Answer:
24
Step-by-step explanation:
hello
let's note x the number we are looking for
[tex]\dfrac{x}{12}=6\\<=> x = 6*12=72[/tex]
so 1/3 of it equals
[tex]\dfrac{72}{3}=24[/tex]
another way to see it is that 12=4*3
so 1/3 of it equals 6*4=24
hope this helps
please - i got this wrong so plz help
Answer:
Area = 108 cm^2
Perimeter = 44 cm
Step-by-step explanation:
Area, -->
24 + 30 + 24 + 30 -->
24(2) + 30(2)
48 + 60 = 108 cm^2
108 = area
10 + 12 + 10 + 12, -->
10(2) + 12(2) = 44 cm
44 = perim.
Hope this helps!
Answer:
Step-by-step explanation:
Draw the diagram.
This time put in the only one line for the height. That is only 1 height is 8 cm. That's it.
The base is 6 + 6 = 12 cm.
The slanted line is 10 cm
That's all your diagram should show. It is much clearer without all the clutter.
Now you are ready to do the calculations.
Area
The Area = the base * height.
base = 12
height = 8
Area = 12 * 8 = 96
Perimeter.
In a parallelagram the opposite sides are equal to one another.
One set of sides = 10 + 10 = 20
The other set = 12 + 12 = 24
Both sets = 20 + 24
Both sets = 44
Answer
Area = 96
Perimeter = 44
Simplify 18 - 2[x + (x - 5)]. 28 - 4 x 8 - 4 x 28 - 2 x
Answer:
[tex]-4x+28[/tex]
Step-by-step explanation:
[tex]18-2(x+x-5)[/tex]
[tex]18+(-2)(x)+(-2)(x)+(-2)(-5)[/tex]
[tex]18+-2x+-2x+10[/tex]
[tex]-2x-2x+10+18[/tex]
[tex]=-4x+28[/tex]
What is the value of AC?
Answer:
0.637
Step-by-step explanation:
The average value of a whole sinusoidal waveform over one complete cycle is zero as the two halves cancel each other out
Consider the graph of the line of best fit, y = 0.5x + 1, and the given data points. A graph shows the horizontal axis numbered negative 4 to positive 4 and the vertical axis numbered negative 4 to positive 4. Points show an upward trend. Which is the residual value when x = 2? –2 –1 1 2
Answer
its -1
Step-by-step explanation:
ED 2020 boiiiii
The residual value of the line of the best fit when x = 2 is -1
How to determine the residual value?The equation of the line is given as:
y = 0.5x + 1
When x = 2, we have:
y = 0.5 * 2 + 1
Evaluate
y = 2
The residual is the difference between the actual value and the predicted value.
From the complete graph, the actual value is 1.
So, we have:
Residual = 1 - 2
Evaluate
Residual = -1
Hence, the residual value when x = 2 is -1
Read more about residuals at:
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Find the slope of the line that goes through the given points.
(6,1) and (9,-1)
Answer:
m = -2/3
Step-by-step explanation:
Slope Formula: [tex]m = \frac{y2-y1}{x2-x1}[/tex]
So,
[tex]m = \frac{-1-1}{9-6}[/tex]
m = -2/3
A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.
Y
p(x,y), 0 1 2
0 .10 .04 .02
x 1 .08 .20 .06
2 .06 .14 .30
a. What is P(X = 1 and = 1)?
b. Compute P(X land Y 1).
c. Give a word description of the event {X t- 0 and Y 0}, and compute the probability of this event
d. Compute the marginal pmf of X and of Y. Using pX(x), what is P(X 5 1)?
e. Are X and Y independent rv's? Explain.
Answer:
Step-by-step explanation:
Y
p(x,y) 0 1 2
0 0.10 0.04 0.02
x 1 0.08 0.2 0.06
2 0.0 0.14 0.30
a) What is P(X = 1 and = 1)
From the table above we have
P(1,1) = 0.2
b) Compute P(X ≤ 1 and Y ≤ 1).
[tex]=p(0,0)+p(0,1)+p(1,0)+p(1,1)\\\\=0.1+0.04+0.08+0.2\\\\=0.42[/tex]
C)
Let A ={X ≠ 0 and Y ≠ 0}
p{X ≠ 0 , Y ≠ 0}
= p(1,1) + p(1,2) + p(2,1) + p(2,2)
= 0.20 + 0.06 + 0.14 + 0.30
=0.7
d) The possible X values are in the figure 0,1,2
[tex]p_x(0)=p(0,0)+p(0,1)+p(0,2)\\\\=0.1+0.04+0.02\\\\=0.16\\\\p_x(1)=p(1,0)+p(1,1)+p(1,2)\\\\=0.08+0.2+0.06\\\\=0.34\\\\p_x(2)=p(2,0)+p(2,1)+p(2,2)\\\\=0.06+0.14+0.3\\\\=0.5[/tex]
The possible Y values are in the figure 0,1,2
[tex]p_y(0)=p(0,0)+p(1,0)+p(2,0)\\\\=0.1+0.08+0.06\\\\=0.24\\\\p_y(1)=p(0,1)+p(1,1)+p(2,1)\\\\=0.04+0.2+0.14\\\\=0.38\\\\p_y(2)=p(0,2)+p(1,2)+p(2,2)\\\\=0.02+0.06+0.3\\\\=0.38[/tex]
So the probability of x ≤ 1 is
[tex]p(x\leq 1)=p_x(0)+p_x(1)\\\\=0.34+0.16\\\\=0.50[/tex]
e) From the table
[tex]p_x(x=1,y=1)=p(1,1)\\\\=0.2\\\\p_x(1)=0.34\\\\p_y(1)=0.38[/tex]
we multiply both together
0.34 x 0.38
=0.1292
Therefore p(1,1) is not equal px(1), py(1)
Hence x and y are not independent it is not equal
Solve the equation x^3 + 2x^2 - 11x -12 = 0
Answer: there are 4 solutions
x = -2
x = -1/2 = -0.500
x =(3-√5)/2= 0.382
x =(3+√5)/2= 2.618
Step-by-step explanation:
The local food pantry has 1, 600 cans of fruit. They give away 155 cans of fruit each week. Assuming no new donations are made,
how many cans of fruit will remain after 6 weeks?
The solution is
What is the answer for this problem?
Answer:
670 Cans of fruit will be left
Step-by-step explanation:
First you multiply 155 by the 6 weeks.
That equals 930 and then you subtract 930 from 1,600 and that gives you 670.
There are 670 cans of fruit that will remain after 6 weeks the answer is 670 cans.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have:
The local food pantry has 1, 600 cans of fruit. They give away 155 cans of fruit each week.
First term a = 1600
Common difference d = -155
After 6 weeks means on week 7.
n = 7
a(7) = 1600 + (7-1)(-155)
a(7) = 1600 - 930
a(7) = 670
Thus, there are 670 cans of fruit that will remain after 6 weeks the answer is 670 cans.
Learn more about the sequence here:
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. A bag contains 6 red and 3 black chips. One chip is selected, its color is recorded, and it is returned to the bag. This process is repeated until 5 chips have been selected. What is the probability that one red chip was selected?
Answer:
The probability that one red chip was selected is 0.0053.
Step-by-step explanation:
Let the random variable X be defined as the number of red chips selected.
It is provided that the selections of the n = 5 chips are done with replacement.
This implies that the probability of selecting a red chip remains same for each trial, i.e. p = 6/9 = 2/3.
The color of the chip selected at nth draw is independent of the other selections.
The random variable X thus follows a binomial distribution with parameters n = 5 and p = 2/3.
The probability mass function of X is:
[tex]P(X=x)={5\choose x}\ (\frac{2}{3})^{x}\ (1-\frac{2}{3})^{5-x};\ x=0,1,2...[/tex]
Compute the probability that one red chip was selected as follows:
[tex]P(X=1)={5\choose 1}\ (\frac{2}{3})^{1}\ (1-\frac{2}{3})^{5-1}[/tex]
[tex]=5\times\frac{2}{3}\times \frac{1}{625}\\\\=\farc{2}{375}\\\\=0.00533\\\\\approx 0.0053[/tex]
Thus, the probability that one red chip was selected is 0.0053.
Answer:
0.0412
Step-by-step explanation:
Total chips = 6 red + 3 black chips
Total chips=9
n=5
Probability of (Red chips ) can be determined by
=[tex]\frac{6}{9}[/tex]
=[tex]\frac{2}{3}[/tex]
=0.667
Now we used the binomial theorem
[tex]P(x) = C(n,x)*px*(1-p)(n-x).....Eq(1)\\ putting \ the \ given\ value \ in\ Eq(1)\ we \ get \\p(x=1) = C(5,1) * 0.667^1 * (1-0.667)^4[/tex]
This can give 0.0412
The null hypothesis for this ANOVA F test is: the population mean load failures for the three etch times are all different the population mean load failure is lowest for the 15‑second condition and highest for 60‑second condition at least one population mean load failure differs the sample mean load failure is lowest for the 15‑second condition and highest for 60‑second condition the sample mean load failures for the three etch times are all different the population mean load failures for the three etch times are all equal
Answer:
The population mean load failures for the three etch times are all equal
Step-by-step explanation:
For an ANOVA F test, the null hypothesis always assumes that mean which is also the average value of the dependent variable which is continuously are the same/ there is no difference in the means. The alternative is to test against the null and it is always the opposite of the null hypothesis.
Mary is running a marathon which is a total of 26 miles. She is running at a pace of 7.5 miles per hour and
has already run 8 miles. If she stays at the same pace, how much time in hours does she have left?
Answer:
2.4 hours
Step-by-step explanation:
If Mary is running 26 miles at a pace of 7.5 miles per hour, it will take her 3.47 hours to run the full course.
26/7.5 = 3.466666...
If she has run 8 miles, 1.07 hours have passed.
8/7.5 = 1.06666666...
Subtract the total time from the time that has already passed to find the time left.
3.47 - 1.07 = 2.4
Mary has 2.4 hours left.
Can advise on the solution?
Answer:
340
Step-by-step explanation:
If x is the amount of pages in the book we can write:
1/4x + 5 + 3/5(x - (1/4x + 5)) + 10 + 12 + 24 = x
1/4x + 51 + 3/5(3/4x - 5) = x
1/4x + 51 + 9/20x - 3 = x
7/10x + 48 = x
3/10x = 48
x = 160
Please answer this correctly
Answer:
6 pizzas
Step-by-step explanation:
At least 10 and fewer than 20 makes it 10-19
So,
10-19 => 6 pizzas
6 pizzas have at least 10 pieces of pepperoni but fewer than 20 pieces of pepperoni.
The valve was tested on 270 engines and the mean pressure was 6.6 lbs/square inch. Assume the variance is known to be 0.49. If the valve was designed to produce a mean pressure of 6.5 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve does not perform to the specifications
Answer:
[tex]z=\frac{6.6-6.5}{\frac{0.7}{\sqrt{270}}}=2.347[/tex]
The p value for this case would be given by"
[tex]p_v =2*P(z>2.347)=0.0189[/tex]
For this case since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is significantly different from 6.5 lbs/square inch at 10% of significance. So then there is not enough evidence to conclude that the valve does not perform to the specifications
Step-by-step explanation:
Information given
[tex]\bar X=6.6[/tex] represent the sample mean
[tex]s=\sqrt{0.49}= 0.7[/tex] represent the population deviation
[tex]n=270[/tex] sample size
[tex]\mu_o =6.5[/tex] represent the value that we want to test
[tex]\alpha=0.1[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value for the test
Hypothesis to verify
We want to verify if the true mean for this case is equal to 6.5 lbs/square inch or not , the system of hypothesis would be:
Null hypothesis:[tex]\mu= 6.5[/tex]
Alternative hypothesis:[tex]\mu \neq 6.5[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]z=\frac{6.6-6.5}{\frac{0.7}{\sqrt{270}}}=2.347[/tex]
The p value for this case would be given by"
[tex]p_v =2*P(z>2.347)=0.0189[/tex]
For this case since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is significantly different from 6.5 lbs/square inch at 10% of significance. So then there is not enough evidence to conclude that the valve does not perform to the specifications
A manager bought 12 pounds of peanuts for $30. He wants to mix $5 per pound cashews with the peanuts to get a batch of mixed nuts that is worth $4 per pound. How many pounds of cashews are needed
Answer:
18 pounds of cashews are needed.
Step-by-step explanation:
Given;
A manager bought 12 pounds of peanuts for $30.
Price of peanut per pound P = $30/12 = $2.5
Price of cashew per pound C = $5
Price of mixed nut per pound M = $4
Let x represent the proportion of peanut in the mixed nut.
The proportion of cashew will then be y = (1-x), so;
xP + (1-x)C = M
Substituting the values;
x(2.5) + (1-x)5 = 4
2.5x + 5 -5x = 4
2.5x - 5x = 4 -5
-2.5x = -1
x = 1/2.5 = 0.4
Proportion of cashew is;
y = 1-x = 1-0.4 = 0.6
For 12 pounds of peanut the corresponding pounds of cashew needed is;
A = 12/x × y
A = 12/0.4 × 0.6 = 18 pounds
18 pounds of cashews are needed.
Google I would like to purchase 10 bags of chicken wings the store is selling three bags for $51.00 what is the cost of 10 bags of chicken wings
a. 61.00
b. 71.00
c. 170.00
d. 130.00
Answer:
A 61.00
Step-by-step explanation:
51 Added to 10 Equals 61.00 which is the Cost of 10 Bags of chicken Wings. Your Welcome.
Write an equation for a polynomial function that has the given roots
-2. 3i , and 5
Answer:
x^4 - 3x^3 - x^2 - 27x - 90 = 0.
Step-by-step explanation:
If 3i is one root then another is -3i.
In factor form we have:
(x + 2)(x - 5)(x - 3i)(x + 3i) = 0
(x^2 - 3x - 10)(x^2 -9i^2) = 0
(x^2 - 3x - 10)(x^2 + 9) = 0
x^4 + 9x^2 - 3x^3 - 27x - 10x^2 - 90 = 0
x^4 - 3x^3 - x^2 - 27x - 90 = 0.
Please help me or assist me in answering this Thank you 5 2/3 X 6 7/8
Answer: 38 23/24
Step-by-step explanation:
Turn the mixed numbers into improper fractions
5 * 3 = 15
15 + 2 = 17
17/3
————————
6 * 8 = 48
48 + 7 = 55
55/8
————————
Now multiply the improper fractions
17/3 * 55/8
17 * 55 = 935
3 * 8 = 24
Divide 935 by 24 to get the answer as a mixed number.
935 / 24 = 38.95833
0.95833/1 = 23/24
935/24 as a mixed number is 38 23/24
Answer: 119 / 4
Step-by-step explanation:
5 2/3 x 6 7/8
= 17/3 x 6 x 7/8
= 17 x 2 x 7/8
= 17 x 2 x 7/8
= 17 x 7/4
= 119 / 4
In d e f, d f equals 16 and F equal 26. Find Fe to the nearest tenth
Answer:
14.4 units
Step-by-step explanation:
In Trigonometry
[tex]\cos \theta =\frac{Adjacent}{Hypotenuse}\\[/tex]
In Triangle DEF,
[tex]\cos F =\dfrac{EF}{DF}\\\cos 26^\circ =\dfrac{EF}{16}\\EF=16 \times \cos 26^\circ\\=14.4$ units (correct to the nearest tenth).[/tex]
anyone please answer this
Answer:
21
Step-by-step explanation:
1/5 of 30 is 6
10% of 30 is 3
3+6=9
30-9=21
which is 7/10
Answer:
Simon has 7/10 of the cakes left.
A student walk 60m on a bearing
of 028 degree and then 180m
due east. How is she from her
starting point, correct to the
nearest whole number?
Answer:
d = 234.6 m
Step-by-step explanation:
You can consider a system of coordinates with its origin at the beginning of the walk of the student.
When she start to walk, she is at (0,0)m. After her first walk, her coordinates are calculated by using the information about the incline and the distance that she traveled:
[tex]x_1=60cos28\°=52.97m\\\\y_1=60sin28\°=28.16m[/tex]
she is at the coordinates (52.97 , 28.16)m.
Next, when she walks 180m to the east, her coordinates are:
(52.97+180 , 28.16)m = (232.97 , 28.16)m
To calculate the distance from the final point of the student to the starting point you use the Pythagoras generalization for the distance between two points:
[tex]d=\sqrt{(x-x_o)^2+(y-y_o)^2}\\\\x=232.97\\\\x_o=0\\\\y=28.16\\\\y_o=0\\\\d=\sqrt{(232.97-0)^2+(28.16-0)^2}m=234.6m[/tex]
The displacement of the student on her complete trajectory was of 234.6m
Approximately 8% of all people have blue eyes. Out of a random sample of 20 people, what is the probability that 2 of them have blue eyes? Round answer to 4 decimal places. Answer:
Answer:
27.11% probability that 2 of them have blue eyes
Step-by-step explanation:
For each person, there are only two possible otucomes. Either they have blue eyes, or they do not. The probability of a person having blue eyes is independent of any other person. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
8% of all people have blue eyes.
This means that [tex]p = 0.08[/tex]
Random sample of 20 people:
This means that [tex]n = 20[/tex]
What is the probability that 2 of them have blue eyes?
This is P(X = 2).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{20,2}.(0.08)^{2}.(0.92)^{18} = 0.2711[/tex]
27.11% probability that 2 of them have blue eyes
The probability that 2 of them have blue eyes is 27.11%.
Given that,
Approximately 8% of all people have blue eyes.
Out of a random sample of 20 people,
We have to determine,
What is the probability that 2 of them have blue eyes?
According to the question,
People having blue eyes p = 8% = 0.08
Sample of people n = 20
For each person, there are only two possible outcomes. Either they have blue eyes, or they do not.
The probability of a person having blue eyes is independent of any other person.
The probability that 2 of them have blue eyes is determined by using a binomial probability distribution.
[tex]\rm P (X = x) =n_C_x\times p^x \times (1-p)^{n-x}}[/tex]
Therefore,
The probability that 2 of them have blue eyes is,
[tex]\rm P (X = x) =n_C_x\times p^x \times (1-p)^{n-x}}\\\\ \rm P (X = x) = \dfrac{n!}{(n-x)! \times x!} \times p^x \times (1-p)^{n-x}}\\\\[/tex]
Substitute all the values in the formula,
[tex]\rm P (X = 2) = \dfrac{20!}{(20-2)! \times 2!} \times (0.08)^2 \times (1-0.08)^{20-2}}\\\\ P (X = 2) = \dfrac{20!}{(18)! \times 2!} \times (0.0064) \times (0.92)^{18}}\\\\ P (X = 2) = \dfrac{19\times 20}{ 2} \times (0.0064) \times (0.222)\\\\ P(X = 2) = {19\times 10}\times (0.00142)\\\\P(X = 2) = 0.2711\\\\P(X = 2) = 27.11 \ Percent[/tex]
Hence, The required probability that 2 of them have blue eyes is 27.11%.
For more details refer to the link given below.
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Solve for x. 9x-2c=k
The life of an electric component has an exponential distribution with a mean of 8.9 years. What is the probability that a randomly selected one such component has a life more than 8 years? Answer: (Round to 4 decimal places.)
Answer:
[tex] P(X>8)[/tex]
And for this case we can use the cumulative distribution function given by:
[tex] F(x) = 1- e^{-\lambda x}[/tex]
And if we use this formula we got:
[tex] P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070[/tex]
Step-by-step explanation:
For this case we can define the random variable of interest as: "The life of an electric component " and we know the distribution for X given by:
[tex]X \sim exp (\lambda =\frac{1}{8.9}) [/tex]
And we want to find the following probability:
[tex] P(X>8)[/tex]
And for this case we can use the cumulative distribution function given by:
[tex] F(x) = 1- e^{-\lambda x}[/tex]
And if we use this formula we got:
[tex] P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070[/tex]
A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. In a random sample of 36 bins, the sample mean amount was 48.99 pounds and the sample standard deviation was 3.7 pounds. Conduct the appropriate hypothesis test using a 0.01 level of significance.
a) What is the test statistic? Give your answer to four decimal places.
b) What is the P-value for the test? Give your answer to four decimal places.
Answer:
Step-by-step explanation:
Claim: if the mean amount of garbage per bin is different from 50.
Null hypothesis: u=50
Alternative hypothesis : u =/ 50
Using the z score formular for a one sample z test - z = (x - u ) / (sd/√n)
Where x = 48.99, u = 50 sd =3.7 and n = 36
z = 48.99 - 50 / (3.7/√36)
z = -1.01 / (3.7/6)
z = -1.01/0.6167
z = -1.6377
To find the p value at a 0.01 level of significant from the -1.6377 z score for a two tailed test the p value using the p value calculator is 0.1016. The result is not significant at 0.01 level of significant thus we will fail to reject the null and conclude that the mean amount of garbage per bin is 50.
The top figure in the composite figure is called a . And What is the volume?
Answer:
Triangular Prism
volume 748
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 442 gram setting. It is believed that the machine is underfilling the bags. A 44 bag sample had a mean of 438 grams. Assume the population variance is known to be 576. A level of significance of 0.1 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.
Answer:
p value is 0.1343
Step-by-step explanation:
Null: u>= 442
Alternative: u < 442
Using the formula for z score:
(x - u)/sd/√n
Where x is 438, u = 442 sd can be determined from the variance = √variance =√576 = 24 and n = 44
z score = 438-442 / (24/√44)
z score = -4/(24/6.6332)
z = -4/3.6182
z =-1.1055
Now let's find the p value at 0.1 significance level using a z score of -1.1055, using a p value calculator, p value is 0.1343 which greatest than 0.1 meaning the day is not sufficient enough to conclude that the machine is underfilling the bags.
Please answer this correctly
Answer:
33.3%
Step-by-step explanation:
The numbers greater than 6 from the spinner are 7 and 8.
2 numbers out of total 6 numbers.
2/6 = 1/3
= 0.333
= 33.3%
A grasshopper sits on the first square of a 1×N board. He can jump over one or two squares and land on the next square. The grasshopper can jump forward or back but he must stay on the board. Find the least number n such that for any N ≥ n the grasshopper can land on each square exactly once.
Answer:
n=N-1
Step-by-step explanation:
You can start by imagining this scenario on a small scale, say 5 squares.
Assuming it starts on the first square, the grasshopper can cover the full 5 squares in 2 ways; either it can jump one square at a time, or it can jump all the way to the end and then backtrack. If it jumps one square at a time, it will take 4 hops to cover all 5 squares. If it jumps two squares at a time and then backtracks, it will take 2 jumps to cover the full 5 squares and then 2 to cover the 2 it missed, which is also 4. It will always be one less than the total amount of squares, since it begins on the first square and must touch the rest exactly once. Therefore, the smallest amount n is N-1. Hope this helps!
The smallest value of n is N-1.
What is a square?Square is a quadrilateral of equal length of sides and each angle of 90°.
Here given that there are 1×N squares i.e. N numbers of squares in one row.
The grasshopper can jump either one square or two squares to land on the next square.
Let's assume the scenario of 5 squares present in a row.
Let the grasshopper starts from the first square,
so the grasshopper can cover the full 5 squares in 2 methods;
one method is that it will jump one square at a time and reach at last square.
another method is it will jump all the squares to the finish and then backtrace.
If the grasshopper jumps one square at a time, it will take 4 jumps to cover all 5 squares.
Similarly, If a grasshopper jumps two squares at a time and then backtrace, it will take 2 jumps to reach the 5th square and then it will jump 1 square and then 2 squares to cover the 2 squares it missed, for which the number jump is also 4.
From the above it is clear that the number of jumps will always be one less than the total number of squares if the grasshopper begins from the first square and touch every square exactly once.
Therefore, the smallest value of n is N-1.
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Show all work to identify the asymptotes and zero of the faction f(x) = 4x/x^2 - 16.
Answer:
asymptotes: x = -4, x = 4zeros: x = 0Step-by-step explanation:
The vertical asymptotes of the rational expression are the places where the denominator is zero:
x^2 -16 = 0
(x -4)(x +4) = 0 . . . . . true for x=4, x=-4
x = 4, x = -4 are the equations of the vertical asymptotes
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The zeros of a rational expression are the places where the numerator is zero:
4x = 0
x = 0 . . . . . . divide by 4