HELP!!!
What is the unit rate of this graph?
BLUE: 200 beats/minute
TEAL: 75 beats/minute
YELLOW: 100 beats/minute
RED: 150 beats/minute
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Henry earned $850 over the summer working odd jobs. he wants to put his money into a savings account for when he is ready to buy a car. his bank offers a simple interest account at 5%, how much interest will henry have earned after 4 years?
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Answer:
We can use the formula for simple interest to calculate the interest earned by Henry:
Simple Interest = (Principal * Rate * Time)
where,
Principal = $850 (initial amount)
Rate = 5% per year (as given)
Time = 4 years (as given)
Substituting the values, we get:
Simple Interest = (850 * 0.05 * 4) = $170
Therefore, Henry will have earned $170 in interest after 4 years of keeping his money in the savings account.
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1) Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.)
f(x, y) = 5x^2 + 5y^2; xy = 1
2) Find the extreme values of f subject to both constraints. (If an answer does not exist, enter DNE.)
f(x, y, z) = x + 2y; x + y + z = 6, y^2 + z^2 = 4
Answers
The maximum and minimum values for given function f(x, y) = 5x² + 5y² subject to xy = 1 are both 10. The extreme values of f(x, y, z) = x + 2y; x + y + z = 6, y² + z² = 4 subject to both constraints are 7 and -4.
We can use Lagrange multipliers to find the maximum and minimum values of f(x, y) subject to the constraint xy = 1.
First, we set up the Lagrange function
L(x, y, λ) = 5x² + 5y² + λ(xy - 1)
Then, we take partial derivatives of L with respect to x, y, and λ and set them equal to 0
∂L/∂x = 10x + λy = 0
∂L/∂y = 10y + λx = 0
∂L/∂λ = xy - 1 = 0
Solving these equations simultaneously, we get
x = ±√2, y = ±√2, λ = ±5/2√2
We also need to check the boundary points where xy = 1, which are (1, 1) and (-1, -1). We evaluate f at these points and compare them to the values we get from the Lagrange multipliers.
f(√2, √2) = 10, f(-√2, -√2) = 10
f(1, 1) = 10, f(-1, -1) = 10
So the maximum and minimum values of f(x, y) subject to xy = 1 are both 10.
We can use Lagrange multipliers to find the extreme values of f(x, y, z) subject to both constraints.
First, we set up the Lagrange function
L(x, y, z, λ, μ) = x + 2y + λ(x + y + z - 6) + μ(y² + z² - 4)
Then, we take partial derivatives of L with respect to x, y, z, λ, and μ and set them equal to 0
∂L/∂x = 1 + λ = 0
∂L/∂y = 2 + λ + 2μy = 0
∂L/∂z = λ + 2μz = 0
∂L/∂λ = x + y + z - 6 = 0
∂L/∂μ = y² + z² - 4 = 0
Solving these equations simultaneously, we get
x = -1, y = 2, z = 3, λ = -1, μ = -1/2
x = 3, y = -2, z = -1, λ = -1, μ = -1/2
We also need to check the boundary points where either x + y + z = 6 or y² + z² = 4. These points are (0, 2, 2), (0, -2, -2), (4, 1, 1), and (4, -1, -1). We evaluate f at these points and compare them to the values we get from the Lagrange multipliers.
f(-1, 2, 3) = 7, f(3, -2, -1) = -1
f(0, 2, 2) = 4, f(0, -2, -2) = -4
f(4, 1, 1) = 6, f(4, -1, -1) = 2
So the maximum value of f subject to both constraints is 7, which occurs at (-1, 2, 3), and the minimum value of f subject to both constraints is -4, which occurs at (0, -2, -2).
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A peregrine falcon can dive at the speed of 320km/h. Create a problem that you can solve by finding an equivalent rate for this speed. Then solve the problem.
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Calculate the perimeter and area of the shaded region in the drawing of two circles at right. Round to the nearest tenth. Show all work. 10 5cm 21 cm
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The perimeter of the shaded region is approximately 85.67 cm The area of the shaded region is approximately 91.84 cm² (rounded to the nearest tenth).
To calculate the perimeter and area of the shaded region, we first need to find the radius of each circle.
The larger circle has a diameter of 21 cm, which means its radius is 10.5 cm (half of the diameter). The smaller circle has a diameter of 10 cm, so its radius is 5 cm.
To find the perimeter of the shaded region, we need to add the circumference of both circles and subtract the overlap (the length of the shared segment). The circumference of the larger circle is 2π(10.5) ≈ 65.97 cm, and the circumference of the smaller circle is 2π(5) ≈ 31.42 cm.
To find the length of the shared segment, we can use the Pythagorean theorem. The distance between the centers of the circles is 15 cm (the sum of the radii), so we can form a right triangle with legs of 10.5 cm and 5 cm. Using the Pythagorean theorem, we get:
c² = a² + b²
c² = 10.5² + 5²
c² ≈ 137.25
c ≈ 11.72
So the length of the shared segment is approximately 11.72 cm.
Therefore, the perimeter of the shaded region is approximately 65.97 + 31.42 - 11.72 = 85.67 cm (rounded to the nearest tenth).
To find the area of the shaded region, we need to subtract the area of the smaller circle from the area of the larger circle, and then subtract the area of the overlap (the area of the shared segment).
The area of the larger circle is π(10.5)² ≈ 346.36 cm², and the area of the smaller circle is π(5)² ≈ 78.54 cm².
To find the area of the shared segment, we can use the formula for the area of a sector of a circle:
A = (θ/360)πr²
where θ is the central angle of the sector. In this case, the sector has a central angle of 2cos⁻¹(5/10.5) ≈ 105.2°, so:
A = (105.2/360)π(10.5)²
A ≈ 91.84 cm²
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!!PLEASEE HELPPP!! I’m having a hard time!!
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a. A customer would save $492 during the first year by switching from ElectroniSource to Intellivision. b. A customer who would save $207 in the second year. c. Intellivision's total cost of $1654.56.
Describe Algebra?Algebra is a branch of mathematics that deals with the manipulation and properties of variables, symbols, and equations. In algebra, variables represent unknown quantities, and equations represent relationships between those unknown quantities.
The fundamental operations in algebra are addition, subtraction, multiplication, and division. Algebraic equations involve variables and constants, which are combined using these operations to form algebraic expressions. These expressions can be simplified by applying algebraic rules and properties, such as the distributive property, associative property, and commutative property.
a. To calculate the savings during the first year, we need to find the total cost for each company for all three services during a year and compare them.
For ElectroniSource, the total cost for a year would be:
$42/month x 12 months = $504 for phone service
$35/month x 12 months = $420 for Internet service
$59/month x 12 months = $708 for cable TV service
Total cost for a year with ElectroniSource = $504 + $420 + $708 = $1632
For Intellivision, the flat monthly fee is $95, so the total cost for a year would be:
$95/month x 12 months = $1140
Savings during the first year = Cost with ElectroniSource - Cost with Intellivision
= $1632 - $1140
= $492
Therefore, a customer would save $492 during the first year by switching from ElectroniSource to Intellivision.
b. After the first year, Intellivision raises the rates by 25%. The new monthly fee would be:
$95 + 25% of $95 = $118.75
To calculate the savings for the second year, we need to find the total cost for each company for all three services during the second year and compare them.
For ElectroniSource, the total cost for the second year would still be:
$504 for phone service
$420 for Internet service
$708 for cable TV service
Total cost for the second year with ElectroniSource = $504 + $420 + $708 = $1632
For Intellivision, the total cost for the second year would be:
$118.75/month x 12 months = $1425
Savings during the second year = Cost with ElectroniSource - Cost with Intellivision
= $1632 - $1425
= $207
Therefore, a customer who switched from ElectroniSource to Intellivision would save $207 in the second year.
c. If Intellivision raises the rates by 16% for the third year compared to the second year, the new monthly fee would be:
$118.75 + 16% of $118.75 = $137.88
To compare the total cost for each company for the third year, we need to find the total cost for each company for all three services during the third year and compare them.
For ElectroniSource, the total cost for the third year would still be:
$504 for phone service
$420 for Internet service
$708 for cable TV service
Total cost for the third year with ElectroniSource = $504 + $420 + $708 = $1632
For Intellivision, the total cost for the third year would be:
$137.88/month x 12 months = $1654.56
Therefore, ElectroniSource is cheaper for the third year, with a total cost of $1632 compared to Intellivision's total cost of $1654.56.
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During one week, Sheila made several changes to her bank account. She made four withdrawals of 40$ each from an ATM she also used her check card for a 156$ purchase then she deposited her paycheck of $375
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The amount change in her bank account during that week after withdrawals and deposit is equal to $59.
Total number of withdrawals made by Sheila = 4
Amount made at the time withdrawals using ATM = $40
Amount withdraw using check card to purchase = $156
Amount deposited using paycheck = #375
Let us calculate the total amount of money Sheila withdrew from her bank account using ATM,
4 withdrawals of $40 each
= 4 x $40
= $160
So, she withdrew $160 and made a $156 purchase, meaning she spent a total amount of,
= $160 + $156
= $316
Sheila also deposited her paycheck of $375, so the total amount of money in her account changed by is equal to,
$375 - $316 = $59
Therefore, the amount in Sheila's account increased by $59 during that week.
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The above question is incomplete, the complete question is:
During one week, Sheila made several changes to her bank account. She made four withdrawals of $40 each from an ATM. She also used her check card for a $156 purchase. Then she deposited her paycheck of $375. By how much did the amount in her bank account change during that week?
Your parents are buying a house for $187,500. They have a good credit rating, are making a 20% down payment, and expect to pay $1,575/month. The interest rate for the mortgage is 4.65%. What must their realized income be before each month?
Be sure to include the following in your response:
the answer to the original question
the mathematical steps for solving the problem demonstrating mathematical reasoning
Answers
P = (PV * r * (1 + r)^n) / ((1 + r)^n - 1)
where P is the monthly payment, PV is the mortgage principal ($187,500 - 20% down payment = $150,000), r is the monthly interest rate (4.65% / 12 = 0.3875%), and n is the number of months (30 years or 360 months).
Substituting the given values, we get:
P = ($150,000 * 0.003875 * (1 + 0.003875)^360) / ((1 + 0.003875)^360 - 1)
P = $802.62
Therefore, your parents must have a realized income of $1,575 + $802.62 = $2,377.62 before each month to afford the mortgage payment.
Note: This calculation assumes that the monthly payment of $1,575 includes both the principal and interest payments for the mortgage.
Determine the intervals on which the given function is concave up or concave down and find the points of inflection. S(x) = (x - 10)(1 - x) (Use symbolic notation and fractions where needed. Give your answer in three decimal numbers
Answers
There are no points of inflection.
To determine the intervals on which the function S(x) = (x - 10)(1 - x) is concave up or down and find the points of inflection, we need to find the second derivative and analyze its sign.
First, find the first derivative, S'(x):
S'(x) = (x - 10)(-1) + (1 - x)(1) = -x + 10 - 1 + x = 9
Next, find the second derivative, S''(x):
S''(x) = d(S'(x))/dx = d(9)/dx = 0
Since the second derivative S''(x) is constant and equal to 0, there is no concavity, and the function is neither concave up nor concave down. There are no points of inflection.
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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 ___?
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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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The circumference of a circle is 12.56 millimeters. What is the circle's radius?
C=12.56 mm
Use 3.14 for .
Answers
The radius of the circle is 2mm
How to determine the circumferenceIt is important to note that the formula that is used for calculating the circumference of a circle is expressed with the equation.
The equation is written as;
C = 2πr
Such that the parameters are;
C is the cicumference of the circle.r is the radius of the circle.πtakes the constant value of 22/7From the information given, we have thatt;
The radius of the circle = r
The circumference = 12.56mm
Substitute the values, we have;
12. 56 = 2×3.14r
Multiply the values
r = 12. 56/6. 28
divide the values
r = 2mm
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a florida citrus grower estimates that if 60 orange trees are planted, the average yield per tree will be 400 oranges. The average yield will decrease by 4 oranges per tree for each additional tree planted on the same acreage. Express the grower's total yield as a function of the number of additional trees planted, draw the graph and estimate the total number of trees the grower should plant to maximize yield.
Answers
Answer: 80 trees
Step-by-step explanation:
YIELD = (NUMBER OF TREES)*(NUMBER OF ORANGES PER TREE)
Let's assume NUMBER OF TREES = 60 + x, where x is the number of additional trees above 60
The NUMBER OF ORANGES PER TREE will = (400-4x). Hence:
YIELD = (60+x)*(400-4x) = 24000-240x+400x-4x2 = -4x2 + 160x + 24,000
To find the maximum YIELD, take the derivative of YIELD wrt x, set it to zero, and solve for x:
d(YIELD)/dx = -8x + 160
0 = -8x +160
8x = 160
x = 20
The grower should grow 60 + 20 = 80 trees to maximize yield.
Answer: 80 trees
Step-by-step explanation: just bc it is
Part A: Sydney made $18. 50 selling lemonade, by the cup, at her yard sale. She sold each cup for $0. 50 and received a $3 tip from a neighbor. Write an equation to represent this situation. (4 points) Part B: Daria made a profit of $21. 00 selling lemonade. She sold her lemonade for $0. 75 per cup, received a tip of $3 from a neighbor, but also had to buy each plastic cup she used for $0. 10 per cup. Write an equation to represent this situation. (4 points) Part C: Explain how the equations from Part A and Part B differ. (2 points
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a) equation will be 0.5x + 3 = 18.50
b) equation will be (0.75x - 0.10x) + 3 = 21.00
a) Sydney made $18.50 selling lemonade.
she sold each cup for $0.50 and received a $3 tip from a neighbor.
let x be the cost of cup she sold.
equation will be 0.5x + 3 = 18.50
b) Daria made a profit of $21.00 selling lemonade
she sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbor.
equation will be (0.75x - 0.10x) + 3 = 21.00
c) Sydney don't have to pay for the cups used while Daria paid.
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A. An equation to represent the situation in part A is 18.50 = (0.50) x + 3.
B. An equation to represent the situation in part B is 21.00 = (0.75) y - (0.10) y + 3.
C. The equations differ in the fact that one accounts for the cost per cup while the other does not.
What is profit?In general, the profit is defined as the amount gained by selling a product, which should be more than the cost price of the product.
Part A: Let x be the number of cups of lemonade sold.
Then, the total amount of money Sydney made is given by:
Total money = (selling price per cup) × (number of cups sold) + tip
Substituting the given values, we get:
18.50 = (0.50) x + 3
Part B: Let y be the number of cups of lemonade sold.
Then, the total profit made by Daria is given by:
Total profit = (selling price per cup) × (number of cups sold) + tip - (cost per cup) × (number of cups sold)
Substituting the given values, we get:
21.00 = (0.75) y - (0.10) y + 3
Part C: The equation for Sydney's lemonade stand only takes into account the total amount of money she made, which includes the selling price per cup and a fixed tip.
On the other hand, the equation for Daria's lemonade stand takes into account both the total profit made (which includes the selling price per cup and a fixed tip) and the cost per cup of lemonade sold. So, the equations differ in the fact that one accounts for the cost per cup while the other does not.
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Complete question is
Part A : Sydney made $18.50 selling lemonade, by the cup, at her yard sale. She sold each cup for $0.50 and received a $3 tip from a neighbour. Write an equation to represent this situation.
Part B : Daria made a profit of $21.00 selling lemonade. She sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbour, but also had to buy each plastic cup she used for $0.10 per cup. Write an equation to represent this situation.
Part C: Explain how the equation from part A and part B differ.
solve by completing the square x^2-14x+49=16
Answers
ANSWER:
(x+7)^2=16
Step-by-step explanation:
x^2-14x+49=16
x^2-14x+49-16=0
x^2-14x+33=0
subtract -33 on both sides
x^2-14x+33-33=-33
x^2-14x=-33
Add 49 on both sides
x^2-14x+49=-33+49
x^2-14x+49=16
x^2-7x-7x+49=16
x(x-7)-7(x-7)=16
(x-7)(x-7)=16
(x-7)^2=16
Help me with these questions pls
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The volume of the cones are;
1. 84. 78 in³
2. 564. 15 ft³
3. 4710 yd³
How to determine the value
The formula for calculating the volume of a cone is expressed as;
V = 1/3 πr²h
Given that;
r is the radius of the cone.h is the height of the coneFrom the information given, we have;
1. Volume = 1/3 × 3.14 × 3² × 9
Multiply the values and find the square
Volume = 254. 34/3
divide the values
Volume = 84. 78 in³
2. Volume = 1/3 × 3.14 × 7² × 11
Multiply the values
Volume = 1692. 46/3
Volume = 564. 15 ft³
3. Volume = 1/3 × 3.14 × 15² × 20
Multiply the values
Volume = 4710 yd³
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A bag contains 4 white, 3 blue, and 5 red marbles. Find the probability of choosing a red marble, then a white marble if the marbles were replaced.
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The probability of choosing a red marble, then a white marble is 5/36
Finding the probability of choosing a red marble, then a white marbleFrom the question, we have the following parameters that can be used in our computation:
A bag contains 4 white, 3 blue, and 5 red marbles
If the marbles were replaced, then we have
P(Red) = 5/12
P(White) = 4/12
So, we have
The probability of choosing a red marble, then a white marble is
P = 5/12 * 4/12
Evaluate
P = 5/36
Hence, the probability of choosing a red marble, then a white marble is 5/36
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AC B Round your answer to the nearest hundredth.
Answers
Answer:
4.28
Step-by-step explanation:
To find what the length of AC is, we can use the tangent of angle A, which is 35°. Here's the equation:
tan(35)=3/x
multiply both sides by x
x·tan(35)=3
divide both sides by the tangent of 35
x=4.28 (rounded to the nearest hundredth)
This means that AC=4.28
Hope this helps! :)
In a right triangle, angle λ has a measure of 19º. If the hypotenuse of this right triangle has a measure of 24 feet, what is the measure of the side adjacent to angle λ?
Answers
Answer:
22.69 ~ = 23 feet
Step-by-step explanation:
cos 19 = adj/24
24cos 18 = adj
adj = 22.69~= 23
Given that MNPQ is a rectangle with vertices M(3, 4), N(1, -6), and P(6, -7), find the coordinates Q that makes this a rectangle
Answers
Given that MNPQ is a rectangle with verticles M(3, 4), N(1, -6), and P(6, -7), to find the coordinates of point Q, we can use the fact that opposite sides of a rectangle are parallel and have equal lengths.
First, let's find the vector MN and MP:
MN = N - M = (1 - 3, -6 - 4) = (-2, -10)
MP = P - M = (6 - 3, -7 - 4) = (3, -11)
Now, let's add the vector MN to point P:
Q = P + MN = (6 + (-2), -7 + (-10)) = (4, -17)
Therefore, the coordinates of point Q that make MNPQ a rectangle are Q(4, -17).
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I'm fairly new to this concept and I'm a bit confused on these 3 questions. Please help :)
Answers
1) All the solution are,
(x, y) = (√2, 2) , (- √2, 2), (√2, -2) , (- √2, -2), (√2i, 2) , (- √2i, 2), (√2i, -2) , (- √2i, -2),
2) Solutions are,
⇒ x = 3, 3, - √3 / 2, - 5
3) All the even integers which are divisible by 5 is,
⇒ 10, 20, 30, 40, 50, ....
Given that;
1) Expression is,
⇒ x² = y, and y² = 4
2) Expression is,
⇒ (x - 3)² (2x + √3) (x + 5) = 0
Now, We can simplify as;
⇒ x² = y,
⇒ x⁴ = y²
x⁴ = 4
x⁴ - 2² = 0
(x²)² - 2² = 0
(x² - 2) (x² + 2) = 0
This gives,
x² = 2
x = ± √2
x² = - 2
x = ±√2 i
Hence, We get;
y² = 4
y = ± 2
Thus, All the solution are,
(x, y) = (√2, 2) , (- √2, 2), (√2, -2) , (- √2, -2), (√2i, 2) , (- √2i, 2), (√2i, -2) , (- √2i, -2),
Since, 2) Expression is,
⇒ (x - 3)² (2x + √3) (x + 5) = 0
Simplify as;
⇒ (x - 3)² = 0
⇒ x = 3, 3
⇒ (2x + √3) = 0
⇒ x = - √3 / 2
⇒ (x + 5) = 0
⇒ x = - 5
3) All the even integers which are divisible by 5 is,
⇒ 10, 20, 30, 40, 50, ....
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PLS HELP ME WITH THIS 50 POINTS!
Answers
Answer: The transformation is up one and to the left 5
(-5, 1)
Step-by-step explanation:
Please Give brainliest, have a great night!
Answer: h(x) = g(x+5)+1
Step-by-step explanation:
h(x) = g(x+5)+1
You went 5 in the negative direction x direction; take the opposite sign
Also went up 1 in the y direction so add 1 to equation
A wheel has a diameter of 40 cm, to the nearest 10 cm.
Write an inequality to show
a the lower and upper bounds for the diameter d of the wheel
b the lower and upper bounds for the circumference C of the wheel.
Answers
a) The diameter d of the wheel has bounds:
35 cm ≤ d ≤ 45 cm
b) The circumference C has bounds, using C = πd:
π * 35 cm ≤ C ≤ π * 45 cm
How to solveThe inequality representing the lower and upper bounds for the diameter d is:
35 cm ≤ d ≤ 45 cm
b) For the lower bound, we substitute the lower bound of the diameter (35 cm) into the formula:
[tex]C_l_o_w_e_r[/tex] = π * 35 cm
For the upper bound, we substitute the upper bound of the diameter (45 cm) into the formula:
[tex]C_u_p_p_e_r[/tex] = π * 45 cm
The inequality representing the lower and upper bounds for the circumference C is:
π * 35 cm ≤ C ≤ π * 45 cm
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To meet the company’s sales goals, the sales director for the pet food company decided to provide training for some of the sales representatives in the Midwest and Northeast regions. After conducting a one-month training program, the sales director analyzed the effectiveness of the program by conducting a statistical study.
Question 1
The purpose of the sales director’s study is to determine whether attending the training program caused an increase in sales for representatives from the two regions. So the sales director collected sales data from both groups (those receiving training and those receiving no training) for three months after the one-month program and compared the number of orders secured by those who attended the training program with the number of orders secured by those who didn’t attend.
Part A
Question
Select the correct answer from each drop-down menu.
The sales director conducted _______ because a treatment _____ applied to the sales representatives. This is the best statistical study for this situation because the sales director is trying to establish _______.
1. ) An experiment
An observational
A survey
2. ) was
was not
3. ) causality
correlation
Answers
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What is the maximum height of Anna’s golf ball? The equation is y=x-0. 04x^2.
The maximum height is____ feet
Answers
The maximum height of Anna's golf ball is 6.25 feet.
To find the maximum height of Anna's golf ball, we need to determine the vertex of the parabolic equation y = x - 0.04x^2. The x-coordinate of the vertex can be found using the formula:
x = -b / (2a)
In this case, the coefficients a and b are:
a = -0.04
b = 1
Substituting the values into the formula:
x = -1 / (2 * -0.04)
x = -1 / (-0.08)
x = 12.5
Now, we need to find the y-coordinate of the vertex by plugging the x-coordinate back into the equation:
y = 12.5 - 0.04(12.5)^2
y = 12.5 - 0.04(156.25)
y = 12.5 - 6.25
y = 6.25
So, the maximum height of Anna's golf ball is 6.25 feet.
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Find the absolute maximum and minimum of the function f(x,y)=y√x−y2−x+3y on the domain 0≤x≤9, 0≤y≤8
Answers
The absolute maximum of the function f(x,y) = y√(x-y^2)-x+3y on the domain 0≤x≤9, 0≤y≤8 is 2√2, which occurs at the point (2,2).
The absolute minimum of the function is -8, which occurs at the point (0,2).
To find the absolute maximum and minimum of the function f(x,y) = y√(x-y^2)-x+3y on the domain 0≤x≤9, 0≤y≤8, we need to evaluate the function at the critical points and at the boundary of the domain.
The critical points of the function are the points where the partial derivatives with respect to x and y are both zero. Solving these equations, we get:∂f/∂x = -1 + y/(√(x-y^2)) = 0∂f/∂y = √(x-y^2) - 1 + 3 = 0Solving these equations, we get two critical points: (0,2) and (2,2). Evaluating the function at these points, we get:f(0,2) = -8f(2,2) = 2√2Next, we need to evaluate the function at the boundary of the domain. This includes the points (0,y), (9,y), (x,0), and (x,8).
Evaluating the function at these points, we get:f(0,y) = -x+3yf(9,y) = y√(9-y^2)-6f(x,0) = -xf(x,8) = 8√(x-64/9)-x+24Taking the maximum and minimum values of the function at the critical points and on the boundary of the domain, we see that the absolute maximum of the function is 2√2, which occurs at the point (2,2), and the absolute minimum of the function is -8, which occurs at the point (0,2).
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Please hurry I need it ASAP
Answers
BC^2 = AC^2 + AB^2 - 2 AC•AB • cos A.
BC = √(29² + 24² - 2•29•24 • cos 78) = 33.6 ft
Answer: BC = 33.6 ft
A 3 ox serving of roasted skinless chicken breast contain 140 cal, 24 g of protein, 2 g of fat, 11 mg of calcium, and 61 mg of sodium. One half cup of potato salad contains 160 cal, 4 g of protein, 13 g of fat, 21 mg of calcium, and 656 mg of sodium. One brooccoli spear contains 40 cal, 5 g of protein, 1 g of fat, 81 mg of calcium, and 23 mg of sodim. Use this information to complete following parts.
a) Write a 1×5 matrices, C, P, and B that represent the nutritional values of the chicken, potato salad, and broccoli, respectively. Give the nutritional values in the following order: Cal, g of protein, g of fat, mg of calcium, and mg of sodium.
C=
P=
B=
Answers
The matrices are: C = [140, 24, 2, 11, 61] P = [160, 4, 13, 21, 656] B = [40, 5, 1, 81, 23]
To represent the nutritional values of the chicken, potato salad, and broccoli in matrices, we can use a 1x5 matrix for each food, where each column represents a different nutritional value in the following order: calories, protein, fat, calcium, and sodium.
Therefore, we have:
C = [140 24 2 11 61]
P = [160 4 13 21 656]
B = [40 5 1 81 23]
In matrix C, the values are 140 calories, 24 grams of protein, 2 grams of fat, 11 milligrams of calcium, and 61 milligrams of sodium for a 3 ounce serving of roasted skinless chicken breast. In matrix P, the values are 160 calories, 4 grams of protein, 13 grams of fat, 21 milligrams of calcium, and 656 milligrams of sodium for one half cup of potato salad. In matrix B, the values are 40 calories, 5 grams of protein, 1 gram of fat, 81 milligrams of calcium, and 23 milligrams of sodium for one broccoli spear.
These matrices can be used to perform calculations and comparisons between the nutritional values of the different foods.
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If a and b are positive numbers, prove that the equation
a/x^3+2x^2-1 + b/x^3+x-2 = 0
has at least one solution in the interval (- 1, 1).
Answers
The equation has at least one solution in the interval (-1, 1).
To prove that the equation has at least one solution in the interval (-1, 1), we can use the Intermediate Value Theorem.
First, let's simplify the equation by finding a common denominator:
a(x^3+x-2) + b(x^3+2x^2-1) = 0
Now, let's define a new function f(x) = a(x^3+x-2) + b(x^3+2x^2-1). This function is continuous on the interval (-1, 1) because it is a sum of continuous functions.
Next, we will evaluate f(-1) and f(1) to see if the Intermediate Value Theorem can be applied.
f(-1) = a(-1^3-1-2) + b(-1^3+2(-1)^2-1) = -a-b < 0
f(1) = a(1^3+1-2) + b(1^3+2(1)^2-1) = a+3b > 0
Since f(-1) is negative and f(1) is positive, there must be at least one value of x in the interval (-1, 1) such that f(x) = 0, by the Intermediate Value Theorem.
To prove that the given equation has at least one solution in the interval (-1, 1), we can use the Intermediate Value Theorem (IVT). Let's define the function f(x) as follows:
f(x) = a/(x^3 + 2x^2 - 1) + b/(x^3 + x - 2)
Since a and b are positive numbers, we can examine the behavior of f(x) at the endpoints of the interval (-1, 1).
f(-1) = a/((-1)^3 + 2(-1)^2 - 1) + b/((-1)^3 + (-1) - 2)
f(-1) = a/(-1) + b/(-4) < 0
f(1) = a/(1^3 + 2(1)^2 - 1) + b/(1^3 + 1 - 2)
f(1) = a/(2) + b/(0) = a/2 > 0
Since f(-1) < 0 and f(1) > 0, by the Intermediate Value Theorem, there must be at least one point c within the interval (-1, 1) where f(c) = 0. This means that the given equation has at least one solution in the interval (-1, 1).
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Find each arc length. Round to the nearest hundredth.
If EB = 15 cm, find the length of CD.
mCD = ____ cm.
(30 points) will give brainiest for effort
Answers
The length of arc CD, given that the radius, EB = 15 cm, is 29.31 cm
How do i determine the length of arc CD?First, we shall determine ∠CED. Details below:
∠BEC = 68°∠CED =?2∠CED + 2∠BEC = 360
2∠CED + (2 × 68) = 360
2∠CED + 136 = 360
Collect like terms
2∠CED = 360 - 136
2∠CED = 224
Divide both sides by 2
∠CED = 224 / 2
∠CED = 112°
Finally, we shall determine the length of the of arc CD. Details below:
Radius (r) = EB = 15 cmAngle (θ) = ∠CED = 112°Length of arc CD = ?Length of arc = 2πr × (θ / 360)
Length of arc CD = (2 × 3.14 × 15) × (112 / 360)
Length of arc CD = 29.31 cm
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Complete question:
See attached photo
Find all solutions of the equation in radians.
sin(2x)sin(x)+cos(x)=0
Answers
Answer:
[tex]x&=\dfrac{1}{2}\pi +2\pi n,\;\; \dfrac{3}{2}\pi + 2 \pi n[/tex]
Step-by-step explanation:
Given equation:
[tex]\sin(2x)\sin(x)+\cos(x)=0[/tex]
Rewrite sin(2x) using the trigonometric identity sin(2x) = 2sin(x)cos(x):
[tex]\implies 2\sin(x)\cos(x)\sin(x)+\cos(x)=0[/tex]
[tex]\implies 2\sin^2(x)\cos(x)+\cos(x)=0[/tex]
Factor out cos(x):
[tex]\implies \cos(x)\left[2\sin^2(x)+1\right]=0[/tex]
Applying the zero-product property:
[tex]\textsf{Equation 1:}\quad\cos(x)=0[/tex]
[tex]\textsf{Equation 2:}\quad2\sin^2(x)+1=0[/tex]
Solve each part separately.
[tex]\underline{\sf Equation \; 1}[/tex]
[tex]\begin{aligned}\cos(x)&=0\\x&=\arccos(0)\\x&=\dfrac{1}{2}\pi +2\pi n,\;\; \dfrac{3}{2}\pi + 2 \pi n\end{aligned}[/tex]
[tex]\underline{\sf Equation \; 2}[/tex]
[tex]\begin{aligned}2\sin^2(x)+1&=0\\\sin^2(x)&=-\dfrac{1}{2}\;\;\;\;\;\;\leftarrow\;\textsf{No solution}\end{aligned}[/tex]
Therefore, the solutions of the equation in radians are:
[tex]\boxed{x&=\dfrac{1}{2}\pi +2\pi n,\;\; \dfrac{3}{2}\pi + 2 \pi n}[/tex]
7 Plot (6,2) on the grid.
My teacher never thought us this and this was on my homework I give you 59 points if you give me a answer
Answers
Answer:Go to the 6 number on the bottom line.Then go up until you reach 2
Step-by-step explanation:
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Should look like that-ish
Answer:
Step-by-step explanation:
Put the point to the right 6 times and up two times
