Answers
Answer:
5⁴a²
Step-by-step explanation:
(5³a³)÷5a-¹×5-²a²
5³a³÷5a-¹×5-²a²
5³a³÷5¹-²×a-¹+²
5³a³÷5-¹a
5³a³/5-¹a
5³-(-¹)a³-¹
5⁴a²
Related Questions
Two dice are thrown, 1 is the event that the sum of their
dots is a prime number and 2 is the event that 5 is the dot on
the top of second die. Check whether (1 ∩ 2) =
(1). (2)
Answers
Given:
Two dice are thrown.
[tex]E_1[/tex] is the event that the sum of their dots is a prime number
[tex]E_2[/tex] is the event that 5 is the dot on the top of second die.
To find:
Whether [tex]P(E_1\cap E_2)=P(E_1)\cdot P(E_2)[/tex] is true or false.
Solution:
If two dice thrown, then the total possible outcomes are:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6),
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6),
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6).
[tex]E_1[/tex] is the event that the sum of their dots is a prime number.
[tex]E_1=\{(1,1),(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5)\}[/tex]
[tex]P(E_1)=\dfrac{15}{36}[/tex]
[tex]P(E_1)=\dfrac{5}{12}[/tex]
[tex]E_2[/tex] is the event that 5 is the dot on the top of second die.
[tex]E_2=\{(1,5), (2,5),(3,5),(4,5),(5,5),(6,5)\}[/tex]
[tex]P(E_2)=\dfrac{6}{36}[/tex]
[tex]P(E_2)=\dfrac{1}{6}[/tex]
The intersection of these two events is:
[tex]E_1\cap E_2=\{(2,5),(6,5)\}[/tex]
[tex]P(E_1\cap E_2)=\dfrac{2}{36}[/tex]
[tex]P(E_1\cap E_2)=\dfrac{1}{18}[/tex]
Now,
[tex]P(E_1)\cdot P(E_2)=\dfrac{5}{12}\cdot \dfrac{1}{6}[/tex]
[tex]P(E_1)\cdot P(E_2)=\dfrac{5}{72}[/tex]
[tex]P(E_1)\cdot P(E_2)\neq P(E_1\cap E_2)[/tex]
Therefore, the given statement is false because [tex]P(E_1\cap E_2)\neq P(E_1)\cdot P(E_2)[/tex].
{(6,4),(7,−3),(−4,3),(8,−3)}, which point if added would not create a function?
Answers
Answer:
Step-by-step explanation:
What points were you given to choose from?
X- 2y = 3 5x + 3y = 2 The lines whose equations are shown intersect at which point? O (1, -1),(-1,1),(0'3/2)
Answers
The scatter plot below shows what kind of trend?
A positive trend
B no trend
C random trend
D negative trend
Answers
the answer is b no trend
What is the non-negative zero of the function f, where f(x) = 6x^2-9x-6?
Answers
Answer:
The non-negative zero of the function f(x) is x = 2.
Step-by-step explanation:
For a given function f(x), the "zeros" of the function are the values of x such that:
f(x) = 0
In this case, we have the function:
f(x) = 6*x^2 - 9*x - 6
If we want to find the zeros of this function, we need to solve:
f(x) = 0 = 6*x^2 - 9*x - 6
To solve this, we can use the Bhaskara's formula, which says that for a general quadratic equation:
0 = a*x^2 + b*x + c
The zeros are:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]
In this case our equation is:
0 = 6*x^2 - 9*x - 6
then, in the above notation, we have:
a = 6
b = -9
c = -6
Replacing these in our general formula, we get:
[tex]x = \frac{-(-9) \pm \sqrt{(-9)^2 - 4*6*(-6)} }{2*6} = \frac{9 \pm 15 }{12}[/tex]
Then we have two zeros:
x = (9 + 15)/12 = 24/12 = 2
x = (9 - 15)/12 = -6/12 = -1/2
But we want only the non-negative, so we can discard the second one.
Concluding, the non-negative zero of the function f(x) is x = 2.
Ik desperate please help the question is:
how many times more people will there be in the town after 15 years than after 10 years??? I need help ASAP!??!?!?!?!? 20 points?!?!?!!
pleaseeeee
Answers
Answer:
good point I don't know that either
the size of an interior angle of a regular polygon is 3x. It's exterior is (x- 20)°. Find number if the sides of the polygon.
Answers
Answer: 12
Step-by-step explanation: Since the angles are supplements, 3x + x - 20 = 180. Solving this, we find that x = 50, and 3x = 150. Since dodecagons have interior angles of 150 degrees, the answer is 12 sides.
Answer:
Step-by-step explanation:
Since the angles are supplements, 3x + x - 20 = 180. Solving this, we find that x = 50, and 3x = 150. Since dodecagons have interior angles of 150 degrees, the answer is 12 sides.
Can someone help please
Answers
Answer:
2x^2 + 4
Step-by-step explanation:
f(g(x)) just means to first solved g(x) and put the solution into f(x).
Therefore, it becomes f(x)=(10x^2+5)/5 + 3, and you can simplify that into
2x^2 + 4.
One wall inside an art studio is used to display paintings with oval frames and rectangular
frames. There are a total of 68 paintings on this display. There are 3 times as many
rectangular frames as there are oval frames in this display. How many oval frames and
rectangular frames are on the display?
Answers
Answer:
Oval frames = 17
Rectangular frames = 51
Step-by-step explanation:
Given that :
Paintings on wall are either oval or rectangular ;
Let :
Oval painting = x
Rectangular painting = y
According to the information given :
x + y = 68 - - (1)
Rectangular frames = 3 times oval frames
y = 3x - - - (2)
Put y = 3x in equation (1)
x + 3x = 68
4x = 68
x = 68/4
x = 17 frames
From :
x + y = 68
17 + y = 68
y = 68 - 17
y = 51
Oval frames = 17
Rectangular frames = 51
Which table represents an exponential function?
Answers
Answer:
2nd one is the answer if it's the question
Plz help will mark brainliest
Ben and Tom together collected $400 for the Good Friday Appeal. Ben collected seven times as much money as Tom. How much did they each collect?
Answers
Answer:
$400 Altogether.
The main half of 4 is 2 , so I think they all collected 400 Dollars
so if it was 200 for Ben and collected 7 time than what he actually did
so 200 × 7
= $1400
Suppose b is any integer. If b mod 12 = 7, what is 4b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 4b is divided by 12? Fill in the blanks to show that the same answer will be obtained no matter what integer is used for b at the start. Because b mod 12 = 7, there is an integer m such that b = 12m + . Multiply both sides of this equation by 4 and then simplify the right-hand side to find values of q and r such that 4b = 12q + r with 0 ≤ r < 12. The result is q = and r = . Now 0 ≤ r < 12, and q is an integer because ---Select--- . So the uniqueness part of the quotient remainder theorem guarantees that the remainder obtained when 4b is divided by 12 is . Need Help?
Answers
Answer:
4b mod 12 = 4
Step-by-step explanation:
Since b mod 12 = 7, it implies that there is an integer, m such that
b = 12m + 7.
We desire to find 4b mod 12
So, multiplying b by 4, we have
4b = 4(12m + 7)
4b = 4 × 12 m + 4 × 7
4b = 4 × 12 m + 28
4b = 4 × 12 m + 24 + 4
4b = 4 × 12 m + 12 × 2 + 4
Factorizing 12 out, we have
4b = 12(4m + 2) + 4
Since m is an integer 4m + 2 is an integer since the operation of adding and multiplication is closed for the set of integers.
comparing 4b = 12q + r with 4b = 12(4m + 2) + 4,
q = 4m + 2 and r = 4
So 4b mod 12 = 4, that is the remainder when 4b is divided by 12 is 4.
In this exercise we have to calculate the value of the unknown, so we have:
the value is 4
we know that the equation will be given as:
[tex]b = 12m + 7\\[/tex]
we need to multiply both sides by 4 to become another known equation, like this:
[tex]4b = 4(12m + 7)\\4b = 4 * 12 m + 4 * 7\\4b = 4 * 12 m + 28\\4b = 4 * 12 m + 24 + 4\\4b = 4 * 12 m + 12 * 2 + 4[/tex]
So factoring this equation we will find that:
[tex]4b = 12(4m + 2) + 4[/tex]
Thus, when making a comparison between the two equations, we have that:
[tex]4b = 12q + r \\4b = 12(4m + 2) + 4\\q = 4m + 2\\r = 4[/tex]
See more about factoring at brainly.com/question/6810544
Choose all measurements that are equivalent to 45 meters.
a. 450 centimeters
b. 4,500 centimeters
c. 0.045 kilometer
d. 0.45 kilometer
e. 4,500 millimeters
Answers
Answer:
option : b, c
Step-by-step explanation:
1 meter = 100 centimeters
45 meters = 4500 centimeters
1000 meter = 1 kilometer
[tex]45 \ meters = \ \frac{45}{1000} = 0.045 \ kilometers[/tex]
1 meter = 1000 millimeters
45 meters = 45, 000 millimeters
Which descriptions from the list below accurately describe the relationship between ∆ABC and ∆DEF? Check all that apply.
A. Same area B. Same size C. Congruent D. None of the above
Answers
Answer:
D. None of the above
Step-by-step explanation:
The two right triangles have different sizes. Therefore, their areas cannot be the same as well.
Congruent triangles have the same three angles that are congruent to each other and three side lengths that are congruent or equal to each other. The two triangles only have equal angles bit different corresponding side lengths. Therefore, they cannot be congruent.
The correct answer is "None of the above".
Answer:
PROPORTIANAL SIDE LENGTHS
Step-by-step explanation:
I JUST TOOK THE TEST
Which of these four sets of side lengths will form a right triangle?
Answers
You can simply check by
The sum of the square of first two number should be equal to the square of third number to form a right angled triangle (simply use Pythagorean’s theorem)
For example in set four
12²+16²=20²
144+256=400
400=400
So it is a right angled triangle
Hope it helps : )
Can someone please help me?
Answers
Answer:
use the Desmos graphing calculator. Type the first one in. Then type your answer choices in. See which lines are the same.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Just simplify
Use an appropriate series in (2) in Section 6.1 to find the Maclaurin series of the given function. Write your answer in summation notation. 1 5 x
Answers
Answer:
[tex]e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{1}{5}^k \cdot \frac{x^k}{k!}[/tex]
Step-by-step explanation:
Poorly formatted question.
The given parameters can be summarized as:
[tex]e^x = \sum\limits^{\infty}_{k=0} \frac{x^k}{k!}[/tex] ----- the series
Required
Determine [tex]e^\frac{1}{5}^x[/tex]
We have:
[tex]e^x = \sum\limits^{\infty}_{k=0} \frac{x^k}{k!}[/tex]
Substitute [tex]\frac{1}{5}x[/tex] for x
[tex]e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{(\frac{1}{5}x)^k}{k!}[/tex]
Split
[tex]e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{1}{5}^k \cdot \frac{x^k}{k!}[/tex]
Hi, could someone help me solve this. so the question says to find the area of the shaded part (in black) , in terms of pie (π). the length of the square is 12 cm. the radius of the circle is 6cm. i came with the answer of (144-36π)/4. is this ok? below is the picture of the question.
Answers
Answer:
yes but can be simplified
Step-by-step explanation:
area of shaded part = ( area of square - area of circle ) / 4
= [tex]\frac{12^2-\pi (6)^2}{4}[/tex]
= [tex]\frac{144-36\pi }{4}[/tex]
= [tex]\frac{144}{4}[/tex] - [tex]\frac{36\pi }{4}[/tex]
= 36 - 9π
A triangle has sides measuring 2 inches and 7 inches. If x represents the
length in inches of the third side, which inequality gives the range of possible
values for x?
O A. 5sxs 9
O B. 2 sxs7
O C. 2
OD. 5
Answers
Answer is
5 gives the range of possible values for x.
PLEASEEEE HELP QUICKKKK
Answers
Given:
Line A goes through (0,y) and (-2,0).
Line B goes through (1,2) and (3,10).
To find:
The value of y for which the system of given linear equation (equation of line A and line B) has no solutions.
Solution:
Two linear equation has no solutions if they are parallel line.
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We know that the slopes of two parallel lines are the same.
So, the given system of given linear equation has no solutions if
Slope of line A = Slope of line B
[tex]\dfrac{0-y}{-2-0}=\dfrac{10-2}{3-1}[/tex]
[tex]\dfrac{-y}{-2}=\dfrac{8}{2}[/tex]
[tex]\dfrac{y}{2}=4[/tex]
Multiply both sides by 2.
[tex]\dfrac{y}{2}\times 2=4\times 2[/tex]
[tex]y=8[/tex]
Therefore, the required value of y is 8.
There are 1800 students in a school, if the ratio of teachers to students is 2: 7. How many teachers are at the school?
Answers
Answer: 258
Step-by-step explanation:
7/9 = 1800
2/9 = ?
= 258
900 tickets were sold. Adult tickets cost $10, children's cost $4, and a total of $7500 was
collected. How many tickets of each kind were sold?
Answers
Answer:
650 adult tickets and 250 children's tickets.
Step-by-step explanation:
Suppose the true proportion of voters in the county who support a restaurant tax is 0.54. Consider the sampling distribution for the proportion of supporters with sample size n = 168.
What is the mean of this distribution?
What is the standard error of this distribution?
Answers
Answer:
The correct answer is:
(a) 0.54
(b) 0.0385
Step-by-step explanation:
Given:
Restaurant tax,
p = 0.54
Sample size,
n = 168
Now,
(a)
The mean will be:
⇒ μ [tex]\hat{p}= p[/tex]
[tex]=0.54[/tex]
(b)
The standard error will be:
[tex]\sigma \hat{p}[/tex] = [tex]\sqrt{[\frac{p(1-p)}{n} ]}[/tex]
= [tex]\sqrt{[\frac{(0.54\times 0.46)}{168} ]}[/tex]
= [tex]\sqrt{[\frac{(0.2484)}{168} ]}[/tex]
= [tex]0.0385[/tex]
if you are just given the two points it is the same formula. Find the midpoint between the points (4,−5) and (−4,5).
Answers
Answer:
[tex]M = (0,0)[/tex]
Step-by-step explanation:
Given
[tex](4,-5)[/tex] and [tex](-4,5)[/tex]
Required
The midpoint (M)
This is calculated as:
[tex]M = \frac{1}{2}(x_1 + x_2,y_1+y_2)[/tex]
So, we have:
[tex]M = \frac{1}{2}(4-4,-5+5)[/tex]
[tex]M = \frac{1}{2}(0,0)[/tex]
[tex]M = (0,0)[/tex]
Write a linear function g(x) where g(1) = 4 and g(-3) = -2
Answers
Answer:g(x) = 3/2x + 2 and a half?
Step-by-step explanation: sorry not good at college math, but at least i tried.
What is the difference between 5d and d ⁵ ?
Answers
If you’re asking to subtract then it’d be written as 5d - d^5
A die is rolled twice. What is the probability of showing a 3 on the first roll and an even number on the second roll?
Answers
Answer:
1/6 * 1/2 = 1/12
Step-by-step explanation:
1 number on a 6 sided die is 1 out of 6 (1/6) and an even number (2,4,6) on a 6 sided die is 3/6 or 1/2 (always simplify when multiplying fractions)
so 1 times 1 = 1 and 6 times 2 = 12 making it 1/12
A rectangular garage is 12 yards long and 8 yards wide. It costs $1.00 per square yard to put in a new concrete floor. How much would it cost to put a new concrete floor in the garage?
Answers
===========================================================
Explanation:
Compute the area to get 12*8 = 96 square yards
We can think of it like having 96 squares and each square costs $1. So naturally the total cost is 96*1 = 96 dollars.
what is a line passing through the points (1, -1) and (9, 3) in equation form?
Answers
Answer:
[tex]x-2y=3[/tex]
Step-by-step explanation:
[tex]We\ are\ given,\\Line\ passes\ through\ the\ points\ (1,-1) and (9,3). Hence,\ this\ means\ that\ the\\ points\ are\ indeed\ solutions\ of\ the\ equation,\ which\ represents\ the\ line.\\Hence,\\We\ know\ that,\\The\ equation\ of\ a\ line\ (Point-Slope)\ is\ given\ by:\\y-y_1=m(x-x_1),\ where\ m\ is\ the\ slope\ of\ the\ graph.[/tex]
[tex]So\ first,\\Lets\ find\ the\ Slope\ of\ the\ Graph.\\Slope(m)=\frac{Rise}{Run}=\frac{y_2-y_1}{x_2-x_1}\\Hence,\\Here,\\Considering\ (1,-1)\ as\ the\ First\ Point\ and\ (9,3)\ as\ the\ Second\ Point,\ we\ have:x_1=1,x_2=9\ and\ y_1= -1, y_2=3\\Plugging\ the\ values\ in\ the\ Equation\ for\ the\ Slope,\ we\ have:\\[/tex]
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-1)}{9-1}=\frac{3+1}{9-1}= \frac{4}{8}=\frac{1}{2}\\Hence,\\Coming\ back\ to\ our\ Point-Slope\ Formula\ for\ the\ equation:\\\ We\ already\ have:\\y-y_1=m(x-x_1)\\Substituting\ m=\frac{1}{2} , x_1=1,\ y_1=-1,\ we\ have: \\y+1=\frac{1}{2}(x-1)\\\therefore 2(y+1)=x-1\\\therefore 2y+2=x-1\\\therefore 2y-x=-3\\Multiplying\ with\ (-1)\ on\ both\ sides:\\\therefore x-2y=3\\Hence,\\x-2y=3,\ is\ our\ desired\ equation.[/tex]
Help with #15 please
Answers
Answer:
3 gallons of carpet shampoo
Step-by-step explanation:
room area: 16 * 15 = 240 ft
1 gallon carpet shampoo: 80 ft
240/80 = 3
3 gallons of carpet shampoo are needed.