Answer:
the next 3 numbers in the pattern are 1/27 , 1/81. , and 1/243
Step-by-step explanation:
to go from 9 to 3 you either have to subtract 6 or divide by 3. if you subtract 6 it doesn't match with the numbers. if you divide by 3 it matches. you can multiply 1/9 by 1/3 or divide by 3. it end with the same answer
We have that The Next 3 patterns are
1/27,1/81,1/243
From the Question we are told that
Pattern. 9 ,3 ,1 ,1/3, 1/9
Generally
Using in inductive reasoning the pattern progresses as a function of dividing by 3
Therefore
The next three number are
[tex]x_1=\frac{1/9}{3}\\\\x_1=1/27[/tex]
[tex]x_2=\frac{1/27}{3}\\\\x_2=1/81[/tex]
[tex]x_3=\frac{1/81}{3}\\\\x_3=1/243[/tex]
Therefore
The Next 3 Numbers are
1/27,1/81,1/243
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can i please get some help on this one ASAP!
Answer:
This is a 4th degree polynomial!
Step-by-step explanation:
Because the polynomial starts of the a number with a 4th degree and decreases down with lower numbers. Simply put, because (x^4) has the largest degree.
Hope this helps, good luck! :)
Which equation represents an exponential function with an initial value of 500?
f(x) = 100(5)x
f(x) = 100(x)5
f(x) = 500(2)x
f(x) = 500(x)2
Answer:
y = 500 * (2)^x is an exponential function
Step-by-step explanation:
An exponential function is of the form
y = a b^x where a is the initial value and b is the growth/decay factor
y = 500 * (2)^x is an exponential function
The correct equation that represents an exponential function with an initial value of 500 is:
f(x) = 500(2)x
What is a logarithmic function?The opposite of an exponential function is a logarithmic function. A log function and an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function is expressed. The formula for the logarithmic function is f(x) = log base b of x.
We are given that the initial value of the exponential function is 500. The initial value refers to the value of the function when x is equal to zero. Therefore, the value of f(0) is 500.
Out of the four given options, only option (c) represents an exponential function with an initial value of 500, since f(0) is equal to 500 when x is equal to zero:
f(x) = 500(2)^x
Option (a) represents an exponential function with an initial value of 100 and a base of 5.
Option (b) represents a power function, not an exponential function.
Option (d) represents an exponential function with an initial value of 0 and a base of x^2, which can take any value including negative values, thus it doesn't satisfy the conditions of a valid exponential function.
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Find the sum of a 22-term arithmetic sequence, where the first term is 7 and the last term is 240.
Answer:
The sum of the arithmetic series is 2717.
Step-by-step explanation:
The sum of an arithmetic sequence is given by:
[tex]\displaystyle S = \frac{k}{2}\left( a + x_k\right)[/tex]
Where k is the number of terms, a is the initial term, and x_k is the last term.
There are 22 terms, the first term is 7, and the last term is 240. Hence, the sum is:
[tex]\displaystyle \begin{aligned} S &= \frac{(22)}{2}\left((7) + (240)} \\ \\ &= 11(247) \\ \\ &= 2717\end{aligned}[/tex]
In conclusion, the sum of the arithmetic series is 2717.
A box contains a yellow ball, an orange ball, a green ball, and a blue ball. Billy randomly selects 4 balls from the box (with replacement). What is the expected value for the number of distinct colored balls Billy will select?
Answer:
[tex]Expected = 0.09375[/tex]
Step-by-step explanation:
Given
[tex]Balls = 4[/tex]
[tex]n = 4[/tex] --- selection
Required
The expected distinct colored balls
The probability of selecting one of the 4 balls is:
[tex]P = \frac{1}{4}[/tex]
The probability of selecting different balls in each selection is:
[tex]Pr = (\frac{1}{4})^n[/tex]
Substitute 4 for n
[tex]Pr = (\frac{1}{4})^4[/tex]
[tex]Pr = \frac{1}{256}[/tex]
The number of arrangement of the 4 balls is:
[tex]Arrangement = 4![/tex]
So, we have:
[tex]Arrangement = 4*3*2*1[/tex]
[tex]Arrangement = 24[/tex]
The expected number of distinct color is:
[tex]Expected = Arrangement * Pr[/tex]
[tex]Expected = 24 * \frac{1}{256}[/tex]
[tex]Expected = \frac{3}{32}[/tex]
[tex]Expected = 0.09375[/tex]
find the missing segment in the image below
Answer:
3
Step-by-step explanation:
Intercept theorem
DE // CB ⇒ [tex]\frac{AD}{AC} = \frac{AE}{AB}[/tex]
⇒ [tex]\frac{6}{6+?} =\frac{4}{4+2}[/tex]
⇒ ? = 3
Find the sum of the second multiple of 9 and the fifth multiple of 6.
Answer:
48
Step-by-step explanation:
9,18
6,12,18,24,30
18 + 30 = 48
if an angle is 10 degree less than its complement, find the angle.
Let one be x
Other one is x-10ATQ
[tex]\\ \sf \longmapsto x+x-10=90[/tex]
[tex]\\ \sf \longmapsto 2x-10=90[/tex]
[tex]\\ \sf \longmapsto 2x=90+10[/tex]
[tex]\\ \sf \longmapsto 2x=100[/tex]
[tex]\\ \sf \longmapsto x=\dfrac{100}{2}[/tex]
[tex]\\ \sf \longmapsto x=50[/tex]
[tex]\\ \sf \longmapsto x-10=50-10=40[/tex]
What would -4|5+-3| be
Answer:
-8
Step-by-step explanation:
Find the values of the unknown angles marked with letters. please help me- it is about alternate angles
100 points!!!
a ?
b ?
c ?
d ?
Answer:
Step-by-step explanation:
Find either c or d first. Those are easy and everything will fall into place after those 2 are found.
c: angle c is supplementary with 115. That means that they add up to equal 180; therefore, 115° + c° = 180° so c = 65°.
d: angle d is supplementary with 70. Therefore, 70° + d° = 180° so d = 110°.
a and c are same side interior, so they are also supplementary. That means that a = 115°.
b and d are also same side interior, so they are also supplementary. That means that b = 70°.
You order CDs for $14.25 each and the website charges $4.50 for each shipment.
The expression $14.25p + $4.50 represents the cost of p CDs. Find the total cost for
ordering 4 CDs.
Answer:
$61.50
Step-by-step explanation:
14.25(4) + 4.50
= 57.00 + 4.50
= 61.50
Mark all the relative minimum points in the graph.
Please help I don't understand what to do.
Answer:
Step-by-step explanation:
The thing to remember is that absolute can be relative but relative can't be absolute. In other words, absolute min is the very lowest point on the graph and there's usually only one (unless there are 2 absolute mins that have the same y value) while relative mins can occur at several points on a graph. That means that the only relative min point on the graph occurs at (-3, 4); the absolute min occurs at (5, -6).
using appropriate properties , find 7/5 × 5/12 − 3/12 × 7/5 − 1/15
Answer:
[tex] \frac{1}{6} [/tex]
Step-by-step explanation:
[tex] \frac{7}{5} \times \frac{5}{12} - \frac{3}{12} \times \frac{7}{5} - \frac{1}{15} = \frac{7}{5} ( \frac{5}{12} - \frac{3}{12} ) - \frac{1}{15} = \frac{7}{5} \times \frac{1}{6} - \frac{1}{15} = \frac{7}{30} - \frac{2}{30} = \frac{5}{30} = \frac{1}{6} [/tex]
Triangle ABC is a right triangle.
Triangle A B C. Angle A is x degrees, B is 90 degrees, C is (x minus 10) degrees. The exterior angle to angle C is (2 x + 40) degrees.
Which equations can be used to find the value of x? Check all that apply.
x + 90 + (x minus 10) = 180
x + 90 + (2 x + 40) = 180
2 x + 80 = 180
x + 90 = 2 x + 40
(x minus 10) + 90 = 2 x + 40
Answer:
x + 90 + (x minus 10)= 180° can be used to find the value of x.
Answer:
A) X+90+ (x-10) - 180
C) 2x+80 = 180
D) x+90 = 2x+40
Step-by-step explanation:
PLEASE HELP IM TRYING TO FINISH THIS BY NEXT MONDAY AND IVE BEEN STUCK ON THIS
Answer:
Step-by-step explanation:
Choice A is the only one that is applicable.
Answer:
A. F(x) has 1 relative minimum and maximum.
Step-by-step explanation:
[tex]{ \bf{F(x) = 2 {x}^{3} - 2 {x}^{2} + 1 }}[/tex]
As x and F(x) tend to positive and negative infinity:
[tex]{ \sf{x→ \infin : f(x) = \infin}} \\ { \sf{x→ {}^{ - } \infin : f(x) → {}^{ - } \infin}}[/tex]
❎So, B and C are excluded.
Roots of the polynomial:
[tex]{ \sf{f(x) = 2 {x}^{3} - 2 {x}^{2} + 1}} \\ { \sf{f(x) = - 0.6 \: \: and \: \: 0.8}}[/tex]
❎, D is also excluded.
✔, A
A rectangular bathroom mirror has a perimeter of 22 feet. Its area is 18 square feet. What are the dimensions of the mirror?
Answer:
The dimensions of the mirror is 9 feet and 2 feet
Step-by-step explanation:
Keep in mind that the area and perimeter of a rectangle is:
Area - length x width
Perimeter - 2 (l + w)
List the factors of 18 (the area of the mirror):
1, 2, 3, 6, 9, 18
POSSIBLE DIMENSIONS OF MIRROR:
1 ft and 18 ft
Area = 18 ft^2
Perimeter = 38 feet
2 ft and 9 ft
Area = 18 ft^2
Perimeter = 22 feet
3 ft and 6 ft
Perimeter = 18 feet
The rectangle with dimensions 2 feet and 9 feet corresponds with the area and perimeter of the mirror mentioned. So those are the correct dimensions.
Hope these helps!
#What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x?
Discriminant = b2 – 4ac
–8
4
8
16
Answer:
16
Step-by-step explanation:
the quadratic equation –3 = –x2 + 2x can be changed into :
x²-2x-3= 0
a=1, b= -2 , and c = -3
so, the discriminant = (-2)²-4(1)(-3)
= 4 + 12 = 16
shop sells shirts. In
January they reduce the
price of all their £50 shirts
by 50%. In February they
decide to increase the price
of all their shirts by 50%. In
March they decide to
reduce the price of their
shirts by 50% again. What is
the cost of a shirt in March?
HELP ME PLEASEEEE
TAXI RATES A New York City taxi charges $2.50, plus $.40 for each fifth of a
mile if it is not delayed by traffic. Write an expression for the cost of the ride
if you travel x miles in the taxi with no traffic delays.
Step-by-step explanation:
C(x) = 2.50 + 5(0.40x)
<=> C(x) = 2.50 + 2.00 x
The required expression for the taxi charges is C(x) = $2.50 + 0.4 * x/5.
Given that,
A New York City taxi charges $2.50, plus $.40 for each fifth of a
mile if it is not delayed by traffic. To determine an expression for the cost of the ride, if travel x miles in the taxi with no traffic delays to determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Let the number of miles be x,
The total charge be C(x)
Now accoding to the condition total charge could be the sum of the cost of every fifth mile and $2.40. So, every fifth mile = x / 5
Now,
C(x) = 2.40 + 0.40 * x/5
Thus, the required expression for the taxi charges is C(x) = $2.50 + 0.4 * x/5.
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Write an equation in point-slope form of the line that passes through the given point and has the given slope.
(16,-4);m=-3/4
Use the substitution method to solve the system of equations. Choose the correct ordered pair.
y= -2x+11
y=-3x+21
Answer:
x=10
y=-9
Step-by-step explanation:
eqn 2-1
-1x+10=0
x=10
in eqn 1
y=-2 ×10+11
-20+11
-9
Answer hurry which one 1 2 3 or 4?
Answer:
Option: 1Step-by-step explanation:
Let,
Footprints that Adele will find be = f
So, Footprints that Yumiko finds = 2f = f + f
Since,
As given that,
Yumiko finds 16 Footprints so it will be,
2f = f + f = 16
And,
f = 16 / 2
= 8
Which is half of Footprints found by Yumiko.
So the bar model 1 represents it correct.
Answer:
option 1
Step-by-step explanation:
i did the quiz
50 apples cost 25$ how much would 75$ apples cost?
Answer:
100
Step-by-step explanation:
Hey there!
First, to find the cost of one apple, 50 ÷ 25, which equals 2.
At this point, i am not very sure if you meant to say 75 apples, or $75 apples, so I am just going to give both solutions.
If you meant 75 apples: 75 x 2 = $150
If you meant $75 apples: $75 ÷ 2 = 37.5
Since it isn't realistic to buy 37 apples and one half, round it to 37 apples.
Hope this helps!
Have a great day!
What is the equation of the graph
Answer:
y=6^x-2
Step-by-step explanation:
Start with the parent function, a^x. The graph looks like it has been translated b units down, so our function is a^x+b. Now at x=0, y=-2. So b=-2. Next at x=1, y=3. 3=a^(1)-2, a=6. y=6^x-2 is the equation
A plank 6m long leans against a vertical wall so that the foot of the plank is 4m away from the wall. A lizard climbs 2m up the plank. Calculate the horizontal distance between the lizard and the wall.
Answer: [tex]\dfrac{8}{3}\ m[/tex]
Step-by-step explanation:
Given
Length of the plank is [tex]6\ m[/tex]
Foot of the flank is [tex]4\ m[/tex] away from the wall
Lizard climbs 2 m up the wall
from the figure, the two triangles are similar
[tex]\therefore \dfrac{2}{6}=\dfrac{x}{4}\\\\\Rightarrow x=4\times \dfrac{2}{6}\\\\\Rightarrow x=\dfrac{4}{3}\ m[/tex]
So, the distance from the wall is
[tex]\Rightarrow 4-x\\\\\Rightarrow 4-\dfrac{4}{3}\\\\\Rightarrow \dfrac{8}{3}\ m[/tex]
Olympia ate lunch at a restaurant. The amount of her check was $6.89. She left $8.00 on the table, which included the amount she owed plus a tip for the waiter. Which equation shows t, the amount of her tip, in dollars?
6.89 + t = 8.00
6.89 - t = 8.00
6.89t = 8.00
6.89 = 8.00 Divided by t
Answer:
not sure if the answer is obvious but I'd say $6.89 + t = $8.00
Step-by-step explanation:
so to make it more understandable you have to first go over the question and ask your self is the tip included in the totally amount owed or is it apart
after you figure out that its apart all you have to do is plug in the numbers you could verify this by checking every equation like this
$6.89 + t = $8.00 (t) in this case is the tip which would be $1.11 all you do to arrive at that answer is subtract the amout owed from the amount given like this $8.00 - $6.89 = $1.11 which will be your tip
now continue checking your answer next is , $6.89 - t = $8.00
which would be $6.89- $1.11 = $5.78 not quite right because now she is short on the pay , on to the next its $6.89t= $8.00 which would be $6.89 x $1.11= $7.65 rounded to neartest tenth which would included the amount but not all the tip given meaning tip would be short 0.35 cents and finally $6.89= $8.00 divided by t , now this takes the amount give which is $8.00 and divides by t which is $1.11 doing this $6.89 = $8.00/$1.11 which it is trying to imply that $6.89 is equal to $7.21 which would be incorrect making the only reasonable equation $6.89 + t = $8.00 reaveling that the tip given was $1.11
hopefully that help maybe i can get brainlist?!
Answer:
6.89 + t = 8.00
Step-by-step explanation:
it's A
Edge 2021
Solve the equation sin(x° − 20°) = cos(42°) for x, where 0 < x < 90. A. 22 B. 28 C. 62 D. 68
[tex] \sin(x - 20°) = \cos(42°) [/tex]
[tex] \sin(x - 20°) = \sin(90° - 42°) [/tex]
[tex] \sin(x - 20°) = \sin 48°[/tex]
[tex]x - 20° = 48°[/tex]
[tex]x = 48° + 20°[/tex]
[tex]x = 68°[/tex]
______________________________■ HOPE IT HELPS YOU DEAR!!!______________________________Answer:68
Step-by-step explanation:
need help asap pls !
Answer:
L={∅}
Step-by-step explanation:
Please Help Me With This Geometry Problem
Answer:
Remember that the area of a square of sidelength L is:
A = L^2
And the area of a circle of diameter D is:
A = pi*(D/2)^2
If we inscribe a square in a circle, we will get four segments, like the ones shaded in the image below:
Notice that the diameter of the circle will be equal to the diagonal of the square.
And the diagonal of a square of side length L is:
d = √(2)*L
knowing that the side length of our square is 6 inches, the diameter of the circle will be:
D = √2*6in
Now, the total area of the four shaded parts will be equal to the difference between the area of the circle and the area of the square.
The area of the circle is:
A = pi*(√2*6in/2)^2 = (pi/2)*36in^2
The area of the square is:
A' = (6in)^2 = 36in^2
The difference is:
A - A' = (pi/2)*36in^2 - 36in^2 = (pi/2 - 1)*36in^2
And there are 4 of these segments, then the area of every single one is one-fourth of that:
a = (1/4)*(pi/2 - 1)*36in^2 = (pi/2 - 1)*9 in^2
The area of each segment is:
a = (pi/2 - 1)*9 in^2
if we replace pi by 3.14, the exact area will be:
a = (3.14/2 - 1)*9in^2 = 5.13 in^2
pls help i will give brainliest for answer and explanation.
Answer:
36
Step-by-step explanation:
girls:boys=2:3
2units=24
1unit=24÷2=12
boys have 3 units
3units=12 x 3 =36
There are 36 boys
Monica makes tomato sauce with the plants she grows in her garden. She uses 3 basil leaves in her sauce for every 8 tomatoes. She is making a big batch of sauce with 32 tomatoes from her garden.
Answer: 12 Basil leaves
Step-by-step explanation:
Given
Monica uses 3 basil leaves for every 8 tomatoes
For 32 tomatoes she needs
[tex]\Rightarrow 3\ \text{basil leaves}\equiv8\ \text{Tomatoes}\\\\\Rightarrow 4\times 3\ \text{basil leaves}\equiv4\times 8\ \text{Tomatoes}\\\\\Rightarrow 12\ \text{basil leaves}\equiv 32\ \text{Tomatoes}[/tex]
Thus, she needs 12 basil leaves.
