The 56th term of the following arithmetic sequence 7,10,13,16 is 172.
What is the arithmetic sequence?
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.
Here, we have
Given
Arithmetic sequence 7,10,13,16.
We have to find the 56th term.
The common difference between terms: 10 - 7 = 3
Using the arithmetic progression formula:
nth term = first term + (n-1)* common difference
56th term = 7 +(56-1) 3
56th term = 7 + 55×3
56th term = 7 + 165
56th term = 172
Hence, the 56th term of the following arithmetic sequence 7,10,13,16 is 172.
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Is -6,-3 a solution to 2x-9y=15
Answer: Yes
Step-by-step explanation:
Assuming that (-6, -3) is a coordinate, you just plug in the x and y values. When doing this you multiply 2 * - 6 and add that to -9 * -3This gives you -12 + 27 = 15This gives you 15 = 1515 is equal to 15 therefore, this is a solution to the problem.I hope this makes sense! : )
A continuous random variable X has probability density function f(x) = c(1+x)(1 - 2 over the domain -1<<1. (a) i. Evaluate the constant e (the integration can be done by MATLAB). ii. Plot the probability density function over the domain (-1,1). Is this density function skewed to the right, skewed to the left, or symmetric? (b) Use MATLAB to evaluate I i. the mean y = E(X)= |- «f(x) dx; ii. E(X)= (- 22 f(x) dx; iii. the variance o2 = Var(X) = E(X) – H?, and the standard deviation o. *(c) i. Use MATLAB to find an expression for the cumulative distribution function F(x). ii. Check the result in (i) by differentiation. Hint: simplify (ans) might help! iii. Evaluate P(-0.2 X <0.2).
(a)i. Evaluating the constant:
\($$\int_{-1}^{1} c(1+x)(1-2x) dx = 1$$$$\implies c = \frac{3}{4}$$\)
Therefore, the probability density function is:
\($$f(x) = \frac{3}{4} (1+x)(1-2x), -1< x < 1$$\) ii. Plotting the probability density function:
From the graph, it is observed that the density function is skewed to the left.
(b)i. The mean:
\($$E(X) = \int_{-1}^{1} x f(x) dx$$$$E(X) = \int_{-1}^{1} x \frac{3}{4} (1+x)(1-2x) dx$$$$E(X) = 0$$\)
ii. The second moment about the origin:
\($$E(X^2) = \int_{-1}^{1} x^2 f(x) dx$$$$E(X^2) = \int_{-1}^{1} x^2 \frac{3}{4} (1+x)(1-2x) dx$$$$E(X^2) = \frac{1}{5}$$\)
Therefore, the variance is:
\($$\sigma^2 = E(X^2) - E(X)^2$$$$\implies \sigma^2 = \frac{1}{5}$$\)
iii. The standard deviation:
$$\sigma = \sqrt{\sigma^2} = \sqrt{\frac{1}{5}} = \frac{\sqrt{5}}{5}$$(c)
i. The cumulative distribution function:
\($$F(x) = \int_{-1}^{x} f(t) dt$$$$F(x) = \int_{-1}^{x} \frac{3}{4} (1+t)(1-2t) dt$$\)
ii. The probability density function can be obtained by differentiating the cumulative distribution function:
\($$f(x) = F'(x) = \frac{3}{4} (1+x)(1-2x)$$\)
iii. Evaluating\(P(-0.2 < X <0.2):$$P(-0.2 < X <0.2) = F(0.2) - F(-0.2)$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} f(x) dx$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} \frac{3}{4} (1+x)(1-2x) dx$$$$P(-0.2 < X <0.2) = 0.0576$$\)
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In trapezoid ABCD below, angles B and C are right angles.
(a) Circle the two sides from the four choices below that are parallel.
AB
BC
CD
DA
b) Find the area of the right trapezoid by breaking it
into a rectangle and right triangle and summing
their areas.
Rectangle:
Sum of areas:
Right Triangle:
D
24 cm
A
6 cm B
16 cm
C
The parallel sides are AB and CD while the area of the Trapezium is 240cm²
A.)
Parallel sides are directly opposite one another and their lines never meet. lines AB and CD.
Therefore, the two parallel sides are AB and CD
B.)
Area of Trapezium = Area of Rectangle + Area of Triangle
Area of rectangle = Length * width
Area of rectangle = 6 * 16 = 96 cm²
Area of Triangle = 1/2*base*height
Area of Triangle= 1/2 * 18 * 16
Area of Triangle = 144 cm²
Hence, area of Trapezium is 240 cm²
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Why do the pole and zero of a first order all pass filter's transfer function representation on the s-plane have to be at locations the Symmetrical with respect to jW axis? Explain.
In a first-order all-pass filter, the transfer function in the Laplace domain can be represented as H(s) = (s - z) / (s - p), where 'z' represents the zero and 'p' represents the pole of the filter. To understand why the pole and zero locations must be symmetrical with respect to the jω axis (imaginary axis), let's examine the filter's frequency response.
When analyzing a filter's frequency response, we substitute s with jω, where ω represents the angular frequency. Substituting into the transfer function, we get H(jω) = (jω - z) / (jω - p). Now, consider the magnitude of the transfer function |H(jω)|.
If the zero and pole are not symmetric with respect to the jω axis, then their distances from the axis would differ. As a result, the magnitudes of the numerator and denominator in the transfer function would not be equal for any given ω. Consequently, the magnitude response of the filter would be frequency-dependent, introducing gain or attenuation to the signal.
To maintain the all-pass characteristic, which implies that the filter only introduces phase shift without changing the magnitude of the input signal, the pole and zero must be symmetrically positioned with respect to the jω axis. This symmetry ensures that the magnitude response is constant for all frequencies, guaranteeing an unchanged magnitude but only a phase shift in the output signal, fulfilling the all-pass filter's purpose.
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Clare mixes 2 1/2 cups of water with 1/3 cup of orange juice concentrate
Han mixes 1 2/3 cups of water with 1/4 cup of orange juice concentrate
Who's juice is stronger?
when u logically think it should be 1 2/3cups of water with 1/4 cup of concentrated orange juice
Help please!
So far this basketball season, all of Nikkis points have come
from two-point and three-point field goals. She has scored a
total of 43 points. The number of three-point field goals she
has made is one more than twice as many two-point field
goals. How many of each type of field goal has Nikki made?
Answers:
5 two-pointers11 three-pointers=====================================================
Explanation:
x = number of two-pointers made
2x+1 = number of three-pointers made
This is because of the fact that she made one more than twice as many three-pointers than two-pointers.
In other words,
number of three pointers = 2*(number of two pointers) + 1
number of three pointers = 2x + 1
-------------------
If she made x two-pointers, then she gets 2x points from just those made shots.
If Nikki made 2x+1 three-pointers, then she gets 3(2x+1) = 6x+3 points from just the stuff beyond the arc.
In total, she earns (2x)+(6x+3) = 8x+3 points from both types of shots.
-------------------
Set this equal to the stated total 43 points and solve for x.
8x+3 = 43
8x = 43-3
8x = 40
x = 40/8
x = 5
Nikki made 5 two-pointers and 2x+1 = 2*5+1 = 11 three-pointers
--------------------
Check:
A = points from two-pointers only = 2*5 = 10 points
B = points from three-pointers only = 3*11 = 33 points
A+B = total points = 10+33 = 43 points
The answer has been confirmed.
CAN SOMEONE PLEASEEEE HELP/EXPLAIN THIS ASAP !!!
Answer:
5th figure is not symmetrical
comment if doubt
anyone knows the answer?
Answer:
20 miles
Step-by-step explanation:
x = break even miles
$10 + x($1.50 = x($2.00)
10 + 1.5x = 2x
0.5x=10
x = 20 miles
Solve the right triangle.
Round your answers to the nearest tenth.
Answer:
A = 32°. b = 22.4. c = 26.4
Step-by-step explanation:
Opposite is called opposite because it is the side that is opposite the angle we need to find. in this case, b is opposite side.
Hypotenuse (c) is always facing the 90-degree angle.
Adjacent (14) is the remaining side.
Sine = O/H = b/c
Cosine = A/H = 14/c
Tangent = O/A = b/14
In a right-angled triangle, a^2 + b^2 = c^2
Sine rule: a/SIN A = b/SIN B = c/SIN C
angles in a triangle add up to 180
angle A = 180 - 90 - 58 = 32°.
b/SIN 58 = 14/SIN 32, b = (14 X SIN 58) / SIN 32 = 22.4.
c² = 14² + 22.4². c = 26.4
Which number is greatest?6. 23 times 10 superscript 126. 23 times 10 superscript 86. 23 times 10 superscript negative 66. 23 times 10 superscript 3.
From the given numbers, the greatest number is 23 × 10^126
The first number = 23 × 10^126
The second number = 23 × 10^86
The third number = 23 × 10^66
The fourth number = 23 × 10^3
The scientific notation is defined as the easiest method to represents the very smallest or the largest number. The scientific notation consist of a whole number multiplied by the power of ten
Here, the whole number is same in all cases, only the power of the 10 is different . To find the largest number we have to find the number with largest power of 10
The number with largest power of 10 = 23 × 10^126
Hence, the greatest number is 23 × 10^126
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Optically active compounds rotate plane-polarized light. Match the direction of rotation with the correct term.
A. Clockwise
B. Counterclockwise
C. Dextrorotatory
D. Levorotatory
Optically active compounds can rotate plane-polarized light in
A - Clockwise rotation
B - Counterclockwise rotation
C - Dextrorotatory
D - Levorotatory
Optically active compounds can rotate the plane of polarization of light, which can be either clockwise or counterclockwise. The direction of rotation is usually expressed as either dextrorotatory (abbreviated as +) or levorotatory (abbreviated as -), depending on whether the compound rotates the plane of polarization to the right or left, respectively.
For example, a compound that rotates the plane of polarization to the right (clockwise) is said to be dextrorotatory (+), while a compound that rotates the plane of polarization to the left (counterclockwise) is said to be levorotatory (-).
Therefore, A corresponds to clockwise rotation, B corresponds to counterclockwise rotation, C corresponds to dextrorotatory, and D corresponds to levorotatory.
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-p(51+z) = Dz+84
Z=?
Answer:
\(z=\frac{3 (28 + 17p)}{p + D}\)
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
community college faculty is negotiating a new contract with the school board. The distribution of faculty salaries is skewed right by several faculty members who make over $100,000 per year. If the faculty impression that they deserve higher sales should they a r e the meanor median of their current salaries? A. The faculty should use the mean to make their argument. The mean will be higher than the median since the mean is influenced by the few extremely high res.B. The faculty should use the mean to make o rgument. The man will be lower than the median since it will be henced by the few high salariesC. The faculty should use the median to make their argument. The median will be higher than the mean since the media is unced by the high e s D. The faculty should use the median to make their argument. The median will be lower than me since the means i nced by the extremely histories
Option D. The faculty should use the median to make their argument. The median will be lower than the mean since the mean is influenced by the few extremely high salaries.
Mean is the average of any data set whereas the median is the middle value we get after arranging the data in ascending order.
So for example, if the salaries of any 5 faculty members are as follows:
$10,000 , $50,000 , $80,000 , $150,000 , $160,000
Mean= (10,000+50,000+80,000+150,000+160,000) / 5
Mean= $90,000
Median= (5+1) / 2
Median= 6/2
Median= 3rd value
As the data is already arranged in ascending order, Median is $80,000
Hence, if the faculty want to give the community the impression that they deserve higher salaries, they should advertise the median of their current salaries.
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a variable x is normally distributed with mean 10 and standard deviation 3. find the percentage of all possible values of the variable that:
The percentage of all possible values of the variable is 5.05 and 14.95
Given, mean= 10, and variance= 3.
P(6 <X<7)= P( (6-10)/3< Z< (7-10)/3 )
=P(-1.33<Z<-1)
=P(Z<-1)- P(Z<-1.33)
=0.669
P(X<=17.5)= P(Z<=(17.5-10)/3)
=P(Z<=2.5)
=0.9938
We need to find x’, such that P(X>=x’)=0.15
=>P(Z>= (x’-10)/3)= 0.15
=>P(z<= (x’-10)/3)= 0.85
Using the Normal table, (x’-10)/3 = 1.04
x’=13.11
We need to find x” such that P(X<=x”)= 0.05
>=P(Z<=(x”-10)/3)= 0.05
Using the Normal Table, (x”-10/3)= -1.65
x”= 5.05
Also, another value x’’’=> 10+ 1.65*3= 14.95
Therefore, the two values are 5.05 and 14.95
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if m is a nonzero integer then m 1/m is always greater than 1
T/F
If m is a nonzero integer, then m^(1/m) is not always greater than 1.
The statement is false.
To determine if m^(1/m) is greater than 1, we can consider different values of m. For positive values of m, such as m = 2, m^(1/m) = 2^(1/2) = √2, which is approximately 1.414 and greater than 1.
However, if we consider negative values of m, such as m = -2, m^(1/m) = (-2)^(1/(-2)) = (-2)^(-1/2), which is equal to 1/√(-2). Since the square root of a negative number is not defined in the real number system, the value of m^(1/m) is not defined for negative values of m.
Therefore, the statement that m^(1/m) is always greater than 1 for nonzero integers m is false.
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A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. What is the smallest possible sum for this series?
The smallest possible sum for this series is 20736 = 12^4.
Given:
A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power.
S = a + (a+2) + (a+4) + ... + (a+2*287) = 288(a+(a+574))/2 = 288(a+287)
288 = 2^5 * 3^2
smallest value of (a+287) that will make S = 288(a+287) a perfect fourth power is:
a + 287 = 2^3 * 3^2 = 72
a = −215
Smallest sum = 288*72 = 20736 = 12^4
Smallest odd integer in series = −215
−215 + −213 + −211 + ... + −1 + 1 + 3 + ... + 213 + 215 + ... + 359
= 20736 = 12^4.
Therefore the smallest possible sum for this series is 20736 = 12^4.
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Guillermo is a professional deep water free diver. His altitude (in meters relative to sea level), xxx seconds after diving, is modeled by g(x)=\dfrac{1}{20}x(x-100)g(x)= 20 1 x(x−100)g, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 20, end fraction, x, left parenthesis, x, minus, 100, right parenthesis How many seconds after diving will Guillermo reach his lowest altitude?
Answer: 140
Step-by-step explanation:
Answer: 50
Step-by-step explanation:
Khan academy answer
Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data. What do the results tell us? 40 39 8 82 25 53 97 1 28 41 94
Answer:
(a)Range = 96
(b)Variance=1059.36
(c)Standard Deviation =32.55
Step-by-step explanation:
(a)Range
Highest Value = 97Lowest Value = 1Range = Highest Value - Lowest Value
=97-1
=96
(b)Variance
The variance of a sample for ungrouped data is defined by the formula:
\(Variance, s^2 = \dfrac{\sum(x-\overline{x})^2}{n-1}\)
First, we determine the mean of the sample data.
\(Mean = \dfrac{40 +39+ 8+ 82+ 25+ 53+ 97+ 1+ 28+ 41+ 94}{11} \\=\dfrac{508}{11}\\\\ \overline{x}=46.2\)
\(\sum(x-\overline{x})^2=(40-46.2)^2 +(39-46.2)^2+ (8-46.2)^2+ (82-46.2)^2+ (25-46.2)^2+ (53-46.2)^2+ (97-46.2)^2+ (1-46.2)^2+ (28-46.2)^2+ (41-46.2)^2+ (94-46.2)^2\\\\=38.44+51.84+1459.24+1281.64+449.44+46.24+2580.64+2043.04+331.24+27.04+2284.84\)
=10593.64
Therefore:
Variance, Variance,
\(Variance, s^2 = \dfrac{10593.64}{11-1}\\\\=1059.36\)
(c)Standard Deviation
\(s=\sqrt{Variance}\\ =\sqrt{1059.36}\\s=32.55\)
The results tell us that there is great variability in the number of jerseys of the player as evidenced by the high standard deviation and range.
heh I kinda don't have my notes on this problem please look at the picture and help me thank you
Answer:
Step-by-step explanation: 6^4 would be 1296 because its 6 times 6 times 6 times 6. Then 6 times 6 times 6 times 6 times 6 times 6 times 6 times 6 would be 1,679,616. 6 times 6 times 6 would be 216. 1,679,616/216 would be 7776. 1296 times 7776 is 10,077,696.
Hoped This Helped!
Which angle is formed by a secant and tangent line?
A) ANG
B) GSE
B) EGS
C) NGL
The angle formed by a secant and tangent line is GSE (Given-Secant-Exterior).
A tangent is a straight line or curve that touches a given curve exactly once but does not cross it. The tangent is a fundamental concept in geometry and calculus that is used to study the behavior of functions at a specific point.
An external angle is the angle formed by a secant and tangent line at a point on a circle. The abbreviation for this angle is EGS (External Angle-Secant-Tangent).
A secant line intersects a circle at two points, whereas a tangent line intersects the circle at only one. The external angle is formed at the point of tangency by the intersection of the secant and tangent lines outside the circle.
Full question.
Which angle is formed by a secant and tangent line?
A) ANG
B) GSE
B) EGS
C) NGL
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Label the sides with its corresponding ratio in the special right triangle given below. The answer choice may be used more than once.
50 points.
HELP PLEASE :)
Answer:
See belowStep-by-step explanation:
It is isosceles right triangle so the sides will be a for legs, √2a for hypotenuse:
Legs 1 and 1, hypotenuse √2Legs √2 and √2, hypotenuse 2in a large ball pit, 20% of the balls are red. you plan to jump in and randomly select 10 balls. which statement is true? you are guaranteed to have exactly two red balls in your sample. you will likely have one to three red balls in your sample. you will most likely have eight red balls in your sample. it is unlikely that you will have exactly two red balls in your sample.
Answer:
You will likely have 1-3 balls in your sample.
Step-by-step explanation:
Samples aren't perfect, so you aren't guaranteed to have exactly 20% of your sample be red balls. However that isn't unlikely either. This eliminates the 1st and last options.
As for having 8, that's unlikely. While again it's
possible, to have a sample very so greatly from the actual percentages is unlikely.
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use the grid to create a model to solve the percent problem. what is 20% of 90? responses 12 12 14 14 16 16 18
The solution of 20% of 90 is, 18
We have,
Use the grid to create a model to solve the percent problem.
Here, We can simplify as,
= 20% of 90
= 20/100 x 90
= 18
Therefore, The solution of 20% of 90 is, 18
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What is the solution to the system of linear equations? Show your work using either substitution or elimination.
Need help rlly soon! Also please show work!
Answer:
x = 11 ; y =13
Step-by-step explanation:
3x - 2 y = 7 -------------(I)
y = x + 2 -----------(II)
Substitute y = x + 2 in equation (I)
3x - 2(x + 2) = 7
3x - 2*x + 2*(-2) = 7
3x - 2x - 4 = 7
x - 4 = 7
x = 7 + 4
x = 11
Plugin x = 11 in equation(II)
y = 11 + 2
y = 13
In circle G with m/FGH = 60 and FG = 18 units, find the length of arc FH
Round to the nearest hundredth
The length of arc FH is approximately 9.42 units when rounded to the nearest hundredth.
To find the length of arc FH in circle G, we need to use the formula:
Arc Length = (Central Angle / 360°) \(\times\) Circumference
First, let's calculate the central angle m/FGH in degrees:
m/FGH = 60°
Next, we need to find the circumference of the circle. We know that the radius of the circle is equal to half the length of FG:
Radius = FG/2 = 18/2 = 9 units
Circumference = 2 \(\times\) π \(\times\) Radius = 2 \(\times\) π \(\times\) 9
Now, let's substitute the values into the formula to calculate the arc length:
Arc Length = (60/360) \(\\\times\) (2 \(\times\) π \(\times\) 9)
Simplifying this expression:
Arc Length = (1/6) \(\times\) (18π) = 3π units
To round the answer to the nearest hundredth, we can substitute the value of π as approximately 3.14:
Arc Length ≈ 3 \(\times\) 3.14 ≈ 9.42 units
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Make x the subject:
y= (x+10)^2
Answer:
x = - 10 ± \(\sqrt{y}\)
Step-by-step explanation:
y = (x + 10)² , or
(x + 10)² = y ( take square root of both sides )
x + 10 = ± \(\sqrt{y}\) ( subtract 10 from both sides )
x = - 10 ± \(\sqrt{y}\)
what is the answer to 28r+24
Answer:
\(\boxed{\sf{4(7r+6)}}\)Step-by-step explanation:
In order to solve this problem, you must find the factor to use the distributive property.
Distributive property:
→ A(B+C)=AB+AC
28r+24
4*7=28
4*6=24
Rewrite the problem down.
4*7r+4*6
Solve.
4*7r=28r
4*6=24
28r+24
Therefore, the final answer is 4(7r+6).I hope this helps! Let me know if you have any questions!
if Anna's grade is a D and she gets a D on her final what will her new grade be?
Answer:
D or an F depends on the grading system
Step-by-step explanation:
Which expression is equivalent to 8 + 20 using the Distributive Property? A. 4(4+20) B. 4(2+5) C. 2(2+10) D. 2(6+18) EASY QUESTION PLZ HELP
Answer:
B. 4(2+5)
Step-by-step explanation:
4 * 2 = 8
4 * 5 = 20
Add the equation in and you get 8+20
Answer:
B
Step-by-step explanation:
4(5+2)
add the brackets.
4(7)
multiply
=28
(8+ 20 also equals 28)
In square units, what is the area of the blue sector in the figure above? Round to the nearest tenth.
Given:
A figure of a circle with radius 8. The central angle of the blue sector is 60 degrees.
To find:
The area of the blue sector.
Solution:
Area of a sector is:
\(A=\pi r^2\dfrac{\theta}{360^\circ}\)
Where, r is the radius and \(\theta \) is the central angle of the sector in degrees.
Putting \(r=8, \theta=60^\circ, \pi=3.14\), we get
\(A=(3.14)\cdot (8)^2\cdot \dfrac{60^\circ}{360^\circ}\)
\(A=(3.14) \cdot (64)\cdot \dfrac{1}{6}\)
\(A=33.49333....\)
Approximate the value to the nearest tenth.
\(A\approx 33.5\)
Therefore, the area of the blue sector is about 33.5 sq. units.