Give an example of a function with both a removable and a non-removable discontinuity.

Answers

Answer 1

Answer:

(x+5)(x-3) / (x+5)(x+1)

Step-by-step explanation:

A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator.  It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x.  In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.


Related Questions

Gsggagsgsvhdgdvdvdvdvdg help me fast I’ll give you brainliste

Answers

The answer is D

Hope that was fast enough

X+ y = 18
X = 2y
What is the solution of the system of equations?
i need the answer asap lol!!!!

Answers

Answer:

( 12 , 6 )  or x=12,y=6

Step-by-step explanation:

Answer:

Step-by-step explanation:

if  x = 2y then

2y+y=18

3y=18

=6

At a bake sale, pies cost $8 each. One customer buys $64 worth of pies.

Answers

The customer bought 8 pies.

To find the total amount of pies the customer bought, simply divide 64 by 8 to recieve your answer of 8 pies.

I hope this is correct and helps!

Eight pies would be the answer

Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.5 feet and a standard deviation of 0.4 feet. A sample of 45 men’s step lengths is taken. Step 1 of 2 : Find the probability that an individual man’s step length is less than 1.9 feet. Round your answer to 4 decimal places, if necessary.

Answers

Answer:

0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.

Step-by-step explanation:

Normal Probability Distribution:

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

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with a mean of 2.5 feet and a standard deviation of 0.4 feet.

This means that [tex]\mu = 2.5, \sigma = 0.4[/tex]

Find the probability that an individual man’s step length is less than 1.9 feet.

This is the p-value of Z when X = 1.9. So

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

[tex]Z = \frac{1.9 - 2.5}{0.4}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a p-value of 0.0668

0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.

a, b, c are prime numbers and 5≤a

Answers

Answer:

a=5

Step-by-step explanation:

What is the equation of the line that is perpendicular to
and has the same y-intercept as the given line?
(0,0)
(5,0)
O y = x+1
O y = x+5
o y = 5x + 1
O y = 5x + 5
-6 -5 -4 -3 -2 -1
23
4 5 6
Mark this and return
Save and Exit
Nyt
Submit

Answers

Answer:

y = 5x + 1

Step-by-step explanation:

Given the coordinate points (0,1) and (5,0)

First, get the slope

Slope m =(0-1)/5-0

m = -1/5

Since the required line is perpendicular, then the required slope is;

M = -1/(-1/5)

M = 5

Since 1the y intecept id (0,1) i.e. 1

Required equation is y = mx+b

y = 5x + 1

This gives the required equation

Note that the coordinate (0,1) was used instead os (0,0)

Using the simple spinner below what is the probability of landing on either 2, 4, or 7?

Answers

Answer:

3/10

Step-by-step explanation:

Total possibilities = 10

favourable possibilities = 3

Answer:

A

Step-by-step explanation:

There is a 1 out of 10 chance that it will land on 2.

There is a 1 out of 10 chance that it will land on 4.

There is a 1 out of 10 chance that it will land on 7.

[tex]\frac{1}{10}\cdot3=\frac{3}{10}[/tex] so the anwser is A.

Unit sales for new product ABC have varied in the first seven months of this year as follows:
Month Jan Feb Mar Apr May Jun Jul
Unit Sales 314 285 158 482 284 310 281
What is the (population) Pearson's coefficient of skewness of the data?
Unit sales for new product ABC have varied in the first seven months of this year as follows:
Month Jan Feb Mar Apr May Jun Jul
Unit Sales 314 285 158 482 284 310 281
What is the (population) standard deviation of the data?

Answers

Answer:

Coefficient of skewness = 0.5785

Population standard deviation = 88.154

Step-by-step explanation:

Given the data:

Month Jan Feb Mar Apr May Jun Jul

Unit Sales 314 285 158 482 284 310 281

Reordered data : 158, 281, 284, 285, 310, 314, 482

The population mean of the data :

Mean, μ = Σx / n = 2114 / 7 = 302

The median :

1/2(n+1)th term

n = 7

1/2(8)th term

Median = 4th term = 285

The population standard deviation, s :

s = √(Σ(x - μ)²/n)

s = √[(158-302)^2 + (281-302)^2 + (284-302)^2 + (285-302)^2 + (310-302)^2 + (314-302)^2 + (482-302)^2] / 7

s= √(54398 / 7)

s = √7771.1428

s = 88.154

The Pearson Coefficient of skewness :

[3(μ - median)] / s

3(302 - 285) / 88.154

3(17) / 88.154

51 / 88.154

= 0.5785


12
х
8
6
Find the value of x.
A) 9
B) 16
C) 14
D) 10

Answers

Answer:

The answer is 10, hope this helps!

Step-by-step explanation:

Write the quadratic equation in standard form:
3x2 – 3x = 11

Answers

Answer:

[tex]3x^{2} -3x-11 = 0[/tex]

Step-by-step explanation:

PLEASE HELP!!! Choose the best graph that represents the linear equation:
6x = y + 8
Graph A
On a coordinate plane, a line goes through (negative 2, 4) and (0, negative 8).
Graph B
On a coordinate plane, a line goes through (0, negative 8) and (2, 4).
Graph C
On a coordinate plane, a line goes through (negative 2, negative 4) and (0, 8).
Graph D
On a coordinate plane, a line goes through (0, 8) and (2, negative 4).
a.
Graph A
c.
Graph C
b.
Graph B
d.
Graph D



Please select the best answer from the choices provided


A
B
C
D

Answers

Answer:

b.

Graph B

Step-by-step explanation:

We are given the following linear equation:

[tex]6x = y + 8[/tex]

When x = 0:

[tex]6(0) = y + 8[/tex]

[tex]y = -8[/tex]

Thus, the line goes through (0,-8).

When y = 4:

[tex]6x = y + 8[/tex]

[tex]6x = 4 + 8[/tex]

[tex]6x = 12[/tex]

[tex]x = \frac{12}{6} = 2[/tex]

So also through (2,4).

Thus means that the correct answer is given by Graph B.

Does anyone know this question?

Answers

Step-by-step explanation:

this is a relatively easy function. Just plug in the value for x

For a particular species of wolf, 55% are female, 20% hunt in medium-sized packs, and 15% are both female and hunt in medium-sized packs. What is the percent of wolves that are female but do not hunt in medium-sized packs?

Answers

20% is the answer
55%-20%-15%=20%

Marina spent $13.50 at the grocery store. She bought pears, kiwis, and pineapples. Pears cost $0.50 each, pineapples cost $1.50 each, and kiwis are $0.30 each.How many of each kind did she buy if she bought 9 more pears than pineapples and 2 fewer kiwis than pears? Branliest if correct.

Answers

Answer:

Number of pineapples = 10

Number of pears = 10 + 9 = 19

Number of kiwis = 10 - 2 = 8

Step-by-step explanation:

Money = $ 13.5

Cost of a pear = $ 0.5

Cost of a pineapple = $ 1.5

Cost of a kiwi = $ 0.3

let the number of pineapple = p  

Number of pears = p + 9

Number of kiwis = p - 2

Cost is

0.5 (p + 9) + 0.15 p + 0.3 (p - 2) = 13.5

0.5 p + 4.5 + 0.15 p + 0.3 p - 0.6 = 13.5  

0.95 p = 9.6

p = 10

So, number of pineapples = 10

Number of pears = 10 + 9 = 19

Number of kiwis = 10 - 2 = 8  

Answer:

3 pineapples  12 pears  10 kiwis

Winning the jackpot in a particular lottery requires that you select the correct two numbers between 1 and 65 ​and, in a separate​ drawing, you must also select the correct single number between 1 and 60. Find the probability of winning the jackpot.

Answers

Answer:  1/ 233856 chance changed to 233856  x 2 = 467712

= 1 / 467712 chance as there are 2 drawings

Workings;

1 and 65 = 64

1 and 65 - 1 ball drawn = 63

1 and 60 -1 = 58

1/64 x 1/63 x 1/58 = 233856

1/4032 x 1/58 and to make these the same we 4038/58 =  69.62

then convert properly = 1/4032  x 69.62/4032 4032 x 4032 = 69.62/16257024 then 16257024/69.62 =233510.83

= 233511 chance if rounding before

1/ (233511 x 2) = 1/467022

Then one part is our actual probability

P) = 1/233856

But as they specified a special drawing

you need to repeat this as 64 x 63 x 58 x 2 as the last one cannot be in 1 drawing it has to be in 2nd drawing

233856  x 2 = 467712

= 1 / 467712 chance not rounding down before hand.

Can someone help me ASAP. All them added together is = 454 .thanks

Answers

Answer:

the answer is 86°

Step-by-step explanation:

look at the photo

The answer is in the image.

______are used to represent an unknown quantity in a mathematical expression.

Answers

Answer:

Variables are used to represent an unknown quantity in a mathematical expression.

Step-by-step explanation:

Variables are used to represent an unknown quantity in a mathematical expression.For example : x + 2 = 4, here x is the variable.We can denote variable by any alphabet i.e, a,b,c,d etc.

Solve the system of inequalities to decide if the point (-3,2) is part of the solution; y<=-4x-3, +8y>=7

Answers

Answer:

[tex](x,y) = (-3,2)[/tex] is a solution

Step-by-step explanation:

Given

[tex]y \le -4x + 3[/tex]

[tex]x + 8y \ge 7[/tex]

Required

Determine if [tex](x,y) = (-3,2)[/tex] is a solution

[tex]y \le -4x + 3[/tex] becomes

[tex]2 \le -4 * -3 + 3[/tex]

[tex]2 \le 15[/tex] --- this is true

[tex]x + 8y \ge 7[/tex]

[tex]-3+ 8 * 2 \ge 7[/tex]

[tex]13 \ge 7[/tex] --- this is also true

Hence,

[tex](x,y) = (-3,2)[/tex] is a solution

Given that the area of a triangle ABC is 4.5 m², a=4, b=3, find two possible measures for angle C. Round your answer to the nearest tenth

Answers

Answer:

[tex]C = 48.6[/tex]

Step-by-step explanation:

Given

[tex]Area= 4.5m^2[/tex]

[tex]a =4[/tex]

[tex]b = 3[/tex]

Required

Find angle C

The area of the triangle will be calculated using:

[tex]Area = \frac{1}{2}ab \sin C[/tex]

So, we have:

[tex]4.5= \frac{1}{2} * 4 * 3 * \sin C[/tex]

[tex]4.5= 6 * \sin C[/tex]

Divide both sides by 6

[tex]0.75= \sin C[/tex]

Take arc sin of both sides

[tex]\sin^{-1}(0.75)= C[/tex]

[tex]48.6 = C[/tex]

[tex]C = 48.6[/tex]

Which of the following can be constructed by drawing an angle on tracing
paper and then folding the paper so that the rays forming the angle lie upon
each other?
A. Parallel lines
• B. Angle bisector
• C. Median of a line segment

D. Perpendicular line segment

Answers

B. angle bisector.

i hope this helps

Choose the correct answers for (a) the total installment price, (b) the carrying charges, and (c) the number of months needed to save money at the monthly rate to buy the item for its cash price.
A bunk bed with a cash price of $1,998, at $143 per month for 15 months

Answers

Answer:

$2,145 ; $147 ; 14 months

Step-by-step explanation:

Given that :

The cash price, that is, the amount that would be paid if customer is to pay the entire amount item is worth at once = $1998

Monthly payment = $143

Period = 15 months

The total installment price ; total amount paid on a monthly pay for 15 months :

(monthly payment * period)

($143 * 15)

= $2,145

The carrying charge :

Installment pay - Cash amount

$(2,145 - 1,998)

= $147

The number of month needed to save at Monthly rate to buy item at it's cash price :

Cash price / monthly payment

$1998 / $143

= 13.97

= 14 months

There are 200 blue balls and 10 red balls in an urn. Suppose that 10 balls are taken random;ly from the urn and let X denote the number of red balls selected.
a) The distribution of the random variable X is___.
i) Binomial.
ii) Hypergeometric.
iii) Poisson.
iv) Normal.
v) Exponential.
vi) Uniform
b) Find P(all 10 balls are red).
c) Which distribution from those listed in part (a) can be used as an approximation to the distribution of X? With this approximation find P(X = 10).

Answers

Answer:

Hypergeometric

Kindly check explanation

Step-by-step explanation:

For a hypergeometric distribution, the following conditions must be met :

1.) The total number of samples must be fixed.

2.) Sample size will be a portion of the population

3.) The probability of success changes per trial. This is because sampling is done without replacement

The above scenario meets the condition described:

Total number of samples = 210

Sample size, n = 10

Blue balls = 200 ; red balls = 10

P(10 red balls)

Using the hypergeometric distribution function and the calculator :

X ~ H(n, N, M)

X ~ (10, 200, 210) = 0.6072

Find the inverse of the given function. (pictured below)

Answers

Answer:

4

3

0

Step-by-step explanation:

f(x) = y = -1/2 × sqrt(x+3)

2y = -sqrt(x+3)

4y² = x + 3

x = 4y² - 3

now renaming this, so that the normal symbols and names are used for this function definition, so that the input variable is called "x" :

f-1(x) = 4x² - 3

basically, just by itself, this function would be defined for all possible real values of x.

but because it is the inverse of the original function, which generates only values of y<=0, then for the inverse function that same range applies for its input variable x

x<=0

Mark draws one card from a standard deck of 52. He receives $ 0.30 for a heart, $ 0.55 for a queen and $ 0.90 for the queen of hearts. How much should he pay for one draw

Answers

Answer

$0.1346

Explanation:

Find probability of each card and the value of each card and then add them together.

Probability of getting a heart = 13/52

Price of one heart =$0.30

Pay for one heart = 13/52×0.30=$0.075

Probability of getting a queen =4/52

Price of one queen =$0.55

Pay for one queen =4/52×$0.55=$0.0423

Probability of getting a queen of hearts =1/52

Price of one queen =$0.90

Pay for one queen =1/52×$0.90=$0.0173

Therefore the pay for one draw= $0.075+$0.0423+$0.0173=$0.1346

A system of equations is said to be redundant if one of the equations in the system is a linear combination of the other equations. Show by using the pivot operation that the following system is redundant. Is this system equivalent to a system of equations in canonical form?
a) x1 +x2 −3x3 = 7
b) −2x1 +x2 +5x3 = 2
c) 3x2 −x3 = 16

Answers

Answer:

prove that The given system of equations is redundant is attached below

Step-by-step explanation:

System of equations

x1 +x2 −3x3 = 7

−2x1 +x2 +5x3 = 2

 3x2 −x3 = 16

To prove that the system is redundant we will apply the Gaussian elimination ( pivot operation )

attached below is the solution

A small radio transmitter broadcasts in a 69 mile radius. If you drive along a straight line from a city 93 miles north of the transmitter to a second city 78 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?

Answers

Answer:

See Explanation

Step-by-step explanation:

According to the Question,

We have A small radio transmitter that broadcasts in a 69-mile radius. If you drive along a straight line from a city 93 miles north of the transmitter to a second city 78 miles east of the transmitter.

Thus,

The distance that you get reception is the length of the chord created by the intersection of the circle defining the edge of transmission and the line defining the car trip.

 x2 + y2 = 69²               this is the circle

And,

The Transmitter at the origin

City to the north at (0,93)  & City to the east at (78,0)  

the Slope is M=(-93/78)

Intercept is B= y - mx ⇒  93 - (-93/78)(0) = 93

The equation of the line between the cities is y = (-93/78)x + 93

y = -93x/78 + 93           this is the line

Now, Solve the above two Equations

The intersection is gotten from the picture or solving:

x^2 + [(-93/78)*x + 93]^2 = 69^2

on solving we get, the points approximately are: (67.952,11.98 ) and (23.6277, 64.82)

Now,

From the Pythagorean theorem the total distance of the trip is:  

d1 = √(93^2 + 78^2) ≈ 121.37miles  

And the distance when the signal is picked up is:

d2 =√ [(67.952-23.627)^2 + (64.82 - 11.98)^2] ≈ 68.96 miles

You will pick up a signal from the transmitter in (d2/d1)*100 = 56% of the drive.

You are dealt one card from a​ 52-card deck. Find the probability that you are dealt a king or a red card.

Answers

Answer:

7/13

Step-by-step explanation:

Half the deck is red so there are 26 reds.

There are 4 kings but we already counted two of these in the 26.

So there are 26+2 red or king cards total.

The probability of selecting a king or red is 28/52.

This can be reduced by dividing top and bottom by 4: 7/13.

every student from different schools planted as many plants of their number if they planted 4225 plants how many students were there

Answers

Answer:

65 students.

Step-by-step explanation:

Given that :

Every student planted as many plant as their number ;

Then let the number of student = x

Then the number of plant planted by each student will also = x

The total number of plants planted by all the students = 4225

The Number of students can be obtained thus ;

Total number of plants = Number of plants * number of plants per student

4225 = x * x

4225 = x²

√4225 = x

65 = x

Hence, there are 65 students

NEED ANSWER QUICK

Timmy and Tommy are two boys whose ages add up to 23. Timmy is 5
years older than Tommy. How old are they?

Answers

Let’s assume that age of Timmy is x yrs.
Then we can conclude that age of Tommy is =
(23 -x) yrs.

Now we know that Timmy is 5 years older than Tommy, therefore,
x = 5 + (23-x)
x = 5 + 23 - x
x + x = 28
2x = 28
x = 28/2
x = 14 Answer. (Age of Timmy)

So, the age of Tommy is 23 - x = 23 - 14 = 9 yrs.

Answer:

Tommy's age is 9 years old.

Timmy's age is 14 years old.

Step-by-step explanation:

Take Tommy's age to be x and Timmy's age to be x+5

x+x+5=23

2x+5=23

2x=23-5=18

x=18÷2=9

x+5=9+5=14

two observers, Anna and Bryan. sight a kite at angles 44 degrees and 66 degrees. respictively. if anna is located 20m from the kite. how far is anna from bryan?

Answers

Answer:

28.6m

Step-by-step explanation:

this question is very incomplete. it requires a number of assumptions to give an answer. the main one - where is Bryan located relative to Anna ? I assume diametrically on the opposite side of the kite. because he has the steeper angle, it is clear that he is nearer to the kite.

so, I guess, we have to add his distance to the kite to her distance to the kite to get the distance between her and him.

but he could be on any point on a circle around the kite to have the same viewing angle, and we would have no clue about where on that circle.

as the other extreme alternative, he could be on the same line to the kite as Anna. and then we would have to subtract his distance from her distance.

but again, we assume he is exactly on the other side of the kite.

anyway, each person creates a right-angled triangle with the kite:

there is the direct line of sight as the base line or Hypotenuse (c).

there is the line on the ground from the person to the point on the ground directly under the kite as one side.

there is the line representing the height of the kite above ground as the other side. we let this start at the height of the eyes of the watching person.

and we assume that both persons are of the same height (so the height of the kite relative to their eyes is the same for both).

let's start with Anna.

the side a of Anna's triangle is

a = 20m

angle between a and c = 44 degrees

we know the angle between a and b is 90 degrees.

therefore the angle between b and c = 180-90-44 = 46 degrees.

now we use the law of sines :

a/sin(bc) = b/sin(ac) = c/sin(ab)

we know sin(ab) = sin(90) = 1

20/sin(46) = b/sin(44)

b = 20×sin(44)/sin(46) = 19.31... m = height of the kite

now to Bryan.

now we know his b (height of the kite) = 19.32... m

his angle between a and c is 66 degrees.

his angle between a and b is also 90 degrees.

therefore his angle between b and c = 180-90-66 = 24 degrees.

19.31/sin(66) = a/sin(24)

a = 19.31×sin(24)/sin(66) = 8.6 m

based on our assumption that they are standing opposite from each other in relation to the kite their distance is

20 + 8.6 = 28.6m

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