100 AAA batteries were tested on a particular MP3 player. Suppose the battery has a mean lifetime of 31.7 hours, with a standard deviation of 2.9 hours. How long do we expect the majority of batteries to last?A. Between 2.9 and 31.7 hours
B. Between 28.8 and 31.7 hours
C. Between 31.7 and 34.6 hours
D. Between 28.8 and 34.6 hours
31.7 -2.9 = 28.8
31.7 + 2.9 = 34.6
between 28.8 & 34.6 hours
D is the correct answer
mMelissa is making clothes for her dolls. She has 7/8 yard of fabric. Each doll shirt requires 2/7 of a yard of fabric. How many shirts can she make for her dolls?
need to divide 7/8 by 2/7
7/8 / 2/7 = 7/8 x 7/2 =49/16 = 3 1/16
she will be able to make 3 shirts
A line has a slope of 3/5. It passes through (3,5) and (x,9). What is the value of x?
Final answer:
The value of x for the line with a slope of 3/5 that passes through (3,5) and (x,9) is 9 2/3 or 9.67 when expressed as a decimal.
Explanation:
To find the value of x for the point (x, 9) on a line with a slope of 3/5, we can use the slope formula which is (change in y) / (change in x) = slope. We know two points on this line, (3, 5) and (x, 9).
First, calculate the change in y which is 9 - 5 = 4. Then, use the slope of 3/5 and set it equal to the change in y (which is 4) over the change in x (which is x - 3):
3/5 = 4 / (x - 3)
To find x, we cross-multiply:
3 x (x - 3) = 5 x 4
3x - 9 = 20
Add 9 to both sides: 3x = 29
Divide both sides by 3: x = 29/3
Therefore, x = 9 2/3 or 9.67 when expressed as a decimal.
This calculation shows the x-coordinate for the point where the line passes through y-coordinate 9.
The relationship between the base and rate a plumber charges and his hourly fee is modeled by the linear function f (x) = 25x + 100 where x is the number of hours he works. What is the total bill if the plumber works for 6 hours ?
4a to the fourth power -2b to the second power +40 when a =2 and b =7
American car makers produce 5,650,000 cars each year. In a report, Ben wrote that Americans made 6,550,000 cars. What mistake did Ben make? How can he fix it? Find the error.
Please help. This is summer homework that's due in 2 days!
The volume of a cube is 27n^27 cubic units. What is the length of one side of the cube?
A. 3n^3
B. 3n^9
C. 27n^3
D. 27n^9
Which of the following is not a Pythagorean triple? A. 28,45,53 B. 16,63,65 C. 13,84,85 D. 11,61,62
Tentukan hasil dari (tanpa menghitung satu persatu)
a. 1+3+5+7+9+.....+99
b. 1-2+3-4+5-6+7-8+.....-100
c. -100-99-98-..........-2-1-0+1+2+.....+48+49+50
a . 1 + 3 + 5 + 7 + 9 + ... + 99 = 2500
b. 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... - 100 = -50
c. -100 - 99 - 98 - .... -2 - 1 - 0 + 1 + 2 + ... + 48 + 49 + 50 = -3775
Further explanation
Let us learn about Arithmetic Progression.
Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.
[tex]\large {\boxed {T_n = a + (n-1)d } }[/tex]
[tex]\large {\boxed {S_n = \frac{1}{2}n ( 2a + (n-1)d ) } }[/tex]
Tn = n-th term of the sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
d = common difference between adjacent numbers
Let us now tackle the problem!
Question a :1 + 3 + 5 + 7 + 9 + ... + 99
initial term = a = 1
common difference = d = ( 3 - 1 ) = 2
Firstly , we will find how many numbers ( n ) in this series.
[tex]T_n = a + (n-1)d[/tex]
[tex]99 = 1 + (n-1)2[/tex]
[tex]99-1 = (n-1)2[/tex]
[tex]98 = (n-1)2[/tex]
[tex]\frac{98}{2} = (n-1)[/tex]
[tex]49 = (n-1)[/tex]
[tex]n = 50[/tex]
At last , we could find the sum of the numbers in the series using the above formula.
[tex]S_n = \frac{1}{2}n ( 2a + (n-1)d )[/tex]
[tex]S_{50} = \frac{1}{2}(50) ( 2 \times 1 + (50-1) \times 2 )[/tex]
[tex]S_{50} = 25 ( 2 + 49 \times 2 )[/tex]
[tex]S_{50} = 25 ( 2 + 98 )[/tex]
[tex]S_{50} = 25 ( 100 )[/tex]
[tex]\large { \boxed { S_{50} = 2500 } }[/tex]
Question b :In this question let us find the series of even numbers first , such as :
2 + 4 + 6 + 8 + ... + 100
initial term = a = 2
common difference = d = ( 4 - 2 ) = 2
Firstly , we will find how many numbers ( n ) in this series.
[tex]T_n = a + (n-1)d[/tex]
[tex]100 = 2 + (n-1)2[/tex]
[tex]100-2 = (n-1)2[/tex]
[tex]98 = (n-1)2[/tex]
[tex]\frac{98}{2} = (n-1)[/tex]
[tex]49 = (n-1)[/tex]
[tex]n = 50[/tex]
We could find the sum of the numbers in the series using the above formula.
[tex]S_n = \frac{1}{2}n ( 2a + (n-1)d )[/tex]
[tex]S_{50} = \frac{1}{2}(50) ( 2 \times 2 + (50-1) \times 2 )[/tex]
[tex]S_{50} = 25 ( 4 + 49 \times 2 )[/tex]
[tex]S_{50} = 25 ( 4 + 98 )[/tex]
[tex]S_{50} = 25 ( 102 )[/tex]
[tex]\large { \boxed { S_{50} = 2550 } }[/tex]
At last , we could find the result of the series.
1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... - 100
= ( 1 + 3 + 5 + 7 + ... + 99 ) - ( 2 + 4 + 6 + 8 + ... + 100 )
= 2500 - 2550
= -50
1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... - 100 = -50
Question c :-100 - 99 - 98 - .... -2 - 1 - 0 + 1 + 2 + ... + 48 + 49 + 50
initial term = a = -100
common difference = d = ( -99 - (-100) ) = 1
Firstly , we will find how many numbers ( n ) in this series.
[tex]T_n = a + (n-1)d[/tex]
[tex]50 = -100 + (n-1)1[/tex]
[tex]50+100 = (n-1)[/tex]
[tex]150 = (n-1)[/tex]
[tex]n = 151[/tex]
We could find the sum of the numbers in the series using the above formula.
[tex]S_n = \frac{1}{2}n ( 2a + (n-1)d )[/tex]
[tex]S_{151} = \frac{1}{2}(151) ( 2 \times (-100) + (151-1) \times 1 )[/tex]
[tex]S_{151} = 75.5 ( -200 + 150 )[/tex]
[tex]S_{151} = 75.5 ( -50 )[/tex]
[tex]\large { \boxed { S_{151} = -3775 } }[/tex]
Learn moreGeometric Series : https://brainly.com/question/4520950Arithmetic Progression : https://brainly.com/question/2966265Geometric Sequence : https://brainly.com/question/2166405Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Arithmetic and Geometric Series
Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term
The sum of the series are:
Part(a): [tex]\fbox{\begin\\\ \math S=2500\\\end{minispace}}[/tex]
Part(b): [tex]\fbox{\begin\\\ \math S=-50\\\end{minispace}}[/tex]
Part(c): [tex]\fbox{\begin\\\ \math S=-3775\\\end{minispace}}[/tex]
Further explanation:
A series is defined as a sum of different numbers in which each term is obtained from a specific rule or pattern.
In this question we need to determine the sum of the series given in the part (a), part (b) and part (c).
Part(a):
The series given in part (a) is as follows:
[tex]1+3+5+7+9+...+99[/tex]
All the terms in the given series are odd numbers.
From the given series in part(a) it is observed that the series is an arithmetic series with the common difference of [tex]2[/tex].
An arithmetic series is a series in which each successive member of the series differs from its previous term by a constant quantity.
From the above series it is observed that the first term is [tex]1[/tex], second term is [tex]3[/tex], third term is [tex]5[/tex], fourth term is [tex]7[/tex], fifth term is [tex]9[/tex] and the last term is [tex]99[/tex].
The nth term in a arithmetic series is given as follows:
[tex]a_{n}=a+(n-1)d[/tex] (1)
In the above equation a represents the first term, [tex]n[/tex] represents the total terms and [tex]d[/tex] represents the common difference.
Substitute [tex]99[/tex] for [tex]a_{n}[/tex], [tex]1[/tex] for [tex]a[/tex] and [tex]2[/tex] for [tex]d[/tex] in equation (1).
[tex]\begin{aligned}99&=1+2(n-1)\\2(n-1)&=98\\n-1&=49\\n&=50\end{aligned}[/tex]
Therefore, total number of terms in the series is [tex]50[/tex]. This implies that [tex]a_{50}=99[/tex].
The sum of an arithmetic series is calculated as follows:
[tex]S_{n}=\dfrac{n}{2}(a+a_{n})[/tex] (2)
Substitute [tex]50[/tex] for [tex]n[/tex] in equation (2).
[tex]\begin{aligned}S_{50}&=\dfrac{50}{2}(a+a_{50})\\&=25\times (1+99)\\&=25\times 100\\&=2500\end{aligned}[/tex]
Therefore, the sum of the series for part(a) is [tex]\bf 2500[/tex].
Part(b):
The series given in part (b) is as follows:
[tex]1-2+3-4+5-6+7-8+….-100[/tex]
Express the given series as follows:
[tex]S=(1+3+5+7+...+99)-(2+4+6+8+...+100)\\S=S^{'}-S^{''}[/tex]
The series [tex]S^{'}[/tex] is as follows:
[tex]S^{'}=1+3+5+7+...+99[/tex]
It is observed that the above series [tex]S^{'}[/tex] is exactly same as the series given in the part(a) and the sum of the series of part(a) as calculated above is [tex]2500[/tex].
Therefore, sum of the series [tex]S^{'}[/tex] is [tex]2500[/tex] i.e., [tex]S^{'}=2500[/tex].
The series [tex]S^{"}[/tex] is as follows:
[tex]S^{"}=2+4+6+8+...+100[/tex]
From the above series it is observed that the series [tex]S^{"}[/tex] is an arithmetic series as the difference between each consecutive member is [tex]2[/tex] and the last term is [tex]100[/tex].
Substitute [tex]2[/tex] for [tex]a[/tex], [tex]2[/tex] for [tex]d[/tex] and [tex]100[/tex] for [tex]a_{n}[/tex] in equation (1).
[tex]\begin{aligned}100&=2+(n-1)2\\(n-1)2&=98\\n-1&=49\\n&=50\end{aligned}[/tex]
This implies that [tex]a_{50}=100[/tex].
To calculate the sum of substitute [tex]50[/tex] for [tex]n[/tex] in equation (2).
[tex]\begin{aligned}S_{50}&=\dfrac{50}{2}(a+a_{50})\\&=(25)(2+102})\\ &=25\times 102\\&=2550\end{aligned}[/tex]
Therefore, sum of the series [tex]S^{"}[/tex] is [tex]2550[/tex].
Substitute [tex]2550[/tex] for [tex]S^{"}[/tex] and [tex]2500[/tex] for in equation (3).
[tex]\begin{aligned}S&=S^{'}+S^{"}\\&=2500-2550\\&=-50\end{aligned}[/tex]
Therefore, the sum of the series for part(b) is [tex]\bf -50[/tex].
Part(c):
The series given in part(c) is as follows:
[tex]-100-99-9-...-2-1-0+1+2+...+48+49+50[/tex]
From the above series it is observed that it is an arithmetic series with common difference as [tex]1[/tex], first term as [tex]-100[/tex] and the last term as [tex]50[/tex].
Substitute [tex]-100[/tex] for [tex]a[/tex], [tex]1[/tex] for [tex]d[/tex] and [tex]50[/tex] for [tex]a_{n}[/tex] in equation (1).
[tex]\begin{aligned}50&=-100+(n-1)1\\n-1&=150\\n&=151\end{aligned}[/tex]
Substitute [tex]151[/tex] for [tex]n[/tex] in equation (2).
[tex]\begin{aligned}S_{151}&=\dfrac{151}{2}(a+a_{151})\\&=\dfrac{151}{2}(-100+50)\\&=-25\times 151\\&=-3775\end{aligned}[/tex]
Therefore, the sum of the series for part(c) is [tex]\bf -3775[/tex].
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Series
Keywords: Series, sequence, arithmetic sequence, arithmetic series, 1+3+5+7+9+….+99, 1-2+3-4+5-6+7-8+….-100, -100-99-98-….-2-1-0+1+2+…..+48+49+50, sum of series, first term, common difference.
Earth is approximately 9.3 × 107 miles from the sun. Saturn is approximately 8.87 × 108 miles from the sun. About how much farther is Saturn from the sun than Earth is?
Answer:
B. 7.94 * 10^8 miles
Step-by-step explanation:
is the correct answer
a right triangle has a base that measures 39 inches and a height that measures 80 inches what is the length of the hypotense
The price of an item has been reduced by 85%. The original price was $77.
how to do this problem -9=x-14
Plz answer with showing work. #19
An Internet, telephone,and cable TV package plan costs 85$ each month. The Internet part of the bill is $20. The telephone part bill is $12
if a customer ordered 5 items and the order had a total of 17 wheels,how many wagons were ordered?
A map of square piece of property is drawn at a scale of 1 : 500. If a side of the property on the map is 16 cm, what is the property's actual area?
Answer:
[tex]\text{Actual area of property}}=6400\text{ m}^2[/tex]
Step-by-step explanation:
Let x represent the actual side of square property.
We have been given that a map of square piece of property is drawn at a scale of 1 : 500.
We will use proportions to solve for our given problem.
[tex]\frac{\text{Actual length}}{\text{Map length}}=\frac{500}{1}[/tex]
[tex]\frac{x}{16\text{ cm}}=\frac{500}{1}[/tex]
[tex]\frac{x}{16\text{ cm}}*16\text{ cm}=500*16\text{ cm}}[/tex]
[tex]x=8000\text{ cm}[/tex]
[tex]x=80\text{ m}[/tex]
We know that area of a square is square of its side length.
[tex]\text{Actual area of property}}=(80\text{ m})^2[/tex]
[tex]\text{Actual area of property}}=6400\text{ m}^2[/tex]
Therefore, the actual area of property is 6400 square meters.
What is the area of a trapezoid that has bases of 1 1/4 feet and 14 inches and a height of 3 inches? 43.5 in. 2 87 in. 2 22.9 in. 2 3.6 in. 2
Answer:
13.5 in^2 is the answer
Step-by-step explanation:
I need help with this math problem _:5=72:30
i need to fill in the blank
Two pounds of peaches cost $4.20. How much will five pounds cost?
1). The $70 selling price of a bicycle is the cost increased by 4 times the cost. Find the cost?
2). Three pounds less than twice mikes weight is 215 pounds. What is his weight?
3). If mr Washingtons saving were increased by 5 times his savings. He would then save $36,000. How much has he saved ?
PLEASE SHOW YOUR WORK !!!!
1. The cost of the bicycle is $14.
2. Mike's weight is 109 pounds.
3. Mr. Washington has saved $6,000.
Let's solve each problem step by step:
1. The $70 selling price of a bicycle is the cost increased by 4 times the cost.
Let's assume the cost of the bicycle is C dollars.
According to the given information, the selling price of the bicycle is $70, and it is equal to the cost increased by 4 times the cost:
70 = C + 4C
Combine like terms:
70 = 5C
Now, divide both sides by 5 to solve for C:
C = 70 / 5
C = 14
So, the cost of the bicycle is $14.
2. Three pounds less than twice Mike's weight is 215 pounds.
Let's assume Mike's weight is W pounds.
According to the given information, three pounds less than twice Mike's weight is 215 pounds:
2W - 3 = 215
Add 3 to both sides to isolate 2W:
2W = 215 + 3
2W = 218
Now, divide both sides by 2 to solve for W:
W = 218 / 2
W = 109
So, Mike's weight is 109 pounds.
3. If Mr. Washington's savings were increased by 5 times his savings, he would then save $36,000.
Let's assume Mr. Washington's initial savings is S dollars.
According to the given information, if his savings were increased by 5 times, he would save $36,000:
S + 5S = 36000
Combine like terms:
6S = 36000
Now, divide both sides by 6 to solve for S:
S = 36000 / 6
S = 6000
So, Mr. Washington has saved $6,000.
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About 400,000 people visited an art museum in December. What could be the exact number of people who visited the art museum?
The exact number of people who visited the art museum is; C) 352,483
How to approximate numbers?We are told that about 400,000 people visited an art museum in December.
Now, the given statement makes it clear that the 400000 people is an approximate value. This means that it has been rounded up to the nearest 100000.
Now among the options, the only that when rounded up to the nearest hundred thousand will give 400000 will be Option C which is 353,483.
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Complete question is;
About 400,000 people visited an art museum in December. What could be the exact number of people who visited the art museum?
A) 478,051
B) 452,223
C) 352,483
D) 348,998
A graph is shown below:
A graph is shown. The values on the x axis are 0, 3, 6, 9, 12, and 15. The values on the y axis are 0, 9, 18, 27, 36, and 45. Points are shown on ordered pairs 0, 36 and 3, 27 and 6, 18 and 9, 9 and 12, 0. These points are connected by a line
What is the equation of the line in slope-intercept form?
y = 36x − 3
y = −3x + 36
y = −3x + 12
y = −12x + 3
Answer:
Yeah its B
(y = -3x = 36)
Step-by-step explanation:
The equation of the line in slope-intercept form is y = −3x + 36.
What is slope- intercept form?The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
Given:
x axis are 0, 3, 6, 9, 12, and 15.
y axis are 0, 9, 18, 27, 36, and 45.
slope= 27-36/ 3-0= -3
Slope intercept form
y - y1 = m(x- x1)
y- 36 = -3 ( x- 0)
y - 36 = -3x
y + 3x = 36
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How to factor a polynomial when the leading coefficient isn't 1
Final answer:
To factor a polynomial with a leading coefficient that isn't 1, use the ac method or factoring by grouping, identify common factors, and check your work by expanding the factors.
Explanation:
When factoring a polynomial with a leading coefficient that isn't 1, you should consider each term, and factor out any common factors first. If the polynomial is a quadratic, for instance, with a leading coefficient greater than 1, you can use techniques such as the ac method or factoring by grouping. The ac method involves finding two numbers which multiply to give you the product of the leading coefficient and the constant term, and add up to the middle term's coefficient. Once you have these numbers, you can rewrite the middle term and then factor by grouping.
Step-by-Step Explanation
Identify the leading coefficient, the constant term, and the middle term's coefficient.Find two numbers that multiply to the product of the leading coefficient and the constant term, and add to the middle term's coefficient.Rewrite the middle term using the two numbers found in step 2, splitting it into two terms.Factor by grouping, which involves pairing off the terms in such a way that they have a common factor, and then factoring out the greatest common factor from each pair.If you have factored correctly, you should be able to factor out an additional term from the resulting expression, resulting in a factored polynomial.Simplify further if possible, and check your answer by expanding the factors to ensure you get the original polynomial.Identify the equation that translates y=ln(x) five units down.
A) y= ln(x-5)
B) y=ln(x)+5
C) y=ln(x+5)
D) y=ln(x)-5
The equation that translates (y = ln(x)) five units down is (y = ln(x) - 5) and this can be determined by using the transformation.
Given :
Logarithmic equation -- (y = lnx)
The following steps can be used in order to identify the equation that translates (y = ln(x)) five units down:
Step 1 - The graph of the logarithmic function (y = ln(x)) intersect x-axis at (x = 1).
Step 2 - According to the given data, the graph of (y = ln(x)) is translated down by five units. So, to translate the given function five units down subtract the given function y by 5 unis.
Step 3 - So, the resulting logarithmic equation after transformation is given by:
y = ln(x) - 5
Therefore, the correct option is D).
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hope this helps you out >_>
Simplify (5ab^4c)(-abc^2)
This is the answer that u seek
-5a^2b^5c^3
John needs to make a scale drawing of his school building for art class. If the building is 256.25 meters long, and John scales it down using a ratio of 25 meters to 1 inch, how long will the building be in the sketch?
Answer:
10.25 inches
Step-by-step explanation:
John needs to make a scale drawing of his school building for art class.
The building is 256.25 meters long.
John scales it down using a ratio of 25 meters to 1 inch.
Therefore, 256.25 meters = [tex]\frac{256.25}{25}[/tex] = 10.25 inches
The sketch of the building would be 10.25 inches long.
Write words to match expression 3+(4x12)
Boundary Peak in Nevada is 13,000 feet high. Guadalupe Peak in Texas is 8,749.75 feet high. How much higher than Guadalupe Peak is Boundary Peak? Round your answer to match the less precise measurement.
Answer:
The Boundary peak is 48.58% higher than Guadalupe peak.Step-by-step explanation:
Givens:
Boundary Peak is 13,000 ft high.Guadalupe Peak is 8,749.75 high.To know how much higher is Boundary Peak than Guadalupe peak, we only need to subtract:
Boundary Peak - Guadalupe peak = 13,000 - 8,749.75 = 4250.25 m.
However, the best way to represent this is to express it in percentage. To do that, we need to use the rule of three. If 100% is 8749.75, what percentage would be 13000:
[tex]13000m\frac{100\%}{8749.75m}=148.58 \%[/tex]
Therefore, the Boundary peak is 48.58% higher than Guadalupe peak.