how to solve this with steps?

Answer:

\(3(x - 5) \leqslant 24 \\ 3x - 15 \leqslant 24 \\ 3x \leqslant 24 + 15 \\ 3x \leqslant 39 \\ x \leqslant \frac{39}{3} \\ x \leqslant 13\)

Answer:

x ≤ 13

Step-by-step explanation:

Let's sort out the brackets first, expand them.

3(x-5) --> 3x - 15

Now our equation looks like this.

3x - 15 ≤ 24

Since we are solving the inequality, let's get the x on its own. Add the 15 to remove it from one side.

3x - 15 ≤ 24

     +15   +15

3x ≤ 39

We are still trying to get x on its own so let's divide the 3, to remove it.

3x ≤ 39

 ÷3  ÷3

x ≤ 13

And that is the final answer!

Answer:

\(m = \frac{5}{2} \)

Step-by-step explanation:

Here are the laws which would be used in this question:

Indices:

• \( \sqrt{a} = {a}^{ \frac{1}{2} } \)

• \( \frac{1}{a} = {a}^{ - 1} \)

Logarithm

• \( log_{a}( {x}^{n} ) = n log_{a}(x) \)

\( log_{m}( \sqrt{2} ) + log_{m}(8) + log_{m}( \frac{1}{2} ) \)

\( = log_{m}( {2}^{ \frac{1}{2} } ) + log_{m}( {2}^{3} ) + log_{m}( {2}^{ - 1} ) \)

\( = \frac{1}{2} log_{m}(2) + 3 log_{m}(2) - log_{m}(2) \)

\( = \frac{5}{2} log_{m}(2) \)

The linear model for this data is y = 0.63t + 4.922 and the estimated population of Greensboro in 2015 was 11,530

What is slope?

Slope is a measure of the steepness of a line. It is defined as the change in y-coordinate divided by the change in x-coordinate between any two points on the line.

a. To find the linear model for this data, we need to determine the equation of the line that passes through the two given points: (0, 4.922) and (6, 9.1). The slope of this line can be calculated as:

slope = (change in y) / (change in t)

slope = (9.1 - 4.922) / (6 - 0)

slope = 0.63

Using the point-slope form of a linear equation, we can write the equation of the line as:

y - 4.922 = 0.63(t - 0)

Simplifying, we get:

y = 0.63t + 4.922

Therefore, the linear model for this data is y = 0.63t + 4.922.

b. To estimate the population in 2015, we need to find the value of y when t = 11 (since 2015 is 11 years after 2004). Substituting t = 11 into the linear model, we get:

y = 0.63(11) + 4.922

y = 11.53

Therefore, the estimated population of Greensboro in 2015 was 11,530 (rounded to the nearest whole number).

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The parts of this equilateral triangle ABC are as follows:

The length of side x of the equilateral triangle is determined as follows:

AD = x

AB = 6

DB = 6/2 or 3

AB² = AD² + DB²

6² = x² + 3²

x² = 6² - 3²

x = 27

x = 3√3

Therefore, the length of the perpendicular bisector AD is 3√³ units

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Answer:

the length is 3√³ units

The missing length of the triangle can be found using the Pythagorean Theorem which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can use the formula c² = a² + b² where c is the hypotenuse, a is the opposite side and b is the adjacent side.

To find the missing length, we can rearrange the formula to solve for b: b² = c² - a². Substituting the given values,

we have: b² = (0.5)² - (0.3)².

Simplifying the equation, we get: b² = 0.16.

Taking the square root of both sides, we get: b = 0.4 cm.

Therefore, the missing length of the triangle is 0.4 centimeters.

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The number that the last page will have would be = 232.

The total number of digits that will be used for numbering of pages in a book = 235 digits.

The first page which represents one of the pages of the book to be numbered = page 3

Therefore the last page would be = 235-3 = 232 page.

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Answer:

81

Step-by-step explanation:

The shape is a square so it has all equal sides.

324/4=81

Answer:

P = 10x+4

Step-by-step explanation:

The perimeter of a rectangle is given by

P = 2(l+w) where l is the length and w is the width

P = 2( 3x+2+ 2x)

Combine like terms

P = 2(5x+2)

Multiply by 2

P = 10x+4

Mantago should borrow the money for 72.7 months or approximately 6 years,

We can use the following formula to determine the loan length:

Loan length = Loan amount / (Monthly payment - Monthly interest payment)

We must first determine the monthly interest payment, which may be done by applying the following formula:

Monthly interest payment = (APR / 12) * Loan amount

Plugging in the values:

Monthly interest payment = (7.5 / 12) * $10,000 = $62.5

The values can now be entered into the calculation to determine the length of the loan:

Loan length = $10,000 / ($200 - $62.5) = $10,000 / $137.5 = 72.7 months

Therefore, Mantago should borrow the money for 72.7 months, or approximately 6 years, in order to afford the monthly payment of $200.

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Answer:

The probability that we will obtain a sample mean greater than 21" is 0.00164 (\( \\ P(\overline{x}>21) = P(z>2.94) = 0.00164\)).

Step-by-step explanation:

The fundamental concept to understand to answer this question is, at least, the sampling distribution of means. Roughly speaking, this is the distribution of different means, \( \\ \overline{x}\), of the random variable \( \\ x\) for samples of the same size, \( \\ n\). That is, for each sample, we get its mean, and the probability distribution of them is called the sampling distribution of means.

As the sample size, \( \\ n\), is greater, the distribution of \( \\ \overline{x}\) follows a normal distribution with mean that equals the population mean, \( \\ \mu\), and standard deviation that equals \( \\ \frac{\sigma}{\sqrt{n}}\). This result is known as the Central Limit Theorem, and it is crucial in Statistical Inference. Mathematically:

\( \\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})\) [1]

It is important to remember that this result is valid following the rule of thumb that the sample size, \( \\ n\), must be, at least, greater or equals to 30, that is, \( \\ n \geq 30\), no matter the distribution that follows \( \\ x\) (this result is not important if

Another important concept is that the random variable \( \\ Z\), which is a standardized variable, that is, (roughly speaking) a variable that indicates the distance in standard deviations units from the mean, \( \\ \mu\), of a value in the distribution. In this case, the latter is \( \\ \overline{x}\). We can express this mathematically as follows:

\( \\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\) [2]

This variable \( \\ Z\) follows a standard normal distribution or a normal distribution with \( \\ \mu = 0\) and standard deviation \( \\ \sigma = 1\) or \( \\ Z \sim N(0, 1)\).

With all this information, we can proceed to answer the question.

The probability that we will obtain a sample mean greater than 21

Or calculate \( \\ P(x>21)\).

For doing this, we have:

Well, all we have to do is use [2] to calculate \( \\ P(x>21)\) as follows:

\( \\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\( \\ Z = \frac{21 - 19}{\frac{7}{\sqrt{106}}}\)

\( \\ Z = \frac{2}{\frac{7}{10.29563}}\)

\( \\ Z = \frac{2}{0.67990}\)

\( \\ z = 2.94160 \approx 2.94\)

(We rounded this value to \( \\ z = 2.94\) since standard normal tables have two digits for decimal part of \( z\). Notice we use z lowercase since z = 2.94 is a realization of random variable Z, and also that z is the standardized score for \( \\ \overline{x}\).)

With this value of z = 2.94, we can consult the standard normal table (available in Statistics books or on the Internet), and, specifically for this case, we need to consult the cumulative standard normal table (cumulative probability from \( \\ -\infty\) to the value of z).

Here we have z = 2.94. The entry to consult the table is 2.9 (positive). Then, looking carefully the first row in the table, we need to find the column with value 0.04 (to have z = 2.94). The intersection of these two values "gives us" the cumulative probability for z = 2.94. Then, \( \\ P(z<2.94) = 0.99836\).

This is also the cumulative probability for \( \\ P(\overline{x}<21)\) (as we explained above, z is the standardized value for \( \\ \overline{x}\).)

However, we need to know \( \\ P(\overline{x}>21) = P(z>2.94)\). Since

\( \\ P(z<2.94) + P(z>2.94) = 1\)

Then

\( \\ P(z>2.94) = 1 - P(z<2.94)\)

\( \\ P(z>2.94) = 1 - 0.99836\)

\( \\ P(\overline{x}>21) = P(z>2.94) = 0.00164\)

Therefore, "the probability that we will obtain a sample mean greater than 21" is 0.00164.

Answer:

yo what is your question??????

Step-by-step explanation:

Maybe c 7 to 2

A sample size of at least 538 freshmen to estimate the proportion of freshmen who do not visit their advisors regularly with a margin of error of 4% and a confidence level of 95%.

To answer your question, we need to use the formula for sample size calculation for proportion:
n = [(Z-score)^2 * p(1-p)] / E^2

Where:
n = required sample size
Z-score = the critical value for the desired confidence level (95% confidence level corresponds to a Z-score of 1.96)
p = the estimated population proportion (34% or 0.34)
1-p = the complement of p
E = the desired margin of error (4% or 0.04)

Plugging in the values:
n = [(1.96)^2 * 0.34(1-0.34)] / (0.04)^2
Simplifying the equation:
n = [(3.8416) * 0.2244] / 0.0016
n = 537.38

We need a sample size of at least 538 freshmen to estimate the proportion of freshmen who do not visit their advisors regularly with a margin of error of 4% and a confidence level of 95%. Keep in mind that this is just an estimate based on the historical data and assumes that the population proportion has not changed significantly.

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The computed mean is 58.8 degrees based on frequency distribution.

To find the mean of the data summarized in the frequency distribution, we first need to find the midpoint of each class interval.

Midpoint of 40-44 = (40 + 44) / 2 = 42
Midpoint of 45-49 = (45 + 49) / 2 = 47
Midpoint of 50-54 = (50 + 54) / 2 = 52
Midpoint of 55-59 = (55 + 59) / 2 = 57
Midpoint of 60-64 = (60 + 64) / 2 = 62

Next, we multiply each midpoint by its corresponding frequency and add up the results.

(2 x 42) + (6 x 47) + (12 x 52) + (7 x 57) + (3 x 62) = 1764

Finally, we divide this sum by the total number of values (which is the sum of the frequencies).

2 + 6 + 12 + 7 + 3 = 30

1764 / 30 = 58.8

The computed mean is 58.8 degrees.

When we compare this to the actual mean of 57.8 degrees, we see that the computed mean is slightly higher. This may be due to the fact that there are more values in the higher end of the distribution (i.e. 50-54 and 55-59) compared to the lower end (i.e. 40-44 and 45-49).

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Answer:

15  pieces of chocolate 7.5 s'mores

Step-by-step explanation:

you multiply 15 and 5 and you find the answer is 7.5

The expression used to find the product of the numbers 3,5, and 7 is 3 x 5 x 7.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the numbers are 3,5 and 7. The product will be done as below,

To find the product of the numbers we need to multiply all the numbers.

Product = 3 x 5 x 7

Hence, the product will be calculated by the expression 3 x 5 x 7.

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Answer:

y + 2 = -0.069(x-+5)

Step-by-step explanation:

SInce the two lines intersects, we will equate it

Multiply x + 3y = 0 by 4;

4x + 12y = 0

4x-4y-13 = 0,

Subtracts both

12y +4y + 13 = 0

16y = 13

y = 13/16

get x;

x + 3(13/16) = 0

x = -39/16

The point of intersection is (0.8, -2.4) and (-5,-2)

Get the equation;

m = y2-y1/x2-x1

m = -2+2.4/-5-0.8

m = 0.4/-5.8

m = -0.069

Get the equation;

y - y0 = m(x-x0)

y - (-2)= -0.069(x-(-5))

y + 2 = -0.069(x-+5)

Answer:

\(23\frac{1}{16}\) pulgada

Step-by-step explanation:

\(\frac{16}{9} =\frac{41}{y}\)

16 × y = 9 × 41

16y = 369

16y ÷ 16 = 369 ÷ 16

\(y=23\frac{1}{16}\)

False. The expected cell frequency in statistical analysis, specifically in the context of contingency tables and chi-square tests, is not based on the researcher's opinion. Instead, it is determined through mathematical calculations and statistical assumptions.

In contingency tables, the expected cell frequency refers to the expected number of observations that would fall into a particular cell if the null hypothesis of independence is true (i.e., if there is no relationship between the variables being studied). The expected cell frequency is calculated based on the marginal totals (row totals and column totals) and the overall sample size.

The expected cell frequency is computed using statistical formulas and is not influenced by the researcher's opinion or subjective judgment. It is a crucial component in determining whether the observed frequencies in the cells significantly deviate from what would be expected under the null hypothesis.

By comparing the observed cell frequencies with the expected cell frequencies, statistical tests like the chi-square test can assess the association or independence between categorical variables in a data set.

Thus, the statement "the expected cell frequency is based on the researcher's opinion" is false. The expected cell frequency is derived through statistical calculations and is not subject to the researcher's subjective input.

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The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.

In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:

There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.

Two-way interactions:

There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.

These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:

There is 1 possible three-way interaction that can be tested in this design: AxBxC.

This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.

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Answer:

27 hours

Step-by-step explanation:

We are given the information that it takes 6 hours for 20 workers to seed 40 acres. This means that with 20 workers the rate is 40 acres in 6 hours, or 40/6 = 6.67 acres per hour. When we only have 10 workers, we only have half as many people, therefore the rate will be twice as slow, so with 10 workers, the rate is 6.67/2 = 3.34 acres/hour.

To find how long it takes to seed 90 acres we just need to divide 90 by the rate. 90/3.34 = 27 hours.

Hope this helped!

Answer:

y = -3/4x + 7

Step-by-step explanation:

ok first u need to find the slope so use the slope equation for this (x2 - x1 over y2 - y1) so

1 - 4 = -3

8 - 4 4

so the m is -3/4

now you need to find the y intercept so pick one of the points (let's do (8, 1)) and plug that into the slope intercept form (y = mx+b)

so 1 = -3/4(8) + b

1 = -6 + b

+ 6 + 6

b = 7

so the equation is y = -3/4x + 7. hope this helps

Given the expression:

the given logarithms are written to the base (e), we will change the base to 3

First, we will simplify the expression then change the base to 3

As we know: ln(AB) = ln A + ln B

so, the given expression can be written as:

now, we will change (ln 27) from the base (e) to the base (3) as follows:

Now, taking the logarithm to the base 3

so,

so, the answer will be:

To classify the points for the given equation, we need to examine the behavior of the coefficients and the solutions of the equation near each point.

Point x = 1:

At x = 1, the coefficient (x - 1) becomes zero, indicating a potential singular point. To determine the type of singular point, we need to examine the behavior of the other coefficients and the solutions near x = 1.

Point x = 4:

At x = 4, the coefficient (x^2 - 16) becomes zero, indicating a potential singular point. To determine the type of singular point, we need to examine the behavior of the other coefficients and the solutions near x = 4.

Points at infinity:

To determine the behavior of the equation at infinity, we perform a change of variables: x = 1/z, which transforms the equation into a new equation in terms of z. We then examine the behavior of the coefficients and the solutions near z = 0.

Based on the information provided, we cannot classify each point as ordinary, regular singular, irregular singular, or special points without further analysis. The behavior of the equation and the classification of the points depend on the specific form of the solutions and the coefficients near each point. Additional analysis is needed to classify the points accurately.

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The amount of the markup is $48 + $48 (0.55) .

Option (C) is correct .

Mark up refers to the value that a player adds to the cost price of a product. The value added is called the mark-up. The mark-up added to the cost price usually equals retail price.

As given

An item is purchased for a wholesale price of $48 and will be sold at a 55 percent markup.

55% is written in the decimal form .

                                              = 55/100

                                              = 0.55

Markup price = 0.55 × wholesale price of item .

                      = 0.55 × $48

                     = $48 (0.55)

Price of item after markup = Wholesale price of item + Markup price

                                           = $48 + $48 (0.55)

Thus, the amount of the markup is $48 + $48 (0.55) .

Option (C) is correct .

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Answer:The answer is A

Step-by-step explanation:

Edg 2022 (sometimes the verified ones are wrong)

A completely randomized model in a single factor study means that the assignment of treatments is completely random, with no underlying pattern or bias.

When analyzing the difference in means between treatments in a single factor, a completely randomized model means that each individual or unit in the study has an equal chance of being assigned to any of the treatment groups.

In other words, the assignment of treatments is completely random, with no underlying pattern or bias.

This type of experimental design is important because it helps to minimize the effects of confounding variables and other sources of bias.

By randomly assigning treatments to study participants, researchers can be confident that any observed differences in the outcome variable are due to the treatment itself, rather than to other factors that may vary between the groups.

In statistical analysis, a completely randomized model can be used to test whether there are significant differences in the means between the different treatment groups.

This can be done using methods such as analysis of variance (ANOVA) or t-tests, depending on the number of treatment groups and the type of outcome variable being measured.

Overall, the completely randomized model is an important tool for ensuring that the assignment of treatments in a single factor study is unbiased and that the resulting data are suitable for statistical analysis.

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Answer:

$351.58

Step-by-step explanation:

According to the problem, calculation of given data are as follows,

Current balance = -$250.25

Other charge (debit) = $101.33

So, Now the current balance in the account are as follows,

Current balance = - $250.25 + (- $101.33)          (debit is negative)

Current balance = -$250.25 -$101.33

Current balance =  -$351.58

So, we need $351.58 to bring account balance to $0.

Answer:

146,000

Step-by-step explanation:

Simple math let me know if you need anymore help honey, have a nice day!