The math department needs to buy new textbooks and laptops for
the computer science classroom. The textbooks cost $89.00 each, and
the laptops cost $395.00 each.
a. If the math department has $7200 to spend and purchases 60
textbooks, how many laptops can they buy?
b. Suppose the math department decided to purchase 35
textbooks instead of 60. How does this change the number of
laptops that they can buy?

Answer:

mDF = 90°

(Assuming arc mCE is 5x + 10)

Step-by-step explanation:

When we have two chords crossing in a circle, there is a property where the angle in the cross point is equal half the sum of the corresponding arcs.

So in this case, we have:

70° = (mCE + mDF)/2

Assuming mCE is 5x + 10, we have:

70 = (5x + 10 + 11x + 2)/2

70 = (16x + 12)/2

70 = 8x + 6

8x = 64

x = 8

So the arc mDF is:

mDF = 11x + 2 = 11 * 8 + 2 = 90°

The measure of arc DF should be 90 degrees.

Here we assume arc mCE should be 5x + 10

Since mDF = 90°

Also we know that at the time when two chords should be crossing in a circle so the angle in the cross point should be equivalent to the half the sum of the arcs

So base don this.

[tex]70 = (mCE + mDF)\div 2\\\\70 = (5x + 10 + 11x + 2)\div 2\\\\70 = (16x + 12)\div 2[/tex]

70 = 8x + 6

8x = 64

x = 8

Now the arc mDF is:

mDF = 11x + 2

= 11  (8) + 2

= 90°

Hence, The measure of arc DF should be 90 degrees.

Learn more about an arc here: https://brainly.com/question/3401487

Answer:

Select:

11 x 3

4 x 11

5 x 11

Step-by-step explanation:

Notice that the surface area of the prism consists of three rectangles (whose area formula is the product of "length times the width" of each lateral surface), plus the area of two equal right-angle triangles of base 4 and height 3)

Therefore, the formulas we will need to use are:

1) for one of the rectangular faces = 11 x 3

2) for another rectangular face =  5 x 11

3) for the third  rectangular face = 4 x 11

4) for each of the triangular bases = [tex]\frac{1}{2}\, base\,*\,height=\frac{1}{2}\,*4\,*\,3[/tex]

Therefore only three formula expressions need to be selected from the given list.

Answer:

I am pretty sure its (a) and (c)

Step-by-step explanation:

______________________________

Hey!!

Base=15cm

height=5 cm

Area of parallelogram=b*h

=15*5

=75 cm^2

Hope this helps..

__________________________

Answer:

tan (θ+x)= -33/56

sin (θ+x)=33/65

Step-by-step explanation:

cosθ= -4/5 , sin x = -12/13

cosθ= -4/5; θ is in the third quadrant=> sinθ=-√(1-cos² θ)

sinθ=- √(1-16/25)=- √(9/25)=-3/5

sinx= -12/13; x is in the fourth quadrant=> cosx=+√(1-sin²x)

cosx=√(1-144/169)= √(25/169)=5/13

tgθ= sinθ/cosθ=(-3/5)/(-4/5)=3/4

tgx= sinx/cosx=(-12/13)/(5/13)= -12/5

tan (θ+x)=(tgθ+tgx)/(1-tgθ*tgx)

tan (θ+x)=(3/4-12/5)/(1+3/4*12/5)=(-33/20)/56/20)= -33/56

sin (θ+x)=sinθcosx+coxθsinx=-3/5 *5/13 +-4/5 * (-12/13)=-15/65+48/65=33/65

Answer:  (-2,3)

Explanation:

Subtract 5 from the x coordinate to move the point five units to the left. We go from (3,-1) to (-2,-1) after doing this.

Next up, add 4 to the y coordinate to shift the point up four units. We go from (-2,-1) to (-2,3)

===========================================================

Explanation:

Subtract 5 from the x coordinate to move the point five units to the left. We go from (3,-1) to (-2,-1) after doing this.

Next up, add 4 to the y coordinate to shift the point up four units. We go from (-2,-1) to (-2,3)

See diagram below. Point A is the initial point, B is the second step, and C is the final destination.

-----------

Another way to write out the steps is to use the transformation rule below

[tex](x,y) \to (x-5, y+4)\\\\(3,-1) \to (3-5, -1+4)\\\\(3,-1) \to (-2, 3)\\\\[/tex]

Answer:

7 inches

Step-by-step explanation:

250.4/36= 6.955555 rounded to nearest inch is 7

Answer:

(-3,-2)

Step-by-step explanation:

Rewrite first equation in slope-intercept form ( y = mx + b)

2x -y + 4 = 0

-y = -2x - 4

y = 2x + 4

Now rewrite second equation in slope intercept form

y = -x -5

Graph both equations on a calculator and you see that they intersect at (-3,-2)

Answer:

[tex]42cm^2[/tex]

Step-by-step explanation:

Well there are 6 faces on a cube and if each face is 7, the total should be 42.

The surface area of the cube is A = 42 cm²

The formula for surface area of a cube is equal to six times of square of length of the sides of cube. It is represented by 6a2, where a is the side length of cube.It is basically the total surface area.

Surface area S = 6a² ,

where a is the side of the cube

Given data ,

Let the surface area of cube be A

Now , the value of A is

Let the area of one face S = 7 cm²

So , Surface area A = 6a²

On simplifying , we get

A = 6 x 7 cm²

A = 42 cm²

Hence , the surface area is 42 cm²

To learn more about surface area of cube click :

https://brainly.com/question/12079637

#SPJ3

Answer:

Parallelogram

Step-by-step explanation: You have to plot the points in a coordinate plane. If you do that and connect the dots you will get parallelogram.

Answer:

Alvin can make six servings of salad.

Step-by-step explanation:

2/3 is equal to 6/9.

Hi there!

Convert all denominators into the same denominator:

[tex]\frac{2}{3}=\frac{6}{9}[/tex]

[tex]\frac{1}{9}=\frac{1}{9}[/tex]

Divide each terms:

[tex]\frac{6}{9}*\frac{1}{9}=6[/tex]

Final Result: 6

Answer:

P(A and B) = 0.1344 = 13.44%

Step-by-step explanation:

If the chances are disjoint and you want the chance of both happening, you can multiply their individual chances.

It's easiest to express them as a fraction, i.e., 64% = 0.64 and 21% = 0.21

P(A and B) = 0.64 * 0.21 = 0.1344 which is 13.44%

Answer:

Nn

Step-by-step explanation:

Answer:

The answer is explained below

Step-by-step explanation:

This is a word problem, therefore to solve it the statement have to be writing in form of an equation and then solved.

Let the number of fishes caught by Bryan's son be x fishes. Since Bryan caught as many fish as his son, Bryan caught x fishes

Let the number of fishes caught by Elton's son be y fishes. Since Elton caught three times as many fish as his son, Bryan caught 3y fishes

All together, they caught 25 fish

Therefore it can be represented by the equation:

x + x + y + 3y = 25

2x + 4y = 25

2x = 25 - 4y

x = (25 - 4y)/2

The number of fish caught by Bryan is half of the difference between the total fish caught and four times the number of fish caught by Elton son

Answer:

No

Step-by-step explanation:

y=7x

4=7(1)

4=7

This is not a true statement.

15

Σ  40

n=6

explanation; add all the numbers to get 40

6 is the first number and 15 is the last number

Answer: D on edg

Step-by-step explanation:

     [tex]\sum\limits_{i=3}^{10}\big i^2[/tex]

or:

     [tex]\sum\limits_{i=1}^{8}\left(2+i\right)^2[/tex]

or:

    x₁=3, x₂=4, x₃=5, .... x₈=10

    [tex]\sum\limits_{i=1}^{8}\big x_i^2[/tex]

The sigma notation of 3^2+4^2+5^2+...+10^2 is: [tex]\sum\limits^{10}_{n = 3} n^2[/tex]

The sum is given as;

3^2+4^2+5^2+...+10^2

The above means that the sum of the squares of integers from 3 to 10

Using the above statement, the sigma notation is:

[tex]\sum\limits^{10}_{n = 3} n^2[/tex]

Where n represents the current integer

Read more about sigma notation at:

https://brainly.com/question/14322177

The correct statements are:

A) Several factors affect how sediment settles.

C) Moving water affects where sediment travels.

E) Sediments are carried by a transport medium.

I think the question is incomplete. The whole question has 1 more option and is states that check all statements that apply. The whole question was:

Which statements describe characteristics of deposition? Check all that apply.

A) Several factors affect how sediment settles.

B) Sediment is added to a new surface location.

C) Moving water affects where sediment travels.

D) Rocks are broken into smaller particles.

E) Sediments are carried by a transport medium.

If this was not your question, then you can still relate to this, as the answer would be same.

Sediments are a mixture of different elements that are usually carried by water, air or even ice. This mixture may contain organic and inorganic particles. Several factors effect the flow and settlement of sediments, but as discussed above, they always need an transport medium to travel, and moving water serves as one.

Moving water affects where sediment travels.

Deposition is the process of accumulation of loose mineral material and organic residues on the land surface and at the bottom of water bodies.  

It occurs at the foot of the slopes, in valleys and in other negative landforms of various sizes: from sinkholes to large troughs and depressions of tectonic origin, where the accumulating deposits form thick strata that gradually turn into sedimentary rocks.

At the bottom of oceans, seas, lakes and other bodies of water, deposition is the most important exogenous process.

Learn more in https://brainly.com/question/20625095

Answer:

y+5 = 2x

Step-by-step explanation:

The point slope form of an equation is

y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line

y - -5 = 2(x-0)

y+5 = 2x

Answer & Step-by-step explanation:

First, we must know the formula for finding the circumference of a circle.

Circumference = dπ

(d) represents your diameter. In order to find the diameter, you have to multiply the radius by 2 because the radius is half the size of the diameter.

The radius we are given is 15. So well do 15 multiplied by 2.

15 * 2 = 30

Now, since we have ti put the answer in terms of pi, then you are just going to leave 30 as it is and add the pi symbol.

C = 30π

Answer:

Step-by-step explanation:

If the initial amount of nickel is doubling in value each day, it means that the amount of nickel is increasing in geometric progression. The formula for determining the nth term of a geometric sequence is expressed as

Tn = ar^(n - 1)

Where

n represents the common ratio

a represents the first term of the sequence (initial amount)

n represents number of terms in the sequence (days)

r represents common ratio between consecutive terms(days)

From the information given,

r = 2

n = 10

a = 0.05

Therefore, for 10days, T10

T10 = 0.05 × 2^(10 - 1)

T10 = 0.05 × 2^9

T10 = 25.6

Answer:

Having a nickel doubled for 10 days gives 512 nickels, or 2560 cents.

Step-by-step explanation:

Having a nickel doubled in value each day for 10 days, we first write the amount of nickels we have in the first few days, inspect what pattern these numbers take, write a general formula for the sequence formed, and use the formula to find the 10th number easily.

For the first five days we have:

Day1: 1

Day2: 1 + 1 = 2

Day 3: 2 + 2 = 4

Day 4: 4 + 4 = 8

Day 5: = 8 + 8 = 16

...

This is a geometric progression, where the first term is 1, and the common ratio is 2.

The nth term is given as

Tn = ar^(n - 1)

Tn = 1 × 2^(n - 1)

= 2^(n - 1)

That is

Day n = 2^(n - 1)

Day 10 = 2^(10 - 1) = 2^9 = 512 nickels.

But because 1 nickels = 5 cents

512 nickels = 5 × 512 = 2560 cents.

a squared + b squared = c squared

576+100=c squared

676=c squared

c squared = 26

hope it helps

Answer:

$178,000

Step-by-step explanation:

The calculation of X and Y is shown below:-

Before that we need to do the following calculations

[tex]Depreciation\ in \ 1\ year = 45\%\times Initial\ investment[/tex]

[tex]= 0.45\times\$400,000[/tex]

= $180,000

[tex]Depreciation\ in \ 4\ year = 6\%\times Initial\ investment[/tex]

[tex]= 0.06\times\$400,000[/tex]

= $24,000

Now, Operating cash flow of X in Year 1

[tex]X = (Revenue - Cost)\times (1 - Tax \ rate) + Depreciation\times tax \ rate[/tex]

[tex]X = (\$628,000 - \$552,000)\times (1 - 0.50) + \$180,000\times 0.50[/tex]

= $38,000 + $90,000

= $128,000

and Operating cash flow of Y in Year 4

[tex]Y = (Revenue - Cost)\times (1 - Tax \ rate) + Depreciation\times tax \ rate[/tex]

[tex]Y = (\$628,000 - \$552,000)\times (1 - 0.50) + \$24,000\times 0.50[/tex]

= $38,000 + $12,000

= $50,000

[tex]X + Y = Operating\ cash\ flow\ for\ the\ year\ 1 + Operating\ cash\ flow\ for\ the\ year\ 2[/tex]

= $128,000 + $50,000

= $178,000

hence, the X + Y is $178,000

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

To determine for which value of x a pair of expressions will be equal, we will need to set them equal to each other and then solve for x.

[tex]3x-4=2x+1[/tex]

First, we can add 4 to each side

[tex]3x=2x+5[/tex]

Now we can subtract 2x from each side

[tex]x=5[/tex]

Now, just to check our answer, we can plug in our answer back into the original equation to see whether we get the same result for each side

[tex]3(5)-4=2(5)+1\\\\15-4=10+1\\\\11=11[/tex]

Answer:

5

Step-by-step explanation:

1) make them equal to each other

2) put all the constants on one side and all the ones with x on the other

3) solve

Answer:

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

2 x 4 = 8

8 x 2 = 16

4 x 9 = 36

36 x 2 = 72

9 x 2 = 18

18 x 2 = 36

16 + 72 + 36 = 124

124 = D

Answer:

x < 23 (x is less than 23)

Step-by-step explanation:

x - 3 < 20

x < 20 + 3

x < 23 (x is less than 23)