Answer:
p2+7p+10 = (p + 5)(p + 2)
Step-by-step explanation:
What are the factors of x³ 4x² 11x 30?
The factors of the given expression would be = (x + 2), (x – 3) and (x + 5).
What is factorisation of equations?Factorisation of equations is defined as the expression of a given equation as a product of several other factors.
From the equation given; x³ 4x² 11x 30. it's factorisation would be done by getting the first root by trial and error method∶
Since the sum of the coefficients is not zero, 1 is not a root
Let x = -2
⇒ -8 + 16 + 22 – 30 = 0
∴ -2 is or (x + 2) is a factor
Dividing x3 + 4x2 – 11x – 30 by (x + 2)
Quotient = x2 + 2x – 15
⇒ x2 + 5x – 3x – 15 = 0
⇒ x (x + 5) – 3 (x + 5) = 0
⇒ (x – 3) (x + 5) = 0
Other factors are (x – 3) and (x + 5)
∴ (x + 2), (x – 3) and (x + 5) are the roots of the equation
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Calls to the Help Desk: The phone call to a computer software helpdesk occure at the rate of 2.1 per minute between 3.00p.m. and 4:00p.m. Compute the probability that the number of calls to the help desk between 3:10 p.m. and 3:15 p.m. (a) exactly eight. Interpret the result. (6) fewer than eight. Interpret the result. ( at least eight. Interpret the result. You Explain It! Height of 10-Year-Old Males The heights of 10-year-old males are normally distributed with mean = 55.9 inches and o = 5.7 inches. (a) Draw a normal curve with the parameters labeled. (6) Shade the region that represents the proportion of 10-year-old males who are less than 46.5 inches tall. (C) Suppose that the area under the normal curve to the left of x = 46.5 is 0.0496. Provide two interpretations of this result
The probabilities for exact 8 and less than 8 calls can be obtained as 0.1009 and 0.1785 respectively.
What is Poisson distribution?Poisson distribution is applied for the case where the events occur in a specific period of time with constant rate.
The given case belongs to Poisson distribution,
It can be solved as follows,
(a) The probability of exactly 8 calls can be obtained as,
P(Exact 8 calls) = [tex]e^{-\lambda} \lambda^{x}/x![/tex]
Where x = 8 and λ = 2.1 × 5 = 10.5.
Then, the probability is obtained as,
⇒ e⁻⁸ × 10.5⁸/8!
⇒ 0.1009
It implies that if 100 calls are selected randomly for the interval of 5 minute, 10 calls can be expected.
(b) The probability of less than 8 calls can be obtained as
P(Less than 8) = [tex]\sum_{x =1}^{7}e^{-\lambda}\lambda^{x}/ x![/tex]
⇒ P(Less than 8) = 0.1785
It implies that out of 100 randomly selected 5 minute calls, around 18 have less than 8 calls.
Hence, the required probabilities for the given case are 0.1009 and 0.1785 respectively.
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The Brown’s family paid a total of $19.00 to bowl 3 games and rent shoes. Each game cost $4.00. Write an equation to represent the total cost y to rent shoes and bowl x games. How much is the shoe rental? How is this represented in the equation?
Answer:
Shoes rental cost: $7
The equation to find the cost is 19 = 4x + y
Step-by-step explanation:
Each game = $4
There are 3 games
They paid a total of $19.00
We have the equation to find the cost is
19 = 4x + y
Now let's put 3 in for x to solve for the cost of renting shoes!
19 = 4(3) + y
19 = 12 + y
y = $7
So, the equation to find shoe rental cost is 19 = 4x + y, and the cost to rent shoes is $7
Answer:
Step-by-step explanation:
19=4x+y is the equation .------1
here x is number of games.
y is cost to rent shoes.
it is given that x=3
so equation 1 becomes
19-12=y
so y=7
which is shoe rental cost
simple:)
What is the vertex of f/x )=| x 8 |- 3?
The vertex of the graph of f(x) = |x + 8| - 3 is (-8, -3). It lies in the third quadrant.
Therefore the answer is (-8, -3).
Simplifying the given graph to the form f(x) = a|x - h| + k
f(x) = |x + 8| - 3
f(x) = 1 × |x + 8| - 3
where a = 1, h = -8, k = -3
So f(x) = |x + 8| - 3 is symmetrical about the line x = -8. At x = -8, y = -3.
Therefore, the vertex of the graph is (-8, -3).
--The question is incomplete, answering to the question --
"What is the vertex of the graph of f(x) = |x + 8| - 3?"
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Determine if triangle KLM and triangle NOP are or are not similar, and, if they
are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
The triangle KLM and triangle NOP are similar.
What is a triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
The length of side KLM are KL = 18, LM = 19, MK = 20.
The length of side NOP are NO = 54, OP = 57, NP = 60.
The ratio length of sides is
54/18 = 57/19 = 60/20 = 3
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
According to SSS rule triangle KLM and triangle NOP are similar.
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Schedule A can be filed with any tax form to itemize deductions for items such as property taxes and charitable contributions paid. True or false
Can two different square have equal area?
Answer:
The given statement is true. Reason: Area of a square = side × side Therefore, two squares that have the same area will have sides of the same lengths.
hop this helps
mark me brainliest
Step-by-step explanation:
What are the three types of input parameters used in the scripts?
The three types of input parameters used in the scripts are: Value, Column, or Table
In this question we need to state the three types of input parameters used in the scripts
We know that a script is a computer language with several commands within a file which are capable of being executed without being compiled.
The input type or input parameters used in the scripts can be Value, Column, or Table. Type option defines whether the input parameter can be one or more columns, or just a single value.
Type option specifies which data types are supported by this input parameter.
The parameters required by a script are specified using comments in the header.
Therefore, Value, Column, or Table are the three types of input parameters used in the scripts.
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90 points!!! please help meh out thankssss!!
The table shows the multiplication of two linear expressions. Select the correct reason for each step.
Reason 1:
Reason 2:
Reason 3:
Reason 4:
(A)associative property of multiplication
(B)commutative property of multiplication
(C)istributive property
(D) simplify
Reason 1: Distributive Property
The 1/4 x was distributed to each term in the parentheses.
Reason 2: Commutative Property
The individual factors were moved around to put numbers next to numbers and variables next to variables. (Technically the associative property was also used, to break down the previous parentheses, but I don't think your teacher is thinking about that.)
Reason 3: Associate Property
The similar factors were then regrouped.
Reason 4: Simplify
This is just simplifying.
Reason 1: Distributive property
Reason 2: Commutative property
Reason 3: Associative property
Reason 4: Simplify
What are the basic properties of Maths?What is the property of commutativity?
The rule governing the ordering of variables is the commutative property. It states that the order of the variables does not influence the final answer when they are added or multiplied.
What is the property of associativity?
The associative feature of real numbers relates to grouping variables. It states that altering the grouping of variables added to or multiplied by one another has no effect on the output.
In mathematics, what is a distributive property?
This property states that multiplying the sum of two or more addends by a number yields the same result as multiplying each addend separately by the number and then putting the resulting products together.
Detailed Explanation:First Argument: Distributive Property
[tex]\frac{1}{4x}[/tex]was allocated to each phrase between the parenthesis.
Reason 2: Property of Commutation
The individual elements were rearranged in order to place numbers alongside numbers and variables alongside variables. (Technically, the associative property was also utilized to separate the preceding parenthesis, although I doubt your teacher is aware of this.)
Reason 3: Associative Property
Similar elements were subsequently gathered.
Fourthly: simplify
This is just simplifying.
Reason 1: Distributive property
Reason 2: Commutative property
Reason 3: Associative property
Reason 4: Simplify
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Please help! not very hard, easy points! My test is timed and im having trouble
Solve the following problem. It may be helpful to use draw a chart on scrap paper to organize the information and write the equation. Be sure to show all steps (V.E.S.T.) and work in order to receive full credit.
A grocer wants to make a 10-pound mixture of cashews and peanuts that he can sell for $3.64 per pound. If cashews cost $5.80 per pound and peanuts cost $2.20 per pound, how many pounds of each must he mix?
Please help... I suck at thissss
What are the 3 main root functions?
The 3 main root functions are:
(2) They firmly moor the plant.
(3) They support the storage of nutrients and food.
(4) Water and minerals are delivered to the plant by the roots.
The roots of vascular plants are modified plant organs that serve as anchors for the plant and as a means of absorbing water and nutrients into the body of the plant, enabling the plant to grow higher and more quickly.
The majority of the time, roots are found below the soil's surface, but they can also be aerial or aerating, that is, they can rise above the earth or, particularly, above water.
Roots carry out the following tasks:
(1) The soil's nutrients and water are absorbed through roots.
(2) They firmly moor the plant.
(3) They support the storage of nutrients and food.
(4) Water and minerals are delivered to the plant by the roots.
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What is the value of the first quartile for observations 15 18 10 20 23 28 12 16?
The first Quartile of the given set of data is 13.5.
The value that splits a list of integers into quarters can be calculated with the help of the quartile formula. The information is separated into quartiles after being initially organized in ascending order. While quartiles divide data into four equal halves, the median divides it into two equal portions.
A set of observations can be divided into four equal halves using the quartile formula. Between the first term and the median is where the first quartile is located.
The quartiles are shown when the set of observations is organized in ascending order.
First Quartile (Q1) = ((n + 1)/4)thTerm
Given observations are
15, 18, 10, 20, 23, 28, 12,16
To find the First Quartile/Lower Quartile.
Arrange the given numbers in ascending order.
10, 12, 15, 16, 18, 20, 23, 28
Here there are 8 numbers
median is the = 4th term+5th term / 2 = 16+18/2 = 17
the median of the numbers below the median of the whole data set, 17. These numbers are 10,12,15,16. Since there are also an even number of numbers in this data set, the median is the average of its two middle numbers (12+15)÷2 = 27÷2 or 13.5.
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In a group trivia game, a team earns 5 points for a correct answer, and -2 points for a
wrong answer. There are 15 questions in the game. Let a represent the number of
correct answers
Which expression represents the total number of points a team earns for
their correct answers?
A.-2x
B.5x
C.x
D.15
Answer: 5a (B)
Step-by-step explanation:
a batch of 200 iron rods consists of 50 oversized rods, 50 undersized rods and 100 rods of the desired length. if two rods are drawn at random without replacement, what is the probability of obtaining (a) two rods of the desired length, (b) exactly one of the desired length, (c) none of the desired length? show all steps and clearly write out your formulas and assumptions
(a) The probability of obtaining two rods of the desired length is (100/200) * (99/199) = 0.495.
This can be found by using the formula for independent events:
P(A and B) = P(A) * P(B)
Since the two draws are of rods without replacement,
the probability of the first-rod being of the desired length = 100/200 (there are 100 desired-length rods out of a total of 200).
The probability of the second-rod being of the desired length = 99/199 (since one of the desired length rods has already been drawn). Multiplying these two probabilities gives us the answer.
(b)The probability of obtaining exactly one rod of the desired length
=(100/200) * (100/199) + (100/200) * (100/199)
= 0.990.
This can be found by using the formula for the union of two events: P(A or B) = P(A) + P(B).
Since the two draws are rods without replacement, the first draw has a probability of 100/200 of being of the desired length (there are 100 desired-length rods out of a total of 200).
The probability of the second draw being of the desired length is 100/199 (since one of the desired length rods has already been drawn). Adding these two probabilities gives us the answer.
(c) The probability of obtaining none of the desired length is (50/200) * (50/199) = 0.015.
This can be found by using the formula for independent events
: P(A and B) = P(A) * P(B).
Since the two draws are of rods without replacement, the probability of the first-rod being of the undersized length is 50/200 (there are 50 undersized rods out of a total of 200).
The probability of the second-rod being of the undersized length is 50/199 (since one of the undersized rods has already been drawn). Multiplying these two probabilities gives us the answer.
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The table and graph both represent the same relationship. Which
equation also represents that relationship?
Answer:
y=2x
Step-by-step explanation:
plug in the values from the table
for the first one, x=0
2 times x is 0 so y=0
for the second one, x=2
2 times x is 4 so y=4
for the third one, x=4
2 times x is 8 so y=8
for the last one, x=6
2 times x is 12 so y=12
Given the following formula, solve for t.
v u + at O
A. t = OB. t = O C. t = OD. t = UU a a (v + u) a (v - u) v+u a picture included
Answer: A
Step-by-step explanation:
well first, dont respond to whoever was in your comments. in fact dont even read them. Anyways i got this answer on a website. it wont let me type it together so its math and then way. Its a wonderful website and very useful
Can a 6 year old do algebra?
Answer:
Um no?
Step-by-step explanation:
What is the median of first 10 natural numbers?
The required median of the first ten natural numbers is 5.5.
Natural numbers are a part of the number system, including all the positive numbers from 1 to infinity. Natural numbers are also called counting numbers because they do not include zero or negative numbers.
The median is the number in the middle of a list of numbers in ascending order, from lowest to highest.
The median is the middlemost element if the total number of elements in the list is odd, and the median is the average of the middlemost two values if the total number of elements in the list is even.
The list of the first 10 natural numbers is: 1,2,3,4,5,6,7,8,9,10
Here is the total number of elements in the list is even.
And the two middlemost elements are 5 and 6.
The required median is: 5+6 /2 = 11/2 = 5.5
Hence, the required median of the first ten natural numbers is 5.5.
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The list of the first 10 natural numbers is: 1,2,3,4,5,6,7,8,9,10
the total number of elements in the list is even.
the two middlemost elements are 5 and 6.
The required median is: 5+6 /2 = 11/2 = 5.5
the required median of the first ten natural numbers is 5.5.
Solve the system for x and y. 2y = x + 9 2y − 11 = 2x
The value of x is 2 and y is -7/2 in the equations 2y = x + 9 and 2y − 11 = 2x.
Define elimination method.The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients. Because it allows us to remove one of the variables and solve a more straightforward equation. The elimination approach may also be referred to as the addition method or the linear combination method in some texts. This is due to the fact that we'll be adding two equations together.
Given,
Equations,
2y = x + 9
2y − 11 = 2x
Rearranging variables and constant
Using elimination method,
x - 2y = 9
2x - 2y = 11
-----------------
x = 2
Equating x = 2 in equation 1
x - 2y = 9
-2y = 9 - 2
-2y = 7
y = -7/2
The value of x is 2 and y is -7/2 in the equations 2y = x + 9 and 2y − 11 = 2x.
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What will come in place of X of the Series 2 5 10 x 2637?
On solving the provided question, we can say that 50 will therefore be the missing number in the series 2 5 10 x 2637.
What are odd numbers?
A number that is odd is one that can't be partitioned flawlessly into matches. One remains after dividing an odd number by two. The numbers 1, 3, 5, 7, 9, 11, 13, and 15 are consecutively odd. While odd numbers cannot be divided in half, even numbers can. 3, 5, 7, 9, 11, 13, and 15 are unusual cases. Even numbers include 2, 4, 6, 8, 10, 12, and 14.
According to the given question:
Following the numbers 3, 5, 7, 9, 11, and 13, which are all odd numbers, the provided series moves on to 13.
Therefore,
After 37, there will be a break before 50.
50 will therefore be the missing number.
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How do you write all real numbers for a range?
The optimal response is The ranges below encompass all real numbers: From 0 through all actual numbers. The domain of this function is all real numbers since x can be entered with any value.
What is Range?Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.
answer to the question is that all real numbers or (−∞,∞)
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Patty is ordering vests for her scout troop to wear in the Veterans Day parade. She ordered 12 vests from the Festive Features clothing shop. Since this was a bulk order, Festive Features reduced the price of each vest by $6. The total came to $132.
The equation that can be used to find the amount, v, Festive Features normally charges for a vest is given as follows:
12(v - 6) = 132.
How to obtain the normal price?
The normal price is obtained applying the proportions in this problem, considering the total amount paid and the number of items purchased.
The parameters are given as follows:
12 vests were purchased.The price of each vest was reduced by $6 from the normal price v, hence the discounted price is of v - 6.The total price was of $132.Then the equation used to find the standard price is presented as follows:
12(v - 6) = 132.
Missing InformationThe missing sentence is:
Which equation can you use to find the amount, v, Festive Features normally charges for a vest?
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What does SSS triangle stand for?
If all three sides of one triangle are equal to the corresponding three sides of the second triangle, then it is known as the SSS triangle congruency theorem.
What is the SSS condition?The SSS rule states that two triangles are said to be congruent if their respective corresponding three sides are equal.
If all three sets of comparable sides are present, the triangles are congruent.
Using congruence, the side-side-side shortcut can be used (SSS).
Another shortcut is side-angle-side (SAS), which makes use of two sets of sides and an angle between them that is known to be congruent.
Therefore, if all three sides of one triangle are equal to the corresponding three sides of the second triangle, then it is known as the SSS triangle congruency theorem.
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Correct question:
What does the SSS triangle congruency theorem stand for?
for the function f(x) shown below, find the definite integral∫60f(x)dx.
The definite integral for this function is given as follows:
[tex]\int_{0}^{6} f(x) dx = 18[/tex]
How to calculate the definite integral?The definite integral represents the area of the function in the interval composed by the bounds of the definite integral.
This means that the definite integral in this problem can be found merely obtaining the area of the function.
The function is composed as follows:
Square of side length 2 between x = 0 and x = 2.Square of side length 2 between x = 2 and x = 4.Rectangles of dimensions 2 and 5 between x = 4 and x = 6.Hence the area of the figure is given as follows:
A = 2 x 2² + 2 x 5 = 8 + 10 = 18 units.
Which is the result of the definite integral.
Missing InformationThe figure is given by the image shown at the end of the answer.
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Which best describes sentence 7? it is a compound sentence. It is a compound-complex sentence. It is a simple sentence. It is a dependent sentence.
A Simple sentence best describes sentence 7 (They rule the earthly world of men together)
This means that it consists of only one independent clause - meaning there is only one finite verb in the sentence. In this case, the verb rules.
A compound sentence has at least two independent clauses; a compound-complex sentence has at least two independent clauses plus at least one dependent clause; a dependent clause cannot exist on its own because it is just a fragment of a larger sentence, which is obviously not the case here.
Complete question:
Read the summary of the conclusion of “The World on Turtle’s Back.” [1] When the twins grew up, they continued to fight. [2] One day they decided to hold a contest to determine who was stronger. [3] Though they tried to defeat each other in many different ways, neither one could win. [4] On the last day, they fought with weapons. [5] Using a deer antler, the right-handed twin overpowered his brother, and he threw him off the edge of the Earth. [6] Today, the right-handed twin lives in the Sky-World, and the left-handed twin lives in the dark underworld. [7] They rule the earthly world of men together. Which best describes sentence 7? It is a compound sentence. It is a compound-complex sentence. It is a simple sentence. It is a dependent sentence.
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A Simple sentence best describes sentence 7 (They rule the earthly world of men together)
It only has one independent clause, which means there is only one finite verb in the sentence, according to this definition. This time, the verb is in charge.
A dependent clause cannot exist on its own because it is just a fragment of a larger statement, which is obviously not the case in this sentence. A dependent clause cannot exist on its own because it is just a fragment of a larger sentence, which is obviously not the case in this sentence.
Read the summary of the conclusion of “The World on Turtle’s Back.” [1] When the twins grew up, they continued to fight. [2] One day they decided to hold a contest to determine who was stronger. [3] Though they tried to defeat each other in many different ways, neither one could win. [4] On the last day, they fought with weapons. [5] Using a deer antler, the right-handed twin overpowered his brother, and he threw him off the edge of the Earth. [6] Today, the right-handed twin lives in the Sky-World, and the left-handed twin lives in the dark underworld. [7] They rule the earthly world of men together. Which best describes sentence 7? It is a compound sentence. It is a compound-complex sentence. It is a simple sentence. It is a dependent sentence.
the mean absolute deviation (mad) is used to: group of answer choices eliminate forecast errors. detects random factors. estimate the trend line. measure forecast accuracy.
The mean absolute deviation (MAD) is a measure of forecast accuracy that is used to detect random factors in a data set. It is calculated by taking the mean of the absolute differences between the actual values and the forecast values.
The MAD can be used to eliminate forecast errors by identifying and removing random factors that are causing the errors. It is not typically used to estimate the trend line or measure forecast accuracy. Mean absolute deviation (MAD) is a measure of the variability or dispersion of a data set. It is calculated by taking the mean of the absolute differences between the individual values in the data set and the mean of the data set.
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Use the drawing tool(s) to form the correct answer on the provided graph. The graph of function f(x)=|x| is vertically stretched by a factor of 2, shifted 6 units down, and then shifted 4 units to the right. Draw the transformed function on the provided graph.
Answer:
2*|x-4|-6
Type it into desmos to see what the graph will look like
Given AORS = ATUV, QS = 4v + 3, and TV = 6v - 5, find the length of QS and TV.
How many angles can you form when 2 parallel lines are cut by a transversal line?
When a transversal cuts two parallel lines, 8 angles are created.
When two lines do not cross one another, they are said to be parallel. In addition, parallel lines are two lines that cross each other at infinity.
A transversal line is one that crosses two other lines at two different locations. Line l meets a and b in the image below at two different locations, P and Q. Line l is the transversal line as a result.
Corresponding angles are those that are created when two parallel lines and a transversal intersect, also known as matching corners or corresponding corners.
∠1 and ∠6
∠4 and ∠8
∠2 and ∠5
∠3 and ∠7
When a transversal connects two coplanar lines, alternate interior angles are created.
∠4 and ∠5
∠3 and ∠6
However, each pair of alternate interior angles is equal if a transversal meets two parallel lines.
∠4 = ∠5
∠3 = ∠6
The pair of angles that are created on the outer side of two lines but on the other side of the transversal are known as alternate exterior angles.
Consecutive interior angles, related angles, and co-interior angles are other names for interior angles that are on the same side of the transversal.
∠3 and ∠5
∠4 and ∠6
When a transversal cuts two parallel lines, 8 angles are created.
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∠1 and ∠6
∠4 and ∠8
∠2 and ∠5
∠3 and ∠7
When a transversal connects two coplanar lines, alternate interior angles are created.
∠4 and ∠5
∠3 and ∠6
However, each pair of alternate interior angles is equal if a transversal meets two parallel lines.
∠4 = ∠5
∠3 = ∠6
Consecutive interior angles, related angles, and co-interior angles are other names for interior angles that are on the same side of the transversal.
∠3 and ∠5
∠4 and ∠6