Find the compound amount and the interest earned when the given investment has continuous compounding.

$11,000 at 2.3% for 8 years

The required x = $2,831.49. Option B) is correct.

7-year loan of $20,000 to Breck Inc. To repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from Year 4 through Year 7.

When some apply there money on something so that he can get higher value in returns of his money.

for the final 4 years

20000=2500/1.08+5000/(1.08^2)+7500/(1.08^3)+x/(1.08^4)+x/(1.08^5)+x/(1.08^6)+x/(1.08^7)

x = $2,831.49

Thus the required value of x = $2,831.49.

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Answer:

Step-by-step explanation:

The velocity equation is:

[tex]v(x) = 108 - 24x[/tex]

Such that:

[tex]v(0) = 108 ft/s\\v(2) = 60ft/s\\[/tex]

And the velocity is zero for x = 4.5

We know that the position equation is:

[tex]f(x) = 108*x - 12*x^2[/tex]

To get the velocity, we need to differentiate with respect to x, so we get:

[tex]v(x) = \frac{df(x)}{dx} = 108 - 2*12*x = 108 - 24*x[/tex]

Now we want to get the velocity for x = 0 and x = 2, we will get:

[tex]v(0) = 108 - 24*0 = 108\\\\v(2) = 108 - 24*2 = 60[/tex]

Then, when x = 0, the velocity is 108 ft/s, when x = 2 the velocity is 60 ft/2.

Finally, we need to solve:

[tex]v(x) = 108 - 24*x = 0\\\\x = 108/24 = 4.5[/tex]

The velocity is zero when x = 4.5

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The algebraic expression for the given word problem is 12/y + 7

From the question, we are to write the algebraic expression for the given word problem

The given word problem is

"the quotient of 12 and a number y increased by 7"

First,

"the quotient of 12 and a number y" can be expressed as

12/y

Then,

"the quotient of 12 and a number y increased by 7" becomes

12/y + 7

Hence, the algebraic expression for the given word problem is 12/y + 7

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The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. The correct option is B.

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,

[tex]c =\sqrt{a^2 + b^2 -2ab\cdot Cos\theta}[/tex]

where

c is the third side of the triangle

a and b are the other two sides of the triangle,

and θ is the angle opposite to the third side, therefore, opposite to side c.

The length of the sidelink b using the cosine rule can be written as,

[tex]b = \sqrt{a^2+c^2-2ac\cos(\angle B)}\\\\b = \sqrt{4^2+5^2 - 2(4)(5)(\cos 60^o)}\\\\b = \sqrt{16+25-20}[/tex]

Hence, the correct option is B.

The complete question is:

Consider ABC with the measure of angle B equal to 60 degrees, and side lengths a=4 and c=5. Which option lists an expression that is equivalent to the length of side b?

Options are given in the image below.

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Answer:

let x be thomas age

3x for huilans age since huilans age is 3 time thomas age

both of their ages add to 76

ie. x + 3x =76

solve for x

4x = 76

x = 76 ÷ 4

x = 19. thomas age

to get huilans age : take 19 × 3 = 57

Answer:

Your $19,513 loan has 60 monthly payments of $366.00 at 4.75%.

If you make all of your payments on this loan, and do not prepay any of the principal, the total interest for this loan is $2,447.26.

Step-by-step explanation:Loan Summary

Total payments $21,960.26

Total interest paid $2,447.26

Loan amount $19,513

Monthly payment $366.00

Interest rate 4.75%

Term 60 monthly payments

Step-by-step explanation:

Answer:

The answer would be A. 3/4

Step-by-step explanation:

To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

The ratios for the surface area, volume and width respectively are:

Ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In this exercise, we are given the scale factor for this canoe is 3:14. Thus, the ratio of the surface area of the canoe model to the surface area of the original model would squared as follows:

Ratio of SA = 3²/14²

Ratio of SA = 9/196

Ratio of SA = 9:196.

For the volume, we would take the cube:

Ratio of V = 3³/14³

Ratio of V = 27/2,744

Ratio of V = 27:2,744.

For the width, we have:

Ratio of W = 3/14

Ratio of W = 3:14.

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The time required to clean 200 square feet will be 80 minutes. Option B is correct.

The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.

Let x be the cleaning time for the 200 square feet area;

From the table, it is observed that for a 1 sq. foot area the time needed to clean will be 0.4 minutes.

1 square feet = 0.4 minute

200 square feet = 200 × 0.4

200 square feet  = 80 minute

The time required to clean 200 square feet will be 80 minutes.

Hence, option B is correct.

The table is attached in the attachment.

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In the triangle, the fact that wee are given 2AX = 3XD isn't enough to prove similarity.

a. In the question, we are given 2AX = 3XD. An arbitrary triangle AXB can be drawn where one extends AX and choose a point D on the extended line in order for 2AX = 3XD. Also, extend BX and choose a point C on the line so that 2BX = XC. Even though they both satisfy the condition, they're not similar.

b. We are given that AX/BX = DX/CX. When this is rearranged, we'll have AX/DX = BX/CX. In this case, let AX/DX = k. DX and AX will align upon rotation of 180°. The triangle can then be dilated by a factor of k. This brings about the mapping of triangle DXC to AXB. Therefore, the original triangle DXC is similar to AXB.

c. Lines AB and CD are parallel. Here, the dilation moves line CD onto line AB. Here, since the dilation moves D to a point on ray XA, D must move to A. Therefore, the rotation of triangle DXC is similar to AXB. Therefore, DXC is similar to AXB.

d. Here, angle XAB is congruent to angle XCD. This shows similarity and in this case, XCD is similar to XAB.

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Answer:

I don't know how to answer this, sorry!

Step-by-step explanation:

.

Answer:

See below

Step-by-step explanation:

Isosceles because two sides are same length

                 and

Obtuse because there is an interior angle greater than 90 °

Answer:

There is no definitive answer to this question since different wigs are made with different kinds of synthetic fibers. Some synthetic fibers are more resistant to heat than others, so it really depends on the specific wig. In general, however, it is generally not recommended to use heat on synthetic wigs, as it can damage the fibers.

The algebraic expression that represents the reduced price is p - 125

The reduction is given as:

Reduction = $125

The original price is given as:

Original = P

The reduced price is calculated as:

Reduced price = original - reduction

This gives

Reduced price = p - 125

Hence, the algebraic expression that represents the reduced price is p - 125

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Answer:

no

Step-by-step explanation:

Answer:

7720 mm²

Step-by-step explanation:

area = 2 × 80 mm × 40 mm + 2 × 80 mm × 5.5 mm + 2 × 40 mm × 5.5 mm

area = 7720 mm²

Answer:

x>=2 so B

Hope this helps :)

Answer:

75

Step-by-step explanation:

Since they sold 75% of the raffle tickets and the total is 100 raffle tickets, you simply need to find 75% of 100. To find x% of a, you simply convert x% to a decimal by dividing by 100 and then multiplying it by a. So the general formula to find x% of a would be: [tex]a*\frac{x}{100}[/tex]. In this case a=100, and x=75. So you have the equation: [tex]100*\frac{75}{100} = \frac{100 * 75}{100}=\frac{75}{1} = 75[/tex]

Answer: 75 tickets

Step-by-step explanation:

- percentages are out of 100, they are a rate, number, or amount in each hundred

- for example, (10/100) x 100 (because it’s out of 100) = 10%
- or it could be (6/40) x 100 (because it’s out of 100) = 15%

- so because they started with 100 tickets, it’s just (75/100) x 100 =75

hope this helps :)

The errors Emma made are

From the question, we are to determine the errors that Emma made

The given statement is

"The quotient of six and a number, x, is the same as negative two times the difference of x and 4.5"

"The quotient of six and a number, x", can be expressed as

6/x

"Two times the difference of x and 4.5", can be expressed as

2(x - 4.5)

Hence, the errors Emma made are

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Question 14

As we approaching from the negative side, [tex]|x-3|=3-x[/tex].

So, we have [tex]\lim_{x \to 3^{-}}=\frac{3-x}{x-3}=\frac{-(x-3)}{x-3}=\boxed{-1}[/tex]

and thus the limit exists at x=3.

Question 15

For the top part of the function, [tex](9-9)^{2}=0[/tex]

For the bottom part of the function, [tex]9-9=0[/tex]

As both one-sided limits are equal, L = 0, and thus the limit exists at x=9.

Then the most profitable investment is the first machine (third option) because for each dollar, it produces 2 pounds of candy.

The first option is a worker that costs $10 per hour and produces 8lb, then this worker gives:

8lb/$10= 0.8 pounds per dollar.

The second worker costs $12 per hour, and produces 16lb per hour, so this worker gives:

16lb/$12 = 1.33 pounds per dollar.

The third option is a machine that cost $5 per hour and produces 10lb per hour, then:

10lb/$5 = 2 pound per dollar.

The last option costs $8 per hour, and produces 14 pounds per hour, then:

14lb/$8 = 1.75 pounds per dollar.

Then the most profitable investment is the first machine (third option) because for each dollar, it produces 2 pounds of candy.

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The inverse of the function f(x) = 2x + 5 is; f⁻¹(x) = (x - 5)/2

An inverse function in mathematics is function which reverses the another function.

We want to find the inverse of the function; f(x) = 2x + 5

Thus;

Step 1; y = 2x + 5

Step 2; Subtract 5 from both sides to get;

y - 5 = 2x

Step 3;  Since we want to find the inverse of f(x), then we now have;

x - 5 = 2y

Step 4: Divide both sides by 2 to get;

(x - 5)/2 = y

Step 5; Thus, we have;

f⁻¹(x) = (x - 5)/2

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Answer:

First we have to find the value of x;

then we have to find the value of y;

Step-by-step explanation:

here,

2x= 12

x = 12\2

x = 6

now,

4y = 12

y = 12\4

y = 3

° the value of x is 6

° ° the value of y is 3

Using Pythagoras theorem,  we know that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

Therefore,

c²= a²+ b²

where

Therefore,

3² + 4² = 5²

Hence,

Knowing that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle

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Answer:

a gas can hold 7×10=70 litters of gas

Using linear function concepts, we have that from the information given:

A linear function is modeled by:

y = mx + b

In which:

From the information given, the y-intercept is of 25 and the slope is of $2.50, hence the value after t months is given by:

V(t) = 25 - 2.5t.

Thus:

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Answer:

b = 5.3

A = 48.6

B = 41.4

Step-by-step explanation:

Attached is the Pics contain the Pythagoras Theorem and Trigonometric Identities.

So for our Right-Angled Triangle we have from Pythagoras Identity that

[tex]a^{2} +b^{2} =c^{2}[/tex]  ,, Then [tex]b^{2} =c^{2} -a^{2}[/tex]  where a=6 , c=8

by substituting,

[tex]b^2=8^2-6^2=28\\ b=\sqrt{28} =2\sqrt{7}=5.3[/tex]

Now to find A , we will use the Trigonometric Identities

Since    [tex]sin(A)=\frac{Opposite}{Hypotenuse}=\frac{a}{c} =\frac{6}{8}=\frac{3}{4} \\[/tex]

[tex]A=sin^{-1} (\frac{3}{4} )=48.6\\[/tex]

Since in any Triangle A+B+C=180

Then B=180-A-C=180-48.6-90=41.4

Answer: -2

Step-by-step explanation:

When x = 0, y = -2.

So, f(0) = -2.