Answer:
We can rewrite this as [tex]\frac{200x}{x} + \frac{-300}{x}[/tex].
[tex]\frac{200x}{x}[/tex] simplifies to 200 after eliminating x from the numerator and denominator and [tex]\frac{-300}{x}[/tex] becomes [tex]-\frac{300}{x}[/tex] so the final answer is [tex]200 - \frac{300}{x}[/tex].
1
If the 2nd and 5th terms of a G.P are 6 and 48 respectively, find the sum of the first for term
If the first term is [tex]a[/tex], then the second term is [tex]ar[/tex], the third is [tex]ar^2[/tex], the fourth is [tex]ar^3[/tex], and the fifth is [tex]ar^4[/tex].
We're given
[tex]\begin{cases}ar=6\\ar^4=48\end{cases}\implies\dfrac{ar^4}{ar}=r^3=8\implies r=2\implies a=3[/tex]
So the first five terms in the GP are
3, 6, 12, 24, 48
Adding up the first four gives a sum of 45.
If you were asked to find the sum of many, many more terms, having a formula for the n-th partial sum would convenient. Let [tex]S_n[/tex] denote the sum of the first n terms in the GP:
[tex]S_n=3+3\cdot2+3\cdot2^2+\cdots+3\cdot2^{n-2}+3\cdot2^{n-1}[/tex]
Multiply both sides by 2:
[tex]2S_n=3\cdot2+3\cdot2^2+3\cdot2^3+\cdots+3\cdot2^{n-1}+3\cdot2^n[/tex]
Subtract this from [tex]S_n[/tex], which eliminates all the middle terms:
[tex]S_n-2S_n=3-3\cdot2^n\implies -S_n=3(1-2^n)\implies S_n=3(2^n-1)[/tex]
Then the sum of the first four terms is again [tex]S_4=3(2^4-1)=45[/tex].
Please answer it now in two minutes
Answer: √3
Step-by-step explanation:
Hi, since the situation forms a right triangle we have to apply the next trigonometric function.
Sin α = opposite side / hypotenuse
Where α is the angle (30°), the hypotenuse is the longest side of the triangle (in this case 2), and the opposite side is x. (not t or 2)
Replacing with the values given:
Sin 30 = x /2
Sin 30 (2) = x
x=1
Applying the Pythagorean theorem:
c^2 = a^2 + b^2
Where c is the hypotenuse of the triangle (2) and a and b are the other sides.
2^2 = t^2 + 1^2
4= t^2 +1
4-1 = t^2
3 = t^2
√3 = t
Feel free to ask for more if needed or if you did not understand something.
Of his take-home pay each month, Jerry spends 1/6 on car payment and 1/4 on food. What fraction of his take-home pay is left after paying for these two items?
Answer:
The fraction of Jerry's take-home pay that is left after paying for these two items is 7/12.
Step-by-step explanation:
Consider that the total take-home pay each month Jerry receives is, $x.
It is provided that:
Jerry spends 1/6 on car payment, i.e. Car Payment = [tex]\frac{1}{6}x[/tex].Jerry spends 1/4 on food, i.e. Food = [tex]\frac{1}{4}x[/tex].The remaining amount can be computed by subtracting the amount spent from the total amount.
Compute the amount Jerry has spent so far:
Amount Spent = Car Payment + Food
[tex]=\frac{1}{6}x+\frac{1}{4}x\\\\=[\frac{1}{6}+\frac{1}{4}]x\\\\=[\frac{2+3}{12}]x\\\\=\frac{5}{12}x[/tex]
Compute the remaining amount as follows:
Remaining Amount = Total Amount - Amount Spent
[tex]=x-\frac{5}{12}x\\\\=[1-\frac{5}{12}]x\\\\=[\frac{12-5}{12}]x\\\\=\frac{7}{12}x[/tex]
Thus, the fraction of Jerry's take-home pay that is left after paying for these two items is 7/12.
Which lines are parallel to the graph of 4x - y = 6?
Answer:
Step-by-step explanation:
i cant see answers help my insta is 813.caden
Answer:
y+1=4(x-2)
y=4x+11
8x-2y+6
Step-by-step explanation:
There were some pieces of candy in a bowl. Shirley took half of them. Then Rose took half of the pieces left in the bowl. After that, Susan took half of the remaining pieces of candy. In the end there were 8 pieces of candy left in the bowl. How many candies were there in the bowl at the beginning?
Answer:
Number of pieces of candy in the bowl=64
Step-by-step explanation:
Let
x=number of pieces of candy in a bowl
Shirley took=1/2 of x
=1/2x
Remaining
x-1/2x
= 2x-x/2
=1/2x
Rose took half of the pieces left in the bowl=1/2 of 1/2x
=1/2*1/2x
=1/4x
Remaining
1/2x-1/4x
=2x-x/4
=1/4x
Susan took 1/2 of the remaining pieces of candy=1/2 of 1/4x
=1/2*1/4x
=1/8x
Remaining 8
1/8x=8
x=8÷1/8
=8*8/1
=64
x=64
What is 50 + 30(0) - 30?
Answer:
20
Step-by-step explanation:
30(0)
= 0
50 + 0 - 30
= 50 - 30
= 20
Answer:
20
Step-by-step explanation:
We know that 30 × 0 = 0. Next, we can take 50 and add 0 which is still 50. Now, we take 50 - 30 which equals to 20.
John wants to nail a thumbtack on his circular board, pictured below. If the thumbtack is equally likely to be placed anywhere on the board, what is the probability that the thumbtack will be placed on the inner circle? Use 3.14 for , and round your answer to the nearest whole percent. A. 51% B. 55% C. 57% D. 60%
Answer:
[tex]Probability = 51\%[/tex]
Step-by-step explanation:
Given
Radius of inner circle = 5ft
Radius of outer circle = 7ft
Required
Determine the probability that the thumbtack will be placed on the inner circle
We start by calculating the area of both circles;
Inner Circle
[tex]Area = \pi r^2[/tex]
[tex]Area = 3.14 * 5^2[/tex]
[tex]Area = 3.14 * 25[/tex]
[tex]Area = 78.5[/tex]
Outer Circle
[tex]Area = \pi R^2[/tex]
[tex]Area = 3.14 * 7^2[/tex]
[tex]Area = 3.14 * 49[/tex]
[tex]Area = 153.86[/tex]
At this point, the probability can be calculated;
The probability = Area of Inner Circle / Area of Outer Circle
[tex]Probability = \frac{78.5}{153.86}[/tex]
[tex]Probability = 0.51020408163[/tex]
Convert to percentage
[tex]Probability = 0.51020408163 * 100\%[/tex]
[tex]Probability = 51.020408163\%[/tex]
Approximate
[tex]Probability = 51\%[/tex]
For a chemical reaction to occur, at least one-third of the solution must be an acid. If there are five liters of acid, in interval form, how much solution is present?
A. [5,8)
B. (3/5,5]
C. (5/3,5]
D. [5,15]
Answer:
Amount of solution = 15 liter
Step-by-step explanation:
Given:
One third of solution is acid
Amount of acid = 5 Liter
Find:
Amount of solution
Computation:
Amount of solution = Amount of acid (1 / One third of solution is acid)
Amount of solution = Amount of acid (3)
Amount of solution = (5)(3)
Amount of solution = 15 liter
A particle moves along a straight line. The distance of the particle from the origin at time t is modeled by the equation below. s(t)equals2 sine t plus 3 cosine t Find a value of t between 0 and StartFraction pi Over 2 EndFraction that satisfies the equation s(t)equalsStartFraction 2 plus 3 StartRoot 3 EndRoot Over 2 EndFraction .
Answer:
The value of t that will satisfy the equation is π/6 (which is 30 degrees)
Step-by-step explanation:
The function that models the movement of the particle is given as;
S(t) = 2 sin(t) + 3 cos (t)
Now we want to the value of t between 0 and pi/2 that satisfies the equation;
s(t) = (2+ 3√3)/2 = 1 + 3√3/2
What we do here is simply find that value of t that would ensure that;
2sin(t) + 3cos(t) = 1 + 3√3/2
Without any need for rigorous calculations, this value of t can be gotten by inspection.
From our regular trigonometry, we know that the sin of angle 30 is 1/2 and its cos value is √3/2
We can make a substitution for it in this equation.
We obtain the following;
2 sin(30) + 3cos (30) and that is exactly equal to 1 + 3√3/2
Do not forget however that we have a range. And the range in question is between 0 and π/2
Kindly that π/2 in degrees is 90 degrees
So our range of values here is between 0 and 90 degrees.
So to follow the notation in the question, the value within the range that will satisfy the equation is π/6
What is the effect on the graph of f(x) if it is changed to f(x) + 2 and f(x + 2)?
Answer:
For f(x)+2, it goes along the y axis, 2 units.
For f(x+2), it goes along the x axis, -2 untis.
Step-by-step explanation:
Jakki got a new job that guarantees her a 6% raise every year. If she started out making $40,000, how long will it be before she doubles her current salary?
Answer:
2400months
Step-by-step explanation:
6/100*40,000
maybe
A bus traveled 40 miles during the second hour of a trip. This was 1/3 more than the distance traveled during the first hour. In the third hour the bus traveled a distance that was 1/4 more than in the second hour. What was the total distance that the bus traveled in 3 hours
Answer:
120 miles
Step-by-step explanation:
Distance in 2nd hour: 40 miles
Distance in 1st hour:
40/(4/3) = 30 miles
Distance in 3rd hour:
(5/4) * 40 = 50 miles
Total distance:
40 + 30 + 50 = 120 miles
The slope of the line is -5/7. Write a point-slope equation of the line using the coordinates of the labeled point
Answer:
The answer is C.
Step-by-step explanation:
The formula to find equation is y - y1 = m(x - x1).
Let (x1,y1) be (6,2) and m is -5/7.
So the equation is,
y - 2 = -5/7(x - 6)
A bookcase has 3 shelves with a total of 24 books. The top shelf has 8 mystery books. The middle shelf has 10 math books. The bottom shelf has 6 science books. Two books are now taken off each shelf. What fraction of the books remaining on the three shelves are math books? Express your answer as a common fraction.
Answer:
4/9
Step-by-step explanation:
So, the ratio of the books is 8:10:6. After 2 books were taken off of each shelf, it became 6:8:4. All of these numbers added up is 18. So that means 8/18 of the books are math books, which can be simplified to 4/9.
Answer:
4/9
Step-by-step explanation:
A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $6,000 or $12,000. If the partnership raised $486,000, then how many investors contributed $6,000 and how many contributed $12,000?
Answer:
39 investors contributed $6,000, and 21 investors contributed $12,000.
Step-by-step explanation:
Let's say that x investors contributed $6,000, and y investors contributed $12,000.
x + y = 60
6,000x + 12,000y = 486,000
x + 2y = 81
x + y = 60
y = 21
x + 21 = 60
x = 39
So, 39 investors contributed $6,000, and 21 investors contributed $12,000.
Hope this helps!
Marci has taken out a loan of $5,000 for a term of 24 months (2 years) at an interest rate of 8.5%. Use the amortization table provided to
complete the statement.
Monthly Payment per $1,000 of Principal
Rate | 1 Year 2 Years 3 Years 4 Years 5 Years
6.5% $86.30 $44.55 $59.35 $23.71 $19.57
7.0% $86.53 $44.77 $31.88 $23.95 $19.80
7.5% $86.76 $45.00 $51.71 $24.18 $20.04
8.0% $86.99 $45.23 $31.34 $24.41 $20.28
8.5% $87.22 $45.46 $24.65 $24.65 $20.52
9.0% $87.45 $45.68 $31.80 $24.89 $20.76
Marci's monthly payment will be $
and her total finance charge over the course of the loan will be $
Answer:
$227.30$455.20Step-by-step explanation:
The table tells you that Marci's monthly payment on a 2-year loan at 8.5% will be $45.46 on each $1000 borrowed. For her $5000 loan, her monthly payment will be 5 times the table value, or ...
monthly payment = $5000/$1000 × $45.46
monthly payment = $227.30
__
Her total of 24 payments will be ...
total repaid = 24 × $227.30 = $5,445.20
That amount is $445.20 more than the amount borrowed, so that is Marci's finance charge.
__
Marci's monthly payment will be $227.30, and her total finance charge will be $455.20.
help plz its math and i will give brainlest if u answer
Answer:
not a right triangle
Step-by-step explanation:
We can use the Pythagorean theorem to see if it is a right triangle
a^2 + b^2 = c^2
15^2 + 12^2 = 21^2
225 + 144 = 441
369 = 441
This is not true so it is not a right triangle
Answer:
Step-by-step explanation:
A triangle is a right angled triangle if sum of squares of two sides is equal to the square of third side.
12²+15²=144+225=369
21²=441
so a²+b²≠c²
it is not a right angled triangle.
As mountain climbers know, the higher you go, the cooler the temperature gets. At noon on July 4th last summer, the temperature at the top of Mt. Washington — elevation 6288 feet — was 56◦F. The temperature at base camp in Pinkham Notch — elevation 2041 feet — was 87◦F. It was a clear, still day. At that moment, a group of hikers reached Tuckerman Junction — elevation 5376 feet. To the nearest degree, calculate the temperature the hikers were experiencing at that time and place. When you decided how to model this situation, what assumptions did you make?
Answer:
a. 63 °F
b. When i decided to model the situation, I assumed that the temperature varied inversely as the elevation and that the change in elevation or temperature was linear.
Step-by-step explanation:
a. To model this situation, we assume the temperature varies inversely as elevation decreases since at elevation 6288 ft the temperature is 56 °F and at elevation 2041 ft, the temperature is 87 °F
So, we model this as a straight line.
Let m be the gradient of the line.
Let the (6288 ft, 56 F) represent a point on the line and (2041 ft, 87 °F) represent another point on the line.
So m = (6288 ft - 2041 ft)/(56 °F - 87 °F) = 4247 ft/-31 °F = -137 ft/°F
At elevation 5376 ft, let the temperature be T and (5376 ft, T) represent another point on the line.
Since it is a straight line, any of the other two points matched with this point should also give our gradient. Since in the gradient, we took the point (6288 ft, 56 °F) first, we will also take it first in this instant.
So m = -137 ft/ °F = (6288 ft - 5376 ft)/(56 °F - T)
-137 ft/°F = 912 ft/(56 °F - T)
(56 °F - T)/912 ft = -1/(137 ft/ °F)
56 °F - T = -912 ft/(137 ft/°F)
56 °F - T = 6.66 °F
T = 56 °F + 6.66 °F
T = 62.66 °F
T ≅ 62.7 °F
T ≅ 63 °F to the nearest degree
b. When i decided to model the situation, I assumed that the temperature varied inversely as the elevation and that the change in elevation or temperature was linear.
Most evenings after dinner Duarte spends 30 minutes playing chess with his dad. Write an equation for the number of minutes, m, that Duarte spent playing chess with his dad if they played chess together (e) evenings.
Answer:
m=30e
Step-by-step explanation:
30 minutes for each evening, 2 evenings, 60 minutes
Hope this helped!
The most suitable equation that would express the time Duarte spends to play chess with his dad is m= 30e
How to use equation for expressionsNumber of minutes each evening= 30 mins=m
They played together every evening= e.
Therefore, the equation that would express the time Duarte spends to play chess with his dad is m = 30e.
Learn more about equation here:
https://brainly.com/question/2972832
#SPJ2
11.1/0.01= what is the answer
Answer:
1,110
Step-by-step explanation:
calculator
Give the excluded values for 6/t+5 + 2/t-5 = 3t-1/t^2-25. Do not solve
A)25
B)-5,5
C)5,25
D)-5,5,25
Please help i don’t understand
Answer:
B -5, and 5
Step-by-step explanation:
you can't have zero on the bottom
Determine what type of model best fits the given situation: An Internet phone company presently provides service to 5,000 customers at a monthly rate of $20 per month. After a market survey, it was determined that for each $1 decrease in the monthly rate an increase of 500 new customers would result. A. linear B. quadratic C. none of these D. exponential
Answer:
The best fit is A. Linear model
Step-by-step explanation:
Given:
Monthly Rate = $20, Number of customers = 5000
If there is a decrease of $1 in the monthly rate, the number of customers increase by 500.
To find:
The type of model that best fits the given situation?
Solution:
Monthly Rate = $20, Number of customers = 5000
Let us decrease the monthly rate by $1.
Monthly Rate = $20 - $1 = $19, Number of customers = 5000 + 500 = 5500
Let us decrease the monthly rate by $1 more.
Monthly Rate = $19 - $1 = $18, Number of customers = 5500 + 500 = 6000
Here, we can see that there is a linear change in the number of customers whenever there is decrease in the monthly rate.
We have 2 pair of values here,
x = 20, y = 5000
x = 19, y = 5500
Let us write the equation in slope intercept form:
[tex]y =mx+c[/tex]
Slope of a function:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{5500-5000}{19-20}\\\Rightarrow -500[/tex]
So, the equation is:
[tex]y =-500x+c[/tex]
Putting x = 20, y = 5000:
[tex]5000 =-500\times 20+c\\\Rightarrow c = 5000 +10000 = 15000[/tex]
[tex]\Rightarrow \bold{y =-500x+15000}[/tex]
Let us check whether (18, 6000) satisfies it.
Putting x = 18:
[tex]-500 \times 18 +15000 = -9000+15000 = 6000[/tex] so, it is true.
So, the answer is:
The best fit is A. Linear model
25 POINTS + BRAINLIEST !!!! A fruit bowl contains apples and bananas in the ration 4 : 5. Two apples are removed changing the ratio to 2 : 3. Work out the total number of fruit that remain in the bowl.
Answer:
Total number of fruits remaining = 25
Step-by-step explanation:
Let the number of
apples = 4x
bananas = 5x
Therefore
4x-2 / 5x = 2 / 3
Solve for x, cross multiply
3(4x-2) = 2(5x)
12x - 6 = 10 x
2x = 6
x = 3
Apples = 4*3 = 12
Bananas = 5*3 = 15
Apples remaining = 12-2 = 10
Total number of fruits remaining = 10+15 = 25
Answer:
[tex]\boxed{25 \ fruits}[/tex]
Step-by-step explanation:
Let apples be 4x and Bananas be 5x
So, the given condition is:
[tex]\frac{4x-2}{5x} = \frac{2}{3}[/tex]
Cross Multiplying
5x*2 = 3(4x-2)
10x = 12x - 6
Adding 6 to both sides
10x+6 = 12x
12x - 10x = 6
2x = 6
x = 3
Now, Fruits remaining in the bowl are:
=> 4x-2 + 5x
=> 12 - 2 + 15
=> 10+15
=> 25
Represent the expression
(4 x 1,000) + (3 x 100) + (6 x
1/100) + (7x1000)
as a decimal number.
Answer:
The answer is 11 300.06
[tex](4 \times 1000) + (3 \times 100) + (6 \times \frac{1}{100}) + (7 \times 1000) [/tex]
[tex] = 4000 + 300 + \frac{6}{100} + 7000[/tex]
[tex] = 11 \: 300 + 0.06[/tex]
[tex] = 11 \: 300.06[/tex]
What number :Increased by 130% is 69 i rlly need help!!!
Answer:
53.076923
Step-by-step explanation:
130% as a decimal is 1.3
Divide 69 by 1.3:
69 /1.3 = 53.076923
Answer:
30
Step-by-step explanation:
The unknown number is x.
Start with x.
To increase x by 130%, you need to add 130%of x to x.
x + 130% of x
The sum equals 69.
x + 130% of x = 69
x + 130% * x = 69
1x + 1.3x = 69
2.3x = 69
x = 30
Answer: The number is 30.
Convert 2.41 cm2 into mm2 *the 2 means squared
Answer:
241 mm^2.
Step-by-step explanation:
There are 10 mm in a cm so there are 10*10 = 100 mm^2 in a cm^2.
So the answer is 2.41 * 100 = 241 mm^2.
Answer:
241mm²
Step-by-step explanation:
If 10mm = 1cm,
then 100mm² = 1cm²
2.41 × 100 = 241mm²
By which smallast number must the following number be divided so that the quotient is a perfect cube
(A) 8640
Answer:
60
Step-by-step explanation:
8640/60 is 144. 144 is a perfect square. 12*12 is 144
Hey there! I'm happy to help!
------------------------------------------------------------------
INTRO TO PERFECT CUBES
A perfect cube is any number whose cube root is an integer. In English, that means that if you take any number without a fraction (this is called an integer, such as -7, 8, 100, none have fractions) and multiply it by itself three times, you get a perfect cube.
If you cube the number 4, you get 64, which is (4×4×4). 64 is an example of a perfect cube.
You can use the cube root button on your calculator to see if a number is a perfect cube. If you do the cube root of 64, you get 4, telling you that 64 is a perfect cube. The cube root of 10 is 2.154434...... so 10 is not a perfect square because it does not give you an integer (number that does not have a fraction) as the answer.
------------------------------------------------------------------
SOLVING THE PROBLEM
So, we want to find the smallest numbers we can divide 8640 to equal a perfect cube.
I will assume that we will not be dividing by fractions but only whole numbers (positive integers).
We could try dividing by 1, but we see that 8640 is not a perfect cube because it's cube root is 20.519711....
Let's just keep counting up! The first divisor we run into that gives a quotient that it is a perfect cube is the smallest whole number possible that will give us that result.
8640÷2=4320
∛4320≈16.2865....... Not a perfect cube
8640÷3=2880
∛2880≈14.22757..... Not a perfect cube
8640÷4=2160
∛2160≈12.92660..... Not a perfect cube
8640÷5=1728
∛1728=12, a perfect cube!
Since 12 cubed is equal to 1728, this means that 1728 is a perfect square, so 5 is the smallest number we can divide 8640 by to get a perfect square.
The answer is 5.
I hope that this helps! Have a wonderful day! :D
Last season, a softball team played 18 games. The team won 15 of these games. What is the ratio of the softball team's wins to its total number of games played ?
Answer:
5:6Step-by-step explanation:
Given the total number of games played by the softball team = 18 games
Total games won = 15 games
Ratio of the softball team's wins to its total number of games played can be gotten by simply dividing the total games won by the total games played
Ratio = [tex]\frac{total \ teams's win}{total\ number\ of \ games\ played}[/tex]
[tex]Ratio = \frac{15}{18}[/tex]
Expressing the ratio in its lowest term
[tex]Ratio = \frac{3*5}{3*6} \\\\Ratio = \frac{5}{6}[/tex]
Hence, the ratio of the softball team's wins to its total number of games played is 5:6
On a separate piece of graph paper, graph y = |x - 3|; then click on the graph until the correct one appears.
ps : there's another picture it just didn't let me edit it its the opposite side of the shape facing up the graph.
Answer: Graph is shown in the attached image below
This is a V shaped graph with the vertex at (3,0). The V opens upward
Explanation:
The equation y = |x-3| is the result of shifting the parent function y = |x| three units to the right. The vertex moves from (0,0) to (3,0). The "x-3" portion moves the xy axis three units to the left. If we held the V shape in place while the xy axis moved like this, then it gives the illusion the V shape moved 3 spots to the right.
Side note: the equation y = |x-3| is composed of two linear functions y = x-3 and y = -x+3. The value of x will determine which gets graphed. When x < 3, then we'll graph y = -x+3; otherwise we graph y = x-3. This is known as a piecewise function.
Pls help me I need it pls!! I only need the last question which is "Find the weight of one circle. Show or explain how you got your answer. "