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In order to ride a roller coaster, a rider must be greater than 48 inches tall. Right now, Jeff is 45 inches tall. Write an inequality that describes how many more inches Jeff must grow in order to ride the roller coaster.

The balance in the account after the given period is \(\$6,872.74\)  

we know that

The compound interest formula is equal to  

\(\text{A}=\text{P}(1+\frac{\text{r}}{\text{n}})^{\text{nt}}\)

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

\(\text{t}= 8 \ \text{years}\)

\(\text{P}=\$4,000\)

\(\text{r}=0.07\)

\(\text{n}=1\)

substitute in the formula above

\(\text{A}=\$4,000(1+\frac{0.07}{1})^{1\times8}=\$6,872.74\)  

Answer:

a) 615

b) 715

c) 344

Step-by-step explanation:

According to the Question,

Z = (x - mean)/standard deviation

Now,

For x = 4171,  Z = (4171 - 3311)/860 = 1  

Next, multiply that by the sample size of 732.

Z = (1581 - 3311)/860 = -2    

Z1 = (3311 - 3311)/860 = 0

Z2 = (5031 - 3311)/860= 2  

P(0 ≤ Z ≤ 2) = 0.9772 - 0.5000 = 0.4772

  approximately 47% fall between 0 and 1 standard deviation, so take 0.47 times 732 ⇒ 732×0.47 = 344.

The expression that models the area of the garden is A = 5w + 3w².

The area a rectangle occupies is the space it takes up inside the limitations of its four sides.

The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth. In contrast, the circumference of a rectangle is equal to the product of its four sides. Thus, we can say that the area of a rectangle equals the space enclosed by its perimeter. The area of a square will, however, be equal to the square of side-length in the case of a square because all of its sides are equal.

Let us suppose the width of the rectangle = w.

Given that, the length of the patio to be five yards more than three times the width.

The length of the rectangle is l = 5 + 3w

The area of the garden is given as:

A = (l)(w)

A = (5 + 3w)(w)

A = 5w + 3w²

Hence, the expression that models the area of the garden is A = 5w + 3w².

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Answer:

\(236.715\:\mathrm{ft^2}\)

Step-by-step explanation:

The area of the figure consists of a rectangle and two half-circles.

Area of rectangle: \(15\cdot 4=60\)

Area of two half-circles: \(2\cdot \frac{1}{2}\cdot 7.5^2\cdot \pi=176.714586764\)

Thus, the total area of the figure is

\(60+ 176.714586764\approx \boxed{236.715}\)

Answer:

d

Step-by-step explanation:

divide

Answer:X=3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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Answer:

It is B, B, C, B

(x-1) would be the opposite on the x axis so it will be 1 to the right.

If it is (x)-1 is accurate to the horizontal change so it is 1 down.

Step-by-step explanation:

Answer:

21.715 degrees

Step-by-step explanation:

There are 14 vertexes (vertices) for a 14-gon. It is 'regular' so all these angles are equal. So the exterior angle of each is 180-154.285 = 21.715 degrees.

The measure of the exterior angle in a regular 14 sided polygons is 25.72 degree.

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.

We have 14 sides polygon.

We know the sum of the interior angle = (n-2)×180

n is the number of sides

Here n = 14

The sum of the interior angle = (14-2)×180 = 2160 degree

Each interior angle = 2160/14 = 154.285

Measure of the exterior angle = 180 – 154.285 = 25.715 ≈ 25.72 degree

Thus, the measure of the exterior angle in a regular 14 sided polygons is 25.72 degree.

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The equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is: R(x) = 250000 + 375x - 2.5x²

Equations are mathematical statements with two algebraic expressionsοn either sideοf an equals (=) sign. It illustrates the equality between the expressions writtenοn the left and right sides. To determine the valueοf a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

N(x) = 625 + 2.5x

The revenue R(x) will be the productοf the numberοf students enrolled and the fee charged per student. The fee charged per student will be (400 - x) dollars. So, the revenue function can be represented as:

R(x) = (625 + 2.5x)(400 - x)

Simplifying the expression, we get:

R(x) = 250000 + 375x - 2.5x²

Therefore, the equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is:

R(x) = 250000 + 375x - 2.5x²

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Answer:

685

Step-by-step explanation:

11 hours = 660 minutes

660 + 25

You can subtract the right side and factor the result, or you can factor the left side then see what happens.

... 5x² +22x +8 = 5x +2

... 5x² + 2x +20x +8 = 5x +2 . . . . split the x term so we can factor by grouping

... x(5x +2) +4(5x +2) = (5x +2)

Now we can subtract the right side and finish the factoring.

... x(5x +2) +(4 - 1)(5x +2) = 0

... (x +3)(5x +2) = 0 . . . . . the factorization of your equation

_____

If we start by subtracting the right side, we are looking to factor ...

... 5x² +17x +6 = 0

... 5x² +2x +15x +6 = 0 . . . . . split the x-term to help factoring by grouping

... x(5x +2) +3(5x +2) = 0 . . . factor pairs of terms

... (x +3)(5x +2) = 0 . . . . . . . . combine the results

______ _____

Factoring quadratics with the leading coefficient not equal to 1 is similar to factoring when it is equal to 1. Here, (after subtracting the right side), we are looking for factors of 5·6 = 30 that add to 17, the coefficient of the x-term.

... 30 = 1·30 = 2·15 = 3·10 = 5·6

The sums of these factor pairs are 31, 17, 13, 11. We see that the factor pair (2, 15) is the one we want, as its sum is 17. You will note these are the numbers used to divide the x-term for factoring by grouping. We rewrote 17x as 2x +15x. (There are other ways to use these numbers, but this is perhaps the easiest to see and remember.)

Answer:

(5x + 2)(x + 4)

Step-by-step explanation:

So, we have the equation \(5x^2+22x+8\) right?

To get the \(x^2\) we are going to need 'something' x in the first x slots of our factor form, like this:

(?x ± ?)(?x ± ?)

5 is a prime number, so one of the x's will be a 5x, and the other one a 1x:

(5x ± z)(x ± q)

z * q must be 8, and 5 * q + z must be 22

2 * 4 is 8

Let's plug these values in:

(5x + 2)(x + 4)

Let's multiply this out:

\(5x^2+22x+8\)

This matches with our original equation!

So, our answer is:

(5x + 2)(x + 4)

The angle from the options given that is shown in the drawing is: D. <LIJ.

An angle is a geometric figure that is formed by two rays that share the same endpoint, called the vertex. The rays are called the sides of the angle, and the endpoint is called the vertex.

In the drawing given,  IJ and LI are two segments that have a common endpoint called vertex I.

Points L, I, and J forms an angle whose vertex is at I, as shown in the image given. Thus, the angle shown in the drawing is: D. ∠LIJ.

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Answer:

Step-by-step explanation:

The given figure has a perimeter of 10 lines, each 1 unit long.

If the perimeter is 30 for the new figure, then the scale factor is 3, because 30 is 3 * 10

Answer:

81 degrees

This is an acute angle since it’s less then 90 degrees

Step-by-step explanation:

All three angles of a triangle always equal 180 degrees

180-(78+31)

180-109

81 degrees

Hopes this helps please mark brainliest

Answer:

(657)

Step-by-step explanation:

Simplify the following:

3 (300 - 70/5 - (3×23 - (8 - 2×3)))

The gcd of -70 and 5 is 5, so (-70)/5 = (5 (-14))/(5×1) = 5/5×-14 = -14:

3 (300 + -14 - (3×23 - (8 - 2×3)))

-2×3 = -6:

3 (300 - 14 - (3×23 - (-6 + 8)))

8 - 6 = 2:

3 (300 - 14 - (3×23 - 2))

3×23 = 69:

3 (300 - 14 - (69 - 2))

| 6 | 9

- | | 2

| 6 | 7:

3 (300 - 14 - 67)

300 - 14 - 67 = 300 - (14 + 67):

3 ((300 - (14 + 67)))

| 1 |

| 6 | 7

+ | 1 | 4

| 8 | 1:

3 (300 - 81)

| | 9 |

| 2 | | 10

| | |

- | | 8 | 1

| 2 | 1 | 9:

3 (219)

3 (219) = (3×219):

(3×219)

3×219 = 657:

Answer: (657)

Susan invested $7000 in the fund that paid a 9% profit, and the remaining (10,000 - 7000) = $3000 in the stock that suffered a 3% loss.

Let's assume that Susan invested x dollars in the fund that paid a 9% profit, and the remaining (10,000 - x) dollars in the stock that suffered a 3% loss.

The net profit from the investment in the fund would be 9% of x, or 0.09x dollars.

The net loss from the investment in the stock would be 3% of (10,000 - x), or 0.03(10,000 - x) dollars.

Given that her overall net profit was $540, we can write the equation:

0.09x - 0.03(10,000 - x) = 540

Now let's solve for x:

0.09x - 0.03(10,000 - x) = 540

0.09x - 300 + 0.03x = 540

0.12x = 540 + 300

0.12x = 840

x = 840 / 0.12

x = 7000

So, Susan invested $7000 in the fund that paid a 9% profit, and the remaining (10,000 - 7000) = $3000 in the stock that suffered a 3% loss.

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Answer:

22 1/2

Step-by-step explanation:

Answer:

A. 18

Step-by-step explanation:

Recall: the Mid-segment Theorem states that the length of the mid-segment theorem of a triangle is half the length of its third side.

DE = ½(AC) (Triangle Mid-segment Theorem)

AC = 36 (given)

Plug in the value

DE = ½(36)

DE = 18

Answer:

Step-by-step explanation:

$100x0.5x1=$5

Answer:

a) The curved surface area of the frustum of the cone is given by:

= (1 + 2)

where is the slant height of the frustum, 1 is the top radius, and 2 is the bottom radius.

We can find the slant height using the Pythagorean theorem:

= √(ℎ^2 + (2 − 1)^2)

= √(28^2 + (14 − 6)^2)

= √(784 + 64)

= √848

= 29.12

Substituting the values into the formula, we get:

= × 29.12 × (6 + 14)

= 1138.5 m^2

Therefore, the curved surface area of the frustum of the cone is 1138.5 square meters.

b) The total surface area of the frustum of the cone is given by:

= 1^2 + 2^2 + (1 + 2)

Substituting the values into the formula, we get:

= × 6^2 + × 14^2 + × 29.12 × (6 + 14)

= 1138.5 + 1070.88 + 1138.5

= 3347.88 m^2

Therefore, the total surface area of the frustum of the cone is 3347.88 square meters.

c) The volume of the frustum of the cone is given by:

= 1/3 × × ℎ × (1^2 + 2^2 + 12)

Substituting the values into the formula, we get:

= 1/3 × × 28 × (6^2 + 14^2 + 6 × 14)

= 1/3 × × 28 × (36 + 196 + 84

9514 1404 393

Answer:

  54

Step-by-step explanation:

The fraction of the total that work outside the home is ...

  outside/(outside +inside) = 6/(6+4) = 6/10

Then the number of those surveyed who work outside the home is ...

  (6/10)(90) = 54 . . . work outside the home

Answer:

162 cm

Step-by-step explanation:

Perimeter =35+35+46+46

=162cm

Perimeter is basically adding up all the sides of the length

Answer:

(1.75,0)

Step-by-step explanation:

The point charges placed 0.500 m apart are 10.4 nC and 43.9 nC. Then, the electric field halfway between these charges will be -4824 N/C.

The physical field that surrounds particles with an electrical charge is called an electric field. All other charged particles in the field are affected by it, either being attracted to it or being repelled by it.

The electric field because of a point charge q is written as \(E=\frac{kq}{r^2}\)

Positive point charges cause the electric field to point away from the point, whereas negative point charges cause the electric field to point in the direction of the point. Then, the electric field of the midpoint p in the diagram is written as,

\(\begin{aligned}E_p&=\mathrm{\frac{k(10.4\;nC)}{(0.25\;m)^2}-\frac{k(43.9\;nC)}{(0.25\;m)^2}}\\&=\mathrm{\frac{k(10.4-43.9)\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{\frac{9\times 10^9\;Nm^2/C^2\times 33.5\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{4824\;N/C}\end{aligned}\)

The required answer is -4824 N/C.

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Answer:

Step-by-step explanation:

Hence, it costs $87.5 to ship 500 pounds.

Hoped this helped.

\(BrainiacUser1357\)

1. Relation 1 is a function

2. Relation 2 is a function

3. Relation 3 is not a function

4. Relation 4 is a function

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

The relations (1) to (4)

Relation (1)

This relation is a function

This is because each range value point to unique domain values

Relation (2)

This relation is a function

This is because each range value point to unique domain values

Relation (3)

This relation is not a function

This is because domain values w have different range values.

Relation (4)

This relation is a function

This is because each range value point to unique domain values

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