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3 years ago

1/3(x-10)=-4 solve for x with steps

Mathematics

1 answer:

mrs_skeptik [129]3 years ago

6 0

Answer:

X = 5 2/3

Step-by-step explanation:

1/3 (x - 10) = - 4

- 1/3 - 1/3

(x - 10) = - 4 1/3

+ 10 + 10

x = 5 2/3

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Construct a 99% confidence interval for the population mean, mu. Assume the population has a normal distribution. A group of 1

Zarrin [17]

Answer:

99% confidence interval for the population mean is [19.891 , 24.909].

Step-by-step explanation:

We are given that a group of 19 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8 years.

Assuming the population has a normal distribution.

Firstly, the pivotal quantity for 99% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean age of selected students = 22.4 years

s = sample standard deviation = 3.8 years

n = sample of students = 19

$\mu$ = population mean

<em>Here for constructing 99% confidence interval we have used t statistics because we don't know about population standard deviation.</em>

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.878 < $t_1_8$ < 2.878) = 0.99 {As the critical value of t at 18 degree of

freedom are -2.878 & 2.878 with P = 0.5%}

P(-2.878 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 2.878) = 0.99

P( $-2.878 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.878 \times {\frac{s}{\sqrt{n} } }$ ) = 0.99

P( $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ) = 0.99

<u>99% confidence interval for</u> $\mu$ = [ $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ , $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ]

= [ $22.4 -2.878 \times {\frac{3.8}{\sqrt{19} }$ , $22.4 +2.878 \times {\frac{3.8}{\sqrt{19} }$ ]

= [19.891 , 24.909]

Therefore, 99% confidence interval for the population mean is [19.891 , 24.909].

6 0

3 years ago

HELP PLEASE!!!!!! Find x and y so the quadrilateral is a parallelogram.

adell [148]

Answer:

x is on R,Q and Q,P and y is R,S to S,P

Step-by-step explanation:

picture it on a coordinate plane

8 0

3 years ago

Both the diameter and height of a cylinder vase are 2.5 times greater than a dimilar vase. The surface area of the smaller vase

faust18 [17]

Both diameter and height are scaled by 2.5.

Area is measured in squared units ( square centimetres).

Square the scale factor:

2.5^2 = 6.25

Multiply the area of the smaller vase by the scale:

2826 x 6.25 = 17,662.5 square cm.

7 0

3 years ago

For f(x)= 3x+1 and g(x)= x^2-6, find (g/f)(x).

o-na [289]

D. The exclusion is important because we cannot divide by zero. Apart from that we are simply looking at a function.

4 0

3 years ago

Read 2 more answers

Agnes Hammer is a senior majoring in management science. She has been interviewing with several companies for a job when she gra

stiks02 [169]

Answer:

Mean = 30516.67

Standard deviation, s = 3996.55

P(x < 27000) = 0.0011518

Step-by-step explanation:

Given the data:

28500 35500 32600 36000 34000 25700 27500 29000 24600 31500 34500 26800

Mean, xbar = Σx / n = 366200 /12 = 30516.67

Standard deviation, s = [√Σ(x - xbar) / n-1]

Using calculator, s = 3996.55

The ZSCORE = (x - mean) / s/√n

Zscore = (27000 - 30516.67) / (3996.55/√12)

Zscore = - 3516.67 / 1153.7046

Zscore = - 3.048

P(x < 27000) = P(Z < - 3.049) = 0.0011518

3 0

3 years ago