A gym teacher placed golf balls into 9
buckets so that each bucket had at least 15
balls. How many total golf balls are there?

Answer:

a) 0.8802 = 88.02% probability that the shipment is accepted

b) 0.1756 = 17.56% probability that the shipment is accepted if 15% of the total shipment is defective.

Step-by-step explanation:

For each item, there are only two possible outcomes. Either it is defective, or it is not. The probability of an item being defective is independent of any other item. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

20 randomly selected video streaming devices

This means that \(n = 20\)

a. Find the probability that the shipment is accepted if 3% of the total shipment is defective.

3% defective means that \(p = 0.03\)

Probability of at most 1 defective is:

\(P(X \leq 1) = P(X = 0) + P(X = 1)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{20,0}.(0.03)^{0}.(0.97)^{20} = 0.5438\)

\(P(X = 1) = C_{20,1}.(0.03)^{1}.(0.97)^{19} = 0.3364\)

\(P(X \leq 1) = P(X = 0) + P(X = 1) = 0.5438 + 0.3364 = 0.8802\)

0.8802 = 88.02% probability that the shipment is accepted.

b. Find the probability that the shipment is accepted if 15% of the total shipment is defective

Now \(p = 0.15\). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{20,0}.(0.15)^{0}.(0.85)^{20} = 0.0388\)

\(P(X = 1) = C_{20,1}.(0.15)^{1}.(0.85)^{19} = 0.1368\)

\(P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0388 + 0.1368 = 0.1756\)

0.1756 = 17.56% probability that the shipment is accepted if 15% of the total shipment is defective.

The area of the composite figures are:

The total area of Shape A is = 115.5 in²

and, total area of Shape B is = 51ft².

Here, we have,

from the given diagram we get,

Shape A.)

Part 1: it is a rectangle,

l= 13 and w = 7

so, area = 91 in²

Part 2: it is a triangle,

b = 7 and h = 7

so, area = 1/2 *7 * 7 = 24.5 in²

So, The total area of Shape A is = 115.5 in²

now, Shape B.)

part 1 : it is a rectangle,

l=4 and w = 6

so, area = 24 ft²

part2: it is a square,

side = 3

so, area = 9 ft²

part 3: it is a trapezium,

a = 6, b = 3, h =4

so, area = 1/2 * (6+3) * 4 = 18ft²

So, total area of Shape B is = 51ft².

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There are  0.09779 grams in 7.4 x 10^19 Atoms of copper.

The number of grams in a given number of atoms of an element, we need to use the concept of molar mass and Avogadro's number.

The molar mass of an element represents the mass of one mole of that element. For copper (Cu), the molar mass is approximately 63.546 grams per mole.

Avogadro's number, denoted as N_A, is the number of atoms or molecules in one mole of a substance. It is approximately 6.022 x 10^23 atoms/molecules per mole.

To calculate the mass of a given number of atoms, we can use the following steps:

Step 1: Determine the number of moles of copper atoms.

Given: 7.4 x 10^19 atoms of copper

Number of moles = (Number of atoms) / (Avogadro's number)

Number of moles = (7.4 x 10^19) / (6.022 x 10^23)

Step 2: Calculate the mass using the molar mass of copper.

Mass = (Number of moles) x (Molar mass)

Mass = (7.4 x 10^19) / (6.022 x 10^23) x 63.546

Now, we can perform the calculations:

Mass ≈ 0.09779 grams

Therefore, there are approximately 0.09779 grams in 7.4 x 10^19 atoms of copper.

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Answer:

C. 1/2

Step-by-step explanation:

Just trust me bro

The function that describes his distance from the finish line after x minutes is given by, f(x) = 3-x/2.

Given that a student is running a 3 kilometer race.

He runs 1 kilometer every 2 minutes.

So in 1 minute he runs 1/2 kilometers.

So in x minutes he runs x/2 kilometers.

So his distance from finish line of 3 kilometers race after x minutes = 3-x/2

So the suitable function which shows the his distance he runs after x minutes from finish line is given by,

f(x) = 3-x/2

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Answer:

79 boxes

Step-by-step explanation:

1500-155= 1345

1345/17=79.11

Answer:

See below

Step-by-step explanation:

Part A

\(f(g(x))=f(\frac{x}{3})=3(\frac{x}{3})=x\\g(f(x))=g(3x)=\frac{3x}{3}=x\)

Since BOTH \(f(g(x))=x\) and \(g(f(x))=x\), then \(f\) and \(g\) are inverses of each other

Part B

\(f(g(x))=f(\frac{x+1}{2})=2(\frac{x+1}{2})+1=x+1+1=x+2\\g(f(x))=g(2x+1)=\frac{(2x+1)+1}{2}=\frac{2x+2}{2}=x+1\)

Since BOTH \(f(g(x))\neq x\) and \(g(f(x))\neq x\), then \(f\) and \(g\) are NOT inverses of each other

A function is a rule that generates one unique output value for every specified input value. Therefore, the fourth statement is true.

In mathematics, the function is something that relates an input to an output. The output obtained will somehow be related to the input. We write the function as f(x). For example, consider f(x) = x². This means that the function f takes the value of x and squares this value. Like when we input x=4. Then the output is f(x)=4²=16.

So, here see the function assigns a single and a unique output value of 16 for the input value of 4. Therefore, option 4 is correct. That is function gives every input value a unique, separate output value.

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Answer:

Step-by-step explanation:

lets remove the parenthesis

-29+7-9-11=-42

Answer:

-42

Step-by-step explanation:

(-29+7)= -22

(9+11) = 20

-22-20= -42

1. The velocity at time t , v(t) = (18t² + 3 ) m/s

2. The velocity at time t = 3 seconds = 165 m/s

3. The acceleration at time t, a(t) =( 36t )m/s²

4. The acceleration at time t = 3 seconds = 108 m/s²

The quantity that tells us how fast an object is moving anywhere along its path is the instantaneous velocity.

Instantaneous acceleration is defined as the ratio of change in velocity during a given time interval such that the time interval goes to zero.

1. s(t) = 6t³ + 3t +9

to find the velocity at time t, we differentiate s(t)

= 18t² + 3

2. at t = 3s

= 18(3)² +3

= 165 m/s²

3. v(t) = 18t² + 3

to get the acceleration at time t, we differentiate v(t)

= 36t

4. when t = 3

a = 36 × 3

= 108 m/s²

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Answer:

Step-by-step explanation:

You have to use the quadratic formula

x = -b +/- \(\sqrt{(b^{2} -4ac)/2a\)

and then you can simplify both answers so the first one would be -13/2 and the second would be -27/2

you usually have to reject an answer but since there is no equal sign in the question, you should be fine

The equation for the line of best fit from the given data, will be y = 2.12 x + 4.42.

The line of best fit would be the line that has an equal number of points above it, as the number of points beneath it.

Going by this definition, two points that would be on the line are (6, 17) and ( 7, 19 ).

The slope of this line would be:

= ( Y2 - Y1 ) / ( X 2 - X1)

= ( 19 - 17 ) / (7 - 6 )

= 2.12

The y intercept would be:

y = mx + c

19 = 2.12 (7 ) + c

c = 4.42

The equation of the  line of best fit is then :
y = 2.12 x + 4.42

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Answer:

The left side of the histogram has a cluster.

Step-by-step explanation:

The others don't make since.

It's not evenly distributed,

it's not symmetrical, and

it is definitely not a mirror image of the right side.

Answer:

A

Step-by-step explanation:

Answer:

8.7, 8.9, 9.0

Step-by-step explanation:

Answer:

8.7, 8.9, & 9.1

Step-by-step explanation:

The decimal places go up by tens like all other numbers. Therefore, 8.7, 8.9, and 9.1 are all in between 8.6 and 9.2

Answer:

  \(x\log_2{5}\)

Step-by-step explanation:

The relevant rule of logarithms is ...

  log(a^b) = b·log(a)

__

Here, that means ...

  log(5^x) = x·log(5) . . . . . where the log is to the base 2 in each case

Answer:

45°

Step-by-step explanation:

complementary angles add up to 90° so it's 90-45

Answer:

3n>15

Step-by-step explanation:

So basically, this three times a number, 3n, is greater than 15. So, this is 3n>15.

The six terms of the series 247 are 2, 2, 2, 2, 2, and 2.

To find the six terms of a series, we need to first understand what a series is. A series is defined as the sum of the terms of a sequence. A sequence is a set of numbers in a specific order.

Therefore, a series is a sum of terms from a sequence. There are different types of series, and they have different formulas for calculating their terms.In this case, we are required to find the six terms of the series 247. Since this is a finite series, we can use a formula to calculate the nth term of a finite series.

The formula is given as follows:Tn = a + (n - 1) dWhere Tn is the nth term of the series, a is the first term of the series, n is the number of terms in the series, and d is the common difference between the terms of the series.To find the six terms of the series 247, we need to know the value of a and d. In this case, we can see that the first term of the series is 2. Therefore, a = 2.

Since this is a constant series, we can see that the common difference between the terms is 0. Therefore, d = 0.Substituting these values in the formula, we get:T1 = a + (1 - 1) dT1 = 2 + 0T1 = 2T2 = a + (2 - 1) dT2 = 2 + 0T2 = 2T3 = a + (3 - 1) dT3 = 2 + 0T3 = 2T4 = a + (4 - 1) dT4 = 2 + 0T4 = 2T5 = a + (5 - 1) dT5 = 2 + 0T5 = 2T6 = a + (6 - 1) dT6 = 2 + 0T6 = 2.

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Answer:

Step-by-step explanation:

Drop an altitude from the left angle so that it is perpendicular to x

The hypotenuse created by this altitude is 15 cm

The 28 degree angle is opposite the altitude.

Sin(28) = opposite / hypotenuse

opposite = the altitude

hypotenuse = 15 cm

Reference angle = 28 degrees.

Sin(28) = altitude / 15     Multiply both sides by 15

15 sin(28) = altitude

Sin(28) = 0.4695

altitude = 15*0.4695

altitude = 7.0421

Now we can solve for x

Area = 1/2 altitude * x

Area = 1/2 * 7.0421 * x

60 cm^2 = 3.521 * x                        Divide both sides by 3.521

60 / 3.521 = x

x = 17.04

Answer:

\((\frac{dy}{dx})x_{= \frac{\pi }{2} } = f^{1} (\frac{\pi }{2} ) =2\)

Step-by-step explanation:

Step(i):-

Given that

 \(f(x) = \frac{5x}{sinx} -3xsinx\)

Apply (UV )¹ = UV¹+VU¹

\(\frac{d}{dx} (\frac{U}{V} ) = \frac{V U^{l} -VU^{l} }{V^{2} }\)

Step(ii):-

\(f^{1} (x) = 5\frac{sin x(1)-x(cos x)}{sin^{2}x } - 3(x cos x + sin x(1))\)

put  \(x = \frac{\pi }{2}\)

\(f^{1} (\frac{\pi }{2} ) = 5\frac{sin \frac{\pi }{2} (1)-\frac{\pi }{2} (cos \frac{\pi }{2} )}{sin^{2}(\frac{\pi }{2} ) } - 3(\frac{\pi }{2} cos \frac{\pi }{2} + sin(\frac{\pi }{2}) (1))\)

we know that  

\(cos(\frac{\pi }{2}) = 0\)  

\(sin(\frac{\pi }{2} ) = 1\)

\(f^{l} (\frac{\pi }{2} ) = \frac{5(1-0)}{1} -3(0+1)\)

\(f^{1} (\frac{\pi }{2} ) = 5-3 =2\)

Final answer:-

\((\frac{dy}{dx})x_{= \frac{\pi }{2} } = f^{1} (\frac{\pi }{2} ) =2\)

Explanation:

You would use this law under two conditions:

Hence, you have your answer.

* Just make sure to use the inverse function towards the end, or elce you will throw your answer off!

_______________________________________________

Now, you would use the Law of Sines under three conditions:

* I HIGHLY suggest you keep note of all of this significant information. You will need it going into the future.

I am delighted to assist you at any time.

Answer:

\(f(x)=\sqrt{8-7}=\sqrt{1}=1\)

Step-by-step explanation:

\(f(x)=\sqrt{x-7}\\\\f(x)=\sqrt{8-7}=\sqrt{1}=1\)

Answer:

30

Step-by-step explanation:

100-65

=35

Katie Collected 35

65-35 = 30

Emily collected 30 more pieces of candy

Answer:

  C

Step-by-step explanation:

If ∆MNP is equilateral, then each of the arcs MN, NP and PM will be 120°. An inscribed angle from anywhere that intercepts one of these arcs will have measure 60°. That is, angle MQP is 60°. We already know angle MOQ is 60° (half of arc MN), so ∆MOQ is equilateral, and MO=MQ=PO.

Points M and N were drawn using Q as a center, and PO as a radius.

Do u have a screenshot

Step-by-step explanation:

Answer:

144 - 36×3.142 = 30.888

30.888 ÷4 = 7.722

Answer:

MN= 17.9in

ST=  3.8cm

CE= 13.0yd

Step-by-step explanation:

Step-by-step explanation:

\( \frac{19695}{x - 15605} = 100\)

\(19695 = 100(x - 15605)\)

\(19695 = 100x - 1560500\)

\(19695 + 1560500 = 100x\)

\(15801 95 = 100x\)

\( \frac{1580195}{100} = x\)

\(x = 15801.95\)