InstructionGary is making a casserole but only needs 1/3 of theoriginal serving size. If the number of servings Garyneeds is 4. how many servings did the original recipemake?How many servings did the original recipe make?Show result
Answers
12 servings
Explanation
you can easily solve this by using a rule of three
Step 1
Gary is making a casserole( 4 servings) but only needs 1/3 of the
original serving size,then
\(\begin{gathered} if\text{Gary} \\ \frac{1}{3}\text{ of the original serving size}\rightarrow4\text{ serving } \\ \text{the relation is} \\ \frac{\frac{1}{3}}{\frac{4}{1}}=\frac{1}{12} \end{gathered}\)Step 2
Let
x represents the number of servings in the original recipe(1),then
\(\begin{gathered} 1\rightarrow x \\ \text{the relation is the same, so} \\ \frac{1}{x}=\frac{1}{12} \end{gathered}\)Step 3
solve for x
\(\begin{gathered} \frac{1}{x}=\frac{1}{12} \\ 12\cdot1=1\cdot x \\ x=12 \end{gathered}\)the original recipe made 12 servings
Related Questions
The amount of workers varies inversely with the time, in days, to complete a project. Five workers can complete a certain project in 24 days. How many workers will be needed to complete the project in 15 days?
Answers
9514 1404 393
Answer:
8
Step-by-step explanation:
The number of days has gone down by a factor of 15/24. The number of workers is inversely proportional, so must increase by a factor of 24/15 = 8/5.
(5 workers) × (8/5) = 8 workers
8 workers are needed to complete the project in 15 days.
Prove that if A and B are m x n matrices, then A and B are row equivalent if and only if A and B have the same reduced row echelon form
Answers
We have proven that if A and B are m x n matrices, then A and B are row equivalent if and only if A and B have the same reduced row echelon form.
What is matrices?Matrices are a type of mathematical structure used to store and analyze data. They are represented as a series of rows and columns, with each cell in the matrix containing a number or other value. Matrices are used to solve systems of equations, perform matrix multiplication and determine the inverse of a matrix. They are also used in linear programming, cryptography, and other areas of mathematics.
Row equivalence is defined as a pair of matrices A and B being row equivalent if there is a sequence of row operations that can transform A into B, or vice versa. This means that if A and B are row equivalent, then A and B can be transformed into one another by a series of row operations.
A reduced row echelon form is defined as a matrix in which all non-zero rows are above any rows of all zeroes and the leading coefficient of each non-zero row is 1. In other words, all of the non-zero rows have a leading coefficient of 1, and any rows of all zeroes are below the non-zero rows.
Therefore, if A and B are row equivalent, then A and B can be transformed into one another by a series of row operations. This means that we can use the same series of row operations to transform A and B into the same reduced row echelon form. This proves that if A and B are row equivalent, then A and B have the same reduced row echelon form.
On the other hand, if A and B have the same reduced row echelon form, then they must have been transformed into the same form by a series of row operations. This means that the same series of row operations must have been used to transform A and B into the same reduced row echelon form, which means that A and B are row equivalent. This proves that if A and B have the same reduced row echelon form, then A and B are row equivalent.
To prove that if A and B are m x n matrices, then A and B are row equivalent if and only if A and B have the same reduced row echelon form, we can use the definition of row equivalence and the definition of a reduced row echelon form.
Therefore, we have proven that if A and B are m x n matrices, then A and B are row equivalent if and only if A and B have the same reduced row echelon form.
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Which of the following steps indicates the addition property of equality while solving the equation –1 – 6x = x – 15?
A) x = 14∕2
B) –1 – 6x = x – 15
C) 23 – 6x – 24 = x – 15
D) –1 – 6x + 15 = x – 15 + 15
Answers
Answer:
-1 - 6x = x - 15
Add 15 to both sides using the addition property of equality.
14 - 6x = x
14 = 7x
2 = x
D) -1 - 6x + 15 = x - 15 + 15
Answer and Step-by-step explanation:
Please refer to the photo for the solution!
the sum of the first twenty-one terms of a linear sequence is 28 and the sum of the first twenty-eight terms is 21. find which term of the sequence is 0 and also the sum of the terms preceding it
Answers
The sum οf the terms preceding the 49/5th term is 38/21.
What is Iinear equatiοn?A Iinear equatiοn is a mathematicaI equatiοn that describes a straight Iine in a twο-dimensiοnaI pIane.
Let the first term οf the Iinear sequence be represented by 'a' and the cοmmοn difference be represented by 'd'. Then, we have:
The sum οf the first 21 terms:
S21 = (21/2) * [2a + (21-1)d] = 28
The sum οf the first 28 terms:
S28 = (28/2) * [2a + (28-1)d] = 21
SimpIifying these equatiοns, we get:
42a + 420d = 28 -----(1)
56a + 1540d = 21 -----(2)
MuItipIying equatiοn (1) by 2 and subtracting it frοm equatiοn (2), we get:
112d = -35
d = -35/112
Substituting this vaIue οf d in equatiοn (1), we get:
42a - (35/8) = 28
42a = 329/8
a = (329/8) * (1/42) = 329/336
Therefοre, the nth term οf the sequence is given by:
an = a + (n-1)d
an = (329/336) + (n-1)(-35/112)
We want tο find the term in the sequence that is equaI tο 0, sο we set an = 0 and sοIve fοr n:
0 = (329/336) + (n-1)(-35/112)
35n = 329/8 + 35/112
35n = 343/8
n = 49/5
Therefοre, the term in the sequence that is equaI tο 0 is the 49/5th term.
Tο find the sum οf the terms preceding this term, we need tο find the sum οf the first (49/5 - 1) = 44/5 terms. This can be fοund using the fοrmuIa fοr the sum οf the first n terms οf an arithmetic sequence:
Sn = (n/2) * [2a + (n-1)d]
S44/5 = (44/10) * [2(329/336) + (44/5 - 1)(-35/112)]
S44/5 = 38/21
Therefοre, the sum οf the terms preceding the 49/5th term is 38/21.
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This question has two parts. First, answer Part A. Then, answer Part B. The question is below
Answers
Both relation (year, percent of men) and (year, percent of women) are functions.
What is a function?
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.
Now,
In given data
For every input (i.e. year) there is a unique output (i.e. percent of men/ percent of women)
Hence, Given relation (year, percent of men) and (year, percent of women) are functions.
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This subject is called substitution
Answers
Pls send only answers - no work
Answers
Answer:
No
Step-by-step explanation:
If you are just seeking answers, you are basically cheating and trying to get someone to do your work...which will not help you learn the material ....sad.
A pyramid has a square base with an area of 144 ft. Mark each statement as true or false and correct any false statements.
T/F? - The length of one side of the pyramids base can be found using the equation s^2=144.
T/F? - The Length of one side of the pyramids base is 72 feet.
Answers
Answer:
1) true
2) false
Step-by-step explanation:
1) area of a square is s²
in this case s²=144. by taking the square root of 144 to solve for s, you get s=12
√144=s=12
2) False because the area for a square is s², and if you plug in 72 into this equation, you get 72²=5184, which isn't the area given in the problem
The equation s^2=144 can be used to find the length of one side of a pyramid with a square base and an area of 144 ft^2, which is true. However, the length of one side is not 72 feet, but rather it is 12 feet.
Explanation:The answers to the questions are as follows:
True - The length of one side of the pyramid's base can indeed be found using the equation s^2=144. This is because the area of a square is calculated by squaring the length of one of its sides. False - The length of one side of the pyramid's base is not 72 feet. If we rearrange the equation to solve for s (which represents the length of a side), we get that s equals to the square root of 144 (s=sqrt(144)), so s = 12 feet. Therefore, each side of the pyramid's base is 12 feet long.Learn more about Square roots here:https://brainly.com/question/1540542
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If the toss of a coin comes down heads, you win two dollars. If it comes down tails, you lose fifty cents. How much would you expect to gain after 25 tosses (in $ dollars)
Answers
Answer:
$30.00
Step-by-step explanation:
Because if you think about it, about half of them are going to be heads and the other half are going to be tails.
hope this helped
We could expect $30.00 to gain after 25 tosses.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
It is given that If the toss of a coin comes down heads, you win two dollars. If it comes down tails, you lose fifty cents.
We need to find How much would you expect to gain after 25 tosses (in $ dollars).
Because if you think about it, you will see that about half of them are going to be heads and the other half are going to be tails.
Therefore, We could expect $30.00 to gain after 25 tosses.
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IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answers
Applying the congruent chords theorem, the value of x is: 7.
Length of segment LP is: 6 units.
What is a Chord in Geometry?In geometry, a chord is defined as the line segment that joins two points on the circumference of a circle.
What is the Congruent Chords Theorem?In a circle, if two chords are congruent, then they are equidistant from the center of a circle, according to the congruent chords theorem.
In the circle given, chords JK = LM = 12 units. This means both chords are congruent, therefore, they are equidistant from the center of the circle S.
According to the congruent chords theorem, NS = PS, thus:
8 = 2x - 6
8 + 6 = 2x
14 = 2x
Divide both sides by 2
14/2 = 2x/2
7 = x
x = 7
LP = 1/2(12)
LP = 6 units.
In summary, applying the congruent chords theorem, the value of x is: 7.
Length of segment LP is: 6 units.
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Compute the limit \(\lim_{n \to \ 0} \frac{log(1+x)}{cos(x)+e^{x} -1}\)
Answers
I assume you mean
\(\displaystyle \lim_{x\to0} \frac{\log(1+x)}{\cos(x) + e^x - 1}\)
since the limand is free of n. As x goes to 0, the numerator converges to log(1 + 0) = 0, while the denominator converges to cos(0) + e⁰ - 1 = 1, so the overall limit is
\(\displaystyle \lim_{x\to0} \frac{\log(1+x)}{\cos(x) + e^x - 1} = \frac01 = \boxed{0}\)
PLEASE HELP ASAP!! (Please do this if ur good at Scientific Notation) please tell me which 4 should I put in the box! (Click picture) ‼️‼️
Answers
Answer:
1st one is 6.9 X 10^6
2nd one is 2 x 10^5
Step-by-step explanation:
Let x represent the number of television show episodes that are taped in a season. Enter an expression for the number of episodes taped in 8 seasons.
Please help this is due soon!!!
Answers
Answer:
x=8 ???
Step-by-step explanation:
??? not 100% sure but im pretty sure ;w;
Answer:
=> 8x
Step-by-step explanation:
=> Take X as the number of episodes taped in 8 seasons.
=> So, it's 8x
Question 1 (1 point)
In the context of elevation, what would | -7 | feet mean?
O a
O b
Oc
Od
The vertical distance between the point at 7 feet and sea level (0 feet).
The vertical distance between the point at -7 feet and sea level (0 feet).
The horizontal distance between the point at 7 feet and sea level (0 feet).
The horizontal distance between the point at -7 feet and sea level (0 feet).
Answers
The correct answer is option (b) The vertical distance between the point at -7 feet and sea level (0 feet)
What is elevation?
The elevation is the height of an object or point above a given reference point, usually sea level. It is often used to describe the height or altitude of a geographic location, such as a mountain peak or a city, and is commonly measured in feet or meters.
In the context of elevation, | -7 | feet would mean the vertical distance between the point at -7 feet and sea level (0 feet).
The vertical distance between two points is calculated by taking the absolute value of the difference between their elevations. So, in this case, the absolute value of -7 is 7, which means the point is 7 feet below sea level.
The correct answer is option (b) The vertical distance between the point at -7 feet and sea level (0 feet).
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How to solve adjacent angles?
Answers
Answer:
D
Step-by-step explanation:
1 + 4x and 57° are corresponding angles and are congruent , so
1 + 4x = 57 ( subtract 1 from both sides )
4x = 56 ( divide both sides by 4 )
x = 14
please help find the surface area. i will give brainliest
Answers
Answer:
The first one is 145 in^2 and the other is 250 in^2
Step-by-step explanation:
For the first one you have to find the base first so 5*5=25, then you find the area of the other faces and since theres 4 of them dont bother diving them by 2 and just do it twice, so the faces would be 120 in^2 in all add it together and you get 145
For the second one its the same thing but instead of a square base its a triangle so theres only 3 faces. 8*10 = 80/2 =40, 2 of the faces are 140 in all and to find the last one just 14*10=140/2=70 and you add them together and get 250
In the diagram a || b. Use the diagram to answer the question. Name the alternate interior angle to <2
Answers
The angle 7 is the alternative interior angle to angle 2.
Given that,In the diagram a || bWe need to find the alternate interior angle to <2 .Alternate interior angles are the angles that are formed when a transversal crosses two parallel lines.
They are the angles that are on opposite sides of the transversal and inside the two parallel lines.
Thus, in the given diagram, the angle that is opposite to angle <2 and is inside the two parallel lines a and b is the alternate interior angle to angle <2.
We can see that the alternate interior angle to angle <2 is <7. Therefore, the alternate interior angle to angle <2 is <7.
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For the function N(t)=t2−8t−1, evaluate N(6).
Answers
The function N(t)=t2−8t−1, for evaluating N(6) will be -13.
A function is the rule which assigns a unique output value for each input value. The input values are typically called the domain of the function, and the output values are called the range of the function.
To evaluate means to find the value of an expression or a function at a particular point or set of points. This typically involves substituting given values for any variables in the expression or function and then simplifying or solving the resulting equation to obtain a numerical result.
To evaluate N(6), we substitute t = 6 into the expression for N(t);
N(6) = 6² - 8(6) - 1
Simplifying;
N(6) = 36 - 48 - 1
N(6) = -13
Therefore, N(6) = -13.
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Acylinder has a volume of 400 cubic feet. If the height of the cylinder is 25 feet, what is the radius of the cylinder? Use 3.14 for me and round to the nearest hundredth
adius hype your answer...
1
Answers
The radius of the cylinder is 2.25 feet.
To find the radius of the cylinder, we can use the formula for the volume of a cylinder:
V = πr²h
Given that the volume V is 400 cubic feet and the height h is 25 feet, we can substitute these values into the formula and solve for the radius r.
400 = 3.14 r² x 25
Dividing both sides of the equation by (3.14 * 25) to isolate r^2, we have:
r² = 400 / (3.14 x 25)
r² ≈ 5.08
Taking the square root of both sides to solve for r, we get:
r ≈ √5.08
r ≈ 2.25
Therefore, the radius of the cylinder is 2.25 feet.
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it is math can someone help me, please
Answers
Answer:
Less than 3,
9/4
Step-by-step explanation:
A rectangular prism has a length of 5 cm, a width of 7 cm, and a height of 4 cm. What is the volume of the prism?
Answers
Answer:
140
Step-by-step explanation:
V=whl=7·4·5=140cm³
Answer:
140cm^3
Step-by-step explanation:
It is 140 because volume is base x length x height so 7 x 5 x 4 = 35 x 4 = 140 cm cubed so 140cm^3
Hope this helps
8. Training for a race can provide a goal to focus on when running. True False
Answers
I have the answers for the first three but confused on number four (practice assessment)
Answers
If "x" is the rental fee, and the total taxes collected is 0.07x, the if the rental fee is:
\(\text{0}.07\times220=15.4\)Therefore, she collects $15.4 in taxes.
the total amount in tax and gratuity is:
\(15.4+35=50.4\)Therefore, in taxes and gratuity the total amount is $50.4
The members of the Junior National Honors Society at Franklin Middle School are required to complete community service hours. The box plots show the volunteer service hours performed by the 7th and 8th graders. 7th Graders 8th Graders 3.5 4 4.5 Community Service 5 5.5 6 6.5 7 7.5 Number of Hours Which statement is best supported by the information in the box plots?
Answers
Answer:
The statement that is best supported by the information in the box plots is:
* The 8th graders completed more community service hours than the 7th graders.
The 8th grade box plot is shifted to the right of the 7th grade box plot, which indicates that the 8th graders had a higher median number of community service hours. The 8th grade box plot also has a wider spread, which indicates that there was more variation in the number of community service hours completed by the 8th graders.
However, it is important to note that the box plots do not provide information about the total number of community service hours completed by each group of students. It is possible that some 7th graders completed more community service hours than some 8th graders.
Step-by-step explanation:
Answer:The 8th graders completed more community service hours than the 7th graders
Step-by-step explanation:
what does the x mean in this problem 12x- 15 =6 3x
Answers
Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.3 years with a standard deviation of 1.1 years.
Step 1 of 2: If a sampling distribution is created using samples of the ages at which 35 children begin reading, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.
Answers
Answer:
The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3 years.
give thanks for more! your welcome!
Step-by-step explanation:
Paul had 30 candy bars. After giving each of his p friends 3 candy bars, he still has some left. Select two expressions that represent the number of candy bars Paul has left.
Answer:
3(10-p)
30-3p
3(p-10)
3p-30
Answers
Answer:
30-3p and 3(10-p)
Step-by-step explanation:
We know that he starts with 30 candy bars.
Now, we know that he has p friends, and that each friend received 3 candy bars.
Therefore, the answer is 30-3p
However, if you divide 30-3p by 10, you get the expression 3(10-p)
Thus, either answer is acceptable.
Simplify the following polynomial expression.
Answers
Answer:
3x² - 10x + 8
Step-by-step explanation:
(5x² + 13x - 4) - (17x² + 7x - 19) + (5x - 7)(3x + 1)
Distribute the first 2 parenthesis and expand the product of factors using FOIL
= 5x² + 13x - 4 - 17x² - 7x + 19 + 15x² - 16x - 7 ← collect like terms
= 3x²- 10x + 8
Simplify the algebraic
expression
4(x + 1) + 7(x + 3).
a. 11x + 4
b. 2x + 215
C. 11x + 25
d. 5x + 11
Someone help pleaseeee
Answers
Answer:
C.
Step-by-step explanation:
4(x + 1) + 7(x + 3)= 4*x+4*1 + 7*x+7*3 = 4x+4 +7x +21 = 11x + 25
C
Step-by-step explanation:
4x+4+7x+21
11x+25
you have to combine like terms
What is the constant up a proportionally in a equation y=x/g
Answers
Answer:
Step-by-step explanation:
\(y=(\frac{1}{g} )x\)
Constant up a proportionally is \(\frac{1}{g}\).