In terms of x and y, Julia's withdrawal from her savings account was equal to y/4 + x/12.
What does algebraic expression mean?An expression obtained by performing a finite number of algebraic fundamental operations on symbols representing numbers.
What is an illustration of an algebraic expression?Algebraic expressions have at least one variable and one operation (addition, subtraction, multiplication, division). 2(x + 8y) is an example of an algebraic expression.Both Ang and Julia have savings balances of x and y dollars, respectively.
Ang = x dollars
Julia = y dollars
Ang offers Julia a third of his savings, which she then transfers to her own savings account.
Amount in Julia's account = (1/3)x + y
Julia then spends a quarter of the total into her savings account.
Amount of money Julia spent = 1/4 × [(1/3)x + y]
= (1/12)x + (1/4)y
= y/4 + x/12
Therefore, in terms of x and y, the amount Julia spent from her savings account is y/4 + x/12.
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Order the following expressions from least to greatest.
Answer:
[tex]\boxed{a} \quad \boxed{|b - c|} \quad \boxed{|a - b|} \quad \boxed{|a - c|}[/tex]
Step-by-step explanation:
The bars either side of an expression or a value are the absolute value symbol. "Absolute value" means how far a number is from zero. Therefore, the absolute value of a number is its positive numerical value.
The values of a, b and c are negative. All expressions except "a" are absolute values, and are therefore positive numerical values. Therefore, "a" is the least expression.
The simplest way to calculate each expression's numerical value is by assigning approximate numbers to each value, then carrying out each calculation.
From inspection of the graph:
a ≈ -3.8b ≈ -1.3c ≈ -0.7[tex]\begin{aligned} \implies |a - b| & \approx |-3.8 - (-1.3)|\\ & = |-2.5| \\ &= 2.5\end{aligned}[/tex]
[tex]\begin{aligned} \implies |b - c| &\approx |-1.3 - (-0.7)| \\ &= |-0.6| \\ &= 0.6\end{aligned}[/tex]
[tex]\implies a \approx -3.8[/tex]
[tex]\begin{aligned} \implies |a - c| &\approx |-3.8 - (-0.7)| \\ &= |-3.1| \\ &= 3.1\end{aligned}[/tex]
Therefore: -3.8 < 0.6 < 2.5 < 3.1
Hence, the expressions from least to greatest are:
[tex]\boxed{a} \quad \boxed{|b - c|} \quad \boxed{|a - b|} \quad \boxed{|a - c|}[/tex]
Ramu's sister's age is 28 years old. She is 3 years older than five times Ramu's Age? What is Ramu's age?
Answer:
Ramu's sister's Age= 28
ramus age=×
28=5×+3
5×=28-3
=25
×=25/5
×=5
so the age of Ramu is 5 years old.
Answer:
25 because 5×5= 25 and 25+3=28 so ramu's age is 25
ASAP PLEASE
Solve the following word problem using elimination. Set up a system of equations before solving in order to receive full credit.
The difference between two numbers is 4. The sum of the smaller number and three times the larger number is 36. What are the two numbers?
The two numbers are 10 and 6.
Now, let's take the larger number to be x and the smaller number to be y.
According to the question,
We have the following details:
The difference between two numbers = 4
So, we have the following expression:
(x-y) = 4 .... (1)
The sum of the smaller number and three times the larger number = 36
So, we have the following expression:
(3x+y) = 36 ....(2)
Now, we will use the elimination method to solve these equations. So, we will add equation 1 and 2.
(Please note that the left hand side is added to the left hand side and the right hand side numbers are added to the right hand side numbers.)
(x-y+3x+y) = (4+36)
4x = 40
x = 40/4 (4 is in multiplication on the left hand side. So, it is in the division on the right hand side.)
x = 10
Now, putting the value of x in equation 1,
(x-y) = 4 .... (1)
(10-y) = 4
-y = 4-10
-y = -6
y = 6
Hence, the larger number is 10 and the smaller number is 6.
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suppose that the weight, x, in pounds, of a 40-year-old man is a normal random variable with mean 147 and standard deviation 16. calculate p(120≤x≤153). round your answer to four decimal places.
0.6004 is standard deviation of equation .
Why is there a standard deviation?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.An individual collection of data is compared to the average of several other sets of data using the standard deviation. You can compute two different forms of standard deviation: When data are gathered from every person in a population or collection, it is the population standard deviation.=0.6004$P(120≤X≤153)=0.6004
The mean is μ=147, and the standard deviation is σ=16.
0.6462−0.0458=0.6004.
Thus, P(120≤X≤153)=0.6004.
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Write the equation in slope-intercept form of a line that has a slope of and passes through the point (-6, 0)
3
0 >=²x
xy=
y=x-6
O 0y=x-2
O
0 >=²x+2
The equation of the line in slope intercept form with slope 1/3 and passes through ( - 6, 0) is y = 1/3x + 2.
In mathematics, the slope or gradient of a line is a number that indicates the line's steepness as well as its X and Y directions. The letter "m" stands for slope. The ratio of the "vertical change" to the "horizontal change" between any two separate points on a line is used to compute the slope.
The equation of the line in point-slope form is expressed as:
y - y₁ = m( x - x₁ )
where m is the slope.
So, m = 1/3
( x₁, y₁ ) is the point on the line = ( - 6, 0)
Substituting the values,
y - 0 = 1/3( x + 6 )
y = 1/3( x + 6 )
y = 1/3x + 6/3
y = 1/3x + 2
Hence, the equation in slope-intercept form of the line is y = 1/3x + 2.
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Simplify:
5/8(-8j+24)
Answer: -5j+15
step by step equation
Normally a chef uses 13 ounces of chocolate to make chocolate chip cookies. But he started using 16.12 ounces instead. He should advertise the cookies as having _____ percent more chocolate
Group of answer choices
Answer:
24%
Step-by-step explanation:
[tex]16.12 - 13 = 3.12\\3.12 * 100 = 312 \\312 / 13 = 24[/tex]
24% more chocolate
1.00 + 0.24 = 1.24
13 * 1.24 = 16.12
I need help on 5,6, and 7 !
In the picture there are 2 problems. The similarity is they two have to find 2 question. The difference is given question are different.
Given that,
In the picture there are 2 problems.
We have to find the difference and similarities of question in the picture.
The similarities are they 2 are word problems.
Another similarity is they two have to find 2 question.
1. How much money for 10 days and How many days to collect the money $1.05?
2.How much gallon of water need for 50 minutes and How much time take to fill the pool?
Another similarity is they two have to justified the answer in a mathematical model.
Now,
The difference is,
First question has given sisters and money problem where as the second has given pool and gallon water problem.
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given the expression 3x^4 - 5x + 2 state what each of the following represents
-5
2
3x^4
4
Given the algebraic expression 3x⁴ - 5x + 2, each of following represents:
-5 = coefficient.2 = constant3x⁴ = monomial4 = exponent.What is an algebraic expression?An algebraic expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables, numerical quantities (constants), accompanied with the use of different mathematical operations.
What is a coefficient?In Mathematics, a coefficient simply refers to a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.
In conclusion, an exponent is an operation that raises a numerical value or quantity to the power of another and it is generally written as bⁿ.
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Combine like terms to simplify the expression. 2x - 10 - 5x - 1 + x
Combine X. which is 2x, -5x, x.
we combine -2x and -5x and gives me -3x.
2x -10 -5x -1 +x
now i combine the last x, which is -3x and x and gives us -2x.
-3x -10 -1 +x
now we just combine the rest of the numbers. -10 and -1 and gives me -11.
-2x -10 -1
we have now combine all the numbers and there's nothing else to combine. we're done combining. :))
ANSWER:
-2x-11
help me i am helpless.
Answer: -5x >[-3x,4x,1.5x] 10>[11] 6xy>[-7.85xy, -98xy, 155xy]
Step-by-step explanation:
Which equation is the inverse of y = 16x2 + 1?
y = plus-or-minus StartRoot StartFraction x Over 16 EndFraction minus 1 EndRoot
y = StartFraction plus-or-minus StartRoot x minus 1 EndRoot Over 16 EndFraction
y = StartFraction plus-or-minus StartRoot x EndRoot Over 4 EndFraction minus one-fourth
The inverse of the given function, y = 16x² + 1 is: B. y = ±√(x - 1)/16
What is an inverse function?In Mathematics, an inverse function can be defined as a type of function that is obtained by reversing (undoing) the operation of a given function (f(x)).
Generally speaking, a given function (f(x)) and its inverse function has the following property f⁻¹(f(x)) = x.
In order to determine the inverse of the given function, we would interchange input value (x) and the output value (y) as follows:
y = 16x² + 1
x = 16y² + 1
Subtracting 1 from both sides, we have:
16y² + 1 - 1 = x - 1
16y² = x - 1
Dividing both sides by 16, we have:
y² = (x - 1)/16
Taking the square root of both sides, we have:
y = ±√(x - 1)/16
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Expand
−
10
(
b
−
9
)
Answer:
Step-by-step explanation:
Expand · Evaluate Fractions · Linear Equations · Quadratic Equations ... 7 + 4 s = 10 ( 6 - 9 s ). 7+4s=10(6−9s) ... 7 + 4 s = 10 ( 6 - 9 s ).
Answer:
-10b × 90
Step-by-step explanation:
-10 * b =-10b
10 *9=90
Your welcome :)
at what rate percent compound interest wil Rs2000 amount to Rs2420 in 2 years.
The Compound Interest of Principle 2000 will become 2420 within 2 years when the rate of interest is 21%
Compound interest = P(1 + R ÷ 100) to the power of n,
where P = Principle
R = Rate of Interest
n = no. of years
According to the given question,
Principle(P) =Rs2000
Rate of interest (R) =?
no. of years(n) = 2 years
given CI (Compound Interest) = Rs2420
CI = 2000(1 + R ÷ 100)² = 2420
= 20(100 +R) = 2420
= 100 + R = 2420 ÷ 20
= 100 + R = 121
= R = 121 - 100
= R = 21%
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1. the sum of three and seven divided
by two
2.the sum of four and nine times three
3.ten divided by the product of four
and five
4.the sum of one and two divided
by twenty
Answer:
1. (3 + 7) ÷ 2 = 5
2. (4 + 9) x 3 = 39
3. 10 ÷ (4 x 5) = 1/2
4.(1 + 2) ÷ 20 = 3/20
Write the equation that is the translation of y = |x| left 9 units and up 11 units.
The translation of y = |x| left 9 units and up 11 units is y = |x+9|+11 .
The process of translating an existing graph or equation into a new graph is known as graph translation.
The alteration of algebraic equations is a typical form of algebraic challenge.A translation modifies the graph of a parent function. Dilations, reflections, and translations are the three distinct types of translation. The y-values of a function can be changed vertically, or the x-values can be changed horizontally (affects the x-values).We know that for translation we have to change the x-coordinate and the y-coordinate by the amount that is stated in the translation.
Therefore from the graph we can see that the graph of y =|x| is represented by the blue line and the graph of translation y = |x+9|+11 is represented by the red line.
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If f(x) = x/2 - 3 and g(x) = 4x^2 + x - 4, find (f +g)(x).
A. 4x^2 + 3/2 x -1
B. 4x^2 + 3/2 x -7
C. 4x^2 + 1/2 x -1
D. 6x^2 -7
Apex Functions!
Answer: B
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\=\frac{x}{2}-3+4x^2 +x-4\\\\=4x^2 +\frac{3x}{2}-7[/tex]
Tom sold t-shirts and hats at a festival. He made a $5 profit for each t-shirt he sold. He also made a profit of $40 from selling hats. If he made a total profit of $125, how many t-shirts did he sell?
The total number of t-shirts sold by Tom equals to 17 t-shirt.
What is a profit?Basically, a profit refers to the difference between the revenue that an entity has received from its outputs and the opportunity costs of its inputs.
We need to note that he made a total profit of $125. From here, we will proceed to use that data to solve other sections.
From the total profit of $125, he also made a profit of $40 from selling hats. That means that the T-shirt sales alone gives him a profit of $85 ($125 - $40).
Total quantity of t-shirt sold is computed as follows:
= Total profit from t-shirt / Profit per shirt
= $85 / $5
= 17 t-shirt
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Anna is following this recipe to make biscuits.
Anna uses 120 g of chocolate.
How many grams of margarine will she need?
Recipe: Makes 24 biscuits
80 g sugar
120 ml syrup
200 g oats
120 g margarine
40 g chocolate
Anna uses 120 g of chocolate and 360 grams of margarine to needed to bake biscuits.
We have data as follows; To make 24 biscuits Anna uses following proportion of Ingredients;
80 g sugar
120 ml syrup
200 g oats
120 g margarine
40 g chocolate
Now We can analysis that anna uses 40 g chocolate to make 24 biscuits
So for 120 g of chocolate Anna can bake [tex] \frac{24(120)}{40} [/tex]
= 24 (3)
= 72 biscuits
∴ Anna can bake 72 biscuits if she uses 120 g of chocolate.
We want to find how many grams of margarine will she need to make 72 biscuits and this can be done as follows;
Ingredients for 24 biscuits require 120 g margarine
∴ For 72 biscuits anna require [tex] \frac{72(120)}{24} [/tex] g of margarine
= 3 (120)
= 360 g of margarine.
Hence 360 grams of margarine anna needed.
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a grocery store sells a bag of 4 oranges for $1.72 . if christopher spent $1.29 on oranges how many did he buy
Christopher would be able to purchase 3 oranges but if the grocery store only sells them in bags of 4 then he would not have enough money to purchase any.
To find our answer we do 4 divided by 1.29 and that is how many he can afford which is 3.1
pls give brainliest
Answer:
He bought 3 oranges
Step-by-step explanation
Divided $1.72 by 4 which gives $0.43
So each orange cost $0.43
0.43 times 3 equals $1.29
What is the domain of the following ordered pairs?
(2, 3), (-12, 7), (4, 7)
Answer:
Yes, the relation {(3,2), (4,1), (5,9), (6,12), (7,12)}is a function.
Step-by-step explanation:
Answer:
It's a triangle just like you, except you're acute one.
Step-by-step explanation:
-¾ ÷ (-0.06)
Can someone help me with this question please
Answer:
12.5
Step-by-step explanation:
-3\4÷[-0.06]
convert -0.06to fraction
-3\50
then divide
-3\4÷-3\50
sign changes
-3\4 ÷ 50\3
=50\4
=12.5
WILL GIVE BRAINLIEST
The average daily profit of an electronics store is $31,435. The company estimates that 15% is lost each day to returns, with a margin of error of ±4%. What is the maximum the company can expect for returned items?
$3457.85
$4621.13
$5972.65
$6638.22
The maximum that the company can expect for returned items is C. $5972.65
How to calculate the value?From the information, the average daily profit of an electronics store is $31,435 and the company estimates that 15% is lost each day to returns, with a margin of error of ±4%.
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.
The maximum the company can expect for returned items will be:
= (15% + 4%) × Profit
= 19% × $31,435
= 0.19 × $31,435
= $5972.65
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a 13-foot ladder is leaning against a wall. if we pull the ladder away from the wall at a rate of 6ft/s, how fast is the top of the ladder moving down the wall when the bottom of the ladder is 12ft from the wall?
Answer:
Below in bold.
Step-by-step explanation:
The relation between the height of the ladder and distance from the ground is given by Pythagoras Theorem:
h^2 = 13^2 - L^2
h = (169 - L^2)^1/2
Finding the derivative:
dh/dL = 1/2(169 - L^2)^-1/2 * -2L
= -L / (169 -L^2)^1/2
dL/dt = 6
So, dh/dt = dh/dL * dL/dt
= -6 * L/ (169 - L^2)^1/2
= -6 * 12 / (169 - 12^2)^1/2
= -72/5 ft /second
= -14.4 ft/second.
It's negative because the distance from the ground is decreasing.
Mrs. Ellis has 4 children. She is going to feed them leftover pizza for dinner. If she has 2/3 of pizza left, how much pizza will each child get?
PLEEASE HELP ASAP AAA
Stanley ate 3/8 of a pizza. his brother ate 3/4 of a pizza how much pizza did they eat in all
Answer:
The Answer is 1 1/8
Step-by-step explanation:
When Stanley ate 3/8 of a pizza and his brother ate 3/4 of a pizza, the amount eaten in all is 1 1/8 of the pizza.
What is a fraction?A fraction simply means a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, Stanley ate 3/8 of a pizza and his brother ate 3/4 of a pizza.
Therefore, the amount eaten by both of them will be:
= 3/8 + 3/4
= 3/8 + 6/8
= 9/8
= 1 1/8.
The amount is 1 1/8.
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Please help!!! What are the domain and range of the function?
Answer: Option D
Step-by-step explanation:
Step-by-step explanation:
As we know domain of a function is represented by x values on the graph and y values represents the range of the function.
From the given table domain will be the set of all real numbers.
Range of the same function will be y > 4
Option D is the answer. there you go o(*￣︶￣*)o it was hard to but now its easy
45 percent of what number is 99
actually the number is "x", which oddly enough is the 100%, so we know that 45% of "x" is 99, what is "x" anyway?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 99& 45 \end{array} \implies \cfrac{x}{99}~~=~~\cfrac{100}{45} \\\\\\ \cfrac{x}{99}=\cfrac{20}{9}\implies 9x=1980\implies x=\cfrac{1980}{9}\implies x=220[/tex]
3*19*14+18/2 whats the awnser
Answer:
807
Step-by-step explanation:
because u multipy 3x19x14+18/2 and u get 807
Answer:
807
Step-by-step explanation:
3*19*12=798
18/2 = 9
798 + 9 = 807
In Exercises 12-15, graph the linear function.
12. r(x) = 2
14. g(x) = ²x − 3
How do I graph it? Can someone PLEASE explain!!??
This is due tomorrow so pls help
Answer:
Step-by-step explanation:
Problem 12:
r(x) = 2
Since x will always be 2, it will always be a straight line.
Problem 14:
(I'm assuming the square is on the x)
g(x) = x^2-3
First, start on the y-intercept, and go down 3 as the starting value is -3. You can then substitute a number to find the next point.
For example, if you want to find if x = 1, what y will be:
1^2-3
1-3
-2
You can then do this for the rest of the points to the point.