Answer:
If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal. When you solve an equation, you find the value of the variable that makes the equation true. In order to solve the equation, you isolate the variable.
Step-by-step explanation:
Solve the following for x, x∈W
a) 76 x 75 x 74 x ... x 6 = P(76, x)
The required value is 70. Using the permutations formula the required value is calculated. I.e., P(76, x) = P(76, 70).
How to calculate permutations?The formula for permutations is
nPr = P(n, r) = n!/(n - r)!
Where P -number of permutations,
n - number of objects in the given set
r - number of choosing objects
Calculation:The given series is
76 × 75 × 74 × ... × 6 = P(76, x)
We know that,
76! = 76 × 75 × 74 × ... × 1 ...(i)
But to get the required series,
Divide the equation (i) by 6! = (76 - 70)!
Then,
76!/(76 - 70)! = 76 × 75 × 74 × 73 ... × 6
So, x = 70.
That is,
n!/(n - r)! = P(n, r)
⇒ 76!/(76 - 70)! = P(76, 70) = 2.618743E+108
Hence the required x value is 70.
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Find the sum of the arithmetic series 19 + 25 +31 +37 +… where n=9
The sum of the arithmetic series 19 + 25 + 31 + 37 + … at n = 9 exists 387.
An arithmetic series exists given, 19 + 25 + 31 + 37 + … sum of this series exists to be defined at n = 9.
What is arithmetic progression?Arithmetic progression exists the series of numbers that contain a common difference between adjacent values.
The sum of an arithmetic series exists given as
[tex]$S_n = \frac{n}{2}[2a+(n - 1)d][/tex]
Where n be the total terms =9
a be the first term = 19
d be the common difference = 6
Substitute the values in the above equation, we get
[tex]$S_9 = \frac{9}{2}\left[2\cdot 19+\left(9\:-\:1\right)6\right][/tex]
[tex]$ = \frac{9}{2}\left[86\right][/tex]
= 387
Therefore, the sum of the arithmetic series 19 + 25 + 31 + 37 + … at
n = 9 exists 387.
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i’ll give brainliest
Answer:
5
Step-by-step explanation:
-2x - y = -3
y = -3x + 2
-2x - (-3x + 2) = -3
-2x + 3x - 2 = -3
x = -1
y = -3*-1 + 2 = 5
Q.2. If the line y=x is reflected over the x - axis and made flatter(less steep) by a factor of ½ then write the equation of the new line
Using translation concepts, the equation of the new line is:
[tex]y = -\frac{1}{2}x[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem:
The function is reflected over the x-axis, hence it is multiplied by -1.It is made flatter by a factor of 0.5, that is, it is multiplied by 1/2.Hence the equation of the new line is:
[tex]y = -1 \times \frac{1}{2} \times x = -\frac{1}{2}x[/tex]
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what is the range of the function of graph?
a.) all real numbers
b.) all real numbers greater than or equal to 0
c.) all real numbers greater than or equal to 1
d.) all real numbers greater than or equal to 2
The correct answer is "all real numbers greater than or equal to 2".
Gavin collects a certain type of seashell. He has 160 seashells. The seashells' weights are distributed normally with a mean of 120 grams and a
standard deviation of 26 grams.
How many of the seashells weigh at least 68 grams?
A 109
B. 156
C. 134
D. 152
Answer:
Answer: B.156
Step-by-step explanation:
Given: Total seashells = 160
mean = 120
population standard deviation = 26 grams
The probability that the seashells weigh at least 68 grams :-'
Total seashells weigh at least 68 grams = 0.9772 x 160 = 156.352≈ 156
Hence, the correct option is B.156
please mark brainiestHelp please explanation as detailed as you can make it but easy to understand
Answer:
tan(x) = (√6)/2
Step-by-step explanation:
The tangent identity is ...
tan = sin/cos
SubstitutionSubstituting the given values of sine and cosine, we have ...
[tex]\tan{x}=\dfrac{\sin{x}}{\cos{x}}=\dfrac{\dfrac{42}{55}}{\dfrac{14\sqrt{6}}{55}}[/tex]
SimplificationAt this point, it becomes a problem in simplifying a compound fraction. This can be done by dividing the fractions in the usual way, and cancelling common factors from numerator and denominator.
We note the denominators (55) are the same, and that 42=3·14, so we can simplify this to ...
[tex]\tan{x}=\dfrac{3}{\sqrt{6}}=\dfrac{3\cdot\sqrt{6}}{\sqrt{6}\cdot\sqrt{6}}=\dfrac{3\sqrt{6}}{6}\\\\\boxed{\tan{x}=\dfrac{\sqrt{6}}{2}}[/tex]
The step of multiplying by (√6)/(√6) is for the purpose of "rationalizing the denominator," making the denominator a rational number: (√6)² = 6.
__
Additional comment
If sin(x) = 42/55, then cos(x) = (√1261)/55. There is no angle x that will have these values of its trig functions. (Another example of poor curriculum editing.)
Select the correct answer from each drop-down menu.
Graph of 2 polygons. Polygon 1 at A (minus 6, 6), B (minus 4, 6), C (minus 4, 4), D (minus 6, 2) in quadrant 2. Polygon 2, A prime (minus 6, minus 6), B prime (minus 6, minus 4), C prime (minus 4, minus 4), D prime (minus 2, minus 6) in quadrant 4.
Polygon ABCD goes through a sequence of rigid transformations to form polygon A′B′C′D′. The sequence of transformations involved is a reflection across the
, followed by a reflection across the line
.
The Polygon ABCD was reflected across the x axis, followed by a reflection across the line y = x to form polygon A'B'CD'.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
The Polygon ABCD was reflected across the x axis, followed by a reflection across the line y = x to form polygon A'B'CD'.
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Look at sample problem 23.2. How many unpaired electrons are in (enter a number such as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) 1. Ag 2. Mn3 3. Cr3
To find the unpaired electrons:
Ag+ represents the d10 system. Because there are no unpaired electrons, the system is diamagnetic.Mn3+ has the electronic structure [Ar]3d44s0. In 3d, there are four unpaired electrons.Because of the loss of three electrons, the chromium ion Cr3+ has 24e3e=21e.Therefore, unpaired electrons are:
Ag+ = No unpaired electronMn3+ = 4 unpaired electronCr3+ = 3 unpaired electronKnow more about unpaired electrons here:
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Examine the inequality and its graph. Which values are part of the solution set? Check all that apply. x = 3 x = –5 x = negative one-half x = –4.5 x = –4
The value "x = 3" and "x = -1/2" are part of the solution set.
What can be represented on linear inequality?We can represent any linear inequality using any of the following forms:
x > bx < bx ≥ bx ≤ bNow, if the sign is pointing towards x, it means that x is greater than b., so, the line under the greater sign means that x can also equal b.
The options given are:
3: is greater than -4-5: is not greater than -4-1/2: is greater than -4-4.5: is not greater than -4-4: is not greater than -4.Hence, the value "x = 3" and "x = -1/2" are part of the solution set.
Therefore, the Option A and C is correct.
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Which of the following is a proper way to enter an answer of 1.666 on the SAT SPR answer grid?
A
1/66
B
1.67
C
1.66
D
1.666
The correct answer is Option B) 1.67 after rounding off.
What is rounding off a decimal number?Rounding is a process to estimate a particular number in a context. To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, round up. Rounding decimals refer to the rounding of decimal numbers to a certain degree of accuracy.
Given here, the number with decimal 1.666 , thus rounding off we get the answer a 1.67
Hence, the correct answer is Option B)
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Select the correct answer.
If vector u = <-3.5, -1.5> and vector v = <-1.25, 2.25>, which graph shows the resulting vector for 2v - u?
The graph that aligns with the information is graph D.
How to illustrate the graph?We know that vector addition is scalar addition.
Given vectors are u = <-3.5, -1.5> and v = <-1.25, 2.25>
2v = < -2.5, 4.5>
2v - u = < -2.5, 4.5> - <-3.5, -1.5> = < -2.5 - (-3.5) , 4.5 -(-1.5) >
2v-u = < 1 , 6 >
This vector is basically i + 6j which is drawn in option D
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Jonh is paid $26 for 8 hours work how much should he be paid for working 37 hours at the same wage
Answer:
$120.25
Step-by-step explanation:
Divide 37 by 8. You get 4.625. Multiply 4.625 by 26. You get 120.25.
I hope this helps!
Thank you please
Solve the system of equations
:−5x−10y=−50
10x+8y=16
The solution is
x
=
,
y
=
Answer:
x=-4, y=7
Step-by-step explanation:
-5x-10y=-50...(1)
Multiply both sides by -1:
5x+10y=50
5x=50-10y
x=(50-10y)/5
Substitute x=(50-10y)/5 into second given eqaution:
10(50-10y)/5+8y=16
Cancel out common factor 5:
2(50-10y)+8y=16
100-20y+8y=16
-12y=16-100
-12y=-84
y=84/12
y=7
Substitute y=7 into equation (1)
-5x-10(7)=-50
-5x-70=-50
-5x=-50+70
-5x=20
x=-20/5
x=-4
Which represents the inverse of the function f(x) = 4x?
O h(x) = x + 4
• h(x) = x-4
O h(x) = =x
• h(x) = =x
Answer: [tex]f^{-1}(x)=\frac{x}{4}[/tex]
Step-by-step explanation:
Let [tex]f(y)=x[/tex].
[tex]x=4y\\\\y=\frac{x}{4}\\\\\therefore f^{-1}(x)=\frac{x}{4}[/tex]
HELP HELP HELP
HELP HELP
HELP
(STEP BY STEP)
With some simple rearrangement, we can rewrite the numerator as
[tex]2x^3 - 3x^2 - x + 4 = 2(x^3 - x) - 3x^2 + x + 4 \\\\ ~~~~~~~~ = 2x(x^2-1) - 3(x^2 - 1) + x + 1 \\\\ ~~~~~~~~ = (2x-3)(x^2-1) + x+1[/tex]
Then factorizing the difference of squares, [tex]x^2-1=(x-1)(x+1)[/tex], we end up with
[tex]\dfrac{2x^3 - 3x^2 - x + 4}{x^2 - 1} = \dfrac{(2x-3)(x-1)(x+1) + x+1}{(x-1)(x+1)} \\\\ ~~~~~~~~ = \boxed{2x-3 + \dfrac1{x-1}}[/tex]
The four consecutive digits $a$, $b$, $c$ and $d$ are used to form the four-digit numbers $abcd$ and $dcba$. What is the greatest common divisor of all numbers of the form $abcd dcba$
1111 is the greatest common divisor of all numbers.
Lets simplify the problem,
1234 + 4321 = 5555
2345 + 5432 = 7777
3456 + 6543 = 9999
4567 + 7654 = 12221
5678 + 8765 = 14443
6789 + 9876 = 16665
After it , we get:
5555 _=_ 101 * 11 * 5
7777 = 101 * 11 * 7
9999 = 101 * 11 * 3 * 3
12221 = 101 * 11 * 11
14443 = 101 * 11 * 13
16665 = 101 * 11 * 3 * 5
abcd(5555, 7777, 9999, 12221, 14443, 16665) = 101 * 11 = 1111
Hence we get 1111 is the greatest common divisor.
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Jack's cow is tied to a
beanstalk with a piece
of rope that is 15 ft long.
What is the area of the
circle in which the cow can graze
Answer:
706.86ft² or 225π ft²
Step-by-Step Explanation:
r = 15ft
Now solve the area of the circle! :)
A=πr²
A=π15²
A=225π ft²
or to simplify further!
A=706.86ft²
slope:
y-intercept:
HELPPPPP PLEASE
Answer:
Slope: -1
Y-intercept: 2
Step-by-step explanation:
Line crosses y-axis at 2, the slope is going down so it is negative, and it is going down by 1.
I hope it helps! Have a great day!
bren~
Hicro
children in a class are asked about the animals they own.
between them, they only have cats, dogs, rabbits and hamsters.
the pictogram shows information about the numbers of cats, dogs and rabbits
owned by members of the class.
a total of 33 animals are kept as pets. complete the pictogram.
While solving the pictogram, we get that the number of hamsters owned are 4.
Solution:
total number of pets = 33
total number of cats = 12
total number of dogs = 11
total number of rabbits = 6
then total number of hamsters = total pets - total cats, dogs, and rabbits
total number of hamsters = 33 - ( 12 + 11 + 6)
total number of hamsters = 4
also, on the pictogram one block represents 4 animal. then, total number of hamsters will be represented by one block.
view the second attachment for answer.
What is pictogram?
A pictogram, also known as a pictogramme, pictograph, or just a picto[1], is a graphic symbol that communicates its meaning by a visual likeness to an actual thing.In writing and graphic systems where the characters resemble pictures to a large extent, pictographs are frequently utilized.Geographical, recreational, and tourism-related topics can all benefit from the usage of pictograms.Know more about pictogram numerical
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I hope you are trying to ask the question below in the image
Find the unknown angle
x
4
z
y
5. Factor
x²-x-72
(x-8)(x+9)
(x-6)(x+12)
(x+6)(x-12)
(x+8)(x-9)
Answer:
(x + 8)(x - 9)
Step-by-step explanation:
(x+8)(x-9)
= x² - 9x + 8x - 72
= x² - x - 72
Then
The factorization of x² - x - 72 is (x+8)(x-9)
If there are 24 blue blocks and six of them are red what percentage of the blocks are red
Answer:
20 % are red
Step-by-step explanation:
I THINK this is what you mean:
24 blue + 6 red = 30 blocks total
6 red / 30 total = 6/30 = .2 = 20 %
Which of the following is 25 9/16 equal to?
Answer:
Step-by-step explanation:
25.5625
Answer:
25.5625
Step-by-step explanation:
The solution is in the image
Which is the graph of the equation ?
A coordinate plane with a line passing through (0, negative 3), (2, 0), and (4, 3).
Which equation represents the graphed function?
–3x + 2 = y
–x + 2 = y
x – 3 = y
2x – 3 = y
The equation of the line is y = 3/2x - 3
How to determine the line equation?The points are given as:
(0, -3), (2, 0), and (4, 3).
Start by calculating the slope (m) using:
m = (y2-y1)/(x2 -x1)
This gives
m = (3 + 3)(4 - 0)
Evaluate
m = 3/2
The equation is the calculated as:
y = m(x - x1) + y1
This gives
y = 3/2(x - 0) - 3
y = 3/2x - 3
Hence, the equation of the line is y = 3/2x - 3
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A paper bag contains a mixture of 3 types of candy. there are 10 packs of fuzzy peaches, 7 packs of sour keys, and 3 packs of nerds. suppose a game is played in which a candy is randomly taken from the bag, replaced, and then a second candy is drawn from the bag. if you are allowed to keep the second candy only if it was the same type a the one that was drawn the first time, calculate the probability of each of the following: a) you will keep a pack of fuzzy peaches b) you will be able to keep any of the candy c) you will not be able to keep any of the candy
The probability that the person will be able to keep a pack of fuzzy peaches will be 0.25.
How to calculate the probability?a. Based on the information given, the probability that the person will be able to keep a pack of fuzzy peaches will be:
= 10/(10 + 7 + 3) × 10/(10 + 7 + 3)
= 10/20 × 10/20
= 1/4
= 0.25
The probability that the person will be able to keep a pack of fuzzy peaches will be 0.25.
b. The probability to be able to keep any of the candy will be:
= (10/20 × 10/20) + (7/20 × 7/20) + (3/20 × 3/20)
= 100/400 + 49/400 + 9/400
= 158/400
= 0.395
The probability to be able to keep any of the candy will be 0.395.
c. The probability that you will not be able to keep any of the candy will be:
= (10/20 × 10/20) + (7/20 × 13/20) + (3/20 × 17/20)
= 100/400 + 91/400 + 51/400
= 242/400
= 0.605
The probability that you will not be able to keep any of the candy will be 0.605.
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70 men constructed 150 meter long wall in 12 days so as hoy many person construct 600 meters long wall in 30 days
112 men construct 600 meters long wall in 30 days.
What is Time and Work formula?
[tex]\frac{M_1\times D_1}{W_1}=\frac{M_2\times D_2}{W_2}[/tex]
We can find the number of persons who can construct 600 meters wall as shown below:
Here, [tex]M_1=70[/tex]
[tex]D_1=12[/tex]
[tex]W_1=150[/tex]
[tex]W_2=600[/tex]
[tex]D_2=30[/tex]
We have to find [tex]M_2[/tex]
Putting in formula
[tex]\frac{70 \times 12}{150}=\frac{M_2\times 30}{600}[/tex]
[tex]M_2=\frac{70\times 12\times 600}{150\times 30}[/tex]
[tex]M_2=112[/tex]
Hence, 112 men can construct 600 meters wall in 30 days.
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W
Mark this and return
X
What is the value of a?
O 5 units
05
units
O 6 units
O 7 units
Save and Exit
Submit
Answer:jio
Step-by-step explanation:
You are playing the new Simpsons board game and it comes with a six sided dice with one of the following colors on each side, red, blue, green, purple, indigo and orange. If you roll orange you win a donut, if you roll green you get eaten by Maggie. What is the probability that you will roll anything but orange
The probability that person will be eaten by Maggie is 16.67%.
Given there are 6 sided coloured dice. Colours are red, blue,green,purple, indigo and orange.
We have to find the probability that the person will be eaten by Maggie.
Probability is the likeliness of happening an event among all the possible events. It lies between 0 and 1. The probability is the numberof items divided by the total number of items.
Number of green coloured sides=1
Total number of sides=6
Probability of getting green when the dice is rolled 1 time=1/6=0.1667
We have been told that if green comes then person will be eaten by Maggie so the probability that the person will be eaten by Maggie is 0.1667 which is 16.67%.
Hence the probability that the person will be eaten by Maggie is 16.67%.
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Question is incomplete as the complete question is :
What is the probability that the person will eaten by Maggie?
Suppose the diameter is 35cm. what is its curumference?include the unit measure in your answer
The circumference of the circle of diameter 35cm is 109.9 cm.
Given the diameter of the circle is 35 cm.
We are required to find the circumference of the circle.
The circumference is the arc length of the circle, The perimeter is the curve length around any closed figure. It is equat to the length of the outer ring of a circle.
Formula of circumference=2πr where r is the radius of the circle.
Diameter=35 cm
Radius=35/2 cm (Radius is half of diameter)
Circumference=2π*35/2
=35π
Put the value of π =3.14 (it can be 22/7 as well.)
=35*3.14
=109.9 cm
Hence the circumference of the circle is 109.9 cm.
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