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jekas [21]
3 years ago
15

If the domain of the function f(x)=2x2- 8is {-2, 3, 5}, then the range is

Mathematics
1 answer:
Simora [160]3 years ago
6 0

Answer:

{0, 10, 42}

Step-by-step explanation:

<em>Domain is set of input values and range is set output values.</em>

For the function f(x) = 2x² - 8 and domain set of {-2, 3, 5}

<u>Range is:</u>

  • f(-2) = 2(-2)² - 8 = 0
  • f(3) = 2*3² - 8 = 10
  • f(5) = 2*5² - 8 = 42

<u>Range:</u> {0, 10, 42}

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If log50=1.699 then what is log(100)50? with the 100 being the subscript of log
Hatshy [7]
\bf \textit{Logarithm Change of Base Rule}\\\\&#10;log_a b\implies \cfrac{log_c b}{log_c a}&#10;\\\\\\&#10;\textit{Logarithm Cancellation Rules}\\\\&#10;\boxed{log_a a^x = x}\qquad \qquad a^{log_a x}=x\\\\&#10;-------------------------------\\\\&#10;log_{100}(50)\implies \cfrac{log_{10}(50)}{log_{10}(100)}\implies \cfrac{log_{10}(50)}{log_{10}(10^2)}\implies \cfrac{log(50)}{2}&#10;\\\\\\&#10;\cfrac{1.699}{2}\implies 0.8495
8 0
3 years ago
with Judy jogging north and Jackie jogging west (on straight roads). When Jackie is 1 mile farther fro m the intersection than J
dolphi86 [110]
Judy's distance from the intersection: d

<span>When Jackie is 1 mile farther from the intersection than Judy:
</span>Jakie's distance from the intersection: d+1

T<span>he distance between them is 2 miles more than Judy’s distance from the intersection: d+2

</span>How far is Jackie from the intersection?
d+1=?

Using the Pythagoras Theorem:
c^2=a^2+b^2; a=d, b=d+1, c=d+2
(d+2)^2=(d)^2+(d+1)^2
(d)^2+2(d)(2)+(2)^2=d^2+(d)^2+2(d)(1)+(1)^2
d^2+4d+4=d^2+d^2+2d+1
d^2+4d+4=2d^2+2d+1
d^2+4d+4-d^2-4d-4=2d^2+2d+1-d^2-4d-4
0=d^2-2d-3
d^2-2d-3=0
Factoring:
(d-3)(d+1)=0

d+1=0→d+1-1=0-1→d=-1<0 (negative): No possible. The distance can't be negative.

d-3=0→d-3+3=0+3→d=3 miles>0 (positive): Ok

Jakie's distance from the intersection=d+1=3+1→d+1=4 miles

Answer: <span>Jackie is 4 miles far from the intersection
</span>
Please, see the attached file.
Thanks


6 0
3 years ago
Translate this phrase into an algebraic expression.
Naily [24]

Answer:

2m + 8

Step-by-step explanation:

It's rather simple to break it down, take "8 more" as (+ 8) and twice Matt's savings into (2 * m) which then becomes simply (2m). Because of pemdas, your final answer should be 2m first then + 8, so 2m+8

5 0
3 years ago
Please help I will mark brainlist if correct
Virty [35]
We have 2 equations  here  ( b = cost of bush and  t = cost of a tree)

10b + 4t = 246........................................................(1)
5b + 3t = 147      Multiply this equation by -2:-
-10b - 6t = -294.......................................................(2)

Adding equations (1) and (2) we get:-

0 - 2t = - 48

t = -48/-2 = 24

Plug t = 24 into the first equation:-
10b + 4(24) = 246
10b = 246 - 96 = 150
b = 15 

The answer is one bush costs $15 and one tree costs $24.



4 0
3 years ago
The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first deter
JulsSmile [24]

Answer:

1) n=114

2) n=59

3) On this case no, because if we survey just the adults of the nearest college that would be a convenience sample. And when we use "convenience sample" we have some problems associated to bias. This methodology it's not appropiate in order to have a good estimation of the parameter of interest. It's better use a random, cluster or stratified sampling.

Step-by-step explanation:

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".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 80% of confidence, our significance level would be given by \alpha=1-0.80=0.2 and \alpha/2 =0.1. And the critical value would be given by:

z_{\alpha/2}=-1.28, z_{1-\alpha/2}=1.28

Part 1

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.06 or 6% points, and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

Since we don't have a prior estimate of \het p we can use 0.5 as a good estimate, replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.06}{1.28})^2}=113.77  

And rounded up we have that n=114

Part 2

On this case we have a prior estimate for the population proportion and is \hat p =0.85 so replacing the values into equation (b) we got:

n=\frac{0.85(1-0.85)}{(\frac{0.06}{1.28})^2}=58.027

And rounded up we have that n=59

Part 3

On this case no, because if we survey just the adults of the nearest college that would be a convenience sample. And when we use "convenience sample" we have some problems associated to bias. This methodology it's not appropiate in order to have a good estimation of the parameter of interest. It's better use a random, cluster or stratified sampling.

5 0
3 years ago
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