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2 years ago

Please help me with the below question.

Mathematics

1 answer:

marta [7]2 years ago

4 0

Let y = f(x). By the fundamental theorem of calculus, differentiating f(x) twice yields

$f'(x) = \dfrac1{4 + x + 3x^2}$

$f''(x) = -\dfrac{1 + 6x}{(4 + x + 3x^2)^2}$

y is concave upward wherever f''(x) > 0. The denominator is positive for all real x, so the numerator determines the sign of f''(x). We have 6x + 1 = 0 when x = -1/6, and

• for x ∈ (-∞, -1/6), we have e.g. with x = -1, 6x + 1 = -5 < 0

• for x ∈ (-1/6, ∞), we have e.g. with x = 0, 6x + 1 = 1 > 0

Then y is concave upward on the interval (-1/6, ∞).

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40 PTS if u do this correctly! Algebra 1 Do #'s 4,5,6,7,8,9,10,12,13,14

Likurg_2 [28]

4.)
n^2+4n=32
--------------------------
Subtract 32 from each side
n^2+4n-32=32-32
n^2+4n-32=0
--------------------------
Factor left side of equation
(n-4)(n+8)=0
--------------------------
Now set the factors to equal 0
n-4=0
or/and
n+8=0
--------------------------
n=4 and/or n=-8
====================================================================
5.)
t^2-26t=56
Subtract 56 from each side
t^2-26t-56=56-56
t^2-26t-56=0
----------------------------
Factor left side
(t+2)(t-28)=0
--------------------------
Set factors equal to 0
t+2=0
or/and
t-28=0
t = -2 and/or t = 28
===================================================================
As you may have noticed you need to subtract to get 0 on the right side, then you factor the left side and then switch the symbols from the numbers. Negative to Positive and Positive to Negative. I'll keep provided the work for the next 3 or 4 questions
===================================================================
6.)
z^2-14z=72
----------------
Subtract 72 from each side
z^2-14z-72=72-72
z^2-14z-72=0
----------------
Factor left side
(z+4)(z-18)=0
----------------
Set factors equal to 0
z+4=0 or z-18=0
Invert
z = -4 and z = 18
===================================================================
7.)
80+a^2=18a
-------------------------
Simplify
a^2+80=18a
------------------------
Subtract 18a from each side
a^2+80-18a=18a-18a
a^2-18a+80=0
------------------------
Factor left side
(a-8)(a-10)=0
-----------------------
Set factors to equal 0
a-8=0 or a-10=0
Invert
a = 8 and a = 10
===================================================================
8.)
u^2=16u+36
--------------------------
Subtract 16u+36 from both sides.
u^2-(16u+36)=16u+36-(16u+36)
u^2-16u-36=0
--------------------------
Factor left side
(u+2)(u-18)=0
--------------------------
Set factors to 0
u+2=0 or u-18=0
Invert
u = -2 and u = 18
====================================================================
9.)
3h^2+6h=105
--------------------------
Subtract 105 from each side
3h^2+6h-105=105-105
3h^2+6h-105=0
--------------------------
Factor left side
3(h-5)(h+7)=0
--------------------------
Set factors to equal 0
h-5=0 or h+7=0
h = 5 and h = -7
===================================================================
10.)
a^2+14a=-45
---------------------------
Subtract -45 from each side
a^2+14a-(-45)=-45-(-45)
a^2+14a+45=0
--------------------------
Factor left side
(a+5)(a+9)=0
-------------------------
Set factors to equal 0
a+5=0 or a+9=0
Invert
a = -5 and a = -9
===================================================================
12.)
w=5 and w=6
===================================================================
13.)
k=6 and k=-9
===================================================================
14.)
h=5 and h=12

7 0

4 years ago

The average daily high temperature in June in LA is 77 degree F with a standard deviation of 5 degree F. Suppose that the temper

olasank [31]

Answer:

11.51% probability of observing an 83 degree F temperature or higher LA during a randomly chosen day in June

The coldest 10% of the days during June in LA have high temperatures of 70.6F or lower.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 77, \sigma = 5$

What is the probability of observing an 83 degree F temperature or higher LA during a randomly chosen day in June?

This probability is 1 subtracted by the pvalue of Z when X = 83. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{83 - 77}{5}$

$Z = 1.2$

$Z = 1.2$ has a pvalue of 0.8849.

1 - 0.8849 = 0.1151

11.51% probability of observing an 83 degree F temperature or higher LA during a randomly chosen day in June

How cold are the coldest 10% of the days during June in LA?

High temperatures of X or lower, in which X is found when Z has a pvalue of 0.1, so whn Z = -1.28

$Z = \frac{X - \mu}{\sigma}$

$-1.28 = \frac{X - 77}{5}$

$X - 77 = -1.28*5$

$X = 70.6$

The coldest 10% of the days during June in LA have high temperatures of 70.6F or lower.

5 0

3 years ago

Graph the following piecewise function.

disa [49]

Step-by-step explanation:

$for\ 2$

$\ -\ \text{op}\text{en circle}\\\\\leq,\ \geq\ -\ \text{closed circle}$

8 0

3 years ago

What value of x is in the solution set of 2x– 3 > 11 – 5x? -3 0 2 4

eimsori [14]

Answer:

the answer is x > 2

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Assuming these ratios stay consistent, if each plant recycled 350 total bottles in a day, plant B would recycle_______ more red

zmey [24]

Answer:

Step-by-step explanation:

Assuming these ratios stay consistent, if each plant recycled 350 total bottles in a day, plant B would recycle___70____ more red bottles than plant A. Plant C would recycle_____80___________ more red bottles than plant D.

A = We first multiply 150 x 2.333 (2 1/3) = 350 tbottles 60 x 2.333 = 140

B = Then multiply 350/200 = 200 x 1.75 350 tbottles RED = 120 x 1.75=210

First answer = 210-140 = B recycles 70 more than A

C = We first multiply 175 x 2 = 350 tbottles RED = 110 x 2 = 220

D = We first find LCM of 180 and 350

Then find 18x now equals 1/10 x 35x tbottles RED = 72 / 18 = 4 then 4 x 35 = 140

Second answer = 220-140 = C recycles 80 more than D.

6 0

4 years ago

Read 2 more answers