This equals 320 tablespoons.
Find all geometric sequences such that the sum of the first two terms is 24 and the sum of the first three terms is 26.
Answer:
The nth term Tn = -8(-1/4)^(n-1) or Tn = 6(1/3)^(n-1) can be used to find all geometric sequencesStep-by-step explanation:
Let the first three terms be a/r, a, ar... where a is the first term and r is the common ratio of the geometric sequence.
If the sum of the first two term is 24, then a/r + a = 24...(1)
and the sum of the first three terms is 26.. then a/r+a+ar = 26...(2)
Substtituting equation 1 into 2 we have;
24+ar = 26
ar = 2
a = 2/r ...(3)
Substituting a = 2/r into equation 1 will give;
(2/r))/r+2/r = 24
2/r²+2/r = 24
(2+2r)/r² = 24
2+2r = 24r²
1+r = 12r²
12r²-r-1 = 0
12r²-4r+3r -1 = 0
4r(3r-1)+1(3r-1) = 0
(4r+1)(3r-1) = 0
r = -1/4 0r 1/3
Since a= 2/r then a = 2/(-1/4)or a = 2/(1/3)
a = -8 or 6
All the geometric sequence can be found by simply knowing the formula for heir nth term. nth term of a geometric sequence is expressed as
if r = -1/4 and a = -8
Tn = -8(-1/4)^(n-1)
if r = 1/3 and a = 6
Tn = 6(1/3)^(n-1)
The nth term of the sequence above can be used to find all the geometric sequence where n is the number of terms
Going from point A to point B, the cheetah traveled at an average rate of 70 mph. Returning to point A, the cheetah traveled at an average rate of 40 mph. Can we say that this cheetah’s average rate was 55 mph? The average rate for the trip is equal to the total distance traveled divided by the total time traveled. The following equations represent the distance traveled on each leg of the trip. First leg of trip: d=r_1 t_1 Second leg of trip: d=r_2 t_2 Write an equation for the average rate for the trip. Remember, the cheetah runs from point A to point B and back to point A.
Answer:
No.
[tex]\text{Average rate} = \dfrac{\text{Total distance}}{\text{Total time}} = \dfrac{r_{1}t_{1} + r_{2}t_{2}}{t_{1} + t_{2}}\\\\= \text{50.91 mi/h}[/tex]
Step-by-step explanation:
First leg: d = r₁t₁
Second leg: d = r₂t₂
r₁t₁ = r₂t₂
Total distance: 2d = r₁t₁ + r₂t₂
Total time: t = t₁ + t₂
1. Equation for average rate
[tex]\text{Average rate} = \dfrac{\text{Total distance}}{\text{Total time}} = \dfrac{r_{1}t_{1} + r_{2}t_{2}}{t_{1} + t_{2}}[/tex]
2. Average rate
Since r₁t₁ = r₂t₂,
[tex]t_{1} = \dfrac{r_{2}t_{2}}{r_{1}} = \frac{40}{70}t_{2} = \frac{4}{7}t_{2}\\\\\text{Average rate} = \dfrac{2r_{2}t_{2}}{\frac{4}{7}t_{2} + t_{2}} = \dfrac{2 \times 40t_{2}}{\frac{4t_{2}+ 7t_{2}}{7}}= 80t_{2} \times\frac{7}{11t_{2}} = \dfrac{560}{11}\\\\= \textbf{50.91 mi/h}[/tex]
We cannot say truthfully that the average rate is 55 mi/h.
The average rate of a body is the total distance travelled divided by the total time.
The cheetah runs at an average rate of 50.91mph, not 55mph
Let
[tex]d \to[/tex] distance
[tex]r \to[/tex] average rate
[tex]t \to[/tex] time
Given that:
[tex]d = r_1t_1 = r_2t_2[/tex]
So, we have:
[tex]r_1 = 70[/tex]
[tex]r_2 = 40[/tex]
The average rate (r) is calculated as follows:
[tex]r = \frac{Total\ Distance (D)}{Total\ Time (T)}[/tex]
Where:
[tex]D=d + d[/tex]
[tex]D = r_1t_1 + r_2t_2[/tex]
and
[tex]T =t_1 + t_2[/tex]
So, the average rate is:
[tex]r =\frac{r_1t_1 + r_2t_2}{t_1 + t_2}[/tex]
Recall that:
[tex]D = r_1t_1 + r_2t_2[/tex]
[tex]r_1t_1 = r_2t_2[/tex]
Make [tex]t_2[/tex] the subject
[tex]t_2 = \frac{r_1t_1}{r_2}[/tex]
Substitute values for [tex]r_1[/tex] and [tex]r_2[/tex]
[tex]t_2 = \frac{70t_1}{40}[/tex]
So, we have:
[tex]r =\frac{r_1t_1 + r_2t_2}{t_1 + t_2}[/tex]
[tex]r = \frac{70t_1 + 40 \times \frac{70t_1}{40}}{t_1 + \frac{70t_1}{40}}[/tex]
[tex]r = \frac{70t_1 + 70t_1}{t_1 + \frac{70t_1}{40}}[/tex]
[tex]r = \frac{140t_1}{t_1 + \frac{70t_1}{40}}[/tex]
Factor out t1
[tex]r= \frac{140t_1}{t_1(1 + \frac{70}{40})}[/tex]
[tex]r = \frac{140}{(1 + \frac{70}{40})}[/tex]
[tex]r = \frac{140}{\frac{40+70}{40}}[/tex]
[tex]r= \frac{140}{\frac{110}{40}}[/tex]
Rewrite as:
[tex]r = \frac{140 \times 40}{110}[/tex]
[tex]r = 50.91mph[/tex]
Hence, the cheetah's average rate is 50.91mph, not 55mph
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What increase the probability of something happening?
Answer:
Repeating the activity or just waiting for it to happen.
Step-by-step explanation:
I did not really understand but I tried my best.
Ok so this question is about scientific notation. Which isn’t hard. But the numbers given are too much for a calculator. I don’t get how to do it. Please help and please provide an explanation
Answer:
1.1 x 10^24
Step-by-step explanation:
Mass of earth: 5.97 x 10^24
Mass of venus: 4.87 x 10^24
There are 24 numbers in the mass of venus before the 4, in 4.87. So, that is why we use 10^24.
5.97-4.87=1.1
Kristen invests $5,000 in a bank. The bank pays 6.45% interest compounded semi-annually. How much money will she have after 2 years, if she makes no additional contributions or withdrawals to the account?
a:5665.80
b:5327.70
c:4375.80
d:5676.88
Answer:
D. $5,676.88
Step-by-step explanation:
A=P(1+r/n)^n*t
Where
P=principal=$5000
r=interest rate=6.45%=0.0645
n=periods=2(semiannually)
t=time=2 years
A=P(1+r/n)^n*t
=5,000(1+0.0645/2)^2*2
=5,000(1+0.03225)^4
=5000(1.03225)^4
=5000(1.13553756247925)
=5,676.8781
Approximately
$5,676.88
Segment AC bisects angle BAD if the measure of angle BAC is 20 degrees what’s is the measure of angle BAD
Answer:
40°
Step-by-step explanation:
An angle bisector divides an angle into 2 equal angles. 20° x 2 = 40°.
A bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. Two marbles are chosen from the bag. What expression would give the probability that one marble is yellow and the other marble is red?
- 30%
- 40%
- 50%
- 60%
Answer:
2/15 = 13 1/3 %
Step-by-step explanation:
eight yellow marbles, nine green marbles, three purple marbles, and five red marbles = 25
P(yellow) = yellow/ total =8/25
Keep
7 yellow marbles, nine green marbles, three purple marbles, and five red marbles = 24
P(red) = red/total =5/24
P(yellow then red) = 8/25 * 5/24 = 1/15
Then we have (red, yellow) =
P(red) = red/ total =5/25 = 1/5
Keep
8 yellow marbles, nine green marbles, three purple marbles, and four red marbles = 24
P(yellow) = yellow/total =8/24 = 1/3
P(red, yellow) = 1/5*1/3 = 1/15
Add them together
1/15 + 1/15 = 2/15 =
the triangle bounded by the lines y = o, y = 2x
and y = -0.5x + k with k positive is equal to 80 square untits find k
Answer
k = 3.575.
Step-by-step explanation:
Find the number missing from the following equivalent fractions:4/11= ?/66
Answer:
24
Step-by-step explanation:
whatever you add or divide to the numerator, you do to the denominator. the same occurs the other way round,too.
If 11 is multiplied by 6 to give 66.
then, 4 should also be multiplied by 6, for the equivalent fraction. This gives you 24.
Hope this helps. Good Luck
The missing number is 24.
please see the attached picture for full solution
Hope this helps..
Good luck on your assignment..
You are drawing two cards, without replacement, from a standard deck of 52 cards. What is the
probability of drawing a 2. then a face card (King, Queen, or Jack)?
Leave your answer in decimal form to 4 decimal places.
Answer:
Dear student,
Answer to your query is provided below
Probability of drawing a 2 at first is (4/52) = (1/13)
Probability of drawing a face card in second try without replacement = 12/51
Step-by-step explanation:
Total no. Of cards = 52
Total no. Of cards of 2 = 4
Prob. Of drawing 2 = 4/52
Total no. Of face card = 12
Total no.of cards left in deck = 51
Prob. Of drawing face card = 12/51
Jill converted the equation of the line 15 x minus 14 y = negative 2 into slope-intercept form and found the slope and y-intercept of the line as follows. 15 x minus 14 y = - 2. 15 x minus 4 y minus 15 x = - 2 minus 15 x. - 4 y = -2 minus 15 x. - 4 y Over - 4= - 2 minus 15 x Over - 4 Y = - 2 Over -4 minus 15 x Over - 4 . y = one-half minus 15 Over 4 x. y = - 15 Over 4x + one-half. slope = -15 Over 4. y-intercept = one-half. What was her mistake? She mixed up the slope and the y-intercept. She got the sign of the slope wrong. She got the sign of the y-intercept wrong. She found the reciprocals of the slope and the y-intercept.
Answer:
B. She got the sign of the slope wrong.
Step-by-step explanation:
This is the correct answer for edge
Answer:
B
Step-by-step explanation:
She got the sign of the slope wrong.
Help for brainliest answer
Step-by-step explanation:
SA=ph+2A, that is, perimeter × height+ twice area
p=21+20+29=70cm
h=22cm
70×22=1540cm
A=1/2 ×20×21=210×2=420
1540+420=1960cm2
Running from the top of a flagpole to a hook in the ground there is a rope that is 13 meters long. If the hook is 5 meters from the flagpole, how tall is the flagpole?
Answer:
12 meters
Step-by-step explanation:
Looking at the problem we can see that it typifies a right angled triangle. The rope running from the top of the flagpole to the hook on the ground is the hypotenuse of the triangle. Let us call this hypotenuse c. Let the distance between the hook and the foot of the flagpole be b. Let the height of the flagpole be a.
From Pythagoras theorem;
c^2 = a^2 + b^2
a^2= c^2 - b^2
a= √c^2-b^2
From the question
c= 13 metres
b= 5 metres
a= the unknown
a= √c^2-b^2
a= √(13)^2 - (5)^2
a= √169 - 25
a= √144
a= 12 meters
Answer:
The flagpole 12 meters tall
Step-by-step explanation:
Running from the top of a flagpole to a hook in the ground there is a rope that is 13 meters long
∵ The hook is 5 meters from the flag pole
∵ The flagpole and the ground ⊥ to each other
By using Pythagoras theorem:
hypothenus side is 13m
base is 5m
how tall is the flagpole is x
[tex]13^2=x^2+5^2\\\\169=x^2+25\\\\x^2=169-25\\\\x^2=144\\\\x=12m[/tex]
The flagpole 12 meters tall
at davidson's bike rentals it cost $48 to rent a bike for 9 hours. how many hours of bike use does a customer get per dollar?
Answer:
About $5.33
Step-by-step explanation:
If u want to find out How many dollars per hour u do 48 divided by 9
Hope this helps
Given the regular octagon, what is the length of any side?
Answer:110
Step-by-step explanation:x^2+17x=15x+35
x^2+17x-15x-35=0
x^2+2x-35=0
delta=2^2-4*1*(-35)=4+140=144
x1=(-2+V144)/2=(-2+12)/2=10/2
x=5
so 15*5+35=75+35=110
Answer:
110Step-by-step explanation:
In a regular polygon, each side has the same length.
Therefore we have the equation:
[tex]x^2+17x=15x+35[/tex]
We must specify the domain:
[tex]x^2+17x>0\ \wedge\ 15x+35>0\\\\x(x+17)>0\ \wedge\ 15x>-35\\\\(x<-17\ \vee\ x>0)\ \wedge\ x>-\dfrac{7}{3}\Rightarrow x>0[/tex]
[tex]x^2+17x=15x+35\qquad\text{subtract}\ 15x\ \text{from both sides}\\\\x^2+17x-15x=15x-15x+35\\\\x^2+2x=35\qquad\text{add 1 to both sides}\\\\x^2+2x+1=35+1\\\\x^2+2(x)(1)+1^2=36\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1)^2=36\to x+1=\pm\sqrt{36}\\\\x+1=\pm6\qquad\text{subtract 1 from both sides}\\\\x+1-1=\pm6-1\\\\x=-7\ \vee\ x=5[/tex]
[tex]x<-7\notin\text{domain};\ x=5\in\text{domain}[/tex]
The length of a side:
[tex]x^2+17x=5^2+17(5)=25+85=110\\\\15x+35=15(5)+35=75+35=110[/tex]
What is the diameter of a circle with a radius of 9.5 cm ?
Answer:
9.5(2) = 19 is the diameter
Step-by-step explanation:
Answer:
19 cm
Step-by-step explanation:
Diameter is twice the radius, thus 2 x 9.5 cm = 19 cm
Please help me with my question!!
Answer:
14 ornaments.
Step-by-step explanation:
To find the amount of ornaments students can make from 3 1/2 pieces of Bristol board, you will need to divide fractions. Therefore:
Begin by converting '3 1/2' to an improper fraction.
3 1/2 = [tex]\frac{7}{2}[/tex]
Divide '1/4' from the total amount by multiplying by the reciprocal.
[tex]\frac{7}{2} * \frac{4}{1} = \frac{7* 4}{2 *1} = \frac{28}{2} = 14[/tex]
Therefore, the students can make 14 ornaments.
Evaluate Solve 7x + 5 < 3x + 25
Answer:
x < 5
Step-by-step explanation:
7x + 5 < 3x + 25
Subtract 3x from each side
7x-3x + 5 < 3x-3x + 25
4x+5 < 25
Subtract 5 from each side
4x +5-5 < 25-5
4x < 20
Divide by 4
4x/4 < 20/4
x < 5
Answer
x<5
Step-by-step explanation:
7x + 5 < 3x + 25
you would subtract 3x from both sides
Leaving you with 4x+5< 25
next you would subtract 5 from both sides
leaving you with 4x<20
Then you would divide both sides by 4
leaving you with x <5
Hoped this helped
:)
The sides of a polygon have lengths 5, 7, 8, 11, and 19 units. The perimeter of a similar polygon is 75 units. Find the lengths of the sides of the larger polygon
The perimeter of small polygon is 50 units. The length of sides of the larger polygon is 7.5, 10.5, 12, 16.5, 28.5 units.
What is polygon?
Polygon in geometry is "any closed curve consisting of set line segments connected such that two segment across".
According to the question,
Lengths of sides of polygon is 5 units, 7 units, 8 units, 11 units, and 19 units.
Formula for Polygon = sum of sides
Perimeter of first polygon = 5 + 7 + 8 + 11 +19
= 50 units.
Perimeter of second polygon = 75 units.
Divide second polygon by first polygon = 75/50 = 1.5 units
This conclude, second polygon is 1.5 units larger than first polygon.
In order to find the length of the sides of larger polygon by given, first polygon and second polygon are similar polygon multiply 1.5 units to the length sides of first Polygon.
5 * 1.5 = 7.5
7 * 1.5 = 10.5
8 * 1.5 = 12
11 * 1.5 = 16.5
19 * 1.5 = 28.5
Hence, the length of sides of the larger polygon is 7.5, 10.5, 12, 16.5, 28.5 units.
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HOW PLEASE HELP SORRYYYYY FOR ASKING
Answer:
-7 , -5
Step-by-step explanation:
use the AC method, find two numbers that multiply to 35 and add to 12. those numbers are 7 and 5. then u have (m+7)(m+5), so m = -7,-5
Find the perimeter of a rectangle whose length is (4a+b)cm and width (a+6)cm
Answer:
P = 10a +2b+12
Step-by-step explanation:
P = 2 (l+w) for a rectangle
P = 2 ( 4a+b + a+6)
Combine like terms
P = 2(5a+b+6)
Distribute
P = 10a +2b+12
Answer:
Given below
Hope it helps
Step-by-step explanation:
Perimeter= 2(l+b)
= 2(4a+b+a+6)
= 2(5a+b+6)
= 10a+2b+12 cm^2
NEED ANSWERS QUICK, I WILL GIVE BRAINLIEST 1.According to the following image, what is the length of
AB, 2. solve for X
Answer:
the length of ab is 8
x=3
Step-by-step explanation:
Which polynomial is written in descending order of the powers of the variable?
A. -2x^3+6x^2-9x+5
B. 5-9x+6x^2-2x^3
C. 5+6x^2-9x-2x^3
D. -2x^3+5+6x^2-9x^2-9x
Step-by-step explanation:
Descending means from highest to lowest values, so look for the one that goes in order counting down.
Option A is going down all the way unlike any of the other answers, so A is the correct option.
Answer:
A. [tex]-2x^3+6x^2-9x+5[/tex]
There are only red counters and blue counters in a bag the ratio of the number of red counters to the number of blue counters is 4:6 write the ratio in the simplest form
Simplify the following 3 x a x 2 x b
Answer:
6 times ab
Step-by-step explanation:
3 times 2 = 6
a times b = ab
Answer:
6ab
Step-by-step explanation:
An investment group compares returns on an account
against the function represented in the table, where x is the
time in years and f(x) is the total return on investment.
Which describes the function over the interval given in the
table?
х
a decreasing quadratic function
an increasing quadratic function
a decreasing exponential function
an increasing exponential function
0
5
f(x)
10,000
12,201.90
14,888.64
22,167.15
10
20
Answer:
d
Step-by-step explanation:
edge2020
Option D is correct. The exponential function is increasing when time goes and the total return on investment.
What is exponential function?An exponential function is of the form aˣ where 'a' is the base of the function and 'x' is the power of the function.
What is quadratic function?A quadratic function is" a polynomial function with one or more variables in which highest exponent of variable is 2".
According to the question,
Let 'x' is the time in years and f(x) is the total return on investment. The below table shows the function over the interval.
x f(x)
a decreasing quadratic function 10,000
an increasing quadratic function 12,201.90
a decreasing exponential function 14,888.64
an increasing exponential function 22,167.15
Quadratic function f(x) = ax² +b x +c a > 0
A decreasing quadratic function is the vertex of the parabola lies on the axis parabola. The graph of the function is increasing at one side of the axis and decreases at other side of the axis. Clearly it shows as time in years change does not give maximum total return on investment.An increasing quadratic function the vertex of the parabola lies on the axis parabola. The graph of the function is increasing at one side of the axis and decreases at other side of the axis. Clearly it shows change in time in years does not give maximum total return on investment.Exponential function f(x) = a. bˣ +q
The exponential function is decreasing when a < 0 and 0 ≤ b < 1. Then the function f(x) is decreasing exponential function. Clearly it shows time goes, total return on investment is not maximum. The exponential function is increasing when a > 0 and b > 1. Then the function f(x) is increasing exponential function. Clearly it shows time goes, total return on investment is maximum.Hence, the exponential function is increasing when time goes and the total return on investment.
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Question 3: Marla bought one necklace and two bracelets for $67.50. Use the following information to determine the amount she paid for each bracelet: The price of the necklace was $27. The bracelets were both the same price. Enter your numerical answer only in the box; do not include the dollar sign.
Answer:
Each bracelet costs 20.25
Step-by-step explanation:
Here's what was given in the equation:
Total Price: $67.50
Price of necklace: $27
We can subtract the $27 from the $67.50 to get $40.5
Since we know that both bracelets are the same price we can divide the $40.5 by 2 to get two of the exact same prices. The result is $20.25 for each bracelet.
Hope this helps
Answer:
20.25
Step-by-step explanation:
Took test got it right.
(2^8 • 5^negative5 • 19^0) • (5^negative2 / 2^3)^4 • 2^38
i need steps shown and a simplified answer please!
Answer:
6.872* 10^17
Step-by-step explanation:
(2^(8) * 5^(5) * 19^(0)) * ((5^(2))/(2^(3)) ) * 2^(38)
you add the exponent of the same number because it is multiplication
for number two 2 : 8+38=46
for division you subtract the exponents : 46-3=43
and for number 5 : 5+2=7
for 19^0=1
2^43*5^7=6.872*10^17
Si mi disco duro tiene una capacidad de 1.5 Terabytes ¿ cuántas llaves de 32 Gigabits caben en ese disco duro?
Answer:
The number of 32 Gigabit keys that can be fitted on the hard drive is 375.
Step-by-step explanation:
The question is:
If my hard drive has a capacity of 1.5 Terabytes, how many 32 Gigabit keys can fit on that hard drive?
Solution:
1 Terabyte = 8000 Gigabits
Then 1.5 Terabytes in Gigabits is:
1.5 Terabytes = (8000 × 1.5) Gigabits
= 12000 Gigabits
One key is of 32 Gigabits.
Compute the number of 32 Gigabit keys that can be fitted on the hard drive as follows:
[tex]\text{Number of 32 Gigabit keys}=\frac{12000}{32}=375[/tex]
Thus, the number of 32 Gigabit keys that can be fitted on the hard drive is 375.
Which notations accurately represent the range?
Check all that apply.
(-∞ 2) U (2, ∞)
(-∞, -2) U (-2, ∞)
{yly E R, Y ≠ -2}
{yly E R Y≠2}
y<2 or y> 2
Y<-2 or y> -2
Answer:
y < 2 or y > 2 and {y|y ∈ R, y ≠ 2}, (–∞, 2) U (2, ∞)
Step-by-step explanation:
these are the answers i got it right