Answer:
[tex]f(n) = 3T_{n-1}[/tex]; [tex]T_1 = 12[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 4*3^x[/tex]
Required
Write as a recursive function
Substitute 1 for x.
[tex]f(1) = 4*3^1 = 4 * 3 = 12[/tex]
[tex]f(2) = 4*3^2 = 4 * 9 = 36 = 12 * 3[/tex]
[tex]f(3) = 4*3^3 = 4 * 27 = 108 = 36 * 3[/tex]
Following the above pattern:
[tex]f(n) = T_{n-1} * 3[/tex]
[tex]f(n) = 3T_{n-1}[/tex]
Hence, the recursive function is:
[tex]f(n) = 3T_{n-1}[/tex]; [tex]T_1 = 12[/tex]
Your friend and you flip a coin 300 times and got tails 237 times is this normal? Why or why not
Answer:
No. N-O.
Step-by-step explanation:
It's chance. On an average, normal flipping, you have a 50/50 chance (150/300) of getting tails.
This is an anomaly, but of course it's not impossible. Merely, it's just a rare occasion.
i need help like need it pls help
In an orchard, there are 13 apple trees, 25 orange trees, and a cherry tree. What is the ratio of orange trees to cherry trees?
Answer:
1:25
Step-by-step explanation:
Write an equation to solve for b: What is b?
Answer:
Since all angles of a triangle add up to 180 degrees, b+2b+(b+24)=180
b=39 degrees
Step-by-step explanation:
b+2b+(b+24)=180
4b=156
b=39
If entering your answer as a decimal, round your final answer to the nearest hundredth.
Find the perimeter of rectangle LINT.
Answer:
[tex]P = 22.75[/tex]
Step-by-step explanation:
Given:
See attachment for rectangle LINT
Required
Calculate its perimeter
From the attachment:
Considering triangle LYT, we apply Pythagoras theorem.
[tex]LT^2 = LY^2 + TY^2[/tex]
Where:
[tex]LY = 5.2[/tex]
[tex]TY = 3.9[/tex]
The formula becomes:
[tex]LT^2 = 5.2^2 + 3.9^2[/tex]
[tex]LT^2 = 42.25[/tex]
Take positive square root of both sides
[tex]LT = \sqrt{42.25[/tex]
[tex]LT = 6.5[/tex]
Next, we calculate the length of NT.
By comparing triangles LYT and NYT
We make use of the following equivalent ratios to solve for NT
[tex]NT:TY = LT:LY[/tex]
[tex]NT : 3.9 = 6.5 : 5.2[/tex]
Convert to fractions
[tex]\frac{NT}{3.9} = \frac{6.5}{5.2}[/tex]
Make NT, the subject:
[tex]NT = \frac{6.5}{5.2}*3.9[/tex]
[tex]NT = \frac{6.5*3.9}{5.2}[/tex]
[tex]NT = \frac{25.35}{5.2}[/tex]
[tex]NT = 4.875[/tex]
The perimeter (P) is then calculated as:
[tex]P = NT + LT + LI + NI[/tex]
Where
[tex]NT = LI[/tex] and [tex]LT = NI[/tex] -- opposite sides of rectangle.
So:
[tex]P = NT + NT + LT + LT[/tex]
[tex]P = 2NT + 2LT[/tex]
Substitute values for NT and LT
[tex]P = 2*4.875 + 2*6.5[/tex]
[tex]P = 9.75 + 13.0[/tex]
[tex]P = 22.75[/tex]
Hence, the perimeter is 22.75 units
can someone help to fine goths slope, y intercept and equation
Which equation yields the solutions x=−2 and x=−10?
Options:
A. −x2−2x+35=0
B. 5x2+40x+60=0
C. −4x2+24x−20=0
D. x2+12x+20=0
Answer: its not B
sorry it only let me choose once ttm2021
What is 7/9 as a decimal rounded to 3 decimal places?
Answer:
7 ÷ 9 = 0.77777777777
= 0.778
The given fraction 7/9 as a decimal rounded to 3 decimal places is 0.778.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
To convert a fraction to a decimal, we need to divide the numerator by the denominator.
Here, we have:
7/9 = 0.777777...
7 divided by 9 gives us a repeating decimal of 0.7777777... and so on.
To round this to 3 decimal places, we need to look at the fourth decimal place. If it is 5 or greater, we round up the third decimal place. If it is less than 5, we simply leave the third decimal place as is.
In this case, the fourth decimal place is a 7, which means we need to round up the third decimal place.
Therefore, 7/9 as a decimal rounded to 3 decimal places is 0.778.
Learn more about the fraction here:
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What is the variable number in the equation 6=4+2s
Answer:
I believe it is 2s
Step-by-step explanation:
a variable is a symbol which functions as a placeholder, so in this case, the placeholder is "s"
find the coordinates of the missing endpoint if m is the midpoint of ab. a(-9, -4) and m(-7, -2.5)
Answer:
The coordinates of the point b are:
b(x₂, y₂) = (-5, -1)
Step-by-step explanation:
Given
As m is the midpoint, so
m(x, y) = m (-7, -2.5)
The other point a is given by
a(x₁, y₁) = a(-9, -4)
To determine
We need to determine the coordinates of the point b
= ?
Using the midpoint formula
[tex]\left(x,\:y\right)=\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
substituting (x, y) = (-7, -2.5), (x₁, y₁) = (-9, -4)
[tex]\left(-7,\:-2.5\right)=\left(\frac{x_2+\left(-9\right)}{2},\:\:\frac{y_2+\left(-4\right)}{2}\right)[/tex]
Thus equvating,
Determining the x-coordinate of b
[x₂ + (-9)] / 2 = -7
x₂ + (-9) = -14
x₂ - 9 = -14
adding 9 to both sides
x₂ - 9 + 9 = -14 + 9
x₂ = -5
Determining the y-coordinate of b
[y₂ + (-4)] / 2 = -2.5
y₂ + (-4) = -2.5(2)
y₂ - 4 = -5
adding 4 to both sides
y₂ - 4 + 4 = -5 + 4
y₂ = -1
Therefore, the coordinates of the point b are:
b(x₂, y₂) = (-5, -1)
What is 2/3 as a decimal please show steps on how you got there
Answer:
2/3 as a decimal is 0.67 rounded otherwise it is 0.6 recurring
Step-by-step explanation:
Many calculators round the digit up so they dont repeat forever.
Just divide 2 / 3 and that makes 0.6 recurring
During the last schools football game, the Home Team scored 13 more points than the Visiting
denm. The total of their scores was 47. How many points did each team score?
Answer:
Home 30, visitor 17.
Step-by-step explanation:
Visiting team score is x. Home score is then x+13. Total of both is 47 so...
x+(x+13)=47
2x+13=47
2x-34
x=17
x+13=30
The score of Home Team is 30 points.
The score of Visiting team is 17 points.
Here,
During the last schools football game, the Home Team scored 13 more points than the Visiting team.
The total of their scores was 47.
We have to find points of each team score.
What is Number system?
A number system is a system representing numbers. It is also called the system of numeration.
Now,
Let Visiting team score x points.
Then, Home team score is 13 more points than the Visiting team.
Home team score x + 13 points.
The total of their scores was 47.
Hence,
x + (x + 13) = 47
2x + 13 = 47
2x = 47 - 13
2x = 34
x = 17
So, The score of Visiting team is 17 points.
And, The score of Home Team = 17 + 13 = 30 points.
Learn more about the number system visit:
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A case of water contains 24 bottles
and a package of juice boxes
contains 10 boxes. A school needs
a total of 200 individual drinks for
an picnic. If the school purchased
three more juice box packages
than cases of water, how many
packages of each type did they
purchase?
--- Formulate the system of equations please
Plz I might fail if I don’t do this
Answer:
-130
Step-by-step explanation:
f(10) just means you plug in 10 for any X's in the equation
So it would be... f(10) = -10^2-3(10)
Help Please! I'll give branliest!
Two airplanes leave the airport. Plane A departs at a 42° angle from the runway, and plane B departs at a 44° angle from the runway. Which plane was farther away from the airport when it was 7 miles from the ground? Round the solutions to the nearest hundredth.
Plane A because it was 9.428 miles away
Plane A because it was 10.46 miles away
Plane B because it was 10.08 miles away
Plane B because it was 9.73 miles away
Answer: plane a because it was 10.46 miles away
Step-by-step explanation:
1 The length of a rectangle is 10 inches, and the
width is represented by 3x. Which best
represents an equation and solution for x if the
area of the rectangle is 40 square inches?
A 10(3x) = 40; X = 4
B 30x = 40; x = 1;
C 3x = 40; x = 13
D 3x + 10 = 40; X = 10
Answer:
A
Step-by-step explanation:
To find the area of a rectangle, it is length times width (10*3x), and if it equals 40, you could just write that after the equation, and then find out that "x" would equal [tex]\frac{4}{3}[/tex]
Answer:
30x = 40 ; x ≈ 1
Step-by-step explanation:
[tex]A^{}[/tex] = [tex]l^{}[/tex] [tex]w^{}[/tex]
[tex]l^{}[/tex] = 10 inch.
[tex]w^{}[/tex] = 3x
10(3x) = 40
30x = 40 ; x = [tex]1\frac{1}{3}[/tex] ≈ 1
What is the y intercept of the line
Answer:
-2
-2
Step-by-step explanation:
Answer:
it's 1/2 if you move left once and go up 2 it connects with the line
2y-6x=4 if you are solving for y
Answer:
y = 3x + 2
Step-by-step explanation:
Ans : y = 3x + 2
Steps:
(2y-6x=4)/2
y=3x+2
Which container would most likely have a capacity that is measured in liters? A.Drinking Glass
B.Watering Can
C.Baby Bottle
D.Soup Spoon
Bryan bought a canvas for an art project. The canvas has 2 pairs of parallel sides and 4 right angles.The sides are not all of equal length. Which shape is the canvas?
Given:
The canvas has 2 pairs of parallel sides and 4 right angles.
The sides are not all of equal length.
To find:
The shape of the canvas.
Solution:
Rectangle: A rectangle is a quadrilateral whose opposite sides are parallel and equal. All the interior angles of a rectangle are right angles.
Note: All sides of a rectangle are not equal. If they are equal then it is known as square.
It is given that the canvas has 2 pairs of parallel sides and 4 right angles. The sides are not all of equal length.
Therefore, the shape of the canvas is a rectangle.
again helppp! asap!
Answer:
C
Step-by-step explanation:
because 30÷6 is 5 and that is what should be placed
scientific notation --> 2.34* 10^14
written in standard form
Answer:
there's 104 days of summer vacation
you are paid $60 per week plus $5 per sale.At least how many sales do you need to make in order to have over $350? Which inequality best represents this?
Answer:
the answer is 60 + 5x > 350
Lois and Clark own a company that sells wagons. The amount they pay each of their sales employees (in dollars) is given by the expression 12h+30w12h+30w12, h, plus, 30, w where hhh is the number of hours worked and www is the number of wagons sold.
What is the amount paid to an employee that works 666 hours and sells 333 wagons?
\$
Answer:
x=36° (180/5x because 2x+3x)
Step-by-step explanation:
Answer:
162
=12h+30w
=12(6)+30(3)
=72+90
=162
A warehouse has shelves that can hold 8, 12 or 16 each shelf has section holding the same number of skateboards. What is the greatest number of skate boards that can be put in a section
Answer:
4 skate boards
Step-by-step explanation:
We solve this question using Greatest Common Factor method
We find the factors of 8, 12 and 16
The factors of 8 are: 1, 2, 4, 8
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 16 are: 1, 2, 4, 8, 16
Then the greatest common factor is 4.
Thereeft, ,the greatest number of skate boards that can be put in a section is 4 skate boards
Find the sum of 0.5 and -0.5.
Amswer
The answer is 0
I need help on these two questions please
Answer:
For #1= D = 24.25 #2= D= 21Step-by-step explanation:
hope this helps. pls mrk me branliest :)
Answer:
1)24.25
2)21
Step-by-step explanation:
1) (a/4)^2=(20/4)^2=25
b/2/8=6/8=3/4
25-3/4
=100/4-3/4
=97/4
=24.25
2)2(x-y)^2=2(3)^2=18
x-y=3
=18+3
=21
Hope this helps!
Please help! Suppose f(x) = x - 4. Find the graph of
3/4 f(x).
Click on the correct answer.
graph 1
graph 2.
Answer:
Graph 1 because if you just do the Y coordinate its much easier.
Answer:
graph 1
Step-by-step explanation:
the answer is graph 1
The regular price of a scooter is $70. It is on sale for $28 off. What PERCENT do you save? (Guess and Check is a good strategy for this problem)
Answer:
40%
Step-by-step explanation:
Given data
Regular price =$70
Discount =$28
%discount= 28/70*100
%discount =0.4*100
%discount = 40%
Hence you will save 40%
Is (2,3) a solution of the system
Answer:
Yes
Step-by-step explanation: