Help me in question four! Please
The solution of the z-score of the standard deviation is [tex]0.5[/tex].
What is the standard deviation?
The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Here given that,
The weight for twelve month old baby boys are normally distributed wih the mean [tex]22.5[/tex] pounds and a standard deviation of [tex]2.2[/tex] pounds.
Here, [tex]mean=22.5[/tex] , standard deviation [tex]=2.2[/tex]
z-score = (Blood pressure reading - mean)/standard deviation
[tex]=\frac{23.6=22.5}{2.2}\\\\=\frac{1.1}{2.2}\\\\=0.5[/tex]
Hence, the percentage is [tex]0.5[/tex].
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Two-sevenths of the students in the theater club will be in the second show, and three-fifths of them will be in the third show. The rest will be in the first show. If there are 70 students in the theater club, how many of them will be in the first show?
Answer:
8 students
Step-by-step explanation:
Let's say there are x students in the theater club. We can set up the following equations to represent the information given in the problem:
2/7 * x = number of students in the second show3/5 * x = number of students in the third showx - (2/7 * x + 3/5 * x) = number of students in the first showWe are told that there are 70 students in the theater club, so we can substitute 70 for x in the equations above to find the number of students in each show:
2/7 * 70 = 20 students in the second show3/5 * 70 = 42 students in the third show70 - (2/7 * 70 + 3/5 * 70) = 8 students in the first showTherefore, there will be 8 students in the first show.
Please help! It’s asap :(
Answer:
mean is the average of all the values:
( 15.07 + 15.47 + 15.93 + 15.86 + 15.07 ) / 5 = 15.48g
median is the middle value AFTER it has been arranged in increasing order:
the increasing order is: 15.07, 15.07, 15.47, 15.86, 15.93
the middle value is 15.47g making it the median.
the mode is the most repeated value: 15.07g
consider the words consisting of 5 letter "a"'s, 7 letter "b"'s, and 1 letter "c". find the number of such words where there are no two consecutive "b"'s.
Answer:
To avoid consecutive b's, the string of b's must be divided into one or more groups of 1, 2, or 3 b's. There are a total of 5 + 1 = 6 possible places to insert the dividers to create these groups. For example, suppose we have a string of 7 b's and we insert dividers between the 3rd and 4th b's, and between the 5th and 6th b's. This would create the following groups of b's: bb|bb|b. In general, the number of possible ways to divide the string of b's into groups of 1, 2, or 3 b's is equal to the number of ways to insert 6 dividers into a string of 7 b's. This is equal to the number of ways to choose 6 of the 8 possible places to insert the dividers, which is equal to $\binom{8}{6} = 28$.
Since the 5 a's and the 1 c must be arranged in a specific order, there is only 1 way to arrange these letters. Therefore, the total number of words consisting of 5 letter a's, 7 letter b's, and 1 letter c is equal to $1 \times 28 = 28$.
Answer:
6 possible words.-----------------------------------------------
According to the question there are 7 'b' s and we can't have them together. We assume more than two consecutive 'b' s contain two consecutive 'b' s and hence not considering any option of having 3, 4, 6 or 7 'b' s.
There is only one way to place 'b' s apart which leaves us with 6 gaps.
There are 5 + 1 = 6 other letters which is just the number to fill in the gaps between 7 'b' s.
We have only an option for 'c' to have any of the 6 gaps, it gives us 6 options and no other options for 'a' s.
Therefore in total we have 6 possible ways.
a theatre has 36 rows with 26 seats in the first row, 30 in the second row, 34 in the third row, and so forth. how many seats in the theatre.
The Answer is 38 seats for the 30th row! Because...
It is Adding up by 4 seats:)
Glad to help....
Mark me brainlyest ty!
Jackie Pope is a professional singer. She tracks her transportation expenses to and from her performances. Her expense sheet looks like this: Pope budgets $100 per month for transportation. How much more or less are her expenses than the $100 budgeted? a. $13.50 less c. $19.50 less b. $12.50 less d. $12.50 more Gas/Oil Parking Tolls Commuting $30.00 5.00 7.00 45.50
Expenses are $12.50 less than the budget of 100$ given to Jackie Pope.
How to calculate Expenses?Tabulate the expenses of all the things. Calculate the sum of all expenses to get Expenses.
Now for the given question:
Given:
Expenses of travelling of Jackie pope are
It costed $30.00 for Gas/Oil for car;
It costed $5.00 for Parking of car.
It costed $7.00 for Tolls on road.
It costed $45.50 for commuting.
Now total expenses is sum of all the above four expenses:
Expenses=30+5+7+45.5=$87.50.
Now budget=$100.
So, Remaining amount= Budget-Expenses;
Remaining amount= 100-87.5=$12.50;
Remaining amount from the budget is $12.50
Expenses are $12.50 less than the budget of 100$ given to Jackie Pope.
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find a power series representation for the function. f(x) = x^8 tan^−1(x^3)
The Power series representation of f(x) = [tex]x^8tan^-^1x^3[/tex] is [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}[/tex]
What is Maclaurin series?The Maclaurin series expansion method can be used to get the power series of such functions if the function has a composite part, such as the multiplication or quotient form.
What is power series?
An infinite series in mathematics known as a "power series" can be compared to a polynomial with an infinite number of terms.
The Maclaurin series will be used in this instance to expand the function:
[tex]tan^-^1x[/tex] = [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^2^n^+^1}{2n+1}[/tex]
and for [tex]tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{(x^3)^2^n^+^1}{2n+1}[/tex]
=> [tex]tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}[/tex] -------(i)
and f(x) = [tex]x^8tan^-^1x^3[/tex]
now we need to multiply [tex]x^8[/tex] in the above equation to get the power series expansion of f(x)
[tex]x^8tan^-^1x^3[/tex] = [tex]x^8[/tex] [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}[/tex]
=> [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3^+^8}{2n+1}[/tex]
=> [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}[/tex]
so the expansion of f(x) = [tex]x^8tan^-^1x^3[/tex] is [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}[/tex]
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a) In a single throw of 2 dice, find the probability of getting product at most 6.
Answer: There are a total of 6 * 6 = 36 outcomes when two dice are thrown.
The outcomes that result in a product at most 6 are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 1), (3, 2), (3, 3), (4, 1), and (5, 1).
There are a total of 15 outcomes that result in a product at most 6.
Therefore, the probability of getting a product at most 6 in a single throw of 2 dice is 15/36, which is approximately 0.417.
Step-by-step explanation:
Answer:
p(product of at most 6) = 13/36
Step-by-step explanation:
When throwing 2 dice, there are 36 possible outcomes.
Here are the 36 possible outcomes and their products.
1, 1: 1 <---- at most 6
1, 2: 2 <---- at most 6
1, 3: 3 <---- at most 6
1, 4: 4 <---- at most 6
1, 5: 5 <---- at most 6
1, 6: 6 <---- at most 6
2, 1: 2 <---- at most 6
2, 2: 4 <---- at most 6
2, 3: 6 <---- at most 6
2, 4: 8
2, 5: 10
2, 6: 12
3, 1: 3 <---- at most 6
3, 2: 6 <---- at most 6
3, 3: 9
3, 4: 12
3, 5: 15
3, 6: 18
4, 1: 4 <---- at most 6
4, 2: 8
4, 3: 12
4, 4: 16
4, 5: 20
4, 6: 24
5, 1: 5 <---- at most 6
5, 2: 10
5, 3: 15
5, 4: 20
5, 5: 25
5, 6: 30
6, 1: 6 <---- at most 6
6, 2: 12
6, 3: 18
6, 4: 24
6, 5: 30
6, 6: 36
There are 36 possible outcomes.
There are 13 outcomes of at most 6.
p(product of at most 6) = 13/36
CAN someone help me about this?
Answer:
Step-by-step explanation:
[tex]i=\sqrt{-1} \ \ \ \ \ \ \ \ i^2=(\sqrt{-1})^2=-1[/tex]
a) ±2, 3
[tex](x-2)(x-(-2))(x-3)=\\\\(x-2)(x+2)(x-3)=\\\\(x^2-4)(x-3)=\\\\x^3-4x-3x^2+12=\\\\x^3-3x^2-4x+12[/tex]
b) -2, ±i
[tex](x-(-2))(x-i)(x-(-i))=\\\\(x+2)(x-i)(x+i)=\\\\(x+2)(x^2-i^2)=\\\\(x+2)(x^2-(-1))=\\\\(x+2)(x^2+1)=\\\\[/tex]
[tex]x^3+x+2x^2+2=\\\\x^3+2x^2+x+2[/tex]
c) 3, -1 ±i
[tex](x-3)(x-(-1-i))(x-(-1+i)=\\\\(x-3)(x+1+i)(x+1-i)=\\\\(x-3)((x+1)+i)((x+1)-i)=\\\\(x-3)((x+1)^2-i^2)=\\\\(x-3)((x+1)^2-(-1))=\\\\(x-3)((x+1)^2+1)=\\\\(x-3)(x+1)^2+(x-3)(1)=\\\\(x-3)(x^2+2x+1)+(x-3)=\\\\x^3+2x^2+x-3x^2-6x-3+x-3=\\\\x^3-x^2-4x-6[/tex]
d) -1, -2±√2
[tex](x-(-1))(x-(-2-\sqrt{2}))(x-(-2+\sqrt{2}))=\\\\ (x+1)(x+2+\sqrt{2})(x+2-\sqrt{2})=\\\\(x+1)((x+2)+\sqrt{2})((x+2)-\sqrt{2})=\\\\ (x+1)((x+2)^2-(\sqrt{2})^2)=\\\\(x+1)((x+2)^2-2)=\\\\(x+1)(x+2)^2-2(x+1)=\\\\(x+1)(x^2+4x+4)-2x-2=\\\\x^3+4x^2+4x+x^2+4x+4-2x-2=\\\\x^3+5x^2+6x+2[/tex]
a delivery truch travels 21 blocks north , 16 blockd east, and 26 blocks south. what is its displacment form the oriringo
Displacement from the origin will be 16.76 block
Pythagoras Theorem:
Pythagoras theorem can be used to find the unknown side of a right-angled triangle.Theorem stats that,
c² = a² + b²
where 'c' is the hypotenuse and 'a' and 'b' are the two legs.
In figure,
O is origin,
First travel 21 block north that means OA = 21 block.
then,
travel 16 block East that means AB = 16 block.
again finally,
travel 26 block South that means BC = 26 block.
Join OC,
OC = 16 block
CD = 5 block
we have to find the value of OD
Apply Pythagoras theorem,
OD² = OC² + CD²
OD = √(OC² + CD²)
OD =√(16² + 5²)
OD =√(256 + 25)
OD = √(256 + 25)
OD = √281 block
OD = 16.76 block
Thus,
Displacement from the origin will be 16.76 block
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Could the average peron lift the weight of $150 in quarter? HINT: The average quarter weigh 0. 2 oz
Answer: Yes, they can.
Step-by-step explanation: Since quarters weigh 0.2 oz. 1 dollar weighs 0.8 oz. 0.8x150=120oz. 120ozs is about 7.5 pounds, so yes.
Mariol buy 3 pound of cheee and 3 pound of auage for a total cot of $36. The auage cot $2. 00 le per pound than the cheee. What i the combined cot of 1 pound of cheee and 1 pound of auage?How much would Mariol pay for 4 pound of cheee and 1 pound of auage
Mariol pays $12 for a pound of cheese and a pound of sausage, and $42 for 4 pounds of cheese and 1 pound of sausage.
To solve this problem, we can apply simple algebra. Let's use the letter for the initial, C for a pound of cheese, and S for a pound of sausage.
3 C + 3 S = $36
If the sausage cost $2.00 per pound, so
3 C + 3 ($2) = $36
3 C + $6 = $36
To know the price for a pound of cheese, do as follow
3 C = $36 - $6
3 C = $30
1 C = $30 : 3 = $10
Thus, 1 pound of cheese and 1 pound of sausage would be $2 + $10 = $12
Moreover, if 4C + 1S = 4($10) + 1($2) = $40 + $2= $42
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The perimeter of a rectangular field is 308m . If the length of the field is 96m , what is its width?
Answer:
Perimeter = 2(Length + Width)
let x as width308m = 2(96m + x)
308m = 192m + 2x
308m - 192m = 2x + 192m - 192m
116m = 2x
x = 58m
therefore, the width is 58m
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Given || m ||n, find the value of x.
124°
(5x-4)°
Answer:
x=12
Step-by-step explanation:
5x-4 is vertically opposite and 124 + 5x-4 should add up to 180 because they are cointerior anglesthen you look for the value of x by 124+5x-4=180
124-4+5x-4=180
x=12
you recently joined a computer club that now has 14 members. the club has four different leadership positions (president, vice president, treasurer and secretary). if any club member can serve in any of the leadership positions but no one can serve in two positions simultaneously, how many different ways can the club leadership be organized?
There are 14 members in the club, and there are 4 leadership positions. Each position can be filled by any of the 14 members, so there are 14 ways to fill the first position, 14 ways to fill the second position, and so on. However, we have overcounted because we have not taken into account that a member cannot serve in two positions simultaneously. To correct for this overcounting, we divide by the number of ways that a member can serve in two positions simultaneously, which is 1. Therefore, the total number of ways that the club leadership can be organized is:
14 * 14 * 14 * 14 / 1 = 14^4 = 20736 ways.
How many ways can five members of the
100-member United States Senate be
chosen to be put on a committee?
Answer:
75287520
Step-by-step explanation:
Combination formula: [tex]\frac{n!}{r!(n-r)!}[/tex]
n = the amount of members of the US senate (100)
r = number of members chosen to be committee (5)
= [tex]\frac{100!}{5!(100-5)!}[/tex]
= [tex]\frac{100!}{5! * 95!}[/tex]
= 75287520
can someone help me pls?
The value of x that will make the equation of the model true is: x = 5.8.
How to Solve an Equation of a Model?Create an equation using the model given, then isolate the variable in order to determine its value, which will make the equation true.
Given the model above, the following equation would be created below:
x + x + 9.4 = 21
Combine like terms
2x + 9.4 = 21
Subtract 9.4 from both sides
2x + 94 - 9.4 = 21 - 9.4 [subtraction property of equality]
2x = 11.6
Divide both sides by 2:
2x/2 = 11.6/2 [division property of equality]
x = 5.8
The value of x is: 5.8.
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What are complementary and supplementary angles? How do you find the measure of an unknown angle using these relationships? Give an example and show your work.
Two angles are called complementary when their measures add up to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.
Complementary angles add up to 90°- example: 15° & 75° are complimentary
For example:
Suppose if one angle is x then the other angle will be 90° – x.
Now, to find the complement of 2x + 52°, subtract the given angle from 90 degrees.
90o – (2x + 52o) = 90o – 2x – 52o = -2x + 38o
The complement of 2x + 52o is 38o – 2x.
Supplementary angles add up to 180°- example: 50° & 130° are supplementary
if the two angles form a linear angle, such that, if one angle is x, then the other angle is 180° – x
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2+2 please help me k
Answer:
4
Step-by-step explanation:
.....
commpute how many of those cis contain the true mean. assume that the true mean is 25,000 . store this value in sample hits. does this value match the theoretical value?
assume that the true mean is 25,000 . store this value in sample hits.No, this value does not match the theoretical value.
This code is calculating the number of "hits" in a list of "CIS" that match the specified true mean of 25,000. The loop iterates through each item in the list and if the value matches the true mean, the sample_hits counter is incremented by one. After the loop has finished iterating through the list, the sample_hits value should represent the number of times the true mean was found in the list. The result does not necessarily match the theoretical value because it is dependent on the contents of the list and whether or not the true mean is actually present.
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Bryce's faucet leaks at a rate of 7 gallons an hour. Bryce collects data points, where yis the
number of gallons leaked, and x is the number of hours elapsed, and plots them on a graph.
What is the slope of the line that fits Bryce's data?
y = 7 x is the situation's linear equation in two variables and 7 is Slope of line.
How to calculate Slope?To determine a line's inclination or steepness, use the slope formula. By calculating the ratio of the change in the y-axis to the change in the x-axis, it may be used to calculate the slope of any line. A line's slope is determined by how its "y" coordinate changes in relation to how its "x" coordinate changes.
Calculation:The faucet leakage rate is shown here to be 7 gallons per hour.
Since y gallons could leak in x hours , we have
Leakage rate is expressed as gallons per hour divided by the number of hours.
Given that our leakage was y gallons, and
The duration of the leaking is x hours, as well.
7 gallons per hour is the leakage rate, so we have;
Amount of gallons leaked = Gallons leaking per hour × Number of hours
The situation is represented by the linear equation =
y = 7 × x.
By comparing this with y=mx+c, Slope of line is 7
y = 7 x is the situation's linear equation in two variables and 7 is Slope of line.
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Select the correct answer from each drop-down menu.
Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?
A coordinate plane linear graph on inequalities.
The system of inequalities that is represented by the graph is given as follows:
y ≤ -x + 1.y ≥ -0.75x + 0.5.How to define the system of linear inequalities?The system of linear inequalities is defined with linear functions, which have the slope-intercept format given as follows:
y = mx + b.
In which the parameters are given as follows:
m is the slope, representing the change in y when x is increased by one.b is the y-intercept, representing the value of y when the graph of the function crosses the y-axis.For the upper bound of the inequality, we have that the linear function:
Has a slope of -1, as when x increases by one, y decreases by one.Has an intercept of 1, as when x = 0, y = 1.Then the upper bound of the inequality has the definition given by:
y ≤ -x + 1.
For the lower bound of the inequality, we have that the linear function:
Has a slope of -0.75, as when x increases by four, y decreases by three.Has an intercept of 0.5, as when x = 0, y = 0.5.Hence the lower bound of the inequality has the definition given by:
y ≥ -0.75x + 0.5.
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A rectangle has a height-to-width ratio of 6.25:4.
Select all of the choices below that are scaled versions of this rectangle.
A rectangle with a height of 18.75 units and a width of 12 units
A rectangle with a height of 18.75 units and a width of 12 units
A rectangle with a height of 30.25 units and a width of 20 units
A rectangle with a height of 30.25 units and a width of 20 units
A) A rectangle with a height of 400 units and a width of 625 units
B) A rectangle with a height of 400 units and a width of 625 units
C) A rectangle with a height of 50 units and a width of 32 units
D) A rectangle with a height of 50 uxnits and a width of 32 units
E) A rectangle with a height of 1.25 units and a width of 0.8 unit
The scaled versions of the given rectangle are A rectangle with a height of 18.75 units and a width of 12 units, A rectangle with a height of 50 units and a width of 32 units and A rectangle with a height of 1.25 units and a width of 0.8 unit
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.
Given that, A rectangle has a height-to-width ratio of 6.25:4.
4/6.25 = 0.64
The ratio of width to height should be 0.64 for the scaled versions of this rectangle.
A) A rectangle with a height of 18.75 units and a width of 12 units = 12/18.75 = 0.64
B) A rectangle with a height of 50 units and a width of 32 units = 32/50 = 0.64
C) A rectangle with a height of 1.25 units and a width of 0.8 unit = 0.8/1.25 = 0.64
Hence, The scaled versions of the given rectangle are A rectangle with a height of 18.75 units and a width of 12 units, A rectangle with a height of 50 units and a width of 32 units and A rectangle with a height of 1.25 units and a width of 0.8 unit
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On a coordinate plane, a point is at (negative 5, 3). to which linear equations is the coordinate a solution? select two options. y = 2x 13 y = –x – 2 y = 3x – 5 y = negative one-half x 6 y = –2x – 2
The 2 linear equation which passes through point (-5,3) are:
y=2x+13y= -x - 2so option A and B is correct
in order to check the answer we will check for all options which satisfies the the given point (-5,3)
putting the values in equation 1
3 = 5*-2+13 so 3 =3 and the given points satisfies the above equation.
putting the vlaues in equation 2
LHS = y= 3
RHS = -(-5) -2 =5-2 = 3
so LHS = RHS this equation also satisfies
putting the vlaues in equation 3
LHS = y= 3
RHS = 3*-5 -5 = -20
so LHS ≠ RHS so, this equation not satisfies
putting the vlaues in equation 4
LHS = y= 3
RHS = -0.5 *5 + 6 = 3.5
so LHS ≠ RHS so, this equation not satisfies
putting the vlaues in equation 5
LHS = y= 3
RHS = -2*-5- 2=8
so LHS ≠ RHS so, this equation not satisfies
so only equation i and ii is true for the given point
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Complete question :
On a coordinate plane, a point is at (negative 5, 3). to which linear equations is the coordinate a solution? select two options.
A. y = 2x + 13
B. y = –x – 2
C. y = 3x – 5
D. y = negative one-half * 6
E . y = –2x – 2
Why in this case would we expect the sample size to be small? (Mark all that might apply:) There limited amount of time that bat keepers maybe able to devote to this activity. The sample size doesn't have to be small: There are many bats in the wild We wouldnt want to unnecessarily stress the animals. There is limited number of bats in captivity:
When it comes to researching bats in captivity, we expect the sample size to be small for a few reasons.
Firstly, there may be a limited amount of time that bat keepers are able to devote to this activity due to other obligations. Secondly, we would not want to unnecessarily stress the animals by collecting too many samples. Lastly, there is a limited number of bats in captivity, so the sample size will be small.
On the other hand, there are many bats in the wild, which means that the sample size does not have to be small. Researchers can take advantage of this by collecting data from a larger sample size. However, researchers must be mindful of the impact that their research may have on the environment, and the stress that it may cause the animals.
In conclusion, the sample size for studying bats in captivity is likely to be small due to the limited amount of time that bat keepers can devote to this activity, the need to avoid unnecessarily stressing the animals, and the limited number of bats in captivity. On the other hand, a larger sample size is possible when studying bats in the wild, but researchers must be mindful of the impact of their research on the environment and the animals.
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Use the order of operations to simplify.
4x5-10-2(1-2)+5
Answer:the answer is 17
Step-by-step explanation:
The required simplified solution of the given expression is 17.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
= 4×5 -10 -2 (1 - 2) + 5
Following the PEMDAS rule,
= 20 - 10 - 2(-1) + 5
= 20 - 10 + 2 + 5
= 20 + 2 + 5 - 10
= 27 - 10
= 17
Thus, the required simplified solution of the given expression is 17.
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suppose that you are rolling a six sided dice. let a = even what is p(ac)?
Answer:
1/2
Step-by-step explanation:
When you roll a 6-sided die, there are 6 possible outcomes:
1, 2, 3, 4, 5, 6
3 of the outcomes are even, and 3 of the outcomes are odd.
p(A) = p(even) = 3/6 = 1/2
p(Ac) = 1 - p(A) = 1 - 1/2 = 1/2
6.4: Spot the Differences
Let /(x) = (x-2)(x+3)(x-7) and g(x)=(x-2)(x+3)(x-7).
Mathematics
1. Use graphing technology to graph both functions in the same window of
-10 ≤x≤ 10 and -100 ≤ y ≤ 100. Describe how the two graphs are the same and
how they are different.
The differences f(x) = (x-2)(x+3)(x-7) and g(x)=(x-2)(x+3)(x-7) is 0.
What is the polynomial equation?
A polynomial is a function in which the least power of the unknown is 2.
The root of a polynomial is the value of the unknown which makes the polynomial equal to zero.
We have,
f(x) = (x-2)(x+3)(x-7)
g(x) = (x-2)(x+3)(x-7).
( f – g ) ( x ) = ?
( f – g ) ( x ) = f ( x ) – g ( x )
= (x - 2) (x + 3) (x - 7) – (x - 2) (x + 3) (x - 7)
= 0
Hence, the differences f(x) = (x-2)(x+3)(x-7) and g(x)=(x-2)(x+3)(x-7) is 0.
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2. In the March 1998 issue of Great Goatee Magazine, readers could vote online for their
favorite goatee in the Pitt-Brust Bonanza. Readers could either vote for Brad Pitt or Mr. Brust. Brust's
votes equaled 2 times the sum of Pitt's votes and 400. The total number of votes received was 2012.
Model the situation with a linear system.
a.
Pitt?
Total # of votes:
Brust vs Pitt:
Let B # vote for Brust
Let P=#votes for Pitt
= 2(.
= 2012
LON BY SHged Fa
Brust?
Brust's votes equaled 2 times the sum of Pitt's votes and 400:
B = 2(P + 400), this is the first equationThe total number of votes received was 2012:
B + P = 2012, this is the second equationSolve for P by substitution:
2(P + 400) + P = 20122P + 800 + P = 20122P = 2012 - 8002P = 1212P = 606Find B:
B =2012 - 606B = 1406Answer:
a) Total # of votes: B + P = 2012
Brust vs Pitt: B = 2(P + 400)
b) 1608 = votes for Brust
404 = votes for Pitt
Brust won by 1204 votes
Step-by-step explanation:
Given variables:
Let B = the number of votes for BrustLet P = the number of votes for PittGiven information:
Brust's votes equalled 2 times the sum of Pitt's votes and 400.The total number of votes received was 2012.Create a system of linear equations using the given variable and information:
Total # of votes: B + P = 2012Brust vs Pitt: B = 2(P + 400)Substitute the second equation into the first equation and solve for P:
⇒ 2(P + 400) + P = 2012
⇒ 2P + 800 = 2012
⇒ 3P = 1212
⇒ P = 404
Substitute the found value of P into the first equation and solve for B:
⇒ B + 404 = 2012
⇒ B = 1608
Therefore:
1608 = votes for Brust404 = votes for PittTo find how many votes Brust won by, subtract the total number of votes for Pitt from the total votes for Brust:
⇒ 1608 - 404 = 1204
Given the equation. y = x^2 + 4
Write the vertex form equation of each parabola.
A. y = (x + 2)^2 - 4
B. y = (x - 2)^2 + 4
C. y = (x + 4)^2 - 1
D. y = (x + 4)^2 - 2
Answer:
The vertex form equation of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex and a is a constant that determines the shape of the parabola.
To write the vertex form equation of each parabola, we need to find the values of a, h, and k for each equation.
A. y = x^2 + 4 To find a, we can compare the coefficients of x^2 in the given equation and the vertex form equation. We see that a = 1 in this case.
To find h and k, we can complete the square for the x-term in the given equation. We add and subtract (b/2a)^2, where b is the coefficient of x and a is the coefficient of x^2.
y = x^2 + 4 y = x^2 + 4 + (0/2)^2 - (0/2)^2 y = x^2 + 4 + 0 - 0 y = (x + 0)^2 + 4 - 0 y = (x + 0)^2 + 4
We see that h = -0 and k = 4 in this case. The vertex form equation is y = (x + 0)^2 + 4, or y = x^2 + 4.
B. y = (x - 2)^2 + 4 This equation is already in vertex form, so we can directly read the values of a, h, and k. We see that a = 1, h = 2, and k = 4 in this case. The vertex form equation is y = (x - 2)^2 + 4.
C. y = (x + 4)^2 - 1 This equation is also already in vertex form, so we can directly read the values of a, h, and k. We see that a = 1, h = -4, and k = -1 in this case. The vertex form equation is y = (x + 4)^2 - 1.
D. y = (x + 4)^2 - 2 This equation is also already in vertex form, so we can directly read the values of a, h, and k. We see that a = 1, h = -4, and k = -2 in this case. The vertex form equation is y = (x + 4)^2 - 2.