The recommended mass of a Soccer ball is 0.43 kilogram. The actual mass is allowed
to vary by up to 20 grams.
a. Write and solve an absolute value equation to find
the minimum and maximum acceptable soccer ball
masses.
b. A soccer ball has a mass of 423 grams. The soccer
ball loses 0.016 kilogram of mass over time. Is the
mass now acceptable? Explain.
The absolute value equation is:
|M - 430g| = 20g
And the solutions are M = 410g and M = 450g
b) No, the mass is not acceptable.
How to write the absolute value equation?We know that the recomended mass is 0.43kg, with an accepted error of 20 grams.
Where:
0.43kg = 0.43*1000g = 430g
Then the minimum mass accepted is: 430g - 20g = 410g
The maximum mass accepted is: 430g + 20g = 450g
These are the solutions, and the absolute value equation is, if M is the mass:
|M - 430g| = 20g
b) If the ball has a mass of 423g it is in the accepted range, if now it loses 0.016kg:
0.016kg = 0.016*1000g = 16g
The new mass is:
423g - 16g = 407g
This is smaller than the minimum accepted mass, then this mass is not acceptable.
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So i am have homework and it is asking me to show the ratios are equivalent by simplifying any 4 of them and i am stuck in that one i don't understant that can you help me pls can u explain me
The ratios are shown equivalent as by simplification done below.
Ratio is the representative of comparison of part of things in a complete thing. Equivalent ratios are collection of ratios that show same comparison. As per the given question, the equivalent ratios are calculated as follows -
First column -
Ratio = 6:2
Dividing both the parts of ratio by 2
Ratio = 3:1
Second column -
Ratio = 9:3
Dividing both the parts of ratio by 3
Ratio = 3:1
Third column -
Ratio = 12:4
Dividing both the parts of ratio by 4
Ratio = 3:1
Fourth column -
Ratio = 15:5
Dividing both the parts of ratio by 5
Ratio = 3:1
Similarly, for rest of the columns, division by 6, 7 and 8 of both parts of ratio will give the result 3:1. Hence, the given rations are shown as equivalent ratios, by simplifying into 3:1.
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The edge of a circular flower bed, 320 ft in diameter, needs mulch. How many cubic
yards (yd³) of mulch do you need if you want the mulch to cover 2 ft in from the edge to a
depth of 3.5 inches, all the way around
868.34 cubic yards (yd³) of mulch is needed to cover 2 ft in from the edge to a depth of 3.5 inches,
To calculate square feet for a circular area, measure the distance from the center of the bed to the outer edge (this is the radius R) .Then area is given by square meters of circular area = [tex]R\times R\times\ 3.14[/tex] ....(1)To determine the amount of mulch you need 1. Multiply the square feet of your bed by the number of inches of mulch you want to deep . 2. Divide this number by 324 . You will get the amount of mulch you need in a cubic yard.It is given that a circular flower bed, 320 ft in diameter which means radius[tex]=\frac{320}{2}= 160 \ ft[/tex]
Putting r = 160 in equation (1) , we get
[tex]A=160\times160\times3.14\\A=80384 \ ft \ sqaure \ units[/tex]
We need the mulch 3.5 inches deep
[tex]80384\times3.5=281344[/tex]
On dividing the above number by 324 , we will get the required cubic yards [tex]\frac{281344}{324} =868.34[/tex]
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i don’t get it help i need to understand it kinda confusing please help me if u don’t i’ll fail
Answer: Brainliest? It's a lot of questions
Step-by-step explanation:
7) 20*50 = 1000
8) 10^2 = 100
20*6=120
120>100
Yes, she will finish the reading in time because she will read 20 pages more than needed.
9) 10 x 20 x 30 x 40 = (1 x 10) x (2 x 10) x (3 x 10) x (4 x 10)
=(1 x 2 x 3 x 4) x (10 x 10 x 10 x 10)= 24 x 10000 = 240000
10) Called different things different places do yourself
11) (10^3 x 12) + (10^2 x 35)
=(1000 x 12) + (100 x 35)
=12000+3500
=15500
How do I work this out
Answer:
multiply simplify and work out the problem as slow as possible so you can get it right
Simplify the expression.
a + b + 2a + 2b + 5 - b
3a + 2b + 5
3a + 4b + 5
2a + 4b + 5
2a + 2b + 5
Answer:
the answer is 3a+2b+5.
I hope this will help
14/7 into mixed numbers
Is (2,-1) a solution of 2x-y=5? Explai
how your work.
Answer:
Yes, (2, -1) is a solution.
Step-by-step explanation:
Plug in 2 for x and -1 in for y and see if it is a true statement.
2x - y = 5
2(2) - (-1) = 5
4 - (-1) = 5 Subtracting a negative number is the same as adding a positive number
4 + 1 = 5
5 = 5 Since this statement is true, (2,-1) is a solution.
How many 5-letter words can be made from the letters WASTEFUL if
repetition of letters is allowed? And if repetition is not allowed
Answer w a s t e f u l
Step-by-step explanation:
theres 7 words on it
a rectangular plot of land measures 40.0 m by 120.0 m, with a parcel 10.0 m by 12.0 m out of one corner for an electrical transformer. what is the area, in meters squared, of the remaining plot?
The area of the remaining rectangular plot of land is 4680m²
Area of rectangle:
Area of rectangle means the area covered by the rectangle.
The formula for area of rectangle is
A = l x b
where,
l is the length of the rectangle
b is the breadth or width of the rectangle
Given,
A rectangular plot of land measures 40.0 m by 120.0 m, with a parcel 10.0 m by 12.0 m out of one corner for an electrical transformer.
Here we need to find the remaining area of the rectangular plot land.
For that first, we have to find the area of each separately,
Like,
The area of the rectangular plot is,
A₁ = 40.0 x 120.0 m²
A₁ = 4800m²
Similarly, the area of the electric transformer is,
A₂ = 10.0 x 12.0 m²
A₂ = 120m²
Now the remining area is,
A = A₁ - A₂
A = 4800 - 120 m²
A = 4680m²
Therefore, the area of the remaining rectangular plot is 4680m².
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Randy's swimming coach kept track of his average 50-meter lap times during the first 3 weeks of training. How much greater was the percent of change from Week 1 to Week 2 than from Week 2 to Week 3? Round to the nearest tenth of a percent.
The percent of the first change is greater by 2.36%.
Time in 1st week = 28.8 sec
Time in 2nd week = 27.6 sec
Time in 3rd week = 27.1 sec
∴ Change of time from week 1 to week 2 = (28.8 - 27.6) sec
= 1.2 sec
∴ Percent of change from week 1 to week 2 = [tex]\frac{time change}{1st week time} \times 100[/tex] %
= [tex]\frac{1.2}{28.8} \times 100[/tex] %
= 4.17%
∴ Change of time from week 2 to week 3 = (27.6 - 27.1) sec
= 0.5 sec
∴ Percent of change from week 2 to week 3 = [tex]\frac{Time change}{2nd week time} \times 100[/tex] %
= [tex]\frac{0.5}{27.6} \times 100[/tex] %
= 1.81%
∴ The greater change was in the first week. The amount by which it was greater is = (4.17 - 1.81) %
= 2.36%
Answer) The percent of the first change is greater by 2.36%.
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a region is bounded by semicircular arcs constructed on the side of a square whose sides measure $2/\pi$, as shown. what is the perimeter of this region?
The perimeter of this region is 4.
What is perimeter?playing a card game, set of cards that are numbered or outlined (or both) and are utilized for messing around, for schooling, for divination, and for conjuring. Generally, Western playing a card game are made of rectangular layers of paper or slight cardboard stuck together to frame a level, semirigid material. Some have proposed that the playing a card game previously worked as "play cash" and addressed the stakes utilized for other betting games, and later turned out to be essential for the actual games. Others have proposed associations between playing a card game and chess or dice games, yet this is again theoretical. Different games, for example, a 25-card variation of Euchre which involves the Joker as the most elevated trump, make it one of the main in the game. Frequently, the Joker is a special case, and subsequently permitted to address other existing cards.
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Evaluate the expression when x=3 , y=−4 , and z=−6.
z−2xy=
x = 3 , y = −4 , and z = −6
z-2xy =
Substitute the value of x,y and z in the expression.
-6-2(3)(-4)
-6-2(-12)
-6+24
18
Cuánto es 15–4(n–2)=27
Answer:
tu respuesta es -1
Step-by-step explanation:
15-4(n-2) =27
15-4n+8=27
15-4n+8=27
23-4n=27
-4n+23=27
-4n+23-23=27-23
-4n=27-23
-4n=4
[tex]\frac{-4}{4} \frac{4}{4}[/tex] =-1
Any genius willing to help :) , I'll give you a brainliest if you do.
Answer:
00
Step-by-step explanation:
Find the square root of 0.81
A. 0.009
B. 0.09
C. 0.9
D. 9
Answer: C. 0.9
I used a caculator.
26 divided by 7,254 i need help
Answer:
279, Remainder 0
Step-by-step explanation(Using long division):
[tex]72 - 52(26 \times 2) = 20\\20(5) - 182(26 \times 7) = 23\\23(4) - 234(26 \times 9) = 0(Remainder)\\= 279\\= R=0[/tex]
Hiroshi and Giulio share a common investment goal and once they reach their goals, they will withdraw their money.
Giulio starts out with 3
3
times as much money as Hiroshi and it takes Hiroshi 5
5
times longer than Giulio to reach this goal.
They both use the same bank that provides a 5
5
% annual interest rate compounded quarterly.
Work out how long it takes Hiroshi to reach his investment goal?
Give your answer correct to the nearest year.
It takes Hiroshi 30 years to reach his investment goal.
The formula for calculating the amount received on the principal amount (P) after t years at r% rate of interest is-
Amount = P(1 + r/100)^t
Let the principle amount with Hiroshi be P
then, the amount that Giulio starts with = 3P
Let time period for Giulio's investment = t
Then, the time period for Hiroshi's investment = 5t
Rate = 5%
As the investment goals of both the people are equal, they will get the same amount.
Therefore, we get the following equation-
P(1 + 20/100)^5t/4 = 3P(1 + 20/100)^t/4
(1 + 20/100)^5t/4 = 3(1 + 20/100)^t/4
[(1 + 20/100)^5t/4] /[(1 + 20/100)^t/4] = 3
(1 + 20/100)^(5t/4- t/4) = 3
(1 + 20/100)^(4t/4) = 3
(1 +0.2)^t = 3
(1.2)^t = 3
Taking log on both sides-
Log (1.2)^t = log 3
t log 1.2 = log 3
t = log 3/ log 1.2
t = 6.025
Time taken by Hiroshi to reach his investment goal = 5t
= 5(6.025)
= 30.128
Thus, it takes Hiroshi 30 years to reach his investment goal.
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The width of a rectangle is five less than three times the length of the rectangle. If the perimeter of the rectangle is 70 inches what are the dimensions of the rectangle?
Step-by-step explanation:
Do you mean width equal 5
a certain composer wrote 10 symphonies, 4 piano concertos (music for piano and orchestra), and 35 piano sonatas (music for solo piano). a. how many ways are there to play first a symphony and and then a piano concerto? b. the manager of a radio station decides that on each successive evening (7 days a week), a symphony will be played followed by a piano concerto followed by a piano sonata. for how many nights could this be carried out before exactly the same program would have to be repeated? about how many years would this be? (round to the nearest year).
(a) According to the question, a composer wrote [tex]10[/tex] symphonies, [tex]4[/tex] piano concerts (piano and orchestra) and [tex]35[/tex] piano sonatas (solo piano):
Here, determine how many ways are there to play first a symphony and then piano concerto.
So, the probability is [tex](10P1) (4P1) = (10)(4)= 40[/tex]
Therefore, there are [tex]40[/tex] ways to play first a symphony and then piano concerto.
(b)The manager of a radio station decides that on each successive evening, a symphony will be played followed by a piano concerto followed by a sonata.
Here determine how many nights could be carried out before the same program would get repeated.
So, the probability would be [tex](35)(10)(4)=1440[/tex]
Therefore, [tex]1440[/tex] nights are carried out before the same program gets repeated.
Now, to calculate the years: [tex]\frac{1440 nights}{365days} = 3.95 years[/tex]
Therefore, it would be [tex]3.95[/tex] years.
What is probability?
Probability is the method to measure the occurred events or the occurrence of the events. It is also used to analyze the outcomes of random events. For example, to calculate the probability of a playing card which is 52 in numbers. And it is divided into four cards and each are in the count of 13.These four cards are heart, spades, diamond and club.
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) Find the value of x.
V
X+2
91°
44°
Step-by-step explanation:
remember, the sum of all angles in a triangle is always 180°.
and the sum of all angles around a single point on one side of a line is also always 180° (because that line is like a diameter of any circle with that point as center, and half a circle is 180°).
3)
the third inner angle of the triangle is
180 = 63 + 51 + angle = 114 + angle
angle = 66°.
x = 180 - 66 = 114°
4)
the third inner angle of the triangle is
180 = 86 + 45 + angle = 131 + angle
angle = 49°
x + 30 = 180 - 49 = 131°
x = 101
1. Turn this standard notation 25,000,000 into scientific notation.
Answer:
25,000,000 = 2.5 × 10^7
The ^ is raised to the power.
Hope this helps :)
Step-by-step explanation:
2.5 × 10^7 = 25,000,000
Gogglejaws can eat 36 fish in one minute.
How many fish could Gogglejaws eat in 2.2
hours?
Answer:
3752
Step-by-step explanation:
there are 60 minutes in an hour so multiply 2.2 times 60
2.2 • 60 = 132 minutes
132 min • 36 fish = 3752
Rosa ran the hurdles in 58.32 seconds. maya ran the hurdles in 54.078 seconds. what is the difference between the two times? 3.954 seconds 4.242 seconds 4.258 seconds 5.758 seconds
Answer:
Step-by-step explanation: 4.242
The difference of time taken by Rosa and Maya to ran the hurdles is 4.242 seconds .
The correct option is B .
Given, time taken by Rosa and Maya to ran the hurdles.
Time taken by Rosa to ran the hurdle = 58.32 seconds .
Time taken by Maya to ran the hurdle = 54.078 seconds .
Difference between the time taken:
Rosa is taking more time to cover the distance than Maya . Thus the speed of Rosa is less than the speed of Maya .
Relationship between speed, time and distance.
Distance = Speed × Time
Subtract time taken by Rosa to ran the hurdle from time taken by Maya to ran the hurdle.
= 58.32 - 54.078
= 4.242 seconds
Therefore the correct option is B .
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Solve for X
4(5x+6)=12
-3(2x-4)=18
26=2(3x-2)
The value of x in the equations are:
1. x = -3/5
2. x = -1
3. x = 5
How to Solve an Equation?Given the equations above, to solve for x, isolate x as the variable in the equation to one side of the equation.
a. 4(5x+6) = 12
Apply the distributive property
20x + 24 = 12
20x = 12 - 24
20x = -12
x = -12/20
x = -3/5
b. -3(2x - 4) = 18
Apply the distributive property
-6x + 12 = 18
-6x + 12 - 12 = 18 - 12
-6x = 6
x = 6/-6
x = -1
c. 26 = 2(3x - 2)
Apply the distributive property
26 = 6x - 4
26 + 4 = 6x
30 = 6x
5 = x
x = 5
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Where on the number line would you plot the square roots of the numbers 70, 85, 99, and 112?
a. 4
b. 5
c. between 4 and 5
d. between 64 and 125
We have to plot the square roots of the numbers 70, 85, 99, and 112 between 64 and 125 ( d )
First, we must evaluate the square root of given numbers.
√70 = √ ( 2 × 5 ×7 ) = 8.36
√85 = √ ( 5 × 17 ) = 9.22
√99 = √( 9 × 11 ) = 3√11 = 9.95
√112 = √( 4 × 4 × 7 ) = 4 √7 = 10.58
All these numbers ( 8.36, 9.22, 9.95 , 10.58 ) belong between, square roots of √64 and √125 which are 8 and 15. So we have to put these numbers in between the square roots of 64 and 125 on the number table.
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State the property that justifies the statement.
If x/3=-15, then x=-45.
The value of x will be -45 by the multiplicative property for the given expression x/3=-15.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
The given expression is x/3=-15. The value of x will be calculated as below:-
x/3=-15.
x = -15 x 3
x = -45
Therefore, the value of x will be -45 by the multiplicative property.
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NEED HELP FAST, GIVING AWAY 99 POINTS.
Evaluate the numerical expression.
3/2 − (−1/4)
A -1/2
B -3/2
C 7/4
D 4/5
Answer:
The answer is C. 7/4 :)
there are 11 books on a shelf. 9 of these books are new. the rest of them are used
Draw an irregular 14-sided polyhedron which has two congruent bases.
An irregular 14-sided polyhedron which has two congruent bases is as shown in the attached file.
What is a Polyhedron?
A polyhedron is a three dimensional solid shape made by joining together polygons.
For example we can consider a prism having 12-sided regular polygons as bases because then there would be 2 bases and 12 lateral sides for a total of 14 sides for the polyhedron.
Since the lateral faces are rectangles and not 12-sided polygons like the bases, the polyhedron is an irregular polyhedron.
Applying the above, we can draw an irregular 14-sided polyhedron which has two congruent bases as shown in the attached file.
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