There are 5040 ways to place 8 rooks on an 8 x 8 chessboard.
A permutation is a systematic grouping of objects or numbers. Combinations allow you to select objects or numbers from a group of items without having to worry about the order in which they were collected. Contrary to permutations, when selecting components from a collection using the combination method, the order of selection is unimportant.
There are 8! ways to place 8 rooks on an 8 x 8 chessboard such that no two rooks are in the same row or column.
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 5040
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Ten people were chosen at random and surveyed. The survey asked participants for the number of hours they watched TV per day and their ages. Letting X represent the number of hours the participant watched TV per day and Y represent the participant's age, the surveyor calculated the correlation coefficient between X and Y to be 0.19. Interpret the correlation coefficient calculated by choosing the statement below which correctly describes the association between X and Y. A. weak positive association B.weak negative association C. strong positive association D. strong negative association
Answer:
The correlation coefficient of 0.29 indicates that the correlation is a weak positive correlation. Thus option (D) is the correct answer.
What is correlation?
"Correlation is a statistical tool that studies the relationship between two variables. Data sets have a positive correlation when they increase together, and a negative correlation when one set increases as the other decreases".
For the given situation,
Correlation coefficient = 0.29
Positive correlation: the two variables change in the same direction.
Negative correlation: the two variables change in opposite directions.
No correlation: there is no association or relevant relationship between the two variables.
The correlation coefficient lies between 0 to 0.3 indicating that the correlation is a weak positive correlation.
Hence we can conclude that option (D) weak positive correlation is the correct answer.
Researchers created a new fertilizer. They conducted an experiment to compare the new fertilizer to the old fertilizer. They divided tomato plants into two groups. They applied the new fertilizer to one group and the old fertilizer to another group. The variable is the number of tomatoes per plant on a randomly selected day.
Which one of the following statements is valid?
A. The new formula of fertilizer works better. Plants with the new fertilizer had more tomatoes.
B. The old formula of fertilizer was better because the plant with the most tomatoes was treated with the old fertilizer.
C. The average number of tomatoes per plant with the old fertilizer is higher than the average amount of tomatoes per plant with the new fertilizer.
D. We can make no conclusions from this data about which fertilizer is better because the two groups have a different number of plants
The plant that produced the most tomatoes was treated with the old fertilizer, thus it was better. So statement B is correct.
A line plot is one type of graph that helps us to represent the data along the number line. This plot is also referred to as a dot plot. In this plot, we show the data as a check or point above a number line. Each point or check in this plot represents the frequency of each value.
The given plot about fertilizers is a line plot. In this plot, 1 dot over 2 in the old fertilizer treatment means about 2 plants have one tomato.
By comparing the line plot for both the new fertilizer and old fertilizer, we will be able to say that there are more tomatoes produced when the old fertilizer is used than the new fertilizer.
Nearly 65 tomatoes were produced when old fertilizer is used but only 58 tomatoes were produced when new fertilizer is used. Therefore, statement B is correct.
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I Need help quick! Tyyy!
The required answer of given parts are 1) 4500 ft² 2) 2700 ft² 3) $1485.
What is right angled triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The sum of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
According to question:1) Area of design = area of rectangle + 2(area of triangle)
Area of design = (60×30) + 60×45
Area of design = 1800 + 2700
Area of design = 4500 ft²
2) Area covered by grass = 2(area of triangle)
Area covered by grass = = 60×45
Area covered by grass = 2700 ft²
3) installment of grass is $0.55 per ft².
So,
For 2700 ft²
= 2700 ft²(0.55)
= $1485
Thus, required answers are 1) 4500 ft² 2) 2700 ft² 3) $1485.
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Give the length of the line segments in the requested units.
AC = _ mm
CF = _ mm
EG = _ m
I would appreciate a step by step explanation, I’ve never been taught any of this stuff and it’s relatively new to me. Thanks! ^
The lengths of the line segments in the requested units are:
AC = 50 mm
CF = 30 mm
EG = 0.15 m
How to find the length of the line segments in the requested units?A line segment is a part of a line that is defined by two distinct endpoints and all the points on the line between them.
The length of a line segment is the distance between the two endpoints. The two endpoints are also known as the "extremities" of the line segment
The length of the line segments in the requested units is as follow.
From the figure AC = 5 cm and CF = 3cm
Since 1cm = 10mm. Thus:
AC = 50 mm
CF = 30 mm
EG = AB and AB = 15 cm
EG = 15 cm
Since 100 cm = 1m
Thus, EG = 0.15m
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I need help with this problem. Please show work and tell me if its one solution or all or none.
2x-y=9
2x+y=11
Answer:
x = 5, y = 1
Step-by-step explanation:
2x - y = 9
2x + y = 11 subtract equation 2 from equation 1
0 - 2y = -2
y = -2/-2 = 1 substitute into equation 1 or 2 to solve for x
2x - 1 = 9
2x = 10
x = 10/2 = 5
The price of an item has been reduced by 35% . The original price was $60. What is the price of the item now?
===================================================
Explanation:
The price drops by 35%, so it keeps the remaining 65% (since 100-35 = 65)
65% of $60 = 0.65*60 = 39 dollars
-------
A slightly longer method:
35% of 60 = 0.35*60 = 21
You save $21 and the final price is 60-21 = 39 dollars
Earth is about 9. 27 x 107 miles from the Sun. Venus is about 6. 68 x 107 miles
from the Sun. About how much farther from the Sun is Earth than Venus?
Earth is 2.59 x 10⁷ miles farther from the Sun than Venus.
Let us assume that d₁ represents the distance between the earth and the sun.
d₂ represents the distance between the earth and the Venus.
The distance between the earth and the sun is 9.27 x 10⁷ miles.
d₁ = 9.27 x 10⁷ miles
And the distance between the Sun and the Venus is about 6. 68 x 10⁷ miles.
⇒ d₂ = 6. 68 x 10⁷
To find : by how much farther from the Sun is Earth than Venus
We need to find the absolute difference between d₁ and d₂
Let d be the absolute difference between d₁ and d₂
d = |d₁ - d₂|
d = | (9.27 x 10⁷) - (6. 68 x 10⁷ )|
d = |(9.27 - 6.68) x 10⁷ |
d = 2.59 x 10⁷ miles
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Can someone please help me? I need help ASAP
I need to show work btw
Answer:
Step-by-step explanation:
yes the triangle can be formed
The points plotted on the coordinate grid represent the rule y = x + 4. Which table also represents this rule?
Answer:
See below
Step-by-step explanation:
No table was given but it should look something like
x y
-3 1
-2 2
-1 3
0 4
1 5
2 6
3 7
Whatever number you select for x add 4 to it and that will give you your y value
what is (-5x+3)-(-7x7)
Answer: (-5x+3) - (-7x7) = -5x + 3 - (-7x7) = -5x + 3 + 7x7 = 2x7
The expression (-5x+3) - (-7x7) is the result of subtracting two algebraic expressions. When subtracting algebraic expressions, we need to distribute the negative sign to each term before combining like terms.
The first step is to distribute the negative sign to each term in the second expression, (-7x7). This gives us:
(-5x+3) - (-7x7) = -5x+3 + 7x7
Now we can combine the like terms, x7, to get the simplified expression:
-5x+3 + 7x7 = 2x7
So the final answer is 2x7.
Step-by-step explanation:
5. Write the following expression: the product of 10 and 4, taken to the fourth power, minus the quantity of 25 divided by 5.
We can write the given statement as an expression as -
(10 × 4)⁴ - (25/5)
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the mathematical statement as -
" the product of 10 and 4, taken to the fourth power, minus the quantity of 25 divided by 5 ".
We can write the expression as -
(10 × 4)⁴ - (25/5)
Therefore, we can write the given statement as an expression as -
(10 × 4)⁴ - (25/5)
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The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 68%, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
Answer:
Likely
Step-by-step explanation:
68% is more than 2/3, so the event is likely to occur.
Answer: Likely
3/5=?/10=33/?
Complete the empty places
The values in the empty places are 0.6 and 3.3 respectively.
What is division and multiplication?Multiplication is the process of adding a number repeatedly. When m is multiplied by n, m is being added to itself n times in total. The multiplication sign is "." A way to divide or distribute a number into equal parts is by division. The two key arithmetic operations in mathematics are multiplication and division. Similar to addition and subtraction, the processes of multiplication and division are intimately tied to one another. All real numbers are subjected to these processes.
The value of 3/5 can be calculated by dividing the numerator and the denominator.
3/5 = 0.6
The given expression is:
10 = 33/ x
Isolate the value of x:
10x = 33
x = 33/10
x =3.3
Hence, the values in the empty places are 0.6 and 3.3 respectively.
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Plss help 20 points!
Average price is the mean price of an asset or security observed over some period of time.
Define average price in gas?
Weighted Average Gas Price means the total payment made by the Buyer to the Seller for Seller's Gas delivered in a month divided by the total MMBtu of Seller's Gas delivered for that month.In basic mathematics, average price is a representative measure of a range of prices. It is calculated by taking the sum of the values and dividing it by the number of prices being examined.Get the miles traveled from the trip odometer, or subtract the original odometer reading from the new one.Divide the miles traveled by the amount of gallons it took to refill the tank. The result will be your car's average miles per gallon yield for that driving period.To learn more about average refers to:
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Find the area of a circle with diameter, d = 8.6m. Give your answer rounded to 1 DP.
Answer:
58.1 m²
Step-by-step explanation:
d = 8.6 m
r = d/2 = 4.3 m
A = πr²
A = 3.14159 × (4.3 m)²
A = 58.1 m²
what is 10% of 125???
Answer: 10% of 125 is 12.5
Answer:12.5
Step-by-step explanation:
Divide 125 by 10%. 125 divided by 10% is 12.5.
4. Please Help ASAP!
Use this balanced reaction to show that you can write the equation that makes chemical sense.
Explain how your symbols were derived in paragraph form..
The simulation provides information about the concept of balancing a chemical equation through visual representation and interactive tasks.
What is your understanding about given chemical reaction?The user is able to balance the equation by adjusting the coefficients of the reactants and products to ensure that the number of atoms of each element is conserved on both sides.It did not have to research outside the simulation for information about balancing a chemical equation. The simulation provides enough information to understand the concept.The simulation can be used to check learning by allowing the user to practice balancing different chemical equations and receive feedback on their work. This helps to reinforce the understanding of the concept and identify any areas where further improvement is needed.In the balanced reaction CO2 + H2O -> C2H6 + O2, the coefficients were derived by ensuring that the number of atoms of each element was conserved on both sides of the equation. This means that the same number of carbon, hydrogen, and oxygen atoms are present in the reactants and products. To balance the equation, the coefficients were adjusted until this condition was met.To show the molecular representations of a balanced reaction, the molecular structures of the reactants and products can be drawn, showing the individual atoms and their connections. In the case of the reaction CO2 + H2O -> C2H6 + O2, the molecular structure of CO2 is a linear arrangement of two oxygen atoms bonded to a carbon atom. The molecular structure of H2O is a bent arrangement of two hydrogen atoms bonded to an oxygen atom. The molecular structure of C2H6 is a hexagonal arrangement of six hydrogen atoms bonded to a carbon atom. The molecular structure of O2 is a linear arrangement of two oxygen atoms bonded to each other. These representations were derived by following the basic principles of chemical bonding and considering the arrangement of atoms in the molecules.
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noah spent 150$ to buy movie tickets for 15 students and 3 adults. Adult tickets cost $4 more than student tickets Use A as the price for an adult price and S for the price of student tickets.
The amounts of each ticket that were purchased are given as follows:
Adult: $11.67.Student: $7.67.How to obtain the amounts?The amounts are obtained using a system of equations, for which the variables are given as follows:
Variable a: number of adult tickets.Variable s: number of student tickets.Noah spent $150 to buy movie tickets for 15 students and 3 adults, hence:
3a + 15s = 150
a + 5s = 50
a = 50 - 5s
Adult tickets cost $4 more than student tickets, hence:
a = 4 + s.
The solution for s is then obtained as follows:
50 - 5s = 4 + s
6s = 46
s = 46/6
s = $7.67.
Then the price of an adult ticket is of:
7.67 + 4 = $11.67.
Missing InformationThe problem asks for the amounts of each ticket that were purchased.
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Alexa was comparing the price of salmon at two stores. The equation � = 11.54 � y=11.54x represents the total cost, in dollars and cents, � y, that it costs for � x pounds of salmon at SuperGrocery B. At SuperGrocery A, 5 pounds of salmon costs $37.10.
The total cost of x pounds of salmon is y = 11.54x at SuperGrocery B and y = 7.42x at SuperGrocery A
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
The slope intercept form of linear equation is:
y = mx + b
Where m is the rate of change and b is the initial value of y
The standard form of a linear equation is:
Ax + By = C
where A, B and C are constants.
Let y represent the costs for x pounds of salmon.
At the Super Grocery B:
y = 11.54x
At Super Grocery A, 5 pounds of salmon costs $37.10, hence:
y = (37.10/5)x
y = 7.42x
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Fiona wants to earn at least $100 this week. She makes $11 an hour babysitting. Choose the inequality that shows the number of hours Fiona needs to babysit in order to reach her goal.
h≥11
h>9
h>8
h≥9
The inequality that shows the number of hours Fiona needs to babysit in order to reach her goal is h>9.
What is inequality?
The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.
Given that,
Fiona wants to earn at least [tex]\$[/tex]100
She makes [tex]\$[/tex]11/hour
in order to reach her goal = 100/11 = [tex]\$[/tex]9.09 .
The inequality that shows the number of hours Fiona needs to babysit in order to reach her goal is h>9.
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Write the equation of each line given the y-intercept and x-
The equation of each line given the y-intercept and x-intercept
5 and -4 is 4y- 20 = 5x.
The line has an x-intercept at x = -4 and y intercept at y = 5 this means that the line passes through the points(,0) and(,5).
Now we find the pitch m of the line passing through the points(,0) and(,5)(x-intercept).
The pitch of the line is
m = y2- y1/ x2- x1
= 5- 0/ 0-(- 4)
= 5/ 4
Point- pitch Formula y = m(x-x1)
where m is the pitch and( x, y) is the given point.
Now substituting the values
y- 0 = (5/4)( x-(- 4))
y = (5/4)( x 4)
4y- 20 = 5x
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The complete question :
Find the equation of the line that has an y intercept and x-intercept at
5 and -4.
10. Hamal has a new part-time job bagging groceries after school. The 2 po equation y = 10x + 50 shows the relationship between his hours of work (x) and the amount of money in his bank account (y). How much money did he have in his bank account before he started working?*
If the relationship between his hours of work (x) and the amount of money in his bank account (y) is represented by equation "y = 10x + 50" , then the money did he have in his bank account before he started working is $50 .
The equation y = 10x + 50 shows the relationship between Hamal's hours of work (x) and the amount of money in his bank account (y).
When x = 0, the equation becomes y = 10(0) + 50, which simplifies to y = 50. So when Hamal has not worked any hours, he has $50 in his bank account.
In other words, the y-intercept of the equation is 50, which represent the amount of money Hamal had in his bank account before he started working.
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to own and operate a home printer it costs $100 for the printer and additional $0.05 per page for ink
let p represent the number of pages let t represent the total costs
A,write an equation to represent each printing scenario Y=mx+b
The equation that represents each printing scenario will be t = 0.05p + 100.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Owning and operating a home printer costs $100 for the printer and an additional $0.05 per page for ink.
Let 'p' represent the number of pages and 't' represent the total costs. Then the equation is given as,
t = 0.05p + 100
The equation that represents each printing scenario will be t = 0.05p + 100.
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A home improvement store sells lumber by the foot. It costs $24 to buy 8 feet of lumber.
Fill in the table.
Answer:
The price per foot is $3
Step-by-step explanation:
The order for the answers on the chart are 3, 4, 72, 40.
Mateo has 8 liters of punch for a party. Each glass holds 1/5
liter of punch.
How many glasses can Mateo fill with punch?
amswer in simplest from fraction
Mateo can fill 40 glasses with punch and this can be calculated as :
8 liters = 8 x (5/1) = 40 liters
By solving the above equation following will be obtained.
Therefore, Mateo can fill 40 glasses with punch.
Mathematics, where the numerator and denominator are divided. Each is an integer in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.
If numerator value is less than the denominator value, it is a proper fraction.If a numerator value is greater than denominator value, then it is called an improper fraction.
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incoming calls to a customer service center are classified as complaints (73% of calls) or requests for information (27% of calls). of the complaints, 40% deal with computer equipment that does not respond and 57% deal with incomplete software installation; in the remaining 3% of complaints, the user has improperly followed the installation instructions. the requests for information are evenly divided on technical questions (50%) and requests to purchase more products (50%). round your answers to four decimal places (e.g. 0.9876). (a) what is the probability that an incoming call to the customer service center will be from a customer who has not followed installation instructions properly? enter your answer in accordance to the item a) of the question statement (b) find the probability that an incoming call is a request for purchasing more products. enter your answer in accordance to the item b) of the question statement statistical tables and charts
The probability of that an incoming call to the service centre is 0.0219. And the probability that an incoming call is a request for purchasing more products is 0.135.
Probability of an event gives the possibility of an event which is never greater than 1 and the probability of impossible event is 0 and the probability of sure event is 1.
Probability = number of favourable cases/ total number of outcomes
a) The probability that an incoming call to the customer service = Probability of incoming calls to the service centre * probability of remaining number of calls in the centre = 0.73* 0.03 = 0.0219.
b) the probability that an incoming call is a request for purchasing more products = Probability of request of calls in the service centre * probability of request of purchase. = 0.5 * 0.27 = 0.135.
Hence, the probability that incoming call to the service is 0.0219 and of the request of purchase is 0.135.
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4. The two trapezoids below are similar. What
is the length of segment EF?
24 am
A
D
30 cm
B
C
G.
7.5 cm
X
E
H
Help please
The length of the segment EF for the given trapezoids is 6 cm.
How do trapezoids work?Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided shape.
An opposing set of sides are parallel. The four angles of a trapezium add up to 360 degrees, and their diagonals cut each other in half. It has four odd-numbered sides. Thus, the opposing sides of an isosceles trapezium are congruent, as well as the diagonals.
Trapezoids ABCD and EFGH are similar,
Hence, corresponding sides ratio are equal:
Thus, AB/EF = DC/HG
24/x = 30/7.5
30x = 180
x = 180/30
x= 6
Hence, the length of the segment EF is 6 cm.
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C is the circumcenter of isosceles triangle ABD with vertex angle ∠ABD. Does the following proof correctly justify that triangles ABE and DBE are congruent? It is given that triangle ABD is an isosceles triangle, so segments AB and DB are congruent by the definition of isosceles triangle. It is given that C is the circumcenter of triangle ABD, making segment BE a median. By the definition of perpendicular, angles AEB and DEB are 90°, so triangles ABE and DEB are right triangles. Triangles ABE and DEB share side BE making it congruent to itself by the reflexive property. Triangles ABE and DBE are congruent by HL
The incenter is where a triangle's angle bisectors meet. Since C is the incenter, segment BC should be the angle bisector. So, there is an error in line 3; segment AB and BC are congruent.
Any triangle with any 2 sides that are the same length is defined as an isosceles triangle. An isosceles triangle has two equal-sized angles that are opposite from one other and have equal sides.
If all three angles of the three triangles are acute, the circumcenter of an isosceles triangle sits inside the triangle. The circumcircle's chords are the sides of the triangle. In this case, the circumcenter is outside of the triangle since one of the angles is 90 degrees.
The circumcenter of a triangle ABC is the location where the perpendicular bisectors of its sides cross.
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The complete question is given below:
Help me with simplified expressions of a side length of a triangle, please!
Answer:
2w³ +w
Step-by-step explanation:
Given expressions for the sides of a triangle, (-10w³+w) and (4w³-3w), and for the perimeter, (-4w³-w), you want an expression for the third side.
PerimeterThe perimeter is the sum of the side lengths. This relation can be used to find the length of the third side:
Perimeter = side 1 + side 2 + side 3
-4w³ -w = (-10w³ +w) +(4w³ -3w) +side 3
-4w³ -w = -6w³ -2w + side 3 . . . . . . collect terms
side 3 = (-4w³ -w) -(-6w³ -2w) . . . . . . . subtract (-6w³ -2w)
side 3 = 2w³ +w . . . . . . . . . . . . . . . . collect terms
The table shows the costs of movie tickets and large bags of popcorn for two groups of people.
a. Can you determine how much each ticket costs? Explain.
b. A third group buys 5 tickets and 4 large bags of popcorn for $82. How much more does a ticket cost than a large bag of popcorn?
According to the unitary method,
(a) Ticket cost for 5 people is $28.75
(b) The cost for ticket is $28.75 and the cost for popcorn is $53.25
In math the term called unitary method is defined as a basic concept to find the value of a single unit and then using that value to find the value of multiple units.
Here we have know that each person in a group buys a movie ticket, a drink, and a popcorn.
And the cost for each of the product is listed as Ticket is $5.75, Drink is $2.00 and Popcorn is $3.25.
Then the cost of 5 people is calculated as,
=> 5.75 x 5
=> 28.75
And the third group buys 5 tickets and 4 large bags of popcorn for $82.
Then the cost of the ticket is calculated as,
=> 82 - 28.75
=> 53.25
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