A car travels at an average speed of 48 miles per hour. How long does it take to travel 180 miles?

12) Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

never [62]

Answer:

Part a) Domain of f : {-3, -2, -1, 0, 1, 2, 3}

Part b) Domain of g : {-1, 0, 1, 2, 3, 4}

Part c) Domain of f+g = {-1, 0, 1, 2, 3}

Part d) Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Step-by-step explanation:

Part a) Determining the domain of f

Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

Domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of f : {-3, -2, -1, 0, 1, 2, 3}

Part b) Determining the domain of g

Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

As domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of g : {-1, 0, 1, 2, 3, 4}

Part c) Determining the domain of f+g

When there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains.

As,

Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

Domain of f : {-3, -2, -1, 0, 1, 2, 3}

and,

Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

Domain of g : {-1, 0, 1, 2, 3, 4}

As when there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains

So, the domain of f+g = {-1, 0, 1, 2, 3}

Part d) List the ordered pairs of f-g

As

f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

and

g = {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

For f - g, we must focus on subtracting the second (y) coordinates of both function that correspond to the same element in the domain (x)

(f - g)(x) = f(x) - g(x)

(f - g)(x) = f(-1) - g(-1) = 14 - 4 = 10

(f - g)(x) = f(0) - g(0) = 7 - 5 = 2

(f - g)(x) = f(1) - g(1) = 4 - 6 = -2

(f - g)(x) = f(2) - g(2) = 5 - 1 = 4

(f - g)(x) = f(3) - g(3) = 7 - (-16) = 23

So,

Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Keywords: domain, function, f+g, f-g

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7 0

4 years ago

If you write out the numbers from 1 through 40 (including 1 and 40), how many numbers have a "5" in them?

GaryK [48]

Answer:

4

Step-by-step explanation:

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40

6 0

3 years ago

What is the missing number?

JulsSmile [24]

Answer:

y = 2^{x}

Step-by-step explanation:

Given the above data for x and y.

From the algebraic expression;

y = 2^{x}

We can deduce that the value of y is equal to two (2) raise to the power of x.

When x = 1, y = 2

y = 2^{x}

y = 2^{1}

y = 2

When x = 2, y = 4

y = 2^{x}

y = 2^{2}

y = 4

When x = 3, y = 8

y = 2^{x}

y = 2^{3}

y = 8

The above calculations can be used to determine the other values of y with respect to x.

3 0

3 years ago

It is important that face masks used by firefighters be able to withstand high temperatures because firefighters commonly work i

Salsk061 [2.6K]

Answer:

$(-\infty, 0.2661)$

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".

The population proportion have the following distribution

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

n=60 represent the sample size

X=12 represent the number of masks that had lenses pop out at 250°

$\hat p =\frac{12}{60}=0.2$ represent the estimated proportion of masks that had lenses pop out at 250°

p represent the population proportion of masks that had lenses pop out at 250°

Confidence =0.9 or 90%

$\alpha=0.1$ represent the significance level

Confidence interval

On this case we want a interval on this form : $(-\infty,\hat p +z_{\alpha}\sqrt{\frac{\hat p (1-\hat p)}{n}})$

So the critical value would be on this case $z_{\alpha}=1.28$ and we can use the following excel code to find it: "=NORM.INV(1-0.1,0,1)"

We found the lower limit like this:

$0.2 +1.28\sqrt{\frac{0.2 (1-0.2)}{60}}=0.2661$

And the interval would be: $(-\infyt, 0.2661)$

3 0

4 years ago

Of all individual tax returns, 37 percent include errors made by the taxpayer. If IRS examiners are assigned randomly selected r

Dima020 [189]

Answer:

mean=4.44

standard deviation=1.67

Step-by-step explanation:

The mean and standard deviation for the number of erroneous returns per batch can be calculated using binomial distribution. The binomial distribution is used because

i) There are one of two possible outcomes( error or no error) that can be categorized into success and failure.

ii) The experiment is repeated fix number of times 12.

iii) The probability of success remains constant at each trial i.e. 37%

iv) The trails are independent.The mean and standard deviation of binomial distribution are np and √npq

Here, n=12, p=0.37 and q=1-0.37=0.63

mean=12*0.37=4.44

standard deviation=√12*0.37*0.63=√2.8=1.67

8 0

4 years ago