Which of the following has an x-intercept of 2 and a y-intercept of -4?

A. Five-number summary for City A and B are given below. IQR for City A is 10.5; IQR for City B is 11.5

B. There are no outliers present in either data set.

The values in the five-number summary include, lower and upper quartiles, max and min values, and the median.

Interquartile range (IQR) = upper quartile (Q3) - lower quartile (Q1)

Outlier of a data set is any value that is lower than Q1 - 1.5 × IQR or greater than Q3 + 1.5 × IQR.

The five-number summary for City A, 9, 27, 17, 24, 21, 12, 25, 25, 18, is:

IQR = 25 - 14.5 = 10.5

Outlier for City A:

Q1 - 1.5 × IQR = 14.5 - 1.5 × 10.5 = -1.25

Q3 + 1.5 × IQR = 25 + 1.5 × 10.5 = 40.75

No value is less than -1.25 or greater than 40.75, therefore, there is no outlier in City A.

The five-number summary for City B, 6, 20, 26, 15, 23, 25, 14, 14, 11,  is:

IQR = 24 - 12.5 = 11.5

Outlier for City B:

Q1 - 1.5 × IQR = 12.5 - 1.5 × 11.5 = -4.75

Q3 + 1.5 × IQR = 24 + 1.5 × 11.5 = 41.25

No value is less than -4.25 or greater than 41.25, therefore, there is no outlier in City B.

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The transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

The rule that describes the transformation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

To understand this, let's apply the transformation rule to each vertex of the original parallelogram ABCD:

Point A (2, 5) becomes A' (-5, 2).

Point B (5, 4) becomes B' (-4, 5).

Point C (5, 2) becomes C' (-2, 5).

Point D (2, 3) becomes D' (-3, 2).

By applying the transformation rule, we observe that the x-coordinate of each point becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.

This transformation is a 90-degree counterclockwise rotation about the origin (0, 0) on the coordinate plane. The image parallelogram A'B'C'D' is obtained by rotating the original parallelogram ABCD by 90 degrees counterclockwise.

Visually, this transformation can be seen as the original parallelogram being rotated around the origin, where the x-axis becomes the y-axis, and the y-axis becomes the negative x-axis.

Therefore, the transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

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Answer:

\(Base (B) = /frac{15x² + 1 + 2}{x}\)

Step-by-step Explanation:

==>Given:

Dimensions of a rectangular prism are expressed as follow:

Volume (V) = 15x² + x + 2

Height (h) = x²

==>Required:

Expression of the Base area (B)

==>Solution:

Volume (V) = Base (B) × Height (h)

15x² + x + 2 = B × x²

Divide both sides by x²

\(\frac{15x² + x + 2}{x²} = B

\(Base (B) = /frac{15x² + 1 + 2}{x}\)

Answer: c

Step-by-step explanation:

Answer:

Sssssnake ssssssnake sssssnake........../////////////////////////................

Step-by-step explanation:

Answer:

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

a) Use the distance formula:

\(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Substitute the coordinates and calculate:

\(d=\sqrt{(5-(-1))^2+(2-10)^2} =\sqrt{6^2+(-8)^2} =\sqrt{36+64} =\sqrt{100} =10\)

The distance is AB = 10 units

b) Use midpoint formula and find x and y- coordinates of this point:

\(x= \cfrac{x_1+x_2}{2}\)    and    \(y= \cfrac{y_1+y_2}{2}\)

Substitute coordinates and find the midpoint:

\(x= \cfrac{-1+5}{2} =2\)  and  \(y= \cfrac{10+2}{2}=6\)

The midpoint is (2, 6)

Answer:

Length of line segment AB = 10 units

Midpoint of line segment AB = (2, 6)

Step-by-step explanation:

To find length, apply the distance formula :

To find the midpoint :

Tthe probability that two particular people A and B will both be selected is:

P(A and B) = (2! * C(98,10)) / C(100,12)

A) If events A and B are disjoint, it means that they have no elements in common, i.e., A ∩ B = ∅. In this case, AC and BC are disjoint if and only if AC and BC have no elements in common, i.e., (AC) ∩ (BC) = ∅.

B) To find the probability that two particular people A and B will both be selected, we need to find the number of favorable outcomes (where both A and B are selected) and divide it by the number of total possible outcomes (the number of ways to select 12 people from 100).

The number of favorable outcomes is the number of ways to select the two people A and B, which is 2!, and the number of ways to select the remaining 10 people, which is (100-2) choose 10, i.e., C(98,10). So, the number of favorable outcomes is 2! * C(98,10).

The number of total possible outcomes is the number of ways to select 12 people from 100, which is C(100,12).

So, the probability that two particular people A and B will both be selected is:

P(A and B) = (2! * C(98,10)) / C(100,12)

Probability is a mathematical concept that quantifies the likelihood of an event occurring. It is a value between 0 and 1, where 0 represents an event that is impossible to occur, and 1 represents an event that is certain to occur.

Probabilities can be calculated based on the number of favorable outcomes (the number of ways the event of interest can occur) and the number of possible outcomes (the number of possible outcomes in the sample space).

For example, if you roll a fair six-sided die, the probability of rolling a 4 is 1/6, because there is only one favorable outcome (rolling a 4) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).

Probability is used in many fields, including mathematics, statistics, finance, insurance, and the natural sciences, to make predictions and inform decision-making under uncertainty.

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Answer:

2.8 units

Step-by-step explanation:

Think of this distance as the hypotenuse of a right triangle that has a vertical leg and a horizontal one as well.

Going from P to Q, the change in x is 2 and the change in y is also 2.

Thus, by the Pythagorean Theorem, this desired distance is:

d = √(2^2 + 2^2) = 2√2 units, or 2.8 units

Answer:

Got this from the internet.

Step-by-step explanation:

The vertical line dividing the parabola into two equal portions is called the line of symmetry. All parabolas have a vertex, the ordered pair that represents the bottom (or the top) of the curve. The vertex of a parabola has an ordered pair \begin{align*}(h, k)\end{align*}.

Answer:

3

Step-by-step explanation:

Answer:20.25

Step-by-step explanation:

The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
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Answer:627.072

Step-by-step explanation:

The critical value of z separates the rejection region from the nonrejection region while observed value of z is the value calculated for a sample statistic such as x.

A critical value of z is used when the sampling distribution is normal, or close to normal. The critical value of z refers to the point that cuts off area under graph for the standard normal distribution separating the rejection and nonrejection region of the data. The Critical value of z can indicate what probability any particular variable will have. These values are typically obtained from a table such as the standard normal distribution table. The observed value of z is a value determined for a sample statistic x. It is a test statistic for Z-tests that measures the difference between an observed statistic and its hypothesized population parameter in units of the standard deviation.

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the MLE of the unknown variance σ{power}2 of a Normal distribution when the mean μ is known is the sample variance, which is the sum of the squared deviations of the observations from the mean, divided by the sample size.

Suppose X1, . . . , Xn are iid samples from a Normal distribution with mean μ and unknown variance σ{power}2. The likelihood function for this model is given by:

L(σ{power}2|x) = (1/σ{power}(n)) {product} exp(-(1/2σ{power}2) {product}Σ(xi - μ){power}2)

where Σ denotes the sum over i=1 to n.

To find the MLE of σ{power}2, we differentiate the log-likelihood function with respect to σ{power}2 and set the derivative equal to zero:

d/d(σ{power}2) log L(σ{power}2|x) = -(n/2σ{power}2) + (1/2σ{power}4) {product}Σ(xi - μ){power}2 = 0

Solving for σ{power}2, we get:

σ{power}2 = (1/n) {product} Σ(xi - μ){power}2

This means that the MLE of σ{power}2 is the sample variance, which is the sum of the squared deviations of the observations from the mean, divided by the sample size.

To show that this is indeed the MLE, we need to check that it is a maximum. We can do this by computing the second derivative of the log-likelihood function with respect to σ{power2:

d{power}2/d(σ{power}2){power}2 log L(σ{power}2|x) = n/(2σ{power}4) - Σ(xi - μ){power}2/(σ{power}6)

If we plug in the value of σ{power}2 = (1/n) {product} Σ(xi - μ){power}2 into this expression, we get:

d{power}2/d(σ{power}2){power}2 log L((1/n) {product}Σ(xi - μ){power}2|x) = -n/(2((1/n) {product} Σ(xi - μ){power}2){power}2) < 0

This shows that the MLE of σ{power}2 is indeed a maximum.

In conclusion, the MLE of the unknown variance σ{power}2 of a Normal distribution when the mean μ is known is the sample variance, which is the sum of the squared deviations of the observations from the mean, divided by the sample size. This estimator is unbiased and efficient, meaning it has the smallest variance among all unbiased estimators.

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Answer:

x=5

Step-by-step explanation:

7x+15-9x=5

-2x+15=5

-2x=-10

x=5

Answer:

X = 5

Step-by-step explanation:

First expand, 7x + 15 - 9x = 5

Simplify, -2x + 15 = 5

Additive property of Addition/Subtraction , (-2x + 15) - 15 = (5) -15

Simplify, -2x = -10

Divide by -2, (-2x)/-2 = (-10)/-2

Simplify, x = 5

Substitution for checking your answer, 7(5) + 3(5-3(5)) = 5

35 + (15-45), simplify, 35 - 30 = 5

Thus the final answer can be concluded as X = 5

Answer:

Which ordered pairs are solutions to the inequality 2x + y > - 4?

Select each correct answer.

(-1, -1), (4, -12), (5, -12), (0, 1), (-3, 0)

The correct answer is:

(4, -12)

A chart that compares three sets of values in a three-dimension chart is called surface.

A two-dimensional collection of points (flat surface), a three-dimensional collection of points with a curved cross section (curved surface), or the perimeter of any three-dimensional solid are all examples of surfaces in geometry.

A surface is typically a continuous boundary that separates two areas of a three-dimensional space. For instance, a sphere's surface divides its interior from its exterior, and a horizontal plane divides the half-planes above and below it. Despite the fact that regions they contain are three-dimensional and have a volume, surfaces are basically two-dimensional and have an area. Despite this, surfaces are frequently referred to by the names of the regions they surround. Differential geometry studies the characteristics of surfaces, particularly the concept of curvature.

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The probability that at least one of them is defective if three units are picked at random is 0.8560.

We would define Ai as the event that the i th chosen unit is not defective, for I = 1, 2, 3. We are interested in P (A1 ∩ A2 ∩ A3). Note that

P(A1) = 95/100  

Given that the first chosen item was good, the second item will be chosen from 94 good units and 5 defective units, thus

P (A2 ∣ A1) = 94/99

Given that the first and second chosen items were okay, the third item will be chosen from 93 good units and 5 defective units, thus

P (A3∣ A2, A1) = 93/98

Thus, we have

P(A1∩ A2 ∩ A3) =  P(A1) P(A2∣ A1) P(A3∣ A2, A1)

=95/100*94/99*93/98

=0.8560

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a) The approximate sports league salary cap in 1995 was $35.17 million. b) According to the model, the salary cap reached $65 million in the year 2001.

To approximate the sports league salary cap in millions of dollars for a given year using the quadratic model, we substitute the corresponding value of x into the equation \(y = 0.2313x^2 + 2.600x + 35.17\).

a) To approximate the sports league salary cap in a particular year, we need to determine the value of y when x represents that year. Let's calculate:

For the year 1995 (x = 0):

\(y = 0.2313(0)^2 + 2.600(0) + 35.17\)

y ≈ 35.17 million dollars

Therefore, the sports league salary cap in 1995 was approximately 35.17 million dollars.

b) We can use the quadratic equation to determine the year when the salary cap reached 65 million dollars. Let's solve the equation for y = 65:

\(65 = 0.2313x^2 + 2.600x + 35.17\)

To solve this quadratic equation, we can rearrange it to:

\(0.2313x^2 + 2.600x + 35.17 - 65 = 0\)

\(0.2313x^2 + 2.600x - 29.83 = 0\)

To solve this equation, we can use the quadratic formula:

x = (-b ± √(b²- 4ac)) / 2a

where a = 0.2313, b = 2.600, and c = -29.83.

Substituting these values into the quadratic formula, we get:

x = (-2.600 ± √(2.600² - 4 * 0.2313 * (-29.83))) / (2 * 0.2313)

Calculating the expression within the square root:

x = (-2.600 ± √(6.76 + 27.4376)) / 0.4626

x = (-2.600 ± √(34.1976)) / 0.4626

x = (-2.600 ± 5.8456) / 0.4626

Now we can calculate the two possible values for x:

x1 = (-2.600 + 5.8456) / 0.4626 ≈ 6.22

x2 = (-2.600 - 5.8456) / 0.4626 ≈ -14.09

The value of x represents the number of years since 1995. Therefore, -14.09 is not a valid solution in this context.

According to the model, the salary cap reached 65 million dollars approximately 6.22 years after 1995. Adding this to 1995, we find:

1995 + 6.22 ≈ 2001.22

Therefore, according to the model, the salary cap reached 65 million dollars around the year 2001.

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The complete question is:

In 1995, the sports league introduced a salary cap that limits the amount of money spent on players' salaries. The quadratic model y=0.2313x2+2.600x+35.17 approximates this cap in millions of dollars for the years 1995-2006, where x=0 represents 1995, x=1 represents 1996, and so on. Complete parts a and b.

a) Approximate the sports league salary cap in .

b) According to the model, in what year did the salary cap reach 65 million dollars?

Answer:

9

Step-by-step explanation:

9² = 81

10² = 100

81 ... 90 ... 100

90 - 81 = 9

100 - 90 = 10

9 is less than 10

Hence, √90 is closer to 9

\(f(x) = - x + 1 \iff f(-1) = - (-1) + 1 = 1+1 = 2\)

\(\implies \bf f(-1) = 2\)

Answer: f(-1) = 2

Step-by-step explanation:

To find f(-1), we simply need to substitute -1 for x in the given expression for f(x):

f(x) = -x + 1

f(-1) = -(-1) + 1 [substitute x=-1]

f(-1) = 1 + 1

f(-1) = 2

MAKE ME THE BRAINLIEST PLS

Answer:

x= 1

y= 3

Step-by-step explanation:

21(-2+y) +7y = 42

-42 +28y+42

28y = 42+42

28y= 84

divide both sides y= 3

x= -2+3 x=1

x= + (3-2) = 1

42=42

10=10

Answer:

26

Step-by-step explanation:

This is what I got! I hope this helps!

The value of cos2x when sine of x equals negative 15 over 17 and cos x > 0 is -161/289.

The ratio of the neighboring side's length to the longest side, or hypotenuse, in a right triangle is known as the cosine. Let's say that the hypotenuse of a triangle ABC is written as AB, and the angle between the hypotenuse and base is written as.

It's interesting to see that cos's value varies depending on the quadrant. As observed in the above table, cos 0°, 30°, etc. have positive values while cos 120°, 150°, and 180° have negative values. Cos will have a good value in the first and fourth quadrants.

Given that, sin x equals negative 15 over 17.

Using the Pythagoras theorem we have:

(17)² = (- 15)² + y²

y = 8

The value of cos x = 8/17

Then the value of cos2(x) is calculated using the formula:

cos2x = cos²x - sin²x

cos2x = (8/17)² - (15/17)²

cos2x = -161/289

Hence, the value of cos2x when sine of x equals negative 15 over 17 and cos x > 0 is -161/289.

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Answer:

4

Step-by-step explanation:

just 4 -_-

4x^2-20x

=4(x^2-5x)

so the value is 4

By solving the quadratic equation, the value of A is 4

Option (3) is correct.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is \(ax^{2}+bx+c=0\), where a and b are the coefficients, x is the variable, and c is the constant term.

Given quadratic equation

\(4x^{2} -20x+3=0\)

⇒ \(4x^{2} -20x=-3\)

By taking 4 as common in \(4 x^{2}\) and 20x

⇒ \(4(x^{2} -5x)=-3\)...................(1)

According to the question by solving the quadratic equation. Mariya got, \(A(x^{2} -5x)=-3\) .....................(2)

By comparing equation 1 and 2 we can clearly see that A = 4

Hence, by solving the quadratic equation, the value of A is 4

Option (3) is correct.

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Answer:

$12.55

Step-by-step explanation:

20-7.45=12.55

Given:

To find:

Write each given fraction in the simplest form.

Explanation:

Write given terms in numerator and denominator as factorize form,

Cancel out the common terms in numerator and denominator,

Which is the simplest form.

Final answer:

Hence, the required simplest form is:

As given by the question,

There are given that the equation:

Now,

First, suppose any number, for which the given equation has satisfied.

So, the number is, x = 2 and y = 6

Then,

Put both values into the given equation

Then,

Put the same value of x and y into the given option and check whether it is satisfied:

So,

From option 3:

Hence, the correct option is 3.

Answer:

The answer is 4,000.

Step-by-step explanation:

The closest to 35xn= 3,465

Answer:

Step-by-step explanation:

35 to the nearest 10 is 40 and 99 to the nearest 10 is 100 so 4 times 100 is 4,000 so your answer should be d. 4,000