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sergejj [24]
3 years ago
15

If p − 1 is a factor of p4 + p2 + p − k, the value of k is .

Mathematics
1 answer:
LiRa [457]3 years ago
7 0

Answer:

3

Step-by-step explanation:

Since (p - 1) is a factor then p = 1 is a root and p(1) = 0

p(1) = 1^{4} + 1² + 1 - k = 0, that is

3 - k = 0 ⇒k = 3

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Hello me again, answer this question, please show work
Rudik [331]

Answer:

6x

Explanation:

A number is x. 6 x x is written as 6x

8 0
2 years ago
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If f(x) = 5x + 40, what is f(x) when x = -5?<br> 0-8<br> 0.7<br> O 15
Over [174]

Answer:

15

Step-by-step explanation:

f(x) = 5x + 40

…………………………

when x = -5

f(-5) = 5(-5) + 40

      = -25 + 40

      = 40 - 25

      = 15

4 0
2 years ago
Allen�s hummingbird (Selasphorus sasin ) has been studied by zoologist Bill Alther A small group of 15 Allen� s hummingbirds has
Bogdan [553]

Answer:

1) 80% CI: [3.04; 3.26]gr

d= 0.11

2) n= 28 hummingbirds

Step-by-step explanation:

Hello!

The study variable of this experiment is:

X: the weight of a hummingbird. (gr)

And it has a normal distribution, symbolically: X~N(μ;σ²)

And (I hope I got it correctly) its population standard deviation is σ= 0.33

There was a sample of n= 15 hummingbirds taken, its sample mean X[bar]= 3.15 gr

1) You need to construct an 80% Confidence Interval for the population mean of the hummingbird's weight.

Since the study variable has a normal distribution, you can use either the standard normal distribution or the Student's t distribution. Both are useful to estimate the population mean. Since the population standard variance is known, the best choice is the Standard normal.

Z= <u> X[bar] - μ </u>~ N(0;1)

       σ/√n

The formula for the interval is:

X[bar] ± Z_{1- \alpha /2} * (σ/√n)

Z_{1- \alpha /2}= Z_{0.90} = 1.28

3.15 ± 1.28 * (0.33/√15)

[3.04; 3.26]gr

The margin of error (d) of a confidence interval is hal its amplitude (a)

a= Upper bond - Lower bond

d= (Upper bond - Lower bond)/2

d= \frac{(3.26-3.04)}{2} = 0.11

2) You need to calculate a sample size for a 80% Confidence interval for the average weight of the hummingbirds with a margin of error of d= 0.08

As I said before, the margin of error is half the amplitude of the interval, the formula you use to estimate the population mean has the following structure:

"point estamator" ± "margin of error"

Then the margin of error is:

d= Z_{1- \alpha /2} * (σ/√n)

Now what you have to do is rewrite the formula based on the sample size

d= Z_{1- \alpha /2} * (σ/√n)

\frac{d}{Z_{1- \alpha /2}}= σ/√n

√n * \frac{d}{Z_{1- \alpha /2}}= σ

√n = σ * \frac{Z_1- \alpha /2}{d}

n = (σ * \frac{Z_1- \alpha /2}{d})²

n=  (0.33 * \frac{1.28}{0.08})²

n= 27.8784 ≅ 28 hummingbirds.

I hope it helps!

4 0
3 years ago
Which of the following numbers is a rational but not a integer
Temka [501]
Rational numbers are numbers that can be turned into a fraction. They can be negative or positive.
Integers are whole numbers. They can be negative or positive. 

Numbers such as 0.10 are rational because they can be turned into a fraction
0.10 = 1/10....and since it is not a whole number, it is not an integer.
8 0
3 years ago
Suppose you have a bag of colored elastic bands and you choose one without looking. The probability the elastic band you choose
Gekata [30.6K]

Answer:

1/2 is the fraction and 50% is the percentage

Word phrase:

The probability of choosing a P (white) color band its a 50% chance.

sry if i did this wrong

6 0
3 years ago
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