To make a stable structure, the method of joints can be used to calculate the force BD in the truss shown.
This method uses the equations of equilibrium to determine the forces in the members of a truss. To calculate the force BD, one needs to sum the moments about point A and equate them to zero.
The moment is given by M = FxD, where F is the force, and D is the perpendicular distance from the point of interest to the line of action of the force. Therefore, the force BD can be calculated using the equation:
MAB = 0 = (BD)(2) - (AE)(5)
BD = 5AE/2
To find the forces in members CD and CE using the method of sections, one needs to cut through the truss along a line passing through points C and E.
Then, the force in member CD can be found by using the equation of equilibrium, where the sum of the forces in the x-direction and the sum of the forces in the y-direction must be equal to zero. Similarly, the force in member CE can also be calculated using the same method.
To learn more about joints, refer below:
https://brainly.com/question/13441222
#SPJ11
find the number of ways of arranging N people in a straight line if two particular people must always be separated
The number of ways to arrange N people with A and B separated is given by expression N! - 2*(N-1)! .
What exactly are expressions?
In mathematics, an expression is a combination of numbers, variables, operators, and functions that are grouped together in a meaningful way. Expressions can be as simple as a single number or variable, or they can be complex and include many different elements. They are used to represent mathematical relationships and operations, and can be evaluated or simplified using mathematical rules and techniques. Examples of expressions include:
3x + 7(2a - b) / (c + 1)sin(x) + cos(y)Now,
Let the two particular people be A and B.
If we place A in a spot, there are N-1 spots left for B to be placed. Once A and B are placed, there are (N-2)! ways to place the remaining people. Therefore, the number of ways to arrange N people with A and B separated is:
(N-1) * (N-2)!
Alternatively, we can find the total number of ways to arrange N people in a line (N!) and subtract the number of ways to arrange them with A and B together.
To find the number of ways to arrange N people with A and B together, we can treat A and B as a single entity, so there are (N-1)! ways to arrange the remaining people with AB together. However, A and B can be arranged in two ways (AB or BA), so we need to multiply (N-1)! by 2.
Therefore, the number of ways to arrange N people with A and B separated is:
N! - 2*(N-1)!
To know more about expressions visit the link
brainly.com/question/13947055
#SPJ1
Divya has $45 to spend on movie tickets. If each movie ticket is $14 and he pays $1 in tax, how much money does Divya have left over?
Answer:$30
Step-by-step explanation:
45-14=31
31-1=30
so the answer is 30
hope this helps
the final exam scores in a science class were normally distributed with a mean of 60 and a standard deviation of seven. find the probability that a randomly selected student scored more than 70 on the exam. round your answer to four decimal places.
Answer:
Step-by-step explanation:
We can use the standard normal distribution to solve this problem by standardizing the score.
z = (x - mu) / sigma
Where:
x = 70 (score we are interested in)
mu = 60 (mean score)
sigma = 7 (standard deviation)
z = (70 - 60) / 7 = 1.43
Using a standard normal distribution table or calculator, we can find the probability that z is greater than 1.43. The probability is approximately 0.0764.
Therefore, the probability that a randomly selected student scored more than 70 on the exam is 0.0764 (or about 7.64%).
why mean absolute deviation is a better approach to handle outliers in a data than standard deviation
Mean absolute deviation (MAD) is sometimes considered a better approach to handle outliers in a data set than standard deviation because it is less sensitive to extreme values.
The reason for this is that MAD uses absolute differences between each data point and the median of the data set, rather than the squared differences used by standard deviation.
In a data set with extreme values, such as outliers, the squared differences used by standard deviation can significantly inflate the value, leading to a higher estimate of the overall variability in the data. MAD, on the other hand, uses absolute differences, which are not affected by the sign of the difference and thus are less affected by extreme values. Therefore, MAD can be a better measure of variability in a data set that includes outliers.
However, it is important to note that MAD also has some limitations. It is less widely used and less familiar to many analysts than standard deviation, and it has a more complex formula that can be harder to interpret. Additionally, MAD is not as efficient as standard deviation when the underlying distribution is normal, meaning it requires a larger sample size to achieve the same level of precision as standard deviation. Ultimately, the choice between MAD and standard deviation depends on the specific characteristics of the data set and the goals of the analysis.
To know more about Mean absolute deviation, visit: brainly.com/question/10528201
#SPJ4
zero vertical asymptote removable discontinuity
A zero vertical asymptote removable discontinuity means that there is a zero of the function at the input value where the vertical asymptote would occur,
How to explain the termA zero of a function occurs when the value of the function is zero. A vertical asymptote of a function occurs when the value of the function becomes unbounded (either positive or negative) as the input approaches a certain value.
A removable discontinuity of a function occurs when there is a hole in the graph of the function at a certain input value, but the function can be made continuous at that point by defining its value at that input.
In the case of a zero vertical asymptote removable discontinuity, this means that there is a zero of the function at the input value where the vertical asymptote would occur, and the function can be made continuous at that input value by defining its value to be the value of the function at that input.
Learn more about asymptote on
https://brainly.com/question/4138300
#SPJ1
Please solve with workings out
Answer:
1500 g
Step-by-step explanation:
part a) is correct
part b)
The ratio of syrup to oats for one flapjack is 1:4
That means for each g of syrup you will require 4 g of oats
For 12 flapjacks you require 250 g
Therefore quantity of oats needed for 12 flapjacks = 250 x 4 = 1000 g
If you were to make 18 flapjacks then you would need 18/12 x quantity needed for 12 flapjacks
18/12 = 3/2 (dividing numerator and denominator by 6)
Quantity of oats needed for 18 flapjacks
= 18/12 x 1000
= 3/ 2 x 1000
= 3 x 500
= 1500 g
What is the volume of the box?
Simplify: 76 ÷ 72. 7 3 7 8 7 4 7 12
We can simplify the fraction by dividing both numbers by 4 (or by 2 two times), we will get the equivalent fraction 19/18
How to simplify the quotient?Here we have a quotient (or we can also call it a fraction) which is:
76/72
To simplify any fraction, what you need to do is divide both numerator and denominator by the same number.
For example, if we use 2, we will get:
76/2 = 38
72/2 = 36
then we have the equivalent fraction.
38/36
But we can keep simplifying this, divide by 2 again:
38/2 = 19
36/2 = 18
We get:
19/18
We can't simplify this anymore because 19 is prime.
Learn more about fractions at:
https://brainly.com/question/11562149
#SPJ1
solve the pair of simultaneous equations:(step by step, using factorization method)
y²+2y+11=x
x=5-3y
Answer: (-3,-2)
Step-by-step explanation:
y²+2y+11 = 5-3y
y^2+2y+11-5+3y =0
y^2+5y+6=0
y^2+3y+2y+6=0
y(y+3)+2(y+3)=0
(y+3)(y+2)=0
y= -3, -2
All you do is plug in the x value to the equation
Hope it helps:)
george flips an unfair coin $7$ times. the coin has a $\frac{1}{4}$ probability of coming up heads and a $\frac{3}{4}$ probability of coming up tails. what is the probability that he flips exactly $2$ tails?
The probability of getting exactly 2 tails in 7 flips of a coin with a probability of tails being 3/4 is 189/16384 or approximately 0.0115.
We can use the binomial distribution formula to solve this problem. Let X be the number of tails that come up in 7 flips of the coin. Then X follows a binomial distribution with n = 7 and p = 3/4 (since the probability of tails is 3/4).
The probability of getting exactly 2 tails is given by:
P(X = 2) = (7 choose 2) * (3/4)^2 * (1/4)^5
= (21 * 9/16 * 1/1024)
= 189/16384
So the probability that George flips exactly 2 tails is 189/16384, or approximately 0.0115.
To know more about binomial distribution refer here:
https://brainly.com/question/14565246#
#SPJ11
HI! PLEASE SHOW FULL SOLUTIONS FOR BOTH QUESTIONS AND ONLY ANSWER IF YOU KNOW! NO CALCULUS PLEASE! THAT WOULD BE VERY APPRECIATED!!
Answer:
3) p(2) = 22
4) k = 0
Step-by-step explanation:
Remainder theorem: If the polynomial p(x) is divided by the linear polynomial x -a then the remainder is p(a).
3)p(m) = m⁴ - 2m³ + m² + 12m - 6
p(m) is divided by (m - 2).
m -2 = 0
m = 2. The remainder is p(2)
p(2) = 2⁴ - 2*2³ + 2² + 12*2 - 6
= 16 - 16 + 4 + 24 - 6
= 22
p(2) = 22
4) p(x) = 8x³ + 6x² + x + k
p(x) is divided by (2x + 3).
2x + 3 = 0
2x = -3
[tex]x = \dfrac{-3}{2}[/tex]
[tex]p(\dfrac{-3}{2})=-15[/tex]
[tex]8*(\dfrac{-3}{2})^3+6*(\dfrac{-3}{2})^2-\dfrac{3}{2}+k=-15\\\\\\8*\dfrac{-27}{8}+6*\dfrac{9}{4}-\dfrac{3}{2} + k = -15\\\\\\-27 + \dfrac{27}{2}-\dfrac{3}{2}+k=-15\\\\\\-27 + \dfrac{24}{2}+k=-15\\\\[/tex]
-27 + 12 + k = -15
k = -15 + 27 - 12
k = 0
Find the area of the figure.
7 cm
11 cm
8 cm
The area is ? square centimeters.
pls help I'll mark brainlisest
Answer:
Area of the figure=126.5cm²
Step-by-step explanation:
As we can see based on the shape of the figure, we can divide it into a;
→ Triangle
→ Rectangle
Formulas that we need are;
⇒ Area of triangle =1/2×base×height
⇒ Area of rectangle =length × width
Let's solve the area of the triangle first;
Area of triangle =1/2 × base × heightArea of triangle=1/2 × 11cm × 7cmArea of triangle=38.5cm²Then the area of the rectangle;
Area of rectangle =length × widthArea of rectangle =11cm × 8cmArea of rectangle =88cm²Finally, we add the triangle and rectangle together-
Area of Triangle + Area of Rectangle = 38.5cm²+88cm²
Area of the figure=126.5cm²
RevyBreeze
What is y=-2(x-4)^2+2 in factored form?
The factored form of this quadratic equation is equal to y = -2x² + 16x - 30.
How to determine the factored form of a quadratic equation?In this exercise, you are required to determine the factored form of the given quadratic function that is written in vertex form (standard form).
In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided above, we have the following quadratic function:
y = -2(x - 4)² + 2
y = -2(x - 4)(x - 4) + 2
y = -2(x² - 4x - 4x + 16) + 2
y = -2(x² - 8x + 16) + 2
y = -2x² + 16x - 32 + 2
y = -2x² + 16x - 30
Read more on vertex here: brainly.com/question/14946018
#SPJ1
I am mad confused! I will make you Brainlist if correct and show all steps and I will give a thanks on all your answers
Step-by-step explanation:
The surface area of a rectangular prism can be found by adding the areas of all six of its faces.
In this case, the rectangular prism has side lengths of 3, 6, and 12 feet. So, its faces are:
Top and bottom faces: Each of these faces is a rectangle with side lengths of 3 feet and 6 feet. Therefore, the area of each of these faces is 3 ft * 6 ft = 18 ft². Since there are two of these faces, their combined area is 2 * 18 ft² = 36 ft².
Front and back faces: Each of these faces is a rectangle with side lengths of 3 feet and 12 feet. Therefore, the area of each of these faces is 3 ft * 12 ft = 36 ft². Since there are two of these faces, their combined area is 2 * 36 ft² = 72 ft².
Side faces: Each of these faces is a rectangle with side lengths of 6 feet and 12 feet. Therefore, the area of each of these faces is 6 ft * 12 ft = 72 ft². Since there are two of these faces, their combined area is 2 * 72 ft² = 144 ft².
To find the total surface area, we add the areas of all six faces:
Total surface area = 36 ft² + 72 ft² + 144 ft²
Total surface area = 252 ft²
Therefore, the surface area of the rectangular prism is 252 square feet.
Answer:
Step-by-step explanation:
12*3*2= 72 because there are two rectangles with the same length.
6*3*2= 36 because there are two widths with the same area.
6*12*2= 144 because there are a top and bottom with the same area.
72+36+144= 252
Surface area is 252 ft squared.
What is y'all's teacher teaching y'all!? I learned this two months ago!
of a group of 200 workers, 15 are chosen to participate in a survey about the number of miles they drive to work each week
In this situation, the sample consists of the [ ]workers selected to participate in the survey.
the population consists of [ ] workers.
The sample consists of the 15 workers selected to participate in the survey.
The population consists of 200 workers.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Out of a group of 200 workers, 15 are chosen to participate in a survey about the number of Miles they drive to work each week.. In this situation the samples consist of the 15 workers selected to participate in the survey.The population consist of 200 workers
SAMPLE: This is a representative part of a population on which a research is about the population is administered
POPULATION: This is the large collection of people or objects that is the focus of a scientific query or research. Often times, the logistics involved in reaching the entire population may be unavailable, so a sample is taken
To learn more about the probability from the given link
https://brainly.com/question/24756209
#SPJ9
Find the quadratic function
Answer:Get a quadratic function from its roots. Enter the roots and an additional point on the Graph. Mathepower finds the function and sketches the parabola.
Step-by-step explanation:Solve a quadratic equation using the quadratic formula.
Write the quadratic equation in standard form, ax2 + bx + c = 0. Identify the values of a, b, and c.
Write the Quadratic Formula. Then substitute in the values of a, b, and c.
Simplify.
Check the solutions.
5% of a number is 23
1% of the same number is 4. 6
work out 16 % of the number
16 percentage of the unknown number is 73.6
To solve the problem, we can use the relationship between percentages and multiply/divide by factors of 100.
Let's start by finding the whole number that corresponds to 1% of the unknown number
1% of the number = 4.6
100 times 1% of the number = 100 x 4.6
Whole number corresponding to the unknown number = 460
We can now use this value to find 5% of the unknown number:
5% of the number = 5/100 x the number = (5/100) × 460 = 23
So we have confirmed that the number we found is correct.
Finally, to find 16% of the number, we can use the same approach
16% of the number = 16/100 x the number = (16/100) × 460 = 73.6
Learn more about percentage here
brainly.com/question/12715980
#SPJ4
7. Write the unknown value that makes this
statement true:
25% of is 10
Answer: 40
Step-by-step explanation:
25/100 x ? = 10
multiply both sides by 100/25
x= 10 x 100/25
x=10
please help with this!!!
The graph of g can be obtained using a horizontal stretch by a factor of 4 and a vertical translation 3 units up of the graph of f.
What is a translation?In Mathematics, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
In Mathematics, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is represented by this mathematical expression g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent a function.Based on the information provided about the parent function f, a function that represents g(x) is given by:
g(x) = 4f + N
g(x) = 4x + 3
Read more on translation here: brainly.com/question/4521517
#SPJ1
Choose the best estimate for the weight of a cantaloupe. Responses A 2 decigrams2 decigrams B 2 kilograms2 kilograms C 2 grams2 grams D 2 milligrams
The best estimate for the weight of a cantaloupe is 2 kilograms (B).
A decigram is 1/10th of a gram, which would be too small of weight for a cantaloupe. 2 grams (C) is also too small for a cantaloupe as it would only be the weight of a few small seeds. 2 milligrams (D) is an extremely small weight, only suitable for a single grain of salt or a tiny insect.
Therefore, 2 kilograms (B) is the most reasonable estimate for the weight of a cantaloupe as it falls within the typical range of cantaloupe weights.
Learn more about Cantaloupe:
https://brainly.com/question/27861329
#SPJ4
Complete Question:
Choose the best estimate for the weight of a cantaloupe. Responses
A 2 decigrams
B 2 kilograms
C 2 grams
D 2 milligrams
Which equation matches the hanger diagram?
Equations are collections of two or more statements with equal signs.
I must locate the solution that the hanger diagram matches. [tex]3x=4[/tex] is the equation that fits the hanger diagram. Thus, option C is correct.
What is a hanger diagram?The hanger shows a total weight of 7 units on one side that is balanced with 3 equal, unknown weights and a 1-unit weight on the other.
Two or more expressions containing equal signs are called equations. I need to find the equation that corresponds to the hanger diagram. The hanger model is a visual representation of the equation.
Both sides must have the same weight to keep the hanger balanced. Like scales and barbells. There are 3 x on the left side of the hanger and 4 x on the right side.
So [tex]3x=4[/tex] is an equation that satisfies the given trailer diagram.
So option C is correct. [tex]3x=4[/tex] is the equation that fits the hanger diagram.
From the diagram we have,
Left=x+x+x
Right [tex]=1+1+1+1[/tex]
This gives
Left=[tex]3x[/tex]
Right [tex]=4[/tex]
Therefore, the equation [tex]3x =4[/tex]
Learn more about hanger here:
https://brainly.com/question/30382013
#SPJ1
The graph is given below y>x+4 is given below.
Write three points that represent solutions and non-
solutions.
Solutions
Non-Soultions
Answer:
Solutions: (-5, 1), (-10, 1), (-10, 5)
Non-solutions: (0, 4), (5, 4), (10, 4)
Step-by-step explanation:
Solutions are in the shaded area. Non-solutions are in the non-shaded area and on the dashed line.
Solutions: (-5, 1), (-10, 1), (-10, 5)
Non-solutions: (0, 4), (5, 4), (10, 4)
If the circumference of a circle is 70cm. Find the measure of it's radius and diameter. (22/7)
Please Help! I don't understand this question!
Therefore, the inverse of f(x) is not a function, as it fails the vertical line test.
How does a mathematical function appear?One output is produced for one input by a function, a form of rule. The formula y=x2 serves as an illustration of this. A single output for y results from any input for x. Given that x is the input value, it is appropriate to say that y is a function of x.
We can determine if the inverse of f(x) = 8x² + 27 is a function by finding the inverse and checking if it passes the vertical line test.
To find the inverse, we first replace f(x) with y:
y = 8x² + 27
Next, we swap the roles of x and y:
x = 8y² + 27
Solving for y gives:
8y² = x - 27
y² = (x - 27)/8
y = ±√((x - 27)/8)
Notice that we have a ± sign in front of the square root, which means that for each x value, we have two possible y values.
Therefore, the inverse of f(x) is not a function, as it fails the vertical line test.
To know more about function visit:
https://brainly.com/question/30721594
#SPJ1
Help please, Which value of x satisfies the equation 7/3(x+9/28)=20
Answer:
Step-by-step explanation:
[tex]\frac{7}{3} (x+\frac{9}{28} )=20[/tex]
[tex]7 (x+\frac{9}{28} )=60[/tex] (multiplied both sides by 3)
[tex]x+\frac{9}{28} =\frac{60}{7}[/tex] (divided both sides by 7)
[tex]x=\frac{60}{7}-\frac{9}{28}=\frac{240}{28}-\frac{9}{28}=\frac{231}{28} =8.25[/tex] (subtracted [tex]\frac{9}{28}[/tex] both sides and solved)
Lily has a box of candies.
5
6
of the candies are pink.
1
2
of the pink candies are round.
What fraction of the candies are pink and round?
Answer:
1/12
Step-by-step explanation:
Out of the total number of candies, 1/2 of the pink candies are round.
To find the fraction of the candies that are pink and round, we need to multiply the fractions representing the proportion of pink candies and the proportion of round candies among the pink candies:
pink candies = 5/6
round candies among the pink ones = 1/5
Therefore, the fraction of candies that are pink and round is:
(5/6) x (1/2) x 1/5 = 1/12
So, 1/12 of the candies are pink and round.
A parking lot was full of different colored cars. There were 12 red cars, 15 blue cars, and 3 green cars. At this rate, how many blue cars will there be if there were 120 total cars?
w(x)= -5(x-8)(x+4)
What is the maximum height that the stone will reach?
Answer:
(2, 180)
Step-by-step explanation:
w(x)=-5x^2+20x+160
a=-5 b=20
x=-20/2x(-5)
x=2
w(2)=180
2, 180
Cielo's rectangular prism shaped swimming pool has a
side of length 8 yards, width of 6-yards and height of 3
yards. What is the total volume of the pool?
a) 36 yd³
b) 144 yd³
c) 1008 yd³
d) 156 yd³
The total volume of the pool is 156 yd³. Option D
How to determine the volumeFirst, to determine the volume, we need to note the properties of a rectangular prism.
It has 6 faces, 12 edges and 8 vertices.The base and side are always rectangles.It also has three dimensions, that is, length width and height.Pairs of opposite faces are identical or equal.The formula for volume of a rectangular prism is;
Volume = lwh
Given that;
l is the length.w is the width.h is the height.Now, substitute the value
Volume = 8 × 3 × 13/2
Volume = 312/2
Volume = 156 yd³
Learn about volume at: https://brainly.com/question/23963432
#SPJ1
the capacity of a dump truck is listed by the manufacturer as 10 yd3. a construction site requires the removal of 170 m3 of dirt, and the contractor has three identical trucks. how many trips will each need to make?
Trips will each need to make 6 trips.
Given
Capacity = 10yd³
Dirts = 170 m³
Trucks = 4
Required
Count the trips made by each truck.
To determine how much dirt is in each truck, divide the amount of soil by 4.
Each Truck = 170/4 m³
Each Truck = 42.5 m³
Divide the portion of each truck by capacity of each truck to get the number of trip
Trip = Each Truck / 10yd³
Convert m³ to yd³
Trip = 55.587875/10
Trip = 5.5587875
Approximate:
Trip = 6
To know more about Capacity, click the below link
https://brainly.com/question/15899704
#SPJ4