To calculate the deflection at point D on the circular rod, we need to consider the segments BD, CD, and AD. Using the formula δ=∑NLAE, we can calculate the deflection as 0.0516 m.
To calculate the deflection at point D using the formula δ=∑NLAE, we need to first segment the rod and then calculate the deflection for each segment.
Segment the rod
Based on the given information, we need to consider segments BD, CD, and AD to calculate the deflection at point D.
Calculate the internal normal force N for each segment
We can calculate the internal normal force N for each segment using the formula N=F1+F2 (for BD), N=F2 (for CD), and N=0 (for AD).
For segment BD
N = F1 + F2 = 140 kN + 55 kN = 195 kN
For segment CD
N = F2 = 55 kN
For segment AD
N = 0
Calculate the cross-sectional area A for each segment
We can calculate the cross-sectional area A for each segment using the formula A=πd²/4.
For segment BD:
A = πd₁²/4 = π(7.6 cm)²/4 = 45.4 cm²
For segment CD
A = πd₂²/4 = π(3 cm)²/4 = 7.1 cm²
For segment AD
A = πd₁²/4 = π(7.6 cm)²/4 = 45.4 cm²
Calculate the length L for each segment
We can calculate the length L for each segment using the given dimensions.
For segment BD:
L = L₁/2 = 6 m/2 = 3 m
For segment CD:
L = L₂ = 5 m
For segment AD:
L = L₁/2 = 6 m/2 = 3 m
Calculate the deflection δ for each segment using the formula δ=NLAE:
For segment BD:
δBD = NLAE = (195 kN)(3 m)/(100 GPa)(45.4 cm²) = 0.0124 m
For segment CD:
δCD = NLAE = (55 kN)(5 m)/(100 GPa)(7.1 cm²) = 0.0392 m
For segment AD
δAD = NLAE = 0
Calculate the total deflection at point D:
The deflection at point D is equal to the sum of the deflections for each segment, i.e., δD = δBD + δCD + δAD = 0.0124 m + 0.0392 m + 0 = 0.0516 m.
Therefore, the deflection at point D is 0.0516 m.
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--The given question is incomplete, the complete question is given
"For a bar subject to axial loading, the change in length, or deflection, between two points A and Bis δ=∫L0N(x)dxA(x)E(x), where N is the internal normal force, A is the cross-sectional area, E is the modulus of elasticity of the material, L is the original length of the bar, and x is the position along the bar. This equation applies as long as the response is linear elastic and the cross section does not change too suddenly.
In the simpler case of a constant cross section, homogenous material, and constant axial load, the integral can be evaluated to give δ=NLAE. This shows that the deflection is linear with respect to the internal normal force and the length of the bar.
In some situations, the bar can be divided into multiple segments where each one has uniform internal loading and properties. Then the total deflection can be written as a sum of the deflections for each part, δ=∑NLAE.
The circular rod shown has dimensions d1 = 7.6 cm , L1 = 6 m , d2 = 3 cm , and L2 = 5 m with applied loads F1 = 140 kN and F2 = 55 kN . The modulus of elasticity is E = 100 GPa . Use the following steps to find the deflection at point D. Point B is halfway between points A and C.
Segment the rod
For the given rod, which segments must, at a minimum, be considered in order to use δ=∑NLAE to calculate the deflection at D?"--
Instructions: Find the surface area of the figure below. Round your answers to the nearest tenth, if necessary.
The surface area of the figure given is of: 61.3 yd².
What is the combined surface area of a figure?The combined surface area of a figure is the area of each figure.
This figure is composed by:
A circle of radius 3 yd.A triangle with base 6 yd and one leg 11.4 yd.The area of the circle is given as follows:
[tex]A = \pi r^2 = \pi \times 3^2 = 9\pi[/tex]
For the triangle, we need to find it's height, which is the leg of a right triangle, in which one of the sides is 3 and the hypotenuse is 11.4, hence:
h² + 3² = 11.4²
[tex]h = \sqrt{11.4^2 - 3^2}[/tex]
h = 11 yd.
Hence the area of the triangle is:
A = 0.5 x 6 x 11 = 33 yd²
The surface area of the figure is:
9pi + 33 yd² = 61.3 yd².
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If A, B, C, and D, are the only possible outcomes of an experiment, find the probability of D using the table below. . Group of answer choices 1/4 3/7 4/7 1/7
Using it's concept, the probability of D is 4/7.
What is a probability?
A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching this problem on the internet, A, B and C all have a probability of 1/7. The sum of all probabilities is of 1 = 100%, hence:
[tex]3 \times \frac{1}{7} + P(D) = 1[/tex]
[tex]P(D) = 1 - \frac{3}{7}[/tex]
[tex]P(D) = \frac{4}{7}[/tex]
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Which of these numbers is irrational?
-3.5
3.5
ОО
35
√5 help
Answer:
√5 is irrational
Step-by-step explanation:
A rational number is one that can be written exactly as an integer or ratio of integers. Written as a decimal number, it will have a finite number of digits, or a repeating decimal fraction.
ApplicationUsually, a number that can only be expressed exactly using a symbol will be irrational. For square roots, any root of an integer other than a perfect square will be irrational.
The integer 5 is not a perfect square. It is between the squares 2²=4 and 3²=9. The square root of 5 is irrational.
__
Additional comment
A reduced fraction whose denominator has factors other than 2 or 5 will translate to a repeating decimal. The number of repeating digits may be as many as 1 less than the denominator. For example, 1/19 has an 18-digit repeating decimal equivalent.
Factor x4 + xy3 + x3 + y3 completely. Show your work. Hint: First factor out a monomial. x4 + xy3 + x3 + y3 =
Answer:
[tex]x^{3} ( x + 1 ) + y^{3} (x+1)\\= (x+1)(x^{3} + y^{3})[/tex]
Answer:
Step-by-step explanation:
YOU PLUS ALL OF THEM
Given AB=15cm,BC=20cm.Find AB correct 3 significant
(question refer to a triangle ABC which is right -angled at C)
The length of AB is 25 units
How to determine the length AB?The given parameters are
AC = 15 cm
BC = 20 cm
The triangle is right -angled at C.
So, we have:
AB^2 = AC^2 + BC^2
This gives
AB^2 = 15^2 + 20^2
Evaluate
AB^2 = 625
Take the square roots
AB = 25
Hence, the length of AB is 25 units
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What are the inputs of the following function?
{(-3, 2), (-4, 2), (8,3), (7, 1)}
A. {-4, -3, 7, 8}
B. {1, 2, 3, 7, 8}
C. {1, 2, 3}
D. {-4,-3, 1, 2, 3, 7, 8}
Answer:
A. {-4, -3, 7, 8}
Step-by-step explanation:
The ordered pairs representing a function are always written ...
(input, output)
InputsThe set of inputs for the given function is the list of first-numbers of the ordered pairs. Those numbers are -3, -4, 8, 7. When we express them as a set, we like to have the elements of the set in increasing order:
inputs = {-4, -3, 7, 8} . . . . . . matches the first choice
2x-3y=1 2x+3y=2 describe the process of using addition to show that the lines are intersecting
Two lines in a plane can intersect,overlap or be parallel.When two lines intersect they have a common point which lies on both line.This is called solution of the two simultaneous equation which when graphed represent straight lines. Adding the two equations uses Elimination method to solve for x and y. The x and y value obtained is the common point lying on both the lines.
2x - 3y = 1
+ 2x + 3y = 2
4x =3 Or x=3/4
Substituting x value in any of the two-equation we can find the corresponding y value .
2x-3y=1
2(3/4) - 3y =1
Solving for y
y= 1/6
The point of intersection of the two lines is ( 3/4, 1/6)
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The geometry students have designed a hexagonal flowerbed for the Homes for
Humanity landscaping project. The shape indicates the color of the flowers. The
design is composed of two congruent rhombuses (blue), four congruent parallelograms
(red and white), and four congruent trapezoids (red and white). The circular area
surrounding the design is an existing rock bed.
The students have determined the following measurements of each figure:
the bases of the trapezoids are 6 ft and 8 ft,
• the heights of the trapezoid and the parallelogram are 3.5 ft each, and
• the horizontal distances between the left and right vertices of each rhombus is 2
ft.
Trapezoid
[tex]A=\frac{1}{2}(3.5)(6+8)=24.5[/tex]
Parallelogram
[tex]A=(3.5)(6)=21[/tex]
Rhombus
[tex]A=\frac{1}{2}(7 \cdot 2)=7[/tex]
Red Area
[tex]2(21)+2(24.5)=91[/tex]
White Area
[tex]2(21)+2(24.5)=91[/tex]
The circular area surrounding the design is an existing rock bed are 24.5, 21, 27, 91 and 91 ft sq.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
It is given the bases of the trapezoids are 6 ft and 8 ft,
The heights of the trapezoid and the parallelogram are 3.5 ft each, and the horizontal distances between the left and right vertices of each rhombus is 2 ft.
Trapezoid
Area = 1/2(3.5)(6 + 8)
Area = 24.5
Parallelogram
Area = 1/2(3.5)(6)
Area = 21
Rhombus
Area = 1/2(7)(2)
Area = 7
Red Area
Area = 2(21) + 2(2.4)
Area = 91
White Area
Area = 2(21) + 2(2.4)
Area = 91
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If you could help me on 1 and 2 that would be great!!!
The conversion of the vectors into coordinate notation rule are as follows;
(-3, 1) ==> (x-3, y+1)(4, -7) ==> (x+4, y-7)What are the coordinate notation form of the given vectors?It follows from the task content that the vectors given in the task content can be converted to coordinate notation form by mapping x and y to their respective transformation units. It therefore follows that the coordinate notation form of the vectors are;
(-3, 1) ==> (x-3, y+1)(4, -7) ==> (x+4, y-7)Read more on coordinate notation;
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Shara is building a birdhouse. She cuts a 6-foot-long board into sections that are each 1/3 foot long. How many sections of the board will Shara have when she is finished cutting?
A 2
B 6 1/3
C 10 1/3
D 18
Answer:
D
Step-by-step explanation:
Dividing by a fraction is the same as multiplying by its reciprocal.
6 ÷ 1/3
= 6 x 3/1
= 6 x 3
= 18
The number of sections of the board Shara has when she is finished cutting is 18 sections.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Length of the board = 6 feet
Length of the section = 1/3 feet
The number of 1/3 feet sections.
= 6 ÷ 1/3
= 6 x 3
= 18
Thus,
Shara when she is finished cutting will have 18 sections.
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Elena and her friends order a 24-slice party pizza. She and her friends eat 2/3 of the
pizza. How many slices do they eat altogether .
Answer:
16 slices
Step-by-step explanation:
24* 2/3 = 16
15-point question. Pls help
Answer:
44
Step-by-step explanation:
x + (22 - 13) = 53
x + 9 = 53
x = 44
Answer:
44
Step-by-step explanation:
x+(22-13)=53
x+22-13=53
x+9=53
x=44
6x + 4y = 10 slove for x
In how many ways can max select 3 toppings from 10 available toppings for his
12. pizza?
Max can select 3 toppings from 10 available toppings for his pizza in 120 ways.
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order. Combinations can be confused with permutations.
Thus number of ways in which Max can select 3 toppings from 10 available toppings for his pizza is 10C3
=[tex]\frac{10!}{7!3!}[/tex]
= [tex]\frac{8.9.10}{3!}[/tex]
= 120
Thus Max can select 3 toppings from 10 available toppings for his pizza in 120 ways.
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Design your own statistical question that you can ask at least twenty different people. Keep in mind that the question should result in a variety of different numerical answers. What is your statistical question?
Ask at least twenty different people (classmates, family, friends, neighbors, teammates, etc.) your statistical question and record their answers. Describe the people you asked and how you gathered your data.
Organize and list your numerical data in order from least to greatest. Then, determine the values of the five-number summary for your set of data.
Use your five-number summary to create and upload a box plot that displays your data set.
A statistical question you can ask at least 20 different people can be: "How many pets do you have?"
An hypothetical data for the number of pets 20 sixth graders have has been given and the box plot that displays the data set is in the image below.
What is a Statistical Question?A statistical question can be defined as a question that can be answered by collecting a variety of numerical answers that vary. Examples of statistical questions include:
What are the age of students in my class?What are the heights of students in a class?A statistical question you can ask at least 20 different people can be: "How many pets do you have?"
Below is the hypothetical questions that can be assumed you'd get from two people:
0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 5, 5
Description of the people you asked can be: 20 sixth graders in your school.
How you gathered your data can be: Asking them to fill a questionnaire or by interview.
The numerical data from least to the greatest, hypothetically would be:
0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 5, 5
The five-number summary for the hypothetical data would be:
Minimum: 0 (least data point)
Quartile Q1: 1 (middle of the first half of the data distribution)
Median: 1.5 (center of the data)
Quartile Q3: 2.75 (middle of the second half of the data distribution)
Maximum: 5 (greatest data value).
Using the five-number summary generated, the box plot that displays the data set is shown in the image attached below.
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A math class's mean test score is 88.4. The standard deviation is 4.0. If Kimmie scored 85.9, what is her z-score
The z-score of Kimmie is -0.625
Calculating z-scoreThe formula for calculating the z-score is expressed as;
z = x-η/s
where
η is the mean
s is the standard deviation
x is the Kimmie score
Substitute the given parameter
z = 85.9-88.4/4.0
z = -2.5/4.0
z = -0.625
Hence the z-score of Kimmie is -0.625
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Jacob takes 7 classes, each 50.00 minutes long, every day of the 5 day school week. How many hours per week does he spend in class
7×50×5 = 1750 minutes
1750minutes/60minutes = 29.161 hours
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. A shaded polygon A B C D is graphed in an x y plane, where x axis ranges from 0 to 7 in increments of 1 and y axis ranges from 0 to 6 in increments of 1. The vertices are as follows: A (1, 1), B (2, 3), C (5, 4), and D (4, 2). Polygon ABCD, shown in the figure, is dilated by a scale factor of 8 with the origin as the center of dilation, resulting in the image A′B′C′D′. The slope of C'D' is___ .
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.
Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).
Slope of CD = (2 - 4) / (4 - 5) = 2
Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.
Slope of C'D' = slope of CD (because preserves shape) = 2
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
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The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
What is transformation?
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.
Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).
Slope of CD = (2 - 4) / (4 - 5) = 2
Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.
Slope of C'D' = slope of CD (because preserves shape) = 2
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
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The perimeter of a rectangle is 64 feet. If one side of the rectangle has a length of 20 feet, how long is the other side?
Answer:
other side is 12
Step-by-step explanation:
Givens
Perimeter = 64 feet
L = 20
Formula
P = 2L + 2w Substitute Givens
64 = 2*20 + 2w Combine
64 = 40 + 2w Subtract 40 from both sides
64-40 = 40-40+2w Combine
24 = 2w Divide both sides by 2
24/2=2w/2
12 = w
Mike is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start.
The solution of the given exponential equation is 0.688.
Given that Mike is working on solving the exponential equation 37ˣ = 12.
An exponential equation is an exponential equation where the power (or) part of the exponent is a variable.
firstly, we have to slve this equation is by converting it to logarithmic form. Any exponential equation can be transformed into an equivalent logarithmic equation as follows:
aˣ = y
logₐy = x
Now, we will apply this transformation to our equation and we get
log₃₇12=x
Further, we will apply the change of base formula so that solution is written in terms of base 10 logs:
x=log12/log37
So, this is an exact answer to given equation, but we can simplify it further by using decimal approximation of it using a calculator. Remember that these logs are base 10:
x≈1.079/1.568
x=0.688
Hence, the solution of the given exponential equation 37ˣ=12 is 0.688.
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4. For a camping trip, each person packs 1.5 lb of food per day. Let p represent the number of people on the trip, and let f represent the total weight of food packed for each day. What is the independent variable in this relationship? Explain. I need this with explanation please:(
Answer the following regarding Momentum Change and Force
1. Find the force necessary to gain a velocity of 60 m s-1 within 5 minutes, when acted on a mass of 200 kg which is initially at rest.
2. A force of 150 N acts on an object of mass 600 kg for 2 minutes, which was initially at rest. Find the velocity gained by the object at the end of the second minute.
1. The force necessary to gain a velocity of 60 m/s within 5 mins is 40 N
2. The velocity gained by the object at the end of the second minute is 30 m/s
1. How to determine the forceInitial velocity (u) = 0 m/sFinal velocity (v) = 60 m/sMass (m) = 200 KgTime (t) = 5 ms = 5 mins = 5 × 60 = 300 sForce (F) =?F = m(v –u) / t
F = 200(60 – 0) / 300
F = 40 N
2. How to determine the velocity Force (F) = 150 NMass (m) = 600 KgInitial velocity (u) = 0 m/sTime (t) = 5 ms = 2 mins = 2 × 60 = 120 sFinal velocity (v) = ?F = m(v –u) / t
Cross multiply
m(v –u) = Ft
Divide both sides by m
v - u = Ft / m
v - 0 = (150 × 120) / 600
v = 30 m/s
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A cyclist rides her bike at a rate of 21 kilometers per hour. What is this rate in kilometers per minute? How many kilometers will the cyclist travel in 20 mins. Don’t round your answers
Answer:
0.35 km per minute, 7 km in 20 minutes
Step-by-step explanation:
1 hr = 60 minutes
21 km per 60 minutes = 21/60 = 0.35 km per minute
In 20 minutes: 0.35*20 = 7 km
Use the diagram to complete the proof
The missing statements that completes the proof that proves that quadrilateral ACDB is a parallelogram is explained below.
What are the Properties of a Parallelogram?A quadrilateral that has the following properties is a parallelogram, in reference to the quadrilateral ACDB in the image given:
Opposite sides are congruent (AB ≅ CD and AC ≅ BD).Opposite angels are congruent to each other (∠A ≅ ∠D and ∠C ≅ ∠B).Consecutive angles are supplementary (m∠A + m∠C = 180°).Given that ΔCFD ≅ ΔBGA, the proof that quadrilateral ACDB is a parallelogram is given below:
Since we know that ΔCFD ≅ ΔBGA, therefore, CD ≅ BA because corresponding parts of congruent triangles are: congruent.
Since we also know that m∠DCA + m∠CAB = 180°, then we also know that both angles are: supplementary.
Transversal A.F cut the two lines, CD and BA, then the interior angles on the same side of the transversal are: supplementary, thus, we it implies we know that lines CD and BA would be: parallel.
Since one pair of sides (CD and BA) are both parallel and congruent, then we know that quadrilateral ACDB is a parallelogram.
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If a peregrine falcon dove at its maximum speed for half a mile to catch prey, how many seconds would the dive take
The dive of the Peregrine falcon took 7.5 seconds
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed X Time
Assuming the top speed of a Peregrine falcon is 240mph.
Distance travelled by the Peregrine falcon = 0.5 miles
By using the formula we get
0.5 = 240 x time
time = [tex]\frac{1}{480}[/tex] hours
time = [tex]\frac{3600}{480}[/tex] seconds = 7.5 seconds
∴ The dive of the Peregrine falcon took 7.5 seconds
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HALP URGENT PLS im dum
x =x=x, equals
^\circ
∘
Answer:
x = 55°
Step-by-step explanation:
That square box indicates a right angle.
A right angle is 90°.
We know that angle x and the 35° angle are making up this 90° angle together.
So, the equation to show what this ship looks like is the following:
[tex]x+35=90[/tex]
This is a simple equation, that if we solve, we get:
[tex]x=55[/tex]
So, x is 55°.
Considering the angle of the ray, it is found that the value of x is of x = 55º.
What is the angle of the ray?The ray has an angle of 180º. It is composed by:
Angle x.An angle of 35º.An angle of 90º.Hence:
x + 35 + 90 = 180
x = 180 - 125
x = 55º.
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Help me please I’m giving briainly need help ASAP
Answer:
f(-x) = -4x^3 + 9x, f(x) is an odd function
Step-by-step explanation:
We are given that f(x) = 4x^3 - 9x. In order to solve this problem, we first need to understand what an odd function is and what an even function is. When we have an odd function, f(-x) = -f(x). Meaning, that if we plug -x in for x, we should get -f(x). On the other hand, with an even function, f(-x) = f(x). Even if you change the sign, when you simplify, you will get back the same function. In either case, we have to first find f(-x) to figure this problem out:
[tex]f(-x)=4(-x)^3-9(-x)\\f(-x)=-4x^3+9x[/tex]
We can see from our answer for f(-x) that it is equal to -f(x). We can verify this below:
[tex]-f(x)=-(4x^3-9x)\\-f(x)=-4x^3+9x[/tex]
Since f(-x) = -f(x), our function f(x) is an odd function
Find the missing segment in the image below.
Answer:
10.
Step-by-step explanation:
6/9 = x/15
9x = 6*15
9x = 90
x = 10.
Answer:
10
Step-by-step explanation:
[tex]\frac{6}{15} =\frac{x}{x+15}[/tex]
[tex]6(x+15)=15x[/tex]
[tex]6x+90=15x[/tex]
[tex]90=15-6x[/tex]
[tex]90=9x[/tex]
[tex]x=90/9= 10[/tex]
Hope this helps
number 68 is increased by 43%
Answer:
68 increased by 43% is 97.24.
Step-by-step explanation:
Multiply 68 by 1.43.
68×1.43=97.24
The answer is 97.24.
Hope this helps!
Answer:
97.24 Absolute change, And the actual difference is 97.24 - 68 = 29.24.
Step-by-step explanation:
A restaurant has the following items on its three-course menu.
List all the possible three-course meals that could be ordered, assuming diners must order one meal from each category.
Starters:
Salad
Garlic bread
Mains:
lamb
pizza
desserts:
cookie
brownie
Answer:
salad, lamb, cookie
salad, pizza, brownie
garlic bread, lamb, cookie.
garlic bread, pizza, brownie