5. (a) The table below shows the cumulative frequency distribution of the weight of 80 deer recorded by the zookeeper. Weight, w kg Cumulative Frequency 6 15 61-80 36 niger 81-100 58 y Determine the upper class boundary for the class 21-40. Determine the class width for the class 41-60. How many deer were recorded in the class 81-100. (iv) A deer was chosen at random from the 80 deer. What is the probability that the weight of the deer is more than 100.5 kg. Leave your answer as an EXACT value. [2]
Answers
STEP - BY - STEP EXPLANATION
What to find?
• The upper class boundary for the class 21 - 40
,• Class width for 41 - 60
,• The number of deer recorded in the class 81 - 100
Given:
(i) To find the class boundary for the class 21 - 40, we will first subtract 0.5 from 21 and then add 0.5 to 40.
That is;
20.5 - 40.5
Hence, the upper class boundary is 40.5
(ii) The class width for the class 41 - 60
The class width can be determine by subtracting 41 from 60.
That is;
[tex]60-41=19[/tex]Hence, class width = 19
(iii) Number of deer recorded in the class 81 - 100
This can be obtain by subtracting the cumulative frequency in the class from the cumulative frequency before it.
58 - 36 =22
Hence, we have 22 numbers of deer in the class 81 - 100.
(iv) A deer was chosen at random from the 80 deer. What is the probability that the weight of the deer is more than 100.5 kg.
We can solve this by first determining the number of deer that are above 100.5 kg.
Number of beer above 100.5 kg = 15 + 7 = 22
Total number of deer = 80
[tex]Probability=\frac{required\text{ outcome}}{all\text{ possible outcome}}[/tex][tex]=\frac{22}{80}[/tex][tex]=\frac{11}{40}[/tex]ANSWER
(i) 40.5
(ii) 19
(iii) 22
(iv) 11/40
Related Questions
8You are asked to draw a triangle withside lengths of 10 inches, 7 inches, and2 inches. How many triangles like thiscan you draw?A. OneB. ThreeC. TwoD. Zero
Answers
ANSWER
D. Zero
EXPLANATION
The triangle inequality states that the sum of any two sides of a triangle is greater than the third side,
All these inequalities must be true to be able to form a triangle with the given sides,
[tex]\begin{gathered} 7+10>2\Rightarrow17>2\Rightarrow true \\ 2+10>7\Rightarrow12>7\Rightarrow true \\ 7+2>10\Rightarrow9>10\Rightarrow false \end{gathered}[/tex]Hence, no triangle can be formed with these side lengths.
How do I get my answer?
Answers
Answer:
[tex] \frac{2}{9 {d}^{14} } [/tex]
Step-by-step explanation:
[tex] \frac{ {4d}^{ - 5} }{18 {d}^{9} } = \frac{4}{18} \times \frac{ {d}^{ - 5} }{ {d}^{9} } = \frac{2}{9} {d}^{ - 14} = \frac{2}{ {9d}^{14} } [/tex]
Please find the square root. Round your answer to the nearest tenth. [tex] \sqrt{58 } = [/tex]
Answers
Determine the square root of 58.
[tex]\begin{gathered} \sqrt[]{58}=7.615 \\ \approx7.6 \end{gathered}[/tex]So answer is 7.6.
Zachary is designing a new board game, and is trying to figure out allthe possible outcomes. How many different possible outcomes arethere if he spins a spinner with three equal-sized sections labeledWalk, Run, Stop, spins a spinner with four equal-sized sections labeledRed, Green, Blue, Orange, and spins a spinner with 5 equal-sizedsections labeled Monday, Tuesday, Wednesday, Thursday, Friday?
Answers
ANSWER
60 possible outcomes
EXPLANATION
If he spins the 3-section spinner, there are 3 possible outcomes: Walk, Run, Stop.
If he spins the 4-section spinner, there are 4 possible outcomes: red, green, blue, orange.
If he spins the 5-section spinner, there are 5 possible outcomes: Monday, Tuesday, Wednesday, Thursday, Friday.
If he has to spin the three spinners, the total possible outcomes is the product of the possible outcomes of each spinner: 3x4x5 = 60.
Given that the two triangles are similar find the unknowns length of the side labeled in
Answers
The unknown length of the side labeled n is 10.5 units
Explanation:Given:
Two similar triangles with one unknown
To find:
the unknown length of the side labelled n
For two triangles to be similar, the ratio of their corresponding sides will equal
[tex]\begin{gathered} side\text{ with 36 corresponds to side with 27} \\ side\text{ with 14 corresponds to side with n} \\ The\text{ ratio:} \\ \frac{14}{n}\text{ = }\frac{36}{27} \end{gathered}[/tex][tex]\begin{gathered} crossmultiply: \\ 14(27)\text{ = 36\lparen n\rparen} \\ 36n\text{ = 378} \\ \\ divide\text{ both sides by n:} \\ \frac{36n}{36}\text{ = }\frac{378}{36} \\ n\text{ = 10.5} \end{gathered}[/tex]The unknown length of the side labeled n is 10.5 units
An object moves in simple harmonic motion with period 6 seconds and amplitude 4cm. At time =t0 seconds, its displacement d from rest is 0cm, and initially it moves in a negative direction. Give the equation modeling the displacement d as a function of time t.
Answers
The general function for describing the displacement from the mean position in harmonic motion is:
[tex]d(t)=A\cdot\sin (\frac{2\pi}{T}\cdot t+\phi)\text{.}[/tex]Where:
• A is the amplitude,
,• T is the period,
,• φ is initial phase displacement.
From the statement, we know that:
• the amplitude is 4 cm,
,• at time t = 0 its displacement d from the rest is 0 → d(t = 0) = 0,
,• initially, it moves in a negative direction.
s
Fifteen strips, 11/4" wide, are to be ripped from a sheet of plywood. If 1/8" is lost with each cut, how much of the plywood sheet is used in making the 15 strips? (Assume 15 cuts are necessary.)
Answers
The size of the plywood sheet used is;
[tex]\frac{37}{8}^{\doubleprime}[/tex]Here, we want to get the size of the part of the plywood sheet lost
From the question, we are told that 1/8 inches is lost
The size lost would be;
[tex]\frac{1}{8}\times\text{ 15 = }\frac{15}{8}[/tex]This is the size that was lost
To get the total part of the plywood used, we simply add the width of all the strips to the amount of the plywood lost
We have this as;
[tex]\frac{11}{4}\text{ + }\frac{15}{8}\text{ = }\frac{22+15}{8}\text{ = }\frac{37}{8}[/tex]Find the value of each variable.All answers must be in simplest radical form
Answers
Radical
x = √10 • tan 45° = √10• 1 = √10
then
x= √10
y= √x^2 + 10 = √ 10 +10 = √20
Then answer is
x=√10
y= √20
Yoko plans to watch 2 movies each month. Write an equation to represent the total number of movies n that she will watch in m months.
Answers
Answer:
2m because 2 times the months will tell us how many she has watched for example in 2 months she will watch 4 because 2*2 is 4
Determine the value of each limit for the function below.f(x)=x/(x-2)^2(a) lim f(x). (b) lim f(x)x---2^-. x---2^+
Answers
We will have the following:
a)
[tex]\lim _{x\rightarrow2^-}\frac{x}{(x-2)^2}=\infty[/tex]b)
[tex]\lim _{x\rightarrow2^+}\frac{x}{(x-2)^2}=\infty[/tex]The Oldest rocks on Earth are about 4 x 10^9 years old. For which of these ages could this be an approximation?
A. 3,862,100,000 years
B. 3.849999999x10^9 years
C. 0.000000004 years
D.4,149,000,000 years
E.3.45x10^9 years
Answers
4149000000 is the approximation age of oldest rock. The precise amount is not known with certainty. Similar to proximity or approximately, the word "approximation" is derived from the Latin Proximus, which meaning "nearest."
What is approximation age?The precise amount is not known with certainty. Similar to proximity or approximately, the word "approximation" is derived from the Latin Proximus, which meaning "nearest." The closest estimate you can make without knowing something's exact size or measurement is called an approximation.
Despite the fact that approximation is most usually used in relation to numbers, it is also regularly used in relation to mathematical functions, forms, and physical laws. In science, the term "approximation" can refer to using a less complex method or model when the proper one is challenging to use.
For this, sampling techniques like Markov chain Monte Carlo and significance sampling as well as variationally methods like mean-field approximations and assumed density filtering have been used.
To learn more about approximation refer to:
https://brainly.com/question/28802280
#SPJ1
Cameron can run 3.6 miles for every 4 miles Juliette runs. If Juliette ran 7.6 miles, how far will Cameron run? 6.84 miles68.4 miles6 miles68 miles
Answers
lets set up a proportion here
cameroon runs 3.6 miles for every 4 miles Juliette runs
3.6 miles(C).................................................... 4 miles (J)
? miles(C)...........................................................7.6 miles (J)
cameron will run= (7.6*3.6)/4=6.84 miles
Cameron will run 6.84 miles
what's the answer for proportions 7/9=b/b-10
Answers
Answer:
-35
Step-by-step explanation:
[tex]\frac{7}{9}[/tex] = [tex]\frac{b}{b - 10}[/tex] multiply both sides by 9(b -10)
[tex]\frac{9(b - 10)}{1}[/tex] [tex](\frac{7}{9})[/tex] = [tex]\frac{9(b -10)}{1}[/tex] [tex](\frac{b}{b-10})[/tex] On the right side of the equation, the 9's cancel out and on the right side of the equation the (b -10) cancels out to leave
7(b -10) = 9b Distribute the 7
7b - 70 = 9b Subtract 7b from both sides
-70 = 2b Divide both sides by 2
-35 = b
A machine worked for 4hours and used 6kilowatts of electricity.What is the rate ofenergy consumed inkilowatts per hour?*Enter your answer as a decimal
Answers
4 hours ---> 6 kilowatts
1 hour -----> x kilowatts
[tex]\begin{gathered} 4\times x=1\times6 \\ 4x=6 \\ \frac{4x}{4}=\frac{6}{4} \\ x=\frac{3}{2}=1.5 \end{gathered}[/tex]answer:
1.5 kilowatts per hour
x+y+z=12x+4y+2z = -6-x+9y-3z=-49 Can someone please help me solve this system of equation?
Answers
Let's begin by listing out the information given to us:
[tex]\begin{gathered} x+y+z=1 \\ 2x+4y+2z=-6 \\ -x+9y-3z=-49 \end{gathered}[/tex]To solve this 3 variable equation, let's eliminate one of the variables
add equation 1 & 3, we have:
[tex]\begin{gathered} x-x+y+9y+z-3z=1-49 \\ 10y-2z=-48 \\ Make\text{ z the }subject,we\text{ have:} \\ -2z=-10y-48 \\ divide\text{ through by -2} \\ z=5y+24 \end{gathered}[/tex]Substitute z into equation 1, 2 & 3
[tex]\begin{gathered} x+y+5y+24=1 \\ x+6y=1-24 \\ x+6y=-23 \end{gathered}[/tex][tex]\begin{gathered} 2x+4y+2\left(5y+24\right)=-6 \\ 2x+4y+10y+48=-6 \\ 2x+14y=-6-48 \\ 2x+14y=-54 \end{gathered}[/tex][tex]\begin{gathered} -x+9y-3\left(5y+24\right)=-49 \\ -x+9y-15y-72=-49 \\ -x-6y=-49+72 \\ -x-6y=23 \end{gathered}[/tex]Solve as a simultaneous equation, we have:
[tex]\begin{gathered} x+6y=-23 \\ 2x+14y=-54 \\ \text{Multiply the top equation by 2 \& subtract it from the bottom equation} \\ 2\cdot(x+6y=-23)\Rightarrow2x+12y=-46 \\ 2x+14y=-54-(2x+12y=-46) \\ 2x-2x+14y-12y=-54-(-46) \\ 2y=-8 \\ y=-4 \end{gathered}[/tex]Substitute y = -4 into x + 6y = -23, we have:
[tex]\begin{gathered} x+6\left(-4\right)=-23 \\ x-24=-23 \\ x=-23+24 \\ x=1 \end{gathered}[/tex]Substitute y = -4 into z = 5y + 24, we have:
[tex]\begin{gathered} z=5\left(-4\right)+24 \\ z=-20+24 \\ z=4 \end{gathered}[/tex]how do you find the domain in a range of number 2?
Answers
The domain is all the x values included in the function, while the range are all the y values included in the function.
Based on the graph:
Answer:
• Domain:
[tex](-\infty,\text{ }\infty)[/tex]• Range:
[tex](0,\infty)[/tex]Below is the graph of a parabola with its vertex and another point on the parabola labeled.Write an equation of the parabola.(-2,4).(1, -2)
Answers
The vertex form of a parabola is given by:
[tex]x=a(y-k)^2+h[/tex]Where the vertex is:
[tex]\begin{gathered} V(h,k)=(-2,4) \\ so\colon \\ x=a(y-4)^2-2 \\ x=a(y-4)^2-2 \end{gathered}[/tex]for (1,-2):
[tex]\begin{gathered} 1=a(-2-4)^2-2 \\ 1=a(-6)^2-2 \\ 1=36a-2 \\ solve_{\text{ }}for_{\text{ }}a\colon \\ 36a=1+2 \\ 36a=3 \\ a=\frac{3}{36} \\ a=\frac{1}{12} \\ \end{gathered}[/tex]therefore:
[tex]x=\frac{1}{12}(y-4)^2-2[/tex]Find the prime factorization of the following number write any repeated factors using exponents
Answers
Notice that 100=10*10, and 10=2*5. 2 and 5 are prime numbers; therefore,
[tex]\begin{gathered} 100=10\cdot10=(2\cdot5)(2\cdot5)=2\cdot2\cdot5\cdot5=2^2\cdot5^2 \\ \Rightarrow100=2^2\cdot5^2 \end{gathered}[/tex]The answer is 100=2^2*5^2
I need some help solving this It’s from my ACT prep guide
Answers
We can convert a measure from radians to degrees by taking into account that π radians is equivalent to 180°.
Then, we can convert a measure in radians into degrees by multiplying by 180°/π.
We can convert 7π/11 into degrees as:
[tex]\frac{7\pi}{11}\cdot\frac{180\degree}{\pi}=\frac{7\cdot180\degree}{11}\approx114.55\degree[/tex]Answer: 114.55°
Han and clan are stuffing enveloppes Han can stuff 20 envelopes in one minute and Clare can stuff 10 envelopes in one minute. They start working together on a pile of 1000 envelopes. How long does it take them to finish the pile.
Answers
uff = Given
Han can stuff 20 envelopes in one minute
Clare can stuff 10 envelopes in one minute
Together they start working on a pile off 1000 envelope.
Find
How long does it take them to finish the pile.
Explanation
as we have given
in one minute , Han can stuff = 20 envelope
in one minute , Clare can stuff = 10 envelope
together in one minute , they can stuff =
[tex]\begin{gathered} 20+10=30 \\ \\ \end{gathered}[/tex]we know that the number of time it will take to finish stuffing would be number of envelope / joint rate = 1000/30
so , time taken to finish the pile =
[tex]\begin{gathered} \frac{1000}{30} \\ \\ \frac{100}{3} \\ \\ 33\frac{1}{3} \\ or \\ 33min20sec \end{gathered}[/tex]Final Answer
Hence , the time taken by them to finish the pile is 33 minutes 20 seconds
Find the tangent of each angle that is not the right angle. Drag and drop the numbers into the boxes to show the tangent of each angle. B 76 tan ZA tan ZB 2.45 0.38 0.93
Answers
From the trignometric ratio of right angle triangle :
The ratio for the tangent of any angle of right angle triangle is the ratio of the side Opposite to that angle to the adjacent side of that angle :
[tex]\tan \theta=\frac{Opposite\text{ Side}}{Adjacent\text{ Side}}[/tex]In the given triangle :The side opposite to the angle A is BC and the adjacent side AC
So,
[tex]\begin{gathered} \tan \theta=\frac{Opposite\text{ Side}}{Adjacent\text{ Side}} \\ \tan A=\frac{BC}{AC} \end{gathered}[/tex]In the figure : we have AC = 76, BC = 31 and AB = 82.1
Substitute the value and simplify :
[tex]\begin{gathered} \tan A=\frac{BC}{AC} \\ \tan A=\frac{31}{76} \\ \tan A=0.407 \\ \tan A=0.41 \end{gathered}[/tex]Thus, tan A = 0.41
Now, the side opposite to the angle B is AC and the adjacent side is BC
thus :
[tex]\begin{gathered} \tan \theta=\frac{Opposite\text{ Side}}{Adjacent\text{ Side}} \\ \tan B=\frac{AC}{BC} \end{gathered}[/tex]In the figure : we have AC = 76, BC = 31 and AB = 82.1
Substitute the value and simplify :
[tex]\begin{gathered} \tan B=\frac{AC}{BC} \\ \tan B=\frac{76}{31} \\ \tan B=2.451 \end{gathered}[/tex]tan B = 2.451
Answer :
tanA = 0.41
tanB = 2.45
if the area of polygon A is 72 and Q is a scaled copy and the area of Q is 5 what scale factor got 72 to 5
Answers
A area= 72
Q area =5
So, if we multiply the A area by the square of the scale factor ( since they are areas) we obtain area Q:
72 x^2 = 5
Solving for x:
x^2 = 5/72
x = √(5/72)
x= 0.26
Find the length to the nearest whole number of the diagonal (hypotenuse) of a square with 30 cm on a side. Round answers to the nearest tenth if necessary. Your answer
Answers
Notice that we can draw a triangle in the square , and that the length of the square's diagonal is the same as the length of the triangle's hypotenuse. The triangle is a right triangle therefore it satisfies the Phytagorean Theorem. To calculate for it's hypotenuse , we will use:
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse, and a, b are the other legs of the triangle.
[tex]\begin{gathered} c^2=30^2+30^2 \\ c^2=1800 \\ c=\sqrt[]{1800} \\ c=42.43 \end{gathered}[/tex]Since the hypotenuse of the triangle is 42.43 cm. Therefore, the square's diagonal is also 42.43 cm
Answer:
The square's diagonal is 42.43 cm
The position of an open-water swimmer is shown in the graph. The shortest route to the shoreline is one that is perpendicular to the sh Ay 10 00 6 water 4 shore |(2, 1) swimmer 19 -2 2 1 3 4 5X N -2 An equation that represents the shortest path is y=
Answers
Answer:
Explanation:
From the graph, we ca
Which of the following are solutions to the following solutions to the following solutions?
Answers
We have to find the solutions to the equation:
[tex]|x+4|=8[/tex]The absolute value function is in fact a piecewise function, so it may have two solutions.
We consider for the first solution that the argument inside the absolute function is positive, that is x + 4 > 0. Then, we will have:
[tex]\begin{gathered} x+4=8 \\ x=8-4 \\ x=4 \end{gathered}[/tex]Now, we consider that the the argument is negative and is made positive by the absolute value function (it will shift the sign, which can be represented by a multiplication by -1). This means that x + 4 < 0, and the solution will be:
[tex]\begin{gathered} -(x+4)=8 \\ -x-4=8 \\ -x=8+4 \\ -x=12 \\ x=-12 \end{gathered}[/tex]We can see it in a graph as:
Answer: the solutions are x = 4 and x = -12.
What are the domain and range of y = cot x? Select onechoice for domain and one for range.
Answers
ANSWER:
A. Domain: x ≠ n
D. Range: All real numbers
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]y=\cot\left(x\right)[/tex]The domain of a function is the interval of input values, that is, the interval of x while the range is the interval of output values, that is, the interval of y.
In the cotangent function, x cannot take the value of radians (nor its multiples), since it is not defined, while the range is continuous on all real numbers.
That means the correct options are:
A. Domain: x ≠ n
D. Range: All real numbers
The first 19 terms of the sequence 9, 2, -5, -12,... find the sum of the arithmetic sequence
Answers
To find the sum of the ari
cell phone company A charges a fee of $50 per month plus an additional $0.10 for every minute talked. cell phone company B computes its monthly charge by using the equation y=$0.05 + $75 where y is the total cost and X is the number of minutes talked.
Answers
We will first write A equation
Let x be the number of minutes
y = 0.10x + 50
Comparing the above with y=mx + b where m is the rate of change
m = 0.10
Company B
y = 0.05x + 75
comparing with y =mx + b
rate of change (m) = 0.05
Hence, company A has a higher rate of change at $0.10
5. What is the correlation coefficient for the given data?
Answers
Let us plot the data on the graph to obtain its correlation coefficient.
5) 'r' is known to be the symbol for the correlation coefficient.
Hence, the correlation coefficient from the graph is
[tex]r=0.9741[/tex]6) There is a strong correlation for the data set because the r-value is larger than 0.7 which is close to +1.
10. A car dealership offers a loan with 3.9% interest for 36 months, and you plan to purchase a car for $19,500. You can afford a down payment of $2,500.(a) What will your monthly payment be? $(b) How much will you pay in total for the car? $(c) How much will you pay in interest over the life of the loan? $
Answers
The monthly payment formula is :
[tex]M=P\times\frac{r(1+r)^n}{(1+r)^n-1}[/tex]where M is the monthly payment
P is the Financed amount
r is the rate of interest monthly, annual rate divided by 12
n is the number of payments
From the problem,
The financed amount is the difference between the car's cost and the down payment.
P = $19,500 - $2,500
P = $17000
The monthly interest rate is :
r = 3.9%/12 or 0.039/12 = 0.00325
n = 36 months
The monthly payment will be :
[tex]\begin{gathered} M=17000\times\frac{0.00325(1+0.00325)^{36}}{(1+0.00325)^{36}-1} \\ M=501.15 \end{gathered}[/tex]a. M = $501.15
b. The total payment for the car is monthly payment multiplied by the number of payment made together with the downpayment.
501.15 x 36 + 2500 = $20,541.4
c. The interest is the difference between the total payment made and the financed amount.
I = 501.15 x 36 - 17,000 = $1,041.4