A man wants to set up a 529 college savings account for his granddaughter. How much would he need to deposit each year into the account in order to have $50,000 saved up for when she goes to college in 17 years, assuming the account earns a 5% return?

Answer:

x = 8

Step-by-step explanation:

Step 1: Write out the expression

x + 2x = 24

Step 2: Combine like terms

3x = 24

Step 3: Isolate x

x = 8

And we have our final answer!

Answer:

X=8

Step-by-step explanation:

Answer:

I'm not completely sure what you mean by a, "single fraction," but I'm pretty sure the answer you are looking for is [tex]\frac{5-4}{a-b}[/tex]

Step-by-step explanation:

Answer:

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

P-value = 0.166.

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(490+502+505+495+492)\\\\\\M=\dfrac{2484}{5}\\\\\\M=496.8\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}((490-496.8)^2+(502-496.8)^2+(505-496.8)^2+(495-496.8)^2+(492-496.8)^2)}\\\\\\s=\sqrt{\dfrac{166.8}{4}}\\\\\\s=\sqrt{41.7}=6.5\\\\\\[/tex]

Then, we can perform the hypothesis t-test for the mean.

The claim is that the amount of vitamin C in a tablet sample is different from 500 mg.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=500\\\\H_a:\mu< 500[/tex]

The significance level is 0.05.

The sample has a size n=5.

The sample mean is M=496.8.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.5.

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

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6.5}{\sqrt{5}}=2.907[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{496.8-500}{2.907}=\dfrac{-3.2}{2.907}=-1.1[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=5-1=4[/tex]

This test is a left-tailed test, with 4 degrees of freedom and t=-1.1, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.1)=0.166[/tex]

As the P-value (0.166) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

Answer : The value of x is 4.1 cm.

Step-by-step explanation :

As we know that the perpendicular dropped from the center divides the chord into two equal parts.

That means,

AB = CB = [tex]\frac{15.6cm}{2}=7.8cm[/tex]

Now we have o calculate the value of x by using Pythagoras theorem.

Using Pythagoras theorem in ΔOBA :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](OA)^2=(OB)^2+(BA)^2[/tex]

Now put all the values in the above expression, we get the value of side OB.

[tex](8.8)^2=(x)^2+(7.8)^2[/tex]

[tex]x=\sqrt{(8.8)^2-(7.8)^2}[/tex]

[tex]x=\sqrt{77.44-60.84}[/tex]

[tex]x=\sqrt{16.6}[/tex]

[tex]x=4.074\approx 4.1[/tex]

Therefore, the value of x is 4.1 cm.

Answer:

34

Step-by-step explanation:

F(x) = 2x^3 - 7x + 1

Let x= 3

F(3) = 2* 3^3 - 7*3 + 1

      = 2 * 27 -21+1

      = 54 -21 + 1

      = 34

Answer: 34

Step-by-step explanation:

Answer:

india

Step-by-step explanation:

Answer:

x = -2

y = -5

Step-by-step explanation:

We can solve this algebraically (substitution or elimination) or graphically. I will be using elimination:

Step 1: Add the 2 equations together

-8y = 40

y = -5

Step 2: Plug y into an original equation to find x

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

15 + 10x = -5

10x = -20

x = -2

And we have our final answers!

Answer:

[tex]\boxed{\sf \ \ \ x=-2 \ \ \ and \ \ \ y=-5 \ \ \ }[/tex]

Step-by-step explanation:

let s solve the following system

(1) -5y-10x=45

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

let s do (1) + (2) it comes

-5y-10x-3y+10x=45-5=40

<=>

-8y=40

<=>

y = -40/8=-20/4=-5

so y = -5

let s replace y in (1)

25-10x=45

<=>

10x=25-45=-20

<=>

x = -20/10=-2

so x = -2

Answer:  Measure of angle T = 25 degrees and Measure of angle U = 45 degrees

Step-by-step explanation:

Measure of angle T = 25 degrees and TU = 12 is the pair of measurements would eliminate the possibility that the triangles are congruent.

" Triangles are said to be congruent if the corresponding sides and angles of the one triangle are equals to the other triangles."

According to the question,

In triangle KLM,

KM =27millimeters

LM = 20millimeters

KL = 12 millimeters

∠K= 45degrees

∠M= 25 degrees

∠L = 110degrees

From the given measurements of the triangle we have,

side with measure 27millimeters is opposite to angle 110° .

side with measure 12millimeters is opposite to angle 25° .

side with measure 20millimeters is opposite to angle 45°.

From the conditions in triangle TUV to be congruent to triangle KLM ,

Measure of angle T = 25 degrees and TU = 12  is against the given condition of congruent triangle.

As angle T and side TU are adjacent to each other, which is against the correspondence of the given triangle.

Hence, measure of angle T = 25 degrees and TU = 12 is the pair of measurements would eliminate the possibility that the triangles are congruent.

Learn more about congruent triangle here

https://brainly.com/question/12413243

#SPJ2

Answer:

root 61

Step-by-step explanation:

You can use the distance formula or draw a triangle with sides 5 and 6

Answer:

(C)Out of 5,000 randomly chosen children, 250 children carry the virus.

Step-by-step explanation:

[tex]\text{Option A}: \dfrac{210}{5000}=0.042=4.2\% \\\text{Option B}: \dfrac{3}{60}=0.05=5\% \\\text{Option C}: \dfrac{250}{5000}=0.05=5\% \\\text{Option D}: \dfrac{1}{20}=0.05=5\%[/tex]

The higher the research sample, the more credible the results. In options A and C, the research sample was 5000. However, since the relative frequency of children carrying the virus is 5% in both, we take the result with a higher number of positives.

Option C is the correct option.

Answer:

P(B1) = (11/15)

P(B2) = (4/15)

P(A) = (11/15)

P(B1|A) = (5/7)

P(B2|A) = (2/7)

Step-by-step explanation:

There are 11 red chips and 4 blue chips in a box. Two chips are selected one after the other at random and without replacement from the box.

B1 is the event that the chip removed from the box at the first step of the experiment is red.

B2 is the event that the chip removed from the box at the first step of the experiment is blue. A is the event that the chip selected from the box at the second step of the experiment is red.

Note that the probability of an event is the number of elements in that event divided by the Total number of elements in the sample space.

P(E) = n(E) ÷ n(S)

P(B1) = probability that the first chip selected is a red chip = (11/15)

P(B2) = probability that the first chip selected is a blue chip = (4/15)

P(A) = probability that the second chip selected is a red chip

P(A) = P(B1 n A) + P(B2 n A) (Since events B1 and B2 are mutually exclusive)

P(B1 n A) = (11/15) × (10/14) = (11/21)

P(B2 n A) = (4/15) × (11/14) = (22/105)

P(A) = (11/21) + (22/105) = (77/105) = (11/15)

P(B1|A) = probability that the first chip selected is a red chip given that the second chip selected is a red chip

The conditional probability, P(X|Y) is given mathematically as

P(X|Y) = P(X n Y) ÷ P(Y)

So, P(B1|A) = P(B1 n A) ÷ P(A)

P(B1 n A) = (11/15) × (10/14) = (11/21)

P(A) = (11/15)

P(B1|A) = (11/21) ÷ (11/15) = (15/21) = (5/7)

P(B2|A) = probability that the first chip selected is a blue chip given that the second chip selected is a red chip

P(B2|A) = P(B2 n A) ÷ P(A)

P(B2 n A) = (4/15) × (11/14) = (22/105)

P(A) = (11/15)

P(B2|A) = (22/105) ÷ (11/15) = (2/7)

Hope this Helps!!!

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

The mean annual tuition and fees for a sample of 15 private colleges was $35,500 with a standard deviation of $6500. A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from $32,500. State the null and alternate hypotheses. A) H0: 4 = 32,500, H:4=35,500 C) H: 4 = 35,500, H7:35,500 B) H: 4 = 32,500, H : 4 # 32,500 D) H0:41 # 32,500, H : 4 = 32,500

Solution

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 32500

For the alternative hypothesis,

Ha: µ ≠ 32500

This is a two tailed test.

Since the number of samples is small and the population standard deviation is not given, the distribution is a student's t.

Since n = 15,

Degrees of freedom, df = n - 1 = 15 - 1 = 14

t = (x - µ)/(s/√n)

Where

x = sample mean = 35500

µ = population mean = 32500

s = samples standard deviation = 6500

t = (35500 - 32500)/(6500/√15) = 1.79

We would determine the p value using the t test calculator. It becomes

p = 0.095

Assuming alpha = 0.05

Since alpha, 0.05 < than the p value, 0.095, then we would fail to reject the null hypothesis.

Answer:

50 to 60 seconds is the answer

Answer:

3/10

Step-by-step explanation:

Answer:

The value of the sample mean resonance frequency is 112Hz

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

In this problem, we have that:

Lower bound: 111.6

Upper bound: 112.4

Sample mean: (111.6 + 112.4)/2 = 112Hz

The value of the sample mean resonance frequency is 112Hz

The value of the sample mean resonance frequency is 112 Hz.

The value of the sample mean resonance frequency is equivalent to the average of the upper limit and the lower limit.

The sample mean resonance frequency = (lower limit + upper limit) / 2

(111.6 +112.4) / 2

= 224 / 2

= 112 Hz

To learn more about confidence interval, please check: https://brainly.com/question/15905477

area =πr²

6.5²xπ=132.73

2.3²xπ=16.62

132.73-16.62= 116.11

116cm^2

i think its this anyway

Answer:

116 cm^2 to 3 s f's.

Step-by-step explanation:

The area of the shaded part = area of the outer circle - area of the inner circle

= π * 6.5^2 - π *  2.3^2

=  132.732 - 16.619

= 116.113  cm^2.

Answer:  b) the tiles are not similar because both SP:SR is 5:4 and MJ:ML is 5:2

Step-by-step explanation:

We are given that the tiles are rectangular which implies that they both have a 90° angle.

In order to prove similarity, We need to show that the lengths and widths are proportional.

P Q R S

J  K L M

a) PQ : QR         JK : LM

  w=4  L=5        w=2 w=2

                                  ↓

                                 We need Length (not width)

b) SP : SR         MJ : ML

  L=5  w=4        L=5 w=2

      5 : 4               5 : 2

When comparing length to width they do not have the same ratio so the rectangles are not similar.

c) PQ : QR         JK : KL

  w=4  L=5        w=2 L=5

      4 : 5               2 : 5

When comparing width to length they do not have the same ratio so the rectangles are not similar.

d) SR : ML         PQ : JK

  w=4  w=2        w=4 w=2

           ↓                     ↓

  We need Length (not width)

Answer:

-1/4 is the slope and the y intercept is -4

Step-by-step explanation:

Solve for y

x +4y = -16

Subtract x

4y = -x-16

Divide by 4

4y/4 = -x/4 -16/4

y = -1/4 x -4

This is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

-1/4 is the slope and the y intercept is -4

Answer:

For a sample size of n = 609.

Step-by-step explanation:

Central limit theorem for proportions:

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

We have that p = 0.58.

We have to find n for which s = 0.02. So

[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

[tex]0.02 = \sqrt{\frac{0.58*0.42}{n}}[/tex]

[tex]0.02\sqrt{n} = \sqrt{0.58*0.42}[/tex]

[tex]\sqrt{n} = \frac{\sqrt{0.58*0.42}}{0.02}[/tex]

[tex](\sqrt{n})^{2} = (\frac{\sqrt{0.58*0.42}}{0.02})^{2}[/tex]

[tex]n = 609[/tex]

For a sample size of n = 609.

Answer:

54

Step-by-step explanation:

The pink parts are 9 out of total 11 parts.

9/11

Multiply with 66.

9/11 × 66

= 54

Hey there! :)

Answer:

P(Pink) = 54.

Step-by-step explanation:

Begin by calculating the possibility of the spinner landing on pink:

[tex]P(pink) = \frac{pink}{total}[/tex]

Therefore:

[tex]P(Pink) = \frac{9}{11}[/tex]

In this question, the spinner was spun 66 times. Since we have solved for the probability, we can set up ratios to find the probability of the spinner landing on pink out of 66.

[tex]\frac{9}{11}= \frac{x}{66}[/tex]

Cross multiply:

594 = 11x

Divide both sides by 11:

x = 54.

P(Pink) = 54.

Answer: The solution  is [tex](-2,\frac{5}{3} )[/tex]

Step-by-step explanation:

it already gives you the solution for x so just plot it into the equation to solve for y.

y= [tex]\frac{2}{3} *\frac{-2}{1}+3[/tex]  

y= [tex]\frac{-4}{3}+\frac{3}{1}[/tex]

y= [tex]\frac{5}{3}[/tex]

Answer: -2 5/3

Step-by-step explanation:

y= 2/3*-2/1+3

y= -4+3/1

-2 5/3

Answer:

25%

Step-by-step explanation:

The last percentile always contains 25% of the observations.

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

  (x, y) = (7, 4) meters

Step-by-step explanation:

The area of the floor without the removal is x^2, so with the smaller square removed, it is x^2 -y^2.

The perimeter of the floor is the sum of all side lengths, so is 4x +2y.

The given dimensions tell us ...

  x^2 -y^2 = 33

  4x +2y = 36

From the latter equation, we can write an expression for y:

  y = 18 -2x

Substituting this into the first equation gives ...

  x^2 -(18 -2x)^2 = 33

  x^2 -(324 -72x +4x^2) = 33

  3x^2 -72x + 357 = 0 . . . . write in standard form

  3(x -7)(x -17) = 0 . . . . . factor

Solutions to this equation are x=7 and x=17. However, for y > 0, we must have x < 9.

  y = 18 -2(7) = 4

The floor dimension x is 7 meters; the inset dimension y is 4 meters.

Answer:

y = 2/3x + 4

Step-by-step explanation:

Step 1: Find slope

m = (4-0)/(0+6)

m = 2/3

Step 2: Write in y-int (0, 4)

y = 2/3x + 4

Answer:

Step-by-step explanation:

given a point [tex](x_0,y_0)[/tex] the equation of a line with slope m that passes through the  given point is

[tex]y-y_0 = m(x-x_0)[/tex] or equivalently

[tex] y = mx+(y_0-mx_0)[/tex].

Recall that a line of the form [tex]y=mx+b [/tex], the y intercept is b and the x intercept is [tex]\frac{-b}{m}[/tex].

So, in our case, the y intercept is [tex](y_0-mx_0)[/tex] and the x  intercept is [tex]\frac{mx_0-y_0}{m}[/tex].

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph [tex](x_0,\frac{1}{x_0})[/tex]. Which means that [tex]y_0=\frac{1}{x_0}[/tex]

The slope of the tangent line is given by the derivative of the function evaluated at [tex]x_0[/tex]. Using the properties of derivatives, we get

[tex]y' = \frac{-1}{x^2}[/tex]. So evaluated at [tex]x_0[/tex] we get [tex] m = \frac{-1}{x_0^2}[/tex]

Replacing the values in our previous findings we get that the y intercept is

[tex](y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}[/tex]

The x intercept is

[tex] \frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0[/tex]

The triangle in consideration has height [tex]\frac{2}{x_0}[/tex] and base [tex]2x_0[/tex]. So the area is

[tex] \frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2[/tex]

So regardless of the point we take on the graph, the area of the triangle is always 2.

Answer:

Correct statement: "the number is divisible by 3".

Step-by-step explanation:

The statement provided is:

When a number is divisible by 9, the number is divisible by 3.

The general form of a conditional statement in if-then form is:

[tex]p\rightarrow q[/tex]

This implies that if p, then q.

The part after the "if" is known as the hypothesis and the part after the "then" is known as the conclusion.

The if-then form of the provided statement is:

If a number is divisible by 9, then the number is divisible by 3.

So, the conclusion is:

"the number is divisible by 3"

Answer:

a

Step-by-step explanation:

Answer:

You didn't state it but you need to find Angle A.

From the Pythagorean Theorem, we calculate side ac

side ac^2 = 5^2 - 3^2  =25 -9 = 16 Side AC = 4

arc tangent angle A = 3 / 4 = .75

angle A =  36.87 Degrees

Step-by-step explanation:

Answer:

P(7 or 11) = 0.2222

Step-by-step explanation:

First let's find the cases where we get a sum of 7 and a sum of 11:

The cases where we get a sum of 7 are:

(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)

And the cases where we get a sum of 11 are:

(5,6), (6,5)

So we have a total of 8 cases among the 36 total possible outcomes.

So the probability of the sum of the two dice being 7 or 11 is:

P(7 or 11) = 8 / 36 = 0.2222

Answer:

the answer is 3

Step-by-step explanation:

i took the test