The second term of the given sequence aₙ = -5(n² + 1n) when solved gives us; a₂ = -20
How to find the nth term of a sequence?We are given the formula for a sequence as;
aₙ = -5(n² + 1n)
Where n is the position of the term.
Now, for the first term, we will have;
a₁ = -5(1² + 1(1))
a₁ = -10
The second term of the sequence is;
a₂ = -5(2² + 1(2))
a₂ = -20
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Find the 58" term of the following arithmetic sequence.
7, 15, 23, 31, …
See the file attached!!
Hope it helps:)
please help due in 15 mins
Answer:
x is -1
Step-by-step explanation:
-4 multiplied by x is -4x, then -4 x 3 is -12, which makes the problem -4x + -12 and you need to do the opposite so add 4, -4x cancels out and then add 4 to -12 which is 8x
What is the area of this figure?
Please help
Area of centre rectangle
(8+6+2)(7)(16)(7)112mm²Area of right rectangle
6(3)18mm²Area of triangle
1/2(16-12)(8)4(4)16mm²Total
16+18+112146mm²Can you guys help me please :(
Answer:
circumference formula = πd or 2πr .. they are the same thing
G is the answer
By cross multiplication find x and y if
ax + by = a² + b² and bx - ay = 0
[tex] \bold{\underline{\underline{\underbrace{Answer}}}} [/tex]
x = a and y = b
Step-by-step explanation:
To findThe value of x and y
⠀
Givenax + by = a² + b² (equation 1)
bx - ay = 0 (equation 2)
⠀
Solution{Taking equation 2}
[tex] \sf bx - ay = 0 [/tex]
{Taking ay on RHS}
[tex] \sf bx = ay[/tex]
{Dividing both sides by a}
[tex] \sf \frac{bx}{a} = y(equation \: 3)[/tex]
{Now substituting the equation 3 in equation 1}
[tex] \sf ax + b( \frac{bx}{a} ) = {a}^{2} + {b}^{2} \\ \\ \sf ax + \frac{ {b}^{2} x}{a} = {a}^{2} + {b}^{2} [/tex]
{Taking LCM on LHS}
[tex] \sf \frac{ {a}^{2}x + {b}^{2} x }{a} = {a}^{2} + {b}^{2} \\ \\ \sf \frac{x( {a}^{2} + {b}^{2}) }{a} = ( {a}^{2} + {b}^{2} )[/tex]
{Dividing by (a² + b²) both sides}
[tex] \sf \frac{x}{a} = 1 \\ \\ \green{\boxed {\tt{x = a} } }[/tex]
{Now substituting the value of x in equation 3}
[tex] \sf \frac{ba}{a} = y \\ \\ \green {\boxed{ \tt{y = b}} }[/tex]
The Hiking Club plans to go camping in a State park where the probability of rain on
any given day is 0.68. What is the probability that it will rain on at least three of the
five days they are there? Round your answer to the nearest thousandth.
Answer:
0.3386 = 0.339 (rounded).
Step-by-step explanation:
It is the binomial type probability distribution.
The number of trial n= 3; the probability of the success trial is 0.16, and the number of success trial k = 1.
It costs $10 to enter a theme park and $2 for each ticket, t. Which equation represents the total cost, c, of going to the theme park?
Let $a_1, a_2, a_3, \dots$ be a non-constant arithmetic sequence. Suppose that $a_4, a_7, a_{12}$ form a geometric sequence. If $a_7 = 30$, what is $a_1$?
The terms a1, a2 and a3 do not have a common difference, and the value of a1 in the geometric sequence is 10/9
How to determine the value of the first term?The arithmetic sequence is given as:
a₁, a₂ and a₃
The geometric sequence is given as:
a₄, a₇ and a₁₂
The common ratio of a geometric sequence is:
[tex]r = \frac{T_2}{T_1}[/tex]
So,we have:
[tex]\frac{a_7}{a_4} = \frac{a_{12}}{a_7}[/tex]
Cross multiply
[tex]a_{12} * a_4 = a_7 * a_7[/tex]
Given that a7 = 30, the equation becomes
[tex]a_{12} * a_4 = 30 * 30[/tex]
Evaluate the product
[tex]a_{12} * a_4 = 900[/tex]
Rewrite as:
[tex]a_{4} * a_{12} = 900[/tex]
Express 900 as 10 * 90
[tex]a_{4} * a_{12} = 10 * 90[/tex]
By comparison, we have:
a₄ = 10 and a₁₂ = 90
This means that the geometric sequence is:
10, 30, 90 ---- it has a common ratio of 3
The nth term of a geometric sequence is:
[tex]a_n = ar^{n-1}[/tex]
So, we have:
[tex]a_7 = ar^6[/tex]
[tex]a_4 = ar^3[/tex]
Substitute values for a7 and 14
[tex]ar^6 = 30[/tex]
[tex]ar^4 = 10[/tex]
Divide both equations
[tex]r^2 = 3[/tex]
Take the cube of both sides
[tex]r^6 = 27[/tex]
Substitute [tex]r^6 = 27[/tex] in [tex]ar^6 = 30[/tex]
[tex]a * 27 = 30[/tex]
Divide both sides by 27
[tex]a = \frac{10}{9}[/tex]
Hence, the value of a1 in the geometric sequence is 10/9
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Find the surface area
Answer:
should be 1305 yd^2
Step-by-step explanation:
to get the surface area of one of the 3 recanglular sides take 24 x 15 to get 360 then muliply by 3 to get 1080 since all the recanglular sides are the same then do 15 x 15 to get both of the triangle sides to get 225 since the equation is 1/2 B x H then add them together
PLEASE HELP IM SO STUCK ON THIS!!!!!
Based on the number of ways to answer the multiple choice questions and the number of ways to answer true or false, the number of ways to answer the test is 8,192 ways.
How many ways can the test be answered?This can be found as:
= Total number of ways to answer multiple choice questions + Total ways to answer true or false questions
Solving gives:
= (4 x 4 x 4) x (2 x2 x2 x 2 x 2 x 2 x 2)
= 64 x 128
= 8,192 ways
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What is the surface area of this right prism?
Enter your answer in the box.
cm²
NEED HELP ASAP!!! 20 POINTS!!!!
Answer:
Since the 'base' and 'top' of any prism have the same shape, the surface area can be found by
surface area of prism = 2 * area of base + perimeter of base * H
So for the rectangular prism in your example..
surface area = 2LW + 2(L+W)H
= 2 * 7 * 4 + 2*(7+4)*5
= 56 + 2 * 11 * 5
= 56 +110
= 166 sq cm
Hope this helps
What set of transformations could be applied to rectangle ABCD to create A″B″C″D″?
A composite transformation is the production of the image of a figure through two or more transformation
The set of transformations that could be applied to rectangle ABCD to create rectangle A'B'C'D' is the second option;
Reflected over the y-axis and rotated 180°The reason the above selected option is correct is as follows:
Known parameters:
The given coordinates of the vertices of the preimage of the rectangle ABCD are; A(-4, 2), B(-4, 1), C(-1, 1), and D(-1, 2)
The given coordinates of the vertices of the image of the rectangle ABCD, which is rectangle A'B'C'D' are; A'(-4, -2), B'(-4, -1), C'(-1, -1), and D'(-1, -2)
Solution:
The form of the ordered pair of the vertices of the pre-image is negative value for x, positive value for y, which can be written as (-x, y), where x, and y, are positive numbers
The form of the ordered pair of the vertices of the image is (-x, -y)
The location of a point (-x, y) following a reflection over the y-axis is the point (x, y)
The location of a point (x, y) following a 180° rotation is the point (-x, -y)
Therefore, the set of transformations that can be applied to (-x, y), to create (-x, -y), is a reflection over the y-axis, followed by a rotation of 180
Which gives;
The set of transformations that transforms A(-4, 2) to create A'(-4, -2), B(-4, 1), to create B'(-4, -1), C(-1, 1), to create C'(-1, 1), and D(-1, 2), to create D'(-1, -2) is a reflection over the y-axis followed by a rotation of 180°.Therefore, the correct option is; Reflected over the y-axis and rotated 180°
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Answer: B is your correct answer!
Step-by-step explanation:
Reason abstractly. A square has vertices at (3,8),(3,2),(9,8), and (9,2). Determine the area.
Answer:
The area is 9 units^2
Step-by-step explanation:
Let X and Y be the following sets:
X = {5, 6, 10, 12, 15, 18}
Y = {6, 10, 12, 15)
Which of the following is the set X UY?
Answer:
i think the answer is X, because the elements of both X and Y are in X
What is the volume of a cylinder, in cubic centimeters, with a height of 7 centimeters and a base diameter of 18 centimeters? Round to the nearest tenths place
Answer:
the answer is 126 cm
sana makatulong
A sequence has a common second difference of 4 between terms. The first two terms are 3 and 12. Write down the 3rd and 4th terms.
The first two terms of the sequence are 3 and 12 and the 3rd and 4th terms are 25 and 42.
3rd and 4th terms from second level differenceThe 3rd and 4th terms of the sequence is determined from second level difference as shown below;
let the first term = asecond term = bthird term = cfourth term = d(c - b) - (b - a) = 4 ----(1)
(d - c) - (c - b) = 4 ---- (2)
from (1);
(c - 12) - (12 - 3) = 4
(c - 12) - (9) = 4
c - 21 = 4
c = 25
from (2);
(d - 25) - (25 - 12) = 4
d - 38 = 4
d = 42
The sequence = 3, 12, 25, 42
check
first difference = (12 - 3), (25-12), (42-25) = 9, 13, 17
second difference = (13 - 9), (17 - 13) = 4, 4
Thus, the first two terms of the sequence are 3 and 12 and the 3rd and 4th terms are 25 and 42.
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Which of the following function pairs are inverses?
Answer:
The answer is D.
Step-by-step explanation:
f(x) = 5x -3
y = 5x - 3
Switch y and x to find the inverse
x = 5y - 3
Solve for y.
x + 3 = 5y
y = (x+3)/5
g(x) = (x+3)/5
What number is 25% of 168?
Answer:
42
Step-by-step explanation:
You turn the percentage into a decimal, 25%=0.25
then you multiply 0.25 to 168
Then you get 42
0.25 x 168 = 42
Hope this helps <3
HELp!!! 100 POINTS.
What is the formula of g in terms of f?
Answer: C
Step-by-step explanation: bcuz
Answer:
[tex]\textsf{A)} \quad f\left(-\dfrac{1}{2}x\right)[/tex]
Step-by-step explanation:
From observation of the given graph, function f has been reflected across the y-axis.
When a graph is reflected across the y-axis, the y-coordinate stays the same while the x-coordinate is negated.
Therefore, replace y = f(x) with y = f(-x), so:
[tex]\implies g(x) = f(-x)[/tex]
It appears that the graph has also been stretched parallel to the x-axis.
When a graph is stretched parallel to the x-axis the x is multiplied by a constant. If the constant is greater than 1, the graph is compressed. If the constant is greater than zero and less than 1, the graph is stretched.
As the graph has been stretched, the constant is 0 < c < 1, so:
[tex]\implies g(x)=f\left(-\dfrac{1}{2}x\right)[/tex]
A square pyramid with a side length of 5 cm and a slant height 7 cm has a total surface area of ... square centimeter
20
165
95
25
70
Answer:
95
Step-by-step explanation:
Surface Area :
⇒ Area (4 triangle faces) + Area (square base)
⇒ 4 x 1/2 x 5 x 7 + (5)²
⇒ 2 x 35 + 25
⇒ 70 + 25
⇒ 95 square centimeters
(b) A square has a perimeter of 80 ft. What is the length of each side?
Answer:
20 ft
Step-by-step explanation:
There are 4 equal sides to a square so one side is 80/4 = 20 ft
Is anyone here like rlly good at algebra bc im not and I kinda forgot What my teacher told me so-
(b + 516= 1000)
I have no clue what to do so-….
Answer:
The question is asking you to subtract 516 from 1,000 to find b.
[tex]1,000 - 516 = 484[/tex]
Therefore, b = 484
Solve this
4 ∙ 7 1/2 ∙ 1 3/5
Step-by-step explanation:
[tex] = 7 \frac{1}{2} .1 \frac{3}{5} [/tex]
[tex] = \frac{ \red{\cancel{15}}}{ \blue{ \cancel{2}}} . \frac{ \blue{\cancel{8}}}{ \red{\cancel{5}}} [/tex]
[tex] = \frac{3}{1} . \frac{4}{1} [/tex]
[tex] = 12[/tex]
[tex] \: [/tex]
Help please
worth 14 points
Answer:
Ok I can walk you through if you comment the questions ok?
Step-by-step explanation:
Trust me :-)
Answer:
1. obtuse
2.straight
3.right
4. acute
5. <EAF
6. <DAF
7. <BAF
8. They are perpendicular to each other
PLEASE HELP SOLVE GEOMETRY PLEASE HELP SOLVE
help me this is very hard
Answer:
B. 60
Step-by-step explanation:
1. take the square root of 64
2. multiply 8*10 and 5*4
3. subtract
Square root of 64 is 8 so,
10*8 - 5*4
80 - 20 =
60
A researcher wanted to see if different breeds of dogs preferred toys of certain colors. The researcher presented each dog with 3 toys, identical except that each was a different color, and recorded which toy the dog played with the most in a set time period. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts):
The value for the test statistic and the p value on the test when the researcher wanted to see if different breeds of dogs will be x² = 0.9421 and 0.05 < p value < 0.10.
How to illustrate the research?From the information given, the null hypothesis is that the variables have no difference while the alternative hypothesis is that they have a difference.
The degree of freedom will be:
= (3 - 1) × (3 - 1)
= 4
The critical value is 9.4877. In this case, the p value is greater than the significance level. Therefore, we fail to reject the null hypothesis.
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Answer:
Step-by-step explanation:
From Khan
Malachy rolls a fair dice 168 times.
How many times would Malachy expect to roll a number greater than 5?
Answer:
28 times
Step-by-step explanation:
On a fair die, the probability of rolling a 6, the only number greater than 5, is 1/6. So in 168 rolls of this die, Malachy can expect a 6 on 1/6 × 168, or 28 times.
A bag contains 8 black marbles, 16 white marbles, 14 red marbles, and 10 green marbles. A marble is drawn at random from the bag. What is the probability that the marble drawn will not be white? 1/3. 2/3. 3/4. 15/16
Answer:
2/3
Step-by-step explanation:
total marbles is (8 black+ 16 white + 14 red +10 green) = 48
no white cmarbles ( 8+14+10) = 32
32/ 48 = 2/3
32/16= 248/16 =3I need help with this problem, Iceman drove at an average speed of 50 mi/h from her home in Seattle to visit her sister in St. Louis. She stayed in St. Louis for 15 hours, and on the trip back averaged 35 mi/h. She returned home 42 hours after leaving. How many miles is Seattle from St. Louis?
To solve this problem, we have to figure out the time spent travelling and then use the speed-distance-time equation to find the distance between the two places. The distance between Seattle and St. Louis is 2295 miles.
How many miles is Seattle from St. LouisTo calculate the miles or distance between Seattle and St. Louis, we have to take into consideration that out of the 42 hours she spent in her journey, she stayed 15 hours over at St. Louis.
[tex]42 - 15 = 27[/tex]
She spent 27 hours travelling.
Her speed in the first journey was 50mi/h and her speed in the second journey was 35mi/h.
This implies she was faster in her first journey compared to her second journey.
Data;
time = 27 hoursspeed = 85mi/h[tex]speed = \frac{distance}{time} \\distance = speed * time[/tex]
Let's substitute the values
[tex]distance = (50 + 35) * 27 = 2295mi[/tex]
The distance between Seattle and St. Louis is 2295 miles
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