Decompose the terms in the sum as
[tex]4 + 15 + 26 + \cdots + 213 = 4 + (4 + 11) + (4 + 2\times11) + \cdots + (4 + 19\times11)[/tex]
so there are 20 terms in the sum. Then our sum simplifies to
[tex]4 + 15 + 26 + \cdots + 213 = 4\times20 + (0+1+2+\cdots+19)\times11[/tex]
Now, if
[tex]S = 1 + 2 + 3 + \cdots + 17 + 18 + 19[/tex]
we can reverse the order of terms to get the same sum,
[tex]S = 19 + 18 + 17 + \cdots + 3 + 2 + 1[/tex]
so that doubling up the sum gives
[tex]2S = (1 + 19) + (2 + 18) + \cdots + (18 + 2) + (19 + 1) = 19\times20 \implies S=19\times10=190[/tex]
So, our sum evaluates to
[tex]4 + 15 + 26 + \cdots + 213 = 4\times20 + 190\times11 = \boxed{2170}[/tex]
The Green Party at a large university plans to line both sides of a 24-foot-long hallway with posters endorsing a candidate for state senate. Each of the posters costs them $6.25 , they’re 3 feet wide, and there will be 4 feet between posters. Assume the first poster on each end will be exactly even with the start of the hall. Estimate how much this will cost.
The total cost of putting the posters on the wall is $25.
What is the cost of putting the posters on the wall?
If the first poster on each end will be exactly even with the start of the wall, it means that after the two posters have been placed on either side of the wall, the total space left would be 10 feet (24 - 3 - 3 - 4 - 4).
After the first poster has been placed on both ends of the wall, a second poster would be placed on either ends of the wall. Total space now left is 4 feet (10 - 3 - 3). So there can only be four posters on the wall.
Total cost of 4 posters = 4 x $6.25 = $25
To learn more about multiplication, please check: https://brainly.com/question/3385014
#SPJ1
The population P ( ) of a culture of the bacterium Pseudomonas aeruginosa is given by P ( t ) 1684 + 83,000 + 10,000 , where is the time in hours the culture was started .
The maximum time in hours will be equal to 24.64 hours.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given function is P(t) = -1684t² +83000t + 10000
The maximum time will be calculated by differentiating the given function with respect to 't' and equate with zero.
[tex]\dfrac{dP(t)}{dt}[/tex] = -1684t² +83000t + 10000 = 0
[tex]\dfrac{d}{dt}[/tex][-1684t² +83000t + 10000] = 0
-3368t + 83000 = 0
3368t = 83000
t = 24.64 hours
Therefore the maximum time in hours will be equal to 24.64 hours.
The correct question is given below:-
The population p(t) of a culture of the bacterium Pseudomonas aeruginosa is given by,p(t)= -1684t² +83000t + 10000 which is the time in hours since the culture was started. Determine the time the population was at its maximum. Round to the nearest hour.
To know more about Expression follow
https://brainly.com/question/723406
#SPJ1
It would take 15men 8days to dig a trench of 240metres long.How many days would it take 18men to dig a trench of 360meters long working at the same Rate.
Using proportions, it is found that it would take 6.4 days for 8 men to dig a trench of 360 meters long working at the same rate.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the rule of three is given as follows:
8 days - 15 men - 240 meters
x days - 18 men - 360 meters
The number of men is inverse proportional to the number of days, hence we divide 18 by 15 instead of 15 by 18, then:
[tex]\frac{8}{x} = \frac{18}{15} \times \frac{24}{36}[/tex]
[tex]\frac{8}{x} = \frac{6}{5} \times \frac{4}{6}[/tex]
[tex]\frac{8}{x} = \frac{5}{4}[/tex]
Applying cross multiplication:
5x = 32.
x = 32/5
x = 6.4 days.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
In order to slove the following system of equations by addition, which of the following could you do before adding the equations so that one variable will be eliminated when you add them?
4x-2y=7
3x-3y=15
Answer:
B. use multipliers -3 and 2
Step-by-step explanation:
If you're solving the system by "addition," multiplying the equations by the chosen numbers needs to result in opposite coefficients for one of the variables.
Effect of answer choicesA. The system becomes ...
12x -6y = 2112x -12y = 60No variable has opposite coefficients.
__
B. The system becomes ...
-12x +6y = -216x -6y = 30The y-variable has opposite coefficients. This is a good choice.
__
C. The system becomes ...
12x -6y = 216x -6y = 30No variable has opposite coefficients.
__
D. The system becomes ...
4/3x -2/3y = 7/33x -3y = 15No variable has opposite coefficients.
__
Additional comment
The simplest "no brainer" solution is to use the coefficients of one of the variables, negating one of them. Multiply each equation by the opposite equation's coefficient. Here, the y-coefficients are -2 and -3, and the multipliers of answer choice B are -3 and 2, consistent with this advice. (The sign of 2 was changed.)
Answer:
B.
Step-by-step explanation:
Multiply the top equation by -3 and the bottom equation by 2
-12x+6y=-21
6x-6y= 30
-6x = 9 Variable "y" is removed
Hope this helps
find the area of the shaded regions.
Answer: [tex]27\pi \text{ cm}^{2}[/tex]
Step-by-step explanation:
The area of the entire circle is [tex](\pi)(6^{2})=36\pi[/tex]
The area of the sector with the right angle is [tex]\frac{36\pi}{4}=9\pi[/tex]
Subtracting these areas, we get [tex]27\pi \text{ cm}^{2}[/tex]
PLEASE HELP
Find the point that splits segment CD in half if point C is located at (−2, 4) and point D is located at (3, 7)
(2.5, 1.5)
(1, 5)
(0.5, 5.5)
(3, 2)
Answer:
0.5, 5.5
Step-by-step explanation:
ive done this worksheet before
Answer: Choice C
(0.5, 5.5)
===========================================================
Explanation:
Draw out a number line with -2 and 3 on it. These are the x coordinates of the given points. Add up these values and divide by 2 to get the midpoint on the number line.
(A+B)/2 = (-2+3)/2 = 1/2 = 0.5
The value 0.5 is the midpoint of -2 and 3. This midpoint is equally spaced from both endpoints.
Therefore, the x coordinate of the midpoint is 0.5
Repeat this idea for the y coordinates
Add: 4 + 7 = 11
Divide the result in half: 11/2 = 5.5
The y coordinate of the midpoint is 5.5
The overall midpoint itself is located at (x,y) = (0.5, 5.5)
This is why choice C is the final answer.
Visual confirmation is shown below. GeoGebra has a nice handy feature to find the midpoint very quickly with just a few clicks.
Please help!! Very much appreciated!! Consider the following set of real numbers. Which of the following lists all of the rational numbers in the set?
Answer:
The second choice.
Step-by-step explanation:
A rational number means that you are able to write the number as a fraction with integers in the numerator and the denominator. An integers are the whole numbers and their opposites ...-3,-2,-1,0,1,2,3...
The square root of 4 is 2. 2 can be written 2/1 (an integer over and integer)
-square root of 2 cannot be written as an integer over an integer. When this number is written as a decimal number it never repeats and it never terminates so it cannot be written as an integer over and integer.
-2/3 is written in the form of an integer over and integer.
1 can be written 1/1
9/8 is written as an integer over an integer.
The square root of 9/4 would be 3/2. (3/2)(3/2) = 9/4.
2.4 repeating can be written as an integer over an integer. Any decimal that repeats or terminates can be written as an integer over and integer. It actual happens to be 22/9.
The square root of 10 written as a decimal does not repeat or terminate so it is not rational. Only perfect squares are rational.
Classify the triangle by its angle and sides
Answer:
isosceles obtuse triangleStep-by-step explanation:
isosceles obtuse triangle
An isosceles obtuse triangle is a triangle in which one of the three angles is obtuse (lies between 90 degrees and 180 degrees) and the other two acute angles are equal in measurement, and 2 equal sides.
A credit card company charges a 4% balance transfer fee. If you want to transfer a balance of $2,100 to this credit card, what fee would you pay?
Answer:
$84
Step-by-step explanation:
So since it charges 4%, this means you need to find 4% of what you're transferring. To find x% of a number, you need to convert the percentage to a decimal, and then multiply it by the number you're trying to find x% of. So in this case 4%/100 = 0.04. Now take this decimal and multiply it by 2100, and this will give you 84. So the fee would be $84
Answer:
$84
Step-by-step explanation:
= 4% × $2100
= 0.04 × $2100
= $84
Which statement regarding the diagram is true?
m∠WXY = m∠YXZ
m∠WXY < m∠YZX
m∠WXY + m∠YXZ = 180°
m∠WXY + m∠XYZ = 180°
the graph shows the equation x^2+y^2=5 use the slider for a to move the vertical line on the graph based on the vertical line test is this equation a function why or why not
Answer:
Not a function.
Step-by-step explanation:
The vertical line touches the graph at more than one point at once.
What is f(x) = 8x² + 4x written in vertex form?
F(x) = 8x + - 1.
f(x) = 8√(x + 1)² - 1/6
f(x) = 8√x+¹²-2
f(x) = 8(x + 1)² - 4
[tex]8x^{2}+4x\\\\=8\left(x^{2}+\frac{1}{2}x \right)\\\\=8\left(x+\frac{1}{4} \right)^{2}-8\left(\frac{1}{16} \right)\\\\\boxed{f(x)=8\left(x+\frac{1}{4} \right)^{2}-\frac{1}{2}}[/tex]
What is this math problem in Simply form 3-4(-2-7)
1. make sure you understand what the problem really is
3-4(-2-7)
= 3 + -4 × (-2 + -7)
2. always begin with the brakes
3 + -4 × (-2 + -7)
= 3 + -4 × (-9)
3. then ² and [tex] \sqrt{?} [/tex]
4. then × and and ÷
3 + -4 × (-9)
= 3 + 36
5. lastly + and -
3+36
=39
Which could be the entire interval over which the
function, f(x), is positive?
O (-∞, 1)
O (-2, 1)
O (-∞, 0)
O (1,4)
Answer:
(-2, 1)
Step-by-step explanation:
So assuming this table contains all the zeroes of f(x) and all of them having a multiplicity of 0. This quadratic equation can be defined as
[tex]f(x) = a(x+2)(x-1)[/tex]. So if you look at the top where its f(-3) then f(-2) then f(-1) it appears to be increasing and then somewhere in between f(-1) and f(0) it has a turning point in which it starts decreasing. and then after f(1) it no longer outputs positive values and appears to be going towards negative infinity. So the interval in which f(x) is positive seems to be finite and using this table it appears to be at (-2, 1) and make sure to use parenthesis since at f(-2) and f(1) it's not positive, because 0 is not positive, so it's not included in the interval
How do I calculate the 2nd question?
(Attached the file)
Answer:
0.29287
Step-by-step explanation:
You want to use the binomial cumulative distribution function (binomcdf). The purpose of this function is that it allows you to obtain the probability of observing less than or equal to x successes in n trials, with the probability p of success on a single trial.
x in this case is 182, n is 200, and p is 0.9005. Essentially by inputting these values, we find the probability that out of 200 passengers with a 0.9005 chance of getting on the plane, that 182 or less show up.
This gives us P(x <= 182) = 0.70713. (You need your calculator for this step, input the values above in the binomcdf function)
We want to find the probability of more than 182 passengers showing up though, so it would be 1 - 0.70713 = 0.29287.
Thus the probability that when 200 reservations are accepted for the flight, there are more passengers than seats available is 0.29287.
20. An amount of money was shared among five boys Ali, Juma, Musa, Khalid and Mustafa. Ali got /8 of the total amount while Juma got /5 of the remainder. The remaining amount was shared equally among Musa, Khalid and Mustafa, each of which received Kshs 600. a) How much did Juma get? b) How much was shared among the five boys. (3 marks) (2 marks)
Answer:
[tex]x=\frac{18000}{7}=2571\frac{3}{7}[/tex]
Step-by-step explanation:
Let the total amount be x
Then Ali got 1/8x With 7/8x left
Juma got 7/40x with 7/10x left
Musa, Khalid and Mustafa got 7/30x each
since [tex]\frac{7}{30}x=600[/tex]
7x=18000
[tex]x=\frac{18000}{7}=2571\frac{3}{7}[/tex]
Find the area of the following figure:
The area of the figure is 11. 27 cm²
How to find the areaThe figure given is a parallelogram
Note that the formula for area of a parallelogram is given as;
Area = base × height
Base = 2. 3cm
height = 4. 9cm
Area = 2. 3 × 4. 9
Area = 11. 27 cm²
Thus, the area of the figure is 11. 27 cm²
Learn more about a parallelogram here:
https://brainly.com/question/970600
#SPJ1
round the answer to the nearest
By knowing the blood pressure and applying the quadratic formula, the age of a man whose normal blood pressure is 129 mm Hg is 40 years old.
How to use quadratic equations to determine the age of a man in terms of blood pressure
In this problem we have a quadratic function that models the blood pressure as a function of age. As the latter is known, we must use the quadratic formula to determine the former:
129 = 0.006 · A² - 0.02 ·A + 120
0.006 · A² - 0.02 · A - 9 = 0
[tex]A = \frac{0.02 \pm \sqrt{0.006^{2}-4\cdot (0.006)\cdot (- 9)}}{2\cdot (0.006)}[/tex]
A = 1.667 + 38.733
A = 40
By knowing the blood pressure and applying the quadratic formula, the age of a man whose normal blood pressure is 129 mm Hg is 40 years old.
To learn more on quadratic equations: https://brainly.com/question/1863222
#SPJ1
I need the answer pls, any of y'all's answers would help!
Answer:
1
Step-by-step explanation:
The differences in the values on each spot on the line is 2, because -5 is in between -7 and -3. Going to the right means that the values are increasing. We go from -7, to -5, to -3, to -1, and finally, to 1.
Brainliest, please :)
Which of the following determines a plane?
A. 3 non-collinear points
B. line and a point on the line
C. three collinear points
D. a straight line
Answer: A 3 non collinear pts
a plane is a flat surface like a wall
Jacob can take any one of three routes from school to the mall, and one of five possible routes from the mall to his house. If he doesn’t retrace his steps, how many different ways can Jacob walk from school to home?
Answer:
15 routes
Step-by-step explanation:
3 x 5 = 15 routes
fg⊥op, rs⊥qr. FG = 40, RS = 40, OP = 15. Find x.
A. 17
B. 21
C. 20
D. 15
The measure of x from the diagram is 15
Circle theoremsFrom the given diagrams, we are told that fg⊥op, rs⊥qr. Given the following parameters
FG = 40,
RS = 40,
OP = 15.
Since the measure of FG is equal to RS, hence the measure of Op will be equal to OQ to have:
OQ = OP = x
x = 15
Hence the measure of x from the diagram is 15
Learn more on circle theorem here: https://brainly.com/question/26594685
#SPJ1
Answer: 15
Step-by-step explanation:
OP = OQ
they are congruent
Hi- I need help please to get my HS diploma...did not graduate :(
Find the remainder when f(x)=x3−6x2+3x−1 is divided by 2x−3.
The remainder from the division of the algebraic equation is -53/8.
What is the remainder of the algebraic expression?The remainder of the algebraic expression can be determined by using the long division method.
Given that:
[tex]\mathbf{f(x) = \dfrac{x^3 - 6x^2 + 3x - 1}{2x-3}}[/tex]
where:
The divisor = 2x -3Using the long division method, we have:
[tex]\mathbf{= \dfrac{x^2}{2} +\dfrac{-\dfrac{9x^2}{2}+3x -1 }{2x-3}}[/tex]
[tex]\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} +\dfrac{-\dfrac{-15x}{4}-1 }{2x-3}}[/tex]
[tex]\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} -\dfrac{15}{8}+\dfrac{-\dfrac{53}{8} }{2x-3}}[/tex]
[tex]\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} -\dfrac{15}{8}-\dfrac{53 }{8(2x-3)}}[/tex]
Therefore, we can conclude that the remainder is -53/8.
Learn more about the division of algebraic equations here:
https://brainly.com/question/4541471
#SPJ1
Work out 0.8 million - 1.76 thousand
The value of the given task 0.8 million - 1.76 thousand is 798,240.
Place value0.8 million
= 0.8 × 1,000,000
= 800,000
1.76 thousand
= 1.76 × 1000
= 1,760
So,
0.8 million - 1.76 thousand
= 800,000 - 1,760
= 798,240
Therefore, 0.8 million - 1.76 thousand is 798,240
Learn more about place value:
https://brainly.com/question/2041524
#SPJ1
Fifteen hungry kittens found a bucket of sausages. Each time
they cut a sausage or a part of a sausage, they cut it into exactly
two new pieces. They made 18 cuts in all and each kitten got 2
(maybe unequal) pieces of sausage. How many sausages were in
the bucket?
Answer:
2.4 SAUSAGES
Step-by-step explanation:
18 x 2 = 36
36/ 15 = 2.4
DECIDE WHEATHER THE ORDER PAIR(-3,-5) IS A SOLITION OF THE EQUATION 7X-5Y=15
Answer:
(-3, -5) is not a solution of the equation 7x - 5y = 15
Step-by-step explanation:
1) Knowing that coordinates are given to us as (x, y), plug in the ordered pair into the equation. [tex]7(-3)-5(-5)=15[/tex]
2) Do PEMDAS on the left side of the equation
[tex]-21+25=15[/tex][tex]4=15[/tex][tex]4\neq 15[/tex]Answer:
Not a solution
Step-by-step explanation:
Hello!
We can determine if it's a solution by plugging in the x and y-values of the point into the equation. If both sides are equal to each other, then it is a solution.
-3 is the x-value and -5 is the y-value, since an ordered pari is written in the form of (x,y).
Evaluate7x - 5y = 157(-3) - 5(-5) = 15-21 + 25 = 154 ≠ 15Since both sides are not equal to each other, (-3,-5) is not a solution.
Which graph represents a function with direct variation? A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2). A coordinate plane with a line passing through (negative 5, 4) and (0, 3). A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3). A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4).
A line passing through the points (-1,-4),(0,0) and (1,4).
The correct option is (B).
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The only line that passes through origin is having coordinates (-1,-4),(0,0) and (1,4).
m= y/x
m = -4/-1
m=4
Hence, the linear equation is y=4x, which represent in direct variation.
Learn more about this concept here:
https://brainly.com/question/13347203
#SPJ1
Answer:
C
Step-by-step explanation:
If the line is a direct variation it has to go through the origin
A container is shaped like a cylinder with half spheres on each end. The cylinder has a length of 30 centimeters and a radius is 5 centimeters. To the nearest cubic centimeter, how many cubic centimeters can one container hold? Do not round calculations until the final answer. For the final answer, round to the nearest cubic centimeter (no decimals) and use a comma to separate the thousands place. cubic centimeters
The cubic centimeter one container can hold is 2,878.33 cm³.
What is the cubic centimeter one container can hold ?In order to determine the cubic centimeter one container can hold, the volume of the container has to be determined.
Volume of the container = volume of the cylinder + (2 x volume of the hemisphere)
Volume of the cylinder = πr²h
Where:
π = 3.14 r = radius h = height3.14 x 5² x 30 = 2355 cm³
Volume of a hemisphere = (2/3) x π x r³
2 x (2/3 x 3.14 x 5³) = 523.33 cm³
Volume of the container = 523.33 cm³ + 2355 cm³ = 2,878.33 cm³
To learn more about the volume of a hemisphere, please check: https://brainly.com/question/26840364
#SPJ1
what is the approximate radius of a sphere with the volume of
Answer:
4.6cm
Step-by-step explanation:
v=4/3πr^3
128π=4/3π^3
128π×3=4πr^3
384π\4=πr^3
96π\π=r^3
96=r^3
3√96=r
r=4.579
r=4 6cm
Which line has no slope?
a
O Line a
O Line b
O Line c
O Line d