.

So, if his yearly rent is $12564, so per month he must be paying =

12564 / 12 = $1047

Therefore, the equation that represents the amount Mr. Kelly pays per month is: 1047m = c

3) The relation given shows the quantity of apples bought to its corresponding cost,

So, considering the point (4, 10) by which the graph passes,

So, this mean that, 4 pounds of apple cost $10,

So, 1 pound = 10/4 = $2.5

Hence the cost per pound is $2.5.

Hence the answers are 1) B, 2) A and 3) D.

Learn more about linear equations click;

https://brainly.com/question/12974594

#SPJ1

Answer:

d

Step-by-step explanation:

To calculate the average budget across the four quarters, we need to add the budget for each quarter and divide by 4:

Average budget = (5623 + 5892 + 6382 + 5325) / 4 = 5805.5

Next year's estimated budget is £6,032 per quarter.

To calculate the percentage difference, we can use the following formula:

Percentage difference = (new value - old value) / old value x 100%

Percentage difference = (6032 - 5805.5) / 5805.5 x 100% = 3.9%

Therefore, the answer is (d) 3.9%.

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)

<95141404393>

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.

Learn more about curve at:

https://brainly.com/question/31786419

#SPJ1

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

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]

By using trigonometry, the missing sides are

Example 1: x = 16.7

Example 2: x = 3.2

Example 3: x = 23.5

Example 4: x = 9.3

From the question we are to determine the value of the missing sides in the given triangles

We can determine the value of the missing sides by using SOH CAH TOA

Example 1

Angle = 42°

Opposite side = x

Hypotenuse = 25

Thus,

sin (42°) = x / 25

x = 25 × sin (42°)

x = 16.7

Example 2

Angle = 75°

Opposite side = 12

Adjacent side = x

Thus,

tan (75°) = 12 / x

x = 12 / tan (75°)

x = 3.2

Example 3

Angle = 36°

Hypotenuse side = x

Adjacent side = 19

Thus,

cos (36°) = 19 / x

x = 19 / cos (36°)

x = 23.5

Example 4

Angle = 53°

Opposite side = x

Adjacent side = 7

Thus,

tan (53°) = x / 7

x = 7 × tan (53°)

x = 9.3

Hence,

The missing sides are 16.7, 3.2, 23.5 and 9.3

Learn more on Trigonometry here: https://brainly.com/question/29195940

#SPJ1

New Jersey has the greatest population density in 2013

Since we know that,

Population density  is defined as the number of people per square at any given point in time.

Total people / total area = population density

In emerging countries, population density is higher than in developed countries.

Now for the state :  Connecticut

Population = 3596080

Area = 4842

Therefore,

Density = 3596080/4842

             = 742.68

Now for the state :  Massachusetts

Population = 6692824

Area = 7800

Therefore,

Density = 6692824/7800

             = 858.05

Now for the state :  New Jersey

Population = 8899339

Area = 7354

Therefore,

Density = 8899339/7354

             = 1210.13

Now for the state :  New Jersey

Population = 1051511

Area = 1034

Therefore,

Density = 8899339/7354

             = 1016.93

Hence population Density of  New Jersey is greatest.

To learn more about population density visit:

https://brainly.com/question/16894337

#SPJ1

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.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.

We have,

For Matthew's investment, the continuous compounding formula can be used:

[tex]A = P \times e^{rt}[/tex]

Where:

A = Final amount

P = Principal amount (initial investment)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (in decimal form)

t = Time (in years)

In this case,

Matthew's money has tripled,

So A = 3P.

For Parker's investment, the formula for compound interest compounded annually is used:

[tex]A = P \times (1 + r)^t[/tex]

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (in decimal form)

t = Time (in years)

We need to find t when Matthew's money has tripled in value.

Let's set up the equation:

[tex]3P = P \times e^{rt}[/tex]

Dividing both sides by P, we get:

[tex]3 = e^{rt}[/tex]

Taking the natural logarithm of both sides:

ln(3) = rt

Now we can solve for t

t = ln(3) / r

For Matthew's investment,

r = 3 1/8% = 3.125% = 0.03125 (as a decimal).

For Parker's investment,

r = 2 3/4% = 2.75% = 0.0275 (as a decimal).

Now we can calculate t for Matthew's investment:

t = ln(3) / 0.03125

Using a calculator, we find t ≈ 22.313 years.

Now, we can calculate how much money Parker would have in his account at that time:

[tex]A = P \times (1 + r)^t[/tex]

[tex]A = $8,000 \times (1 + 0.0275)^{22.313}[/tex]

Using a calculator, we find A ≈ $13,774.

Therefore,

Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.

Learn more about compound interest here:

https://brainly.com/question/13155407

#SPJ1

Answer:

20,763

Step-by-step explanation:

I saw the answer after I got it wrong

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.

Learn more about systems of equations at:

https://brainly.com/question/13729904

#SPJ1

The required sample size for a margin of error of less than 0.04 is given as follows:

n = 601.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The margin of error is defined as follows:

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

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

We have no estimate, hence the proportion is used as follows:

[tex]\pi = 0.5[/tex]

For a margin of error of 0.04, the sample size is obtained as follows:

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

[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.04\sqrt{n} = 1.96 \times 0.5[/tex]

[tex]\sqrt{n} = \frac{1.96 \times 0.5}{0.04}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 0.5}{0.04}\right)^2[/tex]

n = 601.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

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.

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.

For similar question on linear relationship.

https://brainly.com/question/30300982

#SPJ11

Answer:

subsidiaries hi sus

Step-by-step explanation:

scientific 2 is the answer

The measure of side TR is given as follows:

TR = 6.7.

Similar triangles are triangles that share these two features listed as follows:

As the triangles in this problem are similar, the proportional relationship for the side lengths is given as follows:

TR/35 = 5/26.

Hence the length of side TR is given as follows:

TR = 35 x 5/26

TR = 6.7.

More can be learned about similar triangles at brainly.com/question/14285697

#SPJ1

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

Learn more about combination:

https://brainly.com/question/30676516

#SPJ1