With the help of factorisation we can conclude our answer.
What is factorisation?The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into the product of another entity, or factors, whose multiplication results in the original number or matrix is known as factorization or factoring in mathematics.A polynomial or integer is simply resolved into components that, when multiplied together, produce the original or starting polynomial or integer. The factorization method allows us to simplify any algebraic or quadratic equation by representing the equations as the product of factors rather than by expanding the brackets. Any equation can have an integer, a variable, or the algebraic expression itself as a factor.acc to our question-
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A probablity experiment is conducted in which the sample space of the experiment is S= (5. 6, 7, 8,9, 10, 11, 12, 13, 14, 15. 16}, event F={8,9,10,11,12,13), And event G = {12, 13, 14, 15} Assume that each outcome is equally likely. List the outcomes in F For G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule.
List the outcomes in F or G.
A. For G= {__}
(Use a comma to separate answers as needed)
Using the general addition rule, p(F or G) = 0.667.
What is sample space?
In probability theory, the set of all feasible outcomes or outcomes of an experiment or random trial is referred to as the sample space. The sample points, or potential ordered outcomes, are listed as elements in the set used to represent the sample space.
Let,
S = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
F = {8, 9, 10, 11, 12, 13}
G = {12, 13, 14, 15}
n(S) = number of elements in set S are 12.
n(F) = 6
n(G) = 4
n(F and G) = common elements in F and G = 2
n(F or G) = n(F) + n(G) - (F and G)
n(F or G) = 6 + 4 - 2
n(F or G) = 8
Now, using the general addition rule,
P(F or G) = P(F) + P(G) - P(F and G)
Here,
P(F) = n(F)/n(S) = 6/12 = 1/2
P(G) = n(G)/n(S) = 4/12 = 1/3
P(F and G) = n(F and G)/n(S) = 2/12 = 1/6
⇒ P(F or G) = 1/2 + 1/3 - 1/6
= 5/6 - 1/6
= 4/6
⇒ P(F or G) = 0.667
Hence, using the general addition rule, P(F or G) = 0.667.
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from a group of 12 students, we want to select a random sample of 5 students to serve on a university committee. how many combinations of random samples of 5 students can be selected?
The number of combinations of random samples of 5 students can be 792.
Given, 12 groups of students
We have to select random samples of 5 students,
Here we will use the combination formula,
Cₙ,ₓ = n! / x! (n - x)!
Here n=12 and x=5
Cₙ,ₓ = 12! / 5! (7!)
Cₙ,ₓ = 479,001,600 / (120) × (5040)
Cₙ,ₓ = 792
Therefore the possible ways of selecting the random samples of 5 students are 792.
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When the product of 6 and the square of a number is increased by 5 times the number, the result is 4. Select all of the values that the number could be?
When the product of 6 and the square of a number is increased by 5 times the number, the result is 4. then the values of the number is x = 1/2 and -4/3
The product of 6 and the square of a number
Consider the number as x
Then the product of 6 and the square of a number = [tex]6x^2[/tex]
The product of 6 and the square of a number is increased by 5 times the number, the result is 4
Then the equation will be
[tex]6x^2[/tex] + 5x = 4
Move 4 to the left hand side of the equation
[tex]6x^2[/tex] + 5x - 4 = 0
We have to solve the quadratic equation
Split the middle terms
[tex]6x^2[/tex] + 8x - 3x -4 = 0
2x(3x+4) -1(3x+4) = 0
(2x-1)(3x+4)= 0
Then the value of x will be
2x- 1 = 0
2x = 1
x = 1/2
Similarly
3x+4 = 0
3x = -4
x = -4/3
Hence, when the product of 6 and the square of a number is increased by 5 times the number, the result is 4. then the values of the number is x = 1/2 and -4/3
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on average dog bite victims arrive at carver memorial hospital at a rate of 2 victims per day. which probability distribution is most nearly appropriate to describe the number of dog bite victims who arrive at this hospital on a given day?
The "Poisson distribution" is the probability distribution that comes the closest to accurately describing that many dog bite patients visit this hospital across any given day.
Describe the term Poisson distribution?A discontinuous probability distribution is a Poisson distribution. It provides the likelihood that a response will occur a specific number of times (k) over a specific duration or area. The mean number of occurrences, designated by the letter "lambda," is the single parameter of the Poisson distribution.The chance of a discrete (i.e., countable) result is provided by a Poisson distribution, that is an discrete probability distribution.The discrete result for Poisson distributions is k, that also stands for the frequency of an event.For the given data of,
An average of two dog bite victims show up at Carver Memorial Hospital each day.
A probability distribution that most accurately predicts the number of dog bite victims who visit this hospital on any given day is characterized as the "Poisson distribution."
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A couple buys a $290000 home, making a down payment of 15%. The couple finances the purchase with a 15
year mortgage at an annual rate of 3.4%. Find the monthly payment.
per month.
If the couple decides to increase their monthly payment to $1950, find the number of payments.
payments (give 2 decimal places)
which we would round up to
total payments.
The monthly payment for the first condition is $1750.11 and the total number of payments is 156.
What is the monthly payment?
Monthly payment is defined as the amount paid every month depending on the terms of the mortgage loan. This includes the principal, which is the actual balance on the loan, and the interest on the loan.
The formula for monthly payments on the mortgage is given:
[tex]MP = \frac{P(\frac{r}{n}) }{1- (1+\frac{r}{n})^{-nt} }[/tex]
where, MP = monthly payment
P = principal amount
r = rate of interest
n = number of payments per year
t = number of years
Given, a couple buys a house for $290000 and makes a down payment of 15%
Down payment = 0.15*290000 = $ 43500
First condition,
Present value of loan (P) = $290000 - $43500 = $246500
rate of interest (r) = 3.4% = 0.034
number of payments per year (n) = 12
number of years (t) = 15 years
Then, the monthly payment is calculated by:
[tex]MP = \frac{246500(\frac{0.034}{12}) }{1- (1+\frac{0.034}{12})^{-12*15} } = 1750.11[/tex]
Therefore, monthly payment = $1750.11
Second condition,
monthly payment (MP) = $1950
Present value of loan (P) = $290000 - $43500 = $246500
rate of interest (r) = 3.4% = 0.034
number of payments per year (n) = 12
time in years (t) = x years
Then,
or, [tex]1950 = \frac{246500(\frac{0.034}{12}) }{1- (1+\frac{0.034}{12})^{-12*x} }[/tex]
or, [tex]x = 13.06 = 13[/tex]
So, the total number of payments = 13*12 = 156
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Find the equation of the line that is parallel to another line whose equation is x+2y+8=0 and passes though the point(-2,-3)
There is no line parallel to the line x + 2 · y + 8 = 0, as point (x, y) = (- 2, - 3) lies on the original line.
How to determine the equation of a line parallel to another line and that passes through a given point.
In this problem we need to determine the equation of line based on its slope relationship respect to another line and a given point. Two lines are parallel if and only if they have the same slope (m) and two distinct intercepts (b). First, transform the given equation of the line into slope-intercept form:
x + 2 · y + 8 = 0
2 · y = - x - 8
y = - (1 / 2) · x - 4
Then, the resulting line has a slope of - 1 / 2.
Second, determine the intercept of the resulting line:
y = m · x + b
b = y - m · x
b = - 3 - (- 1 / 2) · (- 2)
b = - 3 - 1
b = - 4
The intercept of the resulting line is - 4.
Third, transform the equation of the resulting line into standard form:
y = - (1 / 2) · x - 4
- 2 · y = x + 8
x + 2 · y + 8 = 0
There is no parallel line for the point (x, y) = (- 2, 3).
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Solve each system by substitution.
4x + y = 19
6x + 7y=1
Step-by-step explanation:
that simply means we use one equation to express one variable by the other, and then we use that identity in the second equation (substituting one variable by the expression of the other variable. and then we solve for that remaining variable.
finally we use one of the original equations to solve for the second variable.
4x + y = 19
so, that gives us
y = 19 - 4x
we use that now in the second equation :
6x + 7(19 - 4x) = 1
6x + 133 - 28x = 1
-22x + 133 = 1
-22x = -132
22x = 132
x = 6
now, let's use e.g.
4x + y = 19
4×6 + y = 19
24 + y = 19
y = -5
Which of the following represents an equation in standard form for the line that passes through (3, -1) and (-5, -3).
O A y-tx-1
OB 7x-4y = 1
OC. x - 4y = 7
D 4x-y=7
Answer:
Step-by-step explanation:
y = ¼x + (-7/4) is the standard form for the line that passes through (3, −1) and (−5, −3)
What is Slope intercept form?
y=mx=c is the slope intercept form of a line, m is the slope.
We need to find equation of line passing through (3, −1) and (−5, −3)
First we need to calculate slope 'm'.
slope m = y2- y1 / x2-x1
y2=-3, y1=-1, x2=-5, x1=3
m= -3 - (-1)/(-5)-3 = -2/-8=1/4
Equation of line, y=mx+c
find C in the equation (y=mx+c)
C = y-mx
C = -1-1/4(3)= -7/4
now replace the values you find in the equation (y=Mx+C)
y =1/4x-7/4
Hence y =1/4x-7/4 is the equation of line passes through (3, −1) and (−5, −3).
write a problem that could be represented by the equation 5n - 6 = 19
Suppose y varies directly with x and inversely with z. When y=3, x=5, and z=9. Find y when x=12 and z=21.
Answer:
3.09
Step-by-step explanation:
check the file attached
Eric's city took a telephone poll about a plan to build a new hotel downtown. 200 people took
the poll. 25% of them were in favor of the new hotel. How many people were in favor of the
new hotel?
Answer:
50 people
Step-by-step explanation:
Solution
25% as a fraction is 25/100 which reduces down to 1/4. What this tells you is that 1/4 of the people asked want the hotel
1/4 * 200 = 50
50 people want the hotel.
draw the full decision tree for the parity function of four boolean attributes, a, b, c, and d. is it possible to simplify the tree? g
The diagramfull decision tree for the parity function of four boolean attributes, a, b, c, and d is shown below picture and it is possible to simplify the tree.
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Which answer is correct?
(A) y = 3x − 2
y = 2x + 5
(B) y = −3x + 2
y = 2x − 5
(C) y = −3x − 2
y = −2x − 5
(D)y = 3x + 2
y = −2x + 5
Step-by-step explanation:
the slow of a line is the factor of x in a "y = ..." firm of equation.
the line going through (1, 5) has a slope of 3 (when x increases by +1, then y increases by +3, so the slope y/x = 3).
(B) and (C) are out, because there is no line with slope 3 (only -3).
the line going through (-2, 9) has a slope of -2 (when x increases by 1, y decreases by 2, so the slope y/x = -2/1 = -2).
(A) is out, as there is no line with the slope -2 (only +2).
so, (D) is the correct answer.
26. Use Patterns and Structure
Amoli says you should use
the Distributive Property to
multiply the two expressions.
Yuji says you should use the
Associative Property. Who is
correct? Explain
(125+y) 1/2y
Amoli is Correct, where distributive property is used to multiply two expressions.
What is Distributive property?
The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.
What is Associative property?
A mathematical principle known as the associative property states that grouping the factors in a multiplication problem does not affect the solution.
Step-by-step explanation:
According to distributive property:
= (125 * (1/2y)) +( y * (1/2y))
= 125/2y + 1/2
Here, Associative property does not held.
Hence, Distributive property should be used.
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What is the answer to this problem?
Answer:
$22,000 at 5%, $10,000 at 11%
Step-by-step explanation:
Let x be the amount invested at 5%.
[tex].05x = .11(32000 - x)[/tex]
[tex].05x = 3520 - .11x[/tex]
[tex].16x = 3520[/tex]
[tex]x = 22000[/tex]
$22,000 at 5%, $10,000 at 11%
help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
0.64 feet
Step-by-step explanation:
make h the subject of this expression
[tex]t = \sqrt{ \frac{h}{16} } [/tex]
[tex] {t}^{2} = \frac{h}{16} [/tex]
[tex]h = 16 {t}^{2} [/tex]
then substitute in the value of t=0.2 into the equation of h:
h = 16 × (0.2)² = 0.64 feet(answer)
the first step of writing an equation when given two points is the same for both strategies, slope-intercept or point-slope forms. What would be the first step in finding the equation of the line that passes through (5, 1) and (3, 5)? create a graph using the two points find the slope find the y-intercept substitute one point’s coordinates into either form
The answer to this question is provided in main body.The equation will be as,
What is equation?
an equation could be a formula that uses the sign to attach 2 expressions to indicate that they're equal.
Main Body:
given : points (5,1) and (3,5).
Since slope of line passing through two points
(x₁,y₁ ) and (x ₂ ,y₂ ) is m= (x₂ −x₁)/(y₂ −y₁)
We now find the slope of the line passing through the points (5,1) and (3,5) as shown below:
⇒m= (5-1)/(3-5)
⇒m= 4/-2
⇒m= -2
Therefore, the slope of the line is -2
Now use the slope and point (5,1) to find the y-intercept.
y= mx+b
⇒1= -2(5) +b
⇒1= -10 + b
⇒b= -11
Write the equation in slope intercept form as:
y= mx+b
y = -2x -11
Hence the equation of line is, 2x + y= -11.
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Five sisters each bought matching scarves and two pairs of socks. the scarves were priced at $15.00.if the total bill for all 5 sisters was $125.00 what was the price of one pair of socks?
Price of one pair of socks are $5.00
The total of 5 sisters each bought scarves and 2 pairs of socks.
Socks price variable defined as x.
Total scarves bought by the sisters are:
5 × 1 = 5
Total socks bought by the sisters are:
5 × 2 = 10
Equation for total bill:
$125.00 = 5 × $15.00 + 10 × x
$125.00 = $75.00 + 10x
10x = $125.00 - $75.00
10x = $50.00
x = $50.00/10
x = $5.00
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For her final project, stacy plans on surveying a random sample of students on whether they plan to go to florida for spring break. From past years, she guesses that about % of the class goes. Is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?.
Less than 10 attempts were successful in this situation. due to the fact that 5 is less than 10. The data does not satisfy the requirement as a result.
Because the data don't fit the success or failure criteria, it is not appropriate to adopt a normal model for the sampling distribution of the sample.
50 students make up the sample. The likelihood that she assumes 10% of the class will attend is 10%. It will be demonstrated by:
1 - p = 1 - 10%
⇒ 1 - 0.10 = 0.90
np = 50 × 0.1
np = 5
This suggests the number of victories.
In this case, fewer than 10 efforts have been successful. Since 5 is less than 10, this is the situation. The data does not meet the criteria as a result.
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. Kendra has a painting canvas that is 23 inches wide by 33 inches high. She painted a red
rose, which covered 30% of the canvas. What was the area of the canvas which was
covered by the red rose?
Answer:
227.7 in²
Step-by-step explanation:
You want to know the area that is 30% of a canvas that is 23 inches by 33 inches.
AreaThe area of the canvas is the product of its length and width.
A = LW
A = (33 in)(23 in) = 759 in²
RoseThe rose covers 30% of that area, so an area of ...
rose = 0.30 × 759 in² = 227.7 in²
The area of the canvas covered by the rose was 227.7 square inches.
What is the image of (1, 0) after a counterclockwise rotation of 60°?
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The volume of the triangular prism is 12.5 m³. The length is 2.5 m and the base is 2 m. What is the width?
Answer:
(4) 5 m
Step-by-step explanation:
You want the length of side x of a right triangular prism with base edge lengths of 2.5 m and 2 m, and a volume of 12.5 m³.
VolumeThe volume of the prism is given by the formula ...
V = Bh
where B is the area of the base:
B = 1/2bh . . . . where b and h are the leg dimensions of the right triangle
Using these formulas together, we have ...
V = 1/2(2.5 m)(2 m)x
12.5 m³ = 2.5x m²
Dividing by 2.5 m², we find x to be ...
(12.5 m³)/(2.5 m²) = x = 5 m
The dimension labeled x has length 5 meters.
If g(x) = -2x² + 3x - 1, find g(x + 1)
The value of the equation g(x+1) is -2x²-x
Given equation,
g(x) = -2x²+3x-1
Replacing x in the equation by x+1
g(x+1) = -2(x+1)² +3(x+1) -1
g(x+1) = -2(x²+1+2x) +3x +3 -1
g(x+1) = -2x² -2 -4x +3x +3 -1
g(x+1) = -2x²- x
Hence the final answer is g(x+1) = -2x²-x
Since this, the question says to find the value g(x+1) we need to replace the value of x in the given equation g(x) by x+1 to find value. After replacing we get -2(x+1)² +3(x+1) -1. Next, we need to solve the bracket (x+1)² which will give us x²+1+2x. We will multiply this by -2, which will give us -2x² -2 - 4x. Next, we will solve 3(x+1) which will give us 3x+3. Finally, we need to solve the whole equation to get the answer -2x²- x
I hope this answer helps.
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The scatter plot shows the number of strawberries that have been picked on the farm during the month of February
1001
Number of Strawberries
116ITTIS ITT2TTAS
Days in February
Part A: Using computer software, a correlation coefficient of r= 0. 01 was calculated. Based on the scatter plot, is that an accurate value for this data? Why
or why not? (5 points)
Part B. Instead of comparing the number of strawberries picked and the day in February, write a scenario that would be a causal relationship for
strawberries picked on the farm. (5 points)
Part A:because the data points are far away from each other.
Part B: A casual relationship would be: the number of strawberries picked and the amount of fertilizers used.
What is Correlation Coefficient?
Correlation coefficient, r, is quantitative measure that measures the extent to which two variables are associated.
The closer the data points are on a scatter plot, the closer the value of r is to 1 or -1.
Part A:
The data points in the scatter plot are farther apart and the trend slopes upwards to the right, this means that the correlation coefficient, r, would be positive but very low.
Thus, based on the scatter plot given, the correlation coefficient of r = 0.01 is most likely accurate because the data points are far away from each other.
Part B:
A casual relationship would be: the number of strawberries picked and the amount of fertilizers used.
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Hannah prepares 44 pies for the thanksgiving feast at her school. each pie is cut into 8 pieces. approximately how many students can hannah feed? round to the nearest ten.
Answer:352
Step-by-step explanation:
3X + 4X - 2 = 12
Please help again I’m not very smart lol
[tex]{ \pink{ \boxed{ \blue{ \sf{x = 2}}}}}[/tex]
Step-by-step explanation:
[tex]{ \red{ \sf{3x + 4x - 2 = 12}}}[/tex]
[tex]{ \red{ \sf{7x = 12 + 2}}}[/tex]
[tex]{ \red{ \sf{7x = 14}}}[/tex]
[tex]{ \red{ \sf{x = \frac{14}{7}}}} [/tex]
[tex]{ \blue{ \boxed{ \green{ \sf{x = 2}}}}}[/tex]
1) 2 more than 5 times x
2) 9 Multiply n by 6, and then divide the product by 5.
Answer:
1. 5x +2
2. 6x/5
Step-by-step explanation:
Help me pls!!!!!!!!!!!!!!
Answer:
it's not possible
because Z^2 = Z*Z
and the condition to multiply two arrays is :
( the column in first array have to equal the row in the second array)
ABCD, BEG and CEF are straight lines. Find a and b
Answer:A=72
B=108
Step-by-step explanation:
The solution is, angle a = 72 & b = 108
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
given that,
from the given figure we get,
∠ABC = 180
∠BCD = 180
so, we have,
∠ABC + ∠BCD = 180 + 180
ABE + EBC + a + b = 360
again, we know that,
EBC + a = 180 - 38 = 142
[we know, from property of triangle's angle]
now, we get,
ABE + 142 + b = 360
or, 110 + 142 + b = 360
or, b = 108
so, we get,
a = 180 - 108 = 72
Hence, The solution is, angle a = 72 & b = 108.
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I need help like asap !!!
only numbers and decimal points