The missing item in the given geometric sequence is: [tex]\frac{4}{15}[/tex].
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: [tex]\frac{2}{5}[/tex], ___, [tex]\frac{8}{45}[/tex]
Here, Let b = missing term of the geometric sequence.
By using the concept of geometric mean, we can find the missing term; geometric mean is used to find the mean, i.e., the middle term between two terms.
GM = [tex]\sqrt{(term_1)(term_2)}[/tex]
Here, b = [tex]\sqrt{\frac{2}{5}\times\frac{8}{45}}[/tex]
=> b = [tex]\sqrt{\frac{16}{25\times9}}[/tex]
=> b = [tex]\frac{4}{5\times3}=\frac{4}{15}[/tex]
Hence, The missing item in the given geometric sequence is: [tex]\frac{4}{15}[/tex].
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Three more than the product of a number and eight is nine
The expression for the given condition is: 8n + 3 = 9
What is the number?
Number is a mathematical word that is used to measure various attributes or count items. In essence, it is arithmetic values. Natural numbers, whole numbers, rational or irrational numbers are among the several types of counting numbers.
The supplied condition is three greater than the product of a number, and eight equals nine, according to the query.
So let's suppose that n is the number.
Three is more than the result of a number and eight, according to the question:
The necessary formula will be: 8n + 3 = 9.
Now, n has been computed to be worth: n = 6/8 = 3/4.
As a result, 3/4 is the value of the supposed integer "n."
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What are the coordinates of the vertices of the image after a 90-degree counter-clockwise rotation about the origin?
Answer:
Well, (2,3) is transformed into (-3,2)
(-3,-1) changes into (1,-3)
and (2,-1) changes into (1,2)
Step-by-step explanation:
Smort
help!! please its easy
The area of the quadrilateral ABCD is 26 square units
How to find the area of quadrilateral ABCD?The quadrilateral ABCD is a trapezoid, and it has the following parameters:
Parallel bases = BC and ADHeight = CEThe lengths of these sides can be calculated using
d = √[(x2 - x1)^2 +(y2 - y1)^2]
So, we have
BC = √[(0 - 4)^2 +(3 + 1)^2] = 4√2
AD = √[(-5 - 4)^2 +(4 + 5)^2] = 9√2
CE = √[(2 - 4)^2 +(-3 + 1)^2] = 2√2
The area of the quadrilateral ABCD is then calculated as
Area = 0.5 * (BC + AD) * CE
This gives
Area = 0.5 * (4√2 + 9√2) * 2√2
Evaluate
Area = 26
Hence, the area of the quadrilateral ABCD is 26 square units
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Bill is planning a circular vegetable garden with a fence around the border. If he can use up to 50 feet of fence, what radius can he use for the garden?
F. 10 G. 9 H. 8 J. 7
The radius that can he use for the garden is H. 8
What is circumference of circle?A circle's outside boundary is called the circumference and can be measured, or calculated, by using
Circumference = 2πr
where r is the radius of circle.
Now it is given that,
Length of fence = 50 feet
⇒ Circumference of vegetable garden = 50 feet
Since, Circumference = 2πr
⇒ 2πr = 50
⇒ r = 50/2π
⇒ r = 50/6.28
⇒ r = 7.96
⇒ r ≈ 8 feet
Thus, the radius that can he use for the garden is H. 8
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Find the missing term of each arithmetic sequence.... 25, 페, 53,...
The missing 2nd term of the given arithmetic sequence 25, _, 53,...(a₂ = 39).
What is the AP arithmetic progression sequence?The difference between the two different numerical orders is a fixed number in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.
We'd come along through a few specific words in AP that were labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)The AP can also be understood in terms of common differences, as shown below.
The operation for reviewing an AP's n-th term is as follows: an = a + (n − 1) × dThe following is the arithmetic progression sum: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, for the given AP; 25, _, 53....
Let the initial term be 'a₁' = 25
Let the second term be 'a₂' = ?
Let the third term be 'a₃' = 53.
The AP must have the same common difference. So,
d = a₂ - a₁ or d = a₃ - a₂
Equating the common difference to find the 2nd missing term.
a₃ - a₂ = a₂ - a₁
Substitute the given values;
53 - a₂ = a₂ - 25
Bring the variable part on one side.
2a₂ = 53 + 25
a₂ = 78/2
a₂ = 39
Therefore, the 2nd missing value of an AP is found to be 39.
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2w=2w+1 I’m very confused and I don’t know how to answer this
Answer:
Step-by-step explanation:
2w = 2w + 1
2w - 2w = 1
w(2 - 2) = 1
0w = 1
w = 1/0
w is undefined
What is one over seven raised to the third powerequal to?
one over ten
three over twenty-one
one over three hundred forty-three
three over two thousand four hundred one
The statement which represents the expression one over seven raised to the third power is Option (C) one over three hundred forty-three is the correct option.
We are given the expression:
one over seven raised to the third power
This can be written as:
(1 / 7) ³
Simplifying and solving the expression by finding the cube of 1 and 7.
1³ = 1
7³ = 343
So, the expression will now become:
(1 / 7) ³ = 1 / 343
which can also be written as:
one over three hundred forty - three
Therefore, option (C) one over three hundred forty-three is the correct option which represents the expression one over seven raised to the third power.
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1/3 +1/5
Greatest common multiple
Right isosceles ΔA B C has hypotenuse length h . DE is a midsegment with length 4 x that is not parallel to the hypotenuse. What is the perimeter of ΔA B C ?
The perimeter of right isosceles ΔABC with midsegment DE is 16 + 8√2.
If right isosceles ΔABC has hypotenuse length h, then the two other sides are congruent.
side a = side b
Using Pythagorean theorem, c^2 = a^2 + b^2
h^2 = a^2 + b^2 a = b
h^2 = 2a^2
a = h/√2
If DE is a midsegment not parallel to the hypotenuse, then it is a segment that connects the midpoints of one side of a triangle and the hypotenuse. See photo for reference.
ΔABC and ΔADE are similar triangles.
a : b : h = a/2 : 4 : h/2
If a/2 = a/2, then b/2 = 4.
b/2 = 4
b = 8
If a = b, then a = 8.
If a = h/√2, then
8 = h/√2
h = 8√2
Solving for the perimeter,
P = a + b + h
P = 8 + 8 + 8√2
P = 16 + 8√2
P = 27.3137085
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If a jar contains 150 peanuts and 60 cashews, what is the approximate probability that a nut selected from the jar at random will be a cashew?
A 0.25
C 0.33
E 0.71
B 0.29
D 0.4
The probability that a nut selected from the jar at random will be a cashew = 0.29
The correct answer is option (B) 0.29
In this question,
A jar contains 150 peanuts and 60 cashews.
So, the total number of nuts = 150 + 60
= 210
We need to find the probability that a nut selected from the jar at random will be a cashew.
To find the probability we use the formula,
P = number of possible outcomes / total number of outcomes
Let event A: a nut selected from the jar at random is a cashew
n(A) = 60
total number of nuts n(S) = 210
So, the probability that a nut selected from the jar at random will be a cashew,
P(A) = 60/210
P(A) = 0.29
Therefore, the probability that a nut selected from the jar at random will be a cashew = 0.29
The correct answer is option (B) 0.29
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4x^2+16x-1
What’s the answer?
Answer:
Step-by-step explanation:
Find the volume of the sphere or hemisphere. Round to the nearest tenth.
sphere: area of great circle =55π in²
The volume of sphere and hemisphere is 7×10⁵ inches and 3.5×10⁵ inches respectively.
We are given the area of circle. From this given information, we will be calculating radius of the circle, which will be further required to calculate volume of sphere and hemisphere.
Area of circle = πr²
Keep the value in formula -
55π = πr²
Cancelling π and taking square root to find the value of radius
r = √55
r = 7.4 inches
Now, volume of sphere is calculated by the formula -
Volume of sphere = 4/3 πr³
Volume of sphere = 4/3 π (55)³
Volume of sphere = 6.97×10⁵ inches
Now, volume of hemisphere is calculated by the formula -
Volume of hemisphere = 2/3 πr³
Volume of hemisphere = 2/3 π (55)³
Volume of hemisphere = 3.48×10⁵ inches
On rounding off, we get volume of sphere and hemisphere as 7×10⁵ inches and 3.5×10⁵ inches
Hence, the volume of sphere and hemisphere is 7×10⁵ inches and 3.5×10⁵ inches respectively.
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How many feet are equivalent to
1|5
mile? (1 mile = 5280 feet)
Answer:
1056 feet
Step-by-step explanation:
5280/5=1056
a has 32 more then b and b has five times as much money as c if c has d dollars how much does a have
The amount A has in terms of d is 5d + 32.
Amount A has in terms of B
The amount A has in terms of B is calculated as follows;
If a has 32 more than b, our equation becomes;
A = b + 32
Amount B has in terms of CThe amount B has in terms of C is calculated as follows;
If B has five times as much money as C and C has d dollars, our equation becomes;
B = 5C = 5d
Amount A has in terms of dollarsThe amount A has in terms of d is calculated as follows;
A = b + 32
A = 5d + 32
Thus, the amount A has in terms of d is 5d + 32.
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14. Let f(x) = -3x+4. Find and simplify f(x + 2).
f(x+2) = (Simplify your answer.)
12. Let f(x) = -2x+5. Find f(1/2) simply ur answer
15. Let f = {(4,0),(-4,4),(1,-9) Find f(4).
Answer:
14. [tex]-3(x+2)+4[/tex]
12. [tex]4[/tex]
15. [tex]0[/tex]
Step-by-step explanation:
Question 14
To find the function in terms of "x+2", simply replace "x" in the original equation with "x+2":
[tex]f(x+2)=-3(x+2)+4[/tex]
Now simplify by distributing the 3:
[tex]f(x+2)=-3x-6+4[/tex]
Finish by adding the constants:
[tex]f(x+2)=-3x-2[/tex]
Question 12
This one follows the same concept! Replace "x" in the original equation with 1/2:
[tex]F(\frac{1}{2})=-2(\frac{1}{2} )+5[/tex]
Simplify:
[tex]f(\frac{1}{2})=-1+5\\f(\frac{1}{2})=4[/tex]
Question 15
For this question, it looks like you are given a set of coordinate pairs in the function. You are asked to find "f(4)". Essentially, you are being asked to find the value of y given 4 as the value of x.
The given coordinate pair (4,0) has 4 as the x value, so the y value when x=4 is 0!
you rent an apartment that cost 1600 per month during the first year but the rest had to go by 12.5 per year what would be the rent of the apartment during the 10th year in
Answer: 2000
12.5÷100=0.125
1600×0.125×10=2000
A baseball glove originally cost 84.50.
Kenji bought it at 40 % off. How much was deducted from the original price?
F. 50.70
H. 33.80
G. 44.50
J. 32.62
33.80 was deducted from the original price costing 84.50.
84.50 × 40% = 33.80
That's it, the answer is H. 33.80
What is original price?The full cost of purchasing an asset is known as the original price. When calculating an asset's original cost, all of the costs associated with buying and using the asset are taken into account.
Included in these expenses are the purchase price as well as things like commissions, shipping, appraisals, warranties, installation, and testing. Equipment, real estate, and security instruments are all examples of asset types that can be valued using original cost.
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Simplify the expression.
10-22 / 8-17
The simplified expression for (10-22 / 8-17) is 4/3 .
The given expression is,
( 10-22 / 8-17 )
First we need to solve the numerator which is (10-22) and on simplifying the numerator we can write,
Numerator = ( 10 - 22 ) = -12 equation 1
Similarly, now we can proceed to solve the denominator which is (8 - 17) and on simplifying the denominator we write,
Denominator = (8 - 17) = -9 equation 2
Now we can substitute the value of numerator and the denominator from equation 1 and equation 2 in the given expression ( 10-22 / 8-17 ) as,
(Numerator / Denominator) = (10-22 / 8-17) = ((-12)/(-9)) = 4/3
The simplified expression for (16-12 / 15-11) is 4/3 .
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Round 67.483 to the nearest whole number
Answer:
67 is the answer
Answer:
67 would be the nearest whole number.
HELP!! I WILL GIVE BRAINLIEST TO THE PERSON WHO ANSWERED IT CORRECTLY AND GAVE A GREAT EXPLANATION!!! PLEASE ANSWER THE QUESTION!! IT IS ALGEBRA AND I AM NO GOOD AT IT!!!
( Hello! I'm bo)red....Can someone talk to me.....anyone...please???
Answer:
I believe the correct answer would be C.
Step-by-step explanation:
Have a great day! :)
Write each number as a percent.
0.25
Answer: 25%
Step-by-step explanation:
0.25
25%
Convert the decimal or whole number to a percent.
1.15 7/8
Answer:
1.15 is 115%
Step-by-step explanation:
7/8 is 0.875 so it makes it 87.5%
The percentage form of the given number is:
1.15 as a percent is 115%
7/8 as a percent is 187.5%
To convert a decimal to a percent,
we need to multiply it by 100.
So for 1.15,
Multiply it by 100 to get 115%.
To convert a mixed number to a percent,
We have to convert it to an improper fraction first.
To do that, we multiply the denominator by the whole number and add the numerator.
Then we put that answer over the original denominator.
For 7/8, the improper fraction would be,
(8 x 1) + 7 = 15/8.
To convert this to a percentage,
We need to divide the numerator by the denominator and multiply by 100.
So 15/8 as a decimal is 1.875, and when we multiply that by 100 we get 187.5%.
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Evaluate r + (-5) < -3.
r < -5
r < 2
r < -2
r < 5
Answer:
r<2
Step-by-step explanation:
r + (-5) < -3
r -5 < -3
r<-3+5
= r<2
Solve for x. Question 8
Step-by-step explanation:
Pythagoras :
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle).a and b are the legs of the right-angled triangle.
so,
x² + 12² = (x + 8)² = x² + 16x + 64
144 = 16x + 64
16x = 80
x = 5
Compute the average rate of change of the given function over the specified interval. f (x) = x^3, [3, 4]
Answer:
Use the given functions to set up and simplify
[
3
,
4
]
Step-by-step explanation:
can someone helppppppppppppppppppppppppp
Answer:
Step-by-step explanation:
p= AB+BC+AC
AB=[tex]\sqrt{(-5-(-5))^2+(4-(-2))^2} =6[/tex]
BC=[tex]\sqrt{(-5-6)^2+(4-(-2))^2} =\sqrt{157}[/tex]
AC=[tex]\sqrt{(6-(-5))^2+(-2-(-2))^2} =11[/tex]
p= 17+[tex]\sqrt{157\\[/tex]
What is the area, in square centimeters, of the isosceles trapezoid below? ¹8 cm 15.5 cm 5.7 cm
The area of the trapezoid is 169.6 cm² for the dimensions as 8 cm, 5.7 cm and 15.5 cm.
We are given that:
The dimensions of the trapezoid are:
Height = 8 cm
Shorter side = 5.7 cm
longer side = 15.5 cm
Area of the trapezoid will be:
A = (a + b) / 2 × h
Substituting the values in the formula, we get that:
A = (5.7 + 15.5) / 2 × 8 cm²
A = 21.2 × 8 cm²
A = 169.6 cm²
Therefore, we get that, the area of the trapezoid is 169.6 cm² for the dimensions as 8 cm, 5.7 cm and 15.5 cm.
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Evie has a price of ribbon that is 80cm long she cuts it into lengths and has no ribbon left over each length is exactly 8.5cm or 12.5cm how many of each length does evie have
Using a function to express the number of pieces of the two lengths, Evie should have 3 pieces of ribbon of length 12.5 cm and 5 pieces of ribbon of length 8.5 cm.
In mathematics, a function is the representation of the relationship of a set of input(X) and its corresponding output(Y).
If Evie has a price of ribbon that is 80cm long that she wants to cut into lengths of exactly 8.5cm or 12.5cm and that no ribbon left over, then the function for this statement is:
12.5x + 8.5y = 80 ⇒ y = (80 - 12.5x)/8.5
where x is the number of pieces of length 12.5 cm and y is the number of pieces of length 8.5 cm, and x and y must be whole numbers(pieces of ribbon)
Listing down the possible integers for the value of x and solving for the corresponding y value.
x = 1 , y = 135/17
x = 2 , y = 110/17
x = 3 , y = 5
x = 4 , y = 60/17
x = 5 , y = 35/17
x = 6 , y = 10/17
Since when x = 3, y = 5 is the only ordered pair that is both integers, then it is the answer.
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Some people think that the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida, resembles a golf ball. The building is a sphere measuring 165 feet in diameter. A typical golf ball has a diameter of approximately 1.5 inches.
b. Find the volume of a golf ball to the nearest tenth.
A typical golf ball having a diameter of approximately 1.5 inches has a volume of 1.8 cubic inches.
Volume refers to the amount of space occupied by a three-dimensional object.
From the problem, the golf ball resembles the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida which is a sphere.
If a typical golf ball has a diameter of approximately 1.5 inches, and radius is half of the diameter, then the radius of the golf ball is approximately 0.75 inches.
The volume of the golf ball can be calculated using the formula for the volume of a sphere given by:
V = 4/3 π r^3
V = 4/3 π (0.75 inches)^3
V = 4/3 π (0.421875 cubic inches)
V = 1.767145868 cubic inches
Rounding off to the nearest tenth,
V = 1.8 cubic inches
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I need the answer and explanation ASAP Complete the perfect square f(x)=x^2+7x+10
The perfect square equation is f(x) = (x + 7/2)^2 - 9/4
How to complete the perfect square?The equation of the function is given as
f(x) = x^2 + 7x + 10
Rewrite the equation as
x^2 + 7x + 10 = 0
Subtract 10 from both sides of the equation
So, we have
x^2 + 7x = -10
-----------------------------------------------------------------------
Take the coefficient of x
k = 7
Divide by 2
k/2 = 7/2
Square both sides
(k/2) = 49/4
-----------------------------------------------------------------------
Add 49/4 to both sides of the equation
So, we have
x^2 + 7x + 49/4 = -10 + 49/4
Express as a perfect square
So, we have
(x + 7/2)^2 = -10 + 49/4
Evaluate the sum
So, we have
(x + 7/2)^2 = 9/4
This gives
(x + 7/2)^2 - 9/4 = 0
So, we have
f(x) = (x + 7/2)^2 - 9/4
Hence, the perfect square equation is f(x) = (x + 7/2)^2 - 9/4
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