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3 years ago

Consider the functions f(x) = x2 − 13 and g(x) = x + 5. What is the value of (f − g)(−4)? ...?

1 answer:

7 0

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.

f(x) = x2 - 13
g(x) = x + 5

and are asked to compute "f-g" when x=-4. there are two ways of doing this. you can either first find f(-4) and g(-4) and then substract one from other like so:

f(−4)=(−4)2−13=16−13=3
g(−4)=−4+5=1

f(−4)−g(−4)=3−1=2

or you can create a new function that represents "f-g", call it "h", and work out h(-4) as follows:

h(x)=f(x)−g(x)=(x2−13)−(x+5)=x2−13−x−5=x2−x−18
h(−4)=(−4)2−(−4)−18=16+4−18=2

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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar. A medical center o

viktelen [127]

Answer:

1) 0.1504

2) 0.432

Step-by-step explanation:

1) The given information are;

The proportion of the morning appointments that are with elderly patients = 60%

The number of patients in the appointments = 10 patients

The proportion of the morning appointments that are with non-elderly patients = 100 - 60 = 40%

The binomial probability distribution is given as follows;

$P(X = r) = \dbinom{n}{r}p^{r}\left (1-p \right )^{n-r}$

$P(X = 0) = \dbinom{10}{0}0.6^{0}\left (1-0.6 \right )^{10}$ = 0.000105

$P(X = 1) = \dbinom{10}{1}0.6^{1}\left (1-0.6 \right )^{9}$ = 0.0016

$P(X = 2) = \dbinom{10}{2}0.6^{2}\left (1-0.6 \right )^{8}$ = 0.01062

$P(X = 3) = \dbinom{10}{3}0.6^{3}\left (1-0.6 \right )^{7}$ = 0.0425

The probability that the first four patients are elderly is 0.000105 + 0.0016 + 0.1062 + 0.0425 = 0.1504

2) The probability that exactly 2 out of 3 morning patients are elderly patient is given as follows

$P(X = 2) = \dbinom{3}{2}0.6^{2}\left (1-0.6 \right )^{1}$ = 0.432

8 0

3 years ago

A lady is 5 years younger to her husband and he is 5 times as old as his daughter. If the daughter was 5 years old 3 years back,

adoni [48]

Answer:

Step-by-step explanation:

5x (5+3)=40-5=35

3 0

2 years ago

Using the digits 1 to 9, at most one time each, fill in the boxes so that the points make a parallelogram. Mathematically, use p

Lera25 [3.4K]

Answer:

$\left\begin{array}{ccc}A\left( \boxed{3} , \boxed{8} \right)&B\left( \boxed{9} , \boxed{6} \right )\\\\C\left( \boxed{1} , \boxed{4} \right)&D\left( \boxed{7} , \boxed{2} \right )\end{array}\right$

Step-by-step explanation:

The coordinates are:

$\left\begin{array}{ccc}A\left( \boxed{3} , \boxed{8} \right)&B\left( \boxed{9} , \boxed{6} \right )\\\\C\left( \boxed{1} , \boxed{4} \right)&D\left( \boxed{7} , \boxed{2} \right )\end{array}\right$

The parallelogram is attached below.

To verify if these coordinates form a parallelogram, we show that:

AB=CD; and
AC=BD

Using Distance Formula

$AB = \sqrt{(6-8)^2+(9-3)^2} = \sqrt{(-2)^2+(6)^2} = \sqrt{40} $ units$

$CD = \sqrt{(2-4)^2+(7-1)^2} = \sqrt{(-2)^2+(6)^2} = \sqrt{40} $ units$

$AC = \sqrt{(8-4)^2+(3-1)^2} = \sqrt{(4)^2+(2)^2} = \sqrt{20} $ units$

$BD = \sqrt{(6-2)^2+(9-7)^2} = \sqrt{(4)^2+(2)^2} = \sqrt{20} $ units$

Since AB=CD; and AC=BD, the coordinates A, B, C, and D form the vertex of a parallelogram.

3 0

3 years ago

Please provide an explanation. Simplify sqrt242

alex41 [277]

Sqrt242 can't be simplified anymore. It doesn't contain any perfect squares factors. For instance,
$\sqrt{150}$
This can be simplified because
$\sqrt{25 \times 6}$
And 25 is a perfect square, and square root of 25 is 5. The simplified version for this would be 5 sqrt (6). For your question, sqrt 242 can't be simplified anymore, its most simplified version is its current state.

6 0

3 years ago

Read 2 more answers

Determine which consecutive integers do not have a real zero of between them. a. (–6, –5) c. (–2, –1) b. (–5, –4) d. (1, 2) Plea

svetoff [14.1K]

We have by the intermediate value theorem that if a continuous function takes values both above and below zero at 2 points, there is a zero of the function in-between. We have that polynomials are continues. Let's calculate f(-6) and f(-5). f(-6)=-36 while f(-5)=-1. Thus, we cannot conclude that there is a root between them.
F(-2)=8, f(-1)=-1, so there is a flip; a zero must exist between them.
F(1)=-1, f(2)=20, so again there is a change of signs.
f(-5)=-1, f(-4)=14 so there is a root still.
We have that the only choice that does not have a root between the integers is choice a.

7 0

3 years ago