Answer:
f(1) = 93
f(n) = f(n - 1) + 4
Step-by-step explanation:
The recursive formula for an arithmetic sequence is given as:
f(1) = a
f(n) = f(n - 1) + d
where a = first term and d = common difference
An arithmetic sequence is in the form:
f(n) = a + d(n - 1)
where a = first term and d = common difference
The common difference in f(n) = 93 + 4(n-1) is 4.
The first term is 93.
The recursive formula is therefore:
f(1) = 93
f(n) = f(n - 1) + 4
Answer:
f(1)=93
f(n)=f(n-1)+4
Step-by-step explanation:
As you can see in the picture, the initial value is 93, which is why it's the first part of the equation. The 4 is multiplying the (n-1) part in the equation and as we complete the recursive formula of N, you have to put the numbers in the correct order.
The length of a rectangular room is 5 feet longer than twice the width If the room's perimeter is 166 feet, what is the length?
A. 67 feet
B. 44 feet
C. None of these
D. 114 feet
E. 57 feet
Answer:
E. 57 feet
Step-by-step explanation:
If you draw a rectangle and label the long side 5+2x, and the short side x, then that represents the rectangular floor.
The 2x is "twice the width".
The 5 added to the 2x is "5 feet longer than"
The x is the width of the room.
If the equation for the whole perimeter is 2(5+2x)+2x=166 <-(The perimeter)
(Both of the long sides)^ ^(Both of the short sides)
Then we need to solve for x.
[tex]2(5+2x)+2x=166\\10+4x+2x=166\\10+6x=166\\6x=156\\x=26[/tex]
Next, we input the value we got into the equation 5+2x (The length of one side) and solve
[tex]5+2x\\5+2(26)\\5+52\\57[/tex]
So the length of the room is 57 feet.
Hope this helps!
Factor the quadratic expression completely
8x^2 + 6x - 5
15 5 6 6 19 4 5 5 3 4 5 19 5 4 6
What is the mean? Round your answer to the nearest tenth.
Write the equation of a line that is parallel to y=6x and that passes through the point (-7,1)
Answer:
so y=6x+43
Step-by-step explanation:
Slope is 6, so using y=mx+b
1=6(-7)+b, b = 43
so y=6x+43
Factor completely −5x3 + 10x2
Answer:
(2 - x)5x²Step-by-step explanation:
-5x³ + 10x² = 10x² - 5x³ (Commutative property of addition)
= 2×(5x²) - x×(5x²)
= 5x² × (2 - x) (Factor out 5x²)
Answer:
−5x2(x − 2)
Step-by-step explanation:
I took the test
Graph a line that contains the point (-7,-4) and has a slope of
2
3
Answer:
y = 2/3x + 2/3
Step-by-step explanation:
just substitute every known value into the parent function on a linear function
y = mx +b
-4 = 2/3(-7) +b
now solve for b (the y-intercept)
-4 = -14/3 + b
-12/3 = -14/3 + b ( made it to same denominator)
2/3 = b
The probability for event A is 0.4, the probability for event B is 0.2, and the probability of events A and B is 0.1. Why are the events are not independent?
Answer:
Since [tex]P(A \cap B) \neq P(A)P(B)[/tex], these events are not independent.
Step-by-step explanation:
Independent events:
Two events, A and B are independent, if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this question, we have that:
[tex]P(A) = 0.4, P(B) = 0.2, P(A \cap B) = 0.1[/tex]
However
[tex]P(A)P(B) = 0.4*0.02 = 0.08[/tex]
Since [tex]P(A \cap B) \neq P(A)P(B)[/tex], these events are not independent.
Answer:
C
Step-by-step explanation:
edg 2020
What is 1200 milligrams converted into grams
Answer:
The answer is 1.2 grams.
Step-by-step explanation: So 1,000 milligrams is 1 gram. So to get this answer you divide 1200 milligrams by 1000 and that gives you 1.2 grams for 1200 milligrams.
what is the circumference of a circle with the radius of 7 units
Answer:
43.98
Step-by-step explanation:
a sector with a central angle measure of 7pi/4 in radians has a radius of 16cm what is the area of the sector
Answer:
The area of this sector is 224*pi cm² or approximately 703.72 cm²
Step-by-step explanation:
In order to calculate the area of a sector for which we have an angle in radians, we need to apply a rule of three in such a way that pi*r² is related to 2*pi radians in the same proportion as the given angle is related to the area of the sector we want to find. This is shown below:
2*pi rad -> pi*r² unit²
angle rad -> sector area unit²
2*pi / angle = pi*r² / (sector area)
2*pi*(sector area) = pi*r²*angle
sector area = [pi*r²*angle]/2*pi
sector area = r²*angle/2 unit²
Applying the data from the problem, we have:
sector area = [(16)²*(7*pi/4)]/2 = [256*(7*pi/4)]/2 = 64*7*pi/2 = 32*7*pi = 224*pi
sector area = 224*pi cm²
sector area = 703.72 cm²
You are going to buy a pizza, and have 3 options. The first option is a rectangular pizza that is 8 inches by 16 inches. The second option is a circular pizza that has a diameter of 10 inches. The third option is a pizza in
the shape of a triangle, with a base of 14 inches, and a height of 10 inches.
Which pizza is the largest? (You must give the area of each pizza to
receive credit)
*
Answer:
The largest pizza is Rectangular Pizza .
Step-by-step explanation:
In order to know which pizza is the largest you have to find the area for each shape using the formulas :
Rectangular pizza,
[tex]area = length \times width[/tex]
Let length = 8 inches,
Let width = 16 inches,
[tex]area = 8 \times 16[/tex]
[tex]area = 128 \: \: {inches}^{2} [/tex]
Circular pizza,
[tex]area = \pi \times {r}^{2} [/tex]
Let r = 5 inches,
[tex]area = \pi \times {5}^{2} [/tex]
[tex]area = 25\pi[/tex]
[tex]area = 78.5 \: \: {inches}^{2} [/tex]
Triangular pizza,
[tex]area = \frac{1}{2} \times base \times height[/tex]
Let base = 14 inches,
Let height = 10 inches,
[tex]area = \frac{1}{2} \times 14 \times 10[/tex]
[tex]area = \frac{1}{2} \times 140[/tex]
[tex]area = 70 \: \: {inches}^{2} [/tex]
Sydney is going to a carnival that has games and rides. Each game costs $1.25 and each ride costs $2.25. Sydney spent $24.25 altogether at the carnival and the number of rides she went on is 3 more than the number of games she played. Determine the number of games Sydney played and the number of rides Sydney went on.
Answer:
number of games played is 5
number of rides road 8
Step-by-step explanation:
8 x 2.25=18
5 x 1.25=6..25
18 + 6.25=24.25
The number of games Sydney played is 5 and the number of rides Sydney went on is 8.
What is linear equation?Linear equation is the type of equation with highest power 1.
Assume the number games Sydney played be x. So, the number of rides she went is x+3.
The cost of 1 game is $1.25. So, the cost of x games will be 1.25x.
The cost of 1 ride is $2.25. So, the cost of x+3 rides will be 2.25(x+3).
The total cost is $24.25. Formulate the linear equation and solve it.
1.25x+2.25(x+3)=24.25
1.25x+2.25x+6.75=24.25
3.5x=17.5
x=5
Substitute x=5 into x+3.
5+3=8
Thus, the number of games Sydney played is 5 and the number of rides Sydney went on is 8.
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Find two numbers, if their sum is 49 and their difference is 1/2 .
This question is for my little sister who needs help with her Math.
I'm too busy to help.
Answer: 49.5 and -0.5
Step-by-step explanation:
a + b =49
a - b = 0.5
a= 49.5
b= -0.5
The two numbers are approximately 24.25 and 24.75.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
Let's call the two numbers x and y.
According to the problem, we have two equations:
x + y = 49 (since their sum is 49)
x - y = 1/2 (since their difference is 1/2)
We can solve this system of equations using the method of substitution.
First, we can rearrange the second equation to solve for one of the variables in terms of the other:
x - y = 1/2
x = y + 1/2
Now we can substitute this expression for x into the first equation:
(y + 1/2) + y = 49
2y + 1/2 = 49
2y = 48.5
y = 24.25
Now we can use this value of y to solve for x:
x = y + 1/2 = 24.25 + 1/2 = 24.75
Therefore, the two numbers are approximately 24.25 and 24.75.
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What is another way to represent 3%?
Answer: 0.03
Step-by-step explanation:
3% in decimal form is 0.03
Answer:
The decimal form, which would be 0.03
People would say the decimal will be 0.3, but that is 30%, so the decimal would be 0.03.
A cafeteria manager can choose from among six side dishes for the lunch menu: applesauce, broccoli, corn, dumplings, egg
rolls, or French fries. He uses a computer program to randomly select three dishes for Monday's lunch.
What is the theoretical probability that applesauce and broccoli will both be offered on Monday?
10%
20%
50%
80%
Answer:
B: 20%
Step-by-step explanation:
The theoretical probability that the applesauce and broccoli dishes will both be offered on Monday is given by P ( A ) = 20 %
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the theoretical probability that the applesauce and broccoli will both be offered on Monday be P ( A )
Now , the equation is
The total number of dishes = 6 dishes
The combination of selecting 3 dishes out of 6 is given by
⁶C₃ = 20 ways
Now , the combination of selecting 2 dishes on Monday = 4 ways
So , P ( A ) = 4 / 20
P ( A ) = 1/5 = 0.20
Therefore , the applesauce and broccoli will both be offered on Monday is given by 20 %
Hence , the probability is 20 %
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Find and interpret the mean absolute deviation of the data. round your answer to the nearest tenth if necessary.
_______________
| 60 | 105 | 80 | 125 |
| 140 | 95 | 65 | 170 |
----------------------------
please help i have asked this questions 3 times and people keep being like " sorry i need these." or " thx for the points!!!" so please help i don't understand this.
The mean absolute deviation of the data is 30.
Given data:
To find the mean absolute deviation (MAD) of the given data, we need to follow these steps:
Calculate the mean (average) of the data set.
Find the absolute difference between each data point and the mean.
Calculate the mean of these absolute differences.
Given data set: 60, 105, 80, 125, 140, 95, 65, 170
Step 1:
Calculate the mean
Mean = (60 + 105 + 80 + 125 + 140 + 95 + 65 + 170) / 8
Mean = 840 / 8
Mean = 105
Step 2:
Find the absolute difference between each data point and the mean
|60 - 105| = 45
|105 - 105| = 0
|80 - 105| = 25
|125 - 105| = 20
|140 - 105| = 35
|95 - 105| = 10
|65 - 105| = 40
|170 - 105| = 65
Step 3:
Calculate the mean of the absolute differences
MAD = (45 + 0 + 25 + 20 + 35 + 10 + 40 + 65) / 8
MAD = 240 / 8
MAD = 30
The mean absolute deviation of the given data set is 30.
Interpretation:
The mean absolute deviation represents the average amount by which each data point deviates from the mean. In this case, the MAD of 30 indicates that, on average, the data points in the set deviate from the mean by approximately 30 units.
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Elimination method using multiplication:3x+2y=0 and x-5y=17
Answer:
(2,-3)
Step-by-step explanation:
have to multiply (-3) to the second equation to get -3x + 15y = 51 then you add both equations .the 3 is remove (postive and negative cancels out )
2y+15y= 17y
0-51+-51
divide both sides by 17 y
-51/17= -3
then you plug -3 into the first equation and get
x= 2
y=-3
Answer:
x=2 y=- 3
Step-by-step explanation:
You are going to the grocery to buy the candies for you and your sisters/brothers. You want to buy
chocolates and gums. Each chocolate costs 1.50 AED and each gum costs 0.50 AED. At the end you spent a total
of 78.50 AED. You bought a total of 87 chocolates and gums combined. You must report the number of
chocolates bought and the number of gums bought. How many chocolates were bought and how many gums
were bought?
Answer: 35 chocolates were bought and 52 gums were bought.
Step-by-step explanation:
c + g = 87 where c is the number of chocolate and g is the number og gums
1.50c + 0.50g = 78.50 solve both equations by elimination.
-1.50c - 1.50g = -130.5
1.50 + 0.50g = 78.50
-1g = -52
g= 52
1.50c + 0.50(52) = 78.50
1.50c + 26 = 78.50
-26 -26
1.50c = 52.5
c = 35
The lines y=x+1 and y=-x-3 are graphed.
What is the solution to the system?
Please help
Answer: (-2, -1)
Step-by-step explanation: Since these lines are already graphed, we are looking for their point of intersection. This point where the two lines intersect will represent the x and y that is the solution to this system of equations.
The two lines intersect in quadrant III
where x and y are both negative.
When finding the coordinates of a given point,
be very careful with your signs.
Let's just do a quick review on the coordinate system. On the x-axis, left means negative and right means positive and on the y-axis, down means negative and up means positive.
So to find the coordinates for this point, we start at the origin.
Then we move to the left 2 and down 1 so that's (-2, -1).
So the solution to this system is (-2, -1).
neli has 3 partically full cans of of white paint.They contain 1/3 gallon,1/5 gallon, and 1/2 gallon of paint.about how much paint does neli have in all
options
^^^^^^^^
Less than 1 1/2 gallons.
More than 2 gallons.
Between 1 1/2 gallons and 2 gallons
(which one?)
(help pls)
Answer:
less than 1 and 1/2
Step-by-step explanation:
1/3 + 1/5 + 1/2 = 31/30 which is also equal to 1 1/30
Answer:so wut the answer?
Step-by-step explanation:im dum i dont know
4
A circle has a radius of
9
units and is centered at (-6.2, 5.8)
Write the equation of this circle.
Answer:
(×6.2)2+(y-5.8)2= 16+81
Step-by-step explanation:
Circle has center (-6.2, 5.8)
r= 4/9
Then simplify the equation.
h,k is the center of the circle
R = Radius
Hope this helps.
Find the particular solution to y ' = 2sin(x) given the general solution is y = C - 2cos(x) and the initial condition y of pi over 2 equals 1 .
-2cos(x)
2 - 2cos(x)
1 - 2cos(x)
-2 - 2cos(x)
I think it is option C. Thank you in advance!
Answer:
1 − 2 cos x
Step-by-step explanation:
y' = 2 sin x
y = C − 2 cos x
1 = C − 2 cos(π/2)
1 = C
y = 1 − 2 cos x
Question 11 point(s) Jared made Ask Your Teacher cups of snack mix for a party. His guests ate Ask Your Teacher of the mix. How much snack mix did his guests eat?
Answer:
[tex]8\frac{1}{2}[/tex] cups
Step-by-step explanation:
To determine the quantity of snack mix Jared guest ate, we multiply the quantity of snack mix the guest ate by the quantity of snack mix Jared made. i.e we determine [tex]\frac{2}{3}of12\frac{3}{4}[/tex] by multiplying both fractions together
quantity of snack mix Jared guest ate = [tex]\frac{2}{3}of12\frac{3}{4}=\frac{2}{3}*12\frac{3}{4}=\frac{2}{3}*\frac{51}{4}=\frac{17}{2} =8\frac{1}{2}[/tex]
Solve for x2= 9/49. Show your step-by-step.
Answer:
x = [tex]\frac{3}{7}[/tex], x = [tex]\frac{-3}{7}[/tex]
Step-by-step explanation:
The first step is to get rid of the square on the x, and to get rid of it, you square root both sides of the equation, like so:
[tex]x^{2} = \frac{9}{49}[/tex]
[tex]\sqrt{x^2} = \sqrt{\frac{9}{49} }[/tex]
A perfect square is when a number has two factors that are identical to one another. In this case, 9 and 49 are both perfect squares, meaning we can break them down:
The square root of 9 is 3. (3 · 3 = 9)
The square root of 49 is 7. (7 · 7 = 49)
x = [tex]\frac{3}{7}[/tex]
The answer is also x = [tex]\frac{-3}{7}[/tex] because a negative · a negative = a positive.
Jeremiah is creating a playlist that has only one song from each of his favorite genres. The following table shows his favorite genres and the number of songs on his MP3 player for each genre.
Answer:
Step-by-step explanation:
well i just dont know whats going on but just times the number of songs times the Genre.
Answer:
448
Step-by-step explanation:
just because
the tape diagram represents an equation write an equation to represent the image
Answer:11=5b or 5b=11
Step-by-step explanation:
Answer is 11=5b or 5b=11
Please help me and show
Work
Thank you
Answer:
120
Step-by-step explanation:
Need help with 1 and 2 please
Answer:
calculator
Step-by-step explanation:
calculator
help me with this question.thank u
Answer:
see below
Step-by-step explanation:
P( yellow) = number of yellow sections / total sections
= 4/20
1/5
20%
Answer:
a.
4 out of 20
1/5
or 20%
b. The probability may not be as much as the other colors on the wheel depending on how many colors and how many sections of each. You have a 20% chance out of all colors to get the color yellow.
please help me i need the last word for this crossword puzzle!!! if i did something wrong let me know...
Answer:
Your other answers all look good - I think the word in the blank is producer, which means an organism that makes its own food. Green plants do so through photosynthesis.
Answer:
producer
Step-by-step explanation:
Because it makes sense
