a deposit of $500 in an account earns 6% simple interest. how long will it be before the total amount is $575?

Answer:

Step-by-step explanation:

an = 6n - 13

If n  = 10  ,  a10 = 6*10 - 13 = 60-13 = 47

If n  = 11 ,  a11 = 6*11 - 13 = 66-13 = 53

If n  = 12  ,  a12 = 6*12 - 13 = 72-13 =  59

The formula to find the nth term of the sequence an, is a(n) = -13 + 6n

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

a(10) = 47

a(11) = 53

a(12) = 59

a(13) = 65

The nth term of an arithmetic sequence can be represented as

a(n) = a(1) + (n - 1) * d

Where,

common difference,

d = 6

So, we have

a(n) = a(1) + (n - 1) * 6

Using the 12th term, we have

a(1) + (12 - 1) * 6 = 59

a(1)  = 59 - 66

a(1)  = -7

So,, we have

a(n) = -7 + (n - 1) * 6

Expand

a(n) = -13 + 6n

Hence, the formula to find an is a(n) = -13 + 6n

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Answer:

77.78

Step-by-step explanation:

Answer:

77.78

Step-by-step explanation:

i had this ? on rsm student portal.

135 cubes are required to fill the prism

Solution:

Given that a rectangular prism with volume of 5 cubic units is filled with cubes with side lengths of [tex]\frac{1}{3}[/tex] units

Then the number of cubes required to fill the prism will be given by:

[tex]\text { number of cubes }=\frac{\text {volume of rectangular prism}}{\text {volume of cube}}[/tex]

Volume of rectangular prism = 5 cubic units

[tex]\text{ Volume of cube}=(\text { side })^{3}$[/tex]

[tex]\text { Volume of cube }=\left(\frac{1}{3}\right)^{3}=\frac{1}{27}[/tex]

Therefore number of cubes required to fill the prism are:

[tex]\text { number of cubes }=\frac{5}{\frac{1}{27}}=5 \times 27=135[/tex]

Therefore 135 cubes are required to fill the prism

Answer:

135

Step-by-step explanation:

Answer:

The centroid is located at (3,3)

Step-by-step explanation:

Centroid Of A Triangle

The centroid of a triangle is the point where its three medians intersect. It is also the center of gravity of the triangle. The medians are lines that go from each vertex to the midpoint of the opposite side.

Given A(ax,by), B(bx,by), C(cx,cy) the points of the vertices, then the coordinates of the centroid [tex]P(x_c,y_c)[/tex] are

[tex]\displaystyle x_c=\frac{ax+bx+cx}{3}[/tex]

[tex]\displaystyle y_c=\frac{ay+by+cy}{3}[/tex]

The vertices are  (0,1) (2,6) (7,2), thus

[tex]\displaystyle x_c=\frac{0+2+7}{3}=3[/tex]

[tex]\displaystyle y_c=\frac{1+6+2}{3}=3[/tex]

The centroid is located at (3,3)

The coordinates of centroid are (3,3)

Step-by-step explanation:

The coordinates of centroid of a triangle are calculated by finding average of x-coordinates of vertices and the average of y-coordinates of vertices.

Given vertices are:

(0,1) (2,6) (7,2)

So,

x-coordinate of centroid:

[tex]x = \frac{0+2+7}{3}\\=\frac{9}{3}\\= 3[/tex]

y-coordinate of centroid:

[tex]y = \frac{1+6+2}{3}\\=\frac{9}{3}\\= 3[/tex]

Hence,

The coordinates of centroid are (3,3)

Keywords: Triangle, centroid

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Answer:

4

Step-by-step explanation:

first add up the xs that gives you 5x because first 3x+4x gives you 7 then minus that with 2x that gives you five,

now add the numbers -76+96 that gives you 20 now the equation becomes

5x=20

now divide 20 by 5 that gives you 4

25% off means it would be selling for 75% of the original price ( 100% - 25% = 75%).

To find the sale price you would multiply the regular price by 75%:

The equation would be y = 0.75x

Answer:

y=x/2−1/2

Step-by-step explanation:

Answer:

The value of each share decreased by $8.

Step-by-step explanation:

Number of shares of a certain stock Linda owned = 4

Total value of shares went down by = $32

So find the change in value of each share.

Solution:

Let the total value of each share in dollars be = [tex]x[/tex]

Value of 4 shares in dollars will be = [tex]4x[/tex]

The total value of shares went down by $32

So, new value of 4 shares = [tex]4x-32[/tex]

New value of each share = [tex]\frac{New\ value\ of\ total\ shares}{4}[/tex]

⇒ [tex]\frac{4x-32}{4}[/tex]

Splitting the denominators.

⇒ [tex]\frac{4x{{4}-\frac{32}}{4}[/tex]

⇒ [tex]x-8[/tex]

Original value of each share in dollars was = [tex]x[/tex]

New value of each share in dollars = [tex]x-8[/tex]

Thus, we can see that the value of each share decreased by $8.

Answer:

A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.

Step-by-step explanation:

find the number line best shows how to solve −8 − (−6)

In the number line first we start with -8 . negative and negative becomes positive

from -8 move 6 units to the right. So it ends at -2

A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.

225

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Answer: 3x-x+2=4

Step-by-step explanation:

absolute value of 225 = | 225 | = 225    

Answer:

x<=5

Step-by-step explanation:

Two things

Answer:

The area of cardboard required is 40750 cm².

Step-by-step explanation:

Given:

Length (L) = 25 cm

Width (W) = 5 m = 5 × 100 = 500 cm

Height (H) = 15 cm

Area of the cardboard is same as the total surface area of the closed rectangular box.

Total surface area of the rectangular box is given as:

[tex]SA=2(LW+WH+LH)\\\\SA=2(25\times 500+500\times 15+15\times 25)\\\\SA=2(12500+7500+375)\\\\SA=2\times 20375=40750\ cm^2[/tex]

So, the area of cardboard required is 40750 cm².

Answer:

No

Step-by-step explanation:

A function is a relation in which no two ordered pairs have the same first element.

A function associates each element in its domain with one and only one element in its range.

After 16 hours, the charges will be same.

Step-by-step explanation:

Given,

Janet's upfront fee = $20

Charges per hour = $7.50

Let,

x be the number of hours.

J(x) = 7.50x+20

Lisa has no upfront fee.

Charges per hour = $8.75

L(x) = 8.75x

For the charges to be equal;

J(x) = L(x)

[tex]7.50x+20=8.75x\\20=8.75x-7.50x\\20=1.25x\\1.25x=20[/tex]

Dividing both sides by 1.25

[tex]\frac{1.25x}{1.25}=\frac{20}{1.25}\\x=16[/tex]

After 16 hours, the charges will be same.

Keywords: function, division

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Answer:

B

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 8) and (x₂, y₂ ) = (2, - 4) ← 2 points on the line

m = [tex]\frac{-4-8}{2+1}[/tex] = [tex]\frac{-12}{3}[/tex] = - 4 → B

Answer:

The slope of the given line is -4.

So, option (B) is correct.

Step-by-step explanation:

We know that, slope (m) of a line passing through points (x₁, y₁) and (x₂, y₂) is given by,

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Now, the given line passes through the point (-1, 8) and (2,-4).

So, (x₁, y₁) = (-1, 8) and (x₂, y₂) = (2, -4)

So, by using the above formula, we get

Slope(m) of the given line passing through (-1, 8) and (2, -4) is given by,

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{-4-8}{2-(-1)}[/tex]

[tex]\implies\;m = \frac{-12}{3}=-4[/tex]

∴The slope of the given line is -4.

Hence, option (B) is correct.

The cost of [tex]1\frac{3}{4}[/tex] pounds chocolate milk is $6.25 more than the cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel.

Step-by-step explanation:

Given,

Cost of one pound of Caramels = $10.28

Cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel = [tex]10.28*1\frac{3}{4}[/tex]

Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]10.28*\frac{7}{4}=\frac{71.96}{4}= \$17.99[/tex]

Cost of one pound of chocolate milk = $13.85

Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]13.85*1\frac{3}{4}=13.85*\frac{7}{4}[/tex]

Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]\frac{96.95}{4}=\$24.24[/tex]

Difference = 24.24 - 17.99 = $6.25

The cost of [tex]1\frac{3}{4}[/tex] pounds chocolate milk is $6.25 more than the cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel.

Keywords: difference, multiplication

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Final answer:

The cost for 1 3/4 pounds of milk chocolate is $6.25 more than the cost for 1 3/4 pounds of caramels, after calculating the total cost of each based on their per pound price.

Explanation:

To find out how much more the cost for 1 3/4 pounds of milk chocolate is than the cost for 1 3/4 pounds of caramels, we first need to calculate the cost of 1 3/4 pounds of each type of candy. Since the cost per pound of caramels is $10.28 and the cost per pound of milk chocolate is $13.85, we can set up our calculations as follows:

Total cost of caramels = 1.75 (pounds) * $10.28 (per pound) = $17.99

Total cost of milk chocolate = 1.75 (pounds) * $13.85 (per pound) = $24.24

Now, we subtract the total cost of caramels from the total cost of milk chocolate to find the difference:

Cost difference = $24.24 - $17.99 = $6.25

So, the cost for 1 3/4 pounds of milk chocolate is $6.25 more than the cost for 1 3/4 pounds of caramels.

Answer:

No.

Step-by-step explanation: Assuming you mean x^3*x-7, these two equations do not produce the same line.

Answer:

Step-by-step explanation:

[tex]x^3\cdot x^{-7}=x^{3+(-7)}=x^{-4}\\\\\text{used}\ a^n\cdot a^m=a^{n+m}\\\\\text{Other way}\\\\a^{-n}=\dfrac{1}{a^n}\\\\x^3\cdot x^{-7}=x^3\cdot\dfrac{1}{x^7}=\dfrac{x^3}{x^7}=\dfrac{x\!\!\!\!\diagup^1\cdot x\!\!\!\!\diagup^1\cdot x\!\!\!\!\diagup^1}{x\!\!\!\!\diagup_1\cdot x\!\!\!\!\diagup_1 \cdot x\!\!\!\!\diagup_1 \cdot x\cdot x\cdot x\cdot x}=\dfrac{1}{x^4}=x^{-4}[/tex]

Answer:

It would be (3,5)

Step-by-step explanation:

On a coordinate plane it would be changed in which the 2nd number becomes first & the + or - changes. Same for the first number.

Answer:

12

Step-by-step explanation:

2/3 x + x = 20

2/3 x + 3/3x = 20

5/3 x = 20   ... times 3/5 both sides

x = 12

check: 2/3 x 12 + 12 = 8 + 12 = 20

For this case we must simplify the following expression:

[tex](2a ^ 3-5a) - (7a+ 3a ^ 2) =[/tex]

By definition of the law of multiplication signs we have to:

[tex]- * + = -[/tex]

Rewriting the expression we have:

[tex]2a ^ 3-5a-7a-3a ^ 2 =[/tex]

We add similar terms taking into account that:

Equal signs are added and the same sign is placed.

[tex]2a ^ 3-3a ^ 2-12a[/tex]

ANswer:

[tex]2a ^ 3-3a ^ 2-12a[/tex]

Answer:

See explanation

Step-by-step explanation:

1. Lines l and k are parallel. These lines are cut be transversal n. Angles 2 and 7 are corresponding angles when parallel lines l and k are cut by transversal n. By Corresponding Angles Ttheorem, angles 2 and 7 are congruent.

2. Lines m and n are parallel. These lines are cut be transversal k. Angles 2 and 10 are alternate interior angles when parallel lines m and n are cut by transversal k. By Alternate Interior Angles Theorem, angles 2 and 10 are congruent.

3. Angles 2 and 7 are congruent (see 1)

   Angles 2 and 10 are congruent (see 2)

  Hence, angles 7 and 10 are congruent by transitive property.

Answer:

3.3 x - (3.3*8) - x = 1.2

2.3 x - (3.3*8) = 1.2

2.3 x - 26.4 = 1.2

2.3 x - 26.4 + 26.4 = 1.2 + 26.4

2.3 x = 27.6

2.3 x / 2.3 = 27.6 / 2.3

x = 12

The y-intercept of [tex]\(12x + y^3 = 2\) is at \((0, \sqrt[3]{2})\).[/tex]

To find the y-intercept of the equation [tex]\(12x + y^3 = 2\)[/tex], we first need to understand what the y-intercept represents. The y-intercept is the point where the graph intersects the y-axis, which means the x-coordinate of this point is 0.

To find the y-intercept, we set [tex]\(x = 0\)[/tex] in the equation and solve for y:

[tex]\[12(0) + y^3 = 2\][/tex]

[tex]\[y^3 = 2\][/tex]

To solve for y, we take the cube root of both sides:

[tex]\[y = \sqrt[3]{2}\][/tex]

So, the y-intercept of the equation is [tex]\((0, \sqrt[3]{2})\).[/tex]

Answer:

16 serving.

Step-by-step explanation:

Given: 3/4 cup servings.

Now, computing the number of serving in 12 cups of cherries.

Using unitary method to solve.

∴ Number of serving= [tex]total\ cups \times number\ of\ serving\ per\ cup[/tex]

Number of serving in one cup is [tex]\frac{4}{3}[/tex]

Number of serving in 12 cups = [tex]12\times \frac{4}{3} = 16 \ serving[/tex]

Number of serving in 12 cups= [tex]16\ serving[/tex]

∴ There are 16 serving is possible in 12 cups of cherries.

Final answer:

To calculate the number of 3/4 cup servings in 12 cups of cherries, divide 12 by 3/4, which equals 16 servings.

Explanation:

To determine how many 3/4 cup servings are in 12 cups of cherries, we can divide the total number of cups by the size of one serving.

First, we express the serving size and the total amount in the same units: 3/4 cup and 12 cups.

Next, we divide the total amount of cherries by the serving size: 12 cups ÷ 3/4 cup.

To perform the division, we can multiply 12 by the reciprocal of 3/4, which is 4/3 (12 × 4/3 = 16).

The result is that there are 16 servings of 3/4 cup in 12 cups of cherries.

Answer:

16.00

Step-by-step explanation:

When you divide twenty percent(0.20) to 20.00 you will get sixteen or 4.00 dollars off

Answer:

answer is y-5=-3(x-3)

Step-by-step explanation:

your y-coordinate is 5 s you would write y-5 and your slope is -3 with your x-coordinate as 3 so that would be written as -3(x-3).  The equation put together correctly would be y-5=-3(x-3)

Answer:

y-5=-3(x-3)

Step-by-step explanation:

y-y1=m(x-x1)

y-5=-3(x-3)

Answer:

x>5

Step-by-step explanation:

-3(2x+5)<-45

2x+5<-45/-3

2x+5<15

2x<15-5

2x<10

x<10/2

x<5

x>5

Answer:

[tex]x>22.5[/tex]

Step-by-step explanation:

Given linear inequality:

[tex]2x+5>50[/tex]

Solving for [tex]x[/tex]

Subtracting both sides by 5.

[tex]2x+5-5>50-5[/tex]

[tex]2x>45[/tex]

Dividing both sides by 2.

[tex]\frac{2x}{2}>\frac{45}{2}[/tex]

∴ [tex]x>22.5[/tex]

The graph of the inequality is shown below.

The line is represented by dotted line because the inequality sign is only greater than which means 22.5 is not included in the solution.  

7/19

bc 2 5/7 = 19/7. the reciprocal is a fraction reversed. or upside down that is. So, your answer is 7/19

Answer:

7/19

Step-by-step explanation:

2 5/7=19/7