The Geometric Progression is [tex]-3_n = -6^n^-^1[/tex] where a is -3 and r is 2.
The general form of geometric sequence is as follows:
[tex]a_n[/tex] = [tex]ar^n^-^1[/tex]
Since, the sum of the 3rd and 5th term of a GP is -60
⇒ a₃ + a₅ = -60
⇒ ar² + ar⁴ = -60
⇒ ar²( 1+r²) = -60 ------- (1)
Similarly, the sum of the 5th term and 7th term is -240
⇒ a₅ + a₇ = -240
⇒ ar⁴ + ar⁶ = -240
⇒ ar⁴ ( 1+ r²) = -240 ------ (2)
Here we will divide equation (2) with equation (1) we get
⇒ r² = 4
∴ r = 2
Putting r=2 in equation (1) we get
⇒ ar²(1+r²) = -60
⇒ 4a( 1+4) = -60
⇒ 20a = -60
⇒ a= -3
Putting the derived values of a and r in the general form of GP
Hence, the GP is [tex]-3_n = -6^n^-^1[/tex]
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Which equation models the following word problem?Find three consecutive odd integers such that the sum of 3 times thesmaller and 5 times the largest is 770.
AExplanations:
• Some examples of odd numbers are 1, 3, 5, 7, 9, and 11, we cand see that this is an addition of 2 to the previous number.
So,
• Let x be the smaller inter ... ................(1)
• let x + 2 = the middle interger.......... (2)
therefore the third odd interger will be
• (x+2) +2 = (x+4) ........................................(3)
Solving this according to the given statement will be :
• the sum of 3 times the smaller = 3x
,• 5 times the largest = 5*(x+4)
combining this would be : 3x + 5(x+4) = 770Option D is correct .A rotating light is located 17 feet from a wall. The light completes one rotation every 4 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 15 degrees from perpendicular to the wall.
the light is 17 feet from the wall
angular speed is found with
w = change in rotation / change in time
2pi / 4
pi / 2
y = 17 tan(θ)
derivative
y = 17 sec^2 (θ)
y = 17 * pi/2 * sec^2(θ)
y = 17 * pi/2 * sec^2(15)
y = 28.62 ft per second
Distribute the negative number and simplify.10 - 2(4 + 3x)
SOLUTION
Step 1 :
In this question, we are meant to distribute the negative number and simplify the linear expression.
Step 2 :
Given:
[tex]\begin{gathered} 10\text{ - 2 ( 4 + 3 x )} \\ \text{Expanding the brackets, then we have that:} \\ =10\text{ - 8 - 6 x } \\ =2\text{ - 6x } \end{gathered}[/tex]CONCLUSION
We can see clearly that:
[tex]10\text{ - 2 ( 4 + 3 x ) = 2 - 6 x }[/tex]
Rounded to the nearest hundredth, how many cm are 26in (1in = 2.54cm)
We are asked to find how many cm are 26in given that (1in = 2.54cm)
Explanation
Let the desired cm be x
[tex]\begin{gathered} if\text{ 1in =2.54cm} \\ \text{ 26in=xcm} \\ xcm=26\times2.54 \\ xcm=66.04 \end{gathered}[/tex]Answer:66.04cm
Select the outlier in the data set. 7 58 62 68 65 86 72 76 74 If the outlier were removed from the data set, would the mean increase or decrease?
7 is an outlier.
Data:
7, 58, 62, 68, 65, 86, 72, 76, 74
Let us rearrange the data
7, 58, 62, 65, 68, 72, 74, 76, 86
To know if a number is an outlier, it is usually either:
1. Lower Outlier Threshold = Less than Q1 + 1.5 x IQR
2. Higher Outlier Threshold = Greater than Q3 - 1.5 x IQR
where IQR is the interquartile range
Q1 is the First Quartile
Q3 is the Third Quartile.
Now we have to find Q1, Q3, and IQR.
The formulas are given below:
[tex]\begin{gathered} Q1=\frac{(1\times(n+1))}{4}^{th} \\ \text{where n is the number of values in the dataset} \\ \\ Q3=\frac{(3\times(n+1))}{4}^{th} \\ \\ \text{IQR}=Q3-Q1 \end{gathered}[/tex]n = 9 (according to the question)
Thus, with these formulas, we can find the Q1, Q3, and IQR
[tex]\begin{gathered} Q1=\frac{(1\times(9+1))^{th}}{4} \\ Q1=\frac{10}{4}^{th}=2.5^{th} \\ Q1\approx3^{rd} \end{gathered}[/tex]Therefore, the first Quartile Q1 is in the third position in the arranged data:
7, 58, 62, 65, 68, 72, 74, 76, 86
Q1 = 62.
Now we solve for Q3:
[tex]\begin{gathered} Q3=\frac{(3\times(9+1))^{th}}{4}=\frac{(3\times10)^{th}}{4}=\frac{30}{4}^{th} \\ Q3=7.5^{th}\approx8^{th} \end{gathered}[/tex]Therefore, the third Quartile Q3, is in the 8th position in the arranged data:
7, 58, 62, 65, 68, 72, 74, 76, 86
Q3 = 76
Now, we can calculate IQR as:
Q3 - Q1 = 76 - 62 = 14
Thus, IQR = 14
Now we can test which values are outliers.
[tex]\begin{gathered} LowerOutlierthreshold=Q1-1.5\times IQR \\ \text{Lower Outlier }threshold\text{ = 62- 1.5}\times14=41 \end{gathered}[/tex]We have a value of 7 which is much lower than the Lower Outlier threshold value.
Thus 7 is an outlier.
Now let us check for the HIgher Outlier:
[tex]\begin{gathered} \text{Higher Outlier threshold = Q3 + 1.5}\times IQR \\ \text{Higher Outlier threshold= 76 + 1.5}\times14 \\ \text{Higher Outlier threshold= 97} \end{gathered}[/tex]We have no value from the dataset that is greater than 97, thus there is no upper outlier
Therefore, the final answer is = 7
suppose tortilla chips cost 35.5 cents per ounce. if a bag costs $4.63, how many ounces are in the bag of chips? round your answer to the nearest hundredth, if necessary
Given:
The cost of tortilla chips = 35.5 cents per ounce
The bag of tortilla chips = $4.63 = 463 cents
To find the number of ounces in the bag, divide 463 by 35.5
so,
The number of ounces =
[tex]\frac{463}{35.5}=13.04225[/tex]Rounding to the nearest hundredth
so, the answer will be 13.04 ounces
Jamie runs 3 2/3 miles on Monday and 1 2/3 miles on Tuesday . Jamie says the total distance she runs is Monday and Tuesday is between 4 and 5 . Is she correct. rewrite 3 2/3 as the fraction ___ and rewrite 1 2/3 as the fraction___ the sum of this fraction is ___ so, the total distance Jamie runs on Monday and Tuesday is between ___ and ___ Jamie ___ correct.
now the sum
[tex]\frac{11}{3}+\frac{5}{3}=\frac{16}{3}[/tex][tex]\frac{16}{3}\longrightarrow5\frac{1}{3}[/tex]
blanks
1)11/3
2)5/3
3)16/3 or 5 1/3
4) 5
5) 6
6) wasnt
Jamie runs 3 2/3 miles on Monday and 1 2/3 miles on Tuesday . Jamie says the total distance she runs is Monday and Tuesday is between 4 and 5 . Is she correct? Rewrite 3 2/3 as the fraction 11/3 and rewrite 1 2/3 as the fraction 5/3, the sum of this fractions is 16/3, so the total distance Jamie runs on Monday and Tuesday is between 5 and 6, and Jamie isn't correct.
Two trains leave stations 224 miles apart at the same time and travel toward each other. One train travels at 75 miles per hour whilethe other travels at 85 miles per hour. How long will it take for the two trains to meet?Do not do any rounding.
The distance between two trains is 224 miles.
The speed of one train is 75 miles per hour and the speed of the second train is 85 miles per hour.
The train is moving towards each other. So the relative speed of the train is,
[tex]\begin{gathered} 75-(-85)=75+85 \\ =160 \end{gathered}[/tex]So the distance between trains 224 miles is covered at the speed of 160 miles per hour.
Determine the time after which trains meet each other.
[tex]\begin{gathered} t=\frac{224\text{ miles}}{160\text{ miles/hour}} \\ =1.4\text{ hours} \end{gathered}[/tex]So two trains meet after 1.4 hours.
Please show how to solve 59.5 minus 40.125
Answer:
19.35
Step-by-step explanation:
59.500
-
40.125
______
(borrow 1 from 5 and add in front of the first zero.
59.4(1)05
-
40.125
(borrow 1 from 10 and add in front of the second zero. (10 - 1)
59.49(1)0
-
40.125
now start your subtraction.
59.49(1)0
-
40.125
________
19.375
schedulefairG GPATurnitinW History NotesHistory Ch 16DashboardFinal - Version 1Solve each related rate problem.6) Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. Theradius of the spill increases at a rate of 4 m/min. How fast is the area of the spillincreasing when the radius is 7 m?A) 63 m²/min B) 54rt m®/min C) 5211 m²/min D) 560 m²/min7) A spherical balloon is inflated so that its radius increases at a rate of 2 cm/sec. How fast
Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The
radius of the spill increases at a rate of 4 m/min. How fast is the area of the spill
increasing when the radius is 7 m?
Area of a circle = Pi r^2
A = Pi (7)^2 = Pi (49) =
start with -8+5= -3a. -8.35+ +5= ?b. -8.55 + +5.3 = ?c. -8.65 + +5.25=?
Answer
(a) -8.35 + +5 = -3.35
(b) -8.55 + +5.3 = -3.25
(c) -8.65 + +5.25 = -3.4
Explanation
Given:
-8 + 5 = -3
So,
(a) -8.35 + +5 = ?
+ x + = +
∴ - 8.35 + 5 = -3.35
(b) -8.55 + +5.3 = ?
+ x + = +
-8.55 + 5.3 = -3.25
(c) -8.65 + +5.25 = ?
+ x + = +
-8.65 + 5.25 = -3.4
The distance between twocities on a map is 4 inches.If the map scale is1 inch : 10 miles, how farapart are the actual cities?miles
Answer:
The actual cities are 40 miles apart.
[tex]40\text{ miles}[/tex]Explanation:
Given that the distance between two cities on a map is 4 inches.
And the scale is;
[tex]1\text{inch : 10 miles}[/tex]It means that 1 inch on the map represent 10 miles on the actual length.
So for 4 inches on the map, the actual length will be;
[tex]\begin{gathered} 4\times10\text{ miles} \\ =40\text{ miles} \end{gathered}[/tex]Therefore, the actual cities are 40 miles apart.
[tex]40\text{ miles}[/tex]7) y = x + 2 x A) Domain: x 2-2 Range: 1 2 0 B) Domain: x 20 Range: y 2 2 C) Domain: { All real numbers.} Range: { All real numbers. D) Domain: x s 2 Range: y = 0
ok
y = x + 2
The answer to your question is letter B.
This is because x must be positive, hold on , I'll grpah the equation
From the graph we concluded that the domain is x >= 0
and the range is y>= 2.
Is (x+1) a factor of f(x) = x^4 - 3x^3 + 2x - 2?
Answer:
[tex]\text{Yes}[/tex]Explanation:
According to the factor theorem, if we set x+1 to zero, the substitute the x value into the polynomial, if we get a value of zero, then x+1 is a factor of the polynomial, otherwise, it is not
We start by setting x+1 to zero:
[tex]\begin{gathered} \text{ x+1 = 0} \\ x\text{ = -1} \end{gathered}[/tex]Substitute -1 into the polynomial:
[tex]\begin{gathered} f(-1)=-1^4-3(-1)^3+2(-1)-2 \\ f(-1)\text{ = 1+3-2-2} \\ f(-1)\text{ = 4-4} \\ f(-1)\text{ = 0} \end{gathered}[/tex]This shows that (x+1) is a factor of the polynomial
To get the 10% discount, a shopper must spend more than $100. Use d to represent the spending (in dollars) of a shopper who gets the discount.
Answer
For a shopper to get the discount,
d > 100
Explanation
To get the discount, a shopper must spend more than $100.
If the amount a shopper must spend to get the discount is represented as d (in dollars), then the inequality that represents that d must be more than $100 is
d > 100
Hope this Helps!!!
Marsha Bought a Birthday Card for $2.86 And a Pen for $1.57 She paid with a 20 dollar bill. How much change should marsha have received. A $15.57B $24.43C $17.77D $16.57
Answer: The answer is D. 16.57
Step-by-step explanation:
First, you do 2.86+1.57 = 4.43. Then you do 20-4.43. You then get the answer. P.S this is answered by a 7th grader so my step-by-step explanation is kinda bad.
P, Q, and R are collinear points with Q between P and R. PQ=4x+7, QR=5x+11, and PR=54. Use the Segment Addition Postulate to solve for x.
This problem is about the sum of segments.
We know that
PR = 54 (the total length of the segment)
PQ = 4x + 7
QR = 5x + 11
By the segment addition postulate, we can say that
[tex]PR=PQ+QR[/tex]Replacing the given information, we have
[tex]54=4x+7+5x+11[/tex]Now, we solve for x
[tex]54-7-11=4x+5x\rightarrow9x=36[/tex]Then, we divide the equation by 9
[tex]\frac{9x}{9}=\frac{36}{9}\rightarrow x=4[/tex]Therefore, the value of x is 4.If FG = 27 yards, find the length of FED.= I need help end of semester and I need to be eligible for sports please help me
SOLUTION
The formula for length of arc is given as
[tex]A_L=\frac{\theta}{360}\times2\pi r[/tex]For the length of arc FEG
[tex]\begin{gathered} \theta=360-47-80 \\ \theta=233 \end{gathered}[/tex]Therefore the length of arc FEG is
[tex]\frac{233}{360}\times2\times\pi\times7[/tex]Calculate the value
[tex]\frac{233}{360}\times2\times\pi\times7=28.47[/tex]Therefore, the length of arc FEG is 28.47 yards
Jamie will Part 9 come at 5 and coordinate plane
The plot coordinates are given as (9, 5).
Note that the coordinates of a point are given in the form (x, y).
x is the value on the x-axis, which is the horizontal axis that moves left to right, while y is the value on the y-axis that moves up and down.
There are two possible first two steps to take to plot (9, 5):
1) Start at the origin.
2) Either take 9 steps to the right, and take 5 steps upwards.
From this, we can pick OPTIONS E and H
I need help finding out the answer to this problem! I tried solving it but it just gave me a point on a graph, not just 1 number.....
y-65=-(x-22) 4x-y=23
Answer:
(22, 65)
x = 22, y = 65
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y-65=-(x-22)\\ 4x-y=23\end{cases}[/tex]
Rearrange the first equation to make y the subject:
[tex]\implies y-65=-(x-22)[/tex]
[tex]\implies y-65=-x+22[/tex]
[tex]\implies y-65+65=-x+22+65[/tex]
[tex]\implies y=-x+87[/tex]
Substitute the rearranged equation into the second equation and solve for x:
[tex]\implies 4x-y=23[/tex]
[tex]\implies 4x-(-x+87)=23[/tex]
[tex]\implies 4x+x-87=23[/tex]
[tex]\implies 5x-87=23[/tex]
[tex]\implies 5x-87+87=23+87[/tex]
[tex]\implies 5x=110[/tex]
[tex]\implies \dfrac{5x}{5}=\dfrac{110}{5}[/tex]
[tex]\implies x=22[/tex]
Substitute the found value of x into the rearranged first equation and solve for y:
[tex]\implies y=-x+87[/tex]
[tex]\implies y=-22+87[/tex]
[tex]\implies y=65[/tex]
Therefore, the solution to the system of equations is:
[tex]x = 22, \quad y = 65[/tex]The solution in (x, y) form is (22, 65).
Note: If the question requires only one number as the answer, it is likely that it wants only the x-value of the solution, which in this case is x = 22.
The solution to the system of equations are (x,y) 22 and 65 respectively.
What is an equation?A system of equations is a group of two or more equations with the same variables. A solution to a system of equations is the values of the variables that make all of the equations in the system true.
Rearranging the first equation which is y - 65 = -(x - 22) will be y = -x + 87.
Substitute the rearranged equation into the second equation and then solve for x.
4x - y = 23
4x - (-x + 87) = -23
Collect like terms
5x = 110
Divide
x = 110 / 5
x = 23
Since y = -x + 87.
y = -22 + 87
y = 65
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Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find the length of BD.
Okay, according with the identities of parallelograms we have: AE=CE and BE=DE.
Replacing we obtain:
AE=CE
2x=x+2
2x-x=2
x=2
BE=DE
y+10=4y−8
10+8=4y-y
18=3y
y=18/3
y=6
And considering that BD=BE+DE, we got:
BD=(y+10)+(4y-8)=(6+10)+(4*6-8)=(16)+(24-8)=16+16=32
So, finally we obtain that the length of BD is 32 units.
What is 0.3% of $4,900?
Answer:
14.7
Step-by-step explanation:
4900*0.3%=14.7
1. The image shown will undergo a dilation at point B, with a scale factor of 2 Which lines will not be changed by the transformation? Select all that apply. Pick up to 2 answers. A. AC B. -- AE C. BE D. CD DE
verify each option
AC is not changed -
ED is not changed
BC is changed
answer is
AC and ED
Solve the inequality for x: x−1x−2≥0
Given:
Inequality is
[tex]\frac{x-1}{x-2}\ge0[/tex]Required:
Solve the inequality.
Explanation:
We have inequality greater than or equal to zero.
So, this can happen only when both numerator and denominator positive or negative.
Fraction will be positive when x less than or equal 1 and when x greater than 2.
So, it is
[tex](-\infty,1]or(2,\infty)[/tex]Answer:
Hence, option B is correct.
two intergers whose absolute value have a product of 24
Given : two integers whose absolute value have a product of 24
Factor the number 24:
24 = 1 x 24
24 = 2 x 12
24 = 3 x 8
24 = 4 x 6
So, the two numbers are one of the following :
• 1 and 24
,• 2 and 12
,• 3 and 8
,• 4 and 6
If we take the negative numbers into accounts so, the set will be :
the product of two negative numbers will give a positive number.
• -1 and -24
,• -2 and -12
,• -3 and -8
,• -4 and -6
volume of a cone = 1/3 pi r^2 h, where r is the radius and h is the
height.
The cone below has a diameter of 14 cm and a height of 11 cm.
What is the volume of the cone?
If your answer is a decimal, give it to 1 d.p.
Answer:
564.7 cm^3
Step-by-step explanation:
volume of cone =1/3*π*r^2*h
=(1/3)*(22/7)*7^2*11
=564.7 cm^3 (1 d.p.)
Find the 52nd term of the given arithmetic sequence-30, -38, -46, -54...
The sequence is given to be:
[tex]-30,-38,-46,-54...[/tex]The nth term of an arithmetic sequence is calculated using the formula:
[tex]a_n=a_1+(n-1)d[/tex]where a₁ is the first term, n is the number of terms, and d is the common difference.
From the given sequence, the following parameters can be gotten:
[tex]\begin{gathered} a_1=-30 \\ d=-38-(-30)=-8 \end{gathered}[/tex]Therefore, the parameters can be substituted into the formula to find the 52nd term:
[tex]\begin{gathered} n=52 \\ \therefore \\ a_{52}=-30+(52-1)(-8) \\ a_{52}=-30+51(-8)=-30-408 \\ a_{52}=-438 \end{gathered}[/tex]The 52nd term is -438.
A certain car is rated to get 26 miles per gallon. How far can it travel on 12.5 gallons of gas?
Our car can do 26 miles with one gallon, so, if we have 12.5 gallons, to find how much we can travel we need to make the product of the amount of gallons we have by the amount of milles we can do with one gallon, wich gives us the expression:
[tex]12.5\times26=325[/tex]So our car can travel 325 miles with 12.5 gallons of gas.
was just working on my math skills but don't know how to to this problem
As shown the figure : there are two parallel lines and a transversal
Given the angles : ( x + 14 ) and (5x - 74)
The angles are congruent because they are a corresponding angles
So,
[tex]5x-74=x+14[/tex]solve the equation to find x , combine the like terms
[tex]\begin{gathered} 5x-74=x+14 \\ \\ 5x-x=14+74 \\ \\ 4x=88 \\ \\ x=\frac{88}{4}=22 \end{gathered}[/tex]so, the answer is x = 22
write the percent as a rate per 100 170/t= ?/100
Answer:
The equation that shows how to find t, the total number of pages in the e-book is;
[tex]\frac{180}{t}=\frac{75}{100}[/tex]Explanation:
Given that after reading 180 pages, he has completed 75% of the book.
It implies that 75% of the total number of pages is 180 pages.
[tex]\begin{gathered} 75\text{\% of t = 180 pages} \\ \frac{75}{100}\times t=180 \\ \frac{75}{100}=\frac{180}{t} \\ \frac{180}{t}=\frac{75}{100} \end{gathered}[/tex]Therefore, the equation that shows how to find t the total number of pages in the e-book is;
[tex]\frac{180}{t}=\frac{75}{100}[/tex]