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3 years ago

P+7 – 5 = –10 – 3p Step by step

Mathematics

1 answer:

oksian1 [2.3K]3 years ago

6 0

Step-by-step explanation:

you add the three p to p and that's 4p and

4p+7-5=-10

4p-2=-10

+2=+2

4p=-8

devide by four on both side so p is-2

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he XO Group Inc. conducted a survey of brides and grooms married in the United States and found that the average cost of a weddi

ahrayia [7]

Answer:

A. P(X<20,000) = 0.0392

B. P(20,000 < x < 30,000) = 0.488

C. Amount = $39,070

Step-by-step explanation:

From XO group website

Cost of a wedding = $29,858

Mean, μ = $29,858

Standard Deviation, σ =$5,600

a. Calculating the probability that a wedding costs less than $20,000

P(X<20,000)?

First, the z value needs to be calculated.

z = (x - μ)/σ

x = 20,000

z = (20,000 - 29,858)/5600

z = -1.76

So, P(X<20,000) = P(Z<-1.76)

From the z table,

P(Z<-1.76) = 0.0392

P(X<20,000) = 0.0392

b. Calculating the probability that a wedding costs between $20,000 and $30,000

P(20,000 < x < 30,000)

First, the z value needs to be calculated.

z = (x - μ)/σ

When x = 20,000

z = (20,000 - 29,858)/5600

z = -1.76

When x = 30,000

z = (30,000 - 29,858)/5600

z = 0.02

P(20,000 < x < 30,000) = P(-1.76 < z <0.02) --- using the z table

P(-1.76 < z <0.02) = 0.508 - 0.0392

P(-1.76 < z <0.02) = 0.4688

P(20,000 < x < 30,000) = 0.488

c. Using the following formula, we'll get the amount it'll a wedding to be among the 5% most expensive

z = (x - μ)/σ where x = amount

Make x the subject of formula

x = σz + μ

Fist we need to get the z value of 5%

z0.05 = 1.645

x = σz + μ becomes

x = 5600 * 1.645 + 29,858

x = $39,070

Amount = $39,070

5 0

3 years ago

57/61 in simplest form

sattari [20]

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7 0

3 years ago

The combined average weight of an okapi and a llama is 450450 kilograms. The average weight of 33 llamas is 190190 kilograms mor

Nataliya [291]

Answer:

Okapi 290 kg

Llama 160 kg

Step-by-step explanation:

Let weight of each llama be $l$

Let weight of each okapi be $o$

Given, combined weight of 1 okapi and 1 llama is 450, we can write:

$l+o=450$

Also, average weight of 3 llama is 190 more than the average weight of 1 okapi, thus we can write:

$3l-190=o$

Now, substituting 2nd equation into 1st equation, we can solve for weight of 1 llama:

$l+o=450\\l+(3l-190)=450\\l+3l-190=450\\4l=450+190\\4l=640\\l=\frac{640}{4}=160$

Each llama weights 160 kg, now using this and plugging into 2nd equation, we get weight of 1 okapi to be:

$o=3l-190\\o=3(160)-190\\o=290$

Each okapi weigh 290 kg

5 0

3 years ago

HELP NEEDED ASAP! Thanks :)

Arlecino [84]

Answer:

Step-by-step explanation:

First we must find the total boxes of pens

15 + 9 = 24

Then we can divide the total cost by the total number of boxes of pens

$72 / 24 boxes = 3

4 0

2 years ago

The function in Exercise represents the rate of flow of money in dollars per year. Assume a 10-year period at 8% compounded cont

anzhelika [568]

Answer:

a) The present value is 688.64 $

b) The accumulated amount is 1532.60 $

Step-by-step explanation:

a) The preset value equation is given by this formula:

$P=\int^{T}_{0}f(t)e^{-rt}dt$

where:

T is the period in years (T = 10 years)
r is the annual interest rate (r=0.08)

So we have:

$P=\int^{T}_{0}(0.01t+100)e^{-rt}dt$

Now we just need to solve this integral.

$P=\int^{T}_{0}0.01te^{-rt}dt+\int^{T}_{0}100e^{-rt}dt$

$P=e^{-0.08t}(-1.56-0.13t)|^{10}_{0}+1250e^{-0.08t}|^{10}_{0}$

$P=0.30+688.34=688.64 $$

The present value is 688.64 $

b) The accumulated amount of money flow formula is:

$A=e^{r\tau}\int^{T}_{0}f(t)e^{-rt}dt$

We have the same equation but whit a term that depends of τ, in our case it is 10.

So we have:

$A=e^{r\tau}\int^{T}_{0}(0.01t+100)e^{-rt}dt=e^{0.08\cdot 10}P$

$A=e^{0.08\cdot 10}688.64=1532.60 $$

The accumulated amount is 1532.60 $

Have a nice day!

6 0

3 years ago