The main show tank has a radius of 70 feet and forms a quarter-sphere. What is the volume
of the quarter-sphere shaped tank? Round your answer to the nearest whole number You
must explain your answer using words, and you must show all work and calculations to
receive credit. (2 points)

Answer:

x = 10

Step-by-step explanation:

2x/3 + 1 = 7x/15 + 3

(times everything in the equation by 3 to get rid of the first fraction)

2x + 3 = 21x/15 + 9

(times everything in the equation by 15 to get rid of the second fraction)

30x+ 45 = 21x + 135

(subtract 21x from 30x; subtract 45 from 135)

9x = 90

(divide 90 by 9)

x = 10

2x/3 + 1 = 7x/15 + 3

(find the LCM of 3 and 15 = 15)

(multiply everything in the equation by 15, then simplify)

10x + 15 = 7x + 45

(subtract 7x from 10x; subtract 15 from 45)

3x = 30

(divide 30 by 3)

x = 10

Answer:

28 i assume.

Answer:

The answer is 28% :))

Step-by-step explanation:

It is given that,

\(u{\cdot}v=4\\\\|u|=5\\\\|v|=3\)

We need to find the value of \(4u{\cdot} (4u-7v)\)

Firstly, we should simplify \(4u{\cdot} (4u-7v)\)

\(4u{\cdot} (4u-7v)=4u{\cdot} 4u-4u{\cdot} 7v\)

Now using distributive property : x(y-z)=xy-yz

So,

\(4u{\cdot} (4u-7v)=4u{\cdot} 4u-4u{\cdot} 7v\\\\=16u{\cdot}u-28{u{\cdot} v}\\\\=16|u|^2-28(u{\cdot}v)\\\\=16\times 5^2-28\times 4\\\\=288\)

So, the value of  \(4u{\cdot} (4u-7v)\) is 288.

Answer:

x° = 41.8°

Step-by-step explanation:

Use trigonometric functions to calculate angles from side lengths.

sOH - cAH - tOA.

Sine:  Opposite/Hypotenuse
Cosine:  Adjacent/Hypotenuse
Tangent:  Opposite/Adjacent

sin(x°) = 4/6

\(x=sin^-1(\frac{2}{3} )\)

x° = 41.8°

Answer:

x − 43 = 90

Step-by-step explanation:

2x + 43 = 180

2x − 43 = 90

x + 43 = 180

x − 43 = 90

Answer:

B/ 5/6

Step-by-step explanation:

5/6 represents a part of a whole while the others represent a part of a whole AND a whole.

Answer:

15

Step-by-step explanation:

Following PEMDAS you would do the equation in the parentheses first.

1 - 15 = -14

13 - 2  ⋅ (-14) divided by 14

-2 ⋅ (-14) = 28

13 + 28 divided by 14

28 divided by 14 = 2

13 + 2 = 15

Your answer is 15

Hope I helped :)

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The number of tiles required to completely cover the floor is approximately 1673 tiles

Let find the area of the floor . Therefore,

where

l = length

w = width

Therefore,

let's convert ft to inches.

9 ft = 108 inches

8 ft = 96 inches

area = 108 × 96

area = 10, 368 inches²

Number of tiles to completely cover the floor = 10368 / 6.2

Number of tiles to completely cover the floor = 1672.25806452

Number of tiles to completely cover the floor ≈ 1673 tiles

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The measure of the unknown angles in the parallel lines AC and DF with transversal HJ are as follow,

m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.

Two lines AC and DF are parallel to each other  in the attached figure

Transversal HJ cut  lines AC and DF at point B and E respectively.

Measure of ∠ABE = 63°.

Using the result based on corresponding angles, alternate interior angles , and vertically opposite angles of a parallel lines we get,

Measure of ∠ABE ≅ Measure of ∠DEH ( corresponding angles)

⇒Measure of ∠DEH = 63°

Measure of ∠ABE ≅ Measure of ∠BEF ( alternate interior angles)

⇒Measure of ∠BEF = 63°

Measure of ∠ABE ≅ Measure of ∠CBJ ( vertically opposite angles)

⇒Measure of ∠CBJ = 63°

Using the result of linear pair angles,

Measure of ∠ABE + Measure of ∠CBE = 180°

⇒ Measure of ∠CBE = 180° -63°

⇒  Measure of ∠CBE = 117°

Measure of ∠CBE ≅ Measure of ∠FEH ( corresponding angles)

⇒Measure of ∠FEH = 117°

Measure of ∠CBE ≅ Measure of ∠BED ( alternate interior angles)

⇒Measure of ∠BED = 117°

Measure of ∠CBE ≅ Measure of ∠ABJ ( vertically opposite angles)

⇒Measure of ∠ABJ = 117°

Therefore, the measure of the seven unknown angles formed in the parallel line are given by m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.

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The above question is incomplete, the complete question is:

Lines AC and DF are parallel. They are cut by transversal HJ with your partner find the seven unknown angle measures in the diagram explain your reasoning. What do you notice about the angles with vertex B and the angles with vertex E.

In the attached figure.

The ability of the twins to divide the oddly shaped plot into two Identical plots along the grid lines depends on the presence of a line of symmetry.

To determine whether the set of twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need to consider the characteristics of the plot and the conditions required for the division.

For the division to be possible, the plot needs to have a line of symmetry that can be used to create two identical halves. A line of symmetry divides an object into two equal and mirrored parts.

If the plot of land has a line of symmetry, the twins can divide it by drawing a line along the symmetry axis. This line should cut the plot into two equal halves, ensuring that both plots are identical.

However, if the plot does not have a line of symmetry, it may not be possible to divide it into two identical plots along the grid lines. In this case, the twins would need to consider alternative methods of division or compromise on the goal of having two identical plots.

To determine if the plot has a line of symmetry, the twins can examine its shape and characteristics. They can look for any symmetrical patterns, such as equal sides or mirrored shapes, that indicate the presence of a line of symmetry.

If the plot does not have an obvious line of symmetry, the twins might need to explore other options, such as dividing the plot into two equal areas based on other criteria, such as the length or width of each half.

the ability of the twins to divide the oddly shaped plot into two identical plots along the grid lines depends on the presence of a line of symmetry. If such a line exists, they can divide the plot by drawing a line along the symmetry axis. However, if the plot lacks symmetry, they may need to consider alternative methods of division or adjust their expectations.

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Note the full question may be :

To determine whether the twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need more specific information about the shape and dimensions of the plot. the shape of the plot (rectangular, triangular, irregular), the lengths of its sides, any existing grid lines or divisions within the plot.

Answer:

It would be proportional.

Step-by-step explanation:

Every 2 numbers on the X value, The y vaulue goes up by 20. It is the same number that it is inreasing by each time.

Answer:

C. $755 i got it right

Step-by-step explanation:

If you make only the minimum payment each month, the total cost of the computer will be $755.00, which is $155 more than the original cost of the computer ($600).

percentage, a relative value indicating hundredth parts of any quantity.

To calculate the total cost of the computer if you make only the minimum payment each month, we need to use the simple interest formula:

A = P(1 + rt)

where A is the total amount paid, P is the principal or balance, r is the annual interest rate expressed as a decimal, and t is the time in years.

P = $600

r = 12.9% or 0.129 (annual interest rate)

t = 2 years

To find the monthly interest rate, we divide the annual interest rate by 12 (the number of months in a year):

Monthly interest rate = 0.129 / 12 = 0.01075

Now, we can use this monthly interest rate to calculate the minimum monthly payment:

Minimum monthly payment = 1% x P = 0.01 x $600 = $6

Therefore, the minimum monthly payment is $6.

To find the total cost of the computer over the 2-year period, we need to calculate the total amount paid (A) by making the minimum monthly payment each month:

A = P(1 + rt)

A = $600(1 + 0.01075 x 2 x 12)

A = $600(1 + 0.258)

A = $755.00

Therefore, if you make only the minimum payment each month, the total cost of the computer will be $755.00, which is $155 more than the original cost of the computer ($600).

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Answer:

total $10.97

tax $0.68

Step-by-step explanation:

apple for $1.25

sandwich for $4.25

chips for $2.49

apple juice for $2.30

Total: $10.29

Calculate sales tax:

6.625% of $10.29 = 0.06625 × $10.29 = $0.68

Calculate total price:

$10.29 + $0.68 = $10.97

Answer:

0

Step-by-step explanation:

4r-10s

4x5-10x2

20-20

= 0

Answer:

0.9

Step-by-step explanation:

It is the second decimal. 1/9 equals 0.9

Answer:

0.7125

Step-by-step explanation:

The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes (with probability p) in a sequence of n independent events.

The probability of getting exactly x successes in n independent Bernoulli trials =  \(n_{C_{x}}(p)^x(1-p)^{n-x}\)

Total number of watches in the shipment = 50

Number of defective watches = 6

Number of selected watches = 10

Let X denotes the number of defective digital watches such that the random variable X follows a binomial distribution with parameters n and p.

So,

Probability of defective watches = \(\frac{X}{n}=\frac{6}{50}=0.12\)

Take n = 10 and p = 0.12

Probability that the shipment will be rejected = \(P(X\geq 1)=1-P(X=0)\)

\(=1-n_{C_{x}}(p)^x(1-p)^{n-x}\\=1-10_{C_{0}}(0.12)^0(1-0.12)^{10-0}\)

Use \(n_{C_{x}}=\frac{n!}{x!(n-x)!}\)

So,

Probability that the shipment will be rejected = \(=1-\left ( \frac{10!}{0!(10-0)!} \right )(0.88)^{10}\)

\(=1-(0.88)^{10}\\=1-0.2785\\=0.7125\)

Step-by-step explanation:

y=kx

25= k(-5)

k= -5

y= -5x

y = -5 ×3 = -15

Answer:

21.8 m/s

Step-by-step explanation:

Given that Tom drops a object from a height of h meters and it hits the ground with a veloc8of v m/s and it is given by function ;

\(\longrightarrow v =\sqrt{19.6h}\)

We need to find out the velocity upon reaching the ground when it is dropped from a height of 24.3 m . On plugging in 24.3 in place of h we have ,

\(\longrightarrow v =\sqrt{19.6\times 24.3 }\ m/s\\\\\longrightarrow v =\sqrt{ 476.28} m/s \\\\\longrightarrow v = 21.823 \ m/s \\\\\longrightarrow \underline{\underline{ v = 21.8 \ m/s }}\)

And we are done !

Answer:

21.8

Step-by-step explanation:

The formula is given :

Given that h = 24.3 m, we need to find v.

Substituting the value of h in the formula :

Yes, 15 miles per gallon would be a unit rate.  

A unit rate is essentially a situation where the quantity is written with a 1 as the denominator (A unit rate is y over x, when x = 1).

Answer: 4.5

Step-by-step explanation:

\(\frac{-36}{-8} = \frac{-9}{-2} = 4.5\)

Answer:

Kinda vague but here...

Step-by-step explanation:

z*(8-4)
z*(4)
4z

Given Data:

The total number of beads in the bag is: 30

The number of orange, green and blue beads in the bag are equal.

Thus, the number of green beeds in the bag is,

Thus, there are 10 green, 10 orange and 10 blue beads in the bag.

The expression to calculate the probability of selecting a green bead from the bag is,

Thus, the probability of selecting a green bead from the bag is 1/3.

Based on the information, there is a t, 2≤ t ≤ 4. using the Mean value theorem and t=2

The given parameters are

t: 2≤t≤4

t is a continuous function between 2≤t≤4

We should equally know that the amount of coffee at the cup at a time y=C

Using the formula  for t

t=C(4) -C(2)/4-2

Inputting the values of t at the extremes values

t=C(4) -C(2)/4-2  = (12.8-8.8)/4-2

Simplifying this to get

4/2

=2

⇒ C(2) is continuous on the coordinates (2,4) and this can be differentiated in the coordinates (2,4)

If we apply the intermediate value theorem, the is t in (2,4)

Therefore, C(t) = [C(4)- C(2)]/ 4-2

This implies that C(t) = 2

In conclusion, based on the information, there is a t, 2≤ t ≤ 4. using the Mean value theorem. and t=2

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Answer:

\( \frac{2}{9 {d}^{14} } \)

Step-by-step explanation:

\( \frac{ {4d}^{ - 5} }{18 {d}^{9} } = \frac{4}{18} \times \frac{ {d}^{ - 5} }{ {d}^{9} } = \frac{2}{9} {d}^{ - 14} = \frac{2}{ {9d}^{14} } \)

The value of x in the parallelogram is 112°.

In a parallelogram, adjacent angles are always supplementary. This means that the sum of two adjacent angles in a parallelogram is always 180 degrees.

To understand this concept, let's consider a parallelogram ABCD. The opposite sides of a parallelogram are parallel and equal in length, and the opposite angles are congruent. Adjacent angles are those that share a side. Let's say angle A and angle B are adjacent angles in the parallelogram.

Since opposite angles of a parallelogram are congruent, we have angle A is congruent to angle C, and angle B is congruent to angle D.

Now, let's consider angle A and angle B. The sum of angle A and angle B is equal to the sum of angle C and angle D because opposite angles are congruent.

Therefore, we can conclude that angle A + angle B = angle C + angle D = 180 degrees.

This property holds true for all parallelograms. So, in any parallelogram, the adjacent angles are always supplementary, meaning their sum is 180 degrees.

For the given question, we know x° + 68° = 180°.

Then x° = 180° - 68°

x° = 112°

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Answer:

y = -2/7(x) + 3

Step-by-step explanation:

The equation of a line can be stated as y = mx + b, where m is the slope and b is the y-intercept (the value of the function when x = 0).  To find the equation of the line, we'll start by finding the slope.

The slope can be expressed as \(\frac{y_{2} - y_{1}}{x_{2}-{x_1}}\)

Substituting in our coordinates, we have:

\(m = \frac{1 - 5}{7 - (-7)} = \frac{-4}{7 + 7} = \frac{-4}{14}\), which can be simplified to \(-\frac{2}{7}\)

Plugging that back into our equation, we have y = \(-\frac{2}{7}\)x + b

Now, to find b, we substitute in one of our sets of coordinates.  Let's use (-7, 5)

x = -7 and y = 5, which gives us:

\(5 = -\frac{2}{7} (-7) + b\)

\(-\frac{2}{7} (-7) = 2\), which gives us:

5 = 2 + b

Subtracting 2 from both sides, we get:

3 = b

Plugging that back into our equation, we have \(y = -\frac{2}{7} x + 3\)

Answer:

0.5: 0.2: 0.4:

Fair Coin Blue Block Blue Marble

Soccer Ball Red Block

Dice Yellow Marble

Tennis Ball

Step-by-step explanation:

Answer:

\(6 \frac{2}{3} \pi \: {in}^{3} \)

Step-by-step explanation:

First, we have to find the area of the base:

\(a(base) = \pi \times {r}^{2} = \pi \times {2}^{2} = 4\pi\)

Now, we can find the volume of the cone:

\(v = \frac{1}{3} \times a(base) \times h = \frac{1}{3} \times 4\pi \times 5 = \frac{20\pi} {3} = 6 \frac{2}{3} \pi\)

The maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.

To convert the maximum effective monthly rate of 1% into an APR with quarterly compounding, we can use the formula:

\(APR = [(1 + \dfrac{r}{n})^n - 1] \times 4\)

Where r is the effective monthly rate and n is the number of compounding periods per year. In this case, we want to find the maximum APR with quarterly compounding that the borrower will accept, so we can substitute r = 1% and n = 3:

\(APR = ((1 + \dfrac{0.01}{3})^3 - 1) \times 4\)

APR = (1.0100333³ - 1) x 4

APR = 0.04033 x 4

APR = 0.16132 or 16.132%

Therefore, the maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.

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