Answer: 1.85
Step-by-step explanation:
PLEASEE HELP ITS DUE TONIGHT!!!
Find the area of the shaded region
Answer: 84
Step-by-step explanation:
Area of whole rectangle = lb = 11x9 = 99
Area of Inner rectangle = lb = 5x3 = 15
Area of Shaded region = Area of whole rectangle - Area of Inner rectangle
= 99 - 15
= 84
Answer:
Area of shaded region = 84 units²
Step-by-step explanation:
Area = Area of bigger - Area of smaller
[tex] { \tt{area = (11 \times 9) - (5 \times 3)}} \\ \\ { \tt{area = 99 - 15}} \\ \\ { \tt{area = 84 \: units {}^{2} }}[/tex]
Problem 2 (Vector and Matrix Refresh) Seven data points are arranged as columns of a data matrix X given as follows: 2 1 0 0 -1 0 -2 X = 2 0 1 0 0 -1 -2 a) Draw all data points on a 2D plane by hand. Properly label the two axes. Clearly provide important tick values to facilitate a precise graphical description of the data. b) Consider each point as a vector. Calculate the angle in between (2 27 and the five other points (excluding [0 07), respectively, using the inner/dot product formula that involves the angle. Note that the angle between two vectors can be negative. c) Calculate the matrix outer product for X, namely, R = XXT. Show the intermediate steps of calculating each element of the 2-by-2 matrix R. d) The matrix outer product can also be calculated via R =
a) The drawing of all data points on a 2D plane is illustrated below.
b) The angle in between the five other points is 27
c) The matrix outer product for X is R = XXT.
d) The matrix outer product can also be calculated via R is (2,27)
The data matrix X is a 2-by-7 matrix, where each column represents a data point with two components. We can visualize each data point as a vector in a two-dimensional plane, where the horizontal axis represents the first component and the vertical axis represents the second component.
To draw all data points on a 2D plane, we can plot each column of X as a vector starting from the origin. Proper labeling of the two axes and providing important tick values will facilitate a precise graphical description of the data.
Next, we can use the inner product formula to calculate the angle between the first data point (2, 27) and the other five data points, respectively.
The inner product, also known as the dot product, is a way to measure the similarity between two vectors by multiplying their corresponding components and summing the products.
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PLEASE HURRY!!
Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed.
What is the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle? Please show your work.
The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%
What is Conditional probability?
Conditional probability is the probability of an event occurring given that another event has occurred or is known to have occurred. It is denoted by P(A|B), which reads as "the probability of A given B."
The formula for conditional probability is:
P(A|B) = P(A and B) / P(B)
where P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.
The total number of Plastic #2 bottles is 8 (correctly placed) + 5 (incorrectly placed) = 13.
The total number of Plastic #4 bottles is 5 (correctly placed) + 2 (incorrectly placed) = 7.
The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is given by:
(number of Plastic #4 bottles correctly placed) / (total number of bottles)
So the probability is:
5/20 = 1/4 = 0.25
Therefore, the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%.
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Last years freshman class at big state university totaled 5,303 students
URGENT
The 1,262 students who received a merit scholarship, the amount they received varied per student and totaled an average of $3,458 ($454). That amount is 78.2% of the full tuition cost of $4,400.
What is merit?Merit is a term used to describe the quality of something or someone that makes them worthy of recognition or respect. It is an indicator of worthiness and is usually based on a person's ability, effort, or accomplishments. Merit is often used when evaluating an individual or a group for a promotion, hiring, or award. Merit is subjective, as different people have different standards for what merits recognition.
Therefore, 21.8% of the students who received a merit scholarship did not receive enough to cover full tuition. Therefore, the percentage of students who received a merit scholarship and did not receive enough to cover full tuition is 21%.
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help plssss explainnn!!
Answer:
[tex]xy^8[/tex]
Step-by-step explanation:
Notice if you have the same base you can ADD the exponent, for example:
[tex]x^{-6} x^{7} =x^{-6+7}=x^{1 }=x[/tex]
[tex]y^{6} y^{2} =y^{6+2}=y^{8 }\\[/tex]
so the answer is
[tex]xy^8[/tex]
Which set of ordered pairs does not represent a function?
1. {(6,5), (3, 5), (−2, 8), (-9,4)}
2. {(-6, -1), (3, 1), (4, −4), (8, 1)}
3. {(-1,9), (-8, 5), (-1, 3), (-9, 1)}
4. {(5,9), (2,-5), (-1,-5), (0, 1)}
The set of ordered pairs does not represent a function is the one in the third option.
{(-1,9), (-8, 5), (-1, 3), (-9, 1)}
Which set of ordered pairs does not represent a function?A relation maps elements from one set, the domain, into elements of other set, the range.
Such that these mappings are of the form (x,y).
A function is a relation where each input is mapped into a single one output, then if you see a relation that has two points with the same value of x and different values of y, then that relation is not a function.
Particularly, if you look at the third option:
{(-1,9), (-8, 5), (-1, 3), (-9, 1)}
You can see that the first and second points have the same input and different outputs, then this is not a function, and that is the correct answer.
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If the gradient of the equation 2x-ay+2=0 is 1. Then find the value of a.
Step-by-step explanation:
2x + ay + 2 = 0
the gradient or slope of the line is the factor m of x in the form
y = mx + b
so let's transform the given equation into that form :
ay = -2x - 2
y = (-2/a)x - 2/a
we know that m = 1.
so,
-2/a = 1
-2 = a
Letsha wants to produce 80 pages information books for school project. She can have this done at local printing company at R0.35 per page.
Answer:
if u want total price then,
=Rs.35×80=Rs.2800
I am in my room (State 1). There is a 65% chance that I stay here and do my work like I am supposed to. There is a 35% chance I go get a snack and procrastinate (State 2). Once I have gone to get the snack, there is a 15% chance that I go back to work (go back to State 1), and there is an 85% chance that I get another snack and procrastinate further (stay in State 2).
Create a diagram and a transition matrix for this case.
Answer:
Here is a diagram and transition matrix for this case:
Diagram:
+---(0.65)---> State 1 (work)
|
Start ---+
|
+---(0.35)---> State 2 (procrastinate)
|
+---(0.15)---> State 1 (work)
|
+---(0.85)---> State 2 (procrastinate)
Transition matrix:
| State 1 | State 2 |
----------+-----------+-----------+
State 1 | 1.00 | 0.00 |
----------+-----------+-----------+
State 2 | 0.15 | 0.85 |
----------+-----------+-----------+
In the transition matrix, the rows represent the starting state and the columns represent the ending state. The entries in the matrix represent the probabilities of transitioning from the starting state to the ending state. For example, the entry in row 1 and column 2 (0.00) represents the probability of transitioning from State 1 to State 2, which is 0.00.
point $p$ lies inside square $abcd$ such that triangle $abp$ is equilateral. find $\angle pcd$ in degrees.
The measurement of angle PCD in equilateral triangle is 67.38°.
Let $s$ be the side length of the square $abcd$, and let $O$ be the center of the square. Then $OP = s/\sqrt{2}$.
Since triangle $ABP$ is equilateral, we have $\angle ABP = 60^\circ$ and $AP=BP=s$. Let $E$ be the foot of the perpendicular from $P$ to $AB$. Then $AE=BE=s/2$ and $EP=s\sqrt{3}/2$.
Since $EP$ is perpendicular to $AB$ and $AB$ is parallel to $CD$, we have $\angle PCD = \angle ACE$.
Since $OP$ is perpendicular to $AB$, we have $\angle OEP = \angle AEP = 30^\circ$. Also, $OE=OP/\sqrt{2}=s/2$.
Using the Pythagorean theorem in triangle $OCE$, we have
CE= [tex]\sqrt{(OE)^{2} + (OC)^{2}} = \sqrt{(s/2)^{2} + s^{2}} = s\sqrt{5}/2[/tex]
Therefore, $\sin \angle ACE = CE/CP = \sqrt{5}/2$. Thus,
∠PCD = ∠ACE = arcsin(√5/2) ≈ 67.38°
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HELP ASAP PLEASE! What is the arc length of an arc with radius 18 inches and central angle 22°? Leave the answer in terms of n. Show your work.
Answer:
arc length = 2.2π inches
Step-by-step explanation:
arc length is calculated as
length = circumference of circle × fraction of circle
= 2πr × [tex]\frac{22}{360}[/tex] ( r is the radius )
= 2π × 18 × [tex]\frac{22}{360}[/tex] ( cancel 18 and 360 by 18 )
= 2π × [tex]\frac{22}{20}[/tex]
= [tex]\frac{44}{20}[/tex] π
= 2.2π inches
If the average aggregate inventory value is $1,200,000 and the cost of goods sold is $600,000, which of the following is weeks of supply?
The inventory turnover ratio can be calculated by dividing the cost of goods sold by the average inventory value. In this case, the inventory turnover ratio is 0.5, and the correct answer is (D) 0.5.
The inventory turnover ratio measures the number of times a company sells and replaces its inventory during a period. It can be calculated by dividing the cost of goods sold by the average inventory value.
The inventory turnover ratio = Cost of goods sold / Average inventory value
In this case, the cost of goods sold is $600,000 and the average inventory value is $1,200,000.
Inventory turnover ratio = $600,000 / $1,200,000 = 0.5
Therefore, the inventory turnover ratio is 0.5, and the correct answer is (D) 0.5.
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Complete question:
If the average aggregate inventory value is $1,200,000 and the cost of goods sold is $600,000, which of the following is inventory turnover?
A)60
B)10.4
C)2
D)0.5
E)None of these
Which of the following products is defined?
GH
FE
EH
FG
All of the above are undefined
Using matrices, we can find that the products of EH and FG are defined, the rest does not satisfy.
Define matrix?A matrix is a rectangular array of values that are defined for mathematical operations including addition, subtraction, and multiplication.
The quantity of rows and columns in a matrix—also referred to as the order of the matrix—determines its size. A 6 4 symbol and 6 by 4 reading are used to symbolise and denote the order of a matrix having 6 rows and 4 columns.
Here in the question,
When the matrices, E and H are multiplied, the resulting matrix is a defined matrix.
Similarly, we can see when F and G are multiplied, the resulting matrix is a defined matrix.
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Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table.
In response to the stated question, we may state that As a result, the overall probability of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.
What is probability?Probability theory is an area of mathematics that calculates the likelihood of an occurrence or a proposition being true. A risk is a number in the range of 0 and 1, whereas 1 implies certainty and a probability of roughly 0 indicates how likely an event seems to be to occur. Probability is a mathematical expression of the chance or chances that a given event will occur. Probabilities can alternatively be stated as integers between 0 and 1 or as % from 0% to 100%. the ratio of occurrences among equally likely choices that result in a certain event in comparison to all other outcomes.
Using the data in the table, we can compute the likelihood of a correct drive-thru order for each fast food chain, as well as the overall chance of an accurate order across all chains.
Divide the number of accurate orders by the total number of orders to find the chance of a randomly picked order being accurate at each chain:
P(accurate order) = 1246 / 1300 = 0.958 for McDonald's
P(accurate order) = 1020 / 1100 = 0.927 Taco Bell
P(accurate order) = 708 / 800 = 0.885 for Burger King
P(accurate order) = 940 / 1000 = 0.94 for Wendy's
P(adequate overall order) = 0.3 * 0.958 + 0.25 * 0.927 + 0.2 * 0.885 + 0.25 * 0.94 = 0.929
As a result, the overall likelihood of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.
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assuming w1, w2, and w3 are 0-1 integer variables, the constraint w1 w2 w3 < 1 is often called a
The constraint w1 w2 w3 < 1, where w1, w2, and w3 are 0-1 integer variables, is often called a packing constraint. The packing constraint w1 w2 w3 < 1 limits the number of variables that can be set to 1 and is used to control the number of items that can be selected in integer programming problems.
A packing constraint is a type of constraint used in integer programming that limits the number of items that can be selected from a set of items. In this case, the constraint limits the number of variables that can take the value 1 to be less than 1.
The term "packing" comes from the idea of packing items into a container. In the context of integer programming, packing constraints are used to limit the number of items that can be "packed" into a container (i.e., set to 1), while ensuring that the total value of the packed items meets certain requirements or constraints.
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Which function represents the following graph?
Oy=√√x-3+3
Oy=√√x+3+3
O y=3√√x-3+3
Oy-3√x+3+3
The correct option b) [tex]\rm y = \sqrt{x+ 3} + 3[/tex] is a function of the given graph.
What particular graph best illustrates a function?The graph οf a relatiοn is said tο reflect a functiοn if a vertical line drawn anywhere οn the graph οnly intersects the graph οnce. In the event when a vertical line can graph is nοt a representatiοn οf a functiοn if there are mοre than twο pοints οn it.
The graphs coordinate is at (-3, 3)
Lets put the value in all the given function to find the correct function
a. [tex]\rm y = \sqrt{x - 3} + 3[/tex]
Using (-3, 3) as x and y
[tex]\rm 3 = \sqrt{(-3) - 3} + 3[/tex]
[tex]\rm 3 = \sqrt{9} + 3[/tex]
[tex]\rm 3 \neq 3 + 3[/tex]
[tex]\rm y = \sqrt{x - 3} + 3[/tex] is not a function of graph.
b. [tex]\rm y = \sqrt{x+ 3} + 3[/tex]
Using (-3, 3) as x and y
[tex]\rm 3 = \sqrt{-3+ 3} + 3[/tex]
[tex]\rm 3 = \sqrt{0} + 3[/tex]
[tex]\rm 3 = 0 + 3[/tex]
[tex]\rm 3 = 3[/tex]
[tex]\rm y = \sqrt{x+ 3} + 3[/tex] is a function of the given graph.
The other two options are no the functions as cube root is used and the value of x wont satisfy there.
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10 of 1710 of 17 Questions
Question
Katherine bought 312
pounds of oranges for $1.45
per pound, as well as 434
pounds of potatoes that cost $1.69
for 2
pounds. She gives the cashier a $10.00
bill.
Which equation represents the situation if x
is the amount of change in dollars Katherine should receive?
A 312(1.45)+434(1.69)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times 1 point 6 9 plus x is equal to 10
B 312(1.45)+434(1.692)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren plus x is equal to 10
C 312(1.45)+434(1.692)−x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren minus x is equal to 10
D (312+434)⋅(1.45+1.69)+x=10
HELP ME I WILL GIVE BRAINLIEST
Answer:
6)-56+567)-/(05(-)9
Step-by-step explanation:
Question
Katherine bought 312
pounds of oranges for $1.45
per pound, as well as 434
pounds of potatoes that cost $1.69
for 2
pounds. She gives the cashier a $10.00
bill.
Which equation represents the situation if x
is the amount of change in dollars Katherine should receive?
A 312(1.45)+434(1.69)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times 1 point 6 9 plus x is equal to 10
B 312(1.45)+434(1.692)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren plus x is equal to 10
C 312(1.45)+434(1.692)−x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren minus x is equal to 10
D (312+434)⋅(1.45+1.69)+x=10
HELP ME I WILL GIVE BRAINLIEST
of the following people, who would be included in the survey conducted by the bureau of labor statistics?
The people who are included in the survey conducted by Bureau of Labor Statistics are (a) certain unpaid workers, (b) part-time workers and (c) workers on vacation, the correct option is (d).
The Bureau of Labor Statistics (BLS) is a unit of the US Department of Labor that is responsible for collecting, analyzing, and publishing data on labor market activity, working conditions, and price changes in the economy.
The Bureau of Labor Statistics (BLS) considers individuals to be employed if they meet any of the given criteria:
(i) Worked at least one hour as paid employees
(ii) Worked at least 15 hours as unpaid workers in a family-owned enterprise
(iii) Were temporarily absent from their regular jobs due to illness, vacation, strike, etc.
⇒ This means that certain unpaid workers, such as family members working in a family-owned business, would be considered employed by the BLS.
⇒ Part-time workers, who work less than 35 hours per week but are paid for their work, are also included in the employed category.
⇒ The Workers on vacation are considered employed by the BLS because they are temporarily absent from their job.
Therefore, all the options are correct , which is Option(d).
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The given question is incomplete, the complete question is
Who of the following are included in the Bureau of Labor Statistics "employed" category?
(a) certain unpaid workers
(b) part-time workers
(c) workers on vacation
(d) All of the above are correct.
Question 4
Let us assume an original starting value of $4 trillion in 2033, but that the actual rate of
decline after 2033 was 10% greater than the 7.6% rate. (Notice that this refers to a 10%
relative increase over the 7.6% rate of decline that was originally estimated in the
lesson, and not an absolute increase of 10 percentage points.) In the questions below,
consider how this would affect the estimated value of the funds in 2038?
What is the new estimated value of the trust funds in 2038? Round to the nearest
The new estimated value of the trust funds in 2038 would be $2.5 trillion.
What is funds?Funds are resources of monetary value that can be used to acquire goods, services, or to meet financial obligations. They are usually obtained through the sale of goods and services or by borrowing. Funds can come from a variety of sources, including individuals, businesses, governments, and other organizations. Funds can be used to purchase assets such as stocks, bonds, real estate, or other forms of investments.
This is because a 10% relative increase over the original estimated 7.6% rate of decline means that the actual rate of decline is 8.36% (7.6% x 1.10 = 8.36%). Applying this rate to the original starting value of $4 trillion, the value of the trust funds in 2038 would be $4 trillion x 0.9164 (which is the equivalent of 1 - 0.0836) = $2.5 trillion.
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The new estimated value of the trust funds in 2038 would be $2.4 trillion.
What is trust fund?A trust fund is a legal arrangement in which a person or organization (the trustor) transfers assets to another person or organization (the trustee) to be managed and distributed for the benefit of a third party (the beneficiary). The trustor sets out a set of instructions (the trust deed) on how the trust funds should be handled, managed, and distributed. The trustee is legally bound to abide by these instructions, and is responsible for the management and distribution of the trust funds according to the trust deed. Trust funds can be used for a variety of purposes, such as providing for a beneficiary's education, medical care, or retirement.
This is because a 10% increase in the rate of decline would result in a rate of decline of 8.36% (7.6% plus 10% of 7.6%).
Using this new rate of decline, the value of the trust funds in 2038 would be $4 trillion multiplied by (1 - 0.0836)⁵,
which is equal to $2.4 trillion.
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Use the Law of Cosines to solve the problem. You must solve for BC first. Solve this order
A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it turn when it changed direction? Show you Work.
answer: 175
Step-by-step explanation:
Answer:
71.9 degrees
Step-by-step explanation:
The find the value of x on the given diagram, we must first find the included angle between the two line segments labelled 94 mi and 119 mi in the triangle. To do this, we can use the Law of Cosines.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
The values to substitute into the formula are:
a = 119b = 94c = 173Solving for the angle C:
[tex]\begin{aligned}173^2&=119^2+94^2-2(119)(94)\cos C\\\\29929&=14161+8836-22372\cos C\\\\29929&=22997-22372\cos C\\\\6932&=-22372\cos C\\\\-\dfrac{6932}{22372}&=\cos C\\\\C&=\cos^{-1}\left(-\dfrac{6932}{22372}\right)\\\\C&=108.0502874...^{\circ}\end{aligned}[/tex]
As angles on a straight line sum to 180°, the value of x can be calculated by subtracting the found value of C from 180°:
[tex]x=180^{\circ}-108.0502874...^{\circ}[/tex]
[tex]x=71.9497125...^{\circ}[/tex]
[tex]x=71.9^{\circ}\; \sf (nearest\;tenth)[/tex]
Therefore, the ship turned 71.9 degrees north of west when it changed direction.
1. A living room measures 4.75 m by 5.2 m. a. What is the area of the living room? 24.7m b. The area of the game room is one and a half times that of the living room. Fi the living room and the game room.
The area of the living room is 24.7 m², and the area of the game room is 37.05 m².
What is area?Area is the measure of the two-dimensional space occupied by a figure or an object. It is usually expressed in square units such as cm2, m2, or in2. It is used to measure the size of a figure or object, and can also be used to calculate the amount of material required for a project.
The area of a living room measuring 4.75 m by 5.2 m can be calculated using the formula A = l × w, where A is the area, l is the length and w is the width. In this case, A = 4.75 m × 5.2 m = 24.7 m².
To calculate the area of the game room, we must multiply the area of the living room by 1.5. Therefore, the area of the game room is 1.5 × 24.7 m² = 37.05 m².
The area of the living room is 24.7 m², and the area of the game room is 37.05 m².
The area of a room can be used to determine how much furniture can fit in the room or how much floor space is available for activities. Knowing the area of a room is also important for calculating the cost of painting, wallpapering, carpeting, and other flooring materials.
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What is the smallest possible average of five distinct positive even integers?
A. 10
B. 8
C. 6
D. 4
E. 0
Answer:
The smallest possible average of five distinct positive even integers will occur if we choose the five smallest even integers. Since we want the integers to be distinct, we start with 2 and add the next four even integers:
2, 4, 6, 8, 10
The average of these five integers is:
(2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6
Therefore, the smallest possible average of five distinct positive even integers is 6, which is answer choice C.
A local service club has monthly luncheon meetings. Each person chooses from a preset menu with three beverage choices, an appetizer of soup or salad, and four sandwiches to choose from. How many different lunches consisting of a beverage, appetizer, and sandwich are possible?
Answer:
24 different lunches
Step-by-step explanation:
There are three choices for the beverage, two choices for the appetizer (soup or salad), and four choices for the sandwich. Therefore, using the multiplication principle of counting, the number of different lunches possible is:
3 choices for beverage x 2 choices for appetizer x 4 choices for sandwich = 24 different lunches.
part b - find the internal axial force in each bar segment using the answer for the support reaction at a determ
As per the axial force, the support reaction at A is equal in magnitude to the axial force that is applied at the other end of the bar.
To determine the support reaction at A, we will draw a free-body diagram of the bar.
Since the bar is fixed at A, the support reaction at that end will be a vertical force, and we will label it as RA.
Using Newton's second law of motion, we can write the equation of equilibrium for the bar in the vertical direction:
ΣFy = 0
where ΣFy is the sum of all the forces in the vertical direction. Since there are only two forces acting on the bar, the axial force and the support reaction, we can write:
-FA + RA = 0
where FA is the axial force that is applied at one end, and RA is the support reaction at the other end.
From this equation, we can solve for RA:
RA = FA
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Complete Question:
Determine the support reaction at A
The axially loaded bar is fixed at A and loaded as shown. Draw a free-body diagram and determine the support reaction at A.
-51+((-5+(-4)) all calculation
Answer:
the answer to that is -31
Converting
What is 3.4 hours in hours and minutes?
By answering the presented questiοn, we may cοnclude that 0.4 οf an expressiοns hοur is 0.4 x 60 = 24 minutes in this situatiοn. As a result, 3.4 hοurs equals 3 hοurs and 24 minutes.
What is expressiοn ?An expressive in mathematics is a collection of numbers, variables, and complicated mathematical operations (such as addition, subtraction, multiplication, division, multiplicands, and others) that convey a quantity's value. Expressions can be as straightforward as "3 + 4" or as complex as "(3x2 - 2) / (x + 1)". They could also include functions like "sin(x)" or "lg(y)".
The real way to evaluate an expression is to insert the variables with their values and carry out the arithmetic operations in the order specified. For instance, the phrase "3x + 5" means 3(2) + 5 = 11 if x = 2. In mathematics, expressions are typically used to describe actual situations, build equations, and decompose challenging mathematical diagrams.
3 hοurs and 24 minutes is cοmparable tο 3.4 hοurs.
Yοu may separate the full number (which represents the hοurs) frοm the decimal tο cοnvert decimal hοurs tο hοurs and minutes (which represents the fractiοn οf an hοur in minutes).
0.4 οf an hοur is 0.4 x 60 = 24 minutes in th
is situation. As a result, 3.4 hours equals 3 hours and 24 minutes.
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T/F. To construct a confidence interval for sigma (or sigma squared), the population from which the sample was drawn must be normally distributed.
To construct a confidence interval for sigma the population from which the sample was drawn must be normally distributed. -
It is not necessary to make the normalcy assumption in order to build a confidence interval for sigma. To employ the central limit theorem, however, the sample size must be adequate which ideally enables the use of the normal distribution to approximate the sampling distribution of the sample variance. Alternative techniques, like t-distribution, can be employed if total sample size is limited.
It's also important to remember that, regardless of sample size, the distribution of sample variance will be normal if population is known and recognizable to have a normally distributed population. As long as the sample size is appropriate, the sample variance may still be utilized to create a confidence range for sigma even if the population is not normally distributed.
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Hunter is an hourly employee, and the line that models his total pay in dollars
as it relates to the number of hours he has worked has a slope of 35 and a y
intercept of 25. Which statement is true?
O A. Hunter's wage is $35 an hour, but it appears that he received no
signing bonus.
• B. Hunter's wage is $35 an hour, and it appears that he received a
signing bonus of $25.
O C. Hunter's wage is $25 an hour, but it appears that he received no
signing bonus.
• D. Hunter's wage is $25 an hour, and it appears that he received a
signing bonus of $35.
Answer: C
Step-by-step explanation:
The correct answer is C.
The slope of the line represents the hourly wage, so Hunter's wage is $35 an hour, as given in option A and B. However, the y-intercept of the line represents the starting pay or the pay for zero hours worked. In this case, the y-intercept is 25, which means Hunter received $25 even if he did not work any hours. Hence, option C is correct as it states that Hunter's wage is $25 an hour, but it appears that he received no signing bonus.
In an effort to figure out why application rates are slipping, your college decides to set up an experiment to determine why students who are interested in the college decide to enroll or not. The college decides to send out a questionnaire to everyone who submitted an application to the college in 2017. What's the population for this study, and what's the sample?
A. The population is all college students everywhere, and the sample is all college students interested in your school.
B. The population is all college students everywhere, and the sample is the individuals who responded to the survey.
C. The population is all students who applied to your college, and the sample is the individuals who responded to the survey.
D. The population is all college students interested in your school, and the sample is everyone who decided to enroll.
The population of interest is the group of students who submitted an application to the college in 2017.
What is sample?A sample is a subset of a population that is selected and studied in order to make inferences or conclusions about the population. The sample is usually selected to be representative of the population in some way, so that the conclusions drawn from the sample can be generalized to the population as a whole.
According to question:The correct answer is C.
The purpose of the study is to determine why students who are interested in the college decide to enroll or not. Therefore, the population of interest is the group of students who submitted an application to the college in 2017.
Option A is incorrect because the population is not all college students everywhere, only those who applied to the college in question.Option B is incorrect because the sample is not just the individuals who responded to the survey, but rather all students who submitted an application in 2017.Option D is incorrect because the sample is not just everyone who decided to enroll, but rather all students who submitted an application, regardless of whether they enrolled or not.To know more about sample visit:
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any point on the parabola can be labeled (x,y), as shown. a parabola goes through (negative 3, 3)
The correct standard form of the equation of the parabola is:
[tex]y = -x^2 - 1[/tex].
To find the standard form of the equation of the parabola that passes through the given points (-3, 3) and (1, -1), we can use the general form of the equation of a parabola:
[tex]y = ax^2 + bx + c[/tex] ___________(1)
Substituting the coordinates of the two given points into this equation, we get a system of two equations in three unknowns (a, b, and c):
[tex]3 = 9a - 3b + c[/tex]
[tex]-1 = a + b + c[/tex]
To solve for a, b, and c, we can eliminate one of the variables using subtraction or addition. Subtracting the second equation from the first, we get:
[tex]4 = 8a - 4b[/tex]
Simplifying this equation, we get:
[tex]2 = 4a - 2b[/tex]
Dividing both sides by 2, we get:
[tex]1 = 2a - b[/tex]___________(2)
Now we can substitute this expression for b into one of the earlier equations to eliminate b. Using the first equation, we get:
[tex]3 = 9a - 3(2a - 1) + c[/tex]
Simplifying this equation, we get:
[tex]3 = 6a + c + 3[/tex]
Subtracting 3 from both sides, we get:
[tex]0 = 6a + c[/tex]
Solving for c, we get:
c = -6a __________(3)
Substituting this expression for c into the second equation, we get:
[tex]-1 = a + (2a - 1) - 6a[/tex]
Simplifying this equation, we get:
[tex]-1 = -3a - 1[/tex]
Adding 1 to both sides, we get:
[tex]-3a =0[/tex]
Solving for a, we get:
[tex]a = 0[/tex]
Substituting this value of a into the equation(3) for c, we get:
c = 0
Substituting a = 0 into the equation(2) for b that we found earlier, we get:
[tex]1 = 0 - b[/tex]
Solving for b, we get:
[tex]b = -1[/tex]
Putting the values of a, b and c in (1), we get
[tex]y = -x^2 - 1[/tex]
Therefore, the equation of the parabola that passes through the given points (-3, 3) and (1, -1) is:
[tex]y = -x^2 - 1[/tex]
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Complete question:
A parabola goes through (-3, 3) & (1, -1). A point is below the parabola at (-3, 2). A line above the parabola goes through (-3, 4) & (0, 4). A point on the parabola is labeled (x, y).
What is the correct standard form of the equation of the parabola?
The figure is in the image attached below
