Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.

Assume that you take out a $3000 loan for 30 months at 8.5% APR. What is the monthly payment? (Round your answer to the nearest cent.)

Answer:

(1/32π)in/seconds or 0.0099471839 inches per seconds.

Step-by-step explanation:

From the question, we have the following information

Rate = 2 cubic inches per second. Radius(r) = 4 inches

Time = 4 seconds

(a) How fast is the radius of the balloon growing at t=4 seconds = dr/dt

Volume of a Sphere = 4/3πr³

We solve using Differentiation

Rate = V(t) = 4/3πr(t)³

dv/dt = 2 cubic inches per second.

Radius at time(t) = 4 inches

Rate = V(t) = 4/3πr(t)³

dv/dt = 4πr(t)²× dr/dt

dv/dt = 4π(4)² × dr/dt

2 = 4π × 16 × dr/dt|t = 2

Making dr/dt the subject of the formula

dr/dt = 2/64π

dr/dt at t = 4 seconds = (1/32π)inches/seconds

= 0.0099471839 inches per seconds.

The radius of the balloon growing at t=4 seconds is growing at a rate or speed of (1/32π) inches/seconds

= 0.0099471839 inches per seconds.

In a case whereby a boat travels with velocity vector (25, 25√3) the directional bearing of the boat is ON 30° E.

The given velocity vector are; 25 and  25√3)

horizontal  components =25

vertical components =25√3

Then the angle

Tan(θ) = {vertical component / horizontal component }

= 25√3 / 25

= √3 / 1

= √3

Tangent √3= 60 degrees, Then the directional bearing of angle 60 degrees is 30° E

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Answer:

1629.24m

Step-by-step explanation:

starting with the easy ones

1) Rectangle 1:

Surface area of rectangle=Length x width

SAR= 24x21

= 504m

2) Rectangle 2:

SAR= 19x21

=399

3) Rectangle 3

SAR= 21x8

=168

4) Rectangle 4:

SAR= 21x11

=231

*because the top and bottom are trapeziums the formular for it is

A=1/2(a+b)h

although those trapeziums don't have h(Height)

it needs to be broken down into two triangles and a rectangle. to find the height*

5) side/height of triangle A:

formula: C squared= a squared + b squared

in this case we already have C and A. meaning we have to rearrange the formula to:

x = c^2 - a^2

x = 8^2 - 2.5^2

x = sqrt 57.75

x = 7.61

6) Trapezium

SA= 1/2(a+b)h

SA= 1/2(19+24)7.61

=163.62

7) add all surface area together

which should equal 1629.24m

Camila can have 300 different combinations to choose from.

A permutation is an arrangement of things where order matters, AB and BA are two different permutations.

The combination is a selection of things where order does not matter, AB and BA are the same combinations.

The statement, This afternoon, she can ice skate, make a snowman, or ski has \(^3C_1\) different things to choose from.

Similarly, all the options have \(^3C_1\times^4C_1\times^5C_1\times^5C_1\) different combinations.

= 3×4×5×5 different combinations.

= 300 different combinations.

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The expression JK||GI implies line JK and GI are parallel lines

The ratio of HK : KI is 3 : 1

A ratio is used to show the relationship between two related quantities

The given parameter is:

HJ : JG = 3 : 1

Given that JK||GI , then it means that:

HJ : JG = HK : KI

This gives

HK : KI = 3 : 1

Hence, the ratio of HK : KI is 3 : 1

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Answer:

B. 107

Step-by-step explanation:

Demand for soccer balls at a new sporting goods store is forecasted using the following regression equation: Y = 98 + 2.2X where X is the number of months that the store has been in existence. Let April be represented by X = 4. April is assumed to have a seasonality index of 1.15. What is the forecast for soccer ball demand for the month of April (rounded to the nearest integer)?

y = 98 + 2.2x when x = 4

y = 98 + 2.2(4)

y = 98 + 8.8

y = 106.8

A. 123

B. 107

C. 100

D. 115

There are 13 nickels and 5 pennies.

Given that,
A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢,
To determine the number of pennies and nickels.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
A single value of a nickel coin is 0.05
A single value of a pennies coin is 0.01
A pile of 18 coins consists of pennies and nickels.
x + y = 18  - - - - -(1)
where
x = number of nickels and y = number of pennies
The total amount of the coins is 38¢
0.05x + 0.01y = 0.38   - - - - -(2)

solving equations 1 and 2
0.05 (18 - y) + 0.01y = 0.38
0.90 - 0.05y + 0.01 = 0.38
-0.04y = - 0.52
y = 13
Now put 13 in equation 1,
x + 13 = 18
x = 5

Thus, there are 13 nickels and 5 pennies.

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Answer:

the sales tax percentage is 6%

Step-by-step explanation:

To solve this you want to first find what percent $95.40 is of $90. Then we can subtract 100% to find the extra percent (the sales tax).

95.40 is what percent of 90?

95.40 = X · 90

Divide by 90 on both sides.

1.06 = X

So now we know that 95.40 is 106% of 90. We subtract 100% from 106% to get 6%. Therefore the sales tax percentage is 6%.

Answer:

($775.20 - $408.00)/$775.20 =

$367.20/$775.20 = 47.4%

Answer: 7xy + 2x^2t

Step-by-step explanation:

Answer:

\(m=\frac{9}{10}\)

Step-by-step explanation:

To find the slope between any two points, we can use the following slope formula:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Let (-7, -1) be (x₁, y₁) and let (3, 8) be (x₂, y₂). Substitute them into the slope formula:

\(m=\frac{8-(-1)}{3-(-7)}\)

Evaluate:

\(m=\frac{9}{10}\)

Therefore, the slope between the two points is 9/10.

The expression that is equal to the given Polynomial expression is (x^3-4)(2x+5).

The polynomial expression given is 2x^4+5x^3-8x-20. We have to identify the expression that is equal to this given polynomial expression.

We will factor the given polynomial expression to determine the equivalent expression. We can use factorization by grouping to factor the expression completely and determine the equivalent expression .

Factorization by grouping:

We can group the first two terms 2x^4 and 5x^3 together and factor out x^3 from them. We can also group the last two terms -8x and -20 together and factor out -4 from them.

This gives us;2x^4+5x^3-8x-20= x^3(2x+5)-4(2x+5) =(x^3-4)(2x+5)

Therefore, the expression that is equal to the given polynomial expression is (x^3-4)(2x+5).

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Answer:

6

Step-by-step explanation:

hope this helps

Answer:

I think you were right, that it was A.

3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Answer:

BE= 19

Step-by-step explanation:

   4x+3   = 12x-10

2(4x+3)   = 12x-10

  8x+6   = 12x-10

8x-8x+6 = 12x-8x-10

          6 = 4x-10

    10+6 = 4x-10+10

        16 = 4x

     16/4 = 4x/4

         4  = x

BE 8(4)+6   = 38         38/2 = 19

AC 12(4)-10 = 38

The diagonals of a rectangle are equal.

Answer:

2.57 - 1.75 = 0.82

Step-by-step explanation:

Let us assume that we need to find the value of 2.57 - 1.75 i.e. we need to subtract 1.75 from 2.57. It can be done as follows :

The first number is 2.57 and other no is 1.75.

In 2.57, 2 is in ones place, 5 is in tenths place and 7 is in hundredths place.

In 1.75, 1 is in ones place, 7 is in tenths place and 5 is in hundredths place.

Subraction :

  2.57

-  1.75

= 0.82

Hence, the value of 2.57 - 1.75 is 0.82

Answer:

Length = 8 ft.

Step-by-step explanation:

The perimeter of a rectangle can be represented by the formula P = 2w + 2l, where w is the width and l is the length.

Given what we're told, we can represent the length for this problem using the equation l = w + 3

Thus, to find the length, we plug in everything we know:

26 = 2(w +3) + 2w

26 = 2w + 6 + 2w

26 = 4w + 6

20 = 4w

5 = w

l = 5 + 3 = 8

Answer:

a

Step-by-step explanation:

when you divide it the last decimal nubers keep on repeating its self so you put a line above the decimals

Answer:

It is a rational number and a repeating decimal

Step-by-step explanation:

A,F,B

Hence, \(n^2 + 1\geq 2^n\) when \(n\) is a positive integer with \(1 \leq n \leq 4\).

Use principle of mathematical induction, put \(n=1,2,3,4\) in the given inequality

For \(n=1\)

\(1^2+1\geq2^1\)

\(2\geq2\), which is true.

So, \(n^2+1\geq2^n\) is true for \(n=1\)

For \(n=2\)

\(2^2+1\geq2^2\)

\(5\geq4\), which is true.

So, \(n^2+1\geq2^n\) is true for \(n=2\)

For \(n=3\)

\(3^2+1\geq2^3\)

\(10\geq8\), which is true.

So, \(n^2+1\geq2^n\) is true for \(n=3\)

For \(n=4\)

\(4^2+1\geq2^4\)

\(17\geq16\), which is true.

So, \(n^2+1\geq2^n\) is true for \(n=4\)

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Let's assume the number of cookies Lily bought is represented by "C," and the number of brownies is represented by "B."

According to the problem, the cost of one cookie is $2, and the cost of one brownie is $3. Lily spent a total of $144.

We can set up two equations based on the given information:

C + B = 60 (equation 1, representing the total number of sweets)

2C + 3B = 144 (equation 2, representing the total cost in dollars)

To solve this system of equations, we can use substitution or elimination method. Here, we'll use the substitution method.

From equation 1, we can rewrite it as C = 60 - B.

Now substitute this value of C in equation 2:

2(60 - B) + 3B = 144

Simplify the equation:

120 - 2B + 3B = 144

Combine like terms:

120 + B = 144

Subtract 120 from both sides:

B = 144 - 120

B = 24

Now substitute the value of B back into equation 1 to find C:

C + 24 = 60

C = 60 - 24

C = 36

Therefore, Lily bought 36 cookies and 24 brownies.

Answer:

32 red cars.

Step-by-step explanation:

Let the red cars be denoted by R

Let the green cars be denoted by G

Translating the word expression into an algebraic equation;

\( R + G = 36\) ...........equation 1

\( R = 8G\) ...........equation 2

Substituting equation 2 into equation 1;

\( 8G + G = 36\)

\( 9G = 36\)

\( G = \frac{36}{9}\)

G = 4

The number of green cars are 4.

From, \( R = 8G\)

\( R = 8*4\)

R = 32

Therefore, the number of red cars that Susan counted are 32.

The angle of elevation of the sun when a 10-foot tree creates a shadow that is 15 feet long  is 33.69 degrees

To find the angle of elevation of the sun, we can use trigonometry and the concept of similar triangles.

Given that:

The tree's height is 10 feet.

The length of the shadow is 15 feet.

Let's assume that the tree's height is "h"  feet.

Length of its shadow is represented by "s" feet

The angle of elevation of the sun is the angle between the ground and the line from the top of the tree to the tip of its shadow.

The angle can be determined using the tangent function.

\(tan\theta\) = \(\dfrac{h}{s}\)

Now, substitute the given values:

\(tan\theta\)= \(\dfrac{10}{15}\)

\(tan\theta\) = \(\dfrac{2}{3}\)

The angle of elevation can be obtained by  taking the inverse tangent of 2/3

angle of elevation =\(\tan^-1\dfrac{2}{3}\)

angle of elevation ≈ 33.66 degrees

So, the angle of elevation of the sun is approximately 33.69 degrees.

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Answer:

E

Step-by-step explanation:

using the Sine rule in Δ ABC

\(\frac{a}{sinA}\) = \(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)

where a is the side opposite ∠ A , b opposite ∠ B , c opposite ∠ C

we require to calculate ∠ C

∠ C = 180° - (64 + 85)° = 180° - 149° = 31°

then to find a , using

\(\frac{a}{sinA}\) = \(\frac{c}{sinC}\)

\(\frac{a}{sin64}\) = \(\frac{9.3}{sin31}\) ( cross- multiply )

a × sin31° = 9.3 × sin64° ( divide both sides by sin31° )

a = \(\frac{9.3sin64}{sin31}\) ≈ 16.23 ( to 2 decimal places )

then to find b , using

\(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)

\(\frac{b}{sin85}\) = \(\frac{9.3}{sin31}\) ( cross- multiply )

b × sin31° = 9.3 × sin85° ( divide both sides by sin31° )

b = \(\frac{9.3sin85}{sin31}\) ≈ 17.99 ( to 2 decimal places )

Answer:

thousands

Step-by-step explanation:

Answer:

The answer would be the Thousands place.

Step-by-step explanation:

The order goes like this.

ones

tens

hundreds

thousands

ten-thousands

one hundred-thousands

millions

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