d) Jerry, Barry, and Harry went fishing and they each caught a giant fish! Jerry's fish is 62 inches long. Barry's fish is 7 feet long. Harry's fish is 2 yards long. Who caught the longest fish?
Answers
Related Questions
In the expansion of (2+3x)^n, the coefficients of x^3 and x^4 are in the ratio of 8:15. FIn the expansion of (2+3x)^n, the coefficients of x^3 and x^4 are in the ratio of 8:15. Find the value of n.ind the value of n.
Answers
The value of n is 8.
What is Binomial Theorem?Binomial theorem is the method of expanding an expression consisting of two terms raised to any power.
Using the expansion of Binomial theorem, we can write,
(2 + 3x)ⁿ = ⁿC₀ (2)ⁿ (3x)⁰ + ⁿC₁ (2)ⁿ⁻¹ (3x)¹ + ⁿC₂ (2)ⁿ⁻² (3x)² + ⁿC₃ (2)ⁿ⁻³ (3x)³ + ⁿC₄ (2)ⁿ⁻⁴ (3x)⁴ + .............
Coefficient of x³ is ⁿC₃ (2)ⁿ⁻³ (3)³ and the coefficient of x⁴ is ⁿC₄ (2)ⁿ⁻⁴ (3)⁴.
Ratio of these coefficients is 8 : 15.
[ⁿC₃ (2)ⁿ⁻³ (3)³] / [ⁿC₄ (2)ⁿ⁻⁴ (3)⁴] = 8 / 15
Simplifying,
(4 × 2) / [(n - 3) 3] = 8/15
8 / 3n - 9 = 8 /15
Equating, we have,
3n - 9 = 15
3n = 24
n = 8
Hence the value of n is 8.
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2. aₙ-1=aₙ-1 ÷ 2 where a₁=50 for n≥2
Answers
The nth term of the sequence is aₙ = 48 + 2n
How to determine the value of nth term?The definition of the function is given as
a₁= 50
aₙ = aₙ₋₁ + 2
The above definitions imply that we simply add 2 to the previous term to get the current term
Using the above as a guide, we have:
The common difference, d = 2
First term, a = 50
The nth term of the sequence is calculated as
aₙ = a₁ + (n - 1)* d
Substitute the known values in the above equation
So, we have the following representation
aₙ = 50 + (n - 1)* 2
So, we have
aₙ = 50 + 2n - 2
Evaluate the like terms
aₙ = 48 + 2n
Hence, the nth term is aₙ = 48 + 2n
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is this a rigid motion
Answers
The transformation in this problem is a translation combined with a reflection, hence yes, it is a rigid motion, as the side lengths of the transformed figure are equal to the side lengths of the original figure.
What are transformations on the graph of a function?Examples of transformations are given as follows:
Translation: Translation left/right or down/up.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor.The dilation is the only transformation that is not a rigid motion, as it changes the side lengths of the figure.
The transformation for this problem has the rule defined as follows:
(x,y) -> (x + 2, -y).
The transformations are defined as follows:
x -> x + 2 is a translation right two units.y -> -y is a reflection over the x-axis.Neither transformation is a dilation, hence it is a rigid motion.
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Kinda confused!! need help!!
Answers
Answer:
I think last option is correct
Answer:
Option 2. EG, DH, CG, FH
Step-by-step explanation:
Skew lines are lines that do not lie on the same plane, and they also never intersectLet's verify options
Option 1
AC is an exception, it intersects ABOption 2
All good, all lines are skew with ABOption 3
GH is an exception, Can be on the same plane with ABOption 4
CD is an exception, can be on the same plane with ABWrite a division problem with a quotient greater than 20 less than 25? What do you guys think?
Answers
Answer:
hmmm, how about 242 divided by 11? the answer is 22 r0
Step-by-step explanation:
what's the answer for this equation
x^3 - 3x^2 + 3x - 1 > 3/2x(x - 1)
Answers
hello
the answer to the question is:
x³ - 3x² + 3x - 1 > (3/2)x(x - 1)² ---->
(x - 1)³ > (3/2)x(x - 1)² ----> x - 1 > (3/2)x ---->
(1/2)x < - 1 ----> x < 2
0.00000083 in scientific notation
Answers
Answer:
8.3x10^7
Step-by-step explanation:
Answer:
8.3 x 10⁻⁷
Step-by-step explanation:
0.0000083 in scientific notation
To put numbers in scientific notation, you have one (1) non-zero digit in the ones place.
8.3 x 10ˣ
From 8.3, we would have to move the decimal place seven (7) places to the left (this means you put a negative sign in front of the exponent).
8.3 x 10⁻⁷
the displacement of a mass suspended on a spring is modeled by the function y=5sin(pit) where y is measured in inches and t in seconds. the amplitude period and frequency of the motion of the mass given by
Answers
The amplitude , period and frequency of the motion of the mass are :
Amplitude = 5 inches, Period = 2 seconds, Frequency = 0.5 cycles per second.
In the equation y = 5sin(πt), the function represents the displacement of a mass suspended on a spring.
Amplitude: The amplitude of the motion is the coefficient of the sine function, which is 5 in this case. The amplitude represents the maximum displacement of the mass from its equilibrium position. In this case, the maximum displacement is 5 inches.
Period: The period of the motion is the time it takes for the mass to complete one full cycle of oscillation. In this equation, the coefficient of t inside the sine function is π (pi). The period of the motion can be calculated using the formula T = 2π/ω, where T is the period and ω is the angular frequency. In this case, the angular frequency is π, so the period T is 2π/π, which simplifies to 2 seconds.
Frequency: The frequency of the motion is the reciprocal of the period and represents the number of cycles per unit of time. In this case, the frequency is 1/T, which is 1/2, or 0.5 cycles per second.
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A bag of trail weighs 1.625 pounds. Round 1.625 to the nearest hundredth. Use the number line for help.
Answers
Answer:
1.63 lb
Step-by-step explanation:
1.625 \|\ the five would round the two up to a three
1.63
which of the following is the correct point-slope equation for the line that passes through the point (2, -5) and is parallel to the line given by y = -4x + 25? A. y+5=-4(x-2) B. y-20=-4(x-2) C. y-20=-4x-2 D. y-5=-4(x+2)
Answers
Answer:
Step-by-step explanation:
y + 5 = -4(x - 2)
the answer is A
K > 18 Which value for K would make the inequality false? a) 33 b) 7 C) 21 d) 19
Answers
Answer:
b. 7
If the value of the K is 7 then the inequality K> 18 would be false.
Hope it will help :)❤
Answer:
B
Step-by-step explanation:
7 is not greater than 18
No links please! Which expression has the same value as
Look below
Answers
Answer:
-5 1/3 - 3 1/3
Step-by-step explanation
both expressions equal -8 2/3
Lin bought 4 bags of apples. Each bag had the same number of apples. After eating 1 apple from each, she had 28 apples left.
Write an equation that represents the story.
Answers
Answer:
Step-by-step explanation:
4(a-1) = 28
a = 8 apples per bag
you manage a restaurant and need to replace a broken dishwasher
Answers
Answer:
B
Step-by-step explanation:
3f–4g=1
6f–6g=5
use the elimination method
Answers
6f-6g= 5 —(2)
(1)x2:6f-8g= 2 —(1a)
(1a)-(2):(6f-8g)-(6f-6g)= 2-5
6f-8g-6f+6g= -3
-2g= -3
g= 3/2
Substitute g= 3/2 into (1):
3f-4(3/2)=1
3f-6=1
3f=7
f =7/3
I’m taking my dog to get groomed in the morning
Answers
A tank is draining water such that the volume is given which an exponentially decreasing graph as shown in the graph below. If the volume was modeled with an equation of the form V=a(b)^t, where t is the number of hours then which of the following is the best value for b?
(1) b=20
(2) b=0.6
(3) b=2.8
(4) b=0.3
Answers
Answer:
\(b = 0.3\)
Step-by-step explanation:
Given
\(V = ab^t\)
See attachment for graph
From the graph
V = 20 when t = 0
This implies that:
\(V = ab^t\)
\(20 = ab^0\)
\(20 = a * 1\)
\(20 = a\)
\(a = 20\)
Also:
V = 4 when t = 1.5
So:
\(4 = ab^{1.5\)
Substitute 20 for a
\(4 = 20 * b^{1.5\)
Divide by 20
\(0.2 =b^{1.5\)
\(b^{1.5} = 0.2\)
Take 1.5th root of both sides
\(b = 0.34199518933\)
\(b = 0.3\) --- approximated
The points A, B and C have position vectors a, b, c, referred to an origin O. i. Given that the point X lies on AB produced so that AB : BX = 2 : 1, find x, the position vector of X, in terms of a and b. ii. If Y lies on BC, between B and C so that BY : Y C = 1 : 3, find y, the position vector of Y, in terms of a and b iii. Given that Z is the midpoint of AC, Calculate the ratio XY : Y Z.
Answers
i. The position vector of X is 2b - a.
ii. The position vector of Y is (3b + c)/4.
iii. The ratio XY : Y Z is \(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\). Simplifying this expression will give us the final ratio.
i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.
ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.
iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =\(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\).
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Write an inequality for the graph
Answers
The inequality that represents the line in the figure will be y > - (2/3) x + 3.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
From the figure, the points of the line are (0, 3) and (3, 1). And the region above the line is a consideration. Then the equation of the line is given as,
(y - 3) > [(3 - 1) / (0 - 3)](x - 0)
Simplify the equation, then we have
(y - 3) > [(3 - 1) / (0 - 3)](x - 0)
(y - 3) > - (2/3)x
y > - (2/3) x + 3
The disparity that addresses the line in the figure will be y > - (2/3) x + 3.
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What is the volume of this prism?
23.9
47.7
9.0
4.5
Answers
This simple question does not require any statistical calculations, only statistical knowledge. The showerhead heights at a men’s athletic locker room were designed to be 72 inches which is well above the mean height of 69.5”. The heights of the athletes are normally distributed. From the choices listed below, which is more likely to be true: a, b or c?
a.The mean height for a randomly selected sample of 20 players is more than 72 inches.
b.The height of one randomly selected player is more than 72 inches.
c.Both a and b are equally likely.
Why? (Justify your answer with a short answer.)
Answers
That both a and b are equally likely, is also not true since the Probability of option b is higher than that of option a.
Option b is more likely to be true. This is because the given information states that the showerhead heights were designed to be 72 inches, which is well above the mean height of 69.5 inches. Therefore, it is reasonable to assume that the majority of the players' heights are below 72 inches. Since the heights of the athletes are normally distributed, the probability of selecting a player at random with a height above 72 inches is relatively low. On the other hand, option a suggests that the mean height of a sample of 20 players is more than 72 inches, which is less likely than option b. Option c, which suggests that both a and b are equally likely, is also not true since the probability of option b is higher than that of option a.
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Carter shared his post with 10 friends, who each share with only 2 people each day. Carter shared his post with 10 friends, who each share with only 2 people each day.
write an exponential function to represent the spread of carters social media post.
Answers
The exponential function will be equal to y = 20ˣ.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Carter shared his post with 10 friends, who each share with only 2 people each day.
The exponential function will be written as,
y = abˣ
y = 10(2)ˣ
y = 20ˣ
Therefore, the exponential function will be equal to y = 20ˣ.
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Answer:
f(x) = 10(2)^x
Step-by-step explanation:
Rule for solving: The first number is the first part of the equation, and the second number is in parenthesis.
The figure shows how the yard lines on a football field are numbered. The goal lines are labeled G. A referee was standing on a certain yard line as the first quarter ended. He walked 41
3
4
yards to a yard line with the same number as the one he had just left. How far was the referee from the nearest goal line? Express your answer as a simplified mixed number.
The referee was BLANK yards away from the goal line before moving.
Answers
YOU WILL DO YOU GOOD LUCK
Step-by-step explanation:
please help me answer this math question
Answers
Answer:
k>0: ]-∞, 1[ v ]9 , +∞[
Step-by-step explanation:
we know that D > 0 because the anwser has to have two outcomes so:
b²-4.a.c>0 => (k-3)²-4.k.1>0 <=> k²-6k+9-4k>0 <=> k²-10k+9>0
=> D=8² : x1 = 9 v x2 = 1
k>0: ]-∞, 1[ v ]9 , +∞[
A manufacturer of athletic footwear finds that the sales of a popular brand of running shoes is a function of the selling price (in dollars) for a pair of shoes. Suppose that pairs of shoes and pairs of shoes per dollar. The revenue that the manufacturer will receive for selling pairs of shoes at dollars per pair is Find What impact would a small increase in price have on the manufacturer's revenue
Answers
Answer:
Hello your question is poorly written attached below is the complete question
Answer :
a) R'( 120 ) = 3000
b) Increase the manufacturers revenue
Step-by-step explanation:
Given data:
F (120) = 9000 pairs
F' (120) = -50 pairs of shoes
R(p) = P * F(p)
a) find R' ( p )
R'(p) = P * F'(p) + F(p) * 1
∴ R' ( 120 ) = 120 * ( -50 ) + 9000 * 1
= 3000
b) A small Increase in price by $3000 will Increase the manufacturers revenue
Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0.
x y squared StartRoot 8 x cubed EndRoot
2 x cubed y cubed StartRoot x y squared EndRoot
2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot
4 x cubed y Superscript 4 Baseline StartRoot x EndRoot
Answers
The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.
To understand why this is the case, let's break down each expression and simplify them step by step:
StartRoot \(8 x^7 y^8\) EndRoot:
We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.
Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.
(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:
Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.
Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.
Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.
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an arts academy requires there to be 6 teachers for every 132 students and 3 tutors for every 27 students . how many students does the academy have per teacher ? per tutor ? how many tutors does the academy need if it has 72 students ?
Answers
Answer:
3
Step-by-step explanation:
The number of necessary tutors when you divide 27 into 72, is 2.6; therefore the necessary number of tutors is 3 because you can’t have .6 of a tutor. Hope this helps!
I = PRT
C = 2r A = r2
Answers
Answer: Calculate Total Amount Accrued (Principal + Interest), solve for A. A = P(1 + rt)
Calculate Principal Amount, solve for P. P = A / (1 + rt)
Calculate rate of interest in decimal, solve for r. r = (1/t)(A/P - 1)
Calculate rate of interest in percent. ...
Calculate time, solve for t
Step-by-step explanation:
Check out this triangular prism:
5
7
6
Find the surface area of the triangular
prism (above) using its net (below).
7
6
5
5
4
units2
Answers
Answer:
Step-by-step explanation:
b- base of the triangle = 6
h - height of the triangle = 4
L = length of the rectangles = 7
s₁ = breadth of the base rectangle = 6
S₂ = breadth of the right rectangle = 5
s₃ = breadth of the left rectangle = 5
Surface area of the prism = bh + L*(s₁ + s₂ + s₃)
= [ 6*4 ] + 7 * (6+5+5)
= 24 + 7*16
= 24 + 112
= 136 square units
What is the diameter of a circle with a circumference of 11.27pi ft? Use pencil and paper.
The diameter is ... ft
Answers
Answer:
\(circumference = \pi \: d \\ 11.27\pi = \pi \: d \\ d = 11.27 \: ft\)