Answer:
The given sequence is decreasing by a factor of 2 each time, so each term is half of the previous term.
We can write the nth term of the sequence as:
a_n = a_1 * (1/2)^(n-1)
where a_1 is the first term of the sequence (12 in this case) and n is the position of the term we want to find.
For example, to find the 4th term of the sequence, we would have:
a_4 = 12 * (1/2)^(4-1)
= 12 * (1/2)^3
= 12 * 1/8
= 1.5
Therefore, the formula for the nth term of the sequence 12, 6, 3, ... is:
a_n = 12 * (1/2)^(n-1)
A spherically shaped hot air balloon has a
diameter of about 27 meters when fully inflated.
What is the volume of the hot air balloon when it
is fully inflated?
Answer: 7725.5775
Step-by-step explanation:
d=27
r=d/2=27/2=13.5
the volume of the spherical balloon= 3.14*r^3
= 3.14*(13.5)^3
= 7725.5775
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which of the following representations show y as a function of x
The option that is a representation that shows y as a function of x is the graph in option 2. The answer is B.
What is a Function?A function is any relation or table of values which may be represented in a graph that has only one possible y value that is assigned to each x-value.
The first option is not a function because x-value 0 has two corresponding y-values, 4 and 9.
In the third option, we also have two y-values, 5 and -5, that is assigned to one x-value, 0. So, it is not a function.
The graph in option 2 represents y as a function of x, because no two y-values is assigned to the same x-value.
The answer is: B.
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The makers of a new app recorded the number of times the app was downloaded each day for the first year the app was available.
Select the correct methods they could use to describe the data.
To describe how the number of daily downloads varies, they could use the median value. To describe how the number of daily downloads varies, they could use the mean absolute deviation.
To describe how the number of daily downloads varies, they could use the maximum value. To summarize the number of daily downloads with a single number, they could use the mean value.
To summarize the number of daily downloads with a single number, they could use the interquartile range. To summarize the number of daily downloads with a single number, they could use the minimum value.
The best method to describe data is use median value for how number of daily downloads varies, and mean value or interquartile range for number of daily downloads. So, correct options are A, D and E.
The median value is a measure of central tendency that represents the middle value of a set of data. It is useful to describe how the number of daily downloads varies, as it gives an idea of the typical value of the dataset.
However, mean absolute deviation is a measure of dispersion that describes how far the data values are from the mean. It is not an appropriate method to describe how the number of daily downloads varies, as it does not give information about the distribution of the data.
The maximum value is a measure of the largest value in a dataset, which can provide information on the upper limit of the number of daily downloads. However, it is not an appropriate method to describe how the number of daily downloads varies, as it does not give information on the spread or distribution of the data.
The mean value is a measure of central tendency that summarizes the data with a single number, but it may not be the best choice if the data is skewed or has outliers.
The interquartile range is a measure of dispersion that summarizes the spread of the middle 50% of the data. It can be used to summarize the number of daily downloads with a single number, but it does not give information on the typical or extreme values of the dataset.
The minimum value is a measure of the smallest value in a dataset, which can provide information on the lower limit of the number of daily downloads. However, it is not an appropriate method to summarize the number of daily downloads with a single number, as it does not give information on the spread or distribution of the data.
So, correct options are A, D and E.
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Tom made some beads and packed all the bead in 14 small boxes and 3 large boxes. She filled each small box with the same number of beads and each large box with the same number of beads. There were 4 more beads in each large box than in each small box. 7/9 of the beads made were packed in the small boxes. How many beads were there in each small box?
Answer:
Each small box has 24/17 beads.
Step-by-step explanation:
Let's call the number of beads in each small box "s" and the number of beads in each large box "l".
We know that there are 14 small boxes, so the total number of beads in the small boxes is 14s. We also know that there are 3 large boxes, so the total number of beads in the large boxes is 3l.
From the problem, we know that there are 4 more beads in each large box than in each small box, so we can write:
l = s + 4
We also know that 7/9 of the total number of beads were packed in the small boxes, so we can write:
14s + 3l = 7/9(total number of beads)
We can simplify this expression by substituting l = s + 4:
14s + 3(s + 4) = 7/9(total number of beads)
Expanding and simplifying:
17s + 12 = 7/9(total number of beads)
Now, we need one more equation to solve for s. We know that the total number of beads is equal to the sum of the beads in the small and large boxes:
total number of beads = 14s + 3(s + 4)
Simplifying:
total number of beads = 17s + 12
Now we have two equations that we can use to solve for s:
17s + 12 = 7/9(total number of beads)
total number of beads = 17s + 12
We don't know the total number of beads, but we do know that it is a multiple of both 14 and 3 (since there are 14 small boxes and 3 large boxes). The smallest multiple of both 14 and 3 is 42, so let's assume that the total number of beads is 42x, where x is some number.
Substituting 42x for "total number of beads" in the two equations:
17s + 12 = 7/9(42x)
42x = 17s + 12
Simplifying:
153s + 108 = 98x
42x = 17s + 12
Now we have two equations and two unknowns (s and x). We can solve for s in terms of x by isolating s in the second equation:
17s = 42x - 12
s = (42x - 12)/17
We can substitute this expression for s into the first equation:
17((42x - 12)/17) + 12 = 7/9(42x)
Simplifying:
42x - 12 + 12 = 14x
28x = 24
x = 24/28 = 0.857
Now we know that the total number of beads is:
42x = 42(0.857) = 36
And we know that each small box has:
s = (42x - 12)/17 = (36 - 12)/17 = 24/17
So each small box has 24/17 beads.
solve for x x/3=? please help me image attached
The value of x is 5.48 units
Let us assume that the left right triangle be ABC and the right triangle on the right side be ABD.
So, the larger right triangle would be DAC.
Consider thr outer right triangle DAC.
The length of the hypotenuse DC would be,
DC = CB + BD
DC = 3 + 7
DC = 10 units
Also right triangle ABC and DAC are similar triangles.
We know that the sides of the smilar triangles are in proportion.
Using the definition of similar triangles for DAC and ABC,
DA/AB = AC/BC = DC/AC
Consider, AC/BC = DC/AC
x/3 = 10/x
this is the required proportion.
x² = 3 × 10
x² = 30
x = 5.48 units
Thus the value of x = 5.48 units
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Select the correct answer.
If the temperature outside is 86°F, the heat index can be found using the equation y = 0.004x²-0.1243x 84.028. This equation is also the curve of
best fit for the values in the table. In the equation, x represents the relative humidity and y represents the heat index.
Relative Humidity
Heat
If the temperature outside is 86°F and the relative humidity is 55%, the heat index is: C. 89°F.
How to determine the equation of line of best fit?In this scenario, the relative humidity would be plotted on the x-axis (x-coordinate) of the scatter plot while the heat index would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
From the scatter plot which models the relationship between the x-values and y-values, a quadratic equation for the line of best fit when the temperature outside is 86°F, is given by:
y = 0.004x²- 0.1243x + 84.028
when x = 55%, the heat index can be calculated as follows;
y = 0.004(55)²- 0.1243(55) + 84.028
y = 89.2915 ≈ 89°F
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I need help please geometry not my strong suit
The image point of (-7, -8) after the sequence of transformations is given as follows:
(-4.5, -4).
How to obtain the coordinates of the image point?The original coordinates are given as follows:
(-7, -8)
The first transformation is a dilation with a scale factor of 1/2, meaning that each coordinate is multiplied by 1/2, hence:
(-3.5, -4).
The second transformation is a translation of one unit left, meaning that one is subtracted from the y-coordinate, thus the image point after the sequence of transformations is given as follows:
(-4.5, -4).
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Determine whether the statement below is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
logb (x3 + y3) = 3 logb x + 3 logby
Using rules for logarithms we can see that the statement is false.
Is the statement true or false?Here we have the equation:
logₐ(x^3 + y^3) = 3logₐ(x) + 3logₐ(y)
And we want to see if it is true.
First, remember two rules:
logₐ(x^n) = n*logₐ(x)
and:
logₐ(x) + logₐ(y) = logₐ(x*y)
Then, the right side of the statement can be rewritten as:
3logₐ(x) + 3logₐ(y)
3(logₐ(x) + logₐ(y)) = 3*logₐ(x*y) = logₐ((x*y)^3)
And that is different to what we got in the statement, so the statement is false.
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Hello, I hope you are having a great day so far, I was wondering if someone ca (seriously) help me and not play around. I really need an Answer asap as soon as possible
PLEASE HELP (I NEED AN ANSWER QUICK!)
Answer:
the corresponding sides are proportional
hi can someone help with this question
Based on the information, we can infer that the investment was made 11.53 years ago.
How to calculate how many years ago was the investment made?To calculate how many years ago was the investment mafe we have to can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial amount invested)
r = the interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Let's start by finding the initial principal (P) by working backwards from the final amount (A):
A = P(1 + r/n)^(nt)
31372.0 = P(1 + 0.022/1)^(14)(1 + 0.022+0.007/1)^(1(t-4))
Simplifying, we get:
31372.0 = P(1.093248)(1.029)^(t-4)
P = 27500 euros (initial investment)
Now we can solve for t:
31372.0 = 27500(1.093248)(1.029)^(t-4)
1.1412 = (1.029)^(t-4)
log(1.1412) = log(1.029)^(t-4)
t - 4 = log(1.1412)/log(1.029)
t = log(1.1412)/log(1.029) + 4
t = 11.53
Therefore, the investment was made about 11.53 years ago.
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The data table shows the numbers of eggs laid by
individual chickens in a year
What is the median number of eggs laid in a year?
A. 231
B. 229
C. 230
D. 234,6
The value of the median number of eggs laid in a year is,
⇒ 231
We have to given that;
The data table shows the numbers of eggs laid by individual chickens in a year.
Now, We can arrange it into ascending order as;
⇒ 222, 229, 229, 231, 234, 235, 262
Since, There are 7 terms
Hence, Median is,
= (7 + 1)/2
= 4th term
= 231
Thus, The value of the median number of eggs laid in a year is,
⇒ 231
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Answer:
A. 229 is correct
answer D.231 is wrong
14. During 2006, a swimming lesson at a particular school lasted 45 minutes.
(a) In 2007, the lesson time will be 50 minutes.
Find the increase in the lesson time from 2006 to 2007 as a percentage of the lesson time in 2006.
(b) The lesson time in 2007 will be 25% more than it was in 2005. Find how long the lesson lasted in 2005.
(c) At present, James takes 240 seconds to swim 100 metres. In a year's time, he would have improved his swimming time by 25%. Calculate the time he will take to swim 100 metres in a year's time.
m (d) Robert, at present, also takes 240 seconds to swim 100 metres. In a year's time, he would have increased his swimming speed by 25%. Calculate the time he will take to swim 100 metres in a year's time.
(e) Who will be the faster swimmer, James or Robert, in a year's time?
(a) The lesson time in 2007 is 11.1% more than the lesson time in 2006.
(b) The lesson lasted 40 minutes in 2005.
(c) James will take 180 seconds to swim 100 meters in a year's time.
(d) Robert will also take 180 seconds to swim 100 meters in a year's time.
(e) James and Robert will swim equally which means that their speed will be same and they will be complete at same time.
(a) The increase in lesson time from 2006 to 2007 is:
Increase = 50 - 45 = 5 minutes
The percentage increase is:
Percentage increase = (5 / 45) x 100% = 11.1%
Therefore, the lesson time in 2007 is 11.1% more than the lesson time in 2006.
(b) Let x be the lesson time in 2005. The lesson time in 2007 is 25% more than it was in 2005, so:
1.25x = 50
Solving for x, we get:
x = 40
Therefore, the lesson lasted 40 minutes in 2005.
(c) James currently takes 240 seconds to swim 100 meters. If he improves his time by 25%, his new time will be:
New time = 240 - (0.25 x 240) = 180 seconds
Therefore, he will take 180 seconds to swim 100 meters in a year's time.
(d) Robert currently takes 240 seconds to swim 100 meters. If he increases his speed by 25%, his new time will be:
New time = 240 - (0.25 x 240) = 180 seconds
Therefore, he will also take 180 seconds to swim 100 meters in a year's time.
(e) Both James and Robert will take the same time to swim 100 meters in a year's time, so they will be equally fast.
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A man earns $65000. He pays 18% of that in tax. (a) Calculate how much he has left, after paying the tax. (b) He invests $4500 and earns 6% interest per annum. Calculate the interest after 2 years. (c) He takes out a loan to buy a car. The price of the car is $24750. He pays $25740 altogether. What is the percentage interest?
a) The amount left after paying the tax is $53300.
(b) The interest after 2 years is $540.
(c) The percentage interest is 4%.
We have,
a)
The amount of tax the man pays.
= $65000 x 0.18
= $11700
Therefore, he has left.
= $65000 - $11700
= $53300
(b)
The interest earned after 2 years.
= $4500 x 0.06 x 2
= $540
(c)
The total amount of interest paid on the loan.
= $25740 - $24750
= $990
The percentage interest.
= ($990 / $24750) x 100%
= 4%
Thus,
(a) The amount left after paying the tax is $53300.
(b) The interest after 2 years is $540.
(c) The percentage interest is 4%.
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Jasmine sold 5 cherry pies and 12 Lemmon mer
Answer:
6
Step-by-step explanation:
this is if you meant: Jasmine sold 5 cherry pies and 12 lemonade how much more did Jasmine sell of lemonade than cherry pies
y = 2x X 0 2 3 4 6 4 8 5 10 Click to select points on the graph. 10 9 8 0 7 5
Answer:
The points selected on the graph are:
(0, 0), (2, 4), (3, 6), (4, 8), (6, 12), (4, 8), (8, 16), (5, 10)
Here is a table showing the coordinates of the selected points:
x y
0 0
2 4
3 6
4 8
6 12
4 8
8 16
5 10
a. Find x. The figure is not drawn to scale. b. Is the triangle equilateral, isosceles, or scalene? Explain.
*
0 points
Captionless Image
Answer: Based on the given figure above, we can conclude that the triangle is an isosceles triangle. By definition, an isosceles triangle is a triangle that has at least two equal sides. Since this is an isosceles triangle, 8x-10 =6x. Now we can solve for x. So,
8x-10 =6x
8x-6x = 10
2x =10
x= 5.
Therefore, the value of x in the figure is 5. Hope this is the answer that you are looking for.
question in the picture
1.) The average monthly income for Brianna would be = $1,850
2.) The average monthly expenses for Brianna would be =$3,145
3.) The total monthly cash flow = =$ −1,295
How to calculate the monthly income for Brianna?The monthly pay check after tax = $1600
The annual scholarship stipend = $3000
That is 3000/12 = $250
Therefore, the average monthly income = 1600+250 = $1,850.
The average monthly expenses = 700+120+75+140+25+110+100+300+250+(12000+1000+1500+800+600/12)
= 1820 + 15900/12
= 1820 + 1325
= $3,145
The monthly cash flow = 1850-3145 =$ −1,295
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GIVNING BRINLIE$T
Order the numbers from greatest to least based on their absolute value.
|−25
|, |0.5|, |−34
|, |0.35|
Answer:
|-34|, |-25|, |0.5|, |0.35| is the correct order.
Name the characteristics a shape has to have to be defined as the following
quadriatera
Triangle
square
Answer:
A quadrilateral is a shape that has four straight sides and four angles.
A triangle is a shape that has three straight sides and three angles.
A square is a special type of quadrilateral that has four straight sides of equal length and four right angles.
What’s the equation and solution?
The equation for the rectangle is adding the interior angles:
x + x - 5 + 71 + y + 21 = 360°
Solving that for y, we will get:
2x + y + 87 = 360
How to find the equation?Remember that the sum of the interior angles of any figure with 4 sides must be 360°.
Then we can write an equation:
x + x - 5 + 71 + y + 21 = 360°
2x + y + 87 = 360
Solving it for y:
y = 273 - 2x
Now there is a clear problem in the diagram because the angle in the bottom left is clearly larger than 90°, but it says that the angle measures 71°, so there we have a problem.
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Jodi’s car used 12 gallons of gas to travel 456 miles. How many miles did her car travel per gallon of gas? Show work
Answer:
To find the number of miles Jodi's car traveled per gallon of gas, we need to divide the distance traveled by the amount of gas used:
miles per gallon = distance traveled / amount of gas used
distance traveled = 456 miles
amount of gas used = 12 gallons
miles per gallon = 456 miles / 12 gallons
miles per gallon = 38 miles/gallon
Therefore, Jodi's car traveled 38 miles per gallon of gas.
Answer:
38 miles
Step-by-step explanation:
Set up your division: 456 / 12
456 divided by 12 is 38
So, Jodi's car travels at 38 miles per gallon of gas.
You invest a lump sum of $1,500 into a bank account that offers 7.75%
simple interest.
1) How much interest is earned each year? $
2) How much money will be in the account after 20 years? $
1. intrest earned per year $116.25
2. total after 20 years $3,825
116x20= $2325
$1500+ 2325=3825
Prove: 36 + 324 + 900+. . . +(12n − 6)2 = 12n(4n2 − 1)
By mathematical induction, the given formula holds for all natural numbers n:
S(n) = 36 + 324 + 900 + ... + (12n - 6)² = 12n(4n² - 1)
How to solveTo demonstrate our point, mathematical induction can be employed.
We want to prove that the given formula holds for all natural numbers n:
S(n) = 36 + 324 + 900 + ... + (12n - 6)² = 12n(4n² - 1)
Using mathematical induction:
Step 1: Base case (n=1)
S(1) = 6² = 36
12 * 1 * (4 * 1² - 1) = 36
Since S(1) holds true, the base case is proven.
Step 2: Inductive step (Assume it's true for n=k, and show it's true for n=k+1)
Assumption: S(k) = 36 + 324 + 900 + ... + (12k - 6)² = 12k(4k² - 1)
We follow the exhaustive process to prove:
= 12(4k³ + 12k² + 11k + 3)
Since both expressions for S(k+1) are equal, the inductive step is proven.
Thus, by mathematical induction, the given formula holds for all natural numbers n:
S(n) = 36 + 324 + 900 + ... + (12n - 6)² = 12n(4n² - 1)
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ELECTRICAL POTENTIAL The electrical potential between two electrons is given by a formula has the form 1/r + 1/ 1-r
In a case whreby the electrical potential between two electrons is given by a formula has the form 1/r + 1/ 1-r the simpification of the expression is 1/r(1-r).
How can the expression be simplified?Looking at the expression we can see that it is adion of two expression which implies that we will need to perform an addition operation then later simplified the result, this is been done below
We can find the LCM as r(1-r)
(1-r +r)/ r(1-r)
=1/r(1-r)
Therfore, after performing the addition operation as well as the simplification, then the the simpification of the expression is 1/r(1-r).
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complete question;
The electrical potential between two electrons is given by a formula has the form 1/r + 1/ 1-r simplify the expression.
HELP DUE IN 30 MINUTES! I have an ice cream cone that has a radius of 1in and a height of 3in. How can you find how much ice cream could fit in the cone?
Answer:
Step-by-step explanation:
just do how tall times the diamiter divided by the
Use a net to find the surface area of the prism.
A. 426m2
B. 213m2
C. 306m2
D. 336m2
The surface area of the rectangular prism in this problem is given as follows:
A. 426 m².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas. -> net method.
The dimensions for this problem are given as follows:
5 m, 12 m and 9 m.
Hence the surface area of the prism is given as follows:
S = 2(5 x 12 + 5 x 9 + 12 x 9)
S = 426 m².
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13x−6y=22
x=y+6
Please help first come first surve
Answer:
The answer is
x= -2
y= -8
Step-by-step explanation:
x=y+6
substitute into equation 1
13(y+6)-6y=22
13y+78-6y=22
13y-6y=22-78
7y=-56
divide both sides by 7
7y/7= -56/7
y= -8
x=y+6
x= -8+6
x= -2
10. A pizza with a diameter of 5 inches is divided into 8 sectors
of equal area.
What is the approximate area of each pizza slice? Round
your answer to the nearest hundredth.
O
O
The approximate area of each pizza slice is 2.45 sq inches
What is the approximate area of each pizza slice?From the question, we have the following parameters that can be used in our computation:
Diameter = 5 inches
This means that
Radius, r = 5/2 inches
Evaluate
Radius, r = 2.5 inches
The approximate area of each pizza slice is calculated as
Area = Circle area/number of sectors
So, we have
Area = 3.14 * 2.5^2/8
Evaluate
Area = 2.45 sq inches
Hence, the approximate area of each pizza slice is 2.45 sq inches
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10. i’d the area of a circle is 201.06 cm^2, find its diameter and circumference.
11. if m < MPL =63 degrees, find each measure
The diameter of the circle is 16.04 cm.
The circumference is 50.39 cm
How to solve for the diameterA = πr²
where A is the area of the circle and r is its radius.
square both sides
r = √(A/π) = √(201.06/π) = 8.02 cm
The diameter of the circle is twice the radius, so we can find it by multiplying the radius by 2:
d = 2r = 2(8.02) = 16.04 cm
Therefore, the diameter of the circle is 16.04 cm.
To find the circumference of the circle, we can use the formula:
C = 2πr
where C is the circumference and r is the radius. We already know the value of the radius, so we can substitute it into the formula:
C = 2π(8.02) = 50.39 cm
Therefore, the circumference of the circle is 50.39 cm.
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Solve for BC: 3√2 A B C
Sides AB = 3√2 and BC = 6.
The given triangle ABC is a right-angled triangle, as ∠BAC = 90°.
In the given right triangle ABC,
Hypotenuse of the triangle = BC
Base and height = AC and AB.
Also, we see from the diagram that ∠ACB and ∠ABC are equal.
∴ Triangle ABC is isosceles, with sides AC = AB = 3√2.
Now, by Pythagoras' theorem,
Hypotenuse² = Base² + Height²
Or, BC² = AC² + AB²
Or, BC² = (3√2)² + (3√2)²
⇒ BC² = 36
Or, BC = 6
Hence, sides AB = 3√2 and BC = 6.
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