Simplify. Rewrite the expression in the form 4^n (4^9 ) / ( 4^5)

Scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. What perce

Alla [95]

Answer:

The percentage is $P(350 < X 650 ) = 86.6\%$

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 500$

The standard deviation is $\sigma = 100$

The percent of people who write this exam obtain scores between 350 and 650

$P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100}$

Generally

$\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )$

$P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100}$

$P(350 < X 650 ) = P(-1.5$

$P(350 < X 650 ) = P(Z < 1.5) - P(Z < -1.5)$

From the z-table $P(Z < -1.5 ) = 0.066807$

and $P(Z < 1.5 ) = 0.93319$

=> $P(350 < X 650 ) = 0.93319 - 0.066807$

=> $P(350 < X 650 ) = 0.866$

Therefore the percentage is $P(350 < X 650 ) = 86.6\%$

3 0

3 years ago

A half circle is joined to an equilateral triangle whose

MArishka [77]

We want to find the perimeter of the given figure. We will find that the perimeter of the figure is 35.7 units.

Remember that for a circle of diameter D, the perimeter or circumference is:

p = pi*D

where pi = 3.14

So we have a half-circle and an equilateral triangle, and we know that the equilateral triangle sides measure 10 units each.

Notice that the diameter of the half-circle is equal to the side length of the triangle, then the diameter is D = 10

Then the length of the arc of the half-circle is just given as half the circumference of a circle with a diameter of 10 units, this is:

C = (1/2)*3.14*10 = 15.7

And to this we must add the two sides of the triangle that belong to the perimeter, remember that each one measures 10 units, then the total perimeter is:

Perimeter = 15.7 + 10 + 10 = 35.7

If you want to learn more, you can read:

brainly.com/question/9350935

8 0

3 years ago

If y varies inversely as x and y is 2.5 when x is 6, what is y when x is 4?

Lady_Fox [76]

Yvaries as x means
y=kx where k is constant
y=2.5
x=6
find k
2.5=k6
divide bot sides by 6
2.5/6=k (leave as that an simplfy later)

if x=4, what is y
y=(2.5/6)*4
y=10/6
y=5/3
y=1 and 2/3

5 0

3 years ago

Help a brother out with some math? Jane bought a desk that was marked down 60% from an original price of $100. If she paid 5% sa

OlgaM077 [116]

Answer:

45 i think

Step-by-step explanation:

i could be totally wrong about this but im pretty sure that if an initial price is 100 percentages are really easy. so 100 minus 60 is 40 and with a 5 percent tax thats 45.

6 0

3 years ago

A factory produces widgets whose length must be within 1.5 mm of an ideal length of 47 mm. A factory supervisor wants to mark ru

Nat2105 [25]

Using absolute value, it is found that:

The situation is described by the following equation: $|l - 47| = 1.5$
The markings should be between 45.5mm and 48.5mm.

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

The definition of the absolute value function is as follows:

$|x| = x, x \geq 0$

$|x| = -x, x < 0$

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

The length should be set to 47mm with an allowance of 1.5mm, which means that the absolute value of the difference between the length and 47 should be 1.5, thus:

$|l - 47| = 1.5$

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

The solutions are:

$l - 47 = -1.5 \rightarrow l = 45.5$

$l - 47 = 1.5 \rightarrow l = 48.5$

The markings should be between 45.5mm and 48.5mm.

A similar problem is given at brainly.com/question/24514895

3 0

3 years ago