A survey of Mr. Thorne’s class shows that 5 out of 8 students will buy lunch today. Based on this result, how many of the 720 students in the school will buy today?

Answer:

(-12+6+7+12-6+1)÷ 6

=8÷6

=1.3333

The complete solution is:

∫4\(sin^{-1}(2x) dx = sin^{-1}(2x)\) x 4x + √(1 - (2x)²) + C, where C is the constant of integration.

We have,

\(u = sin^{-1)}(2x)\)

dv = 4 dx

Taking the derivative of u, we get:

du/dx = 1 / √(1 - (2x)²)

Integrating dv, we get:

v = ∫4 dx = 4x

Now, applying the integration by parts formula:

∫4 \(sin^{-1}(2x) dx\) = uv - ∫vdu

Plugging in the values, we have:

∫4 \(sin^{-})(2x) dx = sin^{-1}(2x) \times\) 4x - ∫(4x / √(1 - (2x)²)) dx

At this point, we need to evaluate the integral on the right side.

Let's perform a substitution to simplify it:

Let u = 1 - (2x)²

Differentiating u with respect to x, we get:

du/dx = -4(2x) = -8x

Solving for dx, we have:

dx = -du / (8x)

Substituting these values, the integral becomes:

∫(4x / √(1 - (2x)²)) dx = ∫(-4x / (8x x √u)) (-du / (8x))

Simplifying, we get:

∫(4x / √(1 - (2x)²)) dx = ∫(-1 / (2√u)) du

= -∫(1 / (2√u)) du

= -√u + C

Substituting back the value of u, we have:

∫(4x / √(1 - (2x)²)) dx = -√(1 - (2x)²) + C

Therefore,

The complete solution is:

∫4\(sin^{-1}(2x) dx = sin^{-1}(2x)\) x 4x + √(1 - (2x)²) + C, where C is the constant of integration.

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The complete question:

a) Evaluate the integral ∫4 sin^(-1)(2x) dx using integration by parts.

Answer:

2

Step-by-step explanation:

The slant height of the cone with a height of 12 cm and radius of 9 cm is 15 cm.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

( hyotenuse )² = ( leg 1)² + ( leg 2)².

In the cone with a right angle formed between the height and radius, we can use the Pythagorean theorem to find the slant height.

Here, the height of the cone ( leg 1) is one of the sides, the radius of the cone ( leg 2) is the other side, and the slant height is the hypotenuse.

( hyotenuse )² = ( leg 1)² + ( leg 2)²

Plug in the values:

( hyotenuse )² = 12² + 9²

( hyotenuse )² = 144 + 81

( hyotenuse )² = 225

Hypotenuse = √225

Hypotenuse = 15

Therefore, the slant height is 15.

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Answer:

111,865.74

Step-by-step explanation:

it is that answer because you want to multiply then divide

Answer:

Step-by-step explanation:

You need to know trigonometry for this.\

You can't solve this without a scientific calculator.

TOA means Tan x = Opposite/Adjacent or in this case, 5.1/4.2

tan x = 5.1/4.2

arctant(tanx) = arctan(5.1/4.2)

x = arctan(5.1/4.2)

≈ 50.5°

arctan x is also known as tan inverse x

1.)  Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.

2.) The sum of probabilities of all possible outcomes is equal to 1.

1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.

A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.

Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.

2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.

Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.

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Answer:

(a) 10.3

(b) 11

Step-by-step explanation:

(a) Step 1: mean is the average of a set of numbers. Add them all together and then divide by how many numbers you were given

11+12+5+11+8+13+12 = 72

Step 2: There are 7 numbers so you divide 72 by 7

72/7 = 10.28

(a) The mean equals 10.3

(b) Step 1: Median is the middle number in a list of numbers. Line the numbers up in order and find the middle one.

5, 8, 11, 11, 12, 12, 13

(b) the median equal 11

There are 48 possible poker hands that contain all four aces, and the probability of getting one of these hands is 0.002%.

A poker hand that contains all four aces can be formed in 48 ways.

This is because there are 48 cards remaining in the deck after the four aces are removed, and any one of these cards can be chosen to complete the hand.

The number of ways to choose 5 cards from a deck of 52 is 52C5 = 2,598,960.

So the probability of getting a hand with all four aces is 48/2,598,960 = 0.0000185, or about 0.002%.

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Answer:

The numbers can be either -8,-7,-6, or 6, 7, 8.

n(n−1)(n+1)=16(n−1+n+n+1)  

⟹n(n2−1)=16×3n  

⟹n(n2−1)n=48nn  

⟹(n2−1)−48=48−48  

⟹n2−49=0  

⟶(n−7)(n+7)=0  

n  can be  7  or  −7 , so the numbers can be either  −8,−7,−6  

Or

6,7,8

Step-by-step explanation:

Answer: 24

To get this number, you do 60 x .40, and you get 24 (Amount of right handed people.)

Answer:

24

Step-by-step explanation:

24 because 40% of 60 is 24

Answer:

x = 2

Step-by-step explanation:

3x+4y=36

Y=-1/2+8

Now we substitute y with -1/2+8.

3x + 4(-1/2+8) = 36

3x + 4(7.5) = 36

3x + 30 = 36

3x = 6

x = 2

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Answer:

the file is 20 kb

Step-by-step explanation:

16kb/80%

xkb/100%

1600=80%

80       80

20KB

Which shows the following expression after the negative exponents have been eliminated

\(a^{2} b^{2}\)

Given the algebraic expression:

\(\frac{a^{3}b^{-2} }{ab^{-4} }, a\neq 0, b\neq 0\)

We are required to eliminate the negative exponents and find the resulting expression.

Using the Negative Exponent Law of Indices: \(x^{-y} = \frac{1}{x^{y} }\)

Using the Division Law of Indices: \(\frac{t^{x} }{t^{y} } = t^{x-y}\)

Therefore:

\(\frac{a^{3}b^{-2} }{ab^{-4} } = a^{3-1}.b^{-2-(-4)}\\ \\ Simplifying\\ \\a^{3-1}.b^{-2-(-4)} = a^{2}b^{-2+4}\\ \\ =a^{2} b^{2}\\\\Therefore:\\\\\frac{a^{3}b^{-2} }{ab^{-4} } =a^{2} b^{2}\\\)

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Answer:

Yes.

Step-by-step explanation:

The difference of two rational numbers is always a rational number because the numbers are always complete. There will never be a running number. Think of it as multiplying two positive numbers, you can never receive a negative from two positives.

Hey there!

4x + 3x = -21

7x = -21

x = -21/7

x = -3

Hope it helps ya!

Answer:

\(4x + 3x = - 21\)

\(7x = - 21\)

\(x = \cancel \frac{ - 21}{7} \)

\(x = - 3\)

To calculate the number of combinations for the car color and optional equipment, we multiply the number of color choices by the number of equipment choices.

For the car color, there are 7 different options available. Since you can choose only one color, there are 7 possibilities for this selection.

Regarding the optional equipment, there are 10 different types available, but you can only afford 2 of them. This means you have 10 options for the first equipment choice and 9 options for the second equipment choice.

The total number of combinations for your car can be determined by multiplying the number of color choices by the number of options for the equipment. Therefore, the total number of combinations for your car is 7 (color choices) multiplied by 10 (choices for the first equipment) multiplied by 9 (choices for the second equipment), which equals 630 combinations.

So, you have a total of 630 combinations for your car, taking into account the different color options and the two affordable equipment choices.

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Answer:

C. x = 1 + 3i or x = 1 - 3i

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

x² - 2x + 10 = 0

Step 2: Identify Variables

a = 1

b = -2

c = 10

Step 3: Find roots

a) Φ(63) =?  b) Let A = 99...9 be a 36 digit number. Prove that 63|A.

The value of Φ(63) is 36.

To prove that 63 divides the number A, which consists of 36 nines, we need to show that A is divisible by both 7 and 9.

First, let's examine the divisibility by 7. We can observe that A can be expressed as A = 10^36 - 1. Since 10 ≡ 3 (mod 7), we can rewrite A as A ≡ 3^36 - 1 (mod 7). By applying Fermat's Little Theorem (which states that if p is a prime number and a is an integer not divisible by p, then a^(p-1) ≡ 1 (mod p)), we can deduce that 3^6 ≡ 1 (mod 7). Therefore, 3^36 ≡ (3^6)^6 ≡ 1^6 ≡ 1 (mod 7). Hence, A ≡ 1 - 1 ≡ 0 (mod 7), indicating that A is divisible by 7.

Next, let's examine the divisibility by 9. Since A consists of 36 nines, we can express it as A = 9(111...1), where the number of ones is 36. By the divisibility rule for 9, we know that a number is divisible by 9 if and only if the sum of its digits is divisible by 9. In this case, the sum of the digits of A is 9 × 36 = 324, which is clearly divisible by 9.

Therefore, since A is divisible by both 7 and 9, it follows that A is divisible by their least common multiple, which is 63. Thus, 63 divides the number A.

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This statement is - true.

Two angles that lie in the same plane and have a common vertex and a common side but have no common interior points are the meaning of adjacent angles.

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Answer:

0.25 Hope this helps :)

Step-by-step explanation:

You add the 5 red and 3 green

8 Mables besides blue

so that's 2/8

simplified 1/4

1/4=0.25

Answer:

yes this is function ,because function it can go to minus and plus

Step-by-step explanation:

Answer:

617/1000

Step-by-step explanation:

61.7% as a percent in case u need it :)

Answer:

-4/2

Step-by-step explanation:

Answer:

A) s=32t

B) 224 ft/s

Step-by-step explanation:

A)

In the form (time, speed), the question gives us the following data: (1,32) and (5,160). Since we are told that the relationship between​ time, t, and​ speed, s, is linear, we know the equation will fit the formula y=mx+c, where m is slope c is the y-intercept and y and x are the co-ordinate values. Plug in (1,32) and (5,160) to find the formula:

y=mx+c

s=mt+c

32=1m+c

c=32-m

160=5m+C

160=5m+32-m

128=4m

m=32

c=32-m

=32-32=0

So our equation is s=32t

B)

s=32t

s=32(7)=224 ft/s

The five-number summary for the given data set is:

Minimum: 1.5

Q1: 1.6

Median (Q2): 2.6

Q3: 4.0

Maximum: 7.6

To calculate the five-number summary and construct a box plot for the given data set:

Step 1: Arrange the data in ascending order:

1.5, 1.5, 1.6, 1.6, 1.7, 2.0, 2.1, 2.2, 2.6, 3.2, 4.0, 4.9, 5.5, 7.5, 7.6

Step 2: Find the minimum and maximum values:

Minimum value: 1.5

Maximum value: 7.6

Step 3: Find the median (Q2):

Since the data set has an odd number of values, the median is the middle value.

Median (Q2): 2.6

Step 4: Find the lower quartile (Q1):

The lower quartile is the median of the lower half of the data set.

Lower half: 1.5, 1.5, 1.6, 1.6, 1.7, 2.0, 2.1

Median of lower half (Q1): 1.6

Step 5: Find the upper quartile (Q3):

The upper quartile is the median of the upper half of the data set.

Upper half: 2.2, 2.6, 3.2, 4.0, 4.9, 5.5, 7.5, 7.6

Median of upper half (Q3): 4.0

Step 6: Find the interquartile range (IQR):

IQR = Q3 - Q1 = 4.0 - 1.6 = 2.4

Step 7: Calculate the lower and upper fence:

Lower fence = Q1 - 1.5 * IQR = 1.6 - 1.5 * 2.4 = -2.1 (Since it is below the minimum value, we ignore it for the box plot)

Upper fence = Q3 + 1.5 * IQR = 4.0 + 1.5 * 2.4 = 7.4

Step 8: Construct the box plot:

Using the minimum, Q1, median (Q2), Q3, and maximum, we can construct the box plot. The fences are represented by whiskers (lines) outside the box. Any data points beyond the fences are considered outliers.

Box plot:

| o

| o---o---o

| | |

+--+-------+--

Minimum Maximum

Q1 Q2 Q3

The five-number summary for the given data set is:

Minimum: 1.5

Q1: 1.6

Median (Q2): 2.6

Q3: 4.0

Maximum: 7.6

Note: The box plot representation might not be accurate due to the limitations of text formatting.

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Answer:

5x=3+x

Step-by-step explanation:

5 times X is equal to 5x

3 more than X is equal to 3+x

Answer:

5 - 15 = -10

Step-by-step explanation:

Answer:

5 - 15 = -10

Step-by-step explanation:

If you start with 5 and then subtract 15, you end up at -10.