Clarence likes to make desserts for bake sales. Last month, he made 2 batches of brownies and 2 batches of cookies, which called for 6 eggs total. The month before, he baked 2 batches of brownies and 1 batch of cookies, which required a total of 4 eggs. How many eggs did Clarence use for a batch of each dessert?
Answers
To find out how many eggs Clarence used for a batch of each dessert, we can set up a system of equations based on the information provided.
Clarence used 1 egg for a batch of brownies and 2 eggs for a batch of cookies based on the information and the solution to the system of equations.
Let's represent the number of eggs used for a batch of brownies as 'b' and the number of eggs used for a batch of cookies as 'c'.
From the given information:
In the previous month, 2 batches of brownies and 2 batches of cookies required a total of 6 eggs:
2b + 2c = 6 -- Equation 1
In the month before, 2 batches of brownies and 1 batch of cookies required a total of 4 eggs:
2b + c = 4 -- Equation 2
We can now solve this system of equations to determine the number of eggs used for a batch of each dessert.
Multiplying Equation 2 by 2, we have:
4b + 2c = 8 -- Equation 3
Subtracting Equation 3 from Equation 1, we can eliminate 'b':
(2b + 2c) - (4b + 2c) = 6 - 8
-2b = -2
b = 1
Now that we have found the value of 'b' to be 1, we can substitute it back into Equation 2 to solve for 'c':
2(1) + c = 4
2 + c = 4
c = 2
Therefore, Clarence used 1 egg for a batch of brownies and 2 eggs for a batch of cookies.
In conclusion, Clarence used 1 egg for a batch of brownies and 2 eggs for a batch of cookies based on the given information and the solution to the system of equations.
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Related Questions
Rewrite the problem using substitution and simplify the expression using order of operations and show your work.
3. Evaluate:
Suppose you want to buy something for $60, and you have $15 saved up so far. Then your grandmother calls and says she will chip in for your purchase. She doesn’t tell you the amount of money she will give you yet, so you just consider it x dollars.
Answers
The algebraic expression for the scenario is 15 + x = 60
How to evaluate the algebraic expression for the statement?From the question, we have the following parameters that can be used in our computation:
Amount saved up = $15
Cost of item = $60
Amount gifted by your grandma = x
The above parameters means that the mathematical statement is an equation statement
So, we have the following representation
Amount saved up + Amount gifted by your grandma = Cost of item
Substitute the known values in the above equation, so, we have the following representation
15 + x = 60
Hence, the algebraic expression is 15 + x = 60
The question does not require that the equation be solved
However, when it is solved, we have:
15 + x = 60
Subtract 15 from both sides
x = 45
So, the amount is 45
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A new pet store is offering 12% off for their grand opening! A parakeet originally costs $17. What is the sale price after the discount?
Answers
Let:
Oc = original cost = $17
Sp = Sale price
D = Discount percent = 12% = 12/100 = 0.12
The sale price will be:
\(\begin{gathered} Sp=Oc-0.12\cdot Oc \\ Sp=17-0.12\cdot17 \\ Sp=17-2.04 \\ Sp=14.96 \end{gathered}\)The sale price is $14.96
12% of 17 is 2.04
17-2.04=14.96
Write an equation in point-slope form.
a. m= -3, (-2,-1)
Answers
Given the error function e(t) where its z-transform is: E(z) = 3z3/ z^3-9z^2+27z-27.
Prove that E(z) can be written as product of two z-transform equations E₁(z) and E₂(z) in the form E(z) = E₁ (z) x E₂ (z), where E₁(z) and E₂(z) are fractional polynomial of z of first order numerators.
Answers
The given error function E(z), with its z-transform E(z) = 3z³ / (z³ - 9z² + 27z - 27), can be expressed as the product of two z-transform equations E₁(z) and E₂(z), where E₁(z) and E₂(z) are fractional polynomials of z with first-order numerators.
To express E(z) as the product of two z-transform equations E₁(z) and E₂(z), we factorize the denominator of E(z):
E(z) = 3z³ / (z³ - 9z² + 27z - 27)
The denominator can be factored as follows:
z³ - 9z² + 27z - 27 = (z - 3)(z - 3)(z - 3)
Now, we define E₁(z) = 3z / (z - 3) and E₂(z) = z - 3. Multiplying them together, we obtain:
E₁(z) x E₂(z) = (3z / (z - 3)) x (z - 3) = 3z³ / [(z - 3)(z - 3)(z - 3)]
This expression is equal to E(z), as shown by the factored denominator. Therefore, we have proven that E(z) can be written as the product of two z-transform equations E₁(z) and E₂(z), where E₁(z) has a first-order numerator 3z and E₂(z) has a first-order numerator z - 3.
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What is the y intercept
Answers
Answer:
the answer is A) -7
Step-by-step explanation:
-7 is the y-intercept
Samantha's mother spent $78 at a farmers market. She bought the same number of pounds of apples for $1. 50 per lb as tomatoes for $2. 50 per lb. She also bought half that weight of a farmers cheese that sold for $4. 00 per lb. The number of pounds of peaches she bought for $3. 00 per lb was one more pound than the farmers cheese. How many pounds of each product did samantha's mother buy?.
Answers
Answer:
6.36 Lbs
Step-by-step explanation:
Donell buys 13 bags of soil to put around the bases of 6 trees how much soil should Donell put around the base of each tree
Answers
Answer:
2.16 is the amount donmel has to put around each base
At a local gardening store, there is a small group of plants located near the gardening
supplies, and the remainder of the plants are arranged in equal-sized rows in the field
behind the store. The function 9(x) = 18x+23 represents the total number of plants at the
gardening store if there are x rows of plants in the field. What is the value of g(27)), the
total number of plants when there are 27 rows?
Answers
Answer:
uuuuuuuuu
Step-by-step explauuuuuuuuuuu
The required number of plants from the function is 509 when there are 27 rows.
Given that,
The function g(x) = 18x+23 represents the total number of plants at the gardening store if there are x rows of plants in the field. What is the value of g(27) is to be determined.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Number of plants,
g(x) = 18x+23
Since the number of rows is 27
Now, the number of plants,
g(27) = 27 * 18 + 23
g(27) = 486 + 23
g(27) = 509
Thus, The required number of plants from the function is 509 when there are 27 rows.
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what is the value of x and y?
Answers
Answer: (x,y) has the meaning of plane's point coordinates. The first x is the horizontal coodinate (abscisa) and second is the vertical coordinate (ordenate). Both are coordinates. (x,y) has the meaning of a complex number: x is the real part and y is the imaginary part: x+yi.
Step-by-step explanation:
write an equation in slope intercept form of the line that passes through (0,2) and has a slope of m
Answers
Answer:
Step-by-step explanation:
\(y = mx + 2\)
So for math class they gave me this equation and it is 6 ÷ 3(1+2) it makes no sense, I just keep getting stumped
Answers
Answer:
The answer is 6.
Step-by-step explanation:
6 ÷ 3 = 2
2+4 = 6
How long does it take for an investment to double in value if it is invested at 2% compounded monthly? Compounded continuously
Answers
Answer:
34.69 years for the first part.
Step-by-step explanation:
I got it right
Kim works as a server in a restaurant. She is serving the table where a group of her friends are eating. Her friends always tip 15%. If the cost of the meal is $23.60, how much of a tip will Kim earn?
Answers
if the bill was $23.60, and the tip was 15%, kim will earn $3.54. the overall total of the meal would be $27.14 :)
Anwser will be $3.54
15% = .15 ( to convert percent to decimal, change the % to . and move the decimal two places to the left)
23.60 * .15 = 3.54
correctly rounded, 20.0030 - 0.491 g =
Answers
The calculation for correctly rounded 20.0030 - 0.491 g is as follows:
20.0030
- 0.491
= 19.5120
To correctly round this answer, we need to consider the significant figures of the original values. The value 20.0030 has five significant figures, while 0.491 has only three. Therefore, the answer should be rounded to three significant figures, which gives us:
19.5 g
When subtracting values with different significant figures, the answer should be rounded to the least number of significant figures in either value. In this case, the value 0.491 has only three significant figures, so the answer should be rounded to three significant figures.
The correctly rounded answer for 20.0030 - 0.491 g is 19.5 g. It is important to consider the significant figures when rounding the answer, as this ensures that the result is accurate and precise.
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PLEASE ASAP PLEASE A.S.A.P
HELP
Four lines are shown on the grid above
A)(i) write the equation of line L1
(ii) write the equation of line L2
(iii)write the value of (m) and the value of (n) for the line (y=mc+n)
(iv)write the value (p) and (q) for the line y=px+q
B) which of the letters A to K lie in the region where
(i) x >=2. y>=mx +n. and y>=px+q
(ii) y<=2. y<=mx+n. And y<=px+q
C)what is the maximum value of x+y in the region G
Answers
Answer:
A) x = 2; y = 2; (m, n) = (1/2, 0); (p, q) = (-3/2, 12)
B) K; A and E
C) 11
Step-by-step explanation:
With the exception of the vertical line, the equations of the lines can be written in terms of their slope and y-intercept. The slope is the ratio of "rise" to "run". The "rise" is the vertical change between points, and the "run" is the horizontal change between the same points. Changes to the right or up are taken as positive. The change amounts can be read from the graph by counting grid squares, or by subtracting coordinate values.
The regions described by an inequality will be to the right of a boundary line for x > (boundary), and above the boundary line for y > (boundary). When these inequalities are reversed, the region will be left or below the boundary, respectively.
__
A)The slope-intercept equation for a line is ...
y = mx +b . . . . where m is the slope, and b is the y-intercept
(i) x = 2 . . . . . . points on the vertical line have an x-value of 2
(ii) y = 2 . . . . . 0 slope, y-intercept of 2
(iii) m = 1/2, n = 0 . . . . rise = 1 for run = 2; y-intercept = 0
(iv) p = -3/2, q = 12 . . . . rise = -3 for run = 2; y-intercept = 12
__
B)(i) Region K is to the right of the vertical line, and above the two slanted lines
(ii) Regions A and E are below y=2 and the two slanted lines
__
C)The maximum value of x+y will be found at the point on the line x+y=c, where c is the largest possible value. That is, it will lie on the line ...
y = -x +c . . . . a line with a slope of -1
such that the line is as far as possible from the origin.
For region G, the point that maximizes "c" in the above equation is point (2, 9), so ...
c = x +y = 2 +9 = 11
The maximum value of (x+y) in region G is 11.
4 Solve the system to find the y-value of the
solution:
7x – 4y = – 18
x + 12y = 10
A. No Solution
B. 1
C. -2
D. 5
A
B
с
D
Answers
Answer: B
Step-by-step explanation:
7(-2) - 4(1) = -18
-14 - 4 = -18
-18 = -18
TRUE
(-2) + 12(1) = 10
-2 + 12 = 10
10 = 10
TRUE
Potassium-42 has a half-life of 12.4 hours. How much of a 746-gram sample will be left after 62 hours?
Answers
the amount of potassium-42 remaining after 62 hours is approximately 23.31 grams (option B)
Explanation:half life = 12.4 hours
initial amount = 746g
time elapsed = 62 hours
Using the half-life formula:
\(\begin{gathered} N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{_{\frac{1}{2}}}}} \\ N(t)\text{ = amount remaining} \\ N_0\text{ = initial amount = 746g} \\ t\text{ = 62 hours} \\ t_{\frac{1}{2}\text{ }}\text{ = 12.4 hours} \end{gathered}\)Substitute for the values:
\(\begin{gathered} N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{_{\frac{1}{2}}}}} \\ N(t)\text{ = }746(\frac{1}{2})^{\frac{62}{12.5}} \\ N(t)\text{ = }746(\frac{1}{2})^5 \\ N(t)\text{ = }746(\frac{1}{2^5}) \end{gathered}\)\(\begin{gathered} N(t)\text{ = }(\frac{746}{32})^{} \\ N(t)\text{ = }23.3125 \end{gathered}\)Hence, the amount of potassium-42 remaining after 62 hours is approximately 23.31 grams (option B)
which distribution is described by predicting the number of girls amoung 5 children randomly selected from a group of 10 girls and 10 boys
Answers
The distribution described is a binomial distribution.
A binomial distribution describes a discrete probability distribution, which means the values are countable. This distribution has two possible outcomes, in this case, either a girl or a boy. The probability of getting a girl is 0.5, as there are 10 girls and 10 boys in the group.
The binomial distribution is described by the following formula: P(x) = nCx * p^x * (1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success in each trial.
In this case, n=5, x= number of girls, and p=0.5. Thus, P(x)= 5Cx * 0.5^x * 0.5^5-x. To predict the number of girls among 5 randomly selected children from the group, we need to calculate P(x) for x=0,1,2,3,4, and 5. This will give us the probabilities of selecting 0, 1, 2, 3, 4, and 5 girls in the group.
The sum of all these probabilities should be equal to 1, indicating that all the possibilities have been accounted for. This binomial distribution will help us predict the number of girls among 5 randomly selected children from the group of 10 girls and 10 boys.
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A rancher wishes to fence in a rectangular corral enclosing 1300 square yards and must divide it in half with a fence down the middle. If the perimeter fence costs $5 per yard and the fence down the middle costs $3 per yard, determine the dimensions of the corral so that the fencing cost will be as small as possible.'
Answers
The dimensions of the corral that will minimize the cost of the fencing are x = 4 yards (width) and y = 325 yards (length).
To begin solving this problem, we need to use the given information to set up an equation that represents the cost of the fencing. Let's start by defining the dimensions of the rectangular corral. We can use x to represent the width and y to represent the length.
Since the area of the corral is 1300 square yards, we know that:
xy = 1300
Now, let's think about the fencing. We need to divide the corral in half with a fence down the middle, which means we have two equal sections with a width of x/2. The length of each section is still y.
To find the perimeter of each section, we add up all the sides. For the top and bottom, we have two lengths of y and two widths of x/2. For the sides, we have two lengths of x/2 and two widths of y. This gives us a perimeter of:
2y + x + 2x + 2y = 4y + 2x
Since we have two sections, the total perimeter is:
2(4y + 2x) = 8y + 4x
We can now set up an equation for the cost of the fencing:
Cost = (8y + 4x)($5) + (x)($3)
The first part of the equation represents the cost of the perimeter fence, while the second part represents the cost of the fence down the middle.
Now, we want to find the dimensions of the corral that will minimize the cost of the fencing. To do this, we can use calculus. We take the derivative of the cost equation with respect to x and set it equal to zero:
dCost/dx = 20y + 3 = 0
Solving for y, we get:
y = -3/20
Since we can't have a negative length, this solution is not valid. However, we can find the minimum cost by plugging in the value of y that makes the derivative equal to zero into the original equation for the cost of the fencing. This gives us:
Cost = (8y + 4x)($5) + (x)($3)
Cost = (8(-3/20) + 4x)($5) + (x)($3)
Cost = (-(12/5) + 4x)($5) + (x)($3)
Cost = -24x + 3x^2 + 3900
To minimize the cost, we take the derivative with respect to x and set it equal to zero:
dCost/dx = -24 + 6x = 0
x = 4
Plugging this value of x back into the equation for the cost of the fencing gives us:
Cost = -24(4) + 3(4^2) + 3900
Cost = $3892
Therefore, the dimensions of the corral that will minimize the cost of the fencing are x = 4 yards (width) and y = 325 yards (length).
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Need help ASAP !!! And show work please
Answers
Answer:
\(\sqrt{40}\) or 6.32
Step-by-step explanation:
We can find the distance between two points by using this formula
\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
where the x and y values are derived from the given points
The points given are ( -2 , 5 ) and ( 4 , 3 )
So we plug in the x and y values of those coordinates into the distance formula
\(\sqrt{(4-(-2)^2+(3-5)^2} \\4-(-2)=6\\3-5=-2\\d=\sqrt{6^2+-2^2} \\6^2=36\\-2^2=4\\36+4=40\\d=\sqrt{40}\)
or 6.32
A game of chance has a spinner with five equal sized sections. The results of 625 spins are shown below.
For which color is the experimental probability closest to the theoretical probability? Use the drop down menus to explain your answer.
(Brown,Orange,Yellow,Green,Purple) The experimental probability is (22.72%, 18.88%, 21.92%, 19.52%) and the theoretical probability is (10%, 25%, 20%)
For which color is the difference between the theoretical probability and experimental probability greatest? Use the drop down menus to explain your answer.
Brown,Green,Yellow,Orange,Purple) The experimental probability is (16.96%, 22.72, 18.88%, 21.92%) and the theoretical probability is (25%, 10%, 20%).
Answers
Answer:
https://e-eduanswers.com/mathematics/question176807332
Step-by-step explanation:
Solve the following polynomial equation. Identify all solutions.
x^(3)+54x^(2)+53x=0
Brainlest + Thanks :)
help asap
Answers
With factoring!
Hope this helps!
y = -2x - 5
6x + 3y = -15
A.one line
B.parallel lines
C.intersecting lines
Answers
Answer:
A. One line
Step-by-step explanation:
Let rearrange the system of equations into explicit forms:
\(y = -2\cdot x - 5\)
\(6\cdot x + 3\cdot y = -15\)
\(3\cdot y = -6\cdot x - 15\)
\(y = -2\cdot x - 5\)
The second equation is identical to the first one, which means that there is just one line.
HELP DUE IN 10 MINS! Finish the statement.
Corresponding sides of similar figures are??
Answers
Answer:
proportional
Step-by-step explanation:
Answer:
Proportional
Step-by-step explanation:
Shania is working in a clothing store at the freehold raceway mall. she earns $30 per day, plus $5 commision for each sale. write and algebraic equation for the amount of money shania could earn today.
Answers
Shania is working in a clothing store at the freehold raceway mall. she earns $30 per day, plus $5 commision for each sale. Write and algebraic equation for the amount of money Shania could earn today.
Algebraic Equation:The total amount of money that Shania can earn today is the sum of her daily wage of $30 and commission on sales of $5 per sale.The total sales made by Shania can be represented by the variable "s".Therefore, the total amount of money that Shania can earn today can be expressed as:
Shania, who is working in a clothing store at the Freehold Raceway Mall, is earning $30 per day, plus $5 commission for each sale. The equation for the amount of money that she could earn today can be written as the sum of her daily wage and commission on sales made by her. The total sales made by her can be represented by the variable "s."
Therefore, the equation is written as, "Earnings = $30 + $5s." Based on the sales made, the value of "s" can change, which will ultimately change the total earnings.
Shania's earnings will depend on the number of sales she makes, and the total amount of money that she could earn today is the sum of her daily wage and commission on sales.
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Part 2 out of 2 Isabella spends $5.86 on paint brushes and paint. How many of each item does she buy? Complete the explanation how you found your answer. By using compatible numbers, you find a total of used guess and check to find that she buys items that had a total cost of $5.86. Then you paint brushes and jars of paint. Check Next
Answers
Based on the information, it can be concluded Isabella bought 2 paintbrushes and 3 jars of paint.
How many items can Isabella buy?The average of buying a product is 0.97, which means Isabella can buy a total of 5 items (0.97 x 5 = 4.85)
Based on this different combinations of products are possible, for example, 1 paintbrush and 4 jars or 3 jars and 2 paintbrushes. However, the one that fits the final price is:
2 paintbrushes x 0.95 = $1.9
3 jars of paint x 0.99 = $2.97
$2.97 + 1.9 = $4.87
Note: This question is incomplete, here is the missing information
The paintbrushes cost $0.95 and the jar of paint cost $.099
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Why couldn't Abbie and Ben buy locally-grown corn in May or June in Rhode Island?
Answers
Abbie and Ben would not be able to buy locally-grown corn in Rhode Island until late October.
What is amount?Amount is an indefinite quantity of something, typically money, that is to be paid or received. It is often used in the context of a purchase, loan, or other financial transaction. Amounts can be expressed as a numerical value, such as a dollar amount, or as a percentage of the total transaction. In accounting, the term "amount" is used to refer to the total amount of money that is owed or received.
Abbie and Ben could not buy locally-grown corn in May or June in Rhode Island because the growing season for corn in Rhode Island runs from late June through late October. This is the typical growing season for corn in the Northeastern United States and is largely dependent on the region's climate. Corn is a warm-season crop, meaning it requires temperatures of at least 50 degrees Fahrenheit for germination and growth. In early spring, most of Rhode Island is still too cold for corn to be planted. This means that the earliest corn grown in Rhode Island is planted in late June, and it is not harvested until late October. Thus, Abbie and Ben would not be able to buy locally-grown corn in Rhode Island until late October.
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A clay specimen, 25 mm thick, has been tested in an oedometer apparatus with two way rainage, and it is observed that 50% of the consolidation settlement occurs in 1 hour. A ayer of the same clay is observed to settle 10 mm in 10 years and after many years to settle (total primary consolidation) by 35 mm. Determine the thickness of the clay layer if it drains only from upper surface
Answers
The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.
The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.
Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.
Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.
To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.
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For the angles shown in the diagram, which statements are true? Select all that apply. The sum of m∠3 and m∠4 is 180°. The sum of the measures of the adjacent interior angle and one of the remote interior angles is equal to the measure of the exterior angle. ∠3 is supplementary to ∠1. m∠4 = m∠1 + m∠2. m∠1 + m∠2 + m∠3 = 180°
Answers
The statements that are correct from the given once {in reference to the figure shown) are -
- The sum of m∠3 and m∠4 is 180°.
- m∠4 is equivalent to the sum of m∠1 and m∠2.
- The sum of the m∠1, m∠2 and m∠3 is equivalent to 180°.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted ΔABC.
In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
Area : ½ × base × heightPerimeter : sum of side lengths of the triangleNumber of vertices : 3Number of edges : 3Internal angle : 60° (for equilateral)Sum of interior angles : 180°Right angle : 90 degreesGiven is a triangle as shown in the figure attached.
The given statements are correct for the given figure -
The sum of m∠3 and m∠4 is 180°. {∠3 and ∠4 form a linear pair}.m∠4 = m∠1 + m∠2.m∠1 + m∠2 + m∠3 = 180° {Sum of interior angles : 180°}Therefore, the statements that are correct from the given once {in reference to the figure shown) are -
The sum of m∠3 and m∠4 is 180°.
m∠4 is equivalent to the sum of m∠1 and m∠2.
The sum of the m∠1, m∠2 and m∠3 is equivalent to 180°.
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55% of what number is 330? pls help meee
Answers
Answer:
600
Step-by-step explanation:
Assume x=target number
55%(x)=300
55%=0.55
0.55x=300
x=300/0.55
x=600
Answer
600
Step-by-step explanation:
Here is the formula/format:
Part %
------ = --------
Whole 100
We are trying to find the "whole" in this case, so I did:
330 55
------- = ------- (this says that 55% of the number we are looking for is 330)
x 100
Then, I cross multiplied and got: 55x= 33,000
From there, I divided 33,000 by 55 (inverse operations) to get x = 600.
I hope this helps! :)