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maks197457 [2]
4 years ago
6

How do you solve 4n-4(n-5)

Mathematics
2 answers:
Bad White [126]4 years ago
8 0

Answer: -4(-2x-5

Step-by-step explanation:

inysia [295]4 years ago
6 0

-4(n) -4(-5)

4n-4n+20

N+20

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An educational organization in California is interested in estimating the mean number of minutes per day that children between t
Hatshy [7]

Answer:

The critical value for a 98% CI is z=2.33.

The 98% confidence interval for the mean is (187.76, 194.84).

Step-by-step explanation:

We have to develop a 98% confidence interval for the mean number of minutes per day that children between the age of 6 and 18 spend watching television per day.

We know the standard deveiation of the population (σ=21.5 min.).

The sample mean is 191.3 minutes, with a sample size n=200.

The z-value for a 98% CI is z=2.33, from the table of the standard normal distribution.

The margin of error is:

E=z\cdot \sigma/\sqrt{n}=2.33*21.5/\sqrt{200}=50.095/14.142=3.54

With this margin of error, we can calculate the lower and upper bounds of the CI:

LL=\bar x-z\cdot\sigma/\sqrt{n}=191.3-3.54=187.76\\\\\\UL=\bar x+z\cdot\sigma/\sqrt{n}=191.3+3.54=194.84

The 98% confidence interval for the mean is (187.76, 194.84).

4 0
3 years ago
Rearrange the formula to make a the subject
PilotLPTM [1.2K]

Answer:

Step-by-step explanation:

p = (3n + a)/(n + a)

Cross multiply

p(n + a) = 3n +a

pn + pa = 3n + a

pa - a = 3n - pn

a(p - 1) = n(3 - p)

Dividing by p - 1

a = n(3 - p)/(p - 1)

7 0
3 years ago
Evaluate triple integral ​
kaheart [24]

Answer:

\\ \frac{1}{8} e^{4a}-\frac{3}{4}e^{2a}+e^{a} -\frac{3}{8} \\\\or\\\\ \frac{e^{4a}-6e^{2a}+8e^{a}-3}{8}

Step-by-step explanation:

\\ \int\limits^{a}_{0} \int\limits^{x}_{0} \int\limits^{x+y}_{0} {e^{x+y+z}} \, dzdydx \\\\=\int\limits^{a}_{0} \int\limits^{x}_{0} [\int\limits^{x+y}_{0} {e^{x+y}e^z} \, dz]dydx \\\\\\=\int\limits^{a}_{0} \int\limits^{x}_{0} [e^{x+y}\int\limits^{x+y}_{0} {e^z} \, dz]dydx\\\\=\int\limits^{a}_{0} \int\limits^{x}_{0} [e^{x+y}e^z\Big|_0^{x+y}]dydx \\\\\\=\int\limits^{a}_{0} \int\limits^{x}_{0} [e^{x+y}e^{x+y}-e^{x+y}]dydx \\\\\\=\int\limits^{a}_{0} \int\limits^{x}_{0} e^{2x+2y}-e^{x+y}dydx \\\\\\

\\=\int\limits^{a}_{0} [\int\limits^{x}_{0} e^{2x}e^{2y}-e^{x+y}dy]dx \\\\\\=\int\limits^{a}_{0} [\int\limits^{x}_{0} e^{2x}e^{2y}dy- \int\limits^{x}_{0}e^{x}e^{y}dy]dx \\\\\\u=2y\\du=2dy\\dy=\frac{1}{2}du\\\\\\=\int\limits^{a}_{0} [\frac{e^{2x}}{2}\int e^{u}du- e^x\int\limits^{x}_{0}e^{y}dy]dx \\\\\\=\int\limits^{a}_{0} [\frac{e^{2x}}{2}\cdot e^{2y}\Big|_0^x- e^xe^{y}\Big|_0^x]dx \\\\\\=\int\limits^{a}_{0} [\frac{e^{2x+2y}}{2} - e^{x+y}\Big|_0^x]dx \\\\

\\=\int\limits^{a}_{0} [\frac{e^{4x}}{2} - e^{2x}-\frac{e^{2x}}{2} + e^{x}]dx \\\\\\=\int\limits^{a}_{0} \frac{e^{4x}}{2} -\frac{3e^{2x}}{2} + e^{x}dx \\\\\\=\int\limits^{a}_{0} \frac{e^{4x}}{2}dx -\int\limits^{a}_{0}\frac{3e^{2x}}{2}dx + \int\limits^{a}_{0}e^{x}dx \\\\\\u_1=4x\\du_1=4dx\\dx=\frac{1}{4}du_1\\\\\u_2=2x\\du_2=2dx\\dx=\frac{1}{2}du_2\\\\\\=\frac{1}{8}\int e^{u_1}du_1 -\frac{3}{4}\int e^{u_2}du_2 + \int\limits^{a}_{0}e^{x}dx \\\\\\

\\=\frac{1}{8}e^{u_1}\Big| -\frac{3}{4}e^{u_2}\Big| + e^{x}\Big|_0^a \\\\\\=\frac{1}{8}e^{4x}\Big|_{0}^a -\frac{3}{4}e^{2x}\Big|_{0}^a + e^{x}\Big|_0^a \\\\\\=\frac{1}{8}e^{4x} -\frac{3}{4}e^{2x} + e^{x}\Big|_0^a \\\\\\=\frac{1}{8}e^{4a} -\frac{3}{4}e^{2a} + e^{a}-\frac{1}{8} +\frac{3}{4} -1\\\\\\=\frac{1}{8}e^{4a} -\frac{3}{4}e^{2a} + e^{a}-\frac{3}{8}\\\\\\

Sorry if that took a while to finish. I am in AP Calculus BC and that was my first time evaluating a triple integral. You will see some integrals and evaluation signs with blank upper and lower boundaries. I just had my equation in terms of u and didn't want to get any variables confused. Hope this helps you. If you have any questions let me know. Have a nice night.

6 0
3 years ago
Evaluate the expression 1/4[x(2y+3z)] x=8 y=3z=5/3​
ladessa [460]

Answer:

Step-by-step explanation:

x = 8  ; y = 5/3

3z = \dfrac{5}{3}

\dfrac{1}{4}[x(2y+3z)] =\dfrac{1}{4}[8*(2*\dfrac{5}{3}+\dfrac{5}{3})]\\\\=\dfrac{1}{4}(8*(\dfrac{10}{3}+\dfrac{5}{3})]\\\\=\dfrac{1}{4}(8*\dfrac{15}{3})\\\\=\dfrac{1}{4}*8*5\\\\=2*5\\\\=10

4 0
3 years ago
the formula P = 2l + 2w ives the promoter P of a rectangular room with length l and width w. A rectangular living room is 26 ft
jonny [76]

Answer:

Therefore the Perimeter of the room is 94 ft.

Step-by-step explanation:

Given:

P=2l+2w

Where ,

P = Perimeter

l = Length = 26 ft

w = Width = 21 ft

To Find:

Perimeter of the room = ?

Solution:

Perimeter of Rectangle is given as

P=2l+2w

Substituting 'l' and 'w' we get

P=2\times 26+2\times 21=52+42=94\ ft

P=94\ ft

Therefore the Perimeter of the room is 94 ft.

5 0
4 years ago
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