HELP PLEASE I JUST CANT DO IT ANYMORE!! The table shows the monthly salaries for employees at a company.



a. Find the mean, median, and mode of the data.

The mean is $
. The median is $
. The mode is $
.


Question 2
b. Each employee receives a 5% raise. Find the mean, median, and mode of the data with the raise. How does this increase affect the mean, median, and mode of the data? Round to the nearest cent.

The mean is $
. The median is $
. The mode is $
.

The raise increases the mean, median, and mode by
%.


Question 3
c. Use the original monthly salaries to calculate the annual salaries. Find the mean, median, and mode of the annual salaries. How are these values related to the mean, median, and mode of the monthly salaries?

The mean is $
. The median is $
. The mode is $
.

These values are
times the mean median, and mode of the monthly salaries.

Answer:

A(t) = 50(0.97)^t

Step-by-step explanation:

3% = 0.03

1 - .03 = 0.97

A(t) = 50(1 - 0.03)^t

A(t) = 50(0.97)^t

Kayla would have approximately $554.93 in the account after 12 years, rounded to the nearest dollar.

Learn more about To calculate the amount Kayla would have in the account after 12 years, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

Where:

A = the final amount

P = the principal amount (initial deposit)

r = the annual interest rate (in decimal form)

n = the number of times interest is compounded per year

t = the number of years

In this case, Kayla deposits $380 every quarter, so the principal amount (P) is $380. The annual interest rate (r) is 3.3% or 0.033 as a decimal. The interest is compounded quarterly, so n = 4. The number of years (t) is 12.

Plugging these values into the formula:

A = $380 * (1 + 0.033/4)^(4*12)

Calculating the exponent:

A = $380 * (1 + 0.00825)^(48)

A = $380 * (1.00825)^(48)

Using a calculator, we can calculate the value of (1.00825)^(48) ≈ 1.464096

A = $380 * 1.464096

A ≈ $554.93

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Answer:

40

Step-by-step explanation:

I hope you know the basics of algebra.

Divide becomes multiply. Add becomes subtract...

The approximate z-score that corresponds to a right tail area of is standard normal distribution

In a right-tailed scenario, we are interested in finding the z-score that corresponds to a specific area or probability in the right tail of the standard normal distribution. This area represents the probability of obtaining a z-score greater than a certain value.

To determine the z-score corresponding to a right tail area, we can use either a z-table or statistical software. A z-table lists the cumulative probabilities or areas under the standard normal distribution curve. These tables provide the area to the left of a given z-score. However, since we are interested in the right tail, we need to find the complementary area or subtract the given area from 1.

For example, if the right tail area is 0.05, we need to find the z-score that corresponds to an area of 0.95 (1 - 0.05). We can use a z-table to find the z-score that has an area of 0.95 to its left. By looking up this area in the z-table, we can find the corresponding z-score.

Alternatively, statistical software or online calculators can also provide us with the z-score for a given right tail area. These tools allow you to input the area or probability directly and retrieve the corresponding z-score.

It's important to note that finding the exact z-score can be challenging because z-tables usually provide values rounded to two decimal places. However, these approximations are typically sufficient for most practical purposes.

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Answer:

4 dollars per hour

Step-by-step explanation:

Answer:

Move all terms that don't contain  x  to the right side and solve.

x =  5 /3 −  4 y /3

Answer:4y+3x=5

Step 1: Add -4y to both sides.

3x+4y+−4y=5+−4y

3x=−4y+5

Step 2: Divide both sides by 3.

3x

3

=

−4y+5

3

x=

−4

3

y+

5

3

Step-by-step explanation:

The equation of the given circle is (x - 2)² + (y - 4)² = 36. In general form, the equation of a circle can be written as x² + y² + Dx + Ey + F = 0, the equation of the circle in general form is x² + y² - 4x - 8y + 36 = 0.

Expanding the equation, we get (x² - 4x + 4) + (y² - 8y + 16) = 36.

Rearranging the terms, we have x² + y² - 4x - 8y = 16.

To complete the square for x, we add (4/2)² = 4 to both sides of the equation, resulting in x² - 4x + 4 + y² - 8y = 16 + 4.

Similarly, to complete the square for y, we add (8/2)² = 16 to both sides of the equation, giving us x² - 4x + 4 + y² - 8y + 16 = 16 + 4 + 16.

Simplifying further, we obtain (x - 2)² + (y - 4)² = 36.

Therefore, the equation of the circle in general form is x² + y² - 4x - 8y + 36 = 0.

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The measure of side LJ would be 88 + 11 = 99. Round to the nearest tenth, LJ is 99.0.

To find the measure of side LJ, we need to use the concept of similarity between triangles.

If two triangles are similar, then the ratio of their corresponding side lengths is equal.

In this case, triangle GHI is similar to triangle JKL.

Let's assume the measure of side GH is x.

Then, the measure of side GI would be 8x and the measure of side HI would be 41x.

The measure of side JK would be x and the measure of side KL would be 8x.

By using the ratios of the side lengths,

we can set up an equation:

x/8x = JK/KL

Solving for x, we get x = 11. So, the measure of side KL is

8x = 8 * 11 = 88

The measure of side LJ would be 88 + 11 = 99. Round to the nearest tenth, LJ is 99.0.

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Step 1: Start by drawing a circle.

Step 2: On the circle, choose any point. Label its endpoints A and C.

Step 3: Set the width of the compass larger than the radius of the circle. Draw arcs centered at A and C on each side of the diameter.

Step 4: Connect the arcs and the center of the circle. Label the points of intersection with the circle as B and D.

Step 5: Draw chords AB, BC, CD, and DA.

A circle is a fundamental geometric shape in mathematics. It is a two-dimensional figure that consists of all points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is known as the radius.

A circle is defined by its center and radius. The center is usually represented by the coordinates (h, k), where 'h' represents the horizontal position and 'k' represents the vertical position. The radius is the distance between the center and any point on the circle.

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Answer:

input the formula of acceleration and the the answer will be

8.928571429

The plane and ship are 7.5 km apart.

Given that the displacement vector from plane to ship is

−3.078i−6.47j+2.20k km

(b) How far apart are the plane and ship

To determine the magnitude of the displacement vector, we will use the distance formula.

Let the components of the displacement vector be:

A = -3.078, B = -6.47, C = 2.20

∴ The magnitude of the displacement vector is

|d| = √(A² + B² + C²)|d|

= √((-3.078)² + (-6.47)² + (2.20)²)|d|

= √9.47 + 41.98 + 4.84|d|

= √56.29|d|

= 7.5 km.

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Rounding to the nearest degree, we get x = 53 degrees.

We can use the inverse sine function (sin⁻¹) to find the value of x.

From the sine rule,

sin(x) = opposite/hypotenuse

\(sin(x) = 7/9\\x = sin^{-1}(7/9)\)

Using a calculator, we find that x is approximately 53.13 degrees. Rounding to the nearest degree, we get x = 53 degrees.

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the standard meridian for vladivostok is 120 degrees east

The standard meridian for Vladivostok would be the line of longitude that corresponds to the local mean time of the city. To determine the standard meridian, you need to consider the time zone of Vladivostok.

Vladivostok is located in the UTC+10 time zone. Each time zone typically spans 15 degrees of longitude. Since Vladivostok has a longitude of 132 degrees east, you can calculate the standard meridian by finding the closest multiple of 15 degrees within the range of longitudes for that time zone.

To do this, you can divide 132 by 15 and round down to the nearest whole number. In this case, 132 divided by 15 equals 8.8, so rounding down gives us 8.
Therefore, the standard meridian for Vladivostok would be 8 times 15 degrees east, which is 120 degrees east.

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Answer: .416666667

Step-by-step explanation: Take 80 and divide it by 192.0= .416666667

The travel time x is 41.162 min such that 17.36% of the 60 days have a travel time that is at least x.

We have to determine the travel time such that 17.36% of the 60 days have a travel time that is at least.

Total work days to work = 60 days

The travel mean time = 35.6

Standard deviation = 10.3

For normal distribution,

P(X < A) = P(Z < (A - mean)/standard deviation)

P(X > x) = 0.2946

P(X < x) = 1 - 0.2946 = 0.7054

P(Z < (x - 35.6)/10.3) = 0.7054

Take the z value that corresponds to 0.7054 in the table of the standard normal distribution.

(x - 35.6)/10.3 = 0.54

x = 41.162 min

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The probability that you will win three rounds in a row is 1/8, or 12.5%.

The probability of winning a single round of ring toss is 50%. To calculate the probability of winning three rounds in a row, we must multiply the probability of winning each round together. So, the equation would be 0.5 x 0.5 x 0.5 which equals 0.125, or 12.5%. This means that the probability of winning three rounds in a row is 1/8, or 12.5%.

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The angle based on the diameter is always right

Then <ABC=90 and ∠BAC=∠ACB=45° ;  and ∠BCD=180-45=135 then                x=(180-135):2=22,5°

Answer:

x^2 - x + 2.

Step-by-step explanation:

Answer:

x² - x + 2

Explanation

Work out using the given functions to set up and simplify (f + g) (x)

The original number is -21/5 or -4.2 which is divided by 3 more than the number.

In mathematics, an equation is a statement or formula which shows two expressions having equal value and connected by an equal sign. The two expressions consist of variables and/or numbers.

Let the number be 'x' Two times the number = 2x3 more than the number = x + 3

According to the question,two times a number is divided by 3 more than the number is equal to 7 which means 2x / (x+3) = 7

By applying cross multiplication,2x = 7 × ( x+3)2x

= 7x + 7×32x

= 7x + 212x - 7x

= 21-5x = 21x = 21/ (-5)x

= -4.2

Hence the original number is -4.2

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In the 8 Axioms, 4 and 6 axioms fails to holds and S is not a vector space. Rest of the axioms try to hold the vector space.

To demonstrate that S is not a vector space, we must demonstrate that at least one of the eight vector space axioms fails to hold. Let us examine each axiom in turn:

Therefore, axioms 4 and 6 fail to hold, and S is not a vector space.

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The correct question:

Let S be the set of all ordered pairs of real numbers. Define scalar multiplication and addition on S by α(x₁, x₂) = (αx₁, αx₂); (x₁, x₂) ⊕ (y₁, y₂) = (x₁ + y₁, 0). We use the symbol ⊕ to denote the addition operation for this system in order to avoid confusion with the usual addition x + y of row vectors. Show that S, together with the ordinary scalar multiplication and the addition operation ⊕, is not a vector space. Which of the eight axioms fail to hold?

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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The length of chord XY is 5√2.

What is the length of the chord?

It is described as the line segment that connects any two points on the circle's circumference without going through the circle's center. As a result, the diameter is the chord of a particular circle that is the longest and goes through its center. In mathematics, determining the chord's length can be crucial at times.

Here, we have

Given: A circle with center O and radius 5 has a central angle XOY. X and Y are points on the circle. ​If the measure of arc XY is 90 degrees.

We have to find the length of chord XY.

∠XOY = 90°

OX = OY = 5

We draw a perpendicular from the center to chord XY bisect XY at D.

Now, since OD bisects ∠XOY

∠XOD = ∠YOD = 90°/2 = 45°

Now, in ΔXOD

sin45° = XD/OX

1/√2 = XD/5

5/√2  = XD...(1)

In ΔYOD

sin45° = YD/OY

5/√2  = YD...(2)

Adding (1) and (2), we get

XD + YD = 5/√2 + 5/√2

XY = 5√2

Hence, the length of chord XY is 5√2.

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Answer:

56 kilograms is equal to approximately 123.456 pounds.

Answer:

last option:  9200 + 80c ≤ 25,000

Step-by-step explanation:

the options showing ≥ 25,000 cannot be solutions because the weight must be less than 25,000

if there already is 9200 then that would be added to 80c and, when solved, would tell you how many 80kg containers can be loaded

80c ≤ 25,000 - 9,200

80c ≤ 15,800

c ≤ 15,800 ÷ 80

c ≤ 197.5

Answer:

Step-by-step explanation:

y+11<30

subtract 11 from both sides

y+11-11<30-11

y< 19

choice A

Step-by-step explanation:

y + 11 < 30       Original inequality

y + 11 - 11 < 30 - 11    Isolating the variable

y < 19                The answer / Simplification

The answer is A, I hope this helps!!!

Let X={1,2,3,4} and Y={a,b,c,d}. Let f={(1,d),(2,a),(3,b),(4,c),(3,b)}. a. f is an injection (one-to-one) b. f is a surjection (onto) c. f is a bijection,  The correct answer is: c. f is a bijection

To determine whether f is an injection (one-to-one), we need to check if each element in X is mapped to a distinct element in Y. Since f(3) = b and f(3) = b, f is not an injection.

To determine whether f is a surjection (onto), we need to check if every element in Y has at least one preimage in X. By examining the mappings in f, we can see that each element in Y (a, b, c, d) has a preimage in X. Therefore, f is a surjection.

Since f is both an injection and a surjection, it satisfies the conditions for a bijection. Hence, the correct answer is c. f is a bijection.

We can also note that f is a function from X to Y since each element in X is mapped to exactly one element in Y. Therefore, option d is also correct.

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Answer:

\(3x - 9 = 2x + 21 \\ 3x - 2x - 9 = 2x - 2x + 21 \\ x - 9 = 21 \\ x - 9 + 9 = 21 + 9 \\ x = 30\)

m<DGI = 80°

\(3x - 9 = \\ 3(30) - 9 = \\ 90 - 9 = 81\)

The measure of angle ∠DGI can be obtained by finding the solution of the equation as 81°.

A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.

It can be represented as a straight line on a graph.

The ray GI bisects ∠DGH.

It implies that the new angles are equal in measurement.

⇒ m∠DGI = m∠IGH

⇒ 3x - 9 = 2x + 21

⇒ x = 30

Then, in order to calculate m∠DGI, plug x = 30 in  3x - 9 as,

3 × 30 - 9 = 81

Hence, the measure of angle ∠DGI is given as 81°.

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Answer:

See answers below

Step-by-step explanation:

Equation of a line in point slope form is expressed as;

y-y0 = m(x-x0)

m is the slope

(x0, y0) is a point on the line

Given the line y = x

The slope of the line is 1.

The slope of the line perpendicular is M = -1

Given the point (2,2)

x0 = 2 and y 0 = 2

Substitute

Recall y-y0 = m(x-x0)

y - 2 = -1(x-2) (Point slope form)

Express in slope intercept form;

y - 2 = -1(x-2)

Make y the subject of the formula;

y -2 = -x + 2

y = -x + 2 + 2

y = -x + 4 (slope intercept form)

The general form of linear equation is expressed as the slope intercept form which is y = -x+4

let y = f(x)

f(x) = -x+4

f(x) = 4-x (Linear equation)