What is the area of the rhombus?

marta [7]

To solve this problem, we first must rewrite each term in the form k times a^n so that we can compute the multiplication afterwards. To do this, we must remember that the square root of a is equivalent to a^(1/2) and that variables in the denominator have negative exponents. Using this knowledge, we can rewrite the given expression as:

a^(1/2) * (2a² - 4a^(-1))

Now, we must recall that when terms with the same base are multiplied together, we must add the exponents when simplifying. This step is shown below.

2a^(1/2 + 2) - 4a^(1/2 - 1)

The next step is to perform the addition of the exponents and obtain our final answer.

2a^(5/2) - 4a^(-1/2)

The above expression is your final answer.

Hope this helps!

6 0

3 years ago

7.2 x 10^-2 and 3 x 10^-1

Tom [10]

Answer:

7.2 × 10(24) 5.3 ×10-1

(7×2)×(10×24)×(5×3)×10-1

14×240×15×10-1

50400×10-1

504000-1=5403999

❥ʜᴏᴘᴇ \: ɪᴛ \: ʜᴇʟᴘs \: ʏᴏᴜ

5 0

3 years ago

(2-8i)^2 show work please

Archy [21]

(2 - (8 * i))^2 =
-60 - 32 i

that’s all i know idk how to show it but you can search it up

6 0

3 years ago

A classic rock radio station claims to play an average of 50 minutes of music every hour. However, it seems that every time you

tia_tia [17]

Answer:

a) $47.917-1.796\frac{2.811}{\sqrt{12}}=46.460$

$47.917+1.796\frac{2.811}{\sqrt{12}}=49.374$

b) Null hypothesis: $\mu =50$

Alternative hypothesis: $\mu \neq 50$

And after analyze the interval obtained the upper limit not contains the value of 50, so then we can conclude that the claim is not satisfied for this case, and the population mean seems to be lower than 50 at 10% of significance.

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".

We have the following data: 44 49 45 51 49 53 49 44 47 50 46 48

And we can calculate the sample mean and deviation with the following formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s= \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

And replacing we got:

$\bar X= 47.917, s= 2.811$

$\mu$ population mean (variable of interest)

n=12 represent the sample size

Part a: Calculate the confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom are given:

$df= n-1= 12-1=11$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,11)".And we see that $t_{\alpha/2}=1.796$

Now we have everything in order to replace into formula (1):

$47.917-1.796\frac{2.811}{\sqrt{12}}=46.460$

$47.917+1.796\frac{2.811}{\sqrt{12}}=49.374$

Part b

For this case the system of hypothesis are:

Null hypothesis: $\mu =50$

Alternative hypothesis: $\mu \neq 50$

And after analyze the interval obtained the upper limit not contains the value of 50, so then we can conclude that the claim is not satisfied for this case, and the population mean seems to be lower than 50 at 10% of significance.

6 0

3 years ago

What is the image of the point (0,5)(0,5) after a rotation of 180^{\circ}180

almond37 [142]

The image of the point (0,5) after a rotation of 180° counterclockwise about the origin is (0, -5).

<h3>What is geometric transformation?</h3>

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

The question is incomplete.

The complete question is:

What is the image of the point (0,5) after a rotation of 180° counterclockwise about the origin?

The rule for the above transformation:

(x, y) → (-x, -y)

(0, 5) → (0, -5)

Thus, the image of the point (0,5) after a rotation of 180° counterclockwise about the origin is (0, -5).

Learn more about the geometric transformation here:

brainly.com/question/16156895

#SPJ1

3 0

1 year ago