Given that2x - 2 < g(x) < x^2 + 2x - 3, use the Sandwich Theorem to

Answer:

43%

Step-by-step explanation:

443.50 divided by 1015 is 0.43 when rounded; 0.43 as a fraction is 43%. So therefore, the answer is 43%.

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

Answer:

p = 1,400

Step-by-step explanation:

In the simple interest rate formula, each year the same amount of interest is applied, as it's based off the initial amount invested and the interest rate.

\(I=P*r*t\)

Where "r" is the interest rate, "t" is time, and "p" is the principle amount, or initial amount invested.

We're given the following values:

Now the only thing is generally speaking, interest is applied annually rather than monthly. So we would need to convert the 3 months into years, which we can do by dividing by 12, giving us: 0.25 years

So we actually have: t = 0.25 years

Now from here we can plug in known values, and leave anything we don't know alone. So we start with our initial formula of:

\(I=P*r*t\)

Now from here we plug in i = 21, t = 0.25, r = 0.06 and leave "P" as "P"

\(21=P*0.25*0.06\)

Now let's simplify the multiplication on the right side:

\(21 = 0.015P\)

Divide both sides by 0.015:

\(1,400=P\)

And now we have our missing value!

Answer:

x-intercept = -6      y-intercept = 9

Step-by-step explanation:

The regression equation is: y = -0.0068824x + 36.8881

So, the correct option is:

D) None of these.

To compute the regression equation based on the given data, we can use the formulas for slope (b1) and y-intercept (bo):

b1 = (NΣXY - ΣXΣY) / \((N\sum X^2 - (\sum X)^2)\)

bo = (ΣY - b1ΣX) / N

Where:

N = Number of data points (in this case, 11)

ΣX = Sum of all X values (prices)

ΣY = Sum of all Y values (average number of pounds sold per day)

ΣXY = Sum of the product of X and Y values

\(\sum X^2\) = Sum of the squares of X values

Using the provided data:

Ex = 210

Xy = 450

Zcy = 10387

Zz = 7275

Xy = 42471

Let's calculate the required values:

N = 11

ΣX = Ex + Zcy + Zz = 210 + 10387 + 7275 = 17872

ΣY = Xy = 450

ΣXY = Xy = 450

\(\sum X^2 = (Ex)^2 + (Zcy)^2 + (Zz)^2 = (210)^2 + (10387)^2 + (7275)^2 = 239208144\)

Now, substitute these values into the formulas to find b1 and bo:

\(b1 = (11 \times450 - 17872 \times 450) / (11 \times239208144 - (17872)^2)\)

= -14112250 / 2050445128

≈ -0.0068824

bo = (450 - (-0.0068824 \(\times\) 17872)) / 11

= (450 + 122.7790368) / 11

≈ 36.8881

Therefore, the regression equation is:

y = -0.0068824x + 36.8881

So, the correct option is:

D) None of these.

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The complete question may be like:

Over a period of one year, retailer sells widgets at 11 different prices. He Calculates the average number of oiunds sold per day at each different price. From theese data, the following are calculated. Ex = 210, Xy = 450, Zcy = 10387, Zz? 7275 Xy? 42471 Compute the regression equation , SELEC A) y 0.20261x + 0.549951 B) y = 0.549951x + 30.410021 C) y = 0.20261. + 30.410021 D) none of these =b1x + bo.

4 cm² is its height in centimetres (cm) in triangle .

How do triangles work?

The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point.

                        The triangle's three angles add up to a total of 180 degrees. Three sides, three angles, and three vertices make up the closed, two-dimensional shape of a triangle. A triangle is a type of polygon.

The area of this triangle is 12 cm².

The area of this triangle = 1/2 * b * h

                          12 = 1/2 * 6 * h

                          h = 4 cm²

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If Group 1 trees produce 25 percent more coconuts than Group 2, proportionately, Group 2 trees produce 120 coconuts.

Proportion refers to the two ratios equated to each other.

Proportion shows how much quantity or value is contained in another.

We depict proportions using fractional values, such as fractions, decimals, and percentages.

The number of coconuts produced by Group 1 trees = 150

The percentage by which Group 1 trees produce more than Group 2 = 25%

Let Group 1's production compared to Group 2's = 1.25 (100% + 25%)

Let Group 2's production = 100% = 150/125 x 100

= 120 coconuts

Thus, Group 2 trees would produce 120 coconuts compared to Group 1 trees that produced 150, which was proportionately, 25% more.

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Answer:

Step-by-step explanation:

4=y/8+1

rewrite equation

y/8 + 1 = 4

move all terms not containing y to the right of the equation

y/8 = 3

multiply both sides of the equation by 8

8 x y/8 = 8 x 3

simplify both sides of the equation.

y = 24

Answer:

The person can correct this error two ways.  The first is by multiplying every part of the right side by 8 instead of only the \(\frac{y}{8}\):

\(8(4) = (\frac{y}{8} + 1)(8)\\32 = y + 8\\24 = y\)

Another way to fix it is to subtract 1 from both sides before multiplying both sides by 8.

\(4 - 1 = (\frac{y}{8} + 1) - 1\\3 = \frac{y}{8} \\8(3) = \frac{y}{8}(8)\\24 = y\)

Please be sure to mark brainliest if this satisfies your question.

The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.

the greatest common divisor of 5! and 7! is 120.

To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.

First, let's calculate the values of 5! and 7!:

5! = 5 * 4 * 3 * 2 * 1 = 120

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Now, let's factorize both numbers:

Factorizing 120:

120 = 2^3 * 3 * 5

Factorizing 5,040:

5,040 = 2^4 * 3^2 * 5 * 7

To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).

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The total out-of-pocket expense for one month is $677. The correct option is D.

The first step is to calculate the amount of the prescription costs that will be covered by the insurance plan.

Since the family will fill 6 prescriptions per month and the total cost is $850, the average cost per prescription is $850/6 = $141.67 per prescription.

The insurance plan covers 90% of the first $450 in prescription costs, which is $450 * 0.9 = $405.

The remaining $141.67 - $405 = -$263.33 of the first prescription is not covered, since it is below the $450 threshold. This means that the family will have to pay the full cost of the first prescription, and the insurance will not contribute anything to it.

For the remaining 5 prescriptions, the insurance will cover 80% of the cost, since they are over the $450 threshold. The remaining 20% will be the family's responsibility.

The cost of the remaining 5 prescriptions is $141.67 x 5 = $708.35.

The insurance will cover 80% of this amount, which is $708.35 x 0.8 = $566.68.

The family will be responsible for the remaining 20% of the cost, which is $708.35 x 0.2 = $141.67.

Adding up all the costs, the total out-of-pocket expense for one month is:

$405 (first prescription) + $141.67 (20% of remaining prescription costs) + $48 (monthly premium) = $594.67

Therefore, the correct answer is option D: $677.

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Answer: C

Step-by-step explanation:

The cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

To find the cost of one hosta and one geranium, we can set up a system of equations based on the given information.

Let's assume the cost of one hosta is represented by 'h' and the cost of one geranium is represented by 'g'.

From the information given, we can set up the following equations:

Eugene's spending:

18h + 6g = $150

Jessica's spending:

7h + 16g = $113

We can now solve this system of equations to find the values of 'h' and 'g'.

Multiplying the first equation by 2 and the second equation by 3 to eliminate 'g', we get:

36h + 12g = $300

21h + 48g = $339

Now, we can subtract the second equation from the first to eliminate 'h':

(36h + 12g) - (21h + 48g) = $300 - $339

36h - 21h + 12g - 48g = -$39

15h - 36g = -$39

Simplifying further, we have:

15h - 36g = -$39

Now we can solve this equation for 'h' and substitute the value back into any of the original equations to find 'g'.

Let's solve for 'h':

15h = 36g - $39

h = (36g - $39) / 15

Substituting this value of 'h' into Eugene's equation:

18[(36g - $39) / 15] + 6g = $150

(648g - $702) / 15 + 6g = $150

648g - $702 + 90g = $150 * 15

738g - $702 = $2250

738g = $2250 + $702

738g = $2952

g = $2952 / 738

g ≈ $4

Now, substituting the value of 'g' back into Eugene's equation:

18h + 6($4) = $150

18h + $24 = $150

18h = $150 - $24

18h = $126

h = $126 / 18

h ≈ $7

Therefore, the cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

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62 = 12.

7 x 0 = 7.

Four hundred and eight is written as 4008.

0.10 = point ten.

0.5 x 10 = 0.50.

6 -:- ½ = 3.

- 5 + 3 = -8.

4% is 0.4 as a decimal.

Answer:

1st

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the answer would be a because it is shown more than the others

Answer:

D

Step-by-step explanation:

x coordinates are horizontal and it goes up so it is going right

Answer:

At x = 13, the expression inside the absolute value bars becomes 0, so F(13) = |0| + 11 = 11. Therefore, the vertex of the graph of F(x) is the point (13, 11).

Step-by-step explanation:

The graph of the function F(x) = |x - 13| + 11 is the graph of the absolute value function shifted 13 units to the right and 11 units up from the origin. The vertex of this graph is the point where the absolute value function changes direction, which is at the point (13, 11).

To see why this is the case, consider the definition of the absolute value function:

|x| = x, if x >= 0

|x| = -x, if x < 0

The function F(x) = |x - 13| + 11 is a translation of the absolute value function by 13 units to the right and 11 units up. This means that the vertex of the graph will occur at the point where the absolute value function changes direction, which is at x = 13.

At x = 13, the expression inside the absolute value bars becomes 0, so F(13) = |0| + 11 = 11. Therefore, the vertex of the graph of F(x) is the point (13, 11).

Using a TI-83, TI-83 Plus, or TI-84 Population standard deviation is 56.4 and Population variance is 3178.5 .

To calculate the population standard deviation and variance using a TI-83, TI-83 Plus, or TI-84 calculator, we can use the following steps:

Enter the data into a list on the calculator. To do this, press the STAT key, then select Edit. Enter the data into L1.

Calculate the sample mean by pressing STAT, then CALC, then 1-Var Stats. Make sure L1 is selected as the list, then press ENTER.

Find the population variance by pressing STAT, then CALC, then 2-Var Stats. Make sure L1 is selected as the list, then press ENTER. The variance will be displayed as sX².

Take the square root of the population variance to find the population standard deviation. To do this, press the MATH key, then select PRB, then select 5:√(. Enter the population variance, then press ENTER.

Using this method, we find that the population standard deviation is approximately 56.4 and the population variance is approximately 3178.5.

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Complete question is:

A statistics professor gives a survey to each of the 10 students in an introductory statistics course. The survey asks the students how many text messages they think they sent yesterday. The data are included below. Use a TI-83, TI-83 Plus, or TI-84 to calculate the population standard deviation and the population variance. Round your answers to one decimal place .

Texts sent yesterday: 29 211 130 21 5 21 19 67 60 95

Answer:

a

Step-by-step explanation:

inverse ----> y = x

x = 2y - 7

2y = x + 7

y = (x+7)/2

Answer:

What is the expected value for the insurance company?

E(x) = 0.9986*161 + 0.0014*(-99839) = $21.00

Step-by-step explanation: Ur welcome

There is a 0.9986 probability that a randomly selected 30 year old male lives through the year. A life insurance company charges $161 for insuring that the male lives through the year. If the male does not survive the year, the policy pays out $100,000 as a death benefit.

Answer:

18

Step-by-step explanation:

The solution set of the equation will be;

⇒ x = 18

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

''2/3 of a number is 12."

Now,

Since, The expression is,

''2/3 of a number is 12."

Let a number = x

So, We can formulate;

⇒ 2/3 of x = 12

⇒ 2/3 × x = 12

⇒ 2x = 12 × 3

⇒ 2x = 36

⇒ x = 36/2

⇒ x = 18

Thus, The solution set of the equation will be;

⇒ x = 18

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Answer:

Step-by-step explanation:

5,7,9

trust the process.

Answer:R’ (-10,2) S’(-6,8) T’(4,-2)

Step-by-step explanation:

Did it in class

After dilation of ΔRST with the given scale factor we have vertices of ΔR'S'T' as R'(-10, 2), S'(-6, 8) and T'(4, -2).

Given that, ΔRST with vertices R(-5,1), S(-3,4), and T(2,-1).

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

Given, scale factor is k=2.

So, with using scale factor

R(-5,1)→2(-5, 1)= R'(-10, 2)

S(-3,4)→2(-3,4)=S'(-6, 8)

T(2,-1)→2(2,-1)=T'(4, -2)

Therefore, after dilation of ΔRST with the given scale factor we have vertices of ΔR'S'T' as R'(-10, 2), S'(-6, 8) and T'(4, -2).

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Answer:

3:25

Step-by-step explanation:

The photo shows how it's solved.

Answer: 3:25

Step-by-step explanation:

Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator

0.12 = 0.12/1

Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.
0.12 x 100

------------ = 12/100
1 x 100

Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)

12 ÷ 4

---------  = 3/25  

100 ÷ 4

Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:  

3  

25   =  3:25

Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%