Answer:
[tex]f(x) = x^{4}[/tex], [tex]g(x) = x-1[/tex]
Step-by-step explanation:
Let be [tex]F(x) = f\circ g (x) = (x-1)^{4}[/tex], then expression for [tex]f(x)[/tex] and [tex]g(x)[/tex] are, respectively:
[tex]f(x) = x^{4}[/tex] and [tex]g(x) = x-1[/tex]
Suppose that 22 inches of wire costs 66 cents.
At the same rate, how much (in cents) will 17 inches of wire cost?
cents
Х
?
Answer:
51 cents for 17 inches of wire
Step-by-step explanation:
22 = 66
17 = x
22x = 66 * 17
22x = 1122
x = 51 cents
or
22 inches costs 66 cents
1 inch costs 3 cents (66 / 22 = 3 cents)
17 inches costs 51 cents (17 * 3 = 51 cents)
The concentration of a drug in the body decreases exponentially after a dosage is given. In one clinical study, adult subjects averaged 14 micrograms/milliliter (mcg/mL) of the drug in their blood plasma 1 hr after a 1000-mg dosage and 3 micrograms/milliliter 4 hr after dosage.
a) Find the value k, and write an equation for an exponential function that can be used to predict the concentration of the drug, in micrograms/milliliter, t hours after a 1000-mg dosage.
b) Estimate the concentration of the drug 3 hr after a 1000-mg dosage.
c) To relieve a fever, the concentration of the drug should go no lower than 4 mcg/mL. After how many hours will a 1000-mg dosage drop to that level?
k = ________(Round to three decimal places as needed.)
Answer:
Step-by-step explanation:
14 = 1000 [tex]e^{ k*1}[/tex]
.014 = [tex]e^{k*1}[/tex]
ln(.014) = k ln(e)
k = -4.268
~~~~~~~~~~~~~~~~~~
after 3 hrs
1000 [tex]e^{ -4.268*3}[/tex]
0.00274
~~~~~~~~~~~~~~~
4 = 1000 [tex]e^{ -4.268*t}[/tex]
.004 = [tex]e^{ -4.268*t}[/tex]
ln(.004)/-4.268 = t
t = 1.29368 hrs
h(x) = -x² + 3x + 10
Answer:
x = 5 or x = -2 or 3 - 2 x (derivative)
Step-by-step explanation:
Solve for x over the real numbers:
-x^2 + 3 x + 10 = 0
Multiply both sides by -1:
x^2 - 3 x - 10 = 0
x = (3 ± sqrt((-3)^2 - 4 (-10)))/2 = (3 ± sqrt(9 + 40))/2 = (3 ± sqrt(49))/2:
x = (3 + sqrt(49))/2 or x = (3 - sqrt(49))/2
sqrt(49) = sqrt(7^2) = 7:
x = (3 + 7)/2 or x = (3 - 7)/2
(3 + 7)/2 = 10/2 = 5:
x = 5 or x = (3 - 7)/2
(3 - 7)/2 = -4/2 = -2:
Answer: x = 5 or x = -2
____________________________________
Find the derivative of the following via implicit differentiation:
d/dx(H(x)) = d/dx(10 + 3 x - x^2)
Using the chain rule, d/dx(H(x)) = ( dH(u))/( du) ( du)/( dx), where u = x and d/( du)(H(u)) = H'(u):
(d/dx(x)) H'(x) = d/dx(10 + 3 x - x^2)
The derivative of x is 1:
1 H'(x) = d/dx(10 + 3 x - x^2)
Differentiate the sum term by term and factor out constants:
H'(x) = d/dx(10) + 3 (d/dx(x)) - d/dx(x^2)
The derivative of 10 is zero:
H'(x) = 3 (d/dx(x)) - d/dx(x^2) + 0
Simplify the expression:
H'(x) = 3 (d/dx(x)) - d/dx(x^2)
The derivative of x is 1:
H'(x) = -(d/dx(x^2)) + 1 3
Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 2.
d/dx(x^2) = 2 x:
H'(x) = 3 - 2 x
Simplify the expression:
Answer: = 3 - 2 x
Answer two questions about Equations A and B: A.5x=20 \ B.x=4 1) How can we get Equation B from Equation A? Choose 1 answer: (Choice A) Multiply/divide both sides by the same non-zero constant (Choice B,) Multiply/divide both sides by the same variable expression (Choice C) Add/subtract the same quantity to/from both sides (Choice D) Add/subtract a quantity to/from only one side
Answer:
Multiply/divide both sides by the same non-zero constant
Step-by-step explanation:
5x = 20
Divide each side by 5
5x/5 = 20/5
x = 4
To obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"
Given the equations :
5x = 20 ___ (A)x = 4 _____ (B)To obtain the value ; x = 4 from A
We multiply (A) by the same non-zero constantHere, the constant value which can be used is 5 in other to isolate 'x'
5x/5 = 20/5
x = 4
Therefore, to obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"
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The scale on a scale drawing is 1 : 30. What should you do with each measurement on the drawing to get the actual dimensions? Provide an example of a drawing that uses this scale. Include both the original and new dimensions.
Answer:
see below
Step-by-step explanation:
For the first question, you should multiply the scale dimension by 30 to get the actual dimension. This is because the scale is 1:30 where the scale dimension is the 1 and the actual dimension is 30, so therefore, the scale dimension is 1/30th of the actual dimension, so to get the actual dimension, we can multiply the scale dimension by 30. I'm not totally sure how to attach pictures from my phone on my computer (sorry) but an example of a drawing could be two rectangles, the first (this is the scale drawing) having dimensions of 1 by 2 units and the second (this is the actual drawing) having dimensions of 30 by 60 units. I hope this helps!
Records indicate that x years after 2008, the average property tax on a three bedroom home in a certain community was T(x) =20x^2+40x+600 dollars.
Required:
a. At what rate was the property tax increasing with respect to time in 2008?
b. By how much did the tax change between the years 2008 and 2012?
Answer:
a) 40 dollars
b) 480 dollars
Step-by-step explanation:
Given the average property tax on a three bedroom home in a certain community modelled by the equation T(x) =20x²+40x+600, the rate at which the property tax is increasing with respect to time in 2008 can be derived by solving for the function T'(x) at x=0
T'(x) = 2(20)x¹ + 40x° + 0
T'(x) = 40x+40
At x = 0,
T'(0) = 40(0)+40
T'(0) = 40
Hence the property tax was increasing at a rate of 40dollars with respect to the initial year (2008).
b) There are 4 years between 2008 and 2012. To know how much that the tax change between the years 2008 and 2012, we will find T(4) - T(0)
Given T(x) =20x²+40x+600
T(4) =20(4)²+40(4)+600
T(4) = 320+160+600
T(4) = 1080 dollars
Also T(0) =20(0)²+40(0)+600
T(0) = 0+0+600
T(0)= 600 dollars
T(4) - T(0) = 1080 - 600
T(4) - T(0) = 480 dollars
Hence, the tax has changed by $480 between 2008 and 2012
8.What side of the road will you see speed, yield, and guide signs on ?
Answer:
we see it in our left side of the road
Help me please thank you
Answer: 60°
Step-by-step explanation:
apply concept: the interior angle sum of triangle is 180°
x+x+x=180
3x=180
x=60
---------------
this is also an equilateral triangle which if you know it, you will know that each angles are all 60°
Answer: x=60°
Step-by-step explanation:
We know that the sum of the angles in a triangle is 180°. Since all of the angles are x°, we know that they are equal in degrees. Since there are 3x, we can use that to solve for x.
3x=180 [divide both sides by 3]
x=60°
what is the diameter of a circular swimming pool with a radius of 9 feet? enter only the number
Answer:
The answer is 18 feet
Step-by-step explanation:
To find the diameter of a circle given it's radius we use the formula
diameter = radius × 2
From the question
radius = 8
So the diameter is
diameter = 9 × 2 = 18 feetHope this helps you
Answer:
18
Step-by-step explanation:
Hey there!
Well radius is half the diameter so,
D = r*2
Plug in 9
D = 9*2
D = 18
Hope this helps :)
How many countries expect to have an increase in population from 1950 to 2000 and from 2000 to 2050 ?
one
two
three
four
Answer:
three
Step-by-step explanation:
The three countries expect to have an increase in population. Then the correct option is C.
What is a histogram?A diagram is made up of rectangles whose size is related to a variable's frequency and whose width is comparable to the training sample.
The bar chart of the countries is shown.
From the bar chart, the population from 1950 to 2000 and from 2000 to 2050 of Australia increased.
From the bar chart, the population from 1950 to 2000 and from 2000 to 2050 of Hungary first increases then decreases.
And from the bar chart, the population from 1950 to 2000 and from 2000 to 2050 of Canada increased.
From the bar chart, the population from 1950 to 2000 and from 2000 to 2050 in South Korea first increases then decreases.
From the bar chart, the population from 1950 to 2000 and from 2000 to 2050 of Egypt increased.
The three countries expect to have an increase in population.
Then the correct option is C.
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Two cards are dealt at random from a standard 52 card deck (without replacement). (Ace, King, Queen, Jack are face cards.)
Required:
a. Find the probability that the first card is a face card and the second is NOT a face card.
b. Find the probability that they are both face cards.
c. Find the probability that the second is a face card given the first is NOT a face card.
Answer:
The answer is below
Step-by-step explanation:
There are 52 cards in a deck, 12 of these cards are face cards (4 kings, 4 queens and 4 jacks) and 40 are not face cards
a. Find the probability that the first card is a face card and the second is NOT a face card.
There are 12 first card, the probability that the first card is a face card is 12/52.
Since there are no replacement, after picking 1 face card the number of cards remaining is 51, the probability of the second card not being a face card = 40/51. Therefore:
The probability that the first card is a face card and the second is NOT a face card = P(first is face card) × P(second is not face card) = 12/52 × 40/51 = 40/221
b) Find the probability that they are both face cards.
The probability that the first card is a face card is 12/52.
Since there are no replacement, after picking 1 face card the number of cards remaining is 51 and the number of face card remaining is 11, the probability of the second card is a face card = 11/51. Therefore:
The probability that they are both face cards = P(first is face card) × P(second is face card) = 12/52 × 11/51 = 11/221
c) Find the probability that the second is a face card given the first is NOT a face card.
The probability that the first card is not a face card = 40/52
Since there are no replacement, after picking the first card the number of cards remaining is, the probability of the second card is a face card = 12/51. Therefore:
The probability that the second is a face card given the first is NOT a face card = P(first is not a face card) × P(second is face card) = 40/52 × 12/51 = 40/221
A segment bisector is a line, ray or segment that divides a line segment into two equal parts. in the triangle formed by points A(-1,7), B(1,2), C(7,6) what is the slope of the line that goes through point A and bisects BC?
In decimal form, this is equivalent to -0.6
=================================================
Explanation:
This segment bisector is cutting side BC in half. So we have a point D such that it is between B and C. Also, we can say BD = DC. Refer to the diagram below.
To find the location of D, we'll apply the midpoint formula to points B and C.
B(1,2) and C(7,6) have x coordinates of 1 and 7 respectively. Average those x values to get (1+7)/2 = 8/2 = 4. This is the x coordinate of point D.
Repeat this idea for the y coordinates. We'll get (2+6)/2 = 8/2 = 4 which is the y coordinate of D.
Point D is located at (4,4)
---------------------
The takeaway from that last section, if we were to summarize it in one sentence, is that D is located at (4,4).
Now focus on the points A(-1,7) and D(4,4)
We'll apply the slope formula
m = (y2-y1)/(x2-x1)
m = (4-7)/(4-(-1))
m = (4-7)/(4+1)
m = -3/5 is the slope
Notice that to go from A to D, we can drop down by 3 units and move to the right 5 units. We can say rise = -3 and run = 5; therefore, slope = rise/run = -3/5
You meet with the financial aid office to discuss your costs for attending LSU next semester.Tuition is $113.67 per credit hour, and fees are a flat rate of $660. You have a grant of $350 and a scholarship of $400. If you are taking 15 credit hours what amount will you need go pay for your classes next semester?
Show you work
Answer:
$1615.05Step-by-step explanation:
Scholarship and grants are money given to the candidates to support his financial needs in school. It will serves as the means of revenue for the student.
Revenue generated = Grant + Scholarship amount
Revenue generated = $350 + $400
Revenue generated= $750
Total money needed to be spent in school = Tuition + fees
If tuition is $113.67 per credit hour and I used 15 credit hours, total amount of tuition paid = 15* $113.67 = $1705.05
Total fees = $660
Total money needed to be spent in school = $1705.05 + $660
Total money needed to be spent in school = $2365.05
Amount I will need to pay for classes next semester = Total money that will be spent - (grant+scholarship)
= $2365.05 - $750
= $1615.05
Hence, the amount I will need to pay for classes next semester is $1615.05
Tyler and Gabe went to the arcade and played the same two games, Tyler played five rounds of each game for 30$. Write two equations for the amounts the two boys spent. Then find the cost for one round each game.
Equations:
1. (30)(5)= 150
2. 30 + 30 + 30 + 30 + 30 = 150
I round:
30 dollars divided by 5 rounds = 6 dollars per round.
The total amount spent by the two boys is $300.
What is algebraic expression?An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
Given is that Tyler and Gabe went to the arcade and played the same two games. Tyler played five rounds of each game for 30$.
We can write the total amount spent by the two boys as -
total amount = 2 x cost of each game x total number of games played
total amount = 2 x 30 x 5
total amount = 10 x 30
total amount = 300
Therefore, the total amount spent by the two boys is $300.
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Chelsea played her tuba from 4:25 pm until 5:07
Answer:
42 minutes
Step-by-step explanation:
if you are asking how long it takes Chelsea to play her tuba then you do: 67 - 25 = 42
Answer:
Step-by-step explanation:
jhngjnh
3a-27=0
How to solve
Answer:
a = 9
Step-by-step explanation:
3a - 27 = 0
3a = 27
a = 27/3
a = 9
3*9 - 27 = 0
27 - 27 = 0
Answer:
a = 9
Step-by-step explanation:
3a-27=0
Add 27 to each side
3a = 27
Divide by 3
3a/3 = 27/3
a = 9
In December 2004, a report based on the National Survey on Drug Use and Health estimated that 20% of all Americans aged 16 to 20 drove under the influence of drugs or alcohol in the previous year. We would like to update this information by calculating a 98% confidence interval. How large a sample is necessary in order for the bound on the error of estimation to be 0.04?
Answer:
542
Step-by-step explanation:
We are required to find the sample size at 98% confidence interval in this question
E = 0.04
P* = 20% = 0.20
n = p* x (1-p)(Zα/2÷E)²
α = 1 - 0.98
= 0.02
To get Critical value
= 0.02/2 = 0.01
The critical value at 0.01 is 2.33
Inserting values into formula:
O.2 x 0.8(2.33/0.04)²
= 0.8 x 0.2 x 58.25²
= 542.89
The value of n must be an integer therefore the answer is 542.
In the diagram, the vertices of the square lie at the centers of the four partial circles. What is the area of the entire shape? Use the value pi = 3.1416
The area of the entire shape is 33,562 square units
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
The figure is made up of a square and four 3/4 circles. So the total area will be equal to the sum of the area of the square and the sum of the 3/4 th circles.
Area of Square:-
= 100 x 100 = 10,000
Area of each circle
= π r² = 3.1416 x 50 x 50 = 7854
Area of each 3/4 circle
= 7854 x ( 3/4 ) = 5890.5
Area of all four 3/4 circles
= 5890.5 x 4=23562
The TOTAL area will be the sum of all the areas
A = 23562 + 10,000 = 33,562 square units
Therefore the area of the entire shape is 33,562 square units
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The area of the entire shape is 33,562 square units.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
Here, we have,
The figure is made up of a square and four 3/4 circles.
So the total area will be equal to the sum of the area of the square and the sum of the 3/4 the circles.
Area of Square:-
= 100 x 100 = 10,000
Area of each circle
= π r² = 3.1416 x 50 x 50 = 7854
Area of each 3/4 circle
= 7854 x ( 3/4 ) = 5890.5
Area of all four 3/4 circles
= 5890.5 x 4=23562
The TOTAL area will be the sum of all the areas
A = 23562 + 10,000 = 33,562 square units
Therefore the area of the entire shape is 33,562 square units
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Abel and Cedric will share a total of $180. Abel will receive half as much as Cedric. What amount. in dollars, will Cedric receive (Disregard the $ sign when gridding your answer.)
Answer:
Abel receives $60, and Cedric receives $120
Step-by-step explanation:
Let Abel's share = A
Let Cedric's share = C
we are given the following
A + C = 180 - - - - - (1) (Abel and Cedric will share a total of $180)
[tex]A = \frac{C}{2}\ - - - - - - - (2)[/tex] (Abel will receive half as much as Cedric. )
from equation 2:
[tex]A = \frac{C}{2}\\ C = 2A\ - - - - - - (3)[/tex]
putting this value of C in eqn (3) into eqn (1)
A + (2A) = 180
3A = 180
∴ A = 180 ÷ 3 = 60
to find C, let us replace the value of A in eqn (3) with 60
C = 2A - - - - (3)
C = 2 × 60
C = 120
Therefore, Abel receives $60, and Cedric receives $120
Solve for X, 3^x + 3^2 = 90
3^x + 3^2 = 90
Simplify the known power:
3^x + 9 = 90
Subtract 9 from both sides:
3^x = 81
Take the cubic root of both sides:
X = 4
look at the image below
Answer:
1520.5 yd²
Step-by-step explanation:
Surface area of a sphere = 4πr², where r is the radius
so,
4πr²
= 4×π×11²
= 484π
= 1520.5 yd²
rite
8x8*8X8X8 as
power
Answer:
8×8×8×8×8
= 8^5
because there are five 8 number
I hope this helps
if u have question let me know in comments ^_^
[tex]8\cdot8\cdot8\cdot8\cdot8=8^5[/tex]
20.) The area of a circle is given by the equation A = nr2. If the radius of a circle is equal to 6 centimeters,
which of the following is closes to the area of the circle? (Use it = 3.14.)
113.04
18.84
36
28.26
please provide explanation
Answer:
113.04 cm^2
Step-by-step explanation:
The area of a circle is
A = pi r^2
We know the radius is 6 cm
A = 3.14 * 6^2
A = 3.14 * 36
A =113.04
A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month. The results of a study of 140 fatal accidents were recorded. Is there enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month? Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fatal Accidents 8 15 9 8 13 6 17 15 10 9 18 12
Answer:
There is enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month, as the Variance is 14 and the Standard Deviation = 4 approximately.
There is a high degree of variability in the mean of the population as explained by the Variance and the Standard Deviation.
Step-by-step explanation:
Month No. of Mean Squared
Fatal Accidents Deviation Difference
Jan 8 -4 16
Feb 15 3 9
Mar 9 -3 9
Apr 8 -4 16
May 13 1 1
Jun 6 -6 36
Jul 17 5 25
Aug 15 3 9
Sep 10 -2 4
Oct 9 -3 9
Nov 18 6 36
Dec 12 0 0
Total 140 170
Mean = 140/12 = 12 Mean of squared deviation (Variance) = 170/12 = 14.16667
Standard deviation = square root of variance = 3.76386 = 4
The fatal accidents' Variance is a measure of how spread out the fatal accident data set is. It is calculated as the average squared deviation of the number of each month's accident from the mean of the fatal accident data set. It also shows how variable the data varies from the mean of approximately 12.
The fatal accidents' Standard Deviation is the square root of the variance, and a useful measure of variability when the distribution is normal or approximately normal.
Give an example of when and why one would use a continuity correction factor?
Answer:
An example of when a continuity correction factor can be used is in finding the number of tails in 50 tosses of a coin within a given range .
and continuity correction factor is used when a continuous probability distribution is used on a discrete probability distribution
Step-by-step explanation:
An example of when a continuity correction factor can be used is in finding the number of tails in 50 tosses of a coin within a given range .
continuity correction factor is used when a continuous probability distribution is used on a discrete probability distribution, continuity correction factor creates an adjustment on a discrete distribution while using a continuous distribution
what's the standard answer for (5×1)+(7×.2)+(2×0.4)
9514 1404 393
Answer:
7.2
Step-by-step explanation:
The order of operations tells you that quantities in parentheses are evaluated first.
(5×1)+(7×.2)+(2×0.4) = 5 + 1.4 + 0.8
Then the addition is performed, left to right.
= 6.4 +0.8
= 7.2
_____
Your calculator can work this problem for you, if necessary.
Add 5/20 + 1/20. Simplify your answer.
Answer:
3/10
Step-by-step explanation:
1) 5/20+1/20= 6/20
2) Both 6 and 20 lowest number on dividing: 2
6 divide by 2= 3 20 divide by 2= 10
5/20+1/20
= 5+1/20
= 6/20
= 3/10
How to convert 2cm to feet?
Answer:
Divide by 30.48: It would be 0.0656168 feet.
Step-by-step explanation:
Answer:
0.0656
Step-by-step explanation:
2.54 cm = 1 in
12 in = 1 ft
2.54 * 12 = 30.48
2/30.48 = 0.0656167979
Timothy invested $2,000 in an account earning 3.5% annual interest that is compounded continuously. How long will it take the investment to grow to $3,500?
Answer: 16 years
Step-by-step explanation:
The exponential function for continuous growth is given by :-
[tex]P=Ae^{rt}[/tex]
, where A = initial amount, r= rate of growth and t = time.
As per given , we have
A= $2,000, =r 3.5%=0.035 and P= $3500
put these vales in equation , we get
[tex]3500=2000e^{0.035t}\\\\\Rightarrow\ \dfrac{3500}{2000}=e^{0.035t}\\\\\Rightarrow\ 1.75=e^{0.035t}[/tex]
Taking log on both sides , we get
[tex]\ln 1.75=0.035t\\\\\Rightarrow\ t=\dfrac{\ln1.75}{0.035}=\dfrac{0.560}{0.035}=16[/tex]
Hence, it will take 16 years to grow to $3,500.
quick i need help so bad :(
There are 4 triangles with base of 5 and height of 8.4
Area of triangle = 1/2 x base x height
Area of triangle = 1/2 x 5 x 8.4 = 21 m^2
Multiply by 4 = 21 x 4 = 84 m^2
Area of the base = length x width = 5 x 5 = 25 m^2
Total area = 84 + 25 = 109 m^2