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krek1111 [17]
3 years ago
11

solve each equation below for the given variable. Please explain how u got ur answer:) a. 4x/5=x-2/7 b. -3(2b-7)= -3b+21-3b c.6-

2(c-3)=12​

Mathematics
1 answer:
nadya68 [22]3 years ago
3 0
This is a answer of question A

You might be interested in
A linear regression model is fitted to the data x y 37.0 65.0 36.4 67.2 35.8 70.3 34.3 71.9 33.7 73.8 32.1 75.7 31.5 77.9 with x
andrey2020 [161]

Answer:

b0= 144.59

b= -2.12

Se²= 1.02

99%CI E(Y/X=35): [68.78; 71.99]

Step-by-step explanation:

Hello!

I've arranged the given data:

X: 37.0, 36.4, 35.8, 34.3, 33.7, 32.1, 31.5

Y: 65.0, 67.2, 70.3, 71.9, 73.8, 75.7, 77.9

The equation of the linear regression model is:

Yi= β₀ + βXi + εi

Where

Yi is the dependent variable

Xi is the independent variable

εi represents the errors or residues

β₀ is the intercept of the line

β is the slope

The conditions to make a linear regression analysis are:

For each given value of X, there is a population of Y~N(μy;σy²)

Each value of Y is independent of the others.

The population variances of each population of Y are equal.

From these conditions the following characteristic is deduced:

εi~N(0;σ²)

The parameters of the regression are:

β₀, β, and σ²

If the conditions are met then you can estimate the regression line:

Yi= bo * bXi + ei.

And the point estimation of the parameters can be calculated using the formulas:

β₀ ⇒ b0= (∑y/n)-b(∑x/n)

β ⇒ b= [∑xy- ((∑x)(∑y))/n]/(∑x²-((∑x)²/n))

σ²⇒ Se²= 1/(n-2)*[∑y²-(∑y)²/n - b²(∑x²-(∑x)²/n)]

n= 7

∑y= 501.80

∑y²= 36097.88

∑x= 240.80

∑x²= 8310.44

∑xy= 17204.87

b0= 144.59

b= -2.12

Se²= 1.02

The estimated regression line is:

Yi= 144.59 -2.12Xi

You need to calculate a 99%CI E(Y/X=35), the formula is:

(b0 + bX0) ± t_{n-2;1-\alpha /2}*\sqrt{S_e^2(\frac{1}{n}+\frac{(X_0-X[bar])^2}{sumX^2-(\frac{(sumX)^2}{n} )} )}

(144.59 + (-2.12*35)) ± 4.032*\sqrt{1.02(\frac{1}{7}+\frac{(35-34.4)^2}{8310.44-(\frac{(240.80)^2}{7} )} )}

[68.78; 71.99]

With a 99% confidence level youd expect that the interval [68.78; 71.99] contains the true value of the average of Y when X= 35.

I hope it helps!

6 0
3 years ago
Why does it say this am i supposed to be ranked up or what?
tatiyna

Answer:

idk that's weird ( I'm just trying to get more points)

4 0
3 years ago
6. If f(x) = 3x +3 and g(x)=-3+2x, find the rule of the function 2g(x)+2f(x).
mars1129 [50]
<h3>Answer:</h3>

10x

Solution:

If f(x) = 3x +3 and g(x) = -3 +2x, then 2g(x) +2f(x) is:

2(-3 +2x) +2(3x +3) \\ -6 +4x +6x +6 \\ (-6 +6) +(4 +6)x \\ 0 +10x \\ 10x

5 0
3 years ago
Greg’s house is 0.8 miles from the library. So far, Greg has walked 5/6 of the distance. How many miles has he walked in fractio
Anastaziya [24]

Greg has walked \frac{2}{3} miles

<em><u>Solution:</u></em>

Given that, Greg’s house is 0.8 miles from the library

Distance between house and library = 0.8 miles

Greg has walked \frac{5}{6} of the distance

Therefore,

Distance walked = \frac{5}{6} of the distance between house and library

Here "of" means multiplication

Thus we get,

\text{Distance walked } = \frac{5}{6} \text{ of } 0.8

\rightarrow \frac{5}{6} \times 0.8 = \frac{5}{6} \times \frac{8}{10}\\\\\text{Simplify the above fraction by reducing to lowest terms }\\\\\rightarrow \frac{5}{6} \times \frac{8}{10}=\frac{2}{3}

Thus Greg has walked \frac{2}{3} miles

8 0
3 years ago
What does the fundamental theorem of algebra state about the equation 2x^2−6x+10=0 ?
Temka [501]

Answer:

B. The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are ​ x=3±i√11/2 .  

Step-by-step explanation:

We know that,

Fundamental theorem of algebra states that ' a polynomial of degree n will have n number of roots'.

Since, the polynomial y=2x^{2}-6x+10 has degree 2, so it will have 2 roots.

We know that the polynomial ax^{2}+bx+c=0 has roots given by x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}.

So, the roots of polynomial 2x^{2}-6x+10=0 will be,

x=\frac{6 \pm \sqrt{(-6)^{2}-4 \times 2 \times 10}}{2 \times 2}

i.e. x=\frac{6 \pm \sqrt{36-80}}{4}

i.e. x=\frac{6 \pm \sqrt{-44}}{4}

i.e. x=\frac{6 \pm 2i \sqrt{11}}{4}

i.e. x=3 \pm \frac{\sqrt{11}i}{2}

Hence, the roots are given by 3 \pm \frac{\sqrt{11}i}{2}

So, option B is correct.

5 0
3 years ago
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