Answers
Answer:
The correct option is (A).
Step-by-step explanation:
The given expression is :
[tex]\dfrac{14x^4y^6}{7x^8y^2}[/tex]
The numerator contains 14x⁴y⁶ and the denominator is 7x⁸y².
We can write it as :
[tex]\dfrac{14x^4y^6}{7x^8y^2}=\dfrac{7\times 2\times x^4\times y^2\times y^4}{7x^4\times x^4\times y^2}[/tex]
Canceling the common terms,
[tex]=\dfrac{2y^4}{x^4}[/tex]
So, the correct option is (A).
Related Questions
A positive real number is 1 more than another. When -2 times the smaller is added to the square of the larger, the result is 33. Find the numbers.
Answers
Answer:
The smaller number is 4√2 and the larger number is (4√2 + 1).
Step-by-step explanation:
Let the two numbers be x and y, where y is the larger of the two numbers.
Since y is the larger number, it is one more than the smaller number. So:
[tex]y=x+1[/tex]
When negative two times the smaller is added to the square of the larger, the result is 33. In other words:
[tex]-2x+y^2=33[/tex]
Substitute:
[tex]-2x+(x+1)^2=33[/tex]
Solve for x. Square:
[tex]-2x+(x^2+2x+1)=33[/tex]
Simplify:
[tex]x^2+1=33[/tex]
Subtract one from both sides:
[tex]x^2=32[/tex]
And take the square root of both sides:
[tex]x=\pm\sqrt{32}=\pm 4\sqrt{2}[/tex]
Since y is positive, we can ignore the negative case. So, the smaller number is:
[tex]x=4\sqrt{2}\approx5.66[/tex]
And the larger number is:
[tex]y = 4\sqrt{2} + 1 \approx6.66[/tex]
which is the graph of g(x)
Answers
Answer:
The 1st graph is the answer and matches
-x/2 + 2 -2 ≤ x < 2 because it is equal to -2
The 4th graph is incorrect slightly at = 2x - 3 x ≥ 2
as the graph is descending and shows x = -1/2 as the gradient 4/-2 = -1/2
m = -1/2 would be the equation.
Therefore 2 (-1/2) = -1 and -1 - 3 = -4 and 4 is not greater than 2 so is wrong/.
Step-by-step explanation:
Use logarithmic differentiation to differentiate the question below
[tex]y = x \sqrt[3]{1 + {x}^{2} } [/tex]
Answers
Answer:
[tex] \orange{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]
Step-by-step explanation:
[tex]y = x \sqrt[3]{1 + {x}^{2} } \\ assuming \: log \: both \: sides \\log y = log(x \sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + log(\sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + \frac{1}{3} log({1 + {x}^{2} } ) \\ differentiating \: both \: sides \: w.r.t.x \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{1}{3} . \frac{1}{(1 + {x}^{2}) } (0 + 2x) \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{2x}{3(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3(1 + {x}^{2}) + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 3{x}^{2} + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 5{x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{dy}{dx} =\frac{y(3 + 5{x}^{2} )}{3x(1 + {x}^{2}) } \\ \\ \frac{dy}{dx} =\frac{x \sqrt[3]{1 + {x}^{2} } (3 + 5{x}^{2} )}{3x(1 + {x}^{2}) }\\ \\ \frac{dy}{dx} =\frac{(3 + 5{x}^{2} )\sqrt[3]{1 + {x}^{2} } }{3(1 + {x}^{2}) }\\ \\ \purple{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]
Answer for brainlest plssss
Answers
Answer:
[tex] \displaystyle d) 36 \: {in}^{2} [/tex]
Step-by-step explanation:
the polygon can be separated in two parts
rectangletrianglelet's figure out the area of the rectangle
recall that,
[tex] \displaystyle A_{ \rm rect} =l \times w[/tex]given that,
l=9w=3thus substitute:
[tex] \displaystyle A_{ \rm rect} =9\times 3[/tex]simplify multiplication:
[tex] \displaystyle A_{ \rm rect} =27[/tex]let's figure out the area of the triangle
remember that,
[tex] \displaystyle A_{ \rm triangle} = \frac{1}{2} \times b\times h[/tex]
substitute the value of b and h:
[tex] \displaystyle A_{ \rm triangle} = \frac{1}{2} \times 9\times 2[/tex]
reduce fraction:
[tex] \displaystyle A_{ \rm triangle} = 9[/tex]
now the area of the polygon would be the total area of the rectangle and triangle thus
[tex] \displaystyle A_{ \rm polygon} = 27 + 9[/tex]
simplify addition:
[tex] \displaystyle A_{ \rm polygon} = 36[/tex]
hence our answer is D)
A card is drawn randomly from a standard 52 card deck. Find the probability of drawing the given card. NO LINKS!!!!
Answers
Answers:
Problem 7) 1/26Problem 8) 1/13Problem 9) 10/13Problem 10) 1/2Problem 11) 11/13Problem 12) 3/13===================================================
Explanations:
Problem 7)
There are 2 red aces (hearts, diamonds) out of 52 cards total, so 2/52 = 1/26 is the probability of picking a red ace.
---------------------------
Problem 8)
There are 4 kings out of 52 cards total, so 4/52 = 1/13 are the odds of picking a king.
This is the same as say focusing on one suit (eg: clubs) and finding the probability of pulling out a king.
---------------------------
Problem 9)
There are 3 face cards per suit (Jack, Queen, King) so 3*4 = 12 face cards in all. The odds of picking a face card are 12/52 = 3/13. That makes 10/13 the odds of not picking a face card, since 3/13+10/13 = 1.
---------------------------
Problem 10)
The answer is 1/2 because half of the cards are red.
You could say 26/52 = 1/2 since there are 26 red cards out of 52 cards total.
---------------------------
Problem 11)
There are 4 copies of '2' and 4 copies of '3', so there are 4+4 = 8 cards we want to avoid. The probability of picking either of them is 8/52 = 2/13. The odds of not picking any of these cards is 11/13 (refer to problem 9).
---------------------------
Problem 12)
We have 4 copies each of '7', '8' and '9'
That gives 4*3 = 12 cards total we want to pick.
So 12/52 = 3/13 is the answer.
Please help me!!! WILL MARK BRAINLIEST AND THANK
Answers
Answer:
2 is the same as 4
Step-by-step explanation:
find the area of the following figure.
Answers
Explanation:
Divide figure into two triangles:
Area of triangle to the left (1/2•base•height):
1/2 • 6 • 4 = 12 square meters
Area of triangle to the right:
1/2 • 6 • 9 = 27 square meters
Add the area of both triangles:
27 + 12 = 39
FINAL ANSWER: 39 square meters
Hope this helps!
gold that is 24 karat is 100% pure gold. gold that is 14 karat is 14 parts pure gold and 10 parts another metal, such as copper,zinc,silver, or nickel. What percent of 14 karat gold if pure gold.
help im confused
Answers
100% is 14+10=24
14 divided by 24 = 0.583
Move decimal over to the right twice is 58.3%
Use the method of least squares to solve the following problem.
Given the data set below, find the line of best fit? Then find the y-value for when x=7. Yes, there are supposed to be
two 6's.
Х
1
2
4
5
6
6
8
9
Y
14
10
12
8
9
6
3
4
Answers
If y varies directly as x and y = 24 when x = -3, find the constant of variation k
and then determine y when x = 12.
Answers
Answer:
I. k = -8
II. y = -96
Step-by-step explanation:
Given the mathematical expression and data;
y = 24
x = -3
y = kx (y varies directly as x).
To find the constant of proportionality k;
y = kx
Substituting the values into the expression, we have;
24 = k(-3)
24 = -3k
k = -24/3
k = -8
Next, to find the value of y when x = 12
y = kx
Substituting the values, we have;
y = -8 * 12
y = -96
Teresa is playing a video game. She earns 10 points when she completes Level 1. Each time she completes a level, she earns three times as many points as the previous level.
How many points will Teresa earn when she completes Level 7?
Enter your answer in the box.
Answers
Answer: 7290
Step-by-step explanation:
Three times is asking you to multiply the points before them by three. Level one, as we know is 10. Then, to get level two's points, you would multiply 10 by 3, to get 30, & so on.
Level One:10
Level Two: 10x3=30
Level Three: 30x3=90
Level Four: 90x3=270
Level Five: 270x3=810
Level Six: 810x3=2430
Level Seven: 2430x3= 7290
*** If you are still confused, comment on this question, & I will be happy to walk you through the whole question. ***
Answer:
7290 :)
Step-by-step explanation:
Took the quiz.
I need help please asp !!!!
Answers
There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.08 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.03 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm.
What is the probability that the first machine produces an acceptable cork? (Round your answer to four decimal places.)
What is the probability that the second machine produces an acceptable cork? (Round your answer to four decimal places.)
Please explain the math behind your answer so I am able to understand!(:
Answers
Answer:
0.7888 = 78.88% probability that the first machine produces an acceptable cork.
0.9772 = 97.72% probability that the second machine produces an acceptable cork.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
First machine:
Mean 3 cm and standard deviation 0.08 cm, which means that [tex]\mu = 3, \sigma = 0.08[/tex]
What is the probability that the first machine produces an acceptable cork?
This is the p-value of Z when X = 3.1 subtracted by the p-value of Z when X = 2.9. So
X = 3.1
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.1 - 3}{0.08}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a p-value of 0.8944
X = 2.9
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.9 - 3}{0.08}[/tex]
[tex]Z = -1.25[/tex]
[tex]Z = -1.25[/tex] has a p-value of 0.1056
0.8944 - 0.1056 = 0.7888
0.7888 = 78.88% probability that the first machine produces an acceptable cork.
What is the probability that the second machine produces an acceptable cork?
For the second machine, [tex]\mu = 3.04, \sigma = 0.03[/tex]. Now to find the probability, same procedure.
X = 3.1
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.1 - 3.04}{0.03}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772
X = 2.9
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.9 - 3.04}{0.03}[/tex]
[tex]Z = -4.67[/tex]
[tex]Z = -4.67[/tex] has a p-value of 0
0.9772 - 0 = 0.9772
0.9772 = 97.72% probability that the second machine produces an acceptable cork.
What is the value........
Answers
Answer:
[tex]a_5 = 120[/tex]
Step-by-step explanation:
Given
[tex]a_1 = 1[/tex]
[tex]a_n = n(a_{n-1})[/tex]
Required
[tex]a_5[/tex]
This is calculated as:
[tex]a_5 = 5(a_{5-1})[/tex]
[tex]a_5 = 5*a_4[/tex]
Calculate [tex]a_4[/tex]
[tex]a_4 =4(a_{4-1})[/tex]
[tex]a_4 =4*a_3[/tex]
Calculate [tex]a_3[/tex]
[tex]a_3 =3*a_2[/tex]
Calculate [tex]a_2[/tex]
[tex]a_2 = 2 * a_1[/tex]
[tex]a_2 = 2 * 1[/tex]
[tex]a_2 = 2[/tex]
So:
[tex]a_3 =3*a_2[/tex]
[tex]a_3 = 3 * 2 = 6[/tex]
So:
[tex]a_4 =4*a_3[/tex]
[tex]a_4 = 4 * 6 =24[/tex]
Lastly;
[tex]a_5 = 5*a_4[/tex]
[tex]a_5 = 5 * 24[/tex]
[tex]a_5 = 120[/tex]
In science class sara needed 8 test tubes for 3 different experiments. The first experiment required 2 test tubes and the other two experiments required the same number of test tubes. How many test tubes were needed for each of the the other two experiments
Answers
Answer:
as we know Sara need 8 tube in 3 experiment
she will use 2 tube in 1 experiment
now she have 6 tube in other experiments
so the question said to find how many tube were used in both experiment equally so 3,3 test tube were needed for each of the other two experiment
Step-by-step explanation:
total tube=8 (3 experiment)
used =2tube (1 experiment)
remaining=8-2=6
now ,
dividing 6 into 2 equal part
so,=6/2=3
so 3 tube were used in 2nd experiment and 3in 3rd experiment
why is the growth factor 0.9?
Answers
Answer:
Actual growth of population - Birth - Death + In migration - Out Migration. ...
Evaluate the following expression. "12 more than 5"
Answers
Answer:
17
Step-by-step explanation:
12+5
Only answer if you're very good at Math.
What is the sum of 7x/x^2 - 4 and 2/x + 2?
A: 7x + 2/x^2 - 4
B: 9x - 4/x^2 - 4
C: 7x + 2/ x^2 + x - 2
D: 9/x
Answers
Answer:
Solution given:
B: 9x - 4/x^2 - 4
Step-by-step explanation:
.k
HELP ME PLEASEEEEEEEEEEEE
Answers
Answer:
x=in5
Step-by-step explanation:
A rectangular prism has a base area of 2 square feet and a height of 5 feet. What
is the volume of the prism in cubic feet?
10
15
12
11
Submit
Answers
PLEASE HELP! WILL MARK BRAINLIEST!
Answers
Answer:
at first put the value of X
after that do the equation.
Step-by-step explanation:
hope it will help you
Answer:
a = 2
Step-by-step explanation:
substitute x with the number 5.
5+8a=25+5a-7a
subtract 5a from both sides
5+3a=25-7a
add 7a to both sides
5+10a = 25
subtract 5 from both sides
10a=20
divide both sides by 10
a = 2
Mariana baked 14 cakes. She gave 1/7 of them to her family before she took the rest to a party. How many cakes did Mariana give to her family?
Answers
Answer:
2
Step-by-step explanation:
14·[tex]\frac{1}{7}[/tex]=2
Answer:
2
Step-by-step explanation: 1/7th's of 14 is 2.
1/7 x 14 = 2.
Find an equation of the circle that satisfies the given conditions. (Give your answer in terms of x and y.) Radius 7 and center (2, −4)
Answers
Let's start by writing the equation of a circle.
(x - h)² + (y - k)² = r²The center of the circle is (h, k), and the radius, r, is 4 so
we can simply plug these values into the formula.
So we have [(x) - (2)]² + [(y) - (-4)]² = (7)².
Notice that I changed the parenthses that were in the original formula
to brackets so that we wouldn't have too many sets of parenthses
when plugging our values into the formula.
Finally, we simplify inside the brackets.
So we have (x - 2)² + (y + 4)² = 49.
Now, I changed the brackets back to parenthses in the final answer.
Find the surface area of the regular pyramid.
Answers
Answer:
B
Step-by-step explanation:
Base area = side^2 = 3^2 = 9 m^2
Base perimeter = side x 4 = 3 x 4 = 12 m
LA = (base perimeter x slant height)/2 = (12 x 5)/2 = 30 m
SA = base area + LA = 9 + 30 = 39 m^2
Write an equation for a line perpendicular to y=3x+1 and passing through the point (6,2)
Answers
Answer:
[tex]y = -\frac{1}{3}x + 4[/tex]
Step-by-step explanation:
Required
Equation of line
passes through [tex](6,2)[/tex]
In an equation of the form [tex]y =mx + b[/tex]; the slope is [tex]m[/tex]
So, by comparison;
The slope of [tex]y = 3x + 1[/tex] is: [tex]m =3[/tex]
From the question, we understand that the required equation is perpendicular to [tex]y = 3x + 1[/tex]
This means that its slope is:
[tex]m_2 =-\frac{1}{m}[/tex]
So, we have:
[tex]m_2 =-\frac{1}{3}[/tex]
The line equation is:
[tex]y = m_2(x - x_1) + y_1[/tex]
Where:
[tex](x_1,y_1) = (6,2)[/tex]
So, we have:
[tex]y = -\frac{1}{3}(x - 6) + 2[/tex]
[tex]y = -\frac{1}{3}x + 2 + 2[/tex]
[tex]y = -\frac{1}{3}x + 4[/tex]
Type SSS, SAS, ASA, SAA, or HL to
justify why the two larger triangles are
congruent.
Answers
Answer:
ASA
Step-by-step explanation:
The two small angles which are the base angles of the small triangle in the middle are marked as equal.
The two large angles of the two triangles are also marked as conguent.
The base of the small triangle in the middle is common to both the larger triangles by the reflexive property (a line is always equal to itself). The line is between two sets of congruent angles. Therefore the two large triangles are congruent by ASA
Explanation:
It might help to peel the triangles apart as I have done so below.
We have two pairs of congruent angles, as shown by the distinct angle markers. Between the congruent angles, we have a pair of congruent sides.
The side (S) is between the angles (A), which is why we use ASA.
Note: SAA is slightly different where the congruent sides are not between the congruent angles.
The salaries of professional baseball players are heavily skewed right with a mean of $3.2 million and a standard
deviation of $2 million. A baseball analyst randomly selects 40 athletes and records the mean salary. What is the shape
of the distribution of the sample mean for all possible random samples of size 40 from this population?
skewed left
skewed right
approximately Normal
approximately uniform
Answers
Answer:
approximately Normal with a mean of 3.2 million and a standard deviation of 0.32 million
Step-by-step explanation:
For normal distribution conditions
1) Sample size is greater than 30
2) Population standard deviation is known
3) population is normal distributed
Above any condition given problem if satisfied than it's distribution will approximately normal.
n = 40 > 30
Sample size(n) greater than 30 and population standard deviation is known.
So the distribution will approximately be normal
Hope this helps!
The shape of the distribution of the sample mean for all possible random samples of size 40 from this population is approximately Normal
The following any or all conditions should be there for normal distribution:
The Sample size is more than 30 .Population standard deviation is known .The Population is normal distributed
Now
n = 40 > 30
Here
Sample size(n) more than 30 and population standard deviation is known.
Learn more: brainly.com/question/17429689
Sand is being dumped from a conveyor belt and forms a conical pile. Assuming that the height of this cone is always exactly 3 times the size of the radius of its base, and that thesand is added at the rate of 10 m^3/min, how fast is the height increasing when the pile is15 m high?
Answers
Answer:
dh/dt = 0.4 m/min
Step-by-step explanation:
The volume of the cone is:
V(c) = (1/3)*r² *h if always h = 3r then r = h/3
The volume of the cone as a function of h will be:
V(h) = (1/3)* (h/3)²*h
V(h) = (1/27)*h³
The increasing rate of the volume is equal to the rate of sand added the:
D(V)/dt = (1/27)*3*h²*dh/dt
D(v) / dt = 10 m³/min
h = 15 m and dh/dt is the rate of increasing of the height
By substitution
10 m³/min = ( 1/9)* 225 * dh/dt (m²)
dh/dt = 90 / 225 m/min
dh/dt = 0.4 m/min
This one says (cos) , help it’s timed ! Take me through the process !
Answers
Answer:
4/5 is ur answer
Step-by-step explanation:
ok just like the last one but this one is COS
ok so we know that COS is A/H
A= adjacent and ofc H= hypotenuse
so lets see its the COS of a which means it will be A/H
A= 4 and the H=5
It costs Beverly $0.50 to produce each bracelet she makes. She sells each bracelet for $20, plus three times the production cost per bracelet. Which equation below shows the amount Beverly charges, C, per bracelet, b?
Answers
Answer:
(0.5b+20b)*3b=c
Step-by-step explanation:
The requried equation that shows the amount Beverly charges per bracelet is C = 21.5b
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
The amount Beverly charges, C, per bracelet, b, is given by:
C = 20 + 3(0.5)
C = 20 + 1.5
C = 21.5
So the equation that shows the amount Beverly charges per bracelet is:
C = 21.5b
Learn more about models here:
https://brainly.com/question/22591166
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