Mathematics College

What is the sixth term of the sequence?

an= −3 ⋅ 2n+1

Enter your answer in the box.

a6=

Answers

Answer 1
-3*2n+1
-3*2(6)+1
-3*12+1
-36+1
-35=a6
Answer 2

Answer: its actually -384 and I TOOK THE TEST I promise !!!

Step-by-step explanation:

Related Questions

Evaluate the expression 9p6

Answers

Answer:
9P6 = 60480

Explanation:
In general:
nPx = n! / (n-x)!
In the given, we have:
n = 9 and x = 6
Therefore:
9P6 = 9! / (9-6)! 
       = 9! / 3!
       = (9*8*7*6*5*4*3*2*1) / (3*2*1)
       = 60480

Hope this helps :)

Answer:

60,480

Step-by-step explanation:

I got it correct on founders edtell

Mr. Young has a section of his parking lot, measuring 10 yards by 12 yards, that needs to be repaved. The paving company told Mr. Young the workers complete square yards every hour. How long should it take to pave the parking lot?

Answers

To discover the area of the parking lot , you just need to multiply the length by the width ( 10 × 12 )
10 yards × 12 yards = 120 yards^2
if the take 1 hour to complete 1 square yard , the would take 120 hours to complete the intire parking lot.

I hope you understood my brief explanation
And please consider marking this as the Branliest awnser if you think it deserves it! Thank you :)

Find the exact length of the curve.x = y48 + 14y2, 1 ≤ y ≤ 2

Answers

The original question I assume was:
[tex]x=\frac{y^4}{8}+\frac{1}{4y^2},1\leq y\leq 2[/tex]
We'll use the formula for the arc length of a function which is the following:
[tex]L=\int ds\\ ds=\sqrt{1+\lef(\frac{dx}{dy} )^2}dy[/tex]
Now let's get the derivative of x:
[tex]\frac{dx}{dy}=\frac{4}{8}y^3-\frac{2}{4}\frac{1}{y^{3}}\\=\frac{1}{2}(y^3-\frac{1}{y^3})[/tex]
Alright now plug this into ds formula to get:
[tex]ds=\sqrt{1+\frac{1}{4}(y^3-\frac{1}{y^3})^2}[/tex]
Notice that:
[tex]1+\frac{1}{4}(y^3-\frac{1}{y^3})^2=1+\frac{1}{4}y^6-\frac{1}{2}+\frac{1}{4y^6}\\ =(\frac{1}{2}y^3+\frac{1}{2}y^{-3})^2 [/tex]
Now the integral will be more simple:
[tex]L=\int_1^2\sqrt{(\frac{1}{2}y^3+\frac{1}{2}y^{-3})^2}dy=\int_1^2\frac{1}{2}y^3+\frac{1}{2}y^{-3}dy\\=[\frac{1}{8}y^4-\frac{1}{4}y^{-2}]_2^1\\ =\frac{33}{16}[/tex]

Final answer:

The exact length of the curve x = y^48 + 14y^2, for 1 ≤ y ≤ 2, can be found by differentiating x with respect to y, substituting into the formula for arc length, and solving the integral from y=1 to y=2.

Explanation:

To solve this problem, we use the formula for the arc length of a curve given by a function in parametric form. This formula is L = ∫sqrt(1+(dx/dy)^2)dy, with integration done over the interval [1,2].

In this case, our function is given as x = y^48 + 14y^2. First, we differentiate x with respect to y to get dx/dy = 48y^47 + 28y. We then substitute this into the formula to get L = ∫sqrt(1+(48y^47 + 28y)^2)dy. To solve this integral, you can use a standard calculus method or a calculator with integral functions. Make sure to evaluate the definite integral from y=1 to y=2.

Learn more about Arc Length here:

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Solve the equation on the interval [0,2pi) 4sin^2x-3=0

Answers

4sin²x-3=0
4sin²x=3
sin²x=3/4
sinx=√3/2 or -√3/2
x=π/3, 2π/3, 4π/3, or 5π/3

The equation 4sin^2x-3=0 has a solution of x=π/3,2π/3,4π/3,5π/3.

What is equation?

An equation is basically a relationship between two variables in equal to form. In an equation each variable must have a solution or value.

How to solve an equation?

The equation given as 4sin²x-3=0

We have to first find the value of x in the equation itself  which is  4sin²x=3

sin²x=3/4

sinx=√3/2 or -√3/2

x=π/3, 2π/3, 4π/3, or 5π/3.

Hence the solution for the equation 4[tex]sin^{2}x-3[/tex]=0 is x=π/3,2π/3,4π/3,5π/3.

Learn more about equation at https://brainly.com/question/2972832

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Write the equation of the line that passes through (–2, 1) and is perpendicular to the line 3x – 2y = 5.

Answers

To make the perpendicular line, it is convenient to swap the x- and y-coefficients and negate one, then offset the x- and y- by the point value:
.. 2(x +2) +3(y -1) = 0

This equation can now be put into any desired form. Based on the given equation, it looks like you would like "standard form."
.. 2x +3y = -1

To find the equation of a line that is perpendicular to the line 3x - 2y = 5 and passes through the point (-2, 1), we determine that the slope of the perpendicular line must be -2/3. Using the point-slope form, the equation of the desired line is y = (-2/3)x - (1/3).

Finding the Equation of a Perpendicular Line

To write the equation of a line that is perpendicular to another line, you first need to determine the slope of the original line. The given equation, 3x - 2y = 5, can be rewritten in slope-intercept form (y = mx + b) by solving for y:
3x - 2y = 5
=> -2y = -3x + 5
=> y = (3/2)x - (5/2)
The slope (m) of this line is 3/2. Perpendicular lines have slopes that are negative reciprocals of each other. Thus, the slope of the line perpendicular to the original line is -2/3.

To find the equation of the line passing through the point (-2, 1) with this slope, use the point-slope form of the equation:
y - y1 = m(x - x1)
=> y - 1 = (-2/3)(x + 2)
Simplifying, we have:

y - 1 = (-2/3)x - (4/3)
=> y = (-2/3)x - (4/3) + 1
=> y = (-2/3)x -(1/3)

This is the equation of the line that passes through (-2, 1) and is perpendicular to the line 3x - 2y = 5.

You owe $976.34 on a credit card that has an interest rate of 10.75% APR. You pay $100.00 at the end of each month.

You place the $100.00 in a savings account that earns a 2.75% APR. What is the difference in interest between savings earned and credit card interest paid

answer: $8.52

Answers

You already wrote the answer. Do you want to check if this answer is correct?
1. $976.34*1075= 104.96
976.34*104=871.38
 2. 100.00*0275=2.75 

John bought a house. He decided to reduce his square backyard by 40 inches along its width. The area of the new backyard is given by the function below, where z represents the length in inches.

A(z)=z^2-40z

Which statement best describes the term 40z?

* The area of the playground after expansion
* The width of the backyard
* The area of the backyard before reduction
* The area reduced from the backyard

Answers

Ans: The area reduced from the backyard

Weight Gain after gaining 25 pounds, a person is 115 pounds lighter than double his previous weight. How much did the person weigh before gaining 25 pounds? How could I write this problem

Answers

Equation: x + 25 = 2x - 115
Cross 115 over the 'bridge' and add it with 25: x+140 = 2x
Cross x over the 'bridge' and subtract with 2x: 140 = x

ANSWER: x

Use the empirical rule to solve the problem. ed's monthly phone bill is normally distributed with a mean of $65 and a standard deviation of $11. what percentage of his phone bills are more than $76?

Answers

By the empirical rule, 84% of the distribution is below one standard deviation above the mean.

16% of Ed's monthly phone bills are more than $76.

Answer:

16% of his phone bills are more than $76

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 65

Standard deviation = 11

What percentage of his phone bills are more than $76?

76 = 65 + 11

So 76 is one standard deviation above the mean.

By the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean. The other 100-68 = 32% are more than 1 standard deviation from the mean. Since the normal probability distribution is symmetric, 16% of them are more than 1 standard deviation below the mean and 16% are more than 1 standard deviation above the mean. So

16% of his phone bills are more than $76

Your brother is 13 your age. Your sister is 6 years older than your brother. Your sister is 10 years old. Write and solve an equation to find your age a.

Answers

By setting up equations using the information about your siblings' ages, we find out that you are 12 years old.

To find your age, we can set up an equation based on the information given:

Your sister is 10 years old.

Your brother is 13 your age, meaning 1/3 of your age.

Your sister is 6 years older than your brother. Therefore, if your brother's age is b, your sister's age is b + 6.

Since your sister is 10, this allows us to write the equation for your brother's age as:

b + 6 = 10

Solving for b, we get:

b = 10 - 6 => 4

Now we know your brother is 4 years old, and since he is 13 your age, we can write another equation:

a ÷3 = 4

Multiplying both sides by 3 to solve for a:

a = 4 × 3 => 12

You are 12 years old.

subtracting/adding mixed fractions

Answers

a)
= 3 2/4
= 3 1/2

b)
= 7 10/15 + 2 3/15
= 9 13/15

If the cubic function P(x) includes the points (−4, 0), (0, 0), and (2, 0), which of the following represents this function?

Answers

Final answer:

The function cannot be determined with the given information.

Explanation:

The given points (-4, 0), (0, 0), and (2, 0) indicate that the function is a cubic function with three real roots. A cubic function is of the form P(x) = ax^3 + bx^2 + cx + d. Since the function passes through the x-axis at (-4, 0), (0, 0), and (2, 0), the roots of the cubic function are -4, 0, and 2. Therefore, the function can be written as P(x) = a(x + 4)(x - 0)(x - 2). However, since a cubic function with three real roots has an odd degree, the coefficient 'a' must be negative or positive. This means that the function can also be written as P(x) = -a(x + 4)(x - 0)(x - 2) or P(x) = a(x + 4)(x - 0)(x - 2). So, the correct representation of the function cannot be determined with the given information.

Gas costs $1.64 a gallon. Elaine spent $23.78 at the gas station.How many gallons of gas did she but?

Answers

$1.64 per gallon
she paid $23.78
23.78÷1.64
She paid for 14.5 gallons

To check:
1.64 * 14.5 
23.78

Hope this helps

Answer:

23.78

Step-by-step explanation:

Does the following equation represent growth or decay? Y=10,000(0.97)x

Answers

decay because it  is being multiplied by a decimal so the number will go down.

Given is Y = 10000·(0.97)ˣ

This is an exponential equation whose general form is y = a·bˣ

where 'a' is the initial value and 'b' is the growth or decay factor.

If value of b is greater than 1, then it is growth of population.

If value of b is lesser than 1 but greater than 0, then it is decay of population.

On comparison of the given equation with its general form, we get a = 10000, b = 0.97

So initial value is 10000.

Since value of b is 0.97 i.e. lesser than 1, so it is decay of population.

Hence, the given equation represents "Decay".

The height of a rock thrown off a cliff can be modeled by h=-16t^2-8t+120, where h is the height in feet and t is time in seconds. How long does it take the rock to reach the ground?

Answers

The rock hits the ground after 4 seconds.

----------------------
Here is the work in how you can find this answer...:
----------------------

The height, h, of an object thrown upward from an initial height, H, with an initial velocity, Vo, is given by the function h as a function of time, t:

h(t) = -16t^2 + Vot + H

Since Vo = 48 ft/sec and H 64 ft, then: 

h(t) = -16t^2 + 48t + 64

You want to know at what time, t, will the rock hit the ground (h = 0). Set the above function = 0. 

-16t^2 + 48t + 64 = 0

Solve this quadratic equation for t. First, factor -16.

-16 ( t^2 - 3t -4 ) = 0

Apply the zero products principle.

t^2 - 3t - 4 = 0

Factor.

( t - 4 )( t + 1 )

Again, apply the zero products principle.

t - 4 = 0 and/or  t + 1 = 0

If t - 4 = 0, then t = 4 seconds

If t + 1 = 0, then t = -1 second...Discard this solution as negative time is not meaningful in this problem.

---
OVERALL = THE ROCK HITS THE GROUND AFTER 4 SECONDS
---

How to do this because I do not understand how to do it

Answers

Answer: 24.52%

-------------------------------------------

Work Shown:

Convert the time 7:45, which represents 7 min 45 sec, to seconds only
7:45 = (7 min) + (45 sec)
7:45 = (7*60 sec) + (45 sec)
7:45 = (420 sec) + (45 sec)
7:45 = (420+45) sec
7:45 = 465 sec

Do the same for 5:51
5:51 = (5 min) + (51 sec)
5:51 = (5*60 sec) + (51 sec)
5:51 = (300 sec) + (51 sec)
5:51 = (300+51) sec
5:51 = 351 sec

So the initial time is 465 seconds and it drops to 351 seconds
Subtract the values to find the amount dropped: 465-351 = 114

Divide that difference over the initial time: 114/465 = 0.24516

Move the decimal over 2 spots to the right to convert to a percentage: 0.24516 --> 24.516%

Then round to the nearest hundredth of a percent (2 decimal places) to go from 24.516% to 24.52% which is our final answer

So the reduction is roughly 24.52%
This means if you took 24.52% of the initial time and subtracted it off, then you'd get to about 351 seconds.

Answer:

24.52%

Step-by-step explanation:

What are the values of a and b?

Answers

See also
https://brainly.com/question/8861591

Short Side : Long Side is the same for all triangles
.. a/20 = 20/21
.. a = 400/21

Hypotenuse : Long Side is the same for all triangles
.. b/20 = 29/21
.. b = 580/21

The 1st selection is appropriate.

Choose the correct classification of x6 + 3x3 by number of terms and by degree.
Third degree polynomial
Fourth degree trinomial
Third degree binomial
Sixth degree binomial

Answers

 x⁶ + 3x³

Since there are 2 terms, this is a binomial 

The degree of these is found by looking at the largest exponent on its variables. The highest degree in this binomial is the power 6

Therefore, it is a sixth degree binomial

The uploaded picture below will be helpful
it is a sixth degree polynomial

Find the markup and the selling price of the following item. Round answers to the nearest cent. A chemistry set costing $38.50, marked up 32% on cost. Markup = ? Selling price = ?

Answers

In order to compute the markup, compute the percentage like this:
[tex]38.50\times0. 32=12,32[/tex]
The markup is then $12,32.
The selling price is the sum of the cost and the markup:
[tex]38.50+12,32=50,82[/tex]

Answer:

markup, 12.32

selling price, 50.82

Step-by-step explanation:

Which statement about the population shown in this graph is true? A. The number of individuals will increase endlessly. B. The number of individuals will eventually drop to zero. C. The population has increased until it reached its carrying capacity. D. There are no limiting factors to control population growth.

Answers

D is the answer to this question
Hello


D will be your correct answer.

Hope this helps 

(64-2^2)-(8+7)
answer please

Answers

Hello there!

64 - 2² - (8 + 7)

= 64 - 4 - 15

= 60 - 15

= 45

Let me know if you have any misunderstanding!

As always, I am here to help!

PLEASE HELP BABES!!

How likely is it that you would pick the number 67 if you closed your eyes?
A) certain
B) impossible
C) probable
D) unlikely

Answers

The answer is D. Unlikely
I think the correct answer will be  (c probably)

What is the geometric mean of 6 and 13?

What is the Geometric mean a 5 and 45?

Answers

What is the geometric mean of 6 and 13? 
√(6·13) = √78

What is the Geometric mean a 5 and 45?
√(5·45) = √225 = 15

Answer: [tex]\sqrt{78}[/tex] and [tex]15[/tex]

Step-by-step explanation:

Given: (1) two numbers [tex]6[/tex] and [tex]13[/tex].

           (2) two numbers [tex]5[/tex] and [tex]45[/tex].

To Find: Geometric number of numbers in [tex](1)[/tex] and [tex](2)[/tex]

Solution:

Let first number be [tex]=\text{a}[/tex]

Let second number be [tex]=\text{b}[/tex]

Geometric mean of two numbers [tex]\text{a}[/tex] and [tex]\text{b}[/tex] is

                                     [tex]\sqrt{\text{a}\text{b}}[/tex]

Now,

[tex](1)[/tex] First number is [tex]=6[/tex]

            Second number is [tex]=13[/tex]

Geometric mean of both numbers is

      [tex]\sqrt{6\times13}[/tex]

      [tex]\sqrt{78}[/tex]

Geometric mean is  [tex]\sqrt{78}[/tex]

[tex](2)[/tex] First number is [tex]=5[/tex]

            Second number is [tex]=45[/tex]

Geometric mean of both numbers is

      [tex]\sqrt{5\times45}[/tex]

      [tex]\sqrt{225}[/tex]

      [tex]15[/tex]

Geometric mean is  [tex]15[/tex]

If a couple plans to have 9 ​children, what is the probability that there will be at least one girl​? assume boys and girls are equally likely. is that probability high enough for the couple to be very confident that they will get at least one girl in 9 ​children?

Answers

Second question: maybe but nothing is certain when you're talking about anything between men and women. This is not part of the answer. It's just an observation.

Figure this question out first as though you don't get any females. They are all males. The total number of ways that you can distribute 9 children by gender is 2^9 = 512
There is only one way that you can get all males and that is M M M M M M M M M  so the chances are 1 chance in 512 or 1/512 
All males = 0.001953

So the chances of there being at least 1 female is
1 - 1/512 = 0.998

Which contrary to my opening remark is almost certainty.



A store is having a sale where all jeans are 1/4 off the regular price.Find the constant of proportionality, then write an equation relating to the sale price to the regular price.

Answers

1 to 25% so just simplify the fraction

Assume the method dosomething has been defined as follows: public static void dosomething (int[] values, int p1, int p2) { int temp = values[p1]; values[p1] = values[p2]; values[p2] = temp; } what does the method do?3

Answers

First step is to analyze input and output variables:
INPUT:
list of integers with name "values"
integer with name "p1"
integer with name "p2"
OUTPUT:
there is no output variable as in declaration of a method there is void

ANALYSIS:
"int temp = values[p1]"
this line creates variable "temp" which is integer. then this line goes to the list "values" and takes value that is at position "p1" and stores it into variable "temp"

"values[p1] = values[p2]"
this line goes to the list "values" and takes value that is at position "p2" and stores it into variable that is at position "p1"

"values[p2] = temp"
this line takes value of the variable "temp" and stores it into list values at position "p2"

Short explanation:
this code replaces values of the list at between positions p1 and p2

When 2/3 of a number is added to 10 the result is 5 more than the number find the number g?

Answers

[tex]g-the\ number\\\\\dfrac{2}{3}g+10=g+5\qquad\text{multiply both sides by 3}\\\\2g+30=3g+15\qquad\text{subtract 30 from both sides}\\\\2g=3g-15\qquad\text{subtract 3g from both sides}\\\\-g=-15\qquad\text{change the signs}\\\\\boxed{g=15}[/tex]

Myron bought a dozen eggs for $1.75 per dozen. If he bought 8 dozen eggs, how much did they cost?]

Answers

That would be 8×1.75, which is 14. He bought 8 dozen eggs for $14.
Hey there!

So, if 1 (dozen) of eggs equal ($1.75), we would want to multiply this by (8).

[tex] \left[\begin{array}{ccc}\boxed{\boxed{1.75*8}}\end{array}\right] \ =\left[\begin{array}{ccc}\boxed{14}\end{array}\right][/tex]

This would cost then ($14).

Hope this helps you!

Sarah has grades of 98 and 98 on her first two test if she want to average at least 80 after her third test what must she make on that test

Answers

So add together 98 plus 98 plus 44. This gives you 240. 240 divided by three is 80.
So sarah need to get a 44 percent on her next test!

Hope this helps!
♤MidnightQueen
98+98+44

240\80=44 Answer is 44

given the equation W=CE2/2, solve for C

Answers

W=CE^2/2
CE^2 = 2W
C = 2W/E^2 Answer

Answer:

[tex]C=\frac{2W}{E^2}[/tex]

Step-by-step explanation:

[tex]W=\frac{CE^2}{2}[/tex]

Solve for C

To solve for C, we need to get C alone

LEts start with eliminating 2 from the denominator

Multiply the equation by 2 on both sides

[tex]2W= CE^2[/tex]

To isolate C, divide both sides by E^2

[tex]\frac{2W}{E^2} =C[/tex]

[tex]C=\frac{2W}{E^2}[/tex]

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