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2 years ago

What is the domain and range of the function

Mathematics

1 answer:

Stells [14]2 years ago

7 0

Answer:

Option d is correct.

Domain = all real number

range = positive real numbers

Step-by-step explanation:

Given the function: $y=f(x) = a^x$

Domain of the function is all real numbers except where the expression is undefined.

In this case, there is no real number that makes the expression undefined.

Domain of f(x) = $(-\infty , \infty)$ = {a | a∈R}

Range is the set of all valid f(x) values.

$(0,1) \cup (1, \infty)$

$\{y | y\neq 1 , y>0\}$

Therefore, Domain is all real number and the range of function is positive real number

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Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. Th

denpristay [2]

Answer:

(1) Correct option is B.

(2) Correct option is C.

Step-by-step explanation:

The information provided is:

$n_{1}=200,\ \bar x_{1}=22.7,\ s_{1} = 4.5\\n_{2}=200,\ \bar x_{2}=19.7,\ s_{2} = 4.3$

The (1 - <em>α</em>)% confidence interval for the difference between two mean is:

$CI=\bar x_{1}-\bar x_{2}\pm t_{\alpha/2, (n_{1}+n_[2}-2}\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}} }$

The critical value of <em>t</em> is:

$\alpha /2=0.05/2=0.025$

degrees of freedom $=n_{1}+n_{2}-2=200+200-2=398$

$t_{\alpha/2, n_{1}+n_{2}-2}=t_{0.025, 398}=1.96$

Compute the 95% confidence interval for the difference between two mean as follows:

$CI=22.7-19.7\pm 1.96\sqrt{\frac{4.5^{2}}{200}+\frac{4.3^{2}}{200} }\\=3\pm0.8624\\=(2.1376, 3.8624)\\\approx(2.14, 3.86)$

Thus, the 95% confidence interval, (2.14, 3.86) implies that the true mean difference value is contained in this interval with probability 0.95.

Correct option is B.

The null value of the difference between means is 0.

As the value 0 is not in the interval this implies that there is a difference between the two means, concluding that priming does have an effect on scores.

Correct option is C.

4 0

2 years ago

Please help me, I don’t know how to solve for x on this one

Brums [2.3K]

Use trigonometry to solve for x.

The tangent function is defined to be opposite side divided by the adjacent side.

tan(78) = x/10

tan(78)(10) = x

47.0463010948 = x

We now round off to two decimal places. In other words, we round off to the nearest tenths.

47.05 = x

Done!

5 0

2 years ago

5 divide 15x 15squared

Goryan [66]

Answer:

Step-by-step explanation:

(5 /15) x (15 squared = 75

4 0

2 years ago

PLEASE HELP ASAP!!!

Sonbull [250]

2x^2 - 7x - 6 = 0

$x1 = \frac{- b + \sqrt{ {b}^{2} - 4ac }}{2a}$
$x2 = \frac{- b - \sqrt{ {b}^{2} - 4ac }}{2a}$
where a=2
where b=-7
where c=-6

solve for x1 and x2

x1=4.21
x2=-0.71

6 0

2 years ago

At the local gas station gasoline costs $2.75 for per gallon and diesel costs $3.02 per gallon. Gabriel needs to purchase 15.2 g

Ainat [17]

Answer:

The total amount paid by Gabriel at the local gas station is $70.49.

Step-by-step explanation:

Cost of gasoline per gallon = $2.75

Cost of diesel per gallon = $3.02

Amount of gasoline Gabriel needs = 15.2 gallons

Amount of diesel Gabriel needs = 9.5 gallons

Compute the total amount paid by Gabriel at the local gas station as follows:

Total Cost = Cost of gasoline × Amount of gasoline

+ Cost of diesel × Amount of diesel

$=(2.75\times 15.2)+(3.02\times 9.5)\\\\=41.8+28.69\\\\=70.49$

Thus, the total amount paid by Gabriel at the local gas station is $70.49.

7 0

2 years ago