a trapazoid is a quadrilateral with one or more pairs of paralllel sides true or false

Answer:

Options (c) and (f)

Step-by-step explanation:

In the given triangle,

Measure of one angle is 90°.

Therefore, it's a right angle triangle.

Since two angles of the given triangle are equal, opposite sides of this triangle will be equal.

Therefore, the given right triangle is an isosceles triangle.

Options (c) and (f) will be the answer.

Answer:

y+8 = 3(x-3)

Step-by-step explanation:

The point slope form of the equation for a line is

y-y1 = m(x-x1)

y- -8 = 3(x -3)

y+8 = 3(x-3)

Answer:

x = 7

Step-by-step explanation:

<ACF = 90° (since AB is the diameter and it is perpendicular to EF)

But <ACF = 2(7x-4)

So

2(7x-4) = 90

14x-8 = 90

14x = 90+8

14x = 98

Dividing both sides by 14

x = 7

Answer:

a) 0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less

b) 0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours

c) 0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours

d) 86 should have a battery life of at least 9 hours.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]

The probability of being higher than x is:

[tex]P(X > x) = \frac{b - x}{b-a}[/tex]

The probability of being between c and d is:

[tex]P(c \leq X \leq d) = \frac{d-c}{b-a}[/tex]

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

This means that [tex]a = 8.5, b = 12[/tex]

a. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]

[tex]P(X \leq 10) = \frac{10 - 8.5}{12 - 8.5} = 0.4286[/tex]

0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less.

b. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

[tex]P(X > x) = \frac{b - x}{b-a}[/tex]

[tex]P(X > 11) = \frac{12 - 11}{12 - 8.5} = 0.2857[/tex]

0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours

c. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

[tex]P(c \leq X \leq d) = \frac{d-c}{b-a}[/tex]

[tex]P(9.5 \leq X \leq 11.5) = \frac{11.5 - 9.5}{12 - 8.5} = 0.5714[/tex]

0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours.

d. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

Proportion of iPad Minis with a battery life of at least 9 hours.

[tex]P(X > 11) = \frac{12 - 9}{12 - 8.5} = 0.8571[/tex]

Out of 100:

0.8571*100 = 85.71

To the nearest whole number

86 should have a battery life of at least 9 hours.

Answer:

Total time of flight= 6.3 s

Total Max height= 60.87ft

Step-by-step explanation:

Height above ground = 15ft

Velocity=30ft/sec

Angle = 90°

Max height traveled= U²Sin²tita/2g

Max height traveled= ( 30²*1²)/(2*9.81)

Max height traveled= 900/19.62

Max height traveled= 45.87 ft

Total Max height= 15+45.87= 60.87ft

Time travel to Max height

=( usin90)/g

Time travel to initial position

= (30*sin90)/9.81

= 3.1 s

Time to travel to the ground from Max height

H = 1/2gt²

60.87= 1/2 * 9.81*t²

(60.87*2)/9.81= t²

3.5 = t

Total time of flight = 3.5+3.1

Total time of flight= 6.3 s

Answer:

43.46% probability that the person will need to wait at least 9 minutes total

Step-by-step explanation:

To solve this question, we need to understand conditional probability and the exponential distribution.

Conditional probability:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Expontial distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

In this question:

Event A: Waited at least 4 minutes.

Event B: Waiting at least 9 minutes.

The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 6 minutes.

This means that [tex]m = 6, \mu = \frac{1}{6}[/tex]

Probability of waiting at least 4 minutes.

[tex]P(A) = P(X \geq 4) = P(X > 4)[/tex]

[tex]P(A) = P(X > 4) = e^{-\frac{4}{6}} = 0.5134[/tex]

Intersection:

The intersection between a waiting time of at least 4 minutes and a waiting time of at list 9 minutes is a waiting time of 9 minutes. So

[tex]P(A \cap B) = P(X > 9) = e^{-\frac{9}{6}} = 0.2231[/tex]

What is the probability that the person will need to wait at least 9 minutes total

[tex]P(B|A) = \frac{0.2231}{0.5134} = 0.4346[/tex]

43.46% probability that the person will need to wait at least 9 minutes total

Answer:

StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U

Step-by-step explanation:

The expression below means RS/VU = ST/UT

See the attachment for better explanation.

Answer:

A

Step-by-step explanation:

I took the test

*The question is incomplete. Attached below is the diagram of the box plots being referred to followed by the complete question and options.

Answer:

D. The median for town A, 20 degrees, is less than the median of town B, 30 degrees

Step-by-step Explanation:

From the given diagram of the box plots showing the daily low temperatures for town A and B, the median of town A and B is shown on the box plots by the line that divides the box. Therefore, the median of town A is where the line that divides the box is. Median for town A is 20⁰. Same applies for town B. Town B median is 30⁰.

Therefore, option D is the most appropriate comparison of the centers. Median of town A is less than median of town B.

Answer:

10 : 6

Step-by-step explanation:

1km / min = 1000m / 60 sec = 100/6 m/s

Ratio :

100/6 : 10

10/6 : 1

10 : 6

Step-by-step explanation:

Hope you understand this

Answer: 16875x³-13500x²+3600x-320

Step-by-step explanation:

[gοfοh](x) means g(f(h(x))). So you plug in h(x) into f(x) and that into g(x).

f(3x)=5(3x)-4=15x-4

g(f(3x))=5(15x-4)³

g(f(3x))=5(3375x³-2700x²+720x-64)

g(f(3x))=16875x³-13500x²+3600x-320

Answer:

A

Step-by-step explanation:

Step-by-step explanation:

a. If x is the total numbers of students in school, 35%x = 140.

0.35x = 140

x = 140/0.35 = 400

b. Since there are 400 kids in the school, 15% of them take the bus which is 0.15 * 400 = 60 kids.

Answer:

3 [tex]\frac{31}{35}[/tex] mph ≈ 3.8857 mph

Step-by-step explanation:

Speed = distance/time

1) Plug the numbers in.

Speed = 3 ⅖ / ⅞

2) Convert the numbers to decimals.

Speed = 3.4 / 0.875

3) Solve.

Speed ≈ 3.8857 mph = [tex]\frac{136}{35}[/tex] mph = 3 [tex]\frac{31}{35}[/tex] mph

ANOTHER WAY TO SOLVE

Speed = distance/time

1) Plug the numbers in.

Speed = 3 ⅖ / ⅞

2) Convert into improper fractions

Speed = [tex]\frac{17}{5}[/tex] / [tex]\frac{7}{8}[/tex]

3) Multiply by the reciprocal

Speed =  [tex]\frac{17}{5}[/tex] × [tex]\frac{8}{7}[/tex] = [tex]\frac{136}{35}[/tex] mph = 3 [tex]\frac{31}{35}[/tex] mph

Answer:

a, b

Step-by-step explanation:

a and b  cause  all  the data are  not in a form of a line

Answer:

a. Attached.

b. Mean = 0.5

Step-by-step explanation:

This random number generator con be modeled with an uniform continous random variable X that has values within 0 and 1, each with the same constant probability within this range.

The probability for the values within the interval [a,b] in a continous uniform distribution can be calculated as:

[tex]f(x)=\dfrac{1}{b-a}\;\;\;x\in[0; 1][/tex]

In this case, b=1 and a=0, so f(x)=1.

The sketched curve of the probability distribution of this random variable is attached.

The mean of this distribution can be calculated as the mean for any uniform distribution:

[tex]E(X)=\dfrac{a+b}{2}=\dfrac{0+1}{2}=0.5[/tex]

14. Was the perimeter calculated correctly?

We know that,

Perimeter of rectangle = 2 ( l + b )

= 2 ( 4 + 7 / 5 )

= 2 ( 20 + 7 / 5 )

= 2 × 27/5

= 54 / 5

= 1 * 4/5

No ...

Range of the given function  y=-x-5 includes -4

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

For the given function,

y = -x-5

Wen we put x = -1

we get y = -4

Also,

The range of this function is (-∞, ∞)

Hence,

The function  y = -x-5 includes the -4.

To learn more about function visit:

https://brainly.com/question/8892191

#SPJ7

Answer:

8  5/648

Step-by-step explanation:

y = 5x ^ -3 + 4x^2

dy /dx = 5 * -3 x^ -4 + 4 * 2x ^ 1

           = -15 x ^ -4 + 8x

Now take the second derivative

dy^2/ dx^2 = -15  * -4 x^-5 +8

                   = 60 x^ -5 +8

                   = 60 /x^5   +8

Evaluate at x = 6

                   = 60 / 6^5  +8

                    60/7776 +8

                   5/648 + 8

                  8  5/648

Answer:

(a) The probability mass function of X is:

[tex]P(X=x)={4\choose x}\ (0.33)^{x}\ (1-0.33)^{4-x};\ x=0,1,2,3...[/tex]

(b) The most likely value for X is 1.32.

(c) The probability that at least two of the four selected have earthquake insurance is 0.4015.

Step-by-step explanation:

The random variable X is defined as the number among the four homeowners  who have earthquake insurance.

The probability that a homeowner has earthquake insurance is, p = 0.33.

The random sample of homeowners selected is, n = 4.

The event of a homeowner having an earthquake insurance is independent of the other three homeowners.

(a)

All the statements above clearly indicate that the random variable X follows a Binomial distribution with parameters n = 4 and p = 0.33.

The probability mass function of X is:

[tex]P(X=x)={4\choose x}\ (0.33)^{x}\ (1-0.33)^{4-x};\ x=0,1,2,3...[/tex]

(b)

The most likely value of a random variable is the expected value.

The expected value of a Binomial random variable is:

[tex]E(X)=np[/tex]

Compute the expected value of X as follows:

[tex]E(X)=np[/tex]

         [tex]=4\times 0.33\\=1.32[/tex]

Thus, the most likely value for X is 1.32.

(c)

Compute the probability that at least two of the four selected have earthquake insurance as follows:

P (X ≥ 2) = 1 - P (X < 2)

              = 1 - P (X = 0) - P (X = 1)

              [tex]=1-{4\choose 0}\ (0.33)^{0}\ (1-0.33)^{4-0}-{4\choose 1}\ (0.33)^{1}\ (1-0.33)^{4-1}\\\\=1-0.20151121-0.39700716\\\\=0.40148163\\\\\approx 0.4015[/tex]

Thus, the probability that at least two of the four selected have earthquake insurance is 0.4015.

Answer:

Step-by-step explanation:

We assume your intended attendance equation is ...

  A = -1.95x^3 +70.1x^2 -188x +2150

a. For x=0 (corresponding to 1985), the first three terms are 0, so we have ...

  A = 2150 . . . . the initial value of the function

__

b. For x=13 (corresponding to 1985) we have ...

  A = ((-1.95(13) +70.1)(13) -188)(13) +2150 = (44.75(13) -188)(13) +2150

  = 393.75(13) +2150 = 7268.75

Attendance in the year 1998 is modeled to be about 7269.

Answer:

D.) 9m

Step-by-step explanation:

Answer:

its d

Step-by-step explanation:

i just did the question

Answer:

x= -6 broo

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

The formula that relates two independent events is provided as below:

P(A) x P(B) = P(A⋂B)

=> P(A) x (1/3) = 1/6

=> P(A) = (1/6) x 3

=> P(A) = 3/6 = 1/2

=> Option D is correct

Hope this helps!

Answer:

The ball is at a maximum height when t = 0.125s.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

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

It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]

In which

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

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]

In this question:

[tex]h(t) = -32t^{2} + 8t + 3[/tex]

So [tex]a = -32, b = 8[/tex]

When is the ball at a maximum height

[tex]t_{v} = -\frac{8}{2*(-32)} = 0.125[/tex]

The ball is at a maximum height when t = 0.125s.

Answer:

[tex] y^2 -4y +6=0[/tex]

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

Where [tex] a = 1, b= -4 ,c =6[/tex]

And replacing we got:

[tex] y = \frac{-(-4) \pm \sqrt{4^2 -4(1)(6)}}{2*1}[/tex]

And solving we got:

[tex] y = \frac{4 \pm \sqrt{-8}}{2} =2 \pm 2\sqrt{2} i[/tex]

Where [tex] i =\sqrt{-1}[/tex]

And the possible solutions are:

[tex] y_1=2 + 2\sqrt{2} i , y_2 = 2 - 2\sqrt{2} i [/tex]

Step-by-step explanation:

For this case we use the equation given by the image and we have:

[tex] -y^2 +4y -6=0[/tex]

We can rewrite the last expression like this if we multiply both sides of the equation by -1.

[tex] y^2 -4y +6=0[/tex]

Now we can use the quadratic formula given by:

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

Where [tex] a = 1, b= -4 ,c =6[/tex]

And replacing we got:

[tex] y = \frac{-(-4) \pm \sqrt{4^2 -4(1)(6)}}{2*1}[/tex]

And solving we got:

[tex] y = \frac{4 \pm \sqrt{-8}}{2} =2 \pm 2\sqrt{2} i[/tex]

Where [tex] i =\sqrt{-1}[/tex]

And the possible solutions are:

[tex] y_1=2 + 2\sqrt{2} i , y_2 = 2 - 2\sqrt{2} i [/tex]

Answer:

All Lake Tahoe Community College math students

Step-by-step explanation:

From the question itself it is clear that the instructor is interested in the average number of days Lake Tahoe Community College math students are absent from class during a quarter that lasts 9 weeks, which clearly indicates that the teacher is interested in population of all Lake Tahoe Community College math students.

Answer:

[tex](C)\dfrac{1}{4}[/tex]

Step-by-step explanation:

In a standard deck,

The table below gives the distribution of the cards.

[tex]\left|\begin{array}{c|c|c|c}&$Club&$Not a club\\----&----&---&----\\$Face card&3&9&12\\$Not a face card&10&30&40\\----&----&---&----\\$Total&13&39&52\end{array}\right|[/tex]

[tex]P($Club$ | $Not a Face Card)$=\dfrac{10}{40}\\ =\dfrac{1}{4}[/tex]

The correct option is C.

Answer:

150

Step-by-step explanation:

Given the following parameters;

Time, T = 150mins

Cooker setting, H = 7

Since the time for a pot of water to boil is inversely proportional to the cooker setting;

[tex]T * 1/H[/tex]

[tex]T = K/H[/tex] ........equation 1

Where, K is the constant of proportionality.

Substituting the parameters into the equation 1, we have;

150 = K/7

K = 150*7

K = 1050

To find the cooker setting at 7mins;

[tex]T = K/H[/tex]

H = K/T

H = 1050 ÷ 7

H = 150.

Hence, the cooker setting must be at 150.