The missing term in the geometric sequence 45, ___, 1620 is 270.
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Given the geometric sequence: 45, ___, 1620, we need to find the missing term.
Let's denote the missing term as a2 and the common ratio as r. The terms of the geometric sequence are determined by the formula:
an = a1 * rn-1
For our sequence:
The first term, a1, is 45.The third term, a3, is 1620.We express the third term in terms of the first term and common ratio:
1620 = 45 * r2
Solving for r2:
r2 = 1620 / 45
r2 = 36
r = 6
Since the common ratio, r, is 6, we can find the missing second term, a2:
a2 = a1 * r
a2 = 45 * 6 = 270
Thus, the complete sequence is 45, 270, 1620.
A spherical gas tank has a 10 foot diameter when filled with propane it provides 358,000,000 BTUs how many BTUs does 1 cubic foot of propane yield? Round to the nearest thousand
The number of BTUs does 1 cubic foot of propane yield is 684,000 BTUs/ft³ (in thousand)
Calculation of the number of BTUs:
Since we know that
The volume of the spherical tank is
[tex]V=4\div 3\pi r^3[/tex]
Now the volume of the tank will be:
[tex]V=4\div 3\times \pi \times (10/2)^3[/tex]
=523.59877756
= 523.6 ft³
Now the number should be
= [total amount] ÷ [total volume]
=358,000,000 ÷ 523.6
=683,728.0367 BTUs/ft³
= 684,000 BTUs/ft³ (in thousand)
Therefore, The number of BTUs does 1 cubic foot of propane yield is 684,000 BTUs/ft³ (in thousand)
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What is the slope of the line shown on the graph?
What is the solution to the following system? 3x+3y+6z=9 x+3y+2z=5 3x+12y+12z=18
(3, 1, 0)
(0, 1, 0)
(2, 1, 0)
(–2, 1, 0)
Answer:
C. (2, 1, 0)
Step-by-step explanation:
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In how many ways can 3 identical emeralds 2 identical diamonds and 2 different opals be arranged in a row in a display case
They can be arranged in 210 ways.
We have given that, 3 identical emeralds 2 identical diamonds and 2 different opals
What is the arrangement of n object where n₁ is one kind, n₂ is a second kind, and n₃ is a third kind?The arrangement of n objects where n₁ is one kind, n₂ is a second kind, and n₃ is a third kind is given by
[tex]\frac{n!}{n_1!*n_2!*n_3!}[/tex]
The total number of gems =7
3 of the first kind, 2 of the second kind and 2 of the third kind
Therefore, we get
[tex]\frac{7!}{2!*2!*3!}=210[/tex]
Therefore ,they can be arranged in 210 ways.
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How many combinations of four books can be made from eight different books? 24 70 1,680?
Answer:
70
Step-by-step explanation:
four books can be made from eight different books
4 books to be chosen from 8 books
The order does not matters so we use Combination.
four books can be made from eight different books, so we find 8C4
[tex]nCr= \frac{n!}{r!(n-r)!}[/tex]
[tex]8C4= \frac{8!}{4!(8-4)!}[/tex]
[tex]8C4= \frac{8!}{4!(4)!}[/tex]
[tex]8C4= \frac{8*7*6*5*4!}{4!(4)!}=70[/tex]
Answer:
70
Step-by-step explanation:
Bob bought 3 packs of model cars. He gave 4 cars to Ann.Bob has 11 model cars left how many model cars were in each pack.
A rancher has 4000 ft. of fence for constructing a rectangular corral that is divided into 3 equal sections. one side of the corral will be bounded by his barn and needs no fencing. what are the dimensions of the corral that will maximize the area? what is the area of the corral?
Factor this expression completely and then place the factors in the proper location. Note: Place factors alphabetically!
mn - 4m - 5n + 20
To solve this problem you must apply the proccedure shown below:
1. You have the following expression given in the problem above:
[tex] mn - 4m - 5n + 20 [/tex]
2. The first thing you must do to factor the expression is to group the terms, as following:
[tex] (mn-4m)+(-5n+20) [/tex]
3. Now, choose the greatest common factor of each group:
[tex] m(n-4)-5(n-4) [/tex]
4. Now, you need to factor the expression by factoring out the [tex] n-4 [/tex]
[tex] (m-5)(n-4) [/tex]
The answer is: [tex] (m-5)(n-4) [/tex]
Determine the values of x on which the function f(x)=2x^2-x-15/4x^2-12x is discontinuous and verify the type of discontinuity at each point.
A.There is a vertical asymptote at 0 and a hole at 3.
B.There are vertical asymptotes at -5/2 & 0 and a hole at 3.
C.There is a vertical asymptote at 3 and a hole at 0.
D.There are vertical asymptotes at 0 & 3.
There is a vertical asymptote at x = 0 (because the denominator becomes 0). We need to further analyze the behavior at x = 3 to see if it's a hole (cancellation) or the function is continuous there (Option A or B might be the answer).
Step 1: Identify Potential Discontinuities
A rational function (like f(x)) is discontinuous when its denominator is zero. So, we need to find the values of x that make the denominator 0:
Denominator = 4x^2 - 12x = 0
Factor the denominator: 4x(x - 3) = 0
This gives us two possible values for x: x = 0 and x = 3.
Step 2: Verify Discontinuity Type at Each Point
Check if the function is defined (has a value) at these points.
x = 0: If we plug x = 0 in the original function, we get 0/0, which is indeterminate. This suggests a potential vertical asymptote at x = 0.
x = 3: If we plug x = 3 in the original function, the expression doesn't become 0/0. The function might have a hole or be continuous at x = 3.
Step 3: Analyze for Holes (Optional):
To further investigate x = 3, we can try to simplify the function by factoring the numerator (possible because the denominator is already factored). If the simplification gets rid of the term that causes the 0/0 at x = 3, it creates a hole.
28 - 2(5a - 3) = 47
A. -1.3
B. 1.3
C. -2.5
D. 8.1
(6a −? )5a =? a2 − 35a
Solve 3/10 n-3 1/5 = -1 1/5
Answers-
A.n =-12 2/3
B.n = 6 2/3
C.n = 8
D.n = -6/25
Answer: B. n = 6 2/3
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Rovide an appropriate response.4) assume that adults have iq scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the wechsler test). find the iq score separating the top 14% from the others. 4)
x 0 2 4 6 8 f(x) 15 15.5 17 19.5 23 Write the quadratic function that corresponds to the given table of values in standard form, f(x) = ax2 + bx + c, where a, b and c are constants.
f(x)=ax^2+bx+c
Answer with Step-by-step explanation:
We are given that:
f(x)=ax²+bx+c
also at x=0 f(x)=15
Putting x=0 in f(x)
a×0+b×0+c=15
⇒ c=15
now, f(2)=15.5
⇒ a×2²+b×2+c=15.5
⇒ 4a+2b+15=15.5
⇒ 4a+2b=0.5 -------(1)
f(4)=17
⇒ a×4²+b×4+c=17
⇒ 16a+4b+15=17
⇒ 16a+4b=2 --------(2)
equation (2)- 2×equation(1)
⇒ 16a+4b-8a-4b=2-2×0.5
⇒ 8a=2-1
⇒ 8a=1
⇒ a=1/8
⇒ a=0.125
Putting value of a and c in equation (1)
⇒ 4×0.125+2b=0.5
⇒ 0.5+2b=0.5
⇒ 2b=0
⇒ b=0
Hence
a=0.125
b=0
c=15
and f(x)=0.125x²+15
Today Jan put a necklace on layaway by making a down payment of $75 and agreeing to pay $15 per month, starting next month, for 18 months. When will Jan receive the necklace?
Answer:
The answer is 18 months.
Step-by-step explanation:
Today Jan put a necklace on layaway by making a down payment of $75 and agreeing to pay $15 per month, starting next month, for 18 months.
So, she will receive the necklace in 18 months.
Layaway is a system of paying a deposit for your product to secure it for later purchase. When all your payments are done, the product is given to you.
In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 8 in.?
8√ in.
88√ in.
28√ in.
82√ in.
Yo! For anyone who comes across this..answer is D; 8√2in.
Hope this helps!!
The length of the hypotenuse when the length of one of the legs is 8 in. is 8√2 in option (D) is correct.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
It is given:
In a 45-45-90 triangle
The length of one side = 8 in
The length of other side = 8 in (because 45-45-90)
Using Pythagoras theorem:
Hypotenuse = √8² + 8²
= 8√2
Thus, the length of the hypotenuse when the length of one of the legs is 8 in. is 8√2 in option (D) is correct.
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What is the range of the function y = -x2 + 1?
Final answer:
The range of the function y = -x^2 + 1 is all real numbers less than or equal to 1, represented as ]-∞, 1].
Explanation:
The range of the function y = -x^2 + 1 refers to the set of all possible values that y can take as x varies over all real numbers. Since the function is a downward-opening parabola (due to the negative coefficient of x^2), the maximum value of y is at the vertex of the parabola. The vertex, in this case, occurs at x=0, which gives us the maximum y value of y = 1. As x moves away from zero in either direction, the value of y decreases and approaches negative infinity. Hence, the range of this function is ]-∞, 1], or all real numbers less than or equal to 1.
Use graphing calculator to solve system the equations in the interval from 0+2pi.round to the nearest hundredth. 7cos 2t=3
The solutions of the trigonometric equation are approximately 0.56, 2.58, 3.71 and 5.72, all in concordance with the results found beside the analytical approach.
How to solve trigonometric equations
Trigonometric functions are periodic functions, cosine function has a standard period of 2π radians. There are two approaches to solve the expression given, an analytical one and a graphical one. Now we proceed to show each approach:
Analytical method
Now we proceed to apply algebraic handling and inverse trigonometric functions to solve the expression for t:
7 · cos 2t = 3
cos 2t = 3/7
2 · t = cos⁻¹ (3/7)
There are two solutions:
2 · t₁ ≈ 0.359π + 2π · i ∨ 2 · t₂ ≈ 1.641π + 2π · i
t₁ ≈ 0.180π + π · i ∨ t₂ ≈ 0.821π + π · i
t₁₁ ≈ 0.180π ∨ t₁₂ ≈ 1.180π ∨ t₂₁ ≈ 0.821π ∨ t₂₂ ≈ 1.821π
The solutions of the trigonometric equations in [0, 2π] are approximately 0.18π, 0.82π, 1.18π and 1.82π.
Graphical approach
First, we add the definition of the following two functions (f(x) = 7 · cos 2t and g(x) = 3) and plot in the calculator through a graphing tool. The solutions of this trigonometric function are the points of intersection of the two functions.
According to the image attached below, the solutions of the trigonometric equation are approximately 0.56, 2.58, 3.71 and 5.72, all in concordance with the results found beside the analytical approach.
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use the graph of y=sin theta to find the value of 2theta for theta = pi/4 radians
How much greater is the median number of pairs of shoes in the inventory at the Golf pro Shop than the median number of pairs of shoes in the inventory at the Tennis Pro Shop?
What is the value of x?
a. 7
b. 7√2
c. 14
d. 14√2
Geometry A Problem! Help! Line AC
The path of a rocket ship is given by the parametric equations x(t)=3t and y(t)=4t^2+1, where t is the time in seconds after launch. Where is the ship after 10 seconds?
(3, 4)
(3, 5)
(30, 401)
(30, 501)
Help please ! A B Or C
Answer:
B) 46
Step-by-step explanation:
What you have to do here is plug in the numbers 2, 3, 4, and 5 in for i in the equation and then add the sums together:
3(2) + 1 = 7
3(3) + 1 = 10
3(4) + 1 = 13
3(5) + 1 = 16
Add those together and they equal 46
Which of the following is a solution of x2 + 6x = −18?
The correct option are a. [tex]\(x = -3 + 3i\)[/tex] and b. [tex]\(x = -3 - 3i\)[/tex].The solutions are complex numbers [tex]\(x = -3 + 3i\)[/tex] and [tex]\(x = -3 - 3i\)[/tex].
To find the solution of the quadratic equation [tex]\(x^2 + 6x = -18\)[/tex], we need to solve it for [tex]x[/tex].
Starting with the given equation:
[tex]\[x^2 + 6x = -18\][/tex]
Rearranging it to the standard form of a quadratic equation:
[tex]\[x^2 + 6x + 18 = 0\][/tex]
Now, to find the solutions, we can use the quadratic formula:
[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]
where [tex]\(a = 1\), \(b = 6\)[/tex], and [tex]\(c = 18\).[/tex]
Substituting the values:
[tex]\[x = \frac{{-6 \pm \sqrt{{6^2 - 4 \cdot 1 \cdot 18}}}}{{2 \cdot 1}}\]\[x = \frac{{-6 \pm \sqrt{{36 - 72}}}}{2}\]\[x = \frac{{-6 \pm \sqrt{{-36}}}}{2}\]\[x = \frac{{-6 \pm 6i}}{{2}}\]\[x = -3 \pm 3i\][/tex]
So, the solutions are complex numbers [tex]\(x = -3 + 3i\)[/tex] and [tex]\(x = -3 - 3i\)[/tex].
The complete question is:
Which of the following is a solution of [tex]\(x^2 + 6x = -18\)[/tex]?
a) [tex]\(x = -3 + 3i\)[/tex]
b) [tex]\(x = -3 - 3i\)[/tex]
c) [tex]\(x = -3\)[/tex]
d) [tex]\(x = 3\)[/tex]
An angle measuring between 90° and 180° is called _____. A.obtuse B.acute C.straight D.small
Benson has a bankruptcy on his credit report, so he pays higher interest rates on his current loans. He calculates that the extra money he pays in additional interest each year, if invested at the rate of 2% for one year, could earn him simple interest totaling $180. How much does Benson pay in additional interest each month? a. $360 b. $750 c. $900 d. $1,000
Answer:
The correct answer is letter b, $750
Step-by-step explanation:
Tomas can do a job in 4 hours. julia can do the same job in 6 hours. how many hours will it take the two of them to do the job if they work together?
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