Cooper invested $3,100 in an account paying an interest rate of 2%
compounded quarterly. Robert invested $3,100 in an account paying an
interest rate of 3 % compounded continuously.After 12 years, how much
more money would Robert have in his account than Cooper, to the nearest
dollar?

Answer:

a) SAT score = 1075

b) ACT score = 19.2.

c) ACT score = 27.9.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score

SAT scores have mean 1070 and standard deviation 204, so [tex]\mu = 1070, \sigma = 204[/tex]

51th percentile means that Z has a p-value of 0.51, so Z = 0.025. The score is X. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.025 = \frac{X - 1070}{204}[/tex]

[tex]X - 1070 = 0.025*204[/tex]

[tex]X = 1075[/tex]

SAT score = 1075.

(B) What would be the equivalent ACT score for this student?

ACT scores have mean of 19.1 and standard deviation of 5.2, which means that [tex]\mu = 19.1, \sigma = 5.2[/tex]. The equivalent score is X when Z = 0.025. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.025 = \frac{X - 19.1}{5.2}[/tex]

[tex]X - 19.1 = 0.025*5.2[/tex]

[tex]X = 19.2[/tex]

ACT score = 19.2.

(C) If a student gets an SAT score of 1417, find the equivalent ACT score.

Z-score for the SAT:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1417 - 1070}{204}[/tex]

[tex]Z = 1.7[/tex]

Equivalent score on the ACT:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.7 = \frac{X - 19.1}{5.2}[/tex]

[tex]X - 19.1 = 1.7*5.2[/tex]

[tex]X = 27.9[/tex]

ACT score = 27.9.

Answer:

Step-by-step explanation:

First,

7 times 8 = 7 × 8 = 56

Then,

The product divided by 2 = 56 ÷ 2 = 28

Hence,

The required answer is 28

Answer:

He can lift 160 pounds

Step-by-step explanation:

125 (from last year) + 35 (more pounds) = 160 (total pounds)

125 + 35 = 160

Answer:

the volume is 600

Step-by-step explanation:

15*8*5=600

v=w*h*l

Answer:

[tex](a)\ Pr = \frac{2}{5}[/tex]

[tex](b)\ Pr = \frac{9}{20}[/tex]

[tex](c)\ E(Orange) = 100[/tex]

[tex](d)\ E(Orange) = 62.5[/tex]

Step-by-step explanation:

Solving (a): Theoretical probability of green or yellow

Here, we consider the spinner itself

From the attached image, we have:

[tex]n= 5[/tex] --- i.e. 5 sections

[tex]Yellow = 1[/tex]

[tex]Green = 1[/tex]

So, the probability is:

[tex]Pr = P(Yellow)\ or\ P(Green)[/tex]

[tex]Pr = \frac{Yellow}{n} + \frac{Green}{n}[/tex]

[tex]Pr = \frac{1}{5} + \frac{1}{5}[/tex]

Take LCM

[tex]Pr = \frac{1+1}{5}[/tex]

[tex]Pr = \frac{2}{5}[/tex]

Solving (b): Experimental probability of green or yellow

Here, we consider the result of the experiment

From the attached image, we have:

[tex]n= 40[/tex] --- i.e. 40 spins

[tex]Yellow = 12[/tex]

[tex]Green = 6[/tex]

So, the probability is:

[tex]Pr = P(Yellow)\ or\ P(Green)[/tex]

[tex]Pr = \frac{Yellow}{n} + \frac{Green}{n}[/tex]

[tex]Pr = \frac{12}{40} + \frac{6}{40}[/tex]

Take LCM

[tex]Pr = \frac{12+6}{40}[/tex]

[tex]Pr = \frac{18}{40}[/tex]

Simplify

[tex]Pr = \frac{9}{20}[/tex]

Solving (c): Expectation of orange outcomes in a spin of 500 times, theoretically.

Here, we consider the spinner itself

From the attached image, we have:

[tex]n= 5[/tex] --- i.e. 5 sections

[tex]Orange = 1[/tex]

So, the probability of having an outcome of orange in 1 spin is:

[tex]Pr = P(Orange)[/tex]

[tex]Pr = \frac{Orange}{n}[/tex]

[tex]Pr = \frac{1}{5}[/tex]

In 500 spins, the expectation is:

[tex]E(Orange) = Pr * 500[/tex]

[tex]E(Orange) = \frac{1}{5} * 500[/tex]

[tex]E(Orange) = 100[/tex]

Solving (c): Expectation of orange outcomes in a spin of 500 times, base on experiments.

Here, we consider the spinner itself

From the attached image, we have:

[tex]n= 40[/tex] --- i.e. 40 spins

[tex]Orange = 5[/tex]

So, the probability of having an outcome of orange is:

[tex]Pr = P(Orange)[/tex]

[tex]Pr = \frac{Orange}{n}[/tex]

[tex]Pr = \frac{5}{40}[/tex]

[tex]Pr = \frac{1}{8}[/tex]

In 500 spins, the expectation is:

[tex]E(Orange) = Pr * 500[/tex]

[tex]E(Orange) = \frac{1}{8} * 500[/tex]

[tex]E(Orange) = 62.5[/tex]

Answer:

28 in.

Step-by-step explanation:

Since the right portion of the figure is a square, the unlabeled bottom must be the same as the top or 6 in., therefore just add up the pieces starting on the right side. (5 + 6 + 2 + 5 + 4 + 6 = 28)

Answer:

28.3 (b)

Step-by-step explanation:

To solve circumference, you will need to use the equation C = 2 *pi* r

for this, we will use 3.14 for pi and the radius is 4.5 so this is how we need to solve it

C= 2 pi (4.5)             Solve 2*4.5

C= 9 pi                     Now we input 3.14 for pi and multiply

C= 9(3.14)

C= 28.26                  Now we round to the nearest tenth to get

C=28.3

Answer:

Subject : Tomato plant

Explanatory variables : Watering condition ; Fertilizer addition

Treatment : daily watering ; half fertilizer ; full fertilizer

Response variable = Number of tomato picked

Step-by-step explanation:

Subjects are the individuals, animals or plants upon which treatment is applied. The subject here are the tomato plants

The Explanatory variables are the independent variables upon which we want base the variation of the dependent variable. The Independent variables are the watering condition a d the amount of fertilizer added.

Treatment : These are the actual changes made or applied on the subject, they include, daily watering, full or half fertilizer application.

Response variable : The number of tomatoes picked. This is also called the dependent variable, it is the outcome which may be due to the effect of the independent variable.

Answer:

1,408 packs can be made, and 2 pens will be left out.

Step-by-step explanation:

Given that a manufacturer has 5,634 pens to divide into packs of 4 pens, and the manufacturer makes as many packs as possible, to determine how many packs of pens does the manufacturer make, and how many pens are left over, the following must be done calculation:

5.634 / 4 = X

1,408.5 = X

5,634 - (1,408 x 4) = X

5.634 - 5.632 = X

2 = X

Therefore, 1,408 packs can be made, and 2 pens will be left out.

Answer: 1,408 packs can be made and 2 will be left out

Step-by-step explanation:

Answer:

a.

Approximately [tex]24.7\; \rm in[/tex].

b.

While there are three diagonals in a box (a rectangular prism,) all three diagonals goes through the same point- the centroid of this box.  

For a maximum-length poster to fit in this box, it would have to be on one of the main diagonals of this box. Hence, any maximum-length poster that fits in this box would go through the centroid of this box.

It's not possible to force more than one posters to go through the same point (i.e., the centroid) in space. Hence, it would not be possible to fit a second maximum-length poster into this box.

This argument does not apply to  [tex]21.5\; \rm in[/tex] posters. These posters are shorter than the diagonal of this box; they could fit inside the box without having to go through a particular point in space.

Step-by-step explanation:

The longest poster that could be fit into this box (a rectangular prism) would be as long as the longest line segment in this box. That line segment would be one of the three diagonals of this box.

Apply the Pythagorean theorem twice to find the length of that diagonal.

Start by finding calculating the diagonal of the base of this box. The base of this box is a rectangle with width [tex]8\; \rm in[/tex] and length [tex]10\; \rm in[/tex]. The length of its diagonal would be [tex]\sqrt{8^2 + 10^2}[/tex] inches.

Combine that with the height of this box to find the length of the diagonal of this box.

[tex]\begin{aligned}& \sqrt{{\left(\sqrt{8^2 + 10^2}\right)}^2 + 12^2 \\ &= \sqrt{8^2 + 10^2 + 12^2} \\ &\approx 24.7 \end{aligned}[/tex].

Answer:

1.004728

Step-by-step explanation:

Mark as brainllest

Answer:

The 95% confidence interval for the proportion of water specimens that contain detectable levels of lead is (0.472,0.766).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead.

This means that [tex]n = 42, \pi = \frac{26}{42} = 0.619[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.619 - 1.96\sqrt{\frac{0.619*0.381}{42}} = 0.472[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.619 + 1.96\sqrt{\frac{0.619*0.381}{42}} = 0.766[/tex]

The 95% confidence interval for the proportion of water specimens that contain detectable levels of lead is (0.472,0.766).

Answer:

A

Step-by-step explanation:

This can be rearranged as 4^3 * 1/(4^6)

or (4^3)/(4^6)

This can be changed to:

(4^3)/((4^3)*(4^3)

Which is equal to 1/(4^3)

or

4^(-3)

Answer:

simple interest

Step-by-step explanation:

An additional amount of money added to borrowed money only on the principal could be simple interest.

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

Since, the initial amount (also called as principal amount) is P, and the interest rate is R% per unit of time, it is left for T unit of time for that compound interest.

we can conclude that the additional amount of money added to borrowed money only on principal is simple interest.

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Given:

The given sum is:

[tex]\sum _{k=4}^9(5k+3)[/tex]

To find:

The expanded form and find the sum.

Solution:

We have,

[tex]\sum _{k=4}^9(5k+3)[/tex]

The expanded form of given sum is:

[tex]\sum _{k=4}^9(5k+3)=(5(4)+3)+(5(5)+3)+(5(6)+3)+(5(7)+3)+(5(8)+3)+(5(9)+3)[/tex]

[tex]\sum _{k=4}^9(5k+3)=(20+3)+(25+3)+(30+3)+(35+3)+(4+3)+(45+3)[/tex]

[tex]\sum _{k=4}^9(5k+3)=23+28+33+38+43+48[/tex]

[tex]\sum _{k=4}^9(5k+3)=213[/tex]

Therefore, the correct option is C.

Answer:

I DONT SEE TRIANGLES

Step-by-step explanation:

Answer:

I think its

ai. fx-f3

ii. 5gx

Answer:

It would take 4 years. The formula for continuously compounded interest is: where P is the principal, r is the interest rate as a decimal number, and t is the number of years.

Step-by-step explanation:

You deposit $800 in an account that pays 3.6% annual interest compounded quarterly. after 11 years your balance first exceed $1200.

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

You deposit $800 in an account that pays 3.6% annual interest compounded quarterly.

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

[tex]1200 = 800(1 + \dfrac{3.6}{4})^{4t}\\\\300 = (1 + 0.9)^{4t}\\\\t = 11.4[/tex]

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Answer:

x=3

Step-by-step explanation:

y=-x+3

0=-x+3

x=3

Answer:

this whole sentence confused me a lot

Step-by-step explanation:

yes there is, but it depends on how you want to do it

Answer:

I don't really get what you're implying can you please explain?

Step-by-step explanation:

haha this just really confused me :)

Answer:

80 cups

Step-by-step explanation:

1 gallon = 128 oz

5x128= 640 oz

640/8=80

Answer:

x = 2 , 1

Step-by-step explanation:

Answer:

2.5 or 3.5

Step-by-step explanation:

The quadratic formula is [tex]x = -b +/- \frac{\sqrt{b^2 + 4ac}}{2a}[/tex] .

a, b, and c are determined by the terms in the formula ax^2 + bx + c

They gave you the equation x^2 - 3x - 2, which fits that formula. a is 1, b is -3, and c is -2. So plug those values into the equation:

[tex]x = -(-3) +/- \frac{\sqrt{(-3)^2 + 4(1)(-2)}}{2(1)}[/tex]

[tex]x = 3 +/- \frac{\sqrt{9 -8}}{2}[/tex]

[tex]x = 3 +/- \frac{\sqrt{1}}{2}[/tex]

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

So x is 3 plus or minus -1/2. 3 plus -1/2 is 2.5

3 minus -1/2 is 3.5

So the 2 possible x values are 2.5 and 3.5.

Answer:

Here is the picture

Step-by-step explanation:

The number lies between x-values 4 and 6 and y-values 6 and 9.

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

Given that scatter plot lies in quadrant 1 of a coordinate plane, and the 14 points are plotted in the first quadrant.

We need to find the range of x and y values for this scatter plot.

The x values of the 14 points are given as;

2, 4, 4,1, 5, 5, 5, 5, 6, 6, 7, 8, 9.5, 9.5

The y values of the 14 points are given as;

5, 6, 9, 7.2, 6, 6.8, 8, 9, 7, 8.5, 10, 10.5, 9.5, 11.4

We can conclude that that most of the points are clustered between x-values 4 and 6 and y-values 6 and 9.

Therefore, the points are clustered between the x-values 4 and 6 and y-values 6 and 9.

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The complete question is

Select the correct answer. Scatter plot in quadrant 1 of a coordinate plane. 14 points are plotted at (2, 5), (4, 6), (4, 9), (4.1, 7.2), (5, 6), (5, 6.8), (5, 8), (5, 9), (6, 7), (6, 8.5), (7, 10), (8, 10.5), (9.5, 9.5), and (9.5, 11.4). Between which x-values and y-values does the cluster in this scatter plot lie? A. It lies between x-values 2 and 4 and y-values 4 and 6. B. It lies between x-values 4 and 6 and y-values 9 and 10. C. It lies between x-values 4 and 6 and y-values 6 and 9. D. It lies between x-values 7 and 9 and y-values 10 and 11.

sum of observations

no. of observations

50+55+58+90+58+92+99 502

7 7

awnser is 71.7

Answer:

[tex]Width = 4ft[/tex]

[tex]Height = 4ft[/tex]

[tex]Length = 8ft[/tex]

Step-by-step explanation:

Given

[tex]Volume = 128ft^3[/tex]

[tex]L = 2W[/tex]

[tex]Base\ Cost = \$9/ft^2[/tex]

[tex]Sides\ Cost = \$6/ft^2[/tex]

Required

The dimension that minimizes the cost

The volume is:

[tex]Volume = LWH[/tex]

This gives:

[tex]128 = LWH[/tex]

Substitute [tex]L = 2W[/tex]

[tex]128 = 2W * WH[/tex]

[tex]128 = 2W^2H[/tex]

Make H the subject

[tex]H = \frac{128}{2W^2}[/tex]

[tex]H = \frac{64}{W^2}[/tex]

The surface area is:

Area = Area of Bottom + Area of Sides

So, we have:

[tex]A = LW + 2(WH + LH)[/tex]

The cost is:

[tex]Cost = 9 * LW + 6 * 2(WH + LH)[/tex]

[tex]Cost = 9 * LW + 12(WH + LH)[/tex]

[tex]Cost = 9 * LW + 12H(W + L)[/tex]

Substitute: [tex]H = \frac{64}{W^2}[/tex] and [tex]L = 2W[/tex]

[tex]Cost =9*2W*W + 12 * \frac{64}{W^2}(W + 2W)[/tex]

[tex]Cost =18W^2 + \frac{768}{W^2}*3W[/tex]

[tex]Cost =18W^2 + \frac{2304}{W}[/tex]

To minimize the cost, we differentiate

[tex]C' =2*18W + -1 * 2304W^{-2}[/tex]

Then set to 0

[tex]2*18W + -1 * 2304W^{-2} =0[/tex]

[tex]36W - 2304W^{-2} =0[/tex]

Rewrite as:

[tex]36W = 2304W^{-2}[/tex]

Divide both sides by W

[tex]36 = 2304W^{-3}[/tex]

Rewrite as:

[tex]36 = \frac{2304}{W^3}[/tex]

Solve for [tex]W^3[/tex]

[tex]W^3 = \frac{2304}{36}[/tex]

[tex]W^3 = 64[/tex]

Take cube roots

[tex]W = 4[/tex]

Recall that:

[tex]L = 2W[/tex]

[tex]L = 2 * 4[/tex]

[tex]L = 8[/tex]

[tex]H = \frac{64}{W^2}[/tex]

[tex]H = \frac{64}{4^2}[/tex]

[tex]H = \frac{64}{16}[/tex]

[tex]H = 4[/tex]

Hence, the dimension that minimizes the cost is:

[tex]Width = 4ft[/tex]

[tex]Height = 4ft[/tex]

[tex]Length = 8ft[/tex]

Answer:

90°

Step-by-step explanation:

It's simple, the angle of a line is 180°

∠EFG=90°

Line GD-∠EFG=180°-90°=90°

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9514 1404 393

Answer:

  3.  2n - 4 = 7(n + 8)

Step-by-step explanation:

Two times a number is 2n. Four less than 2n is (2n-4). The sum of a number and 8 is (n+8). Seven times that sum is 7(n+8). The statement says these values are equal:

  2n -4 = 7(n +8)

Answer:

Step-by-step explanation:

1/48 + 5/6    

The LCD of 48 and 6 is 48 so we have:

1/48 + 40/48

= 41/38

Answer:

41/48

Step-by-step explanation: