Answer:
8
Step-by-step explanation:
8*25=2.00
2.00+.90=2.90
The box plots show Theo’s math scores and language arts scores.
Math
2 box plots. The number line goes from 50 to 100. For math, the whiskers range from 55 to 90, and the box ranges from 60 to 85. A line divides the box at 80. For language arts, the whiskers range from 50 to 90, and the box ranges from 60 to 80. A line divides the box at 70.
Language Arts
About 50% of Theo’s scores are in which range for each subject?
Based on the upper and lower quartiles of the box plots:
Range for Maths is 60 to 85
Range for Language arts is 60 to 80.
What is the Upper Quartile and the Lower Quartile?In a box plot, the about half of the data set lies between the upper quartile and the lower quartile which are represented at the beginning and the end of the edges of the box respectively. This makes up 50% of a data distribution.
Thus, for Maths, the Upper and lower quartiles are between 60 to 85, hike that for Language arts are between 60 to 80.
Therefore, 50% of Theos scores for Maths ranges from: 60 to 85, while for Language arts is: 60 to 80.
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what is the missing pattern 7, 11, 2, 18, -7
The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].
What is the missing element in a sequence?
A sequence is a set of elements which observes at least a defined rule. In this question we see a sequence which follows this rule:
[tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex] (1)
Now we prove that given expression contains the pattern:
n = 0
7
n = 1
7 + (- 1)² · 2² = 7 + 4 = 11
n = 2
7 + (- 1)² · 2² + (- 1)³ · 3² = 11 - 9 = 2
n = 3
7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² = 2 + 16 = 18
n = 4
7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² + (- 1)⁵ · 5² = 18 - 25 = - 7
The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].
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I will give brainliest to whoever answers!
Answer:
C 34 cm
Step-by-step explanation:
Area = L x W
72 = 8 x W then W = 9
Perimeter = 2 ( L+W) = 2 ( 8+ 9) = 34 cm
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{Area of rectangle: A = wl; whereas \boxed{\textsf a} is \underline{area}, \boxed{\textsf w} is \underline{width}, \& \boxed{\textsf{l}} is}\\\large\text{\underline{length}.}[/tex]
[tex]\large\text{a = wl}\\\\\large\text{wl = a}\\\\\large\text{w(8) = 72}\\\\\large\text{8w = 72}\\\\\large\textsf{DIVIDE 8 to BOTH SIDES}\\\\\rm{\dfrac{8w}{8} = \dfrac{72}{8}}\\\\\large\text{SIMPLIFY IT!}\\\\\rm{w = \dfrac{72}{8}}\\\\\rm{w = 9}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{width = \bf 9}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Please Expand the following:
3q(r – 2q)
Answer:
3qr - 6q²
Step-by-step explanation:
3q(r - 2q) ← multiply each term inside the parenthesis by 3q
= 3qr - 6q²
Answer:
3qr – 6q²
Step-by-step explanation:
3q(r – 2q)
E X P A N D I N G :-
3qr – 6q²
The following data represent the high-temperature distribution for a summer month in a city for some of the last 130 years. Treat the data as a population. Complete parts (a) through (c
Temperature Lower Limit Upper Limit Days
50-59 50 59 4
60-69 60 69 316
70-79 70 79 1426
80-89 80 89 1532
90-99 90 99 345
100-109 100 109 7
Answer:
The Mean and Standard deviation for the given data would be as follows:
μ =79.7
б =7.81
Step-by-step explanation:
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Standard deviation is the square root of the arithmetic mean of the squares of deviations of the items from their mean values.
Frequency Distribution
Given that,
Temperature Lower Limit Upper Limit Days([tex]f_{i}[/tex])
50-59 50 59 2
60-69 60 69 313
70-79 70 79 1419
80-89 80 89 1503
90-99 90 99 319
100-109 100 109 9
Average([tex]x_{i\\}[/tex])
[tex]\frac{50+59}{2} = 54.5\\ \\\frac{60+69}{2} = 64.5\\ \\\frac{70+79}{2} = 74.5\\\\\frac{80+89}{2} = 84.5\\ \\\frac{90+99}{2} = 94.5\\ \\\frac{100+109}{2} = 104.5[/tex]
As we know,
Mean (μ) =∑ [tex](x_{i}f_{i})[/tex]/∑[tex]f_{i}[/tex]
= { (54.5 * 2) + (64.5 * 313) +(74.5 * 1419)+(84.5*1503)+(94.5*319) + (104.5*9)/ (2+313+1419+1503+319)
∵ μ = 79.7
As we know,
Standard Deviation:-
[tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}[/tex]
by putting the values, we get
∵ б = 7.81
Hence, μ = 79.7 and б=7.81 are the correct answers.
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How many Identities are there in algebra?
Name them.
Answer:
the technical number depends on what you are including to be algebraic identities.
There are multiple forms of most identities (pos. / neg. and multiple ways of writing the same identity)
generally, you can consider there to be 10
Step-by-step explanation:
algebraic identity: an equality that holds true for any variable values
standard identities:
square of binomial:
(a+b)² = a² +2ab + b²
(a - b)² = a² - 2ab + b²
difference of squares:
(a + b)(a - b) = a² - b²
----
product of two binomials:
(x + a)(x + b) = x² + (a + b)x + ab
square of trinomial:
(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx
(x - y - z)² = x² + y² + z² -2(xy + yz - zx)
cube of binomial:
(x + y)³ = x³ + y³ + 3xy (x + y)
(x - y)³ = x³ + y³ - 3xy (x - y)
(a - b)³ = a³ - 3a²b + 3ab² - b³
sum of cubes:
a³ + b³ = (a + b)(a² - ab + b²)
x³ + y³ = (x + y)(x² - xy + y²)
x³ + y³ = (x - y)(x² + xy + y²)
difference of cubes:
a³ - b³ = (a - b)(a² + ab + b²)
x³ - y³ = (x - y)³ + 3xy(x - y)
--
x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx)
= 1/2 (x + y + z) [(x -y)² + (y - z)² + (z - x)²]
(a + b + c)³ = a³ + b³ + c³ + 3(a + b)(b + c)(c + a)
--
and
if x + y + z = 0, then x³ + y³ + z³ = 3xyz
hope this helps!!
(this took me a while to write; there are also a few complicated identities also that I've left out)
[tex]( {a + b})^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ \\ {a}^{2} - {b}^{2} = (a + b)(a - b) \\ \\ {a + b + c}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca \\ \\ {a + b}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) \\ \\ {a - b}^{3} = {a}^{3} - {b}^{3} - 3ab(a - b) \\ \\ {a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca).[/tex]
square root of the quantity x plus 7 end quantity minus 11 equals 2
An equation is formed when two equal expressions are equated together. The value of x in the equation [√(x+7)]-11=2 is 162.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution for x in the equation [√(x+7)]-11=2 can be solved as,
[tex]\sqrt{x+7}-11=2\\[/tex]
Using the addition property of equality,
[tex]\sqrt{x+7} -11+11= 2+11\\\\\\\sqrt{x+7} = 13[/tex]
Squaring both the sides of the equation,
x + 7 = 169
Using the subtraction property of equality,
x + 7 - 7 = 169 - 7
x = 162
Hence, the value of x in the equation [√(x+7)]-11=2 is 162.
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Solve the equation.
-x+8+3x = x-6
O x=-18
O x=-14
O x = 2
O x = 4
Answer:
x = -14
Step-by-step explanation:
- x + 8 + 3x = x - 6
- x + 8 + 3x - x + 6 = 0
x + 14 = 0
x = -14
Evaluate the function f(r) = √r + 1 - 1 at the given values of the independent variable and simplify.
a. f(-1) b. f(24) c. f(x-1)
Step-by-step explanation:
I'm going to assume you meant to write [tex]\sqrt{r+1}[/tex] in the equation as +1 - 1 wouldn't make much sense since they would just cancel out.
a. [tex]f(-1) = \sqrt{-1 + 1} - 1\\ f(-1) = \sqrt{0} - 1\\f(-1) = 0-1\\f(-1) = -1[/tex]
b. [tex]f(24) = \sqrt{24 + 1} - 1\\ f(24) = \sqrt{25} - 1\\f(24) = 5 - 1\\f(24) = 4[/tex]
c. [tex]f(x-1) = \sqrt{(x-1)+1} -1\\f(x-1) = \sqrt{x} - 1[/tex]
Emissions of sulfur dioxide by industry set off chemical changes in the atmosphere that result in "acid rain".
The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has pH 7.0, and lower pH values indicate acidity.
Normal rain is somewhat acidic, so "acid rain" is sometimes defined as rainfall with a pH below 5.0.
The pH of rain at one location varies among rainy days according to a Normal distribution with mean 5.43 and standard
deviations 0.54.
What proportion of rainy days have rainfall with pH below 5.0? Use software or Table A to find the answer.
(Enter your answer rounded to four decimal places.)
Using the normal distribution, it is found that 0.2119 = 21.19% of rainy days have rainfall with pH below 5.0.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 5.43, \sigma = 0.54[/tex]
The proportion of rainy days have rainfall with pH below 5.0 is the p-value of Z when X = 5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 5.43}{0.54}[/tex]
Z = -0.8
Z = -0.8 has a p-value of 0.2119.
0.2119 = 21.19% of rainy days have rainfall with pH below 5.0.
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PLS answer quick
Which formula can be used to find the volume, V, of the composite solid figure represented below?
OA V = r2h + ³
r²h +
3
r²2h + 3r3
r²h + ³
OB. V
OC.
V =
V =
V =
OD. V =
The formula to find the volume of the composite solid is: C. V = πr²h + ⅔πr³.
How to Find the Volume of a Composite Solid?The volume of the composite solid in the image given = Volume of cylinder + volume of hemisphere.
Volume of cylinder = πr²h
Volume of hemisphere = ⅔πr³
Therefore, formula to find the volume is: C. V = πr²h + ⅔πr³.
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Answer:
C
Step-by-step explanation:
I Just Took the Test.
Hello, thank all of you that helped me fix my math problems you helped me to succeed and get a good grade !!!
Given the two similar triangles below, which proportion is not true?
The proportion of sides of the triangle which is not true are 13.5/21 = 9/14, 9/13.5 = 6/21 and 14/6 = 21/9
ProportionThe three sides of each of the rectangles should be proportional to each other
Triangle A : Triangle B
9 cm : 13.5 cm
= 9/13.5
14 cm : 21 cm
= 14 cm / 21 cm
6 cm : 9 cm
= 6 cm / 9 cm
Therefore, the proportion of sides of the triangle which is not true are 13.5/21 = 9/14, 9/13.5 = 6/21 and 14/6 = 21/9
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-5x-5<15
Solve the inequality and graph solution set. Write solution set in (a) set builder notation and (b) interval notation
-5x-5<15 [given]-5x<20 [add 5 to both sides]x>-4 [divide both sides by -5, don't forget to flip the inequality sign]
(a) [tex]\{x: x > -4 \}[/tex]
(b) [tex](-4, \infty)[/tex]
Unas deportivas cuestan $600 he visto que hay una rebaja del 20% cuánto dinero rebajado las reporteras
Answer:
600/100*20=6*20=120
600-120=480$
(LOOK AT PHOTO) What is the quotient of the rational expression below?
x²-49 x²-14x+49
x+2
3x+6
The quotient [tex]\frac{x^2 - 49}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex] is [tex]\frac{3(x +7)}{(x -7)}[/tex]
How to determine the quotient?The expression is given as:
[tex]\frac{x^2 - 49}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex]
Express x^2 - 49 as difference of two squares
[tex]\frac{(x + 7)(x- 7)}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex]
Factorize other expressions
[tex]\frac{(x + 7)(x- 7)}{x + 2} \div \frac{(x -7)(x-7)}{3(x + 2)}[/tex]
Express as product
[tex]\frac{(x + 7)(x- 7)}{x + 2} \times\frac{3(x + 2)}{(x -7)(x-7)}[/tex]
Cancel the common factors
[tex]\frac{(x + 7)}{1} \times\frac{3}{(x -7)}[/tex]
Evaluate the product
[tex]\frac{3(x +7)}{(x -7)}[/tex]
Hence, the quotient [tex]\frac{x^2 - 49}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex] is [tex]\frac{3(x +7)}{(x -7)}[/tex]
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Plss HELPP I neeed help on this question
Answer: 180 degrees
Step-by-step explanation:
The measure of the arc of a semicircle is 180 degrees.
Find the inverse of the function y = 3x + 5 Find the inverse of the function y=3x+5
Answer:
First Inverse function= f^-1(x)=x/3-5/3
Second Inverse function=f^-1(x)=x/3-5/3
Step-by-step explanation:
Nigel bought 10 pencils and 5 erasers for 8$. The price of 2
pencils was 1$. What was the price of 2 erasers?
Answer:
2 erasers cost $1.20
Step-by-step explanation:
Nigel bought 10 pencils and 5 erasers for $8.
We can write this algebraically:
10p + 5e = 8
We know that the price of 2 pencils is $1. That is $0.50/Pencil.
So, p = $0.50. Now we can plug that into out equation and find the price of one eraser:
10(0.50) + 5e = 8
5 + 5e = 8
5e = 3
e = $0.60
Now, we have the price of one eraser, $0.60, and we can multiply this by 2 to find the price of 2 erasers, which equates to $1.20.
Choose True or False, (T or F). Data are recorded observations used for explaining conditions of particular phenomenon
Answer:
true
Step-by-step explanation:
this is absolutely true
Evaluate: √121m²n6 if m = 3, n = 2
Answer:
1188
Step-by-step explanation:
√121 (3^2)(2(6)) = 1188
Answer:
264
Step-by-step explanation:
√(121m^2 n^6) = 11 m n^3
sub in the values given for m and n
11 (3)(2^3) = 11 * 3 * 8 = 264
2/5x - 1/2 = 1/3 + 5/6x
Answer:
[tex]x = \frac{25}{13} [/tex]
Step-by-step explanation:
Given:
[tex] \frac{2}{5} x - \frac{1}{2} = \frac{1}{3} + \frac{5}{6} x[/tex]
Combine like terms:
[tex] \frac{2}{5} x - \frac{5}{6} x = \frac{1}{3} + \frac{1}{2} [/tex]
Find GCF :
[tex] \frac{12}{30} x - \frac{25}{30} = \frac{2}{6} + \frac{3}{6} [/tex]
Subtraction and Addition :
[tex] \frac{13}{30} x = \frac{5}{6} [/tex]
Divide both sides by 13/30 :
[tex] \frac{ \frac{13}{30} }{ \frac{13}{30} } x = \frac{ \frac{5}{6} }{ \frac{13}{30} } [/tex]
Simplify :
Multiplication (Reciprocal) :
[tex]x = \frac{5}{6} \times \frac{30}{13} [/tex]
[tex]x = \frac{150}{78} [/tex]
[tex]x = \frac{25}{13} [/tex]
Answer :
[tex]x = \frac{25}{13} [/tex]
Hope it helps
Students returning to a secondary school have to pass through a check point at the rate of 50 per though. The average time for checking is 35 seconds. The arrival rate and service rate follow a Poisson distribution. There is a delay and the principal is willing to include another check point to reduce the average time of checking to 28 seconds if the idle time is less than 10% and the average queue length is more than 10 students, check whether the introduction of an extra check point is justifiable.
The average queue length is greater than 10 students, the introduction of an extra checkpoint is justifiable.
How to explain the information?Since the arrival rate and service rate follow a Poisson distribution, we can use the Poisson arrival rate formula to calculate the average queue length.
Average queue length = (arrival rate * service time) / (1 - arrival rate * service time)
For the given problem, the average queue length is:
Average queue length = (50 * 35) / (1 - 50 * 35)
= 175
Since the average queue length is greater than 10 students, the introduction of an extra checkpoint is justifiable.
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If 462 subjects were studied and 99 of them expressed a preference for Brand Y, what percentage
expressed a preference for Brand Y? Round to the nearest tenth percentage. Enter the numerical value
only. For example, if your answer is 12.2%, enter 12.2 in the blank.
Answer:
20
Step-by-step explanation:
492/99x100=21.43
nearest tenth percentage is 20
Anjali wrote a 30-item multiple choice exam and answered every question. She got 8 points for each correct item. She lost 2 points for each incorrect item. Her total score was 150 points. How many items did she answer correctly?
She did 21 question correctly.
Correct Answer :Let number of correct answers : x
Let number of wrong answer : y
Given, Total question wrote : 30
So,
x + y = 30 (i) - equation
Got 8 point on each correct answer, total point : 8*x
Got -2 point on each wrong answer, total point : (-2)*y
Total point she score was : 150 (given)
so, our next equation is
8*x - 2*y = 150 (ii) - equation
y = 30 - x [from (i) - equation]
put in (ii) - equation, we get
8*x - 2*(30 - x) = 150
8*x - 60 + 2*x = 150
10*x = 210
x = 21
Therefor, only 21 answers are correct.
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20
Apply the 50-30-20 Rule to the context below and determine how much money is left over.
You share an apartment with two friends, and the rent and utilities are split equally by all three tenants. Find the
amount left for savings if your bi-weekly net income is $1,391.50.
Total Rent: $1,100
Public Transportation: $88
Cell Phone: $68
Total Utilities: $327
Renter's Insurance: $48.20
Gym Membership: $50
Cable & Streaming Services: $175
Dining Out / Entertainment: $300
3% of Gross into a 401k Savings Plan
Credit Cards: $102
Student Loans: $150
1. Given this monthly budget, how much net income gets applied to each of the "Need/Wants/Debt-Savings"
categories?
50%
30%
20%
2. Subtract each deduction from the monies found in 1). How much remains in each category?
50%
30%
20%
3 How much money remains? What changes would you recommend to improve this budget?
Placement Assessment
A certain drug is made from only two ingredients: compound A and compound B. There are 7 milliliters of compound A used for every 4 milliliters of compound
B. If a chemist wants to make 946 milliliters of the drug, how many milliliters of compound A are needed?
milliliters of compound A
X
Time Remaining: 22:11:23 I Question 17
?
Libbi
Est
Answer:
[tex]7 469.8.56[/tex]
nossa nem sei como é bom saber se fala com a mãe e o pai do mundo e vc não tem mais nada pra comer e não tem como fazer a gente vai ficar muito tempo sem fazer a mãe dela não e vc como tá o trabalho rede de nada em casa e é só pra mim né não é fácil de fazer a mãe dela e a mãe dele tá bem né não é fácil de fazer o que vc quer que Deus quiser vai dar pra mim né e não tem como fazer d id da x não vou poder é o que eu te abençoe e ilumine e ilumine todos os dias entre?01029)
The Research Triangle in North Carolina is formed by Raleigh, Durham, and Chapel Hill. Is this triangle a right triangle? Explain.
The triangle is not a right triangle. This is because the sum of the square of the two shorter lengths is not equal to the square of the longest length.
Is the triangle a right triangle?
In order to determine if the triangle is a right triangle, Pythagoras theorem would be used.
The Pythagoras theorem: a² + b² = c²
where a = length
b = base
c = hypotenuse
12 ² + 24²
= 144 + 576 = 720
29² = 841
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there are 1,500 pupils in school , 0.6 are boys how many pupils are girls
Answer:
1491 girls (99.4 percent)
Step-by-step explanation:
explanation is in the attached picture
An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability that during a given week the airline will lose less than 20 suitcases?
Answer:
[tex] \frac{?}{?} [/tex]
