2. Fiona is studying how income taxes impact various families and their finances. She creates a table with various amounts of taxes owed and estimates


that this represents 9% of each family's gross income.


Solve for the gross income for each family based off of their taxes owed.

Blake should invest $6,000 at 4% interest and the remaining $5,000 (11000 - 6000) at 5% interest to earn exactly $490 at the end of 1 year.

Let's denote the amount of money Blake invests at 4% interest as "x" (in dollars) and the amount he invests at 5% interest as "11000 - x" (since the total investment is $11,000).

To earn interest, we can use the formula: Interest = Principal × Rate × Time

For the 4% interest account, the interest earned is:

0.04x × 1 (1 year) = 0.04x

For the 5% interest account, the interest earned is:

0.05(11000 - x) × 1 (1 year) = 550 - 0.05x

According to the problem, the total interest earned is $490. Therefore, we can set up the equation:

0.04x + (550 - 0.05x) = 490

Simplifying the equation:

0.04x + 550 - 0.05x = 490

-0.01x + 550 = 490

-0.01x = -60

x = 6000

Blake should invest $6,000 at 4% interest and the remaining $5,000 (11000 - 6000) at 5% interest to earn exactly $490 at the end of 1 year.

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Answer: \(3^{\circ}C\)

Step-by-step explanation:

Given

The temperature on Monday was \(-5^{\circ}C\)

By Tuesday, it becomes \(-2^{\circ}C\)

Change in temperature is the difference between the two temperatures.

\(\Rightarrow \Delta T=-2-(-5)\\\Rightarrow \Delta T=-2+5\\\Rightarrow \Delta T=3^{\circ}C\)

Therefore, the change in temperature is \(3^{\circ}C\).

Answer:

x =127

Step-by-step explanation:

Since this is a 6 sided figure, the sum of the interior angles is 720

128+133+112+x+120+100 = 720

Combine like terms

x+593=720

Subtract 593 from each side

x+593-593 = 720-593

x =127

Hint :

Sum of angles of the 6 sided figure = \( {720}^{o} \)

Answer:

\( {x}^{o} = {127}^{o} \)

Step-by-step explanation:

\( {x}^{o} + {112}^{o} + {133}^{o} + {128}^{o} + {100}^{o} + {120}^{o} = {720}^{o} \\ {x}^{o} + {593}^{o} = {720}^{o} \\ {x}^{o} = {720}^{o} - {593}^{o} \\ {x}^{o} = { 127}^{o} \)

Answer:

for the first one : 0.91 or 0.916 either one

for the second answer : 1 11/20

Step-by-step explanation:

Here is the explanation for the second question>>>To find the total of 3/4 and 4/5 is to add them together. However, in order to add them together you need to find the least common denominator (LCD). And the LCD of both denominators would be 20, because that is the smallest number both 4 and 5 can divide into. And here is the tricky part, now you have to change the numerators. So since 3/4th's now has a denominator of 20 you have to make the 3 match the 20. So 4 times what it 20? It is 5. So now multiply 5 by three and that will give you 15/20, which can reduce to 3/4 which means that you did this correctly! Now repeat the same steps with 4/5:

4/5=4/20

20÷5=4

4•4=16

16/20    (16/20 can reduce to 4/5 which means you did this correctly.

Now to add them keep the denominators the same and only add the numerators:

15/20 + 16/20 = 31/20

Now this as a mixed number would be 1 11/20. I hope this was helpful!

Answer:

1.) 1  1/12

2.) 1  11/20

Step-by-step explanation:

5/6+1/4

convert to common denominators

5/6 x 2/2 = 10/12

1/4 x 3/3 = 3/12

10/12+3/12=13/12

Convert to a mixed number

1 1/12

3/4+4/5

convert to common denominators

3/4 x 5/5 = 15/20

4/5 x 4/4 = 16/20

15/20+16/20=31/20

Convert to a mixed number

1 11/20

Using it's formula, it is found that the geometric mean between 6 and 12 is of 8.4853.

The geometric mean between n numbers is given by the nth root of the product of the numbers.

In this problem, there are 2 numbers, 6 and 12, hence the geometric mean is given by:

\(M_g = \sqrt{6 \times 12} = \sqrt{72} = 8.4853\)

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Answer:

average

Step-by-step explanation:

The midpoint is always the average or middle of the line. So here it would be the average of the two x endpoints.

Step-by-step explanation:

102^2 = 10404

102×102=10404

The image quality is significantly superior to what it was on previous scanners, but the number of patients served per day remains the same. this situation attests to the fact that the service sector has seen improvement in quality of service, but productivity remains about the same.

Improvement in quality of service:

Putting the customer first, balancing efficiency and customer satisfaction (experience), and focusing on employee engagement are three key strategies for improving contact center service quality.

Productivity:

Productivity is the efficiency with which goods and services are produced and is represented by a scale. A measure of productivity is often expressed as a ratio of total output to a single input or total input in a production process. Typically the output per unit of input over a period of time. The most common example is a measure of (aggregate) labor productivity, an example of which is GDP per worker. There are various definitions of productivity (including those not defined by the ratio of outputs to inputs), and the choice depends on the purpose of measuring productivity and the availability of data gain. The main reason for differences in different measures of productivity usually has to do with how outputs and inputs are aggregated (directly or indirectly) to obtain such relative measures of productivity doing conduct.

Importance of Productivity:

Productivity gains are defined as the process of getting more out of every hour of work. Improving productivity can take many forms, including: Capital, Investments in equipment, software, infrastructure, machinery, etc. equate to labor. Productivity is important for individuals (workers and consumers), business leaders, and analysts(such as policy makers and government statisticians).

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The average rate of change for the function will be 234.

It is the average amount by which the function is modified per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph that represents the function. The average rate of change of the function is given as,

Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]

The function is given below.

f(x) = 3ˣ + 17

The value of the function at x = 3 will be

f(x) = 3³ + 17

f(x) = 27 + 17

f(x) = 44

The value of the function at x = 6 will be

f(x) = 3⁶ + 17

f(x) = 729 + 17

f(x) = 746

Then the average rate of change for the function will be

Average rate = [746 - 44] / [6 - 3]

Average rate = 702 / 3

Average rate = 234

The average rate of change for the function will be 234.

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Step-by-step explanation:

A parenthesis is used when the number next to it is NOT part of the solution set

   like :   all numbers up to but not including 3 .    

  Parens are always next to  infinity  when it is part of the solution set .

  A bracket is used when the number next to it is included in the solution set.

The difference between the height (h) and the slant height (L) of the pyramid is that the height measures the vertical distance from the apex to the base, while the slant height measures the length along the surface of the pyramid from the apex to any point on the base's edge.

The height (h) of a pyramid refers to the perpendicular distance between its base and its apex. It is the vertical measurement from the highest point of the pyramid to the base. In the given context, the specific value of the height (h) is not provided, so we cannot determine its exact value.

On the other hand, the slant height (L) of a pyramid refers to the length of the line segment that connects the apex of the pyramid to any point on the edge of its base. The slant height is measured along the surface of the pyramid, forming an inclined line from the apex to the base. In this case, the slant height is given as 10.50 units.

Therefore, the difference between the height (h) and the slant height (L) of the pyramid is that the height measures the vertical distance from the apex to the base, while the slant height measures the length along the surface of the pyramid from the apex to any point on the base's edge.

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The correlation coefficient is 0.9541. This can be determined from the information provided in the ANOVA table, specifically the regression sum of squares (SSR) and the total sum of squares (SST).

The correlation coefficient, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where values closer to -1 or 1 indicate a stronger relationship, and values closer to 0 indicate a weaker relationship.

To calculate the correlation coefficient, we can use the formula:

r = sqrt(SSR/SST)

From the ANOVA table provided, we can see that SSR = 12,323.64 and SST = 13,538.4. Plugging these values into the formula gives:

r = sqrt(12,323.64/13,538.4) = 0.9541

Therefore, the correlation coefficient for this model is 0.9541, indicating a strong positive linear relationship between the independent variable and the dependent variable

Complete Question:

Using the following information. Coefficients -12.8094 Intercept Independent variable 2.1794 ANOVA df SS MS F 1 90.0481 Regression Residual Total 12,323.64 1,214.762 13,538.4 12,323.64 136.8550 8 1° 9 What is the correlation coefficient? Multiple Choice 0.9103 0.9541 -0.9541

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This measure of central tendency can be considered the most precise in option c. mean

The mean is a measure of central tendency that calculates the average of a set of values. It is often considered the most precise measure because it takes into account all the values in the dataset and provides a balanced representation.

The mean is calculated by summing all the values and dividing by the total number of values. Unlike the mode, which only identifies the most frequently occurring value, and the median, which represents the middle value, the mean incorporates all the values and provides a comprehensive summary of the dataset.

However, it is important to note that the mean can be sensitive to extreme values or outliers in the data.

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Answer:

a. 5/12

Step-by-step explanation:

there are 5 vowels out of 12 letters

Answer:

42, 122, 202,

Step-by-step explanation:

.................

Answer:

42, 122, 202

Step-by-step explanation:

The sequence is going up by 20s.

Answer:

19.4 cm

Step-by-step explanation:

Hi there!

This is a right triangle. We're given an angle, the side adjacent to the angle and we're solving for the hypotenuse. Given this information, we can use the cosine ratio:

\(cos\theta=\frac{adj}{hyp}\)

Plug in the given angle and side

\(cos71=\frac{6.3}{BC}\\BC=\frac{6.3}{cos71} \\BC=19.4\)

Therefore, the length of BC is 19.4 cm when rounded to 3 significant figures.

I hope this helps!

Answer:

8.30662386292= mas o menos 8

Step-by-step explanation:

Para este pregunta, se necesita encontrar el raiz cuadrada de 69, porque 69 esta triplicada, entonces la temperatura inicial era  mas o menos 8

Standard deviation is used for interval-ratio variables and is the square root of the average of the squared deviations from the mean.

What is measure of variability?

Measures of variability provide descriptive information about the dispersion of scores within data.

Standard deviation uses all the values in the distribution in it's calculation hence the standard deviation provides the most information.

Therefore standard deviation is used for interval-ratio variables and is the square root of the average of the squared deviations from the mean.

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Answer:

3 ft 3 in

Step-by-step explanation:

The radius is half the diameter.  

If the diameter is 6 ft 6 in, then the radius is 3 ft 3 in.

The indicated angles in the parallel lines cut by the transversal are as follows:

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, linear angles, vertically opposite angles, alternate exterior angles etc.

Therefore, according to the diagram the two parallel lines are cut by a transversal. Let's use the angle relationships to find the m ∠1 and m∠3.

m ∠6 = 78 degrees.

m ∠1 = m ∠ 7 (alternate exterior angles)

Alternate exterior angles are congruent.

Hence,

m ∠7 = 180 - 78 = 102 degrees

m ∠ 1 = 102 degrees

m ∠ 1 = m ∠ 3 (vertically opposite angles)

vertically opposite angles are congruent.

m ∠ 3 = 102 degrees.

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Answer:

Step-by-step explanation:

The proper loop condition test to quit iterating if x < 10 and y > 3 would be:

while (!(x < 10 && y > 3))

This condition will be true as long as either x is not less than 10 or y is not greater than 3. Once both conditions are met, the loop will exit.

The output of the code fragment would be:

"That is all. Goodbye"

Since the condition "x > 5" in the if statement is not true (x is equal to 5), the printf statement inside the if block will not be executed. The following printf statements outside the if block will be executed and will print the corresponding text.

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Answer:

The expressions for the payment made to Mary are,

(Monday) 90 = 15m + b

(Tuesday) 62 = 8m + b

where m and b are the fee per student and the base fee, respectively. Solving for m and b, the values are 4 and 30.

The equation that represents Mary's earning is

y = 4x + 30

For 20 students,

y = 4(20) + 30 = 110

For Lisa's earnings,

y = 8x + 15

Substituting 20,

y =8(20) + 15 = 175

Thus, Lisa would earn more than Mary by $65.

(Btw this is not my work, I got it from someone else on brainly and wanted to help lol)

Answer:

u = 3

Step-by-step explanation:

\( {u}^{3} = 27\)

\( {3}^{3} = 27\)

\(3 \times 3 \times 3 = 27\)

Answer:

u = 3 , − 3 − 3 i √ 3 /2 , − 3 + 3 i √ 3 /2

Step-by-step explanation:

Factor using difference of cubes and set each factor equal to  0 .

The orthogonal projection of vector y onto the span of u₁ and u₂ is \([-2, 2.1481, -8.7037]^T\).

To verify if {u₁, u₂} is an orthogonal set, we need to check if the dot product of u₁ and u₂ is zero.

Let's calculate the dot product:

u₁ · u₂ = (7 * 1) + (-1 * -1) + (-2 * 4) = 7 + 1 - 8 = 0

Since the dot product of u₁ and u₂ is zero, we can conclude that {u₁, u₂} is an orthogonal set.

Given:

y = \([-1, 2, -9]^T\)

u₁ = \([7, -1, -2]^T\)

u₂ = \([1, -1, 4]^T\)

Let's calculate the orthogonal projection:

Step 1: Calculate dot products:

y · u₁ = (-1 * 7) + (2 * -1) + (-9 * -2) = -7 - 2 + 18 = 9

y · u₂ = (-1 * 1) + (2 * -1) + (-9 * 4) = -1 - 2 - 36 = -39

Step 2: Calculate norm squared of u₁ and u₂:

||u₁||² = (7 * 7) + (-1 * -1) + (-2 * -2) = 49 + 1 + 4 = 54

||u₂||² = (1 * 1) + (-1 * -1) + (4 * 4) = 1 + 1 + 16 = 18

Step 3: Calculate the orthogonal projection:

Projᵤ(y) = ((y · u₁) / ||u₁||²) * u₁ + ((y · u₂) / ||u₂||²) * u₂

         = \((9 / 54) * [7, -1, -2]^T + (-39 / 18) * [1, -1, 4]^T\)

         = \([0.1667, -0.0185, -0.0370]^T + [-2.1667, 2.1667, -8.6667]^T\)

         = \([-2.0000, 2.1481, -8.7037]^T\)

Therefore, the orthogonal projection of vector y onto the span of u₁ and u₂ is \([-2, 2.1481, -8.7037]^T\).

Complete Question:

Verify that {\(u_1, u_2\)} is an orthogonal set, and then find the orthogonal projection of y onto Span{\(u_1,u_2\)}. \(y =[-1 2 -9]^T, u_1 = [7 -1 -2]^T, u_2 = [1 -1 4]^T\)

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Answer:

\(12\ gallons\)

Step-by-step explanation:

Step 1:  Determine the unit rate

\(Miles / Gallons\)

\(162\ miles / 9\ gallons\)

\(18\ miles/gallon\)

Step 2:  Determine the amount of gasoline used for 216 miles

\(216\ miles * (gallon / 18\ miles)\)

\(12\ gallons\)

Answer:  \(12\ gallons\)

Answer:

12

Step-by-step explanation:

1. Figure out how many miles the car can go with one gallon of gasolline

162 ÷ 9 = 18

1 gallon = 18 miles

2. Figure out how many times 18 can go into 216

216 ÷ 18 = 12

12 gallons = 216 miles

*We do this because we know that every time the car drives 18 miles its uses another gallon of gas.

The car will use 12 gallons of gasoline to travel 216 miles.

Answer:

1,792 c = 112 gal.

Step-by-step explanation:

Because their 16 cups in 1 gallon, we will divide 1,793 by 16 and we get 112.  Therefore, 112 is our answer.

Answer:

112 gallons

Step-by-step explanation:

there are 16 cups in 1 gallon

1=16

?=1792

to solve this, divide 1792 by 16 to get 112 gallons

112*16 is 1792

Answer:

volume = 174.8 sq. units.

Answer:

61.5752159 units³

Step-by-step explanation:

The height of a cone can be found using the following formula:

\(v=\frac{1}{3} \pi r^2h\)

We know that the height is 14.7 and the radius is 2.

\(h=14.7 \\r=2\)

Substitute the values into the formula.

\(v=\frac{1}{3} \pi (2)^2(14.7)\)

Evaluate the exponent.

⇒ 2²= 2*2 = 4

\(v=\frac{1}{3} \pi (4)(14.7)\)

Multiply 4 and 14.7

\(v=\frac{1}{3} \pi (58.8)\)

Multiply 1/3 and pi.

\(v=1.04719755*58.8\)

Multiply the two numbers together.

\(v=61.5752159\)

Add appropriate units. Volume is cubic units, and we aren't given units. So, we should use cubic units.

\(v=61.5752159 units^3\)

The volume of the cone is 61.5752159 cubic units.

StartFraction 36 + 9 StartRoot 7 EndRoot + 4 StartRoot 2 EndRoot + StartRoot 14 EndRoot Over 9 EndFraction is the Square root.

What in mathematics is a square root?

It is possible to multiply an integer by its square root in order to obtain the original value.

                         Square root is represented by the symbol sqrt, which stands for square root of, end square root. The opposite of squaring an integer is finding its square root.

(9 + sqrt(2))/(4 - sqrt(7))

Multiply and divide by 4 + sqrt(7)

[(9 + sqrt(2))(4 + sqrt(7))]/(4² - 7)

[36 + 4sqrt(2) + 9sqrt(7) + sqrt(14)]/9

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x = 19 is the value of x in triangle .

What is triangle explain?

angle R + angle S + angle T = 180

(5+ 2x) + (7x - 16) + (x + 1) = 180

10x - 10 = 180

10x = 190

x = 19

Therefore

angle R = 5 + 2(19) = 43 degrees

angle S = 19 + 1 = 20 degrees

angle T = 7(19)-16 = 117 degrees

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