Sample response: Start by calculating the volume of the original prism. The area of the base, B, is 4(6) = 24 m2. Multiply that by the height to get the volume: 24(10) = 240 m3. Now, if you double all of the dimensions, you would have a rectangular prism with a base that is 8 m by 12 m and a height of 20 m. The area of the base, B, is 8(12) = 96 m2. Multiply that by the height to get the volume: 96(20) = 1,920 m3. To compare, look at the ratio of the original prism to the new prism: 96/1,920 = 1/8. The volume increases by 8 times the original volume.

Check all that you included in your response.
Find the original volume. The area of the base, B, is 4(6) = 24 m2. Multiply that by the height to get the volume: 24(10) = 240 m3.
If you double all of the dimensions, you would have a rectangular prism with a base that is 8 m by 12 m and a height of 20 m.
Find the new volume. The area of the base, B, is 8(12) = 96 m2. Multiply that by the height to get the volume: 96(20) = 1,920 m3.
The volume increases by 8 times the original volume.

Answer:

8/225

Step-by-step explanation:

The probability of each event would be the number of the type of currency that you have specified divided by the total number of coins, in this case the total amount of coins does not change as the coin returns to the bag.

The total number of coins is: 10 + 12 + 8 = 30

The probability of finding a quarter is:

10/30

The probability of finding dime is:

8/30

The probability of finding nickel is:

12/30

The final probability then is:

(10/30) * (8/30) * (12/30) = 960/27000

If we simplify this, dividing both numbers by 120, we are left with:

8/225

Answer :

9

Explanation :

The expression above signifies the Permutation expression

Permutation expression is given as nPr

The Permutation expression is calculated as:

nPr = P(n, r) = n! / (n - r)!

It the above question, we were asked to evaluate the expression 9P1

From the above question, we can see that:

n = 9 and r = 1

Therefore, the expression

9P1 = 9! / ( 9 - 1) !

9P1 = 9! / 8!

= 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 362880 /40320

= 9

Therefore, the evaluation of the expression 9P1 = 9

Final answer:

To evaluate the expression 9P1, we calculate the permutation for selecting 1 item from 9, which simplifies to 9/1, giving us the answer of 9.

Explanation:

The student has asked to evaluate the expression 9P1, which is a permutation problem. To find 9P1, we use the permutation formula, which is P(n, k) = n! / (n-k)!, where n is the total number of items to choose from, and k is the number of items to choose. In this case, since we want to choose 1 item from 9, the permutation is calculated as:

Therefore, the value of 9P1 is 9.

Answer:

The integers are:

44,46,48

Step-by-step explanation:

Answer:

9.8

Step-by-step explanation:

Answer:

9.8 that is the answer

Step-by-step explanation:

To increase £258 by 43%, convert the percentage to a decimal, calculate the increased amount, and add it to the original amount. The increased amount to the original amount is £368.94

To increase £258 by 43% using the multiplier method:

Convert the percentage to a decimal: 43% = 0.43

Calculate the increased amount: £258 x 0.43 = £110.94

Add the increased amount to the original amount: £258 + £110.94 = £368.94

Answer:

The answer is "$ 4450"

Step-by-step explanation:

Purchased policy price = $50,000

10th anniversary cash value = ?

The after calculation its final value is = $ 4450

Answer:

B. Opposite angles add up to 180 degrees.

Step-by-step explanation:

Answer Choice B is incorrect because opposite angles are actually congruent. However, adjacent angles of a parallelogram do add up to 180 degrees.

Answer:

[tex]y = 66.25(1.11)^x[/tex]

Step-by-step explanation:

Let's plug in 9 for x and 171 for y into the given exponential equation:

y = [tex]ab^x[/tex]

171 = [tex]ab^9[/tex]

Now do the same with (10, 190):

190 = [tex]ab^{10}[/tex]

Write them both in terms of a and set them equal:

a = 171/[tex]b^9[/tex]

a = 190/[tex]b^{10}[/tex]

171/[tex]b^9[/tex] = 190/[tex]b^{10}[/tex]

Multiply both sides by [tex]b^{10}[/tex]:

171b = 190

b = 190/171 = 10/9 ≈ 1.11

Plug this in to find a:

a = 171 / (10/9)^9 ≈ 66.25

So, the exponential model is:

[tex]y = 66.25(1.11)^x[/tex]

Answer:

y = 66.25[(10/9)^x]

Step-by-step explanation:

171 = a(b⁹)

b⁹ = 171/a

190 = a(b¹⁰)

190 = a(171/a) × b

b = 190/171

b = 10/9

(10/9)⁹ = 171/a

a = 66.24890362

Answer:

5

Step-by-step explanation:

If e = 7, you would replace e in the expression e - 2 with 7 so that the expression becomes 7 - 2 which results in 5.

Does that help?

Answer:

2(2-n)

Step-by-step explanation:

4 - 2n

Factor out a 2

2*2 -2n

2(2-n)

Answer:

see below

Step-by-step explanation:

V = l*w*h for the rectangular  tank

V = 70* 40*40

  =112000 cm^3 = 1mL

The water is 84000

Make this a fraction

84000/112000  = 3/4

The water fills 3/4 of the tank

1-3/4 = 1/4

It is 1/4 from the top

Find the volume of the treasure chest

V = 12*10*8 =960

Tower

V = pi r^2

  3.14 * 10^2 *10

  =3140

Water + chest + tower

84000+960+3140 =88100

This is less than 112000 so the water will not overflow

Answer:

a) 10 cm

b) Will not overflow

Step-by-step explanation:

8400 = base area × height

84000 = 70 × 40 × h

h = 30

From the top: 40 - 30 = 10cm

b) Capacity of the tank:

70 × 40 × 40

112,000 cm³

Combined volume of the two vessels:

(12 × 10 × 8) + (3.14 × 10² × 10)

960 + 3140

4,100 cm³

4100 = 70 × 40 × rise

rise = 1.464285715 cm

Since 1.464285715 < 10

It will not overflow

Answer:

5940 y

Step-by-step explanation:

Simplify the following:

-11 (-9)×5×3×4 y

-9×3 = -27:

-11×5×-27×4 y

-27×4 = -108:

-11×5×-108 y

-11×5 = -55:

-108-55 y

-55 (-108) = 5940:

Answer: 5940 y

Answer:

339604.65 cubic feet

Step-by-step explanation:

We are given that 1 m is equal to 3.3 ft.

1 m = 3.3 ft

This means that if we find the volume of a cube of 1 m, we have its volume as:

[tex]1^3 = 1 m^3[/tex]

In the same way, the volume of a cube of 3.3 ft (1 m) is:

[tex]3.3^3 = 35.937 ft^3[/tex]

This means that:

[tex]1m^3 = 35.937 ft^3[/tex]

The Kuroshio sea tank has volume of [tex]9450 m^3[/tex]. Its volume in cubic feet is therefore:

[tex]1m^3 = 35.937 ft^3\\\\9450 m^3 = 9450 * 35.937 = 339604.65 ft^3[/tex]

The volume of the tank is 339604.65 cubic feet.

Answer:

21

Step-by-step explanation:

(9g+4)-55=

(72+4)-55=

76-55=

21

Final answer:

To find the answer, first multiply 9 by 8, then add 4, resulting in 76. Finally, subtract 55 to get the answer, which is 21.

Explanation:

To solve the problem, we need to first calculate the sum of 9g and 4 when g=8. This will be 9 × 8 + 4.

After calculating the sum, we will subtract 55 from this amount to get the final answer.

Following the steps:

Therefore, when g = 8, subtracting 55 from the sum of 9g and 4 results in  21.

Answer:

The center of data is a single number that summarizes the entire data set.

Step-by-step explanation:

Answer:

24.75m ≤ 30m < 35.75m

Step-by-step explanation:

Minimum area:

5.5 (lower bound of 6m) * 4.5 (lower bound of 5m) = 24.75m

Maximum area:

6.5 (upper bound of 6m) * 5.5 (upper bound of 5m) = 35.75m

Normal area:

6*5=30m

I hope that makes some sense or helps a little!

Answer:

8

Step-by-step explanation:

3m + 9 -9m = 2m + 25

3m + 9 = 11m + 25

9 = 8m + 25

16/2 = 8m/2

M = 8

the actual distance between the two towns is 360 miles.

The ratio used to depict the relationship between the dimensions of a model or scaled figure and the corresponding dimensions of the real figure or object is called the scale. On the other hand, a scale factor is a value that is used to multiply all of an object's parts in order to produce an expanded or decreased figure.

Given, On a map, the distance between two towns is 12 centimeters.

Also given, 3 centimeters represent 90 miles on the map.

Since 12 centimeters represent the distance between the two towns on the map, we can set up the proportion:

3 centimeters : 90 miles = 12 centimeters : x miles

where x represents the actual distance between the two towns in miles.

To solve for x, we can cross-multiply and simplify:

3 centimeters * x miles = 90 miles * 12 centimeters

3x = 1080

x = 360

Therefore, the actual distance between the two towns is 360 miles.

Learn more about scale here:

https://brainly.com/question/1287267

#SPJ6

Answer:

A. Circle

Step-by-step explanation:

Perpendicular to m is parallel to the base of the cones (circular).

Therefore the cross section would be a circle (except at the vertex)

In one year, the Perseid meteor shower had a meteor appear every 1 1/5 minutes on average. That same year, the Leonid meteor shower had a meteor appear every 4 2/3 minutes on average. How many more meteors fell during the Perseid meteor shower?

Answer:

325,452 meteors

Step-by-step explanation:

We all know that :

We have 365 days in a year and in each day there are 24 hours, Likewise an hour has 60 minutes

SO, the total number of minutes in a year is :

365 × 24 × 60 = 525600 minutes

For Perseid  meteor:

[tex]1 + \frac{1}{5} \\ \\ = 1 + 0.2 \\ \\ = 1.2[/tex]

So one meteor fall at 1.2 minutes interval Thus, in a year, we will have :

1 meteor - 1.2 minutes.

x meteor - 525600 minutes.

1.2x = 525600

[tex]x = \frac{525600}{1.2}[/tex]

x = 438000

∴  438,000 meteors fell during the Perseid shower.

For  Leonid meteor shower:

[tex]4 + \frac{2}{3} = 4.67[/tex]

So one meteor fall at 4.67 minutes interval Thus, in a year, we will have :

1 meteor - 4.67 minutes.

x meteors - 525600 minutes.

[tex]4.67x = 525600[/tex]

[tex]x = \frac{525600}{4.67}[/tex]

x = 112548

112,548 meteors fell during the Leonid Shower.

Finally , the numbers of more meteors that  fell during the Perseid meteor shower is calculated by the difference in the number of Perseid meteor shower and Lenoid meteor shower. i.e

438,000 - 112,548 = 325,452

325,452 more meteors fell during the Perseid meteor shower

Answer:

For Leonid meteor shower: So one meteor fall at 4.67 minutes interval Thus, in a year, we will have : 1 meteor - 4.67 minutes. x meteors - 525600 minutes

Step-by-step explanation:

Answer:

416 x 5 = 2080

721 x 8 = 5768

5768 + 2080 = 7848. Have a great day.

We have been given that the 5th term in a geometric sequence is 160. The 7th term is 40. We are asked to find the possible values of 6th term of the sequence.

We know that an geometric sequence is in form [tex]a_n=a\cdot r^{n-1}[/tex], where,

[tex]a_n[/tex] = nth term of sequence,

a = First term,

r = Common ratio,

n = Number of terms.

We will get two equations using our given information as:

[tex]160=a\cdot r ^{5-1}...(1)[/tex]

[tex]160=a\cdot r ^{4}...(1)[/tex]

[tex]40=a\cdot r ^{7-1}...(2)[/tex]

[tex]40=a\cdot r ^{6}...(2)[/tex]

Upon dividing equation (2) by equation (1), we will get:

[tex]\frac{40}{160}=\frac{a\cdot r^6}{a\cdot r^4}[/tex]

[tex]\frac{1}{4}=r^{6-4}[/tex]

[tex]\frac{1}{4}=r^{2}[/tex]

[tex]r^{2}=\frac{1}{4}[/tex]

[tex]\sqrt{r^{2}}=\pm\sqrt{\frac{1}{4}}[/tex]

[tex]r=\pm\frac{1}{2}[/tex]

Let us solve for a.

[tex]160=a\cdot (\frac{-1}{2})^{4}[/tex]

[tex]160=a\cdot \frac{1}{16}[/tex]

[tex]160\cdot 16=a\cdot \frac{1}{16}\cdot 16[/tex]

[tex]2560=a[/tex]

So our formula would be [tex]a_n=2560\cdot (\pm\frac{1}{2})^{n-1}[/tex].

We cannot determine whether the common ratio would be positive or negative, so we will take both values.

[tex]a_6=2560\cdot (\pm\frac{1}{2})^{6-1}[/tex]

[tex]a_6=2560\cdot (\pm \frac{1}{2})^{5}[/tex]

[tex]a_6=2560\cdot \pm \frac{1}{32}[/tex]

[tex]a_6=\pm 80[/tex]

Therefore, the 6th term of the sequence would be [tex]\pm 80[/tex] and option C is the correct choice.

Answer:

C.+- 80

Step-by-step explanation:

Answer:

the first and third

Step-by-step explanation:

Answer:

A and C

Step-by-step explanation:

Answer:

Three students voted for horns.true

Step-by-step explanation:thats all i know

Answer:

B, D, E, F

Step-by-step explanation:

Three students voted for horns.

Thirteen students voted for piano or guitar.

Twice as many students voted for piano as horns.

Eleven students voted for flute or guitar.

Answer: 1/24

Step-by-step explanation:

If one fourth was split into six pieces, you would multipli six by one fourth to get 1.24==

Answer:

18pi, or 56.52

Step-by-step explanation:

To start off, if you were to find the area of any whole circle, you would use the formula: pi x radius^2 = area of circle

However, since this is a semi-circle (half of a whole circle) you would divide the whole expression by 2, and then solve:

(pi x radius^2)/2 = area of semi-circle

(pi x 6^2)/2 = area of semi-circle

(36 x pi)/2 = area of semi-circle

18 x pi = area of semi-circle

18 x 3.14 = area of semi-circle

56.52 = area of semi-circle

The area of a circle is

[tex]\pi \: {r}^{2} [/tex]

So the area of a semicircle would be half of that, or

[tex] \frac{\pi}{2} {r}^{2} [/tex]

So just plug in the radius, six, to get this

[tex]18\pi[/tex]

Answer:

The answer is $321,631.08

Step-by-step explanation:

I just did a test on it. Got it wrong, but it showed me the right answer.

Answer:

321,621,numbers

Step-by-step explanation:

Answer:

x= [tex]2-\sqrt{3}[/tex]          and          x=[tex]2+\sqrt{3}[/tex]

Step-by-step explanation:

- transfer the -1 to the other side so that the equation reads as [tex]x^{2} -4x+1[/tex]

- factor! think about what numbers add -4 but also multiply to be 1

- you may then realize that there are no numbers with those characteristics

- since that is the case, we have to use the quadratic formula, which is:

               [tex]\frac{-b+\sqrt{b^{2}-4ac }}{y}[/tex]        and         [tex]\frac{-b-\sqrt{b^{2}-4ac }}{y}[/tex]

- the equation is shown as [tex]a^{2}+b^{2}=c^{2}[/tex]

- using the numbers that correspond with those lettered values, plug it in the quadratic formulas

the solutions to the equation [tex]\( x^2 - 4x = -1 \) are \( x = 2 + \sqrt{3} \) and \( x = 2 - \sqrt{3} \)[/tex].

To find the solutions to the equation [tex]\( x^2 - 4x = -1 \)[/tex], we can follow these steps:

1. Move all terms to one side of the equation to set it equal to zero:

 [tex]\[ x^2 - 4x + 1 = 0 \][/tex]

2. We can solve this quadratic equation using the quadratic formula:

  [tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

  where [tex]\( a = 1 \), \( b = -4 \), and \( c = 1 \).[/tex]

3. Plug in the values and simplify:

  [tex]\[ x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(1)}}{2(1)} \] \[ x = \frac{4 \pm \sqrt{16 - 4}}{2} \] \[ x = \frac{4 \pm \sqrt{12}}{2} \] \[ x = \frac{4 \pm 2\sqrt{3}}{2} \] \[ x = 2 \pm \sqrt{3} \][/tex]

So, the solutions to the equation [tex]\( x^2 - 4x = -1 \) are \( x = 2 + \sqrt{3} \) and \( x = 2 - \sqrt{3} \)[/tex].

Answer:

360.82 units

Step-by-step explanation:

The circle has a circumference of 1,133.54 units.

The circumference of a circle is given as:

C = πD

where D = diameter

This implies that:

1133.54 = πD

=> D = 1133.54 / π

D = 360.82 units

Its diameter is 360.82 units