The difference in volume between the two boxes would be = 156in³
How to calculate the difference in volume between the boxes?To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;
Volume = length×width×height.
For box 1 = length = 12in, width = 7¾in, height= 2in
Vol = 12×7¾×2 = 186in³
For box 2; length = 3⅔in, width = 3½in, height= 2⅓in
Volume = 3⅔×3½×2⅓ = 30
The difference = 186-30 = 156in³
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What is 625x25 what is the answer to this problem
Answer
15,625
Step-by-step explanation:
Solution of expression 625 x 25 is, 15,625
We have to given that,
An expression to solve,
625 x 25
Since,To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We can multiply is,
625 x 25
= 15,625
Therefore, Solution of expression 625 x 25 is, 15,625
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help me and thank you
Answer:
Option A, is 8x^6.
Step-by-step explanation:
4x³ × 2x³ = (4 × 2) x^(3+3) = 8x^6
Therefore, 4x³ × 2x³ simplifies to 8x^6.
You're welcome. :)
A) 8x⁶
Step-by-step explanation:Exponents have different rules for operations such as multiplication.
Multiplying Coefficients
When multiplying different terms with exponents, the first thing we should do is multiply the coefficients. Even though there are variables with different exponents, we still multiply the coefficients like normal. This means that the coefficient of the answer should be 8 because 4 * 2 =8. However, you should note that you can only multiply the coefficients and simply the expression if the terms have the same variable.
Multiplying Exponents
To multiply 2 terms with exponents, you should add the exponents together. For example, x⁴ * x⁶ = x¹⁰. No matter what the coefficients are, if the variables are the same, then this method will work. This means that x³ * x³ = x⁶. Then, combine this with the coefficient from before and 4x³ * 2x³ = 8x⁶.
In circle S with m/RUT = 17°, find the m/RST.
S
U
Q
R
T
The value of measure of ∠ RST is,
⇒ ∠ RST = 34°
We have to given that;
In circle S with m ∠RUT = 17°
Hence, We get;
⇒ ∠ RST = 2 × ∠ RUT
⇒ ∠ RST = 2 × 17°
⇒ ∠ RST = 34°
Thus, The value of measure of ∠ RST is,
⇒ ∠ RST = 34°
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The number of people applying for financial aid has gone up in the past 10 years by 6.74%. If the number of people that used to apply was 9,720,000, then how many people are applying now (10 years later)?
There are currently about 10,361,248 people requesting financial aid, which is an increase of 6.74% from ten years ago.
How are financial aid amounts determined?By reducing the financial barrier, it supports the advancement of your academic and professional ambitions.
Its current number of applications can be determined by multiplying 9,720,000 with 1.0674 (which equals a 6.74% increase)
If there were 9,720,000 people asking for financial help 10 years ago and there have been 6.74 times as many applicants since then. As a result, there are currently 10,361,248 applicants for financial aid, or 9,720,000 x 1.0674.
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Which is true about the relationship between 1 inch and 1 foot? A. 1 inch is 12 times as long as 1 foot. B. 1 foot is 12 times as long as 1 inch. C. 1 foot is 6 times as long as 1 inch. D. 1 inch is 6 times as long as 1 foot.
The true-relationship between 1 inch and 1 foot is (b) 1 foot is 12 times as long as 1 inch.
An "inch" is a unit to measure length and is equal to 1/12th of a foot. It is denoted by symbol "in"
A "foot" is a unit which measures the length and is equal to 12 inches. It is denoted as "ft" .
In the imperial system, the unit of length is the foot, and it is divided into 12 smaller units called inches,
So, 1 foot is equal to 12 inches, and we can write this as : 1 foot = 12 inches,
We rearrange this equation to get the relationship between 1 inch and 1 foot,
⇒ 1 inch = 1/12 foot,
This means that 1 inch is equal to one-twelfth of a foot. In other words, it takes 12 inches to make 1 foot.
Therefore, the correct option is (b).
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Hourly Wage Your wage is $8.00 per hour plus $0.75 for
each unit produced per hour. So, your hourly wage y in terms of the number of units produced is
y = 8 +0.75x.
(a) Find the inverse function.
(b) What does each variable represent in the inverse function?
(c) Determine the number of units produced when your hourly wage is $22.25.
(1) The inverse function is: [tex]f^-1 (y)[/tex] = (y - 8)/0.75 (2) In the inverse function, y represents the number of units produced and x is the hourly wage.(3) an hourly wage of $22.25 is approximately 14.93.
How do you know if a graph is a function?If a vertical line drawn anywhere on the graph of a relation only intersect at one point on the graph, then this graph represents a function. If a vertical line can intersect the graph at two or more points, the graph does not represent a function.
(a) To find the inverse function, we must solve for x in terms of y.
y = 8 + 0.75x
y - 8 = 0.75x
x = (y - 8)/0.75
So the inverse function is:
[tex]f^-1 (y)[/tex] = (y - 8)/0.75
(b) In the inverse function, y represents the number of units produced and x is the hourly wage.
(c) To determine the number of units produced when the hourly wage is $22.25, we need to plug y = 22.25 into the inverse function we found in part (a):
[tex]f^{-1}[/tex](22.25) = (22.25 - 8)/0.75
[tex]f^{-1}[/tex](22.25) = 14.93
Therefore, the number of units produced at an hourly wage of $22.25 is approximately 14.93.
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Sophia has the following data:
131213141313h
If the range is 3, which number could h be?
A. 10
B. 11
Answer:
To determine the possible values of h, we need to first understand what is meant by the range.
The range is the difference between the highest value and the lowest value in a set of numbers. In this case, we don't know what the full set of numbers is, but we know that the range is 3.
The highest number in the set is 4 (since there are no higher numbers in the set than 4), and the lowest number in the set is either 1 or 2. This is because the range is 3, and there are only two possible sequences of three consecutive integers that include the number 4: 2, 3, 4 and 1, 2, 3.
So to find the possible values of h, we need to add 3 to each of the possible lowest numbers in the sequence.
If the lowest number is 1, then the possible highest numbers are 4 and 5 (4 + 3 = 7 but the sequence only goes up to 4 so the highest should be 5). Therefore, the possible values of h are either 10 or 11.
Therefore, the correct answer is B. 11.
In July 1964, an elderly woman was mugged in Costa Mesa, California. In the vicinity of the crime a tall, bearded man sat waiting in a yellow car. Shortly after the crime was committed, a young, tall woman, wearing her blond hair in a ponytail, was seen running from the scene of the crime and getting into the car, which sped off. The police broadcast a description of the suspected muggers. Soon afterward, a couple fitting the description was arrested and convicted of the crime. Although the evidence in the case was largely circumstantial, the two people arrested were nonetheless convicted of the crime. The prosecutor based his entire case on basic probability theory, showing the unlikeness of another couple being in that area while having all the same characteristics that the elderly woman described. The following probabilities were used. Characteristic Assumed probability Drives yellow car 1 out of 12 Man over 6 feet tall 1 out of 10 Man wearing tennis shoes 1 out of 4 Man with beard 1 out of 11 Woman with blond hair 1 out of 3 Woman with hair in a ponytail 1 out of 13 Woman over 6 feet tall 1 out of 100 Compute the probability of another couple being in that area with the same characteristics. Would you use the addition or multiplication rule? Why? Are the characteristics independent or dependent? How are the computations affected by the assumption of independence or dependence? Should any court case be based solely on probabilities? Would you convict the couple who was arrested even if there were no eyewitnesses? Comment on why in today’s justice system no person can be convicted solely on the results of probabilities. In actuality, aren’t most court cases based on uncalculated probabilities?
No, any court case should not be based solely on probabilities as probability does not imply certainty.
How to solveCompute the probability of another couple being in that area with the same characteristics
CHARACTERISTIC ASSUMED PROBABILITY
Drives a yellow car 1 out of 12
Man over 6 feet tall 1 /10
Man wearing tennis shoes 1/4
Man with beard 1/11
Woman with blond hair 1/3
Woman with hair in a ponytail 1 /13
Women over 6 feet tall 1/100
We will use the multiplication rule as all the characteristics should be present in the couple.
The probability of another couple being in that area with the same characteristics is given as
P(Drives a yellow car) x P(Man with beard) x P(Woman with blond hair) x P(Woman with hair in a ponytail) x P(Woman over 6 feet tall) = 1/12 x 1/11 x 1/3 x 1/13 x 1/100 = 1/514800
The characteristics dependent on the sum of the probabilities is not equal to 1.
The assumption of independence would lead to use of the addition rule instead of the multiplication rule, and hence the probability would change (the probability would increase).
No, any court case should not be based solely on probabilities as probability does not imply certainty.
No, the couple who was arrested should not be convicted if there were no eyewitnesses as probability does not imply certainty.
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Please see the attached.
Answer:
min: 56
lower quartile: 70
median: 74
upper quartile: 80
max: 86
Let A and B be two events such that P(A) = 1⁄5 While P(A or B) = 1⁄2. Let P(B) = P. For what values of P are A and B independent?
The value of P for A and B to be independent is 3/8.
What is probability of something?Probability is a mathematical concept used to determine the likelihood or chance of an event occurring. It's a measure of how likely it is that a specific outcome will happen in a given situation. Probability values are expressed as numbers between 0 and 1, where 0 means the event is impossible, and 1 means it is certain to occur.
The probability of an event is calculated by dividing the number of outcomes that favor the event by the total number of possible outcomes. The total number of outcomes is the number of ways the event could happen, while the number of favorable outcomes is the number of outcomes that satisfy the event's conditions.
Probability theory has many applications in various fields, including finance, economics, science, engineering, and statistics. It is an essential tool for analyzing data, predicting outcomes, and making decisions.
Two events A and B are independent if and only if P(A and B) = P(A) * P(B).
Using the formula for the probability of the union of two events, we have:
P(A or B) = P(A) + P(B) - P(A and B)
Substituting the given values, we get:
1/2 = 1/5 + P - P(A and B)
Simplifying, we get:
3/10 = P - P(A and B)
We also know that P(A) = 1/5. Using the formula for the probability of the intersection of two events, we have:
P(A and B) = P(A) * P(B | A)
Substituting the given values, we get:
P(A and B) = (1/5) * P
Since we want to find the values of P for which A and B are independent, we can substitute this expression for P(A and B) in the earlier equation:
3/10 = P - (1/5) * P
Simplifying and solving for P, we get:
P = 3/8
Therefore, A and B are independent if and only if P = 3/8.
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Write the system first as a vector equation and then as a matrix equation.
7 x 1
plus
x 2
minus
3 x 3
equals
7
3 x 2
plus
2 x 3
equals
0
Question content area bottom
Part 1
Write the system as a vector equation where the first equation of the system corresponds to the first row. Select the correct choice below and fill in any answer boxes to complete your choice.
The given system of equations can be written as a vector equation [tex]7x^1+x^2-3x^3[/tex] = 7 and as a matrix equation = , where A = [7 1 -3 3 2 2] and B = [7 0].
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It usually consists of two expressions separated by an equals sign (=). The expressions may contain numbers, variables, and operations, such as addition, subtraction, multiplication, and division. The solution of an equation is the value of the variable that makes the equation true.
Vector equation:
[tex](7x^1+x^2-3x^3)=7[/tex]
Part 2
Write the system as a matrix equation. Select the correct choice below and fill in any answer boxes to complete your choice.
Matrix equation:
=
A =
[7 1 -3
3 2 2]
B =
[7
0]
Conclusion:
The given system of equations can be written as a vector equation [tex](7x^1+x^2-3x^3)[/tex] = 7 and as a matrix equation = , where A = [7 1 -3 3 2 2] and B = [7 0].
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please i need help i literally have an hour and 45 minutes to finish this
Answer:
0.506
0.516
0.609
0.615
Step-by-step explanation:
Matt's parents pay him $5.50 for each half hour he babysits his sister, plus a two dollar tip. If Matt made $18.50, fo how long did he babysit
The number of hours Matt babysits his sister is 1 and half hours.
Given that, Matt's parents pay him $5.50 for each half hour he babysits his sister, plus a two dollar tip.
Let the number of half an hours Matt babysits his sister be x.
Matt made $18.50
So, equation is 5.50x+2 =18.50
5.50x=16.50
x=16.50/5.50
x= 3
Which means 1 and half hours he babysits his sister.
Therefore, the number of hours Matt babysits his sister is 1 and half hours.
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Module Test Form B (RM C3 M8) Second Version) mo
13) Determine whether the following statement is true or false.
The capital letter N produces the same capital letter after being rotated 180°.
O True
O False
The statement "The capital letter N produces the same capital letter after being rotated 180°" is true.
If you rotate the capital letter N 180°, it will produce the same capital letter, as it has rotational symmetry.
The letter N has a vertical line of symmetry in the center, which means that if you rotate it 180°, it will overlap perfectly with its original position, producing the same letter.
So, the statement "The capital letter N produces the same capital letter after being rotated 180°" is true.
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Divide. Write your answer as a fraction or mixed number in simplest form 9÷4⅔
An above ground pool drains at a rate of 20
gallons every 3 minutes. The swimming pool
holds 5,000 gallons of water. How many hours
will it take to completely drain the swimming
pool?
The amount of time it would take to drain the swimming pool is equal to 75 minutes..
How to determine time it would take to drain the swimming pool?Generally speaking, a mathematical model for any quantity (water) that decreases by r percent per unit of time is an exponential function of this form:
[tex]P(t) = I(1 - r)^t[/tex]
Where:
P(t ) represents the volume of water in gallons.t represents the time or number of years.I represents the initial volume of water.r represents the decay rate.Next, we would determine the amount of time it would take to have 0 gallons in the swimming pool:
20 gallons = 3 minutes
5,000 gallons = x minutes
20x = 1500
x = 1500/20
x = 75 minutes.
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Jacob took out a loan from a bank today (now). The original agreement stated that to pay off the loan he had to make two equal payments: The first payment of $3000 was due 6 months from now, and the second payment of $3000 was due 12 months from now.
Suppose he renegotiated with the bank so that instead of the original agreement he will make a single payment 24 months from now to pay off the two original obligations.
What single payment 24 months from now will he have to make if the simple interest rate is 10%? The agreed focal date is 24 months from now.
The single payment Jacob would make in 24 months from now, to pay off the two obligations under the new agreement is $7,620.
We shall be solving this using the formula for Simple Interest,
What is the formula for Simple Interest?The interest accrued on each payment can be calculated using the formula for Simple Interest:
Interest = Principal × Rate × Time
where:
Principal = amount borrowed,
Rate = simple interest rate,
Time = time period in years.
Under the original agreement, Jacob shall make two payments of $3000 each, one 6 months from now and the other 12 months from now.
For payment1, the interest accrued would be:
Interest1 = $3000 × 0.10 × (6/12) = $150
For payment2, the interest accrued would be:
Interest2 = $3000 × 0.10 × (12/12) = $300
So the total amount Jacob was to pay under the original agreement is:
Total1 = $3000 + $150 + $3000 + $300 = $6,450
Now let's calculate the amount Jacob would have to pay under the new agreement.
Original principal for each payment is $3000.
The interest accrued on the sum of both payments can be calculated using the same formula for simple interest:
Interest3 = ($3000 + $150 + $3000 + $300) × 0.10 × (24/12) = $720
So the total amount Jacob would pay under the new agreement is:
Total2 = $3000 + $150 + $3000 + $300 + $720 = $7,620
So, Jacob would make a single payment of $7,620, 24 months from now,
to pay off both loans under the new agreement.
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Juan buys candy that costs $8 per pound. He will spend at least $48 on candy. What are the possible numbers of pounds he will buy?
Use p for the number of pounds Juan will buy.
Write your answer as an inequality solved for p.
In a case whereby Juan buys candy that costs $8 per pound and will spend at least $48 on candy the possible numbers of pounds he will buy written in inequality is is p>5 (at least 5 pounds).
How can these number be determined?Inequality in math refers to a statement that one quantity is either greater than, less than, or not equal to another quantity. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), or "≤" (less than or equal to) and "≥" (greater than or equal to). For example, the inequality "x > 3" states that the variable "x" is greater than the value of 3. The inequality "y ≤ 5" means that the variable "y" is less than or equal to 5.
From the question, p = number of pounds Juan will buy.
candy=costs $8 per pound
$20/$4 = 5 pounds
p>5
at least 5 pounds
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The quadrilateral
�
�
�
�
GRAY is shown below. Find the image of quadrilateral
�
�
�
�
GRAY if it has a translation of 4 units left and 2 units down and then is dilated by a scale factor of
1
2
2
1
The coordinates of the figure after translation & dilation are A''(1,3) ,R''(-1/2,1) , G''(-1,-3/2), Y''(5/2,5/2).
What is quadrilateral?A quadrilateral is a polygon with four sides and four vertices. Some examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses.
What is meant by scale factor?Scale factor refers to the ratio of the length or size of an object in one dimension to the length or size of a corresponding object in another dimension. It is commonly used in mathematics and geometry to describe the relationship between two similar figures. For example, if one square has a side length of 4 cm and another square is similar to it with a side length of 8 cm, the scale factor between the two squares is 2:1.
A(2,8) R(3,4) G(2,-1) Y(9,7)
Translate it to 4 units left gives the result:
A'(-2,6) ,R'(-1,2) ,G'(-2,-3), Y'(5,5)
Now dilate it:
A''=(-1,3), R''(-1/2,1), G''(-1,-3/2), Y''(5/2,5/2)
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I need help!
What is the volume of the prism? Be sure to state your answer with the units included
Answer: 105m
Step-by-step explanation:
Hope this helps! :)
50 Points! Multiple choice algebra question. Find the inverse of f(x)=3+5x. Photo attached. Thank you!
the inverse of the function f(x) = 3 + 5x is f^(-1)(x) = (x - 3) / 5.To find the inverse of the function f(x) = 3 + 5x, we need to solve for x in terms of y, then replace y with the inverse notation f⁻¹(x).
what is inverse of the function ?
The inverse of a function is a new function that "undoes" the effect of the original function, meaning that if we apply the inverse function to the output of the original function, we get back the input.
In the given question,
To find the inverse of the function f(x) = 3 + 5x, we need to solve for x in terms of y, then replace y with the inverse notation f⁻¹(x). The steps to find the inverse are as follows:
Step 1: Replace f(x) with y.
y = 3 + 5x
Step 2: Solve for x in terms of y.
y - 3 = 5x
x = (y - 3) / 5
Step 3: Replace x with f⁻¹(x) to get the inverse function.
f⁻¹(x) = (x - 3) / 5
Therefore, the inverse of the function f(x) = 3 + 5x is f⁻¹(x) = (x - 3) / 5.
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Try These questions out and I’ll give you brainliest
Answer:
1) -8m
2) -x
3) -4y
4)
[tex] - 17x {y}^{3} [/tex]
5) p
6) 0
7) 15m + 10
8) r - 7
9) 5x - 22
10)
[tex]3 {m}^{2} [/tex]
11)
[tex]7 {x}^{2} - x[/tex]
12) 22pq - 8p
13)
[tex] - 13 {r}^{2} - 6r[/tex]
14) -19
15) 0
16) 3.07y
17)
[tex] - 4 {m}^{2} - 35m[/tex]
18)
[tex]x {y}^{2} - 3 {x}^{2} y[/tex]
19) .3mn + 4.7m
20) 3r + 2j + m + 3
21)
[tex] - 4 {x}^{2} - 16x + 11[/tex]
22)
[tex]3 {y}^{4} - {y}^{2} + 11[/tex]
What is the lateral surface area
Answer:
A- 304.8 cm²
Step-by-step explanation:
Find the area for the 4 sides (excluding both the top and base).
(2(12×7.5))+(2(12×5.2)) = 302.8
Answer:
A. 304.8 cm²
Step-by-step explanation:
The rectangular prism has a total of 6 rectangular sides
~ two at the bottom and top both of equal dimensions 5.2 x 7.5
~ two at the front and back both of equal dimensions 12 x 7.5
~ two one on the left side and the other on the right side both of equal dimensions 12 x 5.2
The question is asking only for the lateral surface area. This means we ignore the top and bottom surfaces
For each of the other two pairs of rectangles, the surface area is nothing but the product of the dimensions for each rectangle
Therefore area of all the 4 rectangles is
2(5.2 x 7.5 + 12 x 5.2)
We multiply by 2 since there are 2 of each rectangular surface
2(5.2 x 7.5 + 12 x 5.2) = 304.8 cm² ANSWER
If 2-1=3 3-4=7 4-9=13 5-16=21 3-81=0 6-25=?
The result of (6 - 25) = (6² - √25) = (36 - 5) = 31
What is a sequence of series?A sequence is a list of numbers arranged in a specific order, while a series is the sum of the terms of a sequence. In other words, a sequence is a collection of numbers that follow a particular pattern or rule, and a series is the result obtained by adding these numbers together.
The sequence of equations, it appears that each result is obtained by subtracting the square of first number to the square root of second number:
2 - 1 = 2² - √1 = 4 - 1 = 3
3 - 4 = 3² - √4 = 9 - 2 = 7
4 - 9 = 4² - √9 = 16 - 3 = 13
5 - 16 = 5² - √16 = 25 - 4 = 21
3 - 81 = 3² - √81 = 9 - 9 = 0
Similarly,
6 - 25 = 6² - √25 = 36 - 5 = 31
Therefore, the result of 6 - 25 = 6² - √25 = 36 - 5 = 31
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A. Using the given variables, translate the following to mathematical
expressions.
1. the sum of n and 8
2. M reduced by x
3. 12 subtracted from z
4. cincreased by d
5. 20 more than twice f
6. the square of the sum of x and y
7. twice the product of m and n
8. six less than twice b
9. the sum of the squares of u and v
10.the product of x and y divided by 2
Answer:
n + 8
M - x
z - 12
c + d
2f + 20 or 20 + 2f
(x + y)^2 or (x + y) × (x + y)
2mn or 2 × m × n
2b - 6 or 6 - 2b
u^2 + v^2 or v^2 + u^2
(xy)/2 or xy/2
Mr. Hernandez has a high-speed printer that can produce 32 pages per minute.
Write an equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y.
y =
An equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y is y = 32x
The equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y, can be obtained using the following formula:
y = r * x
where r represents the rate of printing in pages per minute, which in this case is 32 pages per minute.
Therefore, the equation becomes:
y = 32x
This equation states that the number of pages printed, y, is directly proportional to the print time in minutes, x, at a rate of 32 pages per minute.
For example, if Mr. Hernandez wants to print 128 pages, we can use the equation to find out how long it will take him:
128 = 32x
x = 128/32
x = 4
Therefore, it will take Mr. Hernandez 4 minutes to print 128 pages on his high-speed printer.
In summary, the equation y = 32x represents the relationship between the print time in minutes, x, and the number of pages printed, y, when using a high-speed printer that can produce 32 pages per minute.
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Select all of the following that are potential roots of
p(x)=x²-9x²
- 4x + 12?
00
00
+2
NI ###
+4
+9
O +3
+6
+12
The potential roots of the function p(x) = x² - 9x² - 4x + 12 are x = 1, -1.5, and 12.
What is the degree of a polynomial?Degree of a polynomial is the highest power of the variable in that polynomial. For example, in a cubic polynomial, the variable [[tex]\bold{x}[/tex]] has the highest power of 3.
Given is the following function with degree of 2 as -
We will plot the graph and find the roots of this function. The number of x - intercepts [coordinates where the graph cuts the x axis] will give us the roots or zeroes of the polynomials. Refer to the graph attached, it shows that the graph intercepts the x - axis at three different coordinates which are → x = 1, x = -1.5, and x = 12. Hence, these three values of [x] are the potential roots of the function p(x) = x² - 9x² - 4x + 12.
Therefore, the potential roots of the function p(x) = x² - 9x² - 4x + 12 are x = 1, -1.5, and 12.
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The potential roots of the given polynomial equation are +4 and -3. These roots are found by factoring the equation, setting each factor equal to zero and solving for x.
Explanation:To find the potential roots of the polynomial equation p(x) = x² - 9x - 12, we can set the equation to zero and solve for x: 0 = x² - 9x - 12.
Next, we look for the factors of 12 which when multiplied would give you -12 and when subtracted would give you 9. There we have -4 and +3. Therefore the factors of the equation are (x - 4)(x + 3) = 0.
So, Final answer:
The potential roots of the given polynomial equation are +4 and -3. These roots are found by factoring the equation, setting each factor equal to zero and solving for x.
Explanation:To find the potential roots of the polynomial equation p(x) = x² - 9x - 12, we can set the equation to zero and solve for x:
0 = x² - 9x - 12.
Next, we look for the factors of 12 which when multiplied would give you -12 and when subtracted would give you 9. There we have -4 and +3. Therefore the factors of the equation are (x - 4)(x + 3) = 0.
So, potential roots of the equation are x = 4 and x = -3 if we set each factor equal to zero and solve for x. This means that from the given options, the potential roots to the equation would be +4 and -3 (though -3 is not mentioned). of the equation are x = 4 and x = -3 if we set each factor equal to zero and solve for x. This means that from the given options, the potential roots to the equation would be +4 and -3 (though -3 is not mentioned).
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Kevin answered 62 questions correctly on his multiple choice history final and earned a grade of 31%. How many total questions were on the final exam?
Answer:
200
Step-by-step explanation:
Turn the 31% back to a decimal = 0.31
62/ x = 0.31
multiply each side of the equation by x to cancel it out from under the fraction
62 = 0.31x
divide each side by 0.31 to have to x alone
200 = x
Check work:
62/200 = 0.31 x 100 = 31%
Use the definition of Ax
to write the vector equation as a matrix equation.
The matrix equation is enter your response here
If the vector is drawn from (0,0) to (5, -1), the outcome or the required vector is drawn.
Describe vector?A mathematical concept known as a vector has both a magnitude and a direction. Physical quantities like force, velocity, and acceleration are represented by it. In the physical sciences, engineering, and computer graphics, vectors are frequently employed. They can also be used to represent abstract concepts like magnitude, directions, and other things.
Here in the question,
(0, 0) is the beginning position. There should be an arrow above each vector name listed below.
Ink a line beginning at (3, -1). A vector has an origin of (0,0) and a destination of (3, -1).
Put a line through points (2,2). The vector B has a start point of (0, 0) and an end point of (2, 2).
These two vectors add up to: a + b = (3-1) + (2,2) = (5,1) when combined.
Whatever order they are in, b + a = (2,2) + (3, -1) = (5,1) regardless.
Either way, the same conclusion is reached.
The terminal point of A + B is at (5, 1).
If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.
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The monthly rents (in dollars) paid by 10 people are given below. (Note that these are already ordered from least to greatest) 905, 940, 955, 965, 1020, 1040, 1045, 1085, 1090, 1105 Send data to calculator Suppose that one of the people moves. His rent changes from $905 to $ 1055 Answer the following (a) What happens to the mean ? decreases by It increases by s Box It stays the same . (b) What happens to the median ? It decreases by s It increases by It stays the same .
Therefore , the solution of the given problem of mean comes out to be $1055 is more expensive than $1020 it increases by.
What is mean?The total of all values variable divided by all of the values constitutes the outcome of a collection, sometimes referred to as the arithmetic mean. It's one of the key trend indicators that's utilised the most and is typically referred as the "mean." To obtain the answer, multiply the collection's overall number of numbers by each value. Either the raw data or information that has been combined into frequency charts can be used for calculations.
Here,
The average rent is determined by adding up all the rents and dividing by the total number of rents.
This is known as the mean.
Given that the person's rent increased by
=>$150, $1055 - $905 = $150.
The entire sum of all rentals would therefore rise, but the overall number of rents would stay the same at 10.
The mean would therefore rise by
=> $150/10
=> $15.
(b) The median rent at the moment is $1020 because the rents are already arranged from lowest to highest.
The new median would be the middle value of the revised list, which would include the new price of $1055,
if one person's rent increased from $905 to $1055.
The median would rise given that $1055 is more expensive than $1020.
Thus , it increases by.
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