Carson is going on a work trip. He will get reimbursed for his expenses for
driving his own car. He will get a flat rate of 30, plus $1.25 per mile (m) he
drives. Write the equation representing the total reimbursement (R) he
should expect to see in his bank account when he comes back.z s

By applying the median concept, it can be concluded that the median of the series is 78.

The median of a series of numbers is the middle number when the numbers are arranged in ascending or descending order.

We have the following series of numbers 80,78,73,69,100.

This number can be arranged in ascending order as 69,73,78,80,100 or descending order as 100,80,78,73,69.

Since there are 5 numbers in the series, the middle number in this series is the 3rd number, which is 78.

Therefore, the median of the series is 78.

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Full question:

2. Find the median in this series of numbers: 80,78,73,69,100.

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

The system of equations is.

\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)

And the solutions are y = 50 and x = 10.

Let's define the two variables:

With the given information we can write two equations, then the system will be:

\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)

Now let's solve it.

We can isolate x on the first  to get:

\(\text{x} = 60 - \text{y}\)

Replace that in the other equation to get:

\(15\times(60 - \text{y}) + 10\text{y} = 800\)

\(-2\bold{y} = 900 - 800\)

\(-2\bold{y} = 100\)

\(\text{y} = \dfrac{100}{-2} = \bold{50}\)

Then \(\bold{x=10}\).

Therefore, the solutions are y = 50 and x = 10.

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We can use the given formula for the rate of change of the weight of the solid to estimate the amount of solid 1 second later.

If there is 6 grams of solid at time t, then f(t) = 6 g.

To estimate the amount of solid 1 second later, we can use the derivative formula:

f'(t) = −2f(t)(5+ f(t))

We want to estimate the value of f(t+1), which represents the weight of the solid 1 second later.

To do this, we can use Euler's method, which is an approximation method for solving differential equations.

Euler's method uses the formula:

f(t+1) ≈ f(t) + f'(t)Δt

where Δt is the time step (in minutes).

Since we want to estimate the amount of solid 1 second later, we can set Δt = 1 minute.

Plugging in the values for f(t) and f'(t), we get:

f(t+1) ≈ f(t) + f'(t)Δt

f(t+1) ≈ 6 - 2(6)(5+6)

f(t+1) ≈ -66

Therefore, the estimated weight of the solid 1 second later is -66 grams. However, this result does not make physical sense since weight cannot be negative.

It is possible that the given formula for f'(t) does not accurately describe the behavior of the solid, or that there was an error in the calculation.

or maybe im just bad at maths

if we notice the tickmarks on the triangle, we can see the all sides are equal, namely is an equilateral triangle, and if all sides are equal, then all interior angles are equal as well.

Let's recall that the sum of all interior angles in a triangle is 180°, now if we divide that by 3, that gives us 60, namely each angle in the equilateral triangle is 60°, that means

\(10x=60\implies x=\cfrac{60}{10}\implies \boxed{x=6} ~\hfill 12y=60\implies y=\cfrac{60}{12}\implies \boxed{y=5}\)

Answer:

3,280/38650 x 100% = 8%

The height of the kite from the ground when the angle is 50 degrees is 232 feet.

The study of the correlations between triangles' sides and angles is the focus of the mathematic branch known as trigonometry. To link the angles of a right triangle to the lengths of its sides, it makes use of trigonometric functions like sine, cosine, and tangent.

Numerous industries, including physics, engineering, and navigation, use trigonometry. It can be used, for instance, to determine a building's height or the separation between two locations on a map, as well as to examine how waves and oscillations behave.

To find the height of the kite above the ground we use the trigonometric identity of tangent.

Thus, we have:

tan(50°) = h/200

Now, using cross multiplication:

h = 200 tan(50°) ≈ 232 feet

Hence, the height of the kite from the ground when the angle is 50 degrees is 232 feet.

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The correct form for the quotient and remainder, written as partial fractions, is A + B/(x + 3) + C/(2x - 7).

Option A is the correct answer.

We have,

To express (8x³- 2x² - 67x - 24) / (2x² -x - 21) as partial fractions, we need to factor the denominator.

The denominator factors to (2x - 7)(x + 3).

Therefore, we can write:

(8x³ - 2x² - 67x - 24) / (2x² -x - 21) = A/(2x - 7) + B/(x + 3)

To find A and B, we need to solve for them using the method of equating coefficients.

Multiplying both sides by the denominator (2x - 7)(x + 3) gives:

8x³ - 2x² - 67x - 24 = A(x + 3) + B(2x - 7)

Expanding the right-hand side and collecting like terms gives:

8x³ - 2x² - 67x - 24 = (A + 2B)x + (3A - 7B)

We now have two equations with two unknowns:

A + 2B = 8

3A - 7B = -67

Solving for A and B, we get:

A = -19/5

B = 54/5

Thus,

The correct form for the quotient and remainder, written as partial fractions, is:

(8x³ - 2x² - 67x - 24) / (2x² -x - 21) = -19/5/(2x - 7) + 54/5/(x + 3)

A + B/(x + 3) + C/(2x - 7)

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Answer:

0.35

Step-by-step explanation:

Answer:

The decimal form of 28/80 is 0.35.

Answer:

Step-by-step explanation:

first step: 0.5 * x

second step: 3* (0.5x) = 1.5x

third step: (1.5x)^2

fourth step: (1.5x)^2 + 1 = 50

(1.5x)^2 + 1 = 50                    Subtract 1 from both sides

(1.5x)^2 = 49                          Take the square root of both sides

1.5x = sqrt(49)

1.5x = +/- 7

1.5x = +7

x = 7/1.5

x = 4.67

1.5x = - 7

x = - 7 / 1.5

x = - 4.67

Answer:

x = 8/3 and y = 32/3

Step-by-step explanation:

Add the two equations, getting -3y = -32, thus y = 32/3

Sub for y in first equation, getting 5x + 32/3 = 24

5x = 40/3

x = 8/3

The vector shown in figure is, (- 2, 1 , - 4)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The graph of the vectors is shown below.

Now, By definition of vectors the sign of coordinates are, ( - , + , - )

Thus, By options the coordinate of vectors are,

⇒ (- 2, 1 , - 4)

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Step-by-step explanation:

Let use the following rules to construct a polynomial,

Rule 1:

If r is a zero of some polynomial, f(x), then

\((x - r)\)

is a factor of the polynomial

We first know that one of our zeroes are real, which is 0.

So since r=0

\((x - 0) = x\)

is a factor

However, since the root ,0, has a multiplicty of 4, that basically means we have 0 as a root 4 times or basically we multiply the factor 4 times.

\(x \times x \times x \times x = x {}^{4} \)

This leads to an another rule:

If a polynomial has a zero, r that has a multiplicty of k,

we represent the factor as

\((x - r) {}^{k} \)

where k is all integers greater than 0.

So to reinforce myself, since 0 has a multiplicty of 4, we have

\((x - 0) {}^{4} = {x}^{4} \)

So our first factor is

\( {x}^{4} \)

Part 2: Complex Zeroes.

When dealing with complex zeroes, we must note this rule.

if (a+bi) is a zero of some polynomial, p then its conjugate (a-bi) is a factor as well.

So if 3-2i is a factor, then

3+2i is a factor as well.

Using Rule 1, our factors now become

\((x - (3 + 2i))\)

and

\((x - (3 - 2i))\)

So our factors are

\( {x}^{4} (x - (3 - 2i)(x - (3 + 2i))\)

To simplify use FOIL Method,

\( {x}^{4} ( {x}^{2} - x(3 + 2i) - x(3 - 2i) + 9 - 4 {i}^{2} )\)

\( {x}^{4} ( {x}^{2} - 6x + 13)\)

\( {x}^{6} - 6 {x}^{5} + 13 {x}^{4} \)

So our polynomial is

\( {x}^{6} - 6 {x}^{5} + 13 {x}^{4} \)

Answer:

Step-by-step explanation:

(180 - 127) / 2 = 26.5°

Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.

To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.

Rental: 1/5

Food: 1/10

Bank: 1/4

To find the fraction spent on miscellaneous:

Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)

Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40

Fraction spent on miscellaneous = 1 - 17/40 = 23/40

So, Mr. Marshal spent 23/40 of his salary on miscellaneous.

To find the amount spent on rental, we multiply the fraction spent on rental by his salary:

Amount spent on rental = (1/5) \(\times\) $8,400 = $1,680

Therefore, Mr. Marshal spent $1,680 on rental.

If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.

Fraction spent on the trip = (4/9) \(\times\) (23/40) = 92/360 = 23/90

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Answer:

35x48=1680

Step-by-step explanation:

1680

Answer:

0.1212...

Step-by-step explanation:

as you see there is another 12 repeating itself, so if on computer you show by:

ellipsis (…) or the repeat bar, when had writing.

The slope and intercept of the linear functions are written as follows

a. 2y + 3x = 10

slope = -3/2

intercept = 5

b. x + 2y = 6

slope = -1/2

intercept = 3

c. 3y + 12 = 5x

slope = 5/3

intercept = -4

6. The coordinates of common point in the linear function is

(-6, -14)

The slope and intercept of linear function is gotten by rewriting the equation to be in the form

y = mx + b

m = slope

b = intercept

a. 2y + 3x = 10

rearranging the equation

2y = -3x + 10

y = -3/2 x + 5

slope = -3/2

intercept = 5

b. x + 2y = 6

rearranging the equation

2y = -x + 6

y = -1/2 x + 3

slope = -1/2

intercept = 3

c. 3y + 12 = 5x

rearranging the equation

3y = 5x - 12

y = 5/3 x - 4

slope = 5/3

intercept = -4

6. The coordinates of common point in the linear function is solved using graph. From the graph the point is (-6, -14)

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Based on the provided information, we can say that Kibo has a volume of approximately 54.01 cubic meters.

To compare the volume of Kibo, Destiny, and Columbus, we need to calculate the volumes of each module.

The volume of a chamber can be determined utilizing the equation V = πr^2h, where r is the span and h is the level (or length for this situation) of the chamber.

For Kibo:

Radius (r) = 2.2 meters

Length (h) = 11.2 meters

V_kibo = π * (2.2^2) * 11.2

      = 4.84 * 11.2

      ≈ 54.01 cubic meters

For Destiny and Columbus, we would need their respective dimensions to calculate their volumes using the same formula.

Destiny is a U.S. laboratory module on the International Space Station. It is a multi-sided module, so we would need the measurements of each side to calculate its volume.

Columbus is a European laboratory module, which is also multi-sided.

Without the specific dimensions of Destiny and Columbus, we cannot accurately compare their volumes to Kibo. However, based on the provided information, we can say that Kibo has a volume of approximately 54.01 cubic meters.

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Answer:

y=1x-7

Step-by-step explanation:

Answer:

\( {4a}^{4} \times {7a}^{5} \\ \\ = (4 \times 7)( {a}^{4} \times {a}^{5} ) \\ \\ = 28( {a}^{4} \times {a}^{5} )\)

from law of indices:

\( {n}^{x} \times {n}^{y} = {n}^{(x + y)} \)

therefore:

\( = 28 \{ {a}^{(4 + 5)} \} \\ \\ = 28 {a}^{9} \)

Answer:

28a^9

Step-by-step explanation:

The only rule to follow is

Divide dividend by divisor and the mention the quotient and things left after remains in place of remainder

Here is a sample

\(\sf\Large\qquad\quad16\\ \begin{array}{cc} \cline{2 - 2}\sf 20 )&\sf \ 327\\&\sf - 20 \downarrow\\ \cline{2-2}& \sf \ \ \ \ 127\\ &\sf \ - 120 \\ \cline{2-2} & \sf \ \007 \\ \cline{2-2} \end{array}\\\\\\ \sf Divisor \rightarrow 20 \\ \\ \sf Quotient \rightarrow 16\\\\ \sf Remainder \rightarrow 7\)

Answer:

The probability that all four received a raised when they asked for one is 0.370.

Step-by-step explanation:

Let the random variable X represent the number of business executives who received a pay raise when they asked for one.

The probability that a business executives received a pay raise when they asked for one is, p = 0.78.

A random sample of n = 4 executives was selected.

The events of any executive receiving a pay raise when they asked for one is independent of the others.

The random variable X follows a Binomial distribution with parameters n = 4 and p = 0.78.

The probability mass function of X is:

\(P(X=x)={4\choose x}\ (0.78)^{x}\ (1-0.78)^{4-x};\ x=0,1,2,3...\)

Compute the probability that all four received a raised when they asked for one as follows:

\(P(X=4)={4\choose 4}\ (0.78)^{4}\ (1-0.78)^{4-4}\)

                \(=1\times 0.37015056\times 1\\\\=0.37015056\\\\\apporx 0.370\)

Thus, the probability that all four received a raised when they asked for one is 0.370.

Answer:

10 * $1 = $ 10

$10 / 10 = 1

one 10$ bill

pretty simple

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

it's basically asking what is the y value that corresponded to x = 2

that value is 3.

Answer:

"Type II error" is the right answer.

Step-by-step explanation:

Thus the above is the right answer.

Answer:

2 or 3 I think

I gessssssssssing

Answer:1,708,984,375

Step-by-step explanation: Dont feel like doin those numbers but that's the answer :)

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

The nth term of a geometric sequence is given as,

nth term = a \(r^{n-1}\)

The 13th term of the geometric sequence is 39062500.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Example:

2, 4, 8, 16, 32 is a geometric sequence.

We have,

7, -35, 175

a = 7

The common difference.

= -35 / 7

= -5

Now,

The nth term of a geometric sequence is given as,

nth term = a \(r^{n-1}\)

Now,

n = 13

13th term:

= 7 x \((-5)^{13-1}\)

= 7 x \((-5)^{12}\)

= 39062500

Thus,

The 13th term of the geometric sequence is 39062500.

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