NO LINKS!! Describe the domain and range (in BOTH interval and inequality notation) for each function shown part 1a​

For statement one:

We need to add up to complex numbers and their sum must give us equal to 10.

Also, we need to use the complex numbers:

5+i√15 and 5-i√15.

Then, we can use:

(5+i√15)+( 5-i√15) =

5+i√15+5-i√15 =

5+5+ i√15-i√15 =

= 10 + 0

= 10

For the second statement:

We need to show the product of complex numbers:

Then, we use:

(5+i√15)(5-i√15))=

5*5 - 5*i√15) +5*i√15) +√15*√15=

25 + 0 + 15=

40

The distance traveled by airplane is 180 miles.

The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°

The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.

Then, the total distance traveled by airplane will be:

= 100 miles + 80 miles = 180 miles.

The speed can be defined as the distance traveled by the total time taken.

Speed = distance/time

Speed = 180 miles/ 1 hour

Speed = 180 miles/60 minutes

Speed = 3 miles per minute

The angle of direction from its origin will be:

tan (x) = 100 miles/80 miles

x = tan⁻¹ ( 100/80)

x = tan⁻¹ ( 10/8) =  tan⁻¹ ( 5/4)

x = 51.34°

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x = 0,1 are the real solutions of the equation .

What are real solutions in math?

 4x³ - 8x² + 4x = 0

x( 4x² - 8x + 4 ) = 0

x( 4x² - 4x - 4x + 4 ) = 0

x ( 4x ( x - 1) -4 ( x - 1 )) = 0

x ( ( 4x - 4 ) ( x - 1 ) ) = 0

x = 0

4x - 4 = 0 ⇒ x = 1

x - 1 = 0 ⇒ x = 1

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Given the expression

express in sen and cos terms

then the correct answer is option C

Cos (angle)

We will see that the function f(x) is:

f(x) = 15*(x - 3)

Evaluating it in x = -3 we can see that:

f(-3) =  -90

We know that when we divide f(x) by (x - 3), the quotient is 15. (that is the statement given in the question)

so we can write the equation:

f(x)/(x - 3) = 15

And we can solve this for f(x) as if it were a variable, then we get:

f(x) = 15*(x - 3)

Now, if we evaluate the function in x = -3 (this is replacing the variable x with the number -3), we will get:

f(-3) = 15*(-3 - 3) = 15*(-6) = -90

So the statement:

f(-3) = 15

Is false

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5x + 2y = -12 (a)

3y + 5x =-8 (b)

First, write (b) in the ax+by=c form:

5x + 3y = -8 (b)

Now, subtract (b) to (a) to eliminate x

5x + 2y = -12

-

5x + 3y = -8

__________

-y = -4

solve for y:

Multiply both sides by -1

y=4

Replace y=4 on (a) and solve for x:

5x + 2 (4) = -12

5x + 8 = -12

5x = -12-8

5x = -20

x = -20/5

x = -4

Solution: (-4,4)

The tangent-secant theorem states that given the segments of a secant segment and a tangent segment that share an endpoint outside of the circle, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment.

Graphically,

In this case, we have:

Now, we can solve the equation for x:

Therefore, the value of x is 20/3 or approximately 6.67.

We will have the following:

The surface area of the onion can be best modeled by a sphere. Base on the model, the approximate area of the onion is 38.5 square inches:

Given that two cars are 188 miles apart, travelling at different speeds, meet after two hours.

To Determine: The speed of both cars if the faster car is 8 miles per hour faster than the slower car

Solution:

Let the slower car has a speed of S₁ and the faster car has a speed of S₂. If the faster speed is 8 miles per hour faster than the slower car, then,

It should be noted that the distance traveled is the product of speed and time. Then, the total distance traveled by each of the cars before they met after 2 hours would be

It was given that the distance between the faster and the slower cars is 188 miles. Then, the total distance traveled by the two cars when they meet is 188 miles.

Therefore:

Combining equation 1 and equation 2

Substitute equation 1 into equation 2

Divide through by 4

Substitute S₁ in equation 1

Hence,

The slower car travels at 43 miles per hour(mph), and

The faster car travels as 51 miles per hour(mph)

We need to know how to calculate compound interest to solve this problem. The present value is $2577.32

Compound interest is the interest that is earned on interest. Inorder to calculate the compound interest we need to know the principal amount, the rate of interest, the time period and how many times the interest is applied in per time period. In this question we know the amount after 9 years and the rate of interest is 9.5% and the interest is compounded quarterly. We will use the formula for compound interest get the principal value.

A=P[tex](1+\frac{r}{n}) ^{nt}[/tex]

where A= amount, P= principal, t=time period, n= number of times interest applied per time period, r=rate of interest

A=$6000

r=9.5%

t=9 yrs

n=4

6000=P[tex](1+\frac{9.5}{400} )^{36}[/tex]

6000= P x 2.328

P=6000/2.328=2577.32

Therefore the present value that will grow to $6000 in 9 years is $2577.32

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In order to corroborate that the points belong to the equation, we must subtitute the points into the equation.

If we substitute the points from option A, we get

for (1,8), we have

then, option A is false.

Now, if we substitute the points in option B, for point (2,5), we have

which is correct. Now, for point (-1.8) we obtain

Since all the points fulfil the equation, then option B is an answer.

Lets continue with option C and D.

If we substitute point (1,8) from option C, we have

then, option C is false.

If we substite point (4,11) from option D, we get

then, option D is false.

Therefore, the answer is option B.

To solve our question, first we need to know that a prime factorization is a way to represent a number by a sequence of prime numbers that multiplied together gives us the original number.

So let's calculate our first prime factorization:

As we can see, we divide our number by the smallest prime number and then the factor we follow the same rule until we get "1" (for all divisions we just have integers).

Now, for the second number we have:

And both prime factorizations are our final answers.

Explanation

Step 1

Let

then

I hope this helps you

Answer:

B. 1

Explanation:

Given the inequality:

To find the critical number, first, change the inequality sign to the equality sign :

Next, solve for x:

Therefore, from the options, 1 is the critical number.

The correct option is B.

Multiply both sides by t:

Multiply both sides by 10:

Divide both sides by 12:

The confidence interval for the mean score of the 30 randomly selected students is: 99% CI {78.26, 89.73}

Confidence interval is the range of values for which which is expected to have the values at a certain percentage of the times.

Given data form the question

99% confidence interval

30 randomly selected students

mean sample = 84

Standard deviation = 12.2

Definition of variables

confidence level, CI = 99%

mean sample, X = 84

standard deviation, SD = 12.2

Z score, z = 2.576

sample size, n = 30

The formula for the confidence interval is given by

[tex]CI=X+Z\frac{SD}{\sqrt{n} }[/tex]    OR    [tex]CI=X-Z\frac{SD}{\sqrt{n} }[/tex]  

[tex]=84+2.576\frac{12.2}{\sqrt{30} }[/tex]

=[tex]=84+2.576*2.2274[/tex]

= 84 + 5.7378     OR       84 - 5.7378

= 89.7378           OR        78.2622

=  89.73 to 78.26  

The confidence interval for the mean score of all students is 78.26 to 89.78

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Integers are numbers such as

And odd numbers are

step1: Write out the formula for exponential growth

Hence we have

Step2: substitute into the formula in step 1

Hence the right option is A

The number of kilometers per hour in 880 feet / minute can be found to be 16.09 kilometers per hour

Based on the conversion rates between kilometers and feet, the number of feet per minute for each kilometer per hour is 54.6807 feet per minute.

In other words, 1 km / h is equal to 54.6807 feet per minute.

If there are 880 ft / minute therefore, the number of kilometers per hour is:

= Speed in feet per minute / feet per minute per kilometer per hour

= 880 / 54.6807

= 16.09 kilometers per hour

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Remember that

The compound interest formula is equal to

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is the number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

P=$2,000

t=5 years

r=6%=6/100=0.06

n=12

substitute the given values in the above formula

therefore

Given:

The sequence of number of stars is 2,4,8,16

a) To find the common ratio of the pattern.

Hence the common ratio is 2.

b) To find the explicit formula for the pattern.

The general for a geometric progression sequence is,

Hence, the formula for the above pattern will be,

c) To find the number of stars in 11th set.

Substitute n=11 in the explicit formula of the pattern.

Hence, the number of stars in 11th set will be 2048.

To complete the perfect square ((x-h)²) we add and subtract constants:

ok! to graph your first point, you know the y-intercept is 1, so your point is (0,1)

graph that

because we knkow the slope is 2/3 and it's y change/x change, move up 2 and left 3 for your next point, which is (2,4)

we can graph a third point for accuracy, and move up 2 and left 3 again to get (4,7)

create a line connecting all the points

We are given two functions:

h(x) = x^2 + 1

and k(x) = x - 2

We are asked to find the value of:

(h - k) (3) (the value of the difference of the two functions at the point x = 3

So we performe the difference of the two functions:

(h - k) (x) = x^2 + 1 - (x - 2) = x^2 + 1 - x + 2 = x^2 - x + 3

So, this expression evaluated at 3 gives:

(h-k)(3) = 3^2 - 3 + 3 = 9

One could also evaluate what was asked by evaluating each function independently and subtracting the results of such evaluation:

h(3) = 3^2 + 1 = 10

k(3) = 3 - 2 = 1

Then, the difference is : h(3) - k(3) = 10 - 1 = 9

So use whatever method feels more comfortable for you.

The Solution:

Given:

By formula,

From the z-score tables:

Convert to percent by multiplying with 100.

Thus, the number of people that have an IQ score less than 90 is 25.25%

Therefore, the correct answer si 25.25%

we have the following:

Therefore:

50 + 10m = 90 Reason: This is a right angle, which sum up to 90 degree.

10m = 90 - 50

10m = 40

m = 40/10

m = 4

The formula for the logistic regression model that best fits the data is,

The graph, tables and details of the population data will be shown below

a) The equation that best fits the regression model is,

Substitutes the data above into the equation

Hence,

b) In the year 2030, t = 20

Hence, the answer is

c) Given that

Multiply both sides by 1+3.98e^{-0.02t}

Subtract 1 from both sides

Divide both sides by 3.98

Apply exponent rule

Divide both sides by -0.02

Hence, the population will reach 23million in the year 2023.

d) The carrying capacity for Florida's population is equal to the value of a.

Hence, the carrying capacity fof Florida's population is

Explanation:

The equation for a line in the slope-intercept form is:

Where 'm' is the slope and 'b' is the y-intercept.

We can find both with only two points from the line. The slope is:

(x1, y1) and (x2, y2) are points on the line.

With only one of these points, once we know the slope, we can find the y-intercept by replacing x and y by the point. For example:

And then solve for b.

In this problem we can use any pair of points from the table. I'll use the first two:

• (3, -4.5)

• (5, -9.5)

The slope is:

And the y-intercept - I'll use point (3, -4.5) to find it;

Answer:

• Slope: -5/2

• y-intercept: 3

The correct answer is option B

Answer

The least likely to occur is Event C

Explanation

A.

P(spade card) = 13/52

P(queen) = 4/51 Note: Without replacement

⇒ 13/52 x 4/51

= 52/2652

= 0.0196

B.

P(a spade) = 13/52

P( another spade) = 12/51 Note: Without replacement

⇒ 13/52 x 12/51

= 156/2652

= 0.0588

C.

P(an ace) = 4/52

P(king) = 4/51

⇒ 4/52 x 4/51

= 16/2652

= 0.006

∴ The least likely to occur is Event C