Answer:
[tex]\large\boxed{\dfrac{1}{4}+-\dfrac{2}{3}=-\dfrac{5}{12}}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{4}+\left(-\dfrac{2}{3}\right)=\dfrac{1}{4}-\dfrac{2}{3}\\\\\text{You must find the common denominator.}\\\\\text{List of multiples of 3:}\ 0,\ 3,\ 6,\ 9,\ \boxed{12},\ 15,\ ...\\\text{List of multiples of 4:}\ 0,\ 4,\ 8,\ \boxed{12},\ 16,\ ...\\\\\text{The common denominator is}\ \boxeed{12}.\\\\3\cdot4=12\\\\\dfrac{1}{4}=\dfrac{1\cdot3}{4\cdot3}=\dfrac{3}{12}\\\\\dfrac{2}{3}=\dfrac{2\cdot4}{3\cdot4}=\dfrac{8}{12}\\\\\\\dfrac{1}{4}-\dfrac{2}{3}=\dfrac{3}{12}-\dfrac{8}{12}=\dfrac{3-8}{12}=-\dfrac{5}{12}[/tex]
Find the absolute extrema of the function \(f(x)= xe^{- x^2/18}\) on the interval \([-2,4]\).
if a debt of $480 is reduced by 20% find the new debt
To find the new debt after a 20% reduction, subtract 20% of the original debt from the original debt.
Explanation:To find the new debt after a 20% reduction, we need to subtract 20% of the original debt from the original debt. Here's how to calculate it:
Convert 20% into a decimal by dividing it by 100: 20% = 0.20Multiply 0.20 by $480 to find the reduction amount: 0.20 x $480 = $96Subtract $96 from $480 to find the new debt: $480 - $96 = $384Therefore, the new debt after a 20% reduction is $384.
The new debt after being reduced by 20% is $384.
Explanation:To find the new debt after it has been reduced by 20%, we can use the following steps:
Calculate 20% of $480 by multiplying 480 by 0.20. 20% of 480 is $96.Subtract the amount calculated in step 1 from the original debt. The new debt is $480 - $96 = $384Therefore, the new debt after being reduced by 20% is $384.
what is 107,609 divided by 72 with a remainder with no decimal?
a pail holds 4 4/1 gallons of water.How much is this in cups
To convert gallons to cups, multiple conversion factors can be used. Assuming a typo in '4 4/1 gallons' and correcting it to '4 gallons,' the conversion shows that there are 16 cups in a gallon. Thus, 4 gallons of water is equivalent to 64 cups.
Explanation:To convert gallons to cups, you can use conversion factors that relate these two units of volume. First, we need to correct the expression given for the volume of water in the pail. It seems there is a typo because '4 4/1 gallons' isn't a proper number. Assuming it's intended to be '4 gallons,' we can proceed with the conversion.
Since 1 gallon is equivalent to 4 quarts and 1 quart is equivalent to 2 pints, and 1 pint is equivalent to 2 cups, we can create a chain of multiplications to convert from gallons to cups.
1 gallon = 4 quarts1 quart = 2 pints1 pint = 2 cupsMultiplying these together gives us:
1 gallon = 4 x 2 x 2 = 16 cups
Therefore, to find out how many cups are in 4 gallons:
4 gal x 16 cups/gal = 64 cups
So, 4 gallons of water is equivalent to 64 cups.
Final answer:
To convert 4 gallons to cups using the provided conversion factors, multiply the gallons by 4 to get quarts, then multiply by 2 to get pints, and again multiply by 2 to get cups, resulting in a total of 64 cups.
Explanation:
The student's question involves converting a quantity of gallons into cups, which is a Mathematics problem specifically dealing with units of volume conversion. The amount given, 4 4/1 gallons, seems to be a typo, but assuming the intention was to convert 4 gallons into cups, we can use the given conversion factors:
1 gallon = 4 quarts1 quart = 2 pints1 pint = 2 cupsTo find out how many cups are in 4 gallons, we follow these steps:
Multiply the number of gallons by 4 to convert gallons to quarts.Since 1 gallon is equal to 4 quarts, 4 gallons is equal to 4 x 4 quarts, which is 16 quarts.Since 1 quart is equal to 2 pints, we can then convert quarts to pints by multiplying the number of quarts by 2.16 quarts is equal to 16 x 2 pints, which is 32 pints.Finally, since 1 pint is equal to 2 cups, to convert pints to cups, multiply the number of pints by 2.32 pints is equal to 32 x 2 cups, which equals 64 cups.Therefore, 4 gallons is equivalent to 64 cups.
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Jane ran 3/8 of the distance that Jack ran. If Jane ran 2/3 of a mile, how far did Jack run?
Which of these could be used to solve the problem?
A. 3/8 * = 2/3
B. 2/3 * = 3/8
C. x=(2/3) (3/8)
D. x=3/8 *- 2/3*
Using proportions, it is found that the distance that Jack ran is given by:
A. [tex]\frac{3}{8}x = \frac{2}{3}[/tex]
The distance ran by Jane was of [tex]\frac{2}{3}[/tex] of a mile.This distance was also [tex]\frac{3}{8}[/tex] of the distance ran by Jack, which is given by x.Applying the proportion, we have that [tex]\frac{3}{8}[/tex] multiplied by x is equals to [tex]\frac{2}{3}[/tex], hence:
[tex]\frac{3}{8}x = \frac{2}{3}[/tex]
Which means that the correct option is given by a.
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The equation of the line in this graph is y=____x+____
If a truck traveled 75.648 miles per year how many miles did it travel monthly
choices are (mode, mean, median)
A sample was selected and the eye color of every person in the sample was recorded.
{Brown,Brown,Green,Blue,Brown,Green,Hazel,Brown,Green,Hazel}
The ___________ should be used.
A Girl Scout troop sold cookies. The number of boxes each scout sold is listed below.
{35,45,47,27,50,43,25,52,37,312}
The ___________ should be used.
A pizza parlor sold the follow number of pizzas each day from January 27-28.
{30,28,23,25,35,27,29}
The __________ should be used.
A chemist has two large containers of sulfuric acid solution, with different concentrations of acid in each container. Blending 305 mL of the first solution and 580 mL of the second gives a mixture that is 10.24% acid, whereas blending 85 mL of the first mixed with 490mL of the second gives a 6.10% acid mixture. What are the concentrations of sulfuric acid in the original containers?
The concentrations of sulfuric acid in the original containers as per the system of equation is equals to 24% in first container and 3% in second container.
What is system of equation?" A system of equations is finite set of equations for which we find the common solution."
According to the question,
'a' represents the concentration of acid in first container
'b' represents the concentration of acid in second container
Situation1: 305 mL of the first solution and 580 mL of the second gives a mixture that is 10.24% acid, it represents the equation as,
a% of 305 + b% of 580 = 10.24% of 885
⇒ 305a + 580b = 9062.4 _______(1)
Situation 2:85 mL of the first mixed with 490mL of the second gives a 6.10% acid mixture, it represents the equation as,
a% of 85 + b% of 490 = 6.10% of 575
⇒ 85a + 490b = 3507.5 ______(2)
Solve system of equation by multiplying (1) by 85 and (2) by 305 we get,
25925a + 49300b = 770303 _______(3)
25925a + 149450b = 1069787.5 _______(4)
Subtract system of equation (3) from (4) we get,
100150b = 299483.5
⇒ b = 2.9
⇒ b≈ 3%
Substitute the value of 'b' in (2) we get,
85a + 490(3) = 3507.5
⇒85a + 1407 = 3507.5
⇒ 85a = 2037.5
⇒ a = 23.9
⇒ a ≈24%
Hence, concentration of sulfuric acid in first container 24% and second container 3% as per the system of equation.
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The ratio of the height to the width of a packaging label is 5 to 19. If the height of the label is 2 inches, what is its width? HINT: Set up and solve as a proportion and find x.
Answer:
7.6 inches
Step-by-step explanation:
The ratio of the height to the width of a packaging label is 5 to 19, that is,
h/w = 5/19 [1]
If the height of the label is 2 inches, and its width is unknown (x), that is,
h/w = 2 in/x [2]
We can set up a proportion with [1] and [2],
5/19 = 2 in/x
We use the cross product property of proportions.
5 × x = 19 × 2 in
x = 19 × 2 in/ 5 = 7.6 in
The width is 7.6 inches.
How many elements does each of these sets have where a and b are distinct elements?
a.p({a, b,{a, b}})
b.p({∅, a,{a},{{a}}})
c.p(p(∅))?
Change 5 2/3 to a mixed decimal and round to the nearest hundredth.
A concrete stepping stone measures 20 square inches. What is the area of 30 such stones
simplify (7x−13)−(x+5)
a=9y+3yx solve for y
Answer:
[tex]y=\frac{a}{(9+3x)}[/tex]
Step-by-step explanation:
we have
[tex]a=9y+3yx[/tex]
Solve for y
That means -----> isolate the variable y
Step 1
Factor the variable y in the right side
[tex]a=y(9+3x)[/tex]
Step 2
Divide by [tex](9+3x)[/tex] both sides
[tex]a/(9+3x)=y(9+3x)/(9+3x)[/tex]
Step 3
Simplify
[tex]y=\frac{a}{(9+3x)}[/tex]
An arrow is shot vertically upward from a platform 25ft high at a rate of 172ft/sec. When will the arrow hit the ground?
Jack wants to buy a skateboard that usually sells for $79.40. All merchandise is discounted by 12%. What is the total cost of the skateboard if Jack has to pay a state sales tax of 6.75%. Round your intermediate calculations and answer to the nearest cent.
Gerard bought 9 hamburgers and 3 orders of fries for 24.75. Chris bought 6 hamburgers and 4 orders of fries for 19.50. Each hamburger cost the same amount. Each Order of fries cost the same amount. Wrote a system of equations that can be used to find how much one hamburger and one Order of fries cost.
Answer:
System of equations:
9x+3y=24.75
6x+4y=19.50
x: cost of a hamburger
y: cost of an order of fries
Step-by-step explanation:
We define the variables of the system of equations:
x: cost of a hamburger
y: cost of an order of fries
We propose the system of equations:
To Gerard: 9x+3y=24.75
To Chris: 6x+4y=19.50
where, the coefficients in the equations represent the quantity that was purchased from each product and the variables represent the costs of each product.
(1 pt) let x be an exponential random variable with parameter \lambda = 4, and let y be the random variable defined by y = 2 e^x. compute the probability density function of y:
What is the value of s 0.7(3s+4)-1.1s=7.9
Rewrite the expression 3a^2b^3c^5/8x^4y^3z so that it has no denominator.
Answer: 3*2^-3a^2b^3c^5x^-4y^-3z^-1 (graded correct)
Step-by-step explanation:
meaganblatcher (original poster)
you take away 8 and multiply and get 3a^2b^3c^5 * x^4y^3z or something
This becomes 3a^2b^3c^5x^-4y^-3z^1/8
Then you move the 8 up using multiplication and get -24a^2b^3c^5x^4y^3z^1
This can be simplifed as 3*2^-3a^2b^3c^5x^-4y^-3z^-1
regardless that's the real answer.
Which of the following represents the vertical asymptotes of the function
The linear equation y=3x−5y=3x−5 y equals 3 x , minus 5 is in what form.
What is the value of x? Enter your answer in the box
using Pythagorean Theorem
x^2 +b^2 = c^2
x^2 +12^2 = 13^2
x^2 +144 = 169
x^2 = 25
x = sqrt(25) = 5
x = 5
1.all real numbers that are less than -3 or greater than or equal to 5
A.x < -3 or x≥5
B.x < 5 or x ≥-3
C.x ≤ -3 or x >5
D.x ≤-3 or x ≤ 5
2.The time a cake must bake is between 25 minutes and 30 minutes, inclusive.
A.25 < x < 30
B.25 ≤ x ≤ 30
C.25 ≤x ≥ 30
D.25 < x > 30
3. Solve. 5 < x -2 <11
A.5 < x < 11
B.7 < x < 13
C.7 < x < 11
D.5 < x < 16
4. Which graph shows the solution of 9 - c < 2 or -3c > 15?
Answer:
Kramer is wrong trust me
The answers are:
1. A
2. B
3. B
4. C
100% just took it :)
Lesson 6 - Compound inequalities
Step-by-step explanation:
A doctor's office has a computer file showing the heights of 100 male patients of one of the doctors of the practice. the heights range from 18 inches to 68 inches. by accident, the greatest height has been recorded as 680 inches, instead of 68 inches. (a) does this affect the average? if so, by how much? (b) does this affect the median? if so by how much?
The effect of the mistake is:
The mean value obtained is larger. The median value is not affected.The average value recorded is larger than it actually is. Hence , the average value is affected by the mistake. Given the information supplied, we can only deduce that the mean value will be greater than the actual average.
The mean involves taking the sum of all the values and dividing it by the number of values.
Using a value of 680 instead of 68 will mean that, the sum obtained is greater than the actual sum.
The median on the other hand isn't affected by this error, because, the arrangement of the values isn't changed.
The sorting of values is very crucial to calculating the Median. However, either 68 or 680. The position of the maximum value remains unchanged.
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A School raised $13,809 during it's fall fundraiser and $20,786 during it's winter fundraiser. The total fundraising goal for the school year is $50,000. How much more money does the school need to raise during the spring fundraiser to reach its goal?
Show your work...
The extra fundraiser school should get is $15405.
What is a fundraiser?A fundraiser is an event which is intended to raise money for a particular purpose, for example, for a charity.
Given that, A School raised $13,809 during its fall fundraiser and $20,786 during its winter fundraiser. The total fundraising goal for the school year is $50,000.
The yet total fundraised = fall fundraiser + winter fundraiser
= $13,809 + $20,786
= $34595
Since, they need $50000 in total,
Therefore, remaining amount = total - collected
= $50000 - $34595
= $15405.
Hence, the extra fundraiser school should get is $15405.
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What is the relationship between the values of the 4s in the number 4,438
Answer:
The leftmost 4 has a positional value of [tex]4\times10 ^ 3[/tex]. While the other 4 that appears in the displayed figure has a positional value of [tex]4\times10^2[/tex]. Then, it can be said that the relationship between the major and the minor is: [tex]\frac{4\times10 ^ 3}{4\times10 ^ 2} = 10[/tex]. That is, the relationship is that the 4 on the left is 10 times greater than the other 4 .
Step-by-step explanation:
On a winter day in Alaska, the temperature at noon was -0.6°C. From noon to 3:00, the temperature increased by 1.2°C. From 3:00 to 6:00, it dropped 0.4°C, and from 6:00 to 9:00, it decreased by 0.6°C. What expression shows the temperature in °C at 9:00 p.m.?
At 9:00 p.m, the temperature would be equal to -0.4°C
How are Kelvin, Celsius, and Fahrenheit related?We have got an equation that can relate these three units of measurement of temperature, as given below:
[tex]\dfrac{C}{5} = \dfrac{F - 32}{9} = \dfrac{K - 273}{5}[/tex]
where C represents the measurement of a fixed temperature in celsius, F represents the measurement of that same intensity temperature in fahrenheit, and K represents the measurement of equally intense temperature in kelvin.
We are given that
On a winter day in Alaska, the temperature at noon = -0.6°C.
Then From noon to 3:00, the temperature increased by 1.2°C. From 3:00 to 6:00, it dropped 0.4°C, and from 6:00 to 9:00, it decreased by 0.6°C.
-0.4
Therefore, the expression could be;
-0.6+1.2-0.4-0.6
=-0.4
The expression that shows the temperature in °C at 9:00 p.m is -0.6+1.2-0.4-0.6
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the amount of money in an account with continuously compounded interest is given by the formula A = Pert, where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the nearest tenth of a year how long it takes for an amount of money to double if interest is compounded continuously at 5.2%. 5.9 years 13.3 years 1.3 years 0.6 years