Answer:
The volume of existing cage = length x widht x height = 3 x 2 x 3 = 18 cubic ft
Now she wants cage with volume four times of this cage
New Volume = V1 = 18 x 4 = 72 cubic ft
Keeping length same = 3 ft
Length x width x height = V1
3 x Width x height = 72
Width x height = 72 /3
Width x height = 24
Now multiple of 24 must be the width and height.
Taking width = 6 ft and height = 4 ft, we will get our answer
Proof:
Length x width x height = V1
3 x 6 x 4 = 72
Together they ran a total of 30 laps. Runner B ran 6 more than twice as many laps as Runner A. Part A: Write an equation for this situation. Use a variable to represent the number of laps for Runner A. Part B: How many laps did Runner A run? Part C: How many laps did Runner B run?
Answer:
Step-by-step explanation:
Number of laps run by Runner A = x
Number of laps run by Runner B = y
Runner B ran 6 more than twice as many laps as Runner A.
b = 6 + 2a
Together they ran a total of 30 laps.
a + b = 30
Part A: Write an equation for this situation. Use a variable to represent the number of laps for Runner A.
Part B: How many laps did Runner A run?
a + b = 30
b = 6 + 2a
Hence:
a + 6 + 2a = 30
3a = 30 - 6
3a = 27
a = 27/3
a = 9 laps
Part C: How many laps did Runner B run?
a + b = 30
b = 30 -9
b = 21 laps
please help with numbers 5-18..ik its a lol but please this a 4 page packet and please show work
Answer:
5-18 answers below ↓
Step-by-step explanation:
5) 14/2=7
7^2=49
10^2=100
h^2+49=100
-49 -49
h^2=51 h=✓51= 3•17
6) 48/2= 24
24^2=576
44^2=1936
h^2+576=1936
-576 -576
h^2=1360 h=✓1360= 4•340
7) 24^2+b^2=32^2 (leg is short side & hypo.. is long side)
576+b^2=1024
-576 -576
b^2= 448 b=✓448=4•112 length of 3rd side it's hypo..
8) 24^2+b^2=45^2
576+b^2=2025
-576 -576
b^2=1449 b=✓1449=9•161 length of 3rd side hypo..
9) 40^2+b^2=85^2
1600+b^2=7225
-1600 -1600
b^2=5625 b^2=✓5625 b=75 length of 3rd side leg
10) 49^2+b^2=168^2
2401+b^2=28,224
-2401 -2401
b^2=25,823 b=✓25,823 b=49•527 length of 3rd side hypo..
11) 72^2+b^2=78^2
5184+b^2=6084
-5184 -5184
b^2=900 b=✓900=30 length of 3rd side leg
12) 7^2+x^2=10^2
49+x^2=100
-49 -49
x=51=3•17
13) 12^2+x^2=28^2
144+x^2=784
-144 -144
x=✓640=4•160
14) 44^2+x^2=52^2
1936+x^2=2704
-1936 -1936
x=✓768=4•192
15) 120^2+h^2=125^2
14,400+h^2=15,625
-14,400 -14,400
h^2=1,225 h=✓1225 h=35
16) might be wrong but worth a try 8+8=16
16^2+x^2=16^2
256+x^2=256 x=0 don't know these challenge ones sorry, but the rest of the questions are correct hope this helps u (:
Your classmates Sarah, Gene and Paul are proposing plans for a class fundraiser. Each presents his or her proposal for the amount of money raised, y, for x number of hours worked, in different ways.
Answer:
yx
Step-by-step explanation:
The answer is yx
We can draw the conclusion that linear functions can be used to represent each of the ideas. Due to the fact that each proposal's linear function has an initial value, the class now has money in its accounts (b).
What is "Linear Function" ?A linear function is denoted by the equation y = mx + b, where m is the slope or unit rate between the two variables, x and y, and b is the beginning value or y-intercept.
The initial value is b.
A linear function is a graph with straight lines.
A unit rate exists for all linear functions (b).
here, we have,
given that,
Sarah's suggestion can be expressed by a linear function because the graph that represents it is a straight line.
Gene's Proposal's table displays the unit rate as change in y/change in x = 7. As a result, a linear function can be used to express it.
Paul's idea has a linear function as its equation.
This leads us to the conclusion that linear functions can be used to represent each of the ideas.
Due to the fact that each proposal's linear function has an initial value, the class now has money in its accounts (b).
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The price of an object with 13% value added tax is 5763 . what will be the value added tax amount ? find it
Answer:
100. ~113
x ~ 5763(assume that X is price without VAT)
100×5763=113×x
X. =(5763×100)/113. (5763/113=51)
X= 51×100
X =5100
VAT=5763-5100
=RS.663
Given:
Interest rate,
13%Object price,
5763The value added tax will be:
→ [tex]\frac{13 \ percent}{100+13} = \frac{VAT}{5763}[/tex]
→ [tex]VAT = 5763\times \frac{0.13}{1.13}[/tex]
[tex]= 663[/tex]
Thus the approach above is right.
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PLEASE HELP!!! DISTRIBUTIVE PROPERTY
What is 1/8 x 5/6 x 4/5 you will need paper.
Answer:
This would equal [tex]\frac{1}{12}[/tex]
Step-by-step explanation:
We do this by just multiplying straight across
Numerators go first
[tex]1*5*4[/tex]
This equals 20
Now the denominators
This would be done by
[tex]8*6*5[/tex]
This equals 240
now all together this is
[tex]\frac{20}{240}[/tex]
Simplify
[tex]\frac{1}{12}[/tex]
A trapezoid with an area of 36 inches squared.
What is the area of the enlarged trapezoid?
54 in.²
81 in.²
576 in.²
864 in.²
Answer:
B. 81 in.²
Step-by-step explanation:
We have been given that the trapezoid shown in the attachment has been enlarged by a scale of 1.5. We are asked to find the area of the enlarged trapezoid.
The area of the original trapezoid is 36 square inches.
Since each side of the trapezoid is enlarged 1.5 times, so the area of new trapezoid would be 2.25 times greater than area of original trapezoid.
The area would be 2.25 times greater because area is product of sum of lengths of parallel sides and height.
1.5 × 1.5 = 2.25
Area of new trapezoid: 2.25 × 36 in²
Area of new trapezoid = 81 in²
The area of the enlarged trapezoid would be 81 in² or option B.
4. Kevin can clean a large aquarium tank in about 9 hours. When Kevin and Lara
work together, they can clean the tank in 6 hours. Write a rational equation that
could be used to determine how long it would take Lara to clean the tank if she
works by herself. You do not have to solve the equation. You may solve the
equation for extra credit.
Answer:
Part A
The rational equation that can be used to determine how long it would take Lara to clean the tank alone is; 6/9 + 6/x = 1
Part B
It would take Lara 18 hours to clean the tank if she works by herself
Step-by-step explanation:
Part A
The time it takes Kevin to clean an aquarium tank alone = 9 hours
The time it takes Kevin and Lara to clean the tank together = 6 hours
Let '1/x' represent Lara's cleaning rate, we have;
The time it would take Lara to clean 1 tank alone = 1/(1/x) = x
Kevin's cleaning rate, y = 1/9 tank per hour
The number of tanks, z = tank
The total time it takes both of them to clean the tank, t = 6 hours
Therefore, we get;
t × y + t × 1/x = z
When t = 6, y = 1/9, and z = 1, we get;
6 × (1/9) + 6·(1/x) = 1
Therefore, the rational equation that can be used to determine how long it would take Lara to clean the tank if she work by herself, '1/x', is given as follows;
6/9 + 6·(1/x) = 1
6/9 + 6/x = 1
Part B
Solving the rational equation gives;
1/x = (1 - 6/9)/6 = 1/18
∴ 1/x = 1/18)
∴ x = 18
The time it would take Lara to clean the tank if she worked by herself, x = 18 hours
PLEASE HELP WITH THIS AND SHOW WORK.
Answer:
RECT and ANGL are similar triangles with a ratio of 9:16, and for TR, we have TR:24 in the ratio 9:16 so TR = 13.5
Hope this helps!
What is the area of triangle ABC
Answer:
A = 24 cm²
Step-by-step explanation:
The area (A) of Δ ABC is calculated as
A = [tex]\frac{1}{2}[/tex] × AB × AC
Calculate AC using Pythagoras' identity
AC² + AB² = BC²
AC² + 6² = 10²
AC² + 36 = 100 ( subtract 36 from both sides )
AC² = 64 ( take the square root of both sides )
AC = [tex]\sqrt{64}[/tex] = 8
Then
A = 0.5 × 6 × 8 = 24 cm²
Car survey in a survey of 1200 people who owned a certain type of car,600 said they would buy that type of car again.What percent of people surveyed were satisfied with the car?
Answer:
50 percent
Step-by-step explanation:
Total number of people in this car survey = 1200
Total number of people who they would still buy same car type = 600 (these are the satisfied people)
The percentage = 600/1200 x 100
= 0.5 x 100
= 50 percent
So the percentage of satisfied people who would buy this type of car again is 50%
Two heads 35 Two tails 23 One head, One tail 52 What is the theoretical probability that a coin toss results in two heads showing?
Answer:
[tex]Pr = 0.25[/tex]
Step-by-step explanation:
Given
Two heads ---> 35
Two tails ---> 23
One head, One tail ---> 52
Required
The theoretical probability of 2 heads
When a coin is tossed, the probabilities are:
[tex]P(Head) = 0.5[/tex]
[tex]P(Tail) = 0.5[/tex]
So, the theoretical probability of 2 heads is:
[tex]Pr = P(Head) * P(Head)[/tex]
[tex]Pr = 0.5 *0.5[/tex]
[tex]Pr = 0.25[/tex]
Notice that the given parameters were not used. Using them will only give us the result of the experimental probabilities, because they are recorded from an experiment
Gracie and Mark are having a
contest to see who can sell the most
cupcakes. For every 3 that Mark
sold, Gracie sold 4. If Gracie sold 4
more than Mark, how many total
cupcakes were sold?
Answer:
Mark sold 12 cupcakes, meaning Gracie sold 16.
4 threes, and 4 fours.
Mark Gracie
O O O O O O O
O O O O O O O
O O O O O O O
O O O O O O O
Answer:
Step-by-step explanation:
m/g=3/4
m=3g/4, now we can express m in terms of g
g=4+m, using m found above in this equation gives you
g=4+(3g)/4
4g=16+3g
g=16, since m=3g/4
m=3(16)/4
m=48/4
m=12
So total cupcakes sold is 12+16=38.
38 cupcakes were sold.
If g(x)=−5x2−11 and f(x)=10x+5, find (f⋅g)(x).
Answer: -50x^3 - 25x^2 - 110x - 55
Step-by-step explanation: brainliets if its right
kevin's garden is rectangular and measures 12 metres by 15 metres. He plans to lay new turf in the garden which will cost £8 per square metre. how much turf will he need to buy and how much will this cost?
Answer:
Kevin’s garden is rectangular and measures 12 metres by 15 metres. He plans to lay new turf in the garden which will cost £8 per square metre. How much turf will he need to buy and how much will this cost? 4)Inga needs to buy enough skirting board to replace the old skirting board in her bedroom. The bedroom is 5m 20cm long and 4m 80cm wide.
Step-by-step explanation:
please anyone know anything abt geometry i really need it
Answer:
8,14,9 = yes
8 + 14 > 9 ✅
17,4,13 = yes
17 + 4 > 13 ✅
9,9,9 = yes
9 + 9 > 9 ✅
22,23,60 = no
22 + 23 > 60 ❌
If I have a meal that cost 6.14 and I have $8 how much change do I get
Answer:
8-6.14= 1.86
That's what you get
Answer:
you would get $1.86 back
I need help with this math problem ASAP plsssss helppp. The problem is attached below
Answer:
234.67 in³
Step-by-step explanation:
volume of full sphere = 4/3(π)(r³) = 4/3(3.14)(5³) = 523.33 in³
volume of half sphere = 523.33/2 = 261.67 in³
volume of cube = LWH = 3³ = 27 in³
261.67 - 27 = 234.67 in³
What is the surface area of the rectangular prism?
36 cm²
108 cm²
72 cm ²
54 cm²
Answer:
SA = 108cm² (the 2nd option)
Step-by-step explanation:
h = 4
l = 3
w = 6
SA = 2(lw + lh + wh)
SA = 2((3)(6) + (3)(4) + (6)(4))
SA = 2(18 + 12 + 24)
SA = 2(54)
SA = 108cm²
The surface area of the rectangular prism is 108cm².
Calculation of the surface area of the rectangular prism:Since
height = 4
length = 3
width = 6
So, here the surface area is
SA = 2(lw + lh + wh)
= 2((3)(6) + (3)(4) + (6)(4))
= 2(18 + 12 + 24)
= 2(54)
= 108cm²
hence, The surface area of the rectangular prism is 108cm².
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Lamar used 7/8 of a cup of raisins to make snacks mix. he used 3/4 of a cup of raisins to make cookies what expression could be used to determine the amount of raisins in cups Lamar used together
A: 7/8 + 3/8
B: 7/8 + 6/8
C: 7/12 + 3/12
D: 11/12 + 11/12
I NEED TO KNOW NOWW PLEASEEE!!!!
NEED HELP ASAP!! Please show steps and answer correctly! :)
One car traveled 240 miles and drove 20 mph hour faster than a second car drove 160 miles. If the cars were traveling for the same time, how fast was the first car traveling?
Answer:
190
Step-by-step explanation:
Jake's parents want $100,000 at the end of 40 years. They put their money in an account that yields 4% per year compounded continuously. How much money should jakes parents deposit?
Answer:
$ 20,189.65
Step-by-step explanation:
Jake's parents want $100,000 at the end of 40 years. They put their money in an account that yields 4% per year compounded continuously. How much money should jakes parents deposit?
From the above question, we are to find the Principal. The formula for Principal compounded continuously =
P = A / e^rt
Where:
A = Amount after time t = $100,000
r = Interest rate = 4%
t = Time in years = 40 years
First, convert R percent to r a decimal
r = R/100
r = 4%/100
r = 0.04 per year,
Then, solve our equation for P
P = A / e^rt
P = 100,000.00 / e ^(0.04×40)
P = $ 20,189.65
Therefore, the amount Jake's parents should invest = $ 20,189.65
Select all values that would make the following inequality true: x ≥ -10
-10
-14
-2
0
Answer: -10; -2; 0
Step-by-step explanation:
≥ means greater or equal than.
-10 is equal -10, true.
-14 is less than -10, so false.
-2 is greater than -10, true
0 is greater than -10, true
so the answer is -10, -2 and 0 can make this inequality true.
Estimate the quotient.6.2 ÷ 8
Answer:
0.775
Step-by-step explanation:
is 5he answer
Step by step
Please help with this! Please don't get it wrong T0T
Answer:
45
Step-by-step explanation:
angle E is 115
angle C and B 20 degrees
180 - 135= 45
Shalini blusex batting scores were 13144 155 142 167 172 what was his score
Figure ZANY is a square. If ZY = 7x - 3 and ZA = 6x, what is the value of x
Rectangle QUAD has coordinates Q(0,0), U(0,2), A(7,3), and D(7,0). Q'U'A'D' is the image of QUAD after a dilation with center (0,0) and scale factor 6. What are the coordinates of point U '?
Answer:
U': (0 , 12)
Step-by-step explanation:
(0 , 2) -> (0*6, 2*6) -> (0 , 12)
Craig collects stamps he collected a total of 150 stamps if 88% of the stamps be collected were foreign how many stamps did he collect
Answer:
18 Non Foreign Stamps
Step-by-step explanation:
Given data
Total stamps= 150
Foreign Stamps= 88% of the total stamps
Hence the number of foreign stamps is
=88/100*150
=0.88*150
=132 Foreign Stamps
The number of stamps that is Non Foreign Stamps is
=150-132
=18 Non Foreign Stamps
Find the volume of the pentagonal base is 33.5 cm2 and the height of the prism is 15 cm. Do not include units in your answer.
Answer:
[tex]V=502.5\ cm^3[/tex]
Step-by-step explanation:
The area of the pentagonal base, A = 33.5 cm²
The height of the prsim,h = 15 cm
We need to find the volume of the pentagonal base prism. The formula for the volume of the pentagonal base prism is given by :
[tex]V=A\times h\\\\V=33.5\times 15\\\\V=502.5\ cm^3[/tex]
So, the required volume is [tex]502.5\ cm^3[/tex].