A person invested $810 in an account growing at a rate allowing the money to double
every 10 years. How long, to the nearest tenth of a year would it take for the value of
the account to reach $1,690?

The approximate area of the mulch around the merry-go-round is 126.228 feet².

Diameter of the merry go round = 10.4 feet

Radius is half of the diameter.

Radius of the merry go round = 10.4/2 = 5.2 feet

Before the piece can be installed, a solid circular pad of mulch must be put down which extends 3 feet beyond the edge of the merry-go-round.

Radius of the merry go round with mulch = 5.2 + 3 = 8.2 feet

Total area of the merry go round with the mulch is,

Area = π (8.2)² = 67.24π feet²

Area of the merry go round = π (5.2)² = 27.04π feet²

Area of the mulch = 67.24π feet² - 27.04π feet² = 40.2π = 126.228 feet²

Hence the required area is 126.228 feet².

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Answer:

Step-by-step explanation:

1. Put the words into math

3  3 1/4 divided by 2 3/8 equals a b/c.= 3 1/4/2 3/8

3 1/4/2 3/8=

1 7/19

2. Answer: 1 7/19

A graph of the cube root function g(x) = 1/2x³ is shown in the image below.

In Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

This ultimately implies that, the dimension (size) or side lengths of the dilated geometric object would be stretched or shrunk depending on the scale factor that is applied.

When the parent cube root function f(x) = x³ is vertically shrunk by a scale factor of 1/2, the transformed function g(x) is given by;

g(x) = kf(x)

g(x) = 1/2f(x)

g(x) = 1/2x³.

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Betsy needs to  invest $32,000 in the B-rated bonds paying 13% interest and $28,000 in the certificate of deposit paying 3% interest.

Interest is calculated by multiplying the rate with the principal.

Let x = the amount Betsy will invest in the B-rated bonds paying 13% per annum. The remaining amount, $60,000-x , she will invest in the certificate of deposit paying 3% per annum.

We can express the earnings on these two investments, after converting the percentages to their decimal equivalents, as: 0.13x+0.03(60000-x) and this is to earn a total of $5,000

Now we can write the necessary equation to solve for x.

or, 0.13x+0.03(60000-x) = 5000

or, 0.13x+1800-0.03x = 5000

or, 0.1x+1800 = 5000

or, 0.1x = 3200

or, x = 32000

So Betsy needs to invest $32,000 in the B-rated bonds paying 13% interest and the remainder ($60,000-$32,000 = $28,000) in the certificate of deposit paying 3% interest to obtain $5,000 in interest per annum.

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The area of the space available for onions is:n12 square feet - 0.12x square feet. number of onion bulbs Mark can plant is: (12 - 0.12x) / y

What is percentage?

Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".

Mark has marked off a certain percentage of the 12 square feet to save for a tomato plant, which means the remaining space will be used for onions.

Let's say Mark marks off x% of the space for the tomato plant. That means he will have (100-x)% of the space for onions.

The area of the space reserved for the tomato plant is:

12 square feet x (x/100) = 0.12x square feet

The area of the space available for onions is:

12 square feet - 0.12x square feet

Let's say each onion bulb needs y square feet of room to grow. Mark can plant as many onion bulbs as can fit in the remaining space, which is:

(12 square feet - 0.12x square feet) / y

So the number of onion bulbs Mark can plant is:

(12 - 0.12x) / y.

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Answer:e

Step-by-step explanation:

-(5/3)=-5/3

Step-by-step explanation:

so, we calculate the perpendicular slope, and then we start with the point-slope form (since we were given a specific point of the line), and transform into the regular slope-intercept form.

the slope in

y = 2x + 2

is the factor of x : 2 or 2/1

the perpendicular slope is turning this upside down and flips the sign : -1/2

the point- slope form is

y - y1 = a(x - x1)

"a" being the slope, (x1, y1) being the point.

y - 9 = -1/2(x - -2)

y - 9 = (-1/2)x - 1

y = (-1/2)x + 8

You know that the lines are parallel and they are intersected by a transversal.

Then, it is important to remember the following pair of angles:

1. Vertical angles are congruent. They share the same vertex.

2. Corresponding angles are congruent. They are located on the same side of the transversal. One angle is exterior and the other angle is interior. They are non-adjacent angles.

In this case, you can identify that the angle "b" and the angle that measures 130 degrees are Corresponding angles. Then:

You can also identify that the angle "b" and the angle "c" are Vertical angles. Then:

Therefore, the answer is:

The measure of angle DCE in this problem is given as follows:

m < DCE = 22.5º.

The triangles in this problem are right triangles, meaning that the trigonometric ratios are used to find the measures.

The three trigonometric ratios are given as follows:

The segment DB is adjacent to angle of 38º, while the hypotenuse is of 12.2 cm, hence the length of segment DB is calculated as follows:

cos(38º) = DB/12.2

DB = 12.2 x cosine of 38 degrees

DB = 9.6 cm.

BE:ED = 3:1, means that segment DE is one-fourth of segment DB, and thus it's length is given as follows:

DE = 1/4 x 9.6

DE = 2.4 cm.

Then for the angle DCE, we have that the opposite side is of 2.4 cm while the adjacent side is of 5.8 cm, hence the tangent is used to find it's measure, as follows:

tan(x) = 2.4/5.8

x = arctan(2.4/5.8)

x = 22.5º

m < DCE = 22.5º.

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Answer:

x = 22.5°

Step-by-step explanation:

Answer:

b=20

r=15

Step-by-step explanation:

OK...

hope helpful for you

Explanation: Working with scientific notation all we need to do is to move the point to the left or to the right.

Letter a. Let's Illustrate below

As we can see above, we just needed to move the point 3 times to the right which represents the

at the end of the scientific notation.

Letter b. Let's represent it as below

As we can see above we are doing the inverse representation so we needed to move the point 7 timer to the right.

Answer:

The number of gallons of gas were in the tank minus 9 leves 3 gallons

I don't know that

Answer:

f(g(x)) = x + 11

g(f(x)) = √(x² + 11)

Step-by-step explanation:

f(x) = x² + 5

g(x) = √(x + 6)

f(g(x)) = f(√(x + 6))

= (√(x + 6))² + 5

= x + 6 + 5

f(g(x)) = x + 11

g(f(x)) = g(x² + 5)

= √(x² + 5 + 6)

g(f(x)) = √(x² + 11)

Answer:

Step-by-step explanation:

The given equation of the line is y = (-3/4)x - 3.

To find the equation of a line perpendicular to this line, we need to determine its slope first.

The slope of the given line is -3/4.

Since the line we are looking for is perpendicular, its slope will be the negative reciprocal of -3/4, which is 4/3.

So the slope of the line passing through (0, -1) and perpendicular to the given line is 4/3.

Using the point-slope form of the equation of a line, we can write:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the given point.

Substituting the values we have, we get:

y - (-1) = (4/3)(x - 0)

Simplifying, we get:

y + 1 = (4/3)x

Subtracting 1 from both sides, we get:

y = (4/3)x - 1

Therefore, the equation of the straight line passing through the point (0, -1) and perpendicular to the line y = (-3/4)x - 3 is y = (4/3)x - 1.

Answer:

y = (4/3)x - 1.

Step-by-step explanation:

we have

y=-3/4x-3

comparing it with y=mx+c

where m is the slope and is c the y-intercept.

we get

slope (m) = -3/4.

Any line perpendicular to it will have a slope that is the negative reciprocal of -3/4, which is 4/3.

Let's call the equation of the line we're trying to find y = mx + b, where m is the slope and b is the y-intercept.

We know that the line passes through the point (0, -1), so we can substitute these values into the equation to get:

-1 = (4/3)(0) + b

Simplifying this, we get:

-1 = b

So the y-intercept of our line is -1.

Now we can substitute the slope and y-intercept into the equation to get:

y = (4/3)x - 1

Therefore, the equation of the straight line passing through the point (0, -1) which is perpendicular to the line y=-3/4x-3 is y = (4/3)x - 1.

The correct options are -

When something is bought on credit, an initial payment is made in the form of a down payment.

Given is that Renata is purchasing a condominium for $125,000. She wants to put down a down payment of 20%.

We can calculate the amount she is putting in down payment as -

{x} = 20% of 125000

{x} = 20/100 x 125000

{x} = 20 x 1250

{x} = 25000

Therefore, the correct options are -

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Step-by-step explanation:

Flip f(x) about the x-axis by multiplying it by -1

  - f(x)

  the squish it skinnier by multiplying it by 4

g(x) = - 4 f(x)   = -4 x^2

Answer:

Debbie runs 9 feet per second: 9 ft/s

Jessica runs 1 mile  in 440 seconds: 414/50 ft/s = 207/25 ft/s = 8 7/25 ft/s

jesssica runs 131 feet in 10 seconds: since 1 mile = 5280 ft we have 1/470 mi/s = 5280/470 ft/s = 528/47 ft/s = 11 11/47 ft/s

ron runs 603 feet in 1 minute: 547 ft/min = 603/60 ft/s = 201/20 ft/s = 10 1/20 ft/s

Since:

11 11/47 > 10 1/20 > 9 > 8 7/25

Emily runs the fastest.

Answer:

-4 < 2 - a < -8

Step-by-step explanation:

Answer:

ANSWER: 1 31/40

Step-by-step explanation:

You would need to find common denominators!

Finding the common denominator 40 is what they all have in common because 5*8 = 40, 8*5 = 40, and 10 * 4 = 40.

You would then multiply the numerator by the number you used to get 40.

This gets you:

24/40 + 35/40 + 12/40 = 71/40

Then you would have to simplify this problem!

ANSWER: 1 31/40

a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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The equation solved for the variable are;

h = S- 2B/p

b = S - hp/2

To determine the equation, we need to know that the subject of formula for  an equation is described as the variable that is made to stand on one end of the equality sign.

It is the variable that is being worked out.

From the information given, we have that;

S= hp + 2B.

To make the height with the variable 'h' the subject, we have;

collect the terms

hp = S - 2B

Divide by the coefficient

h = S- 2B/p

For b, we have;

S - hp = 2b

divide by the coefficient

b = S - hp/2

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Functions f(x) = x² + 1 and g(x) = x – 4, the value equivalent  to f(g(10)) is, 37

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

f(x) = x² + 1

g(x) = x – 4

f(g(10)) = ?

f(g(x))  =  (x - 4)² + 1

           =  x² - 8x + 16 +1

           =   x² - 8x + 17

f(g(10)) =  10² - 8×10 + 17

            = 100 - 80 + 17

            = 37

The value of  f(g(10)) is 37

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Answer:

i know

Step-by-step explanation:

but I don't have pen

Answer:

15$

Step-by-step explanation:

24.00 increased by 15% is 27.60

the increase is 3.60

so the answer is 15%

The 95 percent confidence interval is (0.20, 0.32).

a. We can construct a 95% confidence interval to estimate the percentage of yellow peas as follows:

Let p = proportion of yellow peas = 155/595 = 0.26

Sample size = n = 595

Standard error = SE = √(p × (1-p) / n) = √(0.26 × (1-0.26) / 595) = 0.03

95% confidence interval = p ± 1.96 × SE

= 0.26 ± 1.96 × 0.03

= 0.26 ± 0.06

So, the 95% confidence interval is (0.20, 0.32).

b. Yes, the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow, as the 95% confidence interval does not include the expected value of 0.25.

Therefore, the 95 percent confidence interval is (0.20, 0.32).

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The required number of small prism that would be fill in the large prism is given as 6

As mentioned in the question, a large rectangular prism is 12 inches long, 9 inches wide, and 6 inches tall. A small rectangular prism is also 12 inches long, but it's only 3 inches wide and 3 inches tall.

Here,
The volume of the large prism = 12 × 9 × 6
                                              = 648 inches cube
The volume of the small prism = 12 × 3 × 3
                                              = 108 inches cube,

The ratio of the volume of the large prism to a small prism will give the number of small prisms needed to fill the large prism. So,
n = 648 / 108  = 6 / 1

Thus, the required number of small prism that would be filled in the large prism is given as 6.

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Answer:

It would be C.

Step-by-step explanation:

Y would be the Amount he would pay plus the one time fee. So there for it would be Y=12.5+37.00

Answer:

8 months

Step-by-step explanation:

if you can get 120 per month then 950/120 = ~8

Answer:

She needs $350.

Step-by-step explanation:

120 x 5 = 600

$950 - $600 = $350

Answer:

x ≈ 0.6385

Step-by-step explanation:

using the rule of logarithms

log \(x^{n}\) = nlog x

then

\(7^{2x}\) = 12 ( take ln of both sides )

ln \(7^{2x}\) = ln12

2x ln7 = ln12 ( divide both sides by 2ln7 )

x = \(\frac{ln12}{2ln7}\) ≈ 0.6385 ( to the nearest ten thousandth )

Answer

Linear equations

Step-by-step explanation:

that’s what they look like linear equations are how you graph a line

The formula is y=Mx+b

The M is the slope which is how many times u move up or down, and  left or right on the line. In this case its 5 you would move up 5 and right 1

With negative slope, for example -5 you would move either up 5 left 1 or down 5 right 1.

The B is the y-intercept which is when x is equal to 0 in your case its 1 for the first problem and -1 for the second problem

that’s kinda all to know about linear equations for now!