The functions f(x)=8x^2+x+3, g(x)=4x-1, h(x)=3x+6 C.Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g is true.
What is increasing function?
⇒ The function is said to be increasing if the y value increases as the x value increase over a given range
What is average rate of change?
⇒An average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another
As x approaches infinity the value of f(x) eventually exceeds the value of both g(x) and h(x)
And it is true for the interval [0,2]
The faster the growth rate higher the average rate of change
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Answer:
C.
Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g.
You are offered two jobs selling college textbooks. One company offers an annual salary of $30,000 plus a year-end bonus of 1% of your total sales. The other company offers an annual salary of $25,000 plus a year-end bonus of 2% of your total sales. How much would you need to sell in a year to make the second offer the better offer?
Answer:
at least $500,000 in sales
Step-by-step explanation:
A 2-liter bottle of juice costs $2.80. A box containing six 1/2 liter bottles sells for $3.90. Which option has a higher cost per liter? What is that cost?
A. 2-liter bottle; $1.40
B. Box of six 2-liter bottles; $1.30
C. 2-liter bottle; $2.80
D. Box of six-liter bottles; $3.90
Answer:
A. 2-liter bottle;$1.40
Step-by-step explanation:
We have to find out which option has the higher cost per liter. To do this we must find out how much each option would be if it was a liter.
1st set up each equation
2-liter = $2.80 we can divide by 2 on both sides of the equal sign and we get 1 liter = $1.40.
6(1/2) liter bottles = $3.90 this becomes 3 liters = $3.90 then we divide by 3 on both sides of the equal sign and we get $1.30
2nd we compare
$1.40(2 liter bottle) > $1.30 (6 1/2 liter bottles)
5 and 6 thousandths in standard form
5 and 6 thousandths in standard form is 5.006
How to express the number in standard form?The number is given as:
5 and 6 thousandths
This can be rewritten as
5 + 6 thousandths
Express as numbers
5 + 0.006
Evaluate the sum
5.006
Hence, 5 and 6 thousandths in standard form is 5.006
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If the volume of the cone is 180 in³, what is its surface area?
Answer:
Hi, to find the surface area of a cone is πrl
if your radius and length is given.
hope this helps (•‿•)
Ramiro was on a 2-day road trip. On the first day he drive at an average speed 40 mph. On the second day he drove at an average speed of 60 mph. If he drove 2 hours. If he drove 2 hours longer and went 20 miles farther on the first day, find the total distance Ramiro traveled on his first road trip
The total distance Ramiro travelled is 380 miles.
What is equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side).
Parts of an EquationThere are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation.
let x be the first day hours
let y be the second day hours.
now,
x = y + 2
40x = 60y + 20
Putting x= y+2
40(y + 2) = 60y + 20
40y + 80 = 60y + 20
60 = 20y
y = 3 hours
For, first day
x = y + 2
x = 3 + 2
x = 5 hours
Thus,
Total distance = 40(5) + 60(3)
=200 + 180
=380 miles
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in mongolia the temperature can dip down to -45C in January. The temperature in July may reach 40C. What is the temperature range in Mongolia?
Answer:
85 C
Step-by-step explanation:
Temperature range means the difference between the maximum and minimum in temperature for an area. 40C-(-45C)=85 C
john likes to walk the steps of the department he works for during lunch break. There are s steps in his department. Today John would like to walk the steps of the taller building next door. The number of steps in the taller building next door is 27 less than 6 times the number of steps in John's department. Which expression represents the number of steps in the taller building next door in terms of s?
The next two terms of 2;6;18;54
5) What problems have a negative slope?
A negative slope can be illustrated when a line that is trending downward from left to right, has a negative value.
What is a negative slopeIt should be noted that a negative slope implies that two variables are negatively related.
This implies that when x increases, y decreases, and also when x decreases, y increases.
Graphically, a negative slope implies that as the line on the line graph moves from left to right, the line will fall.
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ASAP help me with this PLEASE
Answer:
98 degrees
Step-by-step explanation:
In a quadrilateral, we have 4 angles whose sum is 360 degrees which can be derived using the Exterior Angle Sum Theorem which essentially states that any convex polynomial will have a sum of 360 degrees for it's exterior angles.
Since we know that two of the angles are equal, we can just represent angle A and D as "x", and since they're congruent, and there is two of them, the sum can be represented as "2x"
So using all the known values we can set up the following equation:
[tex]2x+64+100=360[/tex]
Simplify on the left side
[tex]2x+164=360[/tex]
Subtract 164 from both sides
[tex]2x=196[/tex]
Divide both sides by 2
[tex]x=98[/tex]
Since we know that "x" represents both angle A and B, then the angle A is 98 degrees.
Can someone please help meee<3
Answer:
36
Step-by-step explanation:
[tex]\sqrt{24a}=12\sqrt{6} \\ \\ 24a=864 \\ \\ a=36[/tex]
Write the equation y=-3x+3 in function notation using f(x) to denote the function.
The function notation form of the given equation; y = -3x +3 as in the task content is; f(x) = -3(x) +3.
What is the function notation form of the equation?According to the task content, the equation given; y = -3x +3 is to be written in function notation.
Consequently, since the function expression given is linear in variable X, it follows that the required function notation is;
f(x) = -3x +3.
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What length of skirting board is needed for a room which is 4m by 4m square if the room has a 800mm door?
Answer:
15.2m2
Step-by-step explanation:
hope it helps.good day
Tried doing it myself multiple times , multi choice question, not getting any availabile answer.
Answer: The given integral is impossible to solve.
Step-by-step explanation: I tried solving it right now with integration by parts and trigonometric substitution, and I was unable to solve it.
So I looked at two math solvers and tried inputting the question, and it either says "There is nothing more you can do with this problem," or "We are unable to solve this problem."
First, let's substitute [tex]x=\frac w4[/tex] and [tex]dx=\frac{dw}4[/tex] to get rid of the fraction.
[tex]\displaystyle \int \csc^6\left(\dfrac w4\right) \cot^4\left(\dfrac w4\right) \, dw = 4 \int \csc^6(x) \cot^4(x) \, dx[/tex]
Recall that
[tex]\cot^2(x) + 1 = \csc^2(x)[/tex]
[tex]\dfrac{d}{dx} \cot(x) = -\csc^2(x)[/tex]
We can the rewrite the integrand as
[tex]\displaystyle 4 \int \csc^6(x) \cot^4(x) \, dx = 4 \int \left(\cot^2(x) + 1\right)^2 \cot^4(x) \csc^2(x) \, dx[/tex]
then substitute [tex]y=\cot(x)[/tex] and [tex]dy=-\csc^2(x)\,dx[/tex] to get
[tex]\displaystyle -4 \int (y^2 + 1)^2 y^4 \, dy[/tex]
Expand the integrand.
[tex]\displaystyle -4 \int (y^4 + 2y^2 + 1) y^4 \, dy = -4 \int (y^8 + 2y^6 + y^4) \, dy[/tex]
Now integrate with the power rule.
[tex]\displaystyle -4 \left(\frac{y^9}9 + \frac{2y^7}7 + \frac{y^5}5\right) + C[/tex]
[tex]\displaystyle -\frac{4y^9}9 - \frac{8y^7}7 - \frac{4y^5}5 + C[/tex]
Put everything back in terms of [tex]x[/tex], then [tex]w[/tex].
[tex]\displaystyle -\frac{4\cot^9(x)}9 - \frac{8\cot^7(x)}7 - \frac{4\cot^5(x)}5 + C[/tex]
[tex]\displaystyle \boxed{-\frac49 \cot^9\left(\dfrac w4\right) - \frac87 \cot^7\left(\dfrac w4\right) - \frac45 \cot^5\left(\dfrac w4\right) + C}[/tex]
So confused please help me thank u
15. Find the young modulus of a brass rod of diameter 25mm and of length 250mm which is
subjected to a tensile load of 50KN when the extension of the rod is equal to 0.3mm.
The Young Modulus of the brass rod ≈ 8.5 × 10¹⁰ Pa or N/m².
How to find the young modulus of a brass rod?
Given: Physical Properties of the Brass rod exist
Length, L = 250 mm
Radius, R = Diameter / 2 = 25/2 mm
Load of 50 kN hanging on the brass rod which results in elongation of the rod to 0.3 mm.
To estimate the Young Modulus of the brass rod we will require Stress on the rod, Ratio of elongation to the total length.
To find the stress on the rod,
Stress(Pressure) = Force / Area
⇒ Stress = 50,000 / (Area of cross-section)
The rod exists shaped like a cylinder then the area of its cross-section will be πR² ( R = radius)
⇒ Stress = 50000 / (π (25/2 mm)² )
The force exists given in newton, then we must convert the unit of the area into m² to obtain the solution in pascal.
1 mm = 0.001 m
⇒ Stress = 50,000 / 22/7 ( 25/2 × 10⁻³ m)²
take, π = 22/7
⇒ Stress = 50000 / ( 22/7 × 625 / 4 × 10⁻⁶ )
⇒ Stress = 50000 / ( 11/14 × 625 × 10⁻6 )
⇒ Stress = 50000 × 14 × 10⁶ / 625×11
⇒ Stress = 80 × 14 × 10⁶ / 11
⇒ Stress = 1120/11 × 10⁶ Pa
Now, that we maintain Stressed, to estimate Strain (ratio of elongation to original length),
⇒ Strain = (Elongation) / (Original length)
⇒ Strain = 0.3 / 250
⇒ Strain = 3 / 2500
Therefore, Young Modulus, Y = Stress / Strain
⇒ Y = 1120/11 × 10⁶ / 3/2500
⇒ Y = 1120/11 × 2500/3 × 10⁶
⇒ Y = 101.8 × 833.3 × 10⁶
⇒ Y = 84829.94 × 10⁶
⇒ Y ≈ 8.5 × 10¹⁰ Pa
Therefore, the Young Modulus of the brass rod ≈ 8.5 × 10¹⁰ Pa or N/m².
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Equivalent fraction statement
Answer:
x=18
Step-by-step explanation:
[tex]\frac{4}{12} =\frac{6}{x} \\[/tex]
[tex]\frac{4}{12}[/tex] ÷ [tex]\frac{2}{2}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{6}{x}[/tex]
[tex]\frac{2}{6} = \frac{6}{x}[/tex]
2×3 =6
6×3=18
x=18
Exercise 18: 3 1. The populations of a city increased from 4 million to 1.1 million. Write in digits the number by which the population increased.
pls as fast as u can!!!!!!!!!!!!!!!!
Answer:
bro it had been decreased
so total had been decreased is (4,000,000-2,900,000)=1,100,000Jason wants to receive monthly payments of $3,250 for 15 years. How much does he have to invest now in an annuity that has an annual interest rate of 3.6% to achieve his goal? Round your answer to the nearest hundred.
Answer: $451,500
The amount she should invest today in the annuity is $455,450.40.
How much should be invested today?The first step is to determine the future value of the monthly annuity.
Future value = monthly payment x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 3.6/12 = 0.3%n = number of periods : 15 x 12 = 180Future value : 3250 x [(1.003^180) - 1] / 0.003 = 774,171.92
The second step is to determine the present value of this future annuity:
774, 171.92 / (1.036^15) = $455,450.40
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Mr. Gosain?(1 Aana = 31.8 m²) b) A real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 20,00,000 altogether. If he immediately sold the land in the shape of a quadrilateral at Rs 15,00,000 per Kattha, find his profit or loss.(1 Kattha= 338.63 sq. m) danta Excel in Mathematics - Book 9 86 36 m Approved by Curriculum Development Cen 20 m 29 m 25 m 21 m aktapur
The information given regarding the computation of the profit or loss shows that there's a loss of RS 500,000.
How to calculate the profit?From the information given, it was stated that the real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 2000,000 altogether.
It was further depicted that he sold the land in the shape of a quadrilateral at Rs 1,500,000. In their case, the sale is less than the cost and therefore, there's a loss.
The loss will be:
= 2,000,000 - 1,500,000
= 500,000
Therefore, the information given regarding the computation of the profit or loss shows that there's a loss of RS 500,000.
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From the top of the Eiffel tower, which is 984 feet tall, you look down and see your friend at a 60°
angle of depression. How far is your friend from the foot of the tower?
The answer is 492 feet.
If we picture the scenario as a right triangle, using trigonometric ratios, this problem can be solved.
cos 60° = x / 984
1/2 = x/984
x = 984/2
x = 492 feet
ASAP HELP ME WITH THIS
Answer:
isosceles trapezoind
Step-by-step explanation:
An isosceles trapezoid is a trapezoid with congruent base angles.
2/120=X/80=Y/300
x=? & y=?
X=1.33
Y=4.9875;approx. 5.0
Answer:
(2/120=X/80)=Y/300
2×80=120×X
X=160/120
X=1.33
X/80=Y/300
But X=1.33
By substituting
X=1.33, We have that
1.33/80=Y/300
80×Y=1.33×300
80Y=399
Y=399/80
Y=399/80
Y=5.0 approx.
simply the following expression by combining like terms 5w + 7v - 8w + v - w + 2y
Mr. and Mrs. Chan want to buy new furniture that has a cash price of $6230. On the installment plan, they must pay %25 of the cash price as a down payment and make twelve monthly payments of $415. How much interest did they pay due to financing?
The interest due on financing option is $307.50
What is interest on financing?
Interest on financing is the extra amount paid by the couple when their total payments are compared to the cash price of $6,230.
The total payments would be the 25% down payment plus the sum of the twelve monthly payments of $415 each
Down payment=cash price*25%
Down payment=$6230*25%
Down payment=$1,557.50
Total monthly payments=amount of each monthly payment*number of monthly payments
monthly payment=$415
number of monthly payments=12
Total monthly payments=$415*12
Total monthly payments=$4,980
Total payment under financing=Down payment +Total monthly payments
Total payment under financing=$1,557.50+$4,980
Total payment under financing=$6,537.50
Interest=$6,537.50-$6,230
Interest on financing=$307.50
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What is the common denominator of x+5/x+8=1+6/x+1?
Answer:
(x+8) (x+1)
Step-by-step explanation:
To find the common denominator, we need to find the least common multiple of the terms in the denominator
(x+8) from the first term
(1) from the second term
(x+1) from the third term
The least common denominator is
(x+8) (1)(x+1)
Simplifiying
(x+8) (x+1)
Did you ever purchase a bag of M & M Peanut candies and wonder about the distribution of the colors ? A recent article reported that 30 percent of the candies are brown , 20 percent yellow , 20 percent red , 20 percent green , and 10 percent orange . A one - pound bag of M & M peanut candies was purchased at Wal - Mart here in Lubbock . A total of 188 candies were in the bag , with 67 brown , 22 yellow , 51 red , 24 green , and 24 orange .
Filling in the frequency table according to the colors observed and expected on the M & M Peanut candies is as follows:
Frequency Table:Color Brown Yellow Red Green Orange Total
Absolute FrequenciesObserved Frequency 67 22 51 24 24 188
Expected Frequency 56 38 38 38 18 188
Relative Frequencies:
Observed Frequency 36% 12% 27% 13% 13%
Expected Frequency 30% 20% 20% 20% 10%
What is a frequency table?A frequency table is a display of the number of occurrences of a particular value or characteristic.
A frequency table makes it easy to display and interpret a distribution of data.
The absolute frequencies shows the absolute values of the observed and expected frequencies, while the relative frequencies shows the percentage values of the observed and expected frequencies.
Data and Calculations:Color Brown Yellow Red Green Orange Total
Observed Frequency 67 22 51 24 24 188
Expected Frequency 30% 20% 20% 20% 10% 100%
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Question Completion:Fill in the following table on the frequency of the colors, indicating the absolute and relative frequencies of the distributions.
Find one value of x for which h(x)=4 and find h (-2)
the solutions are:
h(x) = 4 for x = 0h(-2) = 2How to find the value of x for which h(x) = 4?The only information of h(x) that we have is the given graph.
To find the value of x, we need to go to the vertical axis and find y = 4, then we move horizontally to the left until we meet the curve.
That intersection will give the value of x for which h(x) = 4.
Doing that, we conclude that h(x) = 4 when x = 0 (on the vertical axis).
Now we want to find h(-2), and we can do that using the graph.
By finding x = -2 on the horizontal axis and then moving up until we intercept the graph, we can see that:
h(-2) = 2
Concluding, the solutions are:
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Find the sum of the infinite geometric sequence that begins 1/12, 1/18, 1/27, …
Answer:
1/4
Step-by-step explanation:
The sum of an infinite geometric series is given by the formula ...
S = a/(1 -r)
where 'a' is the first term, and r is the common ratio.
ApplicationHere, the first term is 1/12, and the common ratio is ...
(1/18)/(1/12) = 12/18 = 2/3
Then the sum is ...
S = (1/12)/(1 -2/3) = (1/12)/(1/3) = 3/12 = 1/4
The sum of the infinite series is 1/4.
jelissa determined she needs to have 800000 for retirement in 30 years. her account earns 6% interest
a. how much would she need to deposit in the account each month
b. how much total money will she put into the account.
c. how much total interest will she earn
The monthly payment is $796.40.
The total amount she would deposit is $286,705.51
The total interest earned is $513,294.49
What is the monthly payment, total amount deposited and interest?The payments made by Jessica are known as deferred annuities. Deferred annuities are when a series of payments are made in exchange for an amount of money in the future.
The formula that can be used to determine the amount of monthly deposit is: future value / annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 6%/12 = 0.5%
n = number of years = 30 x 12 = 360
Annuity factor = ](1.005^360) - 1] / 0.005 = 1004.515
Monthly payments = 800,000 / 1004.515 = $796.40
Total amount she would deposit = monthly payment x number of years x number of months in a year
$796.40 x 30 x 12 = 286,705.51
Total interest earned = value of the retirement account - total amount deposited
800,000 - 286,705.51 = 513,294.49
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