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ivann1987 [24]
3 years ago
7

Solve for the variable z to 4 = 8/5

Mathematics
1 answer:
Shkiper50 [21]3 years ago
5 0

Answer:

Alright well solve for z by simplifying by both sides of the equation, then isolating the variable

Exact form: z = 2/5

Decimal form: o.4 Hope this helps :)

Step-by-step explanation:


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18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:
Ksenya-84 [330]

a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}

S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525

8 0
3 years ago
Suppose you want to accumulate $25,000 as down payment on a house and the best you can do is to put aside $200 a month. If you d
Sunny_sXe [5.5K]

Answer:

It will take 88.2 months to accumulate the amount

Step-by-step explanation:

Given;

Future value of money, FV = $25,000

investment per compound period, P = $200

interest rate, i = 0.75% x 12 = 9%

The number of monthly installments required to amount to FV is given by;

n = \frac{ln(FVi +cp)-ln(cp)}{ln(c+i)-ln(c)}\\\\ n = \frac{ln(25000*0.09 +200*12)-ln(200*12)}{ln(12+0.09)-ln(12)}\\\\n = \frac{8.4446 -7.7832}{2.4924-2.4849}\\\\n = 88.2 \ months

Therefore, it will take 88.2 months to accumulate the amount.

7 0
3 years ago
6. Marcus sold 6 pizzas. Sue sold 4 pizzas.
mestny [16]

Answer:

6*$10= $60

4*$10=$40

60+40= $100

$100

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Find A and B. Using the image above.
NeX [460]

Answer:

a = 7, b = \frac{7\sqrt{3} }{3}

Step-by-step explanation:

Using the sine ratio in the left right triangle and the exact value

sin45° = \frac{1}{\sqrt{2} } , then

sin45° = \frac{opposite}{hypotenuse} = \frac{a}{7\sqrt{2} } = \frac{1}{\sqrt{2} } ( cross- multiply )

a × \sqrt{2} = 7\sqrt{2} ( divide both sides by \sqrt{2} )

a = 7

--------------------------------------------------------

Using the tangent ratio in the right triangle on the right and the exact value

tan60° = \sqrt{3} , then

tan60° = \frac{opposite}{adjacent} = \frac{a}{b} = \frac{7}{b} = \sqrt{3} ( multiply both sides by b )

b × \sqrt{3} = 7 ( divide both sides by \sqrt{3} )

b = \frac{7}{\sqrt{3} } × \frac{\sqrt{3} }{\sqrt{3} } = \frac{7\sqrt{3} }{3}

7 0
2 years ago
I don’t know how to do it, please teach me !!!
cricket20 [7]

As described in z-distribution the answers are given below:

a) The 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month is given as follows: (747, 853).

b) The sampling error at 95% confidence level is of: $35.78.

What is a z-distribution ?

The normal distribution with a mean of 0 and a standard deviation of 1 is referred to as the standard normal distribution (also known as the Z distribution) (the green curves in the plots to the right). It is frequently referred to as the bell curve since the probability density graph resembles a bell.

solution:

The bounds of the confidence interval are given as follows:

In which:

is the sample mean.

z is the critical value.

n is the sample size. is the standard deviation for the population.

The parameters for this problem are given as follows:

Hence the lower bound of the interval is of:

800 - 200 x 1.96/square root of 55  = 747.

The upper bound of the interval is of:

800 + 200 x 1.96/square root of 55  = 853.

The sampling error for a sample size of 120 is calculated as follows:

200 x 1.96/square root of 120 = $35.78.

To learn more about the z-distribution from the given link

brainly.com/question/4079902

#SPJ1

5 0
1 year ago
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