PLEASE HELP IM STUCK PLS

The expression for the volume of the pyramid in terms of the radius of the cone is  [tex]V=\pi r^{3}[/tex].

The expression for the volume of the pyramid in terms of the radius of the cone:

B= base area of the cone.

[tex]V=\pi r^{2}[/tex]

The volume of the Pyramid,

[tex]V=\frac{1}{3} *B*height[/tex]

[tex]$\Rightarrow V=\frac{1}{3} \times \pi r^{2} \times 3 \gamma$[/tex]

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

The expression for the volume of the pyramid in terms of the radius of the cone is [tex]V=\pi r^{3}[/tex]

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Answer:

Width is 11 inches

Step-by-step explanation:

I am not sure what the question is.  I think you might be looking for the width length.  The perimeter is the distance around a rectangle.  If the whole distance around is 48.  We have 2 lengths and 2 widths.  They tell us that the length is 13.  We have two lengths so the lengths add up to 26.  We can subtract that from 48 and that leaves us with 22 (48-26)  This is the total for the 2 widths.  Since the 2 widths are the same length we divide that number by 2 to get 11.

11 + 11+ 13 + 13 = 48

Answer:

[tex]12.50 \space\ h = 2500.75[/tex]

Step-by-step explanation:

We know from the question that the student earned $12.50 per hour.

Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.

We also know that the total money they earned is $2500.75.

∴ Therefore, we can set up the following equation:

[tex]\boxed {12.50 \times h = 2500.75}[/tex]

From here, if we want to, we can find the number of hours worked by simply making h the subject of the equation and evaluating:

h = [tex]\frac{2500.75}{12.50}[/tex]

  = 200.6 hours

Answer: 12.50h = 2500.75

Step-by-step explanation:

We know from the question that the student earned $12.50 per hour.

Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.

We also know that the total money they earned is $2500.75.

(C) [tex]8x^{3} -7x^{2} -6x+5[/tex] represents a cubic expression.

To determine which expression represents a cubic expression:

Therefore, (C) [tex]8x^{3} -7x^{2} -6x+5[/tex] represents a cubic expression.

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The complete question is given below:

Choose the expression that represents a cubic expression.

(A) −7x + 14

(B) 7x2 − 5x + 6

(C) 8x3 − 7x2 − 6x + 5

(D) 9x4 + 8x3 − 6x2 − 2x + 11

The equation of the directrix is x = -3

A mirror-symmetrical, roughly U-shaped plane curve known as a parabola. It corresponds to a number of mathematical models that appear to be superficially dissimilar but yet all define the exact same curves. A point and a line are one way to describe a parabola.

Given the general equation of a parabola expressed as

(y-y0)² = 4a(x-x0) ... 1

Equation of the directrix will be expressed as x = x0 - a

From the equation given;

y² = 12x ... 2

Comparing 1 and 2;

x - x0 = x

-x0 = x - x

-x0 = 0

x0 = 0

Similarly;

y-y0 = y

-y0 = y - y

-y0 = 0

y0 = 0

Also;

4a = 12

a = 12/4

a = 3

Substituting x0 =0, y0 = 0 and a = 3 into the equation of the directrix above, we will have;

x = x0 - a

x = 0 - 3

x = -3

Hence,

the equation of the directrix is x = -3

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Answer:

17, 5

Step-by-step explanation:

Let the width be x

width = x

length = x + 12

length x width = x(x + 12)

length x width = x² + 12x

x² + 12x = 85

x² + 12x - 85 = 0

Now it is just a quadratic:

The 2 numbers we need are 17 and -5

(x + 17)(x - 5) = 0

x = -17 or x = 5.

Since width and length cannot be negative, x must equal 5.

Width = 5

length = 17

The answer is 17, 5.

We are given two things :

We can represent the length and width as x + 12 and x respectively.

Now, the formula for the area of a rectangle is :

Area = Length x width

Now, let's substitute the values for length and width in the formula along with the area.

We now have a quadratic equation, which can either be solved by splitting the middle term, or by using the quadratic formula. For convenience purposes, we'll go with the first one.

Using the Fundamental Counting Theorem, there are 20 possibilities for their big night out.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For this problem, we have that:

The number of possibilities is given by:

N = 5 x 4 = 20.

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Answer:

ur answer is B

Step-by-step explanation:

Answer:

B

As root over 72 is 8.48 and after we round off we get 8.5 so no B is correct

Proved that the cofunction identity sec([tex]\frac{\pi }{2}[/tex]) - u = csc(u)

We have to prove that the cofunction identity using the addition and subtraction formulas.

sec([tex]\frac{\pi }{2}[/tex]) - u = csc(u)

We can prove this by using the identities given below:

[tex]sec(u)=\frac{1}{cos(u)}[/tex]

[tex]\frac{1}{sin(u)} =csc(u)[/tex]

cos(a-b) = cos a cos b + sin a sin b

Now the explanation,

[tex]sec(\frac{\pi }{2} -u) = csc(u)[/tex]

By using trignometric identities,

[tex]cos(u)=\frac{1}{sec(u)}[/tex]   ∴[tex]sec(u)=\frac{1}{cos(u)}[/tex]

So,

[tex]\frac{1}{cos(\frac{\pi }{2}-u) } =csc(u)[/tex]

By substituting the given identities we get,

  [tex]\frac{1}{cos(\frac{\pi }{2})cos(u)+sin(\frac{\pi }{2} )sin(u) }[/tex]

= [tex]\frac{1}{0.cos(u)+(1).sin(u)}[/tex]

=[tex]\frac{1}{sin(u)}[/tex]

= csc(u)

csc(u) = csc(u)

Here we proved that the cofunction identity sec([tex]\frac{\pi }{2}[/tex]-u) = csc(u)

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Answer:

The answer is 314

Step-by-step explanation:

You need to do

3.14(pie) times the radius times the height divided by 3

Answer:

C. 314 [tex]in^{3}[/tex]

Step-by-step explanation:

The volume of a cone is: 1/3[tex]\pi[/tex][tex]r^{2}[/tex]h'

1/3 x 3.14 x [tex]5^{2}[/tex] x 12

1/3 x 3.14 x 25 x 12

1/3 x 3.14 x 300

100 x 3.14

V = 314

Answer:

a = 97° , b = c = 146°

Step-by-step explanation:

a and 83° are same- side interior angles and sum to 180°

a + 83° = 180° ( subtract 83° from both sides )

a = 97°

34° and b are same- side interior angles and sum to 180°

b + 34° = 180° ( subtract 34° from both sides )

b = 146°

b and c are corresponding angles and are congruent , so

c = b = 146°

Answer:

< a = 97 degrees.

< b = 146 degrees.

< c = 146 degrees.

Step-by-step explanation:

We have 2 lines crossing 2 parallel lines.

Internal angles between the 2 parallel lines add up to 180 degrees, so

34 + <b = 180

<b = 180 - 34 = 146 degrees

Also

<a + 83 = 180 degrees (also internal angles)

---> <a = 97 degrees

< c and < b are corresponding angles so are congruent, therefore

<c = < b = 146 degrees.

The probability of drawing a red card from a standard deck of cards is 1/2.

Given that there is a standard deck of cards.

We are required to find the probability of drawing a rd card from a standard deck of cards.

Probability is the calculation of chance of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.

Probability=Number of items/Total items.

Total number of cards=52

Number of red cards =26

Number of black cards=26

Probability of drawing a red card =Number of red cards/ Total cards.

=26/52

=1/2

Hence the probability of drawing a red card from a standard deck of cards is 1/2.

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The standard deviation exists as the positive square root of the variance.

So, the standard deviation = 4.47.

Given data set: 13 17  9 21

To calculate the mean of the data.

We know that mean exists as the average of the data values and exists estimated as:

Mean [tex]$=\frac{13+17+9+21}{4} \\[/tex]

Mean [tex]$=\frac{60}{4} \\[/tex]

Mean = 15

To find the difference of each data point from the mean as:

Deviation:

13 - 15 = -2

17 - 15 = 2

9 - 15 = -6

21 - 15 = 6

Now we have to square the above deviations we obtain:

4, 4, 36, 36

To estimate the variance of the above sets:

variance [tex]$=\frac{4+4+36+36}{4}$[/tex]

Variance [tex]$=\frac{80}{4}$[/tex]

Variance = 20

The standard deviation exists as the positive square root of the variance. so, the standard deviation [tex]$=\sqrt{20 }=4.47$[/tex].

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Answer:

4.4

Step-by-step explanation:

The answer above is correct.

Answer:

B={1,2,3,4,6and12}

n (B) =6

Step-by-step explanation:

Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

Hope it helps!

Using proportions, it is found that the value of n is of [tex]n \geq 11[/tex].

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

On the first 15 games, the team wins 2 games and losses 13. Then, in each week, the team plays 3 games, winning 2. Then:

The proportion of wins is given as follows:

[tex]\frac{2 + 2n}{15 + 3n}[/tex]

The proportion is of at least 50%, hence:

[tex]\frac{2 + 2n}{15 + 3n} \geq 0.5[/tex]

We solve the inequality for n, similarly to how we would solve an equality, applying cross multiplication. Then:

[tex]2 + 2n \geq 7.5 + 1.5n[/tex]

[tex]0.5n \geq 5.5[/tex]

[tex]n \geq \frac{5.5}{0.5}[/tex]

[tex]n \geq 11[/tex]

The value of n is of [tex]n \geq 11[/tex].

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Answer:

7/10

Step-by-step explanation:

take 3, 2, 1 from the equation and your left with 7 numbers. Add those together you get 10. 7/10 is the probability that you will draw a number greater than 3

Answer:

$0.03

Step-by-step explanation:

2.31/11 =.21

2.70/15 =.18

.21-.18 = .03

The answer is B.

If the terminal point of θ is at (0, -1), then tanθ is equal to :

The tangent of the given angle is undefined, so the correct option is B.

The tangent function is one of the main six trigonometric functions and is generally written as tan x. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.

Given that on a unit circle, the terminal point of θ is (0, - 1) we need to determine tan θ,

We know that the terminal point of θ is (0, -1).

Now, the tangent of an angle is equal to the quotient between the y-component and the x-component of the terminal point, then we have:

tan(θ) = =1/0

And we can't divide by zero, so it is undefined, then the correct option is B.

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If the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.

Given that the speed of the ball after kicking is 48 feet per second and the function that represents the height of the ball is [tex]-16t^{2} +48t[/tex].

We are required to find the time that the ball took to travel before returning the ground.

We know that speed is the distance a thing covers in a particular time period.

The height of the ball after t seconds is as follows:

h(t)=[tex]-16t^{2} +48t[/tex]

It is at ground at the instants of t.

Hence,

[tex]-16t^{2} +48t[/tex]=0

-16t(t-3)=0

We want value of t different of 0, hence :

t-3=0

t=3.

Hence if the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.

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Answer:

B. t=3

Step-by-step explanation:

i took the test and got it right

The probability that the service time will be more than three minutes is 0.3012.

Given that the average wait time at the Rivertown bank's neighborhood branch is 2.5 minutes and has an exponential distribution,

The time it takes to succeed in a continuous sequence of independent trials is described by the exponential distribution, which is a continuous probability distribution.

At the River Town Bank's neighborhood branch, the random variable X service time has an exponential distribution with a mean value of 2.5 minutes. Therefore,

[tex]f(x)=\left\{\begin{array}{ll}\theta e^{-\theta x},& \theta \geq 0,0\leq x\leq \infty\\0&\text{otherwise}\end{array}[/tex]

E(x)=1/θ

θ=1/2.5

θ=0.4

The probability that the service time will be longer than three minutes:

[tex]\begin{aligned}P(X > 3)&=1-P(X\leq 3)\\ &=1-(1-e^{-0.4\times 3}\\ &=e^{-1.2}\\ &=0.3012\end[/tex]

Since the service duration has an exponential distribution and a mean of 2.5 minutes, the needed chance that it will exceed 3 minutes is 0.3012.

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The value of the missing side x is 38.40 units given the triangle is a right angled triangle with angle 38° and side opposite to the angle is 30 units. This can be obtained by using trigonometric ratios.

Trigonometric identities,

If in a right triangle ΔABC where A is the right angle

In the question,

x is the adjacent side of the angle 38° and 30 units is the opposite side.

The ratio with opposite side and adjacent side is tan A

Therefore,

⇒ tan 38° = [tex]\frac{opposite\ side}{adjacent\ side}[/tex]

⇒ tan 38° = 30/x

⇒ x = 30/tan 38°

∵ tan 38° = 0.781285627

⇒ x = 30/0.781285627

⇒ x = 38.398249

⇒ x = 38.40

Hence the value of the missing side x is 38.40 units given the triangle is a right angled triangle with angle 38° and side opposite to the angle is 30 units.

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Answer:

  0.33 ⋅ 10^−15

Step-by-step explanation:

Scientific notation requires exactly one non-zero digit to the left of the decimal point.

The number ...

  0.33 ⋅ 10^−15

has no non-zero digits to the left of the decimal point. It is not in "scientific notation."

__

Additional comment

Expressed in scientific notation, it would be ...

     3.3 ⋅ 10^−16

There are 105 numbers in the  the first 1000 positive integers contain only 0s and 1s when written in base 3

The number base is given as:

Base 3

To determine the count of numbers, we make use of the following Python program

count = 0

for n in range(1,1001):

   digits = []

   while n:

       digits.append(int(n % 3))

       n //= 3

   myStr = ''.join(map(str,digits[::-1]))

   if(myStr.count('0')+myStr.count('1') == len(myStr)):

       count+=1

print(count)

The above program counts the numbers in the  the first 1000 positive integers contain only 0s and 1s when written in base 3

The output of the program is 105

Hence, there are 105 numbers in the  the first 1000 positive integers contain only 0s and 1s when written in base 3

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from 2007 to 2012 is only 5 years, so we can see this as a compound interest with a rate of 1.2% per annum for 5 years, so

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$113505\\ r=rate\to 1.2\%\to \frac{1.2}{100}\dotfill &0.012\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=113505\left(1+\frac{0.012}{1}\right)^{1\cdot 5}\implies A=113505(1.012)^5\implies A\approx 120481[/tex]

2 x 10² kcal are in the serving report your answer to 2 significant figures.

According to the question

A serving of fish contains 50 g of protein and 4. 0 g of fat.

i.e. content of protein = 50 g

Content of fat = 4 g

kcal are in the serving report your answer to 2 significant figures:

As the serving of fish contains 50g of protein that is 4.0kcal/g

Calories in 50 g protein = (Content of protein) × (caloric value in protein)

50g × (4.0kcal/g) = 200kcal

That means the kcal of the serving is 200kcal

In 2 significant figures: 2 x 10² kcal

Hence,

2 x 10² kcal are in the serving report your answer to 2 significant figures.

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Answer:

not sure but I think it is this

Answer:

The rope is worth 13.

The shoe is worth 5.

The clock is worth 3.

Step-by-step explanation:

We know that the weights are 8 so we will use 8 for the weights.

Let s = show

Let r = rope

Let c = clock

We have three unknowns so we need three equations.

8 + s = r                      c + s = 8                                 s= c +2

There are a number of ways that we can approach this.  Let's substitute

c + 2 for s in the first 2 equations.

8 + s = r

8 + c + 2 = r

10 + c = r

c + s = 8

c + c + 2 = 8

2c + 2 = 8  

2c = 6

c = 3  we found the value of the clock.

Now, let's substitute 3 in for 3 in the bold equation above.

10 + c = r

10 + 3 = r

13 = r we found the value of the rope.

We can use any of the equations to find the shoe.

s= c + 2

s = 3 + 2

s = 5

This is tricky.  It takes a lot of practice.  Don't give up!

Shoe= 5

Rope= 13

Clock= 3

We can start by giving each item a variable. Shoe= s, rope= r, clock= c. The weight is 8, so we don't need to give it a variable. Our equations are now:

8+s= r

c+s= 8

s= c+2

Now, we can isolate a variable to solve for it using the substitution method. Let's start with s.

c+s=8

-c    -c

s= 8-c

Now, we'll take another equation and plug s in.

8-c=c+2

 +c +c

8= 2c+2

-2      -2

6=2c

c=3

Now we know that the clock is 3. Put 3 into the last equation, and add 3+2 to get 5 for the shoe. 5 in the first equation for the shoe plus 8 as the weight means the rope is 13.

hope this helped!

Answer:

A

Step-by-step explanation:

the means is less than the median

Solving a system of equations we can see that:

Let's define:

When the airplane travels against the wind, the total speed is:

(A - W)

In this way, we know that the airplane travels 1350 miles in 5 hours, then:

(A - W) = 1350mi/5h

When the airplane travels with the wind, it takes 3.75 hours to travel the same distance, then:

(A + W) = 1350mi/3.75h

We have now a system of equations:

(A - W) = 1350mi/5h

(A + W) = 1350mi/3.75h

If we isolate A on the first equation, we get:

A = 270mi/h + W

Replacing that in the other equation we get:

270mi/h + W + W = 360 mi/h

Solving for W we get:

2*W = 360mi/h - 270mi/h = 90mi/h

W = 90mi/h = 45mi/h

And the airplane rate is:

A =  270mi/h + W = 270mi/h + 45mi/h = 315 mi/h

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