Answer:
S= -3
Step-by-step explanation:
3s-12=-21
3s= -21+12
3s= -9
s= -9/3
s= -3
Answer:
s = -3
Step-by-step explanation:
[tex]3s - 12 = - 21[/tex]
Collect like terms
[tex]3s = - 21 + 12[/tex]
Add the numbers :
[tex] - 21 + 12 = - 9 \\ \\ 3s = - 9[/tex]
Divide both sides of the equation by 3
[tex] \frac{3s}{3} = \frac{ - 9}{3} [/tex]
Simplify
[tex]s = - 3[/tex]
Evaluate the expression and enter your answer in the box below.
-7 • (5+ 3) +216 ➗ 4
Answer:
= -2
-7(5+3)+216/4
-7(8)+216/4
-56+54
= -2
Which led to the formation of oceans after water on Earth’s surface evaporated?
Answer:
The sun released a strong burst of water vapor. As Earth cooled, water in the atmosphere condensed. Materials collided due to strong gravitational forces. The ozone layer formed to protect against harmful UV ray exposure
Step-by-step explanation:
Answer:
As Earth cooled, water in the atmosphere condensed
Step-by-step explanation:
dues to high temps, water evaporated.
as the earth's surface cooled, water condensed and formed oceans
rocks hardened to form continents
Introduction to Interval Notation
What is the domain and range?
2.
The domain of this function is 3≤x≤5 in interval notation that is [3,5]
The range is -3≤y≤3. In interval notation that is [-3,3]
4.
The domain of this function is -5≤x≤-1 in interval notation that is [-5,-1]
The range is 1≤y≤5. In interval notation that is [1,5]
:)
Solve for all possible values of x.
Vx+7-11=2
Ox= 6
O x = 20
Ox= 162
Ox = 169
How do you do this problem?
Answer:
Your answer is absolutely correct
Step-by-step explanation:
The work would be as follows:
[tex]\int _0^{\sqrt{\pi }}4x^3\cos \left(x^2\right)dx,\\\\\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx\\=> 4\cdot \int _0^{\sqrt{\pi }}x^3\cos \left(x^2\right)dx\\\\\mathrm{Apply\:u-substitution:}\:u=x^2\\=> 4\cdot \int _0^{\pi }\frac{u\cos \left(u\right)}{2}du\\\\\mathrm{Apply\:Integration\:By\:Parts:}\:u=u,\:v'=\cos \left(u\right)\\=> 4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\int \sin \left(u\right)du\right]^{\pi }_0\\\\[/tex]
[tex]\int \sin \left(u\right)du=-\cos \left(u\right)\\=> 4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\left(-\cos \left(u\right)\right)\right]^{\pi }_0\\\\\mathrm{Simplify\:}4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\left(-\cos \left(u\right)\right)\right]^{\pi }_0:\quad 2\left[u\sin \left(u\right)+\cos \left(u\right)\right]^{\pi }_0\\\\\mathrm{Compute\:the\:boundaries}:\quad \left[u\sin \left(u\right)+\cos \left(u\right)\right]^{\pi }_0=-2\\=> 2(-2) = - 4[/tex]
Hence proved that your solution is accurate.
Answer:
[tex]\int\limits^{\sqrt{\pi}}_0 {4x^3\cos(x^2)} \, dx=-4[/tex]
Step-by-step explanation:
So we have the integral:
[tex]\int\limits^{\sqrt{\pi}}_0 {4x^3\cos(x^2)} \, dx[/tex]
As told, let's use u-substitution first and then use integration by parts.
For the u-substitution, we can let u to be equal to x². So:
[tex]u=x^2[/tex]
Differentiate:
[tex]du=2x\, dx[/tex]
We can rewrite our integral as:
[tex]\int\limits^{\sqrt{\pi}}_0 {2x(2x^2)\cos(x^2)} \, dx[/tex]
Therefore, by making our u-substitution, our integral is now:
[tex]\int\limits {2u\cos(u)} \, du[/tex]
We also need to change our bounds. Substitute them into u. So:
[tex]u=\sqrt{\pi}^2=\pi\\u=(0)^2=0[/tex]
Therefore, our integral with our new bounds is:
[tex]\int\limits^{\pi}_{0} {2u\cos(u)} \, du[/tex]
Now, let's use integration by parts. Integration by parts is given by:
[tex]\int\limits {v}\, dy=vy-\int y\, dv[/tex]
(I changed the standard u to y because we are already using u).
Let's let v be 2u and let's let dy be cos(u). Thus:
[tex]v=2u\\dv=2\,du[/tex]
And:
[tex]dy=\cos(u)\\y=\sin(u)[/tex]
So, do integration by parts:
[tex]=2u\sin(u)-\int \sin(u)2\,du[/tex]
Simplify:
[tex]=2u\sin(u)-2\int \sin(u)\,du[/tex]
Evaluate the integral:
[tex]=2u\sin(u)+2\cos(u)[/tex]
Now, use the bounds. So:
[tex](2(\pi)\sin(\pi)+2\cos(\pi))-(2(0)\sin(0)+2\cos(0))[/tex]
Evaluate:
[tex]=(2\pi(0)+2(-1))-(0(0)+2(1))[/tex]
Simplify:
[tex]=(-2)-(2)[/tex]
Subtract:
[tex]=-4[/tex]
And we're done!
A village fete has a children’s running race each year, run in heats of up to ten children. For each heat the first three contestants past the finishing line qualify for the final. There are three prizes in the final for 1st, 2nd and 3rd places. One year 29 children enter the race so there are three heats, of ten, ten and nine children. One year 29 children enter the race so there are three heats, of ten, ten and nine children. 1) What is the probability that three randomly chosen competitors win prizes? 2) What is the probability that two randomly chosen competitors win prizes? 3) How many ways are there to select ten competitors for the first heat? 4) Once the competitors have been selected for the first heat, how many different groups of three qualifiers are possible from this heat
Answer: 1) 1/3,654 2) 3/406 3) 72,684,900,288,000 4) 120
Step-by-step explanation:
1) First and Second and Third
[tex]\dfrac{3\ total\ prizes}{29\ total\ people}\times \dfrac{2\ remaining\ prizes}{28\ remaining\ people}\times \dfrac{1\ remaining\ prize}{27\ remaining\ people}=\dfrac{6}{21,924}\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad =\large\boxed{\dfrac{1}{3,654}}[/tex]
2) First and Second
[tex]\dfrac{3\ total\ prizes}{29\ total\ people}\times \dfrac{2\ remaining\ prizes}{28\ remaining\ people}=\dfrac{6}{812}=\large\boxed{\dfrac{13}{406}}[/tex]
[tex]3)\quad \dfrac{29!}{(29-10)!}=\large\boxed{72,684,900,288,000}[/tex]
[tex]4)\quad _{10}C_3=\dfrac{10!}{3!(10-3)!}=\large\boxed{120}[/tex]
State the domain and range in set notation
Answer:
Image result for State the domain and range in set notation
The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range. Domain: all x-values that are to be used (independent values).
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
The last option is not complete, but since the first three options are incorrect, the last option is correct
when examining distributions of numerical data, what three components should you look for
Answer:
The three components you should look for when examining distributions of numerical data are Shape, center, and spread
-Source(I took AP statistics in senior year of high school and passed the AP test)
The three components for examining distributions of numerical data are Shape, centre, and spread.
What is distribution of data?
A normal distribution is a common probability distribution. It has a shape often referred to as a "bell curve." Many everyday data sets typically follow a normal distribution: for example, the heights of adult humans, the scores on a test given to a large class, errors in measurements.
When examining the distribution of a quantitative variable, one should describe the overall pattern of the data (shape, centre, spread), and any deviations from the pattern (outliers). When describing the shape of a distribution, one should consider: Symmetry/skewness of the distribution Peakedness (modality) - the number of peaks (modes) the distribution has. Not all distributions have a simple, recognizable shape. Outliers are data points that fall outside the overall pattern of the distribution. It is always important to interpret the features of the distribution (as they appear in the histogram) mean in the context of the data.
Hence, The three components for examining distributions of numerical data are Shape, centre, and spread.
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x = - 4y + 37x + 3y = 29 pls help i need this grade!!!!!!!!
a right rectangular prism has these dimensions:
Length: 1 1/3
width: 5/6
height: 2/3
Solve for the missing angle?
A) 32*
B)44*
C)61*
D)50*
Answer:
using question mark as reference angle
Base = 13
hypotenuse = 18
usimg trigonometric ratios
cos? = B/h
? = inverse(13/18) = 43.74 = 44°
Step-by-step explanation:
Here, we are given with two sides and the triangle is a right angled triangle. Here, we can use trigonometry to find the missing angle.
Note: Always remember that the perpendicular, base and hypotenuse changes with the reference angle.According to missing angle, cos theta can be used because we are given with base and hypotenuse. No need to find the perpendicular.
[tex] \cos( \theta) = \frac{base}{hypotenuse} \\ [/tex]
[tex] \cos( \theta) = \frac{13}{18} [/tex]
Now for finding the missing angle theta, inverse of cosine will be applied on the other side. Because, inverse of multiplication is division.
[tex] \theta = \cos {}^{ - 1} ( \frac{13}{18} ) [/tex]
[tex] \theta = \cos {}^{ - 1} (0.7222222222) [/tex]
[tex] \boxed{ \theta \approx \: 43.76174269 \degree}[/tex]
━━━━━━━━━━━━━━━━━━━━
Which set of ordered pairs represents a function?
o {(5,-2), (-5,2), (-5, -4),(4, -5)}
{(9,6),(-1,7), (9,–7), (4,7)}
o {(-1,0),(-8, 9), (7,0), (1,3)}
{(8,6), (8, –4), (-7, -2),(-1, —8)}
Answer:
{(-1,0),(-8, 9), (7,0), (1,3)}
Step-by-step explanation:
number 3 is the only one with no colliding outputs.
If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability that all 4 cards are picture cards .
Answer:
If we defelt 4 cards from 52 cards
Step-by-step explanation:
P(b) favorable outcome /total number of outcomes
48/52
The probability that all 4 cards are picture cards is 0.00183
How many kinds are in a deck of 52?A standard 52-card deck comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠). Each suit includes three court cards (face cards), King, Queen and Jack, with reversible (double-headed) images.
as, we know
A face card is any of the twelve cards in a deck which has a picture of a face. The face cards are kings, queens, and jacks.
So, the possibilities to get a picture card is are 3*4=12.
Now, he probability that all 4 cards are picture cards
=(12/52) * (11/51) * (10/50) * (9/49)
=( 11880 / 6497400 )
= ( 0.0018284237 )
= 0.00183
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which answer is right?
Answer: D
Step-by-step explanation:
Since we know that the area of the square is 900 in², we can use that to find the length of each side.
900=x² [square root both sides]
x=30
Now that we know each side is 30 in, we know that the diameter of the circle is also 30 in. To find the radius, divide the diameter by 2.
2r=30 [divide both sides by 2]
r=15
With the radius, we can find the area of the circle.
A=π(15)² [exponent]
A=225π
Since the problem said to leave in terms of π, the area is A=225π in².
Graph the line with slope -1/2
passing through the point (-2, 4).
This image should help with that.
(7)/(9)-2n+(1)/(9) please helpppppp
Answer:
-2n + 8/9
Step-by-step explanation:
Try that tell me I it don't work
Evaluate the expression and enter your answer in the box below.
[(8 + 10) /3] +3 • (7-3)
Answer:
38.6
Step-by-step explanation:
The endpoints of (MP)are M(2,1) and P(12,6). If point K partitions (MP) in a ratio of MK:KP = 3:2, what are the coordinates of K?
Answer:
K(8, 4)
Step-by-step explanation:
Given:
M(2, 1), P(12, 6)
MK:KP = 3:2
Required:
Coordinates of K
SOLUTION:
Coordinates of K can be determined using the formula below:
[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]
[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]
Where,
[tex] M(2, 1) = (x_1, y_1) [/tex]
[tex] P(12, 6) = (x_2, y_2) [/tex]
[tex] m = 3, n = 2 [/tex]
Plug in the necessary values to find the coordinates of K:
[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]
[tex] x = \frac{3(12) + 2(2)}{3 + 2} [/tex]
[tex] x = \frac{36 + 4}{5} [/tex]
[tex] x = \frac{40}{5} [/tex]
[tex] x = 8 [/tex]
[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]
[tex] y = \frac{3(6) + 2(1)}{3 + 2} [/tex]
[tex] y = \frac{18 + 2}{5} [/tex]
[tex] y = \frac{20}{5} [/tex]
[tex] y = 4 [/tex]
The coordinates of K = (8, 4)
when do historians believe that Euclid complete his work
Answer:
2.999 millions hours ago
Step-by-step explanation: :)
(6n-7)+(8n+2)=23 HELP FAST PLEASE
Answer:
n=2
Step-by-step explanation:
(6n-7)+(8n+2)=23
14n-5=23
14n=28
n=2
Solve for x. 6x−24=x−2
Answer:
22/5
Step-by-step explanation:
6x-24=x-2
6x-x=-2+24
5x=22
x=22/5
Find the nth term of the sequence:
23, 19, 13, 5, -5.......
Answer:
Step-by-step explanation:
Given the sequence :
23, 19, 13, 5, -5.......
From the sequence, the common difference is unequal, as their is a constant Increment in the difference after successive numbers.
19 - 23 = -4
13 - 19 = -6
5 - 13 = -8
-5 - 5= -10
Hence an constant difference of - 2 after each successive difference.
Hence, this is a quadratic sequence
With the formula
an² + bn + c
Wich is equivalent to 12(3 2/3)!?
Answer:
1/5 = 2/10 = 3/15 = 4/20
= 5/25 = 6/30 = 7/35 = 8/40
= 9/45 = 10/50 = 11/55 = 12/60
= 13/65 = 14/70 = 15/75 = 16/80
= 17/85 = 18/90 = 19/95 = 20/100
= 21/105 = 22/110 = 23/115 = 24/120
= 25/125 = 26/130 = 27/135 = 28/140
= 29/145 = 30/150 = 31/155 = 32/160
= 33/165 = 34/170 = 35/175 = 36/180
= 37/185 = 38/190 = 39/195 = 40/200
= 41/205 = 42/210 = 43/215 = 44/220
= 45/225 = 46/230 = 47/235 = 48/240
= 49/245 = 50/250 = 51/255 = 52/260
= 53/265 = 54/270 = 55/275 = 56/280
= 57/285 = 58/290 = 59/295 = 60/300
= 61/305 = 62/310 = 63/315 = 64/320
= 65/325 = 66/330 = 67/335 = 68/340
= 69/345 = 70/350 = 71/355 = 72/360
= 73/365 = 74/370 = 75/375 = 76/380
= 77/385 = 78/390 = 79/395 = 80/400
= 81/405 = 82/410 = 83/415 = 84/420
= 85/425 = 86/430 = 87/435 = 88/440
= 89/445 = 90/450 = 91/455 = 92/460
= 93/465 = 94/470 = 95/475 = 96/480
= 97/485 = 98/490 = 99/495 = 100/500
Step-by-step explanation:
all of these are equivalent
Answer: 36/11 Or 3 3/11
Step-by-step explanation:
sun^4A+sin^2Acos^2A=sin^2A
Step-by-step explanation:
sin⁴A + sin²Acos²A = sin²A
Proving the left hand side ( LHS)
That's
sin⁴A can be written as ( sin²A)(sin ²A)
So we have
( sin²A)(sin ²A) + sin²Acos²A
Next factor sin²A out
That's
sin²A ( sin²A + cos²A)
Using trigonometric identities
That's
sin²A + cos²A = 1Simplify the expression
That's
sin²A × 1
We have the final answer as
sin²AAs proven
Hope this helps you
-4 1/2 divided by (-2 2/3
Answer:
1 11/16
Step-by-step explanation:
Answer:
1 11/16
Step-by-step explanation:
Convert mixed numbers into improper fractions:
-4 1/2
Step 1: whole number x denominator + numerator
-4 x 2 + 1 = -9
Step 2: write that number over your original denominator
-9/2
Step 3: repeat for other fraction
-2 2/3
-2 x 3 + 2 = -8
-8/3
Step 4: copy, dot, flip
-9/2 × -3/8
Step 5: solve
27/16
Step 6: convert back to mixed number
1 11/16
*note* Negative x negative = positive
Write Three and eight thousandths in standard form? What is it
Thousandths is the 3rd decimal place
The answer is 3.008
helppp please I have limited time
Answer:
p = T - a - b
Step-by-step explanation:
Hope that helps, not sure if it is correct though.
Help...plzz giving 25 points
Answer: the integers are closed under addition, multiplication, and subtraction, but NOT division.
Step-by-step explanation:
A cylinder has a volume of 320x cubic inches and a height of 5 inches.
What is the radius of the cylinder?
Answer: 8 inches
Step-by-step explanation:
320π in³= π (r²) (5 in)
64 in² = r²
r = 8 in
It takes Dariya 35 seconds to download 5 songs from the Internet. How can the number of seconds it would take Dariya to download 7 songs at this rate be determined? ( need help )
By dividing 35 by 7.
By multiplying 35 by 7.
By finding the unit rate and dividing it by 7.
By finding the unit rate and multiplying it by 7.
To determine the number of seconds it would take Dariya to download 7 songs at the same rate, we first find the unit rate and multiply it by 7.
Hence, option 4. By finding the unit rate and multiplying it by 7 is the right option.
Unit Rate = 7second/song.
Time to download 7 songs = 49 seconds.
What do we mean by unit rate?A unit rate is a quantity taken for a unit of another quantity.
How do we solve the given question?We are given that it takes Dariya 35 seconds to download 5 songs from the Internet. We are asked about the time it will take Dariya to download y songs at the same rate.
We will first determine the unit rate of the time taken for downloading a song.
5 songs take 35 seconds.
∴ 1 song takes 35/5 = 7 seconds.
∴ Unit rate is 7seconds/song.
Now to determine the time for downloading 7 songs, we multiply the unit rate by 7.
∴ Time taken to download 7 songs = 7 songs * unit rate
or, Time taken to download 7 songs = 7 songs * 7 second/song
or, Time taken to download 7 songs = 49 seconds.
∴ To determine the number of seconds it would take Dariya to download 7 songs at the same rate, we first find the unit rate and multiply it by 7.
Hence, option 4. By finding the unit rate and multiplying it by 7 is the right option.
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