Answer:
f(g(-1)) = -8
Step-by-step explanation:
⭐ The two equations we are given are:
[tex]f(x) = 1-x^2[/tex][tex]g(x) = 2x + 5[/tex]This problem is an example of composite functions.
⭐What are composite functions?
Composite functions are functions inside of a functionYou compute the value of an x-value for one function, and use that value for another function.First, we have to compute the value for the 2nd function you see. The 2nd function is inside f(x), and it is g(-1).
Essentially, we have to find the corresponding y-value for when x = -1 in g(x)
[tex]g(-1) = 2(-1) + 5[/tex]
[tex]g(-1) = 3[/tex]
Next, take this value and substitute it as the x-value for f(x).
[tex]f(3) = 1-x^2[/tex]
Now we have to find the y-value for f(x) for when x = 3.
[tex]f(3) = 1 -3^2[/tex]
⚠️⚠️⚠️!!! CAUTION !!! ⚠️⚠️⚠️
Some people may make the mistake of computing f(3) like this:
[tex]f(3) = 1 - 3^2[/tex]
[tex]f(3) = 1+9\\f(3) = 10[/tex]
This is wrong because only 3 is being squared, not -3. Make sure to read the equations you are given carefully to avoid mistakes like this.
[tex]f(3) = 1-3^2\\f(3) = 1-9\\f(3) = -8[/tex]
∴ f(g(-1)) = -8
In the figure, Line a is parallel to line b. If angle 1 = 105º what is the measurement of angle 6?
Answer:
75
Step-by-step explanation:
angle 4 is 75 because it forms a linear pair with angle 1, and 6 is alternate interior with 4 which makes it equal
The sum of a number and twice its reciprocal is
9/2. If the number is an integer, find the number.
Answer:
x + 2/x = 9/2
multiply through by x
x2 + 2 = (9/2)x
multiply through by 2
2x2 + 4 = 9x
2x2 - 9x + 4 = 0
We can factor by grouping. 2(4) = 8 ...
taken from coefficient of square term and the constant ...
Factors of 8 that add to -9 are (-8)(-1):
Replace -9x with -8x - x
2x2 - 8x - x + 4 = 0
(2x2 - 8x) - (x - 4) = 0
2x(x - 4) - (x-4) = 0
(2x-1)(x-4) = 0
2x-1 = 0 and x = 1/2
OR
x-4 = 0 and x = 4
Your two answers are {1/2, 4}
Please mark brainliest for further answer :)Vx
Which two figures have the same number of lateral faces?
O sphere and cylinder
O triangular prism and rectangular prism
O rectangular prism and cube
O triangular prism and cylinder
Two hockey teams, the Winnipeg Jets (yay!) and the Toronto Maple Leafs (boo!), miraculously make it to
the Stanley Cup finals. As soon as a team wins 3 games, the championship is over.
The schedule for the playoffs (for home games) is: Jets - Leafs - Jets - Leafs - Jets
If the Jets are playing at home, there is a 60% chance they'll win. If they are playing on the road, there is
a 45% chance they'll win.
Find the probability that the Jets win the Stanley Cup. Round answers to at least 4 decimal places.
Can anyone help me. answer with full explanation. No links please
Answer:
There is a 54% chance that the Jets will win the Stanley Cup.
Step-by-step explanation:
Since two hockey teams, the Winnipeg Jets and the Toronto Maple Leafs, miraculously make it to the Stanley Cup finals, where as soon as a team wins 3 games, the championship is over, and the schedule for the playoffs for home games is: Jets - Leafs - Jets - Leafs - Jets; since if the Jets are playing at home, there is a 60% chance they'll win, while if they are playing on the road, there is a 45% chance they'll win, to find the probability that the Jets win the Stanley Cup the following calculation must be performed:
(0.60 + 0.45 + 0.60 + 0.45 + 0.60) / 5 = X
2.70 / 5 = X
0.54 = X
Thus, there is a 54% chance that the Jets will win the Stanley Cup.
I have to show work of how i get the values of x, y and z
x= -3
y=4
z=5
Answer:
use symbolab, it helps explain your math problems step by step.
Step-by-step explanation:
pls answer quick Doug makes a parallelogram-shape sign for his shop.
What is the area of this parallelogram?
Round to the nearest hundredth.
5.32 ft²
8.96 ft²
14.28 ft²
17.02 ft²
Answer: 1.9x2.8 + 3.2+2.8 = 14.28
HOPE THIS HELPS
blank minus 1/2 equals to 1/6
Answer:
Blank = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
blank = x
[tex]x-\frac{1}{2} =\frac{1}{6} \\\\x=\frac{1}{6} +\frac{1}{2} \\\\x=\frac{1}{6} +\frac{3}{6} \\\\x=\frac{4}{6} \\\\x=\frac{2}{3}[/tex]
1. What is the median of the following numbers? 36,42,28, 52, 48, 36, 31
36
O 42
O 48
Tú tienes la mitad de lo que tenías y tendrás el triple de lo que tienes. Si tuvieras lo que tienes, tenías y tendrás, tendrías lo que yo tengo que es 180 dólares más de lo que tú tendrás ¿Cuánto tenías?
Answer:
Step-by-step explanation:
PLEASE HELP ASAP GIVING BRAINLIEST W/ POINTS PLSS
9514 1404 393
Answer:
108 ft²
Step-by-step explanation:
When x=6, the length is 6+6 = 12 ft, and the width is 6+3 = 9 ft. The area is given by ...
A = LW
A = (12 ft)(9 ft) = 108 ft²
The area of Cameron's garden is 108 ft².
53 POINTS!!!!!!!!!!!!!
Evaluate the expression when c=6 and d=4. d+7c
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{d + 7c}\\\large\textsf{= 4 + 7(6)}\\\large\textsf{= 4 + 7 + 7 + 7 + 7 + 7 + 7}\\\large\textsf{= 4 + 14 + 14 + 14}\\\large\textsf{= 4 + 28 + 14}\\\large\textsf{= 4 + 42}\\\large\textsf{= 46}\\\\\large\textsf{Therefore, your answer should be: 46 }\large\checkmark\\\\\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\frak{\star \ Amphitrite1040:) \ \heartsuit}[/tex]
Last month we had only five sunny days. There were 30 days in all last month.
What was the ratio of sunny days to the total number of days? What was the ratio
of sunny days to days that were not sunny?
Answer:
6
Step-by-step explanation:
30 ÷ 5 = 6
Answer:
6
Step-by-step explanation:
it is 6
Is {(-3,0), (13,4), (6,3), (13,-4), (22,5)} a function? Please explain if possible
please help me with this asap
What is an equivalent ratio to 3:4?
Answer:
12:16
Step-by-step explanation:
3 x 4 = 12
4 x 4 = 16
Answer:
6:8, 9:12, or 12: 16
Step-by-step explanation:
don't know how many you need but hope this helps! :))
Express as a trinomial.
(3x+1)(2x-1)
Answer:
6x^2-x-1
Step-by-step explanation:
Use the FOIL method.
HELPP IM FAILING MATH RN!!
LC is 40°. What is the measure of arc CB?
I hope this helps you
Hi there!
[tex]\large\boxed{100^{o}}[/tex]
∠C = 40° and triangle ABC is isosceles, therefore:
∠C = ∠A = 40°
Angles in a triangle sum up to 180°, so:
180 = 40 + 40 + ∠A
180 = 80 + ∠A
100 = ∠A
Thus, arc CB has a measure of 100°.
The diameter of each circular hole in a paint palette is 42 millimeters.
Find the circumference of each hole. Use 3.14 as an approximation for .
A 128 millimeters
B 131.88 millimeters
C 120 millimeters
D 42 millimeters
Answer:
B
Step-by-step explanation:
The circumference is just diameter x π (3.14 in this case) so 42 x 3.14 = 131.88
Answer:
B
Step-by-step explanation:
the circumference of a circle is
2×pi×r
with r being the radius (half the diameter).
2r is then the diameter.
so, in our case the circumference is
42×pi = 42 × 3.14 = 131.88 mm
A sample of a radioactive isotope had an initial mass of 450 mg in the year 2005 and decays exponentially over time. A measurement in the year 2012 found that the sample's mass had decayed to 310 mg. What would be the expected mass of the sample in the year 2017, to the nearest whole number?
Answer: 238
Step-by-step explanation:
I need help this is due today
Answer: the amount of money after the purchase depends on the amount of money before the purchase
Step-by-step explanation:
Expand 4(8y-12)......
Answer:
(4 * 8y) - (4 * 12)
Step-by-step explanation:
We have the equation 4(8y - 12) and are asked to expand, this equation can be solved through distribution, and to expand it, we need to separate the "4" to multiplying into "8y" and "-12"
Therefore :
(4 * 8y)(4 * -12)
Now this may seem correct, but we have to keep in mind that we are not multiplying both answers within the parenthesis but yet subtracting, therefore :
(4 * 8y) - (4 * 12)
Please help asap Find the area of this circle. Use
3.14 for it.
108 in.
The area of the circle is about in.2.
(Round to the nearest hundredth as needed.)
Answer:
I know what the answer is if you be more clear. Is 108 the diameter?
44% of all statistics classes require a statistical calculator and 27% require the use of a computer that has statistical software. Of the classes that require a statistical calculator, 15% also require the use of a computer. If a statistics course is selected at random find: (round to 4 decimal places where possible) a. P(Statistical Calculator) = Correct b. P(Statistical Software) = Correct c. P(Require a Statistical Calculator and Statistical Software) = d. P(Require a Statistical Calculator GIVEN Require Statistical Software) =
Answer:
I'm not exactly sure what this is asking, so i'm going to answer each part
A. 44%
B. 27%
C. 11.88% (assuming independence)
D. 61.36%
Step-by-step explanation:
Honestly I'm not really sure what he's asking but for A and B the answer is in the question. For C i assumed independence and multiplied the respective probabilities. For D I divided .27/.66 since it is a dependency probability
The probabilities of the events are
a. 0.44
b. 0.27
c. 0.1188
d. 0.2444.
What is probability?
Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
Statistics classes require a statistical calculator = 44% = 0.44
Statistics classes require a computer that has statistical software = 27% = 0.27
Of the classes that require a statistical calculator, classes also require the use of a computer = 15% = 0.15
a. P(Statistical Calculator) = 0.44
b. P(Statistical Software) = 0.27
c. P(Require a Statistical Calculator and Statistical Software) = [tex](0.44)(0.27)[/tex]
⇒ [tex]0.1188[/tex]
d. P(Require a Statistical Calculator GIVEN Require Statistical Software)
⇒ [tex]\frac{0.066}{0.27}[/tex]
⇒ [tex]0.244[/tex]
Hence we can conclude that the probabilities of the events are
a. 0.44
b. 0.27
c. 0.1188
d. 0.2444.
Learn more about probability here
https://brainly.com/question/19130157
#SPJ2
Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails. C[0, 1], the set of all continuous functions defined on the interval [0, 1], with the standard operations
Answer:
It is a vector space
Step-by-step explanation:
The set of all continuous functions C[0,1 ] defined on the interval [0,1] is a vector space
as proven below ( attached below is a required proof that it is a vector space )
The set checks out for additivity, scalar multiplication and associativity hence it is a vector space
The yield of a certain chemical reaction is believed to be related to temperature. A study collected the yield from 15 such reactions selected at random to test the belief and producedthe following results.
Variable Estimate
Intercept 1 15.5 2.96
Temp 1 0.05 0.017
R-sq = 0.73
Which of the following is the appropriate test statistic for the test?
a. t=0.05/0.73
b. t=15.5/0.73
c. t=0.05/15.5
d. t=15.5/0.05
Answer:
t = 0.05 / 0.017
Step-by-step explanation:
Given the table :
Variable ____ Estimate
Intercept 1 ____ 15.5 ____2.96
Temp 1 _______0.05 ___ 0.017
R-sq = 0.73
The test statistic for a regression test :
t = b1 / E
Where ;
b1 = slope ; E = Standard error of the slope
From the result table ;
b1 = 0.05 ;
E = 0.017
The test statistic, t = 0.05 / 0.017
The appropriate test statistic for the test is t = 0.05 / 0.017.
Calculation of the test statistic for the test:Since
Variable ____ Estimate
Intercept 1 ____ 15.5 ____2.96
Temp 1 _______0.05 ___ 0.017
R-sq = 0.73
So here the test statistic should be
t = b1 / E
here,
b1 = slope ;
E = Standard error of the slope
So,
The test statistic, t = 0.05 / 0.017
learn more about random here: https://brainly.com/question/24172316
Kimi buys a box of blueberry, poppy seed, and chocolate-chip muffins. There are 17 blueberry
muffins and 17 chocolate-chip muffins in the box. How many muffins are in the box?
42
50
61
There is not enough information to solve this
problem.
Answer:
we need more info
Step-by-step explanation:
Evaluate the expression : (4 x 5)2 – 6 + 3 II
help I'm doing a test online
Answer:
8x5−3
Step-by-step explanation:
which two quadrilaterals have 4 congruent sides
Answer:
rhombus and parallelogram .
Step-by-step explanation:
A survey of 64 informed voters in Kenya revealed the following information:
45 believe that Voting is a waste of time
49 believe that they have been abducted by space aliens
42 believe both of these things
REQUIRED
i). How many believe neither of these things?
ii). How many believe Voting is a waste of time but don't believe that they have been
abducted by space aliens?
Answer:
i) 12 believe neither of these things.
ii) 3 believe voting is a waste of time but don't believe that they have been abducted by space aliens.
Step-by-step explanation:
I'm going to solve these question treating these events as Venn sets.
I am going to say that:
Event A: Voting is a waste of time.
Event B: They have been abducated by space aliens.
45 believe that Voting is a waste of time
This means that [tex]A = 45[/tex]
49 believe that they have been abducted by space aliens
This means that [tex]B = 49[/tex]
42 believe both of these things
This means that [tex]A \cap B = 42[/tex]
i). How many believe neither of these things?
Total of 64.
At least one is:
[tex]A \cup B = A + B - A \cap B[/tex]
With the values we have
[tex]A \cup B = 45 + 49 - 42 = 52[/tex]
None:
[tex]64 - 52 = 12[/tex]
12 believe neither of these things.
ii). How many believe Voting is a waste of time but don't believe that they have been abducted by space aliens?
This is:
[tex]A - B = A - (A \cap B) = 45 - 42 = 3[/tex]
3 believe voting is a waste of time but don't believe that they have been abducted by space aliens.