Statistics 1

You are buying uniforms for young male military recruits. You know the mean chest size and the standard deviation of the chest size. About what proportion of the chest sizes of the recruits would you expect to be within one standard deviation of the mean chest size? Choose the best answer below


A. 50%, if the mean chest size is Normally distributed

B. 2/3

C. 50%, if the chest sizes are Normally distributed

D. 68%, if the chest sizes are Normally distributed

E. 95%

Answer:

∠G=110°

Step-by-step explanation:

The 4 interior angles of a kite add up to 360. 100+40=140. 360-140=220. E and G are the only angles left so we know together they must equal 220. And ∠E and ∠G are congruent angles beceause of kite rules. So, we divide by 2 to get how much angle E and G are individually.

Distance is the product of speed and time. The rate at which the distance between the ships changes at 4:00 p.m is 27.293 km/h.

Distance is the product of speed and time. It is given by the function,

[tex]\rm Distance = Time \times speed[/tex]

Given at noon the distance between two ships is 170 km. Furter ship A is moving towards the east at a speed of 40 km/h, therefore, the distance covered by Ship A in 4 hours will be,

[tex]\rm \text{Distance covered by Ship A in 4 hours} = 4 \times 40 = 160\ km[/tex]

The distance covered by Ship B in 4 hours will be,

[tex]\rm \text{Distance covered by Ship B in 4 hours} = 4 \times 15= 60\ km[/tex]

At 4 pm the distance between the two ships is the hypotenuse of the red triangle as shown below,

[tex]\rm Hypotenuse = \sqrt{10^2 + 60^2} = \sqrt{100+3600 }= 60.827\ km[/tex]

The rate of change in the distance between the two ships can be written as,

[tex]\rm \text{Rate of change of distance} = \dfrac{170-60.827}{4} = 27.293\ km/h[/tex]

Hence, the rate at which the distance between the ships changes at 4:00 p.m is 27.293 km/h.

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Answer: About 800 thousand

The more accurate value is 807,528 but this is also an approximation.

=======================================================

Work Shown:

[tex]t = \text{number of years since the year 2000}[/tex]

[tex]P_0 = \text{population (in millions) in the year 2000}[/tex]

[tex]P = P_0(1.2)^t\\\\5 = P_0(1.2)^{10}\\\\5 \approx P_0*6.1917364224\\\\P_0 \approx \frac{5}{6.1917364224}\\\\P_0 \approx 0.80752791444922\\\\P_0 \approx 0.807528\\\\[/tex]

That's the rough population of wild pigs (in millions) for the year 2000.

Multiply by [tex]10^6[/tex] to get it in terms of units instead.

[tex]0.807528\times10^6 = 807,528[/tex]

There were roughly 800 thousand wild pigs in the year 2000.

Answer:

t = 7.46, 0.42

Explanation:

h = 126t - 16t²    [ "h" is height, "t" is time ]

when height is 50 feet

==================

[tex]\sf use \ quadratic \ formula : x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ ax^2 + bx + c = 0[/tex]

==================

[tex]\Longrightarrow \sf t = \dfrac{-126\pm \sqrt{126^2-4\left(-16\right)\left(-50\right)}}{2\left(-16\right)}[/tex]

[tex]\Longrightarrow \sf t = \dfrac{63\pm\sqrt{3169}}{16}[/tex]

[tex]\Longrightarrow \sf t = 7.46, \ 0.42[/tex]

Let's find

Put h=50

Use quadratic formula

[tex]\\ \rm\Rrightarrow t=\dfrac{-126\pm\sqrt{126²-4(-16)(-50)}}{-32}[/tex]

[tex]\\ \rm\Rrightarrow t=7.5s,0.4s[/tex]

Answer:

B

Step-by-step explanation:

Because of inflation, prices at restaurants would go up.

Answer:

A=1

4πd2=1

4·π·122≈113.09734

Step-by-step explanation:

Answer:

113.04 feet :)

Step-by-step explanation:

First we divide 12 by 2 to find the radius!

12/2 = 6

Now we can solve!!

3.14(6^2)

3.14(36)

113.04

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Answer:

Seventy-two million, six hundred and seven thousand games remaining

please mark brainliest

Answer:

72607000

Step-by-step explanation:

just subtract 5312 from 72612312

Answer:

about 11

Step-by-step explanation:

Answer:

A= 57.79 degrees

B= 32.58 degrees

C= 89.63 degrees

Step-by-step explanation:

hope this helps!

Answer:

A. 57.79

Got it right on Plato

Answer:

[tex]41\frac{1}{8}[/tex]

Answer:

$7.50

Step-by-step explanation:

the question can be represented with:
12.5/5 and x/3

12.5/5 is 2.5, so that means each bag of dog food is $2.5  
So then you multiply 2.5 by 3, = 1.20, so 3 bags of dog food is $7.50.

Answer:

Step-by-step explanation:

Remark

I take it you mean 5 and not 0.5.

If that is the case, this is a proportion question. A proportion consists of 4 parts. If you know 3 of the parts, you can solve for the 4th one.

Formula

Number of bags/Cost = new number of bags/Cost of the new number

Givens

original Number of bags  = 5

Cost = 12.50

New number of bags = 3 bags

Cost = x

Solution

5/12.50 = 3/x           Cross Multiply

5x = 12.50 * 3          Combine the right

5x = 37.5                  Divide by 5

5x/5 = 37.5/5

x = 7.5

Answer: 3 bags cost 7.50 dollars.

Answer:

y= -12/x + 3

Step-by-step explanation:

Here's my answer

Answer:

  38.0 m/s

Step-by-step explanation:

Units conversion can be done by multiplying by appropriate conversion factors. Each conversion factor has a value of 1: the numerator is equal to the denominator, but the units are different. The units are chosen so that cancelling unwanted units gives the set of units you want.

__

  [tex]\dfrac{85\text{ mi}}{1\text{ h}}\times\dfrac{1.61\text{ km}}{1\text{ mi}}\times\dfrac{1000\text{ m}}{1\text{ km}}\times\dfrac{1\text{ h}}{3600\text{ s}}=\dfrac{85\cdot1.61\cdot1000\text{ m}}{3600\text{ s}}\\\\\approx\boxed{38.0\text{ m/s}}[/tex]

Using the histogram, it is found that the percentage of simulations is the average for group A at least 1.6 higher than the average for group B is given by:

A: 1.

An histogram is a graph that shows the number of times each element of x was observed.

In this problem, the histogram shows that out of the 100 simulations, only 1 had a difference of at least 1.6, as the bin corresponding to [1.6, 2] has value of 1 and the bins to the right of this have values of 0.

Hence, the percentage is given by:

P = 1/100 x 100% = 1%.

Which means that option A is correct.

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Answer:

7C

Step-by-step explanation:

Answer:

A.) 21.95

B.)22.47

Step-by-step explanation:

A.) An easy way to solve this is to use the Pythagorean theorem. Since the only person between Cyrus and Jane is Adriana, we will use her as a measuring point. Adriana's distance to Jane is 19, we will set a = 19, Adriana also is 11 miles away from Cyrus, and we will set b = 11. Now we plug it into the Pythagorean theorem.

[tex]a^2+b^2=c^2\\19^2+11^2=c^2\\\sqrt{482} =\sqrt{c^2}\\ 21.95=c[/tex]

B.) Using the same principle but for Adriana and Madisyn, we will use Jane as she is between them. Adriana is 19 miles from Jane, so we will set a=19, Madisyn is also 12 miles from Jane, so we will set b=12. Plug it for the Pythagorean theorem.

[tex]a^2+b^2=c^2\\19^2+12^2=c^2\\505=c^2\\\sqrt{505}=\sqrt{c^2}\\ 22.47 = c[/tex]

Answer:

tangina napaka pogi ko +41

Answer:

the answer is 56in2

Step-by-step explanation:

[tex]b = 14in \\ h = 8in \\ area \: of \: triangle = \frac{1}{2} b \times h \\ = \frac{1}{2} \times 14 \times 8 \\ = 56inches[/tex]

Answer:

D

Step-by-step explanation:

The equation of the circle is (d) (x -3)^2 +(y - 1)^2 = 58

The given parameters are:

Start by calculating the radius using:

r^2 = (x -a)^2 +(y - b)^2

So, we have:

r^2 = (0 -3)^2 +(-6 - 1)^2

Evaluate

r^2 = 58

The circle equation is then calculated using:

(x -a)^2 +(y - b)^2 = r^2

This gives

(x -3)^2 +(y - 1)^2 = 58

Hence, the equation of the circle is (d) (x -3)^2 +(y - 1)^2 = 58

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Answer:

y=x/2

Step-by-step explanation:

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The value of x from the given figure is 8

A triangle is a 2-dimensional shape with 3 sides an interior angle

Since the sum of the interior angles of a triangle is 180 degrees, hence;

8x - 4 + 76 + 44 = 180

8x + 116 = 180

8x = 180 - 116

8x = 64

x = 64/8

x = 8

Hence the value of x from the given figure is 8

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So, we need to solve the quadratic equation from quadratic formula as per the question, but before starting, let's first recall that, for any quadratic equation of the form ax² + bc + c = 0, the discriminant is given by D = b² - 4ac, and the value of x is given by :

Also, their are no real solutions of x i.e their are only imaginary values of x iff D < 0, equal and real roots iff D = 0 and real and distinct roots iff D > 0. So, let's convert the given equation to the standard form ax² + bx + c = 0 and then we will find the discriminant and then we will be solving for k ;

[tex]{:\implies \quad \sf 2k(k+5)=-25}[/tex]

[tex]{:\implies \quad \sf 2k^{2}+10k=-25}[/tex]

[tex]{:\implies \quad \sf 2k^{2}+10k+25=0}[/tex]

Now, on comparing this with the standard equation, we will get a = 2, b = 10 and c = 25, and then D = (10)² - 4 × 2 × 25 = 100 - 200 = - 100, now as D < 0, so their will be imaginary values of k, so now solving for k will yield by using the Quadratic Formula ;

[tex]{:\implies \quad \sf k=\dfrac{-10\pm \sqrt{-100}}{2\times 2}}[/tex]

[tex]{:\implies \quad \sf k=\dfrac{-10\pm 10\iota}{2\times 2}}[/tex]

[tex]{:\implies \quad \sf k=\dfrac{2(-5\pm 5\iota)}{2\times 2}=\dfrac{-5\pm 5\iota}{2}}[/tex]

[tex]{:\implies \quad \boxed{\bf{k=\dfrac{-5+5\iota}{2}\:\:,\:\: \dfrac{-5-5\iota}{2}}}}[/tex]

This is the required answer

Answer:

the answer to this question is 52.18

[tex]\begin{array}{lcccl} &\stackrel{solution}{gallons}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{gallons of }}{pure~alcohol}\\ \cline{2-4}&\\ \textit{25\% solution}&x&0.25&0.25x\\ \textit{5\% solution}&y&0.05&0.05y\\ \cline{2-4}&\\ mixture&20&0.08&1.6 \end{array}~\hfill \begin{cases} ~\hfill x + y &= 20\\\\ 0.25x+0.05y&=1.6 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=20\implies \underline{y = 20-x}} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.25x~~ + ~~0.05(\underline{20-x})~~ = ~~1.6}\implies 0.25x+1-0.05x=1.6 \\\\\\ 0.20x+1=1.6\implies 0.2x=0.6\implies x=\cfrac{0.6}{0.2}\implies \boxed{x=3}[/tex]

Answer:

8/6

Step-by-step explanation:

Sam has 8 times the number of eggs Kyle has can be expressed as:

[tex]\displaystyle \large{8\cdot \dfrac{1}{6}}[/tex]

As given, the number of eggs Kyle has is 1/6 so out of 6 eggs, Kyle only had 1.

Therefore, 8 multiplies/times the number of eggs is:

8/6