The chairs in the auditorium illustrates an arithmetic sequence
The recursive rule is: an = an-1 + 8; a1 = 26The explicit rule is: an = 18 + 8nThere are 74 seats in the 7th row840 chairs can fit the auditoriumThe recursive ruleFrom the question, we have the following sequence:
Seats: 18, 26, 34
Rewrite as:
26 = 18 + 8
34 = 26 + 8
The above means that:
The number of seats on a row is 8 added to the the number of seats on the previous row.
Hence, the recursive rule is:
an = an-1 + 8; a1 = 26
The explicit ruleIn (a), we have:
a1 = 26 and d = 8
The explicit rule is calculated using:
an = a1 + (n -1) * d
This gives
an = 26 + (n - 1) * 8
Expand
an = 26 - 8 + 8n
Evaluate the difference
an = 18 + 8n
Hence, the explicit rule is:
an = 18 + 8n
The number of seats in the row 7This means that n = 7.
So, we have:
a7 = 18 + 8 * 7 = 74
Hence, there are 74 seats in the 7th row
The sigma notationWe have the maximum number of rows to be 12.
So, the sigma notation would be:
[tex]\sum\limits^{12}_{n=1} {18 + 8n}[/tex]
The total number of seats is:
Sn = n/2(2a + (n -1) * d)
This gives
S12 = 12/2(2 * 26 + (12 -1) * 8)
S12 = 840
Hence, 840 chairs can fit the auditorium
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The slope of a given line is. 3/5 What is the slope of the line parallel / perpendicular to
it? Write your answer as a fraction in simplest form.
Perpendicular lines have negative reciprocal slopes. That means the fraction is flipped and multiplied by negative 1. So if one line has a slope of 3/5, then a line perpendicular to it has a slope of -5/3.
A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. The negative reciprocal of the original line is –2, and is thus the slope of its perpendicular line
Show all steps when completing the square to solve 2x^{2} - 4x - 5 = 25.
Answer:
x = 5,-3
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Answer:
See attachments
Step-by-step explanation:
Hope this helps! (I hope you can open them)
20. What is the area in square feet of the sidewalk shown
below? Round off to the next largest foot.
Answer:
it doesnt say any numbers or pictures of the question can you add them
Solve 2x+4> 16.
O A. X> 10
B. x <10
C. x< 6
O
D. X>6
Answer:
D
Step-by-step explanation:
First subtract 4 from both sides and divde both sides by 2.
Solution:
=2x+4>16
=2x+4-4>16-4
=2x>12
=2x÷2>12÷2
=x>6
Milk is on sale for 40% off when it is normally $3.75 per gallon. How much will a gallon of milk cost?
The discounted price for milk is $____(Round to the nearest cent.)
Answer:
$2.25
Step-by-step explanation:
You have to set up a proportion to show how much the cost of milk is when discounted per gallon. 0% off, the milk would be $3.75. 40% off, the milk would be x. Now I flipped the percents because that is how much you are actually paying.
Proportion would look something like this:
3.75/100 = x/60
solve for x:
225 = 100x
x= 2.25
Use translation (x,y) to (x-8, y+4)
What is the image of A (2,6)
Answer:
(-6,10)
Step-by-step explanation:
This is simple, you just subtract 8 from the x value, and add 4 to the y value.
Hope this helps
Help with this please
Answer:
f(4)=-10
x=0
Step-by-step explanation:
On Friday, a local hamburger shop sold a combined total of 468 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Friday?
Hello, can you help me out with this please i will give brainlist :D
Answer:
2.23
Step-by-step explanation:
Which of the following functions best models the data represented by the scatterplot shown below
y=25x+20
y=160x−100
y=8x2+10
y=2x+12
Answer:
I am pretty sure the answer is going to be y=25x+20 :)
Have an amazing day!!
Please rate and mark brainliest!!
The correct function for the given data representation will be,
y = 8x² + 10
What is Function?
A relation between a set of inputs having one output each is called a function.
Data representation is given by the scatterplot in the graph.
Now,
Take a function y = 8x² + 10
Then, Check each point on the x - axis for the value of y - axis.
So. Substitute x = 1 in the function we get;
y = 8 × 1 + 10
y = 8 + 10
y = 18
So, Point is (1, 18)
For, x = 3
y = 8 × 3² + 10
y = 72 +10
y = 82
So, Point is (3, 82)
For, x = 5
y = 8 × 5² + 20
y = 200 + 20
y = 220
So, Point is (5, 220)
Thus, All points are satisfy the given scatterplot graph.
So, The correct function for the given data representation will be,
y = 8x² + 10
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Answer the question below:
Answer:
5 students did.
Step-by-step explanation:
20 students. 1/4 of 20 is 5
Solve for the missing angles. Can somebody please help in stuck!
Answer:
A = C = 115°
B = 65°
D = E = 45°
Step-by-step explanation:
65° + C = 180° or 65° + A = 180°, They are supplementary angles that are linear pair that add up to 180°.
A = C = 115°
B° = 65° Vertical Angles meaning they are equal to each other.
D and E are equal to cheat other since the lines on the sides mean that are isosceles.
D + E + 90° = 180°
D + E = 90°
2x = 90
x = 45°
D = E = 45°
Find the missing length. Round to the nearest tenth, if necessary. A right triangle has legs measuring 8 units and x units and a hypotenuse measuring 21 units.
Answer:
168
Step-by-step explanation:
In the diagram, BD is a diameter of circle A. If the slope of BE is 3/2, what is the slope of BD
Answer:
Step-by-step explanation:
the slopes are perpendicular
find a slope perpendicular to 3/2
how to find:
change the sign of the slope and flip the fraction
-2/3 is the slope
The slope of BD is -2/3.
What is slope?Numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it.
Given:
BD is a diameter of circle A. If the slope of BE is 3/2.
We have to find the slope of BD.
According to given question we have
We know that the slope of a perpendicular line from the slope of a given line is obtained by taking the negative reciprocal of the slope of the given line. If the slope of the given line is [tex]m_{1}[/tex] and the slope of a perpendicular line is [tex]m_{2}[/tex] then we have
[tex]m_{2} = -1/m_{1}[/tex]
So, the slope of BD is -2/3.
Therefore, the slope of BD is -2/3.
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People use water to cook, clean, and drink every day. An estimate of 22.8% of the water used each day is for cleaning. If a family uses 68.4 gallons of water a day for cleaning, how many gallons do they use every day?
Answer:
I got 15.6
Step-by-step explanation:
I subtracted 28.8 percent from 68.4 then subtracted that number from 68.4
Dora is making invitations for her party. Dora needs to make invitations for 54 of her friends. On Friday you helped her make 1/2 of the invitations. How many did you make?
Answer:
[tex] \frac{1}{2} of \: the \: invitations = \frac{1}{2} \times 54 \\ = 27invitations[/tex]
you made 27 of the invitations
The circumference of a circle is 11 inches. What is the area, in square inches, of the circle? Express your answer in terms of pi
Answer
A = 30.25pi. PLS GIVE BRAINLIEST
Step-by-step explanation:
so if circumference is 11, and formula for circumference is 2pi*r, we can work backwards to find the radius.
Radius: 11pi/2 = 5.5pi = 5.5 is radius
Area = pi * r^2
so Area = pi*5.5^2
so A = 30.25pi left in terms of pi
Answer: 11/4pi
Step-by-step explanation:
In a call center that stays open all the time, calls arrive as a poisson process with a mean rate of 0.3 complaints per hour.(a) (5 points) after receiving a call (the 1st call), what is the probability that the 51st call arrives within 150 hours?(b) (5 points) after receiving a call, what is the probability that the next call arrives after 2 hours?(c) (5 points) the number of calls received each day is recorded for 50 consecutive days. find the probability that the sum of these 50 numbers is less than 356.
The probability the 51st call arriaves within 150hours is 0.0431, the probability the next call arrives within the next 2 hours 0.5488, the probability the sum of these 50 numbers is less than 356 is 0.4165.
Data;
Mean rate = 0.3x = 50standard deviation = ?Poission RuleUsing poission formula,
[tex]P(x=x) = \frac{e^-^\lambda - \lambda^x}{x!}\\\lambda = 0.3 per minute[/tex]
Let's substitute the values into the formula.
For 50 calls in 150 hours
For 150 hours = x = 0.3 * 150 = 45
[tex]p(x=50) = \frac{e^-^4^5 * 45^5^0}{50!} = 0.0431[/tex]
b)
The probability the next call arrives after 2 hours.
[tex]\lambda = 0.3 * 2 = 0.6\\p(x=0) = \frac{e^-^0^.^6 * 0.6^0}{0!} = 0.5488[/tex]
c)
The number of calls recieved each day is recorded for 50 consecutive days.
for 50 days;
[tex]\lambda = 0.3 * 50 * 24 = 360[/tex]
The mean = 360
The standard deviation is given as
[tex]S.D = \sigma =\sqrt{360} = 18.974\\[/tex]
The probability the sum of these 50 number is less than 356 is
[tex]p = (x < 356) = z = \frac{356 - 360}{18.974} = -0.2108\\p(z < -0.2108) = 0.4165[/tex]
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pleessss helpppp for brainlyyyyy
$37.51 - the third option above
Step-by-step explanation:
A
1600 x 1.053^3= 1868.12
B
1600x1.06^3 =1905.63
Difference
1905.63-1868.12= 37.51
$37.51
Hope this helps!
2 m
6 m
Volume = Base x height
Find the volume of this cylinder.
The electrician charges a $20 service fee, plus $60 per
hour for electrical repairs, shown by the equation below.
Solve the equation 60h + 20 = 140 and explain the
meaning of the solutions• (What does h represent?
What do the numbers in the equation represent, etc.)
Now let's change this equation into an inequality:
60h + 20 < 140
How does the change from an equation to an inequality
impact the meaning? Give one scenario that could
account for the less than sign.
Answer:
1a) h = 2
1b) "h" represents the amount of hours the electrician worked, so the electrician worked two hours. "60" represents the cost per hour. "20" represents the beginning service fee. "140" represents the total cost in the end.
2a) This impacts the meaning because instead of the equation, meaning that the customer of the electrician payed exactly $140, it is turned into an inequality, which means the customer payed $140 at most.
2b) The electrician charges a $20 service fee, plus $60 per hour for electrical repairs. The customer payed $140 at most. This is shown with the following equation: 60h + 20 < 140
Step-by-step explanation:
60h+20=140
60h=120
h=2
Kalvin's sister Kate finds yet another way for him to pick his
breakfast. She places one blue marble and one red marble in each
of two bags. She says that each morning he can choose one marble
from each bag. If the marbles are the same color, he eats Cocoa Blast.
If not, he eats Health Nut Flakes. Explain how selecting one marble
from each of the two bags and tossing two coins are similar.
Answer:
The probability of each is 50-50.
Step-by-step explanation:
With the marbles, there are four different outcomes: red-blue, blue-red, red-red, and blue-blue. Because one outcome is for same colors and the other is different colors, the probability of either is 2/4, or 1/2, or 50%. This is the same as tossing a coin. Hope this helps!
A plot of corn is 8 1/2 yards wide. It is 9 1/4 times as long as it is wide. How long is the plot of corn?
Answer:
[tex]78 \frac{5}{8} [/tex]
Step-by-step explanation:
[tex]for \: the \: width = 8 \tfrac{1}{2} \\ = \frac{17}{2} \\ sine \: the \: width \: is \: 9 \frac{1}{4} a \: long \\ 9 \ \frac{1}{4} = \frac{37}{4} \\ lenht \: of \: the \: plot = \ \frac{17}{2} \times \frac{37}{4} = \frac{629}{8} = 78 \ \frac{5}{8} \\ it \: will \: be78 \ \frac{5}{8}long [/tex]
Help ASAP!!! Will Mark Brainliest!!! Don't Know, Don't Answer!!!
Answer:
the question is blurry, please resend it
With the equation of the circle that has a center at the origin and passes through the point (1-6),
Answer:
[tex]\sf x^2+y^2=37[/tex]
Step-by-step explanation:
Equation of a circle: [tex]\sf(x-h)^2+(y-k)^2=r^2[/tex]
where (h, k) is the center and r is the radius
Given the center is at (0, 0)
[tex]\sf \implies (x-0)^2+(y-0)^2=r^2[/tex]
[tex]\sf \implies x^2+y^2=r^2[/tex]
Given the circle passes through point (1, -6):
[tex]\sf \implies (1)^2+(-6)^2=r^2[/tex]
[tex]\sf \implies r^2=37[/tex]
Therefore, the equation of the circle is:
[tex]\sf \implies x^2+y^2=37[/tex]
Equation of a circle passing through origin
x²+y²=r²So
As (1,-6) lies on circle it will satisfy
1²+(-6)²=r^21+36=r²r²=37Now
equation of the circle
x²+y²=37y is directly proportional to (x-4) when x=16, y=3 find y in terms of x
Answer:
y = ¼(x-4)
Step-by-step explanation:
Before solving the question, let's look at one example,
A is directly proportional to B means A∝B which also means A=kB where k is a constant.In this case, y is directly proportional to (x-4) means that y∝(x-4) which can also mean that y=k(x-4).
Hence, to find the value of k, substitute x=16, y=3 into y=k(x-4),
3=k(16-4)
k=3/12
k=1/4
After that, substitute the k value into the equation,
y = ¼(x-4)Find the volume of a cone that has a diameter of 14 feet and a height of 11 feet. Use 3.14 for pi
Answer:
564.15 cubic ft[tex] \: [/tex]
Step-by-step explanation:
In the question, it is given that a cone has a diameter of 14 feet and a height of 11 feet and we have to find the volume of the cone.
[tex] \: [/tex]
To Find the volume of the cone, we must know this formula :
[tex] \\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { Volume_{(cone) }= \dfrac{1}{3} \: \pi {r}^{2}h }}}}}}} \\ \\[/tex]
Where,
r refers to the radius of the cone. As the diameter is 14 ft, therefore the radius will 7 ft.h refers to the height of the cone.Now, we will substitute the values in the formula :
[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times {(7)}^{2} \times 11 }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times 49 \times 11 }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times 539 }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 1692.46 }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1692.46}{3} }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \: \: \underline{ \boxed{ \frak{564.15 } }} }}}}}}} \: \: \bigstar \\ \\[/tex]
Therefore,
The volume of the cone is 564.15 ft³ .Step-by-step explanation:
Given :-
Height of cone :- 11 feet Diameter of cone :- 14 feet , radius = 7 feetTo Find :-
Volume of coneSolution:-
Formula for volume of cone = 1/3πr²h
putting the known values ,Volume = 1/3×3.14×7²×11 cubic ft.
Volume = 564.15 cubic ft.
Please help me out I’m really bad
Find the area of the parallelogram below, after the
purple triangle-sized hole was removed.
Answer: 75
Step-by-step explanation:
Separate the parallelogram into two identical triangles (0.5 length by 10 height) and a rectangle (8 length by 10 height).
Work out the area of the rectangle - 8 * 10 = 80
Work out the area of the triangle - 0.5 * 10 = 5 (you don't need to halve it as you have two triangles)
Work out the area of the parallelogram - 80 + 5 = 85
Work out the area of the purple rectangle? (it says triangle in your description but I'm pretty sure that's not a triangle) - 5 * 2 = 10
Work out final area of the parallelogram - 85 - 10 = 75
I'm not sure if this is right but either way I hope you get your answer :)
Q. Find the volume
10
8
12
3
2
answer choices
A. 128
B. 180
C. 124
D. 182
Answer:
A.128
Step-by-step explanation:
First you break the prism apart so that you have one 7x4x2 rectangular prism and one 12x3x2 prism. Find the volume of both, then add them together.
Volume of 12x3x2:
12 x 3 = 36. 36 x 2 = 72.
Volume of 7x4x2:
7 x 4 = 28. 28 x 2=56.
Then add both volumes: 72 + 56 = 128.