Simplify each expression
{5√2}/{√10-3}

Answer:

r = 14 cm

Step-by-step explanation:

Circumference = 2πr = 88

=> r = 88 / 2 x 22/7

=> r = 88 x 7 / 44

=> r = 2 x 7

=> r = 14 cm

Answer: 4,856

Step-by-step explanation:

YEEE

Answer:

A

Step-by-step explanation:

28 + 8 is 26

Answer:

1) 314.38 m

2) Je ne sais pas.

The quadratic equation that would model this scenario is

[tex]x^{2} = 2x(x-16)[/tex]

Let us take the side of the square = x

Area of the square = x²

Length of the rectangular garden = 2x

Width of the rectangular garden = x-16

So, the area of the new vegetable garden = length*width

Area of the new or rectangular vegetable garden = 2x(x-16)

The polynomial equation whose highest degree is two is called a quadratic equation. The equation is given by [tex]ax^2+bx+c[/tex]coefficient [tex]x^{2}[/tex]non-zero.

Since it is given that

Area of square garden = area of the rectangular garden

[tex]x^{2} = 2x(x-16)[/tex]

Thus, the quadratic equation that would model this scenario is

[tex]x^{2} = 2x(x-16)[/tex]

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Answer:

its a

Step-by-step explanation:

Answer:no the correct answer should be (4,1)

Step-by-step explanation:

I reduced the equations to linear form then I used substitution to find the cordinents.

Answer:

[tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \frac{1}{12}[/tex]

General Formulas and Concepts:
Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                                [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Special Limit Rule [L’Hopital’s Rule]:                                                                       [tex]\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}[/tex]

Differentiation

Derivative Property [Addition/Subtraction]:                                                        [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Derivative Rule [Basic Power Rule]:

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36}[/tex]

Step 2: Find Limit Pt. 1

We see that we get 0 divided by 0, an indeterminate form.

Step 3: Find Limit Pt. 2

Use L'Hopital's Rule.

∴ the limit as x approaches 36 of the given function is equal to one-twelfths.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

We are given with a limit and we need to find it's value , but first recall the identity which is the main key to this question :

Now , consider the limit we have ;

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{\sqrt{x}-6}{x-36}}[/tex]

Let's try direct substitution first ;

[tex]{:\implies \quad \displaystyle \sf \dfrac{\sqrt{36}-6}{36-36}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{6-6}{0}=\dfrac00}[/tex]

Here , we get an indeterminate form , so direct substitution didn't worked. So , consider again :

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{\sqrt{x}-6}{x-36}}[/tex]

Can be further written as ;

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{\sqrt{x}-6}{(\sqrt{x})^{2}-6^{2}}}[/tex]

Using the above identity we have ;

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{(\sqrt{x}-6)}{(\sqrt{x}-6)(\sqrt{x}+6)}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{\cancel{(\sqrt{x}-6)}}{\cancel{(\sqrt{x}-6)}(\sqrt{x}+6)}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{1}{\sqrt{x}+6}}[/tex]

Now , put the limit

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{\sqrt{36}+6}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{6+6}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{12}}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{\displaystyle \bf \lim_{x\to 36}\dfrac{\sqrt{x}-6}{x-36}=\dfrac{1}{12}}}}[/tex]

Answer:

60%

Step-by-step explanation:

10 + 15

25

15/35 = 60%

We need to first find the total number of games so 15 plus 10 gets us 25. Then we take and divide the number of games won by the total number played, getting us 60%.

Have an amazing day!!

PLEASE RATE!!

Answer:

3 ------------- √9

6 ------------- ³√216

7 ------------- ³√343

8 ------------- √64

9 ------------ ³√729

10 ----------- √100

Step-by-step explanation:

Hope this helps .

Answer:

[tex]1. \sqrt{9} =3[/tex]

[tex]2. \sqrt[3]{729}=9[/tex]

[tex]3. \sqrt{100} =10[/tex]

[tex]4. \sqrt[3]{216} =6[/tex]

[tex]5. \sqrt{64} =8[/tex]

[tex]6. \sqrt[3]{343} = 7[/tex]

Step-by-step explanation:

[tex]1. \sqrt{9} =3[/tex]    [tex]3*3=9[/tex]

[tex]2. \sqrt[3]{729}=9[/tex]

[tex]\sqrt[3]{9^3}=9[/tex]

[tex]3. \sqrt{100} =10[/tex]    [tex]10*10=100[/tex]

[tex]4. \sqrt[3]{216} =6[/tex]

[tex]\sqrt[3]{6^3}=6[/tex]

[tex]5. \sqrt{64} =8[/tex]     [tex]8*8=64[/tex]

[tex]6. \sqrt[3]{343} = 7[/tex]

[tex]\sqrt[3]{7^3}=7[/tex]

Hope this helps!

The average distance that he travelled every hour is; 2.4357 miles per hour

He drove 275 miles in 212 hours.

Now, to find the rate of distance per hour;

Distance per hour = 275/212 = 1.2972 miles per hour

He drove 357.5 miles in 314 hours.

Distance per hour = 357.5/314

Distance per hour = 1.1385 miles per hour

Thus, his average distance per hour = 1.2972 + 1.1385 = 2.4357 miles per hour

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Answer:

Train A : 143 tons ; Train B : 18 tons

Step-by-step explanation:

Call train A as A, train B as B

A + B = 161t
A - B = 125t

A = (161+125) : 2 = 143t
B = 143t - 125t = 18t

Answer:

B) y < 3/4x -2

Step-by-step explanation:

First, to eliminate 2 options let's see what sign we should use. The ≤ is a solid line where < is a dotted line. Next, you need to know which way to flip the sign. If it is under the line it is the < symbol.

Answer:

10 x 20

Step-by-step explanation:

it's 10 on the side of the shaded area, and 20 on the opposing side, so in this case, it must be 10 x 20 = 200.

hope it helps

Answer:

Your answer would be B!

Hope this helps.

The graph of the function is defined in the attached file please find it.

[tex]\to \bold{x=4}[/tex]

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2 + 3x

= 5

Have a Nice day

The two events out of the listed events which are independent events are given by: Option A: A and C

For two events A and B, by chain rule, we have:

[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(A|B)[/tex]

Suppose that the sample space is divided in n mutual exclusive and exhaustive events tagged as

[tex]B_i \: ; i \in \{1,2,3.., n\}[/tex]

Then, suppose there is event A in sample space.

Then probability of A's occurrence can be given as

[tex]P(A) = \sum_{i=1}^n P(A \cap B_i)[/tex]

Using the chain rule, we get

[tex]P(A) = \sum_{i=1}^n P(A \cap B_i) = \sum_{i=1}^n P(A)P(B_i|A) = \sum_{i=1}^nP(B_i)P(A|B_i)[/tex]

Suppose two dimensions are there, viz X and Y. Some values of X are there as [tex]X_1, X_2, ... , X_n[/tex] values of Y are there as [tex]Y_1, Y_2, ..., Y_k[/tex]rows and left to the columns. There will be [tex]n \times k[/tex]values will be formed(excluding titles and totals), such that:

Value([tex]i^{th}[/tex] row, [tex]j^{th}[/tex] column) = Frequency for intersection of [tex]X_i[/tex] and [tex]Y_j[/tex]values are going in rows, and Y values are listed in columns).

Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.

For n = 2, and k = 2, the table would look like:

[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]

where S denotes total of totals, also called total frequency.

n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

Suppose that two events are denoted by A and B.

They are said to be independent event if and only if:

[tex]P(A \cap B) = P(A)P(B)[/tex]

The given frequency table is:

[tex]\begin{array}{ccccc} &\text{Public}&\text{Own}&\text{Others}&\text{Total}\\\text{Male}&12&20&4&36\\\text{Female}&8&10&6&24\\\text{Total}&20&30&10&60\end{array}[/tex]

The probability table for the same labels would be:

[tex]\begin{array}{ccccc} &\text{Public}&\text{Own}&\text{Others}&\text{Total}\\\text{Male}&12/60&20/60&4/60&36/60\\\text{Female}&8/60&10/60&6/60&24/60\\\text{Total}&20/60&30/60&10/60&1\end{array}[/tex]

The events A, B,C,D and E are given as:

Checking all the listed options one by one, for them being independent:

P(A) = P(The employee is male. ) = 36/60

P(C) = P(The employee takes public transportation.) = 20/60[tex]P(A \cap C) = 12/60 \\\\ P(A)P(C) = \dfrac{36 \times 20}{60^2} = 12/60[/tex]

[tex]P(A \cap C) = P(A)P(C)[/tex]

Thus, A and C are independent events.

P(A) = P(The employee is male. ) = 36/60

P(D) = P(The employee takes his/her own transportation.) = 30/60

[tex]P(A\cap D) = 20/60\\\\P(A)P(D) = \dfrac{30 \times 36}{60^2} = 12/60 \neq P(A \cap D)[/tex]

Thus, A and D are not independent events.

P(B) = P(The employee is female. ) = 24/60

P(D) = P(The employee takes his/her own transportation.) = 30/60

[tex]P(B \cap D) = 10/60 \neq P(B)P(D)=\dfrac{24 \times 30}{60^2} = 12/60[/tex]

Thus, B and D are not independent events.

P(B) = P(The employee is female. ) = 24/60

P(E) = P(The employee takes some other method of transportation.) = 10/60

[tex]P(B \cap E) = 6/60 \neq P(B)P(E)= \dfrac{24 \times 10}{60^2} = 4/60[/tex]

Thus, B and E are not independent events.

Thus, the two events out of the listed events which are independent events are given by: Option A: A and C

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Answer:

First option!!

"A and C"

Step-by-step explanation:

Edge 2022

Answer:

112

Step-by-step explanation:

There are 400 employees. If 72 of them work part-time, then 72% of 400 = 400*72%. This equals 288. Then you subtract that from 400 because the rest of them should be full-time workers. 400-288=112.

Answer:

112

Step-by-step explanation:

400 x 0.72 = 288, so that's the number of part-time employees.

400 - 288 = 112

(6,5)

If you start at the origin (which is (0,0)) and go 6 right, that's six for x. If you then go 5 up, that means y is 5.

(6,5)

Answer:

(6,5)

Step-by-step explanation:

6 is on the x-axis, and 5 is on the y-axis

Answer:

Angles on a straight line add up to 180 degrees so for the 129 degrees you will take 180 - 129 = 51. In the triangle you will add 51 and 55 = 106 but remember in a triangle all angles should be equal to 180. So 180 - 106 = 74. X=74degrees

Answer:

Thursday

Step-by-step explanation:

Positive sign denotes that it has gained

Account A is having $1,093 after 3 years. and Account B is having $1,120 after 3 years.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

Elisa put $1,000 in each bank.

Account A: gives her at a rate of 3% per annum compounded annually.

Account B: $40 bonus is added to the account each year.

After 3 years, account A will have

[tex]\rm Account \ A = 1000(1.03)^3\\\\Account \ A = 1093[/tex]

Account A is having $1,093 after 3 years.

After 3 years, account B will have

[tex]\rm Account \ B= 1000 + 3(40)\\\\Account \ B= 1,120[/tex]

Account B is having $1,120 after 3 years.

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Answer:

A ; 1092.73

B ; 1120

Step-by-step explanation:

The function to model the path of the fireworks in the new location is -4.9(t - 4)^2 + 50

Given the height reached by the flight expressed as:

h(t) = -4.9(t - 4)^2 + 80

If the barge is relocated 30 meters to the east, the new function will be derived by subtracting 30 from the initial function

New function = -4.9(t - 4)^2 + 80 - 30

New function = -4.9(t - 4)^2 + 50

Hence the function to model the path of the fireworks in the new location is -4.9(t - 4)^2 + 50

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Answer:

40

Step-by-step explanation:

since you can just add 4 to 36 to get 40.

Answer:

40

Step-by-step explanation:

Let n represent the number then...

n-4=36

Add 4 to both sides

n-4+4=36+4

n=40

The number is 40

Answer:

I would say B

Step-by-step explanation:
A. would make no sense and the graph will always have a straight line unless its compairing something and it does not have anything to do with 0 because it shows where it starts

Answer:

The balance when the account went into overdraft was -38.02

Explanation:

Let x be the balance when the account went into overdraftTo get back to a positive balance he deposited money at a steady rate of $20.06 per week. Amount deposited per week = $20.06Amount deposited 8 weeks = Now amount in account after 8 weeks =x+160.48We are given that After 8 weeks, he had $122.46 in the account.So,x+160.48=122.46x=122.46-160.48x=-38.02

Step-by-step explanation:

a²+b²=c²

THIS is the Pythagorean theorem which is:

Hypotenuse² + Base² = perpendicular ²

Thus inputting values:

(√117)² + (6)² = (x)²

117 + 36 = x²

x² = 153

x= √153 (ans)

The sides and angles of a triangle can be determined using trigonometry ratios

The values of x, y and z are [tex]x = 14\sqrt 2[/tex], [tex]y =14[/tex] and [tex]z = 14\sqrt 3[/tex]

The upper triangle is a right triangle with an angle measure of 45 degrees.

So, the value of x is:

[tex]x = 14\sqrt 2[/tex]

Next, we calculate the hypotenuse (h) of the lower triangle using:

[tex]h^2 = (14\sqrt 2)^2 + (14\sqrt 2)^2[/tex]

So, we have:

[tex]h^2 = 784[/tex]

Take the square roots of both sides

[tex]h = 28[/tex]

The value of y is then calculated using the following sine ratio

[tex]\sin(30) = \frac y{28}[/tex]

Make y the subject

[tex]y =28 * \sin(30)[/tex]

Evaluate

[tex]y =14[/tex]

The value of z is then calculated using the following cosine ratio

[tex]\cos(30) = \frac z{28}[/tex]

Make z the subject

[tex]z =28 * \cos(30)[/tex]

Evaluate

[tex]z =28 * \frac{\sqrt 3}{2}[/tex]

[tex]z = 14\sqrt 3[/tex]

Hence, the values of x, y and z are [tex]x = 14\sqrt 2[/tex], [tex]y =14[/tex] and [tex]z = 14\sqrt 3[/tex]

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Answer:

380.16

Step-by-step explanation:

To find the capacity of a tank: multiply the length by the width to get the area. Then multiply the area by height to get volume. Finally, multiply the volume by 7.48 gallons per cubic foot to get capacity.