a) 2338 ≡ 42 • 55 + 28 ≡ 28 (mod 55)
b) We want to find a such that
23a ≡ 1 (mod 55)
Use the Euclidean algorithm:
55 = 2 • 23 + 9
23 = 2 • 9 + 4
9 = 2 • 4 + 1
⇒ 1 = 9 - 2 • 4
⇒ 1 = 9 - 2 • (23 - 2 • 9) = 5 • 9 - 2 • 23
⇒ 1 = 5 • (55 - 2 • 23) - 2 • 23 = 5 • 55 - 12 • 23
Solve for a :
5 • 55 - 12 • 23 ≡ 1 (mod 55)
⇒ -12 • 23 ≡ 1 (mod 55)
⇒ a ≡ -12 ≡ 43 (mod 55)
The scores of a recent test taken by 1200 students had an approximately normal distribution with a mean of 225 and a standard deviation of 18. determine the number of students who scored between 200 and 245
If the probability will be 0.7842. Then the number of students who scored between 200 and 245 will be 941.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The scores of a recent test taken by 1200 students had an approximately normal distribution with a mean of 225 and a standard deviation of 18.
Then the number of students who scored between 200 and 245 will be
Then the z-score for x = 200
[tex]z = \dfrac{200-225}{18}\\\\z = -1.389[/tex]
Then the z-score for x = 245
[tex]z = \dfrac{245-225}{18}\\\\z = 1.1111[/tex]
Then we have
[tex]\begin{aligned} P(-1.39 < z < 1.11) &= P(z < 1.11) - P(z < -1.389)\\\\&= P(z < 1.11)- [1-P(z > -1.389)] \\\\&=0.8665 - (1-0.9177) \\\\&=0.7842 \end[/tex]
Then the number of students who scored between 200 and 245 will be
→ 0.7842 × 1200
→ 941.04 ≅ 941
More about the normal distribution link is given below.
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I NEED HELP WITH THIS QUESTION PLEASE, i don't have much time T^T
i'll give brainliest and points, thank you in advancee <33
an explanation for future reference would be appreciated!!^^
Answer:
Option b is the correct answer
Step-by-step explanation:
[tex]\cos x = -\frac{12}{13}[/tex] (Given)Formula relating sin x and cos x is given as below:[tex]\sin^2x = 1-\cos^2x[/tex][tex]\implies \sin^2x = 1-\bigg(-\frac{12}{13}\bigg)^2[/tex][tex]\implies \sin^2x = 1-\frac{144}{169}[/tex][tex]\implies \sin^2x = \frac{169-144}{169}[/tex][tex]\implies \sin^2x = \frac{25}{169}[/tex][tex]\implies \sin x =\pm\sqrt{ \frac{25}{169}}[/tex][tex]\implies \sin x =\pm \frac{5}{13}[/tex]It is given that: 180° < x < 270°. This means x falls in the third quadrant. In third quadrant sin ratio is negative.[tex]\implies \sin x =- \frac{5}{13}[/tex]Now, we will find the value of tanx by dividing sinx by cosx.[tex]\implies \tan x =\frac{\sin x}{\cos x}[/tex][tex]\implies \tan x = \frac{-5/13}{-12/13}[/tex][tex]\implies\red{\bold{ \tan x =\frac{5}{12}}}[/tex]tan (90° + x) and tan x both lie in the interval 180° < x < 270°. So, the values of both will be equal.[tex]\implies \tan (90\degree + x ) =\tan x[/tex][tex]\implies \huge{\purple{\tan (90\degree + x ) =\frac{5}{12}}}[/tex]Jackson is told that he will be given 1 cent for working today. However, for each day he works, he will get double the pay. So, on day 2, he gets 2 cents, on day 3, 4 cents, and so on. Jackson thinks, no way, that’s not much money. But if he agrees, how much will he make on day 20?
Question
Jackson is told that he will be given 1 cent for working today. However, for each day he works, he will get double the pay. So, on day 2, he gets 2 cents, on day 3, 4 cents, and so on. Jackson thinks, no way, that’s not much money. But if he agrees, how much will he make on day 20?
Answer:
48 cents
Step-by-step explanation:
Yes yes yes
If the volume is 7 and the density is 1.420 what's thr mass
Answer:
9.94
Step-by-step explanation:
Density = mass/ volume
1.420 = mass / 7
7 x 1.42 = mass
9.94 = mass
Austin worked 28 hours last month and won $8 per hour. he was already spent $19 of your income. How much money does he have left?
Answer:
[tex]\huge\boxed{\sf \$\ 205}[/tex]
Step-by-step explanation:
Work hours = 28 hours
Earning = $8 per hour
1 hour = $8
28 hours = $8 × 28
28 hours = $224
He has earned $224 last month.
Spent = $19
Left:
= Earning - Spent
= $224 - $19
= $205
[tex]\rule[225]{225}{2}[/tex]
what is 2 times 2 times 5 times 6 divided by 3 and subtracted 3 and plus 1?
Answer:
38
Step-by-step explanation:
2(2) = 4
4(5) = 20
20(6) = 120
120/3 = 40
40 - 3 = 37
37 + 1 = 38
HELPPP!! I’ll give brainliest
Ram has two plots in two different places. Both are square in shapes. The side of the first field is 350m and the side of the other field is 220m. Find the total area of the fields that Ram has?
The total area of the fields that Ram has is 170,900 square meters ( 170900 m²)
Calculating the areas of squaresFrom the question, we are to determine the total area of the fields that Ram has
Since the fields are square in shapes, we will use the formula for calculating the area of a square
The area of a square can be calculated by using the formula,
A = s²
Where A is the area
and s is the side
For the first field
s = 350 m
∴ A = 350²
A = 122500 m²
For the second field
s = 220 m
∴ A = 220²
A = 48400 m²
Then,
The total area of the fields = 122500 m² + 48400 m²
The total area of the fields = 170900 m²
Hence, the total area of the fields that Ram has is 170,900 square meters ( 170900 m²)
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Factor the quadratic trinomial x²- 9x+18
(x + ) (x+ )
Answer:
(x - 6)(x - 3)
Step-by-step explanation:
x² - 9x + 18
consider the factors of the constant term (+ 18) which sum to give the coefficient if the x- term (- 9 )
the factors are - 6 and - 3 , since
- 6 × - 3 = + 18 and - 6 - 3 = - 9 , then
x² - 9x + 18 = (x - 6)(x - 3) ← in factored form
Answer:
(x - 3)(x - 6)
Step-by-step explanation:
x²- 9x+18
= x^2 - 6x - 3x + 18
= x(x - 6) - 3(x - 6)
= (x - 3)(x - 6).
HURRY UP 10 MIN LEFT (100 points)!!!!!!!!!!!
Which of the following words is not a translation for "=?"
equals
similar
is
equal to
Answer:
similar
Step-by-step explanation:
Answer:
Similar
Step-by-step explanation:
For similarity or congruence we use ~ symbol not equal to
Is equal to also denote to =Equals is generally=If overhead is applied to individual jobs at a rate of 50% of direct labor costs incurred per job, and $50,000 in direct materials were used and $25,000 of direct labor was required, what was the total cost of the job?
a) $25,000
b) $50,000
c) $12,500
d) $87,500
The total cost of the Job in the question is; D: $87,500
How to find the total Cost?
We are given that;
Direct Labor = $25000
Cost of direct materials used = $50000
Overhead is 50% of direct labor costs. Thus;
Overhead Cost = 50% * $25000 = $12500
Total Cost of Job = Overhead Cost + Materials Cost + Labor Cost
Total Cost of Job = $87,500
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please help me with this problem i will give brainliest please :) <3
Answer:
I believe it would be 3,000,000 by the end of 12 years since nothing is being taken out or deposited but instead, she put a compound interest so the numbers would go up from what i gather
Step-by-step explanation:
P(Head, Diamond AND Head, Heart) = ?
Using it's concept, it is found that the desired probability is given as follows:
P(Head, Diamond AND Head, Heart) = 1/64.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, for each trial, there are 8 equally as likely outcomes, hence:
P(Head, Diamond) = 1/8.P(Head, Heart) = 1/8.Hence the probability of both outcomes is given by:
P(Head, Diamond AND Head, Heart) = 1/8 x 1/8 = 1/64.
More can be learned about probabilities at https://brainly.com/question/14398287
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What are irrational and rational numbers?
An irrational number is a type of real number which cannot be represented as a simple fraction.
A rational number is a number that can be expressed as an integer or the quotient of an integer divided by a nonzero integer.
Answer:
here is the definition of irrational and rational numbers
12250 depreciates by 6% per year how much is the tractor worth after six years
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &12250\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &6\\ \end{cases} \\\\\\ A=12250(1 - 0.06)^{6}\implies A=12250(0.94)^6\implies A\approx 8450.90[/tex]
what is the slope of the liner equation y=7x-2
Answer:
Hence, slope of y=7x−2 is 7 and y -intercept is −2.
Step-by-step explanation:
The equation of any straight line can be written as y=mx+c, where m is its slope and c is its y-intercept.
Comparing the equation y=7x−2 with the standard form of the equation, we get:
m=7,c=−2
Hence, slope of y=7x−2 is 7 and y -intercept is −2
Hope this helps :)
10z + 2z - 4
please thx
What is the equation of the line shown in the graph?
Answer:
y = -x – 2
Step-by-step explanation:
Slope is ΔY/ΔX = -1
plug this into the equation:
1=-(-3) +b
= -2=b
so we get; y = -x – 2
Answer: y = -x - 2
Step-by-step explanation:
I will be writing this equation in slope-intercept form.
First, we will find our m value, also known as the slope.
[tex]\displaystyle \frac{\text{change in y}}{\text{change in x}} =\frac{1--4}{-3-2} =\frac{5}{-5}=-1[/tex]
Now, we will find our b value, or the y-intercept.
-> The line intercepts the y-axis at (0, -2), so our y-intercept is -2.
Lastly, we will write our equation.
y = mx + b
y = -x - 2
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The square to solve the quadratic equation x^2-15x+2=0
The roots of the equation [tex]x^{2}[/tex]-15x +2 =0 are 14.865 and 0.135
What is completing the square method?Completing the square method is one of the methods to find the roots of the given quadratic equation.
Given equation is:
[tex]x^{2}[/tex]-15x +2 =0
Using Completing the Square method we have
[tex]x^{2}[/tex]-15x +2 + [tex](\frac{15}{2})^{2}[/tex] - [tex](\frac{15}{2})^{2}[/tex] =0
Now,
[tex]x^{2}[/tex]-15x + [tex](\frac{15}{2})^{2}[/tex] - [tex](\frac{15}{2})^{2}[/tex] +2=0
or, [tex][x-(\frac{15}{2})]^{2}[/tex] - 225/4 +2 =0
or, [tex][x-(\frac{15}{2})]^{2}[/tex] -217*4 =0
or, [tex][x-(\frac{15}{2})]^{2}[/tex] = 217/4
or, [tex]x[/tex] = [tex]\pm \frac{14.73}{2} + \frac{15}{2}[/tex]
or, [tex]x_1[/tex]= 14.865, [tex]x_2[/tex]= 0.135
Thus, the roots of the quadratic equation are: 14.865 and 0.135
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What is the value of x in this figure?
Enter your answer in the box.
x =
The figure contains a pair intersecting lines. One angle is labeled 114 degrees. The angle that is opposite and not adjacent to this angle is labeled x degrees.
Answer:
114°
Step-by-step explanation:
Non-adjacent angles where two lines cross are called "vertical angles." They are congruent.
x = 114°
PLSS HELP ILL GIVE BRAINLIEST ASAP
Find the surface area of the regular pyramid
Find the area of triangle
Answer:
C- 17 cm
A- 9cm
Step-by-step explanation:
C - because plus 9 and 8 is 17 cm
A - because plus 4 and 5 is 9 cm
Writing fractions with a common denominator to add or subtract
Answer:
5/6-1/9=45/54-6/54=39/54.
Step-by-step explanation:
hey!
To make fractions have a common denominator, multiply both the numerator and denominator by the same number. For example, 5/6=45/54 because I multiplied 5 and 6 both by 9, and 1/9= 6/54 because I multiplied 1 and 9 by 6. This is the same for all fractions.
Hope this helped :)
Answer:
13/18
Reasoning:
First. We have to find the GCD
Second. Multiply both fractions with the number that creates the GCD
5/6 x 3/3 - 1/9 x 2/2 = 15/18 - 2/18
Third. Subtract 15/18 - 2/18 = 13/18
( Would appreciate if you marked me brainliest )
its wrong someone help me with it
Answer:
the answer is π^8
Step-by-step explanation:
the math program has got some bugs in it. See your teacher and tell him or her about it
factor the quadratic trinomial x^2-8x+18
(x+ )(x+ )
Answer:
This is prime.
No factors.
Step-by-step explanation:
a triangle had sides with lengths 5, 12, and 13.
verify this is a pythagorean triple
It is a pythagorean triple.
A rectangular plot measures 140m by 20m find the area in ares
Answer:
28ares
Step-by-step explanation:
that's the correct way.i hope you will understand it. if there's any question feel free to ask. nice day.
Which of the following is a valid probability distribution?
Answer:
first one is the valid probability distribution
A cylinder has a base of 8 feet and a height of 29 ft what is its volume in cubic feet
Answer:
1457.7 cubic ft
Step-by-step explanation:
Volume of a cylinder= πr²h
where, r = radius = 8/2 = 4 ft
h = 29
Volume= π × 4² × 29 = 1457.7 cubic ft
[tex]\rule{300}{1}[/tex]
[tex]\diamond\large\blue\textsf{\textbf{Given question:-}}}[/tex]
A cylinder has a base of 8 feet and a height of 29 ft. What is its volume
in cubic feet (ft³)?
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
We are asked to find the volume of a cylinder, which can be found using the following formula:-
[tex]\hookrightarrow\boxed{\bold{V=\pi r^2h}}[/tex]
Where:-
V=volumer=radiush=heightProvided Information:-
r=4 ft (base = 8ft, divided by 2=4ft)h=29 ftSolving for Volume:-
Substitute 4 in lieu of r and 29 in lieu of h:-✳︎ [tex]\sf{V=\pi (4)^2(29)}[/tex]
On simplification,
✳︎ [tex]\sf{V=\pi (16)(29)}[/tex]
On further simplification,
✳︎ [tex]\sf{V=464\pi }[/tex]
Final step:-
✳︎ [tex]\sf{V\approx1,457.7\:ft^3}[/tex]
So we conclude that the volume of the given cylinder is
[tex]\ast[/tex] [tex]\sf{V\approx{1,457.7\:ft^3}}}[/tex]
Good luck with your studies.[tex]\rule{300}{1}[/tex]
What is the surface area of the rectangular prism below?
Answer:
the answer is A. 612
Step-by-step explanation:
SA=2(wl+hl+hw)
parenthesis() mean multiply
x means multiply
SA= 2 x width x length + height x length + height x width
