Evaluate a + b for a = 12 and b = 6.

The probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

Given that:

Find how many ways the 4 oldest people can be selected from the group.

Since the 4 oldest people are already determined, there is only 1 way to select them.

To calculate the probability, to determine the total number of ways to select 4 people from the group of 11. This can be found using the combination formula:

Number of ways to choose k items from n items :

C(n,k) = n! / (k!(n-k)!)

Calculate the total number of ways to select 4 people from the group:

Plugging n and k value from given data:

C(11,4 )= 11! / (4!(11-4)!)

On simplifications gives:

C(11, 4) = 330.

Calculate the probability:

Probability = Number of ways 4 oldest people selected / Total number of ways to select 4 people

Plugging the given data:

Probability = 1 / 330

Probability ≈ 0.00303 or 0.303%.

Therefore, the  probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

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Answer:

fourth option

Step-by-step explanation:

∠ FTC = ∠ MTL ( vertical angles )

Since FC and ML are parallel, then

∠ FCT = ∠ TML (corresponding angles )

Thus

Δ TCF ~ Δ TML by the AA postulate

Answer:

[tex]\large \boxed{\mathrm{similar, \ AA \ similarity}, \ \Delta TML}[/tex]

Step-by-step explanation:

The two triangles are similar.

We can prove by angle-angle similarity, in [tex]\mathrm{AA}[/tex] similarity, there are two pairs of congruent corresponding angles in two triangles, this proves the two triangles are similar.

[tex]\angle U[/tex] and [tex]\angle M[/tex] are a pair of congruent corresponding angles.

[tex]\angle V[/tex] and [tex]\angle L[/tex] are a pair of congruent corresponding angles.

Therefore,

[tex]\Delta TUV \sim \Delta TML[/tex]

Ernie will owe an interest of $268

Answer:

9  3  -7  -13

4  -4  11  8

0  9  2  -4

Step-by-step explanation:

9  3  -7  -13

4  -4  11  8

0  9  2  -4

Answer: 9  3  -7  -13

4  -4  11  8

0  9  2  -4

Step-by-step explanation:

Answer:$40.00

Step-by-step explanation:first divide 20 by 5 and the answer will be 4. now multiply 10 into 4 and you'll get the answer $40.00

Answer:

length: 9cm

width: 9cm

Step-by-step explanation:

9×9=81

Answer:

yd^2

Step-by-step explanation:

I took the test :)

The farmer calculate surface area in unit of [tex]yd^{2}[/tex]

The surface area of any given object is the area or region occupied by the surface of the object.

Thus , The farmer calculate surface area in unit of [tex]yd^{2}[/tex]

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Answer: an equation that has one term which is nameless and squared also no term which gets raised to higher power.

Step-by-step explanation:

[tex]f(x)=\sqrt{x+3}\\g(x)=8x-7\\\\f(g(x))=\sqrt{8x-7+3}=\sqrt{8x-4}[/tex]

Answer:

5x+4f-1(x)=3 this is short answer

Answer:

1. add 1/2x to both sides

a. you want to combine the like terms. in this case, it is the x variable.

you are left with 7/6x = 5

2. multiply by 6/7

a. the reciprocal of 7/6 will cancel out the values

Answer:

  C. G(x) = x - 9

Step-by-step explanation:

You know that the transformation ...

  g(x) = f(x -h) +k

causes parent function f(x) to be shifted right h units and up k units.

You're looking for a function that is shifted right, so you want something that looks like ...

  g(x) = f(x -constant) = x - constant

Choice C has that form:

  C. G(x) = x - 9

_____

A. the function is shifted up 2 units

B. the function is vertically expanded by a factor of 4 (no shift)

C. shifted right

D. the function is reflected over the y-axis (no shift)

Answer: C [G(x) = x-9]

Step-by-step explanation:

I got it right

Answer:

bonds: $65,000

cd's: $30,000

stocks: $20,000

Step-by-step explanation:

b + c + s = 115000

0.045b + 0.0325c + 0.082s = 5540

b = c + 35000

b = 65,000

c = 30,000

s = 20,000

Step-by-step explanation:

Hey, there!

Given, equations are,

2x+y=10.............(i)

-3x+y= -5...........(ii)

From equation (i)

y=10- 2x...........(iii)

Putting the value of "y" from equation (iii) in equation (ii).

-3x+y= -5

-3x + (10-2x)= -5

-3x + 10-2x= -5

- 5x = -15

[tex]x = \frac{ - 15}{ - 5} [/tex]

Therefore, x= 3.

Now, putting the value of "x" in equation (iii).

y= 10- 2x

y= 10- 2×3

Therefore, y= 4.

Hope it helps...

Answer:

[tex]\boxed{6.875 \text{\: grams}}[/tex]

Step-by-step explanation:

Half-lives are how long it takes for half of a substance to decay. If you start with a certain amount and it decays for a certain amount of half-lives, you are dividing by [tex]2^{x}[/tex], where x  is equal to the amount of half-lives.

In order to solve this question, simply divide the starting value by 2 raised to the value of half-lives.

[tex]\large\boxed{\frac{220}{2^{5}}=6.875\text{\: grams}}[/tex]

Answer:

As the calculated value of t is greater than critical value reject H0. The tests supports the claim at ∝= 0.05

If the p-value for the test statistic for this hypothesis test is 0.014, then the critical region is t ( with df=9) for a right tailed test is 2.821

then we would accept H0. The test would not support the claim at ∝= 0.01

Step-by-step explanation:

Mean x`= 518 +548 +561 +523 + 536 + 499+  538 + 557+ 528 +563 /10

x`= 537.1

The Variance is  = 20.70

H0 μ≤ 520

Ha μ > 520

Significance level is set at ∝= 0.05

The critical region is t ( with df=9) for a right tailed test is 1.8331

The test statistic under H0 is

t=x`- x/ s/ √n

Which has t distribution with n-1 degrees of freedom which is equal to 9

t=x`- x/ s/ √n

t = 537.1- 520 / 20.7 / √10

t= 17.1 / 20.7/ 3.16227

t= 17.1/ 6.5459

t= 2.6122

As the calculated value of t is greater than critical value reject H0. The tests supports the claim at ∝= 0.05

If the p-value for the test statistic for this hypothesis test is 0.014, then the critical region is t ( with df=9) for a right tailed test is 2.821

then we would accept H0. The test would not support the claim at ∝= 0.01

Answer:

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval

(3) A survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

Step-by-step explanation:

We are given that a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                         P.Q.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of Americans who decide to not go to college = 48%

           n = sample of American adults = 331

           p = population proportion of Americans who decide to not go to

                 college because they cannot afford it

Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.

So, 90% confidence interval for the population proportion, p is ;

P(-1.645 < N(0,1) < 1.645) = 0.90  {As the critical value of z at 5% level

                                                        of significance are -1.645 & 1.645}  

P(-1.645 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.645) = 0.90

P( [tex]-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]\hat p-p[/tex] < [tex]1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90

P( [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90

90% confidence interval for p = [ [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

 = [ [tex]0.48 -1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] , [tex]0.48 +1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] ]

 = [0.4348, 0.5252]

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) The interpretation of the above confidence interval is that we can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.

3) Now, it is given that we wanted the margin of error for the 90% confidence level to be about 1.5%.

So, the margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]

              [tex]0.015 = 1.645 \times \sqrt{\frac{0.48(1-0.48)}{n} }[/tex]

              [tex]\sqrt{n} = \frac{1.645 \times \sqrt{0.48 \times 0.52} }{0.015}[/tex]

              [tex]\sqrt{n}[/tex] = 54.79

               n = [tex]54.79^{2}[/tex]

               n = 3001.88 ≈ 3002

Hence, a survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

Answer:

  C.  -1

  D.  1

Step-by-step explanation:

A perfect linear relationship is indicated by a correlation with a magnitude of 1. The sign of the correlation coefficient is the sign of the slope of the line describing the relationship. It may be positive or negative.

The appropriate choices are ...

  C.  -1

  D.  1

Answer:

c=-1

d=1

Step-by-step explanation:

Answer:

22.57 x 28

Step-by-step explanation:

10.86 + 4x = 101.14

-10.86           -10.86

            4x = 90.28

             /4       /4

              x = 22.57

5.43 + 22.57 = 28

22.57

Answer:

5 seconds

Step-by-step explanation:

Well we know that when the soccer ball is on the ground the height will be 0.

So we replace y with 0 and solve for x.

0=-12x²+60x

factor out and divide x, (this x is x=0, which is before he kicked it)

0=-12x+60

subtract 60 from both sides

-60=-12x

x=5

Answer:

600

Step-by-step explanation:

first, 40% of 15000 is 6000,

10% of 6000, which is the number of students studying mathematics as well as science, 600

Answer:

•600 students studied both the subject.

Answer:

infinite solutions along the line y = 2x+1

Step-by-step explanation:

3y – 6x = 3

y = 2x + 1

Replace y in the first equation with the second equation

3 ( 2x+1) -6x =3

6x +3 -6x = 3

3=3

This is always true so there are infinite solutions along the line y = 2x+1

Step-by-step explanation:

Hi, there!!!

you mean to solve it, right.

then let's begin...

3y-6x=3..........epuation 1.

y = 2x+1..........equation 2.

now, substituting the value y of equation 2 in equation 1. so, we get,

3y-6x=3

or, 3(2x+1) -6x = 3

or, 6x+3-6x=3

by simplifying it we get, 3=3

so, this equation can have infinite solution.

you may have wrote wrong question ..

0riginal break even point:

285000/ 60/35 = $166,250

New break even point = new fixed costs / ( selling price - variable cost/ selling price)

New break even point = 285,000 + 15,900. / ( 60-( 35-4.50)/60

300,900 / 60-30.50/60 = $612,000

The new break even point increases.

Answer:

1. $-50

2. $25

Step-by-step explanation:

1. If she had $150 in her bank account and bought a bike for $200, then that means she spent all of her money PLUS $50 extra then what she had.  That means $200-$150=$50.  Her $150 is spent and that $50 becomes negative because she paid $200 when she only had $150.

2.  If she deposits $75 in her account then it will be $75+(-50).  That translates to $75-$50 which is $25.  

+ and - = -

+ and + = +

- and - = +

Answer:

1. $-50

2. $25

Step-by-step explanation:

1.

We know that Clare originally had $150 in her account. She then buys a bike, which means she must have taken money out of her account for this purchase.

Since she spent $200, we need to subtract 200 from 150:

150 - 200 = -50

So, her account balance is $-50.

2.

Clare earns $75 later, which means she's receiving the money and can add it back into her account. Her current balance is -50, so we add 75 to -50:

-50 + 75 = $25

Thus, her account balance is now $25.

~ an aesthetics lover

x = number of 1-cent stamps

y = number of 8-cent stamps

z = number of 12-cent stamps

We have 31 stamps all together, so x+y+z = 31.

"I have 4 more 1-cent stamps than 8-cent stamps" means we have the equation x = y+8. Whatever y is, add 8 to it to get x. Solve for y to get y = x-8.

You also have "twice as many one cent stamps as 12 cent stamps", so x = 2z. Solving for z gets you z = 0.5x

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

x+y+z = 31

x+x-8+z = 31 ... y replaced with x-8

x+x-8+0.5x = 31 ... plug in z = 0.5x

2.5x-8 = 31

2.5x = 31+8

2.5x = 39

x = 39/2.5

x = 15.6

Your teacher made a typo somewhere because we should get a positive whole number result for x (since x is a count of how many 1-cent stamps we have).

The number of one-cent stamps is 14.

Total stamps = 31
We have three types of stamps: 1-cent stamps, 8-cent stamps, and 12-cent stamps.

The person has 4 more 1-cent stamps than 8-cent stamps.

The person has twice as many 1-cent stamps as 12-cent stamps.

We have to make equations with the given above statement.

Consider,

1-cent stamp = A

8-cent stamp = B

12-cent stamp = C

4 more 1-cent stamps than 8-cent stamps: A = 4 + B.

A = 4 + B

B = A - 4..........(1)

Twice as many 1-cent stamps as 12-cent stamps: A = 2C.

A = 2C

C = A/2...............(2)

Total number of stamps = 31

A + B + C = 31................(3)

Putting (1) and (2) in (3)

we get,

A + ( A - 4 ) + A / 2 = 31

A + A - 4 + A / 2 = 31

2A - 4 + A / 2 = 31

2A + A / 2 = 31 + 4

(4A + A) / 2 = 35

4A + A = 35 x 2

5A = 70

A = 70 / 5

A = 14

Thus the number of 1-cent stamps is 14.

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Answer:

x=9; one ticket is $9

Step-by-step explanation:

4x+12=48

4x=48-12

4x=36

x=36/4

x=9

Answer:

The passenger train is moving at 45 miles per hour

Step-by-step explanation:

Let the amount of time it took the two trains to travel the distance = t.

Since the two trains traveled the distance at the same time,

Rate of the passenger train =[tex]\frac{180}{t}[/tex]

Rate of the freight train = [tex]\frac{120}{t}[/tex]

Where t is in hours.

From the problem, we can see that the rate of the freight train was 15 miles per hour slower than the rate of the passenger train. Mathematically, we can represent this as

[tex]\frac{120}{t}= \frac{180}{t}-15[/tex]

from the above equation, we can now get our value for t  as

[tex]\frac{120-180}{t}=-15\\\frac{-60}{t}=-15\\t=4 hours[/tex]

We have our time of travel for the two trains as 4 hours.

The rate of the passenger train can now be calculated by 180/4 = 45 miles per hour

Answer:

a. 4

Step-by-step explanation:

-1(-4) = 4

Answer:

A 4

Step-by-step explanation:

opposite of –4 = 4

Answer:

Step-by-step explanation:

Given the inequality [tex]|z+4|>15[/tex], we are to find the solution set of the inequality. Since the the function is an absolute value, this means that the function will be positive and negative.

For the positive value of the function;

[tex]z+4>15\\\\subtract\ 4\ from \ both \ sides\\z+4-4 > 15 -4\\\\z>11[/tex]

For the negative value of the function we have;

[tex]-(z+4) > 15\\\\-z-4> 15\\add\ 4 \ to\ both \ sides\\\\-z-4+4> 15+4\\\\-z> 19\\\\[/tex]

Multiplying both sides of the inequality by -1 will change the sense of the inequality sign;'

[tex]-(-z)< -19\\\\z<-19[/tex]

Hence the solution sets are [tex]z> 11 \ and \ z< -19 \\[/tex] OR z less-than negative 19 or z greater-than 11

Answer:

z less-than negative 19 or z greater-than 11

Step-by-step explanation:

Answer:

(d-4)(c-9)

Step-by-step explanation:

cd-9d-4c+36

d(c-9)-4(c-9)

pull out the (c-9),

(d-4)(c-9)