Which of these is an example of a recurring-payment variable annuity

Answer: [tex]2 sin(5 \theta) cos \theta[/tex]

Step-by-step explanation:

According to the trigonometric identities we have the following formula:

[tex]sin (x) + sin (y)=2 sin(\frac{x+y}{2}) cos(\frac{x-y}{2})[/tex]

Now, we have the following:

[tex]sin (6\theta)+ sin (4\theta)[/tex]

Where [tex]x=6\theta[/tex] and [tex]y=4\theta[/tex]

Hence:

[tex]sin (6\theta)+ sin (4\theta)=2 sin(\frac{6\theta+4\theta}{2}) cos(\frac{6\theta-4\theta}{2})[/tex]

[tex]sin (6\theta)+ sin (4\theta)=2 sin(\frac{10\theta}{2}) cos(\frac{2\theta}{2})[/tex]

Finally:

[tex]sin (6\theta)+ sin (4\theta)=2 sin(5\theta) cos(\theta)[/tex]

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Simplify 17q−q−8q−4  to  8q-48q−4.

8q - 4 = 20

8q = 20 + 4

8q = 24

q = 24/8

q = 3

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Answer:

84

Step-by-step explanation:

7x12

Answer:

3/-7

Step-by-step explanation:

They’re correct!

Answer:

Step-by-step explanation:

(-2,6),(1,1)

slope = (1 - 6) / (1 - (-2) = -5/3

y - y1 = m(x - x1)

slope(m) = -5/3

(-2,6)....x1 = -2 and y1 = 6

and we get :

y - 6 = -5/3(x - (-2)...which can further be simplified to :

y - 6 = -5/3(x + 2) <=== ur answer

Answer:

D. A line can be contained in more than one plane .

Step-by-step explanation:

A. is wrong because a line can't be said as coplanar . We can draw infinite number of planes through a line .

B. is wrong because a line can be contained in infinite number of planes.

C. is wrong because a line can't be contained in a point as a line is a collection of points.

D. is the right answer as every line passes through infinite number of planes.

Answer:

-1

Step-by-step explanation:

A function assigns the values. The right-hand limit of this function at x=2 is -1.

A function assigns the value of each element of one set to the other specific element of another set.

The right-hand limit of the function when the value of x=2, can be found by substituting the value of x as 2 in the given function, therefore, the right-hand limit of this function at x=2 is,

g(x) = (x²-3)/(x-3)

g(2) = (4-3)/(2-3)

g(2) = -1

Hence, the right-hand limit of this function at x=2 is -1.

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Answer:

A related subtraction fact would be either

12-5=7  or

12-7=5

Step-by-step explanation:

Answer:

a related subtraction fact for 5+7=12 would be 12-7=5

Answer:

[tex]4^7[/tex]

Step-by-step explanation:

If we use one of the property of exponents rules:

[tex]4^4*4^3=4^4^+^3=4^7[/tex]

Answer:

The measure of arc AC is [tex]136^o[/tex]

Step-by-step explanation:

Notice that angle BAC (whose measure is given as 34 degrees) is an inscribed angle, and according toe the inscribed angle theorem, the measure of an inscribed angle is half the measure of the central angle that subtends the same chord.

Then, the central angle that subtends the cord BC, is twice 34 degrees ([tex]2\,*\,34^o = 68^o[/tex])

Then, since they give us also the measure of the arc AB which is [tex]156^o[/tex], then the measure of arc AC can be estimated as the needed measure to complete [tex]360^o[/tex] as the sum of all three arcs. That is:

[tex]AC + AB+ BC = 360^o\\AC + 156^o+2\,*\,34^o = 360^o\\AC + 156^o+68^o = 360^o\\AC=360^o-156^o-68^o\\AC=136^o[/tex]

Answer:

8 vehicle.

Step-by-step explanation:

Given: Monthly salary of salesperson is $2400

          Incentive of salesperson is $250 per vehicle sold.

First, lets compute income to earned apart from salary.

∴ Deduct salary from the target amount

[tex]\$ 4400-\$ 2400= \$ 2000[/tex]

∴ $2000 need to be earned only through incentive, which is $250 per vehicle sold.

Now, solving to get number vehicles to be sold to earn $2000 as incentive.

Number of vehicle= [tex]\frac{2000}{250}= 8\ vehicles[/tex]

∴ 8 vehicles need to be sold by salesperson to get total earning as $4400.

The salesperson needs to sell 8 vehicles to earn a total of $4400 in a month.

To determine the number of vehicles a salesperson needs to sell to earn a total of $4400, we can set up an equation based on the information provided.

The salesperson earns a fixed monthly salary of $2400 and an additional $250 for each vehicle sold. Let's denote the number of vehicles sold as x

We want the total earnings  E to be $4400, so we set up the equation:

 4400 = 2400 + 250x

Now, we solve for x

250x = 4400 - 2400

x= 8

 Therefore, the salesperson needs to sell 8 vehicles to earn a total of $4400 in a month.

Step-by-step explanation:

Point B(2, 8) reflect to x-axis

It means the x value won't change, the only thing that will change is the y value.

According to it, we can know that B' is (2, -8)

(2, -8) → (-8, 2+4) = (-8, 6) = B''

Final answer:

To obtain the coordinates of B'' after a reflection across the x-axis and a translation of (x,y)
ightarrow(y,x+4), point B(2,8) becomes B'(2,-8) after reflection and then B''(-8, 6) after translation.

Explanation:

The student is asking about the results of performing a geometric transformation on a point in the coordinate plane. Specifically, point B(2,8) is first reflected across the x-axis, and then is translated according to the rule (x,y)
ightarrow(y,x+4). To find the coordinates of B'', we follow these steps:

Reflect B across the x-axis: The x-coordinate remains the same, but the y-coordinate changes sign, resulting in B'(2,-8).

Apply the translation rule: We then take the coordinates of B' and apply the rule. The x-value of B' becomes the y-value of B'' and the y-value of B', decreased by 4, becomes the new x-value. Therefore, B'' = (-8, 2+4) = (-8, 6).

The final coordinates of B'' after the reflection and translation are (-8,6).

Answer:

The unit rate for her riding in miles per hour is given by 2 miles per hour.

Step-by-step explanation:

Amber rides m miles in h hours according to the equation m=2h .......... (1)

Putting h = 1 hour, we get m = 2 miles.

Therefore, Amber rides 2 miles height within a period of time 1 hour.

Therefore, the unit rate for her riding in miles per hour is given by 2 miles per hour. (Answer)

Again, differentiating equation (1) with respect to h we get,

[tex]\frac{dm}{dh} = 2[/tex] miles per hour.

So, here also we get the unit rate of her riding is 2 miles/hr.

Answer:

21 miles

Step-by-step explanation:

Hence, the actual distance between Paige's house and the mall is [tex]21[/tex] miles.

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Here given that,

Sonoma bikes [tex]5[/tex] miles to Paige's house. On a map, they measure that distance as [tex]\frac{5}{6}[/tex]cm. The same map shows that the mall is [tex]3\frac{1}{2}[/tex]cm from Paige's house.

Let the actual distance between Paige's house and the mall is [tex]x[/tex]

So,

[tex]\frac{5}{\frac{5}{6}}=\frac{x}{\frac{7}{2}}\\\\\\5(\frac{6}{5})=x(\frac{2}{7})\\\\\\6=\frac{2x}{7}\\\\\\x=6(\frac{7}{2})\\\\\\x=\frac{42}{2}\\\\\\x=21[/tex]

Hence, the actual distance between Paige's house and the mall is [tex]21[/tex] miles.

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Final answer:

To find the amount of cloth left over, subtract the amount used from the total amount. Jaquan had 9.5 yards of cloth left over, which can be expressed as the fraction 19/50.

Explanation:

To find the amount of cloth left over, we need to subtract the amount used from the total amount. Jaquan bought 25 yards of cloth, used 4.9 yards for a decoration, and used 10.6 yards to make costumes. To find the amount left over, we subtract the sum of 4.9 yards and 10.6 yards from 25 yards: 25 - 4.9 - 10.6 = 9.5 yards.

The amount of cloth left over can be expressed as a fraction by dividing the amount left over by the total amount. So, 9.5 yards can be written as the fraction 9.5/25, which can be simplified by dividing both the numerator and denominator by 0.5 to get 19/50. Therefore, the amount of cloth left over is 19/50.

Answer: 2 bookcases.

Step-by-step explanation:

Let be "x" the number of bookcases that the custodian will be able to repaint completly with 5 gallons of paint.

According to the data given, the custodian needs 2 gallons of paint to repaint one bookcase. Since all the bookcases are equal, you can set up the following proportion:

[tex]\frac{2}{1}=\frac{5}{x}[/tex]

Now you must solve for "x" in order to find its value:

[tex](x)(\frac{2}{1})=5\\\\2x=5\\\\x=\frac{5}{2}\\\\x=2.5[/tex]

Notice that the custodian will be able to repaint 2 bookcases completely, then you can say that:

[tex]x\approx2[/tex]

The custodian will be able to repaint 2 bookcases with 5 gallons of paint.

To determine the number of bookcases the custodian will be able to repaint with 5 gallons of paint, we need to divide the total amount of paint by the amount of paint required for each bookcase. Each bookcase requires 2 gallons of paint, so we divide 5 gallons by 2 gallons per bookcase:

5 gallons ÷ 2 gallons/bookcase = 2.5 bookcases

Since we cannot have 0.5 of a bookcase, the custodian will be able to repaint 2 bookcases with 5 gallons of paint.

Answer:

1/256

Step-by-step explanation:

1/256

4^-4 as a fraction is 1/256. It cannot be further simplified because 1 and 256 have no common factors other than 1, making it the simplest form.

To express 4^-4 as a fraction and simplify it, we can apply the rule that states any non-zero number raised to a negative exponent is equivalent to 1 divided by that number raised to the positive exponent.

So, for 4^-4, we can write it as:

4^-4 = 1 / 4^4

Now, let's calculate 4^4:

4^4 = 4 * 4 * 4 * 4 = 256

So, we have:

4^-4 = 1 / 256

This is the fraction representation of 4^-4. To determine if it can be further simplified, we can check if the numerator and denominator have any common factors other than 1. In this case, 1 and 256 have no common factors other than 1.

Therefore, 1/256 is already in its simplest form. It represents the fraction equivalent of 4^-4, which is a small value. It means that 4 raised to the power of -4 is a very small positive number, specifically 1/256, indicating that the original number 4^-4 is less than 1 and quite close to zero in value.

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Answer:

[tex]293,148\ mm^2[/tex]

Step-by-step explanation:

The cup has cylivdrical shape. Find the volume of the cylinder using formula

[tex]V=\pi r^2h,[/tex]

where

r = base radius

h = height

In your case,

r = 36 mm

h = 72 mm

then

[tex]V=\pi \cdot 36^2\cdot 72=93,312\pi \ mm^2\approx 293,148\ mm^2[/tex]

The house will be 10.9 inches high on the blueprint.

Step-by-step explanation:

Given,

Scale on blue print;

6 inch = 11 feet

We will find unit rate in terms of foot.

1 foot = [tex]\frac{6}{11}\ inches[/tex]

Therefore;

20 feet = [tex]\frac{6}{11}*20 = \frac{120}{11}[/tex]

20 feet = 10.9 inches

The house will be 10.9 inches high on the blueprint.

Keywords: unit rate, division

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The house would be approximately 10.91 inches tall on the blueprint to represent a 20-foot actual height.

The student asked how many inches high a house would be on a blueprint if the actual home is to be 20 feet tall, and a blueprint states that a 6-inch line represents 11 feet on the actual home. To solve this, we set up a proportion to determine the blueprint's height. The proportion is 6 inches/11 feet = x inches/20 feet, where x represents the height on the blueprint. First, write the proportion as 6 inches/11 feet = x inches/20 feet. Then, cross-multiply to get 11 feet * x inches = 6 inches * 20 feet. To find x, divide both sides of the equation by 11 feet, getting x = (6 inches * 20 feet) / 11 feet. After calculating, we find that x ≈ 10.91 inches. Therefore, on the blueprint, the house would be approximately 10.91 inches tall to represent an actual height of 20 feet.

Answer:

164 minutes

Step-by-step explanation:

Assuming that Jerome's seed is maintained, we say that for every 1 mile, he takes 13 minutes and 40 seconds which is equivalent to[tex]13\frac {2}{3}[/tex] since 1 minute has 60 seconds hence [tex]\frac {40}{60}[/tex]=[tex]\frac {2}{3}[/tex]

Now if

1 mile = [tex]13\frac {2}{3}[/tex]

12 miles=??

We cross multiply hence 12\times[tex]13\frac {2}{3}=164[/tex]

Therefore, Jerome needs 164 minutes, equivalent to 2 hours 44 minutes

Answer:

Option E) is correct

If n is an odd number then 2(n+1) represents an even number.

Step-by-step explanation:

Let X=set of all odd numbers

that is [tex]X={\{1,3,5,7...}\}[/tex]

Let Y=set of all even numbers

that is [tex]Y={\{2,4,6,8...}\}[/tex]

Verify that 2(n+1) represents an even number where n is an odd number:

Put n=1 in 2(n+1) we get

2(1+1)=2(2)=4

Put n=3 in 2(n+1) we get

2(3+1)=2(4)=8

Put n=5 in 2(n+1) we get

2(5+1)=2(6)=12

and so on.

From above results we get 2(n+1) represents an even number and is belongs to the set Y when n is an odd number.

Therefore Option E) is correct

If n is an odd number then 2(n+1) represents an even number.

Answer: the answer that actually makes since is multiply 8 times 41.75 that also equals out to 334 which would be accurate

Step-by-step explanation:

Answer:

multiply 8 times 41.75

Step-by-step explanation:

i got it right on my test

Answer:

circumference is 59.6075

area is 282.743

Step-by-step explanation:

   To find the circumference and area of the circle, we need to first find the radius. This can be achieved using the distance formula.

   The distance formula goes as follows: for any two points on an coordinate plane, the distance can be calculated using a certain method. This method is the derived from the Pythagorean Theorem. Basically, you find the distance from right to left and square it, and then find the distance from up to down and square it. You add these two values together and then square root the whole thing. I know, its complicated.

   To apply this to your problem, we do 2-(-1) to find the distance from right to left (x-distance) and then we do 5-(-4) to find the distance from up to down (y-distance). 2-(-1)=3 and squaring that we get 9. 5-(-4)=9 and squaring that we get 81. Adding these two values together, we get 90 and square rooting it we get [tex]\sqrt{90}[/tex].

   The formula for circumference of a circle is 2Pi * radius and plugging in our values we get 2Pi * [tex]\sqrt{90}[/tex] which gives us approximately 59.6075.

   The formula for area of a circle is Pi * radius^2 and plugging in our values we get Pi * [tex]\sqrt{90}[/tex] ^2 which gives us approximately 282.743.

Answer:

[tex]y=8x-2[/tex]

Step-by-step explanation:

Here is the complete question: At a restaurant jars of tomato are stored in boxes in the pantry. each box contains 8 jars of tomato sauce. A cook uses 2 jars from 1 of the boxes. Which function shows the relationship between y, the total number of jars of tomato sauce remaining in the pantry, and x, the number of boxes in the pantry?

Given: Each boxes contain 8 jars of tomato sauce.

           Cook uses 2 jars from 1 of the boxes.

As we know total number of boxes is "x".

Number of jars in the pantry is [tex]8\ jars \times x\ boxes= 8x \ jars[/tex]

∵ cook uses 2 jars from one box.

∴ [tex]y=8x-2[/tex] ( y is used to show relationship)

The relationship between y, the total number of jars of tomato sauce remaining in the pantry, and x, the number of boxes in the pantry is [tex]y=8x-2[/tex].

Answer:

[tex]A=\$584.43[/tex]  

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=17\ years\\ P=\$150\\ r=8\%=8/100=0.08[/tex]  

substitute in the formula above

[tex]A=150(e)^{0.08*17}[/tex]  

[tex]A=150(e)^{1.36}[/tex]  

[tex]A=\$584.43[/tex]  

Answer:

[tex] \: \: \: \: \: \: 15 - d = 6 \\ = > - d = 6 - 15 \\ = > - d = - 9 \\ = > d = 9[/tex]

Verification :

[tex] \: \: \: \: \: \: 15 - d = 6 \\ = > 15 - 9 = 6 \\ = > 6 = 6[/tex]

The required polynomial that should be subtracted from the polynomial [tex]y^2-5y+1[/tex] to get the difference equal to 5  is [tex]y^2-5y-4[/tex]

Step-by-step explanation:

We need to find polynomial that should be subtracted from the polynomial [tex]y^2-5y+1[/tex] to get the difference equal to 5

Let the required polynomial be x

We are given:

[tex]y^2-5y+1-(x)=5[/tex]

We need to find the value of x

[tex]-x=5-y^2+5y-1\\-x=-y^2+5y+4[/tex]

Divide both sides by - 1

[tex]x=y^2-5y-4[/tex]

So, the required polynomial that should be subtracted from the polynomial [tex]y^2-5y+1[/tex] to get the difference equal to 5  is [tex]y^2-5y-4[/tex]

Keywords: Solving Polynomials

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43 pounds is a reasonable range for the total weigh of 6 packages.

Step-by-step explanation:

Given,

Number of packages shipped = 6

Weight of lightest = 24 pounds

Weight of heaviest = 67 pounds

Let,

a, b, c, d be the weight of other four packages.

24, a, b, c, d, 67 (written in lighter to heavier weight order)

Range is defined as the difference between the lowest and highest values.

Range = Highest weight - Lowest weight

Range = 67 - 24 = 43 pounds

43 pounds is a reasonable range for the total weigh of 6 packages.

Keywords: range, difference

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The reasonable range for the total weight of the 6 packages is 24 pounds to 67 pounds.

The reasonable range for the total weight of the 6 packages is 24 pounds to 67 pounds.

Since the lightest package weighs 24 pounds and the heaviest package weighs 67 pounds, any total weight between these two values would be reasonable.

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