Given: MNOK is a trapezoid, MN=OK, m∠M=60°, NK⊥MN, MK=16cm
Find: The midsegment of MNOK

ANSWER

[tex]|^{ \to} _{YZ}| = \sqrt{13} [/tex]

EXPLANATION

Given the points, y(-2,5),z(1,3)

[tex] ^{ \to} _{YZ} = \binom{1}{3} - \binom{ - 2}{5} = \binom{3}{ - 2} [/tex]

Therefore the ordered pair is <3,-2>

The magnitude is

[tex] |^{ \to} _{YZ}| = \sqrt{ {3}^{2} + ( - 2)^{2} } [/tex]

[tex] |^{ \to} _{YZ}| = \sqrt{ 9 +4} [/tex]

[tex]|^{ \to} _{YZ}| = \sqrt{13} [/tex]

Answer: AAAAAAAAAAAAAAAAAAAAAAAAAAa

To convert 88 square yards to square meters, we use the conversion factor 1 square yard = 1.196 square meters. By multiplying 88 by 1.196, we find that 88 square yards is approximately 105.3 square meters.

The question is part of the mathematics subject, specifically in the area of unit conversion. We have a conversion factor to use, which is 1 square yard = 1.196 square meters, based on the provided reference information.

So to convert 88 square yards to square meters, you multiply 88 by 1.196.

88 yards2 * 1.196 m2/yard2 = 105.3 m2.

so 88 square yards is approximately = 105.3 square meters.

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Answer:

a. X is the number of adults in America that need to be surveyed until finding the first one that will watch the Super Bowl.

b. X can take any integer that is greater than or equal to 1. [tex]\rm X\in \mathbb{Z}^{+}[/tex].

c. [tex]\rm X \sim NB(1, 0.40)[/tex].

d. [tex]E(\rm X) = 2.5[/tex].

e. [tex]P(\rm X = 7) = 0.0187[/tex].

f. [tex]P(\text{X} = 3) +P(\text{X} = 4) = 0.230[/tex].

Step-by-step explanation:

In this setting, finding an adult in America that will watch the Super Bowl is a success. The question assumes that the chance of success is constant for each trial. The question is interested in the number of trials before the first success. Let X be the number of adults in America that needs to be surveyed until finding the first one who will watch the Super Bowl.

It takes at least one trial to find the first success. However, there's rare opportunity that it might take infinitely many trials. Thus, X may take any integer value that is greater than or equal to one. In other words, X can be any positive integer: [tex]\rm X\in \mathbb{Z}^{+}[/tex].

There are two discrete distributions that may model X:

[tex]\rm NB(1, p)[/tex] (note that [tex]r=1[/tex]) is equivalent to [tex]\sim Geo(p)[/tex]. However, in this question the distribution of [tex]\rm X[/tex] takes two parameters, which implies that [tex]\rm X[/tex] shall follow the negative binomial distribution rather than the geometric distribution. The probability of success on each trial is [tex]40\% = 0.40[/tex].

[tex]\rm X\sim NB(1, 0.40)[/tex].

The expected value of a negative binomial random variable is equal to the number of required successes over the chance of success on each trial. In other words,

[tex]\displaystyle E(\text{X}) = \frac{r}{p} = \frac{1}{0.40} = 2.5[/tex].

[tex]P(\rm X = 7) = 0.0187[/tex].

Some calculators do not come with support for the negative binomial distribution. There's a walkaround for that as long as the calculator supports the binomial distribution. The r-th success occurs on the n-th trial translates to (r-1) successes on the first (n-1) trials, plus another success on the n-th trial. Find the chance of (r-1) successes in the first (n-1) trials and multiply that with the chance of success on the n-th trial.

[tex]P(\text{X} = 3)+P(\text{X} = 4) = 0.230 [/tex].

The events “cheering for Team A” and “being a female” are not mutually exclusive. The probability that a randomly selected attendee is female or cheers for Team A is approximately 0.741.

(a) No, the events “cheering for Team A” and “being a female” are not mutually exclusive. This is because there are females who are cheering for Team A. Mutually exclusive events cannot happen at the same time.

(b) To find the probability that a randomly selected attendee is female or cheers for Team A, we need to add the probabilities of each event happening and subtract the probability of both events happening at the same time. We can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

In this case, P(A) is the probability of cheering for Team A, P(B) is the probability of being female, and P(A and B) is the probability of being a female who cheers for Team A.

Given the numbers provided, the probability of cheering for Team A is 2118/4997 and the probability of being female is 2568/4997. The probability of being a female who cheers for Team A is 982/4997. Plugging these values into the formula, we get:

P(Female or Team A) = P(Team A) + P(Female) - P(Female and Team A) = 2118/4997 + 2568/4997 - 982/4997 = 3704/4997 ≈ 0.741

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Let's call them: W and L

Then area: A = W × L

We can replace: L = 2 × W

So: A = W × 2W=98→

2W^2=98 →W^2=98/2=49

→W=√49=7

→L=2×W=2×7=14

Conclusion: The rectangle is 7*14 ft

Hope this helps :)

Answer:

7 and 14 in simple terms, i got this right.

HAVE A BLESSED DAY!!!!!!

Answer:

Box 2

Step-by-step explanation:

Volume= l*w*h

            =2*3*1

            = 6ft3

Answer:

Box 2 is your answer

Step-by-step explanation:

ANSWER

[tex]x = \frac{ 5 - \sqrt{ 5} }{4} \: or \: \: x = \frac{ 5 + \sqrt{ 5} }{4} [/tex]

EXPLANATION

The given quadratic equation is

[tex]4 {x}^{2} - 10x + 5 = 0[/tex]

We compare this to

[tex]a {x}^{2} + bx + c = 0[/tex]

to get a=4, b=-10, and c=5.

The quadratic formula is given by

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

We substitute these values into the formula to get:

[tex]x = \frac{ - - 10 \pm \sqrt{ {( - 10)}^{2} - 4(4)(5)} }{2(4)} [/tex]

This implies that

[tex]x = \frac{ 10 \pm \sqrt{ 100 - 80} }{8} [/tex]

[tex]x = \frac{ 10 \pm \sqrt{ 20} }{8} [/tex]

[tex]x = \frac{ 10 \pm2 \sqrt{ 5} }{8} [/tex]

[tex]x = \frac{ 5 \pm \sqrt{ 5} }{4} [/tex]

The solutions are:

[tex]x = \frac{ 5 - \sqrt{ 5} }{4} \: or \: \: x = \frac{ 5 + \sqrt{ 5} }{4} [/tex]

Answer:

[tex]\large\boxed{x=\dfrac{5-\sqrt5}{4},\ x=\dfrac{5+\sqrt5}{4}}[/tex]

Step-by-step explanation:

[tex]\text{The quadratic formula for}\ ax^2+bx+c=0\\\\\text{if}\ b^2-4ac<0,\ \text{then the equation has no real solution}\\\\\text{if}\ b^2-4ac=0,\ \text{then the equation has one solution:}\ x=\dfrac{-b}{2a}\\\\\text{if}\ b^2-4ac,\ ,\ \text{then the equation has two solutions:}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\==========================================[/tex]

[tex]\text{We have the equation:}\ 4x^2-10x+5=0\\\\a=4,\ b=-10,\ c=5\\\\b^2-4ac=(-10)^2-4(4)(5)=100-80=20>0\\\\x=\dfrac{-(-10)\pm\sqrt{20}}{2(4)}=\dfrac{10\pm\sqrt{4\cdot5}}{8}=\dfrac{10\pm\sqrt4\cdot\sqrt5}{8}=\dfrac{10\pm2\sqrt5}{8}\\\\=\dfrac{2(5\pm\sqrt5)}{8}=\dfrac{5\pm\sqrt5}{4}[/tex]

Answer:

Volume of the Right Triangular Prism is 1771 m³.

Step-by-step explanation:

Given:

A Right Triangular base Prism.

Length of the legs of the right triangle of the base is 14 m , 23 m

Hypotenuse of the triangle is 26.9 m

Height of the Prism is 11 m

To find: volume of the Prism.

We know that Volume of the Prism = Base Area × Height

Volume of the Right Triangular Prism = Area of Base Triangle × Height

                                                              = 1/2 × 14 × 23 × 11

                                                              = 7 × 23 × 11

                                                              = 1771 m³

Therefore, Volume of the Right Triangular Prism is 1771 m³.

Answer:

1,771

Step-by-step explanation:

0.3 or 30%. The probability that Ace pick a banana from a basket that content others fruits is 0.3.

The key to solve this problem is using the equation of probability [tex]P(A)=\frac{n(A)}{n}[/tex] where n(A) the numbers of favorables outcomes and n the numbers of possible outcomes.

There are in the basket 10 fruits in total (3 bananas + 4 apples + 3 oranges = 10fruits). Then, extract a fruit can occur in 10 ways, this is n. There is only 3 bananas in the basket, so the fruit that ACE will pick be a banana can occur in 3 ways out of 10,  so 3 is n(A).

Solving the equation:

[tex]P(A)=\frac{3}{10}=0.3[/tex]

The probability that Ace will pick a banana from the basket is 3/10, as there are 3 bananas out of a total of 10 pieces of fruit.

The question asks for the probability that Ace will pick a banana from a basket containing 3 bananas, 4 apples, and 3 oranges. To calculate this, you sum up the total number of pieces of fruit, which is 3 bananas + 4 apples + 3 oranges = 10 pieces of fruit. The probability is then the number of desired outcomes (bananas) over the total number of possible outcomes (all pieces of fruit), which is 3 bananas / 10 pieces of fruit = 3/10 or 30%.

Answer:

D. 15P15 * 10P5

Step-by-step explanation:

Since you have to place all first-grade students in the first three rows, and nowhere else, we have to make a special calculation for that, then another for the rest of the bus.

These are permutations since the order is important. If we sit John, Paul, Ringo, George and Pete in this order in the first row it's a different way than seating them (in the same order) in the second row for example.

For the 15 first-graders of the first three rows (15 seats), we have 15P15 since all 15 places have to be occupied by all 15 first-graders.

Then we have 10 remaining seats left to be assigned to the 5 second-graders.  That is 10P5.

We then multiply the permutation numbers of those two arrangements to get the total ways:

15P15 * 10P5, answer D.

Answer:

The correct answer option is D. 15P15 x 10P5.

Step-by-step explanation:

We know that there are 15 students in first grade and we have 5 rows of 5 seats to accommodate them. So first grade students can be arranged to occupy the seats in [tex]15P15[/tex].

Also, we have 5 students in the second grade with a total of 25 seats from which 15 seats are already occupied so we are left with 10 seats now.

Therefore, the students can be seated in 15P15 x 10P5 ways.

Answer:

[tex]\large\boxed{x=\dfrac{5-\sqrt5}{4},\ x=\dfrac{5+\sqrt5}{4}}[/tex]

Step-by-step explanation:

[tex]\text{The quadratic formula for}\ ax^2+bx+c=0\\\\\text{if}\ b^2-4ac<0,\ \text{then the equation has no real solution}\\\\\text{if}\ b^2-4ac=0,\ \text{then the equation has one solution:}\ x=\dfrac{-b}{2a}\\\\\text{if}\ b^2-4ac,\ ,\ \text{then the equation has two solutions:}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\==========================================[/tex]

[tex]\text{We have the equation:}\ 4x^2-10x+5=0\\\\a=4,\ b=-10,\ c=5\\\\b^2-4ac=(-10)^2-4(4)(5)=100-80=20>0\\\\x=\dfrac{-(-10)\pm\sqrt{20}}{2(4)}=\dfrac{10\pm\sqrt{4\cdot5}}{8}=\dfrac{10\pm\sqrt4\cdot\sqrt5}{8}=\dfrac{10\pm2\sqrt5}{8}\\\\=\dfrac{2(5\pm\sqrt5)}{8}=\dfrac{5\pm\sqrt5}{4}[/tex]

Answer:

116.75 oceanic miles

Step-by-step explanation:

A graph of the data shows the distance to be between 110 and 120 miles (closer to 120). There is only one answer choice in that range.

In 2 hours, the ship travels 42.5 miles, so in 1 hour will travel 21.25 miles. Adding that distance to the distance at 4 hours gives the distance at 5 hours, ...

  95.5 +21.25 = 116.75 . . . . "oceanic" miles

_____

In order for the distance from the lighthouse to be uniformly increasing, the ship must be traveling directly away from the lighthouse. Traveling at any other angle, the distances will not fall on a straight line. (That is one reason I wanted to graph the data.)

Answer:

C. there is a common difference of 3 for f(x) when x increases by 1

Step-by-step explanation:

As 3 is the slope of this function, there will be a common difference of 3 when x increases by 1.

f(x) = 3x  - 7

Let's think, whenever we add 1 to x it i'll increase 3 in the result

f(0) = 3.0 - 7 = 0 - 7 = -7

f(1) = 3.1 - 7 = 3 - 7 = -4

f(2) = 3.2 - 7 = 6 - 7 = -1

So we can know that there's a common difference of 3 for f(x) when x increase by 1.

Answer:

D. 7

Step-by-step explanation:

The given expression is

[tex]\frac{5x-18}{x-7}[/tex]

This is a rational expression.

This expression undefined, when the denominator is zero.

We equate the denominator to zero  to get;

[tex]x-7=0[/tex]

This implies that;

x=7

Answer:

The correct answer option is 7.

Step-by-step explanation:

We are given the following expression and we are to determine whether which of the given options for the value of x would the expression become undefined:

[tex] \frac { 5 x - 1 8 } { x - 7 } [/tex]

We know that the expression is undefined when the denominator equals zero. So to make the denominator zero, the value of x should be 7.

Answer: A

Step-by-step explanation:

Answer:

a.

“Let’s go outside. It’s really noisy in here and I can’t really hear what you are saying.”

Step-by-step explanation:

Which of the following statements reflects the principles of avoiding distractions and being other-oriented?

a. “Let’s go outside. It’s really noisy in here and I can’t really hear what you are saying.”

This is clear from option A - the person is saying that its noisy here and he cannot listen to the other person.

Answer:

Associative property of multiplication

Step-by-step explanation:

To show that 9(3x) = 27(x), we need to show that 9(3x) = (9 * 3)x.

The APM does just that. By this property, in multiplication, the order of which numbers are multiplied do not matter.

So, 9(3x) = (9 * 3)x.

And by multiplication, (9 * 3)x = 27x.

So 9(3x) = 27x

Answer:

78(0.50)+87(0.25)+80(0.15)+90(0.10)=x

Step-by-step explanation:

Let

x-----> the final average

we know that

To find the final average multiply each performance by its weight in decimal and then sum the results

x=78(0.50)+87(0.25)+80(0.15)+90(0.10)

x=39+21.75+12+9

x=81.75

Answer:

165

Step-by-step explanation:

[tex]5c^{2} -3d+15[/tex]

c = 6 and d = 10

[tex]5c^{2}[/tex] = 5 × 6² = 5 × 36 = 180

[tex]5c^{2}[/tex] - ( 3 d ) = 180 - ( 3 × 10 ) = 180 - 30 = 150

[tex]5c^{2}[/tex] -  3 d  ( + 15 ) = 150 + 15 = 165

Answer:

165

Step-by-step explanation:

Substitutet 6 for c and 10 for d in  5c^2 - 3d + 15​ .

Note that " ^ " is used here to denote exponentiation; c2 is meaningless.

Then we have 5(6)^2 - 3(10) + 15, or   180 - 30 + 15, or 165.

Answer:

The correct answer option is x = 4.

Step-by-step explanation:

We are given the following logarithmic equation and we are to determine whether which of the given options shows its extraneous solution:

[tex] log _ 7 ( 3 x ^ 3 + x ) - log _ 7 ( x ) = 2 [/tex]

We can rewrite it as:

[tex]log7[\frac{3x^3+x}{x} ]=2[/tex]

But we know that [tex]log_7(49)=2[/tex]

So, [tex]log7[\frac{3x^3+x}{x} ]=log_7(49)[/tex]

Cancelling the log to get:

[tex]\frac{3x^3+x}{x} =49[/tex]

Further simplifying it to get:

[tex]3x^2+1=49[/tex]

[tex]3x^2=48[/tex]

[tex]x^2=\frac{48}{3}[/tex]

[tex]x^2=16[/tex]

x = 4

Answer:

The extraneous solution to the logarithmic equation is [tex]x=-4[/tex]

Step-by-step explanation:

We have the equation:

[tex]Log_{7} (3x^3+x)-Log_7(x)=2[/tex]

By properties of logarithms:

[tex]LogA-LogB=Log(\frac{A}{B})[/tex]

So, with the equation we have:

[tex]Log_{7} \frac{(3x^3+x)}{x}=2[/tex]

[tex]Log_{7}( \frac{3x^3+x}{x})=2\\Log_{7}( \frac{3x^3}{x}+\frac{x}{x})=2\\Log_{7}( \frac{3x^3}{x}+1)=2\\Log_{7}(3x^2+1)=2[/tex]

This logarithm base is 7 and this equation is equal to 2,  the number 7 passes as the base on the other side of the equation and the two as an exponent, after that we just to find x:

[tex]7^2=(3x^2+1)\\49=3x^2+1\\49-1=3x^2\\\frac{48}{3} =x^2\\16=x^2[/tex]

Now, we can find x with square root

[tex]16=x^2\\\sqrt{16} =\sqrt{x^2} \\x_1=4\\x_2=-4[/tex]

This equation has two answers because it is a quadratic equation, so with this logic the strange solution is -4

[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{csc(\theta )-sin(\theta )}{cos(\theta )}\implies \cfrac{~~\frac{1}{sin(\theta )}-sin(\theta )~~}{cos(\theta )}\implies \cfrac{~~\frac{1-sin^2(\theta )}{sin(\theta )}~~}{cos(\theta )}[/tex]

[tex]\bf \cfrac{1-sin^2(\theta )}{sin(\theta )}\cdot \cfrac{1}{cos(\theta )}\implies \cfrac{\stackrel{cos(\theta )}{\begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}} }{sin(\theta )}\cdot \cfrac{1}{\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\implies \cfrac{cos(\theta )}{sin(\theta )}\implies cot(\theta )[/tex]

Answer:

cot Ф

Step-by-step explanation:

Recall that sin²Ф + cos²Ф = 1, (which also says that cos²Ф - 1 = sin²Ф).

Also recall the definitions of the csc, sin and cos functions.

Your expression is equivalent to:

   1               sin Ф

----------  -  -------------

sin Ф              1

===================

           cos Ф

There are three terms in your expression:  csc, sin and cos.  Multiply all of them by sin Ф.  The result should be:

 1 - sin²Ф

---------------

sin Ф · cos Ф

Using the Pythagorean identity (see above), this simplifies to

  cos²Ф

------------------

sin Ф·cos Ф

and this whole fraction reduces to

   cos Ф

--------------   and this ratio is the definition of the cot function.

   sin Ф

Thus, the original expression is equivalent to cot Ф

Answer:

Eric’s share in the profit is $30,000 ⇒ answer B

Step-by-step explanation:

* We will use the ratio to solve this problem

- At first lets find the ratio between their invested

∵ Eric has invested $400,000

∵ George has invested $300,000

∵ Denzel has invested $300.000

- To find the ratio divide each number by 100,000

∴ Eric : George : Denzel = 4 : 3 : 3

- They will divide the profits among themselves in the ratio of their

  respective investments

- The total profit will divided by the total of their ratios

∵ The total of the ratios = 4 + 3 + 3 = 10

∴  Eric : George : Denzel : Sum = 4 : 3 : 3 : 10

- That means the profit will divided into 10 equal parts

- Eric will take 4 parts, George will take 3 parts and Denzel will take

 3 parts

∵ The profit = $75,000

- Divide the profit by the sum of the ratio

∴ Each part of the profit = 75,000 ÷ 10 = $7,500

- Now lets find the share of each one

∴ The share of Eric = 4 × 7,500 = $30,000

∴ The share of George = 3 × 7,500 = $22,500

∴ The share of Denzel = 3 × 7,500 = $22,500

* Eric’s share in the profit is $30,000

# If you want to check your answer add the shares of them, the answer

  will be the total profit (30,000 + 22,500 + 22,500 = $75,000), and if

  you find the ratio between their shares it will be equal the ratio

  between their investments (divide each share by 7,500 to simplify

  them the answer will be 4 : 3 : 3)

Answer:

B

Step-by-step explanation:

Explanation:

To find the value, put 320 where x is and do the arithmetic.

f(320) = 0.11·320 +43 = 35.20 +43 = 78.20

The meaning is described by the problem statement:

"how much Derek pays for phone service" for "the number of minutes, [320], used for international calls in a month."

Derek pays 78.20 for 320 minutes of international calls in a month.

__

The units (dollars, rupees, euros, pounds, ...) are not specified.

Answer:

Given the function f(x) = 0.11x + 43, this shows the relationship between how much Derek has to pay for phone service for the amount of minutes he uses on international calls a month.  f(320) can be solved by substituting x = 320, and this is shown below: f(x) = 0.11x + 43 f(320) = 0.11(320) + 43 f(320) = 78.2 This means that Derek has to pay $78.20 for the 320 minutes of calls. Among the choices, the correct answer is B.

Answer:

The recursive rule is a1 = 3 , an = (1/6) a(n-1)

Step-by-step explanation:

* Lets revise the recursive formula for a geometric sequence:

1. Determine if the sequence is geometric (Do you multiply, or divide,

  the same amount from one term to the next?)

2. Find the common ratio. (The number you multiply or divide.)

3. Create a recursive formula by stating the first term, and then

   stating the formula to be the common ratio times the

   previous term.

# a1 = first term;

# an= r • a(n-1)

- Where:

- a1 = the first term in the sequence

- an = the nth term in the sequence

- an-1 = the term before the nth term  

- n = the term number

- r = the common ratio

* Lets solve the problem

∵ an = 3(1/6)^(n-1) ⇒ geometric sequence

∵ The explicit rule is an = a1(r)^n-1

∴ a1 = 3 and r = 1/6

- Lets write the recursive rule

∵ a1 = first term;

∵ an= r • a(n-1)

∴ a1 = 3

∴ an = (1/6) a(n-1)

* The recursive rule is a1 = 3 , an = (1/6) a(n-1)

Answer:

a1 = 3
an = 1/6a n-1

Step-by-step explanation:

i took the test

will you receive the grade immediately?

Answer:

21

Step-by-step explanation:

√(35x)

The prime factorization of 35 is 5×7.  To simplify the radical, the expression underneath must be a multiple of a perfect square.  So we need to choose a value of x that has either 5 or 7 as a factor.

21 has a factor of 7.  Let's see:

√(35×21)

√(5×7×3×7)

√(15×7²)

7√15

Answer:

see below

Step-by-step explanation:

The number of columns of A is equal to the number of rows of B, so multiplication is possible. It works well to have a calculator do this for you. It involves 27 multiplications and 18 additions, tedious at best.

Each product term is the sum of products ...

p[row=i, column=j] = a[i, 1]b[1, j] +a[i, 2]b[2, j] +a[i, 3]b[3, j]

For example, the product term in the 3rd row, 2nd column is ...

p[3, 2] = a[3, 1]b[1, 2] +a[3, 2]b[2, 2] +a[3, 3]b[3, 2]

= (-4)(-5) +(-1)(3) +(-9)(4) = 20 -3 -36

p[3, 2] = -19

Answer:

B

Step-by-step explanation:

The volume of a sphere is given by

[tex]V=\frac{4}{3}\pi r^3[/tex]

where r is the radius

For $2.75, we can get 1 large  OR  2 small scoops.

Giant scoop has diameter 6, so radius is half of that, which is 3, hence the volume is:

[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}\pi (3)^3\\V=113.1[/tex]

Regular scoop's diameter is 4, hence radius is 2. So volume of 1 regular scoop is:

[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}\pi (2)^3\\V=33.51[/tex]

We can get 2 of those, so total volume is 33.51 + 33.51 = 67.02

Hence, the max volume for $2.75 is around 113, answer choice B.

By Pythagoras' Theorem:

Sum of the squares of the two side  = Square of longest side

a² + b² = c²

a)

So let's check 7, 24, 25

Is 7² + 24² = 25²  ?

7*7 + 24*24

49 + 576  

=625.

Let us perform the other side 25²

25² = 25 * 25 = 625

Therefore the left hand side = Right hand side.

Therefore 7, 24, 25 is a Pythagorean Triple

b)

Let's check 9, 40, 41

Is 9² + 40² = 41²  ?

9² + 40²

9*9+ 40*40  

81 + 1600

=1681

Let us perform the other side 41²

41² = 41 * 41 = 1681

Therefore the left hand side = Right hand side.

Therefore 9, 40, 41 is a Pythagorean Triple.

Answer:

  80 cm²

Step-by-step explanation:

Trapezoid LPKB has area ...

  A = (1/2)(b1 +b2)h = (1/2)(4 +20)(20) = 240 . . . . cm²

Triangle BPN has area ...

  A = (1/2)bh = (1/2)(20)(20) = 200 . . . . cm²

Triangle BKN has a height that is 4/5 the height of triangle BPN, so will have 4/5 the area:

  ΔBKN = (4/5)(200 cm²) = 160 cm²

The area of quadrilateral LPKB is that of trapezoid LPNB less the area of triangle BKN, so is ...

  240 cm² - 160 cm² = 80 cm²

Answer:

  1557/1892

Step-by-step explanation:

Your calculator can do this:

[tex]\dfrac{18M}{K}=\dfrac{18\cdot 3\cdot 11\cdot 173}{2\cdot 33\cdot 11\cdot 172}=\dfrac{18\cdot 173}{2\cdot 11\cdot 172}\\\\=\dfrac{1557}{1892}[/tex]

Answer:

6433.98 ft

Step-by-step explanation:

In order to find what 25% of the tank's capacity is, we know to know the full capacity of the tank then take 25% of that.  The volume formula for a right circular cone is

[tex]V=\frac{1}{3}\pi r^2h[/tex]

We have all the values we need for that:

[tex]V=\frac{1}{3}\pi (16)^2(96)[/tex]

This gives us a volume of 25735.93 cubic feet total.

25% of that:

.25 × 25735.93 = 6433.98 ft

Answer:

The height of the water is [tex]60.5\ ft[/tex]

Step-by-step explanation:

step 1

Find the volume of the tank

The volume of the inverted right circular cone is equal to

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

we have

[tex]r=16\ ft[/tex]

[tex]h=96\ ft[/tex]

substitute

[tex]V=\frac{1}{3}\pi (16)^{2} (96)[/tex]

[tex]V=8,192\pi\ ft^{3}[/tex]

step 2

Find the 25% of the tank’s capacity

[tex]V=(0.25)*8,192\pi=2,048\pi\ ft^{3}[/tex]

step 3

Find the height, of the water in the tank  

Let

h ----> the height of the water  

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

[tex]\frac{R}{H}=\frac{r}{h}[/tex]

substitute

[tex]\frac{16}{96}=\frac{r}{h}\\ \\r= \frac{h}{6}[/tex]

where

r is the radius of the smaller cone of the figure

h is the height of the smaller cone of the figure

R is the radius of the circular base of tank

H is the height of the tank

we  have

[tex]V=2,048\pi\ ft^{3}[/tex] -----> volume of the smaller cone

substitute

[tex]2,048\pi=\frac{1}{3}\pi (\frac{h}{6})^{2}h[/tex]

Simplify

[tex]221,184=h^{3}[/tex]

[tex]h=60.5\ ft[/tex]