Find the value of x in the triangle shown below.

For what values of the variable are the following expressions defined?

Rom4ik [11]

Answer:

The Expression will be defined if the denominator is not equal to 0 since any number divided by 0 is undefined.
Therfore our main priority here is to check the denominator only because it's the only part that can make the expression undefined
the expression will be defined for all real numbers (a) BUT 3+a must not equal to 0 therfore (a) can be all real numbers but must never be equal to -3

Step-by-step explanation:

$a \: is \: an \: element \: of \: all \: real \: numbers \: but \: not \: not \: equal \: to \: -3$
HOPE THIS HELPS!

3 0

2 years ago

A quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain bra

tensa zangetsu [6.8K]

Answer:

We conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

Step-by-step explanation:

We are given that a quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain brand of soft drink contains 120 calories as the labeling indicates.

Using a random sample of 10 cans, the manager determined that the average calories per can is 124 with a standard deviation of 6 calories.

Let $\mu$ = average calorie content of a 12-ounce can.

So, Null Hypothesis, $H_0$ : $\mu \leq$ 120 calories {means that the average calorie content of a 12-ounce can is less than or equal to 120 calories}

Alternate Hypothesis, $H_A$ : $\mu$ > 120 calories {means that the average calorie content of a 12-ounce can is greater than 120 calories}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

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

where, $\bar X$ = sample average calories per can = 124 calories

s = sample standard deviation = 6 calories

n = sample of cans = 10

So, test statistics = $\frac{124-120}{\frac{6}{\sqrt{10} } }$ ~ $t_9$

= 2.108

The value of t test statistics is 2.108.

Now, at 0.05 significance level the t table gives critical value of 1.833 at 9 degree of freedom for right-tailed test. Since our test statistics is more than the critical values of t as 2.108 > 1.833, so we have sufficient evidence to reject our null hypothesis as it will in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

7 0

3 years ago

PLEASE HELP ME

earnstyle [38]

So here you're using system of equations. You can solve systems by graphing, elimination, or substitution. Ill use substitution. First lets solve for x. take the second equation and add y to both sides to get x by itself:
x - y = 75
x = y + 75 now plug y+75 in for x in the first equation
x + y = 743
(y +75) +y = 743 solve for y
2y +75 = 743 subtract 75
2y = 668 divide both sides by 2
y = 334
now plug this into any of the 2 equations to solve for x i chose the second one
x - y = 75
x - 334 = 75 add 334 to both sides
x = 409
This means x, sold before the tournament is 409 and y, sold at the door is 334. That means the assistant is wrong and accidentally flipped the two answers

8 0

3 years ago

Read 2 more answers

This table shows a proportional relationship between the number of cups of bananas and apples used for a smoothie.

mixer [17]

Answer:

For every 1 cup of banana you have to add 6 cups of apples. So it means there's six times as much apples as there is bananas. If there's 3 cups of apples, which is half of 6, it means the banana would now also have to be halved from 1 to half a cup.

Whatever you do to the bananas or the apples, you have to maintain the same ratio. Which is that apples is 6 times as much as bananas.

So 1 cup of apple would need to be divided by 6, to get banana. That would be approximately 1÷6= 0.167 cups

7 0

3 years ago

Tabitha and her parents drive to Dallas for a wedding. After 90 minutes, Tabitha's father tells her they have traveled 105 miles

BARSIC [14]

Im pretty sure it would be 70 mi/h

6 0

2 years ago