Hello There!
WHAT WE KNOW 25 students in a class and 16 out of the 25 students in the class are girls. There are 9 boys in the class because "25-9=16"
HOW TO SOLVE If we know that 9 out of the 25 students in the class are girls, we can represent it as the fraction [tex]\frac{9}{25}[/tex]. Next, we divide 35 by 9 to get a quotient of 0.36 and then multiply by 100 to get our percent of girls in the class which is 36%
HAVE A GREAT DAY!
To find the percentage amount of girls in the class, we need to first find the amount of girls in the class.
Since 16 of the 25 students are boys, the rest must be girls. Subtract 16 from 25 to find the amount of girls in class.
25-16=9
Now, to find out what percent of 25 9 is, divide 9 by 25.
9/25= .36
The percentage of girls in the class was 36%.
Hope this helps!
8. Let f(x) = x 2 + 3x − 12 what is the average rate of change from x = 3 and x = 5?
[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)= x^2+3x-12\qquad \begin{cases} x_1=3\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(3)}{5-3} \\\\\\ \cfrac{[(5)^2+3(5)-12]~~-~~[(3)^2+3(3)-12]}{2}\implies \cfrac{[25+3]~~-~~[9-3]}{2} \\\\\\ \cfrac{28-6}{2}\implies \cfrac{22}{2}\implies 11[/tex]
HELLLLLLPPPPPP!!!!!!!!!
Answer:
A
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x)
= 3x² - 2x + 4 - (5x² + 6x - 8) ← distribute parenthesis by - 1
= 3x² - 2x + 4 - 5x² - 6x + 8 ← collect like terms
= - 2x² - 8x + 12 → A
Please answer now and please explain thank you
Hello There!
The answer would be the first one.
This is saying that Tom can not save exactly 50.25 but he must save more than that
20points! What is the percent of change from 134 to 106? Round to the nearest percent!
Answer:
Step-by-step explanation:
it's -2
The percentage change of 134 to 106 will be -20.89% .
Given ,
Number changed from 134 to 106 .
Now,
Here initially the number was = 134
After reduction the number was = 106
Percentage change = final - initial / initial * 100
Final number = 106
Initial number = 134
so,
Percentage change = 106 -134/134 * 100
Percentage change = -28/134 *100
Percentage change = -20.89%
Thus the percentage change is -20 .89% and the negative sign shows the declining nature of number .
Know more about percentages,
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Factor completely 3x4 − 30x3 + 75x2. 3(x − 5)2 3x2(x − 5)2 3x2(x2 − 10x + 25) 3x2(x + 5)(x − 5)
Answer:
The complete factorization is 3x² (x - 5)² ⇒ 2nd answer
Step-by-step explanation:
* Lets revise how to factorize a trinomial
- Find the greatest common factor of the coefficients of the three terms
∵ The trinomial is 3x^4 - 30x³ + 75x²
- The greatest common factor of 3 , 30 , 75 is 3
∵ 3 ÷ 3 = 1
∵ 30 ÷ 3 = 10
∵ 75 ÷ 3 = 25
∴ 3x^4 - 30x³ + 75x² = 3(x^4 - 10x³ + 25x²)
- Now lets find the greatest common factor of the variable x
∵ x² is the greatest common factor of the three terms
∵ x^4 ÷ x² = x²
∵ 10x³ ÷ x² = 10x
∵ 25x² ÷ x² = 25
∴ 3(x^4 - 10x³ + 25x²) = 3x² (x² - 10x + 25)
- Lets factorize (x² - 10x + 25)
∵ √x² = x
∵ √25 = 5
∵ 2 × 5 × x = 10x
∴ x² - 10x + 25 is a completing square
∴ (x² - 10x + 25) = (x - 5)²
∴ 3x² (x² - 10x + 25) = 3x² (x - 5)²
* The complete factorization is 3x² (x - 5)²
Answer:
3x^2 (x-5)^2
Step-by-step explanation:
3x^4 − 30x^3 + 75x^2
We can factor out a 3x^2 from each term
3x^2 (x^2 -10x +25)
The term inside the parentheses can be factored
What 2 numbers multiply to 25 and add to -10
-5*-5 = 25
-5+-5 = -10
3x^2 (x-5) (x-5)
3x^2 (x-5)^2
Which expression is equivalent to (x + 2)(3x – 3)?
Multiply the two brackets together
(x+2)(3x-3)
x(3x)*(-3)(x)+2(3x)(2*-3)
3x^2-3x+6x-6
3x^2+3x-6
Answer is : 3x^2+3x-6
Answer
A. x5y3
Step-by-step explanation:
Vertical? Obtuse? Straight or acute
Answer:
D. Acute
Step-by-step explanation:
This is an acute angle because the angle is less then 90 degrees.
<FOA is an Acute angle (D).
How I know...
Acute angles are angles are below 90 degrees (aka LESS then a right angle)
Hope this helped!
~Just a girl in love with Shawn Mendes
6. The ratio of red ribbons to green ribbons is 4 to 6. If
there are a total of 30 red ribbons, then how many green
ribbons are there?
Answer:
45
Step-by-step explanation:
The 4 part of the ratio represents 30 red ribbons
Divide 30 by 4 to find the value of one part of the ratio
30 ÷ 4 = 7.5, hence
6 × 7.5 = 45 ← number of green ribbons
A 52-inch pipe is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.
Answer:
The length of the shorter piece is 13 inches
Step-by-step explanation:
Let's represent the longer piece of pipe with the variable L and the shorter piece of pipe with variable S.
Since the pipe is going to be the length of L and S together, we can make this equation:
L+S=52
Also we know that the longer piece is three times the shorter piece or
L=3S
Substitute the second equation into the first equation.
L+S=52
3S+S=52
4S=52
Divide both sides by 4
4S/4=52/4
S=13 inches
The length of the shorter piece is 13 inches....
To find the length of longer piece, put the value S=13 in L=3S
L=3S
L=3(13)
L=39 inches
The length of the longer piece is 39 inches....
Witch table shows a proportional relationship between a and b
Answer:
Option B is correct.
Step-by-step explanation:
A proportional relationship is a relationship between two variables where the ratio between the two variables is always the same.
Divide b/a for each option, the option having same ratio for the complete tables have proportional relationship
a)
9/3 = 3
12/4 = 3
20/5 = 4
b)
25/20 = 5/4
30/24 = 5/4
40/32 = 5/4
c)
12/4 = 3
15/5 = 3
24/6 = 4
d)
4/3 = 4/3
9/6 = 3/2
12/16 = 3/4
So, Option B is correct.
Answer: Second Option
Step-by-step explanation:
It is said that two variables a and b are propocionales if when b increases then a increases in a constant rate.
That is, a and b are proportional if the quotient between b and a is always equal to a constant k.
[tex]\frac{b}{a}=k[/tex]
To know which of the tables shows a proportional relationship identify in which of the tables the division of b between a always is constant
You can verify that the table where the quotient of b enters a is always constant is in the second table
[tex]\frac{b}{a}=\frac{5}{4}[/tex]
What is the simplified form of the following expression?
Oo oo
Answer:
[tex]\frac{\sqrt[3]{100x}}{5}[/tex]
Step-by-step explanation:
we have
[tex]\sqrt[3]{\frac{4x}{5}}[/tex]
Multiply inside by [tex]\frac{25}{25}[/tex]
so
[tex]\sqrt[3]{\frac{4x*25}{5*25}}[/tex]
[tex]\sqrt[3]{\frac{100x}{125}}[/tex]
Remember that
[tex]\sqrt[3]{125}=5[/tex]
substitute
[tex]\sqrt[3]{\frac{100x}{125}}=\frac{\sqrt[3]{100x}}{\sqrt[3]{125}}=\frac{\sqrt[3]{100x}}{5}[/tex]
(29 PTS) Explain how the Quotient of Powers Property was used to simplify this expression. 3^4/9 = 3^2
A/ By simplifying 9 to 32 to make both powers base three and adding the exponents
B. By simplifying 9 to 32 to make both powers base three and subtracting the exponents
C. By finding the quotient of the bases to be 1/3 and simplifying the expression
D. By finding the quotient of the bases to be 1/3 and cancelling common factors
Answer:
B. By simplifying 9 to [tex]3^{2}[/tex] to make both powers base three and subtracting the exponents
Step-by-step explanation:
When you have a division the quotient of powers property states that the exponents should be substracted, and by simplifying 9 to [tex]3^{2}[/tex] you end up with an equation like this:
[tex]\frac{3^{4} }{3^{2} }[/tex]=[tex]3^{2}[/tex]
Then you just have to substract the exponent from the denominator from the numerator´s exponent, which would be:
4-2=2
and the resultant equation would be:
[tex]3^{2} =3^{2}[/tex]
The Quotient of Powers Property allows you to subtract exponents when dividing expressions with the same base. The expression 3^4/9 simplifies to 3^2 because 9 can be expressed as 3^2, therefore their exponents are subtracted (4-2=2).
Explanation:In this question, the Quotient of Powers Property is used. This property states that to divide where the base remains the same, you subtract the exponents. In the expression 3^4/9 = 3^2, we know that 9 can be expressed as 3^2.
Therefore, it becomes 3^4/3^2. According to the Quotient of Powers Property, we subtract the exponent of the denominator from the exponent of the numerator (4-2=2). Hence the expression simplifies to 3^2. The correct choice is B: By simplifying 9 to 3^2 to make both powers base three and subtracting the exponents.
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What is the product -9x(5x-2x)
Answer:
−27x2
Step-by-step explanation:
It's -27x to the second power so the small 2 at the end
What is the answer to 4 • 4.
Answer:
16
Step-by-step explanation:
4 groups of 4 is 16:
[tex]\left\begin{array}{cccc}*&*&*&*\*&*&*&*&*\*&*&*&*&*\*&*&*&*&*\end{array}\right[/tex]
what is the distance between the points (2 -3) and (-6 4) on the coordinate plane
Answer:
√113
or
10.6301458127
Step-by-step explanation:
Plug the coordinated into this equation and make sure you match up the corrdinates in the correct order
d = √(x2 - x1)^2 + (y2 - y1)^2
The number next to the number does NOT mean multiply it mean like this
(x2, y2) and (x1, y1) so you would plug them in like this:
d = √(-6 - 2)^2 + (4 - (-3))^2
d = √(-8)^2 + (7)^2
d = √(64 + 49
d = √113
or 10.6301458127
Answer with Step-by-step explanation:
The distance(d) between the points (a,b) and (c,d) is given by:
[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]
Here, we have to find distance between (2,-3) and (-6,4)
(a,b)=(2,-3) and (c,d)=(-6,4)
[tex]d=\sqrt{(-6-2)^2+(4-(-3))^2}[/tex]
[tex]d=\sqrt{8^2+7^2}[/tex]
[tex]d=\sqrt{64+49}[/tex]
[tex]d=\sqrt{113}[/tex]
Hence, the distance between the points (2 -3) and (-6 4) on the coordinate plane is:
[tex]\sqrt{113}[/tex]
The system shown is _____.
consistent
equivalent
inconsistent
Answer:
consistent
Solution at (3,2)
Step-by-step explanation:
A consistent and independent solution to a system of linear equations is one point
A consistent and dependent solution to a system of linear equations is where they are the same line ( they could also be called equivalent)
An inconsistent solution is where there is no solution, the lines do not cross
Since the lines cross at exactly one point, this is a consistent and dependent solution
The solution is at x = 3 ( 3 units to the right of the origin)
and y = 2 ( 2 units up from the origin)
(3,2)
Answer:
Consistent :)
Step-by-step explanation:
In a singing competition, there are
150 participants. At the end of each
round, 40% of the participants are
eliminated. How many participants
are left after n rounds?
Answer:
150(.40)^n is your equation
Step-by-step explanation:
Answer:
[tex]=150\cdot{0.4^n}[/tex]
Step-by-step explanation:
Let n be the number of rounds. Lets look at n=1 which is round one. Therefore if 40% of the contestants are eliminated then we can write an expression of the number of contestants eliminated:
[tex]=150\cdot{0.4}[/tex]
For round two, n=2:
[tex]=150\cdot{0.4)\cdot{0.4}=150\cdot{0.4^2}[/tex]
Therefore for the n number of rounds:
[tex]=150\cdot{0.4^n}[/tex]
Simplify the expression. 8P3
Answer:
336
Step-by-step explanation:
Using the definition of n[tex]P_{r}[/tex] = n ! / (n- r) !
where n ! = n(n - 1)(n - 2).... × 3 × 2 × 1
8[tex]P_{3}[/tex]
= 8 ! / (8 - 3) !
= 8 ! / 5 !
= [tex]\frac{8(7)(6)(5)(4)(3)(2)(1)}{5(4)(3)(2)(1)}[/tex]
[ cancel 5(4)(3)(2)(1) on numerator/denominator
= 8 × 7 × 6 = 336
ANSWER
[tex]^8P_3 = 336[/tex]
EXPLANATION
Recall that;
[tex]^nP_r = \frac{n!}{(n - r)!} [/tex]
The given expression is:
[tex]^8P_3[/tex]
We substitute n=8 and r=3
[tex]^8P_3 =\frac{8!}{(8- 3)!} [/tex]
[tex]^8P_3 =\frac{8!}{(5)!} [/tex]
This simplifies to :
[tex]^8P_3 =\frac{8 \times 7 \times 6 \times 5!}{5!} [/tex]
We cancel out the common factors to get:
[tex]^8P_3 = 8 \times 7 \times 6[/tex]
[tex]^8P_3 = 336[/tex]
find the area of the smaller sector (please help me(
Answer:
27
Step-by-step explanation:
Area of circle with radius of 2
Answer:
[tex]4\pi[/tex] or 12.56
Step-by-step explanation:
[tex]\pi r^{2}[/tex] is the formula to find the area of a circle.
if we plug '2' in... [tex]\pi2^{2}[/tex]
which equals to [tex]4\pi[/tex]
if we multiply 4 with pi, it equals to 12.56
Answer:
Area of circle = 12.56 sq. units
Step-by-step explanation:
radius = 2
Area of circle = π r² sq. units
= 3.14 * 2 * 2 = 12.56 sq. units
Simplify this expression HELP ASAP
Answer:
B
Step-by-step explanation:
Noting the following rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex]
Given
([tex]\sqrt{2}[/tex] + [tex]\sqrt{3}[/tex])( [tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex] )
Each term in the second factor is multiplied by each term in the first factor
= [tex]\sqrt{2}[/tex]([tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex]) + [tex]\sqrt{3}[/tex]([tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex]) ← distribute parenthesis
= [tex]\sqrt{10}[/tex] - [tex]\sqrt{14}[/tex] + [tex]\sqrt{15}[/tex] - [tex]\sqrt{21}[/tex]
log; (3x+2) = log,(4x-6)
Answer:
x = 8
Step-by-step explanation:
Using the rule of logarithms
log x = log y ⇔ x = y
Given
log(3x + 2) = log(4x - 6), then
4x - 6 = 3x + 2 ( subtract 3x from both sides )
x - 6 = 2 ( add 6 to both sides )
x = 8
For what values of y does 125=(1/25)^y-1
[tex]125 = \frac{1}{125} {}^{y - 1} \\ 125 = ( {5}^{ - 2} ) {}^{y - 1} \\ \\ {5}^{3} = {5}^{2 - 2y} \\ 3 = 2 - 2y \\ - 0.5 = y[/tex]
Answer:
The answer is [tex]y=-0.5[/tex]
Step-by-step explanation:
In order to determine the "y" value, we have to change the way of we see the equation.
In these cases, when the variable is in the exponent and it is possible to make two exponents in each side of the equation, we have to equal bases and then we have to make other equation between the exponents of both sides.
So,
[tex]125=(\frac{1}{25})^y^-^1\\(5)^3=(5^-^2)^y^-^1\\(5)^3=(5)^-^2^*^y^+^2\\[/tex]
Then, we have to make an equation between the exponents of both sides:
[tex]3=-2*y+2\\2*y=2-3\\2*y=-1\\y=\frac{-1}{2}=-0.5\\ y=-0.5[/tex]
Finally, the value of "y" is -0.5
1. Two lines, A and B, are represented by the following equations: Line A: 2x + y = 6 Line B: x + y = 4 Which statement is true about the solution to the set of equations? (4 points) It is (2, 2). There are infinitely many solutions. It is (4, 0). There is no solution.
Answer:
It is (2, 2).
Step-by-step explanation:
1. You have a piece of land where you want to grow a garden. You only
have 20 yards of fencing to surround the garden. Work through the steps
below to figure out the maximum space you can create to grow plants.
A) you decide to make the width 3 yards.
Length: _____ yards
Area: _____ square yards
select the two values of x that are roots of this equation 2x^2 + 7x + 6=0
A. X=-3
B. X=-3/2
C. X=-4
D. X=-2
Answer:
x = -2 or x = -3/2 thus B. & D. are the answer
Step-by-step explanation:
Solve for x:
2 x^2 + 7 x + 6 = 0
Hint: | Factor the left hand side.
The left hand side factors into a product with two terms:
(x + 2) (2 x + 3) = 0
Hint: | Find the roots of each term in the product separately.
Split into two equations:
x + 2 = 0 or 2 x + 3 = 0
Hint: | Look at the first equation: Solve for x.
Subtract 2 from both sides:
x = -2 or 2 x + 3 = 0
Hint: | Look at the second equation: Isolate terms with x to the left hand side.
Subtract 3 from both sides:
x = -2 or 2 x = -3
Hint: | Solve for x.
Divide both sides by 2:
Answer: x = -2 or x = -3/2
Answer:
B and D
Step-by-step explanation:
Given
2x² + 7x + 6 = 0
To factorise the quadratic
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × 6 = 12 and sum = + 7
The factors are + 4 and + 3
Use these factors to split the x- term
2x² + 4x + 3x + 6 = 0 ( factor the first/second and third/fourth terms )
2x(x + 2) + 3(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(2x + 3) = 0
Equate each factor to zero and solve for x
x + 2 = 0 → x = - 2 → D
2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex] → B
what is −7−4p−(−5) ??
Answer:
Step-by-step explanation:
−7−4p+5
−4p+(−7+5)
Ans
−4p−2
your answer is: -4p - 2
Explanation:
first, ignore the -4p for now. do the small equation without the variable. SO, we would do 7 - 5 = 2.
there aren't any addition symbols being used in the equation and there aren't any other numbers with the p variable. this means that the -4p will stay the same. so we would end up with -4p - 2
(this isn't the normal way of solving this, but I did my own way and got the same answer)
What is the midpoint of (3.2,2.5) and (1,6,-4.5)
Answer:
(2.4 , -1)
Step-by-step explanation:
Too many commas in second ordered pair but this is how I will interpret the question:
Find the midpoint of (3.2,2.5) and (1.6,-4.5)
So just average x's : (3.2+1.6)/2 =4.8/2=2.4
And
just average y's : (2.5+-4.5)/2=-2/2=-1
The midpoint is (average x's , average y's)
Your midpoint is (2.4 , -1 )
answer (2.4 , -1)
The manufacturer of a new product developed the following expression to predict the monthly profit, in thousands of dollars, from sales of t
product when it is sold at a unit price of x dollars.
-0.5x2 + 221 – 224
What is represented by the zero(s) of the expression?
A.
the unit price(s) when the profit is equal to 0
B.
the unit price(s) when profit is greatest
c.
the profit when the unit price is equal to 0
OD.
the profit when the unit price is greatest
Reset
Next
Answer:
A. The answer is our unit prices when our profit is 0
Step-by-step explanation:
The zeros are the x-intercepts, when the curve passes through the x-axis.
I'm going to call our function P
P(x)=-0.5x^2+221x-224 is equal to 0 (our profit is equal to 0) when x (the unit price is such and such)
The answer is our unit prices when our profit is 0
The expression represents the monthly profit from sales of a product at a given unit price. The zero(s) of the expression represent the unit price(s) when the profit is equal to 0.
Explanation:The expression -0.5x^2 + 221x - 224 represents the monthly profit, in thousands of dollars, from sales of a product when it is sold at a unit price of x dollars.
The zero(s) of the expression are the unit price(s) when the profit is equal to 0. To find the zero(s), we need to set the expression equal to 0 and solve for x.
-0.5x^2 + 221x - 224 = 0We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.The zero(s) of the expression will give us the unit price(s) at which the profit is equal to 0.Learn more about Quadratic equations here:https://brainly.com/question/30098550
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the first quartile of a data set is 72, and the third quartile is 92. Which of these values in the data set is an outlier ?
A. 61
B. 121
C. 101
D. 41
Answer: Option D
D. 41
Step-by-step explanation:
A value [tex]x_i[/tex] is considered an outlier if
[tex]x_i> Q_3 + 1.5IQR[/tex]
or
[tex]x_i <Q_1 - 1.5IQR[/tex]
Where
[tex]Q_3[/tex] is the third quartile
[tex]Q_1[/tex] is the first quartile
IQR is the interquartile range.
[tex]IQR = Q_3-Q_1[/tex]
In this case:
[tex]Q_3=92\\Q_1=72[/tex]
So
[tex]IQR = 92-72 =20[/tex]
[tex]Q_3 + 1.5IQR = 92 + 1.5*20 = 122[/tex]
[tex]Q_1 - 1.5IQR=72-1.5*20=42[/tex]
Then the outlier values will be all those greater than 122 or less than 42
Therefore the answer is the option D.