Write an equation for this sentence

The difference of twice x and four times the quantity x plus y is equal to twelve

The power to which a number or expression is raised is called the exponent.

1. An exponent is a mathematical notation that represents the power to which a number or expression is raised. It is written as a superscript number or variable placed above and to the right of the base number or expression.

2. The base number or expression is the number or expression that is being multiplied repeatedly by itself, raised to the power of the exponent.

3. The exponent tells us how many times the base number or expression should be multiplied by itself. For example, in the expression \(2^3\), the base is 2 and the exponent is 3. This means that 2 should be multiplied by itself three times: 2 * 2 * 2 = 8.

4. The exponent can be a positive whole number, a negative number, zero, or a fraction. Each of these cases has different interpretations:

  - Positive exponent: Indicates repeated multiplication. For example, \(2^4\)means 2 multiplied by itself four times.

  - Negative exponent: Indicates the reciprocal of the base raised to the positive exponent. For example, \(2^{-3\) means 1 divided by \(2^3\).

  - Zero exponent: Always equals 1. For example, \(2^0\) = 1.

  - Fractional exponent: Represents a root. For example, \(4^{(1/2)\)represents the square root of 4.

5. Exponents follow certain mathematical properties, such as the product rule \((a^m * a^n = a^{(m+n)})\), the quotient rule \((a^m / a^n = a^{(m-n)})\), and the power rule \(((a^m)^n = a^{(m*n)})\).

Remember to use these rules and definitions to correctly interpret and evaluate expressions involving exponents.

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Answer:

5x-4

Step-by-step explanation:

-(x+4)+6x           Hope this helps

-x-4+6x

       -1x

  5x-4

Answer:

20.8mm

Step-by-step explanation:

We know that an octagon has 8 sides, and since this is a regular octagon we can safely say that all sides are equal.

This means all sides are 2.6mm.

So if we run the calculation:

2.6mm × 8 = 20.8mm (Side Length × Number of Sides = Perimeter)

We have our final answer!

The average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

Given,

Benny's arcade has five video game machines

The average time between failures = 34 hours

The maintenance engineer can repair a machine in about = 13 hours

The failure time and repair times are both exponentially distributed

The formula for the mean of an exponential distribution is mean = 1/λ where λ is the rate parameter of the distribution.

In this problem, the rate parameter of both the failure time and repair time is the reciprocal of their respective averages. Therefore,

λ_f = 1/34λ_r = 1/13

Now, let's find the average time from when a machine breaks until it is fixed using the fact that the sum of two independent exponential distributions with rate parameters λ1 and λ2 is itself an exponential distribution with rate parameter λ1+λ2.

So, the rate parameter for the time from when a machine breaks until it is fixed is λ_f+λ_r = 1/34+1/13

= 0.0885 hours⁻¹ (approximately)

Hence, the average time from when a machine breaks until it is fixed is mean = 1/λ= 1/0.0885 ≈ 11.3 hours (approximately).

Therefore, the average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

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The sample size increases, the probability of obtaining a sample mean less than 3500 decreases. The mean of the sample mean distribution is equal to the population mean, which is 7500.

a) The probability that, on a single test, x is less than 3500 can be calculated using the standard normal distribution. We need to standardize the value using the z-score formula: z = (x - μ) / σ. Substituting the given values, we get z = (3500 - 7500) / 1750 ≈ -2.286.

Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of -2.286. The probability is approximately 0.0116, or 1.16%. Therefore, there is a 1.16% chance that a single test result will be less than 3500, indicating leukopenia.

(b) When the doctor uses the average x (sample mean) for two tests taken about a week apart, the probability distribution of x (sample mean) follows a normal distribution. The mean of the sample mean distribution is equal to the population mean, which is 7500. The standard deviation of the sample mean distribution is equal to the population standard deviation divided by the square root of the sample size. In this case, the sample size is 2.

The probability distribution of x (sample mean) < 3500 can be calculated by standardizing the value using the z-score formula and then finding the corresponding probability from the standard normal distribution table or a calculator. With two tests, the probability distribution will be narrower compared to a single test. The exact probability depends on the specific value of the sample mean and the standard deviation of the sample mean distribution.

(c) When considering three tests taken a week apart, the process is similar to part (b). The mean of the sample mean distribution remains the same at 7500, but the standard deviation of the sample mean distribution is now divided by the square root of 3, since the sample size is 3. As the sample size increases, the standard deviation of the sample mean distribution decreases, resulting in a narrower distribution.

The probability distribution of x (sample mean) < 3500 can be calculated using the z-score formula and finding the corresponding probability from the standard normal distribution table or a calculator. With three tests, the probability distribution will be even narrower compared to two tests.

In summary, as the sample size increases, the probability of obtaining a sample mean less than 3500 decreases. With more tests, we can have greater confidence in the accuracy of the sample mean and draw stronger conclusions about the individual's condition. If a person had a sample mean less than 3500 based on three tests, it would indicate a higher level of certainty about the presence of leukopenia, potentially leading to further investigation or treatment options.

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Answer:

$1,296

Step-by-step explanation:

kelly earns $288 during her first 8 hour shift. how much would kelly earn on a full paycheck of 36 hours? interpret your answer.

288/8 = $36 per hour

If she worked 36 hours at $36 per hour:

36* $36 = $1,296

The expression is restricted for x = -9, x = 3, and x = -3. These values should be excluded from the domain

To simplify the expression (2x² - 6x) / (x² + 18x + 81) * (9x + 81) / (x² - 9), we can first factor the denominators and cancel out any common factors:

(2x² - 6x) / (x² + 18x + 81) × (9x + 81) / (x² - 9)

The denominator (x² + 18x + 81) can be factored as (x + 9)(x + 9) or (x + 9)².

The denominator (x² - 9) is a difference of squares and can be factored as (x - 3)(x + 3).

Now we can simplify the expression by canceling out common factors:

(2x² - 6x) / (x + 9)² × (9x + 81) / (x - 3)(x + 3)

Next, we can simplify further by multiplying the numerators and denominators:

(2x² - 6x)(9x + 81) / (x + 9)²(x - 3)(x + 3)

To multiply the numerators, we can distribute:

(18x³ + 162x² - 54x² - 486x) / (x + 9)²(x - 3)(x + 3)

Combining like terms in the numerator:

(18x³ + 108x² - 486x) / (x + 9)²(x - 3)(x + 3)

Therefore, the simplified expression is (18x³ + 108x² - 486x) / (x + 9)²(x - 3)(x + 3).

As for the restrictions on the variables, we need to consider the denominators. The expression is undefined when any of the denominators equals zero:

(x + 9)² = 0 --> x = -9

(x - 3) = 0 --> x = 3

(x + 3) = 0 --> x = -3

So, the expression is undefined for x = -9, x = 3, and x = -3. These values should be excluded from the domain.

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The proportion of all registered voters, based upon a 99% confidence interval, would be 65% ± 4.6%. (Answer as a percentage rounded to two decimal spaces)

We have: Sample size, n = 250

Proportion of registered voters who intend to vote, p = 0.65q = 1 - p = 1 - 0.65 = 0.35

Confidence level = 99%

We are to find the margin of error.

We use the formula for the margin of error: ME = zα/2 * √(pq/n)

Where: zα/2 = the critical value at the 99% confidence level√(pq/n) = the standard error of the proportion

The critical value, zα/2 for a 99% confidence interval can be found using a Z-score table or calculator.

We can use an online calculator to obtain zα/2, which is 2.576.

The standard error of the proportion is given by: SE = √(pq/n)SE = √(0.65 * 0.35/250)SE = 0.034

The margin of error is: ME = zα/2 * √(pq/n) ME = 2.576 * 0.034ME ≈ 0.0874 = 0.0874 * 100% ≈ 4.6%

Therefore, the proportion of all registered voters, based upon a 99% confidence interval, would be 65% ± 4.6%. (Answer as a percentage rounded to two decimal spaces)

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Answer: 1 3/10

Step-by-step explanation:

Since we are informed that Annie has two boxes of markers and that the first box is 7/10 full while the second box is 6/10 full.

Therefore, the total markers that Annie has will be the addition of both boxes and this will be:

= 7/10 + 6/10

= 13/10

= 1 3/10

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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9/16 as a decimal is 0.5625.

A decimal number is a number that is written in the base-ten numeral system, which is the system we use in everyday life. In the decimal system, there are ten digits, from 0 to 9, and each digit has a place value that is ten times greater than the digit to its right.

To convert the fraction 9/16 to a decimal, you can divide the numerator (the top number) by the denominator (the bottom number) using long division or a calculator. Here's how to do it:

Write down the fraction 9/16.

Divide the numerator (9) by the denominator (16).

The quotient is the decimal equivalent of the fraction. In this case, the quotient is 0.5625.

Write the decimal as 0.5625.

Therefore, 9/16 is 0.5625.

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Answer:

x=12

Step-by-step explanation:

4x-10=3x+2

Subtract 3x on both sides:

x-10=2

Add 10 on both sides:

x=12

Hope this helps!

Answer:

50 gallons of each.

Step-by-step explanation:

Answer:

11.since diagonal are equal of rectangle

QS=RT

4x+6=6x-4

6+4=6x-4x

2x=10

x=10/2

x=5

now

diagonal :4x+6=4*5+6=26

12.

again

QS=RT

9x+12=11x-10

12+10=11x-9x

2x=22

x=11

now

diagonal=9*11+12=99+12=111

Answer:

x=-12

x=10

x=-8

x=-5

Step-by-step explanation:

Answer:

1.x=-12

2.x=10

3.x=-8

4.x=-5

Step-by-step explanation:

Answer:

D - T-H is negative

Step-by-step explanation:

So lets go through what we know:

M is on the left side of 0, so M is negative.

A is also one the left side of 0, so A is negative.

T is on the right side of 0, so T is postive

H is also on the right side of 0, so H is postive

Lets go through each answer and see if it is accurate or not:

The sum of M and H is postive.

With what we know, M is negative and H is postive.

Looking at the graph, we can see that M is farther to the left than H is to the right.

So this means that M is a larger negative than H is postive, meaning when we add them together, the answer will be negative, not postive.

Next we have the answer to A divided by H is negative

We know A is negative, and M also negative

Remember, a negative divided or multiplied by a negative is postive.

This is not what our answer states, as it says it should be negative.

So next off, we have the product of H and A is postive.

Product means multipication.

A is negative and H is postive

Since it is multipication, and we know a negative and postive make another negative, this would make it incorrect

The answer states it must be postive, but this is negative.

Finally we have the answer as T-H is negative.

We see that T is postive, and H is postive.

T is less than H is, so when you subtract H from T, you would get a negative.

So D is the answer

Hope this helps!

The answer is 4/15

2/5 * 2/3 = 2 · 2/5 · 3 = 4/15

Multiply the numerators and denominators together. Keep the result fraction to the smallest possible denominator GCD(4, 15) = 1. It cannot further simplify the fraction result by canceling in the following intermediate step.

In other words, two fifths times two thirds equals four fifteenths.

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Answer:

5/3

Step-by-step explanation:

"of" means times so so so often. It is not a hard math rule/definition. But more like a soft English-Math translation.

So, "2/5 of what"

means 2/5x (but make sure the 2/5 is a fraction beside the x, NOT the x on the bottom with the 5)

"is" means equals.

2/5x = 2/3

Multiply both sides by 5/2.

5/2 • 2/5x = 2/3•5/2

x = 2/3 • 5/2

x = 5/3

You get 5/3 either by "cancelling" the 2's OR by

fraction multiplication where you times top×top and bottom×bottom and simplify.

x = 10/6

x = 5/3

2/5 of 5/3 is 2/3.

The "what" in the question is 5/3.

Answer:

Step-by-step explanation:

The difference between two consecutive even integers  is 2

and even integer is always twice some integer

So:

2x   ← smaller of numbers

2x+2  ←  larger of numbers  

2×2x     ←  twice the smaller of numbers

3(2x+2)      ←  three  times the larger

3(2x+2)-26   ← 26 less than 3 times the larger

twice the smaller is  26 less than 3 times the larger:

3(2x+2) - 26 = 2×2x

6x + 6 - 26 = 4x

       +20         +20

6x - 4x = 20

       2x = 20

2x+2 = 20 + 2 = 22        

Check:   2×20=40; 40+26 = 66; 66÷3=22

Answer:

Todd (but only by like 0.2%)

Step-by-step explanation:

If you convert 1/7 to a percentage(by multiplying it by 100)

you get 14.285%

Round this off and you get 14.3%

Step-by-step explanation:

The horse eats 9/12 in 9 days.

The elevation of the hole relative to ground level is 23,956 feet.

Elevation:

The height to which something is elevated: such as. : the angular distance of something (such as a celestial object) above the horizon. : the degree to which a gun is aimed above the horizon. : the height above the level of the sea: altitude.

Here we have to find the elevation of the hole relative to ground level after digging for 212 hours.

Data given:

Rate of digging the hole = is 113 feet every hour

Time = 212 hours

Elevation of ground level = 0

Elevation = digging rate × number of hours

                = 113 × 212

                = 23,956 feet

Therefore the elevation is 23,956 feet.

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Answer: 21 < t  unless it is subtraction then its t - 21

Each friend gets 1/6 pan of brownie

What is Fraction?

A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.

Solution:

Given that, 1/2 pan of brownie is left and it is shared in 3 people

To find the share of each person / fraction that each friend gets we need to

divide 1/2 by 3

(1/2)/3

It means each person/friend gets 1/6 pan of brownie

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The reduced cost matrix for travelling salesperson problem in the given instance is shown below. The Travelling Salesperson Problem (TSP) is a classical combinatorial optimization issue that belongs to the category of NP-Hard problems.

This problem can be resolved using a branch and bound algorithm or by using dynamic programming.The reduced cost matrix for the given travelling salesperson problem instance The computation of the reduced cost matrix for travelling salesperson problem involves two steps: Identify the smallest element of each row and subtract the value from all the values in the row.

Identify the smallest element of each column and subtract the value from all the values in the column.In the given instance, the smallest element of each row is highlighted in bold. Therefore, after performing Step 1 the matrix becomes the matrix becomes Hence, the reduced cost matrix for the travelling salesperson problem is obtained.

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Answer:

a=16 b =10 or any other combination that gives 160

a = 20 b=8

a = 32 b = 5

Step-by-step explanation:

The area of a triangle using the lengths of two sides and the sine of the included angle is ½ ab sin C  where a and b are sides and C is the angle.

A =40 = 1/2 ab sin 30°

sin 30° = 1/2 so

40 = 1/2*ab*1/2

40 =1/4 ab multiply each side by 4

160 = ab

any combination of sides that gives you 160 will work

Let's check if a=16 b =10

A = 1/2*16*10 sin 30°

A = 1/2*160*1/2

A = 40

Answer:

total balls 5+4 = 9

Probability of getting blue ball in the first try

                                                                   =\(\frac{5}{9}\)

After replacing, total number of balls  = 9

Probability of getting blue ball in the second try

                                                                  \(= \frac{5}{9}\)

Therefore probabilty of getting 2 blue balls

                                                               =\(\frac{5}{9}*\frac{5}{9} =\frac{25}{81}\)

Answer:

The solution to the system of equations is (x, y). To find the value of x, we need to solve for x in one of the equations, and then substitute that value into the other equation to check if it holds.

One way to solve the first equation is to add 6y to both sides and then divide both sides by 5:

5x - 6y = 2.7

5x = 2.7 + 6y

x = (2.7 + 6y)/5

We can then substitute this expression for x into the second equation:

10((2.7 + 6y)/5) + 7 = 1.6

Simplifying this equation we get:

8.4 + 3y = 1.6

3y = -6.8

y = -2.27

Now we can substitute y = -2.27 back into the first equation to find the value of x:

5x - 6(-2.27) = 2.7

5x + 13.62 = 2.7

5x = -10.92

x = -2.184

So the value of x is approximately -2.184 .