Write in if-then form: “Being 35 years old is a necessary condition for being President.”

Answer:

3

Step-by-step explanation:

there are two solutions in the given system of two equations:

a=10; b=7 and a=7; b=10.

|a-b|=3.

Answer with explanation:

Sample mean of 81 full Professor = $ 77,220

Sample Standard Deviation (S)= $ 4500

Sample mean= $77,220

[tex]Z_{98 \text{Percent}=\frac{98}{100}}\\\\Z_{98 \text{Percent}=0.8365}\\\\Z_{\text Score=\frac{\bar x -\mu}{\sigma}}\\\\0.84=\frac{77220- \mu}{4500}\\\\\mu=77220-3780\\\\ \mu=73440[/tex]

So, When , z=98% , then Mean Salary ( μ)=73,440

Answer:

[tex]\$13,013.17[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=10/12\ years\\ P=?\\ A=\$14,000\\r=0.091[/tex]

substitute in the formula above  

[tex]\$14,000=P(1+0.091*(10/12))[/tex]

[tex]P=\$14,000/(1+0.091*(10/12))[/tex]

[tex]P=\$13,013.17[/tex]

Answer:

A

Step-by-step explanation:

14 is A because its dividing and operating

Answer:

D, D

Step-by-step explanation:

Nickels are $0.05, Dimes are $0.10 and quarters are $0.25

Simply work out the options and see which one gives you $1.95

A) By observation, we see that this combination has 16 coins, but the question says only 15 coins. Hence we can remove this as an option.

B) 5($0.05) + 7($0.10) + 3($0.25) = $1.70 ≠ $1.95 (wrong)

C) 7($0.05) + 6($0.10) + 2($0.25) = $1.45 ≠ $1.95 (wrong)

D) 3($0.05) + 8($0.10) + 4($0.25) = $1.95 (Correct)

FOr next question, D is not a function because if you observe the values in D, an input of 7 should give 11 i.e (7,11), but there is another option where 7 gives an output of 13 i.e (7,13).

Because for a function to be valid, one input cannot give 2 different outputs, D is not a function.

By definition of expectation,

[tex]\displaystyle E[X]=\sum_xx\,P(X=x)=\sum_{x=1}^n\frac xn=\frac{n(n+1)}{2n}=\boxed{\frac{n+1}2}[/tex]

and variance,

[tex]V[X]=E[(X-E[X])^2]=E[X^2-2X\,E[X]+E[X]^2]=E[X^2]-E[X]^2[/tex]

Also by definition, we have

[tex]E[f(X)]=\displaystyle\sum_xf(x)\,P(X=x)[/tex]

so that

[tex]E[X^2]=\displaystyle\sum_{x=1}^n\frac{x^2}n=\frac{n(n+1)(2n+1)}{6n}=\frac{(n+1)(2n+1)}6[/tex]

and finally,

[tex]V[X]=\dfrac{(n+1)(2n+1)}6-\dfrac{(n+1)^2}4=\boxed{\dfrac{n^2-1}{12}}[/tex]

Answer:

[tex]\frac{n^{2} - 1 }{12}[/tex]

Step-by-step explanation:

Data:

We collect the variables and simplify the result:

E[X] = [tex]\SIGMA \\[/tex]Σ x · p(x) = [tex]\frac{1}{n}[/tex]= ....

E[X²] =∑ x²· p(x) = ∑x²·[tex]\frac{1}{n}[/tex] = ....

Var [X] = E[X²] - E[X]² = ...

We then use the identities:

∑x = [tex]\frac{n(n+1)}{2}[/tex] and ∑ x² = [tex]\frac{n(n+1)(2n+1)}{6}[/tex]

simplifying the identities above gives:

[tex]\frac{n^{2-1} }{12}[/tex]

Answer:

The value of x = 96°

Step-by-step explanation:

Here we consider two angles be <1, <2 and < 3, where <1 is the linear pair of angle measures 130° and <2 be the linear pair of angle measures 134°

To find the value of m<1

m<1 = 180 - 130 = 50°

To find the value of m<2

m<2 = 180 - 134 = 46°

To find the value of m<3

By using angle sum property,

m<1 + m<2 + m< 3 = 180

m<3 =180 - (m<1 + m<2)

 = 180 - (50 + 46 = 96

 = 84°

To find the value of x

Here x and <3 are linear pair,

x + m<3 = 180

x = 180 - m<3

 = 180 - 84 = 96°

Therefore the value of x = 96°

Answer: 0.05699

Step-by-step explanation:

The total number of cards in a deck = 52

The total number of black cards = 26

Then ,[tex]\text{P(Black)}=\dfrac{C(26,4)}{C(52,4)}=0.00182842367\approx0.00183[/tex]

The total number of face cards = 12

Then , [tex]\text{P(Face)}=\dfrac{C(12,4)}{C(52,4)}\approx0.05522[/tex]

The number of cards that are black and face cards = 6

Then , [tex]\text{P(Black and Face )}=\dfrac{C(6,4)}{C(52,4)}\approx0.00006[/tex]

Then , the probability that a randomly drawn hand of four cards contains all black cards or all face cards is given by :-

[tex]\text{P(Black or Face)}=\text{P(Black)+P(Face)-P(Black and Face)}\\\\\Rightarrow\ \text{P(Black or Face)}=0.00183+0.05522-0.00006\\\\\Rightarrow\ \text{P(Black or Face)}=0.05699[/tex]

Answer:

Step-by-step explanation:

It’s nothing

Answer:

  7

Step-by-step explanation:

The function can be written in vertex form as ...

  f(x) = -(x +1)^2 +7

The vertex is then identifiable as (-1, 7). The y-coordinate is 7.

_____

Vertex form is ...

  f(x) = a(x -h)^2 +k

where "a" is the vertical scale factor, and (h, k) is the vertex point. It is convenient to arrive at this form by factoring "a" from the first two terms, then adding and subtracting the square of the remaining x-coefficient inside and outside parentheses.

  f(x) = -(x^2 +2x) +6

  f(x) = -(x^2 +2x +1) + 6 -(-1) . . . . completing the square

  f(x) = -(x +1)^2 +7 . . . . . . . . . . . . vertex form; a=-1, (h, k) = (-1, 7)

The y-coordinate of the vertex of the parabola defined by the function f(x)= -x² - 2x + 6 is 3. This is found by using the vertex formula and then substituting the x-coordinate back into the original function.

To find the y-coordinate of the vertex of the parabola defined by the quadratic function f(x)= -x² - 2x + 6, we can use the vertex formula for a parabola in standard form, which is y = ax² + bx + c. The x-coordinate of the vertex is given by the formula -b/(2a), and the y-coordinate can then be calculated by applying the x-coordinate to the original function.

First, let's find the x-coordinate of the vertex:

x-coordinate of the vertex, x_v = -(-2)/(2*(-1)) = -(-2)/(-2) = 1

Now, substitute x_v back into the function to find the y-coordinate:

y-coordinate of the vertex, y_v = f(1) = -1² - 2*1 + 6 = -1 - 2 + 6 = 3

Therefore, the y-coordinate of the vertex is 3.

Answer:

[tex]x^{2} \neq -\frac{1}{14}[/tex]

Step-by-step explanation:

The equation will hold true as long as the denominator does not equal zero:

so take the denominator and set it equal to zero and find x. when you find x, that will be your answer:

-14x^2 -1=0

-14x^2=1

-x^2=1/14

x^2=-1/14

For this case we have that by definition, the area of a rectangle is given by:

[tex]A = ab[/tex]

Where:

a, b: They are the sides of the rectangle

We have as data that the area of the rectangle is given by:

[tex]x ^ 2-4x-12[/tex]

IF we factor the expression, we must find two numbers that when multiplied give as a result "-12" and when summed give as result "-4". These numbers are: -6 and +2:

[tex](x-6) (x + 2)[/tex]

Thus, the sides of the rectangle are given by:

[tex](x-6) (x + 2)[/tex]

Answer:

Option A

Note that adding the first two equations gives

[tex](4x-y+3z)+(x+4y+6z)=12+(-32)\implies5x+3y+9z=-20[/tex]

But the third equation says [tex]5x+3y+9z=20[/tex], so there is no solution.

Answer:

The price is $3.36 per infinity stone

Step-by-step explanation:

we know that

Five infinity stones cost $16.80

so

To find the price of each infinity stone (unit rate) divide the total cost by five

[tex]\frac{16.80}{5} =3.36\frac{\$}{infinity\ stone}[/tex]

Answer: C. -4 percent

Step-by-step explanation:

Nominal interest rate is the interest rate before taking inflation into account.

Real interest rate takes the inflation rate into account.

The equation that links all three values is

nominal rate - inflation rate = real rate

6 - 10 = -4

-4 percent

The real interest rate can be calculated by subtracting the inflation rate from the nominal interest rate. In this case, the real interest rate is -4%, suggesting an investor would lose value due to inflation.

The calculation of the real interest rate involves subtracting inflation from the nominal interest rate. This is essential since inflation erodes the purchasing power of money, making it an important factor to consider when dealing with interest rates. In this case, you need to subtract the inflation rate (10 percent) from the nominal interest rate (6 percent).

So, performing this calculation:
6% (Nominal Interest Rate) - 10% (Inflation Rate) = -4%

Thus, in this scenario, the correct option would be C. -4 percent. This implies that an investor would actually lose ground when considering the effect of inflation.

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Answer:

[tex]\large\boxed{\left(r+\dfrac{1}{4}\right)\left(r-\dfrac{1}{4}\right)=r^2-\dfrac{1}{16}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ (a+b)(a-b)=a^2-b^2\\\\\left(r+\dfrac{1}{4}\right)\left(r-\dfrac{1}{4}\right)=r^2-\left(\dfrac{1}{4}\right)^2=r^2-\dfrac{1^2}{4^2}=r^2-\dfrac{1}{16}[/tex]

[tex](a+b)(a-b)=a^2-b^2[/tex]

[tex]\left(r+\dfrac{1}{4}\right)\left(r-\dfrac{1}{4}\right)=r^2-\dfrac{1}{16}[/tex]

The cost to run a 1500 W hair dryer for 10 minutes in Los Angeles during July 2017 is:

                   4.45 cents

Electric power costs 17.8 cents per kWh in Los Angeles in July 2017.

Now we are asked to find the cost to run  a 1500 W hair dryer for 10 minutes in Los Angeles during July 2017.

We know that: 1 w=0.001 kW

This means that:

   1500 W= 1.500 kW

Also, it is used for 10 minutes

i.e. 1/6 hours

Hence, the electric power used to run the hair dryer is: 1.500×(1/6)

i.e. Electric power to used by hair dryer is: 0.25 kWh

Cost of 1 kwh is: 17.8 cents

This means that cost of 0.25 kwh is: 17.8×0.25

                                                        =  4.45 cents

Hence, the answer is:

                      4.45 cents

Answer:

Your answer should be -8.

Answer:

A.

[tex]y - 5 = -2(x-6)[/tex]

Negative reciprocal gives you the perpendicular slope so negative reciprocal of 1/2 is -2.

Then apply point-slope form.

B. The answer is x = 6.

The midpoint of JK is

[tex]\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{8+ 4}{2}, \frac{4 + 4}{2} \right) = \left(6,4\right)[/tex]

The line that goes through JK is just a horizontal line [tex]y = 4[/tex] because the y-coordinate does not change. So its perpendicular bisector is the vertical line that goes through the x-coordinate of the midpoint, that is, [tex]x = 6[/tex].

Answer:

The average rate of change is [tex]\frac{18}{5}[/tex]

Step-by-step explanation:

Given function that shows the population of a culture of cells,

[tex]P(t)=\frac{90t}{t+1}------(1)[/tex]

Where, t represents the number of weeks.

Thus, the average rate of change in the population over the interval [0,24],

[tex]m=\frac{P(24)-P(0)}{24-0}[/tex]

From equation (1),

[tex]=\frac{\frac{90\times 24}{24+1}-\frac{90\times 0}{0+1}}{24}[/tex]

[tex]=\frac{\frac{2160}{25}-\frac{0+1}{0}}{24}[/tex]

[tex]=\frac{2160}{25\times 24}[/tex]

[tex]=\frac{2160}{600}[/tex]

[tex]=\frac{18}{5}[/tex]

The graph approaches positive infinity at a constant rate.

The end behavior of this graph is:

As x → -∞, f(x) → +∞

For the first notation it looks at the behavior of the left side of the graph. As x approaches negative infinity (or positive xs) y or f(x) approaches positive infinity (or positive ys)

and

As x → +∞, f(x) → +∞

For the second notation it looks at the behavior of the right side of the graph. As x approaches positive infinity (or positive x's) y or f(x) approaches positive infinity (or positive ys)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: The graph approaches positive infinity at a constant rate.

Step-by-step explanation:

For this case we propose a system of equations:

x: Variable representing the anticipated tickets

y: Variable representing the same day tickets

So:

[tex]x + y = 45\\25x + 35y = 1375[/tex]

We clear x from the first equation:

[tex]x = 45-y[/tex]

We substitute in the second equation:

[tex]25 (45-y) + 35y = 1375\\1125-25y + 35y = 1375\\10y = 1375-1125\\10y = 250\\y = 25[/tex]

We look for the value of x:

[tex]x = 45-25\\x = 20[/tex]

Thus, 20 of anticipated type and 25 of same day type were sold.

Answer:

20 of anticipated type and 25 of same day type were sold.

Answer: 20 advance tickets and 25 same-day tickets.

Step-by-step explanation:

Set up a system of equations.

Let be "a" the number of advance tickets and "s" the number of same-day tickets.

Then:

[tex]\left \{ {{25a+35s=1375} \atop {a+s=45}} \right.[/tex]

You can use the Elimination method. Multiply the second equation by -25, then add both equations and solve for "s":

[tex]\left \{ {{25a+35s=1,375} \atop {-25a-25s=-1,125}} \right.\\.............................\\10s=250\\\\s=\frac{250}{10}\\\\s=25[/tex]

Substitute [tex]s=25[/tex] into an original equation and solve for "a":

[tex]a+(25)=45\\\\a=45-25\\\\a=20[/tex]

Answer:

  diagonal ≈ 18.43 cm

Step-by-step explanation:

Let L represent the length of the rectangle. Then the width is ...

  w = 2L -4 . . . . . . 4 less than twice the length

The area is ...

  A = wL = (2L -4)L = 2L² -4L

The area is said to be 153 cm², so we have ...

  2L² -4L = 153

  2L² -4L -153 = 0 . . . . . . subtract 153 to put into standard form

We can find the solution to this using the quadratic formula. It tells us the solution to ax²+bx+c=0 is given by ...

  x = (-b±√(b²-4ac))/(2a)

We have a=2, b=-4, c=-153, so our solution for L is ...

  L = (-(-4) ±√((-4)²-4(2)(-153)))/(2(2)) = (4±√1240)/4

Only the positive solution is of interest, so L = 1+√77.5.

__

Now we know the rectangle is 1+√77.5 long and -2+2√77.5 wide. The diagonal (d) is the hypotenuse of a right triangle with these leg lengths. Its measure can be found from ...

  d² = w² +L² = (-2+2√77.5)² +(1+√77.5)²

It can work well to simply evaluate this using a calculator, or it can be simplified first.

  d² = 4 -8√77.5 +4·77.5 + 1 +2√77.5 +77.5 = 392.5 -6√77.5

Taking the square root gives the diagonal length:

  d = √(392.5 -6√77.5) ≈ 18.43 . . . . cm

Answer with explanation:

For, a 3 × 3, matrix

[tex]r_{1}=(3,-2,0)\\\\r_{2}=(0,1,1)\\\\r_{3}=(2,-1,0)[/tex]

which are entries of First, Second and Third Row Respectively.

So, if written in the form of Matrix (A)

 [tex]A=\left[\begin{array}{ccc}3&-2&0\\0&1&1\\2&-1&0\end{array}\right][/tex]

⇒Adjoint A= Transpose of Cofactor of A

[tex]a_{11}=1,a_{12}=2,a_{13}=-2\\\\a_{21}=0,a_{22}=0,a_{23}=-1\\\\a_{31}=-2,a_{32}=- 3,a_{33}=3\\\\Adj.A=\left[\begin{array}{ccc}1&0&-2\\2&0&-3\\-2&-1&3\end{array}\right][/tex]

⇒≡ |Adj.A|=1 ×(0-3) -2×(-2-0)

            = -3 +4

            =1     --------(1)

⇒For, a Matrix of Order, 3 × 3,

| Adj.A |=| A|²---------(2)

[tex]|2 A^{-2}|=2^3\times |A^{-2}|\\\\=2^3\times |A|^{-2}\\\\=\frac{8}{|A^{2}|}\\\\=\frac{8}{|Adj.A|}\\\\=\frac{8}{1}\\\\=8[/tex]

                                              --------------------------------------------(Using 1 and 2)

[tex]\rightarrow|2 A^{-2}|=8[/tex]

Answer:

yes

Step-by-step explanation:

it is absolutely true that biononmials always gives biononmials when added

If X and Y are independent, then X+Y is not a binomial random variable and so it is a false statement.

This term is known to be a binomial random variable that occurs when all the parts of the variables is said to have similar success probability.

The best method to check if two random variables are said to be independent is through the  calculation of the covariance of the two specific random variables.

Note that if If the variables are said to be independent (X and Y), then their difference is said to be not binomially distributed.

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Answer:

a. 0.047

b. Unlikely.

Step-by-step explanation:

a. The probability of a test result being wrong for a person not using mrijuana  = 8 / 170 = 0.047.

b. As the probability for a wrong result is < 0.05 we can say that the test is unlikely to be wrong.

Answer:

25.8

Step-by-step explanation:

Answer: 0.0026

Step-by-step explanation:

Given: Mean : [tex]\mu=8.4\text{ hours}[/tex]

Standard Deviation : [tex]\sigma = 1.8\text{ hours}[/tex]

Sample size : [tex]n=40[/tex]

Formula to calculate z-score :-

[tex]z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For X=7.6 hours.

[tex]z=\dfrac{7.6-8.4}{\dfrac{1.8}{\sqrt{40}}}=-2.81091347571\approx-2.8[/tex]

[tex]P(X<7.6)=P(Z<-2.8)=0.0025551\approx0.0026[/tex]

Hence, the probability that their mean rebuild time is less than 7.6 hours = 0.0026

The probability that their mean rebuild time is less than 7.6 hours is 0.0026

A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 7.6 hours.

The Chevrolet Cavalier is the line of small cars produced for the model years 1982 until 2005 by Chevrolet. Mechanics is the physics area concerned with the motions of macroscopic objects. The mean is the number average. To calculate we add up all the numbers then divide by how many numbers there are. In other words it is the sum divided by the count.

[tex]\mu = 8.4 hours[/tex]

[tex]\sigma = 1.8 hours[/tex]

[tex]n=40[/tex]

[tex]z = \frac{Xbar -\mu}{\frac{\sigma}{\sqrt{r} } } = \frac{7.6-8.4}{\frac{1.8}{\sqrt{40} } } = -2.81[/tex]

Therefore the value of  Xbar < 7.6 hours. from the standard normal table is 0.0026

Hence, the probability that their mean rebuild time is less than 7.6 hours is  0.0026  = 0.26%.

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Answer:

x < 2

Step-by-step explanation:

[tex]2x+1 <5\\ 2x <4\\x <2[/tex]

For this case we have the following inequality:

[tex]2x + 1 <5[/tex]

Subtracting 1 from both sides of the inequality we have:

[tex]2x <5-1\\2x <4[/tex]

Dividing between 2 on both sides of the inequality:

[tex]x <\frac {4} {2}\\x <2[/tex]

Thus, the solution is given by all values of "x" less than 2.

Answer:

[tex]x <2[/tex]

Answer:

About 0.3 billion dollars

Step-by-step explanation:

5 years = 60 months.

The 150 of the first month will be 150*1.07^60 in 5 years.

The 150 of the second month will be 150*1.07^59 in 5 years.

The 150 of the third month will be 150*1.07^58 in 5 years.

And so forth.

So we sum that up:

( sum_(n=1)^(60) 150×1.07^n)

And multiply with

× 1.07^(5×23)

to account for the increase in value in the following 23 years.

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y\geq -x^{2}-1[/tex]

The solution of the inequality is the shaded area above the solid line of the equation of the  parabola [tex]y= -x^{2}-1[/tex]

The vertex of the parabola is the point (0,-1)

The parabola open downward (vertex is a maximum)

using a graphing tool

see the attached figure