LO. Gabe has 60 coins consisting of quarters and dimes.
The combined value of the coins is $9.45.
How many
quarters and dimes does Gabe have?

Answer:

y = 1/2x + 5

Step-by-step explanation:

We can use point slope form since we are given a point and the slope

y -y1 = m( x-x1)

where ( x1,y1) is a point and m is the slope

y -0 = 1/2 (x- -10)

y = 1/2( x+10)

y = 1/2x + 5

The equation of line passing through the point (-2,5) that is perpendicular to the line 6x+2y=0 is y = 3x + 11.

To find the equation of a line perpendicular to another line, we need to use the fact that the slopes of perpendicular lines are negative reciprocals of each other.

First, let's determine the slope of the given line. The equation of the given line is 6x + 2y = 0. We can rewrite it in the slope-intercept form, y = mx + b, by solving for y:
2y = -6x
y = -3x
The slope of this line is -3.

Since the line we are looking for is perpendicular, its slope will be the negative reciprocal of -3, which is 1/3.

Now, we have the slope and a point (-2,5) on the line we want to find the equation for. We can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Plugging in the values, we get:
y - 5 = (1/3)(x - (-2))
y - 5 = (1/3)(x + 2)
y - 5 = (1/3)x + 2/3
y = (1/3)x + 2/3 + 5
y = (1/3)x + 2/3 + 15/3
y = (1/3)x + 17/3
Multiplying through by 3 to get rid of the fraction, we have:
3y = x + 17
Rearranging, we get the final equation:
x - 3y + 17 = 0

So, the equation of the line passing through the point (-2,5) that is perpendicular to the line 6x + 2y = 0 is x - 3y + 17 = 0.

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Answer:

1 ≤ x < 7

Step-by-step explanation:

−2+3≤x−3+3<4+3 (Add 3 to all parts)

Wider spans of control have become more popular in recent years due to their ability to increase efficiency, improve communication, and promote collaboration within an organization.

A) Narrower spans of control: This traditional approach has been found to be less efficient, as it requires more levels of management and bureaucracy. This leads to slower decision-making and reduced agility in responding to market changes.

B) Wider spans of control: Wider spans of control allow managers to oversee more employees directly, thus reducing the number of management levels, resulting in increased efficiency and faster decision-making. This approach also fosters better communication and collaboration among team members.

C) A span of control of four: While a specific number may vary depending on the organization, a span of control of four is considered too narrow for many modern organizations. It may limit the organization's ability to respond quickly to change and make it less adaptable.

D) An ideal span of control of six to eight: Some experts suggest that an ideal span of control is between six and eight employees, as it strikes a balance between effective oversight and management efficiency.

E) Eliminating spans of control in favor of team structures: In some organizations, especially those with flatter hierarchies, spans of control are being replaced by team structures. This approach enables employees to work collaboratively, share responsibilities, and make decisions collectively, which can lead to increased innovation and productivity.

In conclusion, wider spans of control have become more popular in recent years due to their ability to increase efficiency, improve communication, and promote collaboration within an organization.

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Answer:

5.99 • .25 = 1.50

4.99 • 1.5 = 7.48

6.99 • 1 = 6.99

3.99 • 0.75 = 2.99

The costumer will pay approximately $18.96 before taxes.

Step-by-step explanation:

Answer:

In geometry, area is the 2-dimensional space or region occupied by a closed figure, while perimeter is the distance around a closed figure i.e. the length of the boundary. Two shapes may have the same perimeter, but different areas or may have the same area, but different perimeters.

Step-by-step explanation:

Answer maybe

Step-by-step explanation:

ANSWER

x = 41

EXPLANATION

The given angles are supplementary, so their measures add up to 180°,

Now we have an equation for x. First, add like terms,

Then subtract 16 from both sides of the equation,

And finally, divide both sides by 4,

Hence, x = 41.

The roots of the system of equations are x = 3.38586 and y = 2.61414, the error converges to 0 after the third iteration.

To solve this system of equations, we can use the Newton-Raphson method. This method starts with an initial guess and then uses a series of iterations to converge on the solution. In this case, we can use the initial guess x = y = 4.

The following table shows the results of the first few iterations:

Iteration | x | y | Error

------- | -------- | -------- | --------

1 | 4 | 4 | 0

2 | 3.38586 | 2.61414 | 0.06414

3 | 3.38586 | 2.61414 | 0

As you can see, the error converges to 0 after the third iteration. Therefore, the roots of the system of equations are x = 3.38586 and y = 2.61414.

The Newton-Raphson method is a relatively simple and efficient way to solve systems of equations.

However, it is important to note that it is only guaranteed to converge if the initial guess is close enough to the actual solution. If the initial guess is too far away from the actual solution, the method may not converge or may converge to a different solution.

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Step-by-step explanation:

The problem bothers on fractions, here we are being presented with mixed fractions.

what we are going to do bascially is to subtract the sum of all the uloaded

peat moss in sites 1 and 2 to get from the peat moss to get the remaining for the third site

therefore

\(10\frac{2}{5}-(2\frac{2}{3}+ 2\frac{1}{4})\)

we then have to convert the mixed fraction to further simplify the problem we have

\(\frac{52}{5}-(\frac{8}{3}+ \frac{9}{4})\)

we then solve the fraction to the right of the negative symbol first

\(=\frac{52}{5}-(\frac{8}{3}+ \frac{9}{4})\\\\=\frac{52}{5}-\frac{32+27}{12} \\\\=\frac{52}{5}-\frac{59}{12} \\\\\=\frac{624-295}{60} \\\\=\frac{329}{60}\)

We can now convert to mixed fraction

\(=\frac{329}{60}\\\\ =5\frac{12}{25}\)

For the third site the remainder is 5 12/25

Answer:

30

Step-by-step explanation:

We can ignore the fact they are similar altogether. It's known that all 3 angles of a triangle add up to 180, so:

180=102+48+m

180=150+m

30=m

Answer:

A. 30 degrees

Step-by-step explanation:

They are similar aka the same or congruent and since you know all three angles you just match them up.

Answer:

19/8

Step-by-step explanation:

Step-by-step explanation:

just divide them jk but umm it is 19/8

Answer:

y=2x-5

Step-by-step explanation:

y=mx+c

mx=slope

In this case, the slope is already given to you which means the m=2.

y=2x+c.

The coordinates are (14, 23) and when you put -5 into c, the line goes through the coordinates (14, 23).

Hope this helps!

The correct statements that are true about experimental probability is choices A, C, and D.

Experimental probability is a probability that is determined on the basis of a series of experiments.

A random experiment is done and is repeated many times to determine their likelihood and each repetition is known as a trial.

The experiment is conducted to find the chance of an event to occur or not to occur. It can be tossing a coin, rolling a die, or rotating a spinner. In mathematical terms, the probability of an event is equal to the number of times an event occurred ÷ the total number of trials.

Also, experimental probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trials,  not in a theoretical sample space but in an actual experiment.

Thus, The correct statements that are true about experimental probability is choices A, C, and D.

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Below you have the graph:

The equation of the line in the form ax+by=c whose x-intercept is -20 and y-intercept is -5 would be x - 4y = -20.

What is Slope point form of a line?

For linear equations, the general form y-y1=m(x-x1) is used. It accentuates the line's slope and a point on the line (that is not the y-intercept)

To find the equation of the line with the given x-intercept and y-intercept, we can use the point-slope form of a line. First, we find the slope of the line using the x-intercept and y-intercept:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

Since the x-intercept is (-20, 0) and the y-intercept is (0, -5), we use these two points to find the slope:

m = (0 - (-5)) / (-20 - 0)

m = 5 / -20

m = -1/4

Next, we use the point-slope form of a line and the x-intercept to find the equation of the line:

y - 0 = -1/4 (x - -20)

y = -1/4 x + 5

To simplify, we can multiply the coefficients by 4 to get rid of the fraction:

4y = -x + 20

-x + 4y = 20

And since a > 0, we can rearrange the equation to make the coefficient of x positive:

x - 4y = -20

This is the equation of the line with x-intercept -20 and y-intercept -5, in the form ax + by = c.

Hence, The equation of the line in the form ax+by=c whose x-intercept is -20 and y-intercept is -5 would be x - 4y = -20.

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The length vector is 1. So the sketch vector field f is given below. So the option a is correct.

In the given question, the vector field F by drawing a diagram like this figure.

The given vector field F is:

F(x, y) = (yi + xj)/√(x^2 + y^2)

We can write the vector field as:

F(x, y) = yi/√(x^2 + y^2) + xj/√(x^2 + y^2)

Here

F(x, y) = [y/√(x^2 + y^2)]^2 + [x/√(x^2 + y^2)]^2

F(x, y) = y^2/(x^2 + y^2) + x^2/(x^2 + y^2)

F(x, y) = (y^2+ x^2)/(x^2 + y^2)

F(x, y) = 1

F(0, y) = y/|y| = ±1

F(x, 0) = x/|x| = ±1

So the length vector is 1.

So the sketch vector field f is given below:

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The complete question is:

Sketch the vector field F by drawing a diagram like this figure.

F(x, y) = (yi + xj)/√(x^2 + y^2)

4.82 × 10⁻⁴

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  10 . If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:

4.82 x 10^-4

Step-by-step explanation:

8.2 x 10^-4 + .0004= enter into calculator

.000482, move decimal behind first whole number and count places

it moves 4 spaces and because it starts in front of the number your exponent is negative

To calculate the amount in the account at the end of 5 years, we can use the formula for compound interest. At the end of 5 years, the amount in the account would be approximately $1561.41.

To calculate the amount in the account at the end of 5 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial investment)

r is the annual interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the number of years

Given:

P = $1200

r = 6.12% = 0.0612 (converted to decimal form)

n = 4 (compounded quarterly)

t = 5 years

Using the formula, we can calculate the final amount:

A = 1200(1 + 0.0612/4)^(4*5)

A = 1200(1 + 0.0153)^(20)

A ≈ $1561.41

Therefore, at the end of 5 years, the amount in the account would be approximately $1561.41.

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Answer:

-2(2-5x)

Step-by-step explanation:

3+2×(5x)-7

Calculate the difference

-4+2×(5x)

Factor out -2 from the expression

-2(2-5x)

Thats the answer: -2(2-5x)

Hope this helps

Answer:

\(f(-1)=-5\)

Step-by-step explanation:

Numeric Value of a Function

Given:

\(f(x)=4x^2-9\)

It's required to find f(-1).

It can be calculated by substituting the value x=-1 in the function:

\(f(-1)=4(-1)^2-9\)

Calculating:

\(f(-1)=4*1-9\)

\(f(-1)=4-9\)

\(\boxed{f(-1)=-5}\)

The sentence "64% of women in the sample are the principal investor in their household" serves as an example of descriptive statistics.

This sentence provides a summary of the survey's data and a descriptive statistic (percentage) that characterizes the sample's characteristics.

According to the survey's findings, "there is a correlation between American women and being the principal investor in their household." The sample data are used to draw this conclusion about the population. Despite the fact that the sample is not representative of all American women, the findings indicate that a sizable number of the women in the sample are the principal investors in their households.

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The scale factor of the drawing is  \(2/1\), and the drawing is half the size of the actual diner.

To find the scale factor of the drawing, we need to determine the ratio of the size of the drawing to the actual size of the diner. Since the scale is given in terms of inches and feet, we need to convert the units to a common measure before we can compare them.

First, let's convert the scale to the same unit of measurement. We know that 1 foot is equal to 12 inches, so we can rewrite the scale as:

10 inches = 5/12 feet

Next, we can simplify this fraction by multiplying the numerator and denominator by 12:

10 inches = 60/12 inches = 5 feet

Now we can see that the scale factor is:

Size of drawing / Actual size = 10 inches / 5 feet = 2 inches per foot

So the scale factor of the drawing is 2, which means that every inch on the drawing represents 2 feet in the actual diner.

To compare the size of the drawing to the actual size of the diner, we can use the scale factor to determine how much smaller the drawing is.

Since the scale factor is 2, the drawing is half the size of the actual diner. In other words, every linear measurement on the drawing is half the length of the corresponding measurement in the actual diner.

Therefore, the scale factor of the drawing is 2/1, and the drawing is half the size of the actual diner.

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The given question is complete. The complete question is given below:

Tristan drew a scale drawing of a diner, with the scale of 10 inches = 5 feet. What is the scale factor of the drawing, and how does it compare to the actual size of the diner?

Answer:

y=2/5x-7

Step-by-step explanation:

2x−5y=35

Step 1: Add -2x to both sides.

2x−5y+−2x=35+−2x

−5y=−2x+35

Step 2: Divide both sides by -5.

-5y/5=-2x+35/-5

y=2/5x-7

(a) The magnitude of the cross product of a and b is |a × b| = 41.51. (b) The dot product of a and b is a⋅b ≈ 42.9. c)  (a+b)⋅b ≈ 100.57.  (d) The component of a along the direction of b ≈ 6.87.

To find the required values using the given vectors a = \(6.6i^ + 7.1j^\) and b =\(6.5i^ + 2.1j^:\)

(a) ∣a×b∣ (Magnitude of the cross product of a and b):

The cross product of two vectors a and b is given by the formula: |a × b| = |a| |b| sin(θ), where θ is the angle between the two vectors.

|a × b| = \(|6.6i^ + 7.1j^ × 6.5i^ + 2.1j^|\)

Using the determinant form of the cross product:

|a × b| = |\(i^ j^ k^\)|

              |6.6   7.1   0|

              |6.5   2.1   0|

|a × b| = \((6.6 * 2.1 - 7.1 * 6.5)k^\)

Evaluating the determinant:

|a × b| = \((-41.51)k^\)

Therefore, the magnitude of the cross product of a and b is |a × b| = 41.51.

(b) a⋅b (Dot product of a and b):

The dot product of two vectors a and b is given by the formula: a⋅b = |a| |b| cos(θ), where θ is the angle between the two vectors.

a⋅b = \((6.6i^ + 7.1j^) ⋅ (6.5i^ + 2.1j^)\)

a⋅b = (6.6 * 6.5) + (7.1 * 2.1)

Evaluating the dot product:

a⋅b ≈ 42.9

Therefore, the dot product of a and b is a⋅b ≈ 42.9.

(c)   (a+b)⋅b (Dot product of (a+b) and b):

(a+b)⋅b = \((6.6i^ + 7.1j^ + 6.5i^ + 2.1j^) ⋅ (6.5i^ + 2.1j^)\)

(a+b)⋅b =\((13.1i^ + 9.2j^) ⋅ (6.5i^ + 2.1j^)\)

(a+b)⋅b = (13.1 * 6.5) + (9.2 * 2.1)

Evaluating the dot product:

(a+b)⋅b ≈ 100.57

Therefore, (a+b)⋅b ≈ 100.57.

(d) The component of a along the direction of b:

The component of a along the direction of b can be calculated using the formula: (a⋅b) / |b|.

Component of a along the direction of b = (a⋅b) / |b|

Component of a along the direction of b = (a⋅b) / √(b⋅b)

Component of a along the direction of b = (a⋅b) / \(√(|b|^2)\)

Component of a along the direction of b = (a⋅b) / \(√((6.5)^2 + (2.1)^2)\)

Component of a along the direction of b ≈ 42.9 / √(42

.25 + 4.41)

Calculating the component:

Component of a along the direction of b ≈ 42.9 / √(46.66)

Therefore, the component of a along the direction of b ≈ 6.87.

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After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

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Population: All American households.

Sample: The 1780 American households surveyed.

Individuals: The American households participating in the survey.

In the given scenario, we have a survey of 1780 American households that found 59% of the households own a computer. Let's identify the population, sample, and individuals in the study:

Population: The population refers to the entire group or larger set of individuals that we are interested in. In this case, the population would be all American households.

Sample: The sample is a subset of the population that is chosen to represent the population accurately. In this situation, the survey includes 1780 American households. Therefore, the sample is the 1780 households that were surveyed.

Individuals: The individuals in the study are the specific units or elements being surveyed or examined. In this case, the individuals are the American households that participated in the survey. Each household represents an individual within the study.

To summarize:

Population: All American households.

Sample: The 1780 American households surveyed.

Individuals: The American households participating in the survey.

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Answer:

D. 2 1/4.

Step-by-step explanation:

First, convert both -5 1/4 and -7 1/2 into improper fraction. These would be -21/4 and -15/2.

-21/4 - (-15/2)

Two negatives in a row make a positive.

-21/4 + 15/2

Double both the numerator and denominator of 15/2 to make it have the same denominator as -21/4. This would 30/4.

-21/4 + 30/4

Put -21 + 30 over 4 to make it a single fraction.

(-21 + 30)/4

Add -21 and 30 to get 9.

9/4

Convert 9/4 into a mixed number: 2 1/4

The answer to -5 1/4 - (-7 1/2) is 2 1/4, which is D.

Answer:

A is the answer

Step-by-step explanation:

the center of the circle is (-2,-1) so you're going to reverse their signs and insert that value in for x and y. the radius is 5, but the equation of a circle is

\(x ^{2} + {y}^{2} = {r}^{2} \)

so you're going to square the radius, this making it 25.

Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10