A geometric sequence is given by:
\(a_n=a\cdot r^{n-1}\)Where:
a = First term of the sequence
r = Common ratio
Using the data provided:
\(\begin{gathered} a=256 \\ a_2=64=256\cdot r \\ r=\frac{1}{4} \end{gathered}\)Therefore, the geometric sequence is:
\(\begin{gathered} a_n=256(\frac{1}{4})^{n-1} \\ _{\text{ }}since \\ a_3=16 \end{gathered}\)We can conclude it is a geometric sequence and its common ratio is 1/4
Answer:
c) yes, 1/4
Answer:
Yes; \(\frac{1}4}\)
Step-by-step explanation:
Divide the second term by the first term, then the third term by the second term, and so on.
\(\frac{64}{256} = 0.25, or \frac{1}{4} \\\frac{4}{16} = 0.25, or \frac{1}{4} \\\\\frac{64}{256} = 0.25, or \frac{1}{4} \\\)
The common ratio is \(\frac{1}{4}\).
A card is drawn randomly from a standard 52-card deck. Find the probability event. (a) The card drawn is 8 of the given 2 The probability is:______(b) The card drawn is a face card (Jack, Queen, or King) The probability is:______(c) The card drawn is not a face card The probability is:_______
The probability of selecting an 8 is \(\frac{4}{52}\) since there are 4 total 8's available (8 of hearts/spades/diamonds/clubs) out of 52 cards. This simplifies to \(\frac{1}{13}\). The probability of selecting a face card is \(\frac{12}{52}\) since there are 4 Jacks, 4 Queens, and 4 Kings. This simplifies to \(\frac{3}{13}\). 1 - \(\frac{3}{13}\) = \(\frac{13}{13}\) - \(\frac{3}{13}\) =\(\frac{10}{13}\).
There are four suits (hearts, spades, diamonds, and clubs), each with 13 cards from Ace to King, in a conventional 52-card deck of playing cards. As a result, there are four of each potential card.
(A) The probability of selecting an 8 is \(\frac{4}{52}\) since there are 4 total 8's available (8 of hearts/spades/diamonds/clubs) out of 52 cards. This simplifies to \(\frac{1}{13}\).
(B) The probability of selecting a face card is \(\frac{12}{52}\) since there are 4 Jacks, 4 Queens, and 4 Kings. This simplifies to \(\frac{3}{13}\).
(C) The probability of NOT selecting a face card is \(\frac{40}{52}\) since there are 4 of each card from Ace through 10 that are not face cards. This simplifies to 10/13. The solution to part B's question can be used as another way to approach this issue. If the probability of selecting a face card is 3/13, then the probability of NOT selecting a face card has to be 1 - \(\frac{3}{13}\) = \(\frac{13}{13}\) - \(\frac{3}{13}\) =\(\frac{10}{13}\). Recall that you must deduct from 1 since the probability of all conceivable outcomes must add up to 1, or 100%.
Therefore, the probability of selecting an 8 is \(\frac{4}{52}\) since there are 4 total 8's available (8 of hearts/spades/diamonds/clubs) out of 52 cards. This simplifies to \(\frac{1}{13}\). The probability of selecting a face card is \(\frac{12}{52}\) since there are 4 Jacks, 4 Queens, and 4 Kings. This simplifies to \(\frac{3}{13}\). the probability of NOT selecting a face card has to be 1 - \(\frac{3}{13}\) = \(\frac{13}{13}\) - \(\frac{3}{13}\) =\(\frac{10}{13}\).
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Can isosceles triangles be an equilateral triangle?
Answer:
IT CAN BE
Step-by-step explanation:
BECAUSE ISOSCELES TRIANGLE IS A TRIANGLE WITH 2 SIDES EQUAL....
EQUILATERAL TRIANGLE HAS ALL SIDES AND ANGLES EQUAL, so equilateral triangle also has 2 sides equal
Answer:
no it is not can you look at your coments
Use implicit differentiation to find dy/dx and d^2y/dx^2.
Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.
Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.
Given the equation x² + xy + y² = 5,
we can differentiate both sides with respect to x using the chain rule as follows:
2x + (x(dy/dx) + y) + 2y(dy/dx) = 0
Simplifying this equation yields:
(x + 2y)dy/dx = -(2x + y)
Hence, dy/dx = -(2x + y)/(x + 2y)
Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.
That is:
d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))
= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))
Simplifying this equation yields:
d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³
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What is the length of the apothem of the regular pentagon shown below? Round to one decimal place
The length of the apothem of the regular pentagon shown is 5.2 meters
How to determine the length of the apothem?Represent the central angle of the regular pentagon using x
The value of the central angle of the regular pentagon is then calculated as:
x = 360/n
Where n represents the number of sides
i.e n = 5
So, we have:
x = 360/5
Evaluate the quotient
x = 72
Represents the apothem with y.
The apothem is then calculated as:
tan(x/2) = (Side length/2)/Apothem
This gives
tan(72/2) = (7.6/2)/y
Evaluate the quotient
tan(36) =3.8/y
Multiply both sides by y
y tan(36) = 3.8
Divide both sides by tan(36)
y = 3.8/tan(36)
Evaluate the quotient
y = 5.2
Hence, the length of the apothem of the regular pentagon shown is 5.2 meters
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what is the range of function m?
The range of the function m is [1, ∞). Thus, B is correct option.
What are a function's range and domain?The dοmain οf a functiοn is the cοllectiοn οf values that can be plugged intο it. This set represents the x values in a functiοn like f. (x). A functiοn's range is the set οf values that the functiοn can take οn. This is the set οf values returned by the functiοn when we enter an x value.
Tο determine the range οf functiοn m, we must first determine the set οf all pοssible functiοn οutput values.
Looking at the function graph, we can see that the lowest point is (3, 1) and the highest point is (∞, ∞).
As a result, the function m has a range of [1, ∞).
We can write: in interval notation:
m ∈ [1, ∞) range.
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PLEASE HELP ASAP
solve -1/6[3-15(1/3)2]
Answer:
C) -2/9
Step-by-step explanation:
\(\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}\)
Answer:
Hence, Option (C) - 2/9 is the Answer:
Step-by-step explanation:
-1/6 [3 -15(1/3)^2]
-1/6(3 -15)(1/9))
-1/6(3 - 5/3)
-1/6 (4/3)
Hence, Option (C) - 2/9 is the Answer:
I hope it helps!
Solve for x. Round to the nearest hundredth if necessary.
Answer:
x is 34.28 rounded to the nearest hundredth
Step-by-step explanation:
Since it is a right-angled triangle, using Pythagoras' rule; SOH/CAH/TOA
Since the known variables are: Opposite(19), Adjacent(x), and Theta(29°);
So, TOA would be used;
tan 29° = 19 / x (cross multiply) Making x the subject of the formula;
x = 19 / tan 29° = 34.276 = 34.28 rounded to the nearest hundredth
x = 34.28
Cuantas Escuelas de administración hay ?
Jo bought 5 lb potatoes for 2.89 a loaf of bread for 1.79 and a can of soup for 1.63 she gave the clerk 10 dollars how much should she get back
it should be easy but i just forgot how to get thhe awnser
Answer:
$3.69 in change
Step-by-step explanation:
10-2.89-1.79-1.63=3.69
Answer : 3.69 Dollars
Explanation : 2.89 + 1.79 + 1.63 = 6.31 10-6.31 = 3.69
YusuCr
Please look at the picture for question.
Answer:
a c and e
Can i have brainliest if im right?
Step-by-step explanation:
Find the mean of the data set:
87,79,92,71,88,70,91,82,85
Round your answer to the nearest tenth.
Provide your answer below:
The mean of the data set is 82.77
How to calculate the mean of the data set?If we want to find the mean, we would have to put it at the back of our minds that the mean is the same as the average. As such, we would have to take the sum of all the values that have been listed in the data set and divide by the total number of the data.
The first step is to arrange the data set orderly from smallest to largest;
70, 71,79, 82,88,85,87,91,92
We have nine values in the data set thus the mean is;
70+71+79+82+88+85+87+91+92/9= 745/9= 82.77
Hence the mean of the data set is 82.77
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A group of student volunteers at the animal shelter is helping feed the dogs. Each day, small dogs eat 1/2 cup less dog food than medium-sized dogs, and large dogs eat cup more dog food than the 3/4 medium-sized dogs. The shelter currently has 22 small dogs, 14 medium-sized dogs, and 8 large dogs.
Write an expression for the total amount of dog food the dogs eat each day. Explain what your variable represents and what each term in your expression represents.
The expression is that the total amount of dig food is 44x - 5.
How to calculate the expression?Based on the information, the small dogs will be:
= ( x - 1/2)
Large dogs = (x + 3/4)
The total amount of dogs food will be:
= 22(x - 1/2) + 14x + 8(x + 3/4)
= 22x - 11 + 14x + 8x + 6
= 44x - 5
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I see that the amount i owe has been reduced from $90. 00 to $75. 00 yes, the discount has saved you.
Answer:
Step-by-step explanation:
90.00 - 75.00 = 15.00
Commitment to goals can be promoted in which of the following ways?
Commitment to goals can be promoted in through:
by imagining how you will feel when you achieve themby identifying who or what might keep you from achieving themWhat is goal commitment?Goal commitment is the degree of determination a person uses to achieve an accepted goal, and it is determined by two major factors: importance and self-efficacy. The reasons a person has for achieving a goal, including expectations of certain outcomes, are significant. Commitment helps you stick to your goals in both good and bad times, when obstacles arise. Commitment is influenced by two factors: importance and
Goal commitment is generally defined as an individual's determination to devote time and effort to achieving a goal.
Goal commitment is the degree of determination a person uses to achieve an accepted goal, and it is determined by two major factors: importance and self-efficacy. The reasons a person has for achieving a goal, including expectations of certain.
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At a factory, the number of workers cars produced is directly proportional to the number of hours factory workers are making the cars. It takes 45 hours to make 60 cars. Use a proportion to find how long it will take to make 250 cars?
9514 1404 393
Answer:
187.5 hours
Step-by-step explanation:
Let x represent the number of hours required to make 250 cars.
hours/cars = 45/60 = x/250
Multiply by 250:
x = 250(45/60) = 187.5 . . . hours
It will take 187.5 hours to make 250 cars.
Select all situations that are are accurately described by the expression 15*35.
A. A population begins at 15,000. The population triples each hour.How many bacteria are there after 5 hours?
B. A population begins at 15,000. The population triples each hour.How many thousand bacteria are there after 5 hours?
C. A population begins at 15,000. The population triples each hour.How many thousand bacteria are there after 3 hours?
D. A bank account balance is $15. The account balance triples each year. What is the bank account balance,in dollars,after 5 years?
E. A bank account balance is $15,000.It grows by 3,000 each year. What is the bank account balance,in thousands of dollars,after 5 years?
Answer:
If the total truly is 15 x 35 = 525
None of the situations work
Step-by-step explanation:
The correct situations that are are accurately described by the expression 15 × 3⁵ is,
D. A bank account balance is $15. The account balance triples each year. What is the bank account balance ,in dollars, after 5 years?
What is Multiplication?Multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The expression is,
⇒ 15 × 3⁵
Hence, By option D;
The situation is,
A bank account balance is $15. The account balance triples each year. What is the bank account balance ,in dollars, after 5 years?
Hence, We can formulate;
⇒ Amount after 5 years is,
⇒ 15 × 3⁵
Thus, The correct situations that are are accurately described by the expression 15 × 3⁵ is,
D. A bank account balance is $15. The account balance triples each year. What is the bank account balance ,in dollars, after 5 years?
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T(x,y,z)=x^2yz^3 với M(1,1,1)
Answer:
A= (2xy^2)^3. (-1/2x^2yz) (gạch chéo là phần)
B=(-4x3y2z)( x2y3)3xy
Step-by-step explanation:
ok :)
given the following trigonometric ratio, enumerate the meaning ratio
Answer:
The trigonometric ratios are presented below:
\(\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}\)
\(\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}\)
\(\cot \theta = \frac{BC}{AC}\)
\(\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}\)
\(\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}\)
Step-by-step explanation:
From Trigonometry we know the following definitions for each trigonometric ratio:
Sine
\(\sin \theta = \frac{y}{h}\) (1)
Cosine
\(\cos \theta = \frac{x}{h}\) (2)
Tangent
\(\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x}\) (3)
Cotangent
\(\cot \theta = \frac{\cos \theta}{\sin \theta} = \frac{x}{y}\) (4)
Secant
\(\sec \theta = \frac{1}{\cos \theta} = \frac{h}{x}\) (5)
Cosecant
\(\csc \theta = \frac{1}{\sin \theta} = \frac{h}{y}\) (6)
Where:
\(x\) - Adjacent leg.
\(y\) - Opposite leg.
\(h\) - Hypotenuse.
The length of the hypotenuse is determined by the Pythagorean Theorem:
\(h = \sqrt{x^{2}+y^{2}}\)
If \(y = AC\) and \(x = BC\), then the trigonometric ratios are presented below:
\(\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}\)
\(\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}\)
\(\cot \theta = \frac{BC}{AC}\)
\(\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}\)
\(\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}\)
I don't need help but I am giving the answer to everyone :) hope it helps
The number of cannonballs in illustration is 506.
What is illustration?Math Illustrations enables you to produce more useful geometry figures for your students in less time by fusing the constraint-based design of Geometry Expressions with simple-to-use sketching and graphing features.
The number of cannonballs in the first layer = 1² = 1
Number of cannonballs in the second layer = 2² = 4
Number of cannonballs in the third layer = 3² = 9
So, the generalized formula to count the balls is given as
= n(n + 1) (2n + 1)/ 6
Here, n= the total number of layers
Put n =11
11(11 + 1)(2(11) + 1) / 6
= 11(12)(23)/6
= 3036/6
= 506
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find the area of the circle
Answer:
113.04 square feet
Step-by-step explanation:
A = π\(r^{2}\)
A = π \((6\)\()^{2}\)
A = 3.14 (36)
A = 113.04
A bowl holds 4 cups of rice if I use a measuring cup that holds 1/8 of a cup how many times will I need to fill the measuring cup in order to fill the entire bowl
Answer:
32 times
Step-by-step explanation:
It's SUPER easy, all you have to do is take that 1/8 and make it into a regular 8. Now all you do is multiply 4 by 8.
I know there's probably some way the teachers taught that's so much harder then it already is, but if you try to look at it from an easier perspective, you'll be a pro!
Try some more so you'll slowly start getting better at them! Anyway I hope this helped!!
A ladder rests against the top of a wall. The head of a person 6 feet tall just touches the ladder the person is 9' from the wall and 6' from the foot of the ladder. find the height of the wall
Answer:
15 ft
Step-by-step explanation:
Let the height of the wall be represented bad x
Applying the theorem of similarity, we would have the following equation:
\( \frac{x}{6} = \frac{9 + 6}{6} \)
\( \frac{x}{6} = \frac{15}{6} \)
\( \frac{x}{6} = \frac{5}{2} \)
Cross multiply
\( x*2 = 5*6 \)
2x = 30
Divide both sides by 2
x = 15
Thus, the height of the wall = 15 ft
The tangent of the curve f(t) =2+nt+mt^2 at point (1,1/2) is parallel to the normal g(t)= t^2+6t+13(-2,2), calculate the values m and n.
Step-by-step explanation:
The slope of g(t) as (-2,2) is given by
\(g'(t)=2t+6\)
\(g'(-2)=2(-2)+6=2\)
Since the normal is parallel to the tangent of f(t) at (1, 1/2),
The tangent line of f(t) has a slope of
\(\dfrac{d}{dx}f(t)=n+2mt=2\)
At point (1, 1/2), we know
\(f'(1)=n+2m=2\)
\(f(1)=2+n(1)+m(1)^2=2+n+m=\frac12\)
Solving,
\(n=5, m=-\frac72\)
Among all the pairs of numbers whose difference is 18 18 , find the pair with the smallest product. What is the product?
Answer:2-b= 18-a+b now their product is F=a.b-f(b)=18+b)b Dt/db =18+2b-0=18+2b-0=9+b-9=b
so, that's our only critical point, run a first-derivative test on it, and you'll notice is a minimum
Step-by-step explanation:
When converted to a household measurement, 9 kilograms is approximately equal to a
Answer:
D) 19.8 lbs
Explanation:
1kg in household measurement is equal to 35.274 ounces. 35.274*9=317.466 ounces.
1kg is also equal to 2.205 lbs. 9*2.205=19.8416
9 kg is also equal to 9000 grams, but grams are not a part of the household measurement system
a) 9000 grams. b) 9000 ounces. c) 19.8 ounces. d) 19.8 pounds.
This leaves us with 19.8 lbs
Which angle is congruent to angle 3?
I would really appreciate it if someone could help and answer this problem:)
Answer:
Angle 6
Step-by-step explanation:
Angles on opposite ends are congruent if they are formed by the same two lines or in other words, if the two angles are vertical angles.
Find the area of the figure. 5in 2in 4in 5in
Answer: Your answer is 23.5in²
Hope it helped :D
Good Luck!
Pedro is solving this number riddle using guess and check. Fourteen less than my number is eleven. What is my number? Which statements about solving the riddle are true? Check all that apply. Less than means subtraction. Subtract 14 from the unknown number to get 11. 14 – 11 = 3 25 – 14 = 11 The unknown number is 25.
The answer is 1, 2, 4, 5
Have a GREAT day!
Please help me in this math problem
Answer:
Step-by-step explanation: well, you will more than likely get it at least 60%-80% of the time! If this doesn't help i can try to explain in a lot more detail unless someone does for me!
what is the h.c.f of 24 and 40
Answer:
i think hcf of
24 and 40 is 8.