Why can you use cross products to solve the proportion 18/5 equals x/100 for x?

Debora [2.8K]

I am assuming you meant to write the following options

A. f(x)=x+3; g(x)=√x
B. f(x)=x; g(x)=x+3
C. f(x)=√x; g(x)=x+3
D. f(x)=3x; g(x)=√x

You need to find a fucntion f(x) that once evaluated in g(x) gives us as a result h(x)

h(x) = g(f(x))

Looking at the options, the answer is A.

g(f(x)) = sqrt(f(x)) = sqrt (x + 3) = h(x)

8 0

3 years ago

Read 2 more answers

A right triangle has legs measuring 18 in. and 26 in. What is the length of the hypotenuse? Round to the nearest tenth. A) 18.8

Evgen [1.6K]

Answer:

a

Step-by-step explanation:

3 0

3 years ago

A grinding wheel manufacturer designed a new grinding wheel. Repeated tests were conducted on wheels of approximately the same w

sergejj [24]

Answer:

a) $a=225 +0.674*16.5=236.121$

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.

b) $P(X \geq 3) = 1-P(X$

c) $P(\bar X \geq 225)=1- P(\bar X$

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".

2) Part a

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

$X \sim N(225,16.5)$

Where $\mu=225$ and $\sigma=16.5$

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

$P(X>a)=0.25$ (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 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

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:

$z=0.674=\frac{a-225}{16.5}$

And if we solve for a we got

$a=225 +0.674*16.5=236.121$

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.

Part b

For this case we know that the individual probability of select one wheel with a cutting rate higher than the calculated value in part a is 0.25, and we select n =10 so then we can use the binomial distribution for this case:

$X\sim Bin(n=10, p=0.25)$

And we want this probability:

$P(X \geq 3) = 1-P(X$

We can find the individual probabilities like this:

$P(X=0)=(10C0)(0.25)^0 (1-0.25)^{10-0}=0.0563$

$P(X=1)=(10C1)(0.25)^1 (1-0.25)^{10-1}=0.1877$

$P(X=2)=(10C2)(0.25)^2 (1-0.25)^{10-2}=0.2816$

$P(X \geq 3) = 1-P(X$

Part c

For this case we know that the distribution for the sample mean is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we want this probability:

$P(\bar X \geq 225)$

And for this case we can use the complement rule and the z score given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we replace we got:

$P(\bar X \geq 225)=1- P(\bar X$

4 0

3 years ago

Two complex numbers are given byz1= 3 +j4 andz2= 2 +j3. Determine in both polar andCartesian forms

Marat540 [252]

Answer:

Cartesian

z₁= 3 +4*j

z₂= 2 +3*j

Polar

z₁=5 * e^ (0.927*j)

z₁=√13 * e^ (0.982*j)

Step-by-step explanation:

for the complex numbers z the cartesian form of is

z= x + y*j

then

1) z₁= 3 +4*j (cartesian form)

2) z₂= 2 +3*j (cartesian form)

the polar form is

z= r* e^jθ

where

r= √(x²+y²) → r₁ = √(3²+4²) = 5 , r₂ = √(2²+3²) = √13

and

θ = tan⁻¹ (y/x) → θ₁ = tan⁻¹ (4/3)= 0.927 rad , θ₂ = tan⁻¹ (3/2)= 0.982 rad

then

z₁=5 * e^ (0.927*j)

z₁=√13 * e^ (0.982*j)

3 0

3 years ago

Please answer this question, thx :)

dusya [7]

Answer:

49.5

Step-by-step explanation:

just put into you calculator

47+(15/3)/2

3 0

3 years ago