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The mean lifespan of a sylvania light bulb is 1600 hours with a standard deviation of 300 hours, an iqr of 450 hours, and a rang

IgorLugansk [536]

Given that t<span>he mean lifespan of a sylvania light bulb is 1600 hours with a standard deviation of 300 hours, an iqr of 450 hours, and a range of 690 hours. the lifespan distribution is relatively symmetric.

Since, the distribution is relatively symmetric, the measure of spread that is the best measurement is the standard deviation.</span>

6 0

3 years ago

A right rectangular prism has a length of 5 cm, a width of 4 cm, and a height of 3 cm. The dimensions of the prism are doubled.

yKpoI14uk [10]

Answer:

376 square centimeters

Step-by-step explanation:

When doubled, the new length is 5*2=10 cm, new width is 4*2=8 cm, and new height is 3*2=6 cm.

The surface area of a rectangular prism is given by : $2(lw+wh+lh)$

Where l is length, w is width, and h is height

Plugging in the new values we get:

$2(lw+wh+lh)\\=2((10)(8)+(8)(6)+(10)(6))\\=2(80+48+60)\\=2(188)\\=376$

The surface area of the enlarged prism = 376 cm^2

6 0

4 years ago

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If light travels at 3. 108 m/s and its frequency is 6. 1015 Hz, then its wavelength is:

Sergio039 [100]

Answer:

$5 * 10^{-8} m$

Step-by-step explanation:

The speed of light is $3 * 10^8 m/s$ and its frequency is $6 * 10^{15} Hz$ .

The speed of light is given as:

c = λ * f

where λ = wavelength of light

f = frequency of light

Therefore, the wavelength is given as:

λ = c / f

=> λ = $\frac{3 * 10^8}{6 * 10^{15}}$

=> λ = $5 * 10^{-8} m$

The wavelength of the light is $5 * 10^{-8} m$

7 0

3 years ago

The polynomial P(x) = 2x^3 + mx^2-5 leaves the same remainder when divided by (x-1) or (2x + 3). Find the value of m and the rem

Zigmanuir [339]

Answer:

m=7

Remainder =4

If q=1 then r=3 or r=-1.

If q=2 then r=3.

They are probably looking for q=1 and r=3 because the other combinations were used earlier in the problem.

Step-by-step explanation:

Let's assume the remainders left when doing P divided by (x-1) and P divided by (2x+3) is R.

By remainder theorem we have that:

P(1)=R

P(-3/2)=R

$P(1)=2(1)^3+m(1)^2-5$

$=2+m-5=m-3$

$P(\frac{-3}{2})=2(\frac{-3}{2})^3+m(\frac{-3}{2})^2-5$

$=2(\frac{-27}{8})+m(\frac{9}{4})-5$

$=-\frac{27}{4}+\frac{9m}{4}-5$

$=\frac{-27+9m-20}{4}$

$=\frac{9m-47}{4}$

Both of these are equal to R.

$m-3=R$

$\frac{9m-47}{4}=R$

I'm going to substitute second R which is (9m-47)/4 in place of first R.

$m-3=\frac{9m-47}{4}$

Multiply both sides by 4:

$4(m-3)=9m-47$

Distribute:

$4m-12=9m-47$

Subtract 4m on both sides:

$-12=5m-47$

Add 47 on both sides:

$-12+47=5m$

Simplify left hand side:

$35=5m$

Divide both sides by 5:

$\frac{35}{5}=m$

$7=m$

So the value for m is 7.

$P(x)=2x^3+7x^2-5$

What is the remainder when dividing P by (x-1) or (2x+3)?

Well recall that we said m-3=R which means r=m-3=7-3=4.

So the remainder is 4 when dividing P by (x-1) or (2x+3).

Now P divided by (qx+r) will also give the same remainder R=4.

So by remainder theorem we have that P(-r/q)=4.

Let's plug this in:

$P(\frac{-r}{q})=2(\frac{-r}{q})^3+m(\frac{-r}{q})^2-5$

Let x=-r/q

This is equal to 4 so we have this equation:

$2u^3+7u^2-5=4$

Subtract 4 on both sides:

$2u^3+7u^2-9=0$

I see one obvious solution of 1.

I seen this because I see 2+7-9 is 0.

u=1 would do that.

Let's see if we can find any other real solutions.

Dividing:

1 | 2 7 0 -9

| 2 9 9

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

2 9 9 0

This gives us the quadratic equation to solve:

$2x^2+9x+9=0$

Compare this to $ax^2+bx+c=0$

$a=2$

$b=9$

$c=9$

Since the coefficient of $x^2$ is not 1, we have to find two numbers that multiply to be $ac$ and add up to be $b$ .

Those numbers are 6 and 3 because $6(3)=18=ac$ while $6+3=9=b$ .

So we are going to replace $bx$ or $9x$ with $6x+3x$ then factor by grouping:

$2x^2+6x+3x+9=0$

$(2x^2+6x)+(3x+9)=0$

$2x(x+3)+3(x+3)=0$

$(x+3)(2x+3)=0$

This means x+3=0 or 2x+3=0.

We need to solve both of these:

x+3=0

Subtract 3 on both sides:

x=-3

----

2x+3=0

Subtract 3 on both sides:

2x=-3

Divide both sides by 2:

x=-3/2

So the solutions to P(x)=4:

$x \in \{-3,\frac{-3}{2},1\}$

If x=-3 is a solution then (x+3) is a factor that you can divide P by to get remainder 4.

If x=-3/2 is a solution then (2x+3) is a factor that you can divide P by to get remainder 4.

If x=1 is a solution then (x-1) is a factor that you can divide P by to get remainder 4.

Compare (qx+r) to (x+3); we see one possibility for (q,r)=(1,3).

Compare (qx+r) to (2x+3); we see another possibility is (q,r)=(2,3).

Compare (qx+r) to (x-1); we see another possibility is (q,r)=(1,-1).

6 0

3 years ago

How to tell if an inverse is a function without graphing?

Y_Kistochka [10]

A function's inverse will itself be a function if the original function is one-to-one. Meaning it passes the horizontal line test.

7 0

3 years ago