The function f(x) is decreasing on the interval x∈(1/2,∞) and all the real values.
What is meant by a function?A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.
The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.
Given function,
f(x)=[tex]e^{2 x^{2} +5}[/tex]/-6x
f'(x)=-1/6x([tex]e^{2 x^{2} +5}[/tex])(4x)+[tex]e^{2 x^{2} +5}[/tex](1/6x²)
=[tex]e^{2 x^{2} +5}[/tex]/6x((1/x)-4x)
f'(x)=0
((1/x)-4x)=0
1-4x²=0
4x²=1
x=±1/4
Given that, f(x) is decreasing function then,
f'(x)<0
((1/x)-4x)<0
(1-4x²)/x<0
1-4x²<0
1<4x²
1/4<4x²
x²>1/4
x>1/2
x∈(1/2,∞)
Hence, f(x) is decreasing on the interval x∈(1/2,∞)
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Please help!
Find the amount of money( future value) in an account where 8,800 is deposited ( present value) at an interest rate 6.5% per year compounded continuously and the money is left in the account for 7 years.
The final amount is $ ?
Round your answer to 2 decimal places.
By using the formula for amount of money in a compound interest, it can be calculated that
Amount received after 7 years is $13675.08
What is a compound interest?
If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, then the interest earned is called compound interest.
If p is the principal, r is the rate and n is the time in years, then
amount = [tex]p(1+\frac{r}{100})^n[/tex]
Difference between amount and principal gives the compound interest.
Principal = $8800
Rate = 6.5 %
Time = 7 years
Amount received = [tex]8800(1 + \frac{6.5}{100})^7[/tex]
$13675.08
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What is the equation of the line in standard form?
A. x-2y=4
B. x+2y=4
C. 2x+y=2
D. 2r-y-2
Answer:
D. 2x -y = 2
Step-by-step explanation:
You want to know the standard-form equation of the line through points (-1, 4) and (2, 2) as shown on the graph.
Intercept formThe graph shows the x-intercept of the line is a=1, and the y-intercept of the line is b=-2. This means the intercept form of the equation is ...
x/a +y/b = 1
x/1 +y/(-2) = 1
Standard formMultiplying this equation by 2 gives ...
2x -y = 2 . . . . the standard form equation for the line
__
Additional comment
The standard form equation can also be developed from the coordinates of points on the line:
(y2 -y1)x -(x2 -x1)y = (y2 -y1)x1 -(x2 -x1)y1
(2 -(-4))x -(2 -(-1))y = (2 -(-4))(-1) -(2 -(-1))(-4)
6x -3y = -6 +12
Dividing by 3 gives the standard form equation ...
2x -y = 2
Suppose a large consignment of compact discs contained 13% defectives.
If a sample of size 329 is selected, what is the probability that the sample proportion will differ from the population proportion by more than 3%? Round your answer to four decimal places.
The probability that the sample proportion will differ from the population proportion by more than 3% is 0.8948
How to calculate the probability?The requirement to solve the probability between z-values is to know that the probability between the z-values is the difference between the probability of the greatest z-value and the lowest z-value.
In this case, the sample proportion:
= ✓[p(1 - p)/n]
= ✓(0.13 × 0.87)/329
= 0.01854.
The probability will be:
P(-0.03 / 0.01854) < z < (0.03 / 0.01854)
P(-1.62 < z < 1.62)
Looking at the z table, the probability is 0.08948
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A ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The distance along the ramp to the building is 5 feet. What is the angle of elevation of the ramp to the nearest degree?
A. 11°
B. 0°
C. 12°
D. 1°
Using the trigonometry ratio, he angle of elevation of the ramp to the nearest degree is 11°.
In the given question,
A ramp goes from a doorway of a building to the ground.
The end of the ramp connected to the doorway is 1 foot above the ground.
The distance along the ramp to the building is 5 feet.
We have to find the angle of elevation of the ramp to the nearest degree.
The distance is 5 feet.
The height is 1 foot.
To find the angle of elevation we used the trigonometry ratio.
According the trigonometry ratio, we know that tangent is the ratio between height and distance.
We can write it as
tan A=height/distance
Now putting the value
tan A=1/5
tan A=0.2
So A = arctan(0.2)
A = 11.30°
A ≈ 11°
Hence, the angle of elevation of the ramp to the nearest degree is 11°.
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if q is 3x+ 6 and AC is 8x+8 what is the length of AC? Round your answer to the nearest hundredth
Answer:
AC = 24Step-by-step explanation:
AC is the diagonal of the parallelogram ADCB.
q is half of AC, therefore:
AC = 2qSubstitute values and solve for x:
8x + 8 = 2(3x + 6)8x + 8 = 6x + 128x - 6x = 12 - 82x = 4x = 2Find the length of AC:
AC = 8*2 + 8 = 16 + 8 = 24To go to the theater you would pay $8.00 for each ticket you purchase. Which answer choice correctly represents the algebraic expression for the cost of t tickets?
A. 8t
B. 8 + t
C. 8 – t
D.
Answer:
Step-by-step explanation:
a
For f(x)=3x+18, what is the value of x for which f(x) =21
a. x=2
b. x=5
c. x=1
d. x=-1
Answer:
I believe the answer is C
Step-by-step explanation:
a. would = 24b. would = 33c. would = 21d. would = 15 :)Find the slope of the line using rise/run formula please help
Answer:
20/5 is the slope, or 4.
Step-by-step explanation:
It went up 20 units on the y axis, and over 5 units on the x-axis. So 20/5 is the slope.
-Hope this helped
Anna Marie goes to dinner at a restaurant where the sale tax on meals is 9%. she leaves a tip that is 175% of the amount of sales tax. if her total bill is $45 what was the cost of her meal and what percent tip did she leave
Answer: $78.75
Step-by-step explanation:
You have to multiply the price by tax and add
What percent is 199 is 761
Answer:
Step-by-step explanation:
Solutionx% of 199 is 761 is 382.41206…% Answer
Convert x% into a decimal and multiply by 199
In order to convert a percent to a ratio, divide it by 100:
a%=a100
a=x
x% =x100
Convert to decimal form=0.01x
Multiply 0.01x by 199
=0.01x· 199=1.99x
Solve 1.99x=761
1.99x=761
x=761/1.99
x=382.41206%
Please Help!!!!
Kim and Tracy are collecting data for their final project in their psychology
class, in which they are conducting a survey about people’s overall job
satisfaction. They decide to go to the local mall to collect their data. To get a
more varied sample, Kim surveys shoppers coming out of store A, a discount
clothing store, while Tracy surveys shoppers coming out of store B, a high-end
boutique.
A. Identify a possible problem with this type of sampling method. (6 points)
B. How might Kim and Tracy improve on their sample design so as to get more
accurate information from the shoppers at the mall?
Answer:
below
Step-by-step explanation:
A problem would be that they are not surveying people from multiple places. They are doing it at 2 opposite stores, at the same times. They should try multiple different stores at other days and times to get more objective data.
NEED HELP ASAP
What is the value of y in the solution to this system of equations 6y+x= -59 x= -2y+9?
Answer:
y = - 17
Step-by-step explanation:
6y + x = - 59 → (1)
x = - 2y + 9 → (2)
substitute x = - 2y + 9 into (1)
6y - 2y + 9 = - 59
4y + 9 = - 59 ( subtract 9 from both sides )
4y = - 68 ( divide both sides by 4 )
y = - 17
Notebook paper is about 0.003 in. thick. If you cut a sheet of paper in half, stack one piece on top of the other, cut those in half, stack all the pieces together, repeating this process 20 times, how high will the stack of paper be?
Answer:
765
Step-by-step explanation:
if h(x)= 1-7x find the value of 23-h(9)=
85
Step-by-step explanation:
Given,
[tex]{ \pink{ \sf{h(x) = 1 - 7x}}} \: { \to} \: { \tt{eq}^{n} (1)}[/tex]
Put x = 9 in Eqⁿ (1)
[tex]{ \pink{ \sf{h(9) = 1 - 7(9)}}}[/tex]
[tex]{ \pink{ \sf{h(9) = 1 - 63}}}[/tex]
[tex]{ \red{ \boxed{ \pink{ \sf{h(9) = - 62}}}}}[/tex]
Let
[tex]{ \green{ \sf{23 - h(9)}}} \: { \to} \: { \tt{ {eq}^{n} (2)}}[/tex]
Substitute the value of h(9) in Eqⁿ (2)
[tex]{ \green{ \sf{23 - ( - 62)}}}[/tex]
[tex]{ \green{ \sf{23 + 62}}}[/tex]
[tex] = { \pink{ \boxed{ \red{ \sf{85}}}}}[/tex]
the length of a rectangle is 2 feet more than the width. Find the minimum dimensions if the perimeter is more than 16 feet and the length and width are integers.
Answer:
L = 6 feet ; W = 4 feet
Step-by-step explanation:
l = 2 + w
perimeter/2 = 8
l + w > 8
2 + w + w > 8
2 + 2w > 8
2w > 8-2
2w > 6
2/2 w > 6/2
w > 3
smallest integer > 3 = 4
W= 4
L = 4 + 2 = 6
a nutrition label on a protein bar shows that the bar contains 7% of the daily recommended amount of carbohydrates. there are 20 grams of carbohydrates are recommended in the protein bar. how many grams of carbohydrates ar recommended per day? round your answer to the nearest whole. PLEASE HELP WITH N EXPLANATION
The daily amount in grams of the recommended carbohydrates is 2587.15 grams
How to solve for the amount of recommended carbohydrateThe amount of daily recommended carbohydrate is solved by dividing the quantity of carbohydrate in the protein bar by the percentage contained in the bar
The problem deals with percentage and 7% is written as
7%
= 7 percent
= 7 / 100
= 0.07
The factor 0.07 of the daily recommended amount of carbohydrates gives 20 grams of carbohydrate
let the daily recommended amount of carbohydrates be x
0.07 * x = 200
0.07x = 200
x = 200 / 0.07
x = 2587.15 grams
The daily recommended amount of carbohydrates is 2587.15 gram
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4.5,3,1.5,0 fin the difference in the following sequence
-1.5 is the difference in the sequence
How determine the difference in a sequence?
An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms are the same.
The difference is usually called the common difference. For example, the sequence 3, 6, 9, 12 have a common difference of 3 i.e. 6-3 = 3 or 9-6 = 3
Given: the sequence 4.5,3,1.5,0
The difference = 3 - 4.5 = -1.5 or 1.5-3 = -1.5
Note: You can pick any two consecutive terms to get the difference
Therefore, the difference in the sequence is -1.5
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Given f(x)=3x^2+kx+4 and the remainder when f(x) is divided by x-4 is 68 then What is the value of k?
Answer:
k = 4-----------------------------
GivenFunction f(x) = 3x² + kx + 4,Remainder of f(x) / (x - 4) is 68.According to the remainder theorem, if we subtract 68 from the given trinomial it should be divisible by x - 4. In other words, one of zero's will be x = 4.
f(x) = 3x² + kx + 4 - 68 = 3x² + kx - 64 = 0When x = 43*4² + k*4 - 64 = 048 + 4k - 64 = 04k - 16 = 04k = 16k = 4NEED HELP ASAPPPPPPPP
1) In figure 4, the area of the square os 16cubes. The shaded part is 7cubes, being one less than 4^2 or 4*4. The formula is n+n-1. This can be put in for 5 too. 5+5-1=9.
2) Using the formula, 50+50-1=99. Therefor, the shaded squares in the 50th figure would be 99.
Complete sentence:
1) The formula for the number of shaded squares in the Nth figure is n+n-1.
2) There would be 99 shaded squares in the 50th figure.
explanation: Knowing that the area of a square is length*width, in this case because the figures are squares, the length and the width are both the same number. From this, we can tell that for figure 45, the length is 45 and so this the width. The one square in the corner is both the length and the width so this is why we take 1 away or -1.
Solve for r.
r/3 + 16 = 19
Answer:
r = 9
Step-by-step explanation:
Hello!
Solve for r by isolating the variable.
Solve for r[tex]\frac r3 + 16 = 19[/tex] Subtract 16 from both sides[tex]\frac r3 = 3[/tex] Multiply both sides by 3[tex]r = 9[/tex]The value of r is 9.
What is the simplest fraction equal to 9%?
HELPP ME PLEASEEEEEE
Answer:
We can see that as x increases, y decreases. This indicates a negative slope meaning that the two variables are negatively related.
Hope this helps! :)
81 to the 5th power = 3x
x=?
The value of x according to the given equation as in the task content is; 3¹⁹.
What is the value of x according to the given expression?It follows from the task content that the value of x is to be determined from the equation given in the task content.
Therefore, since the equation given in the task content is;
(81)⁵ = 3x
(3⁴)⁵ = 3x
3²⁰ = 3x
Therefore, the value of x can be evaluated as;
x = 3²⁰/3
x = 3¹⁹.
Ultimately, the value of x from the given equation is; 3¹⁹.
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ANSWER PLEASE!
Armando lost 975 coins playing his
favorite video game. He lost the same number of coins in each of the 15 levels he played. What was the change in Armando's coins at the end of each level of the game?
Answer: 81.25
Step-by-step explanation:
Answer:
Armando lost 65 coins each level.
Step-by-step explanation:
Given information,
→ Armando lost 975 coins playing his favorite video game.
→ He lost the same number of coins in each of the 15 levels he played.
Forming the equation,
→ 15x = 975
Now required value of x will be,
→ 15x = 975
→ x = 975/15
→ [ x = 65 ]
Hence, he lost 65 coins each level.
Need help solving this problem 35)210.35
Answer: The answer is 0.16638935108
Step-by-step explanation:
I don't understand how to do this, pls help :(
Answer: A
Step-by-step explanation:
Describe the transformers of the parent function, f(x)=x, performed to create g(x).
g(x)= -3 • f(x) + 1
The function g(x) is a reflection over the x-axis and stretch by 3 units and shifted upward by 1 unit of the parent function f(x).
What is a function?A capability is a declaration, idea, or rule that lays out a relationship between two factors. Capabilities might be found all through science and are fundamental for the advancement of huge connections.
The functions are given below.
f(x) = x
g(x) = -3f(x) + 1
g(x) = -3x + 1
The parent function is a reflection over the x-axis and stretch by 3 units and shifted upward by 1 unit.
The functions g(x) and f(x) are shown below.
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do we have to find x using quadratic formula or what?
Step-by-step explanation:
The base of the separated triangle is (x+5) - (2x - 4) = x + 5 - 2x + 4 = 9 - x
So, area of the separated triangle would be:-
1/2 * b* h
or, 1/2 * (9-x)* (x+3)
or, (6x + 27 - x² )/2
Total area of trapezium = (6x + 27 - x²)/2 + (2x-4)(x + 3)
or, 60 = (6x + 27 - x²)/2 + 2x² + 2x - 12
or, 60 = (6x + 27 - x² + 4x² + 4x - 24)/2
or, 120 = 10x + 3x² + 3
or, 0 = 3x² + 10x + 3 - 120
hence, 3x² + 10x - 117 = 0 (proved)
Again,
Use quadratic formula to figure out value of x.
(It woun't be a natural number)
Write the value of x with only one digit after it's decimal.
A hospital is trying to cut down on emergency room wait times. It is interested in the amount of time patients must wait before being called back to be examined. An investigation committee randomly surveyed 70 patients. The sample mean was 1.5 hours with a sample standard deviation of 0.5 hours.
Which distribution should you use for this problem? (Enter your answer in the form z or tdf where df is the degrees of freedom.)
The distribution that is needed for the problem that we have here is the t distribution.
What is the t distribution?With its bell-shaped structure and heavier tails, the t-distribution, commonly referred to as the Student's t-distribution, is a kind of probability distribution that resembles the normal distribution.
When there are insufficient samples or unknown variances, it is used to estimate population parameters. T-distributions have broader tails than normal distributions because they are more likely to contain extreme values.
We have tn-1
where n = 70
so that we would have
t70 - 1
= t69
Therefore we would have to use the t distribution here.
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A line is perpendicular to y = 6x +3
and intersects the point (6, 1).
Find the equation for this line.
y-1=-(x-[?])
Answer:
1
Step-by-step explanation:
Perpendicuar lines have slopes that are opposite reciprocals: 6 ==> -1/6
y=mx+b
y=-x/6 + b ==> plug in slope -1/6 into slope equation
1 = -6/6 + b ==> plug in x and y values into slope equation
1 = -1 + b
1 + 1 = -1 + 1 + b
b = 2 ==> solve for b
y = -x/6 + 2 ==> plug in the value of b into the equation
y - 1 = -x/6 + 2 - 1
y - 1 = -x/6 + 1
y - 1 = -(x/6-1) ==> answer: 1
