78% of all laboratory mice can make it through a maze. If 600 randomly selected mice attempt the maze. Write out the formula to calculate the confidence interval

First You add all given angles up to equal 180 to give you x then you plug x into equations

A= 125 degrees

C= 35 degrees

Answer:

0.0482 = 4.82% probability that at least 6 computers are functioning beyond 6 years

Step-by-step explanation:

For each computer, there are only two possible outcomes. Either it works beyond 6 years, or it does not. The probability of a computer working beyong 6 years is independent of any other computes. This means that the binomial probability distribution is used to solve this question.

As the lifetime of a computer is an exponential variable, the probability of a computer working beyond 6 years is found using the exponential distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

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]

Probability of a computer working beyong 6 years:

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

The probability is:

[tex]P(X > 6) = e^{-0.2*6} = 0.3012[/tex]

What is the probability that at least 6 computers are functioning beyond 6 years?

10 computers means that [tex]n = 10[/tex]

0.3012 probability of a computer working beyond 6 years means that [tex]p = 0.3012[/tex]

This probability is:

[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 6) = C_{10,6}.(0.3012)^{6}.(0.6988)^{4} = 0.0374[/tex]

[tex]P(X = 7) = C_{10,7}.(0.3012)^{7}.(0.6988)^{3} = 0.0092[/tex]

[tex]P(X = 8) = C_{10,8}.(0.3012)^{8}.(0.6988)^{2} = 0.0015[/tex]

[tex]P(X = 9) = C_{10,9}.(0.3012)^{9}.(0.6988)^{1} = 0.0001[/tex]

[tex]P(X = 10) = C_{10,10}.(0.3012)^{10}.(0.6988)^{0} \approx 0[/tex]

[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0374 + 0.0092 + 0.0015 + 0.0001 + 0 = 0.0482[/tex]

0.0482 = 4.82% probability that at least 6 computers are functioning beyond 6 years

Answer:

123456789101112131415161718192021222324252627

Answer:

$30

Step-by-step explanation:

Plus in 10 into the equation

Price=2(10)+10

Price=20+10

Price=30

Answer:

6.28 units²

Step-by-step explanation:

The formula for finding the area of a circle:

πr²

We are given r = 2. So,

π(2)²

12.56 units²

However, it is a semicircle. So, only half of this value is needed.

12.56/2 = 6.28 units²

Answer:

area =12.56

Step-by-step explanation:

area of a semicircle=(pi(r)^2)/2

(3.14(2)^2)/2

(3.14(4))/2

12.56/2

6.28

Step-by-step explanation:

Under 18 tickets: 5062-3484=1578

Total money: 3484*18+1578*12=81648$

100%-85%=15% goes to community projects

So, (15/100)*81648=12247.2 $

Answer:

570 m³

Step-by-step explanation:

The volume of water is the product of flow rate of water and the time taken. We are to get the volume of water used between 6 am and 9 am, that is for 3 hours (9 - 6).

We are given the flow rate at 6 am and the flow rate at 9 am, but this flow rate changes between 6 am and 9 am. To get the estimate of the water used, Let us assume that it flows at the same flow rate as it was at 6 am throughout, hence:

[tex]V_L= 100 m^3/h * 3h=300\ m^3[/tex]

Also, let us assume that it flows at the same flow rate as it was at 9 am throughout, hence:

[tex]V_R= 280 m^3/h * 3h=840\ m^3[/tex]

To get the best estimate of the total volume, let us find the average of the two values, hence:

[tex]Volume=\frac{V_L+V_R}{2} =\frac{300+840}{2}=570\ m^3[/tex]

Answer:

35

Step-by-step explanation:

you multiply like it is a rectangle then you cut your answer in half in this case 7x10=70 cut in half is 35

Answer:

D) 675 units per day.

Step-by-step explanation:

We can write a function to model the situation.

The company is currently producing 275 units per day.

And it will increase its production by 50 units after each year.

Therefore, after y years, its production in units per day will be:

[tex]f(y)=275+50y[/tex]

Then 8 years from now, the company will be producing:

[tex]f(8)=275+50(8)=275+400=675\text{ units per day.}[/tex]

Our answer is D.

Answer:

x = 2

y = 1

Step-by-step explanation:

Answer:

x= 2

y= -1

Step-by-step explanation:

Answer:

226.78579

Step-by-step explanation

first, find k in 90(3^kx)

90(e^0) = 90 [when time is 0 years, the population is 90]

180=90(e^k3), 2=e^3k

ln2 = 3k, k=(ln2)/3

90(e^4(ln2)/3) = 90(e^ln(16)/3)

it is about 226.78579

Answer:

142°

Step-by-step explanation:

Minor arc QN = m(MN) + m(QM)

n(MN) = m<MKN = 90° (central angle = measure of intercepted arc)

m(NO) = m<NKO = 38° (measure of intercepted arcs)

m(QM) = 180° - (m(MN) + m(NO)) (half circle)

Substitute

m(QM) = 180° - (90° + 38°)

m(QM) = 52°

✔️Minor arc QN = m(MN) + m(QM)

Substitute

Minor arc QN = 90° + 52° = 142°

Answer:

y = 1/2x+4

Step-by-step explanation:

First find the slope

m= (y2-y1)/(x2-x1)

   = (3 - 5)/(-2 -2)

    = -2/-4

   = 1/2

Using point slope form

y -y1 = m(x-x1)  where m is the slope and (x1,y1) is a point on the line

y-5 = 1/2(x-2)

Distribute

y-5 = 1/2x -1

Add 5 to each side

y-5+5 = 1/2x -1+5

y = 1/2x+4

Answer:

perimeter = 71.4 m

Step-by-step explanation:

using the Pythagorean theorem:

CD² = 15.3² + (24 - 13.6)² = 234.09 + 108.16 = 342.25

CD = √342.25 = 18.5

perimeter = 24 + 15.3 + 13.6 + 18.5 = 71.4 m

Answer: x=1.21

Step-by-step explanation:

Given

Function is [tex]f(x)=0.8e^{2x}-9[/tex]

To find the zeroes, equate the function equal to zero

[tex]\Rightarrow 0.8e^{2x}-9=0\\\\\Rightarrow e^{2x}=\dfrac{9}{0.8}\\\Rightarrow e^{2x}=11.25[/tex]

taking natural logarithm both sides

[tex]\Rightarrow \ln (e^{2x})=\ln (11.25)\\\Rightarrow 2x=2.42\\\Rightarrow x=1.21[/tex]

The zero of the equation is 1.21

Answer:

13.5

Step-by-step explanation:

your teacher wrote all the tools you need down already.

we only need to apply them.

is that really so difficult ?

because of the law of sines we have

sin(27)/11 = sin(34)/x

we can also turn this upside down to simplify the calculation.

11/sin(27) = x/sin(34)

x = 11×sin(34)/sin(27) = 13.549 ≈ 13.5

there, that was all there was to it ...

Answer:

3.87

Step-by-step explanation:

? = a

b = 1

c = 4

a² + b² = c²

a² + 1² = 4²

a² + 1 = 16

a² = 15

a = 3.8729

Rounded to hundredths: 3.87

Answer:

AB = √17     4.1

GH = 4√2    5.7

Step-by-step explanation:

AB = 1²+4²=c²

1+16=c²

17=c²

√17=c

c=4.1

GH = 4²+4²=c²

16+16=c²

32=c²

√32=c

4√2=c

C=5.7

Answer:

$75

Step-by-step explanation:

he makes $44 and then you add the dollar per 31 books making $75

Answer:

Read the claim. Schools should stop doing standardized testing. Read the counterclaim. The Department of Education says that teaching students to do well on standardized tests helps to motivate students and keep them focused on important subjects. Read the rebuttal. On the contrary, being forced to focus on testing stresses students and limits the amount of knowledge they can gain. How can the writer revise the rebuttal to make it stronger

Answer:

B 113

Step-by-step explanation:

on edg

From the information given, the area of the circle is: "113 sq. cm".

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

The formula to find the area of a circle is,

Area = πr².

Now, Using the side as the radius of the circle, we can calculate the area of the base area.

Here,

Radius r = 6

Thus, We get;

A = π x 6²

A = (22/7) x 36

A = 3.14285714286 x 36

A = 113.12

A ≈ 113 square unit.

Hence, The area of the circle is,

⇒ A =  113 sq. cm.

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The length of arc GJ is equivalent to 26π/3 units.

Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

Given is the value of 3 in 728.36.

In 728.36, the digit 3 is at tenths place. The digit 6 is at units place. We can say that the digit 3 is at tenths place in the decimal number 728.36.

Therefore, the digit 3 is at tenths place in the decimal number 728.36.

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Answer:

y= -|x - 3| graph

Step-by-step explanation:

Answer:

A) The higher the grade, the larger the average donation

Answer:

The Answer is A

Step-by-step explanation:

Answer:

24.3

Step-by-step explanation:

30% of 81 can be found by converting the percentage into the fraction 0.30 and then multiplying:  0.30(81) = 24.3

Answer:

4

Step-by-step explanation:

The domain of a function consist of all possible values of x that will give us corresponding values of y.

From the graph given, the points plotted indicates on the x-axis that the largest possible value we can have on the x-axis which represents Maya's Domain function is x = 4.

4 is the highest domain of Mayas function.

Answer:

b cuz its cosine but i flipped the numbers so it can be 20 over 12 and gave me exactly 0

The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of cos(θ) in the given triangle is 0.6.    

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm \sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\\cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\\tan \theta=\dfrac{Perpendicular}{Base}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

In a right angle, the cosine function of trigonometry is the ratio of the base of the triangle and the hypotenuse of the triangle.

For angle θ, the dimension of the triangle will be,

Perpendicular = 16

Base = 12

Hypotenuse = 20

Now, the measure of cos(θ) will be,

Cos(θ) = Base / Hypotenuse

           = 12 / 20

           = 6 / 10

           = 0.6

Hence, the value of cos(θ) in the given triangle is 0.6.

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