How much should be invested at 7% compounded daily for 15 years to make $200,000?

Answer:

area = 82 cm²

Step-by-step explanation:

The figure comprises a trapezoid, a triangle and a square.

Calculating areas of the three shapes separately and then adding them will give us the required area of the composite figure.

Area of square : (side)²

= (2)²

= 4 cm²

Area of triangle : ½ × b × h

= ½ × 3 × 12

= 3 × 6

= 18 cm²

Area of trapezoid : ½ × (a + b) × h

= ½ × (5+5) × 12

= ½ × 10 × 12

= 5 × 12

= 60 cm²

Now, area of the composite figure :

= 4 + 18 + 60

= 22 + 60

= 82 cm²

Answer:

Step-by-step explanation:

If you exclude the square on the bottom, you have a trapezoid with bases of 5 cm and 8 cm and the height of 12 cm.

Its area is:

Add the area of the square with sides of 2 cm:

Total area is:

Step-by-step explanation:

Simply graph the two equations....the intersection of the two graphs is the solution

There are 384 ways to arrange these given letters as per the given situation.

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Given, different ways can the 8 letters a, b, c, d, e, f, g, and h be arranged if the letters a and b must be next to one another, the letters c and d must be next to one another, the letters e and f must be next to one another, and the letters g and h must be next to one another.

In this question, we have 2 ways where A and B (AB, BA) are next to each other and 2 ways where C and D (CD, DC) are next to each other.  2 ways where g and h (gh, hg) are next to each other and 2 ways where e and f (ef, fe) are next to each other.

The total number of arrangements is = 4! * 2 * 2 *2*2

The total number of arrangements is = 24 * 16

The total number of arrangements is = 384

Therefore, the Different ways to arrange these letters are 384.

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The function represents exponential decay with a percentage rate of decrease of 9.8%.

The given exponential function y = 660(0.902) represents decay because the base of the exponent is less than one.

This means that the output value of the function will decrease as the input value increases.

To determine the percentage rate of decrease, we need to find the value of the base of the exponent subtracted from one and then multiply it by 100.

The base of the exponent is 0.902, so we subtract it from one to get 0.098.

Multiplying by 100 gives us a percentage rate of decrease of 9.8%.

This means that for every unit increase in the input value, the output value of the function will decrease by approximately 9.8%.

For example, if the input value increases from 1 to 2, the output value will decrease by 9.8%, and if the input value increases from 2 to 3, the output value will again decrease by 9.8%.

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Answer:

d. alternate interior angles are congruent

Answer: 980

Step-by-step explanation:

Answer:

980

Step-by-step explanation:

I really don't think you need an explanation

The next terms of the sequences 1; 2; 4; 7; 11; ... and -3; 0; 3; 6; ... are 16, 22 and 9, 12.

The given sequence is: 1; 2; 4; 7; 11; ...

To get the next term, we need to observe the differences between consecutive terms:

2-1 = 1; 4-2 = 2; 7-4 = 3; 11-7 = 4

The differences are increasing by 1 in each step. So, to get the next term, we add 5 to the last term:

11 + 5 = 16

Similarly, to get the term after that, we add 6 to the previous term:

16 + 6 = 22

Therefore, the next two terms of the sequence are 16 and 22, and the term-to-term rule is to add consecutive integers starting from 1 to the previous term.

The given sequence is: -3; 0; 3; 6; ...

To get the next term, we add 3 to the previous term:

6 + 3 = 9

Similarly, to get the term after that, we add 3 to the previous term:

9 + 3 = 12

Therefore, the next two terms of the sequence are 9 and 12, and the term-to-term rule is to add 3 to the previous term.

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Check the picture below.

\(\cfrac{17.5+14}{17.5}~~ = ~~\cfrac{x}{12.5}\implies \cfrac{(17.5+14)(12.5)}{17.5}~~ = ~~x\implies 22.5=x\)

The sampling distribution of the difference in the sample mean length of candles between Machine 1 and Machine 2 is approximately normally distributed with a mean of 0 and a standard deviation of 0.0212 centimeters.

When we take a random sample of 49 candles from each machine, the sampling distribution of the difference in the sample mean length of candles follows a normal distribution. The shape of this distribution is symmetric and bell-shaped.

This means that the majority of the differences in sample means will be close to zero, representing little to no difference between the machines. The center of the sampling distribution is at 0, indicating that, on average, there is no difference in the sample mean length between the two machines.

The variability of the sampling distribution is represented by the standard deviation, which is calculated using the formula for the standard error of the difference in sample means. In this case, the standard deviation is 0.0212 centimeters, which indicates the average amount of variation or spread in the differences of sample means.

It's important to note that the shape, center, and variability of the sampling distribution are based on the assumptions of random sampling and independence of the samples from each machine.

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The real solutions of the polynomial equation x⁴ = 16 are x = ±2.To find the real or imaginary solutions of the polynomial equation x⁴ = 16, we can start by rewriting it as x⁴ - 16 = 0.

We can then factor the equation as a difference of squares: (x²)² - 4² = 0. Now, we have a quadratic equation in the form a² - b² = 0, which can be factored using the difference of squares formula: (x² - 4)(x² + 4) = 0. From this equation, we get two possible cases: Case 1: x² - 4 = 0. Solving for x, we have: x² = 4; x = ±2. Case 2: x² + 4 = 0.  

This equation has no real solutions because the square of a real number is always positive. Therefore, the real solutions of the polynomial equation x⁴ = 16 are x = ±2.

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Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

Maria can arrange the books on her shelf in (n-2)! ways, where n represents the total number of books excluding the first and last spots.

Since Maria has already decided to place "Pride and Prejudice" in the first spot and "Little Women" in the last spot, the remaining books can be arranged in between these two fixed positions. The number of ways to arrange the books in the remaining spots depends on the total number of books excluding the first and last spots.

Let's say Maria has a total of n books (including "Pride and Prejudice" and "Little Women"). Since these two books are fixed, she needs to arrange the remaining (n-2) books in the remaining spots.

The number of ways to arrange (n-2) books is given by (n-2)!. The factorial (n!) represents the number of ways to arrange n distinct objects.

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To show that the closure of a relation R with respect to a property P, if it exists, is the intersection of all relations with property P that contain R, we need to prove two things:

1. The closure of R with respect to P is a subset of every relation with property P that contains R.

2. The intersection of all relations with property P that contain R is a subset of the closure of R with respect to P.

Let's proceed with the proof:

1. The closure of R with respect to P is a subset of every relation with property P that contains R:

Assume that C is the closure of R with respect to P, and let's consider any relation S that contains R and has property P. We need to show that C ⊆ S.

Since C is the closure of R with respect to P, it means that C satisfies property P, and C contains R. Since S is a relation that contains R and has property P, it also satisfies property P and contains R.

Now, if x and y are two elements in C, then there exists a sequence of elements (x₁, x₂, ..., xₙ) such that x = x₁, y = xₙ, and (xi, xi+1) ∈ R for each i = 1 to n-1. Since R is a subset of S, (xi, xi+1) ∈ S for each i = 1 to n-1.

Therefore, we can conclude that (x, y) ∈ S, which means C ⊆ S. This holds for any relation S that contains R and has property P.

2. The intersection of all relations with property P that contain R is a subset of the closure of R with respect to P:

Assume that I is the intersection of all relations with property P that contain R. We need to show that I ⊆ C, where C is the closure of R with respect to P.

Since I is the intersection of all relations with property P that contain R, it means that I satisfies property P, and I contains R.

Now, let's consider any pair (x, y) ∈ I. By definition of intersection, (x, y) ∈ S for every relation S with property P that contains R. Therefore, (x, y) ∈ C as well since C is the closure of R with respect to P, and C contains R.

Hence, we can conclude that I ⊆ C.

Combining both proofs, we have shown that the closure of R with respect to P is the intersection of all relations with property P that contain R.

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Answer:

20 miles.

Explanation:

2x + 20 = 3x

x = miles driven

The left side of the equation represents Laguna's, and the right side Salvatori's.

You can multiply the miles driven by their price per mile. This gives you (2x) on the left, for Laguna's $2 per mile, and (3x) for Salvatori's $3 per mile.

The (+20) represents the initial payment for Laguna's, but Salvatori's doesn't have this, so we can leave it out.

Finally, eliminate.

Subtract 2x from 3x on the right. This leaves you with 20 = 1x.

Answer:

They are shown together to find units of 4 total

4 (j/ total + s/total )

= 4 (1/4 + 3/4)

=  4/4 + 12/4

= 4 cups total

Then show letters and work out for j + s

4(j/3 + 3/4) = 4

4j/3 + 12/4 = 4

4j/3 + 3 = 4

4j/3 = 4-3

4j/3= 1

j = 1/3     s = 3/4 * 4 = 3  

You would rearrange 4 within the brackets to find total

3 (1/3 + 4t) = 4

   1 + 12t = 4

         12t = 4-1

         12t = 3

             t = 12/3 of the total

            t = 4

Por lo tanto, la respuesta es la opción A: 2065.

El ingreso promedio mensual original es de S/. 1750.

Un incremento del 10% en el ingreso original es:

(10/100)*1750 = 175

Por lo tanto, el nuevo ingreso promedio mensual, considerando el incremento del 10%, es:

1750 + 175 = 1925

Luego, se suma el bono por movilidad de S/. 140:

1925 + 140 = 2065

Por lo tanto, el nuevo ingreso promedio mensual con el incremento del 10% y el bono de movilidad es de S/. 2065.

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Answer:

First even = 24

Second even = 26

Step-by-step explanation:

let x be the first even integer.

let 2x be the second even integer.

\(x + 2x = 50\)

\(x + x = 50 - 2 \)

\(2x =48\)

\( x = 24\)

Therefore, The first even number is 24.

\(second \: \: number= 50 - x \\ = 50-24 \\ = 26\)

Therefore, The second even number is 26.

Answer:

11x represents the total area of the rectangular playground

Answer:

The term 11x represents the area of the playground that contains the slide. The side lengths of this area are 11 feet and x feet.

Step-by-step explanation:

Answer:

,.........................................

Therefore, the volume of the paper cone to the nearest tenth is 418.7 inches cubed.

The volume of the paper cone that Gretchen made to hold a gift for a friend is given by;V= (1/3)πr²hWhere;r = radius of the paper coneh = height of the paper coneπ = 3.14

Given that;Height of the paper cone (h) = 16 inches Radius of the paper cone (r) = 5 inchesWe are to find the volume (V) of the paper cone to the nearest tenth of an inch.

To obtain the volume of the paper cone, we can substitute the values of r and h in the formula above to obtain;

\(V= (1/3)\pir^2hV\)= \((\frac{1}{3} ) \times 3.14\times5^2 \times16V = (\frac{1}{3} ) \times 3.14\times25\times16V = (\frac{1}{3}) \times 1256V=418.7\)

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Equivalent expression is the expression which is equal to the original equation but the way of representation is different. The equivalent expression of the given expression are,

\(x+x+6-7+x\)

\(3-x+2x-4+2x=3x-1\)

Given information

The given expression in the problem is,

\(6+(-x)+2x+(-7)+2x\)

Equivalent expression is the expression which is equal to the original equation but the way of representation is different.

The given equation is,

\(6+(-x)+2x+(-7)+2x\)

As the product of the negative and positive is negative. Thus solve the equation by opening the bracket.

\(6+(-x)+2x+(-7)+2x=6-x+2x-7+2x\\ 6+(-x)+2x+(-7)+2x=-x+2x+2x+6-7\\ 6+(-x)+2x+(-7)+2x=3x-1\)

Check all the option,

\(x+x+6-7+x\)

Solve it further,

\(x+x+6-7+x=x+x+x+6-7\\ x+x+6-7+x=3x-1\\\)

The result is equal to the result of the given expression. Thus the expression of the option 1 is equivalent to the expression given in the problem.

\(2x+2+x\)

Solve it further,

\(2x+2+x=2x+x+2\\2x+2+x=3x+2\)

The result is not equal to the result of the given expression. Thus the expression of the option 2 is not equivalent to the expression given in the problem.

\(3-x+2x-4+2x\)

Solve it further,

\(3-x+2x-4+2x=3x-1\)

The result is equal to the result of the given expression. Thus the expression of the option 3 is equivalent to the expression given in the problem.

\(x-1\)

The expression of the option 4 is not equivalent to the expression given in the problem.

\(x+1\)

The expression of the option 5 is not equivalent to the expression given in the problem.

Hence the equivalent expression of the given expression are,

\(x+x+6-7+x\)

\(3-x+2x-4+2x=3x-1\)

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Answer:

A, C edge 2022

Step-by-step explanation:

have a great day <3

Answer:

n = 8

Step-by-step explanation:

\(m \angle 1 = 9n \\ m \angle \: 2 = n + 10 \\ \\ \because \: m \angle 1 + m \angle 2 = 90 \\ \therefore \: 9n + n + 10 = 90 \\\therefore \: 10n = 90 - 10 \\ 10n = 80 \\ n = \frac{80}{10} \\ \huge \red{ \boxed{ n = 8}}\)

Step-by-step explanation:

total=x kg × 1.50 + y kg × 2.25

=1.50x + 2.25y

=3.75xy

Answer:

1.5 lb

Step-by-step explanation:

Steps to determining the answer

Lb that would be needed for 1 square foot = 0.6 lb / 100 = 0.006

Lb needed for 250 square foot = 0.006 x 250 = 1.5 lb

The vertex of your parabola lies at those two coordinates .The axis of symmetry, x is 1, was already discovered.

To locate a parabola's vertex, you must first determine x (or y, if your parabola is sideways) using the axis of symmetry formula. The quadratic equation will then be used to solve for y (or x, if your parabola opens to the side) using that value. The vertex of your parabola lies at those two coordinates.

The axis of symmetry is shown as a line, hence x=1. Since it is the highest or lowest point of the parabola, the vertex of a quadratic equation also serves as its maximum and minimum. We need to do a few things in order to locate the vertex: The axis of symmetry, x=1, was already discovered.

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The region enclosed by the curves y = sqrt(x) and y = x^2, for 0 <= x <= 4, can be sketched as shown below:

To find the region enclosed by the curves y = sqrt(x) and y = x^2, we can plot both curves on a graph for the given range of x values (0 to 4). The curve y = sqrt(x) represents a half-parabola opening upwards, while the curve y = x^2 represents a parabola opening upwards.

The region enclosed by these curves is the area between the two curves. By sketching the curves, we can visualize the region and determine its boundaries.

To find the area of the enclosed region, we can use integration techniques to calculate the definite integral of the difference between the two curves over the given range of x values.

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Answer:

b

Step-by-step explanation:

Answer:

If 250 per 600

Step-by-step explanation:

600 x 3 is 1800, so 250 x 3 is 750.

So you're answer would be 750

To calculate Nathan's net worth, we need to determine his total liabilities (debt) and subtract that from his total assets. The debt ratio tells us that Nathan's liabilities are 80% of his total net worth.

Total liabilities = Car loan + Mortgage + Student loans = $2,000 + $150,000 + $15,000 = $167,000

Nathan's net worth = Total assets = Total liabilities / Debt ratio = $167,000 / 0.8 = $208,750

So, Nathan's net worth is $208,750.

False. The expected cell frequency in statistical analysis, specifically in the context of contingency tables and chi-square tests, is not based on the researcher's opinion. Instead, it is determined through mathematical calculations and statistical assumptions.

In contingency tables, the expected cell frequency refers to the expected number of observations that would fall into a particular cell if the null hypothesis of independence is true (i.e., if there is no relationship between the variables being studied). The expected cell frequency is calculated based on the marginal totals (row totals and column totals) and the overall sample size.

The expected cell frequency is computed using statistical formulas and is not influenced by the researcher's opinion or subjective judgment. It is a crucial component in determining whether the observed frequencies in the cells significantly deviate from what would be expected under the null hypothesis.

By comparing the observed cell frequencies with the expected cell frequencies, statistical tests like the chi-square test can assess the association or independence between categorical variables in a data set.

Thus, the statement "the expected cell frequency is based on the researcher's opinion" is false. The expected cell frequency is derived through statistical calculations and is not subject to the researcher's subjective input.

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