Find the total area of the prism.

Answer:

3.6

Step-by-step explanation:

1/9+1/6

1/3^2+1/2x3=1/x

2+3/3^2x2=1/x

5/3^2x2=1/x

x.5=18

5x=18

5x/5= 18/5

x=18/5

x=3.6

To paint the room if they worked​ together in 4 hours 14 min.

To find time if they work together.

science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers.An arithmetic sequence is a sequence where the difference between each successive pair of terms is the same. The explicit rule to write the formula for any arithmetic sequence is this:

an = a1 + d (n - 1).

Given that:

(1 room/Sally's time) + (1 room/Steve's time) = (1 room)/(time working together)

1/9+1/6+=+1/x

Multiply both sides by 54x

6x+9x=54

15x=54

x=3.6hours

Working together, they can paint the room in 3 hours 6 min.

So, to paint the room if they worked​ together in 3 hours 6 min.

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Answer:

There is a solution. The ordered pair is (4, 2).

Step-by-step explanation:

Solve the system of equations by using the substitution method.

[tex]x+y=6\\x=2y[/tex]

Substitute x as 2y in the first equation and solve for y.

[tex]2y+y=6\\ 3y=6\\(3y)/3=6/3\\y=2[/tex]

Substitute y as 2 in the second equation and solve for x.

[tex]x=2(2)\\x=4[/tex]

Answer:-8

Step-by-step explanation:

Answer:

(a) C = 80 a = 5.938cm c = 9.097cm

(b) unsure

(c) b= 22.147cm

A = 48.16 degrees

C = 22.82 degrees

Note angle sum higher than 180 due to rounding inaccuracies

Step-by-step explanation:

(a) <C == 180 - (40 + 60) == 80 (Interior angles on triangle have sum of 180 degrees)

side a = (8*sin(40))/sin(60) == 5.938cm by law of sines

side c = (8*sin(80))/sin(

60) == 9.097cm by law of sines

(b) unsure

(c) b^2 = 17^2 + 11^2 - 2(17)(11)cos(104) --> Law of cosines

b^2 = 289 + 121 - 2(187)cos(104)

b^2 = 400 - -90.479

b^2 = 490.479

b = 22.147 cm

sin(A)/17cm = sin(104)/22.147cm

A = arcsin((17/22.147)*sin(104))

A = 48.16 degrees

sin(C)/11cm = sin(104)/22.147cm

C = arcsin((11/22.147)*sin(104))

C = 28.82 degrees

Answer:

35.25

Step-by-step explanation:

Give the data set:

23 37 49 34 35 41 40 26 32 22 38 42

We are expected to calculate the midquartile of the given data set.

22 23 26 32 34 35 37 38 40 41 42 49

First step is to find the lower quartile which comprises of

22 23 26 32 34 35

Here the Q1 is (26+32)/2 = 58/2= 29

Second step to find the upper quartile which comprises of

37 38 40 41 42 49

Here the Q3 is (40+41) /2 = 81/2 = 41.5

Then to find the midquartile which is (Q1+Q3) /2 where Q1 is 29 and Q3 is 41.5

= (29+41.5)/2

= (70.5) /2 = 35.25

Answer:

72

Step-by-step explanation:

There are 12 inches in a foot.

Therefore in 8 feet there are 96 inches

Therefore the square floor is 96 * 96.

Therefore the area of the square floor is 9216 inches squared.

Each tile is 8 inches by 8 inches meaning it has an area of 64 inches squared.

9216 / 64 = 144.

Therefore 144 tiles are needed to tile the floor

Since each tile is 50 cents, 144 * 0.5 = 72

Therefore it costs 72 dollars to tile the floor.

Answer:

[tex]\large \boxed{\sf \ \text{2 feet, 4 seconds, 258 feet } \ }[/tex]

Step-by-step explanation:

Hello,

To know the height of the baseball when it is hit we have to compute h(0), as t = 0 is when the baseball is hit into the air.

[tex]h(0)=-16\cdot 0^2+128 \cdot 0+2=2[/tex]

So, the answer is 2 feet.

h(x) is a parabola which can be written as [tex]ax^2+bx+c[/tex], it means that the vertex is the point (-b/2a,h(-b/2a)).

The baseball reached its maximum height after

   [tex]\dfrac{-b}{2a}=\dfrac{-128}{-2*16}=\boxed{4 \text{ seconds}}[/tex]

And the maximum height of the baseball is h(4).

[tex]h(0)=-16\cdot 4^2+128 \cdot 4+2=-256+512+2=\boxed{258 \ \text{feet}}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Where is the table

Step-by-step explanation:

I cant answer without it

Answer:

0, 22, 44, 66

Step-by-step explanation:

Given the equation for the model, [tex] d = 11t [/tex] , you can complete the table above by simply plugging in each value of "t" has given in the table to solve for "d".

*When t (seconds) = 0, distance (feet) would be:

[tex] d = 11(0) [/tex]

[tex] d = 0 [/tex]

*When t (seconds) = 2, distance (feet) would be:

[tex] d = 11(2) [/tex]

[tex] d = 22 [/tex]

*When t (seconds) = 4, distance (feet) would be:

[tex] d = 11(4) [/tex]

[tex] d = 44 [/tex]

*When t (seconds) = 6, distance (feet) would be:

[tex] d = 11(6) [/tex]

[tex] d = 66 [/tex]

Answer:

a = 8

b = -8

Step-by-step explanation:

You have the following function:

[tex]f(x)\\\\=at+b;\ \ t<2\\\\2t^2-1;\ \ 2\leq t[/tex]

A function is differentiable at a point c, if the derivative of the function in such a point exists. That is, f'(c) exists.

In this case, you need that the function is differentiable for t=2, then, you have:

[tex]f'(t)=a;\ \ \ \ t<2 \\\\f'(t)=4t;\ \ \ 2\leq t[/tex]

If the derivative exists for t=2, it is necessary that the previous derivatives are equal:

[tex]f'(2)=a=4(2)\\\\a=8[/tex]

Furthermore it is necessary that for t=2, both parts of the function are equal:

[tex]8(2)+b=2(2)^2-1\\\\16+b=8-1\\\\b=-8[/tex]

Then, a  = 8, b = -8

Answer:

The  confidence interval is     [tex]0.20644 < p <0.36984[/tex]

Step-by-step explanation:

From the question we are told that

     The  sample is n  = 118

     The  confidence level is  C   =  95 %  

     The  number of people with high blood pressure is  k  =  34

The proportion of those with high blood pressure is evaluated as

          [tex]\r p = \frac{k}{n}[/tex]

substituting values

        [tex]\r p = \frac{34}{118}[/tex]

       [tex]\r p = 0.288136[/tex]

Given that the confidence level is 95%  then the level of significance is evaluated as

       [tex]\alpha = 100 -95[/tex]

      [tex]\alpha = 5[/tex]%

     [tex]\alpha = 0.05[/tex]

Now the critical values of  [tex]\frac{\alpha }{2}[/tex] obtained from the normal distribution table is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

The reason we are obtaining values for  is because  is the area under the normal distribution curve for both the left and right tail where the 95% interval did not cover while   is the area under the normal distribution curve for just one tail and we need the  value for one tail in order to calculate the confidence interval

 Now the margin of error is evaluated as

      [tex]MOE = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1- \r p)}{n} }[/tex]

substituting values

      [tex]MOE = 1.96 * \sqrt{\frac{ 0.288136 (1- 0.288136)}{118} }[/tex]

      [tex]MOE = 0.0817[/tex]

Thus the 95% confidence interval for the true percentage of all adults that have high blood pressure is evaluated as

      [tex]\r p - MOE < p < \r p + MOE[/tex]

substituting values

      [tex]0.288136 - 0.0817 < p <0.288136 + 0.0817[/tex]

     [tex]0.20644 < p <0.36984[/tex]

Answer:

y = -x + 0

Step-by-step explanation:

well the equation of a line is y = mx + b

m = the slope , b = the y-intercept

m = y2 - y1 / x2 - x1

m = -1

and b is the y-intercept of the line.

finally:

y = -1x + 0

She can either have 24 people since there are more slices of pizza there will be extras

Answer:

sin(O) = 2/sqrt(5)   or 2sqrt(1/5)

Step-by-step explanation:

using 1+cot^2(x) = csc^2(x)

we have, taking reciprocal on both sides,

sin(x) = 1/sqrt(1+cot^2(x)

= 1/sqrt(1+(-1/2)^2)

= 1/sqrt(5/4)

= 2/sqrt(5)   or 2sqrt(1/5)

Since angle x is in the second quadrant, sin(x) is positive.

Answer:

x =2

Step-by-step explanation:

3 = 1/2x + 1/2x + 1/2x

Combine like terms

3 = 3/2 x

Multiply each side by 2/3 to isolate x

3 * 2/3 = 2/3 * 3/2 x

2 =x

Answer:

The options that have two angles, which are A and D prove both triangles to be similar.

Step-by-step explanation:

The postulate AA is exactly what it sounds like, and you can find the two angles, which will prove the similarity of two triangles sharing those two angles.

The reason being is if two angles are the same between the two triangles, the third can't be different.

Answer:

The adult ticket costs $18 and the children ticket costs $13.

Step-by-step explanation:

Let the price of the adult ticket be a.

Let the price of the children ticket be c.

Three adults and four children must pay $106. This implies that:

3a + 4c = 106 _______(1)

Two adults and three children must pay $75. This implies that:

2a + 3c = 75 ________(2)

We have two simultaneous equations:

3a + 4c = 106 _____(1)

2a + 3c = 75 ______(2)

Multiply (1) by 2 and (2) by 3 and subtract (1) from (2):

  6a + 9c = 225

- (6a + 8c = 212)

             c = $13

Put this value of c in (2):

2a + 3*13 = 75

2a + 39 = 75

=> 2a = 75 - 39

2a = 36

a = 36/2 = $18

Therefore, the adult ticket costs $18 and the children ticket costs $13.

Answer:

Answer is 24288.

Step-by-step explanation:

Given that there are 18 senior and 22 junior partners.

To find:

Number of ways of selecting at least one junior partner to form a committee of 3 partners.

Solution:

At least junior 1 member means 3 case:

1. Exactly 1 junior member

2. Exactly 2 junior member

3. Exactly 3 junior member

Let us find number of ways for each case and then add them.

Case 1:

Exactly 1 junior member:

Number of ways to select 1 junior member out of 22: 22

Number of ways to select 2 senior members out of 18: 18 [tex]\times[/tex] 17

Total number of ways to select exactly 1 junior member in 3 member committee: 22 [tex]\times[/tex] 18 [tex]\times[/tex] 17 = 6732

Case 2:

Exactly 2 junior member:

Number of ways to select 2 junior members out of 22: 22 [tex]\times[/tex] 21

Number of ways to select 1 senior member out of 18: 18

Total number of ways to select exactly 2 junior members in 3 member committee: 22 [tex]\times[/tex] 21 [tex]\times[/tex] 18 = 8316

Case 3:

Exactly 3 junior member:

Number of ways to select 3 junior members out of 22: 22 [tex]\times[/tex] 21 [tex]\times[/tex] 20 = 9240

So, Total number of ways = 24288

Answer:

Graph A

So it has two distinct real roots.

Graph B

It has one repeated real root

Graph C

So it has two complex roots.

Graph D

One real root and one complex root

Step-by-step explanation:

For graph A

The value of the roots is x= 1 and x= 3

And the minimum value = -3

It's a positive graph

So it has two distinct real roots.

For graph B

The value of the roots is x = 2 and x= 2

That is x= 2 twice

Has a maximum value of 0

It's an inverse graph

It has one repeated real root

For graph C

It's a positive graph but on the negative of x

Has a minimum value of 1

It didn't touch x at y = 0

And it's root will be negative

So it has two complex roots.

For Graph D

Value of the roots is x= 2 and x= -2

It's a positive graph

Minimum value of -4

One real root and one complex root

Answer:

Henry had the best record for the number of shots made

Step-by-step explanation:

From the given information.

Four friends are on a basketball team.

Henry

Allison

Arthur

Trevor

We are being told that Henry made 0.45  of his shots out of all his attempts

Allison made Arthur made of her shots  of his shots.

i,e Arthur did the work for Allison , so out of Arthur's shot , we have to  figured out Allison shots,

Trevor missed 58% of his shots.

i.e Trevor failed 0.58 of his shot, If he failed 0.58 shot

Then the attempts Trevor made is :

= 1 - 0.58

= 0.42

SO , Trevor made 0.42 shots out of all his attempt

N:B We are not given any information about Arthur's shots , so we can't determine Allison shot as well.

Therefore; we will focus on only Henry and Trevor shots

So ;

Henry made 0.45  of his shots

Trevor made 0.42 out of his shots

We can thereby conclude that :

Henry had the best record for the number of shots made

Answer:

8.3

Step-by-step explanation:

Answer:

A. $500.00

Step-by-step explanation:

IRS popularly known as  Internal revenue service charges an IRS fee under the authority of the Federal Law and policy agencies. This implementation of IRS fee is to recuperate the cost of rendering a service to the masses.  

From the given information in the question:

Suppose you invest $15,000 at the age of 35 and agree to start receiving  payments at the age of 45.

At age 41, you decide you want to withdraw $5000  from your account.

Since the investor is still 41 years of age ; IRS will charge 10% of the withdrawal amount.

IRS fee = 10% of $5000

IRS fee = 0.1 × $5000

IRS fee = $500

Answer:

true

Step-by-step explanation:

There is only one distinct triangle possible, with m N= 33º. Therefore, option B is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in ΔMNO, m = 20, n = 14, and m∠M = 51°.

Now, sin51°/20=sinN/14

0.7771/20=sinN/14

0.038855=sinN/14

sinN=14×0.038855

sinN=0.54397

N=33°

Therefore, option B is the correct answer.

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Answer:

A...............................

Answer:

3x + 2y =60

Step-by-step explanation:

x = socks

y = shoes

3x + 2y =60

Answer:

3x + 2y =60

Step-by-step explanation:

Hope this Helps you !

Answer:

The Man needs to run at 9 mph

Step-by-step explanation:

Let M stand for the man's speed in mph.  When the man  

runs toward point A, the relative speed of the train with respect  

to the man is the train's speed plus the man's speed (45 + M).  

When he runs toward point B, the relative speed of the train is the  

train's speed minus the man's speed (45 - M).

When he runs toward the train the distance he covers is 2 units.  

When he runs in the direction of the train the distance he covers  

is 3 units. We can now write that the ratio of the relative speed  

of the train when he is running toward point A to the relative speed  

of the train when he is running toward point B, is equal to the  

inverse ratio of the two distance units or

              (45 + M)          3

              -----------  =      ---

              (45 - M)          2

          90+2 M=135-3 M

⇒5 M = 45

⇒ M = 9 mph

The Man needs to run at 9 mph

Answer: 9 mph

Step-by-step explanation:

Given that a man walking on a railroad bridge is 2/5 of the way along the bridge when he notices a train at a distance approaching at the constant rate of 45 mph .

If the man tend to run in the forward direction, he will cover another 2/5 before the train reaches his initial position. The distance covered by the man will be 2/5 + 2/5 = 4/5

The remaining distance = 1 - 4/5 = 1/5

If the man can run at a constant rate in either direction to get off the bridge just in time before the train hits him, the time it will take the man will be

Speed = distance/time

Time = 1/5d ÷ speed

The time it will take the train to cover the entire distance d will be

Time = d ÷ 45

Equate the two time

1/5d ÷ speed = d ÷ 45

Speed = d/5 × 45/d

Speed = 9 mph

Answer:

Step-by-step explanation:

If [tex]\sum a_n[/tex] is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

[tex]\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho[/tex]

If [tex]\rho[/tex] < 1, the series converges absolutely

If [tex]\rho > 1[/tex], the series diverges

If [tex]\rho = 1[/tex], the test fails.

Given the series [tex]\sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}[/tex]

To test for convergence or divergence using ratio test, we will use the condition above.

[tex]a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}[/tex]

[tex]\frac{a_n_+_1}{a_n} = \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\[/tex]

[tex]\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\[/tex]

aₙ₊₁/aₙ =

[tex]\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\[/tex]

note that any constant dividing infinity is equal to zero

[tex]|\frac{1+2/\infty+1/\infty^2}{5}|\\\\[/tex]

[tex]\frac{1+0+0}{5}\\ = 1/5[/tex]

[tex]\rho = 1/5[/tex]

Since The limit of the sequence given is less than 1, hence the series converges.

Answer:

43 mountain climbers have not climbed either mountain.

Step-by-step explanation:

Total number of mountain climbers, i.e. n(U) = 60

Number of mountain climbers who have climbed Mt. Everest, n(E) = 10

Number of mountain climbers who have climbed Mt. Rainier, n(R) = 15

Number of mountain climbers who have climbed both, n(E [tex]\cap[/tex] R) = 15

Using the formula to find number of climbers who have climbed either of the mountains:

[tex]n(A \cup B) = n(A)+n(B)-n(A\cup B )[/tex]

[tex]\therefore n(E \cup R) = n(E)+n(R)-n(E\cup R )\\\Rightarrow n(E \cup R) = 10+15-8 = 17[/tex]

To find, who have not climbed either mountain:

[tex]n(E\cup B)'=n(U) - n(E\cap B)\\\Rightarrow n(E\cup B)'=60 - 17 = \bold{43}[/tex]

So, the answer is:

43 mountain climbers have not climbed either mountain.