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Related Questions
Share £747 in the ratio 2:7 between Tom and Ben
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747 / 9 =83
83 * 2 = 166
83*7 = 581
Tom gets 166 and Ben gets 581
9x=747 x83
((83(2)=166/83(7)518))
A rectangular prism has a length of 12 in., a width of 5 in., and a height of 4 1/4 in.
The prism is filled with cubes that have edge lengths of 1/4 in.
How many cubes are needed to fill the rectangular prism?
Enter your answer in the box.
To fill the rectangular prism, how many cubes are needed.
Answers
Answer:
64
Step-by-step explanation:
took the test
Share £747 in the ratio 2:7 between Tom and Ben
Answers
then 373.5 in a ratio = 3:7
The correct answer is £166, £581.
To share £747 in the ratio of 2:7 between Tom and Ben.
Let's define the total parts: 2 + 7 = 9
Tom's share: [tex]\frac{2}{9} \times 747 = \frac{1494}{9} = £166[/tex]
Ben's share: [tex]\frac{7}{9} \times 747 = \frac{5229}{9} = £581[/tex]
Therefore, the calculation to share £747 in the ratio of 2:7 between Tom and Ben is:
[tex]\text{Tom's share} &= \frac{2}{9} \times 747 = \frac{1494}{9} = £166[/tex]..
[tex]\text{Ben's share} &= \frac{7}{9} \times 747 = \frac{5229}{9} = £581\end{aligned}[/tex]
Where Tom receives £166, and Ben receives £581.
A hockey game between two teams is 'relatively close' if the number of goals scored by the two teams never differ by more than two. In how many ways can the first 12 goals of a game be scored if the game is 'relatively close'?
Answers
This question falls under the combinatorial mathematics branch. Due to the complex nature of the problem which involves permutations and combinations, it's necessary to use a systematic approach or a computer algorithm to find the total number of scoring sequences that keeps the game 'relatively close'. Hence, the actual numerical answer would require a stronger background in combinatorics.
Explanation:This question belongs to the subject of combinatorial mathematics, particularly involving permutations and combinations. In this scenario, 'relatively close' is defined as the number of goals scored by the two teams never differing by more than two. The total number of goals scored in the game is twelve.
Let's denote the two teams as Team A and Team B. The game can start in three ways: either Team A scores twice, Team B scores twice, or each team scores once. After that, at any point, the next goal can either maintain the score within the 'relatively close' range of two goals or equalize the score.
Determining the total number of scoring sequences under these conditions requires generating a tree diagram and counting all the possible paths, subject to the condition that the absolute difference between the number of goals for the two teams does not exceed two at any stage. Due to the combinatorial complexity, this task could be difficult without using a systematic approach or computer algorithm.
Therefore, to actually answer this question, one would require a stronger background in combinatorics, and most likely the assistance of programming or mathematics software to execute a brute force count or implement a more advanced mathematical solution.
Learn more about Combinatorial Mathematics here:https://brainly.com/question/32415345
#SPJ5
a bird is in a tree 30 feet off the ground and drops at Twigs at lands on a rose bush 25 ft below. the function h(t)=-16t^2+30, where T represents the time in seconds gifts the height H and feet of The Twig above the ground as it falls when will The Twig land on the bush
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First, we will start with what we are given the equation: h(t) = -16t^2 + 30
Now, we should input a 5 for the h(t) because we want the seconds that will give us a height of 5 seconds.
5 = -16t^2 + 30
Solve the equation:
0 = -16t^2 + 25
To solve this, you could use the quadratic formula or factor out a -1 and you will have the difference of two squares.
Either way the answer is 1.25 seconds.
Answer:
After 1.25 seconds the twig land on the bush.
Step-by-step explanation:
Given function that shows the height of twig from the ground after t seconds,
[tex]h(t)=-16t^2+30[/tex]
When twig is on the bush,
h(t) = 5 feet ( ∵ the distance from bush to ground = 30 - 25 = 5 feet )
[tex]\implies -16t^2+30=5[/tex]
[tex]-16t^2=-25[/tex]
[tex]t^2=\frac{25}{16}[/tex]
[tex]\implies t=\pm \frac{5}{4}[/tex]
Since, time can not be negative,
Hence, t = [tex]\frac{5}{4}[/tex] ≈ 1.25
Therefore, after 1.25 seconds the twig land on the bush.
Maria spent 4/7 of her money on a book and saved the rest. What fraction of her money did Maria save?
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Since all, or one whole of a book is equal to 1, we subtract:
1 - 4/7 = 3/7
So, Maria has 3/7 of her money left.
Hope this helps!
Maria spent 4/7 and saved the rest, so you can subtract 7 and 4 to find out what fraction of her money she saved . . .
7 - 4 = 3 <-------
This means 3/7 of her money was saved.
3/7 is the fraction of money Maria saved.
Hope this helps you.
Have a great day!
HELP ASAP PLEASE HELP FAST
I want to exchange $500 to yen. How many yen will I receive if the rate of a Japanese yen to the U.S. dollar is 116.22 to 1?
A. 58,115 yen
B. 58,110 yen
C. 5,811 yen
D. 4.3 yen
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58110 Is the Answer.
if an arc has a measure of 97° and the circle has radius = 10, what is the arc length
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97/360 x 62.8 = 16.92
arc length = 16.92 ( round answer as needed)
Final answer:
The arc length of a circle with a radius of 10 units and a central angle of 97° is calculated using the formula for arc length, yielding an arc length of approximately 16.975 units.
Explanation:
The question asks us to find the arc length of a circle with a certain radius when a central angle is given. To find the arc length, we use the formula:
Arc length (s) = (θ/360) × 2πr
Where θ is the central angle in degrees, r is the radius of the circle, and π is approximately 3.14159. Since we know the central angle is 97° and the radius is 10, we can plug these values into the formula:
s = (97/360) × 2×π×10
s ≈ (97/360) × 2× 3.14159 × 10
s ≈ 16.975
Therefore, the arc length is approximately 16.975 units.
Find the area of the triangle or quadrilateral.
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A = 1/2 · h · (b₁ + b₂)
A = area
h = height
b₁ = base 1
b₂ = base 2
Plug in the numbers given for trapezoid AWEV
1/2 · 3 · (3 + 6)
Then solve
1/2 · 3 · 9 = 13.5
The area of trapezoid AWEV = 13.5 ft²
Follow the same steps for the second trapezoid (Trapezoid EFGH)
A = 1/2 · h · (b₁ + b₂)
A = area
h = height
b₁ = base 1
b₂ = base 2
Plug in the numbers given for trapezoid EFGH
1/2 · 4 · (13 + 8)
Then solve
1/2 · 4 · 21 = 42
The area of trapezoid EFGH = 42 ft²
please help and explain how u got your answer :)
Answers
square=area of 16
triangle=base times height divided by 2
triangle=24/2
triangle =12
28yd^2
Square Area= a^2
=(4)^2
=16 yards squared
Triangle Area= 1/2 base * height
add 4 yards + 4 yards to equal whole side of triangle
=1/2 (6)(4+4)
=1/2(6)(8)
=1/2(48)
=24 yards squared
Add the area of the square and the area of the triangle together.
=16 + 24
=40 yards squared
ANSWER: 40 yards squared (second choice)
Hope this helps! :)
Angles ABC is dilated using scale factor of 2. what happens to its angle measures?
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When you are dilating a shape you are simply making the sides larger or smaller. However, the angles will remain the same.
Imagine a stop sign being made twice as large. The side would be twice a long, however all of the angles will remain the same.
Good luck,
MrEQ
radical functions. please help me!
Answers
1) Quesion 1:
9+√2
---------
4 - √7
Answer: the third option:
36 + 9√7 + 4√2 + √14
-----------------------------
9
Explanation:
Multiply both numerator and denominator by the conjugate of the denominator.
The conjugate of 4 - √7 = 4 + √7
=>
[tex] \frac{9+ \sqrt{2} }{4- \sqrt{7} } . \frac{4+ \sqrt{7} }{4+ \sqrt{7} } = \frac{(9)(4)+9 \sqrt{7}+4 \sqrt{2} + \sqrt{2} . \sqrt{7} }{(4)^2-( \sqrt{7})^2 } =[/tex]
[tex]= \frac{36+9 \sqrt{7} +4 \sqrt{2} + \sqrt{14} }{16-7} [/tex]
2) Question 2: sum
[tex]5x (\sqrt[3]{x^2y})+2( \sqrt[3]{x^5y})[/tex]
Answer: fourth option
[tex]7x( \sqrt[3]{x^2y} )[/tex]
Explanation:
Take x^5 out of the second radical which will result in a like term of the first radical:
[tex]5x( \sqrt[3]{x^2y} )+2( \sqrt[3]{x^5y}) =5x( \sqrt[3]{x^2y} )+2x( \sqrt[3]{x^2y})=7x( \sqrt[3]{x^2y}) [/tex]
which is the fourth option
3) Question 3. Which expression is equivalent to:
[tex] \frac{ \sqrt{10} }{ \sqrt[4]{8} }[/tex]
Answer: the first option
Explanation
[tex] \frac{ \sqrt{10} }{ \sqrt[4]{8} } = \frac{ \sqrt[4]{10^2} }{ \sqrt[4]{8} } = \frac{ \sqrt[4]{100} }{ \sqrt[4]{8} } . \frac{ \sqrt[4]{8^3} }{ \sqrt[4]{8^3} } = \frac{ \sqrt[4]{(100)(512)} }{8} = \frac{ \sqrt[4]{51200} }{8} = \frac{4 \sqrt[4]{200} }{8} = \frac{ \sqrt[4]{200} }{2} [/tex]
4) Question 4 What is the simplest form?
Answer: the second option
Explanation:
[tex] \sqrt[4]{81x^8y^5}=x^2 y\sqrt[4]{3^4y} =3x^2y \sqrt[4]{y} [/tex]
5) Question 5 Product
Answer: the fourth option:
[tex]104x^4+16x^4 \sqrt{30} [/tex]
Explanation:
Use the square of a binomial product: (a + b)^2 = a^2 + 2ab + b^2
[tex](4x \sqrt{5x^2} )^2+2(4x \sqrt{5x^2})(2x^2 \sqrt{6}) +(2x^2 \sqrt{6} )^2=[/tex]
[tex]=16x^2(5x^2)+16x^4( \sqrt{30} )+4x^4(6)=80x^4+16x^4 \sqrt{30} +24x^4=[/tex]
[tex]=104x^4+16x^4 \sqrt{30} [/tex]
which is the fourth option.
6) Question 6 Product
Answer: fourth option
Explanation:
[tex] \sqrt[3]{16x^7} . \sqrt[3]{12x^9} = \sqrt[3]{2^4.2^2.3x^7x^9} = \sqrt[3]{2^6.3.x^{16}}=2^2 x^5 \sqrt[3]{3x} =4 x^5\sqrt[3]{3x} [/tex]
which is the fourth option.
7) Question 7. Simplified form of 2√18 + 3√2 + √162
Answer: 18√2
Explanation:
[tex]2 \sqrt{18}+3 \sqrt{2} + \sqrt{162}=2(3) \sqrt{2} + 3 \sqrt{2} +9 \sqrt{2} =18 \sqrt{2} [/tex]
which is the second option.
8) Question 8 which function is undefined for x = 0.
Answer: second option y = √ (x - 2)
Explanation.
The square root function is not defined for negative values.
When x = 0, x - 2 = -2, whose square root is not defined.
Therefore, the square root of x - 2 is not defined for x = 0.
if x <0, which integer does not satisfy the inequality x+2 <1
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x<1-2
x<-1
-1 does not satisfy the inequality because though-1 is lesser than 0 but not lesser than -1.
Answer:x+2<1x<1-2x<-1-1 does not satisfy the inequality because though-1 is lesser than 0 but not lesser than
Plz help me with this
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or 3.3repeating
or 10/3
Select all that apply. Which of the following decimal numbers are examples of terminating decimals? Here is all the choices... 0.6868 14.1 832.15902... 23.7 9.125 1,087.59014
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Explain what each variable in the formula represents.
Will give brainlist
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Hi where is the formula.
Part 1:
P is the principal amount of the loan
i is the interest rate of the loan
t is the term of the loan
Part 2:
Increasing the principal and interest rate will result to a higher monthly payment. Increasing the term of the loan will produce the opposite result.
what is the area of this trapezoid
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8 + 3 = 11 * 12 = 132
Hope it helps
You sell 3 hamburgers at $2.10 each plus 0.38 tax. A customer gives you a $10.00 bill. How much change does he get?
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Given is the Rate of each hamburger = 2.10 dollars each.
The number of hamburgers that we sell = 3 hamburgers.
Charges for all 3 hamburgers = 3 x 2.10 = 6.30 dollars.
Tax charged on these 3 hamburgers = 0.38 dollars.
Total Bill = Charges for 3 hamburgers + Tax
Total Bill = 6.30 + 0.38 = 6.68 dollars.
Customer paid = 10 dollars.
The amount to be returned to customer = Bill paid by customer - Total Bill charged = 10 - 6.68 = 3.32 dollars.
Hence, the customer would get a change of 3.32 dollars.
a picture of a school mascot is 18 in. Wide and 24 in. Long. It is enlarged proportionally to banner size. If the width is enlarged to 63 in., what is the length of the banner?
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find the value of this pronumeral
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x = 70 ;
y = 50 .
_____________________________________________________
Explanation:
_____________________________________________________
y = 50 ; since vertical angles are congruent.
180 – (50 + 60) = x ; since all angles in any triangle add up to 180 degrees.
↔ x = 180 – (50 + 60) = 180 – (110) = 70.
_____________________________________________________
I really need the answer I’ve been stuck on this all day
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You do 72/6 which is 12.
So the answer is 12
Hope this helps!
The area is 72
72=6*b
Base= 12
Two angles are complementary. If the measure of one angle is twice the measure of the other angle, what is the measure of the larger angle?
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x = 2y
plug in 2y for x
2y + y = 90
3y = 90
3y/3 = 90/3
y = 30
plug in 30 for y
x = 2y
x = 2(30)
x = 60
x (the largest angle) = 60°
hope this helps
Answer:
70 is the answer choise I picked it and got it correct
Step-by-step explanation:
7.2 + ( -5.55) = -5.5 + 7.2 identify what property is shown
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Help I don’t understand
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By what percent will a fraction increase if its numerator is increased by 60% and its denominator is decreased by 20%?
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= 160% * 5/4
= 200%
80%hope this hell
The period T of a pendulum in seconds depends on its length L in feet, and is given by the formula T=
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T = 2πsqrt(7/32)
T = (6.28319...)(0.46771...)
T is about 2.93871 seconds
Suppose a ball is completely submerged inside a cylinder filled with water displacing some of the water in the cylinder. Assume the ball and the cylinder both have a diameter of 10 centimeters, and the diameter of the ball is the same as the height of the cylinder. Determine the volume of water that can remain in the cylinder after the ball is inserted so that the water rises to the top edge of the cylinder without spilling
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.. Vc = πr²×(2r) = 2πr³
In terms of radius, the volume of the sphere is
.. Vs = (4/3)πr³
Then the volume of water is the difference
.. Vw = Vc -Vs
.. = (2 -4/3)πr³
.. = (2/3)πr³
For the given dimensions, this is
.. Vw = (2π/3)*(5 cm)³
.. = 250π/3 cm³
.. ≈ 261.8 cm³ . . . . . . . . volume of water in the cylinder
Answer:the volume of cylinder is 785
volume of the sphere is 523.33
the volume of the water that can remain is 261.8
Step-by-step explanation: algebra nation answer
Milo's pancake recipe makes 9 servings. It calls for 3/4 cup milk. Milo wants to make 6 servings. How much milk will he need?
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It says that the recipe for 9 servings would require 3/4 cup milk.
He wants to prepare recipe for 6 servings. Let's assume it requires X cups milk.
Now we can use concept of proportions to solve this problem.
The proportion of X cups for 6 servings would be same as 3/4 cup milk for 9 servings. Mathematically, we can write it as follows :-
[tex] \frac{X \;cups \;milk}{6 \;servings} = \frac{\frac{3}{4} \;cups \;milk}{9 \;servings} \\\\
Or\; \frac{X \;cups \;milk}{\frac{3}{4} \;cups \;milk} = \frac{6 \;servings}{9 \;servings} \\\\
\frac{X }{\frac{3}{4} } = \frac{6 }{9 } \\\\
X = \frac{6}{9}*\frac{3}{4} \\\\
X = \frac{6*3}{9*4} \\\\
X = \frac{18}{36} \\\\
X = \frac{1}{2} \;cup \;milk [/tex]
Hence, we require [tex] \frac{1}{2} [/tex] cup milk for 6 servings.
9x+10y=29
10x+9y=28
Solve by elimination
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[tex](10x + 9y = 28) - 10[/tex]
[tex]81x + 90y = 261[/tex]
[tex] - 100x - 90y = - 280[/tex]
[tex] - 19x = - 19[/tex]
[tex]x = 1[/tex]
[tex]9(1) + 10y = 29[/tex]
[tex]9 - 9 + 10y = 29 - 9[/tex]10y=20
y=2
Given: ΔABC; a= 10; b = 4, and c = 11. Find the measurement of ∠B to the nearest tenth of a degree. A) 21.3° B) 24.7° C) 25.1° D) 31.4°