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What ratio is equivalent to 14/21?
A. 2/3 B. 1/7 C. 3/4 D. 2/7

Answer: 3

Step-by-step explanation:

1. Convert the mixed number to fraction:

- Multiply the denominator of the fraction by the whole number.

- Add the product obtained and the numerator of the fraction.

- Write the sum obtained as the numerator and rewrite the original denominator of the fraction.

Then:

[tex]1\ 1/2=\frac{(1)(2)+1}{2}=\frac{3}{2}[/tex]

2. Multiply the numerators.

3. Multiply the denominator.

4. Reduce the fraction.

Then:

[tex](\frac{3}{2})(\frac{2}{1})=\frac{6}{2}=3[/tex]

Answer:

76.16

Step-by-step explanation:8 multiplied by 9.52

The system has Infinite solutions

Answer:

3 x 5 = 15

4 x 7 = 28

the answer is 15/28

;)

The rule is add 3. The next three terms are 36, 39, 42

Answer:

D

Step-by-step explanation:

The sides of a regular hexagon are congruent

Given that 1 side = 15in, then

perimeter = 6 × 15 = 90 in → D

31.5in² hopefully this helps

The area of a sector can be calculated using a given formula. After adjusting for the given radius and angle, the approximate area of the sector is 31.1 cm^2.

Without specifications about the figure, let's consider it as a sector of a circle.

The area of a sector can be calculated using the formula Area = (angle / 360) * π * (radius)^2.

But here we are given the base length, which is actually the diameter for the whole circle.

Hence, the radius would be base/2 which is 9/2 = 4.5 cm.

So, by substituting the given values in the formula, the area will be Area = (140 / 360) * π * (4.5)^2 = 31.07 cm^2 approx. So, the area of the figure to the nearest tenth is 31.1 cm^2.

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Answer: 5.6?

Step-by-step explanation:

x^= 16+16

x^= 32

find the square root of 32 which is 5.6 pretty sure

Answer:

11.02 = a, rounded to the nearest 10th

Step-by-step explanation:

The length of the ladder (13 ft) forms the hypotenuse of the triangle when leaned against the house.  The distance the ladder goes up the wall is the side opposite to the angle we are working with, so we can use the sine function to solve.  

Sin X = (opposite side)/(hypotenuse)

Sin 58 = a/13

     13(Sin 58) = a

              11.02462525 = a

                  11.02 = a, rounded to the nearest 10th    

A 13-foot ladder making a 58-degree angle with the ground will reach approximately 6.9 feet up a wall when we use the cosine function to calculate the height.

To find how many feet up a wall a 13-foot ladder will reach when it makes a 58-degree angle with the ground, we can use trigonometric functions, specifically the cosine function for adjacent and hypotenuse in a right-angled triangle.

The formula we will use is:

cosine(angle) = [tex]\frac{height}{hypotenuse}[/tex]

Re-arranging the equation to solve for the adjacent side, we get:

adjacent side = cosine(angle) * hypotenuse

Now plug in the values:

adjacent side = [tex]cosine(58 ^0) * 13 feet[/tex]

We can calculate the cosine of 58 degrees using a calculator and multiply it by 13, which will give us the height the ladder reaches on the wall. Let's calculate:

adjacent side = 0.5299 * 13 feet

adjacent side = 6.8887 feet

Therefore, a 13-foot ladder at a 58-degree angle with the ground will reach approximately 6.9 feet up a wall.

Answer:

The doubling time of this investment would be 9.9 years.

Step-by-step explanation:

The appropriate equation for this compound interest is

A = Pe^(rt), where P is the principal, r is the interest rate as a decimal fraction, and t is the elapsed time in years.

If P doubles, then A = 2P

Thus, 2P = Pe^(0.07t)

Dividing both sides by P results in 2 = e^(0.07t)

Take the natural log of both sides:  ln 2 = 0.07t.

Then t = elapsed time = ln 2

                                       --------- = 0.69315/0.07 = 9.9

                                         0.07

The doubling time of this investment would be 9.9 years.

To calculate the doubling time for an investment earning 7% interest compounded continuously, the Rule of 70 is used, which suggests that the investment will double in approximately 10 years.

To find the doubling time of an investment earning 7% interest compounded continuously, we can use the Rule of 70. The Rule of 70 is a quick and useful formula that estimates the number of years it takes for an investment to double given a fixed interest rate, specifically for interest rates below 10%. Here's how you can use it:

The Rule of 70 assumes continuous compounding. Thus, if an investment has a consistent return of 7% per year, compounded continuously, it will take roughly 10 years to double.

It's also worth noting that the Rule of 72 can be used in a similar way to estimate the doubling time more roughly. In this case, using the Rule of 72, dividing 72 by the interest rate of 7% would provide an estimation of approximately 10.3 years. This is a close approximation and often used due to its simplicity.

The answer for your question is:

C: Rectangle

If a parallelogram is inscribed in a circle, then it must be a Rectangle

Any quadrilateral in which opposites sides are parallel is called a parallelogram.

Any 2 dimensional figure bounded by 3 sides and sum of all the angles is 180° is called a triangle.

A parallelogram with four equal sides and sometimes one with no right angles is called a rhombus.

A rectangle is a four sided quadrilateral, having all the internal angles equal to 90 degrees and opposite sides are equal.

A trapezoid is a quadrilateral with one pair of opposite sides parallel.

This follows the characteristics features of a circle.

So the required parallelogram will be a rectangle.

Option C is correct.

So, options A , B, D are incorrect.

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Answer:

One eighth is one part of eight equal sections. Two eighths is one quarter and four eighths is a half. It's easy to split an object, like a cake, into eighths if you make them into quarters and then divide each quarter in half.

There are two eighths of an inch in a quarter of an inch.

The student is asking how many eighths of an inch are in 1/4 of an inch. To get the answer, you have to ask "how many 1/8's fit into 1/4". Since 1/4 is the same as 2/8, there are two eighths in one quarter.The student is asking how many eighths of an inch are in 1/4 of an inch. To get the answer, you have to ask "how many 1/8's fit into 1/4". Since 1/4 is the same as 2/8, there are two eighths in one quarter.The student is asking how many eighths of an inch are in 1/4 of an inch. To get the answer, you have to ask "how many 1/8's fit into 1/4". Since 1/4 is the same as 2/8, there are two eighths in one quarter.

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Answer:

[tex]49,987.24\ ft[/tex]

Step-by-step explanation:

Let

x-----> distance from the two towns

we know that

In the right triangle ABC

[tex]tan(32\°)=37,000/(x+y)\\x+y=37,000/tan(32\°)[/tex]

In the right triangle ABD

[tex]tan(76\°)=37,000/(y)\\y=37,000/tan(76\°)[/tex]

see the attached figure to better understand the problem

Remember that

(x+y)-y=x

so

[tex]x=\frac{37,000}{tan(32\°)} -\frac{37,000}{tan(76\°)}[/tex]

[tex]x=49,987.24\ ft[/tex]

Answer: C≈47.12m

Step-by-step explanation:

C=2π r=2· π· 7.5≈47.12389m

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Gallons would provide a more precise measurement when measuring water evaporation from a swimming pool.

If you are measuring the amount of water evaporated from a swimming pool, gallons would give you a more precise measurement. Gallons is a larger unit of measurement than quarts and therefore provides a more accurate representation of the amount of water evaporated from a swimming pool due to its larger capacity.

Answer:

B: 192pi - 144

Step-by-step explanation:

Area of the sector = (120/360) * pi * r^2

Area of the sector = 1/3 * pi * 24 * 24

Area of the sector = 192 * pi

Now to find the area of the triangle.

The triangle is an isosceles triangle That means two of its sides are equal. They are equal to the radius of the circle, which is 24.

the small angles are equal to

2x + 120 = 180    Subtract 120 from both sides

2x = 60               Divide by 2

x = 60/2

x = 30

The height of the triangle is derived from sin(30) = opposite / hypotenuse

sin(30) = 1/2

hypotenuse = 24

1/2 = opposite / hypotenuse

1/2 = opposite / 24                      Multiply both sides by 24

1/2 * 24 = opposite

opposite = 12

The height = 12

r = 24

Area of the triangle = 1/2 * 12 * 24

Area of the triangle = 144

So the area of the shaded area = 192*pi - 144 which looks like B

The area of the shaded region of the circle in terms of pi is 192π - 144√3 m².

The correct option is B) 192π - 144√3 m².

The shaded area of the circle is a segment, to determine the area of the segment, we simply subtract the area of the triangle from the area of the sector.

Note that; the area of a sector is expressed as:

Area = (θ/360) × πr²

Area of a triangle can be expressed as:

Area = ab × (sinθ)/2

Hence, the area of the shaded region will be:

Area = ( (θ/360) × πr² ) - ( ab × (sinθ)/2 )

Plug in the values and simplify:

Area = ( (120/360) × π × 24² ) - ( 24 × 24 × (sin120)/2 )

Area = ( 192π ) - ( 144√3 )

Area = 192π - 144√3

Therefore, the shaded area measures 192π - 144√3 square meters.

Option B) 192π - 144√3 m² is the correct answer.

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Answer:

x=3 (double root)

Step-by-step explanation:

We are told that y = x - 3.

Substituting x - 3 for y in the second equation yields:

x - 3 = x² - 5x + 6.

We need to rewrite this in the standard form of a quadratic equation:

Subtracting (x - 3) from both sides results in:

0 = x² - 5x + 6 - x + 3.

Combining like terms gives us:

0 = x² - 6x + 9,

which factors into (x - 3)(x - 3) = 0.  Thus, there are two real, equal roots:  x = 3 and x = 3.

Subbing 3 for x in the first equation gives us 3 - 3 = 0 = y..

Thus, the solution of this system of equations is (3, 0).

Answer:

(3,0)

Step-by-step explanation:

The question is asking to determine whether given sets of sides form a right triangle using Pythagorean theorem. The theorem is verified if the square of the length of the longest side equals the sum of the squares of the two other sides. However, some approximations might not perfectly fit the theorem but still form a right triangle.

The subject of this question is the Pythagorean Theorem in the field of Mathematics. The theorem is a fundamental principle in Geometry which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² = b² + c².

To determine whether or not a set of sides forms a right triangle, you would need to check if the lengths satisfy the Pythagorean theorem. If they do, then the sides are potentially those of a right triangle. For instance, if you're given sides with lengths 3, 4, and 5, you can check if 5² equals 3² + 4². Since 5² = 25 and 3² + 4² = 9 + 16 = 25, the sides do form a right triangle.

However, checking with the Pythagorean theorem is only conclusive if the lengths already satisfy the theorem. There might be situations where the length measurements are approximations and might not perfectly fit the theorem despite forming a right triangle.

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It would be D because 45.60-.01 would mean you subtract the .01 from the .60

Answer:

D)4.193

Step-by-step explanation:

[tex]5(2x + 7) = 10x + 35[/tex]

The given expression 5(2x+7) is equivalent to (10x+35).

The distributive property is the property that expresses the distributive law of algebraic multiplication. similarly, in polynomial expression we can use the distributive property for example we can write a(c+b)  in the form of (ac+bc).

We have a polynomial expression:

= 5(2x+7)

By using the distributive property we get

=(5×2x+5×7)

= (10x+35)

Thus, the given expression 5(2x+7) is equivalent to (10x+35).

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Answer: option a

Step-by-step explanation:

You must apply the formula for calculate the distance between the two points. which is shown below:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Therefore, keeping on mind that the points given in the problem are (6, 11), (0, 3), when you substitute values into the formula shown above, you obtain that the distance between these two points is the following:

[tex]d=\sqrt{(0-6)^2+(3-11)^2}\\d=10[/tex]

Answer:

a. 10

Step-by-step explanation:

We have been given two points (6, 11) and  (0, 3). Now we need to find the distance between points (6, 11) and  (0, 3) and check which of the following choices are correct:

(6, 11), (0, 3) a. 10 b. 14 c. 15 d. 100

Also we should round to the nearest tenth if necessary.

Apply distance formula :

[tex]distance =\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

[tex]distance =\sqrt{\left(0-6\right)^2+\left(3-11\right)^2}[/tex]

[tex]distance =\sqrt{\left(-6\right)^2+\left(-8\right)^2}[/tex]

[tex]distance =\sqrt{36+64}[/tex]

[tex]distance =\sqrt{100}[/tex]

[tex]distance =10[/tex]

Hence correct choice is a. 10

Answer:

Step-by-step explanation:

yes i did and it was sad because it was so hard mabey some questions where easy but other than that it was hard i whould cry throught the whole pert test but nah i didint

The PERT test's Math portion mainly covers algebra and geometry. It includes topics such as fractions, decimals, percentages, ratios and proportions, linear equations, inequalities, polynomials, quadratic equations, and basic geometry concepts. Preparation, practice, and study guides are recommended to perform well.

The PERT (Postsecondary Education Readiness Test) is a placement test used by colleges in Florida to assess a students' college readiness in Reading, Writing, and Mathematics. If you're concerned about the Math section, understanding the content breakdown can be very helpful.

The Math portion of the PERT test primarily includes algebraic and geometry questions, with the main focus being algebra. Topics include but aren't limited to fractions, decimals, percentages, ratios and proportions, linear equations, inequalities, polynomials, quadratic equations, and basic geometry concepts.

Preparing for this test may include using study guides, practice tests, and brushing up on your algebra and geometry skills. Remember utilizing all available resources and allotting ample time to study can greatly help you perform better on the test.

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Answer:

expression a

Step-by-step explanation:

The given expression is 15+0.25(d−1).

let suppose,

15 = a

0.25(d−1) = b

we get  a + b

It clearly indicates the given expression is sum of two entities, we can exclude  option b and option d.

Now we are left with option a and c, for that we have to evaluate the term b

b = 0.25(d−1) that is the additional amount after d days

Therefore, expression a is correct.

Answer:

It is the sum of the initial amount and the additional amount after d days.

Step-by-step explanation:

It is the sum of the initial amount and the additional amount after d days. i have ttm

Answer:

Option D. y=6x

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each case

case a) y=(1/6)x+6

Is a linear equation, but is not a direct variation. The line not passes through the origin

case b)  y=6/x

The equation represent an inverse variation

case c) y=6x-6

Is a linear equation, but is not a direct variation. The line not passes through the origin

case d) y=6x

The equation represent a direct variation

Final answer:

Among the options provided, option d. y = 6x is the equation of a direct proportion because it follows the form y = kx where k is the constant of proportionality and there is no added or subtracted constant.

Explanation:

The equation of a direct proportion is one where the dependent variable changes at the same rate as the independent variable. In mathematical terms, if two variables y and x are directly proportional, it implies that y = kx, where k is the constant of proportionality.

Looking at the options provided:

a. y = 1/6x + 6 is not directly proportional because of the addition of the constant 6.

b. y = 6/x is an inverse proportion because y changes inversely with x.

c. y = 6x - 6 is also not directly proportional due to the subtraction of the constant 6.

d. y = 6x perfectly fits the definition of direct proportionality as there is no added or subtracted constant and it follows the form y = kx.

Therefore, the equation of a direct proportion among the options given is d. y = 6x.

Answer: C

Explanation:

If a store paid x dollars to buy the computer and they sold it for 10 percent extra, it would be x+.1x. We can use the distributive property to get that x+.1x=x(1+.1) to get 1.1x, or C

Answer: c.1.1x

Step-by-step explanation:

Hi, the correct option is c.1.1x.

Since the price they paid for the computer is 100%, if they sell them for 10% more:

100%+10% =110% (sales percentage)

So, for a price x, to obtain the selling price we have to multiply the price (x) by the sales percentage in decimal form (110/100= 1.1)

The final expression is:

1.1x

$260 divided by 10 weeks equals $26 a week

I say 8 is the answer.

Proof:

[tex]3 + 2 + 3 = 8[/tex]

So 8ft is my answer.

Answer:

36 square feet outdoor carpet will be required for this hole.

Step-by-step explanation:

A triangle colored in green with a rectangular hole has been given in the figure.

Area of the outdoor carpet will be calculated by the expression,

Area of the carpet = Area of the right triangle - Area of the rectangle removed from the triangle

Area of the right triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                         = [tex]\frac{1}{2}\times (12)\times (7)[/tex]

                                         = 42 square ft

Area of the rectangle = Length × Width

                                   = 3×2

                                   = 6 square ft

Area of the remaining area to be covered with the carpet = 42 - 6

= 36 square feet

Therefore, area of the outdoor carpet required for the hole = 36 feet²

Answer:98 I believe

Step-by-step explanation:

Answer:

98.

Step-by-step explanation:

Number of cats = 28 * 3.5

= 98 cats.

That's a zoo!!

Answer:

the answer would be 3,-5

Step-by-step explanation:

you rotate it in a 90 degree clockwise rotation and you end up with 3,5 and when you reflect it upon the x-axis your point ends up at 3,-5

Answer:

3,-5

Step-by-step explanation:

If you rotate it in a 90 degree rotation in the clock direction you will end in 3.5 and your x-axis will result in 3.5.