7 is the slope of BD in Quadrilateral.
What in arithmetic is a quadrilateral?
Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional form. Concave and convex are the two most common forms. Additionally, there are several subgroups of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombus, and squares.
There are four closed sides to a quadrilateral. Quadrilaterals are the following figures: produced by Raphael. a quadrilateral form. The form features a single pair of parallel sides and no right angles.
points A(4, 9) and C(3, 2)
slope = y₂ - y₁/x₂ - x₁
= 2 - 9/3 - 4
= - 7/-1
= 7
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As as you approach zero from the left on a number line the integers ____ , but the absolute values of those integers ___?
As you approach zero from the left on a number line, the integers become increasingly negative, but the absolute values of those integers remain positive.
A number line is a visual representation of numbers placed in order on a straight line. It is a graphical tool used to represent the real numbers, starting from negative infinity on the left side and extending to positive infinity on the right side. The number line is divided into equal intervals, and each point on the line corresponds to a specific value or number. The distance between any two points on the number line represents the numerical difference between the corresponding numbers. The number line is a fundamental tool in mathematics for understanding the order and magnitude of numbers, as well as for performing operations such as addition, subtraction, and comparison.
As you approach zero from the left on a number line, the integers become increasingly negative, but the absolute values of those integers remain positive.
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Consider the graph of function g
y4
If f(x)=x², which equation represents function g?
OA. g(z) f(27)
OB. g (2) f(42)
M
2
O C. g(z) = 2 f(z)
(2)
D. 9(2) -
Answer:
D
Step-by-step explanation:
7) Roy buys pizza for his friends. A whole pizza costs P 190. 00 and P 40. 00 for every
additional topping. If he spent P 1070 for pizza with 3 sets of additional toppings, how
many whole pizzas did he buy?
8) There are 4 large gifts. Inside each large gift are 2 medium-sized gifts and inside each
medium-sized gift are 3 small gifts. How many gifts are there altogether?
9) Mang Cardo has cows and chickens in his farm. If he counted 13 heads and 36 feet,
how many cows and chickens does he have?
10) Alexander travelled at 6:00 a. M. And started driving at an average speed of 70 km per
hour. After two hours of driving, he stopped for 30 minutes for a rest. He continued
driving and reach his hometown at 9:30 a. M. How far did he travel?
7) Roy buys 5 whole pizzas.
8) There are 36 gifts altogether.
9) There is 5 cows and 8 chickens.
10) He travel 210 km.
We have the four parts of question:
Now, We have the information:
7) A whole pizza costs P 190.00 and P 40. 00 for every additional topping.
If he spent P 1070 for pizza with 3 sets of additional toppings.
So, The formation of equation is:
=> (1070 - 3 × 40) ÷ 190
=> 5
8) Total gifts are : 4
and Inside each large gift are 2 medium-sized gifts and inside each
medium-sized gift are 3 small gifts.
So, the formation of equation;
=> 4 × 2 = 8
=> 8 × 3 = 24
The total is:
8 + 24 + 4 = 36
9) There are 13 heads and 36 feet .
We know:
Cows have (C) 4 legs
Chickens have (c) 2 legs
So, The equation will be:
C + c=13 ....eq.(1)
Multiply by 4, we get:
4C+2c=36
Then,
4C+4c=52
4C+2c=36
--------------- (-)
2c=16
c = 8 chickens
We put the value of c in eq.(1), we get
C=13 - 8
C = 5 cows
Hence, There is 5 cows and 8 chickens.
10) Alexander travelled at 6:00 a.m.
and, average speed is 70 km per hour.
So, He travelled 140 km in 2 hours.
After two hours of driving, he stopped for 30 minutes for a rest.
He continued driving and reach his hometown at 9:30 a.m.
So, therefore he continues driving at 8:30
then he arrived at his destination at 9:30
So after his break for driving he travels 1 more hour
So in total he travelled 3 hours to arrive at his destination
3 × 70 = 210.
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Determine if the sequence is a geometric sequence. If it is, find the common ratio and write the explicit formula and recursive definition. 45, 15, 5, 5/3
The type of sequence is a geometric sequence with a common ratio of 1/3
Checking the type of sequenceTo determine whether the given sequence is a geometric sequence, we need to check if there is a common ratio between any two consecutive terms.
The common ratio, denoted by "r", is calculated by dividing any term of the sequence by its preceding term.
Let's check if there is a common ratio between any two consecutive terms of the given sequence:
15/45 = 1/3
5/15 = 1/3
5/3 / 5 = 1/3
Since the ratio between any two consecutive terms is the same (1/3), the sequence is a geometric sequence.
To find the explicit formula for a geometric sequence, we use the formula:
an = a1 * r^(n-1)
So, we have
an = 45* (1/3)^(n-1)
For the recursice sequence, we have
an = a(n - 1) * 1/3
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FRANK IS DESIGNING 30-KILOMETERS TRAIL RUN WATER WILL BE GIVEN TO THE RUNNERS 4000 OW MANY WATER STATIONS WILL THERE BE
Based on the above, Frank will need to have about 533 water stations per kilometer for the 30-kilometer trail run.
What is the water stations?If each runner is said to have about 250 milliliters (0.25 liters) of water per station and there are said to be 4000 liters of water available in total, we have to calculate the total number of water stations by:
4000 liters of water ÷ 0.25 liters of water per station
= 16000 stations
we have 30-kilometer run, we have to divide the total number of stations by the distance and it will be:
16000 stations ÷ 30 kilometers
= 533.33 stations per kilometer
Therefore, about 533 water stations per kilometer for the 30-kilometer trail run is needed by Frank.
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see full question below
frank is designing a 30-kilometers trail run water that will be given to runners. if 4000 liters of water is available, each runner was given about 250 milliliters (0.25 liters) of water per station. how many water stations will there be 30-kilometer run.
Consider the geometric sequence 1,3,9,27. If n is a integer, which of these functions generate the sequence?
a(n)= 3^n for n>0
b(n) = 3(3)^n for n>0
c(n)= 3^n for n>2
d(n) = 3^n-1 for n>2
The function d(n) = 3^n-1 for n>2 generates the given geometric sequence.
The common ratio of the given geometric sequence is 3, which means that each term is obtained by multiplying the previous term by 3.
a(n)= 3^n for n>0 generates the sequence 3^1, 3^2, 3^3, 3^4, ... = 3, 9, 27, 81, ..., which is not the same as the given sequence.
b(n) = 3(3)^n for n>0 generates the sequence 3(3)^1, 3(3)^2, 3(3)^3, 3(3)^4, ... = 9, 27, 81, 243, ..., which is not the same as the given sequence.
c(n)= 3^n for n>2 generates the sequence 3^3, 3^4, 3^5, 3^6, ... = 27, 81, 243, 729, ..., which is not the same as the given sequence.
d(n) = 3^n-1 for n>2 generates the sequence 3^2, 3^3, 3^4, 3^5, ... = 9, 27, 81, 243, ..., which is the same as the given sequence starting from the third term.
Therefore, the function d(n) = 3^n-1 for n>2 generates the given geometric sequence.
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Answer: A
a(n) = 3^n for n > 0
Step-by-step explanation: Khan
Choose the correct answer.
Find the quadratic equation given the points (6,0), (-1,0), and (7,4).
h(x) = 1/2(x + 1)(x − 6)
h(x) = 2(x+6)(x − 1)
h(x) = 2(x + 1)(x - 6)
h(x):1/2(x+6) (x - 1)
The quadratic equation given the points (6,0), (-1,0), and (7,4).
The correct answer is h(x) = 1/2(x + 1)(x - 6).
To find the quadratic equation given the points (6,0), (-1,0), and (7,4), we can use the general form of a quadratic equation, which is [tex]h(x) = ax^2 + bx + c.[/tex]
First, let's substitute the coordinates of the given points into the equation to create a system of equations:
For the point (6,0):
[tex]0 = a(6)^2 + b(6) + c ---- (1)[/tex]
For the point (-1,0):
[tex]0 = a(-1)^2 + b(-1) + c ---- (2)[/tex]
For the point (7,4):
[tex]4 = a(7)^2 + b(7) + c ---- (3)[/tex]
We now have a system of three equations with three unknowns (a, b, c). We can solve this system to find the values of a, b, and c.
Solving the system of equations (1), (2), and (3), we find:
a = 1/2
b = -3/2
c = 0
Thus, the quadratic equation that satisfies the given points is:
h(x) = 1/2(x + 1)(x - 6).
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Juanita keeps 25% of the monthly sales from her ice cream shop as a profit. If the shop makes an average of $750 in sales this month, how much money will Juanita keep as profit this month?
Juanita will keep $187.50 as profit from her ice cream shop's sales this month.
Juanita will keep 25% of the monthly sales as profit, which is equivalent to $750 x 0.25 = $187.50. This means that out of the total monthly sales of $750, Juanita will keep $187.50 as her profit, while the remaining $562.50 will go towards the expenses of running the ice cream shop.
Profit is the amount of money that a business earns after deducting all its expenses. It is the excess revenue that remains after all the costs of doing business have been taken into account. Profit is essential for businesses as it helps them to sustain their operations, invest in growth opportunities, and generate returns for their owners or shareholders.
In Juanita's case, her profit is 25% of the monthly sales, which is a significant amount that can help her to keep her ice cream shop running smoothly. By keeping a portion of the sales as profit, Juanita can use the money to pay for her expenses, such as rent, utilities, and supplies, while still having enough left over to reinvest in her business or save for her personal use.
Overall, understanding the concept of profit is crucial for entrepreneurs and business owners to ensure that they can generate enough revenue to cover their expenses and make a profit that will help them to grow and succeed in the long run.
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The profit from selling tickets to a musical can be modeled by the function P(x) = -100x2 + 2,400x - 8,000, where x is the price per ticket, in dollars. What ticket price will maximize the profit?
The profit is maximized at $16,400 when the ticket price is $12.
To find the ticket price that maximizes the profit, we used the fact that the maximum or minimum value of a quadratic function occurs at its vertex. For a quadratic function in the form of P(x) = ax^2 + bx + c, the x-coordinate of the vertex can be found using the formula x = -b / 2a.
In this case, we were given the function [tex]P(x) = -100x^2 + 2400x - 8000,[/tex]where x represents the price per ticket. The coefficient of [tex]x^2[/tex] is negative, which tells us that the graph of this function is a downward-facing parabola. The vertex of this parabola represents the maximum value of the function.
Using the formula x = -b / 2a, we found the x-coordinate of the vertex to be x = -2400 / 2(-100) = 12. This means that a ticket price of $12 will maximize the profit.
To verify that this is indeed the maximum profit, we substituted x = 12 into the profit function P(x):
[tex]P(12) = -100(12)^2 + 2400(12) - 8000 = 16,400[/tex]
We can see that the profit is maximized at $16,400 when the ticket price is $12.
In summary, to find the ticket price that maximizes the profit, we used the formula x = -b / 2a to find the x-coordinate of the vertex of the quadratic function representing the profit from selling tickets to a musical. The maximum profit occurs at the ticket price that corresponds to the x-coordinate of the vertex.
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Analyzing Solution Sets to Linear Equations with the Variable on Both Sides
2x + 5 = 3 + 2(x + 1)
Answer: it will need to be rewritten so that the variable is only on one side of the equation
Step-by-step explanation:f the equation contains fractions, you may elect to multiply both sides of the equation by the least common denominator
IN A CLASS OF 100 STUDENTS ,35 LIKE SCIENCE ,45 LIKE MATH , 10 LIKE BOTH. HOW MANY LIKE EITHER OF THEM , HOW MANY LIKE NEITHER OF THEM
Answer: 5 like either, 5 like neither.
Step-by-step explanation: If we add up those who like science, math and both, we get 90. That leaves 10 students, and because all the other numbers end in 5’s or 0’s, I’d say we split this evenly. So 5 like either, and 5 like neither.
Answer:
Like either science or math but not both: 60
Like neither: 30
Step-by-step explanation:
Total: 100
Like science: 35
Like math: 45
Like both: 10
Subtract 10 from "like science" and 10 from "like math"
Like only science: 25
Like only math: 35
Like both science and math: 10
Total who like math, science, or both: 70
Like either science or math but not both: 25 + 35 = 60
Like neither: 100 - 70 = 30
Which triangle will always have the same area, no matter how it is drawn? A А a right triangle that has two 45° angles an obtuse triangle that has two 30° angles © a right triangle that has two 5-inch-long sides an obtuse triangle that has two 5-inch-long sides
The triangle that will always have the same area, no matter how it is drawn, is a right triangle that has two 45° angles. The correct answer is option A
This is because any right triangle with two 45° angles is a special type of triangle called an isosceles right triangle. In an isosceles right triangle, the two legs are congruent, which means they have the same length. Therefore, no matter how the triangle is drawn, its area will always be the same.
To see why this is true, let's use the formula for the area of a right triangle:
Area = (base x height) / 2
In an isosceles right triangle, the base and height are congruent, so we can write:
Area = (leg x leg) / 2
Simplifying this expression, we get:
Area = (leg^2) / 2
Since the legs of an isosceles right triangle are congruent, we can substitute leg for both legs in the formula:
Area = (leg^2) / 2 = (leg x leg) / 2
No matter how the triangle is drawn, the legs will have the same length, so the area of the triangle will always be the same.
Therefore, the correct answer is option A, a right triangle that has two 45° angles.
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help me please Which choice below is NOT a possible feature of a conjecture?
Group of answer choices
A) It’s a declarative statement
B) It’s a falsehood
C) It’s the truth.
D) It’s a question
Solve this system.
Select one:
a.
No solution
b.
(4,-2)
c.
(5,10)
d.
Infinite solutions
The solution to this system of equations are x =5 and y =10
Calculating the x and y coordinates of the solution to this system of equations.From the question, we have the following parameters that can be used in our computation:
5x - 2y = 5 2x + 2y = 30
Express properly
So, we have
5x - 2y = 5
2x + 2y = 30
Add the equations to eliminate y
7x = 35
Divide both sides by 7
x = 5
Next, we have
2(5) + 2y = 30
So, we have
2y = 20
y = 10
Hence, the value of y is 10
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What’s the answer I need help pls?
Answer:
A, C, F
Step-by-Step:
The amplitude is whatever the coefficient is behind the trig function
A.
kyle swam 4 laps in the pool on monday. he swam
6 times as many laps on tuesday. choose true or false
for each statement.
a. the expression 6 x 4 represents the number of
x
laps kyle swam on tuesday.
b. the words 6 times as many as 4 represents the
number of laps kyle swam on tuesday.
c. the number of laps kyle swam on tuesday can be
found by solving the equation ? = 6 x 4.
d. kyle swam 10 laps on tuesday.
A. Kyle swam 4 laps in the pool on Monday. He swam 6 times as many laps on Tuesday.
a. The expression 6 x 4 represents the number of laps Kyle swam on Tuesday.
b. The words "6 times as many as 4" represent the number of laps Kyle swam on Tuesday.
c. The number of laps Kyle swam on Tuesday can be found by solving the equation x = 6 x 4.
d. Kyle swam 10 laps on Tuesday.
a) True. Since Kyle swam 6 times as many laps on Tuesday as he did on Monday (4 laps), you would multiply 6 by 4 to find the number of laps he swam on Tuesday.
b) True. This phrase means that Kyle swam 6 times the number of laps he swam on Monday (4 laps), which gives you the number of laps he swam on Tuesday.
c) True. This equation represents the total number of laps Kyle swam on Tuesday. By solving the equation, you can determine that Kyle swam 24 laps on Tuesday.
d) False. Based on the information given and the calculations made, Kyle actually swam 24 laps on Tuesday, not 10.
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You roll a 6-sided die two times.
What is the probability of rolling a number greater than 1 and then rolling a number less than
3?
Answer:
Step-by-step explanation:
The possible outcomes of rolling a fair six-sided die are the numbers 1, 2, 3, 4, 5, and 6, each of which has an equal probability of $\frac{1}{6}$ of appearing.
The probability of rolling a number greater than 1 is $\frac{5}{6}$, since there are five out of six possible outcomes that satisfy this condition (namely, 2, 3, 4, 5, and 6).
The probability of rolling a number less than 3 is $\frac{2}{6}=\frac{1}{3}$, since there are two out of six possible outcomes that satisfy this condition (namely, 1 and 2).
To find the probability of both events happening (rolling a number greater than 1 and then rolling a number less than 3), we can multiply their respective probabilities:
$\frac{5}{6}\cdot\frac{1}{3}=\frac{5}{18}$
Therefore, the probability of rolling a number greater than 1 and then rolling a number less than 3 is $\boxed{\frac{5}{18}}$.
6.) Marissa's class is having a Read-a-Thon. The 34 students in her class have read a total of 817 books. On average, how many books has each student read? (5th grade answer)
Answer:
24 with a remainder of 1 (or Q.24 R.1)
Explanation:
divide the amount of books by the amount of students.
Apply the Distributive Property to the right side.
12
enter your response herex
enter your response here (Type integers or fractions.)
The rewritten expression of 12 using the distributive property is 3(2 + 2)
Rewriting the equation using the distributive property.From the question, we have the following parameters that can be used in our computation:
12 distributive property
This means that
12
Express as 6 + 6
So, we have
12 = 6 + 6
Factor out 3 from the equation
So, we have
12 = 3(2 + 2)
The above equation has been rewritten using the distributive property.
Hence, the rewritten expression using the distributive property is 3(2 + 2)
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11. On a basketball court, the free throw lane is marked off geometrically. This area of the court is called the
key and is topped by a semicircle that has a diameter of 12 feet. Find the arc length of the semicircle to the
nearest foot. Find the area of the semicircle to the nearest square foot.
The area of the semicircle is approximately 57 square feet.
The arc length of the semicircle can be found using the formula:
arc length = (θ/360) × 2πr
where θ is the angle in degrees, r is the radius, and π is approximately 3.14.
In this case, the diameter of the semicircle is 12 feet, so the radius is half of that, or 6 feet. The angle of the semicircle is 180 degrees, since it is a semicircle. Plugging these values into the formula, we get:
arc length = (180/360) × 2π(6) ≈ 18.85 feet
Therefore, the arc length of the semicircle is approximately 19 feet.
To find the area of the semicircle, we can use the formula:
area = (πr^2)/2
Plugging in the value of the radius from before, we get:
area = (π(6^2))/2 ≈ 56.55 square feet
Therefore, the area of the semicircle is approximately 57 square feet.
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Please Help Fast!!!!!!!!!!!!!!!!!!!!!!!!!
The number of solutions that are there for the pair of equations for lines Q and S is zero solution (no solution) because the lines are parallel with no point of intersection.
What is no solution?In Mathematics and Geometry, no solution is sometimes referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.
This ultimately implies that, a system of equations would have no solution when the line representing each of the equations are parallel lines and have the same slope i.e both sides of the equal sign are the same and the variables cancel out.
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A farmer of a large apple orchard would like to estimate the true mean number of suitable apples produced per tree. He selects a random sample of 40 trees from his large orchard and determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520. Which of these statements is a correct interpretation of the confidence level?
The confidence level represents the degree of certainty that the interval contains the true population parameter.
The statement "determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520" means that if the farmer were to repeat the sampling process many times and calculate the confidence interval each time, 95% of those intervals would contain the true mean number of suitable apples per tree.
Therefore, we can be 95% confident that the true mean number of suitable apples produced per tree is within the interval of 375 to 520 for this particular sample of 40 trees.
The confidence level represents the degree of certainty that the interval contains the true population parameter.
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The figure below is made of 222 rectangles
The volume of the figure, which is made up of 2 rectangular prisms, would be 276 cm ³.
How to find the volume of the rectangular prism ?The figure shown is made up of two rectangular prisms which means that we can find the volume of the entire figure by finding the volumes of the rectangular prisms and then adding up these volumes to find the total volume.
Volume of the first rectangular prism:
= Length x Width x Height
= 10 x 6 x 3
= 180 cm ³
Volume of the second rectangular prism:
= Length x Width x Height
= 4 x 6 x 4
= 96 cm ³
The total volume of the figure:
= 180 + 96
= 276 cm ³
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Find (A) f'(x). (B) the partition numbers for f', and (C) the critical numbers of f. f(x) = x³ - 75x - 2 (A) f'(x)= (B) Find the partition numbers for f' Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The partition number(s) is/are x = (Use a comma to separate answers as needed) B. There are no partition numbers (C) Find the critical numbers for f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The critical number(s) is/are x = (Use a comma to separate answers as needed) B. There are no critical numbers
The critical numbers of f are x = -5 and x = 5.
(A) To find the derivative f'(x), we differentiate f(x) = x³ - 75x - 2 with respect to x:
f'(x) = 3x² - 75
(B) There are no partition numbers for f' as partition numbers are related to integer partitions, which are not applicable in this context.
(C) To find the critical numbers of f, we set f'(x) equal to 0 and solve for x:
3x² - 75 = 0
x² = 25
x = ±5
So the critical numbers of f are x = -5 and x = 5.
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Your local dry cleaners is running a special. The dry cleaner is offering a 13% discount for any drop off that is over $40. Also, they are running a neighborhood special of an additional 5% off. Given this information, determine the decay factor corresponding to each percent decrease. A. 34. 8; 33. 06 c. 0. 87; 0. 95 b. 0. 384; 0. 3306 d. 87; 95
The decay factor corresponding to each percent decrease is 0.87. The correct option is c. The customer would save a total of $17.35, or 17.35% off the original price.
To determine the decay factor corresponding to each percent decrease, we need to use the formula:
decay factor = (100% - percent decrease)/100%
For the first discount of 13%, the decay factor would be:
decay factor = (100% - 13%)/100% = 0.87
For the additional neighborhood discount of 5%, the decay factor would be:
decay factor = (100% - 5%)/100% = 0.95
So the correct answer is option C, with a decay factor of 0.87 for the 13% discount and 0.95 for the neighborhood discount.
These decay factors represent how much of the original price is left after the discount has been applied. For example, if the original price was $100, after the 13% discount, the price would be:
price after first discount = $100 x 0.87 = $87
Then, after the additional 5% discount, the final price would be:
final price = $87 x 0.95 = $82.65
So the customer would save a total of $17.35, or 17.35% off the original price.
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Find a quadratic function that models the
number of cases of flu each year, where y is years since 2012. What is the coefficient of x? Round your answer to the nearest hundredth
Using regression analysis, we get the following quadratic function:
y = 557[tex]x^{2}[/tex] + 1,690x + 60,000
How to explain the functionWe can use the data given and fit a quadratic equation in the form of y = a[tex]x^{2}[/tex] + bx + c, where y represents the number of flu cases and x is the number of years since 2012.
x (years since 2012) y (number of flu cases)
0 60,000
1 62,000
2 63,000
3 64,000
4 65,000
5 66,000
6 67,000
7 68,000
8 69,000
9 70,000
10 71,000
11 72,000
12 73,000
13 74,000
14 75,000
15 76,000
Next, we can use this table to find the coefficients a, b, and c that give us the best-fit quadratic function.
Using a regression analysis, we get the following quadratic function:
y = 557[tex]x^{2}[/tex] + 1,690x + 60,000
Here, the coefficient of x is 1,690, which represents the linear term in the quadratic equation. It tells us how much the number of flu cases changes with each year since 2012, assuming a quadratic relationship.
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Year Number of Flu Cases
2000 20,000
2001 22,000
2002 25,000
2003 28,000
2004 32,000
2005 35,000
2006 38,000
2007 42,000
2008 45,000
2009 50,000
2010 55,000
2011 58,000
2012 60,000
2013 62,000
2014 63,000
2015 64,000
Find a quadratic function that models the number of cases of flu each year, where y is years since 2012. What is the coefficient of x?
Omar Cuts A Piece of wrapping paper with the shape and dimensions as shown.Find The Area Of The Wrapping Paper.Round Your Answer To The Nearest Tenth Of Needed
Answer:
72.5 square inches
Step-by-step explanation:
See attachment.
The areas of the 2 shapes are in blue, but when added together:
60+12.5=72.5
Hope this helps!
5. A 40-kg ornamental star is suspended by two chains fastened to
horizontal beams at different heights with angles as shown.
Determine the tension in each chain.
The diagram is shown below; I also know we have to split up the triangles to make two right angle triangles but I’m not sure where to go from there
Answer:We can start by resolving the forces acting on the ornamental star in the vertical direction and in the horizontal direction. Since the star is stationary, these forces must balance each other out.
Let's call the tension in the higher chain T1 and the tension in the lower chain T2. We can use trigonometry to find the vertical and horizontal components of each tension force.
For T1:
The vertical component is T1cos(40°) and the horizontal component is T1sin(40°).
For T2:
The vertical component is T2cos(30°) and the horizontal component is T2sin(30°).
Now, resolving the forces in the vertical direction, we have:
T1cos(40°) + T2cos(30°) - mg = 0
where m is the mass of the star and g is the acceleration due to gravity.
Substituting the values:
T1cos(40°) + T2cos(30°) - (40 kg)(9.81 m/s^2) = 0
T1cos(40°) + T2cos(30°) = 392.4 N
Next, resolving the forces in the horizontal direction, we have:
T1sin(40°) = T2sin(30°)
Now we have two equations with two unknowns:
T1cos(40°) + T2cos(30°) = 392.4 N
T1sin(40°) = T2sin(30°)
Solving these equations simultaneously, we get:
T1 = 266.4 N
T2 = 205.1 N
Therefore, the tension in the higher chain (T1) is 266.4 N and the tension in the lower chain (T2) is 205.1 N.
Step-by-step explanation:
2. Mandy is walking in the woods. She completes 70% of her walk in 3 hours. She continues walking at that same rate. How much time, in hours, will Mandy's entire walk take?
A 3 4\5
B. 5
C. 6
D. 6 1\2
Answer:
If Mandy completed 70% of her walk in 3 hours, then we can find her walking rate as follows:
Let's assume that the entire walk takes t hours. Then, 70% of the walk would take 0.7t hours. We know that Mandy completes 70% of her walk in 3 hours, so we can set up the following equation:
0.7t = 3
Solving for t, we get:
t = 3 ÷ 0.7 ≈ 4.29
So, the entire walk will take approximately 4.29 hours. Since Mandy has already walked for 3 hours, the remaining time she needs to complete her walk is:
4.29 - 3 = 1.29 hours
Therefore, the answer is closest to option A, 3 4/5 hours.
Learn more about Walking Rates here:
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Which number sequence follows the rule subtract 15 starting from 105? 15, 30, 45, 60, 75 15, 10, 25, 20, 35 105, 100, 95, 90, 85 105, 90, 75, 60, 45
The number sequence that follows the rule of subtracting 15 starting from 105 is 105, 90, 75, 60, 45.
To obtain this sequence, we start with 105 and subtract 15 from it to get 90. Then we subtract 15 from 90 to get 75, and so on until we reach 45. Each term in the sequence is obtained by subtracting 15 from the previous term.
It is important to note that this is an arithmetic sequence with a common difference of -15. The formula for finding the nth term of an arithmetic sequence is: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference. Using this formula, we can find any term in the sequence by plugging in the appropriate values.
To know more about sequence refer here:
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