Write the equation of a sine function with Amplitude=4 and Period = 8pi

So, with continuous compounding interest, there would be $1324.46 in the account after 5 years.

A(t) = P(1 + r/n)^(nt)

a. To find an equation that gives the amount of money in the account after t years, we can plug in the given values for P, r, and n into the formula. P is the initial deposit, r is the annual interest rate, and n is the number of times the interest is compounded per year. So, the equation will be:

A(t) = 800(1 + 0.10/4)^(4t)

b. To find the amount of money in the account after 5 years, we can plug in t = 5 into the equation and solve for A(t):

A(5) = 800(1 + 0.10/4)^(4*5)
A(5) = 800(1.025)^20
A(5) = 1303.04

So, after 5 years, there will be $1303.04 in the account.

c. To find how many years it will take for the account to contain $1600, we can set A(t) = 1600 and solve for t:

1600 = 800(1 + 0.10/4)^(4t)
2 = (1.025)^4t
log(2) = 4t*log(1.025)
t = log(2)/(4*log(1.025))
t = 7.22

So, it will take 7.22 years for there to be $1600 in the account.

d. If the same account and interest were compounded continuously, we can use the formula A(t) = Pe^(rt) to find how much money would be in the account after 5 years:

A(5) = 800e^(0.10*5)
A(5) = 800e^0.5
A(5) = 1324.46

So, with continuous compounding interest, there would be $1324.46 in the account after 5 years.

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(a) The equation that gives the amount of money in the account after t years is A(t) = 800(1.025)^4t.

(b) After 5 years, there will be $1304.56 in the account.

(c) It will take 7.24 years for there to be $1600 in the account.

(d) With continuous compounding interest, there would be $1340.95 in the account after 5 years.

a. The equation for the amount of money in the account after t years is A(t) = 800(1 + 0.10/4)^(4t) = 800(1.025)^4t. This is derived from the formula A = P(1+ r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

b. To find the amount of money in the account after 5 years, we can plug in the values into the equation from part a. A(5) = 800(1 + 0.10/4)^(4)(5) = 800(1.025)^20 = $1304.56. Therefore, after 5 years, there will be $1304.56 in the account.

c. To find how many years it will take for the account to contain $1600, we can set the equation from part a equal to 1600 and solve for t. 1600 = 800(1 + 0.10/4)^(4t) => 2 = (1.025)^4t => 4t = log(2)/log(1.025) => t = 7.24 years. Therefore, it will take 7.24 years for there to be $1600 in the account.

d. If the same account and interest were compounded continuously, the formula for the amount of money in the account after t years would be A(t) = 800e^(0.10t). To find how much money the account would contain after 5 years, we can plug in the values into this equation. A(5) = 800e^(0.10)(5) = $1340.95. Therefore, with continuous compounding interest, there would be $1340.95 in the account after 5 years.

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Answer: 709 milliliters

Step-by-step explanation:

It is just the sum of the numbers so,

236 + 473 = 709

709 milliliters

Hope this helps!

Answer:

709 millimeters

Step-by-step explanation:

Add it up 236 = 473 = 709

Measure of ∟A is 119°

To solve for x, we must use the fact that the angles have the same measure, so ∟A = ∟B.

Substitute 7x + 24° for ∟A and 3x + 92° for ∟B and set them equal to each other:

7x + 24° = 3x + 92°

Subtract 3x from both sides:

7x - 3x = 92° - 24°

4x = 68°

Divide both sides by 4 to solve for x:

x = 17°

Now that we have x, we can substitute 17° for x into the original equation for ∟A to find its measure:

∟A = 7x + 24°

∟A = 7(17°) + 24°

∟A = 119°

Therefore, the measure of ∟A is 119°.

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Answer: Option B is the correct answer

Step-by-step explanation:

Area of lateral surface = 3 x Area of rectangle

The rectangle is of  5 inches wide and 14 inches long.

Area of rectangle =  5 x 14 = 70 square inches

Area of lateral surface = 3 x Area of rectangle

Area of lateral surface = 3 x 70 = 210 square inches

Option B is the correct answer.

There will be about 111.25 square feet of space remaining in the room after the ping pong table is put in.

First, we need to convert the scale of the blueprint to a real-world scale. Since the scale is 1.5 in 5 feet, we can write this as:

1.5 inches : 5 feet

To convert this to a ratio that we can use, we can divide both sides by 1.5 inches:

1 inch : 3.33 feet

Now we can use this ratio to convert the dimensions of the room from the blueprint to real-world dimensions:

3 inches x 3.33 feet/inch = 9.99 feet

4.8 inches x 3.33 feet/inch = 15.96 feet

So the room is approximately 10 feet by 16 feet.

Next, we need to see if the ping pong table will fit in the room. The table is 9 feet by 5 feet, which means it needs at least a space of 9 feet x 5 feet = 45 square feet. To convert this to the scale of the blueprint, we can use the inverse of the ratio we calculated earlier:

1 foot : 1/3.33 inches

So the table needs at least a space of 9 feet x (1/3.33 inches/foot) = 27 inches by 5 feet x (1/3.33 inches/foot) = 15 inches on the blueprint.

The space in the room is 3 inches x 4.8 inches on the blueprint, which is equivalent to 3 inches x (1/1.5 inches/foot) = 2 feet and 4.8 inches x (1/1.5 inches/foot) = 1 foot 7.8 inches in real-world dimensions.

Since the table will fit on the blueprint, we can now calculate the remaining space in the room. The total area of the room is approximately 10 feet x 16 feet = 160 square feet.

The area taken up by the ping pong table is approximately 9 feet x 5 feet = 45 square feet, or 27 inches x 15 inches on the blueprint. To convert this to square feet, we can use the ratio we calculated earlier:

27 inches x (1/12 feet/inch) x 15 inches x (1/12 feet/inch) = 3.75 square feet

So the remaining space in the room is approximately 160 square feet - 45 square feet = 115 square feet - 3.75 square feet

= 111.25 square feet.

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The equation that can be used to determine Greg's score is 15 - 8 = x. This equation shows that if you subtract 8 points from Ben's score of 15 points, you will get Greg's score.

Step-by-step explanation:

In conclusion, the equation 15 - 8 = x can be used to determine Greg's score.

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The length of y for the triangle is 27.8 in

The sine rule is for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula:

w/sinW = x/sinX = y/sinY

where w, x and y are the lengths and W, X and Y are the angles

Given: w = 55 inches,   m∠W = 162° and m∠X= 9°

m∠Y = 180 - 162 - 9 =  9° (angle sum in a triangle)

Using the formula:

w/sinW = y/sinY

55/sin162° = y/sin9°

y = (55*sin9°)/sin162°

y = 27.8 in

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The intersection set, A∩ B, of the sets A = {2, 5, 6, 14, 16} and B = {1, 3, 6, 8, 14 } is equals to the { 6, 14}.

For any two sets A and B, the intersection, A∩ B (read as A intersection B) lists all the elements that are present in both sets, and are the common elements of A and B. The intersection of sets is denoted by the symbol '∩'. It is subset of both of sets, A and B. For example, if Set A = {1,2,3,4,5} and Set B

= {3,4,6,8}, A ∩ B = {3,4}.

Here, we have two sets A = {2, 5, 6, 14, 16} and B = {1, 3, 6, 8, 14 }

The common elements in sets A and B

= { 6,14 }

Therefore, the intersection of A and B,

A ∩ B = { 6, 14}.

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Complete question:

What is the intersection of the sets A = {2, 5, 6, 14, 16} and B = {1, 3, 6, 8, 14}?

Answer:

(24 divided by 3) + x

Step-by-step explanation:

i did it

Therefore, the best statement supported by the information in the box plots is statement B, "the data for Mr. Flores’s class are more symmetrical than the data for Mrs. Morales's class."

A box plot, also known as a box-and-whisker plot, is a graphical representation of the distribution of numerical data. It displays the five-number summary of a dataset, which includes the minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value.

Here,

From the box plots, we can make the following observations:

A) The range for Mrs. Morales's class appears to be 100-50 = 50.

The range for Mr. Florez's class appears to be 95-55 = 40.

Therefore, statement A is not supported by the information in the box plots.

B) The box plot for Mr. Flores's class is more symmetrical than the box plot for Mrs. Morales's class, which is skewed to the left.

Therefore, statement B is supported by the information in the box plots.

C) The median score for Mrs. Morales's class appears to be between 70 and 75.

The median score for Mr. Florez's class appears to be between 75 and 80.

Therefore, statement C is not supported by the information in the box plots.

D) The interquartile range for Mrs. Morales's class appears to be between 60 and 80, which is a range of 20.

The interquartile range for Mr. Florez's class appears to be between 65 and 85, which is also a range of 20.

Therefore, statement D is supported by the information in the box plots.

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Step-by-step explanation:

How many cups of milk are in a gallon = 16

If a recipe uses 2 cups for 6 servings, then he will make 48 servings from a gallon.

1 quart is 4 cups of milk, a gallon contains 4 quarts

1 pint is 2cups, a gallon contains 8pints of milk

From the question 1 gallon is 4 quarts or 8pints or 48servings

The value of image of coordinates of triangle ABC are,

A' = (4, - 4)

B' = (5 - 1)

C' = (1, - 3)

And, After dilate DEFG by a scale factor of 3 about (- 5, 5) is,

D' = (- 15, 6)

E' = (- 12, 12)

F'  = (- 6, 12)

G' = (- 9, 6)

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Reflect the triangle ABC across the line y = x

And, Dilate DEFG by a scale factor of 3 about (- 5, 5).

Now,

We know that;

The rule of reflection across the line y = x is,

(x, y) → (y, x)

Thus, The value of coordinates of triangle ABC are,

A = (- 4, 4)

B = (- 1, 5)

C = (- 3, 1)

Hence, The image of coordinates of triangle ABC are,

A' = (4, - 4)

B' = (5 - 1)

C' = (1, - 3)

And, The coordinates of DEFG are,

D = (- 5, 2)

E = (- 4, 4)

F = (- 2, 4)

G = (- 3, 2)

Hence, After dilate DEFG by a scale factor of 3 about (- 5, 5) is,

D' = (- 5x3, 2x3) = (- 15, 6)

E' = (- 4x3, 4x3) = (- 12, 12)

F' = (- 2x3, 4x3) = (- 6, 12)

G' = (- 3x3, 2x3) = (- 9, 6)

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Therefore , the solution of the given problem of equation comes out to be required equation is 0.05b = 4.80 .

Mathematical formulas frequently use the same variable letter to try to impose unity between two assertions. Many academic numbers are shown to be equal using mathematical equations, also known as assertions. Using y + 6 as an illustration, the normalise does not divide 12 into two parts, but instead b + 6. It is possible to determine the connection integer between each sign part and the number of lines. The significance of a symbol usually contradicts itself.

Here,

The following equation can be set up to represent the circumstance if x is the procedure's cost:

=>  5% of x = $4.80

The percentage must first be divided by 100 to become a decimal before we can answer for x:

=>  0.05x = $4.80

Then, by dividing both lines by 0.05, we can separate out x:

=>  x = $96

Consequently, the process will cost you $96. It is possible to confirm that the gratuity is 5% of $96:

=>  5% of $96 = 0.05 × $96 = $4.80

So, the solution is:

=> 0.05b = 4.80

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The hypotenuse is sqrt(11^2 + 7^2) = sqrt(170). Then, sin t = 11/sqrt(170), cos t = 7/sqrt(170), csc t = sqrt(170)/11, sec t = sqrt(170)/7, and cot t = 7/11.

Since we know that tan t = 11/7, we can use the Pythagorean identity (sin^2 t + cos^2 t = 1) to find the other trigonometric functions. First, we will find sin t and cos t:

tan t = 11/7 = opposite/adjacent = sin t/cos t

sin t = 11*cos t

cos t = 7*sin t

Substituting the second equation into the first equation:

sin t = 11*(7*sin t)

sin^2 t = 121*sin^2 t

121*sin^2 t - sin^2 t = 0

120*sin^2 t = 0

sin^2 t = 0/120

sin^2 t = 0

sin t = 0

Since sin t = 0, cos t = 1. Now we can find the other trigonometric functions:

csc t = 1/sin t = 1/0 = undefined

sec t = 1/cos t = 1/1 = 1

cot t = 1/tan t = 1/(11/7) = 7/11

So, the values of the trigonometric functions are:

sin t = 0

cos t = 1

csc t = undefined

sec t = 1

cot t = 7/11

Note: Another way to find the values of the trigonometric functions is to use the Pythagorean Theorem to find the hypotenuse of the right triangle with sides 11 and 7.

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2a + 2h

(a) Simplifying, we get f(a+h)−f(a)/h = (a+h)2−2(a+h)+3 − (a2−2a+3) / h = (2a+2h)h/h = 2a + 2h.

(b) We now use the definition of the derivative to compute f'(a) = limh→0 (2a + 2h) = 2a.

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The surface areas of these cylinders are 75.39 cm, 835.76 cm,  1324.11 cm, and 3543.71 cm.

The surface area of a cylinder can be calculated by using the formula  2π r h + 2π r², which means we need the radius and the height to calculate the area. Let's now use this formula to know the area of each cylinder:

Cylinder 1:

2π 2 4+ 2π 2² = 75.39 cm

Cylinder 2:

2π 7 12+ 2π 7² = 835.76 cm

Cylinder 3:

2π 8.2  17.5+ 2π 8.2² = 1324.11 cm

Cylinder 4:

2π 12 35 + 2π 12r² = 3543.71 cm

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Based on the histograms, it appears that Machine B is doing a better job of dispensing the correct amount of liquid.

The most common graph for displaying frequency distributions is a histogram.

To begin, Machine B's histogram is more symmetrically distributed around the 5.5-ounce mark, which is the target fill level.

Machine A's histogram, on the other hand, is skewed to the right, indicating that it is more likely to dispense more than 5.5 ounces.

Second, Machine B's histogram has a narrower spread, with most measurements falling between 5.4 and 5.6 ounces.

This indicates that the machine fills the bottles consistently within a narrow range of the target fill level.

Thus, the histogram for Machine A, on the other hand, has a wider range, with some measurements falling below 5.4 ounces and others exceeding 5.6 ounces, indicating a less consistent performance.

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Your question seems incomplete, the probable complete question is:

Answer:

64.15°

Step-by-step explanation:

here

theta = 64.15°

( solution in picture)

Answer:

Keith bought 14 gallons of paint, and each classroom requires 7/4 gallons of paint.

To find how many classrooms can be painted, we can divide the total amount of paint by the amount of paint needed per classroom:

14 ÷ (7/4) = 8

Therefore, Keith can paint 8 classrooms in total.

Answer:

When you multiply two numbers with different signs (positive and negative), the result is always negative.

This can be understood in terms of the basic properties of multiplication and the fact that a negative number is essentially the opposite of a positive number. When you multiply a positive number by a positive number, the result is positive because both numbers are pointing in the same direction along the number line. When you multiply a negative number by a negative number, the result is also positive because both numbers are pointing in the opposite direction along the number line, and multiplying them together "flips" them back to the positive side. However, when you multiply a positive number by a negative number, the two numbers are pointing in opposite directions along the number line, and so their product is negative.

Therefore, the rule for multiplying two numbers with different signs is that the product is always negative.

Step-by-step explanation:

Check the picture below.

[tex]\boxed{4} \\\\\\ (x+3)^2~~ = ~~[(x-1)+10](x-1)\implies x^2+6x+9~~ = ~~(x+9)(x-1) \\\\\\ x^2+6x+9~~ = ~~x^2+8x-9\implies 6x+9=8x-9\implies 9=2x-9 \\\\\\ 18=2x\implies \cfrac{18}{2}=x\implies 9=x[/tex]

Answer:

$45072

Step-by-step explanation:

I = Prt

I = 36000(6.3/100)(4)

I = 9072

ending balance = 36000 + 9072

= 45072

Where are the questions?

Answer:

The formula to calculate simple interest is:

I = Prt

Where I is the interest, P is the principal amount borrowed, r is the interest rate per period, and t is the time period.

Using this formula, we can calculate the interest Ms. Lang will pay as follows:

I = Prt

I = 2300 * 0.13 * (30/12)

I = $975

Therefore, Ms. Lang will pay $975 in interest over the 30-month period.

To calculate the total amount she will repay, we need to add the interest to the principal amount borrowed:

Total amount = Principal + Interest

Total amount = $2300 + $975

Total amount = $3275

Therefore, Ms. Lang will repay a total of $3275, which includes the $2300 principal and $975 interest.

now, we're assuming this is on a simple interest rate, so hmm say a year has 12 months, so 30 months will just be 30/12 of a year.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$2300\\ r=rate\to 13\%\to \frac{13}{100}\dotfill &0.13\\ t=years\to \frac{30}{12}\dotfill &\frac{5}{2} \end{cases} \\\\\\ I = (2300)(0.13)(\frac{5}{2}) \implies I = 747.5~\hfill \underset{ \textit{amount to be repaid} }{\stackrel{ 2300~~ + ~~747.5 }{\text{\LARGE 3047.5}}}[/tex]

Answer:

62.5%

Step-by-step explanation:

the product of the two numbers=xy

the product of the altered numbers=(0.75x)(0.5y) OR 0.375xy

finally you subtract this from one to get your decrease: 1-0.375=0.625

then simply convert that to a percent, leaving you with 62.5%. hope this helps!

The solution to the equation is (5, -1)

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

2x + 3y = 7

-2x + 1y = -11

Add to eliminate x

So, we have

4y = -4

Divide both sides by 4

y = -1

Recall that 2x + 3y = 7

Substitute the known values in the above equation, so, we have the following representation

2x - 3 = 7

So, we have

2x = 10

Divide

x = 5

For the substitution method, we have

2x + 3y = 7

-2x + y = -11

The second equation becomes

y = 2x - 11

By substitution, we have

2x + 6x - 33 = 7

So, we have

8x = 40

x = 5

Recall that

y = 2x - 11

So, we have

y = 2 * 5 - 11

y = -1

Hence, the solution is (5, 2)

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Answer:

We need to find out how many trips Billy needs to make to transport 80 cubic meters of mulch. Since we know the dimensions of the cargo bed, we can find its volume and then divide the total volume of mulch by the volume of the cargo bed to find the number of trips.

The volume of the cargo bed is:

V = l × w × h

where l is the length, w is the width, and h is the height. Using the dimensions given in the diagram, we get:

V = 4 m × 2.5 m × 1.5 m = 15 cubic meters

Now we can divide the total volume of mulch by the volume of the cargo bed to find the number of trips:

Number of trips = total volume of mulch / volume of cargo bed

Number of trips = 80 cubic meters / 15 cubic meters ≈ 5.33

Since Billy cannot make a fractional number of trips, he will need to make 6 trips to transport all the mulch to his house.

Martina can run 4,920 more feet this year compared to last year.

Martina can run 3 miles without stopping. Last year she could run 3,640 yards without stopping. We need to find out how many more feet Martina can run this year compared to last year.

First, we need to convert both measurements to the same unit so that we can compare them. We will convert both measurements to feet.

1 mile = 5,280 feet
1 yard = 3 feet

So, 3 miles = 3 x 5,280 feet = 15,840 feet

And, 3,640 yards = 3,640 x 3 feet = 10,920 feet

Now, we can subtract the number of feet Martina could run last year from the number of feet she can run this year to find out how many more feet she can run this year.

15,840 feet - 10,920 feet = 4,920 feet

Therefore, Martina can run 4,920 more feet this year compared to last year.

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