Answers
A common formula/theorem when working with right triangles is called the Pythagorean Theorem.
Pythagorean Theorem: a^2 + b^2 = c^2
---a and b are legs of the triangle
---c is the hypotenuse
8^2 + 6^2 = c^2
64 + 36 = c^2
100 = c^2
c = 10
Answer: The length of the hypotenuse of the triangle is 10cm.
Hope this helps!
Related Questions
When entering class, each student is given a card labeled with either A, B. or C. The sample space showing the possibilities for being given a letter over two days can be represented as {(A,A), (A,B), (A,C), __}. Which outcomes would be part of the sample space? Select all that apply.
Answers
The value of sample space are:
⇒ (B,A), (B,B), (B,C), (C,A), (C,B), (C,C)
We have to given that;
When entering class, each student is given a card labeled with either A, B or C.
And, The sample space showing the possibilities for being given a letter over two days can be represented as {(A,A), (A,B), (A,C), __}.
Hence, the possible outcomes for being given a letter over two days are:
{(A,A), (A,B), (A,C), (B,A), (B,B), (B,C), (C,A), (C,B), (C,C)}
So, the options that would be part of the sample space are:
(B,A), (B,B), (B,C), (C,A), (C,B), (C,C)
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p(x) = 2x^3 -5x^2 + 7x - 3 find p(2) , p(0), p(-1), p(-2)
POLYNOMIAL CLASS 9 QUESTION
PLS, I NEED ANSWER FAST
Answers
The value of p(2) = 7, p(0) = -3 , p(-1) = -17 and p(-2) = -53 when polynomial is p(x) = 2x³ - 5x² + 7x - 3 with one variable.
Given that,
The polynomial is p(x) = 2x³ - 5x² + 7x - 3
We have to find the value of p(2), p(0), p(-1) and p(-2).
We know that,
Take polynomial,
p(x) = 2x³ - 5x² + 7x - 3
Now, to find p(2) take x = 2 in polynomial
By substituting,
p(2) = 2(2)³ - 5(2)² + 7(2) - 3
p(2) = 16 - 20 + 14 - 3
p(2) = 30 - 23
p(2) = 7
Now, to find p(0) take x = 0 in polynomial
p(0) = 2(0)³ - 5(0)² + 7(0) - 3 [multiplication]
p(0) = 0 - 0 + 0 - 3
p(0) = -3
Now, to find p(-1) take x = -1 in polynomial
p(-1) = 2(-1)³ - 5(-1)² + 7(-1) - 3
p(-1) = -2 - 5 - 7 - 3 [subtraction]
p(-1) = -17
Now, to find p(-2) take x = -2 in polynomial
p(-2) = 2(-2)³ - 5(-2)² + 7(-2) - 3
p(-2) = -16 - 20 - 14 - 3
p(-2) = -53
Therefore, The value of p(2) = 7, p(0) = -3 , p(-1) = -17 and p(-2) = -53.
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find the confidence interval. thirty students received scholarship averaging $7,000 with a standard deviation of $500. find the 99% confidence interval.
Answers
We can use the formula for the confidence interval for a population mean with a known standard deviation. Plugging in the values, we get the interval (6817.22, 7182.78).
To find the 99% confidence interval for the scholarship averages of thirty students, we need to use the following formula:
CI = X ± zα/2 * (σ/√n)
Where
X = sample mean ($7,000 in this case)
zα/2 = the z-score corresponding to the desired confidence level (99% in this case), which is 2.576
σ = population standard deviation ($500 in this case)
n = sample size (30 in this case)
Substituting these values into the formula, we get:
CI = 7000 ± 2.576 * (500/√30)
Simplifying this expression, we get:
CI = 7000 ± 182.78
Therefore, the 99% confidence interval for the scholarship averages of thirty students is
(7000 - 182.78, 7000 + 182.78)
= (6817.22, 7182.78)
So we can say with 99% confidence that the true population mean scholarship amount lies within this interval.
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Meghan has a jar containing 15 counters. There are only blue counters, green counters and red counters in the jar.
Hector is going to take at random one of the counters from his bag of 12 counters. He will look at the counter and put the counter back into the bag.
Hector is then going to take at random a second counter from his bag. He will look at the counter and put the counter back into the bag.
Meghan is then going to take at random one of the counters from her jar of counters. She will look at the counter and put the counter back into the jar.
The probability that the 3 counters each have a different colour is 7/24
(c) Work out how many blue counters there are in the jar.
Answers
The probability that the first two counters Hector draws are different colors is 1 - (the probability that the first two counters are the same color).
The probability that the first two counters Hector draws are the same color is:
(number of counters of that color in the bag / total number of counters in the bag) * (number of counters of that color in the bag - 1 / total number of counters in the bag - 1)
There are three cases to consider:
1. The first two counters are both blue:
(x/15) * ((x-1)/(15-1))
2. The first two counters are both green:
((15-x)/15) * ((15-x-1)/(15-1))
3. The first two counters are both red:
((15-x)/15) * ((15-x-1)/(15-1))
So the probability that the first two counters are the same color is:
(x/15) * ((x-1)/(14)) + ((15-x)/15) * ((14-x)/(14))
Simplifying:
= (x^2 - x + 210 - 15x^2 + 15x) / (15 * 14)
= (14x^2 + 210) / 210
= (2x^2 + 30) / 30
= (x^2 + 15) / 15
The probability that the three counters each have a different color is 7/24, so:
Probability (three different colors) = Probability (first two are different colors) * Probability (third is a different color)
= (1 - (x^2 + 15) / 15) * (x/15 + (15-x)/15 * x/14)
= [(225 - x^2 - 15) / 225] * [(15x + 210 - x^2) / 210]
= [(210 - x^2) / 225] * [(15x + 210 - x^2) / 210]
= (14 - x^2) / 15 * (3x + 42 - x^2) / 14
= (2 * 7 - x^2/15) * (3x + 42 - x^2) / 14
= (14 - x^2/15) * (3x + 42 - x^2) / 14 = 7/24
Multiplying both sides by 14:
(14 - x^2/15) * (3x + 42 - x^2) = 7/24 * 14
(14 - x^2/15) * (3x + 42 - x^2) = 49/12
Expanding:
42 - 3x^2/15 + 42x/15 - x^2 + x^3/15 = 49/12
Simplifying:
4x^3 - 36x^2 + 168x - 280 = 0
Dividing both sides by 4:
x^3 - 9x^2 + 42x - 70 = 0
By trying integer values for x, we find that x=5 is a solution to the equation.
Therefore, there are 5 blue counters in the jar.
Find the value of sides RS
Answers
Answer:
RS = 15 units
Step-by-step explanation:
Given:
RT = 9
TS = 12
To find: Length of RS
Proof:
In right triangle RTS,
[tex]RT^{2} + TS^{2} = RS^{2}[/tex]
[tex]9^{2} + 12^{2} = RS^{2}[/tex]
[tex]81 + 144 = RS^{2}[/tex]
[tex]225 = RS^{2}[/tex]
[tex]\sqrt{225} = RS[/tex]
15 = RS
∴ The length of RS is 15 units.
Work out 3.4 cos 13 degrees rounded to 2 d.p
Answers
Answer:
To work out 3.4 cos 13 degrees, you can use a calculator or a table of trigonometric functions that includes cosine values.
Using a calculator, you can simply enter "3.4 * cos(13)" and get the answer. Rounding to 2 decimal places gives:
3.4 * cos(13) ≈ 3.298
Therefore, 3.4 cos 13 degrees, rounded to 2 decimal places, is approximately equal to 3.30.
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differentiate the function. y = tan[ln(ax + b)]
Answers
Answer:
sec² [㏑(ax + b)] X a/(ax +b)
Step-by-step explanation:
chain rule is if y = f(c) and z = f(e), and y = f[f(e)], then:
dy/de = dy/dc X dc/de
This might look complicated. Much easier with example, as in this question.
y = tan [㏑(ax + b)]
y = tan (u),
where u =㏑(v), v = ax + b
so we have y = tan (u), u = ㏑(v), v = ax + b.
dy/du = sec² (u), du/dv = 1/v, dv/dx = a.
dy/dx = dy/du X du/dv X dv/dx
= sec² (u) X (1/v) X a
= sec² [㏑(v)] X (1/(ax + b)) X a
= sec² [㏑(ax + b)] X a/(ax + b)
If x = 5, then which equation is NOT true?
-2x ≤ 12
x - 2>7
2x < 12
x-7<2
Answers
Answer:
x - 2 > 7
Step-by-step explanation:
Substitute the value 5 for x.
x = 5
-2x ≤ 12
-2(5) ≤ 12
-10 ≤ 12 True
-10 is less than or equal to 12
x - 2 > 7
5 - 2 > 7
3 > 7 Not true
3 is greater than 7
2x < 12
2(5) < 12
10 < 12 True
10 is less than 12
x - 7 < 2
5 - 7 < 2
-2 < 2 True
-2 is less than 2
Which measure of central tendency is used to determine the average annual percent
increase?
A) Mode
B) Arithmetic mean
C) Median
D) Weighted mean
E) Geometric mean
Answers
The geometric mean is used to determine the average annual percent increase, as it accurately accounts for compounding growth over multiple periods. The correct option is E.
The measure of central tendency that is typically used to determine the average annual percent increase is the arithmetic mean. This measure takes the sum of all the values and divides it by the total number of values.
It is important to note that other measures, such as the geometric mean, can also be used in certain situations. But for most cases, the arithmetic mean is the go-to measure for determining the average annual percent increase.
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you are a bank officer. Elena comes to you seeking a loan. She tells you that she has sure-fire idea for a business that simply cannot fail. She stays further that the bank will not be risking a penny by granting her the loan. Do Elenas claims encourage you of discourage you from approving the loan.
Answers
As a bank officer, Elena's claims would not be enough to encourage me to approve the loan. It's important to look at the details of her business plan, her financial history and her credit score before making a decision. Even if Elena believes that her business idea cannot fail, there is always a risk involved in lending money. It's important to assess the risk and make a decision based on the facts, rather than on promises or guarantees.
Answer:
Step-by-step explanation:
Her claims encourage you.
Find the value of x in the figure. Figure is not drawn to scale.
Answers
Answer:
[tex]x^{0} =105^{0}[/tex]
Step-by-step explanation:
[tex]x^{0} =180-(180-(180-110)-(180-145))[/tex]
[tex]x^{0} =180-(180-70-35)[/tex]
[tex]x^{0} =180-75[/tex]
[tex]x^{0} =105[/tex]
Hope this helps
Answer:
x=105
Step-by-step explanation:
Two methods
Method 1. Solving with Exterior Angles
Method 2. Solving with Interior Angles
Method 1. Solving with Exterior Angles
So that we can keep things organized, let's call the angle in the bottom left of the triangle, Angle 1, the angle in the top of the triangle, Angle 2, and the angle in the bottom right of the triangle, Angle 3.
An Exterior Angle is formed by continuing the line segment of a side, and is the angle that forms a linear pair with the interior angle.
Observe that all of the angles given are Exterior Angles to the Polygon (in this case, a triangle), and only one exterior angle is given for each vertex (we don't want to double-count things).
For any polygon, the sum of its exterior angles is always 360 degrees.
Therefore, we can setup the following equation:
[tex]360^o=m \angle 1_{exterior} + m \angle 2_{exterior} + m \angle 3_{exterior}[/tex]
[tex]360^o=(145^o) + (110^o) + (x^o)[/tex]
Combining like terms on the right hand side...
[tex]360^o=x^o +255^o[/tex]
Isolating x by subtraction 255 degrees from both sides...
[tex](360^o)-255^o=(x^o +255^o)-255^o[/tex]
[tex]105^o=x^o[/tex]
So, x = 105
Method 2. Solving with Interior Angles
An Interior Angle is the angle we usually think of inside of a polygon (in this case, a triangle).
The sum of the Interior angles of any polygon is given by [tex]Interior~Angle~Sum=180^o*(n-2)[/tex], where "n" is the number of sides of the polygon. For triangles, n=3, so
[tex]Interior~Angle~Sum=180^o*((3)-2)[/tex]
[tex]Interior~Angle~Sum=180^o*(1)[/tex]
[tex]Interior~Angle~Sum=180^o[/tex]
In this case, we're given exterior angles for two of the vertices, and we've been asked to find the exterior angle for the third vertex. Each Exterior angle forms a linear pair with the interior angle, and thus is supplementary, meaning a pair of Interior and Exterior angles have measures that add to 180 degrees.
Keeping with our angle numbering described in Method 1, we have the following 3 true equations about each interior/exterior pair, where we can substitute in the known values, and solve for / isolate the unknown angle measure (in the last case, we'll get an expression containing "x" for its measure):
[tex]\begin{array}{ccc}180^o=m \angle 1+m \angle 1_{exterior}&180^o=m \angle 2+m \angle 2_{exterior}&180^o=m \angle 3+m \angle 3_{exterior}\\180^o=m \angle 1+(145^o)&180^o=m \angle 2+(110^o)&180^o=m \angle 3+(x^o)\\180^o-145^o=m \angle 1&180^o-110^o=m \angle 2&180^o-(x^o)=m \angle 3\\35^o=m \angle 1&70^o=m \angle 2&180^o-(x^o)=m \angle 3\end{array}[/tex]
Additionally, since the sum of the interior angles of a triangle is 180 degrees, we also have the following equation...
[tex]m \angle 1 + m \angle 2 + m \angle 3 = 180^o[/tex]
Making substitutions with the quantities found above...
[tex](35^o) + (70^o) + (180^o-x^o) = 180^o[/tex]
Rewriting subtraction as addition of a negative...
[tex]35^o + 70^o + 180^o + (-x^o) = 180^o[/tex]
Adding x degrees to both sides, and subtracting 180 degrees from both sides...
[tex]35^o + 70^o =x^o[/tex]
Combining like terms..
[tex]105^o =x^o[/tex]
So, again, x=105
The points D(−3,−4), E(5,0), F(3,4), and G(−5,0) form rectangle DEFG. Plot the points then click the "Graph Quadrilateral" button. Then find the area of the rectangle.
Answers
If the points D(−3,−4), E(5,0), F(3,4), and G(−5,0) form rectangle DEFG then the area is 40 square units.
The length of the rectangle can be found by finding the distance between D and E (or F and G), which is:
√(5 - (-3))² + (0 - (-4))²] = √8² + 4²
= √80
= 4√5
The width of the rectangle can be found by finding the distance between D and G (or E and F), which is:
√-5 - (-3))² + (0 - (-4))²
= √(-2)²+ 4²
= √20
= 2√5
Therefore, the area of the rectangle is:
length x width = 4√5 x 2√5
= 8 x 5
= 40
Hence, 40 square units is area of the given rectangle DEFG.
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Please help me. I have so much late work I need this asap;
Answers
Answer: 7, 6 ,7
Step-by-step explanation:
a customer can choose one of two amplifiers, one of four compact disc players, and one of eight speaker models for an entertainment system. determine the number of possible system configurations.
Answers
There are 64 possible system configurations that can be made from the given choices of two amplifiers, four CD players, and eight speaker models.
To determine the number of possible configurations, we multiply the number of choices available for each component of the system. Since the customer can choose one of two amplifiers, one of four CD players, and one of eight speaker models, the total number of possible configurations is given by:
2 (amplifiers) × 4 (CD players) × 8 (speakers) = 64
Therefore, there are 64 possible system configurations that can be made from the given choices of two amplifiers, four CD players, and eight speaker models.
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Find the perimeter of quadrilateral PQRS given that the coordinates of its vertices are
P(1,3),Q(3,1),R(1,−1), and S(−2,−1). You may round your answer to one decimal place.
Answers
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill PQ=\sqrt{(~~ 3- 1~~)^2 + (~~ 1- 3~~)^2} \\\\\\ ~\hfill PQ=\sqrt{( 2 )^2 + ( -2)^2} \implies \boxed{PQ=\sqrt{ 8}}[/tex]
[tex]Q(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad R(\stackrel{x_2}{1}~,~\stackrel{y_2}{-1}) ~\hfill QR=\sqrt{(~~ 1- 3~~)^2 + (~~ -1- 1 ~~)^2} \\\\\\ ~\hfill QR=\sqrt{( -2)^2 + ( -2)^2} \implies \boxed{QR=\sqrt{ 8}} \\\\\\ R(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad S(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1}) ~\hfill RS=\sqrt{(~~ -2- 1~~)^2 + (~~ -1- (-1)~~)^2} \\\\\\ ~\hfill RS=\sqrt{( -3)^2 + ( 0)^2} \implies RS=\sqrt{ 9}\implies \boxed{RS=3}[/tex]
[tex]S(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad P(\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) ~\hfill SP=\sqrt{(~~ 1- (-2)~~)^2 + (~~ 3- (-1)~~)^2} \\\\\\ ~\hfill SP=\sqrt{( 3)^2 + ( 4)^2} \implies SP=\sqrt{ 25}\implies \boxed{SP=5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Perimeter} }{\sqrt{8}+\sqrt{8}+3+5} ~~ \approx ~~ \text{\LARGE 13.7}[/tex]
how many liters of oil are recquired to supply the electricalenergy needs of an average home for a year?
Answers
Approximately 897 liters of oil would be required to supply the electrical energy needs of an average home for a year. Keep in mind that this is a rough estimate, as factors like energy consumption and power plant efficiency can vary.
To answer your question, we need to consider a few factors such as the size of the home and the energy consumption of the household. However, on average, a household consumes around 10,000 kilowatt-hours (kWh) of electricity per year. If we convert this into liters of oil, we can use a conversion factor of 0.2778 liters of oil per kWh. Therefore, an average household would require around 2,778 liters of oil per year to supply their electrical energy needs.
It is important to note that this is just an estimate and the actual amount of oil required may vary depending on various factors such as the efficiency of the heating system and the energy usage habits of the household. It is also worth considering alternative energy sources such as solar or wind power, which can reduce the dependence on oil and lower the carbon footprint of the household.
In conclusion, an average household would require approximately 2,778 liters of oil to supply their electrical energy needs for a year. However, it is important to explore alternative energy sources and implement energy-saving measures to reduce the reliance on oil and minimize environmental impact.
The number of liters of oil required to supply the electrical energy needs of an average home for a year depends on the home's energy consumption and the efficiency of the power plant converting the oil into electricity. On average, a US household consumes about 10,649 kilowatt-hours (kWh) of electricity per year.
A typical oil-fired power plant can produce around 1,885 kWh of electricity from one barrel (159 liters) of oil, with an efficiency rate of around 33%. To calculate the number of liters needed for a year, we can use the formula:
(Number of kWh per year) / (kWh per liter of oil) = Liters of oil needed
First, let's find the kWh per liter of oil: 1,885 kWh/barrel * (1 barrel/159 liters) ≈ 11.86 kWh/liter
Now we can calculate the liters of oil needed: 10,649 kWh/year / 11.86 kWh/liter ≈ 897 liters/year
So, approximately 897 liters of oil would be required to supply the electrical energy needs of an average home for a year. Keep in mind that this is a rough estimate, as factors like energy consumption and power plant efficiency can vary.
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which of the following facts should make you the most worried about the reliability of the results of the test in this case? there is no need to worry because all of the expected cell counts are above 5. the sample was only 300 black women and is not representative of all black women. two of the six observed counts are 5 or less. not all of the cells' contributions to the chi-squared statistic are greater than 1. two of the six expected counts are less than 5.
Answers
Therefore, the reliability of the results may be questioned due to the small sample size and the fact that the observed and expected counts in some cells are too small.
The fact that two of the six observed counts are 5 or less should make you the most worried about the reliability of the results of the test in this case. This is because when the observed counts in a cell are too small, it is difficult to draw reliable conclusions from them. In such cases, the chi-squared statistic may not accurately reflect the true relationship between the variables being studied. This is because the chi-squared statistic is based on the difference between the observed counts and the expected counts, and if the observed counts are too small, the chi-squared statistic may be biased and not accurately reflect the true relationship between the variables.
Moreover, the fact that two of the six expected counts are less than 5 also raises concerns about the reliability of the results. This is because when the expected counts in a cell are too small, it may indicate that the sample size is too small or that the sample is not representative of the population being studied. In this case, the sample size was only 300 black women, which may not be representative of all black women.
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Find the limit of the following sequence or determine that the sequence diverges.
StartSet StartFraction left parenthesis 9 n plus 1 right parenthesis exclamation mark Over left parenthesis 9 n right parenthesis exclamation mark EndFraction EndSet(9n+1)!(9n)!
Answers
The term (9n+1) grows without bound as n approaches infinity, the limit does not exist. Therefore, the sequence diverges.
To find the limit of the given sequence, we can use the ratio test:
StartFraction
(9(n+1)+1)! / (9(n+1))!
Over
(9n+1)! / (9n)!
EndFraction
Simplifying the expression, we get:
StartFraction
(9n+10)(9n+9)(9n+8)...(9n+2)(9n+1)
Over
(9n+1)(9n)(9n-1)...(2)(1)
EndFraction
The terms cancel out and we are left with:
StartFraction
(9n+10)(9n+9)
Over
9n(9n+1)
EndFraction
Taking the limit as n approaches infinity, we get:
lim (n → ∞) StartFraction
(9n+10)(9n+9)
Over
9n(9n+1)
EndFraction
= lim (n → ∞) StartFraction
81n² + 81n + 90
Over
81n² + 9n
EndFraction
= lim (n → ∞) StartFraction
n² + n + 10 / n² + n / 9
EndFraction
As n approaches infinity, the higher order terms dominate, so we can ignore the constants and simplify the expression to:
lim (n → ∞) StartFraction
n² / n²
EndFraction
= 1
Since the limit exists and is finite, the sequence converges. Therefore, the limit of the sequence is 1.
To find the limit of the given sequence or determine if it diverges, consider the sequence:
a_n = (9n+1)! / (9n)!
We can rewrite the sequence using the properties of factorials:
a_n = [(9n+1)(9n)(9n-1)...(9n-(9n-1))] / (9n)!
a_n = (9n+1)
Now, we'll examine the limit as n approaches infinity:
lim (n -> ∞) a_n = lim (n -> ∞) (9n+1)
Since the term (9n+1) grows without bound as n approaches infinity, the limit does not exist. Therefore, the sequence diverges.
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help me variance and standard deviation help me
Answers
The variance is 7521.2 and the standard deviation is 86.7.
The variance is 18630.08 and the standard deviation is 136.4.
The variance is 0.0325 and the standard deviation is 0.18.
The variance is 252.8418 and the standard deviation is 15.91.
We have,
1)
Step 1: Find the mean
Mean = (106 + 121 + 152 + 234 + 347) / 5 = 192
Step 2: Find the variance
Variance = [(106-192)^2 + (121-192)^2 + (152-192)^2 + (234-192)^2 + (347-192)^2] / 5
Variance = 37606 / 5 = 7521.2
Step 3: Find the standard deviation
Standard deviation = sqrt(Variance) = sqrt(7521.2) = 86.7
2)
Step 1: Find the mean
Mean = (1450 + 1250 + 1776 + 1388 + 1340) / 5 = 1440.8
Step 2: Find the variance
Variance = [(1450-1440.8)^2 + (1250-1440.8)^2 + (1776-1440.8)^2 + (1388-1440.8)^2 + (1340-1440.8)^2] / 5
Variance = 93150.4 / 5 = 18630.08
Step 3: Find the standard deviation
Standard deviation = sqrt(Variance) = sqrt(18630.08) = 136.4
3)
Step 1: Find the mean
Mean = (7.7 + 7.4 + 7.3 + 7.9) / 4 = 7.575
Step 2: Find the variance
Variance = [(7.7-7.575)^2 + (7.4-7.575)^2 + (7.3-7.575)^2 + (7.9-7.575)^2] / 4
Variance = 0.0325
Step 3: Find the standard deviation
Standard deviation = sqrt(Variance) = sqrt(0.0325) = 0.18
4)
Step 1: Find the mean
Mean = (112 + 100 + 127 + 120 + 134 + 118 + 105 + 110) / 8 = 117.375
Step 2: Find the variance
Variance = [(112-117.375)^2 + (100-117.375)^2 + (127-117.375)^2 + (120-117.375)^2 + (134-117.375)^2 + (118-117.375)^2 + (105-117.375)^2 + (110-117.375)^2] / 8
Variance = 2022.7344 / 8 = 252.8418
Step 3: Find the standard deviation
Standard deviation = sqrt(Variance) = sqrt(252.8418) = 15.91
Therefore,
The variance is 7521.2 and the standard deviation is 86.7.
The variance is 18630.08 and the standard deviation is 136.4.
The variance is 0.0325 and the standard deviation is 0.18.
The variance is 252.8418 and the standard deviation is 15.91.
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Approximate the area under the function between a and b using a left-hand sum with the given number of intervals. f(x) = x² − x a = 0 b=3 3 Intervals
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a growing farming conglomerate increases its water usage at a rate of 7% every year. if it used 28,390 megaliters of water this year, then how much water will it use 5 years from now?
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The farming conglomerate will use approximately 36,912.51 megaliters of water 5 years from now.
To calculate the amount of water the farming conglomerate will use 5 years from now, we can use the given information that its water usage increases at a rate of 7% every year.
Let's denote the current water usage as W₀ and the water usage after 5 years as W₅.
We know that W₅ = W₀ * (1 + r)^n, where r is the growth rate (in decimal form) and n is the number of years.
In this case, W₀ = 28,390 megaliters, r = 7% = 0.07, and n = 5.
Substituting these values into the formula, we have:
W₅ = 28,390 * (1 + 0.07)^5
Calculating this expression, we get:
W₅ ≈ 28,390 * (1.07)^5 ≈ 36,912.51 megaliters
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Find the y-intercept of the line on the graph.
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Step-by-step explanation:
'y - intercept' is shorthand for ' y-axis intercept' ....or the value of the graph where it crosses the y - axis
this one is point (0,3) or y-intercept = 3
What multiplies to -25 and adds to 0?
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Answer:
-5 and 5
Step-by-step explanation:
[tex]-5*5=-25\\\\-5+5=0[/tex]
Find the sector area for the following
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[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta = \frac{2\pi }{3} \end{cases}\implies A=\cfrac{~~ \frac{2\pi }{3 }6^2 ~~}{2}\implies A=12\pi \stackrel{ using~\pi =3.14 }{\implies A=37.68}[/tex]
use quantifiers and logical connectives to express the factthat every linear polynomial (that is, polynomial of degree 1) with real coefficients and where the coefficient ofx is nonzero, has exactly one real root.
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The expression states that for every linear polynomial p with real coefficients and a nonzero coefficient of x, there is exactly one real root r.
For all linear polynomials with real coefficients and a nonzero coefficient of x, there exists exactly one real root. This can be expressed using the universal quantifier "for all" and the existential quantifier "there exists", connected by the logical connective "and". Additionally, the statement "exactly one real root" can be expressed using the quantifier "there exists" and the logical connective "and".
Using quantifiers and logical connectives, we can express the given fact as follows:
∀p ∃!r ((isLinearPolynomial(p) ∧ hasRealCoefficients(p) ∧ coefficientOfX(p) ≠ 0) → hasRealRoot(p, r))
Explanation:
- ∀p: For every polynomial p
- ∃!r: There exists exactly one real root r
- isLinearPolynomial(p): p is a linear polynomial (degree 1)
- hasRealCoefficients(p): p has real coefficients
- coefficientOfX(p) ≠ 0: The coefficient of x in p is nonzero
- hasRealRoot(p, r): p has a real root r
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Find the y-intercept of the line on the graph.
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A basket of beads contains 8 red beans , 6 yellow beads, and 6 greens . A bead will be drawn from the basket and replaced 150 times. What is the reasonable prediction for the number of times a green bead is drawn
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Step-by-step explanation:
green is 6 out of a total of ( 8+6+6 = 20 ) beads
so 6/20 ths of the time it should be a green bead
6/20 * 150 = 45 times should be green
6/20 or 3/10
3/10 x 150 = 45
Or you could do 6 x 150 to get 900, and then divide by 20, the denominator, to get 45 as well :)
describe the pattern 9;16;25;36;49 by words and algebraically
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Given the pattern:
9, 16, 25, 36, 49
In words, this pattern represents:
the sequence of perfect squares of consecutive integers starting from 3.The numbers are obtained by squaring the integers 3, 4, 5, 6, and 7, respectively.
Algebraically, we can represent the pattern using the formula:
t(n) = (n + 2)², where t(n) is the nth termI really need help please ️
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The solution to all parts is shown below.
1. Using a standard normal distribution table (z-table), the corresponding percentile left of the score for a z-score of 1.93 is approximately 97.65. Therefore, the percentile can be written as an integer of 98.
2. The percentile left of the score corresponding to z-score 1.94 can be found using a standard normal distribution table (z-table).
Looking up the value of 1.94 in the z-table, we find the area under the curve to the left of 1.94 is 0.9732, or 97.32% when rounded to two decimal places.
Therefore, the corresponding percentile left of the score for z-score 1.94 is 97%.
4. Since the normal distribution is symmetrical, we know that the area in the right tail is also 0.0158.
Therefore, the total area of the shaded region is:
= 0.0158 + 0.0158 = 0.0316
7. To determine the percentage of test takers who scored lower than Lorena, we need to find the area to the left of her z-score on the standard normal distribution.
First, we calculate the z-score of Lorena's score:
z = (554 - 495) / 20 = 2.95
Using a standard normal distribution table or calculator, we find that the area to the left of z = 2.95 is approximately 0.9985. This means that approximately 99.85% of test takers scored lower than Lorena.
Therefore, Lorena scored better than about
100% - 99.85% = 0.15% of test takers, which can be rounded to 0.2%.
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Wyatt’s math teacher wrote the following data set on the board.
10, 2.8, 6.5, 21.6, 8.2, 9.3, 4, 2.8
What is the range of the data?
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Answer:
18.8
Step-by-step explanation:
To find the range of a data set, you subtract the smallest value from the largest value.
In this case, the smallest value is 2.8 and the largest value is 21.6.
Range = largest value - smallest value = 21.6 - 2.8 = 18.8
Therefore, the range of the data set is 18.8.
Your highest is: 21.6
Your lowest is: 4.
I believe you subtract both of them and that’ll give you your answer. try that and let me know if it’s right :)!. if it’s not i’m sorry :((
