Answer:
A. an = 1(4)^n-1
Step-by-step explanation:
Geometric sequence:
In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio, and the sequence is given by:
[tex]a_n = a_1(q)^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term and q is the common ratio.
We are given the following sequence:
[tex]a_1 = 1[/tex]
[tex]a_n = 4a_{n-1}[/tex]
So
[tex]a_2 = 4a_1 = 4[/tex]
[tex]a_3 = 4a_2 = 16[/tex]
[tex]a_4 = 4a_3 = 64[/tex]
That is, the quotient between consecutive terms is 4, so [tex]q = 4[/tex].
The first term is already given, [tex]a_1 = 1[/tex]. So
[tex]a_n = a_1(q)^{n-1}[/tex]
[tex]a_n = 1(4)^{n-1}[/tex]
And thus, the correct answer is given by option A.
The hours of daylight, y, in Utica in days x from January 1, 2013 can be modeled by the equation y = 2.89sin(0.0145x-1.40) + 10.99. How many hours of daylight, to the nearest tenth, does this model predict for February 21, 2013?
Answer:
9.3 hours
Step-by-step explanation:
Given
[tex]y = 2.89\sin(0.0145x-1.40) + 10.99.[/tex]
Required
Hours of sunlight on Feb 21, 2013
First, calculate the number of days from Jan 1, 2013 to Feb 21, 2013
[tex]days = 52[/tex]
So:
[tex]x = 52[/tex]
So, we have:
[tex]y = 2.89\sin(0.0145x-1.40) + 10.99.[/tex]
[tex]y = 2.89\sin(0.0145*52-1.40) + 10.99.[/tex]
[tex]y = 2.89\sin(0.754-1.40) + 10.99.[/tex]
[tex]y = 2.89\sin(-0.646) + 10.99.[/tex]
[tex]y = 2.89*-0.6020 + 10.99.[/tex]
[tex]y = -1.740 + 10.99.[/tex]
[tex]y = 9.25[/tex]
[tex]y = 9.3[/tex] --- approximated
find the derivative
f (x ) = (x-5)^2 (3-x)^2
Given:
The function is
[tex]f(x)=(x-5)^2(3-x)^2[/tex]
To find:
The derivative of the given function.
Solution:
Chain rule of differentiation:
[tex][f(g(x))]'=f'(g(x))g'(x)[/tex]
Product rule of differentiation:
[tex][f(x)g(x)]'=f(x)g'(x)+g(x)f'(x)[/tex]
We have,
[tex]f(x)=(x-5)^2(3-x)^2[/tex]
Differentiate with respect to x.
[tex]f'(x)=(x-5)^2\dfrac{d}{dx}(3-x)^2+(3-x)^2\dfrac{d}{dx}(x-5)^2[/tex]
[tex]f'(x)=(x-5)^2[2(3-x)(0-1)]+(3-x)^2[2(x-5)(1-0)][/tex]
[tex]f'(x)=(x^2-10x+25)(-6+2x)+(9-6x+x^2)(2x-10)[/tex]
[tex]f'(x)=(x^2)(-6)+(-10x)(-6)+(25)(-6)+(x^2)(2x)-10x(2x)+25(2x)+(9)(2x)+(-6x)(2x)+x^2(2x)+9(-10)+(-6x)(-10)+x^2(-10)[/tex]
On further simplification, we get
[tex]f'(x)=-6x^2+60x-150+2x^3-20x^2+50x+18x-12x^2+2x^3-90+60x-10x^2[/tex]
[tex]f'(x)=(2x^3+2x^3)+(-6x^2-20x^2-12x^2-10x^2)+(60x+50x+18x+60x)+(-90-150)[/tex]
[tex]f'(x)=4x^3-48x^2+188x-240[/tex]
Therefore, the derivative of the given function is [tex]f'(x)=4x^3-48x^2+188x-240[/tex].
A survey of 2392 adults ages 18 and over asked what type of food they would be most likely to choose at a restaurant. The results are shown in the figure.
A circle graph titled Survey Results is divided into 6 regions showing different types of restaurants. Starting from the top right, the regions are labeled, American 670, Italian 526, Mexican 407, Chinese 383, Japanese 167, Other 239.
What is the probability that an adult chosen at random prefers Italian food? Round your answer to the nearest whole percent.
Answer:
22%
Step-by-step explanation:
their is a total of 2392 adults, the number of people, who would be most likely to chose Italian food is 526.
p= 526/ 2392=22%
The probability of choosing Italian food is 21.9%.
What is probability?"Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one".
For the given situation,
Total number of adults = 2392
American food = 670
Italian food = 526
Mexican food = 407
Chinese food = 383
Japanese food = 167
Others = 239
The event is the probability of choosing Italian food.
[tex]P(e)=\frac{526}{2392}[/tex]
⇒[tex]P(e)=0.219[/tex]
Rounded to nearest whole percent = [tex]0.219[/tex] × [tex]100[/tex]
⇒[tex]21.9\%[/tex]
Hence we can conclude that the probability of choosing Italian food is 21.9%.
Learn more about probability here
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Which pair of diagrams best models the equation 3/4 = 6/8.
the one we barely see in the photo you took seems a good fit. on the left wich 3 blue stripes and one white. and with stripes of half the size, 6 blue and two white
Answer:
Answer is a because it has
Step-by-step explanation:
3 blue and 6 blue trust me
How do I do this ahh!?
Based on data from the U.S. Census Bureau, a Pew Research study showed that the percentage of employed individuals ages 25-29 who are college educated is at an all-time high. The study showed that the percentage of employed individuals aged 25-29 with at least a bachelor's degree in 2016 was 40%. In the year 2000, this percentage was 32%, in 1985 it was 25%, and in 1964 it was only 16%.+
What is the population being studied in each of the four years?
a. college educated individuals
b. college educated individuals aged 25-29
c. individuals aged 25-29
d. employed individuals aged 25-29
e. employed individuals
Answer:
d. employed individuals aged 25-29
Step-by-step explanation:
"Population" in a research study is the comprehensive group that the experimenter or the researcher is interested in.
It is given that US Census Bureau, showed that percentage of the employed individual who are of age group 25 years to 29 years are college educated and is at all time high.
The research study focuses on the specific age group of individuals those who graduated form college or at least have a bachelor degree.
Thus the population of the research study those who studied in each of the four years are the employed individuals aged from 25-29.
help please jfisaljfdlsajflsd
9514 1404 393
Answer:
108 square units
Step-by-step explanation:
The area of a trapezoid is given by the formula ...
A = 1/2(b1 +b2)h
This trapezoid has bases 8 and 1, and a height of 24. Its area is ...
A = (1/2)(8 +1)(24) = 108 . . . square units
The product of a and the sum of a and 34?
please help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
9514 1404 393
Answer:
the correct answer is marked
Step-by-step explanation:
The circle with center (h, k) and radius r has equation ...
(x -h)² +(y-k)² = r²
For the given center, that is ...
(x -1)² +(y +1)² = r²
The value of r² can be found by using the given point for x and y, and seeing what value of r² makes the equation true.
(5 -1)² +(7 +1)² = 4² +8² = 16 +64 = 80
So, r² = 80 makes the equation true, and that equation is ...
(x -1)² +(y +1)² = 80
The correlation coefficient for practicing violin and getting better grades in a group of people is 0.8. Analyze the following statement:
Playing violin causes students to get better grades.
Is this a reasonable conclusion?
Answer:
D No; even though there is a strong positive correlation, playing violin doesn't cause students to get better grades
I need help with #7. Please help. I have to show all work so please explain
Answer: 2√17 A website to use for this would be "M a t h w a y"!!! Good luck, hope I helped!!!
find the median of the data in the dot plot below. Mass of each rock in Nija's collection
Answer:
40
Step-by-step explanation:
The median is the middle number
There are 10 numbers
The middle is between 5th and 6th number
Take the 5th and 6th numbers and average them
(39+41)/2 = 80/2 = 40
The median is 40
Mass of each rock in Nija's collection is 40.
Answer:
The median is the middle number
n=10 numbers
The middle is between 5th and 6th number
Taking the 5th and 6th numbers:
average(39+41)/2 = 80/2 = 40
Find the amount of interest for a 18-year investment of $4300 at a simple annual rate
of 4.07%
PLEASE ANSWE QUICK
Tamara uses a coupon to save 20% off her purchase at the bookstore. The original cost of Tamara's purchase is d dollars.
Which expressions represent the cost, in dollars, of Tamara's purchase after using the coupon? Choose all that apply.
Answer:
The equation would be d - (d×0.2)
An ice cube is melting, and the lengths of its sides are decreasing at a rate of 0.8 millimeters per minute At what rate is the volume of the ice cube decreasing when the lengths of the sides of the cube are equal to 18 millimeters? Give your answer correct to the nearest cubic millimeter per minute. Rate of decrease: millimeters3 per minute.
Answer:
The rate of decrease is: [tex]43.2mm^3/min[/tex]
Step-by-step explanation:
Given
[tex]l = 18mm[/tex]
[tex]\frac{dl}{dt} = -0.8mm/min[/tex] ---- We used minus because the rate is decreasing
Required
Rate of decrease when: [tex]l = 18mm[/tex]
The volume of the cube is:
[tex]V = l^3[/tex]
Differentiate
[tex]\frac{dV}{dl} = 3l^2[/tex]
Make dV the subject
[tex]dV = 3l^2 \cdot dl[/tex]
Divide both sides by dt
[tex]\frac{dV}{dt} = 3l^2 \cdot \frac{dl}{dt}[/tex]
Given that: [tex]l = 18mm[/tex] and [tex]\frac{dl}{dt} = -0.8mm/min[/tex]
[tex]\frac{dV}{dt} = 3 * (18mm)^2 * (-0.8mm/min)[/tex]
[tex]\frac{dV}{dt} = 3 * 18 *-0.8mm^3/min[/tex]
[tex]\frac{dV}{dt} = -43.2mm^3/min[/tex]
Hence, the rate of decrease is: 43.2mm^3/min
(doesnr let me put 2 pictures) what name length describes the center of the data? (a question to the number line) (i mark brainlist)
Work it out yourself lad
Answer:
three
Step-by-step explanation:
answer might be 3... shortest name length
uppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.5 and a standard deviation of 0.37. Using the empirical rule, what percentage of the students have grade point averages that are no more than 3.24
Answer:
[tex]P(x \le 3.24) = 0.97725[/tex]
Step-by-step explanation:
Given
[tex]\bar x = 2.5[/tex]
[tex]\sigma = 0.37[/tex]
Required
Percentage that is not more than 3.24
The above implies that:
[tex]x = 3.24[/tex]
Calculate z score
[tex]z = \frac{x - \bar x}{\sigma}[/tex]
[tex]z = \frac{3.24 - 2.5}{0.37}[/tex]
[tex]z = \frac{0.74}{0.37}[/tex]
[tex]z = 2[/tex]
So, the probability is represented s:
[tex]P(x \le 3.24) = P(z \le 2)[/tex]
From z probability
[tex]P(z \le 2) = 0.97725[/tex]
Hence:
[tex]P(x \le 3.24) = 0.97725[/tex]
What is the value of x?
O 20
(x + 40)
(3x)
R
O 35
w
O 60
S
070
Answer:
Hello! answer: 20
Step-by-step explanation:
These are vertical angles meaning they will have the same measure so... 20 + 40 = 60 20 × 3 = 60 therefore x = 20 hope that helps!
In the given scenario, the value of x is 20. The correct option is A.
What is parallelogram?A parallelogram is a quadrilateral with two pairs of parallel sides. This means that opposite sides of a parallelogram are parallel and congruent, and opposite angles are congruent as well.
To find the value of x in the given diagram, we need to use the fact that the opposite sides of a parallelogram are equal in length.
Therefore, we can set the expressions for the opposite sides equal to each other and solve for x:
x + 40 = 3x
Simplifying the equation, we get:
40 = 2x
Dividing both sides by 2, we get:
x = 20
Therefore, the value of x is 20.
For more details regarding parallelogram, visit:
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What is the surface area of the solid that this net can form?
8 mm
25 mm
8 mm
5 mm
5 mm
8 mm
8 mm
5 mm
5 mm
8 mm
8 mm
25 mm
O 730 square millimeters
O 875 square millimeters
O 1,000 square millimeters
O 1,444 square millimeters
Answer:
730
Step-by-step explanation:
separate each rectangle
use the formula to calculate the area of each rectangle.
1st rectangle
area = length ×breadth
length =5, breadth =8+25+8=41
A1=5×41=205
2nd rectangle
A2=8×25=200
....
A3=5×25=125
A4=8×25=200
Add all As and you have your ans 730
I need help, please answer A and B.
Answer:
a. 81 square inches
b. 108 inches
Step-by-step explanation:
The area of all 5 squares combined is 405 square inches. This is 5 times the area of 1 square. 405/5 = 81. The area of 1 square is 81 square inches.
Since this is a square, the sides are equal. Thankfully the area of 1 square is a perfect square so the length of one side of the square is a full number, which is 9. All of the squares are congruent as shown in the diagram so we simply add every length together (there are 12 sides, each side is 9 inches).
12*9 = 108 and that is the perimeter.
Answer:
area
Step-by-step explanation:
a = 405/5 = 81
a =81 square inches
perimeter
p = √81
= 9
=4×9×5
=180 inches
Consider the function f(x) = 2^x
and function g
g(x) = f(x) + 6
How will the graph of function g differ from the graph of function ?
Answer:
The graph of function g is the graph of function f shifted 6 units up
Step-by-step explanation:
If you plug in the values, [tex]g(x) = 2^{x} + 6[/tex]. If the 6 was added or subtracted from the x in the exponent, it would shift horizontally (left and right), but adding 6 to f(x) separately moves the graph vertically (up and down). Hope this helps.
Complete the factored form of the linear expression.
15x + 12y = ( )( + )
Answer:
3(5x + 4y)
Step-by-step explanation:
Given
15x + 12y ← factor out 3 from each term
= 3(5x + 4y) ← in factored form
Find the angle(s) of intersection between the equations f (x) = x^2 + 2x + 1 and g(x) = 1.
There could be more that one answer
18.4
26.6
71.6
63.4 (already know that this is definitely one of the options)
Answer:
seems to be the same as the other angle
Step-by-step explanation:
i use desmos for these graphs btw
12 ducks fly overhead. Each of 6 hunters picks one duck at random to aim at and kills it with probability 0.6. What's the expected number of hunters who hit the duck they aim at?
Answer:
The expected number of hunters who hit the duck they aim at is 3.6
Step-by-step explanation:
Given;
number of hunters, n = 6
the probability of killing a duck, p = 0.6
The expected number of hunters who hit the duck they aim at?
In binomial distribution, the expected value is equal to the product of the number of trials and the probability of success.
The expected number of hunters who hit the duck they aim at is calculated as follows;
E = np
E = 0.6 x 6
E = 3.6
Therefore, the expected number of hunters who hit the duck they aim at is 3.6
What is the probability that you roll a dice and get 3, then get an ace from a deck, then (without replacing the other card) draw a black 2?
I Really need help!
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Explanation:
1/6 is the probability of rolling a '3' since there is one side we want out of 6 total.
The probability of getting an ace is 4/52 because there are 4 aces out of 52 cards total.
If that card isn't put back, then we have 52-1 = 51 cards left. That means the probability of drawing a black 2 is 2/51. The numerator 2 has nothing to do with the card value of '2'. It has to do with the fact we have 2 black cards (2 of spades, 2 of clubs) out of 51 left over.
We multiply the fractions to get the final answer
(1/6)*(4/52)*(2/51)
(1*4*2)/(6*52*51)
8/15912
1/1989
When using a calculator, we can see that,
1/1989 = 0.0005 = 0.05%
There is a very small chance of all three events happening at the same time.
usain bolt broke the world record for the mens 100 m sprint with a time of 9.58 seconds. Florence Griffith Joyner broke the world record for the womens 100 m sprint with a time of 10.49 seconds. If florence and usain were running at their world-record speed in the same race, how many metres behind usain would florence finish?
Answer:
If Florence Griffith Joyner and Usain Bolt were running at their world-record speed in the same race, Florence Griffith Joyner would finish 8.67 m behind Usain Bolt.
Step-by-step explanation:
Step 1: Determine the speed of each athlete in m/s
Speed = distance / time
Distance = 100 m
Usain Bolt's speed: 100m / 9.58 s = 10.438 m/s
Florence Griffith Joyner's speed: 100 m/ 10.49 s = 9.533 m/s
Step 2: Determine the distance covered by Florence Griffith Joyner in 9.58 s
Distance = Speed × time
Distance covered by Florence Griffith Joyner = 100 m/ 10.49 s × 9.58 s = 91.32 m
Step 3: Determine the difference in the distance covered by Usain Bolt and Florence Griffith Joyner after 9.58 s
After 9.58 s, Usain Bolt have covered a distance of 100 m
After 9.58 s, Florence Griffith Joyner have covered a distance of 91.33 m
Difference between the distances = (100 - 91.33) m = 8.67 m
Therefore, if Florence Griffith Joyner and Usain Bolt were running at their world-record speed in the same race, Florence Griffith Joyner would finish 8.67 m behind Usain Bolt
Select the correct answer.
What is the factored form of this expression?
-12x+36
ОА.(x - 12)(x-3)
O B. (x - 6)^2
OC. (x + 6)^2
OD. (x-6)(x+6)
The answer is B
the method use to solved this is called foil
Simplify: -8x +7-5-5x + 5x
A
- 8x + 2
B
-18x+12
-x-5
D
-X+12
Answer:
A) -8x+2
Step-by-step explanation:
-8x + 7 - 5 - 5x + 5x
-8x -5x + 5x + 7 - 5
- 8x+2
1)Light travels at the speed of 3,00,000 km in one second ,if it has
already travelled 1,05,342 km, how much more distance is left for the
ray of light to travel?
Answer:
1,94,658km
Step-by-step explanation:
If you are talking about how much distance it has to travel in 1 second then you can simply subtract 1,05,342 from 3,00,000. This process gives total of 1,94,658km remaining for it to travel.
Goodluck
Right answers only pls I am gonna fail rn pls help
Answer:
y = 5x – ¼
Step-by-step explanation:
The equation for the slope intercept form is given by:
y = mx + c
Where m and c are the slope and intercept on the y-axis respectively.
From the equation i.e y = mx + c, we can see that y is the subject of the equation.
Now, comparing the equation of the slope intercept form (i.e y = mx + c) with those given in the question above, we can see that only the equation:
y = 5x – ¼
has y as the subject of the equation.
Therefore, y = 5x – ¼ gives the correct answer to the question.