Answers
A) 4n² - 3n
Related Questions
Anyone help please!!!!
Answers
cos(α-B)-cos(α+B) = 2 sinα sinβ
Left hand side = cos(α - B)-cos(α + B)
= cosα cosβ + sinα sinB - (cosα cosB - sinα sinβ)
= cosα cosβ + sinα sinB - cosα cosB + sinα sinβ)
= sinα sinβ + sinα sinβ
= 2 sinα sinβ
= Right Hand side
cos(a-B)-cos(a+B)
cosucosv - sinusinv = cos(u+v)
cosucosv + sinusinv = cos(u-v)
cos(a-B)-cos(a+ B) = cosa cosB + sina sinB - (cosa cosB - sina sinB)= cosa cosB + sina sinB - cosacosB + sinb sinB= 2 sina sinB
please verify my probability answer!!!
Answers
The probability that the second student likes to play baseball:[tex]P(B)=\dfrac{15}{24}=\dfrac{5}{8}[/tex]
Together:
[tex]P(A)\cdot P(B)=\dfrac{2}{5}\cdot\dfrac{5}{8}=\dfrac{1}{4}[/tex]
Answer:
1/4
Step-by-step explanation:
Hope this helped :)
WILL GIVE BRAINLIEST IF YOU HAVE THE REST OF THE ANSWERS
Answers
I completed this a few months ago but don't remember the rest of the answers. Message me and I'll be able to find them for you, but anyway, I'm positive the answer is A.
Proof:
A=(123-55)/2=34
In which type of quadrilateral are consecutive sides congruent?
Select the best answer from the choices provided.
trapezoid
parallelogram
square
rectangle
Answers
Final answer:
A square is the quadrilateral with congruent consecutive sides. It is an equilateral rectangle and a special type of parallelogram with equal-length sides and right angles.
Explanation:
The type of quadrilateral in which consecutive sides are congruent is a square. A square is a special type of parallelogram where all sides are equal in length and all angles are right angles. When considering a square as a rectangle (which technically it is), its diagonals (which are equal in length) bisect one another at right angles, suggesting the property of being an equilateral rectangle. Furthermore, in a larger context, if we treat the sides of any parallelogram symmetrically, such as in a notation [PQRS], the order can change to [QRSP], [QPSR], and [PRQS] without affecting its properties, which aligns with the symmetric nature of a square's sides.
What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 18 cm?
a. 5,832 cm
b. 2,916 cm
c. 1,944 cm
d. 972 cm
Find the volume of the cylinder in terms of Pie. The diagrams are not drawn to scale.
a. 52.8 m
b. 58.08 m
c.127.78 m
d. 29.04 m
Answers
we know that
[volume of a square pyramid]=(1/3)*b²*h
where
b is the length side of the square base-----> 18 cm (is equal to the length side of cube)
h is the height---------> 18 cm (is equal to the length side of cube)
[volume of a square pyramid]=(1/3)*18²*18----> 1944 cm³
the answer Part 1) is
c. 1,944 cm³
Part 2) Find the volume of the cylinder in terms of Pie. The diagrams are not drawn to scale.
volume of a cylinder=pi*r²*h
for r=2.2 m
h=12 m
volume of a cylinder=pi*2.2²*12-----> volume=58.08*pi m³
the answer Part 2) is
58.08*pi m³
Which box plot represents the data?
30, 35, 25, 5, 5, 25, 40, 45, 50, 10, 15, 40
Answers
1. In an auditorium, there are 21 seats in the first row and 26 seats in the second row. The number of seats in a row continues to increase by 5 with each additional row.
(a) Write an iterative (explicit) rule to model the sequence formed by the number of seats in each row. Show your work.
(b) Use the rule to determine how many seats are in row 15. Show your work.
2. Rhonda started a business. Her business made $40,000 in profits the first year. Her annual profits have increased by an average of 6% each year since then.
(a) Write an iterative rule to model the sequence formed by the profits of Rhonda’s business each year.
(b) Use the rule to determine what the annual profits of Rhonda’s business can be predicted to be 20 years from the start of her business. Round your answer to the nearest dollar. Do not round until the end. Show your work.
3. The sequence 3, 12, 48, 192, … shows the number of pushups Kendall did each week, starting with her first week of exercising.
(a) What is the recursive rule for the sequence?
(b) What is the iterative rule for the sequence?
Answers
[tex]s_n=s_{n-1}+5[/tex]
Since [tex]s_1=21[/tex], we have
[tex]s_2=s_1+5[/tex]
[tex]s_3=s_2+5=s_1+2\cdot5[/tex]
[tex]s_4=s_3+5=s_1+3\cdot5[/tex]
[tex]\cdots[/tex]
[tex]s_n=s_{n-1}+5=\cdots=s_1+(n-1)\cdot5[/tex]
So the explicit rule for the sequence [tex]s_n[/tex] is
[tex]s_n=21+5(n-1)\implies s_n=5n+16[/tex]
In the 15th row, the number of seats is
[tex]s_{15}=5(15)+16=91[/tex]
2. Let [tex]p_n[/tex] be the amount of profit in the [tex]n[/tex]-th year. If the profits increase by 6% each year, we would have
[tex]p_2=p_1+0.06p_1=1.06p_1[/tex]
[tex]p_3=1.06p_2=1.06^2p_1[/tex]
[tex]p_4=1.06p_3=1.06^3p_1[/tex]
[tex]\cdots[/tex]
[tex]p_n=1.06p_{n-1}=\cdots=1.06^{n-1}p_1[/tex]
with [tex]p_1=40,000[/tex].
The second part of the question is somewhat vague - are we supposed to find the profits in the 20th year alone? the total profits in the first 20 years? I'll assume the first case, in which we would have a profit of
[tex]p_{20}=1.06^{19}\cdot40,000\approx121,024[/tex]
3. Now let [tex]p_n[/tex] denote the number of pushups done in the [tex]n[/tex]-th week. Since [tex]3\cdot4=12[/tex], [tex]12\cdot4=48[/tex], and [tex]48\cdot4=192[/tex], it looks like we can expect the number of pushups to quadruple per week. So,
[tex]p_n=4p_{n-1}[/tex]
starting with [tex]p_1=3[/tex].
We can apply the same reason as in (2) to find the explicit rule for the sequence, which you'd find to be
[tex]p_n=4^{n-1}p_1\implies p_n=4^{n-1}\cdot3[/tex]
Answer:
i will look but i think she was right
Step-by-step explanation:
At a particular music store, CDs are on sale at $14.00 for the first one purchased and $12.00 for each additional disc purchased. Maria spends $86.00 on CDs. How many CDs has Maria purchased?
Answers
So:
$ 86- $ 14 = 72
The rest of the CDs cost $ 12.
Then we divide $ 72 between $ 12
$ 72 / $ 12 = 6.
That means that 6 CDs were bought at $ 12 plus the first one bought at $ 14.
So the number of CDs that María bought was 7
Answer: 7
Step-by-step explanation:
Solve for x: 12(x-7)+3(2x+2)=50x-62
Answers
Hope this helps
This is because
12 (-1/2 - 7) + 3 (2 x -1/2 + 2) = 50x - 62
12 x -7.5 + 3 x 1 = -25 - 62
-87 = -87
The equation of the line through ab *write your answer in slope-intercept form
Answers
But we can assume that A:(a,b) and B:(c,d), find the slope and then write the equation of the line thru points A and B:
d - b
m = -----------
c - a
d - b
then the equation of the line is y-d = ----------- (x-c)
c - a
Please ensure that you are sharing all of the info given (e. g., the coordinates of the points A and B).
What does a residual value of 1.3 mean when referring to the line of best fit of data set?
-a data point is 1.3 units above the line of best fit
-a data point is 1.3 units below the line of best fit
-the line of best fit has a slope of -1.3
-the line of best fit has a slope of 1.3
Answers
A residual value of 1.3, when referring to the line of best fit of a data set, means that,
⇒ a data point is 1.3 units above the line of best fit.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
To find a residual value of 1.3 mean when referring to the line of best fit of data set.
Since, A residual is defined as the difference between the observed value of a dependent variable and the predicted value of that variable using the regression equation.
Hence, In this case, the residual value of 1.3 indicates that the observed value of the dependent variable is 1.3 units above the predicted value, or the line of best fit.
Thus,
A residual value of 1.3, when referring to the line of best fit of a data set, means that,
⇒ a data point is 1.3 units above the line of best fit.
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Solve the problem. 13) from the edge of a 1000-foot cliff, the angles of depression to two cars in the valley below are 21° and 28°. how far apart are the cars? round your answers to the nearest 0.1 ft.
Answers
The problem is about finding the distance between the cars using the angles of depression and the height of the cliff. Calculate individual horizontal distances first and then find their difference which gives us the distance between the cars.
Explanation:This problem can be solved using trigonometry. We've a 1000-foot cliff and a valley below where the two cars are located. From the edge of the cliff, if we draw two lines of sight to the cars, we can get two right triangles. The angles of depression to the cars are 21° and 28°, which are the angles between these lines of sight and a horizontal line.
We can use the tangent of these angles, which is the ratio of the opposite side (the vertical distance from the cliff to the cars) and the adjacent side (the horizontal distance from the cliff baseline to the cars). We know the vertical distance - it's 1000 ft (height of the cliff). So, we can calculate the horizontal distances (D1 and D2) to the cars as D1 = 1000/tan(21°) and D2 = 1000/tan(28°) respectively.
The difference between D1 and D2 will give the distance between the cars.
The calculations might give the distance in decimals, and the problem asks to round the answer to the nearest 0.1 ft.
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GIVING AWAY 50 POINTS TO WHOEVER SHOWS LEGIT WORK!
The lengths of the sides of three squares are s, s + 1, and s + 2. If their total area is 365 cm squared (^2), find their total perimeter.
Answers
S+1 = one length square 2
S+2= one length square 3
Our equation would be
S^2+(S+1)^2+(S+2)^2=365
Idk if it would be called distribute but.. distribute
S^2+S^2+2S+1+S^2+4S+4=365
Add like terms
3S^2+6S-360=0
Divide everything. By 3
S^2+2S-120=0
Factor
(S-10)(S+12)=0
The two solutions are:
S-10=0
S=10
S+12=0
S=-12
Since a length can’t be a negative the only possible solution would be 10
Since a perimeter is all lengths added together we can multiply the length by four to get the perimeter
Square 1
10*4=40
Perimeter is 40cm
Square 2
S+1 =11
11*4=44
Perimeter is 44cm
Square 3
S+2=12
12*4=48
Perimeter is 48cm
Add all the perimeters together to get the total perimeter:
Total perimeter:
40+44+48=132
The total perimeter is 132cm
I hope this helps. Sorry if I messed up anything on here it was kinda hard to keep track of everything. Feel free to ask if you need anything cleared up :)
What is the area of a square
Answers
For example, if a square's length is 4cm, then you can assume the width is going to be 4cm. Finding area, you multiply 4 and 4 to get 16, and the unit of measurement (cm) and square it (^2). Thus meaning this answer would be 16cm^2.
I hope this helps!
two angles are drawn below. the measure of angle x is 90
a. 20
b. 60
c. 100
d. 120
Answers
So the answer is B) 60
Beacuse that that is an acute angle and acute is less then 90
In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population fall below 1,200,000?
a. 2024
b. 2027
c. 2036
d. 2049
Answers
Rate of decrease, R = 1.1% = 0.011
Applicable formula
P(n) = P(o) *(1-R)^n
Where P(n) = population after n years, n = Number of years
From information given,
1,200,000 = 1,405,233 (1-0.011)^6
1,200,000/1,405,233 = (0.989)^n
0.85395 = (0.989)^n
ln (0.85395) = n ln (0.898)
n = [ln (0.85395)]/[ln (0.989)] = 14.27 years ≈ 14 years
Year in which population will fall below 1,200,000 = 2010+14 = 2024
Then, the correct answer is a.
Answer:
2024
Step-by-step explanation:
took the test
Is 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a number?
Answers
A lucky integer is a positive integer which is divisible by the sum of its digits. what is the least positive multiple of 9 that is not a lucky integer?
Answers
It is not divisible by 18. Before that they are all added up to 9.
Bricklayers use the formula N = 7LH to estimate the number of bricks N needed to build a wall of height H and length L. What is the height of a wall that is 30 feet long and that requires 2,310 bricks to build? a. 12 ft c. 11 ft b. 10 ft d. 20 ft
Answers
dy/dx = y/x^2
dy/y = dx/x^2
ln y * ln c = -1/x
cy = e^(-1/x)
y = ce^(-1/x)
Answers
dy/y = dx/(x^2)
int[dy/y] = int[dx/(x^2)] ... apply integral to both sides
ln(|y|) = (-1/x) + C
|y| = e^{(-1/x) + C}
|y| = e^C*e^(-1/x)
|y| = C*e^(-1/x)
y = C*e^(-1/x)
So you have the correct answer. Nice job.
------------------------------------------------
Check:
y = C*e^(-1/x)
dy/dx = d/dx[C*e^(-1/x)]
dy/dx = d/dx[-1/x]*C*e^(-1/x)
dy/dx = (1/(x^2))*C*e^(-1/x)
is the expression for the left hand side (LHS)
y/(x^2) = [C*e^(-1/x)]/(x^2)
y/(x^2) = (1/(x^2))*C*e^(-1/x)
is the expression for the right hand side (RHS)
Since LHS = RHS, this confirms the solution for dy/dx = y/(x^2)
A bag contains 3 red, 4 black and 2 white balls. what is the probability of drawing a red ball and then a white ball, if each ball is returned to the bag immediately after it is drawn? 2/27 1/9 1/3 4/27 2/9
Answers
red ball = 3
white ball = 2
P(red, then white) = (3/9)(2/9) = 6/81 = 2/27
Answer: 2/27
Explain how the difference of a fraction or a rational number and its additive inverse is equal to zero.
Answers
Hope This Helped =3
Bricklayers use the formula N = 7LH to estimate the number of bricks N needed to build a wall of height H and length L. What is the height of a wall that is 30 feet long and that requires 2,310 bricks to build? a. 12 ft c. 11 ft b. 10 ft d. 20 ft
Answers
N = 7LH
Clearing H we have:
H = N / (7L)
Substituting the values we have:
H = 2310 / (7 (30))
Rewriting we have:
H = 2310/210
H = 11 feet
Answer:
the height of a wall that is 30 feet long and that requires 2,310 bricks to build is:
c. 11 ft
) a pair of fair dice is rolled. what is the probability that the sum of the top faces is a number 10 or greater?
Answers
the probability is 16.7%
Hope this helps.
WILL GIVE BRAINLIEST... HELP ASAP!!!!!!
1. Circle A with center at (3, 4) and radius 2 is similar to circle B with center at (−4, −5) and radius 3. Below is an incorrect informal argument for proving two circles are similar:
Step 1 Translate circle B to the right 9 units and up 7 units to form concentric circles.
Step 2 Dilate circle B to be congruent to circle A using scale factor of k = r sub two over r sub one equals two over three
Step 3 When an object is dilated, the dilated object is similar to the pre-image, thus the two circles are similar.
What is the first incorrect step, and how can it be fixed?
A. All steps are correct
B. Step 1, translate circle B to the right 7 units and up 9 units
C. Step 2, use scale factor of K= r^2/r^1=3/2
D. Step 3, replace dilated with translated.
An image of two concentric circles is shown with r2 = 8 and r1 = 3:
2. Image shows a pair of concentric circles. The radius of the smaller circle is r sub 1 and the radius of the second is r sub 2.
In order to prove the two circles are similar, the radius r1 was increased to make the circles congruent. What is the scale factor used in the above image?
A. k=8/3
B. K=3/8
C. K=1/5
D. K=5
Answers
First one is B. Because if you're moving from -4 to 3 you don't move 9 units right instead you move 7.
The sum of the squares of two consecutive positive even integers is 100. find the two integers
Answers
6^2= 36
8^2=64
36+64=100
Let's denote the two consecutive positive even integers as x and x+2.
We know their squares sum up to 100, represented mathematically as:
x^2 + (x + 2)^2 = 100.
Expanding this equation, we get:
x^2 + x^2 + 4x + 4 = 100.
Combining like terms gives us:
2x^2 + 4x - 96 = 0.
This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 2, b = 4, and c = -96.
We can solve this quadratic equation for x using the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / 2a.
Substituting a, b, and c into this formula, we find that:
x = [-4 ± sqrt((4)^2 - 4*2*-96)] / 2*2,
x = [-4 ± sqrt(16 + 768)] / 4,
x = [-4 ± sqrt(784)] / 4,
x = [-4 ± 28] / 4.
So the solutions are x = (28 - 4) / 4 = 6 and x = (-28 - 4) / 4 = -8.
Since we are looking for positive even integers, we discard the negative solution.
Therefore, the two consecutive positive even integers are 6 and 6 + 2 = 8.
A card is drawn from a standard deck of cards. Determine whether the events are mutually exclusive or inclusive. Then, find the probability.
P(a red card or a queen)
a.
inclusive, 15/26
c.
inclusive, 7/13
b.
mutually exclusive, 15/26
d.
mutually exclusive, 7/13
Answers
The two events are inclusive because they can both happen at the same time.
This means we find the probability using
P(A or B) = P(A) + P(B) - P(A and B)
P(r or Q) = P(r) + P(Q) - P(r and Q)
There are 26 red cards out of 52 cards.
There are 4 queens out of 52 cards.
There are 2 red queens out of 52.
26/52+4/52-2/52 = 28/52 = 7/13
The events are mutually inclusive and the required probability is p(getting a red or a queen) is 28/52 = 7/13
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here A card is drawn from a standard deck of cards. Now There are some events that can impact each other or that are overlapping. They have one or more outcomes in common. When events have outcomes in common, they are said to be overlapping events, also known as mutually inclusive events. Thus this event is defenitely inclusive.
Now the probability that a red card or a queen is =( 26 red cards + 2 black queens ) /52
= 28/52
=7/13
Hence, The events are mutually inclusive and the required probability is p(getting a red or a queen) is 28/52 = 7/13
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12 POINTS
Simplify i38.
i
−1
−i
1
Answers
Note that i^38 = i^32 * I^4 * I^2.
Note that i^0, i^4, i^8, etc., all equal 1. Therefore,
i^38 = (1)(1)i^2 = 1*(-1) = -1 (answer)
Answer:
-1
Step-by-step explanation:
I got this correct on my quiz
i^38 = -1
Which of the following is not needed when making a box plot?
A - Mean
B - Minimum
C - Median
D - Third Quartile
Answers
I hoped this helped!
You use the median as the center of the boxplot. The first and third quartiles (Q1 and Q3) make up the left and right edges of the box. The min and max are the furthest points on the left and right side of each whisker. The mean is not used at all. With outliers, the mean is skewed. If you have any outliers then its best to use the median instead.
How many terms are in the arithmetic sequence 6, 2, −2, …, −102?
Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference
27
28
29
30
Answers
6, 2, −2, …, −102
will evaluated as follows:
the explicit formula is:
an=a1+d(n-1)
a1=first term
d=common difference
n=number of terms
thus from the question:
a1=6
d=2-6=-4
an=-102
plugging the values in the expression we get:
-102=6-4(n-1)
solving for n we shall have:
-102-6=-4(n-1)
-108=-4(n-1)
27=n-1
thus
n=27+1
n=28
Answer: 28 terms
Final answer:
Calculate the number of terms in the arithmetic sequence 6, 2, -2, ..., -102 using the provided formula to find it is 28.
Explanation:
In mathematics, an Arithmetic Progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference, denoted by d.
Arithmetic sequence: 6, 2, -2, ..., -102
Formula: an = a1 + d(n - 1)
Identify a1 = 6 and an = -102Calculate d = an - a1 = -102 - 6 = -108Substitute the values into the formula and solve for n to find the number of termsTherefore, the number of terms in the arithmetic sequence is 28.