We can then check the sum of each set of three integers and see which one adds up to 26. We find that the set 2, 8, 16 has a sum of 26, so these are the three distinct integers that multiply to 144.Therefore, the sum of the squares of the three integers is 324.
To solve this problem, we can start by listing all the factors of 144 and looking for three distinct integers that multiply to 144. The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144. We can eliminate any factor that is not a positive integer or is repeated, leaving us with the following possibilities:
- 1, 2, 72
- 1, 3, 48
- 1, 4, 36
- 1, 6, 24
- 2, 3, 24
- 2, 4, 18
- 2, 8, 9
- 3, 4, 12
- 3, 6, 8
To find the sum of their squares, we simply square each integer and add them together:
2² + 8² + 16² = 4 + 64 + 256 = 324
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The sum of the squares of the three distinct positive integers is 589.
Let's denote the three distinct positive integers as a, b, and c. We know the following:
1. a * b * c = 144
2. a + b + c = 26
Our goal is to find the sum of their squares, i.e.,[tex]a^2 + b^2 + c^2.[/tex]
Find the prime factorization of 144. It is [tex]2^4 * 3^2[/tex]
We need to find three distinct factors of 144 that add up to 26.
By analyzing the factors, we find that the integers are 2, 3, and 24.
Calculate the sum of their squares:
[tex]a^2 + b^2 + c^2 = 2^2 + 3^2 + 24^2 = 4 + 9 + 576 = 589[/tex].
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ALL MY POINTS TO WHOEVER ANSWERS THIS FIRST
IN ΔABC, m∠A=70° and m∠B=35°.
Select the traingle that is similar to ΔABC.
The answer is B
The internal angles of a triangle have to be 180
IN ΔABC, m∠A=70° and m∠B=35°.
70°+35°+x=180°
105°+x=180°
x=180°-105°
x=75°
Answer B meets the requirements because in ΔPQR m∠P=70° and m∠R=75°
70°+75°+x=180°
145°+x=180°
x=180°-145°
x=35°
The angles of both triangles measure the same
X and y represent positive integers such that 18x+11y= 2020. What is the greatest possible value of x+y
Answer:
To find the greatest possible value of x + y, we need to maximize the values of x and y such that they are still positive integers and satisfy the given equation 18x + 11y = 2020.
We can start by rearranging the equation to solve for y:
11y = 2020 - 18x
y = (2020 - 18x)/11
For y to be a positive integer, 2020 - 18x must be divisible by 11. We can test values of x starting from x = 1 and increasing by 1 until we find the largest possible value of x that satisfies this condition.
When x = 1, 2020 - 18x = 2002, which is divisible by 11. This gives us a value of y = 182/11, which is not a positive integer.
When x = 2, 2020 - 18x = 1984, which is divisible by 11. This gives us a value of y = 180/11, which is not a positive integer.
When x = 3, 2020 - 18x = 1966, which is divisible by 11. This gives us a value of y = 178/11, which is not a positive integer.
When x = 4, 2020 - 18x = 1948, which is divisible by 11. This gives us a value of y = 176/11, which is not a positive integer.
When x = 5, 2020 - 18x = 1930, which is divisible by 11. This gives us a value of y = 174/11, which is not a positive integer.
When x = 6, 2020 - 18x = 1912, which is divisible by 11. This gives us a value of y = 172/11, which is not a positive integer.
When x = 7, 2020 - 18x = 1894, which is divisible by 11. This gives us a value of y = 170/11, which is not a positive integer.
When x = 8, 2020 - 18x = 1876, which is divisible by 11. This gives us a value of y = 168/11, which is not a positive integer.
When x = 9, 2020 - 18x = 1858, which is divisible by 11. This gives us a value of y = 166/11, which is not a positive integer.
When x = 10, 2020 - 18x = 1840, which is divisible by 11. This gives us a value of y = 164/11, which is not a positive integer.
When x = 11, 2020 - 18x = 1822, which is divisible by 11. This gives us a value of y = 162/11, which is not a positive integer.
When x = 12, 2020 - 18x = 1804, which is divisible by 11. This gives us a value of y = 160/11, which is not a positive integer.
When x = 13, 2020 - 18x = 1786, which is divisible by 11. This gives us a value of y = 158/11, which is not a positive integer.
When x = 14, 2020 - 18x = 1768, which is divisible by 11. This gives us a value of y = 156/11, which is not a positive integer.
When x = 15, 2020 - 18x = 1750, which is divisible by 11. This gives us a value of y = 154/11, which is not a positive integer.
When x = 16, 2020 - 18x = 1732, which is divisible by 11. This gives us a value of y = 152/11, which is not a positive integer.
When x = 17, 2020 - 18x = 1714, which is divisible by 11. This gives us a value of y = 150/11, which is not a positive integer.
When x = 18, 2020 - 18x = 1696, which is divisible by 11. This gives us a value of y = 148/11, which is not a positive integer.
When x = 19, 2020 - 18x = 1678, which is divisible by 11. This gives us a value of y = 146/11, which is not a positive integer.
When x = 20, 2020 - 18x = 1660, which is divisible by 11. This gives us a value of y = 144
Explain why the triangles are similar, then find AB. Hint: redraw as 2 triangles
We can see that they are similar because the ratio of the corresponding sides of the triangle are the same = 5/3.
What is triangle?A triangle is a polygon with three sides and three angles. It is one of the most basic shapes in geometry and is formed when three non-collinear points are connected by straight lines. The three sides of a triangle can have different lengths, and the three angles can have different measures. Triangles can be classified based on their sides and angles.
BC/DE = AD/AB
15/9 = AB/6
AB = (15 × 6)/9 = 90/9 = 10.
15/9 = 10/6 = 5/3.
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data from a sample of randomly selected students is shown below. the variables collected are: exercise - the number of hours a student exercise per week debt - the amount of student loan debt (in thousands of dollars) a student is expected to graduate with age - the age of a student gpa - the gpa of a student descriptive statistics exercise debt age gpa n 241 196 254 248 lo 95% ci 7.0769 8.8655 20.069 3.2702 mean 7.8133 11.311 20.500 3.3200 up 95% ci 8.5497 13.757 20.931 3.3822 sd 5.8032 17.361 3.5000 0.3400 minimum 0.0000 0.0000 17.000 1.7500 1st quartile 4.0000 0.0000 19.000 3.0200 median 7.0000 3.0000 20.000 3.3600 3rd quartile 10.000 20.000 21.000 3.6950 maximum 35.000 100.00 41.000 4.0000 someone claims that the mean exercise time of all students is 10 hours per week. how would you respond? group of answer choices at the 95% confidence level, the mean exercise time of all students might be 10 hours per week. i am 95% confident that the mean exercise time of all students equals 7.8133 hours per week. i am 95% confident that the mean exercise time of all students is greater than 10 hours per week. i am 95% confident that the mean exercise time of all students is less than 10 hours per week.
The most appropriate response to the claim would be: "At the 95% confidence level, the mean exercise time of all students might not be 10 hours per week based on the sample data."
How do you 95% confident about the claim?Based on the given data, we can see that the sample mean exercise time is 7.8133 hours per week. The standard deviation of the exercise time is 5.8032, indicating that there is some variability in the data.
To determine whether the claim that the mean exercise time of all students is 10 hours per week is reasonable, we can conduct a hypothesis test.
Our null hypothesis would be that the mean exercise time of all students is equal to 10 hours per week, and the alternative hypothesis would be that the mean exercise time is different from 10 hours per week.
We can then calculate a test statistic and compare it to a critical value based on a t-distribution with n-1 degrees of freedom, where n is the sample size.
Alternatively, we can use the confidence interval provided in the table to make a statement about the claim.
We can see that the 95% confidence interval for the mean exercise time is [7.0769, 8.5497]. Since 10 is outside of this interval, we can say that at the 95% confidence level, the claim that the mean exercise time of all students is 10 hours per week is not supported by the data.
Therefore, the most appropriate response to the claim would be: "At the 95% confidence level, the mean exercise time of all students might not be 10 hours per week based on the sample data."
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Please help offering 15 points
More people that rode the roller coaster are between the ages of 11 and 30, than people that are between the ages of 41 and 60 is the best description of the data which is obtained by using the arithmetic operations.
What are arithmetic operations?
Any real number may be explained using the four basic operations, also referred to as "arithmetic operations." Operations like division, multiplication, addition, and subtraction come before operations like quotient, product, sum, and difference in mathematics.
We are given a chart. From the chart we get the following data:
Number of people aged 11 - 20 riding roller coaster = 20
Number of people aged 21 - 30 riding roller coaster = 15
Number of people aged 31 - 40 riding roller coaster = 10
Number of people aged 41 - 50 riding roller coaster = 5
Number of people aged 51 - 60 riding roller coaster = 0
Using addition operation, we get
Total people = 20 + 15 + 10 + 5 + 0
Total people = 40
Now,
Total riders between 11 - 30 = 20 + 15
Total riders between 11 - 30 = 35
Similarly,
Total riders between 41 - 60 = 5 + 0
Total riders between 41 - 60 = 5
Hence, the fourth option is the correct answer.
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if you used this version of the equation (including your new conversion factor, how would this have changed the intercept of your log-log graph? what would its value have been?
The equation with the new substitutions and conversion factor is a'B'T' = (1/6) * (2/3)^(1/3) * a^(1/3) * d^(1/2)*a^6/6 where k is (1/6) * (2/3)^(1/3) * a^(1/3) * d^(1/2) The intercept value of the log-log graph would have been -1.108.
Starting with Equation 4: T = ka^6/6, we can substitute a = (d/k)^(1/6) and b = (2/3)^(1/2) * (d/k)^(1/3) to get
T = k[(d/k)^(1/6)]^6/6
T = k(d/k)^(1/2)/6
T = (k^(1/2)/6) * d^(1/2)
Now we can rearrange the equation so that a, b, and t are on the left side
a'B'T' = ka^6/6
(a/d)^(1/6) * b^(2/3) * T' = k[(a/d)^(1/6)]^6/6 * T'
(a/d)^(1/6) * (2/3)^(1/2) * (d/k)^(1/3) * T' = (k^(1/2)/6) * d^(1/2) * T'
(2/3)^(1/2) * (a/d)^(1/6) * d^(1/3) * T' = (k^(1/2)/6) * d^(1/2) * T'
(2/3)^(1/2) * (a/d)^(1/6) * d^(1/3) = k^(1/2)/6
k = [(2/3)^(1/2) * (a/d)^(1/6) * d^(1/3)]^2/6
k = (1/6) * (2/3)^(1/3) * a^(1/3) * d^(1/2)
With this new conversion factor, the intercept of the log-log graph would have changed. The intercept represents the value of T when a = 1 (since log(1) = 0). Using the new conversion factor, we have
T = (1/6) * (2/3)^(1/3) * d^(1/2) * a^(1/3)
T = (1/6) * (2/3)^(1/3) * d^(1/2)
log(T) = log[(1/6) * (2/3)^(1/3) * d^(1/2)]
log(T) = log(1/6) + log[(2/3)^(1/3)] + log(d^(1/2))
log(T) = log(1/6) + (1/3) * log(2/3) + (1/2) * log(d)
So the intercept of the log-log graph would be log(1/6) + (1/3) * log(2/3) = -1.108, assuming that d is held constant. This intercept represents the value of log(T) when log(a) = 0, or when a = 1. In other words, when a = 1, the predicted value of T would be 0.162 (or 16.2% of its maximum value).
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--The given question is incomplete, the complete question is given
" Plug the two substitutions into Equation 4 (T = ka^6/6)). Rearrange the equation so that a, b,t are on the left side of the equation and d remains on the right side, e.g. a'B'T' = ka^6/6 you will figure out what the "k" if you used this version of the equation (including your new conversion factor, how would this have changed the intercept of your log-log graph? what would its value have been?"--
PLEASE HELP!!!! I NEED HELP ASAP PLEASE!!!!!!!! IM TRYING SO HARD TO GET MY GRADE UP !!!
Determine the likelihood that the following event will occur:
Rolling a number greater than 7 on a number cube with sides numbered 1 through 6.
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Determine the likelihood that the following event will occur:
Picking the 8 of Hearts from a standard deck of playing cards.
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Determine the likelihood that the following event will occur:
A spinner with 6 equal sections labeled 1 through 6 lands on a number less than 7.
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Determine the likelihood that the following event will occur:
Flipping a coin and having it land with the heads side facing up.
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Determine the likelihood that the following event will occur:
Rolling a sum of 14 with two number cubes with sides 1-6.
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What is the probability of rolling an even number on a dice? The dice is numbered 1-6
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The following M & M colors are in the bowl: 4 yellow, 6 orange, 3 green, 5 blue, 2 brown. What is the probability of selecting a blue candy?
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A number cube is labeled 1 through 6. The probability of randomly rolling a 4 is 1 over 6. What is the probability of not rolling a 4?
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Determine the likelihood that the following event will occur:
Picking a purple ball from a bag containing 7 purple balls and 1 green ball.
-----------------------------------------------------------------------
Answer:
Step-by-step explanation:
Rolling a number greater than 7 on a number cube with sides numbered 1 through 6: The probability of rolling a number greater than 7 on a number cube with sides numbered 1 through 6 is 0, as it is not possible to roll a number greater than 6 on a standard six-sided die.
Picking the 8 of Hearts from a standard deck of playing cards: The probability of picking the 8 of Hearts from a standard deck of playing cards is 0, as there is no 8 of Hearts in a standard deck of playing cards.
A spinner with 6 equal sections labeled 1 through 6 lands on a number less than 7: The probability of a spinner with 6 equal sections labeled 1 through 6 landing on a number less than 7 is 1, as all the sections are labeled with numbers less than 7.
Flipping a coin and having it land with the heads side facing up: The probability of flipping a coin and having it land with the heads side facing up is 0.5 or 50%, assuming the coin is fair and has two equally likely sides.
Rolling a sum of 14 with two number cubes with sides 1-6: The probability of rolling a sum of 14 with two number cubes with sides 1-6 is 0, as the highest possible sum that can be obtained by rolling two number cubes with sides 1-6 is 12 (6 + 6).
What is the probability of rolling an even number on a dice? The dice is numbered 1-6: The probability of rolling an even number on a dice numbered 1-6 is 0.5 or 50%, as there are three even numbers (2, 4, and 6) and three odd numbers (1, 3, and 5) on a standard six-sided die.
The following M & M colors are in the bowl: 4 yellow, 6 orange, 3 green, 5 blue, 2 brown. What is the probability of selecting a blue candy? The probability of selecting a blue candy from the bowl is 5/20 or 1/4, as there are 5 blue candies in the bowl out of a total of 20 candies.
A number cube is labeled 1 through 6. The probability of randomly rolling a 4 is 1 over 6. What is the probability of not rolling a 4? The probability of not rolling a 4 on a number cube labeled 1 through 6 is 5/6, as there are 5 possible outcomes that are not 4 (1, 2, 3, 5, and 6) out of a total of 6 possible outcomes.
Picking a purple ball from a bag containing 7 purple balls and 1 green ball: The probability of picking a purple ball from a bag containing 7 purple balls and 1 green ball is 7/8, as there are 7 purple balls out of a total of 8 balls in the bag.
im sorry I don't know how to delete this but i now realize that my awnser was completely wrong.
super sleep hotel has 1,700 guests who stayed for two nights and rented 150 rooms. how many guest nights did the hotel have during this period?
In linear equation, 4,000 guest nights did the hotel have during this period.
What is a linear equation in mathematics?
A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables.
According to question,
Guest nights = Number of guests × Number of nights
= 2,000 × 2
= 4,000
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The shaded area of a circle is 25 cm squared. if the diameter of the circle is 10cm, determine what percentage of the circle is shaded
If the shaded area of a circle is 25 cm squared. if the diameter of the circle is 10cm, the percentage of the circle is shaded is: 31.83% .
What percentage of the circle is shaded?We can start by finding the area of the entire circle. The formula for the area of a circle is:
A = πr^2
where A is the area and r is the radius. Since the diameter of the circle is 10 cm, the radius is half of that, or 5 cm. Therefore, the area of the entire circle is:
A = π(5 cm)^2 = 25π cm^2
Next, we can find what percentage of the circle is shaded by dividing the shaded area by the total area of the circle and multiplying by 100:
Percentage shaded = (shaded area / total area) x 100
Percentage shaded = (25 cm^2 / 25π cm^2) x 100
Percentage shaded = 100 / π ≈ 31.83%
Therefore, approximately 31.83% of the circle is shaded.
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a numerical measure of linear association between two variables is the . a. z-score b. correlation coefficient c. variance d. standard deviation
The numerical measure of linear association is b. correlation coefficient.
What is the statistical term used to describe a quantifiable measure of the linear relationship between two variables?The correlation coefficient is a statistical measure that represents the degree of linear relationship between two variables. It takes values between -1 and 1, where -1 represents a perfect negative linear correlation, 0 represents no linear correlation, and 1 represents a perfect positive linear correlation.
A positive correlation means that when one variable increases, the other variable also tends to increase, while a negative correlation means that when one variable increases, the other variable tends to decrease.
The correlation coefficient is calculated using the formula:
[tex]r = (nΣxy - ΣxΣy) / sqrt[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)][/tex]
where r is the correlation coefficient, n is the sample size, Σxy is the sum of the products of the corresponding values of x and y, Σx and Σy are the sums of x and y respectively, and Σx^2 and Σy^2 are the sums of the squares of x and y respectively.
In summary, the correlation coefficient is a measure of the strength and direction of the linear association between two variables.
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What is the mean of this data set?
Please help
Answer:
Step-by-step explanation:
Find the area of the circle with a circumference of
. Write your solution in terms of
.
Area in terms of
: ______
Triangle ABC is shown below and has vertices
A (-5, -2), B(-3, -4), and C(-2, 1). After a 180°
counterclockwise rotation of triangle ABC about the point (1, -2),
the result is triangle A'B'C'.
Check the picture below.
What is the smallest positive integer divisible by 6 and 2 you can write using at least one 2 and one 6?
The smallest positive integer divisible by 6 and 2 that can be written using at least one 2 and one 6 is 6.
The smallest positive integer that is divisible by both 2 and 6 is their least common multiple (LCM), which is equal to the product of the highest power of each prime factor that appears in the factorization of 2 and 6.
The prime factorization of 2 is simply 2, while the prime factorization of 6 is 2 × 3. The highest power of 2 that appears in the factorization of 6 is just 2 itself, so the LCM of 2 and 6 is 2 × 3 = 6.
We are asked to write this integer using at least one 2 and one 6. We can do this by simply writing 6, which is the LCM of 2 and 6 and is divisible by both of them. Since 6 contains one 2 and one 6, this meets the requirement of the problem. Therefore, the smallest positive integer divisible by 6 and 2 that can be written using at least one 2 and one 6 is 6.
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a bacteria culture starts with 40 bacteria and grows at a rate proportional to its size. after 2 hours there are 180 bacteria. find the number of bacteria after 5 hours.
The number of bacteria after 5 hours is approximately 1013.8.
We can use the formula for exponential growth to solve this problem. If a population grows at a rate proportional to its size, then we can writ
N(t) = N₀ × e^(rt),
where N(t) is the size of the population at time t, N₀ is the initial size of the population, r is the growth rate, and e is the mathematical constant approximately equal to 2.71828.
We know that the culture starts with 40 bacteria, so N₀ = 40. We also know that after 2 hours, the size of the population is 180. We can use this information to solve for r:
180 = 40 × e^(2r)
180/40 = e^(2r)
ln(180/40) = 2r
r = ln(180/40)/2
r ≈ 0.6931
Now we can use the formula to find the size of the population after 5 hours:
N(5) = 40 × e^(0.6931×5)
N(5) ≈ 1013.8
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PLS HURRY!!
The length of ribbons found at a seamstress are listed. 3, 6, 9, 11, 12, 13 What is the appropriate measure of variability for the data shown, and what is its value?
Thus, the appropriate measure of variability found for the given data is 10.
Explain about the range of the data:The difference here between maximum and smallest values in a data set is known as the range. Utilizing the exact same units as the data, it measures variability. More variability is shown by larger values.
The range in statistics refers to the distribution of your data between the lowest and greatest value in the distribution. It is a widely used indicator of variation. Measures of variability provide you with descriptive statistics for summarising your data set in addition to measurements of central tendency.Given length of ribbons:
3, 6, 9, 11, 12, 13
Minimum value = 3
Maximum value = 13
Actually, the range, which is determined by deducting the lowest value from the greatest value in the dataset, would be the proper measure of variability for this data.
Range = Maximum value - Minimum value
Range = 13 - 3
Range = 10
Thus, the appropriate measure of variability found for the given data is 10.
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Find a congruence transformation that maps triangle RST to triangle UVW
A congruence transformation that maps triangle RST to triangle UVW is a reflection along the line y = 1, followed by a translation 2 units right and down by 1 units.
A congruence transformation that maps triangle RST to triangle UVW is a rotation of 180°, followed by a translation 2 units left and down by 5 units.
What is a transformation?In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;
What is a reflection?In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.
By critically observing the geometric figures, we can reasonably infer and logically deduce that the pre-image underwent a sequence of congruence transformation to produce the image.
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Please only do 9,11, and 13! And please help!! 40 points!!!
9. The volume of the triangular pyramid is given by:
V = (1/3)Bh
Here, B is the base area.
The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:
h = sqrt(26.7² - 11.7²) = 23.274 km
The area if the base is:
B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km
Now, the volume is:
V = (1/3)(136.89)(15) = 2053.35 cubic km
Hence, the volume of the triangular pyramid is 2053.35 cubic km.
9. The volume of the triangular pyramid is 2053.35 cubic km. 11. The area of the shaded portion is 348.19 cubic in 13. The slant height of the cone is 8.53 meters.
What is Pythagoras Theorem?A fundamental conclusion in geometry relating to the lengths of a right triangle's sides is known as Pythagoras' theorem. According to the theorem, the square of the length of the hypotenuse, the side that faces the right angle, in any right triangle, equals the sum of the squares of the lengths of the other two sides, known as the legs.
9. The volume of the triangular pyramid is given by:
V = (1/3)Bh
Here, B is the base area.
The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:
h = √(26.7² - 11.7²) = 23.274 km
The area if the base is:
B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km
Now, the volume is:
V = (1/3)(136.89)(15) = 2053.35 cubic km
Hence, the volume of the triangular pyramid is 2053.35 cubic km.
11. The volume of a cone is given by:
V = (1/3)πr²h
The dimension of the bigger cone is radius is 9 in, and height 15 in:
V1 = (1/3)π(9 in)²(15 in) = 381.7 cubic in
The dimension of the smaller cone is radius is 4 in, and height 10 in:
V2 = (1/3)π(4 in)²(10 in) = 33.51 cubic in
Now, the area of the shaded portion is:
V1 - V2 = 381.7 - 33.51 = 348.19
13. The volume of a cone is given by:
V = (1/3)πr²h
Substituting the values we have:
542.87 = (1/3)π(6 m)²h
h = 542.87 / [(1/3)π(6 m)²] = 6.05 m
Now, using the Pythagoras Theorem for the slant height we have:
s² = r² + h²
s² = (6 m)² + (6.05 m)²
s² = 72.9
s = √(72.9) = 8.53 m
The slant height of the cone is 8.53 meters.
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q= 2-4t/t+3
make t the subject of the formula
(please include steps!!!!) ty
Therefore (t) can be written as **(2 - 3Q) / (Q + 4)**.
Define Q?Within the given equation, Q is a variable. It stands for an unknowable amount or value that can be ascertained by equation-solving.
What exactly is variable?A quantity that can take on any one of a number of values is referred to as a variable. A variable in mathematics is a symbol or letter that denotes an unknowable amount or value. The variable Q in the given equation stands for an unknowable quantity or value that can be ascertained by resolving the equation.
The equation is as follows:
Q = (2 - 4t) / (t + 3)
When we divide both sides by (t + 3), we obtain:
Q(t + 3) = 2 - 4t
When we increase the left side of the equation, we obtain:
Qt + 3Q = 2 - 4t
The result of adding 4t to both sides of the equation is:
Qt + 3Q + 4t = 2
Combining related concepts gives us:
t(Q + 4) = 2 - 3Q
The result of dividing both sides by (Q + 4) is:
t = (2 - 3Q) / (Q + 4)
t can therefore be written as **(2 - 3Q) / (Q + 4)**.
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is $60 a resonable tax for a purchase of $120 what likey caused herschel to make the mistake
Four friends want to play a game. In how many ways can the friends from teams, if both team dont have name
The friends can form teams in 6 different ways.
If the four friends want to form two teams, we can count the number of ways they can do this using combinations.
The number of ways to choose two people out of four is given by the combination formula,
C(4,2) = 4! / (2! * (4-2)!) = 6
We can list them as follows, where each team is represented by the letters A and B,
AB | CD
AC | BD
AD | BC
BC | AD
BD | AC
CD | AB
This means that there are 6 different ways the four friends can be split into two teams.
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Can please someone help me ASAP? It’s due tomorrow. I will give brainliest if it’s all correct!!
Please do part a, b, and c
The sample space are:
{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}
The favorable outcomes care:
{RS, RT, SR, ST, TR, TS}
The probability is 0.3 or 30%
How to find the sample spacePart A:
The sample space represents all possible outcomes that can occur when two cards are randomly selected without replacement from the given pile of cards.
The sample space can be represented as follows:
{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}
Part B:
The favorable outcomes are those outcomes in which both cards are consonants. In this case, the consonants are R, S, and T.
The favorable outcomes can be represented as follows:
{RS, RT, SR, ST, TR, TS}
Part C:
To calculate the probability of selecting 2 cards that are consonants, we need to find the ratio of favorable outcomes to the sample space.
The number of favorable outcomes is 6, and the size of the sample space is 20.
Therefore, the probability of selecting 2 cards that are consonants is:
P(consonants) = favorable outcomes / sample space
P(consonants) = 6 / 20
P(consonants) = 0.3 or 30%
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2)
Phillip has 8 red balls, 3 green balls, 6 yellow balls, 3 orange balls, 13 black balls
and 15 blue balls in his bag.
Mean: | 0,2, Median :
Mode:
Range
The results of the balls in Phillip's bag are:
The mean = 8.
The median = 7.
The mode = blue
The range = 12
How do we calculate the Mean, Median, Mode and Range?The mean (or the average) is the sum of all the values divided by the total number of values. Let's calculate the mean for the given data:
Total number of balls = 8 + 3 + 6 + 3 + 13 + 15 = 48
Mean = (8 + 3 + 6 + 3 + 13 + 15) / 6 = 48 / 6 = 8
Mean = 8.
The median is the middle value when a set of values is arranged in ascending or descending order.
Let's arrange the given data in ascending:
3, 3, 6, 8, 13, 15
As the total number of values is even, the median will be the average of the two middle values, which are 6 and 8.
Median = (6 + 8) / 2 = 7
The median = 7.
The mode is the value that appears most frequently in a set of values. Let's find the mode of the given data:
Red balls: 8
Green balls: 3
Yellow balls: 6
Orange balls: 3
Black balls: 13
Blue balls: 15
Blue balls have the highest frequency (i.e., 15) among all the colors.
The range is the difference between the highest and lowest values in a set of values. Let's find the range of the given data:
Highest value = 15 (blue balls)
Lowest value = 3 (green balls and orange balls)
Range = Highest value - Lowest value = 15 - 3 = 12
Range = 12.
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what is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes? (round your answer to four decimal places.)
The Probability that a student will complete the exam 0.2676.
The probability of completing the exam in one hour or less is:
[tex]P (x < 60)[/tex]
= [tex]P (z < (60-83)/13)[/tex]
=[tex]P (z < -1.77)[/tex]
= 0.0384.
The probability that a student will complete the exam in more than 60 minutes, but less than 75 minutes is.
[tex]P (60 < x < 75)[/tex]
= [tex]P (x < 75)-P (x < 60)[/tex]
Now,
[tex]P (x < 75)[/tex]
=[tex]P (z < (75-83)/13)[/tex]
= [tex]P (z < -0.62)[/tex]
=0.2676.
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scenic cinemas surveyed its audience and found that while most movie goers prefer weekends, seniors visit on weekdays. how should the theatre respond?
Scenic Cinemas should offer discounted weekday matinee showings for seniors and continue to focus on weekend showings for their broader audience.
How should Cinemas tailor their offerings to accommodate both preferences?Based on the survey results, it would be wise for Scenic Cinemas to tailor their offerings to accommodate both preferences.
One option would be to offer discounted weekday matinee showings targeted toward seniors. This could incentivize them to visit on weekdays while also offering them a more affordable option. At the same time, Scenic Cinemas could continue to focus on weekend showings to cater to their broader audience.
Another approach would be to offer more diverse programming during the weekdays, such as classic films or independent movies that may appeal more to seniors. This could create a niche for Scenic Cinemas and attract a more loyal customer base.
Ultimately, it's important for Scenic Cinemas to balance the needs of their different audience segments to maximize revenue and customer satisfaction. By offering targeted promotions and programming, they can ensure that both seniors and other moviegoers feel valued and have a reason to visit the theatre.
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What is the solution to the system of equations graphed below? A. (0,6) B. (6,0) C. (0,3) D. (1,5)
The correct option is - D. (1,5). The solution to the system of equations for the given graph is at (1,5).
Explain about the solution of system of equations:A collection of values for a variable that simultaneously fulfil each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.
The points where the lines representing the intersections where two linear equations intersect are referred to as the conclusion of a linear equation. In other words, the set of all feasible values for the variables that satisfy the specified linear equation constitutes the solution set of both the system of linear equations.For the given graph, the solution of the system of equation is obtained as the point where the lines intersect.
The two lines in the graph intersect at the (1,5). Thus, the solution to the system of equations for the given graph is at (1,5).
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rewrite the following without an exponent 4^-3
Step-by-step explanation:
4^-3 = 1/4^3 = 1/64
Find the volume of this sphere using 3 for pie
The volume of this sphere is equal to 4,000 cm³.
How to calculate the volume of a sphere?In Mathematics and Geometry, the volume of a sphere can be calculated by using this mathematical equation (formula):
Volume of a sphere = 4/3 × πr³
Where:
r represents the radius.
Note: Radius = diameter/2 = 20/2 = 10 cm.
By substituting the given parameters into the formula for the volume of a sphere, we have the following;
Volume of a sphere = 4/3 × 3 × (10)³
Volume of a sphere = 4 × 1000
Volume of a sphere = 4,000 cm³
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7. Volunteer drivers are needed to bring 80 students to the championship baseball
game. Drivers either have cars, which can seat 4 students, or vans, which can seat 6
students. The equation 4c +6v = 80 describes the relationship between the number
of cars c and number of vans v that can transport exactly 80 students.
Answer: To solve for c and v, we need to use the equation:
4c + 6v = 80
We have two variables and one equation, so we need another equation to solve for c and v. We can use the fact that the number of students transported by the drivers is 80. Since each car can seat 4 students and each van can seat 6 students, we can write:
4c + 6v = 80
c + v = number of drivers
Since we want to minimize the number of drivers, we want to minimize the value of c + v. We can use substitution to solve for c and v in terms of one variable. Solving for c in terms of v from the first equation, we get:
4c + 6v = 80
4c = 80 - 6v
c = (80 - 6v)/4
Substituting this expression for c into the second equation, we get:
c + v = number of drivers
(80 - 6v)/4 + v = number of drivers
Multiplying both sides by 4 to clear the fraction, we get:
80 - 6v + 4v = 4(number of drivers)
80 - 2v = 4(number of drivers)
20 - 0.5v = number of drivers
We want to minimize the value of c + v, so we want to minimize the value of v. Since v must be a whole number, we want to find the smallest integer value of v that satisfies the equation. We can plug in integer values of v and find the corresponding value of c, and check if the sum of c and v is less than or equal to the current minimum. Starting with v = 1, we get:
v = 1 -> c = 19.5 -> c + v = 20.5
v = 2 -> c = 18.0 -> c + v = 20.0
v = 3 -> c = 16.5 -> c + v = 19.5
v = 4 -> c = 15.0 -> c + v = 19.0
v = 5 -> c = 13.5 -> c + v = 18.5
v = 6 -> c = 12.0 -> c + v = 18.0
The smallest integer value of v that satisfies the equation is v = 6, which gives c = 12. Therefore, we need 12 cars and 6 vans to transport 80 students.
Step-by-step explanation:
Reflect Teresa writes 8(4) - 8x to represent the area of the Quotations section.
Adnan writes 8(4- x) to represent the area of the Quotations section. Explain
what information each expression tells you.
Teresa's expression, 8(4) - 8x, represents the area of the Quotations section. The expression is comprised of two parts: 8(4) and -8x.
What does the expression 8(4) - 8x contains?8(4) represents the width of the Quotations section, as it is multiplied by the length of 4 units. This indicates that the Quotations section has a fixed width of 8 units.
-8x represents the variable length of the Quotations section. The term -8x indicates that the length of the section can vary based on the value of x, which is a variable. The negative sign indicates that the length decreases as the value of x increases, and vice versa.
Adnan's expression, 8(4 - x), also represents the area of the Quotations section. The expression is slightly different from Teresa's, as the subtraction operation (4 - x) is contained within the parentheses.
What does the expression 8(4 - x) contains?(4 - x) represents the variable width of the Quotations section. The expression indicates that the width of the section is determined by the value of x. As x changes, the width of the section changes accordingly.
8(4 - x) then multiplies the variable width by a fixed length of 8 units, indicating that the Quotations section has a fixed length of 8 units.
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ASAP Please help me do a two column proof for this. I am struggling
∠A = ∠C in trapezoid ABCD with arcAB = arcCD, can be proven with the property of isosceles triangles.
How to prove the relation?Since arcAB = arcCD, the lengths of the two arcs are equal. This implies that the lengths of the segments subtended by these arcs, AB and CD, are also equal.
Let E and F be the midpoints of the non-parallel sides AD and BC, respectively. Connect E and F with a line segment EF.
Since E and F are midpoints, DE = EA and BF = FC. In addition, since AB = CD = L, we can say that:
DE + EA = BF + FC
EA = FC
So, by the Hypotenuse-Leg (HL) theorem of congruence, triangles AEF and CFE are congruent:
ΔAEF ≅ ΔCFE
Now, since the triangles are congruent, their corresponding angles are equal:
∠A = ∠C
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