Step-by-step explanation:
we need the least or smallest common multiple for both numbers, 5 and 6.
this is very simple for the small numbers here, but in general we look at the prime factors of both numbers :
6 has the prime factors 2 and 3.
5 has only 5.
so, the LCM is 2×3×5 = 30.
they will meet again after 30 days.
FYI -
the LCM is for larger numbers a and b not automatically a×b. if both numbers share prime factors, the LCM can be smaller than a×b, as the LCM is using every overlapping prime factor only once.
Let a and ß be first quadrant angles with cos(a)=
√11/7
and sin(B)=
√11/4
Find cos(a+B)
Since both α and β are in the first quadrant, we know each of cos(α), sin(α), cos(β), and sin(β) are positive. So when we invoke the Pythagorean identity,
sin²(x) + cos²(x) = 1
we always take the positive square root when solving for either sin(x) or cos(x).
Given that cos(α) = √11/7 and sin(β) = √11/4, we find
sin(α) = √(1 - cos²(α)) = √38/7
cos(β) = √(1 - sin²(β)) = √5/4
Now, recall the sum identity for cosine,
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
It follows that
cos(α + β) = √11/7 × √5/4 - √38/7 × √11/4 = (√55 - √418)/28
Reese, Greg, and Brad meet once a week for coffee. They each have their favorite café and, to be fair, they use
randomization to choose where they will meet. Each person has a colored marble: red (R) for Reese, green (G) for
Greg, and blue (B) for Brad. Each week, all three marbles are mixed well in a bag and a marble is selected. The
favorite café of the person associated with the selected marble is chosen for that week's meeting. Which of the
following represents the sample space for choosing a café for the first two weeks?
OR & G, R & B, G & R, G & B, B &R, B & G
OR&R, R&G, R & B, G & G, G & B, B & B
R&R, R&G, R & B, G & R, G & G, G & B, B &R, B&G, B & B
R&R, R&G, R & B, R & G, G&R, G & G, G & B, B &R, B & G, B & B
OO
All the samples are given as {R&R, R&G, R&B, G&R, G&G, G&B, B&R, B&G, B&B}.
What are sample?A sample is a group of clearly specified components. The number of items in a finite sample is denoted by a curly bracket.
Reese, Greg, and Brad meet once a week for coffee.
They each have their favorite café and, to be fair, they use randomization to choose where they will meet.
Each person has a colored marble: red (R) for Reese, green (G) for Greg, and blue (B) for Brad.
Each week, all three marbles are mixed well in a bag and a marble is selected.
The favorite café of the person associated with the selected marble is selected for that week's meeting.
Then the total number of the outcomes will be
Total outcomes = 3 × 3
Total outcomes = 9
All the samples are given below.
{R&R, R&G, R&B, G&R, G&G, G&B, B&R, B&G, B&B}
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Jen wants to save money for the future. Jen invests $1,100 in an account that pays interest rate of 4%.
How many years will it take for the account to reach $2,900? Round your answer to the nearest hundredth.
The number of years it will take for the money to be $2900 is 40.91 years
How to find the years the money will accrue to 2900 dollars?Using simple interest formula,
I = prt / 100
we are looking for t
where
p = principalr = ratet = timeI = simple interestTherefore,
I = 2900 - 1100 = 1800
1800 = 1100 × 4 × t / 100
cross multiply
180000 = 4400t
t = 180000 / 4400
t = 40.9090909091
t = 40.91 years
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What is the sum of the first 40 positive odd integers?
Answer:
1600
Step-by-step explanation:
[tex]\text{Number of terms}, ~n = 40\\\\\text{Sum of n odd integers} = n^2 = 40^2 = 1600[/tex]
Find the side of an equialateral triangle if it's area is 9√3 cm2
Step-by-step explanation:
We know that the area of an equilateral triangle of side a cm is
[tex] \rm \: Equilateral \: Triangle = \cfrac{ \sqrt{3} }{4} {a}^{2} \: cm[/tex]Let a cm here be 9√3 then we could get our solution.
[tex] \rm\implies \rm 9 \sqrt{3} = \cfrac{ \sqrt{3} }{4} \: a {}^{2} [/tex]
[tex] \implies \rm \: \cfrac{ \sqrt{3} }{4} {a}^{2} = 9 \sqrt{3} [/tex]
[tex] \implies \rm \: a {}^{2} = 36[/tex]
[tex] \implies \rm \: a = \sqrt{36} = \sqrt{6 \times 6} [/tex]
[tex] \implies \rm \: a = 6 \: cm[/tex]
Thus, the side of the equilateral triangle is 6 cm.
The load requirement in your plan is 60 psf at a joist spacing of 16 inches . If the room dimensions are length 13 feet 2 inches and width 11feet 7 inches are 2 by 10 boards appropriate
The correct answer is; No, because the 2 x 10 boards can support neither the width nor length of the room.
How to find the dimensions?
We are given;
Load requirement = 60 psf
Joist Spacing = 16 inches
Length of room; 13 feet 2 inches
Width of room; 11 feet 7 inches.
Since we want to consider whether 2 by 10 boards are appropriate, this length of 2 by 10 will not be appropriate because it cannot cover up for a room with dimensions of 13 feet 2 inches and 11 feet 7 inches.
Thus, we can conclude that No, because the 2 x 10 boards can support neither the width nor length of the room.
The missing options are;
A. Yes, because 2 x 10 boards can support the width and length of the room
B. Yes, because 2 x 10 boards support the 70 psf
C. No, because 2 x 10 boards can support only the width of the room
D. No, because the 2 x 10 boards can support neither the width nor length of the room
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Calculate the distance between the points H=(4,-8) and C=(9,-4) in the coordinate plane.
Answer:
[tex]find the functions whose derivative is 0[/tex]
The radius of a semicircle is 5 centimetres. What is the semicircle's diameter?
The diameter [tex]d = 2r[/tex], where [tex]r[/tex] is the radius. Thus, [tex]d = 2 \times r = 2 \times 5 = 10cm[/tex]
He was, without a doubt, the most prolific writer of mathematics of all time. Euler is credited as being the first mathematician to define function in the way we currently think of functions. In his book, Introductio in analysin infinitoriumin, he stated, “A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.”
Based on what we know a function to be today, what did Euler mean by an analytic expression?
an expression formed with many variables and no numbers
an expression formed with many numbers and no variables
an expression formed from operations such as addition, multiplication, powers, and roots
an expression formed using only multiplication of a variable and a number
Based on what we know a function to be today, Euler mean an analytic expression "an expression formed from operations such as addition, multiplication, powers, and roots"
Euler's definition of a functionAccording to Euler, a function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.”
The function is. combination of expression which includes variables and constants using various operations such as roots, power and multiplication.
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What is the length of a diagonal of a square with a side length of 8?
A. 4
B. 42
C. 4√3
D. 8√√2
Which is a conditional statement for the sentence?
For all real numbers a, b, and c, a = b implies that a−c=b−c.
A.If a, b, and c are real numbers, then a = b.
B.For all real numbers a, b, and c, if a−c=b−c, then a = b.
C.For all real numbers a, b, and c, if a = b, then a−c=b−c.
D.If a, b, and c are real numbers, then a−c=b−c.
The conditional proposition for the given sentence is:
"For all real numbers a, b, and c, if a = b, then a−c=b−c."
Which one is a conditional statement?
A conditional statement is of the form:
If P, then Q.
Where P and Q are two propositions.
The sentence is:
"For all real numbers a, b, and c, a = b implies that a−c=b−c."
So the propositions are:
P = "a = b"
Q = " a - c = b - c"
Where we need to define that this works for all real numbers.
So the conditional proposition is:
"For all real numbers a, b, and c, if a = b, then a−c=b−c."
So the correct option is C.
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A cake has two layers. Each layer is a regular hexagonal prism. You cut and remove a slice that takes away one face of each prism as shown. What is the volume of the slice? What is the volume of the remaining cake? Use pencil and paper. Describe two ways to find the volume of the slice.
P.S. pls help me
The volume of the slice is 40 in³. The volume of the remaining cake is 197.014 in³.
What is a regular hexagon?A regular hexagon is defined as a closed shape consisting of six equal sides and six equal angles.
Here we have two regular hexagons
one top small hexagon cake with side length = 3 in, height = 3 in
One big hexagon cake, side length = 4 in, Height = 4 in
A slice cut such that it removes a side segment is equivalent to an equilateral triangle with side length = length of hexagon side
Also, all angles within the equilateral triangle are 60° each
Therefore, the length of the side of the removed equilateral triangle side
Top small cake slice triangle side = 3 in.
Area of surface of small slice = 1/2 x b x h = 1/2 x 3 x 3 x sin 60
= 9√3/ 4
The volume of a small slice
= Area of surface small slice × Height of small cake
= 9√3/ 4 x 3
= 11. 69
Big cake slice triangle side = 4 in.
Area of the surface of big slice = 1/2 x 4 x 4 x sin 60
= 4√3
The volume of big slice = Area of surface of big slice × Height of big slice
= 16√3
= 28
Total volume of slice = Volume of small slice + Volume of big slice
Total volume of slice = 12 in³ +28 in³ = 40 in³
For the small cake, the remaining volume = 5 x 11.69 = 58.45
For the big cake the remaining volume = 5 x 27.71 = 138.56
Total volume remaining cake = 58.45 in³ + 138.56 in³ = 197.014 in³
a = Length of side
h = Height of hexagon
The volume of each slice is, therefore,
= a^2 x h x √3/4
For the small cake, we have
a = 3 in.
h = 3 in.
Volume of small slice = a^2 x h x √3/4
= 9 x 3 x √3/4 = 27√3/4
For the big cake, we have
a = 4 in.
h = 4 in.
Volume of big slice = a^2 x h x √3/4
= 16 √3
The total volume of slice = Volume of small slice + Volume of a big slice
Total volume of slice = 27√3/4 + 16 √3
The total volume of slice = 39404 in³.
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only answer if you know! no spams :)
Multiply:
(x+y)by (x+y)
a+b by a^2-b^2
(a+5) by (a^2-2a-3)
(a^2-ab+b^3) by (a+b)
Answer:
Multiply:
[tex](x+y)by (x+y)[/tex]
[tex] : \implies(x + y)(x + y)[/tex]
[tex] : \implies \: x(x + y) + y(x + y)[/tex]
[tex] : \implies {x}^{2} + xy + xy + {y}^{2} [/tex]
[tex] : \implies{x}^{2} + 2xy + {y}^{2} [/tex]
Multiply:
[tex]a+b \: by \: a^2-b^2[/tex]
[tex]: \implies( {a}^{2} + {b}^{2} ) \times (a + b)[/tex]
[tex]: \implies \: {a}^{2} (a + b) - {b}^{2} (a + b)[/tex]
[tex]: \implies \: {a}^{3} + {a}^{2} b - {ab}^{2} - {b}^{3} [/tex]
Multiply:
[tex](a+5) by (a^2-2a-3)[/tex]
[tex]: \implies{(a + 5) \times ( {a}^{2} - 2a - 3) }[/tex]
[tex]: \implies \: a({a}^{2} - 2a - 3) + 5( {a}^{2} - 2a - 3)[/tex]
[tex]: \implies(a \times {a}^{2} - a \times 2a - a \times 3) + (5 \times {a}^{2} - 5 \times 2a - 5 \times 3)[/tex]
[tex]: \implies{a}^{3} - {2a}^{2} - 3a + 5 {a}^{2} - 10a - 15 [/tex]
[tex]: \implies{ {a}^{3} + {3a}^{2} - 13a - 15}[/tex]
Multiply:
[tex](a^2-ab+b^3) by (a+b)[/tex]
[tex]: \implies{(a + b) \times ( {a}^{2} - ab + {b}^{3} )}[/tex]
[tex]: \implies \: a( {a}^{2} - ab + {b}^{3}) + b( {a}^{2} - ab + {b}^{3} ) [/tex]
[tex]: \implies {a}^{3} - {a}^{2} b + a {b}^{3} + {a^2b} - {ab}^{2} + {b}^{4} [/tex]
[tex]: \implies{ {a}^{3}+ab^3 - ab^2+ {b}^{4} }[/tex]
Step-by-step explanation:
[tex] \blue{ \frak{Seolle_{aph.rodite}}}[/tex]
In triangle ABC, AP is an angle bisector of angle BAC. What is the length of PC? Round you answer to the nearest whole number.
A) 6 B) 7 C) 8 D) 9
Answer:
D) 9
Step-by-step explanation:
x = ½ × 13 = 6.5
y = ½ × 5 = 2.5
6.5 + 2.5 = 9
So the length of PC is 9
HOPE THIS HELPS AND HAVE A NICE DAY <3
Living on less than what you make means not
Answer:
living beyond your means.
Step-by-step explanation:
Pay for what you need and don't go into debt.
y = 2(6 + 1) + 5(3 + 2)
Step-by-step explanation:
According to PEMDAS parentheses are first.
2(6+1) can be simplified to 12+2.
5(3+2) can be simplified to 15+10
Add these two together.
12+2+15+10
14+15+10
29+10
y=39
Note - when you have something like this in math 2(6+1) it means you need to do 2 x 6 and 2 x 1
what is it pls help? multiple choice
Answer:
around 904.78
Step-by-step explanation:
i got 904.78 but i cant read the answers properly so choose the closest one
need help with this math
Answer:
x = -12
y = 10
(x, y) = (-12, 10)
Step-by-step explanation:
(07.03 MC)
Victoria used a probability simulator to pull 3 colored marbles from a bag and flip a coin 50 times. The results are shown in the tables below:
Color of
Marble Number of
Times Rolled
Blue
18
Green
20
Yellow
12
Heads Tails
20 30
Using Victoria's simulation, what is the probability of pulling a blue marble and the coin landing tails up?
48 over 50
38 over 50
540 over 2500
360 over 2500
The probability of pulling a blue marble and the coin landing tails up is 360/2500
How to determine the probability?The tables of values are given as:
Color Times
Blue 18
Green 20
Yellow 12
Heads Tails
20 30
The probability of obtaining a blue marble is:
P(Blue) = 18/50
The probability of landing tails up is:
P(Tail) = 20/50
The required probability is:
P = P(Blue) * P(Tail)
This gives
P = 18/50 * 20/50
Evaluate the product
P = 360/2500
Hence, the probability of pulling a blue marble and the coin landing tails up is 360/2500
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Answer and explanation please
Step-by-step explanation:
So, let the N=10a+b
N=10a+b,P(N)=ab,S(N)=a+b
10a+b=ab+a+b
9a-ab=0
a(9-b)=0
a=0 and 9-b=0, b=9. the number is 9. but 9 is not two-digit number. So there is no N which satisfied previous conditions.
Determine the value of x using a trigonometric
ratio. Image below with answers.
This is an identity used to determine the measure of sides and angles of a triangles. The value of x from the given diagram is 7.18 units
Trigonometry identityThis is an identity used to determine the measure of sides and angles of a triangles
From the given triangle
Opposite = 5.5
Hypotenuse = x
According to the theorem
sin 50 = 5.5/H
x = 5.5/sin50
x = 7.18units
Hence the value of x from the given diagram is 7.18 units
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(-1,-4) and (-201,-49)
Find the distance between the two points
Answer:
205 units
Step-by-step explanation:
The distance formula is D = √(x2-x1)^2 + (y2-y1)^2
Lets say -1 is x1 ; -4 is y1; -201 is x2 ; and -49 is y2
we just need to plug it into the formula and solve now
√ (-201 - -1)^2 + (-49 - -4)
√-200^2 + -45^2
√40000 + 2025
√42025 = 205
The distance between the two points is 205 units.
A candidate for office plans to visit 6 cities before the state primary.
How many different ways can the campaign staff arrange her travel route?
Enter your answer as a whole number, like this: 42
Question 2
A candidate for office plans to visit 6 cities before the state primary.
How many different ways can the campaign staff arrange her travel route?
Enter your answer as a whole number, like this: 42
There are 720 different ways the campaign staff can arrange her travel route
How to determine the number of route?The given parameter is:
Cities = 6
The candidate cannot be at all 6 cities at the same time.
This means that we make use of factorial.
So, we have:
Ways = 6!
Evaluate the factorial expression
Ways = 720
Hence, there are 720 different ways the campaign staff can arrange her travel route
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Which choice is equivalent to the expression below?
√-27
OA. -3√3
OB. 3143
O C. -√√27
OD. -3√√37
OE. 3√3
The equivalent expression for the given expression is 3i√3.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is √-27
= i√27
= i√(9×3)
= 3i√3
Therefore, the equivalent expression for the given expression is 3i√3.
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Which of the following describes the polynomial function?
A graph shows the number of texts, numbered 10 to 100, on the x-axis, and the total cost in dollars, numbered 3 to 27, on the y-axis. A straight red line with a positive slope, labeled Emilia, begins at (0, 10), and a straight blue line with a positive slope, labeled Hiroto, begins at (0, 20). Both lines intersect at point (50, 22.5).
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent.
Both plans cost the same when 22 texts are sent.
Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent.
Both plans cost the same when 50 texts are sen
Answer: Both plans cost the same when 50 texts are sent.
Step-by-step explanation:
When x=50 (meaning 50 texts are sent), the y coordinate (which represents the cost) is the same.
what is the effect of the “-“ when y= (x+3)^ is changed to y=-(x+3)^?
Answer + Step-by-step explanation:
The effect of the “-“ when y = (x+3) is changed to y = -(x+3) is creating a negative slope and y-intercept,
y = -(x+3) distributed is y = -x - 3
Visual representation:
The red line: y = (x+3)
The blue line: y = -(x+3)
17
24
12
X
What is the value of x?
Answer: 8.5
Step-by-step explanation:
By the intersecting chords theorem,
[tex]17(12)=24x\\204=24x\\x=\boxed{8.5}[/tex]
MANY POINTS! PLEASE HELP
Answer:
B. 51.7699^2
Step-by-step explanation:
Last 2 wrong because it is positive.
101.... is not the definite integral for the curve
51... purrfecto