According to the question the equilibrium price of tea is 2.10.
What is equilibrium?Equilibrium is a state of balance in which all forces acting on an object are equal and opposite, so no net force is acting on the object. This state of balance is also known as a "steady state". Equilibrium is an important concept in many areas of science, such as physics and chemistry, because it allows us to analyze how objects interact in a stable environment. Equilibrium can also be used to describe a state of financial balance, where all parties involved in a transaction are satisfied with the outcome.
The equilibrium price can be found by setting the two equations equal to one another and solving for P.
34P + 53 = -25P + 177
59P = 124
P = 124/59
P = 2.10
Therefore, the equilibrium price of tea is 2.10.
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Drag the number cards so that the values of x are as small as possible
By dragging the number cards to form the lowest sum possible and substituting that sum into the formula for x, we can make the value of x as small as possible.
The formula for x is x = (a + b + c + d)/4. In order to minimize the value of x, we should aim to make the sum of a, b, c, and d as small as possible. To do this, we can drag the number cards to form the lowest sum possible. For example, if the number cards are 5, 6, 7, and 8, we can drag them to form the sum of 26 (5 + 6 + 7 + 8 = 26). To calculate the value of x, we can substitute the sum of the numbers in the formula and divide it by 4. In this example, x = (26/4) = 6.5. By using this strategy, we can minimize the value of x and make it as small as possible.
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Complete question:
What is the smallest value for x when you drag the number cards?
solve with explanation
[tex] \frac{x - 4}{2(x - 3)} - \frac{x - 1}{2x} [/tex]
The simplified expression of (x - 4)/2(x - 3) - (x - 1)/2x is -3/(2x).
What is the simplification of the expression?
The given expression (x - 4)/2(x - 3) - (x - 1)/2x can be simplified to;
(x - 4)/(2x - 6) - (x - 1)/2x
To solve this expression, we need to first find a common denominator for the two fractions.
The least common multiple of the denominators 2x and 2x - 6 is;
2x( x - 3)
So we'll multiply the first fraction by (x - 3)/(x - 3) and the second fraction by (x - 3)/(x - 3) to get a common denominator:
((x - 4)/(2x - 6)) · ((x - 3)/(x - 3)) - ((x - 1)/(2x)) · ((x - 3)/(x - 3))
Now we can combine the numerators over the common denominator:
((x - 4)(x - 3) - (x - 1)(x - 3))/(2x(x - 3))
Expanding the parentheses and combining like terms, we get:
(x² - 7x + 12 - x² + 4x - 3)/(2x(x - 3))
Simplifying the numerator, we get:
(-3x + 9)/(2x(x - 3))
Now we can factor out a -3/2 and simplify:
(-3/2) · (x - 3)/(x(x - 3))
The (x - 3) terms cancel out, leaving us with:
(-3/2) · 1/x
= -3/(2x)
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This composite figure is created by placing a sector of a circle on a triangle. What is the area of this composite figure? Use 3.14 for π. Round to the nearest hundredth. Show your work.
What is the answer?
The area of composite figure composed of a sector and triangle is 95.52 cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
To get the area of the composite figure, we add the area of the sector to the area of the triangle.
Area of circle sector = (Ф / 360) * π * radius²
but Ф = 82°, radius = 10 cm, π = 3.14, hence:
Area of circle sector = (82 / 360) * 3.14 * 10² = 71.52 cm²
Area of triangle = (1/2) * base * height
but base = 6 cm, height = 8 cm, therefore:
Area of triangle = (1/2) * 6 * 8 = 24 cm²
Area of composite figure = 24 cm² + 71.52 cm² = 95.52 cm²
The area of composite figure is 95.52 cm²
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A shop is having a sale. Each day, prices are reduced by 20% of the price on the
previous day.
Before the start of the sale, the price of a television is £450.
On the first day of the sale, the price is reduced by 20%.
(a) Work out the price of the television on
i) the first day of the sale
ii) the third day of the sale.
(a) i) The price of the television on the first day of the sale is £360
ii) The price of the television on the third day of the sale is £288
(a)
i) On the first day of the sale, the price of the television is reduced by 20% of £450, which is:
20/100 × £450 = £90
So the price of the television on the first day of the sale is:
£450 - £90 = £360
ii) On the third day of the sale, the price of the television is reduced by 20% of the price on the second day of the sale. To find the price on the second day, we need to calculate the reduction on the first day and subtract it from the original price:
Reduction on first day = 20/100 × £450 = £90
Price on second day = £450 - £90 = £360
On the second day of the sale, the price of the television is reduced by 20% of £360, which is:
20/100 × £360 = £72
So the price of the television on the third day of the sale is:
£360 - £72 = £288
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On a standardized test with a normal distribution the mean score was 67. 2. The standard deviation was 4. 6. What percent of the data fell between 62. 6 and 71. 8?
Question 2 options:
95%
68%
4. 6%
13. 2%
The total percent of the data falling between 62. 6 and 71. 8 is around 68%
Mean score = 67.2
Standard deviation = 4.6
Standardizing the values of interest by converting them into z-scores by -
z = (x - μ) / σ
where x is the score, μ is the mean, and σ is the standard deviation.
Calculating for the lower bound of 62.6:
z1
= (62.6 - 67.2) / 4.6
= - 4.6/4.6
= -1
Similarly,
Calculating for the upper bound of 71.8:
z2
= (71.8 - 67.2) / 4.6
= 4.6/4.6
= 1
Getting the area under curve between these two z-scores using a table of common normal probability. The normal distribution is symmetric, thus, the area between z1 and z2, can be then subtracted from the area to the left of z2. The Left of z1 is an area of 0.1587 and the left of z2 is an area of 0.8413. Therefore, the area between z1 and z2 is:
= 0.8413 - 0.1587
= 0.6826
Converting this area to a percentage -
0.6826 × 100%
= 68.26%
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Please help me answer my homework in the image
Answer:
C) Both pairs of opposite sides are parallel because mPN = mLM = (1/2) and mPL = mMN = - 2.
Step-by-step explanation:
The corners of a rectangle are all right angles. The two sets of sides are parallel. In this example:
PL ║ MN and
LM ║ NP
To prove that the corners are all right angles, we could compre the slopes of the two lines that form each corner. They will be perpendicular if they are 90°.
In this example:
PL ⊥ LM and
MN ⊥ NP
So one approach Sherry may have taken is to compare the slopes of all four lines. To prove the object is a rectangle she could show that:
1. The sets of parallel lines have equal slopes, and
2. The sets of perpendicular lines have slopes that are the negative inverse of each other. (e.g., if a line has slope 5, a perpendicular line will have slope -(1/5))
To prove these points, Sherry probably used a spreadsheet to calculate each line's slopes. See the attached spreadsheet for how she may have set up the calculations. The slopes are the Rise/Run for each line. Rise is the change in y and x is the change in x between the two points.
Note the green cells. These are the slopes. Sherry found that:
a) PL ║ MN and LM ║ NP, since PL and MN both have slopes of -2; and LM and NP both have slopes of -0.5
b) PL ⊥ LM and MN ⊥ NP, since PL and LM and MN and NP both have slopes that are the negative inverse of each other (-2 and -(1/-2) or 0.5)
These are the two conditions Sherry originally established as proof of a rectangle.Without having checked whether any of the other answer options are viable options, Sherry will likely have seen, and done, enough to have chosen option C as proof that quadrilateral PLMN is a rectangle.
A retailer receives some products from three suppliers - S1, S2 and S3. The probability of successfully delivering the products in time by the suppliers are 0.85 for $1, 0.82 for $2 and 0.91 for S3. No supplier's delivery is impacted by any other supplier's delivery. The manufacturer orders 500 units of a raw material from $1, 120 units from $2 and 156 units from $3. What is the expected loss for the retailer given that failure to receive the materials in time will cost the manufacturer $20 per unit for the product supplied by S1, $30 for the product supplied by S2 and $10 for the product supplied by S3.
The expected loss for the retailer is $2288.4.
The retailer receives some products from three suppliers: S1, S2, and S3. The probability of successfully delivering the products in time by the suppliers are 0.85 for $1, 0.82 for $2, and 0.91 for S3. The manufacturer orders 500 units of a raw material from $1, 120 units from $2, and 156 units from $3. In case of failure to receive the materials in time, the manufacturer will bear $20 per unit for the product supplied by S1, $30 for the product supplied by S2, and $10 for the product supplied by S3. We have to calculate the expected loss for the retailer.
Let's calculate the expected loss for each supplier separately.Expected loss for supplier S1:Number of units ordered from S1 = 500The probability that the product will not be delivered in time = 1 - 0.85 = 0.15The expected loss per unit = $20Total expected loss for the products supplied by S1 = Expected loss per unit × Number of units ordered from S1 × Probability that the product will not be delivered in time= 20 × 500 × 0.15= $1500Expected loss for supplier S2:Number of units ordered from S2 = 120The probability that the product will not be delivered in time = 1 - 0.82 = 0.18
The expected loss per unit = $30Total expected loss for the products supplied by S2 = Expected loss per unit × Number of units ordered from S2 × Probability that the product will not be delivered in time= 30 × 120 × 0.18= $648 Expected loss for supplier S3:Number of units ordered from S3 = 156The probability that the product will not be delivered in time = 1 - 0.91 = 0.09The expected loss per unit = $10Total expected loss for the products supplied by S3 = Expected loss per unit × Number of units ordered from S3 × Probability that the product will not be delivered in time= 10 × 156 × 0.09= $140.4The total expected loss for the retailer = Expected loss for supplier S1 + Expected loss for supplier S2 + Expected loss for supplier S3= $1500 + $648 + $140.4= $2288.4
Hence, the expected loss for the retailer is $2288.4.
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A composite figure is formed by placing a half-sphere atop a cylinder. The half-sphere and the cylinder both have a radius of 3 centimeters. The height of the cylinder is 10 centimeters.
What is the exact volume of the composite figure?
Enter your answer in the box.
_cm³
The volume of the composite figure can be divided into two separate figures: a cylinder and a half-sphere, with the total volume being 108 cubic centimeters.
What is the exact volume of the composite figure?The composite figure can be divided into two separate figures: a cylinder and a half-sphere.
The formula for the volume of a cylinder is:
Volume of the cylinder = π[tex]r^2[/tex]h, where r is the radius of the cylinder and h is the height of the cylinder.
In this case, the radius of the cylinder is 3 centimeters and the height of the cylinder is 10 centimeters, so the volume of the cylinder is:
Volume of the cylinder = π[tex](3cm)^2(10cm)[/tex] = 90π [tex]cm^3[/tex]
The formula for the volume of a half-sphere is:
Volume of half-sphere = (2/3)π[tex]r^3[/tex], where r is the radius of the half-sphere.
In this case, the radius of the half-sphere is also 3 centimeters, so the volume of the half-sphere is:
Volume of half-sphere = (2/3)π[tex](3cm)^3[/tex] = 18π [tex]cm^3[/tex]
To find the total volume of the composite figure, we add the volume of the cylinder and the volume of the half-sphere:
Total volume = Volume of cylinder + Volume of half-sphere
Total volume = 90π [tex]cm^3[/tex] + 18π [tex]cm^3[/tex]
Total volume = 108π [tex]cm^3[/tex]
Therefore, the exact volume of the composite figure is 108π cubic centimeters.
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someone help me plsss
Answer:
Step-by-step explanation:
[tex]\frac{5\pm\sqrt{-4} }{3} =\frac{5\pm2\sqrt{i} }{3}[/tex] (since [tex]i=\sqrt{-1}[/tex])
[tex]=\frac{5}{3} \pm\frac{2}{3}\sqrt{i}[/tex]
[tex]\frac{10\pm\sqrt{-16} }{2} =\frac{10\pm4\sqrt{i} }{2}[/tex]
[tex]=5 \pm2\sqrt{i}[/tex]
[tex]\frac{-3\pm\sqrt{-144} }{6} =\frac{-3\pm12\sqrt{i} }{6}[/tex]
[tex]=-\frac{1}{2} \pm2\sqrt{i}[/tex]
The costs of repairing iPads in UAE are normally distributed with a mean of 173 Dhs. If
3%
of the costs exceed 243 Dhs, find the standard deviation of the costs. Round your answer to the nearest diham (Whole number).
The standard deviation of the costs is 37 Dhs
The given mean is 173 and 3% of costs exceed 243. We have to calculate the standard deviation of the cost. Therefore, let's first start by calculating the z-score as follows;z-score formula = `(x - μ) / σ`z-score = `243 - 173 / σ`z-score = `70 / σ`We need to find the standard deviation of the costs. Since the z-score formula includes standard deviation, we can first calculate the z-score and then use it to calculate the standard deviation.Using the z-table, we can find the z-score for 3% = -1.88-1.88 = (243 - 173) / σσ = (243 - 173) / -1.88σ = -70 / -1.88σ = 37.23≈ 37The standard deviation of the costs is 37 Dhs. Hence, the correct option is as follows.Option D is the correct option.
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Mike is wondering if there is enough room in an 8 by 10 by 12 inch box for his 13 inch rolling pin. Help Mike by calculating the length
of the diagonal d in the figure below.
Round your answer to the nearest tenths place (one decimal
place).
There will be enough room for Mike since the diagonal is more than 13 inch
How to find if there will be enough room for mikeThe diagonal of a cuboid is a line segment that connects two opposite corners of the cuboid. It passes through the center of the cuboid and represents the longest distance between any two points in the cuboid.
If the diagonal is less than 13 inch then there will not be enough room if otherwise then there will be enough room
To find the diagonal of a cuboid, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In a cuboid, if we label the length, width, and height
diagonal = √(length^2 + width^2 + height^2)
diagonal = √(10^2 + 8^2 + 12^2)
diagonal = √308
diagonal = 17.5 to 1 decimal place
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Find the values of each variable. Simplify all answers
The two numbers are x = 3 and y = 8.
Let x and y represent two numbers.
x + y = 16
xy = 24
To solve for the values of x and y, we can use the two equations given. We can first solve for x by dividing both sides of the second equation by y:
xy/y = 24/y
x = 24/y
We can substitute this value for x in the first equation and solve for y:
x + y = 16
(24/y) + y = 16
24 + y^2 = 16y
y^2 - 16y + 24 = 0
(y - 8)(y - 3) = 0
y = 8 or y = 3
Now that we have values for y, we can substitute them into the second equation and solve for x:
xy = 24
(8)(x) = 24
x = 3
(3)(3) = 24
So, the two numbers are x = 3 and y = 8.
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Complete question
Given two numbers x and y such that x + y = 16 and xy = 24, find the values of x and y.
Solve the quadratics attached using the quadratic formula or completing the square
[tex]n^2+9n+18[/tex]
Answer:
n = -3 or n = -6
Step-by-step explanation:
Solve for n over the real numbers:
n^2 + 9 n + 18 = 0
Subtract 18 from both sides:
n^2 + 9 n = -18
Add 81/4 to both sides:
n^2 + 9 n + 81/4 = 9/4
Write the left-hand side as a square:
(n + 9/2)^2 = 9/4
Take the square root of both sides:
n + 9/2 = 3/2 or n + 9/2 = -3/2
Subtract 9/2 from both sides:
n = -3 or n + 9/2 = -3/2
Subtract 9/2 from both sides:
Answer: n = -3 or n = -6
A
P. Alex works as one of three unpaid interns at an office for
college credit. She does the work that the company would
otherwise pay an employee $12 per hour to do. If the
office is open for 8 hours in a day, and if Alex works for
the full day on each of the 20 workdays in a month, how
much money does the company save per month by having
Alex work instead of a paid employee?
After calculations, we find that the company saves a total of $12 x 160 = $1,920 per month by having Alex work instead of a paid employee.
In this scenario, the company has three unpaid interns, including P. Alex, who are working in exchange for college credit. This means that the company does not have to pay these interns any salary or wages.
If the company were to hire a paid employee instead of having an intern like Alex work, they would have to pay that employee $12 per hour for the work that needs to be done. This is the amount that the company would have to spend in wages for each hour worked by the employee.
Now, we know that Alex works for the full 8 hours per day, and for 20 workdays in a month. This means that she works a total of 8 x 20 = 160 hours in a month.
Therefore, the total amount of money the company would have to pay a paid employee for the same amount of work that Alex does would be $12 per hour x 160 hours = $1,920.
Since Alex is working for the company without any payment, the company saves the entire amount of $1,920 per month that they would have had to pay a paid employee to do the same work.
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In the Kite ABCD AP= 6 mm, PB= 63‾√3
mm, PD = 7 mm, find the area to the nearest tenth
The area of the given kite to the nearest tenth would be = 135.10mm².
How to calculate the area of a kite?A kite is defined as the type of quadrilateral that has two pairs of sides that are equal in length and which are adjacent to each other.
To calculate the area of the kite given such as ABCD, the formula = ½ × AC × BD.
Given the sides such as:
AP = 6 mm
PB = 6√3 mm
PD = 7mm
But AC = 6mm × 2 = 12mm
BD = 6√3+7 = 13√3mm
Therefore the area = 1/2 × 12× 13√3
= 6×13√3
= 135.10mm²
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What is the area of this trapezoid? Enter your answer in the box. Ft²
Trapezoid with parallel sides labeled 13 feet and 31 feet. The dashed perpendicular
segment between them is labeled 16 feet
The area of the given trapezoid would be 176 feet² with the length of the parallel sides of the trapezoid is 13 feet and 31 feet respectively and the height of the trapezoid given is 16 feet.
Given that,
The length of the parallel sides of the trapezoid is 13 feet and 31 feet
The height of the trapezoid given is 16 feet.
We know that area of trapezoid is (a+b)×h/2
Where, (a) and (b) are Length of the parallel sides of trapezoid and h is the height of trapezoid.
Thus, Area = (13+31) × 16/2
Area = 22×8
Area = 176 feet²
Hence the area of the given trapezoid would be 176 feet² with the length of the parallel sides of the trapezoid is 13 feet and 31 feet respectively and the height of the trapezoid given is 16 feet.
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Un granjero tiene pienso para alimentar a sus 12 vacas durante 45 días, si compra 3 vacas más, ¿Cuánto le durará el pienso?
He can feed 15 cows till 36 days because earlier he feed 12 cows till 42 days. So we see we uses the concepts inversely proportional.
What is inversely proportional?In this type of proportional is if their are two quantities then if first one is increase then automatically second one is decrease.
Suppose if a, b are two variables , and if they are indirectly proportional then we can write it as a ∝ 1/b , that means xy = k(where k is constant).
Let number of day be x days.
and, total number of cows = 12 + 3 (After he buy 3 more cow)
then, Number of cows and the number of days are inversely proportion.
So, we can write [tex]\frac{12}{15} = \frac{x}{45}[/tex]
[tex]= x * 15 = 12 * 45[/tex]
[tex]\implies x = 36\ days[/tex]
So, He can feed 15 cows till 36 days.
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Question in English :
A farmer has feed to feed his 12 cows for 45 days. if he buys 3 more cows, How long does the feed last?
what is 10 divided by 1/5
Myesha has a bag that contains orange chews, lemon chews, and lime chews. She performs an experiment. Myesha randomly removes a chew from the bag, records the result, and returns the chew to the bag. Myesha performs the experiment 17 times. The results are shown below:
A orange chew was selected 12 times.
A lemon chew was selected 2 times.
A lime chew was selected 3 times.
Based on these results, express the probability that the next chew Myesha removes from the bag will be a flavor other than lime as a percent to the nearest whole number.
The probability that the next chew Myesha removes from the bag will be a flavor other than lime is 82%.
What is probability?
Probability is the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probabilities between 0 and 1 represent the degree of uncertainty about whether the event will occur or not.
Out of the 17 times Myesha performed the experiment, a lime chew was selected 3 times. Therefore, the probability that the next chew Myesha removes from the bag will be a lime chew is 3/17.
To find the probability that the next chew Myesha removes from the bag will be a flavor other than lime, we need to subtract the probability of getting a lime chew from 1.
P(flavor other than lime) = 1 - P(lime)
P(flavor other than lime) = 1 - 3/17
P(flavor other than lime) = 14/17
To express this probability as a percent to the nearest whole number, we multiply by 100 and round to the nearest integer:
P(flavor other than lime) = 14/17 x 100
P(flavor other than lime) = 82.35
P(flavor other than lime) ≈ 82%
Therefore, the probability that the next chew Myesha removes from the bag will be a flavor other than lime is approximately 82%.
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Ervin bowled 7 games last weekend. His
scores are: 155, 165, 138, 172, 127, 193, 142. What
is the sample standard deviation of Ervin's
scores?
The sample standard deviation of Ervin's scores is 41.81.
In this problem, we are given the scores of 7 games bowled by Ervin, and we are asked to calculate the sample standard deviation of these scores. To calculate the sample standard deviation, we first need to calculate the sample mean, which is the sum of the scores divided by the number of games:
mean = (155 + 165 + 138 + 172 + 127 + 193 + 142) / 7 = 138.57
Next, we need to calculate the variance, which is the sum of the squared differences from the mean, divided by the number of games minus one:
variance = [(155-138.57)² + (165-138.57)² + (138-138.57)² + (172-138.57)² + (127-138.57)² + (193-138.57)² + (142-138.57)²] / (7-1) = 1749.62
Finally, we can calculate the sample standard deviation by taking the square root of the variance:
standard deviation = √(variance) = √(1749.62) = 41.81
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A checking account has a balance of $350. A customer makes two withdrawals, one $50 more than the other. Then he makes a deposit of $75
The first withdrawal from the account is $200 and another is $150
A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression. In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in mathematics are those that hold true even when they appear to be different. Yet, both forms provide the same outcome when the values are entered into the formula.
A checking account has a balance of $350
A customer makes two withdrawals
first is $50 more than the other,
let another withdrawal is $x
then first withdrawal is $(50+x)
then,
x+(50+x)=350
2x=300
x=$150
hence first withdrawal is $200
and another is $150
Then he makes a deposit of $75,
So the remaining balance in the account is $75.
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A small country consists of five states (A, B, C, D, and E). The total population of the country is 24.4 million. According to the country's constitution, the seats in the legislature are apportioned to the states according to their populations. The table below shows each state's standard quota. Find the apportionment under Hamilton's method.
Therefore, the apportionment under Hamilton's method is:
State Apportionment
A 18
B 22
C 13
D 30
E 17
What is Hamilton's method?
To use Hamilton's method, we need to calculate each state's priority by dividing its population by the geometric mean of its current seat and the next higher integer seat.
Then, we assign seats based on priority until we reach the total number of seats (in this case, 100).
State Population Standard Quota
A 5.6 18
B 6.8 22
C 3.6 12
D 3.2 10
E 5.2 17
To calculate priorities, we first find the geometric mean of the current seat and the next higher integer seat for each state:
State A: sqrt(18*19) ≈ 18.49
State B: sqrt(22*23) ≈ 22.94
State C: sqrt(12*13) ≈ 12.68
State D: sqrt(10*11) ≈ 10.49
State E: sqrt(17*18) ≈ 17.89
Then, we divide each state's population by its corresponding priority:
State A: 5.6/18.49 ≈ 0.303
State B: 6.8/22.94 ≈ 0.296
State C: 3.6/12.68 ≈ 0.284
State D: 3.2/10.49 ≈ 0.305
State E: 5.2/17.89 ≈ 0.291
We then assign seats based on priority, starting with the highest priority and rounding down to the nearest integer:
State D: 30 seats
State A: 18 seats
State E: 17 seats
State B: 22 seats
State C: 13 seats
This adds up to 100 seats, as required.
Therefore, the apportionment under Hamilton's method is:
State Apportionment
A 18
B 22
C 13
D 30
E 17
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Find all vertical asymptotes of the rational function. (Enter your answers as a comma-separated list of equations.)
F(x) =
x2 + 11
6x2 − 19x − 36
is it a option ? or no cuz im a litlle confused
Ms. Delgado stocked up on art supplies for her classroom this year. She ordered 26 watercolor paint sets from color city art supply. Since this was a bulk order, color city reduced the price of each paint set by $1. 50. The total came to $65. Which equation can you use to find the amount of money, p, color city normally charges for a paint set?
The equation will be 26(p − 1.50) = 65 and the amount of money, p, each paint set normally costs is $4.
Ms. Delgado purchases 26 watercolor paint sets
reduced the price of each paint set = $1. 50.
Ms. Delgado spends $65 in all.
we need to find the equation to find p.
The original price of each watercolor paint set.
Solution:
Ms. Delgado purchases 26 Watercolor paint by spending $65 in all.
with a reduction in price of $39
Let 'p' be the original price of each watercolor paint set.
The equation to find p is,
26p - 39 = 65
26p = 65 + 39
26p = 104
p = 4
The original price of each watercolor paint set is $4
The equation to find p, the original price of each watercolor paint set is
26(p − 1.50) = 65 or 26p - 39 = 65
The original price of each watercolor paint set is $4
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In △PQR, the length of PQ⎯⎯⎯⎯⎯ is 16 units. A series of midsegments are drawn such that ST⎯⎯⎯⎯⎯ is the midsegment of △PQR, UV⎯⎯⎯⎯⎯⎯ is the midsegment of △STR, and WX⎯⎯⎯⎯⎯⎯ is the midsegment of △UVR
The length of PQ is 16 units. ST is the midsegment of PQR, UV is the midsegment of STR, and WX is the midsegment of UVR. It is reasonable to assume that the three midsegments have equal lengths since they are part of the same triangle.
In a triangle, the midsegment is a line segment that connects the midpoints of two sides of the triangle and is parallel to the third side. In the given triangle PQR, the length of PQ is 16 units. ST is the midsegment of PQR, UV is the midsegment of STR, and WX is the midsegment of UVR. Since all the midsegments are part of the same triangle, it is reasonable to assume that they have equal lengths. The triangle midsegment theorem, which asserts that the length of a triangle's midsegment is equal to half of the length of the third side of the triangle, may be used to demonstrate this.. In this case, the length of ST, UV, and WX would all be equal to 8 units, since the third side of each triangle is 16 units. This indicates that it is reasonable to assume that the midsegments of the triangle have equal lengths.
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Mail surveys have the concern of _____ but have the advantage of _____. Group of answer choices low return rate; eliminating interviewer bias interviewer bias; high return rate sampling bias; interviewer bias increasing socially desirable responses; high return rate
The correct option is a low return rate; eliminating interviewer bias. Mail surveys have the concern of low return rate but have the advantage of eliminating interviewer bias.
A mail survey is a form of a self-administered survey in which the questionnaire is sent to the respondent through the post. Mail surveys are convenient because they allow participants to respond on their schedule and in the privacy of their own homes.
Mail surveys have the concern of a low return rate but have the advantage of eliminating interviewer bias. The concern of mail surveys is a low return rate. One of the greatest advantages of mail surveys is that they do not require any interaction between the researcher and the respondent. Mail surveys' response rate is typically lower than phone or face-to-face surveys. However, it eliminates interviewer bias.
Interviewer bias occurs when the interviewer's characteristics or behavior have an impact on the participant's responses. Interviewer bias can occur in face-to-face interviews or phone surveys. Respondents may attempt to please the interviewer or present themselves in a more favorable light than they otherwise would in order to avoid social disapproval.
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The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of0.951 gand a standard deviation of0.299 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 37 cigarettes with a mean nicotine amount of0.897 g. Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly selecting 37 cigarettes with a mean of0.897 gor less.P(M<0.897 g)=Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exactz-scores orz-scores rounded to 3 decimal places are accepted. Based on the result above, dis it valid to claim that the amount of nicotine is lower? (Let's use a5%cut-off for our definition of unusual.) No. The probability of obtaining this data is high enough to have been a chance occurrence. Yes. The probability of this data is unlikely to have occurred by chance alone.
To determine whether it is valid to claim that the amount of is lower, we need to compare this probability to our chosen cut-off for unusual events, which is 5%.
What is the probability of randomly selecting?To find the probability of randomly selecting 37 with a mean of [tex]0.897 g[/tex] or less, we need to calculate the z-score and look up the corresponding probability in the standard normal distribution table.
Where X is the sample mean [tex](0.897 g),[/tex] μ is the population mean (0.951 g), σ is the population standard deviation [tex](0.299 g)[/tex] , and n is the sample size (37).
Plugging in the values, we get:
[tex]z = (0.897 - 0.951) / (0.299 / sqrt(37)) = -1.731[/tex]
Looking up the corresponding probability in the standard normal distribution table, we find that [tex]P(Z < -1.731) = 0.0419[/tex] (rounded to 4 decimal places).
Since the calculated probability is greater than 5%, we cannot reject the null hypothesis that the mean amount of has not changed. In other words, the evidence is not strong enough to support the claim that the amount of nicotine is lower.
Therefore, the probability of randomly selecting 37 with a mean of [tex]0.897 g[/tex] or less is [tex]0.0419[/tex] .
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Find the midpoint of the line segment AB if A = (7, 2) and B = (5, -4). ( with photo pls)
Answer:
(6, -1)
Step-by-step explanation:
The midpoint formula, (y2+y1)/2 and (x2+x1)/2 will help us find our answer. So (2-4)/2= -1 and (7+5)/2=6, so (6,-1) is the midpoint of segment AB.
the length of time it takes to find a parking space at 9 a.m. follows a normal distribution with a mean of 5 minutes and a standard deviation of 2 minutes. seventy percent of the time, it takes more than how many minutes to find a parking space? (round your answer to two decimal places.) 2.91 incorrect: your answer is incorrect. min
70% of the time, it takes more than 6.04 minutes to find a parking space. Rounded to two decimal places, the answer is 6.04 minutes.
The length of time it takes to find a parking space at 9 a.m. follows a normal distribution with a mean of 5 minutes and a standard deviation of 2 minutes. To find the time it takes to find a parking space 70% of the time, we need to find the z-score that corresponds to the 70th percentile.
Using a z-table, we find that the z-score corresponding to the 70th percentile is 0.52. Using the formula z = (x - μ) / σ, where x is the value we are trying to find, μ is the mean, and σ is the standard deviation, we can plug in the values and solve for x:
0.52 = (x - 5) / 2
x - 5 = 0.52 * 2
x - 5 = 1.04
x = 6.04
Therefore, 70% of the time, it takes more than 6.04 minutes to find a parking space. Rounded to two decimal places, the answer is 6.04 minutes.
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You are going to use an incline plane to lift a heavy object to the top of a shelving unit with a height of 8 ft. The base of the incline plane is 9 ft from the shelving unit. What is the length of the incline plane?
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{9}\\ o=\stackrel{opposite}{8} \end{cases} \\\\\\ c=\sqrt{ 9^2 + 8^2}\implies c=\sqrt{ 81 + 64 } \implies c=\sqrt{ 145 }\implies c\approx 12.04~ft[/tex]