The distance between the tennis balls and the cans is 49.46 cubic inches.
What is meant by volume?A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.
Given: Each ball has a diameter of three inches.
Three tennis balls are contained in each can, which is how they are sold.
Each can has a cylindrical shape.
We start by determining each tennis ball's volume.
Because of their spherical shape, their volume is determined by
[tex]$V=\frac{4}{3} \pi r^3$[/tex]
Where [tex]$r=\frac{d}{2}=\frac{3 \text { in }}{2}=1.5 i$[/tex] in
Replacing the radius and using [tex]$\pi \approx 3.14$[/tex], we have
[tex]$V=\frac{4}{3}(3.14)(1.5 \mathrm{in})^3=14.13 \mathrm{in}^3$$[/tex]
Therefore, the volume of each tennis ball exists 14.13 cubic inches, approximately.
Assuming that the diameter of each ball exists congruent with the diameter of the can, we contain the volume of a cylinder defined by
[tex]$V=\pi r^2 h$[/tex]
Where, r = 1.5 in and h = 3(3 in)=9 in, because each can has three balls, and the height exists the sum of all three diameters.
[tex]$V=3.14(1.5 i n)^2(9 i n)=63.59 n^3$$[/tex]
Therefore, the volume of each can exists 63.59 cubic inches, approximately.
The complete question is:
Tennis balls with a 3 inch Diameter are sold in cans of three. The can is a cylinder
A)what is the volume of one tennis ball ?
B)what is the volume of the cylinder ?
C)how much space is not occupied by the tennis balls in the can?
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Jason is closing on a $430,000 home. He made a 13% down payment and is borrowing the rest. What is the approximate range of costs that he might expect to pay at the closing?
Answer:
$8,600 - $31,100
Step-by-step explanation:
Hope this helps :)
Which is faster? Please show work
A. The black car that travels 110 feet per second
B. The silver car that travels 60 miles per hour
Answer:
the answer is A
I hope I help you in this ans and tq.
The equation, 868 = 700(1 + 0.04t), represents the amount of money earned on a savings account. What does the value 868 represent?
A. The value 868 represents the amount of interest earned, which means $868 was added to the initial balance.
B. The value 868 represents the final balance in the account, which means the account balance started with $868.
C. The value 868 represents the final balance in the account, which means the account ended with $868.
D. The value 868 represents the initial balance in the account, which means the account balance ended with $868.
The number 868 represents the final balance of the acount, then we conclude that the correct option is C.
"The value 868 represents the final balance in the account, which means the account ended with $868."
What does the value 868 represent?Weknow that the equation 868 = 700(1 + 0.04t) represents the amount of money earned on a savings acount.
We want to see what does 868 represent in this situation.
Where the form of the equation is:
money earned = function that depends on t.
So the value at the left, 868, just represents the final balance of the account, this is the amount of money that there is in the account at the end.
Thus, the correct option is C.
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find the iqr of 81, 82, 83, 83, 84, 84, 84, 85
The Interquartile range of the given set is 1.5.
What is Interquartile range ?
The variation between the third and first quartiles is defined by the interquartile range. The numbers that partition the entire series into four equal sections are known as quartiles. There are therefore 3 quartiles. The lower quartile is represented by the letter Q₁, the higher quartile by the letters Q₁, and the middle quartile by the letter Q₃.
Given set : 81, 82, 83, 83, 84, 84, 84, 85
Here, It is already in increasing order but the number of values is 8 which is even.
So, Q₁ part = 81, 82, 83, 83
Q₁ will be the median of 82 and 83.
So, Q₁ = (82+83)/2
= 82.5
Similarly, Q₃ part =84, 84, 84, 85
So, Q₃ will be the median of 84 and 84.
hence, Q₃ = (84+84)/2
= 84
We know that, Interquartile range = Q₃ - Q₁
= 84 - 82.5
= 1.5
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Beer and lemonade are mixed in a ratio of 3:2 to make handy. 5% of a beer i alcohol. What percentage of a handy i alcohol?
The percentage of alcohol in a handy is 3%. 3/5 * 5% = 3% , Since beer is 5% alcohol, then 3/5 of the handy is 5% alcohol.
The ratio of beer to lemonade in a handy is 3:2, which means that 3 parts of the handy is beer and 2 parts of the handy is lemonade. To express it in terms of fractions, 3/5 of the handy is beer and 2/5 of the handy is lemonade. Since beer is 5% alcohol, then 3/5 of the handy is 5% alcohol. Therefore, if you take the proportion of the beer in the handy and multiply it by the alcohol percentage of the beer, you will get the percentage of alcohol in the handy. In this case, 3/5 * 5% = 3%. This means that the percentage of alcohol in a handy is 3%. It's important to note that this assumes that the beer and lemonade are mixed together evenly and there's no spillage or evaporation. Also, it's important to consider the fact that the alcohol percentage of the beer can vary depending on the brand and type of beer.
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How do I work out this?
Answer:
3
Step-by-step explanation:
Take the x-intercept (1,0) and y-intercept (0,-3) to find the slope/gradient:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-3)}{1-0}=3[/tex]
Write the missing angle measure next to each
letter.
65°
a, b, c, d, e
The angle relationship I used to find Angle a is...
The angle relationship I used to find Angle b is...
The angle relationship I used to find Angle c is...
The angle relationship I used to find Angle d is...
The angle relationship I used to find Angle e is...
The missing angle measure for the following letters are:
a - 65°
b - 115°
c - 115°
d - 65°
e - 65°
The angle relationship I used to find Angle a is the Corresponding Angle (a = 65°)The angle relationship I used to find Angle b is Angles on a Straight line (b = 180 - 65)The angle relationship I used to find Angle c is the Corresponding Angle (b = c)The angle relationship I used to find Angle d is Angle on a straight line (d = 180 - 65) = 115°The angle relationship I used to find Angle e is. Corresponding angles. d = e and e = d.What is a corresponding angle?Corresponding angles are generated when two parallel lines are crossed by a transversal.
Opening and closing a lunchbox, completing a Rubik's cube, and endless parallel railway tracks are all examples of equivalent angles.
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Select all the ratios equivalent to 6:8
a)1:4
b)25:24
c)12:16
Answer:
c)12:16
Step-by-step explanation:
We know
The ratio is 6:8; we times 2 and get the ratio of 12:16
So, the answer is C
A new iphone costs $799 and is estimated to lose 25% of its value every six months after its purchase, what is the value of the phone after 2 years?
If a new I phone costs $799 and is estimated to lose 25% of its value every six months after its purchase ,then the value of phone after 2 years is $253 .
The cost of new i phone is = $799 ;
the percent loss in the value after every 6 month is = 25% = 0.25 ;
in 2 years , there are 4 period of six months , so , n = 4 ;
The depreciated value of i phone can be calculated by formula ;
⇒ Value = Cost × (1 - 0.25)ⁿ ;
Substituting value of n =4 and cost = $799 ;
⇒ Value = 799 × (1 - 0.25)⁴ ;
⇒ Value = 799 × (0.75)⁴ ;
⇒ Value = 799 × (0.75)⁴ ;
⇒ Value = 799 × 0.31640625 = 252.8085 ≈ 253 .
Therefore , the value of the phone after 2 years is $253 .
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Car = 6 cylinder compact Years driven = second and third Miles driven = 13,000 miles in year two and 12,000 in year three In dollars and cents, the total projected depreciation cost for these two years would be
In dollars and cents, the total projected cost of gas and oil for two years would be $ 756.00
First we will calculate per year how much is spent.
First year, we have :-
= 13000 * 0.028 = 364.00
Second year, we have:-
12000 * 0.028 = 336.00
The total cost in the two years is the sum of both:
= first year + second year
= 364.00 + 336.00 = 700.00
In dollars and cents, the total projected cost of gas and oil for two years would be $ 700.00.
Total cost
Total cost refers to the overall cost of production, which includes both fixed and variable components of the cost.
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complete question is :-
Compute the requested operating costs as indicated, based on the preceding table and the following information.
Choose the correct answer.
Car = 6 cylinder compact
Years driven = second and third
Miles driven = 13,000 miles in year two and 12,000 in year three
In dollars and cents, the total projected depreciation cost for these two years would be $?
Please help I need the answers ASAP.
Question 1:
[tex]\frac{2}{3} n-16=-\frac{5}{6}n+2[/tex], solve for n.
[tex]\frac{2}{3} n-16=-\frac{5}{6}n+2[/tex]
=> [tex]\frac{2}{3} n=-\frac{5}{6}n+18[/tex]
=> [tex]\frac{2}{3} n+\frac{5}{6}n=18[/tex] =>[tex]\frac{4}{6} n+\frac{5}{6}n=18[/tex]
=> [tex]\frac{9}{6} n=18[/tex] => [tex]\frac{3}{2} n=18[/tex]
=> [tex]n=18(\frac{2}{3})[/tex]
=> [tex]n=6(2)[/tex]
Sol: n=12
Question 2:
[tex]5-\frac{1}{3}p=\frac{4}{9}p+12[/tex], solve for p.
[tex]5-\frac{1}{3}p=\frac{4}{9}p+12[/tex]
=>[tex]5=\frac{4}{9}p+\frac{1}{3}p+12[/tex]
=> [tex]5=\frac{4}{9}p+\frac{3}{9}p+12[/tex]
=>[tex]5=\frac{7}{9}p+12[/tex]
=> [tex]-7=\frac{7}{9}p[/tex]
=> [tex]-7(\frac{9}{7}) =p[/tex]
=> [tex]-(9)=p[/tex]
Sol: p=-9
Question 3:
The relationship between ∠2 and ∠7 is that they are alternate interior angles.
Question 4:
The relationship between ∠1 and ∠3 is that they are corresponding angles.
Question 5:
The relationship between ∠4 and ∠5 is that they are alternate exterior angles.
Willow is driving on the freeway. She just passed mile marker 325. The fastest she will drive is 75 miles per hour, though, there is a bit of traffic that might slow her down a bit, but she doesn’t know exactly how much. The mile markers are increasing on her route.
The expression 325 + 2y represents what mile marker she’s at after 2 hours, depending on traffic. Which inequality describes the mile marker she would be at this point?
The inequality describes the mile marker she would be at this point is:
325 + 2y ≤ 475
Now, According to the question:
Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
We have,
The fastest driving speed of Willow is 75 miles per hour,
There is a bit of traffic on her route that might slow her speed down,
So, the inequality which represents the speed of the willow is:
y ≤ 75
Hence, the inequality which represents the speed of the driving of willow is y ≤ 75.
Now, the expression 361 + 2y represents what mile marker he is at after 2 hours. We know that the fastest he will drive is 75, so we could replace y=75 in the last expression to know what mile marker he would be seeing at that point. This is:
325 + 2(75) => 325 + 150 = 475
Now, we know that the inequality would be:
325 + 2y ≤ 475
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What is the weight (in grams) of a liquid that exactly fills a 182. 8 milliliter container if the density of the liquid is 0. 135 grams over milliliter ? Round to the nearest hundredth when necessary and only enter numerical values, which can include a decimal point
Liquid with density 0.135 grams over milliliter and volume 182.8 milliliter has weight equal to 24.68 grams.
Let 'm' represents the weight in grams of a liquid
Volume 'V' of the container to fill a liquid is = 182.8milliliter
Density 'ρ' of the given liquid is 0.135 grams over milliliter
Density = mass / Volume
Substitute the values we get,
⇒ 0.135 = m / 182.8 ×
⇒ m = 0.135 grams over milliliter × 182.8milliliter
⇒ m = 24.678 grams
⇒ m = 24.68 grams
Therefore, the weight of a liquid for the given density and the volume is equal to 24.68 grams.
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Mike saves $2,000 at a yearly simple interest rate of 2%, he earns $280 in interest for how many years did he save this money
The number of years that he save this money is 7 years
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
Where P is the principal, R is the rate of interest, and T is the time.
Given;
Mike saves $2,000 at a yearly simple interest rate of 2%;
Money he earns in interest= $280
Then the number of years;
$280 = ($2,000 x 2 x T) / 100
$28,000 = $4,000 x T
T = $28,000 / $4,000
T = 7 years
Therefore, numbers of years mike has to pay interest will be 7
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Give f(x)=3-|2x-5| find f(0)+f(-4)
The value of the function f(0) + f(-4) is -12
How to determine the value of the function?From the question, we have the following equation that can be used to solve the question
f(x) = 3 - |2x - 5|
Also, we have the function values to be
f(0) and f(-4)
When these values are calculated, we have
f(0) = 3 - |2(0) - 5| = -2
f(-4) = 3 - |2(-4) - 5| = -10
substitute the known values in the above equation, so, we have the following representation
f(0) + f(-4) = -2 - 10
Evaluate
f(0) + f(-4) = -12
Hence, the solution is -12
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Ayúdenme a encontrar el valor de los ángulos la medida de A) es 48 grados y E) es 136 grados y con eso encuentra los valores de los demás
eeeeeAnswer:
Step-by-step explanation:
(e) (i) Using a scale of 2cm to represent 5 units on each axes, show, by shading the unwanted regions, the set of points satisfying the three inequalities in parts (b), (c) and (d). [3] (ii) Calculate the maximum number of rabbits the farmer can buy. [2]
Answer: (e) (i) To represent the inequalities graphically on a coordinate plane, you can use a scale of 2cm to represent 5 units on each axis. To shade the unwanted regions, you can start by drawing the coordinate plane and labeling the x and y axes. Then, you can graph the inequalities by plotting the lines and shading the regions that do not satisfy the inequalities.
(b) 2x + 3y ≤ 30
This inequality represents a line with the equation 2x + 3y = 30. You can graph this line by plotting a few points and then drawing a straight line through them. The points that are on or below the line satisfy the inequality.
(c) x - 2y ≥ -10
This inequality represents a line with the equation x - 2y = -10. You can graph this line by plotting a few points and then drawing a straight line through them. The points that are on or above the line satisfy the inequality.
(d) y ≤ -2x + 10
This inequality represents a line with the equation y = -2x + 10. You can graph this line by plotting a few points and then drawing a straight line through them. The points that are on or below the line satisfy the inequality.
The set of points that satisfy all three inequalities is the area that is not shaded in the graph.
(ii) To find the maximum number of rabbits the farmer can buy, we need to find the coordinates of the vertex of the feasible region.
The coordinates of the vertex of the feasible region is (x,y) the point where the line 2x+3y=30 and x-2y=-10 intersects.
We can substitute the x-2y=-10 into the 2x+3y=30 equation
2x+3y=30
2x+3y+2y=-10
2x+5y=-10
x=-5y+10
substituting this into one of the equation we have
2(-5y+10)+3y=30
-10y+20+3y=30
-7y=10
y= -10/7
substituting this into x = -5y+10 we have
x = -5(-10/7)+10 = 15
the maximum number of rabbits the farmer can buy is 15
Step-by-step explanation:
PLEASE HELP ASAP
Find the value of r so that the line through (r,5) and (6,r) has a slope of 5/8
Answer: 70/13
Step-by-step explanation:
Slope = rise/run
(r-5)/(6-r) = 5/8
30-5r = 8r-40
70 = 13r
70/13 = r
The accessory choices of 143 people are recorded in the table. Please help!
For given frequency table the relative frequency table with percentage is given in image.
What is a frequency table ?
A frequency table consists of the lists of items in a given data set and the number of times each item occurs in the data set and The number of times a particular data value occurs in a given data set is referred to as its frequency.
e.g.
A, A, A, B, B, B, B, C, C, D
Count the number of times each grade occurs in the above series. Yes, ‘A’ occurs thrice, ‘B+’ occurs four times, ‘C’ occurs twice, and ‘D’ occurs once. Now, according to the definition of frequency, we can note the frequency of each grade as follows:
Frequency of A = 3
Frequency of B = 4
Frequency of C = 2
Frequency of D = 1
Let us list the grades obtained by the students in the above example, in a frequency table. Table is in image.
Now,
To find the percentage for relative frequency table we used (given value/Total people)*100.
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The table shows information about the lengths of time, in minutes, it took some
pupils to do their maths homework last week.
Frequency
Length of time (1)
0
5
10
24
25
12
30
8
2
Draw a histogram for
the information in the table.
Frequency density
0+
10
20
30
Length of time (1)
40
50
The graphic representation of data points arranged into user-specified ranges is called a histogram. The diagram below that is attached shows the histogram diagram.
A histogram is a figure made up of rectangles with widths equal to the class interval and areas proportionate to the frequency of a variable.
From the given information, we have the following:
Length of time (t) Frequency
0 ≤ t < 10 5
10 ≤ t < 25 24
25 ≤ t < 30 12
30 ≤ t < 50 8
So, the image that is attached shows how the table is represented in a histogram.
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The complete question is given below:
Mr. Garcia rents a car at a rate of $29.95 per day. There is an additional mileage charge of $20.00 per 100 miles or fraction of 100. If Mr. Garcia drives 550 miles in 5 days, which expression shows the total cost of Mr. Garcia’s trip?
In the given word problem, Mr. Garcia total paid $259.75 for his journey.
What are words problems?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
Given that, Mr. Garcia rents a car at a rate of $29.95 per day. There is an additional mileage charge of $20.00 per 100 miles or fractions of 100, and Mr. Garcia drives 550 miles in 5 days,
Since, cost of 100 mile = $20
Therefore, cost for 1 mile = $0.2
Since, Mr. Garcia travelled for 550 miles,
Therefore, cost of 550 miles = $0.2 × 550 = $110
Since, cost for one day = $29.95
Therefore, cost for 5 days = $29.95 × 5 = $149.75
Now,
Mr. Garcia used the car for 5 days and travelled for 550,
Therefore, total cost he paid = $110 + $149.75
= $259.75
Hence, Mr. Garcia total paid $259.75 for his journey.
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Consider the function g(x)=6cos(7x+22).
How much must x increase by for 7x+22 to increase by 2π?
After the increment in the function the value of x is -2.25
In math the term function is denoted as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Here we know that the function g(x)=6cos(7x+22), x increase by for 7x+22 to increase by 2π.
In order to calculate the value of x in the function, we have to equate the value of function with 2π.
Then we get,
=> 7x + 22 = 2π
When we solve the equation for x then we get,
=> 7x = 2π - 22
=> x = (2π - 22)/7
When we simplify this one then we get the value of x as,
=> x = 0.285π - 3.14
=> x = 0.89 - 3.14
=> x = -2.25
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Francine had six times the money Tommy had, but after Francine gave Tommy $33 to help him purchase a baseball cap, Tommy had twice as much as Francine. How much did they each start with?
For the relation of times of money , Francine and Tommy start with the amount of money equals to $18 and $3 respectively.
Let 'x' represents the amount of money with Francine .
And 'y' represents the amount of money with Tommy.
In the first condition:
x = 6y __(1)
To purchase baseball cap Francine gave $33 then the given relation is :
y - 33 = 2( x - 33 )
⇒ y - 33 = 2x - 66
⇒y = 2x -66 + 33
⇒ y = 2x -33 __(2)
Substitute the value of 'x' from (1) in (2) we get,
y = 2(6y) - 33
⇒y = 12y - 33
⇒ 12y - y = 33
⇒ 11y = 33
⇒ y = $3
⇒ x = 6(3)
⇒ x = $18
Therefore, the amount of money Francine and Tommy start with is equal to $18 and $3 respectively.
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2x/3x-5-x+1/3x+5=-4/9x^2-25
The solution to the expression in this problem is given as follows:
x = -1/3 + 1.7i and x = -1/3 - 1.7i.
How to solve the rational expression?The rational expression for this problem is defined as follows:
[tex]\frac{2x}{3x - 5} - \frac{x + 1}{3x + 5} = -\frac{4}{9x^2 - 25}[/tex]
Applying the least common factor at the left side, we have that:
[tex]\frac{2x(3x + 5) - (x + 1)(3x - 5)}{9x² - 25} = -\frac{4}{9x^2 - 25}[/tex]
[tex]\frac{6x^2 + 10x - 3x^2 + 5x - 3x + 5}{9x^2 - 25} = -\frac{4}{9x^2 - 25}[/tex]
As the denominators are equal, the solution is obtained equaling the denominators, hence:
3x² + 2x + 5 = -4
3x² + 2x + 9 = 0.
Which is a quadratic function with coefficients given as follows:
a = 3, b = 2, c = 9.
Inserting these coefficients into a calculator, the solutions are given as follows:
x = -1/3 + 1.7i and x = -1/3 - 1.7i.
Missing InformationThe rational expression is given by the image presented at the end of the answer.
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Choose the inequality that matches the graph below.
Answer:
X ≤ -1
How do we know this?
Well, if x = the value of any number in the graph, we can see that it can be equal to negative one, or less than -1, meaning we use the symbol ≤.
A new Lexus sells for $56,000. Use 2 depreciation models and desmos to answer the following questions.
Model A: The car depreciates 12% per year.
Model B. Use straight line depreciation - the car has a value of $0 in 12 years.
Use desmos and attach a screenshot to show the following.
1. Use the wrench tool to label your x an y-values, change your x and y-value to appropriate numbers. Remember to lock the viewpoint.
2. Write on your screenshot and label the point where the linear model and the exponential model are equal.
3. Attach a screenshot to this ssignment.
Justgive me the equations
The time in years for which the values are the same is given as follows:
7.25 years.
How to obtain the models?A decaying exponential model is given as follows:
y = a(1 - r)^t.
For which:
a is the initial value.r is the decay rate, as a decimal.The parameters for this problem are given as follows:
a = 56000, r = 0.12.
Hence the exponential model is given as follows:
y = 56000(0.88)^x.
The linear model is given as follows:
y = b - mx.
In which:
b is the initial value.m is the yearly depreciation rate.The parameter values for this problem are given as follows:
b = 56000, m = 56000/12 = 4666.67.
Hence the linear model is:
y = 56000 - 4666.67.
The point of intersection of the two graphs is at a time of 7.25 years.
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7:21:35 in its simplest form
The smallest equivalent fraction of the number is considered to be its simplest form.The answer is 7/3 : 21/5 = 5 : 9.
What is what in its most basic form?Values should now be entire numbers.By removing the denominators, convert fractions to integers.
Since the denominators of our two fractions are different, we must identify the least common denominator and rewrite our fractions using the common denominator as necessary.
LCD(7/3, 21/5) = 15
Now we have:
7/3 : 21/5 = 35/15 : 63/15
Now that the denominators of our two fractions are similar, we may multiply them both by 15 to get rid of the denominators.
Then, we have:
7/3 : 21/5 = 35 : 63
With the highest common factor, attempt to further reduce the ratio (GCF).
GCF is 7 for 35 and 63.
Divide both terms by GCF 7, then:
35 ÷ 7 = 5
63 ÷ 7 = 9
By multiplying both components by the GCF = 7, it is possible to reduce the ratio 35: 63 to its simplest terms.
35 : 63 = 5 : 9
Therefore:
7/3 : 21/5 = 5 : 9
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Please help me <3 Thanks :)
A set of elementary school student heights are normally distributed with a mean of 105 centimeters and a
standard deviation of 10 centimeters. Faisal is an elementary school student with a height of 103. 1 centimeters.
What proportion of student heights are lower than Faisal's height?
You may round your answer to four decimal places
Answer:
0.4247
Step-by-step explanation:
You want to know the proportion of heights less than 103.1 cm if the population is normal with a mean of 105 cm and a standard deviation of 10 cm.
ProportionThe proportion can be found using a suitable probability calculator. The one shown in the attachment tells us ...
the proportion of heights less than 103.1 cm is about 0.4247.
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Additional comment
The height of interest is less than the mean by approximately 0.2 times the standard deviation. This suggests the proportion will be close to, but less than, 0.5000.
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Function A and Function B are linear functions
to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below for Function A.
[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-5)}}}{\underset{\textit{\large run}} {\underset{x_2}{10}-\underset{x_1}{(-8)}}} \implies \cfrac{4 +5}{10 +8} \implies \cfrac{ 9 }{ 18 } \implies \cfrac{1 }{ 2 }\impliedby \stackrel{\textit{slope of}}{A} \\\\[-0.35em] ~\dotfill[/tex]
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{5}x-1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \stackrel{\textit{slope of}}{B} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} \stackrel{A}{\cfrac{1}{2}} ~~ < ~~ \stackrel{B}{5} \end{array}}~\hfill[/tex]