Heart rate refers to the number of times the heart beats per minute, and is an indicator of cardiovascular health and fitness. It can be affected by factors such as age, activity level, and overall health.
Hours of exercise per week refers to the amount of time spent engaging in physical activity or exercise over a period of seven days. It is often recommended for maintaining good physical and mental health.
Based on the information provided, the study investigates the relationship between hours of exercise per week and resting heart rate. Here's a step-by-step explanation:
1. Identify the population model being estimated: The appropriate model is one where resting heart rate ('HeartRate') is the dependent variable, and hours of exercise per week ('Exercise') is the independent variable. From the given options, this corresponds to:
Answer 1: C. Heart Rate = bo + b Exercise
2. Determine the intercept and slope using the graph: Based on the plot provided, we can approximate the intercept (bo) and slope (b) of the line of best fit. These values represent the starting point (resting heart rate without exercise) and the change in heart rate for each additional hour of exercise per week, respectively.
Answer 2: Intercept (bo) ≈ 79
Answer 3: Slope (b) ≈ -4
So, the estimated population model is: HeartRate = 79 - 4 * Exercise
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there are two samples, a and b, ere tested by rockwell hardness test. sample a is tested in b scale, shows hardness value 59 hrb. sample b is tested in f scale, shows hardness value 90.5 hrf. which sample is harder? (use your conversion chart if it is necessary)
sample B is harder than sample A.To compare the hardness values of samples A and B, we need to convert them to the same scale.
Rockwell hardness scales are designated by a letter, such as B or F, and each scale has a different range and units of measurement.
To convert sample A's hardness value from the B scale to the F scale, we can use the conversion chart. According to the chart, the conversion formula from B to F scale is HRF = (HRB x 1.000) + 18. Therefore, the converted hardness value for sample A is:
HRF = (59 x 1.000) + 18 = 77 HRF
Now we can compare the hardness values of both samples, and we see that sample B has a higher hardness value of 90.5 HRF, compared to sample A's value of 77 HRF. Therefore, we can conclude that sample B is harder than sample A.
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What is the surface area of this complex shape?
408 ft
458 ft
545 ft
720 ft
680 ft
1000 ft
GIVING BRAINLIEST TO WHO ANSWERS IT CORRECTLY
The surface area of the figure will be 458 square feet. Then the correct option is B.
What is the area?The quantity area demonstrates the amount of a sector on a planar or hemispherical cup. Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.
The surface area of the figure is given as,
[tex]\sf SA = 2 [(12 \times 5) + (12 \times 5) + (7 \times 7) + (5 \times 12)][/tex]
[tex]\sf SA = 2 (60 + 60 + 49 + 60)[/tex]
[tex]\sf SA = 2 (229)[/tex]
[tex]\sf SA = 458 \ square \ feet[/tex]
The surface area of the figure will be 458 square feet. Then the correct option is B.
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if x initially contains the value 3, which of the following sets x to 7?
To set x to 7 when it initially contains the value 3, you would need to add 4 to x. Therefore, the option that would set x to 7 is x = x + 4.
This statement adds 4 to the current value of x (which is 3), resulting in x being equal to 7. It is important to note that there may be other ways to set x to 7 depending on the specific context and code. However, in the absence of further information, adding 4 to x is the most direct and simple solution.
Let's consider that x initially contains the value 3. We want to find an operation that sets x to 7. Since we're looking for a change of +4 (7 - 3), we can perform the following operation: x = x + 4. By adding 4 to the initial value of x, we get x = 3 + 4, which results in x = 7. Thus, the operation that sets x to 7 when it initially contains the value 3 is x = x + 4.
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Twenty percent of the 640 pitches Kendall threw last year were strikes. Which table can be used to find the number of strikes she threw?
Number of Pitches
A 3-column table with 6 rows. Column 1 has entries 20 percent, 20 percent, 20 percent, 20 percent, 20 percent = 100 percent. Column 2 has entries 0. 2, 0. 2, 0. 2, 0. 2, 0. 2 = 1. Column 3 has entries 128, 128, 128, 128, 128 =640. Number of Pitches
A 3-column table with 6 rows. Column 1 has entries 20 percent, 20 percent, 20 percent, 20 percent, 20 percent = 100 percent. Column 2 has entries 0. 2, 0. 2, 0. 2, 0. 2, 0. 2 = 1. Column 3 has entries 256, 256, 256, 256, 256 = 1,280. Number of Pitches
A 3-column table with 5 rows. Column 1 has entries 25 percent, 25 percent, 25 percent, 25 percent = 100 percent. Column 2 has entries 0. 25, 0. 25, 0. 25, 0. 25 = 1. Column 2 has entries 160, 160, 160, 160 = 640. Number of Pitches
A 3-column table with 5 rows. Column 1 has entries 25 percent, 25 percent, 25 percent, 25 percent = 100 percent. Column 2 has entries 0. 25, 0. 25, 0. 25, 0. 25 = 1. Column 2 has entries 320, 320, 320, 320 = 1,280
A 3-column table with 5 rows. Column 1 has entries 25 percent, 25 percent, 25 percent, 25 percent = 100 percent. Column 2 has entries 0.25, 0.25, 0.25, 0.25 = 1. Column 3 has entries 320, 320, 320, 320 = 1,280.
The correct table that can be used to find the number of strikes Kendall threw is:
A 3-column table with 5 rows.
Column 1 has entries 25 percent, 25 percent, 25 percent, 25 percent = 100 percent.
Column 2 has entries 0.25, 0.25, 0.25, 0.25 = 1.
Column 3 has entries 320, 320, 320, 320 = 1,280.
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the model of a river is constructed to a scale of 1/60. if the water in the river is flowing at 38 ft/s, how fast must the water flow in the model?
The water in the given model must flow at a constant speed of 2,280 ft/s to represent the actual water flow of 38 ft/s.
The speed of water flow in the model can be calculated as follows:
Model speed = Actual speed / Scale factor
Since the scale factor is 1/60, the model speed will be:
Model speed = 38 ft/s / (1/60) = 2,280 ft/s
Therefore, the water in the given model must flow at a constant speed of 2,280 ft/s to accurately and precisely represent the actual water flow of 38 ft/s.
Note: The calculated model speed seems unreasonably high, and it is likely that there is an error in the given values or in the calculation.
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The triangle above has the following measures.
s = 23 in
r = 75 in
Find the mzQ.
Round to the nearest tenth and include correct units.
Show all your work
The measure of the angle of the triangle is ∠Q = 72.1°
Given data ,
Let the triangle be represented as ΔQRS
Now , the measure of sides of the triangle are
SQ = 75 inches
And , RS = 23 inches
From the trigonometric relations , we get
cos θ = adjacent / hypotenuse
On simplifying , we get
cos Q = 23/75
cos Q = 0.3066667
Taking inverse on both sides , we get
The inverse of the cosine function is Q = cos⁻¹ ( 0.306667 )
Q = 72.14°
Hence , the angle is Q = 72.1°
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the vector equation ,0
Hello! It seems like your question might be incomplete or missing some details. However, I'll provide you with a brief explanation of a vector equation, and if you need more help, please provide additional information.
A vector equation is an expression that describes a vector in terms of its components, magnitude, and/or direction. It is often used to represent , such as displacement, velocity, and force, which have both magnitude and direction. In general, a vector equation can be written as:
Vector V = ai + bj + ck
Here, V is the vector, and a, b, and c are its components along the x, y, and z axes, respectively. i, j, and k are the unit vectors along the x, y, and z axes.
If you need help with a specific vector equation or problem, please provide more details, and I'll be happy to assist you.
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six shapes are shown bellow, some of these are regular polygons, some are regular some are not polygons in the table write down the letter of each shape in the correct column below
Table 1 is filled with option C, table 2 is filled with option A, B, and E, and table 3 is filled with option D.
There are six different shapes given in the questions.
We need to fill the table that is given in the question. The table is asked to segregate the figures into regular polygons, irregular polygons, and not polygon.
Therefore,
A regular polygon is only the option (C)
Irregular polygon is options A, B, and E.
Not a polygon is the only option (D)
Thus, table 1 is filled with option C, table 2 is filled with option A, B, and E, and table 3 is filled with option D.
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For the given cost function C(x) = 1900 + 390x + 1.5x2 and the demand function p(x) = 1170 (i.e. the price p at the given volume of demand x). Find the production level that will maximaze the profit P(x)=r(x)-c(x), where r(x) is the revenue function.
The production level that will maximize the profit P(x)=r(x)-c(x) [where r(x) is the revenue function] is x = 260 units.
For the given cost function C(x) = 1900 + 390x + 1.5x^2 and the demand function p(x) = 1170, we will find the production level that will maximize the profit P(x) = r(x) - c(x), where r(x) is the revenue function.
Determine the revenue function r(x) by multiplying the demand function p(x) by x (i.e., the quantity sold):
r(x) = p(x) * x = 1170 * x
Calculate the profit function P(x) by subtracting the cost function C(x) from the revenue function r(x):
P(x) = r(x) - C(x) = 1170x - (1900 + 390x + 1.5x^2)
Simplify the profit function:
P(x) = 780x - 1900 - 1.5x^2
Step 4: To find the production level that maximizes the profit, we need to find the critical points of the profit function by taking its first derivative and setting it to zero:
P'(x) = d(P(x))/dx = 780 - 3x
Now set P'(x) to 0 and solve for x:
780 - 3x = 0
3x = 780
x = 260
The production level that will maximize the profit is x = 260 units.
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look at cliped pic please help
Answer:
[tex]( { \frac{4}{7} )}^{2} = \frac{ {4}^{2} }{ {7}^{2} } = \frac{16}{49} [/tex]
the region r in the first quadrant is enclosed by the lines x=0 and y=5 and the graph of y=x^2+1
Therefore, the area of the region r is 8 square units.
To start, let's graph the two lines and the equation y=x^2+1 in the first quadrant:
As we can see from the graph, the region r is a triangle with a curved bottom. To find the area of this region, we can use integration.
First, we need to find the x-coordinates of the points where the line y=5 intersects with the curve y=x^2+1. To do this, we set the two equations equal to each other:
5 = x^2 + 1
Subtracting 1 from both sides gives us:
4 = x^2
Taking the square root of both sides, we get:
x = ±2
Since we are only interested in the positive x-value (since we are in the first quadrant), we have:
x = 2
Next, we need to set up our integral to find the area of the region r. Since the region is bounded by the lines x=0 and y=5, and the curve y = x^2+1, we can integrate with respect to y, using the limits of integration y=1 and y=5 (since the curve starts at y=1 when x=0).
The area of the region r can be found using the following integral:
A = ∫[1,5] [√y - 1] dy
Integrating, we get:
A = [2/3 y^(3/2) - y] [1,5]
A = [2/3 (5)^(3/2) - 5] - [2/3 (1)^(3/2) - 1]
A = 25/3 - 1/3
A = 8
Therefore, the area of the region r is 8 square units.
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slope of (-9,6) and (3,6)
Answer: Slope of 0
Step-by-step explanation: Both points are 6 on the y-axis.
PLEASE HELP!! LIMITED TIME WILL GIVE BRAINLIEST/POINTS!
The number of cars waiting at a bank for 60 minutes is as follows.
Find the probability of 3 cars waiting in line.
P( 3 ) = [?]
Answer:
The probability is 1/5 or 0.2
Step-by-step explanation:
Probability of 3 cars waiting in the line= the number of 3 cars waiting in the line/Total number of cars
T(c)=2+9+16+12+8+6+4+2+1=60
P=12/60
P=1/5 or 0.2
Think of a proportional relationship you may see in your daily life . Make a table of data and graph the data. explain how u know that the data show a proportional relationship
One example of a proportional relationship in daily life could be the relationship between the distance traveled by car and the time it takes to travel that distance, assuming a constant speed.
We have,
Let's say we have a car that is traveling at a constant speed of 60 miles per hour.
We can create a table of data to show the relationship between distance and time:
Distance (miles) Time (hours)
60 1
120 2
180 3
240 4
300 5
We can see from the table that as the distance traveled increases by a factor of 2, the time it takes to travel that distance also increases by a factor of 2.
This is a proportional relationship.
Thus,
One example of a proportional relationship in daily life could be the relationship between the distance traveled by car and the time it takes to travel that distance, assuming a constant speed.
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22. Look at the given triangles.
4x + 2
7x+7
C.
x+3
2x-5
X+7
5x-4
a Write an expression in simplest form for the perimeter of each triangle.
b. Write another expression in simplest form that shows the difference between the perimeter
of the larger triangle and the perimeter of the smaller triangle.
Find the perimeter for each triangle when x = 3
U
a. The perimeter of the first triangle is and the perimeter of the second triangle is
b. The difference between the perimeters is
c The perimeter of the triangles when x is 3 are
What is perimeter of triangle?Perimeter is a math concept that measures the total length around the outside of a shape.
The perimeter of a triangle = a+b+c
1. 4x+2 + 7x+7 + x+3
= 4x+7x+ x +2+7+3
= 12x +12
Perimeter of the second triangle
= 2x-5+x+7+5x-4
= 2x+5x+x-5+7-4
= 8x-2
2. The difference of the perimeters
= 12x+12 -( 8x-2)
= 12x-8x +12+2
= 4x +14
3. when x is 3
The perimeter of the first triangle
= 12(3) +12
= 36+12
= 48 units
The perimeter of the second triangle
= 8(3)- 2
= 22 units
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(7) Mary is 4 years older than Toni. Sam is twice as old
as Mary. The sum of their three ages is 8 times
Toni's age. How old are they?
Solving a system of equations we can see that:
Toni is 3 years old, Mary is 7 years old, and Sam is 14 years old.
How old are they?
First let's define the variables:
M = Mary's age.T = Toni's age.S = Sam's age.With the given information we can write 3 equations:
M = T + 4
S = 2*M
M + T + S = 8T
Now let's solve the system.
Replace thefirst equation into the second one to get:
S = 2*(T + 4)
Now we can replace the two equations in the last one to get:
T + 4 + T + 2*(T + 4) = 8*T
Now we can solve this for T.
4T + 12 = 8T
12 = 8T - 4T
12 = 4T
12/4 = T = 3
Now that we know that value, we can get the other two:
M = 4 + T = 4 + 3 = 7
S = 2*M = 2*7 = 14
These are the 3 ages.
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Which set of two variables is most likely to have a cause-and-effect relationship? A. The age of a teacher and the income of the teacher B. The height of a person and the weight of a person C. The weight of a box and the postage rate we have to pay to ship the box to California D. The make of a car and the mileage of the car
Out of the given options, the set of variables that is most likely to have a cause-and-effect relationship is A. The age of a teacher and the income of the teacher. A cause-and-effect relationship implies that one variable is the cause of changes in the other variable.
In this case, it is possible to argue that the age of a teacher can cause changes in their income. For example, as teachers gain more experience and seniority, they may be eligible for higher salaries. Additionally, teachers who have been in the profession for longer may have more qualifications or skills that make them more desirable to schools and therefore more likely to earn higher incomes. On the other hand, the other options do not necessarily have a clear cause- and- effect relationship. For example, while a person's weight may influence their height to some extent, it is not a direct cause-and-effect relationship. Similarly, while the make of a car may influence its mileage, it is not a direct cause-and-effect relationship. In conclusion, while it is important to consider all variables when analyzing data, it is essential to identify which variables have a direct cause-and-effect relationship. In this case, the set of variables with a cause-and-effect relationship is A. The age of a teacher and the income of the teacher. Based on the given options, the set of two variables most likely to have a cause-and-effect relationship is C. The weight of a box and the postage rate we have to pay to ship the box to California.This relationship is likely cause-and-effect because shipping companies typically charge postage rates based on the weight of the package being sent. As the weight of a box increases, the cost to ship it usually increases as well, demonstrating a direct cause-and-effect relationship between these two variables
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HELP ASAP !!!!
The coordinates of a triangle are described by a matrix, where the rows represent each point, A, B, and C, from top row to bottom row, and column 1 represents the x coordinates and column 2 represents the y coordinates. What transformation does the following matrix represent when added to the first matrix?
A. A rotation about the origin clockwise by 90°
B. A flip over the y-axis
C. A translation to the left by 20 units and down by 20 units
D. A translation to the right by 20 units and down by 20 units
Answer:
D. A translation to the right by 20 units and down by 20 units
Step-by-step explanation:
You want to know the effect of adding (20, -20) to the (x, y) coordinates of the vertices of a triangle.
TransformationThe x-coordinate of a point tells you its position to the right of the y-axis. Adding 20 to the x-coordinate moves its position 20 units farther to the right.
The y-coordinate of a point tells you its position above the x-axis. Subtracting 20 from the y-coordinate moves its position down 20 units.
The matrix represents the transformation ...
A translation to the right by 20 units and down by 20 units, choice D.
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What is the best estimate for the volume of the pyramid
The best estimate for the volume of the pyramid is 1386.67 cubic units.
To calculate the volume of a pyramid, we use the formula V = (1/3) * B * h, where B is the area of the base and h is the height of the pyramid. In this case, we are given that the base of the pyramid is a rectangle with dimensions 15 units by 20 units, so the area of the base is B = 15 * 20 = 300 square units. We are also given that the height of the pyramid is 14 units. Therefore, the volume of the pyramid is V = (1/3) * 300 * 14 = 1400 cubic units. However, since this is an estimate, we should round our answer to a reasonable number of decimal places. In this case, we can round to two decimal places to get a final answer of 1386.67 cubic units. This estimate gives us a good approximation of the volume of the pyramid based on the information provided.
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T/F: a dss can do a follow-up assessment on how well a solution is performing.
True, a decision support system (DSS) can conduct a follow-up assessment on how well a solution is performing. This is because a DSS is designed to analyze and evaluate data, as well as provide ongoing feedback on the effectiveness of decisions made using the system.
By monitoring key performance indicators and other metrics, a DSS can provide valuable insights into the success of a particular solution or course of action, allowing users to make more informed decisions going forward.
True: A Decision Support System (DSS) can do a follow-up assessment on how well a solution is performing. This allows for continuous improvement and optimization of the implemented solution based on the collected data and feedback.
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The table of values represents an exponential function f(x). What is the average rate of change over the interval −2≤x≤2? Enter your answer, as a decimal rounded to the nearest hundredth, in the box. −3 64 −2 16 −1 4 0 1 1 1/4 2 1/16 3 1/64
Rounded to the nearest hundredth, the average rate of change over the interval -2 ≤ x ≤ 2 is approximately -3.98.
To find the average rate of change of the exponential function over the interval -2 ≤ x ≤ 2, we need to calculate the slope between the endpoints of the interval.
At x = -2, the corresponding value is 16, and at x = 2, the corresponding value is 1/16.
The change in y (Δy) between these two points is 1/16 - 16 = -255/16.
The change in x (Δx) is 2 - (-2) = 4.
The average rate of change is Δy/Δx = (-255/16)/4 = -255/64.
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I need help pls quick
Answer:
14
Step-by-step explanation:
I think what you're asking is how many study Spanish. In the diagram, the spot for Spanish has the number 14.
determine the angular velocity of the gear and the velocity of its center o at the instant shown
For the angular velocity of the gear, you'll need to gather relevant information about the gear, calculate the linear velocity, and use the formula = v / r. The velocity of the center "O" is always 0 as it does not move linearly.
To determine the angular velocity and the velocity of the center 'O' of the gear at the given instant, you will need to follow these steps:
Step 1: Identify the relevant information.
First, gather information about the gear, such as its radius, the speed at which it is rotating, and any other relevant details. To determine the angular velocity of the gear and the velocity of its center at the instant shown, we need to know the radius of the gear and the speed of its rotation. The angular velocity of the gear can be calculated by dividing the speed of rotation by the radius of the gear. The velocity of the center of the gear can be calculated by multiplying the angular velocity by the radius of the gear.
Step 2: Calculate the angular velocity.
Angular velocity () can be calculated using the formula = v / r, where 'v' is the linear velocity at the edge of the gear and 'r' is the radius of the gear.
Step 3: Find the linear velocity at the edge of the gear.
This can typically be given or can be determined based on the information provided.
Step 4: Calculate the angular velocity.
Plug the values of linear velocity (v) and radius (r) into the formula = v / r to find the angular velocity.
Angular velocity = (speed of rotation) / (radius of gear)
Velocity of center = (angular velocity) x (radius of gear)
Step 5: Determine the velocity of the center 'O'
Since the center 'O' of the gear is the point around which the gear rotates, its velocity is 0, as it does not move linearly.
In summary, to find the angular velocity of the gear, you'll need to gather relevant information about the gear, calculate the linear velocity, and use the formula = v / r. The velocity of the center "O" is always 0 as it does not move linearly.
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Please try this ! Ill mark u as brainliest is do!!!
Answer: (50, 40)
Step-by-step explanation:
I am not a 100% sure if it is 40, but try that. if c is an equal distance to both a and b and the total distance between a and be is 40 (because 100-60 is 40), the middle of that would be 20. given that, 60 from the y axis minus 20 is 40.
* so try (50,40)
A cone has a volume of 4.5pi cubic inches and a height of 13.5 inches. which measure is closest to the radius of the cone in inches?
Answer: The volume of a cone can be expressed as:
V = (1/3)πr^2h
where V is the volume, r is the radius, and h is the height of the cone.
We are given that the volume of the cone is 4.5π cubic inches and the height is 13.5 inches. Substituting these values into the equation above, we get:
4.5π = (1/3)πr^2(13.5)
Simplifying this equation, we get:
r^2 = (4.5π * 3) / (13.5π)
r^2 = 1
Taking the square root of both sides, we get:
r = 1 inch
Therefore, the measure closest to the radius of the cone is 1 inch.
A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 4 hours. The company has only 800 work hours to use in manufacturing each day, and the packaging department can package only 300 trimmers per day. If the company sells the cord-type model for $22. 50 and the cordless model for $45. 00, how many of each type should it produce per day to maximize its sales?
The company should produce 200 cord-type trimmers and 100 cordless trimmers per day to maximize its sales. The total sales will be $10,500.
To maximize the sales, the company needs to determine how many units of each type of electric hedge trimmers it should produce, subject to the constraints of manufacturing time and packaging capacity. Let x be the number of cord-type trimmers and y be the number of cordless trimmers that the company produces per day.
Since the cord-type trimmer requires 2 hours to make and the cordless model requires 4 hours, the total manufacturing time can be expressed as:
2x + 4y ≤ 800
Similarly, the packaging department can package only 300 trimmers per day, which means:
x + y ≤ 300
We also know that the company sells the cord-type model for $22.50 and the cordless model for $45.00, so the total sales can be expressed as:
total sales = 22.50x + 45.00y
To maximize the total sales subject to the above constraints, we can use linear programming. Solving the above equations using the graphical method, we get the feasible region bounded by the lines 2x + 4y = 800 and x + y = 300. The corners of this feasible region are (0, 300), (200, 100), and (400, 0).
Now, we need to determine the values of x and y that maximize the total sales. We can evaluate the total sales at each of the corners of the feasible region and choose the corner that gives the maximum total sales.
At (0, 300), the total sales = 22.50x + 45.00y = 45.00 * 300 = $13,500.
At (200, 100), the total sales = 22.50x + 45.00y = 22.50 * 200 + 45.00 * 100 = $10,500.
At (400, 0), the total sales = 22.50x + 45.00y = 22.50 * 400 = $9,000.
Therefore, the company should produce 200 cord-type trimmers and 100 cordless trimmers per day to maximize its sales. The total sales will be $10,500.
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let p(x, y) be the terminal point on the unit circle determined by t. then sin(t) =
We can use the parametric equation of the unit circle to find the values of sin(t) and cos(t) for a given terminal point (x, y). The parametric equation of the unit circle is given by:
x = cos(t)
y = sin(t)
Since the terminal point (x, y) is on the unit circle, we know that x^2 + y^2 = 1. Substituting the expressions for x and y from the parametric equation, we get:
cos^2(t) + sin^2(t) = 1
Simplifying this equation, we get:
sin^2(t) = 1 - cos^2(t)
Taking the square root of both sides, we get:
sin(t) = ±sqrt(1 - cos^2(t))
Since the unit circle is defined to have radius 1, we know that -1 ≤ cos(t) ≤ 1, and therefore 0 ≤ cos^2(t) ≤ 1. This means that 0 ≤ 1 - cos^2(t) ≤ 1, and therefore 0 ≤ sqrt(1 - cos^2(t)) ≤ 1.
Since we are given that the terminal point (x, y) is on the unit circle, we know that x^2 + y^2 = 1, and therefore cos^2(t) + sin^2(t) = 1. This implies that cos^2(t) = 1 - sin^2(t).
Substituting this expression for cos^2(t) into the equation for sin(t), we get:
sin(t) = ±sqrt(1 - cos^2(t)) = ±sqrt(1 - (1 - sin^2(t))) = ±sqrt(sin^2(t))
Since sin(t) is always non-negative on the unit circle, we can take the positive square root and simplify to get:
sin(t) = sqrt(sin^2(t)) = sin(t)
Therefore, the value of sin(t) is simply the y-coordinate of the terminal point (x, y) on the unit circle, which is given by sin(t).
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A student organization holds meetings every week, with one chosen leader and two assistants to run the meeting efficiently. If there are 14 weeks in a semester, how many students must be in the organization to guarantee that they can have a different set of leaders/assistants at every meeting?
To guarantee a different set of leaders/assistants at every meeting, the organization would need at least 45 students.
To see why, consider the first meeting. There are three students chosen to lead/assist, leaving (total number of students - 3) students who did not lead/assist.
For the second meeting, we need to choose three different students from the remaining pool of (total number of students - 3) students. This can be done in (total number of students - 3) choose 3 ways, which is equal to:
(total number of students - 3)! / [3!(total number of students - 6)!]
For there to be a different set of leaders/assistants at every meeting, we need this number to be greater than or equal to 14 (the number of meetings in a semester). So we have:
(total number of students - 3)! / [3!(total number of students - 6)!] >= 14
Simplifying this inequality and solving for total number of students, we get:
(total number of students) * (total number of students - 1) * (total number of students - 2) >= 126
Since we want the smallest possible value for total number of students, we can start by guessing that it is around 10. If we plug in total number of students = 10, we get:
10 * 9 * 8 = 720
This is greater than 126, so we know that the organization needs at least 10 students. Trying total number of students = 11 gives:
11 * 10 * 9 = 990
This is also greater than 126, so we know that the organization needs at least 11 students. Continuing this way, we find that the smallest integer value of total number of students that satisfies the inequality is 45.
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5,322,093.05 in words
Answer:
five million three hundred twenty-two thousand ninety-three and five hundredths
Step-by-step explanation:
have a great day and thx for your inquiry :)
Answer:
five million, three hundred and twenty two thousand and ninety three point zero five
liam is buying tickets for a group of families going to an amusement park. he wants to have at least 20 tickets. each adult ticket costs $15.75 and each child ticket costs $13. liam wants to spend no more than $250. which system of inequalities can liam use to find the number of tickets he can buy?
Inequalities ensure that Liam buys enough tickets (at least 20), and also that he stays within his budget (spends no more than $250).
Let's use the variables "a" and "c" to represent the number of adult and child tickets Liam buys, respectively. Then the total number of tickets he buys is a + c, and the total cost of the tickets is 15.75a + 13c.
To find the system of inequalities, we need to use the given information:
Liam wants to have at least 20 tickets: a + c ≥ 20
Each adult ticket costs $15.75 and each child ticket costs [tex]$13: 15.75a[/tex] + 13c ≤ 250 (since Liam wants to spend no more than [tex]$250)[/tex]
So the system of inequalities is:
a + c ≥ 20
15.75a + 13c ≤ 250
These inequalities ensure that Liam buys enough tickets (at least 20), and also that he stays within his budget (spends no more than [tex]$250).[/tex]
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