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3 years ago

Evaluate the following expression using the values given: Find -a^2-3b^3+c^2+2b^3-c^2 if a=3, b=2, and c=-3.

1 answer:

7 0

Ok so substitute the values. a=3 b=2 and c=-3
-3^(2)-3(2)^(3)+(-3)^(2)+2(2)^(3)-(-3)^(2)=-9-24+9+16-9=-33+25-9=-42+25=-17

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In triangle KLM, if K is congruent to L, KL = 9x - 40, LM = 7x - 37, & KM = 3x + 23, find x & the measure of each angle.

Dennis_Churaev [7]

Answer: x = 15, ∠K = 45.7°, ∠L = 45.7°, ∠M = 88.6°

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

Since ∠K ≅ ∠L, then ΔKLM is an isoceles triangle with base KL

KM ≅ LM

3x + 23 = 7x - 37

23 = 4x - 37

60 = 4x

15 = x

KM = LM = 3x + 23

= 3(15) + 23

= 45 + 23

= 68

KL = 9x - 40

= 9(15) - 40

= 135 - 40

= 95

Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.

Since N is the midpoint of KL and KL = 95, then NL = 47.5
Since ∠N is 90°, then NL is adjacent to ∠l and ML is the hypotenuse

Use trig to solve for ∠L (which equals ∠K):

cos ∠L = $\frac{adjacent}{hypotenuse}$

cos ∠L = $\frac{47.5}{68}$

∠L = cos⁻¹ $(\frac{47.5}{68})$

∠L = 45.7

Triangle sum Theorem:

∠K + ∠L + ∠M = 180°

45.7 + 45.7 + ∠M = 180

91.4 + ∠M = 180

∠M = 88.6

7 0

3 years ago

In a semiconductor manufacturing process, three wafers from a lot are tested. Each wafer is classified as pass or fail. Assume t

Angelina_Jolie [31]

Answer:

$P(X = 0) = 0.027$

$P(X = 1) = 0.189$

$P(X = 2) = 0.441$

$P(X = 3)= 0.343$

Step-by-step explanation:

The probability mass function P(X = x) is the probability that X happens x times.

When n trials happen, for each $x \leq n$ , the probability mass function is given by:

$P(X = x) = pe_{n,x}.p^{x}.(1-p)^{n-x}$

In which p is the probability that the event happens.

$pe_{n,x},$ is the permutation of n elements with x repetitions(when there are multiple events happening(like one passes and two not passing)). It can be calculated by the following formula:

$pe_{n,x} = \frac{n!}{x!}$

The sum of all P(X=x) must be 1.

In this problem

We have 3 trials, so $n = 3$

The probability that a wafer pass a test is 0.7, so $p = 0.7$

Determine the probability mass function of the number of wafers from a lot that pass the test.

$P(X = 0) = (0.7)^{0}.(0.3)^{3} = 0.027$

$P(X = 1) = pe_{3,1}.(0.7).(0.3)^{2} = 0.189$

$P(X = 2) = pe_{3,2}.(0.7)^{2}.(0.3) = 0.441$

$P(X = 3) = (0.7)^{3} = 0.343$

5 0

4 years ago

Kelvin and Lewie each design surveys in order to determine the number of people who buy food at the mall. Kelvin surveys every o

timurjin [86]

Answer: A.Kelvin’s because he surveyed people leaving an area where food is sold

Step-by-step explanation:

Given: Kelvin and Lewie each design surveys in order to determine the number of people who buy food at the mall.

Kelvin surveys every other person leaving the food area.

Thus, he doesn't know about the people who do not buy food at mall whereas Lewie surveys every fifth person leaving the mall’s main entrance.

Thus, by this systematic random sampling he knows out of how many people the number of people buy food at mall.

Hence, Kelvin’s survey is likely to produce less valid results because he surveyed people leaving an area where food is sold.

6 0

3 years ago

Read 2 more answers

Decide if the following is a true or false statement - explain how you

NARA [144]

Answer:

true

Step-by-step explanation:

(-3) -(-4.25) = -3 + 4.25 = 1.25 (positive)

6 0

3 years ago

Plz answer i'll give brainliest but it has to be right.

Alex17521 [72]

3 -3/4 and 2 pls brainlest

8 0

3 years ago