what expression is equal to(5+x-2)×2

When the student recalculates their grades by including the fifth exam (95), the grade that changes the most is the lowest grade, which increases from 80 to 95.

Initially, the student had four exam grades of 80, 80, 85, and 90. These grades have a range of 10 points, from the lowest grade of 80 to the highest grade of 90. When the student includes their fifth exam grade of 95, the range increases to 15 points, as the lowest grade increases by 15 points.

The lowest grade of 80 experiences the most significant change because it increases by 15 points to become 95. In comparison, the other grades remain the same or change by smaller margins. The two initial grades of 80 remain unchanged, while the grade of 85 increases by 10 points to 95, and the grade of 90 remains the same. However, since the lowest grade undergoes the largest increase, it has the most significant impact on the overall grade calculation.

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The rank that should be assigned to a score of x=6 is 4.

The given scores are already sorted from smallest to largest. The scores before x=6 are 1, 1, and 3, which are ranked 1, 2, and 3, respectively. The next score after x=6 is also 6, and since we are asked to rank x=6, we need to skip the next two 6s and assign it the rank 4.

Arrange the given scores in ascending order, which has already been done: 1, 1, 3, 6, 6, 6, 9 Identify the position of the first occurrence of the score x = 6. In this case, the first 6 appears in the 4th position.

The rank assigned to a score of x = 6 is 4, based on the order of the given scores.

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We need to calculate the numerical integration of this function using the Trapezium rule over the interval [0, 2].The formula of the Trapezium rule is given by:

\($$ \int_{a}^{b}f(x)dx \approx \frac{(b-a)}{2n}[f(x_0) + 2f(x_1) + 2f(x_2) + ... + 2f(x_{n-1}) + f(x_n)] $$\)

where, \($$ x_0 = a, x_n = b \space and \space x_i = a + i \frac{(b-a)}{n}$$\)

Now,

a) We are given a function as: $$ f(x) = 0.2 + 25x + 3x^2$$

we can calculate the numerical integration as:\($$ \begin{aligned}\int_{0}^{2}f(x)dx & \approx \frac{(2-0)}{2}[f(0) + f(2)] + \frac{(2-0)}{2n}\sum_{i=1}^{n-1}f(x_i) \\& \approx (1)(f(0) + f(2)) + \frac{1}{n}\sum_{i=1}^{n-1}f(x_i) \end{aligned}$$\)

We can find the value of f(x) at 0 and 2 as:

\($$ f(0) = 0.2 + 25(0) + 3(0)^2 = 0.2 $$$$ f(2) = 0.2 + 25(2) + 3(2)^2 = 53.2 $$\)

Now,

let's find the value of f(x) at some other points and calculate the sum of all values except for the first and last points as:

\($$ \begin{aligned} f(0.2) &= 0.2 + 25(0.2) + 3(0.2)^2 = 1.328 \\ f(0.4) &= 0.2 + 25(0.4) + 3(0.4)^2 = 3.248 \\ f(0.6) &= 0.2 + 25(0.6) + 3(0.6)^2 = 6.068 \\ f(0.8) &= 0.2 + 25(0.8) + 3(0.8)^2 = 9.788 \\ f(1.0) &= 0.2 + 25(1.0) + 3(1.0)^2 = 14.4 \\ f(1.2) &= 0.2 + 25(1.2) + 3(1.2)^2 = 19.808 \\ f(1.4) &= 0.2 + 25(1.4) + 3(1.4)^2 = 26.128 \\ f(1.6) &= 0.2 + 25(1.6) + 3(1.6)^2 = 33.368 \\ f(1.8) &= 0.2 + 25(1.8) + 3(1.8)^2 = 41.528 \\\end{aligned}$$\)

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the correct choice is option C: The series converges because ak is nonincreasing in magnitude for k greater than some index N and lim ak = 0 as k approaches infinity.

To analyze the convergence of the series, we first examine the behavior of the magnitude of its terms, represented by ak = 20. From the given expression, we can observe that the magnitude of the terms does not decrease or increase monotonically with increasing values of k. Therefore, options B, C, D, and E can be eliminated.

Next, we consider the alternating sign (-1)^(k+1) in the series. This alternating sign indicates that the series follows an alternating pattern of positive and negative terms.

Since the magnitude of the terms does not exhibit a clear monotonic pattern, the alternating nature of the series is significant. In this case, we can apply the Alternating Series Test, which states that if the magnitude of the terms is nonincreasing and approaches zero as k approaches infinity, then the series converges.

Based on the given information, it is mentioned that the magnitude of the terms is nonincreasing (ak is nonincreasing in magnitude). Additionally, as k approaches infinity, the terms indeed approach zero.

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Answer:

3

Step-by-step explanation:

15.839 rounded to the nearest hundredths place would be 15.83.

Answer:

4

Step-by-step explanation:

If rounded to the nearest hundredth of a second, you would get 15.84, as you round up if the last number is 5 or above.

For the given information, the value of the test statistic is -1.724 and its associated p-value is 0.0426.

In order to calculate the p value of students with GPA of 3.00 or below, the standard score (z -score or test statistic) must be determined first. In statistics, the standard score refers to the number of standard deviations by which the scores differs from the mean value of the observed or measured data. Scores above the mean have positive standard scores, while those below the mean have negative standard scores.

In a sample of 190 graduates, 28 students have a GPA of 3.00 or below, x = 28/190 = 0.15

The standard deviation = √(p(1 – p)/n) = √(0.2(1-0.2)/190) = 0.029 (where p is the probability of success and n is the total number of data)

The z-score = (x - µ)/σ = (0.15 – 0.2)/0.029 = - 1.724

From the table,

The P (z < -1.724) = 0.0426 or 4.26%.

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The given matrix is :$$
A = \(\begin{bmatrix}2 & 1 & 2\\1 & 2 & 2\\1 & 1 & 3\\\end{bmatrix}$$\)Now we need to find out the eigenvalues and eigenvectors of the given matrix.

For that, we need to find out the roots of the characteristic equation. The characteristic equation of matrix A is given as :\($$\begin{vmatrix}2 -\lambda & 1 & 2\\1 & 2 -\lambda & 2\\1 & 1 & 3-\lambda\\\end{vmatrix}=0\)
$$On solving the above equation, we get the eigenvalues as :λ1 = 1, λ2 = 3, λ3 = 3Now we have to find the eigenvectors for the corresponding eigenvalues. For λ1 = 1 :We need to find the nullspace of matrix (A - λ1I). The nullspace is given by:\($$(A - \lambda_1I)X = 0$$$$\)
\(\Rightarrow \begin{bmatrix}1 & 1 & 2\\1 & 1 & 2\\1 & 1 & 2\\\end{bmatrix}\begin{bmatrix}x\\y\\z\\\end{bmatrix} = \begin{bmatrix}0\\0\\0\\\end{bmatrix}$$$$\)
\(\Rightarrow x + y + 2z = 0$$Putting z = 1, we get $x = -1$ and $y = 1$.\)Therefore, the eigenvector corresponding to λ1 is :$$
\(v_1 = \begin{bmatrix}-1\\1\\1\\\end{bmatrix}$$Similarly for λ2 = 3\):We need to find the nullspace of matrix (A - λ2I). The nullspace is given by:\($$(A - \lambda_2I)X = 0$$$$\)
\(\Rightarrow \begin{bmatrix}-1 & 1 & 2\\1 & -1 & 2\\1 & 1 & 0\\\end{bmatrix}\begin{bmatrix}x\\y\\z\\\end{bmatrix} = \begin{bmatrix}0\\0\\0\\\end{bmatrix}$$$$\)
\(\Rightarrow -x + y + 2z = 0$$$$\Rightarrow x = y + 2z$$Putting z = 1, we get $x = y + 2$ and $y = -2z$\). Therefore, the eigenvector corresponding to λ2 is :\($$v_2 = \begin{bmatrix}1\\-2\\1\\\end{bmatrix}$$\)We know that if there are n linearly independent eigenvectors corresponding to n distinct eigenvalues, then those eigenvectors will form a basis for Rn. Here, we have two distinct eigenvalues λ1 = 1 and λ2 = 3 and we have two linearly independent eigenvectors . Hence, these two vectors form a basis for R2.

So the correct choice is :A. There are two distinct eigenvalues, λ1 = 1 and λ2 = 3. Bases for the corresponding eigenspaces are v1 = [-1 1 1] and v2 = [1 -2 1]. C. In ascending order, the three distinct eigenvalues are λ1 = 1, λ2 = 3 and λ3 = 3. Bases for the corresponding eigenspaces are v1 = [-1 1 1], v2 = [1 -2 1] and v3 = [0 0 0].

In ascending order, the distinct eigenvalues are -3, -1, 0, and 2, with algebraic multiplicities 1, 1, 6, and 3, respectively. Bases for the corresponding eigenspaces are {[0,1,0,0,0,0,0,0,0,0,0,0]T, [0,0,1,0,0,0,0,0,0,0,0,0]T}, {[1,0,0]T, [0,1,0]T, [0,0,1]T}, and {[−1,0,1,0,0,0,0,0,0,0,0,0]T, [−1,0,0,0,1,0,0,0,0,0,0,0]T, [0,−1,0,0,0,1,0,0,0,0,0,0]T, [0,0,−1,0,0,0,1,0,0,0,0,0]T, [0,0,0,1,0,0,0,0,0,0,0,0]T, [0,0,0,0,1,0,0,0,0,0,0,0]T, [0,0,0,0,0,1,0,0,0,0,0,0]T, [0,0,0,0,0,0,1,0,0,0,0,0]T, [0,0,0,0,0,0,0,1,0,0,0,0]T, [0,0,0,0,0,0,0,0,1,0,0,0]T, [0,0,0,0,0,0,0,0,0,1,0,0]T, [0,0,0,0,0,0,0,0,0,0,1,0]T, [−1,−1,0,1,0,0,0,0,0,0,0,0]T, [−1,0,−1,0,1,0,0,0,0,0,0,0]T}.

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The expected gain or loss from playing the game 15 times is -$75.00, indicating an expected loss of $75.00.

To determine the expected gain or loss from playing the game 15 times, we need to calculate the expected value.

The probability of getting three tails (winning) in a single coin toss is (1/2) * (1/2) * (1/2) = 1/8, since each coin toss is independent and has a 1/2 probability of landing tails.

The probability of losing in a single coin toss is 1 - 1/8 = 7/8.

If we play the game 15 times, the expected number of wins is (1/8) * 15 = 15/8, and the expected number of losses is (7/8) * 15 = 105/8.

The amount gained from winning is $10, and the amount lost from losing is $2.

Therefore, the expected gain or loss can be calculated as follows:

Expected gain or loss = (Expected number of wins * Amount gained) - (Expected number of losses * Amount lost)

= (15/8 * $10) - (105/8 * $2)

Simplifying this expression, we find:

Expected gain or loss = $187.50 - $262.50

= -$75.00

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Let's define the next variable:

x: the original second prize (in tickets)

The first time, she won 50 tickets. The second time, she won 4 times the number of tickets of the original second prize, that is, 4x. Altogether she won 200 tickets. That is,

50 + 4x = 200

50 is adding on the left, then it will subtract on the right

4x = 200 - 50

4x = 150

4 is multiplying on the left, then it will divide on the right

x = 150/4

x = 37.5

The original second prize was 37.5 tickets

Answer:

x = 2

Step-by-step explanation:

Answer:

-3x2

Step-by-step explanation:

x=2:(-3)2=(-6)

not (-3)(-2) negative times negative is always positive, negative times positive is always negative

Answer:

x = 100 , x = 3

Step-by-step explanation:

(a)

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × 3 = 540°

sum the angles and equate to 540

x + x + 125 + 125 + 90 = 540 , that is

2x + 340 = 540 ( subtract 340 from both sides )

2x = 200 ( divide both sides by 2 )

x = 100

(b)

the 2 given angles are alternate exterior angles and are congruent , then

6x + 18 = 2x + 30 ( subtract 2x from both sides )

4x + 18 = 30 ( subtract 18 from both sides )

4x = 12 ( divide both sides by 4 )

x = 3

Step-by-step explanation:

your answer would be d trapezoid

The coordinate (3, -2) will be a solution to the given equation since it lies on the line.

A line is defined as the shortest distance between two points. The equation of a line is described by the linear equation y = mx + b

Given the equation y = -3x +7, in order to determine the coordinate that represents a solution, we will substitute the value of x and check if we are going to get the corresponding y-value.

For the coordinate (1, 10)

y = -3(1) +7

y = 4

Hence (1, 10) is not a solution

For the coordinate (1, -4)

y = -3(1) +7

y = 4

Hence (1, -4) is not a solution

For the coordinate (3, -2)

y = -3(3) +7

y = -2

Since the equivalent y-value is -2, hence the coordinate (3, -2) is a solution.

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Answer:

Cone Volume = (PI * radius^2 * height) / 3

96 cc = (PI * radius^2 * 14) / 3

(96 * 3) / (PI * 14) = radius^2

radius ^ 2 = 6.5480890872

radius = 2.5589234235

diameter = radius *2 = 5.117846847  cm

diameter = 5.12 cm (rounded)

Step-by-step explanation:

Answer:

4 small cars

7 large cars

Step-by-step explanation:

To determine the number of small cars rented and the number of large cars rented by the group of college students, we can set up and solve a system of equations.

Let x be the number of small cars.

Let y be the number of large cars.

If the students rented 3 more large cars than small cars, then:

\(y = x + 3\)

Given each small car can hold 4 people, each large car can hold 6 people, and the total number of people that the rented cars could hold is 58, then:

\(4x + 6y = 58\)

Therefore, the system of equations is:

\(\begin{cases} y = x + 3\\4x + 6y = 58\end{cases}\)

To solve the system of equations, substitute the first equation into the second equation and solve for x:

\(\begin{aligned}4x+6(x+3)&=58\\4x+6x+18&=58\\10x+18&=58\\10x&=40\\x&=4\end{aligned}\)

Substitute the found value of x into the first equation and solve for y:

\(y=4+3\)

\(y=7\)

Therefore, the number of cars rented was:

Answer:

likley

Step-by-step explanation: edge 2021 on the quiz for me its question 6

Answer:

C. likely

Step-by-step explanation:

It is likely because if the bag holds red and green grapes then its not impossible to get a green grape because there are green grapes in the bag. It is not unlikly because there are 11/15 green grapes there, so there are more green grapes than red. But its still not certain that you will get a green grape, remember there are still quite a few red grapes too! So you would likely get a green grape.

I hope this helps!

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{k = 53}}}}}\)

Step-by-step explanation:

\( \bigstar{ \sf{ \: \: \frac{3 + k}{14} = 4}}\)

\( \tt{Step \: 1 \: }\) : Do cross multiplication

\( \hookrightarrow{ \sf{3 + k = 4 \times 14}}\)

\( \tt{Step \: 2}\) : Multiply the numbers : 4 and 14

\( \hookrightarrow{ \sf{3 + k = 56}}\)

\( \tt{Step \: 3 \: }\) Move 3 to right hand side and change it's sign

\( \hookrightarrow{ \sf{k = 56 - 3}}\)

\( \tt{Step \: 4 \: }\) Subtract 3 from 56

\( \hookrightarrow{ \sf{k = 53}}\)

The value of k is 53

Hope I helped!

Best regards! :D

~TheAnimeGirl

Answer:

Step-by-step explanation:

k/14 + 3 = 4

k/14 = 1

k = 14

Answer:

Its easy

Step-by-step explanation:

\(20 = 5 \times 4\)

\(20 = 5 \times x \\ x = 4\)

So we know the x is four so it will be like this

\(6 \times 4 =x \\ x = 24\)

So there were sold 24 chocolate milks

Hope this helps

Answer:

24

Step-by-step explanation:

because

5____6

20___x

Proportion: x=20*6/5=24

Answer:the answer is 16

Step-by-step explanation:

:) hi

Answer:25

Step-by-step explanation: Mangekyou Sharingan

Answer:

240 pencils

Step-by-step explanation:

10 (24) =  240

The definite integral in this problem has the value given as follows:

B. 42.

The definite integral in the context of this problem is given as follows:

\(\int_0^2 (x^7 + 5) dx\)

Applying the power of x integral rule, the result of the integral is given as follows:

\(\frac{x^8}{8} + 5x\)

At x = 2, the numeric value of the integral is given as follows:

\(\frac{2^8}{8} + 5(2) = 42\)

At x = 0, the numeric value of the integral is given as follows:

0.

(as both terms involve a multiplication by x and x = 0).

Applying the Fundamental Theorem of Calculus, the result of the integral is given as follows:

42 - 0 = 42.

Hence option B is the correct option in the context of this problem.

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Answer:

mx is the slope. b is the y-intercept

Step-by-step explanation:

the first thing you should always do is identify your slope this is key for graphing. remember your slope is b so what ever b is you locate that point in the x axis.

then whatever your slope is remember that it is rise over run so say your equation is y=3x+5 you plot the point on the y intercept which is 5. now 3x is your slope so you put it as a fraction to make it easier this is what it looks like in a fraction "3/1" so you go up 3 on the graph and over 1 because of rise/run

Answer:

3a-2a+7-4

a+3

Step-by-step explanation:

like and unlike terms arranging

and add and subtraction

Applying the knowledge of quotient and fractions, we have:

The number of soda each person will drink is: \(1\frac{2}{3} \) glasses.

The fraction of sugar to be used per cupcake is: \(1\frac{3}{5} \)

Problem 1:

The expression that matches the situation is: 7 ÷ 3 (quotient of 7 and 3)

7/3 = \(1\frac{2}{3} \)

The number of soda each person will drink is: \(1\frac{2}{3} \) glasses.

Problem 2:

The expression that matches the situation is: 8 ÷ 5 (quotient of 8 and 5)

8/5 = \(1\frac{3}{5} \)

The fraction of sugar to be used per cupcake is: \(1\frac{3}{5} \)

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Answer:

Statement H : The difference of 2/8 is reasonable because 1 – 3/4 = 1/4 .

Step-by-step explanation:

Given - Gina subtracted 6/8 from 1 and found a difference of 2/8 .

To find - Which statement best describes the difference of 6/8 from 1 is 2/8 ? Statement F : The difference of 2/8 is not reasonable because 1 – 3/4 = 1/4 .

Statement G : The difference of 2/8 is reasonable because 3/4 – 1/4  = 1/2 .

Statement H : The difference of 2/8 is reasonable because 1 – 3/4 = 1/4 .

Statement J : The difference of 2/8 is not reasonable because 3/4 – 1/4 = 1/2 .

Proof -

If we subtract 6/8 from 1 , we get

\(1 - \frac{6}{8} = \frac{8 - 6}{8} = \frac{2}{8}\)

So, the difference is 2/8

It is reasonable.

So,

The correct statement is - Statement H : The difference of 2/8 is reasonable because 1 – 3/4 = 1/4 .

Reason -

As we can write

\(\frac{6}{8} = \frac{3}{4}\) and \(\frac{2}{8} = \frac{1}{4}\)

So,

either we subtract 6/8 from 1 or 3/4 from 1 , we get the same result because both the values are equal

So the correct statement is - H : The difference of 2/8 is reasonable because 1 – 3/4 = 1/4 .

Question D. Highlight -1, -2, -3, -4, -5, 0, 1, 2, 3

Question C. Highlight -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6

Question B. Highlight 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10

Answer:

commutative property of addition

Step-by-step explanation:

Name the property used: commutative property of additionAnswer: commutative property of addition