Determine whether a quadratic model exists for the set of values below. If so, write the model.
f(0) = -1, f(3) = -13, f(-1) = -5

The interquartile range IQR for the given data set is IQR=10

A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary. A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.

Finding the median, lower quartile, and upper quartile of a given set of data (Q2, Q1, and Q3) is the first stage in creating a box-and-whisker figure. Now that you know how to calculate the interquartile range (IQR). The distance between the upper and lower quartiles is known as the interquartile range.

Lower data set:

70 73 81 84

Q1=73+81/2=77

Middle data set

65 70 75 80

Q2= 70+75/2=72.5

Upper data set

85 87 90

Q3=87

IQR=Q3-Q1=87-77=10

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Answer:

7

Step-by-step explanation:

This is a geometric sequence with first term -2 and common ratio 3.

From the sum of a geometric series formula,

\(\frac{-2(1-3^n)}{1-3} =-2186 \\ \\ 1-3^n=-2186 \\ \\ -3^n =-2187 \\ \\ 3^n=2187 \\ \\ n=\log_{3}(2187) \\ \\ n=7\)

A Gaussian random variable X has mean μ=1 and variance σ2=4.  Therefore, the probability P[X ≤ 2] can be expressed in terms of the Gaussian Q-function as Q[0.5].

A Gaussian random variable X with mean μ = 1 and variance σ² = 4. We are asked to express the following probabilities in terms of the Gaussian Q-function.(a) P[1 - 2]

We know that P[1 - 2] is the probability that the random variable X is less than 2 standard deviations below the mean. Since the mean is μ = 1 and the standard deviation is σ = 2, we can express this probability as follows: P[1 - 2] = P[X < μ - 2σ] = P[X < 1 - 4] = P[X < -3]

This probability cannot be expressed in terms of the Gaussian Q-function because the Q-function is only defined for non-negative arguments. Thus, we cannot use the Q-function to calculate P[1 - 2].(c) P[X ≤ 2]

We want to find the probability that the random variable X is less than or equal to 2. We can express this probability as follows: P[X ≤ 2] = Q[(2 - μ) / σ] = Q[(2 - 1) / 2] = Q[0.5]

Therefore, the probability P[X ≤ 2] can be expressed in terms of the Gaussian Q-function as Q[0.5].

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The quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

To solve the quadratic equation 2a^2 = -6 + 8a, we need to rearrange it into standard quadratic form, which is ax^2 + bx + c = 0, where a, b, and c are coefficients.

Step 1: Move all the terms to one side of the equation to set it equal to zero:

2a^2 - 8a + 6 = 0

Step 2: The equation is now in standard quadratic form, so we can apply the quadratic formula to find the solutions for 'a':

a = (-b ± √(b^2 - 4ac))/(2a)

Comparing with our equation, we have:

a = (-(-8) ± √((-8)^2 - 4(2)(6)))/(2(2))

Simplifying further:

a = (8 ± √(64 - 48))/(4)

a = (8 ± √16)/(4)

a = (8 ± 4)/(4)

Now, we can calculate the two possible solutions:

a1 = (8 + 4)/(4) = 12/4 = 3

a2 = (8 - 4)/(4) = 4/4 = 1

Therefore, the quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

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Answer:

Step-by-step explanation:

If a line is parallel to a side of a triangle, then the intersected sides are divided proportionally

4/2=y/3

2=y/3

y=2*3 = 6

next,

If the angles of one triangle are equal to the angles of another triangle, then the triangles are said to be equiangular.

(4+2)/4=6/x

6/4=6/x

x=4

Since overtime is paid at one and one-half, Tonya's overtime pay for this week is $36.56.

The overtime pay is the product of the overtime pay rate and the number of overtime hours.

The normal work week is 40 hours.  The overtime hours, in this situation, are 2.5 hours.

The total number of hours Tonya worked this week = 42.5 hours

The hourly pay rate = $9.75

Overtime pay rate = $14.625 ($9.75 x 1.5)

Overtime hours worked = 2.5 hours (42.5 - 40)

Overtime pay = $36.56 ($14.625 x 2.5)

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Answer:

x = 4,  x = 8

Step-by-step explanation:

Given the quadratic equation, x² - 12x + 38 = 6

Subtract 38 from both sides:

x² - 12x + 38 - 38 = 6 - 38

x² - 12x = -32

You'll need to rewrite the equation in the form, x² + 2ax + a². To find the value of a:

2ax = -12x  

Divide both sides by 2x to solve for the value of a :

\(\frac{2ax}{2x} = \frac{-12x}{2x}\)

a = -6

Substitute the value of a into the quadratic form, x² + 2ax + a²

x² - 12x + a² = -32 + a²

x² - 12x + (-6)² = -32 + (-6)²

x² - 12x + 36 = -32 + 36

x² - 12x + 36 = 4

Rewrite the perfect square trinomial into its binomial factors:

x² - 12x + 36 = 4

(x - 6)² = 4

To solve for x, take the square root of each side of the inequality:

\(\sqrt{(x - 6)^{2}} = +/- \sqrt{4}\)

\(\sqrt{(x - 6)^{2}} = \sqrt{2^{2} } = (x - 6) = 2\)

For (x - 6) = 2, start by adding 6 to both sides of the equation:

x - 6 + 6 = 2 + 6

x = 8

\(\sqrt{(x - 6)^{2}} = -\sqrt{2^{2} } = (x - 6) = -2\)

For (x - 6) = - 2, start by adding 6 to both sides of the equation:

x - 6 + 6 = - 2 + 6

x = 4

Therefore, the solutions to the quadratic equations using the perfect square strategy are: x = 4, x = 8.

Answer:

It is A

Step-by-step explanation:

You have 4 muffins or 4m with a 2 dollar off coupon so therefore it is 4m-2

Answer:

4m-2

Step-by-step explanation:

The cost, m, is subtracted by 2. There are 4 muffins being bought, so the term would be 4m, making the equation 4m-2.

8400000cm

84 kilometer is 8400000 centimeter.

Here given 84 km ,

We know that 1 km = 1000 meter

               so 84 km  = 84 x 1000 meter

                                 = 84000 meter

 and 1 meter = 100 cm

 so here 84000 meter = 84000 x 100 cm

                                       = 8,400,000 Centimeters

∴ 84 km = 8400000cm

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Answer:

m=-3

Step-by-step explanation:

Answer:

y = -3x - 1

Step-by-step explanation:

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (1,-4), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=1 and y1=-4.

Also, let's call the second point you gave, (-2,5), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-2 and y2=5.

To find b, think about what your (x,y) points mean:

(1,-4). When x of the line is 1, y of the line must be -4.

(-2,5). When x of the line is -2, y of the line must be 5.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-3x+b. b is what we want, the -3 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (1,-4) and (-2,5).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(1,-4). y=mx+b or -4=-3 × 1+b, or solving for b: b=-4-(-3)(1). b=-1.

(-2,5). y=mx+b or 5=-3 × -2+b, or solving for b: b=5-(-3)(-2). b=-1.

See! In both cases we got the same value for b. And this completes our problem.

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

25&36

Step-by-step explanation:

25 is a square number and so is 36 and there product is 900. They are also consecutive.

Just assemble the square numbers from the least i.e 4 and try solving as asked to see if it gives 900.

Thus you'll land on 25&36

Answer:

5² and 6²

Step-by-step explanation:

Use trial and error

Start from the product of 1² and 2²

1×2²

1×4=4

4<900 (incorrect)

2²×3²

4×9=36

36<900(incorrect)

3²×4²

9×16=144

144<900(incorrect)

4²×5²

16×25=400

400<900(incorrect) *but close

5²×6²

25×36 =900

900=900(correct)

: . 5² and 6² are the two consecutive square numbers.

Answer: The first one :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

b/c we can fairly say,  that the parallelgram is also a rectangle of size 24 x 11, we can just solve that area

24*11= 264

We can see, this is a parallelogram.

The formula to calculate the area of a parallelogram is b x h, where b is base and h is height.

Given that base = 24 in, height = 11 in, we can calculate the area as : 24 x 11 = 264 in2.

Given that the function f is linear, f(1) = −4, and f intersects the x-axis at an angle of 150° (measured counterclockwise from the x-axis, as usual). To find a formula for f and leave the answer in exact form, let's proceed as follows: Let a be the slope of the linear function, f(x) = ax + b.

Given that the function f is linear, f(1) = −4, and f intersects the x-axis at an angle of 150° (measured counterclockwise from the x-axis, as usual). To find a formula for f and leave the answer in exact form, let's proceed as follows: Let a be the slope of the linear function, f(x) = ax + b.

At point (1, -4), we have-4 = a(1) + b ...(1)

Also, given that f intersects the x-axis at an angle of 150° (measured counterclockwise from the x-axis), we can use the angle θ that f makes with the positive x-axis to find the slope as follows: tan θ = a ...(2)

Since the angle with x-axis is 150°, the angle made with the positive x-axis is 30°.

Hence, tan 30° = 1 / √3

Therefore, a = 1 / √3. Hence, from equation (1), -4 = (1 / √3) + b ⇒ b = -4 - (1 / √3)

Thus, the equation of the linear function f is

f(x) = (1 / √3)x - (4 + 1 / √3).

Therefore, the formula for f is given by f(x) = (1 / √3)x - (4 + 1 / √3).

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The value of the number will be;

⇒ x = - 11

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''Three times the quantity of a number increased by 7 is equal to the same number decreased by 15''

Now,

Let the quantity of a number = x

So, We can formulate;

⇒ 3x + 7 = x - 15

Solve for x as;

⇒ 3x - x = - 15 - 7

⇒ 2x = - 22

⇒ x = - 11

Thus, The value of the number will be;

⇒ x = - 11

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Answer:

3

it is asking for the slope of the line

(0,0) , (1,3)

3-0/1-0 = 3/1 = 3

Step-by-step explanation:

Answer:

\(\huge\boxed{slope=-\dfrac{1}{3}}\)

Step-by-step explanation:

The formula of a slope:

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

Substitute the coordinates of the given points (-1, -1) and (2, -2):

\(m=\dfrac{-2-(-1)}{2-(-1)}=\dfrac{-2+1}{2+1}=\dfrac{-1}{3}=-\dfrac{1}{3}\)

Volume of a cylinder is given as,

Hence the required volume is approximately 200 cubic units.

The appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

To find the appropriate test statistic for a 2-sample z-test for two proportions, we need to calculate the standard error and then use it to compute the z-score. The formula for the standard error is:

SE = sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]

Where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.

In this case, we have the following values:

X1 = 24 (number of successes in sample 1)

n1 = 200 (sample size 1)

X2 = 17 (number of successes in sample 2)

n2 = 150 (sample size 2)

To calculate the sample proportions, we divide the number of successes by the respective sample sizes:

p1 = X1 / n1 = 24 / 200 = 0.12

p2 = X2 / n2 = 17 / 150 = 0.1133

Now, we can plug these values into the formula to calculate the standard error:

SE = sqrt[(0.12 * (1 - 0.12) / 200) + (0.1133 * (1 - 0.1133) / 150)]

SE ≈ 0.0319

Finally, the test statistic (z-score) is calculated by subtracting the two sample proportions and dividing by the standard error:

Z = (p1 - p2) / SE

Z = (0.12 - 0.1133) / 0.0319

Z ≈ 0.2103

Therefore, the appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

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Answer:

x=17

Step-by-step explanation:

Answer:

(i)unique solution

Explanation:

We solve for x1 thus in the first equation:

x1-3x3=-3

x1-9=-3

x1=-3+9

x1= 6

We solve for a thus in the second equation:

2x1+ax2-x3=-2

2+a2-x3=-2

a2-x3=-4

a2=-4+x3

Step-by-step explanation:

(m-3)w²-8w+8=0........colllecting like terms

m+w²-8w=3-8

m-7w=-5

mw=-5+-7

mw=-12

mw/mw=-12/mw.....mw will be cancled out by mw so the answer is -12/mw

It will take 2 days for the car to cover the route.

To determine how many days it will take a car to cover a route of length M kilometers, we need to use the given formula:

Distance = Rate × Time

where distance is M kilometers, and rate is N kilometers per day.

We want to find the time in days.

Therefore, rearranging the formula, we have: Time = Distance / Rate

Substituting the given values, we get: Time = M / N

Therefore, the function days(n, m) that returns the number of days to cover the route can be defined as follows: def days(n, m):    return m / n

Now, let's use this function to calculate the number of days it will take for a car that covers a distance of 700 kilometers per day to cover a route of length 750 kilometers:

days(700, 750) = 1.0714...

Since the number of days should be a whole number, we need to round up the result to the nearest integer using the ceil function from the math module: import mathdef days(n, m):    return math.ceil(m / n)

Now, we can calculate the number of days it will take for a car that covers a distance of 700 kilometers per day to cover a route of length 750 kilometers as follows: days(700, 750) = 2

Therefore, it will take 2 days for the car to cover the route.

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Based on the calculations, the volume of this louvre pyramid is equal to 8,983 cubic meter..

Given the following data:

Base width = 35 meters.

Height = 22 meters.

Mathematically, the volume of a pyramid can be calculated by using this formula:

Volume = 1/3 × base area × height

For the base area, we have:

Area = w²

Area = 35² = 1,225 m².

Substituting the parameters into the formula, we have;

Volume = 1/3 × 1,225 × 22

Volume = 1/3 × 26,950

Volume = 8,983 cubic meter.

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Answer:

No.

Step-by-step explanation:

If you substitute x = 2 and y = 3 into the equation, you get 3 = 2 which is not true.

The correct option id D. There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than our sample's 36 working full-time

A study was conducted to determine if more than 30% of Cal State East Bay students work full-time.

The sample of Cal State East Bay students selected was random.

Out of 100 students, 36 were found to be working full-time.

The p-value was calculated to be 0.0952.

The probability of having more than 36 Cal State East Bay students working full-time out of a random sample of 100 students is 9.52% if exactly 30% of Cal State East Bay students work full-time.

Therefore, it is concluded that the null hypothesis cannot be rejected.

The p-value is greater than 0.05 which shows the significance level.

Hence, we accept the null hypothesis.

The null hypothesis states that the proportion of Cal State East Bay students who work full-time is not greater than 30%.

The alternate hypothesis states that the proportion of Cal State East Bay students who work full-time is greater than 30%.

The test is a right-tailed test.

The sample proportion is p = 0.36. The test statistic is given as Z = (p - P0) / √ [P0 (1 - P0) / n]Z = (0.36 - 0.30) / √ [(0.30) (0.70) / 100] = 1.76The p-value is given as 0.0392.

Since the p-value is less than 0.05, we can reject the null hypothesis.

Thus, we can conclude that more than 30% of Cal State East Bay students work full-time.

Hence, option D is the correct answer.

There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than 30% working full-time.

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The expression that shows 18 + 15 as a product of two factors is 3(6 + 5)

The expression is given as:

18 + 15

Factor out 3 from the expression

18 + 15 = 3 * (6 + 5)

Hence, the expression that shows 18 + 15 as a product of two factors is 3(6 + 5)

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Answer:

14 squared

Step-by-step explanation:

Answer:

amor no te enojes conmigo hacienda

Answer:

2 boxes

Step-by-step explanation:

im sorry this is a bit late but this is for other people