Complex fractions level 4

Answer:

30

Step-by-step explanation:

22/33=20/x

cross multiply

22x=33x20

22x=660

x=660/22

x=30

Answer:

(x^3+2x-1) * (x^4-x^3+3)

Step-by-step explanation:

To simplify this expression, we can multiply each term in the first expression by each term in the second expression and combine like terms:

(x^3)(x^4) + (x^3)(-x^3) + (x^3)(3) + (2x)(x^4) + (2x)(-x^3) + (2x)(3) + (-1)(x^4) + (-1)(-x^3) + (-1)*(3)

Simplifying further:

x^7 - x^6 + 3x^3 + 2x^5 - 2x^4 + 6x - x^4 + x^3 - 3

Combining like terms:

x^7 - x^6 + 2x^5 - 3x^4 + 4x^3 + 6x - 3

Therefore, the expression representing the product of (x^3+2x-1) and (x^4-x^3+3) is x^7 - x^6 + 2x^5 - 3x^4 + 4x^3 + 6x - 3.

(a) The average cost in 2010 is $2088.82.

(b) A graph of the function g for the period 2006 to 2015 is: D. graph D.

(c) Assuming that the graph remains accurate, its shape suggest that: B. the average cost increases at a slower rate as time goes on.

Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:

g(x) = -1736.7 + 1661.4Inx

where:

x = 6 corresponds to the year 2006.

For the year 2011, the average cost (in dollars) is given by;

x = (2010 - 2006) + 6

x = 4 + 6

x = 10 years.

Next, we would substitute 10 for x in the function:

g(10) = -1736.7 + 1661.4In(10)

g(10) = $2088.82

Part b.

In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.

Part c.

Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.

Read more on exponential functions here: brainly.com/question/28246301

#SPJ1

Step-by-step explanation:

If we wanted to extend the discussion beyond what has been shared so far, an additional question we could ask is:

"What is the ratio of adult tickets to children's tickets sold in a day?"

This question would provide insight into the distribution of ticket sales between adults and children and help us understand the demand for different movie genres or screenings among the audience.

Answer:

31

Step-by-step explanation:

you add the hats to get the total number of hats then divide the answer by

No, it is much too high. Then the correct option is B.

An equation is a statement of equality between two expressions consisting of variables and/or numbers.

Given the question above, we need to find if the hats is to high or low.

Calculating the total numbers of hats made, we have

[tex]21 + 29 + 12 = 62 \ \text{hats}[/tex]

If Edna wants to split 62 hats evenly between two hospital, then each hospital will get

[tex]\dfrac{62}{2} = 31 \ \text{hats}[/tex]

Therefore, if Edna works out that each hospital gets 62 hats, No it is too high, as that is the total of all the hat that is available

Hence, the correct option is B.

Learn more on equations at:

https://brainly.com/question/29657983

Edna just joined a group that makes hats for babies in the hospital. Two weeks ago they made 21 hats. Last week they made 29 hats. This week they made 12 hats. All these hats will be split evenly between 2 nearby hospitals. Edna works out that's 62 hats for each hospital. Does that sound about right?

A. Yes

B. No, it is much too high

C. No, it is much too low

Answer:

a)

[tex] \frac{1}{( - 7)^{4} } [/tex]

Answer:

[tex](-7)^-^4=\frac{1}{(-7)^4}[/tex]

Step-by-step explanation:

The user aswati already wrote the correct answer, but I wanted to help explain why their answer is correct so that you'll understand.

According to the negative exponent rule, when a base (let's call it m) is raised to a negative exponent (let's call it n), we rewrite it as a fraction where the numerator is 1 and the denominator is the base raised to the same exponent turned positive.

Thus, the negative exponent rule is given as:

[tex]b^-^n=\frac{1}{b^n}[/tex]

Thus, [tex](-7)^-^4[/tex] becomes [tex]\frac{1}{(-7)^4}[/tex]

Answer:

Step-by-step explanation:

Answer:

i believe by creating radii of equal lengths.

Step-by-step explanation:

it gives a path to create an angle congruent to angle APB. The angle APB would have the same radii (BP and AP) and the same width as the congruent angle that would be created.

Wish you good luck.

Answer:

Step-by-step explanation:

60 minutes per hour
2.82gal *60mins = 169.2gal per hour.
303 gallons / 169.2 gph = about 1.7907 hours

a) Option a) 9 - 1/2 is equal to 17/2.

b) Option b) 27 - 2/3 is equal to 79/3.

a) The expression 9 - 1/2 can be simplified by finding a common denominator for the terms. The common denominator for 9 and 1/2 is 2.

Multiplying 9 by 2/2, we get:

9 * (2/2) = 18/2

So, the expression 9 - 1/2 can be simplified to:

18/2 - 1/2 = 17/2

Therefore, option a) 9 - 1/2 is equal to 17/2.

b) The expression 27 - 2/3 can be simplified in a similar manner by finding a common denominator for the terms. The common denominator for 27 and 2/3 is 3.

Multiplying 27 by 3/3, we get:

27 * (3/3) = 81/3

So, the expression 27 - 2/3 can be simplified to:

81/3 - 2/3 = 79/3

Therefore, option b) 27 - 2/3 is equal to 79/3.

for such more question on simplified

https://brainly.com/question/11680269

#SPJ8

Answer:

Step-by-step explanation:

Step 1.   Determine the dollar amount of the markup

          175 - 79 = 96

Step 2:   Divide the markup Amount by the Cost

          96/79 = 1.215

Step 3:   Multiply by 100 and add the % sign

           1.215 x 100 = 121.5%

The best measure of center of the data is (a) mean; because the data are close together

From the question, we have the dataset of 10 values

In the given dataset, we can see that there are no outliers present in the dataset

By definition, outliers are extreme values.

Since there are no outliers, it means that the mean is the best measure of center

This is because the mean is affected by the presence of outliers and since no outlier is present, we use the mean

From the list of options, we have the mean value to be 42.536

Hence, the true statement is (a)

Read more about mean and median at:

https://brainly.com/question/14532771

#SPJ1

Answer:

The consecutive interior angles are supplementary, so we have:

3x + 20 + 2x = 180

5x + 20 = 180

5x = 160, so x = 32

The area of the region bounded by the graphs of [tex]f(x) = x^3 + x^2 - 6x[/tex] and [tex]g(x) = 2x - x^2[/tex] is 69 1/3 square units.

To find the area of the region bounded by the graphs of the functions [tex]f(x) = x^3 + x^2 - 6x[/tex] and [tex]g(x) = 2x - x^2[/tex], we need to determine the points of intersection and evaluate the definite integral.

First, let's find the points of intersection by setting f(x) equal to g(x):

[tex]x^3 + x^2 - 6x = 2x - x^2[/tex]

Rearranging the equation, we get:

[tex]x^3 + 2x^2 - 8x = 0[/tex]

Factoring out an x, we have:

[tex]x(x^2 + 2x - 8) = 0[/tex]

Using the quadratic formula, we find the solutions for [tex]x^2 + 2x - 8 = 0[/tex] to be x = -4 and x = 2. Therefore, the points of intersection are (-4, -16) and (2, 4).

To calculate the area, we integrate the difference of the two functions within the bounds of -4 to 2:

Area = ∫[from -4 to 2] (f(x) - g(x)) dx

Evaluating the definite integral, we have:

Area = ∫[-4 to 2] [(x^3 + x^2 - 6x) - (2x - x^2)] dx

= ∫[-4 to 2] (x^3 + 2x^2 - 8x) dx

Integrating each term and evaluating the integral, we find:

Area = [1/4x^4 + 2/3x^3 - 4x^2] from -4 to 2

= [(1/4)(2)^4 + (2/3)(2)^3 - 4(2)^2] - [(1/4)(-4)^4 + (2/3)(-4)^3 - 4(-4)^2]

= [4/4 + 16/3 - 16] - [16/4 + (-128/3) - 64]

= 1/3 + 128/3 - 16 + 4 - 128/3 + 64

= 1/3 + 4 + 64

= 69 1/3

For more such questions on area

https://brainly.com/question/2607596

#SPJ8

Taking into account the definition of a system of linear equations, on Sunday 77 adult tickets were sold.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

So, the system of equations to be solved is

a + c= 131

9.60a + 5.20c= 1020

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable c from the first equation:

c= 131 -a

Substituting the expression in the second equation:

9.60a + 5.20×(131 -a)= 1020

Solving:

9.60a + 5.20×131 -5.20a= 1020

9.60a + 681.2 -5.20a= 1020

9.60a -5.20a= 1020 - 681.2

4.4a= 338.8

a= 338.8÷ 4.4

a= 77

In summary, 77 adult tickets were sold that day.

Learn more about system of equations:

brainly.com/question/14323743

#SPJ1

By analyzing the temperature-altitude relationship on a mountain, we can establish a linear model that describes how temperature changes with varying altitudes.

Step-by-step explanation:

a) Knowing the altitude and temperature data, we can use the formula for the slope of a line:

m = (y2 - y1) / (x2 - x1),

where (x1, y1) and (x2, y2) are two points on the line.

Using the altitude and temperature values provided:

(x1, y1) = (4800, 79) and (x2, y2) = (6400, 67),

we can calculate the slope:

m = (67 - 79) / (6400 - 4800)

= -12 / 1600

= -0.0075.

Now, to find the y-intercept (b), we can substitute one of the points (4800, 79) into the equation:

79 = (-0.0075)(4800) + b.

Solving for b, we have:

b = 79 + 0.0075(4800)

= 79 + 36

= 115.

Therefore, the linear model is T(x) = -0.0075x + 115.

b) The units of the slope (m) can be determined by looking at the units of the y values (temperature) and x values (altitude). In this case, the units of temperature are degrees, and the units of altitude are feet. Therefore, the units of the slope (m) are degrees per foot.

c) To find T(5800), we can substitute x = 5800 into the linear model:

T(5800) = -0.0075(5800) + 115

= -43.5 + 115

= 71.5.

Answers:

a) T(x) = -0.0075x + 115.

b) The units of the slope (m) can be determined by looking at the units of the y values (temperature) and x values (altitude). In this case, the units of temperature are degrees, and the units of altitude are feet. Therefore, the units of the slope (m) are degrees per foot.

c) 71.5 degrees.

Answer:

Step-by-step explanation:

To determine the percentage of adults who had 2 children, we need to first find the total number of adults questioned.

Looking at the bar graph, we can see that the bar representing 2 children has a height of 2.5. This means that 2.5 adults indicated having 2 children.

Let's assume the total number of adults questioned is "m". According to the bar graph, the sum of the heights of all the bars represents the total number of adults questioned.

From the bar graph, we can see the following:

The bar representing 4+ children has a height of 4.

The bar representing 3- children has a height of 3.5.

The bar representing 2- children has a height of 2.5.

The bar representing 1- children has a height of 1.5.

The bar representing 1 child has a height of 1.

The bar representing 0.5- children has a height of 0.5.

The bar representing 0 children has a height of 0.

To find the total number of adults questioned (m), we sum up the heights of all the bars:

m = 4 + 3.5 + 3 + 2.5 + 2 + 1.5 + 1 + 0.5 + 0

m = 18

Therefore, the total number of adults questioned is 18.

To find the percentage of adults who had 2 children, we divide the number of adults with 2 children (2.5) by the total number of adults questioned (18) and multiply by 100:

Percentage = (2.5 / 18) * 100

Percentage ≈ 13.9 (rounded to 1 decimal place)

Therefore, approximately 13.9% of the adults questioned had 2 children.

1. The missing value is b ≈ 10.

2. The missing value is a ≈ 12.

3. The missing value is b ≈ 13.

4. The missing value is b ≈ 10.

5. The missing value is a ≈ 4.

6. The missing value is b ≈ 5.

7. The missing value is a ≈ 11.

8. The missing value is b ≈ 6.

9. The missing value is b ≈ 20.

10. The missing value is a = 0.

Using the Pythagorean theorem, we can solve for b:

[tex]b^2 = c^2 - a^2b^2 = 10^2 - 4^2b^2 = 96b ≈ 10[/tex]

2. Using the Pythagorean theorem, we can solve for a:

[tex]a^2 = c^2 - b^2a^2 = 12^2 - 3^2a^2 = 135a ≈ 12[/tex]

3. Using the Pythagorean theorem, we can solve for b:

[tex]b^2 = c^2 - a^2b^2 = 14^2 - 6^2b^2 = 160b ≈ 13[/tex]

4. Using the Pythagorean theorem, we can solve for b:

[tex]b^2 = c^2 - a^2b^2 = 12^2 - 7^2b^2 = 95b ≈ 10[/tex]

5. Using the Pythagorean theorem, we can solve for a:

[tex]a^2 = c^2 - b^2a^2 = 10^2 - 9^2a^2 = 19a ≈ 4[/tex]

6. Using the Pythagorean theorem, we can solve for b:

[tex]b^2 = c^2 - a^2b^2 = 6^2 - 3^2b^2 = 27b ≈ 5[/tex]

7. Using the Pythagorean theorem, we can solve for a:

[tex]a^2 = c^2 - b^2a^2 = 14^2 - 11^2a^2 = 123a ≈ 11[/tex]

8. Using the Pythagorean theorem, we can solve for b:

[tex]b^2 = c^2 - a^2b^2 = 12^2 - 10^2b^2 = 44b ≈ 6[/tex]

9. Using the Pythagorean theorem, we can solve for b:

[tex]b^2 = c^2 - a^2b^2 = 25^2 - 15^2b^2 = 400b ≈ 20[/tex]

10. Using the Pythagorean theorem, we can solve for a:

[tex]a^2 = c^2 - b^2a^2 = 12^2 - 12^2a^2 = 0a = 0[/tex]

For such more questions on value

https://brainly.com/question/843074

#SPJ8

Answer:

Step-by-step explanation:

The cost of a single unit is given as follows:

$1.05.

El costo de un plátano es el seguiente:

$1.05.

The cost of a single unit is obtained applying the proportions in the context of the problem.

The cost of 22 units is of $23.10, hence the cost of a single unit is obtained dividing the total cost by the number of units, as follows:

23.1/22 = $1.05.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

99

Step-by-step explanation:

since the height is 9 and the base is 11 we use the formula BH=V

substitute 9x11 and get 99

Answer:

try (gauth math) could be helpful take screen shot and upload it it may be there or not hopefully it is

Answer:

W = V/(LH)

Step-by-step explanation:

All we are doing is isolating W. Since V=LWH, then dividing both sides by LH will put W by itself on the right-hand side, you have V/(LH) = W as your equation

The tangent line at that point is:

y = (-3/25)*x + 6/5

so m = -3/25, and b = 6/5

To find the slope at that point, we need to evaluate the derivative at that point.

y = 3/x

The derivative is:

y' = -3/x²

When x = 5, we have:

y' = -3/5² = -3/25

So that is the slope, m.

Now let's find the line.

The line must pass trhough the point (5, 3/5), then:

3/5 = (-3/25)*5 + b

3/5 = -3/5 + b

3/5 + 3/5 = b

6/5 = b

The equation of the line is:

y = (-3/25)*x + 6/5

Learn more about the tangent line:

https://brainly.com/question/30162650

#SPJ1

Answer:

Step-by-step explanation:

To find the maximum width of an aircraft seat that will accommodate 98% of all adult women, we need to determine the corresponding z-score for the 98th percentile of the normal distribution.

First, we find the z-score corresponding to the 98th percentile using a standard normal distribution table or calculator. The z-score for the 98th percentile is approximately 2.05.

Next, we use the z-score formula to find the corresponding value in the original distribution:

z = (x - μ) / σ

Solving for x (the maximum width of the aircraft seat):

x = z * σ + μ

Substituting the values given:

x = 2.05 * 4.36 + 37.6

x ≈ 45.98

Therefore, the maximum width of an aircraft seat that will accommodate 98% of all adult women is approximately 46 cm (rounded to one decimal place).

Answer:

Step-by-step explanation:

To calculate the future value of Francine's 401k account in 10 years, considering an annual contribution of $8,000 and an average annual return of 4%, we can use the formula for the future value of a series of regular payments, also known as an annuity.

The formula for the future value of an annuity is:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value

P is the payment amount

r is the interest rate per period

n is the number of periods

In this case:

P = $8,000 (annual contribution)

r = 4% or 0.04 (annual interest rate)

n = 10 (number of years)

Calculating the future value:

FV = $8,000 * [(1 + 0.04)^10 - 1] / 0.04

FV = $8,000 * (1.04^10 - 1) / 0.04

FV ≈ $8,000 * (1.480244 - 1) / 0.04

FV ≈ $8,000 * 0.480244 / 0.04

FV ≈ $8,000 * 12.0061

FV ≈ $96,048.80

Therefore, Francine will have approximately $96,048.80 in her 401k account in 10 years if the account averages a 4% annual return and she contributes $8,000 each year.

Common ratio of the geometric sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.

As we know that,

Common ratio of any G.P. is a constant number that is multiplied by the previous term to obtain the next term.

So, r= (n+1)th term / nth term

where r ⇒ common ratio

          (n+1)th term⇒ succeeding term

          nth term⇒ preceding term

According to the given question, r = (9/8) / (3/4)

                                                       r = (2/3)

We also know,

Any term of a G.P. [nth term] can be obtained by the formula:

Tₙ= a[tex]r^{n-1}[/tex]

where, Tₙ= nth term

            a= first term of G.P.

            r=common ratio

Since last term of the G.P. is given to be 8/81; putting this in the above formula will yield us the total number of terms.

   Tₙ= a[tex]r^{n-1}[/tex]

⇒ (8/81) = (9/8) x ([tex]2/3^{n-1}[/tex])

⇒ (64/729)= ([tex]2/3^{n-1}[/tex])

⇒[tex](2/3)^{6}[/tex] = ([tex]2/3^{n-1}[/tex])

⇒ n-1 = 6

⇒ n = 7

∴ The total number of terms in G.P. is 7.

Therefore, Common ratio of the sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.

Read more about Geometric Progression (G.P.):

https://brainly.com/question/29084446

The Common Ratio for this geometric sequence is 2/3 and the total number of terms in the sequence is 6.

The given mathematical sequence appears to be a geometric sequence, which is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the Common Ratio. In a geometric sequence, you can find the Common Ratio by dividing any term by the preceding term.  

So in this case, the second term (3/4) divided by the first term (9/8) equals 2/3. Therefore, the Common Ratio for this geometric sequence is 2/3.

To find the total number of terms in this sequence we use the formula for the nth term of a geometric sequence: a*n = a*r^(n-1), where a is the first term, r is the common ratio, and n is the number of terms. This gives us: 8/81 = (9/8)*(2/3)^(n-1). Solving this for n gives us n = 6. Therefore, the total number of terms in this sequence is 6.

https://brainly.com/question/34721734

#SPJ2