Answer:
part 1- 1/3
part 2- a.n = 22/3+(n-1)1/3
part 3- size 12
Step-by-step explanation:
The common difference of the arithmetic sequence is 0.5 inches.
To find the common difference of the arithmetic sequence, we can use the given information about the shoe sizes and corresponding foot lengths.
Let's denote the common difference by [tex]\( d \)[/tex]. In an arithmetic sequence, the[tex]\( n \)-th[/tex] term is given by [tex]\( a_n = a_1 + (n - 1)d \)[/tex], where [tex]\( a_1 \)[/tex] is the first term.
Given that a women's size 3 fits a foot 8 inches long, we can consider this as the first term of the arithmetic sequence:
[tex]\[ a_1 = 8 \][/tex]
We are also given that a women's size 7 fits a foot[tex]\( 9\frac{1}{3} \)[/tex] inches long. Since this corresponds to the 5th term in the sequence (because [tex]\( 7 - 3 = 4 \)[/tex] and we start counting from 0), we can write:
[tex]\[ a_5 = a_1 + 4d \][/tex]
[tex]\[ a_5 = 8 + 4d \][/tex]
We know[tex]\( a_5 = 9\frac{1}{3} \),[/tex]which is [tex]\( 9 + \frac{1}{3} \) or \( \frac{28}{3} \)[/tex] inches. Now we can set up the equation:
[tex]\[ 8 + 4d = \frac{28}{3} \][/tex]
To solve for [tex]\( d \)[/tex], we first convert[tex]\( \frac{28}{3} \)[/tex] to a decimal or a fraction with a denominator of 1 to match the units of the other terms:
[tex]\[ 8 + 4d = \frac{28}{3} \times \frac{1}{1} \][/tex]
[tex]\[ 8 + 4d = \frac{28}{3} \][/tex]
[tex]\[ 8 + 4d = 9\frac{1}{3} \][/tex]
[tex]\[ 8 + 4d = 9.333... \][/tex]
Now, we solve for[tex]\( d \)[/tex]:
[tex]\[ 4d = 9.333... - 8 \][/tex]
[tex]\[ 4d = 1.333... \][/tex]
[tex]\[ d = \frac{1.333...}{4} \][/tex]
[tex]\[ d = 0.333... \][/tex]
However, we need to express[tex]\( d \)[/tex] in inches, and since [tex]\( \frac{1}{3} \)[/tex] of an inch is [tex]\( 0.333... \)[/tex]inches, we convert it to a fraction that has a denominator of 2 to match the format of the options given:
[tex]\[ d = \frac{1}{3} \times \frac{2}{2} \][/tex]
[tex]\[ d = \frac{2}{6} \][/tex]
[tex]\[ d = \frac{1}{3} \][/tex]
[tex]\[ d = 0.5 \][/tex]
Therefore, the common difference of the arithmetic sequence is[tex]\( 0.5 \)[/tex]inches."
A coffee merchant wants to make 6 pounds of a blend of coffee costing five dollars per pound. The blend is made using a six dollar per pound grade coffee and a three dollar per pound grade of coffee. How many pounds of each of these grades should be used?
Answer:
We should use 4 pounds of $6 coffee and 2 pounds of $3 coffee for the blend.
Step-by-step explanation:
The blend should,
Cost = $5
Weigh = 6 pounds.
Lets take the weight of $6 coffee as [tex]x[/tex] pounds
And lets take the weight of $3 coffee as [tex]y[/tex] pounds.
Lets write an equation for the weight of the blend,
[tex]x+y=6[/tex] <---------- 1st equation.
[tex]\frac{6x+3y}{x+y} =5[/tex]
=[tex]6x+3y=5x+5y[/tex]
=[tex]x=2y[/tex] <---------- 2nd equation
We can substitute to x in 1st equation from 2nd equation,
⇒[tex]2y+y=6[/tex]
=[tex]2y+y=6[/tex]
=[tex]3y=6[/tex]
=[tex]y=2[/tex]
We can substitute y value to 2nd equation to find x,
⇒[tex]x=2y[/tex]
=[tex]x=2*2[/tex]=[tex]x=4[/tex]
Therefore, we should use 4 pounds of $6 coffee and 2 pounds of $3 coffee for the blend.
You have a normal distribution of hours per week that music students practice. The mean of the values is 8 and the standard deviation of the values is 4. According to the normal distribution model that corresponds to this population, what percentage of the students practice between 6 to 10 hours per week? Use the graph of the standard normal distribution given below to find the percentage. 19% 30% 34% 38%
Answer:
38%
Step-by-step explanation:
Given that X,the hours per week the music student practice follow a normal distribution.
X:N(8,4)
We have to find the percentage of students who practice between 6 and 10 hours.
6<x<10 implies converting to z
We know z = (x-mean)/sigma = (x-8)/4
Hence 6<x<10 is equivalent to (6-8/4)<Z<(10-8/4)
= |z|<0.5
From std normal table we find this area equals = 0.1915+0.1915
=0.3830 = 0.38 (rounded off)
Hence required percentage = 0.38x100 = 38%
Final answer:
To determine the percentage of music students practicing between 6 to 10 hours, we convert these hours to z-scores and use the standard normal distribution table, which reveals that approximately 38.2% of students practice within this range.
Explanation:
To find the percentage of music students who practice between 6 to 10 hours per week, we can use the properties of the normal distribution. We first need to convert the range values to z-scores using the formula Z = (X - μ) / σ, where X is the value from the data set, μ is the mean, and σ is the standard deviation.
Converting 6 hours to a z-score:
Z = (6 - 8) / 4 = -0.5
Converting 10 hours to a z-score:
Z = (10 - 8) / 4 = 0.5
Now we use the standard normal distribution table to find the probability corresponding to these z-scores. The area under the curve between z-scores -0.5 and 0.5 gives us the desired percentage. Looking up the z-scores in the standard normal distribution table, we find that the area between these scores is approximately 38.2%. Thus, 38% is the closest option provided.
What’s the product of 4(-3)
A jug contained 6qt of Kolkata. Tom drank 3/8 of the jug. How much did he drink?
Tom drank 2.25qt of the jug, in fraction form it would be 2 1/4
I need help with this please
The Sumerian civilization believed in the divine right of kings.
True False
5 decimal jumps to the right is a shortcut to what math
In this Decimal Point Movement question, Moving the decimal five places to the right in mathematics is a shortcut for multiplication by 105 (one hundred thousand). This uses the principle of powers of ten.
In mathematics, moving the decimal five places to the right is actually a shortcut for multiplying by 105, or 100,000. This concept utilizes the patterns in powers of ten. For instance, for any given number, we can count the zeros in the power of ten and then move the decimal point that same number of places to the right.
Illustrating with an example, let's say we have the number 5.27. If we multiply it by 105, we move the decimal five places to the right to get 527000. This aligns with the multiplication principle: when we multiply by 10, 100, 1000, and so on, each time, we are essentially incrementing the decimal place to the right.
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Line JK has the slope 3/4 and is perpendicular to line LM. What is the slope of line LM?
Answer:
The slope of line [tex]LM[/tex] is [tex]-\frac{4}{3}[/tex]
Step-by-step explanation:
Line [tex]JK[/tex] has the slope [tex]\frac{3}{4}[/tex] and is perpendicular to line [tex]LM[/tex]
Suppose, the slope of line [tex]LM[/tex] is [tex]m[/tex]
We know that, the product of the slopes of two lines which are perpendicular to each other is always [tex]-1[/tex]. So, the equation will be..............
[tex]\frac{3}{4}*m= -1\\ \\\frac{3m}{4}=-1\\ \\ 3m= -4\\ \\ m=-\frac{4}{3}[/tex]
So, the slope of line [tex]LM[/tex] will be [tex]-\frac{4}{3}[/tex]
How to round 4.66 to the nearest hundredth
48 times 24 pleaseeee
48 times 24 is 1,152.
48x24=672
Hope I helped!
ΩωΩ
6-x=5x+30
but I need it solved like the picture pls thanks!
6-x=5x+30
-x=5x+30-6
-x=5x+24
-x-5x=24
-6x=24
x=24/-6
x=-4
Hello there!
[tex]6-x=5x+30\\[/tex]
Explanation:
↓↓↓↓↓↓↓↓↓↓↓↓
First you had to subtract by 6 from both sides of the equation.
[tex]6-x-6=5x+30-6[/tex]
Simplify
[tex]-x=5x+24[/tex]
Then you subtract by 5x from both sides of the equation.
[tex]-x-5x=5x+24-5x[/tex]
Simplify
[tex]-6x=24[/tex]
Divide by -6 from both sides of the equation.
[tex]\frac{-6x}{-6}=\frac{24}{-6}[/tex]
Simplify it should be the correct answer.
[tex]x=-4[/tex]
Answer⇒⇒⇒⇒⇒x=-4
Hope this helps!
Thank you for posting your question at here on Brainly.
Have a great day!
-Charlie
What is the solution to this equation? 2x+4=16
[tex]2x+4=16\\\\2x=12\\\\x=6[/tex]
The solution to the equation 2x + 4 = 16 is x = 6.
What is the solution to the equation?Given the equation in the question:
2x + 4 = 16
To solve the equation 2x + 4 = 16, first, isolate the variable term on one side by moving the constant term to the other side of the equation.
2x + 4 = 16
Subtract 4 from both sides of the equation:
2x + 4 - 4 = 16 - 4
2x = 16 - 4
Subtract 4 from 16:
2x = 12
Divide both sides of the equation by 2 to isolate the variable x:
2x/2 = 12/2
x = 12/2
x = 6
Therefore, the value of x is 6.
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Jina is chosing a 2-letter password from the letters A,B,C, and D. The password cannot have the same letter repeated in it. How many such passwords are possible?
I need help on this
Answer in the attachment.
HE;P ME!!!!!
The average rainfall in Annette, Alaska is 0.31 inches per day. How much rain falls over the course of an average September?
The average amount of rain fall is 9.61 inches
The average rainfall in Annette, Alaska is 0.31 inches per day. Over the course of an average September, the total amount of rain that falls is 9.3 inches.
Explanation:To find out how much rain falls over the course of an average September, we need to know the number of days in September. Let's assume there are 30 days. Given that the average rainfall in Annette, Alaska is 0.31 inches per day, we can calculate the total rainfall by multiplying the average rainfall per day by the number of days in September: 0.31 inches/day * 30 days = 9.3 inches.
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3x+10y=13
4(-2y+x)-9x=13
Answer:
[tex]x=-9[/tex]
[tex]y=4[/tex]
Step-by-step explanation:
[tex]3x+10y=13[/tex] ← Equation 1
[tex]4(-2y+x)-9x=13\\[/tex]
By simplifying the above equation we get,
[tex]-8y+=4x-9x=13[/tex] (Simplifying the brackets)
[tex]-8y-5x=13[/tex] (By subtracting [tex]-9x[/tex] from [tex]+4x[/tex]) ← Equation 2
Multiply Equation 1 by 5 and Equation 2 by 3 and add them together.
Equation 1 multiplied by 5 will give,
[tex]15x+50y=65[/tex]
Equation 2 multiplied by 3 will give,
[tex]-24y-15x=39[/tex]
Add those together,
[tex]15x+50y-24y-15x=65+39[/tex]
[tex]26y=104[/tex] (After simplifying [tex]x[/tex] values)
Therefor [tex]y=4[/tex]
By substituting [tex]y=4[/tex] to Equation 1 we get,
[tex]3x+10*4=13[/tex][tex]3x+40=13\\3x=-27\\x=-9[/tex]
Therefor we can say,
[tex]x=-9[/tex]
[tex]y=4[/tex]
Determine whether the given lengths can be sides of a right triangle.
10 in., 26 in., 24 in.
Can 10, 26, and 24 be the lengths of the sides of a right triangle?
The length of a rectangle is seven times the width. To express the length and the width in terms of the same variable, let W be the width. Then the length is
100e^0.125t=200
A. t= ln(16)
B. t= ln(256)
C. t= 8ln(100)
D. t= 0.08ln(200)
To solve the equation 100e^0.125t=200 for t, divide by 100, apply the natural logarithm, and rearrange to find t=ln(2)/0.125, which simplifies to t=ln(16).The Correct Answer is Option. A.
Explanation:The question involves solving for the variable t in the exponential equation 100e^0.125t=200.
To solve this, we need to isolate the exponent on one side. Here are the steps to find the correct value of t:
Divide both sides by 100 to get e^0.125t = 2.Apply the natural logarithm (ln) to both sides to obtain ln(e^0.125t) = ln(2).Simplify the left side using the property ln(e^x) = x, resulting in 0.125t = ln(2).Finally, divide both sides by 0.125 to find t. This gives t = ln(2)/0.125.The correct answer from the given options is A. t= ln(16), as ln(2) / 0.125 = ln(16).
Kathy Stood on the middle rung of a ladder. She climbed up three rungs, moved down five rungs, and then climbed up 7 rungs. Then she climbed up the remaining 6 rungs to the top of the ladder. How many rungs are there in the whole ladder?
There are 13 rungs on the ladder :)
Answer:
23 rungs
Step-by-step explanation:
Let the number of rungs on the ladder be h and make the necessary adjustments based on this
Given that she is on the middle rung of a ladder this is equivalent to
= (h + 1)/2
She climbed up three rungs
= (h + 1)/2 + 3
moved down five rungs
= (h + 1)/2 + 3 - 5
and then climbed up 7 rungs
= (h + 1)/2 + 3 - 5 + 7
Then she climbed up the remaining 6 rungs to the top of the ladder
(h + 1)/2 + 3 - 5 + 7 + 6 = h
(h + 1)/2 + 11 = h
h + 1 + 22 = 2h
2h - h = 23
h = 23
The scale on the map is 1 cm to 10 km. The distance from Clevend to Cincinnati is 40cm. The scale on the second map is 1 cm to 50 km. What is the distance from Clevend to Cincinnati on the second map? Explain your reasoning
Using the concept of scale, we find that the distance between Cleveland and Cincinnati on the first map (1 cm to 10 km) is 40 cm, equivalent to 400 km in real-world distance. On the second map with a scale of 1 cm to 50 km, the equivalent distance is calculated to be 8 cm.
To calculate the distance between Cleveland and Cincinnati on the second map, we use the concept of scale. On the first map, the scale is 1 cm to 10 km, and the distance is represented as 40 cm. Scaling this to the real-world distance gives us 40 cm × 10 km/cm = 400 km between the two cities.
Now, let's apply the second map's scale of 1 cm to 50 km. To find the corresponding map distance, we set up a proportion: 10 km/cm (first map) / 50 km/cm (second map) = 40 cm (distance on the first map) / X cm (distance on the second map). Simplifying this, we find that X = 40 cm ×(10 km/cm) / (50 km/cm) = 40 cm × 1/5 = 8 cm.
Therefore, the distance between Cleveland and Cincinnati on the second map, which has a scale of 1 cm to 50 km, would be 8 cm.
which are discrete variables ????
Answer:
E, C
Step-by-step explanation:
which of the following sets of constraints forms an unbounded feasible region?
x≤0, y≥0, y≤2
x≥0, x≤2, y≥0, y≤3
x≥-2, x≤0, y≥0, y≤2
x≥0, x≤2, y≥0, y≤2
The third one is the right answer
Answer:
its a :)
Step-by-step explanation:
What is the value of f? 6f − 12 = −4f + 6
A. −9
B. −3/5
C. 1 4/5
D. 9
The answer is D! Aight hope it helped
The value of f in the equation 6f − 12 = −4f + 6 is 1 4/5.
Explanation:To answer the student's question, we need to solve the algebraic equation 6f − 12 = −4f + 6 for the unknown variable f. First, we want to get all terms with f on one side of the equation, and all constant terms on the other side. Thus, we'll add 4f to each side of the equation to eliminate -4f from the right side of the equation and get 6f + 4f = 6 + 12. This simplifies to 10f = 18, then we divide each side by 10, and we get f = 18/10 which reduces to f = 1 4/5 (Option C).
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Divide 3,724 ÷ 6. What is the remainder? The remainder is?
The answer is 620.6666666666667
The remainder is 620.7 or 620.6
Plz help ASAP thanks !! 30 points!
What is the value of x ?
Remark
The 2 angles are vertically opposite and that means they are equal.
Equation
(3x - 3) = [6(x - 10)]
Solution
Remove the brackets.
3x - 3 = 6(x - 10)
3x - 3 = 6x - 60 Subtract 3x from both sides
- 3 = 6x - 60 - 3x Combine like terms
-3 = 3x - 60 Add 60 to both sides
-3 + 60 = 3x
57 = 3x Divide by 3
57 / 3 = 3x / 3
19 = x Answer
I need help with this!
Solution
f(r) = 3.14[tex]r^{2}[/tex]
Now we have to find the area of the circle when the radius (r) = 4.
Plug in r = 4 in f(r) to get the area of the circle.
f(4) = 3.14[tex](4^{2} )[/tex]
f(4) = 3.14 * 4 * 4
f(4) = 3.14 *16
f(4) = 50.24
The answer is C. 50.24
Shane and Karen want to measure the length of a soccer field. Should they use centimeters or meters to measure it. Explain
Hello!
They should most definitely use meters. Meters are much bigger than centimeters as centimeters are 1/100th of a meter. Meaning, it will take 100 centimeters to get 1 meter. A soccer field is a large surface, and to get a simpler number, you should use meters.
Hope this helps!
one pump can empty the pool in 5 days, whereas a second pump can empty the pool in 7 days. how long it will take the two pumps, working together, to empty the pool?
Can I get some help on 3-5 please I don't understand how to do this :']