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1 year ago

In the equation below, a and b are constants. If a = b, what is the value of x in terms of y ? 2xa=8yb Select one:

Mathematics

1 answer:

Bas_tet [7]1 year ago

7 0

Answer: $x=4y$

Step-by-step explanation:

The equation is $2xa=8yb$ .

To find the value of the variable "x" in terms of "y", you need to apply the Division property of equality and divide both sides of the equation by "2a". Then:

$\frac{2ax}{2a}=\frac{8yb}{2a}$

$x=\frac{8yb}{2a}$

You know that the costants "a" and "b" are equal ( $a=b$ ), then:

$\frac{b}{a}=1$

Knowingt this, you can simplify.

Therefore, you get that the value of "x" in terms of "y" is:

$x=4y$

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From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that ag

Jlenok [28]

Answer:

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we to reject the null hypothesis, and the the actual mean starting age of smokers is significantly lower than 19.

Step-by-step explanation:

1) Data given and notation

$\bar X=18.1$ represent the mean age when smokers first start to smoke varies

$s=1.3$ represent the standard deviation for the sample

$\sigma=2.1$ represent the population standard deviation

$n=37$ sample size

$\mu_o =5.7$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean starting age is at least 19, the system of hypothesis would be:

Null hypothesis: $\mu\geq 19$

Alternative hypothesis: $\mu < 19$

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{18.1-19}{\frac{2.1}{\sqrt{37}}}=-2.607$

Calculate the P-value

Since is a one-side lower test the p value would be:

$p_v =P(z$

Conclusion

4 0

2 years ago

George took a nonstop flight from Dallas to

In-s [12.5K]

It is given in the question that,

George took a nonstop flight from Dallas to Los Angeles, a total flight distance of 1,233 miles. The plane flew at a speed of 460 miles per hour for the first 75 minutes of the flight and at a speed of 439 miles per hour for the remainder of the flight.

Let for x hours, the flight travelled with a speed of 439 miles per hour .

So we have,

$460* \frac{75}{60} + 439*x = 1233$

$575 + 439x =1233
\\
439x = 1233 - 575
\\
439x = 658
\\
x = \frac{658}{439} hours$

And to convert it in minutes, we have to multiply by 60. And on doing so, we will get

$x = \frac{658}{439}*60 =approx \ 90 \ minutes$

5 0

2 years ago

A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1 2 pound o

Valentin [98]

Answer:

47.25 pounds

Step-by-step explanation:

$\dfrac{dA}{dt}=R_{in}-R_{out}$

First, we determine the Rate In

Rate In=(concentration of salt in inflow)(input rate of brine)

$=(0.5\frac{lbs}{gal})( 6\frac{gal}{min})\\R_{in}=3\frac{lbs}{min}$

Change In Volume of the tank, $\frac{dV}{dt}=6\frac{gal}{min}-4\frac{gal}{min}=2\frac{gal}{min}$

Therefore, after t minutes, the volume of fluid in the tank will be: 100+2t

Rate Out

Rate Out=(concentration of salt in outflow)(output rate of brine)

$R_{out}=(\frac{A(t)}{100+2t})( 4\frac{gal}{min})\\\\R_{out}=\frac{4A(t)}{100+2t}$

Therefore:

$\dfrac{dA}{dt}=3-\dfrac{4A(t)}{100+2t}\\\\\dfrac{dA}{dt}=3-\dfrac{4A(t)}{2(50+t)}\\\\\dfrac{dA}{dt}=3-\dfrac{2A(t)}{50+t}\\\\\dfrac{dA}{dt}+\dfrac{2A(t)}{50+t}=3$

This is a linear differential equation in standard form, therefore the integrating factor:

$e^{\int \frac{2}{50+t}dt}=e^{2\ln|50+t|}=e^{\ln(50+t)^2}=(50+t)^2$

Multiplying the DE by the integrating factor, we have:

$(50+t)^2\dfrac{dA}{dt}+(50+t)^2\dfrac{2A(t)}{50+t}=3(50+t)^2\\\{(50+t)^2A(t)\}'=3(50+t)^2\\$Taking the integral of both sides\\\int \{(50+t)^2A(t)\}'= \int 3(50+t)^2\\(50+t)^2A(t)=(50+t)^3+C $ (C a constant of integration)\\Therefore:\\A(t)=(50+t)+C(50+t)^{-2}$

Initially, 20 pounds of salt was dissolved in the tank, therefore: A(0)=20

$20=(50+0)+C(50+0)^{-2}\\20-50=C(50)^{-2}\\C=-\dfrac{30}{(50)^{-2}} =-30X50^2=-75000$

Therefore, the amount of salt in the tank at any time t is:

$A(t)=(50+t)-75000(50+t)^{-2}$

After 15 minutes, the amount of salt in the tank is:

$A(15)=(50+15)-75000(50+15)^{-2}\\=47.25$ pounds$

8 0

1 year ago

What is the 12th term of the sequence? 3, −9, 27, −81, 243, ...

mestny [16]

The answer is 27 because not only does it refer to the number line sequence it doesn't actually mean a big number comes behind it. what ever it starts with,it multiplies the same pass the big number

6 0

2 years ago

What is the angle θ that the field e⃗ makes with the surface of the slab, which is perpendicular to the x direction? express you

Virty [35]

The angle θ that the field e⃗ makes with the surface of the slab, which is perpendicular to the x direction is θ = -1.57 rad

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1 year ago

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