20% of 400 is what number

Answer:

113 hours is the right answer

Answer:

1 7/8

Step-by-step explanation:

Have a blessed day

Answer: The top three finishers can be arranged in 15 x 14 x 13 ways, since there are 15 choices for the first place, 14 choices for the second place (since one person has already been selected for first place), and 13 choices for the third place (since two people have already been selected for first and second place).

So the answer is:

15 x 14 x 13 = 2730

Therefore, the top three finishers can be arranged in 2730 different ways. Answer: 2730.

Step-by-step explanation:

Answer:

\(2730\)

Step-by-step explanation:

We can solve this problem without using any complex formulas, though there is a formula for solving such problems

Out of the 15 participants, only one participant can be in first place but this can be any one of the participants

So choice for first place = 15 participants

Once a participant has won in the first place, there are 14 remaining participants who can come second place

For third place there are only 13 participants who can make it

The total number of ways in which top three participants can be arranged is

15 x 14 x 13 = 2730 ways

The formula is

\(P(n, r ) = \dfrac{n!}{(n-r)!}\)

where n is the population to be considered; here n = 15

r = number of items to be considered ; here r = 3

\(P(n, r)\) sometimes written as \(_nP_r\) represents the number of subsets  r that can be taken from a larger set  n when the order of the subset matters.

using the formula we get

\(P(n, r ) = \dfrac{15!}{(15-3)!} = \dfrac{15!}{12!} = 15 \times \ 14 \times 13 = 2730\)

To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.

The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.

Therefore, the fraction of pocket money left can be written as 17/35.

According to the equation the given all necessary math work are:

\(A: (x -f)^2 +(y -g)^2 = h^2\)

B:  domain: [-5, 11]; range: [-9, 7]

C:  yes, inside

The hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides if a triangle has a straight angle (90 degrees), accοrding tο the Pythagοras theοrem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypοtenuse BC are all used in this equatiοn. The lοngest side οf a right-angled triangle is its hypοtenuse, it shοuld be emphasized.

Part A:

Use οf the Pythagοrean theοrem gets yοu tο the equatiοn fοr a circle in essentially οne step:

sum οf squares οf sides = square οf hypοtenuse

\((x -f)^2 +(y -g)^2 = h^2\) . . . . . . circle cantered οn (f, g) with radius h

Part B:

The circle will be defined fοr values οf x in the dοmain f ± h, and fοr values οf y in the range g ± h.

dοmain: 3 ± 8 = [-5, 11]

range: -1 ±8 = [-9, 7]

Part C:

The distance frοm pοint (10, -4) tο (f, g) is ...

\(h^2 = (10 -3)^2 +(-4 -(-1))^2\)

\(h^2 = 7^2 +(-3)^2 = 49 +9 = 58\)

h = √58 < 8 . . . . the distance tο the pοint is less than h=8.

The pοint is inside the circle.

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The value of \(log_35 \times log_{25}9\) is 1.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

\(log_35 \times log_{25}9\)

\(log_ab = \frac{logb}{loga}\)

So,

= log 5 / log 3 x log 9 / log 25

= log 5 / log 3 x log 3² / log 5²

\(logm^n = n~logm\)

So,

= log 5 / log 3 x log 3² / log 5²

= (log 5 / log 3) x (2 log 3 / 2 log 5)

= (log 5 / log 3) x (log 3 / log 5)

= 1

Thus,

1 is the value.

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The Correl function is the easiest way to for calculating correlation between two variables.

What is correlation ?

correlation can be defined as the measure of relation between two variables.

In case you want to measure of degree the power of a dating between two variables, you can accomplish that through using a complicated or on line calculator. you could additionally placed your mathematical abilities to apply and calculate it through hand. while calculating a correlation coefficient via hand.

To find correlation using data points are as follows  :

Determine your data sets.

Calculate the standardized value for your x variables.

Calculate the standardized value for your y variables.

Multiply and find the sum.

Divide the sum and determine the correlation coefficient.

Hence, The Correl function is the easiest way to for calculating correlation between two variables.

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Answer:

hope this helps you

option B

Step-by-step explanation:

ecf-zutd-cpt.

The probability that the dice faces add up to either 4 or 6 is 0.222.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Here, After two six sided dice are rolled,

Total outcomes = 36

Probability of getting sum 4 = 3/36     {(1, 3), (2, 2), (3, 1)}

Probability of getting sum 6 = 5/36

Total Probability of getting sum either 4 or 6 = 3/ 36 + 5/36

                                                                          = 8/36

                                                                          = 2/9

                                                                          = 0.222

Thus, the probability that the dice faces add up to either 4 or 6 is 0.222.

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Answer: 8,982,596 cm

Step-by-step explanation:

Rectangular Prism Volume = Height * Length * Width/base

238 cm * 113 cm * 334 cm = 8,982,596 cm

Answer:

P [ β / Def]  = 0,6521     or      65,21 %

Step-by-step explanation:

Tree diagram:

0,20 (α)       Defective  0,02

0,50 (β)       defective   0,06

0,30 (γ)       defective    0,04

According to Baye´s Theorem

P [ A/B]  = P[A] * P [ B/A] / P[B]

if we call

β = A   and  Defective = B       then  P[β] = P[A]  and P[Defective] = P[B]

we get :

P [ β / Def]  = P[β] * P [ def./β] / P[def]

Then

P[β] = 0,5

P[def/β] = 0,06

P [Defective] = 0,02* 0,2 + 0,06*0,5 + 0,04*0,3

P [Defective] = 0,004 + 0,03 + 0,012

P [Defective] = 0,046

P [ β / Def]  = 0,5 * 0,06 / 0,046

P [ β / Def]  = 0,6521     or      65,21 %

Answer:

1625

Step-by-step explanation:

multiply 6.5x250 since each cm is 250 and you have 6.5 cm

ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

y - 1 = (1/2)x - 2

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

y = (1/2)x - 1/2

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

y = (1/2)x - 1/2

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

The value of the integral  \(\int _1^3\:\:4e^{x+5}\:dx\)  is  \(4e^6(e^2-1)\) by using properties of integrals.

To evaluate the integral \(\int _1^3\:\:4e^{x+5}\:dx\) we can use the property of definite integrals that allows us to factor out constants and add the exponents of the same base.

This property states:

\(\int\limits^a_b {cf(x)} \, dx =c\int\limits^a_bf(x)dx\)

where c is a constant.

Applying this property to our integral, we get:

\(\int _1^3\:\:4e^{x+5}\:dx\) \(=4\int _1^3\:\:e^{x+5}\:dx\)

\(=4e^5\int _1^3\:\:e^{x}\:dx\)

From given we have \(\int\limits^3_1{e^x} \, dx =e^3-e\)

So, \(\int _1^3\:\:4e^{x+5}\:dx=4e^5(e^3-e)\)

\(=4e^5.e^3-4e.e^5\)

\(=4e^8-4e^6\)

\(=4e^6(e^2-1)\)

Hence, the value of the integral \(\int _1^3\:\:4e^{x+5}\:dx\) is \(4e^6(e^2-1)\).

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Complete question:

Given that\(\int\limits^3_1{e^x} \, dx =e^3-e\)use this result to evaluate \(\int _1^3\:\:4e^{x+5}\:dx\)

Answer:

\(\huge\boxed{\sf x = 5}\)

Step-by-step explanation:

g(x) = -3x + 8

Given that, g(x) = -7

-7 = -3x + 8

Subtract 8 to both sides

-7 - 8 = -3x

-15 = -3x

Divide -3 to both sides

5 = x

OR

x = 5

\(\rule[225]{225}{2}\)

Answer:

\(\frac{3375}{512}\) or ≈6.59

Step-by-step explanation:

We can first begin by simplifying each of the numbers with exponents. Recall that in a fraction exponent, the numerator is the power, while the denominator is the root.

Take \(25\frac{3}{2}\) for example. The '2' in the fraction means we must take the square of 25. √25 = 5.

The '3' in the fraction means we take the power, which means we must cube '5'.

5³ = 125. Therefore, \(25\frac{3}{2}\)  = 125. Use this process for the other numbers:

\(25^{\frac{3}{2} } = 125\\243^{\frac{3}{5} } = 27\\16^{\frac{5}{4} } = 32\\ 8^{\frac{4}{3} } = 16\)

The new fraction would look like:

\(\frac{125 * 27}{32 * 16}\)

Which simplifies to:

\(\frac{3375}{512}\) or ≈6.59

Answer:

Step-by-step explanation:

(25) raise to 3/2 = (5^2) raise to 3/2 and 2 gets cancelled when the bracket is opened which leaves 5^3.

(243) raise to 3/5 = (3^5) raise to 3/5 and 5 gets cancelled when the brackets are opened which leaves 3^3.

(16) raise to 5/4 = (2^4) raise to 5/4 and 4 gets cancelled when the bracket is opened which leaves 2^5.

(8) raise to 4/3 = (2^3) raise to 4/3 and 3 gets cancelled when the brackets are opened which leaves 2^4.

5^3 * 3^3 divided by 2^5 * 2^4

= (5 x 3)^ 3 / 2^5+4                   [∵a^m x b^m = (ab)^m] & [a^m x a^n = a^m+n]

15^3 / 2^9

This when simplified gives 6.591.

So,  15^3 / 2^9 is approximately equal to 6.59

PLS MARK IT AS BRAINLIEST

The velocity required to escape the gravitational attraction of Mars is approximately 5.03 km/s.

The velocity required to escape the gravitational attraction of Mars is given by the formula:

\(v = sqrt(2GM/r)\)

where v is the velocity required, G is the gravitational constant, M is the mass of Mars, and r is the distance from the center of Mars to the spacecraft (which is equal to the radius of Mars plus the altitude of the orbit).

The mass of Mars is approximately 6.39 x 10^23 kg, and the radius of Mars is approximately 3,389.5 km. Therefore, the distance from the center of Mars to the spacecraft is:

r = 3,389.5 km + 384 km = 3,773.5 km

Substituting these values into the formula for velocity, we get:

\(v = sqrt(2 x 6.6743 x 10^-11 m^3 kg^-1 s^-2 x 6.39 x 10^23 kg / 3,773.5 km x 1000 m/km)\)

Simplifying, we get:

v ≈ 5.03 km/s

Therefore, the velocity required to escape the gravitational attraction of Mars is approximately 5.03 km/s.

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Answer:

No

Step-by-step explanation:

Using the given lengths if we say this is a right triangle then 8 would be length of hypotenuse

From the Pythagorean theorem 

8^2 = 5^2 + 7^2

64 = 25 + 49

64 = 74 is not a correct equation so the triangle is not a right triangle for the given lengths

Answer:

1/2

Step-by-step explanation:

9/10 - 4/10 =  (9-4) / 10 = 5/10 = 1/2

Answer:

9/10 - 4/10 = 5/10 (0.5) zero and a half.

Step-by-step explanation:

The denominators are the same so you only need to subract 4 from nine, you could even simplify it after by dividing the top of the fraction and the bottom by the same number. goodluck btw

Answer:

I dont know

Step-by-step explanation:

Answer:

Maybe. But look at me, I have two F's and all D's in the last quarter when I had A's a B's and one C for the 1st, 2nd, and 3rd quarter. I am going to get kicked out if I have ONE F. Yay.... :,)

Step-by-step explanation:

A square root function that is represented by the graph include the following: A. f(x) = √(4x + 8).

In Mathematics and Geometry, a square root function can be defined as a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

Therefore, the required square root function is given by;

f(x) = √(4x + 8)

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Answer:

-5 =x

Step-by-step explanation:

0 = In(x + 6)

Raise each side to base e

e^0 = e^ ln (x+6)

1 = x+6

Subtract 6 from each side

1-6 = x

-5 =x

Answer:

area of base is 9pi

circumference of base is 6pi

lateral surface 24

surface area is 42

Step-by-step explanation:

Answer:

x=-1

Step-by-step explanation:

4x+35x-15=9x-45
39x-15=9x-45
39x-9x=-45+15
30=+-30
x=-1

Answer:

\( \sf \: x = - 1\)

Step-by-step explanation:

Given equation,

→ 4x + 5(7x - 3) = 9(x - 5)

Now the value of x will be,

→ 4x + 5(7x - 3) = 9(x - 5)

→ 4x + 35x - 15 = 9x - 45

→ 39x - 15 = 9x - 45

→ 39x - 9x = -45 + 15

→ 30x = -30

→ x = -30 ÷ 30

→ [ x = -1 ]

Hence, the value of x is -1.

x is a hypergeometric random variable, p(x=0) is 0.033.

Hypergeometric random distribution is a discrete probability distribution that describes k success in n draws without replacement from a finite population  size of N that exactly contains K objects.

Given x is a  hypergeometric random variable ,

    \(P(X=k)=\frac{KC_{k} .(N-K)C_{n-k} }{NC_{n} }\)

Here, N=10,n=3,r=6, P(x=0)

By using the above formula we get,

            =\(\frac{6C_{0} .4C_{3} }{10C_{3} }\)

            =\(\frac{4}{120}\)

 p(x=0) =0.033

Hence, P(x=0) is 0.033, where x is a hypergeometric random variable.

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Therefore, after 4 weeks, Liz will have $275 in her savings account and Fareed will have $300 in his savings account.

After 1 week

Liz will have saved $75 + $50 = $125, and

Fareed will have saved $100 + $50 = $150.

After 2 weeks,

Liz will have saved a total of $125 + $50 = $175, and

Fareed will have saved a total of $150 + $50 = $200.

After 3 weeks,

Liz will have saved a total of $175 + $50 = $225, and

Fareed will have saved a total of $200 + $50 = $250.

After 4 weeks,

Liz will have saved a total of $225 + $50 = $275, and

Fareed will have saved a total of $250 + $50 = $300.

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a) The event E, that the sum of the numbers showing face up is equal to 6, can be written as the set:

E = {11, 15, 24, 33, 42, 51}

b) The probability of E is 6/36 = 1/6.

c) The event F, that the sum of the numbers showing face up is at most 4, can be written as the set:

F = {11, 15, 22, 31, 33, 42, 44, 51}

d) The probability of F is 2/9.

Probability is a measure of the likelihood of an event occurring in a statistical experiment. It is a number between 0 and 1, where 0 indicates that the event will never happen and 1 indicates that the event will always happen. Probability can be used to make predictions about the outcome of statistical experiments, and it is a useful tool in many fields, including economics, finance, and science. It is also used in gambling and games of chance to determine the odds of winning.

The probability of event E is the number of outcomes in the event divided by the total number of outcomes in the sample space. There are 6 outcomes in the event E and 36 outcomes in the sample space.

So, the probability of E is 6/36 = 1/6.

The probability of event F is the number of outcomes in the event divided by the total number of outcomes in the sample space. There are 8 outcomes in the event F and 36 outcomes in the sample space.

So, the probability of F is 8/36 = 2/9.

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Answer:

B

Step-by-step explanation:

the first fish tank has 100 gallons of water and 1 gallon is removed every hour which makes 100-h

the second tank has 40 gallons in it and 2 gallons are added every hour which makes 40+2h

after 20 hours the second tank will have more gallons than the first tank

this means that 40+2h would be greater than 100-h since it's also asking you "After how many hours will the first tank  have less water than the second?"