Lee put $10,000 into a stock market index mutual fund that grew at an average of 7% per year for 10 years. About how much is in Lee's mutual fund account after 10 years? Ignore compounding.

Answer:

Y=150

Step-by-step explanation:

Just apply the proportionality rulw and solve for k. Then substitute the value of k into the equation.

Answer:

90

Step-by-step explanation:

Let the constant of proportionality be K

So that;

Y= K(x+2)^2

This means

For two corresponding points (x1,y1) and (x2,y2) we have;

Y1/(x1+2)^2= Y2/(x2+2)^2

If we consider x=8 y=250 as point (x1,y1) and y when x=4 as (x2,y2) we have ;

250/(8+2)^2 =y/(4+2)^2

250/(10)^2 = y/(6)^2

250/100 = y/36

250/100 × 36 = y

90= y

y=90

Answer:

  F ∪ H = {c, d, e, f, g, h}

  F ∩ H = { }

Step-by-step explanation:

The union is the list of elements that are in either of the two sets.

  F ∪ H = {c, d, e, f, g, h}

The intersection is the list of only those elements that appear in both sets. (There are none.)

  F ∩ H = { } . . . . the empty set

Answer:

Systematic Sampling

Step-by-step explanation:

yes the answer is( true).

Answer:

The answer is (True)

Step-by-step explanation:

Answer:

3.72kg

$29.76

See explanation below

Step-by-step explanation:

The question is incomplete as we are not told what we are to determine. Consider the following question

Question:

Tomas has two boxes to be shipped. One box weighs 3 kilograms. The other box weighs 720 grams.

a) What is the total weight of the boxes in kilogram?

b) If the shipping cost $8 per kilogram, what is the total cost of shipping.

Solution:

This is a question on measuring mass.

a) Total weight of the two boxes = weight of 1st box + weight of 2nd box

1st box = 3kg

2nd box = 720g

1000 g is equal to 1 kg

720g = (720/1000)kg = 0.72 kg

2nd box = 0.72 kg

Total weight of the two boxes = 3kg + 0.72kg

Total weight of the two boxes = 3.72kg

b) cost of shipping per kg = $8

cost of shipping for 3.72 kg = 8 × 3.72

Total cost of shipping for both boxes = $29.76

Answer: from my calculations its 3.72

which is also 3720 grams

Answer:

B. n=36, p=0.98, x=12

Step-by-step explanation:

98% of bottles have the correct amount.

The probability is equal to 0.98

That is p = 0.98

A bottle of water is supposed to have 12 ounces.

That is the expected value is 12

X = 12

36 bottles has all bottles properly filled

The possible sample space is 36

N = 36

Answer:

240cc

Explanation:

From the expression of the relationship between pressure and volume, we can state mathematical that for two successive volume V1 and V2 and Pressure P1 and P2 we have:

P1V1 = P2V2

V2 = P1V1 / P2

=400×300/500= 240cc

Answer:

846^% and then to rond it is 850^%

Step-by-step explanation:

e radius of a 10” pizza is 5”. Using A= pi2, what is the area of the 10” pizza? (Round to the nearest tenth)

Answer:

Step-by-step explanation:

One half

Answer:

a. December 16

Step-by-step explanation:

18 June + 180 days = 15 December

Since 2 options given,

a. December 16 is the answer

Answer:

A : We keep the middle 97% of values by chopping off 1.5% from each tail.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.97}{2} = 0.015[/tex]

This means that for a 97% confidence interval, 1.5% of each tail is removed, while the middle 97% of values are kept.

So the corect answer is:

A : We keep the middle 97% of values by chopping off 1.5% from each tail.

Answer:

factor out 12

[tex]12(14cx - 5 + 2x)[/tex]

Answer:

135

Step-by-step explanation:

Based on the following information:

- There are 150 dog lovers

- There are 120 cat lovers

So:

The null hypothesis:

H, there are an equal number of dog lovers and cat lovers, so the expected frequency in each cell will be the same and that is:

f = (150 + 120) / 2

f = 270/2 = 135

then the first option of 135 is correct

Answer:

The expected revenue is $984.6.

Step-by-step explanation:

The tourist operator sells 21 non-refundable tickets, as the tourist may not show up.

The tourist have a probability of 0.02 of not showing up, independent of each other.

The income is the selling of the 21 tickets at $50 each.

[tex]I=21*50=1,050[/tex]

The only cost considered in this problem is the refund if a tourist show up and a seat is not available.

This only happens when the 21 tourists show up. If each tourist has a probability of 0.02 of not showing up, they have a probability of 0.98 of showing up.

For the event that the 21 tourists show up, we have the probability:

[tex]P=0.98^{21}\approx0.654[/tex]

For each of this event, the tour operator has to pay $100, so the expected revenue of the tour operator is:

[tex]E(R)=I-E(C)=1,050-0.654\cdot 100=1,050-65.4=984.6[/tex]

In this case, the complement would be selecting a number less than or equal to 7; the probability of this occurring is [tex]\boxed{\frac{7}{10}}.[/tex]

Answer:

it is 3/10

Step-by-step explanation:

Answer:

  C.  7, 14, 21, 28

Step-by-step explanation:

Since you know your times tables, you know that multiples of 7 are ...

   7, 14, 21, 28

Answer:

.

Step-by-step explanation:

[tex]answer = (3x + 1)\\ solution \\ {9x}^{2} + 6x + 1 \\ = {9x}^{2} + (3 + 3)x + 1 \\ = {9x}^{2} + 3x + 3x + 1 \\ = 3x(3x + 1) + 1(3x + 1) \\ = (3x + 1)(3x + 1) \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer:

[tex]z=\frac{0.480 -0.42}{\sqrt{\frac{0.42(1-0.42)}{1045}}}=3.930[/tex]  

The p value for this case would be given by:

[tex]p_v =P(z>3.930)=0.0000443[/tex]  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis so then we can conclude that the true proportion is significantly higher than 0.42

Step-by-step explanation:

Information given

n=1045 represent the random sample selected

X=502 represent the college graduates with a mentor

[tex]\hat p=\frac{502}{1045}=0.480[/tex] estimated proportion of college graduates with a mentor

[tex]p_o=0.42[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to test if the true proportion is higher than 0.42, the system of hypothesis are.:  

Null hypothesis:[tex]p \leq 0.42[/tex]  

Alternative hypothesis:[tex]p > 0.42[/tex]  

The statistic is given by:

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

Replacing the info we got:

[tex]z=\frac{0.480 -0.42}{\sqrt{\frac{0.42(1-0.42)}{1045}}}=3.930[/tex]  

The p value for this case would be given by:

[tex]p_v =P(z>3.930)=0.0000443[/tex]  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis so then we can conclude that the true proportion is significantly higher than 0.42

Answer:

32.738ft³

32.7ft³

Step-by-step explanation:

This is half a sphere therefore volume=4/3πr³×1/2

4/3×22/7×2.5³×1/2

=32.738ft³

Answer:

[tex] x = \frac{12 \pm \sqrt{(-12)^2 -4(5)(-7)}}{2(5)}[/tex]

And we got for the solution:

[tex] x_1= 2.885 , x_2 = -0.485[/tex]

And the value sof y are using the function y =2x-3:

[tex] y_1=2.77, y_2=-3.97[/tex]

Step-by-step explanation:

For this case we have this function given:

[tex] y = 2x-3[/tex]  (1)

And the circle with center the origin and radius 4 is given by;

[tex] x^2 +y^2 = 16[/tex]  (2)

We can solve fro y from the last equation and we got:

[tex] y = \pm \sqrt{16-x^2}[/tex]   (3)

Now we can set equal equations (3) and (1) and we got:

[tex] 2x-3 = \sqrt{16-x^2}[/tex]

[tex] (2x-3)^2=16-x^2[/tex]

[tex] 4x^2 -12x +9 = 16-x^2[/tex]

[tex] 5x^2 -12x -7=0[/tex]

And using the quadratic equation we got:

[tex] x = \frac{12 \pm \sqrt{(-12)^2 -4(5)(-7)}}{2(5)}[/tex]

And we got for the solution:

[tex] x_1= 2.885 , x_2 = -0.485[/tex]

And the value sof y are using the function y =2x-3:

[tex] y_1=2.77, y_2=-3.97[/tex]

Answer: 6 1/6

Step-by-step explanation:

6 can go into 37 6 times

6x6=36

with 1 left over

The fraction 37/6 can be changed to the mixed number​ as 6 1/6 if the fraction is 37/6.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The fraction is:

= 37/6

We can write the above number as:

= (36 + 1)/6

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

= 36/6 + 1/6

= 6 + 1/6

Or

= 6 1/6 (mixed fraction)

Thus, the fraction 37/6 can be changed to the mixed number​ as 6 1/6 if the fraction is 37/6.

Learn more about the fraction here:

brainly.com/question/1301963

#SPJ2

Answer:

Null hypothesis is [tex]\mathbf {H_o: \mu > 937}[/tex]

Alternative hypothesis is [tex]\mathbf {H_a: \mu < 937}[/tex]

Test Statistics z = 2.65

CONCLUSION:

Since test statistics is greater than  critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.

P- value = 0.004025

Step-by-step explanation:

Given that:

Mean [tex]\overline x[/tex] = 960 hours

Sample size n = 36

Mean population [tex]\mu =[/tex] 937

Standard deviation [tex]\sigma[/tex] = 52

Given that the mean  time between failures is 937 hours. The objective is to determine if the mean time between failures is greater than 937 hours

Null hypothesis is [tex]\mathbf {H_o: \mu > 937}[/tex]

Alternative hypothesis is [tex]\mathbf {H_a: \mu < 937}[/tex]

Degree of freedom = n-1

Degree of freedom = 36-1

Degree of freedom = 35

The level of significance ∝ = 0.01

SInce the degree of freedom is 35 and the level of significance ∝ = 0.01;

from t-table t(0.99,35), the critical value = 2.438

The test statistics is :

[tex]Z = \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \dfrac{960-937 }{\dfrac{52}{\sqrt{36}}}[/tex]

[tex]Z = \dfrac{23}{8.66}[/tex]

Z = 2.65

The decision rule is to reject null hypothesis   if  test statistics is greater than  critical value.

CONCLUSION:

Since test statistics is greater than  critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.

The P-value can be calculated as follows:

find P(z < - 2.65) from normal distribution tables

= 1 - P (z ≤ 2.65)

= 1 - 0.995975     (using the Excel Function: =NORMDIST(z))

= 0.004025

Answer:

C.

Step-by-step explanation:

Hello!

Given the variable:

X: childhood asthma prevalence

With mean μ= 2.22%

and standard deviation σ= 1.39%

You have to calculate the probability of the sample average of childhood asthma prevalence in a sample of n= 30 cities is greater than 2.5%

We don't know the distribution of the variable, but remember that thanks to the central limit theorem, since the n ≥ 30, we can approximate the sampling distribution to normal:

X[bar]≈N(μ;σ²/n)

And use the standard normal distribution to calculate the asked probability:

P(X[bar]>2.5)= 1 - P(X≤2.5)

Calculate the Z value for the given X[bar] value:

[tex]Z= \frac{X[bar]-Mu}{\frac{Sigma}{\sqrt{n} } } = \frac{2.5-2.22}{\frac{1.39}{\sqrt{30} } }= 1.10[/tex]

Using the Z-tables you have to look for the value of

P(Z≤1.10)= 0.86433

1 - 0.86433= 0.13567

Then P(X[bar]>2.5)= 1 - P(X≤2.5)= 1 - P(Z≤1.10)= 1 - 0.86433= 0.13567

13.567% of the 30 cities will have a mean childhood asthma prevalence greater than 2.5%

I hope this helps!

Answer:

The dimensions of the rectangular box is 36.23 ft×36.23 ft×4.345 ft.  

Minimum cost=2046.16 cents      

Step-by-step explanation:

Given that a rectangular box with a volume of 684 ft³.

The base and the top of the rectangular box is square in shape

Let the length and width of the rectangular box be x.

[since the base is square in shape,  length=width]

and the height of the rectangular box be h.

The volume of rectangular box is = Length ×width × height

                                                      =(x²h) ft³

[tex]x^2h=684\Rightarrow h=\frac{684}{x^2}[/tex]  (1)

The area of the base and top of rectangular box is = x² ft²

The surface area of the sides= 2(length+width) height

                                               =2(x+x)h

                                               =4xh ft²

The total cost to construct the rectangular box is

=[(x²×20)+(x²×15)+(4xh×1.5)] cents  

=(20x²+15x²+6xh) cents

=(25x²+6xh) cents

Total cost= C(x).

C(x) is in cents.

∴C(x)=25x²+6xh

Putting [tex]h=\frac{684}{x^2}[/tex]

[tex]C(x)=25x^2+6x\times\frac{684}{x^2} \Rightarrow C(x)=25x^2+\frac{4104}{x}[/tex]

Differentiating with respect to x

[tex]C'(x)=50x-\frac{4104}{x^2}[/tex]

To find minimum cost, we set C'(x)=0

[tex]\therefore50x-\frac{4104}{x^2}=0\\\Rightarrow50x=\frac{4104}{x^2}\\\Rightarrow x^3=\frac{4104}{50}\Rightarrow x\approx 4.345[/tex] ft.

Putting the value x in equation (1) we get

[tex]h=\frac{684}{(4.345)^2}[/tex]

 ≈36.23 ft.

The dimensions of the rectangular box is 36.23 ft×36.23 ft×4.345 ft.  

Minimum cost C(x)=[25(4.345)²+10(4.345)(36.23)] cents

                               =2046.16 cents      

Answer:

4y

Step-by-step explanation:

y - -3y

Subtracting a negative is like adding

y+3y

Combine like terms

4y

Answer:

[tex]4y[/tex]

Step-by-step explanation:

[tex]y - ( - 3y) \\ y + 3y \\ = 4y[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

(a)[tex]x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3[/tex]

(b) 12

(c)[tex]2\frac{3}{4}[/tex]

Step-by-step explanation:

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

We are to compute the quadratic form [tex]x^TAx[/tex] for A.

Part A

[tex]x=\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right][/tex]

[tex]x^TAx = \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3&2&0\\2&2&1\\0&1&0\end{array}\right]\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right][/tex]

[tex]= \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3x_1+2x_2+0x_3\\2x_1+2x_2+1x_3\\0x_1+1x_2+0x_3\end{array}\right][/tex]

[tex]= x_1(3x_1+2x_2+0x_3)+x_2(2x_1+2x_2+1x_3)+x_3(0x_1+1x_2+0x_3)\\= x_1(3x_1+2x_2)+x_2(2x_1+2x_2+x_3)+x_3(x_2)[/tex]

[tex]= 3x_1^2+2x_1x_2+2x_1x_2+2x_2^2+x_2x_3+x_2x_3\\\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3[/tex]

Part B

[tex]x=\left[\begin{array}{ccc}-2\\-1\\5\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(-2)^2+4(-2)(-1)+2(-1)^2+2(-1)(5)\\=3*4+4*2+2-10\\=12+8+2-10\\=12[/tex]

Part C

[tex]x=\left[\begin{array}{ccc}\frac{1}{2}\\\frac{1}{2}\\\frac{1}{2}\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(\frac{1}{2})^2+4(\frac{1}{2})(\frac{1}{2})+2(\frac{1}{2})^2+2(\frac{1}{2})(\frac{1}{2})\\\\=\frac{3}{4}+1+ \frac{1}{2}+\frac{1}{2}\\\\=2\frac{3}{4}[/tex]

Theoretical probability formula: Favorable Outcomes/All Possible Outcomes

So let's find the theoretical probability for each option.

"Not picking a square"

So, there are 2 squares out of the 8 total shapes (2 circles + 4 triangles + 2 squares) So do 8-2=6... This is subtracting the number of squares out. So we are now left with 6/8.. Reduce the fraction: GCF is 2, so 6/8 simplifies to 3/4. So, "Not picking a square" is an option!

"Picking a square"

Okay so there are 2 squares (favorable outcome) out of 8 shapes in total (all possible outcomes) so the fraction is 2/8. Now simplify: GCF = 2, so 2/8 = 1/4. "Picking a square" is NOT an option

"Picking a triangle"

There are 4 triangles out of 8 shapes, so the fraction is 4/8 which = 1/2. The theoretical probability of picking a triangle is 1/2 and thus NOT an option.

"Picking a shape that has only straight edges"

So this basically means every shape that's not a circle. So, there are 4 triangles + 2 squares = 6 total shapes with straight edges. So there are 6 shapes with straight edges out of 8 total shapes: 6/8 reduces to 3/4. "Picking a shape that has only straight edges" IS an option! :D

LASTLY!

"Not picking a circle"

There are only 2 circles out of 8 total shapes, so 8-2=6 so the fraction is 6/8. This reduces to 3/4. "Not picking a circle" Is an option!

CORRECT ANSWERS:

Not picking a square

Picking a shape that has only straight edges

Not picking a circle

Have a good day!

Answer:

A, D, and E

Step-by-step explanation:

got it right on edge