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3 years ago

Use rhombus ABCD and the given information to find each value.

Mathematics

1 answer:

Semmy [17]3 years ago

4 0

Answer: (c) 31 (d) 30 (e) 41 (f) 10

<u>Step-by-step explanation:</u>

NOTES about angles of a rhombus:

diagonals are angle bisectors (cut the angle into 2 equal parts)
diagonals are perpendicular to each other (90°)
two adjacent triangles of a rhombus form an isosceles triangle

Per rule 2 → ∠BEC = 90°

Triangle Sum Theorem: sum of the angles of a triangle = 180°

∠CBD + ∠BEC + ∠BCE = 180°

59° + 90° + ∠BCE = 180°

149° + ∠BCE = 180°

∠BCE = 31°

(d) Given: ∠BCD = 120°

Per rule 3 → ∠CBD = ∠CDB

Triangle Sum Theorem: sum of the angles of a triangle = 180°

∠CBD + ∠CDB + ∠BCD = 180°

2∠CBD + 120° = 180°

2∠CBD = 60°

∠CBD = 30°

(e) Given: ∠AED = 2x+8

Per rule 2 → ∠AED = 90°

2x+8 = 90

2x = 82

x = 41

(f) Given: ∠BCE = 3x + 3 and ∠ECD = 5x - 17

Per rule 1 → ∠BCE = ∠ECD

3x + 3 = 5x- 17

3 = 2x - 17

20 = 2x

10 = x

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Certain transportation company has a fleet of 210 vehicles. The average age of the vehicles is 4.25 years, with a standard devia

-BARSIC- [3]

Answer:

$z = \frac{4-4.25}{\frac{1.5}{\sqrt{40}}}= -1.054$

And we can find the following probability:

$P(z$

And the last probability can be founded using the normal standard distribution or excel.

Step-by-step explanation:

For this case we define the random variable X as the ages of vehicles. We know the following info for this variable:

$\bar X = 4.25$ represent the mean

$\sigma =18/12=1.5$ represent the deviation in years

They select a sample size of n=40>30. And they want to find this probability:

$P(\bar X$

Since the sample size is large enough we can use the central limit theorem and the distribution for the sample mean would be:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

We can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for 4 we got:

$z = \frac{4-4.25}{\frac{1.5}{\sqrt{40}}}= -1.054$

And we can find the following probability:

$P(z$

And the last probability can be founded using the normal standard distribution or excel.

3 0

3 years ago

The m∠ACD = (4x + 4)° and m∠ABD = (6x - 14)°. Find m∠ACD.

densk [106]

The anwser is C because your suppose to line it up like this, 4x+4=6x-14, then you solve for x. Once you have x then you plug it in and solve. For your x you will get 9.

8 0

3 years ago

Read 2 more answers

Find the axis of symmetry:<br> Picture is below.

trapecia [35]

Answer:

x = -3

Step-by-step explanation:

<h3>Axis of symmetry: </h3>

Axis of symmetry is the vertical line that divides the parabola into two equal halves and it passes through the vertex of the parabola.

From the graph, Vertex (-3, 4)

Axis of symmetry: x = -3

4 0

2 years ago

Find the mixed number equivalent to the im<br> proper fraction 22/6

Naddik [55]

Answer:

$3\frac{2}{3}$

Step-by-step explanation:

Given the following question:

$\frac{22}{6}$

In order to convert a mixed number into an improper fraction we have to divide the numerator (in this case; 22) by the denominator (in this case; 6) to find your answer.

$\frac{22}{6}$
$\frac{22}{6} \div2=\frac{11}{3}$
$\frac{11}{3}=11\div3=3\frac{2}{3}$
$=3\frac{2}{3}$

Let three represent how many times 3 goes into 11, let 2 represent the remainder while of course keeping the denominator the same. Your answer is "3 2/3."

Hope this helps.