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3 years ago

Find the length of dm in the given fig.

Mathematics

1 answer:

lesya692 [45]3 years ago

4 0

Answer:

$DM=12$

Step-by-step explanation:

(Let the point where the altitude from $D$ intersects $AB$ be called as point $E$ .) First, let's find the area of parallelogram $ABCD$ . The area of a parallelogram is simply $b*h=bh$ , where $b$ is the parallelogram's base and $h$ is the parallelogram's height. If we let $AB$ and $DE$ be the base and height respectively, since we are already given their lengths, we know that the area of parallelogram $ABCD$ will be $AB*DE=15*8=120$ .

Now, how does this information matter, you might ask? Well, we can take either $AB$ <em>or </em> $CB$ to be the base and either $DE$ or $DM$ to be the height. In this case, let's take the latter two options, as we are looking to find the length of $DM$ .

Therefore, we know that the area of parallelogram $ABCD$ can also be found by calculating $CB*DM$ . Since we know the values of the area and $CB$ , we can write the following equation to solve for $DM$ :

$Area = CB*DM$

$120=10*DM$ (Substitute $Area=120$ and $CB=10$ into the equation)

$\frac{120}{10}=\frac{10*DM}{10}$ (Divide both sides of the equation by $10$ to get rid of $DM$ 's coefficient)

$12=DM$ (Simplify)

$DM=12$ (Symmetric Property of Equality)

Hope this helps!

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If there bill was 58.65 and they gave a sever a 15% tip, how much did they pay altogether

masha68 [24]

Answer:

<u>$67.43 altogether</u>

Step-by-step explanation:

A 15% percent tip means 15% OF the bill.

15% of 58.65

$0.15*58.65=8.7975$

You can't really pay $8.7975, so you would round to the nearest one hundredth which is $8.78.

Now you add the $8.78 to $58.65 which will give you $67.43.

I hope that helps!

7 0

3 years ago

Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in the number of rooms oc

Anit [1.1K]

Answer:

a) $\hat \sigma^2 =s^2 =30^2 = 900$

b) $567.277 \leq \sigma^2 \leq 1690.224$

Rounded to the nearest number would be:

$567 \leq \sigma^2 \leq 1690$

c) $23.818 \leq \sigma \leq 41.112$

And rounded :

$23.8 \leq \sigma \leq 41.1$

Step-by-step explanation:

Data given and notation

s=30 represent the sample standard deviation

$\bar x=290$ represent the sample mean

n=20 the sample size

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 mean or variance 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.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

Part a

The best point of estimate for the population variance is the sample variance, so on this case:

$\hat \sigma^2 =s^2 =30^2 = 900$

Part b

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=20-1=19$

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 values.

The excel commands would be: "=CHISQ.INV(0.05,19)" "=CHISQ.INV(0.95,19)". so for this case the critical values are:

$\chi^2_{\alpha/2}=30.144$

$\chi^2_{1- \alpha/2}=10.117$

And replacing into the formula for the interval we got:

$\frac{(19)(30)^2}{30.144} \leq \sigma \leq \frac{(19)(30)^2}{10.117}$

$567.277 \leq \sigma^2 \leq 1690.224$

Rounded to the nearest number would be:

$567 \leq \sigma^2 \leq 1690$

Part c

In order to find the confidence interval for the deviation we just need to take the square root for the interval of the variance, and we got:

$23.818 \leq \sigma \leq 41.112$

And rounded :

$23.8 \leq \sigma \leq 41.1$

7 0

3 years ago

How would i graph the solution set for 1/3x (greater than or equal to) y+2?

Leto [7]

1/3x ≥ y + 2

You’ll have to transform the equation into its slope-intercept form, y = mx + b, so that you could graph the line. Set y to “=“

1/3x = y + 2
Subtract 2 from both sides

1/3x -2 = y + 2- 2

1/3x - 2 = y or y = 1/3x - 2

Next, to graph the solid line, you need at least two points to plot. We can start with the y-intercept, (0, -2). Another point to use is the x-intercept. To solve for the x-intercept, (a, 0), set y = 0:

0 = 1/3x - 2
Add 2 on both sides:

0 + 2 = 1/3x - 2 + 2
2 = 1/3x

Multiply both sides by 3 to solve for x:
2(3) = (3) 1/3x

6 = x

Therefore, the x-intercept = (6,0).

Plot the intercepts on the graph and connect those two points to create line.

Next, to identify which half-plane region to shade, choose a convenient test point (not on the line) to see whether it part of the solution. We could use the point of origin, (0, 0). Substitute its values into the linear inequality:

1/3x ≥ y + 2

1/3(0) ≥ (0) + 2
0 ≥ 2 (false statement). Therefore, you must shade the half-plane region where it doesn’t contain the test point, (0, 0).

Attached is the graph where it shows that the shaded lower half-plane region.

Please mark my answers as the Brainliest if you find my explanations helpful :)

6 0

2 years ago

Michael is walking from home to work. The function graphed represents the remaining distance to his work, in kilometers, x hours

Karolina [17]

x intercept- the number of remaining hours it takes to walk to work.

y intercept- the remaining distance from home to work.

Just took the quiz. Hope this helps you guys baiii <33

3 0

4 years ago

Read 2 more answers

Joseph went to the market and bought 5 9/10 pounds of tomatoes, 4 3/5 pounds of corn, 6 1/5 pounds of lemons, and 3 3/10 pounds

77julia77 [94]

Answer:

20 pounds

Step-by-step explanation:

5.9+4.6+6.2+3.3=20

7 0

2 years ago

Find the length of dm in the given fig.​

Find the length of dm in the given fig.