A fish tank has 45 gallons of water in it. If it is 90% full, what is the full capacity of the fish tank? The fish tank can hold gallons of water when full to capacity.​

Answers

Answer 1
the answer is 50 gallons because 45 gallons is 90% of 50 gallons
Answer 2

Answer:

My answer is 55 or 60  which would be 100%

Step-by-step explanation:


Related Questions

(X+m)(c+n) if m=5 and n=-7

Answers

Answer: -7/5

Step-by-step explanation:

x = - 5cm^2 - 7m^2 + 35/ m (5c - 7), C = (cross out the equal sign) 7/5 and m = (cross out the equal sign) 0 and n = -7/5



Compare [tex]99![/tex] and [tex]50^{99}[/tex].

Hint: Identity [tex](a+b)(a-b)=a^2-b^2[/tex].​

Answers

50^99 is greater than 99!

How to compare the numbers?

The numbers are given as:

99! and 50^99

When the above numbers are estimated using a calculator, we have:

99! = 9.332622e+155

50^99 = 1.577722e+168

Next, we compare the exponents

168 and 155

168 is greater than 155

Hence, 50^99 is greater than 99!

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11 points
please help me

Answers

Answer:

40%

8%

15%

37%

Step-by-step explanation:

The solutions are in the image

Revenue function: r(x) = 60x cost function: c(x) = 12 + 7x profit function: p(x) =

Answers

Profit function : p(x) = 53 x - 12

Cost is the total cost of producing the output.

The cost function consists of two different types of costs:

- Variable costs

- Fixed costs.

Variable costs vary with output (number of units produced). Total variable costs can be

expressed as the product of variable costs per unit and the number of units produced. If there are multiple items

manufactured costs are higher.

Fixed costs usually do not vary with performance.

Revenue is the total payment received from the sale of goods or the provision of a service.

The revenue function R() reflects the revenue from selling “” quantity of output items at price

"p" after item.

() =

Profit functions

The profit function P() is the difference between the revenue function R(x) and the total cost function C()

So P() = R() – C()

=−

Now, Profit = Revenue - Cost

= 60 x - ( 12 + 7 x)

= 60 x -12 -7 x

Profit = 53 x - 12

Hence, Profit function : p(x) = 53 x - 12

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What are the possible lengths of the third hallway? between 30 yards and 60 yards between 30 yards and 90 yards between 30 yards and 120 yards between 30 yards and 150 yards

Answers

The possible length of the third hallway is between 30 yards and 150 yards.

How to find the third length of a triangle?

The hallway forms a triangle .

Therefore,  using triangle inequality theorem, It states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

Hence,

90 + 60 > x

Where

x is the third side

x + 60 > 90

x + 90 > 60

Therefore, the possible length of the third hallway is between 30 yards and 150 yards.

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Answer:

D: between 30 yards and 150 yards

Ben has typed 180 and can type 30 words per minute. millie has typed 60 and can type 50 words per minute. how many minutes will it take for millie to catch up with ben.

Answers

The time taken by Millie to catch up with Ben is 6 minutes, solved using the linear equation in one variable and the unit rates provided.

We assume the minutes taken by Millie to catch up with Ben to be x minutes.

The number of words Ben has already typed = 180.

The unit rate for Ben for the typing of words = 30 per minute.

Therefore, words typed by Ben in x minutes = 30x words.

Therefore, the total number of words typed by Ben = 180 + 30x words.

The number of words Millie has already typed = 60.

The unit rate for Millie for the typing of words = 50 per minute.

Therefore, words typed by Millie in x minutes = 50x words.

Therefore, the total number of words typed by Millie = 60 + 50x words.

As Millie needs to catch up with Ben after x minutes, the total number of words typed by them needs to be equal, that is, 60 + 50x = 180 + 30x, which is the required linear equation in one variable.

To find the minutes taken by Millie to catch up with Ben, we solve this linear equation in one variable as follows:

60 + 50x = 180 + 30x,

or, 60 + 50x - 30x = 180 + 30x - 30x {Subtracting 30x from both sides},

or, 60 + 20x = 180 {Simplifying},

or, 60 + 20x - 60 = 180 - 60 {Subtracting 60 from both sides},

or, 20x = 120 {Simplifying},

or, 20x/20 = 120/20 {Dividing both sides by 20},

or, x = 6 {Simplifying}.

Thus, the time taken by Millie to catch up with Ben is 6 minutes, solved using the linear equation in one variable and the unit rates provided.

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Rewrite each equation in factored form and solve using zero product property. Find the solutions of each equation. Use the notes about r * k = c and r + k = b. In the first problem c is 6 and b is -7. So you need the same r and k that multiply to be 6 but also add to be -7. The numbers you find will be the solutions

Answers

The factored form of the equation are as follows;

(d - 6)(d - 1) = 0(x + 9)(x + 9) = 0(u + 12)(u - 5) = 0

How to write equation in factored form?

Converting a quadratic function to factored form is called factoring.

Therefore,

let's factor the equation,

a.

d² - 7d + 6 = 0

d² - d - 6d + 6 = 0

d(d - 1) - 6(d - 1) = 0

(d - 6)(d - 1) = 0

b.

x² + 18x + 81 = 0

x² + 9x + 9x + 81 = 0

x(x + 9) + 9(x + 9) = 0

(x + 9)(x + 9) = 0

c.

u² + 7u - 60 = 0

u² - 5u + 12u - 60 = 0

u(u - 5) 12(u - 5) = 0

(u + 12)(u - 5) = 0

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20pts and brainliest !! please help quick

Answers

Need a little more information

Answer:

y = -1.3x + 10

Step-by-step explanation:

x_avg = (-2 + -1 + 1 + 2 + 3 + 4)/6 = 1.166666...

y-avg = (21 + 8.6 + 1 + 1 + 5 + 14.3) = 8.48333...

x      y       x-x_avg       y-y_avg          (x-x+avg)²           (x-x_avg)(y-y_avg)

-2    21     -3.1666        12.51666       10.02777                    -39.63611

-1    8.6     -2.1666        0.11666        4.69444                     -0.252777

1      1        -0.1666       -7.48333        0.02777                     1.247222

2      1       0.83333     -7.48333         0.69444                    -6.236111

3      5       1.8333        -3.48333        3.3611111                     -6.386111

4     14.3    2.8333        5.81666         8.02777                     16.480555

sum of (x-x_avg)(y-y_avg) = -34.858

sum of (x+x_avg)² = 26.8333

slope = [(x-x_avg)(y-y_avg)/[(x+x_avg)²]

slope = -34.858/26.8333

slope = -1.29907

y = mx + b

y_avg = m(x_avg) + b

8.48333 = -1.3(1.1666) + b

b = 9.9989

y = -1.3x + 10

The angle measurements in the diagram are represented by the following expressions.

Answers

The angle measurements of angle B as represented in the diagram shown is 150°

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

From the diagram:

∠A = ∠B (alternate interior angles)

Hence:

8x - 10 = 3x + 90

x = 20

∠B = 3(20) + 90 = 150°

The angle measurements of angle B as represented in the diagram shown is 150°

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Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout ($)
1 2 5 8 10
Probability 0.35 0.2 0.1 0.2 0.15
Expected Value = [? ]
Round to the nearest hundredth.
Enter

Answers

Answer:

4.35

Step-by-step explanation:

The expected value can be defined as: [tex]\sum{x_i*p_i}[/tex] where x_i = the payout, and p_i = the probability of it occurring.

This gives us the expression: [tex](1 * 0.35) + (2 * 0.2) + (5 * 0.1) + (8 * 0.2) + (10 * 0.15) = 0.35 + 0.4 + 0.5 + 1.6 + 1.5 = 4.35[/tex]

So the expected payout is 4.35

Cost of 4 tables and 3 chairs is $225 and 3 tables and 4
chairs cost $195. Find the cost of 2 chairs and 1 table.

Answers

The cost of 2 chairs is = $30

The cost of 1 table = $60

Step-by-step explanation:

Let a table represent x

A chair represents y

4x + 3y = 225.......eq 1

3x + 4y = 195........eq 2

Use elimination method

x - y = 30

x= 30 + y...... Eq 3

Substitute the value of x into equation 1

4(30+ y) + 3y= 225

120 + 4y + 3y= 225

7y + 120= 225

7y= 225-120

7y= 105

y= 15

Substitute the value of y in eq 2

3x + 15 = 195

3x= 195-15

3x= 180

x= 60

Therefore, the cost of 2 chairs is 15 * 2= $30

The cost of 1 table = $60

Answer:

65

Step-by-step explanation:

0.00000007 as a fraction

Answers

Answer:

7/100000000

Step-by-step explanation:

to find this out we can start by saying that 0.7 is 7/10

every 0 in front of 7 after that is adding another 0 to 10

so

0.07 is 7/100

0.00000007 is 7/100000000

Select the correct answer from each drop-down menu. a comic-strip writer churns out different numbers of comic strips each day. the writer logged the number of comic strips he wrote each day for 16 days and sorted the data in ascending order to create this data set. 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8 the data in the distribution is . if the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference of the mean and the median for the new data set is .

Answers

Mean = 3.5

Median = 3

Distribution is negatively skewed.

What is skew in the distribution?

The distribution has no skewness if the mean and median are equal.

The median exceeds the mean in a favorably skewed distribution.

The distribution is also negatively skewed if the median is lower than the mean.

Given,

Data set : 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8

Mean = [tex]\frac{1+1+2+2+2+3+3+3+3+4+4+4+5+5+6+8}{16}[/tex]

Mean = [tex]\frac{56}{16}[/tex]

Mean = [tex]3.5[/tex]

Median = mid value of the data set when the values are arranged in   ascending order

Here,

the two mid values = [tex]3, 3[/tex]

Median = [tex]\frac{3+3}{2}[/tex]

Median = [tex]\frac{6}{2}[/tex]

Median = [tex]3[/tex]

Now, as the mean is larger than the median therefore the distribution will be skewed negatively.

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The data in the distribution is positively skewed (skewed to the right). If the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference between the mean and the median for the new data set is 0.28.

ヾ(•ω•`)o

iteration-Find the first 3 iterates of the function look at pic pls help!!!!!

Answers

The first 3 iterates of the function are D. 3, -3, 9.

How to calculate the value?

The function given is:

f(x) = -2x + 3

= -2(0) + 3

= 3

When x = 3

f(x) = -2x + 3

= -2(3) + 3

= -6 + 3

= -3

When x = -3

f(x) = -2x + 3

= -2(-3) + 3

= 9

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Solve the simultaneous equations x - 5y = 0 and 15x + 10y = 17

Answers

x - 5y = 0 (1)
15x + 10y = 17 (2)

From (1),
2x - 10y = 0 (3)

(2) + (3),
17x = 17
x= 1

Sub x=1 into (1)
x - 5y = 0
- 5y = -1
y = 1/5

Therefore x = 1, y = 1/5.

Hope it helps : )

The solutions of the equations x - 5y = 0 and 15x + 10y = 17 at x and y is 1 and 1/5 respectively.

Two algebraic expressions separated by an equal symbol in between them and with the same value of the expression are called equations.

Given that:

The linear equations are:

x - 5y = 0

15x + 10y = 17

Solve the equations using elimination method:

Multiply equation 1 by 2

2(x - 5y) = 0

15x + 10y = 17

This can be solved as:

2x-10y = 0.....(1)

15x + 10y = 17....(2)

On subtracting equation 1 from 2

17x = 17

x = 1

The value of x is 1.

Substitute the value of x in equation (1)

2(1)-10y = 0

2=10y

y = 1/5

Thus, the value of x and y is 1 and 1/5 respectively.

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Gerri purchases a coupon book with discounts for her favorite coffee shop. every coupon for the coffee shop offers the same discount. the table shows her total savings, y, based on the number of coupons, x, used from the book. a table showing coffee shop coupon savings with 2 columns and 6 rows. the first column, x, has the entries, 0, 5, 10, 15, 20. the second column, y, has the entries. negative 20, negative 10, 0, 10, 20.

Answers

Slope 2 and y intercept is 10

The question seems to be incomplete and complete and the complete question is shown in the image

The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases.

When x = 0, the corresponding y-value is the y-intercept. In the particular context of word problems, the y-intercept (that is, the point when x = 0) also refers to the starting value.

Y-intercept is the point  at which the line intersects the y axis- meaning x = 0

From the table y = -20 when x= 0

y-intercept: -20

To find the slope

m = ΔY/ΔX

m = -20+10/0-5 = 2

Hence the slope is 2 and y intercept is 10

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Compared to the graph of f(x) = x², the graph of g(x) = (x − 2)² +3
is the result of translating f(x)

Answers

Answer:

Vertical shift up 3

Horizontal shift to the right 2

Brainliest, please :)

Answer:

Step-by-step explanation:

f(x) is moved 2 units to the right followed by 3 units up,

Which expression can be used to find the volume of the sphere?

A sphere with diameter 10 inches.
V = four-thirds pi r squared = Four-thirds (3.14) (5) squared
V = four-thirds pi r cubed = Four-thirds (3.14) (5) cubed
V = four-thirds pi r cubed = Four-thirds (3.14) (10) cubed
V = four-thirds pi r squared = Four-thirds (3.14) (10) squared

Answers

I think its (B)

V = four-thirds pi r cubed = Four-thirds (3.14) (5) cubed

Clark works for Acme Bank and asks for your assistance. He wants you to look at a property that's about to go into foreclosure and provide him with a report on its current marketability and an approximate market value. What's Clark most likely asking you to provide

Answers

The information that Clark is asking me to provide for him regarding the property is called  Brokers Price Opinion (BPO).

What is BPO?

The term BPO refers to Brokers Price Opinion. It is the opinion of a genuine real estate professional regarding the accurate pricing of a property.

The information that Clark is asking me to provide for him regarding the property is called  Brokers Price Opinion (BPO).

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3. A gardener uses 2 packages of lettuce seeds for 3 garden rows, each 5 feet long. How many packages of seeds does the gardener need to plant 45 feet of lettuce rows? Use the table to help.
Seeds (pkg) 2,4
Lettuce (rows) 3, 6



A 27
B 16
C 6
D 80


I need this with explanation please:(​

Answers

Answer:

C) 6

Step-by-step explanation:

3 garden rows = 3*5 = 15 feet

we know we need 2 packages per each 15 feet

45/15=3 so 3 15 in 45, we just multiply 3 and 2 to get 6 packages

Find the value of X. Round to the nearest tenth HELP ASAP!!!!

Answers

Answer: 22.5

Step-by-step explanation:

[tex]\sin 64^{\circ}=\frac{x}{25}\\\\x=25 \sin 64^{\circ}\\\\x \approx 22.5[/tex]

pls help :,)

What is the area of this triangle?

units²

Answers

Answer:

6 [tex]units^{2}[/tex]

Step-by-step explanation:

The formula for the area of a triangle is A = [tex]\frac{1}{2} bh[/tex]. The base in this case is the length of DE, 4 - 1 = 3 units. The height of this triangle is 1 + 3 = 4 units.

A = [tex]\frac{1}{2} bh[/tex] = [tex]\frac{1}{2} *3*4[/tex] = 6

A badminton net is tethered to the ground with a strand of rope that forms a 50 angle with the ground. What is the length of the rope, x? Write an equation and show work below. Round to the nearest tenth.

Answers

Answer:

5.4 ft to nearest tenth.

Step-by-step explanation:

We know the adjacent side  of the right triangle  and we need the hypotenuse so we use the cosine:

cos 50 = 3.5/x

x = 3.5 / cos 50

  = 5.445 ft.

can someone help me i know nothing about graphs

Answers

with the +4 it means that the graph will move 4 units up

Answer:

The answer is B.

Step-by-step explanation:

The function F(x) = x would be the “parent function”. Meaning the +4 we see in G(x) would be a translation, because the function is not multiplied.


if you have ever seen the formula y = mx + b then you should be able to see that +4 would be referencing b in the linear equation, and because m is the same in both lines, we can say that the two functions only change is b, because b represents the y-intercept, if b was 0 in f(x)=x and was 4 in g(x)=x+4, the graph would be shifted 4 units up.


if you want to learn how to understand functions and linear equations, I recommend using khan academy. It is really helpfull in explaining topics of math.

Find the area of each figure as described or shown. Write final answer on blank provided. Show work. Include units as part of your answer. If needed, round answer to 2 decimal places.

Answers

Answer:

482.84u², 42.5cm², 51.5ft²

Step-by-step explanation:

1) A = 2(1 + √2)a²

A = 2(1 + √2)(80 / 8)²

A = 482.84units²

2) Square = 5²

Square = 25

T1 = 3 x 5 / 2

T1 = 7.5

T2 = 4 x 5 / 2

T2 = 10

Total = 10 + 7.5 + 25

Total = 42.5cm²

3) Rect = 4(8 + 3)

Rect = 44

T1 = 2 x 3 / 2

T1 = 3

T2 = 3 x 3 / 2

T2 = 4.5

Total = 3 + 4.5 + 44

Total = 51.5ft²

A 2-column table with 7 rows. The first column is labeled x with entries negative 6, negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries 8, 2, 0, negative 2, negative 1, 0, 4.

Which is a possible turning point for the continuous function f(x)?


(–2, 0)

(0, –2)

(2, –1)

(4, 0)



On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 2, 2), (0, 1), (1, 3), (2, negative 4), (4, negative 1).


On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 2, 1), (negative 2, negative 1), (0, negative 2), (0, negative 4), (2, negative 5).

Answers

A possible critical point of the function f(x) is given by: (0,-2)

What are the critical points of a function?

The critical points of a function are the values of x for which:

[tex]f^{\prime}(x) = 0[/tex]

At these points, the function can change from decreasing to increasing, or vice-versa.

For the table described, we have that the function is decreasing until (0,-2), then it starts to increase, hence there can be a critical point at (0,-2).

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Help me with alg 2 please!

Answers

The probability that 5 boys would be selected would be 5/6720

How to determine the probability

From the information given, the probability can be calculated using permutation

The formula for permutation is given as;

Permutation = [tex]\frac{n!}{n - r!}[/tex]

Where;

n is number of sets = 8r is the number of objects selected = 5

Substitute the values into the formula

Permutation = [tex]\frac{8!}{8 - 5!}[/tex] = [tex]\frac{8!}{3!}[/tex] = [tex]\frac{40, 320}{6}[/tex] = 6720

The probability that 5 boys would be selected is 5/6720

Thus, the probability that 5 boys would be selected would be 5/6720

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If f(x) = x-2, what is f¹(x)?
f¹(x) = 9x + 18
ƒ²¹(x) = x + 2
f¹(x) = 9x+2
ƒ¹ (x) = -2x +

Answers

y=1/9x-2

Interchange x and y

[tex]\\ \tt\leadsto x=\dfrac{1}{9}y-2[/tex]

Solve for y

[tex]\\ \tt\leadsto \dfrac{1}{9}y=x+2[/tex]

[tex]\\ \tt\leadsto y=9(x+2)[/tex]

[tex]\\ \tt\leadsto y=9x+18[/tex]

That's the inverse

[tex]\\ \tt\leadsto f^{-1}(x)=9x+18[/tex]

Answer:

[tex]f^{-1}(x)=9x+18[/tex]

Step-by-step explanation:

[tex]f^{-1}(x)[/tex] is the notation for the inverse of a function.  

The inverse of a function is its reflection in the line y = x.

Given function:

[tex]f(x)=\dfrac{1}{9}x-2[/tex]

To find the inverse of the given function:

Replace f(x) with y to get an equation for y in terms of x:

[tex]\implies y=\dfrac{1}{9}x-2[/tex]

Rearrange the equation to make x the subject:

[tex]\implies y+2=\dfrac{1}{9}x[/tex]

[tex]\implies 9(y+2)=x[/tex]

[tex]\implies x=9y+18[/tex]

Replace x with [tex]f^{-1}(x)[/tex] and y with x:

[tex]\implies f^{-1}(x)=9x+18[/tex]

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Call line that passes through the point x, y with a y intercept of b and a slope of m can be represented by the equation y=mx + b. a line is drawn on the coordinate plane that passes through the .3, -6 and has a slope of four the y-intercept of the line is

Answers

Answer: (0, -7.2)

Step-by-step explanation:

Substituting into point-slope form, the equation is

[tex]y+6=4(x-0.3)[/tex]

The y-intercept is when x=0, so substituting in x=0,

[tex]y+6=4(-0.3)\\\\y+6=-1.2\\\\y=-7.2[/tex]

So, the y-intercept is (0, -7.2).

ASAP PLEASE I NEED YouR HELP

Subtract − 4 b 2 + 4 b − 4 from 3 b 2 + 2 b − 5 .

Answers

Step-by-step explanation:

I assume the question really looks like

-4b² + 4b - 4 is to be subtracted from 3b² + 2b - 5.

so,

3b² + 2b - 5 - (-4b² + 4b - 4) =

= 3b² + 2b - 5 + 4b² - 4b + 4 =

= 7b² - 2b - 1

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Please i need help urgently pls 13. Consider a man-in-the-middle attack on an SSL session between Alice and Bob.a. At what point should this attack fail?b. What mistake might Alice reasonably make that would allow this attack to succeed? Adders Chapter 4 ManoGiven:Find c1,,c4 and S0,,S3 if C0 = 0 andA = (A0,,A3) =(1001) AND B =(1101)Whis is the answer if c0 =1Modify the diagram to subtract B-A and c0Modify the diagram, B, and c0 to find A Using the original A and B, how can this diagram be used to findA +B then B-A? suppose that a consumer is faced with the utility function u(x, y) = x 4 xy. calculate the marginal rate of substitution (mrs) for this consumer. ______ is an attempt to forbid sacred or historical imagery by destroying and defacing it (often due to the belief in its error, misuse, or superstition). an exchange rate that is used to take care of business in the future is called a_____ exchange rate. Fatoumata has a bag that contains orange chews, apple chews, and watermelon chews. She performs an experiment. Fatoumata randomly removes a chew from the bag, records the result, and returns the chew to the bag. Fatoumata performs the experiment 29 times. The results are shown below: A orange chew was selected 6 times. A apple chew was selected 10 times. A watermelon chew was selected 13 times. Based on these results, express the probability that the next chew Fatoumata removes from the bag will be orange or apple as a percent to the nearest whole number step 6: only an aldehyde and a ketone remain. the two carbonyl groups have similar carbonyl absorbance, but you can differentiate the two by looking for an additional ch stretch of the aldehyde. 2. if a cylinder has a volume of 2908.33 in^3 and a radius of 11.5 in. what is the height of the cylinder Select the characteristics of complex media used in microbial culturing. (Check all that apply.)Check All That ApplyThe chemical composition is precisely known.The chemical composition is precisely known.They provide a rich mixture of nutrients for microbial growth.They provide a rich mixture of nutrients for microbial growth.They may contain blood, serum, or meat extracts.They may contain blood, serum, or meat extracts.They are also referred to as synthetic media.They are also referred to as synthetic media.Examples include chocolate agar and MacConkey agar. 8. 160 people attended a carnival where five persons sat on each table. Each tablewas served kg of chocolate cake. How many kilograms of cake was served?What was the quantity of cake meant for each person? The vapor pressure of ethanol, ch3ch2oh , at 40.0 c is 17.88 kpa . if 2.28 g of ethanol is enclosed in a 3.00 l container, how much liquid will be present? Which of the following is incorrect?a) The level of significance is the probability of making a Type I error.b) Lowering both and at once will require a higher sample size.c) The probability of rejecting a true null hypothesis increases as n increases.d) When Type I error increases, Type II error must decrease, ceteris paribus. TRUE OR FALSE polyamory refers to extramarital relationships that involve emotional commitment. People in your neighborhood pay annual dues to a neighborhood association. This association refunds neighborhood dues to selected homeowners who do a particularly nice job of beautifying their yards.a. Why might the neighborhood association provide this refund?b. At the most recent homeowners' association meeting, homeowners voted to end this practice because they felt that it was unfair that some people would not have to pay their share of the costs of maintaining the neighborhood. What is likely to happen to the overall level of neighborhood beautification? Explain. what techniques can the sonographer utilize to demonstrate acoustic shadowing with small gallstones Which of the following is not a common security feature used by database management systems? a. backward recovery b. authentication c. encryption d. authorization . . 1. Imagine youve decided to invest in a mutual fund. Pick one of the three starting amounts and one of the three ratesof annual return (choose any pair they dont have to be vertical to each other). Circle your choices. (3 points each)Starting amount $400 $600 $900Rate of annual return 5% 7% 9%1 b) If you dont make any other deposits or withdrawals, how much money will be in your account in 30 years? (Youmay use a calculator, but you should still show your steps. Round correctly to the nearest cent. )2. Harper and Khalid start new food truck businesses in the same week. The graph shows the function (), which givesHarpers weekly profits for the first eight weeks. The table shows Khalids weekly profits for the first eight weeks. 2 a) Write the function that can be used to calculate Khalids weekly profits, (), based on the number of weeks. (4 points. Show your work. )2 b) Graph the curve () that represents Khalids profits on the same graph as () above. (3 points)2 c) What is the solution to this system of equations? (What is the solution to the equation () = ()?) What doesthat solution represent about this real-world situation? (3 points)2 d) What is the average rate of change of () from week 3 to week 6? What does the average rate of changerepresent about this real-world situation? (4 points)Weeks, Khalids profit, ()0 $2001 $2602 $3383 $439. 404 $571. 225 $742. 596 $965. 367 $1254. 978 $1631. 4 A 5kg block is resting on a surface for which the coefficient of friction between the surface and the block is 0.25. The 5kg block is attached to a massless string that passes over a pulley, causing it to turn without slipping, andis attached to a hanging 3kg block. The pulley is a uniform disk of radius 6cm and mass Tkg 9. The linear acceleration of the blocks is a. 2.02 m/s2, b. 1.44 m/s. (C)2.23 m/s2. d. 2.35 m/s2 e. None of these answers is correct. x p(x) 2 0.84 3.28 51.2 13 1638.4 ? 6553.6 What is x such that p(x) = 6553.6?