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3 years ago

Triangle DEF is a right triangle and angles D and F are equal but are not right angles. What is the measure of angle E?

1 answer:

5 0

If it’s a right triangle 1 side is a right angle and if those 2 sides are equal and not right angles then E needs to be a right angle and a right angle is 90 degrees so it’s D

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What is the arc measure of BDC in degrees?<br> (4k + 159)<br> P<br> (2k + 153)

andre [41]

<h2>Explanation:</h2><h2></h2>

The diagram is missing but I'll assume that the arc BDC is:

$(4k + 159)^{\circ}$

And another arc, let's call it FGH. measures:

$(2k + 153)^{\circ}$

If those arc are equal, then this equation is true:

$(4k + 159)^{\circ}=(2k + 153)^{\circ} \\ \\ (4k + 159)=(2k + 153) \\ \\ \\ Solving \ for \ k: \\ \\ 4k-2k=153-159 \\ \\ 2k=-6 \\ \\ k=-\frac{6}{2} \\ \\ k=-3$

Substituting k into the first equation:

$\angle BDC=(4(-3)+159)^{\circ} \\ \\ \angle BDC=(-12+159)^{\circ} \\ \\ \boxed{\angle BDC=147^{\circ}}$

3 0

3 years ago

Read 2 more answers

Below are survival times (in days) of 13 guinea pigs that were injected with a bacterial infection in a medical study:

tresset_1 [31]

Outliers are data that are relatively far from other data elements.

The dataset has an outlier and the outlier is 120

The dataset is given as:

91 83 84 79 91 93 95 97 97 120 101 105 98

Sort the dataset in ascending order

79 83 84 91 91 93 95 97 97 98 101 105 120

<h3>The lower quartile (Q1)</h3>

The Q1 is then calculated as:

$Q1 = \frac{N +1}{4}th$

So, we have:

$Q1 = \frac{13 +1}{4}th$

$Q1 = \frac{14}{4}th$

$Q1 = 3.5th$

This is the average of the 3rd and the 4th element

$Q1 = \frac{1}{2} \times (84 + 91)$

$Q1 = 87.5$

<h3>The upper quartile (Q3)</h3>

The Q3 is then calculated as:

$Q3 = 3 \times \frac{N +1}{4}th$

So, we have:

$Q3 = 3 \times \frac{13 +1}{4}th$

$Q3 = 3 \times 3.5th$

$Q3 = 10.5th$

This is the average of the 10th and the 11th element.

$Q_3 =\frac12 \times (98 + 101)$

$Q_3 =99.5$

<h3>The interquartile range (IQR)</h3>

The IQR is then calculated as:

$IQR = Q_3 -Q_1$

$IQR = 99.5 - 87.5$

$IQR = 12$

Also, we have:

$IQR(1.5) = 12 \times 1.5$

$IQR(1.5) = 18$

<h3>The outlier range</h3>

The lower and the upper outlier range are calculated as follows:

$Lower = Q_1 - IQR(1.5)$

$Lower = 87.5- 18$

$Lower = 69.5$

$Upper = Q_3 + IQR(1.5)$

$Upper = 99.5 + 18$

$Upper = 117.5$

120 is greater than 117.5.

Hence, the dataset has an outlier and the outlier is 120

Read more about outliers at:

brainly.com/question/9933184

6 0

2 years ago

Find all the powers of 4 in the range 4 through 1000

marissa [1.9K]

Powers of 4 are like 4^1, 4^2, 4^3 and so on
remember that 4^x means 4 times itself x times for example
4^3=4 times iteslef 3 times=4 times 4 times 4

so the multipules of the powers of 4 are just 4 times of the previous
so we will list

4^1=4
4^2=16
4^3=64
4^4=256
4^5=1024

1024 is already more than 1000 so the list stops and is
1,16,64,256

8 0

3 years ago

Find the median of 30 , 40, 35, 50 and 55 degrees angle measures

ELEN [110]

We know that
the median <span>is the middle number when listed in order from least to greatest.
</span>
step 1
listed in order from least to greatest
[<span>30,40, 35, 50, 55]--------> [30, 35, 40, 50, 55]

step 2
find the middle number

the middle number is 40

therefore

the answer is
the median is 40</span>°<span>

</span>

6 0

3 years ago

Which is true about the polynomial 9x²y – 6x - 5y^2

Ostrovityanka [42]

Answer:

Step-by-step explanation:

It is a trinomial with a degree of 3.

This is the correct answer on the exam.

7 0

3 years ago