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2 years ago

Consider this polynomial, where a is an unknown real number.

Mathematics

1 answer:

DENIUS [597]2 years ago

8 0

Answer:

Step-by-step explanation:

Correct steps to find the value of 'a' should be,

Braulio's synthetic division should be,

-1 | 1 5 a -3 11

-1 -4 (4 - a) (a - 1)

1 4 (a - 4) (1 - a) (a + 10)

Here remainder is (a + 10).

So (a + 10) = 17 ⇒ a = 7

Braulio Incorrectly found a value of 'a' because he should have used (-1) instead of 1.

Zahra's calculation by remainder theorem should be,

p(x) = x⁴ + 5x³ + ax² - 3x + 11

p(-1) = (-1)⁴ + 5(-1)³ + a(-1)² - 3(-1) + 11

= 1 - 5 + a + 3 + 11

= (a + 10)

Since, remainder of the solution is 17,

(a + 10) = 17 ⇒ a = 7

Zahra incorrectly found the value of 'a' because she incorrectly solved the powers to (-1).

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Mia has 1/2 of a pizza. She divides it equally among 4 people. Which model shows the fraction of a whole pizza each person gets

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Each person gets $\frac{1}{8}$ of whole pizza

Solution:

Given that Mia has $\frac{1}{2}$ of a pizza

She divides it equally among 4 people

To find: Fraction of a whole pizza each person gets

From statement,

$\frac{1}{2}$ of pizza is divided equally among 4 people

Therefore, to find the fraction of whole pizza each person gets, we can divide the $\frac{1}{2}$ by 4 people

$\text{fraction each person gets } = \frac{\frac{1}{2}}{4}\\\\\text{fraction each person gets } = \frac{1}{2} \times \frac{1}{4}\\\\\text{fraction each person gets } = \frac{1}{8}$

Thus each person gets $\frac{1}{8}$ of whole pizza

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2 years ago

On January 1, year 1, Klondike issued 10-year bonds with a stated rate of 10% and a face amount of $100,000. The bonds pay inter

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Answer:

91,000

Step-by-step explanation:

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2 years ago

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The probability that a professional baseball player will get a hit is 1/3. Calculate the exact probability that he will get at l

Evgesh-ka [11]

It is given here that there is 1/3 probability of professional baseball player will get a hit. Hence if at least three hits are gained out of 5 attempts, the calculation goes: 5C3* (1/3)^3*(2/3)^2 + 5C4* (1/3)^4*(2/3)^1 +5C5 *(1/3)^5*(2/3)^0 equal to 0.21.

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2 years ago

High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capa

zalisa [80]

Answer:

The students have to score 0.74 standard deviations above the mean to be publicly recognized.

Step-by-step explanation:

A random variable X is said to have a normal distribution with parameters µ (mean) and σ² (variance).

If $X \sim N (\mu, \sigma^{2})$ , then $z=\frac{X-\mu}{\sigma}$ , is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, $Z \sim N (0, 1)$ .

The distribution of these z-scores is known as the standard normal distribution.

The z-score is a standardized form of the raw score, X. It is a numerical measurement of the relationship between a value (X) and the mean (µ) in terms of the standard deviation (σ). A z-score of -1 implies that the data value is 1 standard deviation below the mean. And a z-score of 1 implies that the data value is 1 standard deviation above the mean.

Let X be defined as the scores of students at the National Financial Capability Challenge Exam.

It is provided that the students who score in the top 23% are recognized publicly for their achievement by the Department of the Treasury.

That is, P (X > x) = 0.23.

⇒ $P(\frac{X-\mu}{\sigma}>\frac{x-\mu}{\sigma})=0.23$

⇒

$P(Z>z)=0.23\\1-P(Z$

The value of z for this probability value is:

z = 0.74.

*Use a z-table.

Thus, the students have to score 0.74 standard deviations above the mean to be publicly recognized.

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2 years ago

A chi-square test for goodness of fit is used to examine the distribution of individuals across three categories, and a chi-squa

aleksandrvk [35]

Answer:

Equal df

Step-by-step explanation:

Given that a chi square test for goodness of fit is used to examine the distribution of individuals across three categories,

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Here degree of freedom = (r-1)(c-1) where r = no of rows and c =no of columns

= (2-1)(3-1) = 2

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