Write an equation of the parabola that passes through the points (-4, 7), (-3, 9), and (4,-5)

An equation of the parabola is y =

Variation refers to differences in characteristics between individuals of the same species or between different genera or species. The formula is y = 0.25x.

Therefore,

y=0.25 x

the initial statement is y ∝ x

to convert to an equation multiply by k  the constant of

⇒ y=k x

to find k use the given condition

y=0.5 when x=2

[tex]$y=k x \Rightarrow k=\frac{y}{x}=\frac{0.5}{2}=0.25$$[/tex]

the equation is y = 0.25x

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The variation equation  is [tex]y=\frac{1}{5} x[/tex]

Calculation

Given, y =2 and x=10

we know the direct relation in y∝ x

so, y = kx, where k is the proportionality constant

2= k*10

k = [tex]\frac{2}{10} =\frac{1}{5}[/tex]

Therefore, the direct variation equation for this situation is [tex]y=\frac{1}{5} x[/tex]

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The correct answer is Option A.

Randomization important because it is used to ensure all treatment groups receive experimental units .

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Answer:

the answer is c. to ensure that all treatment groups are roughly equivalent regarding the variability within the experimental units

Step-by-step explanation:

The value of 3 times 4 times 4 times 3 times 3 times 4 in exponent is 3³ × 4³

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, the expression given is 3 times 4 times 4 times 3 times 3 times 4. It should be noted that the 4 occurs three times as well as the 3.

Therefore, this will be 3³ × 4³.

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Answer:

3x^2-2x+3+1/x+2

Step-by-step explanation:

The angle of pairs = 170.

The scalar product is the product between two vectors whose result is a scalar.

Where A and B are the vectors, |A| and |B| are the modules of the vectors and θ at the angle between them.

The vector is given in Cartesian coordinates and the unit vectors in these coordinates are perpendicular.

We look for the modulus of each vector.

In conclusion using the dot product we can find the angle between the two vectors is:

Hence, the angle θ = 170º

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The probability that the sample proportion of the Republicans will differ from the population by more than 4% is 95.56%

The probability is calculated using z score, this is used to determine the amount of difference a sample, X is from the standard deviation

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

population mean, μ  = p = 50% = 0.5

sample size, n = 629

standard deviation, σ

= √{(p(1 - p)) / n}

= √{(0.50(1 - 0.50)) / 629}

= √{(0.50 * 0.50) / 629}

= 0.0199

Differ by more than 4% is differ by 50% + 4%

X = 50% + 4% = 54% = 0.54

The probability of more than 54% P = P(p > 54%) = P(p > 0.54)

P(p > 0.54) = 1 - P(p < 0.54)

Z score for z < 0.54

z = (X - μ) / σ

= (0.54 - 0.50) / 0.0199

= 2.01

p value for z < 2.01 = 0.0444

P(p > 0.54) = 1 - P(p < 0.54)

= 1 - 0.0444

= 0.9556

= 95.56%

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Answer:

$26

Step-by-step explanation:

Answer: 15√11z

Step-by-step explanation:

The equation of line passing through points (4,−2) and (8, 3) is 4y - 5x + 28 = 0

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

Given pair of points are  (4,−2) and (8, 3).

The equation of line passing through two points (x₁, y₁) and (x₂, y₂) is given as,

y = ((x - x₁) / (x₁ - x₂)) (y₁ - y₂) + y₁

Substitute the respective values to get the equation of line as,

y = ((x - 4 ) / (4 - 8)) (-2 - 3) + (-2)

y = ((x - 4 ) / 4) × 5 - 2

4(y + 2) = 5(x - 4)

4y - 5x + 28 = 0

Hence, the equation of line for the given points is 4y - 5x + 28 = 0.

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Regarding the data-set of the temperatures, it is found that:

a) The mean and the standard deviation are given as follows:

b) The histogram is bell shaped.

c) 95% of the days will be between 63.75 ºF and 97.07 ºF.

The first step towards obtaining the mean and the standard deviation is obtaining the relative frequencies, which are the absolute frequencies divided by the number of observations.

The number of observations is:

5 + 309 + 1496 + 1521 + 533 + 6 = 3870.

Considering the midpoint of each interval, the following distribution is built:

The mean is given by the sum of each value multiplied by it's relative frequency, hence:

E(X) = 54.5 x 0.0013 + 64.5 x 0.0798 + 74.5 x 0.3866 + 84.5 x 0.3930 + 94.5 x 0.1377 + 104.5 x 0.0016 = 80.41.

The standard deviation is given by the square root of the sum of the differences squared between each observation and the mean, multiplied by their relative frequencies, as follows:

S(X) = sqrt((54.5-80.41)² x 0.0013 + (64.5-80.41)² x 0.0798 + (74.5-80.41)² x 0.3866 + (84.5-80.41)² x 0.3930 + (94.5-80.41)² x 0.1377 + (104.5-80.41)² x 0.0016) = 8.33.

From the histogram, most values are around the mean, with a small percentage of around 0.3% around the bounds, accordingly with the Empirical Rule, hence the distribution is normal.

By the Empirical Rule, a percentage of 95% of the observations is within two standard deviations of the mean, hence:

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1/1728 is the value of negative integers .

What in math is an integer?

= 12⁻³

= 1/12³

=  1/1728

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Answer:

option c

y = -1

Step-by-step explanation:

2x - y = 3 -----------------(1)

x - 3y = 4 ------------------(2)

from equation (2)

x = 4 + 3y-------------------(3)

substituting the value of x in equation (1)

2(4+3y) - y = 3

8 + 6y - y = 3

5y = 3-8

5y = -5

y = -1

substituting the value of y in equation (3)

x = 4 - 3

x = 1

The missing terms in the two column proof are;

Reason 4; Opposite Angles

Reason 5; AAS Congruency Postulate

From the given image, we want to use the two column proof to prove that ΔAEC ≅ ΔDEB.

Now, we have the two column proof as follows;

Statement 1; AC ║ BD

Reason 1; Given

Statement 2; AC ≅ BD

Reason 2; Given

Statement 3; ∠ACE ≅ ∠DBE

Reason 3; Alternate angles

Statement 4; ∠AEC ≅ ∠BED

Reason 4; Opposite Angles

Statement 5; ΔAEC ≅ ΔDEB

Reason 5; AAS Congruency Postulate

The final proof is AAS Congruency postulate because it has 2 congruent angles and the non-included congruent side.

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The 95% confidence interval for the proportion of respondents who say yes is of:

(0.5562, 0.6176)

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The remaining parameters, which are the sample size and the estimate, are given as follows:

[tex]n = 990, \pi = \frac{581}{990} = 0.5869[/tex]

The lower bound of the interval is of:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5869 - 1.96\sqrt{\frac{0.5869(0.4131)}{990}} = 0.5562[/tex]

The upper bound of the interval is of:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5869 + 1.96\sqrt{\frac{0.5869(0.4131)}{990}} = 0.6176[/tex]

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Answer:

second option

Step-by-step explanation:

the solution to the system of equations is at the points of intersection of the two graphs.

the graphs intersect at (- 2, - 3 ) and (1, 0 ) , then

the solutions are (- 2, - 3 ) and (1, 0 )

Answer:

There is only one solution

Step-by-step explanation:

4x - 7 = 2x + 15

+7        +7

4x = 2x + 22

-2x   -2x

2x = 22

divide by 2 into both sides

x = 11

Since there is only one answer, there is only ONE solution.

The correct option regarding the proportional relationships for the costs of the Peanut Brittle and for the Almond Bark are given as follows:

Almond bark costs $0.25 more per ounce than peanut brittle.

A proportional relationship is a special case of a linear function, with slope k and intercept 0, hence the output variable y is obtained with the multiplication of the input variable x and the slope k, as follows:

y = kx.

The Peanut Brittle graph goes through the point (10, 10), hence the constant, which is the price per candy, is obtained as follows:

10k = 10

k = 10/10

k = 1.

For Almond Bark, the price per candy is obtained as follows, from the table:

4k = 5

k = 5/4

k = 1.25.

Hence the difference of the prices is:

1.25 - 1 = $0.25.

Which means that the first option is correct.

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Answer:

Almond bark costs $0.25 more per ounce than peanut brittle.

Step-by-step explanation:

Answer:

$208

Step-by-step explanation:

$79.50 x 24 = 1908

$1908 + 400 = 2308

$2100/2308 = 9%

Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.

Interest is a financial concept that represents the cost of borrowing money or the return on invested capital. It is a fee charged for the use of borrowed funds or the compensation received for lending money or investing in assets.

Total number of monthly payments

= 12 months/year x 2 years

= 24 months

and, Monthly payment amount = $79.50

Total amount paid in monthly installments

= Monthly payment amount x Total number of monthly payments

= $79.50 x 24

= $1,908

Next, we can subtract the initial down payment from the total amount paid to find the interest paid:

Total interest paid = Total amount paid - Down payment

= $1,908 - $400

= $1,508

Therefore, Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.

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The quotient when ([tex]x^{2} -25[/tex]) is divided by (x+5) is (x-5) and the remainder is 0.

According to the question,

We have the following information:

([tex]x^{2} -25[/tex]) is divided by (x+5)

Now, we can solve this using two ways. First method is to use the long division method and second is to solve the expression using an identity.

We know that the following identity can used to expand the dividend:

[tex]a^{2} -b^{2} = (a+b)(a-b)\\[/tex]

In this case, we have a = x and b = 5.

[tex]x^{2} -(5)^{2} = (x-5) (x+5)[/tex]

Now, we have the following expression:

(x+5)(x-5)/(x+5)

(x-5)

Now, the remainder is 0.

Hence, the quotient when ([tex]x^{2} -25[/tex]) is divided by (x+5) is (x-5) and the remainder is 0.

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The number of voters that each volunteer call is 18.

It is important to note that voting is done to choose a particular person during elections.

In this case, the candidate for mayor is calling 882 registered voters to remind them about the upcoming election and the candidate has 49 volunteers.

Since they gave same number of voters, this will be:

= Number of voters / Number of volunteers

= 882 / 49

= 18

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Answer:

30 lb bag is cheaper by about $2.40

Step-by-step explanation:

to find per pound we divide

19.49/4= 4.8725

$4.87per pound

$73.99/30=2.46633

$2.47 per pound

30 lb bag is cheaper per pound

4.87-2.47=2.40

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The solutions for the graphed linear inequality are (-4, 0), (-1, 4), (0, 0), and (-2, 0). The correct options are A. (-4, 0), B. (-1, 4), C. (0, 0), and E. (-2, 0)

From the question, we are to determine all of the solutions for the linear inequality whose graph is given

To do this, we will find the points that fall in the solution region (shaded portion of the graph)

The point (-4, 0) falls in the solution region. Thus, it is a solution for the linear inequality.

The point (-1, 4) falls in the solution region. Thus, it is a solution for the linear inequality.

The poi0nt (0, 0) falls in the solution region. Thus, it is a solution for the linear inequality.

The point (4, -1) does not fall in the solution region. Thus, it is not a solution for the linear inequality.

The poi0nt (-2, 0) falls in the solution region. Thus, it is a solution for the linear inequality.

The point (0, -2) does not fall in the solution region. Thus, it is not a solution for the linear inequality.

Hence, the solutions are (-4, 0), (-1, 4), (0, 0), and (-2, 0).

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A 95% confidence interval for the proportion who believe immigration is a good thing is; CI = (0.4173, 0.7173)

The formula for the confidence interval of proportions is;

CI = p ± z√(p(1 - p)/n)

where;

p is sample proportion

z is z-score at confidence level

n is sample size

We are given;

Number of success; x = 631

Sample size; n = 1095

Thus;

sample proportion; p = x/n = 631/1095 = 0.5763

The z-score at 95% confidence level is 1.96. Thus;

CI = 0.5673 ± 1.96√(0.5673(1 - 0.5673)/1095)

CI = 0.5673 ± 0.015

CI = (0.5673 - 0.15), (0.5673 + 0.15)

CI = (0.4173, 0.7173)

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The Minimum value is y(min) = 48 , x = 5 and The maximum value is   [tex]y = -2(x -5)^2+48[/tex]

Given,

In the question:

The given Function is :

[tex]y = -2x^2 + 20x -2[/tex]

To find the maximum or minimum value of the function:

Now, According to the question:

For maximum value:

The given Function is :

[tex]y = -2x^2 + 20x -2[/tex]

Take out the leading coefficient is :

[tex]y = -2(x^2 + 10x) -2[/tex]

Complete the square:

[tex]y = -2(x^2 + (2(-5))x +(-5)^2+(-2-(-2).(-5)^2)[/tex]

Express the function in vertex form:

[tex]y = -2(x -5)^2+48[/tex]

For Minimum Value:

y(min) = 48

x = 5

Hence, The Minimum value is y(min) = 48 , x = 5 and The maximum value is   [tex]y = -2(x -5)^2+48[/tex].

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Answer:

60, 80, 100

Step-by-step explanation:

All 3 of these numbers are between 55 and 101, and can be divided by all 3 numbers provided.

The first five terms of the sequence defined by the given function are f(1) = 10 f(2) = 22  f(3) = 48.4 f(4) = 106.48 and f(5) = 234.256.

What is a sequence?

A collection of events or items that occur one after the other in a specific order is referred to as a sequence.

Here, we have

Given the function is f(n) = 2.2 [ f(n-1) ] Here, f(1) = 10 then we have to create the first five terms of the sequence defined by the function.

Since f(1) = 10

f(2) = 2.2 [ f (2-1) ] = 2.2× [ f (1) ]

    = 2.2 × 10 = 22

f (3) = 2.2 [ f (3-1)] = 2.2 × [ f (2) ]

       = 2.2 × 22 = 48.4

f(4)  = 2.2 [ f(4-1) ] = 2.2× [ f(3)]

       = 2.2 × 48.4 = 106.48

f(5)  = 2.2 [ f(5-1) ] = 2.2× [ f(4)]

        2.2× 106.48 = 234.256

Hence the first five terms of the sequence defined by the given function are f(1) = 10 f(2) = 22  f(3) = 48.4 f(4) = 106.48 and f(5) = 234.256.

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The probability that the boy will select a palindrome number is 1/900.

A number that reads the same both forward and backward is known as a palindrome.

The 6 digits palindrome numbers can be formed starting from 100 and writing the reverse of 100 before 100 like 100-001, 101-101, 102-201,...,

995-599, 996-699, 997-799, 998-899,999-999.

Therefore, the 6 digits palindrome numbers can be formed using three digits starting from 100 to 999.

Since we are starting from 100, subtract 99 from 999 to get the total number of 6 digits palindrome numbers,

999-99

=900

Therefore, there are 900 six digits palindrome numbers.

The probability of selecting one palindrome number out of a total of 900 numbers is,

1/900

Therefore, the probability that the boy will select a palindrome number is 1/900.

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Answer:

I will help you okay????

Cut off for the failing score is 60.

Percentage of the student failed is 12.5%.

What is standard deviation?

The term "standard deviation" (or "SD") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

What is normail distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

Given that,

mean = 72

standard deviation = 6

So,

(a) Cutoff score = mean-(2 x standard deviation)  [tex]=72-(2\times 6)[/tex][tex]= 72-12[/tex]  [tex]=60[/tex].

(b) In a normal distribution, 95% of students fall on both sides of mean in 2 standard deviations range. i.e., [tex]\frac{95}{2} = 47.5[/tex] of students between mean and (mean-2 x standard deviation). So, the percentage of students below 2 standard deviations from mean = 60-47.5 = 12.5%.

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