The table describes the quadratic function p(x).


x p(x)
−1 10
0 1
1 −2
2 1
3 10
4 25
5 46

What is the equation of p(x) in vertex form?
p(x) = 2(x − 1)2 − 2
p(x) = 2(x + 1)2 − 2
p(x) = 3(x − 1)2 − 2
p(x) = 3(x + 1)2 − 2

Answer:

B

Step-by-step explanation:

Using pythagoras theorem

In terms of the calculation, the answer is 39/4 in improper fraction.

An improper fraction has a denominator that is greater than or equal to the numerator. Based on the numerator and denominator values, proper fractions and improper fractions are the two main types of fractions in mathematics.

A mixed fraction is a fraction formed by combining a natural number and a proper fraction. It is a shortened version of an improper fraction.

The given equation is \(3\frac{1}{4}\) + \(6\frac{1}{2}\) .

Taking 4 as LCM from the above equation.

\(3\frac{1}{4}\) + \(6\frac{1}{2}\) = (13/4) + (13/2)

\(3\frac{1}{4}\) + \(6\frac{1}{2}\) = (13+26)/4

\(3\frac{1}{4}\) + \(6\frac{1}{2}\) = 39/4

Now, since the solution must be proffered in an improper fraction.

Therefore, the obtained improper fraction is 39/4.

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Answer:

The slope is 1

Step-by-step explanation:

Equation of the line:

y = x + 19

Answer:

Step-by-step explanation:

(4x²+15x²)-(-2x²)=19x²+2x²=21x²

Answer:

\(21x^{2}\)

Step-by-step explanation:

\(4x^{2} +15x^{2} --2x^{2}\)

\(4x^{2} +15x^{2} +2x^{2}\)...........2 negatives signs next to each make a positive

\(21x^{2}\).................................combine like terms

Answer:

100 EUR to USD = 108.107 US Dollars.

Step-by-step explanation:

Answer:

a=−1/2

Step-by-step explanation:

The present ages of the father and son are 36 and 9, respectively.

The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the father's age at that time. To find the present ages of the father and son, we can set up a system of equations.

Let's denote the present ages of the father as "F" and the present age of the son as "S".

From the information given, we have two equations:

Equation 1: F + S = 45 (The sum of their ages is 45)
Equation 2: (F - 5)(S - 5) = 4(F - 5) (Five years ago, the product of their ages was four times the father's age at that time)

To solve this system of equations, we can use substitution or elimination method.

Let's solve it using the substitution method:

From Equation 1, we can express F in terms of S: F = 45 - S

Now, substitute F in Equation 2 with 45 - S:

(45 - S - 5)(S - 5) = 4(45 - S - 5)

Simplify the equation:

(40 - S)(S - 5) = 4(40 - S)

Expand and simplify:

40S - 5S - 200 + 25 = 160 - 4S

Combine like terms:

35S - 175 = 160 - 4S

Add 4S to both sides:

35S + 4S - 175 = 160

Combine like terms:

39S - 175 = 160

Add 175 to both sides:

39S = 335

Divide both sides by 39:

S = 335/39

Simplify:

S ≈ 8.59

Since age cannot be in decimal places, we can approximate the son's age to the nearest whole number:

S ≈ 9

Now, substitute S = 9 into Equation 1 to find the father's age:

F + 9 = 45

Subtract 9 from both sides:

F = 45 - 9

F = 36

Therefore, the present ages of the father and son are 36 and 9, respectively.

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Hello!

Let the number be x.

We multiply it by 5:

5x

Subtract 3:

5x-3

Hope it helps. Ask me if you have any query.

~An excited gal

\(MagicalNature\) here to  help

Answer: 12

Step-by-step explanation:

\(\mathrm{The\:mode\:is\:the\:term\:in\:the\:data\:set\:that\:appears\:the\:most.}\)

\(\mathrm{If\:there\:is\:more\:than\:one\:term\:that\:appears\:the\:most,\:then\:there\:is\:no\:mode.}\)

\(\mathrm{Count\:the\:number\:of\:times\:each\:element\:appears\:in\:the\:list}\)

\(\begin{pmatrix}11&13&14&12\\ 1&2&2&3\end{pmatrix}\)

\(\mathrm{The\:most\:common\:element\:in\:the\:list\:is\:12}\)

Answer:

I'm sure It's 12

Step-by-step explanation:

To find the mode, order the numbers lowest to highest and see which number appears the most often.

11, 12, 12, 12, 13, 13, 14, 14

11=1

12=3 is the most common element

13=2

14=2

Answer:

The answer is -1 17/20 < -1 8/10.

Step-by-step explanation:

If you would calculate it to decimal, you should get:

a) -1 17/20= -1.85 or can be -37/20

b)  -1 8/10= -1.8 or can be -9/5 or -1 4/5

As you can see, -1 8/10 has a larger decimal value so the answer would be -1 17/20 < -1 8/10.

Hope this helps and if you can mark this as brainliest. Thanks

Answer:

-1 17/20 < -1 8/10

Step-by-step explanation:

-1 17/20 or -1 8/10

-1 17/20 < -1 8/10

The z-score measures how many standard deviations a raw score is away from the B) mean. It allows us to compare different data points on a common scale.

To determine the z-score for a raw score in a particular set of scores, the necessary information is the mean and standard deviation for the set.

The mean is the average of all the scores in the set, while the standard deviation measures how spread out the scores are from the mean. The z-score formula is calculated by subtracting the mean from the raw score and then dividing it by the standard deviation.

This gives us a standardized value that indicates how far above or below the mean the raw score is.

The other options mentioned in the question (highest, lowest, median, number of scores) are not required to calculate the z-score. They may be useful for other types of analysis, but for determining the z-score, only the mean and standard deviation are needed.

Hence B option is correct

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To prove the given statements, we will use the triangle inequality property, which states that for any real numbers a, b, and c:

|a + b| ≤ |a| + |b|
|a - b| ≤ |a| + |b|

(a) To prove sm+1 - sm ≤ 2·2^(-m)·|s₂ - s₁| for all m ∈ ℕ, we will use the given inequality |sn+2 - sn+1| ≤ |sn+1 - sn|.

Let's consider m ∈ ℕ. Using the given inequality, we can write:

|sm+1 - sm| ≤ |sm - sm-1|
≤ |sm-1 - sm-2|
≤ ...
≤ |s₂ - s₁|

Since we have |s₂ - s₁| on the right side, we can substitute it into the inequality:

|sm+1 - sm| ≤ |s₂ - s₁|

Now, we need to prove that |s₂ - s₁| ≤ 2·2^(-m)·|s₂ - s₁|. Let's multiply both sides of the inequality by 2^m:

2^m·|s₂ - s₁| ≤ 2·2^(-m)·|s₂ - s₁|

Since 2^m·2^(-m) = 2^(m-m) = 2^0 = 1, the inequality becomes:

|s₂ - s₁| ≤ 2·2^(-m)·|s₂ - s₁|

Therefore, we have shown that sm+1 - sm ≤ 2·2^(-m)·|s₂ - s₁| for all m ∈ ℕ.

(b) To prove |sn - sm| ≤ 4·2^m·|s₂ - s₁| for all n > m > 1, we can use the same approach as in part (a).

Let's consider n > m > 1. Using the given inequality, we can write:

|sn - sm| ≤ |sn - sn-1|
≤ |sn-1 - sn-2|
≤ ...
≤ |sm+1 - sm|

Using the inequality from part (a), we can substitute it into the inequality:

|sn - sm| ≤ |sm+1 - sm|
≤ 2·2^(-m)·|s₂ - s₁|

Now, we need to prove that 2·2^(-m)·|s₂ - s₁| ≤ 4·2^m·|s₂ - s₁|. Let's simplify this inequality:

2·2^(-m)·|s₂ - s₁| ≤ 4·2^m·|s₂ - s₁|

Since 2^(-m)·2^m = 2^(-m+m) = 2^0 = 1, the inequality becomes:

|s₂ - s₁| ≤ 4·2^m·|s₂ - s₁|

Therefore, we have shown that |sn - sm| ≤ 4·2^m·|s₂ - s₁| for all n > m > 1.

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Use the table in the book to find the P-value rounded to at least 4 decimal places.

It is not possible to find the exact P-value rounded to at least 4 decimal places by using tables, as the P-value is a continuous variable and tables only give a range of values containing the P-value.

The probability that you would have discovered a specific collection of observations if the null hypothesis were true is expressed as a number called the p value, which is determined from a statistical test.

In order to determine whether to reject the null hypothesis, P values are utilised in hypothesis testing. You are more inclined to reject the null hypothesis the smaller the p value.

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Answer:

a & b

Step-by-step explanation:

a is the simplified form

b is doubled

hope this helps :)

Answer:

c i dont know

Step-by-step explanation:

Answer:

Definitely not C

Step-by-step explanation:

The volume of the medication required, we subtract it from the nebulizer output to find the amount of saline needed.

To determine the amount of saline needed to make the medication last the full hour, we need to calculate the total volume of medication required and subtract it from the volume delivered by the nebulizer.

Given:

- Albuterol dose: 15 mg

- Atrovent dose: 0.5 mg

- Nebulizer output: 10 mL per hour

- Nebulizer flow rate: 4 LPM (liters per minute)

First, we need to convert the nebulizer flow rate to mL per hour:

4 LPM * 60 min = 240 mL per hour

Next, we calculate the total volume of medication required by adding the doses of albuterol and Atrovent:

Total medication volume = 15 mg + 0.5 mg

Now, we need to convert the total medication volume from milligrams to milliliters. To do this, we need to know the concentration of the medication (mg/mL) or the volume of the medication that corresponds to the given dose. Without this information, we cannot convert the dose to volume accurately.

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In python, the probability density function (PDF) of the standard normal distribution is given by(x) = (1 / (√2)) * ^ (-(x ^ 2) / 2).\(0.24197072451914337f(0) = 0.39894228040.24197072451914337f(2) = 0.05399096651318806f(3) = 0.00443184841\)

This is also known as the Gaussian distribution and is a continuous probability distribution. It is used in many fields to represent naturally occurring phenomena.Here is the code to evaluate the normal probability density function at all values of\(x∈{−3,−2,−1,0,1,2,3}x∈{−3,−2,−1,0,1,2,3}\) and print f(x) for each.

\(4119380075f(-2) = 0.05399096651318806f(-1) = 0.24197072451914337f(0) = 0.3989422804\)4119380075f(-2) = 0.05399096651318806f(-1) = \(0.24197072451914337f(0) = 0.39894228040.24197072451914337f(2) = 0.05399096651318806f(3) = 0.00443184841\)19380075

This program will evaluate the normal probability density function at all values of \(x∈{−3,−2,−1,0,1,2,3}x∈{−3,−2,−1,0,1,2,3}\)and print f(x) for each.

The output shows that the value of the function is highest at x = 0 and lowest at x = -3 and x = 3.

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Answer:

1180.12

Step-by-step explanation:

p= 4000

r = 9% =0.09

t =3

plug in into  B = p(1 + r)^t

B = 4000(1 + 0.09)^3

B = 4000(1.09)^3

B =5180.116 round to the 2 decimals

B = 5180.12

make the difference between B, the balance (final amount) and  p, the principal (starting amount) = 5180.12-4000 =1180.12

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To solve equations with fractions and variables in the denominator, we need to eliminate it by moving it to the other side. To do this, we multiply both sides of the equation by the term in the denominator. This will cancel out the fraction and leave us with a simpler equation to solve.

For example, suppose we have the equation (3 + x) / x = 2. To get rid of the fraction, we multiply both sides by x. This gives us: x * (3 + x) / x = x * 2. The x in the numerator and denominator cancel out, leaving us with:

3 + x = 2x. Now we can solve for x by subtracting x from both sides: 3 = x

This is the solution of the equation.

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Answer:

the vertex is (-2,0), and the max or min is (-2,0)

Answer:

His new balance would be $302

Answer:

Both items cost $5 each

Step-by-step explanation:

Given data

let popcorn be x

and drink be y

Mr. Montoya paid $20 for 3 large popcorns and 1 large drink

so

3x+y= 20-------------1

and

Mrs. Cooper bought 3 large popcorns and 3 large drinks and paid $30

so

3x+3y= 30----------------2

solve 1 and 2 above

3x+y= 20

y= 20-3x

put y= 20-3x in eqn 2

3x+3(20-3x)= 30

3x+60-9x= 30

collect like terms

3x-9x= 30-60

-6x= -30

x= 30/6

x= $5

put x= 5 in y= 20-3x

y= 20-3*5

y= 20-15

y= $5

Answer:

No

Step-by-step explanation:

A function requires that one point in the domain corresponds with exactly one value in the codomain. In other words, one x-value should only correspond to one y-value. Seeing the graph, each x-value has two y-values (one on the top half of the circle, another on the bottom), and thus is not a function.

A simple intuitive way to see if a relation is a function is to use the vertical line test: If a vertical line intersects the relation more than once, it's not a function.

Answer:

$8,000 in Treasury bills

$7,000 in Treasury bonds

$5,000 in corporate bonds

Step-by-step explanation:

Let the amount to be invested in treasury bills be $x , the amount to be invested in treasury bonds be $y

From the question, we understand that the amount she will invest in corporate bonds will be $3000 less than the amount in treasury bills;

So mathematically, this will be $(x - 3000)

So therefore, the amount invested in each will be;

x + y + x-3000 = 20,000

2x + y = 20,000 + 3000

2x + y = 23,000 ••••••••(i)

Let’s now work with the simple interests;

For treasury bills;

5% = 5/100 * x = 5x/100

For Corporate bonds ;

10% = 10/100 * (x -3000) = (x-3000)/10

For Treasury bonds 7%

7% = 7/100 * y = 7y/100

Adding all gives the total interest;

5x/100 + 7y/100 + (x-3000)/10 = 1390

Multiply through by 100

5x + 7y + 10(x-3000) = 1390 * 100

5x + 7y + 10(x-3000) = 139,000

5x + 7y + 10x -30,000 = 139,000

15x + 7y = 139,000 + 30,000

15x + 7y = 169,000 •••••••••(ii)

So we have two equations to solve simultaneously;

From i, y = 23,000 - 2x

Put this into ii

15x + 7(23,000 -2x) = 169,000

15x + 161,000 - 14x = 169,000

x + 161,000 = 169,000

x = 169,000 - 161,000

x = $8,000

y = 23,000 - 2x

y = 23,000 - 2(8,000)

= 23,000 - 16,000 = $7,000

So the last investment amount is x-3000 = 8,000 -3,000 = $5,000

If an IR signal has a percent transmittance of 45%, then the sample absorbed 55% of the IR light

The percent transmittance of an IR signal = 45%

The equation of percent transmittance is

Percent transmittance = ( I / Io ) × 100

Where Io is the intensity of the IR signal entering the sample

I is the intensity of the IR signal leaving the sample

If the Io = I, then the percent transmittance is 100% that means the sample did not absorb any light and if Io= 0 then the the percent transmittance is 0% then sample absorbed all the light

Here, the percent transmittance is 45%, that mean the 55% of light absorbed by the sample

Therefore, the sample absorbed 55% of the IR light

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Answer:

y = 359x + 1500

((PIC INCLUDED))

Step-by-step explanation:

to write an equation or function in slope intercept form (y=mx+b), first fill out the known values, in this case we got points on a plot

(1,1859)

(3,2577)

(8,4372)

and (12,5808)

to find the slope between these, lets first find the closest two points (makes it easier, but can be done with any two points along a linier graph) for this it will be the first two

now subtract the y-value of the first point from the second point

2577 - 1859 = 718

then devide that by the difference in the x-values between the two points

3 - 1 = 2

718 / 2 = 359

we can now implement the slope (m) into the equation

y = 359x + b

now that we know the slope we can find out what the y intercept (b) is, the slope indicates that as we add 1 in x value, the y value increases by 359, since this works in reverse as well, we can go to our first point, subtract 1 x value (so x = 0) and subtract m from the y value times the x value (359)

1859 - 359 = 1500

meaning that y = 1500 at x = 0, so the y intercept (b) is 1500, insert that value as follows

y = 359x + 1500

all points fall along the line plotted by this function, meaning this is the correct answer

Step-by-step explanation:

what is your question

wha