17. 17. The scores for a math test are shown below, ordered from smallest to largest. 60 61 62 63 63 64 64 65 66 66 66 69 72 72 72 74 75 80 82 84 86 86 87 87 89 89 90 93 94 98 Fill out the stem and leaf plot below for this data. Enter the leaves separated by commas (ex: 1,1,2,3). Stems Leaves
Answers
Answer:
Filling the values we have;
Explanation:
Given the data on the given table, we want to fill them in a stem leaves plot.
The tens values would be in the stems while the unit values will be written in their corresponding leaves.
Filling the values we have;
Related Questions
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Required information
Problem 8-63 (LO 8-1) (LO 8-3) (Static)
[The following information applies to the questions displayed below.]
Henrich is a single taxpayer. In 2021, his taxable income is $450,000. What is his income tax and net investment income
tax liability in each of the following alternative scenarios? Use Tax Rate Schedule. Dividends and Capital Gains Tax Rates
for reference. (Do not round intermediate calculations. Leave no answer blank. Enter zero if applicable. Round your
final answers to 2 decimal places.)
Problem 8-63 Part-b (Static)
b. His $450,000 of taxable income includes $2,000 of long-term capital gain that is taxed at preferential rates.
Income tax
Net investment income tax
Total tax liability
Amount
Answers
Total income & net investment income tax $ 124,556.00
Tax on preferentially taxed income $ 9,022.50
Given :
In 2021, his taxable income is $450,000.
Use Tax Rate Schedule.
His $450,000 of taxable income includes $2,000 of long-term capital gain that is taxed at preferential rates.
Income tax
Final answer is
Total income & net investment income tax $ 124,556.00
Tax on preferentially taxed income $ 9,022.50
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A piece of land is in the shape of a rectangle. What is the ratio of the length to the width?
Answers
Answer: A: 3-5
Step-by-step explanation:
multiply each by their respective ratios, 120*3=360, and 72*3=360
The illustration below shows the graph of yyy as a function of xxx.
Complete the following sentences based on the graph of the function.
This is the graph of a
function.
The yyy-intercept of the graph is the function value y=\:y=y, equals
.
The smallest positive xxx-intercept of the graph is located at x=\:x=x, equals
.
The greatest value of yyy is y=\:y=y, equals
, and it occurs when x=\:x=x, equals
.
For xxx between x=\pix=πx, equals, pi and x=2\pix=2πx, equals, 2, pi, the function value y\:yy
\:000.
Answers
Based on the graph (see attachment) of this function, the sentences should be completed as follows:
This is the graph of a nonlinear functionThe y-intercept of the graph is the function value y = 1.The smallest positive x-intercept of the graph is located at x = π.The greatest value of y is y = 1 and it occurs when x = 0.For x between x = π and x = 2π, the function value y ≤ 0.What is y-intercept?In Mathematics, the y-intercept of any graph such as a trigonometric function, generally occurs at the point where the value of "x" is equal to zero (x = 0).
By critically observing the graph (see attachment), the coordinates of the y-intercept of the parabola is given by y-intercept = (0, 1). Additionally, the greatest value of y is equal to 1 (y = 0) and it occurs when x is equal to 0 (x = 0).
What is y-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-axis and the value of "y" is equal to zero (0).
From the graph (see attachment), the smallest positive coordinate of the x-intercept of the parabola is given by:
x-intercept = (π, 0).
In conclusion, when x is between x is equal to π (x = π) and x is equal to 2π (x = 2π), the range of the function is given by y ≤ 0.
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6)What is the frequency of the 4th class?POINTSOut OF37)How many dogs were weighed?8)What is the midpoint of the 4th class?6)What is the frequency of the 4th class?POINTSOut OF37)How many dogs were weighed?8)What is the midpoint of the 4th class?
Answers
The first question 6) requires us to see how many "events" lies in the 4th class, which is 35 in this case. Then the answer for 6) is 35.
Next, we have to sum the all heights of the rectangles, which are the total dogs weighed as follows:
[tex]total\text{ dogs}=5+15+24+35+16+6+4=105[/tex]Hence the answer for 7) is 105
Finally, the midpoint of a class is the half of the x-coordinate. The 4th class is for dogs which weight between 30 and 39, so:
[tex]midpoint=\frac{30+39}{2}=34.5[/tex]Then the answer for 8) is 34.5
Find the equation for the line with slope-= -4 and passing through (-9,40) write your equation in the form y=mx+b
Answers
Slope m = Y/X
m = -4
Now find b
b = y - mx
replace now by (-9,40)
b = 40 - (-4)•(-9) = 40 - 36 = 4
Then finally write whole equation
y = -4x + 4
Write an equation of the line that is perpendicular to the line
2x+5y=-15 and contains the point (-8,3)
Answers
Welcome to Gboard clipboard, any text you copy will be saved here.Welcome to Gboard clipboard, any text you copy will be saved here.Welcome to Gboard clipboard, any text you copy will be saved here.Welcome to Gboard clipboard, any text you copy will be saved here.
Is 8.21 repeating a rational number?
Answers
We want to know if the number 8.21212121 (repeating) is a rational number.
So, the answer is yes and we will find the rational representation:
[tex]8.212121\ldots=8+0.21212121\ldots=8+\frac{21}{99}=\frac{8\cdot99+21}{99}=\frac{813}{99}[/tex]For any repeating number we can convert to a rational representation taking the repeating number and divided by the the number of 9 with equal number of digits as the repeating number.
In this case, the repeating number is 21, it has two digits so we have to divide by 99 (two digits of 9).
Which exponential function is represented by thegraph?f(x) = 2(34)f(x) = 3(3*)f(x) = 3(2x)O f(x) = 2(2)
Answers
The graph of function passes through points (1,6), (0,3) and (-1,1.5).
Determine the function that satify all the points.
For point (1,6)
[tex]\begin{gathered} f(1)=2(3^1) \\ =2\cdot3 \\ =6 \end{gathered}[/tex]Function satisy the point.
For point (0,3);
[tex]\begin{gathered} f(0)=2(3^0) \\ =2\cdot1 \\ =2 \end{gathered}[/tex]Function not satify the points.
Check for the scond function.
For point (1,6);
[tex]undefined[/tex]There are many numbers which divide 109 with a remainder of 4. List all two-digit numbers that have that property
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15, 21, and 35 are two-digit numbers that divide 109 with a remainder of 4. These are the only numbers by which 109 can be divided to yield a remainder of 4.
What is the Remainder?The remainder is the amount "left over" after performing some computation in mathematics. The remainder is the integer "left over" after dividing one integer by another to produce an integer quotient in arithmetic (integer division).
What are the division rules?RULE 1: A positive integer's quotient with a negative integer is negative. RULE 2: A positive integer is the quotient of two positive integers.
RULE 3: The product of two negative integers is a positive number. If the signs do not match, the answer is negative.
here 109 is dividend and 4 is remainder.
109–4=105.
105=3*5*7.
It is divided by,
3*5=15.
3*7=21.
5*7=35.
Thus, there are three 2 digit numbers 15,21,35 which divide 109 with 4 as remainder.
Two-digit numbers 15, 21, and 35 divide 109 with a remainder of 4. These are the only figures that can divide 109 to leave a remainder of 4.
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3/6+1/6+2/3= Adding fractions
Answers
Given:
[tex]\frac{3}{6}+\frac{1}{6}+\frac{2}{3}[/tex]Let's perform the addition of the fractions.
The first step is to find the Lowest Common Multiple (LCM) of the denominators.
LCM of 6 and 3 = 6
Now, divide the LCM by each denominator and multiply the the corresponding numerator.
We have:
[tex]\begin{gathered} \frac{3}{6}+\frac{1}{6}+\frac{2}{3} \\ \\ =\frac{(3)1+1(1)+(2)2}{6} \\ \\ =\frac{3+1+4}{6} \\ \\ =\frac{8}{6} \\ \\ =\frac{4}{3} \end{gathered}[/tex]5. Select ALL the values of x that are solutions to the inequality: -7 - 3x - 2<-8(x + 1) *X = -0.11x = 0x = 0.1X = 0.2x = 0.3
Answers
Answer:
Explanation:
Given:
-7 - 3x - 2<-8(x + 1)
To find the values of x, we simplify the given inequality first.
So,
[tex]\begin{gathered} -7-3x-2<-8\mleft(x+1\mright) \\ \text{Simplify and rearrange} \\ =-3x-9<-8\mleft(x+1\mright) \\ =-3x-9<-8x-8 \\ =-3x<-8x-8+9 \\ =-3x<-8x+1 \\ =-3x+8x<1 \\ =5x<1 \\ \text{Divide both sides by 5} \\ =x<\frac{1}{5} \\ or \\ =x<\text{ 0.2} \end{gathered}[/tex]Therefore, the values of x should be less than 1/5 or 0.2. Based on the given choices, the values of x are:
x= -0.1
x=0
x=0.1
. (15 points) You work at a canning factory that's producing cans for a new brand of soup. You needto decide what size the cans should be. The soup cans can have a radius of either 2 in, 2.5 in, 3 in, or3.5 in. The cans need to hold a volume of exactly 90 in. The company wants the cans to be no morethan 5 inches tall, and it wants the cans to have the greatest lateral surface area possible so it canprint more information on the side of the cans.To solve this problem, you will fill in this table with the surface area and volume of each cylinder:
Answers
A can is shaped like a cylinder. The formula to find the volume of a cylinder is
[tex]\begin{gathered} V=\pi r^2h \\ \text{ Where} \\ \text{ V is the Volume} \\ r\text{ is the radius and} \\ h\text{ is the height of the cylinder} \end{gathered}[/tex]Now, you calculate the height that each can should be, given the radius and the volume. For this you can clear at once, the height of the formula shown:
[tex]\begin{gathered} V=\pi r^2h \\ \text{ Divide by }\pi r^2\text{ from both sides of the equation} \\ \frac{V}{\text{ }\pi r^2}=\frac{\pi r^2h}{\text{ }\pi r^2} \\ \frac{V}{\text{ }\pi r^2}=h \end{gathered}[/tex]Then, you have
*Radius = 2in
[tex]\begin{gathered} \frac{V}{\text{ }\pi r^2}=h \\ \frac{90in^3}{\text{ }\pi(2in)^2}=h \\ \frac{90in^3}{\text{ }\pi\cdot4in^2}=h \\ \frac{90in^3}{4\pi in^2}=h \\ \frac{90}{4\pi^{}}in=h \\ 7.2^{}in=h \end{gathered}[/tex]*Radius = 2.5 in
[tex]\begin{gathered} \frac{V}{\text{ }\pi r^2}=h \\ \frac{90in^3}{\text{ }\pi(2.5in)^2}=h \\ \frac{90in^3}{\text{ }\pi\cdot6.25in^2}=h \\ \frac{90in^3}{6.25\pi in^2}=h \\ \frac{90^{}}{6.25\pi}in=h \\ 4.6in=h \end{gathered}[/tex]*Radius = 3 in
[tex]\begin{gathered} \frac{V}{\text{ }\pi r^2}=h \\ \frac{90in^3}{\text{ }\pi(3in)^2}=h \\ \frac{90in^3}{\text{ }\pi9in^2}=h \\ \frac{90in^3}{9\pi in^2}=h \\ \frac{90}{9\pi}in=h \\ 3.2in=h \end{gathered}[/tex]*Radius = 3.5 in
[tex]\begin{gathered} \frac{V}{\text{ }\pi r^2}=h \\ \frac{90in^3}{\text{ }\pi(3.5in)^2}=h \\ \frac{90in^3}{\text{ }\pi12.25in^2}=h \\ \frac{90in^3}{\text{ }12.25\pi in^2}=h \\ \frac{90}{\text{ }12.25\pi}in=h \\ 2.3in=h \end{gathered}[/tex]Then, the table filled out with the radii, heights, and volumes of the cans would be:
Now, you can calculate the lateral surface area of each can using this formula:
[tex]\begin{gathered} \text{ Lateral Surface Area }=2\pi rh \\ \text{ Where} \\ r\text{ is the radius and} \\ h\text{ is the height of the cylinder} \end{gathered}[/tex]Then, you have
*2 in radius can:
[tex]\begin{gathered} r=2in \\ h=7.2in \\ \text{ Lateral Surface Area }=2\pi rh \\ \text{ Lateral Surface Area }=2\pi(2in)(7.2in) \\ \text{ Lateral Surface Area }=2\pi\cdot14.4in^2 \\ \text{ Lateral Surface Area }=90.5in^2 \end{gathered}[/tex]*2.5 in radius can:
[tex]\begin{gathered} r=2.5in \\ h=4.6in \\ \text{ Lateral Surface Area }=2\pi rh \\ \text{ Lateral Surface Area }=2\pi(2.5in)(4.6in) \\ \text{ Lateral Surface Area }=2\pi\cdot11.5in^2 \\ \text{ Lateral Surface Area }=72.3in^2 \end{gathered}[/tex]*3 in radius can:
[tex]\begin{gathered} r=3in \\ h=3.2in \\ \text{ Lateral Surface Area }=2\pi rh \\ \text{ Lateral Surface Area }=2\pi(3in)(3.2in) \\ \text{ Lateral Surface Area }=2\pi\cdot9.6in^2 \\ \text{ Lateral Surface Area }=60.3in^2 \end{gathered}[/tex]*3.5 in radius can:
[tex]\begin{gathered} r=3.5in \\ h=2.3in \\ \text{ Lateral Surface Area }=2\pi rh \\ \text{ Lateral Surface Area }=2\pi(3.5in)(2.3in) \\ \text{ Lateral Surface Area }=2\pi\cdot8.1in^2 \\ \text{ Lateral Surface Area }=50.6in^2 \end{gathered}[/tex]Then, the table filled out with the radii, heights, lateral surface areas, and volumes of the cans will be:
Therefore, the cans must have a radius of 2.5 inches and a height of 4.6 inches, since they will have a volume of 90 cubic inches, will not exceed 5 inches in height, and will have the maximum possible lateral surface.
Write the expression with positive exponents only. Then simplify, if possible.
Answers
Given:
2^-3
3^-2
By making the expression into positive exponents:
= 1/2^3
1/3^2
The simplifying:
= 1/8
1/9
lets make division into multiplication by turning the numerator
= 1/8 x 9
= 9/8
= 1 1/8 (Being simplified)
What is the solution to × + 9 = 24A. × = 9 B. × = 18C. × = 15D. × = 33
Answers
Your grandmother gives you $1500 to invest in a savings account on your 15th birthday. The only condition is that you may NOT use it until you have graduated high school at 18. After researching savings accounts, you come up with two options.1) A high interest savings account, with 2.5% simple interest annually or2) A High Yield Savings account with 2% interest compounded annually.Which account will you chose and why?
Answers
.Explanation.
To determine the best account to choose, we will have to check for the amount each account will yield
For the first account, with 2.5% simple interest annually
To find how much this account will yield at 2.5% simple interest annually, we will use the formula
[tex]A=P+\frac{P\times R\times T}{100}[/tex]Where
[tex]\begin{gathered} p=\text{ \$1500} \\ r=2.5\text{ \%} \\ t=18-15=3years \end{gathered}[/tex]Thus, the first account will yield
[tex]\begin{gathered} A=1500+\frac{1500\times2.5\times3}{100} \\ \\ A=1500+15\times7.5 \\ A=1500+112.5 \\ A=\text{ \$1612.5} \end{gathered}[/tex]For the second account with 2% interest compounded annually
[tex]\begin{gathered} A=P(1+\frac{r}{100})^t \\ where \\ P=1500 \\ r=2\text{ \%} \\ t=3 \end{gathered}[/tex]Thus the account will yield
[tex]\begin{gathered} A=1500(1+\frac{2}{100})^3 \\ A=1500(1.0612) \\ A=\text{ \$}1591.81 \end{gathered}[/tex]We can see that the first account with 2.5% simple interest annually yields $1612.50 and
The second account with 2% interest compounded annually yields $1591.81
The difference in the accounts will be
[tex]\text{ \$}1612.50-\text{ \$}1591.81=\text{ \$20.69}[/tex]Thus, I will choose the first account with 2.5% simple interest annually, because it yields $20.69 more than the second account after 3 years
Damin works 32 hours per week and earns 10.75 per hour
Answers
Answer:
32 • 10.75 = $344
Step-by-step explanation:
IF the question is asking how much they earned in 32 hours then your answer is $344. Its simple really, they already gave you the "unit rate" so you're all good 2 go. Good luck
I really need help on this, I don't get it at all. I need help on all of them
Answers
The if-then statement can be called a conditional statement.
In an If-then statement, the part attached to the if is the hypothesis while the part attached to then is the conclusion.
Therefore, we have the following:
• If it is January, then there is snow.
Hypothesis: If it is January
Conclusion: there is snow
Rewite the statement:
A straight angle has a measure of 180 degrees.
If an angle is straight, then it has a measure of 180 degrees.
12. Complete the missing values by writing the equivalent percent.
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Notice that every line represents 1/10. Thereby, the blanks to fill would be:
[tex]\begin{gathered} \frac{2}{10}\rightarrow\frac{1}{5} \\ \frac{4}{10}\rightarrow\frac{2}{5} \\ \frac{6}{10}\rightarrow\frac{3}{5} \\ \frac{8}{10}\rightarrow\frac{4}{5} \\ \end{gathered}[/tex]Thereby,
help meeeeeeee pleaseee
thank you
Answers
The domain of the relationship is: -∞ < x < ∞
The range of the relationship is: -∞ < y ≤ -3
The domain of a function is the defined set of x values, and the scope of the function is the defined set of y values.
The graph's domain is,
The curve on the x-axis begins x = -∞, and it concludes at x = ∞
So, the domain of the relation is: -∞ < x < ∞ .
The graph's range is,
On the y-axis, the curve begins at y = -∞, and it concludes at y = -3.
The connection has a range of -∞ < y ≤ -3.
As a result, the domain and range of the graph are: -∞ < x < ∞ and -∞ < y ≤ -3.
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F(-1)=-5 and g(-1) = 10 find (f+g)(-1)
Answers
The fucntion are given as
[tex]f(-1)=-5,g(-1)=10[/tex]To determine the expression for the function.
[tex](f+g)(-1)[/tex][tex](f+g)(-1)=f(-1)+g(-1)[/tex][tex](f+g)(-1)=-5+10[/tex][tex](f+g)(-1)=5[/tex]Thus the answer is 5.
(6.8 x 10^4)+(2.3 x 10^4) as a scientific notation?
Answers
We have the fortune that the power of ten is equal in both adding up. So
[tex]6.8\cdot10^4+2.3\cdot10^4=9.1\cdot10^4[/tex]Because the integer before the dot is less than 10, we need not do modifications and our answer is 9.1x10^4.
Which of these strategies would eliminate a variable in the system of equations?
6z+5y = 1
6z-5y=7
Choose all answers that apply:
Answers
Equivalent formulas to A=1/2h(b1+b2). Select ALL that apply
b1=b2 - 2A/H
b2=2A/h - b1
h=24/b1 + b2
1/2 b1 + 1/2 b2
b1=A/2h - b2
Answers
The equivalent formulas to A = [tex]\frac{1}{2h}(b_{1}+ b_{2})[/tex] are:
[tex]b_{2}[/tex] = 2A/h - [tex]b_{1}[/tex]
h = 2A / ([tex]b_{1}+ b_{2}[/tex])
[tex]b_{1}[/tex] = 2A/h - [tex]b_{2}[/tex]
A/h = 1/2[tex]b_{1}[/tex] + 1/2[tex]b_{2}[/tex]
Option B and Option D are correct.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
A = [tex]\frac{1}{2h}(b_{1}+ b_{2})[/tex]
We need to find equivalent equations such as:
[tex]A = \frac{1}{2}h(b_{1} +b_{2} ) \\[/tex]
Multiply both sides by 2/h.
2/h x A = [tex]b_{1}+ b_{2}[/tex]
2A/h = [tex]b_{1}+ b_{2}[/tex] _____(a)
Subtract [tex]b_{1}[/tex] on both sides.
2A/h - [tex]b_{1}[/tex] = [tex]b_{2}[/tex] _____(1)
From (a)
2A/h = [tex]b_{1}+ b_{2}[/tex]
Multiply both sides by h.
2A = h ([tex]b_{1}+ b_{2}[/tex])
h = 2A / ([tex]b_{1}+ b_{2}[/tex]) _____(2)
From (a)
2A/h = [tex]b_{1}+ b_{2}[/tex]
Subtract [tex]b_{2}[/tex] on both sides
2A/h - [tex]b_{2}[/tex] = [tex]b_{1}[/tex] _____(3)
From (a)
2A/h = [tex]b_{1}+ b_{2}[/tex]
Divide both sides by 2
A/h = 1/2[tex]b_{1}[/tex] + 1/2[tex]b_{2}[/tex] _____(4)
Thus,
From (1), (2), (3), and (4) we get the equivalent formulas:
[tex]b_{2}[/tex] = 2A/h - [tex]b_{1}[/tex]
h = 2A / ([tex]b_{1}+ b_{2}[/tex])
[tex]b_{1}[/tex] = 2A/h - [tex]b_{2}[/tex]
A/h = 1/2[tex]b_{1}[/tex] + 1/2[tex]b_{2}[/tex]
Option B and Option D are correct.
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Find the slope and y-Intercept of the line in the graph. Express the answers as simplified fractions, If necessary. COM ty 6 4 3 3 W 5 07 The slope is m = The y-intercept is b =
Answers
In order to find the slope and y-intercept of the line, first we can identify the point where the line intersects the y-axis, and that will be the y-intercept.
Looking at the graph, the line intersects the y-axis in the value y = -4, so the y-intercept is -4.
Now, to calculate the slope, we can identify two points on the line and use the following definition:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then, using the points (0, -4) and (3, 1), we have:
[tex]m=\frac{1-(-4)_{}}{3-0}=\frac{5}{3}[/tex]So the slope of the line is 5/3.
stevie's age is 2/3 ella's age. together, their ages sum to 20. find stevens age
Answers
Answer: Stevie's age = 8, Ella's age = 12
Step-by-step explanation:
What we know is that Stevie is 2/3 of Ella's age, and Stevie's age + Ella's age = to 20.
In order to figure out what is Stevie's age, we need to figure out Ella's age first. We will use variable e for Ella's age, and variable s for Stevie's age.
We will use these variables to build our equation
we can put [tex]\frac{2}{3}e[/tex] since we know 2/3 of Ella's age is equal to Stevie's age
[tex]\frac{2}{3}e[/tex] + e = 20
now we isolate the variable, (e) by multiplying by 3 on both sides of the equation
SO it will look like this,
2e+3e=60
then, we collect like terms, by adding 3e+2e
5e=60
then we divide both sides by 5 to isolate the e from the 5,
e=12.
Now we have found out Ella's age and we can plug that in to our second equation s=[tex]\frac{2}{3}e[/tex] to find out Stevie's age
s = [tex]\frac{2}{3}(12)[/tex]
and two-thirds of twelve is 8, so s=8
Stevie's age is 8 and Ellie's age is 12
a bit confusing to understand exactly. not so much on the math part, to get exactly what to compare.
Answers
77/125
Explanation:Probability of ordering sandwich that is either without cheese or is on sourdough bread = Probability of ordering a sandwich without cheese + probability of ordering a sourdough sandwich - probability of a sourdough sand wich without cheese
Sandwich without cheese = 425 + 700 = 1125
Sandwich with cheese = 800+ 1200 = 2000
Total of sandwich with or without cheese = 1125 + 2000 = 3125
Probability of ordering a sandwich without cheese = 1125/3125
Probability of ordering a sandwich without cheese = 9/25
ordering a sourdough sandwich = 800 + 425 = 1225
probability of ordering a sourdough sandwich = 1225/3125
probability of ordering a sourdough sandwich = 49/125
sourdough sandwich without cheese = 425
probability of a sourdough sandwich without cheese = 425/3125
probability of a sourdough sandwich without cheese = 17/125
Probability of ordering sandwich that is either without cheese or is on sourdough bread:
[tex]\begin{gathered} =\frac{9}{25}+\frac{49}{125}-\frac{17}{125} \\ =\text{ }\frac{5(9)+49-17}{125}=\frac{45+49-17}{125} \\ =\frac{77}{125} \end{gathered}[/tex]I need good, clearly explaining for this qustion.NOTE: Harry can fill an order in s minutes.
Answers
We have to find how long does it take for each person to fill an order.
We will use the concept of "capacity", that is the amount of order they can make in a minute. Then, when two persons work together, their capacities can be added.
We have Harry, Hermione and Ron.
Lets call C1: capacity of Harry, C2: capacity of Hermione, and C3: capacity of Ron.
Then, we can write:
[tex]\begin{gathered} C_1=\frac{1}{s} \\ C_2=\frac{1}{s-2} \\ C_3=\frac{1}{s+1} \end{gathered}[/tex]Note that the capacity is the inverse of the time it takes for them to fill one order.
We know that when Harry and Hermione work together, they take 1 minute and 20 seconds to fill an order. We can express this in minutes as:
[tex]T=1\min +20s\cdot\frac{1\min}{60s}=1+\frac{20}{60}=1+\frac{1}{3}=\frac{4}{3}\min [/tex]Then, we can write that the sum of the capacities of Harry and Hermione is equal to the inverse of the time it took them to fill an order:
[tex]C_1+C_2=\frac{1}{T}[/tex]If we replace C1, C2 and T, we get:
[tex]\begin{gathered} C_1+C_2=\frac{1}{T} \\ \frac{1}{s}+\frac{1}{s-2}=\frac{1}{\frac{4}{3}} \\ \frac{1}{s}+\frac{1}{s-2}=\frac{3}{4} \end{gathered}[/tex]We can solve for s as:
[tex]\begin{gathered} \frac{1}{s}+\frac{1}{s-2}=\frac{3}{4} \\ \frac{s+s-2}{s(s-2)}=\frac{3}{4} \\ \frac{2s-2}{s^2-2s}=\frac{3}{4} \\ 4\cdot(2s-2)=3\cdot(s^2-2s) \\ 8s-8=3s^2-6s \\ 0=3s^2-6s-8s+8 \\ 0=3s^2-14s+8 \end{gathered}[/tex]We have a quadratic equation, so we can find the solutions for s as:
[tex]\begin{gathered} s=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ s=\frac{-(-14)\pm\sqrt[]{(-14)^2-4\cdot3\cdot8}}{2\cdot3} \\ s=\frac{14\pm\sqrt[]{196-96}}{6} \\ s=\frac{14\pm\sqrt[]{100}}{6} \\ s=\frac{14\pm10}{6} \\ s_1=\frac{14-10}{6}=\frac{4}{6}=\frac{2}{3} \\ s_2=\frac{14+10}{6}=\frac{24}{6}=4 \end{gathered}[/tex]We have 2 solutions for s.
We can check that s = 2/3 is not a valid solution because it would make Hermione fill the order in negative time: s has to be greater than 2 for Hermione to have a valid time to fill the order:
[tex]s-2>0\Rightarrow s>2[/tex]Then, the value of s is 4.
Then, if we replace s we can calculate the time it takes for each member to fill an order:
[tex]\begin{gathered} \text{Harry}\longrightarrow t_1=s=4\min \\ \text{Hermione}\longrightarrow t_2=s-2=4-2=2\min \\ \text{Ron}\longrightarrow t_3=s+1=4+1=5\min \end{gathered}[/tex]Now, if the three work together, the capacities add, so we can express the time T it would take as:
[tex]C_1+C_2+C_3=\frac{1}{T}[/tex]We can replace the capacities and calculate T as:
[tex]\begin{gathered} \frac{1}{T}=\frac{1}{s}+\frac{1}{s-2}+\frac{1}{s+1}=\frac{1}{4}+\frac{1}{2}+\frac{1}{5} \\ \frac{1}{T}=\frac{1}{4}\cdot\frac{5}{5}+\frac{1}{2}\cdot\frac{10}{10}+\frac{1}{5}\cdot\frac{4}{4} \\ \frac{1}{T}=\frac{5}{20}+\frac{10}{20}+\frac{4}{20} \\ \frac{1}{T}=\frac{5+10+4}{20} \\ \frac{1}{T}=\frac{19}{20} \\ T=\frac{20}{19} \\ T\approx1.0526 \end{gathered}[/tex]It would take them approximately 1.0526 minutes, that can be expressed as 1 minute and 3 seconds. Note that this time is less than the time it takes Hermione and Harry when they work together, as we are adding a new person and increasing the capacity.
Answer:
a) Harry: 4 min, Hermione: 2 min, Ron: 5 min
b) It would take 1 minute and 3 seconds approximately.
Brad is deciding if he should buy six flags season pass. A pass costs $120 and $6 for food each day. Without the pass, the costs is $18. How many days does Brad need to go to break even?
Answers
Answer:
10 times
Step-by-step explanation:
Subtract the price of food per day from the daily cost and divide the season pass price by the daily cost without food.
120+(6•x) x=days 120+(6•x)=18•x
In a pet store, there are 8 puppies, 10 kittens and 6 parakeets. If a pet is chosen at random, what is the probability of choosing a puppy or a kitten?1234144
Answers
FORMULAS
If A and B are any events then:
[tex]P\mleft(AorB\mright)=P\mleft(A\mright)+P\mleft(B\mright)-P\mleft(AandB\mright)[/tex]If A and B are mutually exclusive events then P(A and B) = 0, so then:
[tex]P\mleft(A\text{ }or\text{ }B\mright)=P\mleft(A\mright)+P\mleft(B\mright)[/tex]The probability of an event happening is given to be:
[tex]P=\frac{\text{Number of required events}}{Number\text{ of total events}}[/tex]SOLUTION STEPS
The total number of pets in the store is calculated to be:
[tex]Total=8+10+6=24[/tex]The probability of picking a puppy is:
[tex]P(p)=\frac{8}{24}[/tex]The probability of picking a kitten is:
[tex]P(k)=\frac{10}{24}[/tex]Therefore, the probability of choosing a puppy or a kitten is gotten to be:
[tex]P(p\text{ }or\text{ }k)=\frac{8}{24}+\frac{10}{24}=\frac{18}{24}=\frac{3}{4}[/tex]ANSWER
The probability is 3/4 or 0.75.
Pls help fast !!!!!!
Answers
10 is the distance between two points .
What is Distance?
Distance is the overall movement of an object without consideration of direction. Regardless of an object's starting or ending position, distance can be defined as the amount of ground it has covered.In coordinate geometry, the distance between two given points is calculated using the distance formula. The formula D=(x2x1)2+(y2y1) is used to determine the distance between two points (x1,y1) (x 1, y 1) and (x2,y2) (x 2, y 2). 2 D = (x 2 − x 1) 2 + (y 2 − y 1) 2distance between points are ( -5 , -1 ) and ( 1 , - 9).
d = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1} )^{2} }[/tex]
d = [tex]\sqrt{( 1 - ( - 5 )^{2} + ( -9 - ( -1)^{2} }[/tex]
d = [tex]\sqrt{( 6 )^{2} + ( -8)^{2} }[/tex]
d = [tex]\sqrt{36 + 64}[/tex]
d = [tex]\sqrt{100}[/tex]
d = 10
Learn more about distance
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