Answer:
The correct option is;
[tex]4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )[/tex]
Step-by-step explanation:
The given expression is presented as follows;
[tex]\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right )[/tex]
Which can be expanded into the following form;
[tex]\sum\limits _{n = 1}^{50} \left (4\cdot n^2 + 3 \cdot n\right ) = 4 \times \sum\limits _{n = 1}^{50} \left n^2 + 3 \times\sum\limits _{n = 1}^{50} n[/tex]
From which we have;
[tex]\sum\limits _{k = 1}^{n} \left k^2 = \dfrac{n \times (n+1) \times(2n+1)}{6}[/tex]
[tex]\sum\limits _{k = 1}^{n} \left k = \dfrac{n \times (n+1) }{2}[/tex]
Therefore, substituting the value of n = 50 we have;
[tex]\sum\limits _{n = 1}^{50} \left k^2 = \dfrac{50 \times (50+1) \times(2\cdot 50+1)}{6}[/tex]
[tex]\sum\limits _{k = 1}^{50} \left k = \dfrac{50 \times (50+1) }{2}[/tex]
Which gives;
[tex]4 \times \sum\limits _{n = 1}^{50} \left n^2 = 4 \times \dfrac{n \times (n+1) \times(2n+1)}{6} = 4 \times \dfrac{50 \times (50+1) \times(2 \times 50+1)}{6}[/tex]
[tex]3 \times\sum\limits _{n = 1}^{50} n = 3 \times \dfrac{n \times (n+1) }{2} = 3 \times \dfrac{50 \times (51) }{2}[/tex]
[tex]\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right ) = 4 \times \dfrac{50 \times (50+1) \times(2\times 50+1)}{6} +3 \times \dfrac{50 \times (51) }{2}[/tex]
Therefore, we have;
[tex]4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )[/tex].
feet.
The radius of Cylinder A measures
10
7
14
Answer:
14 I think
Step-by-step explanation:
Tell me if I'm wrong
Answer:
14
mark me brainy plz!
Step-by-step explanation:
If 4 pounds of sugar cost $2, the cost of 1 pound of sugar is $ and the cost of 10 pounds of sugar is $ Bryan drives at an average speed of 60 miles per hour. At this rate, it will take him 3 hours to drive how many miles does Bryan
Answer:
The cost of one pound of sugar is $0.5 and the cost of 10lbs of sugar is $5
Bryan is driving 180 miles
Step-by-step explanation:
Pleaseeeee hurryy need help!!
it is the last one
Step-by-step explanation:
by simplifying powers it becomes
8g^8/64h ^5
simplifying it further gives
g^8/ 8h^5
Please Help ASAP! Will name Brainliest! Question: Minimize the objective function P = 5x + 8y for the given constraints. x ≥ 0 y ≥ 0 2x + 3y ≥ 15 3x + 2y ≥ 15 Answer: 25, 46, 39, 37.5
Answer:
Option D.
Step-by-step explanation:
Minimize the objective function P = 5x + 8y for the given constraints.
[tex]x\geq 0,y\geq 0[/tex]
[tex]2x+3y\geq 15[/tex]
[tex]3x+2y\geq 15[/tex]
The related equations of above inequalities are
[tex]2x+3y=15[/tex]
[tex]3x+2y=15[/tex]
For [tex]2x+3y=15[/tex],
x y
0 5
7.5 0
Plot (0,5) and (7.5,0) and join them by straight line.
For [tex]3x+2y=15[/tex],
x y
0 7.5
5 0
Plot (0,7.5) and (5,0) and join them by straight line.
Check the inequalities for (0,0).
[tex]2(0)+3(0)\geq 15\Rightarrow 0\geq 15[/tex] False
[tex]3(0)+2(0)\geq 15\Rightarrow 0\geq 15[/tex] False
It means both lines are solid lines and shaded region for each lies opposite side of (0,0).
From the below graph it is clear that the vertices of feasible region are (0,7.5), (3,3), (7.5,0).
Point P = 5x + 8y
(0,7.5) P=5(0)+8(7.5)=60
(3,3) P=5(3)+8(3)=15+24=39
(7.5,0) P=5(7.5)+8(0)=37.5 (Minimum)
So, minimum value is 37.5.
Therefore, the correct option is D.
confused on this one
1. Assume that m26 = 60°. What must be true about 26 and 23 for the
lines to be parallel? Name the postulate or theorem that you used in
this justification
Answer:
The other measurement has to be 120 degrees. In other words, the two angles have to add up to 180 degrees. The method for that is same side interior.
Step-by-step explanation:
In same side interior angles, the sum of the two angles has to be 180 degrees. So we know that one of the angles is 60 degrees so we do 180-60=120.
Evaluate 2y - 10 + 8y when y is 4
Answer:
30Step-by-step explanation:
Given,
y = 4
Now, let's evaluate:
[tex]2y - 10 + 8y[/tex]
Plug the values
[tex] = 2 \times 4 - 10 + 8 \times 4[/tex]
Multiply the numbers
[tex] = 8 - 10 + 32[/tex]
Calculate the sum of positive numbers
[tex] = 40 - 10[/tex]
Subtract the numbers
[tex] = 30[/tex]
Hope this helps...
Best regards!!
Answer:
30
Step-by-step explanation:
To solve your question we must first replace y with the given number. In this case, the number given is 4 so,
2 (4) - 10 + 8 (4)
We can now solve by multiplying 2 by 4 and 8 by 4
2 * 4 = 8
8 * 4 = 32
8 - 10 + 32 = 30
Hope this helps!!
1. What solid is represented by this net? (Image 1). A. cylinder B. triangular pyramid C. rectangular prism D. triangular prism E. cone F. rectangular pyramid 2. Choose all the solids from the list below. A. Rectangle B. Circle C. Cone D. Pyramid E. Prism F. Cylinder 3. The volume of the following figure = ___________ cm3. (Image 2) A. 288 B. 72 C. 216 D. 144
Answer:
c rectangular prism i think
Step-by-step explanation:
6/3x = 3. What is x?
Steps to solve:
6/3x = 3
~Multiply 3/6 to both sides
x = 3/2
Best of Luck!
Answer:
x = 3/2
Step-by-step explanation:
Hey there!
To solve this equation, let's rewrite it for cohesive purposes. This would result in (6/3)(x) = 3.
Now, we can simplify the fraction because it reduces to a whole number. Three will go into six two times, so 6/3 is equivalent to 2.
This leaves us with 2x = 3.
Now, we need to isolate the x. Because there is a coefficient leading the variable, we can divide the entire term (2x) by 2 as well as dividing the 3 on the righthand side of the equation by 2.
Remember the mathematical rule of thumb: what you do to one side of the equation, you must perform to the other side. Therefore, if we divide by 2 on the left side of the equation, we must also divide the righthand side of the equation by 2.
By performing this step, it leaves us with x = 1.5.
[tex]{\frac{2x}{2}=\frac{3}{2}}\\\\\bold{x = \frac{3}{2}}[/tex]
We can reduce [tex]\frac{3}{2}[/tex] to a decimal, which transfers to 1.5. However, it's best to leave the answer in fractional form. This leaves our final answer as [tex]\bold{x=\frac{3}{2}}[/tex].
Please answer this!!! Thank you!!!
I hope this helped! Good luck with the rest of your class :)
The price of a vase was increased by 10% to £22. What was the price before the increase?
Answer:
Step-by-step explanation:
Let the price of the vase before increase = x
110 % of x = £ 22
[tex]\frac{110}{100}*x=22\\\\x=22*\frac{100}{110}\\\\x=2*10\\[/tex]
x = £ 20
You have linear functions p(x) and q(x). You know p(2)=3, and p(q(x))=4x+7 for all x. Find q(-1).
Answer:
q(-1)=-2
Step-by-step explanation:
1) flip the equation:
4x+7=-1
2) subtract 7 from both sides:
4x=-8
3) divide both sides by 4:
x=-2
HOPE THIS HELPS!!!! :)
Select all the examples of categorical data. colors number of siblings favorite pet profits genre of music
Answer:
Color, favorite pet, genre of music
Step-by-step explanation:
Categorical variables are simply statistical variables which are non - numeric, usually employed in characterization and groupings based on a certain number of fixed attributes, categories. In the options atated above, the categorical variables fall under a heading with a limited and fixed attributes such as color, pet and genre of music. However, options such as number of siblings and profit are purely numeric variables which can take up any numeric digits and allow for direct numeric computation. They are called quantitative variables.
Answer:
colors, genre of music, favorite pet
What is the value of x in the equation ( x +
({ x + 12) = {(x +
4x + 14) – 3?
-24
-6
2
0
Answer:
3
Step-by-step explanation:
(x+(×+12)=(×+4×+14)-3
×+×+12=×+4×+14-3
2×+12=5×-2×
+12-11=5×-2×
-1=3×
WILL MARK BRAINLIEST Give a real world example of an equation which the constant of proportionality is 15. What would the graph look like?
Answer:
Let's say someone is selling lemonade at a lemonade stand. The more cups of lemonade this person sells, the more money they get. If 1 cup= $1, then he would get $2 for 2 cups.
Step-by-step explanation:
The price of the lemonade cup and the lemonade cup are a constant of proportionality. They are proportional to each other. The more lemonade you sell, the more money you get.
The graph would be a straight diagonal line. The y would be the money, and the x would be the amount of lemonade sold. Since they are the same and proportional, they would go in a straight line.
The pair of points is on the graph of an inverse variation. Find the missing value.
(5, 4) and (x, 7)
Answer:
20/7 or 2 and 6/7
Step-by-step explanation:
convert it into the equation 5=k/4
so 5x4 is 20
k=20
then x=20/y
and y is 7
so the answer is 20/7
Graphs are sometimes______by the way they present information.
Answer:
Misleading?
Step-by-step explanation:
Graphs can have mislabeled axes or different values on the axes, making them hard to understand.
I think this is the right answer, but the question was way too vague. Next time, put some options or at least explain the problem better.
HLP ! HLP ! Please and thank you
Answer:
Yes, it is an exponential function. The base is 2.
Step-by-step explanation:
As you can see, the function is f(x) = 2^(2x).
Since there is an exponent, the function is exponential. Graphing functions is another way to make sure if it's exponential or not.
The base is 2 because 2x, the exponent, is applied to it.
---
I hope this helps, let me know if you have any questions.
When multiplying or dividing two numbers with opposite signs, the answer will be 1.negative 2.positive
Answer:
Negative when multiplying
and
Negative when dividing
Step-by-step explanation:
Answer:
I hope these help
Multiplication ;[tex] - \times - = + \\ - \times + = - \\ + \times + = + \\ + \times - = - [/tex]Division ;[tex] + \div - = - \\ + \div + = + \\ - \div - = + \\ - \div + = - [/tex]
Which of the following is most likely the next step in the series?
Answer:
C.
Step-by-step explanation:
Well if 1 is blue and 2 is tan and 3 is blue and across from 1.
Then 4 will be tan because it is across from 2 which is tan.
C.
Answer:
C
Step-by-step explanation:
It goes blue, blue pink, blue pink blue, so according to the pattern the next would be pink.
p.s. thank you so much for all the points!!!!! Like the other answer said brainliest is always appreciated. Here I am, question #2. You can award it to them now 8-D
Of a classroom filled with 20 students, 2 will be selected to stay after school and correct homework for extra credit. How
many combinations are possible?
Answer: 10
Step-by-step explanation:
20/2=10
pairs of two
Answer:
10 pair
Step-by-step explanation:
20/2=10
10 pairs of students staying after school for extra credit
A cougar can run 25 miles per hour. A cheetah can run 55 miles per hour. if they both run at 3 hours full speed, how much farther will the cheetah run
Answer:
Step-by-step explanation:
( in 3hrs calculate distance)
,the cheetah will run 90 miles farther the cougar
pls mark my answer as the brainliest
Please help i will mark brainliest for correct answers!
Answer:
7. 1/3 8. 3/8
Step-by-step explanation:
7. 5 - 1/6 chance 1 out of 6 possibilities
6 - 1/6 chance 1 out of 6 possibilities
1/6+1/6 = 1/3
8. 3 a's out of 8 letters. 3/8
Answer:
7. 2/3
8. 3/8
Step-by-step explanation:
5 - 1/6
1/6
6 - 1/6
1/6
1/6+1/6 = 2/6 = 1/3
3 out of 8
3/8
P(n) models the probability, when rolling a pair of dice, of obtaining two numbers whose sum is n 2 6 7 P(n) 1/36 5/36 6/36 when does the probability increase faster? a)Between a sum of 2 and a sum of 6 b) Between a sum of 6 and a sum of 7 c)the probability increases at the same rate over both intervals
Answer:
Option c.
Step-by-step explanation:
From the given table, it is clear that
[tex]P(2)=\dfrac{1}{36}[/tex]
[tex]P(6)=\dfrac{5}{36}[/tex]
[tex]P(7)=\dfrac{6}{36}[/tex]
The increasing rate of probability between a sum of 2 and a sum of 6 is
[tex]r_1=\dfrac{P(6)-P(2)}{6-2}[/tex]
[tex]r_1=\dfrac{\dfrac{5}{36}-\dfrac{1}{36}}{4}=\dfrac{1}{36}[/tex]
The increasing rate of probability between a sum of 6 and a sum of 7 is
[tex]r_2=\dfrac{P(7)-P(6)}{7-1}[/tex]
[tex]r_2=\dfrac{\dfrac{6}{36}-\dfrac{5}{36}}{1}=\dfrac{1}{36}[/tex]
Since [tex]r_1=r_2[/tex], therefore the probability increases at the same rate over both intervals.
Hence, the correct option is c.
Answer:
c)the probability increases at the same rate over both intervals
Step-by-step explanation:
it was right on khan academy
Which expression can you simplify by combining like terms? 12b2+4ab−3ba−6 17a2−6b2a+4ba−9 5b2−5a2+8a−b 14a2+6ab−3b−3a
Answer:
12b^2+4ab−3ba−6
Step-by-step explanation:
12b2+4ab−3ba−6
The two middle terms are like terms, the order in which you multiply does not matter ab =ba
12 b^2 +4ab -3ab -6
12 b^2 +ab -6
The correct answer is....
A.) A 12b2+4ab-3ba-6If the degree and variables of two terms are same, then they are called like terms.
Here, 4ab and -3ab are like terms because both have same variables a and b with degree 1.
By combining like terms we get
In options B, C and D, there are no like terms, So only the expression we can simplify by combining like terms.
Let f(x) = 5x + 4 and g(x) = −2x + 1. Find the indicated value f(-2) plz respond quickly
Answer:
f(-2) = -6
Step-by-step explanation:
f(x) = 5x + 4
Let x=-2
f(-2) = 5*-2 +4
= -10+4
= -6
Answer:
[tex]\boxed{f(-2) = -6}[/tex]
Step-by-step explanation:
[tex]f(x) = 5x-4[/tex]
Put x = -2
[tex]f(-2) = 5(-2)+4\\f(-2) = -10+4\\f(-2) = -6[/tex]
Two bicycles are driving on the circle in the same direction with speeds of 9 mph and 5 mph respectively. How many points are there on the circle where the two bicycles meet?
Answer:
4 points
Step-by-step explanation:
.
Let L be the circumference of the circle.
Then the faster cyclist will catch the slower cyclist first time when the faster cyclist will cover
the distance which exactly 1 circumference longer than the distance covered by the slower cyclist
9t-5t=l
It gives the time to get first meeting point
t=l/9-5=l/4 hours
and the distance which the faster cyclist covered during this time is
d1=9t=9l/4 miles
The distance which the slower cyclist covered during this time is
d2=5t=5l/4
The meeting point is geometrically the same point on the circle for both cyclists, and its angle measure on the circle is
(1/l)(5l/(4)-l)=1/4
of the full angle of 2pi radians, or 90 degrees.
So, they started simultaneously, and their first meeting point is at the 90 degrees angle.
Next, they started from this point SIMULTANEOUSLY and . . . and everything was repeated.
Hence, their next meeting point is the point on the circle with the angle of 180 degrees.
So, there are 4 remarkable points on the circle: first point is the starting point, and 3 other points
(the points where whey meet/catch each other) are the images of the starting point, rotated 90°, 180°, and 270° along the circle.
There are 4 remarkable points on the circle which is the first point is the starting point and 3 other points.
What is the circumference of the circle?The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
The circumference of the circle = 2πr
Let L represent the circumference of the circle.
Then the faster cyclist will catch the slower cyclist the first time when the faster cyclist will cover the distance which is exactly 1 circumference longer than the distance covered by the slower cyclist
9t - 5t = L
It gives them time to get the first meeting point
t = L/9 - 5
t = L/4 hours
The distance which the faster cyclist covered during this time;
d1 = 9t = 9L/4 miles
The distance that the slower cyclist covered during this time is
d2 = 5t = 5L/4
The meeting point is geometrically the same point on the circle for both cyclists, and its angle measured on the circle;
(1/l)(5l/(4)-l)=1/4
Therefore, their next meeting point is the point on the circle with an angle of 180 degrees.
So, there are 4 remarkable points on the circle which is the first point is the starting point and 3 other points.
Learn more about circumference here;
brainly.com/question/12512221
#SPJ2
Bryce is picking out a new lamp at a furniture store. There are 5 kinds of lamp bases and
3 different lampshades. Each lampshade comes in 3 different colors. Bryce also needs to
choose one of the 2 kinds of lightbulbs available. How many different lamps can Bryce choose?
Answer:
80 lamps
Step-by-step explanation:
number of lamp bases*no. of lampshades*no. of lightbulbs= total number of lamp choices
5*(3*3)*2
=5*9*2
=40*2
=80
hope it helps :)
60 points
Lana uses factoring by grouping to factor the polynomial 8x2y−10xy2+12x−15y. Her work is shown below, but the last two lines of work are missing.
8x2y−10xy2+12x−15y
(8x2y−10xy2)+(12x−15y)
__[blank 1]__
__[blank 2]__
Select one statement for each blank to correctly complete Lana’s work.
blank 1: 2xy(4x−5y)+3(4x−5y)
blank 1: −4x(2xy+3)+5y(2xy+3)
blank 2: (2xy−3)(4x+5y)
blank 1: −2xy(4x+5y)−3(4x+5y)
blank 2: (2xy+3)(4x−5y)
blank 2: −(2xy+3)(4x−5y
NEED PROOF FOR POINTS
Answer:
blank 1: 2xy(4x-5y)+3(4x-5y)
blank 2: (2xy+3)(4x-5y)
Step-by-step explanation:
Using factoring group to factor the polynomial 8x²y−10xy²+12x−15y
Step 1: Group the polynomial function
(8x²y−10xy²)+(12x−15y)
Step 2: Factor the common value and variables from the functions in parentheses.
= (2xy*4x - 2xy(5y)) + (3(4x) - 3(5y))
= 2xy(4x-5y)+3(4x-5y)
Step 3: Rearrange the expression by selecting one of the function in parentheses and combine those not in parenthesis.
(2xy+3)(4x-5y)
The final expression gives the factor form of the polynomial.
Hence the statement for each blank that correctly completes Lana's work are;
blank 1: 2xy(4x-5y)+3(4x-5y)
blank 2: (2xy+3)(4x-5y)
pls help me i give brainliest
Answer: I Thing the answer may be 7units. Please correct me if i'm wrong
Step-by-step explanation:
At the grocery store, you can purchase lemons at 2 for $0.99. you can also buy a bag of 6 lemons for $2.50. Which is the better buy?
Answer:
The 6 lemons for 2.50 is the better deal.
Step-by-step explanation:
2*3=6
3*0.99=2.97
2.97>2.50