How many number less than 300 is exactly divisible by 8, 12, 18?
Count how many multiples of 8, 12, or 18 there are in the range {1, 2, 3, …, 300}:
⌊300/8⌋ = 37
⌊300/12⌋ = 25
⌊300/18⌋ = 16
(where ⌊n⌋ denotes the floor of n, i.e. the largest integer that is smaller than n; for instance, 300/8 = 37.5, so ⌊300/8⌋ = ⌊37.5⌋ = 37)
Take pairwise LCMs, as well as the LCM of all three numbers:
LCM(8, 12) = LCM(2³, 2²×3) = 2³×3 = 24
LCM(8, 18) = LCM(2³, 2×3²) = 2³×3² = 72
LCM(12, 18) = LCM(2²×3, 2×3²) = 2²×3² = 36
LCM(8, 12, 18) = LCM(2³, 2²×3, 2×3²) = 2³×3² = 72
Count how many multiples there are of each of these LCMs that are less than 300:
⌊300/24⌋ = 12
⌊300/72⌋ = 4
⌊300/36⌋ = 8
Then, using the inclusion/exclusion principle, the number of numbers less than 300 that are exactly divisible by 8, 12, or 18 is
{multiples of 8} + {multiples of 12} + {multiples of 18}
- {multiples of 24} - {multiples of 72} - {multiples of 36}
+ {multiples of 72}
= 37 + 25 + 16 - 12 - 4 - 8 + 4 = 58
Please help me with this, I am stu pid. UnU
Which equations are equivalent to Three-fourths + m = negative StartFraction 7 over 4 EndFraction? Select three options.
Answer:
m = negative StartFraction 10 over 4 EndFraction
m = negative five-halves
Step-by-step explanation:
Given equation :
Which equations are equivalent to Three-fourths + m = negative StartFraction 7 over 4 EndFraction
3/4 + m = - 7/4
Subtracting 3/4 from both sides
3/4 + m - 3/4 = - 7/4 - 3/4
m = - 10/4
m = - 5/2
if tanA=2ab/a square-b square.find the value of cosA and sin A
Answer:
[tex]\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \tan A = \frac{2ab}{a^2 - b^2}[/tex]
And we want to find the value of cos(A) and sin(A).
Recall that tangent is the ratio of the opposite side to the adjacent side.
Therefore, the opposite side measures 2ab, and the adjacent side measures a² - b².
Using the Pythagorean Theorem, solve for the hypotenuse:
[tex]\displaystyle \begin{aligned} c^2 &= a^2 + b^2 \\ \\ c&= \sqrt{(2ab)^2 + (a^2-b^2)} \\ \\ &= \sqrt{(4a^2b^2)+(a^4-2a^2b^2+b^4)} \\ \\ &= \sqrt{a^4 + 2a^2b^2 + b^4 } \\ \\ &= \sqrt{(a^2 +b^2)^2} \\ \\ &= a^2 + b^2\end{aligned}[/tex]
Thus, our hypotenuse is given by a² + b².
Cosine is the ratio between the adjacent side and the hypotenuse. Thus:
[tex]\displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}[/tex]
And sine is the ratio between the opposite side and the hypotenuse. Thus:
[tex]\displaystyle \sin A = \frac{2ab}{a^2 + b^2}[/tex]
In conclusion:
[tex]\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}[/tex]
Answer:
Step-by-step explanation:
[tex]sec^2A-tan^2A=1\\sec^2A=1+tan^2A=1+\frac{4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2-b^2)^2+4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2+b^2)^2}{(a^2-b^2)^2} \\cos^2A=\frac{(a^2-b^2)^2}{(a^2+b^2)^2} \\cos A=\frac{a^2-b^2}{a^2+b^2} \\sin A=\sqrt{1-cos^2A} =\sqrt{1-(\frac{a^2-b^2}{a^2+b^2} )^2} =\sqrt{\frac{(a^2+b^2)^2-(a^2-b^2)^2}{(a^2+b^2)^2} } =\sqrt{\frac{4a^2b^2}{(a^2+b^2)^2} }=\frac{2ab}{a^2+b^2}[/tex]
19. Charlotte has a success rate of about 20%
for making baskets in attempts during
basketball games. She wants to determine
the probability that she will have to make at
least 5 attempts during a game in order to
make a basket. She designed a simulation
where she spun a spinner that was divided
into 5 equal sections, one of which was
colored red. She counted how many times
she had to spin the spinner in each trial
before it landed on red. The results of her
20 trials are shown below.
5, 2, 7, 2, 3, 4, 10, 6,4,6,
3, 6, 6, 4, 8,5,7,7,1,5
According to this simulation, what is the
probability that Charlotte will have to
make at least 5 attempts in order to make
a basket?
Answer:
[tex]P(x \ge 5) = 0.60[/tex]
Step-by-step explanation:
Given
[tex]S = \{5, 2, 7, 2, 3, 4, 10, 6,4,6,3, 6, 6, 4, 8,5,7,7,1,5\}[/tex]
[tex]n(S) = 20[/tex]
Required
[tex]P(x \ge 5)[/tex]
First, we count the number of trials that are at least 5
[tex]x = \{5, 7, 10, 6,6, 6, 6, 8,5,7,7,5\}[/tex]
So, we have:
[tex]n(x \ge 5) = 12[/tex]
So, we have:
[tex]P(x \ge 5) = \frac{n(x \ge 5)}{n(S)}[/tex]
This gives
[tex]P(x \ge 5) = \frac{12}{20}[/tex]
[tex]P(x \ge 5) = 0.60[/tex]
If f(x)= sqrt x, which equation describes the graphed function.
Answer:
C. y = -f(x) - 3
Step-by-step explanation:
The given (parent) function is f(x) = √x
The given graph shows a real curve that starts from y = -3, when x = 0 and the y-value increases in magnitude in the negative direction as the x-values increases positively from left to right, by the same amount that the parent function increases from left to right
Therefore;
The graph is real, therefore, the value of x in √x is x ≥ 0, and y ≠ f(-x) + D
Where, D, is the vertical shift
The graph starts at x = 0, y = -3, compared to the parent function, the vertical shift, D = -3
The y-value of the given curve increases in the opposite direction (negatively) as the y-value of the parent function increases in magnitude in the positive direction
Therefore, the equation of the given curve comprises of the reflection of the parent function or -f(x)
The graph shows the reflection of the parent function, across the x-axis, and we have, reflection of the parent function, f(x) which is -f(x)
Therefore, the equation that describes the graphed function is y = -f(x) - 3
Make sure to round it to tge nearest 10th
Answer:
13.9
Step-by-step explanation:
For the 41° angle, x is the opposite leg, and 16 is the adjacent leg. The trig ratio that relates the opposite leg and the adjacent leg is the tangent.
tan A = opp/adj
tan 41° = x/16
x = 16 * tan 41°
x = 13.9085...
Answer: 13.9
Pure mathematicsssss
Answer:
(i) a = 2
b = -1
c = -1
(ii) x= 1
Step-by-step explanation:
Step 1: Factorise
[tex]f(x) = 2(x^{2} -2x+\frac{1}{2})[/tex]
Step 2: Use the complete square method.
[tex]f(x)=2(x^{2} -2x+(\frac{-2}{2})^{2} + \frac{1}{2} - (\frac{-2}{2})^{2} )[/tex]
Step 3: Have it to [tex]a(x+b)^{2} +c[/tex]
[tex]f(x)=2((x-1)^{2} -\frac{1}{2} )\\ = 2(x-1)^{2} -1[/tex]
Line of symmetry:
To find line of symmetry, we use -b/2a formula.
Based from [tex]2x^{2} -4x+1[/tex]:
a=2, b=-4
-b/2a = -(-4)/2(2) = 1
square of 2x+3y.Please help me
Answer:
(2x+3y)^2
= (2x)^2 + 2(2x)(3y) + (3y)^2
= 4x^2 + 12xy + 9y^2
Answer:
4x^2 12xy +9y^2
Step-by-step explanation:
(2x+3y)^2
(2x+3y)(2x+3y)
FOIL
4x^2 + 6xy+6xy + 9y^2
4x^2 12xy +9y^2
what is simplfiled for x^8 y^2 / x^3 y^9
Answer:
x^5/y^7
Step-by-step explanation:
x^8 y^2 / x^3 y^9
We know that a^b/ a^c = a^(b-c)
Simplify the x terms
x^8 / x^3 = x^(8-3) = x^5
Simplify the y terms
y^2 / y^9 = y^(2-9) = y^-7
We know a^-b = 1/a^b
y^-7 = 1/y^7
Put the terms back together
x^5/y^7
You roll a six-sided number cube and flip a coin. What is the probability of rolling a number greater than 1 and flipping heads? Write your answer as a fraction in simplest form.
Answer:
5/12Step-by-step explanation:
Number cube:
Numbers greater than 1 → 5 options out of 6Coin:
Heads → 1 out of 2Required probability:
P(>1 & H) = 5/6*1/2 = 5/12Answer: Probability of rolling a number more than one: 5/6
Probability of heads: 1/2
Probability of both: 1/2 + 5/6 = 4/3
Step-by-step explanation:
please please please answer!! will give brainliest and extra points!
solve for θ.
sin(74) = cos(θ)
1. 6°
2. 74°
3. 36°
4. 16°
Sin74 = Cos16
cause 16 + 74 = 90
Whenever the sum of two angles is equal with 90, the Sin of one is equal with the Cos of the other like :
Sin(30) = Cos(60)
and also
Tan(30) = Cot(60)
Answer:
16
Step-by-step explanation:
sin(74) = cos(x)
sin(x)=cos(90-x)
sin (74) = cos(90-74)
sin 74 = cos( 16)
Suppose we have a stick of length 1.a) We randomly uniformly choose a point and break the stick into two pieces.Find the expected length of the smaller piece.b) We randomly uniformly choose two points (independently) and break thestick into three pieces. Find the probability that the three resulting piecescan be arranged to form a triangle (i.e. all triangle inequalities are satisfied;i.e no piece is longer than the sum of the other two).
Answer:
Step-by-step explanation:
1) The smaller sticks will range in length from almost 0 unit up to a maximum of 0.5 unit, with each length equally possible.
Therefore, the average length will be about (0 + 0.5)/2 = 0.25 unit
2)If you assume that each break in the stick is uniformly distributed along the length of the stick and is independent of the location of the other break, then the odds are 25% that you will be able to form a triangle with the 3 pieces.
We'll call the length of the stick 1, so each break can occur at a position in the interval [0,1]. Let x and y represent the two breaks. Then we can look at the area of the region in the square bounded x=0, x=1, y=0, y=1, which represents combinations of x and y, for which we can form a triangle. Since the area of the whole square is 1, the area of the region inside is our probability.
If y>x, then the lengths of the pieces are x, y-x, and 1-y.
The triangle inequality must hold for each combination of edges.
for y>x ...
x+y−x≥1−y
x+1−y≥y−x
y−x+1−y≥x
these simplify to...
for y>x ...
y≥1/2
x+1/2≥y
x≤1/2
If we cut our 1x1 square into two triangles along the line x=y,
then the region in the upper triangle which satisfies the inequalities above forms a smaller triangle which connects the midpoints of the upper triangle.
The lower triangle (x>y), is just a reflection about x=y of the upper triangle, so together, the entire region looks like a bow-tie at a 45 degree angle.
This region takes up 25% of the square, so the probability that you can form a triangle is 25%
16. Sandra is choosing an Internet service provider.
• Smart Dot Company costs $12 per month plus $0.50 for each hour of Internet used.
• Communication Plus costs $2.50 for every hour of Internet used.
a. Create an equation to represent the cost of using the internet with each company. (2 marks) Let C represent the cost of using internet in any month.
Let t represent the number of hours used.
Answer: See explanation
Step-by-step explanation:
Since Smart Dot Company costs $12 per month plus $0.50 for each hour of Internet used, the equation to represent the cost of using the internet with them will be:
C = 12 + 0.5t
Since Communication Plus costs $2.50 for every hour of Internet used, the equation to represent the cost of using the internet with them will be:
C = 2.5t
UDISJKDFJSFJDGLFS HELP
Answer:
I think E
Step-by-step explanation:
You know the shortest building is 25 m.
to find the rest, use trigo so Tan(20)=opposite/adjacent.
Adjacent is 50. Do the math and add the answer with 25.
Answer:
The answer would be E. 43.2
According to TOA, The opposite side is tan(20) x adjacent side( 50m)
the answer is 18.2( to 1 dp). Add the height of the second building together with 18.2 and you will get ur answer. HOpe this helps:)
Algebraic expression for 2a+3b-c if a=3 b=-4 c=-2
Answer:
-4
Step-by-step explanation:
a = 3
b = -4
c = -2
2a + 3b - c
= 2(3) + 3(-4) - (-2)
= 6 + (-12) + 2
= -4
20
2, Nine people fit comfortably in a 3 ft. by 3 ft. area. Use this value to
estimate the size of a crowd that is 8 yards deep and 1 mile long.
Determine the Area of the crowd?
A. Area = 3 feet x 3 feet
B. Area = 8 yards v 1 mile = (8 x 3 feet) x (1 x 5280 feet)
C. Area = 24 feet x 1 feet.
D. Area = 8 feet x 5280 feet
.
Answer:
B
Step-by-step explanation:
8 yards = 3 * 8 = 24 ft^2
1 mile = 5280
3*3 = 9 square feet
9 square feet holds 9 people.
1 square foot holds 1 person
8*3 * 5280 people could stand in an area of 8 yards * 1 mile
Though it's not quite correct, the answer is B
A number is doubled and 7 is subtracted from the answer, if the result is -25.
-create an equation
-solve the equation to find the number
Please Respond
answer i guess i will give brainly for corret answers.
Answer:
B. Never
Step-by-step explanation:
When a number is irrational, it means that it cannot be written as a fraction.
I hope this helps!
pls ❤ and mark brainliest pls!
Answer:
c) when it is improper fraction
look at image for question and answer
helpp me solve it and pls explain
tyyy
Answer:
2=124 124/2
4=248 248/4
5=310 310/5
8=496 496/8
Step-by-step explanation:
40 + 22 = 62
62 x 2 = 124
62 x 4 = 248
62 x 5 = 310
62 x 8 = 496
i think
the quotient of a number and -9 is increased by 10 the result is 11 what is the number?
Answer:
so the division of a number and -9 or
x/-9+10=11 or
(x/-9)+10=11
subtract 10 from both sides
x/-9=1
multiply both sides by -9
x=-9
what is the volume of the circular cone below?
Answer:
200.96
Step-by-step explanation:
Volume of cone=(1/3)*pi*r^2*h
Volume=(1/3)*pi*16*12=64*3.14=200.96
SOMEONE PLEASE HELP ME ITS URGENT (PICTURE)
Answer:
Question #1
x and its opposing side are equal in length. One of the sides have no fence.Set up an equation to find x:
[tex]x+x+10=26\\2x=26-10\\2x=16\\x=8[/tex]
The length of the side marked x is 8.0 m.
Question #2
New length = 10 + 1 = 11 cmNew width = xNew perimeter = old perimeter = 34 cmSet up an equation to find x
[tex]11+11+x+x=34\\2x=34-22\\2x=12\\x=6[/tex]
The new width is 6 cm.
Helppp!! Summer math Packet!
(+4) +(-7) =
Step-by-step explanation:
(+4)+(-7)
=4-7
=-3
Hope it will help you..
Find the value of the following (-42) + 15 + (-63) can someone say this and fast
[tex]\\ \sf\longmapsto (-42)+15+(-63)[/tex]
[tex]\\ \sf\longmapsto -42+15+(-63)[/tex]
[tex]\\ \sf\longmapsto -27+(-63)[/tex]
[tex]\\ \sf\longmapsto -27-63[/tex]
[tex]\\ \sf\longmapsto -90[/tex]
Answer:
42 + 15 + (-63) = -90
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
PLS HELP ASAP! 20 PTS
evaluate
Answer:
Step-by-step explanation:
Cos^-1(1/2) = 60
To get from a degree to radian, simply multiply by pi then divide by 180. So the final answer is 1/3pi or approximately 1.0472
I hope this helped! :D
A basketball is shot into the air. Its height is represented by the polynomial equation h(t) = –16t2 + 35t + 5, where h is the height of the basketball at t seconds. What's the height of the basketball at 1.5 seconds?
Question 4 options:
20.2 feet
18.8 feet
21.5 feet
16.7 feet
Answer:
height = 21.5 ft
Step-by-step explanation:
Substitute t = 1.5 into h(t) and evaluate
h(1.5) = - 16(1.5)² + 35(1.5) + 5
= - 16(2.25) + 52.5 + 5
= - 36 + 57.5
= 21.5 ft
Answer:
21.5 feet.
Step-by-step explanation:
Let t = 1.5
[tex]h(1.5)=-16(1.5)^2+35(1.5)+5\\h(1.5)=-36+52.5+5\\h(1.5)=21.5[/tex]
Therefore, at 1.5 seconds, the basketball is 21.5 feet in the air.
Set A and the universal set U are defined as follows.
U={1,2,3,4,5,6)
A= {2,4,6}
Find the following sets.
Write your answer in roster form or as Ø.
Part (a)
Answer: ØThis is the empty set
------------------
Explanation:
It doesn't matter what set A is composed of. Intersecting any set with the empty set Ø will always result in the empty set.
This is because we're asking the question: "What does some set A and the empty set have in common?". The answer of course being "nothing" because there's nothing in Ø. Not even the value zero is in this set.
We can write Ø as { } which is a set of curly braces with nothing inside it.
=========================================================
Part (b)
Answer: {1,2,3,4,5,6}-----------------
Explanation:
When you union the universal set with any other set, you'll get the universal set.
The rule is [tex]A \cup B = B[/tex] where I've made B the universal set to avoid confusion of the letter U and the union symbol [tex]\cup[/tex] which looks nearly identical.
Why does this rule work? Well if an item is in set [tex]\overline{A}[/tex], then it's automatically in set U (everything is in set U; it's the universe). So we're not adding anything to the universe when applying a union involving this largest set.
It's like saying
A = set of stuff inside a persons house[tex]\overline{A}[/tex] = set of stuff outside a persons house (ie stuff that is not in set A)U = set of every itemwe can see that [tex]\overline{A} \cup U[/tex] will basically form the set of every item, aka the universal set.
