X-2626.626(-0.3733+257.23373) ÷ -75y = -656 ÷ (55) 66^ x 26 = 99(368.386) -0.368 = ???

Factor 4n^2 - 5n -6

Allushta [10]

Answer:

(n-2) • (4n+3)

Step-by-step explanation:

4n2-5n-6

Final result :

(n - 2) • (4n + 3)

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(22n2 - 5n) - 6

Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring 4n2-5n-6

The first term is, 4n2 its coefficient is 4 .

The middle term is, -5n its coefficient is -5 .

The last term, "the constant", is -6

Step-1 : Multiply the coefficient of the first term by the constant 4 • -6 = -24

Step-2 : Find two factors of -24 whose sum equals the coefficient of the middle term, which is -5 .

-24 + 1 = -23

-12 + 2 = -10

-8 + 3 = -5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 3

4n2 - 8n + 3n - 6

Step-4 : Add up the first 2 terms, pulling out like factors :

4n • (n-2)

Add up the last 2 terms, pulling out common factors :

3 • (n-2)

Step-5 : Add up the four terms of step 4 :

(4n+3) • (n-2)

Which is the desired factorization

Final result :

(n - 2) • (4n + 3)

3 0

4 years ago

Two sides of a triangle are 6 m and 10 m in length and the angle between them is increasing at a rate of 0.06 rad/s. find the ra

Soloha48 [4]

Since this problem talks about rates of change, then the concept of calculus is very useful. But first, let's find at least two equations in order to solve this system. The first one is the area of a triangle written as

A = 1/2 ab sin θ, where a and b are the sides that from the angle θ. So, we substitute a=6 and b=10. That makes it:
A = 1/2 (6)(10)sin θ = 30 sin θ

Now, you differentiate implicitly (both sides simultaneously) with respect to time.

dA/dt = 30 cosθ (dθ/dt)

We replace dθ/dt = 0.06 rad/s, as mentioned in the problem. Then, the rate of change of the area of the triangle when θ = π/3 rad with respect to time is

dA/dt = 30cos(π/3) (0.06)
dA/dt = 1.8 m²/s

Therefore, the rate of change of the area of the triangle is 1.8 m² per second.

8 0

4 years ago

A motorboat can maintain a constant speed of 15 miles per hour relative to the water. The boat makes trip upstream to a certain

Ira Lisetskai [31]

Answer:

The speed of the current is 2 miles per hours

Step-by-step explanation:

Given as :

The speed of motorboat = x = 15 miles per hour

The time taken by motorboat trip upstream = 51 minutes

The time taken by motorboat trip downstream = 39 minutes

Let The speed of the current = y miles per hour

Let The total distance cover = A miles

So ,

Speed = $\dfrac{\textrm Distance}{\textrm Time}$

So, x - y = $\dfrac{A}{51}$

I.e 15 - y = $\dfrac{A}{51}$

And x + y = $\dfrac{A}{39}$

I.e 15 + y = $\dfrac{A}{39}$

$\dfrac{x-y}{x+y}$ = $\dfrac{39}{51}$

I.e $\dfrac{x-y}{x+y}$ = $\dfrac{13}{17}$

Or, 17 × (x - y) = 13 × (x + y)

Or, 17 x - 17 y = 13 x + 13 y

Or, 17 x - 13 x = 13 y + 17 y

Or, 4 x = 30 y

Now, ∵ x = 15 miles per hour

So, 4 × 15 = 30 y

Or, y = $\dfrac{60}{30}$

∴ y = 2 miles per hour

Hence The speed of the current is 2 miles per hours Answer

8 0

3 years ago

Favorite type of music, choose the correct level of measurement

otez555 [7]

Answer:

The answer is "Nominal"

Step-by-step explanation:

Some of the data is missing which is defined in the attached file. please find it.

The standard measuring degree is nominal for the favorite type of music because the type of music it can be listening for depends on a variety of factors, like age, social or local environment, etc, and the wrong choice can be defined as follows:

It is wrong because the Ordinal does have a nominal or measuring element, however, the name system allows a ranked or a specific series of variables for all the variables to also be organized.
The ratio has the structure infections rate property, as well as the quantities ranges of the variable, provide value, that's why it is incorrect.
It is wrong because the internal has the property of ordinal level rate as well as the vector values have significance.

6 0

3 years ago

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 225 vinyl? glov

romanna [79]

Answer:

a)

H₀: ρ₁ ≤ ρ₂

H₁: ρ₁ > ρ₂

b)

Z= $\frac{('p_{1} - 'p_{2}) - (p_{1} - p_{2})}{\sqrt{'p(1-'p)[\frac{1}{n_1} + \frac{1}{n_2} ]} }$ ≈ N(0;1)

c)

p-value < .00001

d)

Reject the null hypothesis.

The population proportion vinyl gloves that leak viruses is greater than the population proportion of latex gloves that leak viruses.

Step-by-step explanation:

Hello!

The objective is to test if the population proportion of vinyl gloves that leak viruses (population 1) is greater then the population proportion of latex gloves that leak viruses (population 2).

Sample 1 (Vinyl)

n₁= 225

Sample proportion 'ρ₁= 0.60

Sample 2 (Latex)

n₂= 225

Sample proportion 'ρ₂= 0.09

Pooled proportion: 'ρ= (x₁+x₂)/(n₁+n₂)= ( 'ρ₁ + 'ρ₂)/2= (0.60 + 0.09)/2= 0.345 ≅0.35

The hypothesis is:

H₀: ρ₁ ≤ ρ₂

H₁: ρ₁ > ρ₂

α: 0.05

The statistic to use is a pooled Z

Z= $\frac{('p_{1} - 'p_{2}) - (p_{1} - p_{2})}{\sqrt{'p(1-'p)[\frac{1}{n_1} + \frac{1}{n_2} ]} }$ ≈ N(0;1)

The critical region is one-tailed to the right (positive), the critical value is:

$Z_{1-\alpha } = Z_{0.95} = 1.64$

If Z ≥ 1.64, you will reject the null hypothesis.

If Z < 1.64, you will not reject the null hypothesis.

Z= $\frac{(0.6 - 0.09) - (0}{\sqrt{0.35(1-0.35)[\frac{1}{225} + \frac{1}{225} ]} }$ = 11.34

Since the calculated Z- value is greater than the critical value, the decision is to reject the null hypothesis. The population proportion vinyl gloves that leak viruses is greater than the population proportion of latex gloves that leak viruses.

P-value approach:

p-value < .00001

If you compare with the level of signification, you reach the same decision.

I hope it helps!

8 0

4 years ago