Answer:
[tex]a_5 = 21[/tex]
Step-by-step explanation:
Arithmetic sequence:
In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + d(n-1)[/tex]
In which [tex]a_1[/tex] is the first term and d is the common difference.
In this question:
[tex]a_1 = 5, d = 4[/tex]. So
[tex]a_n = a_1 + d(n-1)[/tex]
[tex]a_n = 5 + 4(n-1)[/tex]
Find the value of a_5
[tex]a_n = 5 + 4(n-1)[/tex]
[tex]a_5 = 5 + 4(5-1) = 5 + 16 = 21[/tex]
So
[tex]a_5 = 21[/tex]
The [tex]a_{5}[/tex] term of an arithmetic sequence is 21.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant, and this difference is called the common difference.
The nth term of the sequence is given by
[tex]\rm a_{n} =a_{1} + (n-1)d\\[/tex]
[tex]a_{1}[/tex]= the first term of the sequence and d is a common difference.
[tex]\rm a_{1} = 5, d=4\\\rm a_{n} =a_{1} + (n-1)d\\\rm a_{n} = 5 + 4(n-1)\\\rm a_{5} = 5 + 4(5-1)\\\rm a_{5} = 21[/tex]
Therefore, The [tex]a_{5}[/tex] term of an arithmetic sequence is 21.
Learn more about arithmetic here;
https://brainly.com/question/2171130
HELP TIMER Write the equation of a hyperbola centered at the origin with x-intercept +/- 4 and foci of +/-2(squareroot 5)
Given:
x-intercepts of the hyperbola are ±4.
The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].
Center of the hyperbola is at origin.
To find:
The equation of the hyperbola.
Solution:
The general equation of a hyperbola:
[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex] ...(i)
Where, (h,k) is the center of the hyperbola, ±a are x-intercepts, [tex](\pm c,0)[/tex] are foci.
Center of the hyperbola is at origin. So, h=0 and k=0.
x-intercepts of the hyperbola are ±4. So,
[tex]\pm a=\pm 4[/tex]
[tex]a=4[/tex]
The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].
[tex]\pm c=\pm 2\sqrt{5}[/tex]
[tex]c=2\sqrt{5}[/tex]
We know that,
[tex]a^2+b^2=c^2[/tex]
[tex](4)^2+b^2=(2\sqrt{5})^2[/tex]
[tex]16+b^2=20[/tex]
[tex]b^2=20-16[/tex]
[tex]b^2=4[/tex]
Taking square root on both sides, we get
[tex]b=\sqrt{4}[/tex] [b>0]
[tex]b=2[/tex]
Substituting [tex]h=0,k=0,a=4,b=2[/tex] in (i), we get
[tex]\dfrac{(x-0)^2}{4^2}-\dfrac{(y-0)^2}{2^2}=1[/tex]
[tex]\dfrac{x^2}{4^2}-\dfrac{y^2}{2^2}=1[/tex]
Therefore, the correct option is (d).
Multiply and combine like terms to determine the product of these polynomials. (3x−6)(4x+1)
m) Factorise:
x2/9+1+9/x2
Answer:
Cannot be factored
Step-by-step explanation:
Given
[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2}[/tex]
Required
Factorize
Take LCM
[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2} = \frac{x^4+9x^2+81}{9x^2}[/tex]
The expression cannot be factored
Element X is a radioactive isotope such that its mass decreases by 73% every
hour. If an experiment starts out with 680 grams of Element X, write a
function to represent the mass of the sample after t hours, where the rate of
change per minute can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the
percentage rate of change per minute, to the nearest hundredth of a percent.
Mi
Answer:
Step-by-step explanation:
The element decay percentage rate of change 2.22% per minute.
What is radioactive isotope?
Radioisotope, radionuclide, or radioactive nuclide, any of several species of the same chemical element with different masses whose nuclei are unstable and dissipate excess energy by spontaneously emitting radiation in the form of alpha, beta, and gamma rays.
Here, mass decreases by 73% every hour.
Weight of element X is 680 grams.
According to question,
f(t) = 680 (1 - 73%)ⁿ
f(t) = 680 (1 - 0.73)ⁿ
f(t) = 680 X 0.27ⁿ
f(t) = 680 X 0.9778ⁿ
f(t) = 680 X (1 - 0.02322)ⁿ
Thus, the element decay percentage rate of change 2.22% per minute.
Learn more about radioactive isotope from:
https://brainly.com/question/1907960
#SPJ2
Find the area of the figure shown below. Use 3.14 for π. Use the formula π x r^2 to find the area of a full circle.
A)32.84 in
B)38.13 in
C) None of these answers
D)62.13 in
E)161.04 in
Answer:
c
Step-by-step explanation:
none of the answers are correct. The area of the figure is 51.53 in^2 and none of the answers are 51.53 in^2, therefore it is c.
Answer:
D. 62.13 in²
Step-by-step explanation:
the area = (8×6)+(½×3.14×3²)
= 48+14.13
= 62.13
Please help and show work please and please no sending links
What is the equation of the line through (4, 2) and (0, -2)?
Answer:
y=x-2
Step-by-step explanation:
4-0=4 = (change in y)
2--2=4 = (change in x)
change in y/change in x=4/4=1=x
gradient = x
y=x+c
Subtitute any coordinate
2=4+c
c=-2
so
y=x-2
Answer:
y=x-2
Step-by-step explanation:
Slope Intercept Form
y=x-2
Find Slope using equation below
Chose points I chose 2 as y2 and -2 as y2
4 is x2 and 0 as x1
Slope is 1
now choose a point and plug it in for x and y and plug slope in Equation
I chose (4,2)
2=4+b
subtract 4 by both sides
-2=b
Slope Form
So... y=x-2 is the answer
Leila buys candy that costs 8 dollars per pound. She will spend more than 40 dollars on candy. What are the possible numbers of pounds she will buy?
Answer:
She must buy more than 5 lbs
Step-by-step explanation:
First write the inequality
cost per pound * number of pounds > total cost
8 * lbs > 40
Divide each side by 8
8 lbs /8 > 40/8
lbs > 5
She must buy more than 5 lbs
Find the slope of the line that passes through the points (-5,-6) and (5,10)
what is equivalent to 7w +7w
Answer:
14w
Step-by-step explanation:
Hope this helps
GIVING OUT BRAINLIEST HELP ME OUT PLSSS
Answer:
90 degrees but mom not too sure
Find the median and mean of the data set below:
48,32,5, 13, 11, 22, 2
Answer:
the median is 13 and the mean is 13
1
Calculate the height, A. and the width, B. of the spice
cabinet shown in the figure. Don't forget to include the
1
--inch thickness of the wood where needed. The symbol
hardwood for all framing parts.
" means inches,
This
3
The height, A, of the spice cabinet is inches
(Type an integer, proper fraction, or mixed number.)
on
Answer:
Height A = [tex]12\frac{3}{4}[/tex] inches
Step-by-step explanation:
Height A = Sum of widths of all sections of the cabinet + thickness of the wood
Height A = [tex]1\frac{1}{4}+\frac{1}{4}+4\frac{1}{2}+\frac{1}{4}+4\frac{1}{2}+2[/tex]
= [tex](1+4+4+2)+(\frac{1}{4}+\frac{1}{4}+\frac{1}{2}+\frac{1}{4}+\frac{1}{2})[/tex]
= [tex]11+(\frac{1+1+2+1+2}{4} )[/tex]
= [tex]11+\frac{7}{4}[/tex]
= [tex]11+1\frac{3}{4}[/tex]
= [tex]11+1+\frac{3}{4}[/tex]
= [tex]12\frac{3}{4}[/tex] inches
SOMEONE HELP ME PLEASE
Answer:
y = 90
Step-by-step explanation:
You can use proportions to answer this question.
[tex]\frac{30}{-3} =\frac{y}{-9}[/tex]
Cross multiply 30 to -9; -3 to y
[tex]-270=-3y[/tex]
Isolate y by dividing -3 on both sides
[tex]y=90[/tex]
Answer:
90
Step-by-step explanation:
30/-3 = ?/-9
Cross Multiply-
30 × -9 = -270
-3 × ? = -3
-270 ÷ -3 = 90
y = 90
A sensor output was acquired for 32 seconds at a rate of 200 Hz and spectral analysis was performed using FFT. If the data set was split into 5 segments (each 6.4 seconds long), what is the resulting: F minimum
Complete Question
A sensor output was acquired for 32 seconds at a rate of 200 Hz and spectral analysis was performed using FFT. If the data set was split into 5 segments (each 6.4 seconds long), what is the resulting:
a)F minimum
b) F maximum
c) Frequency resolution
Answer:
a) [tex]Fmax=100Hz[/tex]
b) [tex]Fmin=0Hz[/tex]
c) [tex]F_r=0.0313[/tex]
Step-by-step explanation:
From the question we are told that:
Time [tex]t=32sec[/tex]
Frequency[tex]F=200Hz[/tex]
Segments [tex]\mu=5[/tex]
Generally the equation for Frequency Range is mathematically given by
[tex]Fmax=\frac{F}{2}[/tex]
[tex]Fmax=100Hz[/tex]
Therefore
a) [tex]Fmax=100Hz[/tex]
b) [tex]Fmin=0Hz[/tex]
c)
Generally the equation for Frequency Resolution is mathematically given by
[tex]F_r=\frac{F}{N}[/tex]
Where
N=The Total dat points
N=Sampling Frequency *Time
[tex]N=200*32[/tex]
[tex]N=6400[/tex]
Therefore
[tex]F_r=\frac{200}{6400}[/tex]
[tex]F_r=0.0313[/tex]
(a)
There are 3 liters of orange juice at a school party. 10 students want to drink all of the orange juice, and they all want to get exactly the same amount. How much orange juice can each get?
Answer: 0.3
Step-by-step explanation:
The point ( - 14,12) is on the graph of y = f(x). Find the corresponding point on the graph of y= qe), where gex) = arcus.
The corresponding point on the graph of y = g(x) is
(Simplify your answer. Type an ordered nair
Answer:
[tex](-14,4)[/tex]
Step-by-step explanation:
Given
[tex](-14,12)[/tex] [tex]\to[/tex] [tex]y =f(x)[/tex]
[tex]g(x) = \frac{1}{3}f(x)[/tex]
Required
The corresponding point on [tex]y = g(x)[/tex]
[tex](-14,12)[/tex] [tex]\to[/tex] [tex]y =f(x)[/tex] means:
[tex]12 = f(-14)[/tex]
or
[tex]f(-14)=12[/tex]
[tex]g(x) = \frac{1}{3}f(x)[/tex] is calculated
[tex]g(-14) = \frac{1}{3} * f(-14)[/tex]
[tex]g(-14) = \frac{1}{3} * 12[/tex]
[tex]g(-14) = 4[/tex]
So, the corresponding point on [tex]y = g(x)[/tex] is: [tex](-14,4)[/tex]
3.4 0.8 0.6 find the volume of the rectangular prism in cubic feet
Given:
Consider the dimensions of the rectangular prism are 3.4 ft by 0.8 ft by 0.6 ft.
To find:
The volume of rectangular prism.
Solution:
The volume of a cuboid or rectangular prism is:
[tex]V=l\times b\times h[/tex]
Where, l is length, b is breadth and h is height of the prism.
The dimensions of the rectangular prism are 3.4 ft by 0.8 ft by 0.6 ft. So, the volume of the prism is:
[tex]V=3.4\times 0.8\times 0.6[/tex]
[tex]V=1.632[/tex]
Therefore, the volume of the rectangular prism is 1.632 cubic feet .
two mangoes cost $60.00. what is the cost of 5 mangoes
Answer:
Im not 100% sure but i think it would be $150.00
Step-by-step explanation:
Because if 2 mangos are $60
whats half of 60$
30
so 1 mango = $30
the person wants 5 mango so
multiply
$30*5
which would give you
$150.00
Answer:
$150
Step-by-step explanation:
If 2 mangoes cost $60, then 1 mango would be 60/2=30.
5 mangos would be 30×5=$150
Please help translate into an algebraic expression.
Five more than the product of 15 and a number.
Answer:
15a + 5
Step-by-step explanation:
Determine if each proportion on the left is True or False. Answer options on the right side may be used more than once.
True
False
28/16=14/8
3/5=9/15
4/32=10/78
3/4=12/16
Answer:
28/16=14/8 true
3/5=9/15 true
4/32=10/78 false
3/4=12/16 true
Step-by-step explanation:
DID IT ON BRIDGE
Suppose Duarte is one of the ten cities in the air pollution survey. We found that the number of manufacturing enterprises employing 20 or more workers in Duarte is 200, and the annual mean concentration of sulfur dioxide in Duarte is 18 micrograms per cubic meter. What is the residual for the city of Duarte
Kindly check complete question in the attached picture below.
Answer:
2.2236
Step-by-step explanation:
From the R output given, we can obtain the linear regression model in the form ;
y = bx + c
Intercept, c = 9.4764
Slope, b = 0.0315
x = number of manufacturing enterprise employing 20 or more workers
y = annual mean concentration of Sulphur dioxide
Hence, The regression equation model as obtained from the R output is :
y = 0.0315x + 9.4764
For the city of Duarte;
x = 200
Actual annual mean concentration of Sulphur dioxide is 18 micrograms per cubic meter.
Residual = Actual value - predicted value
Prediction using the regression equation to obtain the predicted annual mean concentration ;
The predicted y value, when x = 200
y = 0.0315(200) + 9.4764
y = 15.7764
The residual, if actual annual concentration = 18
Y residual = 18 - 15.7764 = 2.2236
Sara makes a triangle using three sticks of lengths 20 cm, 21 cm, and 28 cm. Is the triangle a right triangle ? Please explain
Answer:
No, 20^2 + 21^2 ≠ 28^2
Step-by-step explanation:
The sides of which diagram are correctly labeled with respect to angle A?
A right triangle is shown. Angle A is opposite to the side labeled adjacent.
A right triangle is shown. Angle A is opposite to the side labeled opposite. The hypotenuse is opposite to the right angle.
A right triangle is shown. Angle A is opposite to the side labeled opposite. The side labeled adjacent is opposite to the right angle.
A right triangle is shown. Angle A is opposite to the side labeled hypotenuse. The side labeled adjacent is opposite to the right angle.
9514 1404 393
Answer:
(b) Angle A is opposite to the side labeled opposite. The hypotenuse is opposite to the right angle.
Step-by-step explanation:
The hypotenuse is always opposite the right angle.
The side considered "opposite" is opposite the angle of interest, angle A in this case.
Answer:
Other person is correct
Step-by-step explanation:
Find the volume in the shape
Answer:
1205.76 m^3
Step-by-step explanation:
given:
radius = 8m
height = 18 m
volume of a cone = πr2h/3
=3.14 * (8)^2 * 18/3
=3.14 *64 *18/3
=3617.28/3
=1205.76 m^3
An English teacher needs to pick 4 books to put on his reading list for the next school year. He has narrowed down his choices to 8 novels and 6 plays.
a. How many different ways can he choose the books to put on the list if he wants to include at least two plays?
b. Find the standard deviation.
Answer:
A) 3 ways
B) sorry don't know.
Step-by-step explanation:
2 P and 2 N
3P and 1 N
4P
So 3 ways.
How many factors does the following number have?
Step-by-step explanation:
myballsnahajahahahahahahahhahajaajjaajjaaaaaja
Answer: 135
exponents are :2,4,8
add on to each: 3,5,9
3*5*9 = 135
Step-by-step explanation:
Helppppppppppppppppppppppppppppppppppppp
Answer:
diiiiifiiiciiillllllñ
Answer:
Step-by-step explanation:
a - yes
b - yes
c - yes
d - yes
e - yes
PLEASE HELP!!!
WORTH 20 POINTS!!!
WILL MARK BRAINLIEST!!!
Use the triangle below to answer the following questions.
Thank you!
Answer: 1. 1/2
2. √3\2
3. √3
A mountaineer climbed 1,000 feet
Answer:
please complete your question
Answer:
its a (i had to find ur question online hopefully i found the right one)
