How much interest does a $482 investment earn at 5% over 3 years?

Answer:

D

Step-by-step explanation:

Using the midpoint formula

midpoint of 2 points (x₁, y₁ ) and (x₂, y₂ ) is

[ [tex]\frac{1}{2}[/tex](x₁ + x₂), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]

let (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (5, 5), then midpoint is

[ [tex]\frac{1}{2}[/tex](- 1 + 5), [tex]\frac{1}{2}[/tex](5 + 5) ]

= (2, 5) → D

The midpoint of the segment is (2,5).

To find the midpoint of a line segment with endpoints [tex]\((-1, 5)\) and \((5, 5)\)[/tex], we can use the midpoint formula:

[tex]\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]

Given the endpoints:

[tex]\( x_1 = -1 \), \( y_1 = 5 \)[/tex] (coordinates of the first point)

[tex]\( x_2 = 5 \), \( y_2 = 5 \)[/tex] (coordinates of the second point)

Now, let's plug these values into the midpoint formula:

[tex]\[ \text{Midpoint} = \left( \frac{-1 + 5}{2}, \frac{5 + 5}{2} \right) \][/tex]

[tex]\[ = \left( \frac{4}{2}, \frac{10}{2} \right) \][/tex]

[tex]\[ = \left( 2, 5 \right) \][/tex]

Therefore, the midpoint of the segment is (2, 5)

Among the given options, the correct one is option D: (2, 5).

Answer:

Domain = {3,4,9}

Range = {2, 6, 8, 9.5}

Given relation is NOT a function.

Step-by-step explanation:

Given relation is relation is ((9,6), (3,8),(4,9.5), (9,2)}.

Now we need to determine if given relation is a function or not.

We also need to find the domain and range.

((9,6), (3,8),(4,9.5), (9,2)}

​Domain is basically the collection of x-values

So Domain = {3,4,9}

Range is basically the collection of y-values

So Range = {2, 6, 8, 9.5}

Since given relation contains repeated x-value "9".

So the given relation is NOT a function.

Answer:

5

Step-by-step explanation:

(3 1/3)/(2/3) = (10/3)/(2/3) = 10/2 = 5

In the above, both the numerator fraction and the denominator fraction have the same denominator (3), so the result is the ratio of their numerators.

____

The other way to divide fractions is to "invert and multiply". For this, the denominator gets inverted (from 2/3 to 3/2) and that is then used to multiply the numerator.

(3 1/3)/(2/3) = (10/3) · (3/2) = (10·3)/(2·3) = 10/2 = 5

You will note that the denominators of 3 cancel, resulting in 10/2 as above.

Answer:

5

Step-by-step explanation:

Expression: 3 ¹/₃ ÷ ²/₃

Mixed to improper: ¹⁰/₃ ÷ ²/₃

Divide by fraction = multiply by its reciprocal:

Change: ¹⁰/₃ × ³/₂

Simplify: ¹⁰/₁ × ¹/₂

Simplify: ⁵/₁ × ¹/₁

Multiply: 5

Answer:

A. [tex]h=\dfrac{2A}{b}[/tex]

Step-by-step explanation:

You are given formula

[tex]A=\dfrac{1}{2}bh[/tex]

Multiply this equation by 2 to get rid of fraction:

[tex]2A=bh[/tex]

Divide this equation by b to find h in terms of A and b:

[tex]h=\dfrac{2A}{b}[/tex]

Answer:

a) Domain: -∞ < x < ∞

b) Cost required to manufacture 3500 items is $15,900.

c) Number of items she can manufacture is 5208 if cost is kept at $20,000

Step-by-step explanation:

a) What is the reasonable domain of the function?

The function is C(x) = 7,500 + 2.4x

The domain of the function is the set of values for which the function is defined and valid.

In the given function there is no constraint or undefined points so domain is:

-∞ < x < ∞

b) What is the cost of 3,500 items?

We are given x = 3500 and we need to find the cost.

Putting values in the function given:

C(x) = 7,500 + 2.4x

C(x) = 7,500 + 2.4 (3500)

C(x) = 7500 + 8400

C(x) = 15,900

Cost required to manufacture 3500 items is $15,900.

c) If costs must be kept below $20,000 this month, what is the greatest number of items she can manufacture?

We are given cost, and we need to find x

C(x) = 7,500 + 2.4x

20,000 = 7500 +2.4x

20,000 - 7500 = 2.4x

12500 = 2.4 x

=> x = 12500/2.4

x= 5208.3 ≅ 5208

So, Number of items she can manufacture is 5208 if cost is kept at $20,000

Answer:

Other division expression that have the same value as 61.12 divided by 3.2 are

122.24 divided by 6.4 AND

183.36 divided by 9.6

Step-by-step explanation:

61.12/3.2 = 19.1

Other division expression that have the same value as this:

122.24/6.4 = 19.1

183.36/9.6 = 19.1

Answer:

a ≈ 14 or 6

Step-by-step explanation:

264 = π × a × (20 - a)

a(20 - a) = [tex]\frac{264}{Pi}[/tex] ≈ 84 (rounded off to nearest whole number)

Opening the brackets we get;

a² - 20a + 84 = 0

Applying the quadratic formula we get:

a ≈ 14 or 6

Answer:

It's option 2.

Step-by-step explanation:

- 1/2x > 6

Divide both sides by -1/2:

x < -12   (Note the inequality sign flips when we divide by a negative value).

Answer: {x |x ∈ R, x < -12}

Step-by-step explanation:

Given the following inequality:

[tex]-\frac{1}{2}x>6[/tex]

You can find the solution set by solving for the variable "x".

Then, to solve for the variable "x" you need to multiply both sides of the inequality:

[tex](-\frac{1}{2}x)(2)>(6)(2)[/tex]

[tex]-x>12[/tex]

And finally, you must multiply both sides of the inequality by (-1). Notice that the direction of the symbol of the inequality will change:

[tex](-x)(-1)>(12)(-1)[/tex]

[tex]x<-12[/tex]

Therefore, the solution set is: {x |x ∈ R, x < -12}

Answer:

203 minutes

Step-by-step explanation:

This can be expressed as an arithmetic sequence, that is

20, 23, 26, 29,...

With first term a = 20 and common difference d = 3

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a + (n - 1)d ], hence

[tex]S_{7}[/tex] = [tex]\frac{7}{2}[/tex] [ (2 × 20) + (6 × 3) ]

                        = 3.5 ( 40 + 18) = 3.5 × 58 = 203

It might have come from

9/n  =  10/m

Answer: Hi, in the equation 9*m = 10*n the proportion is 9 to 10, which means that 9 times the number m is equal to 10 times the number n.

So n is proportional to m in the way that n= (9/10)*m

and m is proportional to n in the way that m= (10/9)*n

This means that the proportion can be written as 9 to 10, or 9:10.

Answer: 4

Step-by-step explanation:

The degree is the highest exponent , in which in this problem it is 4. The 3x counts as an exponent of 1 because the variable x is 1, and the 2 counts as an exponent of zero. Which means the degree is 4.

Answer:

-3

Step-by-step explanation:

We have

y = F(x) = x + 3

so

x = y  - 3

so

F⁻¹(y) = y - 3

which we can write

F⁻¹(x) = x - 3

We solve

0 = F⁻¹(x) = x - 3

x = 3

Answer: 3

Answer:

The fourth

Step-by-step explanation:

It has 4 terms

ANSWER

4)x^3+ 5x^2- 9x- 45=0

EXPLANATION

Factoring by grouping is used to factor expressions that have four terms.

Among the given options, the fourth option is

[tex]x^3+ 5x^2- 9x- 45=0[/tex]

There are already four terms in this expression.

So we group the first two and the last two and factor.

We can see that x² is common to the first two terms and -5 is common to the last 2 terms.

The fourth choice is correct.

The numbers added together resulted in 8419.

In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as an addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.

To find the addition of all 177 numbers.

First, we arrange in ascending terms, we get,

16, 17, 18, 19, 22, 23, 24, 24, 25, 25, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 28, 29, 29, 29, 30, 30, 30, 31, 31, 31, 32, 34, 35, 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 36, 36, 37, 37, 37, 38, 38, 38, 38, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39, 40, 40, 41, 41, 41, 41, 41, 42, 42, 42, 42, 42, 42, 42, 42, 43, 43, 43, 43, 43, 44, 45, 45, 45, 46, 46, 46, 47, 47, 47, 48, 48, 48, 48, 48, 48, 49, 49, 49, 49, 50, 50, 51, 51, 51, 51, 52, 53, 53, 53, 53, 53, 53, 53, 53, 53, 54, 54, 54, 55, 55, 57, 60, 61, 61, 61, 61, 62, 62, 62, 62, 62, 63, 64, 64, 65, 65, 65, 67, 67, 68, 68, 68, 70, 70, 71, 72, 72, 73, 74, 75, 75, 75, 76, 78, 80, 82, 84, 85, 86, 89, 91, 93, 102, 104, 124.

Therefore, the sum is 8419.

To learn more about the addition;

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The question 'what is 48 35 26 31 27 52 55 63... added all together?' is asking for the sum of all the provided numbers. This can be calculated with a calculator or by manual addition. Be aware it may take time due to the large number of values.

To answer the question, 'what is 48 35 26 31 27 52 55 63 18 74 35 61 28 42 76 35 38 64 71 26 53 65 47 41 102 38 35 84 41 26 73 62 35 39 62 49 104 62 54 19 28 64 36 39 53 89 26 53 43 75 35 39 29 26 45 39 31 30 70 42 37 54 85 42 36 91 25 28 53 65 78 42 68 44 41 50 46 48 75 29 53 72 17 28 38 30 48 43 27 46 36 48 62 31 42 48 61 22 124 27 53 86 60 47 41 37 27 36 45 80 45 70 53 25 29 16 30 36 38 42 48 51 38 39 43 61 75 38 42 55 72 39 28 51 43 49 67 25 37 39 46 41 50 93 53 82 47 36 38 51 42 40 24 68 38 36 34 49 65 68 62 53 67 23 51 40 43 49 57 61 26 54 35 32 38 39 24 added all together?', you would have to add up all the numbers provided. Calculating this would involve simply adding the given values together. To get the answer, you can use a calculator or manually add each number, but it may take a bit of time due to the large number of values given.

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Check the picture below.

so then, the perimeter of that hexagon will  just be the sum of all its 6 sides, or namely 3⅖ + 3⅖ + 3⅖ + 3⅖ + 3⅖ + 3⅖, or just 6( 3⅖ ).

[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=3\\ p=6\left(3\frac{2}{5} \right) \end{cases}\implies A=\cfrac{1}{2}(3)\left[ 6\left(3\frac{2}{5} \right) \right]\implies A=\cfrac{1}{2}(3)\left[ 6\left(\cfrac{17}{5} \right) \right] \\\\\\ A=\cfrac{1}{2}(3)\left(\cfrac{102}{5} \right)\implies A=\cfrac{1}{2}\left( \cfrac{306}{5} \right)\implies A=\cfrac{153}{5}\implies A=30\frac{3}{5}[/tex]

Answer:

[tex]f(-1) = 1[/tex]

Step-by-step explanation:

Given

f(x) = [tex]-x^{3}-x^{2} +1[/tex]

Finding f(-1) means, we have to put -1 in the places of x in the function,

So, putting x=-1 in the function

[tex]f(-1) = (-1)^{3} - (1)^{2} +1[/tex]

As the power 3 is odd, the minus will remain the same, while in the 2nd term minus will be eliminated due to even power. So,

=> [tex]-1-1+1[/tex]

=> 1

Hence,

[tex]f(-1) = 1[/tex]

Answer:

[tex]\large\boxed{\bold{one\ solution}\ (1,\ -4)\to x=1,\ y=-4}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=2x-6\\y=-x-3\end{array}\right\\\\\text{These are linear functions. We only need two points to draw a graph.}\\\\\text{Choice two values of x, substitute to the equation,}\\\text{and calculate the values of y.}\\\\y=2x-6\\for\ x=0\to y=2(0)-6=0-6=-6\to(0,\ -6)\\for\ x=3\to y=2(3)-6=6-6=0\to(3,\ 0)\\\\y=-x-3\\for\ x=0\to y=-0-3=0-3=-3\to(0,\ -3)\\for\ x=-3\to y=-(-3)-3=3-3=0\to(-3,\ 0)\\\\\text{Look at the picture}[/tex]

[tex]\text{The intersection of the line is the solution of the system of equations:}\\\\(1,\ -4)\to x=1,\ y=-4[/tex]

Answer:

Step-by-step explanation:

z score= x - mean/standard deviation

1.20= x -100/15

18= x -100

118=x

z score= x - mean/standard deviation

0.5=x-73/4

2=x-73

75= x

see if u understand, note that the degree is 90

The height of the kite is 9 feet.

Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.

Let h represent the height of the kite. Hence, using trigonometric ratios:

sin(30) = h / 18

h = 9 feet

Therefore the height of the kite is 9 feet.

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Answer:

3 left

Step-by-step explanation:

If she starts out with 73 and drops 5 she is left with 68, an you cannot evenly divide 68 and 13 so you divide it as much as you can evenly which is five containers leaving 3 extra cupcakes.

For this case we have that initially there are 73 cupcakes, if Leda dropped 5 then we are left with:

[tex]73-5 = 68[/tex]

Now, you must equally divide the 68 cupcakes into 13 containers:

putting 5 cupcakes in each of the 13 containers we have;

[tex]13 * 5 = 65[/tex]

[tex]68-65=3[/tex]

So, we have 3 cupcakes left.

Answer:

3 cupcakes

I think it is bottom right because it goes through the most points.

Answer:

21 + 4(3^2 - 5 = 37

Step-by-step explanation:

The answer is D.

If you multiply them all together the answer (without simplifying), it should equal 210/9, you then simplify the numerator and denominator by 3 and you get 70/3.

Answer:

D

Step-by-step explanation:

Given

[tex]\frac{5}{3}[/tex] × [tex]\frac{2}{3}[/tex] × [tex]\frac{21}{1}[/tex]

Multiply numerators/ denominators

= [tex]\frac{5(2)(21)}{3(3)(1)}[/tex]

= [tex]\frac{210}{9}[/tex]

Cancel the numerator/denominator by dividing both by 3

= [tex]\frac{70}{3}[/tex] → D

q=5 the first one is 2 so T1=2

and for the end we use the formula:

[tex]an = 2 \times {5}^{(n - 1)} [/tex]

Answer:

circle area = PI * radius^2

circle area = 11^2 * PI

circle area = 121 * PI

That would be the area for the ENTIRE area but the circle but we are only dealing with 135 degrees of a circle so the area equals

121 * (135 / 360) * PI

= 45.375 PI

Answer is C

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation:

Subtract the total computers from the old computers.

40-15=25

Then put the number of new computers over the total computers

25/40

Then, simplify

5/8

Answer:

The height of the tree is [tex]64.94\ ft[/tex]

Step-by-step explanation:

Let

y ----> the height of the tree

we know that

[tex]tan(33\°)=y/100[/tex] ----> the function tangent is equal to divide the opposite side angle of 33 degrees by the adjacent side angle of 33 degrees

Solve for y

[tex]y=(100)tan(33\°)=64.94\ ft[/tex]

The height of the tree can be calculated using the formula 'Height of tree = tan(33 degrees) * distance from the tree'. Substituting the given values, the tree should be approximately 65.45 feet tall.

John can measure the height of the tree using trigonometric principles. In this case, the problem involves a right triangle, where the height of the tree forms one side (opposite to the angle of elevation), the distance John is from the tree forms the base (adjacent to the angle of elevation), and the line of sight to the top of the tree forms the hypotenuse. The tangent of the angle of elevation (33 degrees in this case) is equal to the height of the tree divided by the distance from the tree.

Therefore, to calculate the height of the tree, we need to find the tangent of the given angle and multiply it by the distance from the tree:
Height of tree = tan(33 degrees) * distance from tree

= tan(33) * 100 feet
Approximately, the tree should be around 65.45 feet tall.

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Answer:

TELL HIM TO STOP BEING SO CHEAP!!!!!!!!! <3

and i oop-

Step-by-step explanation:

[tex]\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} {-2}~~\ast&{4}~~\ast\\ 0&2\\ 1&1\\ {3}~~\ast&{-1}~~\ast\\ \cline{1-2} \end{array}~\hspace{10em} (\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-4}{3-(-2)}\implies \cfrac{-5}{3+2}\implies \cfrac{-5}{5}\implies -1[/tex]

The slope of this line is -1.

The slope formula is useful:

m = (y2 -y1)/(x2 -x1)

where:

m is the slope of the line

y1 and y2 are the y-coordinates of two points on the line

x1 and x2 are the x-coordinates of the two points on the line

 m = (2 -4)/(0 -(-2)) = -2/2 = -1

The slope of this line is -1.

The points on the line drop 1 unit for each 1 unit to the right.

 m = rise/run = -1/1 = -1

Answer:

The value 1.8 represent the club's total number of members today or the present number of members

Step-by-step explanation:

Given an exponential function;

[tex]y=ab^{x}[/tex]

b is the base or the growth factor

a is the initial value, that is the value of y when x = 0

We have been given the exponential function;

[tex]y=1.8(1.02)^{12t}[/tex]

The value 1.8 simply represents the initial value of y. Plug in t = 0 in the equation;

[tex]y=1.8(1.02)^{12(0)}=1.8[/tex]

Therefore, the value 1.8 represent the club's total number of members today or the present number of members.