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.
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).
For more information, refer to the link given below:
https://brainly.com/question/17267403
hope this helps you out >_>
A regular octagon has side lengths of 11 centimeters. Determine the perimeter of the octagon. 66 cm 77 cm 88 cm 99 cm
an octagon has 8 sides
the perimeter would be 8 x length of side
8x11 = 88 cm
Answer:
8*11 = 88 cm
Step-by-step explanation:
simple
identify the following probability as theoretical or empirical. After tossing the same coin 10 times, you are surprised to find that tails has come up 8 times. You therefore conclude that this coin is not fair and that the probability of getting tails with this coin is 0.80. A. Empirical B. Theoretical
Answer:
A. Empirical
Step-by-step explanation:
Theoretical probability is defined as a probability which is based on reasoning. This is written in a ratio form - of the number of favorable outcomes to the number of possible outcomes.
And the empirical probability gives an estimation of an event occurring based on how often that event occurred after collecting the data from large number of trials.
So, based on the definitions, the given scenario is empirical or experimental probability.
The price of an item has been reduced by 85%. The original price was $77.
Can someone please help me? person who helps gets brainly
−5r+8r+5
5+ 1/7b = -2
whats be and explanation
(don't get it cause its a fraction)
Olga saves $15 from every paycheck to save up for a new game system that cost $399. Currently, she has $360 saved. Ignoring the purchase, how many more paychecks does she have until she has enough money saved to buy the game system
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
Learn more about slope- intercept form here:
https://brainly.com/question/9682526
#SPJ2
I need help with this math problem _:5=72:30
i need to fill in the blank
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].
Learn more:
1. A problem on greatest integer function https://brainly.com/question/8243712
2. A problem to find radius and center of circle https://brainly.com/question/9510228
3. A problem to determine intercepts of a line https://brainly.com/question/1332667
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.
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.
Please help. This is summer homework that's due in 2 days!
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.
What is the solution to this system of equations?
What is the sum of 2/5 and 2/4
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
NEED HELP FAST!
3.
(08.01 MC)
The graph shows two lines, A and B:
Based on the graph, which statement is correct about the solution to the system of equations for lines A and B? (1 point)
(3, 4) is the solution to both lines A and B.
(3, 4) is the solution to line A but not to line B.
(0, 2) is the solution to both lines A and B.
(0, 2) is the solution to line A but not to line B.
Answer:
(3,4) For both
Both lines meet up at that point. X is the thicker ones in the middle going across the graph while y is upward.
(x,y)
In the polynomial below, what number should replace the question mark to produce a difference of squares?
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
Round this number to the nearest 1,000 25,386
Round this number to the nearest 100,000 5,370,288
Round this number to the nearest 10,000 7,298,341
Round this number to the nearest 1,000,000 6,289,002
I know thi is a lot but please pretty pleas this is the hardest one:(
An elephant can run one over four mile in 36 seconds. Which of the following correctly shows this rate as miles per hour?
thirty-six seconds over one-fourth mile = 25 miles per hour
one-fourth mile over thirty-six seconds = 144 miles per hour
one-fourth mile over thirty-six seconds = 25 miles per hour
thirty-six seconds over one-fourth mile = 144 miles per hour
Answer:
The answer is 1/4 mile over 36 seconds = 24 miles per hour
Step-by-step explanation: I hope this helps :)
How do you add subtract multiply and divide complex numbers and polynomials
Final answer:
To operate on complex numbers, add or subtract real and imaginary parts separately, multiply using the distributive property, and divide by multiplying by the conjugate of the denominator. Polynomial operations similarly involve combining like terms, using the distributive property, and performing long or synthetic division.
Explanation:
Adding, Subtracting, Multiplying, and Dividing Complex Numbers and Polynomials
To add complex numbers, combine the real parts and the imaginary parts separately. For example, (3 + 2i) + (1 + 4i) = (3 + 1) + (2i + 4i) = 4 + 6i. For subtracting complex numbers, similarly subtract the real and imaginary parts: (3 + 2i) - (1 + 4i) = (3 - 1) + (2i - 4i) = 2 - 2i.
To multiply complex numbers, use the distributive property (FOIL), and remember that i² = -1. For instance, (3 + 2i)(1 + 4i) = 3 + 12i + 2i + 8i² = 3 + 14i - 8 = -5 + 14i.
For dividing complex numbers, multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. For example, (3 + 2i) ÷ (1 + 4i), multiply numerator and denominator by (1 - 4i) to get [(3 + 2i)(1 - 4i)] ÷ [(1 + 4i)(1 - 4i)] = (3 - 12i + 2i - 8i²) ÷ (1 - 16i²) = (11 - 10i) ÷ 17 = (11÷ 17) - (10i÷ 17).
Polynomial operations are similar, but instead of imaginary units, we work with variables. For adding polynomials, combine like terms. For subtracting polynomials, change the sign of each term in the polynomial being subtracted and combine like terms. Multiplying polynomials also requires the distributive property, and for division, you can use either long division or synthetic division depending on the polynomials involved.
Write words to match expression 3+(4x12)
Multiply (2.4 ⋅ 1014) ⋅ (4 ⋅ 107). Express the answer in scientific notation. 9.6 ⋅ 1021 9.6 ⋅ 1022 96 ⋅ 1021 96 ⋅ 1022
Answer:
9.6 × [tex]10^{21} )[/tex].
Step-by-step explanation:
Given : Multiply [tex](2.4 * 10^{14} ) * ( 4 *10^{7} )[/tex].
To find : Express the answer in scientific notation.
Solution : We have given that
[tex](2.4 * 10^{14} ) * ( 4 *10^{7} )[/tex].
Combine the like terms
(2.4 * 4 )( [tex](10^{14} ) (10^{7} )[/tex].
By the exponent same base rule : if the base of two exponent are same then exponent will be add.
9.6 × [tex]10^{14 + 7} )[/tex].
9.6 × [tex]10^{21} )[/tex].
Therefore, 9.6 × [tex]10^{21} )[/tex].
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 ?
The average number of rainy days in Seattle, Washington is listed below: Month January February March April Rainy days 18 16 17 14 If the data was only accurate to the tens place, which month's rainy day total would be different from the others?
Answer: April's rainy days are different from the others.
Step-by-step explanation:
Since we have given that
Months Rainy days
January 18
February 16
March 17
April. 14
When we round the rainy days to nearest tens then we get that
January has 20 rainy days
February has 20 rainy days.
March has 20 rainy days.
But April has 10 rainy days.
So, April's rainy days is different from others.
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
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.
PLZ Help
The tables show the cost of different numbers of t-shirts ordered at two different stores, Store A and Store B:
Store A
Number
of T-shirts Cost (in $)
2 $6
4 $12
8 $24
Store B
Number
of T-shirts Cost (in $)
3 $12
6 $24
9 $36
Which of these explains which store has a better buy?
Store A, because the ratio of the number to the cost is 3:1 in Store A and 4:1 in Store B
Store B, because the ratio of the number to the cost is 2:8 in Store A and 3:15 in Store B
Store B, because the ratio of the number to the cost is 8:2 in Store A and 15:3 in Store B
Store A, because the ratio of the number to the cost is 1:3 in Store A and 1:4 in Store B
Answer:
The last one.
Step-by-step explanation:
I tried it and got it right. Bye. If it helped please let me know. Also if u need anymore help try reaching out to me.