Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes a $ 1700 investment to earn $ 500 interest if it is invested at 2 % interest compounded quarterly.
$ 500 interest will be earned in approximately years. (Round to the nearest tenth.)

The final cost of a skateboard after all the discounts and reductions is $53.775.

Given that, during a clearance sale at a sporting goods store, skateboards were marked down 30%. On Saturday, an additional 25% was taken off already reduced prices of skateboards.

We need to find the final price after all discounts had been taken.

What is the discount?

The basic way to calculate a discount is to multiply the original price by the decimal form of the given percentage rate. To calculate the sale price of any item, we need to subtract the discount from the original price.

Given, that the original cost of the skateboard is $119.50.

Now, 30+25=55

So, the total decrease in percentage is 55%.

The final cost of a skateboard=119.50-55% of 119.50

=119.50-0.55 × 119.50

=119.50-65.725

=$53.775

Therefore, the final cost of a skateboard after all the discounts and reductions is $53.775.

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15 green marbles are there among 56 marbles.

A bag contains 56 marbles, so Total marbles =56.

In That, There are Green and red marbles contained in a ratio of 3:4.

Now we have to assume that

Let 3x = the number of green marbles and 4x = the number of red marbles

By using the ratios and the total we can know how many green and red marbles are there in a bag. so the formula is:

ax+bx=t-------(1)

a and b are ratios of given marbles

t is the total number of marbles

x is to find the value

substituting the values in the above equation we get

3x + 4x =35

7x = 35

x = 5

substitute the x value in 3x we get:

Green: 3x = 15

Therefore,15 green marbles are present among 56 marbles

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Answer:

2n + 16

Step-by-step explanation:

he adds 8 then doubles the sum

2(n + 8) which is 2n + 16

Answer:

Step-by-step explanation:

B

The error occur from line 2 to line 3(optionB)

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation forms a straight line.

A linear equation can have one or two variables. For example 5 = y+ 3y is an example of linear equation with one variable and y = 5 +3x is an example of linear equation with two variables.

8x-4= 2(4x+1)-6

8x-4= 8x+2-6

8x-4= 8x-4

Therefore the error is made where the parentheses is been solved, 2 is to multiply both 4x and 1.

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Because the range is supplied as the difference between the side and the total of the sides given, option C, which is 9 cm<x<17 cm, is the right choice.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Here,

The range of possible lengths for the third side,

13-4<x<13+4

9<x<17

The correct option is C that is 9 cm < x < 17 cm because the range is given in difference between the side and sum of sides given.

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Answer:

2   (the first choice)

Step-by-step explanation:

This is a matrix of size 3 rows and 5 columns  (3 x 5)

Any element of the matrix can be reference by row and column number

C₃₂  refers to the element in the 3rd row, 2nd column which is 2

Answer:

x=29 and y=53

Step-by-step explanation:

let y=3x-34 be the first equation (1) and y=2x-5 be the second equation (2)

Using the elimation method, (1)-(2): 0=x-29

-x=-29

x=29

Substitute x=29 into (2),

y=2(29)-5

y=58-5

y=53

So, x=29 and y=53

Answer:

-9

Step-by-step explanation:

[tex]f(-2)=2(-2)=-4 \\ \\ g(-2)=|-2-3|=5;\\ \\ (f-g)(2)=-4-5=-9[/tex]

The sample size required to estimate the mean score on a standardized test within 4 points of the true mean with 95% confidence. Assume that s = 13 based on earlier studies is 40.58.

Making use of the given data to determine the sample size.

Sample size (n) =?

The confidence level = 95% or 0.95

Z-score for 95% confidence interval  =1.960

Using this formula

Margin of error = Zα/2 × α/√n

Solving for n

4 =   1.960 × 13/√n

√n = 6.37

n = 40.58

Therefore the sample size is 40.58.

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The snow melted in 3 hours would be 1.5 inches, and the expression which represents the amount of snow left after 't' hours of snow melting S(t) = 12.5 - 0.5t

What is a constant rate of change?

A rate of change is a rate that describes how one quantity changes in relation to another quantity.

Constant rate is also called uniform rate which involves something traveling at a fixed and steady pace or else moving at some average speed.

The snow started melting at a rate of 0.5 inches per hour and it is known that 3 hours after the storm ended, the depth of snow was down to 11 inches.

Snow melted in 3 hours = 0.5 * 3 = 1.5 inches

Thus;

The Initial depth of snow = 11 + 1.5 inches = 12.5 inches.

Now, depth of snow on Gabriella's lawn = Initial depth - 0.5(Number of hours)

Let S(t) be the depth of snow on  Gabriella's lawn, in inches, t hours after the snow stopped falling.

Hence, the snow melted in 3 hours would be 1.5 inches, and the expression which represents the amount of snow left after 't' hours of snow melting S(t) = 12.5 - 0.5t

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Since the Polynomial has three non zero terms then the type of the polynomial is Trinomial

What are Polynomials?

A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Solution:

Yes the mentioned Ploynomial

7y - 6y² - y^5 is a Polynomial

Since the Polynomial has three non zero terms then the type of the polynomial is Trinomial

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The following assets is not an example of a fixed asset for a manufacturer of road building equipment is " cans of yellow paint for refurbishing equipment warehouse building for storing finished equipment " .

Given :

which of the following assets is not an example of a fixed asset for a manufacturer of road building equipment  group of answer choices employee parking lot production equipment for assembling engines shipping area for finished goods .

What is fixed asset ?

A fixed asset is a long-term tangible property or piece of equipment that a company owns and uses in its operations to generate income.

It is clear that the paints cans cannot a property so it is not an example of fixed assets .

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Answer:

inverse proportion

Step-by-step explanation:

2=k240/16

The following are the actions she could take to solve the quadratic equation: 2(x² + 6x + 9) = 18 + 3.

Following is the determination of the quadratic equation's solution;

2x² + 12x - 3 = 0

2x² + 12x = 3

Divide equation by 2.

x² + 6x = 3/2

Add both of the equation's sides after squarely multiplying the x-coefficient by half:

(x + 3)² = 3/2 + 3²

x² + 6x + 9 = 9 + 3/2

2(x² + 6x + 9) = 18 + 3

Thus, in order to calculate the quadratic equation, she could follow these steps: 2(x² + 6x + 9) = 18 + 3.

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The correct part is (d) i.e. Fail to reject the null hypothesis.

What is hypothesis testing?

By evaluating whether or not the observed test statistic is more extreme than would be anticipated if the null hypothesis were true, the critical value approach determines whether something is "likely" or "unlikely." This means that the alternative hypothesis is accepted in place of the null hypothesis when the observed test statistic is more extreme than a cutoff number, known as the "critical value." The null hypothesis is not disproved if the test statistic does not deviate significantly from the crucial value.

Here, The critical value is 1.6257 and the sample's test statistic value is 1.3994.

We can see that the sample's test statistic value is not extreme as the critical value, So the null hypothesis should not be rejected.

Hence, It fails to reject the null hypothesis.

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The correct option A) Sunday and Monday, is the days employee 3 does not need to work.

For the stated question-

A medical center's manager wants to schedule employees so that they work 5 days and take 2 days off in a row.

Thus, they are reportedly mandated to have consecutive days off on Saturday and Monday, and there is no better option than A.

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a) The function in vertex form is; y = -16(x - 3.5)² + 198

b) The maximum height if the arrow is; 198 feet

c) The time that it takes the arrow to hit the ground is; 16 seconds

We are given the function as;

y = -16t² + 112t + 2.

where;

y is the height (in feet) of an arrow

t is the time in seconds after it is shot from a bow

This is the equation of a vertical parabola open downward

The vertex is a maximum

The general form of a  quadratic equation in vertex form is;

y = a(x - h)² + k²

where (h, k) is the vertex coordinate

a) y = -16t² + 112t + 2

This is in standard form and using completing the square, we can write in vertex form as;

y = -16(x - 3.5)² + 198

b) The vertex is the point (3.5, 198)

The maximum height of the arrow represents the y-coordinate of the vertex of the function

Thus, the maximum height of the arrow is 198 feet

c) We know that when the arrow hits the ground, the value of y is equal to zero. Thus, at y= 0, we have;

-16(x - 3.5)² + 198 = 0

Rearranging gives;

(x - 3.5)² = (198/16)

(x - 3.5) = ±√(198/16)

(x - 3.5) = ±12.375

x = 12.375 + 3.5

x = 15.875 ≈ 16 seconds which is the time it will take to hit the ground.

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The required step to be taken is to factor the trinomial in the derivation.

The general form of a quadratic equation is given as ax^2 + bx + c = 0.

Here, a ≠ 0 and b and c are integers.

The degree of a quadratic equation is 2.

It can be factorized by completing square method.

The given problem can be solved as follows,

The derivation made by Jimmy is given as,

ax² + bx + c = 0

=> x² + (b/a)x + c/a = 0

=>  x² + (b/a)x =  -c/a

=> x² + (b/a)x + (b/2a)² = -c/a + (b/2a)²

Now, in order to solve the equation the trinomial on the LHS can be factored as follows,

(x + b/2a)² = -c/a + (b/2a)²

Hence, the next step taken by jimmy should be to factorize the trinomial on LHS.

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The different possibilities

The value of each digit in a number is known as place value. Every digit in a number has a distinct value depending on where it is located. The value of a digit depends on its position in the number, which might result in a number having two comparable digits with distinct values.

Given:

5.4  

Now, filling with different possibilities

Tens       Ones     Tenths     Hundredths

0                5               4                     0

0                5               3                    10

0                5               2                   20

0                 5              1                   30

0                 5              0                   40

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Answer:

3 ln(abs ln(7x)) +C

Step-by-step explanation:

Do not forget to add the absolute value!

Answer:

the expression is constant, which means it can be rewritten with a factor of x⁰.

The degree is the largest exponent on the variable.

0

Avoiding discrimination is extremely important because this is an attitude that goes against human dignity and different values.

Some alternatives to overcome discrimination are:

No group should be discriminated against because discrimination promotes negative values and does not allow the correct development of people.

To avoid discrimination you can:

¡Hope this helped!

Answer:

Step-by-step explanation:

There are several ways to write an equation for the money collected as a function of the number of t-shirts sold. One possible equation is $y = x \cdot p$, where $p$ is the price of each t-shirt. This equation says that the total amount of money collected is equal to the number of t-shirts sold multiplied by the price of each t-shirt.Another possible equation is $y = p \cdot (x - c)$, where $c$ is the cost of producing each t-shirt. This equation says that the total amount of money collected is equal to the price of each t-shirt multiplied by the number of t-shirts sold minus the cost of producing each t-shirt.These are just two examples of how to write an equation for the money collected as a function of the number of t-shirts sold. The exact equation will depend on the specific details of the situation.

Answer:

1

Step-by-step explanation:

-5 -2=-7

Keep in mind that negative is below zero. by adding eight we have reach 1 point to the right of zero. Thus, explaining tha answer of positive 1.

-7+8=1

Final Answer: 1

Answer:

<A ≅ <X

<B ≅ <Y

Method

AAS Congruence Theorem

Step-by-step explanation:

The end behavior of the polynomial is, rises to the left and falls to the right.

What is end behavior of polynomial?

A polynomial function typically behaves at its end in the same way that its leading term, or the term with the largest exponent, does at its end.

Look at the leading term of the polynomial function to understand its end behavior. Given that the leading term has the highest power, its behavior will dominate the graph because it will grow much more quickly than the other terms as x gets very large or very small.

Consider, the given polynomial g(x) = x^2 (6 - x)

From the graph of the polynomial function we can see that the maximum point of the polynomial is at its vertex.

The vertex of the polynomial is (10, 90).

So this is the maximum value of the function is (10, 90).

Now to find the end behavior of the polynomial.

The degree of the polynomial is 3 and the leading coefficient of the polynomial is, -1.

By using: Odd degree and Negative leading coefficient the graph Rises to the left and falls to the right.

Hence, the end behavior of the polynomial is, rises to the left and falls to the right.

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The function and the estimated value for the given population of fox are obtained as P(t) = P₀(1 + r)^t and 35346 respectively.

In order to model the population growth first find the value of the growth rate then substitute it into the expression P(t) = P₀(1 + r)^t.

Now, the value of P₀ can be found for t = 0 and thus the function is obtained.

The given problem can be solved as follows,

(a) The population of fox in year 2000 is given as 25800.

And, the growth rate is 4%.

Suppose t = 0 for year 2000.

And for some value of t, the population is P(t).

Now, the following expression for the population can be written as,

P(t) = P₀(1 + r)^t

Where P₀ is the population at the year 2000.

Thus, the expression can be written as,

P(t) = 25800(1 + 4/100)^t

(b) In the year 2008, the value of t is 8.

Substitute t = 8 in the expression of the population to get,

P(t) = 25800(1 + 4/100)^8

⇒ 25800 × 1.37

⇒ 35346

Hence, the function that models the population and the estimated population for year 2008 are given as P(t) = P₀(1 + r)^t and 35346 respectively.

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The remainder of 4 when f(x) is divided by x - 5 means that f(5) = 4

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

The function is given as

Polynomial = f(x)

Remainder = 4

The function is represented as

z(x)

This means that

x = 5 in f(x)

So, we add -5 to both sides of the equation

This gives

x - 5 = 0

Also, we have

A remainder of 4 when divided by x-5

So, when the equation in interpreted, it means

The remainder when f(x) is divided by x - 5 is  4

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