the probability that in bot rolls we have a sum of, at most, 8, is:
P = 47/ 1,296 = 0.036
How to find the probability?The pair is tossed twice. A pair of dice has 36 possible outcomes, so if we toss twice the pair, the total number of outcomes is:
36*36 = 1,296
Now if we define the outcomes as:
{dice 1 (roll1), dice2(roll1), dice 1 (roll2), dice2(roll2) }
The outcomes that give at most a sum of 8 are:
{1, 1, 1, 1}
{2, 1, 1, 1} ( 3 permutations)
{2, 2, 1, 1} ( 6 permutations).
{2, 2, 2, 1} ( 3 permutations)
{3, 1, 1, 1} ( 3 permutations)
{3, 2, 1, 1} ( 12 permutations)
{3, 3, 1, 1} (6 permutations)
{4, 1, 1, 1} (3 permutations)
{4, 2, 1, 1} (6 permutations)
{5, 1, 1 , 1} (3 permutations)
{2, 2, 2, 2}
These are all the outcomes that give a sum of, at most, 8.
If we add all the outcomes we get 47 outcomes.
Then the probability that in bot rolls we have a sum of, at most, 8, is:
P = 47/ 1,296 = 0.036
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6 x 3-2x2+9x-8+4x3-2x+6
Combine like terms: [tex]6x^{3}[/tex] and [tex]4x^{3}[/tex] make [tex]10x^{3}[/tex]. At that point, disentangle constants: -8 + 6 rise to -2. Result:[tex]10x^{3} - 2x^{2} + 9x - 2[/tex].
How to simplify the expressionTo simplify the given expression, take after the arrangement of operations (PEMDAS/BODMAS):
Perform operations inside parentheses/brackets.Assess examples (powers).Perform increase and division from cleared out to right.Perform expansion and subtraction from cleared out to right.Given expression: [tex]6x^{3} - 2x^{2} + 9x - 8 + 4x^{3} - 2x + 6[/tex]
Step 1: Combine like terms (terms with the same variable and example):
[tex]6x^{3} + 4x^{3} = 10x^{3}[/tex]
Step 2: Combine the steady terms:
-8 + 6 = -2
The expression presently gets to be:
[tex]10x^{3} - 2x^{2} + 9x - 2[/tex]
So, the disentangled expression is [tex]10x^{3} - 2x^[2} + 9x - 2.[/tex]
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The complete question:
Simplify the expression:
6 x 3-2x2+9x-8+4x3-2x+6
A carpenter purchased 60 ft of redwood and 80 ft of pine for a total cost of $308. A second purchase, at the same prices, included 90 ft of redwood and 70 ft of pine for a total cost of $397. Find the cost per foot of redwood and of pine?
Answer:
Price of redwood= $3.4
Pine =$1.3
The value of n from the set {6, 7, 8, 9} that holds true for 4n − 12 < 2n + 2 is
The value of n that satisfies the inequality is 6.
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
4n − 12 < 2n + 2
For n= 6
4(6) - 12 = 12
2(6) + 2 = 14
Thus, n=6 satisfies
For n= 7
4(7) - 12 = 16
2(7) + 2 = 16
Thus, n=7 not satisfies
For n=8
4(8) - 12 = 20
2(8) + 2 = 18
Thus, n=8 not satisfies.
For n= 9
4(9) - 12 = 24
2(9) + 2 = 20
Thus, n=9 not satisfies.
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In the plane figure, only downward motion (movement leaving you relatively lower than where you were) is allowed. Find the total number of paths from A to B.
Plane figures are shapes with straight sides. Considering the movement to be lower than the initial path, there are eleven (11) paths from A to B.
A plane figure is given shape with straight sides. And these sides connect each edge of the figure one to another. Examples are triangles, quadrilaterals, polygons, etc.
A path is a connection or link between two reference points. This could be a footpath or a motorable path or other forms of the path.
Considering the given plane figure in the question, it can be observed that the total number of paths from A to B with respect to the given condition is eleven.
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Write the domain and range of the function using interval notation.
A graph of an upward-facing parabola with endpoints (2,-2) and (6,-2). Both endpoints are solid circles. The vertex is (4,-6).
The domain is [2,6] and the range is [-2,0].
What is the Domain and Range of a Function?The Domain is all the possible input values to the function, while the range is all the possible values a function can have as an output.
The parabola has endpoints of (2,-2) and (6,-2).
The vertex is (4,-6)
The domain is [2,6]
The range is [-2,0]
Therefore, the domain is [2,6] and the range is [-2,0].
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PLEASE ANSWER THIS QUESTION! I BEG OF YOU
Two function are represent below.
FUNCTION A FUNCTION B
y=35x. (image below)
What is the difference in the rate of change between Function A and Function B? Be sure to include the rate of change of each function in your answer.
EXPLAIN THE ANSWER!j
Rate of change for Function A is: 35
Rate of change for Function B is: 50
Difference is: 15.
What is the Range of a Linear Function?
Rate of change = change in y / change in x.
The graph for function B is a proportional graph, therefore, rate of change = y/x.
Using a point on the line, (1, 50), rate of change for function B = 50/1 = 50.
Function A is given as y = 35x. Rate of change, is 35.
The difference = 50 - 35 = 15.
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The Smiths have a pool that is 20 feet by 35 feet. A 5 foot wide deck completely surrounds the pool. The average depth of the pool is 6 feet. How much surface area is covered by the proposed pool deck?
Answer:
550 square feet
Step-by-step explanation:
There are 4 areas where the pool deck is situated on:
Top, Left, Right, and Bottom of the pool.
So if the deck is 5 feet wide:
Top = (35 feet * 5 feet) = 175
Bottom = (35 feet * 5 feet) = 175
Left = (20 feet * 5 feet) = 100
Right = (20 feet * 5 feet) = 100
175 + 175 + 100 + 100 = 550 square feet
andrew has a cell phone plan that provides 300 free minutes each month fo a flat rate of $19 . for any minutes over 300, andrew is charged 0.39 per minute
The precise equation that represents the situation is as follows:
$19, x ≤ 300x > 300, f(x) = 19 + 0.39(x - 300)How to represent an equation?His cell phone plan provides 300 free minutes each month for a flat rate of $19.
let
x = number of minutes used
Therefore,
$19, x ≤ 300
For any minutes over 300, Andrew is charged 0.39 per minute.
Therefore,
if x > 300
f(x) = 19 + 0.39(x - 300)
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In 1898, L. J. Bortkiewicz published a book called The Law of Small Numbers, where using data he collected for twenty years, he showed that the number of soldiers killed by horse kicks each year in the Prussian army followed a Poisson distribution with a mean of 0.61. What is the probability that there will be exactly three deaths in two years?
hurry please will pick brainly and step by step appreacite it
Answer:
given : 0.61 per year
formula poisson probability : p(x=k)=xke-x/k!
(a) The parameter λ is the product of the rate per year and the number of years. The number of years is 1 year in this case.
λ=0.61×1=0.61
Evaluate the formula of the Poisson probability at k=0,1:
P(X=0)= 0!
(0.61)
0
e
−0.61
≈0.5434
P(X=1)=
1!
(0.61)
1
e
−0.61
≈0.3314
Add the corresponding probabilities:
P(X≤1)=P(X=0)+P(X=1)=0.5434+0.3114=0.8748
Use the complement rule:
P(X>1)=1−P(X≤1)=1−0.8748=0.1252
Note: The solution in the back of the book is the probability of at least one death instead of more than 1 death, thus the solution in the back of the book is not correct.
Step-by-step explanation:
this is prob wrong so im sorry in advance!
the students in Mrs. Aubrey's class brought in 15 cans during week 1 of the food drive. during week 2 the students brought in 4 times as many cans. how many cans did the students bring in during week 2?
Answer:
30 cans :)
Step-by-step explanation:
We need to divide to solve so lets do that now :)
15 x 4 = 60
60/2 = 30
Have an amazing day!!
Please rate and mark brainliest!!
Mandy has $10.65. she wants to share it with herself and her 2 friends. How much will each friend get
Answer:
3.55 per person
Step-by-step explanation:
To find the amount of money per person, take the total amount of money and divide by the number of people
10.65 /3
3.55 per person
Answer:
$3.55 for everyone
the admission ticket to tyler amussement park is $1.25 per person. A total of 815 tickets were sold on saturday. the attendance decreased by 96 on sunday. how much money did the park receive from ticket sales in all?the admission ticket to tyler amussement park is $1.25 per person. A total of 815 tickets were sold on saturday. the attendance decreased by 96 on sunday. how much money did the park receive from ticket sales in all?the admission ticket to tyler amussement park is $1.25 per person. A total of 815 tickets were sold on saturday. the attendance decreased by 96 on sunday. how much money did the park receive from ticket sales in all?
The total revenue for Saturday and Sunday is $1917.50
How much money did the park receive from ticket sales in all?We know that 815 tickets were sold on Saturday, and on Sunday the number of tickets sold decreased by 96.
Then the total number of tickets sold in the two days is:
(815) + (815 - 96) = 1534
And we know that each ticket costs $1.25
Then the total revenue is:
R = $1.25*1534 = $1917.50
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What type of polynomial is: 3x+x2+4
Answer:
Quadratic polynomial (Biggest power is 2). It's also a trinomial (3 unlike terms)
Find the sum of the first five terms of the geometric sequence: - 1, - 6, - 36
The sum of the first five terms of the geometric sequence is -1555
Sum of geometric sequenceThe formula for calculating the sum of geometric sequence is expressed as:
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
where
r is the common ratio = 6/1 = 6
a is the first term = -1
n = 5 (number of terms)
Substitute
[tex]S_5=\frac{-1(6^5-1)}{6-1}\\S_5=\frac{-7776+1}{5}\\S_5=-1555[/tex]
Hence the sum of the first five terms of the geometric sequence is -1555
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PLEASE HELP ME ASAP!!!!
Part A: Identify the diagonals in the parallelogram.
Part B: Determine the value for x and y. Show your work.
Part C: Identify the length of each diagonal. Show your work.
Part A
[tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex]
Part B
Diagonals of a parallelogram bisect each other, so
[tex]BE=ED \implies 2x+3=3y-4 \implies 3y=2x+7 \implies y=\frac{2}{3}x+\frac{7}{3}\\\\AE=EC \implies y+4=4x-6 \implies y=4x-10[/tex]
Solving by substitution,
[tex]\frac{2}{3}x+\frac{7}{3}=4x-10[/tex]
Multiplying both sides by 3,
[tex]2x+7=12x-30\\\\37=10x\\\\x=3.7[/tex]
So, [tex]y=\frac{2}{3}\left(\frac{37}{10} \right)+\frac{7}{3}=\frac{24}{5}[/tex]
Part C
[tex]BE=ED=2(3.7)+3=10.4\\\\AE=EC=4(3.7)-6=8.8[/tex]
[tex]\therefore BD=2(10.4)=20.8, AC=2(8.8)=17.6[/tex]
Garden table and bench is 657 total. Garden table is $43 less than bench. What cost of bench?
Answer:
$350
Step-by-step explanation:
Let the bench cost $x
Then the garden table costs $x - 43
x + (x - 43) = 657
2x = 657 + 43
2x = 700
x = 350
The cost of the bench is $350.
Nice day to you!
Write an equation of the line that passes through the point (5, 6) with slope 3.
Answer:
the answer to that would be y=3x-9
Find all polar coordinates of point P where P = ordered pair 6 comma negative pi divided by 5.
A) (6, negative pi divided by 5 + 2nπ) or (-6, negative pi divided by 5 + 2nπ)
B) (6, negative pi divided by 5 + 2nπ) or (-6, negative pi divided by 5 + (2n + 1)π)
C)(6, negative pi divided by 5 + (2n + 1)π) or (-6, negative pi divided by 5 + 2nπ)
D) (6, negative pi divided by 5 + 2nπ) or (6, pi divided by 5 + (2n + 1)π)
All polar coordinates of point P where P = ordered are given are mathematically given as
(6, negative pi divided by 5 + 2nπ) or (-6, negative pi divided by 5 + (2n + 1)π)
Option B is correct.
What are all polar coordinates of point P where P = ordered pair 6 commas negative pi divided by 5.?Generally, the equation for all polar coordinates is mathematically given as
[tex]P= 6,\frac{-pi}{5}[/tex]
Finding the whole set of polar coordinates for An arbitrary point's polar coordinates may be written as (r, ), where (r, ) = (r, +2n) for some n and r.
If n is a positive integer and r is negative, then (r,) = (-r, +(2n+1)).
In conclusion, we may solve the problem by setting r = 6 and = -/6.
If n is an integer and r is positive, then P(6,-/6) = (6, -/6) + 2n, and if n is an integer and r is negative, then P(-6,-/6) = (-6, -/6) + (2n+1).
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What is the least 6 digit multiple of 4 that has all different numbers?
Answer:
We can now take 2 as the third digit, 3 as the fourth digit, 4 as the fifth digit and finally 5 as the sixth digit. Therefore, the smallest 6-digit number having all different digits is 102345.
The smallest 6-digit multiple of 4 with all different numbers is 102,564. This number is obtained by incrementing from 100,000 until finding a divisible number with distinct digits.
A number that is the result of a given number plus another natural number is said to be a multiple of that number.
Since the smallest 6-digit number, is 100,000.
Check if this number is divisible by 4.
In this case, it is not.
Increment the number by 1 to get 100,001.
Repeat step 2. Not divisible by 4.
Increment the number by 1 to get 100,002.
Repeat step 2. Not divisible by 4.
Increment the number by 1 to get 100,003.
Repeat step 2. Not divisible by 4.
Continue this process until you find a number that is divisible by 4 and has all different digits.
After following these steps, we find that the smallest 6-digit multiple of 4 with all different numbers is 102,564.
Hence,
The required number is 102564.
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Identify the area of the figure
Answer:
184cm²
Step-by-step explanation:
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Area = 184 cm²[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Divide the figure into two parts,
Part 1 : rectangle with, width = 7 cm and length = 20 cm
Area of part 1 :
[tex] \qquad❖ \: \sf \:20 \times 7[/tex]
[tex] \qquad❖ \: \sf \:140 \: \: {cm}^{2} [/tex]
Part 2 : Trapezoid with parallel sides - 7 cm and 4 cm,and height 8 cm
Area of part 2 :
[tex] \qquad❖ \: \sf \: \cfrac{1}{2} \cdot (7 + 4) \sdot(8)[/tex]
[tex] \qquad❖ \: \sf \:11 \times 4[/tex]
[tex] \qquad❖ \: \sf \:44 \: \: {cm}^{2} [/tex]
Area of whole figure =Area of part 1 + part 2
[tex] \qquad❖ \: \sf \:140 + 44 \: \: {cm}^{2} [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex] \qquad❖ \: \sf \:area =184\: \: {cm}^{2} [/tex]
Three randomly selected households are surveyed. the numbers of people in the households are 1,3,8 assume that samples of size n =2 are randomly selelcted with replacement from the population of 1,3,8. Listed below are the nine different sample 3,5 3,5 3,10,5,3 5,5 5,10 10,3 10,5 10,10 find the variance of each of the nine samples then summerize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values
The estimator sample proportion is mathematically unbiased
What is the estimator sample proportion?Generally, the equation for is mathematically given as
Population sample \mu=1.3
The sample to sample proprotion table will have
first column= 3,5 3,5 3,10,5,3 5,5 5,10 10,3 10,5 10,10
Second coumn= 0,0,0.5,0,0,0.5,05,0.5, total 3
The probability distribution of the distinct variance values table will have
p row=0,0.5,1, Total
probability row= 4/9, 4/9, 1/9, 1
In conclusion, The mean sample
x=3/9
x=1.3
Where
population sample \mu=1.3
\mu= x
Therefore the estimator sample proportion is unbiased for population mean
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Question pictured below
Answer:
The third answer is correct.
Step-by-step explanation:
The city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asked the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information.
City Police Number of Crimes City Police Number of Crimes
Oxford 12 17 Holgate 15 6
Starksville 15 13 Carey 8 18
Danville 20 6 Whistler 6 21
Athens 22 7 Woodville 17 7
Click here for the Excel Data File
a. Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.)
The regression equation is calculated as: ŷ = -0.99299X + 26.39918
How to solve for the regression equationWe have these data for the x axis
12 15 20 22 15 8 6 17
These are the values for the y axis
17 15 6 7 6 18 21 7
Sum of X = 115
Sum of Y = 97
Mean X = 14.375
Mean Y = 12.125
Sum of squares (SSX) = 213.875
Sum of products (SP) = -212.375
Regression Equation = ŷ = bX + a
b = SP/SSX = -212.38/213.88 = -0.99299
a = MY - bMX = 12.13 - (-0.99*14.38) = 26.39918
ŷ = -0.99299X + 26.39918
These values where inputted into a regression analysis calculator and the output is ŷ = -0.99299X + 26.39918
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The price of tickets for the dance was 1 ticket for $5 (for individuals) or 2 tickets for $8 (for couples). She looked inside the cash box and found $200 and ticket stubs for the 47 students in attendance. Does the dollar belong inside the cash box or not? Explain your reasoning.
The $1 belongs in the box.
What are the equations that represent the question assuming the $1 does not belong in the box?s + c = 47 equation 1
5s + 4c = 200 equation 2
How many singles and couples bought the ticket assuming that the $1 does not belong in the box?Multiply equation 1 by 5
5s + 5c = 235
Subtract equation 2 from equation 3
c = 35
Subtract 35 from 47
c = 47 - 35 = 12
35 couples tickets and 12 individual tickets were sold. This is not possible since the couples tickets were sold in 2.
What are the linear equations that represent the question if the 1 dollar belonged in the box?s + c = 47 equation 1
5s + 4c = 201 equation 2
How many couples tickets were sold?Multiply equation 1 by 5
5s + 5c = 235
Subtract equation 2 from equation 3
c = 34
34 is divisible by 2 so the $1 belongs in the box.
Here is the complete question:
Nola was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a dollar lying on the floor next to it. She said,
I wonder whether the dollar belongs inside the cash box or not.
The price of tickets for the dance was 1 ticket for $5 (for individuals) or 2 tickets for $8 (for couples). She looked inside the cash box and found $200 and ticket stubs for the 47 students in attendance. Does the dollar belong inside the cash box or not?
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$15,074 is invested, part at 14% and the rest at 5%. If the interest earned from the amount invested at 14% exceeds the interest earned from the amount invested at 5% by $1694.07, how much is invested at each rate? (Round to two decimal places if necessary.)
The rate at 14% and 5% are $12, 883 and $2191 respectively.
How to determine the rateGiven that;
Invested amount = $ 15, 074 at 14% and 5%
Let rate at 14% = x
rate at 5% = y
We have rate at 9% exceeds that of 5% by $1694. 07
Hence,
0. 14x = 0. 05y + $1694. 07 ⇒ equation 1
x + y = $15, 074 ⇒ equation 2
Make 'x' the subject
x = [tex]15, 074 - y[/tex]
Substitute in equation 2
[tex]0. 14(15, 074 - y) = 0. 05y + $1694. 07[/tex]
Expand the expression
[tex]2, 110. 36 - 0. 14y = 0.05y + 1694. 07[/tex]
Collect like terms
[tex]416. 29 = 0. 19y[/tex]
Make 'y' the subject
y = [tex]\frac{416. 29}{0. 19}[/tex]
y = [tex]$2, 191[/tex]
Substitute the value in equation 2
x + y = $15, 074
x = $15, 074 - y
x = [tex]$15, 074 - 2191[/tex]
x = $12, 883
Therefore , the rate at 14% and 5% are $12, 883 and $2191 respectively.
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Find sin(c)
1.08
0.38
0.92
0.42
The measure of sin C from the figure is 0.92
Sine-tan-cos identityThese identity is used to determine the measure of sides and angles of a triangle.
From the triangle
Opposite side to m<C = 12
'Hypotenuse = 13
Using the expression
sinC = BC/ACC
sinC = 12/13
sinC = 0.92
Hence the measure of sin C from the figure is 0.92
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Graph the image using the given transformation
1) First find the coordinates of the shape:
G(-1, -2), F(-1, -1), E(2,2), D(2, -2)
2)It asked for dilation of 2 about the origin.
*What is dilation?
Dilation is the expanding/enlarging a transformation by a scale factor
Now we multiply all the coordinates with the factor of 2
G(-1*2, -2*2) = G'(-2, -4)
F(-1*2, -1*2) = F'(-2, -2)
E(2*2, 2*2) = E'(4, 4)
D(2*2, -2*2) = D'(4, -4)
3) Now plot these points and graph the transformation:
What are the vertices of A'B'C if ABC is dilated by a scale factor of 2?
The vertices of A'B'C' if A(0, 10), B(8, 6), C(4, 2) is dilated by a scale factor of 2 are;
C. A'(0, 20), B'(16, 12), C'(8, 4)Which method can be used to find the vertices of A'B'C'?Given that triangle ABC is dilated by a scale factor of 2, we have;
A'B' = 2 × AB
A'C' = 2 × AC
B'C' = 2 × BC
Length of AB = √((8-0)^2 + (6-10)^2) = 4•√5
Length of AC = √((4-0)^2 + (2-10)^2) = 4•√5
Length of BC = √((8-4)^2 + (6-2)^2) = 4•√2
By multiplying the given coordinates by the scale factor, we have;
A' = 2 × (0, 10) = (0, 20)
B' = 2 × (8, 6) = (16, 12)
C' = 2 × (4, 2) = (8, 4)
A'B' = √((16-0)^2 + (12-20)^2) = 8•√5
A'C' = √((8-0)^2 + (4-20)^2) = 8•√5
B'C' = √((16-8)^2 + (12-4)^2) = 8•√2
Therefore when we have;
A'(0, 20), B'(16, 12), C'(8, 4), we get;
A'B' = 2 × ABA'C' = 2 × ACB'C' = 2 × BCThe correct option is therefore;
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Pls, I request ya all, exams are near, I am not able to figure out the answer (along with process) of this question. Pls, I will mark as brainliest tose who answer me with the correct process.
Thank You
What this question is asking us is
A) From -40C to 5 0c How much did it rise
The formula for this would be
Risen Temperature - Initial Temperature
The risen temparauture is 5 so we plug the 5 in first then the 4 so it would look like
5-(-4)=9
And remeber when you have 2 negatives it becomes a positie, 5+4=9
The asnwer for A is 9 degress
B) The tempurater then fell by 7 degress from 5 so we just have to do
5 - 7
which is -2 Celcius
Answer:
a was i believe 10 degrees and b dropped 3- degrees
Step-by-step explanation:
Because 4- 3- 2- 1- 0 1 2 3 4 5
1 2 3 4 5 6 7 8 9
4 is the start don't forget that
And for b 5 dropped from 7 degrees just take 5 now ur at 0 and u have 3 more to take boom ur at 3- hope this hellped :)
A vase with a circular base exerts a force of 15 N on a table with a pressure of 750 N/m2.
Find the radius of the base of the vase in cm to 2 dp.
The radius of the base of the vase in cm to 2 dp is 0.08m
Pressure of an objectThe formula for calculating the pressure of a object is expressed as;
Pressure = Force/Area
Area = Force/Pressure
Area = 15/750
Areas = 0.02m²
Since the area of the circular base is πr², then;
πr² = 0.02
r² = 0.02/3.14
r = 0.0798m
Hence the radius of the base of the vase in cm to 2 dp is 0.08m
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