Find the VOLUME of the right circular cone:
26 m
10 m

Answer:

\(t=\frac{203.8-221.4}{\frac{21.6}{\sqrt{100}}}=-8.148\)    

The degrees of freedom are given by:  

\(df=n-1=100-1=99\)  

and the p value would be given by:

\(p_v =P(t_{(99)}<-8.148) \approx 0\)  

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly less than 221.4 the value of study.

Step-by-step explanation:

Information given

\(\bar X=203.8\) represent the sample mean    

\(s=21.6\) represent the sample standard deviation

\(n=100\) sample size  

\(\mu_o =221.4\) represent the value to verify

\(\alpha=0.01\) represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

\(p_v\) represent the p value for the test

Hypothesis to test

We want to verify if the true mean is lower than 221.4, the system of hypothesis would be:  

Null hypothesis:\(\mu \geq 221.4\)  

Alternative hypothesis:\(\mu < 221.4\)  

The statistic is given by:

\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\)  (1)  

Replacing the info we got:

\(t=\frac{203.8-221.4}{\frac{21.6}{\sqrt{100}}}=-8.148\)    

The degrees of freedom are given by:  

\(df=n-1=100-1=99\)  

and the p value would be given by:

\(p_v =P(t_{(99)}<-8.148) \approx 0\)  

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly less than 221.4 the value of study.

Answer:

You need to ask yourself what times 20  gives you 600.  Then ask yourself what times 20 gives you 160.  Then that will give you your answer.

Step-by-step explanation:

f ' ( x ) = 1 ( x + 1 ) 2

Explanation:

differentiating from first principles

f ' ( x ) = lim h → 0

f ( x + h ) − f ( x ) h

f ' ( x ) = lim h → 0

 x + h x + h + 1 − x x + 1 h

the aim now is to eliminate h from the denominator

f ' ( x ) = lim h =0  

( x + h ) ( x + 1 )− x ( x + h + 1) h ( x + 1 ) ( x + h + 1 )

f ' ( x ) = lim h → 0

 x 2 + h x + x + h − x 2 − h x − x h ( x + 1 ) ( x+h + 1 )

f ' ( x ) = lim h → 0

h 1 h 1 ( x + 1 ) ( x + h +1 )

f ' ( x ) = 1 ( x + 1 ) 2

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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STEP BY STEP:

13x - 8 + 7x – 2 = 11+ 6x -- 14x – 5

Combine like terms

20x-8-2 = 20x+11-5

20x-10 = 20x+6

Subtract with -20x on both sides and the result is:

\(-10\neq 6\)

The answer is NO SOLUTION

Answer:

Step-by-step explanation:

According to SOH in SOH, CAH TOA;

SOH means  sin theta = opposite/hypotenuse = 2/3

This shows that opposite = 2 and hypotenuse = 3. Before we can determine which of the expression is possible, we need to find the third side of the rigt angled triangle which is the adjacent.

According to Pythagoras theorem; hyp² = opp²+adj²

adj² = hyp² - opp²

adj² = 3² - 2²

adj² = 9 - 4

adj² = 5

adj = √5

Hence the adjacent side is √5.

From the trigonometry identity above;

cos theta = adj/hyp = √5/3 and tan theta = opp/adj = 2/√5

Since sec theta = 1/cos theta then sec theta = 1/(adj/hyp)

sec theta = hyp/adj = 3/√5

From the above calculation, the following are possible:

cos theta = √5/3, tan theta = 2/√5 and sec theta = 3/√5

The correct options are C and D

There are 21 different city combinations possible for Peter's summer traveling.

To determine the number of different city combinations possible for Peter's summer traveling, we need to calculate the number of combinations of choosing 5 cities out of the 7 available cities.

Since the order in which he visits the cities does not matter, we are dealing with combinations rather than permutations.

The formula to calculate the number of combinations is given by the binomial coefficient, also known as "n choose k," denoted as C(n, k) or (nCk).

In this case, we have 7 cities to choose from, and Peter will visit 5 cities. Thus, we can calculate the number of city combinations as follows:

C(7, 5) = 7! / (5! * (7-5)!)

= 7! / (5! * 2!)

= (7 * 6 * 5!) / (5! * 2)

= (7 * 6) / 2

= 42 / 2

= 21

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Answer:

1800

Step-by-step explanation:

Well the easiest way to do this is just do

9 x 2 = 18 and since in 20 and 90 there are two zeroes, add two zeroes at the end of 18!

Answer:

its equals 1,800

Step-by-step explanation:

Answer:

y = (1/2)x - 3

The slope is m = 1/2 and the y-intercept is (0, -3).

Step-by-step explanation:

Assuming that you meant 6y = 3x - 18, we solve this equation for y to obtain the slope-intercept formula y = mx + b for this particular case:

y = (3/6)x - (18/6), or

y = (1/2)x - 3

The slope is m = 1/2 and the y-intercept is (0, -3).

All the probabilities associated with the contingency table based on the given information are;

A) 82/150

B) 39/150

C) 94/150

D) 22/36

E) 68/150

A contingency table is defined as a type of table that is in a matrix format that displays the frequency distribution of the variables. Thus, the probability would be defined as the likelihood of occurrence of the items in this contigency table.

A) The total number of violent crimes committed was 82. Since the total number of crimes committed was 150 crimes, then the probability of selecting a case to analyze and finding it involved a violent crime is; 82/150

B)  The total number of crimes committed by someone less than 20 years old is 39. Since the total number of crimes committed was 150 crimes, then the probability of selecting a case to analyze and finding the crime was committed by someone less than 20 years old is; 39/150

C) The probability of selecting a case that involved a violent crime or an offender who is less than 20 years old is; (82 + 39 - 27)/150 = 94/150

D) The number of crimes that are non violent involving someone over 40 years old is 22. Thus, the probability of selecting a case to analyze and finding it involved a nonviolent given that this criminal is over 40 is; 22/36

E)  The probability of selecting a case to analyze and finding it involved a Non-violent crime is; 68/150

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Complete question is;

A total of 150 crimes were reported by the sheriff last year. Of the 150 crimes, 39 were committed by criminals under 20 years of age, 36 were committed by criminals over 40 , and 82 were violent crimes. There were 27 violent criminals under the age of 20 and 14 violent criminals over the age of 40 . From the contingency table filled, find the following;

a. What is the probability of selecting a case to analyze and finding it involved a violent crime?

b. What is the probability of selecting a case to analyze and finding the crime was committed by someone less than 20 years old?

c. What is the probability of selecting a case that involved a violent crime or an offender who is less than 20 years old?

d. What is the probability of selecting a case to analyze and finding it involved a nonviolent given that this criminal is over 40?

e. What is the probability of selecting a case to analyze and finding it involved a Non-violent crime?

The probability that either event will occur is P ( C ) = 0.89

Given data ,

Let the probability that either event will occur  be P ( C )

P ( A ) = 20/36

P ( B ) = 12/36

where P ( A or B ) = P ( C )

P ( C ) = P ( A ) + P ( B )

P ( C ) = 32/36

P ( C ) = 0.88888

Hence , the probability is P ( C ) = 0.89

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Answer:

84 miles in 12 hour

Step-by-step explanation:

12/4 = 3

3*28=84

Answer:

84 miles.

Step-by-step explanation:

First, find the rate of miles travel per hour.  It is given that the boat covers 28 miles in 4 hours. Simply divide 28 with 4:

28/4 = 7

The boat covers 7 miles per hour.

Now, multiply 12 hours with 7:

12 hours x 7 miles per hour = 84 miles per 12 hours.

84 miles is your answer.

~

Answer:

3

Step-by-step explanation:

Plug in 6 for the y value. Solve for x.

Answer:

x=3 (3,6)

Step-by-step explanation:

Y = 15 - 3x

Y = 6

6= 15-3x

-15 from each side

-9 = -3x

devide each side

ny -3

x=3

(check)

15-3(3) = 6

Answer:

The total will be 4.59. Since we have 2 dollars and then we have 3 dimes which a dime is equal to 10 cents, it is now 2 dollars and 30 cents. Now we have the 4 pennies, which a penny is 1 cent. So we have 2 dollars and 34 cents. Now we have a dollar and 5 quarters. A quarter is equal to 25 cents. So 4 quarters is equal to 1 dollar. So it will be 2 dollars and 25 cents for the other quarter that we have. Now we add 2.34 and 2.25 which we get 4.59 dollars(i tried my best ok).

Quick equation:2d+3(10)+4(1)=$2.34

                          2d+5(25)=$2.25

Answer:

Perimeter = 64cm

Perimeter is the sum of all sides.

working with the ratio now = 7:1

there 7 + 1 = 8

length = 7/8y

width = 1/8y

Perimeter = (2 x 7/8y) + (2 x 1/8y) = 64

1.75y + 0.25y = 64

2y = 64

y = 32

Length = 7/8 x 32 = 28cm

Width = 1/8 x 32 = 4cm

The vertex of the parallelogram is (5, 13)

We know that in a parallelogram the opposite sides are equal

AB=√(-3-4)²+(-6+3)²

=√49+9

=√58 units

BC=√(6-4)²+(2+3)²

=√4+25

=√29 units

AD=√(-3-x)²+(-6-y)²

AD=√58 units

√58 units=√(-3-x)²+(-6-y)²

58 units=(-3-x)²+(-6-y)²

Now CD=√(6-x)²+(2-y)²

29 units=(6-x)²+(2-y)²

x=5 and y=13 satisfies the equation

Hence, the vertex of the parallelogram is (5, 13)

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Answer:hi

Step-by-step explanation:

Answer:

Please look below:

Step-by-step explanation:

The linear equation consists of the points (1,3) and (-2,-6) [more points are shown on the graph provided below]. If you would like to find the slope, you can use the formula (y2 - y1) / (x2 - x1). Hope that helps!

Answer:

$16

Step-by-step explanation:

This method is probbaly working backwards. I'm not sure.

12 - 4 = 8 (How much she was left with if she didn't wash the car for 4 dollars)

8 x 2 = 16 (They mentioned she spent half of her weekly allowance)

Answer:

\( 6 + 5\sqrt{5} \)

irrational

cannot

does not

Step-by-step explanation:

\( 5\sqrt{5} + 2\sqrt{9} = \)

\( = 5\sqrt{5} + 2 \times 3 \)

\( = 5\sqrt{5} + 6 \)

\( = 6 + 5\sqrt{5} \)

Answer:

See below.

Step-by-step explanation:

First, find the sum:

\(5\sqrt{5}+2\sqrt{9}=5\sqrt{5}+2(3)=5\sqrt{5} +6\)

As long as part of the equation is irrational, the entire answer will also be irrational. Thus:

The result is irrational because it cannot be written [as] the ratio of two integers and its decimal expansion does not terminate or repeat.

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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Answer:

Can not be determined.

Step-by-step explanation:

From the figure attached,

In ΔHFS and ΔIFS,

Side HS ≅ Side HI [Given]

∠HFS ≅ ∠IFS [Given]

Side FS ≅ Side FS [Reflexive property]

But there is no property of SSA (Side-side-angles for the congruence of two triangles)

Therefore, answer is "can not be determined".

Answer:

y= 2x -3

Step-by-step explanation:

Let's rewrite the given equation into the form of y=mx+c, so that we can find the gradient of the line. In this form, m (coefficient of x) is the gradient.

4x -2y= 3

2y= 4x -3

Divide by 2 throughout:

\(y = 2x - 1 \frac{1}{2} \)

Thus the gradient is 2.

Parallel lines have the same gradient thus the line would also have a gradient of 2.

Substitute m=2 into the equation:

y= 2x +c

To find the value of c, substitute a pair of coordinates.

When x=2, y=1,

1= 2(2) +c

1= 4 +c

c= 1 -4

c= -3

Thus, the equation of the line is y= 2x -3.

Answer:

2/5

Step-by-step explanation:

Rearrange terms:

4(2 + a) = 24a

4(a + 2) = 24a

Distrbute:

4(a + 2) = 24a

4a + 8 = 24a

Subtract 8 from both sides of the equation:

4a + 8 = 24a

4a + 8-8 = 24a-8

Simplify:

4a = 24a - 8

Subtract 24a from both sides of the equation:

4a = 24a - 8

4a - 24a = 24a - 8 - 24a

Combine like terms:

-20a = -8

Divide both sides of the equation by the same term:

-20a = -8

-20a/-20 = -8/-20

Simplify:

Cancel terms that are in both the numerator and denominator

Divide the numbers

a = 2/5

I hope that helps! :D

Answer:

46

Step-by-step explanation:

Answer:

4.18 inch^3

Step-by-step explanation:

use the sphere volume formula :

V = (4/3)*pi*r^3

the radius of this sphere is 2/2 = 1 ( diameter / 2)

plugging in the values :

V = (4/3)*3.1415*1^3 = 4.18

Answer:

5:2

Step-by-step explanation:

A ratio is basically a fraction but horizontally for eg. this: 5:8! This question is asking us to find the ratio of the emails that Jamie received to the emails that she answered.

According to the question, Jamie got 20 emails and responds to 8 of them. The ratio would look like this: 20:8 (because a ratio is just a fraction but horizontal, doesn't mean that there will be mixed numbers!) but not this 8:20. Ratios have a specific order that they have to be in and that will vary depending on the question. If the question says to find the ratio of emails that Jamie responded to to the emails that she received, then in this case 8:20 would be correct.

For now, the answer is 20:8. However, we still need to simplify it by finding its lowest common factor (unless the question asks you to not simplify it, it's better to simplify the answer like a fraction). The lowest common factor would be 4 for 20 and 8. 4 goes in 20 5 times sand 4 goes into 8 2 times.

Your final answer should be: 5:2

If you have any further questions please ask!

Answer:

7

Step-by-step explanation:

2 x (3-1) + 3

Evaluate using PEMDAS

Parenthesis

Exponents

Math and Division ( left to right )

Addition and Subtraction ( left to right )

2 x (3-1) + 3

According to PEMDAS we do the operations inside of the parenthesis first

3 - 1 = 2

We now have: 2 x 2 + 3

Next we do exponents

There are no exponents so let's move on to multiplication and division

There is indeed multiplication so we do it

2 x 2 = 4

We now have: 4 + 3

Finally we do the addition

4 + 3 = 7

The answer is 7