Find the volume of given solid figure.​

Answer:

a₈ = 39366

Step-by-step explanation:

The terms have a common ratio between consecutive terms

r = 54 ÷ 18 = 162 ÷ 54 = 3

This indicates the sequence is geometric with nth term

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = 18 and r = 3 , then

a₈ = 18 × [tex]3^{7}[/tex] = 18 × 2187 = 39366

Answer:

Step-by-step explanation:

First coordinate of a point we read from X-axis and the second coordinate of a point we read from Y-axis

The question is incomplete. The complete question is :

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 54 meters cubed. Amie found the volume of the sphere. A sphere with height h and radius r. A cylinder with height h and radius r. Her work is shown below. V = two-thirds + 54. V = two-thirds + StartFraction 162 Over 3 EndFraction. V = StartFraction 164 Over 3 EndFraction meter cubed. What is Amie's error?

Solution :

Amie should have multiplied 54 by two-thirds.

Given that sphere and the cylinder have the same radius as well as same height. The volume of the cylinder is 54 inch cube.

Volume of the sphere = [tex]$\frac{4}{3}\pi r^3$[/tex]      .......... (i)

Volume of cylinder = [tex]$\pi r^2h$[/tex]   ....................(ii)

Therefore, the ratio of sphere volume to cylinder volume is,

[tex]$\frac{4}{3}\pi r^3 : \pi r^2 h$[/tex]   ......(iii)

Divide both the sides by [tex]$\pi r^2$[/tex] , we get

[tex]$\frac{4}{3} \ r : h$[/tex]          ..........(iv)

We know that the height of the sphere = diameter of the sphere

The diameter of the sphere is D = 2r

Also the sphere height = cylinder height

So, the height of the cylinder = 2r

Therefore, substituting the height of the cylinder as 2r that is represented as h in equation (iv) is given by :

[tex]$\frac{4}{3} \ r : 2r$[/tex]        .............(v)

Now dividing both the sides by 2r, we get

[tex]$\frac{2}{3} : 1$[/tex]   ..................(vi)

Thus for equation (vi), we see, sphere volume = [tex]$\frac{2}{3}$[/tex]  of the cylinder volume

∴  sphere volume = [tex]$\frac{2}{3}\times 54$[/tex]

                              = 36 meter cube

Thus, Amie should have multiplied 54 by [tex]$2/3$[/tex] .  

The value of the length will be 17920cm.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Since the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³.

The value of the length will be:

= 7 / (7 +5+2) × 35840

= 7/14 × 35840

= 17920cm

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the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³. Find the value of the length

Answer:

x ≈ 25.4

Step-by-step explanation:

Using the sine ratio in the right triangle

sin37° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{15.3}{x}[/tex] ( multiply both sides by x )

x × sin37° = 15.3 ( divide both sides by sin37° )

x = [tex]\frac{15.3}{sin37}[/tex] ≈ 25.4 ( to the nearest tenth )

The length of the sides RS, ST and TR are √72, √41 and √37 in the scalene triangle RST.

The distance between any two points A(a,b) and B(c,d) in the plane is given by,

AB = √((c-a)²+(d-b)²)

Here, it is given that the points of the triangle are R(-4,4) S(-2,-2) T(2, 3).

The triangle is scalene so length of every side is different.

Now, Using the above formula,

RS = √((2+4)²+(-2-4)²)

RS = √(36+36)

RS = √72

ST = √((2+2)²+(3+2)²)

ST = √(16+25)

ST = √41

TR = √((2+4)²+(3-4)²)

TR = √(36+1)

TR = √37

So, Brian is correct, the triangle is a scalene triangle.

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Answer:

Step-by-step explanation:

The sum of Annie's, Bobby's, Ciro's, and Denise's answers is $ 1140.1.

A number is simplified when it is rounded off, preserving its value while moving it closer to the next number. It is done for whole numbers as well as decimals at various places of hundreds, tens, tenths, etc.

If the number following the decimal is between 0 and 4, a number may be rounded off to its lowest value. If the number after it is between 5 and 9, the number will be rounded off to a greater value.

Annie rounds $ 280.05 to the nearest hundred

$ 280.05 will be equal to $ 300

Bobby rounds $ 280.05 to the nearest ten

$ 280.05 will be equal to = $ 280

Ciro rounds $ 280.05 to the nearest integer

$ 280.05 will be equal to = $ 280

Denise rounds $ 280.05 to the nearest tenth

$ 280.05 will be equal to = $ 280.1

Then, the sum of Annie's answer, Bobby's answer, Ciro's answer, and Denise's answer = $ 300 + $ 280 + $ 280  + $ 280.1 = $ 1140.1

Therefore,

The sum of Annie's, Bobby's, Ciro's, and Denise's answers is $ 1140.1.

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There is a probable (>50%) that two people in a room with 23 people will share the same birthday.

Probable means likely to occur or prove true, or having more evidence for than against, or evidence that inclines the mind to belief but leaves some room for doubt, or affording ground for belief.

Even while it may appear odd that only 23 people are needed to achieve a 50% likelihood of a shared birthdate, this conclusion is made more logical by keeping in mind that birthday comparisons will be done between all potential pairs of people.

There is a 50% chance that two people in a room with 23 people will share the same birthday. Though it may seem strange, it is mathematically accurate.

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Answer:

48 hours

Step-by-step explanation:

Answer:

48 hours

Step-by-step explanation:

328.80 a week, and a 6.85 hourly rate.

To find hours worked:

$328.80 (total earned) / $6.85 (earned hourly) = 48 hours

Answer:

a) B

b) C

Step-by-step explanation:

The surface area of the triangular prism is 156cm² when the triangle sides are 8cm  and 15 cm rectangle sides are 17cm and 2 cm.

Given that,

We have to find the total surface area of the triangular prism in the given picture.

We know that,

First, we need to calculate the area of ​​the triangle

a = area of triangle

a = 1/2 ×15 cm × 8 cm

a = 60 cm²

Now,

We must determine the three rectangles' areas.

a₁ = 2cm × 17cm

a₁ = 34cm²

a₂ = 2cm × 15cm

a₂ = 30cm²

a₃ = 2cm ×8cm

a₃ = 16cm²

Now, we must multiply the triangle by two and sum all the estimated areas.

a₁ + a₂ + a₃ + 2a =60cm² + 34cm² + 30cm² + 2 × 16cm² = 156cm²

Therefore, The surface area of the triangular prism is 156cm² when the triangle sides are 8cm  and 15 cm rectangle sides are 17cm and 2 cm.

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a) To write an equation in slope-intercept form to represent the growth of the Magnolia trees over time, we can use the formula y = mx + b, where x represents the number of years, y represents the height of the tree in feet, m represents the slope (or rate of growth) of the tree, and b represents the y-intercept (or the height of the tree at x = 0).

In this case, the slope (m) of the tree is 3/4 feet per year and the y-intercept (b) is 3 feet, as the trees are initially 3 feet tall when they are purchased. Plugging these values into the formula gives us:

y = (3/4)x + 3

This equation represents the growth of the Magnolia trees over time.

b) The y-intercept of an equation in slope-intercept form represents the value of y when x is equal to 0. In this case, the y-intercept of the equation y = (3/4)x + 3 is 3 feet. This means that when x is equal to 0 (when no years have passed), the height of the tree is 3 feet.

c) To determine the height of the tree in 3 years, we can substitute 3 for x in the equation y = (3/4)x + 3 and solve for y. This gives us:

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

= 9/4 + 3

= 21/4

= 5.25 feet

Therefore, the height of the tree in 3 years is approximately 5.25 feet.

Answer: 62 inches

Step-by-step explanation:

26÷13 =2

so 2 is the scale factor

so 36÷2= 18

18+18+13+13=62

I HOPE THAT HELPED

Answer:

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Step-by-step explanation:

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Answer:

They are both identical triangles with the same angles and lenght which means they are congruent and so their hypotenuses lines AC and CB are also congruent.

Step-by-step explanation:

Hope this helps

Answer:

they are congruent because they are on a perpendicular line

Answer: 7:20

Step-by-step explanation:

It seems like there are no options to choose from, but if that is one of the options, here's how:

You can simplify ratios by finding if there is a common multiple.

For 35 and 100, there is a common multiple of 5, so you can divide both sides by 5 to simplify the equation.

That leaves us with 7:20. Since one is a prime number, we can't simplify this further.

Answer:

The ratio equivalent to 35:100 is 7:20

Step-by-step explanation:

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

What is the Ratio?

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,

Given ratio,

= 35 / 100

= 5× 7 / 20 × 5

= 7 / 20

Answer:

(4,-1,6)

Step-by-step explanation:

x=4

y=-1

z=6

Over the course of the three hours, 41.25 gallons of water passed through the pipe in total.

We know that the rate of flow for the first hour was 50% slower than the rate of flow for the second hour. So, if the rate of flow in the second hour was 15 gallons per hour, the rate of flow in the first hour would be:

15 gallons/hour * (100% - 50%) = 15 gallons/hour * 50% = 7.5 gallons/hour

We also know that 25% more water flowed through the pipe in the third hour than in the second. So the rate of flow in the third hour would be:

15 gallons/hour * (1 + 25%) = 15 gallons/hour * 1.25 = 18.75 gallons/hour

To find the total number of gallons of water that flowed through the pipe during the entire three hours, we can multiply the rate of flow for each hour by the number of hours:

First hour: 7.5 gallons/hour * 1 hour = 7.5 gallons

Second hour: 15 gallons/hour * 1 hour = 15 gallons

Third hour: 18.75 gallons/hour * 1 hour = 18.75 gallons

Adding these values we can find the total amount of water that flowed through the pipe during the entire three hours

7.5 gallons + 15 gallons + 18.75 gallons = 41.25 gallons

So, in total 41.25 gallons of water flowed through the pipe during the entire three hours.

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Answer:

A) 2⁵*3

Step-by-step explanation:

96

2*48

2*2*24

2*2*2*12

2*2*2*2*6

2*2*2*2*2*3

2⁵*3

Therefore, A is the correct answer.

Answer:

[tex]speed = \frac{distance}{time} \\ speed = \frac{150}{3} \\ = 50 \: miles \: per \: hour[/tex]

1(t) = 12(t) (2,2,4) +t(2,4,6) and Ia(t) = 12(t) (2,2,4) +t(2,4,6) represents the same line, as they are both equivalent to 12(t)(2,2,4) + t(2,4,6). So Option A is correct.

The equation of a line in 3-dimensional space can be represented in the form "r(t) = a + tb" where "r(t)" is a vector that represents any point on the line, "a" is a vector that represents a point on the line, and "b" is a vector that represents the direction of the line.

The given equations are:

1(t) = 12(t) (2,2,4) +t(2,4,6)

Ia(t) = 12(t) (2,2,4) +t(2,4,6)

As we can see that both equations are identical to equation 12(t) (2,2,4) +t(2,4,6) thus these three equations represent the same line.

The other given options B, C, and D are not equivalent to each other or to the original equation, thus they do not represent the same line.

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Answer:

4 and 72

Step-by-step explanation:

Answer:

4 and 72 !

Step-by-step explanation:

Thus, It is possible to visually assess whether a limit exists as x approaches a by looking at the function f (x) and g (x) graphs, which are 1 and 5 when x is very close to x=a.

In mathematics, a limit is the value that a function, a sequence, or an index approaches as an input or an index gets closer to a particular value. Limits are essential to the study of calculus and mathematical analysis since they are used to define continuity, derivatives, and integrals.

Here,

From the function f (x) and g graphs shown here ( x)

1) lim f (x) plus lim g ( x )

= -1 + 2 = 1

2) f (-1) + lim g ( x)

= 3 + 2

= 5

Therefore , the solution of the given problem of limit comes out be 5.

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Answer:

The value of the 3 in the tenths place is 10 times the value in the hundredths place

Step-by-step explanation:

Ok

Answer:

supplementary, complementary, acute 45, supplementary, x=10

Step-by-step explanation: