Answer:
[tex]a_{20} = 1/1048576[/tex]
Step-by-step explanation:
Given
[tex]Sequence: -1/2;1/4;-1/8;1/16[/tex]
Required
Determine [tex]a_{20[/tex]
Since it is a geometric sequence, first we need to calculate the common ratio (r)
[tex]r = \frac{a_2}{a_1}[/tex]
From the sequence:
[tex]a_2 = 1/4[/tex]
[tex]a_1 = -1/2[/tex]
[tex]a_1[/tex] is the same as [tex]a[/tex]
So:
[tex]r = \frac{a_2}{a_1}[/tex]
[tex]r = \frac{1/4}{-1/2}[/tex]
[tex]r = -1/2[/tex]
[tex]a_{20[/tex] is then calculated as:
[tex]a_n = ar^{n-1}[/tex]
Where
[tex]n = 20[/tex]
[tex]a_{20} = ar^{20-1}[/tex]
[tex]a_{20} = ar^{19}[/tex]
[tex]a_{20} = (-1/2) * (-1/2)^{19}[/tex]
Apply law of indices
[tex]a_{20} = (-1/2)^{1+19}[/tex]
[tex]a_{20} = (-1/2)^{20}[/tex]
Evaluate the exponent
[tex]a_{20} = 1/1048576[/tex]
I need help please. aaaaaannnnnnnnndddddddddd thannkyou
Answer:
7:58
Step-by-step explanation:
The little hour hand is a bit past the 7. The long minute hand is closest to 12, which is 60 minuets. Just look the the mark that the little hand points at.
Find the product. Write your answer in decimal form. Three-tenths × 1.71 =
Answer:
0.3x1.71=0.513
Answer:
0.513 is the 100% correct answer for this question. Hope this helps! :)
Step-by-step explanation:
Becicy is renting a car for her vacation. The rental costs 5350 per week plus 20 cents per mile. If Becky can spend no more than $500,
how far can she travel
Answer:
750 miles
Step-by-step explanation:
Given that,
The rental costs 350 per week plus 20 cents per mile.
Becky can spend no more than $500.
Let he travel x miles. We can form an equation as follows :
350 + 0.2x = 500
0.2x = 500-350
0.2x = 150
x = 750 miles
Hence, she can travel 750 miles.
Which of these equations are in slope-intercept form?
y-y1=m(x-x1)
y=mx+b
m=y2-y1/x2-x1
ax+by=c
Answer:
y = mx + b
Step-by-step explanation:
The value V of a certain automobile that is t years old can be modeled by V(t) = 14,651(0.81). According to the model, when will the car be worth each of the following amounts?
(a) $8000
(b) $6000
(c) $1000
- The car will be worth $8000 after years.
(Type an integer or a decimal rounded to the nearest tenth as needed.)
Answer:
a) The car will be worth $8000 after 2.9 years.
b) The car will be worth $6000 after 4.2 years.
c) The car will be worth $1000 after 12.7 years.
Step-by-step explanation:
The value of the car after t years is given by:
[tex]V(t) = 14651(0.81)^{t}[/tex]
According to the model, when will the car be worth V(t)?
We have to find t for the given value of V(t). So
[tex]V(t) = 14651(0.81)^{t}[/tex]
[tex](0.81)^t = \frac{V(t)}{14651}[/tex]
[tex]\log{(0.81)^{t}} = \log{(\frac{V(t)}{14651})}[/tex]
[tex]t\log{(0.81)} = \log{(\frac{V(t)}{14651})}[/tex]
[tex]t = \frac{\log{(\frac{V(t)}{14651})}}{\log{0.81}}[/tex]
(a) $8000
V(t) = 8000
[tex]t = \frac{\log{(\frac{8000}{14651})}}{\log{0.81}} = 2.9[/tex]
The car will be worth $8000 after 2.9 years.
(b) $6000
V(t) = 6000
[tex]t = \frac{\log{(\frac{6000}{14651})}}{\log{0.81}} = 4.2[/tex]
The car will be worth $6000 after 4.2 years.
(c) $1000
V(t) = 1000
[tex]t = \frac{\log{(\frac{1000}{14651})}}{\log{0.81}} = 12.7[/tex]
The car will be worth $1000 after 12.7 years.
HELP MEEEEEEE PLEASE
Answer:
C
Step-by-step explanation:
no of rulers each student gets,=,no of rulers ÷ no of students
........=83÷s OR
83/s
The speed s in m/s of an athlete can be modeled by the
function
s = 9.8 – 9.8e-0.88t
where t is the time (in seconds) after the
athlete starts running. Graph this model and use the graph to
estimate the speed of the athlete 2 seconds after his launch.
Round your answer to the nearest whole m/s.
speed m/s
Answer:
Step-by-step explanation: The equation is s = 9.8 – 9.8e-0.88t and we need to find the speed if t or time = 2 so to solve this equation algebraically you would;
[tex]s = 9.8-9.8e-0.88(2)[/tex]
[tex]s = 9.8-9.8e-1.76[/tex]
[tex]s = 8.04-9.8e[/tex]
and after graphing it you would get
[tex]-18.5991619189[/tex]
which after rounding and using absolute value would be
[tex]s=18.6[/tex]
Shilpa's gym membership includes a one-time fee
of $20. She then pays a discounted fee of $5 for
each visit. The function that shows her average
cost after x visits is:
f(x)=20+5x/x
Recall the general form of a rational function:
Answer:
if she goes 5 days a week then she will pay 45 dollars
she only had 2 pay 20$ one time and she pays 5 dollars each visit and she goes 5 times a week
5x5 is 25 and plus 20 will be 45 just within only that weel
I need help its urgent ASAP will mark you the brainliest
9514 1404 393
Answer:
BE = 266 2/3
PE = 233 1/3
Step-by-step explanation:
Part A: The figure has 3 triangles, all similar. In order of shortest-to-longest side lengths, they are ...
ΔBPE ~ ΔBCG ~ ΔGRE
__
Part B: They can be declared similar by the AA postulate. For BPE and BCG, the angles at B are vertical angles, so are congruent. The angles at C and G are alternate interior angles, so are congruent.
For triangles BPE and GRE, angle E is congruent to itself, The angles at R and P are corresponding angles, so are congruent.
(Remember, GRPC is a parallelogram, so any line in the figure is a transversal crossing parallel lines.)
__
Part C:
From parts A and B, we know ΔBPE ~ ΔBCG. Corresponding sides are proportional:
BP/BC = BE/BG = PE/CG
200/300 = BE/400 = PE/350
BE = (400)(2/3) = 266 2/3
PE = (350)(2/3) = 233 1/3
Members of a community garden grow 500 vegetable plant
sprouts. They donate 10% of the sprouts to a school. They
sell 20% of the remaining sprouts to a local park. They plant
5% of those left in a greenhouse. Then they plant the rest of
the sprouts outside. How many sprouts do the members
plant outside? Show your work.
Answer:
342 sprouts are planted outside.
Step-by-step explanation:
500 sprouts
500*0.10=50
500-50=450
450*0.20=90
450-90=360
360*0.05=18
360-18=342
Dorothy opens a savings account with $80 that earns 8.5% interest
per year, not compounded.
How much money, to the nearest penny, will Dorothy have in 1 year?
Give your answer in dollars.
Answer:
$86.8
Step-by-step explanation:
Given that,
Principal, P = $80
Rate of interest, R = 8.5%
We need to find the money he will have in 1 year. As the interest is not compounded, it must be simple interest. The simple interest can be calculated by the formula,
[tex]I=\dfrac{PRT}{100}\\\\I=\dfrac{80\times 8.5\times 1}{100}\\\\=\$ 6.8[/tex]
We know that,
Amount = Principal + interest
= $80 + $6.8
= $86.8
Hence, the amount will become $86.8.
In a sequence of numbers, a4=9, a5=13, a6=17, a7=21, and a8=25.
Which equation can be used to find the nth term of the sequence, an?
A = an=4n+9
B = an=7n−4
C = an=4n−7
D = an=9n+4
Answer:
The answer is C i.e an=4n-7
What type of polynomial is 14x2 + 3x – 15?
Answer:
Step-by-step explanation:
There are three terms. So, 14x² + 3x -15 is a trinomial
Find the conjugate and product of
i2 + 9
Answer:
i2 - 9
-85
Step-by-step explanation:
Conjugate of an expression is gotten by simply changing the sign to the opposite sign. For example, the conjugate of 5 is -5, the conjugate of x+2 is x-2. Given the complex value 2i+9, the conjugate will be -85
Taking their product
(2i+9)(2i-9)
Expand
2i(2i)-9(2i)+9(2i)+9(-9)
= 4i²-18-+18i-81
= 4i² - 81
Since i² = -1
= 4(-1) - 81
= -4-81
= -85
Hence the product will give -85
Decide whether the following statement is true or false. An infinite number of triangles can be created using the same three angle measures
Answer:
True
Step-by-step explanation:
I took the test!
Answer:
true is the answer
There are an infinite number of triangles which can be constructed with angles measuring this.
There are an infinite number of lengths the sides of the triangles can be while the angles stay the same measure.
There are 15 balls in an urn. 5 red balls, 5 blue balls and 5 white balls. Three balls are taken simultaneously. Let X represent the number of Blue balls. Please Help (Random Variable)
Answer:
X = 33.3 percent
Step-by-step explanation:
Write an
equation of the cosine function with amplitude 3 and period 81.
Answer:
y = 3cos(81x)
Step-by-step explanation:
Hello!
Here is the foundational equation to find sine and cosine:
y = A sin(B(x + C)) + D
Any cosine function can be written as a sine function. y = A sin(Bx) and y = A cos(Bx). The number, A, in front of sine or cosine changes the height of the graph. The value A (in front of sin or cos) affects the amplitude (height). B is the period by which the width of the wavelengths are measrured. C is known as the phase shift, which is positive to the left on graph. D is the vertical shift of function.
The amplitude changes the heaight of the cosine function by 3 units. The period is indicated as 81 and , but usually we must first use the equation that is the usual given: period = [tex]\frac{2\pi }{|B|}[/tex] . B must always have an absolute sign to have a psotive value. In this case, the period was given to us.
So, the final equation looks like this:
y = 3cos(81x)
Hope this helps!
NEED HELP FAST‼️‼️
What are the vertices of Triangle A'B'C' after Triangle ABC is reflected across the y-axis?
A (-5,3), B(-1,-3) and C(2,0)
Answer:
Step-by-step explanation:
A ' = (-2, -3)
B ' = (0, -3)
C ' = (-1, 1)
=======================================================
Explanation:
To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.
Algebraically, the reflection rule used can be written as
Applying this rule to the three given points will mean....
Point A = (-2, 3) becomes A ' = (-2, -3)
Point B = (0, 3) becomes B ' = (0, -3)
Point C = (-1, -1) becomes C ' = (-1, 1)
The diagram is provided below.
Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.
If g(x) = 3^Vx-123, find g( - 2).
Answer:
g(-2) = -5
Step-by-step explanation:
We are given the following function:
[tex]g(x) = \sqrt[3]{x - 123}[/tex]
Find g( - 2).
This means that we find g when [tex]x = -2[/tex]. So
[tex]g(-2) = \sqrt[3]{-2 - 123} = \sqrt[3]{-125} = \sqrt[3]{-5^3} = -5[/tex]
So
g(-2) = -5
The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool?
O: The height of the water increases 2 inches per minute.
O: The height of the water decreases 2 inches per minute.
O: The height of the water was 2 inches before any water was added.
O: The height of the water will be 2 inches when the pool is filled
Answer:
answer is a
the height of the water increases 2 inches per minute
Answer:
The height of the water increases 2 inches per minute.
Step-by-step explanation:
—statistics and probability, rules of probability
Question:
Mary has 10 blouses hanging in her closet— 5 are blue, 2 are black, and the rest are red. if she hangs the blouse in a random order, what is the probability that the first and last blouse are both red?
A. 0.011
B. 0.067
C. 0.042
D. 0.001
Answer:
B. 0.067
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Number of arrangements:
The number of possible arrangements of n elements is given by:
[tex]A_{n} = n![/tex]
Desired outcomes
First red(10 - (5+2) = 3 possible)
Last red(2 possible).
Middle 8 arranged in any way.
So
[tex]D = 3*A_{8}*2 = 3*8!*2 = 241920[/tex]
Total outcomes:
Arrangements of 10 elements. So
[tex]T = A_{10} = 10! = 3628800[/tex]
What is the probability that the first and last blouse are both red?
[tex]p = \frac{D}{T} = \frac{241920}{3628800} = 0.067[/tex]
The correct answer is given by option B.
Approximate, in miles, the circumference of a circle with radius equal to 7/11 miles. (Use 22/7 to approximate .)
Answer: 4 miles
Step-by-step explanation:
The circumference of a circle can be calculated by using the formula:
= 2πr
where,
π = 22/7
r = radius = 7/11 miles
Therefore, circumference = 2πr
= 2 × 22/7 × 7/11
= 4 miles
Th circumference is 4 miles.
Quarterback Joe Tarkenton can throw a football downfield at a speed of 60 feet per second. When releasing the ball, his arm is 6 feet above ground. The height of the ball after seconds is given by the function: h(t)=−16^2+60+6.
What is the maximum height of the football?
If the ball is not caught, how many seconds will it take to reach the ground after being thrown?
A: maximum height=3.58 feet; time=62.25 seconds
B: maximum height=62.52 feet; time=3.58 seconds
C: maximum height=62.25 feet; time=3.85 seconds
D: maximum height=3.85 feet; time=62.52 seconds
Answer:
C: maximum height=62.25 feet; time=3.85 seconds
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
In this question:
The height of the ball, after t seconds, is given by the following equation:
[tex]h(t) = -16t^2 + 60t + 6[/tex]
Which is a quadratic equation with [tex]a = -16, b = 60, c = 6[/tex]
Maximum height:
Since a < 0, we can find the maximum value of the function. We have that:
[tex]\Delta = 60^{2} - 4(-16)(6) = 3984[/tex]
[tex]y_{v} = -\frac{3984}{4(-16)} = 62.25[/tex]
The maximum height is of 62.25 feet.
Seconds to reach the ground:
[tex]x_{1} = \frac{-60 + \sqrt{3984}}{2*(-16)} = -0.1[/tex]
[tex]x_{2} = \frac{-60 - \sqrt{3984}}{2*(-16)} = 3.85[/tex]
Since time is a positive measure, 3.85 seconds.
The correct answer is given by option C.
Can someone help me with this please ?
Answer:
radius is 2.5 cm
hope it helps.
Answer:
radius = 2 1/2 cm or 2.5 cm
Step-by-step explanation:
diameter = 5 cm
radius = 5/2 = 2 1/2 cm
Arithmetic Summation
Find the sum of the first n terms of the arithmetic series.
40 + 37 + 34 +31 +...
n=20
Answer:
142
Step-by-step explanation:
hope this help love y all!
Automobile repair costs continue to rise with and average cost now at $367 per repair. Assume that the cost for an automobile repair has a standard deviation of $88.
F/2 + 9 =4
-9 -9
F/2=
Answer:
your wrong lol im sry btw this is a alt XDDD
Step-by-step explanation:
Trigonometry problem
Answer:
22.3923
Step-by-step explanation:
Calculated based on 2 given angles and 1 given side.
∠A = 180° - B - C = 1.309 rad = 5/12π = 75°
a = b·sin(A)/sin(B) = 22.3923
c = b·sin(C)/sin(B) = 23.18222
Answer:
this would be 90 because you would need to multiply to answer it
Step-by-step explanation:
P+p+p/2+p/4+1=100
Polinomios
Answer:
=
3
6
Step-by-step explanation:
+
+
2
+
4
+
1
=
1
0
0
{\color{#c92786}{p}}+{\color{#c92786}{p}}+\frac{p}{2}+\frac{p}{4}+1=100
p+p+2p+4p+1=100
2
+
2
+
4
+
1
=
1
0
0. 2
+
2
+
4
+
1
=
1
0
0
2p+\frac{p}{2}+\frac{p}{4}+1=100
2p+2p+4p+1=100
2
+
2
+
4
+
1
−
1
=
1
0
0
−
1. Subtract the numbers
Subtract the numbers
2
+
2
+
4
=
9
=
3
6
.
Math..
from the four letters L,O,V,E, choose one letter if order is not important