Need to find the greatest common factor

Answer:

The circle's circumference is approximately 106.81 centimeters.

Explanation:

The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is pi (approximately 3.14), and r is the radius of the circle.

So, for a circle with a radius of 17 centimeters, its circumference can be found by:

C = 2πr

C = 2 x 3.14 x 17

C ≈ 106.81 cm

Therefore, the circumference of the circle is approximately 106.81 centimeters.

John will need 36 feet of fence to enclose his 9-foot square garden.

A sqaure is simply a polygon made up of four equal sides, with all the interior angles measuring 90 degrees.

The perimeter of a square is expressed as:

Perimeter = 4 × side length

Given that, the side length of the square garden is 9 ft.

To calculate the amount of fence John will need to enclose his 9-foot square garden, we need to determine the perimeter of the square.

Perimeter = 4 × side length

Plug in the side length

Perimeter = 4 × 9 ft

Perimeter = 36 feet

Therefore, the perimeter of the garden is 6 feet.

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The amount of profit that will be reinvested is 5/12 million.

Profit is the excess of revenue over cost.

Profit = revenue - total cost

In order to determine the profit that will be reinvested, multiply the fraction that is reinvested by the value of the profit.

Amount that will be reinvested = profit x fraction that is reinvested

1 1/4 x 1/3 =

5/4 x 1/3 = 5/12 million

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The HCF (highest common factor) of 20 and 10 is 10.

To determine the 20 and 10's highest common factor (HCF).

We must identify the highest number that can divide both 20 and 10 without producing a remainder in order to determine the HCF.

1, 2, 4, 5, 10, and 20 are the variables that make up 20.

1, 2, 5, and 10 make up the number 10.

The biggest element that both 20 and 10 have as a shared component is 10.

The HCF of 20 and 10 is hence 10.

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Answer:

a=25

b=92

Step-by-step explanation:

Because the average of the five numbers is 51, the sum of the five numbers is 255.

a+b+73+65=255

138+a+b=255

a+b=117

a+67=b

Therefore,

a=25

b=92

Feel free to tell me if I made a mistake! :)

The graph represents

[tex]{y \to -\infty}[/tex] as [tex]{x \to \infty}[/tex]

[tex]{y \to \infty}[/tex] as [tex]{x \to -\infty}[/tex]

From the given graph we can see that,

The curve represent cubic function

And we know that such cubic function is of the form

f(x) = y = -(ax³ + bx² + cx + d)

Since,

A function can approach two separate limits: one in which the variable approaches its limit by using values more than the limit, and one in which the variable approaches its limit by using values less than the limit.

Case 1:

Take limit of x approaching to infinity,

[tex]\lim_{n \to \infty} f(x) = y = -\infty[/tex]

Hence,

As x approaches to infinity the  

y approaches to negative  infinity.

Case 2:

Take limit of x approaching to negative of infinity,

Now since degree of function is 3 which is odd

Therefore,

[tex]\lim_{n \to -\infty} f(x) = y = \infty[/tex]

Hence,

As x approaches to negative infinity then  

y  approaches to infinity.

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Answer:

x = 9

Step-by-step explanation:

6/(x - 1) = 21/(3x + 1)

21(x - 1) = 6(3x + 1)

21x - 21 = 18x + 6

3x = 27

x = 9

Answer:

Step-by-step explanation:

To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

This helped me when i was learning to solve for x

The total area of the composite figure which has triangle and rectangle is  24.41 square inches

The given composite figure has two triangles and one rectangle

Area of rectangle =length × width

=4.6×3.15

=14.49 square inches

Area of left side triangle, it has base of 3.3 in and height 3.15 inches

Area of triangle = 1/2×3.3×3.15

=5.1975 square inches

Area of triangle on right side

Base = 3 in

Height = 6.3-3.15=3.15 in

Area of triangle = 1/2×3×3.15

=4.725 square inches

Total area = 14.49 + 5.1975  + 4.725

=24.41 square inches

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The value of the variable t of the exponential equation [tex]-5\cdot e^{10\cdot t} = - 30[/tex], t = (1 / 10) · ㏑ 6 (EXACT), t = 0.179 (APPROXIMATE).

In this problem we need to clear the variable t of an exponential equation with one variable, this can done by means of relationship of exponential and logarithmic functions, logarithm properties and algebra properties.

Now we proceed to present the complete procedure for the solution to the exponential equation:

[tex]-5\cdot e^{10\cdot t} = - 30[/tex]

[tex]e^{10\cdot t} = 6[/tex]

10 · t = ㏑ 6

t = (1 / 10) · ㏑ 6

t = 0.179

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The equation of the quadratic function is y=x2−4x, the correct option is E

We are given that;

x=-4,-2,1

y=5,-5,0

Now,

The first three rows of the table, we get:

​y=−4 when x=−5y=5 when x=−2y=−3 when x=1​

Substituting into the general form, we get:

​−4=25a−5b+c5=4a−2b+c−3=a+b+c​

Solving this system of equations, we get:

​a=1b=−4c=0​

Therefore, the equation of the quadratic function is y=x2−4x.

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Based on the assumptions, the estimated Federal Withholding Tax for Franklin Lyons would be approximately $191.68.

Determine Franklin's taxable income:

To calculate the taxable income, we need to subtract any deductions or exemptions from his gross pay. We'll consider his gross pay as the taxable income.

Taxable Income = Gross Pay = $958.38

Estimate the Federal Withholding Tax rate:

The Federal Withholding Tax rate depends on the taxable income and the individual's filing status. Let's assume a general tax rate of 20% for this estimation.

Federal Withholding Tax rate = 20%

Calculate the Federal Withholding Tax:

To find the withholding tax, multiply the taxable income by the tax rate:

Federal Withholding Tax = Taxable Income * Federal Withholding Tax rate

= $958.38 * 0.20

= $191.68

Thus, the answer is $191.68.

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To determine whether there is a difference of opinion between doctors and nurses regarding a new postoperative procedure, the researcher conducted a survey and tabulated the data in a table form. The next step is to analyze the data using statistical methods and a significance level of 5%.

To begin the analysis, the researcher can use a statistical test such as the chi-square test for independence. This test will examine whether there is a significant association between the opinions of doctors and nurses regarding the procedure.

The chi-square test will compare the observed frequencies in each category (e.g., doctors who feel differently, doctors who feel the same, nurses who feel differently, nurses who feel the same) with the frequencies that would be expected if there was no association between the profession and opinion.

If the calculated chi-square value exceeds the critical value at a significance level of 5%, it suggests that there is a significant difference in opinion between the two groups.

The researcher should calculate the chi-square value, degrees of freedom, and compare it to the critical value from the chi-square distribution table.

If the calculated chi-square value exceeds the critical value, the researcher can conclude that there is a significant difference of opinion between doctors and nurses regarding the postoperative procedure.

It is important to note that statistical significance does not imply practical significance. Even if there is a significant difference, the magnitude of the difference should be considered in the context of the study.

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The odds against a direct hit is 3 to 1.

Given that the probability of a hurricane hitting at a coast is 1/4 = 0.25.

Therefore, the probability of not hitting = 1-0.25

= 0.75

we know that,

Odds against direct hit = [P(no direct hit)]/P[(direct hit)] = 0.75/0.25 = 3/1

= 3:1

Hence the odds against a direct hit is 3 to 1.

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The parabola y = x² scaled vertically by a factor of 1/10 gives y = x²/10

From the question, we have the following parameters that can be used in our computation:

The parabola y = x² is scaled vertically by a factor of 1/10

The rule of this transformation is

Image = (x, ay)

Where

a = 1/10

So, we have

y = 1/10 * x²

Evaluate

y = x²/10

Hence, the image of the function is y = x²/10

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Answer:

4(1/2)(3)(5) + (3^2) = 30 + 9 = 39 ft^2

The height of the cylinder whose surface area is given would be = 85 yards.

The cylinder is a type of shape that has three sides which consists of two opposite circles that are joined by a curved surface.

To calculate the height of a cylinder, the formula that should be used is given as follows:

Surface area of cylinder = 2πrh + 2πr²

radius = 29 yards

surface area = 20,761.68 square yards

height = ?

That is ;

20,761.68 = 2×3.14× 29×h + 2×3.14× 29×29

20,761.68 =182.12h + 5281.48

182.12h = 20,761.68-5281.48

182.12h = 15480.2

h = 15480.2/182.12

= 85 yards

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The measure of <MNL is (71 - 3x²)/2.

We have,

Far Arc = 59 - 2x²

Near Arc = 12 - x²

Angle = 180- 2x²

Using the Formula

Angle= Average of vertical chords

180 - 2x² = (59 - 2x² + 12 - x²)/2

360 - 4x² = 71 - 3x²

289 = x²

x= 17

So, the measure of <MNL

= (71 - 3x²)/2

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Answer:

16 tvs

Step-by-step explanation:

Maura's earnings for the week equal her weekly salary (460) plus she earns 6.5% commission x number of flat screens sold x $414.

So: Total Earnings = 460+ 0.065*414*t where t is the number of tvs she has sold.

If total earnings = 890.56, just substitute that above and solve for t.

890.56= 460+ 0.065*414*t

430.56=0.065*414*t

430.56=26.91*t

430.56/26.91 = t

16 = t

She sold 16 tvs to earn 890.56.

Answer: If 34% of the mixed fruit juice is apple juice, then 66% of it is a combination of other fruit juices. We can assume that the ratio of apple juice to other fruit juices remains the same in the ice cream and mixed fruit juice mixture.

Let the volume of ice cream in each batch be 3x litres and the volume of mixed fruit juice be 2x litres. Then the total volume of mixture in each batch is 5x litres.

If 34% of the mixed fruit juice is apple juice, then the volume of apple juice in each batch is 0.34 × 2x = 0.68x litres. The volume of other fruit juices in each batch is 2x − 0.68x = 1.32x litres.

The ratio of ice cream to mixed fruit juice is 3 : 2, so we have:

3x : 2x = ice cream : mixed fruit juice

Simplifying, we get:

ice cream = 1.5 × mixed fruit juice

Substituting the values we obtained earlier, we have:

3x = 1.5 × 2x

x = 0.75

Therefore, the volume of ice cream in each batch is 3x = 2.25 litres, and the volume of mixed fruit juice is 2x = 1.5 litres.

To make 1.5 litres of mixed fruit juice, we need 0.68 litres of apple juice and 0.82 litres of other fruit juices.

To make 12.5 litres of smoothies, we need 2.25 litres of ice cream and 10.25 litres of mixed fruit juice. Of this, 0.68 litres is apple juice and 9.57 litres is other fruit juices.

Therefore, to make 12.5 litres of smoothies, we need 0.68/1.5 × 12.5 = 5.67 litres of apple juice.

To make 51 litres of apple juice, we can make a maximum of 51/5.67 ≈ 9 batches of smoothies.

The algebraic rule for the translation in this problem is given as follows:

(x,y) -> (x + 9, y - 1).

The four translation rules are defined as follows:

Comparing the equivalent vertices, the translations for this problem are given as follows:

Hence the algebraic rule for the translation in this problem is given as follows:

(x,y) -> (x + 9, y - 1).

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Answer:

d² - 24d + c = (d - 12)² - 144 + c

The measures of the following arcs are :

m∡AB = 49°

m∡ABC = 253°

m∡BAC = 156°

m∡ACB = 311°

Note that the sum total of the arcs in a circle is 360°

m∡AB = 49° - Given

m∡ABC =  360°  107° =  253°

m∡BAC =  107 + 49 = 156°

m∡ACB = 360 - 49 = 311°

A curve's arc length is significant because it represents the distance between two locations on the curve. The circumference of a circle is equal to its arc length. The arc length of an ellipse equals the ellipse's perimeter.

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The surface area of the composite solid is 255 square inches.

We will compute the surface area of each component and then add them together to find the surface area of the composite solid.

First, the surface area of the square prism:

Given: The square prism has a width, length, and height of 5 inches each.

Formula for the surface area of a rectangular prism: 2lw + 2lh + 2wh

Surface area of the prism = 2(5 * 5) + 2(5 * 5) + 2(5 * 5)

= 2(25) + 2(25) + 2(25)

= 50 + 50 + 50

= 150 square inches

Next, the surface area of the square pyramid at the bottom:

Given: The slant height of the pyramid on the bottom of the prism = 7.5 inches.

The base of the pyramid is a square with a side length of 5 inches.

Formula to find the lateral surface area of a square pyramid: (perimeter of base) * slant height / 2.

The base is a square, the perimeter is 4 times the side length.

Lateral surface area of the bottom pyramid = (4 * 5) * 7.5 / 2

= 20 * 7.5 / 2

= 150 / 2

= 75 square inches

Then, the Surface area of the square pyramid at the top:

Given: The height of the pyramid on top of the prism = 3 inches.

The base of the pyramid is a square with a side length of 5 inches.

Lateral surface area of the top pyramid = (4 * 5) * 3 / 2

= 20 * 3 / 2

= 60 / 2

= 30 square inches

Finally, we shall find the total surface area by summing up the surface areas of each component in this way:

Total surface area = Surface area of the prism + Surface area of the bottom pyramid + Surface area of the top pyramid

= 150 + 75 + 30

= 255 square inches

Therefore, the surface area of the composite solid = 255 square inches.

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Answer:

3)  A = 35.2°, B = 38.6°, C = 106.2°

4)  B = 70.4°, C = 31.6°, a = 18.7

Step-by-step explanation:

To solve for the remaining angles of the triangle ABC given its side lengths, use the Law of Cosines for finding angles.

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]

Given sides of triangle ABC:

Substitute the values of a, b and c into the Law of Cosines formula and solve for angle C:

[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

[tex]\implies \cos(C)=\dfrac{12^2+13^2-20^2}{2(12)(13)}[/tex]

[tex]\implies \cos(C)=\dfrac{-87}{312}[/tex]

[tex]\implies \cos(C)=-\dfrac{29}{104}[/tex]

[tex]\implies C=\cos^{-1}\left(-\dfrac{29}{104}\right)[/tex]

[tex]\implies C=106.191351...^{\circ}[/tex]

To find the measure of angle B, swap b and c in the formula, and change C for B:

[tex]\implies \cos(B)=\dfrac{a^2+c^2-b^2}{2ac}[/tex]

[tex]\implies \cos(B)=\dfrac{12^2+20^2-13^2}{2(12)(20)}[/tex]

[tex]\implies \cos(B)=\dfrac{375}{480}[/tex]

[tex]\implies B=\cos^{-1}\left(\dfrac{375}{480}\right)[/tex]

[tex]\implies B=38.6248438...^{\circ}[/tex]

To find the measure of angle A, swap a and c in the formula, and change C for A:

[tex]\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}[/tex]

[tex]\implies \cos(A)=\dfrac{20^2+13^2-12^2}{2(20)(13)}[/tex]

[tex]\implies \cos(A)=\dfrac{425}{520}[/tex]

[tex]\implies A=\cos^{-1}\left(\dfrac{425}{520}\right)[/tex]

[tex]\implies A=35.1838154...^{\circ}[/tex]

Therefore, the measures of the angles of triangle ABC with sides a = 12, b = 13 and c = 20 are:

[tex]\hrulefill[/tex]

Given values of triangle ABC:

First, find the measure of side a using the Law of Cosines for finding sides.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]

As the given angle is A, change C for A in the formula and swap a and c:

[tex]\implies a^2=c^2+b^2-2cb \cos (A)[/tex]

Substitute the given values and solve for a:

[tex]\implies a^2=10^2+18^2-2(10)(18) \cos (78^{\circ})[/tex]

[tex]\implies a^2=424-360\cos (78^{\circ})[/tex]

[tex]\implies a=\sqrt{424-360\cos (78^{\circ})}[/tex]

[tex]\implies a=18.6856038...[/tex]

Now we have the measures of all three sides of the triangle, we can use the Law of Cosines for finding angles to find the measures of angles B and C.

To find the measure of angle C, substitute the values of a, b and c into the formula:

[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

[tex]\implies \cos(C)=\dfrac{(18.6856038...)^2+18^2-10^2}{2(18.6856038...)(18)}[/tex]

[tex]\implies \cos(C)=0.852040063...[/tex]

[tex]\implies C=31.565743...^{\circ}[/tex]

To find the measure of angle B, swap b and c in the formula, and change C for B:

[tex]\implies \cos(B)=\dfrac{a^2+c^2-b^2}{2ac}[/tex]

[tex]\implies \cos(B)=\dfrac{(18.6856038...)^2+10^2-18^2}{2(18.6856038...)(10)}[/tex]

[tex]\implies \cos{B}=0.334888270...[/tex]

[tex]\implies B=\cos^{-1}(0.334888270...)[/tex]

[tex]\implies B=70.434256...^{\circ}[/tex]

Therefore, the remaining side and angles for triangle ABC are:

The value of x is 9.

Given,

Trapezoid with two bases and median.

base 1 = 44

base 2 = 2x + 10

median = 36

Now,

In trapezoid two bases will be parallel to each other.

Median = 1/2(sum of two bases)

From the formula of median the value of x will be,

Median = 1/2( base 1 + base 2 )

Substitute the values,

36 = 1/2( 44 + 2x + 10 )

72 = 54 + 2x

x = 9

Hence both the bases of trapezoid are obtained.

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The principal amount of $2,287.26 from compound interest at a rate of 4.5% per year owed after six years on a loan of $1300

Since n is the number of times the interest is compounded each year, and 'r' is the rate of compound interest annually, sothe final amount after 't' years would be:

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

Given that certain loan program offers an interest rate of 4.5%, compounded continuously.

Assuming no payments are made so;

First, convert R as a percent to R as a decimal

r = R/100

r = 4.5/100

r = 0.045 per year,

Then, solve the equation for P

P = A / (1 + r/n)^nt

P = 1300/ (1 + 0.045 /365)(365)^(15)

P = 1300/ (1 + 0.00010137)^(4745)

P = $2,287.26

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Answer:

220 in²

Step-by-step explanation:

surface area = [area of the 4 vertical faces] + area of the base + area of top.

surface area = [2(4 X 10) + 2(5 X 10)] + (4 X 5) + (4 X 5)

= (80 + 100) + 20 +  20

= 220 in²

The height of the cylindrical container is approximately 5 inches.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given that:

Volume V = 251 cubic inches

Radius r = 4 inches

Height h = ?

Plug the given values into the above formula and solve for height.

V = π × r² × h

251 = 3.14 × 4² × h

251 = 3.14 × 16 × h

251 = 50.24 × h

h = 251/50.24

h = 5 inches.

Therefore, the measure of the height is 5 inches.

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Answer: q=13

Step-by-step explanation:

add the separate the q, add 4 to the 9= 13

13=q

Answer:

6/MN = 8/9

8MN = 54

MN = 6 3/4

The correct answer is B.