The mail arrival time to a department has a uniform distribution over 5 to 45 minutes. What is the probability that the mail arrival time is more than 25 minutes on a given day? Answer: (Round to 2 decimal places.)

Answer:

41

Step-by-step explanation:

[tex]24*2-7=\\48-7=\\41[/tex]

Answer:

plane

Step-by-step explanation:

Answer:

D. Plane

Step-by-step explanation:

A plane extends in two dimensions. This figure is a plane. It is not a point, a segment or a ray.

Answer:

Minimum population of fish in lake = 2400 - 155 = 2245

Maximum population of fish in lake = 2400 + 155 = 2555

Step-by-step explanation:

population of fish in lake = 2400

Variation of fish = 155

it means that while current population of fish is 2400, the number can increase or decrease by maximum upto 155.

For example

for increase

population of fish can 2400 + 2, 2400 + 70, 2400 + 130 etc

but it cannot be beyond 2400 + 155.

It cannot be 2400 + 156

similarly for decrease

population of fish can 2400 - 3, 2400 - 95, 2400 - 144 etc

but it cannot be less that 2400 - 155.

It cannot be 2400 - 156

Hence population can fish in lake can be between 2400 - 155 and 2400 + 155

minimum population of fish in lake = 2400 - 155 = 2245

maximum population of fish in lake = 2400 + 155 = 2555

Answer:

infinite solutions

Step-by-step explanation:

it means that all x are solution of this equation as 6=6 is always true

Answer:

225º or 3.926991 radians

Step-by-step explanation:

The area of the complete circle would be π×radius²: 3.14×8²=200.96

The fraction of the circle that is still left will be a direct ratio of the angle of the sector of the circle.

[tex]\frac{125.6}{200.96}[/tex]=.625. This is the ratio of the circe that is in the sector. In order to find the measure we must multiply it by either the number of degrees in the circle or by the number of radians in the circle (depending on the form in which you want your answer).

There are 360º in a circle, so .625×360=225 meaning that the measure of the angle of the sector is 225º.

We can do the same thing for radians, if necessary. There are 2π radians in a circle, so .625×2π=3.926991 radians.

Answer:

225º

Step-by-step explanation:

Answer:

20 4/5

Step-by-step explanation:

13/5 times 8/1

104/5

which is simplify

to 20 4/5\

hope this helps

Answer:

Center, radius, chord, diameter... are Words related to circle

Answer:

-10

Step-by-step explanation:

Use the Order of Operations - PEMDAS

Do what is in parentheses first - (4-2) = 2

Next multiply 3 and 4 = 12

Last, perform 2 - 12; which equals -10

Answer:

100 possible extensions

Step-by-step explanation:

we can calculated how many possible extensions they have to try using the rule of multiplication as:

___1_____*___10_____*___10_____*____1____ = 100

1st digit        2nd digit        3rd digit         4th digit

You know that the 1st and 4th digits of the extension are 5. it means that you just have 1 option for these places. On the other hand, you don't remember nothing about the 2nd and 3rd digit, it means that there are 10 possibles digits (from 0 to 9) for each digit.

So, There are 100 possibles extensions in which the 5 is the first and last digit.

Answer:

21/55

Step-by-step explanation:

Simply multiply the top 2 together:

3 x 7 = 21

And the bottom 2 together:

5 x 11 = 55

21/55 is your answer!

Answer:

x = 3, -7

Step-by-step explanation:

Since you already have the factored form, all you need to do is set the equations equal to zero to find you roots:

x - 3 = 0

x + 7 = 0

x = 3, -7

Answer:

3 or -7

Step-by-step explanation:

For it to equal 0, x must be 3 or -7 because anything multiplied by 0 is 0. So you take each part, x-3 and see how you can make that a 0. x-3=0, therefore x must be 3. Other part x+7=0, x must be -7.

Answer:

Raspberry: 30%

Strawberry: 15%

Apple: 20%

Lemon: 35%

Step-by-step explanation:

18 + 9 + 12 + 21 = 60 (there are 60 gummy worms)

18 out of 60 = 30%

9 out of 60 = 15%

12 out of 60 = 20%

21 out of 60 = 35%

Please mark Brainliest

Hope this helps

Answer:

Raspberry Worms: 30%

Strawberry Worms: 15%

Apple Worms: 20%

Lemon Worms: 35%

Step-by-step explanation:

Raspberry Worms: [tex]\frac{18}{18+9+12+21}=\frac{18}{60}=\frac{30}{100}[/tex] or 30%

Strawberry Worms: [tex]\frac{9}{18+9+12+21}=\frac{9}{60} =\frac{15}{100}[/tex] or 15%

Apple Worms: [tex]\frac{12}{18+9+12+21} =\frac{12}{60} =\frac{20}{100}[/tex] or 20%

Lemon Worms: [tex]\frac{21}{18+9+12+21} =\frac{21}{60} =\frac{35}{100}[/tex] or 35%

Answer:

96 degrees

Step-by-step explanation:

Since x is half of 168, its angle measure is 84 degrees. Since x and y are a linear pair, their angle measures must add to 180 degrees, meaning that:

y+84=180

y=180-84=96

Hope this helps!

Answer:

Your answer is 3.16227766

Step-by-step explanation:

Answer:

2x/3 + 2= 16

=21

Step-by-step explanation:

Standard form:

2

3

x − 14 = 0  

Factorization:

2

3 (x − 21) = 0  

Solutions:

x = 42

2

= 21

Answer:

Step-by-step explanation:

given a field of the form F = (P(x,y),Q(x,y) and a simple closed curve positively oriented, then

[tex]\int_{C} F \cdot dr = \int_A \frac{dQ}{dx} - \frac{dP}{dy} dA[/tex] where A is the area of the region enclosed by C.

In this case, by the description we can assume that C starts at (0,0). Then it goes the point (pi,0) on the path giben by y = sin(x) and then return to (0,0) along the straigth line that connects both points. Note that in this way, the interior the region enclosed by C is always on the right side of the point. This means that the curve is negatively oriented. Consider the path C' given by going from (0,0) to (pi,0) in a straight line and the going from (pi,0) to (0,0) over the curve y = sin(x). This path is positively oriented and we have that

[tex] \int_{C} F\cdot dr = - \int_{C'} F\cdot dr[/tex]

We use the green theorem applied to the path C'. Taking [tex] P = x+4y^3, Q = 4x^2+y[/tex] we get

[tex] \int_{C'} F\cdot dr = \int_{A} 8x-12y^2dA[/tex]

A is the region enclosed by the curves y =sin(x) and the x axis between the points (0,0) and (pi,0). So, we can describe this region as follows

[tex]0\leq x \leq \pi, 0\leq y \leq \sin(x)[/tex]

This gives use the integral

[tex] \int_{A} 8x-12y^2dA = \int_{0}^{\pi}\int_{0}^{\sin(x)} 8x-12y^2 dydx[/tex]

Integrating accordingly, we get that [tex]\int_{C'} F\cdot dr = 8\pi - \frac{16}{3}[/tex]

So

[tex] \int_{C} F cdot dr = - (8\pi - \frac{16}{3}) = \frac{16}{3} - 8\pi [/tex]

Answer:

1 .angle S is 90 degree

2. 12

3. 155 degree

1. x = 3

hope it helps .....

Answer:

44.93% probability that the person will need to wait at least 7 minutes total

Step-by-step explanation:

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

Exponential 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]

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.

The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 5 minutes

This means that [tex]m = 5, \mu = \frac{1}{5} = 0.2[/tex]

Assume a person has waited for at least 3 minutes to be served. What is the probability that the person will need to wait at least 7 minutes total

Event A: Waits at least 3 minutes.

Event B: Waits at least 7 minutes.

Probability of waiting at least 3 minutes:

[tex]P(A) = P(X > 3) = e^{-0.2*3} = 0.5488[/tex]

Intersection:

The intersection between waiting at least 3 minutes and at least 7 minutes is waiting at least 7 minutes. So

[tex]P(A \cap B) = P(X > 7) = e^{-0.2*7} = 0.2466[/tex]

What is the probability that the person will need to wait at least 7 minutes total

[tex]P(B|A) = \frac{0.2466}{0.5488} = 0.4493[/tex]

44.93% probability that the person will need to wait at least 7 minutes total

Answer:

No

Step-by-step explanation:

It is not divisible by 6, for if you divide by 6, you will get a non natural number,

It is obviously divisible by 2.

So, No.

Answer:

no

Step-by-step explanation:

only by 2

614/2 = 307

614/6 = 102.33

Answer:

[tex] 211600 = 225000 -k*6700[/tex]

[tex] k = \frac{225000-211600}{6700}= 2[/tex]

[tex] 238400 = 225000 +k*6700[/tex]

[tex] k = \frac{238400-225000}{6700}= 2[/tex]

So then the % expected would be:

[tex] 1- \frac{1}{2^2}= 1- 0.25 =0.75[/tex]

So then the answer would be 75%

Step-by-step explanation:

For this case we have the following info given:

[tex] \mu = 225000[/tex] represent the true mean

[tex]\sigma =6700[/tex] represent the true deviation

And for this case we want to find the minimum percentage of sold homes between $211,600 and $238,400.

From the chebysev theorem we know that we have [tex]1 -\frac{1}{k^2}[/tex] % of values within [tex]\mu \pm k\sigma[/tex] if we use this formula and the limit given we have:

[tex] 211600 = 225000 -k*6700[/tex]

[tex] k = \frac{225000-211600}{6700}= 2[/tex]

[tex] 238400 = 225000 +k*6700[/tex]

[tex] k = \frac{238400-225000}{6700}= 2[/tex]

So then the % expected would be:

[tex] 1- \frac{1}{2^2}= 1- 0.25 =0.75[/tex]

So then the answer would be 75%

Answer:

a=b

Step-by-step explanation:

When the denominator is zero, the expression is undefined

a-b=0

a=b

Answer:

y-7=1/2(x-8)

y-4=1/2(x-2)

Step-by-step explanation:

Slope: 3/6, or 1/2

y-7=1/2(x-8)

y-4=1/2(x-2)

Answer:

The 90% confidence interval for the difference in mean number of days meeting the goal  is (4.49, 18.11).

Step-by-step explanation:

The (1 - α)% confidence interval for the difference between two means is:

[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]

It is provided that:

[tex]\bar x_{1}=45\\\bar x_{2}=33.7\\SE_{\text{diff}} =4.14\\\text{Confidence Level}=90\%[/tex]

The critical value of z for 90% confidence level is,

z = 1.645

*Use a z-table.

Compute the 90% confidence interval for the difference in mean number of days meeting the goal as follows:

[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]

    [tex]=45-33.7\pm 1.645\times 4.14\\\\=11.3\pm 6.8103\\\\=(4.4897, 18.1103)\\\\\approx (4.49, 18.11)[/tex]

Thus, the 90% confidence interval for the difference in mean number of days meeting the goal  is (4.49, 18.11).

Answer:

A

Step-by-step explanation:

We can use the trigonometric ratios. Recall that sine is the ratio of the opposite side to the hypotenuse:

[tex]\displaystyle \sin(C)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

The opposite side with respect to ∠C is 24 and the hypotenuse is 26.

Hence:

[tex]\displaystyle \sin(C)=\frac{24}{26}=\frac{12}{13}[/tex]

Our answer is A.

Answer:

  9.233 ft, 23.233 ft

Step-by-step explanation:

If the shorter leg is x, then the longer leg is x+14 and the Pythagorean theorem tells you ...

  x^2 + (x +14)^2 = 25^2

  2x^2 +28x +196 = 625

  x^2 +14x = 214.5

  x^2 +14x +49 = 263.5

  (x +7)^2 = 263.5

  x = -7 +√263.5 ≈ 9.23268

The two leg lengths are √263.5 ± 7 feet, {9.23 ft, 23.23 ft}.

Answer: 9 ft, 23 ft

Step-by-step explanation:

We know the Pythagorean Theorem is a²+b²=c². Since one leg is 14 less than the other leg, we can use x-14 and the other leg would be x. We can plug these into the Pythagorean Theorem with the given hypotenuse.

(x-14)²+x²=25²

(x²-28x+196)+x²=625

2x²-28x+196=625

2x²-28x-429=0

When we solve for x, we get [tex]x=\frac{14+\sqrt{1054} }{2}[/tex] and [tex]x=\frac{14-\sqrt{1054} }{2}[/tex].

Note, since we rounded to 23, the hypotenuse isn't exactly 25, but it gets very close.

Answer:

[tex]6cm^2[/tex]

Step-by-step explanation:

Let x and y be the sides of the rectangle.

Area of the Triangle, A(x,y)=xy

From the diagram, Triangle ABC is similar to Triangle AKL

AK=4-y

Therefore:

[tex]\dfrac{x}{6} =\dfrac{4-y}{4}[/tex]

[tex]4x=6(4-y)\\x=\dfrac{6(4-y)}{4} \\x=1.5(4-y)\\x=6-1.5y[/tex]

We substitute x into A(x,y)

[tex]A=y(6-1.5y)=6y-1.5y^2[/tex]

We are required to find the maximum area. This is done by finding

the derivative of Aand solving for the critical points.

Derivative of A:

[tex]A'(y)=6-3y\\$Set $A'=0\\6-3y=0\\3y=6\\y=2$ cm[/tex]

Recall that: x=6-1.5y

x=6-1.5(2)

x=6-3

x=3cm

Therefore, the maximum rectangle area is:

Area =3 X 2 =[tex]6cm^2[/tex]

Answer:

Height of tank = 50cm

Step-by-step explanation:

Volume of water from tank that the water is 10cm down is 84000cm³

Length = 60cm

Width = 35cm

Height of water = x

Volume = length* width* height

Volume= 84000cm³

84000 = 60*35*x

84000= 2100x

84000/2100= x

40 = x

Height of water= 40cm

Height of tank I = height of water+ 10cm

Height of tank= 40+10= 50cm

Height of tank = 50cm

Answer:

  [tex]\dfrac{x^2+8x+16}{x-1}[/tex]

Step-by-step explanation:

In general, "over" and "divided by" are used to mean the same thing. Parentheses are helpful when you want to show fractions divided by fractions. Here, we will assume you intend ...

  [tex]\dfrac{\left(\dfrac{x^2+7x+12}{x+3}\right)}{\left(\dfrac{x-1}{x+4}\right)}=\dfrac{(x+3)(x+4)}{x+3}\cdot\dfrac{x+4}{x-1}=\dfrac{(x+4)^2}{x-1}\\\\=\boxed{\dfrac{x^2+8x+16}{x-1}}[/tex]

Answer:

See below in bold.

Step-by-step explanation:

We can write the equation as

y = a(x - 28)(x + 28)   as -28 and 28  ( +/- 1/2 * 56) are the zeros of the equation

y has coordinates (0, 32) at the top of the parabola so

32 = a(0 - 28)(0 + 28)

32 = a * (-28*28)

32 = -784 a

a = 32 / -784

a = -0.04082

So the equation is y = -0.04082(x - 28)(x + 28)

y = -0.04082x^2 + 32

The second part  is found by first finding the value of x corresponding to  y = 22

22 = -0.04082x^2 + 32

-0.04082x^2 = -10

x^2 = 245

x = 15.7 inches.

This is the distance from the centre of the door:

The distance from the edge = 28 - 15.7

= 12,3 inches.