Let the time taken to read the whole be y
If he reads 1/8 of the whole book (x), it can be expressed as,
[tex]\frac{1}{8}\text{ of x =}\frac{1}{8}\times x=\frac{x}{8}[/tex]If it takes Adam to read x/8 of a book in 1/6 hours,
To read the whole book, it will take Adam,
[tex]\begin{gathered} Adam\text{ read }\frac{x}{8}\text{ in }\frac{1}{6} \\ To\text{ read the whole book (x) in y time} \\ y\times\frac{x}{8}=x\times\frac{1}{6} \\ \frac{xy}{8}-\frac{x}{6} \\ \text{Crossmultiply} \\ 6\times xy=8x \\ \text{Divide both sides by }6x \\ \frac{6xy}{6x}=\frac{8x}{6x} \\ y=\frac{4}{3}=1\frac{1}{3}hours \end{gathered}[/tex]Hence, it will take 1 1/3 hours for Adam to read the whole book.
Three vertices of a rectangle are (2,-2), (-3,-2), and (-3,4). What are the coordinates for the fourth vertex?
In order to find the missing coordinate, start graphing the three points given
then, ubicate the point where a 90° angle is formed in the missing corner, keeping the x-coordinate from the point below and the y-coordinate from the point to the left.
Solve y3 = −8. Please help im desperate
Answer:
-2
Step-by-step explanation:
y^3=-8.
y=cube root of -8 = -2
Whitney,Andrew,and Lena all have summer jobs.Whitney earns 312 in 26 hours of work.Andrew earns 451 in 41 hours of work.Lena earns 10 per hour.Who earns the most money per hour
According to the given data we have the following:
Whitney earns 312 in 26 hours of work
Andrew earns 451 in 41 hours of work
Lena earns 10 per hour
In order to calculate who earns the most money per hour we would have to calculate the rate of money per hour of Whitney and Andrew and the compare it with Lena.
So, money per hour of whtiney=312/26
money per hour of whtiney=12 per hour
money per hour of Andrew=451/41
money per hour of Andrew=11 per hour
Therefore, Whitney is the person that earns most money per hour.
Find θ to four significant digits for 0 < θ< 2 pi if cos θ= 0.6725
First, we need to solve for θ:
[tex]\cos\theta=0.6725[/tex][tex]\theta=\cos^{-1}(0.6725)[/tex][tex]\theta=0.8332147[/tex]But, since the cosine is a function that takes the same values every 3π/2, if we add this to the solution:
[tex]\theta_2=0.8332147+\frac{3\pi}{2}\approx5.5456[/tex]Thus, the two solutions are:
[tex]\theta=0.8332,5.5456[/tex]a wheel on a toy has a radius of 3 inches. what is the area of the wheel?
Answer:
28.27 inches squared
Step-by-step explanation:
A = π r²
A = π (3)²
A = π 9
π*9 = 28.2743338823
A = 28.27
how many significant figures are in 7003.01
The significant figures are the digits of the number that provide information about the measurement that number represents.
In this case, all the digits has to be included because all of them are giving information about the measurement.
Hence, there are 6 significant figures.What is the slope of a line perpendicular to the segment AB, which has endpoints A(-8.1, 4.9) and B(-7.6, 2.9)? Express your answer as a common fraction.
The slope of the line perpendicular to the segment AB is 1/4
Explanation:The slopes of perpendicular lines are negative reciprocals of each other.
Given the endpoints A(-8.1, 4.9) and B(-7.6, 2.9), the slope of this line is as follows:
(2.9 - 4.9)/[-7.6 - (-8.1)]
= (2.9 - 4.9)/(-7.6 + 8.1)
= -2/0.5
= -4
The negative reciprocal of -4 is 1/4
Therefore, the slope of the line perpendicular to the segment AB is 1/4
A plane leaves the ground with an elevation angle of 6 degrees. The plane travels 10 miles horizontally.How high is the plane at the time?What's the distance of the plane's path?
Answer
The height of the plane at that time is 1.1 miles
The distance of the plane's path is 10.1 miles
Explanation
The situation models a right angle triangle as shown below
Using trigonometric ratio,
tan 6° = opposite / adjacent
The opposite side of the triangle is the height of the plane. The distance traveled horizontally is the adjacent side. Therefore,
[tex]\begin{gathered} \tan 6^{^0}=\frac{a}{10} \\ 0.1051=\frac{a}{10} \\ \text{Cross multiply} \\ a=10\times0.1051 \\ a=1.051 \end{gathered}[/tex]The height of the plane at that time ≈ 1.1 miles
The hypotenuse of the triangle formed is the distance of the plane path.
Therefore, this distance can be calculated using Pythagoras rule as follows:
[tex]\begin{gathered} c^2=a^2+b^2 \\ a=1.051\text{ miles} \\ b=10\text{ miles} \\ \Rightarrow c^2=1.051^2+10^2 \\ c^2=1.104601+100 \\ c^2=101.104601 \\ c=\sqrt[]{101.104601} \\ c=10.05507837\text{ miles} \end{gathered}[/tex]The distance of the plane's path = 10.1 miles
how to prove that the difference between squares of consecutive even numbers is always a multiple of 4
Let x be an even integer then x+2 is the next consecutive even integer.
We need to look at [tex](x+2)^2 - x^2[/tex], since that's the difference between the squares of any two consecutive even integers.
[tex](x+2)^2 - x^2 = x^2 + 4x + 4 - x^2[/tex]
[tex]=4x+4[/tex]
[tex]=4(x+1)[/tex]
Since that difference is 4 times something, it is a multiple of 4.
What is the solution of the inequality shownbelow?x-1< -10
x - 1 < -10
add 1 to both sides
x - 1 + 1 < -10 + 1
x < -9
Which shape has at least one pair of perpendicular sides? 1 Done Progress > night 2020 by Curriculum Asmates. All rights reserved. These materials, or any portion thereatmay nat be reproduced or shared in any manner without express written consent of Curriculum Assad
the last three pictures have at least 1 pair of perpendicular sides
linear regression and Correlation graphs.sending pic
We have a set of points and we have to calculate the least squares line that fits the data.
Bob needs $.50 to ride the bus. He has 3 quarters, 5 dimes, and 2 nickels. What is the probability he will pull two quarters in a row from his pocket without replacement? Show work.
Step 1:
Probability formula
[tex]\text{Probability of any event = }\frac{n\text{umber of required outcomes}}{n\text{umber of possible outcomes}}[/tex]Step 2:
Number of possible outcomes
Quarters = 3
Dimes = 5
Nickels = 2
Total possible outcomes = 10
Step 3:
[tex]\begin{gathered} \text{Probability of picking two quarters one after the other without} \\ \text{replacement = }\frac{3}{10}\times\frac{2}{9}=\frac{1}{15}\text{ } \end{gathered}[/tex]Final answer
The probability he will pull two quarters in a row from his pocket without replacement = 1/15
geometry » triangle angle-sum theorem y+27°+4y+113=180what is the value of y?y= [ ]°
1) Considering that the sum of the interior angles of a triangle is 180º, i.e., what the triangle angle-sum theorem means
2) Let' solve for y
y+27°+4y+113=180 Combine like terms
5y +140 = 180 Subtract 140º from both sides.
5y = 40 Divide both sides by 5
y=8
2) Hence y = 8
Tell wether the given value is a statistic or a parameter.
Answer:
• 8. Statistic
,• 9. Parameter
,• 10. Statistic
,• 11. Statistic
,• 12. Statistic
,• 13. Parameter
,• 14. Statistic
,• 15. Statistic
Explanation:
A parameter is a number describing a population in its entirety while a statistic is a number that describes a sample.
Number 8
25 people were selected for the research. This is a part of a population.
Thus, this describes a statistic.
Number 9
The number of moons in Jupiter is 67. This describes the entire population of moons on Jupiter. The given value is a parameter.
Number 10
The Statistics teacher randomly selected 35 questions from previous questions to be given in the coming second periodic examination.
The given value is a statistic since the statement describes a sample.
Number 11
It was found out that 10 of the teachers in a certain private high school have doctorate degrees.
The given value is a statistic since the statement describes a sample.
Number 12
In a survey of 1500 bulbs manufactured by a company, it was found out that 120 of them were defective.
The given value is a statistic since the statement describes a sample.
Number 13
The Philippine Senate is composed of 24 senators.
The given value is a parameter since the statement describes the entire population of the Philippine Senate.
Number 14
Based on the sample of 1,200 surveyed students, it was found out that 20% of them needed financial aids.
The given value is a statistic since the statement describes a sample.
Number 15
The manager randomly selected 35 employees to participate in Sports Fest.
The given value is a statistic since the statement describes a sample.
What is the form of the Difference of Squares identity?O A. a? - b - (a - b)(a - b)B. 22 - 62 = (a + b)(a + b)C. 22 - 61 = (a + b)(a - b)D. 3° +6+ = (2-b)(a - b)
The difference of squares identity can be expressed as
[tex]a^2-b^2=(a-b)(a+b)[/tex]this is because when expanding the expression on the left the term ab needs to be cancelled like this
[tex]\begin{gathered} (a-b)(a+b)=a\cdot a+a\cdot b-a\cdot b-b\cdot b \\ =a^2+ab-ab-b^2 \\ =a^2-b^2 \end{gathered}[/tex]Can you help me please I need help with this assignment
a) Consider the experiment of picking 3 tax returns at random as 3 related experiments (due to the fact that it is without replacement); then, as for the first time one selects a tax return,
[tex]P_1(NonError)=\frac{61}{61+9}=\frac{61}{70}[/tex]As for the second time we grab a tax return, there are 69 tax returns in total and 9 of them contain errors; thus,
[tex]P_2(NonError)=\frac{60}{69}[/tex]Similarly, as for the third picking round,
[tex]P_3(NonError)=\frac{59}{68}[/tex]Finally, the probability of experiment a) is
[tex]\begin{gathered} P_1(NonError)*P_2(NonError)*P_3(NonError)=\frac{61*60*59}{70*69*68}=0.657471...\approx65.7\% \\ \end{gathered}[/tex]Rounded to one decimal place, the probability of event a) is 65.7%
b) Similarly, in the event of all three tax returns containing errors,
[tex]\begin{gathered} P_1(Error)=P_1(E)=\frac{9}{70} \\ P_2(E)=\frac{8}{69} \\ P_3(E)=\frac{7}{68} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \Rightarrow P(b)=P_1(E)*P_2(E)*P_3(E)=0.00153... \\ \Rightarrow P(b)\approx0.2\% \end{gathered}[/tex]The probability of event b) is 0.2%. It is quite unusual.
c) The condition 'at least one of those containing errors' includes the cases when 1, 2, or 3 tax returns of the ones selected have errors. Notice that
[tex]1=P(0Errors)+P(1Errors)+P(2Errors)+P(3Errors)[/tex]Therefore,
[tex]P(1o2o3Errors)=P(1E)+P(2E)+P(3E)=1-P(0Errors)[/tex]And we found the probability of picking 3 tax returns without any errors in part a); thus,
[tex]P(c)=1-0.657471...=0.342528...\approx34.3\%[/tex]The probability of event c) is 34.3%.
d) Analogously to part c), the probability of selecting at least one without errors is
[tex]P(d)=1-P(0NonErrors)=1-P(3Errors)=1-P(b)=0.998465...\approx99.8\%[/tex]The probability of event d) is 99.8%, and it is not improbable at all.
1. The monthly revenue from selling x units of a certaincommodity is given to beR(x) = 12x - 0.01x2dollars. Determine the number ofunits that must be sold each month maximize the revenue. What is the correspondingmaximum revenue?
Monthly revenue:
[tex]R(x)=12x-0.01x^2[/tex]As the monthly revenue is given by a quadratic equation, the number of units that must be sold each month maximize the revenue and the maximum revenue are the coordinates of the vertex for the parabola that correspond to the given function.
x is the number of units
y is the maximum revenue
To find the x coordinate of the vertex, use the next formula:
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ \\ x=-\frac{b}{2a} \\ \\ \\ x=-\frac{12}{2(-0.01)}=-\frac{12}{-0.02}=600 \end{gathered}[/tex]Use the x-coordinate in the function to find the y-coordinate (R(600)):
[tex]\begin{gathered} R(600)=12(600)-0.01(600)^2 \\ R(600)=7200-0.01(360000) \\ R(600)=7200-3600 \\ R(600)=3600 \end{gathered}[/tex]Then, the number of units that must be sold each month to maximize the revenue is 600 and the maximum revenue is $3,600Need some help pleaseee
Answer: A=56/5 ft^2
Step-by-step explanation:
A=Area of triangle. b=base. h=height
A=1/2 * b * h
A=1/2 * (5+3/5) * 4
A=1/2 * (25/5 + 3/5) * 4
A=1/2 * 28/5 * 4
A=28/10 * 4
A=28*4/10
A=112/10
A=56/5 ft^2
Melissa has reached her credit card limit of $ 6,500. Since Melissa has poor credit history, the annual interest rate on her credit card is 19%. Using an online calculator, Melissa determined that if she pays $ 220 per month and does not make any additional purchases with her credit card, it will take her 41 months to pay off the credit card. Which of the follow represents the total interest Melissa will pay when her credit card is paid off?
Problem
Melissa has reached her credit card limit of $ 6,500. Since Melissa has poor credit history, the annual interest rate on her credit card is 19%. Using an online calculator, Melissa determined that if she pays $ 220 per month and does not make any additional purchases with her credit card, it will take her 41 months to pay off the credit card. Which of the follow represents the total interest Melissa will pay when her credit card is paid off?
Solution
For this case we can start the amount of money paid by Mellissa with this operation:
220$/month *41 months = $9020
And since the credit card limit is $6500 we can calculate the interest paid with this difference:
$9020- $ 6500=$2520
And the best answer for this case would be $2520
If y=g(x), Find g(-3)= I've already tried 3, 4, 3.25, and 3
The function g(-3) has a value of 3.5
How to evaluate the function?From the question, we have the following parameters that can be used in our computation:
The graph of the function g(x)
Also, we have
y = g(x)
To calculate g(-3), we set x = -3
So, we have the following representation
y = g(-3)
Also from the graph
We have the following representation such that
When x = -3, the function is 3.5 (approximately)
So, we have the following representation
y = 3.5
Hence, the value of the function is 3.5
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Please list the measurements of the8 interior angles on the map usingwhat you know about Angle Pairsand that Lombard and the roadpassing by i jump and Surge Bikewill never intersect.
Let's begin by identifying key information given to us:
We are given 8 interior angles & which are listed below:
[tex]\begin{gathered} \angle KDC=? \\ \angle DCH=? \\ \angle LDC=? \\ \angle DCH=? \\ \angle MEF=? \\ \angle HEF=? \\ \angle EFJ=? \\ \angle EF=? \end{gathered}[/tex]Reading the value of the protractor, we will get the following angle for KDC = 130 degrees.
Angle DC = 50 degrees (Alternate Interior Angles with LDC)
Angle LDC = 50 degrees (Supplementary Angle with KDC)
Angle DCH = 130 degrees (Alternate Interior Angles KDC)
Angle MEF = 50 degrees (Corresponding Angle with DC)
Angle HEF = 130 degrees (Corresponding Angle with CDH)
Angle EFJ = 50 degrees (Alternate Interior Angles with MEF)
Angle EF = 130 degrees (Supplementary angle with EFJ)
Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution. (-8,0) and (1,5)
The standard form of the equation is 9y = 5x + 40
What is standard form of Equation of line?The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y. The values of x and y represent the coordinates of the point on the line represented in the coordinate plane
The given points are (-8, 0) and (1,5)
We find the slope first,
Slope(m) = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Where [tex]y_{1}[/tex] = 0, [tex]x_{1}[/tex] = -8 and [tex]y_{2}[/tex] = 5 and [tex]x_{2}[/tex] = 1
slope(m) = [tex]\frac{5 - 0}{1 - - 8}[/tex]
slope = 5/9
But equation o line is y = mx + c
To find c, take values of x = -8 and y = 0
so that the equation y = mx + c becomes
0 = 5/9(-8) + c
c = 40/9
substitute for the values of m and c into y = mx + c
y = 5/9x + 40/9
Multiply through by 9, we have
9y = 5x + 40
writing it in standard form, 9y -5x - 40 = 0
In conclusion, the equation of the line in standard form is 9y -5x - 40 = 0
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which equation can be represented by the number line below
the equation that represents the number line below is:
[tex]-4-(-5)=1[/tex]Katie has $32 to spend on party supplies after buying 9 packs of noisemaker she has $20 left how much did each pack of noise maker cost
total money she has is 32 $
now after buying she has left only with 20$
so she spent 32 - 20 = 12 $
she spent 12 $ for buying 9 packs of noisemaker,
9 Pack cost = 12 $
1 pack cost = 12 / 9
= 4/3 = 1.3333 $
so cost of each pack of noise is 1.33 $
3-4i/2+iCan you help me to solve this problem please
To solve this problem, we multiply and divide the given expression by 2-i:
[tex]\frac{3-4i}{2+i}(\frac{2-i}{2-i}).[/tex]Recall that:
[tex](a+ib)(a-ib)=a^2+b^2.[/tex]Therefore:
[tex]\frac{3-4i}{2+i}(\frac{2-i}{2-i})=\frac{(3-4i)(2-i)}{2^2+1^2}=\frac{(3-4i)(2-i)}{5}.[/tex]Finally, multiplying the factors in the numerator, we get:
[tex]\frac{6-3i-8i-4}{5}.[/tex]Finally, simplifying the above result, we get:
[tex]\frac{2-11i}{5}=\frac{2}{5}-\frac{11}{5}i.[/tex]Answer: [tex]\begin{equation*} \frac{2}{5}-\frac{11}{5}i. \end{equation*}[/tex]As a student you are able to earn extra money by assisting your neighbors with odd jobs. If you charge 10.25 broken over an hour for your assistant, about how many hours would you need to work to earn $8,425?
For solving our problem we have to divide our total which is $8425 by the hourly charge $10.25
$8425 / $10.25 = 821,95
The rounded answer is 822 hours.
Keith made a rectangular sign that had a perimeter of 48 inches. Which model could represent the sign Keith made
the perimeter is equal to the sum of all the sides, therefore:
[tex]\begin{gathered} P=w+w+l+l=48 \\ so\colon \\ w=12 \\ l=12 \\ P=12+12+12+12=48 \end{gathered}[/tex]----------------------------------------
The area of a rectangle is given by:
[tex]\begin{gathered} A=w\cdot l \\ where \\ l=24 \\ w=17 \\ A=24\cdot17 \\ A=408in^2 \end{gathered}[/tex]Select the correct answer from each drop-down menu.Some of the images in the diagram are images of polygon 1 from similarity transformations.ty2422B20১ম ৪ ৪ ০ ০ ২ ০18polygon 11614Do12Epolygonpolygon 486polygon 3polygon 5N02 4 6 8 10 12 14 16 18 20 22 24 26Polygon✓ and polygon
Solution
By definition of similar figures:
Similar figures are two figures having the same shape
The polygons that are similar to poly gone 1 are
Polygon 3 and Polygon 4
Suppose that both the radius and height ℎ of a circular cone are increasing at a rate of 2cm/s. How fast is the volume of the cone increasing when =20cm and ℎ=15cm? (simplify to one decimal place
1727.88 cm³/sec is the volume of the cone .
How much volume do a cone and a cylinder have?
The volume of a sphere is calculated using the formula 43r3. The equation is r2h for cylinders. A cone has a volume that is 13 (or 13r2h) that of a cylinder.Two right circular cone formulas are necessary to understand: (r2h)/3 is the formula for calculating a cone's volume. The formula for a right circular cone's surface area is rs+r2.Volume of cone V = 1/3πr²h
r/h = 15/20 = 3/4
V = 1/3πr²h
dv/dt = 1/3 [π[r²dh/dt + 2rhdr/dt]
dr/dt = dh/dt = 2cm/sec
r = 15 cm h = 20 cm
dv/dt = π/3[15² × 2 + 2 × 15 × 20 × 2 ]
550π = 1727.88 cm³/sec
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