Answer:
Step-by-step explanation:
The sum of two perfect cubes breaks down into two factors, the first is the sum of their cube roots, and the second is made up of the square of the first root minus the product of both roots plus the square of the second root.
The difference of two perfect cubes is decomposed into two factors, the first is the difference of their cube roots, and the second is made up of the square of the first root plus the product of both roots plus the square of the second root.
If the general term of a sequence is 4, then the sequence is
A)4,4,4,4,
B)4,16,64.216
C)4, 8, 12, 16,
Answer:
Correct answer is A) 4,4,4,4
Find the range of the following data set.
11,5, 1, 11, 12
01
1.
017
Answer:
range 11
Step-by-step explanation:
The range is the largest number minus the smallest number
The largest number is 12 and the smallest number is 1
12 - 1 = 11
On a coordinate plane, triangle A B C has points (negative 9, 3), (negative 9, 6), (0, 3) and triangle A double-prime B double-prime C double-prime has points (3, negative 1), (3, negative 2), and (0, negative 1).
Which transformations could be performed to show that △ABC is similar to △A"B"C"?
a reflection over the x-axis, then a dilation by a scale factor of 3
a reflection over the x-axis, then a dilation by a scale factor of One-third
a 180° rotation about the origin, then a dilation by a scale factor of 3
a 180° rotation about the origin, then a dilation by a scale factor of One-third
Answer: D 180 degrees rotation about the origin.then a dilation by a scale factor of one-third.
Step-by-step explanation:
A( -9,3) B(-9,6) C (0,3)
After a rotation of 180 degrees you will have the new points as
A (9,-3) B( 9,-6) C (0, -3)
The you after dilating it by a scale factor of 1/3
you will get the coordinates
A ( 3,-1) B( 3,-2) C(0,-1)
which match is what was given in the question.
Answer:
a 180° rotation about the origin, then a dilation by a scale factor of One-third
Step-by-step explanation:
took the test
What is the first step of the following division problem? (8x3 – x2 + 6x + 7) ÷ (2x – 1)
Answer:
The first step is to determine how many times 2x goes into 8x^3
Step-by-step explanation:
The first step is to determine how many times 2x goes into 8x^3
4x^2
--------------------------
2x-1 | (8x3 – x2 + 6x + 7
8x^3 -4x^2
Answer:
A
Step-by-step explanation:
i just took the test
Score: 0 of 1 pt
7.4.41
From a standard 52-card deck, how many 5-card hands consist entirely of black cards?
Answer:
so halve the deck is black and halve the deck is red so you have 26 black cards then divide by 5 and you get 5 with 1 card leftover
A real estate purveyor purchases a 60{,}00060,00060, comma, 000 square foot \left(\text{ft}^2\right)(ft 2 )(, start text, f, t, end text, squared, )warehouse and decides to turn it into a storage facility. The warehouse's width is exactly \dfrac 2 3 3 2 start fraction, 2, divided by, 3, end fraction of its length. What is the warehouse's width? Round your answer to the nearest foot.
Answer:
200 feet
Step-by-step explanation:
Area of the warehouse [tex]=60,000$ ft^2[/tex]
Let the length of the warehouse=l
The warehouse's width is exactly [tex]\dfrac23[/tex] of its length
Therefore: Width of the warehouse[tex]=\dfrac23l[/tex]
Area =Length X Width
Therefore:
[tex]\dfrac23l*l=60000\\$Cross multiply\\2l^2=60000*3\\2l^2=180000\\$Divide both sides by 2\\2l^2 \div 2=180000 \div 2\\l^2=90000\\l^2=300^2\\$Length, l=300 feet\\Recall: Width =\dfrac23l\\$Therefore, Width of the warehouse=\dfrac23*300=200$ feet[/tex]
find the value of the expression :1/216^-2/3 + 1/256^-3/4 + 1/243^-1/5
Answer:
103
Step-by-step explanation:
A number to the power of a negative exponent, means 1 divided by that same number to the power of the positive exponent.
1/(216^(-2/3)) + 1/(256^(-3/4)) + 1/(243^(-1/5))
Break it apart into three pieces.
1/(216^(-2/3))
216^(2/3) = 36
1/(256^(-3/4))
256^(3/4) = 64
1/(243^(-1/5))
243^(1/5) = 3
So...
1/(216^(-2/3)) = 36
1/(256^(-3/4)) = 64
1/(243^(-1/5)) = 3
Add the numbers gives:
36 + 64 + 3 = 103
Please answer this correctly
The right answer is 40 cm
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Reflect on the concept of function. What concepts (only the names) did you need to accommodate the concept of function in your mind? What is the simplest function you can imagine? In your day to day, is there any occurring fact that can be interpreted as a function? Is it possible to view a function? What strategy are you using to get the graph of a function?
Answer:
Step-by-step explanation:
For this kind of question you'd be better off if you'd write down and share your own answers to these conceptual questions and then ask for Brainly feedback on what you have written. You'll need to understand the concept of "function" often in algebra and beyond.
What concepts (only the names) did you need to accommodate the concept of function in your mind? input, output, rule, domain, range, mapping, variation (direct and inverse)
Simplest function: y = c (there's only one x-value and y equals that value)
In your day to day, is there any occurring fact that can be interpreted as a function? An electronic parking meter: the amount of time you can park at the meter without risking getting a ticket is dependent upon the number of quarters you insert into the meter, e. g, 15 minutes for 25 centers, 30 minutes for 50 cents, and so on.
Is it possible to view a function? Sure. Graph the function.
What strategy are you using to get the graph of a function? Set up a coordinate plane. Label the horizontal axis "x" and the vertical axis "y". Choose x (input) values that are included in the domain of the function. If the domain includes '0' you will be finding the 'y-intercept' of the function. Write the input and output as a point: (x, y). Plot that point. Choose other x values within the domain and calculate the corresponding y value for each. Plot several more points and draw a line or a curve through them. Of course there are more sophisticated strategies for graphing functions. Remember: If you're working with a function, there is never more than one output or y value for any particular input value.
A man is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet, all from different wineries. a) If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? (2 points) b) If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (4 points) c) If 6 bottles are randomly selected, what is the probability that all of them are the same variety?
Answer:
a. 336
b. 14.01%
c. 0.2%
Step-by-step explanation:
a. We have that the number of zinfandel bottles is 8 and that the number of zinfandel served is 3, therefore:
n = 8 and r = 3
we can calculate it by means of permutation:
nPr = n! / (n-r)!
replacing:
8P3 = 8! / (8-3)!
8P3 = 336
Which means there are 336 ways.
b. First we must calculate the ways to choose 2 bottles of each variety, through combinations:
nCr = n! / (r! * (n-r)!
We know that there are 8 bottles zinfandel, 10 of merlot, and 12 of cabernet, and we must choose 2 of each, therefore it would be:
8C2 * 10C2 * 12C2
8! / (2! * (8-2)! * 10! / (2! * (10-2)! * 12! / (2! * (12-2)!
28 * 45 * 66 = 83160
Now we must calculate the total number of ways, that is, choose 6 bottles of the 30 total (8 + 10 + 12)
30C6 = 30! / (6! * (30-6)! = 593775
Thus:
83160/593775 = 0.1401
In other words, the probability is 14.01%
c. In this case, we must calculate the number of ways of 8 bottles zinfandel, 10 of merlot, and 12 of cabernet choose 6, that is to say that they are all of the same variety, therefore:
8C6 + 10C6 + 12C6
8! / (6! * (8-6)! + 10! / (6! * (10-6)! + 12! / (6! * (12-6)!
28 + 210 + 924 = 1162
And that divide it by the total amount that we calculated the previous point, 30C6 = 593775
Thus:
1162/593775 = 0.002
In other words, the probability 0.2%
There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 2 9 . There are 45 marbles in total in the bag and each is equally likely to be chosen. Work out how many red marbles there must be
Answer:
10 red marbles
Step-by-step explanation:
Total= 45 marbles
Probability of red= 2/9
Number of red= 45*2/9= 10
Each roll of tape is 30.5 feet long. A box contains 454 rolls of tape. How many yards are there in total
Answer:
Answer: 4615.66667
Steps: 1 foot=0.33333
total feets=30.5×454=13847
13847 feets=46.1566667 yards
of 5 points)
2. The two figures are similar. Write the similarity statement. Justify you
37.5
(Score for Question 2:
45
Y
40
30
Z
Answer:
Answer:
f\left(x\right)=x^3-x
Step-by-step explanation:
A service club is organizing a concert to raise funds for a retirement home. The club determines that the revenue from the concert can
be represented by R(x) = 0.0027x3 - 125, where x is the number of tickets sold. The cost to put on the concert is represented by the
function C(X) = 21x + 11,305.
Which of the following functions describes the funds raised, F(x), as a function of the number of tickets sold?
FX) = 0.0027x3 - 21x - 11,430
FAX) = 0.0027x3 + 21x - 11,180
FX) = 0.0027x3 - 21x - 11,180
F(X) = 0.0027x3+
+ 21-11,430
Answer:
maybe is a
Step-by-step explanation:
Answer:
F(x) = 0.0027x^3 - 21X - 11,430
Step-by-step explanation:
Three security cameras were mounted at the corners of a triangles parking lot. Camera 1 was 110 ft from camera 2, which was 137 ft from camera 3. Cameras 1 and 3 were 158 ft apart. Which camera had to cover the greatest angle
Answer:
Camera 2nd has to cover the maximum angle, i.e. [tex]78.70^\circ[/tex].
Step-by-step explanation:
Please have a look at the triangular park represented as a triangle [tex]\triangle ABC[/tex] with sides
a = 110 ft
b = 158 ft
c = 137 ft
1st camera is located at point C, 2nd camera at point B and 3rd camera at point A respectively.
We can use law of cosines here, to find out the angles [tex]\angle A, \angle B, \angle C[/tex]
As per Law of cosine:
[tex]cos C = \dfrac{a^{2}+b^2-c^2 }{2ab}\\cos B = \dfrac{a^{2}+c^2-b^2 }{2ac}\\cos A = \dfrac{b^{2}+c^2-a^2 }{2bc}[/tex]
Putting the values of a,b and c to find out angles [tex]\angle A, \angle B, \angle C[/tex].
[tex]cos C = \dfrac{110^{2}+158^2-137^2 }{2\times 110 \times 158}\\\Rightarrow cos C = \dfrac{12100+24964-18769 }{24760}\\\Rightarrow cos C =0.526\\\Rightarrow C = 58.24^\circ[/tex]
[tex]cos B = \dfrac{110^{2}+137^2-158^2 }{2\times 110 \times 137}\\\Rightarrow cos B = \dfrac{12100+18769 -24964}{30140}\\\Rightarrow cos B = \dfrac{5905}{30140}\\\Rightarrow cos B =0.196\\\Rightarrow B = 78.70^\circ[/tex]
[tex]cos A = \dfrac{158^{2}+137^2-110^2 }{2\times 158 \times 137}\\\Rightarrow cos A = \dfrac{24964+18769-12100}{43292}\\\Rightarrow cos A = \dfrac{31633}{43292}\\\Rightarrow cos A = 0.731\\\Rightarrow A = 43.05^\circ[/tex]
Camera 2nd has to cover the maximum angle, i.e. [tex]78.70^\circ[/tex].
29.) in Mongolia the temperature can dip down to - 45°C
in January. The temperature in July may reach 40°C.
What is the temperature range in Mongolia?
Answer:
The temperature range is [tex]95^o[/tex] , going from [tex]-45^0[/tex] to [tex]40^o[/tex]
Step-by-step explanation:
The temperature range is the difference between the maximum and the minimum temperature:
[tex]40^o-(-45^o)=40^o+45^o=95^o[/tex]
The temperature range is [tex]95^o[/tex] , going from [tex]-45^0[/tex] to [tex]40^o[/tex]
Find the equations for a conical helix that has a radius of 8, a height of 12 and does exactly two complete revolutions (starting at the xy-plane). Include a plot of your conical helix.
Answer:
The equation are
[tex]x =\frac{ 12-z }{h} 8 cos (2 z)[/tex]
[tex]y = \frac{12-z }{12} 8sin (2z)[/tex]
z = z
Step-by-step explanation:
From the question we are told that
The radius of the conical helix is [tex]r= 8[/tex]
The height of the conical helix is [tex]h = 12[/tex]
The angular frequency is [tex]w = 2[/tex]
The plot of the conical helix is shown on the first uploaded image
Generally the parametric equation of a conical helix is mathematically represented as
for x -axis
[tex]x =\frac{ h-z }{h} r cos (wz)[/tex]
substituting values
[tex]x =\frac{ 12-z }{h} 8 cos (2 z)[/tex]
for y-axis
[tex]y = \frac{h-z }{h} rsin (wz)[/tex]
substituting values
[tex]y = \frac{12-z }{12} 8sin (2z)[/tex]
for z-axis
z = z
What is the area of the figure?
A figure can be broken into a rectangle and triangle. The rectangle has a base of 5 feet and height of one-third feet. The triangle has a base of 3 and two-thirds feet and height of 2 feet.
5One-third ft2
6 and two-thirds ft2
7 ft2
9 ft2
plzzzz help in a test!!! i only have 18 pts sry!!!
Answer:
5 one-third ft²
Step-by-step explanation:
rectangle=5ft (base) / 1/3ft (height)
triangle1=3ft (base) / 2ft (height)
triangle2=2/3ft (base) / 2ft (height)
area of rectangle=5x1/3
=5/3ft²
area of triangle1=3x2(1/2)
=3ft²
area of triangle2=2/3x2(1/2)
=2/3ft²
Total area=5/3+6+2/3
=16/3ft² or 5 one-third ft²
Answer:
A
Step-by-step explanation:
took the test on edg 2021
please hurry I’ll make brainiest
The number of people at a concert can be modeled by the following
equation where p is the number of people and t is the time passed in
minutes.
P = 30(1.10) + 20
Based on the model, which of the following statements is true?
Answer:
There were 30 people attending at the start of the concert
Step-by-step explanation:
The coefficient of the value raised to an exponent in these types of functions is always the "starting" value. In your case, '30' is the coefficient, so it is the starting value. FYI: 1.10 is the rate at which the people increase, t is time passed, 20 is a constant, and P is the total number of people after the time goes by.
Answer:
There were 30 people attending at the start of the concert.
Step-by-step explanation:
30 is the coefficient, so that's your starting point, basically.
1.82 /6 pls answer with rounding to the nearest cent plzzzz I'll mark the 1st answer brainlist
Answer:
.30
Step-by-step explanation:
the answer is .30333 (with the 3 repeating) and since 3 is less than 5 you leave the second number as is.
The radius of a circle is 5 cm. Find its area to the nearest tenth.
Answer:
78.5 cm^2
Step-by-step explanation:
The area of a circle is found by
A = pi r^2
A = pi (5)^2
A = 25pi
Letting pi = 3.14
A = 25(3.14)
A =78.5 cm^2
Letting pi be the pi button
A =78.53981634
Rounding to the nearest tenth
78.5
Answer:
78.5 cm²
Step-by-step explanation:
The area of a circle can be found using the following formula.
a=πr²
We know the radius of the circle is 5 centimeters.
r=5
Substitute 5 in for r.
a=π(5²)
Evaluate the exponent. 5² is equal to 5*5, which equals 25.
a=π(25)
Multiply 25 and pi
a=78.5398163397
Round to the nearest tenth. The 3 in the hundredth place tells use to leave the 5 in the tenths place as is.
a≈78.5
Add appropriate units. Area always uses units², and the units in this case are centimeters.
a≈78.5 centimeters²
The area of the circle is about 78.5 square centimeters.
NEED GEOMETRY HELP ASAP
Answer:
HJ > KP
Step-by-step explanation:
Form the figure attached,
Two triangles PKL and JGH have been given with HG ≅ KL and PL ≅ GJ
m∠HGJ = 90°
m∠KLP = 85°
Since m∠HGJ > m∠PLK
Therefore, measure of opposite sides of these angles have the same relation.
HJ > KP
PLEASE HELP!!!!!
This is edge!
A b c d
Will mark brainliest!!!!
Answer:
D. [tex] \frac{7}{12} \: of \: a \: pound[/tex]
Step-by-step explanation:
[tex]total \: candies = 2 \frac{1}{4} + \frac{2}{3} \\ \\ = \frac{9}{4} +\frac{2}{3} \\ \\ = \frac{9 \times 3 + 2 \times 4}{3 \times 4} \\ \\ = \frac{27 + 8}{12} \\ \\ = \frac{35}{12} \\ \\ share \: of \: brother = \frac{1}{5} \times \frac{35}{12} \\ \\ = \frac{7}{12} \: of \: a \: pound[/tex]
Answer:
[tex]\fbox{\begin{minipage}{10em}Option D is correct\end{minipage}}[/tex]
Step-by-step explanation:
Step 1: Let's find the total amount of candy that Loret and her sister have:
Loret has [tex]2\frac{1}{4}[/tex] pound of candy
Loret's sister has [tex]\frac{2}{3}[/tex] pound of candy
=> Total amount: [tex]A =2\frac{1}{4} + \frac{2}{3} = \frac{9}{4} + \frac{2}{3} = \frac{27}{12} + \frac{8}{12} = \frac{35}{12}[/tex] pound of candy
Step 2: Let's find the amount of candy Loret's brother could get:
If Loret's brother did the chores, he can get [tex]\frac{1}{5}[/tex] total amount of candy that Loret and her sister have.
=> The amount Loret's brother can get:
[tex]B = A*\frac{1}{5} = \frac{35}{12} * \frac{1}{5} = \frac{7}{12}[/tex] pound of candy
=> Option D is correct
Hope this helps!
:)
A bank wants to attract new customers for its credit card. The bank tries two different approaches in the marketing campaign. The first promises a cash back reward; the second promises low interest rates. A sample of 500 people is called the first brochure; of these, 100 get the credit card. A separate sample of 500 people is called the second brochure; 125 get the credit card. The bank wants to know if the two campaigns are equally attractive to customers. What is a 95% confidence interval for the difference in the two proportions
Answer:
Step-by-step explanation:
Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p= x/n
Where x = number of success
n = number of samples
For the first brochure,
x = 100
n1 = 500
p1 = 100/500 = 0.2
For the second brochure
x = 125
n2 = 500
p2 = 125/500 = 0.25
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, the z score for confidence level of 95% is 1.96
Margin of error = 1.96 × √[0.2(1 - 0.2)/500 + 0.25(1 - 0.25)/500]
= 1.96 × √0.000695
= 0.052
Confidence interval = (0.2 - 0.25) ± 0.052
= - 0.05 ± 0.052
can someone please help meee!???
Write the equation of the line shown in the graph above in slope-intercept form. Question 3 options: A) y = –2∕3x + 1 B) y = –x + 2∕3 C) 2x + 3y = 3 D) y = 2∕3x + 1
Answer:
A) y = -2/3x + 1
Step-by-step explanation:
Slope - intercept form is y = mx + b, where m is the slope and b is the y - intercept.
The line is falling from left to right, so it has a negative slope.
y = -mx + b
The line has a slope of -2/3.
y = -2/3x + b
The line has a y - intercept of 1.
y = -2/3x + 1
I hope this helps :)
A) y = -2/3x + 1, the equation of the line shown in the graph above in slope-intercept form.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
Slope - intercept form is y = mx + b,
where m is the slope and b is the y - intercept.
The line is falling from left to right, so it has a negative slope.
y = -mx + b
As, the line passes through (0,1) and (1.5,0)
The line has a slope of -2/3.
y = -2/3x + b
The line has a y - intercept of 1.
y = -2/3x + 1
hence, A) y = -2/3x + 1, the equation of the line shown in the graph above in slope-intercept form.
To learn more on Equation 0f Straight-Line click:
brainly.com/question/11116168
#SPJ2
A shopkeeper buys 1 dozen of pens at Rs 15 each and sells them at Rs 18
ch. Find his profit and profit percent.
Answer:
20%
Step-by-step explanation:
Cost price (C. P.) of each pen = ₹ 15
Selling price (S. P.) of each pen = ₹ 18
Profit = S. P. - C. P. = 18 - 15 = ₹3
[tex]profit \: percent \\ \\ = \frac{profit}{c.p.} \times 100 \\ \\ = \frac{3}{15} \times 100 \\ \\ = \frac{3}{3} \times 20 \\ \\ = 20\%[/tex]
plz answer this asap
Answer: 20
Step-by-step explanation: 5 times 4 is 20 times 2 is 40, but when you divide by 1/2 you drop down to 20.
Find the median of the following set of data: 4, 7, 2, 1, 4, 6,
2,6
Answer:
(4+4)/2 = 4
Hope this helps
Answer:
4
Step-by-step explanation:
1,2,2,4,4,6,6,7
The median is the number in the middle however there are an even amount of numbers so you get the number between 4 and 4 which is just 4
An ethologist is interested in how long it takes a certain species of water shrew to catch its prey. He only has access to a sample of 100 shrews. On multiple occasions each day he lets a dragonfly loose inside the cage of the shrews and times how long it takes until the shrews catch the dragonfly. After months of research the ethologist concludes 1) that the mean prey catching time was 30 seconds, 2) the standard deviation was 5.5 seconds and 3) that the scores he has collected are normally distributed. What is the percentage of shrews that: a) catch a dragonfly in less than 18 seconds; b) catch a dragonfly in between 22 and 45 seconds; c) take longer than 45 seconds to catch a dragonfly? d) take less than 30 seconds to catch its prey;
Answer:
a) 1.46%.
b) 92.33%.
c) 0.32%.
d) 50%
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 30, \sigma = 5.5[/tex]
a) catch a dragonfly in less than 18 seconds;
This is the pvalue of Z when X = 18. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{18 - 30}{5.5}[/tex]
[tex]Z = -2.18[/tex]
[tex]Z = -2.18[/tex] has a pvalue of 0.0146
So the percentage of shrews is 1.46%.
b) catch a dragonfly in between 22 and 45 seconds;
This is the pvalue of Z when X = 45 subtracted by the pvalue of Z when X = 22.
X = 45
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{45 - 30}{5.5}[/tex]
[tex]Z = 2.73[/tex]
[tex]Z = 2.73[/tex] has a pvalue of 0.9968
X = 22
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22 - 30}{5.5}[/tex]
[tex]Z = -1.45[/tex]
[tex]Z = -1.45[/tex] has a pvalue of 0.0735
0.9968 - 0.0735 = 0.9233
So the answer is 92.33%.
c) take longer than 45 seconds to catch a dragonfly?
From b), when X = 45, Z = 2.73 has a pvalue of 0.9968
1 - 0.9968 = 0.0032
So the answer for this item is 0.32%.
d) take less than 30 seconds to catch its prey;
This is the pvalue of Z when X = 30.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 30}{5.5}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
So the answer for d) is 50%.
