Find the unit rate (How much for
one shirt?):
$98.73 for 6 shirts (round to the
nearest hundredth).

The slope-intercept equation of a line has the form

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

Now, there is a very interesting relationship between the slopes (m_1 and m_2) of perpendicular lines:

Looking at the given equation, we can say that its slope is 1/2. Then,

Then, our desired equation becomes

Now, we know that our line passes through (-2,5). This means that

Solving this equation for b, we get

The desired line has equation

Answer:

The answer is 1050

Step-by-step explanation:

The value of f(-0.01) is approximately 0.99005.

To evaluate f(-0.01), we substitute -0.01 into the function f(x) = (1+x)^(1/x). Thus, we have f(-0.01) = (1+(-0.01))^(1/(-0.01)).

Using a calculator, we simplify this expression to f(-0.01) = 0.99005. Therefore, the value of f(-0.01) rounded to five decimal places is approximately 0.99005.

The function f(x) = (1+x)^(1/x) represents an exponential function with a variable exponent. In this case, we are evaluating the function at x = -0.01.

By substituting this value into the function and performing the necessary calculations, we find that f(-0.01) is approximately 0.99005. This means that when x is equal to -0.01, the function value is approximately 0.99005.

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The total principal and interest payment that Nelson will have to pay after 2 months is $4665.50.

To calculate the total principal and interest payment, we need to determine the interest amount and add it to the principal.

First, let's find the interest amount:

Interest = Principal x Interest Rate x Time

Given:

Principal = $4650

Interest Rate = 2% per year

Time = 2 months

Since the interest rate is given on an annual basis, we need to convert the time from months to years. There are 12 months in a year, so 2 months is equivalent to 2/12 = 1/6 years.

Interest = $4650 x 0.02 x (1/6) = $15.50

Now, we can calculate the total principal and interest payment:

Total Payment = Principal + Interest

Total Payment = $4650 + $15.50 = $4665.50

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Answer:

Step 1: Read the entire problem. Students will find themselves reading the story numerous times. Each time will have a different purpose in the model drawing process. Step 2: Turn the question into a sentence with a space for the answer.

The number of square meters that the space that Araceli rents is, is 30. 66 square meters.

The space that Araceli rents has a rectangular space so to find the area of the rectangular space that Araceli rents, we need to multiply the length by the width.

The given width is 4. 2 meters and the length is 7. 3 meters.

The area of the space in square meters is therefore :

Area = Length × Width

Area = 7. 3 meters × 4. 2 meters

Area = 30. 66 square meters

In conclusion, the space that Araceli rents has an area of 30. 66 square meters.

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Answer:

constant: 4

coefficient:-5

variable:x

Step-by-step explanation:

You can easily search up the definition of each word and figure it out just saying. It's fine if u wanna do this-

The surface areas for each figures are:

1. The surface area of the cuboid is:

Top and bottom: 2(10 ft x 4 ft) = 80 ft²

Front and back: 2(10 ft x 5 ft) = 100 ft²

Sides: 2(4 ft x 5 ft) = 40 ft²

Total surface area = 80 + 100 + 40 = 220 ft²

2. The surface area of the cuboid is:

Top and bottom: 2(18 cm x 5 cm) = 180 cm²

Front and back: 2(18 cm x 5 cm) = 180 cm²

Sides: 2(5 cm x 5 cm) = 50 cm²

Total surface area = 180 + 180 + 50 = 410 cm²

3. The surface area of the prism is:

Top and bottom: 2(5 cm x 14 cm) = 140 cm²

Front and back: 2(5 cm x 12 cm) = 120 cm²

Sides: 2(12 cm x 14 cm) = 336 cm²

Total surface area = 140 + 120 + 336 = 596 cm²

4. The surface area of the stacked cuboids is:

Top and bottom of first cuboid: 2(6 cm x 7 cm) = 84 cm²

Front and back of first cuboid: 2(6 cm x 2 cm) = 12 cm²

Sides of first cuboid: 2(7 cm x 2 cm) = 28 cm²

Front and back of second cuboid: 2(7 cm x 2 cm) = 28 cm²

Sides of second cuboid: 2(2 cm x 4 cm) = 8 cm²

Front and back of third cuboid: 2(2 cm x 10 cm) = 40 cm²

Sides of third cuboid: 2(10 cm x 8 cm) = 160 cm²

Total surface area = 84 + 12 + 28 + 28 + 8 + 40 + 160 = 360 cm²

5. The surface area of the cylinder is:

Top and bottom: 2π(6 mm)² = 72π mm²

Side: 2π(6 mm)(5 mm) = 60π mm²

Total surface area = 72π + 60π = 132π mm²

6. The surface area of the cylinder is:

Top and bottom: 2π(1 ft)² = 2π ft²

Side: 2π(1 ft)(10 ft) = 20π ft²

Total surface area = 2π + 20π = 22π ft²

7. The surface area of the cylinder stacked on a cube is:

Top and bottom of cylinder: 2π(5 m)² = 50π m²

Side of cylinder: 2π(5 m)(8 m) = 80π m²

Surface area of cube: 6(10 m x 13 m) = 780 m²

Total surface area = 50π + 80π + 780 = (130π + 780) m²

8. The surface area of the cylinder is:

Top and bottom: 2π(9 in)² = 162π in²

Side: 2π(9 in)(4 in) = 72π in²

Therefore, the total surface area of the cylinder is:

2(162π in²) + 72π in² = 396π in²

So the surface area of the cylinder is 396π square inches.

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Image transcribed:

Find the surface area of each figure.

10 ft

18 cm

5 cm

4 ft

5 ft

3.

4.

6 cm

7 cm

2 cm

5 cm

12 cm

14 cm

4 cm

10 cm

8 cm

Find the surface area of each cylinder. Leave your answer in terms of π.

5.

6 mm

6.

1 ft

5 mm

10 ft

7.

5 m

8.

4 in.

8 m

10 m

9 in.

13 m

11 m

247

Journal and Practice Workbook

Geometry

Answer:

log(3x⁹y⁴) = log 3 + 9 log x + 4 log y

Answer:

\(\log 3+ 9\log x +4 \log y\)

Step-by-step explanation:

Given logarithmic expression:

\(\log 3x^9y^4\)

\(\textsf{Apply the log product law:} \quad \log_axy=\log_ax + \log_ay\)

\(\log 3+\log x^9 +\log y^4\)

\(\textsf{Apply the log power law:} \quad \log_ax^n=n\log_ax\)

\(\log 3+ 9\log x +4 \log y\)

Answer:

26+a

Step-by-step explanation:

(12+a)+14

(12+14)+a

26+a

Answer:

Step-by-step explanation:

160,150,158,159,160,160,162,165,166,167,170,175

Write the 12 numbers in ascending order:

     150, 158, 159, 160, 160, 160, 162, 165, 166, 167, 170, 175

We need the middle number but there is no middle number:

      150, 158, 159, 160, 160, 160,       162, 165, 166, 167, 170, 175

We have split the numbers into 2 even amounts and there is no number in the middle so we take the middle 2 number and find there average:

      150, 158, 159, 160, 160,      160, 162,      165, 166, 167, 170, 175

Average of 160 and 162 \(=\frac{160+162}{2} =161\).

SOLUTION: Median is 161cm.

The inverse of the function f(x) = 1/3x^2 - 3x + 5 is  f-1(x) = 9/2 + √[3(x + 7/4)], the sum of the arithmetic series is 1078 and the common ratio of the sequence is 2

The function is given as:

f(x) = 1/3x^2 - 3x + 5

Next, we rewrite the function as in vertex form

Using a graphing calculator, the vertex form of the function f(x) = 1/3x^2 - 3x + 5 is

f(x) = 1/3(x - 9/2)^2 - 7/4

Express f(x) as y

y = 1/3(x - 9/2)^2 - 7/4

Swap x and y

x = 1/3(y - 9/2)^2 - 7/4

Add 7/4 to both sides

1/3(y - 9/2)^2 = x + 7/4

Multiply through  by 3

(y - 9/2)^2 = 3(x + 7/4)

Take the square root of both sides

y - 9/2 = √[3(x + 7/4)]

Add 9/2 to both sides

y = 9/2 + √[3(x + 7/4)]

Rewrite as an inverse function

f-1(x) = 9/2 + √[3(x + 7/4)]

Here, we have:

5 + 18 + 31 + 44 + ... 161

Calculate the number of terms using:

L = a + (n -1)d

So, we have:

161 = 5 + (n - 1) * 13

This gives

(n - 1) * 13 = 156

Divide by 13

n - 1 = 12

Add 1

n = 13

The sum is then calculated as:

Sn = n/2 * [a + L]

This gives

Sn =13/2 * (5 + 161)

Evaluate

Sn = 1078

Hence, the sum of the arithmetic series is 1078

Here, we have:

T11  = 32 * T6

The nth term of a geometric sequence is

Tn = ar^(n-1)

This gives

ar^10 = 32 * ar^5

Divide by ar^5

r^5 = 32

Take the fifth root

r = 2

Hence, the common ratio of the sequence is 2

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Answer:

x+y=40 and 6x+9y=288

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1200\\ P=\textit{original amount deposited}\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}\)

\(1200 = P\left(1+\frac{0.07}{12}\right)^{12\cdot 15} \implies 1200=P\left( \frac{1207}{1200} \right)^{180} \\\\\\ \cfrac{1200}{ ~~ \left( \frac{1207}{1200} \right)^{180} ~~ }=P\implies 421.21\approx P\)

For part a, you can use a chi-squared test to determine whether the variance in the sample exceeds the maximum acceptable variance in the population.

The null hypothesis for this test is that the variance in the sample is equal to or less than the maximum acceptable variance, and the alternative hypothesis is that the variance in the sample is greater than the maximum acceptable variance.

To perform the test, you need to first calculate the chi-squared statistic, which is given by:

X² = (n-1) * s² / σ²

where n is the sample size (in this case, 15), s is the sample standard deviation (in this case, 0.014 inches), and σ is the maximum acceptable variance (in this case, 0.0001 inches).

Plugging in the values, you get:

X² = (15-1) * .014² / .0001² = 27.44

Next, you need to determine the degrees of freedom for the test. In this case, the degrees of freedom is equal to the sample size minus 1, so the degrees of freedom is 14.

With the chi-squared statistic and the degrees of freedom, you can look up the p-value in a chi-squared table or use a chi-squared calculator to determine the p-value. The p-value is the probability of observing a chi-squared statistic as large or larger than the one you calculated, assuming the null hypothesis is true.

If the p-value is less than the significance level (in this case, .10), then you can reject the null hypothesis and conclude that the variance in the sample exceeds the maximum acceptable variance. In this case, the p-value is between 0.01 and 0.025, so you can reject the null hypothesis and conclude that the variance in the sample exceeds the maximum acceptable variance.

For part b, you can use a t-test to construct a 90% confidence interval estimate of the variance in the population. The confidence interval is an interval estimate of the true variance in the population, and the 90% confidence level means that there is a 90% probability that the true variance in the population falls within the confidence interval.

To construct the confidence interval, you first need to calculate the standard error of the variance, which is given by:

SE = s / √(n-1)

where s is the sample standard deviation and n is the sample size. Plugging in the values, you get:

SE = 0.014 / √(15-1) = 0.0041

Next, you need to determine the t-value for the confidence interval. The t-value is based on the degrees of freedom and the confidence level. With 14 degrees of freedom and a 90% confidence level, the t-value is 1.76.

With the standard error and the t-value, you can construct the confidence interval as follows:

Lower bound = s² - t * SE = .014² - 1.76 * 0.0041 = 0.00012 inches

Upper bound = s² + t * SE = .014² + 1.76 * 0.0041 = 0.00042 inches

Therefore, the 90% confidence interval estimate of the variance of the ball bearings in the population is .00012 to .00042 inches.

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The Lim household used 225 kWh of electricity in that month. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers are thought to be adequately described by the four basic operations, often known as "arithmetic operations." The mathematical operations quotient, product, sum, and difference come after division, multiplication, addition, and subtraction.

We are given that the Lim household paid $45 for electricity usage in a certain month and each electricity (in kWh) is charged at $0.20​.

Let the electricity used be x.

So, we get an equation as

⇒ 0.20x = $45

Using the division operation, we get

⇒ x = 225 kWh

Hence, the Lim household used 225 kWh of electricity in that month.

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Answer:

Step-by-step explanation:

sin (B) = \(\frac{2}{5}\)

(A) The range and IQR for boxplot 1 is 10 and 6 respectively.

(B) The range and IQR for boxplot 2 is 12 and 7 respectively.

The interquartile range defines the difference between the third and the first quartile.

The formula for the interquartile range is given below.

Interquartile range = Upper Quartile – Lower Quartile = Q­3 – Q­1

The range is the difference between the lowest and highest values.

The formula for the interquartile range is given below.

Range = Maximum – Minimum

(A) For boxplot 1, we need to find the range and IQR from the given data set.

So, let 34 be the maximum and 24 be the minimum.

\(\text{Range}=\sf 34-24\)

\(\text{Range}=\sf10\)

Therefore, the range is 10.

Now time to find the IQR.

So, let 33 be Q3 and 27 be Q1.

\(\text{IQR}=\sf 33-27\)

\(\text{IQR}=\sf 6\)

Therefore, the IQR is 6.

(B) Now for boxplot 2, we will do the same thing as from part A.

Let's find the range.

So, let 24 be the maximum and 12 be the minimum.

\(\text{Range}=\sf 24-12\)

\(\text{Range}=\sf12\)

Hence, the range is 12.

Now for the IQR.

So, let 22 be Q3 and 15 be Q1.

\(\text{IQR}=\sf 22-15\)

\(\text{IQR}=\sf 7\)

Hence, the IQR is 7.

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Answer: a=1,b=1

Step-by-step explanation:

b

The p-value can also be calculated using a t-distribution table or a statistical software package. Using a two-tailed test with 7 degrees of freedom and a significance level of 0.05, we obtain a p-value of 0.073.

How to solve the question?

To determine whether the fitness program has had a significant effect on reducing employee absenteeism, we need to conduct a hypothesis test.

Null hypothesis: The average number of absences before and after the fitness program are the same.

Alternative hypothesis: The average number of absences after the fitness program is less than before the program.

To test this hypothesis, we can use a one-tailed paired t-test with a significance level of 0.05. We will calculate the difference between the number of absences before and after the program for each employee, and then compute the mean and standard deviation of the differences. The t-test statistic will then be calculated as the mean difference divided by the standard deviation of the differences, multiplied by the square root of the sample size.

Using the given data, we calculate the differences and obtain the following results:

Employee Before After Difference (d) d²

1 8 7 -1 1

2 7 3 -4 16

3 8 2 -6 36

4 8 4 -4 16

5 6 5 -1 1

6 7 10 3 9

7 6 4 -2 4

8 8 9 1 1

Mean difference (d-bar) = -1.25

Standard deviation of differences (s) = 3.27

Sample size (n) = 8

The t-test statistic can now be calculated as:

t = (d-bar / (s / √(n))) = (-1.25 / (3.27 / √(8))) = -1.63

The degrees of freedom for the t-test is n-1 = 7, which can be used to obtain the p-value from a t-table or calculator. Using a one-tailed test with a significance level of 0.05 and 7 degrees of freedom, the critical t-value is -1.895.

Since our calculated t-value (-1.63) is greater than the critical t-value (-1.895), we fail to reject the null hypothesis. In other words, we do not have sufficient evidence to conclude that the fitness program has resulted in a significant reduction in employee absenteeism.

The p-value can also be calculated using a t-distribution table or a statistical software package. Using a two-tailed test with 7 degrees of freedom and a significance level of 0.05, we obtain a p-value of 0.073. Since this p-value is greater than the significance level, we again fail to reject the null hypothesis.

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Answer:

\(18x^2+85x+18 = 0\)

Step-by-step explanation:

Given Equation is

=> \(2x^2+7x-9=0\)

Comparing it with \(ax^2+bx+c = 0\), we get

=> a = 2, b = 7 and c = -9

So,

Sum of roots = α+β = \(-\frac{b}{a}\)

α+β = -7/2

Product of roots = αβ = c/a

αβ = -9/2

Now, Finding the equation whose roots are:

α/β ,β/α

Sum of Roots = \(\frac{\alpha }{\beta } + \frac{\beta }{\alpha }\)

Sum of Roots = \(\frac{\alpha^2+\beta^2 }{\alpha \beta }\)

Sum of Roots = \(\frac{(\alpha+\beta )^2-2\alpha\beta }{\alpha\beta }\)

Sum of roots = \((\frac{-7}{2} )^2-2(\frac{-9}{2} ) / \frac{-9}{2}\)

Sum of roots = \(\frac{49}{4} + 9 /\frac{-9}{2}\)

Sum of Roots = \(\frac{49+36}{4} / \frac{-9}{2}\)

Sum of roots = \(\frac{85}{4} * \frac{2}{-9}\)

Sum of roots = S = \(-\frac{85}{18}\)

Product of Roots = \(\frac{\alpha }{\beta } \frac{\beta }{\alpha }\)

Product of Roots = P = 1

The Quadratic Equation is:

=> \(x^2-Sx+P = 0\)

=> \(x^2 - (-\frac{85}{18} )x+1 = 0\)

=> \(x^2 + \frac{85}{18}x + 1 = 0\)

=> \(18x^2+85x+18 = 0\)

This is the required quadratic equation.

Answer:

α/β= -2/9      β/α=-4.5

Step-by-step explanation:

So we have quadratic equation  2x^2+7x-9=0

Lets fin the roots  using the equation's  discriminant:

D=b^2-4*a*c

a=2 (coef at x^2)   b=7(coef at x)  c=-9

D= 49+4*2*9=121

sqrt(D)=11

So x1= (-b+sqrt(D))/(2*a)

x1=(-7+11)/4=1   so   α=1

x2=(-7-11)/4=-4.5    so  β=-4.5

=>α/β= -2/9       => β/α=-4.5

Answer:

35/16

Explanation:

(5*7)/2^4

= 35/2^4

= 35/16

Note:

Please mark as brainliest! <3

Answer:

the answer would be 4m

hope this helped

Answer:

4m

Well there's 4 m's being added so to put it in simple terms, it would be 4m.

Answer:

0.5

Step-by-step explanation:

Add everything together 33+66+33 = 132

Then 66/132, = 1/2 or 0.5

Answer:

\( c = 15.5 \)

Step-by-step explanation:

Using the Law of Cosines, c² = a² + b² - 2ab*cos(C), let's find c.

Where,

a = 15 ft

b = 20 ft

C = 50°

Thus:

\( c^2 = 15^2 + 20^2 - 2*15*20*cos(50) \)

\( c^2 = 625 - 600*0.6429 \)

\( c^2 = 625 - 600*0.6429 \)

\( c^2 = 625 - 385.74 \)

\( c^2 = 239.26 \)

\( c = \sqrt{239.26} \)

\( c = 15.5 \) (nearest tenth)

Answer:

c sorry gotta get points.

Step-by-step explanation:

Answer:

- 72 - 48i

Step-by-step explanation:

note that i² = - 1

(6i)(- 2i)(- 6 - 4i)

= - 12i²(- 6 - 4i)

= - 12(- 1)(- 6 - 4i)

= 12(- 6 - 4i) ← distribute parenthesis by 12

= - 72 - 48i

Two lines are parallel if their slopes are equal. To find the slope of the line through the points (1,2) and (1,a), we can use the formula:

(y2 - y1) / (x2 - x1) = (a - 2) / (1 - 1) = a - 2

To find the slope of the line 6x + 2y = -2, we can rewrite it in slope-intercept form (y = mx + b) by isolating y:

2y = -6x - 2

y = -3x - 1

So the slope of this line is -3.

Since the line through the points (1,2) and (1,a) is parallel to 6x + 2y = -2, we know that the slopes must be equal. Therefore:

a - 2 = -3

Solving for a:

a = -1

So the value of a is -1.

Answer:

|3| < |-7| and 3>-7

Step-by-step explanation:

The absolute value of -7 = 7, and 3 < 7.