EVALUATE THE FOLLOWING:
A) 85!/82!
B) nC0
C) nPn

Last box

As it's 7:2

Difference between x and y must increase in big number as x and y increases

Option D is correct in that manner

Let's double check

Using it's concept, the experimental probability that in a group of 4 students, at least one of them has green eyes is of 0.45 = 45%.

A probability is given by the number of desired outcomes divided by the number of total outcomes. An experimental probability is calculated considering the results of previous trials.

In this problem, there were 20 trials. The digit 9, which represents a student with green eyes, appears at least once in 9 of the the trials, hence the probability is:

p = 9/20 = 0.45 = 45%.

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Answer:

Step-by-step explanation:

why is it so hard omg

f(x) = 12(x - 1)/[(x + 2)(x - 3)] is the equation of the function graphed as in the figure. This can be obtained using the formula of f(x) = P(X)/Q(X) by vertical asymptotes and factors of the polynomial.

Let  where P(X) and Q(X) are polynomial function.

The function has the following:

This means that, -3 and 2 are roots of the denominator. Thus, the equation of the denominator is:

⇒ Q(X) = (x + 2)(x - 3)

Let a be the leading coefficient of P(X)

⇒ P(X) = a(x - 1)

Now for finding the value of a we can rewrite the equation as,

⇒ f(x) = P(X)/Q(X)

⇒ f(x) = a(x - 1)/[(x + 2)(x - 3)]

⇒ f(0) = a(0 - 1)/[(0 + 2)(0 - 3)]

Since from the graph we can say that the y-intercept is (0, - 2), this means that when x = 0, y = -2, f(0) = - 2

⇒ - 2 = -a/[(2)(- 3)]

⇒ a = - 2 × 2 × 3

⇒ a = - 12

By putting a = -12 in f(x) we get,

⇒ f(x) = 12(x - 1)/[(x + 2)(x - 3)]

Hence f(x) = 12(x - 1)/[(x + 2)(x - 3)] is the equation of the function graphed as in the figure.

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Answer: -6

Step-by-step explanation:

[tex]x+3y=-5\\\\3y=-x-5\\\\y=-\frac{1}{3}x-\frac{5}{3}[/tex]

So, since parallel lines have the same slope, the slope of the line we need to find is -1/3.

Substituting into point-slope form, the equation is

[tex]y-2=-\frac{1}{3}(x+7)\\[/tex]

Converting to the required form,

[tex]y-2=-\frac{1}[3}x-\frac{7}{3}\\\\\frac{1}{3}x+y=-\frac{1}{3}\\\\-3x-9y=3[/tex]

So, B-A is equal to -6.

Answer:

a. 33

Step-by-step explanation:

a straight line is 180° so

3x = 180 - 81

3x = 99

to find x divide by 3

x = 99/3

x = 33

The options Patel has to solve the quadratic equation 8x² + 16x + 3 = 0 is x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot.

8x² + 16x + 3 = 0

8x² + 16x = -3

8(x² + 2x) = -3

8(x² + 2x + 1) = -3 + 8

8(x² + 1) = 5

(x² + 1) = 5/8

(x + 1) = ± √5/8

x = -1 ± √5/8

Therefore,

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

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Answer:

[tex]a_{n} = -3n + 10[/tex]

Step-by-step explanation:

The arithmentic function formula is:

[tex]a_{n} = a_{1} + d(n-1)[/tex]

Let's plug in what we know. [tex]a_{1}[/tex] (the first term in our sequence) is 7. d (the common difference) is -3. This means we are subtracting 3 every time.

Plugging that in to the formula, we get

[tex]a_{n} = 7 -3(n-1)[/tex]

Now we distribute and combine like terms.

[tex]a_{n} = 7 - 3n +3[/tex]

[tex]a_{n} = 10 - 3n[/tex]

Change the order to fit the format and you get

[tex]a_{n} = -3n + 10[/tex]

When [tex]n=1[/tex],

[tex]10^{2\cdot1 - 1} + 1 = 10^1 + 1 = 11[/tex]

which is of course divisible by 11.

Assume this holds for [tex]n=k[/tex], that

[tex]11 \mid 10^{2k - 1} + 1[/tex]

In other words,

[tex]10^{2k - 1} + 1 = 11\ell[/tex]

for some integer [tex]\ell[/tex].

Use this to show the claim is true for [tex]n=k+1[/tex].

[tex]10^{2(k+1) - 1} + 1 = 10^{2k + 1} + 1 \\\\ ~~~~~~~~~~~~~~~~~~~~ = 10^{2k+1} + \left(10^{2k-1} + 10^{2k-1}\right) + 1 \\\\ ~~~~~~~~~~~~~~~~~~~~ = \left(10^{2k+1} - 10^{2k-1}\right) + \left(10^{2k-1} + 1\right) \\\\ ~~~~~~~~~~~~~~~~~~~~ = 10^{2k-1} \left(10^2 - 1\right) + 11\ell \\\\ ~~~~~~~~~~~~~~~~~~~~ = 99\times10^{2k-1} + 11\ell \\\\ ~~~~~~~~~~~~~~~~~~~~ = 11\left(9\times10^{2k-1} + \ell\right)[/tex]

which is indeed divisible by 11. QED

On the off-chance you meant [tex]10^{2^n-1}+1[/tex], notice that [tex]2n-1[/tex] is odd for any integer [tex]n[/tex]. Similarly [tex]2^n-1[/tex] is odd for all [tex]n[/tex], so the above proof actually proves this automatically.

Answer:

To know the final result we have to make 30% of 56 dollars and add the result to the 56 dollars to know the original price.

Operations:

30% de 56 = (30x56)/100= 16,8 dollars.

56+16,8= 72,8 dollars (final result)

A pair of shoes is reduced by 30% down to a price of £56 then the original price of the pair of shoes was £80.

To find the original price of a pair of shoes using a mathematical approach. We are given that the shoes were reduced by 30% and their final price is £56. We will use algebraic equations to determine the original price of the shoes.

Let's denote the original price of the shoes as "P". Since the shoes were reduced by 30%, we can express this reduction as a decimal, which is 0.30 (30% = 30/100 = 0.30).

The amount of reduction is then given by 0.30 multiplied by the original price, which is 0.30P.

The final price of the shoes after the reduction is £56. We can set up an equation to represent this:

P - 0.30P = 56

Now, let's simplify the equation:

0.70P = 56

Next, we need to isolate "P" on one side of the equation. To do this, we divide both sides by 0.70:

[tex]\[ \frac{{0.70P}}{{0.70}} = \frac{{56}}{{0.70}} \][/tex]

This simplifies to:[tex]\[ P = \frac{{56}}{{0.70}} \][/tex]

Now, let's calculate the value of "P":

[tex]\[ P = \frac{{56}}{{0.70}} = 80 \][/tex]

So, the original price of the pair of shoes was £80.

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The graph of the parabola can be seen in the image below.

We need to find some points on the parabola, and then draw a curve that connects them.

On the graph you already have the x-intercepts, so you already have two points.

Now let's get another point which is the vertex.

For our parabola:

[tex]y = -x^2 + 10x - 24[/tex]

The vertex is at:

[tex]x = -10/(2*-1) = 5[/tex]

Evaluating in x = 5 we get:

[tex]y = -5^2 + 10*5 - 24 = 1[/tex]

So we also have the point (5, 1), now we can just connect the points and get the parabola:

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Answer:

c

Step-by-step explanation:

consider points (0,2) and (-4,0)

slope=(0-2)/(-4-0)=-2/-4=1/2

y-intercept=2

y=mx+c

y=1/2 x+2

Answer:

y=1/2x+2

Step-by-step explanation:

The critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881

The scatter plot of the election is added as an attachment

From the scatter plot, we have the following highlights

Start by calculating the degrees of freedom (df) using

df =n - 2

Substitute the known values in the above equation

df = 8 - 2

Evaluate the difference

df = 6

Using the critical value table;

At a degree of freedom of 6 and significance level of 0.01, the critical value is

z = 0.834

From the list of given options, 0.834 is between  -0.881 and 0.881

Hence, the critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881

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There is no answer because there cannot be one to one function inverse.

[tex]s = c(1 + in) \\ s = 4000(1 + 0.03 \times 1) [/tex]

[tex]s = 4120.00[/tex]

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]x + y = 10\implies y = -x+10\implies y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+10 \leftarrow \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so, we're really looking for the equation of al ine whose slope is -1 and that passes through (-1 , 5)

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{-1}( ~~ x-\stackrel{x_1}{(-1) ~~ }) \\\\\\ y-5 = -(x+1)\implies y-5=-x-1\implies y=-x+4[/tex]

It can be said that the total amount of fuel that was used by Michael when he was away to his friends was 12 gallons.

The question said that the tank was full before he left to his friends. This was after he checked the gauge of the gas tank.

The question says that the required quantity needed to fill up this tank is 24 gallon. Hence if it is full, then the total gallon it had before he made this trip was 24 gallon.

Then we are told that he went ahead to check the gauge when he finished and was at home. The quantity of fuel he had at this time was 1/2 of what was there.

This would be 1/2 * 24

12

Hence he made use of 12 gallons when he was away.

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The table that represents exponential growth is the second table.

Exponential growth simply means a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.

Exponential growth is the pattern of data which shows sharper increases over time. In finance, compounding creates exponential returns and the savings accounts with a compounding interest rate can show exponential growth.

In this case, the second table described represents an exponential function. It has a common ratio of 4, meaning that each y-value is multiplied by 4 to get to the next value. Here, every time the Xs increase by 1, the Ys increase by a multiple of 4.

One of the best examples of exponential growth is observed in bacteria. Here, it takes bacteria roughly an hour to reproduce through prokaryotic fission. This illustrates exponential growth.

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Answer: B

Step-by-step explanation:

answer

is true statement w= 4

Answer:

√3/2

Step-by-step explanation:

This is compound angle of cosine

cos(11+19)

=cos(30)

=√3/2

Answer: slope is 1/3

Step-by-step explanation: make a graph of y=1/3x+9

The cost to rent each chair is $1.5 and cost to rent each table is $6.5

From the question, we are to determine the cost to rent each chair and each table

Let c represent chair

and

t represent table

From the given information,

The total cost to rent 5 chairs and 3 tables is $27

That is,

5c + 3t = 27 ------------ (1)

Also,

The total cost to rent 2 chairs and 12 tables is $81

That is,

2c + 12t = 81 ---------- (2)

Now, solve the equations simultaneously

5c + 3t = 27 ------------ (1)

2c + 12t = 81 ---------- (2)

Multiply equation (1) by 2 and multiply equation (2) by 5

2 × [5c + 3t = 27 ]

5 × [2c + 12t = 81 ]

10c + 6t = 54        ------------- (3)

10c + 60t = 405   ------------- (4)

Subtract equation (4) from equation (3)

10c + 6t = 54        

10c + 60t = 405

---------------------------

-54t = -351

t = -351/-54

t = 6.5

Substitute the value of t into equation (2)
2c + 12t = 81

2c + 12(6.5) = 81

2c + 78 = 81

2c = 81 - 78

2c = 3

c = 3/2

c = 1.5

∴ The cost of chair is $1.5 and cost of table is $6.5

Hence, the cost to rent each chair is $1.5 and cost to rent each table is $6.5

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Step-by-step explanation:

(52900 ÷ 28.7) × 100 = 184320 ( rounded to nearest whole number, since you cannot have half humans)

Answer:

[tex]\frac{5}{100}\times35[/tex]

[tex]0.05\times35[/tex]

Step-by-step explanation:

Given:

Which of the following options have the same value as 5% 35, percent of 35?

Following Options:

[tex]5 \times 35[/tex]

[tex]\frac{5}{100}\times35[/tex]

[tex]0.5\times0.35[/tex]

[tex]0.05\times35[/tex]

[tex]\frac{5}{10}\times35[/tex]

Solve:

[tex]5[/tex] % [tex]= 0.05=\frac{5}{100}[/tex]

Thus the following options:

[tex]5 \times 35[/tex]           [ False x ]

5 does not equal 5%

[tex]\frac{5}{100}\times35[/tex]         [True √ ]

[tex]5[/tex]% [tex]=\frac{5}{100}[/tex]

[tex]0.5\times0.35[/tex]      [ False x ]

[tex]0.5 = 0.50[/tex]

[tex]0.05\times35[/tex]       [True √ ]

[tex]5[/tex]% [tex]= 0.05=\frac{5}{100}[/tex]

[tex]\frac{5}{10}\times35[/tex]          [ False x ]

[tex]\frac{5}{10}=0.50[/tex]

Therefore, the options [B] [tex]\frac{5}{100}\times35[/tex] and [D] [tex]0.05\times35[/tex] is True.

Kavinsky

Answer: 40

Step-by-step explanation:

Sub x=4 into 3x²-2x+1

∴ 3(4)²-2(4)+1

=3(16)-8+1

=48-8+1

=40

Answer:

41

Step-by-step explanation:

substitute the x to 4

so 3(4)² - 2(4) + 1 = 41

With the use of formula, the amount of Iodine-125 that would remain in the tumor after 60 days is 0.45 grams

First analyze the problem and represent them in exponential function. The decay rate is different from increase rate with minus and plus sign.

Given that a tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. Let

An exponential model representing the amount of Iodine-125 remaining in the tumor after t days will be

A = I( 1 - R%)^t

Let us use the formula to find the amount of Iodine-125 that would remain in the tumor after 60 days by substituting all the given parameters into the formula

A = 0.9 ( 1 - 1.15/100)^60

A = 0.9 ( 1 - 0.0115)^60

A = 0.9 ( 0.9885)^60

A = 0.9 x 0.4995

A = 0.45 grams

Therefore, the amount of Iodine-125 that would remain in the tumor after 60 days is 0.45 grams

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9x - 4(x - 2) =x + 20

We move all terms to the left:

Multiply

We get rid of the parentheses.

We add all the numbers and all the variables.

We move all terms containing x to the left hand side, all other terms to the right hand side

Step-by-step explanation:

(2^2x²/xy²) for x=3 and y=2

we have

2^2(3)²/((3)(2²))

2^2(9)/((3)(4))

2^18/12

262144/12

21845.3

The value of  expression [tex]2^{2} x^{2}/xy^{2}[/tex]  for x=3 and y=2 is, 3

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,  [tex]2^{2} x^{2}/xy^{2}[/tex]

The value of expression when, x = 3 & y = 2

⇒  2²×3²/3×2²

⇒  3

Hence, The value is 3

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Proportionately, if they do half and half of 50% and 80% of the two bags, Bob is correct.

A proportion is a mathematical measure that compares two variables or numbers.

Proportions can be stated in percentages or ratios, as decimals or fractions.

Content of 16-ounce bag of nuts = 60% chocolate-covered nuts

Content of first bag = 50/50 plain and chocolate-covered nuts

Content of second bag = 80% chocolate-covered nuts

A mixture of half of 50% bag with half of 80% bag will result in 65% (50% + 80%)/2.

Thus, since the promise for each 16-ounce bag is for at least 60% chocolate-covered nuts, Bob is correct.

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Is Bob correct?