All categories

3 years ago

Write each of the following expressions without using absolute value. |z−6|−|z−5|, if z<5

Mathematics

2 answers:

lina2011 [118]3 years ago

6 0

Answer: 1

Step-by-step explanation: first you need to pretend that the absolute value bars are parentheses. Then substitute a with any number less that five, for example z=3

Now we can write our new equation: (3-6)-(3-5)

now we have to determine if the final answer inside the parentheses is positive or negative. In the first parentheses 3-6=-3 with is negative. In our second parentheses we have 3-5=-2 which is a also negative.

Knowing that both parentheses are negative results we can set up an equation using z instead of 3:

-(z-6)-(-(z-5)) is our new equation. If we simplify this equation we get 1 for an answer

Andre45 [30]3 years ago

3 0

Answer: 6 - 5

Step-by-step explanation:

|z - 6| - |z - 5| ; z < 5

Since z < 5, then

|z - 6| will be the absolute value of a negative number. Replace the absolute value with a negative and parentheses:

-(z - 6) = -z + 6

|z - 5| will be the absolute value of a negative number. Replace the absolute value with a negative and parentheses:

-(z - 5) = -z + 5

Now subtract them without the absolute value signs:

-z + 6 - (-z + 5)

Distribute the negative sign:

-z + 6 + z - 5

-z + z = 0 which leaves:

6 - 5

You might be interested in

Consuelo paid $16.72 for an item which was discounted

Alexeev081 [22]

Ok so if e=mc squared then the answer= abcd :)

6 0

3 years ago

Members of the millennial generation are continuing to be dependent on their parents (either living with or otherwise receiving

Morgarella [4.7K]

Answer:

$\bf H_0:$ The mean of adults aged 18 to 32 that continue to be dependent on their parents is 0.3

$\bf H_a:$ The mean of adults aged 18 to 32 that continue to be dependent on their parents is greater than 0.3

b) 34%

c) practically 0

d) Reject the null hypothesis.

Step-by-step explanation:

Since an individual aged 18 to 32 either continues to be dependent on their parents or not, this situation follows a Binomial Distribution and, according to the previous research, the probability p of “success” (depend on their parents) is 0.3 (30%) and the probability of failure q = 0.7

According to the sample, p seems to be 0.34 and q=0.66

To see if we can approximate this distribution with a Normal one, we must check that is not too skewed; this can be done by checking that np ≥ 5 and nq ≥ 5, where n is the sample size (400), which is evident.

We can then, approximate our Binomial with a Normal with mean

$\bf np = 400*0.34 = 136$

and standard deviation

$\bf \sqrt{npq}=\sqrt{400*0.34*0.66}=9.4742$

Since in the current research 136 out of 400 individuals (34%) showed to be continuing dependent on their parents:

$\bf H_0:$ The mean of adults aged 18 to 32 that continue to be dependent on their parents is 0.3

$\bf H_a:$ The mean of adults aged 18 to 32 that continue to be dependent on their parents is greater than 0.3

So, this is a right-tailed hypothesis testing.

According to the sample the proportion of "millennials" that are continuing to be dependent on their parents is 0.34 or 34%

Our level of significance is 0.05, so we are looking for a value $\bf Z^*$ such that the area under the Normal curve to the right of $\bf Z^*$ is ≤ 0.05

This value can be found by using a table or the computer and is $\bf Z^*$ = 1.645

Applying the continuity correction factor (this should be done because we are approximating a discrete distribution (Binomial) with a continuous one (Normal)), we simply add 0.5 to this value and

$\bf Z^*$ corrected is 2.145

Now we compute the z-score corresponding to the sample

$\bf z=\frac{\bar x -\mu}{s/\sqrt{n}}$

where

$\bf \bar x$ = mean of the sample

$\bf \mu$ = mean of the null hypothesis

s = standard deviation of the sample

n = size of the sample

The sample z-score is then

$\bf z=\frac{136 - 120}{9.4742/20}=16/0.47341=33.7759$

The p-value provided by the sample data would be the area under the Normal curve to the left of 33.7759 which can be considered zero.

Since the z-score provided by the sample falls far to the left of $\bf Z^*$ we should reject the null hypothesis and propose a new mean of 34%.

7 0

3 years ago

X X X X X X X Barrette Length (inches) What would be the total length of the 24-inch barrettes if Mikayla places them end-to-end

svlad2 [7]

B or d are most likely it I could be wrong if I am, I am so sorry:)

6 0

3 years ago

Read 2 more answers

Steven estimates how long his computer repairs will take. He discovers that ABC Tech and Tech Squad will charge the

katrin2010 [14]

You didn't include the costs of doing repairs at both computer repair firms. I fixed that for you.

ABC Tech ------- $20 service charge plus $15 per hour.

Tech squad ------- $30 service charge plus $10 per hour.

Answer:

Steven's estimate of the repair time is 2 hours.

Step-by-step explanation:

Now in this case, we were told that ABC Tech normally charges $20 service charge and $15 per hour of computer repair service. The second tech firm charges $30 service charge and $10 per hour for computer repair service. We are now simply required to find out or calculate the number of hours of computer repair service whereby the cost of doing repairs at both tech firms become equal.

Let us use "x" to represent that unknown number of hours. The equation needed to calculate this is:

20 + 15x = 30 + 10x

We then pair like terms

15x - 10x = 30 - 20

5x = 10

x = 10/5

x = 2

Therefore the number of hours of computer repair service whereby the cost of doing repairs at both tech firms become equal is 2 hours.

8 0

3 years ago

Use the graph below to determine the equation of the circle in a center radius form and a general form

likoan [24]

Mml omggggg … not fun times

3 0

3 years ago