Answer:
The dimensions of the rectangular box is 36.23 ft×36.23 ft×4.345 ft.
Minimum cost=2046.16 cents
Step-by-step explanation:
Given that a rectangular box with a volume of 684 ft³.
The base and the top of the rectangular box is square in shape
Let the length and width of the rectangular box be x.
[since the base is square in shape, length=width]
and the height of the rectangular box be h.
The volume of rectangular box is = Length ×width × height
=(x²h) ft³
[tex]x^2h=684\Rightarrow h=\frac{684}{x^2}[/tex] (1)
The area of the base and top of rectangular box is = x² ft²
The surface area of the sides= 2(length+width) height
=2(x+x)h
=4xh ft²
The total cost to construct the rectangular box is
=[(x²×20)+(x²×15)+(4xh×1.5)] cents
=(20x²+15x²+6xh) cents
=(25x²+6xh) cents
Total cost= C(x).
C(x) is in cents.
∴C(x)=25x²+6xh
Putting [tex]h=\frac{684}{x^2}[/tex]
[tex]C(x)=25x^2+6x\times\frac{684}{x^2} \Rightarrow C(x)=25x^2+\frac{4104}{x}[/tex]
Differentiating with respect to x
[tex]C'(x)=50x-\frac{4104}{x^2}[/tex]
To find minimum cost, we set C'(x)=0
[tex]\therefore50x-\frac{4104}{x^2}=0\\\Rightarrow50x=\frac{4104}{x^2}\\\Rightarrow x^3=\frac{4104}{50}\Rightarrow x\approx 4.345[/tex] ft.
Putting the value x in equation (1) we get
[tex]h=\frac{684}{(4.345)^2}[/tex]
≈36.23 ft.
The dimensions of the rectangular box is 36.23 ft×36.23 ft×4.345 ft.
Minimum cost C(x)=[25(4.345)²+10(4.345)(36.23)] cents
=2046.16 cents
If prices increase at a monthly rate of 2.7 by what do they increase in a year
Answer:
37.67%
Step-by-step explanation:
Suppose initially a price of $ 100
Increasing per month at a rate of 2.7%. Which is equal to 0.027
Now applying the formula:
Vf = Vi * (1 + m) ^ n
where Vf is the final quantity, Vi is the initial value, m is the rate and n is the number of months.
We know that 1 year, is 12 months, since the rate is monthly means, n = 12, we replace:
Vf = 100 * (1 + 0.027) ^ 12
Vf = 137.67
It means price increase in 1 year = 137.67 - 100 = 37.67
Which means that n a year increases to 37.67%
Find the function for this...
Answer:
Step-by-step explanation:
Midline is the horizontal line that passes exactly in the middle between the graph's maximum and minimum points.
Amplitude is the vertical distance between the midline and one of the extremum points.
Period is the distance between two consecutive maximum points, or two consecutive minimum points (these distances must be equal).
To find the formula for [tex]g(x)[/tex]. First, let's use the given information to determine the function's amplitude, midline, and period.
The midline of a sinusoidal function passes exactly in the middle of its extreme values. So we can find the midline by finding the average of the maximum and minimum values.
The midline passes exactly between the minimum value 1, and the maximum value 11, so the midline equation is
[tex]midline=y=\frac{11+1}{2} =6[/tex]
The extremum points are 5 units above or below the midline, so the amplitude is 5.
The maximum point is 0.5 units to the right of the minimum point, so the period is [tex]2\cdot 0.5 =1[/tex]. We multiply by 2 because the distance between consecutive minimum and maximum points is always [tex]\frac{1}{2}[/tex] of the period.
The general sinusoidal equation [tex]y=a\cos(bx)+d[/tex] is the result of horizontal and vertical shifts, reflections, and stretches of the parent equation [tex]y=\cos(x)[/tex] where
The amplitude is [tex]|a|[/tex].The midline is [tex]y=d[/tex].The period is [tex]\frac{2\pi }{|b|}[/tex].The amplitude is 5, so [tex]|a|=a=5[/tex].
The midline is y = 6, so d = 6.
The period is 1, so b = [tex]\frac{2\pi }{1}=2\pi[/tex].
The formula for [tex]g(x)=5\cos(2\pi x)+6[/tex].
Suppose you draw a card from the set of cards, record the letter, return the card to the set, and shuffle the cards. You can repeat this experiment 22 times. Would you expect the experimental probability of drawing a vowel to be the same as the theoretical probability?
Answer:
They should not be exactly the same but they should be close.
Step-by-step explanation:
The first thing that we must take into account is the following:
Experimental probability is the result of an experiment, and theoretical probability is based on the mathematical model developed in probability theory. With the above, we can affirm that the precision of the results of the experiments depends directly on the sample size of the experiment and the precision is greater when the sample size is greater.
This means that the odds are most likely not the same, they must be very close since it has been repeated a considerable number of times and the more times it is done the closer they will be to being the same.
Boxes A and B contained 112 pencils. When 1/5 of the pencils in box A were transferred to box B, both boxes combined the same number of pencils. How many more pencils were there in box A than in Box B at first?
Answer:
The number of pencils in the box A is 70
The number of pencils in the box B is 42
Step-by-step explanation:
The number of pencils in the box A is a
The number of pencils in the box B is b
We have:
a + b = 112
a - (1/5)a = b + (1/5)a
or
a + b = 112
a - (2/5)a = b
or
a + b = 112
(3/5)a = b
or
a + (3/5)a = 112
or
(8/5)a = 112
or
a = 112*(5/8)
or
a = 70
=> b = 112 - 70 = 42
Hope this helps!
Salid bought 30 feet of window trim at a hardware store. The trim cost $1.75 per foot including sales tax. If Salid paid with a $100.00 bill, how much change should he have received?
Answer:
47.50
Step-by-step explanation:
According to the question above Salid bought 30 feet of window at a hardware trim store
The trim cost of each window is $1.75 per foot with an inclusion of sales tax added to this amount
= $1.75×30
= 52.5
Since Salid paid for the trim service with a cash of $100.00, his change is calculated as follows
=$100-52.5
= $47.50
Hence Salid change is $47.50
According to the general equation for conditional probability, if P(A, B) =4/7
and P(B) =7/8 - what is P(AIB)?
Answer:
[tex]P(A|B) = \frac{32}{49}[/tex]
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)}[/tex]
In which
P(A|B) is the probability of event A happening, given that B happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(B) is the probability of B happening.
We have that:
[tex]P(A \cap B) = \frac{4}{7}, P(B) = \frac{7}{8}[/tex]
So
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{4}{7}}{\frac{7}{8}} = \frac{4}{7}*\frac{8}{7} = \frac{32}{49}[/tex]
Then
[tex]P(A|B) = \frac{32}{49}[/tex]
Determine the maximized area of a rectangle that has a perimeter equal to 56m by creating and solving a quadratic equation. What is the length and width?
Answer:
Area of rectangle = [tex]196\,m^2[/tex]
Length of rectangle = 14 m
Width of rectangle = 14 m
Step-by-step explanation:
Given:
Perimeter of rectangle is 56 m
To find: the maximized area of a rectangle and the length and width
Solution:
A function [tex]y=f(x)[/tex] has a point of maxima at [tex]x=x_0[/tex] if [tex]f''(x_0)<0[/tex]
Let x, y denotes length and width of the rectangle.
Perimeter of rectangle = 2( length + width )
[tex]=2(x+y)[/tex]
Also, perimeter of rectangle is equal to 56 m.
So,
[tex]56=2(x+y)\\x+y=28\\y=28-x[/tex]
Let A denotes area of rectangle.
A = length × width
[tex]A=xy\\=x(28-x)\\=28x-x^2[/tex]
Differentiate with respect to x
[tex]\frac{dA}{dx}=28-2x[/tex]
Put [tex]\frac{dA}{dx}=0[/tex]
[tex]28-2x=0\\2x=28\\x=14[/tex]
Also,
[tex]\frac{d^2A}{dx^2}=-2<0[/tex]
At x = 14, [tex]\frac{d^2A}{dx^2}=-2<0[/tex]
So, x = 14 is a point of maxima
So,
[tex]y=28-x=28-14=14[/tex]
Area of rectangle:
[tex]A=xy=14(14)=196\,m^2[/tex]
Length of rectangle = 14 m
Width of rectangle = 14 m
In a certain area an average of 13 new swarms of honeybees are seen each spring. If the number of swarms stays constant each year, what is the probability of observing between 9 and 15 (inclusive) swarms?
Answer:
The probability of observing between 9 and 15 (inclusive) swarms is 0.6639.
Step-by-step explanation:
The random variable X can be defined as the number of swarms of honeybees seen each spring.
The average value of the random variable X is, λ = 13.
A random variable representing the occurrence of events in a fixed interval of time is known as Poisson random variables.
For example, the number of customers visiting the bank in an hour or the number of typographical error is a book every 10 pages.
So, the random variable X follows a Poisson distribution with parameter λ = 13.
The probability mass function of X is as follows:
[tex]P(X=x)=\frac{e^{-\lambda}\ \lambda^{x}}{x!}; x=0,1,2,3...[/tex]
Compute the the probability of observing between 9 and 15 (inclusive) swarms as follows:
P (9 ≤ X ≤ 15) = P (X = 9) + P (X = 10) + P (X = 11) + ... + P (X = 15)
[tex]=\sum\limits^{15}_{x=9}{\frac{e^{-\lambda}\ \lambda^{x}}{x!}}\\\\=0.06605+0.08587+0.10148+0.10994\\+0.10994+0.10209+0.08848\\\\=0.66385\\\\\approx 0.6639[/tex]
Thus, the probability of observing between 9 and 15 (inclusive) swarms is 0.6639.
In performing a chi-square goodness-of-fit test with multinomial probabilities, the ___________ the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are correct.
Answer:
Step-by-step explanation:
The smaller/closer the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are correct concluding that the data fits that particular distribution given.
State the null and alternative hypotheses for each of the following situations. (That is, identify the correct number μο and write to : μ analogous expression for Ha) Ao and the appropriate
a. The average time workers spent commuting to work in Verona five years ago was 38.2 minutes. The Verona Chamber of Commerce asserts that the average is less now
b. The mean salary for all men in a certain profession is $58,291. A special interest
c. The accepted figure for the caffeine content of an 8-ounce cup of coffee is 133 mg. A dietitian believes that the average for coffee served in a local restaurants is higher
d. The average yield per acre for all types of corn in a recent year was 161.9 bushels. An economist believes that the average yield per acre is different this year.
e. An industry association asserts that the average age of all self-described fly fishermen is 42.8 years. A sociologist suspects that it is higher.
Answer:
a) The null hypothesis is given as
H₀: μ₀ ≥ 38.2 minutes
The alternative hypothesis is given as
Hₐ: μ₀ < 38.2 minutes
b) The null hypothesis is given as
H₀: μ₀ = $58,291
The alternative hypothesis is given as
Hₐ: μ₀ ≠ $58,291
c) The null hypothesis is given as
H₀: μ₀ ≤ 133.0 mg
The alternative hypothesis is given as
Hₐ: μ₀ > 133 mg
d) The null hypothesis is given as
H₀: μ₀ = 161.9 bushels
The alternative hypothesis is given as
Hₐ: μ₀ ≠ 161.9 bushels
e) The null hypothesis is given as
H₀: μ₀ ≤ 42.8 years
The alternative hypothesis is given as
Hₐ: μ₀ > 42.8 years
Step-by-step explanation:
In hypothesis testing, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that, with random chance responsible for the outcome or results of any experimental study/hypothesis testing, its statement is true.
The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in its own statement.
Taking the statements one at a time
a) The assertion is that the new average time workers spent commuting to work in Verona is now less than the old average.
The null hypothesis would be there isn't enough evidence to conclude that the new average time workers spent commuting to work in Verona is now less than the old average. That is, the new average time workers spent commuting to work in Verona is now equal to or more than the old average.
The alternative hypothesis is that the new average time workers spent commuting to work in Verona is now less than the old average.
Mathematically, if μ₀ = new average time workers spent commuting to work in Verona.
The null hypothesis is given as
H₀: μ₀ ≥ 38.2 minutes
The alternative hypothesis is given as
Hₐ: μ₀ < 38.2 minutes
b) Although the question isn't complete,
The null hypothesis is that there isn't a significant difference between whatever is being compared in the complete question and the mean salary for all men in that profession.
The alternative hypothesis is that there is significant difference between whatever is being compared in the complete question and the mean salary for all men in that profession.
Mathematically, if μ₀ = Mean of whatever is being compared in the complete question
The null hypothesis is given as
H₀: μ₀ = $58,291
The alternative hypothesis is given as
Hₐ: μ₀ ≠ $58,291
c) The claim to be proved is that the average caffeine content for coffee served in a local restaurants is higher.
The null hypothesis is that the average caffeine content for coffee served in a local restaurants is not higher than the standard figure of 133 mg for an 8 ounce cup. That is, the average caffeine content for coffee served in a local restaurants is not higher than the standard figure of 133 mg for an 8 ounce cup.
The alternative hypothesis is that average caffeine content for coffee served in a local restaurants is higher than the standard figure of 133 mg for an 8 ounce cup.
Mathematically, if μ₀ = average caffeine content for coffee served in a local restaurants.
The null hypothesis is given as
H₀: μ₀ ≤ 133.0 mg
The alternative hypothesis is given as
Hₐ: μ₀ > 133 mg
d) The economist claims that the average yield per acre this year is different from the average yield per acre in recent years.
Hence, the null hypothesis is that there is no significant difference between the average yield per acre this year and the average yield per acre in recent years.
The alternative hypothesis is that there is significant difference between the average yield per acre this year and the average yield per acre in recent years.
Mathematically, if μ₀ = the average yield per acre this year
The null hypothesis is given as
H₀: μ₀ = 161.9 bushels
The alternative hypothesis is given as
Hₐ: μ₀ ≠ 161.9 bushels
e) The sociologist suspects that the average age of all self-described fly fishermen is higher than 42.8 years.
Hence, the null hypothesis is that the average age of all self-described fly fishermen is not higher than 42.8 years. That is, the average age of all self-described fly fishermen is equal to less than 42.8 years.
The alternative hypothesis is that the average age of all self-described fly fishermen is higher than 42.8 years.
Mathematically, if μ₀ = average age of all self-described fly fishermen.
The null hypothesis is given as
H₀: μ₀ ≤ 42.8 years
The alternative hypothesis is given as
Hₐ: μ₀ > 42.8 years
Hope this Helps!!!
An ice-cream shop uses the following ingredients to make one sundae.
Ingredients. Amount
Ice-cream- 2 scoops
Sprinkles- 4 spoonful's
Whipped Cream- 2 tablespoons
How many sundaes did the shop make if they used 32 spoonful's of whipped cream?
Answer:
16
Step-by-step explanation:
there are 2 tbs of whipped cream per sundae so you have to divide 32 by 2 and get 16
Answer: 8
Step-by-step explanation:
For every 1 sundae, the shop uses 4 spoonfuls of sprinkles. The ratio of sundaes to spoonfuls of sprinkles is 1:4.
The shop used 32 spoonfuls of sprinkles.
Since the number of spoonfuls of sprinkles was multiplied by 8, we also need to multiply the number of sundaes by 8.
The shop made 8 sundaes.
The ice cream shop has 7 types of toppings available, and you decide to add 4 toppings to your bowl of 5 scoops of ice cream. How many combinations of 5 scoops of ice cream and 4 toppings are possible
Answer: 35
Step-by-step explanation:
The number of combinations of r things selected out of n things is given by
[tex]^nC_r= \dfrac{n!}{r!(n-r)!}[/tex]
Given , the total number of types of toppings available = 7
The number of toppings needed to be selected = 4
Then, the number of ways to do this would be
[tex]^7C_4=\dfrac{7!}{4!(7-4)!}\\\\=\dfrac{7\times6\times5\times4!}{4!3!}\\\\=\dfrac{7\times5}{1}=35[/tex]
Hence, the number of combinations of 5 scoops of ice cream and 4 toppings are possible = 35.
Please answer this correctly
Answer:
B) Mia Hamm helped her soccer team at the University of North Carolina at Chapel Hill win four NCAA titels.
Step-by-step explanation:
The first option is an opinion, not a fact.
Of 585 samples of seafood purchased from various kinds of food stores in different regions of a country and genetically compared to standard gene fragments that can identify the species, 19% were mislabeled. a) Construct a 99% confidence interval for the proportion of all seafood sold in the country that is mislabeled or misidentified. b) Explain what your confidence interval says about seafood sold in the country. c) A government spokesperson claimed that the sample size was too small, relative to the billions of pieces of seafood sold each year, to generalize. Is this criticism valid? a) What is the 99% confidence interval? The 99% confidence interval is from nothing% to nothing%. (Round to one decimal place as needed.)
Answer:
a) The 99% confidence interval is from 14.8% to 23.2%.
b) The confidence interval tells us that the true proportion of mislabeled is within 14.8% and 23.2%, with a 99% confidence. In other words, if we take samples of the same size, 99% of the samples will have a proportion within 0.148 and 0.232.
c) The confidence interval calculation take into account the sample size, so the width (or precision) of the interval depends on the sample size.
The only criticism that could be analyzed is to see if the sample is representative of the population.
Step-by-step explanation:
a) We have to calculate a 99% confidence interval for the proportion.
The sample proportion is p=0.19.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.19*0.81}{585}}\\\\\\ \sigma_p=\sqrt{0.000263}=0.016[/tex]
The critical z-value for a 99% confidence interval is z=2.576.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=2.576 \cdot 0.02=0.042[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.19-0.042=0.148\\\\UL=p+z \cdot \sigma_p = 0.19+0.042=0.232[/tex]
The 99% confidence interval for the population proportion is (0.148, 0.232).
Use slopes and y-intercepts to determine if the lines y=5x+5 and 5x−y=−5 are parallel.
Answer: They are not parallel, they are coincident
Step-by-step explanation:
If two lines have the same slope but a different y-intercept, the lines are parallel. If two lines have the same slope and the same y-intercept, the lines are coincident.
We can rewrite 5x−y=−5 adding -5x to both sides and multiplying by -1:
5x - y =-5
5x - y -5x = -5 - 5x (adding -5x to both sides)
-y = -5 - 5x
Multiplying by -1
y = 5x + 5
Both equations look the same so they are coincident. They have the same intercept y=5 and the same slope m=5.
a discount voucher offering 15% off is used to pay a bill. after using the voucher the bill is reduced to £36.72.
how much was the bill before applying the voucher discount?
A recent gasoline survey said that the national average price of gasoline was $1.298 a gallon. It was felt that gasoline price in Texas was significantly lower than the national average. A study of 37 different suburbs in Dallas, Texas, found the average price of gasoline to be $1.192 a gallon with a standard deviation of $0.0436. What is the alternative hypothesis
Answer:
alternative hypothesis : H₁ :
Recent Gasoline surveys felt that gasoline price in Texas was significantly lower than the national average
Alternative Hypothesis : H₁: μ < $1.298 a gallon
Step-by-step explanation:
Explanation:-
Given A recent gasoline survey said that the national average price of gasoline was $1.298 a gallon
Population average μ= $1.298 a gallon
sample size 'n' = 37
Sample mean (x⁻) = $1.192 a gallon
Sample standard deviation 'S' = $0.0436
Null hypothesis :H₀ : μ = $1.298 a gallon
Alternative Hypothesis : μ < $1.298 a gallon
Degrees of freedom : ν = n-1= 37-1=36
t₀.₀₂₅ = 1.688
Test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{1.192-1.298 }{\frac{0.0436}{\sqrt{37} } }[/tex]
t = -14.8044
|t| = |-14.8044| > 1.688
Null hypothesis is rejected
Alternative hypothesis is accepted
Recent Gasoline surveys felt that gasoline price in Texas was significantly lower than the national average
Select all statements below that are true about the binomial distribution shown on the right. The bar for any number k represents the probability of getting k successes in 5 flips. The number of successes, k, can range from 0 (no success) to 5 (all successes). Each coin flip is independent; it is not affected by any other coin flip. For 5 coin flips, P(2 heads) = P(3 heads). The sum of the probabilities shown in the binomial distribution is p.
Answer:
Step-by-step explanation:
Hello!
Distribution in attachment.
The variable of interest is:
X: Number of successes after flipping a coin 5 times.
If you check the binomial criteria:
The number of trials is fixed: n=5
There are only two possible outcomes "success" or "failure"
Each flip of the coin is independent of the others.
The probability of success in the same from one trial to another, in this case, if we consider the coin to be balanced, the probability of success is p=0.5
The histogram shows the probability of obtaining X number of success in 5ve flips of a coin (y-axis) vs the number of successes counted each (x-axis)
Statements:
1) The bar for any number k represents the probability of getting k successes in 5 flips. Correct. The histogram shows the probability of obtaining X number of success in 5ve flips of a coin (y-axis) vs the number of successes counted each (x-axis). Each bar represents the probability of success for each possible value.
2) The number of successes, k, can range from 0 (no success) to 5 (all successes). Correct. The variable count the number of successes after flipping a coin 5 times. It can happen that you flip it and all the flips turn to be failures (X=0), that you flip it 5 times and only one turns out to be a success and the other 4 are failures (X=1), and so on until you flip it 5 times and all flips are successes (X=5)
3) Each coin flip is independent; it is not affected by any other coin flip. Correct, if not, this variable wouldn't have a binomial distribution as specified in the text.
4) For 5 coin flips, P(2 heads) = P(3 heads). Correct
Looking at the histogram, the bars for "2 successes" and "3 successes" have the same height, a little above 0.3, this means that both values have the same probability of occurrence.
5) The sum of the probabilities shown in the binomial distribution is p.
Incorrect.
For the binomial distribution "p" represents the probability of success for each trial, in this case, flipping the coin once.
For this distribution, as well as for other probability distribution, the sum of all probabilities is always 1, if not, then it is not a probability distribution.
I hope this helps!
Answer:
Lets make this easier for you guys. The correct answers are 1 through 4.
The bar for any number k represents the probability of getting k successes in 5 flips.
The number of successes, k, can range from 0 (no success) to 5 (all successes).
Each coin flip is independent; it is not affected by any other coin flip.
For 5 coin flips, P(2 heads) = P(3 heads
Step-by-step explanation:
Correct on edge :))
About 70,000 people live in a 6-mile radius of a city's town hall. Find the population density in people per square mile. Round your answer to the nearest whole number.
The population density is about _
people per square mile.
Answer:
The population density is 618.93 per square mile.
Step-by-step explanation:
It is given that,
No. of people, N = 70,000
The radius of a city's town hall, r = 6 miles
We need to find the population density. It can be calculated by the formula i.e. number of people divided by area of land such that,
[tex]P=\dfrac{N}{A}\\\\P=\dfrac{N}{\pi r^2}\\\\P=\dfrac{70000}{\pi (6)^2}\\\\P=618.93\ \text{per square mile}[/tex]
So, the population density is 618.93 per square mile.
What is
3 1/6 - 2 5/6 =??
The answer is 1/3
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer: 1/3
Step-by-step explanation: To subtract mixed numbers, first subtract the fractions.
Notice here however that we have 1/6 - 5/6
which will give us a negative fraction.
Since this will cause us a lot of trouble, instead,
let's rewrite the first mixed number.
We can do this by thinking of 3 and 1/6 as 2 + 1 and 1/6 or 2 + 7/6
by changing 1 and 1/6 into an improper fraction.
So 3 and 1/6 can be written as 2 and 7/6.
So we have 2 and 7/6 - 2 and 5/6.
Now, subtract the fractions.
So we have 7/6 - 5/6 which is 2/6.
Then subtract the whole numbers.
2 - 2 is 0.
However, we don't need to include 0 in our answer.
We can write our answer as 2/6.
However, 2/6 is not in lowest terms.
So divide the numerator and denominator by 2 to get 1/3.
So 3 and 1/6 - 2 and 5/6 is 1/3.
You need to remove a tree from your front yard. You have climbed the tree and trimmed off the branches, and you are now ready to chop down the trunk. It is very important that the tree falls in the right direction… away from your house. You have attached a wire to the top of the trunk. You will attach the other end of the wire to the ground and pull it tightly so that when the trunk begins to fall, the wire will pull it in the right direction. The trunk is 24 feet tall and you are going to attach the wire to the ground 10 feet away from the base of the trunk. a) How long must your wire be to reach the ground?
Answer:
26 feet
Step-by-step explanation:
Let the length of the required wire =l
The height of the tree =24 cm
We want the tree to fall to the ground 10 feet away from the base.
Ths problem forms a right triangle which I have drawn and attached below.
To determine the length of the wire l required, we use Pythagoras theorem to solve for the hypotenuse of the right triangle.
[tex]B$y Pythagoras theorem: Hypotenuse^2=Opposite^2+Adjacent^2\\$Therefore:\\l^2=24^2+10^2\\l^2=676\\$Take the square root of both sides\\l=\sqrt{676}\\ l=26$ feet[/tex]
Thw wire must be 26 feet long to reach the ground.
A square matrix AA is called half-magic if the sum of the numbers in each row and column is the same. The common sum in each row and column is denoted by s(A)s(A) and is called the magic sum of the matrix AA. Let VV be the vector space of 2×22×2 half-magic squares.
A) Find an ordered basis BB for VV.
B) Find the coordinate vector [M]_B of M [-2 -7, -7 -2]
Answer:
A) [tex]B = \{\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right], \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right] \}[/tex]
B) [tex]M_{B} = \left[\begin{array}{ccc}-2\\-7\end{array}\right][/tex]
Step-by-step explanation:
Let [tex]A = \left[\begin{array}{ccc}a&b\\c&d \end{array}\right][/tex] where a, b, c and d are real numbers
Since A is said to be a half magic square matrix, a = d, b = c.
The matrix A therefore becomes [tex]A = \left[\begin{array}{ccc}a&b\\b&a \end{array}\right][/tex] where [tex]a,b \epsilon R[/tex]
A can therefore be manipulated as:
[tex]A = a \left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] + b \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex]
The matrices [tex]\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right][/tex] and [tex]\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex] are apparently linearly independent and therefore form a basis B for V
[tex]B = \{\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right], \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right] \}[/tex]
B) Find the coordinate vector [M]_B of M [-2 -7, -7 -2]
[tex]M = \left[\begin{array}{ccc}-2&-7\\-7&-2 \end{array}\right][/tex]
[tex]M[/tex] can be written in the form [tex]M = a\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] + b\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex]
[tex]M = \left[\begin{array}{ccc}-2&-7\\-7&-2 \end{array}\right] = -2\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] -7\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex]
The coordinate vector is therefore, [tex]M_{B} = \left[\begin{array}{ccc}-2\\-7\end{array}\right][/tex]
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answer:
260
20
Step-by-step explanation:
speed of plane= p
speed of wind =w
(p+w)*3=840 p+w=840/3=280and
(p-w)*3.5=840p-w= 840/3.5= 240added up the 2 equations we get:
2p= 280+240p=260 mphthen
w= 20 mph14d+21 and 7 (2d+3) choose yes or no to see if the expression is equivalent
Answer:
Yes- these answers are equivalent.
Step-by-step explanation:
In the expression 7(2d+3), the 7 is outside the parentheses, meaning everything inside the parentheses is multiplied by 7.
2d X 7 = 14 d
3 X 7 = 21
7(2d+3) = 14d + 21
Yes, the expressions are equivalent.
What is expression ?By combining numbers, variables, functions in mathematics we get an expression.
Example : 4p+2, 3x-4y etc
What is the required result ?Given expressions are 14d+21 and 7(2d+3)
Here, simplifying the expression 7(2d+3) we get,
7(2d+3) = (7×2d)+(7×3) = 14d+21
Therefore, the given two expressions are equal to each other, i.e same.
Learn more about expression here :
https://brainly.com/question/723406
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What are all the methods to finding zeros and factors of higher degree polynomial functions?
Answer:
Use the Rational Zero Theorem to list all possible rational zeros of the function. Use synthetic division to evaluate a given possible zero by synthetically dividing the candidate into the polynomial. Repeat step two using the quotient found with synthetic division.
Step-by-step explanation:
One of the methods to finding zeros and factors of higher degree polynomial functions is using the Remainder theorem.
What are the zeros of the polynomial function?The zeros of polynomial refer to the values of the variables present in the polynomial equation for which the polynomial equals 0.
The methods to finding zeros and factors of higher degree polynomial functions
Evaluate a polynomial using the Remainder Theorem.Use the Rational Zero Theorem to find rational zeros.Use the Factor Theorem to solve a polynomial equation.Use synthetic division to find the zeros of a polynomial function.Hence, one of the methods to finding zeros and factors of higher degree polynomial functions is using the Remainder theorem.
To learn more about the polynomial function visit:
https://brainly.com/question/12976257.
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The rental shop charges $16 plus $9 an hour to rent a bicycle. If Luis spends $70, for how
many hours did he rent the bicycle?
Answer:
2.8 hours or 2hrs 8 min
Step-by-step explanation:
money paid per hour=16+9=$25
money paid by luis=70
time=70/25= 2.8 hrs
=2 hours and 8 minutes
hope this helps u :)
Which statement accurately describes chemical rocks?
Answer:
Chemical rocks form when minerals dissolve in a solution and crystalize.
Answer:
Chemical rocks don't form from solidification from a melt
Step-by-step explanation:
Solve the equation 4c=3
c =
Answer:−2x=−8
4sin2(x)−1=0
2x+3=3
Step-by-step explanation:
State the negation of the following statement:
It is cloudy.
saying it is cloudy is the defining that it's so gloomy outside or is probably paraphrasing to how someone feels
hope this helps
Rewrite the equation by completing the square. x^2 +16x +64=0
Answer: (x+8)²
Step-by-step explanation:
When you complete the square, the factor is squared. You want to first factor the equation.
x²+16x+64=0
(x+8)(x+8)=0
Now that we have factored the equation, we can put in into squares.
(x+8)²
Answer
8 and 0 (Khan)
