The time is 1:25 A.M. What time will it be in 6 hours and 55 minutes?

The sum of three consecutive even numbers is 114. what is the smallest of the three numbers?

saul85 [17]

Answer:

36

Step-by-step explanation:

Let's let n be any number.

If we multiply n by 2, we get 2n. Since anything multiplied by 2 is even, 2n <em>must</em> be even. Therefore, let 2n be our first number.

So, the consecutive even number will be (2n+2) followed by (2n+4).

We know that their sum must be 114. Therefore, we can write the following equation:

$(2n)+(2n+2)+(2n+4)=114$

Solve for n. Combine like terms on the left:

$6n+6=114$

Subtract 6 from both sides:

$6n=108$

Finally, divide both sides by 6. Therefore, the value of n is:

$n=108/6=18$

Therefore, our first even number is 2n or 2(18) which equates to 36.

And the consecutive even numbers will be 38 and 40.

So, the smallest of them, the first term, is 36.

4 0

3 years ago

Read 2 more answers

A random sample of 100 observations from a quantitative population produced a sample mean of 22.8 and a sample standard deviatio

natima [27]

Answer:

We conclude that the population mean is 24.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 24

Sample mean, $\bar{x}$ = 22.8

Sample size, n = 100

Alpha, α = 0.05

Sample standard deviation, s = 8.3

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 24\\H_A: \mu \neq 24$

We use Two-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{22.8 - 24}{\frac{8.3}{\sqrt{100}} } = -1.44$

We calculate the p-value with the help of standard z table.

P-value = 0.1498

Since the p-value is greater than the significance level, we accept the null hypothesis. The population mean is 24.

Now, $z_{critical} \text{ at 0.05 level of significance } = \pm 1.96$

Since, the z-statistic lies in the acceptance region which is from -1.96 to +1.96, we accept the null hypothesis and conclude that the population mean is 24.

7 0

3 years ago

Nate paid $13.25 for a shirt. This amount includes a sales tax of 6%. What was the cost of the shirt before tax?

kolbaska11 [484]

12.45
I hope
ᕦ(ò_óˇ)ᕤ

7 0

3 years ago

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The domain of a function is

kramer

Answer:

The domain of a function is the complete set of possible values of the independent variable. In plain English, this definition means: The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

Step-by-step explanation:

I hope this helped ;)

4 0

3 years ago

What if this function simplified?

almond37 [142]

Hi!

Let's first expand the cotangent of theta.

You'll probably know that tangent will be "y/x", or $\frac{sin(x)}{cos(x)}$ , and cotangent is the reciprocal of this, meaning that it is "x/y" or $\frac{cos(x)}{sin(x)}$ .