If you have $100 in a savings account earning 3% interest per year, how much will you have in
two years?

Answer:

6 years

Step-by-step explanation:

A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:

[tex]y=ab^x[/tex]

Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8

[tex]y=ab^x\\8=ab^0\\a=8[/tex]

Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2

Therefore:

[tex]y=ab^x\\y=8(1.2^x) \\[/tex]

To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x

[tex]20=8(1.2)^x\\20/8=1.2^x\\1.2^x=2.5\\Taking \ natural\ log\ of \ both\ sides:\\ln(1.2^x)=ln2.5\\xln(1.2)=0.9163\\x=0.9163/ln(1.2)\\x=5.026[/tex]

x = 6 years to the nearest year

Answer:

5 years

Step-by-step explanation:444

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   Hi my lil bunny!

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[tex]\frac{(17)(3.141593)}{12}[/tex]

= [tex]\frac{53.407075}{12}[/tex]

= [tex]4.45059[/tex]

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If this helped you, could you maybe give brainliest..?

Also Have a great day/night!

❀*May*❀

I have an answer and explanation but I can't type so search up the question you asked and you should get an answer and explanation from s0cratic.

Answer:

  0.4 meters

Step-by-step explanation:

The volume is ...

  V = LHB

  12.8 m³ = (8(5B))(5B)(B) = 200B³ . . . fill in given values

  0.064 m³ = B³ . . . . . simplify

  ∛0.064 m = B = 0.4 m

The breadth of the wall is 0.4 meters.

Answer:

3 miles

Step-by-step explanation:

5 + m=8

Subtract 5 from each side

5-5 + m=8-5

m = 3

She needs to swim 3 more miles

Answer:

Yelena needs to swim 3 more miles

Step-by-step explanation:

You need to solve for the variable "m", which represents the miles. Based on the information, Yelena swam 5 miles and she needs to swim 8. Solve:

[tex]5+m=8[/tex]

To find the value of m, you need to isolate it on one side of the equation. To do this, you need to get the 8 and 5 on the same side of the equal operation. For this, you need to use reverse operations. This undoes the value from one side and does the same on the other, keeping the equation balanced. Since we have a "positive 5", we take the opposite, which would be a "negative 5". So subtract 5 from both sides of the equation:

[tex]5-5+m=8-5[/tex]

Simplify. The 5's cancel each other out, leaving 0. 8-5 is 3:

[tex]m=3[/tex]

The total miles left that Yelena needs to swim is 3 miles.

:Done

Answer:

c. It does not appear to be within statistical control because there is an upward trend.

Step-by-step explanation:

Statistical process control is a method for quality control which employs statistical method to monitor and control process. It ensures operation efficiency and ensuring required specification to reduce wastes in production lines. Here the process variation is out of control because the statistical control has an upward trend.

Answer:

[tex]\large \boxed{31/63}[/tex]

Step-by-step explanation:

5/7 - 2/9

Make denominators equal by LCM.

(5 × 9)/(7 × 9) - (2 × 7)/(9 × 7)

45/63 - 14/63

Subtract fractions since denominators are equal.

(45 - 14)/63

31/63

Answer:

[tex]\frac{31}{63}[/tex]

Step-by-step explanation:

Therefore, the answer is [tex]\frac{31}{63}[/tex].

Answer:

(a) The probability that X is at most 30 is 0.9726.

(b) The probability that X is less than 30 is 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is 0.7406.

Step-by-step explanation:

We are given that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked. A random sample of 200 shafts is taken.

Let X = the number among these that are nonconforming and can be reworked

The above situation can be represented through binomial distribution such that X ~ Binom(n = 200, p = 0.11).

Here the probability of success is 11% that this much % of all steel shafts produced by a certain process are nonconforming but can be reworked.

Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).

So, the new mean of X, [tex]\mu[/tex] = [tex]n \times p[/tex] = [tex]200 \times 0.11[/tex] = 22

and the new standard deviation of X, [tex]\sigma[/tex] = [tex]\sqrt{n \times p \times (1-p)}[/tex]

                                                                  = [tex]\sqrt{200 \times 0.11 \times (1-0.11)}[/tex]

                                                                  = 4.42

So, X ~ Normal([tex]\mu =22, \sigma^{2} = 4.42^{2}[/tex])

(a) The probability that X is at most 30 is given by = P(X < 30.5)  {using continuity correction}

        P(X < 30.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{30.5-22}{4.42}[/tex] ) = P(Z < 1.92) = 0.9726

The above probability is calculated by looking at the value of x = 1.92 in the z table which has an area of 0.9726.

(b) The probability that X is less than 30 is given by = P(X [tex]\leq[/tex] 29.5)    {using continuity correction}

        P(X [tex]\leq[/tex] 29.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{29.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] 1.70) = 0.9554

The above probability is calculated by looking at the value of x = 1.70 in the z table which has an area of 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is given by = P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = P(X < 25.5) - P(X [tex]\leq[/tex] 14.5)   {using continuity correction}

       P(X < 25.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{25.5-22}{4.42}[/tex] ) = P(Z < 0.79) = 0.7852

       P(X [tex]\leq[/tex] 14.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{14.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] -1.70) = 1 - P(Z < 1.70)

                                                          = 1 - 0.9554 = 0.0446

The above probability is calculated by looking at the value of x = 0.79 and x = 1.70 in the z table which has an area of 0.7852 and 0.9554.

Therefore, P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = 0.7852 - 0.0446 = 0.7406.

Answer:

The answer is "253"

Step-by-step explanation:

In the given- equation there is mistype error so, the correct equation and its solution can be defined as follows:

Given:

[tex]\bold{\frac{dn}{dt} = 6\sqrt{t+1}}\\[/tex]

[tex]\to dn= 6\sqrt{t+1} \ \ dt.....(a)\\\\[/tex]

integrate the above value:

[tex]\to \int dn= \int 6\sqrt{t+1} \ \ dt \\\\\to n= \frac{(6\sqrt{t+1} )^{\frac{3}{2}}}{\frac{3}{2}}+c\\\\\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}+c\\\\[/tex]

When the value of n=1 then t=0

[tex]\to 1= \frac{12(0+1)^{\frac{3}{2}}}{3}+c\\\\ \to 1= \frac{12(1)^{\frac{3}{2}}}{3}+c\\\\\to 1-\frac{12}{3}=c\\\\\to \frac{3-12}{3}=c\\\\\to \frac{-9}{3}=c\\\\\to c=-3\\[/tex]

so the value of  n is:

[tex]\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}-3\\\\[/tex]

when we put the value t= 15 then,

[tex]\to n= \frac{(12\sqrt{15+1} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\sqrt{16} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\times 64)}{3}-3\\\\\to n= (4\times 64)-3\\\\\to n= 256-3\\\\\to n= 253[/tex]

Answer:

We conclude that the population mean is equal to 490.

Step-by-step explanation:

We are given that a random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9.

Let [tex]\mu[/tex] = population mean.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 490      {means that the population mean is equal to 490}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 490     {means that the population mean is different from 490}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                               T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_1_4[/tex]

where, [tex]\bar X[/tex] = sample mean = 495

            s = sample standard deviation = 9

             n = sample of observations = 15

So, the test statistics =   [tex]\frac{495-490}{\frac{9}{\sqrt{15} } }[/tex]  ~ [tex]t_1_4[/tex]

                                     =  2.152

The value of t-test statistics is 2.152.

Now, at a 0.01 level of significance, the t table gives a critical value of -2.977 and 2.977 at 14 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that the population mean is equal to 490.

13226/29= 456.068965517

Answer:

0.0618

Step-by-step explanation:

z = (x - μ)/σ, where

x is the raw score = 69

μ is the sample mean = population mean = 65

σ is the sample standard deviation

This is calculated as:

= Population standard deviation/√n

Where n = number of samples = 25

σ = 13/√25

σ = 13/5 = 2.6

Sample standard deviation = 2.6

z = (69 - 65) / 2.6

z = 4/2.6

z = 1.53846

Approximately to 2 decimal places = 1.54

Using the z score table to determine the probability,

P(x = 69) = P(z = 1.54)

= 0.93822.

The probability that the sample mean is greater than 69 is

P(x>Z) = 1 - 0.93822

P(x>Z) = 0.06178

Approximately to 4 decimal places = 0.0618

Answer:

 $900

Step-by-step explanation:

To begin with let us estimate the total cash value of the prices

$1000 x 1= 1000

$500 x 1=  500

$50 x 2= 100

Total = $1600

Now let us calculate the total cost of tickets sold at $2.50 per tickets for 1000 tickets

2.5*1000= $2,500

Assuming worse case that the lottery had winners in all three categories and i.e the total prices given out is $1600

Then the expected profit is = $2,500-$1600= $900

Answer:

d. all of the above

Step-by-step explanation:

A one sample z test measures whether the mean of a population is greater, less or equal to a specific value. It is called one sampl z test since the standard normal distribution is used in calculation of critical values. It makes use of the null hypothesis and alternative hypothesis in determining if the mean is greater than or equal or less than the reference value. Variance and standard deviation is assumed to be known and at least one population is used

Answer:

Option A (repeated measures design) is the correct option.

Step-by-step explanation:

The other three options are not related to the given instance. So that alternative A would be the correct choice.

Answer:

a) f(6)=(6)^2+4(6)+1=65

b)f (x+9)=(x+9)^2+4 (x+9)+1=(x^2+18x+81)+(4x+36)+1=x^2+22x+117

f (-x)=(-x)^2-4x+1

Answer:

symmetric

Step-by-step explanation:

it kind of evenly falls to the left and right from the highest value in the middle

skewed would be different and would look like a straight line not a quadratic equation

Question Completion:

WACC = 10.0%

Opportunity cost = $100,000

Net equipment cost (depreciable basis) = $65,000

Straight-line deprec. rate for equipment = 33.333%  

Sales revenues, each year = $123,000

Operating costs (excl. deprec.), each year = $25,000

Tax rate = 35%

Answer:

Century Roofing

Project's NPV is: ($6,578)

Step-by-step explanation:

a) Data and Calculations:

WACC = 10.0%

Opportunity cost = $100,000

Net equipment cost (depreciable basis) = $65,000

Straight-line deprec. rate for equipment = 33.333%  

Sales revenues, each year = $123,000

Operating costs (excl. deprec.), each year = $25,000

Tax rate = 35%

Cash outflow in year 0 = $165,000 (Opportunity and new equipment costs)

Annual Cash inflow = $123,000 - $25,000 - $34,300 = $63,700

PV of annuity for 3 years at 10% = $158,422 ($63,700 x 2.487)

NPV = Cash inflow minus Cash outflow

= $158,422 - $165,000

= ($6,578)

Negative NPV

b) Since Century Roofing could have realized $100,000 from the sale of the building if it decides not to open the new warehouse, this opportunity cost is factored into the calculation of the Net Present Value.  It becomes a present cash outflow.  Century Roofing's opportunity cost is defined as the loss of $100,000 being the future return from the best alternative project when it chooses to build the new warehouse instead of selling off the building.

Answer:

x >162

Step-by-step explanation:

x+54 > 216

Subtract 54 from each side

x+54-54 > 216 - 54

x >162

Answer:

[tex]\huge \boxed{{x>162}}[/tex]

Step-by-step explanation:

[tex]x+54 > 216[/tex]

[tex]\sf Subtract \ 54 \ from \ both \ parts.[/tex]

[tex]x+54 -54> 216-54[/tex]

[tex]x>162[/tex]

Answer:

To find the volume of this cube, you would have to multiply 1.08 by 5.25 by 3.3 feet. If you did this, you would get: 18.711 feet^3. This is the volume of the rectangular prism.

Hope this helped!

Answer:

0.2207

Step-by-step explanation:

Here, we want to find the probability that the sample mean is greater than 25.

What we use here is the z-scores statistic

Mathematically;

z-score = (x-mean)/SD/√n

From the question;

x = 65, mean = 63, SD = 13 and n = 25

Plugging these values in the z-score equation, we have

Z-score = (65-63)/13/√25 = 2/13/5 = 0.77

So the probability we want to calculate is ;

P(z > 0.77)

This can be obtained from the standard normal distribution table

Thus;

P(z > 0.77) = 0.22065 which is 0.2207 to 4 d.p

36×7

=252

Explaination :

First Multiply 6 and 7 we get 42 !

Write 2 and 4 will be added to the product of 3×7

We get 21 and add 4 here

So we get 252

Answer:

[tex]36 \times 7 = 252[/tex]

Step-by-step explanation:

Firstly multiply 6 with 7 you have to write 2 and take 4 carry and then multiply 7 with 3 u get 21 now add the number u carry in 21 u get ur answer. 252.

Hope it helps u mate

Answer:

8

Step-by-step explanation:

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

8x→1

7y→1

The largest exponent is the degree of the polynomial.

1

The leading term in a polynomial is the term with the highest degree.

8x

The leading coefficient of a polynomial is the coefficient of the leading term.

____________________________________________________________

The leading term in a polynomial is the term with the highest degree.

8x

The leading coefficient in a polynomial is the coefficient of the leading term.

8

List the results.

Polynomial Degree: 1

Leading Term: 8x

Leading Coefficient: 8

Hope This Helps!!!

Answer:

6/50

Step-by-step explanation:

There are 50 tiles

6 purple

18 pink

26 orange

P( purple) = purple/ total

                = 6/50

Answer:

3x18 = 3 (10+8) is an example of the commutative property of multiplication

Step-by-step explanation:

Answer: commutative property of multiplication

Step-by-step explanation:

Add up the P(x) values that correspond to x = 2 through x = 4

0.07+0.22+0.22

So we have a 51% chance of getting an x value such that 1 < x < 5

By using the probability distribution table, the value of P(1<x<5) is 0.51

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true

A probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events

Given,

We have to find the value of P(1<x<5)

P(1<x<5) = P(2)+P(3)+P(4)

P(2)=0.07

P(3)=0.22

P(4)=0.22

P(1<x<5) = 0.07+0.22+0.22 =0.51

Hence, the value of P(1<x<4)= 0.51

Learn more about Probability and Probability distribution here

https://brainly.com/question/14210034

#SPJ2

Answer:

M= 521.1 g

Step-by-step explanation:

1st.  Find the volume of the cube:   V=3³=27 cm³

As the weight of V= 1 cm³ cube  is 19.3 g the weight of the cube=27 cm³ is

M=27*19.3= 521.1 g

Answer:

Step-by-step explanation:

∠a is alternate interior angle to ∠ECD

∠b is alternate interior angle to ∠BCD

so:

If AB || CD then:

m∠a = m∠ECD = 25° + 42° = 67°

m∠b = 42°