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pishuonlain [190]
3 years ago
15

Find the zeros of the function by rewriting the function in intercept form

Mathematics
1 answer:
galben [10]3 years ago
5 0
y=3x^2+2x\\
y=x(3x+2)\\
y=x(x+\frac{2}{3})\\
x=0 \vee x=-\frac{2}{3}\\\\
f(x)=5x^2-25x+30\\
f(x)=5(x^2-5x+6)\\
f(x)=5(x^2-2x-3x+6)\\
f(x)=5(x(x-2)-3(x-2))\\
f(x)=5(x-3)(x-2)\\
x=3 \vee x=2


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2.A production process manufactures items with weights that are normally distributed with mean 10 pounds and standard deviation
Vesna [10]

Answer:

Step-by-step explanation:

Given that:

population mean = 10

standard deviation = 0.1

sample mean = 9.8 < x > 10.2

The z score can be computed as:

z = \dfrac{\bar x - \mu}{\sigma}

if x > 10.2

z = \dfrac{10.2- 10}{0.1}

z = \dfrac{0.2}{0.1}

z = 2

If x < 9.8

z = \dfrac{9.8- 10}{0.1}

z = \dfrac{-0.2}{0.1}

z = -2

The p-value = P (z ≤ 2) + P (z ≥ 2)

The p-value = P (z ≤ 2) + ( 1 -  P (z ≥ 2)

p-value = 0.022750 +(1 -   0.97725)

p-value = 0.022750 +  0.022750

p-value = 0.0455

Therefore; the probability of defectives  = 4.55%

the probability of acceptable = 1 - the probability of defectives

the probability of acceptable = 1 - 0.0455

the probability of acceptable = 0.9545

the probability of acceptable = 95.45%

4.55% are defective or 95.45% is acceptable.

sampling distribution of proportions:

sample size n=1000

p = 0.0455

The z - score for this distribution at most 5% of the items is;

z = \dfrac{0.05 - 0.0455}{\sqrt{\dfrac{0.0455\times 0.9545}{1000}}}

z = \dfrac{0.0045}{\sqrt{\dfrac{0.04342975}{1000}}}

z = \dfrac{0.0045}{\sqrt{4.342975 \times 10^{-5}}}

z = 0.6828

The p-value = P(z ≤ 0.6828)

From the z tables

p-value = 0.7526

Thus, the probability that at most 5% of the items in a given batch will be defective = 0.7526

The z - score for this distribution for at least 85% of the items is;

z = \dfrac{0.85 - 0.9545}{\sqrt{\dfrac{0.0455\times 0.9545}{1000}}}

z = \dfrac{-0.1045}{\sqrt{\dfrac{0.04342975}{1000}}}

z = −15.86

p-value = P(z ≥  -15.86)

p-value = 1 - P(z <  -15.86)

p-value = 1 - 0

p-value = 1

Thus, the probability that at least 85% of these items in a given batch will be acceptable = 1

6 0
2 years ago
On the first day after the new moon, 2% of the Moon's surface is illuminated. On the second day, 6% is illuminated. Based on thi
maxonik [38]

Answer:

50%: day 13

100%: day 26

Step-by-step explanation:

We are given two days and the amount of the moon that is illuminated. The two days are points on a straight line.

(1, 0.02), (2, 0.06)

y = mx + b

m = (0.06 - 0.02)/(2 - 1) = 0.04

y = 0.04x + b

0.02 = 0.04(1) + b

b = -0.02

y = 0.04x - 0.02

We want y = 50% = 0.5

0.04x - 0.02 = 0.5

0.04x = 0.52

x = 13

y = 100% = 1

0.04x - 0.02 = 1

0.04x = 1.02

x = 25.5

7 0
2 years ago
Read 2 more answers
What is 2/5 of 26 ?
grandymaker [24]
2/5 × 26 equals 10.4
4 0
3 years ago
Help please today the teachers are grading it help!!!
Lemur [1.5K]
#6
D. 3.0 x 10^8

#7
A. y = 3.5x + 7

#8
B. 5
3 0
3 years ago
Read 2 more answers
What if there is more than one variable?
Nadya [2.5K]

Answer:

a10 b10

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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