A couple plans to invest money into an account that earns 9% interest, compounded quarterly, for their child's college education. What principal must be deposited by the parents in order to have $25,000 after 13 years?

Answer:

The chance that there will be exactly 2 heads among the first five tosses and exactly 4 heads among the last 5 tosses is P=0.0488.

Step-by-step explanation:

To solve this problem we divide the tossing in two: the first 5 tosses and the last 5 tosses.

Both heads and tails have an individual probability p=0.5.

Then, both group of five tosses have the same binomial distribution: n=5, p=0.5.

The probability that k heads are in the sample is:

[tex]P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{5}{k}\cdot0.5^k\cdot0.5^{5-k}[/tex]

Then, the probability that exactly 2 heads are among the first five tosses can be calculated as:

[tex]P(x=2)=\dbinom{5}{2}\cdot0.5^{2}\cdot0.5^{3}=10\cdot0.25\cdot0.125=0.3125\\\\\\[/tex]

For the last five tosses, the probability that are exactly 4 heads is:

[tex]P(x=4)=\dbinom{5}{4}\cdot0.5^{4}\cdot0.5^{1}=5\cdot0.0625\cdot0.5=0.1563\\\\\\[/tex]

Then, the probability that there will be exactly 2 heads among the first five tosses and exactly 4 heads among the last 5 tosses can be calculated multypling the probabilities of these two independent events:

[tex]P(H_1=2;H_2=4)=P(H_1=2)\cdot P(H_2=4)=0.3125\cdot0.1563=0.0488[/tex]

Answer:

[tex] 3x - y = 5 [/tex]

Step-by-step explanation:

The two pint equation of a line:

[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]

We have

[tex] x_1 = 4 [/tex]

[tex] x_2 = 3 [/tex]

[tex] y_1 = 7 [/tex]

[tex] y_2 = 4 [/tex]

[tex] y - 7 = \dfrac{4 - 7}{3 - 4}(x - 4) [/tex]

[tex] y - 7 = \dfrac{-3}{-1}(x - 4) [/tex]

[tex] y - 7 = 3(x - 4) [/tex]

[tex] y - 7 = 3x - 12 [/tex]

[tex] 5 = 3x - y [/tex]

[tex] 3x - y = 5 [/tex]

Answer:

HL (try HL, I believe that's the right answer)

Answer:

HL

Step-by-step explanation:

BRO TRUST ME

Answer:

a) E(X) = 16.09 ft³

E(X²) = 262.22 ft⁶

Var(X) = 3.27 ft⁶

b) E(22X) = 354 dollars

c) Var(22X) = 1,581 dollars

d) E(X - 0.01X²) = 13.470 ft³

Step-by-step explanation:

The complete Correct Question is presented in the attached image to this solution.

a) Compute E(X), E(X2), and V(X).

The expected value of a probability distribution is given as

E(X) = Σxᵢpᵢ

xᵢ = Each variable in the distribution

pᵢ = Probability of each distribution

Σxᵢpᵢ = (13.5×0.20) + (15.9×0.59) + (19.1×0.21)

= 2.70 + 9.381 + 4.011

= 16.092 = 16.09 ft³

E(X²) = Σxᵢ²pᵢ

Σxᵢ²pᵢ = (13.5²×0.20) + (15.9²×0.59) + (19.1²×0.21)

= 36.45 + 149.1579 + 76.6101

= 262.218 = 262.22 ft⁶

Var(X) = Σxᵢ²pᵢ - μ²

where μ = E(X) = 16.092

Σxᵢ²pᵢ = E(X²) = 262.218

Var(X) = 262.218 - 16.092²

= 3.265536 = 3.27 ft⁶

b) E(22X) = 22E(X) = 22 × 16.092 = 354.024 = 354 dollars to the nearest whole number.

c) Var(22X) = 22² × Var(X) = 22² × 3.265536 = 1,580.519424 = 1,581 dollars

d) E(X - 0.01X²) = E(X) - 0.01E(X²)

= 16.092 - (0.01×262.218)

= 16.0926- 2.62218

= 13.46982 = 13.470 ft³

Hope this helps!!!

Answer:

V = number of ounces

56 = 2V

Step-by-step explanation:

Answer:28

Step-by-step explanation:V times 2= 56

Answer:

  both

Step-by-step explanation:

Both of the equations shown here are linear equations in standard form.

  5x + 3y = 210

  x + y = 60

Answer:

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

And replacing we got:

[tex]t=\frac{69.5-69}{\frac{11.2}{\sqrt{147}}}=0.541[/tex]  

Step-by-step explanation:

Information given

[tex]\bar X=69.5[/tex] represent the sample mean    

[tex]s=11.2[/tex] represent the sample standard deviation

[tex]n=69[/tex] sample size  

[tex]\mu_o =69[/tex] represent the value that we want to test

t would represent the statistic (variable of interest)  

Hypothesis to test

We want to check if the true mean is 69, the system of hypothesis would be:  

Null hypothesis:[tex]\mu =69[/tex]  

Alternative hypothesis:[tex]\mu \neq 69[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

And replacing we got:

[tex]t=\frac{69.5-69}{\frac{11.2}{\sqrt{147}}}=0.541[/tex]  

Hey there! :)

Answer:

y = 1/4x - 3.

Step-by-step explanation:

Use the slope-formula to find the slope of the line:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in two points from the line. Use the points (-4, -4) and (0, 3):

[tex]m = \frac{-3 - (-4)}{0 - (-4)}[/tex]

Simplify:

m = 1/4.

Slope-intercept form is y = mx + b.

Find the 'b' value by finding the y-value at which the graph intersects the y-axis. This is at y = -3. Therefore, the equation is:

y = 1/4x - 3.

Answer:

7,000,000,000

Step-by-step explanation:

since the closest number is less than 5 (1<5) you round down making the nearest billion 7

Answer:

7,000,000,000 OR 7 Billion

Step-by-step explanation:

Since the 1 is millions place and its less than 5, you need to round down meaning that 7,125,000,00 rounded to the nearest billion is 7 billion.

Answer:

[tex] P(A) = 0.25, P(B= 0.3[/tex]

And if we want to find [tex] P(A \cap B)[/tex] we can use this formula from the definition of independent events :

[tex] P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075[/tex]

And the best option would be:

[tex] P(A \cap B) =0.075[/tex]

Step-by-step explanation:

For this case we have the following events A and B and we also have the probabilities for each one given:

[tex] P(A) = 0.25, P(B= 0.3[/tex]

And if we want to find [tex] P(A \cap B)[/tex] we can use this formula from the definition of independent events :

[tex] P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075[/tex]

And the best option would be:

[tex] P(A \cap B) =0.075[/tex]

Answer:

A) Null and alternative hypothesis

[tex]H_0: \mu=2\\\\H_a:\mu\neq 2[/tex]

B) M = 2.2 hours

C) s = 0.52 hours

D) P-value = 0.255

E) At a significance level of 0.05, there is not enough evidence to support the claim that the mean tree-planting time significantly differs from two hours.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the mean tree-planting time significantly differs from two hours.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=2\\\\H_a:\mu\neq 2[/tex]

The significance level is 0.05.

The sample has a size n=10.

The sample mean is M=2.2.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.52.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.52}{\sqrt{10}}=0.1644[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2.2-2}{0.1644}=\dfrac{0.2}{0.1644}=1.216[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=10-1=9[/tex]

This test is a two-tailed test, with 9 degrees of freedom and t=1.216, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t>1.216)=0.255[/tex]

As the P-value (0.255) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.05, there is not enough evidence to support the claim that the mean tree-planting time significantly differs from two hours.

Sample mean and standard deviation:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(1.7+1.5+2.6+. . .+2.3)\\\\\\M=\dfrac{22}{10}\\\\\\M=2.2\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((1.7-2.2)^2+(1.5-2.2)^2+(2.6-2.2)^2+. . . +(2.3-2.2)^2)}\\\\\\s=\sqrt{\dfrac{2.4}{9}}\\\\\\s=\sqrt{0.27}=0.52\\\\\\[/tex]

Answer:

C

Step-by-step explanation:

[tex]-5x-49\geq 113[/tex]

[tex]-5x\geq 162[/tex]

[tex]x\leq -32.4[/tex]

(Multiplying or dividing by a negative flips the sign).

This is a great question!

When we are given ( r - c )( 3 ), we are being asked to take 3 as x in the functions r( x ) and c( x ), taking the difference of each afterwards -

[tex]r( 3 ) = ( 3 )^2 + 5( 3 ) + 14,\\x( 3 ) = ( 3 )^2 - 3( 3 ) + 4[/tex]

____

Let us calculate the value of each function, determine their difference, and multiply by 100, considering r( x ) and c( x ) are measured in hundreds of dollars,

[tex]r( 3 ) = 9 + 15 + 14 = 38,\\x( 3 ) = 9 - 9 + 4 = 0 + 4 = 4\\----------------\\( r - c )( 3 ) = 38 - 4 = 34,\\34 * 100 = 3,400( dollars )\\\\Solution = 3,400( dollars )[/tex]

Therefore, ( r - c )( 3 ) " means " that George's new store will have a profit of $3,400 after it's third month in business, given the following options,

( 1. The new store will have a profit of $3400 after its third month in business.  

( ​​2. The new store will have a profit of $2400 after its third month in business.

( 3. ​The new store will sell 2400 items in its third month in business.

( 4. The new store will sell 3400 items in its third month in business.

The required answer is , [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.

The substitution method is the algebraic method to solve simultaneous linear equations.

Given function is,

[tex]r(x) = x^2+5x+14[/tex]...(1)

And [tex]c(x) = x^2-4x+5[/tex]...(2)

Now, substituting the value into the equation (1) and (2).

[tex]r(5) = (5)^2+5(5)+14=64[/tex]

[tex]c(5) = (5)^2-4(5)+5=10[/tex]

Therefore,

[tex](r-c)(5)=r(5)-c(5)\\=64-10\\=54[/tex]

Now, [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.

Learn more about the topic Substitution:

https://brainly.com/question/3388130

Answer:

1 because jahahdhekskdbsks

Answer

so I need to know the coordinates for me to tell you the answer but I think I can still help you by explaining.

In order for E to become E' the rule for reflection over y=x is (y, x) so you basically switch the x and the Y to have E'. so for you to be able find out E, you need to witch the x and the y.

for example:

if E' was (-2, 3)

E in the pre image would be (3, -2)

hope this helps :)

Answer:

(-2,6)

Step-by-step explanation:

Just did it edge 2021

Answer:

C. We are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

For 95% confidence interval, it means that we are 95% confident that the mean of the population is between the given upper and lower bounds of the confidence interval.

For the case above, the interpretation of the 95% confidence interval is that we are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.

Answer:

  a) 207 mph

  b) x = (1260-w)/1.17

  c) 1000 mb

Step-by-step explanation:

a) Put the pressure in the equation and solve.

  w(900) = -1.17(900) +1260 = 207

The wind speed for a hurricane with a pressure of 900 mb is 207 mph.

__

b) Solving for x, we have ...

  w = -1.17x +1260

  w -1260 = -1.17x

  x = (1260 -w)/1.17 . . . . inverse function

__

c) Evaluating the inverse function for w=90 gives ...

  x = (1260 -90)/1.17 = 1170/1.17 = 1000 . . . millibars

The approximate barometric pressure for a hurricane with a wind speed of 90 mph is 1000 millibars.

Answer:

20 years old.

Step-by-step explanation:

Let us say that the man's age is represented by x and the son's age is represented by y.

As of now, x = 2y.

In 20 years, both ages will increase by 20. We can have an equation where the son's age increased by 20 equals 2/3 of the man's age plus 20.

(y + 20) = 2/3(x + 20)

Since x = 2y...

y + 20 = 2/3(2y + 20)

3/2y + 30 = 2y + 20

2y + 20 = 3/2y + 30

1/2y = 10

y = 20

To check our work, the man's age is currently double his son's, so the man is 40 and the son is 20. In 20 years, the man will be 60 and the son will be 40. 40 / 60 = 2/3, so the son's age is 2/3 of his father's.

So, the son's present age is 20 years old.

Hope this helps!

Answer:

Answer is option 2

Step-by-step explanation:

We know that Angle M = Angle G (given in diagram)

We also know that Angle L in triangle LMN is equal to Angle L in triangle LGH

As two angles are equal in both triangles they are similar.

But why is it Triangle LGH instead of Triangle HGL?

As we know M=G therefore they should be in the same place in the name Of the triangle. In triangle LMN M is in the middle therefore Angle G should also be in the middle

Answer:

D. *6F

Step-by-step explanation:

C=(F-32)*5/9

30=(F-32)*5/9

F = (30*9)/5+32

F = 86

Answer:

2x+50

Step-by-step explanation:

Distributive property: 2(x)+2(25)

Simplify: 2x+50

Answer: 2x + 50

Step-by-step explanation: In this problem, the 2 distributes through the parenthses, multiplying by each of the terms inside.

So we have 2(x) + 2(25) which simplifies to 2x + 50.

Answer:

what's a bit

Step-by-step explanation:

Answer:

[tex]( x_1 , y_1 , z_1 ) = < -7 + 4\sqrt{3} , -4 + 2\sqrt{3} , 7 - 2\sqrt{3} >\\\\( x_2 , y_2 , z_2 ) = < -7 - 4\sqrt{3} , -4 - 2\sqrt{3} , 7 + 2\sqrt{3} >\\[/tex]

Step-by-step explanation:

Solution:-

- We are given a parametric form for the vector equation of line defined by ( t ).

- The line vector equation is:

                        L: < 3 + 2t , t + 1 , 2 -t >

- The same 3-dimensional space is occupied by a unit sphere defined by the following equation:

                          [tex]S: x^2 + y^2 + z^2 = 1[/tex]

- We are to determine the points of intersection of the line ( L ) and the unit sphere ( S ).

- We will substitute the parametric equation of line ( L ) into the equation defining the unit sphere ( S ) and solve for the values of the parameter ( t ):

                        [tex]( 3 + 2t )^2 + ( 1 + t )^2 + ( 2 - t)^2 = 1\\\\( 9 + 12t + 4t^2 ) + ( t^2 + 2t + 1 ) + ( 4 + t^2 -4t ) = 1\\\\t^2 + 10t + 13 = 0\\\\[/tex]

- Solve the quadratic equation for the parameter ( t ):

                       [tex]t = -5 + 2\sqrt{3} , -5 - 2\sqrt{3}[/tex]

- Plug in each of the parameter value in the given vector equation of line and determine a pair of intersecting coordinates:

                      [tex]( x_1 , y_1 , z_1 ) = < -7 + 4\sqrt{3} , -4 + 2\sqrt{3} , 7 - 2\sqrt{3} >\\\\( x_2 , y_2 , z_2 ) = < -7 - 4\sqrt{3} , -4 - 2\sqrt{3} , 7 + 2\sqrt{3} >\\[/tex]

Answer:

93.5 square units

Step-by-step explanation:

Diameter of the Circle = 12 Units

Therefore:

Radius of the Circle = 12/2 =6 Units

Since the hexagon is regular, it consists of 6 equilateral triangles of side length 6 units.

Area of the Hexagon = 6 X Area of one equilateral triangle

Area of an equilateral triangle of side length s = [tex]\dfrac{\sqrt{3} }{4}s^2[/tex]

Side Length, s=6 Units

[tex]\text{Therefore, the area of one equilateral triangle =}\dfrac{\sqrt{3} }{4}\times 6^2\\\\=9\sqrt{3} $ square units[/tex]

Area of the Hexagon

[tex]= 6 X 9\sqrt{3} \\=93.5$ square units (to the nearest tenth)[/tex]

Answer:

I didn't know which one you wanted...

Step-by-step explanation:

1. Finding the x an y-intercepts

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (2,0)

y-intercept(s): (0,−24)

2. Finding the slope and y-intercept

Use the slope-intercept form to find the slope and y-intercept.

Slope: 12

y-intercept: −24

Answer:

  (x, y, z) = (13/7, 19/7, 25/7)

Step-by-step explanation:

You know that the vector whose components are the coefficients of the equation of the plane is perpendicular to the plane. That is (1, 2, 3) is a vector perpendicular to the plane.

The parametric equation for a line through (1, 1, 1) with this direction vector is ...

  (x, y, z) = (1, 2, 3)t +(1, 1, 1) = (t+1, 2t+1, 3t+1)

The point of intersection of this line and the plane will be the point in the plane closest to (1, 1, 1). That point has a t-value of ...

  (t +1) +2(2t +1) +3(3t +1) = 18

  14t +6 = 18

  t = 12/14 = 6/7

The point in the plane closest to (1, 1, 1) is ...

  (x, y, z) = (6/7+1, 2(6/7)+1, 3(6/7)+1)

  (x, y, z) = (13/7, 19/7, 25/7)

First find the distance it is reflected:

D = 20.0 x 10.0 /(20-10) = 200/10 = 20cm away.

Now calculate the magnification: -20/ 20 = -1

Now calculate the height:

-1 x 2.50 = -2.50

The negative sign means the image is inverted.

The mirrored image would be inverted, 2.50 cm tall and 20 cm in front of the mirror.

Answer:

[tex] g(x) = 2x+2[/tex]

Let's find g(a+h):

[tex] g(a+h)=2*(a+h) +2= 2a +2h +2[/tex]

And now let's find g(a)

[tex] g(a)= 2a+2[/tex]

And now finally:

[tex] g(a+h) = 2a +2h +2 -2a-2 = 2h +2-2= 2h[/tex]

Step-by-step explanation:

We have the following function given:

[tex] g(x) = 2x+2[/tex]

Let's find g(a+h):

[tex] g(a+h)=2*(a+h) +2= 2a +2h +2[/tex]

And now let's find g(a)

[tex] g(a)= 2a+2[/tex]

And now finally:

[tex] g(a+h) = 2a +2h +2 -2a-2 = 2h +2-2= 2h[/tex]