Answer:
60 people left each year so -60
Step-by-step explanation:
-300 is the total population change over the past 5 years
The population decreased.
Divide 300/5 to find the amount of people who left each year
300/5= 60
60 people left each year.
The change in the towns population is (-60)
Kam can make 72 cookies in 3 hours at his house, while Madison can make 120 cookies in 4 hours at her house. How long would it take for them to make a total of 200 cookies together
Answer:
The answer to your question is: 3.7 hours
Step-by-step explanation:
Kam can make 72 cookies/ 3 hours
Madison can make 120 cookies/4 hours
Time to make 200 cookies together = ?
First, calculate the number of cookies make per hour
Kam 72 ---------------- 3
x ---------------- 1 hour
x = 72/3 = 24 cookies/h
Madison
120 ------------- 4 hours
x --------------- 1 hour
x = 120 / 4 = 30 cookies
Now we write and equation where "t" will be time
24t + 30t = 200 and solve it
54t = 200
t = 200/54
t = 3.7 hours
The time taken by both of them will be 3.7 hours.
What is the ratio of two numbers?The ratio of two numbers a and b can be written as a : b = a/b.
The ratio of two quantities is the unit rate of one quantity with respect to the other.
The given problem can be solved as follows,
The number of cookies made by Kam in 1 hour = 72/3 = 24.
The number of cookies made by Madison in 1 hour = 120/4 = 30.
The total number of cookies made by them in one hour = 30 + 24 = 54.
The time taken to make 200 cookies is the ratio of 200 and 54 as given below,
Time taken by both to make 200 cookies = 200/54 = 3.7 hours.
Hence, Kam and Madison would take 3.7 hours to make the cookies together.
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A seed company sells two grades of seed. A 100-pound bag of a mixture of rye and Kentucky bluegrass sells for $235, and a 100-pound bag of bluegrass sells for $341. How many bags of each are sold in a week when the receipts for 17 bags are $4,949?
Answer:
The company sold 8 bags of a mixture of rye and Kentucky bluegrass and 9 bags of bluegrass
Step-by-step explanation:
This is a classical problem that can be solved using a system of equations:
Let us first define our variables:
[tex]x[/tex] as the number of 100-pound bags which contain a mixture of rye and Kentucky bluegrass and,
[tex]y[/tex] as the number of 100-pound bags of bluegrass.
The problem tells us that in a week a total of 17 bags were sold, therefore, we can say that this number must be equal to the number of bags containing the mixture of rye and Kentucky bluegrass plus the number of bags containing bluegrass. Then, according to our variable names:
[tex]x+y=17[/tex] (1)
The problem also says that the company got a receipt for $4,949 in total. Hence, this number has to be equal to the total number of bags that contain rye and Kentucky bluegrass seeds times its price plus the number of bags containing bluegrass multiplied by its price. Then,
[tex]235x+341y=4949[/tex] (2)
Now we have the system of equations:
[tex]x+y=17[/tex] (1)
[tex]235x+341y=4949[/tex] (2)
Solving for [tex]x[/tex] in equation (1)
[tex]x+y=17\\x=17-y[/tex] (3)
And substituting [tex]x[/tex] in equation (2)
[tex]235x+341y=4949\\235(17-y)+341y =4949\\3995 - 235y +341y=4949\\-235y+341y = 4949-3995\\106y=954\\y=\frac{954}{106}\\ y=9[/tex]
Then, substituting [tex]y=9[/tex] in equation (1):
[tex]x+y=17\\x+9=17\\x=17-9\\x=8[/tex]
Thus, the company sold 8 bags of a mixture of rye and Kentucky bluegrass and 9 bags of bluegrass.
8 bags of the 100-pound mixture are sold, and 9 bags of the 100-pound bag of bluegrass are sold in a week.
Explanation:Let's assume that:
x = number of bags of the 100-pound mixture of rye and Kentucky bluegrass sold
y = number of bags of the 100-pound bag of bluegrass sold
We can set up a system of equations based on the given information:
x + y = 17 (The total number of bags sold is 17) 235x + 341y = 4949 (The total cost of the receipts is $4949)
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:
Multiply equation (1) by 235 to eliminate x: 235x + 235y = 3955 Subtract equation (2) from the result of step 1: (235x + 235y) - (235x + 341y) = 3955 - 4949
Simplifying the equation in step 2 gives us -106y = -994. Solving for y, we get y = 9.
Substituting the value of y back into equation (1), we get x + 9 = 17. Solving for x, we get x = 8.
Therefore, 8 bags of the 100-pound mixture are sold, and 9 bags of the 100-pound bag of bluegrass are sold in a week.
plz help!
Find the equation of the line in slope-intercept form that passes through the following point with the given slope. Simplify your answer.
Point (5,−2); Slope=5
Answer:
5x - y = 27
Step-by-step explanation:
Slope is the direction of line and it is calculated as,
[tex]Slope = \frac{y-y_{1}}{x-x_{1}} [/tex]
where (x₁, y₁) is any two points on the line.
Here, we have given that
Slope = 5 and (x₁, y₁) = (5, -2)
∴ [tex]5 = \frac{y-(-2)}{x-5} [/tex]
⇒ 5(x - 5) = y + 2
⇒ 5x - 25 = y + 2
⇒ 5x - y = 27
Hence, the equation of a line is: 5x - y = 27
Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. To determine customer opinion of their check dash in service, American Airlines randomly selects 110 flights during a certain week and surveys all passengers on the flights.
Answer:
This is cluster sampling.
Step-by-step explanation:
American Airlines randomly selects 110 flights during a certain week and surveys all passengers on the flights.
This is a type of cluster sampling.
This type of sampling is done by dividing the population into different groups and a simple random sample of clusters is selected from the population.
Lean ground beef is advertised at $1.78/lb. What is the price per kilogram? (There are approx. 2.2 lbs in 1 kg)
Answer:
The answer to your question is: $ 3.92 / kg
Step-by-step explanation:
Data
Lean ground beef cost = $1.78
price of 1 kg = ?
Equivalence 1 kg = 2.2 lbs
Process (rule of three)
$1.78 ------------------- 1 pounds
x ------------------- 2.2 pounds
x = 2.2(1.78) / 1 = $ 3.92 / kg
HELP PLEASE!!! :( ONLY TWO QUESTIONS
1.)The ratio of the angle measures in a quadrilateral is 4: 5 :8 :7 . What is the measure of each angle? ** Must show ALL work and steps for credit!
2.)JKLM~QRST with a scale factor of 4:7 MJ. = 58M. What is the value of TQ ?
Answer:
1) 60°, 75°, 120°, 105°
2) 101.5 m
Step-by-step explanation:
1) The sum of ratio units is 4+5+8+7 = 24, which corresponds to the sum of angles, 360°. Then each ratio unit must stand for 360°/24 = 15°. Multiplying the given ratio units by 15° gives the angle measures:
4×15° = 60°5×15° = 75°8×15° = 120°7×15° = 105°__
2) The similarity statement and the scale factor mean ...
MJ : TQ = 4 : 7
7·MJ = 4·TQ . . . . . . . . . "cross multiply"
TQ = 7/4×MJ = 7/4(58 m) . . . . . divide by 4, substitute the value of MJ
TQ = 101.5 m
This table represents a quadratic function with a vertex at (1,0). What is the
average rate of change for the interval from x = 5 to x = 6
Answer:
9 (option D)
Step-by-step explanation:
Hi Dlynjen! How are you?
Well, as maybe you know a quadratic function is a polynomial of degree 2, that is, the highest exponent in the variable is 2 (formula: y = ax^2 + bx + c). The graph of a quadratic function is a parabola (it has a U-shape).
The vertex of a parabola is the highest or lowest point of the curve (depending on whether the U opens up or down). In this case the parabola opens up because the exercise mentions the vertex is the point (x = 0, y = 1) and then for the other values of “x” (1, 2, 3, etc.) the values of “y” are higher (1, 4, 9, etc.), that's why the vertex is the lowest point in this case.
The exercise asks you to calculate the slope (or average rate of change) of the curve between x = 5 and x = 6, all you know so far is that as the curve opens up it is assumed that the slope will be positive but to calculate the slope must apply the following formula:
M = (y2 - y1) / (x2 -x1)
But we only know x1 = 5, x2 = 6, y1 = 16 (value of the table that corresponds to x1 = 5) and we must first know how much y2 is worth (for x2 = 6). For this we must know what is the quadratic function (formula) that gives rise to our parable.
If we analyze the table, we see that for each value of “x”, the value of “y” is equal to the square of (x-1), that is, if we take x = 3 as an example, the value of Y = (3 -1) ^ 2 = (2) ^ 2 = 4. And so with all the values. Having obtained this formula we can now calculate the value of “y” for x2 = 6:
Y2 = (6-1) ^ 2 = (5) ^ 2 = 25
Finally, we calculate the average exchange rate with the previous formula, knowing x1 = 5, x2 = 6, y1 = 16 and y2 = 25:
m = (y2 - y1) / (x2 -x1)
m = (25-16) / (6-1)
m = (9) / (1)
m = 9
I hope I've been helpful!
Regards!
Write an equation of the line with the given slope, m, and y-intercept (0.b).
m=8, b = 3
The equation is______
(Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)
Answer:
y = 8x + 3
Step-by-step explanation:
The slope-intercept form of the equation of a line is ...
y = mx + b
Putting 8 where m is, and 3 where b is, we get ...
y = 8x + 3
_____
Yes, it's really that simple.
The equation of the line with a slope of 8 and a y-intercept of 3 is y = 8x + 3. This is found by substituting the given values into the slope-intercept formula, which is y = mx + b.
Explanation:In Mathematics, the slope-intercept form of a linear equation is given by the formula y = mx + b, where 'm' represents the slope of the line and 'b' represents the y-intercept of the line. So, for the question, since the given slope, m = 8, and the y-intercept, b = 3, you can substitute these values into the formula to get the equation of the line. This results in the equation y = 8x + 3.
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gx+mp=c
Solve for X please
Answer:
x = (c -mp)/g
Step-by-step explanation:
Subtract the term not containing x, then divide by the coefficient of x.
gx +mp = c . . . . . given
gx = c - mp . . . . . subtract mp
x = (c -mp)/g . . . . divide by g
_____
Comment on the process
This process can be described various ways. A usual description is "get the x term by itself on one side of the equal sign, then divide by the x-coefficient."
I like a more general description of the solution to "solve for" problems: undo what is done to the variable, in reverse order.
Here, the variable x is multiplied by g, then added to mp. To undo those operations (in reverse order), first we undo the addition of mp. We accomplish that by subtracting mp, or by adding the opposite of mp, as you wish.
Having done that, we undo the multiplication by g by dividing by g.
(gx)/g = (c -mp)/g
x = (c -mp)/g
The steps we actually perform here are identical to the steps in "get the x-term by itself, ...". However, the process we have described can be applied to any sort of equation, not just a 2-step linear equation.
I don’t know how to do this help :(
A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 1 unit of protein, 2 units of carbohydrates, and 1 unit of fat. Each ounce of nuts will supply 1 unit of protein, 1 unit of carbohydrates, and 1 unit of fat. Every package must provide at least 7 units of protein, at least 11 units of carbohydrates, and no more than 10 units of fat. Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package.
a. Write a system of inequalities to express the conditions of the problem.
b. Graph the feasible region of the system.
a. Fill in the chart.
Fruit
Nuts
Requirements per package
Protein
nothing unit(s) per ounce
nothing unit(s) per ounce
At least
nothing unit(s)
Carbohydrates
nothing unit(s) per ounce
nothing unit(s) per ounce
At least
nothing unit(s)
Fat
nothing unit(s) per ounce
nothing unit(s) per ounce
No more than
nothing unit(s)
Answer:
See explanation
Step-by-step explanation:
Each ounce of fruit will supply
1 unit of protein, 2 units of carbohydrates, 1 unit of fat.Each ounce of nuts will supply
1 unit of protein, 1 unit of carbohydrates, 1 unit of fat.Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package.
Then x ounces of fruit will supply
x units of protein, 2x units of carbohydrates, x units of fatand y ounces of nuts will supply
y units of protein, y units of carbohydrates, y units of fat.Every package must provide
at least 7 units of protein, then x+y≥7,at least 11 units of carbohydrates, then 2x+y≥11,and no more than 10 units of fat, then x+y≤10.A. You get the system of three inequalities
[tex]\left\{\begin{array}{l}x+y\ge 7\\ 2x+y\ge 11\\x+y\le 10\end{array}\right.[/tex]
B. See attached diagram
[tex]\begin{array}{cccc}&\text{Protein}&\text{Carbohydrates}&\text{Fat}\\\text{Fruit}&x&2x&x\\\text{Nuts}&y&y&y\\&\text{at least 7}&\text{at least 11}&\text{no more than 10}\end{array}[/tex]
Three inequalities were formulated: 1x + 1y ≥ 7 for protein, 2x + y ≥ 11 for carbohydrates and x + y ≤ 10 for fat, with x being fruit and y being nuts. These needs to be graphed to find a feasible region that meets all conditions. A table summarizing the needed unit amount per ounce for protein, carbohydrates, and fats for both fruits and nuts was also provided.
Explanation:To solve your question, first, let's express the given conditions as inequalities:
For Protein: The amount of protein per ounce for the fruit is 1 and for the nuts is 1. So we will have 1x + 1y ≥ 7 units of protein. For Carbohydrates: The units of carbohydrates per ounce for fruit is 2 and for nuts is 1. Therefore, the inequality will be 2x + y ≥ 11 units of carbohydrates.For Fat: Each fruit and each nut both contains one unit of fat per ounce. The inequality for total fat units will be x + y ≤ 10 units of fat.Graphing
these inequalities would result in a feasible region that should fulfill all conditions.
The following table summarizes this:
Fruit
Nuts
Requirements per package
Protein1 unit per ounce1 unit per ounceAt least 7 unitsCarbohydrates2 units per ounce1 unit per ounceAt least 11 unitsFat1 unit per ounce1 unit per ounceNo more than 10 units
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what is multiplicative inverse of 2 and 1/4
WILL GIVE 15 FREE POINTS PLUS BRAINLIEST HELP ASAP!!!
Which expression is equivalent to 3 square root x^5y?
the answer is b) 5/3 1/3
x y
Solve by Substitution
Show Steps
−2x + 3y + 5z = −21
−4z = 20
6x − 3y = 0
−2x + 3y + 5z = −21
−4z = 20
6x − 3y = 0
do -4z=20 first
divide both sides by -4 to get z by itself
-4z/-4=20/-4
z=-5
Use z=-5 into −2x + 3y + 5z = −21
-2x+3y+5(-5)=-21
-2x+3y-25=-21
move -25 to the other side
sign changes from -25 to +25
-2x+3y-25+25=-21+25
-2x+3y=4
6x-3y=0
find x by eliminating y
Add the equations together
-2x+6x+3y+(-3y)=4+0
-2x+6x+3y-3y=4
4x=4
Divide by 4 for both sides
4x/4=4/4
x=1
Use x=1 into 6x − 3y = 0
6(1)-3y=0
6-3y=0
Move 6 to the other side
6-6-3y=0-6
-3y=-6
Divide both sides by -3
-3y/-3=-6/-3
y=2
Answer:
(1, 2, -5)
Help Me ASAP!!!!! PLS
Luca bought his home for $115,000 in 2007. Property values have increased 5% every year since she has owned the home. Which of the following equations can be used to represent the price of the home x years after 2010?
y = 115,000(1.5)x
y = 115,000(0.95)x
y = 115,000(1.05)x
y = 115,000(0.05)x
Answer:
C. y = 115 000(1.05)^x
Step-by-step explanation:
The formula for the amount accrued on an investment earning compound interest is
[tex]A = P(1 + r)^{t}[/tex]
where
P = the amount of money invested (the principal)
r = the interest rate per period expressed as a decimal fraction
t = the number of periods
In this problem,
P = $115 000
r = 5 % = 0.05
By 2010, Luca's house will have increased in value for three years. Its value will be
[tex]A = 115000(1 + 0.05)^{3}\\\text{The correct formula for the value of his home x years after 2010 is}\\ y = 115000(1.05)^{x}[/tex]
Answer:
C: y = 115,000(1.05)x
Step-by-step explanation:
(havn’t actually did any math, but this is just process of elemination.)
{I’m just looking at the end of these, because the start is all the same}
if the number with the (perenthese) is below 1, it is a decreas, and the problem says it’s increasing by 5%. (1.5) Is equal to 50% increase so that means your answer would be (1.05) Because anything times 1 is the larger number, but when u add that 0.5, it’s raising the number up by 5%.
Ticket sales for a spaghetti dinner total $2475. There are four times as many adult tickets sold as children's tickets. The prices of the tickets for adults and children are $10 and $5, respectively. Find the number of children's tickets sold.
Answer:
55 children's tickets
Step-by-step explanation:
Let the number of adult tickets sold = a
Let the number of children tickets sold = c
As per the statement "The adult tickets were sold four times as many as children's tickets".the equation will be
a = 4c ----- (1)
As per second statement "the prices of the tickets for adults and children are $10 and $5 respectively."
The total price of the adult tickets = 10a
the total price of the children tickets = 5c
total tickets were sold for = $2,475
So the equation will be
10a + 5c = 2,475 ------(2)
Now substitute the the value of a from equation (1) to equation (2).
10(4c) + 5c = 2,475
40c + 5 c = 2,475
45c = 2,475
c = [tex]\frac{2475}{45}[/tex]
c = 55
The number of children's tickets 55.
Final answer:
To find the number of children's tickets sold in a spaghetti dinner event with given total sales and ticket prices, set up and solve the relevant equations step by step.
Explanation:
Given:
Total ticket sales for a spaghetti dinner = $2475
Adult ticket price = $10
Children's ticket price = $5
Number of adult tickets sold = 4 times the number of children's tickets sold
To find: Number of children's tickets sold
Step-by-Step Solution:
Let the number of children's tickets sold be x
Number of adult tickets sold = 4x
Write the equation: 5x + 10(4x) = 2475
Solve for x to find the number of children's tickets sold
x = 55
A phone company charges 15.99 a month and 9 cents for every minute above 130 minutes. Write an expression for the monthly phone charge, P, in dollars, as afunctionof the number of minutes, m, used that month.
Answer:
[tex]p=\left \{ {{15.99,m[tex]\leq[/tex]130} \atop {15.99+0.09*(m-130),m>130}} \right.[/tex]
Step-by-step explanation:
We will have a partial funcion to define an expression for the monthly phone charge, because we have a condition that changes the monthly cost.
For months under 130 minutes, there will not be any additional charge other that tha base monthly cost, so the expression for the months under 130 minutes will be the monthly fee.
For months over 130 we will have the same information than above, but we have to add a fee for every minute over 130 minutes. To find the amaunt of minutes over 30 minutes we will just subtract 130 to the amount of minutes used: (m-130). Then we will multiply that number times the cos of each minute over 130 minutes: 9*(m-130). Finally we will add the basic phone fee: 15.99 + (0.09*(m-130)).
Now we set the conditions and use the correct notation for a partial function and we get:
[tex]p=\left \{ {{15.99,m[tex]\leq[/tex]130} \atop {15.99+0.09*(m-130),m>130}} \right.[/tex]
A function follows the rule y = -75 - 5x. When the function's output is 25, the equation is 25 = -75 - 5x. What is the function input when the output is 25?
Answer:
The function input is -20 when the output is 25
Step-by-step explanation:
we have
[tex]y=-75-5x[/tex]
where
y is the dependent variable or output
x is the independent variable or input
If the output is 25
then
y=25
substitute
[tex]25=-75-5x[/tex]
Solve for the function input is the same that solve for x
Isolate the variable x
Adds 5x both sides
[tex]25+5x=-75-5x+5x[/tex]
[tex]25+5x=-75[/tex]
subtract 25 both sides
[tex]25+5x-25=-75-25[/tex]
[tex]5x=-100[/tex]
Divide by 5 both sides
[tex]x=-20[/tex]
therefore
The function input is -20 when the output is 25
Final answer:
To find the function input when the output is 25, solve the given equation 25 = -75 - 5x to find x = -20.
Explanation:
When the function's output is 25, the equation is 25 = -75 - 5x. To find the function input when the output is 25, solve for x:
25 = -75 - 5x
100 = -5x
x = -20
Therefore, the function input when the output is 25 is -20.
The man entered an orchard that had 7 guards and picked some apples. When he left, he gave the first guard half his apples and 1 apple more. To the second guard, he gave half his remaining apples and 1 more. He did the same to each of the remaining five guards and left the orchard with 1 apple. How many apples did he gather in all? Explain how you solved the problem.
Answer:
896 apples
Step-by-step explanation:
We need to order this data to solve the problem. "X" will be the total number of apples he collected.
"He gave the first guard half of his apples and 1 apple more". Mathematically:
[tex]Guard 1 = \frac{X}{2}+1\\[/tex]
"To the second guard, he gave half his remaining apples and 1 more". Mathematically:
[tex]Guard2 = \frac{X}{4}+1[/tex]
"He did the same to each of the remaining five guards". Mathematically:
[tex]Guard3to7 = \frac{X}{8}+1+\frac{X}{16}+1+\frac{X}{32}+1+\frac{X}{64}+1+\frac{X}{128}+1[/tex]
Now we need to calculate "X" (total number of apples he collected). Let's sum all of the data above, that's our "X":
[tex]X= \frac{X}{2}+1 + \frac{X}{4}+1 + \frac{X}{8}+1+\frac{X}{16}+1+\frac{X}{32}+1+\frac{X}{64}+1+\frac{X}{128}+1[/tex]
Solving this equation results in X = 896 apples.
The school board asked Han to conduct a study on the attitudes of faculty regarding the proposed school uniform policy. Han stops by the teachers' lounge and surveys the faculty present. Which nonrandom sampling approach did Han employ?
Answer:
Han used a convenience nonrandom sampling approach
Step-by-step explanation:
The convenience nonrandom sampling approach consists in collecting a sample just because it is convenient. This means that the subjects are easy to select.
Han did precisely this, he went to the teacher's lounge and surveyed the faculty present there. He did not put any further effort like, for example, wait for more teachers to have a larger sample or make sure the ratio between female and male teachers was the same.
Please help justify these steps. First one to solve gets brainliest, hearts, and 5 stars. This question is worth 50 points!!!!!!!!
What is the justification for each step in solving the inequality?
2x+1≤3(x+1/)2
Select from the drop-down menus to correctly justify each step.
Answer:
Step-by-step explanation:
2x+1 ≤ 3(x+1)/2
2x+1 ≤ 3x+3/2
Multiply by 2 on both sides
4x+2 ≤ 3x + 3
Subtract 2 on both sides
4x ≤ 3x + 1
Subtract 3x from both sides
x ≤ 1
I think this is what you were asking?
Solve
An airplane went 20 miles an hour faster than twice the speed of a car that ran x miles an hour
Answer: B
Because you can eliminate the ones that don’t have an inequality symbol so that leaves you with B and D and the 20 should be on the right by itself since that is the constant we are given and it’s not altered in the question
The algebraic expression for the given problem is:
Speed of airplane = 2x + 20
What is Expression?In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, −, ×, ÷, ^) used to represent a quantity or a mathematical relationship between quantities.
" An airplane went 20 miles an hour faster than twice the speed of a car that ran x miles an hour"
The algebraic expression for the given problem is:
Speed of airplane = 2x + 20
Where x is the speed of the car in miles per hour.
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Clavins home is located at the midpoint between Fast pizza and pizza now,Fast pizza is a quarter mile away from calvins home.How far away is pizza now from calvins home?How far are the two pizzerias?
Answer:
q.1 quarter mile
q.2 half mile
:)
addition!
Step-by-step explanation:
Listed below are the commissions earned ($000) last year by a sample of 15 sales representatives at furniture patch inc. $4.2 $6.3 $7.5 $11.2 $13.0 $13.6 $15.2 $15.8 $16.7 $17.4 $18.6 $22.3 $37.6 $43.2 $83.6
a. Determine the mean, median, and the standard deviation. (round your answers to 2 decimal places.) mean $ median $ standard deviation $
b. Determine the coefficient of skewness using pearson's method. (round your answer to 3 decimal places.) coefficient of skewness
c. Determine the coefficient of skewness using the software method. (round your answer to 2 decimal places.)
Analyzing the data, the following values were
Mean = 21.84
Median = 15.8=
Standard deviation = 18.97
Coefficient of skewness = 0.955
How to determine the meana. To find the mean, median, and standard deviation, you can use the following formulas:
Mean = sum of all values / number of values
Median = middle value when the values are arranged in ascending order
Standard deviation = square root of [(sum of squared differences from the mean) / (number of values - 1)]
Mean = (4.2 + 6.3 + 7.5 + ... + 83.6) / 15 = 21.84
Median = 15.8 (the 8th value when arranged in ascending order)
Standard deviation = √([(4.2 - 21.84)² + (6.3 - 21.84)² + ... + (83.6 - 21.84)²] / 14) = 18.97
b. To find the coefficient of skewness using Pearson's method, you can use the following formula:
Coefficient of skewness = (3 * (mean - median)) / standard deviation
Coefficient of skewness = (3 * (21.84 - 15.8)) / 18.97 = 0.955
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Dorothy and Rosanne are baking cookies for a party. Working alone, Rosanne can finish the cookies in 6 hours. Dorothy can finish them in 8 hours if she is working alone. How long will it take them to bake the cookies if they are working together? Round your answer to the nearest hundredth if necessary.
Answer:
It will take them 3.43 hours.
Step-by-step explanation:
Let T denote the total cookies that need to be cocked. Observe that:
If Rosanne finishes the cookies in 6 hours, that means that she can make [tex]\frac{T}{6}[/tex] cookies per hour. If Dorothy finishes the cookies in 8 hours, that means that she can make [tex]\frac{T}{8}[/tex] cookies per hour.Then, by 1) and 2), if they work together would we able to make
[tex]\frac{T}{6}+\frac{T}{8}=\frac{8T+6T}{48}=\frac{14}{48}T=\frac{7}{24}T[/tex]
cookies per hour.
Therefore, in order to finish the T cookies they will need [tex]\frac{24}{7}\approx3.43 hours[/tex]
A recipe calls for cup of applesauce, cup of nuts, cup of flour, and cup of raisins. Which statement about the amount of apple sauce, nuts, flour, and raisins in the recipe is true? The recipe contains more raisins than flour. The recipe contains more nuts than raisins. The same amount of applesauce and flour is used. The same amount of applesauce, nuts, flour, and raisins is used.
Answer:
The same amount of applesauce, nuts, flour, and raisins is used.
Step-by-step explanation:
Have you ever heard of the question, "which weighs more, a pound of steel, or a pound of feathers?" And then everyone is shocked when they weigh the same, even though they both were said to weigh a pound?
This question is like that.
One cup of each is used, so they are all a cup, which means an equal amount of all of them were used.
A single microvillus is a rod-like structure that is 1.0 μm in height. It has a hemispherical top approximately 0.1 μm in diameter. Calculate the surface area of the cylinder that forms the "sides" of the microvillus rod. Use 3.14 for π.
Answer:
so, the figure here is a cylinder with a semi sphere on the top, we know the height of whole structure, and the radius of the semi sphere, which is the same as the radius of the cylinder (you can see it because the radius of the semisphere is constant, and you can thin on it as half a sphere over a cylinder).
First, the cylinder will be the structure without the semi sphere, so his height will be te total height minus the radius of the semi sphere, which is 0.9μm.
so now we know the height and the radius of the cylinder, the surface or the sides of it is 2*3.14*r*h = 2*3.14*0.9μm*0.1μm = 0.5662[tex]μm^{2}[/tex].
The surface area of the cylindrical part of the microvillus is calculated by multiplying pi (3.14) with the diameter (0.1μm) and height (1.0μm) to yield a result of 0.314μm².
Explanation:To calculate the surface area of the cylindrical 'sides' of the microvillus, which we can consider to be a cylinder without its top and bottom parts, the formula used is: π * diameter * height. In this case, the diameter of the microvillus is 0.1μm (which is the diameter of the hemispherical top) and the height is 1.0μm.
Substitute these values into the formula:
Surface area = π * diameter * height = 3.14 * 0.1μm * 1.0μm = 0.314μm².
Thus, the surface area of the cylindrical part of the microvillus is 0.314 micrometers squared.
Learn more about Surface area of a cylinder here:https://brainly.com/question/29015630
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At 9:00 PM the temperature in Chicago was -6°F. By morning the
temperature was +7°F. How many degrees did the temperature rise
overnight?
Answer:13
Step-by-step explanation: Six down to zero. Then zero up to seven.
A scale drawing of a square has a side length of 5 millimeters. The drawing has a scale of 1 mm : 5 km. Find the actual perimeter and area of the square.
Answer:
Actual Perimeter = 100 km
Actual Area = 625 km²
Step-by-step explanation:
A scale drawing of a square has a side length of 5 millimeters.
The drawing has a scale of 1 mm : 5 km (which represents 1 mm is equal to 5 km)
We need to find the actual measurement of 5 mm square on scale.
1 mm = 5 km
5 mm = 5 × 5 km
= 25 km
The actual length of the side of square is 25 km
Now, we find the perimeter and area of the square.
Perimeter of square = 4 × side= 4 × 25
= 100 km
Area of the square = side × side= 25 × 25
= 625 km²
Hence, The actual perimeter is 100 km and area of the square is 625 km²
how many times could a 3 minute song play in a hour?
Answer: 20 times
Step-by-step explanation:
1 hour = 60 minutes.
Duration of the song = 3 minutes each time = 3minutes/time
So, the number of times the song can be played in an hour=
= 60minutes÷3minutes/time = 20 times
So, you can play that song in an hour for 20 times.
Answer: 20 times
[tex]\textit{\textbf{Spymore}}[/tex]
Final answer:
A 3-minute song can play 20 times in an hour by simply dividing the 60 minutes in an hour by the length of the song, which is 3 minutes.
Explanation:
A 3-minute song can play 20 times in an hour. Here's a step-by-step breakdown of the math:
Understand that there are 60 minutes in an hour.
Divide the total minutes in an hour (60) by the length of the song (3 minutes).
The result is the number of times the song can be played in one hour, which is 20 times.
The question seems to diverge from the provided information about the collection of songs with varying lengths. However, for the direct question asked, we do not need those details.