Point A is 4 miles due west of home. Point B is 6 miles due north of
home. Point C is 7 miles due east of home. Kayla goes on a bike trip
along the triangular path from home to point A, to point B, to Point
C and back to home. How far, in miles, does Kayla travel?
Answers
The distance covered on the triangular path to home along point A to B to C is 23.42 miles.
What is Pythagorean theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.
Given that the trip to home goes from point A to point B and then to point C.
The path traced thus, represents the hypotenuse of the two triangles. Triangle BHA and triangle BCH.
The Pythagorean theorem is given as follows:
a^2 + b^2 = c^2
For triangle BHA substitute the value of a = 4 and b =6.
4^2 + 6^2 = c^2
16 + 36 = c^2
c = 7.21
For triangle BHC, substitute the value of a = 7 and b =6.
7^2 + 6^2 = c^2
49 + 36 = c^2
c = 9.21
Now, from point B to point H the additional distance is 7 miles, hence the total distance traveled is:
D = 7.21 + 9.21 + 7
D = 23.42
Hence, the distance covered on the triangular path to home along point A to B to C is 23.42 miles.
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Related Questions
During a quality control check, a factory found that 5% of the parts it produces are defective. The factory recently completed an order for 144,000 parts. Approximately how many of the parts from the order may be defective?
Answers
The approximate number of defective parts the factory produced is 7200.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, During a quality control check, a factory found that 5% of the parts it produces are defective.
Let, 'x' be the number of defective parts.
Therefore, 'x' is 5% of 144000 which can be numerically expressed as,
(5/100)×144000.
= 5×1440.
= 7200.
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A kitchen sink has a volume of 65.9dm3 . Find how many milliliters of water it would take to completely fill the kitchen sink. Use the table of conversion facts, as needed.
Answers
Answer:
65,900 mL
Step-by-step explanation:
You want to know the volume in mL of a sink with a volume of 65.9 dm³.
ConversionThe relation between dm³ and mL is ...
1 dm³ = 1000 mL . . . . . . . . . . also, 1 L (liter)
ApplicationMultiplying the above relation by 65.9, we have ...
65.9 dm³ = 65,900 mL
__
Additional comment
For many problems involving volumes in liters and dimensions in centimeters or meters, it can be convenient to convert the dimensions to decimeters (dm). Since 1 dm³ = 1 L, that can make the desired volume easily calculated.
The function f shown in the graph is an even
function. The graph has been hidden for x ≥ 0.
Complete the following sentences.
over the interval 0 < x < 2.
fis
DONE
f(2)=
DONE
fis
DONE
over the interval 2 < x < 5.
#
6
4
2
y
x
Answers
The given function f is increasing over the interval 0 < x < 2 and
decreasing over the interval 2 < x < 5.
What is a function?
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.
An example of a simple function is f(x) = x^2. In this function, the function f(x) takes the value of “x” and then squares it. For instance, if x = 3, then f(3) = 9. A few more examples of functions are: f(x) = sin x, f(x) = x^2 + 3, f(x) = 1/x, f(x) = 2x + 3, etc.
Now,
As the given function f is increasing till x<2 and increasing after x>2
Hence,
f is increasing over the interval 0 < x < 2 and
decreasing over the interval 2 < x < 5.
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4.) A grade six class went on a field trip. of this group of pupils, only 98% or 49 joined the activity. what is the total techan triangle
Answers
The total number of candidates in the group will be 50.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the grade six class went on a field trip. of this group of pupils, only 98% or 49 joined the activity.
The total number will be calculated as,
Total number = [ 49 x 100 ] / 98
Total number = 50
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How long will it take 5300 to become 7500 if it’s invested at 9% and us compounded quarterly?
Answers
It would take approx 4 years for 5300 to become 7500 if it’s invested at 9% and us compounded quarterly.
What is compound interest?The interest earned on a deposit is known as compound interest because it is computed using both the initial principal and the interest accrued over the course of previous periods. Compound interest is simply interest that is earned on interest, to put it another way. Interest can be compounded daily, monthly, or yearly, among other frequency schedules.
Compound interest increases with a higher number of compounding periods. A snowball-like image comes to mind. Your snowball will grow faster if you start saving early and contribute more money to it.
The compound interest formula is given by:
[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]
Where,
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Here,
A = 7500
P = 5300
r = 9%
n = 4 (quarterly)
t = year to find
Putting the values in the formula
[tex]$7500 = 5300 (1 + \frac{0.09}{4})^{4t}[/tex]
t = 3.90
Thus, It would take approx 4 years for 5300 to become 7500 if it’s invested at 9% and us compounded quarterly.
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Use the intermediate value theorem to show that there is a root of the equation x5 - 2x4 - x - 3 = 0 in the interval (2,3).
Answers
Using the intermediate value theorem, the equation x5 - 2x4 - x - 3 = 0 is continuous on the closed interval [2, 3], there is a root of the equation in the interval (2,3).
Given, the equation is x5 - 2x4 - x - 3 = 0
We have to find the root of the equation in the interval (2, 3) using the intermediate value theorem.
Let f(x) = x5 - 2x4 - x - 3
f(2) = (2)5 - 2(2)4 - 2 - 3
f(2) = 32 - 32 - 5
f(2) = -5
f(3) = (3)5 - 2(3)4 - 3 - 3
f(3) = 243 - 162 - 6
f(3) = 75
Intermediate value theorem states that if a continuous function f(x) on the interval [a,b] has values of opposite sign inside an interval, then there must be some value x = c on the interval (a,b) for which f(c) = 0.
f(x) is continuous on the interval [2, 3] because it is a polynomial function, and is continuous at each point in the interval.
Here, f(2) is negative and f(3) is positive.
Therefore, f(x) is continuous on the closed interval [2, 3], there must be some value x = c on the interval [2, 3] for which f(c) = 0.
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Prove or give a counterexample: if U1; U2; W are subspaces of V such that : U1+ W = U2 + W; then U1 = U2.
Answers
U1 ≠ U2. The claim is therefore false in general
Let V = R2 over R, U1 the x-axis, U2 the y-axis, and W = V.
Obviously, U1 + W, U2 + W ⊆ V is clear since U1,U2,W ⊆ V .
Let v ∈ V be any vector. Then v ∈ W = V .
Here, instead of vectors, U1, U2, and W are vector spaces. Therefore, we are unable to demonstrate the evidence by using U1, U2, and W as separate vectors.
Here we assume that U1={(x, 0), x ∈ R} and U1={(0, y), y ∈ R} and W=V={(x, y), x,y ∈ R}
So v = 0 + v ∈ U1 + W. Also, v = 0 + v ∈ U2 + W.
Hence, V ⊆ U1 +W, U2 +W.
Thus, U1+W = U2+W = V.
But U1 ≠ U2. The claim is therefore false in general.
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Part B Find the minimum initial height hmin at which the car can be released that still allows the car to stay in contact with the track at the top of the loop: Express your answer numerically; in meters_
Answers
The minimum equation initial height at which the car can be released and still stay in contact with the track at the top of the loop is 8.90 m.
hmin = 8.90 m
We can use the equation for centripetal force to solve for the minimum initial height hmin at which the car can be released and still stay in contact with the track at the top of the loop.
Fc = mv2/r
where Fc is the centripetal force, m is the mass of the car, v is the speed of the car, and r is the radius of the loop.
We know that the mass of the car is 250 kg, the speed of the car is 14 m/s, and the radius of the loop is 20 m.
We can rearrange the equation to solve for hmin:
Fc * r = m * v2
hmin = (m * v2) / Fc
hmin = (250 kg * (14 m/s)2) / (25000 N)
hmin = 8.90 m
The minimum initial height at which the car can be released and still stay in contact with the track at the top of the loop is 8.90 m.
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A farmer wishes to study the effect of three different fertilizers on crop yields. He takes a rectangular field and divides it into four plots of equal area. Then he randomly assigns the three different fertilizers to one of the four plots. One plot receives no fertilizer. The plots are harvested after a growing period and the yields are measured and compared. Which of the following statements best describes the design of the study?
I.This design has matched pairs.
II.This design has blocks.
III.This is a completely randomized design.
answer choices
I only
I and III only
I and II only
II only
III only
Answers
Option E is the correct option
In this experiment, a farmer completed 4 stages of therapy using the Randomized Design idea.
Complete randomization of the design
In terms of comfort and ease of data processing, a totally random design is essentially the simplest experimental design. Subjects are randomly assigned to treatments in this design.
In fact, randomization is what this fully randomized design depends on to account for the impacts of unimportant factors. In reality, the investigator anticipates that uncontrollable variables will generally impact treatment conditions in an equal manner, so any meaningful variations across conditions may be accurately assigned to the independent variable.
Design for double blinds:
In an experiment, the placebo effect will be diminished or abolished if participants in the control group are aware that they are getting a placebo, and the placebo will no longer function as a control.
Blinding fundamentally involves withholding information about whether or not a person is getting a placebo. Thus, the placebo effect is equally felt by participants in the control and treatment groups. It's common practice to hide the fact that certain groups get placebos from analysts who review the trial. Double blinding is the term for this procedure. It ensures that their appraisal is not affected by knowledge of real treatment circumstances and stops the analysts from "spilling the beans" to the participants through subtle indications.
Designing Matched Pairs .
A randomized block design is a specific example of the matched pairs design. It can be employed when there are essentially just two treatment conditions in an experiment, and participants can be paired off based on some sort of blocking variable. The individuals are then randomly randomized to various treatments within each pair.
Block design using randomization:
In a randomized block design, participants are really split up into smaller groups called blocks so that the variance within blocks is less than the variance between blocks. After that, patients within each block are allocated to treatment scenarios at random.
So, in this experiment, the farmer applied 4 doses of therapy.
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Ms. Morales bought the kiddie pool shown below for her children. A diagram of a kiddie pool is shown. The height of the pool is labeled twelve inches. A line drawn under the pool from one side of the pool to the other is labeled fifty-four inches.
If she filled the pool 3/4 of the way with water, how much water did Ms. Morales put in the pool in terms of π?
A) 5,832π in.^3
B) 6,561π in.^3
C) 7,776π in.^3
D) 8,748π in.3
Answers
The quantity of water that Ms. Morales put in the pool in terms of π would be = =6561π in³
What is the volume of the pool?The volume of the pool can be calculated by using the formula of the volume of a cylinder which is = πr²h
Where,
r = 54/2 = 27in
volume = π × 27²× 12
= π × 8748
= 8748π in³
Therefore the quantity of the pool that's as filled with water = 3/4 of 8748π
= 3× 8748/4
= 26244/4
=6561π in³
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the following segmented bar chart shows the number of flights that were either on time or delayed at three different airports on one day.
Answers
The correct answer is C. Airport S has 100 on-time flights, and Airport T has 200 on-time flights. Since 100 is one-half of 200, Airport S has one-half the number of on-time flights that Airport T has.
Given that,
The number of flights that were either on time or delayed at three separate airports on a given day is depicted in the segmented bar chart below.
Which of the following statements is the bar chart evidence for?
The options are : In comparison to the other two airports, A Airport T has the highest proportion of on-time flights.
In comparison to the other two airports, B Airport R has the lowest percentage of on-time flights.
C The proportion of on-time flights at Airport S is less than half that at Airport T.
D The proportion of on-time flights at Airport R is lower than that at Airport S.
E There are exactly as many flights at Airport T as there are at Airports R and S put together.
As the number of flights that were either on time or delayed at three different airports on one day can be exactly represented by
The correct answer is less than half as many flights arrive on time at Airport S than at Airport T.
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The Complete Question is :
Which of the following statements is the bar chart evidence for the number of flights that were either on time or delayed at three different airports on one day.?
determine the set of all real x satisfying (x^2 3x-1)^2<9. enter your answer in interval notation.
Answers
The required sets of all real and satisfying numbers are:
(-∞ , -4) , (-4, -2), (-2, - 1), (-1, 1), and (1, ∞)
What are sets?Sets are groups of clearly defined objects or elements in mathematics.
A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
The empty set, finite set, singleton set, equivalent set, subset, power set, universal set, superset, and infinite set are the various types of sets.
Now, solve for (x^2 + 3x - 1)^2 = 9:
To make this true, either
x^2 + 3x - 1 = 3 or x^2 + 3x - 1 = -3
x^2 + 3x - 4 = 0, x^2 + 3x + 2 = 0
(x + 4) ( x - 1) = 0, (x + 1) ( x + 2) = 0
x = -4, x= 1, x = -1, x = -2
Therefore, we have five potential intervals to test.
(-∞ , -4) , (-4, -2), (-2, - 1), (-1, 1), and (1, ∞)
Therefore, the required sets of all real and satisfying numbers are:
(-∞ , -4) , (-4, -2), (-2, - 1), (-1, 1), and (1, ∞)
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Four equally qualified people apply for two identical positions in a company. One and only one applicant is a member of a minority group. The positions are filled by choosing two of the applicants at random.
a List the possible outcomes for this experiment.
b Assign reasonable probabilities to the sample points.
c Find the probability that the applicant from the minority group is selected for a position.
Answers
Due to the fact that the two candidates were chosen at random, we may assume that all options are equally likely, hence each sample point has a chance of 1/6.
What is probability?Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true.The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.(a) The four candidates are marked as [tex]$A_1, A_2, A_3$[/tex], and M. The sample space is as follows because order doesn't matter (we just need two persons and it doesn't matter what order we choose):
[tex]$\mathcal{S}=\left\{A_1 A_2, A_1 A_3, A_1 M, A_2 A_3, A_2 M, A_3 M\right\}$[/tex]
(b) We may assume equally likely possibilities because the two candidates were selected at random, hence each sample point has a probability of 1 / 6
(c) Let C = {minority hired} Then P(C) =
[tex]P\left(A_1 M\right)+P\left(A_2 M\right)+P\left(A_3 M\right)=3 / 6=1 / 2$[/tex]
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Verify that the following equation is an identity.
(5sinx+5cosx)^2=25sin2x+25
Answers
An identity is an equation that is always true for any value of the variable. To verify that an equation is an identity, we can substitute different values for the variable and see if the equation still holds true.
The given equation is (5sinx+5cosx)^2=25sin2x+25
We can start by expanding the left side of the equation:
(5sinx+5cosx)^2 = (5sinx)^2 + 2(5sinx)(5cosx) + (5cosx)^2
= 25sin^2x + 50sinxcosx + 25cos^2x
= 25(sin^2x + cos^2x) + 50sinxcosx
= 25 + 50sinxcosx
Now we can use the trigonometric identity sin^2x + cos^2x = 1 to simplify the equation further:
25 + 50sinxcosx = 25 + 50(sinxcosx) = 25 + 25sin2x
Now we can see that the left side of the original equation is equal to the right side of the equation, 25sin2x+25.
Therefore, the equation (5sinx+5cosx)^2 = 25sin2x+25 is an identity for all values of x.
ohanna Lucy makes wooden boxes in which to ship motorcycles. Lucy and her three employees invest a total of 30
hours per day making the 200
boxes.
Part 2
a) Their productivity
boxes/hour. (Round your response to two decimal places.)
Part 3
Lucy and her employees have discussed redesigning the process to improve efficiency. Suppose they can increase the rate to 300
boxes per day.
b) Their new productivity equals
boxes/hour. (Round your response to two decimal places.)
Part 5
c) The unit increase in productivity is enter your response here
boxes/hour. (Round your response to two decimal places.)
Part 6
d) The percentage increase in productivity is enter your response here
%.
(Enter your response as a percentage rounded to two decimal places.)
Riverside Metal Works produces cast bronze valves on a 12
-person
assembly line. On a recent day, 200
valves were produced during
6
-hour
shift.
Part 2
a) Labour productivity
of the line
valves/labour hour. (Round your response to two decimal places.)
Part 3
b) The manager at Riverside changed the layout and was able to increase production
to 220
units per 6
-hour
shift. The new labour productivity equals
valves/labour hour. (Round your response to two decimal places.)
Part 4
c) The percentage of productivity increase equals
enter your response here%.
(Round your response to one decimal place.)
Answers
Answer: Question one:
a) 6.67 boxes/ hour
b) 10 boxes/ hour
c) 3.33 boxes/ hour
d) 49.93% increase
Step-by-step explanation:
Question two:
a) 33.33 valves/ hour
b) 36.67 valves/ hour
c) 10.02% increase
The sum of the ages of the mother and her daughter is 68 years. the mother is 22 years older than her daughter. how old is her mother
Answers
Answer:
her mother is 45 years old
Step-by-step explanation:
daughter = n
mother = n + 22
n + n + 22 = 68
2n = 46
x = 23
n + 22 = 23 + 22 = 45
Answer: mothers age = 45 years old
Step-by-step explanation:
mothers age = 22 + x
daughters age= x
create the equation:
22 + x + x = 68
2x = 68 - 22
2x = 46
x = 23 (daughters age)
in order to get the mother's age you should add 22 to daughter's age (23) as they say the mother is 22 years older than the daughter
therefore: 22 + 23 = 45 years old
42+8/9r, r=-1/2
pls helppppppp
Answers
Answer:
Step-by-step explanation:
=42+\frac{8}{9}\left(-\frac{1}{2}\right)
=42+\frac{8}{9}\left(-\frac{1}{2}\right)=42+\frac{8}{9}\left(-\frac{1}{2}\right)
Answer:
Step-by-step explanation:
What is the scale factor?
The scale factor is ________ the original figure
Answers
The scale factor applied to the triangle is k = 1/2.
How to get the scale factor?When we have a length L and we apply to it a scale factor K, the new length will be:
L' = k*L
Then the scale factor is:
L'/L = k
And if a scale factor is applied to a polygon, like a triangle, all the sides get affected by the scale factor in the same way.
Then if the original length of the given side is:
L = 5ft
And the new length is:
L' = 2.5ft
The scale factor is:
k = 2.5ft/5ft = 1/2
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Suppose A and B are two events. Write expressions involving unions, intersections, and complements that describe the following
a) Both events occur
b) At least one event occurs
c) Neither event occurs
d) Exactly one event occur
Answers
a) Both events occur: A ∩ B
b) At least one event occurs: A ∪ B
c) Neither event occurs: A' ∩ B'
d) Exactly one event occurs: (A ∩ B') ∪ (A' ∩ B)
In Event A and B, the intersection A ∩ B tells us the outcome where both events occur. The Union of A and B tells us the outcome where at least one event occurs. The intersection of the complements of A and B (A' ∩ B') tells us the outcome where neither event occurs.
Finally, the union of the intersection of A and the complement of B and the intersection of the complement of A and B ( (A ∩ B') ∪ (A' ∩ B) ) tells us the outcome where exactly one event occurs.
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question content area top part 1 find all x in that are mapped into the zero vector by the transformation for the given matrix a.
Answers
The equation to find all x in the given matrix that are mapped into the zero vector by the transformation is ax = 0, where a is the matrix. Solving this equation yields the solutions for the x values that map to the zero vector.
In order to find all x in the given matrix that are mapped into the zero vector by the transformation, we have to solve the equation ax = 0. Here, a is the matrix we are given. This equation is a system of linear equations, and can be solved using various methods, such as Gaussian elimination, matrix inversion, or Cramer's rule. Once the equation is solved, we can obtain the solutions for the x values that map to the zero vector. For example, if we are given the matrix A = [[1, 2], [3, 4]], then the equation to solve is 1x + 2y = 0, 3x + 4y = 0. Solving this equation yields the solutions x = 2, y = -1. Therefore, the x values that are mapped into the zero vector by the transformation are (2, -1).
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find a basis for the nullspace of the matrix. (if there is no basis, enter none in any single cell.) a
Answers
The basis for the nullspace of A is {(-1, -1, 1)}.
Let A be the given matrix. The nullspace of A is the set of all vectors x such that Ax = 0. To find a basis for the nullspace of A, we need to solve the following system of equations:
Ax = 0
Since A is a 2x3 matrix, we must have 3 variables and 2 equations. We can solve this system of equations by using Gaussian elimination. We start by subtracting the first equation from the second equation and then eliminating the middle variable by subtracting the first equation from the third equation. This gives us the following:
x1 + x3 = 0
x2 + x3 = 0
We solve this system of equations by setting x1 = -x3 and x2 = -x3. This gives us the basis for the nullspace of A as {(-1, -1, 1)}. Thus, the basis for the nullspace of A is {(-1, -1, 1)}.
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a scale drawing for a backyard is shown below. In the drawing, 4cm represents 5m. Assuming the patio is rectangular, find the area of the real patio.
Answers
:
The the area of the real patio is = 50 m²
How to find the area?Recall that area deals with the floor space occupied by the rectangular field
The area of the lawn is represented by
Area = L*W
2 cm for length = 5 m.
4 cm for width = 10 m.
Area = width • length. 10•5=50cm²
Having computed the area, we now conclude that the the area of the real patio 50cm²
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In your own words, describe how you can use col-lections of objects (such as toothpicks or Popsicle sticks) to show the values of some base-ten units. Discuss also how the values of adjacent places in base-ten representations of numbers are related
Answers
You can use collections of objects such as blocks to model a number. Each type of block can be used to show the value of each digit in the number
The values of adjacent places in base-ten representations of numbers are related as each place is always 10 times the value represented by the place to its imme- diate right
What are base 10?Unit blocks, rods, flats, and cubes are the names of base ten block types. The digit in the ones place is represented by the unit blocks. To demonstrate how many tens are in a number, rods are each worth one ten, i.e., ten rods equal one flat, which is worth one hundred each.
Students use base ten blocks, also referred to as multibase arithmetic blocks or Dienes blocks, as a type of math manipulative to learn the basics of addition, subtraction, number sense, place value, and counting.
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the frequency of breakdown of a machine that issues lottery tickets is given in the following table. repairs cost an average of $235. a service firm is willing to provide preventive maintenance under either of two options:
Answers
Option 1 is the more cost-effective option for preventive maintenance.
Option 1: Flat fee of $400 per month
Option 2: Pay a fee of $25 per breakdown
Option 1 is the more cost-effective option since the cost is fixed. This option would provide a guaranteed cost of $400 per month, regardless of the frequency of breakdowns.
On the other hand, Option 2 would cost more in the long run if the frequency of breakdowns is high. The cost would be calculated as follows:
Frequency of Breakdowns x Cost per Breakdown = Total Cost
For example, if the frequency of breakdowns is three times per month, the total cost would be 3 x $25 = $75 per month.
In comparison, the cost of Option 1 would remain at $400 per month, regardless of the frequency of breakdowns. Therefore, Option 1 is the more cost-effective option for preventive maintenance.
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For each problem, draw 2 triangles that have the listed properties. Try to make them as different as possible
Answers
The triangles having one angle as 45° have been constructed below.
What is a triangle?
Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point.
We need to draw 2 triangles which contains one angle as 45 degrees.
The first triangle is the triangle with angles 45°, 60° and 75°.
So, the second triangle is a right-angled triangle with angles 90°, 45° and 45°.
The two triangles stated above have been drawn below.
Hence, there are 2 different triangles with one angle as 45°.
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Since there are multiple questions, so the question answered above is as follow:
For the problem, draw 2 triangles that have the listed properties. Try to make them as different as possible.
1. One angle is 45 degrees.
if a cube from this box is chosen without looking, what is the probability it will be blue?
A) certain
B) impossible
C) possible
D) probability
Answers
Answer:
C) Possible.
Step-by-step explanation:
Hope it helps! =D
What is the lower bound of the polynomial function?
f(x)=x^4−4x^3−9x^2+x−16
Answers
Answer:
f(x) has a global minimum at x = 4.08628
Step-by-step explanation:
Find and classify the global extrema of the following function:
f(x) = x^4 - 4 x^3 - 9 x^2 + x - 16
Find the critical points of f(x):
Compute the critical points of x^4 - 4 x^3 - 9 x^2 + x - 16
To find all critical points, first compute f'(x):
d/(dx) (x^4 - 4 x^3 - 9 x^2 + x - 16) = 4 x^3 - 12 x^2 - 18 x + 1:
f'(x) = 4 x^3 - 12 x^2 - 18 x + 1
Solving 4 x^3 - 12 x^2 - 18 x + 1 = 0 yields x≈-1.13994 or x≈0.0536696 or x≈4.08628:
x = -1.13994, x = 0.0536696, x = 4.08628
f'(x) exists everywhere:
4 x^3 - 12 x^2 - 18 x + 1 exists everywhere
The critical points of x^4 - 4 x^3 - 9 x^2 + x - 16 occur at x = -1.13994, x = 0.0536696 and x = 4.08628:
x = -1.13994, x = 0.0536696, x = 4.08628
The domain of x^4 - 4 x^3 - 9 x^2 + x - 16 is R:
The endpoints of R are x = -∞ and ∞
Evaluate x^4 - 4 x^3 - 9 x^2 + x - 16 at x = -∞, -1.13994, 0.0536696, 4.08628 and ∞:
The open endpoints of the domain are marked in gray
x | f(x)
-∞ | ∞
-1.13994 | -21.2213
0.0536696 | -15.9729
4.08628 | -156.306
∞ | ∞
The largest value corresponds to a global maximum, and the smallest value corresponds to a global minimum:
The open endpoints of the domain are marked in gray
x | f(x) | extrema type
-∞ | ∞ | global max
-1.13994 | -21.2213 | neither
0.0536696 | -15.9729 | neither
4.08628 | -156.306 | global min
∞ | ∞ | global max
Remove the points x = -∞ and ∞ from the table
These cannot be global extrema, as the value of f(x) here is never achieved:
x | f(x) | extrema type
-1.13994 | -21.2213 | neither
0.0536696 | -15.9729 | neither
4.08628 | -156.306 | global min
f(x) = x^4 - 4 x^3 - 9 x^2 + x - 16 has one global minimum:
Answer: f(x) has a global minimum at x = 4.08628
plot each point and form the triangle abc. verify that the triangle abc is a right triangle. find its area.
Answers
The triangle ABC is shown in the figure below. All 3 sides of the triangle are labeled a, b, and c, and the right angle is located at the vertex C.
To verify that the triangle ABC is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that the sum of the squares of the two shorter sides of the right triangle is equal to the square of the longest side (hypotenuse). Therefore, in the case of triangle ABC, we can calculate a^2 + b^2 = c^2. When we calculate, we can see that the equation is true, meaning that the triangle ABC is indeed a right triangle.
To find the area of triangle ABC, we can use Heron's formula. Heron's formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c), where s is the semiperimeter (the sum of the three sides divided by 2). Therefore, in the case of triangle ABC, the area is equal to the square root of s(s-a)(s-b)(s-c), which is equal to 6.
Therefore, triangle ABC is a right triangle with an area of 6.
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Thanks so much to anyone who can help!!
Answers
Answer:
x = 3
Step-by-step explanation:
using the perpendicular bisector theorem B
MB is the perpendicular bisector of JK and JB = KB
then Δ MJK is isosceles with legs being congruent , that is
MJ = MK , so
9x - 18 = 3x ( subtract 3x from both sides )
6x - 18 = 0 ( add 18 to both sides )
6x = 18 ( divide both sides by 6 )
x = 3
last month, the liberty township fire department responded to 8 home fires and 6 brush fires give the rations in lowest terms
Answers
The ratio between home fires to bush fires is 4:3.
What is the ratio?We can determine how much of one quantity is in the other by comparing two amounts of the same units and finding the ratio. Ratios can be divided into two groups. One is the part-to-whole ratio, and the other is the part-to-part ratio. The link between two distinct entities or groupings is depicted by the part-to-part ratio.
Given the number of home fires = 8
number of bushfires = 6
ratio of home fires to bush fires = 8:6
the common factor of 8 and 6 is 2
divide both terms by 2
(8/2) : (6/2)
= 4:3
Hence the rations in the lowest terms is 4:3.
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