Comparing a T distribution to a Z distribution, a test statistic with a larger absolute value is more likely by chance alone with a T distribution. Group of answer choices True False
Answers
False - A test statistic with a larger absolute value is less likely by chance alone with a T distribution.
False - When comparing a T distribution to a Z distribution, a test statistic with a larger absolute value is less likely by chance alone with a T distribution.
The T distribution has heavier tails compared to the Z distribution, meaning it has more probability in the tails and less in the center. As a result, extreme values or larger absolute values of the test statistic are less likely to occur by chance alone in a T distribution compared to a Z distribution.
The T distribution is typically used when dealing with smaller sample sizes and when the population standard deviation is unknown and estimated from the sample. In such cases, the T distribution accounts for the added uncertainty associated with smaller sample sizes, resulting in a more conservative approach when evaluating the likelihood of extreme test statistics.
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Related Questions
For the equation 2xy' + y = 6x determine y(4) if y(1) = -2 -6 -3 0 3 6
Answers
The value of y(4) when the differential equation is 2xy' + y = 6x and y(1) = -2 is 5.51.
Given the differential equation is,
2xy' + y = 6x
y' + y/2x = 6x/2x [On dividing 2x from both the sides]
y' + y/2x = 3
Comparing with the general form y' + P(x) y = Q(x) we get,
P(x) = 1/2x and Q(x) = 3
So the integrating factor is
= \(e^{\int{\frac{1}{2x}.dx}}\)
= \(e^{\frac{1}{2}\ln x}\)
= \(e^{\ln \sqrt{x}}\)
= ln √x
So multiplying integrating factor with both sides of the equation we get,
d/dx (y ln √x) = 3 ln √x
d(y ln √x) = (3/2) ln x . dx
Integrating the above equation we get,
y ln √x = (3/2) [x ln x - x] + C
Given that y(1) = -2 so,
-2 ln √1 = (3/2) [1 ln 1 - 1] + C
0 = -3/2 + C
C = 3/2
Hence the main equation is,
y ln √x = (3/2) [x ln x - x] + 3/2
So y(4) is given by,
y ln √4 = (3/2) [4 ln 4 - 4] + 3/2
y ln 2 = (3/2) [4 ln 4 - 4 + 1]
y ln 2 = (3/2) [4 ln 4 - 3]
y = (3/(2 ln 2)) [4 ln 4 - 3]
y = 5.51 [Rounding off to nearest hundredth]
Hence the value of y(4) is 5.51.
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for which equation is x = 1 not a solution?
A. 2x - 1 =1
B. 2x + 1 = 5
C. 3x + 2 = 5
D. 4x - 1 =3
Answers
Answer:
OPTION B (2x + 1 = 5)
Step-by-step explanation:
Let's list them:
Option A:
2(1) -1 = 1
2 - 1 = 1
1 = 1 (Satisfies Equation)
Option B:
2(1) + 1 = 5
2 + 1 = 5
3 = 5 (DOES NOT Satisfy Equation)
Therefore, this is the answer to your question!
(G.11b, 1 point) Circle P, with a radius of 6 centimeters and tangent XY, is shown below. Y 8 cm 6 cm Хо If the length of XY is 8 centimeters, what is the length of PX? O A. 12 cm B. 10 cm O C. 5 cm OD. 13 cm
Answers
According to the picture, we can find the length of PX by using the pythagorean theorem, where PX would be the hypotenuse.
\(\begin{gathered} PX=\sqrt[]{6^2+8^2} \\ PX=\sqrt[]{36+64} \\ PX=\sqrt[]{100} \\ PX=10 \end{gathered}\)The length of PX is 10 cm
At store A is costs $8.36 for 2 board games. At store B you can get 3 board games for $12.84, Which store has the better deal? Explain how you would solve this problem and how you determined the better deal
Answers
Divide the total cost by the number of games bought. The store with the lowest amount is the better buy.
Store A : 8.36/2 = $4.18 each game
Store B: 12.84/3 = $4.28 each game
Store A has the lower price per game so Store A has the better deal.
Solve each equation. Check each solution.2 / x+2 - 1/x} = -4/x(x+2)
Answers
The equation has no solutions.
To solve the given equation, we can start by simplifying the expression on the left side.
The expression can be simplified by finding a common denominator for the fractions. The common denominator is x(x + 2), so we can rewrite the equation as follows:
2(x)(x + 2) - (x + 2)(1) = -4
Simplifying further:
2x^2 + 4x - x - 2 = -4
Combining like terms:
2x^2 + 3x - 2 = -4
Moving all terms to one side:
2x^2 + 3x - 2 + 4 = 0
2x^2 + 3x + 2 = 0
Now, we can try to solve this quadratic equation by factoring, completing the square, or using the quadratic formula. However, upon further examination, we can see that this equation does not factor nicely, and the discriminant of the quadratic formula is negative, indicating that there are no real solutions.
Therefore, the equation has no solutions to satisfy the given equation. When we substitute any value for x, the equation will not hold true.
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Multiply the input by 2. Then add 4 to the result to get the output.
Answers
Answer:
2x +4
Step-by-step explanation:
The Expression for "Multiply the input by 2 and then add 4 to the result to get the output" is 2x+ 4.
What is expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
Multiply the input by 2.
let the input be x.
So, 2x
Now, add the result to 4
Then, 2x+ 4
Hence, the expression is 2x+ 4.
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The polynomial p(x) = 2x^3 - 3x^2 + qx +56 has a factor x-2 a) show that q= -30? b) factorise p(x) completely and hence state all the solutions of p(x)=0
Answers
(a)The polynomial p(x) = 2x^3 - 3x^2 + qx +56 has a factor x-2 . Therefore, q = -30. (b) Therefore, the solutions of p(x) = 0 are x = 2, x = -1/2, and x = 2.
a) To show that q = -30, we can use the factor theorem. According to the factor theorem, if a polynomial p(x) has a factor (x - c), then p(c) = 0.
In this case, the given polynomial p(x) has a factor (x - 2), so we substitute x = 2 into p(x) and set it equal to 0.
p(2) = 2(2)^3 - 3(2)^2 + q(2) + 56 = 2(8) - 3(4) + 2q + 56 = 16 - 12 + 2q + 56 = 4 + 2q + 56 = 2q + 60
Setting this equal to 0, we have: 2q + 60 = 0 Now, solving for q: 2q = -60 q = -30
Therefore, q = -30.
b) To factorize p(x) completely, we can use synthetic division to divide p(x) by (x - 2).
Using synthetic division, we get: The remainder is 2q + 56.
Since we know q = -30, we can substitute it in: 2q + 56 = 2(-30) + 56 = -60 + 56 = -4
So, the remainder is -4. Now, we can write the factored form of p(x): p(x) = (x - 2)(2x^2 - 7x - 4)
To find the solutions of p(x) = 0, we can set each factor equal to zero and solve for x: x - 2 = 0
=> x = 2 2x^2 - 7x - 4 = 0
Using factoring or the quadratic formula, we find the solutions of the quadratic equation to be: x = 2, x = -1/2, x = 4/2
Therefore, the solutions of p(x) = 0 are x = 2, x = -1/2, and x = 2.
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3a. let’s explore the data. what are the mean lengths of yellowfish in each location? what are the variances? do they meet the assumption of equal variances?
Answers
(3a) The 95% confidence interval of σ\(_{1}^{2}\)/σ\(_{2}^{2}\) is: [0.1932 , 1.2032].
What is variance?Variance is the anticipated squared deviation of a random variable from its population mean or sample mean in probability theory and statistics.
F test for variances, using F distribution (\(df_{num}\)=19,\(df_{denom}\)=20) (two-tailed) (validation).
Hypotheses
\(H_{0}:sigma_{1} = sigma_{2}\\\\H_{1}:sigma_{1}\neq sigma_{2}\)
1. H0 hypothesis
Since p-value > α, H0 is accepted.
The sample standard deviation (S) of LaJolla.res' population is considered to be equal to the sample standard deviation (S) of Pt.Loma.ke's population.
In other words, the difference between the sample standard deviation (S) of the LaJolla.res and Pt.Loma.ke populations is not big enough to be statistically significant.
2. P-value
The p-value equals 0.1152, ( p(x≤F) = 0.05759 ). It means that the chance of type I error, rejecting a correct \(H_{0}\), is too high: 0.1152 (11.52%).
The larger the p-value the more it supports \(H_{0}\).
3. The statistics
The test statistic F equals 0.4796, which is in the 95% region of acceptance: [0.3986 : 2.4821].
S1/S2=0.69, is in the 95% region of acceptance: [0.6313 : 1.5755].
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What is the answer for page 785 CPM textbook
Answers
Step-by-step explanation:
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Calculate the maturity value of a simple interest, 3-month loan
of $3800. The interest rate is 6%. (whole number)
Answers
The maturity value of a simple interest, 3-month loan of $3800 at an interest rate of 6% is $3856. (whole number)
To calculate the maturity value, we can use the formula for simple interest:
Maturity Value = Principal + (Principal × Interest Rate × Time)
In this case, the principal (P) is $3800, the interest rate (R) is 6% (which can be expressed as a decimal as 0.06), and the time (T) is 3 months.
Substituting these values into the formula, we have:
Maturity Value = $3800 + ($3800 × 0.06 × 3/12)
Simplifying the calculation, we get:
Maturity Value = $3800 + ($570)
Maturity Value = $4370
Therefore, the maturity value of the 3-month loan is $4370.
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Jayla bought 4.3 pounds of apples. Jaden bought 2.73 pounds of apples. How many
more pounds of apples did Jayla buy than Jaden?
Answers
helpppp pleaseeeeeeeeeee
Answers
Answer:
y=5
Step-by-step explanation:
if the slope is 0, its just a horizontal line passing through 7,5
have a good day lovely :)
Determine the value of x. images attached.
Answers
Answer:
The answer is option AStep-by-step explanation:
Since it's a right angled triangle we can use trigonometric ratios to find the value of x
To find the value of x we can use either sine or cosine
Using sine we have\( \sin(30) = \frac{5}{x} \\ x \sin(30) = 5 \\ x = \frac{5}{ \sin(30) } \\ x = \frac{5}{0.5} \\ \\ \\ \boxed{x = 10}\)
Using cosine we have\( \cos(60) = \frac{5}{x} \\ x \cos(60) = 5 \\ x = \frac{5}{ \cos(60) } \\ x = \frac{5}{0.5} \\ \\ \\ \boxed{x = 10}\)
Hope this helps you
let x1, x2 ..., x100 all be independent bernoulli variables, which take a value of 1 with probability 0.5
Answers
Using the normal approximation to the binomial, there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.
What is the missing information?This problem is incomplete, but researching it on a search engine, it asks the probability that the sum of these Bernoulli variables is of less than 60.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with \(\mu = np, \sigma = \sqrt{np(1-p)}\).The binomial distribution is a series of n Bernoulli trials with p probability of a success on each trial, hence the parameters for the binomial distribution are given as follows:
n = 100, p = 0.5.
The mean and the standard deviation are given by:
\(\mu = np = 100(0.5) = 50\).\(\sigma = \sqrt{np(1-p)} = \sqrt{100(0.5)(0.5)} = 5\)Using continuity correction, the probability that the sum is less than 60 is P(X < 59.5), which is the p-value of Z when X = 59.5, hence:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (59.5 - 50)/5
Z = 1.9
Z = 1.9 has a p-value of 0.9713.
Hence there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.
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which of the following factors would lead the cpi to overstate the true rate of inflation.
Answers
The following factors can lead the Consumer Price Index (CPI) to overstate the true rate of inflation:
Quality Improvements: If the quality of goods and services improves over time, but their prices remain the same or increase slightly, the CPI may not fully account for these quality improvements and could overstate the inflation rate.
Substitution Bias: The CPI assumes that consumers' spending patterns remain constant over time, without considering that consumers may switch to lower-priced alternatives when the prices of certain goods or services increase. This substitution bias can lead to an overstatement of the inflation rate.
New Product Bias: The CPI may not account for the introduction of new products or services that provide better value for consumers at the same or lower prices. This omission can lead to an overstatement of the inflation rate.
Outlet Bias: The CPI is based on prices collected from a sample of outlets, and it may not accurately reflect price changes in different types of stores or online retailers. If price increases are more prevalent in outlets not adequately represented in the CPI sample, it can lead to an overstatement of the inflation rate.
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Q3 - Gandalf, Thranduil, Thorin, Rhosgobel and Azog love riding their favorite animals that are, respectively, White Horse, Great Elk, Bighorn Sheep, Giant rabbits and Warg Matriarch. How many pairs can there be between the five characters and the five animals listed above, that are described in "The Hobbit" and "Lord of the Rings", If only two of the above personals got their favorite animals while the remaining three got animals they do not really prefer? a) 5 b) 10 c) 20 d) 40 e) 8011 Q4 - We have four different dishes, two dishes of each type. In how many ways can these be distributed among 8 people? a) 1260 b) 2520 c) 5040 d) 10080 e) 645120
Answers
There can be 1200 pairs between the five characters and the five animals listed above.
There are 201, 600 ways to distribute the four dishes among 8 people.
When only two of the characters got their favorite animals, and the remaining three got the animals they do not really prefer, the number of pairs that can be formed will be:C(5, 2) × C(3, 3) × P(5, 5) = 10 × 1 × 120 = 1200
Therefore, there can be 1200 pairs between the five characters and the five animals listed above.
There are 4 different dishes and 2 dishes of each type.
Therefore, there are 4!/2!2! = 6 ways of choosing two distinct dishes of each type.
Since there are 8 people, one can distribute the dishes in P(8, 2)P(6, 2)P(4, 2)P(2, 2) = 201, 600 ways.
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the number of seconds remaining when a song is playing displayed as a negative number
Answers
answer:
are you asking:
the number of seconds remaining when a song is playing displayed as a negative number
or
is the number of seconds remaining when a song is playing displayed as a negative number?
or
why is the number of seconds remaining when a song is playing displayed as a negative number?
if so,
these are my answers:
1. yes
2. yes
3. because that is the number of minutes & or seconds remaining!
step-by-step explanation:
i answered your questions & hope you have a great day!
pls give me brainliest <3
Caroline,Colin & Sarah share some money in the ratio 5:9:6.
In total, Caroline and Sarah receive £44. How much does Colin get?
Answers
Answer:
Caroline gets 4*5 = 20 pounds
Colin gets 9 * 4 = 36 pounds
Sarah gets 6*4 = 24 pounds.
Step-by-step explanation:
The ratios are 5x + 9x + 6x
5x + 6x = 11x
Caroline and Sarah get a total of 44 pounds. They don't get 44 pounds each.
11x = 44 Divide by 11
x = 44/11
x = 4
Colin gets 9x
x = 4
9*4 = 36
Colin gets 35 pounds.
Caroline gets 4*5 = 20 pounds
Colin gets 9 * 4 = 36 pounds
Sarah gets 6*4 = 24 pounds.
Caroline and Sarah get 20 + 24 = 44
Now, using the best fit function for the data, y = -465.4569x + 17,267.6, perform extrapolation to estimate the principal balance of the loan after 15, 20, and 30 payments.
Type the correct answer in each box. Round your answers to the nearest cent.
You'll get brainliest! :)
Answers
The principal balance of the loan after 30 payments is -$3,206.98. However, a negative principal balance doesn't make sense, so we can conclude that the loan would be fully paid off before 30 payments.
To estimate the principal balance of the loan after 15, 20, and 30 payments using the best fit function y = -465.4569x + 17,267.6, we need to substitute the given values of x in the equation and solve for y.
For 15 payments:
y = -465.4569(15) + 17,267.6
y = -6,982.3035 + 17,267.6
y = 10,285.2965
Therefore, the principal balance of the loan after 15 payments is $10,285.30.
For 20 payments:
y = -465.4569(20) + 17,267.6
y = -9,309.226 + 17,267.6
y = 7,958.374
Therefore, the principal balance of the loan after 20 payments is $7,958.37.
For 30 payments:
y = -465.4569(30) + 17,267.6
y = -20,474.575 + 17,267.6
y = -3,206.975
Therefore, the principal balance of the loan after 30 payments is -$3,206.98. However, a negative principal balance doesn't make sense, so we can conclude that the loan would be fully paid off before 30 payments.
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Let f:N→N be a function given by f(x)=x+1. Which number belongs to the co-domain but not to the range of f ? Enter your answer as a whole number.
Answers
Therefore, the number 1 belongs to the co-domain but not to the range of f.
The function f(x) = x + 1 maps natural numbers to natural numbers. Since the co-domain is also the set of natural numbers (N), every natural number belongs to the co-domain. However, there is one number in the co-domain that does not belong to the range of f. That number is 1.
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Which of these equations have no solution? Check all that apply.
2(x+2)+2 =2(x+3)+1
2x + 3(x+5) = 5(x-3)
4(x + 3) = x + 12
4-(2x+5)= 1/2 (-4x-2)
5(x+4) - x = 4(x+5)-1
Answers
2x+3(x+5)=5(x-3)
5(x+4)-x =4(x+5)-1
i need you to solve 6x+3=21
Answers
Answer:
x = 3
Step-by-step explanation:
6x + 3 = 21
6x = 18
x = 3
Let's Check the answer.
6(3) + 3 = 21
18 + 3 = 21
21 = 21
So, x = 3 is the correct answer.
Write the value of pi correct to
six decimal places.
Please answer quick
Answers
Answer:
3.141592
Step-by-step explanation:
the probability distribution table shows the proportion of people living in the five different regions of a city. there are now 24,200 residents in the city. how many live in the central region? probability distribution table question responses 24,200 24,200 4840 4840 10,648 10,648 12,100
Answers
There are 9,680 people living in the central region of the city.
To determine how many people live in the central region of the city, we need to use the probability distribution table and calculate the actual number of residents based on the proportions given.
According to the table, the proportions for the five different regions are:
- Region 1: 24,200
- Region 2: 24,200
- Region 3: 4,840
- Region 4: 4,840
- Region 5: 10,648
To find the number of people living in the central region, we need to add the proportions for Region 3 and Region 4, as they represent the central region.
Number of people in the central region = Region 3 + Region 4
= 4,840 + 4,840 = 9,680
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Amy invests $10,000 in an account that pays 1% compound interest annually. She uses the expression P(1+r)t to find the total value of the account after t years.
What will be the total value of the account after 10 years?
Answers
Answer:10000(1+0.01)^10 = 11046.22
The value would be $11046.22
Step-by-step explanation:
uppose the investigators had made a rough guess of 175 for the value of s before collecting data. what sample size would be necessary to obtain an interval width of 50 ppm for a confidence level of 95%?
Answers
To determine the necessary sample size to obtain an interval width of 50 ppm for a confidence level of 95%, we need to use the formula for sample size calculation for estimating a population mean.
The formula for sample size calculation is:
n = (Z * σ / E)^2
n is the sample sizeZ is the Z-score corresponding to the desired confidence levelσ is the standard deviation of the populationE is the desired margin of error (half the interval width)In this case, the desired margin of error is 50 ppm, which means the interval width is 2 * E = 50 ppm. Therefore, E = 25 ppm.
The Z-score corresponding to a 95% confidence level is approximately 1.96.
Given that the investigators made a rough guess of 175 for the value of σ (standard deviation) before collecting data.
We can substitute these values into the sample size formula:
n = (1.96 * 175 / 25)^2
Simplifying the calculation:
n = (7 * 175)^2
n = 1225^2
n ≈ 1,500,625
Therefore, a sample size of approximately 1,500,625 would be necessary to obtain an interval width of 50 ppm for a confidence level of 95%.
To obtain an interval width of 50 ppm with a confidence level of 95%, a sample size of approximately 1,500,625 is required. This is calculated using the formula for sample size estimation, considering a desired margin of error of 25 ppm and a standard deviation estimate of 175. The Z-score corresponding to a 95% confidence level is used to determine the sample size.
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A baseball card collector has 225 plastic pages filled with a total of 3,375 cards.
Which rate represents the relationship between the cards and the number of pages?
15 cards per page
25 cards per page
15 pages per card
33 pages per card
Answers
Answer:
15 cards per page
Step-by-step explanation:
Two siblings, Miko and Cheko, receive some pocket money every month. This month, the ratio of Miko's pocket money to Cheko's pocket money is 8:12. Cheko's pocket money is $660. How much must Cheko give to Miko such that each of them have an equal amount of pocket money?
Answers
Cheko must give $110 to Miko so that each of them has an equal amount of pocket money, which is $550.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
The ratio of Miko's pocket money to Cheko's pocket money.
= 8:12
= 2:3
Now,
Let's represent Miko's pocket money as 2x and Cheko's pocket money as 3x.
We know that,
3x = $660
x = $220
Miko's pocket money.
= 2x
= 2($220)
= $440.
To make their pocket money equal,
Cheko needs to give half of the difference between their pocket money to Miko.
The difference between their pocket money.
= $220 (i.e., $660 - $440).
Half of that is $110.
Therefore,
Cheko must give $110 to Miko so that each of them has an equal amount of pocket money, which is $550.
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The weights of bushels of corn produced by a large farm are approximately normally distributed with a mean of 89.46 pounds and a standard deviation of 2.31 pounds. A store is buys 5 bushels of corn from the farm. Assume the 5 bushels the store receives is a random sample of all bushels of corn the farm produces. What is the approximate probability that the 5 bushels will have a mean weight of more than 90 pounds
Answers
The approximate probability that the 5 bushels will have a mean weight of more than 90 pounds is 0.41
How to determine the probability?The given parameters are:
Mean, μ = 89.46
Standard deviation, σ = 2.31
The z-score at x = 90 is calculated using
\(z = \frac{x - \mu}{\sigma}\)
This gives
\(z = \frac{90 - 89.46}{2.31}\\\)
Evaluate
z = 0.234
The probability is then calculated as:
P(x >90) = P(z > 0.234)
From z table of probabilities, we have:
P(x >90) = 0.41
Hence, the approximate probability that the 5 bushels will have a mean weight of more than 90 pounds is 0.41
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Oscar is planning to paint his house. For stability, the foot of his 17-foot ladder should be placed 4 feet from the house. How far up the side of the house will the ladder reach?
Answers
Answer: The side of the house will the ladder reached by ladder = 16.52 feet
Step-by-step explanation:
House is standing vertical on the ground.
By placing ladder, it will become a right triangle with hypotenuse as ladder.
By Pythagoras theorem,
\((hypotenuse)^2=(perpendicular)^2+(base)^2\)
i.e.
\((17)^2=(Height \ of\ wall\ reached\ by\ ladder)^2+4^2\\\\\Rightarrow\ (Height \ of\ wall\ reached\ by\ ladder)^2=289-16\\\\\Rightarrow\ (Height \ of\ wall\ reached\ by\ ladder)^2=273\\\\\Rightarrow\ (Height \ of\ wall\ reached\ by\ ladder)=\sqrt{273}\approx16.52\)
Hence, the side of the house will the ladder reached by ladder = 16.52 feet (approx)
