The length of the room are y2 – 5y = 750 , y(y – 5) + 750 = 0 and (y + 25)(y – 30) = 0
How to determine the expressionit is important to note that the formula for calculating the area of a rectangle is expressed as;
A = lw
Such that;
A is the area of the rectanglel is the length of the rectanglew is the width of the rectangleFrom the information given, we have that;
Length = y
Width = y - 5
Area = 750 square feet
Substitute the values into the formula
750 =y(y - 5)
expand the bracket
750 = y² - 5y
y² - 5y- 750 = 0
This is factorized to give;
(y + 250 (y - 30)
Hence, the expression is y² - 5y- 750 = 0
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Choose all that are correct. Refer to image.
The apothem of a regular pentagon exists [tex]$4.6797 \mathrm{~cm}$[/tex], and the perimeter exists [tex]$34 \mathrm{~cm}$[/tex]. The area equals [tex]$79.55 \mathrm{~cm}^2$[/tex].
What is meant by regular pentagon?It is a regular pentagon if all of its sides and angles are equal in size. It is not normal if not. Each angle inside the regular pentagon is 108°, while each angle outside is 72°. There are 5 equal sides in an equilateral pentagon.
Five congruent sides (sides of identical length), five congruent inner angles (each measuring 108°), and five congruent outer angles of 72° are necessary for a regular pentagon to exist.
If a polygon's sides and angles are equal, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a regular quadrilateral is a square.
Therefore, the correct answer is option c) The apothem of a regular pentagon is [tex]$4.6797 \mathrm{~cm}$[/tex], and the perimeter is [tex]$34 \mathrm{~cm}$[/tex]. The area equals [tex]$79.55 \mathrm{~cm}^2$[/tex].
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Explain why the value of 0.6 is greater than the value of 0.39.
A 0.39 is greater than 0.6 because 9 hundredths is greater than 6 tenths.
B 0.39 is less than 0.6 because 3 tenths is less than 6 tenths.
C 0.6 is greater than 0.39 because 6 tenths is greater than 9 hundredths.
D 0.6 is less than 0.39 because 6 tenths is less than 9 hundredths.
The value of 0.6 is greater than the value of 0.39 because; C 0.6 is greater than 0.39 because 6 tenths is greater than 9 hundredths.
How to evaluate decimal number digits?When we are talking about decimals, the left hand side before the decimal are referred to as whole numbers while the first digit after the decimal represents the tenths place, the next digit after the tenths place represents the hundredths place, the next digit after the hundredths place represents the thousandths place and so on.
Now, we are given two decimals 0.6 and 0.39.
We see clearly that 0.6 has a greater tenths digit than the hundredths digit in 0.39. This is seen as;
0.6 = 6/10 while 0.39 = 39/100
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Help. WILL GIVE BRAINLIEST!!!!
This suggests that the translation vector [tex]$\mathbf{t}$[/tex] has a component of -1 in the y-direction. Therefore, we have:
t=(3,−1)
How to find translation vector?To find the translation vector that maps quadrilateral ABCD to quadrilateral $A"B"C"D"$, we can subtract the coordinates of corresponding vertices. Let $\mathbf{t}$ be the translation vector. Then:
[tex]$$ \begin{align*}\\\mathbf{A}" - \mathbf{A} &= \langle -3 - t_x, -3 - t_y \rangle - \langle -3, -2 \rangle \\\&= \langle -3 - t_x + 3, -3 - t_y + 3 \rangle \\\&= \langle -t_x, -t_y \rangle\end{align*} $$[/tex]
Similarly, we have:
[tex]$$ \begin{align*}\mathbf{B}" - \mathbf{B} &= \langle 0 - t_x, -1 - t_y \rangle - \langle 0, -2 \rangle \\\&= \langle -t_x, 1 - t_y \rangle \\\\\\mathbf{C}" - \mathbf{C} &= \langle 1 - t_x, -3 - t_y \rangle - \langle 1, 0 \rangle \\\&= \langle -t_x, -3 - t_y \rangle\end{align*}[/tex]Since [tex]$\mathbf{D}"$[/tex] is not given, we cannot use it to solve for the components of [tex]$\mathbf{t}$[/tex]. However, note that the x-coordinate of [tex]$\mathbf{A}"$[/tex] is -3, which is 3 less than the x-coordinate of [tex]$\mathbf{A}$[/tex]. This suggests that the translation vector [tex]$\mathbf{t}$[/tex] has a component of 3 in the x-direction. Similarly, the y-coordinate of [tex]$\mathbf{B}"$[/tex] is -1, which is 1 more than the y-coordinate of [tex]$\mathbf{B}$[/tex]. This suggests that the translation vector [tex]$\mathbf{t}$[/tex] has a component of -1 in the y-direction. Therefore, we have:
t=(3,−1)
which means that the correct answer is [tex]$\boxed{\langle 3, -1 \rangle}$[/tex]
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Samuel buys 3 bottles of juice that each have an original price of 2.80. He uses a coupon for 35% off. Then, he is changed sales tax at a rate of 6.5%. How much does samuel pay 3 bottles of juice?
Samuel pay 5.81 for the 3 bottles of juice.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
Samuel buys 3 bottles of juice that each have an original price of 2.80.
And, He uses a coupon for 35% off. Then, he is changed sales tax at a rate of 6.5%.
Here, The original cost of 3 bottles of juice = 3 × 2.80
= 8.40
Now, He uses a coupon for 35% off.
Hence, The off price = 35% of 8.40
= 35/100 × 8.40
= 2.94
So, The amount of 3 bottles of juice = 8.40 - 2.94
= 5.46
And, He is changed sales tax at a rate of 6.5%.
Thus, The sales tax on bottles = 6.5% of 5.46
= 6.5/100 × 5.46
= 0.35
Thus, The actual amount of 3 bottles of juice = 5.46 + 0.35
= 5.81
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Which are solutions of the equation 4x2 – 7x = 3x + 24? Check all that apply
Answer:
x=5/2 and x=0
Step-by-step explanation:
To solve this equation, we first need to get all the terms on one side of the equation by subtracting 3x from both sides:
4x^2 - 7x - 3x = 24
Simplifying, we get:
4x^2 - 10x = 24
Now, we can factor out the GCF (Greatest common factor) on the left side of the equation:
2x(2x-5) = 24
Now we can divide both sides of the equation by 2x(2x-5) to get the solutions for x:
x = 5/2 , x = 0
So the solutions of the equation 4x^2 - 7x = 3x + 24 are x=5/2 and x=0
3. The graph of a polynomial function f is shown. Select all the true statements about
the polynomial.
-4 -3 +2
YA
12
9
6
3
1
2 B
-6
-9
-12
-15
A. The degree of the polynomial is even.
B. The degree of the polynomial is odd.
C. The leading coefficient is positive.
D. The leading coefficient is negative.
E. The constant term of the polynomial is positive.
F. The constant term of the polynomial is negative.
4
After inspecting the graph, when x=0 y is 6 so the constant is +6 which is Positive
What is polynomial function ?
A polynomial characteristic is a function that includes handiest non-bad integer powers or simplest tremendous integer exponents of a variable in an equation like the quadratic equation, cubic equation, and so forth. for example, 2x+5 is a polynomial that has exponent same to one.
Given ,
The graph is a polynomial function.
This is an odd degree polynomial since end behavior is +infinitely when x is positive and -infinity when x is negative
For an even degree polynomial en behavior will be positive regardless of the sign as a negative number raised to an even power is always positive
The leading coefficient is positive other wise the function would be flipped around the x axis
Inspect the graph. when x=0 y is 6 so the constant is +6 which is Positive
Hence , After inspecting the graph, when x=0 y is 6 so the constant is +6 which is Positive
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Given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8, select the statement that could be true for g.
The only option that is true for the function g is; Option D: g(3) = 18
How to interpret the domain and range of a function?The function, g, has;
Domain; -1 ≤ x ≤ 4
Range: 0 ≤ g(x) ≤ 18
g(-1) = 2 and g(2) = 8
Then the following properties must hold to be true;
The value(s) of x must be between -1 and 4
The values of g(x) must be between 0 and 18.
We consider the options and state why they are true or otherwise.
Option A: g(5) = 12
When x = 5, g(5) = 12. This contradicts property 1 stated above and as such it is not true.
Option B: g(1) = -2
When x = 1, g(x) = -2. This contradicts property 2 stated above and as such, it is not true.
Option C: g(2) = 4
When x = 2, g(2) = 4. However by property 4 stated above, g(2)=9. Therefore, we can say that it is not true.
Option D: g(3) = 18
When x =3 means that its domain lies between -1 and 4 and its range lies between 0 and 18.
Therefore, Option D is true.
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The missing options are;
A) g(5)=12
B) g(1) = -2
C) g(2) = 4
D) g(3) = 18
if johnny has 23 candy and casey have only 3 candy how many times of 3 candy do we need to add more to 23 and try it
We would need to add 8 more sets of 3 candies to 23 candies in order to have the same amount as Casey.
To find this, we can divide the total amount of candy Johnny has (23) by the amount of candy Casey has (3) and round up to the nearest whole number:
(23) / (3) = 7.666...
Since we can't have a fraction of a set of candies, we must round up to the nearest whole number, which is 8.
So, to have the same amount of candy as Casey, we would need to add 8 more sets of 3 candies to Johnny's 23 candies.
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PLSSS HELP IF YOU TURLY KNOW THISSS
Answer: x=10
Step-by-step explanation:
x is an unknown number trying to figure out what number equals 20? You subtract 10 from 20 to figure out x.
when
�
=
1
p=1p, equals, 1 and
�
=
7
q=7q, equals, 7
The resultant answer of the given equation 7 – 5p + 3q is 23.
What are equations?A math formula is a formula that uses the equal sign to represent the equivalence of two expressions.
The meanings of the word equation and its cognates in various languages can vary slightly.
For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.
by inserting the provided values, we must determine the value of the given equation.
The result is obtained by changing the values of p and q in the above equation.
Thus, if p = 1 and q = 7.
So, we get the equation: 7 – 5p + 3q
Calculate as follows:
7 – 5(1) + 3(7)
7 – 5 + 21
28 – 5
23
Therefore, the resultant answer of the given equation 7 – 5p + 3q is 23.
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Correct question:
Evaluate 7-5{p}+3q7−5p+3q7, minus, 5, p, plus, 3, q when p=1p=1p, equals, 1 and q=7q=7q, equal, 7.
a personnel director for a corporation has hired ten new engineers. if three (distinctly different) positions are open at a cleveland plant, in how many ways can she fill the positions?
There are 720 ways that personnel director for a corporation fills the positions
What is permutation?It is the ordered arrangement of members belonging to a set with no repeats.
To solve this problem the formula and the permutation procedure we must use is:
nPr = n! / (n-r)!
Where:
nPr = permutationn = total number of objectsr = number of selected objects! = factorial of the numberInformation about the problem:
n = 10r = 3Applying the permutation formula we have:
nPr = n! / (n-r)!
10P3 = 10! / (10-3)!
10P3 = 10! / 7!
10P3 = 10*9*8*7! / 7!
10P3 = 10*9*8
10P3= 720
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accidents on highways are one of the main causes of death or injury in developing countries and the weather conditions have an impact on the rates of death and injury. in foggy, rainy, and sunny conditions, 1/6, 1/9, and 1/23 of the accidents result in death, respectively. sunny conditions occur 58% of the time, while rainy and foggy conditions each occur 21% of the time. given that an accident without deaths occurred, what is the conditional probability that it was foggy at the time? round your answer to three decimal places (e.g. 0.987). p
The probability that a death will result from an accident is 0.105, or 10.5%.
Given:
In foggy conditions, 25% of accidents result in fatalities.
Rain-related accidents result in fatalities in 12.5% of cases.
In sunny weather, 5% of accidents result in fatalities.
To find : The probability that a death will result from an accidents
The likelihood that a death will ensue from an accident
5% of 60%(sunny) (sunny)
25% of 20%(foggy) (foggy)
12.5% of 20%(rainy) (rainy)
Probability = 0.05 x 0.6 x 0.25 x 0.125 x 0.22
Chance is 0.105
Chance is 10.5%.
There is a 10.5% chance that a fatal accident may occur.
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ANAGNOS: Possible. I should warn you, she is much given to tantrums.
ANNIE: Means something is inside. Well, so am I, if I believe all I hear. Maybe you should warn them.
ANAGNOS [FROWNS]: Annie. I wrote them no word of your history. You will find yourself among strangers now, who know nothing of it.
ANNIE: Well, we’ll keep them in a state of blessed ignorance.
Which statement best describes Annie’s attitude toward her upcoming assignment in this excerpt?
The statement that best describes Annie’s attitude toward her upcoming assignment in this excerpt is "she is studious and eager to share her knowledge"
What is the main message of Annie?Annie is all about maintaining optimism and hope throughout life's journey, no matter the circumstances.
The young orphan Annie has led a difficult life in the cruel matriarch Miss Agatha Hannigan's anything-but-cheerful orphanage. With a shattered necklace, she stealthily leaves her orphanage and goes in search of her parents, who she hopes would adopt her.
She may be the offspring of a Marleyan and an Eldian liaison, and her parents abandoned her when she was a baby. But after being transported to the Internment Zone, a guy took her up and started to train her as a warrior so that he could live better in Marley.
Therefore, Annie is studious and eager to share her knowledge.
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5. Ken will flip a fair coin and then randomly choose one of three colored cards. The
possible outcomes are shown below.
Heads
Red
Blue
Green
Red
Blue
Green
What is the probability that tails will turn up and that he will choose a red card?
Tails
The probability that tails will turn up and that he will choose a red card is 1/6.
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
The probability of choosing a tail is 0.5.
The probability of choosing ref card is 1/3.
Therefore, the probability will be:
= 1/2 × 1/3
= 1/6
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Joy can choose to ride the bus,subway,or take a taxi on monday and tuesday which list show the possible outcomes of day one method of travel
A list that shows the possible outcomes of one day one method of travel:
Monday, bus,
Monday, subway,
Monday, taxi,
Tuesday, bus,
Tuesday, subway,
Tuesday, taxi
The correct answer is an option (B)
Let A represents the set of days.
A = {Monday, Tuesday}
And set B represents the method of transportaion/travel.
B = {bus, subway, taxi }
To find the list of possible outcomes of one day one method of travel we find the product of set A and set B.
We know that for non-empty sets A and B the Cartesian Product is given by AxB = {(a,b) | a ∈ A and b ∈ B}.
It is a set of all ordered pairs (a, b)
For above sets A and B,
A × B = {(Monday, bus), (Monday, subway), (Monday, taxi), (Tuesday, bus), (Tuesday, subway), (Tuesday, taxi)}
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Find the complete question below.
what is the solution to the equation 7.5z-2=8.5.
Answer:
z=1.4
Step-by-step explanation:
honestly, I'm not that smart so i just looked it up.
but Im pretty sure thats the right answer.
A farmer's conveyor belt carries bales of hay from the ground to the barn loft. The conveyor belt moves at 100 ft/min.
Q1:How many Second does it take for a bale of hay to go from the ground to the barn loft?
Q2:Which part of a right triangle does the conveyor belt represent?
Q3:You know the speed. What other information do you need to find time?
Q4:How are minutes and seconds related?
Answer for the conveyer belt moves at 100ft/min from bales of hay to barn loft is given by :
1. Seconds taken by conveyer belt is 60 seconds.
2. Hypotenuse represents the conveyer belt in right triangle.
3. Distance is other information to calculate time.
4. 1 minute = 60 seconds.
Rate at which conveyer belts moves = 100ft/min
⇒1 minute = 100ft
⇒60seconds = 100 ft
1. Seconds taken by bale of hay to move from ground to barn loft is 60 seconds.
2. Conveyer felt represent the hypotenuse of the right triangle.
Feet represents the height , and minutes (time) represents the base.
3. Speed is given to us , to calculate time we should have distance.
4. Relation between minutes and seconds is given by:
1 minute = 60 seconds.
Therefore, for the given conveyer belt moves with 100ft/min answer of the following question are:
1. Seconds taken by moving bale of hay to barn loft is 60 seconds.
2. Conveyer belt represent hypotenuse.
3. To calculate time we need distance apart from speed.
4. One minute is equal to sixty seconds.
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1/2+1/3w=1/6
Please help it’s urgent
Answer:
See below
Step-by-step explanation:
1/2 + 1/3 w = 1/6 subtract 1/2 from both sides of the equation
1/3 w = - 2/6 multiply both sides by 3
w = -1
5x+y =9
10x - 7y = -18
Find X and Y.
Answer:
x=1, y=4
Step-by-step explanation:
5x+y=9
10x-7y=-18
(Multiply top equation by -2)
-10x-2y=-18
10x-7y=-18
(Add)
-9y=-36
(Divide -36 by -9)
y=4
(Substitute y(4) into the top equation)
5x+4=9
(Subtract 4)
5x=5
(Divide 5)
x=1
Answer: x=1 , y=4
Step-by-step explanation:
5x+y =9 y=9-5x
10x - 7y = -18
10x-7(9-5x)=-18 y=9-5x
10x-63+35x=-18 y=9-5(1)
45x-63=-18 y=4
45x=-18+63
45x=45
x=1
Find the annual interest rate I= 20$ P=1000 t= 4 months
keeping in mind that since a year is 12 months, then 4 months is really 4/12 of a year, so
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 20\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{4}{12}\dotfill &\frac{1}{3} \end{cases} \\\\\\ 20 = (1000)(\frac{r}{100})(\frac{1}{3})\implies 20=\cfrac{1000r}{300} \implies 6000=1000r \\\\\\ \cfrac{6000}{1000}=r\implies \stackrel{\%}{6}=r[/tex]
a survey among tenants of shared apartments asked each tenant what percentage of the cleaning around the apartment he or she does. the survey found that aggregating the percentages for each apartment produces an average of much more than 100%. this result may be due to what bias?
The result of an average of more than 100% in a survey of tenants on cleaning chores in shared apartments is likely due to social desirability bias.
The average tenant response of more than 100% in a study about cleaning duties in shared apartments is probably the product of social desirability bias. Social desirability bias occurs when respondents give answers that they think are socially acceptable or desirable, rather than their true opinions or behavior.
In this case, tenants may have overstated their contribution to cleaning the apartment, in order to appear more helpful or responsible, leading to an average percentage higher than 100%.
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annalise works out with a treadmill program that varies the amount of time she runs and walks she has the treadmill set to a walking speed of 15 minutes per mile and a running speed of 9 minutes per mile. The amount of time running and walking can be different for every workout, but she always does a total of 6 miles. (a) suppose that one day, Annalise only walks. How much time would she spend on the treadmill. show your work or explain your answer. (c) write three other combinations for running and walking rimes would she spend on the treadmill. (d) on the graph below, plot the running and walking combinations you determined in parts a, b, and c.
The graph would be a line, where the x-axis represents the distance in miles running, and the y-axis represents the time spent on the treadmill. The points on the graph would be (0,90), (2,78), (4,66), (3,72).
How to solve the problem?(a) If Annalise only walks on the treadmill, she would spend 15 minutes per mile walking. Since she does a total of 6 miles, she would spend 15 minutes/mile * 6 miles = 90 minutes on the treadmill.
(c) Here are three other combinations for running and walking times on the treadmill:
2 miles running and 4 miles walking: 2 miles * 9 minutes/mile running + 4 miles * 15 minutes/mile walking = 18 minutes + 60 minutes = 78 minutes
4 miles running and 2 miles walking: 4 miles * 9 minutes/mile running + 2 miles * 15 minutes/mile walking = 36 minutes + 30 minutes = 66 minutes
3 miles running and 3 miles walking: 3 miles * 9 minutes/mile running + 3 miles * 15 minutes/mile walking = 27 minutes + 45 minutes = 72 minutes
(d) The graph would be a line, where the x-axis represents the distance in miles running, and the y-axis represents the time spent on the treadmill. The points on the graph would be (0,90), (2,78), (4,66), (3,72).
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Broderick has $420 in his checking account. He made 6 deposits of 35. 50 each. He needs to write 6 checks for 310. 75 each
Broderick needs $610.00 in his account to cover his checks.
We know that the balance Boderick has is $420.
First, we will calculate the total amount of the 6 deposits made by Broderick each of $35.50 deposit as follows -
$35.50 x 6 = $213.00
Hence, the total amount of the 6 deposits made by Broderick is $213.00
Next, we will calculate the total amount of the 4 checks he needs to write-
$310.75 x 4 = $1243.00
Hence, the total amount of the 4 checks that Broderick needs to write is $1243.00
Now we will find the final balance of Broderick's account after all the deposits and check withdrawals. We can do this by adding the total amount of the deposits to his initial balance and subtracting the total amount of the checks as follows-
$420.00 + $213.00 - $1243.00 = -$610.00
Thus, Broderick needs $610.00 in his account to cover his checks.
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The complete question is -
Broderick had $420 in his checking account. He made 6 deposits of $35.50 each. He needs to write 4 checks for $310.75 each. How much money does Boderick need to add to his account to cover his checks? Show your work.
Sophia is a student at Windsfall High School.These histograms give information about the number of hours
spent volunteering by each of the students in Sophia's homeroom and by each of the students in the tenth-
grade class at her school.
Number of Students
10
Sophia's Homeroom
0-9 10-19 20-29 30 or
more
Hours Spent Volunteering
Number of Students
70
222882
60
50
10
Tenth-Grade Class at
Windsfall High School
0-9 10-19 20-28 30 or
more
Hours Spent Volunteering
Compare the medians of the data in the histograms.
The median of the number of hours spent volunteering by each student in Sophia's homeroom is more than the median
of the number of hours spent volunteering by each student in the tenth-grade class
O The median of the number of hours spent volunteering by each student in Sophia's homeroom is less than the median of
the number of hours spent volunteering by each student in the tenth-grade class
The median of the number of hours spent volunteering by each student in Sophia's homeroom is same as the median of
the number of hours spent volunteering by each student in the tenth-grade class
O No sufficient data to compare median
The correct option regarding the median of each data-set is given as follows:
The median of the number of hours spent volunteering by each student in Sophia's homeroom is less than the median of the number of hours spent volunteering by each student in the tenth-grade class.
How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.
For Sophia's Homeroom, the total number of students is given as follows:
4 + 9 + 3 + 7 = 23.
Hence the median is the 12th element, which is on the interval 10-19.
For the Tenth Grade class, the total number of students is given as follows:
42 + 38 + 65 + 40 = 185.
Hence the median is the element at the position (185 + 1)/2 = 93, which is on the interval 20-29.
Hence the median is the 12th element, which is on the interval 10-19.
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if the earth's spin axis were perpendicular to the earth's orbital plane (the ecliptic plane), then the seasons and seasonal variation would be
The correct answer is Non-existent. If the Earth's spin axis were perpendicular to the Earth's orbital plane, the seasons and seasonal variation would be greatly reduced or eliminated.
This is because the tilt of the Earth's axis (currently at 23.5 degrees) causes the change in the amount of sunlight received at different latitudes during the year, leading to the seasons we experience.
After all, it causes our seasons in the first place. If the Earth's axis were vertical to its orbital airplane, there would be no seasons. Still, there would be minor variations in temperatures and rush throughout each time as Earth moves slightly closer and further down from the sun If the earth and ringed in an upright position around the sun.
If the Earth's spin axis were perpendicular to the ecliptic plane, the Northern and Southern hemispheres would receive roughly the same amount of sunlight throughout the year, and there would be little temperature variation, thus leading to little or no seasonal changes.
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The right response is Nonexistent. Seasons and seasonal fluctuation would be significantly diminished or completely gone if the Earth's spin axis were parallel to its orbital plane.
This is so that the seasons we experience may be attributed to the tilt of the Earth's axis, which is now 23.5 degrees, which affects the quantity of sunlight received at various latitudes throughout the year.
After all, it is the primary cause of our seasons. Seasons wouldn't exist if the Earth's axis were vertical to its orbital plane. If the earth were circled in an upright position around the sun, there would still be modest fluctuations in temperature and rush throughout each period as Earth travels a little closer to and further away from the sun.
The Northern and Southern hemispheres would get nearly the same amount of sunshine throughout the year, and there would be no temperature difference, which would result in little to no seasonal variations if the Earth's spin axis were perpendicular to the ecliptic plane.
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What is the value of 4.3x10^5
Which of the following graphs has a slope of negative three halves and a y-intercept of 3?
graph of a line passing through the points 0 comma 2 and 3 comma 0
graph of a line passing through the points 0 comma 2 and 2 comma negative 1
graph of a line passing through the points 0 comma 3 and 2 comma 0
graph of a line passing through the points 0 comma 3 and 3 comma 1
The line y = -3/2(x) + 3 has a slope of negative three halves and a y-intercept of 3.
The correct option is C.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given:
We have a graph that has a slope of negative three halves and a y-intercept of 3.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂),
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁).
A). Line passing through the points (0, 2) and (3, 0).
y - 2 = 2/3(x)
y = 2/3(x) + 2.
This is not a required line.
B). Line passing through the points (0, 2) and (2, -1).
y - 2 = -3/2(x)
y = -3/2(x) + 2.
This is not a required line.
C). Line passing through the points (0, 3) and (2, 0).
y - 3 = -3/2(x)
y = -3/2(x) + 3.
This is a required line.
D). Line passing through the points (0, 3) and (3, 1).
y - 3 = -2/3(x)
y = -2/3(x) + 3.
This is not a required line.
Therefore, y = -3/2(x) + 3 is a required line.
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Answer:
The line y = -3/2(x) + 3 has a slope of negative three halves and a y-intercept of 3.
The correct option is C.
Step-by-step explanation:
Please help me w this!!!
Answer:
Step-by-step explanation:
X =90
Whats the answer to my equations.
The equation for the linear function is y=3x -5.
Linear FunctionA linear function can be represented by a linear equation. The standard form for the linear equation is: y= mx+b , for example, y=10x+6.
The standard for the linear equation( y= mx+b), also it is known as the Slope-Intercept Form.
Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given example: m=10 and b=6.
The question gives some points of the linear function, see below.
x y
1 -2
2 1
3 4
4 7
From the given data you can find the slope by solving the system linear equation.
For example, you can write a system linear equation from the points: (1,-2) and (4,7).
-2=m+b (1)
7=4m+b (2)
Multiplying equation 1 by -1, you have
2= -m -b (1)
7= 4m+b (2)
Summing the previous equation, you can find the slope (m):
9=3m
m= 9/3
m= 3
If m=3, from equation 2, you can find the coefficient b.
7 = 4m + b
7 = 4*3 +b
7=12 + b
b= 7-12
b= -5
Thus, the standard form for the linear equation represented by the given table is y=3x -5.
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Pleasee Help !!!!
Given: ∆KLM, KL = LM m∠K = 17°, R = 1. 08 Find: KM
triangle is inside a circle with a midpoint O
From the triangle KLM inside the circle, the value of KM is calculated. And, the value is 1.2079.
A triangle is a polygon made up of three vertices, three angles, and three sides. First, draw a circle with a midpoint represented by O. Then, draw a triangle KLM inside a circle. Now, construct the line segments KO, MO, and LO because they form the circle's radius.
Given that KL = LM. Since two sides of the triangle KLM is equal, it is an isosceles triangle. Also, ∠K=∠M=17°. The total angle of this triangle is 180°. Then, ∠L=180°-17°-17°=146°.
Half the angle L is 73°. Then, ∠KLO=∠MLO=73°.
Consider triangle KLO, this triangle is also isosceles because KO = LO. Then, ∠KLO=∠OKL=73°.
Now, ∠KOL is calculated as follows from the triangle KLO,
[tex]\begin{aligned}\angle KOL&=180^{\circ}-73^{\circ}-73^{\circ}\\&=34^{\circ}\end{aligned}[/tex]
Similarly, consider triangle MLO, this triangle is also isosceles because LO=MO. Then, ∠MLO=∠OML=73°.
Now, ∠LOM is calculated as follows from the triangle MLO,
[tex]\begin{aligned}\angle LOM&=180^{\circ}-73^{\circ}-73^{\circ}\\&=34^{\circ}\end{aligned}[/tex]
Then,
[tex]\begin{aligned}\angle KOM&=\angle KOL+\angle LOM\\&=34^{\circ}+34^{\circ}\\&=68^{\circ}\end{aligned}[/tex]
Using, the cosine law of the triangle KOM, we get,
[tex]\begin{aligned}(KM)^2&=1.08^2+1.08^2-2(1.08)(1.08)\cos 68^{\circ}\\&=2.3328-2.3328(\cos 68^{\circ})\\&=2.3328(1-\cos 68^{\circ})\\&=2.3328(0.6254)\\&=1.4589\\KM&=\sqrt{1.4589}\\&=1.2079\end{aligned}[/tex]
Therefore, the required answer is 1.2079.
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