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Step-by-step explanation:

1/2×2/2

2/4

2/3×2/2

4/6

The following can be shown about the diagonals of parallelogram PQRS to compare the proof that diagonals of a parallelogram bisect each other: B. PR and SQ have the same midpoint.

In Mathematics and Geometry, a parallelogram is a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

In order for any quadrilateral to be considered as a parallelogram, two pairs of its parallel opposite sides must be equal (congruent). This ultimately implies that, the diagonals of a parallelogram would bisect one another only when their midpoints are the same:

(Line segment PR)/2 = (Line segment SQ)/2

Line segment PR = Line segment SQ

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The Probability of red light is 0.3

P(red) = 0.3

The probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light be 0.25.

P(exactly three get stopped by red light)=0.25

The correct option is (d) P(red)=.3,P(exactly 3 get stopped)=.25

A binomial distribution can be thought of as simply the probability of a SUCCESS or FAILURE outcome in an experiment or survey that is repeated multiple times.

The occurrence,

p= probability of a red light

 =\(\frac{15}{15+5+30}\)

 = \(\frac{15}{50}\)

 = 0.3

Hence, Probability of getting red light be,

P (red)= 0.3

Now, the Binomial distribution formula,

Probability=( \(_r^nC\))\(\;p^{r} \;q^{n-r}\)

where, r = number of times for a specific outcome within n trials

\(_r^nC\)   = number of combinations

p = probability of success on a single trial

q = probability of failure on a single trial

n = number of trial

According to question,

          = 1- 0.3

          = 0.7

Now using the formula, ( \(_r^nC\))\(\;p^{r} \;q^{n-r}\)

P( exactly 3  get stopped) = ( \(_3^8C\))\(\;(0.3)^{3} \;(0.7)^{8-3}\)

                                            = \(\frac{8!}{3!(8-3)!}\) \((0.027) \; (0.7)^{5}\)

                                           =  \(\frac{8!}{3!(5)!}\)\((0.027) \; (0.16807)\)

                                           = \(\frac{8 * 7 * 6 }{3 * 2}\) x 0.027 x 0.16807

                                           = 56 x 0.00453789

                                           = 0.25412184

                                          ≈ 0.25

Hence, Probability of next eight eastbound so that exactly three will stopped by a red light be 0.25.

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Answer:

B. 50

Step-by-step explanation:

Answer:

B. 50

Step-by-step explanation:

52 = 4/5m + 12

52 - 12 = 4/5m

40 = 4/5m

40 : 4/5 = m

40 x 5/4 = m

200/4 = m

50 = m

The definite integral of 0.2 * x^5 from 0 to 1, approximated to six decimal places using a power series, is 0.033333.

The definite integral of 0.2 * x^5 from 0 to 1 using a power series with an accuracy of six decimal places. To do this, we can use the power series representation of the integrand and then integrate term by term.

1. Find the power series representation of the integrand:
The integrand is a polynomial, 0.2 * x^5, so its power series representation is simply itself.

2. Integrate term by term:
Now, we integrate the power series term by term. In this case, we have only one term, which is 0.2 * x^5.
∫(0.2 * x^5) dx = (0.2/6) * x^6 + C = (1/30) * x^6 + C

3. Evaluate the definite integral:
Now, we can find the definite integral by evaluating the antiderivative at the given limits (0 and 1):
i = [(1/30) * (1^6)] - [(1/30) * (0^6)] = (1/30)

4. Convert to a decimal:
i ≈ 0.033333

Thus, the definite integral of 0.2 * x^5 from 0 to 1, approximated to six decimal places using a power series, is 0.033333.

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Answer:

254.34

Step-by-step explanation:

\(r^{2}\)x3.14(\(\pi\))

so then substitute

9x9=81

81x3.14=254.34

Answer:

Classify the sequence {1, 6, 11, 16, 21, …}.

The pattern is +5:

1 + 5 = 6

6 + 5 = 11

11 + 5 = 16

16 + 5 = 21

21 + 5 = 26

And so on

Step-by-step explanation:

You're welcome

Answer:

-6200-2150+4780

-8350+4780

Overall, they lost $3570

The loan amount that Ahmad needs to relay will be RM 901600

From the information, Ahmad obtained a car loan of RM 700000 from a bank with an interest rate of 3.2% per annum for 9 years.

The interest based on the information will be:

= Principal × Rate × Time

= 700000 × 3.2% × 9

= $201600

The loan amount that Ahmad needs to relay will be:

= 700000 + 201600

= 901600

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Answer:

Use n(u) formula of chapter sets

Step-by-step explanation:

Have a good day

11 students were majoring in math only; 13 students were not majoring in computer science; and 2 students were not math or computer science majors.

Given that in a class of 25 students, 18 were math majors, 12 were computer science majors, and 7 were dual majors in math and computer science, to determine A) how many students were majoring in math only; B) how many students were not majoring in computer science; and C) how many students were not math or computer science majors; the following calculation must be performed:

Therefore, 11 students were majoring in math only; 13 students were not majoring in computer science; and 2 students were not math or computer science majors.

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Answer:

A. National Labor Relations Act

Step-by-step explanation:

Answer:

-1/10 < 1/2 < 0.666666666 < √12 < 6.33333

Step-by-step explanation:

You have to covert them to decimal

-1/10=-0.1

1/2= 0.5

0.666666666=0.666666666

√12 =3.464

6.33333=6.33333

Answer:

(B) 2x5x7

Step-by-step explanation:

Answer:

B

hope this helps! :)

Answer:

hii

x=30

Step-by-step explanation:

x+3x+5x-90=180

9x=270

x=30

Answer:

set everything equal to itself, like for #3 do 7x+14=9x-2 and solve for x, the same goes for the first two

Step-by-step explanation:

follow my insta anthony.cb8

Answer:

x= 0.0505 or 101/2000

Explanation:

Using Inverse Operations Do The Equation

-1+1=0

100+1=101

2000×=101

2000x/2000=x

101/2000

-

Answer: x=101/2000

Answer:

The distributive property states that 5×(7+6)= 5(7)+5(6). 5(7)+5(6)=35+30, so the answer is 65.

Answer:

65

Step-by-step explanation:

5x7=35

5x6=30

35+30=65

or

7+6=13

13x5=65

Answer: Both p and q are 8cm long.

Step-by-step explanation:

BE created a similar triangle that is exactly half of the larger triangle.

So if BE is 4 and AE is 8 then we know that CD is 8 and AD is 16.

However we only need segment q which is half of AD so the answer is:

p=8 and q=8

;)

The Ministry of Education can make informed decisions about the project's continuation, adjustments, or expansion to further promote math participation and achievement among high school students.

The Ministry of Education is launching a project aimed at encouraging high school students to participate more in math. The project involves two schools, and their performance over the term has been collected.

To further analyze and evaluate the project, we can follow these steps:

Collect and analyze the performance data: Examine the collected performance data from the two schools involved in the project. Look at various metrics such as test scores, participation rates, improvement over time, and overall engagement in math-related activities.

Identify patterns and trends: Analyze the data to identify any patterns or trends in the performance of the students. Look for variations between the two schools and assess whether there are any notable differences in their math participation and performance.

Assess the effectiveness of the project: Compare the performance data before and after the implementation of the project. Evaluate if there has been a positive impact on math participation and performance in both schools. Consider factors such as increased student engagement, improved test scores, and a higher level of interest and involvement in math-related activities.

Make informed decisions: Based on the analysis of the performance data and the assessment of the project's effectiveness, the Ministry of Education can make informed decisions about the project's continuation, adjustments, or expansion to further promote math participation and achievement among high school students.

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I) and II) are true because the limit of the function at x=2 is 5, which implies that f is continuous and differentiable at x=2. III) is false because the derivative of f does not need to be continuous at x=2.

Let f be a function such that lim h→0 (f(2+h) - f(2)) / h = 5.

We can calculate this limit as follows:

lim h→0 (f(2+h) - f(2)) / h = lim h→0 (f(2+h) / h) - (f(2) / h)

= lim h→0 f(2+h) / h - lim h→0 f(2) / h

= lim h→0 f(2+h) / h - 0

= lim h→0 f(2+h) / h

= 5

Therefore, I) and II) are true because the limit of the function at x=2 is 5, which implies that f is continuous and differentiable at x=2. III) is false because the derivative of f does not need to be continuous at x=2.

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100 miles is the distance we know traveled in 2 hours. Therefore we can make this equation:

100 = 2x

100 / 2 =x

50 = x

We travel 50 miles an hour.

Now we know the x, 3.5 so lets plug that in:

3.5x = y

3.5(50) = y

175 = y

Therefore we travelled 175 miles in 3.5 hours.

I hope this helps! :)

Answer:

The speed is distance / time and speed times time equals distance

Step-by-step explanation:

speed = 100/2=50 mi/hr

distance =f(t)=50t

f(3.5)=50×3.5=175miles

hope that helps

Answer:

im stuck on this to

Step-by-step explanation:

Answer:

1656

Step-by-step explanation:

Length of room, l = 3x + 1 ft.

Breadth of room, b = x² -1 ft.

Now, it is given that university wants each room to have 195 ft² of living space.

So,

\(lb = A\\\\(x^2-1)(3x+1)=195\\\\3x^3+x^2-6x-1=195\\\\3x^3+x^2-6x-196=0\)

So, above equation has two complex root and one real root i.e x = 4.08 ft .

Therefore, Length of room is 13.24 ft and breadth is 15.65 ft.

Hence, this is the required solution.

Answer:

ans) 4G and 6/x+y

Step-by-step explanation:

10) it says the product of both so when both multiply each other , we get the product

An equation is formed when two equal expressions. The solution of the system of equation is (-3,1).

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Multiply the first equation by 2 and the other equation by -3. Therefore, the two equations will be,

         14x - 18y = -60

         9x + 18y = -9

Add the two equations,

14x - 18y + 9x + 18y = -9 -60

23x = -69

x = -3

Substitute the value of x in any one of the two given equations,

7(-3) - 9y =-30

-21 - 9y = -30

-9y = -9

y = 1

Hence, the solution of the system of equation is (-3,1).

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It would take Jimbo 24 minutes to solve a 3-variable substitution problem alone.

Let's assume that Jimbo takes x minutes to solve a 3-variable substitution problem alone.

We know that Jimmy takes 8 minutes to solve the same problem alone, so his work rate is 1/8 of the problem solved per minute.

Together, Jimbo and Jim Bob can solve the same problem in 6 minutes. This means that their combined work rate is 1/6 of the problem solved per minute.

We can set up the following equation to represent the work rates:

1/8 + 1/x = 1/6

To solve for x, we can multiply both sides of the equation by 24x:

3x + 24 = 4x

x = 24

Therefore, it would take Jimbo 24 minutes to solve a 3-variable substitution problem alone.

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Thus, we can write that the value of λ=3 is an eigenvalue of the given matrix A and the corresponding eigenvector is v=[-2 5 1]T.

Given matrix is:\($$A = \begin {bmatrix} 2 & 0 & -1 \\ 2 & 2 & 3 \\ -4 & 3 & -4 \end {bmatrix}$$\)Now, to check whether λ = 3 is an eigenvalue of the given matrix A, we will find the determinant of the matrix (A - λI), where I is the identity matrix. If the determinant is zero, then λ is an eigenvalue of the matrix A. The matrix (A - λI) is\(:$$\ {bmatrix} 2 - 3 & 0 & -1 \\ 2 & 2 - 3 & 3 \\ -4 & 3 & -\)end {bmatrix}$$Now, finding the determinant of the above matrix using the cofactor expansion along the first row:$${\begin{aligned}\det(A-\lambda I)&=-1\cdot \begin{vmatrix} -1 & 3 \\ 3 & -7 \end{vmatrix}-0\cdot \begin{vmatrix} 2 & 3 \\ 3 & -7 \end{vmatrix}-1\cdot \begin{vmatrix} 2 & -1 \\ 3 & 3 \end{vmatrix}\\&=-1((1\cdot -7)-(3\cdot 3))-1((2\cdot 3)-(3\cdot -7))\\&=49\end{aligned}}$$Since the determinant is non-zero, hence λ = 3 is an eigenvalue of the matrix A.

Now, to find the corresponding eigenvector, we will solve the equation (A - λI)v = 0, where v is the eigenvector and 0 is the zero vector. The equation becomes:\($$\begin{bmatrix} -1 & 0 & -1 \\ 2 & -1 & 3 \\ -4 & 3 & -7 \end{bmatrix}\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}$$$$\Rightarrow -x - z = 0$$$$2x - y + 3z = 0$$$$-4x + 3y - 7z = 0$$\)Solving the above system of equations using substitution method, we get y = 5z and x = -2z. Taking z = 1, we get the eigenvector as\(:$$v = \begin{bmatrix} -2 \\ 5 \\ 1 \end{bmatrix}$$\)Therefore, λ = 3 is an eigenvalue of the given matrix A and the corresponding eigenvector is v = [-2 5 1]T.

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