Help me please I will give 20 points and mark u as brainliest

Answer:

∠A = 90  

∠B = 30

∠C = 60

Step-by-step explanation:

Let ∠B = x

∠A = 3x

∠C = x + 30

Angle sum property of triangle: Sum of three angles of triangle is 180

x + 3x + x + 30 = 180   {Combine like terms}

         5x  + 30 = 180

                    5x = 180 - 30

                   5x = 150

                     x = 130/5

x = 30

∠A = 3*30 = 90

∠C = 30 + 30 = 60

Answer:

if both the shorter ends are as long as or longer than the longer end when combined.

Step-by-step explanation:

Answer:

Exact: A = (3.28 + 8π) cm²

Approximate: A = 57.13 cm²

Step-by-step explanation:

The right part of the red figure is a rectangle which is half of the square.

The left half of the red figure is a semicircle.

A = LW + ½πr²

A = (4 cm)(8 cm) + ½(π)(4 cm)²

A = (32 + 8π) cm² (exact)

A = 57.13 cm² (approximate)

In a certain fraction, let the numerator be x and the denominator be x + 4. By adding 5 to both the numerator and denominator, the resulting fraction is 6/10. The original fraction can be found by solving the given conditions.

Let's assume the original fraction is x/(x + 4). According to the given conditions, when we add 5 to both the numerator and denominator, we get (x + 5)/(x + 4 + 5) = 6/10. Simplifying this equation, we have (x + 5)/(x + 9) = 6/10.

To solve this equation, we can cross-multiply, which gives us 10(x + 5) = 6(x + 9). Expanding and simplifying, we get 10x + 50 = 6x + 54. Further simplification leads to 4x = 4, and dividing both sides by 4 gives x = 1.

Therefore, the original fraction is 1/(1 + 4), which simplifies to 1/5. Hence, the original fraction is 1/5.

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a) it takes 9.61 seconds for the automobile to overtake the truck. b) The automobile was initially 165.34 meters behind the truck. c) During the overtaking, the speed of the truck is 21.142 m/s, and the speed of the automobile is 33.635 m/s.

To solve this problem, we can use the equations of motion to calculate the time it takes for the automobile to overtake the truck, the initial distance between them, and their speeds during the overtaking.

Let's denote the time it takes for the automobile to overtake the truck as t.

(a) For the truck:

Using the equation of motion s = ut + (1/2)a\(t^{2}\), where s is the distance covered, u is the initial velocity (0 in this case), a is the acceleration (2.2 m/s^2), and t is the time, we can find the distance covered by the truck when the automobile overtakes it.

s_truck = (1/2) * 2.2 * \(t^{2}\)

s_truck = 1.1 *  \(t^{2}\)

For the automobile:

s_automobile = (1/2) * 3.5 * \(t^{2}\)

s_automobile = 1.75 *  \(t^{2}\)

Given that the truck has moved 60 m when the automobile overtakes it, we can set up the equation:

s_truck = s_automobile + 60

1.1 *  \(t^{2}\)  = 1.75 *  \(t^{2}\)  + 60

Simplifying the equation:

0.65 *  \(t^{2}\)  = 60

\(t^{2}\)  = 60 / 0.65

\(t^{2}\)  ≈ 92.3077

t ≈ √92.3077

t ≈ 9.61 seconds

Therefore, it takes approximately 9.61 seconds for the automobile to overtake the truck.

(b) To find the initial distance between the automobile and the truck, we can substitute the value of t into either of the equations:

s_automobile = (1/2) * 3.5 *  \(t^{2}\)

s_automobile = (1/2) * 3.5 * \((9.61)^{2}\)

s_automobile ≈ 165.34 meters

Therefore, the automobile was initially approximately 165.34 meters behind the truck.

(c) To find the speeds of the automobile and the truck during overtaking, we can use the equation of motion v = u + at, where v is the final velocity, u is the initial velocity (0 in this case), a is the acceleration, and t is the time.

For the truck:

v_truck = 0 + 2.2 * 9.61

v_truck ≈ 21.142 m/s

For the automobile:

v_automobile = 0 + 3.5 * 9.61

v_automobile ≈ 33.635 m/s

Therefore, during the overtaking, the speed of the truck is approximately 21.142 m/s, and the speed of the automobile is approximately 33.635 m/s.

Correct Question :

An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. Then truck has a constant acceleration of 2.2 m/s2 and the automobile has an acceleration of 3.5 m/s 2. The automobile overtakes the truck when it (truck) has moved 60 m.

(a) How much time does it take to automobile to overtake the truck?

(b) How far was the automobile behind the truck initially?

(c) What is the speed of each during overtaking?

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Answer:

(4,-2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

P jkijm

Answer:

145 degrees

The correct answer is C

Sebastian is incorrect. The correct greatest common factor of the given expression is 9mn.

The greatest common factor (GCF) of a set of numbers refers to the largest factor that all the numbers shares. The greatest common factor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For an expression, the greatest common factor is the largest expression that is a factor of all the expressions. In the given expression, 27m²n + 36m³n³ + 18mn⁴, take out the common factor out.

27m²n + 36m³n³ + 18mn⁴

Take out 3

3(9m²n + 12m³n³ + 6mn⁴)

As the expression can be divided by three again, Take out 3

3*3(3m²n + 4m³n³ + 2mn⁴)

9(3m²n + 4m³n³ + 2mn⁴)

Similarly,

Take out m

9m(3mn + 4 m²n³ + 2n⁴)

Take out n

9mn(3m + 4 m²n2 + 2n3)

Hence, the common greatest factor is 9mn and not 9m²n⁴.

Note: The question is incomplete. The complete question probably is: Sebastian wants to factor the greatest common factor out of the expression, 27m²n + 36m³n³ + 18mn⁴. Sebastian determines that the greatest common factor is 9m²n⁴. Is Sebastian correct? If he is, explain why. If he is not correct, determine the correct answer and explain your reasoning.

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(0, -2) is a point and 2 is the slope of the line represented by the equation: y - 2 = 2(x - 3).

How to find a point in a given line?
A point in a given line can be found out by substituting either the value of 'x' or 'y' and then solving the given equation to find the value of the other corresponding variable.
How to find the slope of a given line?
For a line having the equation as y = mx + c, the slope for the same can be defined with the mathematical value of 'm'.

Given,
The line is: y - 2 = 2*(x - 3) ⇒ y = 2 + 2x - 6 = 2x + (-4) ⇒ y = 2x + (-4) --(i)
For x = 0 in (i), y will be: y = 2(1) + (-4) = 2 - 4 = -2
Therefore, (0, -2) is a point on the line given by y - 2 = 2*(x - 3)
Also, on comparing the equation in (i), with the equation established in the literature above, we have:
m = slope of line = 2
∴ The slope of the given line is 2.
Thus, (0, -2) is a point and 2 is the slope of the line represented by the equation: y - 2 = 2(x - 3).

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Answer:

Solution :  (− 3, 5, 6)

Step-by-step explanation:

We have the following system of equations that we have to solve for,

\(\begin{bmatrix}x+3y-z=6\\ 4x-2y+2z=-10\\ 6x+z=-12\end{bmatrix}\)

To solve this problem we can start by writing the matrix with their respective coefficients --- (1)

\(\begin{bmatrix}1&3&-1&|&6\\ 4&-2&2&|&-10\\ 6&0&1&|&-12\end{bmatrix}\)

Now we can reduce this to row echelon form, receiving our solution --- (2)

\(\begin{pmatrix}1&3&-1&6\\ 4&-2&2&-10\\ 6&0&1&-12\end{pmatrix}\) Swap row 1 and 3,

\(\begin{pmatrix}6&0&1&-12\\ 4&-2&2&-10\\ 1&3&-1&6\end{pmatrix}\) Cancel leading coefficient in row 3,

\(\begin{pmatrix}6&0&1&-12\\ 0&-2&\frac{4}{3}&-2\\ 0&3&-\frac{7}{6}&8\end{pmatrix}\) Swap row 2 and 3

\(\begin{pmatrix}6&0&1&-12\\ 0&3&-\frac{7}{6}&8\\ 0&-2&\frac{4}{3}&-2\end{pmatrix}\) Cancel leading coefficient in row 3

\(\begin{pmatrix}6&0&1&-12\\ 0&3&-\frac{7}{6}&8\\ 0&0&\frac{5}{9}&\frac{10}{3}\end{pmatrix}\)

At this point you can see that we have to cancel the leading coefficient in each row, to row echelon form. Continuing this pattern we have the following matrix,

\(\begin{bmatrix}1&0&0&|&-3\\ 0&1&0&|&5\\ 0&0&1&|&6\end{bmatrix}\)

As you can see, x = - 3, y = 5, and z = 6, giving us a solution of (− 3, 5, 6). This is the fourth option.

The sampling technique used in each study is as follows: (a) convenience sampling, (b) systematic sampling, and (c) stratified random sampling.

(a) In the first study, where a journalist goes to a campground to ask people about their feelings regarding air pollution, the sampling technique used is convenience sampling. This is evident because the journalist approaches individuals who are readily available and easily accessible at the campground. However, convenience sampling may introduce bias as it does not ensure a representative sample of the population.

(b) In the second study, where every tenth machine part is selected from an assembly line for measurement, the sampling technique used is systematic sampling. Systematic sampling involves selecting every nth element from a population after establishing a sampling interval. In this case, every tenth machine part is selected to ensure a systematic and unbiased approach to quality assurance.

(c) In the third study, where attitudes about smoking are studied at a college and students are divided by class and then randomly sampled from each class for interviews, the sampling technique used is stratified random sampling. Stratified random sampling involves dividing the population into homogeneous subgroups (strata) and then randomly selecting samples from each subgroup. By dividing the students into different class strata and randomly selecting samples from each class, this study aims to ensure representation from each class in the final sample.

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The selection chances and the required probability for 9 women and 6 men is given by ,

Different groups of applicants selection = 3003

Selection of trainee entirely of women = 126

Probability of selection of entirely women from 15 people = 4.19%

Total number of women = 9

Total number of men = 6

Total = 9 + 6

        = 15

The total number of groups of applicants that can be selected for the positions can be calculated using the combination formula,

nCr = n! / r!(n-r)!

where n is the total number of applicants (15),

And r is the number of positions to be filled (5).

Number of different groups of applicants that can be selected for the positions is,

15C5

= (15! )/(15-5)!5!

=(15! )/(10)!5!

= 3003

Number of different groups of trainees that consist entirely of women can be calculated by selecting 5 women from the 9 available,

9C5

= (9! )/(9-5)!5!

=(9! )/(4)!5!

= 126

Probability of selecting a group of five trainees ,

Consist entirely of women can be calculated by dividing the number of different groups of all-women trainees (126) by the total number of different groups of trainees (3003),

Required probability

= 126/3003

≈ 0.0419

Probability that the trainee class will consist entirely of women is approximately 0.0419, or 4.19% (rounded to four decimal places).

Therefore, for a group of 15 people,

Selection of different groups of people = 3003

Selection of trainee represents entirely women =126

probability of selecting entirely women = 4.19%

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Answer:

D. -29.5

Step-by-step explanation:

−14.160÷−0.48

Expand -14.16 over -0.48 by multiplying both numerator and the denominator by 100.

-1416 / -48

and lastly reduce the fraction -1416 / -48 to lowest terms by extracting and canceling out -24 to get 592/2 and

59/2 = 29 1/2 = 29.5

Given:

Simplife:

The given simplifies equation is:

After the compare the both inequality:

a=2

b=2

c=2

d=6

e=1

f=9

The angle ACS is equal to the sum of the angles ACR adn RCS.

The first option is the correct one:

mSCR+mRCA = mSCA

The false statement based on the given interval is: c) The sample average is 36 inches.

In the given information, the 90% confidence interval for the average annual precipitation in the US is stated as 33 inches to 39 inches. This interval is calculated based on a random sample of 100 US cities.

The midpoint of the confidence interval, (33 + 39) / 2 = 36 inches, represents the sample average or the point estimate for the average annual precipitation in the US. It is the best estimate based on the given sample data.

Therefore, statement c) "The sample average is 36 inches" is true, as it corresponds to the midpoint of the provided confidence interval.

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Answer:

322

Step-by-step explanation:

40a + b

40(8) + 2

320 + 2

322

Answer:

2x+1         (2,7)        

Step-by-step explanation:

y=mx+b

The room in the art gallery, as measured on the blueprint, is 3 1/2 inches long. To calculate its length in feet, we need to use the scale of 1 in : 4 ft. This means that for every 1 inch on the blueprint, there is 4 feet in the actual room.

To figure out the length of the room, we will need to multiply the length of 3 1/2 inches on the blueprint by 4 to get its length in feet. Thus, 3 1/2 inches on the blueprint is equal to 14 feet in the actual room. To double check this answer, we can divide the length of the room (14 feet) by the scale of 1 in : 4 ft., and it should equal 3 1/2 inches. 14 ft. / 4 ft. = 3 1/2 in.

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Answer:

10.5

Step-by-step explanation:

v=158

l×w×h =158

l×5×3=158

l×15=158

L =158÷15=10.5

The values of angles x and y in the trapezium are 48 and 115 degrees.

A trapezium is a quadrilateral with one pair of sides parallel to each other. Sum of angles pair between parallel line is 190 degrees.

Therefore, let's find x and y in the trapezium.

y + 132 = 180

subtract 132 from both sides of the equation

y + 132 - 132 = 180 - 132

y = 48 degrees

x + 65 = 180

subtract 65 from both sides of the equation

x + 65 - 65 = 180 - 65

x = 115 degrees.

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Answer:

he pays 24,00 and he is left with 56000

Step-by-step explanation:

100% = 80000

30%  = X

100%X= 2400000

2400000/100= 24,000

80,000-24,000= 56,000

(a) The solution be Bi = ∑ xi(yi - ßo)/xi

(b) The standard errors of the maximum likelihood estimators are given by the square roots of the diagonal elements of V.

(a) To derive the maximum likelihood estimators for ßo and Bi,

we have to find the values of Bo and Bi that maximize the likelihood function, which is given by,

⇒ L(ßo, 3₁) = (2π)-n/2 ∏\([di]^{(-1/2)}\) exp{-1/2 ∑(yi - ßo - Bixi)/di}

Taking the log of the likelihood function and simplifying, we get,

ln L(ßo, 3₁) = -(n/2) ln(2π) - 1/2 ∑ln(di) - 1/2 ∑(yi - ßo - Bixi)/di

To find the maximum likelihood estimators for ßo and Bi,

Take partial derivatives of ln L(ßo, 3₁) with respect to ßo and Bi,

set them equal to zero, and solve for ßo and Bi.

Taking the partial derivative of ln L(ßo, 3₁) with respect to ßo, we get,

⇒ d/dßo ln L(ßo, 3₁) = ∑ (yi - ßo - Bixi)/di = 0

Solving for ßo, we get,

⇒ ßo = (1/n) ∑ (yi - Bixi)/di

Taking the partial derivative of ln L(ßo, Bi) with respect to Bi, we get,

⇒ d/dBi ln L(ßo, Bi) = ∑xi(yi - ßo - Bixi)/di = 0

Solving for Bi, we get,

⇒ Bi = ∑ xi(yi - ßo)/xi

(b)

To compute the distribution of Bo and Bi,

we need to find the variance-covariance matrix of the maximum likelihood estimators.

The variance-covariance matrix is given by,

⇒ V =\([X'WX]^{-1}\)

where X is the design matrix,

W is the diagonal weight matrix with Wii = 1/di, and X' denotes the transpose of X.

The standard errors of the maximum likelihood estimators are given by the square roots of the diagonal elements of V.

The distribution of Bo and  Bi is assumed to be normal with mean equal to the maximum likelihood estimator and variance equal to the square of the standard error.

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Answer :

hmmm ... :0 ?

Answer:

true

Step-by-step explanation:

The weight of the plant on an nth day can be expressed as 2 x 3ⁿ⁻¹.

The weight of a certain plant is measured every day in a laboratory. The weight on the first day was 2g and on the following days was 6g, 18g, and 54g.

This question is asking to find out how to express the weight of the plant on an nth day. For this question, the formula for the nth term of a geometric sequence will be applied. The formula for the nth term of a geometric sequence is given by, an = a₁rⁿ⁻¹Where,a₁ = 2r = 3 (common ratio)n = nth term of the sequence. Putting values of a₁, r, and n in the

formula = a₁rⁿ⁻¹an = 2 x 3ⁿ⁻¹.

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The completed proof is presented as follows;

By definition of a rhombus \(\overline{JK} \cong \overline{KM}\) and by the reflexive property of

congruence \(\overline{KP} \cong \overline{KP}\), because the diagonals of a rhombus bisect a pair

of opposite angles, ∠JKP ≅ ∠MKP, making ΔJKP ≅ ΔMKP by the SAS

congruency postulate, because CPCTC, ∠JPK ≅ ∠MPK, and these angles

are right angles because two angles that form a linear pair are congruent,

thereby making, \(\overline{JK} \perp \overline{KM}\) by definition of perpendicular segments.

Reasons:

Please find attached the drawing of the given rhombus JKMH, that show

the point of intersection of the diagonals JM and HK at point P.

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Answer:

B is the correct answer.

Step-by-step explanation:

Pi=3.14

So, 7+3.14=10.14

So yes, B is your correct answer.

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