A trapezoid has an area given by A =1-2(b1+b2)h,where b1,is the length of one base, b2 is the length of the other
base, and h is the height. If the trapezoid has an area of 14 square units, solve for b in terms of the other variables.

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:

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

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.

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

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:

56.45  

Step-by-step explanation:

Coefficient skewness=(Third quartile+ first quartile)-n*Median/Third quartile-first quartile

Third quartile is the unknown?

First quartile is 30.8

n is the number of steps taken from first quartile to reach third quartile which is 2 steps.

coefficient skewness is -0.38

let p represent third quartile

-0.38=(p+30.8)-2(48.5)/p-30.8

by cross multiplication

-0.38(p-30.8)=(p+30.8)-97

-0.38p+ 11.704  =p+30.8-97

-0.38p-p=30.8-97-11.704

-1.38p=-77.904

p=-77.904 /-1.38= 56.45  

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:

perimeter

Step-by-step explanation:

She would choose perimeter

Because perimeter is the outside of a object and she ran the outside of the soccer field so ya mark be as brainliest plssss

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:

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:

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:

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:

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: 5 people

Step-by-step explanation: I was the killer... lol

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:

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:

[tex]P(28<X<31.5)=P(\frac{28-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{31.5-\mu}{\sigma})=P(\frac{28-30}{2}<Z<\frac{31.5-30}{2})=P(-1<z<0.75)[/tex]

We can find this probability with this difference

[tex]P(-1<z<0.75)=P(z<0.75)-P(z<-1)[/tex]

If we use the normal standard distribution or excel we got:

[tex]P(-1<z<0.75)=P(z<0.75)-P(z<-1)=0.773-0.159=0.614[/tex]

Step-by-step explanation:

Let X the random variable that represent the weights for a can of pumpkin pie, and for this case we know the distribution for X is given by:

[tex]X \sim N(30,2)[/tex]  

Where [tex]\mu=30[/tex] and [tex]\sigma=2[/tex]

We are interested on this probability

[tex]P(28<X<31.5)[/tex]

We can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula we got:

[tex]P(28<X<31.5)=P(\frac{28-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{31.5-\mu}{\sigma})=P(\frac{28-30}{2}<Z<\frac{31.5-30}{2})=P(-1<z<0.75)[/tex]

We can find this probability with this difference

[tex]P(-1<z<0.75)=P(z<0.75)-P(z<-1)[/tex]

If we use the normal standard distribution or excel we got:

[tex]P(-1<z<0.75)=P(z<0.75)-P(z<-1)=0.773-0.159=0.614[/tex]

Answer:

36.23 kilograms of roasted beef

Step-by-step explanation:

If deli sliced 13.7 kilograms (kg) of roasted beef one week

He sliced 22.53 kilograms (kg) the next week

Total sliced kilograms of roasted beef=13.7 kg + 22.53 kg

=36.23 kg

The deli sliced a total of 36.23 kilograms of roasted beef in the two weeks.

Answer:

closed questions are questions with fixed answer options

A. Closed questions allow the respondent to go​ in-depth with their answers.

B. It is possible to automate the collection of results for closed questions.

C. Closed questions allow for new solutions to be introduced.

D. It is easy to quantify and compare the results of surveys with closed questions.

*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:

  5

Step-by-step explanation:

When the factors are linear, as here, the total number of roots is the sum of the exponents of the factors:

  3 + 1 + 1 = 5 . . . . sum of factor exponents

f(x) has 5 roots.

Answer:

C.  ​No, the distribution is not symmetric and the frequencies do not start off low.

Step-by-step explanation:

Hello!

You have the data of daily rainfall for one month (inches)

To arrange a data set in a frequency table you have to determine the number of class intervals you want to make, then you calculate their widths as: "total observations"/"desired number of intervals". Once you have the class width, you can determine the limits of the intervals. For the first interval, you select the minimum value of the sample and add the width to obtain the upper limit. Then you have to use that limit as the lower limit of the next interval and add the width to obtain the next limit. And so on until the last one.

In this example you have a given class width of 0.20 and the lower limit for the first interval is 0.00.

Once you have all intervals determined, you have to arrange the data set from least to greatest and count how many observations correspond to each interval.

The symbol [;) in the intervals indicates that the interval is "closed" on the lower limit and "open" on the upper limit. Meaning, if you have for example the observation "0.20" and the intervals [0.00; 0.20) and [0.20; 0.40), the first interval has a limit equal to 0.20 but is open, meaning that the observation does not belong to it, it belongs to the next interval.

(See table in attachment)

Does the frequency distribution appear to be roughly a normal​ distribution?

A.  ​No, although the distribution is approximately​ symmetric, the frequencies do not start​ low, increase to some maximum​ frequency, then decrease.

B.  ​No, although the frequencies start​ low, increase to some ​maximum, then​ decrease, the distribution is not symmetric.

C.  ​No, the distribution is not symmetric and the frequencies do not start off low.

D.  ​Yes, all the requirements are met.

As you can see not all defined intervals have at least one observed frequency, most of the observations belong to the first and second one. And there is value, 1.28 inches, that shifts the distribution to the right making it strongly skewed. This distribution is far away from being normally distributed.

Hope it helps!

Answer:

D.) 9m

Step-by-step explanation:

Answer:

its d

Step-by-step explanation:

i just did the question

Answer:

12

Step-by-step explanation:

One part is 1 so 13 minus 1 is 12

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

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:

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