What is the result of..
4! / (4!4!)

Answers

Answer 1

Answer: $(4!)/(4!4!)$

$(4*3*2*1)/(4*3*2*1*4*3*2*1)$

$(1)/(4*3*2*1)$

$(1)/(24)$

Answer 2

Answer: $(4!)/(4!4!)=(1)/(4!)=(1)/(24)$

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Using a tape measure Becky Jo found that the circumference of the great redwood was 900cm. She estimated that its diameter was 300cm. Was her estimate a little too large or a little too small? Why?
What value of x will satisfy the equation 0.2(x −2,700) = x?
(2+7i)(2-7i)= ==========

Help please and thank you!

Answers

Answer:

25. (x, y) = (5, 11)

26. (x, y) = (-1, 1)

Step-by-step explanation:

Both equations are of the form y=( ), so you can set the expressions for y equal to each other. Or, you can subtract the equation with the smaller y-coefficient from the other one.

25.

x +6 = y = 2x +1 . . . . . equate expressions for y

5 = x . . . . . . . . . . . subtract x+1

y = 5+6 = 11 . . . . . using the first equation to find y

(x, y) = (5, 11)

26.

(y) -(y) = (3x +4) -(x+2) . . . . subtract the first equation from the second

0 = 2x +2 . . . . . . . . . . . . . . simplify

0 = x + 1 . . . . . . . . . . . . . . . . divide by the x-coefficient

x = -1 . . . . . . . . . . . . . . subtract the constant

y = -1 +2 = 1 . . . . . . . . . use the first equation to find y

(x, y) = (-1, 1)

_____

Of course, when we say "subtract ..." or "divide ..." we mean that you should do the same operation to both sides of the equation. That way the equal sign remains valid. You can always use an expression or variable in place of its equal (this is the substitution property of equality).

The expression (x+1) that we subtract in problem 25 is the smaller x-term plus the constant on the opposite side of the equal sign. That way, we eliminate both the unwanted x-term and the unwanted constant. You can do these operations one at a time (and you were probably taught to do it that way). That is, subtract x; subtract 1.

For 26, the method of solution that puts both the variable and the constant on the same side of the equation and 0 on the other side has certain advantages. Subtracting one side of the equation from both sides (to make an expression equal to zero) will always work, regardless of the expressions involved. After simplification, you can divide by the coefficient of the variable to get the form x+constant=0, and the answer is always x = -constant. These simple instructions require no judgment. You may find it easier to choose to subtract the side with the smaller coefficient, so the result has a positive coefficient. That's not necessary, but it can reduce anxiety and errors.

The highest temperature on a given winter day is 5°F what is the temperature in C What is the temperature for C

Answers

Answer:

5F = -15C ( 1F=-17.2222222)

Final answer:

The highest temperature on a winter day of 5°F is equivalent to -15°C. This is derived by using the formula to convert Fahrenheit to Celsius: C = (5/9)*(F - 32). Therefore, the temperature in Celsius is -15°C.

Explanation:

The problem is asking for the conversion of temperature from Fahrenheit to Celsius. The formula to convert Fahrenheit to Celsius is C = (5/9)*(F - 32). Let's use it to solve the question.

Given that the Fahrenheit (F) temperature is 5°F, the Celsius (C) temperature would be calculated as: C = (5/9)*(5 - 32), resulting in a Celsius temperature of about -15°C. This means that 5°F is equivalent to -15°C.

Learn more about Temperature Conversion

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How many leaves on a tree diagram are needed to represent all possible combinations tossing a coin 4 times?

Answers

Answer with explanation:

When you toss a coin once , total possible outcome =2={H, T}

When you toss a coin twice , total possible outcome =2²=4={HT,TH,T T,H H}

When you toss a coin thrice , total possible outcome =2³=8

={T T T,T TH, T HT,H T T,H HT,H TH,T H H,H H H}

When you toss a coin 4 times , total possible outcome

$2^4=16$

={T T T T, T T TH, H T T T,T H T T,T T HT,T T H H,H H T T,T H HT,H T TH,H TH T,T H TH, H H HT,H T H H,TH H H,H H TH,H H H H}

=16

There are 16 possible outcomes in all.

So, total number of leaves needed on the tree Diagram = 16 Leaves

1/2 x 1/2 x 1/2 x 1/2 = 1/16

Answer: 16

Use the quadratic formula to solve 2y2 + 6y – 8 = 0. A {–4, –1} B {4, –1} C {–4, 1} D {4, 1}

Answers

y = [-6 +/- sqrt(6^2 -4*2*-8)] / 2*2
= (-6 +/- sqrt 100) / 4
= (-6+10) / 4 , (-6-10) / 4
= (1 , -4)

the answer is C

Allie deposited $300.00 into a new savings account that earns 13% interest compounded quarterly. How long will it take for the balance to grow to $995.00? Round your answer to the nearest month. years and months

Answers

Answer:

9 years 4 months

Step-by-step explanation:

To find out how long it will take for Allie's initial deposit of $300to grow to $995 in a savings account with a 13% annual interest rate compounded quarterly, we can use the compound interest formula:

$\boxed{\begin{array}{l}\underline{\textsf{Compound Interest Formula}}\n\nA=P\left(1+(r)/(n)\right)^(nt)\n\n\textsf{where:}\n\phantom{ww}\bullet\;\;\textsf{$A$ is the final amount.}\n\phantom{ww}\bullet\;\;\textsf{$P$ is the principal amount.}\n\phantom{ww}\bullet\;\;\textsf{$r$ is the interest rate (in decimal form).}\n\phantom{ww}\bullet\;\;\textsf{$n$ is the number of times interest is applied per year.}\n\phantom{ww}\bullet\;\;\textsf{$t$ is the time (in years).}\end{array}}$

In this case:

A = $995
P = $300
r = 13% = 0.13
n = 4 (quarterly)

Substitute the values into the formula and solve for t:

$995=300\left(1+(0.13)/(4)\right)^(4t)$

Simplify the expression inside the bracket:

$995=300\left(1.0325\right)^(4t)$

Divide both sides of the equation by 300:

$(995)/(300)=\left(1.0325\right)^(4t)$

Take natural logs (ln) of both sides of the equation:

$\ln\left((995)/(300)\right)=\ln\left(1.0325^(4t)\right)$

$\textsf{Apply the power law:} \quad \ln x^n=n \ln x$

$\ln\left((995)/(300)\right)=4t\ln\left(1.0325\right)$

Divide both sides of the equation by 4ln(1.0325) to isolate t:

$(\ln\left((995)/(300)\right))/(4\ln\left(1.0325\right))=t$

$t=(\ln\left((995)/(300)\right))/(4\ln\left(1.0325\right))$

Evaluate using a calculator:

$t=9.37184241...$

Therefore, it will take 9.37 years for the balance to grow to $995.00.

To determine the number of months, subtract 9 from the value of t and multiply by 12:

$\textsf{Months}=12(9.37184241...-9)=4.46210895...$

Therefore, it will take 9 years and 4 months (rounded to the nearest month) for the balance to grow to $995.00.

Additional comments

In the case of quarterly compounding, the interest is calculated and added to the account balance every three months (once every quarter). So, even though it will take 9 years and 4 months for the balance to reach $995.00, Allie's account will not show this exact amount at that specific time. It will show a balance of $979.61 at 9 years and 3 months, and a balance of $1,011.45 at 9 years and 6 months, so technically, the account balance will still show as $979.61 at 9 years and 4 months.

Answer:

9 years and 4 months

Step-by-step explanation:

In order to calculate the number of years and months it will take for Allie's savings account balance to grow to $995.00, we can use the following compound interest formula:

$\sf A = P\left(1 + (r)/(n)\right)^(nt)$

where:

A is the future value
P is the present value
r is the annual interest rate
n is the number of compounding periods per year
t is the number of years

We can use the following values for the variables in the formula:

P = $300.00

r = 13% = 0.13

n = 4 (compounding quarterly)

A = $995.00

Substituting value, we get

$\sf 995 = 30000\left(1 + (0.13)/(4)\right)^(4\cdot t)$

$\sf 995 = 300.00\left(1.0325\right)^(4\cdot t)$

$\sf (995)/(300)=\left(1.0325\right)^(4\cdot t)$

$\sf 3.316 = \left(1.0325\right)^(4\cdot t)$

In order to solve the exponential equation, we can take the natural log of both sides:

$\sf ln(3.316) = ln(1.0325) ^ {4t}$

Using the properties of logarithms, we can bring the exponent down in front of the log:

$\sf 4t * ln(1.0325) = ln(3.316)$

Dividing both sides by ln(1.0325), we get:

$\sf t =( ln(3.316) )/(4ln(1.0325))$

Evaluating this expression, we get:

$\sf t = 9.3702710709672$

In the nearest hundred:

$\sf t \approx 9.37$

Therefore, year = 9 year

month = 37% of 12 = 4.44≈ 4 month

So, it will take Allie 9 years and 4 months for her savings account balance to grow to $995.00.

A manager of a grocery store wants to determine if consumers are spending more than the national average. The national average is $150.00 with a standard deviation of $30.20. The manager collects 40 random receipts and finds that the average is $160. Complete a hypothesis test with a significance level of 2.5% to determine if the average customer spends more in his store than the national average. Which of the following is a valid conclusion for the manager based on this test?a.The customers spend more than the national average in his store.b.The manager should decrease prices in his store.c.The customers do not spend more than the national average in his store.d.The customers in his store just come from a rich neighborhood.

Answers

Answer:

The correct answer is:

The customers spend more than the national average in his store

Step-by-step explanation:

The national average is $150.00 with a standard deviation of $30.20.

Sample size n =40

H0: x bar = mu

Ha: x bar >mu

(one tailed test for a single mean)

Sample average x bar = 160

Mean difference = 160-150 =10

std error = 30.20/sqrt 40

=4.775

Test statistic = 2.094

Z critical for 2.5% = 1.96 (one tailed)

Since test statistic > z critical we reject null hypothesis.

Hence the correct answer is:

The customers spend more than the national average in his store.

Answer:

Option A) The customers spend more than the national average in his store.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $150.00

Sample mean, $\bar{x}$ = $160

Sample size, n = 40

Alpha, α = 0.025

Population standard deviation, σ = $30.20

First, we design the null and the alternate hypothesis

$H_(0): \mu = 150\text{ dollars}\nH_A: \mu > 150\text{ dollars}$

The null hypothesis states that the consumers are spending equal to the national average. The alternative hypothesis states that consumers are spending more than the national average.

We use One-tailed z test to perform this hypothesis.

Formula:

$z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }$