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3 years ago

Simplify (−8 + 8i) − (5 + 4i).

2 answers:

7 0

Hey there!

<span>Simplify (−8 + 8i) − (5 + 4i).

</span>( - 8 + 8i) - ( 5 + 4i<span>) = </span>
( - 13 + 4i<span>) </span>

Hope this helps.
~Jurgen

RUDIKE [14]3 years ago

7 0

So this is how you would do this

(-8 + 8i) - (5 + 4i)

Distribute the negative and take away parenthesis

-8 + 8i -5 -4i

add like terms

4i - 13

or

-13 + 4i

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the morgan famili and the alexander family each ised their sprinkles last summer. the water output was 20. l per hour. The water

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Answer:

number of hours Alexander family ‘s sprinkler work = 20

number of hours Morgan family ‘s sprinkler work = 30

Step-by-step explanation:

Given in the question,

water output rate for the Alexander family ‘s sprinkler = 40 L

water output rate for the Morgan family ‘s sprinkler = 20 L

Suppose, number of hours Alexander family ‘s sprinkler work = x

Suppose, number of hours Morgan family ‘s sprinkler work = y

Equation1

x + y = 50

Equation 2

40x + 20y = 1400

x = 50 - y

Put this value of x in equation 2

40(50-y) + 20y = 1400

2000 - 40y + 20y = 1400

-20y = 1400 - 2000

-20y = -600

y = 30

Put this value of y in equation 1 to get the value of x

x + 30 = 50

x = 50 - 30

x = 20

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3 years ago

The hypothesis H0: \mu=350H 0 : μ = 350 versus H_a:\mu<350H a : μ < 350 are examined using a sample of size n = 20. The on

Zolol [24]

Answer:

The statistic for this case is given $t =-1.68$

The degrees of freedom are given by:

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

Since is a one-side lower test the p value would given by:

$p_v =P(t_{19}$

Step-by-step explanation:

Data given and notation

$\bar X$ represent the sample mean

$s$ represent the sample standard deviation

$n=20$ sample size

$\mu_o =350$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is lower than 350, the system of hypothesis are :

Null hypothesis: $\mu \geq 350$

Alternative hypothesis: $\mu < 350$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

The statistic for this case is given $t =-1.68$

P-value

The degrees of freedom are given by:

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

Since is a one-side lower test the p value would given by:

$p_v =P(t_{19}$

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How many triangles can you make with two side lengths of 6 inches that meet at a 50 degree angle.

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<h3>Answer: Exactly One Triangle</h3>

======================================================

Explanation:

Recall that by the SAS (side angle side) congruence theorem, if we know that two pairs of sides are the same length and the angles between them are also congruent, then we can conclude the triangles are congruent. This further means that we can only construct exactly one triangle with two side lengths of 6 inches, and they form a 50 degree angle between them. Applying transformations such as rotations, translations, or reflections will not change the triangle.

Side note: This triangle is isosceles because two sides are the same length. It is not equilateral because we would need to have all three angles to be 60 degrees.

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