If Ax) = 5x - 1 and g(x) = 2x^2 + 1, what is the value of (f x g)(-3)?

A women who is 5 feet 5 inches tall is standing near the Space Needle in Seattle, Washington. She casts a 13-inch shadow at the

Varvara68 [4.7K]

The space needle if 605 ft. high

3 0

3 years ago

Permutations and combination question ^^

mario62 [17]

Answer: 22) A

Step-by-step explanation:

First, order doesn't matter so it is a Combination.

In other words, it doesn't matter which person was chosen 1st, 2nd, 3rd, or 4th to bring food because they are all bringing "food".

Next, If you are going to choose person to 4 people to bring food out of a total of 4 + 3 + 1 = 8 people, you get → ₈C₄

And you are going to choose 3 people to bring decorations out the remaining 8 - 4 = 4 people, you get → ₄C₃

And you are going to choose 1 person to be the host out of the remaining 4 - 3 = 1 person, you get → ₁C₁

"And" means multiplication so altogether you get ⇒ ₈C₄ × ₄C₃ × ₁C₁

3 0

3 years ago

Find the equation of the line through (0,4) perpendicular to the line y = 3x

Rufina [12.5K]

Answer:

$y = - \frac{1}{3} x + 4$

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx+c, where m is the gradient and c is the y-intercept.

The product of the gradients of perpendicular lines is -1.

Gradient of given line= 3.

(Gradient of line)(3)= -1

3m= -1

m= $- \frac{1}{3}$

subst. m= $- \frac{1}{3}$ into the equation:

$y = - \frac{1}{3} x + c$

To find the value of c, substitute a coordinate.

When x=0, y=4,

$4 = - \frac{1}{ 3} (0) + c \\ 4 = c \\ c = 4$

Thus the equation of the line is $y = -\frac{1}{3} x + 4$ .

3 0

3 years ago

Maths!

Ber [7]

Answer:

(1) Variance = 4.5 and Standard deviation = 2.121.

(2) Variance = 4.5 and Standard deviation = 2.121.

(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged.

Step-by-step explanation:

We are given with the following set of data below;

X $X-\bar X$ $(X-\bar X)^{2}$

5 5 - 8 = -3 9

8 8 - 8 = 0 0

10 10 - 8 = 2 4

9 9 - 8 = 1 1

6 6 - 8 = -2 4

Total 72 36

Firstly, the mean of the above data is given by;

Mean, $\bar X$ = $\frac{\sum X}{n}$

= $\frac{72}{9}$ = 8

(1)Now, the variance of the given data is;

Variance = $\frac{\sum (X-\bar X)^{2} }{n-1}$

= $\frac{36}{9-1}$ = 4.5

So, the standard deviation, (S.D.) = $\sqrt{\text{Variance}}$

= $\sqrt{4.5}$ = 2.12

(2) Now, each value is added by 2; so the new data set is given by;

X $X-\bar X$ $(X-\bar X)^{2}$

7 7 - 10 = -3 9

10 10 - 10 = 0 0

12 12 - 10 = 2 4

11 11 - 10 = 1 1

8 8 - 10 = -2 4

Total 90 36

Firstly, the mean of the above data is given by;

Mean, $\bar X$ = $\frac{\sum X}{n}$

= $\frac{90}{9}$ = 10

(1)Now, the variance of the given data is;

Variance = $\frac{\sum (X-\bar X)^{2} }{n-1}$

= $\frac{36}{9-1}$ = 4.5

So, the new standard deviation, (S.D.) = $\sqrt{\text{Variance}}$

= $\sqrt{4.5}$ = 2.12

(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged as we see in the case of variance or standard deviation.

4 0

3 years ago

What is the equation of a line with a slope of 3 and contains point (4.1)

cricket20 [7]

Answer:

y = 3x - 11

Step-by-step explanation:

y=mx+b

1=3(4)+b

1=12+b

b=-11

5 0

3 years ago

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