(1) False. [tex]\{0\}\in\mathscr{U}[/tex] is saying "the set containing only 0 (that is, {0}) is an element of [tex]\mathscr U[/tex]", but this is not the case. [tex]\mathscr U[/tex] is the set containing only 0 and 1.
(2) True. [tex]\{0\}\subset\mathscr{U}[/tex] means "the set {0} is a subset of [tex]\mathscr{U}[/tex]". 0 itself is an element of [tex]\mathscr U[/tex], so {0} is indeed a subset of [tex]\mathscr U[/tex].
(3) True. 0 is clearly an element of [tex]\mathscr U[/tex].
(4) False. This statement says "0 is a subset of [tex]\mathscr U[/tex]" but 0 itself is not a set, it's a number.
2x2
The value of the expression + x(100 - 15x) when x = 5 is
X
Answer:
129
Step-by-step explanation:
2*2+x(100-15x)
2*2+5(100-15*5)
2*2+5(100-75)
2*2+5*25
4+125
129ans
Question 4 of 40
If cose= -
5
in quadrant II, what is sine?
Step-by-step explanation:
cosx=adjacent/hypotenuse
adj=3, hyp=5
by pythagoras theorem,
opp^2+3^2=5^2
opposite=4
sine=opp/hyp
sinex=4/5 (second quadrant so sin is positive)
The solution is, The value of sin ∅ in quadrant 2 is 4/5.
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
here, we have,
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
here, we have,
given that,
cos∅ = - 3/5, in quadrant II,
We have;
adjacent = -3
hypotenuse = 5
Let's find the opposite side, using Pythagorean theorem
5^2 = x^2 + (-3)^2
25 = x^2 + 9
collect like terms
x^2 = 25 - 9
x^2 = 16
x = √ 16
x = 4
We have that
sin ∅ = opposite/hypotenuse
sin ∅ = 4/5
It is important to note that the trigonometric identity 'sine' is positive in quadrant 2
sin ∅ = 4/5
Hence, the value of sin ∅ in quadrant 2 is 4/5
Learn more about trigonometric relations here:
brainly.com/question/863849
#SPJ7
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Answer: y= 3+x
Step-by-step explanation:
Answer: y = x - 3
First, find two points on the graph:
(x₁, y₁) = (3, 0)(x₂, y₂) = (0, -3)Substitute in the points to the slope formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] to find the slope:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{-3-0}{0-3}=\frac{-3}{-3}=1[/tex]
Substitute in a point to the function [tex]y=1x+b[/tex] to find the y-intercept(b):
[tex]-3=1(0)+b\\b=-3[/tex]
Therefore, the function is:
[tex]y=x-3[/tex]
I need help finding the domain and range of y+9x=15
Answer:
domain) all real numbers
range) all real numbers
Step-by-step explanation:
y=15-9x
there are no illegal values for x that would make the equation invalid so domain is all real numbers
this line is not flat so range is also all real numbers
The amount of grain that a shape will hold is called the surface area.
True
False
Answer:
false =D
Step-by-step explanation:
PLEASE HELP!! I'LL GIVE OUT BRAINLIEST.
Convert. Simplify your answer and write it as a proper fraction or as a whole or mixed number.
? yards = 3/4 of a mile.
Answer:
1320 yds
Step-by-step explanation:
1 mile = 1760 yds
3/4 mile * 1760 yds/ 1 mile
1320 yds
Answer:
1 mile = 1720 yard
______ ________
0.75 x
cross multiply and solve for x
1320 yards is the answer
good luck in the future..
find the largest value :
A=5-x^2+2x
Answer:
6
Step-by-step explanation:
A=5-x^2+2x
Rewriting
A = -x^2 +2x+5
This is a downward opening parabola so the maximum value is at the vertex
Factor out the negative sign out of the first two terms
A = -(x^2 -2x) +5
Complete the square
-2/2 = -1 -1^2 = 1
Add 1 inside the parentheses Remember the negative sign out front so -1(1) is really adding -1 so we need to add 1 outside of the parentheses
A = -(x^2-2x+1) +1 +5
A = -(x-1)^2 +6
This is in vertex form
y = a(x-h)^2 +k where (h,k) is the vertex
The maximum occurs at x=h and the value is k
The maximum is 6
HELP PLEASE !!
find the surface area of the cylinder and round it to the nearest tenth.
Answer:
18.8
Step-by-step explanation:
Surface area=2*pi*r*(r+h)=2*pi*1*(3)=18.8
2(x-y)(x+y)+(x+y)*2+(x-y)
Answer:
2 x ^2 − 2 y^ 2 + 3 x + y
Step-by-step explanation:
Two high school basketball players each played 5 games. Their stats are summarized below:
Player A: Stats on 5 games → mean points scored = 25, standard deviation = 4
Player B: Scored 23, 27, 28, 22, 25 points on 5 consecutive games
Suppose a university basketball scout (a person who finds new players for a university's team) is deciding which player to recruit. Who should they choose? Justify your response. [3 marks]
HINT: Compare mean and variance of each player.
Answer:
Player B.
Step-by-step explanation:
Player A has a mean score of 25.
Let's calculate Player B's mean score and compare it to Player A's.
23 + 27 + 28 + 22 + 25 / 5 = 125 / 5 = 25.
So, Player A and Player B have the same mean score.
This doesn't tell the scout which player is "better", so let's look at the variance.
The other statistic given for Player A is the standard deviation for their points. The given number is 4. Let’s calculate the standard deviation for Player B, and compare it to player A.
Recall that we add up the squares of the difference between each score and the mean, divide it by the total number of data, and square root that. So, the standard deviation for player B is sqrt(2^2 + 2^2 + 3^2 + 3^2 + 0^2 / 5) = sqrt (26/5) = sqrt (5.2) = 2.3.
Excellent. We have player A’s standard deviation, as well as player B’s standard of deviation. Since player B’s standard deviation is less than player A’s, it can be inferred that player B has more consistent results than player A, and the scout should get Player B.
Hope this helps!
Which of the following is the function for the graph? Choices/graph below.
set x=0 to get insights.
at x=0 to the functions are
-2(0-2)²+3 = -5
-2(0+2)²-3 = -11
-2(0-2)²+3 = -5
-2(0-2)²-3 = -11
weird, for some reason option 1 and 3 seem to be the same, maybe that's an accident by the author.
maybe a + was intended inside the parentheses, dunno.
option 1 and 3 seem fine, although I think there is an error in the options. they shouldn't be exactly the same
c=1/21.22.23+1/22.23.24+................+1/200.201.202
. = là dấu nhân
It looks like you have to find the value of the sum,
[tex]C = \displaystyle \frac1{21\times22\times23} + \frac1{22\times23\times24} + \cdots + \frac1{200\times201\times202}[/tex]
so that the n-th term in the sum is
[tex]\dfrac1{(21+(n-1))\times(21+n)\times(21+(n+1))} = \dfrac1{(n+20)(n+21)(n+22)}[/tex]
for 1 ≤ n ≤ 180.
We can then write the sum as
[tex]\displaystyle C = \sum_{n=1}^{180} \frac1{(n+20)(n+21)(n+22)}[/tex]
Break up the summand into partial fractions:
[tex]\dfrac1{(n+20)(n+21)(n+22)} = \dfrac a{n+20} + \dfrac b{n+21} + \dfrac c{n+22}[/tex]
Combine the fractions into one with a common denominator and set the numerators equal to one another:
[tex]1 = a(n+21)(n+22) + b(n+20)(n+22) + c(n+20)(n+21)[/tex]
Expand the right side and collect terms with the same power of n :
[tex]1 = a(n^2+43n+462)+b(n^2+42n+440) + c(n^2+41n + 420) \\\\ 1 = (a+b+c)n^2 + (43a+42b+41c)n + 462a+440b+420c[/tex]
Then
a + b + c = 0
43a + 42b + 41c = 0
462a + 440b + 420c = 1
==> a = 1/2, b = -1, c = 1/2
Now our sum is
[tex]\displaystyle C = \sum_{n=1}^{180} \left(\frac1{2(n+20)}-\frac1{n+21}+\frac1{2(n+22)}\right)[/tex]
which is a telescoping sum. If we write out the first and last few terms, we have
C = 1/(2×21) - 1/22 + 1/(2×23)
… … + 1/(2×22) - 1/23 + 1/(2×24)
… … + 1/(2×23) - 1/24 + 1/(2×25)
… … + 1/(2×24) - 1/25 + 1/(2×26)
… … + … - … + …
… … + 1/(2×198) - 1/199 + 1/(2×200)
… … + 1/(2×199) - 1/200 + 1/(2×201)
… … + 1/(2×200) - 1/201 + 1/(2×202)
Notice the diagonal pattern of underlined and bolded terms that add up to zero (e.g. 1/(2×23) - 1/23 + 1/(2×23) = 1/23 - 1/23 = 0). So, like a telescope, the sum collapses down to a simple sum of just six terms,
C = 1/(2×21) - 1/22 + 1/(2×22) + 1/(2×201) - 1/201 + 1/(2×202)
which we simplify further to
C = 1/42 - 1/44 - 1/402 + 1/404
C = 1,115/1,042,118 ≈ 0.00106994
How many lbs. of mixed nuts that contain
37% peanuts must Ashley add to 17 lbs. of
peanuts to make a mixture with 88%
peanuts?
-Answer:
4 lbs of 37% mixed nuts
Step-by-step explanation:
[tex]\frac{\left(17+.37x\right)}{17+x}\:=\:.88[/tex]
x = 4
4 yards 2 feet 7 inches + 2 yards 1 foot 6 inches
what is the answer?
Answer:
6 yards 4 feet 1 inch
Step-by-step explanation:
First, we have the equation:
4 yards 2 feet 7 inches + 2 yards 1 foot 6 inches
Now, let's add each:
6 yards
3 feet
13 inches
But 13 inches would be 1 foot and 1 inch, so now we have plus 1 foot and replace the inches with just 1 inch:
6 yards
4 feet
1 inch
There you have it!
Happy learning!
--Applepi101
Answer:
7 yds 1 ft 1 inch
Step-by-step explanation:
4 yards 2 feet 7 inches
+ 2 yards 1 foot 6 inches
------------------------------------------
6 yards 3 feet 13 inches
13 inches is more than 12 inches ( =1 ft) so subtract 12 inches and add 1 ft
6 yards 3 feet 13 inches
=1 ft - 12 inches
-----------------------------------------
6 yds 4 ft 1 inches
4 ft is more than 3f which is 1 yd ( subtract 3 ft and add 1 yd)
6 yds 4 ft 1 inches
+1 yd - 3ft
------------------------
7 yds 1 ft 1 inch
find the solution for -2.5x +5 < - 2.5 on a number line
Answer:
X>3
Step-by-step explanation:
-2.5x +5 < -2.5
-2.5x < -2.5-5
-2.5x< -7.5
X> -7.5/-2.5
X>3
Solve the equation for x.
(x - 4) - (x + 7) = 8x
11
a.
c.
11
8
2
AlE NE
b.
1
d.
11
coin
8
4
Answer:
[tex]x=-\frac{11}{8}[/tex]
Step-by-step explanation:
Hi there!
[tex](x - 4) - (x + 7) = 8x[/tex]
Open up the parentheses
[tex]x - 4 - x - 7 = 8x[/tex]
Combine like terms
[tex]x -x - 4 - 7 = 8x\\-4-7=8x\\-11=8x[/tex]
Divide both sides by 8 to isolate [tex]x[/tex]
[tex]-\frac{11}{8}=x[/tex]
I hope this helps!
Find the area of triangle ABC.
A. 35.92 units²
B. 43.79 units²
C. 21.39 units²
D. 22.91 units²
Answer:
[tex]\text{C. }21.39\:\mathrm{units^2}[/tex]
Step-by-step explanation:
The area of a triangle with sides [tex]a[/tex] and [tex]b[/tex] and angle [tex]\gamma[/tex] between them is given by [tex]A=\frac{1}{2}ab\sin \gamma[/tex].
Therefore, in the given triangle, we want to find two sides with the angle between them given. In this case, the angle between the two sides 7.39 and 9.75 is marked as [tex]36.43^{\circ}[/tex]. Assign values:
[tex]a\implies 7.39[/tex] [tex]b\implies 9.75[/tex] [tex]\gamma \implies 36.43^{\circ}[/tex]Substituting these values into our area formula, we get:
[tex]A=\frac{1}{2}\cdot 7.39\cdot 9.75\cdot \sin (36.43)^{\circ},\\A=21.3938371858,\\A\approx \boxed{21.39\:\mathrm{units^2}}[/tex]
Please help!! Which transformations would result in a geometric figure that is exactly the same size and shape as triangle DEF? Check all that apply.
Answer:
A, B, C
Step-by-step explanation:
none of the 4 options changes the shape.
but D changes the size.
C is the only one that also maintains the orientation of the triangle - it only shifts its position.
A and B maintain size and shape, but they do change its orientation.
5. If A, B and C are any three points on a line and B lies between A and C, then prove that AB + BC = AC.
Answer:
B IS THE MID POINT
Step-by-step explanation:
If b lies between AC iy means b is de half
therefore a+b+c=ABC which is the straight line
Resolve into factor :(a+b) ^3+1
use the formula a^3+b^3=(a+b)^3-3ab(a+b)
in above question assume (a+b) as a and 1 as b
take help of file above
Solve for 2. Round to the nearest tenth, if necessary.
B
X
A
7.9
154
Answer: <=
Submit Answer
attempt 1 out of 2
Answer:
x = 10.9
Step-by-step explanation:
Since this is a right triangle, we can us trig functions
tan theta = opp / adj
tan 54 = x / 7.9
7.9 tan 54 = x
x=10.87341
Rounding to the nearest tenth
x = 10.9
Which of the following expressions are equivalent
Answer:
A and B
Step-by-step explanation:
A and B are the correct options
Ya and Yb represent continuous linear relations. Some values from the relations are shown in the
table below. Graphically solve the linear system.
The solution to the continuous linear relation is: (2,-7)
The data on the table can be presented as:
Relation A
[tex](x_1,y_1) = (-8,-5)[/tex]
[tex](x_2,y_2) = (-3,-6)[/tex]
Relation B
[tex](x_1,y_1) = (-8,-15)[/tex]
[tex](x_2,y_2) = (-3,-11)[/tex]
Plot the points of each relation and draw a line through the points (see attachment)
Write out the point of intersection of the two lines.
[tex](x,y) = (2,-7)[/tex]
Hence, the solution to the continuous linear relation is: (2,-7)
Read more at:
https://brainly.com/question/20291958
A shopkeeper selling an article at a discount of 25% looses Rs.125.If he allows 10% discount he gains Rs 250.Find the marked price and the costprice of the article. ..............(Plz send the ans clearly if you send the ans clearly I will mark you as a brainliest)
Answer:
i dont know
but try you will get the answer
Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and prepreview ads before the movie starts. Many complain that the time devoted to previews is too long. A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was 4 minutes. Use that as a planning value for the standard deviation in answering the following questions. Round your answer to next whole number. a. If we want to estimate the population mean time for previews at movie theaters with a margin of error of seconds, what sample size should be used
Answer:
[tex]n=35[/tex]
Step-by-step explanation:
From the question we are told that:
Standard Deviation [tex]\sigma=4min[/tex]
Let
[tex]CI=95\%[/tex]
Since
Significance level [tex]\alpha[/tex]
[tex]\alpha =1-CI[/tex]
[tex]\alpha =1-0.95[/tex]
Therefore
[tex]Z_{\alpha/2}=Z_{0.025[/tex]
[tex]Z_{\alpha/2}}=1.96[/tex]
Generally the equation for Sample size is mathematically given by
[tex]n = (Z_{\alpha/2}* \frac{\sigma}{E})^2[/tex]
[tex]n= \frac{1.96 * 3}{1}^2[/tex]
[tex]n=35[/tex]
What is the total surface area (including the area of the floor) of a building shaped as a hemisphere with radius 106 ft ?
Round your answer to the nearest whole number.
Answer:
105897 ft²
Step-by-step explanation:
let, r be the radius, so r = 106 ft
Surface area of a hemisphere,
2πr²+πr²
= 2π×106²+π×106²
= 105897 (rounded to the nearest whole number)
Finding the missing length in a figure
Answer:
8 cm
Step-by-step explanation:
The length of the whole shape is 13. On the right side, it says the length is 5 cm. You use 13-5 to get the missing length.
Answer:
the answer is 8 cm
Step-by-step explanation:
yx(y+1) + 4x(y + 1) - 5(y + 1) factor
( yx + 4x - 5 )( y + 1 )
.....................................
10
6
What is the length of the missing side?
Solve the system of equations using the substitution method. -x − 2y = 0 y = -8x (x, y) = ( , )
Answer:
[tex] = { \tt{(0, \: 0)}}[/tex]
Step-by-step explanation:
Let:
[tex]{ \bf{ - x - 2y = 0 - - - (a)}} \\ { \bf{y = - 8x - - - (b)}}[/tex]
Substitute for y in equation (b) to equation (a):
[tex]{ \tt{ - x - 2( - 8x) = 0}} \\ { \tt{ - x + 16x = 0 }} \\ { \tt{x = 0}}[/tex]
Also, y = 0