How did knowing what addition and subtraction mean help you figure out how the value of an expression can decrease even if the value of a variable increases?

The total value in cents of all coins in the any row would be 16 cents.

In the pattern you described, the coins are arranged in rows such that each subsequent row has one more coin than the previous row. Let's analyze the values of the coins to determine the total value in cents of all the coins in the th row.

Assuming the values of the coins are as follows:

Penny: 1 cent

Nickel: 5 cents

Dime: 10 cents

We can observe that the pattern repeats after every three coins. The first three coins in the pattern are penny, nickel, dime. These coins have a total value of 1 + 5 + 10 = 16 cents.

For the subsequent rows, the pattern repeats with an offset of 3. For example, in the fourth row, the coins are penny, nickel, dime, which have the same total value as the first row, i.e., 16 cents.

So, regardless of the value of "th" (the row number), the total value in cents of all the coins in that row will always be 16 cents.

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Answer:

x^2 | y^25 |√187x

Step-by-step explanation:

First you simplify the equation then you factor 184 into its prime factors which is   184 = 23 • 23  

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent. Factors which will be extracted are: 4 = 22 Factors which will remain inside the root are: 46 = 2 • 23 To complete this part of the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2: 2 = 2 At the end of this step the partly simplified SQRT looks like this: 2 • sqrt (46x5y50)  Rules for simplifing variables which may be raised to a power: (1) variables with no exponent stay inside the radical (2) variables raised to power 1 or (-1) stay inside the radical (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples: (3.1) sqrt(x8)=x4 (3.2) sqrt(x-6)=x-3 (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples: (4.1) sqrt(x5)=x2•sqrt(x) (4.2) sqrt(x-7)=x-3•sqrt(x-1) Applying these rules to our case we find out that SQRT(x5y50) = x2y25 • SQRT(x) sqrt (184x5y50) = 2 x2y25 • sqrt(46x)  

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Answer:

Starting at the origin (0, 0), go right 3 units, then down 7 units. You will end at (3, -7).

The characteristics of the normal distribution can be used to determine the likelihood that X equals 19.62 because X is a normally distributed random variable with a mean of 12 and a standard deviation of 3.

We must compute the z-score, which counts the number of standard deviations a given result is from the mean, in order to determine this probability. Calculating the z-score is as follows:

z = (x - μ) / σ

If the supplied value, x, the mean, and the standard deviation are all given.In this instance, x=19.62, =12, and =3 respectively. By replacing these values, we obtain:

z = (19.62 - 12) / 3 ≈ 2.54

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Answer:

A. 2

Step-by-step explanation:

First divide the 400 toys by the 5 people to see how many each did:

400 toys/5 people = 80 toys/person

Next let's see how many hours were worked by multiplying the hours per day by the number of days worked:

5 days x 8 hours/day

40 hours

Now to find how many toys were assembled per hour per person, let's divide the toys/person by the number of hours they each worked:

\(\frac{80 toys/person}{40 hours}\)=2 toys/person/hour

The average number of toys per person per hour is 2.

Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

Total number of toys assembled = 400

Total days of work = 5  

Each person work daily for = 8 hrs

Total number of people = 5

Then, the total toys assembled per day

400/5= 80

The number of hours worked by the 5 workers per day = 8 × 5= 40

So, the number of toys assembled per person per hour = 80 / 40= 2

Hence, the average number of toys per person per hour is 2.

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Answer:

2 5$ bills

1 10$  bill

5 2$ bills

Step-by-step explanation:

Using the t-distribution, it is found that we do not reject the null hypothesis, which is convincing evidence that the machine is working properly.

At the null hypothesis, it is tested if the mean is of 1.5 inches, that is:

\(H_0: \mu = 1.5\).

At the alternative hypothesis, it is tested if it is different, hence:

\(H_1: \mu \neq 1.5\).

The test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

The parameters are:

In this problem, their values are:

\(\overline{x} = 1.476, \mu = 1.5, s = 0.203, n = 200\).

Hence, the test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{1.476 - 1.5}{\frac{0.203}{\sqrt{200}}}\)

\(t = -1.672\)

Considering a two-tailed test, as we are testing if the mean is diffrent of a value, with 200 - 1 = 199 df and a standard significance level of 0.05, the critical value is of \(|t^{\ast} = 1.972\).

Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis, which is convincing evidence that the machine is working properly.

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To solve a system of inequalities, find values of x and y satisfying both equations, simplifying and dividing by -1, resulting in x = 4 - 2y and y ≤ 5.

To find the solution of the system of inequalities, we need to find the values of x and y that satisfy both equations.

First, let's solve the equation x + 2y = 4 for x:
x = 4 - 2y

Now, let's substitute this expression for x in the second inequality:
y ≥ - (4 - 2y) - 1

Simplifying the inequality:
y ≥ -4 + 2y - 1

Combining like terms:
y - 2y ≥ -4 - 1

Simplifying further:
-y ≥ -5

Dividing both sides of the inequality by -1 (note that we need to reverse the inequality sign when dividing by a negative number):
y ≤ 5

So, the solution of the system of inequalities is x = 4 - 2y and y ≤ 5.

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Answer:

perimeter is 20 cm

Answer:

None of these choices are correct.

Step-by-step explanation:

75 = perimeter

Answer:

The new value of the list after changing 71° to 93° would be:

58, 61, 93, 77, 91, 100, 105, 102, 95, 82, 66, 57

The measure that changes the most would be the median. Without the change, the median was 86.5°, which was the average of the 7th and 8th values in the list (100 + 77) / 2. However, after changing 71° to 93°, the median becomes 91°, which is the average of the 6th and 7th values in the list (91 + 91) / 2.

Therefore, the median has changed by 4.5° (from 86.5° to 91°).

Answer: C. y=1/5x+1

Step-by-step explanation:

Answer:

5x-9y=2z

Step-by-step explanation:

5x8=40

9x3=27

2x11=22

so 40-27=22

Answer:

Brauilo is wrong because he divided by (x+1) instead of (x-1)

Step-by-step explanation:

The remainder Theorem states that

if polynomial f(x) is divided by binomial x-a, the remainder will equal f(a). The factor is positive so the binomial is the same as

which is why we divide by -1, or subsitue -1 into the equation p(x).

The remainder of a polynomial division can be gotten using remainder theorem or synthetic division.

The true statement is: Brauilo did not find the value of a, because he divided by (x+1) instead of (x-1)

From the question, we have the following parameters:

\(\mathbf{p(x) = x^4 +5x^3 + ax^2 - 3x + 11}\)

\(\mathbf{Divisor =x+ 1}\)

\(\mathbf{Remainder = 17}\)

First, we set the divisor to 0.

\(\mathbf{Divisor =x+ 1 = 0}\)

So, we have:

\(\mathbf{x+ 1 = 0}\)

Solve for x

\(\mathbf{x= -1}\)

The above equation means that, the value of x that will be used to test the polynomial is -1

From the question,

Hence, Braulio is incorrect, because he used the wrong value of x

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The probability that the sample proportion is between 0.2 and 0.42 can be calculated using the standard normal distribution.

To calculate the probability, we need to assume that the sample proportion follows a normal distribution. This assumption holds true when the sample size is sufficiently large and the conditions for the central limit theorem are met.

First, we need to calculate the standard error of the sample proportion. The standard error is the standard deviation of the sampling distribution of the sample proportion and is given by the formula sqrt(p(1-p)/n), where p is the estimated proportion and n is the sample size.

Next, we convert the sample proportion range into z-scores using the formula z = (x - p) / SE, where x is the given proportion and SE is the standard error. In this case, we use z-scores of 0.2 and 0.42.

Once we have the z-scores, we can use a standard normal distribution table or a statistical software to find the corresponding probabilities. The probability of the sample proportion falling between 0.2 and 0.42 is equal to the difference between the two calculated probabilities.

Alternatively, we can use the z-table to find the individual probabilities and subtract them. The z-table provides the cumulative probabilities up to a certain z-score. By subtracting the lower probability from the higher probability, we can find the desired probability.

In conclusion, the probability that the sample proportion is between 0.2 and 0.42 can be calculated using the standard normal distribution and z-scores. This probability represents the likelihood of observing a sample proportion within the specified range.

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Given :-

To Find :-

Solution :-

Cost of the boat is 7200 and tax on it is 504. We can find the tax% as ,

→ Tax% = Tax/Cost *100

→ Tax % = 504/7200*100% = 7%

Hence the tax on boat costing 8000 will be ,

→ Tax = 7% of 8000

→ Tax = 7/100*8000 = 560

Hence the tax on the boat costing 8000 is 560.

The number of miles rode by Abby each day is m.

The number of miles rode by Abby in one week (7days) is 7m.

The inequality can be determined as,

Thus, 7m>70 is the required inequality.

Answer:

5 units cause that ordinates are same abssisae is different

To determine how many times you can ride the rollercoaster at the state fair with 851 tickets, we need to know the cost of the tickets for the ride.

Once we know the cost, we can divide the total number of tickets by the cost of each ticket to find out how many times we can ride the rollercoaster.

Assuming that the cost of one ticket for the rollercoaster ride is 10 tickets, we can divide 851 by 10 to find out how many times we can ride the rollercoaster:

851 ÷ 10 = 85 with a remainder of 1

This means that you can ride the rollercoaster 85 times with 1 ticket left over.

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(a) The total amount Bill ended up paying for the equipment, including the down payment and monthly payments, can be calculated by adding the down payment to the total amount paid through monthly payments over the years.

(b) To determine the amount of interest Bill paid on the loan, we need to subtract the initial loan amount (rest of the equipment cost after the down payment) from the total amount paid.

(a) The total amount Bill ended up paying for the equipment can be obtained by adding the down payment to the total amount paid through monthly payments. The down payment represents the initial contribution made towards the purchase, while the monthly payments gradually cover the remaining cost of the equipment over the years. By summing up these two amounts, we obtain the total amount paid by Bill for the lab equipment.

(b) To calculate the amount of interest Bill paid on the loan, we need to subtract the initial loan amount from the total amount paid. The initial loan amount corresponds to the cost of the equipment minus the down payment. This represents the principal amount that Bill borrowed to finance the purchase. By subtracting the principal amount from the total amount paid, we can determine the interest paid on the loan.

It's important to note that the specific values for the down payment, loan amount, and monthly payments are not provided in the question. To obtain the exact total amount paid and the interest paid, these values would need to be known or provided.

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Answer:

0.075

Step-by-step explanation:

Divide the tax rate by 100. A tax of 7.5 percent was added to the product to make it equal to 4300. So, divide 7.5 by 100 to get 0.075.

To find out how many times greater Aaron's salary is than his backup, we can divide Aaron's salary by his backup's salary.

Aaron's salary = 2.2 * 10^7

Backup's salary = 6.3 * 10^5

Dividing Aaron's salary by the backup's salary:

(2.2 * 10^7) / (6.3 * 10^5)

When dividing numbers in scientific notation, we can divide the coefficients and subtract the exponents:

2.2 / 6.3 = 0.3492063492

10^(7 - 5) = 10^2 = 100

So, Aaron's salary is approximately 0.3492063492 times (or 34.9%) greater than his backup's salary.

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Explanation is\(^{}\) in a file

bit.\(^{}\)ly/3gVQKw3

Answer: 13,500

Step-by-step explanation:

Answer:

a) \(y=\frac{23}{6} x-156\)

b) \(\frac{268}{3}\)

Step-by-step explanation:

Formulas for linear equations:

Slope-intercept: \(y=mx+b\), where m is the slope and b is the y-intercept

Point-slope: \(y-y_1=m(x-x_1)\), where (x₁, y₁) is a point on the function and m is the slope.

a) We are given two points. If you're given two points (x₁, y₁) and (x₂, y₂), the slope m is given by the formula:

\(m = \frac{y_2-y_1}{x_2-x_1}\)

Let's mark the temperature on the x-axis, and the number of chirps per minute on the y-axis. So, we have the following points: (60, 74), and (72, 120). Calculating the slope m between these two points:

\(m=\frac{120-74}{72-60}\)

\(m=\frac{23}{6}\)

Since we have the x and y coordinates of a point on the function, we can write an equation in point-slope form, which will help us to find the y-intercept. We need the y-intercept in order to write the slope intercept form of the equation. We will use the point (60, 74) here, although you can also use (72, 120) if you want.

Point-slope form equation of the linear function:

\(y-74=\frac{23}{6} (x-60)\)

Now that we have the point-slope equation of the function, we can find the y-intercept. The y-intercept is the point on the function where the graph crosses the y-axis (when the x-value is 0). So, we plug in 0 for x into the equation and solve for y:

\(y-74=\frac{23}{6} (0-60)\)

\(y=-230+74\)

\(y=-156\)

Now that we have the y-intercept value of the function, we can write an equation in slope-intercept form:

\(y=\frac{23}{6} x-156\)

b) Since we marked the temperature on the x-axis, we can just plug in the number 64 as the x-value into the equation we have. y will be the number of chirps per minute when the temperature is 64º.

\(y=(\frac{23}{6} *64)-156\)

\(y=\frac{736}{3} - \frac{468}{3}\)

\(y=\frac{268}{3}\)

If you have any questions, leave a comment below.

The length and width of the rectangle are 7 cm and 8 cm

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

The length and width of a rectangle are consecutive integers

This means that

Length = x

Width = x + 1

So, we have

Area = x * (x + 1)

Substitute the known values in the above equation, so, we have the following representation

x * (x + 1) = 56

Express 56 as 7 * 8

So, we have

x * (x + 1) = 7 * 8

This means that

x = 7

So, we have

Length = 7

Width = 7 + 1

Length = 7

Width = 8

Hence, the length is 7 cm

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To find the position vector r(t) at a given time t₁, we substitute the value of t₁ into the expression for r(t). In this case, r(t) = t^2 i + t j. The position vector at t = t₁ is r(t₁) = t₁^2 i + t₁ j.

The position vector r(t) represents the position of a particle in three-dimensional space as a function of time. In this case, the position vector r(t) is given by r(t) = t^2 i + t j.

To find the position vector at a specific time t₁, we substitute the value of t₁ into the expression for r(t). Therefore, the position vector at t = t₁ is r(t₁) = t₁^2 i + t₁ j.

The position vector r(t₁) represents the position of the particle at time t₁. It is a vector with components determined by the values of t₁.

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Answer:

9

Step-by-step explanation:

[1/2]^-1 +[1/3]^-1 +[1/4]^-1=9

You need to simplify the expression.

You end up with the answer: 9