Daniel deposits $300 into an account that earns 16% interest annually. Which equation can be used to model his account balance, y, after x years?

Answer:

6/4

Explanation:

If Alex can file the papers in the cabinets for 6 hours and 4 hours with Millie, then the fraction to represent the papers filed with Millie would be 6/4.

Hope this helps!

Answer:

The 90th percentile for the distribution of the total contributions is $6,342,525.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums of size n, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sqrt{n}*\sigma[/tex]

In this question:

[tex]n = 2025, \mu = 3125*2025 = 6328125, \sigma = \sqrt{2025}*250 = 11250[/tex]

The 90th percentile for the distribution of the total contributions

This is X when Z has a pvalue of 0.9. So it is X when Z = 1.28. Then

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

By the Central Limit Theorem

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

[tex]1.28 = \frac{X - 6328125}{11250}[/tex]

[tex]X - 6328125 = 1.28*11250[/tex]

[tex]X = 6342525[/tex]

The 90th percentile for the distribution of the total contributions is $6,342,525.

Answer:

The sampling method is independent.

Step-by-step explanation:

Samples are said to be dependent when the data chosen in one sample has an effect on the data to be chosen in the other sample, while samples are said to be independent if the data chosen in one sample has no effect on the data to be chosen on the other sample.

Here, the stock analyst wants to know if there is a difference between the mean rate of return from energy stocks and that from financial stocks, so, he randomly selects 13 energy stocks. Since the energy stocks he chose were randomly selected, it means the data he selected from the energy stock will not dictate the type of data to be selected from the financial stock. Thus, the sampling method is said to be independent.

Answer:

a) The CDF of X/Y is calculated as:

[tex]F_{z} (\zeta) = \frac{\zeta}{\zeta + 2}[/tex] for [tex]0 < \zeta < \infty[/tex]  

[tex]F_{z} (\zeta) = 0[/tex] for [tex]\zeta \leq 0[/tex]

Note: Z = X/Y

b) Probability that A finishes before B = 1/3

Step-by-step explanation:

For clarity and easiness of expression, this solution is handwritten and attached as a file. Check the complete solution in the attached file.

Answer:

a

Step-by-step explanation:

(-1.00000005)^n

as n becomes very large, the function increases in both positive and negative direction.

If n=1, -1.00000005

if n=2, 1.0000001

if n= 3, -1.00000015

if n=20, 1.000001

if n=21, -1.00000105

Answer:

x = 2

Step-by-step explanation:

Well the diagonals bisect each other.

4x = 8

x = 2

Answer:

x = 2

Step-by-step explanation:

5x = 3x+4

2x = 4

x = 2

Answer:

x > 1

Step-by-step explanation:

Add 7 to both sides

x > 1

Answer:

-4, -6

Step-by-step explanation:

3x+6= 1x-2

2x+6= -2

2x= -8  

x= -4

Now that you have your x variable, you can go back and plug it in to your original equations:

y= 3(-4)+6,

      y= (-12)+6 therefore y= -6

y=1(-4) -2,

        y= (-4) -2 therefore y = -6

Answer: 5x-3

Step-by-step explanation:

(f+g)(x) means f(x)+g(x). Knowing this, we add the 2 functions together.

2x-6+3x+9

5x-3

Answer:

4/13

Step-by-step explanation:

There are 13 diamonds in a deck and 3 fours that aren't diamond

13+3=16

16/52 = 4/13

Answer:

5

Step-by-step explanation:

3(14+x) = 57

42 +3x = 57

3x = 15

x = 5

Answer:

Greater than 9.

Step-by-step explanation:

[tex]6(x/2 + 4)[/tex]

[tex]3x+24[/tex]

Answer:

2.2 metres squared

Step-by-step explanation:

We need to find the area of this trapezoid.

The area of a trapezoid is denoted by:

[tex]A=\frac{(b_1+b_2)h}{2}[/tex], where [tex]b_1[/tex] and [tex]b_2[/tex] are the parallel bases and h is the height

Here, we already know the lengths of the two bases; they are 0.9 metres and 2.3 metres. However, we need to find the length of the height.

Notice that one of the angles is marked 45 degrees. Let's draw a perpendicular line from top endpoint of the segment labelled 0.9 to the side labelled 2.3. We now have a 45-45-90 triangle with hypotenuse 2.0 metres. As one of such a triangle's properties, we can divide 2.0 by √2 to get the length of both legs:

2.0 ÷ √2 = √2 ≈ 1.414 ≈ 1.4

Thus, the height is h = 1.4 metres. Now plug all these values we know into the equation to find the area:

[tex]A=\frac{(b_1+b_2)h}{2}[/tex]

[tex]A=\frac{(0.9+2.3)*1.4}{2}=2.2[/tex]

The answer is thus 2.2 metres squared.

~ an aesthetics lover

Answer:

  8 full turns

Step-by-step explanation:

80 cm is 8 times 10 cm, so is 8 times around the spool.

Alex must unwind 8 full turns of thread from the spool.

__

He must unwind it once.

Answer:

8 in total turns

Step-by-step explanation:

Answer:

  A, C, D, E

Step-by-step explanation:

According to the rational root theorem, any rational roots will be of the form ...

  ±(divisor of the constant)/(divisor of the leading coefficient)

The constant is 8, and its divisors are 1, 2, 4, 8.

The leading coefficient is 6, and its divisors are 1, 2, 3, 6.

So, no rational root will have 3 in the numerator, eliminating choices B and F. The remaining choices are possible rational roots:

Answer:

-26

Step-by-step explanation:

2(x-4)=3(x+6)

2x-8=3x+18

2x-2x -8 = 3x-2x +18

-8 =X+18

-8-18=x+18-18

-26 = x

The value of the unknown number is -26.

Given that, twice the difference of a number and 4 is equal to three times the sum of the number and 6.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the unknown number x.

Twice the difference of a number and 4 = 2(x-4)

Three times the sum of the number and 6 = 3(x+6)

So, equation is 2(x-4)=3(x+6)

⇒ 2x-8=3x+18

⇒ 3x-2x=-8-18

⇒ x=-26

Therefore, the value of the unknown number is -26.

To learn more about an equation visit:

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Answer:

[tex]t=\frac{20.6-18.7}{\frac{8}{\sqrt{11}}}=0.788[/tex]  

The degrees of freedom are given by;

[tex] df =n-1= 11-1=10[/tex]

And the p value would be:

[tex]p_v =2*P(t_{10}>0.788)=0.449[/tex]  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different than 18.7

Step-by-step explanation:

Information given

[tex]\bar X=20.6[/tex] represent the sample mean

[tex]s=8[/tex] represent the sample standard deviation

[tex]n=11[/tex] sample size  

[tex]\mu_o =18.7[/tex] represent the value to test

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic  

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

Hypotesis to test

We want to verify if the true mean is equal to 18.7, the system of hypothesis would be:  

Null hypothesis:[tex]\mu =18.7[/tex]  

Alternative hypothesis:[tex]\mu \neq 18.7[/tex]  

The statistic is given by:

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

Replacing the info we got:

[tex]t=\frac{20.6-18.7}{\frac{8}{\sqrt{11}}}=0.788[/tex]  

The degrees of freedom are given by;

[tex] df =n-1= 11-1=10[/tex]

And the p value would be:

[tex]p_v =2*P(t_{10}>0.788)=0.449[/tex]  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different than 18.7

Answer:

C. The trails are not independent.

The probability of drawing one marble will not be independent of others thus option (c) is correct.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

As per the given,

Drawing 5 marbles from a bag with 10 red, 8 green, and 12 yellow marbles without replacement.

In without replacement, the remaining balls in each draw will go to be decreased thus they will be dependent events so binomial distribution will not be applied.

Hence "One marble's likelihood of being drawn won't be independent of the other marbles".

For more information about the probability,

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Answer:

[tex]4x -y = 5[/tex]

And if we rewrite this expression we got:

[tex] y= 4x -5[/tex]

If the system have just one solution then we need the slope different and for this reason we can discard the options:

y = 4x-5

-2y = -8x - 10 equivalent to y =4x+5

2y = 8x - 10  equivalent to y = 4x -5

And then the correct answer would be:

y=-4x + 5

Step-by-step explanation:

For this case we have the following equation given:

[tex]4x -y = 5[/tex]

And if we rewrite this expression we got:

[tex] y= 4x -5[/tex]

If the system have just one solution then we need the slope different and for this reason we can discard the options:

y = 4x-5

-2y = -8x - 10 equivalent to y =4x+5

2y = 8x - 10  equivalent to y = 4x -5

And then the correct answer would be:

y=-4x + 5

Answer:

A: y = –4x + 5

Step-by-step explanation:

I got it right on Edge

Answer:

[tex]$ \text {Sample mean} = \bar{x} = \mu = 500 \: hours $[/tex]

Step-by-step explanation:

What is Normal Distribution?

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.  

For the given scenario, it is known from numerous previous samples that when this service life is in control it is normally distributed with a mean of 500 hours and a standard deviation of 20 hours.

On three recent production batches, he tested service life on random samples of four headlamps.

We are asked to find the mean of the sampling distribution of sample means when the service life is in control.

Since we know that the population is normally distributed and a random sample is taken from the population then the mean of the sampling distribution of sample means would be equal to the population mean that is 500 hours.

[tex]$ \text {Sample mean} = \bar{x} = \mu = 500 \: hours $[/tex]

Whereas the standard deviation of the sampling distribution of sample means would be

[tex]\text {standard deviation} = s = \frac{\sigma}{\sqrt{n} } \\\\[/tex]

Where n is the sample size and σ is the population standard deviation.

[tex]\text {standard deviation} = s = \frac{20}{\sqrt{4} } \\\\ \text {standard deviation} = s = \frac{20}{2 } \\\\ \text {standard deviation} = s = 10 \: hours \\\\[/tex]

Answer:

A.

Step-by-step explanation:

A quadrilateral inscribed in a circle has its opposite angles adding up to 180°

So

<NOP + <M = 180

4x+8x-24 = 180

12x = 180+24

12x = 204

Dividing both sides by 12

x = 17

<NOP = 4(17)

= 68°

Answer: a) S'(1) = 136; S'(2) = 104; S'(4) = 76;

b) S''(1) = -38; S''(2) = -26; S''(4) = -2

Step-by-step explanation:

a) S' means first derivative;

[tex]\frac{d}{dt}[/tex](6t³ - 45t² +180t +130) = 6t² - 50t + 180

S'(1) = 6.1² - 50.1 + 180

S'(1) = 136

S'(2) = 6.2² - 50.2 + 180

S'(2) = 104

S'(4) = 6.4² - 50.4 + 180

S'(4) = 76

b) S'' is the second derivative of S:

[tex]\frac{d^2}{dt^2}[/tex](6t² - 50t + 180) = 12t - 50

S''(1) = 12.1 - 50

S''(1) = -38

S''(2) = 12.2 - 50

S"(2) = -26

S"(4) = 12.6 - 50

S"(4) = -2

c) Derivative is the rate of change of a function. The first derivative is the slope of the tangent line to the graph if the function in a determined point, while the second derivative measures how the rate of change is changing.

Analysing the values, we can conclude that the sales of the product after t months is decreasing at a rate of 12.

Answer:

 6x^2 -2x -6

Step-by-step explanation:

f(x) = 6x^2 -4

g(x) = 2x+2

f(x) - g(x) =  6x^2 -4 - (2x+2)

Distribute the minus sign

                   6x^2 -4 - 2x-2

Combine like terms

                  6x^2 -2x -6

Answer:

b

Step-by-step explanation:

6x^2

2x

-4+2=-2

Sequence= 4, 16

Difference=12

16+12=28

Answer is...

33+33=28

Answer:

Given..hope it helps

Step-by-step explanation:

Area of square= 36cm2 = total area

Side of square= √36= 6cm

Ratio a:b = 2:1

so let's take total area as 3x

while a is 2x and b is 1x

3x= 36 (given)

x= 36/3 = 12

so area of each rectangle--

area A= 2x= 24cm2

area B= x= 12cm2

While finding the dimensions, they both have a common length since they are from the same square which will be 6cm (side)

So,

Dimensions of rectangle A= 6cm * 4cm

Dimensions of rectangle B= 6cm * 2cm

Answer:

The volume of the space outside the pyramid but inside the prism is 225 cubic centimeters.

Step-by-step explanation:

To find this, you subtract the volume of the pyramid from the volume of the rectangular prism.

The prism and pyramid's bases is 25 cm²

The pyramid's height is 12÷2 or 6 cm

The volume formula for a prism is l×w×h

The volume formula for a pyramid is [tex]\frac{1}{3}[/tex] ×b×h

The area of the prism is 5×5×12 or 300 cm³

The area of the pyramid is [tex]\frac{1}{3} *25*6[/tex] or 75 cm³

300 cm³-75 cm³=225 cm³

The volume outside the pyramid but inside the prism is 225 cm³.

Answer:

X=4

Step-by-step explanation:

1. Distribute 3 to 2x and -9

2. You will get "6x-27 = -3"

3. Next, add 27 to -27 and -3

4. You will get "6x = 24"

5. Then, you will divide 6x and 24 by 6

6. You will get "6x/6 = 24/6"

7. The 6 will cancel the 6 in 6x.

8. Then, you will divide 24 and 6. which will give you the answer of 4

9. Add the "X=..." and...

10. You will get the answer of "X=4"