Answers
Answer:
[tex]f(0) = -1[/tex]
[tex]f(\pi) = 1[/tex]
Domain: All real numbers
[tex]Range = [-1,1][/tex]
Step-by-step explanation:
Given
The attached graph
Solving (a): f(0)
On the attached graph
[tex]f(x) = -1[/tex] when [tex]x =0[/tex]
So:
[tex]f(0) = -1[/tex]
Solving (b): f(pi)
On the attached graph
[tex]f(x) = 1[/tex] when [tex]x =\pi[/tex]
So:
[tex]f(\pi) = 1[/tex]
Solving (c): Domain
There is no restriction on x.
Hence, the domain is the set of all real numbers
Solving (d): Range
In the attached graph
[tex]y_{min} = -1[/tex]
[tex]y_{max} = 1[/tex]
So, the range is:
[tex]Range = [-1,1][/tex]
Related Questions
solution 2^2x+3-7(2^2x+1)+3=0 introduce Log
Answers
Answer:
[tex]x = \frac{log\sqrt{-1/6}}{log2}[/tex]
Step-by-step explanation:
Given the expression
[tex]2^{2x}+3-7(2^{2x}+1)+3=0[/tex]
Let [tex]P=2^x[/tex]
Substituting into the expression, we will have:
[tex]P^2+3-7(P^2+1)+3=0\\Expand\\P^2+3-7P^2-7+3=0\\-6P^2-1=0\\6P^2=-1\\p^2=-1/6\\P=\sqrt{-1/6}[/tex]
Since:
[tex]P=2^x\\2^x=\sqrt{-1/6}\\xlog2=log(\sqrt{-1/6}) \\x = \frac{log\sqrt{-1/6}}{log2}[/tex]
Solve the above quadratic equation
Answers
Answer:
r = 1
Step-by-step explanation:
Find the intersection.
r = 1
r = 3
r = -1
r = 1
Answer:
r=3, r=1, r= -1
Step-by-step explanation:
48r^3-144r^2-48r=-144
48r^3-144r^2-48r +144 =-144 + 144
48r^3-144r^2-48r+144=0
48(r-3)(r+1)(r-1)
r-3=0 r+1=0 r-1=0
r=3, r=1, r= -1
A movie theater has a seating capacity of 187. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1338, How many children, students, and adults attended?
___ children attended.
___ students attended.
___ adults attended.
Answers
Answer:
A) children attended=98 b) students attended=60 c)adults attended=49
Step-by-step explanation:
system%28a%2Bc%2Bx=207%2Cc%2Fa=2%2C5c%2B7x%2B12a=1498%29
Simplify and solve the system.
-
a%2B2a%2Bx=207
3a%2Bx=207
x=207-3aandc=2a
-
The revenue equation can be written in terms of just one variable, a.
10a%2B7%28207-3a%29%2B12a=1498
Solve for a;
use it to find x and c.
FURTHER STEPS
-
10a%2B1449-21a%2B12a=1498
a%2B1449=1498
a=98-49
highlight%28a=49 -------adults
-
c=2a
c=2%2A49
highlight%28c=98 -------children
-
x=207-a-c
x=207-49-98
highlight%28x=60 ---------students
Keith is trying to figure out the area of his pool section in his backyard he knows that his pool is 20 feet long and 9 feet wide he also knows the sidewalk is 3 feet wide all around the floor what is the total area of the pool section of Keith’s backyard?
Answers
Answer:
The total area of the pool section of Keith's backyard is 390 square feet.
Step-by-step explanation:
Since Keith is trying to figure out the area of his pool section in his backyard, and he knows that his pool is 20 feet long and 9 feet wide, and he also knows the sidewalk is 3 feet wide all around the floor, to determine what is the total area of the pool section of Keith's backyard, the following calculation must be performed:
(20 + 3 + 3) x (9 + 3 + 3) = X
26 x 15 = X
390 = X
Therefore, the total area of the pool section of Keith's backyard is 390 square feet.
p(X)=x²+50 then p(2)=
a) 6
b)7
c)8
d)9
Answers
Answer:
54
Step-by-step explanation:
p(x)=x^2+50, p(2)=2^2+50=54
P(x) = x² + 50
P(2) = 2² + 50
= 54
P(6) = 6²+50
= 86
P(7) = 7²+ 50
= 99
P(8) = 8²+50
= 114
P(9) = 9²+50
= 131
Answered by Gauthmath must click thanks and mark brainliest
A lottery ticket has a grand prize of $30.1 million. The probity of winning the grand prize is .000000038
Deteman the expected value of the lottery ticket
Answers
Answer:
$30.1 million * .000000038
$1.14
did the question say how much the ticket cost?
if it was $1 then you would have to subtract $1 so the expected value would be 14 cents
Step-by-step explanation:
Help me please --------------------
Answers
9514 1404 393
Answer:
139.39 in
Step-by-step explanation:
The length of a semicircle of diameter D is ...
C = (1/2)πD
For the given diameter of 27 inches, the length of the curved edge of the figure is ...
C = 1/2(3.14)(27 in) = 42.39 in
__
The perimeter of the figure is the sum of the side lengths. Clockwise from left, that sum is ...
P = 27 + 35 + 42.39 + 35 = 139.39 . . . inches
The perimeter of the figure is 139.39 inches.
Use AABC to find the value of sin B.
Answers
Answer:
35/37
Step-by-step explanation:
sin(B)=(AC)/(AB) = 35/37
What is the equation of a line that passes through the point (5,-3) and has a slope of -2
Answers
Answer:
y=-2x+7
Step-by-step explanation:
The Slope is obviously -2, and just add a random y and play around with it until it goes through the point (5,-3)
simplify using the laws of exponents (4^3)^-2 × (2^3)^4 ×(8/15)^-2
Answers
Answer:
[tex] \dfrac{225}{64} [/tex]
Step-by-step explanation:
[tex] (4^3)^{-2} \times (2^3)^4 \times (\dfrac{8}{15})^{-2} = [/tex]
[tex]= (2^2)^{-6} \times 2^{12} \times (\dfrac{15}{8})^{2}[/tex]
[tex]= 2^{-12} \times 2^{12} \times \dfrac{225}{64}[/tex]
[tex] = \dfrac{225}{64} [/tex]
A board that measures 3/4 feet long is cut into 6 equal pieces . What is the length of each price
Answers
Step-by-step explanation:
8 cm² is the correct answer for that question
Given:
Board Length = 3/4
6 equal pieces = 3/4 ÷6
= 3/4 × 1/6
= 1/4 × 1/2
= 1/8
Therefore each equal piece will be 1/8 feet long
Answered by GauthMath if you like please click thanks and comment thanks too.
Suppose you have 3 bags. Two of them contain a single $10 bill, and the third contains a single $5 bill. Suppose you pick one of these bags uniformly at random. You then add a $5 bill to the bag, so it now contains two bills. The bag is shaken, and you randomly draw a bill from the bag without looking into the bag. Suppose it turns out to be a $5 bill. If a you draw the remaining bill from the bag, what is the probability that it, too, is a $5 bill
Answers
Answer:
1/2
Step-by-step explanation:
Number of bags = 3
number of bags with $10 bill initially = 2
number of bags with $5 bill initially = 1
assume :
event you pick a $5 bill at first draw = A
event you pick a $5 bill at second draw = B
hence : P ( A n B ) = 1/3 * 1 = 1/3
P( A ) = ( 1/3 * 1 ) + ( 1/3 * 1/2 + 1/3 * 1/2 ) = 2/3
therefore P( that the second drawn bill is $5 )
P( B | A ) = P(A n B ) / P ( A )
= (1/3) / (2/3) = 1/2
The probability that it, too, is a $ 5 bill is 33.33%.
Since you have 3 bags, and two of them contain a single $ 10 bill, and the third contains a single $ 5 bill, supposing you pick one of these bags uniformly at random and you then add a $ 5 bill to the bag, so it now contains two bills, and the bag is shaken, and you randomly draw a bill from the bag without looking into the bag, supposing it turns out to be a $ 5 bill, if a you draw the remaining bill from the bag, to determine what is the probability that it, too, is a $ 5 bill, the following calculation must be performed:
3 bags = 2 with a 10 bill and 1 with a 5 bill 1/3 = 0.3333 0.3333 x 100 = 33.33
Therefore, the probability that it, too, is a $ 5 bill is 33.33%.
Learn more in https://brainly.com/question/13243988
If only the height of a pyramid is doubled its volume is Also doubled true or false
Answers
Answer: true
Step-by-step explanation:
Please help me determine the general equation for the graph above as well as solve for a. Thank you.
Answers
Observe that the x coords of the roots of a polynomial are,
[tex]x_{1,2,3,4}=\{-3,0,1,4\}[/tex]
Which can be put into form,
[tex]y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]
with data
[tex]y=a(x-(-3))(x-0)(x-1)(x-4)=ax(x+3)(x-1)(x-4)[/tex]
Now if I take any root point and insert it into the equation I won't be able to solve for y because they will always multiply to zero (ie. when I pick [tex]x=-3[/tex] the right hand side will multiply to zero,
[tex]y=-3a(-3+3)(-3-1)(-3-4)=0[/tex]
and a will be "lost" in the process.
If we observed a non-root point that we could substitute with x and y and result in a non-loss process then you could find a. But since there is no such point (I don't think you can read it of the graph) there is no other viable way to find a.
Hope this helps :)
need help pls with this question. im struggling with this question.
Answers
Answer:
i can't rn but i could explain to you how... so first put a point on 0,5 then move down one and right one... then keep moving down one and right one
and there you go thats your graph
Step-by-step explanation:
the diameter of a circle is 8 cm what is its area?
Answers
A = πr^2 and d = 2r.
So r = 8/2 = 4 cm.
Now use the first formula
A = π(4 cm)^2 = 50.265 cm^2
Which equation has the same solution as 10(x) - x + 5 = 41
Answers
Step-by-step explanation:
if that is truly the full problem description, then we have
10x - x + 5 = 41
=>
9x = 36
our simply
x = 4
so, I am not sure, what your teacher wants to see as result.
there is an infinite number of equations I could find, all with the solution x = 4.
The BBQ club meets every Thursday. The meetings last 2 1/2 hours. There were 5 Thursdays in
September. How many hours did the BBQ club meet in September?
A.2 1/2 hours
B.5 hours
C.12 1/2 hours
D.10 hours
Answers
Answer:
12 1/2
Step-by-step explanation:
2 x 5 = 10
1/2 x 5 = 2 1/2
10 + 2 1/2 = 12 1/2
A telephone service representative believes that the proportion of customers completely satisfied with their local telephone service is different between the South and the Midwest. The representative's belief is based on the results of a survey. The survey included a random sample of 1300 southern residents and 1380 midwestern residents. 39% of the southern residents and 50% of the midwestern residents reported that they were completely satisfied with their local telephone service. Find the 80% confidence interval for the difference in two proportions. Step 1 of 3 : Find the point estimate that should be used in constructing the confidence interval
Answers
Answer:
The point estimate that should be used in constructing the confidence interval is 0.11.
The 80% confidence interval for the difference in two proportions is (0.0856, 0.1344).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Midwest:
50% of 1380, so:
[tex]p_M = 0.5[/tex]
[tex]s_M = \sqrt{\frac{0.5*0.5}{1380}} = 0.0135[/tex]
South:
39% of 1300, so:
[tex]p_S = 0.39[/tex]
[tex]s_S = \sqrt{\frac{0.39*0.61}{1300}} = 0.0135[/tex]
Distribution of the difference:
[tex]p = p_M - p_S = 0.5 - 0.39 = 0.11[/tex]
So the point estimate that should be used in constructing the confidence interval is 0.11.
[tex]s = \sqrt{s_M^2+s_S^2} = \sqrt{0.0135^2+0.0135^2} = 0.0191[/tex]
Confidence interval:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
80% confidence level
So [tex]\alpha = 0.2[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].
The lower bound of the interval is:
[tex]p - zs = 0.11 - 1.28*0.0191 = 0.0856[/tex]
The upper bound of the interval is:
[tex]p + zs = 0.11 + 1.28*0.0191 = 0.1344[/tex]
The 80% confidence interval for the difference in two proportions is (0.0856, 0.1344).
Select the statement that best justifies the conclusion based on the given information.
l is in plane M,
x is on line l
Conclusion: x is in plane M.
a. A plane contains at least three points not all on the same line.
b. If two points lie in a plane, then the line containing them lies in that plane.
c. If a plane contains a line, it contains the points on the line.
d. Exactly one plane contains a given line and a point not on the line.
Answers
9514 1404 393
Answer:
c. If a plane contains a line, it contains the points on the line.
Step-by-step explanation:
The only statement relating a point on a line to the plane containing the line is the one shown above.
_____
Additional comment
Identifying true statements is a reasonable strategy for many multiple-choice questions. Another strategy that can be employed is finding the one true statement that is relevant to the question being asked.
What is the image of (3, -12) after a dilation by a scale factor of į centered
at the origin?
Answers
Answer:
9 is. ................m.m..mk
What is the distance from point Yto wx in the figure below?
W 16 Z
30
X
1612
34
O A. 4
O B. 162
O C. 16
O D. Cannot be determined
E. 16/3
F. 8
Answers
The length of YZ in the similar triangle given is calculated using Pythagoras theorem which gave us 16√3
What are Similar TriangleSimilar triangles are two or more triangles that have the same shape but may be different sizes. They have the same angles and corresponding sides that are proportional.
In this problem, we need to use the concept of ratio and proportions to find the length of YZ
However, we can simply use Pythagoras theorem to determine the length.
According to Pythagoras' Theorem, the square of the hypotenuse, or side opposite the right angle, in a right-angled triangle, is equal to the sum of the squares of the other two sides.
It is expressed as the equation a² + b² = c².
This is because the triangles forms a right angled triangle and we can easily apply that here.
YZ² = 16² + (16√2)²
YZ² = 768
YZ = √768
YZ = 16√3
The length or distance from point Y to WX which is the same as the length of YZ is calculated as 16√3.
Learn more on similar triangle here;
https://brainly.com/question/14285697
#SPJ1
Answer:
C. 16
Step-by-step explanation:
I hope this helps :)
What is a corresponding pair for f(-7)=5
Answers
Answer:
An ordered pair for a function f(x) looks like (x, f(x)). So the ordered pair here would be (5, f(5)) or (5, 7). Either one would work, as they are the same.
The equation cos(35•) = a/25 can be used to find the length of BC what is the length of BC round to the nearest tenth
Answers
Use the equation d=z–9 to find the value of d when z=10.
d=
Answers
Step-by-step explanation:
d = z - 9
d = 10 - 9 ----> substitute
d = 1
Simplify Square root (150n^2)
Answers
Answer:
12
Step-by-step explanation:
find each measurement indicated round your answers to the nearest tenth. Part 1d. NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Answers
Answer:
see explanation
Step-by-step explanation:
Using the Sine rule in all 3 questions
(1)
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values , firstly calculating ∠ B
[ ∠ B = 180° - (78 + 49)° = 180° - 127° = 53° ]
[tex]\frac{a}{sin78}[/tex] = [tex]\frac{18}{sin53}[/tex] ( cross- multiply )
a sin53° = 18 sin78° ( divide both sides by sin53° )
a = [tex]\frac{18sin78}{sin53}[/tex] ≈ 22.0 ( to the nearest tenth )
(3)
[tex]\frac{c}{sinC}[/tex] = [tex]\frac{a}{sinA}[/tex] , substitute values
[tex]\frac{35}{sinC}[/tex] = [tex]\frac{45}{sin134}[/tex] ( cross- multiply )
45 sinC = 35 sin134° ( divide both sides by 35 )
sinC = [tex]\frac{35sin134}{45}[/tex] , then
∠ C = [tex]sin^{-1}[/tex] ( [tex]\frac{35sin134}{45}[/tex] ) ≈ 34.0° ( to the nearest tenth )
(5)
Calculate the measure of ∠ B
∠ B = 180° - (38 + 92)° = 180° - 130° = 50°
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values
[tex]\frac{BC}{sin38}[/tex] = [tex]\frac{10}{sin50}[/tex] ( cross- multiply )
BC sin50° = 10 sin38° ( divide both sides by sin50° )
BC = [tex]\frac{10sin38}{sin50}[/tex] ≈ 8.0 ( to the nearest tenth )
What is |1-8i|?
A.
B.
C
D
Answers
9514 1404 393
Answer:
(b) √65
Step-by-step explanation:
The modulus of a complex number is the root of the sum of the squares of the real and imaginary parts.
|1 -8i| = √(1² +(-8)²) = √(1+64) = √65
A 90% confidence interval is found to be (120,140). What is the margin of error?
Answers
Answer:
There is 10% error in both minimum and extreme values i.e. 120 & 140 , Error in 120 is 10% i.e. = 12, Since value can be more or less in error ∴ Error in 120 is ±12.
3 lawns in 9 hours.what was the rate of mowing in hours per lawn
Answers
Answer:
3
Step-by-step explanation:
3 = 9 \:th \\ 1 = 3 \\ 3 \times 3 = 9 \\ 9 \div 3 = 3 \\ so \: that \: answer \: is \: 3
