Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.0 millimeters (mm) and a standard deviation of 1.7 mm. For a randomly found shard, find the following probabilities.
a. the thickness is less than 3.0 mm
b. the thickness is more than 7.0 mm
c. the thickness is between 3.0 mm and 7.0 mm

Answer:

K=14

Step-by-step explanation:

A=1/2*b*h

80=1/2*8*(6+k)       multiply by 2 on both sides

160=8*(6+k)            distribute by 8

160=48+8k              subtract 48 from both sides

112=8k                     divide by 8

14=K

Answer:

6,720 ways

Step-by-step explanation:

Since in the problem arrangemnt is being asked this is a problem of permutation.

No . of ways of arranging r things out of n things is given by

P(n,r) =   n!/(n-r)!

In the problem given we have to arrange 5 objects from set of 8 objects.

Here n = 8 and p = 5

it can be done in in

P(8,5) =   8!/(8-5)! ways

8!/(8-5)!  = 8!/3! = 8*7*6*5*4*3!/3! = 8*7*6*5*4 = 6,720

Thus,  number of ways to  arrange 5 objects from a set of 8

different objects is P(8,5) =   8!/(8-5)! =  6,720 .

Answer:

Option C and F

Step-by-step explanation:

=> Square and Plane a two-dimensional objects.

Rest of the objects are either 1 - dimensional or 3- dimensional.

Answer:

The answer is option B

Step-by-step explanation:

Since 12 is greater than - 6

Hope this helps

Answer:

12 > -6

Step-by-step explanation:

A positive number is always greater than a negative number

12 > -6

Answer:

15

Step-by-step explanation:

38=10+13+c

c=38-10-13=15

Hope this helps!

Answer:

125 r. 10

Step-by-step explanation:

Answer:

  Mark the points of intersection between circle A and line AB.

Step-by-step explanation:

The attached shows an inscribed square created using technology. We started with point A and B, drew the circle with radius AB, and drew the line AB. Then we marked point C at the intersection of circle A and line AB.

We had a perpendicular to AB drawn through A, and marked its intersection with circle A as points D and E. Finally, we drew inscribed square BDCE.

__

Other answer choices may somehow be involved. We'd need to see the construction to be sure. The one shown above seemed most likely.

Answer:

20

Step-by-step explanation:

If the two triangles are similar, then corresponding sides must share a constant ratio. This means that:

[tex]\dfrac{10}{6}=\dfrac{25}{15}=\dfrac{x}{12}[/tex]

Let's use the second ratio:

[tex]\dfrac{25}{15}=\dfrac{x}{12}[/tex]

Multiply both sides by 12:

[tex]\dfrac{25\cdot 12}{15}=x \\\\x=20[/tex]

Hope this helps!

Answer:

let’s make a Unit rate.

$20/4 hours = $5 per hour

So you earn $5 in 1 hour if you earn $20 in 4 hours.

hope this helps and pls mark me brainliest if it did ;)

Answer:

$5

Step-by-step explanation:

Let's set up a proportion using the following setup.

money/hours=money/hours

We know that $20 is earned in 4 hours. We don't know how much is earned in 1 hour, so we can say $x is earned in 1 hour.

$20/4 hours= $x/1 hour

20/4=x/1

x/1 is equal to x.

20/4=x

Divide 20 by 4.

5=x

$5 is earned in 1 hour.

Answer:

a) x = 94 units/month

b) s = 51.50 units/month

Step-by-step explanation:

The adequate point estimation of the population mean and standard deviation are the sample mean and sample standard deviation.

a) Point estimation of the population (sample mean)

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(94+105+85+94+92)\\\\\\M=\dfrac{470}{5}\\\\\\M=94\\\\\\[/tex]

b) Point estimation of the population standard deviation (sample standard deviation)

[tex]s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{4}((94-94)^2+(105-94)^2+(85-94)^2+(94-94)^2+(92-94)^2)\\\\\\s=\dfrac{206}{4}\\\\\\s=51.50\\\\\\[/tex]

Using statistical concepts, it is found that:

a) The point estimate for the population mean is of: [tex]\overline{x} = 94[/tex]

b) The point estimate for the population standard deviation is of: [tex]s = 7.18[/tex]

Item a:

In this problem, the sample is: 94, 105, 85, 94, 92.

Thus, the mean is:

[tex]\overline{x} = \frac{94 + 105 + 85 + 94 + 92}{5} = 94[/tex]

Item b:

Then:

[tex]s = \sqrt{\frac{(94-94)^2+(105-94)^2+(85-94)^2+(94-94)^2+(92-94)^2}{4}} = 7.18[/tex]

A similar problem is given at https://brainly.com/question/13451786

Answer: x=3 y=1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Baltimore orioles : 1,000,000 + 1,000,000 + 500,000

Click 2 full bag and 1 half bag

Kansas city royals : 1,000,000 +500,000

Click 1 full bag and 1 half bag

Newyork Yankees  : 1,000,000 + 1,000,000 + 1,000,000 +1,000,000 +1,000,000 + 500,000

Click 5 full bag + 1 half bag

Answer:

24

Step-by-step explanation:

hello

let's note x the number we are looking for

[tex]\dfrac{x}{12}=6\\<=> x = 6*12=72[/tex]

so 1/3 of it equals

[tex]\dfrac{72}{3}=24[/tex]

another way to see it is that 12=4*3

so 1/3 of it equals 6*4=24

hope this helps

Answer:

The length of a 95% confidence interval for mean Age is 3.72.

Step-by-step explanation:

The data is provided for the age of 100 adults.

The mean and standard deviation are:

[tex]\bar x=47.8\\\\s=9.3744[/tex]

As the sample size is too large the z-interval will be used for the 95% confidence interval for mean.

The critical value of z for 95% confidence level is, z = 1.96.

The length of a confidence interval is given by:

[tex]\text{Length}=2\cdot z_{\alpha/2}\cdot\frac{s}{\sqrt{n}}[/tex]

           [tex]=2\times 1.96\times\frac{9.3744}{\sqrt{100}}\\\\=3.6747648\\\\\approx 3.67\\\\\approx 3.72[/tex]

Thus, the length of a 95% confidence interval for mean Age is 3.72.

Answer:

107.9 ft

Step-by-step explanation:

Imagine Kite is a point A. The person ,who keeps the string is point B.

The height of flying is AC=85 ft.  So we have right triangle ABC :angle C=90 degrees, angle B is 52 degrees. Length of AB (triangle ABC hypotenuse) is the length of the string.

AB=AC/sinB=85/sin52=107.8665...=approx 107.9 ft

Answer:

2/6, 4/12, 8/24, 16/48, 32/96 ect....

Step-by-step explanation:

I hope this helps I really didnt know if this is what you were asking about

Answer:

20%

Step-by-step explanation:

Answer:

20%

Step-by-step explanation: All you have to do is 16 divided by 80 which is 0.2. 0.2 as a decimal is 20%.

Answer:

r₁ = 3.583cm

V₁= 192.55cm³

r₂= 5.176cm

V₂ = 580.283cm³

r₃ = 5.255cm

V₃ = 607.479cm³

Step-by-step explanation:

assuming circumferences of each balloons are given as follows C₁ = 22.5cm, C₂ = 32.5cm and C₃ = 33cm

Recall C = 2πr

volume of a sphere is 4/3πr³

Answer:

(x-1)/13

Step-by-step explanation:

y = 13x+1

To find the inverse, exchange x and y

x = 13y+1

Solve for y

Subtract 1 from each side

x-1 =13y+1-1

x-1 = 13y

Divide each side by 13

(x-1)/13 = y

The inverse is (x-1)/13

Answer:

f(x) = 13x + 1

To find the inverse let f(x) = y

y = 13x + 1

x = 13y + 1

13y = x - 1

y = (x-1)/13

The inverse is x-1/13.

Answer:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.28})^2}=655.36[/tex]  

And rounded up we have that n=656

Step-by-step explanation:

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 80% of confidence, our significance level would be given by [tex]\alpha=1-0.80=0.20[/tex] and [tex]\alpha/2 =0.10[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=\pm 1.28 [/tex]

Solution to the problem

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

Since we don't have prior info for the proportion of interest we can use [tex]\hat p=0.5[/tex] as estimator. And on this case we have that [tex]ME =\pm 0.025[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.28})^2}=655.36[/tex]  

And rounded up we have that n=656

Answer:

The bounded area  is: [tex]\frac{73}{6}\approx 12.17[/tex]

Step-by-step explanation:

Let's start by plotting the functions that enclose the area, so we can find how to practically use integration. Please see attached image where the area in question has been highlighted in light green. The important points that define where the integrations should be performed are also identified with dots in darker green color. These two important points are: (2, 6) and (3, 1)

So we need to perform two separate integrals and add the appropriate areas at the end. The first integral is that of the difference of function y=x+4 minus function y=(1/3)x , and this integral should go from x = 0 to x = 2 (see the bottom left image with the area in red:

[tex]\int\limits^2_0 {x+4-\frac{x}{3} } \, dx =\int\limits^2_0 {\frac{2x}{3} +4} \, dx=\frac{4}{3} +8= \frac{28}{3}[/tex]

The next integral is that of the difference between [tex]y=-x^2+10[/tex] and the bottom line defined by: y = (1/3) x. This integration is in between x = 2 and x = 3 (see bottom right image with the area in red:

[tex]\int\limits^3_2 {-x^2+10-\frac{x}{3} } \, dx =-9+30-\frac{3}{2} -(-\frac{8}{3} +20-\frac{2}{3} )=\frac{39}{2} -\frac{50}{3} =\frac{17}{6}[/tex]

Now we need to add the two areas found in order to get the total area:

[tex]\frac{28}{3} +\frac{17}{6} =\frac{73}{6}\approx 12.17[/tex]

Answer:

0.015 = 1.5% of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 39368, \sigma = 2367[/tex]

What percentage of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe?

This is 1 subtracted by the pvalue of Z when X = 44520. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{44520 - 39368}{2367}[/tex]

[tex]Z = 2.18[/tex]

[tex]Z = 2.18[/tex] has a pvalue of 0.985

1 - 0.985 = 0.015

0.015 = 1.5% of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe

Answer:

a2+b2=c2

Step-by-step explanation:

find the saqure roof of two

Answer:

(∞,∞), (a /a∉R)

Step-by-step explanation:

Answer:

Standard errors are 0.049, 0.035, 0.022, and 0.016.

Step-by-step explanation:

The given value of population proportion (P) = 0.56

Given sample sizes (n ) 100, 200, 500, and 1000.

Now standard error is required to calculate.

Use the below formula to find standard error.

When sample size is n = 100

[tex]\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{100}} =0.049[/tex]

When sample size is n = 200

[tex]\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{200}} = 0.035[/tex]

When sample size is n = 500

[tex]\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{500}} =0.022[/tex]

When sample size is n = 1000

[tex]\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{1000}} = 0.016[/tex]

Answer:

  about 50.8 cubic meters

Step-by-step explanation:

The formula for the volume of a cone is ...

  V = (1/3)πr²h

Put the given values into the formula and do the arithmetic.

  V = (1/3)π(3.4 m)²(4.2 m) = 16.194π m³

__

For π to calculator precision, this is ...

  V ≈ 50.84 m³

For π = 3.14, this is ...

  V ≈ 50.82 m³

Answer:

3| 4 4 7

4| 0 3 4

5| 5 5 5

6| 0 1 3 8 9

7| 9

8| 1 4 6 8

hope it helps!

Step-by-step explanation:

Check the numbers and list out the tens digit in stem (that is 3-8) and then write the corresponding leaf values

Answer:

To solve for x we can write:

x² - y² = 55

x² = y² + 55

x = ±√(y² + 55)

To solve for y:

x² - y² = 55

y² = x² - 55

y = ±√(x² - 55)

Answer:

(3a+2b-4c)[4z+1]

Step-by-step explanation:

4z(3a+2b-4c)+(3a+2b-4c)

Factor out (3a+2b-4c)

(3a+2b-4c)[4z+1]

Answer:

3a+2b-4c)[4z+1]

Step-by-step explanation:

4z(3a+2b-4c)+(3a+2b-4c)

Factor out (3a+2b-4c)

(3a+2b-4c)[4z+1]

Step-by-step explanation:

While playing volleyball, probability of getting hurt is

P(A) = 0.1 = 1/10

and in the case of soccer, it is

P(B) = 0.2 = 2/10 = 1/5

Here we see, P(A) < P(B)

Answer: We can conclude that the probability of getting injured while playing soccer is more likely.

Answer:

The graph of the probability density function is attached.

Step-by-step explanation:

The probability function for this random number generator will be like the uniform distribution and defined for X ∈ [0, 1].

The probability density function can be written as:

[tex]f(x)={\begin{cases}{\dfrac {1}{1-0}}=1&\mathrm {for} \ 0\leq x\leq 1,\\[8pt]0&\mathrm {for} \ x<0\ \mathrm {or} \ x>1\end{cases}}[/tex]

The graph of the probability density function is attached.