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Anon25 [30]
3 years ago
12

Write a quadratic equation with roots of 3/4 and -4

Mathematics
1 answer:
Vaselesa [24]3 years ago
4 0

A quadratic equation given roots is solved by using the relation

{x}^{2}  - (sum \: of \: roots)x + product \: of \: roots

from the question,

sum of the root will be

\frac{3}{4}  + ( - 4) =  \frac{3}{4}  - 4

=   \frac{3 - 16}{4}

=  \frac{ - 13}{4}

and also, product of the roots will

be

\frac{3}{4}  \times ( - 4) =  - 3

now substituting the sum of roots and product of roots into the equation

{x}^{2}  - ( -  \frac{13}{4} )x - 3

=  {x}^{2}  +  \frac{13}{4} x - 3

as the quadratic equation for the root 3/4 and -4

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Answer:

There is not enough statistical evidence to conclude that the cumulative incidence of prostrate cancer among 50-year old men differs from that of 70-year old men

Step-by-step explanation:

The population 10 year cumulative incidence of prostrate cancer among 70 year old men, p = 0.06

The number of 50 year old men in the sample, n = 260 men

The number of the sampled men that developed prostrate cancer = 13 men

The significance level, α = 0.05

Let the null hypothesis, H₀: \hat{p} = p

The alternative hypothesis, Hₐ: \hat{p} ≠ p

The standard score, z_{\alpha /2} = 1.96

The test statistic, 'z', is given as follows;

z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p \cdot q}{n}}}

\hat{p} = 13/260 = 0.05

q = 1 - p = 1 - 0.06 = 0.94

Therefore,  \ z=\dfrac{0.05-0.06}{\sqrt{\dfrac{0.06 \times 0.94}{260}}} = \dfrac{\sqrt{9165} }{141} \approx -0.68

From the z-table, we find the p-value as follows;

P(z ≈ -0.68) = 0.24825

Therefore, given that the p-value, 0.24825 is larger than the significance level, α/2 = 0.025, we fail to reject the null hypothesis, and therefore, there is not enough statistical evidence to conclude that the cumulative incidence of prostrate cancer among 50-year old men differs from that of 70-year old men

5 0
2 years ago
For a circle with a radius of 6 feet, what is the measurement of the central angle (in degrees) that intercepts an arc with a le
makkiz [27]

Answer:

135 degrees

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

C=2\pi r

we have

r=6\ ft

substitute

C=2\pi (6)

C=12\pi\ ft

step 2

Remember that the circumference of the circle subtends a central angle of 360 degrees

so

using proportion

Find out the measurement of the central angle (in degrees) that intercepts an arc with a length of 9π/2 ft

\frac{12\pi}{360^o}=\frac{(9\pi/2)}{x}\\\\x=360(9\pi/2)/12\pi\\\\x=135^o

3 0
3 years ago
HELP ME PLZZ I NEED HELP WITH THIS
Natali5045456 [20]

Answer:

5 cups

The Commutative Property of Addition

Step-by-step explanation:

They have a common denominator of 12

21/12+6/12+20/12+4/12+3/12+6/12=60/12=5 cups

or you could group ingredients with the same denominators

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Answer:

This term would not change at all when combining like terms.

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