Answer:
(D) t^4
Step-by-step explanation:
You have defined ...
a3 = a2·a1
a4 = a3·(a2·a1) = a3²
a5 = a4·(a3·a2·a1) = a4² = (a3²)² = a3⁴
Then if a3 = t, a5 = t⁴
Let's begin by understanding the given sequence and the pattern it follows.
We are given the initial terms:
a1 = 3
a2 = 5
For n > 2, the next term is defined as the product of all preceding terms. Therefore,
a3 = a1 * a2
a4 = a1 * a2 * a3
and so on.
Now, let's generalize this for any term an where n > 2. According to the problem, an = t.
The term immediately after an would be an+1, which equals the product of all preceding terms:
an+1 = a1 * a2 * a3 * ... * an-1 * an
Since an = t, and every term before it has been multiplied to give t (by definition of the sequence), we have:
an+1 = t * t
an+1 = t^2
Now, let's find an+2. This term is the product of all preceding terms, which now includes an+1:
an+2 = a1 * a2 * a3 * ... * an-1 * an * an+1
From above, we know an = t and an+1 = t^2. Hence:
an+2 = t * t^2
an+2 = t^3
Therefore, the value of an+2 in terms of t is t^3. The correct answer is (C) t^3.
A study conducted at a certain college shows that 72% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that 5 randomly selected graduates all find jobs in their chosen field within a year of graduating.
Answer:
19.3%
Step-by-step explanation:
Assuming the events are independent, the probability of all five is ...
0.72^5 ≈ 0.19349 ≈ 19.3%
Answer: 19.3%
Step-by-step explanation:
If we randomly select 5 students, we know that each of them has a probability of 72% of finding a job in that year (or 0.72 in decimal form)
The joint probability in where the 5 of them have found a job, is equal to the product of the 5 probabilities:
P = 0.72*0.72*0.72*0.72*0.72 = 0.72^5 = 0.193
Where because all the students are in the same result, the number of permutations is only one.
If we want the percentage form, we must multiplicate it by 100%, and we have that P = 19.3%
9x−9y=0 3x−4y=10 solve by elimination
Answer:
(-10,-10)
Step-by-step explanation:
9x-9y=0
3x-4y=10
In elimination, we want both equations to have the same form and like terms to be lined up. We have that. We also need one of the columns with variables to contain opposites or same terms. Neither one of our columns with the variables contain this.
We can do a multiplication to the second equation so that the first terms of each are either opposites or sames. It doesn't matter which. I like opposites because you just add the equations together. So I'm going to multiply the second equation by -3.
I will rewrite the system with that manipulation:
9x-9y=0
-9x+12y=-30
----------------------Add them up!
0+3y=-30
3y=-30
y=-10
So now once you find a variable, plug into either equation to find the other one.
I'm going to use 9x-9y=0 where y=-10.
So we are going to solve for x now.
9x-9y=0 where y=-10.
9x-9(-10)=0 where I plugged in -10 for y.
9x+90=0 where I simplified -9(-10) as +90.
9x =-90 where I subtracted 90 on both sides.
x= -10 where I divided both sides by 9.
The solution is (x,y)=(-10,-10)
The vertex form of the equation of a parabola is y=(x-3)^2+35 what is the standard form of the equation
Answer:
x^2 -6x+44
Step-by-step explanation:
Develop form of (x-3)^2 is x^2 - 6x +9
Then y= x^2 -6x +9 + 35
So, y= X^2 -6x +44
Answer:
[tex]y=x^2 -6x+44[/tex]
Step-by-step explanation:
The standard form of a quadratic equation is:
[tex]y = ax ^ 2 + bx + c[/tex].
In this case we have the following quadratic equation in vertex form
[tex]y=(x-3)^2+35[/tex]
Now we must rewrite the equation in the standard form.
[tex]y=(x-3)(x-3)+35[/tex]
Apply the distributive property
[tex]y=x^2 -3x -3x +9+35[/tex]
[tex]y=x^2 -6x+9+35[/tex]
[tex]y=x^2 -6x+44[/tex]
the standard form of the equation is: [tex]y=x^2 -6x+44[/tex]
A baboon steals an apple and runs to a nearby boulder 10.0 m to its left. The baboon reaches the boulder in 1.0s with a constant acceleration of 20.0m/s^2 leftward. What was the baboon's initial velocity when it started running to the boulder?
Answer:
Initial velocity is zero.
Step-by-step explanation:
According to second equation of motion
[tex]s=ut+\frac{1}{2} at^2[/tex]
where s = distance traveled
t = time taken
a = acceleration
u = initial velocity
here in the question we have
s = 10 m
t = 1 second
a = 20[tex]ms^{-2}[/tex]
plugging the known value in order to find the unknown which is u (initial velocity)
[tex]10=u(1)+\frac{1}{2} (20)(1)^2[/tex
10 = u +10
gives u =0
therefore initial velocity is zero.
A right rectangular prism has base dimensions of 3 inches by 12 inches. An oblique rectangular prism has base dimensions of 4 inches by 9 inches.
If the prisms are the same height, how do their volumes compare?
The volumes are equal, because the bases are congruent.
The volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.
The volumes are not equal, because their horizontal cross-sectional areas are not the same at every level.
Answer:
The correct option is 2.
Step-by-step explanation:
Given information: Height of both prism are same.
Right rectangular prism has base dimensions of 3 inches by 12 inches.
Volume of a right rectangular prism:
[tex]V=Bh[/tex]
where, B is base area and h is height of the prism.
The volume of right rectangular prism is
[tex]V=(3\times 12)\times h=36h[/tex]
Therefore the volume of right rectangular prism is 36h cubic inches.
An oblique rectangular prism has base dimensions of 4 inches by 9 inches.
Volume of a oblique rectangular prism:
[tex]V=Bh[/tex]
where, B is base area and h is height of the prism.
The volume of right rectangular prism is
[tex]V=(4\times 9)\times h=36h[/tex]
Therefore the volume of oblique rectangular prism is 36h cubic inches.
The volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.
Option 2 is correct .
The volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.
How to find the volume of the prism?The formula for the Volume of a right rectangular prism is:
V = B * h
where,
B is base area.
h is height of the prism.
Thus:
V = 3 * 12 * h
V = 36h
Similarly, the volume of the oblique rectangle is:
V = Bh
V = 4 * 9 * h
V = 36h
Thus, we can see that the volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.
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help pleaseeeeeeeeeeee
Answer:
Step-by-step explanation:
The temperature at a given altitude is
y = 36 - 3x
The temperature on the surface of the planet is the point (0,t) where t is the temperature for the given height.
y = 36 - 3*0
y = 36
So at the surface of the planet is 36 degrees C.
======================
Effectively it is the slope of the equation which is - 3
So ever km going up will mean a loss of 3 degrees. I think they want you to write -3
Subtract the second equation from the first.
6x+5y=16
(6x+2y=10)
-
------------------------
A. 12x = 26
B. 3y = 6
C. –12x = 6
D. 7y = 26
Answer:
B. 3y = 6
Step-by-step explanation:
(6x +5y) -(6x +2y) = (16) -(10)
6x +5y -6x -2y = 6 . . . eliminate parentheses
(6-6)x +(5-2)y = 6 . . . . add like terms
3y = 6 . . . . . . . . . . . simplify
Five consecutive multiples of 3 yield a sum that is equal to the product of 7 and 15. What are these multiples?
Answer:
15, 18, 21, 24, 27
Step-by-step explanation:
Five multiples of 3 means we have 5 terms we are adding together to = 105.
For the sake of having something to base each one of these terms on, let's say that the first term is 3. It's not, but 3 is a multiple of 3 and we have to start somewhere. These terms go up by the next number that is divisible by 3. After 3, the next number that is divisible by 3 is 6. The next one is 9, the next is 12, the last would be 15.
Let's then say that 3 is the first term, and we are going to say that is x.
To get from 3 to 6, we add 3. Therefore, the second term is x + 3.
To get from 3 to 9, we add 6. Therefore, the third term is x + 6.
To get from 3 to 12, we add 9. Therefore, the fourth term is x + 9.
To get from 3 to 15, the last term, we add 12. Therefore, the last term is x + 12.
The sum of these terms will then be set to equal 105:
x + (x + 3) + ( x + 6) + ( x + 9) + ( x + 12) = 105
We don't need the parenthesis to simplify so we add like terms to get
5x + 30 = 105. Subtract 30 from both sides to get
5x = 75 so
x = 15
That means that 15 is the first multiple of 3.
The next one is found by adding 3 to the first: so 18
The next one is found by adding 6 to the first: so 21
The next one is found by adding 9 to the first: so 24
The last one is found by adding 12 to the first: so 27
15 + 18 + 21 + 24 + 27 = 105
Notice that all the numbers are, in fact, consecutive multiples of 3 as the instructions stated.
The five consecutive multiples of 3 that sum up to 105 are 15, 18, 21, 24, and 27.
Explanation:The question posed is regarding five consecutive multiples of 3. The sum of these multiples equals 7x15 (or 105). Let's call the first multiple of 3 as '3x'. Therefore, the five consecutive multiples can be represented as 3x, 3x+3, 3x+6, 3x+9, 3x+12.
The sum of the five consecutive multiples then is 15x + 30 (comprising 5 times 'x', plus 30 from the sum of 3, 6, 9, and 12). We know that this sum equals 105, so we can set up the following equation:
15x + 30 = 105.
Solving this equation for 'x' gives:
x = 5. This means the first multiple is 3x, or 3x5 = 15. The next multiples are therefore 15+3 (18), 18+3 (21), 21+3 (24) and 24+3 (27).
So, the five multiples of 3 that yield a sum of 105 are 15, 18, 21, 24, and 27.
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the radious of each wheel of a car is 16 inches at how many revolutions per minute should a spin balancer be set to balance the tires at a speed of 90 miles per hour is the setting different for a wheel of radious 14 inches
Answer:
revolutions per minute for 16 inches is 946 / minute
revolutions per minute for 14 inches is 1081 / minute
Step-by-step explanation:
Given data
radius = 16 inch
speed = 90 mph = 90/60 = 1.5 miles/minute = 1.5 × 5280 feet /12 inches = 95040 inches /minute
radius 2 = 14 inches
to find out
revolutions per minute
solution
first we calculate the circumference of the wheel i.e. 2×[tex]\pi[/tex]×radius
circumference = 2×[tex]\pi[/tex]×16
circumference = 32[tex]\pi[/tex]
we know that revolution is speed / circumference
revolution = 95040/32[tex]\pi[/tex]
revolution = 945.38 / minute
we have given radius 14 inches than revolution will be i.e.
revolution = speed / circumference
circumference = 2×[tex]\pi[/tex]×14
circumference = 28[tex]\pi[/tex]
revolution = 95040/ 28[tex]\pi[/tex]
revolution = 1080.43 / minute
A widget company produces 25 widgets a day, 5 of which are defective. Find the probability of selecting 5 widgets from the 25 produced where none are defective.
Final answer:
To find the probability of selecting 5 non-defective widgets from 25 produced, we consider the independent probabilities of selecting a non-defective widget for each selection and multiply them together.Therefore, the probability of selecting 5 widgets where none are defective is 1024/3125 or approximately 0.327.
Explanation:
To find the probability of selecting 5 widgets where none are defective, we need to consider the probability of selecting a non-defective widget for each of the 5 selections.
The probability of selecting a non-defective widget from the 25 produced is (25-5)/25 = 20/25 = 4/5.
Since the selections are independent, we can multiply the probabilities. So the probability of selecting 5 non-defective widgets is (4/5)⁵ = 1024/3125.
Therefore, the probability of selecting 5 widgets where none are defective is 1024/3125 or approximately 0.327.
Write an equation in standard form for each parabola.
Answer:
[tex]x=1/4(y-2)^{2}-1[/tex]
Step-by-step explanation:
Use Vertex form: [tex]x=a(y-k)^{2}+h[/tex]
Given: vertek (h, k)=(-1, 2)
[tex]x=a(y-2)^2 -1[/tex]
A point:(x , y) = (3, 6)
[tex]3 = a (6-2)^{2} -1[/tex]
16a=4, a=1/4
The equation is : [tex]x=1/4(y-2)^{2}-1[/tex]
An inlet pipe on a swimming pool can be used to fill the pool in 40 hours. The drain pipe can be used to empty the pool in 42 hours. If the pool is 23 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
Answer:
Pool will be filled in 280 hours
Step-by-step explanation:
Inlet pipe fills in 40 hours = 1 pool
Inlet pipe fills in 1 hours = [tex]\frac{1}{40}[/tex]
Drain pipe empty in 42 hours = 1 pool
Drain pipe empty in 1 hour = [tex]\frac{1}{42}[/tex]
If both pipes are opened together
then in pool fills in 1 hour = [tex]\frac{1}{40}[/tex] - [tex]\frac{1}{42}[/tex]
on simplifying the right side ,we get [tex]\frac{42-40}{(40)(42)}[/tex]
= [tex]\frac{2}{(40)(42)}[/tex]
= [tex]\frac{1}{840}[/tex]
[tex]\frac{1}{840}[/tex] pool fills in 1 hour
1 pool will be filled in 840 hours
[tex]\frac{2}{3}[/tex] pool is filled
empty pool = 1 - [tex]\frac{2}{3}[/tex] = [tex]\frac{1}{3}[/tex]
therfore [tex]\frac{1}{3}[/tex] pool will be filled in [tex]\frac{1}{3}[/tex]X 840 =
= 280 hours
The calculations indicate that 280 hours is the time required to fill 2/3 of the pool with both pipes open.
Inlet Pipe Rate:
The inlet pipe can fill the pool in 40 hours.
Therefore, the rate of the inlet pipe is 1/40 pool per hour.
Drain Pipe Rate:
The drain pipe can empty the pool in 42 hours.
Therefore, the rate of the drain pipe is 1/42 pool per hour.
Combined Rate when both pipes are open:
The net rate when both pipes are open is the difference between their individual rates:
Net rate = (1/40) - (1/42)
Simplify the Net Rate:
Find a common denominator for 40 and 42, which is 840:
Net rate = (42 - 40) / 840 = 2/840 = 1/420
Time to Fill 2/3 of the Pool:
Set up the equation: Net rate * Time = 2/3
Substitute the net rate: (1/420) * Time = 2/3
Cross-multiply to solve for time: Time = (2/3) * (420/1) = 280
Therefore, it takes 280 hours to fill 2/3 of the pool when both the inlet and drain pipes are open.
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Find the value of z such that "0.9544" of the area lies between −z and z. round your answer to two decimal places.
Answer:
z = 2.00
Step-by-step explanation:
This is a number many statistics students memorize.
95.44% of the distribution lies within 2 standard deviations of the mean.
Answer:
z = 2.00
Step-by-step explanation:
The value of z such that "0.9544" of the area lies between −z and z rounded to two decimal places is z = 2.00.
On a set of blueprints for a new home, the contractor has established a scale of 0.5in : 10 ft. What are the dimensions on the blueprints of a bedroom that will be 18 feet by 16 feet.
Answer:
The dimensions on the blueprints are 0.9 inches and 0.8 inches
Step-by-step explanation:
* Lets explain the relation between the drawing dimensions and
the real dimensions
- A scale drawing make a real object with accurate sizes reduced
or enlarged by a certain amount called the scale
- Ex: If the scale drawing is 1 : 10, so anything drawn with the size of
1 have a size of 10 in the real so a measurement of 15 cm on the
drawing will be 150 cm on the real
- In a scale drawing, all dimensions have been reduced by the same
proportion
* Lets solve the problem
- On a set of blueprints for a new home, the contractor has
established a scale of 0.5 in : 10 ft
∵ The drawing scale ratio must be in same unit
∴ Change the feet to inch
∵ 1 foot = 12 inches
∴ 10 feet = 10 × 12 = 120 inches
∴ The scale is 0.5 inches : 120 inches
- Simplify the scale by multiply it by 2
∴ The scale is 1 in : 240 in
- Lets find the dimensions on the blueprints
∵ The real dimensions are 18 feet and 16 feet
- Change the feet to inches
∴ 18 feet = 18 × 12 = 216 inches
∵ 16 feet = 16 × 12 = 192 inches
∵ The scale is 1 : 240
∴ 1/240 = x/216 ⇒ use cross multiplication
∴ 240 x = 216 divide both sides by 240
∴ x = 0.9 inch
∵ The scale is 1 : 240
∴ 1/240 = y/192 ⇒ use cross multiplication
∴ 240 y = 192 divide both sides by 240
∴ y = 0.8 inch
* The dimensions on the blueprints are 0.9 inches and 0.8 inches
Find the derivative of f(x) = 12x^2 + 8x at x = 9.
Answer:
224
Step-by-step explanation:
We will need the following rules for derivative:
[tex](f+g)'=f'+g'[/tex] Sum rule.
[tex](cf)'=cf'[/tex] Constant multiple rule.
[tex](x^n)'=nx^{n-1}[/tex] Power rule.
[tex](x)'=1[/tex] Slope of y=x is 1.
[tex]f(x)=12x^2+8x[/tex]
[tex]f'(x)=(12x^2+8x)'[/tex]
[tex]f'(x)=(12x^2)'+(8x)'[/tex] by sum rule.
[tex]f'(x)=12(x^2)+8(x)'[/tex] by constant multiple rule.
[tex]f'(x)=12(2x)+8(1)[/tex] by power rule.
[tex]f'(x)=24x+8[/tex]
Now we need to find the derivative function evaluated at x=9.
[tex]f'(9)=24(9)+8[/tex]
[tex]f'(9)=216+8[/tex]
[tex]f'(9)=224[/tex]
In case you wanted to use the formal definition of derivative:
[tex]f'(x)=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}[/tex]
Or the formal definition evaluated at x=a:
[tex]f'(a)=\lim_{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}[/tex]
Let's use that a=9.
[tex]f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}[/tex]
We need to find f(9+h) and f(9):
[tex]f(9+h)=12(9+h)^2+8(9+h)[/tex]
[tex]f(9+h)=12(9+h)(9+h)+72+8h[/tex]
[tex]f(9+h)=12(81+18h+h^2)+72+8h[/tex]
(used foil or the formula (x+a)(x+a)=x^2+2ax+a^2)
[tex]f(9+h)=972+216h+12h^2+72+8h[/tex]
Combine like terms:
[tex]f(9+h)=1044+224h+12h^2[/tex]
[tex]f(9)=12(9)^2+8(9)[/tex]
[tex]f(9)=12(81)+72[/tex]
[tex]f(9)=972+72[/tex]
[tex]f(9)=1044[/tex]
Ok now back to our definition:
[tex]f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}[/tex]
[tex]f'(9)=\lim_{h \rightarrow 0} \frac{1044+224h+12h^2-1044}{h}[/tex]
Simplify by doing 1044-1044:
[tex]f'(9)=\lim_{h \rightarrow 0} \frac{224h+12h^2}{h}[/tex]
Each term has a factor of h so divide top and bottom by h:
[tex]f'(9)=\lim_{h \rightarrow 0} \frac{224+12h}{1}[/tex]
[tex]f'(9)=\lim_{h \rightarrow 0}(224+12h)[/tex]
[tex]f'(9)=224+12(0)[/tex]
[tex]f'(9)=224+0[/tex]
[tex]f'(9)=224[/tex]
Which value is needed in the expression below to create a perfect square trinomial?
x2+8x+______
4
8
16
64
Answer:
16
Step-by-step explanation:
i know because i did the test
Answer:
16 for people with ads i really need brainliest
Step-by-step explanation:
Cathy lives in a state where speeders fined $ 10 for each mile per hour over the s speed limit cathy was given a fine for $80for speeding on a road where the speed limit is 50 miles per hour how fast was cathy driving
Answer:
58 miles per hour
Step-by-step explanation:
First you need to divide 80 by 10 to see how many miles she was over the speed limit.
80/10 = 8 miles over the speed limit.
The speed limit was 50, so 50 + 8 = 58 miles.
So Cathy was driving at 58 miles per hour
Answer:
58mph
Step-by-step explanation:
Given:
Each mph over the speed limit gets fined $10
or mathematically, rate of fine = $10/mph
also, total fine was $80.
Number of mph over the speed limit,
= total fine ÷ rate of fine
= $80 ÷ $10/mph
= 8 mph.
Given that the speed limit was 50 mph, Cathy's final speed,
= speed limit + number of mph over speed limit
= 50 + 8
= 58 mph
Write and equation that represents the distance traveled by a person who can bike at a rate of 8 miles per hour. Can someone help me with this?
Answer:
d = 8t
Step-by-step explanation:
A lot of math is about matching patterns. Here, the pattern you can match is given in the problem statement:
d = 6t . . . . . equation for distance traveled at 6 miles per hour
You are asked to write an equation for distance traveled at 8 miles per hour. You can see the number 6 in the above equation matches the "miles per hour" of the traveler. This should give you a clue that when the "miles per hour" changes from 6 to 8, the number in the equation will do likewise.
The equation you want is ...
d = 8t . . . . . equation for distance traveled at 8 miles per hour
The distance traveled by a person biking at 8 miles per hour is represented by the equation d = 8t, where d is the distance, and t is the time in hours. For example, if they bike for 2 hours, they will have traveled 16 miles.
Explanation:The question is about calculating the distance traveled by a person who can bike at a rate of 8 miles per hour. This can be represented by the equation d = rt, where d is the distance, r is the rate, and t is the time.
In this case, the rate (r) is 8 miles per hour. Therefore, the equation becomes: d = 8t, meaning the distance travelled is equal to 8 times the amount of time spent biking.
For example, if the person bikes for 2 hours, we would substitute 2 for t in the equation, which would look like this: d = 8 * 2. The resulting distance (d) is 16 miles.
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You are riding the bus to school and you realize it is taking longer because of all the stops you are making. The time it takes to get to school, measured in minutes, is modeled using the function g(x) = x4 − 3x2 + 4x − 5, where x is the number of stops the bus makes. If the bus makes 2 stops after you board, how long does it take you to get to school?
Answer:
7 minutes
Step-by-step explanation:
start with formula
g(x) = x^4 - 3x^2 + 4x - 5
substitute x with number of stops (2)g(2) = 2^4 - 3(2^2) + 4(2) - 5
simplify using p.e.m.d.a.s: start with exponents
g(2) = 16 - 3(4) + 4(2) - 5
multiplyg(2) = 16 - 12 + 8 - 5
subtract/add16 - 12 = 4
4 + 8 = 12
12 - 5 = 7
input: 2
output: 7
ordered pair: (2,7)
By modeled function, the time taken to reach the school is 7 minutes.
What is modeled function ?A function which depicts the variation of a given dependent parameter represented by the variable in the function is known as a modeled function. For modeled function, we input the value of the dependent parameter in place of the given variable and the solution of function gives us the result of dependency.
How to calculate the time taken to reach the school ?Given that the time it takes to get to school, measured in minutes, is modeled using the function g(x) = [tex]x^{4} - 3x^{2} + 4x - 5[/tex] , where x is the number of stops the bus makes.
Also said that the bus makes 2 stops after we board.
Thus the dependent parameter is stop which is represented by the variable x in the modeled function g(x) and the solution of g(x) gives us the time period. We will get the time period by putting x = 2 in the modeled function.
Putting x = 2 in g(x), we get -
⇒ g(x) = [tex]2^{4} - 3*2^{2} + 4*2 - 5[/tex]
⇒ g(x) = 16 - 12 + 8 - 5
∴ g(x) = 7
Thus the time period is 7 units.
Therefore, by modeled function, the time taken to reach the school is 7 minutes.
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Chester used the regression equation of the weight loss plan to make a prediction within the given data range. Complete his work to calculate the number of weekly hours of aerobic activity needed for a monthly weight loss of 3 pounds. Round to the nearest hundredth.
Interpolated Data
About
hours of weekly aerobic activity will result in 3 pounds of monthly weight loss.
Answer:
The answer is 1.94
You need to have 1.94 hours a week to loose a monthly weight of 3 pounds
Three consecutive multiples of 7 have a sum of 84. What is the greatest these numbering?
A. 7
B. 21
C. 35
D. 42
Answer:
C. 35
Step-by-step explanation:
Let x represent the largest of the multiples of 7. The sum will be ...
x + (x -7) + (x -14) = 84
3x = 105 . . . . . . . . . . . . . add 21 and simplify
x = 35 . . . . . . . . . . . . . . . divide by 3
The greatest of the numbers of interest is 35.
_____
Two consecutive multiples of 7 will differ by 7. If x is the largest, the next-largest is x-7, and the one before that is x-14.
Directions: Answer the questions below. Make sure to show your work and justify all your answers.
15. The city bike rental program is analyzing their growth in member rates. The number of regular members is growing by
4.7% per month. The number of VIP members is growing by 65% per year. Write a function to represent the number of
regular members after t years. Then, write an equivalent function that represents the regular members with only 1
compounding per year. What is the effective yearly rate of growth of regular members? Determine the effective rate of
growth per year for regular members. Which type of member is growing at a faster rate?
a What is the effective YEARLY rate of the growth for regular members?
b. Which type of member is growing at a faster rate?
Answer:
a) 73.52%
b) Regular membership is growing faster
Step-by-step explanation:
a) r(t) = r0·1.047^(12t) . . . . regular members after t years, where r0 is the initial value of regular members at t=0.
Equivalently, this is ...
r(t) = r0·(1.047^12)^t ≈ r0·1.7352^t
This shows the effective annual growth rate for regular members is 73.52%.
__
b) The 74% yearly growth rate of regular members is higher than the 65% yearly growth rate of VIP members. Regular membership is growing faster.
Which of the following inequalities has a solution set that when graphed on the number line, is a single segment of finite length? A. x4 ≥ 1 B. x3 ≤ 27 C. x2 ≥ 16 D. 2≤ |x| ≤ 5 E. 2 ≤ 3x+4 ≤ 6
Answer:
Step-by-step explanation:
E
Answer:
B
Step-by-step explanation:
Edge
Starting at home Jessica traveled uphill to the toy store for 12 minutes at just 10 mph. She then traveled back home along the same path downhill at a speed of 30 mph. What is her average speed for the entire trip from home to the toy store and back?
Answer:
15 miles per hour
Step-by-step explanation:
Average Speed is:
Average Speed = Total Distance/Total Time
Going uphill, she took 12 minuets, that is hours is 12/60 = 0.2 hours
We know D = RT, Distance = Rate(speed) * Time
Thus,
D = 10mph * 0.2 hr = 2 miles
So, total distance (uphill and downhill) = 2 + 2 = 4 miles
Downhill the time she took is
D = RT
2miles = 30mph * T
T = 2/30 = 1/15 hours = 1/15 * 60 = 4 minutes
Hence total time is 12 + 4 = 16 minutes
Note: 16 minutes = 16/60 = 4/15 hours
Now
Average Speed = Total Distance/Total Time
Average Speed = 4 miles/ 4/15 hours = 15 mph
Answer:
The Answer is 15.00000000000000000... miles per hour
Step-by-step explanation: You do tis by doing your work and not checking for answers
In order to estimate the mean amount of time computer users spend on the internet each month, how many computer users must be surveyed in order to be 90% confident that your sample mean is within 13 minutes of the population mean? Assume that the standard deviation of the population of monthly time spent on the internet is 228 min
Answer:
832
Step-by-step explanation:
standard deviation =228 minute
error =13 minute given
confidence level =905% =0.90
α=1-0.90=0.1
[tex]z_\frac{\alpha }{2}=z_\frac{0.1}{2}=1.645[/tex]
we know that sample size should be greater than
[tex]n\geq \left ( z_\frac{\alpha }{2}\times \frac{\sigma }{E} \right )^2[/tex]
[tex]n\geq \left ( 1.645\times \frac{228}{13} \right )^{2}[/tex]
[tex]n\geq 28.850^2[/tex]
[tex]n\geq 832.3668[/tex]
n=832
Jessica has three sports cards, one for football (F), one for baseball (B), and one for soccer (S). She picks one card, replaces it, and then picks another card. The sample space for this compound event is listed.
Answer:
The answer is 9
Answer:
Step-by-step explanation:
9
Water pressure increases 0.44 pounds per square inch (0.44 psi) with each increase of one foot in depth below sea level. Identify the independent and dependent quantity in the situation.
Answer:
Depth below sea level is the independent quantity,
Water pressure is the dependent quantity
Step-by-step explanation:
An independent quantity is a variable that can be changed in an experiment. While, dependent quantity results from the independent quantity or we can say, that depends upon the independent quantity.
Here,
The water pressure increases 0.44 pounds per square inch (0.44 psi) with each increase of one foot in depth below sea level,
So, for measuring the water pressure we took depth below sea level as a variable,
⇒ Depth below sea level is the independent quantity,
While, with increasing depth by 1 foot the pressure is also increase by 0.44 pounds per square inches ⇒ pressure depends upon the depth
⇒ Water pressure is the dependent quantity.
Answer:The best answer I think is depth, water pressure
Step-by-step explanation:
PLEASE HELP ME WITH-THIS MATH QUESTION
Answer:
146 degrees
Step-by-step explanation:
The measure of the arc is the measure of the central angle that the arc is created from.
The central angle has a measure of 146 degrees so that is the measure of the arc there.
PLEASE HELPPPPPPPPPPPP!!!!!!!! Two mechanics worked on a car. The first mechanic charged $115 per hour, and the second mechanic charged $45 per hour. The mechanics worked for a combined total of 35 hours, and together they charged a total of $2975. How long did each mechanic work?
Answer:
First mechanic: 20 hours
Second mechanic: 15 hours
Step-by-step explanation:
First we create two equations where:
x - hours of first mechanic
y - hours of second mechanic
x+y=35
115x+45y=2975
Then, we multiply both sides of the first equation by 45, and then subtract it from the second equation:
45x+45y=1575
|115x+45y=2975
-|45x+45y = 1575
70x = 1400
x=20 hours
Now we know for how many hours the first mechanic worked. Now we just need to subtract that from the combined total to find the second mechanic's hours:
35-20=15 hours
If the length of a diagonal of a square is "a", what is the length of its side?
[tex]b[/tex] - the side of a square
[tex]a=b\sqrt2\\b=\dfrac{a}{\sqrt2}\\\\b=\dfrac{a\sqrt2}{2}[/tex]
Answer:
a√2 / 2.
Step-by-step explanation:
Using the Pythagoras Theorem;
a^2 = s^2 + s^2 where s is the length of each side of the square.
2s^2 = a^2
s^2 = a^2 / 2
s = √(a^2 / 2)
= a / √2
= a√2 / 2 .