Final answer:
The ratio of boys to girls in Mrs. Fronko's class in simplest form is 3:4, obtained by dividing both sides of the given ratio, 6:8, by the greatest common divisor, which is 2.
Explanation:
To find the ratio of boys to girls in Mrs. Fronko's class in its simplest form, we will start with the ratio given, which is 6 boys for every 8 girls. This can be written as 6:8. To simplify ratios, we divide both sides of the ratio by the greatest common divisor. In this case, the greatest common divisor of 6 and 8 is 2. Therefore, we divide both numbers by 2 to find the simplest form of the ratio.
6 ÷ 2 = 3 and 8 ÷ 2 = 4.
After dividing both numbers by 2, the ratio becomes 3:4. This indicates that for every 3 boys, there are 4 girls in Mrs. Fronko's class, and this is the simplest form of the ratio.
In a fruit punch drink, the 3 ingredients are apple juice, orange juice and cranberry juice. If
1/3
of the drink is apple juice and
1/2
is orange juice then write the ratio of cranberry juice to apple juice to orange juice in its simplest form.
The ratio of cranberry juice to apple juice to orange juice, when the drink consists of 1/3 apple juice and 1/2 orange juice, is 1:2:3.
The student asked for the ratio of cranberry juice to apple juice to orange juice in its simplest form, knowing that 1/3 of the drink is apple juice and 1/2 is orange juice. To find the fraction of the drink that is cranberry juice, we subtract the other two parts from the whole (which is 1):
1 - (1/3 + 1/2) = 1 - (2/6 + 3/6) = 1 - 5/6 = 1/6
So the ratio of cranberry juice to apple juice to orange juice can be written as:
Cranberry : Apple : Orange = 1/6 : 1/3 : 1/2
To compare ratios, we need to have the same denominator. Multiplying each part of the ratio by 6 (the least common multiple of 6, 3, and 2) gives us:
Cranberry : Apple : Orange = 1 : 2 : 3
Therefore, the ratio of cranberry juice to apple juice to orange juice in its simplest form is 1:2:3.
Which is equivalent to the expression? x2 + 6x + 4 A) (x + 3)2 + 5 B) (x + 3)2 − 5 C) (x − 3)2 + 5 D) (x − 3)2 − 5
Answer:
Step-by-step explanation:
(x + 3)² − 5 because :
(x + 3)² − 5 = x² +6x+9 -5 =x²+6x+4
Answer:
B) [tex](x + 3)^2 - 5[/tex]
Step-by-step explanation:
the equation is: [tex]x^2 + 6x + 4[/tex]
we have an equation of the form
[tex]ax^2+bx+c[/tex]
where
[tex]a=1,b=6,c=4[/tex]
and we must complete the square to obtain a perfect square binomial,
we must add and substract the following:
[tex](\frac{b}{2a} )^2[/tex]
which is:
[tex](\frac{6}{2*1} )^2=3^2[/tex]
and then the equation becomes:
[tex]x^2 + 6x + 4+3^2-3^2[/tex]
where the terms [tex]x^2+6x+3^2[/tex] are the components of the perfect square binomial: [tex](x+3)^2[/tex]
and thus, the equation now is:
[tex](x+3)^2+4-3^2\\=(x-3)^2+4-9\\=(x+3)^2-5[/tex]
the answer is: B) [tex](x + 3)^2 - 5[/tex]
On a certain map 1.5 inches represent a distance of 120miles. If two cities on this map are 1 foot apart, what is the distance in miles, between the cities?
Answer:
Step-by-step explanation:
16 miles in it
Answer: Should be 16 miles.
I'm not a genius but I know partial of math in my grade. Hope this helped.
What is the solution to 5x+y=13
−x+2y=−7 ?
also What is the solution to
4x+5y=35
−3x+2y=−9 ?
A)
5x+y=13
−x+2y=−7
Multiply each term in the first equation by -2:
5x + y = 13 x -2 = -10x - 2y = -26
Now add that to the second equation:
-10x - 2y = -26 + −x+2y=−7
= -11x = -33
Divide each side by -11
X = -33 / -11
X = 3
Now you have x, replace it in the first equation and solve for y:
5(3) + y = 13
Simplify:
15 + y = 13
Subtract 15 from both sides:
y = 13 -15
y = -2
Solution = (3,-2)
B)
4x+5y=35
−3x+2y=−9
Multiply each term in the second equation by -2.5:
7.5x -5y = 22.5
Add this to the first equation:
4x+5y=35 + 7.5x -5y = 22.5
= 11.5x = 57.5
Divide both sides by 11.5:
x = 57.5 / 11.5
x = 5
Now you have x, replace x in one of the equations to solve for y:
4(5) + 5y = 35
Simplify:
20 + 5y = 35
Subtract 20 from both sides:
5y = 15
Divide both sides by 5:
y = 15/5
y = 3
Solution = (5,3)
ABCD is a rectangular wall in which AB=3.15 m and BC = 1.77m. Find the
length of the diagonal BD.
506 students went on a field trip. Nine buses
were filled and 29 students traveled in cars.
How many students were in each bus?
Answer:
53 students on each bus
Step-by-step explanation:
506-29=477 (take out the students that went by car)
477/9 = 53 (distribute 477 students evenly in 9 buses)
Five times the sum of a number and 6 is 48
The number is 3.6
What is Algebra?Algebra is a branch of mathematics that deals with symbols and the arithmetic operations across these symbols. These symbols do not have any fixed values and are called variables. In our real-life problems, we often see certain values that keep on changing. But there is a constant need to represent these changing values.
Given statement:
Five times the sum of a number and 6 is 48.
Let the number be x.
5(x+6)=48
x+6= 9.6
x= 9.6-6
x= 3.6
Hence, the number is 3.6.
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Between which two integers can the square root of 15 be found?
Answer:
3 and 4
Step-by-step explanation:
Consider squares on either side of 15, that is 9 and 16, so
[tex]\sqrt{9}[/tex] < [tex]\sqrt{15}[/tex] < [tex]\sqrt{16}[/tex], that is
3 < [tex]\sqrt{15}[/tex] < 4
Answer:
[tex]3<\sqrt{15}<4[/tex]
Step-by-step explanation:
We are asked to find the integers such that square root of 15 lies between them.
We know that perfect square less than 15 is 9 and perfect square greater than 15 is 16.
We can represent this information in an inequality as:
[tex]\sqrt{9}<\sqrt{15}<\sqrt{16}[/tex]
[tex]\sqrt{3^2}<\sqrt{15}<\sqrt{4^2}[/tex]
[tex]3<\sqrt{15}<4[/tex]
Therefore, the square root of 15 lies 3 and 4.
Hank’s pickup can travel 75 miles on 5 gallons of gas. How many gallons will Hank’s pickup need to travel 60 miles?
Hank’s pickup will need blank gallons of gas to travel 60 miles.
Answer:
The Answer is 4
Step-by-step explanation:
75 Miles divided by 5 Gallons is 15. Take that and divide 60 miles by 15. Your answer is 4 Gallons.
Hank's pickup consumes gas at a rate of 15 miles per gallon. To travel 60 miles, it would need 4 gallons of gas.
Explanation:To solve this problem, you need to first establish the rate of gas consumption for Hank's pickup. According to the data given, we know that Hank's pickup travels 75 miles with 5 gallons of gas which gives us a rate of 15 miles per gallon. The next step is to find out how much gas Hank's pickup will consume to travel 60 miles. So you divide the 60 miles by the rate of consumption which is 15 miles per gallon. The result is 4 gallons. Therefore, Hank's pickup will need 4 gallons of gas to travel 60 miles.
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HELP ASAP!!! The opposite of -4 is, My answer ***
A.4***
B. -4
C. -(-(-4))
D. -I4I
The opposite of -10 is
A. -(-(-10))
B. -10
C. 10 ***
D. -I10I
Which symbol is used to make -5 ?-8 a true statement?
A. >***
B. <
C. =
Which symbol is used to make -6 ? I-8I a true statement?
A. >
B. < ***
C. =
Which set of integers are in the right order from least to greatest?
A. -8. 8, 6, I-7I, 5
B. I-7I, -8, 8, 6, 5
C. -8, 5, 6, I-7I, 8
D. 5, 6, 8, -8, I-7I***
all of them except the last one is correct, the last one is C). -8, 5, 6, |-7|, 8, because it says least to greatest, the one you picked wasn't even put in greatest to least, but I think where you went wrong is the absolute value of -7, the absolute value of a number is shown with | ? |.
I hope you understand your mistake and won't make it again :)
Right for the most part but, 5 is C. –8, 5, 6, |–7|, 8
Good job overall tho :)
Which polynomial is a monomial?
Answer:
The answer is 5r^2s^3t^4 (the last answer) because it is the only monomial in the bunch.
Step-by-step explanation:
(2x - 1) + (3y + 2)i = 5 – 4i
Solve for x and y
Answer:
The solution for x and y in (2x - 1) + (3y + 2)i = 5 – 4i cannot be determined.
Solution:
From question, the equation given is
(2x - 1) + (3y + 2)i = 5 – 4i
Multiplying the terms inside the bracket (3y + 2) with i, the above equation becomes,
(2x – 1) + 3iy + 2i = 5 – 4i
Removing the parenthesis in (2x – 1), the above equation becomes,
2x -1 + 3iy + 2i = 5 - 4i
2x – 1 + 3iy + 2i – 5 + 4i = 0
Rearranging the terms, the above equation becomes
2x + 3iy + 4i + 2i -1 -5 = 0
2x + 3iy + 6i – 6 = 0
The above equation cannot be simplified further. Hence the solution for x and y cannot be determined.
On a number line, what number is located 8 units away from -11 in the positive direction?
Answer:
-3
Step-by-step explanation:
Take negative 11 and add positive 8 to it because you are going in the positive direction.
What is the prime factors of the numbers 48
Answer:
24,12,6
Step-by-step explanation:
48 is even, so you can factor out 2, your first prime factor
Final answer:
The prime factors of 48 are 2 to the power of 4 and 3. You divide 48 by 2 repeatedly until only prime numbers are left, which are 2´ and 3.
Explanation:
Finding Prime Factors
The prime factors of a number are the prime numbers that multiply together to equal the original number. To find the prime factors of 48, you start by finding the smallest prime number that divides 48. In this case, it would be 2. So, you divide 48 by 2 to get 24. You then repeat this process until you are only left with prime numbers.
Here's a step-by-step breakdown:
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
Now, you're left with 2, 2, 2, 2, and 3, all of which are prime numbers. So the prime factors of 48 are 2´ (2 raised to the power of 4) and 3.
Multiplication Property of Equality---- If 6x divided by 8 = 40, then______
A.) 6x * 8=320
B.) 40=6x*8
C.) 6x=320
D.)40=6x divided by 8
whats the corrects answer and why?? plz help
Answer:
Option C.) 6x=320
Step-by-step explanation:
we know that
The Multiplication Property of Equality states that if you multiply both sides of an equation by the same number, the sides remain equal
we have
[tex]\frac{6x}{8}=40[/tex]
Apply the multiplication property of equality
Multiply by 8 both sides
[tex]\frac{6x}{8}(8)=40(8)[/tex]
[tex]6x=320[/tex]
therefore
The answer is the Option C
Answer:
Option C.
Step-by-step explanation:
Multiplication property of equality states that "if a number is multiplied to one side of the equation then other side of the equation should be multiplied with the same number".
The given equation is [tex]\frac{6x}{8}=40[/tex]
By the multiplication property of equality,
[tex]\frac{6x}{8}\times 8=40\times 8[/tex]
6x = 320
Option C will be the correct option.
Am i correct about this or no? Need answer asap.
Answer: Yep! I agree
Step-by-step explanation: Ok to shows the 10 and 30 are proportional... This means 8 and n would be too
What is the circumference of a circle with a diameter of 10 meters?
Answer:
C=10π
Step-by-step explanation:
Circumference formula: C=πd (or C=2πr)
Two Containers have leaks. Container A begins with 80 ounces and leaks at a rate of 0.6 ounces per minute. Container B begins with 100 ounces and leaks at a rate of 1 ounce per minute. How many minutes before the containers have the same amount of ounces?
Answer:
50 mins
Step-by-step explanation:
Set up the following equation:
80-0.6m=100-1m
1) Add 1m to both sides:
80+0.4m=100
2) Subtract 80 from both sides:
0.4m=20
3) Divide both sides by 0.4:
m=50
Let me know if you have any difficulty understanding how I set up the equation!
Help with homework plzzzzz!!!!!!!!!!!!!
I'm not good with intigers, but if you added two negative intigers together wouldn't it still be negative? If you added -1 to -2 you'd get -3. It would always be less than the two original integers.
Which accurately describes a circle with radius 12 centimeters and center Q?
A.
the collection of all points located 6 centimeters from point Q
B.
the collection of all points on the same plane located 6 centimeters from point Q
C.
the collection of all points located 12 centimeters from point Q
D.
the collection of all points on the same plane located 12 centimeters from point Q
Answer:
option D is correct
the collection of all points on the same plane located 12cm from point Q
Answer:
Option D is correct
Step-by-step explanation:
A circle is a planar shape which has a point called center. All the points on the circle keep equal distance from the centre and the equal distance is called radius.
Here given that radius is 12 cm. Since it is a circle it should be in a plane only. Otherwise this will form a sphere. So this lies in a plane with all points keeping equal distance of [tex]12 cm[/tex] from the center
Option D) the collection of all points on the same plane located 12 centimeters from point Q
14.25 devised by1.9 what is the answer
WILL MARK BRAINLIEST :))
The figure shown has two parallel lines cut by a transversal:
Use the figure to complete the sentence.
∠7 and ____ are alternate exterior angles.
∠2
∠1
∠5
∠8
Answer:
<1
Step-by-step explanation:
I think its <1 as well
What integer is represented by the phrase"decreased by 4"?
The phrase 'decreased by 4' refers to a mathematical operation where you take an integer and subtract 4. Without a specified starting point, it could represent various integers depending upon the starting integer.
Explanation:The phrase 'decreased by 4' in the context of mathematics usually requires a starting point or reference integer. Suppose the starting point was 0, 'decreased by 4' would result in -4. However, if the starting integer isn't mentioned, it could be indicating a function where you take an input integer and subtract 4. Therefore, the phrase 'decreased by 4' could represent an operation applied to integers, resulting in an integer that is four less than the original.
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Dustin has a bag of marbles with 4 blue marbles, 4 white marbles, and 3 red marbles.
Find the following probabilities of Dustin drawing the given marbles from the bag if the first marble(s) is(are) not returned to the bag after they are drawn.
a) A Blue, then a red =
b) A red, then a white =
c) A Blue, then a Blue, then a Blue =
Answer:
A.
[tex]\dfrac{6}{55}[/tex]
B.
[tex]\dfrac{6}{55}[/tex]
C.
[tex]\dfrac{4}{165}[/tex]
Step-by-step explanation:
Dustin has a bag of marbles with 4 blue marbles, 4 white marbles, and 3 red marbles. There are 11 marbles in total.
A. The probability that the first marble drawn is blue marble is
[tex]\dfrac{4}{11},[/tex]
the probability that the second marble drawn is red marble is
[tex]\dfrac{3}{10}[/tex]
The probability that the first marble drawn is blue and the second is red is
[tex]\dfrac{4}{11}\cdot \dfrac{3}{10}=\dfrac{12}{110}=\dfrac{6}{55}[/tex]
B. The probability that the first marble drawn is red marble is
[tex]\dfrac{3}{11},[/tex]
the probability that the second marble drawn is white marble is
[tex]\dfrac{4}{10}[/tex]
The probability that the first marble drawn is red and the second is white is
[tex]\dfrac{3}{11}\cdot \dfrac{4}{10}=\dfrac{12}{110}=\dfrac{6}{55}[/tex]
C. The probability that the first marble drawn is blue marble is
[tex]\dfrac{4}{11},[/tex]
the probability that the second marble drawn is blue marble is
[tex]\dfrac{3}{10},[/tex]
the probability that the third marble drawn is blue marble is
[tex]\dfrac{2}{9},[/tex]
The probability that the first, second and third marbles drawn are blue is
[tex]\dfrac{4}{11}\cdot \dfrac{3}{10}\cdot \dfrac{2}{9}=\dfrac{24}{990}=\dfrac{4}{165}[/tex]
Stephen is baking cookies for his school bake sale. He bakes 300 cookies.
1/2 are chocolate chip cookies
3/20 are peanut butter cookies
1/10 are sugar cookies
The rest are lemon cookies
How many cookies are lemon cookies?
Answer:
The number of lemon cookies is 75
Step-by-step explanation:
we know that
The total cookies are 300
Let
x ----> the number of lemon cookies
[tex]x=300(1-\frac{1}{2} -\frac{3}{20}-\frac{1}{10})[/tex]
Multiply by 20 both sides to remove the fractions
[tex]20x=300(20)-300(10)-300(3)-300(2)[/tex]
[tex]20x=1,500[/tex]
[tex]x=75[/tex]
therefore
The number of lemon cookies is 75
Answer:the geezer is right
Step-by-step explanation:
mmath help pls, will reward!! O_O
Answer:
x = -4, y = 8.
Step-by-step explanation:
Question 16.
8x + y = -24 ........(A)
-3x - 2y = -4 ........(B)
Multiply (A) by 2:
16x + 2y = -48 Adding this to equation (B):
13x = -52
x = -4
Substituting this value of x in Equation (A):
8(-4) + y = -24
y = -24 + 32 = 8.
Answer:
Answer for the first part of question 16 is y =-24 - 8x
1st subtract 8x from both sides: 8x + y - 8x = -24 - 8x
2nd simplify: -24 - 8x
Answer for the 2nd part of Q. 16 is y = -(-4+3x)/2
1st add 3x to both sides: -3x - 2y + 3x = -4 + 3x
2nd simplify: -2y = -4 + 3x
3rd divide both sides by -2: -2y ÷ -2 = 4 ÷ -2 +3x ÷ -2
4th simplify: (-4 + 3x)/2
Answer to the 1st part of Q. 17 is y = (-1 - 2x)/3
1st subtract 2x from both sides 2x + 3y - 2x = -1 - 2x
2nd simplify: -3y= -1 - 2x
3rd divide both sides by -3: -3y ÷ -3 = 1 ÷ -3 - 2x ÷ -3
4th simplify: y = (-1 - 2x)/3
Answer to 2nd part of Q.17: y = 6 + 7x ÷ 10
1st Add 7x to both sides: -7x + 10y + 7x = 6 + 7x
2nd simplify: 10y=6+7x
3rd divide both sides by 10: 10y ÷ 10 = 6 ÷ 10 + 7x ÷ 10
4th simplify: y = 6 + 7x ÷ 10
sorry, but I don't know the answer to Q.18 but I hope I helped on questions 16 and 17 :)
Andre says that 5 3/4 + 2 1/4 = 7 1/2 because 7 4/8 = 7 1/2. Identify his mistake. Draw a picture to prove that he is wrong.
Andre's Mistake in reasoning is assuming that 7 4/8 is equal to 7 1/2. Drawing a number line can prove that the fractions may be equivalent, but the whole numbers are not.
Andre made a mistake in his reasoning.
He incorrectly assumed that 7 4/8 is equal to 7 1/2. The fractions 4/8 and 1/2 are actually equivalent, but the whole numbers 7 and 7 are not.
To prove this, you can draw a number line and divide it into equal parts.
Taking the fractions 4/8 and 1/2, you will see that they represent the same distance, but they start at different points on the number line.
Therefore, 5 3/4 + 2 1/4 is not equal to 7 1/2.
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If a pair of shoes costs $52.50 including a 7.25% tax, what is the original cost of the item before taxes are added?
No other symbols other than the number rounded to the second decimal.
Answer:
The original cost of the pair of shoes before tax is $48.95
Step-by-step explanation:
* Lets explain how to solve the problem
- Assume that the cost of the pair of shoes is 100% before taxes
∵ The cost of the pair of shoes is 100% before taxes
∵ The tax is 7.25%
∴ The price of the pair of shoes after tax = 100% + 7.25% = 107.25%
- This 107.25% equivalent to the price of the pair of shoes including
the tax
∵ The cost of the pair of shoes including tax is $52.50
- Lets use the cross multiplication to find the cost of the pair of
shoes before tax
∵ 100% ⇒ 107.25%
? ⇒ 52.50
- ? represents the cost of the pair of shoes before tax
∴ ? = [tex]\frac{100*52.50}{107.25}=48.95[/tex]
∴ The original cost of the pair of shoes before tax is $48.95
8,407,47
is divisible by 3.
Answer:
Yes, it is divisible by three. The answer would be 280,249
Step-by-step explanation:
A quadrilateral has vertices at A(-5,5), B(1,8), C(4,2), and D(-2,-2). Use slope to determine if the quadrilateral is a rectangle. Show your work.
Answer:
The quadrilateral is not a rectangle
Step-by-step explanation:
we know that
If a quadrilateral ABCD is a rectangle
then
Opposite sides are congruent and parallel and adjacent sides are perpendicular
Remember that
If two lines are parallel, then their slopes are the same
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
A(-5,5), B(1,8), C(4,2), and D(-2,-2)
Plot the figure to better understand the problem
see the attached figure
Find the slope of the four sides and then compare
step 1
Find slope AB
A(-5,5), B(1,8)
substitute in the formula
[tex]m=\frac{8-5}{1+5}[/tex]
[tex]m=\frac{3}{6}[/tex]
[tex]m_A_B=\frac{1}{2}[/tex]
step 2
Find slope BC
B(1,8), C(4,2)
substitute in the formula
[tex]m=\frac{2-8}{4-1}[/tex]
[tex]m=\frac{-6}{3}[/tex]
[tex]m_B_C=-2[/tex]
step 3
Find slope CD
C(4,2), and D(-2,-2)
substitute in the formula
[tex]m=\frac{-2-2}{-2-4}[/tex]
[tex]m=\frac{-4}{-6}[/tex]
[tex]m_C_D=\frac{2}{3}[/tex]
step 4
Find slope AD
A(-5,5), D(-2,-2)
substitute in the formula
[tex]m=\frac{-2-5}{-2+5}[/tex]
[tex]m=\frac{-7}{3}[/tex]
[tex]m_A_D=-\frac{7}{3}[/tex]
step 5
Verify if the opposites are parallel
Remember that
If two lines are parallel, then their slopes are the same
The opposite sides are
AB and CD
BC and AD
we have
[tex]m_A_B=\frac{1}{2}[/tex]
[tex]m_C_D=\frac{2}{3}[/tex]
so
[tex]m_A_B \neq m_C_D[/tex]
It is not necessary to continue verifying, because two of the opposite sides are not parallel
therefore
The quadrilateral is not a rectangle