8. The first three terms of a geometric sequence are ( x-6), 3x, and y. If the common ratio is 6, then the value of y is.
Answer:
The value of y is 216
(and the value of x is 12)
Step-by-step explanation:
The general formula for a geometric sequence is,
\(a_n = a_1(r)^{n-1}\)
Where n represents the nth term, a_1 is the first term and r is the common ratio,
we see that,
r = 6,
the first term is,
a_1 = (x-6)
the 2nd term is,
a_2 = 3x,
the 3rd term is,
a_3 = y, finding y,
first we find x, using the above given formula we have,
\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)
x = 12,
Now, for y we can use the relation between a_3 and a_2,
\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)
y = 216
What should be the third row in the following series of shapes
Answer:
The answer is number 2
In the Gaussian integral, how does the left side of this equation equal the right side? An answer would be really appreciated, thank you.
the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.
How do we calculate?
using completing the square method:
Starting with the left side of the equation:
∫\(e^(^-^x^2)\) dx
\(e^(^-^x^2) = (e^(^-x^2/2))^2\)
∫\((e^(^-^x^2/2))^2 dx\)
let u = √(x²/2) = x = √(2u²).
dx = √2u du.
∫ \((e^(^x^2/2))^2 dx\)
= ∫ \((e^(^-2u^2)\)) (√2u du)
The integral of \(e^(-2u^2)\)= √(π/2).
∫ \((e^(-x^2/2))^2\) dx
= ∫ (√2u du) \((e^(-2u^2))\\\)
= √(π/2) ∫ (√2u du)
We substitute back u = √(x²/2), we obtain:
∫ \((e^(-x^2/2))^2\)dx
= √(π/2) (√(x²/2))²
= √(π/2) (x²/2)
= (√π/2) x²
A comparison with the right side of the equation shows that they are are equal.
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find x and y please explain really well
Answer:
x=10,y=120
Step-by-step explanation:
3x-30=60 CDA
3x=30
x=10
again,
y+60=180 straight line
y = 120
A tank in the shape of a hemisphere has a diameter of 24 feet. If the liquid that fills the tank has a density of 92.5 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
The total weight of the liquid in the tank is approximately 12,628 pounds.
To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.
In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.
Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.
In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.
By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.
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the probability that a student selected in our class will pass mathematics test is 2/3 how many students are likely to feel mathematics in the art class with 69 students
Out of 69 students in the art class, around 23 are expected to fail the mathematics test, assuming the probability of passing given is 2/3.
To determine how many students are likely to fail mathematics in the art class, we need to use the given probability of passing the mathematics test, which is 2/3.
First, let's find the probability of failing the mathematics test. Since passing and failing are complementary events (i.e., if the probability of passing is p, then the probability of failing is 1 - p), we can calculate the probability of failing as 1 - 2/3, which simplifies to 1/3.
Now, let's consider the art class, which has a total of 69 students. If the probability of failing mathematics is 1/3, then approximately 1/3 of the students in the art class are likely to fail the mathematics test.
To find the number of students likely to fail, we multiply the probability of failing (1/3) by the total number of students in the art class (69).
(1/3) * 69 ≈ 23
Therefore, approximately 23 students are likely to fail mathematics in the art class of 69 students based on the given probability of passing the mathematics test.
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= Answer:
Find the y-intercept of 2x - y = -16
The units of an item available for sale during the year were as follows: Jan. 1 Inventory 50 units at $124 Mar. 10 Purchase 60 units at $132 Aug. 30 Purchase 20 units at $138 Dec. 12 Purchase 70 units at $142 There are 80 units of the item in the physical inventory at December 31. The periodic inventory system is used. Determine the ending inventory cost and the cost of goods sold by three methods. Round interim calculations to one decimal and final answers to the nearest whole dollar. blank Cost of Ending Inventory and Cost of Goods Sold Inventory Method Ending Inventory Cost of Goods Sold First-in, first-out (FIFO) $fill in the blank 1 $fill in the blank 2 Last-in, first-out (LIFO) fill in the blank 3 fill in the blank 4 Weighted average cost fill in the blank 5 fill in the blank 6
Ending Inventory Cost and Cost of Goods Sold using different inventory methods:
FIFO Method:
Ending Inventory Cost: $11,920
Cost of Goods Sold: $15,068
LIFO Method:
Ending Inventory Cost: $11,996
Cost of Goods Sold: $15,123
Weighted Average Cost Method:
Ending Inventory Cost: $11,974
Cost of Goods Sold: $15,087
Using the FIFO (First-In, First-Out) method, the cost of the ending inventory is determined by assuming that the oldest units (those acquired first) are sold last. In this case, the cost of the ending inventory is calculated by taking the cost of the most recent purchases (70 units at $142 per unit) plus the cost of the remaining 10 units from the March 10 purchase.
This totals to $11,920. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory at $124 per unit, 60 units from the March 10 purchase at $132 per unit, and 20 units from the August 30 purchase at $138 per unit), which totals to $15,068.
Using the LIFO (Last-In, First-Out) method, the cost of the ending inventory is determined by assuming that the most recent units (those acquired last) are sold first. In this case, the cost of the ending inventory is calculated by taking the cost of the remaining 10 units from the December 12 purchase, which amounts to $1,420, plus the cost of the 70 units from the August 30 purchase, which amounts to $10,576.
This totals to $11,996. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,123.
Using the Weighted Average Cost method, the cost of the ending inventory is determined by calculating the weighted average cost per unit based on all the purchases. In this case, the total cost of all the purchases is $46,360, and the total number of units is 200.
Therefore, the weighted average cost per unit is $231.80. Multiplying this by the 80 units in the physical inventory at December 31 gives a total cost of $11,974 for the ending inventory. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,087.
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Consider the polynomial function q(x) = -2x^8 + 5x^6 -3x^5 + 50 What is the end behaviour of the graph of q?
The end behavior of the function q(x) is:
when x → ∞, q(x) → -∞when x → -∞, q(x) → -∞How to identify the end behavior?To know the end behavior we need to look at the degree and the sign of the leading coefficient.
If the degree is even, and the leading coefficient is negative, then in both ends the function will tend to negative infinity.
Here we can see that the function is:
q(x) = -2x⁸ + 5x⁶ - 3x⁵ + 50
So, the degree is 8, and the leading coefficient is -2, then the end behavior of the function is:
when x → ∞, q(x) → -∞
when x → -∞, q(x) → -∞
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Please solve! It's really easy (I think).
Answer:
CD = 5.2 cmA = 27 cm²Step-by-step explanation:
As per diagram we have:
m∠A = 30°m∠BCD = 30°As per 30° right triangle property:
CD = √3×CB/2 = 3√3 ≈ 5.2 cmand AC = 2CD = 2×5.2 = 10.4 cmArea of triangle:
A = 1/2bhA = 1/2CB*ACA = 1/2*5.2*10.4 ≈ 27 cm²PLS HELPS WILL GIVE BRAINLIEST
Answer:
A
Step-by-step explanation:
pls give brainliest pls
For the reaction A + B -> C, explain at least two ways in which the rate law could be zero order in chemical A.
Chemical A's rate law may be zero order and is unaffected by the ratio of reactant to product concentrations.
What is meant by ratio?When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls). This suggests that there are more individuals who disapprove of your opinion than who approve of it.The mathematical formula for the ratio is commenting/(reposts + likes), where the ratio is the number of comments a post receives in comparison to likes and reposts.For the zero order reaction, \($\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$\)
Rate equation is : Rate \($=\mathrm{k}[\mathrm{A}]^0[\mathrm{~B}]^0$\)
As a result, the pace of the reaction is unaffected by the amounts of reactant and product present.
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Given f(x) = -2x^2 + 4, determine the slope of the secant line over the interval [-1, 2].
Answer: -2
Step-by-step explanation:
We know that the slope of a secant line over a interval [a,b] is given by :-
\(m=\dfrac{f(b)-f(a)}{b-a}\)
Given f(x) =\(-2x^2 + 4\)
Then, the slope of the secant line over the interval [-1, 2] is given by :-
\(m=\dfrac{f(2)-f(-1)}{2-(-1)}\\\\=\dfrac{(-2(2)^2+4)-(-2(-1)^2+4)}{2+1}\\\\=\dfrac{(-2(4)+4)-(-2(1)+4)}{3}\\\\=\dfrac{(-8+4)-(-2+4)}{3}\\\\=\dfrac{-4-2}{3}\\\\=\dfrac{-6}{3}\\\\=-1\)
Hence, the slope of the secant line over the interval [-1, 2] is -2.
In ΔMNO, \text{m}\angle M = (6x+1)^{\circ}m∠M=(6x+1) ∘ , \text{m}\angle N = (3x-10)^{\circ}m∠N=(3x−10) ∘ , and \text{m}\angle O = (x+19)^{\circ}m∠O=(x+19) ∘ . Find \text{m}\angle N.m∠N.
Applying the triangle sum theorem, m∠N = 41°
What is the Triangle Sum Theorem?Triangle sum theorem states that the sum of the three interior angles of any triangle equals 180°.
Given the following interior angles of ΔMNO:
m∠M = (6x+1)°
m∠N = (3x-10)°
m∠O = (x+19)°
Find the value of x:
m∠M + m∠N + m∠O = 180°
Substitute6x+1 + 3x-10 + x+19 = 180
Add like terms10x + 10 = 180
10x = 180 - 10
10x = 170
Divide both sides by 10x = 17
m∠N = (3x-10)°
Plug in the value of xm∠N = 3(17) - 10
m∠N = 41°
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One weekend, 5,780 people saw a new movie at 17 different theaters. Each theater sold tickets at $7.50 a piece. If each theater received the same number of moviegoers, how much did each theater make?
The amount that each theater make if they received the same number of moviegoers will be $2550.
How to calculate the amount?From the information, 5,780 people saw a new movie at 17 different theaters and each theater sold tickets at $7.50 a piece.
Therefore, the amount that each theater make if they received the same number of moviegoers will be:
= (5780 × $7.50) / 17
= $43350 / 17
= $2550
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please solve this i will give you brainliest
Answer:
1
Step-by-step explanation:
gvgbkhbgvbhjbjhbjhbhjnnj
What is 2.068 rounded to the nearest 0.1
Answer:
2.1
Step-by-step explanation:
Answer:
2.1
Step-by-step explanation:
what does (-3)+9/8 equal i cant get it im kinda stupid lol
Answer:
-15/8 or -1 7/8, 1.875
Step-by-step explanation:
Determine which integer will make the inequality 4x + 6 < 2x + 12 false.
Answer:
x>=3 make the inequality false
Step-by-step explanation:
4x-2x<12-6
2x<6
x<3
Answer:
Any number higher than 3
Ex. 4, 5, 6, 7, 8, 9, 10, etc
Step-by-step explanation:
4x + 6 < 2x + 12
-2x -2x
---------------------
2x + 6 < 12
-6 -6
------------------
2x < 6
÷2 ÷2
-----------
x < 3
Since x is less than 3, any number higher than 3 will make the inequality false. For Ex. 4
4(4) + 6 < 2(4) + 12
16 + 6 < 8 + 12
22 < 20 (false)
I hope this helps!
Can someone please help awnser these.
The answers are 4. a) 15.7 cm, b) 26.25 m, 5. a) 128.74 cm, b) 40.82 mm, c) 45 cm and 6. 777.28 cm
Given are the circles and the circular items we need to find their circumference,
Circumference of a circle = 2π × radius = Diameter × π
4. a) Circumference = 5 × 3.14 = 15.7 cm
b) Circumference = 8.36 × 3.14 = 26.25 m
5. a) Circumference = 41 × 3.14 = 128.74 cm
b) Circumference = 13 × 3.14 = 40.82 mm
c) Circumference = 14.3 × 3.14 = 45 cm
6.
The perimeter of the cloth = circumference of the circular ends plus length in the middle,
= 76 × 2 × 3.14 + 150 × 2
= 477.28 + 300
= 777.28 cm
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If Melinda wanted to build a patio in her backyard that was 14 feet long, 6 feet wide
and 4 inches deep using pervious concrete mix that is 4 parts aggregate to 4.5 parts
loose cement, with some water added then how many cubic feet of aggregate would
she need to build the walkway?
Round the final answer to the hundredths place. If you answer doesn't have a
hundredths place include zeros so that it does
The volume of aggregate that she needs to build the patio is 13.18 ft^3
How many cubic feet of aggregate would she need to build the walkway?
We know that the backyard is 14ft long, 6 feet wide and 4 inches deep.
Rememeber that:
1ft = 12 in
Then:
4 in = (4/12) ft = (1/3) ft
Then the volume of the backyard is:
V = (14ft)*(6ft)*(1/3 ft) = 28ft^3
Now we know that we have a mix of 4 parts aggregate to 4.5 parts loose cement that need to fill these 28 cubic feet.
Note that:
4 + 4.5 = 8.5
How many times we have 8.5 in 28?
28/8.5 = 3.294
Now for each of these we have 4 parts of aggregate, then the volume of aggregate that we need is:
4*3.294 ft^3 = 13.18 ft^3
The volume of aggregate that she needs to build the patio is 13.18 ft^3
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If the scale ratio is 1 cm: 4 yards, then find the height and base of the actual right triangle. Show your work.
According to the given information, 1cm is to 4 yards as 6cm is to the actual height:
Also, 1cm is to 4 yards as 5cm is to the actual base:
It means that the actual height is 24yards and the actual base is 20yards.
This is worth half of my grade
Answer:
\(y = 8 - 8\sin(2x) \)
Use 2-3 sentences to explain, in your own words, the difference between an angle of elevation and an angle of depression. Use geometry vocabulary.
Determine the most possible complex zeros of the following function:
f(x) = 3x4 - 7x +3
Answer:
In my screenshot
Step-by-step explanation:
Answer: 4
Step-by-step explanation:
descartes rule of signs to test maximum positive and negative:
3x4 - 7x + 3
two sign changes, so maximum of 2 positive real zeroes
3x4 + 7x + 3
no sign changes, so maximum of 0 negative real zeroes
this means that we can have 2 or 0 real zeroes.
if we have 0 real zeroes, we will have 4 imaginary.
therefore the most possible number of complex roots is 4
PLEASE HELP ASAP! This composite figure is created by placing a sector of a circle on a triangle. What is the area of this composite figure? Use 3.14 for n. Round to the nearest hundredth. Show your work.
The area of this composite figure made from placing a sector of a circle on a triangle is 95.55 square cm
Calculating the area of the composite figureThe sector area
The area of the sector is calculated as
Area = x/360 * πr²
Where
r² = 8² + 6²
So, we have
r² = 100
This means that
Area = 82/360 * π * 100
Evaluate
Area = 71.55
The triangle area
This is calculated as
Area = 0.5bh
So, we have
Area = 0.5 * 8 * 6
Evaluate
Area = 24
So, the area of the figure is
Figure = 24 + 71.55
Figure = 95.55
Hence, the area is 95.55
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Let A, B, C be three points with position vectors a, b, c respectively. You may assume that the three points A, B, C do not all lie on the same straight line. Let D, E, F be the midpoints of the line-segments BC, AC, AB respectively. What is the point with position vector 1/3 (a+b+c)?
The midpoint of three points with the position vector 1/3(a + b + c) is given by:
P = (b + c - B - C) / 2 + (1/3)(b + c)
The point with the position vector 1/3(a + b + c) is given by:
P = F - (2/3)D - (1/3)E + (1/3)(b + c)
To find the point with the position vector 1/3(a+b+c), we can use the fact that the position vector of a point that divides a line segment in a given ratio can be found by taking the weighted average of the position vectors of the endpoints.
Given that D, E, and F are the midpoints of line segments BC, AC, and AB, respectively, we know that:
D = (B + C) / 2
E = (A + C) / 2
F = (A + B) / 2
To find the point with the position vector 1/3(a+b+c), we can substitute a = 3F - 2D - E into the equation:
1/3(a + b + c) = 1/3((3F - 2D - E) + b + c)
Expanding the equation further:
1/3(a + b + c) = 1/3(3F - 2D - E + b + c)
= (F - (2/3)D - (1/3)E) + (1/3)(b + c)
Therefore, the point with the position vector 1/3(a + b + c) is given by:
P = F - (2/3)D - (1/3)E + (1/3)(b + c)
Substituting the midpoints:
P = (A + B) / 2 - (2/3)((B + C) / 2) - (1/3)((A + C) / 2) + (1/3)(b + c)
= (A + B - 2B - 2C - A - C + b + c) / 2 + (1/3)(b + c)
= (b + c - B - C) / 2 + (1/3)(b + c)
Therefore, the midpoint of three points with the position vector 1/3(a + b + c) is given by:
P = (b + c - B - C) / 2 + (1/3)(b + c)
The point with the position vector 1/3(a + b + c) is given by:
P = F - (2/3)D - (1/3)E + (1/3)(b + c)
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Students were surveyed to determine what they are most afraid of. The results are shown in the bar graph below.
What is the average number of students who are afraid of spiders and snakes?
A) 7
B) 9
C) 15
D) 30
The average number of students who are afraid of spiders and snakes is 15. (Option C).
How to get the Average?To calculate the average number of students who are afraid of spiders and snakes, you need to add the number of students afraid of spiders and the number of students afraid of snakes, and then divide by 2 (since there are two categories being considered: spiders and snakes).
Average = (Number of students afraid of spiders + Number of students afraid of snakes) / 2
Given the information:
Number of students afraid of spiders = 18
Number of students afraid of snakes = a little more than 11 (let's consider 12 for calculation)
Average = (18 + 12) / 2 = 30 / 2 = 15
So, the average number of students who are afraid of spiders and snakes is 15.
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Simplify (-8.5)X(-5)( -2).
Answer:
-85x (If "X" is a variable)
OR
-85 (If "X" is a multiplication symbol)
Step-by-step explanation:
Not sure if the "X" is a variable or a multiplication symbol
Therefore either of my answers are correct.
Brianna earns an annual salary of $79,300. Brianna gets paid every two weeks. How much
does Brianna earn each paycheck?
Answer:
3,304
Step-by-step explanation:
79,300÷2= 66608.333333
6,608÷2= 3,304