An insurance agent receives 16% commission on every premium paid. How much commission is paid on a policy with a premium of $497.69?

Final answer:

The Miami Dolphins scored 14 points, while the Buffalo Bills scored 52 points, totaling 66 points as per the equation representing their scores.

Explanation:

Let's denote the number of points the Miami Dolphins scored as D. According to the question, the Buffalo Bills scored 24 more than twice the number of points that the Miami Dolphins did. This can be expressed as 2D + 24 for the Buffalo Bills' score. The total points scored by both teams is given as 66.

We can set up an equation to represent this situation:

D + (2D + 24) = 66

Simplify and solve for D:

Combine like terms: 3D + 24 = 66

Subtract 24 from both sides: 3D = 42

Divide both sides by 3: D = 14

So, the Miami Dolphins scored 14 points. We can then calculate the Buffalo Bills' score by plugging D into the Buffalo Bills' score equation:

2(14) + 24 = 28 + 24 = 52

Therefore, the Buffalo Bills scored 52 points.

In conclusion, the Miami Dolphins scored 14 points, and the Buffalo Bills scored 52 points.

Answer: There will be two different ways of doing so.

Step-by-step explanation:

Since we have given that

Total number of rocks =38

If we want to groups of 10 rocks or as single rocks then there are 2 different ways ;

Case I:

if we group into 10 rocks

there will be four sets in which Ist set contains 10 rocks

Second set contains 10 rocks

Third set contains 10 rocks

and Fourth set remains with 8 rocks only.

Case II:

if we group as single rocks .

There will be 38 sets .

Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side.

Coterminal angles are angles that have the same terminal sides in standard position.

Anytime we complete a full cycle( a complete revolution) we come back to the same terminal side.

Therefore to find all angles which are coterminal with [tex]-271\degree[/tex] we keep adding or subtracting [tex]360\degree[/tex].

For the given interval, that is, [tex]0\degree[/tex] to [tex]360\degree[/tex],

We add [tex]360\degree[/tex] so that we can obtain an angle coterminal with [tex]-271\degree[/tex] within this interval.

This means that

[tex]-271\degree[/tex] is coterminal with [tex]360\degree + \: -271\degree=89\degree[/tex]

Hence the correct and answer is D

Answer:

940 people

Step-by-step explanation:

since we know that 423 is 45% of the vote, we would do

45/100 =423/x, when you simplify the proportion, you find out that 940 people

From my research i found the answer to be that he rented 9 movies.

Final answer:

To find out how many movies Andrew rented, subtract the membership fee from the total bill, then divide by the cost per movie. This reveals Andrew rented 9 movies.

Explanation:

To solve how many movies Andrew rented this month, we first need to subtract the monthly membership fee from the total bill. Knowing the monthly membership fee is $5.00 and the total bill was $16.25, we can calculate the cost of movies rented alone.

First, subtract the membership fee from the total bill: $16.25 - $5.00 = $11.25. This is the amount spent on renting movies.

Next, divide the result by the cost per movie, which is $1.25 per movie. This gives us: $11.25 / $1.25 = 9.

Therefore, Andrew rented 9 movies this month.

In geometry, a solid may exist in three-dimensional space is a TRUE statement.

In geometry, a solid shape is a three-dimensional figure which has width, depth and height.

Examples of such solids are:

Pyramid,cone, cubes etc.

The study of such solid shapes is known as a solid geometry.

Hence, the statement:

In geometry, a solid may exist in three-dimensional space is a TRUE statement.

she reads 49 pages in one hour.

The answer is 49 pages per hour

x * 6 = 3

x = 3 : 6

x = 3/6

x = 1/2 or 0.5

That is 256

We get this by doing 4*4*4*4

so 4*4 is 16, then 16*4 is 64, then 64*4 is 256

So a 100lbs person would weigh 256 pounds on jupiter, or 4^4

Hello there,

Your correct answer is C your work is below

Ok so 4 to the 4th power is 256

we do this by multiplyg 4 times 4 times 4 times 4 and get 256

Also the exact weight of 200 pounds in jupiter is 510.40 and 512 is the nearest

If my answer helped please mark me as brainliest it would help thank you and have the best day ever!

Rule of trigonometric functions:-

sin a = cos(90 - a)

Here a = 90°.

sin 90 = cos (90 - 90)

1 = cos 0.

cos 0 = 1.

So the cos 0 = 1.

Answer:

Step-by-step explanation:

If sin 90 = 1

then cos 0 will be

as we know that

cosx = sin(90-x)

If we plug x = 0 ,

cos0  = sin 90 = 1

Answer:

[tex]t=5x[/tex]

Step-by-step explanation:

So the number of questions in an exam varies with the number of minutes to take the exam.

For each question there are 5 minutes allotted.

Lets say that there are 'x' number of questions in the exam and 't' is the total time taken to finish the exam, in minutes. So the time taken to complete the exam would be

[tex]5 \times x=5x[/tex]

Therefore, the equation relating the time taken to complete the exam and the number of questions is given by:

[tex]t=5x[/tex]

So there are two variables in the equation, 't', and 'x':

t - time taken to complete the exam

x - number of questions on the exam

The husband earns $42,000 per year.

Let's denote the husband's earnings as H.

According to the problem, the wife earns 16,000 less than twice what her husband earns. So, the wife's earnings can be represented as (2H - 16,000).

We know that together they earn 110,000 per year. This can be written as:

H + (2H - 16,000) = 110,000

Combining like terms, this equation simplifies to:

3H - 16,000 = 110,000

Add 16,000 to both sides to solve for H:

3H = 126,000

Divide both sides by 3:

H = 42,000

Therefore, the husband earns $42,000 per year.

The product is 3 because -3/4 * -4 is 3

ANSWER

[tex]x=\frac{14.5\degree}{3}+120\degree n\:or\:x=\frac{165.5\degree}{3} +120\degree n[/tex], for [tex]n\ge 0[/tex], where [tex]n[/tex] is an integer.

EXPLANATION

We want to solve the trigonometric equation;

[tex]Sin(3x)=\frac{1}{4}[/tex]

Since sine ratio is positive, it means the argument,[tex](3x)[/tex] is either the first quadrant or second quadrant.

This implies that;

[tex](3x)=arcsin(\frac{1}{4})[/tex]

[tex](3x)=14.5\degree[/tex] in the first quadrant.

Or

[tex](3x)=180\degree-14.5\degree=165.5\degree[/tex] in the second quadrant.

Since the sine function has a period of [tex]360\degree[/tex], The general solution is given by

[tex](3x)=14.5\degree+360\degree n\:or\:(3x)=165.5\degree +360\degree n[/tex],for [tex]n\ge 0[/tex], where [tex]n[/tex] is an integer.

Dividing through by 3, we obtain the final solution to be;

[tex]x=\frac{14.5\degree}{3}+120\degree n\:or\:x=\frac{165.5\degree}{3} +120\degree n[/tex], for [tex]n\ge 0[/tex], where [tex]n[/tex] is an integer.

The 132 tickets is the childrens tickets and the adult tickets together. So to find the adult tickets you subtract the childrens tickets from the full amount. To find the amount of adult tickets you would take the group of adults which is '1' and the childrens tickets which is '5' so in total six. Then you will divide 132 by six and that should be 22.

Answer:

[tex]y=\dfrac{3}{4}x+7\dfrac{1}{4}[/tex]

Step-by-step explanation:

[tex]k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\ \iff\ m_1m_2=-1[/tex]

Let [tex]k:4x+3y=6\to 3y=-4x+6\ \ \ \ |:3\\\\y=-\dfrac{4}{3}x+2\\\\m_1=-\dfrac{4}{3}[/tex]

[tex]l:y=m_2x+b\\\\l\ \perp\ k\ \iff\ -\dfrac{4}{3}m_2=-1\qquad|\cdot\left(-\dfrac{3}{4}\right)\\\\m_2=\dfrac{3}{4}\\\\l:y=\dfrac{3}{4}x+b[/tex]

The line l passes through the point (-3, 5).

Substitute the coordinates of the point to the equation of the function l:

[tex]5=\dfrac{3}{4}(-3)+b\\\\5=-\dfrac{9}{4}+b\\\\5=-2\dfrac{1}{4}+b\qquad|+2\dfrac{1}{4}\\\\b=7\dfrac{1}{4}[/tex]

Finally [tex]l:y=\dfrac{3}{4}x+7\dfrac{1}{4}[/tex]

Pythagorean Theorem:  

500^2 = 300^2 + x^2  

250,000 = 90,000 + x^2  

160,000 = x^2  

x = +/- 400 use the positive root  

height is 400ft

The kite is 400 feet above the ground.

To determine how high the kite is above the ground if it is 500 feet of string out and the horizontal distance between Tyler and the kite is 300 feet, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the adjacent and opposite sides).

In this scenario, imagine a right triangle where the string of the kite represents the hypotenuse, the horizontal distance from Tyler to the point directly underneath the kite represents the adjacent side, and the height of the kite above the ground represents the opposite side.

The length of the hypotenuse (the string) is given as 500 feet, and the length of the adjacent side (the horizontal distance) is 300 feet. To find the height of the kite (the opposite side), we apply the Pythagorean theorem:

[tex]\( c^2 = a^2 + b^2 \rightarrow 500^2 = 300^2 + b^2 \rightarrow 250000 = 90000 + b^2 \rightarrow \\b^2 = 250000 - 90000 \rightarrow b^2 = 160000 \rightarrow b = \sqrt{160000} \rightarrow b = 400 )[/tex]

Therefore, the height of the kite above the ground is 400 feet.

Answer: 12.817

Step-by-step explanation: hope it helps! PLEASE SELECT ME BRAINLIEST!♡

The answer is: [tex](5x^{6}+6y^{7}) (5x^{6} - 6y^{7})[/tex]

To get answer: Factor [tex]25x^{12} -36y^{14}[/tex]

[tex]-36y^{14} +25x^{12}[/tex]

[tex]= (6y^{7} +5x^{6})(-6y^{7}+5x^{6})[/tex]

(5x⁶+6y⁷)×(5x⁶−6y⁷)

This is your answer hope this helps! Have a good day/night whatever time it is near you!

Step 1. Add 72 to both sides

5y = 7 + 5x + 72

Step 2. Simplify 7 + 5x + 72 to 5x + 79

5y = 5x + 79

Step 3. Divide both sides by 5

y = 5x + 79/5

B is your answer.

(1000x0.0325)/100= 32.50.

Hope this helps & good luck. :)

they all split it and is each going to have 6 dollars each plus the extra 2 for cleaning so 8 dollars each.

Answer - $8 Dollars

Each girl received a total of $8 after dividing the $24 from gardening equally among four girls and adding an extra $2 given by Mrs. Day for cleaning up.

The question asks how much money each girl received in total for helping with gardening and cleaning up. To find the answer, we first calculate how much each girl got from the $24 shared equally and then add the additional money each received from Mrs. Day.

Therefore, each girl received $8 in total from helping Mr. and Mrs. Day with gardening and cleaning up.

Answer:  There are 138 short sleeves t-shirts.

Step-by-step explanation:

Given : In August Emily's clothing store sold 460 shirts with the ratio of short sleeve to long sleeve being 3:7.

Let the number of short sleeves shirts be 3x and the number of long sleeves shirts be 7x.

Then, according to the given question,  we have

[tex]7x+3x=460\\\\\Rightarrow\ 10x=460\\\\\Rightarrow\ x=46[/tex]

Now, the number of short sleeves shirt = 3(46)=138

Hence , there are 138 short sleeves shirts.

Answer:

the answer is b

Step-by-step explanation:

After 5 months, they would both have the same cost. If you were to cancel after 9 months, you would cancel $320 for the first option and $360 for the second option.

To solve this, you need to create an equation. You get $50+30x and let x=number of months. This would tell you how much you need to pay for option 1. In option 2, you would have $40x. This is because there is no setup fee and so there would only be the monthly cost.We then set thos equations both equal to each other because the first question asks for the options to be the same price. For the second question, you would need to substitute 9 for the x in those equations. That would have you find out which is more expensive.

Answer:

So, given a quadratic function, y = ax2 + bx + c, when "a" is positive, the parabola opens upward and the vertex is the minimum value. On the other hand, if "a" is negative, the graph opens downward and the vertex is the maximum value.

Step-by-step explanation:

100% on edg :)

The quadratic function, y = ax²+ bx + c opening upward if the value of 'a' is positive.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have quadratic function,

y = ax² + bx + c

If the value of 'a' is negative, then the function will be opening downside and if the value of 'a' is positive, then the function will be opening upside.

Let say a = 1, b = 1, c = 1

y = x² + x + 1 (upside)

If a = -1, b = 1, c = 1

y = -x² + x + 1 (downside)

Thus, the quadratic function, y = ax²+ bx + c opening upside if the value of 'a' is positive.

Learn more about quadratic equations here:

brainly.com/question/2263981

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