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3 years ago

Mathematics and body temperature? Please answer the questions in 3.

Mathematics

1 answer:

Semenov [28]3 years ago

3 0

Answer:

keep the model answer photo

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Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent v

natka813 [3]

Answer:

Step-by-step explanation:

Hello!

Given the independent variable X and the dependent variable Y (see data in attachment)

The regression equation is

^Y= b₀ + bX

Where

b₀= estimation of the y-intercept

b= estimation of the slope

The formulas to manually calculate both estimations are:

$b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }$

$b_0= \frac{}{y} - b*\frac{}{x}$

n=7

∑X= 42

∑X²= 292

∑Y= 49

∑Y²= 403

∑XY= 249

$\frac{}{y} = \frac{sumY}{n} = \frac{49}{7} = 7$

$\frac{}{x} = \frac{sumX}{n} = \frac{42}{7} = 6$

$b= \frac{249-\frac{42*49}{7} }{292-\frac{42^2}{7} }= -1.13$

$b_0= 7- (-1.13)*6= 13.75$

^Y= 13.75 - 1.13X

Using the raw data you can calculate the coefficient of determination as:

$R^2= \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{[sumY^2-\frac{(sumY)^2}{n} ]}$

$R^2= \frac{(-1.13)^2[292-\frac{(42)^2}{7} ]}{[403-\frac{(49)^2}{7} ]}= 0.84$

This means that 84% of the variability of the dependent variable Y is explained by the response variable X under the model ^Y= 13.75 - 1.13X

I hope this helps!

6 0

4 years ago

(Please show all work) 1. Find f(6) if f(x)= 1/2x + x - 4

dsp73

Answer:

$\large\boxed{1.\ f(6)=5\ or\ f(6)=20}\\\boxed{2.\ d=5}\\\boxed{3.\ vertex=(-3,\ -1)}$

Step-by-step explanation:

$1.\\\text{Put x = 6 to the equation of a function}\ f(x):\\\\\text{If}\ f(x)=\dfrac{1}{2}x+x-4\to f(6)=\dfrac{1}{2}(6)+6-4=3+6-4=5\\\\\text{If}\ f(x)=\dfrac{1}{2}x^2+x-4\to f(6)=\dfrac{1}{2}(6^2)+6-4=\dfrac{1}{2}(36)+2=18+2=20\\\\2.\\\text{The formula of a distance between two points:}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\text{We have the points (2, -4) and (5, -8). Substitute:}\\\\d=\sqrt{(5-2)^2+(-8-(-4))^2}=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5$

$3.\\\text{The vertex formula of a parabola:}\\\\y=a(x-h)^2+k\\\\(h,\ k)-vertex\\\\\text{We have}\ y=(x+3)^2-1=(x-(-3))^2-1\\\\\text{Therefore the vertex is:}\ (-3,\ -1).$

8 0

3 years ago

What is the actual distance between these streets?

scoundrel [369]

It's D 4 3/8 miles

First you have to multiply 2 1/2 for the mile and 1 3/4 for the inches. You will get 4.375.Convert it to fraction which is 35/8 and simplify it to get 4 3/8.

Hope this helps!

8 0

3 years ago

Simplify 10x - (5x-x)

Alex17521 [72]

Answer:

$\boxed{6x}$

Step-by-step explanation:

$10x - (5x-x)$

Distribute the Negative Sign:

$= 10x + -1 (5x - x)$

$= 10x + -1 ( 5x) + -1 (-x)$

$= 10x + -5x + x$

Combine Like Terms:

$= 10x + -5x + x$

$= (10x + -5x + x)$

$= 6x$

Hope this helped you!

3 0

4 years ago

A random sample of 16 students selected from the student body of a large university had an average age of 25 years. We want to d

kenny6666 [7]

Answer:

$z=\frac{25-24}{\frac{2}{\sqrt{16}}}=2$

$p_v =2*P(Z>2)=0.0455$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the true mean differs from 24 at 5% of significance

Step-by-step explanation:

Data given and notation

$\bar X=25$ represent the sample mean

$\sigma=2$ represent the sample population deviation for the sample

$n=16$ sample size

$\mu_o =24$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is different from 24, the system of hypothesis would be:

Null hypothesis: $\mu = 24$

Alternative hypothesis: $\mu \neq 24$

If we analyze the size for the sample is < 30 but we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{25-24}{\frac{2}{\sqrt{16}}}=2$

P-value

Since is a two sided test the p value would be:

$p_v =2*P(Z>2)=0.0455$

Conclusion

6 0

4 years ago