Answer: half
Step-by-step explanation:
The employees of a manufacturing company pledged the following donations in peso
for the establishment of a community pantry: 100, 400, 250, 50, 200, 300, 100, 50, 150, 250,
500, 100, 300, 50, and 150. Using the employees’ contributions, calculate and interpret the
following:
a.) upper quartile b.) 7th decile c.) 35th percentile
Solution:
50, 50, 50, 100, 100, 100, 150, 150, 200, 250, 250, 300, 300, 400, 500
a. Upper quartile or 3
=
4
( + 1) 3 =
3
4
(15 + 1) =
3
4
(16) =
48
4
= 12
3 is in the 12th position. Therefore, 3 = 300.
b. 7
th decile or 7
=
10
( + 1) 7 =
7
10
(15 + 1) =
7
10
(16) =
112
10
= 11.2
Interpolate: 11.2nd position is between the 11th and 12th position which are 250 and
300, respectively. 300-250=50 then 250+0.2=250.2. Hence, D7=250.2
c. 35th percentile or 35
=
100
( + 1) 35 =
35
100
(15 + 1) =
7
20
(16) =
112
20
= 5.6
Interpolate: 5.6th position is between the 5th and 6th position which are 100 and 100,
respectively. Hence, P35=100.
Guide Questions:
1. How did you determine the value of the upper quartile, 7th decile and the 35th
percentile?
2. How will you interpret the results? PLEASE HELP ME
The value of upper quartile is, 300.
The value of 7th decile is, 250.2.
The value of 35th percentile is, 100.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The donations are as follows,
⇒ 50, 50, 50, 100, 100, 100, 150, 150, 200, 250, 250, 300, 300, 400, 500.
Now, We find the values as;
a) The upper quartile is,
⇒ Qₐ = a/4 (n + 1)
Here, n = 15
So, We get;
⇒ Q₃ = 3/4 (15 + 1)
= 3/4 × 16
= 12
So, Q₃ is in 12th position.
So, The value of Q₃ = 300
The value of 7th decile is,
⇒ D₇ = 7/10 (15 + 1)
= 7/10 × 16
= 11.2
Here, 11.2 is between the position 11th and 12th position which are 250 and 300 respectively.
Then, We get;
⇒ 300 - 250 = 50
Hence, The value of D₇ = 250 + 0.2
= 250.2
Now, The value of 35th percentile is,
⇒ Pₐ = a/100 (n + 1)
⇒ P₃₅ = 35/100 (15 + 1)
= 35/100 × 16
= 5.6
Here, 5.6 is between the 5th and 6th position which are 100 and 200 respectively.
Hence, P₃₅ = 100
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The temperature in Williamstown was 38°F. Then a winter storm came through and the temperature dropped 24°F overnight. Which expression represents the change in temperature?
|−24| − |38|
|−24| + |38|
|38| − |−24|
|38| + |−24|
Answer:The temperature dropped 24°F overnight, so the change in temperature would be represented by the expression |-24|, which is the absolute value of -24.
You can also represent it by |38| - |-24| which is equal to 38 - (-24) = 38 + 24 = 62°F.
Step-by-step explanation:
solve the simultaneous equation :
x² + y² = 18
x + 2 = - 3x
The solution to the simultaneous equation is x = -1/2 and y = √71 / 2
What is a Linear Expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.
For example, t² is a variable raised to the second power, but t is a variable raised to the first power.
x² + y² = 18 ----- 1
x + 2 = - 3x ---- 2
From equation 2
x + 2 = - 3x
x + 3x = -2
4x = -2
x = -2/4
x = -1/2
Substitute x in equation 1
(-1/2)² + y² = 18
1/4 + y² = 18
y² = 18 - 1/4
y² = (72 - 1)/4
y² = 71/4
y = √71 / 2
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22. find m/ABD (7q-46) (3q+6)°
So on solving provided question we can say that given angle is m/ABD (7q-46) (3q+6)° = m/ABD = 98
what are angles?An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.
here,
the given angle is m/ABD (7q-46) (3q+6)°
m/ABD = 98
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Arianna is working two summer jobs, washing cars and tutoring. She must work no less than 10 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours washing cars, ww, and the number of hours tutoring, tt, that Arianna can work in a given week.
Let ww represent the number of hours washing cars, and tt represent the number of hours tutoring.
The inequality representing the total number of hours Arianna must work between both jobs is:
ww + tt ≥ 10
This inequality states that the number of hours spent washing cars plus the number of hours spent tutoring must be greater than or equal to 10 hours. This represents all possible combinations of hours washing cars and hours tutoring that Arianna can work in a given week while meeting the requirement that she must work no less than 10 hours altogether between both jobs.
X, y and z are three numbers. x is 10 more than y and y is 8 more than z. The sum of the three numbers is 47. What are the values of x, y, and z?
The values of x, y, and z are 25,15 and, 7 respectively.
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant.
Given that,
x=y+10................(i)
y=z+8..................(ii)
x+y+z=47............(iii)
Solving these equations to find the values of x,y, and z.
Putting The value of x from the first equation in the third equation:
we get,
y+10+y+z=47
Solving this equation further, we get,
=>2y+z=47 -10=37
=>2(z+8)+z=37
=>2z+16+z=37
=>3z=37-16=21
=>z=21/3=7
=>y=z+8=7+8=15
=>x=y+10=15+10=25
Thus, The values of x, y, and z are 25,15 and, 7 respectively.
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jason is driving from his home to his office, which is $20$ miles away. he normally drives at a constant speed of $50$ miles per hour for the whole trip. however today, twelve minutes into his drive, his car breaks down. he calls a taxi, and it arrives fifteen minutes later. the taxi driver then takes him to his office driving at a constant speed of $40$ miles per hour. how much longer was this trip today than his usual drive to work, in minutes?
Jason's trip was 9 minutes longer than his usual drive to work.
Given that,
Distance from Jason's home to office = 20 miles
Speed of driving from home to office = 50 miles/hour
Total time taken to reach from home to office = distance ÷ speed = 20/50 = 0.4 hours = 24 minutes
Thus, on a normal day, Jason takes 0.4 hours to reach his office from home.
Now, Jason drove for 12 minutes when his car broke down,
The taxi arrived 15 minutes later and drove at 40 miles/hour,
Total time spent to reach office from taxi= distance ÷ speed = 20/40 = 0.5 hours= 30 minutes
Although he already spent 12 minutes driving before the taxi arrived so,
30 - 12 = 18 minutes.
But, he waited for the taxi to arrive for 15 minutes so,
18+15 = 33 minutes.
Thus, today Jason took 33 minutes to reach the office from his home.
Therefore, Jason took (33- 24)minutes which is equal to 9 minutes longer than his usual drive to work.
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The equation of line s is y= 3 5 x+ 2 5. Line t, which is parallel to line s, includes the point (2,1). What is the equation of line t? write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
The equation is y = 3x/5 - 1/5.
Based on the position of two lines: m = 3/5
Write the equation of linear function
Substitute: 1 = 3/5 * 2 + b
Rearrange unknown terms to the left side of the equation: -b = 3/5 * 2 -1
Write as a single fraction:
Find common denominator and write the numerators above common denominator: -b = (3*2)/5 - 1
Calculate the sum or difference: -b = (6 - 5 )/5
Divide both sides of the equation by the coefficient of variable: b = -1/5
Substitute: y = 3x/5 - 1/5
Find the required form: y = 3x/5 - 1/5.
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What are the tables in math?
Information organised in rows and columns, such as numbers and descriptions is known as table.
General tables and summary tables are the two broad types into which statistical tables can be divided.
General tables
General tables include a compilation of specific data that is all pertinent to the topic or theme. Such tables are typically included in the appendices of reports and serve the primary function of assembling all the information on a given issue for quick reference.
Summery tables
Summary tables are made to accomplish a number of distinct tasks. They are typically included into the text, smaller in size than regular tables, and focus on a particular component of the data. Because they are generated from the general tables, the summary tables are also known as derivative tables. The data in the summary table is intended for analysis and inference. They are also known as interpretative tables as a result.
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which expression has the same value as 1 2/3 + (-8 1/2)
The given expression 1 2/3+(-8 1/2) is equivalent to -41/6.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
Given expression is 1 2/3+(-8 1/2)
=5/3+(-17/2)
=5/3-17/2
Taking LCM 6
=(10-51)/6
=-41/6
Hence,
The given expression 1 2/3+(-8 1/2) is equivalent to -41/6.
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from an ordinary deck of 52 cards, five cards are drawn randomly. what is the probability of drawing
The probability of drawing exactly three face cards is given as follows:
0.0660 = 6.60%.
What is the hypergeometric distribution formula?The mass probability formula is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.Considering that a standard deck is composed of 52 cards, of which 12 are face cards, and 5 cards are taken, the values of the parameters are given as follows:
N = 52, k = 12, n = 5.
The probability of drawing exactly three face cards is P(X = 3), obtained as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,52,5,12) = \frac{C_{12,3}C_{40,2}}{C_{52,5}} = 0.0660[/tex]
Missing InformationThe problem asks for the probability of drawing exactly three face cards.
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mary needs to make a total of 40 deliveries this week she so far has made 38 oif them what percentage of her total deliveries has mary completed
The percentage of the total deliveries made by the Mary is equal to 95%.
As given in the question,
Total number of deliveries need to be delivered by the Mary this week = 40
Total number of deliveries completed by Mary is equal to 38
Percentage formula = [( Number obtained ) / (Total number ) ] × 100
Substitute the value in the formula we get,
The percentage of the completed deliveries made by Mary is
= ( 38 / 40 ) × 100
= 3800 / 40
= 95%
Therefore, the total percentage of the completed delivery made by Mary is equal to 95%.
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what is the end behavior of:
1. [tex]\sqrt{6x}[/tex]
2. [tex]\sqrt{x-5}-6[/tex]
3. [tex]-3\sqrt{x+3}+7[/tex]
In the given question, none of the function exhibits an end behavior
What is End Behavior of a PolynomialThe end behavior of a polynomial is the way the graph of the polynomial behaves as the input values become very large or very small. Generally, the end behavior of a polynomial is either up, down, or a combination of both. If the highest degree term has a positive coefficient, the end behavior is up; if the highest degree term has a negative coefficient, the end behavior is down. If the highest degree term has a coefficient of zero, the end behavior is a combination of up and down.
In the functions given, we can find the end behavior of each of these functions.
1)
y = √x
The leading coefficient test requires a polynomial and this function is not a polynomial.
2)
y = √(x - 5) - 6
The leading coefficient test requires a polynomial and this function is not a polynomial.
3)
y = -3√(x + 3) + 7
The leading coefficient test requires a polynomial and this function is not a polynomial
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(07.04 mc) what is the general solution to the differential equation dy over dx equals x times y plus 3 times x question mark
The general solution of dy over dx equals x times y plus 3 times x question is [tex]y=e^{\frac{x^{2} }{2} +c_{1}} -3[/tex]
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The given differential equation is dy over dx equals x times y plus 3 times x question
dy/dx=xy+3x
dy/dx=x(y+3)
dy/dx-x(y+3)=0
Solve seperable ODE
[tex]y=e^{\frac{x^{2} }{2} +c_{1}} -3[/tex]
Hence, the general solution of dy over dx equals x times y plus 3 times x question is [tex]y=e^{\frac{x^{2} }{2} +c_{1}} -3[/tex]
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
Therefore , on solving the provided question we can say that inequality will be x < 2.2727272727 .
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two variables values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality.
Here,
Given :
the inequality will be
=> 3(2x – 5) < 5(2 – x)
=> 6x - 15 < 10-5x
=> 11x < 25
=> x < 2.2727272727
Thus ,
x < 2.27
Therefore , on solving the provided question we can say that inequality will be x < 2.2727272727 .
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The complete question is " Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left. "
VX is a midsegment of UWY
If UY = 13p - 1 and VX = 20p - 95, what is UY
Solving for UY. in the figure provided where VX is a midsegment of UWY, UY is 90
What are similar triangles?When the comparable triangles' angles are congruent and their respective sides are proportionate, this is referred to as similar triangles in geometry.
In light of this, if the triangle's corresponding angles are congruent, then the side should be proportionate.
For the given figure, the proportionate sides are
WV and VX, WU and UY
Solving for P
WV / VX = WU / UY
1 / (20p - 95) = 2 / (13p - 1)
cross multiplying
13p - 1 = 2(20p - 95)
13p - 1 = 40p - 190
collecting like terms
190 - 1 = 40p - 13p
189 = 27p
p = 7
solving for UY
= 13p - 1
= 13 * 7 - 1
= 90
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Form a polynomial whose real zeros and degrees are given
Zeros: -2, 0, 7
Degree: 3
Type a polynomial with integer coefficients and a leading coefficient of 1
f(x)= ?
Given ,
[tex]\bold\red{zeroes \: of \: a \: cubic \: polynomial \: are \: - 2 \:, \: 0 \: and \: 7} \\ [/tex]
[tex]let \:, \\ \boxed{\alpha \: = - 2} \\ \boxed{\beta \: = 0} \\ \boxed{\gamma \: = 7} [/tex]
Now ,
[tex]sum \: of \: zeroes \: = \alpha \: + \: \beta \: + \: \gamma \: \\ \dashrightarrow \: sum = - 2 + 0 + 7 = \underline{5} \\ \\ sum \: of \: product \: of \: zeroes \: taken \: two \: at \: a \: time \: = \alpha\beta \: + \beta\gamma \: + \: \alpha\gamma \\ \dashrightarrow \: ( - 2)(0) \: + \: (0)(7) \: + \: (7)( - 2) \: = \: \underline{ - 14} \\ \\ product \: of \: zeroes \: = \: \alpha\beta\gamma \\ \dashrightarrow \: ( - 2)(0)(7) = \underline{0}[/tex]
We know that ,
[tex] \boxed{cubic \: polynomial \: = {x}^{3} - (\alpha \: + \: \beta \: + \: \gamma \:) \:{x}^{2} + (\alpha\beta \: + \: \beta\gamma \: + \: \alpha\gamma) \:x \: - \: \alpha\beta\gamma} [/tex]
Plugging in the values , we get
[tex]\boxed{f(x) = {x}^{3} - 5 {x}^{2} - 14x + 0}[/tex]
since this polynomial has degree 3 , it is called a cubic polynomial.
hope helpful! :)
For her party, Carla bought a 5-pound bag of candy to give as party treats. She invited 15 people. How much candy will each of the 15 people get? Choose the correct equation and answer for this situation.
A) 15 ÷ 5 = [tex]\frac{15}{5}[/tex] = 3 pounds
B) 5 ÷ 15 =[tex]\frac{5}{15}[/tex] = [tex]\frac{1}{3}[/tex] pounds
C) 5 ÷ 15 = 3 pounds
D) 15 ÷ 5 = [tex]\frac{1}{3}[/tex] pounds
If for her party, Carla bought a 5-pound bag of candy to give as party treats. She invited 15 people. The amount of candy that each of the 15 people get is: A) 15 ÷ 5 = 15/5 = 3 pounds.
How to find the amount of candy to gives as party treats?Given data:
Candy bought = 5
Number of people invited = 15
Now let find the amount of candy to gives as party treats
Number of candy = Number of people invited / Candy bought
Number of candy = 15/5
Number of candy = 3 pounds
Therefore we can conclude that the correct option is A.
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how to calculate multiplier in economic
Answer:
1/1-mpc and 1-mps
Step-by-step explanation:
to get the multiplier effect you use the formula
M=1/1-MPC
Help, needed ASAP, Thank you!!
Answer:
x = 4
Step-by-step explanation:
For this question we can use the theorem which states that "if the chords of a circle is equal, it is equidistant from the center."
Therefore, FC = CE
or 3x + 8 = 8x - 12
5x = 20
x = 4
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Look at where the diver started and where she is heading. She started at –5 and descended to –75. That means she dropped 70 feet more.
These two points on the number line describe that she descended by 70 units.
What is a number line?A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.
Here,
She started at –5 and descended to –75.
On the number line, the difference between -75 and -5 is given as
= -5 - (-75)
= 70
Thus, these two points on the number line describe that she descended by 70 units.
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A certain type of bird lives in two regions of a state. The distribution of weight for birds of this type in the northern region is approximately normal with mean 10 ounces and standard deviation 3 ounces. The distribution of weight for birds of this type in the southern region is approximately normal with mean 16 ounces and standard deviation 2.5 ounces.(a) Calculate the z-scores for a weight of 13 ounces for a bird living in the northern region and for a weight of 13 ounces for a bird living in the southern region.(b) Is it more likely that a bird of this type with a weight greater than 13 ounces lives in the northern region or the southern region? Justify your answer. (c) This type of bird can also be found in another state. Suppose the distribution of the weight for birds in the other state is approximately normal. A bird with a weight of 13 ounces is at the 70th percentile. Interpret the percentile in context. If the standard deviation is 2 ounces what is the mean weight of this type of bird in the state?
A bird with a weight greater than 13 ounces lives in the southern region
Z = (x – mean)/standard deviation
Le x be weight for birds
For the northern region
Z = (13 – 10)/3
Z = 1
For the southern region
Z = (13 – 16)/2.5
Z = -1.2
to find in what region is more likely to find a bird with 13 ounces, we calculate the probability for each z value
For the northern region
P (x>13) = P(z > 1)
Then we use the z table to find the area under the curve.
P (x>13) = 0.1587
For the southern region
P (x>13) = P(z > 1.2)
Then we use the z table to find the area under the curve.
P (x>13) = 0.8849
Is it more likely that a bird with a weight greater than 13 ounces lives in the southern region
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negative 3 plus negative 5
Answer: -8
Hope this helps :)
Step-by-step explanation:
Adding two negative integers is just like adding two regular numbers
Answer:
negative 8
Step-by-step explanation:
calculator
Find the slope of the line represented by the data below
Answer:
-4
Step-by-step explanation-
y2-y1
-------- = m = slope
x2-x1
8-12 -4
--------- = ---- = -4
-2-(-3) 1
Diana had a coupon for c dollars off of
each box of crackers. Diana bought 2
boxes of crackers for 4.50 – c dollars
each. She also bought 8 cans of soup
for s dollars each. The total amount, in
dollars, she spent on the cans of soup
and boxes of crackers is represented by
the expression below.
2(4.50 – c)+8s
Which expression also represents the
total amount, in dollars, she spent?
A.6.50 – 2c + 8s B. 6.50 – 2c + 10s
C. 9 – c + 8s D. 9–2c + 8s
Answer:
d. 9 - 2c + 8s
Step-by-step explanation:
we can distribute the two by multiplying it by both 4.50 and -c. our result will be 9 and -2c. simply combine that with the 8s that we already had, and we end up with 9 - 2c + 8s.
the roots of the polynomial 10x3 - 39x2 29x - 6 are the height, length, and width of a rectangular box (right rectangular prism). a new rectangular box is formed by lengthening each edge of the original box by 2 units. what is the volume of the new box?
The volume of the new box is 30 units^3.
We can infer the roots are rational integers from the response options, thus this polynomial ought to be simple to factor. The coefficients of x must multiply by 10, hence they must be in some sequence of 5,2,1 or 10,1. Since we can try each one separately, we can express the factored form as follows:
(5x-p)(2x-q)(x-r)
Due to the fact that p, q, and r must multiply to 6, they must be either 3,2,1 or 6,1,1 in some sequence. Once more, we may test each one in a different place to determine if they multiply properly.
When we multiply the x-terms and attempt (5x-2)(2x-1)(x-3), the answer is 29. Try adding the x^2 terms together; they equal -39. Consequently, the roots are [tex]\frac{2}{5} , \frac{1}{2} and 3.[/tex] Now if you add 2 to each root, you get the volume is
=> [tex]\frac{12}{5} X \frac{5}{2} X 5 =30[/tex]
Therefore, The volume of the new box is 30 units^3.
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A table of values for f, g, f ', and g' is given.
x f(x) g(x) f '(x) g'(x)
1 3 2 4 6
2 1 8 5 7
3 7 2 7 9
(a) If h(x) = f(g(x)), find h'(3).
h'(3) =
(b) If
H(x) = g(f(x)), find H'(1).
H'(1) =
a. The value of h'(3) is 45.
b. The value of H'(1) is 36.
The complete table is in the attachment. h' and H are derivates from function h(x) and H(x). Using the Chain Rules to derivate the function.
Calculate the h'(x) function
h(x) = f(g(x))
h'(x) = d/dx {f(g(x))}
h'(x) = f' (g(x)) × g'(x)
h'(3) = f' (g(3)) × g'(3)
h'(3) = f'(2) × 9
h'(3) = 5 × 9
h'(3) = 45
Calculate the H'(x) function
H(x) = g(f(x))
H'(x) = d/dx {g(f(x))}
H'(x) = g' (f(x)) × f'(x)
H'(1) = g' (f(1)) × f'(1)
H'(1) = g'(3) × 4
H'(1) = 9 × 4
H'(1) = 36
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If you were to make a scatter plot of data, you would be able to determine the line of best fit. Using the regression equation y = 1.73x + 0.39, Predict the number of representatives for Oregon, which has a population of about 3.3 million.
A. 5 representatives
B. 6 representatives
C. 7 representatives
D. 28 representatives
The number of representatives for Oregon, which has a population of about 3.3 million is 6 Representatives (Option B).
The regression equation y = 1.73x + 0.39 is the equation of the line of best fit. To use this equation to predict the number of representatives for Oregon, which has a population of about 3.3 million, we need to substitute the population of Oregon (x = 3.3 million) into the equation and solve for y.
y = 1.73x + 0.39
y = 1.73(3.3) + 0.39
y = 5.659 + 0.39
y = 6.049
So the number of representatives for Oregon is approximately 6.049. The closest answer to that is
B. 6 representatives
Therefore, The number of representatives for Oregon, which has a population of about 3.3 million is 6 Representatives (Option B).
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Starting from 1.5 miles away, a car drives towards a speed check point and then passes it. the car travels at a constant rate of 53 miles per hour. the distance of the car from the check point is given by d=|1.5-53t|. at what times is the car 0.1 miles from the check point?
The time at which the car is 0.1 miles from the checkpoint is 95.1s and 108.7s.
The speed of the car is 53 miles per hour.
The distance of the car from the checkpoint is given by d = |1.5 - 53t|
To be 0.1 miles away from the checkpoint, the car has to travel 1.4 miles OR 1.6 miles.
53 miles = 60 minutes
1.4 miles = 1.4 / 53 × 60
= 1.5849056 minutes
= 1.5849056 × 60 seconds
= 95.1 seconds
1.6 miles = 1.6 /53 × 60
= 1.8113207 minutes
= 1.8113207 × 60 seconds
= 108.7 seconds
So the required time is 95.1s and 108.7s.
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prove by the sum of arithmetic induction that the sum of the first n terms of a n arithmetic sequence
The sum of the first n terms of an arithmetic sequence can be proven using the principle of induction. We assume the formula holds for n = k, and then show it holds for n = k+1, thus showing it holds for all values of n.
The sum of the first n terms of an arithmetic sequence can be determined using the formula S_n = (n/2)(a_1 + a_n), where a_1 is the first term and a_n is the nth term.
We can prove this formula using the principle of induction.
Base Case: Let n = 1. Then S_1 = (1/2)(a_1 + a_1), which simplifies to S_1 = a_1. This is the same result we would get if we added the first term of the sequence.
Inductive Step: Assume that the formula holds for n = k.
Then S_k = (k/2)(a_1 + a_k).
Now consider n = k+1.
S_k+1 = (k+1/2)(a_1 + a_k+1)
= (k/2)(a_1 + a_k) + (1/2)(a_1 + a_k+1)
= S_k + (1/2)(a_k+1 - a_1)
= S_k + (1/2)(a_k+1 - a_k) + (1/2)(a_k - a_1)
= S_k + (1/2)(a_k+1 - a_k) + [S_k - (k/2)(a_1 + a_k)]
= (k+1/2)(a_1 + a_k+1)
= S_k+1
Therefore, we have shown that if the formula holds for n = k, then it also holds for n = k+1. By the principle of induction, the formula holds for all n.
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