Answer:
The sequence is 14, 19, 24, 29, 34, 39.
Step-by-step explanation:
Let's call the common difference (the difference between two consecutive terms) as d. We see that the second term is 19 and the 5th term is 34 and since 5 - 2 = 3, we add d 3 times to 19 to get 34 so therefore:
19 + 3d = 34
3d = 15
d = 5 so the first term is 19 - 5 = 14, the third would be 19 + 5 = 24, the fourth would be 24 + 5 = 29 and the sixth would be 34 + 5 = 39.
5 A machine puts tar on a road at the rate of 4 metres in 5 minutes.
a) How long does it take to cover 1 km of road
b) How many metres of road does it cover in 8 hours?
Answer:
5 a) Total = 20.83 hrs = 20 hrs and 50 mins (1250mins total)
5 b) Total = 96 meters. = 0.096km in 8 hrs.
Step-by-step explanation:
1km = 1000 meters
5 mins = 4 meters
1000/4 = 250 multiplier
250 x 5mins = 1250 minutes
1250/60 = 20hrs + 50 minutes
50 / 60 = 0.83 = 20.83hrs
b) 8 hrs = 8 x 60 = 480 minutes
480/5 = 24 multiplier of 4 meters
24 x 4 = 96 meters
What is (-i)^6 ? Please don’t guess. Thanks
Answer:
-1
Step-by-step explanation:
Hello, please consider the following.
[tex](-i)^6=(-1)^6\cdot(i^2)^3=1\cdot (-1)^3=\boxed{-1}\\[/tex]
Thank you
What is the volume of this rectangular pyramid?
_____ cubic millimeters
Answer:
Step-by-step explanation:
L = 9 mm
W = 9 mm
H = 10 mm
volume = LWH/3 = 9·9·10/3 = 270 mm³
Which of these functions could have been the graph shown below?
Answer:
B
Step-by-step explanation:
we take the only point we know
(0,20)
in A when x =0
[tex]f(x)=e^{20x} =e^{20*0}=1[/tex]
in B when x=0
[tex]f(x)=20e^x=20e^0=20*1=20[/tex]
fits
in C
[tex]f(x)=20^x=20^0=1[/tex]
in D
[tex]f(x)=20^{20x}=20^{20*0}=20^0=1[/tex]
so the only choice is B
What is the equation of the sinusoid?
Answer:
Hello,
Answer A
Step-by-step explanation:
if x=0 then sin(2*0)=sin(0)=0
if x= π/4 then sin(π/2)=1
if x= π/2 then sin(π)=0
The equation of the sinusoid will be y=Sin(2x)
What is an equation?It is defined as the relation between two variables, for a sinusoidal wave the equation will be in the form of Sin or Cos.
if x=0 then sin(2*0)=sin(0)=0
if x= π/4 then sin(π/2)=1
if x= π/2 then sin(π)=0
Hence the equation of the sinusoid will be y=Sin(2x)
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A research center poll showed that % of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief? 78 The probability that someone does not believe that it is morally wrong to not report all income on tax returns is . (Type an integer or a decimal.)
Question:
A research center poll showed that 78% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?
The probability that someone does not believe that it is morally wrong to not report all income on tax returns is . (Type an integer or a decimal.)
Answer:
[tex]q = 0.22[/tex]
Step-by-step explanation:
Given
Let p represent the given proportion
p = 78%
Required
Determine the probability that someone holds a contrary belief
Start by converting the given proportion to decimal
[tex]p = 78\%[/tex]
[tex]p = \frac{78}{100}[/tex]
[tex]p = 0.78[/tex]
In probability, the sum of opposite probability is equal to 1
Represent the probability that someone holds a contrary belief with q
So;
[tex]p + q = 1[/tex]
Make q the subject of formula
[tex]q = 1 - p[/tex]
Substitute 0.78 for p
[tex]q = 1 - 0.78[/tex]
[tex]q = 0.22[/tex]
Hence, the probability that someone does not believe is 0.22
Alice, Bob, and Carol play a chess tournament. The first game is played between Alice and Bob. The player who sits out a given game plays next the winner of that game. The tournament ends when some player wins two successive games. Let a tournament history be the list of game winners, so for example ACBAA corresponds to the tournament where Alice won games 1, 4, and 5, Caroll won game 2, and Bob won game 3.
Required:
a. Provide a tree-based sequential description of a sample space where the outcomes are the possible tournament histories.
b. We are told that every possible tournament history that consists of k games has probability 1/2k, and that a tournament history consisting of an infinite number of games has zero prob- ability. Demonstrate that this assignment of probabilities defines a legitimate probability law.
c. Assuming the probability law from part (b) to be correct, find the probability that the tournament lasts no more than 5 games, and the probability for each of Alice, Bob, and Caroll winning the tournament.
Answer:
I don't know what you think about it is not going to be a great day of school and I don't know what you think about it is not going to be a great day of school
Write and solve a word problem involving a $145.00 price and a 5.5% sales tax.
Your question is not complete but I guess you want to know the total price to be paid. This will be:
= $145 + (5.5% × $145)
= $145 + (0.055 × $145)
= $145 + $7.975
= $152.975
3) Write the operation used to obtain the types of solutions.
Sum:
Difference:
Product:
Quotient:
Answer:
the Sum
hope this helps
The Colonel spots a campfire at a bearing N 59∘59∘ E from his current position. Sarge, who is positioned 242 feet due east of the Colonel reckons the bearing to the fire to be N 34∘34∘ W from his current position.
Determine the distance from the campfire to each man, rounded to the nearest foot.
Colonel is about............................ feet away from the fire
Sarge is about............................... feet away from the fire
Answer:
i. Colonel is about 201 feet away from the fire.
ii. Sarge is about 125 feet away from the fire.
Step-by-step explanation:
Let the Colonel's location be represented by A, the Sarge's by B and that of campfire by C.
The total angle at the campfire from both the Colonel and Sarge = [tex]59^{0}[/tex] + [tex]34^{0}[/tex]
= [tex]93^{0}[/tex]
Thus,
<CAB = [tex]90^{0}[/tex] - [tex]59^{0}[/tex] = [tex]31^{0}[/tex]
<CBA = [tex]90^{0}[/tex] - [tex]34^{0}[/tex] = [tex]56^{0}[/tex]
Sine rule states;
[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{b}{Sin B}[/tex] = [tex]\frac{c}{Sin C}[/tex]
i. Colonel's distance from the campfire (b), can be determined by applying the sine rule;
[tex]\frac{b}{Sin B}[/tex] = [tex]\frac{c}{Sin C}[/tex]
[tex]\frac{b}{Sin 56^{0} }[/tex] = [tex]\frac{242}{Sin 93^{0} }[/tex]
[tex]\frac{b}{0.8290}[/tex] = [tex]\frac{242}{0.9986}[/tex]
cross multiply,
b = [tex]\frac{0.8290*242}{0.9986}[/tex]
= 200.8993
Colonel is about 201 feet away from the fire.
ii. Sarge's distance from the campfire (a), can be determined by applying the sine rule;
[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{c}{Sin C}[/tex]
[tex]\frac{a}{Sin 31^{0} }[/tex] = [tex]\frac{242}{Sin 93^{0} }[/tex]
[tex]\frac{a}{0.5150}[/tex] = [tex]\frac{242}{0.9986}[/tex]
cross multiply,
a = [tex]\frac{0.5150*242}{0.9986}[/tex]
= 124.8073
Sarge is about 125 feet away from the fire.
help pls!!! Classify the following question: “President, vice president, and secretary are being chosen for the Environmental Club. In how many different ways can these three offices be filled from a list of ten members?”
the answer is: combation
where p is the price (in dollars) and x is the number of units (in thousands). Find the average price p on the interval 40 ≤ x ≤ 50. (Round your answer to two decimal places.)
THIS IS THE COMPLETE QUESTION BELOW
The demand equation for a product is p=90000/400+3x where p is the price (in dollars) and x is the number of units (in thousands). Find the average price p on the interval 40 ≤ x ≤ 50.
Answer
$168.27
Step by step Explanation
Given p=90000/400+3x
With the limits of 40 to 50
Then we need the integral in the form below to find the average price
1/(g-d)∫ⁿₐf(x)dx
Where n= 40 and a= 50, then if we substitute p and the limits then we integrate
1/(50-40)∫⁵⁰₄₀(90000/400+3x)
1/10∫⁵⁰₄₀(90000/400+3x)
If we perform some factorization we have
90000/(10)(3)∫3dx/(400+3x)
3000[ln400+3x]₄₀⁵⁰
Then let substitute the upper and lower limits we have
3000[ln400+3(50)]-ln[400+3(40]
30000[ln550-ln520]
3000[6.3099×6.254]
3000[0.056]
=168.27
the average price p on the interval 40 ≤ x ≤ 50 is
=$168.27
If why varies with the square of x and Y equals 24 when x equals 10 then the constant of proportionality is ____, and the value of y when x equals 20 is ____. Assume x is greater than or equal to 0. Select two answers
Answer:
Step-by-step explanation:
y varies with the square of x:
y = kx²
y equals 24 when x equals 10
24 = k·10²
constant of proportionality k = 0.24
when x = 20, y = 0.24·20² = 96
"select two answers" —where are the choices?
a college entrance exam company determined that a score of 25 on the mathematics portion of the exam suggests that a student is ready for
Answer:
Student is ready for college level mathematics.
The null hypothesis will be H0 = 25
The alternative hypothesis is Ha > 25
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the z - score for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence to test a hypothesis.
The perimeter of a rectangle is 80 inches, if the width is 18 inches what is the area of the rectangle? A.22 sq.in B.324 sq.in C.396 sq.in D.6,400 sq.in
Answer:
396 in^2
Step-by-step explanation:
The perimeter of a triangle is given by the formula:
● P = 2w+2L
L is the length and w is the width
■■■■■■■■■■■■■■■■■■■■■■■■■■
The width hereis 18 inches and the perimeter is 80 inches.
Replace w by 18 and P by 80 to find L.
● P= 2L+2w
● 80 = 2L + 2×18
● 80 = 2L + 36
Substrat 36 from both sides
● 80-36 = 2L+36-36
●44 = 2L
Divide both sides by 2
● 44/2 = 2L/2
● 22 = L
So the length is 22 inches
■■■■■■■■■■■■■■■■■■■■■■■■■■
The area of a rectangle is given by the formula:
● A= L×w
● A = 22×18
● A = 396 in^2
How do you solve an expansion?
[tex]\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=x\\b=2\\r+1=5\Rightarrow r=4\\n=7\\T_5=\binom{7}{4}x^{7-4}2^4\\T_5=\dfrac{7!}{4!3!}\cdot x^3\cdot16\\T_5=16\cdot \dfrac{5\cdot6\cdot7}{2\cdot3}\cdot x^3\\\\T_5=560x^3[/tex]
Answer:
[tex]\large \boxed{560x^3}[/tex]
Step-by-step explanation:
[tex](x+2)^7[/tex]
Expand brackets.
[tex](x+2) (x+2) (x+2) (x+2) (x+2) (x+2) (x+2)[/tex]
[tex](x^2 +4x+4) (x^2 +4x+4) (x^2 +4x+4)(x+2)[/tex]
[tex](x^4 +8x^3 +24x^2 +32x+16)(x^3 +6x^2 +12x+8)[/tex]
[tex]x^7 +14x^6 +84x^5 +280x^4 +560x^3 +672x^2 +448x+128[/tex]
The fifth term is 560x³.
Determine what type of model best fits the given situation:
The temperature of a cup of coffee decreases by 5 F every 20 minutes.
Álgebra 2 need help
Answer:
first term = -1/5
I cant see part b (sorry its too blurry)
thirteenth term = -0.2
part d: -19a/95a -0.2a
Step-by-step explanation:
socratic
The recipe for gelatin uses 2 cups of water with 4 packages of the gelatin mix. ? How many cups of water will be used with 12 packages of gelatin mix?
Step-by-step explanation:
2 cups of water used with 4 packs
therefore for 12 we use x cups of water
2:4
X :12
therefore 6'cups of water?
In a mixture 60 liters, the ratio of milk and water 2:1.If this ratio is to be 1:2, then what is the quantity of water to be further added?
Answer:
Hello,
60L
Step-by-step explanation:
Quantity of water /Quantity of milk =2/1
Quantity of mixture= Quantity of water +Quantity of milk =60L
Quantity of milk =40 L
Quantity of water =20 L
Let say x the quantity of water to be added
New ratio =1/2=40/(20+x)
20+x=80 (cross products)
x=60 (L)
[tex]4 + \frac{4}{4 } \: = [/tex]
what is answer
Answer:
5Step-by-step explanation:
[tex]4 + \frac{4}{4} [/tex]
= 4 + 1
= 5 (Ans)
there are 40 marbles in an urn: 14 are green and 26 are yellow. you reach into the urn and randomly select 4 marbles without replacement. what is the probability that at least one of the marbles is green
Answer:
p=0,83641536
Step-by-step explanation:
Let's calculate the probability that all 4 marbles are yellow:
p=26/40*25/39*24/38*23/37 ( no replacement)
=0,1635846372688....
probability that at least one of the marbles is green= 1-p
=0,83641536...
What is the measure of the unknown angle?
Image of a straight angle divided into two angles. One angle is thirty five degrees and the other is unknown.
Answer:
145
Step-by-step explanation:
Angles in a straight line = 180
So,
Let unkown angle be x,
x+35=180
x=180-35
x=145
Can someone please help me with this math problem
We have [tex]f\left(f^{-1}(x)\right) = x[/tex] for inverse functions [tex]f(x)[/tex] and [tex]f^{-1}(x)[/tex]. Then if [tex]f(x) = 2x+5[/tex], we have
[tex]f\left(f^{-1}(x)\right) = 2f^{-1}(x) + 5 = x \implies f^{-1}(x) = \dfrac{x-5}2[/tex]
Then
[tex]f^{-1}(8) = \dfrac{8-5}2 = \boxed{\dfrac32}[/tex]
A triangle has vertices at (-4,-6),(3,3),(7,2). Rounded to two decimal places, which of the following is closest aporoximation of the perimeter of the triangle
Answer:
Perimeter= 29.12 unit
Step-by-step explanation:
Perimeter of the triangle is the length of the three sides if the triangle summef up together
Let's calculate the length of each side.
For (-4,-6),(3,3)
Length= √((3+4)²+(3+6)²)
Length= √((7)²+(9)²)
Length= √(49+81)
Length= √130
Length= 11.40
For (-4,-6),(7,2)
Length= √((7+4)²+(2+6)²)
Length= √((11)²+(8)²)
Length= √(121+64)
Length= √185
Length= 13.60
For (3,3),(7,2)
Length=√( (7-3)²+(2-3)²)
Length= √((4)²+(-1)²)
Length= √(16+1)
Length= √17
Length= 4.12
Perimeter= 4.12+13.60+11.40
Perimeter= 29.12 unit
Write the equation of the line shown in the graph above in slope intercept form
A) y=2/3x+1
B) y=-x+2/3
C) y=-2/3x+1
D) 2x+3y=3
Answer:
C, y=-2/3x+1
Step-by-step explanation:
using points (0, 1) and (3, -1) obtained from the graph:
slope = -1-1/3-0 = -2/3
use one of the points above lets take (1, 0) and another point (x,y)
slope = y-0/x-1 = -2/3
y=-2/3x+1
Need help finding the value for A
Answer:
[tex]\text{n}(A \bigcup B)[/tex] = 6.
Step-by-step explanation:
We are given that n(A) = 4, n(B) = 5, and [tex]\text{n}(A \bigcap B)[/tex] = 3.
And we have to find the value of [tex]\text{n}(A \bigcup B)[/tex].
As we know that the union formula is given by;
[tex]\text{n}(A \bigcup B) = \text{n}(A) + \text{n}(B) - \text{n}(A \bigcap B)[/tex]
Now, substituting the values given in the question in the above formula, we get;
[tex]\text{n}(A \bigcup B) = 4+5-3[/tex]
[tex]\text{n}(A \bigcup B) = 9-3[/tex]
[tex]\text{n}(A \bigcup B) = 6[/tex]
Hence, the value of [tex]\text{n}(A \bigcup B)[/tex] = 6.
A manufacturer knows that their items have a lengths that are skewed right, with a mean of 5.1 inches, and standard deviation of 1.1 inches. If 49 items are chosen at random, what is the probability that their mean length is greater than 4.8 inches? How do you answer this with the answer rounded 4 decimal places?
Answer:
0.9719
Step-by-step explanation:
Find the mean and standard deviation of the sampling distribution.
μ = 5.1
σ = 1.1 / √49 = 0.157
Find the z score.
z = (x − μ) / σ
z = (4.8 − 5.1) / 0.157
z = -1.909
Use a calculator to find the probability.
P(Z > -1.909)
= 1 − P(Z < -1.909)
= 1 − 0.0281
= 0.9719
The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
What is Standard deviation?In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values.
What is Mean?The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.
Given,
Mean = 5.1 inches
Standard deviation = 1.1 inches
Sample size = 49
New mean = 4.8
Z score = Difference in mean /(standard deviation / [tex]\sqrt{sample size}[/tex])
Z score = [tex]\frac{4.8-5.1}{1.1/\sqrt{49} }=-1.909[/tex]
Z score = -1.909
Then the probability
P(Z>-1.909)
=1-P(Z>-1.909)
=1-0.0281
=0.9719
Hence, The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719
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I need help ASAP please please please
Answer:
n=39/5
Step-by-step explanation:
24=5(n-3)
24=5n-15
-5n= -15-24
-5n=39
n= 39/5
Write the function in terms of unit step functions. Find the Laplace transform of the given function. f(t) = 5, 0 ≤ t < 7 −3, t ≥ 7
Rewrite f in terms of the unit step function:
[tex]f(t)=\begin{cases}5&\text{for }0\le t<7\\-3&\text{for }t\ge7\end{cases}[/tex]
[tex]\implies f(t)=5(u(t)-u(t-7))-3u(t-7)=5u(t)-8u(t-7)[/tex]
where
[tex]u(t)=\begin{cases}1&\text{for }t\ge0\\0&\text{for }t<0\end{cases}[/tex]
Recall the time-shifting property of the Laplace transform:
[tex]L[u(t-c)f(t-c)]=e^{-cs}L[f(t)][/tex]
and the Laplace transform of a constant function,
[tex]L[k]=\dfrac ks[/tex]
So we have
[tex]L[f(t)]=L[5u(t)-8u(t-7)]=5L[1]-8e^{-7s}L[1]=\boxed{\dfrac{5-8e^{-7s}}s}[/tex]
In this exercise you have to find the laplace transform:
[tex]L[f(t)]=\frac{5-8e^{-7s}}{s}[/tex]
Rewrite f in terms of the unit step function:
[tex]f(t)=\left \{ {{5, for 0\leq t\leq 7} \atop {-3, for t\geq 7}} \right. \\f(t)= 5(u(t)-u(t-7)-3u(t-7)=5u(t)-8u(t-7)[/tex]
Where:
[tex]u(t)= \left \{ {{1, t\geq 0} \atop {0, t<0}} \right.[/tex]
Recall the time-shifting property of the Laplace transform:
[tex]L[u(t-c)f(t-c)]= e^{-cs}L[f(t)][/tex]
and the Laplace transform of a constant function,
[tex]L[k]=\frac{k}{s}[/tex]
So we have:
[tex]L[f(t)]= L[5u(t)-8u(t-7)]= 5L[1]-8e^{-7s}L[1]= \frac{5-8e^{-7s}}{s}[/tex]
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