A cone is cut out of the center of a pyramid with a rectangular base. The rectangular base has side lengths of 15 and 10 units. The cone has a diameter of 9 and a height of 12. The pyramid and cone have the same height. What is the volume of the shaded portion of the composite figure? Express your answer in terms of π. 519π units3 681π units3 (600π – 81) units3 (600 – 81π) units3

Answer:

Distribute

6(x+2)

= 6×x+6×2

So 6x+12

Answer:

The set of solutions are linearly independent because the wronskian is

e^(2ax) ≠ 0

Step-by-step explanation:

To show that the set of solutions {e^(ax), xe^(ax)} are linearly independent, we find the Wronskian of the set of solutions.

Wronskian of y1 and y2 is given as:

W(y1, y2) = y1y2' - y1'y2

y1 = e^(ax)

y1' = ae^(ax)

y2 = xe^(ax)

y2' = axe^(ax) + e^(ax)

W(y1, y2) = e^(ax)[axe^(ax) + e^(ax)] - ae^(ax).xe^(ax)

= (ax + 1)e^(2ax) - axe^(2ax)

= e^(2ax)

The wronskian of the given set of solutions is e^(2ax), which is not zero.

Because it is not zero, the set of solutions are linearly independent.

Answer:

The correct answer is option A. A and C

Step-by-step explanation:

From the given situation above, here is the solution:

Friend A. 13 hours x $ 6.95 = $90.35 x 8 weeks = $722.80

Friend B. 15 hours x $ 5.85 = $87.75 x 8 weeks = $702

Friend C. 18 hours x $ 5.25 = $94.5 x 8 weeks = $756

Friend D. 11 hours x $ 7.80 = $85.8 x 8 weeks = $686.40

Therefore, the individuals who reached their goal of saving $720 for a vacation are friend A and friend C. The correct answer is option A. A and C.

Answer:

The correct answer is A.     A and C

Step-by-step explanation:

Answer:

Step-by-step explanation:

x + 5 = 20

x = 15

Answer:

x=15

Step-by-step explanation:

We are given the equation:

[tex]\frac{1}{4} = \frac{5}{x+5}[/tex]

We want to solve for x. Therefore, we must isolate x on one side of the equation.

Let's begin by cross multiplying. Multiply the numerator of the first fraction by the denominator of the second. Then, multiply the denominator of the first by the numerator of the second.

[tex]1(x+5)=(4*5)[/tex]

[tex]x+5=(4*5)[/tex]

[tex]x+5=20[/tex]

5 is being added to x. The inverse of addition is subtraction, so subtract 5 from both sides of the equation.

[tex]x+5-5=20-5[/tex]

[tex]x=20-5[/tex]

[tex]x=15[/tex]

Let's check our solution. Plug 15 in for x.

[tex]\frac{1}{4} = \frac{5}{x+5}[/tex]

[tex]\frac{1}{4} = \frac{5}{15+5}[/tex]

[tex]\frac{1}{4} = \frac{5}{20}[/tex]

[tex]\frac{1}{4} = \frac{5/5}{20/5}[/tex]

[tex]\frac{1}{4} = \frac{1}{4}[/tex]

Our solution checks out, so we know it is correct.

The solution to this equation is x=15

Answer:

its a, c and e and 2020 edge.

Answer:

-56

Step-by-step explanation:

It technically means -8 times 7.

Answer:

false; Only square roots can result in irrational numbers. Subtraction of any two real numbers results in a rational number.

Step-by-step explanation:

Rational numbers in any operation with a rational number except square rooting will result in a rational number.

Answer:

13cm

Step-by-step explanation:

104 × 2 = 208

208 ÷ 16 = 13cm

(13 × 16) ÷ 2 = 104cm²

Answer:

13 cm

Step-by-step explanation:

Area = 1/2×base×height

Formula  for area:

Solving for b:

Answer is 13 cm

Answer:

rhombus

Step-by-step explanation:

if you flip a rhombus(diamond) shaped sandwich over it is still shaped like a rhombus

hope i helped

Answer:3 inches

Step-by-step explanation:

For every inch is 3 feet

9 feet ÷3 feet to 1 inch = 3 inches

Answer: $70.73

Step-by-step explanation:

Answer: 400 miles

Step-by-step explanation:

Let x= the amount of miles

120+0.4x=40+0.6x

 80+0.4x=0.6x

          80=0.2x

             x=400

400 miles a day the rental cost will be same

Hope this helps!! :)

Please let me know if you have any question

Answer:

sale price = $145.56

Step-by-step explanation:

The regular price of one bicycle is $181.95

20% discount

sale price = original price - ( % discount x original price )

sale price = $181.95 - (0.20 * $181.95)

sale price = $181.95 - $36.39

sale price = $145.56

Answer:

Step-by-step explanation:

Given a chord of distance of 15cm, if it is 9cm from the center of a circle, this means that the 9cm length will be projecting from the centre of the circle perpendicular to the chord and passing through its centre.

Since the radius of a circle is a line that is drawn from the centre of a circle to ts circumference, the set up will form a right angles triangle within the circle with the hypotenuse as the radius and the other two sides as the opposite and adjacent respectively. Using the Pythagoras theorem to get the length of the radius (hypotenuse);

hyp² = opp² + adj²

Let the opposite be the 9cm length

Adjacent will be half of the chord length = 15/2 = 7.5cm

Substituting this values into the formula we will have;

hyp² = 9² + 7.5²

hyp² = 81+56.25

hyp² = 137.25

hyp² = √137.25

hyp = 11.72

Hence the radius of the circle is approximately 11.72 cm long

Answer:

Q1: Communtative property of multiplication

Q2: Commutative property of addition

Step-by-step explanation:

Hope this helps!!!!!!!

Answer:

0.1949

Step-by-step explanation:

Given a normal distribution with;

Mean(m) = 8.8 inches

Standard deviation (sd) = 0.7 inches

If one item is chosen at random, what is the probability that it is less than 8.2 inches long?

Find the Z-score :

x = 8.2 inches

Z = (x - m) / sd

Zscore = (8.2 - 8.8) / 0.7

Zscore = - 0.6 / 0.7

Zscore = - 0.857 = - 0.86

P(Z < - 0.86) :

From z distribution table :

P(Z < - 0.86) = 0.1949

If one item is chosen at random, there is a probability of 0.1949 that it will be less than 8.2 inches long.

Answer:

24

Step-by-step explanation:

The most important thing to note here is that there are no parentheses defining what to do when.

Therefore, we have to use order of operations - PEMDAS, to find the expression's value.

PEMDAS states that the order you go in is:

1. Parentheses

2. Exponents

3. Multiplication/Division

4. Addition/Subtraction

[tex]6^2-3\cdot4[/tex]

There are no parentheses, so first we have to solve the exponent.

[tex]6^2=36\\\\36-3\cdot4[/tex]

Now we have to multiply.

[tex]36-12[/tex]

And now subtract.

[tex]24[/tex]

Hope this helped!

Answer:

6^2 - 3×4 = 24/1 = 24....

Answer:

13x + 6

Step-by-step explanation:

5x + 2(4x + 3)

distribute the 2

2 • 4x = 8x

2 • 3 = 6

5x + 8x + 6

combine like terms

13x + 6

Answer:

Step-by-step explanation:

5x+2(4x+3)

=5x+8x+6

=13x+6

Answer:

8848 meters

Step-by-step explanation:

[tex]1 \: cm = 0.01\:m\\884800 = x \: m\\\\x = 884800\times 0.01\\\\x = 8848\:meters[/tex]

Answer:

The meter is the international system unit of length, here there are some conversions:

So we know 100 cm are equal to 1 meter and we have to pass the 884800 centimeters to meters.

If 1 meter is equal to 100 centimeters, to pass from meters to centimeters we multiply by 100 and from centimeters to meters we divide by 100.

In this case, we need to pass from cm to m, so we divide by 100 the altitude:

884800/100 = 8848 meters

Answer:

Step-by-step explanation:

[tex](9,9) =(x_1,y_1)\\(6,5)=(x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\[/tex]

Plug-in the values into the equation

[tex]d = \sqrt{(6-9)^2+(5-9)^2}\\ \\d = \sqrt{(-3)^2+(-4)^2}\\ \\d = \sqrt{9+16}\\ \\d = \sqrt{25} \\\\d =5[/tex]

(a) Area of rectangle = 1.67 squares in

(b) Area of rectangle = 3.33 squares in

(c) Area of rectangle = 6.67 squares in

(d) Area of rectangle = 0.53 squares in

(e) Area of rectangle = 1 squares in

The area of a rectangle is defined as the product of the length and width.

(a) Length of rectangle =  5 in and

Width of rectangle =  1/3 in

Area of rectangle = 5 × 1/3 = 5/3 = 1.67 square in

(b) Length of rectangle =  5/2 in and

Width of rectangle =  4/3 in

Area of rectangle = 5/2 × 4/3 = 20/6 = 3.33 square in

(c) Length of rectangle =  5 in and

Width of rectangle = 4/3 in

Area of rectangle = 5 × 4/3 = 20/3 = 6.67 square in

(d) Length of rectangle =  2/5 in and

Width of rectangle = 4/3 in

Area of rectangle = 2/5 × 4/3 = 8/15 = 0.53 square in

(e) Length of rectangle =  7/6 in and

Width of rectangle = 6/7 in

Area of rectangle = 7/6 × 6/7 = 42/42 = 1 square in

Learn more about the Area of the rectangle here:

brainly.com/question/20693059

#SPJ2

Answer:

  2300

Step-by-step explanation:

When you multiply by 10, each place value moves one to the left: hundreds become thousands, tens become hundreds.

(2 hundreds 3 tens) × 10 = 2 thousands 3 hundreds

In numbers (standard form), this is ...

  230 × 10 = 2300

Greetings from Brasil...

The volume of a sphere is given by the expression:

where R = radius

So

V = (4πR³)/3

V = (4.π.12³)/3

V = (4.π.1728)/3

V = 6912π/3

or

V = 7,238.23cm³

Answer:

if its asking for the tenths place its 3.7

if its asking for the ones place its 4

Step-by-step explanation:

Answer:

DC

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

First, let's define each of the terms.

Scalene refers to triangles whose three sides and three angles all have different measures.

Isosceles refers to triangles who has two equivalent angles and sides.

Right triangles are triangles with one right angle.

So we know that the triangle has one 90 degrees and 2 45 degree angles.

In other words, this is an isosceles triangle.

And since it also contains a 90 degree angle, it means that the triangle is an isosceles right.

The answer is D

Answer:

3 customers brought all the three papers.

Step-by-step explanation:

Let, D, O and N represents the three newspapers.

D = The daily times

O = The observer

N = The new Nigeria.

According to the given information,

[tex]n(D\cup O\cup N)=135, n(D)=70,n(O)=60,n(N)=50[/tex]

[tex]n(D\cap O)=17, n(O\cap N)=15, n(D\cap N)=16[/tex]

We know that,

[tex]n(A\cup B\cup C) = n(A) + n(B) + n(C)-n(A\cap B)-n(B\cap C)-n(C\cap A) + n(A\cap B\cap C)[/tex]

Using this formula, we get

[tex]n(D\cup O\cup N) = n(D)+n(O) + n(N)-n(D\cap O)-n(O\cap N)-n(N\cap D) + n(D\cap O\cap N)[/tex]

[tex]135 =70+60+50-17-15-16 +n(D\cap O\cap N)[/tex]

[tex]135 =132+n(D\cap O\cap N)[/tex]

[tex]135 -132=n(D\cap O\cap N)[/tex]

[tex]3=n(D\cap O\cap N)[/tex]

Therefore, 3 customers brought all the three papers.

Answer:

104%

Step-by-step explanation:

if it has to do with percentages

Answer:

sixty-eight and ninety-four hundredths

Step-by-step explanation:

Answer: sixty eight and ninety four hundredths

Step-by-step explanation:

60 = sixty

8 = eight

. = decimal (and)

.9 = nine tenths

.04 = four hundredths

so....

sixty eight and ninety four hundredths