Answer:
Country A won 78 medals
Country B won 26 medals
Country C won 15 medals
Step-by-step explanation:
We have been given with :-
A+B+C=119 _____equation(1)
B=C+11 ____equation(2)
A=B+C+37 ____equation(3)
1) Starting with the 3rd equation,
A=B+C+37
2) Subtract 37 from both sides
A-37=B+C+37-37
3) Cancelling out +37 and -37 from the right side we get,
A-37 = B+C
or
B+C = A-37
4) Plugin B+C= A-37 in the equation 1,
A+B+C = 119
=> A+(A-37) = 119
=> 2A-37 = 119
5) Add 37 to both sides
2A-37+37=119+37
6) Cancelling out -37 and +37 from the left side, we get
2A = 156
7) Divide both sides by 2
[tex]\frac{2A}{2} =\frac{156}{2}[/tex]
8) Cancelling out the 2's on the left side, we get
A = 78
9) Now, we plugin A=78 in the equation 1
A+B+C=119
=> 78+B+C=119
10) Subtract 78 from both sides
78+B+C-78 = 119 -78
11) Cancelling out +78 and -78 from the left side, we get
B+C= 41 ____let it be equation (4)
12) Subtracting C from both the sides of the equation 2, we get
B=C+11
=> B-C = C+11 - C
13) Cancelling out +C and -C from the right side, we get
B-C= 11 _____let it be equation (5)
14) Adding the equations 4 and 5, we get
B+C+B-C=41+11
15) Cancelling out the +C and -C, we get
2B = 52
16) Divide both sides by 2
[tex]\frac{2B}{2}=\frac{52}{2}[/tex]
17) Cancelling out the 2's on the left, we get
B = 26
18) Substituting A= 78 and B= 26 in the equation (1), we get
A+B+C=119
=> 78+26+C=119
=> 104+C=119
19) Subtracting 104 from both the sides, we get
104 + C - 104 = 119 -104
20) Cancelling out +104 and -104 from the left side, we get
C = 15
The problem is a basic algebra problem where we assign variables to the number of medals each country won. We then use given equations related to these variables to solve for each unknown.
Explanation:In this problem, we are trying to solve for the number of medals each country won, so let's start by assigning variables for the number of medals for each country. Let's say, Country A = A, Country B = B, and Country C = C.
According to the problem, we know that Country A won 37 more medals than the sum of the other two countries, that's expressed by this equation: A = B + C + 37.
It's also stated that Country B won 11 more medals than Country C, so we have this equation: B = C + 11.
Further, we know that the total number of medals is 119, so we have this equation: A + B + C = 119.
Now, solve these equations systematically. First, substitute the value of A and B from first and second equation into the third equation and solve the variable C, then substitute the obtained value of C in second equation to find B and finally substitute the obtained values of B and C in first equation to find A.
This is a basic algebraic problem-solving situation. It involves the use of equations and variables to find the solution.
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What is the slope intercept form in equation form of this graph?
Answer:
y = 7/2x+5
Step-by-step explanation:
To find the slope we need two points
(-2,-2) and (0,5)
We can find the slope from the formula
m = (y2-y1)/(x2-x1)
m = (5--2)/(0--2)
m = (5+2)/(0+2)
m = 7/2
The slope is 7/2
The y intercept, or where it crosses the y axis, is 5
Using the slope intercept formula for a line
y= mx+b
y = 7/2x+5
What is the value of X?
X=
B=75
C=50
A=x
Thank u! Sorry i'm dumb:(
Answer:
55
Step-by-step explanation:
70+50=125
180-125=55
A bag contains 6 blue marbles 10 red marbles and 9 green marbles. If 2 marbles are drawn at random without replacement what is the probability that to green marbles are drawn
Answer:
P(1 and 2 are green) = 3/25
Step-by-step explanation:
We need to know the total number of marbles
6 Blue + 10 red + 9 green = 25 marbles
P ( 1st marble is green) = green/ total
= 9/25
Since we don't put it back, there are
6 Blue + 10 red + 8 green = 24 marbles
P ( 2st marble is green) = green/ total
= 8/24 = 1/3
P(1 and 2 are green) = P(1st green) * P(2nd green)
= 9/25 * 1/3
= 3/25
To calculate the probability of drawing two green marbles consecutively without replacement, multiply the probability of drawing a green marble on the first draw (9/25) by the probability of drawing another green marble on the second draw (8/24, or 1/3), which equals 0.12.
Explanation:The question is asking about the probability of drawing two green marbles consecutively from a total of 25 marbles without replacement. The total number of marbles is comprised of 6 blue, 10 red, and 9 green marbles. The probability rule for independent events must be used in this scenario, which states that the probability of both events occurring is the product of the probabilities of each event.
Initially, you have 9 green out of 25 total marbles so the probability of drawing a green is 9/25. After having drawn one green marble, there are now 8 green out of a total of 24 marbles left in the bag, hence the probability of drawing one more green would be 8/24 or 1/3. Therefore, the probability of drawing two green marbles consecutively, without replacement is (9/25) * (1/3) or 3/25 or 0.12.
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given m=1/3, what is the parallel slope? what is the perpendivular slope?
Answer:1/3 and -3
Step-by-step explanation:pararel slope is the same as mane slope, and perpendicular is opicite reciprical.
Answer:
parallel: m = 1/3
perpendicular: m = -3
Step-by-step explanation:
Parallel line:
Slopes of parallel lines are equal.
If the given line has slope 1/3, then the parallel line also has slope 1/3.
Perpendicular line:
The slopes of perpendicular lines are negative reciprocals. That means that the product of the slopes is -1. That also means that to find the slope of a perpendicular line to a given line, first find the reciprocal of the slope of the given line (flip the fraction), then change the sign.
The slope of the perpendicular line and the slope of the line must multiply to -1.
Start with the given slope, 1/3. Now flip it to get 3/1 which is simply 3. Now change the sign to -3. The slope of the perpendicular is -3.
Check: multiply the slopes. They must have a product of -1.
1/3 * (-3) = 1/3 * (-3/1) = -3/3 = -1
The product is -1, so the slope of the perpendicular, -3, is correct.
From a boat on the lake, the angle of elevation to the top of a cliff is 28°16'. If the base of the cliff is 1307 ft from the boat, how high is the cliff (to the nearest foot)
keeping in mind that there are 60 minutes in 1 degree, thus 16' is really 16/60 ≈ 0.2666...., meaning [tex]\bf 28^o16'\implies 28.\overline{27}~^o[/tex].
Check the picture below.
make sure your calculator is in Degree mode.
The graph of the equation Ax+3y=48 passes through the point (-18,7) What value of A accurately completes the equation?
please help
Answer:
A = -1.5
Step-by-step explanation:
Ax+3y=48
Plug in (-18,7)
A(-18) +3(7)=48
-18A + 21 = 48
-18A = 27
A = - 27/18
A = - 3/2
A = -1.5
When you find 100% of a number, how does your answer relate to the original number?
a. the numbers are equal.
b. it is less than the original number.
c. it is greater than the original number.
Answer:
i think c.
Step-by-step explanation:
The numbers are equal (choice A)
This is because 100% of something is that entire thing, not changed at all. It is not added to, or subtracted from. Example: 100% of 78 is 78. If you had 78 people in a room, and selected 100% of them, then you selected all 78 people.
Based on the given information, choose the similarity statement
Answer:
SSS
Step-by-step explanation:
For the triangle to be considered similar, 2 sides and an angle must be similar or two angles and a side or three angle or the three sides are similar.
For the case above the three are similar and this makes triangle ABC similar to DEF.
Answer:
Third option SSS is the correct answer.
Step-by-step explanation:
It is given the BC/EF = 1/2
Consider Two triangle ABC and DEF
To find the ratio of sides
From the given data, we get
AC/DF = 3/6 = 1/2 and AB/DE = 12/24 =1/2
The ratio of sides are equal then the triangles are similar.
Based on the given data we can conclude that triangle ABC and DEF are similar.
what is the following quotient -2 srt8 4+sqrt 12
[tex]\dfrac{-2\sqrt8}{4+\sqrt{12}}=\dfrac{-2\sqrt{4\cdot2}}{4+\sqrt{4\cdot3}}=\dfrac{-2\cdot\sqrt4\cdot\sqrt2}{4+\sqrt4\cdot\sqrt3}=\dfrac{-2\cdot2\sqrt3}{4+2\sqrt3}=\dfrac{-4\sqrt2}{2(2+\sqrt3)}=-\dfrac{2\sqrt2}{2+\sqrt3}\\\\\text{Use}\ (a+b)(a-b)=a^2-b^2\\\\=\dfrac{-2\sqrt2}{2+\sqrt3}\cdot\dfrac{2-\sqrt3}{2-\sqrt3}=\dfrac{-2\sqrt2(2-\sqrt3)}{2^2-(\sqrt3)^2}\\\\\text{Use distributive property and}\ \sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\\\\=\dfrac{-4\sqrt2+2\sqrt6}{4-3}=\dfrac{2\sqrt6-4\sqrt2}{1}=2\sqrt6-4\sqrt2[/tex]
In order for two triangles to be similar, all corresponding pairs of angles must be
How do you solve this ?
Answer:
3y
Step-by-step explanation:
Simplifying
13x + -39y = 0
Solving
13x + -39y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '39y' to each side of the equation.
13x + -39y + 39y = 0 + 39y
Combine like terms: -39y + 39y = 0
13x + 0 = 0 + 39y
13x = 0 + 39y
Remove the zero:
13x = 39y
Divide each side by '13'.
x = 3y
Simplifying
x = 3y
12a + 12b + 12c + 12d Michael writes the expression shown here as 12(a + b + c + d). He is correctly using the ___________ property.
Answer:
He should be using distributive property
Sorry if im wrong
Step-by-step explanation:
Answer:
Michael used distributive property
Step-by-step explanation: I got it correct on my test and I'm also in K12
3(-2x-1)=2(x+5)
A) -13/8
B) -3/4
C) 13/8
D) 3/4
Which is the same as 7/3? A.7 divided by 1/3 B. 3 divided by 7 C.1/7 of3 D. 7 divided by 3
Answer:
D
Step-by-step explanation:
[tex]\frac{7}{3}[/tex] is 7 ÷ 3
Answer:
D. 7 divided by 3
Step-by-step explanation:
A.7 divided by 1/3
7 ÷ 1/3 Copy dot flip 7 * 3/1 = 21 No
B. 3 divided by 7
3 ÷7 = 3/7 No
C.1/7 of3
1/7 * 3 = 3/7 No
D. 7 divided by 3
7÷ 3 = 7/3 Yes
if I had 20 apples but 5 are gone and 2 came back but my friend took 7 and TWO OTHER friends took 2 EACH, how many do I have left?
Answer:
6 apples
Step-by-step explanation:
20 - 5 = 15
15 + 2 = 17
17 - 7 = 10
10 - (2 x 2) = 6
Your answer is 6 apples
Yum yum!!
last weekend,5% of the tickets sold at seaworld were discount tickets. if seaworld sold 60 tickets in all , how many discount ticket did it sell? use the percent proportion
Answer:
3
Step-by-step explanation:
to do this you need to figure out 5 percent of 60
in order to do this you need to find 95 percent of 60 and subtract it from 60
.95x60=57
60-57=3
they sold 3 discount tickets
3/60=5%
lightning strikes the earth 1000 times every ten seconds. how many seconds does it take forr it to strike 7250 times?
Answer:
72.5 seconds
Step-by-step explanation:
7250 ÷ 1000 = 7.25
7.25 x 10 = 72.5 seconds
Answer:
72.50 s
Step-by-step explanation:
Lightning strikes the earth 1000 times every 10 seconds. First calculate time taken for each lightning to strike the Earth by unitary method:
1000 times lightning takes 10 s
1 time lightning would take [tex]\frac{10s}{1000} = 0.01 s[/tex]
Multiply 7250 with this time. It will yield amount of time in which lightning would strike 7250 times:
[tex]\frac{10s}{1000}\times 7250 =72.50 s [/tex]
Katie's orange tree has 30 oranges. Katie's tree has three times as many fruits as Lisa's did before Lisa harvested half of her limes on the tree. How many limes does Lisa have on her tree now?
Lisa has 5 limes left on her tree after harvesting half. So, the correct answer is option 5) 5.
Let's break down the problem step by step:
1. Katie's orange tree has 30 oranges.
2. Katie's tree has three times as many fruits as Lisa's did before Lisa harvested half of her limes.
3. Let's denote the number of limes Lisa originally had as x .
4. After Lisa harvested half of her limes, she was left with [tex]\( \frac{x}{2} \)[/tex] limes.
5. Since Katie's tree has three times as many fruits as Lisa's tree originally had, the total number of fruits on Katie's tree is 3x .
6. The problem states that Katie's tree has 30 oranges, so 3x = 30 .
7. Solving for x , we find [tex]\( x = \frac{30}{3} = 10 \).[/tex]
So, Lisa originally had 10 limes on her tree. After harvesting half of them, Lisa is left with [tex]\( \frac{10}{2} = 5 \)[/tex] limes.
Therefore, the correct answer is option 5) 5.
The Correct question is:
Katie's orange tree has 30 oranges. Katie's tree has three times as many fruits as Lisa's did before Lisa harvested half of her limes on the tree. How many limes does Lisa have on her tree now?
1)10
2)45
3)90
4)15
5)5
Lisa initially had 10 limes on her tree. After harvesting half, she has 5 limes remaining. Therefore, Lisa now has five limes on her tree.
To find out how many limes Lisa has on her tree now, we need to break down the problem step-by-step:
Katie's tree has three times as many fruits as Lisa's: 30 = 3x
Solving for x: x = 10
So, Lisa originally had 10 limes on her tree.
Next, we calculate how many limes Lisa has after harvesting half:
Lisa harvested half of the 10 limes:Number of limes harvested = 10 / 2 = 5 The remaining limes on Lisa's tree: Remaining limes = 10 - 5 = 5Therefore, Lisa has five limes on her tree now.
A computer takes 12 min to download a 48 min movie. How long will it take to download a 2.5 hour movie? how do i do this?
Answer:
37.5 minutes
Step-by-step explanation:
48/12 = 4 (for every 1 minute, 4 minutes of movie is downloaded.
change 2.5 hours to minutes = 60+60+30 = 150 minutes
150/4 = 37.5 minutes to download the 2.5 hour movie
Divide. Give special attention to the order of division. a. 72 ÷ 9 ÷ 2 b. (18 ÷ 6) ÷ 3 c. 45 ÷ 5 ÷ 3 d. 144 ÷ (12 ÷ 2)
Answer:
a. 4
b. 1
c. 3
d. 24
Step-by-step explanation:
a. 72 ÷ 9 ÷ 2
= (72÷9)÷2
= 8÷2
= 4
b. (18 ÷ 6) ÷ 3
= 3÷3
= 1
c. 45 ÷ 5 ÷ 3
= (45÷5)÷3
= 9÷3
=3
d. 144 ÷ (12 ÷ 2)
= 144÷6
= 24
The table shows the price for different numbers of
ice cream cones:
number of ice cream cones || price (in dollars)
2 4
4 8
5 10
8 16
Does this table of numbers represent a proportional relationship?
a ] No, because the price of 4 ice cream cones should be $6
b ] No, because the price of 5 ice cream cones should be $20
c ] Yes, because the price is 2 times the number of ice cream cones
d ] Yes, because 2 times the price is the number of ice cream cones
Answer: C
Step-by-step explanation:
Each of the number of cones multiplied by two equals the reciprocating number so they are all proportional.
Answer Is:
C Please mark me brainliest
( 4 over 4 )x = 4/32 what is the value of x
Answer:
x = [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
The fraction [tex]\frac{4}{4}[/tex] is equal to 1, so putting this into the equation:
1x = [tex]\frac{4}{32}[/tex]
So x = [tex]\frac{4}{32}[/tex]
Or simplified down by dividing the fraction by 4:
x = [tex]\frac{1}{8}[/tex]
Answer:
1/8
Step-by-step explanation:
for this problem, you just have to think about how many times 4 goes into 32, so what times 4 equals 32? the answer is 8. so by simplifying the 4 and 32, you get 1/8
10(d+3)–(−9d–4)=d–5+3
What value of d makes the equation TRUE?
Answer:
d=-2
Step-by-step explanation:
We have
[tex]10(d+3)-(-9d-4)=d-5+3[/tex]
now we remove parenthesis and use distribution property
[tex]10d+30+9d+4=d-5+3[/tex]
now we combine like terms
[tex]10d+9d+30+4=d-2[/tex]
[tex]19d+34=d-2[/tex]
[tex]19d-d+34=-2[/tex] (subtract d from both side )
[tex]18d=-2-34[/tex] ( subtract 34 from both side )
[tex]18d=-36[/tex]
[tex]d=\frac{-36}{18}[/tex] ( divide both side by 18)
[tex]d=-2[/tex]
7.19 divided by 58 estimate the quotients
Answer:
0.124
Step-by-step explanation:
[tex]\frac{7.19}{58}[/tex]
To divide the numbers, we need to remove the decimal point
To remove decimal point , we multiply top and bottom by 100
[tex]\frac{719}{5800}[/tex]
Use long division. After using decimal point at the top we can include any number of zeros with 719
. 1 2 3 9
---------------------
5800 7190
5800
------------------------(subtract)
13900
11600
---------------------------(subtract)
2300 0
1740 0
--------------------------(subtract)
56000
52200
---------------------------(subtract)
3800 0
Division goes on ............
Estimate the quotient to 3 decimal places
Quotient = 0.124
you buy a book for 10.99 dollars and pay $0.91 in sales tax how much change should you receive from a $20 bill explain your work
Answer:
$8.10 would be the change
Step-by-step explanation:
10.99+0.91=11.90 to find the total
$20.00-11.90= 8.10 to find the change
Hope this helped ❤️
Answer:
$8.10
Step-by-step explanation:
The first step is to calculate how much you owe.
10.99 + .91 = 11.90
Change = Cash paid - how much you owe
= 20.00 - 11.90
=8.10
The change is $8.10
One evening 1400 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $20 for covered pavilion seats and $15 for lawn seats. Total receipts were $24,000. How many tickets of each type were sold?
To determine the number of each type of ticket sold, a system of linear equations is set up and solved using the substitution method. The answer is 600 covered pavilion seats and 800 lawn seats were sold.
To solve this problem, we can set up a system of linear equations based on the given information. Let x be the number of covered pavilion seats sold and y the number of lawn seats sold. We have two equations:
x + y = 1400 (since 1400 tickets were sold in total)20x + 15y = 24000 (since the total receipts from ticket sales were $24,000)Now we can solve this system of equations using either substitution or elimination method. For simplicity, let's use the substitution method:
From equation 1, we can express x as:
x = 1400 - y
Now substitute x in equation 2:
20(1400 - y) + 15y = 24000
Simplify and solve for y:
28000 - 20y + 15y = 24000
-5y = -4000
y = 800
Since we know y, we can find x by substituting the value of y in x = 1400 - y:
x = 1400 - 800
x = 600
So, the number of covered pavilion seats sold was 600 and the number of lawn seats sold was 800.
Select the property shown by the statement: -2x×7y=-2×7×X×y
A)communitive
B)associative
C)reflective
D)symmetric
Answer:
If I am correct It is Commutative Property
Hope That Helps!
p^n/p^8 = p^-6 what is N? the arrows pointing up mean the power of the letter
[tex]\text{Use}\ \dfrac{a^n}{a^m}=a^{n-m}.\\\\\dfrac{p^n}{p^8}=p^{-6}\\\\p^{n-8}=p^{-6}\iff n-8=-6\qquad\text{add 8 to both sides}\\\\\boxed{n=2}[/tex]
a submarine travels 90 kilometers in 4 hours find the submarines rate of speed in kilometers per hour
Answer:
22.5
Step-by-step explanation:
To find the rate of speed per hour, you need to divide the kilometer (90) by the hours (4).
90/4=
22.5
The submarine's rate of speed is found by dividing the distance traveled (90 kilometers) by the travel time (4 hours), resulting in a rate of 22.5 kilometers per hour.
You need to use the formula for speed which is speed = distance ÷ time. In this case, the submarine travels 90 kilometers in 4 hours.
To calculate the rate of speed, divide the distance by the time:
Speed = 90 kilometers ÷ 4 hours = 22.5 kilometers per hour.
This means the submarine's rate of speed is 22.5 kilometers per hour.
2x (y^2+3)-5 (3+y^2)
Use distributive property a(b + c) = ab + ac.
[tex]2x(y^2+3)-5(3+y^2)=(2x)(y^2)+(2x)(3)+(-5)(3)+(-5)(y^2)\\\\=2xy^2+6x-15-5y^2[/tex]