Answer:
-6/125
Step-by-step explanation:
well first, the decimal is negative so automatically whatever fraction you write is going to be negative
the you look at the decimal:
-0.048
there is a 0 in the tenths place, a 4 in the hundredths place, and an 8 in the thousandths place
so that means, the fraction would be -48/1000
but since it isnt simplified, that what you have to do
both can be divided by 2
which will give you:
-24/500
but those can be divided by 2 again:
-12/250
these can also be divided by 2 again:
-6/125
since the 125 cannot be divided into 2 evenly again, this is the fraction in simplest form
The simplest form of -0.048 is -6/125.
Use the concept of fraction defined as:
A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.
The given decimal number is -0.048
Since there are 3 numbers after decimal,
Therefore,
In fractional the the number can be written as,
-0.048 = -48/1000
Divide both numerator and denominator by 8,
-0.048 = -6/125
Hence,
The simplest form of -0.048 is -6/125.
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A committee of 4 people is chosen from 8 women and 8 men. How many different committees are possible that consist of 2 women and 2 men?
there are 784 different committees possible that consist of 2 women and 2 men.
To form a committee of 4 people consisting of 2 women and 2 men, we need to choose 2 women from the 8 available women and 2 men from the 8 available men.
We can calculate the number of ways to choose 2 women from 8 using combinations, denoted as ( C(n, k) \), which is calculated as:
[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]
Where:
- ( n ) is the total number of items (in this case, the number of women)
- ( k ) is the number of items to choose (in this case, 2)
- ( n! ) denotes the factorial of ( n ), which is the product of all positive integers up to ( n )
Similarly, we can calculate the number of ways to choose 2 men from 8.
Once we have chosen 2 women and 2 men, we multiply these numbers together to find the total number of possible committees.
Let's calculate it step by step:
1. Choose 2 women from 8:
[tex]\[ C(8, 2) = \frac{8!}{2!(8-2)!} = \frac{8!}{2!6!} = \frac{8 \times 7}{2 \times 1} = 28 \][/tex]
2. Choose 2 men from 8:
[tex]\[ C(8, 2) = \frac{8!}{2!(8-2)!} = \frac{8!}{2!6!} = \frac{8 \times 7}{2 \times 1} = 28 \][/tex]
3. Multiply the number of ways to choose women and men:
[tex]\[ \text{Total number of committees} = 28 \times 28 = 784 \][/tex]
So, there are 784 different committees possible that consist of 2 women and 2 men.
The sum of three integers is 12
12
. The sum of the first and second integers exceeds the third by 32
32
. The third integer is 15
15
less than the first. Find the three integers.
The three integers are 5,17 and -10
Step-by-step explanation:
Let x, y and z be three integers then
[tex]x+y+z=12 \ \ \Eqn\ 1[/tex]
'The sum of the first and second integers exceeds the third by 32'
[tex]x+y=z+32\ \ \ \ Eqn\ 2[/tex]
The third integer is 15 less than the first.
[tex]z=x-15\ \ \ \ Eqn\ 3[/tex]
From Eqn 2:
[tex]x+y=z + 32\\x+y-z=32[/tex]
Subtracting Eqn 1 from eqn 2
[tex]x+y-z-(x+y+z)=32-12\\x+y-z-x-y-z=20\\-2z=20[/tex]
Dividing both sides by -2
[tex]\frac{-2z}{-2}=\frac{20}{-2}\\z=-10[/tex]
Putting z=-10 in Eqn 3
[tex]z=x-15\\-10=x-15\\x=15-10\\x=5[/tex]
Putting x=5 and z=-10 in Eqn 1
[tex]x+y+z=12\\5+y-10=12\\y-5=12\\y=12+5\\y=17\\[/tex]
Hence,
The three integers are 5,17 and -10
Keywords: Linear Equations, Variables
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Answer:
First = 5, second = 17, third = -10
Step-by-step explanation:
First integer = x
The third integer is 15 less than the first, so
Third integer = x - 15
The second integer = y
The sum of the first and second integers exceeds the third by 32, so
The sum of the first and second integers = x + y
The third integer = x - 15
x + y is 32 more than x - 15, hence
x + y - 32 = x - 15
y - 32 = -15
y = 32 - 15
y = 17
The second integer = 17
The sum of three integers is 12, so
x + 17 + x - 15 = 12
2x + 2 = 12
2x = 12 - 2
2x = 10
x = 5
x - 15 = 5 - 15 = -10
it takes one fourth of a gallon of paint covers one fifth of a car how much paint covers the whole car
Answer:
The volume of paint that covers the whole car is [tex]1\frac{1}{4}[/tex] gallons or one and a quarter gallons.
Step-by-step explanation:
Let the volume of paint required to cover whole car be 'x'.
Given:
Volume of paint to cover one-fifth of a car = one-fourth of a gallon.
We use unitary method to determine the volume of paint required.
∵ One-fifth of a car requires paint = [tex]\frac{1}{4}\ gal[/tex]
∴ Whole volume of car requires paint = [tex]\frac{\frac{1}{4}}{\frac{1}{5}}[/tex]
[tex]=\frac{1}{4}\times \frac{5}{1}\\=\frac{5}{4}\\=1\frac{1}{4}\ gal[/tex]
Therefore, the volume of paint that covers the whole car is [tex]1\frac{1}{4}[/tex] gallons or one and a quarter gallons.
This month Jan saved $80 from her babysitting job. Last month she saved $20. How many times more did she save this month than last month?
Answer:
4 times more
Step-by-step explanation:
80/20=4
The price of an air conditioner was reduced from rs 27000 to rs 24000 find the rate of percentage
Answer:
Step-by-step explanation:
On a certain hot summer's day, 196 people used the public swimming pool. The daily prices are $ 1.50 for children and $ 2.00 for adults. The receipts for admission totaled $ 314.00 . How many children and how many adults swam at the public pool that day?
Number of adults = 40
Number of children = 156
Step-by-step explanation:
Let x be the number of adults and
y be the number of children
Then according to given statements
[tex]x+y=196\ \ \ Eqn\ 1\\2.0x+1.50y = 314\ \ \ Eqn\ 2\\[/tex]
From equation 1:
[tex]x+y = 196\\x = 196-y[/tex]
Putting in equation 2
[tex]2(196-y) + 1.50y = 314\\392-2y+1.50y = 314\\392-0.5y = 314\\-0.5y=314-392\\-0.5y=-78[/tex]
Dividing both sides by -0.5
[tex]\frac{-0.5y}{-0.5} = \frac{-78}{-0.5}\\y = 156[/tex]
Putting y = 156 in equation 1
[tex]x+156 = 196\\x = 196 - 156\\x = 40[/tex]
Hence,
Number of adults = 40
Number of children = 156
Keywords: Linear equations, Variables
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a woman is walking at the rate of 90 yards per minute. How fast is she going in feet per second?
Answer:
She is going at the rate of 4.5 feet per second.
Step-by-step explanation:
Given:
The rate of walking is 90 yards per minute.
Now, to find the rate in feet per second.
1 yard = 3 foot.
1 minute = 60 seconds.
So, first we find the rate of walking per second in yard = [tex]90\div 60[/tex]
Therefore by dividing we get = [tex]1.5 yard[/tex]
Now, we find the rate of walking per second in feet = [tex]1.5\times 3[/tex]
So, by multiplying we get = [tex]4.5 feet[/tex]
Therefore, she is going at the rate of 4.5 feet per second.
How can you solve 1/2 divided by 4? Is the answer 0.375 or 2/4
Answer:
2
Step-by-step explanation:
(1/2)/4=(1/2)(4/1)=4/2=2
Answer:
1/8
Step-by-step explanation:
1/2 ÷ 4
= 1/2 x 1/4
= 1x1/2x4
= 1/8
how to solve each equation by completing a square -4x^2+10x-40=-9x^2
Answer:
x = -4 or 2
Step-by-step explanation:
-4x² + 10x − 40 = -9x²
First, move the x terms to one side and the constant to the other.
5x² + 10x = 40
Divide by the leading coefficient:
x² + 2x = 8
Take half of the b coefficient, square it, then add to both sides.
(2/2)² = 1
x² + 2x + 1 = 8 + 1
x² + 2x + 1 = 9
Factor the perfect square:
(x + 1)² = 9
Solve for x:
x + 1 = ±3
x = -1 ± 3
x = -4 or 2
Answer:x=2,-4
Step-by-step explanation:
Andrew draws a scale drawing of his office.If each 5 cm in the scale drawing equals 10ft, what are the actual dimensions of Andre’s office?
Answer:
well if it is a square then 10ft by 10ft. Otherwise, since you haven't given me the scale drawing, just find the area through 5cm. Then multiply your answer by 2 and instead of cm have ft.
Step-by-step explanation:
what is the equation of a line parallel to y-2x=3 that passes through the point (3,1)
Answer:
y = 2x - 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange y - 2x = 3 into this form by adding 2x to both sides
y = 2x + 3 ← in slope- intercept form
with slope m = 2
Parallel lines have equal slopes, thus
y = 2x + c ← is the partial equation
To find c substitute (3, 1) into the partial equation
1 = 6 + c ⇒ c = 1 - 6 = - 5
y = 2x - 5 ← equation of line
The rule which allows us to change the sign of an exponent is called the ____ rule.
Answer:
The rule which allows us to change the sign of an exponent is called the negative exponent rule.
Step-by-step explanation:
Consider the provided information.
The negative exponent rule is the rule which allows to change the sign of an exponent.
[tex]x^{-1}=\frac{1}{x}[/tex]
According to negative exponent rule: A negative exponents in the numerator moved to the denominator and become positive exponents.
If A negative exponents in the denominator moved to the numerator and become positive exponents.
Hence, the required statement is: The rule which allows us to change the sign of an exponent is called the negative exponent rule.
Solve the inequality. Graph the solution.
7z< -28
Answer: The answer is -9
Step-by-step explanation:
7z<-28= -9
Because we take the -28 and add 19 because that's the common denominator and we come up with -9
Round 2034627105 to the nearest hundred thousand
you need to put the decimal somewhere but if it comes at the beginning then 203463is your answer.
Answer:
here is an actual answer
203463
Step-by-step explanation:
Paul Hastings had a checkbook balance of $1345.00. His bank statement showed a deposit of $423.00 and he hadnt recorded a $15 service fee. What should his checkbook balance be?
Answer:
Paul Hastings checkbook balance be $1753
Explanation:
We are given Paul Hastings
current checkbook balance is equal to $1345.00
and a deposit of $423.00 is said to be made in the bank
so the new balance will be addition of this deposit in the current balance also there's a deduction of $15 as service fee.
So the total checkbook balance will be after subtracting $15 from sum of current balance and deposit.
So his checkbook balance = $1345 + $423 - $15
= $1753
which is the required value of checkbook.
math please help me :)
Answer:
D, My original answer was A (-6,2) B (-6,5) but that's particular order is not an option but if you flip it you get answer D
11. Any company plans to connect a total of 20 pF of capacitance to a 7200-V
dine. To make this connection, four capacitors will be connected in series, What is
the capacitance of each capacitori
1 W
oche minimum ac
Answer:
C = 80pF
Step-by-step explanation:
The total capacitance of 4 capacitors connected in series is given by:
[tex]Ct = \frac{1}{1/C1 + /C2 + 1/C3 + 1/C4}[/tex]
[tex]Ct = \frac{1}{1/C + /C + 1/C + 1/C}[/tex]
[tex]Ct = \frac{1}{4/C}[/tex]
[tex]Ct = \frac{C}{4}=20pF[/tex]
Solving for C:
C = 4*20pF
C = 80pF
Solve for x.
X-8=-20
-12
12
-28
28
Answer:
-12
Step-by-step explanation:
x - 8 = -20 (add 8 to both sides)
x = -20 + 8
x = -12
Answer:
-12
Step-by-step explanation:
-12 + -8 is -20.
x= -12 because if you added 28 or 12, the answer would be positive. If you subtracted -28 from -8 your answer would be -36.
So the only answer is -12.
please help answer this math question what is 0.4 X 0.5 =
Answer:
it would be 0.2
Step-by-step explanation:
When you multiply 0.4*0.5 it would equal 0.2 since 4*5=20 then 4.0*0.5= 0.2 since 0.2 in fraction form is 2/10 or 20/100.
Write the number 9.359 × 105 in standard form.
Answer:
982.695
Step-by-step explanation:
9.359 x 105 = 982.695
A book has 150 pages and you read 3 pages per day.after a certain number of days,there are 60 pages left.write an equation to show how many days,x,you read
To determine the number of days you have read, an equation is set up as 150 - 3x = 60, where x represents the number of days. After solving, it reveals that you have read for 30 days.
Explanation:To find the number of days, x, that you have read, given that there are 60 pages left and you read 3 pages per day in a 150-page book, we can set up the following equation:
150 - 3x = 60
This equation represents the total number of pages in the book (150) minus 3 pages for each day that you read (3x) equal to the number of pages left (60).
Now, solve for x to determine the number of days you have been reading:
150 - 60 = 3x
90 = 3x
x = 30 days
Therefore, you have been reading for 30 days.
DO I like AirPods??
if you get this right
you get BrainLiest
and remember this is 50 points
so this is the question of your life
Yes, you like AirPods due to zero wires, comfortable fit and long lasting 24 hours battery life.
Step-by-step explanation:
The current technology employed in Apple devices has attracted most users.For example in the AirPods technology, users can enjoy features such as instant connection to other Apple devices, easy switching from Mac to Os devices, comfortable fit and long battery hours. Even with the current price of AirPods at $159 the advantages outweigh the cost.
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Answer: Yeah you like airpods
Step-by-step explanation:
5= 10x - 5y what’s the slope-intercept
Answer:
y=2x-1
Step-by-step explanation:
What is (8x-30)+6x+(2x+10) simplified?
Answer:
16x-20
Step-by-step explanation:
(8x-30)+6x+(2x+10)
8x-30+6x+2x+10
8x+6x+2x-30+10
14x+2x-20
16x-20
Which statements are true about the ordered pair (−4, 0) and the system of equations?
{2x+y=−8x−y=−4
Select each correct answer.
The ordered pair (−4, 0) is a solution to the first equation because it makes the first equation true.
The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true.
The ordered pair (−4, 0) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (−4, 0) is a solution to the system because it makes both equations true.
The true statements are:
The ordered pair (−4 , 0) is a solution to the first equation because it makes the first equation true ⇒ 1st answer
The ordered pair (−4 , 0) is a solution to the second equation because it makes the second equation true ⇒ 2nd answer
The ordered pair (−4, 0) is a solution to the system because it makes both equations true ⇒ 4th answer
Step-by-step explanation:
To prove that point (a , b) is a solution of an equation
Substitute x and y in the equation by a and bIf the left hand side is equal to the right hand side, then the point is a solution of the equationIf the left hand side doesn't equal the right hand side, the point is not a solution of the equation∵ The system of equations is:
2x + y = -8 ⇒ (1)
x - y = -4 ⇒ (2)
The ordered pair is (-4 , 0)
Substitute x by -4 and y by 0 in each equation
∵ x = -4 and y = 0
∵ The left hand side in equation (1) is 2x + y
∵ 2(-4) + 0 = -8 + 0 = -8
∴ The left hand side = -8
∵ The right hand side = -8
∴ The left hand side = the right hand side
∴ (-4 , 0) is a solution of equation (1)
The ordered pair (−4 , 0) is a solution to the first equation because it makes the first equation true
∵ The left hand side in equation (2) is x - y
∵ (-4) - 0 = -4 - 0 = -4
∴ The left hand side = -4
∵ The right hand side = -4
∴ The left hand side = the right hand side
∴ (-4 , 0) is a solution of equation (2)
The ordered pair (−4 , 0) is a solution to the second equation because it makes the second equation true
∵ The ordered pair (-4 , 0) makes the two equations true
∴ The ordered pair (-4 , 0) is the solution of the system of equations
The ordered pair (−4, 0) is a solution to the system because it makes both equations true
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2) Jim get $200 for 50 sales, $350 for 70 sales, and $500 for
85 sales. This is called
Answer:
salary based on how many sales are made
Step-by-step explanation:
Write the equation of the line that passes through the point (4,3) and is perpendicular to the line y=2x-4
Answer:
y-3=-1/2(x-4)
Step-by-step explanation:
y-y1=m(x-x1)
perpendicular means negative reciprocal of the current slope,
and the negative reciprocal of 2 is -1/2.
y-3=-1/2(x-4)
I WILL GIVE 100 POINTS AND BRAINLIEST IF YOU CAN WRITE 3 SENTECES FOR THIS!!!!!!!
Explain how the zero property in the problem 2/3 (0)= 0 (2/3)= 0 is the same with any rational number.
Answer:
In this problem and with any rational number, the zero product property will be applied. If ab = 0, then either a = 0 or b = 0, or both. A product of factors is zero if and only if one or more of the factors is zero.
And excuse me, but where's the other 75 points?
If triangle ABC = DEF AB = 8 , BC = 19 , AC = 14 , EF = 4x - 1 and DE=y-6, what are the values of x,y, and z
Answer:
x = 5 and y = 14
Step-by-step explanation:
Given [tex]\triangle[/tex]ABC[tex]\cong \triangle[/tex]DEF.
Congruent triangles have congruent corresponding parts, so
[tex]AB\cong DE\\ \\AC\cong DF\\ \\BC\cong EF[/tex]
Since
[tex]AB=8\\ \\BC=19\\ \\AC=14\\ \\EF=4x-1\\ \\DE=y-6,[/tex]
then
[tex]4x-1=19\\ \\4x=19+1\\ \\4x=20\\ \\x=5[/tex]
and
[tex]y-6=8\\ \\y=8+6\\ \\y=14[/tex]
There is a pile of nickles and dimes. The whole pile has 82 coins and is worth 6.75. How many nickles are in the pile?
There are 29 nickles in the pile.
Step-by-step explanation:
Let,
nickles = x
dimes = y
Total coins = 82
Total worth = $6.75 = 6.75*100 = 675 cents
1 nickle = 5 cents
1 dime = 10 cents
According to given statement;
x+y=82 Eqn 1
5x+10y=675 Eqn 2
Multiplying Eqn 1 by 5;
[tex]5(x+y=82)\\5x+5y=410\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](5x+10y)-(5x+5y)=675-410\\5x+10y-5x-5y=265\\5y=265[/tex]
Dividing both sides by 5;
[tex]\frac{5y}{5}=\frac{265}{5}\\y=53[/tex]
Putting y=53 in Eqn 1
[tex]x+53=82\\x=82-53\\x=29[/tex]
There are 29 nickles in the pile.
Keywords: linear equations, subtraction
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