You borrow $300 at a simple interest rate of 4% per year. You make no payments for two years. How much do you owe after two years

Answer:

28 and 37

Step-by-step explanation:

Answer:

28 and 37

Step-by-step explanation:

This is very simple actually!

First subtract the 9:

65 - 9 = 56

Then divide by 2:

56 ÷ 2 = 28

28 is one of your answers. If we want to find the other one, then add back 9

28 + 9 = 37

That's it!

Hope this helped  :)

Answer:

\( y = 2x + 3 \)

Step-by-step explanation:

Given :-

And we need to find the equation in slope intercept form. So here we can find the equation of the line using two point form , as ,

\(\implies y - y_1 = \dfrac{ y_2-y_1}{x_2-x_1}( x - x_1) \)

\(\implies y - 9 = \dfrac{ 3-9}{0-3}( x - 3) \\\\\implies y - 9 =\dfrac{-6}{-3}( x - 3 ) \\\\\implies y - 9 = 2( x - 3 ) \\\\\implies y - 9 = 2x - 6 \\\\\implies y = 2x - 6 +9 \\\\\implies \boxed{ y = 2x + 3 }\)

Hence the equation in slope intercept form is y = 2x + 3.

We will need a sample size of 35 bluejay bills to make a 95% confidence interval estimate of the mean length with a margin of error of 0.6 inches.

We find the sample size required for a 95% confidence interval estimate with a margin of error of 0.6 inches. Here are the terms we need to consider:
Confidence interval:

A range of values within which we can be confident the true population parameter lies.
Margin of error:

The amount added or subtracted from the sample mean to create the confidence interval.
Standard deviation:

A measure of the dispersion of a set of values, denoted as σ.
Sample size:

The number of observations in the sample, denoted as n.
Z-score:

The number of standard deviations a value is away from the mean.
Now let's calculate the sample size, n:
Identify the values from the problem.
- Confidence level: 95%
- Margin of error (E): 0.6 inches
- Population standard deviation (σ): 3 inches.

Find the Z-score for a 95% confidence interval.
For a 95% confidence interval, the Z-score is 1.96 (you can find this value in a Z-score table or through online calculators).
Use the formula to calculate the sample size, n:
n = (Z * σ / E)²
n = (1.96 * 3 / 0.6)²
Calculate n:
n = (5.88)²
n ≈ 34.5744
Round up to the nearest whole number, since we can't have a fraction of a sample.
n ≈ 35.

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Step-by-step explanation:

Flour needed to make birthday cakes = 2x

Flour needed to make holiday cakes = 1y = y

Maximum amount of Flour allowed = 20 (No more than 20)

Therefore

2x + y must not be more than 20

\(2x + y \leqslant 20\)

Answer:

Hmmm.... well for one thing I would at least review a few things, just so you can feel a bit more confident in your work, then if that doesn't work you can review more or get your mind off stuff by going somewhere fun. SLEEP It's kinda hard yes but still staying up all night studying and worrying isn't going to do anything but make you sloppy. Make sure you are well fed before said test. Mainly just don't strain  yourself too much because like I said before it'll make it harder in class.

I'm sure you've heard this before but yeah it works if you really take it to heart

I hope this helps! <3 even a little bit?

Answer:

6+2x=16-x.

Step-by-step explanation:

X will represent the missing number. Sum means 6, twice that number means multiply it by two, equal represents =, minus represents this, therefor the equation 6+2x=16-x represents the correct answer.

Given that a rectangle has an area of 345 square millimeters and a base of 15 millimeters, find the height.

Area of a Rectangle = b x h

So, to find the height, we would reverse it by dividing the area by the base.

Work:

345/15 = 23

So, 23 would be our height.

Thus, the height of the rectangle is 23 millimeters.

Answer:

23 millimeters

Step-by-step explanation:

The area of a rectangle can be found using the following formula.

a=b*h

We know that the area is 345 square millimeters and the base is 15 millimeters, but we don't know that the height is.

a=345

b=15

Substitute these variables into the formula.

345=15*h

We want to find out what the height, or h is.  In order to do this, we have to get h by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

h is being multiplied by 15. The opposite of multiplication is division, so divide both sides by 15.

345/15=15*h/15

345/15=h

23=h

Add appropriate units. In this case, the units are millimeters.

h=23 millimeters

The height of the rectangle is 23 millimeters.

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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EXPLANATION

The perimeter Perimeter is given by the sum of the sides as follows:

P = z + 5 + z + 5 + z + z

Substituting P=26 and adding like terms,

26 = 10 + 4z

Subtracting -10 to both sides:

26 - 10 = 10 - 10 + 4z

Simplifying:

16 = 4z

Dividing both sides by 4:

16/4 = z

Switching and simplifying:

z = 4

So,

Equation: 26 = 10 + 4z

z = 4

Answer:

Lisa's text average is 86 :))

Step-by-step explanation:

add all numbers up then divide them by 3.

The slope of a line is -2.

The slope of a line can be described as follows:

The slope of a line is a measure of its steepness

Slope = rise / run

slope = y₂ - y₁ / x₂ - x₁

using (0, -4)(-1, -2)

x₁ = 0

x₂ = -1

y₁ = -4

y₂ = -2

Therefore,

slope = -2 - (-4) / -1 - 0

slope = -2 + 4 / -1

slope = 2 / -1

slope = -2

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Answer: 7 - 3/v

Our expression is rewritten in mathematical form is  

Step-by-Step Explanation:

Since we have given that

7 minus the quotient of 3 and v

As we know that

The quotient of 3 and v is rewritten as

7 minus from it:

So, our expression is rewritten in mathematical form is

Step-by-step explanation: 7-3/v

\(\large\underline{\rm Solution }:- \)

Given function to us is ,

\(\implies f(x) = 3x^3 - 5x + 1 \)

The domain of the expression will be all real numbers except where the given expression is not defined . Therefore , the domain is ,

\(\underline\text{ In Interval Notation :- }\)

\(\implies \boxed{ Domain : ( -\infty , +\infty ) }\)

\(\underline\text{ In Set Builder Notation :- }\)

\(\implies \boxed{ Domain : \{ x | x \in \mathbb{R} \}}\)

9514 1404 393

Answer:

  1/2

Step-by-step explanation:

The midpoint is the average of the end points:

  (-3 +4)/2 = 1/2

The coordinate of the midpoint is 1/2.

Answer: 3

Step-by-step explanation:

Factor of 15: ±1, ±3, ±5, ±15
Factor of 18: ±1, ±2, ±3, ±6, ±9, ±18
Factor of -45: ±1, ±3, ±5, ±9, ±45
=> GCF of 15, 18, -45 is 3

Answer:

ab//dc

Step-by-step explanation:

When m1 = mB

ab//dc

ad//bc

or

none

Answer:

8

Step-by-step explanation:

2 x 4

The size class interval recommend is 30.

Assume that the observations are more or less evenly distributed across the range, and you should get about 5 observations per class.

It also presumes that your interest in the observations is uniform: you are equally interested in values close to 60 as you are in values close to 480. If you were only interested in values above 450, you could group all values from 56 to 449 into one large class and divide the rest into smaller classes.

It is also necessary to check to see if the distribution is uniform. If it is skewed in either direction, it makes more sense to have smaller classes where the observations are dense and larger classes where they are sparse.

Therefore, the size class interval recommend is 30.

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Answer:

676 pi

Step-by-step explanation:

208 ÷ 4 =52

(each length =52cm)

diameter = 52 cm

radius = 52÷2 = 26cm

area of circle = pi × radius ^2

pi × 26^2 = 676 pi

Answer:

108 mm^3

Step-by-step explanation:

the formula for a right rectangular pyramid is lwh/3, so if you multiply 6, 6, and 9, you'll get 324

324/3=108

Answer:

Im pretty sure ur answers would be

x= -32/27 and X=  -46/27

Step-by-step explanation:

So srry if im wrong tho

The first and third rectangular prisms have the same volume of 30 cubic units.

The second rectangular prism has a volume of 350 cubic units, and the fourth rectangular prism has a volume of 24 cubic units.

The volume of each of the rectangular prisms can be calculated as follows:

1.   length: 1; width: 10; height: 3

volume = 1 x 10 x 3 = 30

2.  length: 5; width: 10; height: 7

volume = 5 x 10 x 7 = 350

3.   length: 2; width: 5; height: 3

volume = 2 x 5 x 3 = 30

4.   length: 4; width: 2; height: 3

volume = 4 x 2 x 3 = 24

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The equation in the form of y= mx +b is y= 4x-1.

We have the equation 4x - y =1.

We know the slope intercept form of line as

y= 3x + b

where m is the slope and b is the y intercept.

Now, writing the equation 4x - y= 1 in slope intercept form as

y = 4x - 1

where the slope is 4 and intercept is -1.

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The rule for combining like terms is a way to simplify algebraic expressions. This will result in a single term with the same base and exponent as the original terms, but with a coefficient that is the sum of the coefficients of the original terms.

The rule for combining like terms is a way to simplify algebraic expressions. It is based on the idea that if two terms have the same base (the number or variable part) and the same exponent (the power of the number or variable), then they can be combined into a single term. For example, if we have the expression 5x2 + 3x2, then the two terms can be combined because they have the same base (x2) and the same exponent (2). To combine these terms, we simply add the coefficients (5 and 3) to get 8x2, which is the simplified form of the expression. The same rule applies for combining terms with different bases, but the same exponent. If we have 5x2 + 3y2, then we can combine the terms by adding the coefficients (5 and 3) to get 8x2 + 3y2. This is the simplified form of the expression. By using this method, we can simplify complex expressions and make them easier to solve.

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Answer:

The vertex is option C: (-6, -2)

Step-by-step explanation:

The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)

Pls mark brainliest.

Answer:

Slope-intercept form of a linear equation:  \(y=mx+b\)

where:

To determine the equation of the line of best fit from the given answer options, examine the relationship between the x and y values.

From inspection of the data, we can see that as x increases, y increases.  Therefore, the slope of the equation will be positive.

(If the y-values decrease as the x-values increase, then the slope would be negative).  

Therefore, we can immediately discount answer options B and D as they have negative slopes.

The x and y values are not very far away from each other.  The options given for the slope are either 1.560 or 4.105.  If the slope was 4.105, we would expect to see values of y that were further away from the x-values.

Therefore, the line of best fit is:

A:  y = 1.560x - 4.105

To prove this, plot the 5 points on a graph and draw a line of best fit (see attached).

Choose 2 points on the line of best fit:  (4, 2) and (11, 13)

Use the slope formula with these points to calculate the approximate slope:

\(\implies \sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}\approx\dfrac{13-2}{11-4}=\dfrac{11}{7}=1.57\)

Thus proving that y = 1.560x - 4.105 is an appropriate option for the equation of the line of best fit.

a.To calculate the past growth rate in earnings, we will use the formula for compound annual growth rate (CAGR): The past growth rate in earnings is approximately 0.0841 or 8.41%.b. $2.815. c. 16.22%.

a. To calculate the past growth rate in earnings, we will use the formula for compound annual growth rate (CAGR):

CAGR = (Ending Value / Beginning Value)^(1 / Number of Years) - 1

In this case, the beginning value is $4.42 in 2013, and the ending value is $6.50 in 2018. The number of years is 5. Plugging these values into the formula, we have:

CAGR = ($6.50 / $4.42)^(1 / 5) - 1

Calculating this expression, the past growth rate in earnings is approximately 0.0841 or 8.41%.

b. To calculate the next expected dividend (d1) assuming that the past growth rate continues, we can use the formula:

d1 = d0 * (1 + g)

where d0 is the last dividend ($2.60) and g is the growth rate (8.41% or 0.0841). Plugging in these values, we have:

d1 = $2.60 * (1 + 0.0841)

Calculating this expression, the next expected dividend (d1) is approximately $2.815.

c. The cost of retained earnings (rs) can be calculated using the dividend growth model formula:

rs = (d1 / P0) + g

where d1 is the next expected dividend ($2.815), P0 is the current stock price ($36.00), and g is the growth rate (8.41% or 0.0841). Plugging in these values, we have:

rs = ($2.815 / $36.00) + 0.0841

Calculating this expression, the cost of retained earnings (rs) is approximately 0.1622 or 16.22%.

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Minimization of  f(x) = |x+3| + x^3 at the endpoints (-2 and 6)  the minimum value of the function is approximately 3.84, which occurs at x= \sqrt{1/3}

within the given interval.

To minimize the function subject to the constraint f(x) = |x+3| + x^3 that x lies in the interval [-2, 6], we need to find the value of x that minimizes f(x) within that interval.

First, let's analyze the function f(x). The absolute value term |x+3| can be rewritten as:

|x+3| =

x+3 if x+3 >= 0

-(x+3) if x+3 < 0

Since the interval [-2, 6] includes both positive and negative values of x+3, we need to consider both cases.

Case 1: x+3 >= 0

In this case, f(x) = (x+3) + x^3 = 2x + x^3 + 3

Case 2: x+3 < 0

In this case, f(x) = -(x+3) + x^3 = -2x + x^3 - 3

Now, we can find the minimum of f(x) within the given interval by evaluating the function at the endpoints (-2 and 6) and at any critical points within the interval.

Calculating the values of f(x) at x = -2, 6, and the critical points, we can determine the minimum value of f(x) and the corresponding value of x.

Since the equation involves both absolute value and a cubic term, it is not possible to find a closed-form solution or an exact minimum value without numerical methods or approximation techniques.

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