Are the expressions 5(m + 1 ) - 1 and 2(2m + 2) + m equivalent

It will take 7 hours to paint a room when Sonia and Roman works together.

Given,

Time taken by  Sonia to paint a room = 12 hours

Time taken by Roma to paint the same room = 15 hours

We have to find the time taken by both of them to paint the room if they work together.

Here,

Sonia takes 12 hours

Roman takes 15 hours

LCM of 12 and 15 = 60

12 × 5 = 60

15 × 4 = 60

Total number of works is 60

Now,

Number of works done by Sonia = 5 in an hour

Number of works done by Roman = 4 in an hour

So,

5 + 4 = 9 work can be done by them together in an hour

Then,

Time taken to complete 60 works;

60/9 = 6.66 ≈ 7 hours

That is,

In 7 hours Sonia and Roman paint a room together.

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The monthly payment amount a woman has to pay for the car is $462.91.

Here we have to find the monthly payment amount.

The cost of car = $23,800

Down payment = $3,500

Rate(r) = 4.5%

time(t) = 4 years

Periodic interest(i) = 0.045/12

Formula to calculate monthly payment:

A = P i( 1 + i[tex])^{n}[/tex] / ( 1 + i[tex])^{n}[/tex] - 1

Loan amount = 23800 - 3500

                      = $ 20300

A = 20300 ( 0.045 /12 ( 1 + 0.045/12[tex])^{48}[/tex])/ (1 + 0.045/12[tex])^{48}[/tex] - 1

  = 20300× 0.004488 / 0.196814

  = 462.91

Therefore the monthly payment is $462.91.

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There is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.

Given, an ice cream truck aims to keep 30 degrees as the mean temperature inside its delivery truck.

one employee claims that the mean temperature inside its delivery truck is more than 30 degrees. the employee conducts a hypothesis test and rejects the null hypothesis.

The mean temperature inside its delivery truck is 32 degrees.

As, the temperature inside the delivery truck should be 30 degrees and should not be greater than 30 degrees then, there is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.

So, there is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.

Hence, there is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.

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Answer:

1

Step-by-step explanation:

The equation to represent this would be (1 - (1 / 3)) / 2

1 - (1 / 3) = 2 / 3

2 / 3 / 2 = 1 / 3

7m-(7n-18m) is an expression which is equivalent to (2mn)^4/6m^-3 n^-2 Assume m=0 n=0​

What is a expression in maths?

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/variable, Math Operator, Number/variable)

for example 4m +5 where 4 is the coefficient of m and 5 is the constant term in other word 4m and 5 are the term of the expression and m is the variable in the expression and addition is the operator.

m=0, n=0.

8m^7n^6/3 10m^7n^6/3 8m^16n^12/3 m^4n^6/3

-7m-(3n-(8m-4n-10m)

-7m-(3n-(8m-4n+10m))

-7m-(3n-(18m-4n))

-7m-(3n-18m+4n)

-7m-(7n-18m)

complete question is

Which expression is equivalent to (2mn)^4/6m^-3 n^-2? Assume m=0 n=0​

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Answer:

Step-by-step explanation: x is the number of days she is booked.

List an equation

748+86x=734+87x

x=14

14 nights and plugging x into the equation 1952 points

Using the table the quadratic equation is y = x² - 2

from the curve the quadratic equation is y = x² + 1

Quadratic equation is written of the form

y = a(x - h)² + k

from the table the vertex is

v(h, k) = v(0, -2)

substituting the values to the formula

y = a(x - 0)² - 2

y = ax² - 2

Using the point (2, 2) from the table

y = ax² - 2

2 = a * 2² - 2

2 = 4a - 2

4a = 2 + 2

4a = 4

a = 1

The equation of the curve is

y = x² - 2

from the graph the vertex is

v(h, k) = v(0, 1)

substituting the values to the formula

y = a(x - 0)² + 1

y = ax² + 1

Assuming a unit on the graph is a unit we take point (1, 2) where the curve passed

y = ax² + 1

2 = a * 1² + 1

2 = a + 1

a = 2 - 1

a = 1

The equation of the curve is

y = x² + 1

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The slope of the straight line is 4/5

The slope of a line is a measure of the ratio between the rise and run of that line. The slope of a line is an integral quantity used to calculate the equation of a line

In general, to find the slope of a line, we need to have the values of any two different coordinates on the line.

The slope of a line basically the change in y-coordinate with respect to change in x-coordinate.

This is easily done with a formula given as

m = y₂ - y₁ / x₂ - x₁

Taking data points from the graph attached;

Substituting the values into the slope equation;

m = -2 - 2 / 0 - 5

m = -4 / - 5

m = 4/5

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The square in RMSE is utilized because it consistently provides a positive number for error, preventing errors from canceling one another out, and grants higher weight to values further from the target function, emphasizing locations for which the estimator is unreliable. To reverse the results of squaring, use the square root. 

What is RMSE?

The difference between values (sample or population values) predicted by a model or estimator and the values observed is typically measured using the root-mean-square deviation (RMSD) or root-mean-square error (RMSE).

The RMSD is the quadratic mean of the square root of the second sample moment of the discrepancies between expected values and observed values.

When computations are made outside of the data sample that was used for estimation, the deviations are referred to as errors (or prediction errors) instead of residuals.

The RMSD is used to combine the sizes of predictions' mistakes for different data points into a single indicator of predictive power. .

RMSD is a metric for accuracy that is used to compare the predicting mistakes of various models.

Hence, The square in RMSE is utilized because it consistently provides a positive number for error, preventing errors from canceling one another out, and grants higher weight to values further from the target function, emphasizing locations for which the estimator is unreliable. To reverse the results of squaring, use the square root. 

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Answer:

2.5a - 1.5 b or

5/2a - 3/2b

Step-by-step explanation:

a + (a - b) + 0.5(a - b) =

a + a - b + 0.5a - 0.5b =

2a - b + 0.5a - 0.5b =

2a - 1.5 b + 0.5a  =

2.5a - 1.5 b

The wire should be anchored to the ground to minimize the amount of wire needed 20 ft from the left pole.

What is the quadratic equation?

ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Let x (ft) be the distance from the base of the left pole to the anchor point. Since 2 poles has a distance of 30 ft, the distance from the anchor point to the right pole is 30 - x.

The wire length from the top of the left pole to the anchor point is

[tex]L^{2} _{l} = 20^{2} + x^{2} = x^{2} + 400[/tex]

Similarly for the 2nd part of the wire

[tex]L^{2} _{t} = 10^{2} + (30 - x^{2})[/tex]

= 100 + 900 - 60x + x²

= x²+ 1000 - 60x

We want to minimize the length of the wires, or [tex]L^{2} _{l} + L^{2} _{r}[/tex]

[tex]\frac{x}{\sqrt{{x}^2 + 400} } + \frac{x - 30}{\sqrt{{x}^2 + 400}} = 0[/tex]

we can take the first derivative of this and set it to 0

x = 20

Hence, the wire should be anchored to the ground to minimize the amount of wire needed  20ft.

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Answer:

4/3

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (-3 - 1)/(-2 - 1)

slope = -4/(-3)

slope = 4/3

Answer:

7

Step-by-step explanation:

if he gets $35 in 5 hours then he gets $7 an hour, and 7*7=49.

Answer: 7 hours

Step-by-step explanation:

$35/5 hours=$7 an hour

$49/$7 an hour=7 hours of mowing

Applying the definition of midpoint, the measure of angle GIH in the triangle shown is: 59°.

The corresponding angles of two similar triangles are always congruent to each other.

Given that H is the midpoint of Eg and I is the midpoint of FG, two similar triangles are created, where angles GFE and GIH are corresponding angles.

Given:

m∠GFE = 87 - 7x

m∠GIH = 51 + 2x

m∠GFE = m∠GIH [corresponding angles are congruent]

Substitute

87 - 7x = 51 + 2x

Solve for x

-2x - 7x = 51 - 87

-9x = -36

Divide both sides by -9:

-9x/-9 = -36/-9

x = 4

m∠GIH = 51 + 2x = 51 + 2(4)

m∠GIH = 59°

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A statement which is true about the graphs of f(x) = x and g(x) = f(x + 7) is: C. g(x) is the graph of f(x) translated 7 units to the left.

In Mathematics, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

In Geometry, g(x + 7) or g(x) = f(x + 7) simply means shifting a graph 7 units to the left as illustrated by the graph shown in the image attached below.

In this context, we can reasonably infer and logically deduce that the parent function f(x) = x was shifted by 7 units to the left.

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Complete Question:

Which of the following statements is true about the graphs of f(x)=x and g(x)=f(x+7)?

A. g(x) is the graph of f(x) translated 7 units down.

B g(x) and f(x) have the same y-intercept.

C g(x) is the graph of f(x) translated 7 units to the left.

D g(x) is the graph of f(x) translated 7 units to the right.

Answer:

it's 20 if u look closely

Step-by-step explanation:

[tex] {3}^{10 - 6} [/tex]

[tex] = {3}^{4} [/tex]

Cara has a 25/216 chance of waiting until her third throw before throwing a six.

for the stated question-

Total times the dice is thrown = 3.

Total number of sample space = 6 x 6 x 6 = 216.

The probability of coming six = 1/6

The probability of not coming six = 1 - 1/6 = 5/6.

Probability of getting 6 in third throw = 5/6 x 5/6 x 1/6

Probability of getting 6 in third throw = 25/216

Thus, Cara has a 25/216 chance of waiting until her third throw before throwing a six.

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If one tries to store a list of single-digit numbers in his or her short-term memory, then he will be able to store 7 numbers on average.

What is short-term memory?

Short-term memory is a concept in psychology that defines the capacity for holding a small amount of information in mind for a short interval. The concept of short-term memory is given by Atkinson-Shiffrin. The information of short-term memory can be transformed into long-term memory through rehearsal.

According to several studies, short-term memory has a space limit of 7 ± 2 chunks of information. The fact is written by a cognitive psychologist of Harvard University named George A. Miller and was published in 1956 in psychological reviews.

Hence, If one tries to store a list of single-digit numbers in his or her short-term memory, then he will be able to store 7 numbers on average.

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The equation representing the number of bottle Barbara need to sell to earn $100 is; 1.49x + 1.25y = 100.

For the given question-

Let the number of iced tea bottle be 'x'.

Let the number of water bottle be 'y'.

Total price = 100

Thus, the equation for the total cost becomes-

1.49x + 1.25y = 100.

Therefore, the equation representing the number of bottle Barbara need to sell to earn $100 is; 1.49x + 1.25y = 100.

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Answer:

i need points

Step-by-step explanation:

To find the margin of error we have to use the formula,

Margin of error =  Z * ơ / √n ,

Where

z = critical factor

ơ = population standard deviation

n = sample size

Now we have to find confidence interval

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

x+/-ME

Where margin of error ME = zr/√n

Given that;

Mean = ц

Standard deviation r = 25

Number of samples n = 41

Confidence interval = 95%

z(at 95% confidence) = 1.96

Xbar = 60.............(1)

Xbar + E = 66.........(2)

from equating both the equations we get

E= 6

and for finding the value of margin of error we know that its the half of the E

Margin of error = E/2

=6/2

=3

Therefore , the Margin of error is 3

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Assuming the population standard deviation is known and the standard deviation of the sample mean x : option (b) is correct : the standard error of the sample mean decreases.

In probability theory, the central limit theorem (CLT) states that the distribution of a sample variable approximates a normal distribution (i.e., a “bell curve”) as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population's actual distribution shape.

Standard deviation is a calculation of the dispersion or variation in a set of numbers. If the standard deviation is a small number, it means the data points are close to their average value. If the deviation is large, it means the numbers are spread out, further from the mean or average.

There are different ways to write out the steps of the population standard deviation calculation into an equation. A common equation is:

                          σ = ([Σ(x - u)2]/N)1/2

Where:

σ is the population standard deviation

Σ represents the sum or total from 1 to N

x is an individual value

u is the average of the population

N is the total number of the population

A sample mean is an average of a set of data . The sample mean can be used to calculate the central tendency, standard deviation and the variance of a data set. The sample mean can be applied to a variety of uses, including calculating population averages.

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a) The probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $210 of the population mean is 0.9482.

b) When trying to estimate the population mean, a greater sample size offers the benefit of improving the estimation's accuracy.

a. The z-score is calculated as follows:

z = (x - μ) ÷ (σ ÷ √n)

Where the sample size is n, the sample mean is x, the population mean is y, and the population standard deviation is z.

By entering the specified values, we obtain:

n = 30: z = (x - 17,545) ÷ (2,160 ÷ √30) = (x - 17,545) ÷ 216

n = 50: z = (x - 17,545) ÷ (2,160 ÷ √50) = (x - 17,545) ÷ 174

n = 100: z = (x - 17,545) ÷ (2,160 ÷ √100) = (x - 17,545) ÷ 132

n = 400: z = (x - 17,545) ÷ (2,160 ÷ √400) = (x - 17,545) ÷ 53

To find the odds that a sampling distribution could be within $210 of both population mean and the z-score, we must first figure out the likelihood that now the z-score would be within 1.96 standard deviations of the mean. This is because the 95th percentile, or the number under which 95% of the data lies, is represented by the z-score of 1.96, which is the value in this case.

To ascertain the likelihood, we must attempt searching up the z-scores in a z-table and get the pertinent probabilities. A z-table is a table that lists the probability associated with various z-scores.

Using the z-scores we used to develop the concept, we could look up the alternatives in a z-table and find the following probability:

n = 30: 0.4056

n = 50: 0.5082

n = 100: 0.6690

n = 400: 0.9482

For each of the aforementioned sample sizes, the likelihood that a sampling of taxpayers from this income category who itemized deductions will exhibit a sample mean that is within $210 of the population mean is:

n = 30: 0.4056

n = 50: 0.5082

n = 100: 0.6690

n = 400: 0.9482

b. The likelihood that the sample means will closely match the true population mean is thereby increased.

The standard deviation averages commonly fall as the sample size rises. In other words, as the sample mean becomes less likely to depart from the actual population mean, the likelihood that the random variable will be close to the population mean increases.

For instance, in the aforementioned case, the likelihood that they would give it a shot would be within 210 of a population mean would rise from 0.4056 for a random sample of just 30 to 0.9482 for a random sample of 400.

This means that the likelihood that they give it a chance will fall within the allowed range of the sample % likewise increases as the sample size increases.

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Unlike fraction 1/7 is converted to equivalent  like fraction 2/14 and the sum of 2/14 + 3/14 = 5/14.

As given in the question,

Given fraction is equal to:

1/7=? + 3/14=?

Here there are two fractions

1/7 and 3/14

LCD( least common denominator) of 7 and 14 is equal to 14.

Now make them like fractions

1/7 is equivalent to

( 1/7) × ( 2/2) = 2/ 14

Now 2/14 and 3/14 are like fractions

Sum of like fractions is:

2/14 + 3/14

= ( 2+ 3) / 14

= 5/ 14

Therefore, the conversion of unlike fraction 1/7 to like fraction is 2/14. And sum of 2/14 + 3/14 = 5/14.

The complete question is:

Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If possible, reduce the final sum. 1/7=? + 3/14=?

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If a jar contains 15 red marbles and 14 blue marbles. If you reach in the jar and pull out 2 marbles at random, the probability that both are red is: 2/812.

Probability

Total marbles:

Total marbles=15+14

Total marbles = 29

Chance that a red will be pulled=2/29

Chance that the second marble will be red =1/28

Hence,

Probability :

Probability = 2/29*1/28

Probability = 0.00246

Therefore  If a jar contains 15 red marbles and 14 blue marbles. If you reach in the jar and pull out 2 marbles at random, the probability that both are red is: 2/812

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A manager be interested in analyzing risk to determine a range of outcomes.

Project managers and their teams undertake risk analysis, such as calculating the likelihood of various undesirable outcomes affecting a project, to avoid or minimize their impacts. The process can help reduce exposure, time, and budget overruns and keep businesses in compliance.

Analyzing risk can help to uncover threats to the success of the projects or business operations, such as: vulnerabilities in security; potential litigations, penalties and non-compliance issues; and, mistakes in budget or scheduling.

In general, there are 4 accepted ways to respond to risks, those are: avoidance, mitigation, acceptance, and transfer.

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