What is the 8th term of the geometric sequence with a1=2 and r=-3.
Please asap last question
Answer:
-4374
Step-by-step explanation:
Given :
a1 = 2 ; r = - 3
The nth term of a geometric series :
A(n) = ar^(n-1)
The 8th term :
A(8) = 2(-3)^(8-1)
A(8) = 2(-3^7)
A(8) = 2(−2187)
A(8) = - 4374
(05.06 MC)
Choose the function to match the graph.
-6
5
3
3
2.
1
-2
0
2.
3
4
5
6
-1
-21
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Answer:
(b) f(x) = log(x) +4
Step-by-step explanation:
The x-intercept of any log function is (1, 0). The graph here has been shifted 4 units up from that, so is a graph of ...
f(x) = log(x) +4
The sample space listing the eight simple events that are possible when a couple has three children is {bbb, bbg, bgb, bgg, gbb,
gbg, ggb, 999). After identifying the sample space for a couple having four children, find the probability of getting one girl and three
boys in any order).
Identify the sample space for a couple having four children.
(Use a comma to separate answers as needed.)
Enter your answer in the answer box and then click
Answer:
bbbb,
bbbg, bbgb, bgbb, gbbb,
bbgg, bgbg, bggb, gbgb, gbbg, ggbb,
bggg, gbgg, ggbg, gggb,
gggg
Step-by-step explanation:
3 children: bbb, bbg, bgb, gbb, bgg, gbg, ggb, ggg
4 children: bbbb, bbbg, bbgb, bgbb, gbbb, bbgg, bgbg, bggb, gbgb, ggbb, bggg, gbgg, ggbg, gggb, gggg
You need to take a methodological approach;
The 2 easiest are the possibility of all boys and all girls;
Then consider 3 boys and 1 girl:
bbbg, bbgb, bgbb, gbbb
Then 2 boys and 2 girls:
bbgg, bgbg, bggb, gbgb, gbbg, ggbb
Lastly, 1 boy and 3 girls:
bggg, gbgg, ggbg, gggb
In total, there are 16 possibilities
P.S. interesting to note is that the number of possibilities here follows the pattern of Pascal's triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
The last row is relevant here;
There is 1 possibility where there are 4 boys;
There are 4 possibilities (in terms of the order of birth) where there are 3 boys and 1 girl;
There are 6 possibilities where there are 2 boys and 2 girls
There are 4 possibilities where there is 1 boy and 3 girls;
There is 1 possibility where there are 4 girls;
The pattern ∴ is 1 4 6 4 1, as the 5th row of Pascal's triangle reads;
If your talking about 3 children, it would match the 4th row of Pascal's triangle;
So, 1 possibility of 3 boys;
3 possibilities of 2 boys and 1 girl;
3 possibilities of 1 boy and 2 girls;
And 1 possibility of 3 girls;
If your talking about 10 children, it would match the 11th row of Pascal's triangle.
(Maths can be so cool XD)
What's the inverse of ƒ(x) = x2 – 16?
the inverse of ƒ(x) = x²– 16
[tex] {f}^{ - 1} (x) = \sqrt{x + 16} [/tex]
Answer:
The inverse function should be f
[tex] {f}^{ - 1}( x) = \sqrt{x + 16} [/tex]
this is the correct answer
Solve the inequality.
|6p+3|>15
A p<2 or p>−3
B p>−2 or p<3
C p<−2 or p>3
D p>2 or p<−3
Step-by-step explanation:
|6p + 3| > 15
6p = 15 - 3
6p = 12
divide both sides by 6
6p÷6 = 12 ÷ 6
p = 2
hence, p >2 or p < - 3
What is the value of m?
[tex] \huge \underline \mathcal{Answer}[/tex]
The given angles forms linear pair, and we know the angles forming linear pair are supplementary,
Therefore,
Angle MHJ + Angle MHL = 180°
Let's solve :
[tex](5m + 100) \degree + (2 m + 10) \degree = 180 \degree[/tex][tex]7m + 110 \degree = 180 \degree[/tex][tex]7m = 70 \degree[/tex][tex]m = 10 \degree[/tex]Value of variable m = 10°
[tex] \mathrm{✌TeeNForeveR✌}[/tex]
Find the answer to b and check if a is correct and explain plsss
Answer:
a. 105.84 cm²
b. 136 cm²
Step-by-step explanation:
a. The prism is a cube
Surface area of the cube = 6a²
a = 4.2 cm
Plug in the value
Surface area = 6*4.2²
Surface area = 105.84 cm²
b. The prism is a triangular prism
Surface area of triangular prism = bh + L(s1 + s2 + s3)
b = 6 ft
h = 4 ft
L = 7 ft
s1 = 5 ft
s2 = 5 ft
s3 = 6 ft
Surface area = 6*4 + 7(5 + 5 + 6)
Surface area = 24 +7(16)
Surface area = 24 + 112
Surface area = 136 cm²
How to solve this please I really need it now
Answer:
x=11
Step-by-step explanation:
the question would be to find x
3x + 28 + 5x + 52 + 2x - 10=180 (sum of angles in a triangle is equal to 180⁰)
10x + 70=180
10x=180-70
10x=110
x=110/10
x=11
Which equation is correct?
cos x° = adjacent ÷ hypotenuse
tan x° = hypotenuse ÷ adjacent
cos x° = hypotenuse ÷ adjacent
tan x° = adjacent ÷ hypotenuse
Answer:
cos x° = adjacent ÷ hypotenuse
Step-by-step explanation:
Option (A) cos x° = adjacent ÷ hypotenuse is correct because cos is the ratio of the side adjacent to the angle to the hypotenuse option (A) is correct.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have given trigonometric ratios in the options.
As we know the trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
In the right angle triangle (It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base)
cos is the ratio of the side adjacent to the angle to the hypotenuse
cos x° = adjacent ÷ hypotenuse
tan is the ratio of the side opposite to the angle to the side adjacent to the angle.
tan x° = opposite ÷ adjacent
Thus, option (A) cos x° = adjacent ÷ hypotenuse is correct because cos is the ratio of the side adjacent to the angle to the hypotenuse option (A) is correct.
Learn more about trigonometry here:
brainly.com/question/26719838
#SPJ5
How much interest will be earned on a $1600 investment at 7.72% compounded
quarterly for 9 years?
Answer:
A = $3,198.17
A = P + I where
P (principal) = $1,600.00
I (interest) = $1,598.17
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 7.72/100
r = 0.0772 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 1,600.00(1 + 0.0772/12)(12)(9)
A = 1,600.00(1 + 0.006433333)(108)
A = $3,198.17
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $1,600.00 at a rate of 7.72% per year compounded 12 times per year over 9 years is $3,198.17.
Given that ABCD is a rectangle, find the perimeter of the figure below. Round your answer to the nearest tenth. *
Options
18 ft
19.7 ft
21 ft
24.4 ft
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Answer:
(b) 19.7 ft
Step-by-step explanation:
The perimeter of the figure is the sum of the lengths of the 3 straight sides and half the circumference of a 3-ft circle.
P = 6 + 3 + 6 + (1/2)(π)(3) = 15 +3/2π ≈ 19.712 . . . feet
The perimeter is about 19.7 feet.
Which out of all these are heavier?
It is airoplane and ambulance
Select the correct answer.
This week, Theo walked x hours at a constant rate of 4 miles per hour and jogged y hours at a constant rate of 6 miles per hour. The total distance he walked and jogged this week was 36 miles. The relationship is modeled by this equation:
4x + 6y = 36.
Which statement is true about the graph of this relationship?
A.
The graph is a line that goes through the points (9,0) and (0,6).
B.
The graph is a line that goes through the points (6,0) and (0,9).
C.
The graph is a line that goes through the points (-9,0) and (0,6).
D.
The graph is a line that goes through the points (-6,0) and (0,9).
Answer:
A. The graph is a line that goes through the points (9,0) and (0,6).
Step-by-step explanation:
Given
[tex]4x + 6y = 36[/tex]
Required
Select the true options
[tex](a)\ (9,0)\ and\ (0,6)[/tex]
This implies that"
[tex](x_1,y_1)= (9,0)[/tex]
[tex](x_2,y_2)= (0,6)[/tex]
So, we have: [tex](x_1,y_1)= (9,0)[/tex]
[tex]4x + 6y = 36[/tex]
[tex]4 * 9 + 6 * 0 = 36 + 0 = 36[/tex]
So, we have: [tex](x_2,y_2)= (0,6)[/tex]
[tex]4 * 0 + 6 * 6 = 0 + 36 = 36[/tex]
Hence (a) is true.
Answer:
the answer would be a-The graph is a line that goes through the points (9,0) and (0,6).
Step-by-step explanation:
i took the test
Two trains leave a train station at the same time. One travels north at 12 miles per hour. The other train travels south at 9 miles per hour. In
how many hours will the two trains be 88.2 miles apart?
O 4.7 hours
O 4.2 hours
O 2.1 hours
O 8.4 hours
Answer:
4.2 hours
Step-by-step explanation:
On a piece of paper, graph y = -x2 + 4x - 3 and identify the zeros. Then determine which answer choice matches the graph that you drew and correctly identifies the zeros.
Answer:
C. 1 and 3
Step-by-step explanation:
Will Mark Brainlest help pleaseeeeee
Answer:
h(2) = 7/4
h(-3) = -2
h(-2) = 11/(-8)
h(-3) - h(-2) = -(5/8)
Step-by-step explanation:
h(x) = (2x^2-x+1) / (3x-2)
h(2) = (2*2^2 - 2 + 1) / (3*2 - 2)
= (8 - 2 + 1) / (6 - 2)
= 7/4
h(-3) = {2*(-3)^2 - (-3) + 1} / {3*(-3) - 2}
= (18 + 3 + 1) / (-9 - 2)
= 22/(-11)
= -2
h(-2) = {2*(-2)^2 - (-2) + 1} / {3*(-2) - 2}
= (8 + 2 + 1) / (-6 - 2)
= 11/(-8)
h(-3) - h(-2) = (-2) - {11/(-8)}
= -(5/8)
Hope this will help. Please give me brainliest.
[tex]h(3) - h( - 2) = - \frac{5}{ 8} \\ \\ [/tex]
[tex]\boxed{h(x) = \frac{2 {x}^{2} - x + 1}{3x - 2}}[/tex]
[tex]h(2) = \frac{2 {(2)}^{2} - (2) + 1}{3(2) - 2} [/tex]
[tex]h(2) = \frac{2 {(4)} - 2 + 1}{6 - 2} [/tex]
[tex]h(2) = \frac{ 8 - 1}{4} [/tex]
[tex]h(2) = \frac{7}{4}[/tex]
[tex]h( - 3) = \frac{2 {( - 3)}^{2} - ( - 3) + 1}{3( - 3) - 2} \\ h( - 3) = \frac{2 (9) + 3 + 1}{ - 9- 2} \\ h( - 3) = \frac{18 + 4}{ - 11} \\ h( - 3) = \frac{22}{ - 11} \\ h(-3) = -2[/tex]
[tex]h( - 2) = \frac{2 {( - 2)}^{2} - ( - 2) + 1}{3( - 2) - 2} \\ h( - 2) = \frac{2 (4) + 2+ 1}{- 6 - 2} \\ h( - 2) = \frac{8 + 3}{- 8} \\ h( - 2) = \frac{11}{- 8} [/tex]
[tex]h(3) - h( - 2) = -2 - \frac{11}{- 8} \\=-2 + \frac{11}{ 8} \\ =- \frac{5}{ 8} [/tex]
Josiah baked 24 cookies. He gave 1/6 of them to his family before he took them to his friend's house. How many cookies did he give his family?
Answer:
4 cookies
Step-by-step explanation:
24 x (1/6) = 24/6 = 4
Answer:
4
Step-by-step explanation:
1/6 can be represented as a percentage 1 divided by 6 = 0.1667...multiply that by 24 and you get 4 with a few decimals that round up to four as you would not want to give them a partial cookie....
If y=e3t is a solution to the differential equation
d2ydt2−9dydt+ky=0,
find the value of the constant k and the general solution to this equation.
Answer:
k=18, general solution does not exist.
Step-by-step explanation:
If f(t)=y=e3t is a solution to the differential equation
d2ydt2−9dydt+ky=0,
then
y = e^(3t)
y' = dy/dt = 3y
y'' = d2ydt2 = 9y
y'' - 9y' + ky = 0
9y - 9(3y) + ky = 0
(9-27+k)y = 0
solve for y
(9-27+k) = 0
k = 18
general solution is when y=e^(3t)=0, or t-> -infinity
Name 2 angles that form a linear pair in the diagram.
24 and 25
27 and 29
22 and 23
and 22
Mark this and retum
Save and
225 ft2
81 ft2
Three squares are joined below at their vertices to form a right triangle. Find X, the side
length of the square marked in the diagram.
12 feet
144 feet
48 feet
17.5 feet
Answer:
12 ft
Step-by-step explanation:
we know the areas of the 2 top squares.
the area of a square is simply the square of its side length.
=>
81 ft² means side length is 9 ft.
225 ft² means side length is 15 ft.
these are also 2 of the sides of the right triangle.
the third side we get by using Pythagoras :
c² = a² + b²
with c being the side opposite of the 90 degree angle.
so,
225 = 81 + x²
as x is also the third side of the triangle.
=> 144 = x²
x = 12 ft
Which equation models this relationship?
Answer:
The one you selected is correct! You can check it by using the four values of m and w given.
i have 30 sweets and 15 chocolate in a basket.If i take five sweets out the basket,what is the ratio(in its simplest form)of the number of chocolate th the number of sweets left in the basket?
Answer:
If you take 5 sweet out of the basket, then the ratio of the number of chocolate to the number of sweet left in the basket is. \frac{5} {30 - 5} = 5/25 = 1/5
Step-by-step explanation:
I need the answer the question is in the picture
Answer:
D) 1 3/4
Step-by-step explanation:
What's the value of x in the figure?
a)33 degrees
b)78 degrees
c)57 degrees
d)76 degrees
Answer:
b
Step-by-step explanation:
please help me with these questions
Answer: 24- b 25- c 26- b 27- c
Step-by-step explanation:
Which of the following is the maximum value of the function y=–2x2 + 5?
Answer:
( 1. 6 )
Step-by-step explanation:
Use the formula:
x = - b/2a
to find the maximum and minimum.
Answer: (1, 6 )
Step-by-step explanation:
This should help:
x = - b/2a
The sales tax on a sofa that cost 575$ was 43.13 What was the percent sales tax? PLS HELP ASAP NEED TO SHOW WORK!! AND STEP BY STEP
Answer:
07.50086956521739% (round it)
Step-by-step explanation:
Find what percent 43.13 (Number A) is of 575 (Number B). To do this you divide Number A by Number B.
43.13 / 575 = 0.0750086956521739
Move the decimal point two places to the right.
007.50086956521739
Get rid of the zeros.
7.50086956521739
Answer:
07.5%
Step-by-step explanation:
Set background
Clear frame
1. A cube has edge length 3 units. What is the volume of the cube?
2. A cube has edge length 4 units. What is the volume of the cube?
3. A cube has volume 8 units. What is the edge length of the cube?
4. A cube has volume 7 units. What is the edge length of the cube?
3*3*3 =
27 U13
Answer:
1. 27cm3
2. 64cm3
3. 512cm3
4. ?
Step-by-step explanation:
you toss six coins at the same time. how many possible outcomes are there?
64
36
12
6
Answer:
64 outcomes
Step-by-step explanation:
Let the number of coins be n.Let the number of outcomes per coin be X.Given the following data;
Number of coins = 6
Number of outcomes for a single coin = 2
A single coin comprises of a head (H) and a tail (T), thus, the number of outcomes for a single coin is two (2).
To find how many possible outcomes we would have from tossing six coins at the same time, we would use the following formula;
[tex] Number \; of \; outcomes = X^{n} [/tex]
Substituting the values, we have;
Number of outcomes = 2⁶
2⁶ = 2 * 2 * 2 * 2 * 2 * 2
2⁶ = 64
Number of outcomes = 64
Therefore, the number of outcomes for a single coin tossed at the same time is equal to sixty four (64). It would have a total of 32 heads (H) and a total of 32 tails (T).
Find the value of x.
A. 30
B. 60
C. 90
D. 120
Some one else didn’t add a picture
QUESTION:- Find the value of x.
A. 30
B. 60
C. 90
D. 120
ANSWER:-
ALL ANGLE SUMS HAVE SAME LOGIC OF STRAIGHT LINE ANGLES = 180°
[tex]y + x + y - x = 180[/tex]
[tex]2y = 180 \\ y = 90[/tex]
[tex]2x + y + x = 180[/tex]
[tex]3x + 90 = 180 \\ 3x = 90 \\ x = 30 \degree[/tex]
Answer:
30 degrees
Step-by-step explanation:
2x + y + x = 180
y + x + y - x = 180
3x + y = 180
2y = 180
y = 90
3x + 90 = 180
3x = 90
x = 30