What is the volume of a cone with radius 7 cm and height 11 cm? Round your answer to two decimal places.

Answer:

  [tex]\dfrac{4x^2+12x+5}{6x^2-3x}[/tex]

Step-by-step explanation:

Invert the denominator and multiply.

  [tex]\dfrac{2x+5}{3x}\div\dfrac{2x-1}{2x+1}=\dfrac{2x+5}{3x}\cdot\dfrac{2x+1}{2x-1}\\\\=\dfrac{(2x+5)(2x+1)}{(3x)(2x-1)}=\boxed{\dfrac{4x^2+12x+5}{6x^2-3x}}\qquad\text{matches choice A}[/tex]

Answer:

[tex]\frac{4x^2+12x+5}{6x^2-3x}[/tex]

Step-by-step explanation:

After using the reciprocal of the second term, the denominator will multiply out to be [tex]6x^2-3x[/tex]. There is only one option with that as the denominator so it must be the correct answer.

Answer:

5x + 10 = 25

Subtract 10 on each side to make x alone

5x = 15

divide by 5 on each side

x=3 so x=3

3x + 12 = 48

48-12=36

3x=36

divide by 3

x=12

4x + 8 = 16

4x = 8

x=2

2x + 15=25

2x=10

x=5

5x + 20 = 50

5x=30

x=6

hope this helps

1. 3

2.12

3.2

4.5

5.6

Step-by-step explanation:

Answer:

Step by step explanation

First:

Solution,

1. 5x + 10 = 25

Move constant to the R.H.S and change its sign:

5x = 25 - 10

Calculate the difference

5x = 15

Divide both sides by 5

5x/5 = 15/5

calculate

X = 3

2. 3x + 12 = 48

or, 3x = 48 - 12

or, 3x = 36

or, 3x/x = 36/3

x = 12

3. 4x + 8 = 16

or, 4x = 16 - 8

or, 4x = 8

or, 4x/x = 8/4

x = 2

4. 2x + 15 = 25

or, 2x = 25 - 15

or, 2x = 10

or, 2x/x= 10/2

x = 5

5. 5x + 20 = 50

or, 5x = 50-20

or, 5x = 30

or, 5x/x = 30/5

x = 6

Hope this helps...

Good luck on your assignment...

Answer:

(a)0.5

(b)0.17

(c)0.625

(b)0.375

Step-by-step explanation:

Pr(E)=0.6​

Pr(F)=0.2

[tex]Pr(E\cap F)=0.1.[/tex]

(a)Pr (E|F )

[tex]Pr (E|F )=\dfrac{Pr(E \cap F)}{Pr(F)} \\=\dfrac{0.1}{0.2}\\\\=0.5[/tex]

(b)Pr (F|E )

[tex]Pr (F|E )=\dfrac{Pr(E \cap F)}{Pr(E)} \\=\dfrac{0.1}{0.6}\\\\=0.17[/tex]

(c)Pr (E|F')​

Pr(F')=1-P(F)

=1-0.2=0.8

[tex]Pr(E \cap F')=P(E)-P(E\cap F)\\=0.6-0.1\\=0.5[/tex]

Therefore:

[tex]Pr (E|F' )=\dfrac{Pr(E \cap F')}{Pr(F')} \\=\dfrac{0.5}{0.8}\\\\=0.625[/tex]

(d)Pr(E'|F')​

[tex]P(E'\cap F')=P(E \cup F)'\\=1-P(E \cup F)\\=1-[P(E)+P(F)-P(E\cap F)]\\=1-[0.6+0.2-0.1]\\=1-0.7\\=0.3[/tex]

Therefore:

[tex]Pr (E'|F' )=\dfrac{Pr(E' \cap F')}{Pr(F')} \\=\dfrac{0.3}{0.8}\\\\=0.375[/tex]

Answer:

  Always true

Step-by-step explanation:

If you can't express the number as a ratio of integers, multiplying or dividing it by integers will not make it so you can.

If π is irrational, 2π is also irrational.

It is always true that the product of a rational and an irrational number is irrational.

Answer:

all ways true

Step-by-step explanation:

Hey there! :)

Answer:

10 miles.

Step-by-step explanation:

To solve for the diagonal side, we can simply visualize the sides of the rectangle as sides of a right triangle with the diagonal being the hypotenuse.

We can use the Pythagorean Theorem (a² + b² = c²), where:

a = length of short leg

b = length of long leg

c = length of the diagonal

Solve:

c² = a² + b²

c² = 6² + 8²

c² = 36 + 64

c² = 100

c = 10 miles. This is the length of the pedestrian route.

Answer:

Solution,

Hypotenuse (h) = R

Perpendicular (p) = 8 miles

Base (b) = 6 miles

Now,

Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

Plugging the values:

[tex] {r}^{2} = {(8)}^{2} + {(6)}^{2} [/tex]

Calculate:

[tex] {r}^{2} = 64 + 36[/tex]

[tex] {r}^{2} = 100[/tex]

[tex]r = \sqrt{100} [/tex]

[tex]r = 10 \: miles[/tex]

Length of route = 10 miles

Hope this helps...

Good luck on your assignment...

Answer:  see below

Step-by-step explanation:

Inverse is when you swap the x's and y's.

The Slope-Intercept form is [tex]y=\dfrac{1}{5}x-\dfrac{3}{5}[/tex]    which isn't convenient to graph.

So take the points from the original equation (-1, -2) & (0, 3) and switch the x's and y's to get the points (-2, -1) & (3, 0).

Draw a line through points (-2, -1) and (3, 0) to sketch the graph of the inverse.

Step-by-step explanation:

to be honest I'm not sure how to do

Answer:

Step-by-step explanation:

According to the central limit theorem, if independent random samples of size n are repeatedly taken from any population and n is large, the distribution of the sample means will approach a normal distribution. The size of n should be greater than or equal to 30. Given n = 100 for both scenarios, we would apply the formula,

z = (x - µ)/(σ/√n)

a) x is a random variable representing the salaries of accounting graduates. We want to determine P( x > 52000)

From the information given

µ = 50402

σ = 6000

z = (52000 - 50402)/(6000/√100) = 2.66

Looking at the normal distribution table, the probability corresponding to the z score is 0.9961

b) x is a random variable representing the salaries of finance graduates. We want to determine P(x > 52000)

From the information given

µ = 49703

σ = 10000

z = (52000 - 49703)/(10000/√100) = 2.3

Looking at the normal distribution table, the probability corresponding to the z score is 0.9893

c) The probabilities of either jobs paying that amount is high and very close.

Answer:

4.7

Step-by-step explanation:

Given :

initial mean length =4.1  minutes.

Final mean length =5.3 minutes

The mid point of the given interval can be determined by the

[tex]Midpoint \ = \frac{Initial\ Mean\ length\ +Final\ Mean\ length }{2} \\Midpoint \ = \frac{4.1\ +\ 5.3\ }{2} \\Midpoint \ = \frac{9.4 }{2} \\Midpoint \ =4.7\\[/tex]

Therefore 4.7 is the midpoint

Answer:

A. y=-1/4x

Step-by-step explanation:

We have the information 3y=12x-9, the lines are perpendicular, and the new line passes through (-4,1). First, you want to put the original equation into slope intercept form by isolating the y, to do this we need to divide everything by 3 to get y=4x-3. The slopes of perpendicular lines are negative reciprocals so you need to find the negative reciprocal of 4, so flip it to 1/4 and multiply by -1, we get the slope of the new line as -1/4. So far we have the equation y=-1/4x+b. We are given a point on the line, (-4,1), we can plug these into the equation as x and y to solve for the y-intercept, b. You set it up as 1=-1/4(-4)+b. First you multiply to get 1=1+b, then you subtract 1 from both sides to isolate the variable and you get b=0. Then you can use b to complete your equation with y=-1/4x, or letter A.

Answer:

When describing a property line drawn down the center of a creek bed

Answer:

4 = 4

Step-by-step explanation:

=> 2x = 4

Putting x = 2

=> 2(2) = 4

=> 4 = 4

Answer:

Solution,

X= 2

Now,

2x=4

plugging the value of X,

2*2= 4

4 = 4 ( hence it is true)

Answer: 132

Step-by-step explanation: To solve this equation we know that x is greater than 81 unless the equation would not make sense. 81 + 51 = 132

Answer: x=132

Step-by-step explanation: Add 51 to 81, as positive 51 is the inverse of -51. You need to get the x alone. Therefore, 51+81=132 and x=132.

Answer:

(7, 5.25) lies on the graph.

Step-by-step explanation:

We are given the following values

x = 4,   6,  8, 12 and corresponding y values are:

y = 3, 4.5, 6, 9

Let us consider two points (4, 6) and (6, 4.5) and try to find out the equation of line.

Equation of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:

[tex]y=mx+c[/tex]

where m is the slope.

(x,y) are the coordinates from where the line passes.

c is the y intercept.

Here,

[tex]x_{1} = 4\\x_{2} = 6\\y_{1} = 3\\y_{2} = 4.5[/tex]

Formula for slope is:

[tex]m = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m = \dfrac{4.5-3}{6-4}\\\Rightarrow m = \dfrac{1.5}{2}\\\Rightarrow m = \dfrac{3}{4}[/tex]

Now, the equation of line becomes:

[tex]y=\dfrac{3}{4}x+c[/tex]

Putting the point (4,3) in the above equation to find c:

[tex]3=\dfrac{3}{4}\times 4+c\\\Rightarrow 3=3+c\\\Rightarrow c =0[/tex]

So, final equation of given function is:

[tex]y=\dfrac{3}{4}x[/tex]

OR

[tex]4y=3x[/tex]

As per the given options, the point (7, 5.25) satisfies the equation.

So correct answer is [tex](7, 5.25)[/tex].

Answer:

(-3x-2/x) multiply by (-15x+12/x) so It's (A)

Hope this helped you!!

Step-by-step explanation:

Answer:

30 dimes and 20 quarters

30×.10=$3.00

20×.25=$5.00

30+20=50

$3+$5=$8

Answer:

7x+7 is obviously divisible by 7.

put in any value high enough and you can find the two three digit numbers.

Step-by-step explanation:

Two three-digit numbers divisible by 7 are 98 and 105.

Two three-digit numbers divisible by 7 are 98 and 105.To create an expression that is divisible by 7, we can use the property that the difference between two numbers is divisible by 7 if the numbers themselves are divisible by 7.

Let's represent a three-digit number divisible by 7 as "7k" where k is an integer. To find two three-digit numbers divisible by 7, we can use the following expression:

7k - 7

For example, if we substitute k = 15, we get:

7(15) - 7 = 105 - 7 = 98

So, the first three-digit number divisible by 7 is 98.

Similarly, for the second three-digit number, let's substitute k = 16:

7(16) - 7 = 112 - 7 = 105

Therefore, the two three-digit numbers divisible by 7 are 98 and 105.

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Answer: 14/11

Step-by-step explanation:

When 14/11 is multiplied by 1/4, you get a repeating decimal.  All repeating decimals are rational.

Hope it helps <3

Behold the quotient of F and the product of r,s, and T:  F / (r·s·T)

The numerical of the statement the quotient of F and the product of r,s, and T is F/(r×s×T).

The number which is being divided is the dividend.

The number with which we are dividing is the divisor.

The result when a dividend is divided by the divisor is the quotient.

A remainder is the extra portion of a number when it isn't completely divisible.

Given, Are some variables F, r, s, and t.

Now, The product of r,s, and T is,

= r×s×T and the complete statement the quotient of F and the product of r,s, and T can be written as,

F/(r×s×T).

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Step-by-step explanation:

n = 61,647, p = 0.26, q = 0.74

μ = p = 0.26

σ = √(pq/n) = 0.00177

At 0.05 significance, z = 1.96.

0.26 ± 1.96 × 0.00177

(0.257, 0.263)

0.25 is outside of the confidence interval, so we can conclude with 95% confidence that the proportion is greater than 0.25.

Answer:

z = 10

Step-by-step explanation:

The value of the z-statistic is given by:

[tex]z = \frac{X - \mu}{s}[/tex]

In which:

X is the measured value.

[tex]\mu[/tex] is the expected value.

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex] is the standard deviation of the sample. [tex]\sigma[/tex] is the standard deviation of the population.

In this question:

The mean length was 2.9 inches, and the population standard deviation is 0.1 inch.

This means that [tex]\mu = 2.9, \sigma = 0.1[/tex]

Random sample of 100 screws.

This means that n = 100.

To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be?

3 inches, so [tex]X = 3[/tex]

[tex]s = \frac{0.1}{\sqrt{100}} = 0.01[/tex]

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{3 - 2.9}{0.01}[/tex]

[tex]z = 10[/tex]

Answer:

-10

Step-by-step explanation:

If we first note the denominator of fraction numerator sigma over denominator square root of n end fraction equals fraction numerator 0.1 over denominator square root of 100 end fraction equals fraction numerator begin display style 0.1 end style over denominator 10 end fraction equals 0.01

Then, getting the z-score we can note it is z equals fraction numerator x with bar on top minus mu over denominator begin display style 0.01 end style end fraction equals fraction numerator 2.9 minus 3 over denominator 0.01 end fraction equals negative 10

This tells us that 2.9 is 10 standard deviations below the value of 3, which is extremely far away.

Answer:

[tex]z=\frac{0.21 -0.31}{\sqrt{\frac{0.31(1-0.31)}{100}}}=-2.162[/tex]  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(z<-2.162)=0.0306[/tex]  

Step-by-step explanation:

Information given

n=100 represent the random sample taken

[tex]\hat p=0.21[/tex] estimated proportion of the readers owned a particular make of car

[tex]p_o=0.31[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We need to conduct a hypothesis in order to test if the true proportion is 0.31 or no.:  

Null hypothesis:[tex]p=0.31[/tex]  

Alternative hypothesis:[tex]p \neq 0.31[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

And replacing we got:

[tex]z=\frac{0.21 -0.31}{\sqrt{\frac{0.31(1-0.31)}{100}}}=-2.162[/tex]  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(z<-2.162)=0.0306[/tex]  

Answer:

Step-by-step explanation:

Let X be the amount of cashews that the nutty professor will mix.

Since, the total weight of the nuts should be 35 lbs

The amount of Brazil nuts = 35 - X

Now,

[tex]6x + 5.30(35 - x) = 5.64(35)[/tex]

[tex]600x + 530(35 - x) = 564 \times 35[/tex]

[tex]600x + 18550 - 530x = 19740[/tex]

[tex]70x = 19740 - 18550[/tex]

[tex]70x = 1190[/tex]

[tex]x = \frac{1190}{70} [/tex]

[tex]x = 17[/tex]

Again,

[tex] 35 - x[/tex]

[tex]35 - 17[/tex]

[tex]18[/tex]

17 pounds of cashew and 18 pounds of Brazil nuts.

Hope this helps...

Good luck on your assignment...

Answer:

[tex]\dfrac{1}{7}[/tex]

Step-by-step explanation:

There are 7 days in a week.

For the first person, we select one day out of the 7 days. The first person has 7 options out of the 7 days.

Let Event A be the event that the first person was born on a day of the week.

Therefore:

[tex]P(A)=\dfrac{7}{7}=1[/tex]

The second person has to be born on the same day as the first person. Therefore, the second person has 1 out of 7 days to choose from.

Let Event B be the event that the second person was born.

Therefore, the probability that the second person was born on the same day as the first person:

[tex]P(B|A)=\dfrac{1}{7}[/tex]

By the definition of Conditional Probability

[tex]P(B|A)=\dfrac{P(B \cap A)}{P(A)} \\$Therefore:\\P(B \cap A)=P(B|A)P(A)[/tex]

The probability that both were born on the same day is:

[tex]P(B \cap A)=P(B|A)P(A) = \dfrac{1}{7} X 1 \\\\= \dfrac{1}{7}[/tex]

Answer:

a) Check Explanation.

b) True. Check Explanation.

c) True. Check Explanation.

Step-by-step explanation:

a) A normal distribution is one which is characterized by four major properties.

- A normal distribution is symmetrical about the center of the distribution. That is, the variables spread out from the center in both directions in the same manner; the right side of the distribution is a mirror image of the left side of the distribution.

The center of a normal distribution is located at its peak, and 50% of the data lies above the mean, while 50% lies below.

- The mean, median and the mode are coincidental. The mean, median and mode of a normal distribution are all the same value.

- A normal distribution is unimodal, that is, has only one mode.

- The ends of the probability curve of a normal distribution never touch the x-axis, hence, it is said too be asymptotic.

b) The sampling distribution of sample means arises when random samples are drawn from the population distribution and their respective means are computed and put together to form a distribution. Hence, the curve of this sampling distribition of sample means will show how the sample means are distributed. Hence, this statement is true.

c) The Central Limit Theorem gives that if the samples are drawn randomly from a normal distribution and each sample size is considerable enough, the mean of the sampling distribution of sample means is approximately equal to the population mean. So, if the conditions stated are satisfied, then thos statement too, is true.

Hope this Helps!!!

Answer:

An object balances itself when a perpendicular line drawn through its Centre of Gravity (CG), passes through its base.

See the picture of a popular toy given below. The horse, the rider and the ball are all joined together as one single unit. This entire unit is balanced on the thin black rod shown. At which of the indicated positions, could the Centre of Gravity (CG) of the horse, rider and ball unit be?

July 10 book Science up55 down8

AA BB

CC DD

Step-by-step explanation:

Answer:

(A)Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle)

Step-by-step explanation:

The steps followed by the student are:

Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle)

Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles)

Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p

Step 4: So, m∠m + m∠n = m∠p

We observe that the student made a mistake in Step 1, it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle).

p is outside the triangle, therefore it cannot form one of the angles in the triangle.

Answer:

245 might be the answer

Step-by-step explanation:

(7*7*10)/2

Answer:

  P = 20000×1.625^(n/4)

Step-by-step explanation:

An exponential equation can be written using the given data:

  value = (initial value)×(growth factor in period)^(n/(period))

Here, the growth is by a factor of 32500/20000 = 1.625, and the period is 4 years. Then your exponential equation is ...

  P = 20000×1.625^(n/4)

Answer:

Option (A).

Step-by-step explanation:

The function f(x) = x² + 4 is defined over the interval (-2, 2)

Total number of equal parts between this interval = 5

If the interval is divided into n equal parts, height of the right endpoint of each rectangle = [tex]\frac{5}{n}[/tex]

Height of the endpoint of the k rectangles = [tex]k.\frac{5}{n}[/tex]

Therefore, height of the endpoint of the kth rectangle = Height of first rectangle + height of k rectangles

= -2 + [tex]k.\frac{5}{n}[/tex]

Option (A). will be the answer.

The height of the right endpoint of the kth rectangle h = -2 + k (5/n)

The height is a vertical distance between two points. In the case of the triangle, the height will be the distance between the base and the top vertex of the triangle.

The function f(x) = x² + 4 is defined over the interval) (-2, 2 )

Total number of equal parts between this interval = 5

If the interval is divided into n equal parts, the height of the right endpoint of each rectangle = (5/n)

Height of the endpoint of the k rectangles = k (5/n)

The height of the endpoint of the kth rectangle:-

= Height of first rectangle + height of k rectangles

= -2   +  k (  5/n )

Therefore the height of the right endpoint of the kth rectangle h = -2 + k (5/n)

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