The required solution of the linear programming problem for the given objective function and subject to constraints are,
Linear programming problem is Maximize 15x1 + 2x2
Subject to:
7x1 + x2 < 23
3x1 - x2 < 5
x1, x2 > 0
Objective function value for rounding up fraction 1/2 solution is 53
Objective function value for rounding up all fraction solution is 23.
Optimal objective function value 53 is lower than optimal value 95.5.
Optimal objective function value is always less than or equal to the LP's optimal objective function value as ILP problem is a more constrained version.
To solve the problem as an LP,
we can ignore the integer constraints
And solve the problem as a continuous linear program.
The problem can be written as,
Maximize 15x1 + 2x2
Subject to:
7x1 + x2 < 23
3x1 - x2 < 5
x1, x2 > 0
Rounding up fractions greater than or equal to 1/2,
The following feasible solution is,
x1 = 3, x2 = 4
The objective function value for this solution is 53.
However, this is not the optimal integer solution since both x1 and x2 are not integers.
Rounding down all fractions, we get the following feasible solution,
x1 = 1, x2 = 4
The objective function value for this solution is 23, which is less than the LP's optimal objective function value of 95.5.
This is not the optimal integer solution either.
Optimal objective function value for the ILP is lower than that for the optimal LP, solve the ILP problem.
In any one constraints
When x1 = 0 ⇒ x2 = 23
x2 = 0 ⇒ x1 = 3.3
Optimal value is ,
15(3.3) + 2(23)
= 49.5 + 46
= 95.5
Optimal objective function value is lower than optimal value.
The optimal objective function value for the ILP problem is always less than or equal to the corresponding LP's optimal objective function value .
Because the ILP problem is a more constrained version of the linear programming problem.
The ILP problem restricts the variables to be integers, which reduces the feasible region and makes the problem more difficult to solve.
The optimal objective function values for the LP and ILP problems are equal.
If the LP problem has an optimal solution that satisfies the integer constraints.
In general, the optimal objective function value of the MILP problem can be better or worse than that of the LP or ILP problem.
It depends on the specific problem instance.
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The above question is incomplete, the complete question is :
Given the following all-integer linear program:
Max 15x1 + 2x2
s. t.
7x1 + x2 < 23
3x1 - x2 < 5
x1, x2 > 0 and integer
a. solve the problem as an lp, ignoring the integer constraints.
b. what solution is obtained by rounding up fractions greater than or equal to 1/2? is this the optimal integer solution?
c. what solution is obtained by rounding down all fractions? is this the optimal integer solution? explain.
d. show that the optimal objective function value for the ilp (integer linear programming) is lower than that for the optimal lp.
e. why is the optimal objective function value for the ilp problem always less than or equal to the corresponding lp's optimal objective function value? when would they be equal? comment on the optimal objective function of the milp (mixed-integer linear programming) compared to the corresponding lp and ilp.
a particular fruit's weights are normally distributed, with a mean of 443 grams and a standard deviation of 34 grams. if you pick 2 fruit at random, what is the probability that their mean weight will be between 360 grams and 491 grams
The probability that the mean weight of two fruits picked at random falls between 360 grams and 491 grams is approximately 0.9554 or 95.54%.
To solve this problem, we need to use the formula for the sampling distribution of the sample mean:
x' = μ/√n
where x' is the sample mean, μ is the population mean, and n is the sample size.
Given that the population mean is 443 grams and the standard deviation is 34 grams, we can calculate the standard error of the sample mean:
SE = σ/√n
= 34/√2
≈ 24.04 grams
Now we need to standardize the sample mean to a standard normal distribution using the z-score formula:
z = (x' - μ)/SE
The probability that the sample mean falls between 360 grams and 491 grams is equivalent to the probability that the z-score falls between:
z = (360 - 443)/24.04 ≈ -3.45 and z = (491 - 443)/24.04 ≈ 1.99
Using a standard normal table or calculator, we can find the probability that the z-score falls between -3.45 and 1.99, which is approximately 0.9554.
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Answer the questions below. Write your answers in simplest form.
Answer:
(a.) 8m
(b.) 12 cm
Step-by-step explanation:
a:
given: area of square = 64m²
formula of area of a square A = s²
We will reverse the formula to find the sum of the sides:
S = √A
S =√64
S = 8
b:
Given: perimeter of a square is 48 cm
formula for a perimeter of a square: P = 4 · s
We will reverse the formula to find the sum of the sides:
S = P ÷ 4
S = 48 ÷ 4
S = 12
PLEASE HELP DUE SOON
Answer:
output = -3n +1
Step-by-step explanation:
Given an input/output table for a linear function, you want an expression for the output when the input is n.
Arithmetic sequenceThe input values count up from 1, so we can consider the output values to be the terms of an arithmetic sequence.
The first term of the sequence is a1 = -2 (when n=1).
The common difference of the sequence is d = (-5 -(-2)) = -3.
The general (n-th) term of an arithmetic sequence is given by the formula ...
an = a1 +d(n -1)
For the known values of a1 and d, we find the n-th term to be ...
an = -2 +(-3)(n -1)
an = -2 -3n +3 . . . . . . . eliminate parentheses
an = -3n +1 . . . . . . . . collect terms
The term corresponding to an input value of n is ...
-3n +1
Solve problem 24 and explain how you solved it
What is the measure of AB?
Answer:
The answer is 22
Step-by-step explanation:
You would first start by solving for the x value. You would do 6x-7=2x+5, then start factoring out number and variable until the variable is on 1 side and the number are on the other, so it'd be 4x=12. After you would calculate for the x which is 3, which you did, then you would plug that back into the values. You'd plug 3 into 2(x)+5 which simplifies down to 6+5 which is 11 and since DB is half of AB you multiply by 2 to get 22.
On June 1, Marika’s Cards and Gifts had 117 birthday cards on hand. Over the month, Marika’s sold 208 of this type of card and received two orders from the distributor, each for 144 cards. The cost of birthday cards to Marika’s is $0.56 each. What is the value of the inventory at the end of the month?
Since the cost of each card is $ [tex]0.56[/tex], you can now multiply the total number of cards by the cost per card. the value of the inventory at the end of the month is $ [tex]343.28[/tex].
What is the value of the inventory?To find the value of the inventory at the end of the month, you need to start by calculating the total number of birthday cards that Marika's Cards and Gifts had at the end of the month.
First, you need to add the number of birthday cards that Marika's sold during the month (208) to the number of cards received from the distributor in two separate orders) [tex](144 \times 2) = 288[/tex]
[tex]117[/tex] (initial inventory) + [tex]208[/tex] (cards sold) + [tex]288[/tex] (cards received from distributor) = [tex]613[/tex] (total number of birthday cards at the end of the month)
Since the cost of each card is $0.56, you can now multiply the total number of cards by the cost per card to get the value of the inventory:
[tex]613 \times[/tex] $[tex]0.56 =[/tex] $[tex]343.28[/tex]
Therefore, the value of the inventory at the end of the month is $343.28.
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Arianna ate 0.45 of the grapes and Alex at 35% of them if there were 18 grapes left how many were in the container at first
There were 90 grapes in the container at first.
What is the percentage?
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.
Let's assume that there were x grapes in the container at first.
Arianna ate 0.45 of the grapes, which means she ate 0.45x grapes.
Alex ate 35% of the grapes, which means he ate 0.35x grapes.
The total number of grapes eaten is the sum of what Arianna and Alex ate:
0.45x + 0.35x = 0.8x
This means that 0.8x grapes were eaten, and the number of grapes left is x - 0.8x = 0.2x.
We know that there were 18 grapes left, so we can set up an equation:
0.2x = 18
Solving for x, we get:
x = 90
Therefore, there were 90 grapes in the container at first.
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If Heidi makes 15.85 an hour and she works 47.50 hours this week what is her overtime pay ?
Answer: $178.31
Step-by-step explanation:
To calculate Heidi's overtime pay, we first need to find out how many hours she worked overtime and then multiply those hours by her overtime pay rate. The standard workweek in the United States consists of 40 hours, and any hours worked beyond 40 hours are considered overtime.
Step 1: Calculate the number of overtime hours:
Total hours worked = 47.50 hours
Standard workweek = 40 hours
Overtime hours = Total hours worked - Standard workweek = 47.50 - 40 = 7.50 hours
Step 2: Calculate Heidi's overtime pay rate:
Hourly wage = $15.85
Overtime pay rate = Hourly wage * 1.5 (overtime is typically paid at 1.5 times the regular hourly rate) = $15.85 * 1.5 = $23.775
Step 3: Calculate Heidi's overtime pay:
Overtime pay = Overtime hours * Overtime pay rate = 7.50 hours * $23.775 = $178.31 (rounded to 2 decimal places)
Heidi's overtime pay for the week is $178.31.
Plssssss!!!! Help SOLVE FOR Y!!!!!!
Answer:
y = 23 degrees
Step-by-step explanation:
115° and 5y° are equal because they are alternate exterior angles
115 = 5y
Divide by 5 to isolate the y
23 = y
so y is 23°
Percy's town had a recycling drive last weekend. 5,320 of the residents of the town participated and 1,680 did not. What percentage of the residents of Percy's town participated in the recycling drive?
Answer:
To find the percentage of residents who participated in the recycling drive, we need to divide the number of participants by the total number of residents and then multiply by 100 to get the percentage. Total number of residents in Percy's town = 5,320 + 1,680 = 7,000 Number of residents who participated = 5,320 Percentage of residents who participated = (Number of participants / Total number of residents) x 100 = (5,320 / 7,000) x 100 = 76% Therefore, 76% of the residents of Percy's town participated in the recycling drive.
Answer:
The correct answer is 76%.
Step-by-step explanation:
To find the percentage of Percy's town that participated in the recycling drive, we must divide the number of people that participated by the total number of residents.
To do this, we should first find the total number of residents. Since residents either participated or did not participate, the total number of residents is the sum of these two values. This is modeled below:
Total number of residents = 5,320 + 1,680 = 7,000 total residents
Now, we can continue with the percentage calculation.
% participation = # of participants/# of residents * 100
% participation = 5,320/7,000 * 100
% participation = 76%
Therefore, we can conclude that 76% of Percy's town participated in the recycling drive.
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URGENT PLEASE HELP!! I WILL MARK BRAINLIEST THE BEST ANSWER PLEASEE WORTH LOTS OF POINTS!!
Geometry: Circle Dilations
For problem 3, Noah created the following diagram: (image provided)
He then made the following measurements and calculations:
- He calculated the ratio OB/OA=2.25
- He measured the perimeter of triangle ARG, And found it to be 4.4 cm.
- he measured angle RAG =180ﾟ
- He calculated the area of triangle ARG, and found it to be 0.8 cm squared
- He calculated the circumference of circle A, and found it to be approximately 8.13 cm.
He would now like to calculate corresponding values for the triangle in the larger circle, and he needs your help.
Calculate the following, using your knowledge that all circles are similar, along with the data already collected by Noah.
1. Find the perimeter of triangle BSH
2. Find the measure of angle SBH
3. Find the area of triangle BSH
4. Find the length of the circumference of circle B
1. Perimeter of AARG = 1.6 × 4.4 cm = 7.04 cm
2. The measure of SBH is 162°.
3. Area of AARG = 2.56 × 0.8 cm² = 2.048 cm²
4. The length of the circumference of circle B is approximately 13.01 cm.
What is perimeter ?The circumference of a this double shape's perimeter is its total length. In other terms, it is the total length of all a shape's sides. For instance, the circumference of a circle is equal to the distance around its outside, or circumference, whereas the perimeter of a rectangle may be computed by combining the measurements of all four sides.
To solve this problem, we can use the fact that all circles are similar. This means that corresponding lengths of the circles are proportional. In particular, if the ratio of the radii of two circles is k, then the ratio of their circumferences is also k, and the ratio of their areas is k².
Let's start with finding the radius of the larger circle. Since OB/OA = 2.25, we can write:
OA + AB = OB
OA + 1 = 2.25 OA
OA = 1 / 1.25 = 0.8
Therefore, the radius of the larger circle is 0.8 cm. Since the circles are similar, the ratio of the radii is 0.8/0.5 = 1.6.
1. The perimeter of ABSH is proportional to the radius of the circle, so we have:
Perimeter of ABSH = 1.6 × Perimeter of AARG = 1.6 × 4.4 cm = 7.04 cm
2. Let x be the measure of SBH. Then we have:
RAG + SBH + HBS = 360°
108° + x + 90° = 360°
x = 162°
Therefore, the measure of SBH is 162°.
3. The area of ABSH is proportional to the square of the radius of the circle, so we have:
Area of ABSH = 1.6² × Area of AARG = 2.56 × 0.8 cm² = 2.048 cm²
4. The circumference of circle B is proportional to the radius of the circle, so we have:
Circumference of circle B = 1.6 × Circumference of circle A ≈ 1.6 × 8.13 cm ≈ 13.01 cm
Therefore, the length of the circumference of circle B is approximately 13.01 cm.
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What is the area of a right triangle with a height of sixteen and three-fourths meters and a base of 45 meters?
The area of a right triangle is given by the formula:
Area = 1/2 * base * height
Substituting the values given in the problem:
Area = 1/2 * 45 meters * 16 and 3/4 meters
To simplify the computation, we convert the mixed fraction 16 and 3/4 to an improper fraction:
16 and 3/4 = (16 * 4 + 3) / 4 = 67/4 meters
Substituting this value, we get:
Area = 1/2 * 45 meters * 67/4 meters
Simplifying:
Area = 843.75 square meters
Therefore, the area of the right triangle is 843.75 square meters.
Answer: 376 7/8
Step-by-step explanation: if you multiply the base and the height you'll get 754 3/4 since this is a triangle we are talking about it would be halved which would make it 376 7/8.
and im doing the exam and its correct.
a hemispherical tank has a radius of 13ft . given that the water weighs is 62.5lb/ft3 , find the work required to pump the water out of the tank.
The work required to pump the water out of the hemispherical tank is 5,930,818.125 ft-lb.
To find the work required to pump the water out of the hemispherical tank, we need to consider the following steps:
Step 1: Determine the volume of the hemispherical tank.
The formula for the volume of a hemisphere is (2/3)πr³,
where r is the radius.
Given the radius is 13 ft, we can calculate the volume as follows:
Volume = (2/3)π(13³)
= (2/3)π(2197)
= 14603.86 ft³.
Step 2: Calculate the weight of the water in the tank.
Given the water weighs 62.5 lb/ft³, we can determine the weight of the water in the tank by multiplying the volume by the water weight:
Water weight = Volume × Weight/ft³
= 14603.86 ft³ × 62.5 lb/ft³
= 912741.25 lb.
Step 3: Determine the average height at which the water must be pumped out.
Since the tank is hemispherical, the average height for pumping the water is half the radius (13 ft).
So, the average height is:
Average height = 13 ft ÷ 2 = 6.5 ft.
Step 4: Calculate the work required to pump the water out of the tank.
Work = Weight × Distance × Force of gravity.
where Force of gravity = 1 (as we're working with pounds and feet, the force of gravity is already accounted for).
Work = 912741.25 lb × 6.5 ft × 1 = 5930818.125 ft-lb.
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HELP!
Follow this link to view Jamie’s work. Critique Jamie’s work by explaining the reasonableness of the scenario and the accuracy of the two parts of the graph he described . For any portion of Jamie’s response in which he has made an error, provide and explain an alternative response.
To enhance Jamie’s explanation, describe both sections of the piecewise function using linear equations. Include any limits to the domain.
The given graph is an illustration of a piecewise linear equation.
Jamie correctly described what the graph could be used for (a relay race)
Jamie wrongly described the axes of the graph, in both sections
The piece-wise function is: [tex]y=\left \{ {{\frac{1}{12}x, 0 < = x < 12} \atop {\frac{1}{8}x+\frac{1}2},12 < x < =20}} \right.[/tex]
See the attachment for the graph and Jamie's work
From the graph, we have:
Time (minutes) = x
Distance (miles) = y
(a) When the runner begins the race
From the graph, we have:
x=[0,12]
y=[0,1]
This means that the runner runs a distance of 1 mile in 12 minutes
So; Jamie's description here is wrong because he misrepresented the axes.
The equation of this part is calculated as follows:
Start by calculating the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{1-0}{12-0}=\frac{1}{12}[/tex]
The equation is then calculated using:
[tex]y=m(x-x_1)+y_1\\\\y=\frac{1}{12}(x-0)+0\\\\y=\frac{1}{12}x[/tex]
(b) When his partner takes over
From the graph, we have:
x=(12,20]
y=(1,2]
This means that his partner runs a distance of 1 mile in 8 minutes
So; Jamie's description here is also wrong because he misrepresented the axes, again.
The equation of this part is calculated as follows:
Start by calculating the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{20-12}=\frac{1}{18}\\\\y=\frac{1}{8}(x-12}+1\\\\y=\frac{1}{8}x-\frac{1}{2}[/tex]
Hence, the piece-wise function can be represented as:
The piece-wise function is: [tex]y=\left \{ {{\frac{1}{12}x, 0 < = x < 12} \atop {\frac{1}{8}x+\frac{1}2},12 < x < =20}} \right.[/tex]
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need help with this question, im stuck on it
Answer:
120° and 60°
Step-by-step explanation:
5x - 10 + 3x - 18 = 180
8x = 180 + 10 + 18
8x = 208 / : 8
x = 26
.
(5x - 10)° = (5 × 26 - 10)° = 120°
(3x - 18)° = (3 × 26 - 18)° = 60°
A Cap is discounted at 25% off. The original price is $60.
What is the sales price?
O $40
O $50
O $45
O $30
Answer:
It's 45.
Step-by-step explanation:
Same as the last question :)
what is the value of 16^1/2?
A. 2
B. 4
C. 8
D. 32
Answer: 8
Step-by-step explanation:
COMPARING METHODS In Exercises 27-32, tell whether you would use the Law of Sines, the Law of Cosines, or the Pythagorean Theorem (Theorem 9.1) and trigonometric ratios to solve the triangle with the given information. Explain your reasoning. Then solve the triangle.
Find the third partial sum of the series. (picture included!!!) please I'm in dire need of help cus my grades a D if I could get help ill be so so happy ill probably cry a little tear of joy
Consequently, 15 is the third partial total of the sequence.
What in mathematics is arithmetic?The area of mathematics known as arithmetic deals with the mathematical study of numbers and the numerous procedures that can be performed on them. Addition, subtraction, multiplication, and division are the fundamental mathematical processes. The icons listed above stand in for these processes.
The given series is an arithmetic series with first term a1 = 2 and common difference d = 3.
To find the third partial sum, we need to add the first three terms of the series:
S₃ = 2 + 5 + 8
S₃ = 15
Therefore, the third partial sum of the series is 15.
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Lydia has a bag that contains orange chews, cherry chews, and peach chews. She performs an experiment. Lydia randomly removes a chew from the bag, records the result, and returns the chew to the bag. Lydia performs the experiment 62 times. The results are shown below:
A orange chew was selected 25 times.
A cherry chew was selected 24 times.
A peach chew was selected 13 times.
Based on these results, express the probability that the next chew Lydia removes from the bag will be orange or peach as a percent to the nearest whole number.
Answer:
The probability of selecting an orange chew is 25/62, and the probability of selecting a peach chew is 13/62. To find the probability that the next chew Lydia removes from the bag will be orange or peach, we add these probabilities:
P(orange or peach) = P(orange) + P(peach) = 25/62 + 13/62 = 38/62
To express this probability as a percent, we divide the numerator by the denominator, then multiply by 100:
P(orange or peach) = 38/62 = 0.6129...
0.6129... × 100 ≈ 61
Therefore, the probability that the next chew Lydia removes from the bag will be orange or peach, expressed as a percent to the nearest whole number, is 61%
suppose that three students are randomly selected from the student body. what is the probability that all three will possess a gpa in excess of 3.0?
The probability that at least three out of five randomly selected students will possess a GPA in excess of 3.0 is approximately 0.1772.
To solve this problem, we need to use the binomial distribution with n = 5 and the probability of success p = P(GPA > 3.0), which can be found using the normal distribution table:
P(GPA > 3.0) = P(Z > (3.0 - 2.7)/0.7) = P(Z > 0.43) = 1 - P(Z < 0.43) = 1 - 0.6664 = 0.3336
Now we can use the binomial distribution to find the probability that at least three students out of five have a GPA greater than 3.0:
P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5)
Using the binomial formula and the probabilities of success and failure:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
we get:
P(X = 3) = (5 choose 3) * 0.3336^3 * 0.6664^2 = 0.1311
P(X = 4) = (5 choose 4) * 0.3336^4 * 0.6664^1 = 0.0421
P(X = 5) = (5 choose 5) * 0.3336^5 * 0.6664^0 = 0.0040
Therefore:
P(X ≥ 3) = 0.1311 + 0.0421 + 0.0040 = 0.1772
So the probability that at least three out of five students have a GPA greater than 3.0 is approximately 0.1772.
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--The given question is incomplete, the complete question is given
" The grade point averages (GPAs) of a large population of college students are approximately normally distributed with mean 2.7 and standard deviation 0.7. Suppose that five students are randomly selected from the student body. What is the probability that at least three will possess a GPA in excess of 3.0? "--
a box contains a combination of solid-colored tickets: 1/10 of the tickets are green, 1/2 are red , 1/4 are blue, and the remaining 30 tickets are white. how many blue tickets are in the box?
There were 50 blue box at total in the box.
What is combination?In mathematics, a cοmbinatiοn is a way οf selecting items frοm a cοllectiοn where the οrder οf selectiοn dοes nοt matter. Suppοse we have a set οf three numbers P, Q and R. Then in hοw many ways we can select twο numbers frοm each set, is defined by cοmbinatiοn.
In smaller cases, it is pοssible tο cοunt the number οf cοmbinatiοns, but fοr the cases which have a large number οf grοup οf elements οr sets, the pοssibility οf a set οf cοmbinatiοn is alsο higher.
The bοx will be represented as (x)
From the question, we form:
White tickets = (1 - 1/10 - 1/2 - 1/4)x = 30
Blue tickets = 3/20 x = 30
Blue tickets = = 30 x 20 / 3 = 200
Blue tickets = 1/4 x 200 = 50
Thus, There were 50 blue box at total in the box
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Ms. Angelino made 2 pans of lasagna and
cut each pan into twelfths. Her family ate
112 pans of lasagna for dinner. How many
pans of lasagna were left? (Lesson 6.7)
A. 11/12
B.1 11/12
C.2 1/12
D.3 1/12
Keith will rent a car for the weekend. he can choose one of two plans. the first plan has an initial fee of $53.98 and cost an additional 0.13 per mile driven. the second plan has an initial fee of $67.98 and cost an additional 0.11 per mile driven. how many miles would Keith need to drive for the two plans to cost the same
Use the discriminant to describe the roots of each equation. Then select the best description. 2x2 + 7x + 6 = 0
real and irrational roots
real and rational roots
double root
non-real roots
Answer:
real and rational roots
Step-by-step explanation:
The discriminant of the given equation is [tex]7^2-4(2)(6)=1[/tex].
Since the discriminant is a perfect square, the equation has real and rational roots.
find all unknown measures in the triangle
Therefore , the solution of the given problem of triangle comes out to be C is an 80-degree angle.
What precisely is a triangle?If a polygon has at least one additional segment, it is a hexagon. Its structure is a simple rectangle. Something like this can only be distinguished from a regular triangular form by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.
Here,
We can use the knowledge that a triangle's total angles equal 180 degrees to determine the missing angle measurements in the given triangle.
Angle A:
=> Angle A = 180 - (90 + 45) = 45 degrees
Angle B:
=> Angle B = 180 - (90 + 35) = 55 degrees
Angle C:
=> Angle C = 180 - (45 + 55) = 80 degrees
As a result, the triangle's sides' measurements are as follows:
=> A is a 45 degree angle.
=> B is a 55 degree angle.
=> C is an 80-degree angle.
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if the median of a set of scores is greater than the mean, what can be said about the distribution? group of answer choices leptokurtic negatively skewed positively skewed platykurtic
If the median of a set of scores is greater than the mean, then the distribution will be option (c) It is positively skewed.
The relationship between the median and mean of a distribution can give an indication of the shape of the distribution. If the median is lower than the mean, it suggests that the distribution is positively skewed.
Option a) It is leptokurtic refers to the degree of peakedness of the distribution, which is not directly related to the relationship between the median and mean.
Option b) It is platykurtic refers to a distribution that has less peakedness than a normal distribution, which is also not directly related to the relationship between the median and mean.
Option d) It is negatively skewed is the opposite of the correct answer and suggests that the median is higher than the mean, indicating a negatively skewed distribution.
Therefore, the correct option is (c) It is positively skewed.
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The given question is incomplete, the complete question is:
If the median of a set of scores is lower than the mean, what does that suggest about the shape of the distribution?
Group of answer choices
a) It is leptokurtic
b) It is platykurtic
c) It is positively skewed
d) It is negatively skewed
Charlie's family is going to relax at the beach all day! In preparation, Charlie made s sandwiches for them to eat when they get hungry. Charlie put 3 slices of turkey and 3 slices of ham on each sandwich
Charlie can ensure that each sandwich contains 3 slices of turkey and 3 slices of ham, and can adjust the recipe as needed to suit his family's tastes and preferences.
Preparing food for a day at the beach can be a fun and fulfilling experience. Charlie decided to make sandwiches for his family to snack on when they get hungry. In this case, each sandwich contains 3 slices of turkey and 3 slices of ham.
The first step in making the sandwiches is to gather all the necessary ingredients. Charlie will need bread, turkey slices, ham slices, and any other desired condiments such as mayonnaise, mustard, lettuce, or tomato. He can choose any type of bread, but a sturdy bread such as a ciabatta, sourdough, or French bread would be ideal for a day at the beach.
To assemble the sandwiches, Charlie can follow these simple steps:
1. Lay out the bread slices. Charlie can choose to use one slice of bread per sandwich or two slices for a heartier sandwich.
2. Add a layer of mayonnaise or mustard if desired. Charlie can choose to spread the condiment on one or both slices of bread.
3. Add a layer of lettuce or tomato if desired. This can add some crunch and freshness to the sandwich.
4. Add 3 slices of turkey on one slice of bread, making sure they are evenly distributed. Charlie can choose to overlap the slices or lay them flat.
5. Add 3 slices of ham on top of the turkey slices, again making sure they are evenly distributed.
6. Top the sandwich with the other slice of bread, condiment-side down.
7. If desired, cut the sandwich in half or quarters for easy sharing and eating.
Charlie can repeat these steps for as many sandwiches as needed for his family. He can also customize the sandwiches by adding or subtracting ingredients, such as cheese, bacon, avocado, or pickles.
In terms of nutritional value, the sandwiches provide a good source of protein from the turkey and ham. The bread provides carbohydrates for energy, while the lettuce and tomato provide vitamins and minerals. The mayonnaise or mustard provides some fat and flavor, but can be skipped if desired.
Overall, making sandwiches for a day at the beach is a simple and convenient way to provide nourishing and satisfying food for the family. By following these steps, Charlie can ensure that each sandwich contains 3 slices of turkey and 3 slices of ham, and can adjust the recipe as needed to suit his family's tastes and preferences.
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Charlie's family is going to relax at the beach all day! In preparation, Charlie made s sandwiches for them to eat when they get hungry. Charlie put 3 slices of turkey and 3 slices of ham on each sandwich how does he adjust the situation ?
I NEED HELP ON THIS ASAP!!!!
Horace says that he determined the area of Rectangle ABCD by determining the product (CD) (CB). Bernice says that Horace is incorrect because he needs to use the base of the rectangle and that the base is AB, not CD. Horace responded by saying that CD is one of the bases. Who’s correct? Explain your reasoning.
Answer:
Horace
Step-by-step explanation:
You want to know if "base" refers to any particular side of a rectangle.
Area formulaThe formula for the area of a rectangle can be written ...
Area = base × height
It can also be written ...
Area = length × width
In each formula, the factors of the area refer to orthogonal dimensions of the rectangle. Any side of the rectangle can be considered to be the "base" or the "length" or the "width" or the "height". The other factor in the area formula is whatever dimension is orthogonal to that choice.
Properties of arithmeticThe commutative property of multiplication tells you that you get the same product if you reverse the order of the numbers.
So, you could have ...
Area = AB·BC
or
Area = BC·AB
If you insist that the fist of these numbers is the "base", then the base can be either AB or BC and the area will be the same.
The substitution property of equality tells you that you can substitute any equal values. Opposite sides of a rectangle are equal length, so either can be substituted for the other. In short, you can write the product for the area any of 8 ways:
Area = AB·BC = AB·AD = BC·AB = AD·AB
= CD·AD = CD·BC = AD·CD = BC·CD
If you want to distinguish between AB and BA, you can write this many more ways.
Horace seems to understand the fundamental interchangeability of the dimensions in the area formula. Horace has the right idea.
Bernice seems more attached to one particular understanding. We wonder what Bernice would call the "base" if the rectangle were drawn at a different angle to the grid.
complete the figure with 4-fold rotational symmetry. the point is the center of rotation.
By following these steps, we will have a figure with 4-fold rotational symmetry around the given center point.
To complete the figure with 4-fold rotational symmetry around the center point, follow these steps:
1. Identify the center of rotation:
As mentioned, the given point is the center of rotation.
2. Determine the existing shape or pattern:
Observe the figure and identify the existing shape or pattern to replicate.
3. Divide the circle around the center point into four equal sections (quadrants):
This can be done by drawing two lines that intersect at the center point, dividing the area around it into four equal parts (90 degrees each).
4. Replicate the existing shape or pattern in each quadrant:
Copy the shape or pattern in the first quadrant to the other three quadrants, keeping them equidistant from the center point.
5. Check for symmetry:
Ensure that when you rotate the figure 90 degrees, 180 degrees, or 270 degrees around the center point, it remains identical in appearance.
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