Answer:
486 and 2187
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ × [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
(1)
here a₁ = 2 and r = 3 , then
a₆ = 2 × [tex]3^{5}[/tex] = 2 × 243 = 486
(2)
here a₁ = [tex]\frac{1}{3}[/tex] and r = 3 , then
a₉ = [tex]\frac{1}{3}[/tex] × [tex]3^{8}[/tex] = [tex]\frac{1}{3}[/tex] × 6561 = 2187
HELLLLP MEEEE PLEASEE
Answer:
34 R 12
Step-by-step explanation:
I will add an explanation later, because I do not have time, I have to go somewhere.
It'll be added in at least 1 day AT MOST.
Add.
24 4/5 + 12 4/5
Answer: Convert the mixed numbers to improper fractions, then find the LCD and combine them.
Exact Form:
188
5
Decimal Form:
37.6
Mixed Number Form:
37
3
5
hope this helped have a nice day! :)
Answer:
Step-by-step explanation:
(124+64) /5
= 188/5
Answer is = 37.5
Imagine a lidless box with height h and a square base whose sides have length x. The box must have a volume of 117 ft^3. Estimate the value of x that produces the box with a minimum surface area.
The closest value of x that would produce the box with the minimum surface area would be 117 ft.
The volume of a lidless box with height h and a square base with sides of length x is given by V = x^2 * h.
To have a volume of 117 ft^3, we have:
x^2 * h = 117
The surface area of a lidless box is given by:
A = 2x^2 + 4xh
We want to minimize this surface area while still keeping the volume of the box at 117 ft^3. To do this, we need to find an expression for h in terms of x, and then minimize A in terms of x.
From the volume equation, we can solve for h:
h = 117 / x^2
Substituting this expression into the surface area equation, we get:
A = 2x^2 + 4x * (117 / x^2)
= 2x^2 + 466 / x
Now, we can use calculus to find the minimum of A in terms of x.
The derivative of A with respect to x is:
dA/dx = 4x - 466 / x^2
Setting dA/dx equal to zero, we find the critical points:
4x - 466 / x^2 = 0
4x = 466
x = 116.5
We now need to check if x = 116.5 is a local minimum or maximum.
To do this, we need to examine the second derivative of A with respect to x:
d^2A/dx^2 = -932 / x^3
Since the second derivative is negative, this means that A has a local minimum at x = 116.5.
Hence, the value of x that produces the box with a minimum surface area is approximately 116.5 ft.
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Enter the exact value in terms of
π
.
Answer:
calculate = 3.14159
Step-by-step explanation:
convert to degrees 189°
positive angle
[tex] 3\pi \: positive \: angle[/tex]
(a) The displacement (in centimeters) of a particle s moving back and forth along a straight line is given by the equation
s = 2 sin(t) + 3 cos(t),
where t is measured in seconds. (Round your answers to two decimal places.)
[1, 2]
[1, 1.1]
[1, 1.01]
[1, 1.001]
(b) Estimate the instantaneous velocity of the particle when
t = 1.
The displacements are 2.84 cm, 2.77 cm, 2.83 cm and 2.83 cm respectively.
Instantaneous velocity of the particle at t =,1 is 0.72 cm/s.
How to calculate displacement and velocity?a. To find the displacement of the particle at various times t, we can simply plug the given value of t into the equation s = 2 sin(t) + 3 cos(t) and evaluate:
[1, 2]: s = 2 sin(1) + 3 cos(1) = 2.84 cm
[1, 1.1]: s = 2 sin(1.1) + 3 cos(1.1) = 2.77 cm
[1, 1.01]: s = 2 sin(1.01) + 3 cos(1.01) = 2.83 cm
[1, 1.001]: s = 2 sin(1.001) + 3 cos(1.001) = 2.83 cm
b. To find the instantaneous velocity of the particle when t = 1, we need to find the derivative of the equation for displacement with respect to time, which will give us the velocity. The derivative is given by:
v(t) = ds/dt = 2 cos(t) - 3 sin(t)
Plugging in t = 1 into this equation, we find:
v(1) = 2 cos(1) - 3 sin(1) = 0.72 cm/s
So, the instantaneous velocity of the particle at t = 1 is approximately 0.72 cm/s.
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Determine the open intervals on which the function is increasing, decreasing, or constant. (Enter your answers using interval notation. If an answer does not exist, enter DNE
The intervals of the function's behavior are given as follows:
Increasing: x > 3.Decreasing: x < -3.Constant: -3 < x < 3.How to classify the function as increasing, decreasing or constant?The function is increasing when the graph moves right and up.The function is decreasing when the graph moves right and down.The function is constant when the graph of the function is an horizontal line.The intervals are composed by the values of x that respect each condition, as follows:
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Which graph shows the solution to the system of linear equations?
y = 2x − 2
4x − 2y = 4
Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0.
Coordinate plane with one line that passes through the points 0 comma negative 1 and 1 comma 1 and another line that passes through the points 0 comma negative 2 and 1 comma 0.
Coordinate plane with one line that passes through the points 0 comma 1 and 1 comma 2.
Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0 and another line that passes through the points 0 comma 1 and 1 comma 2.
The solution of the system of equations can be seen in the image at the end, the system has infinite solutions.
Which graph shows the solution of the system of equations?Here we have the system of linear equations below:
y = 2x - 2
4x - 2y = 4
To find the solution graphically, we need to graph both of the equations on the same coordinate axis and find the point where the lines intersect.
The graph can be seen in the image below, and there you can see only one line, that is because both of the equation of our system represent the same line, and thus, the system has infinite solutions.
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simplify!!
(-2x^2-3x+4)+(-4x^2+x-2)
Answer:
number b is the write answer
Step-by-step explanation:
-2x²-3x+4-4x²+x-2
-2x²-4x²-3x+x+4-2
-6x²-2x+2
Exercise 12. Show that each of these con tautology by using truth tables. a) [p ^ (p V q)] →q
b) [(p → 9)^(q + r)] → (p + r) c) [p ^ (p →q)] →q. d) [(p V q) 4 (p r)^(q + r)] →r
Exercise 14. Show that each conditional statement in Exercise 12 is a tautology using the fact that a conditional statement is false exactly when the hypothesis is true and the conclusion is false. (Do not use truth tables.)
(a) All the values in the last column of the truth table are T, the statement [p ^ (p V q)] → q is a tautology.
(b) All the values in the last column of the truth table are T, the statement [(p → q) ^ (q + r)] → (p + r) is a tautology.
(c) All the values in the last column of the truth table are T, the statement [p ^ (p → q)] → q is a tautology.
Here is the truth table for each of the conditional statements
a) [p ^ (p V q)] → q
p p V q p ^ (p V q) q [p ^ (p V q)] → q
T T T T T
T T T F F
T F F T T
F T F T T
F F F T T
F F F F T
Since all the values in the last column of the truth table are T, the statement [p ^ (p V q)] → q is a tautology.
b) [(p → q) ^ (q + r)] → (p + r)
p q r p → q q + r (p → q) ^ (q + r) p + r [(p → q) ^ (q + r)] → (p + r)
T T T T T T T T
T T F T T T T T
T F T F T F T T
T F F F F F T T
F T T T T T T T
F T F T T T F T
F F T T T T F T
F F F T F F F T
Since all the values in the last column of the truth table are T, the statement [(p → q) ^ (q + r)] → (p + r) is a tautology.
c) [p ^ (p → q)] → q
p p → q p ^ (p → q) q [p ^ (p → q)] → q
T T T T T
T F F T T
F T F T T
F T F T T
Since all the values in the last column of the truth table are T, the statement [p ^ (p → q)] → q is a tautology
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Use law of sines and show all work please!!
Answer:
below
Step-by-step explanation:
sin x is to 13 as sin 28 is to 21
sinx /13 = sin(28)/21
sinx = 13 * sin (28) /21
sin x = .2906
x = arcsin (.2906) = 16.9°
please help me will give u extra points :)
•
(5, 9), open (5), close (9), is the interval graph. This interval is inequitable because: 5 < x ≤ 9
What is meant by inequality?Inequality is the absence of an equality link between two expressions or values. So inequality emerges from an imbalance. A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality.It is most frequently used to compare the sizes of two numbers on the number line. The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 5x 4, is larger than the right part, 2x + 3, in the equation.Therefore,
a) Letter A is erroneous since it implies that the graph should have two shaded areas, but this particular graph only has one.
b) Letter B is erroneous because the graph shows that there must be a parenthesis before point 5 because it is open, and point 9 must come after a because it is shaded.
c) The letter c is also wrong because it implies there are two shaded portions in the graph when there is only one.
The complete question is:
Which compound inequality can be represented by the graph below?
A) x < 5 or x ≥ 9
B) 5 ≤ x < 9
C) x ≤ 5 or x > 9
D) 5 < x ≤ 9
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the first 4 terms in a sequence are 8,5,2,-1... What is the recursive equation?
Currently taking discrete math so this one hits close to home haha :)
Provided that we are given the first term [tex]a_0=8[/tex], the equation is found by subtracting the previous term from the current term. The recursive equation is then used to find the following terms in the sequence.
Notice that each term decreases by three as we move along the sequence, this can be written in the form of the recursive equation:
[tex]a_n = a_n_-_1-3[/tex]
line ab is shown on the grid a is the point (0,3) b is the point (6,6) work out the coordinates of the midpoint of the line ab
Answer:
(3, 4.5)
Step-by-step explanation:
x = [tex]\frac{0 + 6}{2}[/tex] = 3
y = [tex]\frac{3+6}{2}[/tex] = 4.5
ANSWER ASAP OR MY MOM WILL BE MAD CUZ SHES ABOUT TO LOOK AT MY WORK IN MATH
25% of 84 is what value?
3
20
21
59
I need answers to #8 with how to graph it and answer to #9 a-c
On solving the provided question, we can say that by unitary method 6 plate cost = $22.69 and 4 more cost = 32.49; total = 32.49+22.69 = $55.18 and cost of each plate = $5.518
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here, by unitary method
6 plate cost = $22.69
and 4 more cost = 32.49
total = 32.49+22.69 = $55.18
cost of each plate = $5.518
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The correct question is -
Pamela found a style of plate that she loves, but her local home goods store is out of stock. She decides to find the same style online. She has 6 plates in her cart right now and her total cost, including a fixed shipping cost is $22.69 . Later she decides to add 4 more plates to her cart. Her total is now $32.49 ,What is the cost of each plate?
class 10r sat a test
the mean mark was 70%
there are thirty students in class 10r, 20 of whom are boys
the mean mark for the boys in the test was 62%
work out the mean of the girls
Answer:
15% tell me if im wrong
Step-by-step explanation:
3. I am a common multiple of 2, 4, and 30.
I am a factor of 120. The sum of my
digits is 6. What number am I?
Answer: 60
Step-by-step explanation:
1. You can multiply 2*30 to get 60 and with 4 you can do 4*20 would equal 60
2. 120/60 would equal 2 so it would not have any decimals so this shows it is 60.
Ariana is a songwriter who collects royalties on her songs
whenever they are played in a commercial or a movie. She
will earn $30 every time one of her songs is played in a
commercial and she will earn $110 every time one of her
songs is played in a movie. Ariana earned a total of $620
in royalties dn 10 commercials and movies. Write and
solve a system of equations to determine the number of
commercials and the number of movies on which her songs
were played.
number of commercials:
number of movies:
Answer:
number of commercials: 6
Number of movies: 4
Step-by-step explanation:
Let x = the number of commercials
Let y = the number of movies
30x + 110 y = 620
x + y = 10 This can be written y = 10 - x (substitute 10 - x for y)
30x + 110y = 620
30x + 110(10 - x) = 620 Distribute the 110
30x + 1100 - 110x = 620 Combine like terms
-80x + 1100 = 620 Subtract 1100 from both sides
-80x = -480 Divide both sides by -80
x = 6
There are 6 commercials.
Substitute 6 for x
x + y = 10
6 + y = 10 Subtract 6 from both sides
y = 4
There are 4 movies.
Check:
x + y = 10
6 + 4 = 10
10 = 10 checks
30x + 110y = 620
30(6) + 110(4) = 620
180 + 440 = 620
620 = 620 checks
Find the slope of the line described by the table.
M =
The slope of the line describes by the table is 0.1.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
The table represents Bike ride, where x represents the number of minutes in 'x' and y represents the number of kilometers.
We know, slope(m) = (y₂ - y₁)/(x₂ - x₁).
Slope(m) = (1.0 - 0.5)/(10 - 5).
Slope(m) = 0.5/5.
Slope(m) = 0.1
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The table shows values of a function f(x). What is the average rate of change of f(x) over the interval from x = 4 to x = 8? Leave answer as an improper fraction. Show formula and work for credit.
PLEASE HELP!!!!
X 4 5 6 7 8 9 10
f(x) -4 -2 8 10 11 14 18
Answer:
The average rate of change of f(x) over the interval from x = 4 to x = 8 can be calculated as follows:
\frac{f(8)-f(4)}{8-4} = \frac{11-(-4)}{8-4} = \frac{15}{4} = 3 \frac{3}{4}
Therefore, the average rate of change of f(x) over the interval from x = 4 to x = 8 is 3 \frac{3}{4}.
The average rate of change of f(x) over the interval from x = 4 to x = 8 is 3.75.
What is Average Rate of Change?
It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
we have the table,
x 4 5 6 7 8 9 10
f(x) -4 -2 8 10 11 14 18
So, the value of f(4)= -4 and f(8) = 11
Now, average rate of change
= f(8)- f(4) / (8-4)
= 11 - (-4) / 4
= 15 / 4
= 3.75
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Consider a set-up in which a transmit- ter is transmitting either a 0 or a 1 and the receiver indicates that it received either a 0 or a 1. Denote the events that i = 0, 1 was transmitted by Ti, and the events that i = 0, 1 was indicated as received by Ri. It is possible to have transmission errors. In fact, you are given the following data on accuracy and the frequency of transmitted signals: P[R0 | T0] = 0.99, P[R1 | T1] = 0.98, P[T0] = 0.75. Given that the receiver indicated 1, what is the probability that there was an error in the transmission? What is the overall probability that there was an error in transmission?
To find the probability as per the given question and the information provided, we can compute it as:
a) By using the Bayes formula, we get:
[tex]P[T0|R1] = \frac{P[R1|T0]P[T0]}{P[R1|T0]P[T0] + P[R1|T1]P[T1] }
\\
= \frac{(1 − 0.99) × 0.75}{(1 − 0.99) × 0.75 + 0.98 × 0.25} \\
= \frac{3}{101} ∼= 0.030.[/tex]
b) An error is bound to happen if T0 ∩ R1 or T1 ∩ R0 occur, that is
[tex]P[error] = P[T0 ∩ R1] + P[T1 ∩ R0] \\ = P[R1|T0] × P[T0] + P[R0|T1] × P[T1] \\ = (1 − P[R0|T0]) × P[T0]
+ (1 − P[R1|T1]) × (1 − P[T0]) \\ = 0.01 × 0.75 + 0.02 × 0.25
\\ =
1
80
∼= 0.013[/tex]
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 indicates certainty.
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show that an ordered set has the least upper bound property if and only if it has the greatest lower bound property.
An ordered set has the least upper bound property if and only if it has the greatest lower bound property.
Every nonempty subset A0 of an ordered set A is said to have the least upper bound property and has the lowest upper bound that is constrained above. A fulfills this requirement. Assume B0 is a set of any size with a lower bound. We must demonstrate that it has the largest lower bound. Assume LA is the collection of all the set B0's lower bounds.
∃b0∈B0,∀x∈L,x≤b0.
L is therefore bound above. So it has the lowest upper bound. Let b represent the lower limit of L.
∀x∈L,x≤b.
If ∃b′∈B0,b′≤b, which defies the assertion that b is the lowest upper bound of L. As a result,
b≤y,∀y∈B0.
So, b is the lower bound.
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The equation 3x -4y=3
The equation 3x -4 =12
The equation 3x +4y=12
Answer:
The point (4,0) lies on the line.
All the other answers are not applicable for this situatino.
Step-by-step explanation:
3 Coffee 5.85
1 Diet Bev. – lg. 3.38
1 Sparkling Water 2.50
3 Ranch Chicken Sandwich 44.97
1 Classic Burger 12.95
1 Thai Stir-fry Special 11.50
2 Club Sandwich 22.98
Subtotal 104.13
Tax (13%) 13.54
Total 117.67
3. The restaurant recommends that groups of five or more tip 18% of the amount
before tax. Which of the following amounts is closest to 18%?
a) $15 b) $20 c) $25 d) $22
The tip amount is closest to 18% is, $15, So Option A is correct
What is the percentage?The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.
Formula for percentage;
Percentage = (present quantity/whole quantity)×100
Given that,
3 Coffee 5.85
1 Diet Bev. – lg. 3.38
1 Sparkling Water 2.50
3 Ranch Chicken Sandwich 44.97
1 Classic Burger 12.95
1 Thai Stir-fry Special 11.50
2 Club Sandwich 22.98
Subtotal 104.13
Tax (13%) 13.54
Total 117.67
Tip amount 18% = 117.67x18/100
= 14.11
Hence, It is closest to $15
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Please help me with this question.
When revolved over the {x} axis will occupy more volume as compared to when revolved over the {y} axis.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is the volume occupied between the lines -
x = 4, y = x and x - axis.
Refer to the image attached. The reflection over the {x} axis will occupy more volume as compared to the reflection over the {y} axis. The figure generated in both the cases would be a cuboidal prism structure.
Therefore, when revolved over the {x} axis will occupy more volume as compared to when revolved over the {y} axis.
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Based on the completed Form 1040 and 2018 Taxable Income Tiers, what is the total tax
that the employee is responsible for paying?
Answer in complete sentences.
If we assumes that the taxpayer has $100,000 as his income on the completed Form 1040, the total tax that the employee is responsible for paying will be $17,836.
What are tax bracket or income tiers?A tax bracket is a range of incomes that are taxed at a specific rate. Tax brackets are part of a progressive tax system, which means that tax rates increase progressively as an individual's income increases. Low-income taxpayers pay relatively low tax rates, while higher-income taxpayers pay higher rates.
In 2022, for example, a single filer with taxable income of $100,000 will pay $17,836 in taxes, representing an average tax rate of 18%. However, your marginal tax rate or tax bracket is 24%. As a result, the total tax that the employee is responsible for is $17,836.
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Fred’s fish tank is shown below how many cubic feet of water will he need to fill in his fish tank l=8.3ft W=11.5ft H=6
Answer:
611.05
Step-by-step explanation:
To find the number of cubic feet of water needed to fill Fred's fish tank, we need to calculate the volume of the tank. The volume of a rectangular prism (such as a fish tank) can be found by multiplying the length, width, and height together. Using the given measurements, the volume of Fred's fish tank would be:
8.3 ft * 11.5 ft * 6 ft = 611.05 cubic ft
So, Fred will need 611.05 cubic ft of water to fill his fish tank.
Write each expression as a fraction and then reduce the fraction
[tex](1 + {a }^{3} ) \div (1 + a)[/tex]
[tex]\textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) ~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] ~\dotfill\\\\ (1+a^3)\div (1+a)\implies \cfrac{1+a^3}{1+a}\implies \cfrac{1^3+a^3}{1+a} \\\\\\ \cfrac{~~\begin{matrix} (1+a) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(1^2 - (a)(1)+a^2)}{~~\begin{matrix} 1+a \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 1^2 - (a)(1)+a^2\implies \boxed{a^2-a+1}[/tex]
is 12,15,18 a phythagorean triple?
Answer:
Below
Step-by-step explanation:
Put the numbers into the pythagorean theorem to see if true
12^2 + 15^2 = 18^2 ??????
144 + 225 = 324 ?????
369 = 324 ?????? <========= not true ....not a triple
A manager has to choose three products out of five possibilities to take into production. How many different ways are there to choose three products out of five?
