Final answer:
The sum of the series 4+12+36+108+...+8748 is found by observing that it is a geometric progression with a common ratio of 3. By comparing the last term to the options, and understanding the rapidly increasing nature of geometric series, the sum is slightly larger than the last term, which only matches the option 8908.
Explanation:
To find the sum of the geometric series 4+12+36+108+...+8748, we first need to identify the common ratio (r) of the series. Each term is obtained by multiplying the previous term by the constant r. In this case, r = 12 / 4 = 36 / 12 = 108 / 36 = 3. The series is therefore a geometric progression with the first term a = 4 and common ratio r = 3.
We can then use the formula for the sum of the first n terms of a geometric series, which is Sn = a(1-rn) / (1-r), where r ≠ 1. However, we need the number of terms (n). To find n, we use the formula for the nth term of a geometric sequence, which is an = a * rn-1. We can solve for n considering the last term given: 8748 = 4 * 3n-1.
However, instead of manually finding the value of n and then the sum, let us approach the problem with the available options. The sum of a geometric series increases very rapidly due to the exponential nature of each subsequent term. Comparing the last term with the provided options, we can infer that the sum has to be a little bit greater than the last term of the series, 8748.
By inspection of the options, the only number that is slightly greater than 8748 is 8908. Therefore, to the quickest approximation and without going through detailed calculations, the sum of the series is 8908.
If there are 15 girls and 9 boys in an art class, the ____________ of girls to boys in the class is 5:3.
15 4/5% of 50
A. .79 B. 79
C. 790 D. 7.9
"The correct answer is B. 79.
To solve the given problem, we need to calculate 15 4/5 percent of 50. First, let's convert the mixed number to an improper fraction to make the calculation easier.
15 4/5% as a fraction is 15 + 4/5, which can be written as 75/5 + 4/5 = 79/5.
Now, to find the percentage of 50, we multiply 50 by the fraction representing the percentage:
[tex]\[ \frac{79}{5} \times 50 = \frac{79 \times 50}{5} \][/tex]
Next, we simplify the multiplication:
[tex]\[ \frac{79 \times 50}{5} = \frac{3950}{5} \][/tex]
Now, we divide 3950 by 5:
[tex]\[ \frac{3950}{5} = 790 \][/tex]
However, since we are looking for 15 4/5 percent and not 15 4/5 times 50, we need to adjust our calculation by dividing by 100 to get the correct percentage:
[tex]\[ \frac{790}{100} = 79 \][/tex]
Therefore, the final answer is B. 79."
Which of the symbols correctly relates the two numbers below? Check all that apply.
55 ? 35
A.
B.
C. <
D.
E. =
F. >
The other symbols dont want to show so if its another on plz tell me or add me on fb if you guys wanna help me i need to finish this,
The shorter leg of a right triangle is 1414 feet less than the other leg. find the length of the two legs if the hypotenuse is 3434 feet.
In a billiards game, Pete hits a ball that is 20in. from a wall. The ball travels 34 in. until it hits the wall and bounces to a position that is 16 in. from the wall. What proportion can be used to find the distance, x, the ball traveled after it bounces off the wall to get to the ending position? CHECK ALL THAT APPLY!
options
34/x =20/16
20/16 = 34/x
16/20 = x/34
20/16 = x/34
To find the distance the ball traveled after it bounces off the wall, we can use the proportion 34/x = 20/16, which simplifies to x = 27.2 inches.
To find the proportion that can be used to find the distance, x, the ball traveled after it bounces off the wall, we can use the equation:
34/x = 20/16
After cross multiplying, we get:
34 × 16 = 20x
Simplifying further:
544 = 20x
Dividing both sides by 20, we find:
x = 27.2
Therefore, the distance the ball traveled after it bounces off the wall is 27.2 inches.
Raj is 3 years older than Zia. The sum of the squares of their ages is 369. How old are they?
Final answer:
Zia's age is 12 and Raj's age is 15
Explanation:
To solve this problem, we can set up two equations using the given information. Let's assume Zia's age is x. Since Raj is 3 years older than Zia, Raj's age can be represented as x + 3.
The first equation is [tex]x^2 + (x + 3)^2 = 369.[/tex]
Simplifying this equation, we get [tex]x^2 + x^2 + 6x + 9 = 369.[/tex]
Combining like terms, we have [tex]2x^2 + 6x + 9 = 369.[/tex]
Next, we can rearrange the equation by subtracting 369 from both sides and combining like terms to get [tex]2x^2 + 6x - 360 = 0.[/tex]
Now, we can solve this quadratic equation for x using factoring, completing the square, or the quadratic formula. The solutions are x = -15 and x = 12.
Since age cannot be negative, Zia's age is 12 and Raj's age is 12 + 3 = 15.
A function that can be written in the form f(x)=ax2+bx+c, where a, b & c are real numbers and a is not equal to zero.
A quadratic function seems to be a second-order polynomial function. Another quadratic function has the following general form:
[tex]f (x) = ax^2 + bx + c[/tex]here,
a, b, and c = real numbersand,
a ≠ 0The quadratic formula is obtained by completing the square on some kind of quadratic equation instead in the standard format. Because the largest power equals two, it is indeed a 2nd-degree polynomial equation.
As a result, the aforementioned response is correct.
Learn more about quadratic equation here:
https://brainly.com/question/19942005
What is the average of the first n positive even numbers?
Solution:
we have been asked to find the average of the first n positive even numbers.
Let the firm n positive even numbers be
[tex] 2,4,6,8,10,12,.........2(n-1), 2n [/tex]
As we know that average of numbers[tex] =\frac{\text{Sum of Numbers }}{Total number of Numbers}\\ [/tex]
Required Average[tex] =\frac{2+4+6+2(n-1)+2n}{n}\\ [/tex]
Required Average[tex] =\frac{2(1+2+3+....+(n-1)+n)}{n} [/tex]
As we know the sum of first n terms[tex] =\frac{n(n+1)}{2} [/tex]
Required Average[tex] =\frac{2n(n+1)}{2n}=n+1 \\ [/tex]
Describe the vertical asymptotes and holes for the graph of y=x-4/x^2+3x+2,
A plane flies round-trip to Philadelphia. It flies to Philadelphia at 220 miles per hour and back home with a tailwind at 280 miles per hour. If the total trip takes 6.5 hours, how many miles does the plane fly round-trip? 560 miles 800.8 miles 1,300 miles 1,601.6 miles
Using the law of cosines, in triangle RST, if r=14 yd, s=9 yd, t=16 yd find m angle s
Help? Thank you
In a tessellation, what must the sum of the angles be where the vertices meet?
90° 180° 360° 60°
) the length of a rectangle is 5 cm less than twice the width. if the area of the rectangle is 88 , find the dimensions of the rectangle.
Jade is painting a rectangular wall. The wall is 414 yards long and 223 yards high.The formula for the area of a rectangle is A=bh. What is the area of the wall?
The formula for the area of the rectangle is actually A = LW. The length of the rectangular wall is 414 yards while its width is 223 yards. To compute for its area, you just have to follow the formula:
A = 414 (223)
A = 92,322 yards^2
Therefore, the area of the wall is 92,322 square yards.
Answer:
hey the answer is 11 1/3
Step-by-step explanation:
ive taken the quiz and this is the answer 100%
What is the solution of log6x+log6(x+5)=2?
Answer:4
Step-by-step explanation:just did it on edge
To solve log6(x) + log6(x + 5) = 2, combine the logarithms, rewrite in exponential form, and solve the resulting quadratic equation. The solutions are x = -9 and x = 4, but since logarithms of negative numbers are undefined, the final answer is x = 4.
To solve this logarithmic equation, follow these steps:
Combine the logarithms: Use the property of logarithms that states logb(a) + logb(c) = logb(a × c).Final Answer: x = 4.
Rewrite the radical exponent as a radical
when does a rhombus have 4 congruent angles?
Factor completely. x^2−3x−40
To factor the quadratic expression x² -3x -40, we find that the expression factors into (x - 8)(x + 5).
The question involves factoring the quadratic expression x² -3x -40 completely. To factor this expression, we look for two numbers that multiply to -40 and add to -3. The numbers that meet these conditions are -8 and 5, since
(-8) * 5 = -40 and
(-8) + 5 = -3.
Therefore, the expression can be factored into (x - 8)(x + 5).
Multiple Choice
You can model the population of a certain city between 1945-2000 by the radical function P(x)=55,000 sqrt x-1945. Using this model, in which year was the population of that city 165,000?
A)1948
B)1951
C)1954
D)1957,
What is the perimeter of the triangle expressed as a polynomial? 8x-2 5x-4 9x-3
A customer buys an apple pie for $8.04, 6 cloves of garlic for $0./9 each, and a quarts of milk for $1.31. You are working the cash register. The customer gives you a $5 bill, six $1 bills, and a quarter. The register tells you that you ow the customer $0.16 . Round the price of each item to the nearest $0.10 to estimate how much the customer owes.
Final answer:
To estimate the total cost, round each item to the nearest $0.10, sum them up, and subtract from the amount given by the customer. The estimated total cost is $9.80, and the estimated change to be returned is $1.45.
Explanation:
To estimate the total amount the customer owes after rounding to the nearest $0.10, we need to perform the following calculations:
Apple pie: $8.04, rounded to $8.00
6 cloves of garlic: $0.09 each, so $0.09 x 6 = $0.54, rounded to $0.50
Quart of milk: $1.31, rounded to $1.30
The estimated total cost is $8.00 (apple pie) + $0.50 (garlic) + $1.30 (milk) = $9.80.
The customer gives a total of $5 + $6 + $0.25 = $11.25.
Subtracting the estimated total cost from the amount given by the customer:
$11.25 - $9.80 = $1.45, which is the estimated change to be returned to the customer.
Solve the system of equations and choose the correct ordered pair. 2x + 6y = 6 3x – 2y = 20
Answer:
solution is (6,-1)
Step-by-step explanation:
[tex]2x + 6y = 6[/tex]
[tex]3x – 2y = 20[/tex]
WE use elimination method to solve for x and y
Multiply the second equation by 3
[tex]3x – 2y = 20[/tex] times 3
[tex]9x – 6y = 60[/tex]
[tex]2x + 6y = 6[/tex] , add both equations
------------------------------
[tex]11x = 66[/tex]
Divide both sides by 11
[tex]x=6[/tex]
Plug in 6 for x in first equation
[tex]2x + 6y = 6[/tex]
[tex]2(6) + 6y = 6[/tex]
[tex]12 + 6y = 6[/tex], subtract 12 on both sides
[tex]6y = -6[/tex]
divide both sides by 6
[tex]y=-1[/tex]
[tex]x=6 \ and \ y= -1[/tex]
Describe the graph of the following inequality: 2x - 5y ≤ 6
To graph the inequality 2x - 5y ≤ 6, plot the line 2x - 5y = 6 with a solid boundary, test a point to determine the solution region, and shade the region that satisfies the inequality, which is below and to the right of the boundary line.
Explanation:To graph the inequality 2x - 5y ≤ 6, you must first draw the boundary line of the inequality. This line is created by graphing the equation 2x - 5y = 6.
Start by finding the intercepts. For the x-intercept, set y to 0 and solve for x, which gives x = 3. For the y-intercept, set x to 0 and solve for y, which gives y = -6/5. These two points can be used to draw the boundary line. Since the inequality is '≤', this line will be solid to show that points on the line satisfy the inequality.
Now you must determine which side of the line contains the solutions to the inequality. You can do this by choosing a test point that is not on the line, like (0,0). Substitute this point into the inequality: 2(0) - 5(0) ≤ 6 is true, so the area containing (0,0), which is below and to the right of the line, is the solution region. Shade this area to show all points that satisfy the inequality 2x - 5y ≤ 6.
In a class, every student knows French or German (or both). 15 students know French, and 17 students know German. What is the largest possible number of students in that class?
Solution:
we are given that
In a class, every student knows French or German (or both).
15 students know French, and 17 students know German.
Suppose there are x student who knows both French and German.
Then Total number of student in the class will be [tex] (15+17-x)=32-x [/tex]
But to guess the largest possible number of student in the class we can assume x=0
Hence the largest Possible number of Student in the class=32
A line includes the points (2, 10) and (1, 4). what is its equation in slope-intercept form?
Solve this easy question and get points!!!
There are two trains. Both trains are going to the same place, taking the same stops, and are going the exact same speed. But one train arrives in
80 Mins and the other train arrives in 1 Hour and 20 Mins. How is this possible?
Bars of soap come in packages of 6 and packages of 8. The 6-bar pack costs $7.86, and the 8-bar pack costs $8.88. Which is the better deal? What is the
price per bar of the better deal?
Carlos’s credit card has an APR of 14.78% and a grace period of 18 days, and Carlos pays his balance in full every month. If his last billing cycle ended on March 28, 2010, and he made his payment on April 13, 2010, Did he owe any interest on his last statements balance?
which is the directrix of parabola with equation x^2=4y
Answer:
[tex]y=-1[/tex]
Step-by-step explanation:
We have been given an equation of parabola [tex]x^2=4y[/tex]. We are asked to find the directrix of our given parabola.
First of all, we will divide both sides of our given equation by 4.
[tex]\frac{x^2}{4}=\frac{4y}{4}[/tex]
[tex]\frac{x^2}{4}=y[/tex]
[tex]y=\frac{x^2}{4}[/tex]
Now, we will compare our equation with vertex form of parabola:
[tex]y=a(x-h)^2+k[/tex], where, (h,k) represents vertex of parabola.
We can see that the value of a is [tex]\frac{1}{4}[/tex], [tex]h=0[/tex] and [tex]k=0[/tex].
Now, we will find distance of focus from vertex of parabola using formula [tex]p=\frac{1}{4a}[/tex].
Substituting the value of a in above formula, we will get:
[tex]p=\frac{1}{4*\frac{1}{4}}[/tex]
[tex]p=\frac{1}{1}=1[/tex]
We know that directrix of parabola is [tex]y=k-p[/tex].
Substituting the value of k and p in above formula, we will get:
[tex]y=0-1[/tex]
[tex]y=-1[/tex]
Therefore, the directrix of our given parabola is [tex]y=-1[/tex].
HELP!! ASAP!!!!! Which system of equations below has infinitely many solutions?
a) y = –3x + 4 and y = –3x – 4
b) y = –3x + 4 and 3y = –9x + 12
c) y = –3x + 4 and y = -1/3+ 4
d) y = –3x + 4 and y = –6x + 8
Answer:
The correct option is B. [tex]y=-3x+4 \ \text{and}\ \ 3y=-9x+12[/tex]
Step-by-step explanation:
Consider the two linear equation:
[tex]a_1x+b_1y+c_1=0\ \text{and}\ \ a_2x+b_2y+c_2=0[/tex]
The pair of linear equation has infinitely many solutions when:
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]
Now consider the option.
Option a) [tex]y=-3x+4 \ \text{and}\ \ y=-3x-4[/tex]
The above equation can be written as:
[tex]y+3x-4=0 \ \text{and}\ \ y+3x+4=0[/tex]
Therefore,
[tex]\frac{1}{1}=\frac{3}{3}\neq\frac{-4}{4}[/tex]
Thus, this pair has no solution.
Now consider the option B. [tex]y=-3x+4 \ \text{and}\ \ 3y=-9x+12[/tex]
The above equation can be written as:
[tex]y+3x-4=0 \ \text{and}\ \ 3y+9x-12=0[/tex]
Therefore,
[tex]\frac{1}{3}=\frac{3}{9}=\frac{-4}{-12}[/tex]
Thus, this pair has infinitely many solution.
Hence, the correct option is B. [tex]y=-3x+4 \ \text{and}\ \ 3y=-9x+12[/tex]