If a₁ = 4 and an = -4an-1 +5 then the value of a5 is 72, in the given sequence.
What is sequence?A group of enumerated objects where repetitions are allowed and order is crucial is referred to as a sequence in mathematics. Similar to a set, it has members. The sequence's length is expressed in terms of its number of elements.
Given that, sequence
[tex]a_1=4, a_n=4 a_{n-1}+5[/tex]
Now
[tex]a_2=4 a_1+5[/tex]
[tex]a_2=4 \times 4+5[/tex]
[tex]a_2=21[/tex]
[tex]a_2=4 \times 4+5[/tex]
[tex]a_2=21[/tex]
And the common difference d = 21 - 4 = 17
Therefore [tex]a_5=a_1+4 d[/tex]
[tex]a_5=4+4 \times 17[/tex]
[tex]a_5=4+68[/tex]
[tex]a_5=72[/tex]
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The function y= 15.35 (1.0279)^t represents the value y(in dollars) of a share of stock after t days. Identify the initial amount and determine the growth or decay rate.
9514 1404 393
Answer:
initial amount: $15.35growth: 2.79% per dayStep-by-step explanation:
The coefficient is the initial amount: $15.35.
The growth factor is the base of the exponential term: 1.0279. The growth rate is 1 less than this: 1.0279 -1 = 0.0279 = 2.79%. It is positive, so represents a growth of 2.79% per day.
The equation of the line of best fit is y= 1/2x+1 how many laps can a bicycle make around the park in 23 mins
Answer:
The equation of the trend line is y= 1/2x +1. How many laps can a bicycle make around the park in 23 minutes? answer choices. 44 laps. 12 1/2 laps. 23 laps.
Step-by-step explanation:
hope this helped :b
Find the point-slope equation for
the line that passes through the
points (7, -21) and (-4, 23). Use
the first point in your equation.
y- [?] = [ ](x-[])
Answer:
[tex]y+21 = -4(x-7)[/tex]
Step-by-step explanation:
1) First, find the slope of the line between the two points. Use the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of (7, -21) and (-4, 23) into the formula and simplify:
[tex]m = \frac{(23)-(-21)}{(-4)-(7)} \\m = \frac{23+21}{-4-7}\\m = \frac{44}{-11}\\m = -4[/tex]
So, the slope of the line is -4.
2) Now we have all the information we need. To write the equation of the line, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
Since [tex]m[/tex] represents the slope, substitute -4 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, substitute the x and y values of (7, -21) into the equation as well. This gives the following answer:
[tex]y+21 = -4(x-7)[/tex]
Match each type of event with its probability. Unlikely event, 10greater than 0 and less than 0.50.5greater than 0.5 and less than 1Neither likely nor unlikely event likely event
Answer:
Unlikely = greater Than 0 ; less than
Likely = greater than 0.5 ; less than 1
Neither likely nor unlikely = 0.5
Step-by-step explanation:
Probability values usually range between standardized values between 0 and 1. With values closer to 1 depicting greater possibilities of an event. Probability value of zero means certain and probability value of 0 zero means.impossible.
Using this standardized values :
An unlikely event is more of not occurring than occurring (that is the event has higher chances of not happening) ;
Hence; We can categorize unliky events to range from below the mid value to greater Tha.n 0
Unlikely event : greater Than 0 ; less than 0.6
Events with probability above the mid value of 0.5 have higher chances of occurring (greater likelihood) hence, Probability is greater than 0.5 but less than 1.
Neither likely nor unlikely event will take the boundary point between likely and unlikely = 0.5
please answer 13 and 14
Answer:
13. Option 3
14.Option 2
Step-by-step explanation:
Option 3 shows that caleb has $5 or less by using the "less than or equal to" sign
Option 2 uses a closed circle to show that $5 is included in the table.
Things to remember that helped me
Closed circle are used for < and > signs to show that the number is being included. They mean "less than or equal to (<)" and "more than or equal to(>)"
Open circles are used for < and > signs. To show that the number is NOT included in the inequality.
Also when looking at the signs < and >, Picture them as arrows. That will show you the direction on the number line they go. For example < is pointing to the left which would mean "LESS THAN" and same with >, its pointing to the right which would mean "MORE THAN"
Answer:
13 - option 3 and 14 - option 2
Step-by-step explanation:
Can anyone help me plss
Answer:
0.7 km per minute , -0.17 km per minute
Step-by-step explanation:
The computation of the average speed is shown below
As we know that
Average speed = Total distance ÷ total time
= (4 + 2 + 1) ÷ (32 + 22 + 16)
= 0.7 km per minute
Now the velocity is
= Change in displacement ÷ change in time
= (4 - 2 - 1) ÷ (32 -22 -16)
= 1 ÷ -6
= - 0.17km per minute
Angle G in trapezoid FGHJ measures 135 degrees. Jasmine reflects the trapezoid over the x-axis. What is the measure of the image of angle G?
Answer:
Triangle EFG has vertices E(-3, 4), F(-5, -1), and G(1, 1)
Step-by-step explanation:
Answer:
angle g is a 2 and fghj is a 1234 ok
What is the unit rate for the proportional relationship represented by the equation y=4/5x
Answer choices:
A:4/5
B:-2
C:4
D:5
Answer:
A: 4/5
Step-by-step explanation:
The equation for proportionality is y = kx, where k is the constant of proportionality. That is what you're looking for in this question.
So in y = 4/5x, 4/5 is the constant of proportionality/unit rate for the proportional relationship.
The 4/5 is the constant of proportionality/unit rate for the proportional relationship.
We have given that,
the unit rate for the proportional relationship is represented by the equation y=4/5x.
We have to determine the unit rate
What is the equation of proportionality?The equation for proportionality is y = kx, where k is the constant of proportionality.
So in y = 4/5x,
The 4/5 is the constant of proportionality/unit rate for the proportional relationship.
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can i get help please?
Answer:
c) 19
Step-by-step explanation:
9^2+17^2 = 81+289 = 370
sqrt370 = approx 19
Please help will mark brainliest :)
Answer:
Fraction Decimal
4/11 0.36363636 ~ the answer would be "0.36"
Step-by-step explanation:
I hope i helped :)
Pls help also no links pls
Answer:
(A)
Step-by-step explanation:
Well you gotta isolate the variable by perfoming inverse operations so you gotta dd 70 to both sides.
PLEASE ANSWER I DONT WANT TO FAIL
Answer:
88 sq units
Step-by-step explanation:
Area of the rectangle = 14*4= 56 (length*width)
Formula for the area of a Δ = 1/2 * b * h =
1/2 * 8 * 8 =
4*8 = 32
Add:
56+32 = 88
What is the constant of proportionality for this problem?
Answer:
$ 825
Step-by-step explanation:
10 yard = $150
55yard = ?
55yard* $150 /10yard
55*15 =825 then the correct answer of
$55 yard is 825
Jackson bought a jar of 240 marbles. The percent bar graph shows the percentage of each color marble in the jar.
How many of the marbles are blue?
Answer:
84
Step-by-step explanation:
Blue marbles = 35%
35% = 0.35
240(0.35)
84
Answer:
84
Step-by-step explanation:
0.35×240=84
hope this helps
Which of the following equations represents this statement
Answer: 5n = 35
Step-by-step explanation:
The product of a number n and the number 5 is 35. This statement can be formed into an equation as:
n × 5 = 35
5n = 35
The equation is 5n = 35
If we want to get the value of the number, it'll be:
5n = 35
n = 35/5
n = 7
The number is 7
Beatrice has a page of 8 math problems to complete over the weekend. She solved 3 problems on Saturday morning and 2 on Saturday afternoon. Write a number sentence with fractions that describes how much of the page Beatrice has completed.
Answer:
5/8
Step-by-step explanation:
Add 3+2 to get 5
5 is the numerator (the number above the line)
8 is the denominator (the number below the line)
Beatrice has done 5/8 (or 5 out of 8) math problems.
I NEED HELP ASAP I WILL GIVE BRAINLIST
A camera has a listed price of $553.98 before tax. If the sales tax rate is 7.5%, find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary.
519.99(.0825) = 42.899
519.99 + 42.899 = $562.89
Answer:
Sales tax---> 553.98 x 0.075= 41.5485
Total---> 553.98 + 41.5485= 595.5285
Round to nearest tenth---> 595.53 is your answer
PLZ HELP FAST THIS IS TIMED
Answer:
its 12 100%
Step-by-step explanation: i just did the test
Answer:
The answer for the color red is 7 and for the color blue is 13
Rearrange the formula:
C = 5/9 (F - 32)
to make F the subject
help
Answer:
F = [tex]\frac{9}{5}[/tex] C + 32
Step-by-step explanation:
Given
C = [tex]\frac{5}{9}[/tex] (F - 32)
Multiply both sides by [tex]\frac{9}{5}[/tex] to clear the fraction
[tex]\frac{9}{5}[/tex] C = F - 32 ( add 32 to both sides )
[tex]\frac{9}{5}[/tex] C + 32 = F
Find the length of the third side. If necessary, round to the nearest tenth.
Answer:
18.3
Step-by-step explanation:
a^2 + b^2 = c^2
We can call the unknown side x. The hypotenuse (25) is c.
Knowing this, you know that x^2 + 17^2 = 25^2.
Now simpify!
x^2 + 289 = 625
Subtract 289 from both sides:
x^2 = 338
Now take the square root of 338 which is 18.3 rounded to the nearest tenth.
Hope this helped! :)
Lynnette went to the coffee shop to buy coffee beans. She purchased 2.5 pounds of her favorite blend. This blend cost $8.50 per pound. How much did the coffee beans cost?
Answer: $21.25
Step-by-step explanation:
Given
Lynnette purchased 2.5 Pounds of blent, which costs $8.50 per pound
total cost is the Product of the amount of blend and rate of coffee blend
[tex]\Rightarrow C=2.5\times 8.50=\$21.25[/tex]
So, coffee beans cost $21.25
Did i pick the right one?
Answer:
V= 3,14×7×3×5
= 21,98×15
= 131,94
2 + 6x > 38 How can I solved this?
Answer:
Below
Step-by-step explanation:
Move all terms not containing x to the right side of the inequality.
6 x > 36
Divide each term by 6 and simplify.
x > 6
Inequality Form: x > 6
Interval Notation: ( 6 , ∞ )
Hope this helps:)
how many more years is the avearge life span of a alligator then a tiger
Answer:
69 years
Step-by-step explanation:
Oh, hell yeah
Answer: 69 more years
Step-by-step explanation:
192.692 - 58.1987
Estimate The Difference
Answer: 134.4933
Step-by-step explanation: 58.1987 minus 192.692 is 134.4933
1. A rectangular fish tank 60 cm by 15 cm by 34 cm find the volume of water needed to fill the tank 2/3 of the given aquarium.
First correct answer will be brainlist
Please help me with this. I don't know how I can thank you, but I need this ASAP. More questions coming.
Answer:
The answer you have marked is correct
Step-by-step explanation:
The angles added together equal 360
Nicolas has $650 to deposit into two different savings accounts.
• Nicolas will deposit $400 into Account I, which earns 3.5% annual simple interest.
• He will deposit $250 into Account II, which earns interest compounded annually.
Nicolas will not make any additional deposits or withdrawals. Which amount is closest to the total balance of these two accounts at the end of 2 years?
Answer:
694.51
Step-by-step explanation:
Please help me
Please, I beg you.
Answer:
a reflection followed by a translation
Step-by-step explanation:
A random sample of dogs at different animal shelters in a city shows that 10 of the 55 dogs are puppies. The city's animal shelters collectively house 1,485 dogs each year. About how many dogs in all of the city's animal shelters are puppies?
Answer: The number of dogs in all of the city's animal shelters is puppies = 270
Step-by-step explanation:
Given: A random sample of dogs at different animal shelters in a city shows that 10 of the 55 dogs are puppies.
The city's animal shelters collectively house 1,485 dogs each year.
The number of dogs in all of the city's animal shelters is puppies = [tex]1485\times\dfrac{10}{55}=270[/tex]
Hence, The number of dogs in all of the city's animal shelters is puppies = 270