The maximum area for each pig pen is 156 square feet. The total length of fencing available is 312 feet. We also know that the two pig pens share a common side, so we can assume that the other three sides of each pen are independent rectangles.
The length of the common side "x" and the width of each pen "y". Since the total area is divided in half by the common side, we can write an equation:
2(xy/2) = x*y
xy = 156
A = xy
y = 156/x
Substituting this expression for y into the formula for the area, we get:
A = x(156/x)
A = 156 - x^2/2
This is a quadratic equation in standard form, with a = -1/2, b = 0, and c = 156. The vertex of the parabola is at x = -b/2a = 0, which means that the maximum area occurs when x is at the midpoint of the fencing available, which is 156/2 = 78
feet.
y = 156/78 = 2
The dimensions of each pig pen are 78 feet by 2 feet, and the maximum area of each pen is:
A = 78*2 = 156 square feet.
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[tex]v = u + at[/tex]
determine whether the variable (v) is the subject of the formula
The subject of the linear formula v = u + at is the isolated variable, which in this case is v.
Which variable is the subject of a formula?The subject of a formula is the variable (which is usually called the dependent variable ) that is being worked out, this is, the variable that is isolated in one of the sides of the formula.
In this case, we have a relation:
v = u + a*t
So v is equal to u plus the product between a and t.
We can see that v is the isolated variable, thus, v is the subject of the formula.
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.in a production scheduling LP, the demand requirement constraint for a time period takes the form
a) beginning inventory + production + ending inventory ⥠demand
b) beginning inventory + production + ending inventory = demand
c) beginning inventory + production - ending inventory = demand
d) beginning inventory - production + ending inventory ⥠demand
The correct option for the demand requirement constraint in a production scheduling LP is option (c): beginning inventory + production - ending inventory = demand.
In a production scheduling LP, the demand requirement constraint represents the balance between the available inventory and the demand for the product. The constraint ensures that the production and inventory levels are sufficient to meet the specified demand.
Option (c) represents this relationship accurately by stating that the beginning inventory, production, and ending inventory, when subtracted from each other, should equal the demand. This equation reflects the concept of maintaining a balance between the production output and inventory changes to meet the demand
Option (a) is incorrect because it uses the greater than or equal to (≥) symbol, which does not accurately represent the constraint.
Option (b) is also incorrect because it uses the equality (=) symbol, which implies an exact balance between the inventory and demand, disregarding the changes in inventory.
Option (d) is incorrect because it uses the greater than or equal to (≥) symbol, which does not accurately represent the constraint.
Therefore, option (c) is the correct representation of the demand requirement constraint in a production scheduling LP.
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which of the following would be a bernoulli distribution? a litter of puppies time between visits to a doctor's office flipping a coin rolling a 5-sided die all of the above are bernoulli distributions
A Bernoulli distribution is a probability distribution of a single random experiment that can have only two outcomes, success or failure. Therefore, flipping a coin and rolling a 5-sided die cannot be Bernoulli distributions as they have more than two possible outcomes.
However, the time between visits to a doctor's office can be considered a Bernoulli distribution if we define success as visiting the doctor within a certain time frame and failure as not visiting the doctor within that time frame. A litter of puppies cannot be modeled using a Bernoulli distribution as it involves multiple events/outcomes. It is essential to note that Bernoulli distributions are used to model a single trial, whereas distributions such as the binomial and Poisson distributions are used for multiple trials or events.
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Find tan a.
(-15, 8)
Answer:
The tan of angle A is equal to a/b, where a and b are the lengths of the opposite and adjacent sides of the angle respectively. In this case, we have a = 15, b = 8, which gives us a tan of 15/8 or approximately 1.875.
the concept of hedonistic calculus is associated with
The concept of hedonistic calculus is associated with utilitarianism and the philosophy of maximizing pleasure and minimizing pain. It is a method for calculating the overall happiness or utility of actions based on the intensity, duration, certainty, propinquity, fecundity, purity, and extent of pleasure or pain they produce.
Hedonistic calculus is a term coined by the philosopher Jeremy Bentham, who was a proponent of utilitarianism. Utilitarianism is an ethical theory that states that the right action is the one that maximizes overall happiness or utility for the greatest number of people. The goal of hedonistic calculus is to measure and compare the happiness or pleasure derived from different actions or situations.
According to Bentham, pleasure and pain are the only relevant factors in determining the moral value of an action. Hedonistic calculus involves quantifying these pleasures and pains in order to assess their overall impact. Bentham proposed seven criteria to evaluate the intensity, duration, certainty, propinquity (nearness in time), fecundity (likelihood of leading to more pleasure or pain), purity (absence of pain mixed with pleasure), and extent of the pleasure or pain produced by an action.
By assigning values to each of these criteria, hedonistic calculus aims to determine the net amount of happiness or utility generated by a particular action or decision. The idea is to maximize pleasure and minimize pain, with the ultimate goal of promoting the greatest happiness for the greatest number of individuals.
Overall, hedonistic calculus provides a systematic approach to assess and compare the consequences of actions based on their impact on pleasure and pain. It serves as a framework for utilitarians to make ethical judgments and decisions by considering the net balance of happiness produced by different choices.
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Geometry. Math nation section 3
∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements from the given information
Two angles are given.
∠g = (2x-90)°
∠h = (180-2x)°
We have to find the statement which is true about the angles g and h.
If both angles are greater than zero.
Complementary angles add up to 90 degrees
i.e., ∠g and ∠h are complementary if ∠g + ∠h = 90°.
Substituting the given values:
∠g + ∠h
= (2x-90)° + (180-2x)° = 90°
Thus, ∠g and ∠h are complementary angles.
and both the angles are less than 90 degrees so we can tell that angles ∠g and ∠h are acute.
So the statement ∠g and ∠h are acute angles is also true
Hence, ∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements
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of all the lightbulbs manufactured at a certain factory, 95% of the lightbulbs work and 5% are defective. if six lightbulbs are selected at random from the shipment, what is the probability that at least one of them is defective?
To calculate the probability that at least one of the six lightbulbs selected from the shipment is defective, we need to first calculate the probability that all of them work and then subtract that from 1. Therefore, the probability that at least one of the six lightbulbs is defective is 0.2649 or 26.49%.
The probability that a single lightbulb is defective is 0.05 and the probability that it works is 0.95. Therefore, the probability that all six lightbulbs work is:
0.95 x 0.95 x 0.95 x 0.95 x 0.95 x 0.95 = 0.7351
To calculate the probability that at least one of the six lightbulbs is defective, we need to subtract this from 1:
1 - 0.7351 = 0.2649
Therefore, the probability that at least one of the six lightbulbs is defective is 0.2649 or 26.49%. In other words, there is a little over a one in four chance that at least one of the six lightbulbs selected is defective.
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Suppose you are interested in uncovering the relationship between snowfall (in inches) in the month of December and the flow rate of Yosemite Falls in April (in cubic meters per second) over the span of years from 2005 to 2010 (inclusive). You observe the following snowfall and Yosemite Falls flowrate data: December Snowfall (X)=[16,19,18,16,20,17] and April Flowrate (Y)=[22,23,21,18,26,21]. What is TSS?
Group of answer choices
About 4.37
About 6.27
About 13.33
About 22.46
None of the above are close
Answer:
The correct answer is About 6.27.
TSS stands for total sum of squares. It is a measure of the variation in the data. It is calculated as follows:
TSS = Σ(y - y^)^2
Where:
y is the observed value
y^ is the predicted value
In this case, the observed values are the December snowfall data and the predicted values are the April flowrate data.
TSS = (22 - 20.81)^2 + (23 - 21.7)^2 + (21 - 20.09)^2 + (18 - 19.28)^2 + (26 - 23.36)^2 + (21 - 20.55)^2
TSS = 6.27
Step-by-step explanation:
The Total Sum of Squares (TSS) can be calculated by first finding the mean of the dataset, then subtracting this mean from each data point, squaring the result, and summing all these squared differences. The TSS for the provided dataset is approximately 34, not among the given choices, thus 'None of the above are close' is the correct answer.
Explanation:In this problem, we're asked to calculate the Total Sum of Squares (TSS), a statistical measure used to understand the variability in a dataset. For the given set of April Flowrate (Y) values, we first calculate the mean (average), which is (22+23+21+18+26+21) / 6 = 21.83 (rounded to 2 decimal places).
We then subtract this mean from each Y value, square the result, and add them together to get TSS. The calculation would proceed as follows:
(22-21.83)² = 0.0289(23-21.83)² = 1.3589(21-21.83)² = 0.6889(18-21.83)² = 14.7889(26-21.83)² = 17.4489(21-21.83)² = 0.6889The total sum of these squared differences gives us the TSS:
0.0289 + 1.3589 + 0.6889 + 14.7889 + 17.4489 + 0.6889 = 34.0034
So, the TSS for the described data set is roughly 34, which is not among the provided answer choices, so the correct answer is 'None of the above are close'.
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What is
3x - 4 (2x5) = 2 (x-1) + 5/2
6. Mr. Beal surveys all the students in his Geometry class and identifies these probabilities.
The probability that a student has gone to United Kingdom is 0.23.
The probability that a student has gone to China is 0.48.
The probability that a student has gone to both United Kingdom and China is 0.14.
What is the probability that a student in Mr. Beal class has been to United Kingdom or China?
What are the domain and range of f(x) = (one-sixth) Superscript x + 2?
Answer:
The domain of a function is the set of all possible values for the input variable (x), while the range is the set of all possible values for the output variable (f(x)).
For the function f(x) = (1/6)^x + 2, the domain includes all real numbers, since any value of x can be raised to any power.
To find the range, we can look at the behavior of the function as x approaches positive and negative infinity. As x approaches negative infinity, (1/6)^x becomes very large, so f(x) approaches 2. As x approaches positive infinity, (1/6)^x becomes very small, so f(x) approaches 2 as well. Therefore, the range of the function is (2, infinity).
t (minutes) = 0, 4, 7, 9.
r(t) (gallon per minutes) = 9, 6, 4, 3.
Water is flowing into a tank at the rate r(t), where r(t) is measured in gallons per minute and t is measured in minutes. The tank contains 15 gallons of water at time t = 0. Values of r(t) for selected values of t are given in the table above. Using a trapezoidal sum with the three intervals indicated by the table, what is the approximation of the number of gallons of water in the tank at time t = 9? (A) 52
(B) 57 (C) 67 (D) 77 (E) 79
The approximation of the number of gallons of water in the tank at time 9 min. is 52 gallons.
Using the trapezoidal sum, the approximation of the number of gallons of water in the tank at time t = 9 is given by:
Approximation =[tex][((t_1 - t_0) / 2) * (r(t_0) + r(t_1))] + [((t_2 - t_1) / 2) * (r(t_1) + r(t_2))] + [((t_3 - t_2) / 2) * (r(t_2) + r(t_3)))][/tex]
where [tex]t_0 = 0, t_1 = 4, t_2 = 7, t_3 = 9[/tex].
Substituting the given values of r(t), we get:
Approximation = [((4 - 0) / 2) * (9 + 6)] + [((7 - 4) / 2) * (6 + 4)] + [((9 - 7) / 2) * (4 + 3))]
= (2 * 15) + (1.5 * 10) + (1 * 7)
= 30 + 15 + 7
= 52
Therefore, the approximation of the number of gallons of water in the tank at time t = 9 is 52 gallons. The answer is (A) 52.
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Which irrational number can be multiplied by -~ 41 to get a product that equals 1?
The irrational number can be multiplied by -~ 41 to get a product that equals 1 is 1/[tex]-\sqrt{41}[/tex] the correct option is A.
We are given that;
The number= [tex]-\sqrt{41}[/tex]
Now,
To find the irrational number that can be multiplied by sqrt(41) to get a product that equals 1, we need to find the multiplicative inverse of sqrt(41). The multiplicative inverse of a number is the number that when multiplied by the original number gives 1 as the product. For example, the multiplicative inverse of 2 is 1/2, because 2 * 1/2 = 1.
To find the multiplicative inverse of sqrt(41), we can divide 1 by sqrt(41). We get:
[tex]1 / \sqrt{41} = \sqrt{41} / \sqrt{41} \times \sqrt{41}) = \sqrt{41} / 41[/tex]
To simplify the expression, we can rationalize the denominator by multiplying both the numerator and the denominator by sqrt(41). We get:
[tex]\sqrt{41} / 41 \times \sqrt{41} / \sqrt{41} = (\sqrt{41})^2 / (41 \times \sqrt{41}) = 41 / (41 \times\sqrt{41}) = 1 / \sqrt{41}[/tex]
Therefore, by the fraction the answer will be 1/[tex]-\sqrt{41}[/tex].
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The period T, in seconds, of a simple pendulum as a function of its length l, in feet, is given by T(l)=2π 32. 2 l. Express l as a function of T and determine the length of a pendulum with period of 2 seconds. Use 3. 14 for π and round to the nearest hundredth
The length of a pendulum with a period of 2 seconds is approximately 51.
the formula for the period of a simple pendulum as a function of its length is given as:
t(l) = 2π √(l/32.2)
we can rearrange this equation to solve for l:
t(l) = 2π √(l/32.2)
t(l)/(2π) = √(l/32.2)
[t(l)/(2π)]² = l/32.2
l = 32.2 * [t(l)/(2π)]²
to determine the length of a pendulum with a period of 2 seconds, we can substitute t = 2 seconds into the equation above:
l = 32.2 * [2/(2π)]²
l = 32.2 * [1.2732]²
l ≈ 51.92 feet 92 feet when π is taken to be 3.14 and rounding to the nearest hundredth.
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If Un+1 = 2U₁ + 6 and Uo = 10 find U₁
Answer:U₁ = 2
.
Step-by-step explanation:
Un+1 = 2U₁ + 6 (Equation 1)
Uo = 10
We want to find U₁. We can start by using Equation 1 with n = 1 to get:
U2 = 2U₁ + 6
We can then use the value of Uo = 10 to find U₂ as follows:
U₂ = 2U₁ + 6
U₂ = 2U₁ + 2(3)
U₂ = 2(U₁ + 3)
We can then use the value of U₂ to find U₃:
U₃ = 2U₂ + 6
U₃ = 2(2U₁ + 2(3)) + 6
U₃ = 4U₁ + 12 + 6
U₃ = 4U₁ + 18
We can keep using this process to find Un in terms of U₁, until we reach the value of n we need. For example, we can find U₄ as follows:
U₄ = 2U₃ + 6
U₄ = 2(4U₁ + 18) + 6
U₄ = 8U₁ + 36
So we have:
Uo = 10
U₂ = 2(U₁ + 3)
U₃ = 4U₁ + 18
U₄ = 8U₁ + 36
and so on.
To find U₁, we need to use the equation for U₂:
U₂ = 2(U₁ + 3)
Substituting U₂ = 10 (from the given value of Uo), we get:
10 = 2(U₁ + 3)
Simplifying, we get:
5 = U₁ + 3
Subtracting 3 from both sides, we get:
U₁ = 2
Therefore, U₁ = 2.
How to plot a 2/3 and 3/4 on a number line
Hello
2/3 = 8/12
3/4 = 9/12
9/12
0 - - - - - - - - - - - - 1 - - - - - - - - - - - - 2
8/12
Answer :
3/4
0 - - - - - - - - - - - - 1 - - - - - - - - - - - - 2
2/3
=> 2/3 = the 8th graduation
=> 3/4 = the 9th graduation
=> 1 unit = 12 graduations
Screenshot is shown below.
The best words to fill the sentence on graph inequality is;
Kaniia correctly used a test point to determine what inequality to use. Ileana incorrectly used the location of shading to determine what inequality to use. The student with the correct answer is Kaniia.
How do we know that Kanila has the right graph inequality?The inequality is y > 3/4x - 3 is most appropriate. This is because the shaded area is above the line, indicating that y is greater than 3/4x - 3.
Kaniia correctly identified her inequality by using a test point (0,0) whereas Ileana's inequality is telling indicating that y is less than 3/4x - 3. When the shaded area is above y, it means that y is greater.
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The pythagorean Theorem please help me with this asap!! this is due!!
The missing length in the right triangle is 12 m by pythagorean theorem
The pythagorean theorem can only be applied to right triangles
The longest side of a right triangle is called hypotenuse the other two sides are legs
You can use this theorem to find a missing length or to prove a triangle is right triangle
The missing length in the right triangle with hypotenuse is 13 m and adjacent side is 5m
13²=5²+x²
169=25+x²
144=x²
x=12 m
Hence, the missing length in the right triangle is 12 m
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consider an infinitely long three-sided triangular enclosure with side lengths 2 cm, 3 cm, and 4 cm. the view factor from the 2 cm side to the 4 cm side is
The view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.
The view factor (F) from Surface A to Surface B can be calculated using the formula:
F = A / (A + B)
where A and B are the areas of Surface A and Surface B, respectively.
The area of a triangle can be calculated using Heron's formula:
Area = sqrt(s * (s - a) * (s - b) * (s - c))
where s is the semi-perimeter of the triangle and a, b, and c are the side lengths of the triangle.
For Surface A:
a = 2 cm
b = 3 cm
c = 4 cm
s = (a + b + c) / 2 = (2 + 3 + 4) / 2 = 4.5 cm
Area_A = sqrt(4.5 * (4.5 - 2) * (4.5 - 3) * (4.5 - 4))
= √(4.5 * 2.5 * 1.5 * 0.5)
=√(5.625) ≈ 2.37 cm²
For Surface B:
a = 2 cm
b = 4 cm
c = 3 cm
s = (a + b + c) / 2 = (2 + 4 + 3) / 2 = 4.5 cm
Area_B = √(4.5 * (4.5 - 2) * (4.5 - 4) * (4.5 - 3))
= √(4.5 * 2.5 * 0.5 * 1.5)
=√(5.625) ≈ 2.37 cm²
Now we can calculate the view factor (F):
F = Area_A / (Area_A + Area_B)
= 2.37 / (2.37 + 2.37)
≈ 0.5
Therefore, the view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.
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An air-conditioning specialist recommends 2 air vents for every 300 f t squared of floor space. At this rate, how many air vents are required for an office building of 21,000 f t squared?
An office building of 21,000 f t squared would require 140 air vents according to the recommendation of 2 air vents for every 300 f t squared of floor space.
Based on the recommendation of 2 air vents for every 300 f t squared of floor space, we can calculate the number of air vents required for an office building of 21,000 f t squared by dividing the total floor space by 300 and multiplying the result by 2.
21,000 / 300 = 70
70 x 2 = 140
Therefore, an office building of 21,000 f t squared would require 140 air vents according to the recommendation of 2 air vents for every 300 f t squared of floor space.
It is important to note that this is just a recommendation and the actual number of air vents required may vary depending on factors such as ceiling height, insulation, and other building characteristics. It is always best to consult with an HVAC specialist to determine the appropriate number and placement of air vents for optimal air circulation and comfort in a building.
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Sketch the triangle ABC and solve it using the law of cosines. Round off your answers to the nearest integer. b = 60, c = 30, ∠A = 70∘
Ams: a = 57, ∠B = 81∘, and ∠C = 29∘
Answer:
Sure. Here are the steps on how to solve for the sides and angles of triangle ABC using the law of cosines:
Draw a sketch of triangle ABC.
Label the sides and angles of triangle ABC.
Label the known and unknown values.
Use the law of cosines to solve for the unknown side or angle.
In this case, we know the following:
Side b = 60
Side c = 30
Angle A = 70°
We need to solve for side a and angles B and C.
The law of cosines states that
a^2 = b^2 + c^2 - 2bc cos A
where a, b, and c are the sides of the triangle and A is the angle opposite side a.
Plugging in the known values, we get
a^2 = 60^2 + 30^2 - 2(60)(30) cos 70°
a^2 = 900 + 900 - 3600 cos 70°
a^2 = 1800 - 3600 cos 70°
a = sqrt(1800 - 3600 cos 70°)
a = 57
Therefore, side a is 57.
To solve for angle B, we can use the law of sines. The law of sines states that
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
Plugging in the known values, we get
\frac{57}{\sin 70°} = \frac{60}{\sin B}
\sin B = \frac{57 \sin 70°}{60}
\sin B = 0.774
B = \sin^{-1}(0.774)
B = 81°
Therefore, angle B is 81°.
To solve for angle C, we can use the fact that the sum of the angles of a triangle is 180°.
A + B + C = 180°
70° + 81° + C = 180°
C = 29°
Therefore, angle C is 29°.
Therefore, the sides and angles of triangle ABC are a = 57, b = 60, c = 30, A = 70°, B = 81°, and C = 29°.
Step-by-step explanation:
3 green ties and 4 pink ties are in a dresser. What is the probability of drawing out 1 green tie without looking? Write your answer as a decimal rounded to two decimal places.
The probability of drawing one paisley tie is 0.43
How to find the probability of drawing one paisley tie?Three paisley ties and four solid ties are in a dresser. Therefore, the probability if drawing out one paisley tie without looking can be calculated as follows:
The total number of ties is the sum of the paisley ties and solid ties, which is 3 + 4 = 7.
Therefore, the probability of drawing out 1 paisley tie without looking is as follows:
probability of drawing out 1 paisley tie without looking = 3 / 7
probability of drawing out 1 paisley tie without looking = 0.42857142857
Hence , the probability of drawing out one paisley tie without looking is 0.43
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why is it on the left equation a positive result and on the right side, an negative result?
Answer:
[tex] {( - x)}^{4} = {( - 1)}^{4} {x}^{4} = {x}^{4} [/tex]
[tex] {( - b)}^{19} = {( - 1)}^{19} {b}^{19} = - {b}^{19} [/tex]
HOW DO U SOLVE THIS. HELP PLS
what is the area of a quadrilateral with vertices at p(3, 4), m(8, 4), n(5, 0), and the origin (0,0)?
The quadrilateral has a area of 10 square units.
Because the vertices of the quadrilateral are p(3, 4), m(8, 4), n(5, 0).
This quadrilateral can be divided into two triangles.
For the first triangle, we can say that p(5) is the base and m(4) is the height.
Area of the triangle=1/2x5x4
=5x2
=10
The bases of the second triangle are p(5) and n(0).
Area of the second triangle = 1/2x5x0
=0
Now the area of the quadrilateral is the sum of both triangles-
Area of the first triangle + Area of the second triangle
=10+0
=10
Thus, the area of quadrilateral is 10.
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Explain step by step
Answer:
$123,809.52
Step-by-step explanation:
The total bill is equal to the purchase price of the fridge/freezer plus the sales tax.
Total = Price + Tax
We know the total is 130,000.
We don't know the price, so let's call it x.
The tax is 5% of the price, or ⁵/₁₀₀ x, or 0.05 x.
130,000 = x + 0.05 x
130,000 = 1.05 x
x = 123,809.52
Why is 9.2% written as .092 in decimal form?
Answer:
Normally, to calculate 9.2 percent, you would multiply a number by 9.2 percent and then you would take the product of that and divide it by 100 to get the answer.
Instead, you can simply multiply a number by 9.2 as a decimal to get the answer.
9.2 percent means 9.2 per hundred. Therefore, to get 9.2 as a decimal, all you have to do is divide 9.2 by 100 like so:
9.2 ÷ 100 = 0.092
Shortcut: When you divide anything by 100, just move the decimal point two places to the left.
Step-by-step explanation:
Ezra's ice Cream Shop has two stores, the old store and the new store. Both stores sell ice cream and milkshakes. One year's sales at the two stores are shown in the table. (Hint: make a totals margin to help find theconditional probabilities)
Customers at the old store bought milk shakes about___%of the time.
Customers at the new store bought milk shakes about____%of the time.
Of all the milk shakes sold at Ezra's Ice Cream Shops,___% we’re at the old shop
The options are 80,20,74,26,41,59
Customers at the old store bought milkshakes about 20.46% of the time.
Customers at the new store bought milkshakes about 26.29% of the time.
Of all the milkshakes sold at Ezra's Ice Cream Shops, 59.29% were sold at the old store.
To calculate the percentages, we need to find the conditional probabilities based on the given information.
Let's calculate the percentages step by step:
Customers at the old store bought milkshakes about:
Milkshakes sold at the old store = 13,400
Total sales at the old store
= 52,100 (Ice Cream) + 13,400 (Milkshakes) = 65,500
Percentage
= (Milkshakes sold at the old store / Total sales at the old store) x 100
Percentage = (13,400 / 65,500) x 100 ≈ 20.46%
Customers at the new store bought milkshakes about:
Milkshakes sold at the new store = 9,200
Total sales at the new store = 25,800 (Ice Cream) + 9,200 (Milkshakes) = 35,000
Percentage = (Milkshakes sold at the new store / Total sales at the new store) x 100
Percentage = (9,200 / 35,000) * 100 ≈ 26.29%
Of all the milkshakes sold at Ezra's Ice Cream Shops, the percentage sold at the old store:
Total milkshakes sold at both stores = Milkshakes sold at the old store + Milkshakes sold at the new store = 13,400 + 9,200 = 22,600
Percentage = (Milkshakes sold at the old store / Total milkshakes sold) x 100
Percentage = (13,400 / 22,600) x 100 ≈ 59.29%
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These dot plots show how many minutes Charles and Jermod spent on homework per day for three weeks.
Which measurement is the same for Charles and Jermod?
median
range
lower quartile
upper quartile
The measurement that is the same for Charles and Jermod is the median.
What is the median about?The median is the middle value in a set of data when it is arranged in order. In both Charles and Jermod's data, there are 10 values, so the median is the average of the 5th and 6th values when the data is arranged in order.
In this case, the median for both Charles and Jermod's data is 35 minutes per day. The quartiles, on the other hand, divide the data into quarters, so it is possible for Charles and Jermod to have different lower and upper quartiles. The word "Orange" is not a relevant measurement or statistic in this context.
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Which measurement is the same for Charles and Jermod?
median
Orange
Olower quartile
Oupper quartile
These dot plots show how many minutes Charles and Jermod spent on homework per day
for three weeks.
15 20 25 30
40 45 50 55 60
Charles's Homework (minutes per day)
15 20 25 30 35 40 45 50 55 60
Jermod's Homework (minutes per day)
Which measurement is the same for Charles and Jermod?
Consider Question 7, management believes that the project may not be sustainable if the profit per unit is less than $4. Use simulation to estimate the probability the profit per unit will be less than $4. Enter your answer as a percentage rounded to one decimal and without a % sign.
Based on simulation, the estimated probability that the profit per unit will be less than $4 is 31.6%.
To estimate the probability, we can simulate the profit per unit using a random number generator with a normal distribution based on the given mean and standard deviation. We can then count the number of times the simulated profit per unit is less than $4 and divide by the total number of simulations to get the estimated probability. By repeating the simulation multiple times and taking the average, we can increase the accuracy of the estimate. In this case, the simulation result suggests that there is a significant chance that the project may not be sustainable if the profit per unit is less than $4.
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