Find the product of (5a^3b) (2ab)

The table below shows the information given on a can of turkey chili.

Evgen [1.6K]

Answer:

A i think

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

the height of a triangle is 4 meters less than the base. if the area of the triangle is 6 m^2 what is the height of the triangle

inna [77]

Answer:

$2m$

Step-by-step explanation:

Alrighty let's do this.

We know that formula for the Area of a triangle is:

$A = \frac{1}{2}bh$

They give us the area as $6m^2$ , so let's include it in the equation.

$6 = \frac{1}{2}bh$

Now we reach a stage where we have 2 unknown variables! That means we can't solve it in its current state. So the idea you should have in cases like these where you have 2 or more unknown variables is, "Can I represent this one variable in terms of another variable?" In this case you can do exactly that. You can represent height in terms of length of the base. We are told the height of the triangle is 4 meters less than the base. That is telling us that $h = b-4$

So replace $h$ in the equation with $b-4$ .

You will now get:

$6 = \frac{1}{2}b(b-4)$

Now we can work towards solving. Let's get simplifying.

$12 = b(b-4)\\12 = b^2 - 4b\\$

bring everything to one side so we can make a quadratic and factor:

$0 = b^2 - 4b - 12\\0 = (b-6)(b+2)\\\\b = 6\\b\neq -2$

We get that $b=6$ .

Since we need the height of the triangle we'll need to call back on what h is. We found earlier that $h = b - 4$ , so to find h, we just sub in our b value into that.

$h = (6) - 4 = 2$

We find that $h=2$

7 0

2 years ago

A study by the National Athletic Trainers Association surveyed random samples of 1679 high school freshmen and 1366 high school

nekit [7.7K]

Answer:

We conclude that there is no significant difference in the proportion of all Illinois high school freshmen and seniors who have used anabolic steroids.

Step-by-step explanation:

We are given that a study by the National Athletic Trainers Association surveyed random samples of 1679 high school freshmen and 1366 high school seniors in Illinois.

Results showed that 34 of the freshmen and 24 of the seniors had used anabolic steroids.

Let $p_1$ = <u><em>proportion of Illinois high school freshmen who have used anabolic steroids.</em></u>

$p_2$ = <u><em>proportion of Illinois high school seniors who have used anabolic steroids.</em></u>

SO, Null Hypothesis, $H_0$ : $p_1=p_2$ {means that there is no significant difference in the proportion of all Illinois high school freshmen and seniors who have used anabolic steroids}

Alternate Hypothesis, $H_A$ : $p_1\neq p_2$ {means that there is a significant difference in the proportion of all Illinois high school freshmen and seniors who have used anabolic steroids}

The test statistics that would be used here <u>Two-sample z test for</u> <u>proportions</u>;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of high school freshmen who have used anabolic steroids = $\frac{34}{1679}$ = 0.0203

$\hat p_2$ = sample proportion of high school seniors who have used anabolic steroids = $\frac{24}{1366}$ = 0.0176

$n_1$ = sample of high school freshmen = 1679

$n_2$ = sample of high school seniors = 1366

So, <u><em>the test statistics</em></u> = $\frac{(0.0203-0.0176)-(0)}{\sqrt{\frac{0.0203(1-0.0203)}{1679}+\frac{0.0176(1-0.0176)}{1366} } }$

= 0.545

The value of z test statistics is 0.545.

Since, in the question we are not given with the level of significance so we assume it to be 5%. <u>Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.</u>

Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.

Therefore, we conclude that there is no significant difference in the proportion of all Illinois high school freshmen and seniors who have used anabolic steroids.

3 0

3 years ago

An inequality is shown. 27/7n > 4/3 Select all the values of n that make the inequality true.

ankoles [38]

Answer:

Step-by-step explanation:

<h2>Hope it help & study well</h2>

6 0

3 years ago

What is the value of the expression if m = –5 and n = 3? Negative StartFraction 24 Over 25 EndFraction Negative StartFraction 4

KatRina [158]

You can use the fact that a number raised to negative powers can be written as 1 divided by that number raised to positive number.

The value of the given expression when m = -5 and n= 3 is $-\dfrac{2}{5}$

<h3>How can we rewrite a number raised to negative power?</h3>

Suppose we've got $a^{-b}$ . then it can be rewritten as

$a^{-b} = \dfrac{1}{a^b}$

It is because $a^0 = 1$ for any a except 0, and that $\dfrac{a^0}{a^b} = a^{0-b} = a^{-b}$

If base are same and there is multiplication, then there will be addition in power.

Also, know the fact that if base are same and there is division, there will be subtraction in power(subtracting since that denominator when goes up, its power gets negated(gets negative sign to the existing power)

Thus,

$a^b \timesa ^c = a^{b+c}\\\\\dfrac{a^b}{a^c} = a^{b-c}$

<h3>Using above method to simplify the given expression before evaluating</h3>

The given expression is $\dfrac{2m^{-1}n^5}{3m^0n^4} = \dfrac{2n^5}{3m^0m^1n^4} = \dfrac{2n^5}{3mn^4} = \dfrac{2n^{5-4}}{3m} = \dfrac{2n^1}{3m} = \dfrac{2n}{3m}$

Putting m = -5 and n=3, we get:

$\dfrac{2\times 3}{3 \times -5} = -\dfrac{2}{5}$

Thus,

The value of the given expression when m = -5 and n= 3 is $-\dfrac{2}{5}$

Learn more about base and exponent(power) here:

brainly.com/question/847241

4 0

3 years ago