Divisiones que den de residuo 300

The difference between the roots of the equation 3x2+bx+10=0 is equal to 4 1 3 . find<br> b.

inna [77]

Given that the difference between the roots of the equation $3x^2+bx+10=0$ is $4 \frac{1}{3} = \frac{13}{3}$ .

Recall that the sum of roots of a quadratic equation is given by $- \frac{b}{a}$ .

Let the two roots of the equation be $\alpha$ and $\alpha + \frac{13}{3}$ , then

$\alpha + \alpha + \frac{13}{3} =2 \alpha + \frac{13}{3} =- \frac{b}{a} =- \frac{b}{3} \\ \\ i.e.\ \ 2 \alpha + \frac{13}{3}=- \frac{b}{3}$ . . . (1)

Also recall that the product of the two roots of a quadratic equation is given by $\frac{c}{a}$ , thus:

$\alpha \left( \alpha + \frac{13}{3} \right)= \alpha ^2+ \frac{13}{3} \alpha = \frac{c}{a} = \frac{10}{3} \\ \\ i.e.\ \ \alpha ^2+ \frac{13}{3} \alpha=\frac{10}{3}$ . . . (2)

From (1), we have:

$2 \alpha =- \frac{b}{3} - \frac{13}{3} \\ \\ \Rightarrow \alpha =- \frac{b}{6} - \frac{13}{6}$

Substituting for alpha into (2), gives:

$\left(- \frac{b}{6} - \frac{13}{6}\right)^2+ \frac{13}{3} \left(- \frac{b}{6} - \frac{13}{6}\right)= \frac{10}{3} \\ \\ \Rightarrow \frac{b^2}{36} + \frac{13b}{18} + \frac{169}{36} - \frac{13b}{18} - \frac{169}{18} = \frac{10}{3} \\ \\ \Rightarrow \frac{b^2}{36} - \frac{289}{36} =0 \\ \\ \Rightarrow \frac{b^2}{36} = \frac{289}{36} \\ \\ \Rightarrow b^2=289 \\ \\ \Rightarrow b=\pm\sqrt{289}=\pm17$

5 0

3 years ago

HELP PLS I NEED THIS DONE ASAP

Sholpan [36]

Answer:

a = 4, b = 0

Also, a = 0 and b = 0 :)

8 0

3 years ago

A charity receives 2025 contributions. Contributions are assumed to be mutually independent and identically distributed with mea

uysha [10]

Answer:

The 90th percentile for the distribution of the total contributions is $6,342,525.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums of size n, the mean is $\mu*n$ and the standard deviation is $s = \sqrt{n}*\sigma$

In this question:

$n = 2025, \mu = 3125*2025 = 6328125, \sigma = \sqrt{2025}*250 = 11250$

The 90th percentile for the distribution of the total contributions

This is X when Z has a pvalue of 0.9. So it is X when Z = 1.28. Then

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$1.28 = \frac{X - 6328125}{11250}$

$X - 6328125 = 1.28*11250$

$X = 6342525$

The 90th percentile for the distribution of the total contributions is $6,342,525.

3 0

3 years ago

Write 125 as a repeated multiplication 5s. Then write it as a power.

Maru [420]

Answer:

125 = 5 * 5 * 5 = 5^3

Step-by-step explanation:

125 is equal to 5 times 5 times 5, and a power is a way to write repeated multiplication, just by saying what number it is and the putting a ^ sign and then saying how many times there is that number. There is 5 three times, so the power is 5^3.

7 0

3 years ago

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I need help plez and thanks

Brilliant_brown [7]

He has a total of $58.19.
1 day = $2.74

58.19/2.74
21.24

You can't have 21.2 days, so you need to round down to 21.

Jim can buy lunch for 21 days before he runs out of money on his account.

3 0

3 years ago

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Divisiones que den de residuo 300​

Divisiones que den de residuo 300