Answer:
2 and 420
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₃ = 6 and a₁₆ = 32 , then
a₁ + 2d = 6 → (1)
a₁ + 15d = 32 → (2)
Subtract (1) from (2) term by term
13d = 26 ( divide both sides by 13 )
d = 2
Substitute d = 2 into (1) for corresponding value of a₁
a₁ + 2(2) = 6
a₁ + 4 = 6 ( subtract 4 from both sides )
a₁ = 2
The sum of n terms of an AP is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ] , thus
[tex]S_{20}[/tex] = [tex]\frac{20}{2}[/tex] [(2 × 2) + (19 × 2) ]
= 10(4 + 38) = 10 × 42 = 420
A cone with radius 2 units is shown below. Its volume is 29 cubic units.
h
Find the height of the cone.
Use 3.14 form and round your ina answer to the nearest hundredth.
Answer:
[tex]h=6.93units[/tex]
Step-by-step explanation:
1. Use the formula of volume of a cone
Volume of a cone=[tex]\frac{1}{3}\pi r^{2} h[/tex]
2. Collecting the information from a question.
In the question, we know that radius=2 units, Volume of a cone=29 cubic units, height of a cone=?
In this question, we can also know that the question requires us to find the height of a cone.
3. Put the value of variables into the formula.
We can put all the information that are provided by a question into the formula of volume of a cone to find the answer.
[tex]\frac{1}{3} *3.14 * 2^{2} h=29 units^{3}[/tex]
pi replaces with 3.14, radius replaces with 2 units, Volume of a cone replaces with 29 units3 and we don't know what is the value of h.
Now, let's simplify and calculate the value of h.
We can simplify the formula like this,
[tex]\frac{314}{75}h =29 units^{3}[/tex]
[tex]\frac{314}{75}[/tex] is the result of [tex]\frac{1}{3}* 3.14*2^{2}[/tex]
Move [tex]\frac{314}{75}[/tex] to other side.
[tex]h=\frac{29units^{3} }{\frac{314}{75} }[/tex]
[tex]h= 6.92675 units[/tex]
But wait, this is not final answer yet, the question requires the answer to the nearest hundredth. So, we need to convert the answer to the nearest hundredth.
[tex]h= 6.92675 units[/tex]
[tex]h=6.93units[/tex]
So, the final answer is 6.93 units.
I hope my solution and explanation are clear for you. If you still cannot understand my point, you can ask me anytime!! Thank you!
Graph the relation shown in the table. Is the relation a function? Why or why not? {(-1, 9), (0, -1), (-1, 4), (4, 9)}
Answer:
Not a function
Step-by-step explanation:
For an equation to be a function, there should be only one y-coordinate per x-coordinate. Since this relation has both (-1,9) and (-1,4), this is not a function.
Answer:not a function
Step-by-step explanation:
because when you put the points on the coordinate plane your shape will come out as a v shaped object. In mathematics, a function is a binary relation over two sets that associates to every element of the first set exactly one element of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers
Can someone help me with this question please.
Answer:
Cheapest price is £25.38
Step-by-step explanation:
To determine the cheapest price that Sue can get the 10 rolls of wallpaper, calculate the cost of getting 10 rolls at each given price offer
=>Cost of getting 10 rolls at £9.21 per roll:
10 × £9.21 = £92.1
=>Cost of getting 10 rolls at £25.38 per pack of 3 rolls
£25.38 = 3 rolls
x = 10 rolls
x = (25.38*10)/3 = 253.8/3
10 rolls would cost x = £84.6
=>Cost of getting 10 rolls at £42.85 per pack of 5 rolls:
£42.85 = 5 rolls
x = 10 rolls
x = (10*42.85)/5 = 428.5/5
x = £85.7
From our calculation, getting 10 rolls at the price offer of £25.38 per pack of 3 rolls is the cheapest.
Therefore, the cheapest price is £25.38
The following table shows the cost for 4 fruits. For example, apples cost $6 for 5 pounds. -------------------------------------------- Fruit: Cost: pounds: Apples: $6 6 Bananas: $4 5 Peaches: $5 4 Kiwis: $9 6 -------------------------------------------- Which Type of fruit has a cost of $1.25 per pound? A. Apples B. Bananas C. Peaches D. Kiwis
Answer:
C. Peaches
Step-by-step explanation:
To find the cost of each fruit per pound, divide the cost of the fruit by how many pounds of it there are.
Apples: $6 ÷ 6 = $1
Bananas: $4 ÷ 5 = $0.80
Peaches: $5 ÷ 4 = $1.25
Kiwis: $9 ÷ 6 = $1.50
The type of fruit that has a cost of $1.25 per pound is peaches.
Hope that helps.
A librarian has 4 times as many mysteries than romances. She lends out 12 mystery books. How many mystery books she have now if she started with 15 romances?
Answer:
48
Step-by-step explanation:
Can someone PLEASE explain in simple terms which trigonometric ratio to use, like tangent, cosine, or sine, and WHY?
Answer:
Use law of Cosines or Tangent
Step-by-step explanation:
This is a SAS triangle, where you have have an angle adjacent to two side lengths. But given that it is a right triangle, you can find the hypotenuse by just using the tangent formula. You can find the quantity of any angle by applying tan= opposite side/adjacent side length.
However, lets say you want to find the opposite side, side XZ, you can use the law of cosine which basically states:
c=a^2+b^2﹣2abcos(angle number). But since it is a right triangle, just use the hypotenuse theorem which states: C^2 = A^2 + B^2
The answer for XZ would thus be: squareroot of 136 or 2(34)^1/2.
Hope this helps :)
Please Help !! I don’t know what to do :(
Answer:
(5+a)/ ( a-1)
Step-by-step explanation:
f(x) = ( 3+x) / (x-3)
Replace x with a+2
f(a+2) = ( 3+a+2) / (a+2-3)
Combine like terms
= (5+a)/ ( a-1)
Answer:
C. (5+a)/(a-1)
Step-by-step explanation:
f(a+2)=(3+a+2)/(a+2-3)=(5+a)/(a-1)
Answer two questions about Equations A and B: A. 2x−1+3x =0 B. 5x-1=0 1)How can we get Equation B from Equation A?
A company manufactures a 14-ounce box of cereal. Boxes are randomly weighed to ensure the correct amount. If the discrepancy in weight is more than 0.25 ounces, the production is stopped.
Which function could represent this situation? Ede
Answer:
Answer is B on Edge
F(x)=14-x
Step-by-step explanation:
Answer:
B) f(x) = |14 – x|
Step-by-step explanation:
Edge
A cell phone bill provider offers a plan that costs $20 per month plus $0.10 per text message sent or received. A comparable plan costs $30 per month but offers unlimited text messaging. How many texts would have to be sent or received in order for the plans to cost the same each month
Answer:
100 texts
Step-by-step explanation:
20+.1x=30
30-20=10
10 dollar difference in base prices.
10/.1 (to find out how many texts)
100 texts
Evaluate: 5^-2 =
????
Answer:
1/25Step-by-step explanation:
5^-2=1/(5^2)=1/25
At a certain time of day, a 40-foot building casts a 8 foot shadow. How tall is a person who casts a 2 foot shadow? A. 4 feet B. 6 feet C. 8 feet D. 10 feet
Answer:
D. 10 feet
Step-by-step explanation:
40/8 = x/2 --> cross multiply
8x = 80
x = 10
Option D is correct, the person who casts a 2 feet shadow is 10 foot tall.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that At a certain time of day, a 40-foot building casts a 8 foot shadow.
We need to find how tall is a person who casts a 2 foot shadow.
Let x be the height of the person.
Let us form a proportional equation
40/8=x/2
Apply cross multiplication
80=8x
Divide both sides by 8
x=10
Hence, the person who casts a 2 foot shadow is 10 foot tall.
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will give BRAINLY, EASY question, please help ASAP! Please explain your answer! Calculate the area of the block "V" shown below. *Drawing not to scale
Answer:
Answer is 117.86 mm^2
Answer is given below with explanations.
Step-by-step explanation:
[tex]in \: the \: figur \: there \: are \: two \: parllelograms \\ intersecting \: a \: triangle \\ area \: of \: 1 \: parallelogram \: = \: bh \: \\ here \: base\: (b) = 20 \:mm \: \: an d \: height \: (h) = 4 \: mm \\ area \: of \: 1 \: parallelogram \: = 20 \times 4 \\ \: \: = 80 \: {mm}^{2} \\ area \: of \: 2 \: parallelogram \: = bh \\ here \: base \: (b) = 32 \: mm \\ height \: (h) = 2 \: mm \\ area \: of \: 2 \: parallelogram \: = 32 \times 2 \\ \: \: = 64 {mm}^{2} \\ in \: the \: v \: shaped \: figure \: there \: s \: a \: triangle \\ area \: of \: triangle \: is \: calculated \: using \: \\ heron \: s \: formula \\ area \: of \: triangle \: = 26.14 \\ area \: of \: v \: block \\ = area \: of \: 1 \: parallelogram \: + area \: of \: 2 \: parallelogram \: - area \: of \: triangle \\ = 80 + 64 - 26.14 \\ \: \: = 117.86 \: {mm}^{2} [/tex]
HAVE A NICE DAY!
if we subtract 22 from three times of number we get 68 find the number
Answer:
90,30
Step-by-step explanation:
let the three times be 3x then,
3x-22=68
3x=68+22
3x=90
x=90/3
x=30
again,
3x=3*30=90
please support me and give me brainliest
Work out the mean for the data set below:
4004, 4009
Answer:
4006.5
Step-by-step explanation:
4004 + 4009 = 8013
8013 ÷ 2 = 4006.5
Answer:
Hey!
Your answer is 4,006.5
Step-by-step explanation:
We get the MEAN by ADDING ALL THE VALUES UP and DIVIDING IT BY THE TOTAL AMOUNT OF SEPERATE NUMBERS!
So...
4,004 + 4,009 = 8,013
WE DIVIDE 8,013 BY 2...
8,013 / 2 = 4006.5!
Hope this helps!
PLEASE ANSWER I WILL GIVE BRAINLIEST AND THANKS DESCRIBE FULLY THE SINGLE TRANSFORMATION THAT MAPS A ONTO C
Answer:
Triangle A has been rotated 180˚ using the point (0,0)
HELPPPPPPPPPPPP SNOG OR SOMEONE
Answer:
4
Step-by-step explanation:
We see that a point is (1, 4) so the answer is 4/1 = 4.
Hey there! :)
Answer:
Second choice: 4.
Step-by-step explanation:
The constant of proportionality is also the slope, or rate of change. The slope formula can be used to solve this problem:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in points from the graph into the equation.
[tex]m = \frac{4 - 0}{1 - 0}[/tex]
m = 4.
Therefore, the constant of proportionality is 4.
can someone answer this so i can check if im right?
Answer:
Step-by-step explanation:
There are 3 possible triangles to find there within what appears to be one triangle. And since they are all part of the same largest triangle, they are also all similar. Just because 2 shapes may be triangles, so NOT mean they are automatically similar. Remember that!
The largest triangle is ΔABC
The triangle on the "left" is ΔADB, and
The triangle on the "right" is ΔCDB
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party 30 14 12 25
I think 12.
Hope this helps!
Please help with this question
If the bathtub holds a total of 46.2 gallons, how many minutes would it take to fill
the entire tub?
Answer:
takes 3 minutes, at 17 gallons per minute, for the tap to fill the tub, so 51 gallons of water flow into the tub.
The capacity of the tub is 46.5 gallons; so in 3 minutes 51-46.5 = 4.5 gallons have leaked. That's a rate of 4.5/3 = 1.5 gallons per minute.
The amount of time it will take the tub to drain at that rate is 46.5/1.5 = 31 minutes.
Answer:
46.5/1.5 = 31
Step-by-step explanation:
Please help for ten points
Answer:
choice 2
Step-by-step explanation:
the best choice for the baby pool is choice 2 because they need a pool that hold less than 15 cubic feet water and choice 2 when i calculate the volume of the given number : 4ft*3ft*1=12 cubic feet which is less than 15 cubic feet.
the other choices show that the volume of choice 1 : 5ft*5ft*1=25 cubic feet which is greater than what they ask for.
choice 3 : 4ft*4ft*2ft=16 cubic feet greater than 15 cubic feet
im not too sure about this one could i get some help with it?
Answer:
98
Step-by-step explanation:
the measure of angles of a triangle=180
the measure of straight angle=180 find angle HAC:
180-128=52
angle A: 180-52-46= 82
now find IAC : 180-82=98 degrees
Does this table represent a function? Why or why not?
Pick A,B,C or D
The situation that is best modeled by a discrete graph is
Answer:
Hope It helps you :) Cause the graph haves to show two unsame activities
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Given △ABC, AD = 5, BC = 20, AC = 11 BD is an altitude Find: AB
Answer:
13
Step-by-step explanation:
To find AB, we need to find BD.
Do this by using Pythagorean’s theorem
Square root of 20 squared minus 16 squared =Square root of 400-256 = Square root of 144 = 12cm
Use Pythagorus Theorem to find the measure of AB
AB = √DA^2 + BD^2
AB = √25 + 144
AB = √169 = 13
Hope this helps
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5
points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown
represents this situation
x + y = 24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
O The test contains 4 three-point questions and 20 five-point questions.
O The test contains 10 three-point questions and 14 five-point questions
O The test contains 14 three-point questions and 10 five-point questions,
O The test contains 20 three-point questions and 8 five-point questions
3x + 3y = 72
2y = 28
y = 14
x = 24 - 14 = 10
The test contains 10 three-point questions and 14 five-point questions
please mark me brainliest!
Check all of the infinite geometric series that converge.
135 – 405 + 1,215 – 3,645 + . . .
Answer is B &C
Answer:b and c
Step-by-step explanation:
A basketball player is shooting a basketball toward the net. The height, in feet, of the ball t seconds after the shot is modeled by the equation h = 6 + 30t – 16t2. Two-tenths of a second after the shot is launched, an opposing player leaps up to block the shot. The height of the shot blocker's outstretched hands t seconds after he leaps is modeled by the equation h = 9 + 25t – 16t2. If the ball was on a path to reach the net 1.7 seconds after the shooter launches it, does the leaping player block the shot?
THIS IS THE COMPLETE QUESTION
basketball player is shooting a basketball toward the net. The height, in feet, of the ball t seconds after the shot is modeled by the equation h = 6 + 30t – 16t2. Two-tenths of a second after the shot is launched, an opposing player leaps up to block the shot. The height of the shot blocker’s outstretched hands t seconds after he leaps is modeled by the equation h = 9 + 25t – 16t2. If the ball reaches the net 1.7 seconds after the shooter launches it, does the leaping player block the shot?
Yes, exactly 0.6 seconds after the shot is launched.
Yes, between 0.64 seconds and 0.65 seconds after the shot is launched
Yes, between 0.84 seconds and 0.85 seconds after the shot is launched.
No, the shot is not blocked.
Answer:
Yes, between 0.84 seconds and 0.85 seconds after the shot is launched.
Given that the
equation for shot block height h = 9 + 25t – 16t2.
equation for ball height h = 6 + 30t – 16t2.
From the question ,it can be deducted that the shot is made before two tenths of a second or 0.2seconds
CHECK THE ATTACHMENT TO COMPLETE THE DETAILED SOLUTION
We can say that the leaping player do not block the shot and thus, the answer is it is No, the shot is not blocked.
What is a shot?In terms of basketball, a shot is known to be the act of throwing a given basketball to a hoop.
Note that in the scenario above, since the ball has reaches the net at about 1.7 seconds after the shooter launches it, We can say that the leaping player do not block the shot and thus, the answer is it is No, the shot is not blocked as it will be hard for the player to do.
See full question below:
basketball player is shooting a basketball toward the net. The height, in feet, of the ball t seconds after the shot is modeled by the equation h = 6 + 30t – 16t2. Two-tenths of a second after the shot is launched, an opposing player leaps up to block the shot. The height of the shot blocker’s outstretched hands t seconds after he leaps is modeled by the equation h = 9 + 25t – 16t2. If the ball reaches the net 1.7 seconds after the shooter launches it, does the leaping player block the shot?
Yes, exactly 0.6 seconds after the shot is launched.
Yes, between 0.64 seconds and 0.65 seconds after the shot is launched
Yes, between 0.84 seconds and 0.85 seconds after the shot is launched.
No, the shot is not blocked.
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Which best explains how you know that P(2, 7) is on the same line as Q(7, 4) and R(12, 1)?
Answer:
See explanation below
Step-by-step explanation:
The best explanation is noticing that in order to get from the point R (12, 1) to the point Q (7, 4) we move 5 units to the left and 3 units up. And to go from point Q (7, 4) to point P (2, 7) we do exactly the same: move 5 units to the left and 3 units up. That means that these points are all connected via the same rate of change: - 3/5, which is in fact the slope of the line the three points belong to.
Answer:
Step-by-step explanation: