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How is the distributive property used when finding the product of two polynomials? How are polynomials closed under multiplication?

Answer:

warmer

Step-by-step explanation:

-11 is closer to zero the -15

Answer:

warmer

Step-by-step explanation:

-15 is colder.

grusi lob ze cruz?masi pa koi foitaitua leo leone fatua fatui?

(1/3) × the cone's volume = The cylinder's volume.

Step-by-step explanation:

Step 1:

The volume of any cone is obtained by multiplying [tex]\frac{1}{3}[/tex] with π, the square of the radius ([tex]r^{2}[/tex]) and the height ([tex]h[/tex]).

So the volume of the cone, [tex]V=\pi r^{2} \frac{h}{3}[/tex].

Step 2:  

The cylinder's volume is nearly the same as the cone but instead by multiplying [tex]\frac{1}{3}[/tex] we multiply with 1.

So the cylinder's volume is determined by multiplying π with the square of the radius of the cylinder ([tex]r^{2}[/tex]) and the height of the cylinder ([tex]h[/tex]).

So the the cone's volume, [tex]V = \pi r^{2} h[/tex].

Step 3:

Now we equate both the volumes to each other.

The cone's volume : The cylinder's volume = [tex]\pi r^{2} \frac{h}{3}: \pi r^{2} h[/tex] = [tex]\frac{1}{3} : 1[/tex].

So if we multiply the cone's volume with [tex]\frac{1}{3}[/tex] we will get the cylinder's volume with the same dimensions.

Answer:

19.998

Step-by-step explanation:

Take the number and decrease (subtract)  by 9.1% of the original number

22 - 22*9.1%

Change the percent to decimal form

22 - 22*.091

22 -2.002

19.998

Final answer:

The result when the number 22 is decreased by 9.1% is 20.0, after calculating 9.1% of 22, which is 2.002, and subtracting it from 22 and rounding to the nearest tenths place.

Explanation:

To find the result when the number 22 is decreased by 9.1%, you can use the following steps:

Calculate the decrease amount by finding 9.1% of 22: (9.1/100) × 22.

Subtract the decrease amount from the original number: 22 - (9.1% of 22).

Using a calculator, the decrease amount is:
(0.091) × 22 = 2.002.

Then subtract this from the original number:
22 - 2.002 = 19.998.

However, we need to report our final answer to the nearest tenths place since that is the precision of the number 9.1%. Therefore, we round 19.998 to 20.0 to reflect the proper significant figures.

So, the result when the number 22 is decreased by 9.1% is 20.0.

Final answer:

The probability of drawing two green marbles consecutively without replacement from a bag containing 3 green and 3 red marbles is 1/5 or 20%.

Explanation:

The probability that both marbles drawn consecutively from an opaque bag without replacement will be green is calculated by multiplying the probability of the first event by the probability of the second event. Here, we have 3 green marbles out of a total of 6 marbles. So, the probability of drawing the first green marble is 3/6 or 1/2. After drawing one green marble, there are now 2 green marbles left out of 5 total marbles. Therefore, the probability of drawing a second green marble is now 2/5. To find the combined probability, we multiply these two probabilities together: (1/2) × (2/5) which equals 1/5 or 0.2. Hence, there is a 20% chance that both marbles drawn will be green.

The volume of the prop is calculated to be 2,712.96 cubic inches.

Step-by-step explanation:

Step 1:

The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying  [tex]\frac{1}{3}[/tex] with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 9 inches and the height is 14 inches.

The volume of the cone :  [tex]V=\pi r^{2} \frac{h}{3}[/tex] = [tex]3.14 \times 9^{2} \times \frac{14}{3}[/tex] = 1,186.92 cubic inches.

Step 3:

The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying  [tex]\frac{4}{3}[/tex] with π and the cube of the radius (r³).

Here the radius is 9 inches. We take π as 3.14.

The volume of a full sphere =  [tex]V=\frac{4}{3} \pi r^{3}[/tex] =  [tex]\frac{4}{3} \times 3.14 \times 9^{3}[/tex] = 3,052.08 cubic inches.

The volume of the half-sphere =  [tex]\frac{3,052.08}{2}[/tex] = 1,526.04 cubic inches.

Step 4:

The total volume = The volume of the cone + The volume of the half sphere,

The total volume = 1,186.92 + 1,526.04 = 2,712.96 cubic inches.

Answer:

84 minutes

HOPE THIS HELPS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

An hour is 60 minutes

60 x 2/5 = 24

24 minutes plus an hour (60 minutes)

= 84

Answer:

Noah should buy a ladder of length greater than 28.1 ft to reach at least 22 feet height.

Step-by-step explanation:

Given:

Noah has to reach at least 22 ft height.

Angle made by the base of ladder with the ground = 51.5°

To find the length of the ladder.

Solution:

On drawing the situation, we get a right triangle. The hypotenuse of the triangle represents the length of the ladder.

In triangle ABC.

∠C = 51.5°

AB = 22 ft

Applying trigonometric ratio to find AC (length of the ladder).

[tex]\sin\theta = \frac{Opposite\ side}{Hypotenuse}[/tex]

[tex]\sin C=\frac{AB}{AC}[/tex]

Plugging in values.

[tex]\sin 51.5\°=\frac{22}{AC}[/tex]

Multiplying AC both sides.

[tex]AC\sin 51.5\°=\frac{22}{AC}\times AC[/tex]

[tex]AC\sin 51.5\°=22[/tex]

Dividing both sides by [tex]\sin 51.5\°[/tex]

[tex]\frac{AC\sin 51.5\°}{\sin 51.5\°}=\frac{22}{\sin 51.5\°}[/tex]

[tex]AC=\frac{22}{\sin 51.5\°}[/tex]

[tex]AC=28.1\ ft[/tex]

Thus, Noah should buy a ladder of length greater than 28.1 ft to reach at least 22 feet height.

Answer:

5 days

Step-by-step explanation:

First subtract the flat fee so that you know you just have the price of the days

225-75

150       Then divide by 30, the day rate so you know how many days it was

150/30= 5

Selena had the car for 5 days

Solution:

The surface area of cube is given as:

[tex]Surface\ area = 6a^2[/tex]

Where, "a" is the length of side of cube

Given that, surface area = 486 square centimeter

[tex]486 = 6a^2\\\\a^2 = \frac{486}{6}\\\\a^2 = 81\\\\a = 9[/tex]

Find the volume of cube:

[tex]volume\ of\ cube = a^3\\\\volume\ of\ cube = 9^3\\\\volume\ of\ cube = 9 \times 9 \times 9\\\\volume\ of\ cube = 729[/tex]

Thus volume of cube is 729 cubic centimeter

The value of b is 5.4

Explanation:

Given that ABC is a triangle.

It is also given that [tex]a=12[/tex] , [tex]\angle B=25^{\circ}[/tex] and [tex]\angle C=45^{\circ[/tex]

We need to find the value of b.

The value of b can be determined using the law of sine formula, which is given by

[tex]\frac{a}{sin A} =\frac{b}{sin B} =\frac{c}{sin C}[/tex]

First, we shall find the angle of A.

Since, ABC is a triangle and all the angles in a triangle add up to 180°

Thus, we have,

[tex]\angle A+\angle B+\angle C=180[/tex]

  [tex]\angle A+25+45=180[/tex]

          [tex]\angle A+70=180[/tex]

                  [tex]\angle A=110^{\circ}[/tex]

Thus, the value of angle A is 110°

Let us substitute these values in the law of sine formula.

Hence, we get,

[tex]\frac{12}{sin \ 110^{\circ}} =\frac{b}{sin \ 25^{\circ}}[/tex]

Simplifying, we get,

[tex]\frac{12}{0.9397} =\frac{b}{0.423}[/tex]

Multiplying both sides of the equation by 0.423, we get,

[tex]\frac{12\times 0.423}{0.9397} =b[/tex]

Simplifying, we get,

[tex]\frac{0.5076}{0.9397} =b[/tex]

Dividing, we have,

[tex]5.4=b[/tex]

Thus, the value of b is 5.4

Yo sup??

by the property of log we can say that

laga+logb=logab

log4+log5=log4*5

=log20

Hope this helps

Answer:

1/4 and 2/12

Step-by-step explanation:

If you mulitply both the numerater and denominator by 2 (or any number) it will be equivelent.

1/6 is equivelient to 2/12, 3/18, etc.

However, if you divide 3/12, you get 0.25, which is equivelent to 1/4

Answer:

11%

Step-by-step explanation:

The margin of error is the standard error times the critical value.

For a proportion, the standard error is:

σ = √(pq / n)

σ = √(0.132 × 0.868 / 1105)

σ = 0.0102

Since n is large, we can approximate the critical value using a normal distribution.  For 99% confidence, the critical value is 2.576.

The margin of error is:

ME = 0.0102 × 2.576

ME = 0.026

The confidence interval is 0.132 ± 0.026.  So the lower limit is 0.106, or 10.6%.  Rounded to the nearest whole number, that's 11%.

Answer:

90⁰

Step-by-step explanation:

The diagonal of the rectangles forms two angles with the sides, about 32 degrees and 58 degrees respectively. These are found using the Pythagorean theorem to find the length of the diagonal, and then the arctan function to find the angles.

To find the angle that the diagonal makes with the sides of the rectangle, first calculate the length of the diagonal which can be found using the Pythagorean Theorem. In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We can write this as: c² = a² + b². In this case, the length and width of the rectangle are the two sides (a and b) and the diagonal is the hypotenuse (c).

So a = 68 inches, b = 42 inches. Plugging these into our formula gives: c² = 68² + 42², so c = √[(68²) + (42²)] which approximates to 80 inches.

Next, calculate the angles using the inverse tangent (or arctan) function: θ = arctan(opposite/adjacent). In this case, the angles are = arctan(42/68) and arctan(68/42). This gives us angles of approximately 32 degrees and 58 degrees.

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Answer:

center(8x,12y) radius 3

Step-by-step explanation:

If i am doing this correct

Length of the rectangle is 150 m.

Step-by-step explanation:

Step 1:

Let the width of the rectangle be x. Then the length = 3x. Given that perimeter = 400 m, find the length.

Perimeter of the rectangle = 2 (length + breadth)

400 = 2 (3x + x)

400 = 8x

∴ x = 400/8 = 50

⇒ Width is 50 m

∴ Length = 3x = 150 m

Answer:

NO.

Step-by-step explanation:

If it is a right triangle then by the Inverse of the Pythagoras Theorem:

40^2 = 35^2 + 15^2

Testing:

40^2 = 1600

35^2 + 15^2 = 1225 + 225 = 1450

So the answer is NO>

Answer:

Step-by-step explanation:

If a ≤ b ≤ c are sides of a triangle, then a + b > c.

We have a = 15, b = 35, c = 40.

Check:

15 + 35 = 50 > 40           CORRECT

These sides can be the sides of a triangle.

If a ≤ b ≤ c are sides of a triangle, then

if a² + b² = c², then it's a right triangle

if a² + b² < c², then it's an obtuse triangle

if a² + b² > c², then it's an acute triangle

Check:

15² + 35² = 225 + 1225 = 1450

40² = 1600

1450 < 1600 ⇒ 15² + 35²  < 40²

Therefore it's  an obtuse triangle

Answer:

assume an approximate value for the variable that will simplify the equation.

solve for the variable.

use the answer as the second approximate value and solve the equation again.

repeat this process until a constant value for the variable is obtained.

Answer:

1900 ft

Step-by-step explanation:

To find the area where roses will be planted, find the area of the 2 triangles. 60×38 divided by 2 = 1140ft. 40×38 divided by 2 = 760. 760+1140=1900

To estimate 52% of 71, you can use either the proportion method or the multiplication method by setting up a proportion or multiplying 0.52 by 71.

To estimate 52% of 71, you can use either proportion or multiplication. Here's how:

Using the proportion method:

52/100 = x/71

71 * 52 = 100 * x

x = 36.92 (rounded to 37)

Using the multiplication method:

0.52 * 71 = 36.92 (rounded to 37)

Answer:

x = 9.25

y = 13.5

Step-by-step explanation:

area = 33

let length be y and width be x

2x - 5 = y

area of rectangle = length * breadth

(2x-5)(x)=33

2x²-5x=33

2x²-5x-33=0

solving quadratic equation

x = 9.25

y = 13.5

Answer:

A. 0.60

Step-by-step explanation:

make a proportion so

36 over 60 = x over 100

36*100= 3600

3600/60

60

.60

The probability that the student attended the jazz concert is 0.60. The correct answer is option A.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

It is given from the table that the student who attended the jazz concert is 36 out of 60 students. Then the probability that the student attended the jazz concert is calculated as below:-

Probability = Number of favorable outcomes / Number of sample

Probability = 36 / 60

Probability = 0.60

Therefore, the probability that the student attended the jazz concert is 0.60. The correct answer is option A.

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Answer:

length of an arc = 1unit

Step-by-step explanation:

given that the circumference of a circle = 6

central angle = 60

length of the arc =?

recall that the circumference of a circle = 2πr

6 = 2πr

r = 6/2π

now to calculate the length of an arc

recall,

length of an arc = 2πr(Ф/360)

length of an arc = 2π(6/2π) × 60/360

length of an arc = 6 × 60/360

length of an arc = 360/360

length of an arc = 1unit

therefore the length of the arc whose circumference is 6 and arc angle is 60° is evaluated to be 1unit

Final answer:

Roshanda bought the same amount of roast beef as ham, 0 pounds.

Explanation:

To find out how much more roast beef Roshanda bought compared to ham, we need to subtract the weight of the ham from the weight of the roast beef. Roshanda bought 1 pound of ham and 1 pound of roast beef, so the difference is 1 pound minus 1 pound, which equals 0 pounds. Therefore, Roshanda did not buy more roast beef than ham, they bought the same amount.

Roshanda bought 1/4 pound more roast beef than ham.

To find out how much more roast beef Roshanda bought compared to ham, we need to subtract the amount of ham from the amount of roast beef.

Given:

Ham = 5/8 pound

Roast beef = 7/8 pound

To find the difference:

Roast beef - Ham

= (7/8) - (5/8)

To subtract fractions, we need a common denominator, which is 8 in this case.

= (7/8) - (5/8)

= (7 - 5)/8

= 2/8

Now, simplify the fraction:

2/8 = 1/4

So, Roshanda bought 1/4 pound more roast beef than ham.

Question

Roshanda bought 5/8 pound of ham and 7/8 pol 11 d of roast beef. How much more roast beef than ham did she buy? Write in simplest form.

Answer:

1. True

2. False

3.True

4.False

Answer:

A-0.5777miles

B-0.7223miles

Step-by-step explanation:

Let A be truck with 58°, B be truck with 52° elevation and C be the position of the fire. We know that the AB is 1.3 miles apart.

-Using sine rule, we find the length of AB and BC as:

[tex]\angle C=180-(58+52)=70\textdegree\\\\\frac{a}{sin \ A}=\frac{b}{sin \ B}=\frac{c}{sin \ C}\\\\\frac{1.3}{sin \ 70}=\frac{b}{sin \ 52}\\\\b=\frac{1.3 sin \ 52}{sin 70}=1.0902mi\\\\\\c=\frac{1.3 sin \ 58}{sin 70}=1.1732[/tex]

#Bisect angle C, and use sine rule again to find the lengths of bisected AB:

[tex]\frac{a}{sin \ A}=\frac{b}{sin \ B}=\frac{c}{sin \ C}\\\\\frac{1.0902}{sin \ 90}=\frac{x}{sin \ (90-58)}\\\\x=\frac{1.0902\ sin \ 32}{sin \ 90}=0.5777mi[/tex]

Truck B's position is calculated as 1.3mi-0.5777miles=0.7223miles

Hence, truck one is 0.5777miles and truck two is 0.7223 miles from the fire.

Answer:

31/30 gallons

Step-by-step explanation:

finding the lowest common denominator for all three numbers. so 1/3 becomes 10/30, 1/5 becomes 6/30, and 1/2 becomes 15/30. 10/30+6/30+15/30=31/30

Answer:31/30

Step-by-step explanation:

you have to first find a common denominator. Which in this case is 30 so then you have to multiply by the same number for both bottom and top number of the fraction. 1/3 = 10/30 1/5=6/30 1/2=15/30. Then, you just have to add JUST THE TOP NUMBERS. You get 31/30 then divide that and i will leave that last part to you. Hope this helps!

Final answer:

The student needs to find the missing number 'b' in a data set, given that the range is 25. Since we know the smallest value is 1, adding the range to that value gives us the largest possible number, which in this case is 26. Therefore, 'b' must be 26 to achieve the specified range.

Explanation:

The student is asking about finding a missing value in a set of numbers given the range of the data set. To find the value of b, we must remember the definition of range: Range is the difference between the largest and smallest values in a set.

With the knowledge that the range is 25, and having the numbers 14, 14, 16, and 1, we identify 1 as the smallest value.

If we add the range to the smallest number (1 + 25), we get the largest number the set could contain, which is 26.

Since the other numbers in the set are all smaller than 26, b must equal 26 for the range to be 25.