the amount that results when $4000 is compounded at 6% annually over seven years

Answers

Answer 1

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$4000\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &7 \end{cases} \\\\\\ A=4000\left(1+\frac{0.06}{1}\right)^{1\cdot 7}\implies A=4000(1.06)^7[/tex]

Related Questions

If SAT scores are normally distributed with a mean of 1518 and a standard deviation of 325, find the probability that a randomly selected SAT score is between 1550 and 1575.

A.
0.5714

B.
0.9684

C.
0.0316

D.
0.5398

Answers

Mean, x_bar = 1518
Standard deviation, sigma = 325
Range required: 1550 ≤ X ≤ 1575

Z = (X - x_bar)/sigma

Z1 = (1550-1518)/325 ≈ 0.1
Z2 = (1575-1518)/325 ≈ 0.18

From Z tables,
P(Z1) = 0.5398
P(Z2) = 0.5714

P(1550≤X≤1575) = P(Z2) - P(Z1) = 0.5714 - 0.5398 = 0.0316

The correct answer is C.

Answer:

0.0316

Step-by-step explanation:

How many eggs are needed to make 1 dozen waffles, assuming you have enough of all other ingredients? given: 2 cups flour + 3 eggs + 1 tbs oil → 4 waffles
a. 12
b. 48
c. none of these choices is correct
d. 9
e. 16?

Answers

We have been given that

2 cups flour + 3 eggs + 1 tbs oil → 4 waffles

In order to make 4 waffles we need 3 eggs.

Thus, to make 1 waffle we need 3/4 eggs.

Now, in 1 dozen there are 12 waffles. Hence, to make 12 waffles we need

[tex]\frac{3}{4} \times 12\\ \\ =3 \times 3\\ =9[/tex]

Therefore, 9 eggs are needed to make 1 dozen waffles.

D is the correct option.

Final answer:

The correct option is (d) 9. Using the given recipe, we can determine that 9 eggs are needed to make 1 dozen waffles by setting up a proportion and solving for the number of eggs.

Explanation:

The original recipe provided states that 2 cups of flour, 3 eggs, and 1 tablespoon of oil will yield 4 waffles. To find out how many eggs are needed to make 1 dozen (12) waffles, we need to set up a proportion based on the given recipe.

Since 4 waffles require 3 eggs, we can set up the following equation: 4 waffles / 3 eggs = 12 waffles / x eggs. Cross-multiplying gives us 4x = 36, and dividing both sides by 4 gives us x = 9. Therefore, 9 eggs are required to make 1 dozen waffles.

What is the equation of the axis of symmetry of the graph of y + 3x – 6 = –3(x – 2)squared + 4?

Answers

Answer:

x = 3/2

Step-by-step explanation:

That is quite long and drawn out, so we have to get it down to a single quadratic equation, set equal to 0.

Begin by expanding the right side to get

[tex]y+3x-6=-3(x^2-4x+4)+4[/tex]

then multiplying in the -3 to get

[tex]y+3x-6=-3x^2+12x-12+4[/tex]

Now we will combine all the like terms and get everything on one side of the equals sign, and set it equal to 0:

[tex]-3x^2+9x-2=0[/tex]

In order to find the equation of the axis of symmetry we have to put it into vertex form, which is accomplished by completing the square on this quadratic.

In order to complete the square, the leading coefficient has to be a +1. Ours is a -3, so we will factor that out. First, though, now that it is set to equal 0, we will move the constant, -2, over to the other side, isolating the x terms.

[tex]-3x^2+9x=2[/tex]

Now we can factor out the -3:

[tex]-3(x^2-3x)=2[/tex]

The rules for completing the square are as follows:

Take half the linear term, square it, and add it to both sides. Our linear term is 3. Half of 3 is 3/2, and squaring that gives you 9/4. We add into the parenthesis on the left a 9/4, but don't forget about that -3 hanging around out front that refuses to be ignored. We didn't add in just a 9/4, we added in (-3)(9/4) = -27/4:

[tex]-3(x^2-3x+\frac{9}{4})=2-\frac{27}{4}[/tex]

In the process of completing the square we created a perfect square binomial on the left. Stating that binomial and simplifying the addition on the right gives us:

[tex]-3(x-\frac{3}{2})^2=-\frac{19}{4}[/tex]

We can determine the axis of symmetry at this point. Because this is a positive x-squared polynomial, the axis of symmetry is in the form of (x = ) and what it equals is the h coordinate of the vertex. Our h coordinate is 3/2; therefore, the axis of symmetry has the equation x = 3/2

Help

How much will $5,000 invested at 6% compounded annually amount to after 10 years?

Answers

To find one year, here's the equation:
5000 + 0.06(5000)
For 10 years:
5000 + 10(0.06(5000))
Multiply:
5000 + 0.6(5000)
We can make it smaller:
1.6(5000) = 8000
You can make $8000

The longest side of an obtuse triangle measure 20 cm. the two shorter sides measure x cm.and 3x sm round to the nearest tenth,what is the greatedt possible value of x

Answers

22cm is the greatest

It should be greater than17(20-3)

and smaller than 23(20+3)

A wheelchair ramp has a slope of 1 10 . if its rise is 1 5 2 feet, what is its run?

Answers

[tex]slope = \frac{rise}{run} \\ 110 = \frac{152}{run} \\ run \times 110 = 152 \\ run = \frac{152}{110} \\ run = \frac{76}{55} \: \: \: \: or \: \: \: 1.38[/tex]

Solve this inequality: 3q + 11 + 8q > 99. A. q > 8 B. q > 1/8 C. q > 88 D. q > 11

Answers

Hey!

To solve this problem we must first group like terms.

Original Equation :
3q + 11 + 8q > 99

New Equation {Grouped Like Terms} :
3q + 8q + 11 > 99

Now, we'll add our similar elements.

Old Equation :
3q + 8q + 11 > 99

New Equation {Added Similar Elements} :
11q + 11 > 99

Next, we'll have to change the equation. To do this we'll add minus eleven to both sides of the equation. This will give us eleven q on its own.

Old Equation :
11q + 11 > 99

New Equation {Added Subtract 11 to Both Sides} :
11q + 11 - 11 > 99 - 11

Now we simplify.

Old Equation :
11q + 11 - 11 > 99 - 11

New Equation {Old Equation Simplified} :
11q > 88

Now, we'll have to divide both sides by eleven. We do this so as to get the variable ( q ) on its own.

Old Equation :
11q > 88

New Equation {Added Divide Both Sides by 11} :
[tex] \frac{11q}{11} [/tex] > [tex] \frac{88}{11} [/tex]

Once again, we now have to simplify.

Old Equation :
[tex]\frac{11q}{11}[/tex] > [tex]\frac{88}{11}[/tex]

New Equation {Old Equation Simplified} :
q > 8

So, this means that the solution to the inequality given is q > 8.

Hope this helps!

- Lindsey Frazier ♥

Under the normal curve, approximately what percent of scores fall between and -1 to +1 standard deviations around the mean?

Answers

According to the empirical rule, roughly 68% of the scores fall between z = -1 and z = 1

You can use a calculator to get a more approximate answer. If you have a TI calculator, you can use the "normalcdf" function to type in normalcdf(-1,1)

PLEASE HELP !!

2. A cube-shaped aquarium has edges that are 3 ft long. The aquarium is filled with water that has a density of 62 lb/ft³.

(a) Should the aquarium be placed on a table that can support a maximum weight of 200 lb? Explain why or why not.

(b) Would the density of the water change if the aquarium was only half full? Explain.

Answers

Part (a)

Let's find the volume of the tank.

Volume of a rectangular prism = length*width*height
V = L*W*H
V = 3*3*3
V = 27 cubic feet

There is 27 cubic feet of water in the tank if the tank is completely full. Use the fact that
1 cubic foot of water = 62 pounds
so we can convert from volume to weight

(27 cubic feet)*(62 pounds/1 cubic foot) = 27*62 = 1674 pounds

If the tank is completely full, then the water weighs 1674 pounds, which is far greater than the 200 lb max weight limit for the table. The table will fall apart if you place a full aquarium on top of it. Note: this is not including anything else that would go inside the tank such as rocks, plant matter, fish, the glass of the tank itself, etc

In short, the aquarium should not be placed on the table as it exceeds the table's weight limit.

---------------------------------------------------------------------------

Part (b)

The density will not change because the density is how packed in a substance is for any cubic unit of volume. Saying "the density of water is 62 pounds per cubic foot" means that for a cubic foot, water naturally weighs 62 pounds .We can scale this to any size we want and the density will stay the same.

It's like saying that the fractions 1/2 and 2/4 are the same. The 2/4 is the scaled version of 1/2. So back to the water example, if we had 2 cubic feet of water then it would weigh 2*62 = 124 pounds. So the ratio
2 cubic feet: 124 pounds
simplifies back to
1 cubic foot: 62 pounds

note: the larger the density, the heavier the object is assuming the volume is held constant

The weight of the water in the cube-shaped aquarium will be 1674 lb, which is much greater than the table's maximum weight capacity of 200 lb. Therefore, the aquarium should not be placed on the table. The density of the water remains constant at 62 lb/ft³ regardless of how much the aquarium is filled.

To determine if the aquarium can be placed on a table with a weight limit of 200 lb, we must first calculate the weight of the water the aquarium will hold. We calculate the volume of the aquarium, then multiply it by the density of water, as the density is given as weight per unit volume (specifically 62 lb/ft³).

The volume (V) of a cube is given by V = side³, so for our aquarium with 3 ft long edges, V = 3³ = 27 ft³. The weight of the water (W) is therefore W = density x volume = 62 lb/ft³ x 27 ft³ = 1674 lb. Since 1674 lb exceeds the table's maximum weight capacity of 200 lb, the aquarium should not be placed on the table.

As for part (b), the density of the water does not change whether the aquarium is full or half full. Density is an intensive property meaning it's independent of the quantity of the substance present. Therefore, whether the aquarium is filled or only half filled, the density of the water remains at 62 lb/ft³.

Find the volume of the pyramid with height 15 and rectangular base with dimensions 3 and 7.

Answers

the volume of the base is 1.4 how I got the answer is by 3 times 7 that will give you 21 and you do 21 divided by 15 and your answer will be 1.4

How do you find the base of this triangle? (Picture should be able to be seen)

Answers

the idea being, when you run a perpendicular line to the base, from the right-angle in a right-triangle, like in this case, what you end up with is, three similar triangles, a Large triangle containing the two smaller ones, a Medium triangle and a Small one, check the picture below.

since all three are similar, we can use the proportions on the corresponding sides, as you see in the picture, the base of the triangle then will just be x + y.

Find the volume of a cylinder that has the following dimensions. Do not round your answer. (Use 3.14 for π.)

CONVERT M INTO CM

Answers

Convert .25 M to 25 cm. Then multiply 3.14 X 5 X 5 X 25 = 1962.5 cubic cm.

The volume of cylinder is 1962.5 [tex]cm^{2}[/tex].

To find the volume of a cylinder.

What is mensuration?

The part of geometry concerned with ascertaining lengths, areas, and volumes. Mensuration deals with the size, region, and density of different forms both 2D and 3D.

Given that:

Radius= 5 cm

Height= 0.25 m=25 cm

π=3.14

By the formula of volume of cylinder

Volume=π[tex]r^{2} h[/tex]

TO put the value,

Volume=3.14*5*5*25

Volume=1962.5 [tex]cm^{2}[/tex]

So, the volume of cylinder is 1962.5 [tex]cm^{2}[/tex].

Learn more about mensuration here:

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Look at the cylinder below. which of these could not be a cross section of the cylinder? a circle b square c triangle d rectangle

Answers

The correct answer would be a triangle.

If you sliced horizontally across a cylinder standing up, you would have a circle.

If you sliced vertically down a cylinder standing up, you could have either a rectangle or a square.

You would never have a triangle.

Final answer:

A square cannot be a cross section of a traditional circular cylinder when sliced perpendicular to its height. However, circles, rectangles, and triangles can be cross sections depending on the shape of the cylinder and the slicing.

Explanation:

When considering the cross sections of a cylinder, it is important to remember that the cross-sectional shape remains consistent along the height of the cylinder. A cross section made perpendicular to the height of a traditional circular cylinder is always a circle. Therefore, the correct answer to which shape could not be a cross section of a cylinder is a square, option b. Circles, rectangles, and triangles can all be cross sections of a cylinder depending on the shapes of the top and bottom faces of the cylinder and how the cross section is sliced.

If the cylinder is a right circular cylinder, the only possible perpendicular cross-sectional shape is a circle. A square cross section can occur in a cylinder if the top and bottom faces are square and the cylinder is not circular. Similarly, a rectangular cross section can occur if the cylinder has a rectangular type of cross-section to start with. However, for a circular cylinder, a triangle cannot be a cross section because slicing it will always yield a circular shape due to the round nature of its base.

When you have two shapes to compare on a coordinate plane, you can determine the scale factor, knowing that the transformation was a dilation. Generate instructions you would give another student to determine the scale factor.

Answers

Assume that the initial coordinates are (x,y) and that the dilated coordinates are (x',y').

The dilation is therefore:
(x,y) ............> (x',y')

Now, let's assume that the dilation factor is k.
Therefore:
x' = kx
y' = ky

Based on the above, all the student has to do is get the initial coordinates and the final ones and then substitute in any of the above two equations to get the value of k.

Example:
Assume an original point at (2,4) is dilated to coordinates (4,8). Find the dilation factor.
Assume the dilation coefficient is k.
(x,y) are (2,4) and (x',y') are (4,8)
Therefore:
x' = kx .........> 4 = k*2 ..........> k = 2
or:
y' = ky ..........> 8 = k*4 .........> k = 2
Based on the above, the dilation coefficient would be 2.

Hope this helps :)

Sample Response: Locate two corresponding ordered pairs of the two shapes. Calculate how much the pre-image values were multiplied by to obtain the image values. This is your scale factor. You can calculate this by dividing the coordinates of the mage by the corresponding coordinates of the pre-image.

The equation of a circle is (x+9)2+(y+6)2=225 .

What is the center of the circle?

Enter your answer in the boxes.

(
,
)

Answers

You can read off the coordinates of the center of (x+9)2+(y+6)2=225 directly: h= -9 and k= -6, so the center is at (-9, -6).

Answer:

[tex](-9,-6)[/tex]

Step-by-step explanation:

We have been given an equation of a circle [tex](x+9)^2+(y+6)^2=225[/tex]. We are asked to find the coordinates of the center of the given circle.

We know that center-radius form of a circle is in format: [tex](x-h)^2+(y-k)^2=r^2[/tex], where,

[tex](h,k)=\text{Center of circle}[/tex],

[tex]r=\text{Radius of circle}[/tex]

Upon comparing our given equation with center-radius form of a circle we will get,

[tex](x-(-9))^2+(y-(-6))^2=15^2[/tex]

Therefore, the center of our given circle is at point [tex](-9,-6)[/tex].

Wright a real world problem that involves classifying a quadrilateral. Then solve the problem.

Answers

An amusement park ride has a moving platform attached to four swinging arms. The platform swings back and forth, higher and higher, until it goes over the top and around in a circular motion. In the diagram below, AD and BC represent two of the swinging arms, and DC is parallel to the ground (line l). Explain why the moving platform AB is always parallel to the ground.

The shape of quadrilateral ABCD changes as the moving platform swings around, but its side lengths do not change. Both pairs of opposite sides are congruent, so ABCD is a parallelogram by Theorem 8.7.By the definition of a parallelogram, AB DC . Because DC is parallel to line l, AB is also parallel to line l by the Transitive Property of Parallel Lines. So, the moving platform is parallel to the ground.

A bag contains 10 res marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Five marbles are drawn from the bag. what is the approximate probability that exactly two of the five are blue

Answers

One way is to do binomial distribution probability so you can say (5C2) (15/50)^2(1-(15/50))^5-2. This should give you the p(2 yellow)

Factor this expression.

4x – 20

A. 4(x – 16)
B. 4(x – 6)
C. 4(x – 5)
D. 4(x – 10)

Answers

4x - 20 = 4x-4*5=4(x-5)

Answer: C. 4(x – 5)

I don't know how to do this question, help!!

Answers

60-45 = 15 square meters
3.5 - 2.75 = 0.75 hours

0.75 hours / 15 meters = 0.05 hours per meter

WILL GIVE BRAINLIEST
solve for x

A. 70/6
B. 60/16
C. 6
D. 11

Answers

So a line is 180°
Since it gave you options, the easiest way would be to plug it in (plug and chug)
the answer is 11
first what I did was plug 12 into 5x+10 and then found the answer and then added 58°
the answer of that subtracted from 180
with that I then plugged in 11 for x for 11x+2 = 123
180 - 123 = 57 which is the same answer for the missing angle within the triangle

One ounce is equal to 28.35 grams. convert 16 ounces to grams round your answe to the nearest tenth

Answers

The amount 16 ounce into grams using the conversion factor 1 ounce = 28.35 grams is 454.2 grams.

To convert ounces to grams, you can use the conversion factor:

1 ounce = 28.35 grams

Now, to convert 16 ounces to grams:

= 16 ounces * 28.35 grams/ounce

= 454.16 grams

Rounding to the nearest tenth:

454.16 grams rounded to the nearest tenth is 454.2 grams.

Therefore, the required quantity is 454.2 grams.

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Final answer:

To convert 16 ounces to grams, we multiply 16 by the conversion factor of 1 ounce to grams (28.35). This gives us 453.6 grams, when rounded to the nearest tenth.

Explanation:

To convert ounces to grams, we use the conversion factor 1 oz = 28.35 g. Given that we are converting 16 ounces to grams, we multiply the number of ounces by the conversion factor.

So, 16 oz * 28.35 g/oz = 453.6 g. Rounding to the nearest tenth, the result is 453.6 g.

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Can someone please help me with this!!
Will give brainliest!!

Answers

Here are the answers. Hope it helps.

Computer amount of interest earned and the following simple interest from a deposit of 5500 at 6% for three years equals?

Answers

1 year = 6% x 5500 = 0.06 x 5500 = $330

1 year = $330
3 years = $330 x 3 = $990

Answer: $990

) the supplement of an angle is thirty more than twice the angle. find the measure of the angle and its supplement. answer

Answers

supplementary angle is two angles sharing a 180 degree.

50 x 2 = 100

100 + 30 = 130

130 + 50 = 180

The other angle would be 130 degrees. And the original angle would be 50.

What is tan (x)?

20/21

20/29

29/21

29/20

Answers

Answer is choice A) 20/21

The first step is to use the pythagorean theorem a^2+b^2 = c^2 to find the missing side to be 21. Once you know this, you find the ratio of the opposite and adajcent sides. The opposite side is the leg furthest from the angle x (the side labeled 20). The adjacent side is the leg closest to or touching the angle x (the side labeled 21 which was found earlier).

So, tan(x) = opposite/adjacent = 20/21

The side of a square measures 2x^2y^3 what is the area of the square if x=-2 and y=2

Answers

The area of the square is -128.

What is 12.5(18/6)+5³

Answers

Your answer is 162.5

Final answer:

To solve the expression 12.5(18/6) + 5³, divide 18 by 6 to get 3. Multiply 12.5 by 3 to get 37.5. Then, calculate 5³, which equals 125. Adding the results, you get 162.5.

Explanation:

To solve the expression 12.5(18/6) + 5³, follow the order of operations (PEMDAS/BODMAS). First, divide 18 by 6, which equals 3. Next, multiply 12.5 by 3, which equals 37.5. Finally, calculate 5³, which equals 125. Adding the results, 37.5 + 125 = 162.5.

Which equation shows 2x – y = 6 converted to slope-intercept form? y = x – 3 y = 2x – 6 y = –2x + 6

Answers

slope-intercept form is y=mx+b
so you would subtract the 2x over to get -y=-2x+6 then you would divide by -1 to get y=2x-6
so y=2x-6 is the answer

The answer is Y=2x-6

The data set represents a month-to-month progression of gasoline prices over the course of several months in an unspecified city. Use a graphing calculator to determine the quadratic regression equation for this data set.

Answers

Answer:

The correct option is a.

Step-by-step explanation:

The general form of a quadratic regression equation is

[tex]y=ax^2+bx+c[/tex] ..... (1)

Using graphing calculator we get

[tex]a=-0.143393\approx -0.143[/tex]

[tex]b=0.59525\approx 0.595[/tex]

[tex]c=2.82964\approx 2.830[/tex]

Substitute these values in equation (1) to find the quadratic regression equation for this data set.

[tex]y=-0.143x^2+0.595x+2.830[/tex]

Therefore the correct option is a.

Solve 7 + x - 15 = -2
5 1/3
6 1/3
10 2/3
20 2/3

Since the mod decided to delete my question because of a mistake. Please answer. Need it ASAP

Answers

7+x-15=-2

Combine like terms
(7-15)+x=-2

-8+x=-2
+8 +8

x=6

6 is your answer.

Check :
7+6-15=-2

13-15=-2

-2=-2

Correct!

Hoped I helped!

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