Answers
Part (a)
Locate x = -1 on the x axis. Draw a vertical line through this x value until you reach the f(x) curve. Then move horizontally until you reach the y axis. You should arrive at y = 4. Check out the diagram below to see what I mean.
Since f(-1) = 4, this means we can then say
g( f(-1) ) = g( 4 ) = 4
To evaluate g(4), we'll follow the same idea as what we did with f(x). However, we'll start at x = 4 and draw a vertical line until we reach the g(x) curve this time.
Answer: 4==========================================================
Part (b)
We use the same idea as part (a)
f(-2) = 5
g( f(-2) ) = g(5) = 6
Answer: 6==========================================================
Part (c)
Same idea as the last two parts. We start on the inside and work toward the outside. Keep in mind that g(x) is now the inner function for this part and for part (d) as well.
g(1) = -2
f( g(1) ) = f(-2) = 5
Answer: 5==========================================================
Part (d)
Same idea as part (c)
g(2) = 0
f( g(2) ) = f( 0 ) = 3
Answer: 3
Related Questions
Dutchess County, New York, has been experiencing a mean of 35.4 motor vehicle deaths each year. If D = the number of vehicle deaths in Dutchess County in a year, what is the distribution for D (Binomial or Poisson) Explain.
Answers
Answer:
Poisson, as we have the mean number and not a proportion.
Step-by-step explanation:
We have the mean number of vehicle deaths per year, thus, since it is a mean and not a proportion, we use the Poisson distribution.
If we were working with the proportion of accidents that end in death for example, or any other proportion, it would be a binomial random variable.
I need help with this
Answers
bing jhwwjwiwisisuwuwywywywfsfsahajai
Зу = -2 - 6
3y = 2z - 6
Answers
Answer:
y = -8/3, z = -1
Use the given values of n= 93 and p= 0.24 to find the minimum value that is not significantly low, μ- 2σ , and the maximum value that is not significantly high, μ+2σ. Round your answer to the nearest hundredth as needed.
a. Minimum: 30.56; maximum: 14.08
b. Minimum: 14.08; maximum: 30.56
c. Minimum: 18.2; maximum: 26.44
d. Minimum:-11.61; maximum: 56.25
Answers
Answer:
The answer is "Option a".
Step-by-step explanation:
[tex]n= 93 \\\\p= 0.24\\\\\mu=?\\\\ \sigma=?\\\\[/tex]
Using the binomial distribution: [tex]\mu = n\times p = 93 \times 0.24 = 22.32\\\\\sigma = \sqrt{n \times p \times (1-p)}=\sqrt{93 \times 0.24 \times (1-0.24)}=4.1186[/tex]
In this the maximum value which is significantly low, [tex]\mu-2\sigma[/tex], and the minimum value which is significantly high, [tex]\mu+2\sigma[/tex], that is equal to:
[tex]\mu-2\sigma = 22.32 - 2(4.1186) = 14.0828 \approx 14.08\\\\\mu+2\sigma = 22.32 + 2(4.1186) = 30.5572 \approx 30.56[/tex]
Engineering
When p= 3, q. I and r. 2, the
expression 2p² q3 is equal to
Answers
Answer:
[tex]{ \tt{2 {p}^{2} {q}^{3} }} \\ = { \tt{ {2(3)}^{2} . {(1)}^{3} }} \\ = 18[/tex]
The surface area of a melting snowball decreases at a rate of3.8cm2/min. Find the rate at which its diameter decreases when the diameter is13cm. (Round your answer to three decimal places if required)
Answers
Answer:
Step-by-step explanation:
This is a pretty basic related rates problem. I'm going to go through this just like I do in class when I'm teaching it to my students.
We see we have a snowball, which is a sphere. We are talking about the surface area of this sphere which has a formula of
[tex]S=4\pi r^2[/tex]
In the problem we are given diameter, not radius. What we know about the relationship between a radius and a diameter is that
d = 2r so
[tex]\frac{d}{2}=r[/tex] Now we can have the equation in terms of diameter instead of radius. Rewriting:
[tex]S=4\pi(\frac{d}{2})^2[/tex] which simplifies to
[tex]S=4\pi(\frac{d^2}{4})[/tex] and a bit more to
[tex]S=\pi d^2[/tex] (the 4's cancel out by division). Now that is a simple equation for which we have to find the derivative with respect to time.
[tex]\frac{dS}{dt}=\pi*2d\frac{dD}{dt}[/tex] Now let's look at the problem and see what we are given as far as information.
The rate at which the surface area changes is -3.8, and we are looking for [tex]\frac{dD}{dt}[/tex], the rate at which the diameter is changing, when the diameter is 13. Filling in:
[tex]-3.8=\pi(2)(13)\frac{dD}{dt}[/tex] and solving for the rate at which the diameter is changing:
[tex]-\frac{3.8}{26\pi}=\frac{dD}{dt}[/tex] and divide to get
[tex]\frac{dD}{dt}=-.459\frac{cm}{min}[/tex] Obviously, the negative means that the diameter is decreasing.
Find the exact value of the logarithm without using a calculator.
Answers
Answer:
1/11
Step-by-step explanation:
We are asked to find the natural log of
[tex] \sqrt[11]{e} [/tex]
Convert to fractional exponent
[tex] ln(e {}^{ \frac{1}{11} } ) [/tex]
Apply Log of Power rule
[tex] \frac{1}{11} ln(e) [/tex]
Natural log of e is 1 so
[tex] \frac{1}{11} \times 1 = \frac{1}{11} [/tex]
Answer:
[tex]\frac{1}{11}[/tex]
Step-by-step explanation:
First, remember that the ln function is just a log function with a base of e. Here's how it looks
[tex]ln(x) =log_{e}(x)[/tex]
[tex]ln(\sqrt[11]{e} ) = log_{e}(\sqrt[11]{e} )[/tex]
We can take this one step further if we realize that we can rewrite the square root as a simple power to a fraction!
[tex]log_{e}(e^{\frac{1}{11} } )[/tex]
Solving the equation above is really simple. All that function is really saying is can we raise e to some number, where the result would be e^(1/11)? In other words find x.
[tex]e^{x} = e^{\frac{1}{11} }[/tex]
Well x has to be 1/11 in that case. And that ends up being our final answer.
[tex]log_{e}(e^{\frac{1}{11} } ) = \frac{1}{11}[/tex]
A runner is traveling at a constant rate of 8 meters per second. How long does it take for the runner to travel 100 meters? Now before you answer this I know it's 12.5! What I need help with is creating a equation that gives the distance, d, that the person has run if you know the amount of time, t, they have been running. Thank you! :)
Answers
Answer:
see below
Step-by-step explanation:
We know that distance = rate * time
100 meters = 8 m/s * time
100 = 8t
Divide each side by 8
100/8 = 8t/8
12.5 = t
If we know the rate and the time, we can find the distance
d = rt
Coefficient of y in the equation: 3(2x -1/3y) = 0 is equal to a) 3 b) 1 c)-3 d)-1
Answers
Answer:
d is the right answer because the coefficient of y is 3*(-1/3) which results -1 so d is the right answer
The coefficient of y in the given equation is 1. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 3(2x -1/3y)=0.
Now, 6x-1/y=0
A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
Here, coefficient of y is 1.
Therefore, option B is the correct answer.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
Which of the following is equal to -18
Answers
Step-by-step explanation:
9i√2
-18
so therefore the answer is 9i√2
Each spring, Bill's yard has about 950 square feet of space to cover with mulch. One year, trying to save some cash, Bill bought cheapo overseas mulch from a gas station, and the packaging said that each bag covered 1.8 square meters. How many bags did Bill need
Answers
Answer:
161 bags
Step-by-step explanation:
Since we need to know how many square feet a bag can cover, we need to convert the 1.8 square meters to feet. A meter is about 3 feet and 3.5 inches, so to find how many bags he needs we need to convert the bag into feet. First lets convert the meter into inches:
[tex](3*12)+3.5\\(36)+3.5 = 39.5[/tex]
Remember that a foot is 12 inches. Now, we need to multiply the 39.5 inches by 1.8 to find out how many square inches a bag holds.
[tex]39.5*1.8 = 71.1[/tex]
We need square feet though, so let's divide our 71.1 inches by 12 to get a foot measurement.
[tex]71.1/12=5.93[/tex]
A bag holds 5.93 square feet of mulch. Now, to figure out how many bags he needs, we need to divide 950 (total area to cover) by 5.93 (area each bag covers).
[tex]950/5.93=160.2[/tex]
Since Bill cant buy a fifth of a bag, we need to round up so he has enough. So, Bill needs 161 bags of mulch to cover his yard.
The mortgage on your new house is $180,000. Your monthly mortgage payment is $839 for 30 years. How much interest will be paid if the house is kept for the full 30 years?
Answers
9514 1404 393
Answer:
$122,040
Step-by-step explanation:
The interest is the difference between the mortgage value and the total amount paid.
($839/mo)×(12 mo/yr)×(30 yr) -180,000 = $302,400 -180,000 = $122,040
$122,040 will be paid in interest.
!!! I need help with this question !!! I tried using the standard deviation formula but my answers are wrong. Can someone please help me! Thank you for your help!
Answers
Answer:
Step-by-step explanation:
Consider a uniform density curve defined from x = 0 to x = 8. What percent of observations fall between 1 and 5?
a) 0.20
b) 0.50
c) 0.62
d) 0.13
e) 0.63
f) None of the above
Answers
Answer: 0.50, which is choice b
Explanation:
The interval [tex]1 \le x \le 5[/tex] covers 5-1 = 4 units in the horizontal direction.
This is out of 8 units that span from x = 0 to x = 8 (we could say 8-0 = 8).
So we get the final result of 4/8 = 0.50
In other words, the interval from x = 1 to x = 5 covers exactly half of the interval from x = 0 to x = 8.
Which is the graph of the following inequality
Answers
Answer:
graph a is the correct answer
Step-by-step explanation:
The height of Mt.Whitney is approximately 14,490 feet. What is a rounded form of this number written in scientific notation?
Answers
Combine the expressions below
4x+(-2x)+6+(-9)
Answers
=4x-2x=2x
=6-9=-3
=2x-3
Each pizza shown is broken up into different sized slices, but they are all equivalent.
Come up with another ratio of pizza slices that is equivalent to all of these pizzas.
Answers
hope this helps as the denominator is divisible by the ones from the question
Find the mean for the data items
Answers
Answer:
4.5
Step-by-step explanation:
Given the data :
Score, x ____: 1, 2, 3, 4, 5, 6, 7, 8
Frequency, F : 1, 5, 1, 4, 4, 1, 5, 1
This is a grouped data: The mean of a grouped data is given as :
Mean (xbar) = ΣFx / ΣF
ΣFx = (1*1)+(2*5)+(3*1)+(4*4)+(5*4)+(6*1)+(7*5)+(8*1) = 99
ΣF = (1+5+1+4+4+1+5+1) = 22
Mean (xbar) = ΣFx / ΣF = 99 / 22 = 4.5
the length of a rectangle is twice its width the perimeter is 48 cm what are the dimensions of the rectangle
Answers
Answer:
The length=16cm and the width=8cm.
Step-by-step explanation:
Given that the length is twice the breadth or width of the rectangle
Let's assume that the breadth of the rectangle is x.
Thus the length is 2x.
Given perimeter=48cm
The formula for the perimeter of a rectangle is 2(l+b) where l is length and b is breadth.
2(x+2x)=48
(3x)=48/2
3x=24
x=8cm
2x=16cm
Step-by-step explanation:
length=2x
width=x
2x+x+2x+x=48
6x=48
6x÷6=48÷6
x=8
length=16
width=8
Help ASPPP!!!
Name a point that is represented on this graph. Use an ordered pair to give your answer. (Hint:
Look at the shaded region)
Answers
Answer:
(-5, -9)
Step-by-step explanation:
From the graph shown, the perfect ordered pair represented on the graph occurs when x = -5, y = -9. Therefore the required coordinate could be (-5, -9)
What is the value of x in the equation
-%y = 30, when y = 15?
Answers
Answer:
x not given
therefore no answer for x
Solve the following equation. for x
7x - 2 < 10
Answers
Step-by-step explanation:
7x < 10+2
7x<12
x < 12/7
Hope this helps!
Answer:
[tex]7x-2<10[/tex][tex]7x-2+2<10+2[/tex][tex]7x<12[/tex][tex]\frac{7x}{7}<\frac{12}{7}[/tex][tex]x<\frac{12}{7}[/tex]OAmalOHopeO
Which of the following is graphed below?
Answers
G. Find the ratio between a pen and pencil if ten pens cost $22.5 and a dozen pencils cost $18.
Answers
Answer:
Cost ratio of pens:pencils = 9 : 4
Step-by-step explanation:
Pen : Pencil
10/10 : 12/12
22.5 / 10 : 18 / 12
2.25 : 1.5 cost per pen : pencil
HC of 0.25 and 0.5 is 8
8 x 2.25 = 18:
1.5 x 8 = 12
Then place them under their denominator x 10 x 12
pens = 18/10 = 1.8
pencils = 12/12 = 1
HC of 1.8 and 1 is 5
1.8 x 5 = 9
1 x 5 = 5
Answer = 9 : 4
The width of a rectangle measures (7k-2m)(7k−2m) centimeters, and its length measures (5k-m)(5k−m) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answers
Answer:
[tex]P = 24k-6m[/tex]
Step-by-step explanation:
The correct expressions are:
[tex]W = 7k - 2m[/tex]
[tex]L = 5k - m[/tex]
Required
The perimeter (P)
This is calculated as:
[tex]P = 2 *(L + W)[/tex]
So, we have:
[tex]P = 2 *(5k - m + 7k -2m)[/tex]
Collect like terms
[tex]P = 2 *(5k + 7k- m -2m)[/tex]
[tex]P = 2 *(12k-3m)[/tex]
Open bracket
[tex]P = 24k-6m[/tex]
please help me its timed -H.M
Answers
Answer:
f(3) = g(3)
General Formulas and Concepts:
Algebra I
Functions
Function NotationGraphingStep-by-step explanation:
We can see from the graph that the lines intersect at (3, 6). If this is the case, then that means that when x = 3 for both functions, it outputs f(x) = 6.
Rewriting this in terms of function notation:
f(3) = 6, g(3) = 6
∴ f(3) = g(3)
Miller's Steakhouse offers 8 side dishes, 5 types of steak, and 4 toppings. How many different smothered steak dinners can be made if a smothered steak dinner consists of the customer's choice of steak served with 3 different toppings and 3 different side dishes?
Answers
Answer:
1120
Step-by-step explanation:
To find the possible number of steak dinners, you would multiply the number of choices for each part of the dinner. You would used combinations instead of permutations since the order of the toppings chosen or side dishes chosen do not matter. There are 5 choose 1 choices for types of steak, which is just 5. There are 8 choose 3 choices for side dishes, which is 56. There are 4 choose 3 choices for toppings, which is 4. 5*56*4 is 1120, so there are 1120 possible steak dinners.
Which of the following is a geometric sequence where a1 = 4 and r = 3?
A) 4, 7, 10, 13, . . .
B) 3, 7, 11, 15, . . .
C) 4, 12, 36, 108, . . .
D) 3, 12, 48, 192, . . .
Answers
Answer:
C 4,12,36 108
Step-by-step explanation:
the answer is above.
Answer:
C
Step-by-step explanation:
G.P= a,ar,ar^2,ar^3,...,
a1=4
a2=4×3=12
a3=4×9=36
a4=4×27=108
JK=8x+6 KL=6x+20 find JL
Answers
Answer:
14x + 26
Step-by-step explanation:
JL = JK + KL
= 8x + 6 + 6x + 20
= 8x + 6x + 6 + 20
JL = 14x + 26
