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?
Answers
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.
Related Questions
In 1925, Zbigniew Morón published a rectangle that could be dissected into nine different sized squares as shown in the diagram.
The lengths of the sides of these squares are
1
,
4
,
7
,
8
,
9
,
10
,
14
,
15
and
18.
1
,
4
,
7
,
8
,
9
,
10
,
14
,
15
and
18.
What is the area of Morón’s rectangle?
Answers
Answer:
Area of the rectangle = 1056 square units
Step-by-step explanation:
Rectangle published could be dissected into nine different squares with different sizes.
Area of the squares with different measure of sides will be,
For side length = 1 unit
Area of the square = (Side)²
= 1²
= 1 square units
For side length = 4 units
Area of the square = 4² = 16 units²
For side length = 7 units
Area of the square = 7² = 49 units²
For side length = 8 units
Area of the square = 8² = 64 units²
For side length = 9 units
Area of the square = 9² = 81 square units
For side length = 10 units
Area of the square = 10² = 100 square units
For side length = 14 units
Area of the square = 14² = 196 square units
For side length = 15 units
Area of the square = 15² = 225 square units
For side length = 18 units
Area of the square = 18² = 324 square units
Total area of the rectangle by adding these 9 squares
= 1 + 16 + 49 + 64 + 81 + 100 + 196 + 225 + 324
= 1056 square units
What’s the correct answer for this question?
Answers
Answer:
B.
Step-by-step explanation:
Volume of the model of moon = 4/3(πr³)
= 4/3(π)(1)³
= 4.2 feet³
Volume of cylinder = πr²h
= (3.14)(0.5)²(0.5)
= 0.39 feet³
Cylindrical clay boxes to be used = 4.2/0.39
=10.7 ≈ 11
Recently, the average amount of time to foreclose on a house in the U.S. was reported to be 359 days. Assume that the standard deviation for this population is 90.4 days. A random sample of 42 homes that have completed the foreclosure process was selected. What is the probability that the sample average was less than 375 days?
Answers
Answer:
87.49% probability that the sample average was less than 375 days
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 359, \sigma = 90.4, n = 42, s = \frac{90.4}{\sqrt{42}} = 13.95[/tex]
What is the probability that the sample average was less than 375 days?
This is the pvalue of Z when X = 375. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{375 - 359}{13.95}[/tex]
[tex]Z = 1.15[/tex]
[tex]Z = 1.15[/tex] has a pvalue of 0.8749.
87.49% probability that the sample average was less than 375 days
Convert 78% to a decimal
Answers
78% means 78/100=0.78
What’s the correct answer for this question?
Answers
Answer:
PO = 20
Step-by-step explanation:
They are equidistant from the centre
PG = GO
x-4=1/2x+3
Multiplying both sides by 2
2(x-4)=x+6
2x-8=x+6
2x-x = 6+8
x = 14
Now
PO = 14-4+7+3
PO = 10+10
PO = 20
In studies examining the effect of humor on interpersonal attractions, McGee and Shevlin (2009) found that an individual’s sense of humor had a significant effect on how the individual was perceived by others. In one part of the study, female college students were given brief descriptions of a potential romantic partner. The fictitious male was described positively as being single and ambitious and having good job prospects. For one group of participants, the description also said that he had a great sense of humor. For another group, it said that he has no sense of humor. After reading the description, each participant was asked to rate the attractiveness of the man on a seven-point scale from 1 (very unattractive) to 7 (very attractive). A score of 4 indicates a neutral rating. The females who read the "great sense of humor" description gave the potential partner an average attractiveness score of M = 4.53 with a standard deviation of s = 1.04. If the sample consisted of n = 16 participants, is the average rating significantly higher than neutral (μ = 4)? Use a one-tailed test with α = .05
Answers
Answer:
The calculated value t = 2.038< 2.145 at 0.05 level of significance
Null hypothesis is accepted
There is the average rate is less than μ ≤ 4
Step-by-step explanation:
Step(i):-
The Population of the mean 'μ' =4
sample size 'n' = 16
sample mean 'x⁻' = 4.53
given sample standard deviation 's' = 1.04
level of significance α = 0.05
Step(ii):-
Null hypothesis:H₀ : There is no significance difference between two means
Alternative hypothesis : H₁: There is significance difference between two means
Test statistic
[tex]t = \frac{x^{-} - mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{4.53-4}{\frac{1.04}{\sqrt{16} } }[/tex]
t = 2.038
Degrees of freedom ν = n-1 = 16-1 =15
t₀.₀₂₅ = 2.145
Conclusion:-
The calculated value t = 2.038< 2.145 at 0.05 level of significance
Null hypothesis is accepted
There is the average rate is less than μ ≤ 4
2(v-1) + 8 = 6(2v -4)
Choose statement that solves the solution
Answers
Answer:
V=3
Step-by-step explanation:
2(v-1)+8=6(2v-4)
2V-2+8=12v-24(calculate)
2v+6=12v-24(move terms)
2v-12v=-24-6(collect like terms)
-10v=-30(devide both sides by-10)
V=3
hi I hope this helps.
you have 4 reindeer, Bloopin, Balthazar, gloopin abd prance, and you want to have 3 fly your sleigh. you always have your reindeer fly in a single-file line. How many different ways can you arrange your reindeer?
Answers
Answer:
24
Step-by-step explanation:
There are 4 options for the first reindeer.
After the first reindeer is selected, there are 3 options left for the second reindeer.
After the second reindeer is selected, there are 2 options left for the final reindeer.
The number of possible permutations is:
₄P₃ = 4×3×2 = 24
The best player on a basketball team makes 70% of all free throws. The second-best player makes 65% of all free throws. The third-best player makes 55% of all free throws. Based on their experimental probabilities, estimate the number of free throws each player will make in his or her next 60 attempts. Explain.
For the best player, one equation that gives the estimated number of free throws is
▼
The best player will make about
nothing free throws.
Answers
Answer:
Best: 42/60 free throws
Second Best: 39/60 free throws
Third Best: 33/60 free throws
Step-by-step explanation:
List four monthly cost that a homeowner needs to pay?
Answers
Answer:
A homeowner has to pay phone bill, home insurance, cable bill, internet bill
Step-by-step explanation:
If the homeowner doesn't pay these then they won't get to continue using it until they pay for it again.
Answer:
The answer should contain any four of the following:
utility fees
association fees
private mortgage insurance (PMI)
title insurance
homeowners insurance
property taxes
Step-by-step explanation: This is the PLATO answer.
My fourth number is 39 my fifth number is 43 what is my first number ?
Answers
Answer:
27
Step-by-step explanation:
39+4=43
27, 31, 35, 39, 43
Answer:
27
Step-by-step explanation:
When you add u subtract 39 from 43 u will get 4
Therefore u will subtract 4 from 39 to get the third number which is 35 then subtract 4 from it to get the second number which is 31 then subtract another 4 to get the first number that's 27
In a large population, 57 % of the people have been vaccinated. If 3 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
Answers
Answer:0.92
Step-by-step explanation:
Given
[tex]57\%[/tex] of Population is vaccinated
So, Probability of a person being vaccinated is [tex]P=0.57[/tex]
and simultaneously , probability of not vaccinated is [tex]1-P[/tex]
[tex]=1-0.57=0.43[/tex]
Now, Probability that atleast one of them has been vaccinated is given by
[tex]=1-P(\text{None of them is vaccinated})[/tex]
[tex]=1-0.43\times 0.43\times 0.43[/tex]
[tex]=1-0.0795[/tex]
[tex]=0.92[/tex]
Answer:
The probability that AT LEAST ONE of them has been vaccinated
P( X ≥1) = 0.920493
Step-by-step explanation:
Step(i):-
Given 57 % of the people have been vaccinated
p = 57% =0.57
q = 1-p =1-0.57 = 0.43
n = 3
[tex]P(X=r) = n_{C_{r} } p^{r} q^{n-r}[/tex]
Step(ii):-
The probability that AT LEAST ONE of them has been vaccinated
P( X ≥1) = P( x =1) + P(x =2)+P(x=3) [tex]P(X\geq 1) = 3_{C_{1} } (0.57)^{1} (0.43)^{3-1} + 3_{C_{2} } (0.57)^{2} (0.43)^{3-2} + 3_{C_{3} } (0.57)^{3} (0.43)^{3-3}[/tex]
[tex]P(X\geq 1) = 3 (0.57) (0.43)^{2} + 3 (0.57)^{2} (0.43) + 1 (0.57)^{3} (0.43)^{0}[/tex]
= 0.316179 + 0.419121 +0.185193
= 0.920493
Final answer:-
The probability that AT LEAST ONE of them has been vaccinated
P( X ≥1) = 0.920493
Marie bought 5 1/2 gallons of paint. She uses 1/3 of the paint for a bedroom. How many gallons of paint did Marie use?
Answers
Answer:
1 5/6 gallons
Step-by-step explanation:
1. 5 1/2 = 11/2 gallons
2. She uses: 1/3 x 11/2 = 11/6 gallons
3. so: 11/6 = 1 5/6 gallons
I'M MARIE!!!
If the first term in an arithmetic sequence is -3 and the tenth term is 15, what is the common difference?
A. d = 2
B. d = 3
C. d = 6
D. d = 12
Answers
Answer:
2
Step-by-step explanation:
a10=a1+(n-1)d
15=-3+(10-1)d
15+3=9d
d=2
Eric's average income for the first 4 months of the year is $1450.25, what must be his average income for the remaining 8 months so that his average income for the year is $1780.75
Answers
Answer:
$ 1,946.00
Step-by-step explanation:
Average income per year=total income per month/12 months
total income=average income for first 4 months*4+ total income for 8 months
Let x represent total income total income for remaining 8 months
$1780.75=($1450.25*4+x)/12
$1780.75*12=$5,801+x
$21,369==$5,801+x
x=$21,369-$5,801
x=$15,568
The average income for the remaining eight months=x/8=$15568/8 =$1,946.00
The average income for the remaining 8 months is $ 1,946.00
What does the graph of f(x)=(x-3)^2+12 look like
Answers
Answer:
see attached for a graph
Step-by-step explanation:
When g(x) is transformed to
f(x) = f(x -h) +k
The graph of g(x) is translated h units right and k units up.
__
Here, the function g(x) = x^2 is transformed to ...
f(x) = g(x -3) +12 = (x -3)^2 +12
Then the graph of f(x) is the graph of g(x)=x^2 translated 3 units right and 12 units up.
Find the equation of the straight line passing through the point (0, 1)
which is perpendicular to the line
y = -2x + 2
:)
Answers
Answer:
[tex]y = \frac{1}{2} x+1[/tex]
Step-by-step explanation:
Perpendicular => So, it will have a slope of a negative reciprocal to this slope
Slope = m = 1/2
Now,
Point = (x,y) = (0,1)
So, x = 0 and y = 1
Putting this in slope-intercept equation to get b
=> [tex]y = mx+b[/tex]
=> 1 = (1/2)(0) + b
=> b = 1
Now putting m and b in the slope intercept equation to get the required equation
=> [tex]y = \frac{1}{2} x+1[/tex]
Answer:
y = \frac{1}{2} x+1
Step-by-step explanation:
The graph of a line passes through the points (0,5) and (-10, 0). What is the
equation of the line?
Answers
Answer:
The equation is y=1/2x+5
Step-by-step explanation:
Answer:
y=1/2x+5
Step-by-step explanation:
I learned this last year. I know this is the answer
Consider that recycling an aluminum can only requires 6% of the energy needed to make the can in the first place. Given that the energy saved by recycling the can will result in enough energy to run a 100W TV for 3 hours. How much energy does it take to make 19 Aluminum cans
Answers
Answer:
21829787.23 joules
Step-by-step explanation:
The recycling will require 6%energy if initial energy, let's say x.
94% of x will be used to power a 100W TV for 3 hours
X = (100*3*60*60)/0.94
X = 1148936.17 joules.
To make 19 aluminum cans ,
It will take 1148936.17*19
= 21829787.23 joules
An amusement park has 15 roller coasters. In how many ways can you choose 10 of the roller coasters to ride during your visit to the park? *
Answers
Answer:
3003 ways
Step-by-step explanation:
We are in a combination or permutation exercise, the difference between them is if the order matters (permutations) or does not matter (combinations),
in this case the order does not matter, since they only ask us for the ways to choose 10 of 15 roller coasters, therefore it would be a combination:
nCr = n! / (r! * (n-r)!
we know that n = 15 and r = 10, we replace:
15C10 = 15! / (10! * (15-10)!
15C10 = 3003
In other words, there are 3003 ways to choose 10 of the 15.
write the equation of the line that passes through the points(7, —4) and (—1, 3) first point-slope form, and then im slope-intersept form.
Answers
Answer:
The slope of the line is -7/8
When the point (7, –4) is used, the point-slope form of the line is
y+4=(-7/8)(x-7)
The slope-intercept form of the line is y=(-7/8)x+(17/8)
Step-by-step explanation:
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 7 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.
Answers
Answer:
The probability that a randomly selected passenger has a waiting time greater than 2.25 minutes is P=0.68.
Step-by-step explanation:
For a uniform distribution, any value within the minimum and maximum value have the same probability. Outside that interval, the probability is 0.
Then, for a uniform distribution within a and b, the probability P(X>c), being z<c<b is:
[tex]P(X>c)=\dfrac{b-c}{b-a}[/tex]
For our case, with a uniform distribution within 0 and 7 minutes, the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes is:
[tex]P(t>2.25)=\dfrac{7-2.25}{7-0}=\dfrac{4.75}{7}=0.68[/tex]
express 1)32.12353535... 2)2.3333...+4.15151515... as a fraction in simplest form
Answers
(1) Suppose x = 32.12353535... . Then 100x = 3212.353535... and 10000x = 321235.353535... .
Subtracting these gives
10000x - 100x = 321235.353535... - 3212.353535...
9900x = 321235 - 3212
9900x = 318023
x = 318023/9900
(2) By the same process as above, we start with
x = 2.333...
y = 4.151515...
Then
10x = 23.333...
==> 10x - x = 23.333... - 2.333...
==> 9x = 23 - 2
==> x = 21/9
and
100y = 415.151515...
==> 100y - y = 415.151515... - 4.151515
==> 99y = 415 - 4
==> y = 411/99
After this, we get
x + y = 2.333... + 4.151515...
==> x + y = 21/9 + 411/99
==> x + y = 231/99 + 411/99
==> x + y = 642/99 = 214/33
6(a–1.4)=3.5a+1.6
Please answer fast!
Answers
What’s the value of x?
Answers
Answer:
Step-by-step explanation:
here ,
6x +238 = 3x+178 ( vertically opposite angles are equal)
so 6x - 3x = 178 -238
3x =-60
x =-60/3
x=-20
hope it helps / please mark me as the brainliest..
Answer:
x= -20
Step-by-step explanation:
The 2 angles are opposite each other. Therefore, they are vertical angles and congruent. We can set them equal to each other and solve.
6x+238=3x+178
To solve the equation, we want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
First, subtract 3x from both sides
6x-3x+238=3x-3x+178
6x-3x+238=178
3x+238=178
Next, subtract 238 from both sides
3x+238-238=178-238
3x=178-238
3x=-60
Finally, divide both sides by 3.
3x/3= -60/3
x=-60/3
x= -20
plss help bring up my grade please
Answers
The easiest way to solve this problem is by calculating the areas of all the sides and adding them together.
Step 1; Calculate the area of the rectangular front & back
A = 2 * (l * w)
= 2 * (25 * 10)
Step 2; Calculate the area of the rectangular sides
A = 2 * (1 * w)
= 2 * (55 * 10)
= 1100 ft^2
In a certain school district, it was observed that 24% of the students in the element schools were classified as only children (no siblings). However, in the special program for talented and gifted children, 119 out of 415 students are only children. The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the α=0.05 level of significance.What is the hypothesized population proportion for this test?
Answers
Answer:
We conclude that the proportion of only children in the special program is significantly different from the proportion for the school district.
Step-by-step explanation:
We are given that in a certain school district, it was observed that 24% of the students in the element schools were classified as only children
However, in the special program for talented and gifted children, 119 out of 415 students are only children.
Let p = proportion of only children in the special program.
So, Null Hypothesis, [tex]H_0[/tex] : p = 24% {means that the proportion of only children in the special program is equal to the proportion for the school district}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 24% {means that the proportion of only children in the special program is significantly different from the proportion for the school district}
The test statistics that would be used here One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of only children in the special program = [tex]\frac{119}{415}[/tex] = 0.29
n = sample of students = 415
The hypothesized population proportion for this test is 0.24.
So, the test statistics = [tex]\frac{0.29-0.24}{\sqrt{\frac{0.24(1-0.24)}{415} } }[/tex]
= 2.385
The value of z test statistic is 2.385.
Now, at 0.05 significance level the z table gives critical value of -1.96 and 1.96 for two-tailed test.
Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the proportion of only children in the special program is significantly different from the proportion for the school district.
Complete the table to investigate dilations of
exponential functions.
2
2*
3-2
23.x
-2
1
4
3
4
64
1
8
-1
2
2 3 4
0
a
c
d
e
1
2
4.
12
64
Answers
Answer: itz 780
Step-by-step explanation:
One of the great mysteries of the world is my hotdogs and hotdog buns come in packages of different sizes hotdogs come in packs of eight and burns came in packs of 12 at your local store what is the least number of each you can buy in order to have a equal number of hot dogs and buns
Answers
Answer:
3 pack of hot dogs and 2 pack of buns 24
Step-by-step explanation:
hot dogs come in packs of 8
burns came in packs of 12
what is the least number of each you can buy in order to have a equal number of hot dogs and buns
so to get equal number
we have to look for the LCM of 8 and 12 = 24
therefore the packs will be equal to product
hot dogs come in packs of 8 = 8*3 = 24
burns came in packs of 12 = 12 *2 = 24
therefore, 3 pack of hot dogs and 2 pack of buns 24
Solving a Real-World Inequality
Samuel is running a 3-mile race. He would like to finish the race in under 33 minutes. He has already run for 10.5
minutes. The inequality 10.5 +X< 33 represents the situation.
Solve the inequality. How is the solution interpreted in the context of the problem?
O x< 22.5; Sam hasa maximum of 22.5 minutes left to finish running.
Ox<22.5; Sam has fewer than 22.5 minutes left to finish running.
O x>43.5; Sam has at least 43.5 minutes left to finish running.
O x<43.5; Sam has no more than 43.5 minutes left to finish running.
Answers
Answer:
B) x < 22.5; Sam has fewer than 22.5 minutes left to finish running.
Step-by-step explanation:
For this case we have the following inequality:
From here, we define the variable x.
x: number of minutes remaining to finish the race.
From here, we clear the value of x.
We have then:
Therefore, Samuel has less than 22.5 minutes to finish the race in the estimated time.
Answer:
x < 22.5; Sam has fewer than 22.5 minutes left to finish running.
x < 22.5; Sam has fewer than 22.5 minutes left to finish running.
How to solve the inequality?For this case we have the following inequality:
From here, we define the variable x.
x = number of minutes remaining to finish the race.
From here, we clear the value of x.
We have then:
Therefore, Samuel has less than 22.5 minutes to finish the race in the estimated time.
What are examples of inequality?The major examples of social inequality include income gap, gender inequality, health care, and social class. In health care, some individuals receive better and more professional care compared to others.
Learn more about inequality here: brainly.com/question/25275758
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