Answer for x<br><br> y = 1/4x + 1

How do you evaluate cube roots and square roots?

balandron [24]

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

5 0

4 years ago

Erin travels north and south from Main Station. The distance, in km, of the train from Main Station is

AnnZ [28]

Answer:

The times are t = 9, t = 10, t = 11 and t = 12

Step-by-step explanation:

For the train to be more than 16 km South and since south is taken as negative,

d(t) > -16

t³ - 9t² + 6t > -16

t³ - 9t² + 6t + 16 > 0

Since -1 is a factor of 16, inserting t = -1 into the d(t), we have

d(-1) = (-1)³ - 9(-1)² + 6(-1)+ 16 = -1 - 9 - 6 + 16 = -16 + 16 = 0. By the factor theorem, t + 1 is a factor of d(t)

So, d(t)/(t + 1) = (t³ - 9t² + 6t + 16)/(t +1) = t² - 10t + 16

Factorizing t² - 10t + 16, we have

t² - 2t - 8t + 16

= t(t - 2) - 8(t - 2)

= (t -2)(t - 8)

So t - 2 and t - 8 are factors of d(t)

So (t + 1)(t -2)(t - 8) > 0

when t < -1, example t = -2 ,(t + 1)(t -2)(t - 8) = (-2 + 1)(-2 -2)(-2 - 8) = (-1)(-4)(-10) = -40 < 0

when -1 < t < 2, example t = 0 ,(t + 1)(t -2)(t - 8) = (0 + 1)(0 -2)(0 - 8) = (1)(-2)(-8) = 16 > 0

when 2 < t < 8, example t = 3 ,(t + 1)(t -2)(t - 8) = (3 + 1)(3 -2)(3 - 8) = (4)(1)(-5) = -20 < 0

when t > 8, example t = 9,(t + 1)(t -2)(t - 8) = (9 + 1)(9 -2)(9 - 8) = (10)(7)(1) = 70 > 0

Since t cannot be negative, d(t) is positive in the interval 0 < t < 2 and t > 8

Since t ∈ (0, 12]

In the interval 0 < t < 2 the only value possible for t is t = 1

d(1) = t³ - 9t² + 6t = (1)³ - 9(1)² + 6(1) = 1 - 9 + 6 = -2

Since d(1) < -16 this is invalid

In the interval t > 8 , the only possible values of t are t = 9, t = 10.t = 11 and t = 12.

So,

d(9) = 9³ - 9(9)² + 6(9) = 0 + 54 = 54 km

d(10) = 10³ - 9(10)² + 6(10) = 1000 - 900 + 60 = 100 +60 = 160 km

d(11) = 11³ - 9(11)² + 6(11) = 1331 - 1089 + 66 = 242 + 66 = 308 km

d(12) = 12³ - 9(12)² + 6(12) = 1728 - 1296 + 72 = 432 + 72 = 504 km

6 0

4 years ago

Suppose the population of a country is 100 people: 40 work full-time, 20 work half-time but would prefer to work full-time, 10 a

kati45 [8]

Answer:

10

Step-by-step explanation:

Those people who are actively seeking for a job are counted as unemployed. Underemployment is not considered as unemployment. Those who have given up looking for jobs are also not considered as unemployed as well. Hence there are 10 unemployed people.

7 0

3 years ago

An article in Fire Technology describes the investigation of two different foam expanding agents that can be used in the nozzles

kvv77 [185]

Answer:

a) There is no evidence to support the claim that there is no difference in mean foam expansion of these two agents.

b) P=0

c) 90% CI

$-3.2406\leq \mu_1-\mu_2 \leq -2.2614$

This CI tells us that there is a 90% confidence that the real value of the difference between the means is between this two values. We see that both are negative values, so the value 0 is left out of the interval.

That means we can be almost sure both means don't have the same value, confirming the results of the previous test.

Step-by-step explanation:

The null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a: \mu_1-\mu_2\neq 0$

The significance level is 0.10 and it will be a two-tailed test.

The difference of the sample means is:

$M_d=M_1-M_2=4.340-7.091=-2.751$

As the sample size is equal for both samples, the estimated standard error of the difference between means is calculated as:

$s_M_d=\sqrt{\frac{s_1^2+s_2^2}{N}}= \sqrt{\frac{0.508^2+0.430^2}{5}}=\sqrt{\frac{0.442964}{5} }= \sqrt{0.0886}=0.2976$

Then, the statistic z is:

$z=\frac{M_d-(\mu_1-\mu_2)}{s_M_d}=\frac{-2.751-0}{0.2976}=-9.24\\\\P(|z|>9.24)=0$

The P-value (P=0) is much lower than the significance level, so the null hypothesis is rejected. The means are different.

For a 90% confidence interval for the difference of the means, we use a z=1.645.

Then the confidence interval is defined as:

$M_d-z*s_M_d\leq \mu_1-\mu_2 \leq M_d-z*s_M_d\\\\-2.751-1.645*0.2976\leq \mu_1-\mu_2 \leq -2.751+1.645*0.2976\\\\-3.2406\leq \mu_1-\mu_2 \leq -2.2614$

This CI tells us that there is a 90% confidence that the real value of the difference between the means is between this two values. We see that both are negative values, so the value 0 is left out of the interval.

That means we can be almost sure both means don't have the same value.

5 0

3 years ago

Can you choose any two distinct points on a line to calculate the slope? True or False?

marin [14]

True, u can choose any two distinct points on a line to calculate the slope

4 0

3 years ago

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Answer for x y = 1/4x + 1