YOU guys can write a story or a situation that can be represented by the given equation.

4a + 5 = 12a - 11

Thank you :)​

a) The median number of hours per week these Year 12 students spend doing homework is 4 hours.

b) If 10% of Year 12 students spend more than k hours per week doing homework, then the value of k is 5.75 hours.

The median is a central value or a middle value in a distribution. The number of values in a dataset is an important factor that determines the calculation of the median. It is a value that cuts the data set into two equal parts.

The data set consists of 20 Year 12 students. Sort the data in ascending order (or descending order) and find the middle value. Then, use the formula for calculating the median. 

a)The number of hours per week the Year 12 students spend doing homework is given as:

3, 3, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4.5, 5, 5, 5.5, 6, 7, 8, 8.5

Arrange the data in ascending order:

3, 3, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4.5, 5, 5, 5.5, 6, 7, 8, 8.5

Now count the data, which gives us 20 numbers. The middle value is the 10th and the 11th numbers, which are both 4.

So the median of the number of hours per week Year 12 students spend doing homework is 4 hours.

b) If 10% of Year 12 students spend more than k hours per week doing homework, then the value of k can be found using the following formula:

100% - 10% = 90%

So, 90% of students study for k hours or less.

So, the value of k can be found using the median. The median value is 4 hours, and 90% of students are studying for k hours or less. Therefore, 10% of students study for more than k hours.

k = 10% more than the value of the 90th percentile value, which is given by: k = 5.5 + ((8-5.5)/10)*1 = 5.5 + 0.25 = 5.75 hours.

Therefore, 10% of Year 12 students spend more than 5.75 hours per week doing homework.

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Answer:

I am pretty sure it is c

Step-by-step explanation:

Answer:

17 is C

18 is add

19 is C

Step-by-step explanation:

Question 18 is worded a little weird.

so. (x^2)(x^3) = x^5, so you should add the expotents when you are multiplying them.

Answer:

\(\sqrt{73}\)units.

Step-by-step explanation:

We have given a pentagon ABCDE

We need to calculate its length

That means we have to find the distance of AD

So, coordinates of A(1,6) and D(4,-2)

Using distance formula:

Here,

On substituting the values we will get:

On simplification:

Hence, the length of AD is   units.

Answer:

  $21.45

Step-by-step explanation:

You want to know the amount of a 9.75% commission on $220.

The amount of the commission is the product of the commission rate and the sales amount to which it is applicable. A 9.75% commission on $220 will be ...

  9.75% × $220 = 0.0975 × $220 = $21.45

Nathan would earn a commission of $21.45 on the sale.

__

Additional comment

We know that a 10% commission can be found by moving the decimal point on the sale amount. A 10% commission on $220 will be $22.

The commission rate of 9.75% is 1/4% less than 10%. 1/4% can be found in two steps: find 1%, then find 1/4 of that.

As with 10%, the 1% amount can be found by moving the decimal point. 1% of $220 is $2.20. One-quarter of that will be $2.20/4 = $1.10/2 = $0.55.

This is the amount we must subtract from the 10% value to make it be 9.75%.

The 9.75% commission amount is $22.00 -0.55 = $21.45.

(The point of using a strategy like this is that you can do the math mentally.)

The total amount he would have at 69 is $343,347.81.

The formula that can be used to determine the future value of the deferred annuity is:

Future value = annuity factor x monthly deposit

Annuity factor = {[(1+r)^n] - 1} / r

Where:

Amount he would save every 6 months:

Future value : 900 x {[(1.0275^90) - 1] / 0.275}= $343,347.81

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Using for loop we can get the syntax in order to calculate this arithmetic series n is A = 0.9999.

An arithmetic collection is the sum of the phrases in an mathematics collection with a specific range of phrases. Following is a easy system for locating the sum: Formula 1: If S n represents the sum of an mathematics collection with phrases.

This system calls for the values of the primary and ultimate phrases and the range of phrases. Finite Sequence- Finite sequences have countable phrases and do now no longer cross as much as infinity. An instance of a finite mathematics collection is 2, 4, 6, 8. Infinite Sequence- Infinite arithmetic collection is the collection wherein phrases cross as much as infinity.

using while

A=0; n=1; while n<=10000     A=A+(1/(n*(n+1)));     n=n+1; end A

output

A =      0.9999

using  for loop

A=0; for n=1:10000     A=A+(1/(n*(n+1))); end A

output

A = 0.9999.

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Correct Question:

The following series can be written with a shorthand form of sigma notation (A). Use while syntax to calculate this arithmetic series:

1/(1x2) + 1/(2x3) + 1/(3x4) + ... + 1/(n x (n+1)) ......1

A = ∈ 1/(n x (n+1)); n=[1:10000]

The graph is a parabola with its touching the x-axis at (3,0)

A parabola is a curve where any point is at an equal distance from:

a fixed point (the focus ), and

a fixed straight line (the directrix )

its general equation is y = a(x – h)² + k or x = a(y – k)² +h. Here (h, k) denotes the vertex. y = a(x – h)2 + k is the regular form. x = a(y – k)2 +h is the sidewise form.

Given here (x-3)² + 4 = -4/9(x(x-6))

simplifying this we get

9(x²-6x+13) = -4 (x(x-6))

13x²-78x+117 = 0

(x-3)² = 0

thus it has a root at x=3

The graph is attached showing the parabola  touching the x-axis at (3,0)

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ANSWER

EXPLANATION

We want to identify the option that is completely factored.

For an expression to be completely factored, it means that there are no more common terms between the terms in the expression.

That means it can not be factored any further.

Therefore, the only correct option is:

Answer:

0.035 litros

Step-by-step explanation:

V = (pi)*(r^2)*(h)

V = pi * 2.25 * 5

= 35 cm^3

1 cm^3 = 0.001

(35)*(0.001)

= 0.035 litros

Answer:Percent Increase n the number of parts usually made = 80%

Step-by-step explanation:

Percent Increase = (Increase / Initial Number of parts made daily)  X 100/1

Initial Number of parts made daily = 45

Current number of parts ,made daily = 81

Percent Increase = 81-45/ 45 x 100

=36/45 x100/1

= 0.8 x 100

= 80%

Answer:

80 percent

Step-by-step explanation:

Answer:

Angela asked each student in her class about the height of the fence around their house. She made the histogram below to

represent the heights of each student's fence.

Height of Fence

16

14

12

10

Students

8

6

4

2

8

10

12

6

Feet

Which statement is true?

OA. The data distribution is both symmetric

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

(3, -2 )

To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

The domain of the function f(x) = ln(x-3) is x > 3, since the natural logarithm is undefined for non-positive values. The x-intercept occurs when f(x) = 0, so ln(x-3) = 0, which implies x - 3 = 1. Solving for x gives x = 4 as the x-intercept.

There are no vertical asymptotes for the function f(x) = ln(x-3) since the natural logarithm is defined for all positive values. However, the graph approaches negative infinity as x approaches 3 from the right, indicating a vertical asymptote at x = 3.

To sketch the graph of f(x) = ln(x-3), we start with the x-intercept at (4, 0). We can plot a few more points by choosing values of x greater than 4 and evaluating f(x) using a calculator.

As x approaches 3 from the right, the graph approaches the vertical asymptote at x = 3. The graph will have a horizontal shape, increasing slowly as x increases. Remember to label the axes and indicate the asymptote on the graph.

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Answer:

The answer is 2. sin2A-cosA. This can be seen by using the trigonometric identities sin2A=2sinAcosA and cos2A=cos2A-sin2A. The expression tanA-secA can then be simplified to sinA/cosA-1/cosA, which can be further simplified to (2sinAcosA-cos2A)/cosA, which can be further simplified to 2sinAcosA-cosA, which can finally be simplified to sin2A-cosA.

Answer:

B (x^2 +4x -2) + (x^2 -2x +4)= 2x^2 +2x +2

Step-by-step explanation:

The blue are positive and the red are negative

The top line is x^2 +4x -2

The second line is x^2 -2x +4

Adding together  

 x^2 +4x -2 + x^2 -2x +4= 2x^2 +2x +2

Answer:

$1,968

Step-by-step explanation:

If he paid $82 for 24 months when you mulitply 82 by 24 you get 1968. So the total computar was $1,968

The price of the computer if the discount is applied before the rebate is $1225. The composite function is (g.f)(x) = g(f(x))

(g.f)(x) = g(f(x))

f(1500) = 0.95(1500)

= 1425

g(1425) = 1425-20

= 1225

= $1225

Therefore, The price of the computer if the discount is applied before the rebate is $1225. The composite function is (g.f)(x) = g(f(x))

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The point at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j is (3/2, 7/2).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the points at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j, we need to find the gradient vector of the function and equate it to the given direction vector.

The gradient vector of the function f(x, y) is given by:

∇f(x, y) = [∂f/∂x, ∂f/∂y]

Taking partial derivatives of f(x, y) with respect to x and y:

∂f/∂x = 2x - 2

∂f/∂y = 2y - 6

Setting the gradient vector equal to the given direction vector i + j:

[2x - 2, 2y - 6] = [1, 1]

Equating the corresponding components, we have:

2x - 2 = 1

2y - 6 = 1

Solving these equations, we get:

2x = 3  =>  x = 3/2

2y = 7  =>  y = 7/2

Therefore, the point at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j is (3/2, 7/2).

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Step-by-step explanation:

1)  Total rectangle area =  W x H = 12 x 8 = 96 cm^2

 area of triangle (shaded portion) = 1/2 base * height = 1/2 * 7 x 8 = 28 cm^2

              Nonshaded portion = 96 - 28 cm^2 = 68 cm^2

          ratio shaded:nonshaded is then   28 : 68 = 7:17

2)   Look at the two middle triangles :  Height of each = 8 cm

       then reading across the diagram  height + base + height = 21 cm

            so base = 5 cm

   area of ONE triangle = 1/2 * base * height = 1/2 * 5 * 8 = 20 cm^2

        total area for FOUR of them  = 80 cm^2

Stu had quite a collection of baseball cards. One day he decided to give half of them to his brother Seth. Then he gave one-third of what he had left to a friend. Then he gave half of what was left to another friend. Stu now has 50 baseball cards. How many did he start with? It seems that I should work

let Stu have x cards

he gave half to seth

so he had x/2 cards

He had x/2 he gave 1/3 of x/2 to a friend

=x/6.

Now he had x/2 - x/6 = x/3 with him balance

1/2 of x/3 he gave to another friend =x/6

Balance he had was x/3 - x/6 = x/6

x/6 = 50

multiply by 6

x= 300

Answer:

Now he had x/2 - x/6 = x/3 with him balance

1/2 of x/3 he gave to another friend =x/6

Balance he had was x/3 - x/6 = x/6

x/6 = 50

multiply by 6

x= 300

Step-by-step explanation:

The power series representation for the function f(x) = x^2 + x^4 + 81 centered at x = 0 is: f(x) = 81 + x^2 + x^4

To find the power series representation, we start by expanding the function around x = 0. We notice that the function has three terms: x^2, x^4, and 81.

To express these terms as a power series, we need to calculate the coefficients for each power of x. The coefficient for x^2 is 1, the coefficient for x^4 is also 1, and the coefficient for the constant term (81) is 81.

Therefore, the power series representation of the function f(x) centered at x = 0 is:

f(x) = 81 + x^2 + x^4

The power series representation for the function f(x) = x^2 + x^4 + 81 centered at x = 0 is obtained by expressing each term as a power of x and determining the corresponding coefficients. In this case, the power series representation simplifies to f(x) = 81 + x^2 + x^4.

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Hi there,

I'm assuming you're looking for an equation that corresponds to the expression "the sum of twice b and 5".

The expression for twice b or two times b is 2b.

Recall how sum means the result of addition.

Therefore, where you're asked the sum of 2b and 5, you're simply looking to add both values together to achieve the sum.

Let the equation corresponding to this question equal to x.

Therefore, your final equation is:

\(2b+5=x\)

Hope that helps.

The answer is:

Work/explanation:

When we add two numbers together, we have the sum of two numbers.

First, twice b is two times b : \(\boldsymbol{2b}\)

So, the sum of twice b and 5 means we add 2b and 5:

Info related to the question

When we subtract two numbers, the result that we get is called the difference.

When we multiply two numbers, the result is the product.

When we divide two numbers, the result is the quotient.

After the additional registrations, there were 100 more voters registered as Democrats than as Republicans in the district by using the concept ratio.

Let's assume the initial number of registered Republicans in the district is 3x, and the initial number of registered Democrats is 5x.

According to the given information, the ratio of Republicans to Democrats before the additional registrations was 3/5. Therefore, we have the equation:

(3x + 600) / (5x + 500) = 3/5

To solve this equation, we can cross-multiply:

5(3x + 600) = 3(5x + 500)

15x + 3000 = 15x + 1500

By subtracting 15x from both sides, we get:

3000 = 1500

This equation is inconsistent and cannot be satisfied. This means there is no valid solution based on the given information. However, if we assume the ratio before the additional registrations was 5/3 instead of 3/5, we can solve the equation:

(3x + 600) / (5x + 500) = 5/3

Cross-multiplying again:

3(3x + 600) = 5(5x + 500)

9x + 1800 = 25x + 2500

Simplifying and rearranging the equation:

16x = 700

x = 700/16 ≈ 43.75

Now we can find the number of registered Democrats and Republicans after the additional registrations:

Democrats: 5x + 500 = 5(43.75) + 500 ≈ 319.75

Republicans: 3x + 600 = 3(43.75) + 600 ≈ 331.25

The difference between the number of registered Democrats and Republicans is:

319.75 - 331.25 ≈ -11.5

Since we're only interested in the absolute difference, the result is approximately 11.5 voters. Thus, there were approximately 11.5 more voters registered as Republicans than as Democrats after the additional registrations.

Based on the given information, there is no valid solution that satisfies the ratio of 3/5 after the additional registrations. However, if we assume the ratio was 5/3, then there were approximately 11.5 more voters registered as Republicans than as Democrats after the registrations.

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Based on the specific output of the ANOVA test, such as the F-statistic and p-value, further conclusions can be drawn about the differences in mean per customer purchase by the day of the week.

I can explain the general concept of an ANOVA test in this context. In your case, the fast food chain operation wants to determine if the mean per customer purchase differs by the day of the week. To test this hypothesis, they collected random samples of customers for each day of the week.

An ANOVA test is used to compare means across multiple groups or categories. In this scenario, the days of the week would be the different groups. The null hypothesis (H0) would state that there is no difference in the mean per customer purchase across the days of the week. The alternative hypothesis (Ha) would suggest that there are significant differences in the means.

The ANOVA test calculates the F-statistic, which compares the variability between the group means to the variability within the groups. If the F-statistic is large enough and the associated p-value is below a predetermined significance level (e.g., 0.05), then the null hypothesis is rejected, indicating that at least one group mean is significantly different from the others.

Based on the specific output of the ANOVA test, such as the F-statistic and p-value, further conclusions can be drawn about the differences in mean per customer purchase by the day of the week.

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The two adjacent rectangular corrals have dimensions of 50ft by 400/3 ft that will produce a maximum enclosed area.

The term "area" typically refers to the measure of the size or extent of a two-dimensional shape or region. It represents the amount of space enclosed within the boundaries of the shape.

The objective is to maximize the enclosed area of two adjacent rectangular corrals given 800 feet of fencing.

Based on the given problem, we have to consider the adjacent rectangular corral, which means it has a shared fence. Let's assume the shared side of the two adjacent rectangular corrals is 'x'.

Therefore, the total length of the fencing that is used for two adjacent rectangular corrals will be equal to;

2L + 3x = 800ft

Here, L is the length of each rectangular corral.

The enclosed area is given by A = L*W

Where;W = (800 - 2L - 3x) / 2 = 400 - L - (3/2)x

From the equation above, the value of W is a function of L and x.

Then we can use differentiation to find the maximum value of A.

So,Let's differentiate A with respect to L and equate it to 0 to find the value of L that maximizes the enclosed area.

We have; dA/dL = d/dL (L*(400 - L - (3/2)x))

= 400 - 2L - (3/2)x

= 0

On simplification, we have;

2L = 400 - (3/2)xL

= 200 - (3/4)x

Then, we substitute the value of L into the equation for W to get;

W = 400 - 200 + (3/4)x - (3/2)x

= 200 - (3/4)x

Thus, the maximum enclosed area is given by;

A = L*W = (200 - (3/4)x)*(200 - (3/4)x)

= 40000 - 300x + (9/16)x^2

Therefore, we need to differentiate A with respect to x and equate to zero to find the value of x that maximizes the enclosed area.

dA/dx = -300 + (9/8)x = 0

Solving for x, we have;

x = 800/3

Thus, the shared side of the two adjacent rectangular corrals should be 800/3 feet, and the dimensions that will produce a maximum enclosed area are;

L = 200 - (3/4)x = 200 - (3/4)(800/3) = 50ftW = 200 - (3/4)x = 200 - (3/4)(800/3) = 50ft

Therefore, the two adjacent rectangular corrals have dimensions of 50ft by 400/3 ft that will produce a maximum enclosed area.

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The composition of function is g ( x ) f ( x ) = 5x⁴ - 40x

Given data ,

Let the first function be g ( x ) = x³ - 8

Let the second function be h ( x ) = 5x

So, the composition of functions , g(x) x h(x) would be:

(x³ - 8) (5x)

We can distribute the multiplication to get:

5x ( x³ ) - 5x ( 8 )

On simplifying , we get

A = 5x⁴ - 40x

Hence , the result of the operation g(x) x h(x) is 5x⁴ - 40x

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The solution for R2 is:

R2 = (R1*R)/(R1+R)

We can begin by multiplying both sides of the equation by the product of R2 and R1 to eliminate the denominators:

1/R = 1/R1 + 1/R2

Multiplying both sides by R1*R2:

R1R2(1/R) = R1R2(1/R1) + R1R2(1/R2)

Simplifying:

R2 = (R1*R)/((R1+R))

Therefore, the solution for R2 is:

R2 = (R1*R)/(R1+R)

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