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3 years ago

State the domain and range for y=cos(-2x+180)+3

Mathematics

1 answer:

qwelly [4]3 years ago

4 0

Answer:

Domain: All real numbers

Range: $2\le x\le4$

Step-by-step explanation:

The given function is

$y=\cos(-2x+180\degree)+3$

The cosine function is continuous everywhere so the domain is all real numbers.

The range of the parent function $y=\cos(x)$

is $-1\le x\le 1$ .

The given function has been shifted up 3 units.

The range is

$-1+3\le x\le 1+3$ .

$2\le x\le 4$ .

See graph

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A random sample of 10 parking meters in a resort community showed the following incomes for a day. Assume the incomes are normal

GenaCL600 [577]

Answer:

A 95% confidence interval for the true mean is [$3.39, $6.01].

Step-by-step explanation:

We are given that a random sample of 10 parking meters in a resort community showed the following incomes for a day;

Incomes (X): $3.60, $4.50, $2.80, $6.30, $2.60, $5.20, $6.75, $4.25, $8.00, $3.00.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean income = $\frac{\sum X}{n}$ = $4.70

s = sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = $1.83

n = sample of parking meters = 10

$\mu$ = population mean

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-2.262 < $t_9$ < 2.262) = 0.95 {As the critical value of t at 9 degrees of

freedom are -2.262 & 2.262 with P = 2.5%}

P(-2.262 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.262) = 0.95

P( $-2.262 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu$ < $2.262 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.262 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.262 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.262 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.262 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $4.70-2.262 \times {\frac{1.83}{\sqrt{10} } }$ , $4.70+ 2.262 \times {\frac{1.83}{\sqrt{10} } }$ ]

= [$3.39, $6.01]

Therefore, a 95% confidence interval for the true mean is [$3.39, $6.01].

The interpretation of the above result is that we are 95% confident that the true mean will lie between incomes of $3.39 and $6.01.

Also, the margin of error = $2.262 \times {\frac{s}{\sqrt{n} } }$

= $2.262 \times {\frac{1.83}{\sqrt{10} } }$ = 1.31

4 0

3 years ago

If Jenna has $50.00 and Leon has $65.00 and they both want to by a baby bunny giant doll that cost $115.43 how much do they spli

patriot [66]

Even if they both spent all of their money, they would still be $0.43 short.

Leon’s $65 and Jennas $50 makes $115. Since they need $115.43, it doesn’t matter how they split the money as they wouldn’t have enough

Hope this helps :)

3 0

3 years ago

Read 2 more answers

Convert 0.86 into a fraction and reduce the answer to lowest terms

Andrei [34K]

Answer:

43/50

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Carys calculates the total amount EEE, in dollars, that she earns for working hhh hours using the equation E=10hE=10hE, equals,