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3 years ago

F(x)=-x^2+1 find f(-3)

Mathematics

1 answer:

Serjik [45]3 years ago

4 0

Answer:

-8

Step-by-step explanation:

All you have to do to solve this equation is plug "-3" into the equation where you see "x"

$f(x)=-x^2+1\\f(-3)=-(-3)^2+1\\f(-3)=-(9)+1\\f(-3)=-9+1\\f(-3)=-8$

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You’ve bought a cylindrical thermos 8 in. high with a base 6 in. across. How much coffee can you put in the thermos?

lana66690 [7]

Answer:

3.706 liters

Step-by-step explanation:

Hello

assuming that these measures correspond to the internal measures of the thermos,

we can calculate the volume as, the volume of a cylinder, which is given by

$V=\pi r^{2} h$

where r is the radius of the base, and h the height

also

Diameter=2r

r=Diameter/2

Step 1

let

h=8 in

base = diameter = 6 inch

r=diameter/2

r=6/2 inch,r=3 inch

Step 2

Put the values into the equation

$V=\pi r^{2} h\\V=\pi (3in)^{2} (8 in)\\V=\pi *72 \ in^{3} \\\\V=72\pi\ in^{3} \\\\$

Step 3

Now, the unit (cubic inches) is not an usual unit for measuring coffee, let´s convert cubic inches into liters by knowing

1 inch = 2.54 cm

1 litro = 1000 cubic centimeters

$if\ 1\ inch\ = 2.54\ cm\\(1\ inch)^{3} =(2.54\ cm)^{3}\\\\1\ inch^{3}=16.3870\ cm^{3}$

1 cubic inch = 16.3870 cubic centimeters

$1\ cubic\ inch\ = 16.3870\ cubic\ centimeters\\\\\\72\pi =x?\ cubic\ centimeters\\\\x=\frac{72\pi \cubic \ inch\ \*16.3870 }{1\ cubic\ inch} \\\\x=3706.65\ cubic\ centimeters$

Step 4

Finally, convert cubic centimeters into liters $1000\ cubic\ centimeters =1\ liter \\\\\\3706.65\ cubic\ centimeters = x?\ liters\ centimeters\\\\x=\frac{3706.65 \cubic \ centimeters\ \*1 liter}{1000 cubic centimeters} \\\\x=3706.65\ cubic\ centimeters\\x=3.706 Liters$

I can put 3.706 liters in the thermos

Have a good day

4 0

4 years ago

(1 point) The shelf life of a battery produced by one major company is known to be normally distributed with a mean life of 3 ye

NeX [460]

Answer:

$z=-0.994$

And if we solve for a we got

$a=3 -0.994*0.4=2.6024$

So the value of height that separates the bottom 16% of data from the top 84% is 2.6024 years

The answer rounded would be 2.6 years approximately

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the shelf life of a population, and for this case we know the distribution for X is given by:

$X \sim N(3,0.4)$

Where $\mu=3$ and $\sigma=0.4$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.84$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.16 of the area on the left and 0.84 of the area on the right it's z=-0.994. On this case P(Z<-0.994)=0.16 and P(z>-0.994)=0.84

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=-0.994$

And if we solve for a we got

$a=3 -0.994*0.4=2.6024$

So the value of height that separates the bottom 16% of data from the top 84% is 2.6024 years

The answer rounded would be 2.6 years approximately

8 0

4 years ago

Is the graphed function linear?

OLEGan [10]

Answer:

No, because the curve indicates that the rate of

change is not constant.

Im 99.9 sure

Step-by-step explanation:

7 0

3 years ago

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What is the prime factorization of 72?

Bingel [31]

Ik that 9 is one of em
Hope this helps have a nice nite

6 0

4 years ago

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It costs $0.60 per ft² to cover a right triangular field with sod. The side lengths of the field are 300 ft, 400 ft, and 500 ft.

algol [13]

In this triangle, we know base & perpendicular are 300 & 400 'cause 500 is the longest side which is hypotenuse

Now, Area of a triangle = ab/2 = (300)(400)/2 = 120000/2 = 60000

As cost for 1 ft² = $0.60
cost for 60000 ft² = 60000 * 0.60 = $36000

In short, Your Answer would be Option A

Hope this helps!

8 0

4 years ago

Read 2 more answers