Answer:
16
Step-by-step explanation:
Describe the pattern 0.13, 0.65, 3.25, 16.25
Let n be the current term and n+1 be the next term
Then the pattern is: n+1 = n * 5
Step-by-step explanation:
Given series is:
0.13, 0.65, 3.25, 16.25
We can find the ratio between consecutive numbers to find the pattern
So,
[tex]Ratio = \frac{0.65}{0.13}\\=5[/tex]
We can see that multiplying the previous term with 5 gives us the next term
0.13 * 5 = 0.65
0.65 * 5 = 3.25
3.25 * 5 = 16.25
Let n be the current term and n+1 be the next term
Then the pattern is: n+1 = n * 5
Keywords: Pattern, Sequence
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what is 2x + 1 = 15 if x =8
Answer:
17
Step-by-step explanation:
17=15
so this is not equal
You are comparing apples to oranges in a fruit bowl. Is the ratio 2:3 the same as the ratio 3:2?
Answer:
No, the two ratios are not the same.
Step-by-step explanation:
When we are saying "apples to oranges", mathematically it means:
[tex]\frac{Apples}{Oranges}[/tex],
Which could be 2:3 or 3:2, which in fractional from are written as [tex]\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex] respectively.
We see that
[tex]\frac{2}{3} \neq \frac{3}{20}.[/tex]
In words the ratio 2:3 says "for every two apples there are three oranges", and 3:2 says "for every three apples there are two oranges". Again we see that the two sentences are not saying the same thing, therefore the ratio 2:3 is not same as 3:2.
Final answer:
The ratio 2:3 is not the same as 3:2 because they represent different relationships between the quantities of apples and oranges in a comparative scenario or barter trade. These ratios suggest different terms of trade and would result in different exchange outcomes.
Explanation:
The question is whether the ratio 2:3 is the same as 3:2 when comparing apples to oranges. To understand this, we must recognize that a ratio represents a relationship between two quantities, expressing how many times one value contains the other or is contained within it. In the context of a fruit bowl, a ratio of 2:3 would mean for every 2 apples, there are 3 oranges, while the ratio 3:2 means for every 3 apples, there are 2 oranges. Therefore, these two ratios are not the same as they represent different relationships between the quantities of apples and oranges.
Considering ratio comparisons like in barter trading, the terms of trade are critical. If 2 bushels of apples can be traded for 3 bushels of oranges, that is a 2:3 apple-to-orange trade ratio. On the other hand, if we reverse the ratio to 3:2, it would mean something quite different for trade or value comparisons. Specifically, you'd need 3 bushels of apples to get 2 bushels of oranges.
It's essential to compare apples to apples; comparative statistics are only useful when the comparison is logical and applicable. The ratios 2:3 and 3:2 convey different terms and thus would yield different outcomes in any exchange or comparative scenario.
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Ryaan goes skydiving and falls at a constant rate toward the ground. The equation y = -32x + 14,000 represents the situation where y is the height of Ryaan in feet above the ground and x is the seconds since she jumped.
Which statement describes the situation?
a. From a starting position of 14,000 feet above the ground, she is ascending at 32 feet per second.
b. From a starting position of 32 feet above the ground, she is ascending at 14,000 feet per second.
c. From a starting position of 14,000 feet above the ground, she is descending at 32 feet per second.
d. From a starting position of 32 feet above the ground, she is descending at 14,000 feet per second.
MUTIPLE CHOICE ANSWER!!!1
Answer:
C, because
-32 x seconds since she jumped + 14000
because 14000 would be 14000 units above 0, and -32 represents the seconds she had jumped, which would basically be -32+14000, which is the same as saying 14000 - 32.
You take out $50,000 for loans during your college career. You must pay it back with 7% APR for 20 years, making monthly payments. Calculate the minimum monthly payment needed to do this.
Answer:
The monthly payment for the loan amount for 20 years is $806.167
Step-by-step explanation:
The principal loan amount= $ 50,000
The rate of interest = 7 %
the time period of loan = 20 years = 20 × 12 = 240 months
let the amount after 20 years = $ A
From Compounded method
Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm Time}[/tex]
or, A = 50,000 × [tex](1+\dfrac{\textrm 7}{100})^{\textrm 20}[/tex]
or, A = 50,000 × [tex](1.07)^{20}[/tex]
Or, A = 50,000 × 3.8696
∴ Amount = $ 193,480
So, The amount after 20 years = $ 193,480
The monthly payment amount = $ [tex]\frac{193480}{240}[/tex] = $ 806.167
Hence The monthly payment for the loan amount for 20 years is $806.167 Answer
Which expression is equivalent to (x^6×x^10/×^-3)^2 and why?
Answer:
The solution for the given expression is [tex]x^{38}[/tex] , i.e option C
Step-by-step explanation:
Given expression as :
[tex](\dfrac{x^{6}\times x^{10}}{x^{-3}})^{2}[/tex]
Now, From the common radix method
∵ In multiplication of radix , if the radix is same , then power is added
I.e [tex]x^{6}\times x^{10[/tex] = [tex]x^{6+10}[/tex]
Or , [tex]x^{6}\times x^{10[/tex] = [tex]x^{16}[/tex]
Now, The expression can be written as
[tex](\frac{x^{16}}{x^{-3}})^{2}[/tex]
And In Division of radix , if the radix is same , then power is subtracted
So, [tex]\frac{x^{16}}{x^{-3}}[/tex]
Or, [tex]x^{16 - (-)3}[/tex]
Or, [tex]x^{16 + 3}[/tex]
or, [tex]x^{19}[/tex]
∴ The expression is now
[tex](x^{19})[/tex]²
Now, again this is written as
[tex]x^{19}[/tex] × [tex]x^{19}[/tex]
I.e here again the radix is same and in multiple for, so, power is added
∴ [tex]x^{19}[/tex] × [tex]x^{19}[/tex] = [tex]x^{19+19}[/tex]
I.e [tex]x^{19}[/tex] × [tex]x^{19}[/tex] = [tex]x^{38}[/tex]
Hence The solution for the given expression is [tex]x^{38}[/tex] , i.e option C . Answer
In which type of triangle is the orthocenter on the perimeter of the triangle?
a right triangle
an acute triangle
an obtuse triangle
an equilateral triangle
Answer:
its a right triangle
Step-by-step explanation:
i just took the test
Answer: Yes, I can confirm it is right triangle!
what is 3² in xpoient
Answer:
9
Step-by-step explanation:
It saying 3 times to the power of 2
or
3 squared
so basically it's saying
3^3=9
How do I graph and find slope intercept for for x+y=0
Answer:
y = -x + 0
slope intercept: 0
Step-by-step explanation:
You would start at the origin, since your slope intercept is 0. The slope, -1 (since -x is the same as -1x), is telling us the line will be negative, so the line you are graphing will be heading up one space at a time towards the left, up 1 and sideways 1. Rise over Run.
Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochets at a rate of
of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to
skip crocheting some days so she can volunteer in other ways.
Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal.
How many days can Darcie skip to still meet her goal?
Answer:
I believe it's 15 days
Answer:
The maximum number of days that she can skip crocheting is s = 57
Step-by-step explanation:
Darcie wants to crochet a minimum of 3 blankets.
She can crochet at a rate of a blanket per day, so she makes 1 blanket in one day.
She has a total of 60 days to work.
If X is the number of days that she works, we can write it as:
X ≥ 3
This means that she works at least 3 days, so she makes at least 3 blankets.
X < 60
This means that she not can work 60 days or more, in this way she has at least one day to do another volunteer job.
then
3 ≤ X < 60
then we have:
1 ≤ s ≤ 60 - 3 = 57
where s is the days that she can skip, where the less or equal sign is used because we have a bigger or equal sign previously.
The maximum number of days that she can skip
The maximum number of days that she can skip crocheting is when the right equality is true, so s = 57.
What’s the answer ?
Answer:
C. Parallel
D. Segment
F. Ray
Explaination:
Answers A, E, & G (line, point, & plane) are undefined terms.
The number of students who attended the winter school dance was 20% less than the number of students attending the following if 220 students attend the Fall dance how many fewer students attended the winter day
Answer:
44
Step-by-step explanation:
20 percent less than 220
Answer:
The answer to this question is S=44
Step-by-step explanation:
STATE THE DOMAIN OF EACH OF THE FOLLOWING RELATIONS.
1.7) {(x, y): x = root y}
Domain ………
1.8) {(r, s): s = (2r -5)/13r }
Domain ………
1.9) {(a, b): ab = 12}
Domain ………
Step-by-step explanation:
1.7) x = √y
The square root must be non-negative, so the domain is x ≥ 0, or in interval notation, [0, ∞).
1.8) s = (2r − 5) / (3r)
The denominator can't be 0, so r can't be 0. So the domain is r ≠ 0, or in interval notation, (-∞, 0) (0, ∞).
1.9) ab = 12
Solve for b: b = 12/a
The denominator can't be 0, so a can't be 0. So the domain is a ≠ 0, or in interval notation, (-∞, 0) (0, ∞).
What is the area of a regular pentagon with a side of 10in?
Area of a regular pentagon with a side of 10in is 172
Step-by-step explanation:
Given:
Side of the regular pentagon = 10in
To Find:
Area of the regular pentagon=?
Solution:
We know that ,
[tex]Area of Pentagon = 5\times\text{ Area of triangle}[/tex]................(1)
Step 1: Finding the Area of the triangle
we know that in a right angle triangle, there are base, height and hypotenuse [tex]tan(\frac{\pi}{5}) =\frac{ height}{hypotenuse }[/tex]
So, from the above equation,
[tex]height=\frac{(base/2)}{tan(36^{\circ})}[/tex]
[tex]height=\frac{5}{tan(36)}=6.88[/tex]
area of right angle triangle
=> [tex]\frac{1}{2}\times base \times height[/tex]
=> [tex]=\frac{1}{2} \times 5\times 6.88[/tex]
=> 17.20
Area of the triangle =2 x area of right angle triangle
Area of the triangle =2 x 17.20
Area of the triangle= 34.40
Step 2: Finding the Area of the pentagon
Substituting the values in (1)
[tex]Area of Pentagon = 5\times 34.40 [/tex]
Area of Pentagon= 172
write the numerical expression as a power. (4 x4 x 4 = )
Answer:
[tex] {4}^{3} [/tex]
Step-by-step explanation:
your are taking 4 and multiplying it by itself three times hence 4 to the third power
Answer:
4³
Step-by-step explanation:
A simple question:
Is a vector made like or ?
Answer:
A vector is a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another.
The coordinates of the vertices of triangle 1 are A(6,6), B(12,9), C(9,6).
The coordinates of the vertices of triangle 2 are A′(2,2), B′(4,3), C′(3,2).
What transformation was performed on triangle 1 to create triangle 2?
Answer:
A
Step-by-step explanation:
The transformation performed on triangle 1 to create triangle 2 is a translation by the vector (-4, -4), which means each point was moved 4 units to the left and 4 units down.
Explanation:The transformation used can be determined by observing the differences between corresponding coordinates in the two triangles. If we subtract the coordinates of A′(2,2) from A(6,6), for instance, we get a change of -4 in the x-direction and -4 in the y-direction. Similarly, subtracting B′(4,3) from B(12,9) and C′(3,2) from C(9,6) results in changes of -8 and -6 in the x-direction and -6 and -4 in the y-direction, respectively.
This means that every point on triangle 1 was moved 4 units to the left and 4 units down to create triangle 2. Thus, the transformation that took place is called a translation by the vector (-4, -4).
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A radar beacon 40 feet above the ground picks up an airplane approaching at an angle of elevation
of 43 degrees and a distance of 6,390 feet. How high above the ground is the plane in whole feet?
5,998.7714 ft
Step-by-step explanation:
Well find x in the illustration;
First To find the opposite side of the right-angled triangle we'll using tangent of the given angle
Tangent Ф = Length of the opposite side / Length of the adjacent side
Tan 43 = h / 6390
h = Tan (43) * 6390
h = 5,958.7714 ft
Then we'll add the height of the beacon which is 40 ft above ground;
x = 5,958.7714 ft + 40 ft
x = 5,998.7714 ft
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A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to spend on the cab ride, how far could she travel?
Answer: 12.69 miles approx
Step-by-step explanation:
let x represent the number of miles traveled
1.75 + 0.65x = 10
0.65x = 8.25
x = 12.69 miles approx
Lashonda bought a desk on sale for $159.60. This price was 62% less than the original price. What was the original price?
p - 62%p = %=$159.60
p - 62p/100 = $159.60
100p - 62p = $15960
38p = $15960
p = $15960/38
p = $420
- 18 = x-6
solve for x.
Answer:
x=-12
Step-by-step explanation:
-18=x-6
-18+6=x--6+6
-12=x
according to the blueprint, the floor area of the stage in the new auditorium at your college must be rectangular and equal to 1200 square feet. The width of the stagr is key to all of the theatre priductions. therefore, in this situation, the stages depth is a function of its width.
Answer:
[tex]d = \frac{1200}{w}[/tex]
Step-by-step explanation:
According to the blueprint, the floor area of the stage in the new auditorium at my college must be rectangular and equal to 1200 sq. feet.
If the width of the stage is w feet and depth of the stage is equal to d feet, then being a rectangle, we can write
[tex]d \times w = 1200[/tex]
Therefore, the equation that represents the depth d as a function of width w is given by [tex]d = \frac{1200}{w}[/tex] (Answer)
Answer:
the correct answer d=1200[tex]d=1200/w[/tex]
Step-by-step explanation:
The figure below is a rhombus.
z = [ ? 10
Answer:
27
Step-by-step explanation:
x=90 because it's a rhombus
Answer:
27 degrees
Step-by-step explanation:
one property of a rhombus is that the diagonals makes an 90 degree angle. so x= 90 degrees. the angle above x is also 90 degrees as well and since angles in a triangle add up to 180, we do 180-63-90, to get z which is 27 degrees
10 5/12- 12 7/12 = in simplest form
Answer:
-13/6 or (in mixed number form) -2 1/6
Step-by-step explanation:
Rewriting our equation with parts separated
=10+512−12−712
Solving the whole number parts
10−12=−2
Solving the fraction parts
512−712=−212
Reducing the fraction part, 2/12,
−212=−16
Combining the whole and fraction parts
−2−16=−216
Another way to do it:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
125/12−151/12
Applying the fractions formula for subtraction,
=(125×12)−(151×12) / 12×12
=1500 − 1812/ 144
=−312/144
Simplifying -312/144, the answer is
=−2 1/6
the sum of two numbers is 19 and there difference is 7 what are the two numbers
Answer:14 and 5
Step-by-step explanation:
Find the zeros of the function
f(x)=x^2+5x+6
Answer:
x= -3 and x= -2
Step-by-step explanation:
(x+3)(x+2)
Hence, the zeroes are:
-3 and -2
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Fill in the missing term in the equation x/x^2-4x+4 - x/x^2-3x+2= ?/(x-2)^2(x-1)
Answer:3
Step-by-step explanation:
The number 123,456 is divisible by...
Answer:
2
Step-by-step explanation:
Because the # ends in a even number, it can be divisible by 2
|4*(6-10)| algebra
--------------
Answer:
16
Step-by-step explanation:
6-10=-4
4*-4=-16
abs(-16)=16
Answer:
|4(6-10)|
|4(-4)|
|-16|=16
Step-by-step explanation:
do parentheses firstdo multiplicationthe answer is 16 because the distance of a number from zero is positive not negative.
Solve the equation 4(0.2x – 5) = 12.
Simplifying
4(0.2x + -5) = 12
Reorder the terms:
4(-5 + 0.2x) = 12
(-5 * 4 + 0.2x * 4) = 12
(-20 + 0.8x) = 12
Solving
-20 + 0.8x = 12
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '20' to each side of the equation.
-20 + 20 + 0.8x = 12 + 20
Combine like terms: -20 + 20 = 0
0 + 0.8x = 12 + 20
0.8x = 12 + 20
Combine like terms: 12 + 20 = 32
0.8x = 32
Divide each side by '0.8'.
x = 40
Simplifying
x = 40