The first term of the Geometric Series = 3 and its common ratio = 3/2.
What is a geometric Series?An unlimited number of terms with a fixed ratio between each term make up a geometric series.
For 'n' termed GP with a = first term and r = common ratio, [tex]S_{n}=\frac{a(r^{n}-1)}{r-1}[/tex]
Given:
Sum of first three terms of a G.P. = 14.25Sum of first four terms of the G.P. = 24.375To find: First term of the GP and the common ratio.
Finding:
As, [tex]S_{n}=\frac{a(r^{n}-1)}{r-1}[/tex], for n =3,
[tex]S_{3}=\frac{a(r^{3}-1)}{r-1}=14.25[/tex] (eqn 1)
=> Similarly for n = 4,
[tex]S_{4}=\frac{a(r^{4}-1)}{r-1} = 24.375[/tex]
On dividing [tex]S_3 by S_4[/tex], we get:
[tex]\frac{14.25}{24.375}=\frac{r^{3}-1}{r^{4}-1}[/tex]
=> On solving the equations, we get:
[tex]14.25r^{4}-24.375r^{3}+10.125=0[/tex]
r = 3/2 (on factorizing the equation)
Now, substituting this in eqn 1
=> [tex]14.25=\frac{a((\frac{3}{2})^{2}-1)}{\frac{3}{2}-1}[/tex]
=> a = 3 on further solving the equation for a.
Hence, the first term of the Geometric Series = 3 and its common ratio = 3/2.
To learn more about geometric series, refer to the link: https://brainly.com/question/24643676
#SPJ4
Estimate the average rate of change over the interval [-1, 0]. Show your work below or on the graph.
these are the means and standard deviations for samples of building heights in two different cities. city a city b mean: 120 ft mean: 240 ft standard deviation: 20 ft standard deviation: 12 ftselect the two true statements.
The average building height and the standard deviation for two separate cities' samples are shown. The true statements are:
City A’s heights are more spread out than city B’s heights.
City A has a lower average height than city B.
What is average?In daily life, an average is a number chosen to represent a group of numbers; it is often the sum of the numbers divided by the total number of numbers in the group (the arithmetic mean). The average of the integers 2, 3, 4, 7, and 9, for instance, is 5, which equals 25. An average could alternatively be another statistic like the median or mode, depending on the situation. The median is sometimes used in place of the mean since the mean would be unnaturally high if it included the personal incomes of a few billionaires. The median is the amount below which 50% of personal incomes fall and above which 50% of personal incomes rise.
To learn more about average ,visit:
https://brainly.com/question/15570401
#SPJ4
Acme widgets had an order to process 250 widgets. The first unit required 200 minutes to assemble. Before starting, the company estimated the amount of time it would require to assemble all 250 widgets if they learned at an 85% rate. After assembling all 250 widgets, acme realized they had learned at an 80% rate. How much time less than their estimate did acme take? you should be able to compute the answer within plus or minus 2 hours.
91.2 hours less was taken to assemble the parts of the widgets by estimation.
Firstly, we will find out the range:
Using the cumulative unit table to determine the range, we get that-
Range = 88.83 - 61.47
Range = 27.36
Secondly, we will calculate the minutes requires to assemble the widgets.
Number of minutes = 27.36 × 200 minutes
Number of minutes = 5472minutes
Now, we have to calculate how much time less than their estimate did acme take:
Time = 5472 / 60
Time = 91.2
Therefore, we get that, 91.2 hours less was taken to assemble the parts of the widgets by estimation.
Learn more about estimation here:
https://brainly.com/question/24375372
#SPJ1
In the figure, the radius of the large circle is three times the radius of the small circle. About what percent of the large circle is covered by the small circle?
I NEED THIS NOW PLEEEEEASE!!
The percent of the large circle is covered by the small circle will be 33.3%.
How to calculate the percentage?It should be noted that the radius of the small circle will be r.
The radius of the big circle will be 3r.
Therefore, the percent of the large circle is covered by the small circle will be:
= r / 3r × 100
= 1/3 × 100
= 33.3%
The percent of the large circle is covered by the small circle will be 33.3%.
Learn more about percentages on:
brainly.com/question/24877689
#SPJ1
2. Which of the following expressions simplifies to -15a + 30?
a. -3(-5a + 10)
b. 5(-3d-6)
c. -15(a + 2)
d. 6(-2.5a + 5)
Answer:
D
Step-by-step explanation:
D, because 6* -2.5a = -15a and 6*5= 30 so it equals -15a+30.
Emma is planning how much she needs to make next week. She can only work 25 hours, and she needs to make a total of $620. What is the dollar value of sales Emma will need to make?
Answer:
The corrects answer is: Emma will need to make sales totaling $800 next week to meet her goal.
Step-by-step explanation:
Solve the inequality and express your answer in interval notation.
x^2-12x+5<0
Answer:
you solve the main number and you can plus the 1+1 the answer is 2 2=2 the main berb on this answer is no
Step-by-step explanation:
jalok
Answer:
The answer is A.
Step-by-step explanation:
leonard can wash 6 cars in 4.5 hours. assuming that he always washes cars at this same rate, answer the following. how many cars can he wash in 9 hours?
how long will it take him to wash one car?
how many cars can he wash in one hour
He wash 12 cars in 9 hours.
And, He take 45 minutes to wash a car.
And, He wash one and one third part of cars in one hour.
Given that;
Leonard can wash 6 cars in 4.5 hours.
He always washes cars at this same rate.
We have to find number of wash cars in 9 hour and time to wash one car and number of wash cars in one hour.
What is relation between hour and minutes?
The relation between hour and minutes is ;
1 hour = 60 minutes.
Now, we have;
Leonard can wash 6 cars in 4.5 hours.
Time for wash 6 cars = 4.5 hour
So, Time for wash 1 car = 4.5 ÷ 6 = 0.75 hour
Since, 1 hour = 60 minutes
Hence, Time for wash 1 car = 0.75 x 60 = 45 minutes
And, In time 4.5 hour, number of wash cars = 6
So, In 1 hour, number of wash cars = 6/4.5 = 1 1/3
Hence, Number of wash cars in one hour is one and one third part of car.
In 9 hour, number of wash cars = (6/4.5) * 9 = 12
Hence, Number of wash cars in 9 hours is 12.
So, He wash 12 cars in 9 hours.
And, He take 45 minutes to wash a car.
And, He wash one and one third part of cars in one hour.
Learn more about the rate of speed visit:
https://brainly.com/question/24644313
#SPJ1
unit 2 sample work due aug 29 3 of 103 of 10 items question order the integers from least to greatest: -9, 5, 2, -8, 0, 10, -12 0, 2, 5, -8, -9, 10, -12 0, 2, 5, -8, -9, 10, -12 -12, -9, -8, 0, 2, 5, 10 -12, -9, -8, 0, 2, 5, 10 -9, -8, 0, 2, 5, 10, -12 -9, -8, 0, 2, 5, 10, -12 -8, -9, -12, 0, 2, 5, 10
The integers from least to greatest is -12<-9<-8<0<2<5<10.
The given set of numbers are -9, 5, 2, -8, 0, 10, -12.
We need to order the integers from least to greatest.
What is ascending order of integers?Ascending order refers to the arrangement of numbers or other items in increasing order from smallest to largest. Numbers that we see on a number line from left to right are examples of ascending order. We usually represent it by putting commas between numbers or by using the 'less-than symbol (<)' between numbers.
With negative numbers, the highest number with the negative sign has the least value.
So, -12<-9<-8<0<2<5<10.
Therefore, the integers from least to greatest is -12<-9<-8<0<2<5<10.
To learn more about the ascending order visit:
https://brainly.com/question/14404086.
#SPJ4
Select the correct answer from the drop-down menu.
Right triangle MNR is represented with the right angle at vertex M. Angle R measures 34 degrees and angle N measures 56 degrees. Point Q lies on segment RN and point P lies on segment MP. Segments MQ and PQ are drawn. Angle MQP measures 56 degrees.
In the figure, sin ∠MQP =
. Plato
The required measure of the sine of angle ∠ MQP for Right triangle MNR is evaluated as 0.83.
As given in the question, the Right triangle MNR is represented with the right angle at vertex M. Angle R measures 34 degrees, and angle N measures 56 degrees.
We have to determine sin ∠MQP.
The angle can be defined as the one line inclined over another line.
Here,
For right-angle triangle MNR,
To calculate the sin of the angle in the right angle triangle we need hypotenuse and perpendicular.
But in the question value of angle ∠MQP is given, So directly,
sin 56 = 0.83.
Thus, the required value of the sine of angle ∠MQP is 0.83.
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ1
Answer:
hlpp
Step-by-step explanation:
Find the measure of the longest angle
The largest angle of the given triangle is 105 degrees. If its measure of other two angles are (6x +17) degrees and (5x + 14) degrees.
According to the given question.
We have, the measure of the angles of a triangle are 105 degrees,
(6x +17) degrees, (5x + 14) degrees.
As we know that the sum of the angles of a triangle is always 180 degrees.
Therefore, we can say that
105 + (6x +17) + (5x + 14) = 180
⇒ 105 + 6x + 17 + 5x + 14 = 180
⇒ 136 + 11x = 180 (adding the like terms)
⇒ 11x = 180 -136
⇒ 11x = 44
⇒ x = 44/11
⇒ x = 4 degrees.
So, (6x +17) degrees = 6(4) + 17 = 24 + 17 = 41 degrees
and, (5x + 14) degrees = 5(4) + 14 = 20 + 14 = 34 degrees
Hence, the largest angle of the given triangle is 105 degrees. If its measure of other two angles are (6x +17) degrees and (5x + 14) degrees.
Find out more informtaion of measure of the angles of a triangle here:
https://brainly.com/question/27681289
#SPJ1
What is another solution of the equation
x + y = 7?
Enter the correct answer.
The solution of the equation x + y = 7 is equal to (x, y) = (1, 6).
The given equation is of the form of linear equation in two variables. A linear equation in two variables is an equation of the form ax + by c = 0 where a, b and c are coefficients and x, and y are independent and dependent variables respectively.
Now, if we take the equation in the question x + y = 7 and assume (1, 6) as (x, y) then
x + y = 7
Putting (x, y) = (1, 6)
=> 1 + 6 = 7
=> 7 = 7
Thus, we see that L.H.S = R.H.S and thus (1, 6) is the solution of the equation x + y = 7.
Learn more about linear equation in two variables at:
brainly.com/question/19803308
#SPJ9
make b the subject of p=1/2ab^2+c
The variable b as the subject of the formula is b = √2(p -c)/a
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to make b the subject of the equation?The equation is given as
p = 1/2ab^2 + c
Subtract c from both sides of the equation
So, we have
1/2ab^2 = p - c
Multiply through by 2
ab^2 = 2(p -c)
Divide by a
b^2 = 2(p -c)/a
Take the square root of both sides
b = √2(p -c)/a
Hence, b as the subject of the formula is b = √2(p -c)/a
Read more about subject of formula at
https://brainly.com/question/10643782
#SPJ1
The letters a and b represent nonzero constants. Solve ax+b=41 for x .
The given equation is solved to x as x=(41-b)/a.
The given equation is ax+b=41.
We need to solve the given equation for x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, the equation ax+b=41 can be solved as follows:
Keep the variable x on the left-hand side of the equation and bring a to the right-hand side of the equation.
That is, x=(41-b)/a (when you bring a variable from LHS to RHS or vice versa the mathematical operations become inverse that is multiplication changes to division)
Therefore, the given equation is solved to x as x=(41-b)/a.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ1
Which expressions are equivalent to 4m-2+(-8m)4m−2+(−8m)4, m, minus, 2, plus, left parenthesis, minus, 8, m, right parenthesis ?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
-2(4m+1) +4m−2(4m+1)+4mminus, 2, left parenthesis, 4, m, plus, 1, right parenthesis, plus, 4, m
(Choice B)
B
2(2m-1)-8m2(2m−1)−8m2, left parenthesis, 2, m, minus, 1, right parenthesis, minus, 8, m
(Choice C)
C
None of the above
Answer:
Ohayooooooooooooooooooooo
A&B
Anna does sit-ups to get ready for her first triathlon. When she starts, she does a sit-up every 222 seconds. But, as she gets tired, each sit-up takes longer and longer to do.
Answer:
No, the number of sit-ups Anna does, are not proportional to the time she spends doing them.
Step-by-step explanation:
When Anna starts, she does a sit-up every 22 seconds.
1. As c decreases, does the value of x increase, decrease, or stay the same for each equation? Assume c is positive.
Equation | Value of x
x + c = 0 |
—————-|——————
-CX=-C |
—————-|——————
X/C=1 |
The complete statements are:
As c increases in x + c = 0, the value of x decreasesAs c increases in -xc = -c, the value of x stay the sameAs c increases in x/c = 1, the value of x increasesHow to determine the complete statements?
To do this, we evaluate each equation
So, we have
Equation 1
x + c = 0
Make x the subject
x = -c
The above implies that x and c are additive inverses
Hence, as c increases, the value of x decreases
Equation 2
-xc = -c
Divide both sides by -c
So, we have
x = 1
The above implies that c does not have any effect on the value of a
Hence, as c increases, the value of x stay the same
Equation 3
x/c = 1
Make x the subject
x = c
The above implies that x and c have the same value
Hence, as c increases, the value of x increases
Read more about equations at
https://brainly.com/question/2972832
#SPJ1
when addition or subtraction is performed, answers are rounded to the least significant decimal place
For addition and subtraction problems, the answer should be rounded to the least significant decimal places as the measurement with the least number of decimal places
The rightmost digit of a decimal number is the least significant digit or least significant figure. Another way to look at the least significant figure is to consider it to be the rightmost digit when the number is written in scientific notation. Least significant figures are still significant.
Count the number of significant figures in the decimal portion only of each number in the problem. Add or subtract in the normal fashion. Final answer may have no more significant figures to the right of the decimal than the least number of significant figures in any number in the problem.
Learn more about Least significant figures here :
https://brainly.com/question/11566068
#SPJ4
Solve 0. 504 ÷ 8.
answer choices:
−7. 496
0. 063
0. 630
4. 32
Answer:
0.063
Step-by-step explanation:
0.504 divided by 8 is 0.063
Hope It Helps
Sorry If I'm Wrong
Answer: The answer is 0.630
Step-by-step explanation: The picture proves my answer :D
(ross p1.15) consider a group of 20 people. if everyone shakes hands with everyone else, how many handshakes take place?
190 handshakes take place.
What is Combinations?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up. The sequence in which the chosen components are chosen is crucial in permutations, too. For instance, the arrangements ab and ba are distinct in permutations but equivalent in combinations (regarded as one arrangement).
Combinatorics is the study of combinations, although mathematics and finance are two other fields that employ combinations.
EXPLNATION : For a handshake you need two people. Therefore, select two from twenty, that is, 20C2 ways. It is 20*19/2 = 190.
In general, if there are ’n’ number of people there can be nC2 handshakes.
To know more about combinations, visit;
https://brainly.com/question/19692242
#SPJ4
Julie has $538 in her bank account. On Monday, she withdrew $218 from her bank account. On Friday, she deposited $49 into her
bank account. What is the net change in her bank account balance from before she made her withdrawal on Monday until after her
deposit on Friday?
Answer:
Step-by-step explanation:Before her deposit on Monday, she had $538 now she has, 538 - 218 + 49 = $369 in her bank account after her withdraw on Friday. Hope this helps, best of luck!
Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Mariam's account has gone into overdraft. Her balance is $-20.21. To get back to a positive balance, she plans to deposit money at a steady rate of $20.79 per week. How much will be in her account after 4 weeks?
Using a linear function, it is found that $62.95 will be in her account after 4 weeks.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that:
The initial balance is the intercept.The weekly deposit is the slope.Hence, her balance after x weeks is given by the following function:
B(x) = -20.21 + 20.79x.
Her balance after 4 weeks is given by:
B(4) = -20.21 + 20.79(4) = $62.95.
Hence $62.95 will be in her account after 4 weeks.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Oceanside Bike Rental Shop charges 24 dollars plus 7 dollars an hour for renting the bike. Mike paid 49 dollars to rent a bike. How many hours did he pay to have the bike checked out?
Step-by-step explanation:
24+7 =31 for one hour
so 49-31= 18 remaining 18/7 =2 remainder 4 so now we have 3 hrs but what about the remainder 4?
if 7 is to 60 as 4 is to x then...
7/60=4/x which will give you x=34.29 mins. so he rented the bike for 4 hours and 34.29 mins
9y=99
Ingrese su respuesta...
The value of y for which the left hand side of the equation is equal to Right hand side is 11.
What is a solution of a linear equation?Solution of a linear equation is the value of the variable for which the left hand side and right hand side of the equation are equal.
Given is the following equation -
9y = 99
In order to solve the equation. we have to find the value of y for which 9y is equal to 99. Now -
9y = 99
Divide both sides by 9 -
9y/9 = 99/9
y = 11
Therefore, the value of y for which the left hand side of the equation is equal to Right hand side is 11.
To solve more questions on solving equations, visit the link below -
https://brainly.com/question/5830512
#SPJ1
[The given question is written in Spanish. The following is the statement converted onto English as
9y=99 Enter your answer.}
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
An open circle is at 3 and a bold line starts at 3 and is pointing to the left
Inequality expressionsInequalities are expressions that are not equated by an equal sign. Given the expression below:
3(8 – 4x) < 6(x – 5)
Expand to have:
3(8) - 3(4x) < 6x - 6(5)
24 - 12x < 6x - 30
Collect like terms
-12x - 6x < -30 - 24
-18x < -54
Divide both sides by -18
-18x/-18 < -54/-18
x < 54/18
x < 3
Hence the solution of the inequality on the number line A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left
Learn more on inequality here: https://brainly.com/question/24372553
#SPJ1
Factor completely.
100-9x²
someone help please
Answer:
[tex](10+3x)(10-3x)[/tex]
Step-by-step explanation:
[tex]100-9x^2\\\sqrt{100} =10\\\sqrt{9} =3\\3*-3=-9\\\sqrt{x^2} = x \\(10-3x)(10+3x)[/tex]
________________________________________________________
Considering both terms are perfect squares, factor using the difference of squares formula:
[tex]a^2-b^2=(a+b)(a-b)[/tex]
In this situation, a = 10 and b = 3x. With this, now plug in your data into the formula.
(10 + 3x) (10 - 3x)
_________________________________________________________
Hope this helps! If so, lmk! Thanks and good luck!
Which relation is a function of x?
O {(1, 2), (7, 6), (3, 2), (1, 0), (5, 6)}
y
2
-6
X
0
0
0
0
9
-7
Ox=3y²-7
X=
-5-4-3-2
5
4
3
2
-2
2 3 4 5 x
Answer:
x=3y2-7
x=3×1-7
x=3-7
x=-4
Which of the following is a true statement
ax + bx = c please help I’m so confused
Answer:
[tex]x = \frac{c}{a + b} a = - b[/tex]
Simplify. (7^{6})^{2}(7
6
)
2
The result of the exponent given is 7^12
Solving exponentsIn order for us to solve the exponential expression given, we will use the law of exponent below;
(a^m)^n = a^mn (multiply the powers)
Given the expression
[tex](7^{6})^{2}[/tex]
Multiply the exponents to have;
7^6(2)
7^12
Hence the result of the exponent given is 7^12
Learn more on exponent here: https://brainly.com/question/11975096
#SPJ