Think of 5 positive integers that have a mean, median, mode, and range of 6.

Answer:

a) The bullet hits the ground after 64 seconds.

b) The bullet hits the ground 113,511.7 feet away.

c) The maximum height attained by the bullet is of 16,384 feet.

Step-by-step explanation:

Equations of motion:

The equations of motion for the bullet are:

[tex]x(t) = (v_0\cos{\alpha})t[/tex]

[tex]y(t) = (v_0\sin{\alpha})t - 16t^2[/tex]

In which [tex]v_0[/tex] is the initial speed and [tex]\alpha[/tex] is the angle.

Initial speed of 2048 ft/s at an angle of 30o to the horizontal.

This means that [tex]v_0 = 2048, \alpha = 30[/tex].

So

[tex]x(t) = (v_0\cos{\alpha})t = (2048\cos{30})t = 1773.62t[/tex]

[tex]y(t) = (v_0\sin{\alpha})t - 16t^2 = (2048\sin{30})t - 16t^2 = 1024t - 16t^2[/tex]

(a) After how many seconds will the bullet hit the ground?

It hits the ground when [tex]y(t) = 0[/tex]. So

[tex]1024t - 16t^2 = 0[/tex]

[tex]16t^2 - 1024t = 0[/tex]

[tex]16t(t - 64) = 0[/tex]

16t = 0 -> t = 0 or t - 64 = 0 -> t = 64

The bullet hits the ground after 64 seconds.

(b) How far from the gun will the bullet hit the ground?

This is the horizontal distance, that is, the x value, x(64).

[tex]x(64) = 1773.62(64) = 113511.7[/tex]

The bullet hits the ground 113,511.7 feet away.

(c) What is the maximum height attained by the bullet?

This is the value of y when it's derivative is 0.

We have that:

[tex]y^{\prime}(t) = 1024 - 32t[/tex]

[tex]1024 - 32t = 0[/tex]

[tex]32t = 1024[/tex]

[tex]t = \frac{1024}{32} = 32[/tex]

At this instant, the height is:

[tex]y(32) = 1024(32) - 16(32)^2 = 16384[/tex]

The maximum height attained by the bullet is of 16,384 feet.

Answer:

[tex]P(X = 0) = 0.03125[/tex]

[tex]P(X = 1) = 0.15625[/tex]

[tex]P(X = 2) = 0.3125[/tex]

[tex]P(X = 3) = 0.3125[/tex]

[tex]P(X = 4) = 0.15625[/tex]

[tex]P(X = 5) = 0.03125[/tex]

Step-by-step explanation:

For each toss, there are only two possible outcomes. Either it is tails, or it is not. The probability of a toss resulting in tails is independent of any other toss, which means that the binomial probability distribution is used to solve this question.

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.

Fair coin:

Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]

5 tosses:

This means that [tex]n = 5[/tex]

Probability distribution:

Probability of each outcome, so:

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

[tex]P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125[/tex]

[tex]P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625[/tex]

[tex]P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125[/tex]

[tex]P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125[/tex]

[tex]P(X = 4) = C_{5,4}.(0.5)^{4}.(0.5)^{1} = 0.15625[/tex]

[tex]P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]

Answer:

a AND ~c

Step-by-step explanation:

you can find the full explanation in wikipedia:

https://en.m.wikipedia.org/wiki/Material_conditional

under "Negated conditionals"

Answer:

Hence the correct option is option b) Yes, the upper level of one standard deviation is 72.

A score of 74 is not within one standard deviation of the mean.

Step-by-step explanation:

Here the given details are,

Mean = 68  

SD = 4  

Distribution is normal.  

Z-score for x = 74 is given as below:  

[tex]Z = (X - mean)/SD\\Z = (74 - 68)/4\\Z = 1.5[/tex]  

So, the score of 74 is 1.5 standard deviations from the mean.  

[tex]Mean + 1\timesSD = 68 + 1\times4 = 72Mean - 1\timesSD = 68 - 1\times4 = 64[/tex]  

Therefore the score is not lies between 64 and 72.  

Yes, the upper level of one standard deviation is 72.  

Answer:

is it four I am not quite sure

Answer:

4x2+3=

Step-by-step explanation:

Answer: (f-g)(x) = - 5^x + 3x - 2

Step-by-step explanation:

if f(x) = -5^x - 4 and g(x)= - 3x - 2,find (f-g)(x)

(f-g)(x) = -5^x - 4 - (-3x - 2)

(f-g)(x) = -5^x - 4 + 3x + 2

(f-g)(x) = - 5^x + 3x - 2

Answer:

15.000 is cost so relate it with 265..hope it is help u.

Answer:

option D

Step-by-step explanation:

[tex]sin^2 ( \frac{3\pi}{2}) + cos^2(\frac{3\pi}{2}) = 1\\\\( -1)^2 + 0^2 = 1[/tex]

Explanation:

[tex]sin x = cos( \frac{\pi}{2} - x)\\\\sin(\frac{3\pi}{2}) = cos ( \frac{\pi}{2} - \frac{3\pi}{2})\\[/tex]

            [tex]=cos(\frac{\pi - 3\pi}{2})\\\\ =cos(\frac{2\pi}{2})\\\\=cos \ \pi\\\\= - 1[/tex]

Therefore ,

               [tex]sin^2( \frac{3\pi}{2}) = ( - 1)^2[/tex]

Answer:

C: parallelogram

Step-by-step explanation:

Answer:

63 cm and 63 cm

Step-by-step explanation:

Both are 63 cm because 9*7 is 63, and those are the measurements of both faces

Answer:

Kindly check the attached picture

Step-by-step explanation:

The solution to the problem has been explicitly solved in the picture attached below :

We need to find a number that makes the denominator a perfect cube in other to simplify the expression which is 25/25.

Kindly check the attached picture for detailed explanation

Answer:

3.15 seconds is the answer.

Explanation

when the ball touches the ground, h =0

hence,

0=255-21t-16t²

16t²+21t-225=0

here a=16 ,b=21, c= -225

[tex]t= \frac{ - b± \sqrt{ {b }^{2} - 4ac} }{2a} \\ \\ t= \frac{ - 21± \sqrt{ {21}^{2} - 4 \times 16 \times - 225} }{2 \times 16} \\ = \frac{ - 21 ± \sqrt{441 - ( - 14400)} }{32} \\ = \frac{ - 21± \sqrt{14841} }{32} \\ = \frac{ - 21±121.82}{32} \\ \\ t = \frac{ - 21 + 121.82}{32} \: or \: \: t = \frac{ - 21 - 121.82}{32} \\ t = 3.15 \: \: or \: \: t = - 4.46[/tex]

time cannot be negative, hence t = -4.46 can be avoided

The ball takes 3.15 seconds to hit the ground.

9514 1404 393

Answer:

  D  neither

Step-by-step explanation:

Reflection across a vertical line is required to change the figure left-to-right without changing it top-to-bottom. Translation along a directed line segment must then map corresponding points.

Sequence A involves reflection over a horizontal line, so can be rejected immediately. Sequence B does the translation so that point N gets moved to the location of point B. However, point N corresponds to point D (see the similarity statement), so that translation is inappropriate.

Neither sequence will map KLMN to ABCD.

Answer:

He drank 354.882 mills of orange juice

Step-by-step explanation: One ounce is equal to 29.5735 mills, so you multiply 29.5735 by 12

Answer: 355 Millileters

Step-by-step explanation:

ejejejejrjruruehehhr

9514 1404 393

Answer:

Step-by-step explanation:

The graph shows the function value is zero for x=5 and x=7. These are the elements of the solution set.

  x ∈ {5, 7}

__

The graph is below the x-axis between these points, so that is the region where f(x) < 0

  5 < x < 7 . . . . . for f(x) < 0

In interval notation: (5, 7).

Step-by-step explanation:

28:20

Once simplified its 7:5

Answer:

2x=6. I think friend it is correct.

Answer:

2(×-6)

Step-by-step explanation:

Correct me if im wrong thanks ●~●

Answer:

[tex](f + g)(4) = 191[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5x^2 - 5x + 15[/tex]

[tex]g(x) = 6x^2 + 7x - 8[/tex]

Required

[tex](f + g)(4)[/tex]

First, calculate [tex](f + g)(x)[/tex]

This is calculated as:

[tex](f + g)(x) = f(x) + g(x)[/tex]

So, we have:

[tex](f + g)(x) = 5x^2 - 5x + 15+6x^2 + 7x - 8[/tex]

Collect like terms

[tex](f + g)(x) = 5x^2 +6x^2 - 5x+ 7x + 15 - 8[/tex]

[tex](f + g)(x) = 11x^2 + 2x + 7[/tex]

Substitute 4 for x

[tex](f + g)(4) = 11*4^2 + 2*4 + 7[/tex]

[tex](f + g)(4) = 191[/tex]

Answer:

25

Step-by-step explanation:

x = distance of the hike

y = number of friends coming along

so, we are looking for a linear relationship between these two.

y = ax + b

we need to find the factor a and the constant offset b.

19 = a×3 + b

7 = a×5 + b

7 - b = a×5

a = (7-b)/5

19 = (7-b)×3/5 + b

19 = (21 - 3b)/5 + b

95 = 21 - 3b + 5b

74 = 2b

b = 37

a= (7-37)/5 = -30/5 = -6

so, the relationship is

y = -6x + 37

for 2km hiking

y = -6×2 + 37 = -12 + 37 = 25 friends

Answer:

The sum of squared errors for the regression equation is 62.

Step-by-step explanation:

The sum of squared errors can be computed as follows:

X            Y           Y* = 2 + 3X         Y - Y*           (Y - Y*)^2

0            5                  2                      3                    9

3            5                  11                     -6                  36

7            27               23                     4                    16

10          31                32                    -1                     1  

20         68               68                     0                   62

From the above, we have:

Error = Y -  Y*

Error^2 = (Y - Y*)^2

Sum of squared errors = Sum of Error^2 = Total of (Y - Y*)^2 = 62

Therefore, the sum of squared errors for the regression equation is 62.

Answer: 1. When you estimate, it is not an exact measurement. 3ft 8 in gets rounded to 4ft and 12 ft 3 in rounds to 12ft. now find the perimeter. P=2l+2w P= 2*12 +2*4 P=32feet

2. 3ft 8in = 3 8/12 or reduced to 3 2/3  12ft 3in = 12 3/12 or reduced to 12 1/4   The fractional part is referring to a fraction of a foot.

3. The perimeter of the room is P=2l+2w or P=2(12 1/4) + 2(3 2/3) p=24 1/2 + 7 1/3  P= 31 5/6 feet

4. The estimate and the actual are very close. They are 1/6 of a foot apart.

5a. Total baseboard 31 5/6ft - 2 1/4 ft = 29 7/12 feet needed.

5b. Take the total and divide it by 8ft  = 29 7/12 divided by 8= 3.7  You are not buying a fraction of a board so you would need 4 boards.

Answer:

The 95% confidence interval for the population mean of such waiting times is between 19.5 and 24.5 minutes. This means that we are 95% sure that the true mean waiting time of all calls for this company is between 19.5 and 24.5 minutes.

The 99% confidence interval for the population mean of such waiting times is between 18.6 and 25.4 minutes. This means that we are 99% sure that the true mean waiting time of all calls for this company is between 18.6 and 25.4 minutes.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 25 - 1 = 24

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0639

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.0639\frac{6}{\sqrt{25}} = 2.5[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 22 - 2.5 = 19.5 minutes

The upper end of the interval is the sample mean added to M. So it is 22 + 2.5 = 24.5 minutes

The 95% confidence interval for the population mean of such waiting times is between 19.5 and 24.5 minutes. This means that we are 95% sure that the true mean waiting time of all calls for this company is between 19.5 and 24.5 minutes.

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.797

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.797\frac{6}{\sqrt{25}} = 3.4[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 22 - 3.4 = 18.6 minutes

The upper end of the interval is the sample mean added to M. So it is 22 + 3.4 = 25.4 minutes

The 99% confidence interval for the population mean of such waiting times is between 18.6 and 25.4 minutes. This means that we are 99% sure that the true mean waiting time of all calls for this company is between 18.6 and 25.4 minutes.

Answer:

the answer is x = 2 or B, hope this helps

Step-by-step explanation:

Answer:

14 to 132

Step-by-step explanation:

We are given that there are 132 boys and 14 adults. Since the question is only asking for the ratio of adults to boys, we don't have to worry about the number of girls in this question. From here, we see that the question is asking for the ratio of adults to boys, so we put it in that exact order. Our answer is 14 to 132. I hope this helps and please don't hesitate to reach out with more questions!

Answer:

11,000

Step-by-step explanation: