Write the equation of the quadratic function shown in the graph.

Write The Equation Of The Quadratic Function Shown In The Graph.

Answers

Answer 1

Answer:

Step-by-step explanation:

y = a(x-h)² + k, where (h,k) is the vertex.

vertex is clearly (0,0), so y = ax².

Plug in (3,3)  and solve for a:

3 = a3²

a = ⅓

y = ⅓x²


Related Questions

what is the value of x in the equation -6 + x = -5

Answers

ANSWER: 1
-6 + 1 = -5

A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. He wants to construct the 95% confidence interval with a maximum error of 0.19 reproductions per hour. Assuming that the mean is 6.4 reproductions and the standard deviation is known to be 1.8, what is the minimum sample size required for the estimate? Round your answer up to the next integer.

Answers

Answer:

The minimum sample size required for the estimate is 345.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The standard deviation is known to be 1.8.

This means that [tex]\sigma = 1.8[/tex]

What is the minimum sample size required for the estimate?

This is n for which M = 0.19. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.19 = 1.96\frac{1.8}{\sqrt{n}}[/tex]

[tex]0.19\sqrt{n} = 1.96*1.8[/tex]

[tex]\sqrt{n} = \frac{1.96*1.8}{0.19}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*1.8}{0.19})^2[/tex]

[tex]n = 344.8[/tex]

Rounding up to the next integer:

The minimum sample size required for the estimate is 345.

A box contains 6 red marbles, 10 blue marbles and 4 yellow marbles.
Which colour marble is impossible to take from the box?
red blue white yellow

Answers

Answer:

White because there is no white marble.

Step-by-step explanation:

white , there’s every colour but white

1. A company has a cash portfolio measured in millions. The drift is 0.1 per month, variance is 0.16per month. The initial cash is 2.0. a) Find the probability distribution after 6 months and after 1 year. b) Find the probability of a negative cash position at the end of 6 months and the end of 1 year. c) At what time in the future is the probability of a negative distribution greatest.

Answers

Answer:

Step-by-step explanation:

From the information given:

The probability distribution at the end of 6 months is determined as follows:

After 6 months;

Mean of probability distribution =  value of Initial cash  + [tex]\alpha[/tex]T  

=2.0 +(0.1 × 6)

=2.6

After 6 months;

The probability distribution's standard deviation is estimated by using the following formula:

Standard deviation:

[tex]= b\sqrt{T}[/tex]

[tex]= 0.4 \times \sqrt{6}[/tex]

= 0.9798

Hence, after 6 months;

The company's cash position is supposed to be allocated monthly, with the following expenses.

Mean                            2.6

Standard deviation     0.9798

Variance                      0.96

After 12 months, the probability distribution is as follows:

Mean = value of Initial cash  + [tex]\alpha[/tex]T

= 2.0 +(0.1 × 12)

= 3.2

The standard deviation is:

The standard deviation of probability distribution = [tex]b \sqrt{T}[/tex]

[tex]= 0.4 \times \sqrt{12}[/tex]

= 1.3856

Hence, after 6 months;

The company's cash position is supposed to be allocated monthly, with the following expenses.

Mean                            3.2

Sandard deviation      1.3856

Variance                      1.92

b)  

in 6-month distribution, the probability of the negative value of the cash position is as follows.

Now, for us to find the negative cash distribution;

We need to estimate the z -scores value.

The z-score inform us greatly on the concept of how far a particular data point is from the mean.

For a normal distribution;

[tex]z = \dfrac{x-\mu}{\sigma}[/tex]

Here;

the value of x = zero as a result that if it exceeds zero. the cash position will be negative.

[tex]z = \dfrac{x-\mu}{\sigma}[/tex]

[tex]z = \dfrac{0 - 2.6}{0.9798}[/tex]

[tex]z = -2.6536[/tex]

Using the standard distribution tables, it is now possible to calculate that the likelihood N(-2.65) equals 0.004 or 0.4 percent.

As a result, there's a 0.4 percent chance of getting a negative cash balance after six months.

For 12 months distribution:

The Probability of negative cash position is calculated as follows:

[tex]z = \dfrac{x-\mu}{\sigma} \\ \\ z = \dfrac{0-3.2}{1.3856} \\ \\ z = -2.3094[/tex]

Using the standard distribution tables,

N(-2.31) equals 0.0104 or 1.04 percent.

As a result, there's a 1.04 percent chance of getting a negative cash balance after 1 year  

c) To determine the time period over which the likelihood of achieving a negative cash condition is highest, it's necessary to examine the z-score more closely. Essentially, the z-score measures the difference between a given value(x) and the mean of all potential values [tex](\mu)[/tex], expressed in terms of the total set's standard deviation [tex](\sigma)[/tex]

This suggests that the higher the z-score, the greater the difference occurring between x and [tex]\mu[/tex], and thus the likelihood of receiving x is minimal. As a result, the best chance of finding a certain value is when the z-score is the lowest.

To do so, calculate the derivative of the z-score in relation to the time interval. The point where the derivative is equivalent to zero is where the z-scores are at their lowest.

The first step is to go over the z-score formula in more detail, as seen below.;

[tex]z = \dfrac{x-\mu}{\sigma} \\ \\ z = \dfrac{0-(initial \ value + \alpha T)}{b \sqrt{T}} \\ \\ z = \dfrac{-initial \ value }{b\sqrt{T}}-\dfrac{a \sqrt{T}}{b} \\ \\[/tex]

Now, compute the derivative of this equation with respect to T as follows:

[tex]\dfrac{dz}{dT}= \dfrac{initial \ value \times T^{-\dfrac{3}{2}}}{2b} - \dfrac{aT^{-\dfrac{1}{2}}}{2b}[/tex]

Now, figure out the value of T at which this derivative is equal to zero by substituting all values as follows:

[tex]0 = \dfrac{2.0 \times T^{-\dfrac{3}{2}}}{2\times 0.4}- \dfrac{0.1 \times T^{-\dfrac{1}{2}}}{2 \times 0.4} \\ \\ \\ 0.1 \times T^{-\dfrac{1}{2}}= 2.0 \times T^{-\dfrac{3}{2}} \\ \\ \\T = \dfrac{2}{0.1} \\ \\ \\ T = 20[/tex]

As a result, the time period in which achieving a negative cash condition is = 20 months.

Find cos(B) in the triangle.
Choose 1 answer:

Answers

Cosine: adjacent/hypothenuse
Adjacent = 3, hypothenuse = 5

Solution: 3/5

Space shuttle Challengerexploded because of O-ring failure shortly after it was launched. O-ring damage and temperature at time of launch for the 23 space shuttle flights that preceded the Challenger. The data is reproduced below.
Flights with O-ring damage 43 57 58 63 70 70 75
Flights with no O-ring damage 66 67 67 67 68 69 70 70 72 73 75 76 76 78 79 81
Is the mean launch temperature for fights with O-ring damage significantly less than for flights with no O-ring damage? Use 5% level of significance.

Answers

Answer:

The mean launch temperature for flights with O-ring damage is significantly lesser than Flights with No O-ring

Step-by-step explanation:

Let

Null hypothesis : H0 : μ1 ≥ μ2

Alternate hypothesis : Ha : μ1 < μ2

next calculate the test statistic

t = -2.312

calculate the P-value

p-value = T.DIST ( t ,df )  (  excel function )

            = 0.0270

Given that P-value ( 0.020 ) < level of significance ( 0.05 ) we will not fail to reject the null hypothesis

Attached below is the detailed solution


PLEASE HELP , DONT SKIP !

NO LINKS OR FILES.

Answers

Step-by-step explanation:

You have to click the number of Xs for each kilometer travelled. For example, there are 2 "3 km" answers, so under the 3 column, you click 2 Xs.

What is the scale factor from LMN to OPO?



A.1
Β. 4
C. 3
D. 0

Answers

You need to add a picture so others can understand what you are referring to.

Answer:

A. 1

Step-by-step explanation:

Cecilia invested 12,500 in an account that compounds quarterly at 2%. How much money is in her account after 4 years

Answers

6 persent

75,000 infour year's

follow me

nice study

I think 22400 mainly because i did the calculation

12500 * .2 4 times and got that answer.

I need help with this question.
What is the approximate circumference of the circle?
A: 1.57 m
B: 157 m
C: 314 m
D: 3.14 m

Answers

Circumference: 2 * pi * r
2 * pi * 0.5 = 3.14159
The value is pi

Solution: D

Answer:

c=2pie r

2*3.14*0.5

=3.14

option d

complete the inequality statement
4/13 __6/13

Answers

< answer because 4/13 is less than

Please HELP ASAP!!! The dot plot show the number of hours teenagers spent on two different websites last week. Which statement is supported by the data in the dot plots? (F.) the mode of the data for website K is greater than the mode of the data from website L. (G.) the range of the data for website L is equal to the range of data for website K. (H.) the distribution of data for website L is symmetrical. (J.) the distribution of data for website K is skewed to the left. ​

Answers

Answer:

(F.) the mode of the data for website K is greater than the mode of the data from website L

Step-by-step explanation:

Mode simply means the parameter that occurs the most.

In website K, the one that occurs the most is 8 hours while in website L, the one that occurs the most is 2 hours.

This means that mode of website K is greater than that of website L.

Thus,statement F is correct

Range is the difference between the highest value and the lowest value..

For website K, Range = 14 - 1 = 13

For website L, Range = 13 - 1 = 12

Thus,range of both websites are not the same and as such statement G is wrong.

For a symmetrical distribution, the left and right hand sides of the centre value line of the distribution have to mirror each other.

In this case neither website K nor L have that. Thus, statement H is not correct.

Skewed to the left means that more o

dot points are found to the left of the graph.

For website L, more dot points are located to the left while for website K, it's not the case. Thus, statement J is not correct

Answer:

f

Step-by-step explanation:

4 Does the equation y = x represent a function? Explain why or why not.

Answers

Answer:

y=x is a function!

Step-by-step explanation:

The reason it is a function is because it can create a:

A slope

A why y and x intercept

and a graph

Remember that x=1 and Y=1 ALWAYS

please help me! i’m so confused!!

Answers

ok

a I'm sure

14*7*8

Step-by-step explanation:

we should multiple everything

Four friends each took a different path walking from the drinking fountain to the cypress tree. Who walked the farthest?
Rowan 150yd
Janelle 429ft 8in
Domingo 130yd 2ft
Lydia 460ft

Answers

Lydia because when you convert all of the distances into inches, Lydia’s total distance is 5520 inches.


Simplify (8x2 − 1 + 2x3) − (7x3 − 3x2 + 1).

Answers

PEMDAS: parentheses, exponents, multiplication, division, addition, subtraction. That tells you the order you solve problems.

You start by working each part of the problem in parentheses. You multiply before adding/subtracting.

I’ve attached a picture. Please ask any questions.
Thanks for answering!!!!!

HELP ME PLEASE
Classify the triangle by its sides and angles.

-acute, scalene
-obtuse, scalene
-obtuse, isosceles
-acute, isosceles

Answers

Answer:

obtuse, scalene

Step-by-step explanation:

Answer:

obtuse,scalene

Step-by-step explanation:

it is more than 180°but less than 360°

it does not have equal sides

5. The owners of a two-person business make their decisions independently of each other and then compare their decisions. If they agree, the decision is made; if they do not agree, then further consideration is necessary before a decision is reached. The first owner makes the right decision 60% of the time; the second - 70% of the time. Enter your answers as decimals. 5(a) What is the probability that they make the right decision on the first try. 5(b) What is the probability that they make the wrong decision on the first try. 5(c) What is the probability that they delay the decision for further study.

Answers

Answer:

A. 0.42

B. 0.12

C. 0.45

Step-by-step explanation:

A. The probability that they make the right decision on the first try

First person = 60%

Second person = 70%

= 60% * 70%

= 0.42

B. Probability that they make wrong decision

= Wrong decision from first person * wrong decision from second person

Wrong decision = 1- right decision

= 1-0.60 * 1-0.70

= 0.40x0.30

= 0.12

3. Probability they delay decision

= 0.60(1-0.60)+0.70(1-0.70)

= 0.60x0.40 + 0.70x0.30

= 0.24+ 0.21

= 0.45

How many cards are in a standard deck of cards? What are their colors?

Answers

Answer:

52 cards

Step-by-step explanation:

the colors I am not sure of thought sorry

Find the missing measure in a right triangle if a= 9 ft and b = 12 ft.

Answers

Answer:

c = 15 ft

Step-by-step explanation:

a^2 + b^2 = c^2

9^2 + 12^2 = c^2

c^2 = 225

c = √225

c = 15 ft

Recall the following study: Over a 17-year period researchers studied a sample of 707 individuals from a single community. They recorded the number of hours each individual spent watching television during adolescence and early adulthood. In later years, they recorded the number of aggressive acts by individuals in the study, as reported by parents, teachers and police. Science magazine published the results in 2002 in an article titled "Television Viewing and Aggressive Behavior during Adolescence and Adulthood." The following are what kinds of variables?

Answers

Your question is incomplete

I have provided the various variables used in the question and their types

Step-by-step explanation:

The independent/explanatory variable in this question is the number of hours spent watching tv. This variable is what is used to explain the changes that occurs in the dependent variable.

The dependent/response variable is the number of aggressive actions that the individual commits. This is the variable we are interested in. This variable is measured using the independent variable.

The confounding variable is gender. And this variable has an impact on both the dependent and the explanatory variables.

Working Two Jobs. Maggie has a job working in an office for $10 an hour and another job driving a tractor
pays $16 an hour. Maggie works at both jobs and earns $480 in one week.

Answers

Answer:

x*$10 + y*$16 = $480

Step-by-step explanation:

The question seems incomplete, and after a search online I've found a lot of similar questions with similar numbers, so I really can not be sure of which one is the complete question.

I suppose that we want to get a linear equation that describes the given situation:

Let's define two variables:

x = number of hours that Maggie works in the office (for $10 each)

y = number of hours that Maggie works driving a tractor (for $16 each).

Then the total amount of money that Maggie gets is:

x*$10 + y*$16

Now we know that she earns $480 per week, then we know that:

x*$10 + y*$16 = $480

This is a linear equation we wanted to get, where (just to be complete) we need to add the restrictions:

x ≥ 0

y ≥ 0

(this means that she can not work a negative number of hours).

What is 97,000 in scientific notation?

Answers

Answer:

9.7 * 10 to power of 4

Step-by-step explanation:

Answer:

Don't know the meaning of this question

MAFS.4.0A.1.2
2. Eddie has 50 marbles. Manny has m marbles. If Eddie
has 10 times as many marbles as Manny, write an
equation that shows how many marbles Manny has.

Answers

E = 10 * m
(E/10) = m

 Consider the line segment LP with endpoint at L (-3, -5) and P (9, 7) and midpoint M.

What is the x—coordinate of N, the point that partitions segment MP in a 1 : 1 ratio?

A. 4
B. -4
C. -6
D. 6

Answers

Answer:

D. 6

Step-by-step explanation:

Finding M:

M is the midpoint of L and P, which is given by the mean coordinates of L and P.

x for L is -3, and for P is 9. So

(-3 + 9)/2 = 6/2 = 3

Finding N:

N is the midpoint between M and P, that is, the mean between the coordinates of M and P. So

(3 + 9)/2 = 12/2 = 6

The correct answer is given by option D.

Please help I’m really need the help (NO LINKS ) (NO LYING ) PART 2

Answers

Here multiple all your numbers together only for that question tho ok
Add the sides up of whatever is equal to the number it shows

Ninety percent of the 50 members of Clean and Green Movement voted for the new
president. How many did not vote for the new president?

Answers

Answer:

5

Step-by-step explanation:

90% of 50 is 45.

So 50-45

5

Hope this helps

help me plz.................

Answers

Answer:

[tex]\frac{1}{8}[/tex] cup

Step-by-step explanation:

[tex]y=\frac{7}{8} -\frac{1}{4}-\frac{1}{2}[/tex]

[tex]y=\frac{7}{8}-\frac{2}{8}-\frac{4}{8}[/tex]

[tex]y=\frac{7}{8}-\frac{6}{8}[/tex]

[tex]y=\frac{1}{8}[/tex]

5. Which is the best estimate for the sum of 3/8 and 1/12?

Answers

The best estimate is 11/24.

To solve, find a common denominator between both 8 and 12. They can both multiply into 24.

To turn 8 into 24, you multiply by 3, so you must do the same with its numerator. To turn 12 into 24, you multiply by 2, so again, you must do the same with its numerator:

3/8 ---> 9/24

1/12 ---> 2/24

Then, you can add the numerators together and keep the denominator 24:

9/24 + 2/24 = 11/24.

find area of figure
3 yd
8 yd
15 yd
13 yd

Answers

Answer:

C, 15 yd

Step-by-step explanation:

Hope this helps

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