Assume the population is bell-shaped. Between what two values will approximately 95% of the population be

Answer:

15 / 4

Step-by-step explanation:

1 kg = 1000 g

3 kg

= 3 x 1000

= 3000 g

3kg to 800g

= 3kg : 800g

= 3000 : 800

= 30 : 8

= 30 / 8

= 15 / 4

15/4 is the fraction representing the ratio of 3 kilograms to 800 grams.

To express the ratio of 3 kilograms to 800 grams as a fraction in its lowest terms.

we need to convert both the quantities to the same units. Since 1 kg is equal to 1000 g, we can convert 3 kg to grams as follows:

3 kg = 3 * 1000 g = 3000 g

Now, we have the quantities in the same unit, and the ratio becomes:

3000 g to 800 g

To express this ratio as a fraction, we place the quantities over each other:

3000 g

-------

800 g

Now, to simplify the fraction to its lowest terms, we find the greatest common divisor (GCD) of the two numbers (3000 and 800) and divide both the numerator and denominator by this GCD.

The GCD of 3000 and 800 is 200, so dividing both by 200 gives us:

3000 ÷ 200 = 15

800 ÷ 200 = 4

Therefore, the ratio 3 kg to 800 g expressed as a fraction in its lowest terms is 15/4.

In summary, we first converted the units to the same (grams) to make the ratio easier to handle. Then, we represented the ratio as a fraction and simplified it to its lowest terms using the GCD method. The final answer, 15/4, is the fraction representing the ratio of 3 kilograms to 800 grams.

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Answer:

21.4 m

Step-by-step explanation:

Let x represent the sum of the tall metal, medium metal and short metal heights. Since the tall metal has a length of 1.44 m, and the ratio is in 9:8:7, hence:

(9/24) * x = 1.44

x = 3.84 m

For the medium metal pieces:

(8/24) * 3.84 = medium metal height

medium metal height = 1.28 m

For the short metal pieces:

(7/24) * 3.84 = short metal height

short metal height = 1.12 m

Total horizontal metal piece length  = 3 * 1.8 m = 5.4 m

Total tall metal piece length  = 2 * 1.44 m = 2.88 m

Total medium metal piece length  = 5 * 1.28 m = 6.4 m

Total short metal piece length  = 6 * 1.12 m = 6.72 m

Total length of metal = 5.4 + 2.88 + 6.4 + 6.72 = 21.4 m

Answer:

[tex]f(h(xc)) = 2xc-4[/tex]

Step-by-step explanation:

Given

[tex]f(x) = x - 7[/tex]

[tex]h(x) = 2x + 3[/tex]

Required

[tex]f(h(xc))[/tex]

First, calculate h(xc)

If [tex]h(x) = 2x + 3[/tex]

Then

[tex]h(xc) = 2xc + 3[/tex]

Solving further:

[tex]f(x) = x - 7[/tex]

Substitute h(xc) for x

[tex]f(h(xc)) = h(xc) - 7[/tex]

Substitute [tex]h(xc) = 2xc + 3[/tex]

[tex]f(h(xc)) = 2xc + 3 - 7[/tex]

[tex]f(h(xc)) = 2xc-4[/tex]

Answer:

The answer is a

Step-by-step explanation:

Answer:

f(4) = 31

f(0) = 7

f(-1) = 1

Step-by-step explanation:

f(x) = 6x + 7

f(4) = 6(4) + 7

f(4) = 24 + 7

f(4) = 31

f(0) = 6(0) + 7

f(0) = 0 + 7

f(0) = 7

f(-1) = 6(-1) + 7

f(-1) = -6 + 7

f(-1) = 1

Answer:

g(x) = x^3 - 2

Step-by-step explanation:

As you can see on the graph, the line has been translated down 2 units.

If the graph of f has the same shape as the graph of g, then the slope remains the same. The y intercept (k) changes by -2 units, so the k value is -2

g(x) = x^3 - 2

Hope this helps!!

Answer:

1,108 in²

Step-by-step explanation:

SA = (12×20) + (2×20×5 + 2×12×5) + (2×½×12×9)

+ (2×20×11)

= 240+320+108+440

= 1,108 in²

Answer:

the image is hard to read... this is the best that I can see

Step-by-step explanation:

[tex]\sqrt[3]{x^{3} } = x^{3/3} = x\\\sqrt[3]{x^{5} } = x^{5/3} \\\\\sqrt[5]{x } = x^{1/5} \\\\\sqrt[2]{x ^3 } = x^{3/2} \\[/tex]

~~~~~~~~~~~~~~~~~~~

Answer:

Step-by-step B represents the $14 John earned in the 2 hours he worked.

explanation:

(3.1) … … …

[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{2x-y}{x-2y}[/tex]

Multiply the right side by x/x :

[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{2-\dfrac yx}{1-\dfrac{2y}x}[/tex]

Substitute y(x) = x v(x), so that dy/dx = x dv/dx + v :

[tex]x\dfrac{\mathrm dv}{\mathrm dx} + v = \dfrac{2-v}{1-2v}[/tex]

This DE is now separable. With some simplification, you get

[tex]x\dfrac{\mathrm dv}{\mathrm dx} = \dfrac{2-2v+2v^2}{1-2v}[/tex]

[tex]\dfrac{1-2v}{2-2v+2v^2}\,\mathrm dv = \dfrac{\mathrm dx}x[/tex]

Now you're ready to integrate both sides (on the left, the denominator makes for a smooth substitution), which gives

[tex]-\dfrac12\ln\left|2v^2-2v+2\right| = \ln|x| + C[/tex]

Solve for v, then for y (or leave the solution in implicit form):

[tex]\ln\left|2v^2-2v+2\right| = -2\ln|x| + C[/tex]

[tex]\ln(2) + \ln\left|v^2-v+1\right| = \ln\left(\dfrac1{x^2}\right) + C[/tex]

[tex]\ln\left|v^2-v+1\right| = \ln\left(\dfrac1{x^2}\right) + C[/tex]

[tex]v^2-v+1 = e^{\ln\left(1/x^2\right)+C}[/tex]

[tex]v^2-v+1 = \dfrac C{x^2}[/tex]

[tex]\boxed{\left(\dfrac yx\right)^2 - \dfrac yx+1 = \dfrac C{x^2}}[/tex]

(3.2) … … …

[tex]y' + \dfrac yx = \dfrac{y^{-3/4}}{x^4}[/tex]

It may help to recognize this as a Bernoulli equation. Multiply both sides by [tex]y^{\frac34}[/tex] :

[tex]y^{3/4}y' + \dfrac{y^{7/4}}x = \dfrac1{x^4}[/tex]

Substitute [tex]z(x)=y(x)^{\frac74}[/tex], so that [tex]z' = \frac74 y^{3/4}y'[/tex]. Then you get a linear equation in z, which I write here in standard form:

[tex]\dfrac47 z' + \dfrac zx = \dfrac1{x^4} \implies z' + \dfrac7{4x}z=\dfrac7{4x^4}[/tex]

Multiply both sides by an integrating factor, [tex]x^{\frac74}[/tex], which gives

[tex]x^{7/4}z'+\dfrac74 x^{3/4}z = \dfrac74 x^{-9/4}[/tex]

and lets us condense the left side into the derivative of a product,

[tex]\left(x^{7/4}z\right)' = \dfrac74 x^{-9/4}[/tex]

Integrate both sides:

[tex]x^{7/4}z=\dfrac74\left(-\dfrac45\right) x^{-5/4}+C[/tex]

[tex]z=-\dfrac75 x^{-3} + Cx^{-7/4}[/tex]

Solve in terms of y :

[tex]y^{4/7}=-\dfrac7{5x^3} + \dfrac C{x^{7/4}}[/tex]

[tex]\boxed{y=\left(\dfrac C{x^{7/4}} - \dfrac7{5x^3}\right)^{7/4}}[/tex]

(3.3) … … …

[tex](\cos(x) - 2xy)\,\mathrm dx + \left(e^y-x^2\right)\,\mathrm dy = 0[/tex]

This DE is exact, since

[tex]\dfrac{\partial(-2xy)}{\partial y} = -2x[/tex]

[tex]\dfrac{\partial\left(e^y-x^2\right)}{\partial x} = -2x[/tex]

are the same. Then the general solution is a function f(x, y) = C, such that

[tex]\dfrac{\partial f}{\partial x}=\cos(x)-2xy[/tex]

[tex]\dfrac{\partial f}{\partial y} = e^y-x^2[/tex]

Integrating both sides of the first equation with respect to x gives

[tex]f(x,y) = \sin(x) - x^2y + g(y)[/tex]

Differentiating this result with respect to y then gives

[tex]-x^2 + \dfrac{\mathrm dg}{\mathrm dy} = e^y - x^2[/tex]

[tex]\implies\dfrac{\mathrm dg}{\mathrm dy} = e^y \implies g(y) = e^y + C[/tex]

Then the general solution is

[tex]\sin(x) - x^2y + e^y = C[/tex]

Given that y (1) = 4, we find

[tex]C = \sin(1) - 4 + e^4[/tex]

so that the particular solution is

[tex]\boxed{\sin(x) - x^2y + e^y = \sin(1) - 4 + e^4}[/tex]

Answer:

7x+y=-3

Step-by-step explanation:

if m is the slope of a line, then the slope of its parallel line will have the same slope m,

in the given equation, y=-7x-8, the slope is -7

among the options, 1st option has a slope of -7, since,

7x+y=-3

or, y=-7x-3

Answered by GAUTHMATH

Answer:

-36m^3-21n^3+85mn^2+36m^2n

Step-by-step explanation:

That's what the calculator says:).

Answer:

the anwer is B ( i mean second option)

And you can try it

you will find ;

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

HAVE A NİCE DAY

Step-by-step explanation:

GREETİNGS FROM TURKEY ツ

9514 1404 393

Answer:

  3/4

Step-by-step explanation:

It might be easier to start by expressing the ratios with AD as the denominator.

  AD/AC = 2/1   ⇒   AC/AD = 1/2

  AD/AB = 3/1   ⇒   AB/AD = 1/3

From the latter, we have ...

  (AD -AB)/AD = 1 -1/3 = 2/3 = BD/AD

Then the desired ratio is ...

  AC/BD = (AC/AD)/(BD/AD) = (1/2)/(2/3) = (3/6)/(4/6)

  AC/BD = 3/4

Answer:

[tex]\mu = 5.2[/tex]

[tex]\sigma = 2.257[/tex]

Step-by-step explanation:

Given

[tex]n = 260[/tex] -- samples

[tex]p = \frac{1}{50}[/tex] --- one in 50

Solving (a): The mean

This is calculated as:

[tex]\mu = np[/tex]

[tex]\mu = 260 * \frac{1}{50}[/tex]

[tex]\mu = 5.2[/tex]

Solving (b): The standard deviation

This is calculated as:

[tex]\sigma = \sqrt{\mu * (1-p)}[/tex]

[tex]\sigma = \sqrt{5.2 * (1-1/50)}[/tex]

[tex]\sigma = \sqrt{5.2 * 0.98}[/tex]

[tex]\sigma = \sqrt{5.096}[/tex]

[tex]\sigma = 2.257[/tex]

Answer:

Step-by-step explanation:

circumference = πd ≅ 250 ft

d ≅ 250/π ≅80 ft

(a) The region Y₁ < 1/2 and Y₂ > 1/4 corresponds to the rectangle,

{(y₁, y₂) : 0 ≤ y₁ < 1/2 and 1/4 < y₂ ≤ 1}

Integrate the joint density over this region:

[tex]P\left(Y_1<\dfrac12,Y_2>\dfrac14\right) = \displaystyle\int_0^{\frac12}\int_{\frac14}^1 (y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac{21}{64}}[/tex]

(b) The line Y₁ + Y₂ = 1 cuts the support in half into a triangular region,

{(y₁, y₂) : 0 ≤ y₁ < 1 and 0 < y₂ ≤ 1 - y₁}

Integrate to get the probability:

[tex]P(Y_1+Y_2\le1) = \displaystyle\int_0^1\int_0^{1-y_1}(y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac13}[/tex]

Y₁ and Y₂ are not independent because

P(Y₁ = y₁, Y₂ = y₂) ≠ P(Y₁ = y₁) P(Y₂ = y₂)

To see this, compute the marginal densities of Y₁ and Y₂.

[tex]P(Y_1=y_1) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_2 = \begin{cases}\frac{2y_1+1}2&\text{if }0\le y_1\le1\\0&\text{otherwise}\end{cases}[/tex]

[tex]P(Y_2=y_2) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_1 = \begin{cases}\frac{2y_2+1}2&\text{if }0\le y_2\le1\\0&\text{otherwise}\end{cases}[/tex]

[tex]\implies P(Y_1=y_1)P(Y_2=y_2) = \begin{cases}\frac{(2y_1+1)(2y_2_1)}4&\text{if }0\le y_1\le1,0\ley_2\le1\\0&\text{otherwise}\end{cases}[/tex]

but this clearly does not match the joint density.

Answer:

36 (maybe...)

Step-by-step explanation:

Technically there is no way to answer this question, it says that 120 ADULTS were surveyed and then asks how many STUDENTS rank themselves as introverts.  But if we a supposed to assume that all adults are students:

The ratio of 3:7 means that for every 3 introverts, there are 7 extroverts.

In other words for every 10 people (total introvert+extrovert) there are 3 introverts.

So to find the number of introverts in the group of 120, just multiply by 3/10 or 0.3

The answer would be 36

Answer:

Step-by-step explanation:

-2

Step-by-step explanation:

here is the answer to your question

Answer:

The right answer is "0.3193".

Step-by-step explanation:

According to the question,

Mean,

[tex]\frac{1}{\lambda} = 13[/tex]

[tex]\lambda = \frac{1}{13}[/tex]

As we know,

The cumulative distributive function will be:

⇒ [tex]1-e^{-\lambda x}[/tex]

hence,

In the first 5 years, the probability of failure will be:

⇒ [tex]P(X<5)=1-e^{-\lambda\times 5}[/tex]

                    [tex]=1-e^{-(\frac{1}{13} )\times 5}[/tex]

                    [tex]=1-e^(-\frac{5}{13})[/tex]

                    [tex]=1-0.6807[/tex]

                    [tex]=0.3193[/tex]

Answer:

16?

Step-by-step explanation:

I'm not sure. I hope so.

Answer:

3z+3x=2

Step-by-step explanation:

3z+8=12+3x-2

collecting like terms

3z-3x=12-2-8

3z-3x=2

3z=2+3x

divide through by three

z= ⅔+x

Answer:

729π ft³

Step-by-step explanation:

Applying,

Volume of a cone

V = πr²h/3.............. Equation 1

Where r = radius of the base, h = height, π = pie

From the question,

Given: r = 9 ft, h = 27 ft

Substitite these values into equation 1

V = π(9²)(27)/3

V = 729π ft³

Hence the volume of the figure in terms of π is 729π ft³

Answer:

Step-by-step explanation:

B

9514 1404 393

Answer:

  y = 7√2

Step-by-step explanation:

We are given the side opposite the angle, and we want to find the hypotenuse. The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(45°) = 7/y

  y = 7/sin(45°) = 7/(1/√2)

  y = 7√2

__

Additional comment

In this 45°-45°-90° "special" right triangle, the two legs are the same length. Thus, ...

  x = 7

Answer:

Step-by-step explanation:

Total sales = x

Correct choice is C

Answer:

1000

Step-by-step explanation:

Answer:

slope is 2÷3 of giving line points