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2 years ago

Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options.

Mathematics

1 answer:

Verizon [17]2 years ago

7 0

Step-by-step explanation:

8x2 + 16x + 3 = 0

a is 8 b is 16 c is 3

multiply 8 and 3 = 24

what 2 numbers when multiplied make 24 and when added make 16?

use quadratic formula

a is 8 b is 16 c is 3

x= (-b +- (√b^2-4ac))/2a

x= (-16 +- (√b^2-4(8)(3)))/2(8)

x= (-16 +- (√16^2-96))/16

x= (-16 +- (√256-96))/16

x= (-16 +- (√160))/16

x= (-16 +- (4√10))/16

x= -1 +- (√10/4)

split up the + and -

x= -1 - √10/4 = -0.209431

x= -1 + √10/4 = -1.79057

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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)"

3 0

4 years ago

75% of what equals 225? What did you get for 10%, 20% , 30% , 40%, 50% ,60% and 70%?

Lesechka [4]

75% of 225 = 300.

10% = 30
20% = 60
30% = 90
40% = 120
50% = 150
60% = 180
70% = 210
80% = 240
90% = 270

If you need an explanation, just ask.

8 0

3 years ago

Howard invested $5,000 in Certificate of Deposit (CD) that pays 3.75% interest. compounded weekly. What is the value of the CD a

blsea [12.9K]

Answer:

The value of the CD at the end of the 4 years is $5,808.86.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Howard invested $5,000 in Certificate of Deposit (CD) that pays 3.75% interest.

This means that $P = 5000, r = 0.0375$

Compounded weekly

An year has 52 weeks, so $n = 52$

Then

$A(t) = P(1 + \frac{r}{n})^{nt}$

$A(t) = 5000(1 + \frac{0.0375}{52})^{52t}$

What is the value of the CD at the end of the 4 years?

This is A(4). So

$A(4) = 5000(1 + \frac{0.0375}{52})^{52*4} = 5808.86$

The value of the CD at the end of the 4 years is $5,808.86.

6 0

3 years ago

PLEASE ANSWER ITS URGENT! I ALREADY TRIED AND GOT IT WRONG!

Katen [24]

Answer:

x=13

Step-by-step explanation:

We can use proportions. Take the small side over the large side

x 5

--------- = ---------

52 20

Using cross products

20x = 5*52

20x = 260

Divide by 20

20x/20 = 260/20

x= 13

6 0

3 years ago

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, t

7nadin3 [17]

To solve this problem, we can use the tan function to find for the distances covered.

tan θ = o / a

Where,

θ = angle = 90° - angle of depression

o = side opposite to the angle = distance of boat from lighthouse

a = side adjacent to the angle = height of lighthouse = 200 ft

When the angle of depression is 16°18', the initial distance from the lighthouse is:

o = 200 tan (90° - 16°18')

o = 683.95 ft

When the angle of depression is 48°51', the final distance from the lighthouse is:

o = 200 tan (90° - 48°51')

o = 174.78 ft

Therefore the total distance the boat travelled is:

d = 683.95 ft - 174.78 ft

d = 509.17 ft

4 0

3 years ago