All categories

3 years ago

Solve the inequality 3/10 ≥ k - 3/5

Mathematics

1 answer:

balandron [24]3 years ago

8 0

Answer:

The answer to your question is $k \leq \frac{9}{10}$ or (-∞ , 9/10]

Step-by-step explanation:

To solve inequality is similar to solve and equation, we just need to find the values of "k" in order than the inequality be true.

$k - \frac{3}{5} \leq \frac{3}{10}$

Solve for "k"

$k \leq \frac{3}{10} + \frac{3}{5}$

$k \leq \frac{3}{10} + \frac{6}{10}$

$k \leq \frac{9}{10}$

Then the answer is

$k \leq \frac{9}{10}$ or (-∞ , 9/10]

You might be interested in

Tolong di jawab pertanyaan ini ya no 1 sampai 6

umka21 [38]

Que ldixldikxhskzjskjzss

5 0

3 years ago

a survey conducted in a school showed that 65% of the students walked to school. The remaining students took buses to school. Th

Feliz [49]

I fear that there is an error copying your assignment.
65% of the students walked. Are all of the other students on buses? Are there both public buses AND private buses?
Assuming that you need to know BOTH kinds of buses, try this:

65% of the students walked, so since 100% - 65% = 35% then this means that 35% of the students were on buses.
Since we know that there are 360 more walkers than bus riders, then one equation we know is: 65% of S = 360 + 35% of S (let S = total # of students)
.65 S = 360 + .35 S
 - .35 S = - .35 S Subtract .35 S from both sides
 .30 S = 360 Divide both sides by .30 (or .3)
.30 .30
S = 1,200 so we know that this is the total number of students, but that is not what was asked.
They want to know how many are on buses and specifically how many are on public buses, if I read this correctly.
Since the walkers = 65% of 1,2000 and we know of means TIMES, then
.65 (1,200) = 780 walkers
1,200 total students minus 780 walkers = 420 bus riders

Now, if there is not a misprint and we really have to figure out the public bus riders as compared to the private bus riders, then remember the ratio from above in the question: 4 bus: 3 public buses
Now if I read this right, that means that 3/4ths of the bus riders were on public buses
so 3/4 of 420 means 3/4 times 420 = 3 times 105 = 315 public bus riders (which coincidentally leaves 105 private bus riders, but since they are private we don't know much about them. Ha-Ha..... I made a lame joke.)

So your answer is 315 public bus riders

5 0

3 years ago

Read 2 more answers

An airplane travels at a constant speed of 300 miles per hour. How far, in miles, will the airplane travel in 20 minutes?

Strike441 [17]

Answer:

100 miles in 20 minutes.

Step-by-step explanation:

300/60 = x/20

x = 300/60 * 20

x = 100

7 0

2 years ago

The ratio of men to women working for a company is 5 to 6. If there are 198 employees total, how many women work for the company

nignag [31]

Answer: 110 Women !

Step-by-step explanation:

Call their numbers 4x to 5x.

Since there are a total of 198 people,

4x + 5x = 198

9x = 198

x = 22

so that there are

88 men and 110 women.

5 0

2 years ago

2. The National Safety Council routinely analyzes the benefit of seat belt use on driver safety. Their data showed that among 28

JulijaS [17]

Answer:

We conclude that there is difference in the proportion of deaths between the 2 groups.

Step-by-step explanation:

We are given that among 2823 drivers not wearing seat belts, 31 died as a result of injuries, and among 7765 drivers wearing seat belts 16 were killed.

Let $p_1$ = proportion of deaths when drivers were not wearing seat belts.

$p_2$ = proportion of deaths when drivers were wearing seat belts.

So, Null Hypothesis, $H_0$ : $p_1=p_2$ {means that there is no difference in the proportion of deaths between the 2 groups}

Alternate Hypothesis, $H_A$ : $p_1\neq p_2$ {means that there is difference in the proportion of deaths between the 2 groups}

The test statistics that would be used here Two-sample z test for proportions;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of deaths when drivers were not wearing seat belts = $\frac{31}{2823}$ = 0.011

$\hat p_2$ = sample proportion of deaths when drivers were wearing seat belts = $\frac{16}{7765}$ = 0.002

$n_1$ = sample of drivers not wearing seat belts = 2823

$n_2$ = sample of drivers wearing seat belts = 7765

So, the test statistics = $\frac{(0.011-0.002)-(0)}{\sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} } }$

= 4.438

The value of z test statistics is 4.438.

Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that there is difference in the proportion of deaths between the 2 groups.

Also, Margin of error (E) = $1.96 \times \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} }$

= $1.96 \times \sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} }$

= 0.00397

5 0

3 years ago