I need help ASAP will mark the brainliest

Answer:

[tex]f(x) = (x + 19)(x^2 + 1)[/tex]

Step-by-step explanation:

Complex numbers:

The following relation is important for complex numbers:

[tex]i^2 = -1[/tex]

Zeros of a function:

Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.

Has zeros −19 and −i

If -i is a zero, its conjugate i is also a zero. So

[tex]f(x) = a(x - (-19))(x - (-i))(x - i) = a(x+19)(x+i)(x-i) = a(x+19)(x^2 - i^2) = a(x + 19)(x^2 + 1)[/tex]

Output of 40 when x=1

This means that when [tex]x = 1, f(x) = 40[/tex]. We use this to find the leading coefficient a. So

[tex]f(x) = a(x + 19)(x^2 + 1)[/tex]

[tex]40 = a(20)(2)[/tex]

[tex]40a = 40[/tex]

[tex]a = 1[/tex]

The polynomial is:

[tex]f(x) = (x + 19)(x^2 + 1)[/tex]

Answer:

a) 0.1180 = 11.80% probability that exactly 30 of them are spayed or neutered.

b) 0.8665 = 86.65% probability that at most 33 of them are spayed or neutered.

c) 0.4129 = 41.29% probability that at least 31 of them are spayed or neutered.

d) 0.5557 = 55.57% probability that between 24 and 30 of them are spayed or neutered.

Step-by-step explanation:

To solve this question, we use the binomial probability distribution, and also it's approximation to the normal distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

62% of owned dogs in the United States are spayed or neutered.

This means that [tex]p = 0.62[/tex]

48 owned dogs are randomly selected

This means that [tex]n = 48[/tex]

Mean and standard deviation, for the approximation:

[tex]\mu = E(x) = np = 48*0.62 = 29.76[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{48*0.62*0.38} = 3.36[/tex]

a. Exactly 30 of them are spayed or neutered.

This is P(X = 30), which is not necessary the use of the approximation.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 30) = C_{48,30}.(0.62)^{30}.(0.38)^{18} = 0.1180[/tex]

0.1180 = 11.80% probability that exactly 30 of them are spayed or neutered.

b. At most 33 of them are spayed or neutered.

Now we use the approximation. This is, using continuity correction, [tex]P(X \leq 33 + 0.5) = P(X \leq 33.5)[/tex], which is the pvalue of Z when X = 33.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{33.5 - 29.76}{3.36}[/tex]

[tex]Z = 1.11[/tex]

[tex]Z = 1.11[/tex] has a pvalue of 0.8665

0.8665 = 86.65% probability that at most 33 of them are spayed or neutered.

c. At least 31 of them are spayed or neutered.

Using continuity correction, this is [tex]P(X \geq 31 - 0.5) = P(X \geq 30.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 30.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30.5 - 29.76}{3.36}[/tex]

[tex]Z = 0.22[/tex]

[tex]Z = 0.22[/tex] has a pvalue of 0.5871

1 - 0.5871 = 0.4129

0.4129 = 41.29% probability that at least 31 of them are spayed or neutered.

d. Between 24 and 30 (including 24 and 30) of them are spayed or neutered.

This is, using continuity correction, [tex]P(24 - 0.5 \leq X \leq 30 + 0.5) = P(23.5 \leq X \leq 30.5)[/tex], which is the pvalue of Z when X = 30.5 subtracted by the pvalue of Z when X = 23.5.

X = 30.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30.5 - 29.76}{3.36}[/tex]

[tex]Z = 0.22[/tex]

[tex]Z = 0.22[/tex] has a pvalue of 0.5871

X = 23.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{23.5 - 29.76}{3.36}[/tex]

[tex]Z = -1.86[/tex]

[tex]Z = -1.86[/tex] has a pvalue of 0.0314

0.5871 - 0.0314 = 0.5557

0.5557 = 55.57% probability that between 24 and 30 of them are spayed or neutered.

Answer: 16

Step-by-step explanation:

there are 3 feet in one yard so divided 48 by 3 and you get 16

Answer:

16

Step-by-step explanation:

Answer:

No, this can not be a triangle because if you use the Pythagorean theorem 5 squared plus 2 squared doesn't equal 10 squared.

Step-by-step explanation:

You take 5 squared and 2 squared and add them, you then find the square root and that should equal 10, if not its not a triangle.

Answer:

I believe it is -6

Step-by-step explanation:

Answer:2440

Step-by-step explanation:

Answer: G

Step-by-step explanation:

Its g because its on the same side of the cube

Answer: G

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Scatter plot (Use excel with any bivariate data you can find)

Answer:

GOT U

Step-by-step explanation:

Mean = 81.5

Median =93.5

Mode = 98

Answer:

y = 2

Step-by-step explanation:

4x - 3y = -18, then 4x = 3y - 18,                  x = (3y - 18)/4

6x + 7y = -4

substitute for x:

6((3y - 18)/4) + 7y = -4

(18y - 108)/4 + 7y = -4

4.5y - 27 + 7y = -4

combine like terms:

11.5y = 23

y = 2

check:

x = (3(2) - 18)/4 = -12/4 = -3

6(-3) + 7(2) = -4

-18 - 14 - -4

-4 = -4

so y = 2 is correct

Answer:

An method would be ASA

Step-by-step explanation:

Answer:

Y=1/4x+33/4

Step-by-step explanation:

Y=1/4x+b

9=1/4(3)+b

9=3/4+b

8.25=33/4=b

Y=1/4x+33/4

Answer:

38 miles per gallon

Step-by-step explanation:

465 miles / 12 gallons

38 miles / gallon

Answer:

Step-by-step explanation:

Answer:

more information

Step-by-step explanation:

Answer:

w-(v+4)

Step-by-step explanation:

please give brainliest

Answer:

65 x 160  / 100 = 104

Step-by-step explanation:

Answer:

4*3/4* 7=21 bones per week

Answer:

= 4 ¾ × 7

= 33.25 snack bones

Answer:

an equilateral triangle have equal angles and equal sides.

so, side x and side bc are 12.

Answer:

It's going to be 12, so is the other size.

Step-by-step explanation:

You can see that in each corner, it shows the triangle is the same, which means it is equilateral, so the answer is 12 :D

Answer:

x= -6h

Step-by-step explanation:

opening up the bracket

10x+20h=12x+32h

10x-12x=32h-20h

-2x=12h

x=-6h

Answer:

x=-6h

Step-by-step explanation:

Isolate the variable by diviiding each side by factors that don't contain the variable. Hopefully this is helpful :)

Answer:

15, y = 1/2x + 3.75

Step-by-step explanation:

Am not 100% sure but for #15

cuz I graphed it & it looks alike

Answer:

C. F'(x) = x - 6 / 3

Step-by-step explanation:

[tex]y = 3x + 6[/tex]

[tex]x = 3y + 6 \\ x - 6 = 3y + 6 - 6[/tex]

[tex] \frac{x - 6}{3} = \frac{3y}{3} [/tex]

[tex]y = \frac{x - 6}{3} [/tex]

[tex]f1 = \frac{x - 6}{3} [/tex]

Answer:

Step-by-step explanation:

a) To provide an example of a function N → N that is one-to-one but not onto.

Suppose [tex]f:N\to N[/tex]  to be [tex]f(n)=n^2[/tex]

Then; [tex]\text{a function } \ f: A \to B\ \text{is one-to-one if and only if } f(a) = f(b) \implies a = b \ for \ a, b \ \epsilon \ A.[/tex]

[tex]\text{a function } \ f: A \to B\ \text{is onto if and only if for every element } b \ \epsilon \ B \\ \text{there exist an element a} \ \epsilon\ A \ such \ that f(a) = b}[/tex]

Now, assuming [tex]a \ \Big {\varepsilon} \ N \& \ b \ \epsilon \ N;[/tex]

Then [tex]f(a) = f(b)[/tex]

[tex]a^2 = b^2 \\ \\ a = b[/tex]

The above function is said to be one-to-one

[tex]\text{it is equally understandable that not every natural number is the square of a natural number}[/tex]e.g

2 is not a perfect square, hence, it is not regarded as the image of any natural no.

As such, f is not onto.

We can thereby conclude that the function  [tex]f(n) = n^2[/tex] is one-to-one but not onto

b)

[tex]Suppose f: N \to N[/tex] be

[tex]f(n) = [n/2] \\ \\ For \ n =1, f(1) = [1/2] = [0.5] = 1 \\ \\ For \ n=2 , f(2) = [2/2] = [1] = 1[/tex]

It implies that the function is not one-to-one since there exist different natural no. having the same image.

So, for [tex]n \epsilon N[/tex] , there exists an image of 2n in N

i.e.

[tex]f(2n) = [2n/2] = [n] = n[/tex]

Hence, the function is onto

We thereby conclude that the function [tex]f(n) = [n/2] \text{ is onto but not one-to-one}[/tex]

c)

[tex]let f: N\to N[/tex] be  [tex]f(n) = \left \{ {{n+1, \ if \ n \ is \ even } \atop n-1 , \ if \ n \ is \ odd} \right.[/tex]

So, if n, m is odd:

Then:

[tex]f(n) = f(m) \\ \\ n-1 = m-1 \\ \\ n = m[/tex]

Likewise, if n, m is even:

Then;

[tex]f(n) = f(m) \\ \\ n+1 = m+ 1 \\ \\ n = m[/tex]

The function is then said to be one-to-one.

However, For [tex]n \epsilon N[/tex] and is odd, there exists an image of [tex]n - 1[/tex]that is even;

[tex]f(n - 1) = n -1 + 1 =n[/tex]

For [tex]n \epsilon N[/tex] and is even, there exists an image of [tex]n + 1[/tex]that is odd;

[tex]f(n - 1) = n +1 - 1 = n[/tex]

where(; implies such that)

Hence, this function is said to be onto.

We can therefore conclude that the function [tex]f(n) = \left \{ {{n+1, \ if \ n \ is \ even } \atop n-1 , \ if \ n \ is \ odd} \right.[/tex] is both onto and one-to-one.

d)

Here, to provide an example where the [tex]f:N \to N[/tex] is neither one-to-one nor onto.

SO;

Let [tex]f : N \to N[/tex] is defined to be [tex]f(n)=0[/tex]

Then, since every integer has the same image as zero(0), the function is not one-to-one.

Similarly, the function is not onto since every positive integer is not an image of any natural number.

We, therefore conclude that, the function [tex]f(n)=0[/tex] is neither one-to-one nor onto.

Answer:

1(2)+3=5

Step-by-step explanation:

Answer:

there is no expression

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

There are 4 red balls and 8 yellow balls.

Therefore, there are total 12 balls in the bag.

n(S) = 12

Let A be the event when the ball drawn is not a red ball.

The balls which are not red will be yellow balls and there are 8 yellow balls so,

n(A) = 8

Probability that the ball drawn randomly from the bag is not a red ball,

p(A) = n(A) / n(S)

= 8/12

= 2/3

Therefore, the probability of the ball drawn randomly is not a red ball is 2/3.

Answer:

-50y+(-80)

Step-by-step explanation: