2. Select all transformations that must take any point A to any point B.
A. Rotation of 180° around A
B. Rotation of 180°around B
C. Rotation of 180° around the midpoint of segment AB
D. Reflection across the line AB
E. Reflection across the perependicular bisector of segment AB
F. Translation by the directed line segment AB
G. Translation by the directed line segment BA
Answers
The given transformation of reflection, rotation and translation are rigid transformation
The transformation that must take any point A to any point B are;
Rotation of 180° around the midpoint of segment ABReflection across the perpendicular bisectorTranslation by the directed line segment ABReason:
Question: The given quadrilaterals ABCD and A'B'C'D' are congruent
Required; To select all transformation that must take a point A to point B
Solution:
Rotation of 180° around the midpoint of segment ABA rotation of 180° about the midpoint of segment AB will change the places of points A and B
A(x, y) → R₁₈₀ → A'(-x, -y)
Let the coordinates of the origin be the midpoint of segment AB, and let (x, y) represent the coordinate of the point B(x, 0) we have;
∴ The coordinates of point A is A(-x, 0), which gives;
A(-x, 0) → R₁₈₀ → A'(x, 0) = point B
Therefore a rotation about the midpoint of AB must take point A to point B
Reflection across the perpendicular bisectorThe reflection of a point (x, y) about y-axis gives a point (-x, y), therefore, we have;
A(-x, 0) → Reflection across the y-axis → A'(x, 0) = point B
Therefore, a reflection across the perpendicular bisector of the line AB must take the point A to point B
Translation by the directed line segment ABA translation along the directed line segment AB of point A(-x, 0) 2·x units right gives;
A'(-x + 2·x, 0) = A'(x, 0) = Point B
Therefore, the transformations that must take any point A to any point B are;
Rotation of 180° around the midpoint of segment AB
Reflection across the perpendicular bisector
Translation by the directed line segment AB
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Related Questions
If x and y are integers and x = 50y + 69, which of the following must be odd? O xy O x+y O x+2y 3x - 1 O 3x+1
Answers
Since 50 is an even number, we know that x will be even if y is even (50 times an even number is still even) and odd if y is odd (50 times an odd number is odd). Therefore, the only answer choice that must be odd is x+y.
Given that x and y are integers and x = 50y + 69, let's determine which of the following expressions must be odd.
1. xy: Since x is odd (50y + 69), when it is multiplied by any integer y, the result will always be odd. Therefore, xy must be odd.
2. x + y: If x is odd, adding it to an even integer (y) would result in an odd number. However, adding it to an odd integer (y) would result in an even number. Therefore, x + y does not necessarily have to be odd. xy: We can't determine if this is odd or even without knowing the values of x and y.
- x+y: This expression is always odd. To see why, consider two cases:
If x and y are both odd, then x+y is even+odd=odd.
If x and y are both even, then x+y is even+even=even.
If one of x and y is odd and the other is even, then x + y is odd + even =odd.
3. x+2y: We can't determine if this is odd or even without knowing the values of x and y.
3x-1: This expression will be odd if x is odd (3 times an odd number is odd) and even if x is even (3 times an even number is even).
3x+1: This expression will be odd if x is even (3 times an even number plus 1 is odd) and even if x is odd (3 times an odd number plus 1 is even).
x + 2y: Since x is odd and 2y is always even, their sum must be odd. Therefore, x + 2 y must be odd.
4. 3x - 1: This expression is odd, since 3x will always be odd (as x is odd) and subtracting 1 from an odd number results in an even number. Therefore, 3x - 1 does not necessarily have to be odd.
5. 3x + 1: This expression is odd, since 3x will always be odd (as x is odd) and adding 1 to an odd number results in an even number. Therefore, 3x + 1 must be odd.
In conclusion, the expressions that must be odd are xy, x + 2y, and 3x + 1.
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Please help ASAP!!!!!!!!!! Which expression is equivalent to the following complex fraction? 1 + StartFraction 1 Over y EndFraction divided by 1 minus StartFraction 1 Over y EndFraction StartFraction (y + 1) (y minus 1) Over y squared EndFraction StartFraction y + 1 Over y minus 1 EndFraction StartFraction y minus 1 Over y + 1 EndFraction StartFraction y squared Over (y + 1) (y minus 1) EndFraction
Answers
Answer:
\((B)\dfrac{y+1}{y-1}\)
Step-by-step explanation:
We are to find an equivalent expression for:
\(\dfrac{1+\frac{1}{y} }{1-\frac{1}{y}}\)
Step 1: Combine the terms in the numerator into one fraction. Do the same for the denominator.
\(=\dfrac{\frac{y+1}{y} }{\frac{y-1}{y}}\)
Step 2: Write on a straight line and simplify
\(=\dfrac{y+1}{y} \div \dfrac{y-1}{y}\\=\dfrac{y+1}{y} \times \dfrac{y}{y-1}\\=\dfrac{y+1}{y-1}\)
The correct option is B.
This question is based on the solving the fraction. Therefore, the correct option is B, that is \(= {\dfrac{y+1}{y-1}\) is equivalent to the following complex fraction.
Given:
Expression:
\(\dfrac{1+\frac{1}{y} }{1-\frac{1}{y} }\)
We need to calculate the expression which is equivalent to given complex fraction.
According to the question,
Firstly, take LCM of numerator and denominator.
We get,
\(= \dfrac{\dfrac{y+1}{y} }{\dfrac{y-1}{y} }\)
Now, above expression can be written as follows. Solve it further,
\(= {\dfrac{y+1}{y} }\times{\dfrac{y}{y-1} }\)
Therefore, we get,
\(= {\dfrac{y+1}{y-1}\)
Therefore, the correct option is B, that is \(= {\dfrac{y+1}{y-1}\) is equivalent to the following complex fraction.
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If f(x) = 2x² + 3x and g(x) = x - 2, what is (f+ g)(2) ?
Answers
\((f+g)(x)=f(x)+g(x)\\\\f(x)=2x^2+3x\\g(x)=x-2\\\\(f+g)(2)=2\cdot2^2+3\cdot2+2-2=8+6=14\)
one and three hundred twenty four thousandths in decimal form
Answers
One is the whole number, 324 thousandths should be the decimal after
assume that x1, x2, x3, and x4 are independent random variables. read the following statements. (a) the joint pmf or pdf for x1, x2, x3, and x4 is f1(x1)f2(x2)f3(x3)f4(x4). (b) if x1, x2, x3, and x4 are identically distributed then they are considered to be a random sample of size n. (c) if x1, x2, x3, and x4 have the same mean and variance then they are called a statistic. (d) identically distributed x1, x2, x3, and x4 can be thought of as measurements on outcomes of 4 random experiments. now choose the correct answer. group of answer choices all statements (a), (b), (c), and (d) are correct. statements (a) and (d) only are correct. statements (a), (b), and (c) only are correct. statements (a) and (b) only are correct. none of these answers are correct. statements (a), (b), and (d) only are correct.
Answers
On solving the provided question we got to know that, favorable cases for X4 to be the least is that = 0.25
What is probability?Probabilities are mathematical justifications of the probability that an event will happen or that a proposition is true. A number between 0 and 1, where 0 often indicates impossibility and 1 normally indicates certainty, denotes the likelihood of an event.
\(X1, \\X2, \\X3\)
can be arranged in 3! Ways so, in tottal 6 ways
\(Hence, there are 6 cases where X4 is the lowest.\)
Total no. of cases on which \(X1, X2, X3, X4\) be arranged are 4! = 24
Favorable cases for \(X4\) to be the least = \(6/24 = 1/4 = 0.25\)
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-\dfrac{5}{6}x=-\dfrac{10}{3}−
6
5
x=−
3
10
Answers
Answer
ok
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
-5/6 x = -10/3
Multiply by 6 each side:
6(-5/6 x) = 6 (-10/3)
Simplify:
-5x = -20
Divide -5 each side:
-5x/ -5 -20/-5
Simplify:
x= 4
-7x+4= 7x+4
what is the answer.
Answers
Answer:
x=0
Step-by-step explanation:
use math-way it helps
please help! i can never understand these problems
Answers
Answer:
1234567891011121314151617181920
Population parameters are used to estimate sample statistics.
a. true
b. false
Answers
Population parameters are used to estimate sample statistics, and this is true.
Population parameters are used to describe the characteristics of a population, such as the mean, median, and standard deviation, and are used to make inferences about a population. Sample statistics, on the other hand, are used to describe the characteristics of a sample of a population. For example, a sample statistic could be the mean of a sample of people's heights.
To estimate sample statistics, population parameters must first be known. For example, the sample mean can be estimated using the population mean. If the population means are unknown, then the sample means can be estimated using the sample mean.
In conclusion, population parameters are used to estimate sample statistics, and this is true. Population parameters provide useful information about a population that can be used to make inferences about a sample. Knowing the population parameters allows researchers to make more accurate estimates of sample statistics, which in turn can be used to make more reliable inferences about a population.
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Does the following series converge or diverge? You must show work on your written submission to receive full credit. -2n 5n n=1\n+1 O a. The series is convergent. O b. The series is divergent.
Answers
The given series is convergent.
The series you provided is:
-2n / (5n + 1)
To determine if the series converges or diverges, we need to evaluate its behavior as n approaches infinity.
Let's rewrite the series using the limit comparison test by comparing it to a known series:
-2n / (5n + 1) * (1/n) / (1/n)
By multiplying and dividing by 1/n, we can rewrite the series as:
-2 / (5 + 1/n)
As n approaches infinity, 1/n approaches 0. Therefore, the expression simplifies to:
-2 / (5 + 0) = -2/5
Since the resulting value is a finite number, we can conclude that the series converges.
The given series is convergent.
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12 m
9 m
10 m
Area:
Find the area
Answers
Answer:
A= b×h
b=12
h=9
12×9= 108
A=108m
Hope this helps.
. (5) Let x be a real number. The floor of x, denoted |, is the largest integer n such that n < x. (See the Scheinerman "Assorted Notation" section.) Let f R -R be defined by f(x) (a) Determine the domain of f. (b) Determine the image of f. (c) Is f one-to-one? Prove your answer (d) Find sets A-R and B-R which are as large as possible so that f : A → B is a bijection. Prove that f : A → В is a bijection
Answers
Let x be a real number. The floor of x, denoted |, is the largest integer n such that n < x. Therefore, (π²/10)I = 4
The meaning of cos in trigonometry defines the cosine of an angle. This angle is the acute angle in a right triangle and is considered a ratio. So in a right triangle the cosine of an angle is equal to the ratio of the side adjacent to the angle to the hypotenuse of the triangle
According to the Question:
f(x) is periodic with period 2
∴I = ∫ ⁻¹⁰₁₀ f(x)cos πx dx
= 2∫₀¹⁰ f(x)cos πx dx
= 2×5∫₀² f(x)cosπx dx
= 10 [∫₀¹ (1−X)cosπx dx+∫²₁(x−1)cosπx dx ]
= 10(I₁+I ₂)
I₁ =∫₁² (x−1)cosπxdx put x−1=t
I₂ = −∫₀¹ tcosπt dt
Therefore,
I = 10[−2∫₀¹ xcosπx dx ]
= −20[x sinπx/π + cosπx/π²]₀¹
= −20[−
Therefore,
(π²/10)I = 4
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(06.04 mc)
jake tossed a paper cup 50 times and recorded how it landed. the table shows the results
position
open side up closed side up landing on side
number of times landed in position
1
5
44
based on the table, determine the experimental probability of each outcome (landing open side up, landing closed side up, and landing on its side). show your work.
Answers
Based on the given data, the experimental probability of landing open side up is 0.1, landing closed side up is 0.88, and landing on its side is 0.02.
To determine the experimental probability of each outcome (landing open side up, landing closed side up, and landing on its side), we need to calculate the ratio of the number of times the cup landed in each position to the total number of tosses.
Let's calculate the experimental probability for each outcome based on the given table:
1. Landing open side up:
The cup landed open side up 5 times out of 50 tosses.
Experimental Probability = Number of times landed open side up / Total number of tosses
Experimental Probability = 5 / 50
Experimental Probability = 0.1
2. Landing closed side up:
The cup landed closed side up 44 times out of 50 tosses.
Experimental Probability = Number of times landed closed side up / Total number of tosses
Experimental Probability = 44 / 50
Experimental Probability = 0.88
3. Landing on its side:
The cup landed on its side 1 time out of 50 tosses.
Experimental Probability = Number of times landed on its side / Total number of tosses
Experimental Probability = 1 / 50
Experimental Probability = 0.02
Based on the given data, the experimental probability of landing open side up is 0.1, landing closed side up is 0.88, and landing on its side is 0.02. These probabilities indicate the likelihood of each outcome occurring in a toss.
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pls help!!!!!!!!!!!!!!
Answers
Answer:
6 million
Step-by-step explanation:
50% = 1/2
1/2 + 1/3 = 5/6
5/6 people watched or listened, which means 1/6 people did not do either of them.
1/6 of 36 (million) = 6 (million)
So, the answer is 6 million.
1. Find the AREA of the circle.
Answers
12.566
Hope this helped :T
1. The heights of American adult males are normally distributed with a mean of 177 cm and a standard deviation of 7.4 cm. Use the Empirical Rule to find the range of heights that contain approximately(a) 68% of the data cm -- cm(b) 95% of the data cm -- cm(c) 99.7% of the data cm -- cm
Answers
PLEASE HELP!!! the values in the table reresent a function
Answers
Answer:
7/3 or 3/7
Step-by-step explanation:
it says it on the thing you just have to find the numbers and we're they go
Math lib equations of circles
Answers
The equation of the circle passing through the point (-6, 3) having center at (5, - 4) is (x - 5)² + (y + 4)² = 170
The general equation of a circle with (h, k) representing the circle's center, and {r} represents the length of its radius is
(x – h)² + (y – k)² = r²
We can write the equation of the circle as -
(x – h)² + (y – k)² = r²
(x - 5)² + (y + 4)² = (11)² + (-7)²
(x - 5)² + (y + 4)² = 121 + 49
(x - 5)² + (y + 4)² = 170
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what is the greatest 5 digit number which when divided by 2, 3, 4, and 5 leaves a remainder of 1 in each case
Answers
Answer:99904.
Step-by-step explanation:
Find the LCM of
5
10 = 2x5
15 = 3x5
20 = 2x2x5
25 = 5x5
LCM = 2x2x3x5x5 = 300
Take the smallest 5-digit number: 10000 and divide it by 300 to get 33.33. Round it off to 34 and multiply it by 300 to get 10200. Finally add 4 to 10200 to get 10204 which is the smallest final 5-digit number.
Check: 10204/5 = 2040 as quotient and a remainder of 4. Correct.
10204/10 = 1020 as quotient and a remainder of 4. Correct.
10204/15 = 680 as quotient and a remainder of 4. Correct.
10204/20 = 510 as quotient and a remainder of 4. Correct.
10204/25 = 408 as quotient and a remainder of 4. Correct.
Answer: 10204.
To get the greatest 5-digit number take 99999 and divide it by 300 to get 333.33. Round it off to 333 and multiply it by 300 to get 99900. Finally add 4 to 99900 to get 99904 which is the final greatest 5-digit number.
Check: 99904/5 = 19980 as quotient and a remainder of 4. Correct.
99904/10 = 9990 as quotient and a remainder of 4. Correct.
99904/15 = 6660 as quotient and a remainder of 4. Correct.
99904/20 = 4995 as quotient and a remainder of 4. Correct.
99904/25 = 3996 as quotient and a remainder of 4. Correct.
Answer: 99904.
What is 4.5pi minus pi/0.5?
Answers
Answer:
≈ 7.8598
Step-by-step explanation:
Let's round pi to 3.14159. First, we multiply 3.14159 by 4.5, which is around 14.13716. Then, we divide 3.14159 by 0.5, which is around 6.28318. So, 14.13716 - 6.28318 = 7.8598
Evvie has these dight card 4 5 0 8 2 she makes them into 6 digit number larger than 300.000 and smaller than 400.000
Answers
Step-by-step explanation:
500.000 evvie was on the digit card
1. Claretta works part-time at a coffee shop. Her
weekly paychecks in March are: $87.00, $96.00,
$84.25, and $100.75. Find the median of her
paychecks.
Answers
Please help me with the problem and show work, please
Answers
x+6+x+9+x+3 = x+4+x+4+x+1+x+1
Solved x=8
Work:
You select a sample of 20 kids in the Valley Kindergarten and observe that their ages are
9; 9.5; 9.5; 10; 10; 10; 10; 10.5; 10.5; 10.5; 10.5; 11; 11; 11; 11; 11; 11; 11,5; 11,5; 11.5
Find the sample standard deviation of the age distribution in the Wenatchee Valley Kindergarten.
Solution. Please write your detailed solution here:
Answers
Standard deviation of the following data is 0.655.
What is standard deviation?The standard deviation is equal to the variance's positive square root. It is a fundamental statistical analysis method. The amount by which data values deviate from the mean is referred to as "standard deviation," or "SD."
Whereas a big standard deviation implies that the values are much outside the mean, a low standard deviation shows that the values are frequently only a few standard deviations from the mean.
Here in the question,
Total kids = 20.
Mean = 9+9.5+9.5+10+10+10+10+10.5+10.5+10.5+10.5+11+11+11+11+11+11+11.5+11.5+11.5/20
= 10.52
Now square of distance between mean and ages.
(9-10.52) ² = 2.31
(9.5-10.52) ² = 1.04
(10-10.52) ² = 0.27
(10.5-10.52) ² = 0.0004
(11-10.52) ² = 0.23
(11.5-10.52) ² = 0.96
Now sum of all the differences = 2.31 + 1.04 + 1.04 + 4×0.27 + 4× 0.0004 + 6× 0.23+ 3×0.96
= 8.73
Now standard deviation = √8.73/20
= √0.43
= 0.655
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(-12 + 3 ) + 4 = -12 + (3 + 4)
Answers
Answer:
yes
Step-by-step explanation:
(-12+3)+4 = -12+(3+4)
-9+4 = -12+7
-5 = -5
:)
2x^3y + 18xy - 10x^2y - 90y
Part A: rewrite the expression so that the GCF is factored completely
Part B: rewrite the expression completely factored. Show the steps of your work
___________________________
Part A: the area of a square is (9x^2 + 24x + 16) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work.
Part B: the area of a rectangle is (16x^2 - 25y^2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work.
___________________________
f(x) = 2x^2 - 5x + 3
Part A: what are the x-intercepts of the graph of f(x)? Show your work
Part B: is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answer and show your work.
Part C: what are the steps you would use to graph f(x)? Justify that you can use the answer in part A and part B to draw the graph.
Answers
The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)
The expression completely factored in is
\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)
Please refer below for the remaining answers.
We have,
Part A:
To rewrite the expression 2x³y + 18xy - 10x²y - 90y so that the greatest common factor (GCF) is factored completely, we can factor out the common terms.
GCF: 2y
\(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)
Part B:
To completely factor the expression, we can further factor the quadratic term.
\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)
Now,
Part A:
To determine the length of each side of the square given the area expression (9x² + 24x + 16), we need to factor it completely.
The area expression (9x² + 24x + 16) can be factored as (3x + 4)(3x + 4) or (3x + 4)².
Therefore, the length of each side of the square is 3x + 4.
Part B:
To determine the dimensions of the rectangle given the area expression (16x² - 25y²), we need to factor it completely.
The area expression (16x² - 25y²) is a difference of squares and can be factored as (4x - 5y)(4x + 5y).
Therefore, the dimensions of the rectangle are (4x - 5y) and (4x + 5y).
Now,
f(x) = 2x² - 5x + 3
Part A:
To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.
2x² - 5x + 3 = 0
The quadratic equation can be factored as (2x - 1)(x - 3) = 0.
Setting each factor equal to zero:
2x - 1 = 0 --> x = 1/2
x - 3 = 0 --> x = 3
Therefore, the x-intercepts of the graph of f(x) are x = 1/2 and x = 3.
Part B:
To determine if the vertex of the graph of f(x) is maximum or minimum, we can examine the coefficient of the x^2 term.
The coefficient of the x² term in f(x) is positive (2x²), indicating that the parabola opens upward and the vertex is a minimum.
To find the coordinates of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.
For f(x),
a = 2 and b = -5.
x = -(-5) / (2 x 2) = 5/4
To find the corresponding y-coordinate, we substitute this x-value back into the equation f(x):
f(5/4) = 25/8 - 25/4 + 3 = 25/8 - 50/8 + 24/8 = -1/8
Therefore, the vertex of the graph of f(x) is at the coordinates (5/4, -1/8), and it is a minimum point.
Part C:
To graph f(x), we can start by plotting the x-intercepts, which we found to be x = 1/2 and x = 3.
These points represent where the graph intersects the x-axis.
Next,
We can plot the vertex at (5/4, -1/8), which represents the minimum point of the graph.
Since the coefficient of the x² term is positive, the parabola opens upward.
We can use the vertex and the symmetry of the parabola to draw the rest of the graph.
The parabola will be symmetric with respect to the line x = 5/4.
We can also plot additional points by substituting other x-values into the equation f(x) = 2x² - 5x + 3.
By connecting the plotted points, we can draw the graph of f(x).
The steps to graph f(x) involve plotting the x-intercepts, the vertex, and additional points, and then connecting them to form the parabolic curve.
The answer in part A (x-intercepts) and part B (vertex) are crucial in determining these key points on the graph.
Thus,
The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)
The expression completely factored in is
\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)
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how much is ( (8/4)+ 6) x 2?
Answers
Answer:
16
Step-by-step explanation:
((8/4)+ 6) x 2
(2 + 6) x 2 Divided 8 by 4
8 x 2 Added 2 and 6
16 Multiply
I need help solving these
Answers
Let (an) and (bn) be sequences satisfying ∣an−bn∣
Answers
In general, if (an) and (bn) are sequences, then ∣an−bn∣ represents the absolute difference between the terms an and bn for every n. This means that for each value of n, you subtract the corresponding terms an and bn and take the absolute value.
The question states that (an) and (bn) are sequences that satisfy ∣an−bn∣. To answer this, we need to understand what this expression means.
The expression ∣an−bn∣ represents the absolute value of the difference between the terms an and bn. Absolute value means that we ignore the negative sign and only consider the magnitude of the difference.
To find the absolute difference between two terms, you subtract one term from the other and take the absolute value.
For example, if an = 3 and bn = 5, then ∣an−bn∣ = ∣3−5∣ = ∣−2∣ = 2.
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On Monday, the baker makes 36 blueberry muffins. What is the total number of muffins that the baker makes on Monday?
Answers
Answer:
90
Step-by-step explanation:
Answer:
am preety sure the total s 40%
Step-by-step explanation: