A) This event is a union. If a card is of the suit of clubs or a face card or both, then it belongs to the set of "cards with clubs or a face".
For the probability in question, we use the inclusion/exclusion principle:
P(club or face) = P(club) + P(face) - P(club and face)
That is, we add the probabilities of drawing a club and of drawing a face card, and subtract the probability of both conditions being met because, in a certain sense, we've double-counted the event of the card being both of clubs and a face. The sets "club" and "face" are not disjoint; there is overlap between them.
Then we have
P(club) = 13/52
P(face) = 12/52
P(club and face) = 3/52
so that
P(club or face) = 13/52 + 12/52 - 3/52 = 22/52 = 11/26
B) This event is an intersection. If a card is of the suit of clubs and a face card, then it belongs to both the set of clubs and the set of face cards.
We already found the probability of the intersection above:
P(club and face) = 3/52
C) If a given card is not a club and not a face card, this is the same as saying the card is neither a club nor a face card. In other words,
P(not club and not face) = P(not(club or face))
and this probability is complementary to the probability that a card is either a club or face, which is to say
P(not(club or face)) = 1 - P(club or face)
Using the result from part (A), we have
P(not club and not face) = 1 - 11/26 = (26 - 11)/26 = 15/26
A machine cuts a strip of carpet into 2 pieces. the length of the smaller piece is 5 meters greater than 1/4 the length of the larger piece. If the length of the smaller piece is 12 meters, the length of the bigger piece is (A, 13.5 B, 14 C, 20 D, 28) meters and the total length of the carpet is (A- 25.5, B- 26, C- 32, D- 40) meters
Answer:
The answer to the is 28 and 40! hope this helps love
When divding numbers with the same base you________ the exponents
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
When divding numbers with the same base you subtract the exponents ~
Answer:
subtracts
Step-by-step explanation:
hope this helps
what does x equal in 150 = -6(x)^2 + 100x -180
Answer:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Exact Form:
x
=
25
+
√
130
3
,
25
−
√
130
3
Decimal Form:
x
=
12.13391808
…
,
4.53274858
…
Step-by-step explanation:
Answer:
x=\frac{25-\sqrt{130}}{3}
Step-by-step explanation:
x_{1,\:2}=\frac{-100\pm \sqrt{100^2-4\left(-6\right)\left(-330\right)}}{2\left(-6\right)}
x_{1,\:2}=\frac{-100\pm \:4\sqrt{130}}{2\left(-6\right)}
x_1=\frac{-100+4\sqrt{130}}{2\left(-6\right)},\:x_2=\frac{-100-4\sqrt{130}}{2\left(-6\right)}
x=\frac{25-\sqrt{130}}{3},\:x=\frac{25+\sqrt{130}}{3}
wHICH ONE IS BETTER!!!!!!!!??????????????
What is 3.468 rounded to the nearest tenth of an ounce?
Answer:
3.5
Step-by-step explanation:
The tenths place would be 0.1
So in 3.468 the 4 is in the tenths place
Look at the number to the right of it, if it is greater than 5 you round up and if it is 4 or lower you stay the same.
For 3.468 you would round up
So you would have 3.5
Have A GREAT day man
Sincerly, lipor
help help help help help
Answer:
2
Step-by-step explanation:
Check the number or numbers that are in the solution set of the equation
below.
7x > 42
A. 14
B. 5
C.35
D. 6
E. 12
F9
Answer:
A, C, E, F
Step-by-step explanation:
when you multiply the numbers with 7 the answer is greater than 42
The sale price of a swimming pool after a 18.5% discount is $1189.90. Find the original list price of the pool.
Answer:
1460
Step-by-step explanation:
18.5% of 1460 = 270.1
1460 - 270.1 = 1189.9
us
What is the dividend yield on Stock A that sells at
15 $/share, when Company A pays a quarterly
dividend of $0.15 per share?
dividend yield = [?] %
Give your answer as a percent rounded to the
nearest tenth.
Fnter
Answer:4
Step-by-step explanation: $0.15 x 4 = 0.6
0.60 divide by 0.15
= 4.
Gavin deposited $200 into his savings account that is compounded semi-annually at an interest rate of 9%. Gavin hoped he would have enough money in 8 years to buy a $400 gaming console for college. Is Gavin correct? Write and solve an equation, showing your work to justify your answer
Answer:
His answer was correct:
(200*0.09)=18
18*16=288
200+288=488
solve the equation: 4) 12
Ani2n 12)
417
Step 1: Use the distributive property
Step 2: Subtract n from both sides
63
41
Step 3: Simplify:
311
Step 4: Divide both sides by 3
301
3
Step 5: Simplify.
Check the solution to the example problem by replacing
z in the original equation with - 2 and evaluating both
sides. What true statement do you get?
to climinate the fraction in
Answer:
not clear enough
Step-by-step explanation:
What are the roots of the equation x²+2x+17=0 in simplest a+bi form?
Answer:
-1 ±4i
Step-by-step explanation:
The quadratic can be written in vertex form as ...
x² +2x +17 = 0
(x² +2x +1) +16 = 0 . . . . . . . . identify the part that can be a perfect square
(x +1)² = -16 . . . . . . . . . . . . subtract 16
x +1 = ±√(-16) = ±4i . . . . take the square root
x = -1 ±4i . . . . . . . . . . . subtract 1
The roots of the equation are x = -1-4i and x = -1+4i.
_____
Additional comment
It can be worthwhile to remember the form of a perfect square trinomial:
(x +a)² = x² +2ax +a²
If you know the coefficient of x, you can use half of it as the constant in each binomial factor.
In the above, we had 2a=2, so a=1 and a²=1. The constant 17 then is resolved into two parts: one part (1) is used to "complete the square" and the other part (16) is the y-coordinate of the vertex. It is used to find the "radical" portion of the roots.
The roots of the equation [tex]x^2 + 2x + 17 = 0[/tex] are [tex]x = -1 +4i[/tex] and [tex]x = -1 - 4i[/tex].
To find the roots of the equation [tex]x^2 + 2x + 17 = 0[/tex] in simplest a + bi form, we can use the quadratic formula.
The quadratic formula states that for an equation in the form[tex]ax^2 + bx + c = 0[/tex], the roots can be found using the formula:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
We have a = 1, b = 2, and c = 17.
Substituting these values into the quadratic formula, we get:
[tex]x = \frac{-2 \pm \sqrt{4 - 68}}{2}[/tex]
[tex]x = \frac{-2 \pm \sqrt{-64}}{2}[/tex]
[tex]x = \frac{-2 \pm \sqrt{64i^2}}{2}[/tex]
[tex]x = \frac{-2 \pm 8i}{2}[/tex]
[tex]x = -1 \pm 4i[/tex]
So, [tex]x = -1 +4i[/tex] and [tex]x=-1-4i[/tex] are roots.
To learn more on Quadratic equation click:
https://brainly.com/question/17177510
#SPJ6
i need help with how to reason it
Answer:
X=80
Step-by-step explanation:
As 100⁰ is Opposite to B and AD and EH Are PARALLEL so B=100⁰
180-100
=80⁰
MARK ME BRAINLIESTFor the expression five minus 5X to have a negative value what must be true about the value of X
Answer:
x=0
Step-by-step explanation:
honestly this is just filler no reason to explain it hoenstly
Option A: 40 trash bags for $6.29 Option B: 24 trash bags for $3.89
Which is the better option. Explain step by step-by-step.
What is the answer to this
what is the answer is 34 lekende eza
Answer:
Yes
Step-by-step explanation:
This is a function because every value in set A has only 1 value in set B.
when 1760 is divided into 14 equal parts, the remainder is 10. what is the correct way to write the quotient?
Answer:
125 R10
Step-by-step explanation:
You have to do (1760-10)/14=125
Find the perimeter. Simplify your answer.
Answer:
16c-6
Step-by-step explanation:
(7c-6)+(6c-10)+(3c+10)=?
7c-6+6c-10+3c+10=?
Collect like terms.
16c-6-10+10
Add and subtract.
16c-6
Hope this helps :)
help me with this please and thank you
Answer:
a. 2x +5
b. Pic attached
c. f(4) = 2•4 +5
f(4) = 8 +5
f(4) = 13
d. Domain: all the real numbers
Range: all the real numbers
A restaurant customer left $1.10 as a tip. The tip was 10% of the cost including tax. What was the total bill?
Answer:
11
Step-by-step explanation:
so 10% as a decimal is 0.1 if you take 1.10 and divide it be 0.1 you get 11. you do this because with percent you just multiply the decimal and you have your percent and using inverse operations you divide by the decimal instead of multiply
need help!!!!
No guessing,no links
Answer:
d = mn/F
Step-by-step explanation:
F = mn/d
multiply both sides with d
d*F = mn/d*d
dF=mn
divide F from both sides
d/F = mn/F
So..
d = mn/F
Answer:
Given:
[tex] \boxed{ \mathsf{F = \frac{mn}{d} }}[/tex]
Divide both sides by "mn":
[tex] \mathsf{ \frac{F}{mn} = \frac{mn}{d \times mn} }[/tex]
The two mn's on the RHS gets canceled out. So we're left with:
[tex] \mathsf{ \frac{F}{mn} = \frac{1}{d} }[/tex]
Invert the fractions present on either side of the "equals" sign
(In other words, flip it on its head so its numerator becomes its denominator and vice):
[tex] \mathsf{ \frac{mn}{F} = \frac{d}{1} }[/tex]
Hence, we got the value of d:
[tex] \underline{\mathsf{ d= \frac{mn}{F} }}[/tex]
Which equations are true and can be used to find the factors of 32? Check all that apply. A. 32 divided by 1 = 32 B. 32 divided by 2 = 16 C. 32 divided by 3 = 12 Or D. 32 divided by 8 =4
Answer:
A, B, D are correct
Step-by-step explanation:
A. 32 divided by 1 = 32
Works, it is correct
B. 32 divided by 2 = 16
Works, it is correct
C. 32 divided by 3 = 12
Incorrect, 12 x 3 = 36, not 32
D. 32 divided by 8 = 4
Works, it is correct
-Chetan K
Solve by substitution.
x-2y=2
2x-5y=3
I give Brainliest
Please explain step by step.
Cuanto le mide a messi la tula ?
Answer:
5’7”
Step-by-step explanation:
te refieres a lionel messi? el mide 5'7 ".
Perdon, mi español no es muy bueno :)
What is the equation, in slope-intercept form, that relates the cost compared to the miles traveled for a Green Cab?
Step-by-step explanation:
the general slope intercept form is
y = ax + b
a is the slope. it is expressed as ratio of y change / x change when going from one point to another.
b is the y-intercept (the point, where the line crosses the y-axis, meaning the y value when x=0).
we get b by using the point coordinates in the equation and solve for b.
we see costs is on the y axis, and miles is on the x axis.
so what points do we identify on the chart for the green taxi ?
there is right on the y-axis (0, 5). which is already our y-intercept.
and then let's pick e.g. the point where both lines intercept : (3, 8).
for the slope we look at the coordinate changes :
x changes by +3 (from 0 to 3).
y changes by +3 (from 5 to 8).
so, the slope is 3/3 = 1.
and again, the y- intercept is +5.
therefore, the line equation is
y = x + 5
meaning the cost of a fare is the number of miles plus 5.
A car travels 20miles be in 1/2 hour at constant speed is traveling at the same speed as a car that travels 30 miles in 3/4 hour at a constant speed.explain or show why
Answer:
It is true that both cars are traveling at the same speed.
Step-by-step explanation:
Given that car A travels 20 miles over half an hour, we know that this car is traveling at a speed of 40 miles per hour.
Car B travels 30 miles in 3/4 of an hour, let us set up a proportion to solve whether or not Car B is traveling at the same rate as Car A
30 miles / (3/4 hour) = x miles / 1 hour Cross multiply
30 = (3/4) x Divide both sides by (3/4)
40 = x
Therefore, both Car A and Car B are traveling at the same rate.
Step-by-step explanation:
Pharaoh, Diego, and Devonte all got jobs
at different clothing stores. At Pharaoh's
store it costs $48 to get 3 shirts. At Diego's
store it costs $96 to get 16 shirts. At
Devonte's store it costs $56 to get 14
shirts. Which one is the best deal.
Answer:
i think the answer is Devonte's store because you get 14 shirt for $56
Step-by-step explanation:
Pharaoh's good it's not too expensive but you only get 3 shirts , Diego's is too expensive even if you get 16 shirts it's for $96
im timed please help!! (see photo)
learnt this topic a while ago and somehow completely forgot could someone explain?
Answer:
99.5
Step-by-step explanation:
in right angle triangle
sin x = opposite side / hypotenuse
sin 34 = x / 178
x = sin 34 * 178
= 99.5
pls help me with these 2 questions
Answer:
x(2x-1)=0
3x-1x=0
2x=0
x=0/2
x=0
Step-by-step explanation:
LCM
first term =3x
=3×x
second term = 4x²y
=2×2×x×x×y
third term =x(x+1)
LCM=x
Answer:
djeuiiuhjjjcjffvgbftvkrfjjjjjrjrjrjjnnrnrf
