The measure of angle C is 53.13 degrees.
What are trigonometric functions?
Trigonometric functions are a set of mathematical functions used to relate the angles of a right triangle to the lengths of its sides. There are six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. Each function represents a ratio of two sides of a right triangle.The tangent function, denoted as tan(x), is a trigonometric function that represents the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
Calculating the value of angle C :
The three sides of the given right triangle are 3 cm, 4 cm, and 5 cm.
To find the measure of angle C, we can use the trigonometric function called inverse tangent, or arctan, which gives the ratio of the length of the opposite side to the length of the adjacent side.
Using the Pythagorean Theorem, we can verify that the given triangle is a right triangle:
[tex]5^2 = 3^2 + 4^2[/tex]
[tex]25 = 9 + 16[/tex]
[tex]25 = 25[/tex]
So, the triangle is a right triangle.
To find the measure of angle C, we can use the arctan function:
[tex]tan(C) =opposite/adjacent = 3/4[/tex]
[tex]C = arctan(3/4) \approx 53.13[/tex] degrees
Therefore, the measure of angle C is 53.13 degrees (rounded to the nearest hundredth).
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What is the answer for y?
The linear function that models the data is y=3/5x - 2/5 which has the form y=mx+b, where m is the slope and b is the y-intercept.
What is linear function?This can be written in the form y = mx + b where m and b are constants and x is a variable. The graph of a linear function is a straight line that goes through the origin.
To calculate the linear function, we must first calculate the slope. The slope is the numerical change in y (rise) divided by the numerical change in x (run).
Subtracting the y-values for x=-9 and x=-8, we get
-29/5 - (-26/5) = -3/5.
Similarly, subtracting the x-values for x=-9 and x=-8, we get
-9 - (-8) = -1.
Now, -3/5 / -1, we get the slope, m, of 3/5.
Next, we must calculate the y-intercept, b.
To do this, we can use either of the points given.
Using the points (x=-9, y=-29/5), we can substitute the x and y values into the linear equation, y=mx+b.
-29/5 = 3/5(-9) + b, which can be simplified to
-29/5 = -27/5 + b.
Adding 27/5 to both sides, we get b = -2/5.
Therefore, the linear function that models the data is y=3/5x - 2/5.
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The table below shows how much Craig spent on ribbon at two different shops. What is the difference in the price of 300 cm of ribbon between shop A and shop B? Give your answer in pounds (£). Shop A Shop B Length of ribbon 140 cm 215 cm Cost £1.68 £1.72
Therefore, the difference in the price of 300 cm of ribbon between shop A and shop B is £1.20.
What is equation?In mathematics, an equation is a statement that two expressions are equal. It usually contains one or more variables, which are typically represented by letters, and may contain constants and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. An equation can be true or false depending on the values of the variables. Solving an equation means finding the values of the variables that make the equation true.
Here,
To find the difference in price between the two shops, we need to first calculate the cost per centimeter of ribbon for each shop:
Shop A: £1.68 / 140 cm = £0.012 per cm
Shop B: £1.72 / 215 cm = £0.008 per cm
Now, we can calculate the cost of 300 cm of ribbon at each shop:
Shop A: 300 cm x £0.012 per cm = £3.60
Shop B: 300 cm x £0.008 per cm = £2.40
The difference in price between the two shops for 300 cm of ribbon is:
£3.60 - £2.40 = £1.20
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What is the area of this polygon in square units
The area of the polygon is 80 units².
What is a Polygon?
A polygon is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides.
Dividing the polygon into parts marked in the attached figure so as to calculate the area easily.
For triangle, DEF
Area = [tex]\frac{1}{2} bh[/tex]
= [tex]\frac{1}{2}[/tex] × 3 × 4
= 6 units²
For triangle BCD
Area = [tex]\frac{1}{2}bh[/tex]
= [tex]\frac{1}{2}[/tex] × 2 × 4
= 4 units²
For trapezoid ABFG,
Area = [tex]\frac{1}{2} (a + b) h[/tex]
= [tex]\frac{1}{2}[/tex] × (5.5 + 12) × 8
= 70 units²
Hence, total area = 6 + 4 + 70
= 80 units².
Therefore, the total area of the polygon is 80 units².
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Assume a jar has five red marbles and four black marbles. Draw out two marbles with and without replacement. Find the requested probabilities. (Enter the probabilities as fractions.)
(a) P(two red marbles)
with replacement without replacement (b) P(two black marbles)
with replacement without replacement (c) P(one red and one black marble)
with replacement without replacement (d) P(red on the first draw and black on the second draw)
with replacement without replacement
The probability of selecting another black marble is 3/7. As a result, the probability of drawing two black marbles in a row without replacement
(a) P(two red marbles) with replacement:The probability of drawing a red marble from a jar with five red marbles and four black marbles is 5/9, as there are five red marbles and nine total marbles. As a result, the probability of selecting two red marbles in a row with replacement is:P(two red marbles with replacement) = (5/9) × (5/9) = 25/81without replacement:When the first marble is removed, there are now only eight marbles remaining in the jar. Because there are only four black marbles in the jar, the probability of drawing a red marble is now 5/8. Therefore, the probability of selecting two red marbles in a row without replacement is:P(two red marbles without replacement) = (5/9) × (5/8) = 25/72(b) P(two black marbles)with replacement:For the first draw, there are four black marbles in the jar and a total of nine marbles. Therefore, the probability of drawing a black marble on the first draw is 4/9. Since the first marble was not removed, there are now eight marbles in the jar, including three black ones, and there are a total of nine marbles. Therefore, the probability of selecting another black marble is 3/9 or 1/3.
The probability of drawing two black marbles in a row with replacement is:P(two black marbles with replacement) = (4/9) × (1/3) = 4/27without replacement:Since the first marble was removed, there are only eight marbles in the jar, and there are four black ones. Therefore, the probability of selecting a black marble is 4/8 or 1/2. When the first black marble is removed, there are only seven marbles left, including three black ones. Therefore, the probability of selecting another black marble is 3/7. As a result, the probability of drawing two black marbles in a row without replacement is:P(two black marbles without replacement) = (4/9) × (3/7) = 12/63(c) P(one red and one black marble)with replacement:When one red and one black marble are selected with replacement, there are nine marbles in the jar for each draw. The probability of selecting one red and one black marble in a row is:P(one red and one black marble with replacement) = 2 × (5/9) × (4/9) = 40/81without replacement:Since there are five red and four black marbles in the jar, the probability of selecting a red marble first is 5/9. Once the red marble has been drawn and removed, there are only eight marbles remaining, including four black ones. As a result, the probability of selecting a black marble is 4/8 or 1/2.
As a result, the probability of drawing one red and one black marble without replacement is:P(one red and one black marble without replacement) = (5/9) × (4/8) + (4/9) × (5/8) = 20/36 + 20/36 = 10/18 = 5/9(d) P(red on the first draw and black on the second draw)with replacement:There are nine marbles in the jar for each draw. The probability of selecting a red marble first is 5/9. When the red marble is returned to the jar, there are still nine marbles in the jar, but now there are only four black marbles. The probability of selecting a black marble on the second draw is 4/9. As a result, the probability of drawing a red marble first and a black marble second with replacement is:P(red on the first draw and black on the second draw with replacement) = (5/9) × (4/9) = 20/81without replacement:Since there are five red and four black marbles in the jar, the probability of selecting a red marble first is 5/9. Once the red marble has been drawn and removed, there are only eight marbles remaining, including four black ones. As a result, the probability of selecting a black marble is 4/8 or 1/2. As a result, the probability of drawing a red marble first and a black marble second without replacement is:P(red on the first draw and black on the second draw without replacement) = (5/9) × (4/8) = 5/18
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Suppose two students from Georgia State University, working as interns for Select one answer the American National Elections Studies agency (ANES), are both 10 points assigned to survey a random sample of registered voters and ask whether or not they will vote for a certain candidate. The first intern plans to select 500 voters and the second intern plans to select 1500 voters. If each intern conducted the study repeatedly selecting different samples of people each time... but using the same sample size), which one of the following would be true regarding the resulting sample proportion, p, of "yes" responses for each intern? A. For either sample size, using the same size each time, as long as the sampling is done with replacement, their mean would be o. B. Different sample proportions, p, would result for each intern, but for either sample size, they would be centered (have their mean) at the true population proportion, P. C. Different sample proportions, p, would result for each intern, but for the intern using a sample size of 1500 they would be centered (have their mean) at the true population proportion, P, whereas for sample size 500 they would not. D. Different sample proportions, p, would result for each intern, but for sample size 500 they would be centered (have their mean) at the true population proportion, P, whereas for sample size 1500 they would not.
Answer: Different sample proportions, ^p, could result for each intern, but for either sample size, they would be centered (have their mean) at the true population proportion, p.
Step-by-step explanation:
Determine the number of 15 boxes in kilograms
Answer:
Step-by-step explanation:
150
in pascal's triangle, each entry is the sum of the two entries above it. in which row of pascal's triangle do three consecutive entries occur that are in the ratio 3:4:5?
The three consecutive entries in Pascal's Triangle that are in the ratio 3:4:5 occur in the 14th row.
The ratio 3:4:5 can be expressed as 3x, 4x, and 5x, where x is a constant. Using this ratio, we can find the values of the entries in the 14th row of Pascal's Triangle.
Starting from the left, the entries in the 14th row are 1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, and 1.
We can see that the ratio of the 5th, 6th, and 7th entries (715, 1287, and 1716) is 3:4:5. Therefore, the answer is the 14th row.
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The tires on Mavis’ car will have to be replaced when they each have 160 000 km of wear on them. If new tires cost $140.00 each, what is the total cost of the wear on Mavis’ tires for a year in which she drives 25 000 km?
Answer:
If the tires on Mavis’ car have to be replaced when they each have 160 000 km of wear, then the total distance Mavis can drive on a set of tires is:
4 tires * 160,000 km = 640,000 km
If Mavis drives 25,000 km in a year, she will need to replace her tires after:
640,000 km ÷ 25,000 km/year = 25.6 years
Since Mavis will need to replace her tires once every 25.6 years, the cost of the wear on her tires for a single year is:
$140.00/tire * 4 tires = $560.00
So the total cost of the wear on Mavis’ tires for a year in which she drives 25,000 km is $560.00.
Step-by-step explanation:
source: trust me bro
Write the expression in complete factored form.
5a(b + 1) + 3(b + 1) help
Answer:
(b+1)(5a+3)
Step-by-step explanation:
Notice how (b+1) appears on both sides. That means we can "factor it out" by moving it to the very left -
(b+1)
Now we know the form of the answer we can continue doing it.
For the next step, I take the terms 5a and 3 (what's left) and move them to the right as shown:
(b+1)(5a+3)
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Best regards
CONNAIS TU LES LIMITES ?
Answer:
yes
Step-by-step explanation:
Determine whether the graph is that of a function. If it is, use the graph to
find its domain and range, the intercepts, if any, and any symmetry with
respect to the x-axis, the y-axis, or the origin.
Answer:
D
Step-by-step explanation:
First, yes, it is a function. Functions are defined as having one output per input, and given a number on this graph, we can find only one output.
Domain is the range of x-values in a graph. The domain here is from [tex]-\pi[/tex] to [tex]\pi[/tex].
Range is the range of y-values in a graph. The range here is from -1 to 1.
This graph has three intercepts at [tex](-\pi ,0)(0,0)(\pi ,0)[/tex].
Symmetry: This graph has rotational symmetry, meaning it can be rotated about a point to map onto itself. Here, we can rotate it 180 degrees about the origin to map onto itself.
Although I can't see the final two points for answer D, answer A is similar but the symmetry portion is wrong, leading me to believe that it must be D.
Let me know if this helped by hitting thanks or brainliest! If not, comment below and I'll get back to you ASAP.
Binomial Problem:A jury has 12 jurors. A vote of at least 10 out of 12 for "guilty" is necessary for a defendant to be convicted of a crime. Assume that each juror acts independently of the others and that the probability that any one juror makes the correct decision on a defendant is .80. If the defendeant is guitly, what is the probability that the jury makes the correct decision?
The probability that the jury makes the correct decision is approximately 0.7063.
To solve this problem, we need to find the probability that the jury makes the correct decision if the defendant is guilty. Let's break down the problem into smaller steps.
We know that the probability of a single juror making the correct decision is 0.80. If the defendant is guilty, then the probability of a juror making the correct decision is still 0.80. Therefore, the probability that a single juror makes the correct decision if the defendant is guilty is 0.80.
We can use the binomial distribution formula to determine the probability of at least 10 out of 12 jurors making the correct decision. The formula is:
P(X ≥ k) = 1 - Σ(i=0 to k-1) [n!/(i!(n-i)!) x [tex]p^i \times (1-p)^{(n-i)}[/tex] ]
where:
P(X ≥ k) is the probability of at least k successes
n is the total number of trials (in this case, 12 jurors)
p is the probability of success in a single trial (in this case, 0.80)
k is the number of successes we want to find the probability of (in this case, 10)
Plugging in the values, we get:
P(X ≥ 10) = 1 - Σ(i=0 to 9) [12!/(i!(12-i)!) x [tex]0.80^i \times (1-0.80)^{(12-i)}[/tex]]
Using a calculator or software, we can calculate this to be approximately 0.7063.
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Help please I dont know how to do this.
[tex]0.000000778\implies \stackrel{ \textit{rounded up} }{0.000000800} ~\hfill 0.00000000155\implies \stackrel{ \textit{rounded up} }{0.00000000200} \\\\[-0.35em] ~\dotfill\\\\ 0.\underset{ 6~zeros }{\underline{000000}}800\implies 8.00\times 10^{-6}\implies \boxed{8\times 10^{-6}} \\\\\\ \underset{ 8~zeros }{0.\underline{00000000}200}\implies 2.00\times 10^{-8}\implies \boxed{2\times 10^{-8}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{\stackrel{ \textit{dust particle} }{8\times 10^{-6}}}{\underset{ \textit{grain of pollen} }{2\times 10^{-8}}}\implies \cfrac{8}{2}\times\cfrac{10^{-6}}{10^{-8}}\implies 4\times10^{-6}10^{8}\implies 4\times 10^2\implies \boxed{400}[/tex]
4/7+1/8+1/3 prime number
Since 7 is the smallest integer that divides 173/168, we can conclude that the sum is not a prime number.
How to solve?
To add the fractions 4/7, 1/8, and 1/3, we need to find a common denominator.
The prime factorization of 7 is 7, the prime factorization of 8 is 2²3, and the prime factorization of 3 is 3. The least common multiple (LCM) of these three numbers is 7× 2²3× 3 = 168.
So, we can rewrite the fractions with the common denominator of 168:
4/7 = 96/168
1/8 = 21/168
1/3 = 56/168
Now we can add these fractions:
96/168 + 21/168 + 56/168 = 173/168
To check if this sum is a prime number, we can use trial division by checking all the integers between 2 and the√ of 173/168 (which is approximately 1.053):
2 does not divide 173/168
3 does not divide 173/168
4 does not divide 173/168
5 does not divide 173/168
6 does not divide 173/168
7 divides 173/168 (24 times)
8 does not divide 173/168
9 does not divide 173/168
...
Since 7 is the smallest integer that divides 173/168, we can conclude that the sum is not a prime number.
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Complete question:
What is the result of adding 4/7, 1/8, and 1/3, and is the sum a prime number?
Let $ABCD$ be a parallelogram. Extend $\overline{DA}$ through $A$ to a point $P,$ and let $\overline{PC}$ meet $\overline{AB}$ at $Q$ and $\overline{DB}$ at $R.$ Given that $PQ = 735$ and $QR = 112,$ find $RC.$
The x ≤ 32Putting x = 24 in the expression we get RC = 96Therefore, the value of RC is 96.
In order to find RC, we will make use of the given information in the following manner: Given that ABDC is a parallelogram. Hence, AB = DC. We have also been given that PQ = 735 and QR = 112.Now, extend PQ to meet DC at S.Let PS = x; then DS = DC - x = AB - x. (Since AB = DC)We have that PS/SP = QR/RB (Since PQR is similar to DBR)Therefore, we getx/SP = 112/(AB - x)We can cross multiply and simplify to getSP = (112* x)/(AB - x)......(1)Further, we have that AQ/QB = SP/BR (Since PQR is similar to AQB)Therefore, we getx/(AB - x) = SP/BROn substituting the value of SP from equation (1) above, we getx/(AB - x) = (112* x)/(BR*(AB - x))Therefore, we getBR = (x*(AB - x)*QR)/[PQ*(AB - 2*x)]BR = (x*(32 - x)*112)/(735*(32 - 2*x))BR = (56*x*(16 - x))/(245*(16 - x))BR = (56*x/245)Since the sum of all sides of a parallelogram is equal to the sum of its opposite sides, we have thatRC + QR = AB + AQ - QBRearranging the terms we getRC = AB + AQ - QB - QR......(2)Now, AQ = PQ - APSubstituting the values of PQ and AP we get AQ = 735 - (DC - x) = 735 - 32 + x = x + 703Also, QB = AB - AQ = (32 - x) - (x + 703) = -x - 671Substituting the values of AQ and QB in equation (2) above we getRC = 32 + (x + 703) + (x + 671) - 112RC = 48 + 2xRC = 2(x + 24)We know that AB = 32, hence, x ≤ 32Putting x = 24 in the expression we get RC = 96Therefore, the value of RC is 96.
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Evaluate the following integral in cylindrical coordinates.∫3−3∫√9−x20∫2011+x2+y2dzdydx
The value of the integral in cylindrical coordinates is -81π/2.
We have the following integral
∫ from 3 to -3 ∫ from 0 to √(9-x^2) ∫ from 20 to 11+x^2+y^2 dz dy dx
Converting to cylindrical coordinates, we have:
x = r cos(theta)
y = r sin(theta)
z = z
Also, from the equation of the cone, we know that r^2 = x^2 + y^2 = 9. Thus, we have
r = 3
Substituting these values, we get
∫ from 0 to 2π ∫ from 0 to 3 ∫ from 20 to 11+r^2 dz r dr dtheta
Evaluating the z integral, we get:
∫ from 0 to 2π ∫ from 0 to 3 (11+r^2-20) r dr dtheta
= ∫ from 0 to 2π ∫ from 0 to 3 (r^3-9r) dr dtheta
= ∫ from 0 to 2π [ (1/4) r^4 - (9/2) r^2 ] |_0^3 dtheta
= ∫ from 0 to 2π (81/4 - 81/2) dtheta
= -81π/2
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56 tuna sandwiches were sold.
This was 40% of the total number of sandwiches sold.
(a) Work out the total number of sandwiches sold,
Answer:
140 sandwiches
Step-by-step explanation:
56/4=14 which is 10% of the sandwiches sold
14*10=140
Answer:
140 sandwiches.
Step-by-step explanation:
We know
56 tuna sandwiches were sold. This was 40% of the total number of sandwiches sold.
Work out the total number of sandwiches sold.
We Take
56 divided by 40, then time 100 = 140 Sandwiches
So, the total number of sandwiches sold is 140 sandwiches.
Which of the following statements most accurately describes the relationship between cultured yeast preparation conditions and fermented alcohol yield, based on passage data?Neither glucose concentration nor percentage yeast inoculate was positively correlated with fermented alcohol yield.A is correct. Table 1 shows that the maximum fermented alcohol yield was obtained in Broth A, with 10% glucose (not 12%, as in Broth C) and 8% yeast inoculate (not 10%, as in Broth B). Therefore, increasing neither glucose concentration nor percentage yeast inoculate led to more production of alcohol, so neither of those parameters showed a positive correlation with alcohol yield.
Based on the passage data, the most accurate statement describing the relationship between cultured yeast preparation conditions and fermented alcohol yield is: "Neither glucose concentration nor percentage yeast inoculate was positively correlated with fermented alcohol yield."
What this means is that increasing the concentration of glucose or percentage of yeast inoculate did not lead to more production of alcohol. The data in Table 1 shows that the maximum fermented alcohol yield was obtained in Broth A, which had 10% glucose and 8% yeast inoculation. Broth C, which had a higher concentration of glucose at 12%, did not result in a higher yield of alcohol. Similarly, Broth B, which had a higher percentage of yeast inoculate at 10%, did not lead to a higher yield of alcohol.
Therefore, it can be concluded that neither glucose concentration nor percentage of yeast inoculates was positively correlated with fermented alcohol yield.
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what is (2x+45)° x° = what?
Answer:
x = 45.
Step-by-step explanation:
Given a straight line with the equation.
First collect like terms:
2x + x = 180 - 45
Then calculate:
3x = 135
Finally after dividing both sides by 3:
x = 45
define a function named signof that receives an integer argument and returns the value 1 if the argument is positive, 0 if the argument is 0, or -1 if the argument is negative.
The signof function is defined as follows:
def signof(num):
if num > 0:
return 1
elif num == 0:
return 0
else:
return -1
In the above code snippet, we have defined a function named signof which receives an integer argument named num. The if condition checks if the num is greater than 0, if yes, the function will return 1 as it is positive. Else if the num is equal to 0, then it will return 0, as per the requirement. Otherwise, it will return -1 as the number is negative. This code snippet will give the required output as per the requirement of the problem statement.
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Factor
[tex]25x^6 + 10x^3 + 12[/tex]
Answer:
Step-by-step explanation:
To factor 25x^6 + 10x^3 + 12, we can first factor out the greatest common factor of the three terms which is 1, then use a substitution:
Let's substitute y = x^3. Then, the expression becomes:
25y^2 + 10y + 12
We can now try to factor this quadratic expression. However, since the discriminant (b^2 - 4ac) of this quadratic equation is negative (10^2 - 4*25*12 = -440), this expression cannot be factored using real numbers.
Therefore, the final answer for the factoring is:
25x^6 + 10x^3 + 12 = (unfactorable)
Stats... I need help please
Answer:
.
Step-by-step explanation:
...................
what percentage of 23 miles is 27 miles? round your answer to the nearest hundredth of a percentage point.
The percentage of 27 miles in 23 miles is 117.39%.
Percentage is a way of expressing a fraction or a portion of a whole number in relation to 100. It is denoted by the symbol "%". A percentage is calculated by dividing the part (numerator) by the whole (denominator) and multiplying the result by 100. A percentage can also be used to represent a rate or a percentage change over time.
In this case, we are asked to find what percentage of 23 miles is 27 miles. The part is 27 miles and the whole is 23 miles. Therefore, the percentage is:
% = part/whole = 27/23 x 100 = 117.39%
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The null hypothesis is rejected whenever:A. past studies prove it wrong. B. there is a low probability that the obtained results could be due to random error.C. the independent variable fails to have an effect on the dependent variable.D. the researcher is convinced that the variable is ineffective in causing changes in behavior.
The null hypothesis is rejected whenever "there is a low probability that the obtained results could be due to random error." The correct answer is Option B.
What is the null hypothesis?The null hypothesis is a statistical hypothesis used to test the difference between two sample data groups. The null hypothesis is the hypothesis that the sample statistics are not significantly different. Any significant differences between the sample data are seen as supporting the alternative hypothesis.
A null hypothesis is often expressed as "no difference," "no correlation," or "no significant effect." For example, the null hypothesis for an experiment comparing two groups of people could be "there is no difference between the two groups." When the null hypothesis is rejected, it means that the results of the experiment are statistically significant, and the alternative hypothesis is supported.
Therefore, the null hypothesis is rejected whenever there is a low probability that the obtained results could be due to random error.
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Suppose you roll a special 37-sided die. What is the probability that one of the following numbers is rolled? 35 | 25 | 33 | 9 | 19 Probability = (Round to 4 decimal places) License Points possible: 1 This is attempt 1 of 2.
Answer:
5/37
Step-by-step explanation:
There are 37 possible outcomes when rolling a 37-sided die, so the probability of rolling any one specific number is 1/37.
To find the probability of rolling any of the given numbers (35, 25, 33, 9, or 19), we need to add the probabilities of rolling each individual number.
Probability of rolling 35: 1/37
Probability of rolling 25: 1/37
Probability of rolling 33: 1/37
Probability of rolling 9: 1/37
Probability of rolling 19: 1/37
The probability of rolling any one of these numbers is the sum of these probabilities:
1/37 + 1/37 + 1/37 + 1/37 + 1/37 = 5/37
So the probability of rolling any of the given numbers is 5/37, which is approximately 0.1351 when rounded to four decimal places.
For his craft project, James bought
10
1010 pieces of ribbon that were each
2. 1
feet
2. 1 feet2, point, 1, start text, space, f, e, e, t, end text long. How many total yards of ribbon did James buy?
James bought a total of 7 yards of ribbon for his craft project.
To begin with, let's first convert the length of the ribbon from feet to yards. There are 3 feet in a yard. So, to convert 2.1 feet to yards, we need to divide it by 3.
2.1 feet ÷ 3 = 0.7 yards
So, each piece of ribbon is 0.7 yards long.
Now, let's calculate the total length of ribbon James bought by multiplying the length of each piece of ribbon by the total number of ribbons he bought.
Total yards of ribbon = length of one ribbon × number of ribbons
Total yards of ribbon = 0.7 yards × 10
Total yards of ribbon = 7 yards
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Complete Question:
For his craft project, James bought 10 pieces of ribbon that were each 2.1 feet long. How many total yards of ribbon did James buy?
The shedding frequency based on the analysis of Question 3 is to be determined through the use of a small-scale model to be tested in a water tunnel. For the specific bridge structure of interest D=20 cm and H=300 cm, and the wind speed V is 25 m/s. Assume the air is at MSL ISA conditions. For the model, assume that Dm =2 cm. (a) Determine the length of the model Hm needed for geometric scaling. (b) Determine the flow velocity Vm needed for Reynolds number scaling. (c) If the shedding frequency for the model is found to be 27 Hz, what is the corresponding frequency for the full-scale structural component of the bridge? Notes: Refer to the eBook for the properties of air. Assume the density of water
rhoH2O = 1000 kg/m3 and the dynamic viscosity of water μH2O =1×10^−3 kg/m/s
Answer:
Step-by-step explanation:
Show that, the sum of an infinite arithmetic progressive sequence with a positive common difference
is +∞
Answer:
Show that, the sum of an infinite arithmetic progressive sequence with a positive common difference
is +∞
Step-by-step explanation:
To show that the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞, we can use the formula for the sum of the first n terms of an arithmetic sequence:
Sn = n/2 [2a + (n-1)d]
where a is the first term, d is the common difference, and n is the number of terms in the sequence.
Now, if we let n approach infinity, the sum of the first n terms of the sequence will also approach infinity. This can be seen by looking at the term (n-1)d in the formula, which grows without bound as n becomes larger and larger.
In other words, as we add more and more terms to the sequence, each term gets larger by a fixed amount (the common difference d), and so the sum of the sequence increases without bound. Therefore, the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞.
A restaurant bill of $3200 is paid with $500 and $1000 bills. If 16 bills were used, determine how many $1000 and $500 bills were used.
Let's use variables to represent the number of $1000 and $500 bills used.
Let x be the number of $1000 bills used.
Then 16 - x is the number of $500 bills used.
The total amount paid is the sum of the values of the bills used:
$1000(x) + $500(16 - x) = $3200
Simplifying and solving for x:
$1000x + $8000 - $500x = $3200
$500x = $4800
x = 9.6
We can't have a fraction of a bill, so we'll round down to 9 $1000 bills.
Then the number of $500 bills used is:
16 - x = 16 - 9 = 7
Therefore, 9 $1000 bills and 7 $500 bills were used to pay the $3200 restaurant bill.
Data and statistics:
what is each students favorite restaurant at my school
Therefore, we estimate that about 7 sixth graders should be chosen to create a representative sample, given that 9 seventh graders were chosen.
What is statistics?Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data. It provides methods for summarizing and describing data, making inferences about populations based on samples, and testing hypotheses. Statistics is used in many fields, such as business, economics, health care, social sciences, engineering, and more, to make decisions and draw conclusions based on data. Some common techniques used in statistics include descriptive statistics (e.g., mean, median, mode, standard deviation), probability theory, hypothesis testing, regression analysis, and sampling methods.
Here,
To estimate the number of sixth graders that should be chosen to create a representative sample, we can use the proportion of seventh graders in the sample and assume that the proportions of each grade in the sample should match the proportions in the population. We know that the sample contains 9 seventh graders, but we don't know the total size of the sample yet. We can use the following formula to estimate the sample size:
sample proportion = population proportion
where
sample proportion = number of seventh graders in the sample / total sample size
population proportion = number of seventh graders in the population / total population size
We can plug in the values we know:
9 / total sample size = 180 / (160 + 180 + 140)
Simplifying the right-hand side:
9 / total sample size = 0.4
Multiplying both sides by total sample size and simplifying:
total sample size = 9 / 0.4
total sample size ≈ 22.5
This means that the sample size should be about 22.5 students. Since we can't choose a fractional number of students, we should round up to the nearest whole number, giving a total sample size of 23 students.
To estimate the number of sixth graders in the sample, we can use the proportion of sixth graders in the population and assume that the proportion should be the same in the sample:
number of sixth graders in the sample / total sample size = 160 / (160 + 180 + 140)
Simplifying the right-hand side:
number of sixth graders in the sample / total sample size = 0.32
Multiplying both sides by total sample size and simplifying:
number of sixth graders in the sample = 0.32 * 23
number of sixth graders in the sample ≈ 7
To know more about statistics,
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Complete question:
A population of middle school students contains 160 sixth graders, 180 seventh graders, and 140 eighth graders. Nine seventh graders were part of a random sample of the population chosen to participate in a survey. For the sample to accurately represent the population, about how many sixth graders should be chosen for each students favorite restaurant at my school?