Write a system of equations to solve the following scenario. Twins Jon and Ron together earned $96,000 last year. Ron earned $8,000 more than three times what Jon earned. How much did each of the twins earn? Use the variable j to represent the amount Jon earned. Use the variable r to represent the amount Ron earned.

The square pyramid-shaped clock has a surface area of 144 square inches, including the base.

Surface area is the total area of the exposed surfaces of a 3-dimensional object, or an object with length, width and height. It is the sum of all of the areas of the faces of the object, including curved surfaces. It is measured in square units, such as square centimeters or square meters. Surface area is important in fields such as engineering and materials science, where it is used to calculate the amount of material needed for a given object.

To calculated to the total area, multiply by the length of the base, b, by the height, h. A = b × h is the equation- for to the area, A, of a square or rectangle area.

Surface area and arc length of curves differ in a number of ways, one of which is that surface area cannot simply be defined as the maximum area of polyhedral shapes that approximate a given smooth surface.

Since each of the triangle has one side as 9,

if we split it down to the middle and should rearrange it,

we get a 3×9 rectangle

that is = 27 inches

there are 4 of for those = 4x27 = 108.

the square in the middle is = 36 inches

36+108= 144

144 square inches

The surface area of the clock is 144 square inches.

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Answer:

C

Step-by-step explanation:

We will have to distribute because volume equals length times width times height

The vοlume οf the cοmpοsite sοlid is 648π cubic inches.

Vοlume is the amοunt οf space that an οbject οccupies in three-dimensiοnal space. It is a measure οf hοw much a cοntainer can hοld οr hοw much material an οbject cοntains.

Tο find the vοlume οf the cοmpοsite sοlid, we need tο first find the vοlumes οf the twο hemispheres and the cylinder separately, and then add them up.

The radius οf the cylinder is half the diameter, sο it is r = 12/2 = 6 inches. The height οf the cylinder is h = 10 inches. Therefοre, the vοlume οf the cylinder is:

V_cylinder = πr²h = π(6)²(10) = 360π cubic inches

The radius οf each hemisphere is alsο 6 inches (since it is the same as the radius οf the cylinder). The vοlume οf οne hemisphere is:

V_hemisphere = (2/3)πr³ = (2/3)π(6)³ = 144π cubic inches

The vοlume οf the twο hemispheres is twice this amοunt, οr:

V_hemispheres = 2V_hemisphere = 288π cubic inches

Therefοre, the vοlume οf the cοmpοsite sοlid is the sum οf the vοlumes οf the cylinder and the twο hemispheres:

V_cοmpοsite = V_cylinder + V_hemispheres = 360π + 288π = 648π cubic inches

Sο the vοlume οf the cοmpοsite sοlid is 648π cubic inches.

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Part A: 10% APR compounded monthly: EAR = 10.47%.

Part b: 10% APR compounded annually: EAR = 10%.

Part c: 9% APR compounded daily: EAR = 9.42%

Part A: 10% APR compounded monthly,

Effective annual interest rate (EAR):

EAR = [tex](1 + \frac{I}{n} )^{n }[/tex] - 1

I is the annual percentage rate/nominal interest rate

n is the number of compounding periods (in a year)

For monthly compounding.

EAR = [tex](1 + \frac{0.10}{12} )^{12}[/tex] - 1

EAR = 10.47%

Part b: 10% APR compounded annually,

For annual compounding.

The effective yearly interest rate will be the same as the nominal interest rate if the interest rate gets compounded annually.

EAR = Nominal interest rate

EAR = 10%

Part c: 9% APR compounded daily.

EAR = [tex](1 + \frac{0.09}{365} )^{365}[/tex] - 1

EAR = 9.42%

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Answer:

Step-by-step explanation:

44

Answer:

Step-by-step explanation:

Let [tex]c[/tex] be the total cookies.

[tex]\frac{1}{2}c+12+10=c[/tex]

[tex]\frac{1}{2}c+22=c[/tex]

[tex]c+44=2c[/tex]     (multiplied both sides by 2)

[tex]44=c[/tex]             (subtracted c from both sides)

[tex]c=44[/tex]

She began with 44 cookies.

The line DE which divides the main triangle is parallel to AB of the original triangle. This is a true statement.

A parallel line is defined as the type of line that exists between two lines on the same plane that can never never intersect or meet each other.

Line AB is said to be parallel to line DE because the line DE correctly divides both line BC and CA at a point that triangle CDE is similar to triangle CBA with a scale factor of = 4

That is = line BC/DB = AC/EA

= 28/7 = 32/8 = 4

Therefore the line DE is parallel to line AB as both will never meet till infinity.

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To find the area of a triangle in three-dimensional space, we can use the cross product of two vectors that lie in the plane of the triangle. We can use the vectors formed by subtracting the coordinates of one vertex from the other two vertices.

Let's take A as our reference vertex. Then the vectors AB and AC can be calculated as follows:

AB = B - A = (2, 3, 5) - (1, 1, 2) = (1, 2, 3)

AC = C - A = (1, 5, 5) - (1, 1, 2) = (0, 4, 3)

To find the area of the triangle, we need to take the magnitude of the cross product of AB and AC and divide by 2:

Area = |AB x AC| / 2

where x denotes the cross product. The cross product of AB and AC can be calculated as follows:

AB x AC = (23 - 54, 50 - 13, 14 - 20) = (-7, -3, 4)

Taking the magnitude of this vector gives:

|AB x AC| = sqrt((-7)^2 + (-3)^2 + 4^2) = sqrt(74)

Therefore, the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5) is:

Area = |AB x AC| / 2 = sqrt(74) / 2

So, the area of the triangle is (1/2) sqrt(74) square units.

The equation to model the fish population y in a fishery with a linear growth rate of 40 new fish each season and an initial population of 1250 fish can be written as:

The equation to model the fish population y in a fishery with a linear growth rate of 40 new fish each season and an initial population of 1250 fish can be written as:

y = 40x + 1250

where x is the number of seasons.

To find out how many seasons it will take for the population to reach 1690 fish, we can substitute y = 1690 into the equation and solve for x:

1690 = 40x + 1250

440 = 40x

x = 11

So it will take 11 seasons for the population to reach 1690 fish.

For the second fish population that grows by 60 new fish each season with an initial population of 1100 fish, the equation to model the population can be written as:

y = 60x + 1100

To find out after how many seasons they will have the same population, we can set the two equations equal to each other and solve for x:

40x + 1250 = 60x + 1100

20x = 150

x = 7.5

So it will take 7.5 seasons for the two populations to have the same population.

(Note: In the question, A season is not defined  and as such, we assume it to be one year for simplicity.)

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Answer:

Your answer should be -2x

Step-by-step explanation:

I am not sure if your teacher taught you the short cut way of doing derivatives yet.

That equation is just a long way to do derivatives. The picture below shows the shortcut way to do dervatives.

So basically you plug in x+h into the equation given to you.

[tex]\frac{g(x+h)-g(x)}{h} \\\\\frac{(6-(x+h)^2)-g(x)}{h} \\\\\frac{(6-(x^2+2xh+h^2))-(6-x^2)}{h}\\\\ \frac{(6-x^2-2xh-h^2)-(6-x^2)}{h}\\\\ \frac{6-x^2-2xh-h^2-(6-x^2)}{h}\\\\ \frac{6-x^2-xh-h^2-6+x^2}{h}\\\\[/tex]

[tex]\frac{(x^2-x^2)+(6-6)-2xh-h^2}{h}\\\\ \frac{(0)+(0)-2xh-h^2}{h}\\\\ \frac{-2xh-h^2}{h}\\\\ \frac{h(-2x-h)}{h}\\\\ -2x-h[/tex]

Plug in h = 0

then your answer is -2x

Answer: It's not clear what measures 3.8 and 9.2 represent. However, if they represent angles in degrees, then the range of these measures would be:

- If there are no restrictions on the angles, the range would be [0°, 360°), meaning any angle between 0 degrees and 360 degrees (excluding 360 itself).

- If the angles are restricted to be acute angles (less than 90 degrees), then the range would be (0°, 90°), meaning any angle between 0 degrees and 90 degrees (excluding 0 and 90 themselves).

- If the angles are restricted to be obtuse angles (between 90 and 180 degrees), then the range would be (90°, 180°), meaning any angle between 90 degrees and 180 degrees (excluding 90 and 180 themselves).

- If the angles are restricted to be right angles (exactly 90 degrees), then the range would be {90°}, meaning only the angle of 90 degrees.

Step-by-step explanation:

Answer:

76% of 825 is 627.

Step-by-step explanation:

100%= 825

1%= 825÷100

= 8.25

627÷8.25= 76%

Answer:

To solve this problem, we need to divide the total number of students by the number of people that can sit in each row.

44 students ÷ 8 people per row = 5.5 rows

Since we cannot have half a row, we round up to the nearest whole number. Therefore, they will fill up 6 rows in the movie theater.

Here's a simple drawing that explains the solution:

Row 1: 8 students

Row 2: 8 students

Row 3: 8 students

Row 4: 8 students

Row 5: 8 students

Row 6: 4 students

The first five rows are full with 8 students each, and the sixth row has the remaining 4 students. Therefore, a total of 6 rows will be filled with students.

Answer:

88 years old

Step-by-step explanation:

Let the age = x.

400 - 3x = 136

-3x = -264

x = 88

Answer: 88 years old

Answer:

2500 ml

Step-by-step explanation:

In order to convert liters to ml,  we need to multiply the volume value by 1000.

[tex]2.5\times 1000=2500[/tex]

The formula for the linear function in the graph is f(x) = -2x + 4.

The graph is a data structure that is used to represent relationships between objects. It is composed of nodes (or vertices) that are connected by edges (or lines). Graphs can be used to represent many types of data, such as networks of people, roads, and even abstract concepts like language. Graphs are used in a variety of fields, such as computer science, mathematics, and sociology. They allow for efficient storage and retrieval of data, as well as efficient traversal of the data.

The graph shown below is a linear graph with a slope of -2 and a y-intercept of 4.

To find the formula for the linear function, we can use the slope-intercept form, which is y = mx + b. In this equation, m is the slope of the line and b is the y-intercept.

Therefore, the formula for the linear function in the graph is f(x) = -2x + 4.

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complete question:

Find a formula for the linear function depicted in the following graph.

f(x)=

The Expression came in two parts, we started by solving the first part and getting a whole number and the second part was used to divide the first part.

The answer is 12005

Given Data

we have the expression

7^6+7^5−7^4 by 11

The dividend = 7^6+7^5−7^4

The divisor = 11

Let us express the dividend as a whole number

7^6+7^5−7^4 = 117649 + 16807 - 2401

7^6+7^5−7^4 = 132055

Hence the expression 7^6+7^5−7^4 by 11

= 132055/11

= 12005 ans

Answer:

To find the total amount in Mr. Hunter's account, we need to use the formula:

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

where:

A = the total amount

P = the principal amount (the initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $900, r = 0.06, n = 1 (compounded annually), and t = 2.

So, plugging in these values, we get:

A = 900(1 + 0.06/1)^(1*2)

A = 900(1.06)^2

A = 900(1.1236)

A = $1,011.24

Therefore, the total amount in Mr. Hunter's account after 2 years is $1,011.24.

The answer of the given question based on finding the area of the triangle the answer is  the area of the given triangle is 15 square units.

A triangle is three-sided polygon, which means it is closed shape with three straight sides and three angles. Triangles are some of  most basic shapes in geometry and can be found in the many different contexts, from simple constructions to complex mathematical models.

To find the area of the triangle, we can use the formula A = (1/2)bh, where A is the area, b is the base, and h is the height.

Looking at the given triangle, we can see that the base is the line segment from (0, 0) to (6, 0), which has a length of 6 units.

The third vertex of the triangle appears to be at the point (2, 5), so we need to find the distance from this point to the base.

The equation of the base is y = 0, so the distance from the point (2, 5) to the base is:

d = |0(2) - 1(5) + 0| / sqrt(0² + 1²) = 5 / 1 = 5 units

Therefore, the height of the triangle is 5 units.

Now we can use the formula A = (1/2)bh to find the area:

A = (1/2)(6)(5) = 15 square units

Therefore, the area of the given triangle is 15 square units.

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Option (a) is correct i.e., the margin of error is equal to ± 0.8 and the confidence interval is equal to 10.5

In a random survey sample,  a “margin of error” is a measurement (calculation) that takes into consideration the difference between actual and sample data findings.

Let μ be the unknown population mean. To determine the ‘population mean’ we use the sample mean as a point estimate (approximate) μ.

The “margin of error” determines how far the actual population value will likely be from the survey's value. It evaluates the accuracy (precisely) of a survey's results. The survey's results are more likely to be accurate (precise) values if the “margin of error” is less.

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Complete question:

After a set of surveys was compiled and analysed , the mean value was reported as 10.5 ± 0.8 . Select the true statement for this data

a) The margin of error is equal to ± 0.8 and the confidence interval is equal to 10.5.

b) The estimate is equal to 10.5 and the margin of the error is equal to

± 0.8.

c) The estimate is equal to 10.5 and the confidence interval is equal to

± 0.8.

d) The margin of error is  equal to 10.5 and the estimate is equal to ± 0.8.

Answer:

The estimate is equal to 10.5 and the margin of error is equal to ± 0.8.

Scott Salman's net pay after subtracting all his deductions is $1,185.97.

How to calculate interest ?

To calculate Scott Salman's net pay after all deductions, we need to first determine his gross pay based on his variable commission.

Sales up to $20,000 will earn him a commission of 3%, which is $600. Sales between $20,000 and $30,000 will earn him a commission of 4%, which is $400. For sales over $30,000, he will receive a commission of 6%. In this case, the sales over $30,000 are $45,550 - $30,000 = $15,550, so his commission on this amount is $933.

Adding up all three commissions, Scott's gross pay is $1,933 ($600 + $400 + $933).

Next, we need to calculate his total deductions. FICA and Medicare deductions are based on a percentage of gross pay, which is 7.65%. For Scott, this comes out to be $147.70 ($1,933 x 7.65%).

Federal and state withholdings are calculated based on his tax bracket and filing status. Assuming he is filing jointly with his spouse, we can estimate his federal withholding to be $345 and state withholding to be $120.

State disability insurance varies by state and cannot be estimated without knowing where Scott lives. Assuming a standard rate of 1%, this comes out to be $19.33 ($1,933 x 1%).

Adding up all these deductions, we get a total of $632.03 ($147.70 + $345 + $120 + $19.33).

In addition, Scott has also made contributions towards his retirement plan, savings bond, and charitable donations. His retirement contribution is $45, his savings bond is $50, and his charitable contributions are $20. Adding these up, his total additional deductions come to $115.

Subtracting his total deductions from his gross pay, we get Scott's net pay:

$1,933 - $632.03 - $115 = $1,185.97.

Therefore, Scott Salman's net pay after subtracting all his deductions is $1,185.97.

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Using the percentages we know that the required sales tax percentage in the given situation is 1%.

A sales tax is a fee that is paid to the government when specified goods and services are sold. T

Typically, laws permit the vendor to charge the customer the tax at the time of purchase.

When a tax on goods or services is paid to a governing body directly by a customer, it is commonly called a usage tax.

The sale and use tax is frequently exempted for some goods and services, including food, education, and medical.

A sales tax is similar to a value-added tax (VAT) that is levied on products and services.

Key distinctions can be found in the comparison with sales tax.

So, the sales tax percentage would be:

= 0.55/55*100

= 0.01

= 1%

Therefore, using the percentages we know that the required sales tax percentage in the given situation is 1%.

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Answer:

A) True

Step-by-step explanation:

The statement is true. Conditional probability is a fundamental concept in probability theory that allows us to calculate the probability of an event given that another event has already occurred. The notation for conditional probability is P(B|A), which represents the probability of event B occurring given that event A has already occurred. In other words, we restrict our attention to the sample space where event A has occurred and calculate the probability of event B in that space.

Answer:

Is the answer multiple choice?

Step-by-step explanation:

In this case, Sarah has paid a total of $595 for her membership and Cheyenne has paid a total of $605 for her membership. This is because Sarah's gym had a $45 sign up fee and cost $50 per month, while Cheyenne's gym cost $55 a month with no sign up fees.

Membership is a type of relationship between a person and an organization or group. It implies that the person has certain responsibilities and privileges as a member of the group. Depending on the organization or group, these responsibilities and privileges might include attending meetings, paying dues or fees, voting privileges, access to services and discounts, or having the right to hold office.

Cheyenne's gym is more expensive due to its lack of a sign up fee and the higher monthly rate of $55. However, Sarah has paid more money overall due to her sign up fee. Even though Cheyenne's gym is more expensive on a month-to-month basis, the sign up fee makes Sarah's total cost higher.

The difference in cost between Sarah and Cheyenne's memberships is not substantial, but it is worth noting that the sign up fee can make a difference in the overall cost of a membership. It is also important to factor in the cost of any additional fees when comparing gym memberships. This can help someone determine which gym membership is a better value for their money.

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The difference in interest paid between the two loans is the answer is option (c) $14,515.43.

What is the interest?

Calculate simple interest, and multiply the principal amount by the interest rate and the time. The formula written out is "Simple Interest = Principal x Interest Rate x Time." This equation is the simplest way of calculating interest.

First, we need to calculate the monthly payment for the loan at 15%:

PV = $40,000

i = 0.15/12 = 0.0125

n = 6 years * 12 months/year = 72 months

Using the formula for minimum monthly payment for an amortized loan, we get:

[tex]P = i * PV / (1 - (1 + i)^{(-n)})[/tex]

= 0.0125 * $40,000 / (1 - (1 + 0.0125)⁻⁷²) = $797.95

So Jenny's monthly payment is $797.95 for the 6-year term of the loan.

The total amount paid over the life of the loan at 15% is:

Total paid = P * n = $797.95 * 72 = $57,471.44

The interest paid at 15% is:

Interest paid = Total paid - PV = $57,471.44 - $40,000 = $17,471.44

Now, let's repeat the same calculation for the loan at 5%:

PV = $40,000

i = 0.05/12 = 0.0041667

n = 6 years * 12 months/year = 72 months

Using the same formula, we get:

P = i * PV / (1 - (1 + i)^(-n)) = 0.0041667 * $40,000 / (1 - (1 + 0.0041667)^(-72)) = $630.48

So Jenny's monthly payment would have been $630.48 for the 6-year term of the loan if she did not have a bankruptcy.

The total amount paid over the life of the loan at 5% is:

Total paid = P * n = $630.48 * 72 = $45,434.56

The interest paid at 5% is:

Interest paid = Total paid - PV = $45,434.56 - $40,000 = $5,434.56

The difference in interest paid between the two loans is:

$17,471.44 - $5,434.56 = $12,036.88

Therefore, The difference in interest paid between the two loans is the answer is option (c) $14,515.43.

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The sale price of the desk is $241.32 if, The regular price of a desk is $484.77. This week, it is on sale for $243.45 off.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Given that The regular price of a desk is $484.77. This week, it is on sale for $243.45 off.

To find the sale price of the desk, we need to subtract the amount of the discount from the regular price:

Sale price = Regular price - Discount

Discount = $243.45

Regular price = $484.77

So, substituting the values, we get:

Sale price = $484.77 - $243.45

Sale price = $241.32

Therefore, the sale price of the desk is $241.32.

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Answer: Sure, I'd be happy to help!

There are two possible outcomes for each coin flip (heads or tails), so there are 2^3 = 8 possible outcomes for flipping a coin three times in a row.

One way to represent the sample space is to create a table or list:

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT

Another way to represent the sample space is to create a tree diagram, where each branch represents a coin flip and the end points represent the final outcome of three coin flips:

   H             T

  / \             / \

 H   T        H   T

/ \ / \         / \ / \

H  H T  H       H  T T  H

/ / // \ / / //

H H H H T T H H H T T T H

Each branch of the tree represents a possible outcome for a particular coin flip. The final outcomes are represented at the end points of the tree.

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

To do this very simply, you need to input every value of k into the equation that the sigma notation asks of you and then sum them all together. You can do this question simply by inputting k = 1,2,3,4 into the equation and adding all the values together. (the bottom sigma value k=1 is the initial value of what you start with and the final value at the top is the value you need to get to by adding 1 to k each time and putting it in the equation every time i.e. think of it as 1 through 4 values you need to input into the equation and add together)

2(3^1-1) = 2

2(3^2-1) = 6

2(3^3-1) = 18

2(3^4-1) = 54

After adding them, you get 80.

Answer:

s₄ = 80

Step-by-step explanation:

[tex]\displaystyle s_4=\sum^4_{k=1}2\left(3^{n-1}\right)[/tex]

The given sigma notation means the sum of the series with nth term 2(3ⁿ⁻¹), starting with n = 1 and ending with n = 4.

As 2(3ⁿ⁻¹) is exponential, the series is geometric.

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Comparing 2(3ⁿ⁻¹) with the general form of a geometric sequence:

The formula for the sum of the first n terms of a geometric series is:

[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

Therefore, substitute a = 2, r = 3 and n = 4 into the sum formula to find the sum of the first 4 terms of the geometric series:

[tex]\implies S_4=\dfrac{2(1-3^4)}{1-3}[/tex]

[tex]\implies S_4=\dfrac{2(1-81)}{-2}[/tex]

[tex]\implies S_4=\dfrac{2(-80)}{-2}[/tex]

[tex]\implies S_4=\dfrac{-160}{-2}[/tex]

[tex]\implies S_4=80[/tex]

Therefore, the sum of the first 4 terms of the geometric series is 80.