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Answer:

[0.6969, 0.7695]

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

They randomly survey 401 drivers and find that 294 claim to always buckle up.

This means that [tex]n = 401, \pi = \frac{294}{401} = 0.7332.

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.7332 - 1.645\sqrt{\frac{0.7332*0.2668}{401}} = 0.6969[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.7332 + 1.645\sqrt{\frac{0.7332*0.2668}{401}} = 0.7695[/tex]

The 90% confidence interval for the population proportion that claim to always buckle up is [0.6969, 0.7695]

Answer:

Step-by-step explanation:

brilliant has 9 letters

brilliant has 1 B (1/9)

brilliant has 1 R (1/9)

brilliant has 2 I's (2/9)

brilliant has 2 L's (2/9)

brilliant has 1 A (1/9)

brilliant has 1 N (1/9)

brilliant has 1 T (1/9)

Answer:

252 options

Step-by-step explanation:

Please let me know if you want an explanation for why this is the answer (comment on this answer). A lot of people don't actually read the explanations, so I wouldn't want to waste my time. However, if you would like it I would be more than happy to type one out for you. Thanks!

Answer:

what's the problem!?......

angle CDT is the opposite angle of ADN

and the segment DF=FN, so AD= AN

and thats why angle FAN= angle FAD

here, Angle FAN =60,

therefore, FAD=60, and AFD = 90 so angle ADN must be 30 degree

and the opposite of ADN is CDT, and the opposite angles are equal.

Hope u got it.

Answer:

Step-by-step explanation:

In this question, the sample space contains 8 elements and has been given as;

          HHT HHH THH HTH HTT TTT TTH THT

1. For event A:

Outcomes of alternating tail and head = THH HTH HTT THT

                                          = 4 outcomes

Pr(alternating tail and head (with either coming first)) = [tex]\frac{4}{8}[/tex]

                                               = [tex]\frac{1}{2}[/tex]

2. For event B:

Outcomes of no tails on the first two tosses = HHT HHH

                                                   = 2 outcomes

Pr (No tails on the first two tosses) = [tex]\frac{2}{8}[/tex]

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

For event C:

Outcomes of a tail on both the first and the last tosses = THT TTT

                                                       = 2 outcomes

Pr(A tail on both the first and last tosses) = [tex]\frac{2}{8}[/tex]

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

Answer:

a) P(79 <= P <= 81) = 0.9968

b) P( X >  81 ) = 0.0002

Step-by-step explanation:

mean value = 75 GPa

standard deviation = 1.7 GPa

a) Determine P(79 <= P <= 81)

given that : n = 25

attached below is the detailed solution

P(79 <= P <= 81) = 0.9968

b) Determine how likely the sample mean diameter will exceed 81

given that n = 36

mean diameter = 81

P( X >  81 ) = 0.0002

Answer:

hfwhww45 5h wahdaw 5656 adshjdawh bh4 54

Step-by-step explanation:

5767

12345

Sum of digits = 1+2+3+4+5

= 15

Which means divisible by 3

Ends with 0 or 5 = Yes ends with 5

Therefore the number is divisible by 15

12345÷15 = 823

Divisiblity rule of 15 = Any number is divisible by 15 if the sum of the digits is divisible by 3 and the number ends with a 0 or 5.

Must click thanks and mark brainliest

Answer:

1.33

Step-by-step explanation:

62 can only be subtracted from 82 once. So 82.46-62 would be 20.46. Since you can't subtract anymore you put a decimal point. 62x3=186 and 20.46-186=1.86 and you can subtract 186-186=0.

Answer:

77.5

Step-by-step explanation:

Its rising at a constant rate between +10-15 each hour, so we if we were to add 25 or so to the 50, it would be close to 77.5, so I would assume the answer was B

Answer:

4

Step-by-step explanation:

Slope = y2-y1/x2-x1

We need to find two points on the graph, let's take these two points:

(x1, y1) (X2,y2)

(0,-6) and (2,2)

(2-(-6)/ (2-0) = 8/2 = 4

Answered by Gauthmath

Answer:

width: 3

Step-by-step explanation:

Given a length l and a width w, we can say that the perimeter is equal to

2 * l + 2 * w. Then, we also know that the perimeter is 27 plus its width, so

2 * l + 2 * w = 27 + w

and the length is 4 times its width, so length = 4 * width = l = 4 * w

We therefore have the two equations

2 * l + 2 * w = 27 + w

l = 4 * w

What we can do is plug 4* w for l in the first equation and solve from there. We thus have

2 * ( 4 * w) + 2 * w = 27 + w

8 * w + 2 * w = 27 + w

10 * w = 27 + w

subtract w from both sides to isolate the w and its coefficient

9 * w = 27

divide both sides by 9 to isolate w

w = 3

l = 4 * w = 12

Therefore, the width is 3 and the length is 12

Answer:

216 m²

Step-by-step explanation:

Surface area of a cube = 6a², when a = length of one side

so,

6a²

= 6×6²

= 6×36

= 216 m²

Answered by GAUTHMATH

Answer:

216 m²

Step-by-step explanation:

Answer:

19.95

Step-by-step explanation:

Take the amount of his salary and multiply by 5 1/4 %

380 * .0525

19.95

Answer:Perimeter of a rectangle is 2*the length plus 2*the width

P = 2L + 2W and P = 130, so

L + W = 65

Three times the length is equal to 10 times the width, giving

3L = 10W

Substituting into the above for L = 65 – W,

3(65 – W) = 10W

195 – 3W = 10W

195 = 13W

W = 195/13 = 15

W = 15 yards,

And L = (10/3)W = (10/3)*15 = 50

L = 50 yards

Step-by-step explanation:

Answer:

21%

Step-by-step explanation:

Percentage reduction is (999.99-789.99)/(999.99)=21%

Answer:

Step-by-step explanation:

Maximum value is when cos x = 1

So it is -2 + 4(1) = 2.

Minimum value, when  cos x = -1:

= -2  + 4(-1) = -6.

Answer:

The maximum 2 is reached when x=2pi,4pi, and 6pi.

The minimum -6 is reached when x=pi, 3pi,and 5pi.

Step-by-step explanation:

So let's first look at cos(x) on interval (0,21].

How many rotations is that? Does it at least contain 1 full rotation? If it contains one full rotation that means all the values from -1 to 1 (inclusive) are tagged? If it doesn't contain a full rotation, we might have to dig a little deeper.

So we know x=0 isn't included and that's when cosine is first 1,but this doesn't mean 1 won't be hit later.

Let's figure out the number of rotations:

21/(2pi)=3.3 approximately

This means we make at least 3 rotations.

So this means we definitely will have all the values from -1 to 1 tagged (inclusive).

Now let's look at whole function.

f(x) = -2 + 4 cos x

-2+(-4) to -2+4 will be the range of the function

So the minimum is -6 and the maximum is 2.

So the min occurs when cos(x)=-1 and the max occurs when cos(x)=1.

We have a little over three rotations and remember we can't include x=0.

cos(x)=1

when x=2pi (one full rotation)

when x=4pi (two full rotations)

when x=6pi (three full rotations)

We will stop here because cosine won't be 1 again until a fourth full rotation

cos(x)=-1

when x=pi (half rotation)

When x=3pi (one + half rotation)

When x=5pi (two+half rotation)

We can't include x=7pi (three+half rotation)

because this one is actually not in the interval because 3.5 is more than 3.3 .

The maximum 2 is reached when x=2pi,4pi, and 6pi.

The minimum -6 is reached when x=pi, 3pi,and 5pi.

Answer:

mean: 84

median: 85

mode: 85

explainations for d and e below.

Step-by-step explanation:

mean:

(85+80+96+72+78+85+92)/7 = 544/7 = 84

median:

sort them in order from least to greatest first

72, 78, 80, 85, 85, 92, 96

find the middle number in that order, that's your median. in this case, it's 85.

mode:

number that appears the most in the order; the frequency. in this case as well, it's also 85.

answer for d:

the reason why the mean is lower than the median is because of the fact we were figuring out the average and had to divide, unlike the median where it's just the middle of the order we have.

answer for e:

(85+80+96+72+78+85+92+100)/8 = 644/8 = 80.5%

p.s: please subscribe to #gauthmath# sub reddit if you can for more help.

Answer:

A

Step-by-step explanation:

f(x) = 1/(x-3)+7

f(x)-7=1/(x-3)

x=1/(f(x)-7)+3

f^-1(x)=1/(x-7)+3, where x≠7

The correct answer is option (a)  [tex]f^{-1}(x)= \frac{1}{x-7} +3[/tex] where [tex]x\neq 7[/tex].

The domain of a function is the complete set of possible values of the independent variable

Given [tex]f^{}(x)= \frac{1}{x-3} +7[/tex]

Let

[tex]y= \frac{1}{x-3} +7[/tex]

⇒y-7= 1/x-3

⇒x-3 =1/y- 7

⇒ [tex]x= \frac{1}{y-7} +3[/tex]

hence option a is correct

Learn more about domain here-brainly.com/question/24338767

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Answer:

8√2

Step-by-step explanation:

4√(10) -2

= 4√8

=4√4×2

=4×2√2

=8√2

Answer:

x = 2.56, y = -2.63

Step-by-step explanation:

I first multiplied the second equation by two, getting

4x-6y = 26

I then subtracted the equations

 4x+2y = 5

- 4x-6y = 26

--------------------

      8y = -21

y = -2.63

with y solved, I plugged it into the second equation to get x:

2x-3(-2.63) = 13

2x+ 7.89 = 13

2x = 5.11

x = 2.56

I hope this helped! ;D

Answer:

e < 24 is the inequality which shows the possible earnings per share.

Explanation:

x, will stand for the variable for earnings and less than, means it will not be higher nor the same as 24. Thus, being leaves us with one sign. The open part facing 24 means that 24 is the bigger number, therefore the smaller side represents that x has to be smaller than 24.

Answer: x<24

Step-by-step explanation:

x, will stand for the variable for earnings and less than means it will not be higher nor the same as 24. Thus being leaves us with one sign. The open part facing 24 means that 24 is the bigger number therefore the smaller side represents that x has to be smaller than 24.

Answer:

Does the answer help you?

Answer:

65% of 27.69 is 18.

Step-by-step explanation:

Formula = Number x 100

Percent = 18 x 100

65 = 27.69

Following shows the steps on how to derive this formula

Step 1: If 65% of a number is 18, then what is 100% of that number? Setup the equation.

18

65% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

65Y = 18 x 100

65Y = 1800

Y = 1800

100 = 27.69

9514 1404 393

Answer:

  r = 2.5

Step-by-step explanation:

The constant of proportionality can be found by solving the equation for r:

  r = y/x

Then any corresponding values of x and y can be used to find r:

  r = 25/10 = 2.5

The constant of proportionality is 2.5.

Answer:

c) The less than symbol should be replaced with the less than or equal to symbol.

Step-by-step explanation:

3(-4 - n/-2) < 5

The equation written above could be interpreted as :

The product of 3 and the difference of -4 and the quotient of a number, n and -2 is less than 5

This means that the only error in Maddison's representation is the inequality sign, the inequality sign used by Maddison is wrong.

The equation should be used with a ≤ sign and expressed thus :

3(-4 - n/-2) ≤ 5

This means the left hand side (L. H. S) is less than or equal to 5 ; this means the L. H. S is at most 5

Answer:

C

Step-by-step explanation:

Answer:

0.81859

Step-by-step explanation:

Given that the length of recovery days for patients with knee surgery is normally distributed with :

Mean, μ = 123 days

Standard deviation, σ = 1 day

The proportion of patients that will recover with 121 and 124 days :

We obtain the Probability of Z score :

Z = (x - μ) / σ

P(Z < (x - μ) / σ) < Z < P(Z < (x - μ) / σ)

P(Z < (121 - 123) / 1) < Z < P(Z < (124 - 123) / 1)

P(Z < - 2) < Z < P(Z < 1)

Using the normal distribution table :

P(Z < 1) - P(Z < - 2)

0.84134 - 0.02275

= 0.81859

Answer:

All Equal to 0

Step-by-step explanation:

0 = 0

3 - 3 = 0

0/4 = 0

12 - 3*4 = 0