Mathematics College

7/6 - 4/3n = -3/2n + 2(n + 3/2)

Answers

Answer 1

2n/3+25/6 I simplified the question if that is what you wanted me to do.

Related Questions

write the following equation in standard form. x^5+2x^3+6x+1/5

Answers

5x^5 + 0x^4 + 10x^3 + 0x^2 + 30x + 1Hope it helped!

The standard form is x⁵ + 2x³ + 6x + [tex]\frac{1}{5}[/tex].

To write the given equation x⁵ + 2x³ + 6x + [tex]\frac{1}{5} \\[/tex] in standard form, follow these steps:

Identify and list all terms in the polynomial: x⁵, 2x³, 6x, and [tex]\frac{1}{5}[/tex].Arrange the terms in descending order based on the exponent of x:x⁵ + 2x³ + 6x + [tex]\frac{1}{5}[/tex]Ensure all coefficients and constants are in standard form:The polynomial in standard form is: x⁵ + 2x³ + 6x + [tex]\frac{1}{5}[/tex].

The circumference of a circular field is
260.62 yards. What is the diameter of the field? Use 3.14 for π and do not round your answer.

Answers

Final answer:

The diameter of the field is 83 yards.

Explanation:

To find the diameter of a circular field, we can use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius. Given that the circumference of the field is 260.62 yards, we can solve for the radius by dividing the circumference by 2π.

Using the value of π as 3.14, we can calculate:

260.62 / (2 * 3.14) = 41.50 yards

Since the diameter of a circle is twice the radius, the diameter of the field is 2 * 41.50 = 83 yards.

The function f(x) = x2 + 5x – 6 is shifted 4 units to the left to create g(x). What is g(x)?

Answers

Please, use "^" to denote exponentiation: x^2, not x2.

f(x) = x^2 + 5x – 6 becomes g(x) if we replace each x in f(x) with (x+4):

g(x) = (x+4)^2 + 5(x+4) - 6

This can be expanded: g(x) = x^2 + 8x + 16 + 5x + 20 - 6, or
g(x) = x^2 + 13x + 30

Answer:

g(x)=(x+4)^2+5(x+4)-6

The diagram shows an isosceles triangle. All the measurements are in cm. Work out the perimeter of the triangle.
How do I achieve the other 3 marks (putting what shows in the box got me 1/4 marks)? Putting "cm" after the numbers did nothing.

Answers

check the picture below.

therefore, the perimeter is then -> [3(6) - 5] + [ 19 - (6)] + [ 2(6) ].

The final mark you can get by substitute the 6 to the x which you get the total of 38 because you have to calculate the perimeter of the isosceles triangle. You both literally helped me to get the full marks on Mathswatch Thank you!

If the equation y = 15x + 2 is changed to y = 15x - 4, how will the graph of the line change?

Answers

The y-intercept is changed from 2 to -4.

That means that the point that the graph crosses the y axis has been moved down by 6.

Since the slope of the line has not changed, this just means the graph of the line will be moved down by 6.

Hope this helps!
Your fortune is "When given a difficult choice, trust your gut. If you don't have one, then close your eyes and hope for the best."

The graph of the line change is, It will shift down 6 units.

The given function is,

y = 15x + 2

Now, We want to find how the graph of this function will change if the function is transformed to

y = 15x -4

We rewrite this function in terms of the first one to get:

y = 15x + 2 + (-6)

Hence, the function with shift down 6 units.

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The use of the normal probability distribution as an approximation of the sampling distribution of p̄ is based on the condition that both np and n(1 – p) equal or exceed _____.
a. .05
b. 5
c. 15
d. 30

Answers

The use of the normal distribution as an approximation for the sampling distribution of[tex]$ \bar{p} $[/tex] requires both [tex]$ np $[/tex] and [tex]$ n(1 - p) $[/tex] to be at least 5. So, the answer is (b) 5.

The normal approximation for the sampling distribution of [tex]$ \bar{p} $,[/tex] the sample proportion, relies on the conditions that both[tex]$ np $[/tex] and [tex]$ n(1 - p) $[/tex] are greater than or equal to 5. Here, [tex]$ n $[/tex] represents the sample size, and [tex]$ p $[/tex] is the probability of success in a binary outcome. These conditions ensure that the distribution of[tex]$ \bar{p} $[/tex] is approximately normal, allowing for the application of statistical techniques based on the normal distribution. When[tex]$ np $[/tex]and [tex]$ n(1 - p) $[/tex]are both at least 5, the central limit theorem asserts that the distribution of [tex]$ \bar{p} $[/tex] is sufficiently close to normal, facilitating the use of standard normal tables and z-scores for making probability calculations and inferences about the population proportion. This approximation is pivotal in hypothesis testing and confidence interval construction for proportions in statistical analyses.

At your birthday party, 5/8 of the 24 guests were relatives. How many relatives were at your party?

Answers

24 / 8 = 3

3 * 5 = 15

15 of the guests were relatives.

Hope this helps!

15 of the guests were relatives.

Find counter example to disprove the conjecture:

if the quotient of two numbers is positive, then the two numbers must be positive

Answers

[tex] \frac{ - 2}{ - 1} = 2[/tex]
this is an example where the quotient is postive but the two numbers are negative

WILL GIVE BRAINEST
50 POINTS
Identify the explicit function for the sequence in the table

Answers

ur answer would be A

hope this helped have a great wonderful rest to ur day and or nite :)

Jackson is flying at a constant rate of 500 mph from New York, New York, to Austin, Texas, which is a distance of 1,750 miles. If the distance Jackson has traveled in miles is a function of time in hours he has been flying, determine an appropriate domain and range for this problem situation.

Answers

Sent a picture of the solution to the problem (s).

The domain of the function is [tex][0,3.5][/tex] and the range of the function is [tex][0,1750][/tex].

Speed [tex]= 500[/tex] mph

Distance [tex]= 1750[/tex] miles

Distance [tex]=[/tex] Speed [tex]\times[/tex] Time

The distance Jackson has traveled in miles is a function of time in hours he has been flying.

[tex]f(t)=500t.[/tex]

For maximum distance, [tex]f(t)=1750[/tex] miles.

[tex]1750=500t.[/tex]

[tex]t=\frac{1750}{500}[/tex]

[tex]t=3.5[/tex] hours

So, domain [tex]= [0,3.5][/tex]

Range [tex]= [0,1750][/tex]

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What dose 0.07x1.22 eaqual

Answers

Final answer:

When multiplying 0.07 by 1.22, the product is 0.0854. This result is calculated by first multiplying the numbers as whole numbers and then placing the decimal point so that the total number of decimal places in the product matches the sum of the decimal places in the factors.

Explanation:

To calculate the product of 0.07 and 1.22, you follow the standard multiplication procedure for decimals:Multiply as if the numbers were whole numbers; ignore the decimal points for a moment.Count the total number of decimal places in both of the numbers you're multiplying. In 0.07, there are two decimal places. In 1.22, there are two decimal places as well.Add the number of decimal places together. In this case, 2 (from 0.07) plus 2 (from 1.22) equals 4 decimal places in total.Perform the multiplication without considering the decimal, which gives you 7 * 122 = 854.Place the decimal point in the answer (854) so that there are 4 decimal places, giving you 0.0854.

Therefore, 0.07 multiplied by 1.22 equals 0.0854.

Final answer:

When multiplying 0.07 by 1.22, we first ignore the decimals and multiply 7 by 122 to get 854, and then we place the decimal point so the result has the same number of decimal places as the sum of the factors, resulting in 0.0854.

Explanation:

To find the product of two decimal numbers, you multiply them just as you would with whole numbers, taking care to place the decimal point in the correct position in the final answer. For the multiplication of 0.07 by 1.22, you perform the multiplication ignoring the decimals first, and then place the decimal in the final answer so that the total number of decimal places equals the sum of the decimal places in the factors.

Multiplying 7 by 122 equals 854. Since 0.07 has two decimal places and 1.22 has two decimal places, the product must have four decimal places. Therefore, the correct placement of the decimal point in 854 would be after four digits from the right, which gives us a final answer of 0.0854.

Does anyone know a rule that work for all of these

Answers

Divide each term in the y column by 2 to go from this list {8, 2, 0, 2, 8} to this list {4, 1, 0, 1, 4}

This list {4, 1, 0, 1, 4} is a bunch of perfect squares so it suggests that y = x^2

However we must double the values to get back to the original list. So the rule is y = 2*x^2

You have a gift card for your favorite clothing store for the amount of $60. You have found a shirt you want to buy that costs $15. If you don't want to spend more than the amount of the gift card, which of the following inequalities could be used to determine the amount you have left to spend?

Answers

Answer:

D. x + 15 ≤ 60

Step-by-step explanation:

Let x be the amount you have left to spend after you purchase the shirt.

We must add to x the cost of the shirt, $15. This gives us x+15.

We only have $60 to spend; this means we can spend anything up to and including $60. This means we want "less than or equal to." This gives us the inequality

x+15 ≤ 60

The inequality of the form x + 15 ≤ 60 is the correct choice.

What is an inequality ?

An inequality is a comparison between two non equal expression or terms or numbers.

According to the given question You have a gift card for your favorite clothing store for the amount of $60.

You have found a shirt you want to buy that costs $15 but you don't want to spend more than the amount of the gift card.

Assuming the amount you will have is x dollars.

∴ x + 15 ≤ 60

As x ≤ 60 - 15

x ≤ 45.

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Find the slope of the line.

Answers

There are several ways to do this.
I'll show you two methods.

1) Pick two points on the line and use the slope formula.
Look for two points that are easy to read. It is best if the points are on grid line intersections. For example, you can see points (-4, -1) and (0, -2) are easy to read.
Now we use the slope formula.

slope = m = (y2 - y1)/(x2 - x1)

Call one point (x1, y1), and call the other point (x2, y2).
Plug in the x1, x2, y1, y2 values in the formula and simplify the fraction.

Let's call point (-4, -1) point (x1, y1).
Then x1 = -4, and y1 = -1.
Let's call point (0, -2) point (x2, y2).
Then x2 = 0, and y2 = -2.

Plug in values into the formula:

m = (y2 - y1)/(x2 - x1) = (-2 - (-1))/(0 - (-4)) = (-2 + 1)/(0 + 4) = -1/4

The slope is -1/4

2) Pick two points on the graph and use rise over run.
The slope is equal to the rise divided by the run.
Run is how much you go up or down.
Rise is how much you go right or left.

Pick two easy to read points.
We can use the same points we used above, (-4, -1) and (-0, -2).
Start at point (0, -2).
How far up or down do you need to go to get to point (-4, -1)?
Answer: 1 unit up, or +1.
The rise is +1.
Now that we went up 1, how far do you go left or right top go to point (-4, -1)?
Answer: 4 units to the left. Going left is negative, so the run is -4.
Slope = rise/run = +1/-4 = -1/4

As you can see we got the same slope using both methods.

Using the rule of 72, mc003-1.jpg, how long will it take for the principal to double with an annual compound interest rate of 6%?

6 years

9 years

12 years

15 years

Answers

Answer:

Option C. 12 years

Step-by-step explanation:

Let principal amount taken = x

We know the formula of compound interest

Final amount = Principal amount×[tex](1+\frac{r}{n})^{nt}[/tex]

Where r = rate of interest (per year)

n = number of times compounded (annually)

t = time in years (years)

Here we have to find the time in which principal amount is doubled.

From the question r = 6% = .06

n = 1

Principal amount = P

Final amount = 2P

Now we put these values in the formula

[tex]2P=P(1+.06)^{t}[/tex]

[tex]2=(1.06)^{t}[/tex]

Now we take log on both the sides

[tex]log(2)=log(1.06)^{t}[/tex]

0.301 = tlog(1.06)

0.301 = t×(.025)

[tex]\frac{0.301}{0.25}=t[/tex]

t = 12 years.

Option C. 12 years is the answer.

How many solutions does this linear system have?

Answers

y = 2x - 5
-8x - 4y = -20

substitute one equation to the other;
-8x - 4y = -20
-8x - 4(2x - 5) = -20
-16x + 20 = -20

solve for x;
-16x + 20 = -20
-16x = -40
x = 5/2 or 2.5

substitute x = 5/2 to find the y;
y = 2x - 5
y = 2(5/2) - 5
y = 0

one solution; (2.5, 0) is your answer.

hope this helped, God bless!

A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?

Answers

A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?
28-14
Find the slope, m: m = ------------ = 14/2 = 7
4-2

Now find the equation of this line by using the point-slope equation:
y-28 = (7)(x-4)

You could change this to point-slope form: y = 28 + 7(x-4), or y = 7x

Answer:

Sorry that I’m late, answer is C. y=7x

Step-by-step explanation:

14/2 = 7

28/ = 7

hello i need help in this, someone pls!!!

Answers

The given ODE is
[tex] \frac{dy}{dx} = \frac{x}{y} [/tex]

Let y² = x - v
Then
[tex]2y \frac{dy}{dx} =1 - \frac{dv}{dx} \\\\ \frac{dy}{dx} = \frac{1}{2y} (1- \frac{dv}{dx} )[/tex]

Substitute in the original ODE.
[tex] \frac{1}{2y} (1- \frac{dv}{dx}) = \frac{x}{y} \\\\ 1- \frac{dv}{dx} =2x \\\\ \frac{dv}{dx} =1-2x [/tex]

Integrate with respect to x to obtain
v = x - x² + b
Hence obtain
y² = x² + b

When y(x) passes through (0,0), obtain
b = 0
y² = x²
When y(x) passes through (1,0), obtain
0 = 1 + b => b = -1
y² = x² - 1
When y(x) passes through (0,1), obtain
1 = 0 + b => b = 1
y² = x² + 1

A graph of the three solutions is shown below.

how many times greater is the value of the digit 2 in the 23.876 than the value of the digit 2 in 3.254?

Answers

The decimal is 2 to the right so it would be 100 times greater :)

Find the Slope A(4,6) B(-8,-3)

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[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ 4}}\quad ,&{{ 6}})\quad % (c,d) B&({{ -8}}\quad ,&{{ -3}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-3-6}{-8-4}\implies \cfrac{-9}{-12}\implies \cfrac{3}{4}[/tex]

An orchard has 864 orange trees. The number of rows exceeds the number of trees per row by 5 . How many trees are there in each row?

Answers

[tex]\bf \cfrac{rows}{\textit{trees in a row}}\qquad 5:1\qquad \cfrac{5}{1}\qquad \cfrac{5\cdot \frac{864}{5+1}}{1\cdot \frac{864}{5+1}}\implies \cfrac{5\cdot 144}{1\cdot 144}\implies \cfrac{720}{144}[/tex]

Final answer:

Using a quadratic equation, we found that there are 24 orange trees in each row of the orchard.

Explanation:

To determine how many orange trees are there in each row, we will set up an equation based on the information provided. Let's let x represent the number of trees per row. According to the problem, the number of rows is x + 5. Since the total number of trees in the orchard is 864, we can create the following equation:

x * (x + 5) = 864

To solve this quadratic equation, we need to find the value of x that satisfies the equation:

First, expand the left side of the equation: [tex]x^{2}[/tex] + 5x.

Write the equation in standard form: [tex]x^{2}[/tex] + 5x - 864 = 0.

Factor the quadratic equation: (x + 36)(x - 24) = 0.

Solve for x: x = -36 or x = 24.

Since we cannot have a negative number of trees per row, we disregard x = -36.

Therefore, there are 24 trees in each row.

1/4 of 12 bottles of water

Answers

1/4(12)= 3

The answer is 3 bottles of water.

Hope this helps!

the answer will be 3

12 dividd by 4 is 3

Which graph represents the solution set of the system of inequalities?

(1st picture is question and 1st set of answers 2nd picture is 2nd set of answers.

Answers

The inequalities are
y ≤ 2x + 1
and
y > -2x -3

Conveniently, they are already in slope-intercept form. Looking at the inequalities, we know off the bat there will be one dotted line and one solid line, since one is a "greater than" inequality (dotted line) and the other is "greater than or equal to" (solid line). This automatically rules our option B and C.

-The solid line will have a slope of 2 and a y-intercept of 1
-The dotted line will have a slope of -2 and a y-intercept of -3.

Both option A and D satisfy this, so which one has correct shading?
Option D has the shaded region below the solid line and above the dotted line, which agrees with our system of inequalities.

Answer is D

Yikes mctugg bought 1/2 pounds of potato salad. He ate 2/3 of it for lunch. How much potato salad was left for an afternoon snack

Answers

Yikes mctugg has 1/6 pounds of potato salad left :)

What is the value of a in the equation 4a + 3(a + 1) = 24?

Answers

a = 3. Hope this helps! (Was trying to show the work but I can't take pictures at the moment.)

The value of A would be 3

After driving for 2.2 hours (2 hours and 12 mintues), marcos' total distance traveled was 153 miles. at what constant speed (in miles per hour) would he have to travel for the last 5 minutes in order to complete the 155 mile drive in 2 hours and 17 minutes?

Answers

Answer:

24 miles per hour.

Step-by-step explanation:

So in order to calculate this you just need to use the formula for the speed:

Speed=Distance/time

Speed= 2 miles/ 5 minutes

Speed= 2 miles/,083 hours

Speed= 24

So the speed at the final 5 minutes will be 24 miles per hour.

Evaluate using the order of operations. 54 + (9.2 - 1.413)

Answers

the answer is 61.787

The quotient of a number and 0.2 is -2.6

Answers

The answer is -.52
You multiply -2.6 and .2 together to find the answer

Quotients are used to represent the division of numbers

The number is -0.52

Let the number be represented with x.

So, the quotient of a number (x) and 0.2 is -2.6 is represented as:

[tex]\frac x{0.2} = -2.6[/tex]

Multiply both sides of the equation by 0.2

[tex]0.2 * \frac x{0.2} = -2.6 * 0.2[/tex]

Evaluate the quotient, on the left hand side

x = -2.6 * 0.2

Evaluate the product on the right hand side

x = -0.52

Hence, the number is -0.52

Answers

Final answer:

The monthly interest rate on this annuity is approximately 0.4318%.

Explanation:

To find the monthly interest rate on the annuity, we need to use the present value formula for an annuity:

PV = A * (1 -[tex](1+r)^{(-n)[/tex]) / r

Where PV is the present value, A is the monthly payment, r is the monthly interest rate, and n is the total number of payments. In this case, PV = $90,000, A = $850, and n = 15 (since the professor's remaining life expectancy is 15 years).

By plugging in these values and solving for r, we can find the monthly interest rate on the annuity.

$90,000 = $850 * (1 - [tex](1+r)^{-15)[/tex] / r

After solving this equation, we find that the monthly interest rate on this annuity is approximately 0.4318%.

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The monthly interest rate is approximately 0.58%.

To determine the monthly interest rate on the annuity, we need to solve for the rate that equates the present value of the annuity payments to the initial payment of $90,000. The payments of $850 are made for the expected life of 15 years, which translates to 180 monthly payments.

The present value (PV) of an annuity can be calculated using the formula:

[tex]PV = Pmt * [(1 - (1 + r)^{-n}) / r][/tex]

Where:
Pmt = $850 (monthly payment)
r = monthly interest rate
n = 180 (total number of payments)

Given PV = $90,000, we need to solve for r:

$90,000 = $850 × [(1 - (1 + r)^-180) / r]

This requires solving the equation iteratively or using a financial calculator, as it's a non-linear equation. By trial and error or using a financial calculator or spreadsheet:

We find that r ≈ 0.0058 or 0.58%

Thus, the monthly interest rate on this annuity is approximately 0.58%.

Simplify and determine the coefficient of (-2/3x)(3y)(-2x). -4 1 4

Answers

The simplification is 4x2y.

The coefficient would be 4.

This question is a bit problematic because -2/3x can be understood as (-2/3) * (X) or (-2) / (3X)

But since the question is about coefficient, then it should pose no problem to solve it. Assuming the question mean (-2/3) * (X), then
(-2/3) * (X) * 3Y * (-2X) =
(-2/3 * 3*-2) * X^2 * Y =
(4) * X^2 * Y
That means the coefficient will be 4

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