Find the stationary points of the function (where the derivative is zero):
f(x) = ln(x ² + 7x + 14)
→ f '(x) = (2x + 7) / (x ² + 7x + 14)
The denominator is always positive, since
x ² + 7x + 14 = (x + 7/2)² + 7/4 ≥ 7/4 > 0
so f '(x) = 0 when
2x + 7 = 0 → x = -7/2
at which point f (-7/2) = ln(203/4) ≈ 3.927.
Also check the endpoints of the given domain:
f (-4) = ln(2) ≈ 0.693
f (1) = ln(22) ≈ 3.091
Then on the interval [-4, 1], we have max(f ) = ln(203/4) and min(f ) = ln(2).
Which expression is equivalent to 8x-12y+32? 16(0.5x-4y+32) 16(0.5x-0.75y+32) 16(0.5x-0.75+2 16(0.5+4y+2)
Answer:
this one
16(0.5x-0.75+2)
Step-by-step explanation:
Answer:
Third Option is the only equivalent equation :)
Step-by-step explanation:
First Option: NO
16(0.5x - 4y + 32)
distribute
8x - 64y + 512
Second Option: NO
16(0.5x - 0.75 + 32)
distribute
8x - 12y + 512
Third Option: YES16(0.5x - 0.75 + 2)
distribute
8x - 12y + 32
Fourth Option:
16(0.5x + 4y + 2)
distribute
8x + 64y + 32
hope this helps :)
The workers at a nursery plant 37 trees in each of 15 parks. They plant 42 trees in each of 23 parks.
How many trees do the workers plant in all?
WHOEVER ANSWERS FIRST AND BETTER GETS BRAINLEY
What is the slope of the line below? Be sure to scroll down first to see all
answer options.
10
10
118
(7.-5)
(14,-7)
A. -2
B. -
00
NIN
Answer:
i think c
i'm not sure tho
Step-by-step explanation:
an angle of 34°. If the arc is 162 feet tall, how far away is the bus? Round to the nearest tenth.
Answer:
the answer is 134 hope this helps.
PLZ HELP PLZ HELP brainlyist for correct answer
.......,,...............
Answer:
[tex]\boxed{C. 32}[/tex]
Step-by-step explanation:
Hello There!
If you didn't know the exterior angle of a triangle is equal to the opposite interior angles
so
100 = 68 + x
subtract 68
100-68=32
68-68 cancels out
we're left with
x = 32
Example 4:
If sin18° = t determine the following in term of t
(a) cos189 (b) sin36° (c) tan198°
Answer:
sorry but i need the points
Step-by-step explanation:
Explain how to solve 4X5X3. Use math terms in your answer.
Answer:
4 x 5 x 3 = 60
Step-by-step explanation:
4 x 5 = 20 , 20 x 3 = 60
Which angle measure is a complement of an angle whose measure is 62 degrees?
A 96
B 118
C 16
D 28
angle measure is a complement of an angle whose measure is 62 degrees=90-62=28.
Answer:
D 28 is your answer
If k=9 and x=5, find the value of the expression:
2k - X
Please hurry
Answer:
[tex]\huge\boxed{13}[/tex]
Step-by-step explanation:
= 2k - x
Given that k = 9, x = 5
= 2(9) - 5
= 18 - 5
= 13
[tex]\rule[225]{225}{2}[/tex]
Hope his helped!
~AH1807The slope of the line shown below is 1/2
Someone Please Help Me
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: 2
Explanation:
Remember Rise/Run
1/2
So if they went "Run" 4 units
then the equivalent to 1/2 is 2/4
Therefore the value of a is 2!
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
find the slope
!!HELP QUICKLY PLEASE!!
1
Five people visited a local restaurant to get some lunch. A bottle of apple
juice costs 3 dollars and a bag of chips cost 2 dollars. If all five people
ordered a sandwich, a bottle of apple juice, and a bag of chips, write a
numerical expression to show the amount of money the friends spent for
this order. Choose ALL that apply. *
Answer:
y = 5x
y = amount of money all the friends spent.
x = cost of burgers, a bottle of apple juice, and a bag of chips all together
Step-by-step explanation:
Ion know which all apply but okay?
yo sorry xDDDDD ok dis real 1
Answer:
96 dozen (or/aka) 1152 cupcakes
Step-by-step explanation:
I hope this is right, if not I'm very sorry just bad at math.
Phil has completed 1/4 of his shift; Darren has completed 3/7 of his shift; Alice has finished 1/8 of her shift; Lisa has 1/5 of her shift remaining. Out of the four employees, who has completed the least work time?
Answer:
Out of the four employees, Alice is the one who has completed the least work time, since she only completed 12.5% of it.
Step-by-step explanation:
Since Phil has completed 1/4 of his shift; Darren has completed 3/7 of his shift; Alice has finished 1/8 of her shift of her; and Lisa has 1/5 of her shift remaining, to determine, out of the four employees, who has completed the least work time, the following calculation must be performed:
Phil: 4 - 1/4 = 3/4 = 0.75
Darren: 7 - 3/7 = 4/7 = 0.57
Alice: 8 - 1/8 = 7/8 = 0.875
Smooth: 5 - 1/5 = 4/5 = 0.8
Thus, of the four employees, Alice is the one who has completed the least work time, since she only completed 12.5% of it.
If you can drive 340 miles in 5 hours, what is the unit rate? *
(2 Points)
Enter your answer
The extract of a plant native to Taiwan has been tested as a possible treatment for Leukemia. One of the chemical compounds produced from the plant was analyzed for a particular collagen. The collagen amount was found to be normally distributed with a mean of 65 and standard deviation of 7.7 grams per mililiter. Round all answers to 4 decimal places.
Required:
a. What is the probability that the amount of collagen is greater than 60 grams per.
b. What is the probability that the amount of collagen is less than 90 grams per.
c. What percentage of compounds formed from the extract of this plant fall within 1 standard deviation of the mean?
Answer:
a) 0.2578 = 25.78% probability that the amount of collagen is greater than 60 grams per mililiter.
b) 0.9994 = 99.94% the probability that the amount of collagen is less than 90 grams per mililiter.
c) 68.26% of compounds formed from the extract of this plant fall within 1 standard deviation of the mean
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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.
The collagen amount was found to be normally distributed with a mean of 65 and standard deviation of 7.7 grams per mililiter.
This means that [tex]\mu = 65, \sigma = 7.7[/tex]
a. What is the probability that the amount of collagen is greater than 60 grams per.
This is 1 subtracted by the pvalue of Z when X = 60. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60 - 65}{7.7}[/tex]
[tex]Z = -0.65[/tex]
[tex]Z = -0.65[/tex] has a pvalue of 0.2578
0.2578 = 25.78% probability that the amount of collagen is greater than 60 grams per mililiter.
b. What is the probability that the amount of collagen is less than 90 grams per.
This is the pvalue of Z when X = 90.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{90 - 65}{7.7}[/tex]
[tex]Z = 3.25[/tex]
[tex]Z = 3.25[/tex] has a pvalue of 0.9994
0.9994 = 99.94% the probability that the amount of collagen is less than 90 grams per mililiter.
c. What percentage of compounds formed from the extract of this plant fall within 1 standard deviation of the mean?
Between Z = 1 and Z = -1, so the proportion is the pvalue of Z = 1 subtracted by the pvalue of Z = -1
Z = 1 has a pvalue of 0.8413
Z = -1 has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
0.6826*100% = 68.26% of compounds formed from the extract of this plant fall within 1 standard deviation of the mean
x:1≤x≤9,x is a prime
Answer:
1≤x≤9
0,1,0,1,2,3,4,5,6,7,8,9
x is a prime number 2,3,5,7
A random sample of 35 business students required an average of 50.7 minutes to complete a statistics exam. Assume that the population standard deviation to complete the exam was 10.4 minutes. The 95% confidence interval around this sample mean is ________. Group of answer choices (48.9, 52.5) (49.8, 51.6) (47.3, 54.1) (45.4, 56.0)
Answer:
(47.3, 54.1)
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{10.4}{\sqrt{35}} = 3.4[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 50.7 - 3.4 = 47.3
The upper end of the interval is the sample mean added to M. So it is 50.7 + 3.4 = 54.1
The answer is (47.3, 54.1).
Write the quadratic equation in standard form.
- 4(x - x²) = 8
Determine if the quadratic function
Answer:
x² - x - 2 = 0
Step-by-step explanation:
Given:
- 4(x - x²) = 8
Find:
Standards form
Computation:
- 4(x - x²) = 8
(x - x²) = -2
x - x² = -2
x² - x - 2 = 0
A seller has a house that is 1483 square feet. The neighborhood comps show the line of
best fit to be y = 0.071x + 52.48. What is a fair price for this house? Round your answer to
the nearest thousand.
9514 1404 393
Answer:
158,000
Step-by-step explanation:
Using the given square feet for x in the equation, we have ...
y = 0.071×1483 +52.48 = 157.773
We presume this is supposed to represent the estimated value of the house in thousands.
The fair price is estimated to be 158,000.
1. Solve the following equation for all values of x.
10x2 – 5x=0
Answer:
20=0+5x
x=20/5
x=4
x=4
x=4
Answer:
exact form:
x=0, 1/2
decimal form:
x=0, 0.5
Using the method of splitting a complex shape into smaller, standard figures, find the area of Vivian’s house using only points provided in the diagram.
Answer:
Step-by-step expVivian’s house area can be split into two rectangles: FLSU and MNSR.
area of rectangle FLSU
= length × width
= (FU) × (FL)
= 30 × 25
= 750 square feet
area of rectangle MNSR
= length × width
= (MS) × (MN)
= 38 × 25
= 950 square feet
area of Vivian’s house
= area of rectangle FLSU+ area of rectangle MNSR
= 750 square feet + 950 square feet
= 1,700 square feet
The relationship between the height of a tree and the time snice the tree was planted?
Answer:
Answer: It´s correlated. Step-by-step explanation: The graph shows that the height of the tree increases as time passes, meaning that the more time that a three has been planted the more height it has, so there´s a direct correlation between the time passing and the height of the tree.
HELP Question below in the photo linked
Answer:
D. x = 10, m<TRS = 60°
Step-by-step explanation:
m<QRS = 122° (given)
m<QRT = (7x - 8)° (given)
m<TRS = (6x)° (given)
m<QRT + m<TRS = m<QRS (angle addition postulate)
(7x - 8)° + (6x)° = 122° (substitution)
Solve for x
7x - 8 + 6x = 122
Add like terms
13x - 8 = 122
13x = 122 + 8
13x = 130
x = 130/13
x = 10
✔️m<TRS = (6x)°
Plug in the value of x
m<TRS = (6*10)° = 60°
I NEED HELP PLEASE SHOW STEP BY STEP, I NEED THIS ASAP, WILL MARK BRAINLEST TO BEST ANSWER
Answer:
first, dilate triangle ABC with respect to the origin by scale factor of 2.
then rotate it 90 degrees counterclockwise about the origin
Step-by-step explanation:
If a car traveling 40 miles per hour takes 50
feet to stop, then accurate to the nearest
tenth, how many seconds will it take to stop?
Answer:
t = 0.85 s
Step-by-step explanation:
Given that,
The speed of a car, v = 40 mph = 17.8816 m/s
Distance, d = 50 feet = 15.24 m
Let the time be t. The formula for speed is given by distance divided by time. So,
[tex]v=\dfrac{d}{t}\\\\t=\dfrac{d}{v}\\\\t=\dfrac{15.24 }{17.8816 }\\\\t=0.85\ s[/tex]
So, the required time is 0.85 s.
8/15 - 1/10 show work plz
Answer: 13/30
Step-by-step explanation:
8/15 -1/10 = (2×8)/(2×15) - (3×1)/(3×10) = 16/30 - 3/30 = (16-3)/30 = 13/30
Answer:
13/30
Step-by-step explanation:
8/15 - 1/10 (first find a common denominator which can be 30 for example)
Multiply numerator and demomiator
16/30 (x2) - 3/30 (x3) =13/30.
Please help me :) I will give Brainiest to whoever does! PLEASE HURRY
Answer:
18.33
Step-by-step explanation:
Plzzzzzzzzzzzzzzzzzzz help
Answer:
Step-by-step explanation: