Answer:
50 students
Step-by-step explanation:
Hello!
To solve this question, we would first need to look at the data. In this data, there are people who chose their favorite sport, and the number of people who chose that response. In order to solve the problem, we would have to find the ratio of how many people choose baseball over the other sports.
By this, we can add the number of students together. 30+10+5+15=60. Out of those 60 students, only 5 people chose baseball.
Since the ratio of the people who chose baseball is 5/60 (meaning that it is a 5/60 % chance someone would pick this sport), we would need to find the amount of people assumed to pick baseball in 600 student survey.
We can make a relationship with these two numbers.
, since the ratio of the students who chose baseball remain the same.
You can see that the ratio on the denominators just add a zero on the bottom, so the top should add 0 as well, to get 50 for x, what we needed.
You can also solve that relationship by cross multiplication.
5(600)=x(60
3000=60x
50=x
Regardless, the answer is 50 students who would choose baseball in a 600 persons survey.
Answer: 6.8%
Step-by-step explanation:
We need to find both percentage so we can determine the increase.
Finding percentage of $10 return: 1% return
Finding percentage of $78 return: 7.8% return
To find the percent increase we do 7.8%-1.0% = 6.8%
The correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".
The given inequality is -3(2x - 5) < 5(2 - x)
We need to simplify the inequality.
<h3>What is inequality?</h3>
In mathematics, inequality is a statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.
Consider LHS and simplify -3(2x - 5) = -3(2x)-5(-3)
⇒ -3(2x - 5) = - 6x + 15 [∵(-)(-) = (+)]
Consider RHS and simplify 5(2 - x) = 5(2) + 5(-x)
⇒5(2 - x) = 10 - 5x [∵(+)(-) = (-)]
Now, - 6x + 15 < 10 - 5x
By subtracting 15 from both sides, we get
- 6x < -5 - 5x
By adding 5x to both sides, we get - x < - 5
The coefficient of x is -1. So, divide both sides by -1
Then we get x > 5
Hence, the correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".
To learn more about inequalities visit:
brainly.com/question/20383699.
#SPJ1
Answer:
1. this is the definition of a midpoint - bc the definition of a midpoint is: “If a point is a midpoint of a segment, then it divides that segment into two congruent parts” or “If a point divides a segment into two congruent parts, then it's the midpoint of that segment.”
2. this is the division property of equality -"The division property of equality states that when we divide both sides of an equation by the same non-zero number, the two sides remain equal". so, in this situation we want to isolate x which means dividing both sides by 20. This will keep both sides equal just more simplified ( before, it was 20 and 100, after dividing both sides by 20 it is 1 and 5 which is the same ratio therefore they are still equal)
3. this one's the subtraction property of equality- this property means you can subtract the same number from both sides of an equation and get an equivalent equation. in this situation, they subtracted 15 from both sides to get AB = 30 and it ends being still being equal to AB + 15= 45.
4. this is the symmetric property of equality - "This property states that if a = b, then b = a. That is, we can interchange the sides of an equation, and the equation is still a true statement." "it states that values are still equal no matter which side of the equal sign they're on." That's why its possible for XY=ST and ST=XY
5. this is definition of congruence - which basically states that if a value of one thing is equal to the value of another thing those two things can be called congruent.
6. this is substitution property- this is the property that allows you to substitute one value for another in an equation. the property states that if
x = y, then x can be substituted in for y in any equation, and y can be substituted for x in any equation, just like what they show here with 5AB substituting for CD in the equation.
i hope this helped! im not that good at explaining so if u have more questions lmk!
Answer:
x = 14
Step-by-step explanation:
Solve for x:
90 = -4 + 2 x + 3 (x + 8)
3 (x + 8) = 3 x + 24:
90 = 3 x + 24 + 2 x - 4
Grouping like terms, 3 x + 2 x - 4 + 24 = (2 x + 3 x) + (-4 + 24):
90 = (2 x + 3 x) + (-4 + 24)
2 x + 3 x = 5 x:
90 = 5 x + (-4 + 24)
24 - 4 = 20:
90 = 5 x + 20
90 = 5 x + 20 is equivalent to 5 x + 20 = 90:
5 x + 20 = 90
Subtract 20 from both sides:
5 x + (20 - 20) = 90 - 20
20 - 20 = 0:
5 x = 90 - 20
90 - 20 = 70:
5 x = 70
Divide both sides of 5 x = 70 by 5:
(5 x)/5 = 70/5
5/5 = 1:
x = 70/5
The gcd of 70 and 5 is 5, so 70/5 = (5×14)/(5×1) = 5/5×14 = 14:
Answer: x = 14
