5) Fill in the missing fact from the fact family. 6 x 7=42 42÷ 7=6 42 ÷6=7 ?

Use synthetic division to determine whether the number k is an upper or lower bound (as specified for the real zeros of the func

mote1985 [20]

Solution:

The given Polynomial is :

$f(x) = 5x^4 + 4x^3 - 2x^2 + 2x + 4=5( x^4 + \frac{4}{5}x^3 - \frac{2}{5}x^2 + \frac{2}{5}x + \frac{4}{5})$

By Rational Root theorem the of Zeroes of the Polynopmial are:

$\pm\frac{1}{5},\pm\frac{2}{5},\pm\frac{4}{5},\pm1,\pm2,\pm4$

But , $f(\pm\frac{1}{5},\pm\frac{2}{5},\pm\frac{4}{5},\pm1,\pm2,\pm4)\neq 0$

So, no root of this polynomial is real.

Therefore, All the four roots of Polynomial are imaginary.

So, we can't say whether the number k=2, is an upper or lower bound of the polynomial $f(x) = 5x^4 + 4x^3 - 2x^2 + 2x + 4=5( x^4 + \frac{4}{5}x^3 - \frac{2}{5}x^2 + \frac{2}{5}x + \frac{4}{5})$ .

8 0

3 years ago

Read 2 more answers

If sin(x) = squareroot 2 over 2 what is cos(x) and tan(x)

Bumek [7]

Answer:

cos(x) = square root 2 over 2; tan(x) = 1

Step-by-step explanation:

$\frac{\sqrt{2} }{2}$

was, before it was rationalized,

$\frac{1}{\sqrt{2} }$

Therefore,

$sin(x)=\frac{1}{\sqrt{2} }$

The side opposite the reference angle measures 1, the hypotenuse measures square root 2. That makes the reference angle a 45 degree angle. From there we can determine that the side adjacent to the reference angle also has a measure of 1. Therefore,

$cos(x)=\frac{1}{\sqrt{2} }=\frac{\sqrt{2} }{2}$ and

since tangent is side opposite (1) over side adjacent (1),

tan(x) = 1

7 0

3 years ago

100 pts help me please.

Natalija [7]

Answer:

Carly's expenditure was $240 and the number of boxes of cards was required is 24 boxes.

Step-by-step explanation:

We know that:

48 + 8(b) = Carly's expenditure
10(b) = Carly's expenditure
48 + 8b = 10b
B = Boxes of cards

Work:

48 + 8b = 10b
=> 48 + 8b - 8b = 10b - 8b
=> 48 = 2b
=> b = 24

Now, let's substitute the value of b into any equation.

10(24)
=> 240

Hence, Carly's expenditure was $240 and the number of boxes of cards was required is 24 boxes.

Hoped this helped.

$BrainiacUser1357$

7 0

2 years ago

A members-only speaker series allows people to join for $18 and then pay $1 for every event attended.What is the maximum number

Pachacha [2.7K]

The answer is 4 events

3 0

3 years ago

Read 2 more answers

A random sample of 50 recent college graduates results in a mean time to graduate of 4.58 years, with a standard deviation of 1.

Anna007 [38]

Answer:

The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).

Yes, this confidence interval contradict the belief that it takes 4 years to complete a bachelor’s degree.

Step-by-step explanation:

The (1 - α)% confidence interval for population mean μ, when the population standard deviation is not known is:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}$

The information provided is:

$\bar x=4.58\\s=1.10\\\alpha =0.10$

Compute the critical value of t for 90% confidence interval and (n - 1) degrees of freedom as follows:

$t_{\alpha/2, (n-1)}=t_{0.10/2, (50-1)}=t_{0.05, 49}=1.671$

*Use a t-table for the probability.

Compute the 90% confidence interval for population mean μ as follows:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}$

$=4.58\pm 1.671\times \frac{1.10}{\sqrt{50}}\\=4.58\pm 0.26\\=(4.32, 4.84)$

Thus, the 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).

If a hypothesis test is conducted to determine whether it takes 4 years to complete a bachelor’s degree or not, the hypothesis will be:

Hₐ: The mean time it takes to complete a bachelor’s degree is 4 years, i.e. μ = 4.

Hₐ: The mean time it takes to complete a bachelor’s degree is different from 4 years, i.e. μ ≠ 4.

The decision rule based on a confidence interval will be:

Reject the null hypothesis if the null value is not included in the interval.

The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32 years, 4.84 years).

The null value, i.e. μ = 4 is not included in the interval.

The null hypothesis will be rejected at 10% level of significance.

Thus, it can be concluded that that time it takes to complete a bachelor’s degree is different from 4 years.

4 0

3 years ago

5) Fill in the missing fact from the factfamily.6 x 7=4242÷ 7=642 ÷6=7?​

5) Fill in the missing fact from the factfamily.6 x 7=4242÷ 7=642 ÷6=7?