1) Last year a computer cost $1,600 to purchase. A year later the same computer cost $1,850 to purchase. By what percent did the cost of the computer increase? (please show your work)
2)A flock of 50 geese landed at a pond. Later that day there were 75 in the pond. By what percent did the number of geese increase?

a
80%
b
50%
c
2%
d
10%

The sequence 10, 9. 5, 9. 0, 8. 5,. has a common difference on -0.5

The sequence 200, 100, 50, 25, has a common ratio of 1/2

Let's start by discussing the sequence 10, 9.5, 9.0, 8.5. We can observe that each term is decreasing by 0.5. This means that the sequence has a common difference of -0.5.

In mathematical terms, the common difference is the constant value that is added or subtracted from each term in the sequence to obtain the next term. In this case, we can write the sequence as:

10, 10 - 0.5, 10 - 1.0, 10 - 1.5

where the common difference is -0.5.

Now, let's consider the sequence 200, 100, 50, 25. We can observe that each term is obtained by dividing the previous term by 2. This means that the sequence has a common ratio of 1/2.

In mathematical terms, the common ratio is the constant value that is multiplied by each term in the sequence to obtain the next term. In this case, we can write the sequence as:

200, 200/2, (200/2)/2, ((200/2)/2)/2

where the common ratio is 1/2.

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The cross-product of u and v:
w = u × v = (5, -4, 8) × (-8, -4, 5) = (-20, -60, 32)

Thus, w is orthogonal to u. Since we need two vectors in opposite directions, we can negate w:
-w = (20, 60, -32)
Therefore, the two orthogonal vectors in opposite directions are w = (-20, -60, 32) and -w = (20, 60, -32).

To find two vectors that are orthogonal to u, we can use the cross-product. Let v = (4,5,0) and w = (-8,0,5). Then v x u = (40,40,45) and w x u = (20,-40,20). So two vectors orthogonal to u are (40,40,45) and (20,-40,20).

To determine whether two planes are orthogonal, parallel, or neither, we can look at the normal vectors of each plane. Let the first plane be defined by the equation 2x + 3y - z = 4 and the second plane being defined by the equation :

4x + 6y - 2z = 8.

The normal vector of the first plane is (2,3,-1) and the normal vector of the second plane is (4,6,-2).

Since the dot product of these two normal vectors is -2(3) + 3(6) - 1(2) = 14, which is not equal to 0, the planes are not orthogonal.

To determine if they are parallel, we can check if the ratio of their normal vectors is constant. Dividing the second normal vector by the first, we get (4/2, 6/3, -2/-1) = (2,2,2). Since this is a constant ratio, the planes are parallel.

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Its translation is 5×3-3=12

After considering all the given data we come to the conclusion that the volume of the prism is 1440 in³, under the condition that A rectangular pyramid has a volume of 480 in.

The volume of a rectangular pyramid is represented by the formula
(1/3) × base area × height.
Now, the volume of a rectangular prism is given by the formula
base area × height.
Now if we consider the rectangular prism has a base and height congruent to the pyramid, then the base area of the prism is equivalent to the base area of the pyramid. Then, the volume of the prism is equivalent to three times that of the pyramid.

Hence, the volume of the pyramid is 480 in³, we can evaluate the volume of the prism
Volume of prism = 3 × Volume of pyramid
= 3 × (1/3) × Base area × Height
= Base area × Height
Then, the volume of the rectangular prism is
480 × 3
= 1440 in³.
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The fraction is equivalent to a whole number  are 9/3, -16/8, 7/0, 0/5

A fraction can simply be described as the part of a whole variable, a whole numbers, or a whole element.

In mathematics, there are different types of fractions. These fractions are listed thus;

From the information given, we have that;

Equivalent expressions or fractions are fractions with the same solutions

Then, we have;

9/3

Divide the values

3

-16/8

-2

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Answer:

x = -9

Step-by-step explanation:

As this is an absolute value function, the line of symmetry is the x-value of the maximum/minimum point. An absolute value function can be denoted as y = |x - h| + k, where (h, k) is the maximum/minimum point. We only need the x-value of the maximum/minimum point, so we only have to look at "h". Now, we can use y = |x - h| + k and turn it into g(x):

y = |x - h| + k

g(x) = |x - -9| + -11   --> this means h = -9, and the line of symmetry is at x = -9

g(x) = |x + 9| - 11

Answer:

I think x equals --9

Kimo should make 5 loads in the small truck and 4 loads in the large truck per day to minimize the total cost while meeting the delivery and union requirements.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

the total cost will be minimized when the loads are distributed in the following way:

5 loads in the small truck (total capacity of 5 * 50 = 250 cubic yards)

4 loads in the large truck (total capacity of 4 * 70 = 280 cubic yards)

This will result in a total of 9 loads and a total capacity of 530 cubic yards, which meets both the daily minimum delivery requirement of 350 cubic yards and the union contract requirement of 9 loads per day.

The total cost can be calculated as follows:

Cost of 5 loads in small truck = 5 * $87 = $435

Cost of 4 loads in large truck = 4 * $73 = $292

Total cost per day = $435 + $292 = $727

Therefore, Kimo should make 5 loads in the small truck and 4 loads in the large truck per day to minimize the total cost while meeting the delivery and union requirements.

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The cylindrical storage container can hold 549.5 cubic inches of cat litter.

To find the volume of the cylindrical storage container, we need to use the formula:

V = πr²h

Where:

π is a constant approximately equal to 3.14

r is the radius of the container

h is the height of the container

Substituting the given values, we get:

V = 3.14 x 5² x 7

V = 549.5 cubic inches

Since we know that the  vessel can hold549.5 boxy  elevation of cat  waste, we can use this value to determine how  important cat  waste can fit in the  vessel in other units.   For  illustration, if we want to know how  numerous liters of cat  waste can fit in the  vessel, we can convert boxy  elevation to liters using the conversion factor 1 liter = 61.02 boxy  elevation.   boxy  elevation61.02 boxy  elevation per liter = 8.998 liters   thus, the spherical  storehouse  vessel can hold  roughly 9 liters of cat  waste.

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Answer:

Let's solve this problem using algebra. Let x be the cost of one orange and y be the cost of one apple. Then we have the system of equations:

12x + 7y = 5.36

8x + 5y = 3.68

To solve for x and y, we can use elimination. Multiplying the second equation by 3 and subtracting it from the first equation multiplied by 5, we get:

(5*12 - 7*8)x + (5*7 - 3*5)y = 26.8 - 11.04

20x = 15.76

x = 0.788

Substituting x back into one of the equations, we can solve for y:

12(0.788) + 7y = 5.36

y = 0.308

Therefore, one orange costs $0.788 and one apple costs $0.308.

The calculated value of the expression A/the area of XYZ is [tex]\frac{49\sqrt3}{216}[/tex]

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

By the ratio of corresponding sides (see attachment for figure), we have

(x + 2y)/(2x + y) = 3/4

By comparison, we have

x + 2y = 3

2x + y = 4

This gives

(x, y) = (5/3, 2/3)

The triangles are equilateral triangles

So, we have

Area of XYZ = 1/2 * side length² * sin(60)

This gives

Area of XYZ = 1/2 * (2x + y)² * sin(60)

Substitute the known values in the above equation

Area of XYZ = 1/2 * (4)² * sin(60)

Evaluate

Area of XYZ = 4√3

The region A is a trapezoid

So, the area is

A = 1/2 * Sum of parallel sides * height

So, we have

A = 1/2 * (x + y) * (x² - y²)

Recall that (x, y) = (5/3, 2/3)

So, we have

A = 1/2 * (5/3 + 2/3) * ((5/3)² - (2/3)²)

Evaluate

A = 49/18

Finding A/the area of XYZ, we have

A/the area of XYZ = 49/18 ÷ 4√3

This gives

A/the area of XYZ = 49/72 ÷ √3

Rationalize

A/the area of XYZ = [tex]\frac{49\sqrt3}{216}[/tex]

Hence, the value of the expression is [tex]\frac{49\sqrt3}{216}[/tex]

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Complete question

Let G be the center of the equilateral triangle XYZ. A dilation centered at G with scale factor -3/4 is applied to triangle XYZ, to obtain triangle X'Y'Z'.  Let A be the area of the region that is contained in both triangles XYZ and X'Y'Z'. Find A/the area of XYZ.

XY = 2x + y

X'Z' = x + 2y

Region A is a trapezoid with parallel sides y & x and height x² - y²

Answer: 81

Step-by-step explanation: this would be 81 because [tex]3^{3}[/tex] is basically 3 x 3 x 3 and 3 x 3 x 3=27 then multiply 27 by 3, and you get 81

Answer:

3^4. my answer needs to be 20+character sooooooooo

Answer:

A, 48 degrees

Step-by-step explanation:

180 - 42 - 90 = 48 (all interior angles add up to 48)

Answer:

it’s A

Step-by-step explanation:

it’s a because the right triangle is always 90°.As you can see there is 42° so you subtract to find the missing number.

Answer:

Step-by-step explanation:

You're going to want to break up the shape into three parts, two triangles, and the rectangle.

Starting with the left-most triangle: A=(L*W)/2

The length is 4ft and the width is 3ft, multiply and divide by 2 to get:  A=6 square feet.

Do the same with the second triangle on the bottom left (L=2ft, W=2ft) to get A=2 square feet.

Now the rectangle, A=L*W and total length is 10ft (8ft+2ft) and the width is 3ft. Multiply these values to get A=30 square feet.

Last step: add up all three areas for the total area of the entire shape, 6+2+30=38.

Area= 38 square feet.

Marsha would save $26,040 over the life of the loan if she purchases the 3 points.

First, let's calculate the monthly payment if Marsha doesn't purchase any points. We can use a mortgage calculator or the PMT function in Excel to find;

PMT = $1,987.13

Now, let's calculate the monthly payment if Marsha purchases 3 points;

Loan amount = $350,000

Points cost = 3 points × 1% × $350,000 = $10,500

Effective loan amount = $350,000 - $10,500 = $339,500

Interest rate = 4.5% / 12 = 0.375%

Number of payments=20 years × 12 = 240

Using the PMT function, we get;

PMT = $1,878.63

So, by purchasing 3 points, Marsha can save;

$1,987.13 - $1,878.63 = $108.50 per month

Over the life of the loan, which is 20 years or 240 months, the total savings would be;

$108.50 × 240 = $26,040

Therefore, Marsha would save $26,040 amount of money.

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The probability that out of three exactly one car will require a minor repair in the first year = 33%

P(E ) = no. of favorable outcome/total no. of outcome

E here represents exactly one car that requires a minor repair.

out of three cars, exactly one car will need a minor repair

No. of favorable outcome = 1

Total no. of outcome = 3

Now, putting value in P(E) we get

P(E) = 1/3

P(E) = 0.333

To get percentage we multiply by 100

P(E) = 0.333 × 100

P(E) = 33.3

The probability to the nearest percent = 33%

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The Maclaurin series for g(x) is given by g(x) =[tex]x^2 - x^6/3! + x^10/5! -[/tex] [tex]x^14/7![/tex] [tex]+ ⋯ + (-1)^n*x^(4n)/(2n+1)! + ⋯[/tex]

The function g(x) is defined as g(x) = [tex]f(x^2)[/tex], where f(x) is a function with a Maclaurin series expansion.

To find the Maclaurin series for g(x), we substitute [tex]x^2[/tex] into the Maclaurin series of f(x). The resulting series for g(x) is obtained by replacing each occurrence of x in the series for f(x) with x^2:

g(x) = [tex]f(x^2) = (x^2) - (x^2)^3/3! + (x^2)^5/5! - (x^2)^7/7! + ⋯ + (-1)^n*(x^2)^(2n+1)/(2n+1)! + ⋯[/tex]

Simplifying the terms, we have:

g(x) =[tex]x^2 - x^6/3! + x^10/5! - x^14/7! + ⋯ + (-1)^n*x^(4n+2)/(2n+1)! + ⋯[/tex]

This represents the Maclaurin series expansion for the function g(x) in terms of the original function f(x) with the argument squared.

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The prediction for the number of times the event of landing on an even number in 550 rolls is 275

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

The number of times = 550

The sample space of a fair 6-sided die is

S = {1, 2, 3, 4, 5, 6}

And as such the even numbers are

Even = {2, 4, 6}

This means that in a fair 6-sided die, we have

P(Even) = 3/6

When evaluated, we have

P(Even) = 1/2

So, when the die is rolled 550 times, we have

Expected value = 1/2 * 550

Evaluate

Expected value = 275

Hence, the number of times is 275

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The simplified expression is 4.

To simplify the expression (-3)(-2) -2), we need to follow the order of operations, which are parentheses first, then multiplication and division from left to right, and finally addition and subtraction from left to right.

First, we need to simplify (-3)(-2) to get:

(-3)(-2) = 6

Now we can substitute this value into the expression to get:

6 - 2) = 4

Therefore, the simplified expression is 4.

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The derivative of f(x) is: f'(x) = [tan⁻¹(2)/2] - [tan⁻¹(1/2)/2]

The Fundamental Theorem of Calculus is a pair of theorems that link the concept of differentiation and integration. It states that if a function f(x) is continuous on an interval [a, b] and F(x) is the antiderivative of f(x) on the same interval, then:

Part I: The derivative of the integral of f(x) from a to x is equal to f(x):

d/dx ∫a to x[tex]f(t) dt = f(x)[/tex]

Part II: The integral of the derivative of a function f(x) on an interval [a, b] is equal to the difference between the values of the function at the endpoints of the interval:

∫a to b [tex]f'(x) dx = f(b) - f(a)[/tex]

Using Part I of the Fundamental Theorem of Calculus, we have:

f(x) = x∫4 1/(1+4t⁴) dt

Then, by the Chain Rule, we have:

f'(x) = d/dx [x∫4 1/(1+4t⁴) dt] = ∫4 d/dx [x(1/(1+4t⁴))] dt

= ∫4 (1/(1+4t⁴)) dt

= [tan⁻¹(2t)/2]₄¹

= [tan⁻¹(2)/2] - [tan⁻¹(1/2)/2]

Therefore, the derivative of f(x) is:

f'(x) = [tan⁻¹(2)/2] - [tan⁻¹(1/2)/2]

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The minimum value of the function is -13 and the minimum value of the function occurs at the point (4, -13).

The function F(x) is a quadratic function with a negative coefficient of the squared term.

Therefore, the function has a maximum value.

To find the maximum value, we need to find the vertex of the parabola.

The x-coordinate of the vertex is given by x = -b/2a, where a and b are the coefficients of the x² and x terms respectively.

In this case, a = -1 and b = -8, so x = -(-8)/(2(-1)) = 4.

To find the minimum value, we substitute this x-value into the function to get F(4) = -(4²) - 8(4) + 19 = -13.

Therefore, the minimum value of the function is -13.

We found in part (1) that the x-coordinate of the vertex is x = 4.

To find the y-coordinate, we substitute this x-value into the function to get F(4) = -13.

Therefore, the minimum value of the function occurs at the point (4, -13).

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An equation of the line that passes through the pair of points (0,4) and (6, −3) in slope-intercept form is y = -7x/6 + 4.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-3 - 4)/(6 - 0)

Slope (m) = -7/6

At data point (0, 4) and a slope of -7/6, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 4 = -7/6(x - 0)  

y = -7x/6 + 4

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The arc measure of major arc BDC in degrees is 240 degrees.

To find the arc measure of major arc BDC in degrees, you'll need to provide more information about the given circle or angles within it. However, I can guide you on how to find the arc measure once you have the necessary information.

1. Determine the measure of the central angle corresponding to the major arc BDC. This can be done by subtracting the measure of the minor arc from 360 degrees.

2. Use the central angle measure to find the arc measure of major arc BDC. Since the arc measure is equal to the measure of the central angle in degrees, the arc measure of major arc BDC will be the same as the central angle measure you found in step 1.

Please provide more information or details about the given circle or angles to help you find the arc measure of major arc BDC.

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Answer:

(d)

Step-by-step explanation:

Therefore , the solution of the given problem of expressions comes out to be  7n.

Instead of using random estimates, it is preferable to use shifting numbers that may also prove increasing, reducing, variable or blocking. They could only help one another by trading tools, information, or solutions to issues. The justifications, components, or quantitative comments for tactics like further disagreement, production, and blending may be included in the assertion of truth equation.

Here,

By dividing the number of rows by the number of trees in each row, one can calculate the total number of trees in Mr. Lee's apple orchard. Here are two expressions that demonstrate various approaches to determining the overall number of trees:

There are 7n =  trees in all.

=> Total number of trees = (Number of rows) x (Number of trees in each row) = 7n

The total number of trees in the orchard is the outcome of both expressions.

While the second statement more directly depicts the multiplication, the first expression merely merges the two elements into a single term.

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Since each of the bricks is the same exact size, then each brick is 0.6 meters tall.

To determine the height of each glowing brick, we need to divide the total height of the tower (5.4 meters) by the number of bricks (9). This gives us the average height of each brick.

Using the formula for division, we can write this as:

Height of each brick = Total height of tower / Number of bricks

Plugging in the given values, we get:

Height of each brick = 5.4 meters / 9 bricks

Simplifying this expression, we can cancel out the units of "bricks" to get:

Height of each brick = 0.6 meters

Therefore, each glowing brick in the tower is 0.6 meters tall.

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The rate of return is 19%, rounded to the nearest tenth.

Given that a purchased for $ 20/share, are sold for $ 720. $ 6 is the  commission on the sale. We need to calculate the total cost of the investment and the total proceeds from the sale, and then use the formula for rate of return.

The total value should be

= 20 × 30

= $ 600

Since, it is sold for $ 720 along with commission of $6 so final money should be  

= 720 - 6

= $ 714.

Now rate of return is

= (714 - 600)/714*100

= 114/600*100

= 19%

Therefore, the rate of return is 19%, rounded to the nearest tenth.

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The solution to the equation 4x + 17 = 23 is x = 3/2.

It should be noted that to solve this equation, we need to isolate the variable x on one side of the equation.

First, we can subtract 17 from both sides of the equation:

4x + 17 - 17 = 23 - 17

Simplifying the left side of the equation:

4x = 6

Next, we can divide both sides of the equation by 4:

4x/4 = 6/4

Simplifying:

x = 3/2

Therefore, the solution to the equation 4x + 17 = 23 is x = 3/2.

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The future value of the investment when Jack is ready to purchase the vacation home is $44,924.

To solve this problem, we can use the formula for future value of an annuity:

FV = Pmt x [(1 + r)^n - 1] / r

Where:

Pmt = $1000 (quarterly contribution)
r = 0.021 (annual interest rate)
n = 40 (number of quarters until Jack turns 50)

Plugging in the numbers, we get:

FV = $1000 x [(1 + 0.021)^40 - 1] / 0.021
FV = $44,924.38

Therefore, the future value of Jack's investment, rounded to the nearest dollar, is $44,924. So the correct answer is $44,924.

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The positive value of z indicates option e) the value z is to the right of the mean.

A standard normal random variable has a mean of 0 and a standard deviation of 1. Positive values of z represent values above the mean, while negative values of z represent values below the mean.

The probability associated with a value of z is always positive since it represents the likelihood of observing a certain value. The area between zero and z is also always positive since it represents the probability of observing a value between 0 and z.

Therefore, option e) is the correct answer as it reflects the relationship between positive values of z and their location relative to the mean.

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