Find the slope of the line that goes through the following points.
A. –1
B. 1
C. –4
D. –7

The probability that Alice and Bob form a match is \(^{24} C_{5}\) * ((\(^{24} C_{4}\))*20*19) / \(^{24} C_{5}\) * \(^{24} C_{5}\).

To answer the question, we use the probability by its complement.

The complement of an event is the subset of outcomes in the sample space that are not in the event. A complement is itself an event.

In this case, probability space is (\(^{24} C_{5}\))^2 where there is match for 4 or 5.

For number of ways for 5 adjectives match is (\(^{24} C_{5}\)).

For number of ways for 4 adjectives match is (\(^{24} C_{4}\))*20*19.

We first choose 4 adjectives which are match and then there are 20*19 ways for both of them to choose an adjective each from remaining 20 adjectives.

Then, the desired probability is:

\(^{24} C_{5}\) * ((\(^{24} C_{4}\))*20*19) / \(^{24} C_{5}\) * \(^{24} C_{5}\)

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Answer:

30cm

Step-by-step explanation:

Perimeter of a Pentagon=5L

P=5×6cm=30cm

(i) The probability that 2 pears and 1 orange are eaten in any order is equal to \(\frac{14}{55}\)

(ii) The probability that the third fruit eaten is an orange is equal to \(\frac{7}{15}\)

(iii) The probability that the first fruit eaten was a pear, given that the third fruit eaten is an orange is equal to \(\frac{6}{11}\)

What is Probability?

What are Combinations?

Here, it is given that the box contains 4 pears and 7 oranges in the box.

So, the total number of fruits in the box = 4 + 7 = 11

Combination when 2 pears is chosen out of 4 pears from the box \(= {4 \choose 2} = \frac{4!}{2!(4-2)!} =6\)      

Combination when 1 orange is chosen out of 7 oranges from the box \(= {7 \choose 1} = \frac{7!}{1!(7-1)!} =7\)

Combination when 2 pears and 1 oranges are taken from the box containing a total of 11 fruits \(= {11 \choose 3} = \frac{11!}{3!(11-3)!} =165\)

So, the probability that 2 pears and 1 orange are eaten, in any order,

\(P(A) =\frac{ {4 \choose 2} \times {7 \choose 1} }{ {11 \choose 3} } \\\implies P(A) = \frac{6 \times 7}{165} \\\implies P(A) = \frac{14}{55}\)

Now, the probability that the third fruit eaten is an orange is given as,

\(P(B)= \frac{{1 \choose 4}{1 \choose 3}{1 \choose 7}+{11 \choose 4}{1 \choose 7}{1 \choose 6}+{1 \choose 7}{1 \choose 6}{1 \choose 5}}{A(11,3)} \\P(B)=\frac{460}{990} \\P(B)=\frac{7}{15}\)

Next, we can find the probability that the first fruit eaten was a pear, given that the third fruit eaten is an orange is a conditional probability problem where one event depends on another event.

The probability that the third fruit is orange P(A) is equal to 7/15

The probability that the first fruit eaten was a pear is calculated as,\(P(C)= \frac{{1 \choose 4}{1 \choose 3}{1 \choose 7}+{11 \choose 4}{1 \choose 7}{1 \choose 6}}{A(11,3)} \\P(C)=\frac{252}{990} \\P(C)=\frac{14}{55}\)

So, according to conditional probability,

Probability of C given A,

\(P(C/A)=\frac{P(C \cap A)}{P(A)} \\\implies P(C/A)=\frac{\frac{14}{55} }{\frac{7}{15} } \\\implies P(C/A)=\frac{6}{11}\)

There, the (i) probability that 2 pears and 1 orange are eaten in any order is equal to \(\frac{14}{55}\)

(ii) probability that the third fruit eaten is an orange is equal to \(\frac{7}{15}\)

(iii) probability that the first fruit eaten was a pear, given that the third fruit eaten is an orange is equal to \(\frac{6}{11}\)

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The graph is a linear function with a growth factor of 4

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

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

m=y₂-y₁/x₂-x₁

The graph has the shape of a straight line, so it is linear.

The graph starts at point (0, 0). It passes through point (1, 4).

slope = 4/1 = 4

The slope is 4. Growth factor is the same as slope for a linear function.

Hence, the graph is a linear function with a growth factor of 4

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Answer:

Their are many other answers to this question this is one of the ones that are correct.

The number of ways the letters of the word DANCER can be arranged if D and A remain together is 120 ways .

In the question ,

it is given that the word is DANGER ,

the number of letters in the given word is = 6

it is given that the letters D and A are together ,

that means they are a single unit ,

So , the number of letters become = 5 letters

and  5 letters can be arranged in 5! ways ,

which can be simplified  as

5! \(=\) 5 * 4 * 3 * 2 * 1 \(=\) 120 ways

Therefore , the number of ways of arrangement is 120 ways .

The given question is incomplete , the complete question is

How many ways can the letters of the word DANCER be arranged in a row if D and A must remain together (in order) as a unit ?

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The standard form of a linear equation is simply given Ax+By=C. In order to change an equation written in slope-intercept form (y=mx+b) to standard form, one should get the x and y on the same side of the equal sign and the constant on the other side.

One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line.

Using a straight line's slope and the location of its y-axis intersection, the slope intercept equation can be used to determine the general equation of the line. Y = mx + b is the equation in slope intercept form.

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Work Shown:

5% = 5/100 = 0.05

5% of 42 = 0.05*42 = 2.10

tax = $2.10

total cost including tax = $42 + $2.10 = $44.10

----------

An alternative is to multiply 42 by 1.05 to get

1.05*42 = 44.10

We get the same answer. The 1.05 refers to 1 + 0.05 where the "1" is 100% and the 0.05 is 5%, so the two combine to 105%, meaning the total cost is 105% of the cost before tax is considered.

Answer:

5x + 3y = 15

Step-by-step explanation:

As Line CD passes through points C(3, 5) and D(6, 0), x (the "run") increases by 3 and y (the "rise") decreases by 5.  Thus, the slope of line CD is

m = rise / run = -5/3, and in slope-intercept form the following is true:

y = mx + b => 5 = (-5/3)(3) + b, or b = 5.

Then the equation of the line is y = (-5/3)x + 5.  Converting this to standard form, we get:

3y = -5x + 15, or 5x + 3y = 15

You are  57 years old if 400 reduced by one half must subtracted from 257 is your age in the given arithmetic problem.

Mathematical arithmetic, which includes operations on numbers, is its foundation. Addition, subtraction, multiplication, and division are among these operations. The foundation of the subject "Maths" is laid by one of the crucial branches of mathematics: arithmetic.

Despite the fact that the subject involves numerous other modified operations, addition, subtraction, division, and multiplication are the three basic operations under the heading of arithmetic.

Let your age be x

\($x=257-400\frac{1}{2}\)

x = 257 - 200

x = 57

Hence, your age is 57 years old.

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Answer:

25% of the isles are empty

Step-by-step explanation:

48/12 is 25%

Answer:

25%

Step-by-step explanation:

12 + 12 + 12 + 12= 48

if 12 isles are empty, then that is 1/4 of 48 aka 25%

Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

Answer:

blank1: 9

blank2: 30°

blank3: 60°

blank4: 90°

blank5: half

Step-by-step explanation:

The 30°-60°-90° triangle has some great shortcuts associated with it (there are math reasons, trig reasons for these shortcuts)

One of these great shortcuts is that the short leg is half the hypotenuse (or the hypotenuse is double the short leg)

For your question, the kite string, 18ft, is the hypotenuse. The kite height is half that--9ft.

see image.

The area of a disk of radius r is given by the formula, A = πr²Given that the radius of the disk is r = 9 - 9x²We can substitute r in the formula to find the cross-sectional area of the disk.

A = πr²A

= π(9 - 9x²)²

A = π(81 - 162x² + 81x⁴)

A = 81π - 162πx² + 81πx⁴

The cross-sectional area of the disk is given by 81π - 162πx² + 81πx⁴.

The function y = 9 - 9x² intersects the x-axis at the following values of x: When y = 0, we have

0 = 9 - 9x²

9x² = 9

x² = 1

x = ± √1

x = ± 1

The function intersects the x-axis at the values -1 and 1. Hence, the smaller value is -1 and the larger value is 1.

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Answer: \(20\times 20, 16\times 25, 10\times 40\)

Step-by-step explanation:

Given

The volume of the pool is \(1600\ ft^3\)

Depth of water is \(d=4\ ft\)

Suppose A is the base of the pool

\(\Rightarrow V=A\times d\\\Rightarrow 1600=A\times 4\\\Rightarrow A=400\ ft^2\)

This area can be written as

\(\Rightarrow A=10\ ft\times 40\ ft\ or\\\Rightarrow A=16\ ft\times 25\ ft\ or\\\Rightarrow A=20\ ft\times 20\ ft\)

The center of the face of a cube is the midpoint of the face and lies along the line that runs between the opposite vertices of the face.

This is the point of intersection of the two diagonals in a face. In other words, it is the point that is equidistant from all four corners of the face.

To visualize this, imagine dividing the face into four equal triangles by drawing lines from each corner to the center. The center of the face is at the intersection of these lines.

In three-dimensional space, the center of the face of a cube is also the center of the cube itself, as all faces of a cube are congruent (the same shape and size) and meet at the center of the cube.

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a. The median number of calls = 55

b. The first and third quartiles, Q1 = 48 and Q3 = 66

c. The first decile and the ninth decile, D1 = 45 and D9 = 71.

d. The 33rd percentile = 52.5

To answer the questions, let's first organize the data in ascending order:

38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57 59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79

(a) The median is the middle value of a dataset when arranged in ascending order.

Since we have 40 observations, the median is the value at the 20th position.

In this case, the median is the 55th visit.

(b) The quartiles divide the data into four equal parts.

To find the first quartile (Q1), we need to locate the position of the 25th percentile, which is 40 * (25/100) = 10.

The first quartile is the value at the 10th position, which is 48.

To find the third quartile (Q3), we need to locate the position of the 75th percentile, which is 40 * (75/100) = 30.

The third quartile is the value at the 30th position, which is 66.

Therefore, Q1 = 48 and Q3 = 66.

(c) The deciles divide the data into ten equal parts.

To find the first decile (D1), we need to locate the position of the 10th percentile, which is 40 * (10/100) = 4.

The first decile is the value at the 4th position, which is 45.

To find the ninth decile (D9), we need to locate the position of the 90th percentile, which is 40 * (90/100) = 36.

The ninth decile is the value at the 36th position, which is 71.

Therefore, D1 = 45 and D9 = 71.

(d) To find the 33rd percentile, we need to locate the position of the 33rd percentile, which is 40 * (33/100) = 13.2 (rounded to 13). The 33rd percentile is the value at the 13th position.

Since the value at the 13th position is between 52 and 53, we can calculate the percentile using interpolation:

Lower value: 52

Upper value: 53

Position: 13

Percentage: (13 - 12) / (13 - 12 + 1) = 1 / 2 = 0.5

33rd percentile = Lower value + (Percentage * (Upper value - Lower value))

                = 52 + (0.5 * (53 - 52))

                = 52.5

Therefore, the 33rd percentile is 52.5.

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The point that is equally spaced from a triangle's three vertices is known as the circumcenter.Triangle ABC's equilateral circumcenter is (-5, 2) .

The point that is equally spaced from a triangle's three vertices is known as the circumcenter.

The triangle's three vertices are all located at the center of the circle.We may insert the coordinate values for the triangle ABC's vertices A(-5,3), B(5,8), and C(-5.8) into the formulas above to determine its circumcenter.

x = (8 - 3) * (-5.8^2 + 3^2 - 5^2 - 8^2)

- (3 - 8) * (-5^2 + 3^

2 - (-5) (-5)

^2 -3^2) / 2 * (3 - (-5))

* (8 - 3) - (3 - 8) * (-5.8 - (-5))

x = (-5) (-5)

y = (3 - (-5.8))

* (-5^2 + 3^2 - (-5)^2 -3^2)

- (-5 - (-5))

* (3^2 + 3^2 - (-5.8) (-5.8)

^2 - 8^2)

/ 2 * (3 - 8) (3 - 8)

* (-5 - (-5))

- (3 - 8) * (3 - (-5.8))

y = 2

The circumcenter of triangle ABC is hence (-5, 2)

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Answer:

a negative times a positive makes a negative

Step-by-step explanation:

Answer: 5w⁴ + w²

Step-by-step explanation: Pic is attached. Hope this helps. Sorry for bad handwriting, Im writing with a mouse.

The subset K = {1 + n | n ∈ N} of the real numbers R is proven to be compact in the topology T[a,b) in the first paragraph. In the second paragraph, it is shown that the subset K does not satisfy the compactness property in the topology T(a,b], indicating that (R, T(a,b]) is not a compact space.

(a) To prove that K U {1} is compact in (R, T[a,b), we need to show that every open cover of K U {1} has a finite subcover. Let C be an open cover of K U {1}. Since K is a subset of R, it can be expressed as K = {1 + n | n ∈ N}. Therefore, K U {1} = {1} U {1 + n | n ∈ N}. The set {1} is a closed and bounded interval in (R, T[a,b)), so it is compact. For the set {1 + n | n ∈ N}, we can choose a finite subcover from C that covers all the elements of this set. Combining the finite subcover of {1} and {1 + n | n ∈ N}, we obtain a finite subcover for K U {1}. Hence, K U {1} is compact in (R, T[a,b)).

(c) To show that (R, T(a,b]) is not compact, we demonstrate that the subset K = {1 + n | n ∈ N} does not satisfy the compactness property in the topology T(a,b]. Suppose we have an open cover C for K. Since the topology T(a,b] contains open intervals of the form (a, b], we can construct an open cover C' = {(n, n + 2) | n ∈ N} for K. However, this open cover C' does not have a finite subcover for K because the intervals (n, n + 2) are disjoint for different values of n. Therefore, K does not have a finite subcover, indicating that it is not compact in (R, T(a,b]). Consequently, (R, T(a,b]) is not a compact space.

Finally, the subset K U {1} is proven to be compact in the topology T[a,b), while the subset K does not satisfy the compactness property in the topology T(a,b], indicating that (R, T(a,b]) is not a compact space.

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Answer:

y = \(\frac{4}{3}\) x

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - \(\frac{3}{4}\) x + 1 ← is in slope- intercept form

with slope m = - \(\frac{3}{4}\)

Given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{3}{4} }\) = \(\frac{4}{3}\) , thus

y = \(\frac{4}{3}\) x + c ← is the partial equation

To find c substitute (9, 12) into the partial equation

12 = 12 + c ⇒ c = 12 - 12 = 0

y = \(\frac{4}{3}\) x + 0 , which simplifies to

y = \(\frac{4}{3}\) x

Answer:

gimme a sec

Step-by-step explanation:

Answer:

5y - 2

Step-by-step explanation:

1/3 ( 15y - 6 ) = (15y - 6) / 3 = 5y - 2

Done! Hope you learned how to do this/understood this and have a great day! Please mark me as brainliest, vote 5.0 on my answer and thank me to show some support! Bye!

Using the definition of the derivative, we have:
f'(a) = lim (h -> 0) [(f(a+h) - f(a)) / h]

We're asked to use the definition of the derivative, which includes the terms:

limit, h, f(a+h), f(a), and the fraction f(a+h) - f(a) / h.
The definition of the derivative of a function f(x) at a specific point x=a is given by:
f'(a) = lim (h -> 0) [(f(a+h) - f(a)) / h]
f(a+h) represents the value of the function f(x) at the point (a+h).
f(a) represents the value of the function f(x) at the point a.
f(a+h) - f(a) calculates the difference in the function values at these two points.
h is the small change in the x-coordinate (x-axis) between these two points, and we let h approach 0 to ensure we're finding the instantaneous rate of change.
(f(a+h) - f(a)) / h represents the average rate of change between the points (a, f(a)) and (a+h, f(a+h)).
By taking the limit as h approaches 0, we find the instantaneous rate of change at the point x=a, which is the derivative of the function f(x) at x=a.

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Answer:

x = 72

Step-by-step explanation:

By exterior angle theorem:

x° + (x + 10)° = 154°

(x + 10 + x) ° = 154°

(2x + 10)° = 154°

2x + 10 = 154

2x = 154 - 10

2x = 144

x = 144/2

x = 72

All the angles of the Rhombus if B-A=20 is angle A = angle C = 80°, and angle B = angle D = 100°.

In a rhombus ABCD, if angle B minus angle A equals 20 degrees (B-A=20°), we can find the degree measures of all the angles.

Step 1: Recognize that in a rhombus, opposite angles are equal. Therefore, angle A = angle C and angle B = angle D.

Step 2: Remember that the sum of the angles in any quadrilateral is 360 degrees. In a rhombus, since the opposite angles are equal, we can represent this as: 2A + 2B = 360°

Step 3: Use the given information, B - A = 20°, to solve for one of the angles. For this, rearrange the equation to isolate B: B = A + 20°

Step 4: Substitute the expression for B from step 3 into the equation from step 2: 2A + 2(A + 20°) = 360°

Step 5: Solve the equation for angle A. 2A + 2A + 40° = 360° → 4A + 40° = 360° → 4A = 320° → A = 80°

Step 6: Now that we have angle A, use the expression from step 3 to find angle B: B = 80° + 20° = 100°

Step 7: Since A = C and B = D, we can now state all the angles of the rhombus ABCD: angle A = angle C = 80°, and angle B = angle D = 100°.

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Answer: 1693.76

Step-by-step explanation:

The range of feasible values for the multiple coefficients of correlation is from -1 to 1.

The multiple coefficients of correlation, also known as the multiple R or R-squared, measures the strength and direction of the linear relationship between a dependent variable and multiple independent variables in a regression model. It quantifies the proportion of the variance in the dependent variable that is explained by the independent variables.

The multiple coefficients of correlation can take values between -1 and 1.

A value of 1 indicates a perfect positive linear relationship, meaning that all the data points fall exactly on a straight line with a positive slope.

A value of -1 indicates a perfect negative linear relationship, meaning that all the data points fall exactly on a straight line with a negative slope.

A value of 0 indicates no linear relationship between the variables.

Values between -1 and 1 indicate varying degrees of linear relationship, with values closer to -1 or 1 indicating a stronger relationship. The sign of the multiple coefficients of correlation indicates the direction of the relationship (positive or negative), while the absolute value represents the strength.

The range from -1 to 1 ensures that the multiple coefficients of correlation remain bounded and interpretable as a measure of linear relationship strength.

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