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3 years ago

If f(x) = -3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.

Mathematics

2 answers:

sdas [7]3 years ago

8 0

Answer:

2/3

Step-by-step explanation:

just did it on edge

creativ13 [48]3 years ago

5 0

Answer:

the lines meet at (2/3, 2)

Step-by-step explanation:

f(x) = g(x)

plug equations for f(x) and G(x)

-3x+4 = 2

-3x = -2

x = 2/3

since both equations meet at x = 2/3, it doesn't matter which equation you plug x = 2/3 into to find the y-coordinate

for simplicity purposes since g(x) is easier to solve, I am going to plug x = 2/3 into g(x), but plugging it into f(x) will give you same answer

g(x) = 2

g(2/3) = 2

the lines meet at (2/3, 2)

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Jack is a college athlete who has been weighing himself weekly on the same scale in the athletic center for the past few years.

Radda [10]

Answer:

a) Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=\pm 1.64$

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

And the standard error is given by:

$SE = \frac{\sigma}{\sqrt{n}}=\frac{3}{\sqrt{9}}=1$

c) $\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And the margin of error is:

$ME= z_{\alpha/2} \frac{\sigma}{\sqrt{n}} = 1.64$

And then the confidence interval is be given by:

$200-1.64 = 198.36$

$200+1.64 = 201.64$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

$\bar X= 200$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=3$ represent the population standard deviation

n=9 represent the sample size

Part a

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=\pm 1.64$

Part b

The distribution for the sample mean is given by:

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

And the standard error is given by:

$SE = \frac{\sigma}{\sqrt{n}}=\frac{3}{\sqrt{9}}=1$

Part c

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And the margin of error is:

$ME= z_{\alpha/2} \frac{\sigma}{\sqrt{n}} = 1.64$

And then the confidence interval is be given by:

$200-1.64 = 198.36$

$200+1.64 = 201.64$

8 0

3 years ago

Need help on this one. I JUST DONT WHAT TO DO IT

statuscvo [17]

Answer: Bottom Left

Step-by-step explanation:

5 0

3 years ago

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1.) The deer population increases at a rate of 3% per year. There are 1253 deer this year. Write a function that models the deer

BabaBlast [244]

Exponential growth/decay rule with general function is:y=y(0)ekt with k is growth/decay constant rate.
(1) Deer population function y(0) = 1253 k
= 3% t
= 6 (years)
y(6) = 1253 . e^(0.03*6) ~ 1500 (deers)
: 1496 deers
(2) Growth factor b is rate 9.5% = 0.095

4 0

3 years ago

Read 2 more answers

M is the midpoint of QR M = (-2,6) Q= (8,-10) R = ????

Zolol [24]

Answer:

R = (-12, 22)

Step-by-step explanation:

Unfortunately it's not a straight line, so gonna need to put in some extra work. Basically think of it like breaking it into it's horizontal and vertical components then doubling them.

From Q to M you move 10 spaces to the left, so to go from M to R you will go another 10 to the left. Similarly, you start at -10 for the y value and go up 16 to 6, and you will need to go up another 16 to get to R.

So for x, 8 -10 = -2 then -2 - 10 = -12, so R's x value is -12

y we do the same thing. Gonna do it in one step though. -10 + 16 + 16 = 22

So R is (-12, 22)

4 0

3 years ago

Which BEST explains the expression x( y z + 1 2 )? A) x depends on ( y z + 1 2 ). B) ( y z + 1 2 ) depends on x. C) x and ( y z

Alekssandra [29.7K]

9514 1404 393

Answer:

D) x and ( y z + 1 2 ) are independent of each other

Step-by-step explanation:

Assuming this is not intended to be describing a function named x with an argument of yz+12, the variables in any expression are assumed to be independent of each other, unless additional information is provided showing their dependencies.

Here, there is no such additional information, so we must assume ...

x and (yz +12) are independent of each other

_____

Additional comment

The assumption stated in the answer is intended to ensure we're not concerned with something of the form ...

g(x)

which is an expression saying 'g' is dependent on 'x'. If we know 'g' is a function name, then g(yz+12) will make 'g' be dependent on (yz+12).

Similarly, if x(a) is intended to mean that x is a function of 'a', then the corresponding x(yz+12) will mean that x is dependent on (yz+12). This would be quite unusual, since letters toward the end of the alphabet are usually used for variable names, while letters in the middle of the alphabet are used for function names.

8 0

2 years ago