The probability that at least 40 rolls are necessary is 4/15.
What is probability?
Probability shows the likelihood of an event happening. it can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1
Probability P=no. outcomes/total no. of the possible outcomes
From the question;
No of out comes=40
No. of total possible outcome=150
Therefore probability P= 40/150
P=4/15
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8. ¿Cuántos cuadriláteros se pueden formar con los vértices de un pentágono regular?
The number of quadrilaterals that can be formed with the vertices of a regular pentagon is given by:
5.
How to obtain the number of quadrilaterals?The number of vertices for each polygon is given as follows:
Quadrilateral: 4 vertices.Pentagon: 5 vertices.Hence, to build the quadrilaterals, four vertices are taken from the set of five vertices of the pentagon.
The formula to be used is given as follows:
Permutation formula -> order of the vertices is not relevant.Combination formula -> order of the vertices relevant.The order of the vertices is not relevant, hence the combination formula is used, given as follows:
[tex]C_{n,x} = \frac{n!}{x!(n - x)!}[/tex]
Which gives the number of different combinations of x elements from a set of n elements.
Hence, in the context of this problem, the number of quadrilaterals is obtained as follows:
[tex]C_{5,4} = \frac{5!}{4!1!} = 5[/tex]
Translation
The problem asks for how many quadrilaterals can be formed with the vertices of a regular pentagon.
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(x^2+4)/(x^3+x^2+4x+4)=
The solution is 1/(x+1)
From the question, we have
(x^2+4)/(x^3+x^2+4x+4)
=(x^2+4)/(x^2 (x^3/x^2 +x^2/x^2 )+2^2 ((2^2⋅x)/2^2 +2^2/2^2 ) )
=(x^2+4)/(x^2 (x^(3-2)+1)+2^2 (x+1))
=(x^2+4)/(x^2 (x+1)+2^2 (x+1))
=(x^2+4)/((x+1)((x^2 (x+1))/(x+1)+(2^2 (x+1))/(x+1)) )
=(x^2+4)/((x+1)(x^2+2^2 ) )
=(x^2+4)/((x+1)(x^2+4) )
=1/(x+1)
The solution is 1/(x+1)
Divide:
Split is to divide into two or more equal sections, places, groupings, or divisions in its most basic form. To divide something simply means to provide it to a group in equal quantities or to cut it up into equal pieces. Let's imagine a diagonal divides a square into two triangles with equal areas. An integer may or may not be the result of a division operation. Sometimes the result will be expressed as decimal numbers.
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PLS HELP! 30 POINTS!!!!!
A Linear equation in standard form is
2x + y = -4
slope of the function = -2
the perpendicular line equation in standard form -x + 2y = -6
How to find slope of linear equationA standard equation is of the form Ax + By = C
A = 2
B = 1
C = -4
Rearranging the equation to the slope intercept form of the form as
y = mx + c
where
m = slope
c = intercept
x = input variables
y = output variables
Ax + By = C
By = -Ax + C
y = -Ax/B + C
calculation of slope
m = -A/B
substituting the values of A and B
m = - 2/1
m = -2
a new perpendicular slope, m' is given by
m' = -1/m
plug in the value of m
m' = -(1/-2)
m' = 1/2
new equation passing through point (8, 1)
(y - y₁) = m' (x - x₁)
y - 1 = 1/2(x -8)
y - 1 = x/2 - 4
y = x/2 - 3
writing in standard form
y = x/2 - 3
2y = x - 6
-x + 2y = -6
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Hi can someone please help me? Thank you!
Find the solutions of the quadratic equation −x^2 + 3x − 3 = 0
(3^3*6^6)^-3
what is a simplified version of this
The simplified value of the above expression is 5.00248967e-19
we know,'^' this symbol means by times
[tex]3^{3}[/tex] =27
[tex]6^{6}[/tex] =46,656
27 multiplied by 46,656
[tex]27 \times 46,656 = 1,259,712[/tex]
[tex]1,259,712 ^{-3} = 5.00248967e-19[/tex]
if you want you can apply the BODMAS system here.
it is just a fraction try to simplify it.
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The height of a building is proportional to the number of floors The figure shows the height of a building with 9 floors
a. Reasoning write the ratio of height of the building to the number of floors. Then find the unit rate, and explain what it means in this
b. How tall would the building be if it had 15 floors
THIS IS FOR MIDDLE SCHOOL 7TH GRADE
Answer: B
Step-by-step explanation:
it has to do with simallar mathematics of 12th grade so you can do the sum
its pretty ez cuz im a 12th grader
8. The interest on $2,000 for 2 years is $320.
What is the simple interest rate?
$
= $2,000 r.
$
= $
=r
% = r
r
Answer:
8%
Step-by-step explanation:
18. How does the
product change when one of the factors in
a multiplication problem is doubled? Give
two examples to support your conclusion.
The product doubles when one of the factors in a multiplication problem is doubled
What is a product?A product in mathematics is the result of multiplication, or an expression that identifies the objects to be multiplied, known as factors. For instance, 30 is the sum of 6 and 5.
In mathematics, multiplying means adding equal groups. The number of things in the group grows as we multiply. A multiplication problem includes the two factors and the product.
For example, 2 × 3 = 6. When 2 is doubled, it becomes 4 and the product will be:
= 4 × 3 = 12
Therefore, the product doubles too.
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30 years ago zoe was 2/3 as old as luke, 18 years ago zoe was 5/6 as old as luke how old are they now
Based on the mathematical statements, Zoe is 56 years old and Luke is 66 years old, now
How to determine how old they are now?From the question, we have the following statements that can be used in our computation:
30 years ago
Zoe was 2/3 as old as Luke
18 years ago
Zoe was 5/6 as old as Luke
Let their present ages be represented as
Zoe = x
Luke = y
So, we have the following representations
30 years ago
Zoe was 2/3 as old as Luke
x - 36 = 2/3(y - 36)
18 years ago
Zoe was 5/6 as old as Luke
x - 18 = 5/6(y - 18)
So, we have the following system of equations
x - 36 = 2/3(y - 36)
x - 18 = 5/6(y - 18)
Make x the subject in x - 18 = 5/6(y - 18)
x = 5/6(y - 18) + 16
Substitute x = 5/6(y - 18) + 16 in x - 36 = 2/3(y - 36)
5/6(y - 18) + 16 - 36 = 2/3(y - 36)
Open the brackets
5/6y - 15 + 16 - 36 = 2/3y - 24
Evaluate the like terms
5/6y - 35 = 2/3y - 24
Multiply through by 6
5y - 210 = 4y - 144
Evaluate the like terms
y = 66
Substitute y = 66 in x = 5/6(y - 18) + 16
x = 5/6(66 - 18) + 16
Evaluate
x = 56
Recall that
Zoe = x
Luke = y
So, we have
Zoe = x = 56
Luke = y = 66
Hence, they are 56 and 66 years, now
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Which of the following is a Rational Number? √11 √14 √77 15
Answer:
1/2
Step-by-step explanation:
The coordinates of the endpoints of
KL
are K(
–
16,10) and L(
–
9,
–
11). Point M is on
KL
and divides it such that KM:LM is 4:3.
What are the coordinates of M?
Write your answers as integers or decimals.
The coordinates M along the directed line segment is (-12, -2)
How to find the coordinates of the point along the directed line segment?The points are given as:
K = (-16, 10)
L = (-9, -11)
The ratio on the segment can be represented as;
KM : LM, m : n = 4 : 3
So, we have the coordinates of the point M that lies along the directed line segment to be
M = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)
So, we have:
M = 1/(4 + 3) * (4 * -9 + 3 * -16, 4 * -11 + 3 * 10)
Evaluate
M = 1/7 * (-84, -14)
Evaluate
M = (-12, -2)
Hence, the coordinates of the point M is (-12, -2)
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[tex]-2 1\frac{1}{3} w +6=15[/tex]
help me pls
The solution for the variable w according to the given equation; -21 ⅓ w + 6 = 15 as required in the task content is; w = -27/64.
What is the value of variable w?It follows from the task content that the value of variable w is time determined according to the given equation as in the task content.
Given the equation; -21 ⅓ w + 6 = 15.
First, the mixed number must be converted to a fraction so that we have;
-21 ⅓ = -64/3.
Hence, the equation becomes;
-64w/3 + 6 = 15
Multiply both sides of the equation by 3 so that we have;
-64w + 18 = 45
-64w = 45 - 18
-64w = 27
w = -27/64.
Ultimately, the solution for variable w according to the equation as given in the task content is; w = -27/64.
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2. Solve the application problem.
Find the area of a mirror that measures 2 yards by 7/8 yard.
A. 1 3/4 yd^2
B. 5 3/4 yd
C. 1 3/4 yd
D. 5 3/4 yd^2
Answer:
Area = l × w
= 2 × 0.875
= 1 3/4 yd^2 or 1.75 yd^2
hope i helped
Step-by-step explanation:
4x (x + 10) + 55 = 180
x = 5/2 and x = -25/2 are the solutions to the equation 4x (x + 10) + 55 = 180.
What is the solution to the quadratic equation?Given the equation in the question;
4x (x + 10) + 55 = 180
To solve for x, apply distributive property to eliminate the parenthesis.
4x (x + 10) + 55 = 180
4x(x) + 4x(10) + 55 = 180
4x² + 40x + 55 = 180
4x² + 40x + 55 - 180 = 0
4x² + 40x - 125 = 0
Now, we use the quadratic formula to solve the quadratic equation.
x = (-b±√(b² - 4ac)) / (2a)
From 4x² + 40x - 125 = 0
a = 4b = 40 c = -125Plug these into the formula and solve for x.
x = (-b±√(b² - 4ac)) / (2a)
x = ( -40 ± √( (40)² - ( 4 × 4 × -125))) / ( 2 × 4 )
x = ( -40 ± √( 1600 - ( -2000) )) / ( 8 )
x = ( -40 ± √( 1600 + 2000 )) / ( 8 )
x = ( -40 ± √( 3600 )) / ( 8 )
x = ( -40 ± 60) / ( 8 )
x = ( -40 - 60) / ( 8 ), ( -40 + 60) / ( 8 )
x = ( -100 )/( 8 ), ( 20 )/( 8 )
x = -25/2, 5/2
Therefore, the solution to the quadratic equation is x = -25/2, 5/2.
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Jacob and Ryan are plumbers. Jacob charges $50 call-
out fee and $70 per hour. Ryan charges $40 call-out fee
and $75 per hour.
Write an expression for the total cost in dollars that
each electrician charges if they work for h hours.
Jacob
Ryan
Answer:
Lets do Jacob's equation first :)
50$ for fee
70$ per hour (h)
Dollars = 70h + 50
Now lets do Ryan's :)
40$ for fee
75 per hour (h)
Dollars = 75h + 40
Have an amazing day!!
Please rate and mark brainliest!
A self-employed person who completes work on a project-by-project basis is
known as:
A. an independent contractor.
B. a wage-earning employee.
C. an exempt employee.
OD. a salaried employee.
SUBMIT
Answer:
A: Independent contractor
Step-by-step explanation:
Solve. 4h+8=9h-7 step by step
Answer:
h=3
Step-by-step explanation:
4h+8=9h-7
subtract 4h
8=5h-7
add 7
15=5h
divide 3
h=3
Carl is making accessories for the soccer team. He uses 773.85 inches of fabric on headbands for 29 players and 4 coaches. He also uses 279.56 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
Your answer might be 16.31 inches for each headband and wristband for each player.
---------------------------------------
Hope this helps!
Joke: What has ears but can’t hear a thing?
Answer: A cornfield.
Have a great day and God bless! :D
Are the figures congruent?
Yes these triangles are congruent.
What is congruent triangles?
Two triangles live aforesaid to be congruent if all 3 corresponding sides are equal and every one the 3 corresponding angles are equal in measure. These triangles may be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of congruousness is’ ≅’.
Main body:
Firstly we need to find the co-ordinates of each point.
M = (-1,5) R= (1,1)
L = (-2,2) S= (-5,-1)
N= (5,3) Q= (2,-2)
to prove these triangles are congruent we need to show that the distance of their sides are equal.
distance formula= [tex]\sqrt{(x1-x2)^2+(y1- y2)^{2}[/tex]
Now in ΔLMN =
ML = [tex]\sqrt{(-1+2)^{2}+(5-2)^{2} }[/tex]
ML= [tex]\sqrt{10}[/tex] units
LN =[tex]\sqrt{(5+2)^{2}+(3-2)^{2} }[/tex]
LN= [tex]\sqrt{50}[/tex] units
MN =[tex]\sqrt{(5+1)^{2}+(3-5)^{2} }[/tex]
MN=[tex]\sqrt{40}[/tex] units
Now in ΔQRS=
RS= [tex]\sqrt{(1+5)^{2}+(1+1)^{2} }[/tex]
RS = [tex]\sqrt{40}[/tex] units
SQ = [tex]\sqrt{(2+5)^{2}+(1-2)^{2} }[/tex]
SQ = [tex]\sqrt{50}[/tex] units
RQ = [tex]\sqrt{(1-2)^{2}+(1+2)^{2} }[/tex]
RQ = [tex]\sqrt{10}[/tex] units.
We can clearly see on side of each triangle is equal to one side of another one.
Hence ΔLMN≅ΔQRS.
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Name the Inequalities
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. Suppose that the mean income is found to be $20.5 for a random sample of 1190 people. Assume the population standard deviation is known to be $11. Construct the 85% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
At an 85% confidence interval, the mean per capita income in thousands of dollars for the major city in Texas is $20.5 ± 0.459.
What is the confidence interval estimate?The confidence interval estimates the mean estimate by adding or subtracting the margin of error.
In random sampling, the margin of error represents the difference between the actual and projected results.
Mean income = $20.5
Sample size, n = 1,190
Standard deviation = $11
Confidence interval = 85%
Z-score for 85% confidence interval = 1.440
The margin of error = z-score x standard deviation/√n
= 1.440 x 11/√1,190
= 1.440 x 11/34.50
= 1.440 x 0.3188
= 0.459
= $459 (0.459 x $1,000)
Lower Limit = Mean - Margin of Error
= $20,500 - $459
= $20,041
= $20.041
Upper Limit = Mean + Margin of Error
= $20,500 + $459
= $20,959
= $20.959
Thus, for the Texas city, the mean per capita income is $20.5 ± 0.459.
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Solve for value of T
The value of t using straight line angle is 24°.
What is straight line angle ?
A straight angle in geometry is one that has a length of 180 degrees. Because it seems to be a straight line, it is known as a straight angle. In other words, it is an angle whose sides extend in the same straight line in directions opposite to the vertex.
In mathematics, a straight angle is defined as an angle with a degree value of 180. It looks to be a straight line, hence the name "straight." In essence, two rays linked end to end create an angle according to the mathematical concept of angles. As a result, the two rays of the 180-degree angle are subtended in the direction of their endpoints, which are in the opposite direction.
Here we know that sum of angle in straight line at any point is 180° .
Then,
=> (4t-7)°+83°=180°
=> 4t-7+83 = 180
=> 4t+76 = 180
=> 4t = 180-76 = 104
=> t = 104/4 = 26°
Hence the value of t=24°
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The quadratic equation used to model the situation is h(t) = -16t2 + 150t + 4. Graph this equation using the graphing tool. Adjust the axis labels to accurately reflect the variables, and adjust the window to display the entire graph in the first quadrant.
The graph of the coordinate points (4, 348), (75/16, 5689/16), (6, 328) is given below.
The given quadratic equation is h(t) = -16t² + 150t + 4.
What is quadratic equation of graph?A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.
The graph of a quadratic equation is as follows:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex: (75/16,5689/16)
Focus: (75/16,22755/64)
Axis of Symmetry: x=75/16
Directrix: y=22757/64
Plot the points (4, 348), (75/16, 5689/16), (6, 328) on graph
Therefore, the graph of the coordinate points (4, 348), (75/16, 5689/16), (6, 328) is given below.
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Select all the equations that have {4} as its solution set.
Responses
79−3x=12x+19
7−x=12x
x2+3=10x−21
5 + 2x = 3x + 3
SELECT ALL, THIS IS MULTIPLE CHOICE.
Answers:
A. 79 − 3x = 12x + 19
B. 7 − x = 12/x
C. x^2 + 3 = 10x − 21
Helppp pls …………………….
Answer:
B
Step-by-step explanation:
the two angles lies on the same lines and they have the same vertex
Identify the function shown in this graph. 3 17 3 2 12 1 1 2 3 4 5 A. y=-3x +3 B. y = -3x-3 PLEASE HELP ME ANSWER THIS I WILL GIVE 30 POINTS AND A BRAINLYEST
Answer:
It's B. A good way to look at it is the last number. The last number is the y-intercept. Here the y-intercept is -3. That's how I would always figure it out.
How can the narrator's parents be described in chapters 1-4 of Frankenstein?
A. Poor farmers
B. Distinguished counsellors
C. Military officers
D. Migrant workers
Answer: B)
Step-by-step explanation:
If you double a number and then add 16 you will get 2/5of the original number. What is the original number?
Step-by-step explanation:
x = the original number
2x + 16 = 2/5 x
multiply both sides by 5 to get rid of the fraction :
10x + 80 = 2x
divide both sides by 2 :
5x + 40 = x
subtract x from both sides :
4x + 40 = 0
divide everything by 4 :
x + 10 = 0
subtract 10 from both sides :
x = -10
Answer : x = -10
Step-by-step explanation :
x = original number
2x + 16 = 2/5x
Change 2/5 to decimal
2x + 16 = 0,4x
Change the position of 16 and 0,4x
2x - 0,4x = -1
Subtract 2 by 0,4
1,6x = -16
Divide -16 by 1,6
x = -10
You can use this way or the other one but this way is faster than the others
Hope it helps !
Select the correct answer.
Given: ZNMY
ZPOB
Prove: ZXMN ZAOP
kk
M
ZXMY and ZAOB are right angles because that information is given. This means that ZXMN is complementary to ZNMY and
ZAOP is complementary to ZPOB by the linear pair theorem. Since ZNMY ZPOB, by the congruent complements theorem.
ZXMN ZAOP.
Where is the error in the proof? Select all that apply.
O The given cannot be used to state that ZAOB is a right angle.
The linear pair theorem cannot be used to state ZXMN is complementary to ZNMY.
The linear pair theorem cannot be used to state ZAOP is complementary to ZPOB.
The congruent complements theorem cannot be used to state that ZXMN
ZAOP.
The given cannot be used to state that ZXMY is a right angle.
The linear pair theorem cannot be used to state ZAOP is complementary to ZPOB.
What is complementary angles?Complementary angles are two angles with a combined angle of 90 degrees, whereas supplementary angles have a combined angle of 180 degrees.
A good that adds value to another good or service is said to be complimentary. To put it another way, they are two items that the client uses in tandem with one another. For instance, cereal and milk or a DVD and a DVD player.
Because the three angles of a triangle sum up to 180° and the right angle has already taken up 90°, the two non-right angles in a right angled triangle are complimentary. We say two angles "Complement" one other when their sums equal 90 degrees. because a complete angle is what is considered to be the right angle.
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