[tex]\large\bold{{Question :-}}[/tex]The sum of the Squares of three consecutive number is 110. Then determine the Three Numbers.
[tex]\large\bold\red{\underline{Answer :-}}[/tex]
So, First of all The Question is to find out three consecutive Numbers .
First of all let's learn a little about Consecutive Numbers. So, Consecutive Numbers are the Numbers which follows each other. For example :- 1,2,3,4 are consecutive Numbers.
Let's start with Our Question :-
Let The First consecutive number be = xand second number be = x + 1Third number be = x + 2So,
[tex]:\pink\implies[/tex] [tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(x + 1)^{2}}}[/tex] + [tex]\bold{{(x + 2)^{2}}}[/tex] = [tex]\bold{{110}}[/tex]
[tex]:\pink\implies[/tex] [tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(1)^{2}}}[/tex]+ [tex]\bold{{2x}}[/tex] +[tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(4)}}[/tex]+ [tex]\bold{{(4x)}}[/tex] = [tex]\bold{{110}}[/tex]
[tex]:\pink\implies[/tex] [tex]\bold{{3x^{2}}}[/tex] + [tex]\large\bold{{6x}}[/tex] + [tex]\bold{{5}}[/tex] - [tex]\large\bold{{110}}[/tex] = [tex]\bold{{0}}[/tex]
[tex]:\pink\implies[/tex] [tex]\bold{{3x^{2}}}[/tex] + [tex]\bold{{6x}}[/tex] - [tex]\bold{{105}}[/tex] = [tex]\bold{{0}}[/tex]
By taking 3 Out as Common, we are left with the Quadratic Equation :—
[tex]:\pink\implies[/tex] [tex]\large\bold{{1x^{2}}}[/tex]+ [tex]\large\bold{{2x}}[/tex] - [tex]\large\bold{{35}}[/tex] = [tex]\large\bold{{0}}[/tex]
By Using Quadratic Formula,
x = -b ± √(b)^2— 4 × a × c / 2a
x = -2 ± √(2)^2— 4 × 1 × -35 / 2×1
x = -2 ± √144/2
[ As we know that "144" is square of 12 ]
x = -2 ± 12/2
Taking Positivex = -2+12/2x = 5Hence, x = +5
x +1 = 5+1 = +6
x+2 = 5+2 = +7
Taking Negative signx = -2-12/2x = -7Hence, x = -7
x+1 = -7+1 = -6
x+2 = -7+2 = -5
Hence, The Three consecutive Numbers are ±5,±6,±7.Answer:
± (5, 6, 7)Step-by-step explanation:
Let the three consecutive numbers be denoted as :
xx + 1x + 2Identity
(x + a)² = x² + 2ax + a²It is given that the sum of the squares of these numbers add up to 110.
(x)² + (x + 1)² + (x + 2)² = 110x² + x² + 2x + 1 + x² + 4x + 4 = 1103x² + 6x + 5 = 1103x² + 6x - 105 = 0x² + 2x - 35 = 0x² + 7x - 5x - 35 = 0x(x + 7) - 5(x + 7) = 0(x - 5)(x + 7) = 0x = 5 or x = -7Taking x = 5
x² = 5² = 25(x + 1)² = 6² = 36(x + 2)² = 7² = 49⇒ 25 + 36 + 49 = 110Taking x = -7
x² = (-7)² = 49(x + 1)² = (-6)² = 36(x + 1)² = (-5)² = 25⇒ 49 + 36 + 25 = 110Solution
5, 6, 7 ⇔ -7, -6, -5⇒ ± (5, 6, 7)There are 5 blue birds, 6 green ones and 3 black ones. If I randomly catch 2 birds, what is the probability the first bird is black and the second is green?
Answer:
So you must first get the total of all the birds, which is going be a fraction of course , that being 14/14 birds in total, since there are only 3 black birds the probability of me getting a black one 3/14 because there are fourteen in total, and the probability for the green birds is 6/14.
The combined probability that the first bird is black and the second is green is 0.0918
What is Probability?Probability is the likeliness of an event to happen.
Total Blue birds = 5
Total Green birds = 6
Total Black birds = 3
Total birds = 14
The probability of selecting two birds such that the first bird is black and the second is green.
Probability = ( No. of the desired outcome )/( Total outcomes)
The probability of selecting black bird is 3/14
The probability of selecting green bird is 6/14
Therefore, the combined probability that the first bird is black and the second is green is
= (3/14) * (6/14)
= 18/196
= 0.0918
To know more about Probability
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PLEASE HELP! TIMED!
Find the perimeter of a triangle with the measurements of 5cm, 9cm, and 11cm.
Identify the series of transformation that will move figure A to the new location of figure B.
Answer:
translate down 6 units and left 3 units
Please help me Im quite confused!!
Answer:
B
Step-by-step explanation:
As stated in the problem x is the number of hours that he works.
x = 6y
All of the other answers establish y as 6, but B is the only answer that has 6 Infront of y (Pretty much multiplying it)
If you were to plug 6 into Y you would get 6(6)
6 times 6 equals thirty six.
x ≠ 36
Joachim, a third student, noted that the confidence interval in part (a) gives plausible values of the parameter as an interval between two values. He suggested that they develop a one-sided confidence interval because they were only concerned with whether the number 6 was landing face up more often than expected, not less often. The one sided-interval will determine a value L such that all plausible values of p are greater than L.
Answer:
Kindly check explanation
Step-by-step explanation:
pˆ = 43 / 200 = 0.215
A.)
The confidence interval obtained :
0.215 ± 0.057 = (0.158 ; 0.272)
Since, 0.215 is within the confidence interval, we can conclude that, dice will lie face up on baked die more often than fair dice.
B.)
H0:p=16 versus Ha:p>16
Decision :
Reject H0 ; if Pvalue < α
Pvalue = 0.033 ; α = 0.05
0.033 < 0.05 ; we reject H0
HENCE, there is significant evidence to conclude that the proportion of face landing up on a baked dice is greater than 16. HENCE, it agrees with our conclusion in (1).
C.)
L=pˆ+z∗√pˆ(1−pˆ)n
Z critical for a one sided 95% confidence interval is 1.64
pˆ = 0.215
L = 0.215 + 1.64 * √(0.215*0.785) / 200
L = 0.215 + (1.64 * 0.1299134)
L = 0.215 + 0.213057976
L = 0.428
(-∞, 0.428)
Please Help Find the volume
Answer:
0.065 units ³
Step-by-step explanation:
Volume of sphere = 4/3 π r³
=> 4/3 × 22/7 × 1/4 × 1/4 × 1/4
=> 0.065 units³
Answer:
[tex]\frac{1}{48}[/tex] π units³
Step-by-step explanation:
the volume (V) of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex] πr³ ( r is the radius ) , then
V = [tex]\frac{4}{3}[/tex] π × ( [tex]\frac{1}{4}[/tex] )³
= [tex]\frac{4}{3}[/tex] π × [tex]\frac{1}{64}[/tex] ( cancel 4 and 64 on numerator/ denominator by 4 )
= [tex]\frac{1}{3}[/tex] π × [tex]\frac{1}{16}[/tex]
= [tex]\frac{1}{48}[/tex] π units³
Find the sum of all multiples of 7 from 7 to 126, inclusive.
David went to the store and bought a bag of
jellybeans for $1.73, an Easter basket for
$5.04, and a floppy bunny for $8.22. Assuming
there is no sales tax, how much change should
David receive if David gives the cashier a
twenty-dollar bill
Answer:
$5.01
Step-by-step explanation:
20 - (1.73 + 8.22 + 5.04)
20 - (9.95 + 5.04)
20 - 14.99
5.01
Therefore, my answer is right.
on the map, 2 cm equals 1 km. what is the actual length of a street that is 10 cm long on the map?
Answer: 5km
Step-by-step explanation: 2cm=1 km
10cm divided by 2 is 5km
the visual representation of data that is used to show how all the parts of something are related to the whole
Answer:pie charts?
Step-by-step explanation:
The change in the price for day 2 is of the change in the price for day 3. At the end of day 5,
the price of Meredith's stock is $32.05. What is the change, in dollars, in the price of the stock
for day 5?
Answer:
+ 0.26
Step-by-step explanation:
In a certain board game, a player who lands on the Double Spin
space earns two spins of the pointer shown. This player is
awarded a free turn if the pointer lands in the red section both
times. What is the probability that a player who lands on the
Double Spin space will win a free turn?
I
Red
Green
Blue
Make a table to describe the possible outcomes.
a
.
Red (R)
Green (G)
R, G
.
RR
Blue (B)
R, B
GB
BB
Red (R)
Green (G)
Blue (B)
There are 9 possible outcomes.
Each outcome is equally likely.
The one favorable outcome is
circled.
.
GR
G, G
B, G
BR
The probability that a player will win a free turn is P(R, R) = 5.
9.
where does a line and a plane intersect?
a. point
b. plane
c. line
Answer:
A. point
Step-by-step explanation:
An intersection of a line and a plane is at the point.
PLS HELP ME WITH THIS!!!
Answer:PLS HELP ME WITH THIS!!!
PLS HELP ME WITH THIS!!!
Step-by-step explanation:PLS HELP ME WITH THIS!!!
is your correct answer
Natalia is a girl in a math class with a total of 11 girls and 9 boys. If the teacher selects one student at random to go to the board, what is the probability that Natalia will be selected?
A box of pens contains a total of 28 pens. If 4 of the pens are red and the rest are blue, what is the probability that the first pen pulled from the box will be red?
Katelyn has a package of 24 jelly beans. There are 9 cherry jelly beans in the package. What is the probability that the first jelly bean Katelyn pulls out of the package will be a cherry jelly bean?
A marble is drawn at random from a bag containing 2 blue marbles, 3 yellow marbles, and 7 orange marbles. What is the probability that the marble is not yellow and not blue?
(Five Stars & Thanks to whoever answers first)
Answer:
First, let's find how many students there are in total:
11 girls + 9 boys
= 20 students.
Out of those 20 students, we are trying to find the probability if Natalia will be selected first.
There is only one Natalia.
So, out of those students, the probability of selecting Natalia is a:
1/20 probability
(if wanted to convert into a percentage):
1/20 x 100
= 5% probability
Since we already know there are 28 given pens in total and 4 of them are red pens, there is a:
4/28 chance of selecting a red pen which can be simplified to a 1/7 probability.
(if wanted to convert into a percentage):
1/7 x 100
= 14% probability
Since we already know there are 24 jelly beans in total and 9 of them are cherry beans, there is a:
9/24 chance/probability of selecting a cherry jelly bean.
(if wanted to convert into a percentage):
9/24 x 100
= 37.5% probability
Let's first figure out how many marbles there are in total.
2 + 3 + 7
= 12 marbles in total.
Now let's exclude the marbles that are blue and yellow, leaving us with 7 orange marbles.
So the probability of selecting a marble that isn't blue/yellow is a:
7/12 probability
(if wanted to convert into a percentage)
7/12 x 100
= 58% probability
The area formula for rectangular shapes is A=LW. What is the area of a rectangular shape with the dimensions of [tex]\sqrt[4]{11}[/tex] and [tex]\sqrt[4]{3}[/tex]?
Hi!
Given the area formula ~ A = LW
We need to multiply the two values:
[tex]\sqrt[4]{11} * \sqrt[4]{3}[/tex]
Since they have the same root, 4, we can multiply what's inside of the radical and give it the same root.
[tex]11*3=33[/tex]
Now, we apply the same root as before:
[tex]\sqrt[4]{33}[/tex]
Therefore, your answer is [tex]\sqrt[4]{33}[/tex]
Now, if you need that as a numerical value rather than a radical, it's roughly [tex]2.397[/tex]
Answer:
[tex]\textsf{area}=\sqrt[4]{33}\:\textsf{square units}[/tex]
Step-by-step explanation:
Formula
Area of a rectangle = length × width
Given:
[tex]\textsf{length}=\sqrt[4]{11}[/tex][tex]\textsf{width}=\sqrt[4]{3}[/tex]Substitute given values into the formula:
[tex]\implies \textsf{area}=\sqrt[4]{11} \cdot \sqrt[4]{3}[/tex]
[tex]\textsf{Apply radical rule}\quad\sqrt[n]{a} \cdot \sqrt[n]{b}=\sqrt[n]{ab}:[/tex]
[tex]\implies \textsf{area}=\sqrt[4]{11 \cdot 3} =\sqrt[4]{33}\:\textsf{square units}[/tex]
How much was made if 900 raffle tickets were sold at 5 for $20?
Answer:
$3600
Step-by-step explanation:
900/5=180
180*20=3600
Answer:
$3600
Step-by-step explanation:
Since they are being sold 5 at a time, divide 900 by 5 first to get 180. Then, since every 5 are worth 20$, multiply 20 by 180 to get $3600.
50 points each question. Please help. How do I solve?
[tex]~~~~~~\tan^{-1}(xy) = \sin^{-1}(4x+4y)\\\\\\\implies \dfrac d{dx} \left[ \tan^{-1}(xy)\right] = \dfrac d{dx} \sin^{-1}\left( 4x+4y\right)\\ \\\\\implies \dfrac{1}{1+(xy)^2} \left[ \dfrac{d}{dx} (xy)\right] = \dfrac{1}{\sqrt{1-(4x+4y)^2}} \cdot \dfrac{d}{dx}(4x+4y)\\\\\\\implies \dfrac{1}{1+x^2 y^2} \left(x\dfrac{dy}{dx}+y \right)=\dfrac{1}{\sqrt{1-(4x+4y)^2}} \left(4+ 4 \dfrac{dy}{dx} \right)\\\\\\\\[/tex]
[tex]\implies \left(\dfrac{x}{1+x^2y^2} \right) \dfrac{dy}{dx} + \dfrac{y}{1+x^2y^2}=\dfrac{1}{\sqrt{1-(4x+4y)^2}} \left(4+ 4 \dfrac{dy}{dx} \right)\\[/tex]
[tex]\\\\\implies 0 \cdot \dfrac{dy}{dx} +0 = \dfrac{1}{\sqrt{1 -0}} \left(4+4 \dfrac{dy}{dx} \right) ~~~~~~~~~;\left[ \text{at}~~ (0,0) \right]\\\\\\\implies 4+4 \dfrac{dy}{dx} = 0\\\\\\\implies \dfrac{dy}{dx} = -\dfrac 44\\\\\\\implies \dfrac{dy}{dx} = -1\\\\\text{So, the slope of the tangent line at (0,0) is}~ -1\\ \\\\\text{The equation of tangent line,}\\\\~~~~~~y-0 = -1(x-0)\\\\\implies y=-x[/tex]
Assume the annual day care cost per child is normally distributed with a mean of $9000 and a standard deviation of $1000. What percent of day care costs are more than $8600 annually?
Answer:
65.54% (nearest hundredth)
Step-by-step explanation:
Given:
[tex]\sf \mu=9000[/tex][tex]\sf \sigma=1000[/tex][tex]\sf X \sim N(\mu, \sigma^2)\implies X \sim N(9000,1000^2)[/tex]
P(X > 8600) = 1 - P(X ≤ 8600)
= 1 - 0.3445782584
= 0.6554217416
= 65.54%
Find the area of the shape.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
Answer:
Therefore, area is 50.24
Step-by-step explanation:
⇒ Area = [tex] \sf \pi {r}^2 [/tex]
Radius = 4
⇒Area = 3.14 × 4²
⇒Area = 50.24
The answer:= 12π
I got this on khan academy.
Sixth-grade students were asked, "What grade are you in?" Explain why this is not a statistical question.
A police officer recorded the speeds of the first six cars whose drivers he ticketed for speeding today.
Car Speed
(miles per hour)
1 67
2 74
3 85
4 80
5 74
6 82
What is the mean of the cars' speeds?
Answer:
The mean is 77.
Step-by-step explanation:
Step one: add all the numbers
Step two: Divide the sum by the number of values you added
(example: 1,5,8,12,13. You would add them together, since we have 5 numbers, we will divide the sum by 5, then we have the mean)
462 divided by 6 is 77
Hope this helps!
Evaluate the expression. – 5×(6+ – 5 1/ 2 )– – 1 4 /5. Write your answer as a fraction or as a whole or mixed number.
CAN SOMEBODY SOLVE THE EQUATION
Answer:
Step-by-step explanation:
Given
y = x^2 + 10x + 21
Complete the square
y = x^2 + 10x + 21 Put brackets around the first 2 terms
y = (x^2 + 10x) + 21 Take 1/2(10) and square it. Add inside the brackets.
y = (x^2 + 10x + 5^2) + 21 Subtract 5^2 after 21
y = (x^2 + 10x + 25) + 21 - 25 Make (x^2 + 10x + 25) into a perfect square.
y = (x + 5)^2 - 4
Answer: (x + 5)^2 - 4
Find the value of x if
Answer:
X=-1 or x=1/3
Step-by-step explanation:
That is the explanation in the photo
What is Limit of j (x) as x approaches 3?
Answer:
lim x - 3 + f ( x ) - As 3 approaches 3 from the right, the value of f ( x ) approaches 0. lim x - 3 f ( x ) - Since the value of f ( x ) as x approaches 3 from the left does not equal the value as x approaches 3 from the right, this limit does not exist.
Clamentine and jake make cookies for the school bake sale. Clamentine baked 72 cookies. Jake baked twice as many as clementine. How many cookies did they bake altogether?
Answer:
Jake has 144 cookies.
Step-by-step explanation:
Let's say Clementine is x.
Clementine: x
Jake: 2x
Now, let's substitute x with 72 since the number is given.
This means that Jake has 72 * 2 cookies which are 144.
i need help pleaseeeeeeeeeeeeeeeeeeeeee
Answer:
[tex]83[/tex]
Step-by-step explanation:
[tex]5 - (18 \div 6) + (2 + 7)^{2} [/tex]
Divide the numbers ⬇
18 ÷ 3= 3[tex]5 - 3 + (2 + 7)^{2} [/tex]
Add the numbers ⬇
2 + 7= 9[tex]5 - 3 + 9 ^{2} [/tex]
Evaluate the power ⬇
9² = 81[tex]5 - 3 + 81[/tex]
Calculate the sum or difference ⬇
[tex]5 - 3 + 81 = 83[/tex]
Hope this helps!! :)
Dee Wallace's salary was $61,000 in 2006 and increased to $64,300 in 2009.
What was the annual rate of change in his salary?
Answer:
$1,100
Step-by-step Explanation:
Dee Wallace's salary in 2006 = $61,000 Dee Wallace's salary in 2009 = $64,300
The salary increased in => 2009 - 2006 = 3yrs
The amount of salary increased = 64,300-61000 = $3,300
The annual change of salary = 3,300/3 = $1,100
a bottle of ketchup as a net weight of 22 ounces. a serving size is 1/2 ounce. how many servings are in the bottle?
Answer:
44 servings are in the bottle
Answer:
44
Step-by-step explanation:
One trick for dividing fractions is:
1. Keep the first fraction. 22/1 divided by 1/2
2. Change division into multiplication. 22/1 times 1/2
3. Flip the second fraction. 22/1 times 2/1
22*2 is 44
1*1 is 1
The final answer should be 44/1