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Alvin is 9 years older than Elga. The sum of their ages is 89. What is Elga's age?

Mekhanik [1.2K]

Answer:

Alvin: 49

Elga: 40

Step-by-step explanation:

The equation is 89 = x + (x-9).
Remove the parenthesis and combine the like terms. 89 = 2x - 9
Add 9 on both sides. 98 = 2x
Divide by 2 on both sides. x = 49
49 is the age of Alvin. (49-9) 40 is the age of Elga.

7 0

3 years ago

Read 2 more answers

1. If a polynomial of Degree 4 has an imaginary zero at -2i and a real zero at 5, how many imaginary zeros does it have?

Vadim26 [7]

Answer:

Complex roots for polynomials equations will always come in conjugate pairs. Since 1-2i is a root, 1+2i will also be a root. (Just switch the sign of the imaginary part to its opposite.)

Step-by-step explanation:

So far we have 1-2i and 1+2i as roots. We need two more to make a 4th degree polynomial.

x=1 with multiplicity of 2 means that we count the root twice when we write down the polynomial: (x - 1)(x - 1) = (x - 1)2

Putting it all together, we can construct our polynomial of degree 4 as

y = f(x) = (x - 1)(x - 1)[x - (1-2i)][x - (1+2i)]

Multiply the factors (FOIL):

[x - (1-2i)][x - (1+2i)] =

x2 - (1+2i)x - (1-2i)x + (1-2i)(1+2i) =

x2 - x - 2ix - x + 2ix + (1 + 2i - 2i + 4) =

x2 - 2x + 5

(x - 1)(x - 1) = x2 - x - x + 1 = x2 - 2x + 1

Now multiply the two underlined expressions:

y = (x2 - 2x + 5)(x2 - 2x + 1)

= x4 - 2x3 + 5x2 - 2x3 + 4x2 - 10x + x2 - 2x + 5 by multiplying term by term

= x4 - 4x3 + 10x2 -12x + 5 by collecting like terms.

4 0

3 years ago

Determine the critical value or values for a one-mean z-test at the 1% significance level if the hypothesis test is right-tailed

kifflom [539]

Answer:

We need to conduct a hypothesis in order to determine if the mean is greater than specified value, the system of hypothesis would be:

Null hypothesis: $\mu \leq \mu_o$

Alternative hypothesis: $\mu > \mu_o$

For this case the significance is 1%. So we need to find a critical value in the normal standard distribution who accumulates 0.99 of the area in the left and 0.01 in the right and for this case this critical value is:

$z_{crit}= 2.326$

Step-by-step explanation:

Notation

$\bar X$ represent the sample mean

$\sigma$ represent the standard deviation for the population

$n=$ sample size

$\mu_o$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean is greater than specified value, the system of hypothesis would be:

Null hypothesis: $\mu \leq \mu_o$

Alternative hypothesis: $\mu > \mu_o$

For this case the significance is 1%. So we need to find a critical value in the normal standard distribution who accumulates 0.99 of the area in the left and 0.01 in the right and for this case this critical value is:

$z_{crit}= 2.326$

3 0

3 years ago

Which of the following is equal to the fraction below? (3/4)^-5

DaniilM [7]

Answer:

4.21399176955

Step-by-step explanation:

$\frac{3}{4}^{-5}$