In a recent survey of monetary donations made by 489 college graduates, the following information was obtained. 95 has donated to a political campaign, 76 had donated to assist medical research, 133 had donated to preserve the environment, 25 had donated to all three, 38 had donated to a political campaign and to medical research, 46 had donated to medical research and to preserve the environment, and 54 donated to a political campaign and to preserve the environment.
(a) How many college graduates donated to none of the listed causes?
(b) What percent of the college graduates donated to exactly one of the three listed causes?

Answer:

(a). 300r + 425p ≤ 6,600

(b). No, it’s not considered overweight

Step-by-step explanation:

In this question, we are to write an equation that shows the number of refrigerators and pianos the truck could carry.

Let the number of refrigerators be r and the number of pianos be p

By using their individual weights, the equation is as follows;

300r + 425p ≤ 6,600

To the second question, we want to consider if 10 refrigerators and 8 pianos are overload.

To get this, we simply multiply the number of each by their individual weights;

That would be;

300(10) + 425(8) = 3000 + 3,400 = 6,400 lbs

This is not considered overweight as it is less than 6,600 lbs

Complete question is;

In a race that consisted of three parts, the cycling part was 12 1/2 miles long. The running part of the race was 1/4 the distance of the cycling part. The kayaking part of the race was 1/2 the distance of the running part. What was the entire distance, in miles of the race?

Answer:

Total distance of race = 17.1875 miles

Step-by-step explanation:

The 3 parts of the race are; cycling, running and kayaking.

The cycling distance was; 12½ miles

We are told that the running part was ¼ of the cycling distance. Thus;

Running distance = ¼ x 12½ = ¼ x 25/2 = 25/8 miles

Lastly, we are told that the kayaking part was ½ the distance of the running part. Thus;

Kayaking distance = ½ x 25/8 = 25/16

Thus,total distance of race = cycling distance + running distance + kayaking distance = 12½ + 25/8 + 25/16 = 17.1875 miles

Answer:

x(1.25)

Step-by-step explanation:

x is the yards.

so for example if you need 2 yards of fabric replace x with 2.

Answer:

x=1.25

Step-by-step explanation:

edgu

Answer:

5

Step-by-step explanation:

To find the slope given two points, we use the formula

m= (y2-y1)/(x2-x1)

   = (-13-2)/(-2 -1)

   = -15/-3

   =5

Answer:

The slope is 5

Step-by-step explanation:

Δ means the change in

slope = m = Δy/Δx = [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{2-(-13)}{1-(-2)}[/tex] = 15/3 = 5/1 = 5

Slope = 5

Answer:

[tex]\frac{3}{50}[/tex]

Step-by-step explanation:

Answer: 6/10

Step-by-step explanation:

the 6 is in the tenth place which means it is by ten

Since the odds against choosing the lemon-flavored piece wasn't included, let us now assume that it is 2/5

Answer:

The Probability of choosing a lemon-flavored piece is 5/7

Step-by-step explanation:

Please kindly see the attached files for explanation

The answer is zero (0), when you add any number to it's opposite you always get zero

Answer:

Step-by-step explanation:

Given that the base of a solid is the circle [tex]x^2 + y^2 = 9[/tex] and Cross sections of the solid perpendicular to the x-axis are semi-circles.

We know that the cross sections are semicircles with the diameter in the given circle [tex]x^2 + y^2 = 9[/tex]

That is we have to find the formula for the area of any semicircle perpendicular to x-axis, and integrate it from -3 to 3.

Now the area of a semicircle is

[tex]A=\frac{\pi r^2}{2}[/tex] cubic units

Let r = y  and [tex]y^2=9-x^2[/tex]

Then area of the semicircle crossing the x-axis at x is  given by

[tex]A(x)=\frac{1}{2}\pi y^2[/tex] cubic units

[tex]=\frac{1}{2}\pi(9-x^2)[/tex]    

 Now we can find the definite integral of A(x) from x = -3 to x = 3.

Since A(x) is an EVEN function then the definite integral of A(x) from x = -3 to x = 3 is the same as twice the integral of A(x) from x = 0 to x = 3.

We have that

[tex]A(x)=2(\int_0^3 \frac{1}{2}\pi(9-x^2))dx[/tex]

[tex]=2(\frac{\pi}{2}[9x-\frac{x^3}{3}]_0^3)[/tex]

[tex]=\pi[9(3)-\frac{3^3}{3}-9(0)-(-\frac{0^3}{3})][/tex]

[tex]=\pi[27-\frac{27}{3}][/tex]

[tex]=\pi[27-9][/tex]

[tex]=\pi[18][/tex]

[tex]=18\pi[/tex]

The volume of the solid is 18π cubic units.

The base of the solid is defined by the circle’s equation x² + y² = 9, indicating that the radius of the circle is 3 units. The cross-sections perpendicular to the x-axis are semi-circles.

To find the volume, we need to integrate the area of these semi-circular cross-sections. For a slice at a given x-coordinate, the diameter of the semi-circle is the length of the chord of the circle at that x-coordinate, which is given by 2√(9 - x²). The radius of the semi-circle is then √(9 - x²), and the area of the semi-circle is (1/2)πr².

The area of each semi-circular slice is: A(x) = (1/2)π(√(9 - x²))² = (1/2)π(9 - x²).

The volume V of the solid is obtained by integrating this area from x = -3 to x = 3:

V = ∫[from x = -3 to x = 3] (1/2)π(9 - x²) dx

This simplifies to:

V = (π/2) ∫[from x = -3 to x = 3] (9 - x²) dx

We solve the integral:

V = (π/2) [9x - (x³ / 3)] (from x = -3 to x = 3)

Evaluating this, we get:

V = (π/2) [(9×3 - (3³ / 3)) - (9×(-3) - ((-3)³ / 3))]

V = (π/2) [(27 - 9) - (-27 + 9)]

V = (π/2) [18 + 18]

V = (π/2) 36

V = 18π

Thus, the volume of the solid is 18π cubic units.

Answer: 70 times

Step-by-step explanation:

If you were to flip a coin 140 times you would expect it to land on tails 70 since 140 divided by 2 is 70 although coins are normally not evenly weighed meaning that it most likely not going to land evenly on both sides.

Answer:

Last one: 5x - 3√y + 1

Step-by-step explanation:

8x + √1 - √9y - √9x^2

8x + 1 - 3√y - 3x

5x + 1 - 3√y

5x - 3√y + 1

Answer:Answer:

Last One: 5x - 3√y + 1

Step-by-step explanation:

8x + √1 - √9y - √9x^2

8x + 1 - 3√y - 3x

5x + 1 - 3√y

5x - 3√y + 1

Step-by-step explanation:

Answer:

( x - 9 )( x - 3 )

Step-by-step explanation:

plz give brainliest

Answer:

#1: 11 cm

#2: 16.5 in

#3: 2.5 feet

Step-by-step explanation:

#1

[tex]P=2l+2w[/tex] Solve for width by substracting 2l on both sides to isolate 2w

[tex]P-2l=2w[/tex]

or

[tex]2w=P-2l[/tex]

Replace.

[tex]2w=26-2(2)\\2w=26-4\\2w=22\\w=\frac{22}{2}\\ w=11cm[/tex]

----------------------------------------------------------------------------

#2

[tex]P=2l+2w[/tex]

[tex]P=2(3.5)+2(4.75)\\P =7+9.5\\P=16.5in[/tex]

----------------------------------------------------------------------------

#3

[tex]P=2l+2w[/tex]

Solve for l

[tex]2l=P-2w\\2l=7-2(1)\\2l=7-2\\2l=5\\l=\frac{5}{2}\\ l=2.5feet[/tex]

Answer:

He use 120 grams of flour.

Step-by-step explanation:

Given:

Flaky pastry can be made using flour and fat in the ratio 4 : 3. Jake makes some flaky pastry using 90 grams of fat.

Now, to find the weight of flour he use in making flaky pastry.

Let the weight of flour be [tex]x.[/tex]

Weight of fat = 90 grams.

The ratio of flour and fat used in making flaky pastry is 4 : 3.

As, 4 is equivalent to 3.

Thus, [tex]x[/tex] is equivalent to 90.

Now, to solve using cross multiplication method:

[tex]\frac{4}{3} =\frac{x}{90} \\\\By\ cross\ multiplying\ we\ get:\\\\360=3x\\\\Dividing\ both\ sides\ by\ 3\ we\ get:\\\\120=x\\\\x=120\ grams.[/tex]

Therefore, he use 120 grams of flour.

Answer:It would be a decrease of 40 percent

Step-by-step explanation:You go from 10/10 to 6/10 meaning you decrease by 4/10 and 4/10 is the same as 40/100 and anything over 100 is its percent value so you would be going down by 40%

Answer:

40 % decrease or -40%.

Step-by-step explanation:

The decrease is 10 - 6 = 4 feet.

% decrease = (4/10) * 100

= 0.4 * 100

= 40 % decrease.

Answer:

The perimeter is 28 (6 plus 8=14 14x2= 28)

Step-by-step explanation:

Plz mark brainliest!

The perimeter of quadrilateral DOBC that forms two right triangles is: 28 units.

Based on the tangent theorem, triangles ODC and OBC are right triangles that are congruent. Therefore, their corresponding side lengths are equal.

Perimeter of quadrilateral DOBC = OB + DO + BC + CD = 6 + 6 + 8 + 8

Perimeter of quadrilateral DOBC = 28 units.

Learn more about congruent right triangles on:

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Answer:

the answer is 5

Step-by-step explanation:

YW

Answer:

There are 5 faces in a triangular prism

I hope this help. If I'm wrong/made any mistakes please let me know so that I can learn from it!

Answer:

[tex]95.1\ cm^2[/tex]

Step-by-step explanation:

we know that

A square is a quadrilateral that has four equal sides and four equal interior right angles.

The area of the square is given by the formula

[tex]A=b^2[/tex]

where

b is the length side of the square

In this problem we have

[tex]b=9.75\ cm[/tex]

substitute in the formula

[tex]A=(9.75)^2=95.06\ cm^2[/tex]

Round to the nearest tenth

[tex]A=95.1\ cm^2[/tex]

Answer:

95.06cm​

Step-by-step explanation:

Hope this helps

Answer: n=4

Step-by-step explanation: 1:4 = 6:24

Answer:

10 inches.

Step-by-step explanation:

First we need to find what is the bigger dimension of the box, because the relay baton will occupy the box, and the larger dimension of the relay baton (that is, it's length) need to be less or equal than the larger dimension of the box.

The dimensions of the box are: 4 inches, 6 inches and 10 inches.

The larger dimension of the box is 10 inches. So, If we want the relay baton to fit in the box, the maximum length it can have is 10 inches.

Answer:

The answer to your question is 5.7

Step-by-step explanation:

Data

Point A = (2, 3)

Point B = (-2, 7)

Process

To find the distance between points A and B use the formula of the distance between two points, substitute and simplify.

Formula

dAB = [tex]\sqrt{(x2 - x1)^{2}+ (y2 - y1)^{2}}[/tex]

-Identify wich is the value of x1, y1, x2, y2

        x1 = 2   y1 = 3  x2 = -2  y2 = 7

-Substittion

dAB = [tex]\sqrt{(-2 - 2)^{2} + (7 - 3)^{2}}[/tex]

-Simplification

dAB = [tex]\sqrt{(-4)^{2} + (4)^{2}}[/tex]

dAB = [tex]\sqrt{16 + 16}[/tex]

dAB = [tex]\sqrt{32}[/tex]

-Result

dAB = 5.65 ≈ 5.7

Answer:714.1

Step-by-step explanation:

500 times tan(55)

We can use the tangent function from trigonometry to estimate the depth of the crater. The depth is approximately 714.1 meters when the length of the shadow is 500 meters and the angle of sun elevation is 55 degrees.

To solve this problem, we can use trigonometry, specifically the tangent function. The tangent function of an angle in a right triangle is equal to the ratio of the opposite side over the adjacent side. Here, the shadow length of the moon's crater functions as the adjacent side, and the depth of crater is the side opposite to the angle.

So tangent(55°) = depth / 500 meters.

To find the depth, rearrange the equation to multiply both sides by 500: depth = 500 * tangent(55°).

Using a calculator, you'll find that the tangent of 55° is approximately 1.4281. So then your final depth equation would look like: depth = 500 meters * 1.4281. By doing this calculation, we find depth ≈ 714.05 meters, and rounding this to the nearest tenth, we have 714.1 meters. So the estimated depth of the crater is 714.1 meters.

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The expression

is a polynomial. Its type is cubic and the degree is 3.

The given mathematical expression

is a polynomial. A polynomial is an expression that is made up of variables and coefficients, using only the operations of addition, subtraction, and multiplication and non-negative integer exponents. The type of this polynomial is cubic, because the highest power of the variable (the degree) is 3. In this case, the highest degree is the highest exponent of the variable 'x', which is 3. Hence the given polynomial is cubic, with degree of 3.

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N equals 78

The equation: (56+n)/2 - 40=27

Add 40 to 27=67

Multiply everything by 2 leaving you with 56+n=134

Subtract 56 from 134

Leaves you with n=78

If you plug it in you would get 67-40, which equals 27

Answer:

I'm newbie here

Step-by-step explanation:

Elimination Method.

4x + 6/y = 15 → step 1

6x - 8/y = 14 → step 2

so,

4x + 6/y = 15 |×6|

6x - 8/y = 14 |×4|

24x + 6/y(6) = 90

24x - 8/y(4) = 56

24x + 36/y = 90

24x - 32/y = 56

____________ _

68/y = 34

68 = 34y

34y = 68

y = 2

subsitution y = 2 to..

4x + 6/y = 15

4x + 6/2 = 15

4x + 3 = 15

4x = 12

x = 3

So, for x is 3, and for y is 2

Answer:

x = 3, y = 2

Step-by-step explanation:

Multiply equation 1 by -6

-24x - 36/y = -90

Multiply equation 2 by 4

24x - 32/y = 56

Add the two equations:

-36/y - 32/y = -34

-68/y = -34

y = -68/-34

y = 2

4x + 6/2 = 15

4x = 15 - 3

4x = 12

x = 3

Given Information:

Coastline of Canada = 202080 km

Coastline of British Columbia = 2/15 of Coastline of Canada

Required Information:

How long is the coastline of British Columbia = ?

Answer:

Coastline of British Columbia is 26944 km long

Step-by-step explanation:

We are given the length of Coastline of Canada that is 202080 km

We also know that Coastline of British Columbia is 2/15 of the Coastline of Canada.

So,

Coastline of British Columbia = (2/15)*202080

Coastline of British Columbia = 26944 km

Therefore, the Coastline of British Columbia is about 26944 km.

Answer:

$15

Step-by-step explanation:

Let Sam's Money =s

Let Janet's Money =j

[tex]$\frac13$[/tex] of Sam's money equals [tex]$\frac12$[/tex] of Janet's money.

Let n be the number of dollars held by Sam and Jane respectively

Therefore: [tex]$n=\frac13s=\frac12j$[/tex]

s=3n

j=2n

s+j=3n+2n=5n

Together, they have more than $10

Therefore:

5n>10

n>2

The least sum they could have is at n=3

At n=3

s+j=5n=5X3=$15

The least number of dollars they could have combined is $15.

Answer:

The final value owed will be $3416.29.

Step-by-step explanation:

Since this is a compound interest problem we should use the apropriate formula given bellow:

M = C*(1 + r/n)^(n*t)

Where M is the final amount, C is the initial amount, r is the interest rate, t is the total time and n is the rate at which it is compounded. Since it's semiannually the value of n is 2 and we can use the formula to find the desired value.

M = 2000*(1 + 0.11/2)^(2*5)

M = 2000*(2/2 + 0.11/2)^(10)

M = 2000*(2.11/2)^(10)

M = 3416.29

The final value owed will be $3416.29.

Answer:

42 Volunteers

Step-by-step explanation:

The time (T) that it takes a group of volunteers to construct a house varies inversely as the number of volunteers (V).

This is written as:

[tex]V \propto \frac{1}{T} \\$Introducing the variation constant k\\V = \frac{k}{T}\\$It takes 20 volunteers to build a house in 63 hours.$\\When V=20, T=63\\V = \frac{k}{T}\\20 = \frac{k}{63}\\k=20*63=1260\\$Therefore, the equation connecting V and T is:$\\V = \frac{1260}{T}\\$When T=30 hours, we want to determine the number of volunteers needed V$\\V = \frac{1260}{30}=42\\$42 Volunteers will be needed.$[/tex]

Answer:

23 miles per gallon

Step-by-step explanation:

Take the miles and divide by the gallons

218.5 miles/ 9.5 gallon

23 miles per gallon

Answer:

23m/g

Step-by-step explanation:

If a car travels 218.5 miles on 9.5 gallons, you can find how many miles can be traveled on one gallon.

You can make the equation 9.5g=218.5, let g be gallons of gas.

Divide by 9.5 on both sides.

g= 23

The gas mileage is 23 miles for one gallon of gas.