A train leaves Little​ Rock, Arkansas, and travels north at 75 kilometers per hour. Another train leaves at the same time and travels south at 60 kilometers per hour. How long will it take before they are 405 kilometers​ apart?

The two angles are related in that they are supplementary angles

Supplementary angles would add tuo to 180 degrees according to the angle Theorem.

Adding the two given angles :

These angles are supplementary

The angles aren't vertical in that , vertical angles should have the same vertex. Complementary angles on the other hand add to 90 degrees. While the angles doesn't share the same side, hence, they aren't adjacent.

Hence, the angles are related as they are supplementary angles .

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Decentralization is a management approach that involves the delegation and assignment of decision-making rights from top levels of management to lower levels of management. Option A

It is an effective way to empower employees and to improve decision-making processes within an organization. The benefits of decentralization include the following:

It empowers more employees at lower levels of management: Decentralization allows employees to take ownership of their work, to be more accountable, and to make decisions that are in the best interest of the organization. This, in turn, leads to improved job satisfaction, employee engagement, and better overall performance.

It allows for better and more timely decision-making: Decentralization ensures that decisions are made closer to where the work is being done. This leads to faster decision-making, improved responsiveness to changes in the market, and better coordination between different departments and teams.

It trains future managers: Decentralization provides employees with the opportunity to gain valuable management experience, which can help prepare them for future leadership roles within the organization.

However, one benefit of decentralization that is not accurate is that it forces top levels of management to focus on individual units. In fact, decentralization can free up top management to focus on the big picture and long-term strategy, rather than getting bogged down in day-to-day operations.

In conclusion, decentralization is a useful management approach that can help organizations improve decision-making, empower employees, and train future managers.

By delegating decision-making rights to lower levels of management, organizations can improve overall performance and become more adaptable to changes in the market.

So Option A is correct.

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complete question:

The benefits of decentralization i.e. delegation and assignment of decision rights include all of the following except:

a it forces top levels of management to focus on individual units

b it empowers more employees at lower levels of management

c it allows for better and more timely decision making

d it trains future managers

Answer:

b is increased by 17% : A and E

b is decreased by 17%: H and J

Step-by-step explanation: took the test

using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

Answer:

I am confused by this

Step-by-step explanation:

Answer:

red +blue marbles :- 15 +13=28 marbles.

yellow marbles:- 50+28=22 marbles.

probability of yellow marble :- 22/50 i.e 11/25

The binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

Given: Roll an 8-sided die 10 times and to find the probability of getting exactly 3 sevens in those 10 rolls.

Formula: The probability of getting exactly "k" successes in "n" trials of an event with a probability "p" of success in a single trial is given by the binomial probability formula:

P(k successes in n trials) = \(C(n , k) * p^k * (1 - p)^{(n - k)}\)

where:

Step1

Calculate the probability of rolling a seven on an 8-sided die (p).

Since there is 1 "success" outcome (rolling a seven) out of 8 possible outcomes (8-sided die),

p = 1/8.

Step 2

Plug the values into the binomial probability formula for getting exactly 3 sevens in 10 rolls:

P(3 sevens in 10 rolls) = \(C(10, 3) * (1/8)^3 * (1 - 1/8)^{(10 - 3)}\)

On subtracting gives:

=C(10,  3) * (1/8)^3 * (7/8)^{7}

Plugging the value of C(10,3) = 120 in the above equation:

= 120 * (1/8)^3 * (7/8)^{7}

Step 3:

Calculate the final answer using the formula:

P(3 sevens in 10 rolls) = 120 * (1/512) * (343/512)

≈ 0.0142

Therefore, the binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

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For the 21% of a number is 27, the value of 7% of that number is 7.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

⇒ 21% of a number is 27

Let a number is = x

So, We can formulate;

⇒ 27% of x = 27

Solve for x as;

⇒ 27/100 × x = 27

⇒ 27x = 27 × 100

⇒ 27x = 2,700

⇒ x = 2,700 / 27

⇒ x = 100

So, 7% of 100 is,

⇒ 7% of 100

⇒ 7/100 × 100

⇒ 7

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Answer: 2 (x+5)

Step-by-step explanation:

Answer:

x+5

Step-by-step explanation:

The height of the television transmission tower is approximately 1298 feet.

The height of the television transmission tower, we can use trigonometry and the concept of tangent.

Let's denote the height of the tower as h.

We know the length of the shadow is 1130 feet and the angle formed by the ground and the line from the top of the tower to the tip of the shadow is 48.3 degrees.

The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.

The height of the tower is the opposite side and the length of the shadow is the adjacent side.

Using the tangent function, we can set up the following equation:

tan(48.3°) = h / 1130

To solve for h, we can multiply both sides of the equation by 1130:

1130 × tan(48.3°) = h

Using a calculator, we find:

h ≈ 1130 × 1.1477

≈ 1297.601 feet

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The Interpretatiom of the equation is that;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

The algebra word problem can be solved by using variables to denote certain parameters I'm the question.

The general form of equation of a line in slope intercept form is;

y = mx + c

Where;

m is slope

c is y-intercept

We are given the equation:

$25w + $65

This equation represents the amount of money Kelly will have saved after some amount of weeks.

Thus;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

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Answer:About 14 to 15 inches

Step-by-step explanation:

Answer:

Step-by-step explanation: First you must do 70 subtracted by 13 then you have your answer for x.

700 + 30

= 730

Hope it's help you!

Answer:

730

Step-by-step explanation:

So you have 700 ok then you are adding 30 to that so in 700 there are no tens or one's so you can just slide that 30 right in there and make 730.

Hope this helps have a great day:)

Answer:

Step-by-step explanation:

-4x + 2 = x - 3

-5x + 2 = -3

-5x = -5

x = 1

y = 1 - 3

y = -2

(1, -2)

y = - 3 * x + 2

if x = - 1

y = - 3 * (-1) + 2 = 3 + 2 = 5

if x = 0

y = - 3 * 0 + 2 = 2

if .. and so on

Answer:

$117.00

Step-by-step explanation:

-earns $7.00 per hour as a cashier

-earns $6.00 per hour as a bagger

-earns $5.00 per hour as a stocker

-works 4 hours as a cashier

-works 9 hours as a bagger

-works 7 hours as a stocker

First, find the amount of money earned in the week while working as a cashier.  We know from the information we picked out that Surge works $7.00 per hour as a cashier and he works 4 hours that week.  Therefore, we need to multiply the amount of money made per hour by the amount of hours worked in a week.:

$7.00/hr * 4 hrs=$28.00 made as a cashier

Next, find the amount of money Surge made as a bagger.  Do the same thing as you did with the cashier calculations, except that this time, he earns $6.00 per hour and he works 9 hours as a bagger.:

$6.00/hr * 9 hrs=$54.00 made as a bagger

Then, find the amount of money made as a stocker.  It's the same as everything else, just that Surge know earns $5.00 per hour and he works 7 hours as a stocker.  So, do the last set of multiplication:

$5.00/hr * 7hrs=$35.00 made as a stocker

Finally, the question asks for the average amount of money made per week, so add up all you calculations to get that average amount:

$28.00+$54.00+$35.00=$117.00

Surge makes an average of $117.00 in a given week.

The serge average pay per hour will be $117.00.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

It is given that earns $7.00 per hour as a cashier, earns $6.00 per hour as a bagger, earns $5.00 per hour as a stocker, and works 4 hours as a cashier -works 9 hours as a bagger -works 7 hours as a stocker.

First, find the amount of money earned in the week while working as a cashier.  We know from the information we picked out that Surge works $7.00 per hour as a cashier and he works 4 hours that week.  Therefore, we need to multiply the amount of money made per hour by the number of hours worked in a week.:

$7.00/hr  x  4 hrs=$28.00 made as a cashier

Next, find the amount of money Surge made as a bagger.  Do the same thing as you did with the cashier calculations, except that this time, he earns $6.00 per hour and he works 9 hours as a bagger.:

$6.00/hr x 9 hrs=$54.00 made as a bagger

Then, find the amount of money made as a stocker.  It's the same as everything else, just that Surge now earns $5.00 per hour and he works 7 hours as a stocker.  So, do the last set of multiplication:

$5.00/hr x  7hrs=$35.00 made as a stocker.

Finally, the question asks for the average amount of money made per week, so add up all your calculations to get that average amount:

$28.00+$54.00+$35.00=$117.00

Therefore,  the serge average pay per hour will be $117.00.

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Answer:

5

Step-by-step explanation:

Given

3n + 7 = 22

3n = 22 - 7

3n = 15

n = 15 / 3

n = 5

Hope it will help :)

Answer:

n = 5

Step-by-step explanation:

3n + 7 = 22

Solve for n.

----------------------

When we need to find a variable, we need to isolate the variable to the point that it is by itself.

3n + 7 = 22

Subtract 7 from both sides :

3n + 7 - 7 = 22 - 7

3n = 15

Divide both sides by 3 :

n = 5

Answer:

C

Step-by-step explanation:

All sides make a cube

Answer:

D

Step-by-step explanation:

The value of the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)

From the question, we have the following parameters that can be used in our computation:

\(\sqrt[4]{a}^3\)

Consider an expression expressed as xⁿ

The expression can be expanded as

xⁿ = x * x * x .... in n places

Using the above as a guide, we have the following:

\(\sqrt[4]{a}^3 = \sqrt[4]{a} * \sqrt[4]{a} * \sqrt[4]{a}\)

Apply the exponent rule of indices

\(\sqrt[4]{a}^3 = a^\frac14 * a^\frac14 * a^\frac14\)

Apply the power rule of indices

\(\sqrt[4]{a}^3 = a^\frac34\)

Hence, the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)

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Answer:

d=-6.5

Step-by-step explanation:

2d+13=0

2d=-13

d= -13/2

d=-6.5

Case 1: a = 0; b = 0 --> Real Number

Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number

Case 3: a ≠ 0; b = 0 --> Real Number

Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number

For each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.

Case 1: a = 0; b = 0

In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.

Case 2: a = 0; b ≠ 0

Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.

Case 3: a ≠ 0; b = 0

In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.

Case 4: a ≠ 0; b ≠ 0

Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.

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Step-by-step explanation:

I just answered that a few minutes ago.

Slope of line SP: -1

Slope of line FJ: -1

Point-Slope Form of Line FJ: \(y=-x-6\)

What to type inside the orange box? You must type "-x-6".

Concept. A parallel line to line SP. A parallel line is a line that has the same slope as another line, therefore, the line parallel to SP has the same slope of SP.

Let's solve!

1. Find the slope of line SP.

Line SP's expression is: \(y=-x-14\).

The slope of a linear function is always given by the coefficient of x when the equation is solved for y. Hence, the slope of line SP is -1, because x is being multiplied by -1.

2. Form the equation for line FJ.

Use the formula for finding linear equations: \(y-y_{1} =m(x-x_{1} )\), where m is the slope of the line, \(x_{1}\) is the x value of a point where the line passes, and \(y_{1}\) is the y value of a point where the line passes. \(x_1\) and \(y_1\) must be taken from a single point where the function passes.

Let's take the formula and find the equation for line FJ:

a. Substitute in the formula.

\(y-(0) =(-1)(x-(-6) )\)

b. Simplify.

\(y-(0) =(-1)(x-(-6) )\\ \\y=(-1)(x+6)\\ \\y=-x-6\)

3. Express your answers.

Slope of line SP: -1

Slope of line FJ: -1

Point-Slope Form of Line FJ: \(y=-x-6\)

Answer:

The formula for finding the area of a circle using its radius is:

The formula for finding the area of a circle using its radius is:A = πr²

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.Note that π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14

Step-by-step explanation:

Hope it Helps

The formula for finding the area of a circle using its radius is π * r².

The formula for finding the area of a circle using its diameter is (π/4) * d².

The formula for finding the area of a circle using its radius is:

A = π * r²

where:

A represents the area of the circle,

π (pi) is a mathematical constant approximately equal to 3.14159, and

r represents the radius of the circle.

If you have the diameter of the circle instead of the radius, you can use the following formula:

A = (π/4) * d²

where:

A represents the area of the circle,

π (pi) is a mathematical constant approximately equal to 3.14159, and

d is the diameter of the circle.

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Answer:

The regression model is:

y = 20.29 + 0.73·x

Step-by-step explanation:

In this case a regression model is to be formed to predict the final average in the course based on the first test grade.

Use Excel to form the regression model.

The output is attached below.

The regression model is:

y = 20.29 + 0.73·x

Predict the final average of a students who made an 83 on the first test as follows:

y = 20.29 + 0.73·x

  = 20.29 + 0.73 × 83

  = 80.88

The final average of a students who made an 83 on the first test would be 80.88.

From the output:

R² = 0.839

Then the correlation coefficient will be:

\(r=\sqrt{R^{2}}=\sqrt{0.839}=0.91597\approx 0.92\)

The value of r is 0.92.

The coefficient of determination R² specifies the percentage of the variance in the dependent-variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent-variable).

In this case, the R² value of 0.839 implies that 83.9% of the variation in the final average can be explained by the grades in the first test.

The equation of the oscillating circle of the curve y = ¹/₄ x² +2 at point (2,1) is (x - 5/2)² + (y - 1)² = 1/4.

To find the equation of the oscillating circle of the curve y = ¹/₄ x² +2 at point (2,1), we need to follow these steps:

Find the first and second derivatives of the given curve:

y = ¹/₄ x² + 2

y' = ¹/₂ x

y'' = ¹/₂

Use the first and second derivatives to find the equation of the tangent line to the curve at point (2,1):

y - 1 = 1/2(x - 2)

y = 1/2 x + 0.5

Find the perpendicular bisector of the tangent line at point (2,1):

The slope of the tangent line is 1/2, so the slope of the perpendicular bisector is -2.

y - 1 = -2(x - 2)

y = -2x + 5

Find the intersection of the perpendicular bisector with the x-axis:

When y = 0, -2x + 5 = 0, so x = 5/2.

Find the center of the oscillating circle:

The center of the oscillating circle is (5/2,1).

Find the radius of the oscillating circle:

The radius of the oscillating circle is the distance between the center and the point of tangency, which is:

r = √[(2 - 5/2)² + (1 - 1)²]

r = [1/4 + 0] = 1/2.

Write the equation of the oscillating circle in standard form:

The equation of the oscillating circle is:

(x - 5/2)² + (y - 1)² = (1/2)².

Simplifying, we get:

(x - 5/2)² + (y - 1)² = 1/4.

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The complete question is below:

Find the equation of oscillating circle of curve y=1/4 x^2 +2 at (2,1)

The domain of the relation of the graph representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.

The domain of a relation is the set of all possible input values (independent variable) for which the relation is defined.

Looking at the given points, the x-coordinates are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.

Therefore, the domain of the relation is {−4, −2, 0, 3, 5}.

Hence, the correct option is {−4, −2, 0, 3, 5}.

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Answer:

p = 8

Step-by-step explanation:

Divide -5 to both sides

-5p = -40

5p = 40

p = 8

So p = 8