All categories

3 years ago

Given f(x) = -10x + 45, find x when f(x) = 15.

Mathematics

1 answer:

fenix001 [56]3 years ago

3 0

Answer:

3 =x

Step-by-step explanation:

f(x) = -10x + 45

f(x) = 15

15 = -10x +45

Subtract 45 from each side

15-45 = -10x+45-45

-30 = -10x

Divide each side by -10

-30/-10 = -10x/-10

3 =x

You might be interested in

Professor Isaac Asimov was one of the most prolific writers of all time. Prior to his death, he wrote nearly 500 books during a

svp [43]

Answer:

Step-by-step explanation:

n = sample size = 5

a) Let us determine the sum

$\sum x_i= 100+200+300+400+490=1490$

$\sum x_i^2= 100^2+200^2+300^2+400^2+490^2=540100$

$\sum y_i = 237+350+419+465+507=1978$

$\sum y_i^2= 237^2+350^2+419^2+465^2+507^2=827504$

$\sum x_i y_i=100 \times 237 + 200\times350+300 \times 419 + 400 \times 465 + 490 \times 507=653830$

Now we can determine $S_x_x, S_x_y, S_y_y$

$S_x_x = \sum x_i^2-\frac{(\sum x_1)^2}{n} \\= 540100 - \frac{1490^2}{5} \\= 96080$

$S_x_y = \sum x_i y_i -\frac{(\sum x_i)(\sum y_i) }{n} \\\\$

$653830 - \frac{1490 \times 1978 }{5} = 64386$

$S_y_y = \sum y_i^2-\frac{(\sum y_i)^2 }{n} = 82750-\frac{1978^2}{5} \\\\= 45007.2$

The estimate b of the slope β is the ratio of $S_x_y$ and $S_x_x$

$b = \frac{S_x_y}{S_x_x}$

$\frac{64386}{96080} = 0.67$

The mean is the sum of all value divide by number of values

$\bar x= \frac{\sum x_i}{n} \\\\= \frac{100+200+300+400+490}{5} \\\\= \frac{1490}{5} = 298$

$\bar y= \frac{\sum y_i}{n} \\\\= \frac{237+350+419+465+507}{5} \\\\= \frac{1978}{5} = 395.6$

The estimate a of the intercept is

$a = \bar y - b \bar x$

$= 395.6 - 0.69 \times 298\\= 195.9$

General least square equation;

$\bar y = \alpha + \beta x$

replace alpha by a = 3 and beta by b = 0.67 in general least equation

y = a + bx

195.9 + 0.67x

<em>Scatter plot is shown in the attached file</em>

x is on the horizontal axis

y is n the vertical axis

The degree of freedom of regression is 1

because we use one variable s predictor variable

$d_f_R = 1$

The degree of freedom of error is the sample size n decrease by 2

$d_f_E =n-2= 5 - 2=3$

Total df is equal to the sum of seperate degree of freedom dfR and dfE

total df = 1 +3 4

$SSR = \frac{(S_x_y)^2}{S_x_x} = \frac{64386^2}{96080} \\\\= 43146.9296$

Total SS =Syy= 45007.2

SSE + Total SS = SSR

= 45007.2 - 43146.9296

= 1860.2705

7 0

3 years ago

What is the length of the altitude of the equilateral triangle below? A. 6 B. 2 C. 2/3 D. /48 E. 36 F. 6 /3

kolbaska11 [484]

It is C the answer is C

5 0

3 years ago

The area of a rectangle is 192 square centimeters. the length of the rectangle is 16 centimeters. what is the width, in centimet

Valentin [98]

A = L * W
W = A / L
W = 192 / 16
W = 12

7 0

3 years ago

The mammogram is helpful for detecting breast cancer in its early stages. However, it is an imperfect diagnostic tool. According

creativ13 [48]

Answer:

The probability that she will have breast cancer is 0.2375.

Step-by-step explanation:

P(Positive if no Cancer) = 86.6/1000 = 0.0866

P(Positive if Cancer) = 1 − 1.1/1000 = 0.9989, and

P(Cancer) = 1/38 = 0.0263

If a woman between the ages of 50 and 59 has a positive mammogram, the probability that she will have breast cancer will be calculated by using the Bayes rule.

Bayes’s theorem describes the probability of an event.

P(Cancer if Positive) = $\frac{P(Cancer)P(Positive if Cancer)}{P(no Cancer)P(Positive if no Cancer) + P(Cancer)P(Positive if Cancer)}$

= $\frac{(0.0263)(0.9989)}{(1 - 0.0263)(0.0866) + (0.0263)(0.9989)}$

= 0.2375

6 0

3 years ago

Vito uses 9 liters of water to water 24 flower pots. He is wondering how many liters of water it would take to water 40 flower p

MatroZZZ [7]

106.666667 for the water amount

3 0

3 years ago