If a and b, then c means that if both a and b are true, then c must also be true. This is an example of a conditional statement, where the truth of one proposition (c) is dependent on the truth of the other two propositions (a and b).
Now, given that the reverse of the if-then statement is also correct, we can conclude that if b is true, then a is also true. This means that both a and b are true. Therefore, according to the original statement, c must also be true.
In other words, if a and b are both true, then c must also be true. This is because the conditional statement "if a and b, then c" holds true in this scenario. Therefore, we can conclude that the value of c is true.
Overall, understanding the logic behind conditional statements and their reverses can help us make logical conclusions about the truth of propositions based on the truth of other propositions.
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Find the volume of this cylinder using 3.14 as pi
13 ft
20 ft
The value of the volume of the cylinder is 706. 5 cm³
How to determine the valueThe formula for the volume of a cylinder is expressed as;
V = πr²h
Such that the parameters are;
V is the volume of the cylinderπ takes the value 3.14r is the radius of the cylinderh is the height of the cylinderNow, substitute the values into the formula, we get;
Volume, V = 3.14 × 5² × 9
Find the square value and substitute
Volume, V = 3.14 × 25 × 9
Multiply the values
volume, V = 706. 5 cm³
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The base of a prism is a right triangle with legs measuring 3 feet and 4 feet. If the height of the prism is 13 feet, determine its volume
The volume of the prism is 78 cubic feet.The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism.
In this case, the base of the prism is a right triangle with legs measuring 3 feet and 4 feet, so its area is (1/2)(3)(4) = 6 square feet. The height of the prism is 13 feet. Therefore, the volume of the prism is V = Bh = (6)(13) = 78 cubic feet.To understand this calculation, think of the prism as a stack of identical, parallel cross sections. Each cross section is a copy of the base, with an area of 6 square feet.
The height of each cross section is the same, and equal to the height of the prism, which is 13 feet. To find the total volume of the prism, we add up the volumes of all these cross sections, which is equal to the area of the base times the height of the prism.
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The combined math and verbal scores for females taking the SAT-I test are normally distributed with a mean of 998 and a standard deviation of 202 (based on date from the College Board). If a college includes a minimum score of 925 among its requirements, what percentage of females do not satisfy that requirement?
The percentage of females who do not satisfy the minimum score requirement of 925 on the SAT-I test is 35.9%.
Calculating the z-score for the minimum score requirement:
z = (X - Mean) / Standard Deviation
z = (925 - 998) / 202
z = -73 / 202 ≈ -0.361
Now, using the z-score to find the percentage of females below the minimum score:
Since the z-score is -0.361, we can use a z-table (or an online calculator) to find the area to the left of this z-score, which represents the percentage of females who scored below 925. The area to the left of -0.361 is approximately 0.359.
3. Convert the area to a percentage:
Percentage = Area * 100
Percentage = 0.359 * 100 ≈ 35.9%
So, approximately 35.9% of females do not satisfy the minimum score requirement of 925 on the SAT-I test.
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The function f(x) models the height in feet of the tide at a specific location x hours after high tide.
f(x) = 3.5 cos (π/6 x) + 3.7
a. What is the height of the tide at low tide?
b. What is the period of the function? What does this tell you about the tides at this location?
c. How many hours after high tide is the tide at the height of 3 feet for the first time?
a) The height of the tide at low tide is 3.7 feet.
b) The period of the function is 12 hours and it means that the tide goes through a full cycle of high tide.
c) The first time the tide reaches a height of 3 feet is therefore either 23.82 hours or 40.18 hours after high tide.
a. To find the height of the tide at low tide, we need to find the minimum value of the function f(x).
Since cos(π/6 x) has a maximum value of 1 and a minimum value of -1, the minimum value of the entire function occurs when cos(π/6 x) = -1.
This happens when π/6 x = π + 2nπ, where n is any integer.
Solving for x, we get x = 12 + 12n.
Substituting this value of x into the function, we get f(x) = 0 + 3.7 = 3.7 feet.
b. The period of the function is the time it takes for the function to complete one full cycle. Since the period of cos(π/6 x) is 2π/π/6 = 12 hours, the period of the entire function f(x) is also 12 hours. This means that the tide goes through a full cycle of high tide and low tide every 12 hours at this location.
c. To find the first time the tide reaches a height of 3 feet, we need to solve the equation 3 = 3.5 cos (π/6 x) + 3.7 for x.
Subtracting 3.7 from both sides and dividing by 3.5, we get cos(π/6 x) = -0.086.
Taking the inverse cosine of both sides, we get π/6 x = 1.67 + 2nπ or π/6 x = -1.67 + 2nπ, where n is any integer.
Solving for x, we get x = 40.18 + 24n or x = 23.82 + 24n.
The first time the tide reaches a height of 3 feet is therefore either 23.82 hours or 40.18 hours after high tide.
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; 3. Using the complex form, find the Fourier series of the function. (30%) 1, 2k – .25 < x < 2k +.25, k € Z. a. (15%), f (x) = 0, elsewhere S 1,0
The Fourier series Using the complex form of f(x) is
f(x) = 1/2 + ∑[n=1, ∞] [2*(-1)^(n+k)/(nπ)]*sin(nπx), 2k-0.25 < x < 2k+0.25
where k is an integer.
To find the Fourier series of the function f(x) over the interval [-1, 1], we first note that f(x) is periodic with period T = 0.5. We can then write f(x) as a Fourier series of the form
f(x) = a0/2 + ∑[n=1, ∞] (ancos(nπx) + bnsin(nπx))
where
a0 = (1/T) ∫[0,T] f(x) dx
an = (2/T) ∫[0,T] f(x)*cos(nπx) dx
bn = (2/T) ∫[0,T] f(x)*sin(nπx) dx
Since f(x) = 0 for x < -0.25 and x > 0.25, we only need to consider the interval [-0.25, 0.25]. We can break this interval into subintervals of length 0.5 centered at integer values k
[-0.25, 0.25] = [-0.25, 0.25] ∩ [1.5, 2.5] ∪ [-0.25, 0.25] ∩ [0.5, 1.5] ∪ ... ∪ [-0.25, 0.25] ∩ [-1.5, -0.5]
For each subinterval, the Fourier coefficients can be calculated as follows
a0 = (1/0.5) ∫[-0.25, 0.25] f(x) dx = 1/2
an = (2/0.5) ∫[-0.25, 0.25] f(x)*cos(nπx) dx = 0
bn = (2/0.5) ∫[-0.25, 0.25] f(x)sin(nπx) dx = 2(-1)^k/(nπ)
Therefore, the Fourier series of f(x) is
f(x) = 1/2 + ∑[n=1, ∞] [2*(-1)^(n+k)/(nπ)]*sin(nπx), 2k-0.25 < x < 2k+0.25
where k is an integer.
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From a Word Problem
An online camera store charges $3 for every
8x10 picture that you order. The
shipping cost is $8. Write an equation to
model this situation. How much will it cost to
get 5 pictures printed?
The product of 58 and the quantity 8b plus 8.
Expression[tex]58(8b+8)[/tex]simplifies to[tex]464b+464.[/tex]
How to simplify quantity expressions?
Calculate the product of 58 and the quantity 8b + 8
The given expression is:
[tex]58(8b + 8)[/tex]
Multiplying 58 by 8b and 8, we get:
[tex]464b + 464[/tex]
Therefore, the answer is:
[tex]58(8b + 8) = 464b + 464[/tex]
To find the product of 58 and the quantity 8b + 8, we need to use the distributive property of multiplication over addition, which states that the product of a number and a sum is equal to the sum of the products of the number and each term in the sum. In this case, we can distribute 58 over 8b and 8, as follows:
[tex]58(8b + 8) = 58 × 8b + 58 × 8[/tex]
Multiplying 58 by 8b and 8 separately, we get:
[tex]58 × 8b = 464b[/tex]
[tex]58 × 8 = 464[/tex]
Adding the products, we get the final answer:
[tex]58(8b + 8) = 464b + 464[/tex]
Therefore, the expression [tex]58(8b + 8)[/tex]simplifies to[tex]464b + 464.[/tex]
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E J calls people at random to conduct a survey. So far 40 calls have Ben answered and 120 calls have not What is the approximate probability that someone might answer the next call he makes. A. 75%. B. 1/3. C. 0. 25. D. 0. 4
The approximate probability that someone might answer the next call E.J. makes is 0.25 or 25%. The correct answer is C. 0.25.
To find the approximate probability that someone might answer E.J.'s next call, we'll use the information provided and follow these steps:
1. Calculate the total number of calls made: answered calls (40) + unanswered calls (120).
2. Find the proportion of answered calls to the total calls.
3. Express the proportion as a probability (as a percentage or fraction).
Let's do the calculations:
1. Total calls = 40 (answered) + 120 (unanswered) = 160 calls
2. Proportion of answered calls = 40 answered calls / 160 total calls = 1/4
3. Probability = 1/4 = 0.25 (as a decimal) or 25% (as a percentage)
So, the approximate probability that someone might answer the next call E.J. makes is 0.25 or 25%. The correct answer is C. 0.25.
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put the measuraments from greatest to least
The measurements from greatest to least would be ordered as follows:
6 yards 2 1/2 feet 45 inchesHow to order the measurements ?First, we need to convert all the units to the same unit. Let's convert everything to inches, since that is the smallest unit.
6 yards = 6 x 3 = 18 feet
18 feet = 18 x 12 = 216 inches
2 1/2 feet = 2 x 12 + 6 = 30 inches
So now we have:
6 yards = 216 inches
2 1/2 feet = 30 inches
45 inches = 45 inches
Putting these in order from greatest to least, we have:
216 inches, 45 inches, 30 inches
Therefore, the measurements from greatest to least would be ordered as follows:
6 yards, 45 inches, 2 1/2 feet
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The full question is:
Put the measurements from greatest to least. 45 inches, 6 yards, and 2 1/2 feet
Which of the following are areas of sectors formed by Angle ABC?
B = 86.4º
AB=4.1cm
Answer:
about 12.67 cm²
Step-by-step explanation:
The area of a sector of a circle is given by:
A = (θ/360) x πr²
where A is the area of the sector, θ is the central angle of the sector (in degrees), and r is the radius of the circle.
In this case, we are given the central angle of the sector, which is 86.4 degrees, and the radius of the circle, which is 4.1 cm. Therefore, we can calculate the area of the sector formed by angle CBA as follows:
A = (86.4/360) x π(4.1)²
A ≈ 12.67 cm²
So, the area "about 12.67 cm²" is a possible area of the sector formed by angle CBA.
To determine if any of the other given areas are possible, we can calculate the central angle of each sector using the same formula as above, and then check if it matches the given angle of 86.4 degrees.
For the area "about 23.35 cm²":
23.35 = (θ/360) x π(4.1)²
θ ≈ 149.6 degrees
The central angle of this sector is approximately 149.6 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 23.35 cm²" is not a possible area of the sector formed by angle CBA.
For the area "about 3.09 cm²":
3.09 = (θ/360) x π(4.1)²
θ ≈ 19.16 degrees
The central angle of this sector is approximately 19.16 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 3.09 cm²" is not a possible area of the sector formed by angle CBA.
For the area "about 40.14 cm²":
40.14 = (θ/360) x π(4.1)²
θ ≈ 256.4 degrees
The central angle of this sector is approximately 256.4 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 40.14 cm²" is not a possible area of the sector formed by angle CBA.
Therefore, the only possible area of the sector formed by angle CBA is "about 12.67 cm²".
If f(x) = x2 + 4x + 6, find the following values. = 1. f(a) = 2. f(a - 1) = 3. f(a + 1) =
To find the values of f(a), f(a-1), and f(a+1) when f(x) = x^2 + 4x + 6, So, the values are: f(a) = a^2 + 4a + 6, f(a-1) = a^2 + 6a + 3, f(a+1) = a^2 + 6a + 11.
we simply substitute the given values of a into the function.
1. f(a) = a^2 + 4a + 6
2. f(a-1) = (a-1)^2 + 4(a-1) + 6 = a^2 + 2a + 1 + 4a - 4 + 6 = a^2 + 6a + 3
3. f(a+1) = (a+1)^2 + 4(a+1) + 6 = a^2 + 2a + 1 + 4a + 4 + 6 = a^2 + 6a + 11
So, the values are:
1. f(a) = a^2 + 4a + 6
2. f(a-1) = a^2 + 6a + 3
3. f(a+1) = a^2 + 6a + 11
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If x = -3, then which inequality is true?
The inequailty y < x + 3 would be true when x = -3 and all values of y are less than 0
If x = -3, then which inequality is true?From the question, we have the following parameters that can be used in our computation:
The statement that x = -3
The above value implies that we substitute -3 for x in an inequality and solve for the variable y
Take for instance, we have
y < x + 3
Substitute the known values in the above equation, so, we have the following representation
y < -3 + 3
Evaluate
y < 0
This means that the inequailty y < x + 3 would be true when x = -3 and all values of y are less than 0
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A radar antenna is located on a ship that is 4 kilometres from a straight shore. It is rotating at 32 revolutions per minute. How fast does the radar beam sweep along the shore when the angle between the beam and the shortest distance to the shore is Pi/4 radians?
The radar beam moves at a pace of roughly 536.47 kilometers per hour as it scans the coastline.
Let A represent the location of the radar antenna and B represent the shoreline location that is closest to A. Let C represent the radar beam's current location on the coast and Ф represent the angle between the beam and the line AB. As a result, we obtain a right triangle ABC, where AB is equal to 4 km, and BC is the length at which the radar beam sweeps along the shore.
32 rev/min(2π/60 sec) = 3.36 radians/sec. BC = r(Ф) = (4 km)(π/4) = π km.
We may calculate the radar beam's speed down the shore by multiplying these two values:
(536.47 km/hr) = 10.54 km/sec or (3.36 rad/sec)(π km).
Hence, the of sweeping is 10.54 km/sec.
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3. What is the range of the functiony = 3x + 1 for
the domain 2 ≤ x ≤ 67
6 ≤ y ≤ 18
sy≤2
7 ≤ y ≤ 19
1
5
sys 3
A company's profit is linearly related to the number of items the company sells. Profit, P, is a function of the number of items sold, x. If the company sells 4000 items, its profit is $24,100. If the company sells 5000 items, its profit is $30,700. Find an equation for P(x)
The equation for the company's profit, P(x), is P(x) = 6.6x - 2,300, where x is the number of items sold.
To find the equation P(x) for the company's profit, we can first determine the slope (m) and the y-intercept (b) of the linear equation P(x) = mx + b.
1. Calculate the slope (m) using the given information:
m = (P2 - P1) / (x2 - x1)
m = ($30,700 - $24,100) / (5000 - 4000)
m = $6,600 / 1000
m = $6.6
2. Use one of the points to find the y-intercept (b):
P(x) = mx + b
$24,100 = $6.6(4000) + b
$24,100 = $26,400 + b
b = -$2,300
3. Write the equation for P(x):
P(x) = 6.6x - 2,300
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I need help with an assignment over pythagorean therom i have an example with one of the problems i really need to get this turned in asap because i really need to bring my grade up in math if i turn in this assignment so if you can help you are an amazing person thank you there's an example of one of the problems that I need
Step-by-step explanation:
I have provided answer in attachment... this is solution of brainly tutor..
450 cubic centimetres of wood is used to make a solid cylindrical ornament. the radius of the base of the ornament is 5 centimetres. what is the height of the cylindrical ornament? (formula = π x radius² x height)
a) 4.5 cm
b) 5.7 cm
c) 6.3 cm
d) 7.5 cm
The height of the cylindrical ornament is approximately 5.7 centimetres (option b).
To find the height of the cylindrical ornament given that 450 cubic centimetres of wood is used and the radius of the base is 5 centimetres, you can use the formula for the volume of a cylinder: V = π × radius² × height.
Step 1: Write down the given values.
Volume (V) = 450 cubic centimetres
Radius (r) = 5 centimetres
Step 2: Plug the given values into the formula.
450 = π × (5)² × height
Step 3: Solve for the height.
450 = π × 25 × height
450 = 78.54 × height
Step 4: Divide both sides by 78.54 to find the height.
height = 450 / 78.54
height ≈ 5.7 centimetres
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A person completes 68 km in 50 minutes via Jeep. Starting 20 minutes, he travels by x km/hr and
next 25 minutes by 2x km/hr and rest time by 3x km/hr. What is the value of x ?
The value of x is 48 km/hr.
How to solve for X
Total distance = 68 km
Total time = 50 minutes
First part:
Duration = 20 minutes
Speed = x km/hr
Second part:
Duration = 25 minutes
Speed = 2x km/hr
Third part:
Duration = 50 - (20 + 25) = 5 minutes
Speed = 3x km/hr
We can calculate the distance traveled in each part using the formula:
distance = speed × time
For the first part:
distance1 = x × (20/60) = (1/3)x (because 20 minutes = 1/3 hour)
For the second part:
distance2 = 2x × (25/60) = (5/6)x (because 25 minutes = 5/12 hour)
For the third part:
distance3 = 3x × (5/60) = (1/4)x (because 5 minutes = 1/12 hour)
Now, we know that the total distance is 68 km, so:
distance1 + distance2 + distance3 = 68
(1/3)x + (5/6)x + (1/4)x = 68
To solve for x, we'll first find a common denominator for the fractions, which is 12:
(4/12)x + (10/12)x + (3/12)x = 68
Now, add the fractions:
(4+10+3)/12 * x = 68
17/12 * x = 68
To isolate x, we'll multiply both sides by the reciprocal of the fraction (12/17):
x = 68 * (12/17)
x = 4 * 12
x = 48
So, the value of x is 48 km/hr.
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What are the slopes and y-intercept of a graph?
The slopes and y-intercept of a graph are two key components of the equation that describes the relationship between two variables.
The slope of a graph is the measure of how steeply the line is rising or falling. It is calculated by dividing the change in the y-axis by the change in the x-axis between two points on the line. A positive slope indicates that the line is rising, while a negative slope indicates that the line is falling.
The y-intercept of a graph is the point where the line crosses the y-axis. It is the value of y when x=0. The y-intercept is a fixed point on the line and is used to help determine the equation of the line.
Together, the slope and y-intercept of a graph can be used to write an equation in slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.
A buoy is floating in the water near a lighthouse. The height of the lighthouse is 18 meters, and the horizontal distance from the buoy to the base of the lighthouse is 45 meters. What is the approximate angle of elevation from the buoy to the top of the lighthouse, rounded to the nearest whole degree?
The equivalent expression is $\boxed{4^{15} \cdot 5^{10}}$.
Find out the simplified expression inside the parentheses?We can simplify the expression inside the parentheses first, using the rule that says when you raise a power to another power, you multiply the exponents:
$\left(\dfrac{4^{3}}{5^{-2}}\right)^{5} = \left(4^{3} \cdot 5^{2}\right)^{5}$
Now, we can use the rule that says when you raise a product to a power, you raise each factor to the power:
$\left(4^{3} \cdot 5^{2}\right)^{5} = 4^{3 \cdot 5} \cdot 5^{2 \cdot 5}$
Simplifying further:
$4^{3 \cdot 5} \cdot 5^{2 \cdot 5} = 4^{15} \cdot 5^{10}$
we can substitute this expression back into the original expression:
$\left(\dfrac{4^{3}}{5^{-2}}\right)^{5} = \left(4^{3} \cdot 5^{2}\right)^{5}$
To simplify this expression further, we can use the rule that says when you raise a product to a power, you raise each factor to the power:
$\left(4^{3} \cdot 5^{2}\right)^{5} = 4^{3 \cdot 5} \cdot 5^{2 \cdot 5}$
Simplifying the exponents, we get:
$4^{3 \cdot 5} \cdot 5^{2 \cdot 5} = 4^{15} \cdot 5^{10}$
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a laundromat has 5 washing machines. a typical machine breaks down once every 5 days. a repairer can repair a machine in an average of 2.5 days. currently, three repairers are on duty. the owner of the laundromat has the option of replacing them with a superworker, who can repair a machine in an average of 5 6 day. the salary of the superworker equals the pay of the three regular employees. breakdown and service times are exponential. should the laundromat replace the three repairers with the superworker?
Replacing three repairers with a superworker would be cost-effective for the laundromat as the expected repair time would increase and lead to more downtime for the machines.
To determine if the laundromat should replace the three repairers with the superworker, we need to compare the expected repair time under each scenario.
With three repairers, the expected time to repair a machine is the sum of the expected time until a machine breaks down and the expected time for a repairer to fix it
E(time with three repairers) = 5 + 2.5/3 = 6.167 days.
With the superworker, the expected time to repair a machine is
E(time with superworker) = 5/6 = 0.833 days.
Therefore, on average, it takes much less time to repair a machine with the superworker than with three repairers. Since the salary of the superworker is equal to that of three repairers, the laundromat should replace the three repairers with the superworker. It is also more cost-effective.
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Neave is designing a prize wheel for her school. 200 students will each spin the wheel once. Neave wants the expected number of winners to be 60.
If the wheel is split into 40 equally sized sections, how many sections should be marked “win”
Neave should mark 12 sections as "win" on the prize wheel to achieve the expected number of winners of 60 out of 200 students.
To determine how many sections should be marked "win" on Neave's prize wheel, we need to consider the expected number of winners and the total number of sections on the wheel.
Neave wants the expected number of winners to be 60 out of 200 students. This means that the probability of winning should be 60/200 = 0.3 or 30%.
If the wheel is split into 40 equally sized sections, we can assume that each section has an equal probability of being selected by a student. Therefore, to have a 30% chance of winning, we need to mark a proportionate number of sections as "win".
To calculate the number of sections to mark as "win", we multiply the total number of sections by the desired probability of winning:
40 sections * 0.3 = 12 sections.
It's important to note that the concept of expected value assumes an idealized scenario with perfect randomness. In reality, the actual number of winners may vary due to random chance and individual spin outcomes.
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The function C(x) = 25x2 - 98x shows the cost of printing magazines (in dollars) per day at a printing press. What is the rate of change of cost when the number of magazines printed per day is 17?
A. 327$/print
B. 552$/print
C. 752$/print
D. 227$/print
The rate of change of cost when the number of magazines printed per day is 17 is 752 dollars per print. The correct option is C.
The function C(x) = 25x² - 98x represents the cost of printing magazines per day at a printing press. To find the rate of change of cost when 17 magazines are printed per day, we need to calculate the derivative of the function with respect to x (the number of magazines printed), which represents the rate of change at a given point.
The derivative of C(x) with respect to x can be found using the power rule for differentiation. For a function of the form f(x) = [tex]ax^n[/tex], its derivative is f'(x) = [tex]n*ax^{(n-1)[/tex].
Applying the power rule to our function, we get:
C'(x) = 2(25x) - 98 = 50x - 98.
Now, we need to evaluate C'(x) when x = 17 (the number of magazines printed per day):
C'(17) = 50(17) - 98 = 850 - 98 = 752.
Therefore, the rate of change of cost when the number of magazines printed per day is 17 is 752 dollars per print. So, the correct answer is: C. 752$/print.
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Amelia read 5 books in 3 months. what was her rate of reading in books per month?
also where should i resize the right columns represent the unit rate?
Amelia's rate of reading was approximately 1.67 books per month (calculated by dividing the total number of books, 5, by the number of months, 3).
How many books did Amelia read per month, and where should I resize the columns to represent the unit rate?To calculate Amelia's rate of reading in books per month, we divide the total number of books she read (5) by the number of months (3). Therefore, her rate of reading is 5/3 books per month.
To resize the right columns to represent the unit rate, you would need to scale them down. If the left column represents the number of months and the right column represents the number of books read, you could adjust the scale so that each unit on the right column represents 1 book per month.
For example, if each square unit on the left column represents 1 month and each square unit on the right column represents 0.5 books, you could resize the right column so that each square unit represents 1 book. This would ensure that the visual representation accurately reflects the unit rate of books per month.
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She wants to play cornhole, but she does not have enough pink bean bags
with her set. However, Sarah keeps a box of spare bean bags in her garage. If
the box contains one yellow, four blue, three red and two pink bean bags,
what is the probability to the nearest tenth of a percent that she will select
the two pink bean bags from the box on her first two attempts?
The probability that she will select the two pink bean bags from the box on her first two attempts is approximately 2.2%.
To calculate the probability that she will select the two pink bean bags from the box on her first two attempts, we need to;
1. Determine the total number of bean bags in the box. There is one yellow, four blue, three red, and two pink bean bags, which makes a total of 1 + 4 + 3 + 2 = 10 bean bags.
2. Calculate the probability of selecting a pink bean bag on the first attempt. There are two pink bean bags out of 10, so the probability is 2/10 or 1/5.
3. After selecting one pink bean bag, there are now nine bean bags left in the box. Calculate the probability of selecting the second pink bean bag on the second attempt. Since there is only one pink bean bag left, the probability is 1/9.
4. To find the overall probability of selecting two pink bean bags in the first two attempts, multiply the probabilities from steps 2 and 3. So, the probability is (1/5) * (1/9) = 1/45.
5. Convert the fraction to a percentage by dividing the numerator by the denominator and multiplying by 100. (1/45) * 100 = 2.22% (rounded to the nearest tenth of a percent).
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If BA = 5x + 5 and AD = 10x - 20, find BD. It is a parallelogram by the way.
To find the length of BD in a parallelogram where BA = 5x + 5 and AD = 10x - 20, we use the fact that opposite sides of a parallelogram are equal in length. Therefore, BD = BA = 30.
Since it is a parallelogram, we know that opposite sides are equal. So, BD = BA = 5x + 5. To find the value of x, we can use the fact that AD is also equal to BD. So, we can set the two expressions for BD equal to each other
5x + 5 = 10x - 20
Simplifying and solving for x, we get
5x = 25
x = 5
Now we can substitute x back into the expression for BD to get the final answer
BD = 5x + 5 = 5(5) + 5 = 30
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Here is a data set: 51, 47, 48, 51, 50, 8
Answer true or false for the following statements.
If you remove the outlier: 8
- the range will stay the same: false
- the mean will decrease: false
- the median will increase: true
The statements are classified as follows:
- the range will stay the same: false- the mean will decrease: false- the median will increase: true.How to obtain the features of the data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
8 is a low outlier, hence it is a value lower than the mean, meaning that the mean increases if we remove the observation of 8.
The range of a data-set is calculated as the difference between the highest value and the lowest value in the data-set, thus if we remove the low value of 8, the next low value is of 47, meaning that the range decreases.
The ordered data-set is given as follows:
8, 47, 48, 50, 51, 51.
The data-set has an even cardinality of 6, hence the median is calculated as the mean of the two middle elements as follows:
Median = (48 + 50)/2
Median = 49.
Removing 8, the data-set is given as follows:
47, 48, 50, 51, 51.
Hence the median increases, as it will be the middle value of 50.
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PLEASE I NEED HELP ASAP
8.4, 42, 210,....
In the sequence above, each term after the first is equal to the previous term times n. What is
the value of the next term in the sequence?
(A) 650
(B) 825
(C) 1,050
(D) 3,050
(E) 5,250
Answer:
C) 1,050
Step-by-step explanation:
We can see that to get from 8.4 to 42 and to get from 42 to 210, we have to multiply by 5.
To complete the sequence, multiply 210 by 5
210·5
=1,050
Hope this helps!
Help with problem in photo pls
Check the picture below.
16 students at a school were asked about their favorite pasta dish. A graph of the results is on the left.
Create a bar graph showing the possible results for all 400 students in the school. Be sure to number the vertical axis.
Answer:
Step-by-step explanation:
to solve this question, we need to use the graph on the left to find the proportions of students who prefer each pasta dish, and then multiply those proportions by 400 to get the estimated number of students in the whole school who prefer each pasta dish. Then we need to plot those numbers on a bar graph with the pasta dishes on the horizontal axis and the number of students on the vertical axis. The graph below shows one possible way to create the bar graph:
We can see that the vertical axis is numbered from 0 to 120 in increments of 20. The bars show the estimated number of students who prefer each pasta dish, based on the sample of 16 students. For example, since 4 out of 16 students prefer spaghetti, we can estimate that 4/16 x 400 = 100 students in the whole school prefer spaghetti. Similarly, since 3 out of 16 students prefer lasagna, we can estimate that 3/16 x 400 = 75 students in the whole school prefer lasagna. We can repeat this process for the other pasta dishes and plot them on the graph.
✧☆*: .｡. Hope this helps, happy learning! (*✧×✧*) .｡.:*☆
