5p+2= -10
Show your work

The total amount owed by the students for the week is $\($28\).

An amount owed refers to total of the money a person owe us from time to time which can include loan and any unpaid interest, fees and expenses. It can also be an ordinal expenses such as school fee etc.

The total amount owed by the student will be:

= $3.00 + $8.00 + $7.00 + $10.00

= $28

Full question "On the first Monday of each month, the school sends home a note that includes each student's lunch account balance. These students owe money. Student 1 =$3.00, Student 2 - $8.00, Student 3 - $7.00, Student 4 - $10.00. What is the total amount owed by the student?".

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Two other examples of linear relationships are changes of units and finding the total cost for buying a given item x times.

Two examples of linear relationships that are useful are:

Changes of units:

These ones are used to change between units that measure the same thing. For example, between kilometers and meters.

We know that:

1km = 1000m

So if we have a distance in kilometers x, the distance in meters y is given by:

y = 1000*x

This is a linear relationship.

Another example can be for costs, if we know that a single item costs a given quantity, let's say "a", then if we buy x of these items the total cost will be:

y = a*x

This is a linear relationship.

So linear relationships appear a lot in our life, and is really important to learn how to work with them.

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Correct option is C. The probability = 1/5

Given, 5n + 3 ≤ 14

⇒5n ≤ 14 − 3

⇒(5 × n) ≤ 11

⇒n ≤  11/5

⇒n ≤ 2.2

As  ′ n ′

 is a positive integer, n > 0

0 < n ≤ 2.2

′ n ′  can only take integer values.

Hence, n = 1  or  n = 2

If  ′ n ′  is picked at random from the 10 positive integers, only two values can satisfy the given condition.

Number of favorable outcomes = 2

Total number of possible outcomes = 10

From the above, probability that the given condition is satisfied =

Number of favorable outcomes / Total number of possible outcomes

= 2/10

= 1/5

Therefore, the probability for  ′ n ′  that 5n + 3 ≤ 14 is  1/5.

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(a) After 4500 years, the sample will remain 3.9 mg.

(b) The sample will remain 15 mg after 1369 years.

The result is obtained by using the exponential decay equation.

The exponential decay equation can be used to calculate radioactive decay for the activity, the nuclei, and also the mass. The exponential decay equation for the mass is

\(m = m_{o} e^{-\lambda t}\)

Where

The half-life of radium-226 is 1600 years and the mass of a sample is 27 mg.

(a) What is the remaining mass after 4500 years?

(b) What is the decay time if the remaining mass is 15 mg?

First, let's calculate the decay constant.

λ = 0.693/T½

λ = 0.693/1600

λ = 0,000433

After 4500 years, the remaining mass is

\(m = m_{o} e^{-\lambda t}\)

\(m = 27 e^{-0.000433 \times 4500}\)

m = 27 × 0.142

m = 3.8 mg

If the remaining mass is 15 mg, the decay time is

\(m = m_{o} e^{-\lambda t}\)

\(15 = 27 e^{-0.000433 t}\)

\(ln \frac{15}{27} = ln (e^{-0.000433 t})\)

\(ln \frac{15}{27} = -0.000433 t\)

-0.588 = - 0.000433t

t = 1357.9 years

Hence,

(a) After 4500 years, the sample will remain 3.9 mg.

(b) The sample will remain 15 mg after 1369 years.

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The term "analysis of variance" is referred to as ANOVA. Ronald Fisher created a statistical test in 1918, and it has been in use ever since. Simply said, an ANOVA analyzes the statistical significance of differences between the means of three or more independent groups.

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To calculate the probability of drawing two red balls from the bag, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes: When drawing two balls at random without replacement, the total number of possible outcomes is given by the combination formula:

Total outcomes = (10 choose 2) = 10! / (2!(10-2)!) = 45

Number of favorable outcomes: We want to draw two red balls, and there are 4 red balls in the bag. The number of ways to choose 2 red balls from 4 is given by:

Favorable outcomes = (4 choose 2) = 4! / (2!(4-2)!) = 6

Now, we can calculate the probability:

Probability = Favorable outcomes / Total outcomes = 6 / 45 ≈ 0.1333

Therefore, the probability of drawing two red balls from the bag is approximately 0.1333 or 13.33%.

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\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

Let's solve for x :

Using quadratic formula ~

\( \boxed{ \frac{ - b \pm \sqrt{b {}^{2 } - 4ac}}{2a} }\)

where,

let's find the roots ~

\(x = - \dfrac{5}{18} + \dfrac{3 \sqrt{95} }{54} \)

and

\(x = - \dfrac{5}{18} - \dfrac{3 \sqrt{95} }{54} \)

There is no real roots, both the roots are imaginary ~

the correct option is D, the inverse relation is only a function if it passes the vertical line test.

A relation maps elements from one set (called the domain) into elements of another set (called the range).

A relation is a function only if each element in the domain is mapped into only one element of the range. So, there is something called the vertical line test.

It says that if at any part of the graph of the relation you can draw a vertical line that intercepts the graph of the relation more than once, then it is not a function. Passing the vertical line test means that no vertical line intercepts the graph more than once.

Then the correct option is D, the inverse relation is only a function if it passes the vertical line test.

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There are 10 students in a class, 6 of them wear glasses. If a student is chosen at random from the class, then the probability that they do not wear glass is 2/5

Total number of Students = 10

Students who wear glasses = 6

Students who don't wear glasses = 4

Probability is the ratio of favorable outcomes to the total favorable outcomes. The probability formula can be expressed as,

P(E) = (Number of favorable outcomes) ÷ (Total favorable outcomes).

The probability of a student not wearing glasses is,

Probability = Students who don't wear glasses/Total number of Students

Probability = 4/10 i.e., 2/5

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Answer:

$27.5

Step-by-step explanation:

Other solution

38.2 X 0.8 = 30.56 (20% off)

30.56 X 0.9 = 27.504 (Another 10% off)

Answer:

50%

Step-by-step explanation:

Sense there are 4 popsicles in all, and 2 are cherry, there would be 2/4 cherry popsicles, which is 1/2 or 50%

Hope my explanation makes sense :)

Yes, it is possible to find a limit at a location where there is a hole in a graph , such as where a point has been removed or where a graph abruptly stops.

This is because the limit of a function is defined as the value that the function approaches as x approaches a given value. In the case of a hole in the graph, the limit is found by looking at the limit from the left, the limit from the right, and the general limit.

The limit from the left is the limit of the function as x approaches the hole from the left. The limit from the right is the limit of the function as x approaches the hole from the right. The general limit is the overall limit of the function at the point where the hole appears. By considering all of these limits, it is possible to determine the overall limit of the function at the point where the hole is present.

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a) In the least-squares line y = 5 - 2x, the slope is -2 and the y-intercept is 5.  b) Since the slope of the line is -2, a change of 1 unit in x would cause a change of 2 units in y. c) When two variables have a negative linear correlation, the slope of the least-squares line is negative.

The least-squares line, also known as the linear regression line, is a straight line that shows the connection between two variables that are linearly related.

A straight line is used to connect two points, and the least-squares line is the line that connects the points with the smallest amount of error or the smallest amount of distance between the points and the line.

The formula for the least-squares line is given by y = mx + b,

where m is the slope of the line and b is the y-intercept.

In the least-squares line

y = 5 - 2x,

the slope is -2, and the y-intercept is 5.

The slope of the line tells us how much y changes when x changes by one unit. In this case, since the slope is -2, a change of 1 unit in x would cause a change of 2 units in y.

When two variables have a negative linear correlation, the slope of the least-squares line is negative.

A negative correlation means that when one variable increases, the other variable decreases.

For example, if we look at the correlation between temperature and snowfall, we would expect a negative correlation. As temperature increases, we would expect snowfall to decrease.

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Answer:

1. C   Add/subtract the same quantity to/from both sides

2. A  Yes

Step-by-step explanation:

Start with Equation A.

3x - 1 = 7

Add 1 to both sides.

3x = 8

First question:

How can we get Equation B from Equation A?

Answer:

C   Add/subtract the same quantity to/from both sides

Second question:

Based on the previous answer, are the equations equivalent?

Since by doing a valid step (adding 1 to both sides) Equation A became Equation B, the two equations are equivalent.

Answer:

A  Yes

The reduced fraction for 0.202222... is 1/5.

To express the repeating decimal 0.20222222... as a reduced fraction, follow these steps:

1. Let x = 0.202222...
2. Multiply both sides by 100: 100x = 20.2222...
3. Multiply both sides by 10: 10x = 2.02222...
4. Subtract the second equation from the first: 90x = 18
5. Solve for x: x = 18/90

Now, let's reduce the fraction:
18/90 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 18. So, 18 ÷ 18 = 1 and 90 ÷ 18 = 5.

Therefore, the reduced fraction for 0.202222... is 1/5.

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Here's how you can use the Trapezoidal Rule to approximate the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 in MATLAB:

```matlab

a = -2;    % Lower limit

b = 2;     % Upper limit

n = 1000;  % Number of subintervals (increase for higher accuracy)

h = (b - a) / n;   % Step size

x = a:h:b;         % Generate evenly spaced x values

y = 1 ./ (25 + x.^2).^1.5;  % Evaluate the function at x

approximation = h * (sum(y) - (y(1) + y(end)) / 2);  % Trapezoidal Rule approximation

fprintf('Approximation: %.6f\n', approximation);

```

1. We define the lower limit `a` as -2, the upper limit `b` as 2, and the number of subintervals `n` as 1000 (you can adjust `n` for higher accuracy).

2. We calculate the step size `h` by dividing the range (`b - a`) by the number of subintervals (`n`).

3. We generate an array `x` of evenly spaced values from `a` to `b` using the step size `h`.

4. We evaluate the function `f(x)` at each point in `x` and store the results in the array `y`.

5. Finally, we use the Trapezoidal Rule formula to approximate the integral by summing the values in `y` and adjusting for the endpoints, multiplying by the step size `h`.

The Trapezoidal Rule approximation for the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 is the value calculated using the MATLAB code above.

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Answer:

(0,8) (1,7)

Step-by-step explanation:

The vertex is (0,8)

We must find a second point to plot so we will put x as 1, after further simplifying we have 7, so (1,7) is the second point.

Answer: b.164.0 meters

Step-by-step explanation:

The  pieces have a total area of approximately 643.88 square feet.

To find the square footage of 4 out of the 7 equal pieces of a circle with a radius of 21 feet, you can follow these steps:
The area of the whole circle using the formula A = π\(r^2\).

Use 22/7 for π.
Divide the total area by 7 to find the area of one piece.

Multiply the area of one piece by 4 to find the total area of 4 pieces.
The area of the whole circle.
A = π\(r^2\)
A = \((\frac{22}{7} ) 21^{2}\)
A = 9,702 sq. ft.
The total area by 7 to find the area of one piece.
Area of one piece = 9,702 sq. ft.
Area of one piece = 1,386 sq. ft.
The area of one piece by 4 to find the total area of 4 pieces.
Total area of 4 pieces = 1,386 sq. ft. × 4
Total area of 4 pieces = 5,544 sq. ft.
To find the area of one piece, we need to first find the central angle of each piece.

Since the circle is cut into 7 equal pieces, the central angle of each piece is 360 degrees divided by 7, which is approximately 51.43 degrees. Next, we can use the formula for the area of a sector of a circle: (central angle/360) x pi x \(radius^2\).

Plugging in the values we have, we get: (51.43/360) x (22/7) x \(21^2\) = 160.97 square feet So each piece has an area of approximately 160.97 square feet.

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Let's solve the equation w/4 + 16 = 7 step by step:Step 1: Begin by isolating the variable term on one side of the equation. In this case, we want to isolate w/4. To do that, we can subtract 16 from both sides of the equation:

w/4 + 16 - 16 = 7 - 16

This simplifies to:

w/4 = -9

Step 2: Now, to solve for w, we need to get rid of the division by 4. We can do this by multiplying both sides of the equation by 4:

4 * (w/4) = 4 * (-9)

On the left side, the 4s cancel out, leaving us with:

w = -36

Step 3: We have found the solution for w, which is -36. To confirm, we can substitute this value back into the original equation to verify its correctness:

(-36)/4 + 16 = 7

Simplifying the left side:

-9 + 16 = 7

This further simplifies to:

7 = 7

Since the equation is true when w is -36, we can conclude that -36 is the solution to the equation w/4 + 16 = 7.

In summary, the equation is solved by subtracting 16 from both sides to isolate the variable, then multiplying both sides by 4 to eliminate the division by 4. The final solution is w = -36, which satisfies the equation.

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Answer:

a:) combination

b:) permutation

c:) combination

Step-by-step explanation:

There are 330 ways the coach can select a batting order of seven players from an 11 person team. Therefore, option B is the correct answer.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.

To determine the number of ways the coach can select a batting order of seven players from an 11 person team, we can use the combination formula, which is given by:

nCr = n! / r!(n-r)!

where n is the total number of players on the team, and r is the number of players in the batting order. In this case, n = 11 and r = 7.

So, the number of ways the coach can select a batting order of seven players from an 11 person team can be calculated as follows:

11C₇ = 11! / (7!(11-7)!)

= (11 x 10 x 9 x 8) / (4 x 3 x 2 x 1)

= 330

Therefore, option B is the correct answer.

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The radian measure of the central angle intercepting an arc of length 10 cm on a circle with a radius of 7 cm is approximately 1.42857 radians.

To find the radian measure of the central angle intercepting an arc of length 10 cm on a circle with a radius of 7 cm, we can use the formula:

θ = s / r,

where θ is the radian measure of the central angle, s is the length of the arc, and r is the radius of the circle.

In this case, the length of the arc (s) is given as 10 cm, and the radius (r) is 7 cm. Plugging these values into the formula, we have:

θ = 10 cm / 7 cm.

Simplifying the expression, we get:

θ ≈ 1.42857 radians.

Therefore, the radian measure of the central angle intercepting an arc of length 10 cm on a circle with a radius of 7 cm is approximately 1.42857 radians.

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Answer:

3.24 pounds

Step-by-step explanation:

3*1.08=3.24

Answer:

x² + 12x + 36  

Step-by-step explanation:

Given the quadratic expression, x² + 12x + ___,  with a missing constant value, c:

We can find the value of the constant by taking the coefficient of the middle term, dividing it by 2, and squaring its quotient.  In other words, \((\frac{b}{2})^{2}\).  In the given quadratic expression, b = 12.  Substitute the value of b = 12 into \((\frac{b}{2})^{2}\), to find the value of the constant.

x² + 12x + \((\frac{b}{2})^{2}\)

x² + 12x + \((\frac{12}{2})^{2}\)

x² + 12x + (6)²

x² + 12x + 36  ⇒ This is the perfect square trinomial.

Therefore, the missing value for the constant, c, is 36, making the quadratic equation a perfect square trinomial, x² + 12x + 36.

The value of e in the interval (0,32) that satisfies the conclusion of the Mean Value Theorem is e = 2^-20.

To verify that the Mean Value Theorem can be applied to f(x) = x^4/5 on the interval (0,32), we need to check whether the function is continuous on the closed interval [0,32] and differentiable on the open interval (0,32).

First, let's check if the function is continuous on the closed interval [0,32]. Since f(x) is a polynomial function with positive exponents, it is continuous everywhere, including at x = 0 and x = 32. Therefore, f(x) is continuous on the closed interval [0,32].

Next, let's check if the function is differentiable on the open interval (0,32). We can use the power rule of differentiation to find that f'(x) = (4/5)x^-1/5 = 4x^-1/5/5. This derivative exists and is continuous for all x in the open interval (0,32). Hence, f(x) is differentiable on the open interval (0,32).

Since f(x) is continuous on the closed interval [0,32] and differentiable on the open interval (0,32), we can apply the Mean Value Theorem. By the theorem, there exists at least one value e in the open interval (0,32) such that:

f'(e) = (f(32) - f(0))/(32 - 0)

Plugging in the values of f(x) and f'(x) we found earlier, we get:

4e^-1/5/5 = (32^4/5 - 0)/(32 - 0)

Simplifying this equation, we get:

4e^-1/5 = 1024/5

Dividing both sides by 4 and raising to the 5th power, we get:

e = (1024/5/4)^-5 = 2^-20

Therefore, the value of e in the interval (0,32) that satisfies the conclusion of the Mean Value Theorem is e = 2^-20.

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9514 1404 393

Answer:

  company B

Step-by-step explanation:

The growth rate is 1 less than the growth factor. The growth factor is the base of the exponential term.

Company A

  growth factor: 0.70

  growth rate: 0.70 -1 = -0.30 = -30%

__

Company B

  growth factor: 1.90

  growth rate: 1.90 -1 = 0.90 = 90%

__

Company B has a higher growth rate than Company A. (Company A has decreasing sales, not increasing.)

Company B has a higher growth rate than Company A.

Answer:

Step-by-step explanation:

2x + 3x - 10 = 90

Combine like terms

5x - 10 = 90

Add 10  to both sides

5x = 90+10

5x = 100

Divide both sides by 5

x =100/5

x = 20

Answer:

\(Slope = \frac{1}{2}\)

\(y-intercept = 6\)

The y-intercept means that there  were [6] inch(es) of snow on the ground at  the start of the storm and the slope  means that [1/2] inch(es) of snow falls every  hour during the storm.

Step-by-step explanation:

Given

\(d(t) = \frac{1}{2}t + 6\)

Required

- Determine the slope and y intercept

- Fill in the gap

The format of a linear equation is:

\(y = mx + b\)

Where

\(m = slope\)

\(b = y-intercept\)

By comparing \(y = mx + b\) with \(d(t) = \frac{1}{2}t + 6\)

We have:

\(m = \frac{1}{2}\)

i.e.

\(Slope = \frac{1}{2}\)

and

\(b = 6\)

i.e.

\(y-intercept = 6\)

Answer:

Step-by-step explanation:

y=(1/4)(2)+8

y=8.5

Plug the value for x given into the equation and solve.

y = \(\frac{1}{4}\) x 2 + 8

y =  \(\frac{1}{4}\) x 2 + 8 > y = \(\frac{1}{2}\) + 8 - Use PEMDAS. Multiply 1/4 by 2.

y = \(\frac{1}{2}\) + 8 > y = 8 \(\frac{1}{2}\)

So, your final answer is 8\(\frac{1}{2}\) or 8.5!

9514 1404 393

Answer:

  108

Step-by-step explanation:

The common ratio is ...

  972/2916 = 1/3

The ratio of the last two numbers shown is 1/9, indicating a missing number between them:

  2916, 972, 324, 108, 36

The missing number is 108.