25 Points please help me
ASAP and I will mark brainlyist

25 Points Please Help Me ASAP And I Will Mark Brainlyist

Answers

Answer 1

Answer:

(a)

1. 4.6... sample mean2. 4.6.. sample mean3. 4.8... sample mean4. 5.2... sample mean

(b) range of sample means =0.6

(c)

FalseFalseFalseFalse

Related Questions

Help ill mark brainliest and yea answeeer

Answers

2r + t + r

3r + t

The correct answer is C - None of the Above.

When we combine like terms, we combine terms that have the same variables but different coefficients. We cannot add 2r and t because r and t are not the same variables.

Hope this helps!

Answer:

None of the above

Step-by-step explanation:

Because the answer is 3r + t

Help me asap! I will give you marks

Answers

Recall the binomial theorem.

[tex](a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k[/tex]

1. The binomial expansion of [tex]\left(1+\frac x3\right)^7[/tex] is

[tex]\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}[/tex]

Observe that

[tex]k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x[/tex]

[tex]k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2[/tex]

When we multiply these by [tex]8-9x[/tex],

• [tex]8[/tex] and [tex]\frac73 x^2[/tex] combine to make [tex]\frac{56}3 x^2[/tex]

• [tex]-9x[/tex] and [tex]\frac73 x[/tex] combine to make [tex]-\frac{63}3 x^2 = -21x^2[/tex]

and the sum of these terms is

[tex]\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}[/tex]

2. The binomial expansion is

[tex]\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k[/tex]

We get the [tex]a^6b^2[/tex] term when [tex]k=2[/tex] :

[tex]k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2[/tex]

Does anyone know this? Evalute the power type your answer in the open box. Look at picture.

Answers

Since it is an negative number and the exponent is an even number, the sign stays the same. After evaluating, it is -256

I hope that this helps! :)

Do the data in the table represent a direct variation or inverse variation? Write an equation to model the data in the table?
x 2 4 8 12
y 4 2 1 2/3

Answers

Based on the given data; the table represent an inverse variation and the equation that model the data in the table is y = 8/x

Variation

Direct variation

y = k × x

4 = k × 2

4 = 2k

k = 4/2

k = 2

when y = 2 and x = 4

y = k × x

= 2 × 4

y = 8

Indirect variation

y = k/x

4 = k / 2

8 = k

when y = 2 and x = 4

y = k/x

2 = k/4

2 × 4 = k

k = 8

So,

y = k/x

y = 8/x

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Last week the value of an investment changed at a rate of -$3.15 each day. After How many days was the total change in value -$12.60?

Answers

In four days,the total change in value -$12.60.

According to the statement

we have given that the value of an investment changed at a rate of -$3.15 each day. And we have to find that the after how many days the change in value reaches at the -$12.60.

So, here we use division rule to find the solution.

The given change value is :

-$3.15 each day.

The desired change value is :

-$12.60.

Number of days required = -12.60 / -3.15

Number of days required = 12.60 / 3.15

Number of days required = 4 days.

So, in four days the change in value reaches at the desired value of change.

So, In four days,the total change in value -$12.60.

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The order of magnitude for total attended for a high school football team that averages 1,000 fans for each of its 5 home games is

Answers

The order of magnitude for total attended for a high school football team is 3

How to determine the order of magnitude?

The given parameters are:

Average number of fan = 1000

Number of home games = 5

The total number of fans in the 5 games is:

Total number of fans = Average number of fan * Number of home games

Substitute known values in the above equation

Total number of fans = 1000 * 5

Express 1000 as 10^3

Total number of fans = 10^3 * 5

Rewrite the equation as:

Total number of fans = 5 * 10^3

The power of 10 represents the order of magnitude

Since the power of 10 is 3, the order of magnitude is 3

Hence, the order of magnitude for total attended for a high school football team that averages 1,000 fans for each of its 5 home games is 3

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Find the volume of the triangular prism below if B = 12 cm, h = 8 cm, and L = 27 cm.

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{Formula \rightarrow \dfrac{1}{2} \times \bold{b}ase\times\bold{h}eight\times \bold{l}ength}[/tex]

[tex]\mathsf{Your\ equation\ should\ look\ like\rightarrow \dfrac{1}{2}\times12\times8\times27}[/tex]

[tex]\mathsf{Solving\rightarrow \dfrac{1}{2}\times12\times8\times27}[/tex]

[tex]\mathsf{ \dfrac{1}{2}\times12\times8\times27}[/tex]

[tex]\mathsf{= \dfrac{1}{2}\times\dfrac{12}{1}\times\dfrac{8}{1}\times\dfrac{27}{1}}[/tex]

[tex]\mathsf{= \dfrac{1\times12\times8\times27}{2\times1\times1\times1}}[/tex]

[tex]\mathsf{= \dfrac{12\times8\times27}{2\times1\times1}}[/tex]

[tex]\mathsf{= \dfrac{96\times27}{2\times1}}[/tex]

[tex]\mathsf{= \dfrac{2,592}{2}}[/tex]

[tex]\mathsf{= 2.592\div2}[/tex]

[tex]\mathsf{= 1,296}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{Option\ C.\ }\frak{1,296\ cm^3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

A bin in the school gymnasium holds different colored balls. a ball is picked at random and then replaced. the probability of picking a green ball is 0.5, the probability of picking a blue ball is 0.4, and the probability of picking a red ball is 0.1. if a ball is picked and replaced 140 times, how many times should you expect a blue ball to be picked? a. 14 b. 48 c. 56 d. 70

Answers

Correct answer is C. the number of times blue ball appears is 56

Given,

probability of picking a green ball is 0.5,

the probability of picking a blue ball is 0.4,

the probability of picking a red ball is 0.1.

a ball is picked and replaced = 140

Probability = (the number of ways of achieving success) / (the total number of possible outcomes)

Probability provides information about the likelihood that something will happen. Meteorologists, for instance, use weather patterns to predict the probability of rain. In epidemiology, probability theory is used to understand the relationship between exposures and the risk of health effects.

For this item, the number of times that we should expect that a blue ball is picked should be the product of the number of times  and the probability of picking a blue ball (which is equal to 0.4)

                            = (140)(0.4) = 56

Therefore, we should expect that the blue ball will be picked 56 times.

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A bag contains 4 black tiles, 5 white tiles, and 6 blue tiles. event a is defined as drawing a black tile from the bag on the first draw, and event b is defined as drawing a white tile on the second draw. if two tiles are drawn from the bag, one after the other without replacement, what is p(a and b) expressed in simplest form?

Answers

P(A and B) expressed in the simplest form is (B) 2/21.

What is probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

To express P(A and B) in the simplest form:

P(A and B) means that you need to multiply the two probabilities together since both A and B need to happen. The probability of drawing a black tile on the first draw is 4/15 since there are 15 total tiles and 4 of those are black. On the second draw, the bag is already missing a tile, and there are therefore 14 tiles remaining. For the second one, the probability is 5/14, since there are 14 total tiles and 5 of them are white. Multiplying these two together, we get 4/15 × 5/14 = 20 / 210 = 2/21.

Therefore, P(A and B) expressed in the simplest form is (B) 2/21.

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The complete question is given below:

A bag contains 4 black tiles, 5 white tiles, and 6 blue tiles. Event A is defined as drawing a black tile from the bag on the first draw, and event B is defined as drawing a white tile on the second draw.

If two tiles are drawn from the bag, one after the other without replacement, what is P(A and B) expressed in the simplest form?

A. 4/45

B. 2/21

C. 4/15

D. 5/14

Which is a discrete random variable?

Answers

The answer is z result of flipping. Two coins

9. Find the values of x and y.
Write answers in simplest radical form.
x=______ y=_____

Answers

Answer:

  x = 3√3

  y = 6

Step-by-step explanation:

The geometric mean relations between segments intersecting the long hypotenuse and its parts can be used to find the values of interest.

Altitude

  x = √(9·3) = 3√3

Short side

  y = √((9+3)·3) = 6

__

Additional comment

These right triangles are all similar, so corresponding sides are proportional. When the proportions are solved for a missing side, a geometric mean relation results. (The geometric mean of 'a' and 'b' is √(ab).)

Identify the segments above the horizontal line as w, x, y. (x and y are already identified in this figure.)

The ratio of short side to long side is ...

  x/9 = 3/x   ⇒   x² = 9·3   ⇒   x = √(9·3)

The ratio of short side to hypotenuse is ...

  y/(9+3) = 3/y    ⇒   y² = (9+3)·3   ⇒   y = √((9+3)·3)

Likewise, the ratio of long side to hypotenuse is ...

  w/(9+3) = 9/w   ⇒   w² = (9+3)·9   w = √((9+3)·9) = 6√3

i don't know how to solve this. help please?

Answers

Answer:

51   74

Step-by-step explanation:

x = smaller

x +23 = larger

added together   (x   + x+23)    equal to 28 less than 3x      = 3x-28

x    + x+23  = 3x-28      subtract 2x from both sides of the equation

   23 = x -28      add 28 to both sides

 51 = x      then the larger   =  51 + 23 = 74

Answer:

51 and 74

Step-by-step explanation:

Let the smaller of the two numbers be represented by x. The larger of the two numbers is 23 greater than the smaller, and therefore can be written as x + 23.

Set up an Equation

First, we can write the sum of the two numbers in terms of the smaller number. "three times the smaller" is 3x, and "28 less" is 3x-28.

Therefore our equation is:

[tex]x+x+23=3x-28[/tex]

Solve the Equation

Start by adding like terms

[tex]2x+23=3x-28[/tex]

Subtract 23 from both sides

[tex]2x=3x-51[/tex]

Subtract 3x from both sides

[tex]-x=-51[/tex]

Divide both sides by -1

[tex]x=51[/tex]

The larger term is: [tex]x+23\Rightarrow51+23\Rightarrow74[/tex]

Check

[tex]51+74=125[/tex]

[tex]3(51)-28=153-28=125[/tex]

[tex]125=125[/tex]

The smaller number is 51 and the larger number is 74

convert 5.75 hours to minutes

Answers

Every hour is 60 mins so multiple 4 by 60 mins and then add 75 you should get 345
Convert 5.75 hours to minutesKnowing that 1 hour = 60 minutes

[tex]\boldsymbol{\sf{Therefore \to \ 5.75\not{h}*\dfrac{60 \ min}{1\not{h}} =345 \ min }}[/tex]

5.75 hours is equal to 345 minutes.

Qualitative data are made up of words rather than numbers. Because of this, analyzing the data is _____________. (Select all that apply)

Answers

Answer: 6328723894

Step-by-step explanation:

Find the slope of the line grapef below

Answers

Answer:

x = 1

Step-by-step explanation:

No matter what y is, x will always be 1.

(1,-4)

(1,-3)

(1,-2)

(1,0)

(1,1)

(1,2) and so on and so on.

Please Help me its a math question i will give brainlist please !!! the image is attached

Answers

Answer:

D

Step-by-step explanation:

When you reflect the point it goes to point (-2,5).  From that point, go 4 left and 8 down.  That gets you to (-2,-3)

A sports teacher divided a class into two groups. Three-fifth of the first group and 80% of the second group play soccer.
What fraction of the class plays soccer?

Answers


Oh, woah-oh, oh, oh
Oh-oh-oh-oh-oh-oh
I'll get him hot, show him what I've
soccer teacher

A little gamblin' is fun when you're with me (I love it, woo)
Russian roulette is not the same without a gun
And baby, when it's love, if it's not rough, it isn't fun, fun

Answer:

7/5

Step-by-step explanation:

80/100 = 0.8 = 8/10 = 4/5 (to the simplest fraction).

(three-fifth) 3/5 + 4/5 = 7/5

7/5 of the class plays soccer ✅

Hope this helpsGood luck ✅

Quick algebra 1 question for 10 points!

Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!

Answers

Answer:

2, x - 2, x + 4

Step-by-step explanation:

The factors of the given quadratic expression, 2x² - 4x - 16, are 2, (x +2), and (x -4)

Factoring a Quadratic expression

From the question, we are to determine the each of the factors of the given quadratic expression

The given quadratic expression is

2x² - 4x - 16

Factoring

2x² - 4x - 16

First, factor out 2

That is,

2(x² - 2x - 8)

Now, we will factor x² - 2x - 8
x² - 2x - 8

x² - 4x + 2x - 8

x(x - 4) +2(x -4)

(x +2)(x -4)

Thus,

2x² - 4x - 16  = 2(x +2)(x -4)

Hence, the factors of the given quadratic expression, 2x² - 4x - 16, are 2, (x +2), and (x -4)

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Find the sum of 10 x 2 + 7 x + 6 10x 2 +7x+6 and 6 x + 5 6x+5.

Answers

The sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

Sum of expressions

Expressions are equations separated by mathematical signs. This expressions are known to contains certain unknowns

Given the following expression

10x^2 +7x+6 and 6x + 5

We are to take the sum of both expression to have:

f(x) = 10x^2 +7x+6 + 6x + 5

Collect the like terms

f(x) = 10x^2 + 7x + 6x + 6 + 5

f(x) = 10x^2 + 13x + 11

Hence the sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

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In a school of 910 pupils, 3/7 are boys and 2/5 of the boys wear glasses. how many boys wear glasses?

Answers

The number of boys wear glasses are 156 boys.

In this question,

Total number of pupils in the school = 910

Ratio of boys = 3/7

Then, number of boys = 910 × 3/7

⇒ 130 × 3

⇒ 390

Ratio of boys wear glasses = 2/5

Then, number of boys wear glasses = 390 × 2/5

⇒ 78 × 2

⇒ 156

Hence we can conclude that the number of boys wear glasses are 156 boys.

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what is 4.22 x 10^17 seconds

Answers

We can rewrite the given time as:

7.03x10^15 mins 1.17x10^14 hours.4.88x10^12 days.What is 4.22x10^17 seconds in minutes and hours?

First, remember that:

60s = 1 min

Then to write that amount in minutes, we just need to divide by 60, so we get:

(4.22x10^17)/60  mins=  7.03x10^15 mins

Now, remember that:

1 hour = 3600s

Then to get the time in hours, we need to divide by 3600:

(4.22x10^17)/3600 h = 1.17x10^14 hours.

Similarly, you can change to any time unit that you want, for example:

1 day = 24*3600 s

Then the time in days is:

(4.22x10^17)/(24*3600) days = 4.88x10^12 days.

And so on.

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An arc on a circle measures 250 degrees. Within range which range is the radian measure of the central angle?

Answers

If the arc measures 250 degrees then the range of the central angle lies from π to 1.39π.

Given that the arc of a circle measures 250 degrees.

We are required to find the range of the central angle.

Range of a variable exhibits the lower value and highest value in which the value of particular variable exists. It can be find of a function.

We have 250 degrees which belongs to the third quadrant.

If 2π=360

x=250

x=250*2π/360

=1.39 π radians

Then the radian measure of the central angle is 1.39π radians.

Hence if the arc measures 250 degrees then the range of the central angle lies from π to 1.39π.

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please help me if you can


The time, t in seconds that it takes a car to travel a quarter-mile when starting from a full stop can be estimated by using the formula:


[tex]t=5.825\sqrt[3]{w/p\\}[/tex]


Where w = weight of the car


p = power delivered by the engine in horsepower (hp)


If the quarter-mile time for a 3,590-pound car is 13.4 s, how much power does its engine deliver? Round to the nearest pound.

Two students solved this problem. Natasha’s answer was 295 hp and Daniel’s was 679 hp. Why was Daniel wrong? Show each step that led Daniel to the wrong answer

Answers

Natasha got the power right. The power is 295 hp.

How to calculate power?

t = 5.825∛w / p

where,

w = weight of the carp  = power delivered by the engine in horsepowerquarter mile time = t

Therefore,

t = 13.4 s

p = 3590

13.4 = 5.825∛ 3590 / p

cube both sides

13.4³ = 5.825³ × 3590 / p

2406.104 = 197.645890625 × 3590 / p

cross multiply

2406.104 p = 709548.747344

p = 709548.747344 / 2406.104

p = 294.895294361

p = 295 hp

Therefore, Natasha got the power right

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PLEASE HELP! ……………..

Answers

Step-by-step explanation:

I am not sure I can read the original expression right, the picture is too blurry for the small digits.

is it 3^(5/5) ?

or rather 3^(5/6) ?

in any case, you should know that a number written like this always has the structure

a^(b/c)

so,

a = 3

b = 5 (or whatever is the numerator or top of the fraction)

c = 5 (or whatever is the denominator or bottom of the fraction).

the denominator of a fraction in an exponent gives us the grade of root to be taken.

the numerator gives us the power of the base number.

and if the exponent is negative it would mean that the whole thing is a 1/... fraction.

like 3^-2 means 1/3².

Use the method of this example to calculate f · dr,c wheref(x, y) = 2xyi (y2 − x2)j(x2 y2)2 and c is any positively oriented simple closed curve that encloses the origin. f · dr

Answers

The area around the given curve according to the green theorem is [tex]F. dr = 0[/tex].

According to the statement

we have to find the area enclosed by the simple closed curve that encloses the origin.

So, We know that the

The given equation is

[tex]f(x,y) = \frac{2xyi + (y^{2} - x^{2} ) j}{(x^{2} + y^{2} )^{2} }[/tex]

and

If function is in form of,

[tex]F = Pi + Qj[/tex]

and C is any positively oriented simple closed curve that encloses the origin.

Then,by use of Green's theorem

Do the partial differentiation of the given function

Then

[tex]\frac{dQ}{dx} = \frac{2x^{3} - 6xy^{2}}{(x^{2} + y^{2} )^{3}}[/tex]

and

[tex]\frac{dP}{dy} = \frac{2x^{3} - 6xy^{2}}{(x^{2} + y^{2} )^{3}}[/tex]

On substitution in Green's theorem,

We get the value

[tex]F. dr = 0[/tex]

From this it is clear that the area around the given curve is zero.

So, The area around the given curve according to the green theorem is [tex]F. dr = 0[/tex].

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If no denominator equals zero , which expression is equivalent to

Answers

Answer: Choice D

[tex]\frac{-19}{\text{x}-5}[/tex]

=================================================

Work Shown:

[tex]\frac{\text{x}^2+10\text{x}+25}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}+5)}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}+5}{1} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}-5)}{1(\text{x}-5)} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\[/tex]

[tex]\frac{\text{x}^2-25}{\text{x}-5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-(\text{x}^2-6)}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-\text{x}^2+6}{\text{x}-5}\\\\\\\frac{-19}{\text{x}-5}\\\\\\[/tex]

This matches with choice D as the final answer.

Keep in mind that we can only subtract fractions when the denominator is the same. The rule is [tex]\frac{a}{c}-\frac{b}{c} = \frac{a-b}{c}[/tex]

What is the focus point of a parabola with this equation? y = 1 8 (x2 − 4x − 12)

Answers

The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down. (h, k + p) exist (2, 0).

How to estimate the focus point of a parabola?

Given: [tex]$y=\frac{1}{8} (x^{2} -4x-12)[/tex]

[tex]$y=\frac{x^{2}}{8}-\frac{x}{2}-\frac{3}{2}$$[/tex]

Use the form [tex]$a x^{2}+b x+c$[/tex] to find the values of a, b, and c.

[tex]$a=\frac{1}{8}$[/tex], [tex]$b=-\frac{1}{2}$[/tex] and [tex]$c=-\frac{3}{2}$[/tex]

Consider the vertex form of a parabola [tex]$a(x+d)^{2}+e$[/tex]

To estimate the value of d using the formula [tex]$d=\frac{b}{2 a}$[/tex].

Substitute the values of a and b into the formula

[tex]$d=\frac{-\frac{1}{2}}{2\left(\frac{1}{8}\right)}$$[/tex]

[tex]$d=-\frac{1}{2} \cdot \frac{1}{\frac{2}{8}}$$[/tex]

Cancel the common factor 2 and 8.

[tex]$d=-\frac{1}{2} \cdot \frac{1}{\frac{1}{4}}$$[/tex]

[tex]$d=-\frac{1}{2}(1 \cdot 4)$$[/tex]

Multiply the numerator by the reciprocal of the denominator.

[tex]$d=-\frac{1}{2} \cdot \frac{1}{2\left(\frac{1}{8}\right)}$$[/tex]

[tex]$d=-\frac{1}{2} \cdot \frac{1}{\frac{2}{8}}$$[/tex]

equating, we get

[tex]$d=-\frac{1}{2}(1 \cdot 4)$$[/tex]

[tex]$d=-\frac{1}{2} \cdot 4$$[/tex]

The value of [tex]$d=-2$[/tex]

Find the value of e using the formula [tex]$e=c-\frac{b^{2}}{4 a}$[/tex].

Substitute the values of c, b and a into the above formula, and we get

[tex]$e=-\frac{3}{2}-\frac{\left(-\frac{1}{2}\right)^{2}}{4\left(\frac{1}{8}\right)}$$[/tex]

simplifying the equation, we get

[tex]$e=-\frac{3}{2}-\frac{(-1)^{2}\left(\frac{1}{2}\right)^{2}}{4\left(\frac{1}{8}\right)}$[/tex]

Apply the product rule to [tex]$\frac{1}{2}$[/tex].

[tex]$e=-\frac{3}{2}-\frac{1\left(\frac{1}{4}\right)}{4\left(\frac{1}{8}\right)}$$[/tex]

[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{4\left(\frac{1}{8}\right)}$$[/tex]

[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4(1)}{8}}$$[/tex]

simplifying the above equation, we get

[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4 \cdot 1}{4 \cdot 2}}$$[/tex]

[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4 \cdot 1}{4 / 2}}$$[/tex]

[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{1}{2}}$$[/tex]

Multiply the numerator by the reciprocal of the denominator.

[tex]$e=-\frac{3}{2}-\left(\frac{1}{4} \cdot 2\right)$$[/tex]

[tex]$e=\frac{-3-1}{2}$$[/tex]

[tex]$e=\frac{-4}{2}=2$[/tex]

Substitute the values of [tex]$a, d_{t}$[/tex] and e into the vertex form [tex]$\frac{1}{8}(x-2)^{2}-2$[/tex].

Set y equal to the new right side.

[tex]$y=\frac{1}{8} \cdot(x-2)^{2}-2$[/tex]

Use the vertex form, [tex]$y=a(x-h)^{2}+k$[/tex], to determine the values of a, h, and k.

[tex]$a=\frac{1}{8}$[/tex]

[tex]$h=2$[/tex]

[tex]$k=-2$[/tex]

Find the vertex [tex]$(h, k)$[/tex]

[tex]$(2,-2)$[/tex]

Find [tex]$\boldsymbol{p}$[/tex], the distance from the vertex to the focus.

To estimate the distance from the vertex to a focus of the parabola [tex]$\frac{1}{4 a}$[/tex]

Substitute the value of a into the formula

[tex]$\frac{1}{4 \cdot \frac{1}{8}}=\frac{1}{\frac{4(1)}{8}}$[/tex]

[tex]$\frac{1}{\frac{4 \cdot 1}{4-2}}=\frac{1}{\frac{4 \cdot 1}{4 \cdot 2}}$[/tex]

[tex]$\frac{1}{\frac{1}{2}}=2$[/tex]

The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down. (h, k + p)

Substitute the known values of h, p, and k into the formula, we get

(2,0).

Therefore, the correct answer is (2,0).

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35 POINTS!!! PLEASE HELP !!!!!!!!!!!!!!
( I already know the answer isn't -2, -1 so D is out of the question
A function is shown in the table.

x g(x)
−2 2
−1 0
0 2
1 8
Which of the following is a true statement for this function? (5 points)

Group of answer choices

The function is decreasing from x = 0 to x = 1.

The function is decreasing from x = −1 to x = 0.

The function is increasing from x = 0 to x = 1.

The function is increasing from x = −2 to x = −1.

Answers

Answer:

The function is increasing from x = 0 to x = 1.

Step-by-step explanation:

A function is increasing when the y-value increases as the x-value increases.

A function is decreasing when the y-value decreases as the x-value increases.

From x = -2 to x = -1 the function is decreasing as the y-value decreases as the x-value increases:  

x-value -2 to -1 → increasey-value 2 to 0 → decrease

From x = -1 to x = 0 the function is increasing as the y-value increases as the x-value increase:  

x-value -1 to 0 → increasey-value 0 to 2 → increase

From x = 0 to x = 1 the function is increasing as the y-value increases as the x-value increase:  

x-value 0 to 1 → increasey-value 2 to 8 → increase

In step 2, the
property of equality was applied.

In step 4, the
property of equality was applied.

Answers

In step 2, the property of equality applied was addition property of equality.

In step 4, the property of equality applied was multiplication property of equality.

What is the Addition Property of Equality?

The addition property of equality states that, to move a negative number over to the other side of an equation, add the number to both sides of the equation. For example, given the equation: a - c = b, to move c over to the other side of the equation, add c to both sides of the equation. we will have:

a - c + c = b + c

a = b + c.

What is the Multiplication Property of Equality?

According to the multiplication property of equality, if we have, a/c = b, to isolate a, we would multiply both sides of the equation by c. Thus:

a/c × c = b × c

a = bc

In the table given, in step 2, 6 was added to both sides of the equation. This means the property of equality that was applied was: addition property of equality.

In step 4, both sides of the equation was multiplied by -2. Thus, the property of equality that was applied was: multiplication property of equality.

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Answer: step 2 - addition property

              step 4 - multiplication property

Step-by-step explanation:

The following are the distances (in miles) to the nearest airport for 12 families. 6, 7, 8, 8, 16, 19, 23, 24, 26, 27, 34, 35 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:

Answers

Using it's definitions, the five-number summary and the interquartile range for the data-set is given as follows:

Minimum: 6Lower quartile: 8Median: 21.Upper quartile: 27Maximum: 35Interquartile range: 19

What are the median and the quartiles of a data-set?

The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference of the third quartile and the first quartile.

This data-set has 12 elements, which is an even number, hence the median is the mean of the 6th and 7th elements, as follows:

Me = (19 + 23)/2 = 21.

The first quartile is the median of 6, 7, 8, 8, 16, which is the third element of 8.

The third quartile is the median of 23, 24, 26, 27, 34, 35, which is of 27. Hence the interquartile range is of 27 - 8 = 19.

The minimum is the lowest value in the data-set, which is of 6, while the maximum is of 35, which is the largest value in the data-set.

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