Answers
ANSWER
n² + 3n + 2 is always even
EXPLANATION
The expression n² + 3n + 2 can be factorized. The zeros are 1 and 2,
\(n^2+3n+2=(n+2)(n+1)\)Let's say that n is odd. In that case, the result of the first factor (n + 2) is an odd number, while the result of the second factor, (n + 1) is an even number. The product of an even number and an odd number is even, so we proved that if n is odd, then the expression is even.
Let's say now that n is even. The result of adding 2 to an even number, like in the first factor, is another even number. The result of the second factor, on the other hand, is an odd number. Like we stated before when n was odd, the result of multiplying any number by an even number is an even number.
Hence, n² + 3n + 2 is always even.
Related Questions
How many 11-card hands are possible with a 20-card deck?
Answers
There is only 1 possible 11-card hand that can be formed from a 20-card deck.
To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.
The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.
The formula for combinations is:
nCk = n! / (k!(n-k)!)
Where "!" denotes the factorial of a number.
Substituting the values into the formula:
20C11 = 20! / (11!(20-11)!)
Simplifying further:
20C11 = 20! / (11! * 9!)
Now, let's calculate the factorial values:
20! = 20 * 19 * 18 * ... * 2 * 1
11! = 11 * 10 * 9 * ... * 2 * 1
9! = 9 * 8 * 7 * ... * 2 * 1
By canceling out common terms in the numerator and denominator, we get:
20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)
Performing the multiplication:
20C11 = 39,916,800 / 39,916,800
Finally, the result simplifies to:
20C11 = 1
Consequently, with a 20-card deck, there is only one potential 11-card hand.
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Which expression is equal to (1.5)3? Select all that apply. A. 5.0625 B. 3.375 C. 4.5 D. 2.25 × 1.5 E. 2.5 × 1.25
Answers
Answer:
c
Step-by-step explanation:
A box contains 12 transistors, 5 of which are defective. If 5 are selected at random, find the probability of the statements below.
a. All are defective
b. None are defective
Answers
Answer:
a. The probability that all 5 selected transistors are defective is 0.0024 or 0.24%.
To calculate this probability, we use the formula for the probability of the intersection of independent events:
P(all 5 defective) = P(defective) x P(defective) x P(defective) x P(defective) x P(defective)
where P(defective) = 5/12 for each transistor.
Plugging in the values, we get:
P(all 5 defective) = (5/12) x (5/12) x (5/12) x (5/12) x (5/12) = 0.0024
b. The probability that none of the selected transistors are defective is 0.163 or 16.3%.
To calculate this probability, we use the complement rule:
P(none defective) = 1 - P(at least one defective)
To calculate P(at least one defective), we can use the complement rule again:
P(at least one defective) = 1 - P(none defective)
So, we need to find P(none defective) first:
P(none defective) = P(not defective) x P(not defective) x P(not defective) x P(not defective) x P(not defective)
where P(not defective) = 7/12 for each transistor.
Plugging in the values, we get:
P(none defective) = (7/12) x (7/12) x (7/12) x (7/12) x (7/12) = 0.163
Then, we can find P(at least one defective):
P(at least one defective) = 1 - P(none defective) = 1 - 0.163 = 0.837
Finally, we can find P(none are defective) using the complement rule:
P(none defective) = 1 - P(at least one defective) = 1 - 0.837 = 0.163.
Wind and Moisture: To understand how weather and landscape affect the spread of wildfires, an experiment was conducted in a low velocity wind tunnel. A fire was started in pine litter, and the researchers measured the fire spread rate for varying wind speeds and pine litter moisture contents. Data for fires started in pine litter that had a moisture content of 4% are shown in the table below.
Answers
Based on the scatterplot, the form of the relationshipbetween fire spread rate and wind speed can be described as a positive correlation.
How is this so?As wind speed increases,the fire spread rate also tends to increase.
b. Direction -
Based on the given scatterplot,the direction of the relationship between fire spread rate and wind speed appears to be positive.
As the wind speed increases,the fire spread rate generally tends to increase as well.
c. Strength -
The scatterplot suggests a moderate to strong relationship between fire spread rate and wind speed.
The data points exhibit a somewhat linear pattern, indicating that there is a noticeable association between these variables.
The firespread rate tends to increase consistently as the wind speed increases, suggesting a relatively strong positive correlation between the two factors.
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Full Question:
Wind and Moisture: To understand how weather and landscape affect the spread of wildfires, an experiment was conducted in a low velocity wind tunnel. A fire was started in pine litter, and the researchers measured the fire spread rate for varying wind speeds and pine litter moisture contents.
Data for fires started in pine litter that had a moisture content of 4% are shown in the table below.
Wind Speed (miles/hour) Fire Spread Rate (feet/minute)
0.76 0
1.78 2
3.34 4
5.38 6
8.10 8
11.75 10
16.70 12
A scatterplot of these data is shown here -
1. Based on the scatterplot, how would you describe the following with regard to the relationship between fire spread rate and wind speed?
a. Form:
b. Direction:
c. Strength:
help me with this and I will give you a chicken
Answers
Answer:
Mode:15
Mean:149
The Range:4
hope this helps don’t be mad if this is wrong pls don’t be mad if it’s wrong if it’s right hope it helps
Louise had 425 marbles. She sold them in bags of 25. How many bags of
marbles did Louise have to sell? ?
Answers
Answer: 17 bags
Step-by-step explanation:
425/25= 17
. Why is the following arrangment of squares not an array?
Answers
When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.
An array is a set of objects or values that are organized in a specific order. It is used in programming, mathematics, and other fields to make data manipulation and analysis easier.
When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.
For example, if a set of squares is arranged in a random or disorganized manner, it cannot be considered an array because it does not meet the orderly requirement. Additionally, if the number of squares in each row or column is different, it cannot be considered an array because it does not meet the uniformity requirement.
Overall, it is important to remember that an array is a specific type of organization and cannot be applied to any random set of objects or values.
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Which expression correctly shows the difference between the product of 8 and 5 and the sum of 8 and 7?
O 8 x (5-8) +7
O (8 x 5) + (8 + 7)
O 8x (5+8)+7
O (8 x 5) - (8 + 7)
feel
Wacom
aer
Answers
Answer:
D. (8 x 5) - (8 + 7)
Step-by-step explanation:
Evaluate the word problem.
The difference (we will be subtracting.) between the product of 8 and 5 (8 * 5) and the sum of 8 and 7 (8 + 7)?
So set it up.
(8 * 5) - (8 + 7)
This is the correct answer because we are taking the difference of the product of 8 and 5 and the sum of 8 and 7.
Please help if u care pls
1/4x+5/2x-2=4-1/4x
What is the value of x
Answers
Answer: The correct answer is: [A]:
__________________________________________________
" Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1 . That value is the unit rate. "
__________________________________________________
Step-by-step explanation:
__________________________________________________
Note that the "unit rate" is the term that refers to:
a "quantity" / or "quantitative value" ;
→ of some type of "countable units"
{e.g. "currency" — [such as: dollars, cents, pounds] ; "distance/length/ width/ height" — [such as: miles, kilometers, meters, centimeters, yards, feet, inches] ; pieces of fruits — [such as: number of apples; cans of soda, number of red dresses] ;
__________________________________________________
per "single unit" of something — {e.g. per hour; per minute; per mile; per ounce; per hour; per dollar, per kilometer, per day, per week.
{e.g.
→ " 3 apples eaten per [single] apricot eaten" ;
→ " 46 miles per hour.
→ " 8.3 cents per oz." ;
→ " 5 Liters of soda per dollar " ;
→ " 2.3 grams per mole " ;
→ " 4.6 mg solute / kg of solvent " ;
→ " 5 km / hr " ; {that is: " 5 km per hr " } .
→ " 3 yds. per [single] square inch."
→ " 35 parts per hundred" ; {that is: " 35 percent" ; or: " 35 % " . } .
→ " ... The cilantro is on sale for 33 cents per bundle ...} ."
→ ... to provide a few examples.
__________________________________________________
On on Cartesian plane graph, the "x-axis" is located on the "horizontal axis" that represents the "independent variable" (or, at times, the "experimental value" — which can be manipulated — or "controlled" —or be subjected to being "manipulated" / "controlled" / or, "selected".
The "y-axis" is located on the "vertical axis" that represents the "dependent variable" (or, at times, the "control value") that cannot be "manipulated" / controlled/ or "selected" / since it represents the "y-value" of the corresponding coordinate to which the "x-value" happens to corresponds to at the given value for "x" .
So, if the "unit rate" represents the "single unit rate" ; we look at "x = 1 " ; since we are "choosing" this particular "single" rate of per "single" (i.e. "1" ) ; so we do not have a choice in what "y-value" of the particular graph to select. We can control the fact that we are "choosing" to find the "unit" rate, so we select the "independent variable" , "x = 1 " . We then examine the "corresponding y-value" that happens to exist when "x = 1 " .
{Note that we have "no control" over what that "y-value" is ; at the: "[point which: " x = 1 .] . "
_________________________________________________
→ As such, that "y-value" [insert that numeric "y-value" ; followed by the units represented by the "y-axis" ] ;
per " 1 " [insert "single unit" represented by the "x-axis" ] ;
_________________________________________________
→ is the: "unit rate" .
__________________________________________________
So:
The correct answer is: [A]:
__________________________________________________
" Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1 . That value is the unit rate. "
Answer:
Step-by-stbhubhbhnhnkjnkjnep explanation:
The parent function f(x)= x is graphed in red. Write the function for g(x) in blue.
Answers
x-3 is the function for second graph of parent function f(x)= x and for third graph the function is g(x)=-x.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given that the parent function is f(x)=x.
The parent function is in red color.
We need to find the function in blue which is transformed from red color.
Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
As we observe, f(x)=x is red graph and it shifted three units down which forms the blue line.
Therefore, g(x)=f(x)-3
g(x)=x-3.
In graph 3, If we flip red graph about x-axis then get blue graph. B
Therefore, g(x)=-f(x)
Thus, The function of blue graph is g(x)=-|x|
Hence, for second graph g(x) is x-3 and for third graph g(x)=-x for parent function f(x)=x.
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Select whether each of these factors was a reason for or against American neutrality. US trade with Europe was worth almost one billion dollars. for against Intro
________________________
Sunny ko behan mil gayi sonali ✨
Answers
The United States' decision to remain neutral was motivated by its over $1 billion in annual trade with Europe.
Why did American neutrality benefit from commerce with Europe?Early 20th-century American trade with Europe helped the US remain neutral by enabling it to maintain business ties with both the Allied and Central Powers.
The US was able to avoid taking a political stance and maintain its neutral status by supplying goods to both sides of the conflict. Additionally, trade helped the US maintain its economic stability because it would have been detrimental to the nation's economy to break off trade with one party.
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The sum of the angle measures of a triangle is 180°. Find the value of x. Then find the angle measures of the triangle.
Answers
Answer:
x = 4343°, 51°, 86°Step-by-step explanation:
The sum of the angles is ...
x° + (x +8)° + 2x° = 180°
4x +8 = 180 . . . . . . . . . . . collect terms, divide by °
x +2 = 45 . . . . . . . . . . divide by 4
x = 43 . . . . . . . . . . subtract 2
x +8 = 51
2x = 86
The angles are 43°, 51°, 86°.
The tourism industry hires a marketing company to promote overseas vacations. The marketing companies research shows a +0.72 correlation between the number of overseas vacations booked and amount of free time, in days, people have each year. Therefore, the marketing company decides to develop an advertising campaign aimed specifically at people, who have lots of free time.
Which of the following is true about this decision?
a. The decision may not be a good one, since it is possible that there is a "lurking" variable, such as income, behind both the number of booked overseas vacations and the number of free days people have each year.
b. The decision is a good one, since we know that the number of free days people have cause them to book more vacations.
c. The decision is a good one, since there is a strong positive relationship between number of booked vacations and the number of free days people have each year.
d. The decision is may not be a good one, since there is a strong positive relationship between number of booked vacations and the number of free days people have each year.
Answers
Answer:
A: The decision may not be a good one, since it is possible that there is a "lurking" variable, such as income, behind both the number of booked overseas vacations and the number of free days people have each year.
Step-by-step explanation:
The correlation coefficient given alone is not sufficient to find out whether the relationship was linear or not. As such there may be a lurking variable and we may therefore have to see the scatter plot diagram to help us know if the relationship was a linear one or not.
A restaurant stores flour, rice, and sugar in three different cylindrical containers.
Answers
The height of the rice cylinder is 12in.
The volume of the flour cylinder is 50.24 in.
What is a cylinder?A cylinder is a 3-D figure that has a radius and a height.
The volume of a cylinder is given as πr²h.
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume.
= 3.14 x 2 x 2 x 5
= 62.8 cm³
We have,
Sugar cylinder:
radius = 2.5 in
height = 8 in
Volume.
= πr²h
= 3.14 x 2.5 x 2.5 x 8
= 157 in²
Rice cylinder:
radius = 2.5 in
height = h
Volume = πr²h
Volume = 235.5 in²
πr²h = 235.5
3.14 x 2.5 x 2.5 x h = 235.5
196.26 x h = 235.5
h = 12 in
Flour cylinder:
Area of base = 12.56 in²
height = 4 in
Volume = x
Area of base = πr²
12.56 = 3.14 x r²
r² = 12.56/3.14
r² = 4
r = 2
Now,
Volume.
= πr²h
= 3.14 x 2 x 2 x 4
= 50.24 in²
Thus,
The solution for each cylinder is given above.
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what integer is equivalent to 25^3/5
Answers
Answer:
3125
Step-by-step explanation:
25^3 = 15625
15625/5=
3125
Given that the measure of ∠x is 90°, and the measure of ∠y is 60°, find the measure of ∠z
Answers
Answer:
GO SEARCH MATH_WAY its a math calculator gives you
Step-by-step explanation:
A motorboat travels 189 kilometers in hours going upstream and 693 kilometers in 7 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Rate of the boat in still water: km/h
Rate of the current: km/h
Answers
Answer:
rate of the boat in still water: 81 km/h
rate of the current: 18 km/h
Step-by-step explanation:
Rate of the boat in still water:81 km/h
Rate of the current: 18km/h
What is speed?Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took. The formula for speed is speed = distance ÷ time.
Given
b= speed of boat in still water c=speed of current
"boat travels 693 kilometers in 7 hours going downstream" Going downstream, the boat travels b+c km per hour. b+c km/hr = 693 km/7hr = 99 km/hr
b+c=99
"boat travels 189 kilometers in 3 hours going upstream" Going upstream, the boat travels b-c km per hour. b-c km/hr = 189 km/3hr = 63 km/hrb-c=63
Add the equations together to eliminate the c terms: b+c=99 b-c=63 2b = 162, therefore, b= 81
b+c= 99, so c = 99 - b= 18
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Write an explicit formula for each sequence given below.
Part A
1,-10, 100,-1,000, 10,000
Explicit Formula: In =
Part B
10.2, 2.2, -5.8, -13.8, -21.8
Explicit Formula: an =
Answers
Answer:
The first five values are 12, 14, 16, 18 and 20
The recursive formula is as follow
Step-by-step explanation:
Since we need to find the first 5 values we start with n = 1 to n = 5. Note that we don't start from n = 0 as the question states that n ≥ 1.
For the first 5 values we just replace the value of n with 1, 2, 3, 4 and 5 and calculate the answer
The first five values are 12, 14, 16, 18 and 20
A recursive formula is one that
a) Mentions the initial term
b) provides a formula connecting the previous term to the existing term.
Since we know the first term is 12, i.e and we know that the difference between consecutive terms is 2 we can conclude that the recursive formula is made up of the following two formulas
The over all formula is as follow
Step-by-step explanation:
Hope this helps:)
14
Select the correct answer from each drop-down menu.
Given: AOB~ XEOF
Prove:
BOC~ DOE
A
B
E
F
Complete the proof.
Suppose that BOC# *DOE
. By the vertical angles theorem,
. By the transitive property,
◆, which contradicts the given. Therefore, XBOC DOE
and
, and
Answers
Using the vertical angles theorem and the transitive property, we have proven that ∠BOC ≅ ∠DOE as shown below.
Geometry
From the question, we are to prove that ∠BOC ≅ ∠DOE
We are given that
∠AOB ≅ ∠EOF
By vertical angles theorem, we can observe that
∠AOB ≅ ∠DOE and ∠BOC ≅ ∠EOF
Then,
By the transitive property
∠AOB ≅ ∠BOC and ∠EOF ≅ ∠DOE
Therefore, ∠BOC ≅ ∠DOE
Hence, the two angles are equal as proven above.
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Here are the answers -
Vert angl theorem: angle AOB is congruent to angle DOE
and: angle BOC is congruent to angle EOF
Transitive Prop: angle EOF is not congruent to angle DOE
and: angle AOB is not congruent to angle EOF
Cheers!
Kiara's cafe uses 4 bags of coffe every day. How many days will 2 2/3 bags of coffe last?
Answers
2 2/3 bags will last 2/3 day
Here, we want to get the number of days the bags will last
From the question, we are told that 4 bags are used everyday
The number of days it will take the given bag to last is the division of the given number of bags by 4
Mathematically, we have this as;
\(\begin{gathered} 2\text{ }\frac{2}{3}\text{ divided by 4} \\ =\text{ }\frac{8}{3}\text{ divided by 4} \\ \\ =\text{ }\frac{8}{3}\times\frac{1}{4} \\ \\ =\text{ }\frac{2}{3}\text{ days} \end{gathered}\)A certain city prides itself on having sunny days. If it rains one day, there is a 95% chance that it will be sunny the next day. If it is sunny one day, there is a 28% chance that it will rain the following day. (Assume that there are only sunny or rainy days.)If today is sunny, what is the chance that it will be rain the day after tomorrow
Answers
Answer:
56% because the more sunny days the more likely it is to rain
how many pattern blocks rhombuses would 4 triangles create
Answers
Four triangles can create a set of pattern blocks that includes a total of four rhombuses.
To understand why, it's essential first to understand what pattern blocks are. Pattern blocks are shapes that are commonly used in early childhood education to teach math concepts like geometry, spatial reasoning, and fractions. They come in different shapes, including triangles, squares, hexagons, trapezoids, and rhombuses.
To create a set of pattern blocks using triangles, one can use four equilateral triangles with the same side length. When these triangles are arranged together, they form a larger equilateral triangle, as each external side of each small triangle connects to a side of another triangle. This larger equilateral triangle can then be divided into four smaller rhombuses by using two diagonals (lines connecting opposite corners) to form a "X" shape. Each of these four smaller rhombuses is made up of two adjacent triangles and forms a diamond shape. Therefore, it can be said that four equilateral triangles can form a set of four rhombuses within an equilateral triangle pattern block set.
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art sculpture composed of 3,880 craft sticks and 960 pieces of balsa wood. What is the ratio of craft sticks to balsa wood?
Answers
Answer:
3880 ÷ 960 = 4.041
ratio = 4:1
Find the probability that z lies between 0 and 1.56.
Answers
Answer:
P(0 < z < 1.56)=0.4406
Step-by-step explanation:
which no. is greater and by how much 3^3+9 or 2×10^2
Answers
A student wants to compare the amount of money that two local movie theaters make over a two-week period for the last nightly showing of a particular movie. The following box plots show the data for the amount of money each theater makes over the period. Compare the median of each box plot.
Please help it’s due in 3 minutes
Answers
The medians are about the same.
Option C is the correct answer.
How to solveThe median, in statistical terms, refers to the value in the center of a dataset that has been sorted either in ascending or descending order, and it is a commonly used measure of central tendency. This contrasts with the mean, which calculates the total value of all figures, then divides by the number of figures.
We have,
Movie theater 1.
From the box plot given,
The median is 995.
Movie theater 2.
From the box plot given,
The median is 995.
Thus,
The median in both the box plot is the same.
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Help please
15 points
Answers
141.6891
hope this is right
Please help me! No links
Two transformations are performed on a figure on a coordinate plane. The first transformation is a translation 8 units to the left. Which second transformation will result in an image that is similar to, but not congruent to, the original figure?
A: A clockwise rotation of 90° about the center.
B: A clockwise rotation of 180° about the center.
C: A dilation by a scale factor of 1 with the origin as the center of dilation.
D: A dilation by a scale factor of 1/2 with the origin as the center of dilation.
Answers
What is the Domain of the given relation?
Answers
[] The domain is the set of x -coordinates, so in this case, we will take the three x values.
-> These are -1, 4, 4, and 1
Answer
[] The first option - {-1, 1, 4}
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Answer:
The domain of the given relation is the set of all "x" values and the range is set of all "y" values in a set of ordered pairs.
Step-by-step explanation:
A pyramid is composed of six isosceles triangles and a hexagonal base. Each isosceles triangle has a height of 8 inches and a base of 6 inches. The area of the hexagonal base is 93.5 square inches. What is the surface area of the pyramid? Enter your answer in the box. in²
Answers
The surface area of the pyramid is A = 265.23 inches²
What is the surface area of the pyramid?The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid
Surface Area of Pyramid = B + ( 1/2 ) ( P x h )
Given data ,
Let the surface area of hexagonal pyramid be represented as A
Surface area of hexagonal pyramid = Area of base + area of lateral surface
Area of the base = 93.5 inches²
Now , the Area of the lateral surface = 3a √ ( h² + ( 3a²/4 ) )
where a = 6 inches
h = 8 inches
Substituting the values in the equation , we get
Area of the lateral surface = ( 3 x 6 ) √ ( 64 + ( 3 x 36 / 4 ) )
On simplifying the equation , we get
Area of the lateral surface = 171.7 inches²
So , Surface area of hexagonal pyramid = Area of base + area of lateral surface
Surface area of hexagonal pyramid A = 93.5 inches² + 171.7 inches²
Surface area of hexagonal pyramid A = 265.23 inches²
Hence , the surface area of hexagonal pyramid is 265.23 inches²
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