Triangle ABC is a right triangle whose right angle is ZABC.
Find the measure of ZEBF.
ZABC and DBF are vertical angles, so they have the same
measure. Because IZABC is 90°, the sum of m2. DBE and
m2 EBF must also be 90°
Solve for x in this equation.
x + (x - 12) = 90
2x - 12 = 90
2x = 102
X51
m2 EBF = 51°

1.What is m
2.What is m
3.Explain how to find m

Answer:

= 0.0041

Step-by-step explanation:

Given that:

A farmer was interest in determining how many grasshoppers were in his field. He knows that the distribution of grasshoppers may not be normally distributed in his field due to growing conditions. As he drives his tractor down each row he counts how many grasshoppers he sees flying away

mean number of flights to be 57

a standard deviation of 12

fewer flights on average in the next 40 rows

[tex]\mu = 57\\\\\sigma=12\\\\n=40[/tex]

so,

[tex]P(x<52)[/tex]

[tex]=P(\frac{x-\mu}{\sigma/\sqrt{n} } <\frac{52-57}{12/\sqrt{40} } )\\\\=P(z<\frac{-5\times6.325}{12} )\\\\=P(z<\frac{-31.625}{12})\\\\=P(z<-2.64)[/tex]

using z table

= 0.0041

The probability of the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor is 0.0041 and this can be determined by using the properties of probability.

Given :

The probability of the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor, can be determined by using the following calculations:

[tex]\rm P(x<52)=P\left (\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n} }}<\dfrac{52-57}{\dfrac{12}{\sqrt{40} }}\right)[/tex]

[tex]\rm P(x<52)=P\left (z<\dfrac{-5\times 6.325}{12 }}\right)[/tex]

[tex]\rm P(x<52)=P\left (z<\dfrac{-31.625}{12 }}\right)[/tex]

[tex]\rm P(x<52)=P\left (z<-2.64\right)[/tex]

Now, using z-table:

P(x < 52) = 0.0041

For more information, refer to the link given below:

https://brainly.com/question/21586810

Answer:

[tex]y=\frac{3}{2} x-4[/tex]

Step-by-step explanation:

The graph I provided shows it passes thru (4,2) and that it is parallel

Answer:

y = 3/2x -4

Step-by-step explanation:

3x - 2y = - 6

First find the slope by putting it in slope intercept form

Subtract 3x from each side

-2y = -3x-6

Divide by -2

y = -3x/-2  -6/-2

y = 3/2x +3

The slope is 3/2

Parallel lines have the same slope

We have the slope 3/2 and a point (4,2)

y = mx+b where m is the slope and b is the y intercept

y =3/2x+b

Substitute the point into the equation

2 = 3/2(4) +b

2 = 6 +b

Subtract 6

2-6 = 6-6+b

-4 =b

y = 3/2x -4

Answer:

Top prism = 262 in.² Bottom prism = 478 in.²

Step-by-step explanation:

top prism:

front + back: 5 x 3 = 15

sides: 19 x 4 x 2 = 152

bottom: 19 x 5 = 95

15 + 152 + 95 = 262

bottom prism:

front + back: 5 x 6 x 2 = 60

sides: 19 x 6 x 2 = 228

top + bottom: 19 x 5 x 2 = 190

60 + 228 + 190 = 478

Answer:

8 + 15i

Step-by-step explanation:

(-2 + 3i) + 2(5 + 6i) =

= -2 + 3i + 10 + 12i

= 8 + 15i

Answer:

The data support the hypothesis that the proportion of defectives is lower for robots than humans.

Step-by-step explanation:

To know if the proportion of defectives is lower for robots than humans so as to prove if the hypothesis is true.

From the data given:

Total number of cables a robot assembled = 507

Defectives = 9

To get the defect rate =  the number of defects divided by the total number of cables, multiplied by 100.

Defect rate =  (9 / 507) x 100 = 0.01775 x 100

Defect rate for the robot = 1.775‬%

From the question, a robot was used and the defect rate after the calculation is 1.775‬%. While for humans, the defect rate is 3.5%. This implies, if humans were used to assembling the same 507 cables, there will be 17.745‬ defectives.

x / 507 = 3.5%

x (defectives) = 17.745‬

Therefore, the data support the hypothesis that the proportion of defectives is lower for robots than humans.

Corrected Question

At the beginning of the season, Jamie pays full price($49.64) for a ticket to see the panthers, her favorite baseball team. Ticket prices decrease $0.41 for every game the panthers lose this season. the panthers currently have 33 wins and 31 losses.

(a)Represent the total change in the cost of a ticket given their losses.

(b) What is the cost of a ticket for the next game they play?

Answer:

(a)$(49.64-0.41x)

(b)$36.93

Step-by-step explanation:

(a)Cost of a Full Ticket =$49.64

Let x be the number of losses

The ticket price reduces by $0.41 for every loss

Therefore:

Ticket Price after x losses =$(49.64-0.41x)

Therefore, total change in the cost of a ticket given their losses=$(49.64-0.41x)

(b)For this season the Panthers has suffered 31 losses.

Number of Losses, x=31

Therefore, cost of a ticket for the next game they play

= $(49.64-0.41*31)

=49.64-12.71

=$36.93

Answer:

The maximum height reached by the rocket is of 938.56 feet.

Step-by-step explanation:

The height y, after x seconds, is given by a equation in the following format:

[tex]y(x) = ax^{2} + bx + c[/tex]

If a is negative, the maximum height is:

[tex]y(x_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

In this question:

[tex]y(x) = -16x^{2} + 230x + 112[/tex]

So

[tex]a = -16, b = 230, c = 112[/tex]

Then

[tex]x_{v} = -\frac{230}{2*(-16)} = 7.1875[/tex]

[tex]y(7.1835) = -16*(7.1835)^{2} + 230*7.1835 + 112 = 938.56[/tex]

The maximum height reached by the rocket is of 938.56 feet.

Answer:

  parallel lines both have slope 1/3; non-parallel lines both have length 5

Step-by-step explanation:

It generally works well to follow instructions.

A graph of the points shows you that the parallel sides are RA and PT. The difference between the end points of these segments are ...

  A - R = (6, 8) -(-3, 5) = (9, 3) = (Δx, Δy)

So, the slope of RA is Δy/Δx = 3/9 = 1/3

And the other difference and slope are ...

  P -T = (9, 4) -(-3, 0) = (12, 4)   ⇒   Δy/Δx = 4/12 = 1/3

The slope of RA is the same as the slope of PT, so those segments are parallel.

__

The length of segment TR can be found from the differences of the end point coordinates:

  R - T = (-3, 5) -(-3, 0) = (0, 5)

Since these points are on the same vertical line, this tells us the segment length is 5.

The other difference of coordinates is ...

  A - P = (6, 8) -(9, 4) = (-3, 4)

The distance formula tells us the length of AP is then ...

  AP = √((-3)² +4²) = √25 = 5

Non-parallel sides TR and AP have the same lengths, so the trapezoid is isosceles.

Answer:

30%

Step-by-step explanation:

fat ÷ total

15 ÷ 50

.3

30%

Answer:

30%

Step-by-step explanation:

To find the percent from fat, take the calories from fat and divide by the total

15/50

.3

Multiply by 100%

30%

Answer:

The integral is

∫ˣ²ₓ₁ 2π cos 2x √[1 + 4 sin² 2x] dx

x₁ = (-π/5)

x₂ = (π/5)

And the area of the surface generated by revolving = 9.71 square units

Step-by-step explanation:

When a function y = f(x) is revolved about the x-axis, the formula for the area of the surface generated is given by

A = 2π ∫ˣ²ₓ₁ f(x) √[1 + (f'(x))²] dx

A = 2π ∫ˣ²ₓ₁ y √[1 + y'²] dx

For this question,

y = cos 2x

x₁ = (-π/5)

x₂ = (π/5)

y' = -2 sin 2x

1 + y'² = 1 + (-2 sin 2x)² = (1 + 4 sin² 2x)

So, the Area of the surface of revolution is

A = 2π ∫ˣ²ₓ₁ y √[1 + y'²] dx

= ∫ˣ²ₓ₁ 2πy √[1 + y'²] dx

Substituting these variables

A = ∫ˣ²ₓ₁ 2π cos 2x √[1 + 4 sin² 2x] dx

Let 2 sin 2x = t

4 cos 2x dx = dt

2 Cos 2x dx = (dt/2)

dx = (1/2cos 2x)(dt/2)

Since t = 2 sin 2x

when x = (-π/5), t = 2 sin (-2π/5) = -1.90

when x = (π/5), t = 2 sin (2π/5) = 1.90

A

= ∫¹•⁹⁰₋₁.₉₀ π (2 Cos 2x) √(1 + t²) (1/2cos 2x)(dt/2)

= ∫¹•⁹⁰₋₁.₉₀ (π/2) √(1 + t²) (dt)

= (π/2) ∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)

But note that

∫ √(a² + x²) dx

= (x/2) √(a² + x²) + (a²/2) In |x + √(a² + x²)| + c

where c is the constant of integration

So,

∫ √(1 + t²) dt

= (t/2) √(1 + t²) + (1/2) In |t + √(1 + t²)| + c

∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)

= [(t/2) √(1 + t²) + (1/2) In |t + √(1 + t²)|]¹•⁹⁰₋₁.₉₀

= [(1.90/2) √(1 + 1.90²)+ 0.5In |1.90+√(1 + 1.90²)|] - [(-1.9/2) √(1 + -1.9²) + (1/2) In |-1.9 + √(1 + -1.9²)|]

= [(0.95×2.147) + 0.5 In |1.90 + 2.147|] - [(-0.95×2.147) + 0.5 In |-1.90 + 2.147|]

= [2.04 + 0.5 In 4.047] - [-2.04 + 0.5 In 0.247]

= [2.04 + 0.70] - [-2.04 - 1.4]

= 2.74 - [-3.44]

= 2.74 + 3.44

= 6.18

Area = (π/2) ∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)

= (π/2) × 6.18

= 9.71 square units.

Hope this Helps!!!

Answer:

sorry'but I don't know the answer

Step-by-step explanation:

a rectangle has reflectional symmetry when reflected over the line through the midpoints of its opposite sides

Answer: A square always has a four reflection symmetry no matter the size.

Answer:

3

Step-by-step explanation:

0 pairs mean when two "boxes" add together to make 0. For the x's we only have one because x + (-x) = x - x = 0. For the other ones we have two (the + means 1 and the - means -1) because 1 + (-1) = 1 - 1 = 0. Therefore the answer is 1 + 2 = 3.

Answer:

This has multiple answers, A, C, And D

Step-by-step explanation:

Answer:

It is definitely A, C, and D.

Step-by-step explanation:

I just answered this question and got it right. I hope this helps and please mark brainliest!

Answer: B

Step-by-step explanation:

For this problem, to solve for x, you want to move all like terms to one side.

[tex]\frac{1}{4}x-\frac{1}{2}x=\frac{7}{8} +\frac{1}{8}[/tex]

Now that you have moved like terms to one side, you can directly add and subtract to combine like terms.

[tex]-\frac{1}{4} x=1[/tex]

x=-4

Answer:

[tex]x = - 4[/tex]

Second answer is correct

Step-by-step explanation:

[tex] \frac{1}{4} x - \frac{1}{8} = \frac{7}{8} + \frac{1}{2} x \\ \frac{1}{4} x - \frac{1}{2} x = \frac{1}{8} + \frac{7}{8} \\ \frac{1x - 2x}{4} = \frac{8}{8} \\ - \frac{1}{4} x = 1 \\ - 1x = 1 \times 4 \\ - 1x = 4 \\ x = - 4[/tex]

hope this helps you

Answer:

[tex] x =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

Where a = 2 , b= 3, c= -5, replacing we have this:

[tex]x =\frac{-3 \pm \sqrt{(-3)^2 -4(2)(-5)}}{2*2}[/tex]

And simplifying we got:

[tex] x = \frac{-3 \pm \sqrt{49}}{4}[/tex]

And the two solutions are:

[tex] x_1 = \frac{-3+7}{4}= 1[/tex]

[tex] x_2 = \frac{-3-7}{4}= -\frac{5}{2}[/tex]

And the correct options are:

B and C

Step-by-step explanation:

We have the following equation given:

[tex] 2x^2 +3x -5=0[/tex]

And if we use the quadratic formula given by:

[tex] x =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

Where a = 2 , b= 3, c= -5, replacing we have this:

[tex]x =\frac{-3 \pm \sqrt{(-3)^2 -4(2)(-5)}}{2*2}[/tex]

And simplifying we got:

[tex] x = \frac{-3 \pm \sqrt{49}}{4}[/tex]

And the two solutions are:

[tex] x_1 = \frac{-3+7}{4}= 1[/tex]

[tex] x_2 = \frac{-3-7}{4}= -\frac{5}{2}[/tex]

And the correct options are:

B and C

Answer:

B and C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Consider the augments matrix (the right most column is  the extra vector).

[tex]\left[\begin{matrix} 1 & 4 & -2 \\3 & h & -6\end{matrix}\right][/tex]

By multypling the first row by 3 and substracting it from the second row and saving the result in the second row we get the matrix

[tex]\left[\begin{matrix} 1 & 4 & -2 \\0 & h-12 & 0\end{matrix}\right][/tex]

Note that since the value of the third column in the second row is 0, any value of h gives us a consistent system. An inconsistent system is when we get a row of zeros that is equal to a number different from 0.

Answer:

a)0.2240

b)0.5768

Step-by-step explanation:

Given:

µ=3

Poison probability is given by :

[tex]f_k=\frac{\mu^ke^-^\mu}{k!}[/tex]

a) Evaluating at k=3

[tex]f(3)=\frac{3^3e^-^3}{3!} \approx 0.2240[/tex]

b)Evaluating at k=0,1,2:

[tex]f(0)=\frac{3^0e^-^3}{0!} \approx 0.0498[/tex]

[tex]f(1)=\frac{3^1e^-^3}{1!} \approx 0.1494[/tex]

[tex]f(2)=\frac{3^2e^-^3}{2!} \approx 0.2240[/tex]

Use complement rule:

P(x≥3)= 1 - f(0) - f(1) - f(2)= 1- 0.0498 - 0.1494 - 0.2240 =0.5768

Answer:

[tex]x =\frac{14}{3} , y = \frac{25}{3} and z = -3[/tex]

The numbers are    [tex]-3 ,\frac{14}{3} , \frac{25}{3}[/tex]

Step-by-step explanation:

Step(i):-

Given sum of the three numbers is 10

Let x , y , z be the three numbers is 10

x +y + z = 10  ...(i)

Given two times the second number minus the first number is equal to 12

2 × y - x = 12 ...(ii)

Given the first number minus the second number plus twice the third number equals 7

x + y + 2 z = 7 ...(iii)

Step(ii):-

Solving (i) and (iii) equations

                       x + y +   z     =    10  ...(i)

                       x + y + 2 z   =     7 ..   (iii)

                     -      -     -         -              

                     0    0    -z      =   3              

Now we know that    z = -3 ...(a)

from (ii)  equation

           2 × y - x = 12 ...(ii)

               x = 2 y -12  ...(b)

Step(iii):-

substitute equations (a) and (b) in equation (i)

                x+y+z =10

           2 y - 12 + y -3 =10

              3 y -15 =10

              3 y = 10 +15

              3 y =25

               [tex]y = \frac{25}{3}[/tex]

Substitute   [tex]y = \frac{25}{3}[/tex]  and   z = -3 in equation(i) we will get

        x+y+z =10

       [tex]x + \frac{25}{3} -3 = 10[/tex]

       [tex]x +\frac{25-9}{3} = 10[/tex]

      [tex]x +\frac{16}{3} = 10[/tex]

      [tex]x = 10 - \frac{16}{3}[/tex]

     [tex]x = \frac{30 -16}{3} = \frac{14}{3}[/tex]

Final answer :-

[tex]x =\frac{14}{3} , y = \frac{25}{3} and z = -3[/tex]

The numbers are  [tex]-3 ,\frac{14}{3} , \frac{25}{3}[/tex]

Answer:

-2, 5, 7 on Edge.

Step-by-step explanation:

I got the Answer right.

Answer:

The probability that at least one defective card appears in the sample

P(D) = 0.9644 or 96.44%

Step-by-step explanation:

Given;

Total number of cards t = 140

Number of defective cards = 20

Number of non defective cards x = 140-20 = 120

The probability that at least one defective card = 1 - The probability that none none is defective

P(D) = 1 - P(N) ........1

For 20 selections; r = 20

-- 20 cards are selected from the lot without replacement for functional testing

The probability that none none is defective is;

P(N) = (xPr)/(tPr)

P(N) = (120P20)/(140P20)

P(N) = (120!/(120-20)!)/(140!/(140-20)!)

P(N) = (120!/100!)/(140!/120!) = 0.035618370821

P(N) = 0.0356

The probability that at least one defective card appears in the sample is;

P(D) = 1 - P(N) = 1 - 0.0356 = 0.9644

P(D) = 0.9644 or 96.44%

Note: xPr = x permutation r

Answer:

  see below

Step-by-step explanation:

The way the problem is worded, we expect "n" to represent the year number we're at the beginning of. That is the initial balance is that when n=1, and the balance at the beginning of year 5 (after interest accrues for 4 years) is the value of obtained when n=5.

After compounding interest for 4 years, the balance will be ...

  500·1.04^4 = 584.93

The matching answer choice is shown below.

Answer:

b

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

This is the veritcal angles theorem

Answer:

Where is the diagram?

Step-by-step explanation:

Answer:

OC and OE are apposite rays so the Answer is yes

Answer:

Donde didn't multiply 4(1+3i)

Answer: it’s A he did not apply distributive property yo

Step-by-step explanation:

Answer:

5 inches is 5 times as big as 1 inch

Answer:

[tex] f(x+h) = 3(x+h)^2 +(x+h) +2= 3(x^2 +2xh+h^2) +x+h+2[/tex]

[tex]f(x+h) = 3x^2 +6xh +3h^2 +x+h+2= 3x^2 +6xh +x+h+ 3h^2 +2[/tex]

And replacing we got:

[tex] lim_{h \to 0} \frac{3x^2 +6xh +x+h+ 3h^2 +2 -3x^2 -x-2}{h}[/tex]

And if we simplfy we got:

[tex] lim_{h \to 0} \frac{6xh +h+ 3h^2 }{h} =lim_{h \to 0} 6x + 1 +3h [/tex]

And replacing we got:

[tex]lim_{h \to 0} 6x + 1 +3h = 6x+1[/tex]

And the bet option would be:

C. 6x + 1

Step-by-step explanation:

We have the following function given:

[tex] f(x) = 3x^2 +x+2[/tex]

And we want to find this limit:

[tex] lim_{h \to 0} \frac{f(x+h) -f(x)}{h}[/tex]

We can begin finding:

[tex] f(x+h) = 3(x+h)^2 +(x+h) +2= 3(x^2 +2xh+h^2) +x+h+2[/tex]

[tex]f(x+h) = 3x^2 +6xh +3h^2 +x+h+2= 3x^2 +6xh +x+h+ 3h^2 +2[/tex]

And replacing we got:

[tex] lim_{h \to 0} \frac{3x^2 +6xh +x+h+ 3h^2 +2 -3x^2 -x-2}{h}[/tex]

And if we simplfy we got:

[tex] lim_{h \to 0} \frac{6xh +h+ 3h^2 }{h} =lim_{h \to 0} 6x + 1 +3h [/tex]

And replacing we got:

[tex]lim_{h \to 0} 6x + 1 +3h = 6x+1[/tex]

And the bet option would be:

C. 6x + 1

Answer:

6x+1

Step-by-step explanation:

Plato :)

Answer:

Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg = 78.5%

The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.

Step-by-step explanation:

Complete Question

According to one study, brain weights of men are normally distributed with mean = 1.20 kg and a standard deviation = 0.14 kg.

Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. Interpret your answer in terms of sampling error.

Solution

The Central limit theorem allows us to say

The mean of sampling distribution is approximately equal to the population mean.

μₓ = μ = 1.20 kg

And the standard deviation of the sampling distribution is given as

σₓ = (σ/√N)

σ = population standard deviation = 0.14 kg

N = sample size = 3

σₓ = (0.14/√3) = 0.08083

Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg, that is, percentage of all samples of three men with mean brain weights within 1.10 kg and 1.30 kg.

P(1.10 ≤ x ≤ 1.30)

We first normalize or standardize 1.10 and 1.30

The standardized score for any value is the value minus the mean then divided by the standard deviation.

For 1.10 kg

z = (x - μₓ)/σₓ = (1.10 - 1.20)/0.08083 = -1.24

For 1.30 kg

z = (x - μₓ)/σₓ = (1.30 - 1.20)/0.08083 = 1.24

To determine the required probability

P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)

We'll use data from the normal distribution table for these probabilities

P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)

= P(z ≤ 1.24) - P(z ≤ -1.24)

= 0.89251 - 0.10749

= 0.78502 = 78.502%

The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.

Hope this Helps!!!

Answer:

Plan A would be the least expensive

Step-by-step explanation:

Plan A= $0.45x100= 45, 45+40=$85

Plan B= $0.35x100= 35, 35+70= %105

(Each plan is for 100 minutes)

Answer:

72°

Step-by-step explanation:

This is called an isosceles triangle. This means that the 2 angles related to the equal sides, are also equal. Hence, the answer is 72°

Answer:

A

Step-by-step explanation:

Since it is isosceles triangle (two equal sides) therefore, there are 2 equal angles too which at the base (72°)

The total angle of triange is 180°

So 180-72-72=36°

Answer:

A

Step-by-step explanation:

The combinations of decisions and true states of nature for a test of​ hypothesis is given below:

Note that when [tex]H_o[/tex] is False, then the Alternate Hypothesis, [tex]H_a[/tex] is True.

Therefore Option A gives the possible combinations.

The possible choices in Option A are ordered below to correspond to the results above.