how to erite a sequence of 1/4 , 1/2,3 write a rule for the sequence 1/4 1/2 3/4

Answers

Answer 1

The equation for finding the equation of an arithmetic sequence is an=a1+(n-1)d, where n is the input for the sequence, a1 is the first term, and d is the difference between each term.

a1= 1/4
d= 1/4

an= 1/4 + (n-1)(1/2) - First you need to distribute the 1/2 to both the n and -1 to get: an= 1/4 + 1/2n -1/2.

Then you need to add like terms (1/4-1/2) to get an=1/2n-1/4. Hope this helps!

Answer 2

The sequence 1/4, 1/2, 3/4 increases by 1/4 for each subsequent term, defining it as an arithmetic sequence with a common difference of 1/4.

To find a rule for the sequence 1/4, 1/2, 3/4, we can examine the pattern and observe that the sequence consists of fractions that increase by 1/4 each step. Starting with 1/4, when we add 1/4, we get 1/2, and adding another 1/4 to 1/2 gives us 3/4. So the rule of the sequence can be written as 'start at 1/4 and add 1/4 each step'. This pattern is an arithmetic sequence with a common difference of 1/4.

Related Questions

Assuming boys and girls are equally likely, find the probability of a couple having a baby boyboy when their sixthsixth child is born, given that the first fivefive children were all boysall boys.

Answers

Doesn't matter what the first five are. The probability is always 1/2 for the next child. This is like tossing a coin. If you toss a coin 5 times and all the times are tails, what is the probability that the sixth time will be heads. If it's a fair coin, it's 1/2.

Answer:

50% probability of a couple having a baby boyboy when their sixth child is born, given that the first five were all boys.

Step-by-step explanation:

For each child, there are only two possible outcomes. Either it is a boy, or it is a girl. The probability of a child being a boy or a girl is independent of the other children. So we use the binomial probability distribution to solve this question.

The conditional probability formula is also used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Find the probability of a couple having a baby boyboy when their sixth child is born, given that the first five children were all boys.

Event A: First five children being boys.

Event B: Sixth children being a boy.

P(A):

First five children being boys.

P(X = 5) when n = 5.

Equally likely to be boy or girl, so p = 0.5.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(A) = P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]

Intersection:

Intersection between the first five children being boys and the sixth also being a boy, so [tex]P(X = 6)[/tex] when n = 6.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(A \cap B) = P(X = 6) = C_{6,6}.(0.5)^{6}.(0.5)^{0} = 0.015625[/tex]

Probability:

[tex]P(B|A) = \frac{0.015625}{0.03125} = 0.5[/tex]

50% probability of a couple having a baby boyboy when their sixth child is born, given that the first five were all boys.

Where is the vertex of the quadratic y = (x -7)2 + 9

Answers

Try this option:
rule: common equation for a parabola is y=ax²+bx+c. If to re-write this equation in the form y=(x+m)²+n, then point (-m;n) is vertex of this parabola.
According to the described rule vertex is (7;9).
The graph of this function is in the attachment.

Final answer:

The vertex of the quadratic function y = (x -7)² + 9 is at the point (7, 9).

Explanation:

Vertex of a quadratic function is the highest or lowest point on the graph of the function. In this case, the quadratic function is in the form y = (x -7)² + 9.

To find the vertex, we notice that the function is in the form y = (x - h)² + k, where (h, k) represents the vertex. Therefore, the vertex of the given quadratic function is at (7, 9).

Kens turtle competed in a 0.50- meter race. His turtle had traveled 49/100 meter when the winning turtle crossed the finish line. What is 49/100 written as a decimal

Answers

Hello!

There are a couple ways we can convert a fraction to a decimal, but I'll use a simple way.

To convert 49/100 to a decimal, we must divide the numerator (top of the fraction, 49) by the denominator (bottom of the fraction, 100).

49 ÷ 100 = 0.49

So, 49/100 is written as 0.49 as a decimal.

Well, to make it simple it's 0.49. Hope it helps!

Two rectangular prisms have the same volume. The area of the base of the blue prism is 216 square units. The area of the base of the red prism is one third that of the blue prism. Which statement is true?

a) The height of the red prism is one-third the height of the blue prism.

b) The height of the red prism is the same as the height of the blue prism.

c) The height of the red prism is six times the height of the blue prism.

d) The height of the red prism is three times the height of the blue prism.

Answers

V = B*h

Let hb represent the height of the blue prism; let hr represent the height of the red prism.

216*hb = V = (1/3)*(216)*hr
3*hb = hr . . . . . . . . . . . . . . . divide by the coefficient of hr

The 4th selection is appropriate.

Answer:

Step-by-step explanation:

A moving company charges $0.60 per pound for a move from New York to Florida. A family estimates that their belongings weigh about 6 tons. About how much would it cost the family to move from New York to Florida?

Answers

It will cost the family $7,200 to move from New York to Florida

one ton = 2,000 pounds
so 6 tons would be 12,000
because we multiply 6x 2,000
So now we need to find the cost 12,000 Ibs.
0.60*2,000=1,200
1,200*6
=$7,200

Workers in france average 5 fewer days of vacation a year than italians. americans average 24 fewer vacation days than the french. if the italians average 42 vacation days each year (the most in the world), how many does the average american worker have a year?

Answers

42 -24 -5 = 13

The average american worker has 13 vacation days per year.

find the difference of the least common multiple and the greatest common factor of 12 and 32 show your work please

Answers

12. 32
6*2. 8*4
3*2*2. 4*2 2*2
2*2*2*2*2

Do the rest of the math yourself lol

Brooke earns $7 an hour at her job now. She can represent the total she makes in a week using the expression 7r. Brooke has asked for a $1 an hour raise. Which expressing would represent the amount Brooke would make in a week after the raise?

Answers

We have that with the increase made Brooke now earns the following amount per hour:
(7 + 1) = 8 $ / h
Therefore we must now rewrite the weekly expression of your earnings.
Rewriting we have:
(7 + 1) r =
8r
Answer:
the amount Brooke would make in a week after the raise is:
8r

the awnser is sir

8R

HELPPPPPPPPPPP WITH CACULAS

Answers

6) We have that in order to see [tex] \lim_{x \to \infty} f(x) [/tex] we need to see the value of the function as the x-value increases to infinity. Checking the graph, we see that as x increases, the y of the graph stays around 3 (tends to it). Hence the limit in this case is C=3. In general cases, the limit as x approaches infinity could not exist (as in the sine function which is periodic), it could be plus or minus infinity or it could be areal number; in the last case we talk of a horizontal asymptote.
7) As x goes to 1, we have that the function itself is getting closer and closer to the value 4. It is important for this calculation to notice that we do not care about f(4) but rather the value of the function as x is around 4. This function could have been discontinuous at 4 (have a hole there or not be defined) but we would still have that [tex] \lim_{x \to 1} f(x)=4 [/tex] .
8) The value of the investment after 1 year will be equal to 400*(1.051); after 2 years the value will be equal to (400*1.051)*1.051 (the quantity after one year times (1+interest)) and after n years: [tex]400*1.051^n[/tex]. Substituting n=5 we get: 512.95$.
Now for the other part: [tex]400*1.051^n=1000[/tex] (We need to solve for n)
[tex]1.051^n=2.5[/tex] Taking logs each side:
[tex]n*log1.051=log2.5[/tex]
This yields n=18.42 years.
9) Let us take the cost: it has a fixed component of 350$ and a variable component of 20c=0.2$ per serving. Hence C(x)=350+0.2*x
The revenue function has only a variable component, 70 cents per serving. Similarly, R=0.7*x where x is the number of servings.
One has that P(x)=R(x)-C(x)=0.7*x-(350+0.2*x)=0.5x-350
Finally, if the Society breaks even, we have that P(x)=0. Solving that equation, we have: 0=0.5x-350 hence 0.5x=350 hence x=700; thus, 700 servings are needed in order for the society to break even.
10) Let us assume that q=a*p+b (general linear relationship). We have that a and b satisfy:
5000=a*60+b and 3500=a*75+b. We need to solve that system of equations to get the coefficient of our function. Subtracting both equations, we get that 1500=-15*a hence a=-100. Substituting back in the first equation, 5000=-100*60+b, yielding that b=11000. Hence the linear model that we were seeking is q=-100*p+11000.
11) If there is no surplus or shortage, we have that the price is chosen so that supply and demand are equal. Hence -3p+400=7p-500. 10p=900, hence p=90$. The required price is at 90$.

An Native American tepee is a conical tent. Find the number of cubic feet of air in a teepee 10 ft. in diameter and 12 ft. high. 100 cu. ft. 300 cu. ft. 400 cu. ft.

Answers

For this case what you should know is that by definition the volume of the cone is given by:
V = ((pi) * (r ^ 2) * (h)) / (3)
Remembering that:
r = d / 2
Substituting the values:
V = ((pi) * ((d / 2) ^ 2) * (h)) / (3)
V = ((pi) * (((10) / 2) ^ 2) * (12)) / (3)
V = 314.16 ft ^ 3
Answer:
V = 314.16 ft ^ 3
The nearest option is:
300 cu. ft

Answer:

100 pi cubic feet

Step-by-step explanation:

Brent was looking at his cell phone bill and saw that the total number of texts he has sent is tracked, as shown below:

Month
Texts
1
120
2
237
3
354
4
471

The function representing Brent's texting per month is f(m) = 117m + 3. What does the 117 represent?

Answers

It should be the additional texts per month or D

Answer:

The number of texts he sends per month

Step-by-step explanation:

The function f(m) = 117m + 3 is a linear function, which is in the form f(x) = mx+b. In this form, m (the number beside our variable) is the slope, or rate of change, and b (the number added or subtracted) is the y-intercept.

In our function, 117 is the number beside the variable, which makes it the slope. This is the rate of change of this function; it describes how the dependent variable (number of texts) changes for every change in the independent variable (months).

In other words, it tells how many texts he sends per month.

Lines l and m are parallel and intersected by transversals t and s as shown in the figure below.
What is m A) 180 degrees
B) 360 degrees
C) 540 degrees
D) 720 degrees

Answers

Angle W and Y are right angles and equal to 90 degrees each. Angle z and angle x are same side interior angles and they have a sum of 180 degrees because of the same side interior angles postulate.

so W= 90 Y=90 X+Z= 180 . so 90+180+90 =360 degrees. B.

Which of the following would NOT be a deduction from a paycheck?

Select the best answer from the choices provided.
taxes
FICA
hourly wages
health insurance

Answers

the answer would most likely be hourly wages

The answer is hourly wages hoped that helped!.)

4x. (2x^3 — x^2–18x+15) Standard Form

Answers

4x. (2x^3 — x^2–18x+15)=
8x^4 - 4x^3 - 72x^2 + 60x

4x (2x ^ 3 - x ^ 2-18x + 15)
For this case, the first thing to do is multiply the value of 4x for each of the terms within the parenthesis.
You must take into account the following power properties:
Same exponents are added.
We have then:
(8x ^ 4 - 4x ^ 3-72x ^ 2 + 60x)
Answer:
The standard form is:
(8x ^ 4 - 4x ^ 3-72x ^ 2 + 60x)

what are two functions, f(x) and g(x), that would result in a rational function?

Answers

The Rational Function is 4 2 8 4

Use signed numbers to solve. A helicopter descended 1200 feet, rose 800 feet, and then descended 450 feet. What was the net gain or loss in altitude? A. lost 2450 ft B. lost 850 ft C. gained 850 ft D. gained 2450 ft

Answers

The rise or an increase in altitude is represented by positive sign and a decend or decrease in altitude is represented by negative sign.

First the helicopter descended 1200 feet. So the change in altitude will be -1200 feet.

Then the helicopter rose by 800 feet. So the change in altitude will be 800 feet.

Finally the helicopter descended by 450 feet. So the change in altitude will be -450 feet.

The net change in altitude will be the sum of all the above 3 changes.
Change in altitude = -1200 + 800 - 450 = -850 feet

The negative sign indicates a descend i.e. loss in altitude. So the net change in altitude was a loss of 850 feet.

Jack purchased a box of 1,000 candy guitar lollipops to sell in the bakery for $20.00. How much did he pay for each lollipop?

Answers

20 divided by 1,000.

0.02 is the right Anwar

Use the expression below to complete the following tasks. (3a2 - 5ab + b2) - (-3a2 + 2b2 + 8ab) What is the additive inverse of the polynomial being subtracted?

Answers

Remember that the additive inverse are two equal numbers (or expressions) but with different signs.
We have then, that according with the coment below:
(3a2 - 5ab + b2) - (-3a2 + 2b2 + 8ab)
the additive inverse is:
(3a2 - 2b2 - 8ab) Note that is the same expression that
(-3a2 + 2b2 + 8ab)
but with different signs.
Answer:
the additive inverse of the polynomial being subtracted is
(3a2 - 2b2 - 8ab)

Answer:

Option 3

Step-by-step explanation:

edge 2020

NEED HELP ASAP!! WILL GIVE BRAINLIEST
5. Marco wrote the equation below.
cos(-pi/2)=cos(3pi/2)
which statement best describes marcos equation?
a. it is true because the cosine function is odd
b. it is false because the cosine function is even
c. it is true because the cosine function has a period of 2pi
d. it is false because the cosine function has a period of pi.

Answers

The given equation is represented below:

cos(-pi/2)=cos(3pi/2)

The value of cos(-pi/2) is 0 and the value of cos(3pi/2) is also 0

Further a function is defined as an even function if f(x) = f(-x)

Cosine function is an even function.

Therefore it is true and the correct option is c

It is true because the cosine function has a period of 2pi

Hope it helps ..!!

Answer:

Option C - It is true because the cosine function has a period of [tex]2\pi[/tex].

Step-by-step explanation:

Given : Marco wrote the equation below.

[tex]\cos (-\frac{\pi}{2})=\cos (\frac{3\pi}{2})[/tex]

To find : Which statement best describes Macro equation?

Solution :

Since, the period of the given cos function is 360°

So, it holds the property of trigonometric :

[tex]\cos \theta=\cos (2\pi+\theta)[/tex] then the function is an even function.

Taking [tex]\theta =-\frac{\pi}{2}[/tex]

Then , [tex]2\pi+\theta = 2\pi-\frac{\pi}{2}[/tex]

[tex]2\pi+\theta = \frac{4\pi-\pi}{2}[/tex]

[tex]2\pi+\theta = \frac{3\pi}{2}[/tex]

So, the given function is a even function in a period of [tex]2\pi[/tex].

Therefore, Option C is correct.

It is true because the cosine function has a period of [tex]2\pi[/tex].

Help Me Plzzzzzzzzzźzź

Answers

To solve these problems simply place a denominator of 1, for all of the whole numbers and then multiply the top numbers together and then the bottom ones.

So for the first one, it would be 4 • 500/1 • 5

2000/5 = 400.

This is the answer.

John always wears a shirt, pants, socks, and shoes. He owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. How many different outfits can John make?

Answers

12 x 3 x 5 x 5 = 900 different outfits

Answer:

900

Step-by-step explanation:

Khan academy

Noah makes ceramic pots for the market. On the weekends he makes 11 more pots than he does during the week. Noah represented the number of pots he makes on weekends using the expression p + 11. Which expression represents the total mumber of pots Noah made one weekend if he made 14 more than his usual number?

Answers

Answer:
number of pots = p + 25

Explanation:
On weekends, Noah makes 11 pots more than the normal weekdays.
We are given that the equation representing the number of pots is:
number of pots = p + 11
Now, Noah made 14 pots more that his usual numbers, this means that we will add 14 to the usual number of pots that he makes.
Therefore, the equation will become:
number of pots = p + 14 + 11
number of pots = p + 25

Hope this helps :)

Lexi's bulletin board is 40 centimeters wide. each of her ribbons is 4 centimeters wide, and her photos are 12 centimeters wide. what combination of ribbons and photos will fit side by side with no overlap on Lexi's bulletin

Answers

Ribbon, Photo, Ribbon, Ribbon, Photo, Ribbon.
4 x 12 x 4 x 4 x 12 x 4= 40 cm.

Hope this helps!!

Jeannie's restaurant served 58 customers on Monday. After the first day the amount of customers served decreases at a rate of 2.5% each day.

What is the explicit rule for this situation and approximately how many customers will be served on the 6th day?

Round to the nearest customer.

Drag and drop the answers into the boxes to match the situation.

Explicit rule

Number of customers on the 6th day.

A n = 58 x (0.975) n - 1, A n = 58 x (0.025) n - 1, A n = 58 (1.025) n - 1, 51, 49, 48, 46,

Answers

The rule is to find the percentage then divide

Answer:

51 customers

Step-by-step explanation:

Jeannie's restaurant served 58 customers on Monday.

Rate of decrement r =2.5 % = 0.025

Formula : [tex]y=a(1-r)^{n-1}[/tex]

A is the initial amount

r is the rate

n is the no. of days

So, Substitute the values

[tex]y=58(1-0.025)^{n-1}[/tex]

[tex]y=58(0.975)^{n-1}[/tex]

So, explicit rule : [tex]A_n=58(0.975)^{n-1][/tex]

Now to find the no. of customers will be served on the 6th day

Substitute n = 6

[tex]A_6=58(0.975)^{6-1}[/tex]

[tex]A_6=51.1035[/tex]

So, 51 customers will be served on the 6th day

Which of these is a point-slope equation of the line that is perpendicular to y-3=4(x-10) and passes through(-3,7)

A. y+7=4(x-3)
B. y-7= -1/4(x+3)
C. y+7= -1/4(x-3)
D. y-7= -4x(x+3)

Answers

Try this option:
1. rule: if y+a₁=k₁(x+b₁) ⊥ y+a₂=k₂(x+b₂), then k₁*k₂= -1.
for unknown line k= -1/4.
2. substituting the coordinates (-3;7) into the equations, it is possible to find that 'y-7' and 'x+3'.
3. at the end, if to make up the equation: y-7= -1/4(x+3).

Answer: B

The point-slope equation of the line that is perpendicular to y-3=4(x-10) and passes through(-3,7) is:

B. [tex]y-7=\frac{-1}{4} (x+3)\\[/tex]

The slope intercept form is y=mx+b where m is slope.

We have given perpendicular line as:

y-3=4(x-10)

y-3=4x-40

y=4x-37

The slope intercept form of the given line is

y=4x-37

Slope of this line is m=4

Now, as we know the two perpendicular lines have negative reciprocal slope.

Thus the other line have slope [tex]m=-\frac{1}{4}[/tex]

Now. the equation of line passing through point (-3,7) and having slope [tex]\frac{-1}{4}[/tex] is:

[tex]y-7=\frac{-1}{4} (x+3)\\[/tex]

Therefore the correct option is B.

Learn more: brainly.com/question/18595188

The range of F(x) = 6 * 3x is all positive real numbers.

Answers

yes it isssss !!!!!!!!!!!!!

Describe the test grades using the measures of center

Answers

which test grades are you talking about?

Janet makes homemade dolls. Currently, she produces 23 dolls per month. If she increased her production by 18%, how many dolls would Janet produce each month?

Answers

I think she would make 4.14 more dolls per month. Hope this helps.

y = -16x2 + 32x - 10 This parabola has x-intercepts, representing the times when the dolphin's height above water is feet.

Answers

Answer:

two real solutions

Step-by-step explanation:

from edge!!

Final answer:

To find the x-intercepts of the quadratic equation representing the height of a dolphin's jump, we can use the quadratic formula by plugging in the coefficients from the equation y = -16x^2 + 32x - 10. The intercepts indicate the times when the dolphin's height above water is zero feet.

Explanation:

The question involves finding the x-intercepts of a quadratic equation, which represent the points where a parabola crosses the x-axis. In this context, the x-intercepts correspond to the times when the dolphin's height above water is 0 feet. To find the x-intercepts, we can use the quadratic formula:

x = −b ± √(b² − 4ac) / (2a)

For the equation y = −16x² + 32x − 10, the coefficients are a = −16, b = 32, and c = −10. By substituting these values into the quadratic formula, we can calculate the times when the dolphin is at the water level (y=0). Since this is a mathematical problem involving a real-world scenario, it is essential to check that the resulting times make sense within the context. Negative values for time, for example, would not be physically meaningful.

Learn more about Quadratic Equation here:

https://brainly.com/question/30098550

#SPJ3

A guy-wire is attached from the ground to the top of a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the height of the pole (round to 2 decimal places)?

Answers

Answer:

The height of the pole is 322.75 feet.

Step-by-step explanation:

Let the triangle Δ ABC with AC be the length of wire and AB be the Height of the pole

Length between the point of attachment of wire from base of the pole = BC = 137 feet

Angle of elevation to the pole = θ = 67°

We have to find the length of the pole that is AB Let the height of pole be h feet.

According to trigonometry :

[tex]\tan C=\frac{\text{perpendicular}}{\text{base}}[/tex]

Here, C = 67° , perpendicular = AB = h , base = BC = 137

Substitute the values,

[tex]\tan 67^{\circ}=\frac{AB}{BC}[/tex]

[tex]\tan 67^{\circ}=\frac{h}{137}[/tex]

[tex]h=\tan 67^{\circ} \times 137[/tex]

[tex]h=322.75[/tex]

Thus, the height of the pole is 322.75 feet.

Answer:60.1

Step-by-step explanation:

cos

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