Mathematics College

1365=x+(1×x×5%)
Please show all steps on how you got the answer

Answers

Answer 1
[tex]\bf 1365=x+(1\cdot x\cdot 5\%)\\\\ -------------------------------\\\\ whatever\%~of~anything\implies \cfrac{whatever}{100}\cdot anything\\\\ -------------------------------\\\\[/tex]

[tex]\bf 1365=x+\left( 1\cdot x\cdot \frac{5}{100} \right)\implies 1365=x+\left(x\cdot \frac{5}{100} \right) \\\\\\ 1365=x+\left(\frac{x\cdot 5}{100} \right)\implies 1365=x+\cfrac{5x}{100}\impliedby \textit{using LCD of \underline{100}} \\\\\\ 1365=\cfrac{100x+5x}{100}\implies 1365\cdot 100=100x+5x \\\\\\ 136500=105x \implies \cfrac{136500}{105}=x\implies 1300=x[/tex]

Related Questions

A cone is placed inside a cylinder as shown. The radius of the cone is half the radius of the cylinder. The height of the cone is equal to the radius of the cylinder. What is the volume of the cone in terms of the radius, r?

Answers

r = radius of the cylinder
V = (1/3)Pi c^2 h for a cone.
and c = r/2 and h = u
so Volumn of the cone is (1/3)Pi(1/4)(r^2)r = (1/12)Pi r^3

Answer:

(1/12) Pi r^3     option C on plato

Step-by-step explanation:

r = radius of the cylinder

V = (1/3)Pi c^2 h for a cone.

and c = r/2 and h = u

so Volume of the cone is (1/3)Pi(1/4)(r^2)r = r = radius of the cylinder

how do you unsquare something? if i know what r squared is how do i find r?

Answers

you would square root something, so to get r from r² you would do √r² which gives r

Which angle pairs are supplementary? Check all that apply

Answers

Supplementary angles add up to 180 degrees, meaning they are straight lines.

B ∠4 and ∠3
C ∠4 and ∠5
E ∠3 and ∠6

The sum of two angles is equal to [tex]180^\circ[/tex] than the angle pairs are known as supplementary angles. Therefore, from the given diagram angle pairs [tex]\rm \angle 3\;and\;\angle6[/tex], [tex]\rm \angle 5\;and\;\angle6[/tex], [tex]\rm \angle 4\;and\;\angle5[/tex], [tex]\rm \angle 3\;and\;\angle4[/tex] and [tex]\rm \angle 7\;and\;\angle 8[/tex] are supplementary angles. So, the correct options are: B), C), and E).

Given :

[tex]\angle 3 = 90^\circ[/tex]

The sum of two angles is equal to [tex]180^\circ[/tex] than the angle pairs are known as supplementary angles.

From the diagram given in the question it can be clearly observe that if [tex]\angle 3 = 90^\circ[/tex] than [tex]\rm \angle 4,\;\angle 5,\;and\;\angle 6[/tex] are also equal to [tex]90^\circ[/tex].

Than according to the definition of supplementary angles:

[tex]\angle 3 +\angle6 = 180^\circ[/tex]

[tex]\angle 3 +\angle4 = 180^\circ[/tex]

[tex]\angle 4 +\angle5 = 180^\circ[/tex]

[tex]\angle 5 +\angle6 = 180^\circ[/tex]

[tex]\angle 7 +\angle8 = 180^\circ[/tex]

Therefore, angle pairs [tex]\rm \angle 3\;and\;\angle6[/tex], [tex]\rm \angle 5\;and\;\angle6[/tex], [tex]\rm \angle 4\;and\;\angle5[/tex], [tex]\rm \angle 3\;and\;\angle4[/tex] and [tex]\rm \angle 7\;and\;\angle 8[/tex] are supplementary angles.

For more information, refer the link given below:

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Your car is a real gas guzzler getting 15 miles to the gallon on the highway using regular gas which at this time costs $ 4.35/gallon. You have a 25 gallon tank in the car and want to drive to visit a trade show in Memphis, Tennessee which is 1780 miles from Los Angeles. You drive on average 70 miles per hour and spend 2 days and nights at the convention during which time you do not drive your car, You do however check into a hotel room which costs $95.00 per night plus a 12% room tax. Your meals cost a total of $35.00 per day for the 2 days that you are in town. You also decide to leave a tip for the waiter of 20% of your meal bill. On the last day of the trip, you decide to purchase an Apple iPod as a gift for your child and an iPad Tablet for yourself which costs $ 589.00. The iPad costs $589.95 and the iPod costs $ 265.95 plus sales tax of 9.25%. What is the total amount yo will spend for the trip? What are the key elements of the problem and what is the answer?

Answers

Given: (Key elements / factors) 15 Mi/Gal $4.35/Gal 1780 Mi 2 days 2 nights $95/night, +12% tax $35/day, +20% tip iPad- $589.95,+9.25% tax iPod- $265.95, +9.25% tax Find: Total expenses for the trip Solution: Gas- 1780 Mi / 15 Mi/gal = 118.67 gallons of gas 118.67 gal * $4.35/gal = $516.20 (total amount spent on gas) Hotel- 2 nights * $95.00/night = $190.00 $190.00 + ($190.00 * 0.12) = $212.80 (total amount for hotel with tax) Food- 2 days * $35.00/day = $70.00 $70.00 + ($70.00 * .20) = $84.00 (total amount spent on food with tip) Purchases- $589.95 + $265.95 = $855.90 $855.90 + (855.90 * 0.0925) = $935.07 (total amount spent on purchases with tax) Total Spent- $516.20 + $212.80 + $84.00 + $935.07 = $1748.07 (total amount spent on trip) Note: This is only for enough gas to get you to the convention, if you want to include the gas for the trip back, double the cost for gas ($516.20)

What is the recursive formula for this geometric sequence?

Answers

B is the answer because first number is 2 and common ratio is - 5

Answer: B.

[tex]a_1=2\\a_n=a_n\times(-5)[/tex]

Step-by-step explanation:

The given geometric sequence : 2, -10, 50, -250

The first term of the sequence : [tex]a_1=2[/tex]

The common ratio between the terms :[tex]r=\dfrac{-10}{2}=-5[/tex]

We know that the recursive formula for geometric progression is given by :-

[tex]a_n=a_{n-1}r[/tex]

Then , the recursive formula for the given geometric progression will be :-

[tex]a_n=a_n\times(-5)[/tex]

Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is C(x) = 2750 + 7x + 0.1x2 (0 ≤ x ≤ 500). Gymnast Clothing sells the cleats at $150 per pair. Find the revenue and profit functions. How many should Gymnast Clothing manufacture to make a profit? Revenue = Profit = At least pairs

Answers

Final answer:

The revenue function for Gymnast Clothing is R(x) = 150x, and the profit function is P(x) = 150x - (2750 + 7x + 0.1x^2). To make a profit, they need to produce and sell more than the breakeven number of cleats, which can be calculated by setting the profit function to zero and solving for x.

Explanation:

When Gymnast Clothing sells soccer cleats at $150 per pair, the revenue function (R) would be the number of cleats, x, multiplied by the selling price. Therefore, R(x) = 150x. To find the profit function (P), we subtract the cost function (C(x)) from the revenue function, so P(x) = R(x) - C(x) or P(x) = 150x - (2750 + 7x + 0.1x2). A profit is made when P(x) > 0.

To determine the number of cleats needed to make a profit, we need to find the break-even point where P(x) = 0, and then any number greater than the break-even number of cleats would yield a profit. By setting the profit function equal to zero and solving for x, we can find the minimum number of cleats Gymnast Clothing should manufacture to begin making a profit.

If mary ellen invest x dollars at 5%, write an equation that describes the total interest

Answers

.05x = total interest

For a one-year investment, the equation is I = x imes 0.05 imes 1.

If Mary Ellen invests x dollars at an interest rate of 5%, we can write an equation that describes the total interest earned on that investment using the simple interest formula. The formula for calculating simple interest is Interest = Principal imes Rate imes Time. Assuming the investment is for 1 year, the equation for the total interest (I) Mary earns would be:

I = x imes 0.05 imes 1

This equation states that the interest Mary earns is equal to the amount of money she invested (x dollars) multiplied by the interest rate (5% or 0.05 as a decimal) and the time the money is invested (1 year).

If Mary Ellen invests $100, the total interest she would earn in one year at a 5% interest rate would be calculated as follows:

I = $100  imes 0.05 imes 1 = $5

Calculate the rf value for the reactant b spot. estimate the ruler to the nearest tenth, report the answer using two significant figures.

Answers

1. Measure the distance the solvent front traveled from the baseline (m1). 2. Measure the distance the reactant b spot traveled (the center of the spot) (m2). 3. To determine the rf, divide (m2/m1). 4. Significant figures- use 2 so the answer should be written to the hundredths place as the spot will not travel farther than the solvent front.

weight A weighs 50 pounds. weight B weighs 100 pounds. if A is placed 6 feet from the pivot, how far must B be placed from the pivot in order for the bar to achieve balance?

Answers

To achieve balance, the momentum on both sides must be equal so that it cancels out. Momentum is simply the product of mass and distance, therefore:

 

50 pounds * 6 ft = 100 pounds * X

X = 3 ft

 

Hence B must be placed 3 ft from the pivot.

Can anyone gimme the answer ASAP please

Answers

Multiplying each side by 3/4, we get (3/4)V=pir^3. Dividing both sides by pi, we then get r^3=(3/4)V/pi

For the second part, we get that 381.51=(4/3)πr^3, so plugging 381.51 into the equation above we get (3/4)(381.51)/pi=around 91, and r= the cube root of r^3, which would equal around 4.5 here

Simplify the expression: Sqrt(16 − x^2)
as much as possible after substituting "4 sin x" for x.

Answers

[tex]\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\ -------------------------------\\\\ \sqrt{16-x^2}\implies \sqrt{16-[4sin(x)]^2}\implies \sqrt{16-[4^2sin^2(x)]} \\\\\\ \sqrt{16-16sin^2(x)}\implies \sqrt{16[1-sin^2(x)]}\implies \sqrt{16cos^2(x)} \\\\\\ \sqrt{4^2cos^2(x)}\implies \sqrt{[4cos(x)]^2}\implies 4cos(x)[/tex]

Final answer:

Simplify the expression √(16 − x²) by substituting x with '4 sin x' to get 4|cos x|. Use trigonometric identities to arrive at the simplified expression.

Explanation:

The expression to simplify is: √(16 − x²) after substituting '4 sin x' for x.

Step-by-step solution:

Replace x with 4 sin x in the expression: √(16 − (4 sin x)²)

Simplify: √(16 − 16 sin² x)

Apply trigonometric identity: √(16 cos² x) = 4|cos x|

A powdered drink mix calls for a ratio of powder to water of 1:8 if there are 32 cups of powder how many total of water are needed? explain your reasoning

Answers

if you do x- number of water cups 1 over 8 will equal 32 over x ,x=256 so 256
if this makes any sense if not ill try better to explain 

The statement 3+3=6 serves as a/an _ to the conjecture that the sum of two odd numbers is an odd number .

Answers

A statements that contradicts another statement is refered to as a contradiction.

Therefore, the statement 3 + 3 = 6 serves as a contradiction to the conjecture that the sum of two odd numbers is an odd number.

What is the sum of the first five terms of the geometric series 2 − 8 + 32 − . . . ?

Answers

First this is not a geometric series due to the sign changes

The series can be written as A(n)=(-1)^(n-1)×2×4^(n-1)

The sum of first five will be 2-8+32-128+512=410
now, is a geometric sequence, and sometimes called a "serie", but is just a sequence with a common "multiplier" or "common ratio".

so it goes from 2, to -8 and so on, to get the "common ratio" you just simply divide a further term by another, -8/2 = -4  <--- r

[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=2\\ r=-4\\ n=5 \end{cases} \\\\\\ S_5=2\left( \cfrac{1-(-4)^5}{1-5} \right)\implies S_5=2\left( \cfrac{1+1024}{1-5} \right)\implies S_5=2\left( \cfrac{1025}{-4} \right)[/tex]

and surely you'd know how much that is.

What is the square root of 360 rounded to the nearest thousandth

Answers

The square root of 360 is 18.97

what are 2 fractions between 3/5 and 4/5?

Answers

3/5 = 12/20
4/5 = 16/20

two fractions between 3/5 and 4/5 can be 13/20 and 14/20

hope this helps

it is 7 kilometers from Kerry's house to the mall. About what is that distance in miles

Answers

There is 0.62 miles in 1 kilometer

Therefore

7 x 0.62 = amount of miles

4.34 miles is your answer

hope this helps


4,34 miles is the answer cuz 1 km = 0,62 miles

in a fish tank 6/7 of the fish have a red stripe on them . if 18 of the fish have red stripes how many total fish are in the tank?

Answers

well, if 6/7 is 18, and how many is the 7/7 or a 1 whole(total)?

[tex]\bf \begin{array}{ccll} \stackrel{frational}{amount}&\stackrel{quantity}{amount}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{6}{7}&18\\\\ \frac{7}{7}&x \end{array}\implies \cfrac{\frac{6}{7}}{\frac{7}{7}}=\cfrac{18}{x}\implies \cfrac{\frac{6}{7}}{1}=\cfrac{18}{x}\implies \cfrac{6}{7}=\cfrac{18}{x} \\\\\\ x=\cfrac{7\cdot 18}{6}[/tex]

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. 4log x + 2log y

Answers

remember some log rules

log a+log b=log ab

xlog a=log aˣ


so
[tex]4log(x)+2log(y)=[/tex]
[tex]log(x^4)+log(y^2)=[/tex]
[tex]log(x^4y^2)[/tex]

The simplified expression is log (x⁴y²).

What is a logarithm?

Inverse to exponentiation is the logarithm.

The given expression is 4log x + 2log y.

Simplify the expression as follows:

4log x + 2log y

= log x⁴ + log y²

= log (x⁴y²)

Hence, the simplified expression is log (x⁴y²).

Learn more about logarithms:

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A car travels at 65 miles per hours. Going through construction it travels at 3/5 this speed. Write this fraction as a decimal and find the speed.

Answers

3/5 = 6/10 = 0.6
0.6×65=39
Car travels 39 miles per hour through construction.

25 POINTS I NEED HELP

Answers

We know that his woodshed is a parallelepiped, and 8' is the depth, 16' is the lenght and 6' is the height.

A cord of wood is 4' high, 4' deep and 96" long.

96" = 8'

We find the volume of his woodshield.

V = h*d*l = 168*6 = 768 cubic feet

Find the volume of a cord

4*4*8 = 128 cubic feet

Do the ratio: 768/128 = 6

His woodshield can hold 6 cords.

For the second question, simply do a multiplication.

If 1 cord is $120, how much are 6?

120*6 = $720

Angela ordered 2 glass paperweights. The volume of each paperweight is 5 cubic inches, and the density of the glass is 1.5 ounces per cubic inch. Angela can use the calculation below to find the total weight of her order.

2×(5×1.5)

How can Angela simplify the calculation using only the associative property of multiplication?

Drag and drop the appropriate number or expression into each box.

Answers

Answer:

[tex](2\times 5)\times 1.5[/tex]

Step-by-step explanation:

Since, according to associative property of multiplication,

a(bc) = (ab)c,

Where a, b and c are any real numbers,

Here, the given expression,

2 × ( 5 × 1.5 ),

By applying the associative property of multiplication,

( 2 × 5 ) × 1.5,

Hence, the appropriate expression in the first box is '(2×5)'

And, the appropriate number in the second box is '1.5'.

Answer:

first box is (2 times 5) next box is 1.5

Step-by-step explanation:

i took K12 test :)

Find the equation of the line that contains the point (3,9) and is parallel to the line y=4x+1. Write the line in slope-intercept form. Graph the lines

Answers

Final answer:

The equation of the line parallel to y=4x+1 passing through (3,9) is y=4x-3. It has the same slope of 4 but a different y-intercept, showing that the lines are parallel and do not intersect.

Explanation:

To find the equation of the line that contains the point (3,9) and is parallel to the line y=4x+1, we start by noting that parallel lines have the same slope. The given line has a slope of 4, so our new line will also have a slope of 4. The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.

Since we have a point (3,9) and a slope of 4, we can use the point-slope form to find our new line:

y - y₁ = m(x - x₁)

Plugging in our point and slope, we get:

y - 9 = 4(x - 3)

Expanding this, we have:

y - 9 = 4x - 12

Add 9 to both sides to get it into slope-intercept form:

y = 4x - 3

Therefore, the equation of the line parallel to y=4x+1 that passes through (3,9) in slope-intercept form is y = 4x - 3.

When graphing these two lines, you'll notice they never intersect, as they have the same slope but different y-intercepts, which is a distinctive feature of parallel lines.

Final answer:

To find the equation of a line that is parallel to another line, we need to determine the slope of the given line and then use the point-slope form of a linear equation. The equation of the line parallel to y = 4x + 1 and passing through the point (3,9) is y = 4x - 3. The graph of the lines show that they are parallel.

Explanation:

To find the equation of a line that is parallel to another line, we need to determine the slope of the given line and then use the point-slope form of a linear equation.

The given line y = 4x + 1 has a slope of 4 because it is in the form y = mx + b, where m is the slope. Since the line we want to find is parallel to this line, it will also have a slope of 4.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point on the line, we can substitute the values (3, 9) and 4 for x1 and m, respectively, to get the equation:

y - 9 = 4(x - 3)

Expanding and rearranging the equation, we get:

y = 4x - 3

Graphing the lines:

The graph of the given line y = 4x + 1 is a straight line with a slope of 4 and a y-intercept of 1. The line we found, y = 4x - 3, is also a straight line with the same slope but a different y-intercept. By plotting the two lines on the same graph, we can visually see that they are parallel.

If RS=ST then point S is called the midpoint of .

Answers

S is the midpoint of line RT

My clock is 75 inches tall and 28 in wide .What is the ratio of height to wide in fraction form

Answers

The ratio of height to wide in the fraction form of the clock is 75/28.

What are the ratio and proportion?

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Height of clock = 75 inches.

Width of clock = 28 inches.

The ratio of height to width = Height of clock / Width of clock

So,

The ratio of height to width = = 75/28.

Hence "The ratio of height to wide in the fraction form of the clock is 75/28".

For more information about ratio and proportion,

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Josh and Eva are packing first-aid supplies. It takes Josh 12 minutes to fill a box with Bandages. It takes Eva 8 minutes to fill a box with antibiotics. If they start packing boxes at the same time, how long will it be before they start filling a new box at the same time.

Answers

The lowest common multiple of 8 and 12 is 24. So ur answer is 24 minutes
Here, you just want to find the LCM, or the Least Common Multiple, or the closest time when both of their numbers meet.

(If that makes any sense)

So their LCM is 24, because:

12: 12, 24

8: 8, 16, 24

And 24 is the closest number they meet at.

So it will be 24 minutes before they start filling a new box at the same time.

The fraction model below shows the steps that a student performed to find a quotient. Which statement best interprets the quotient?

Answers

There are [tex]\rm 6 \frac{1}{4}[/tex] two - third in [tex]\rm 4 \frac{1}{6}[/tex]. Statement A best interprets the quotient.

What is the definition of a fraction number?

A fraction number is a number that represents a portion of a larger number, where the larger number might be any integer. It has the shape of a numerator and a denominator.

The shaded part in step 1 is;

[tex]\rm 4 + \frac{1}{6} = 4 \frac{1}{6}[/tex]

Divide the shaded part with the unshaded part as ;

[tex]\rm \frac{4 \frac{1}{6} }{\frac{2}{3}}\\\\ \frac{25}{6} \times \frac{3}{2} \\\\\ \frac{25}{4} \\\\ 6 \frac{1}{4}[/tex]

There are [tex]\rm 6 \frac{1}{4}[/tex] two - third in [tex]\rm 4 \frac{1}{6}[/tex].

Hence, statement A best interprets the quotient.

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Answer: A

Step-by-step explanation:

3 Hundredths + 4 hundredths

Answers

0.03 + 0.04
0.07

Hope this helped!

Ben measures the height of two bottles. One is 12 centimeters, and the other is 15 centimeters. In millimeters, what is the difference of the two heights?

Answers

30 millimeters is the difference between the two heights

Answer:

30 millimeters

Step-by-step explanation:

What is the solution to the inequality |x-4|<3

Answers

Unfold it and add 4.
  -3 < x-4 < 3
  1 < x < 7

Answer:

The solution of the given inequality  [tex]|x-4|<\:3\:[/tex] is [tex]1<x<7[/tex]

Step-by-step explanation:

Given inequality [tex]|x-4|<\:3\:[/tex]

We have to find the solution of the given inequality  [tex]|x-4|<\:3\:[/tex]

Using absolute rule, [tex]\mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a[/tex], we have,

[tex]-3<x-4<3[/tex]

Rewrite as [tex]x-4<-3\quad \mathrm{and}\quad \:x-4<3[/tex]

Consider , [tex]x-4>-3[/tex]

Adding 4 both side, we have,

[tex]x-4+4>-3+4[/tex]

Simplify, we have,

[tex]x>1[/tex]

Consider , [tex]x-4<3[/tex]

Adding 4 both side, we have,

[tex]x-4+4<3+4[/tex]

Simplify, we have,

[tex]x<7[/tex]

Combining, we have,

[tex]1<x<7[/tex]

Thus, The solution of the given inequality  [tex]|x-4|<\:3\:[/tex] is [tex]1<x<7[/tex]

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