Shaylee has 77 pennies. She will trade in the pennies to get nickels.

To solve the inequality m/-7<(or equal to) 14 , what should be done to both sides?

Marizza181 [45]

Answer:

$\large\boxed{m\geq-98}$

Step-by-step explanation:

$\dfrac{m}{-7}\leq14\\\\-\dfrac{m}{7}\leq14\qquad\text{change the signs}\\\\\dfrac{m}{7}\geq-14\qquad\text{multiply both sides by 7}\\\\7\!\!\!\!\diagup^1\cdot\dfrac{m}{7\!\!\!\!\diagup_1}\geq(7)(-14)\\\\m\geq-98$

5 0

3 years ago

Read 2 more answers

Health insurance benefits vary by the size of the company (the Henry J. Kaiser Family Foundation website, June 23, 2016). The sa

xxMikexx [17]

Answer:

$\chi^2 = \frac{(32-42)^2}{42}+\frac{(18-8)^2}{8}+\frac{(68-63)^2}{63}+\frac{(7-12)^2}{12}+\frac{(89-84)^2}{84}+\frac{(11-16)^2}{16}=19.221$

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.221)=0.000067$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.221,2,TRUE)"

Since the p values is higher than a significance level for example $\alpha=0.05$ , we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.

Step-by-step explanation:

Previous concepts

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Solution to the problem

Assume the following dataset:

Size Company/ Heal. Ins. Yes No Total

Small 32 18 50

Medium 68 7 75

Large 89 11 100

_____________________________________

Total 189 36 225

We need to conduct a chi square test in order to check the following hypothesis:

H0: independence between heath insurance coverage and size of the company

H1: NO independence between heath insurance coverage and size of the company

The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

The table given represent the observed values, we just need to calculate the expected values with the following formula $E_i = \frac{total col * total row}{grand total}$

And the calculations are given by:

$E_{1} =\frac{50*189}{225}=42$

$E_{2} =\frac{50*36}{225}=8$

$E_{3} =\frac{75*189}{225}=63$

$E_{4} =\frac{75*36}{225}=12$

$E_{5} =\frac{100*189}{225}=84$

$E_{6} =\frac{100*36}{225}=16$

And the expected values are given by:

Size Company/ Heal. Ins. Yes No Total

Small 42 8 50

Medium 63 12 75

Large 84 16 100

_____________________________________

Total 189 36 225

And now we can calculate the statistic:

$\chi^2 = \frac{(32-42)^2}{42}+\frac{(18-8)^2}{8}+\frac{(68-63)^2}{63}+\frac{(7-12)^2}{12}+\frac{(89-84)^2}{84}+\frac{(11-16)^2}{16}=19.221$

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.221)=0.000067$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.221,2,TRUE)"

Since the p values is higher than a significance level for example $\alpha=0.05$ , we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.

3 0

3 years ago

Solve for x round to the nearest tenth.

lesantik [10]

Answer:

x ≈ 15.9

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² + 6² = 17²

x² + 36 = 289 ( subtract 36 from both sides )

x² = 253 ( take the square root of both sides )

x = $\sqrt{253}$ ≈ 15.9 ( to the nearest tenth )

3 0

2 years ago

Read 2 more answers

Rob notices that 55 percent of the people leaving the supermarket chhose plastic bags instead of paper bags. out of 600 people,

Temka [501]

To solve this answer, you are trying to find 55% of 600, because that is the number of people who chose plastic bag.

55% can be re-written as 55/100 OR 0.55 since percentages are always out of 100.

So, we do 0.55*600, which gives us 330. 330 people carry plastic bags.

4 0

2 years ago

Tom knows that in his school 10 out of every 80 students are left-handed. There are 384 students in toms school. How many studen

Vika [28.1K]

Answer:

C (48)

explanation:

firstly, divide 384 by 80. This gives you 4.8. So, since 10 out of every 80 students are left handed we have to times 4.8 by 10 which gives you 48.

4 0

2 years ago