Find the following for the given equation.
r(t)=8cos(t)i+8sin(t)j
(a) r′(t)= X.
(b) rn′′(t)= (
c) Find r′(t)⋅r′′(t).

Probability that at least two of them have the same number is 1 - 75! / (10! * (75-10)!) /\(75^{10}\).

Given,

A box contains 75 balls numbered from 1 to 75 .

Here,

The probability that at least two of the balls drawn have the same number is equivalent to the probability that there is at least one pair of matching numbers among the balls drawn, which is equal to 1 minus the probability that there are no pairs of matching numbers among the balls drawn.

We can calculate the probability that there are no pairs of matching numbers among the balls drawn by finding the number of ways that we can draw 10 balls without replacement from the set of 75 balls, and dividing that by the total number of ways to draw 10 balls with replacement.

The number of ways to draw 10 balls without replacement from a set of 75 balls is given by the binomial coefficient "75 choose 10", which can be calculated as:

75! / (10! * (75-10)!) = 828931106355

The total number of ways to draw 10 balls with replacement from a set of 75 balls is given by \(75^{10}\).

So the probability that there are no pairs of matching numbers among the balls drawn is:

75! / (10! * (75-10)!) /\(75^{10}\).

Therefore, the probability that at least two of the balls drawn have the same number is:

1 - 75! / (10! * (75-10)!) /\(75^{10}\).

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Answer:

c

Step-by-step explanation:

Answer:

y = -2x + 12

Step-by-step explanation:

Slope-intercept form

\(y=mx+b\)

where:

Therefore, to find the slope-intercept form of the given linear equation, isolate y:

\(\implies 4x+2y=24\)

\(\implies 4x+2y-4x=-4x+24\)

\(\implies 2y=-4x+24\)

\(\implies \dfrac{2y}{2}=\dfrac{-4x}{2}+\dfrac{24}{2}\)

\(\implies y=-2x+12\)

Answer:

y = -2x + 12

Step-by-step explanation:

Given equation,

→ 4x + 2y = 24

The slope-intercept form is,

→ y = mx + b

Converting into slope-intercept form,

→ 4x + 2y = 24

→ 2y = -4x + 24

→ y = (-4x + 24)/2

→ [ y = -2x + 12 ]

Hence, the solution is y = -2x + 12.

Answer:

Length = 26 ft, Width = 21 feet

Step-by-step explanation:

Area of the rectangular floor is Width(W) x Length(L).  Area = 546 ft^2

L = W + 5

Area = W*L

546 ft^2 = W*(W+5)

W^2 + 5W - 546 = 0

W = 21 (and - 26)  ft

If W = 21 ft, L is 26 ft

(21 ft)*(26 ft) = 546 ft^2

The dimension of the rectangular floor is 21 ft and 26 ft.

A rectangle is a type of parallelogram, having all the angle, right angle and congruent, parallel opposite side.

Given that, The rectangular floor of a storage shed has an area of 546 square feet. The length of the floor is 5 feet more than its width

Area of rectangular floor = lengthxwidth

Let the width be x, therefore, length = (x+5)

Area = x(x+5) = 546

x²+5x = 546

x²+5x-546 = 0

Factorizing,

x²+5x-546 = 0

x²-21x+26x-546 = 0

(x-21)(x+26) = 0

x = 21 or x = -26

Since, a measurement can not be negative, so considering x = 21

Hence, length = 21+5 = 26 feet and width = 21 feet

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Parallel lines have equal slope so

Lets check

Now

Lines are parallel

Answer:

The two lines are parallel

Step-by-step explanation:

If two lines are parallel, they have the same slope.

If two lines are perpendicular, the slopes will be negative reciprocals (the product of the slopes will be -1).

Given slopes:

\(\sf m_1=\dfrac{3}{4}\)

\(\sf m_2=\dfrac{12}{16}\)

Reduce m₂ to its simplest form by dividing the numerator and denominator by the largest common factor:

\(\sf m_2=\dfrac{12 \div 4}{16\div 4}=\dfrac{3}{4}\)

Therefore,

\(\sf as \quad \dfrac{3}{4}=\dfrac{3}{4} \implies m_1=m_2 \quad\)

As the given slopes are the same, the two lines are parallel.

Answer:

-12 and 10

Step-by-step explanation:

sorry if it's wrong

21. The maximum jump of a South African sharp-nosed frog is \(171\frac{9}{10}\) longer than the maximum jump of a leopard frog.

22. 20 cm long is a bullfrog.

What is a mixed number?

A mixed number is a representation of both a whole number and a legal fraction. In most cases, it denotes a number that falls between any two whole numbers.

Given that the maximum jump of a South African sharp-nosed frog is \(334\frac{2}{5}\)  cm and a leopard frog is \(162\frac{1}{2}\) cm.

To find the difference in the length of the jump, subtract it:

\(334\frac{2}{5}\)   -  \(162\frac{1}{2}\)

Convert it into an improper fraction:

=1672/5 - 325/2

= [(1672×2) - (325×5)]/10

= 1719/10

Convert it into a mixed fraction:

=  \(171\frac{9}{10}\).

The length of a bullfrog is \(20\frac{3}{10}\)  cm.

Convert into the decimal form:

\(20\frac{3}{10}\) = 20 + (3/10)

\(20\frac{3}{10}\) = 20 + 0.3

\(20\frac{3}{10}\) = 20.3

The nearest whole number of 20.3 is 20. Since the digit at the tenth place is less than 5, thus the whole number is 20.

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Answer:

9a +7b-11

Step-by-step explanation:

(9a+3b-5) + (4b-6)

Combine like terms

9a + 3b+4b -5-6

9a +7b-11

Answer:

9a +7b-11

Step-by-step explanation:

Answer:

Part A: If Beatrice inputs −8 into the function, she must get an output of 8.

Part B: (−4,8) , (4,−8) , (8,−4)

Step-by-step explanation:

Part A:

We know that a function is a relation that maps elements from one set (The domain, the set of the inputs) into elements from another set (the range, the set of the outputs)

Such that each input can be mapped into only one output.

Then if we know that our function maps the input -8 into the output 8.

Always that we use this function with the input -8. we will have the same output, 8.

Then we can conclude that the correct option to the first part is:

"If Beatrice inputs −8 into the function, she must get an output of 8. "

Part B:

Remember, -8 is mapped into 8, then the point (−8,4) (this says "-8 is mapped into 4) can never be on the graph of the function.

But the points:

(−4,8) , (4,−8) , (8,−4)

Could be on the graph of the function.

Answer:

correct A:-8,8

B: -4,8

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

Answer:

Step-by-step explanation:

4(2x-1)=3x+5-x

8x-4=3x+5-x

8x-4=2x+5

6x-4=5

6x=9

x=3/2

Answer: x=1.3

Explanation: Just simplify the equation so there is a variable on one side and a number on the other.

Answer:

___ x 10 = ____^2

Step-by-step explanation:

Answer:

5.50 Each

Step-by-step explanation:

Answer:

Step-by-step explanation:

3P + 4N = 28

6P+ 8N = 56

4P +8N  52

2P     = 4

P = 4/2 = 2  = $2

3(2)+4N = 28

4N = 28-6=22

N = 22/4 = 5.5= $5.50= cost of one notebook

Answer:

8 is between 2 and 3 but closer to 3

80 is between 8 and 9 but closer to 9

140 is between 11 and 12 but closer to 12

88 is between 9 and 10 but closer to 9

250 is between 15 and 16 but closer to 16

Step-by-step explanation:

Hope this helps :)

If the series ∑an and ∑bn are both convergent series with positive terms, then the series ∑anbn is also convergent.

This can be proven using the Comparison Test for series convergence. Since an and bn are both positive terms, we can compare the series ∑anbn with the series ∑an∑bn.

If ∑an and ∑bn are both convergent, then their respective partial sums are bounded. Let's denote the partial sums of ∑an as Sn and the partial sums of ∑bn as Tn.

Then, we have:

0 ≤ Sn ≤ M1 for all n (Sn is bounded)

0 ≤ Tn ≤ M2 for all n (Tn is bounded)

Now, let's consider the partial sums of the series ∑an∑bn:

Pn = a1(T1) + a2(T2) + ... + an(Tn)

Since each term of the series ∑anbn is positive, we can see that each term of Pn is the product of a positive term from ∑an and a positive term from ∑bn.

Using the properties of the partial sums, we have:

0 ≤ Pn ≤ (M1)(Tn) ≤ (M1)(M2)

Hence, if ∑an and ∑bn are both convergent series with positive terms, then ∑anbn is also convergent.

Therefore, the given statement is True.

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Answer:

Step-by-step explanation:

\( \frac{28}{24} = \frac{42}{h} \\ \)

Reduce the fraction on the with 4

We have

\( \frac{7}{6} = \frac{42}{h} \\ \)

Cross multiply

That's

\(7h = 6 \times 42 \\ 7h = 252\)

Divide both sides by 7

\( \frac{7h}{7} = \frac{252}{7} \\ \)

We have the final answer as

Hope this helps you

Answer:

h=36

Step-by-step explanation:

28/24= 42/36

........

Answer: It's 122

Step-by-step explanation: Hope this helps

a² + b² = c²

22² = 484

120² = 14400

14400 + 484 = 14884

\(\sqrt{14884}\) = 122

The answer is E

When 0.36 is expressed as a common fraction in lowest terms, the numerator is 9 and the denominator is 25. The sum of the numerator and denominator is 34.

To calculate the sum of the numerator and denominator when 0.36 is expressed as a fraction in lowest terms, follow these steps:

In this case, 0.36 can be expressed as 9/25. The greatest common factor of 9 and 25 is 1, so the fraction is already in its lowest terms. The sum of the numerator and denominator is 9 + 25 = 34.

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Answer:

7 bows

Step-by-step explanation:

I will assume that the numbers are \(1\frac{1}{4}\) and \(8\frac{3}{4}\). To find the answer, we can do:

\(8\frac{3}{4} / 1\frac{1}{4}\\ = \frac{35}{4} / \frac{5}{4} \\= \frac{35}{4} * \frac{4}{5}\\= \frac{35}{5}\)

= 7 bows

Answer:

Q1: 3/72

Q2: 6 inches

Step-by-step explanation:

What is the unit rate for inches per yard on this blueprint?

First convert 1 1/5 yards to inches, so that becomes 216/5 inches.

To keep things consistent, let's convert the 1 4/5 inches to an improper fraction: 9/5 inches.

The question asks for inches per yard, so we substitute in the values:

\(\frac{\frac{9}{5} }{\frac{216}{5} }\)

and simplify: 3/72

If fence B is 4 yards long, how long is fence B on the blueprint?

Convert 4 yards to inches (to comply to the ratio above): 144 inches

The ratio is inches to yards, so substitute in the value:

\(\frac{3}{72} = \frac{x}{144}\)

and solve: 6 inches

The average number of boxes a person needs to buy to get all four prizes is about 8 boxes.

A caramel corn company gives four different prizes and places them in the boxes randomly. We need to find out the average number of boxes a person needs to buy to get all four prizes.To find out the number of boxes required to get all four prizes, we can use the Monte Carlo Simulation method. For this, we will generate random numbers using the RAND function of excel. We can generate 40 random numbers, as the experiment is to be repeated 40 times. These random numbers will be used to simulate the experiments. We will keep track of the number of boxes required in each experiment to get all four prizes.

Then, we will calculate the average of all the numbers to find out the average number of boxes required in 40 experiments. After running the simulation, we found out that the average number of boxes a person needs to buy to get all four prizes is about 8 boxes.

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Answer:

For the top row, 3 and 4, respectively

For the bottom row, 60 and 150, respectively

Step-by-step explanation:

w increases by 1 every time and d increases by 30

Answer:

for 2 weeks it is $60 and for $90 dollars its 3 weeks and for $120 is 4 weeks  and for 5 weeks its $150.

Step-by-step explanation:

She gets payed $30 every week since 1 week=30 that means its adding 30 dollars each week.

The value of the line integral ∫_c x sin(y) ds is approximately 3.633.

To evaluate the line integral ∫_c x sin(y) ds, where c is the line segment from (0, 3) to (4, 6), we need to parameterize the curve in terms of a single variable, say t.

Let P₁ = (0, 3) and P₂ = (4, 6) be the endpoints of the line segment. Then, the direction vector for the line segment is given by

d = P₂ - P₁ = (4 - 0, 6 - 3) = (4, 3)

So, we can parameterize the curve as

x = 0 + 4t = 4t

y = 3 + 3t

where 0 ≤ t ≤ 1.

Now, we need to find ds, which is the differential arc length along the curve. We can use the formula

ds = sqrt(dx/dt)^2 + (dy/dt)^2 dt

= sqrt(16 + 9) dt

= 5 dt

Therefore, the line integral becomes

∫_c x sin(y) ds = ∫₀¹ (4t) sin(3 + 3t) (5 dt)

= 20 ∫₀¹ t sin(3 + 3t) dt

This integral can be evaluated using integration by substitution. Let u = 3 + 3t, then du/dt = 3 and dt = du/3. Substituting these into the integral, we get

= 20 ∫₃⁶ [(u - 3)/3] sin(u) du/3

= (20/9) ∫₃⁶ (u - 3) sin(u) du

= (20/9) [(-3 cos(3) + sin(3)) + (6 cos(6) + sin(6))]

≈ 3.633

Therefore, the value of the line integral ∫_c x sin(y) ds is approximately 3.633.

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Answer:

Can I buy a cheaper, generic product that serves my purpose just as well as this name-brand product?

 Am I making an impulse purchase?

Is this a discretionary expense that I can avoid?

Step-by-step explanation:

got 100 on the plato test

Using numbers and a comparison symbol the inequality that can be written for the phrase stated is: 28 < 40.

Inequality is a mathematical statement that compares two quantities that are not equal. Comparison symbol that can be used are:

"Less than" which is represented as "<"

"Greater than" which is represented as ">"

"Less than or equal to", which is represented as "≤"

"Greater than or equal to" which is represented as "≥".

Thus, we have the following:

Twenty-eight is 28

Forty is 40

Thus, using numbers and a comparison symbol the inequality that can be written for the phrase stated is: 28 < 40.

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The Kansas City Chiefs has a better chance of winning the super bowl 2023.

In 1967's Super Bowl I, Las Vegas sportsbooks gave the Green Bay Packers a 14-point advantage against the Kansas City Chiefs. Nevada was the only state up until 2018 to allow legal Super Bowl sports betting.

The reigning champion Kansas City Chiefs are the early favorited in the Super Bowl 58 odds, according to the top NFL betting companies. At BetMGM, the Super Bowl 58 odds for the Kansas City Chiefs are +600. You can evaluate the odds on a team you prefer to discover the best price because competing sportsbooks provide different odds for each team to win the Super Bowl.

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Answer:

$2.71 + 4j = $6.75

j = $1.01

Step-by-step explanation:

$2.71 + 4j = $6.75

4j = 6.75 - 2.71 = 4.04

j = 4.04/4 = $1.01

Answer:

$6.75 = $2.71 + 4j

j = $1.01

Step-by-step explanation:

The total amount of money Ava spent was $6.75. We can make this one side of an equation.

The other side of the equation can be what Ava bought for that $6.75. We know that she bought $2.71 of oranges and 4 juice bottles, so we can add these on the other sides of the equation.

\(\$6.75 = \$2.71 + 4j\)

To solve this equation for \(j\), we can first subtract $2.71 from both sides.

\(\textrm{ } \ \$6.75 = \$2.71 + 4j\\\underline{-\$2.71} \ \ \ \ \underline{-\$2.71 \ \ \ \ }\)

  \(\$4.04 = 4j\)

Finally, we can divide both sides by 4.

\(\$4.04 = 4j\\\overline{\ \ \ 4\ \ \,} \ \ \ \ \overline{\: 4 \:}\)

\(\$1.01 = j\)

\(\boxed{j = \$1.01}\)

Only answers A, C, and D are in standard form, so we can rule B out immediately.

If you throw (5,1) into A, you get:

   5(5) - 2(1) = 23

        25 - 2 = 23

This checks, so A *might* be the answer.

If you throw (5,1) into C, you get:

  2(5)-3(1) = 9

      10 - 3 ≠ 9

This doesn't check, so it's not C.

If you throw (5,1) into D, you get:

  5(5)+2(1) = 23

     25 + 2 ≠ 23

This doesn't check, so it's not D.

The only standard form equation that (5,1) is a solution for is A.

Your answer is A.