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4 years ago

What is the domain of the function on the graph?

Mathematics

2 answers:

lesya [120]4 years ago

5 0

That would be all numbers equal or greater than -3.

Thats the last choice.

Note the solid dot means that -3 is included in the domain

ivolga24 [154]4 years ago

5 0

Answer:

The correct option is 4. The domain of the function are all real numbers greater than or equal to –3.

Step-by-step explanation:

Domain is the set of all possible inputs or x-values, for which the given function is defined.

The given graph is defined form -3 to positive infinity. The point -3 included in the set of input because there is a closed circle at x=-3.

So, domain of the function are all real numbers greater than or equal to –3.

$Domain=\{x|-3\leq x,x\in R\}$

$Domain=[-3,\infty)$

Therefore the correct option is 4.

You might be interested in

Which expression is equivalent to -2/5(15-20d+5c)

Nataly [62]

Answer:

$- 2 \times 3 + 2 \times 4d - 2c \\ = - 6 + 8d - 2c$

3 0

3 years ago

How can (4x⁵/2x²)³ be solved in 2 different ways

Margaret [11]

We assume that we need to simplify the expression in two different ways.

Answer:

One way: Raise both, the numerator and denominator, to the third power, and then simplify the expression.

Second way: Simplify the terms inside parentheses, and then raise the result to the third power.

The result of both ways is the same: $\\8x^{9}$

Step-by-step explanation:

One way

Raise both, the numerator and denominator, to the third power, and then simplify the expression:

$\\ (\frac{4x^{5}}{2x^{2}})^{3}$

$\\ (\frac{64x^{5*3}}{8x^{2*3}})$

$\\ (\frac{64x^{15}}{8x^{6}})$

$\\ \frac{64}{8}\frac{x^{15}}{x^{6}}$

$\\8x^{9}$

This is the first simplification.

Second way

Simplify the terms inside parentheses, and then raise the result to the third power.

$\\ (\frac{4x^{5}}{2x^{2}})^{3}$

$\\ (\frac{4}{2}*\frac{x^{5}}{x^{2}})^{3}$

$\\ (2*x^{5-2})^{3}$

$\\ (2*x^{3})^{3}$

$\\ (2^{3}*x^{3*3})$

$\\ (8*x^{9})$

or $\\ 8x^{9}$ .

3 0

3 years ago

The function 3 y = 72(2) means y= 72 (2) (2) (2) O True O False

KonstantinChe [14]

Answer:

True

Step-by-step explanation:

y=72(2)

= 576

y=72(2)(2)(2)

=576

7 0

3 years ago

15 POINTS

AnnZ [28]

Answer:

Option(D)

Step-by-step explanation:

Diameter of the Sun (S) = 1.4 × 10⁶ km

Diameter of a planet mars (M) = 7000 km

≈ 7.0 × 10³ km

Ratio of the diameter of the Sun to the diameter of Mars

= $\frac{S}{M}$

= $\frac{1.4\times 10^{6}}{7.0\times 10^{3}}$

= $0.2\times 10^{6-3}$

= $0.2\times 10^3$

= $2\times 10^2$

Option (D) will be the correct option.

5 0

3 years ago

A company surveyed 2400 men where 1248 of the men identified themselves as the primary grocery shopper in their household. a) E

polet [3.4K]

Answer:

a) With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.

b) The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.

c) $\alpha =1-0.98=0.02$

Step-by-step explanation:

If np' and n(1-p') are higher than 5, a confidence interval for the proportion is calculated as:

$p'-z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }\leq p\leq p'+z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }$

Where p' is the proportion of the sample, n is the size of the sample, p is the proportion of the population and $z_{\alpha/2}$ is the z-value that let a probability of $\alpha/2$ on the right tail.

Then, a 98% confidence interval for the percentage of all males who identify themselves as the primary grocery shopper can be calculated replacing p' by 0.52, n by 2400, $\alpha$ by 0.02 and $z_{\alpha/2}$ by 2.33

Where p' and $\alpha$ are calculated as:

$p' = \frac{1248}{2400}=0.52\\\alpha =1-0.98=0.02$

So, replacing the values we get:

$0.52-2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\leq p\leq 0.52+2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\\0.52-0.0238\leq p\leq 0.52+0.0238\\0.4962\leq p\leq 0.5438$

With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.

The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.

Finally, the level of significance is the probability to reject the null hypothesis given that the null hypothesis is true. It is also the complement of the level of confidence. So, if we create a 98% confidence interval, the level of confidence $1-\alpha$ is equal to 98%

It means the the level of significance $\alpha$ is:

$\alpha =1-0.98=0.02$

4 0

3 years ago