Answer The formula df = (c – 1) (r – 1) is used to find the degree of freedom – The degree of freedom of the chi-square test is calculated by the formula df = (c – 1) (r – 1), where c represents the column number of cell and r represents the row number of the cell.
A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory.
Sunglasses Inventory
Number of Days Total Amount of Sunglasses
2 54
5 48
7 44
10 38
Which of the following graphs shows the relationship given in the table?
A graph giving us a idea about relationship between the number of days and total amount of sunglasses is mentioned in the image attached below.
How to construct and plot the data on a graph?In this case, using Microsoft Excel, the number of days would be plotted on the x-axis (x-coordinate) of the scatter plot and the total number of sunglasses would be plotted on the y-axis (y-coordinate).
From the scatter plot (attached image) which shows the relationship between the number of days and total amount of sunglasses, a linear equation for the line of best fit is given by:
y = -2x + 62
Hence, we can reasonably infer and logically deduce that the scatter plot indicates an inverse relationship between the number of days and total amount of sunglasses.
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Answer:C
Step-by-step explanation:
at a fixed operating setting, the pressure in a line downstream of a reciprocating compressos os known to maintain a mean value of 12.0 bar with a standard deviation of 1.0 bar based on its history. what is the probability that the line presure will exceed 13.0 bar during any measurement
The probability that the line pressure will surpass 13.0 bars during any measurement is P [Z > 13] = 0,1587, or 15.87%.
If the line pressure exceeds 13.0 bars, there is a chance that:
P [ Z > 13 ] = 1 - P [ Z ≤ 13]
P [Z 13] will be located in the z table when z (score) =
Z (score) equals (Z - 0) /
Z = (13 - 12)/1 (score).
the z-table, we then discover
P [ Z ≤ 13] = 0,8413
Finally . P [ Z > 13 ] = 1 - P [ Z ≤ 13]
P [ Z > 13 ] = 1 - 0,8413
P [Z > 13] = 0,1587, which is equal to 15,87%.One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprovable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it.
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“The product of r and s is more than 4”
Answer: rs>4
Step-by-step explanation: The product of r and s just means rs. Then, when it says more than, you know its going to be a greater than sign: >. So your inequality would be rs>4
A. A fish is 12 m below the surface of the ocean. What is its elevation?
B. A seabird is 28 m above the surface of the ocean. What is its elevation?
C. If the bird is directly above the fish, how far apart are they?
Answer:
1.) -12
2.) 28
3.) 40
Step-by-step explanation:
The elevation of an object is the height or depth of the object relative to the sea level. If the object is above sea level, its elevation will be positive. However, if the object is below sea level, its elevation will be negative. Therefore, we can conclude that the elevation of the fish is -12 m because it is below sea level.
MODELING REAL LIFE Scientists rope off two excavation sites. Site A is rectangular with a length of $60$ meters and a width of $40$ meters. Site B is similar in shape to Site A but has a length of $45$ meters. How much rope is needed for both sites?
m=
By using unitary methods, the amount of rope is needed for both sites is 350 meters.
Unitary method is a mathematical problem-solving technique that involves finding the value of one unit and using it to calculate the value of other units.
Let's start by looking at Site A, which is a rectangular area with a length of 60 meters and a width of 40 meters. To surround this area with rope, we need to measure the perimeter, which is the distance around the site.
=> Perimeter = 2 (length + width)
=> 2(60 + 40)
=> 2 x 100
=> 200 meters
Therefore, we need 200 meters of rope to surround Site A.
Now let's move on to Site B, which is also rectangular but has a length of 45 meters. To find the width of Site B, we can use the fact that it is similar in shape to Site A. Similar shapes have the same angles and proportional sides, so we can use a unitary method to find the missing dimension.
The length ratio of Site B to Site A is
=> 45/60 = 3/4
Since the shapes are similar, the width of Site B must also be 3/4 of the width of Site A.
Width of Site B = 3/4 x 40 = 30 meters
Now we can use the same formula as before to find the perimeter of Site B:
Perimeter = 2 (length + width)
=> 2(45 + 30)
=> 2 x 75
=> 150 meters
Therefore, we need 150 meters of rope to surround Site B.
To find the total amount of rope needed for both sites, we simply add the two perimeters:
Total rope needed = 200 + 150 = 350 meters
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Pleaseh help me! Find the missing side length using trig!
Answe[tex]3\sqrt{2)[/tex]
Step-by-step explanation:
i need help………………………………
The domain and the range of the piecewise function for this problem are given as follows:
Domain D: All real values.Range R: [-2, ∞).How to find the domain and the range of a function?The domain of a function is the set that contains all the values assumed by the values of x of the function.The range of a function is the set that contains all the values assumed by the values of y of the function.For this problem, the piecewise function is defined for all values of x, hence the domain is all real values.
The range is obtained as follows:
Up to x = 3: Positive infinity to y = -2, which is the least value assumed at x = 3.From x = 3 to x = 5: values from y = 3 to y = 5, which are already in the range for the above interval.x = 5 and greater: constant at y = -1, which is already in the range.Hence the range is given as follows:
[-2, ∞).
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Which situation can be represented by y = 4x?
Responses
There are y cats and x dogs in a shelter. The cats and dogs each have 4 legs.
There are , y, cats and , x, dogs in a shelter. The cats and dogs each have 4 legs.
A recipe uses y cups of flour and x cups of sugar. The amount of flour is 4 times the amount of sugar.
A recipe uses , y, cups of flour and , x, cups of sugar. The amount of flour is 4 times the amount of sugar.
Tricia is y years old. This is 4 years older than her younger brother, Max, who is x years old.
Tricia is , y, years old. This is 4 years older than her younger brother, Max, who is , x, years old.
Sebastian buys y sacks of groceries. Each sack weighs 4 pounds. He carries x pounds of groceries home from the store.
Sebastian buys , y, sacks of groceries. Each sack weighs 4 pounds. He carries , x, pounds of groceries home from the store.
Answer:
a recipe uses y cups of flour and x cups of sugar the amount of flour is 4 times the amount of sugar
my proof I took the quiz
Jamila approximates the areas of circles
using the equation A = 3r², and records areas
of circles with different radius lengths in a table.
Is the relation a linear function? Explain.
Geometry!!!!! help me
The value of the unknown side length, BC, in given diagram is 28.3 ft
Similar triangles: Calculating unknown side length in a triangleFrom the question, we are to determine the value of the unknown side length in the given diagram
By similar triangles theorem, we can write that
AX/XY = AB/BC
From the given information,
AX = 12ft
XY = 17 ft
AB = AX + XB
= 12 ft + 8 ft
= 20 ft
BC = ?
Then, we can write that
12/17 = 20/BC
Cross multiply
12 × BC = 17 × 20
12 × BC = 340
BC = 340/12
BC = 28.3
Hence, the value of BC is 28.3 ft
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Now given your positive test result from test 2, what is doctor b's posterior probability for the hypothesis that you do have cogscitis?
The posterior probability of having cogscitis, given a positive test result from Test 2, is 0.0094 or about 0.94%. This indicates that even though you had a positive Test 2 result, the likelihood that you actually have CNS inflammation is still extremely low less than 1%.
With your positive test result from Test 2, we must apply Bayes' theorem to get Doctor B's posterior probability that you have cogscitis, which is:
P(A|B) = P(B|A) * P(A) / P(B)
The following probabilities are known:
P(A) = 0.001 (the population prevalence and previous likelihood of getting cogscitis)
P(B|A) = 0.95 (the possibility of receiving a positive Test 2 result while having cogscitis)
P(B|not A) = 0.10 (the possibility of receiving a positive test result from Test 2 even if you do not have cogscitis)
The law of total probability, which asserts the following, can be used to determine the marginal probability of a positive test result (P(B)):
P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)
where:
P(not A) = 1 - P(A) = 0.999 (the multiplier of the previous probability of contracting cogscitis)
Substituting the values, we get:
P(B) = 0.95 * 0.001 + 0.10 * 0.999 = 0.1008
The posterior probability of developing cogscitis can now be determined, given a positive test result from Test 2:
P(A|B) = P(B|A) * P(A) / P(B)
= 0.95 * 0.001 / 0.1008
= 0.0094
Therefore, the posterior probability of having cogscitis, given a positive test result from Test 2, is 0.0094 or about 0.94%. This indicates that even though you had a positive Test 2 result, the likelihood that you actually have CNS inflammation is still extremely low less than 1%.
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If all of the diagonals are drawn from a vertex of an n-gon, how many triangles are formed?A) n - 2B) n - 1C) nD) n + 1
The correct answer to the given question about all of the diagonals drawn from a vertex of an n-gon is option b) n-1
If all of the diagonals are drawn from a vertex of an n-gon, the number of triangles formed is equal to the number of non-diagonal sides of the n-gon. To see why, imagine selecting a vertex of the n-gon and drawing all of the diagonals from that vertex. Each diagonal connects that vertex to a non-adjacent vertex of the n-gon, which splits the n-gon into a series of triangles. The total number of triangles formed is equal to the number of non-diagonal sides of the n-gon, because each non-diagonal side forms one triangle with the selected vertex and one of its adjacent vertices. An n-gon has n sides, so the number of non-diagonal sides is equal to n - 3. This is because each vertex is connected to two adjacent vertices, so there are n - 2 diagonal sides emanating from the selected vertex, and the remaining n - 2 sides are non-diagonal. In addition, there are three sides at the selected vertex that are not counted as non-diagonal sides, so we subtract 3 from n - 2 to get n - 3. Therefore, the answer is (B) n - 1.
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Please anyone help me
The expression that represents all the possible widths of the rectangle is given as follows:
0 < x < 5.
How to obtain the area of the rectangle?The area of a rectangle of length l and width w is given by the multiplication of these dimensions, as follows:
A = lw.
For this problem, the length is 5 meters more than five times the width, hence:
l = 5 + 5w.
Hence the area is given as follows:
A = w(5 + 5w)
A = 5w² + 5w.
The area is less than 100m², hence the inequality is given as follows:
5w² + 5w < 100
5w² + 5w - 100 < 0.
w² + w - 20 < 0.
(w + 5)(w - 4) < 0.
Hence the solutions are:
w + 5 < 0 -> w < 5.w - 4 < 0 -> w > -4.The width cannot be negative, hence the interval is:
0 < x < 5.
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Grandpa Mick opened a pint of ice cream. He gave his youngest grandchild 1
5
of the ice cream and his
middle grandchild 1
4 of the remaining ice cream. Then, he gave his oldest grandchild 1
3
of the ice cream
that was left after serving the others
a. The oldest grandchild got the most ice cream.
b. The remaining ice cream will be represented by a fraction of 59/100 of the original amount.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
a. The oldest grandchild got the most ice cream.
b. Let's first calculate the fraction of the ice cream that was left after serving the youngest and middle grandchild.
The youngest grandchild received 1/5 of the ice cream, which means 4/5 was left.
Then the middle grandchild got 1/4 of the remaining 4/5, which is 1/5. So 4/5 - 1/5 = 3/5 of the ice cream is left.
Now, if Grandpa Mick serves himself the same amount as the second grandchild (1/4 of the original amount), he will be taking 1/4 of 1/5 of the original amount, which is 1/20.
So the remaining ice cream will be 3/5 - 1/20 = 59/100 of the original amount.
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The question seems incomplete, the missing part would be as:
Grandpa Mick opened a pint of ice cream. He gave his youngest grandchild 1/5 of the ice cream and his middle grandchild 1/4 of the remaining ice cream. Then, he gave his oldest grandchild 1/3 of the ice cream that was left after serving the other. a. Who got the most ice cream? b. What fraction of the pint of ice cream will be left if Grandpa Mick serves himself the same amount as the second grandchild?
Kofi says the circumference of a circle equals pi times the diameter. Skyla says that the circumference of a circle equals pi times the radius. Who do you agree with? Explain why? the picture is the real problem
I agree with Kofi that the circumference of a circle equals pi times the diameter. This is because the formula for the circumference of a circle is given by:
C = 2πr
Where C is the circumference, π is pi, and r is the radius of the circle. To find the diameter, we can double the radius, so we can write:
C = 2π(r) = π(2r) = πd
Where d is the diameter of the circle.
So, the formula for the circumference of a circle is indeed pi times the diameter, not just pi times the radius.
Alicia's doctor allowed her to eat junk food every fifth day. If Alicia had junk food on Monday and Saturday, what are the next two days that she will be allowed to have junk food?
The next two days when Alicia would be allowed to eat junk foods are Thursday and Tuesday.
When would Alicia eat junk food?The first day after Saturday when Alicia would have junk food can be determined by counting the fifth day after Saturday.
Sunday - first day
Monday - second day
Tuesday - third day
Wednesday - fourth day
Thursday - fifth day
The next day after Thursday when Alicia would have junk food is the fifth day after Thursday.
Friday - first day
Saturday - second day
Sunday - third day
Monday - fourth day
Tuesday - fifth day
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The slope-intercept form of a line is y=2/3x + 2. Which line is perpendicular and shifted down 8?
The slope-intercept form of a line is y=2/3x + 2, the line is perpendicular and shifted down 8 is y = -3/2x - 6.
The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept. In the given equation, y = 2/3x + 2, the slope is 2/3 and the y-intercept is 2.
To find a line that is perpendicular to this line, we need to find a line that has a slope that is the negative reciprocal of the slope of the given line. The negative reciprocal of 2/3 is -3/2, so the slope of the new line will be -3/2.
Now we need to find the equation of the new line in slope-intercept form. We know the slope of the line (-3/2), so we can substitute this value for m in the slope-intercept form and get:
y = -3/2x + b
To find the value of b, which is the y-intercept of the new line, we need to use the fact that the line is shifted down 8 units. We can do this by subtracting 8 from the y-intercept of the given line (which is 2), to get:
b = 2 - 8 = -6
So the equation of the line that is perpendicular to y = 2/3x + 2 and shifted down 8 units is:
y = -3/2x - 6
This line has a slope of -3/2, which is the negative reciprocal of the slope of the given line, and a y-intercept of -6, which is 8 units lower than the y-intercept of the given line.
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What is the end behavior of f(x)?
f(x) = -252x+6x³ +30x² - 864
as x→→∞, f(x) → ∞ and as x→∞, f(x) →∞
as x-x, f(x) → ∞ and as a →∞, f(x) →→∞
as x-x, f(x) → ∞ and as a →x, f(x) →∞
as x→→∞, f(x) →→∞ and as x →∞, ƒ(x) →→∞
Answer: 27
Step-by-step explanation:
jeremy's average for 11 math tests is 80. His teacher announced that the students could eliminate any one of their test grades then recompute their average. Jeremy eliminated 30 on his first test. what is his average now?
Answer: His average is 85 now.
Step-by-step explanation:
Average is the sum of all his math tests divided by the number of the math tests he took, so we get:
[tex]\frac{sum }{11}=80[/tex]
sum = 11 x 80
sum = 880
880 - 30, we get 850, which becomes the new sum of the 10 math test scores, because he eliminated one test score.
[tex]\frac{850}{10} =85[/tex]
His average is 85 now.
Question is in picture - a detailed explanation would be very apricated.
Answer:
$1350.68 to nearest cent.
Step-by-step explanation:
At the beginning $500 is deposited and this accumulates interest for 3 years At the end of first year it increases to 500( 1 + r) dollars
Then at the end of the 2 years its value is
500(1+ r)(1 + r)(
and at the end of 3 years value =
500(1 + r)(1 + r)(1 + r)
= 500(1 + r)^3 dollars
and as 1 + r = x we have:
500x^3 dollars
In the same way 200 for 2 years = 200x^2
and 600 for 1 year = 600x dollars.
Total = 500x^3 + 200x^2 + 600x.
b.
So, if the interest r = 2 % (= 0.02)
and x = 1.02
Total value after 3 years
= 500(1.02)^3 + 200(1.02)^2 + 600(1.02)
= 530.604 + 208.08 + 612
= $1350.684
A company makes short-sleeved and long-sleeved T-shirts. The company checks a random sample of 60 T-shirts of each type. It finds that 4 short-sleeved shirts have problems and 1 long-sleeved shirt has problems. How many T-shirts should the company predict have problems in a shipment of 3,000 shirts of each type?
The company should predict that there will be an estimated 201 short-sleeved T-shirts and 51 long-sleeved T-shirts with problems in a shipment of 3,000 shirts of each type.
To predict the number of T-shirts with problems in a shipment of 3,000 short-sleeved and 3,000 long-sleeved T-shirts, we can use the proportion of T-shirts with problems in the random sample as an estimate of the proportion of T-shirts with problems in the population.
For short-sleeved T-shirts, the proportion of T-shirts with problems in the sample is 4/60 = 0.067. For long-sleeved T-shirts, the proportion of T-shirts with problems in the sample is 1/60 = 0.017.
To estimate the number of short-sleeved T-shirts with problems in a shipment of 3,000, we can multiply the proportion by the total number of short-sleeved T-shirts in the shipment:
Estimated number of short-sleeved T-shirts with problems = 0.067 x 3,000 = 201
Similarly, to estimate the number of long-sleeved T-shirts with problems in a shipment of 3,000, we can multiply the proportion by the total number of long-sleeved T-shirts in the shipment:
Estimated number of long-sleeved T-shirts with problems = 0.017 x 3,000 = 51
Therefore, the company should predict that there will be an estimated 201 short-sleeved T-shirts and 51 long-sleeved T-shirts with problems in a shipment of 3,000 shirts of each type.
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The vector u has length 10 and points at an angle of 5°
The vector has length 16 and points at an angle of 25°
The dot product between u and v is 150.35 units²
What is dot productIn the problem given;
u = 10cos5
v = 16cos25
To find the dot product of two vectors, we need to find the product of the magnitude of the vectors and the cosine of the angle between them. Let's call the angle between the vectors θ.
The dot product of u and v is given by:
u•v = |u| * |v| * cos(θ)
where |u| and |v| are the magnitudes of vectors u and v. We are given the magnitudes of the vectors, which are |u| = 10 and |v| = 16.
To find cos(θ), we need to use the dot product formula with the given angle values:
cos(θ) = (u•v) / (|u| * |v|) = (|u| * |v| * cos(θ)) / (|u| * |v|)
Since u and v are both vectors in 2-dimensional space, we can use the law of cosines to find the angle between them:
cos(θ) = (u•v) / (|u| * |v|) = (u1 * v1 + u2 * v2) / (|u| * |v|)
where u1 and u2 are the components of vector u and v1 and v2 are the components of vector v.
To find the components of the vectors, we need to use the given angle values and the magnitudes of the vectors:
u1 = |u| * cos(5°) = 10 * cos(5°)
u2 = |u| * sin(5°) = 10 * sin(5°)
v1 = |v| * cos(25°) = 16 * cos(25°)
v2 = |v| * sin(25°) = 16 * sin(25°)
Substituting these values into the formula for cos(θ), we get:
cos(θ) = (u1 * v1 + u2 * v2) / (|u| * |v|) = (10 * cos(5°) * 16 * cos(25°) + 10 * sin(5°) * 16 * sin(25°)) / (10 * 16)
θ = 20°
u.v = 10 * 16 * cos 20
u.v = 150.35
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Solve for x. Leave your answer in simplest form
Answer:
Step-by-step explanation:x=28
A fruit Juice blend is made by mixing the juice of oranges and apples in the ratio 7:5 If 168 litres of orange juice is used How much litres of Apple juice must be used ?
A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
If the ratio is 7: 5 (oranges to apples) we can use this equation to solve the problem:
168 × 0.714285714 = 120Why do we multiply by 0.714285714?We multiply by 0.714285714 because we can see that 7 is being multiplied by 0.714285714 to get 5.
Therefore, if the ratio stays proportional, you will need 120 litres of apple juice for every 168 litres of orange juice.
The Jacob family plans to attend a concert. An
adult ticket (a) is $7.50 each and a child's ticket (c)
is $5.00 each. Mr. Jacob purchased a total of 11
tickets for a total of $65. How many of each kind of
ticket was purchased?
Answer:Mr. Jacob purchased 7 adult tickets at $7.50 each, and 4 child tickets at $5.00 each, for a total of 11 tickets at a cost of $65.
Step-by-step explanation:
Lin is shopping for a couch with her dad and hears him ask the salesperson, "How much is your commission?" The salesperson says that her commission is 6% of the selling price. How much commission will the salesperson earn by selling a couch for $495?
The commission amount the salesperson earn is $29.7.
What is a percentage?The percentage formula is dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Selling price = $495
Commission = 6%
Now,
The amount of commission.
= 6% of 495
= 6/100 x 495
= 29.7
Thus,
The commission the salesperson earn is $29.7.
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i need this fast Question 7(Multiple Choice Worth 1 points) (05.02 MC) At a local play, student tickets cost $5 each and adult tickets cost $10 each. If ticket sales were $3,000 for 500 tickets, how many students attended the play? 100 200 300 400
The number of students attended the play are 400 in number.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
At a local play, student tickets cost $5 each and adult tickets cost $10 each. If ticket sales were $3,000
5x+10y=3000
The total number of tickets are 500
x+y=500
y=500-x
Now plug this in above equation
5x+10(500-x)=3000
5x+5000-10x=3000
5000-5x=3000
Add 5x on both sides
5000-3000=5x
2000=5x
Divide both sides by 5
400=x
Hence, the number of students attended the play are 400 in number.
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Daniella and her 10 friends are collecting shells on the beach to make crafts. After
they have collected the shells and put them in a pile, they split them evenly among
the group. Each person gets 4 shells. How many shells did they collect as a group?
Select the correct equation and solve for s.
4+ s = 11; s = 7
s/10 = 4; s = 40
4s = 11; s = 2.75
s/11 = 4; s = 44
Daniella and her friends collected a total of 44 shells.
What is linear equation ?
Linear equation can be defined as equation in which highest degree is one.
Given ,
Daniella and her 10 friends are collecting shells on the beach to make crafts.
After they have collected the shells and put them in a pile, they split them evenly among the group. Each person gets 4 shells.
The correct equation for this problem is:
s = 11 x 4
where s is the total number of shells collected.
Simplifying this equation, we have:
s = 44
Therefore, they collected a total of 44 shells.
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please help solve it
The statement that describes the conversion is To find the weight in pounds, multiply the number of ounce by the unit rate 16 ounces per pound
How to complete the statement that describes the conversionFrom the question, we have the following parameters that can be used in our computation:
The double number line
On the double number line, we have:
16 ounces = 1 pound
This means that
To find the weight in pounds, multiply the number of ounce by the unit rate 16 ounces per pound
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On a hike, William passed a sign that said his elevation was 20 1/2 feet
above sea level. He hiked downhill for a while longer until his elevation had
decreased by 28 feet. What is his new elevation?
Answer:
-7.5 OR -7 1/2
Step-by-step explanation:
20.5 - 28 = -7.5
OR
20 1/2 - 28 = -7 1/2
