Answer:
Ratio = [tex]\frac{Perfect.squares}{non.Perfect.squares}[/tex] = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
The perfect squares from 1-30 are:
1, 4, 9, 16, 25
Total no. of perfect squares = five =5
Total no. of non perfect squares = 30-5 = 25
Ratio =[tex]\frac{Perfect.squares}{non.Perfect.squares}[/tex] = 5 / 25 = [tex]\frac{1}{5}[/tex]
The ratio of perfect squares to non-perfect squares for the numbers 1 to 30 is 1:5.
Explanation:A perfect square is a number that is the square of an integer. For the numbers 1 to 30, the perfect squares are 1, 4, 9, 16, 25, as these numbers are squares of integers 1, 2, 3, 4, 5 respectively. The number of perfect squares is 5.
The total number of tiles is 30. So the number of non-perfect squares is 30 - 5 = 25.
The ratio of perfect squares to non-perfect squares in simplest form, then, is 5 : 25. Simplified, this ratio is 1 : 5.
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Solve for 7(2c-1)-3=6+6c
Answer:
c=2
Step-by-step explanation:
7(2c-1)-3=6+6c
14c-7-3=6+6c
14c-10=6+6c
14c-6c-10=6
8c-10=6
8c=6+10
8c=16
c=16/8
c=2
Answer:
c = 2Step-by-step explanation:
[tex]7(2c-1)-3=6+6c\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(7)(2c)+(7)(-1)-3=6+6c\\\\14c-7-3=6+6c\qquad\text{combine like terms}\\\\14c+(-7-3)=6+6c\\\\14c-10=6+6c\qquad\text{add 10 to both sides}\\\\14c-10+10=6+10+6c\\\\14c=16+6c\qquad\text{subtract}\ 6c\ \text{from both sides}\\\\14c-6c=16+6c-6c\\\\8c=16\qquad\text{divide both sides by 8}\\\\\dfrac{8c}{8}=\dfrac{16}{8}\\\\c=2[/tex]
What is the equation of the line that passes through the point (-2, 7) and has a slope of zero
Answer:
y = 7 is the equation of the line that passes through the point ( -2, 7 ) and has a slope of zero.
Step-by-step explanation:
Given:
Let,
A ≡ ( x1 , y1 ) ≡ ( -2, 7 )
Slope = m = 0
To Find :
Equation of Line:
Solution:
Formula for , equation of a line passing through a point ( x1 , y1 ) and having a slope m is given by
[tex](y - y_{1})=m(x-x_{1})[/tex]
Now substituting the values of x1 = -2 and y1 = 7 and slope m = 0 we get,
[tex]y-7=0\times(x--2) \\y-7=0\times (x+2)\\y-7=0\\\therefore y=7[/tex]
Which is the required equation of a line passing through the point ( -2, 7 ) and slope zero
The equation of a line that passes through a point is an algebraic equation. It can also be referred to as the Slope-Intercept Equation.
The equation of the line that passes through the point (-2, 7) and has a slope of zero is written as: y = 7
The equation of the line through a point (x1, y1) can be represented by the algebraic equation:
y = mx + c
where:
m = slope
c = y - intercept
From the question,
(x1, y1) = (-2, 7)
m = slope = 0
Substituting these values into the algebraic equation,
7 = (0 x -2) + c
7 = 0
Hence, y = 7
The equation of the line that passes through the point (-2, 7) and has a slope of zero is y = 7
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Please help having trouble!
Answer:
Option C is the correct choice that is [tex]y<-\frac{5}{2}x-2[/tex]
Step-by-step explanation:
As this is a multiple choice question we will reduce the options and work on it with the given points [tex](0,-2),(-2,-3)[/tex]
Note:We know that [tex]\leq ,\geq[/tex] where there is [tex]=[/tex] sign associated with it have a straight line graph there is no breaking in the line.
And when there is simply [tex]<,>[/tex] we have a dashed line when we plot it on a graph.
So option B and D are discarded.
Now one-by one we will put the values [tex](x,y)\ (-2,3)[/tex] to know which equation it satisfies.
If we put [tex]y=3[/tex] then [tex]x=-2[/tex].
So working with option A.
[tex]y<-\frac{2}{5}x-2[/tex]
Plugging the values.
[tex]3<-\frac{2}{5}x-2\ ,3<\frac{-2x-10}{5}\ ,15<-2x-10\ ,15+10< -2x\ ,x=\frac{25}{-2}=-12.5[/tex]
And we know that [tex]x[/tex] must be equal to [tex]-2[/tex] so this is not the right answer.
We are left with only one choice that is C .
So option C is the correct option of the above inequality.
What is -2-(-3)? Show your work.
When subtracting with a negative number anywhere in the expression you will do something called "Same-Add-Opposite."
This means that you will keep the first number in the expression (in this case that is -2) the same:
-2 - (-3)
Then turn the subtraction sign into an addition sign.
-2 + (-3)
Finally you will take the "opposite" sign of the second number (in this case you will take the opposite of -3). When I say "opposite sign" I mean that if this number is positive it will become negative. If it was negative it will become positive.
-2 + 3
Now you must solve. When adding a positive number with a negative number you will act as if you are subtracting the two numbers, then the answer will take the sign of the largest number (disregarding the signs).
In this case the largest number is 3 (disregarding the signs) and its sign is positive. Your answer will have a negative sign.
-2 + 3
1
-2 - (-3) = 1
Hope this helped!
~Just a girl in love with Shawn Mendes
Simplify (x − 4)(3x2 − 6x + 2). 3x3 + 6x2 − 22x + 8 3x3 − 18x2 + 26x − 8 3x3 − 18x2 − 22x − 8 3x3 + 6x2 + 22x + 8
Answer:
3x^3-18x^2+26x-8
Step-by-step explanation:
(x-4)(3x^2-6x+2)
3x^3-6x^2+2x-12x^2+24x-8
3x^3-6x^2-12x^2+2x+24x-8
3x^3-18x^2+26x-8
The perimeter of a rectangle is twice the sum
of its length and its width. The perimeter is
40 meters and its length is 2 meters more
than twice its width.
The question is incomplete, here is the complete question:
The perimeter of a rectangle is twice the sum of its length and its width, the perimeter is 40 meters and the length is 2 meters more than twice its width. What is the length?
The length of the rectangle is 14 meters
Step-by-step explanation:
The formula of the perimeter of a rectangle is P = 2(L + W), where
L is its lengthW is its widthAssume that the width of the rectangle is x meters
∵ The width of the rectangle = x meters
∵ Its length is 2 meters more than twice its width
- Multiply x by 2 and then add to the product 2
∴ The length of the rectangle = 2 x + 2 meters
∵ The formula of the perimeter is P = 2(L + W)
- Substitute L by 2 x + 2 and W by x
∴ P = 2(2 x + 2 + x)
- Add like terms in the bracket
∴ P = 2(3 x + 2)
- Simplify the right hand side
∴ P = 6 x + 4
∵ The perimeter of the rectangle = 40 meters
- Equate P by 40
∴ 6 x + 4 = 40
- Subtract 4 from both sides
∴ 6 x = 36
- Divide both sides by 6
∴ x = 6
∴ The width of the rectangle is 6 meters
∵ The length = 2 x + 2
- Substitute x by 6
∴ The length = 2(6) + 2 = 12 + 2 = 14 meters
The length of the rectangle is 14 meters
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1,114,040 in word form
Answer:
one million, one hundred fourteen thousand, forty
Step-by-step explanation:
Deon split 4/5 pounds of candy among 5 people.
What is the unit rate in pounds per person?
Write your Anwser in simplest form.
Answer:
4/25 pounds of candy per person.
Step-by-step explanation:
(4/5)/5=(4/5)(1/5)=4/25
To find the unit rate, you divide the total weight of the candy (4/5 pounds) by the total number of people (5). Therefore, each person received 4/25 pound of candy.
Explanation:The unit rate is found by dividing the total quantity by the total number of units. In this problem, Deon divided 4/5 pounds of candy among 5 people.
To find the amount of candy per person which is the unit rate, you divide the total weight of the candy (4/5 pounds) by the total number of people (5). So, 4/5 divided by 5 equals 4/25. Thus, each person received 4/25 pound of candy.
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What is the quotient of (x^3+3x^2-4x-12) / (x^2+5x+6)?
Answer:
The quotient is x -2
Step-by-step explanation:
1. Let's simplify and find out the quotient of the following division:
(x^3+3x^2-4x-12) / (x^2+5x+6)
(x³ + 3x² - 4x - 12)/ (x² + 5x + 6)
(x + 2) (x² + x - 6) / (x + 2) (x + 3) ⇒ Factorizing on the numerator and the denominator
(x² + x - 6) / (x + 3) ⇒ Eliminating (x + 2) on the numerator and the denominator
(x + 3) (x - 2) / (x + 3) ⇒ Factorizing on the numerator
x - 2 ⇒ Eliminating (x + 3) on the numerator and the denominator
The quotient is x -2
Answer:
The answer is x-2 on EDGE
Step-by-step explanation:
A survey showed that 35% of the students prefer plain white milk over chocolate milk. If the school has 1200 students. How many students prefer chocolate milk?
Answer:
The number of students who prefer chocolate milk is 780 .
Step-by-step explanation:
Given as :
The total number of students in the school = 1200
The percentage of students who prefer plain white milk = 35 %
Let the number of students who prefer chocolate milk = x
Now, ∵ The percentage of students who prefer plain white milk = 35 %
∴ The percentage of students who prefer chocolate milk = 100 % - 35 % = 65%
So , As The number of students who prefer chocolate milk = x
Or, 65 % of total number of students in school = x
So, x = [tex]\frac{65}{100}[/tex] × 1200
or, x = [tex]\frac{65\times 1200 }{100}[/tex]
∴ x = 780
So, the number of students who prefer chocolate milk = x = 780
And students who prefer plain white milk = 1200 - x = 1200 - 780 = 420
Hence, The number of students who prefer chocolate milk is 780 . Answer
Solve for z in the problem below:
4/5 = z/20
A.z = 16
B. z = 80
C. z = 13
D. z = 5
Answer:
A
Step-by-step explanation:
Given
[tex]\frac{4}{5}[/tex] = [tex]\frac{z}{20}[/tex]
Multiply both sides by 20 to clear the fractions
16 = z → A
Answer:
A. z = 16
Step-by-step explanation:
Multiply both sides by 20 isolate the variable z.
[tex]\frac{4}{5} *\frac{z}{20}[/tex]
[tex]\frac{4}{5} *20 = \frac{z}{20} *20[/tex]
[tex]z = \frac{4}{5} *20[/tex]
Multiplying [tex]\frac{4}{5}[/tex] by 20 will give us 16.
[tex]\frac{4}{5} *\frac{20}{1} = \frac{80}{5}[/tex][tex]= 16[/tex]
Therefore, z is equal to 16.
Could anyone help me with this ?!
Answer: 5; PO
6; PM
7; MNO
8; QN
9; OQ
10; PQO
Step-by-step explanation:
value of the expression below on the horizontal span of 0 to 10. (Round your answer to two decimal places.)
x2 + 19x + 2
Answer:
The value of expression increases from [tex]2[/tex] to [tex]292[/tex] on spanning [tex]x[/tex] from [tex]0[/tex] to [tex]10[/tex].Step-by-step explanation:
The expression given here is
[tex]x^2+19x+2[/tex]
Now if we differentiate this expression we can find the portions in its graph where it is increasing and decreasing or neither both.
If the differentiated expression is less than zero with the constant infront of highest degree positive then in the values corresponding to that [tex]x[/tex] the graph is decreasing.
If the differentiated expression is greater than zero with the constant infront of highest degree positive then in the values corresponding to that [tex]x[/tex] the graph is increasing.
[tex]\frac{d}{dx}(x^2+19x+2)[/tex]
⇒[tex]2x+19[/tex]
For [tex]2x+19>0[/tex] ⇔[tex]x>\frac{-19}{2}[/tex]
For [tex]2x+19<0[/tex] ⇔[tex]x<\frac{-19}{2}[/tex]
Now for us the horizontal span is asked from 0 to 10 for the expression which is from [tex]x=0[/tex] to [tex]x=10[/tex] ,in which portion the value of the expression is strictly increasing so the vlaue increases from [tex]0+0+2=2[/tex] to [tex]10^2+190+2=292[/tex].
Plzzzzz someone hurry and help me I will mark as brainliest!!!!!
Jonas solved an equation incorrectly, as shown below:
Step 1: 8x = 56
Step 2: x = 56(8)
Step 3: x = 7
Which statement best explains why Step 2 is incorrect in Jonas's solution?
Group of answer choices
A. He did not subtract 8 from 56.
B. He did not multiply 56 by 8.
C. He did not add 8 to 56.
D. He did not divide 56 by 8.
Answer:
D
Step-by-step explanation:
he did not devide56 by 8
Answer:
D
Step-by-step explanation:
Jonas should have divided 56 by 8.
8x=56
8x/8 = 56/8
x = 7
868 divided by 4 equals
Answer:
217
Step-by-step explanation:
868/4=217
Answer:
217
Step-by-step explanation:
Suppose mr reeds class has 3 hours for presentations how many projects can be presented show your solution by writing both a division equation and a multiplication equation
Number of projects that can be presented is 15.
What is Multiplication and Division?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given that
Time alloted for each team = 1/5
Total time for the presentation = 3 hours
Division equation can be written as :
Number of projects = 3 / (1/5), where 3 hours is divided into 1/5 equal parts.
Number of projects = 15
Multiplication equation can be written as :
Number of projects = 3 × 5 = 15
Hence 15 projects can be presented.
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The complete question is as follows:
Teams of students in Mr. Reed’s classroom are presenting Social Studies projects. Each team has 1/5 hour for their presentation.
Suppose Mr Reeds class has 3 hours for presentations. How many projects can be presented show your solution by writing both a division equation and a multiplication equation.
A Shark Weighs 405 kilograms and 68 grams a second shark weighs 324 kilograms and 75 grams how much more does the first shark weigh in grams than the second shark
Answer:
7 grams
Step-by-step explanation:
If you're asking me grams specifically, and not kilograms, subtract 68 from 75 to get your answer. If it's only kilograms subtract 324 from 405. If it's both of them added together subtract 399 from 473, you're welcome!
Answer:
7 grams
Step-by-step explanation:
What is 6% of 24.77?
Answer: 1.4862
Step-by-step explanation: To find 6% of 24.77, first write 6% as a decimal by moving the decimal point two places to the left to get 0.06.
Next, the word "of" means multiply so we will multiply 0.06 by 24.77.
(0.06) (24.77) = 1.4682
Therefore, 6% of 24,77 is 1.4862.
If five times a number is increased by four, the result is at least 19. Find the least possible number that satisfies these conditions
3 is the least possible number that satisfied these conditions
The solution set is: x≥3
Step-by-step explanation:
Let x be the number
Then according to given statement
If five times a number is increased by four
[tex]5x+4[/tex]
At least 19 means that the result will be equal to or greater than 19
so,
[tex]5x+4\geq 19[/tex]
subtracting 4 from both sides
[tex]5x+4-4 \geq 19-4\\5x \geq 15[/tex]
Dividing both sides by 5
[tex]\frac{5x}{5} \geq \frac{15}{5}\\x\geq 3[/tex]
3 is the least possible number that satisfied these conditions
The solution set is: x≥3
Keywords: Inequality, Variables
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x+4y=13
x-y=3
need help please?
Answer:
X=5
y=2
Step-by-step explanation:
x+4y=13
5+4(2)=13
x-y=3
5-2=3
X=5
Y=2
X+4Y=13
X+Y=13/4=3
X(5)+4Y(*2)=13
subtract 3x squared +7x-4 from 8x squared-6+2 your answer should be polynomial in standard form
Answer:
5x² - 13x + 6
Step-by-step explanation:
8x² - 6x + 2 - (3x² +7x -4)
Simplify the expression:
8x² - 6x + 2 - 3x² -7x + 4
Combine like terms:
5x² - 13x + 6
A total of 814 tickets were sold for the school play. They were either adult tickets or student tickets. There were 64 more student tickets sold than adult tickets. How many adult tickets
Answer:
STUDENT TICKETS SOLD = 439ADULT TICKETS SOLD = 375814 - 64 = 750
750 ÷ 2 = 375
375 + 64 = 439
The problem can be solved by setting up two equations based on the given information, substituting one equation into the other, and then solving for the variable. In this case, 375 adult tickets were sold.
Explanation:The subject of this problem is mathematics, particularly a class of problems known as linear equations. Let's assign variables to each type of ticket: A for the number of adult tickets and S for the number of student tickets.
According to the problem, S = A + 64 (because there were 64 more student tickets sold) and S + A = 814 (because a total of 814 tickets were sold).
With these two equations, you can substitute the value of S from the first equation into the second equation. Therefore, (A + 64) + A = 814. Simplify this to get 2A + 64 = 814.
To find the number of adult tickets, solve the simplified equation for A. Subtract 64 from both sides to get 2A = 750, and then divide by 2 to find that A = 375.
So, 375 adult tickets were sold.
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20 POINTS PLEASE HELP!!
Determine if the function f is an exponential function. If so, identify the base. If not, why not? f(x)= e^x
A pair of standard dice is rolled find the probability that the sum of the two dice is greater than 12
Answer:
Probability that the sum of the two dice is greater than 12 is ZERO.
Step-by-step explanation:
Here, when two dices are rolled together, the sample space is given as:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,6)
(6, 1), (6, 2), (6, 3), (6, 4),(6,5), (6,6) = Total 36 outcomes
Now, E : Event of getting a sum greater than 12.
So here, number of possible outcomes = 0
So, the probability that the sum of the two dice is greater than 12 = 0/36 = 0
So, it is an IMPOSSIBLE EVENT.
It is impossible to roll a sum greater than 12 with two standard six-sided dice, as the maximum sum possible is 12. Therefore, the probability of rolling a sum greater than 12 is zero.
Explanation:The student asked about the probability that the sum of two standard six-sided dice is greater than 12. Since the highest sum one can achieve with two six-sided dice is 12 (when both dice show a 6), it is impossible to roll a sum greater than 12. Therefore, the probability of this event is zero.
When considering every outcome of rolling a die, we must include all possible individual results, which range from 1 to 6 for each die. The sum of two dice ranges from a minimum of 2 (both dice showing 1) to a maximum of 12 (both dice showing 6). Consequently, there are no combinations of dice that can result in a sum that exceeds 12.
The highest sum achievable on two six-sided dice is 6 + 6 which equals 12. This makes sums greater than 12 unattainable, and highlights the importance of considering the specified number of sides on dice when calculating probabilities related to their sums.
Is -9 2/7 bigger equal or less than -9.3
Answer:
-9 2/7 is bigger than -9.3.
Step-by-step explanation:
Imagine these two integers on a number line. On the negative side of the line, these two lie. The way I think of it is that the smaller the value is on the positive side, the bigger it is on the negative side. For example, -1 is bigger than -5. -0.5 is bigger than -1. -13.5 is bigger than -13.7.
The given fraction - 9 2/7 is bigger than the given number - 9.3.
Given the fraction is - 9 2/7
-9 2/7 = - (9 + 2/7)
Now, 2/7 is equal to approximately 0.286.
So, - 9 2/7 = - ( 9 + 2/7 ) = - ( 9 + 0.286) = - 9.286
Thus, 9.286 < 9.3
When negative quantity multiplied then inequality sign changes so,
( -1 ) ( 9.286 ) > ( -1 ) ( 9.3 )
- 9.286 > - 9.3
Therefore the given fraction - 9 2/7 is bigger than the given number - 9.3.
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Mr Anderson has a 10 foot metal pipe that he cut into 4 equal length pieces. What is the length of each piece
Answer:
The length of each piece is 2.5.
Step-by-step explanation:
10/4=2.5
Answer:
2.5 ft
The drawing will help
The sum of two numbers is 48, and their difference is 14. What are the two numbers?
Answer: 17 and 31
Step-by-step explanation:
first number = x
second number = y
x+y=48
-(x-y=14)
---------------
2y=34
y=17
x=31
Answer:
17 and 31
Step-by-step explanation:
17 + 31 = 48, I basically just plugged in random numbers until I got the answer.
Tom bought his fiancée Marie a 3800 diamond engagement ring Marie discovers that the value of the ring appreciates 4% each year what is the value of the ring after 4 years
Value of ring after four years with appreciation of 4 % each year is 4445.46
Solution:Given that
Tom bought his fiancée Marie a 3800 diamond engagement ring
Marie discovers that the value of the ring appreciates 4% each year
Need to determine value of ring after four years
Initial value of the ring = 3800
Appreciation of 4% in value means 4% increase
After 1 years , value increases by 4% which means
Value after 1 year = Initial value of the ring + 4% of Initial value of the ring
[tex]\begin{array}{l}{=3800+4 \% \text { of } 3800} \\\\ {=3800+\frac{4}{100} \times 3800=3952}\end{array}[/tex]
After 2 years, value increases by 4% of Value after 1 year which means
Value after 2 years = Value after 1 year + 4% of Value after 1 year
[tex]\begin{array}{l}{=3952+4 \% \text { of } 3952} \\\\ {=3952+\frac{4}{100} \times 3952=4110.08}\end{array}[/tex]
After 3 years, value increases by 4% of Value after 2 years which means
Value after 3 years = Value after 2 years + 4% of Value after 2 years
[tex]\begin{array}{l}{=4110.08+4 \% \text { of } 410.08} \\\\ {=4110.08+\frac{4}{100} \times 4110.08=4274.4832}\end{array}[/tex]
After 4 years , value increases by 4% of Value after 1 year which means
Value after 4 years = Value after 3 years + 4% of Value after 3 years
[tex]\begin{array}{l}{=4274.4832+4 \% \text { of } 4274.4832} \\\\ {=4274.4832+\frac{4}{100} \times 4274.4832=4,445.46}\end{array}[/tex]
Value of ring after four years with appreciation of 4 % each year is 4445.46
To calculate the future value of a ring appreciating at 4% each year for 4 years, compound interest formula is used. The ring's value after 4 years is approximately $4,445.46.
Explanation:The question refers to the calculation of the future value of an investment, which is a common problem in mathematics dealing with compound interest. Tom bought an engagement ring for $3,800, and its value appreciates at a rate of 4% each year. To find the value of the ring after 4 years, we use the formula for compound interest:
Future Value = Present Value x (1 + Rate of Interest)Number of Years
Step-By-Step Calculation
After applying the compound interest formula, the value of the ring after 4 years would be approximately $4,445.46.
please graph these dont have time to finish
Let x represent one number and let y represent the other number. The sum of two numbers is -11 if one number is subtracted from the other their difference is -3 use the given conditions to write of the equation and solve the system find the numbers
Answer:
look at above image for answer. thank you for the question
Using the given conditions, we formed two equations: x + y = -11 and x - y = -3. We then solved these simultaneous equations to find that the two numbers are -7 and -4.
We have been given two conditions to find the values of two numbers, represented by x and y. The first condition can be expressed as the equation x + y = -11. The second condition gives us the second equation x - y = -3.
adding the first and second equation:
(x + y) + (x - y) = -11 + (-3)
2x = -14
x = -7
We can then substitute the value of x back into one of the original equations to solve for y:
-7 + y = -11
y = -11 + 7
y = -4
Thus, the two numbers are -7 and -4.