What ordered pairs are the solutions of the system of equations shown in the graph below?

The results for each composite function at each x-value are listed below:

Case 13: (f ° g) (1) = 26 (Right choice: D)

Case 14: (f + g) (3) = 20 (Reight choice: E)

In this problem we find two cases of composite functions that must be evaluated at given x-value. The procedure is described below:

Now we proceed to solve for each case:

Case 1: f(x) = x² + x - 4, g(x) = 3 · x + 2

(f ° g) (x) = [(3 · x + 2)² + (3 · x + 2) - 4]

(f ° g) (1) = [(3 · 1 + 2)² + (3 · 1 + 2) - 4]

(f ° g) (1) = (5² + 5 - 4)

(f ° g) (1) = 26

Case 2: f(x) = x² + x, g(x) = x² - 1

(f + g) (x) = (x² + x) + (x² - 1)

(f + g) (x) = 2 · x² + x - 1

(f + g) (3) = 2 · 3² + 3 - 1

(f + g) (3) = 18 + 3 - 1

(f + g) (3) = 20

To learn more on composite functions: https://brainly.com/question/20379727

#SPJ1

The mistake done in the solution is while finding the distance from mean we have not taken the absolute value

To find the MAD (Mean Absolute Deviation), first find the mean of the data set:

mean = (2 + 3 + 4 + 7 + 9 + 11) / 6 = 6

Then, calculate the absolute deviation of each data point from the mean:

|2 - 6| = 4

|3 - 6| = 3

|4 - 6| = 2

|7 - 6| = 1

|9 - 6| = 3

|11 - 6| = 5

Next, find the average of these absolute deviations:

(4 + 3 + 2 + 1 + 3 + 5) / 6 = 2.67

While find the distance from mean we have to use the absolute value or positive value

Hemce, the MAD of the data set {2, 3, 4, 7, 9, 11} is 2.67.

To learn more on Statistics click:

https://brainly.com/question/30218856

#SPJ1

Using the exponential function we can rewrite the expression as:

[tex]H = 10^{-4}[/tex]

Here we start with the equation:

log₁₀(H) = -4

We can rewrite the logarithm part as follows:

log₁₀(H) = ln(H)/ln(10)

Then we can rewrite:

ln(H)/ln(10) = -4

ln(H) = -4*ln(10)

Now we can move the coefficeint -4 as a exponent:

[tex]ln(H) = ln(10^{-4})[/tex]

Now apply the exponential equation to both sides:

[tex]exp(ln(H)) = exp(ln(10^{-4}))[/tex]

[tex]H = 10^{-4}[/tex]

That is what we wanted.

Learn more about logarithms at:

https://brainly.com/question/13473114

#SPJ1

The area of the kite is 47.25 square feet.

Given is a figure of Kite.

We know that the diagonal of a Kite divides the Kite into equal two triangles.

Here same things happened.

For the upper triangle, the length of the base is = 10.5 feet.

And the base of the height corresponding to that base = 4.5 feet.

So the area of the upper triangles = (1/2)*10.5*4.5 = 23.625 square feet.

Since the areas of the triangles are equal so the area of the bottom triangle is also 23.625 square feet.

Hence the area of Kite = sum of the areas of this triangles = 23.625 + 23.625 = 47.25 square feet.

To know more about area here

https://brainly.com/question/26870235

#SPJ1

The type of arrangement used in the picture to pack cans is a linear arrangement.

If the cans are arranged in a straight line, this would be called a linear arrangement. In a linear arrangement, the objects are arranged in a single line or row.

This type of arrangement is commonly used for packing and displaying items that need to be easily accessible or for creating a uniform and organized appearance. It can be used for packing cans, bottles, or other similarly shaped objects.

Learn more about arrangement on

https://brainly.com/question/1427391

#SPJ1

Identify the type of arrangement used in the picture to pack cans

​

The correct answer is:

C) Because the P-value is greater than α = 0.10, there is not convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.

The student set up a hypothesis test to investigate whether there is evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5. The null hypothesis is that the proportion is 0.5, and the alternative hypothesis is that it differs from 0.5.

The student obtained a standardized test statistic of z = -0.80 and a P-value of 0.2119.

To make a conclusion, the student needs to compare the P-value to the significance level α.

The significance level is given as 0.10, which means that the student is willing to accept a 10% chance of making a Type I error (rejecting the null hypothesis when it is actually true).

Since the P-value of 0.2119 is greater than α = 0.10, there is not convincing evidence to reject the null hypothesis. Therefore, the student cannot conclude that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.

Learn more about Null Hypothesis here:

https://brainly.com/question/28920252

#SPJ1

Surface area  of Maya's deck box  is 11.075 square meter and Volume is 2.15625 cubic meters

The dimensions of Maya's deck box are length is 2.3 m, width is 1.25m and height is 0.75m

Surface area =2lw+2lh+2hw.

=2(2.3×1.25) + 2(2.3×0.75) + 2(0.75×1.25)

=2(2.875) + 2(1.725)+2(0.9375)

=5.75+3.45+1.875

=11.075 square meter

Volume = Length×width×height

=2.3×1.25×0.75

=2.15625 cubic meters

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

#SPJ1

Answer:

It sounds like a word problem! Let's solve it together. First, let's use some variables. Let's call the number of child tickets sold "c" and the number of adult tickets sold "a". We know that the total sales were $593.40, so we can write an equation for that:

6c + 9.9a = 593.4

We also know that twice as many adult tickets as child tickets were sold, so we can write another equation:

a = 2c

Now we can substitute the second equation into the first equation:

6c + 9.9(2c) = 593.4

Simplifying this equation, we get:

6c + 19.8c = 593.4

25.8c = 593.4

c = 23

So 23 child tickets were sold that day.

Answer:

The correct sequence of steps to use the offset command is:

1. Select the original object to be offset

2. Select the offset command

3. Add the distance of the offset

4. Select a point anywhere on the screen where you want to offset the object

5. Select the object from the original object

I hope that helps!

Answer :

In the first figure,

△BCA

a = Perpendicular

b = base

c = hypotenuse

In the second figure,

△ABC

a = base

b = perpendicular

c = base

tan B = Perpendicular/Base = b/a

cos B = Base/Hypotenuse = a/c

cos A = Base/Hypotenuse = a/c

sin B = Perpendicular/Hypotenuse = b/c

tan A = Perpendicular/Base = a/b

sin A = Perpendicular/Hypotenuse = a/c

We would need to randomly sample at least 1067 people to estimate the proportion of Americans who ate breakfast this morning with a margin of error of 3 percentage points and a 95% confidence interval.

The formula to calculate the sample size required to achieve a desired margin of error and confidence interval is:

n = (Z² x p x (1-p)) / E²

where n is the sample size, Z is the z-score corresponding to the desired level of confidence (1.96 for 95% confidence), p is the estimated proportion of the population who ate breakfast, and E is the desired margin of error as a decimal (0.03 in this case).

To determine the estimated proportion of Americans who ate breakfast this morning, we could use data from previous studies or surveys. Let's assume that previous studies have found that approximately 60% of Americans eat breakfast regularly. Therefore, we can use p = 0.60 in our formula.

Substituting the values into the formula, we get:

n = (1.96² x 0.60 x 0.40) / 0.03²

n ≈ 1067

To know more about confidence interval here

https://brainly.com/question/24131141

#SPJ1

The volume of the object made up of 3 cubes of 1 inch each is 3 cubic inches.

To find the volume of the object made up of 3 cubes, we need to know the dimensions of the object in terms of the length, width, and height.

If each cube has a length, width, and height of 1 inch, then the object made up of 3 cubes will have a length of 3 inches, a width of 1 inch, and a height of 1 inch.

Therefore, the volume of the object is:

Volume = Length x Width x Height

Volume = 3 inches x 1 inch x 1 inch

Volume = 3 cubic inches

So, the volume of the object made up of 3 cubes is 3 cubic inches.

To know more about volume:

https://brainly.com/question/11168779

#SPJ1

--The given question is incomplete, the complete question is given

" The object is of 3 cubes is made up of 1 inch cubes what is the volume of the object"--

The y-intercept represents the base price of $200 for airfare from NYC.

The slope represent a cost of $0.30 cents per mile traveled.

According to the equation given, someone who traveled 2000 miles from NYC would pay $800 for their fare.

According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1000 miles.

If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y = 50 + 0.30x.

In Mathematics, the slope-intercept form of the equation of any straight line is modeled by this mathematical equation;

y = mx + c

Where:

Based on the information provided about this trip, an equation that represents the situation is given by;

y = mx + c

y = 0.30x + 200

When x = 2000 miles, the price of airfare (y) can be calculated as follows;

y = 0.30(2000) + 200

y = $800.

When y = $500, the distance traveled (x) can be calculated as follows;

500 = 0.30x + 200

300 = 0.30x

x = 1000 miles.

Read more on slope-intercept here: brainly.com/question/7889446

#SPJ1

Answer:

[tex]-\frac{9}{1}[/tex]

Step-by-step explanation:

Its just the same way as making positive 9
a fraction, but just add the negative sign.

Hope this helps :))

The evaluated probability that a randomly choosing a point within the circle falls in the red-shaded triangle is 0.30,  

To evaluate this probability, we have to calculate the ratio of the area of the red-shaded triangle to the area of the circle.

The area of the circle is derived as πr²

Here,

r = radius of the circle.

In this case, r = 5.

Staging the values

π(5)² = 25π.

So, the area of the circle is 25π.

The area of the red-shaded triangle can be evaluated by using the formula for the area of a triangle which is

[tex]1/2 * base * height[/tex]

In this case, the base is 6 and the height is 8. So, the area of the red-shaded triangle is

1/2 x 6 x 8

= 24.

Hence, the probability that a randomly selected point within the circle falls in the red-shaded triangle is

P = (Area of red-shaded triangle) / (Area of circle)

= 24 / (25π)

= 24 / 25 x 3.14

= 24 / 78.5

≈ 0.30

To learn more about probability

https://brainly.com/question/13604758

#SPJ1

Answer:

B is correct. Angle 7 measures 125°.

Step-by-step explanation:

Parallel lines intersected by a transversal form congruent alternate interior angles. Therefore, angles 4 and 5 are congruent, meaning angle 5 measures 55°. Angles 5 and 7 are supplementary angles, so angle 7 measures 125°. B is the correct answer.

The equation of each parabola with the given focus and directrix is:

y = (1/6)x² - (2/3)x - 11/6

Here, we have,

To derive the equation of the parabola, let (x , y) be a point in the parabola. Its distance from the focus should be equal to its distance from the directrix.

we will show here how to do  an equation of each parabola with the given focus and directrix.

1.)  focus: (2, -1); directrix: y = -4​

                      d (point to focus) = d (point to directrix)

                        sqrt ((x - 2)² + (y + 1)²) = (y + 4)

Squaring both sides gives us,

                                 (x - 2)² + (y + 1)² = (y + 4)²

Simplifying gives,

                      x² - 4x + 4 + y² + 2y + 1 = y² + 8y +16

Simplifying leads to,

                                       6y = x² - 4x -11

This leads to our final answer of

                                  y = (1/6)x² - (2/3)x - 11/6

Hence, The equation of each parabola with the given focus and directrix is: y = (1/6)x² - (2/3)x - 11/6

learn more on parabola:

https://brainly.com/question/1615961

#SPJ1

The probability that a person will be exposed to more than 5.20 mrem of cosmic radiation on a flight across the US is 0.0745, or 7.45%.

We want to find the probability that a person will be exposed to more than 5.20 mrem of cosmic radiation on such a flight.

Let X be the amount of cosmic radiation exposure on a flight.

Then we need to find P(X > 5.20).

We need to standardize the random variable X by converting it to a standard normal variable Z with mean 0 and standard deviation 1, using the formula:

Z = (X - μ) / σ

Substituting the given values, we get:

Z = (5.20 - 4.35) / 0.59 = 1.44

Now we need to find the probability that a standard normal variable is greater than 1.44.

Using a standard normal distribution table or a calculator, we can find that this probability is approximately 0.0745.

Therefore, the probability that a person will be exposed to more than 5.20 mrem of cosmic radiation on a flight across the US is 0.0745, or 7.45%.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ1

Answer:

A soup can with a height of 4cm and a radius of 3cm holds approximately 113.1 cubic centimeters of soup.

Explanation:

The volume of a cylindrical can is calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height of the can.

In this case, the radius is 3cm and the height is 4cm. Plugging these values into the formula, we get:

V = π × 3^2 × 4

V = 113.1 cubic centimeters

The equilibrium price and quantity if the government imposes a fixed tax of $36 on each good is $26 and  the corresponding value of the government tax revenue is $648

To find the equilibrium price and quantity, we need to set Qs = Qd and solve for the price.

Qs = Qd

=> p = -3Qd + 80 = Qs + 8

=> -3Qd + 80 = Qd + 8 (substituting Qs = Qd)

=> 4Qd = 72

=> Qd = 18

=> Qs = 18

Therefore, the equilibrium price is:

p = Qs + 8 = 18 + 8 = 26

Now, if the government imposes a fixed tax of $36 on each good, the new supply function becomes:

p = Qs + 8 - 36

=> Qs = p - 28

And the demand function remains the same:

p = -3Qd + 80

Setting Qs = Qd and substituting Qs and Qd in terms of p, we get:

p - 28 = -3Qd + 80

=> -3Qd = p - 52

=> Qd = (52 - p) / 3

The government tax revenue is the product of the tax and the quantity sold, which is:

Tax revenue = tax per unit × quantity sold

=> Tax revenue = 36 ×Qs

Substituting Qs = 18, we get:

Tax revenue = 36 × 18 = $648

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Answer:

The correct option is A. Parallel line.

The range of the given equation is [-1, infinity).

We are given that;

Equation  y= underroot(x+5​)

Now,

The domain of this equation is the set of x values that make the expression under the square root non-negative.

That is, x+5 >= 0, or x >= -5. So the domain is [-5, infinity).

The range of this equation is the set of y values that are obtained by plugging in the domain values into the equation. Since the square root function is always non-negative, and we are subtracting 1 from it, the smallest possible value of y is -1, when x = -5. As x increases, y also increases, and there is no upper bound for y.

Therefore, by the range the answer will be [-1, infinity).

Learn more about the domain and range of the function:

brainly.com/question/2264373

#SPJ1

The Surface Area is 11.075 square m and Volume is 2.15625 cubic m.

we have,

Length = 2.3 m

width= 1.25 m

height = 0.75 m

So, Surface Area

= 2 (lw + wh + lh)

= 2( 2.875 + 0.9375 + 1.725)

= 11.075 square m

Now, Volume = l w h

= 2.3 x 1.25 x 0.75

= 2.15625 cubic m

Learn more about Volume here:

https://brainly.com/question/1578538

#SPJ1

The probability that it ends up centered on the red color is 39/64.

Given that there are four concentric circles on the ice with radii of 4 inches, 3 feet, 5 feet, and 8 feet,

We need to find the probability that it ends up centered on the red color.

So,

The total area = 8²π = 64π

4 inches = 1/3 feet

So, the area of red part = (8²-5²)π = 39π ft²

So, the probability that it ends up centered on the red color = area of red part / total area

= 39/64

Hence the probability that it ends up centered on the red color is 39/64.

learn more about probability click;

https://brainly.com/question/11234923

#SPJ1

Answer: e, an=6n-7.

Step-by-step explanation: Any pair of consecutive terms can be used to determine the arithmetic sequence's common difference (d), which can then be used in conjunction with the given term to determine the nth term using the following formula:

an = a1 + (n - 1) d.

Let's use the pair a11=53 and a10=47 to find d:

d = a11 - a10 = 53 - 47 = 6

Now we can use the formula to find any term of the sequence. Let's use the given value of a13=65 to find a13:

a13 = a1 + (13 - 1)d

65 = a1 + 12(6)

65 = a1 + 72

a1 = -7

Therefore, the formula that can be used to find the nth term of the arithmetic sequence is:

an = -7 + (n - 1)6

Simplifying this expression, we get:

an = 6n - 7.

The value of KL and LMJ in the pie chart are 54 degrees and 198 degrees respectively

The pie chart is an important type of data representation. It contains different segments and sectors in which each segment and sector of a pie chart forms a specific portion of the total(percentage). The sum of all the data is equal to 360°. The total value of the pie is always 100%.

To find the value of angle KL and LMJ, we can proceed as;

a. angle KL;

KL = 15 / 100 = x / 360

KL = 0.15 = x / 360

x = 360 * 0.15

x = 54°

KL = 54°

Let's find LMJ

LMJ = 24 + 31 = 55%

55 / 100 = x / 360

0.55 = x / 360

x = 360 * 0.55

x = 198°

LMJ = 198°

Learn more on pie chart here;

https://brainly.com/question/796269

#SPJ1

If an item has a listed price of $65 and the sales tax rate is 5%, the sales tax will be $3.25 and the total cost will be $68.25.

If the item has a listed price of $65, the sales tax rate is 5%, we can first calculate the amount of sales tax as follows:

Sales Tax = Listed Price x Sales Tax Rate

Sales Tax = $65 x 0.05

Sales Tax = $3.25

So the sales tax on the item is $3.25.

To calculate the total cost, we simply add the sales tax to the listed price:

Total Cost = Listed Price + Sales Tax

Total Cost = $65 + $3.25

Total Cost = $68.25

So the total cost of the item with sales tax is $68.25.

To learn more about tax/cost click on,

https://brainly.com/question/6424173

#SPJ1