For a given interest rate, simple interest varies jointly as principal and time. If $2000 left in an account for 4 yr earned interest of $280, how much interest would be earned in 6 yr?

Answer:

12 Vanilla Frosted Cupcakes

Step-by-step explanation:

30 Cupcakes.

1/5 Of 30 is 6.

30 - 6 = 24.

24/2 = 12.

Answer:

$189

Step-by-step explanation:

35% of 140 = 49

140 + 149 = 189

Tom's total saving this year is $189.

It is a 35 percent increased saving from last year's $140.

Percentages are fractional values where the denominator is fixed to be 100.

To convert percentage into number, we multiply by 100.

In the question, we are informed that Tom was able to save 35% more this year than he did last year.

We are asked if he saved $140 last year, then how much did he save this year.

The increase in Tom's savings = 35% of last year's savings,

or, the increase = 35/100 * 140 (To convert percentage into quantity, we divide by 100).

or, the increase = $49.

Therefore, Tom's total savings this year = Last year's savings + Increase,

or, Tom's total saving this year = $140 + $49 = $189.

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Answer:

2 pi : 1

Step-by-step explanation:

for every one unit of radius, there are two pi units in the circumference!

Answer:

10

Step-by-step explanation:

By the geometric mean theorem,

The total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards.

Total distance if Pete walks from A to B to C:

= 15 + 25 = 40 yards

As we know in the triangle the sum of the two sides is greater than the third side.

25 + 15 > AC

40 > AC

or

AC < 40

The direct distance from A to C is more than 10(25-15) yards.

The inequality w < 30 represents the distance, w, that Pete might save by taking the direct path.

Thus, the total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

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Answer:

40, 10, 30
see picture

Step-by-step explanation:

The area of the surface of the pool is 7322.64 m².

The area of rectangle is product of length and its breadth.

i.e., length * breadth

Given: Length = 100 m, Width = 52 m and Diameter = 52 m

Area of rectangle,

= 100 × 52

= 5200 m²

Now,

Area of semicircle = 1/2 × πr²

=1/2 × 3.14 × 26²

= 1061.32 m²

Hence, area of the surface of the pool is

= 1061.32 + 1061.32 + 5200

= 7322.64 m²

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5200 square meters, 1061, 7322

LHL in not equal to RHL , Therefore the limit does not exists , Option D is the answer.(none)

The limit of a function at a certain point is the value that the function approaches as the argument of the function approaches the same point.

It is given that

lim x->2 for f(x)

[tex]\lim_{x \rightarrow 2^-}f(x) = \lim_{x\rightarrow 2^+}f(x)[/tex]

f(x) = 2x+1 x ≤2

f(x)= x² , x >2

When both the function tends to 2

Left Hand Limit

f(x) = 2 *2 +1

f(x) = 5

Right Hand Limit

f(x) = x² ,

f(x) = 4

LHL in not equal to RHL , Therefore the limit does not exists.

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Answer:

[tex]\sf b.) \ 1 +2\sqrt{7}[/tex]

Explanation:

Foil method: (a + b)(c + d) = ac + ad + bc + bd

Solving steps:

[tex](4 - \sqrt{7} )(2 + \sqrt{7} )[/tex]

[tex](4)(2) + 4(\sqrt{7} ) + (-\sqrt{7} )(2) + (-\sqrt{7} )(\sqrt{7} )[/tex]

[tex]8 + 4\sqrt{7} - 2\sqrt{7} - 7[/tex]

[tex]8 -7 + 4\sqrt{7} - 2\sqrt{7}[/tex]

[tex]1 +2\sqrt{7}[/tex]

option b) 1 + 2√7

Foil property method :-

[tex] \red{ \boxed{ \orange{ \rm (a + b)(c + d) = ac + ad + bc + bd}}}[/tex]

then, on substituting the values,

[tex]\sf⇒ \:  \: 8 + 4 \sqrt{7} - 2 \sqrt{7} - 7[/tex]

[tex]\sf⇒ \:  \: \green{ \underline{\bold{ \red{1 + 2 \sqrt{7} }}}}[/tex]

Answer:

[tex]\fbox {tan A = 0.5333}[/tex]

Step-by-step explanation:

tan A = opposite side of ∠A / hypotenuse

tan A = 8 / 15

tan A = 0.5333

Answer:

tan A = perpendicular/ base

tan A = 8/15

tan A=0.5333

Step-by-step explanation:

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The inverse function of the function f(x) will be f⁻¹(x) = 4x + 48. Then the correct option is D.

The complete question is attached below.

Suppose that the given function is

f: X → Y

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

 f⁻¹: Y → X

It simply means, inverse of 'f' is an undo operator, that takes back the effect of 'f'

The function is given below.

f(x) = (1/4)x – 12

Then the inverse function of the function f(x) will be

(1/4)f⁻¹(x) - 12 = x

            f⁻¹(x) = 4x + 48

Then the correct option is D.

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Answer:

A

Step-by-step explanation:

The parabola opens to the left, so this eliminates C and D.

Also, the vertex is at (-17, 2), and out of A and B, the only parabola with this vertex is A.

The average rate of change in h(t) is 6.

It is a measure of how much the function changed per unit, on average, over that interval.

h(t) = 3 + 70t - 16t²

Average rate of change

At t = 1 second

h(1) = 3 + 70(1) - 16(1)^2

h(1) = 57

At t = 3 second

h(3) = 3 + 70(3) - 16(3)^2

h(3) = 69

Average rate of change = Δh / Δt

=[h(3) - h(1)] / (3 - 1)

= (69 - 57) / 2

= 12 / 2

= 6.

Hence, the rate of change is 6.

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The circumference of this circle with a radius of 7 cm is equal to 44 cm.

Given the following data:

Mathematically, the circumference of a circle can be calculated by using this formula:

Circumference = 2πr

Where:

r is the radius of a circle.

Substituting the given parameters into the formula, we have;

Circumference = 2 × 3.14 × 7

Circumference = 43.96 ≈ 44 cm.

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Answer:

See below

Step-by-step explanation:

The solution will show the NUMBER Of adult and the NUMBER of child tickets purchased .

a = adult tickets         cost = 15 a

c = children's tickets    <=== this is equal to 20 - a    

                  cost for children's tickets equals   10(20 - a)

15 a + 10c   =   225           rememeber c = 20 -a <===put that in

15 a      + 10 ( 20 -a)   = 225    solve for a

15a + 200 - 10 a = 225

5 a = 25

a = 5   tix                 then     c = 20 - a =  15   tix

Answer:

9. 15b + 4

10. 4y + 6

11. 15r+72

12. 130n + 20

Step-by-step explanation:

9. Combine Like terms

10. Combine Like terms

11. Distribute the 8 into (r + 9) then combine like terms

12. Distribute 10 into (3n + 2 + 10n) then combine like terms

Answer:

[tex]\mathsf {9) 15b + 4}\\\mathsf {10) 4y + 6}\\\mathsf {11) 15r + 72}\\\mathsf {12) 130n + 20}[/tex]

Step-by-step explanation:

[tex]\textsf {Question 9}[/tex]

[tex]\mathsf {3 + 8b + 4 + 7b - 3}[/tex]

[tex]\mathsf {8b + 7b + 4 + 3 - 3}[/tex]

[tex]\mathsf {15b + 4}[/tex]

[tex]\textsf {Question 10}[/tex]

[tex]\mathsf {8 + 7y - 3y + 2 - 4}[/tex]

[tex]\mathsf {7y - 3y + 8 + 2 - 4}[/tex]

[tex]\mathsf {4y + 6}[/tex]

[tex]\textsf {Question 11}[/tex]

[tex]\mathsf {8(r + 9) + 7r}[/tex]

[tex]\mathsf {8r + 8(9) + 7r}[/tex]

[tex]\mathsf {8r + 7r + 72}[/tex]

[tex]\mathsf {15r + 72}[/tex]

[tex]\textsf {Question 12}[/tex]

[tex]\mathsf {10(3n + 2 + 10n)}[/tex]

[tex]\mathsf {10(13n + 2)}[/tex]

[tex]\mathsf {10(13n) + 10(2)}[/tex]

[tex]\mathsf {130n + 20}[/tex]

Work Shown:

[tex]m = \frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}\\\\m = \frac{6^{n}*6^2-6^{n}}{6^{n}*6^1+6^{n}}\\\\m = \frac{6^{n}*36-6^{n}}{6^{n}*6+6^{n}}\\\\m = \frac{6^{n}(36-1)}{6^{n}(6+1)}\\\\m = \frac{6^{n}(35)}{6^{n}(7)}\\\\m = \frac{35}{7}\\\\m = 5\\\\[/tex]

Therefore,

[tex]\frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}=5\\\\[/tex]

To eliminate the y terms and solve for x in the fewest steps, the first equation 4x - 3y = 34 should be multiplied by 2, and the second equation 3x + 2y = 17 should be multiplied by 3 before adding them.

Elimination is a process of solving a system of equations to eliminate one variable and solve for the other.

To eliminate the y terms from the equations,

first equation: 4x - 3y = 34, and

second equation: 3x + 2y = 17,

we take the L.C.M. of the coefficients of y, that is 3 and 2, which is 6, and multiply the equation by the value = (LCM of the coefficients/respective coefficient of y).

That is, for :

the first equation, we multiply the equation by (LCM of the coefficients/respective coefficient of y) = 6/3 = 2.

the second equation, we multiply by (LCM of the coefficients/respective coefficient of y) = 6/2 = 3.

Thus, to eliminate the y terms and solve for x in the fewest steps, the first equation 4x - 3y = 34 should be multiplied by 2, and the second equation 3x + 2y = 17 should be multiplied by 3 before adding them.

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Okay, so out of 8 kids, we know that 6/8 are girls and 2/8 are boys. Its asking us what fraction of the kids are girls. The denominator (the bottom part of the fraction will be the amount of kids at the party, 8) and the top part, the numerator, will be 6 as there are 6 girls at the party of the 8 attendees.

So the fraction is 6/8. However we can reduce this by dividing both sides of the fraction by a common factor, 2!

So your final answer is 3/4.


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Using the point-slope equation, the equations that represent the data are:

y - 6 = -1.25(x + 2)

y -3.5 = -1.25x

Given a point (a, b) and slope (m), the point-slope equation is expressed as, y - b = m(x - a).

Find the slope (m) using two pairs from the table of values say, (-2, 6) and (2, 1):

Slope (m) = change in y / change in x = (6 - 1)/(-2 - 2) = 5/-4 = -1.25

Using the point, (a, b) = (-2, 6) and m = -1.25, plug the values into y - b = m(x - a):

y - 6 = -1.25(x - (-2))

y - 6 = -1.25(x + 2)

This cam be rewritten as:

y - 6 = -1.25x - 2.5

y - 6 + 2.5 = -1.25x

y -3.5 = -1.25x

The equations that represent the data in the table are:

y - 6 = -1.25(x + 2)

y -3.5 = -1.25x

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Answer: 6 ft

Step-by-step explanation:

[tex]144\pi =\pi(r^{2})(4)\\\\144\pi=4\pi r^{2}\\\\36=r^{2}\\\\r=\boxed{6 \text{ ft}}[/tex]

[tex] |y + 2| > 6 \\ y + 2 > 6 \: \: \: or \: \: \: y + 2 < - 6 \\ y > 6 - 2 \: \: \: or \: \: \: y < - 6 - 2 \\ y > 4 \: \: \: or \: \: \: y < - 8[/tex]

Solution : ] -♾️ , -8 [ U ] 4, + ♾️ [

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Answer:

This situation of the recipe can be represented as y=x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.

What is the equation for this situation?

It is known the total amount of flour (y) is equivalent to the total amount of whole wheat flour (5.5) added to the total white flour (x). Therefore, the equation is:

y = x + 5.5

The possible values are

x = It is expected x is equalthan 0 or greater to it since the minimum amount of white flour that can be added is 0.

y = It is expected y is equal than 5.5 or greater to it since even if no

white flour is added the minimum total is 5.5.

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Step-by-step explanation:

This situation of the recipe can be represented as equation y = x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

For the given expression

y = x + 5.5

The possible values are

x = It is expected x is equal to 0 or greater to it

since the minimum amount of white flour that can be added is 0.

y = It is expected y is equal than 5.5 or greater to it since even if no

white flour is added the minimum total is 5.5.

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Answer:

y = 1.5x + 1

Step-by-step explanation:

→ Choose 2 points

( 2 , 4 ) ( -2 , -2 )

→ Find the gradient

-6 ÷ -4 = 1.5

→ Write into format

y = 1.5x + c

→ Substitute in ( 2 , 4 )

4 = 3 + c

→ Minus 3 from both sides

1 = c

y = 1.5x + 1

Step-by-step explanation:

since the two angles from a straight line, they make a linear pair and linear pairs are supplementery. by the angle addition postulate, you can determine that the two angles sum to 180. substituting the one angle mearsure that you are guven and using a bit of simple arithmetic and the subtraction property of equality, you can determine that the other angle,angle YXZ, is 45 degrees. I hope this is helpful

There's a neat trick to finding the rational form of a repeating decimal number. Take for instance [tex]x=0.123123123\ldots[/tex]. Then

[tex]x = 0.123123123\ldots \\\\ \implies 1000x = 123.123123\ldots \\\\ \implies 1000x - x = 123.123123\ldots - 0.123123\ldots \\\\ \implies 999x = 123 \\\\ \implies x = \dfrac{123}{999}[/tex]

It's easy to reverse this method to find the repeating decimal form of [tex]\frac7{11}[/tex]. Let

[tex]x = \dfrac7{11}[/tex]

Multiply the numerator and denominator by 9,

[tex]x = \dfrac{63}{99}[/tex]

It follows that

[tex]x = \dfrac{63}{99} \\\\ \implies 99x = 63 \\\\ 100x - x = 63.6363\ldots - 0.6363\ldots \\\\ \implies x = 0.636363\ldots[/tex]

The first 20 digits after the decimal are made up of 10 each of 3 and 6, so the sum is 10 × (3 + 6) = 90.

Answer:

90

Step-by-step explanation:

Using long division, we find that  Every group of two digits after the decimal point has a sum of 9 so the sum of the first 20 digits after the decimal point is 10*9=90