You receive $1,000 to put in the bank. You place it in an account that pays 4% annual interest compounded continuously. How much will you have in 15 years? Round the answer to the nearest dollar.

Final answer:

The rectangle's length to be 20 meters and the width to be 14 meters.

Explanation:

We are given that a rectangle has a perimeter of 68 meters and an area of 280 square meters, and we need to find its dimensions. Let's call the length of the rectangle L and the width W.

The perimeter (P) of a rectangle is given by the formula P = 2L + 2W. We know the perimeter is 68 meters, so we can write the equation:

1. 68 = 2L + 2W

The area (A) of a rectangle is given by the formula A = L × W. We know the area is 280 square meters, so we can write the equation:

2. 280 = L × W

To find L and W, we solve these two equations simultaneously.

Divide the perimeter equation by 2 to simplify:

34 = L + W

We can then express W in terms of L using this equation:

W = 34 - L

Substitute this into the area equation:

280 = L × (34 - L)

This gives us a quadratic equation:

L2 - 34L + 280 = 0

Solving this quadratic equation, we find that L = 20 and W = 14 or L = 14 and W = 20. Since the width is shorter than the length, the dimensions of the rectangle are length 20 meters and width 14 meters.

Before we begin please note that a jar is always cylindrical in shape if not mentioned otherwise. Thus, we will take a cylindrical jar in this case.

Since Kelly eats some of the salsa and the salsa in the jar is now 6 cm high, we know that Kelly ate the amount of Salsa whose volume is missing from the jar.

To find the missing volume on the Salsa jar all that we need to do is to find the height of the missing volume which is given to us as h= 6 cm. We already know that the radius of the jar, r=6 cm. Thus, the amount of Salsa Kelly has eaten is:

[tex] V=\pi(6)^2\times 6\approx678.6\approx679 [/tex] [tex] cm^3 [/tex]

Thus, the third option is the correct answer

Answer:

Answer B

Step-by-step explanation:

The already given answer is correct, but if you need to know what answer it is without getting your calculator out, its B, or

0.049 (square)2 -(square) 2 N

0.049√2-√2 N

Answer:

$261.08

Step-by-step explanation:

Worth of Car=$14,390

Trade-in allowance=$1000

Down Payment= $1500

Value of Loan=14390-(1000+1500)

=$11890

The Monthly Payment for a loan P, taken at a Monthly interest rate, r for a number of m months, is gotten using the formula:

[TeX] Monthly\:Payment=\frac{rP}{1-(1+r)^{-m}} [/TeX]

P=$11890

Monthly Interest Rate,r=0.026/12=0.002167

Number of Months, m=4*12=48 Months

[TeX] Monthly\:Payment=\frac{0.002167*11890}{1-(1+0.002167)^{-48}} [/TeX]

=$261.08

The Monthly Payment on the car loan is $261.08.

The standard form is given by :

[tex] ax^{2} +bx +c=0 [/tex]

So we have to convert given equation in this form by bringing all terms to one side and making 0 on the other side.

[tex] 5x^{2} +9x=4 [/tex]

Now we have to bring 4 to the left side,

subtracting 4 on the left,

[tex] 5x^{2} +9x-4=0 [/tex]

Comparing our equation with standard form,

Answer : a=5, b=9 and c=-4 ( second option is right )

The required value of j is 38.

A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.

Now the given expression is

j/-2 + 7 =-12

Substracting 7 both the side. We get,

j/-2 + 7 -7 = -12 - 7

Solving both sides,

j/-2 = -19

Now multiplying whole equation with -2,so the equation becomes

j = 38

which is the required value of j.

Hence,the required value of j is 38.

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It is given in the question that in the lemon squash 2 parts concentrate is added to 5 parts of water. Thus it makes the concentrate to water ratio as 2:5 or [tex] \frac{2}{5} [/tex]. Now, if this ratio is maintained then the amount of water to be added to 90 ml concentrate in a glass can be calculated as:

[tex] \frac{2}{5}=\frac{90}{x} [/tex]

Where x is the amount of water to be added, in ml (milliliters).

Cross multiplication of the above equation will give us:

[tex] 2x=90\times 5=450 [/tex]

Dividing both sides by 2 we will get:

[tex] x=\frac{450}{2}=225 [/tex]

Thus, if we put 90ml of concentrate in a glass, the water that should be added must be 225 ml.

The amount of water should be added is 225 ml if the lemon squash is 2 parts concentrated to 5 parts of water. if you put 90ml of concentrate in a glass

It is defined as the comparison between two quantities that how many times the one number acquires the other number. The ratio can be presented in the fraction form or the sign: between the numbers.

We have:

Lemon squash 2 parts concentrate to 5 parts of water.

Let's suppose the amount of water is x ml

Then according to the problems the ratios:

[tex]\frac{2}{5} =\frac{90}{x}[/tex]

2x = 90×5

2x = 450

x = 225 ml

Thus, the amount of water should be added is 225 ml if the lemon squash is 2 parts concentrated to 5 parts of water. if you put 90ml of concentrate in a glass

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The payroll deductions among the given choices are Taxes, health insurance premiums and pension fund contributions.

Payroll deductions are those amounts which are deducted from an employee's payroll amount. These amounts are usually withheld by the employer where the employee works. Payroll deductions include insurance pension contributions, wage assignments, child support payments, taxes, and union and uniform dues.

the proportional segments for the given diagram is

[tex]\frac{9}{1.5} =\frac{12}{2}[/tex]

Given:

In the given diagram , QS is parallel to MN

when a line that intersects two sides of the triangle is parallel to third side then the sides are in proportion

From the given the sides are in proportion

[tex]\frac{RM}{MQ} =\frac{RN}{NS} \\\frac{9}{1.5} =\frac{12}{2}[/tex]

so the answer for the given diagram is

[tex]\frac{9}{1.5} =\frac{12}{2}[/tex]

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Let us assume the number of times Bill saved $75 from his paycheck = x

Let us assume he number of times Bill saved $150 from his paycheck = y

Since he saved 75$ or 150$ for the 8 paychecks.

So, x+y=8

y=8-x (Equation 1)

Since Bill saved $825 from his last 8 paychecks using $75 or $150.

So, 75x+150y=825 (Equation 2)

Substituting the value of 'y' from equation 1 in equation 2,

[tex] 75x+150(8-x)=825 [/tex]

[tex] 75x+1200-150x=825 [/tex]

[tex] 75x-150x=825-1200 [/tex]

[tex] -75x=-375 [/tex]

x = 5

Therefore, Bill saved $75, 5 times from his paycheck.

Answer:

5

Step-by-step explanation:

Answer:

It is false

Answer:

Assume at least one angle is not acute.

Step-by-step explanation:

With an indirect proof, instead of proving that something must be true, you prove it indirectly by showing that it cannot be false.

An indirect prove starts assuming that the statement is false and then your goal is to arrive at a contradiction. Then, in this case, the first step of indirectly proving at least one angle is acute is assume at least one angle is not acute.

The 7th term of the sequence is 81

The nth term of a geometric sequence is expressed as:

[tex]T_n=ar^{n-1}[/tex]

Substitute the given parameters into the formula to have:

[tex]T_7=1/9(-3)^{7-1}\\T_7=1/9(-3)^6\\T_7=1/9(729)\\T_7=81[/tex]

Hence the 7th term of the sequence is 81

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Final answer:

To solve 0.98 = log x, you determine the number x for which 10 raised to the power of 0.98 equals x. Using a calculator, you find that x is approximately 95.50.

Explanation:

To solve the equation 0.98 = log x, we need to find the value of x such that when you take the common logarithm (base 10) of x, you get 0.98. A common logarithm is a logarithm with base 10, and the equation informs us that x is 10 raised to the power of 0.98 since y = log10(x) can be rewritten as x = 10y.

To find x, we can use the inverse operation of logarithm, which is exponentiation. We can express this process as follows:

x = 100.98

Using a calculator with exponentiation functionality, we enter the value of 0.98 and use the 10x function (sometimes labeled as INV or SHIFT followed by the LOG key).

The result is that x is approximately 95.50 when rounded to the nearest hundredth.

Final answer:

The rate of change of the area of a circle with a radius increasing at a constant rate can be calculated using the derivative of the area formula. For r = 5 inches, the rate is 30π square inches per minute and for r = 21 inches, the rate is 126π square inches per minute.

Explanation:

The student is asking about the rate of change of the area of a circle when its radius is increasing at a constant rate. This is a calculus problem that involves derivatives and can be solved using the formula for the area of a circle, A = πr² where A is the area and r is the radius. The rate of change of the radius, ℓr/ℓt, is given as 3 inches per minute.

To find the rate of change of the area, denoted as ℓA/ℓt, we take the derivative of A with respect to t, using the chain rule, which gives us ℓA/ℓt = 2πr(ℓr/ℓt). When r = 5 inches, substituting the values, we obtain ℓA/ℓt = 2π(5)(3) = 30π square inches per minute. Similarly, when r = 21 inches, ℓA/ℓt = 2π(21)(3) = 126π square inches per minute.

we have that

the given equation is

[tex]y=0.013x^{2}[/tex]

we know that

The general linear equation is equal to

[tex]y=mx+b[/tex]

where

m and b are real numbers

Every equation in this form is a linear equation. The linear equations represent linear functions. Equations than cannot be written in this form are not linear equations, and therefore are not linear functions

The given equation is not a line, is a quadratic equation, therefore is not a linear equation, is a non linear function.

Only a linear relationship can be proportional,

so

the relationship is not proportional

therefore

the answer is

the relationship between x and y  is a non linear function and is not proportional

The dimensions of the rectangular piece of plastic are either 2mm by 5mm or 5mm by 2mm, based on the given area and perimeter.

We'll use the formula for the perimeter of a rectangle: 2(length + width) = perimeter and the formula for area: length x width = area. Given we have area of 10mm2 and perimeter of 22mm, we can set up two equations. Let's denote the length as 'L' and the width as 'W'.

Formula of perimeter of a rectangle: 2(L + W) = 22

Formula of area of a rectangle: L * W = 10.

We solve these two equations simultaneously. We get two possible solutions: Dimensions could be either {2mm, 5mm} or {5mm, 2mm}. Either the length is 5mm and the width is 2mm, or the length is 2mm and the width is 5mm.

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