The amount of money Conor should save each month for 5 months is £136.
How much should he save each month?Division is the mathematical operation that is used to determine the quotient of a number. It involves grouping a number into equal parts using another number.
The amount of money Conor should save each month = total amount needed / number of month
£680 / 5 = £136
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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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factor the following (in picture)
got really sick and missed a bunch of school, would really appreciate the help !
Step-by-step explanation:
I hope this will help you
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]
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Martha recorded the eye colors of the people who have already signed up for a lecture on genetics.
gray 1
brown 10
hazel 1
green 1
blue 7
Considering this data, how many of the next 16 people to sign up should you expect to be brown-eyed?
Answer:
8
Step-by-step explanation:
since martha counted 10/20 had brown eyes thats about 50 percent, simple ratios 10/20= ×/16 you get 8martha conto 10 de 20 personas con ojos cafes, eso quiere decir que 50 por ciento de los contados tenien ojos cafès, 50 porciento de 16 es 8
Which of the following describes the polynomial function?
please help asap 100 points
Answers:
Problem #1: Option C, 166 yards cubed
Problem #2: Option A, 10
Step-by-step solution:
The first problem may seem a lot more confusing that it really is and this actually happened to me when I looked at it. Just because the cylinder is slanted that actually doesn't change any of the volume that we would have if it was straight up with the same diameter and height.
Using what we know about cylinders, let us plug all the information inside of the formula to determine the volume of the cylinder. However, before doing that we need to determine the radius of the circle from the diameter that was given.
Divide the diameter by two to get the radius
[tex]Radius = \frac{Diameter}{2}[/tex][tex]Radius = \frac{5.2\ yd}{2}[/tex][tex]Radius = 2.6\ yd[/tex]Plug in the values
[tex]V_{cylinder} = (\pi * radius^2)*height[/tex][tex]V_{cylinder} = (\pi * (2.6\ yd)^2)*7.8\ yd[/tex]Simplify the exponent
[tex]V_{cylinder} = (\pi * (2.6)^2 *(yd)^2)*7.8\ yd[/tex][tex]V_{cylinder} = (\pi * 6.76\ yd^2)*7.8\ yd[/tex]Simplify the expression
[tex]V_{cylinder} = (21.237\ yd^2)*7.8\ yd[/tex][tex]V_{cylinder} = 165.65\ yd^3[/tex]Therefore, after simplifying the expression using the cylinder volume formula and the given information we were able to determine that the option that best fits the description of our answer is option C, 166 cube yards.
Now that we completed the first question, we can move onto the second question. In this question we are given a figure along with 3 numbers and one unknown, x, which we need to find the value of. We need to use the Secant-Secant Power Theorem to help determine our solution.
Make an expression to represent the scenario
[tex]32(x + 32) = 28(20 + 28)[/tex]We know have an expression which we can now simplify and get the value of the unknown easily. The first step would be to distribute the 32 and 28.
Distribute both sides
[tex]32(x + 32) = 28(20 + 28)[/tex][tex](32 * x) + (32 * 32) = (28 * 20) + (28 * 28)[/tex][tex]32x + 1024 = 560 + 784[/tex]Simplify the expression
[tex]32x + 1024 = 1344[/tex]We now have a simple expression where we can now subtract both sides by 1024 to help isolate x with its coefficient.
Subtract 1024 from both sides
[tex]32x + 1024 - 1024 = 1344 - 1024[/tex][tex]32x = 1344 - 1024[/tex][tex]32x = 320[/tex]The final step that we have to help fully isolate x by itself is to divide both sides by 32 which would remove the coefficient from x.
Divide both sides by 32
[tex]\frac{32x}{32} = \frac{320}{32}[/tex][tex]x = \frac{320}{32}[/tex][tex]x = 10[/tex]After simplifying the expression completely, we are able to see that the best option that fits our description is option A, 10.
set questions need immediate help
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
only answer if you know! no spams :)
(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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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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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
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.
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
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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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]
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.
William is drafting his fantasy basketball team. He needs to select one player for each position. The following table shows how many players are available for each position.
Position Number of players
Point guard 10
Shooting guard 12
Small forward 7
Power forward 2
Center 9
pls pls pls help!! thanks soooo much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: 15120
Step-by-step explanation:
Given: The number of players at point guard = 10
The number of players at shooting guard = 12
The number of players at small forward = 7
The number of players at power forward = 2
The number of players at center = 9
Then, the number of different teams William could draft is given by :-
10∗12∗7∗2∗9=15120
Hence, William could draft 15120 different teams.
(-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.
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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Lila invested 10000 in one of long life insurance company annuity contracts. When issued, the contract was paying a 5 percent rate of return
The kind of annuity does Lila own is: variable immediate annuity.
What is variable immediate annuity?Variable immediate annuity can be defined as the type of annuity that vary or fluctuate based on the type of investment you choose or pick.
In this type of annuity the payment you will receive will not be fixed reason being that payments that will made to you will always increase or decrease.
Therefore the kind of annuity does Lila own is: variable immediate annuity.
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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]
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]
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
Cost of Bikes ($) at Bike Shop
312, 352, 480, 392, 368, 352, 416, 640
a. mean
The mean is?
Answer:
414
Step-by-step explanation:
312+352+480+392+368+352+416+640 divided by 8 = 414
Select ALL the correct answers. Consider the following graph of function f. Which transformations will change function f into function g given below. a vertical shift down 3 units a vertical shift down 5 units a vertical shift up 5 units a horizontal shift left 7 units a horizontal shift right 7 units a horizontal shift left 4 units
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)
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
worth lots of points thank you :)
please help and write explanation :)
Answer: The original price of the fridge is $585
Explanation:
Given she discounts all prices of the fridges by 20%
This 20% is the reduced price of the original cost.
Solve for per unit:
20% ⇒ $117
1% ⇒ $(117/20) = $5.85
Recall, the original price is always of 100%
100% ⇒ $5.85 × 100 = $585
Answer:
$585
Step-by-step explanation:
If there is a discount of 20% and the price is reduced by $117, then that means :
20% of Original Price (T) = $1170.2T = 117T = 117/0.2T = 117 x 5T = $585An airplane flew 2,304 miles in 6 hours.
How many miles did it fly per hour?
A. 416 miles per hour
B. 384 miles per hour
C. 379 miles per hour
D. 367 miles per hour