Step-by-step explanation:
arithmetic progression
even numbers between 1001 and 10000
1002,1004,.......9998
Tn=a+(n-1)d
Tn = 9998 last term in the progression of even numbers
a = 1002 first term
d = 2 distance
9998=1002+(n-1)(2)
8996=2n-2
8998=2n
n = 4499 the number of terms
sum = n/2 (a+Tn) = 4499/2(1002+9998)
= (4499/2)(11000) = 24744500
Logic:
notice what happens when you add the first and last terms
1002+9998=11000
1004+9996=11000
.......
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.
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What additional information must be known to prove the triangles similar by SSS? options: A) ∠F ≅ ∠Q B) No additional information is needed. C) The lengths of and D) ∠F ≅ ∠D
Answer:
Option A) [tex]\angle F\\[/tex] congruent with [tex]\angle Q[/tex]
Step-by-step explanation:
There is only information about two sides in each triangle, so there is still the need of a third piece of info which can come from an angle like [tex]\angle F\\[/tex] congruent with [tex]\angle Q[/tex], which are angles opposite to one of the given sides on each triangle.
HELP ME ON THIS ONE PLZ NEED ANSWERS
What is the domain and range of each relation?
Drag the answer into the box to match each relation.
{(−7, 2), (−2, 2), (0, 1), (4, 5)}
A mapping diagram. Element x contains negative 4, negative 3, negative 1, and 1. Element Y contains negative 3, negative 1, and 4. Negative four maps to negative 1. Negative three maps to negative 3 and 4. Negative one maps negative 1. One maps to 4.
Answer:
See below.
Step-by-step explanation:
The domain of a relation are simply its x-values, while the range of a relation are its y-values.
1)
We have the relation:
{(-7,2), (-2,2), (0,1), (4,5)}
Again, the domain of this relation are the x-values. Therefore, the domain is:
{-7, -2, 0, 4}
The range of this relation are the y-values. Therefore, the range is:
{2, 1, 5}
Note that even though the 2 repeats, we only count it once because it's the same.
2)
We have the relation:
{(-4,-1), (-3,-3), (-3,4), (-1,-1), (1,4)}
The domain are the x-values. Therefore, the domain is:
{-4, -3, -1, 1}
Again, the -3 repeats so we only count it once.
And the range would be the y-values:
{-3, -1, 4}
It's customary to place them in ascending order.
Answer:
If there are two set A and B. All the elements of set A are called domain and all elements of set B are range.And element of B which are maping with set A elements are codomain
Step-by-step explanation:
domains are -7,-2,0,4
range are 2,1,5
I hope this is helpful for you
The endpoints of a line segment can be represented on a coordinate grid by the points
A(-4, 1) and ((-4, -3). Graph and label each of the endpoints of the line segment on
the coordinate grid below.
A swim team must be chosen from 12 candidates. What is the greatest number of different 3-person teams that can be chosen?
==========================================
Explanation:
We have 12*11*10 = 1320 permutations possible. This is where order matters. However, order does not matter with swim teams as there are no positions or ranks. All that matters is the group overall (rather than any individual in the group).
Consider the set {A,B,C}. We have 3*2*1 = 6 ways to arrange this set of letters. When considering a permutation, there are 6 permutations but only 1 combination since order doesnt matter and ABC is the same as BAC. Therefore, we divide 1320 over 6 to get the final answer of 1320/6 = 220.
---------
You can use the combination formula with n = 12 and r = 3. Doing so will give the following:
[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{12} C _3 = \frac{12!}{3!*(12-3)!}\\\\_{12} C _3 = \frac{12!}{3!*9!}\\\\_{12} C _3 = \frac{12*11*10*9!}{3!*9!}\\\\_{12} C _3 = \frac{12*11*10}{3!}\\\\_{12} C _3 = \frac{12*11*10}{3*2*1}\\\\_{12} C _3 = \frac{1320}{6}\\\\_{12} C _3 = 220\\\\[/tex]
As you can see, we get the same result and note how 1320/6 is also present as well.
The greatest number of different 3-person teams that can be chosen is 220.
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?We can use combinations for this case,
The Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]
So, total number of choices in that case would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called permutation of k items chosen out of m items (all distinct).
Consider the set {A,B,C}.
3*2*1 = 6 ways to arrange this set of letters.
When considering a permutation, there are 6 permutations but only 1 combination since order doesnt matter and ABC is the same as BAC.
We can use the combination formula with n = 12 and r = 3.
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.\\\\^{12}C_3= \dfrac{12!}{3! \times (12-3)!} ways.\\\\\\^{12}C_3= \dfrac{12!}{3! \times (9)!} ways.\\\\^{12}C_3= \dfrac{12 \times 11 \times 10 \times 9}{3! \times (9)!} ways.[/tex]
1320/6 = 220
Thus, the greatest number of different 3-person teams that can be chosen is 220.
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help me meeeeeeeeeeee
Answer:
15 pupcakes
Step-by-step explanation:
Purple is 1 out of 4 sections
1/4 times the number of total pupcakes
1/4 * 60
15
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
Which change can be made to correct the chart?
The expression 3x3 should be 3x2.
The expression 6x should be 6xy.
The expression x2y should be x2y2.
The expression 4y should be 4y2.
Answer:
3x^3/x = 3x^(3-1) = 3x^2
6x*y = 6xy
x^2y *y = x^2y^(1+1) = x^2y^2
4y*y = 4y^2
Step-by-step explanation:
This can be solved using law of Indices.
The expression 3x^3 should be 3x^2.
Here power of x is three while in output power of x is two hence we need to eliminate power of x by one for that we divide 3x^3 by x
Rule: x^a/x^b = x^(a-b)
3x^3/x = 3x^(3-1) = 3x^2 (answer)
_________________________________
The expression 6x should be 6xy.
here term y is missing hence we multiply 6x with y
rule: a*b = ab
6x*y = 6xy (answer)
_________________________________________________
The expression x^2y should be x^2y^2
Here we need power of y as 2, to do that we multiply x^2y by y.
Rule
x^2*x^b = x(a+b)
x^2y *y = x^2y^(1+1) = x^2y^2 (answer)
_____________________________________________
The expression 4y should be 4y^2\
Here we need power of y as 2, to do that we multiply 4y by y.
Rule
x^2*x^b = x(a+b)
4y*y = 4y^2 (answer)
Answer:
b: the expression 6x should be 6xy
Step-by-step explanation:
i just did on edgen 2020
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 :)
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:
Please help me I am bad at this stuff
is the square root of 34 rational or irrational
Answer:
irrational
Step-by-step explanation:
If a square root is not a perfect square, then it is considered an irrational number.
The square root of the number 34 is not a rational number
How to determine the type of the numberFrom the question, we have the following parameters that can be used in our computation:
The square root of the number 34
When evaluated, we have
The square root of the number 34 = √34
So, we have
The square root of the number 34 = 5.83.....
The above number cannot be represented by the quotient of 2 integers
Using the above as a guide, we have the following:
We can conclude that the number is an irrational number
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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.
Mrs. Lobo earns a salary of $50,000 per year plus a 4% commission on her sales. The average price of a share
she sells is $50.
Write an inequality to describe about how many shares Mrs. Lobo must sell to make an annual income of at
least $70,000
Select one:
O a. 50,000 + 2x > 70,000
O b. 50,000 + 2x < 70,000
O c. 50,000 -- 2x > 70,000
d. 50,000 + 2 > 70,000
Answer:
a) 50,000 + 2x > 70,000
Step-by-step explanation:
Mrs. Lobo has an annual salary of $50000 per year plus 4% commission on her sales.
If she makes $y commission from sales, Mrs Lobo total income per year is:
$50000 + $y.
She makes 4% commission on her sales of share with the average price of a share = $50
Average commission from sales = 4% × $50 = 0.04 × 50 = $2
If she sales x shares in a year, her commission would be $2x for the year. Therefore her total income for that year would be:
50000 + 2x
The amount of shares Mrs Lobbo must sell to make an annual income of at
least $70,000 is given by the inequality:
50,000 + 2x > 70,000
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:
What is the middle term of the product of (x - 4)(x - 3)?
Answer:
- 7x
Step-by-step explanation:
Given
(x - 4)(x - 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x - 3) - 4(x - 3) ← distribute both parenthesis
= x² - 3x - 4x + 12 ← collect like terms
= x² - 7x + 12
with middle term = - 7x
Answer:
Step-by-step explanation:
= x(x-3) - 4(x-3)
= x²-3x - 4x + 12
= x² -7x +12
So -7x is the middle term
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×
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
An eraser is in the shape of a triangular prism. Its dimensions are shown in the diagram. What is surface area of the
eraser?
50 mm
40 mm
40 mm
30 mm
3,600 square millimeters
4.800 square millimeters
5,400 square millimeters
6,000 square millimeters
Answer:
6000 square millimeters
Step-by-step explanation:
Side length of the slanting side can be calculated using the Pythagorean theorem,
L = sqrt(30^2+40^2) = 50
sufrace area of a triangular prism
= surface area of the end sections + the surface area of the three side faces
= 2*(30*40/2) + 40*(30+40+50)
= 1200 + 4800
= 6000 mm^2
Answer:
D) 6,000 square mm
Step-by-step explanation:
To find the surface area of the triangular prism, find the are of each face.
40 × 30 ÷ 2 = 600 × 2 sides = 120040 × 50 = 200040 × 30 = 120040 × 40 = 1600After adding all the sides' together, you get 6,000 square mm.
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
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!!
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.
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]
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)
Please answer this!!! Thank you!!!
I hope this helped! Good luck with the rest of your class :)
Blue paper chains 4 inches long. Red paper chains are 3 inches long. How many are needed to have 10 inches of paper chains?
1 blue paper chain and 2 red paper chains
Answer:
1 blue paper chains and 2 red
Step-by-step explanation:
becuase 4 plus 3 plus 3 is 10
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]
Find m∠CBD,,,,,,,,,,
Answer:
angle CBD=125
Step-by-step explanation:
(8x-41)+(9x+17)=180
17x -24 = 180
17x=204
x=12
9(12)+17=125
Answer:
125
Step-by-step explanation:
The two angles from a straight line so they add to 180
ABC + CBD = 180
8x -41+ 9x+17 = 180
Combine like terms
17x -24 = 180
Add 24 to each side
17x -24+24 = 180 +24
17x = 204
Divide by 17
17x/17 = 204/17
x =12
We want angle CBD
CBD = 9x+17
= 9*12+17
=108+17
= 125
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
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.