When the quotient of a long division problem has a remainder, it means the
( divisor / dividend ) does not go into the
(divisor / dividend ) evenly.

(d) The ordered pair solution of this equation 3x/4  + 2y = 15 is (4, 6).

(e) The ordered pair solution of this equation xy ≥ 6 is (-2, -4).

The ordered pair solution of the equations is calculated by simplifying the equations as follows;

The given equations;

(d) 3x/4  + 2y = 15

(e) xy ≥ 6

(d) The solution of this equation 3x/4  + 2y = 15 is calculated as follows;

let the value of x = 4 and the value of y = 6

so we will substitute this value into the equation and check if it will be equal to 15.

(4, 6) = (3 x 4 )/4  +  2(6)

(4, 6) = 3  +  12

(4, 6) = 15

(e) The solution of this equation xy ≥ 6 is calculated as follows;

let x = -2, and let y = - 4

(-2, -4) = (-2)(-4) = 8

8 ≥ 6 (this solution is true)

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8t + 7 means 8 times a number plus 7.

Answer:

118ft

Step-by-step explanation:

dont ask how i got it i just got the answer from my teacher but they didnt show me the work. ur welcome

Answer:

D

Step-by-step explanation:

Trica's survey of students in her computer class about their computer usage may not support a valid inference regarding the time spent on computers by students in her entire school.

The survey results may lack validity due to several reasons. First, the sample size may be limited to only Trica's computer class, which could introduce selection bias and make it unrepresentative of the entire school population. Representativeness is crucial for generalizing the findings to the broader student body accurately.

Second, the self-reported nature of the survey introduces the potential for self-reporting bias, where students may provide inaccurate or exaggerated information about their computer usage.

This could lead to unreliable results and inaccurate inferences. Additionally, the survey design and measurement techniques might not be rigorous enough to capture a comprehensive understanding of computer usage, lacking standardization and reliable measurement tools.

To obtain valid inferences, it would be necessary to employ random sampling techniques to ensure representativeness, include students from various classes or grades, verify the accuracy of reported data through cross-referencing or observation, and utilize validated measurement instruments.

By addressing these limitations, Trica can enhance the validity of the survey results and make more robust inferences about the time spent on computers by students in her school.

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The component form of the vectors shown is (-6, -5)

In order to determine the component of the vectors shown, we will subtract the coordinate points from both each other.

Given the vector coordinates on the line. as (-5, -3) and (1, 2). Take the difference;

Difference = [(-5-1), (-3-2])

Difference = (-6, -5)

Hence the  component form of the vectors shown is (-6, -5)

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The area of the regular octagon is approximately 408.5 square cm.

To find the area of a regular octagon with an apothem of 11.1 cm and each side measuring 9.2 cm, follow these steps:

1. Recall that the area (A) of a regular polygon can be calculated using the formula: A = (1/2) * perimeter (P) * apothem (a).

2. Find the perimeter of the octagon by multiplying the side length by the number of sides: P = 9.2 cm * 8 = 73.6 cm.

3. Substitute the values for the perimeter and apothem into the formula: A = (1/2) * 73.6 cm * 11.1 cm.

4. Calculate the area: A ≈ 408.48 square cm.

To the nearest tenth, the area of the regular octagon is approximately 408.5 square cm.

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The Vector functions are :

a) r(t) = (1-t) <2, 3> + t <-1, 5>

b)r(t) = (1-t) <0, 4> + t <-2, 0>

c) x = 3 cos(t), y = 3 sin(t)

(a) The line segment from (2, 3) to (-1,5):

To draw the line segment from (2, 3) to (-1, 5), we first plot the two points on the Cartesian plane:

        (2, 3)

           *

          /

         /

        /  

(-1, 5) *

The direction of motion along this line segment is from (2, 3) to (-1, 5), so we can write a vector function that starts at (2, 3) and ends at (-1, 5) by using the position vector:

r(t) = (1-t) <2, 3> + t <-1, 5>

where t ranges from 0 to 1. This vector function starts at (2, 3) when t = 0 and ends at (-1, 5) when t = 1.

(b) The part of y=4 – x^2 from (0,4) to (-2,0):

To draw the part of y = 4 - x^2 from (0, 4) to (-2, 0), we first plot the two points on the Cartesian plane:

   (0, 4)    *

             / \

            /   \

           /     \

(-2, 0) *  /       \

          *--------*

The direction of motion along this curve is from (0, 4) to (-2, 0), so we can write a vector function that starts at (0, 4) and ends at (-2, 0) by using the position vector:

r(t) = (1-t) <0, 4> + t <-2, 0>

where t ranges from 0 to 1. This vector function starts at (0, 4) when t = 0 and ends at (-2, 0) when t = 1.

(c) The part of the circle x^2 + y^2 = 9 from (3, 0) to (0, -3), moving counter-clockwise:

To draw the part of the circle x^2 + y^2 = 9 from (3, 0) to (0, -3), moving counter-clockwise, we first plot the two points on the Cartesian plane:

markdown

         * (3, 0)

       / | \

     /   |   \

    *----*----*

(0, -3)

We know that the equation of the circle is x^2 + y^2 = 9, so we can parameterize this curve by writing x and y in terms of cos(t) and sin(t):

x = 3 cos(t)

y = 3 sin(t)

where t ranges from π/2 to π. This vector function starts at (3, 0) when t = π/2 and ends at (0, -3) when t = π. Since we want to move counter-clockwise along the circle, we start at the point (3, 0) and move towards (0, -3) as t increases.

In mathematics, we use vector functions to describe curves in two- or three-dimensional space. Vector functions are functions that map a parameter t to a vector in space, allowing us to describe the position and movement of an object over time.

In this problem, we are asked to draw three different curves in the plane and write vector functions that describe each curve.

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Therefore, the standard error is 6 / sqrt(30) ≈ 1.0959 mg/l.

Based on the given information, the mean concentration of sodium in the drinking water is 18.3 mg/l and the standard deviation is 6 mg/l. The water department selects a simple random sample of 30 water specimens and computes the mean concentration across these specimens.

To answer the question using the distributions tool, you should set the mean and standard deviation parameters on the tool to the expected mean and standard error for the distribution of sample mean concentrations.

The expected mean for the distribution of sample mean concentrations is the same as the mean concentration of sodium in the drinking water, which is 18.3 mg/l.

The standard error for the distribution of sample mean concentrations can be calculated by dividing the standard deviation of the population by the square root of the sample size. In this case, the standard deviation is 6 mg/l and the sample size is 30.

You can use these values to set the mean and standard deviation parameters on the distributions tool.

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Answer:

6 ride passes

4 additional items

Step-by-step explanation:

11.

\(T=5.50R+10*7.25\)

\(for T=105.50\)

\(R=6\)

While

T is total cost.

R number of ride passes.

12.

\(T=1.25n+4.75\)

\(for T=9.75\)

\(n=4\)

While

T is total paid.

n is number of addition items.

Answer:

18

Step-by-step explanation:

3x + 2 = 6x - 4

6 = 3x

2 = x

3(2) + 2 + 6(2) - 4 + 2

8 + 8 + 2

18

Answer: HG = CD.

Step-by-step explanation: If you tilt the second triangle so it's flat like the first triangle, you can see that HG is equal to CD.

Answer:

Surface area of the triangular prism = 186.984 feet²

Step-by-step explanation:

Surface area of the triangular prism is given by the expression,

Surface area = (Perimeter of the triangular base)×Height + Area of the triangular bases

Perimeter of the triangular base = (9.8 + 8.5 + 6.2)

                                                      = 24.5 ft

Height of the prism = 5.5 ft

Area of the triangular base = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                                             = \(\frac{1}{2}(9.8)(5.33)\)

                                             = 26.117 square feet

Surface area of the prism = (24.5 × 5.5) + (26.117 × 2)

                                           = 134.75 + 52.234

                                           = 186.984 square feet

Answer:

\(y=\frac{5}{4}x-8\)

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the slope (m)

\(5x - 4y = 36\)

Rearrange the given equation into y-intercept form (this will help us determine m)

Subtract 5x from both sides

\(5x - 4y-5x = -5x+36\\-4y=-5x+36\)

Divide both sides by -4

\(y=\frac{5}{4} x-9\)

Now, we can see that \(\frac{5}{4}\) is in the place of m, making it the slope. Because parallel lines have the same slopes, the slope of the line we're solving for is therefore \(\frac{5}{4}\). Plug this into \(y=mx+b\):

\(y=\frac{5}{4}x+b\)

2) Determine the y-intercept (b)

\(y=\frac{5}{4}x+b\)

Plug in the given point (8,2) and solve for b

\(2=10+b\)

Subtract 10 from both sides

\(2-10=10+b-10\\-8=b\)

Therefore, the y-intercept is -8. Plug this back into \(y=\frac{5}{4}x+b\):

\(y=\frac{5}{4}x-8\)

I hope this helps!

$444

---

364+80 = 444

--- hope this helped

Answer:

364+80=444 es lo que daría la suma de esos dos valores

Darwin's geometric ratio of increase pertains specifically to the growth rate of populations in biological organisms. According to Darwin's theory of evolution, populations have the potential to increase exponentially over time if certain conditions are met. The geometric ratio of increase, often denoted as "r" or the intrinsic rate of natural increase, represents the factor by which a population multiplies during each reproductive cycle or generation.

In the context of natural selection, individuals with higher reproductive rates (higher r-values) have a greater chance of passing on their genetic traits to the next generation. Over time, this can lead to significant population growth and evolutionary changes within a species. However, the geometric ratio of increase is limited by various factors, such as availability of resources, competition, predation, and environmental constraints, which can result in a balance between population growth and environmental carrying capacity.

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Answer:

Step-by-step explanation:

6\(\sqrt{5\\\)

\(\sqrt{5*36}\)

\(\sqrt{180}\)

If you think about it logically, how can you take 6 out? So there was a number 36 under the root, and because of that there is a possibility to take it out, because 6 squared is 36

Answer:

it is the first one I am sure of it

Answer:

782

Step-by-step explanation:

Since it's asking for the before game miles youd have to take he total yards.

(871)

The you wanna take the total yards ran from that one game.

(89)

Then just subtract by the number of yards total and the number of yards ran in that one game.

871-89=782

The horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

Given that:-

The horizontal distance will be calculated by applying the angle property in the right angle triangle.

tan45  =  (  P  /  B  )

B  =  P  /  tan45

B  =  P                                 Since ( tan45 =1 )

B  =  1140 feet.

Therefore the horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.

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The initial 50 miles distance from the lighthouse and the N 30° W and N 40° W bearing of the ship before and after traveling due east, using the law of sines, indicates.

The law of sines states that in a triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for each of the three sides of the triangle.

The distance of the ship from the lighthouse = 50 miles

Bearing of the lighthouse from the ship = N 30° W

The direction in which the ship travels = due east

The new bearing to the lighthouse = N 40° W

In the triangle formed by the initial and new locations of the ship and the lighthouse, the interior angles, A, B, C are;

m∠A = 30° + 90° = 120°

m∠B = 90° - 40° = 50°

Therefore; m∠C = 180° - (120° + 50°) = 10°

Angle opposite the initial distance of the ship from the lighthouse = ∠B = 50°

The angle opposite the new distance of the ship from the lighthouse = m∠A = 120°

The law of sines indicate that we have;

\(\dfrac{50}{sin(50^{\circ})} = \dfrac{New \, distance}{sin(120^{\circ})}\)

50 × sin(120°) = The new distance of the lighthouse × sin(50°)

The new distance of the lighthouse = 50 × sin(120°)/(sin(50°)) ≈ 56.53

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To calculate the amount of money you will have in the account after 3 years with an interest rate of 6% per year, we can use the formula for compound interest:

A = P(1 + r)^n

Where:

A = the final amount

P = the principal amount (initial deposit)

r = the interest rate per period (in decimal form)

n = the number of periods

In this case:

P = $3,875

r = 6% per year, or 0.06 (in decimal form)

n = 3 years

Substituting the values into the formula:

A = 3,875(1 + 0.06)^3

Calculating:

A = 3,875(1.06)^3

A = 3,875(1.191016)

A ≈ 4,614.76

After rounding to two decimal places, you will have approximately $4,614.76 in the account after 3 years.

The system of equations can be graphed using a graphing utility to find their intersection point, which represents the solution to the system.

To graph the system of equations, we first need to rearrange them in slope-intercept form, which is y = mx + b. For the first equation, we can solve for y by subtracting 2x from both sides and then dividing by -4, which gives us y = -0.5x + (5/4). For the second equation, we can solve for y by dividing both sides by -1.2 and then simplifying, which gives us y = -0.5x + (5/8). We can then enter these equations into a graphing utility, such as Desmos or GeoGebra, to plot their graphs. The intersection point of the two graphs represents the solution to the system. In this case, the intersection point is (4.4, 1.3), which means that x = 4.4 and y = 1.3 is the solution to the system of equations.

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Answer:

4m x 11m

Step-by-step explanation:

4 is your width. 11 is your length.

4 x 4=16 > 11

The net income for Griffin's Goat Farm, Inc., was \(\$184,340\).

The operating cash flow (OCF) for Kerber's Tennis Shop, we can use the following formula:

\(OCF = EBIT + Depreciation - Taxes + \triangle Working Capital\)

where EBIT is earnings before interest and taxes.

Calculate EBIT by subtracting interest expense from operating income:

EBIT = Operating Income - Interest Expense

We do not have the information for operating income, but we can use the fact that interest expense was. \(\$165,000\) to calculate EBIT.

EBIT = Interest Expense / (1 - Tax Rate)

= \(\$165,000 / (1 - 0)\)

= \(\$165,000\)

Calculate the change in working capital (Δ Working Capital). We are told that the company reduced its net working capital investment by \(\$69,000\), which means that working capital increased by  \(\$69,000\).

Therefore:

\(\triangle Working Capital = \$69,000\)

Now, we can calculate OCF:

OCF = EBIT + Depreciation - Taxes + Δ Working Capital

=\(\$165,000 + 0 - 0 +\ $69,000\)

=\(\$234,000\)

Therefore, the firm’s 2018 operating cash flow (OCF) was \(\$234,000\) .

To calculate the net income for Griffin's Goat Farm, we can use the following formula:

Net Income = EBIT - Interest Expense - Taxes

where EBIT is earnings before interest and taxes. We can calculate EBIT as:

EBIT = Sales - Costs - Depreciation

= \(\$686,000 - \$332,000 - \$65,000\)

=\(\$289,000\)

Next, we need to calculate taxes. We are given a tax rate of 24%, so:

Taxes = Tax Rate x (EBIT - Depreciation)

= \(0.24 \times (\$289,000 - \$65,000)= \$56,160\)

Now, we can calculate net income:

Net Income = EBIT - Interest Expense - Taxes

= \(\$289,000 - \$48,500 - \$56,160= \$184,340\)

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Answer:

1100. because the 4% and 44 are the same thing 4% goes into 100% 25 times then 44 times 25 is 1100

The following are solutions to the given problems given f(x)=x²- 5x+7 and g(x)=3x² + 4x - 2;

(f- g)(x) = -2x² - 9x + 9

(g-f)(x) = 2x² + 9x - 9

(f + g)(x) = 4 x² - x + 5

A function can be defined as a relation between a set of inputs having one output each. In other words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain (range). A function is generally denoted by f(x) where x is the input.

The general mathematical representation of a function is y = f(x).

f(x)=x²- 5x+7

g(x)=3x² + 4x - 2

(f- g)(x) = x²- 5x+7 - (3x² + 4x - 2)

(f- g)(x) = x²- 5x+7 - 3x² - 4x + 2

(f- g)(x) = -2x² - 9x + 9

(g-f)(x) = 3x² + 4x - 2 - (x²- 5x+7)

(g-f)(x) = 3x² + 4x - 2 - x² + 5x - 7

(g-f)(x) = 2x² + 9x - 9

(f + g)(x) = x²- 5x+7 + 3x² + 4x - 2

(f + g)(x) = 4 x² - x + 5

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