Answer:
Ok, we have two words:
"Signature"
The letters are: "S I G N A T U R E"
9 different letters.
Now, we can make only words with 9 letters, so we can think on 9 slots, and in each of those slots, we can input a letter of those 9.
For the first slot, we have 9 options.
For the second slot, we have 8 options (because on is already taken)
For the second slot, we have 7 options and so on.
Now, the total number of combinations is equal to the product of the number of options in each selection:
C = 9*8*7*6*5*4*3*2*1 = 362,880.
Now, our second word is Restaurant.
The letters here are " R E S T A U N" such that R, T and A appear two times each, so we have a total of 10 letters and 7 unique letters.
So first we do the same as beffore, 10 slots and we start with 10 options.
The total number of combinations will be:
C = 10*9*8*7*6*5*4*3*2*1 = 3,628,800
A lot of combinations, but we are counting only unique words.
For example, as we have two R, we are counting two times the word:
Restaurant (because we could permutate only the two letters R and get the same word)
So we must divide by two for each letter repeated.
we have 3 letters repeated, we divide 3 times by 2.
C = ( 3,628,800)/(2*2*2) = 453,600
Select the correct answer. Consider matrices A, B, and C:
Answer:
i think it is c. i may be incorrect, i am sorry!
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
I did the math
when Charles eats Oreos , he likes to dunk 2 out of every 5 cookies in a cold glass of milk. if he eats a total of 15 Oreos , how many will he dunk ? how many will ge eat without dunking?
Answer: 6 with milk, 9 without
Step-by-step explanation:
2/5 of the cookies he eats are dunked. Thus, simply do 2/5, or .4*15 to get that 6 cookies are dunked, and 15-6 to get that 9 cookies are not dunked.
Hope it helps <3
how could you correctly rewrite the equation 4(5+3)=2(22-6) using the distributive property?
We can correctly rewrite the equation: 4(5+3) = 2(22-6) by distributing each side.
4(5+3) = 2(22-6)
4(8) = 2(16)
32 = 32
Once you finish distributing each side, you can check to see if it is equal on both sides.
In our case it is since they both equal 32 after distributing the terms.
Let T:V→W be a linear transformation from a vector space V into a vector space W. Prove that the range of T is a subspace of W.
Answer:
The range of T is a subspace of W.
Step-by-step explanation:
we have T:V→W
This is a linear transformation from V to W
we are required to prove that the range of T is a subspace of W
0 is a vector in range , u and v are two vectors in range T
T = T(V) = {T(v)║v∈V}
{w∈W≡v∈V such that T(w) = V}
T(0) = T(0ⁿ)
0 is Zero in V
0ⁿ is zero vector in W
T(V) is not an empty subset of W
w₁, w₂ ∈ T(v)
(v₁, v₂ ∈V)
from here we have that
T(v₁) = w₁
T(v₂) = w₂
t(v₁) + t(v₂) = w₁+w₂
v₁,v₂∈V
v₁+v₂∈V
with a scalar ∝
T(∝v) = ∝T(v)
such that
T(∝v) ∈T(v)
so we have that T(v) is a subspace of W. The range of T is a subspace of W.
In a class full of men and women, 5 9 of the class are women. What is the ratio of men to women in its simplest form?
Consider this quote: "In a recent survey, 65 out of 100 consumers reported that they preferred plastic bags instead of paper bags for their groceries. If there is no difference in the proportions who prefer each type in the population, the chance of such extreme results in a sample of this size is about .03. Because .03 is less than .05, we can conclude that there is a statistically significant difference in preference." Give a numerical value for each of the following.
a. The p-value.
b. The level of significance, α.
c. The sample proportion.
d. The sample size.
e. The null value.
Answer:
Step-by-step explanation:
The p value (probability of obtaining results as extreme the z score if null is true) is usually the value derived to make a conclusion and in this case the p value is 0.03
The level of significance is the value usually compared with the p value which is 0.05
The sample promotion is 65 out of 100 = 65/100 = 0.65
The sample size is the total number of consumers which is 100
The null value is usually the default value. The null value would assume that there is no difference in the proportions who prefer each type in the population. There are two preferences: 100/2 = 50- 0.5 for each preference.
When randomly selecting an adult, let B represent the event of randomly selecting someone with type B blood. Write a sentence describing what the rule of complements below is telling us. P B or B = 1 Choose the correct answer below. A. It is impossible that the selected adult has type B blood or does not have type B blood. B. It is certain that the selected adult has type B blood. C. It is certain that the selected adult has type B blood or does not have type B blood. D. It is certain that the selected adult does not have type B blood.
Answer: The rule of complements is apprising us that, the person selected will.eithwr have a type B blood or will not have a type B blood
Step-by-step explanations:
Find explanations in the attachment
The state of CT claims that the average time on death row is 15 years. A random survey of 75 death row inmates revealed that the average length of time on death row is 17.8 years with a standard deviation of 5.9 years. Conduct a hypothesis to test the state of CT's claim. What type of test should be run? t-test of a mean z-test of a proportion The alternative hypothesis indicates a right-tailed test left-tailed test two-tailed test Calculate the p-value. What is the decision? We reject the claim that the average time on death row is 15 years We fail to reject the claim that the average time on death row is 15 years
Answer:
a)The calculated value t = 4.111 > 1.9925 at 5 % level of significance
Null hypothesis is rejected
The claim that the average time on death row is not 15 years
b) The p-value is 0.000101<0.05
we reject Null hypothesis
The claim that the average time on death row is not 15 years
Step-by-step explanation:
Step(i):-
Sample size 'n' =75
Mean of the sample x⁻ = 17.8
standard deviation of the sample (S) = 5.9
Mean of the Population = 15
Null hypothesis:H₀:μ = 15 years
Alternative Hypothesis :H₁:μ≠15 years
Step(ii):-
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }=\frac{17.8-15}{\frac{5.9}{\sqrt{75} } }[/tex]
t = 4.111
Degrees of freedom
ν = n-1 = 75-1=74
t₀.₀₂₅ = 1.9925
The calculated value t = 4.111 > 1.9925 at 5 % level of significance
Null hypothesis is rejected
The claim that the average time on death row is not 15 years
P-value:-
The p-value is 0.000101<0.05
we reject Null hypothesis
The claim that the average time on death row is not 15 years
Question 15 of 25
What is the solution to this equation?
X + 8 = -3
Answer:
x=-11
Step-by-step explanation:
x+8=-3
x=-3-8 :- collect like term
since we are adding two negative numbers, we will let the number be negative but add them.
x=-11
Hope it helps :)
Answer:
x=-11
Step-by-step explanation:
x+8=-3
collect like terms;
x=-3-8
x=-11
PLEASE ANSWER FAST I WILL MARK BRAINLEIST AMD 20 POINTSBased on the figure below what is the value of X
Answer:
[tex]\boxed{9}[/tex]
Step-by-step explanation:
The two angles are complementary to each other.
That means they add up to 90 degrees.
[tex]5x+15+30=90[/tex]
[tex]5x+45=90[/tex]
[tex]5x=45[/tex]
[tex]x=9[/tex]
Answer:
x = 9
Step-by-step explanation:
So you know that the total is 90 degrees.
What you need to do is create an equation.
5x + 15 + 30 = 90
Then, solve the equation like this.
5x + 15 + 30 = 90
5x + 45 = 90
5x = 90 - 45
5x = 45
x = 45 ÷ 5
x = 9
Hope this helps! :)
The measure of minor arc JL is 60°. Circle M is shown. Line segments M J and M L are radii. Tangents J K and L K intersect at point K outside of the circle. Arc J L is 60 degrees. What is the measure of angle JKL? 110° 120° 130° 140°
Answer:
angle JKL = 120 degrees
Step-by-step explanation:
Since arc JL is 60 degrees, the central angle is also 60 degrees.
Point K is the intersection of tanges at J and L, therefore KJM and KLM are 90 degrees.
Consider quadrilateral JKLM whose sum of internal angles = 360.
Therefore
angle JKL + angle KLM + angle LMJ + angle MJK = 360 degrees
angle JKL + 90 + 60 + 90 = 360
angle JKL = 360 - 90 - 60 -90 = 120 degrees
Answer:
120 degrees
Step-by-step explanation:
Since arc JL is 60 degrees, the central angle is also 60 degrees.
Point K is the intersection of tanges at J and L, therefore KJM and KLM are complementary or equal 90 degrees.
look at quadrilateral JKLM whose sum of internal angles = 360.
Therefore
angle JKL plus angle KLM plus angle LMJ plus angle MJK = 360 degrees
angle JKL + 90 + 60 + 90 = 360
For the functions f(x)=8 x 2 +7x and g(x)= x 2 +2x , find (f+g)(x) and (f+g)(3)
Answer:
(f+g)(x)= 9x² + 9x
(f+g)(3) = 108
Step-by-step explanation:
f(x)=8x² +7x
g(x)= x² +2x
(f+g)(x) = f(x) + g(x) = 8x² +7x +x² +2x = 9x² + 9x
(f+g)(x)= 9x² + 9x
(f+g)(3)= 9*3² + 9*3 = 108
Find the present value of an investment that is worth $19,513.75 after earning 3% simple interest for 512 years.
Answer:
$16,750.00
Step-by-step explanation:
Simple interest:
I = Prt
Value of an investment of value P over t years at r interest rate:
F = P + Prt
F = P(1 + rt)
19,513.75 = P(1 + 0.03 * 5.5)
1.165P = 19,513.75
P = 16,750
Answer: $16,750.00
The present value of the investment was $16,750 which is worth $19,513.75 after earning 3% simple interest for 512 years.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100
We have been given data as:
Rate of Interest (R) = 3% = 3/100 = 0.03
Time (T) = 512 years
Value of an investment of value P over t years at r interest rate:
A = P + Prt
A = P(1 + rt)
19,513.75 = P(1 + 0.03 × 5.5)
19,513.75 = 1.165P
1.165P = 19,513.75
P = 19,513.75/1.165
P = 16,750
Thus, the present value of the investment was $16,750 which is worth $19,513.75 after earning 3% simple interest for 512 years.
Learn more about the simple interest here:
brainly.com/question/22621039
#SPJ2
Which describes the graph in words?
A. All numbers less than -10 and less than or equal to 8.
B. All numbers greater than -10 and less than 8
C. All numbers greater than or equal to -10 and less than or equal to 8
D. All numbers greater than -10 and less than or equal to 8.
D. All numbers greater than -10 and less than or equal to 8
Out of 600 people sampled, 66 preferred Candidate A. Based on this, estimate what proportion of the entire voting population (p) prefers Candidate A.
Required:
Use a 90% confidence level, and give your answers as decimals, to three places.
Answer:
11% of the Total the entire voting population
Step-by-step explanation:
Let's bear in mind that the total number of sample candidates is equal to 600.
But out of 600 only 66 preffered candidate A.
The proportion of sampled people to that prefer candidate A to the total number of people is 66/600
= 11/100
In percentage
=11/100 *100/1 =1100/100
=11% of the entire voting population
(SAT Prep) Find the value of x.
Answer:
x = 65°
Step-by-step explanation:
Naming the sides of the parallelogram formed ABCD as shown in the attached image to this solution.
Angle A = 2x (vertically opposite angles are equal)
Angle A = Angle C (opposite angles of a parallelogram are equal)
Angle A = Angle C = 2x
(Angle C) + 50° = 180° (Sum of angles on a straight line is 180°)
2x + 50° = 180°
2x = 180° - 50° = 130°
x = (130°/2) = 65°
Hope this Helps!!!
Answer:
65 degrees
Step-by-step explanation:
6x²-7x=20 solve the following quadratic equation
Answer:
x = -4/3 and x = 5/2.
Step-by-step explanation:
6x² - 7x = 20
6x² - 7x - 20 = 0
To solve this, we can use the quadratic formula to solve this.
[please ignore the A-hat; that is a bug]
[tex]\frac{-b±\sqrt{b^2 - 4ac} }{2a}[/tex]
In this case, a = 6, b = -7, and c = -20.
[tex]\frac{-(-7)±\sqrt{(-7)^2 - 4 * 6 * (-20)} }{2(6)}[/tex]
= [tex]\frac{7±\sqrt{49 + 80 * 6} }{12}[/tex]
= [tex]\frac{7±\sqrt{49 + 480} }{12}[/tex]
= [tex]\frac{7±\sqrt{529} }{12}[/tex]
= [tex]\frac{7±23 }{12}[/tex]
[tex]\frac{7 - 23 }{12}[/tex] = [tex]\frac{-16 }{12}[/tex] = -8 / 6 = -4 / 3
[tex]\frac{7 + 23 }{12}[/tex] = [tex]\frac{30}{12}[/tex] = 15 / 6 = 5 / 2
So, x = -4/3 and x = 5/2.
Hope this helps!
Answer:
[tex]x1 = - \frac{4}{3} [/tex][tex]x2 = \frac{5}{2} [/tex]Step-by-step explanation:
[tex]6 {x}^{2} - 7x = 20[/tex]
Move constant to the left and change its sign
[tex] {6x}^{2} - 7x - 20 = 0[/tex]
Write -7x as a difference
[tex]6 {x}^{2} + 8x - 15x - 20 = 0[/tex]
Factor out 2x from the expression
[tex]2x(3x + 4) - 15x - 20 = 0[/tex]
Factor out -5 from the expression
[tex]2x(3x + 4) - 5(3x + 4) = 0[/tex]
Factor out 3x + 4 from the expression
[tex](3x + 4)(2x - 5) = 0[/tex]
When the product of factors equals 0 , at least one factor is 0
[tex]3x + 4 = 0[/tex]
[tex]2x - 5 = 0[/tex]
Solve the equation for X1
[tex]3x + 4 = 0[/tex]
Move constant to right side and change its sign
[tex] 3x = 0 - 4[/tex]
Calculate the difference
[tex]3x = - 4[/tex]
Divide both sides of the equation by 3
[tex] \frac{3x}{3} = \frac{ - 4}{3} [/tex]
Calculate
[tex]x = - \frac{4}{3} [/tex]
Again,
Solve for x2
[tex]2x - 5 = 0[/tex]
Move constant to right side and change its sign
[tex]2x = 0 + 5[/tex]
Calculate the sum
[tex]2x = 5[/tex]
Divide both sides of the equation by 2
[tex] \frac{2x}{2} = \frac{5}{2} [/tex]
Calculate
[tex]x = \frac{5}{2} [/tex]
[tex]x1 = - \frac{4}{3} [/tex]
[tex]x2 = \frac{5}{2} [/tex]
Hope this helps...
Best regards!!
Solve 2x2 – 6x + 10 = 0 by completing the square.
Answer: x = 6.32 or -0.32
Step-by-step explanation:
2x² - 6x + 10 = 0
No we divide the expression by 2 to make the coefficient of x² equals 1
We now have
x² - 3x + 5 = 0
Now we remove 5 to the other side of the equation
x² - 3x = -5
we add to both side square of half the coefficient of x which is 3
x² - 3x + ( ⁻³/₂)² = -5 + (⁻³/₂)²
(x - ³/₂)² = -5 + ⁹/₄
Resolve into fraction
(x - ³/₂)² = ⁻¹¹/4
Take the roots of the equation
x - ³/₂ = √¹¹/₄
x - ³/₂ = √11/₂
x = ³/₂ ± 3.32/₂
= 3+ 3.32 or 3 - 3.32
= 6.32 or - 0.32
the result of two forces acting on a body has a magnitude of 80 pounds. The angles between the resultant and the forces are 20 degrees and 52 degrees. find the magnitude of the large force
Answer:
Larger force= 66.28 pounds
Step-by-step explanation:
The angle of the resultant force 80 pounds = 180-(52+20)
The angle of the resultant force 80 pounds = 180-72
The angle of the resultant force 80 pounds = 108°
The larger force is the force with 52°
Let the larger force be x
Magnitude of the larger force
x/sin52 = 80/sin108
X= sin52 *(80/sin 108)
X= 0.7880*(80/0.9511)
X = 0.7780*(84.1131)
X = 66.28 pounds
Find the length of AG
Answer:
[tex]AG=22[/tex]
Step-by-step explanation:
Follow the next steps:
[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F} =\frac{C-D}{F-G} =\frac{A-C}{A-F} =\frac{B-D}{E-G} =\frac{A-D}{A-G}[/tex]
Let:
[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F}\\ \\\frac{4}{A-E} =\frac{5}{10x}\\ \\Solving\hspace{3}for\hspace{3}A-E\\\\A-E=8x[/tex]
Now:
[tex]\frac{C-D}{F-G} =\frac{A-C}{A-F} \\\\\frac{2}{F-G} =\frac{9}{18x} \\\\Solving\hspace{3}for\hspace{3}F-G\\\\F-G=4x[/tex]
Hence:
[tex]A-G=(A-E)+(E-F)+(F-G)=22x[/tex]
Finally:
[tex]\frac{B-D}{E-G} =\frac{A-D}{A-G}\\\\\frac{A-D}{B-D} =\frac{A-G}{E-G}\\[/tex]
[tex]\frac{11}{7} =\frac{22x}{14x} \\\\\frac{11x^{2} }{7} -\frac{11}{7} =0\\\\[/tex]
Hence:
[tex]x=1\\x=-1[/tex]
Since it would be absurd for [tex]x=-1[/tex], the real solution is [tex]x=1[/tex]
Therefore:
[tex]AG=22[/tex]
One number is 6 more than another. Their product is -9. Need help fast
Answer: the numbers are 3 and -3
Step-by-step explanation:
let the unknown number be x
The first UNKNOWN NUMBER = X
The second unknown number is = 6 + x
Their product = -9
(X)(6 + X) = -9
6x +[tex]x^{2}[/tex]=-9
[tex]x^{2}[/tex] +6x +9=0
we multiply the coefficient of x which is 1 with 9
now, we look for two numbers that when multiplied will give us 9 and when added will give 6 and that is 3 and 3
[tex]x^{2}[/tex] +3x+3x +9 = 0
x(x+3) +3(x+3) = 0
(x +3 ) = 0
or (x +3)=0
x +3 =0
x=0 -3
x =-3
x +3=0
x =0-3
x =-3
since the numbers are the same ,we pick one
therefore,the first number =x =-3
the second number is 6 + x=6 + (-3)
6-3=3
Because of a manufacturing error, 3 cans of regular soda were accidentally filled with diet soda and placed into a 24-pack. Suppose that two cans are randomly selected from the 24-pack. Determine the probability that at least one contain regular soda.
Answer:
161/184 or 0.875
Step-by-step explanation:
Total number of cans = 24 cans
Total number of diet soda = 3 cans
Total number of regular soda = 21 cans
We are asked to find the probability that:that at least one contain regular soda if two cans are selected randomly
We have two ways for this happening
a) two of the cans are regular soda
b) one of the cans is regular , while one is diet
Hence,
Probability (that at least one contain regular soda) = Probability(that two of the cans are regular soda) + Probability ( one of the cans is regular , while one is diet)
Probability(that two of the cans are regular soda) = 21/24 × 20/23
= 35/46
Probability ( one of the cans is regular , while one is diet) = 21/24 × 3/23
= 21/184
Probability (that at least one contain regular soda) = 35/46 + 21/184
We find the Lowest common multiple of the denominators = 184
= 35/46 + 21/184
= (35 × 4) + (21 × 1)/184
= 140 + 21/184
= 161/184
= 0.875
Therefore, the probability that at least one can contains regular soda = 161/184 or 0.875
Find the slope of the line passing through the points (8,-4) and (4, -8).
Answer:
1
Step-by-step explanation:
We can find the slope using
m= ( y2-y1)/(x2-x1)
= ( -8 - -4)/( 4 - 8)
= ( -8 +4)/( 4 - 8)
= -4 / -4
= 1
Answer:
slope equals 1
Step-by-step explanation:
To do this you would need to do an equation that is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex] so in this case -8 would be y2 and -4 would be y1 and 4 would be x2 and 8 would b e x1 so if you plug it into the equation we would get [tex]\frac{-8-(-4)}{4-8}[/tex] and if we simplify we get [tex]\frac{-4}{-4}[/tex] which simplifies to 1 so the slope would equal 1
1. Manuel quiere fabricar banderitas chilenas para venderlas en los partidos de la selección nacional. Si se demora 1 hora en hacer 45 banderitas y trabaja 5 horas diarias. ¿Cuántos días se demorará en fabricar 1800 banderitas?
Answer:
[tex]\large \boxed{\text{Eight days}}[/tex]
Step-by-step explanation:
1. Calculate the hours
[tex]\text{Hours} = \text{1800 flags} \times \dfrac{\text{1 h}}{\text{45 flags}} = \textbf{40 h}[/tex]
2. Calculate the days
[tex]\text{Days} = \text{40 h} \times \dfrac{\text{1 da}}{\text{5 h}} = \text{8 da}\\\\\text{It will take $\large \boxed{\textbf{eight days}}$ to make 4500 flags.}[/tex]
In a random sample of 40 refrigerators, the mean repair cost was $150. Assume the population standard deviation is $15.50. Construct a 99% confidence interval for the population mean repair cost. Then change the sample size to n = 60. Which confidence interval has the better estimate?
Answer: ($143.69, $156.31)
Step-by-step explanation:
Confidence interval to estimate population mean :
[tex]\overline{x}\ \pm z\dfrac{\sigma}{\sqrt{n}}[/tex]
, where [tex]\sigma[/tex] = population standard deviation
n= sample size
[tex]\overline{x}=[/tex] Sample mean
z= critical value.
As per given,
n= 40
[tex]\sigma[/tex] = $15.50
[tex]\overline{x}=[/tex] $150
Critical value for 99% confidence level = 2.576
Then, 99% confidence interval for the population mean:
[tex]150\pm(2.576)\dfrac{15.50}{\sqrt{40}}\\\\\Rightarrow\ 150\pm6.31 \ \ (approx)\\\\\Rightarrow(150-6.31,150+6.31)=(143.69,156.31)[/tex]
Hence, the required confidence interval : ($143.69, $156.31)
A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75. If x is the cost of one apple and y is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange. 6x+6y=7.50 10x+5y=8.75 What is the cost of one apple?
Answer:
$0.50
Step-by-step explanation:
Let's remove common factors from the equations.
x + y = 1.25 . . . . divide the first equation by 62x +y = 1.75 . . . divide the second equation by 5Subtracting the first equation from the second, we find the cost of an apple:
(2x +y) -(x +y) = 1.75 -1.25
x = 0.50
The cost of one apple is $0.50.
expand(x+y2)2 plzzzzzzzzzzzzzzzz
Answer:
[tex](x + {y}^{2}) = {x}^{2} + 2x {y}^{2} + {y}^{4} [/tex]
Hope it helps!!❤❤Please mark me as the brainliest!!!Thanks!!!!
Which pairs of angles are alternate exterior angles? select yes or no
A - No
B - No
C - Yes
D - Yes
.
C and D are alternate exterior angles
When testing the claim that p 1p1equals=p 2p2, a test statistic of zequals=2.04 is obtained. Find the p-value obtained from this test statistic.
Answer:
0.0414 with an upper tailed test
Step-by-step explanation:
Claim: P1P1 = P2P2
The above is a null hypothesis
The alternative hypothesis for a two-tailed test would be:
P1P1 \=/ P2P2
Where "\=/" represents "not equal to".
Using a z-table or z-calculator, we derive the p-value (probability value) for the z-score 2.04
With an upper tailed test, the
2 × [probability that z>2.04] = 2[0.0207] = 0.0414
This is the p-value for the test statistic.
Focus is on the alternative hypothesis.
Copy the problem, mark the givens in the diagram, and write a Statement/Reason proof. Given: MN ≅ MA ME ≅ MR Prove: ∠E ≅ ∠R
Answer:
Step-by-step explanation:
Given: MN ≅ MA
ME ≅ MR
Prove: ∠E ≅ ∠R
From the given diagram,
YN ≅ YA
EY ≅ RY
<EMA = <RMN (right angle property)
EA = EY + YA (addition property of a line)
NR = YN + RY (addition property of a line)
EA ≅ NR (congruent property)
ΔEMA ≅ ΔRMN (Side-Side-Side, SSS, congruence property)
<MNR ≅ MAE (angle property of congruent triangles)
Therefore,
<E ≅ <R (angle property of congruent triangles)