Abigail has eaten 3/8 of a pound of candy.
This is the answer because 3/4 is equivalent to 6/8, and if Abigail has eaten 3/8 of a pound of that 6/8 pound of candy, then there will be 3/8 remaining (6/8 - 3/8 = 3/8).
To find out how much candy Abigail has eaten, we subtract the amount of candy she has left (3/8 of a pound) from the original amount she bought (3/4 of a pound). The calculation shows that Abigail has eaten 3/8 of a pound of candy.
The student is asking how much candy Abigail has eaten if she originally bought 3/4 of a pound and now has 3/8 of a pound left. To calculate the amount of candy eaten, we subtract the amount left from the original amount. Since we are working with fractions, we ensure the denominators are the same before subtracting.
The steps to solve the problem are as follows:
Original amount of candy: 3/4 pound
Amount left: 3/8 pound
Calculate how much has been eaten: (3/4) - (3/8)
Convert the first fraction to have a denominator of 8: (6/8) - (3/8)
Subtract the second fraction from the first: (6/8) - (3/8) = 3/8
Abigail has eaten 3/8 of a pound of candy.
A garden patio is covered with grey slabs and yellow slabs
1/5 of the slabs are grey
The ratio of grey to yellow slabs are 1:4
There are 55 slabs in total
Work out number of yellow slabs
Answer:
There are 44 yellow slabs.
Step-by-step explanation:
Multiply 1/5 x 55. This gives you 11. 55 - 11 = 44.
The number of yellow slabs in a garden patio is 44.
Given that, a garden patio is covered with grey slabs and yellow slabs 1/5 of the slabs are grey.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
The ratio of grey to yellow slabs are 1:4.
There are 55 slabs in total.
Number of grey slabs =1/5 ×55
= 11
So, the number of yellow slabs
= 55-11
= 44
Therefore, the number of yellow slabs in a garden patio is 44.
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A gardener is planting two types of trees:
Type A is 6 feet tall and grows at a rate of 12 inches per year.
Type B is 2 feet tall and grows at a rate of 24 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the same height.
It will take 4 years for these trees to be the same height
Step-by-step explanation:
A gardener is planting two types of trees:
Type A is 6 feet tall and grows at a rate of 12 inches per year
Type B is 2 feet tall and grows at a rate of 24 inches per year
We need to find exactly how many years it will take for these trees to be the same height
Assume that it will take x years for these trees to be the same height
Type A:
∵ The initial height of the tree is 6 feet
∵ 1 foot = 12 inches
∴ 6 feet = 6 × 12 = 72 inches
∴ The initial height of the tree is 72 inches
∵ It grows at a rate of 12 inches per year
∵ The number of years is x
∴ The height of the tree in x years = 72 + 12 x
Type B:
∵ The initial height of the tree is 2 feet
∴ 2 feet = 2 × 12 = 24 inches
∴ The initial height of the tree is 24 inches
∵ It grows at a rate of 24 inches per year
∵ The number of years is x
∴ The height of the tree in x years = 24 + 24 x
Equate The heights of the two types
∴ 72 + 12 x = 24 + 24 x
- Subtract 2 from both sides
∴ 48 + 12 x = 24 x
- Subtract 12 x from both sides
∴ 48 = 12 x
- Divide both sides by 12
∴ x = 4
It will take 4 years for these trees to be the same height
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Plz solve all:
4x+3−9x=
5+3.2n−6−4.8n=
2y−5(y−3)
−1/2(8b+3)+3b=
Answer:
4x+3−9x= 3-5x
5+3.2n−6−4.8n= -1.6n-1
2y−5(y−3)= -3y-15
−1/2(8b+3)+3b= -1b-1.5
Step-by-step explanation:
Add the numbers with the variables.
4x-9x= -5x
Then add the rest of the equation to it.
3-5x
Again, add the numbers with the variables and simplify the others.
3.2n- 4.8n= -1.6n
5-6= -1
That leads to....
-1.6n-1
Distribute the 5 into the parenthesis.
2y-5y- 15
Now, subtract the variables.
-3y-15
Distribute into the parenthesis.
-4b+(-1.5)+ 3b
Add the variables together.
-1b-1.5
Direct variation or not a direct variation
y=5/x
Answer:
not direct variation
Step-by-step explanation:
The equation for x and y in direct variation is
y = kx ← k is the constant of variation
y = [tex]\frac{5}{x}[/tex] is not in this form, thus not direct variation.
The equation for x and y varying inversely is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
y = [tex]\frac{5}{x}[/tex] is in this form and represents inverse variation
please solve the equation (15m + 3)/2 = -6
Answer:
m = - 1
Step-by-step explanation:
Given
[tex]\frac{15m+3}{2}[/tex] = - 6
Multiply both sides by 2 to clear the fraction
15m + 3 = - 12 ( subtract 3 from both sides )
15m = - 15 ( divide both sides by 15 )
m = - 1
[tex]\text{Solve:}\\\\\frac{15m+3}{2}=-6\\\\\text{Multiply both sides by 2}\\\\15m+3=-12\\\\\text{Subtract 3 from both sides}\\\\15m=-15\\\\\text{Divide both sides by 15}\\\\\boxed{m=-1}[/tex]
Which of these is the algebraic expression for "3 times the sum of 2 and y?" (1 point) 3(2 + y) 3 ⋅ 2 + y 2 + 3 ⋅ y 2(3 + y)
The algebraic expression of "3 times the sum of 2 and y" is 3(2 + y) ⇒ 1st answer
Step-by-step explanation:
Let us revise some words in the operations of mathematics problems
Sum ⇒ answer of addDifference ⇒ answer of subtractProduct ⇒ answer of multiplyQuotient ⇒ answer of divideTimes ⇒ multiply∵ The algebraic expression is " 3 times the sum of 2 and y "
∵ Sum is the answer of add
∴ add 2 and y
∴ The sum of 2 and y = 2 + y
∵ 3 times means multiply by 3
∴ 3 times the sum
∴ Multiply the sum by 3
∵ The sum = 2 + y
∴ Multiply (2 + y ) by 3
∴ 3(2 + y)
∴ 3 times the sum of 2 and y = 3(2 + y)
The algebraic expression of "3 times the sum of 2 and y" is 3(2 + y)
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Answer:
a
=
Step-by-step explanation:
uo[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[
53 pts!! The function f(x)= 7^x+1 is transformed to function g through a horizontal compression by a factor of 3. What is the equation of function g? Substitute a numerical value for k into the function equation.
The value of k will be 3 if the function is transformed by compression factor of 3
Step-by-step explanation:
The horizontal stretch or compression for a function f(x) is given by g = f(bx) where b is a constant. If b> 0 then the graph of function is compressed.
As it is given in the question that he function is transformed by a compression factor of 3.
Given function
[tex]f(x) = 7^x+1\\To\ transform\\g = f(bx)\\g = 7^{3x}+1[/tex]
The value of k will be 3 if the function is transformed by compression factor of 3
Keywords: Functions, Transformation
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What is the value of this expression (3/7)^0
Answer:
1
Step-by-step explanation:
Using the rule of exponents
[tex]a^{0}[/tex] = 1
Any expression raised to the power of zero will equal 1
Given
[tex](3/7)^{0}[/tex] = 1
What is the following product square root 10* square root 10
Answer: 10
Step-by-step explanation:
Answer:
The answer would be ten.
Step-by-step explanation:
I plugged it into my TI-84 plus calculator.
Simplify each expression. (a2b-3/a-2b2)2 a=/0 b=/0
Answer:
The answer is C.
Step-by-step explanation:
Just failed hah stream fancy
Answer:
Answer is a^8/b^10
Option C
Step-by-step explanation:
((a²b-³)/(a-²b²))² where b and a are not equal zero
To solve this equation we start solving the equation from inside the bracket. And for simplicity we solve the numerator and solve the denominator before dividing them with each other. Now let get started
((a²b-³)/(a-²b²))²
Recall from indices that
a ^ -b = 1/a^b
I.e b-³ = 1/b³... We will apply this here.
((a²b-³)/(a-²b²))²
=((a²* 1/b³)/(b²*1/a²))²
=((a²/b³)/(b²/a²))²
Also recall that
(a/b) / (c/d) = (a/b) * (d/c)
Therefore
=((a²/b³)/(b²/a²))²
=(a²/b³ * a²/b²)²
Recall that: a^b * a^c = a^(b+c)
= (a ^ (2+2) / b ^ (2+3))²
= (a^4/b^5)²
Recall that: (a^b)^c = a^(b+c)
Therefore:
=™(a^4/b^5)²
=(a^(4*2)/b^(5*2))
= a^8/b^10
8/9.3/16+1/12
Order of operations
Answer:
[tex]8\div9\times3\div16+1\div12=\frac{1}{4}[/tex]
Step-by-step explanation:
Given operation:
[tex]8\div9\times3\div16+1\div12[/tex]
Using PEDMAS to evaluate the order of operations.
First division:
[tex]=\frac{8}{9}\times\frac{3}{16}+\frac{1}{12}[/tex]
Next multiplication:
[tex]=\frac{1}{6}+\frac{1}{12}[/tex]
Then addition:
taking LCD of [tex]6\ and\ 12=12[/tex]
[tex]=\frac{2}{12}+\frac{1}{12}[/tex]
[tex]=\frac{3}{12}[/tex]
reducing to simplest fraction by division of both numbers by GCF.
[tex]=\frac{3\div3}{12\div3}=\frac{1}{4}[/tex]
in the picture below x=
Answer:
[tex]\displaystyle 79°[/tex]
Step-by-step explanation:
The m∠x is 79°, according to the Alternate Exterior Angles Theorem.
I am joyous to assist you anytime.
* That does NOT look like an acute angle because 79° is considered an acute angle, since it is less than 90°.
What is the answer ?
Answer:
126
Step-by-step explanation:
621 - x = 495
Subtract 621 from both sides.
-x = -126
Divide by -1
x = 126
Year 11 Maths:
500ml of water is used to make 80g of pasta. How many grams of pasta could be made with 2.5 litres of water?
With 2.5 litres of water, it can be estimated that you can make 400 grams of pasta.
Explanation:The question is asking how many grams of pasta could be made with 2.5 litres (or 2500 ml) of water. According to the initial ratio, 500 ml of water is used to make 80 grams of pasta.
To find out how many grams of pasta can be made with 2.5 liters of water, you first need to find the pasta-to-water ratio which is 80 grams pasta to 500 ml water, or 0.16 grams/ml. You then multiply this ratio by the total amount of water you have:
0.16 grams/ml * 2500 ml = 400 grams of pasta.
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What is the answer to this fraction 9 3/100+76/100
Answer:
169/100
Step-by-step explanation:
93 + 76/100 = 169/100
Answer: 169/100
Step-by-step explanation:
One third of a store’s inventory is children’s clothing. Two fifths of its inventory is women’s clothing. What fraction of the total inventory is children’s or women’s clothing?
Answer:
11/15
Step-by-step explanation:
To answer this, add (combine) 1/3 and 2/5.
First we must rewrite these fractions with the same denominator, the LCD.
The LCD here is obtained by multiplying the denominators 3 and 5 together, obtaining 15.
Thus, 1/3 + 2/5 becomes 5/15 + 6/15, which, in turn, is 11/15.
The fraction of the total inventory that is children’s or women’s clothing
is 11/15.
The circumference of a pizza is about 38 inches. What is the diameter of the pizza? Round to the nearest tenth if necessary
Choices
6 in.
12.1 in.
12.7 in.
24.2 in.
Answer:
The diameter of the pizza is 12 inches
Step-by-step explanation:
Given:
Circumference of a pizza = 38 inches
To Find:
The Diameter of the pizza =?
Solution:
Circumference:
The distance around the edge of a circle (or any curvy shape). It is a type of perimeter.
We know that the shape of the pizza is circle.
So the given circumference is circumference of a circle.
Now,
Circumference of the circle(pizza)=[tex]2\pi r[/tex]
where r is the radius of the circle
circumference of the pizza =38
Thus
[tex]2\pi r= 38[/tex]
[tex]\pi r=\frac{38}{2}[/tex]
[tex]\pi r=19[/tex]
[tex]r=\frac{19}{3.14}[/tex]
r=6.050 inches
Now,
Diameter = [tex]2\times r[/tex]
Diameter = [tex]2\times 6.05[/tex]
Diameter=12.1 inches
Rounding to the nearest tenth
Diameter=12 inches
Final answer:
To find the diameter of a pizza with a circumference of about 38 inches, we apply the formula C = πD, leading to a calculation of 38 / 3.14, which results in approximately 12.1 inches.
Explanation:
The question is about finding the diameter of a pizza given its circumference, which is approximately 38 inches. To calculate the diameter from the circumference, we use the formula C = πD, where C is the circumference and D is the diameter. Since π (Pi) is approximately 3.14, we rearrange the formula to find the diameter: D = C / π. Thus, substituting the given value of C = 38 inches, we get D = 38 / 3.14, which is approximately 12.1 inches.
This year, a small business had a total revenue of 33,500. If this is 34% more than their total revenue the previous year, what was their total revenue the previous year?
Final answer:
To find the previous year's total revenue, divide the current year's revenue by 1.34 since the current revenue is 34% higher than the previous year. The calculation shows that the previous year's revenue was $25,000.
Explanation:
The question asks us to find the total revenue of a small business for the previous year, given that the current year's revenue is 34% higher. To do this, we let x represent the revenue from the previous year. Since this year's revenue is 34% more than last year's, we have the equation:
1.34x = 33,500
To find the value of x, we divide both sides of the equation by 1.34:
x = 33,500 / 1.34
x = 25,000
Therefore, the total revenue for the previous year was $25,000.
Find the common factors and the GCF of 8 and 24
Answer:
8
Step-by-step explanation:
The total cost of a jacket and a pair of shoes was $52.95. If the price of the jacket was $3.87 less than the pair of shoes, what was the price of the jacket? Express your answer as a simplified fraction or a decimal rounded to two places.
The price of jacket was $24.54
Step-by-step explanation:
Let,
Cost of jacket = x
Cost of pair of shoes = y
According to given statement;
x+y=52.95 Eqn 1
x = y-3.87 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex](y-3.87)+y=52.95\\y-3.87+y=52.95\\2y=52.95+3.87\\2y=56.82\\[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{56.82}{2}\\y=28.41[/tex]
Putting y=28.41 in Eqn 2,
[tex]x=28.41-3.87\\x=24.54[/tex]
The price of jacket was $24.54
Keywords: linear equation, division
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Final answer:
The price of the jacket is $24.54, calculated by first finding the price of the shoes from the total cost and the price difference between the jacket and shoes, and then subtracting the difference from the price of the shoes.
Explanation:
The question at hand involves finding the price of a jacket given the total cost of the jacket and a pair of shoes and the relationship between their prices. Let's denote the price of the jacket as J and the price of the shoes as S. According to the information provided, we have the following two equations:
J + S = $52.95 (The total cost of both items)
J = S - $3.87 (The jacket costs $3.87 less than the shoes)
We can substitute the second equation into the first to find the price of the shoes:
(S - $3.87) + S = $52.95
2S - $3.87 = $52.95
2S = $52.95 + $3.87
2S = $56.82
S = $56.82 / 2
S = $28.41
Now we can find the price of the jacket by substituting the price of the shoes back into the second equation:
J = $28.41 - $3.87
J = $24.54
Therefore, the price of the jacket is $24.54.
Find three consecutive even integers whose sum is -132
Answer:
The consecutive even numbers are -42, -44, -46
Step-by-step explanation:
As the numbers are consecutive even integers,
Let,
The first number is "x"
The second number is "x+2"
The third number is "x+4"
According to the equation,
x + (x+2) + (x+4) = -132
As the sum is -132. Now we break the parenthesis by using the addition rule.
or, x + x + 2 + x + 4 = -132
or, 3x + 6 = -132
or, 3x = -132 - 6 (side change)
or, 3x = -138
or, x = -138/3 (interchange)
or, x = -46
Therefore, the first number is -46
The second number is -46+2 = -44
And the third number is -46+4 = -42
The consecutive even numbers are -42, -44, -46
solve the systems of equations using elimination
3x-5y=-2
4x-7y=-3
a.(-1,-1)
b.( -7/3, -1)
c. (-7/3, 1)
d.(1, 1)
Answer:
x=1, y=1. (1, 1). The answer is D).
Step-by-step explanation:
3x-5y=-2
4x-7y=-3
--------------
4(3x-5y)=4(-2)
-3(4x-7y)=-3(-3)
------------------------
12x-20y=-8
-12x+21y=9
--------------------
y=1
3x-5(1)=-2
3x-5=-2
3x=-2+5
3x=3
x=3/3
x=1
Uncle drew scored 28 points in 5 5/6 minutes. How many points did he average per minute
Answer:4.6
Step-by-step explanation:
28/6
Answer:
168/35 points per minute
Step-by-step explanation:
5 5/6=35/6
28/(35/6)=(28/1)(6/35)=168/35
If the price of a stock goes from $4.25 per share to $6.50 per share, by what percent has the
value of the stock increased? Round to the nearest whole percent.
Answer:
53%
Step-by-step explanation:
subtract 6.5 - 4.25 = 2.25
then divide 2.25/4.25 = .529
times answer by 100 = 53% rounded
Answer: 53% increase
=============================================
Work Shown:
A = old value = 4.25
B = new value = 6.50
C = percent change
C = 100*(B-A)/A
C = 100*(6.50 - 4.25)/4.25
C = 52.94%
C = 53%
------------
notes:
The positive C value indicates we have a percent increase. If C was negative, then we'd have a percent decrease.
The formula shown above for C is basically having us compute the difference in price (B-A) and then we divide that difference over the original price A. This computes the decimal form of the answer. The "100*" tacked out front will convert from decimal to percent form.
If you took 52.94% of the original price 4.25, then you would get 0.5294*4.25 = 2.24995 which rounds to 2.25; this is the amount the price increases so we add this to 4.25 and we get 4.25+2.25 = 6.50 which is the new share price.
1. -10x+5y = 40 (1 point)
Ox-intercept is 5; y-intercept is -10.
Ox-intercept is 8; y-intercept is -4.
Ox-intercept is -10; y-intercept is 5.
Ox-intercept is -4; y-intercept is 8.
For question 2, find the x- and y-intercept of the line.
2. 5x + 4y = 80 (1 point)
x-intercept is 4; y-intercept is 5.
x-intercept is 20; y-intercept is 16.
O x-intercept is 5; y-intercept is 4.
Ox-intercept is 16; v-intercept is 20.
Answer:
1. Ox-intercept is -4; y-intercept is 8.
2. Ox-intercept is 16; v-intercept is 20.
Step-by-step explanation:
1. -10x + 5y = 40
Recall the equation of line in slope - intercept form :
y = mx + c , where m is the slope and c is the y - intercept
Writing the given equation in this form,we have:
-10x + 5y = 40
5y = 10x + 40
y = 10/5 x + 40/5
y = 2x + 8
comparing with y = mx +c , then y - intercept is 8 , the x - intercept is the point at which y = 0 , substituting y = 0 into the equation , we have
0 = 2x + 8
2x = -8
x = -8/2
x = -4
2. Following the same procedure:
y = -5x/4 + 20
y - intercept = 20
x - intercept = 16
Admission to a baseball game is $2.50 for general admission and $5.50 for reserved seats. The receipts were $3702.00 for 1140 paid admissions. How many ticket were sold?
1140
Step-by-step explanation:
What is 2 to the power of four thirds equal to?
cube root of 8
square root of 8
cube root of 16
square root of 16
Answer:
Step-by-step explanation:
1. 1 7/9
2. 22
3. 8
4. 64
5. 16
Answer:
Cube root of 16
Step-by-step explanation:
Place 2 inside of the square root and 3 outside and 4 inside
Here's how it looks:
[tex]\sqrt[3]{2} ^{4}[/tex]
then you can quadruple root the 2 which gives you 16 and 16 doesn't simplify any further into a cube root so your answer is the cube root of 16
20 points will mark brainlest please help!!The number has been rewritten in exponential notation. The missing powers of 10 are represented by letters.
Type the powers into the boxes that correspond to each letter. Use a slash (/) to show a fraction. Use a caret (^) before an exponent. Do not add any spaces. For example, to show \frac{1}{10^2}, type 1/10^2.
6.19 = 6 x A + 1 x B + 9 x C
A =
Answer:
A = 10^0B = 1/10^1C = 1/10^2Step-by-step explanation:
The expanded form of the number 234.567 written using exponential notation would be ...
2×10² +3×10¹ +4×10⁰ +5×10⁻¹ +6×10⁻² +7×10⁻³
Note that exponents decrease going left to right (or increase going right to left). The exponent associated with the "ones" place is 0.
Apparently, you're supposed to write the negative powers as fractions, so you would have ...
6.19 = 6×10^0 + 1×(1/10^1) + 9×(1/10^2)
×/76 = 4/12
Solving proportions
Answer:
x = 25.33333333
Step-by-step explanation:
x = 4
76 12
Cross multiply:
x * 12 = 76 * 4
Simplifying
x * 12 = 76 * 4
Reorder the terms for easier multiplication:
12x = 76 * 4
Multiply 76 * 4
12x = 304
Solving
12x = 304
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '12'.
x = 25.33333333
Simplifying
x = 25.33333333
To the nearest hundredth, what is the value of x?
Answer:
60.42
Step-by-step explanation:
tan40 = opposite/adjascent
tan40 =x/72
x=72tan40
x = 72 * 0.8391
x = 60.42