Answer:
(a) 31
(b) 32
Step-by-step explanation:
We will do (b) first since it will help us do (a).
(b)
There are [tex]n(A)=5[/tex] elements in [tex]A[/tex]. Using the formula for the number of subsets of a given (finite) set, the number of subsets of [tex]A[/tex] is
[tex]2^{n(A)}=2^5=32[/tex]
(a)
A subset of [tex]A[/tex] is called proper if it does not equal [tex]A[/tex]. The only subset of [tex]A[/tex] that is not proper is [tex]A[/tex] itself, so simply subtract 1 from the number of subsets to get the number of proper subsets, which is
[tex]32-1=31[/tex]
Carmen Martinez
What is the slope of the line that passes through the point 4,4 and 10,7 write your answer in simplest form
[tex]\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{7-4}{10-4}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{3}{6}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto m\approx0.5[/tex]
Answer:
[tex]m=\frac{1}{2}[/tex]
Step-by-step explanation:
The slope of a line, also known as the change in the line or the ([tex]\frac{rise}{run}[/tex]) can be found using the following formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are points on the line. Substitute the given information into the formula and solve for the slope.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Points on the line: [tex](4,4)\ \ \ (10, 7)[/tex]
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{7-4}{10-4}[/tex]
[tex]m=\frac{3}{6}[/tex]
[tex]m=\frac{1}{2}[/tex]
[tex]m=0.5[/tex]
X
у
Which equation could be used to create the data shown in the
table?
1
5
O y = 5x
4
17
O y = 5x + 1
5
21
O y = 4x + 1
7
29
O y = x + 4
9
37
Answer:
C
Step-by-step explanation:
The equation that represents the table is y=4x+1
Solve the following systems of equations using the substitution method. 6x + 2y = 82 and x − y = 3 y = 4x − 1 and x + y = 9 4x + 3y =17 and y = 5 − x
Step-by-step explanation:
puhhh ! that way of typing can be misleading.
let me sum up what equations I think the problem definition specified :
1)
6x + 2y = 82
x - y = 3
2)
y = 4x - 1
x + y = 9
3)
4x + 3y = 17
y = 5 - x
solving 1)
x - y = 3 => x = y + 3
putting this into the first equation
6×(y+3) + 2y = 82
6y + 18 + 2y = 82
8y +18 = 82
8y = 64
y = 8
x = y + 3 = 8 + 3 = 11
solving 2)
using the first equation in the second equation
x + (4x - 1) = 9
5x - 1 = 9
5x = 10
x = 2
y = 4x - 1 = 4×2 - 1 = 8 - 1 = 7
solving 3)
using the second equation in the first equation
4x + 3×(5 - x) = 17
4x + 15 - 3x = 17
x + 15 = 17
x = 2
y = 5 - x = 5 - 2 = 3
rationalize the denominator 2√7+√3/3√7-√3
Answer:
[tex] \frac{2 \sqrt{7} + \sqrt{3}}{3 \sqrt{7} - \sqrt{3} } = \frac{2 \sqrt{7} + \sqrt{3}}{3 \sqrt{7} - \sqrt{3} } . \frac{3 \sqrt{7} + \sqrt{3} }{3 \sqrt{7} + \sqrt{3} } \\ \\ = \frac{(2 \sqrt{7} + 3)(3 \sqrt{7} + \sqrt{3}) }{(3 \sqrt{7} - 3)(3 \sqrt{7} + \sqrt{3} ) } \\ \\ = \frac{(42 + 2 \sqrt{21} + 9 \sqrt{21} + 3 \sqrt{21} )}{63 - 3} \\ \\ = \frac{42 + 2\sqrt{21} + 9 \sqrt{21} + 3 \sqrt{21} }{60} [/tex]
Answer:
(2√7+√3)/(3√7-√3) =(2√7+√3)(3√7+√3)/(3√7-√3)(3√7+√3) =(2*3*√7² + 2√21 + 3√21 + √3²)/(9√7² - √3²) =(42 + 3 + 5√21)/(63 - 3) = (45 + 5√21)/60 = (9 + √21)/12The distance from the green point on the parabola to the parabolas focus is 11. What is the distance from green point to the directrix?
Answer:
answer 11
Step-by-step explanation:
I think it the right answer
fernando charges a flat fee of 4.50 plus 2.00 per mile for his taxi service, when he got to the airport the cab fare was 12.50, how many miles did he cab travel
Answer:
4 miles, the cab travelled 4 miles.
Step-by-step explanation:
12.50 - 4.50 = 8
8/2.00 = 4
I'm helping someone with her daughter's homework. What is the term for this definition: take a part a number to write it in a new way. In mcgraw hill my math grade 1
Answer:
hello mate.. i am glad ur helping someone for her hw.. nice nice
well as per my understanding
'' take apart a number to write it in a new way ''
this answer must be '' subtraction''
as in subtraction we take apart number and resulting number is new way of writing the difference of first 2 ....
go on.. help more ppl ... we are here to support
x-(-4x-(y + y)); use x = -4, and y = -3 evaluate
please mark this answer as brainlist
please help me with both questions
Answer:
(b) 829 seconds
(c) 13.8 minutes
Step-by-step explanation:
(b) 2.48×10⁸/2.99×10⁵ = 829 seconds
(c) 829/60 = 13.8 minutes
Pls helppppp,,,,,.....
Answer:
yall do school right now???and i forgot how to do these sorry
Answer:
18 = 2x-14
or, 2x =18+14
or, 2x =32
or, x=32/2
x=16
2(6x-7)=10
or, 12x-14=10
or, 12x=10+14
or, x=24/12
x=2
√10 Multiple √15 is equal to
(a) 5√6
(b) 6√5
(c) √30
(d) √25
step by step
Solve :-
Answer:
(a). 5√6
Step-by-step explanation:
[tex] \sqrt{10} \times \sqrt{15} \\ = \sqrt{150} \\ = \sqrt{25 \times 6} \\ = 5 \sqrt{6} [/tex]
If ABCD is a rectangle, and m_ADB = 55°, what is the value of x? A. 80 O B. 90 O C. 40 O D. 70 O E. 110
===========================================================
Explanation:
Label a new point E at the intersection of the diagonals. The goal is to find angle CEB. Notice how angle AED and angle CEB are vertical angles, so angle AED is also x.
Recall that any rectangle has each diagonal that is the same length, and each diagonal cuts each other in half (aka bisect). This must mean segments DE and AE are the same length, and furthermore, triangle AED is isosceles.
Triangle AED being isosceles then tells us that the base angles ADE and DAE are the same measure (both being 55 in this case).
---------------------
To briefly summarize so far, we have these interior angles of triangle ADE
A = 55D = 55E = xFor any triangle, the three angles always add to 180, so,
A+D+E = 180
55+55+x = 180
110+x = 180
x = 180-110
x = 70
The triangle below is equilateral. Find the length of side
x to the nearest tenth
Answer:
Step-by-step explanation:
The hypotenuse is 2 * sqrt(11) because all the sides are equal. 1/2 the base is given as root 11.
x^2 = (2*sqrt(11) )^2 - (sqrt(11) ) ^2
x^2 = 4 * 11 - 11
x^2 = 44 - 11
x^2 = 33
x = sqrt(33)
sqrt(33) = 5.744
sqrt(33) = 5.7 rounded to the nearest 1/10
Last minute question emergency please
Answer:
Mean; 762,143
Median; 800,000
Step-by-step explanation:
Mean;
Add all of the numbers together, then divide by how many there are.
There are seven home prices in total, add them together then divide by 7.
5,335,000 divided by 7 = 762,142.85714285; simplified to 762,143.
Median;
Organize the numbers from least to greatest
455,000, 780,000, 795,000, 800,000, 810,000, 840,000, 855,000
Then find the number in the middle
800,000
[tex] \frac{2}{4} + 5 \times 36 + 2 \frac{6}{3 } = [/tex]
what is answer
Step-by-step explanation:
[tex] \frac{2}{4} + 5 \times 36 + 2 \frac{6}{3} [/tex]
[tex] = \frac{1}{2} + 180 + 2 \times \frac{2}{1} [/tex]
[tex] = \frac{1}{2} + 180 + 4[/tex]
[tex] = \frac{1 + 360 + 8}{2} [/tex]
[tex] = \frac{369}{2} [/tex]
[tex] = 184 \frac{1}{2} \: or \: 184.5(ans)[/tex]
Simplify.
10
3
(2.8 +1.2)
6
16
18.4
20
26
Answer:
see similar to the number of the number
Which is a perfect square?
6’1
6’2
6’3
6’5
Answer:
6'2
Step-by-step explanation:
Question 19 of 20:
Select the best swer for the question
19. The distance from the center of a round table top to the edge of the table top is 4 ft what is the area of the table top
Answer:
50.26 ft^2
Step-by-step explanation:
Area=pi*r^2
Area=pi*(4)^2=pi*16=50.26
Given the arc, name the central angle.
FG
A. ∠GQJ
B. ∠FQG
C. ∠GQI
D. ∠HQI
Answer:
B
Step-by-step explanation:
Given arc FG then the central angle is the angle at the centre subtended by FG , that is
central angle = ∠ FQG
The central angle is B i.e ∠FQG
What is central angle?A central angle exists an angle whose vertex stands present at the center of a circle created by the two radii as the sides of the angle.
In Mathematics, an “arc” exists as a smooth curve joining two endpoints. In general, an arc exists one of the portions of a circle. It is essentially a part of the circumference of a circle. Arc exists as a part of a curve. An arc can be a portion of some other curved constitutions like an ellipse but mostly guides to a circle.
The angle substended by the arc would be ∠FQG.
To learn more about central angle refer to:
https://brainly.com/question/14205090
#SPJ2
Can I please get asap
Answer:
Option B, cotangent is the reciprocal of tangent
That option is correct
8. You recorded the time in seconds it took for 8 participants to solve a puzzle. The times were: 15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1, 29.4. a. Find the mean b. Find the median c. Write the 5-number summary for this data
Answer:
Xbar = 20.813
Median = 19.95
5 - number summary :
Minimum = 15.2
Q1 = 19.05; Q2 = 19.95 ; Q3 = 21.95 ; maximum = 29.4
Standard deviation, s = 4.068
Step-by-step explanation:
Given the data:
X : 15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1, 29.4
Ordered data:
15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1, 29.4
The mean (xbar) :
Xbar = Σx / n ; n = sample size = 8
Xbar = 166.8 / 8 = 20.8125
Xbar = 20.813
The median :
1/2 *(n+1)th term
1/2(9) = 4.5
(4 + 5)th term / 2
(19.7 + 20.2) / 2 = 19.95
The five number summary :
Minimum = 15.2
Lower quartile (Q1) = 1/4(9) = 2.25 ; (2nd + 3rd) term / 2
(18.8 + 19.3) / 2 = 19.05
Median (Q2) = 19.95
Upper quartile (Q3) :
3/4(9) = 6.75 = (6th + 7th) / 2
(21.8 + 22.1) / 2 = 21.95
Maximum = 29.4
The standard deviation, s = sqrt[(x - xbar)²/ (n-1)]
Using calculator ;
s = 4.068
9 and -9 are examples of
A. absolute values
B.oposite integers
C. products
D. Quotients
Answer:
opposites
Step-by-step explanation:
9+-9 = 0
When they add to zero they are opposites
Answer:
Step-by-step explanation:
9 and -9 are examples of opposite integers
q= 3ym/2 make m the subject of the formula
Answer:
m = [tex]\frac{2q}{3y}[/tex]
Step-by-step explanation:
Given
q = [tex]\frac{3ym}{2}[/tex] ( multiply both sides by 2 to clear the fraction )
2q = 3ym ( isolate m by dividing both sides by 3y )
[tex]\frac{2q}{3y}[/tex] = m
im giving you 30 points just help me :((((((((
If you draw one card at random, what is the probability that card is a (n) Heart?
Answer:
1/13
Step-by-step explanation:
There are 52 cards in a deck of cards and 13 of them are hears
P(heart) = hearts / total
= 13/52 = 1/13
The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken?
z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576
Use the table above for the z-score, and be sure to round up to the nearest integer.
========================================================
Explanation:
At 95% confidence, the z critical value is roughly z = 1.960
The population standard deviation is given to be sigma = 3.7
The error is E = 2 since we want to be within 2 inches of the population mean mu
The min sample size needed is:
n = (z*sigma/E)^2
n = (1.960*3.7/2)^2
n = 13.147876
n = 14
We always round up to the nearest whole number to ensure that we clear the hurdle (otherwise, the sample is too small). It doesn't matter that we're closer to 13 than to 14.
Find a 2-digit number smaller than 50, the sum of whose digits does not change after being multiplied by a number greater than 1
To solve this question, it is needed to know that the sum of the digits of numbers which are multiples of 9 greater than 1, add to 9, that is:
Multiples of 9:
9*1 = 9
9*2 = 18 -> 1 + 8 = 9
9*3 = 27 -> 2 + 7 = 9
9*4 = 36 -> 3 + 6 = 9
9*5 = 45 -> 4 + 5 = 9
Find a number:
Thus, there are 4 possible options for the desired 2-digit number less than 50:
18, 27, 36, 45.
For more, you can check https://brainly.com/question/24294485
How high is a tree that cast a 26ft shadow at the same time a6ft post casts a shadow which is 11ft long
Set up a ratio:
6/11 = x/26
Cross multiply:
11x = 156
Divide both sides by 11:
X = 14.18 feet ( round answer as needed.)
what is the decimal equivalent of 7/20
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer
Janet and Michelle begin walking at the same time from the same point. Janet walks directly north, and Michelle walks directly ea
10 km apart, Michelle has walked 2 km farther than Janet has walked. How far has Michelle walked?
08 km
06 km
12 km
10 km
9514 1404 393
Answer:
(a) 8 km
Step-by-step explanation:
Let m represent the distance (in kilometers) Michelle has walked. Then Janet walked a distance of (m-2). These distances are at right angles, so the distance between them can be found using the Pythagorean theorem.
m² +(m -2)² = 10²
m² +m² -4m +4 = 100
2m² -4m = 96 . . . . . . subtract 4, collect terms
m² -2m +1 = 49 . . . . . divide by 2 and add 1
(m -1)² = 7² . . . . . . .write as squares
m -1 = 7 . . . . . . positive square root
m = 8
Michelle walked 8 km.
