A two-digit number's tens digit is three times larger than its units digit. Reversing the digits results in a new number that is 54 less than the original. The reversal of the original number is 651, which equals 156.
Let's name the units digit "u" and the tens digit of the original number "t."
From the first statement, we know that:
t = 2u + 3
From the second statement, we know that when the digits are reversed, the new number is 54 less than the original number. Using an equation, we can visualize this:
10u + t = 10t + u - 54
Now we can substitute the first equation (t = 2u + 3) into the second equation:
10u + (2u + 3) = 10(2u + 3) + u - 54
Simplifying this equation, we get:
12u + 33 = 21u - 24
Subtracting 12u from both sides, we get:
33 = 9u - 24
Adding 24 to both sides, we get:
57 = 9u
Dividing both sides by 9, we get:
u = 6
Now we can use the first equation (t = 2u + 3) to find the value of t:
t = 2u + 3 = 2(6) + 3 = 15
Therefore, the original number is 156 (with tens digit 1 and units digit 6) and the reversed number is 651. And indeed, 651 is 54 less than 156.
The complete question is:-
The tens digit of a 2-digit number is 3 more than twice the units digit. if the digits are reversed, the new number is 54 less than the original number. Find the number.
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buses arrive at a specified stop at 15-minute intervals starting at 7am. if a passenger arrives at the stop at a time that is uniformly distributed between 7am and 7:30am, find the probability that he waits
If buses arrive at stop at "15-minute" intervals, then the probability that he waits more than 10 minutes for a bus is "1/3".
Let us denote the arrival-time of the passenger by X, where X is uniformly distributed between 7am and 7:30am. hence, the probability-density-function (pdf) of "X" is written as :
f(x) = 1/30, for 7am ≤ x ≤ 7:30am
f(x) = 0, otherwise
We observe that, the passenger will wait for more than 10 minutes for a bus only if he arrives between 7:00 a.m. and 7:05 a.m. , or between 7:15 a.m. and 7:20 a.m.
So, the probability for waiting time can be written as ;
⇒ [tex]\int\limits^5_0 {\frac{1}{30} } \, dx[/tex] + [tex]\int\limits^{20}_{15} {\frac{1}{30} } \, dx[/tex],
⇒ (1/30)(5 - 0) + (1/30)(20 - 15);
⇒ 1/3.
Therefore, the required probability is 1/3.
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The given question is incomplete, the complete question is
Buses arrive at a specified stop at 15-minute intervals starting at 7am. If a passenger arrives at the stop at a time that is uniformly distributed between 7am and 7:30am, find the probability that he waits more than 10 minutes.
Multiply
28845by 6502
Answer:
187,550,190
Step-by-step explanation:
cashews cost $11.25/kg. pecans cost $13.00/kg the number of kilograms of cashews is 3 less than the number if kilograms of pecans. How many kilograms of each should be mixed to make a box that will sell for $136
Answer:
4 kg cashews7 kg pecansStep-by-step explanation:
You want the mass of cashews and pecans in a box that sells for $136 if there are 3 fewer kg of cashews at $11.25 per kg than of pecans at $13 per kg.
SetupLet c represent the mass of cashews in kg. Then (c+3) is the mass of pecans. The total value of the mix is ...
11.25c +13(c +3) = 136
SolutionSimplifying the equation gives ...
24.25c +39 = 136
24.25c = 97
c = 4
The mix should contain 4 kg of cashews and 7 kg of pecans.
A glass fish tank is shaped like a triangular
prism. Each base of the aquarium is an
isosceles triangle with dimensions shown.
The tank has a height
of 12 inches. What is
the total surface area
of the tank in square
inches?
answers:
work: 36(12) + 2(48)
solution: 528
work: 36(6) + 2(48)
solution: 312
Step-by-step explanation:
Area of the TWO ends are each 1/2 b*h = 1/2 * 16 * 6 =48 in^2
TWO of them would be 2 * 48 = 96 in^2
Then there are 3 sides
two are 10 * 12 = 120
two would be 120 x 2 = 240 in^2
and ONE side 16 * 12 = 192 in^2
Total area is then 96 + 240 + 192 = 528 in^2
if 11011 is equal to what
Answer:
I'm sorry, it is unclear what you are asking. Can you please provide more context or clarify your question?
Step-by-step explanation:
PLEASE HELP I NEED THIS ASAP!!!
identify any outliners in the graph
Answer:
The outlier in this graph is (4, 55)
Step-by-step explanation:
Outliers can be seen graphically when we first draw a line of best fit. When we draw the line of best fit it connects through the middle of the string of points near the top of our graph. We can see that any given point on the graph is either on the line of best fit or very close to it. This can be said about all points but one... the point (4,55). This point lies far away from the line we've created and can be identified as an outlier for this reason.
the depths (in inches) at which 10 artifacts are found in a remote area are the following: 20.7, 24.8, 30.5, 26.2, 36.0, 34.3, 30.3, 29.5, 27.0, 38.5 what is the range? do not round your answer.
The range of the depths of the 10 artifacts is 18.5 inches.
The range in statistics is a measure of variability, which represents the difference between the largest and smallest values in a data set. To calculate the range, we simply subtract the smallest value from the largest value. In this case, the largest value is 38.5 inches, and the smallest value is 20.7 inches.
Therefore, the range of the depths of the artifacts in the remote area is:
Range = 38.5 - 20.7
Range = 17.8
So the range of depths is 17.8 inches. This tells us that there is quite a bit of variability in the depths at which the artifacts were found. The smallest depth was 20.7 inches, while the largest depth was 38.5 inches.
This information could be useful for archaeologists or other researchers who are interested in understanding the distribution of artifacts in the area, as well as the possible reasons for why some artifacts were found at certain depths while others were found at different depths.
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A triangle has a perimeter of 8z + 11. Two of its side lengths are z + 13
and 2z + 6. Write a simplified expression for the third side length of
the triangle.
To find the third side length, we can use the fact that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. So we can write: (z + 13) + (2z + 6) > third side Simplifying the left side, we get: 3z + 19 > third side Now we also know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can write: (z + 13) + (2z + 6) + third side = 8z + 11 Simplifying this equation, we get: 3z + 19 + third side = 8z + 11 Subtracting 3z + 19 from both sides, we get: third side = 5z - 8 Therefore, the
Let x represent the number of customers arriving during the morning hours and let y represent the number of customers arriving during the afternoon hours at a diner. you are given: i) x and y are poisson distributed.ii) the first moment of x is less than the first moment of y by 8iii) the second moment of x is 60% of the second moment of y. calculate the variance of y
E(y) = Var(y) for a Poisson distribution, the variance of y is equal to the value of E(y) .
To calculate the variance of y, follow these steps:
Recall that for a Poisson distribution, the mean (first moment) is equal to the variance. So, if the first moment of x is less
than the first moment of y by 8, we can write: E(x) = E(y) - 8.
We are also given that the second moment of x is 60% of the second moment of y:
[tex]E(x^2) = 0.6 × E(y^2).[/tex]
Recall that for a Poisson distribution, the second moment is given by [tex]E(X^2) = E(X)² + E(X)[/tex]. Thus, we can write equations
for x and y using this relationship: [tex]E(x^2) = E(x)² + E(x) and E(y^2) = E(y)² + E(y).[/tex]
Plug the expressions from step 1 into the equation from [tex]E(x^2) = (E(y) - 8)² + (E(y) - 8).[/tex]
Plug the expressions from step 2 into the equation from[tex]0.6 × E(y^2) = (E(y) - 8)² + (E(y) - 8).[/tex]
Solve for [tex]E(y^2)[/tex] from the equation in [tex]E(y^2) = (10/6) × ((E(y) - 8)² + (E(y) - 8)).[/tex]
Substitute [tex]E(y^2)[/tex] back into the equation for the second moment of y from [tex]E(y^2) = E(y)² + E(y).[/tex]
Solve for E(y) from the equation in
Since E(y) = Var(y) for a Poisson distribution, the variance of y is equal to the value of E(y) .
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HELP!! I need to find the code to pass.
The side TU of the right triangle is 156.15 metres and the area of the triangle is 6168.07 metres squared.
The side GH of the right triangle is 182.33 metres and the area of the triangle is 8934.27 metres².
How to find the side and area of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
The missing side of the right triangle can be found using Pythagoras's theorem.
Therefore,
a² + b² = c²
where
a and b are the legsc is the hypotenuse sideThe area of the right triangle can be found using the formula as follows:
area of a triangle = 1 / 2 bh
where
b = baseh = heightHence,
1.
TU² = 175² - 79²
TU² = 30625 - 6241
TU² = 24384
TU = √24384
TU = 156.153770368
TU = 156.15 metres
Area = 1 / 2 × 156.15 × 79
area = 6168.07392952
area = 6168.07 metres squared
2.
GH² = 207² - 98²
GH² = 42849 - 9604
GH = √33245
GH = 182.33211456
GH = 182.33 metres
Area of the triangle = 1 / 2 × 98 × 182.33
Area of the triangle = 8934.27361345
Area of the triangle = 8934.27 metres²
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Given: J(-4,1), E(-2,-3), N(2,-1)
Prove triangle JEN is an isosceles right triangle
Triangle is an isosceles right triangle because?
The sum of the squares of JE and EN is approximately 32. Therefore, we can conclude that the triangle formed by J, E, and N is indeed an isosceles right triangle.
An isosceles right triangle is a triangle that has two sides of equal length and one right angle. In this case, we are given the coordinates of three points J(-4,1), E(-2,-3), and N(2,-1) and we need to determine if the triangle formed by these points is an isosceles right triangle.
Firstly, we need to calculate the length of each side of the triangle. We can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by the square root of ((x2-x1)^2 + (y2-y1)^2).
Using this formula, we can find that the length of JE is approximately 4.472, the length of EN is approximately 4.472, and the length of JN is approximately 5.657.
Since two sides of the triangle (JE and EN) have the same length, the triangle is indeed isosceles. To determine if it is also a right triangle, we need to check if one of the angles is a right angle.
We can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we can see that JN is the longest side and its length squared is approximately 32. Therefore, we need to check if the sum of the squares of JE and EN is also approximately 32.
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Please help me choose the right answer?
Answer:
B’C’(bar) is Perpendicular to BC(bar) and does not intersect the point (-2,-2).Step-by-step explanation:
The most famous geyser in the world, Old Faithful in Yellowstone National Park, has a mean time between eruptions of 85 minutes. The interval of time between eruptions is normally distributed with a standard deviation of 21 minutes.
Now assume that you going to collect a sample of 30-time intervals between eruptions.
Would it be surprising that a random sample of 30-time intervals between eruptions has a mean of 97 minutes? Provide a brief explanation.
It would be very surprising to observe a random sample of 30-time intervals between eruptions with a mean of 97 minutes, given the population mean and standard deviation.
Based on the information provided, we know that the mean time between eruptions of Old Faithful is 85 minutes and the standard deviation is 21 minutes. We are also given a sample of 30-time intervals between eruptions, and we want to determine whether it would be surprising to observe a sample mean of 97 minutes.
To answer this question, we need to calculate the standard error of the mean (SEM), which is given by the formula:
SEM = σ / sqrt(n)
where σ is the population standard deviation (21 minutes), and n is the sample size (30). Plugging in the values, we get:
SEM = 21 / sqrt(30) ≈ 3.84
Next, we calculate the z-score for a sample mean of 97 minutes, using the formula:
z = (x - μ) / SEM
where x is the sample mean (97 minutes), μ is the population mean (85 minutes), and SEM is the standard error of the mean (3.84 minutes). Plugging in the values, we get:
z = (97 - 85) / 3.84 ≈ 3.13
Finally, we can look up the probability of observing a z-score of 3.13 or more extreme in a standard normal distribution table (or using a calculator or software). The probability turns out to be very small, less than 0.01.
Therefore, Given the population mean and standard deviation, it would be very unexpected to find a random selection of 30-minute gaps between eruptions with a mean of 97 minutes. This suggests that the sample may not be representative of the population, or there may be some other factors affecting the intervals between eruptions.
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a(n) select is a basic statistical tool that graphically shows the frequency or number of observations of a particular value or within a specified group.
A histogram is a basic statistical tool that graphically shows the frequency or number of observations of a particular value or within a specified group.
A histogram is a chart that displays data by dividing it into intervals, or "bins," and then counting how many data points fall into each bin. The x-axis of a histogram represents the range of values being analyzed, while the y-axis represents the frequency or count of values that fall within each bin.
Histograms are commonly used to illustrate the distribution of data. They provide a visual representation of the central tendency, variability, and shape of the data. In particular, histograms can reveal patterns in the data such as skewness, outliers, or gaps.
Histograms are frequently used in data analysis across many fields, including finance, biology, psychology, and engineering. They can be created using software programs such as Microsoft Excel, R, Python, or MATLAB.
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The given question is incomplete, the complete question is:
A(n)______ is a basic statistical tool that graphically shows the frequency or number of observations of a particular value or within a specified group
A rectangular prism has whole number dimensions It has a height of 24 inches, a square base, and a surface area of 306 inches squared. What are the dimensions of the base of the prism?
Therefore, the prism's base can be either 9 x 9 inches, 6 x 6 inches, or
4 x 4 inches in size.
.
The Surface area is what?The amount of space that an object's surface takes up in total is measured by its surface area. It is usually expressed in square units, such as square inches or square metres.The surface area of a three-dimensional object can be determined by adding up the areas of all of its faces.
For instance, the surface area of a rectangular prism can be calculated using the formula below:
A = lw + lh + lw
The formula SA = 2lw + 2lh + 2wh, where l is the prism's length, w is its width, and h is its height, determines the surface area of a rectangular prism. Inputting the values provided yields:
306 is equal to 2l + 2(24) + 2(24) + 48
306 - 48l = 2w(l+24) 153 - 24
l = wl + 48w 153 - 48w = l(w+24) 153 - 24l - 48w = wl
We can identify all potential values of l and w that meet this equation because they are both whole numbers. Since it is a rectangular prism with a square base, we know that l > w. Given that the surface area cannot be more than 306, we also know that l(w+24) 153. We may therefore begin by identifying all variables of (153-48w) bigger than w.and equal to or less than 12 (since w cannot be greater than 12). We get:
W=1, L=9, L=2, L=6, and L=3
Therefore, the prism's base can be either 9 x 9 inches, 6 x 6 inches, or 4 x 4 inches in size.
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$3,423.55+
$2,737.69+
$2,014.95+
$1,253.34+
$450.76+
$12,752.45+
$13,438.31+
$14,161.05+
$14,922.66+
$15,725.24
Answer:
the final answer is 80800 exactly
Answer: $80 880 US$
Step-by-step explanation:
Add all up
Can someone please help me answer this ?
[tex]3(x+1)(x+7)-(2x+5)^2[/tex] is never positive for any value of x, since it is equal to [tex]-x^2+4x-4.[/tex]
What concludes that the expression is never positive?To prove that [tex]3(x+1)(x+7)-(2x+5)^2[/tex] is never positive, we can use algebraic manipulation and some basic concepts of quadratic equations.
First, let's expand the expression and simplify:
[tex]3(x+1)(x+7)-(2x+5)^2 = 3(x^2+8x+7)-(4x^2+20x+25)[/tex]
[tex]= 3x^2+24x+21-4x^2-20x-25[/tex]
[tex]= -x^2+4x-4[/tex]
Now we want to show that this expression is never positive for any value of x.
We can start by considering the discriminant of the quadratic expression -x²+4x-4, which is b²-4ac, where a = -1, b = 4, and c = -4. The discriminant is:
[tex]b^2-4ac = 4^2-4(-1)(-4) = 16-16 = 0[/tex]
Since the discriminant is zero, the quadratic equation [tex]-x^2+4x-4[/tex] has a double root, which means that it touches the x-axis at exactly one point.
Since the coefficient of x² is negative, this means that the parabola opens downward, which implies that the function has a maximum value at the vertex. The x-coordinate of the vertex is given by -b/2a, which in this case is x [tex]= -4/-2 = 2[/tex] .
So, we can conclude that the expression [tex]-x^2+4x-4[/tex] is never positive for any value of x, since it has a maximum value of -4 at [tex]x = 2[/tex] .
Therefore, [tex]3(x+1)(x+7)-(2x+5)^2[/tex] is never positive for any value of x, since it is equal to [tex]-x^2+4x-4[/tex] .
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Hence [tex]3(x+1)(x+7)-(2x +5)^{2}[/tex] = -1 ([tex]x^{2} + 4x -4[/tex]) as the leading coefficient is -1, therefore is never positive.
How to simplify the equation?Expanding the first and second term and then simplifying it we get,
To solve this equation first we need to simplify the equation and then we need to subtract the simplified term.
[tex](x+1)(x+7) = x^{2} +8x+7\\3(x^{2} +8x+7)=3x^{2} +24x+21\\(2x+5)^{2} =(2x+5)(2x+5)= 4x^{2} +20x+25\\(3x^{2} +24x+21) - (4x^{2} +20x+25)= -x^{2} + 4x - 4 =-1(x^{2} -4x+4)= -1((x+2)(x+2))[/tex]
Because it is always multiplied with -1
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what is the parameter of interest? group of answer choices the mean reaction times (measured in seconds) the mean difference in reaction times between all those who drink no beers and all those who drink two cans of beer the difference between the mean reaction time of the sample of those who drink no beers and the mean reaction time of the sample of those who drink two cans of beer the difference between the mean reaction time of all those who drink no beers and the mean reaction time of all those who drink two cans of beer
The parameter of interest is the difference between the mean reaction time of all those who drink no beers and the mean reaction time of all those who drink two cans of beer.
The difference between the mean reaction time of all those who drink no beers and the mean reaction time of all those who drink two cans of beer.
This parameter represents the average difference in reaction times between the two groups - those who did not drink beer and those who drank two cans of beer. It is a measure of the effect that drinking two cans of beer has on reaction times, and it is the focus of the hypothesis test being conducted.
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is the following statement supported or not supported by the data shown in the graph? the mortality rate of albertosaurus dinosaurs aged between 25% and 50% of their maximum life span was far greater than the mortality rate of dinosaurs that reached 75% of their maximum life span.
The statement cannot be determined from the graph, the reason is that the graph shows only the chances of survivals of Albertosaurus and it does not define the life span of the Albertosaurus.
When we carefully asses the graph, according to the information provided, the mortality rate of Albertosaurus dinosaurs between 25% and 50% of their maximum life span was significantly higher than the mortality rate of dinosaurs who lived to 75% of their maximum life span. This conclusion cannot be inferred from the graph because it only depicts the possibilities of survival for Albertosaurus and does not specify how long they lived.
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find the value of X.
Answer:
x = 122
Step-by-step explanation:
the measure of the chord- chord angle 125° is half the sum of the arcs intercepted by the angle and its vertical angle, that is
125 = [tex]\frac{1}{2}[/tex] (x + 6 + x) ← multiply both sides by 2 to clear the fraction
250 = 2x + 6 ( subtract 6 from both sides )
244 = 2x ( divide both sides by 2 )
122 = x
What is the surface area of the triangular prism? A triangular prism. The base is 6 feet by 9 feet. The 2 rectangular sides are 9 feet by 5 feet. The triangular sides have a base of 6 feet and height of 4 feet.
The surface area of the triangular prism is 168 square feet.
What is Surface Area?Surface area is the total area that the surface of a three-dimensional object occupies in space. It is a measure of the amount of material that would be needed to cover the entire surface of the object.
To find the surface area of the triangular prism, we need to find the area of each of its faces and add them together.
The triangular faces have an area of [tex]\frac{1}{2}bh[/tex], where b is the base and h is the height. In this case, the triangular faces have a base of 6 feet and a height of 4 feet, so their area is:
=>[tex]\frac{1}{2}\times6\times4=12ft^2[/tex]
There are two triangular faces, so their total area is [tex]2\times12=24ft^2[/tex]
The rectangular faces have an area of lw, where l is the length and w is the width. In this case, the rectangular faces have dimensions of 9 feet by 5 feet, so their area is:
=> [tex]9\times5=45ft^2[/tex]
There are two rectangular faces, so their total area is
=> [tex]2\times45=90ft^2[/tex]
Finally, the base of the triangular prism is a rectangle with dimensions of 6 feet by 9 feet, so its area is:
=> [tex]6\times9 = 54 ft^2[/tex]
Adding up the areas of all the faces, we get:
=>[tex]24 ft^2 + 90 ft^2 + 54 ft^2 = 168 ft^2[/tex]
Therefore, the surface area of the triangular prism is 168 square feet.
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please help will give brainliest
The explicit rule is 2000 + 3500n
The salesperson has earned $33500 after 9 months since starting the job.
What is Linear Equation?
A linear equation is a mathematical equation that involves two variables and forms a straight line when graphed. It can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept.
The explicit rule for the amount of money the salesperson has earned since starting the job can be given by:
Earnings = 2000 + 3500n
Where n represents the number of months since the salesperson started the job.
To find out how much money the salesperson has earned after 9 months, we can substitute n = 9 in the above formula:
Earnings = 2000 + 3500(9)
= 2000 + 31500
= $33500
Therefore, the salesperson has earned $33500 after 9 months since starting the job.
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if the mean for 1 hour is 1 pound and the standard deviation is 0.2 pound, what is the probability that the amount dispensed per box will have to be increased?
The probability that the amount dispensed per box will have to be increased is 0.
To answer this question, we need to know the target amount that should be distributed per carton.
Assuming that the target amount is also 1 pound, we can use the concept of the normal distribution to estimate the likelihood that we will have to increase the amount distributed per case.
hence the probability of having to increase the amount is 0.
z = (target volume - mean) / standard deviation
z = (1 - 1) / 0.2
z = 0
A Z-score of 0 indicates that the target volume is equal to the mean. A standard normal distribution table or calculator can be used to find the probability that the amount should be increased.
However, the target amount is equal to the mean value,
In summary, without knowing the target amount to be dispensed in each case, it is not possible to determine the potential for volume increases.
If the target amount is to be £1 and the mean and standard deviation is also £1 and 0.2 respectively, then the probability of having to increase the amount is 0.
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Of the people in Malik's apartment building, 4 like to eat macaroni and cheese and 7 like to eat cookies. 3 people like to eat both macaroni and cheese and cookies. How many people like to eat macaroni and cheese or cookies or both?
8 people in Malik's apartment building like to eat macaroni and cheese or cookies or both
Of the people in Malik's apartment building, 4 like to eat macaroni and cheese, and 7 like to eat cookies.
Three people like to eat both macaroni and cheese and cookies.
To determine how many people like to eat macaroni and cheese or cookies or both, we will employ the principle of inclusion-exclusion.
In Malik's apartment building, to find out how many people like to eat macaroni and cheese, or cookies, or both, we can follow these steps:
Identify the number of people who like macaroni and cheese (4 people) and cookies (7 people).
Determine the number of people who like both macaroni and cheese and cookies (3 people).
Calculate the total number of people who like either macaroni and cheese or cookies by adding the number of people who like macaroni and cheese (4 people) and the number of people who like cookies (7 people).
4 people + 7 people = 11 people
Subtract the number of people who like both macaroni and cheese and cookies (3 people) from the total calculated in Step 3 to avoid double-counting those who like both.
11 people - 3 people = 8 people
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um i need help with this so i can bring my grade up
Answer:
There are 20 students. Of those 20 students, 4 knew 15 capitals. We have:
4/20 = 20/100 = 20% of the students knew 15 capitals.
a statistics teacher wants to know if the student birth month is distributed equally across all months. he uses school records to determine the birth month of all the students at the school and calculates a chi-square statistic to test this hypothesis. why is this not an appropriate use of a chi-square goodness-of-fit test?
The chi-square goodness-of-fit test is not an appropriate statistical test to use in this situation.
A statistics teacher wants to know if the student birth month is distributed equally across all months. He uses school records to determine the birth month of all the students at the school and calculates a chi-square statistic to test this hypothesis.
This is not an appropriate use of a chi-square goodness-of-fit test because chi-square goodness-of-fit tests are used to compare the distribution of categorical data to a theoretical distribution.
The chi-square goodness-of-fit test compares observed frequencies of categorical data to expected frequencies based on a theoretical distribution. It is used to determine if a sample of data comes from a specific population or not.
In this case, the teacher is not comparing observed frequencies to expected frequencies, but instead is testing the hypothesis that the distribution of student birth months is equal across all months.
This is not a proper use of a chi-square goodness-of-fit test because the hypothesis being tested is not related to the expected frequencies of a categorical variable. Therefore, the chi-square goodness-of-fit test is not an appropriate statistical test to use in this situation.
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A grocer has 5 apples and 5 oranges for a window display. The grocer makes a row
of the 10 pieces of fruit by choosing one piece of fruit at random, making it the first
piece in the row, choosing a second piece of fruit at random, making it the second
piece in the row, and so on. What is the probability that the grocer arranges the fruits
in alternating order? (Assume that the apples are not distinguishable and that the
oranges are not distinguishable.)
The probability that the grocer arranges the fruits in alternating order is 5/16.
What is probability?It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
According to question:There are only two ways that the fruits can be arranged in alternating order: apple-orange-apple-orange-apple-orange-apple-orange or orange-apple-orange-apple-orange-apple-orange-apple.
Let's consider the first case where the first fruit is an apple. The probability of this happening is 1/2 since there are 10 total fruits and 5 of them are apples. Once the first fruit is chosen, there are 4 apples and 5 oranges left. The next fruit must be an orange, which has probability 5/9 of occurring since there are now 9 fruits left and 5 of them are oranges. The third fruit must be an apple, which has probability 4/8 (or 1/2) of occurring since there are 8 fruits left and 4 of them are apples. Continuing in this way, we get the following probability:
(1/2) * (5/9) * (4/8) * (4/7) * (3/6) * (3/5) * (2/4) * (2/3) * (1/2) * 1
The second case where the first fruit is an orange is the same as the first case but with the roles of apples and oranges reversed. So the probability of arranging the fruits in alternating order is:
(1/2) * (4/9) * (5/8) * (3/7) * (4/6) * (2/5) * (3/4) * (1/3) * (2/2) * 1
Simplifying both expressions, we get:
(5!/(4!1!)) * (4!/(2!2!)) * 1/(2^5) + (5!/(4!1!)) * (4!/(2!2!)) * 1/(2^5)
= 10/32 + 10/32
= 5/16
Therefore, the probability that the grocer arranges the fruits in alternating order is 5/16.
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A rectangular soccer field and and expressions representing its dimensions, in yards, are shown in the diagram below.
Which of the following expressions represents the perimeter, in yards, of the soccer field?
The Perimeter of the rectangle shaped field is 16x+32 unit.
What exactly is a rectangle?
A rectangle is a four-sided, two-dimensional geometric object with four right angles (90-degree angles) and opposing parallel and equal-length sides. Rectangles are classified as a type of quadrilateral, which is any four-sided polygon.
The opposite sides of a rectangle are also congruent, meaning that they have the same length, and all four angles are congruent, meaning that they have the same measure of 90 degrees. The area of a rectangle can be calculated by multiplying the length and width of the rectangle, while the perimeter can be calculated by adding the lengths of all four sides.
Now,
Given rectangular field has
length = 5x+10
Breadth = 3x+6
As we know Perimeter of a rectangle = 2(L+B)
P=2*(5x+10+3x+6)
P=2(8x+16)
P=16x+32
Hence,
The Perimeter of the field is 16x+32.
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The diameter of the base of the cone is 20 inches the height is 21 inches what is the volume of the cone Xpress to answer in terms of pie and again rounded to the nearest cute pic inches
The volume of the cone is approximately700π/3 inches³.
What exactly is a cone?
A cone is a three-dimensional geometric shape that tapers smoothly from a flat, circular base to a point called the apex or vertex. The base can be any shape, but a circular base is the most common. A cone has a curved surface that extends from the base to the apex, and the distance from the apex to the base along a straight line passing through the center of the base is called the height of the cone.
Now,
As the Volume of cone is given by:
V = (1/3)πr²h
where r is the radius of the base, h is the height, and π is the mathematical constant pi.
In this case, we know that the diameter of the base is 20 inches, which means that the radius is 10 inches. We also know that the height is 21 inches. Therefore, we can plug in these values into the formula to find the volume:
V = (1/3)π(10²)(21) = (1/3)π(100)(21) = 700π/3 inches
Therefore, the volume of the cone is approximately700π/3 inches³, expressed in terms of pi and rounded to the nearest cubic inch.
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The hardware store sells hammers in packs of 3 and nails in packs of 6.
Jess is doing some repairs around the house and wants to buy the same number of each of these items.
What is the least number of packs of nails Jess needs to buy?
The least number of packs of nails Jess needs to buy is 1.
To find the least number of packs of nails Jess needs to buy, we need to find the lowest common multiple (LCM) of the pack sizes of hammers and nails.
Step 1: Identify the numbers
Hammers come in packs of 3, and nails come in packs of 6.
Step 2: Find the LCM of 3 and 6
List the multiples of each number:
Multiples of 3: 3, 6, 9, 12, ...
Multiples of 6: 6, 12, 18, 24, ...
The lowest common multiple of 3 and 6 is 6.
Step 3: Determine the number of packs of nails.
Since the LCM is 6 and nails come in packs of 6, Jess needs to buy 1 pack of nails to have the same number of each item.
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