Answer:
Step-by-step explanation:
We know that the life expectancy of the tires is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. Let X be the life expectancy of the tire. Then X ~ N(40,000, 5,000^2).
To find the percentage of tires that will have a life of 34,000 to 46,000 miles, we need to calculate the z-scores for both values using the formula:
z = (X - μ) / σ
where X is the value we want to find the z-score for, μ is the mean, and σ is the standard deviation.
For X = 34,000:
z = (34,000 - 40,000) / 5,000 = -1.2
For X = 46,000:
z = (46,000 - 40,000) / 5,000 = 1.2
Now, we need to find the area under the standard normal distribution curve between these two z-scores. We can use a table of standard normal probabilities or a calculator to find this area.
Using a standard normal table or a calculator, we find that the area to the left of z = -1.2 is 0.1151, and the area to the left of z = 1.2 is 0.8849. Therefore, the area between these two z-scores is:
0.8849 - 0.1151 = 0.7698
So, approximately 76.98% of the tires will have a life of 34,000 to 46,000 miles.
Solve:
|3x|=9
x= 3
x= 1 and x=-2
x=3 and x=-3
x= 0 and x= 7
The required solutions of the equation |3x| = 9 are x = 3 and x = -3.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.
Here,
We can solve the given equation by isolating the absolute value on one side and simplifying it.
|3x| = 9
| x | = 3
Now, we need to solve two separate equations for x:
When x is positive:
|x| = 3
=> x = 3 (since x is positive)
When x is negative:
|x| = 3
-x = 3 (since x is negative)
x = -3
Therefore, the solutions of the equation |3x| = 9 are x = 3 and x = -3.
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The final RSVP guest count is 60 people Which catering company will offer the best deal for your family? How much money will your family save by choosing that company
a) The family's best deal is with Smokey's BBG which charges $780 for 60 guests.
b) Choosing Smokey's BBG over Bennie's BBQ will save (difference) the family $40.
How is the difference or saving determined?The total cost for each company's catering services is worked out using their cost functions.
Smokey's BBG does not charge a fixed cost, unlike Bennie's BBG.
The difference between the total costs of the companies is obtained by subtraction.
The number of guests = 60
Smokey's BBQ Bennie's BBQ
Catering Fees $0 $100
Charge per person $13 $12
The total charge for 60 $780 ($13 x 60) $820 ($100 + $12 x 60)
Difference between the charges = $40 ($820 - $780)
However, using a system of equations we can determine the number of guests that makes the total cost the same for each company as 100.
Thus, comparing the total costs for the two companies shows the difference or cost savings to be gained by the family.
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Question Completion:Smokey's BBQ charges $13 per person while Bennie's BBG charges a $100 catering fee and $12 per person.
Select all of the expressions that are equivalent to (9x+6)-¹(8x-4).
M. 2(x + 1)
R. 2x+6
R. 2x + 2
S. 2(x + 3)
T. 8x
The expression that is equivalent to 2(9x+6)/3-(8x-4)/2 is 8x, the correct option is T.
What is an expression?Expression in mathematics is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that;
The function=2(9x+6)/3-(8x-4)/2.
Now,
First, let's simplify the expression given:
2(9x+6)/3 - (8x-4)/2 = (18x + 12)/3 - (4x - 2) = 6x + 4 - 2x + 1 = 4x + 5
Now let's check which of the given expressions are equivalent to 4x + 5:
M. 2(x + 1) = 2x + 2 (not equivalent)
R. 2x+6 (not equivalent)
R. 2x + 2 (not equivalent)
S. 2(x + 3) = 2x + 6 (not equivalent)
T. 8x = 8x - 40 + 45 = 4x + 5 (equivalent)
Therefore, the answer of the given expression will be 8x.
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30 gallons= 114 liters
Answer: 113.56235 Liters
Step-by-step explanation:
Which expression represents the prime factorization of 192?
A. 2 x 2 x 2 x 2 x 12
B. 2 x 2 x 2 x 2 x 2 x 3
C. 3 x 2 x 2 x 2 x 2 x 2 x 2
D. 2 x 2 x 2 x 2 x 2 x 3 x 3
The expression represents the prime factorization of 192 is 2×2×2×2×2×2×3. Therefore, option C is the correct answer.
What is factorization?The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.
The given number is 192.
The prime factorization is process of writing the given number into product of prime numbers.
Here, 192= 2×2×2×2×2×2×3
Therefore, option C is the correct answer.
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Kevin put a deposit of 10% on his new car. The deposit was $4000, so how much does he still owe?
Answer:
3600
Step-by-step explanation:
Based on the given conditions, formulate: 4000 x ( 1 - 10\% )
Calculate the sum or difference:4000 x 0.9
Calculate the product or quotient:3600
get the result: 3600
Answer: 3600
3.
1
A decorative wooden piece is made up of four rectangles as shown to the
right. The smallest rectangle measures 4 inches by 7 inches. If 2
inches are added to each dimension as the rectangles get larger, what is
the total area of the entire piece?
The total area of the rectangle with the provided figures will be equal to 280 inches.
How to obtain the area of the rectanglesNote that the area of a rectangle is length * width.
So, given this formula:
The area of the smallest rectangle will be: 4 * 7 = 28
The area of the next rectangle will be: (4 + 2) * (7 + 2)
= 6 * 9
= 54
The area of the next rectangle will be: (6 + 2) * (9 + 2)
= 8 * 11
= 88
The area of the fourth and largest rectangle will be: (8 + 2) * (11 + 2)
10 * 11
= 110
The total area of the angles will be: 28 + 54 + 88 + 110
= 280.
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How to determine the area of all faces in mm2
The surface area of all faces of the cube is found as in 150,100 mm².
Explain about the cube?A solid shape having six square faces is called a cube. Because every square face has an identical side length, each face is the same size.
A cube has 8 vertices and 12 edges. An intersection of three cube edges is referred to as a vertex. A cube has twelve equal-length edges and six faces. Its faces are square-shaped. The cube's angles in the plane were right angles. The cube's faces are connected by four other faces.Area of the cube:
Area = 6*side²
Area = 6*(5)²
Area = 150 cm²
We know:
1 cm = 10 mm
Then,
Area = 150 x 100 mm²
Area = 150,100 mm²
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The complete question is-
The cube has the side length of 5 cm. How to determine the area of all faces in mm2
PLEASE HELP !!!! IM SO CONFUSED
For your question just change domain x=-4,-2,0,2,4 to the function y=-1/2x to find y and graph.
5x ^ 2 y^ prime prime +23xy^ prime +16.2y=0
Answer:
Step-by-step explanation:
5
ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST FOR ANSWER
I think it is C. but i am a little rusty
Mica is going to buy a computer for $2,000. He
can finance it at the store for 14% interest for
2 years, or he can use his credit card at 21%
interest for 1 year.
1. Find the monthly payment for each option.
Answer in the box.
2. Find the total repayment for each option.
Answer in the box.
Answer: To find the monthly payment for each option, we can use the following formula:
Monthly Payment = Total Cost * (Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))
For the option to finance at the store for 2 years at 14% interest:
Total Cost = $2,000
Monthly Interest Rate = 14% / 12 = 0.011667
Number of Months = 2 years x 12 months/year = 24 months
Substituting these values into the formula, we get:
Monthly Payment = $2,000 * 0.011667 / (1 - (1 + 0.011667)^(-24)) = $95.13
Therefore, the monthly payment for financing at the store for 2 years at 14% interest is $95.13.
For the option to use his credit card at 21% interest for 1 year:
Total Cost = $2,000
Monthly Interest Rate = 21% / 12 = 0.0175
Number of Months = 1 year x 12 months/year = 12 months
Substituting these values into the formula, we get:
Monthly Payment = $2,000 * 0.0175 / (1 - (1 + 0.0175)^(-12)) = $185.44
Therefore, the monthly payment for using his credit card at 21% interest for 1 year is $185.44.
To find the total repayment for each option, we can multiply the monthly payment by the number of months:
For the option to finance at the store for 2 years at 14% interest:
Total Repayment = $95.13/month x 24 months = $2,283.12
Therefore, the total repayment for financing at the store for 2 years at 14% interest is $2,283.12.
For the option to use his credit card at 21% interest for 1 year:
Total Repayment = $185.44/month x 12 months = $2,225.28
Therefore, the total repayment for using his credit card at 21% interest for 1 year is $2,225.28.
Step-by-step explanation:
These lists show the ages of attendees in a yoga class and a dance class.
Yoga: 18, 31, 17, 44, 20, 33, 36
Dance: 20, 47, 23, 38, 26, 42, 30
Which statement about attendees in the two classes is true?
A. The median age of the attendees in the yoga class is greater than the median age of
the attendees in the dance class.
B. The median age of the attendees in the dance class is greater than the median age of
the attendees in the yoga class.
C. The median age of the attendees in the yoga class is the same as the median age of the
attendees in the dance class.
D. The median age of the attendees in the yoga class is 44 years and the median age of
the attendees in the dance class is 47.
The true statement is the median age of the attendees in the yoga class is greater than the median age of the attendees in the dance class. (option A).
What is the true statement?
Median is the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order.
Ages of Yoga students arranged in ascending order: 18, 17, 20, 31, 33, 36, 44
Median = 31
Ages of Dance students arranged in ascending order: 20, 23, 26, 30, 38, 42, 47
Median = 30
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Create 5 examples of gains and losses using positive and negative numbers.
Answer:
Step-by-step explanation:
gain
loss
gain loss
gain
Answer:
Gains : +1,+10,+3
loss: -3,-5,-9,-100
Step-by-step explanation: I think this question is basically just asking about givings examples of positive and negative numbers
Fins the center of the radius circle.
(x-1)^2 + (y-5)^2=4
Answer:
the radius is 1
Step-by-step explanation:
please help, need help understanding step by step.
we will need at least 96 bags of sand to cover the base of the circular pool.
what is circle?
A circle is a two-dimensional geometric shape consisting of all the points that are equidistant from a given point, called the center.
The area of a circular pool with a diameter of 22 feet can be calculated using the formula:
A = πr^2
where A is the area of the circle, π is a constant (approximately equal to 3.14), and r is the radius of the circle (which is half the diameter).
In this case, the diameter is 22 feet, so the radius is:
r = d/2 = 22/2 = 11 feet
Now we can calculate the area of the circle:
A = πr^2 = 3.14 x 11^2 = 379.94 square feet (rounded to 2 decimal places)
To cover this area with sand, we need to know how many bags of sand are required. We are told that one bag of sand covers about 4 square feet, so we can calculate the number of bags of sand required as follows:
Number of bags = Area of pool / Area covered by one bag
Number of bags = 379.94 square feet / 4 square feet per bag
Number of bags ≈ 95 bags
Since we need to round up to a whole number of bags, we will need at least 96 bags of sand to cover the base of the circular pool.
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A trapezium is shown below.
Work out the sizes of angles x and y.
Give your answers in degrees (°).
145°
X
Y
62°
PLEASE DO IT FOR 20 points
Answer:
x=118
y= 35
Step-by-step explanation:
180-62= 118
180-145=35
The value of x from the trapezium is 118° and the value of y from the trapezium is 35°.
What is a trapezium?
A trapezium is a quadrilateral with two parallel sides. It has two non-parallel sides that are called the legs of the trapezium, and the other two sides are called the bases.
From the given trapezium 4 angles are x, y, 62° and 145°.
Here, x+62°=180° (Sum of allied angles is 180°)
x=180°-62°
x=118°
Now, y+145°=180°
y=180°-145°
y=35°
Therefore, the value of x from the trapezium is 118° and the value of y from the trapezium is 35°.
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how many solutions are in 16 (3x − 6) = 18 (4x + 8).
Answer:
alot
Step-by-step explanation:
Answer:
One solution, x = -10
Step-by-step explanation:
16 (3x − 6) = 18 (4x + 8)
48x - 96 = 72x + 144
-24x = 240
x = - 10
Please help me solve
Answer:
x = -1 (multiplicity 2)
Step-by-step explanation:
Given the cubic f(x) = x³ -x² -5x -3 has x=3 as a root, you want the other roots.
Quadratic factorYou can find the quadratic factor of the polynomial using synthetic division. That tells you ...
f(x) = (x -3)(x² +2x +1)
You recognize the quadratic factor as the perfect square trinomial ...
x² +2x +1 = (x +1)²
RootsThe remaining roots will be the values of x that make these factors zero:
x +1 = 0 ⇒ x = -1 . . . . . and the other is the same: multiplicity 2
The remaining roots are x=-1 and x=-1.
__
Additional comment
We find a graphing calculator to be a quick and easy way to find the real roots of higher-degree polynomials. They are shown in the second attachment.
Kira works mowing lawns and babysitting. She earns $9.20 an hour for mowing and $7.50 an hour for babysitting. How much will she earn for 6 hours of mowing and 1 hour of babysitting?
Answer:
$62.70
Step-by-step explanation:
of means "x"
and means "+"
6 hours of mowing and 1 hour of babysitting
(6 hours of mowing) + ( 1 hour of babysitting)
6 hours of mowing
6 hours x mowing
6x9.20 = answer 1
1 hour of babysitting
1 hour x babysitting
1 x 7.50 = answer 2
add both answers together to get final answer
Calculate the concentration for the following pH: pH = 2.44
The concentration οf hydrοgen ions in a sοlution with pH 2.44 is [tex]2.754\times 10-12 M[/tex]
What is the pH value?
The pH value is a measure οf the acidity or basicity of a solution. It is defined as the negative lοgarithm (base 10) of the concentration of hydrogen ions (H+) in moles per liter (mol/L) of solutiοn. The pH scale ranges from 0 to 14, where a pH of 7 is considered neutral. Solutions with a pH less than 7 are acidic, while solutiοns with a pH greater than 7 are basic οr alkaline.
a) Given pH = 2.44
We knοw pH + pOH = 14,
pOH = 14 - 2.44 = 11.56
[tex][H+] = 10^{-pH} = 10^{-2.44} = 3.63\times 10 ^{-3} M[/tex]
[tex][OH-] = 10-pOH = 10-11.56 = 2.754\times 10-12 M[/tex]
b) Given ,pOH = 10.85
and it is knοwn that pH + pOH = 14, thus pH = 14 - 10.85= 3.15
[tex][H+] = 10^{-pH} = 10^{-3.15} = 7.07\times10^{-4 M}[/tex]
[tex][OH-] = 10^{-pOH} = 10^{-10.85} = 1.41\times10^{-11} M[/tex]
c) Given pH = -0.65
and it is knοwn that pH + pOH = 14, thus pOH = 14 +0.65 = 14.65
[tex][H+] = 10^{-pH} = 10^{0.65} = 4.466 M[/tex]
[tex][OH-] = 10^{-pOH} = 10^{-14.65} = 2.23 \times10^{15} M[/tex]
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Complete question:
Calculate the [H+] and [OH-] concentrations for the fοllowing solutions with: (a) pH = 2.44 (b) pOH = 10.85 (c) pH = -0.65
Griffin read 27 books about animals and 6 books
about space. How many books did he read?
Answer:
33 27 plus 6 = 33
Step-by-step explanation:
A shop employs one man and one woman as shop assistants. The man works for 10 hours per day and the woman for 8 hours per day, and their wages per hour are in the ratio 7:5 If the woman receives $24 per day, find the man's daily wage.
The man's daily wage is given as follows:
$42.
How to obtain the man's daily wage?The man's daily wage is obtained applying the proportions in the context of the problem.
Their wages per hour are in the ratio 7:5, hence the man's hourly wage is 7/5 of the woman's hourly wage, hence:
7/5 x 24/8 = 7/5 x 3 = 21/5 = $4.2 per hour.
The man works 10 hours a day, hence the daily wage is given as follows:
10 x 4.2 = $42.
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A collectible action figure is worth $1100. The value of the action figure increases by 6% each year.
Which explicit and recursive formulas can be used to model the situation.
Drag and drop each formula to the corresponding box.
In response to the query, we can state that r: the annual rate of increase equation (6% in this case)
What is equation?In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in the equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14. To comprehend the relationship between the two sentences written on opposing sides of a letter, utilise a mathematical formula. The logo and the specific programme typically correspond. An illustration would be 2x - 4 = 2.
Explicit Formula:
[tex]a_n = a_0 \times (1 + r)^n[/tex]
Recursive Formula:
[tex]a_n = a_{n-1} \times (1 + r)[/tex]
where:
[tex]a_n[/tex]: the value of the action figure after n years
[tex]a_0[/tex]: the initial value of the action figure ($1100 in this case)
r: the annual rate of increase (6% in this case)
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V(0) is the initial value of the action figure, and the recursive formula calculates the value of the action figure after n years by adding 6% of the previous year's value to the previous year's value.
What is equation?
In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements.
Let V(n) be the value of the action figure after n years.
Explicit formula:
V(n) = 1100(1 + 0.06)^n
Recursive formula:
V(0) = 1100
V(n) = V(n-1) + 0.06V(n-1)
Therefore, V(0) is the initial value of the action figure, and the recursive formula calculates the value of the action figure after n years by adding 6% of the previous year's value to the previous year's value.
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1. You work at a department store that needs at least 4200 labor hours covered per week. It employs full-time staff 40 hours per week and part-time staff 25 hours per week. The cost to employ a full-time staff member is more because the company pays benefits such as health care and life insurance
Full-time
Part-time
Hours per Week Cost per Hour
40 hr
$25
25 hr
$18
The store manager also knows that to make the store run efficiently, the number of full-time employees must be at least 1.25 times the number of part-time employees. You have been asked to help the store manager determine the number of full-time employees and the number of part-time employees that should be used to minimize the weekly labor cost.
a. Clearly define the variables in this problem.
b. Clearly state the constraints (all inequalities) related to the feasible region.
c. State the objective function.
d. Use the graphical method to
solve: Graph the solution region, showing the intercepts used. Label axes, units, points, and lines. Find and label all corner points. The grid for the graph is on the next page.
Show all necessary work.
e. In a complete sentence, state the number of full-time employees and the number of part-time employees that should be used to minimize the weekly labor cost.
Using linear programming, the minimum weekly labor cost of $2,616 occurs when there are 84 full-time employees and 67.2 part-time employees (which can be rounded up to 68 part-time employees)
What are the variables in this problema. Let x be the number of full-time employees and y be the number of part-time employees.
b. The constraints are:
Full-time employees work 40 hours per week, so the total number of full-time labor hours used must be at least 40x.Part-time employees work 25 hours per week, so the total number of part-time labor hours used must be at least 25y.The total number of labor hours used must be at least 4200: 40x + 25y ≥ 4200The number of full-time employees must be at least 1.25 times the number of part-time employees: x ≥ 1.25yThe number of full-time and part-time employees must be non-negative: x ≥ 0 and y ≥ 0c. The objective function is to minimize the weekly labor cost, which is given by:
Cost = 25x + 18y
d. To graph the solution region, we can first graph the inequality 40x + 25y ≥ 4200 as a line:
Convert the inequality to an equation: 40x + 25y = 4200Solve for y: y = (4200 - 40x)/25 = (168 - 1.6x)Plot the y-intercept: (0, 168)Plot the x-intercept: (105, 0) (found by setting y = 0 and solving for x)Draw the line passing through the two intercepts.Next, we can graph the inequality x ≥ 1.25y as a line:
Convert the inequality to an equation: x = 1.25yPlot two points on the line: (0, 0) and (0, 0) (found by setting y = 0 and x = 0 respectively)Draw the line passing through the two points.The feasible region is the shaded region that satisfies all the constraints and is bounded by the two lines and the x and y axes:
To find the corner points, we can solve the system of equations for the lines that form the boundaries of the feasible region:
40x + 25y = 4200 and x = 0 (y-axis intercept) --> (0, 168)40x + 25y = 4200 and y = 0 (x-axis intercept) --> (105, 0)x = 1.25y and y = 0 (x-axis intercept) --> (0, 0)x = 1.25y and 40x + 25y = 4200 --> (84, 67.2)Now we can evaluate the objective function at each of the corner points:
(0, 0): Cost = 0(0, 168): Cost = 25(0) + 18(168) = 3024(105, 0): Cost = 25(105) + 18(0) = 2625(84, 67.2): Cost = 25(84) + 18(67.2) = 2616Therefore, the minimum weekly labor cost of $2,616 occurs when there are 84 full-time employees and 67.2 part-time employees (which can be rounded up to 68 part-time employees).
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Jack has 7 yards of rope. He wants to cut it into pieces of different sizes. Jacks needs 84 inches of rope to tie some packages and 4 feet of rope for another project. Does Jack have enough rope? Explain.
Jack does have enough length of rope to tie his packages.
Explain about the unit conversions?The same attribute is presented using a unit conversion, but in a differing unit of measurement. For examples, time can be indicated in minutes rather than hours, and distance can be depicted in kilometers, feet, or other types of measurement unit instead of miles.
7 yards of rope belong to Jack. He desires to separate this into pieces of various sizes. Jacks requires 4 feet of rope for one project and 84 inches of rope to bind some items.So, concert all units in inches:
7 yards = 7*36 = 252 inches
4 feet = 4*12 = 48 inches.
Total length of rope = 252 inches.
Required rope = 84 inches + 48 inches
Required rope = 132 inches.
Thus, Jack does have enough rope to tie his packages.
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Noah and his friends are going to an amusement park. the total cost of admission for eight students is $100, and all students share the cost equal. Noah bought $13 for his ticket. did he bring enough money to get to the park? bring your reasoning.
Answer: The correct answer is yes, he brought enough money to get into the park.
Step-by-step explanation:
Well, let's analyze the information provided:
Admission to the amusement park for 8 students is $ 100. If each student agreed to share of cost equally, it means that we must divide those 100, for each of those students.
Therefore it will remain 100/8 = 12.5
If each student must pay 12.5, and Noah brought $ 13, that means he will have enough money to enter the park, and he will even have $ 0.50 left over.
which of the following is a set of complementary angles ?
(PLEASE HELP THIS IS DUE TODAY!!!!)
None of the given angles are complementary angles.
What is angle ?An angle is a geometric figure formed by two rays with a common endpoint called the vertex. The rays are also known as the sides or legs of the angle. Angles are usually measured in degrees or radians and are used to measure the amount of rotation between two lines or planes.
According to given information :The sum of two angles is 90 degrees if and only if they are complementary angles.
Using this concept, we can add up the angles in pairs to see which ones are complementary:
Angle AFB + Angle BFC = 40 + 60 = 100 degrees (not complementary)
Angle BFC + Angle CFD = 60 + 50 = 110 degrees (not complementary)
Angle CFD + Angle DFE = 50 + 30 = 80 degrees (not complementary)
Angle AFB + Angle DFE = 40 + 30 = 70 degrees (not complementary)
Therefore, none of the given angles are complementary angles.
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Answer:
Below
Step-by-step explanation:
BFC = 60 degrees and DFE = 30 degrees <===so they are complementery
because they sum to 90°
Quantitative data can be ___
O discrete
O continuous
O discrete or continuous
O none of the above
Answers:
Quantitative data can be discrete or continuous
Step-by-step explanation:The Qualitative data are also called categorical or attribute data deals with characteristics and descriptors that can't be easily measured but can be observed subjectively. We can say that smells tastes textures attractiveness and color are all examples of qualitative data. We can see that qualitative data are not numerical.for example, dimensions such as height, width, and length, temperature and humidity, prices, area and volume. The Discrete data is a count that cannot be made more precise. Continuous data could be divided and reduced to finer and finer levels.Use the graph of the function to find the indicated values.
The value of the indicated function instances as required to be determined are as follows;
f (π) = -3.f (π/2) = 0.f ( -3π/2 ) = 0.What is the value of the indicated function instances?It follows from the task content that a graph is given and the indicated values are to be determined.
By observation of the graph; it follows that;
On this note, f (π) = -3.
f (π/2) = 0.
f ( -3π/2 ) = 0.
The values above are as obtained from the graph.
Ultimately, the value of the indicated function instances are as evaluated from the graph above.
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