If 84% of products come off the line ready to ship to distributors, then the probability of a product being within specifications is 0.84.
Since we are selecting 12 products randomly from the line each hour, the number of products within specifications (x) follows a binomial distribution with parameters n = 12 and p = 0.84.
Using a binomial cumulative distribution function (CDF), we can calculate the probability that x is less than a certain value. For example, if x is less than 7, the probability of this outcome would be considered unusual and the production line should be repaired.
So, the answer is "fewer than 7".
To learn more about distributors please click on below link.
https://brainly.com/question/14276410
#SPJ4
lim(x→1)〖(2x2+x−1)/(2x−1)
What is the value of x?
Enter your answer in the box.
Answer:
84
Step-by-step explanation:
540 is the sum of angle of a pentagon.
we get the equation,
X + 110 +131 +108 + 107 = 540
X = 540 - 456
X = 84
f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.
Answer:f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.
f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.
Step-by-step explanation:f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.
f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.
The average height of men in the US is 70 inches. If the standard deviation for the heights is 3 inches, and Uncle Bob claims that he is also in the 90th percentile for height, how tall is he?
Using the normal distribution, we have that:
The 99th percentile of height is of 77 inches.1,611,000 males are at this height or taller.What is a z-score?The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
[tex]Z = \dfrac{x-\mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean.
Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
For this problem, the mean and the standard deviation are given as follows:
The 99th percentile is X when Z = 2.327, hence:
[tex]Z = \dfrac{x-\mu}{\sigma}[/tex]
2.327 = (X - 70)/3
X - 70 = 2.327 x 3
X = 77.
The 99th percentile of height is 77 inches. The fact that it is the 99th percentile means that only 1% of the males are at that height or taller, hence, out of the 161.1 million males:
0.01 x 161,100,000 = 1,611,000.
1,611,000 males are at this height or taller.
More can be learned about the normal distribution at brainly.com/question/24372153
#SPJ1
5. Increasing the alpha level (for example from a = .01 to a = .05)_____a. Increases the probability of a Type I errorb. Increases the size of the critical regionc. Increases the probability that the sample will fall into the critical regiond. All of the above
The probability of a Type I error, increases the size of the critical region, and increases the probability that the sample will fall into the critical region.
The alpha level (or significance level) is a probability value used to determine the level of statistical significance of a test. Increasing the alpha level from a = .01 to a = .05 means that the probability of a Type I error (also known as a false positive) increases. This is because the critical region, or range of values that represents a statistically significant result, increases in size.
The critical region is calculated by subtracting the alpha level from 1, then subtracting the result from the alpha level. For a = .01, the critical region is calculated by 1 - .01 = .99, and then .99 - .01 = .98. For a = .05, the critical region is calculated by 1 - .05 = .95, and then .95 - .05 = .90.
The increase in the critical region size means that there is an increased probability that the sample will fall into the critical region, and yield a statistically significant result. This is because the critical region has become larger, meaning that there is a greater chance that the sample will lie within it. In summary, increasing the alpha level from a = .01 to a = .05 increases the probability of a Type I error, increases the size of the critical region, and increases the probability that the sample will fall into the critical region.
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ4
Name the property of real numbers illustrated by the equation (2+x)+3=2+(x+3)
Associate property of real numbers illustrated by the equation (2+x)+3=2+(x+3).
What is Associate property ?
Associative property is defined as, when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped.
For instance,
2 × (7 × 6) = (2 × 7) × 6
Associative property for addition implies that regardless of how numbers are grouped, the final sum of the numbers will remain the same. This can be expressed as:
(x + y) + z = x + (y + z)
Associative property for multiplication implies that regardless of how numbers are grouped, the final product of the numbers will remain the same. This can be expressed as:
p × (q × r) = (p × q) × r
Hence , Associate property of real numbers illustrated by the equation (2+x)+3=2+(x+3).
Learn more about Associate property at:
https://brainly.com/question/13181
#SPJ1
The difference between the measures of two complementary angles is 88°. determine the measures of the two angles ?
The measures of the two complementary angles are 44° and 132°.
Given that the difference between the measures of two complementary angles of any given triangle is 88°, it means that one angle is 88° smaller than the other. To find the measures of the two angles, divide the sum of the difference by 2. That is given as, (88°/2) = 44°. One angle is given as 44°, and the other angle is equal to the sum of the two angles in a triangle, which is 180°, minus the first angle, which is 44°, which is equal to 136°.
Learn more on Complementary Angles:
https://brainly.com/question/20728641
#SPJ4
Does this appear to be a regular polygon? Explain.
No, it is not a regular polygon.
What is a convex hexagon?A hexagon is a six sided polygon. And a convex hexagon means, the hexagon's vertices are pointed outwards.
And no interior angle has an angle measure more than 180°.
Given:
A polygon.
To be a regular polygon:
Given Hexagon,
should have equal sides and equal angles.
We have no information about the angles and sides.
Therefore, it is not a regular polygon.
To learn more about the convex hexagon;
https://brainly.com/question/16615236
#SPJ1
Id like to order 5 halves of a cupcake for my family plus some extra for my 2 friends. They'll each like a quarter of a cupcake
The total number of cupcakes needed will be 3 cupcakes.
How to calculate the fractionA fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Since you 5 halves of a cupcake for my family plus some extra for my 2 friends, the total number of cupcakes needed will be:
= 5 ( 1 /2) + 2 ( 1 / 4)
= 2 1/2 + 1/2
= 3
Learn more about fractions on:
brainly.com/question/78672
#SPJ1
Complete question
Id like to order 5 halves of a cupcake for my family plus some extra for my 2 friends. They'll each like a quarter of a cupcake. What is the total cupcakes needed?
An envelope is 4.7 inches wide, and it measures 7.4 inches along the diagonal. How tall is the envelope? If necessary, round to the nearest tenth.
Answer:The envelope is approximately 6.3 inches tall.
Step-by-step explanation:
Garrett bought 4 pounds of red apples and g pounds of green apples. Choose the expression that shows how many pounds of apples Garrett bought in all.
An expression that shows the total pounds of apples Garrett bought in all include the following: D. 4 + g.
How to write an equation to model this situation?In order to write an equation that model this situation, we would assign a variable to the total pounds of green apples and the total pounds of red apples respectively, and then translate the word problem into algebraic equation as follows:
Let the variable r represent the total pounds of red apples.Let the variable g represent the total pounds of green apples.Since Garrett bought 4 pounds of red apples and g pounds of green apples, an equation that models the total pounds of apples that he bought is given by:
Total pounds of apples = r + g
Total pounds of apples = 4 + g
Read more on equation here: brainly.com/question/18912929
#SPJ1
Find a matrix P such that PTAP orthogonally diagonalizes A. Verify that PTAP gives the proper diagonal form. (Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) าง่า 7 1 (P, PTAP) =
We can find a matrix P such that PTAP orthogonally diagonalizes A, and the diagonal entries of PTAP are the eigenvalues of A, verifying that the diagonal form of A is correct.
We can orthogonally diagonalize a matrix A by finding a matrix P such that PTAP is orthogonal. An orthogonal matrix is a matrix whose columns are orthogonal unit vectors. This means that the dot product of any two columns is 0.
Let's calculate the matrix P to orthogonally diagonalize A. We will use the Gram-Schmidt process to calculate the orthonormal vectors for the columns of P.
Let v1 = (7,1) be the first column vector of A. We will use this vector to calculate the first column of P. We normalize v1 and get an orthonormal vector u1 = (7/sqrt(50), 1/sqrt(50)). We set the first column of P to be u1.
For the second column, we take the second column vector of A and subtract its projection on u1. This gives us a new vector v2 = (7, -6). We normalize v2 and get an orthonormal vector u2 = (7/sqrt(73), -6/sqrt(73)). We set the second column of P to be u2.
Now, we have the matrix P = [[7/sqrt(50), 7/sqrt(73)], [1/sqrt(50), -6/sqrt(73)]]. We can verify that the dot product of the columns of P is 0, which shows that P is an orthogonal matrix.
We can now calculate the product PTAP. We get PTAP = [[7^2/50+7^2/73, 7*7/50-6*7/73], [7*7/50-6*7/73, 7^2/50+6^2/73]]. We can see from this matrix that the diagonal entries are equal to the eigenvalues of A, which were 7 and 1. This shows that PTAP is a diagonal matrix which orthogonally diagonalizes A.
We can find a matrix P such that PTAP orthogonally diagonalizes A, and the diagonal entries of PTAP are the eigenvalues of A, verifying that the diagonal form of A is correct.
Learn more about orthogonal matrix here:
https://brainly.com/question/13155513
#SPJ4
How many kilometers per hour is this? Km/h
The speed of a car is 0.61 kilometer per hour.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
From the figure, time =1.68 minutes and distance =17 meter
Now, in kilometer per hour is
Here, speed = Distance/Time
= 17 meter/1.68 minute
= 0.017 km/0.028 hours
= 0.017/0.028
= 0.61 kilometer per hour
Therefore, the speed is 0.61 kilometer per hour.
To learn more about the speed, distance, and time visit:
brainly.com/question/4978052.
#SPJ1
a) b) c) d) By how much is 78 greater than-12? By how much is -23 less than 23? What must be added to -6 to give 105? What must be added to 15 to give -30?
arulfo deposited 55 into a savings account according to the rulw of 72 what interest rate will cause his money to double in approximately 23 years
The 3.13% interest rate will cause his money to double in approximately 23 years.
What is compound interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
Given that Arnulfo deposited $55 into a savings account for which interest is compounded semiannually.
According to the rule of 72, we should divide 72 by the interest rate to determine how many years it will take to double our money at a specific interest rate (r).
time is taken to double the money = 72/r,
where r represents the interest rate and time is in years.
As we have been given that it will take approximately 23 years to double Arnulfo's money, so we can set an equation as:
23 = 72/r
r = 72/23
r = 3.13
Hence the interest rate is 3.13%.
Learn more about compound interest;
https://brainly.com/question/29335425
#SPJ1
The complete question is,
Arnulfo deposited $55 into a savings account for which interest is compounded semiannually. according to the rule of 72, what interest rate will cause his money to double in approximately 23 years?
Estimate the answer by rounding each number to the nearest hundred. Then find the exact number.
By rounding each number to the closest hundred, the answer is 300. 366 is the precise difference.
What is addition?The practice of adding two or more numbers together to achieve their sum is known as addition. Addition is a fundamental arithmetic operation that is used to compute the sum of two or more integers. For instance, 7 + 7 Equals 14. The combination of at least two integers is known as basic addition. Once students know how to count, they may study basic addition. They can learn from an addition chart by identifying the addend across the top of the chart and tracing down to the row of the second addend.
Here,
528-162=366
528 to be rounded off to 500.
162 to be rounded off to 200.
500-200=300
The answer by rounding each number to the nearest hundred is 300. The exact difference is 366.
To know more about addition,
https://brainly.com/question/29783548
#SPJ1
Match each quadratic function given in factored form
The equivalent form of the given polynomials are A) (x+1) (x-12) B) (x+2) (x-6) C)(x+4) (x-3) D) ( x+2) (x+4)
What are quadratic equations?A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.
Given here: The quadratic equations as
1)
[tex]x^2-11x-12\\x^2-12x+x-12\\x(x-12)+(x-12)\\(x+1)(x-12)[/tex]
2)
[tex]x^2-4x-12\\x^2-6x+2x-12\\x(x-6)+2(x-6)\\(x+2) (x-6)[/tex]
3)
[tex]x^2+x-12\\x^2+4x-3x-12\\x(x+4)-3(x+4)\\(x+4) (x-3)[/tex]
4)
[tex]x^2-x-12\\x^2-4x+3x-12\\x(x-4)+2(x-4)\\(x+2) (x+4)[/tex]
Thus the factorization of the polynomials given are given above.
Hence, The factorization of the given polynomials yields the following results.
Learn more about quadratic equations here:
https://brainly.com/question/17177510
#SPJ1
Answer:
f(x) =(x+2) (x-6) B
f(x) =(x-4) (x+3) D
f(x) =(x-12) (x+1) A
f(x) =(x-3) (x+4) C
Step-by-step explanation:
edge 2023
Write a word problem for 3(2x)=6x
Multiply a number by 2 and then find the product of the number obtained with 3 is the statement required
What is an Algebraic Expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Given here: The equation 3(2x)=6x
Clearly here the associative property of multiplication is used above
First, a number x is multiplied by 2
Then the number obtained above i.e 2x is multiplied again by 3
Thus the word problem can be of the form
Multiply a number by 2 and then find the product of the number obtained with 3
Hence, Multiply a number by 2 and then find the product of the number obtained with 3 is the statement required
Learn more about algebraic expression here:
https://brainly.com/question/29078851
#SPJ1
samples a and b were selected from the same population. the mean of sample a is equal to the mean of the population. which of the following statements must be true?
The mean of sample a is equal to the mean of the population, it is likely that the sample is representative of the population, but it is not a guarantee of it.
If the mean of sample a is equal to the mean of the population, then it can be concluded that sample a is representative of the population. The mean of a sample is an estimate of the population mean, and if the sample mean is equal to the population mean, it indicates that the sample was randomly selected and is representative of the population.
However, it is important to note that the equality of the sample mean and the population mean does not guarantee that all other statistics, such as the standard deviation or the distribution shape, are equal. Sampling variability and the size of the sample can also impact the similarity between the sample and population statistics.
In conclusion, if the mean of sample a is equal to the mean of the population, it is likely that the sample is representative of the population, but it is not a guarantee of it. Further statistical analysis is needed to determine the representativeness of the sample and its similarity to the population.
Learn more about standard deviation :
https://brainly.com/question/23907081
#SPJ4
A business owner in England signs a 15% discount note for 30,000 English pounds (£30,000) with a bank in London. If the proceeds are £28,835.16, find the time of the note in days.
The solution is, the time of the note in days is 95 days.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
A business owner in England signs a 15% discount note for 30,000 English pounds (£30,000) with a bank in London.
If the proceeds are £28,835.16.
Since it's not mentioned in the problem, it can be safely assumed that the discount rate is 15%.
For this problem, we use the formula:
F = P(1+rn)
where
r is the discount rate
n is the number of days
P is the original amount
so, we get,
£28,835.16 =£30,000(1+0.15*n)
by, solving we get,
n = 94.5
i.e. 95 days
Hence, The solution is, the time of the note in days is 95 days.
To learn more on percentage click:
brainly.com/question/13450942
#SPJ1
in this lab, you declare and initialize variables in a c program. the program, which is saved in a file named newage.cpp, calculates your age in the year 2050.
The program calculates the user's age in 2050 by declaring and initializing three integer variables (myNewAge, myCurrentAge, and currentYear) and using them in an expression to determine the user's age in 2050.
Here is the C++ code that implements the instructions:
#include <iostream>
int main() {
int myCurrentAge = 29;
int currentYear = 2023;
int myNewAge = myCurrentAge + (2050 - currentYear);
std::cout << "My Current Age is " << myCurrentAge << ". ";
std::cout << "I will be " << myNewAge << " in 2050." << std::endl;
return 0;
}
The program first declares and initializes two variables, myCurrentAge and currentYear, with the user's current age and the current year, respectively. The third variable, myNewAge, is then calculated by adding the difference between 2050 and the current year to the user's current age. Finally, the program outputs the result using the cout statement.
This question is incomplete and should be written as:
Summary In this lab, you declare and initialize variables in a C++ program. The program, which is saved in a file named NewAge.cpp, calculates your age in the year 2050. Instructions Declare an integer variable named myNewAge. Declare and initialize an integer variable named myCurrentAge. Initialize this variable with your current age. Declare and initialize an integer variable named currentYear. Initialize this variable with the value of the current year. Use four digits for the year. Execute the program by clicking the Run button at the bottom of the screen. Sample program execution: My Current Age is 29. I will be 65 in 2050.Learn more about code to execute here: brainly.com/question/26134656
#SPJ4
Convert the binary number 11011101 to decimal.
Answer:
221 is the answer.
Step-by-step explanation:
(1 x 2^7) + (1 x 2^6) + (0 x 2^5) + (1 x 2^4) + (1 x 2^3) + (0 x 2^2) + (1 x 2^1) + (1 x 2^0) = 128 + 64 + 16 + 8 + 4 + 1 = 221
Enter aT or an F in each answer space below to indicate whether the corresponding statement is true or false. A statement is true only if it is true for all possibilities. You must get all of the answers correct to receive credit. 1. If f(x) is continuous at a, then f(a) is differentiable at a T 2. If lim f(z) =0o and lim g(a) 3. If lim f(x) 0 and lim g(a) 0o, then limf(a)-9(a)]= 0 T 1 z1 5, then lim[f(x)/9()] does not exist z-+1 z-1 z1 4. If f'(1) exists, then then the limit lim f(x) is f(1) T z1 0, then lim f(a)/g()] does not exist 5. If lim f(z) = 5 and lim g(x) z+1 F 1 1 LL
The statements are true, as they can be demonstrated using the definitions of continuity, limit, and derivative.
Let f and g be two functions with domain over the real numbers and let a be a real number.
The following statement is true: If f(x) is continuous at a, then f(a) is differentiable at a. This can be demonstrated by the definition of continuity at a point. If f is continuous at a, then for any ε > 0 there exists a δ > 0 such that |f(x) - f(a)| < ε if 0 < |x-a| < δ. This implies that the function is differentiable at a, since the limit of the difference quotient, lim (f(x) - f(a))/(x-a) exists as x approaches a.
The following statement is true: If lim f(z) = 0 and lim g(a) = 0, then lim (f(x)/g(x)) = 0. This can be demonstrated by the definition of a limit. Since the limit of f(x) as x approaches a is 0, then for any ε > 0 there exists a δ > 0 such that |f(x)| < ε if 0 < |x-a| < δ. Similarly, since the limit of g(x) as x approaches a is 0, then for any ε > 0 there exists a δ > 0 such that |g(x)| < ε if 0 < |x-a| < δ. Thus, |f(x)/g(x)| < ε/ε = 1 if 0 < |x-a| < δ, and the limit of f(x)/g(x) as x approaches a is 0.
The following statement is true: If f'(1) exists, then the limit lim f(x) is f(1). This can be demonstrated by the definition of the derivative. If f'(1) exists, then the limit of the difference quotient, lim (f(x) - f(1))/(x-1), exists as x approaches 1. Thus, |f(x) - f(1)| < ε if 0 < |x-1| < δ. This implies that the limit of f(x) as x approaches 1 is equal to f(1).
The statements are true, as they can be demonstrated using the definitions of continuity, limit, and derivative.
Learn more about derivative here:
https://brainly.com/question/25324584
#SPJ4
A number is multiplied by 6 and then 4 is added. The result is 34. Find the number
Answer:
5
Step-by-step explanation:
subtract: 34-4=30.
divide: 30/6=5
Based on the given values, the unknown number is 5.
How to find the unknown numberLet's use algebra to solve the problem.
Let's call the unknown number "x".
We know that when this number is multiplied by 6 and 4 is added, the result is 34:
6x + 4 = 34
Solve for x by isolating it on one side of the equation.
First, simplify the left side of the equation by subtracting 4 from both sides:
6x = 30
Then, solve for x by dividing both sides by 6:
x = 5
Therefore, the unknown number is 5.
Learn more on multiplied on https://brainly.com/question/10873737
#SPJ2
Which best represents the equation of the line below?
1 y = -1 x + 2
Answer:
Solution to the question of figure : c
Step-by-step explanation:
list a process variable value for each of the 4 process variables, and explain the meaning of the application. (eg. 5gpm flow - would fill a 5 gallon bucket up in 1 minute)
The four process variables are temperature, pressure, flow, and level. The temperature is given in degrees Celsius, the pressure is given in bars, the flow rate is given in gallons per minute, and the level is given in centimeters.
1. Temperature - 70°C: This is the temperature of a given system, likely referring to the temperature of a liquid or gas.
2. Pressure - 4 bar: This is the pressure of a given system, likely referring to the pressure of a liquid or gas.
3. Flow - 5 gpm: This is the flow rate of a given system, likely referring to the flow rate of a liquid or gas. It would fill a 5 gallon bucket up in 1 minute.
4. Level - 10 cm: This is the level of a given system, likely referring to the level of a liquid or gas in a container. It is equivalent to 10 cm, or 4 inches.
The four process variables are temperature, pressure, flow, and level. The temperature is given in degrees Celsius, the pressure is given in bars, the flow rate is given in gallons per minute, and the level is given in centimeters. These variables all refer to the properties of a given system, such as that of a liquid or gas.
Learn more about variable here
https://brainly.com/question/29430246
#SPJ4
after much experimentation, john discovers a which says that the wavelengths of light absorbed by hydrogen gas fit into a pattern which he is able to express in a mathematical formula.
After much testing, John comes up with a "law" that states that the light wavelengths absorbed as hydrogen gas follow a pattern that can be expressed mathematically.
Explain about the wavelengths of light for hydrogen gas?When hydrogen gas is placed in the discharge tube as well as the light released on the passing electrical discharges at low pressure is inspected using a spectroscope.
The emission spectrum or line spectrum for hydrogen is formed. It is discovered to be made up of numerous lines divided into various series.Four wavelengths with in visible spectrum of hydrogen light—410 nm, 434 nm, 486 nm, then 656 nm—are associated with photon emissions by excited electrons transitioning towards the quantum level denoted by the primary quantum number n = 2.Thus, John comes up with a "law" that states that the light wavelengths absorbed as hydrogen gas follow a pattern that can be expressed mathematically.
To know more about the wavelengths of light, here
https://brainly.com/question/10728818
#SPJ4
The correct question is-
after much experimentation, john discovers a _____ which says that the wavelengths of light absorbed by hydrogen gas fit into a pattern which he is able to express in a mathematical formula.
About how many millimeters long is the missing side of the right triangle, to the nearest tenth?
5 mm
7 mm
Using Pythagoras theorem, The missing side of the right triangle is 4,9 mm long.
The Pythagoras Theorem is what?Pythagoras' Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle. The hypotenuse in this example is the longest side because it is located across from the 90° angle. A right triangle's positive integer sides (let's say sides a, b, and c) are squared to produce a Pythagorean triple equation.
Right triangles are what the provided triangle is.
The Pythagorean Theorem is used:
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex](5)^{2} + (7)^{2} = c^{2}[/tex]
25 + 49 =[tex]c^{2}[/tex]
c = 4.9
Hence, the missing side of the right triangle is 4,9 mm long.
Learn more about Pythagoras Theorem here:
brainly.com/question/343682
#SPJ1
A container can hold 40 litres of milk and container can hold 60 litres of milk . What is the maximum capacity of a jar that can be used to measure the milk of both containers ?
The capacity of the two containers can be measured with a jar with a maximum capacity of 20 litres.
How to determine the maximum capacity of a jar that can be used to measure two milk jars
In this problem we find the case of two containers with different capacity, one with a capacity of 40 litres and other with a capacity of 60 litres, we can measure each of them based on the number of adds needed to fill each container. The number of adds (n) is equal to the container capacity (C), in litres, divided by the jar capacity (c), in litres:
n = C / c
If we assume that the number of adds is a natural numbers, then we determine the greatest common factor of both container capacities. First, decompose each number related to each container:
40 = 2³ × 5
60 = 2² × 3 × 5
Second, find the common factors and create the resulting product:
G.C.F. = 2² × 5
G.C.F. = 20
A jar with a maximum capacity of 20 litres can be used to measure the capacity of both containers.
To learn more on greatest common factors: https://brainly.com/question/11221202
#SPJ1
a grain silo is in the shape of a cylindrical prism. the silo is 90ft in diameter and 275ft in height. using the standard acceleration of gravity as , find the total weight exerted to the floor of the silo. additionally, of grain weighs 49lbs
The total weight exerted on the floor of the silo is 138,973,475 lbs
The volume of the cylindrical silo is given by the formula:
V = πr^2h
where r is the radius, h is the height and π (Pi) is approximately 3.14.
First, find the radius:
r = D/2 = 90ft / 2 = 45ft
Next, find the volume:
V = π * 45^2 * 275 = 31,875 * 3.14 * 275 = 2836275 cubic feet
Finally, calculate the weight of the grain:
W = V * w_grain/ft^3 = 2836275 * 49lbs/ft^3 = 138,973,475 lbs
This is the total weight exerted on the floor of the silo.
Learn more about weight exerted on the floor of a cylindrical grain silo. here: https://brainly.com/question/20535172
#SPJ4