Answers
p l l q, { < 2 and <3 } are corresponding angles and they are equal Hence , proved p l l q.
What are parallel lines ?In a Two-dimensional plane, parallel lines are those that, no matter how far they are extended, never cross.
In other words, two or more lines that have the same slope and never intersect are said to be parallel.
It is crucial to understand parallel lines in geometry since they are useful in many areas of mathematics, including trigonometry, calculus, and linear algebra.
Examining the slopes of two lines might help you decide if they are parallel. Two lines are parallel if they have the same slope.
Examining the equations of two lines is another method for figuring out if they are parallel.
If the slopes are the same and the equations for the two lines are of the form y = mx + b (where m is the slope and b is the y-intercept),
then the lines are parallel.
What is Two-dimensional plane ?A flat surface that extends infinitely in two directions is referred to as a two-dimensional (2D) plane and is sometimes depicted as a flat sheet of paper.
A two-dimensional plane is frequently referred to as a coordinate plane, Cartesian plane, or just a plane in mathematics.
The x-axis and y-axis, also known as the x and y axes, respectively, intersect at the origin to form the two-dimensional (2D) plane.
The horizontal direction is represented by the x-axis, while the vertical direction is represented by the y-axis.
An ordered pair of coordinates (x, y), where x is the value along the x-axis and y is the value along the y-axis, uniquely identify each point on the plane.
Prove :-
From the graph , we can get
∠1 ≅ ∠3 ------------ (1) {vertical angles are equal.}
Given what we know,
∠1 ≅ ∠2 -------------(2)
According (1) and (2)
We can get
∠2 ≅ ∠3
According to the theorem.
if corresponding angles are equal,
then two lines are
parallel. we can get ,
p l l q
{ < 2 and <3 }
are corresponding angles and they are equal
Hence , proved p l l q.
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Related Questions
Let u = 4i-j, v = 5i + j. and w=i+6j.
Find the specified scalar
U*V+U*W
Answers
To find the specified scalar, we need to first find the dot product of U and V, and then the dot product of U and W, and add these two dot products together:
U·V + U·W
where U·V denotes the dot product of U and V, and U·W denotes the dot product of U and W.
The dot product of two vectors a = (a1, a2) and b = (b1, b2) is given by:
a · b = a1b1 + a2b2
Using this formula, we can find the dot product of U and V:
U · V = (4i - j) · (5i + j) = 4i · 5i + 4i · j - j · 5i - j · j = 20i^2 + (4i · j - 5i · j) - j^2 = 20 + (-i · j) - 1 = 19 - i · j
Next, we can find the dot product of U and W:
U · W = (4i - j) · (i + 6j) = 4i · i + 4i · 6j - j · i - j · 6j = 4i^2 + (4i · 6j - j · i) - 6j^2 = 4 + (24i · j) - 6 = -2 + 24i · j
Now we can substitute these values into the original expression:
U·V + U·W = (19 - i·j) + (-2 + 24i·j) = 17 + 23i·j
Therefore, the specified scalar is 17 + 23i·j.
can someone help with thiss?
Answers
Step-by-step explanation:
You are given the formula for surface area of the cone
r = 7 cm l = 13 cm
Sooooo ...just plug the numbers into the formula :
SA = pi (7^2) + pi (13)(7) =
= 22/7 * 49 + 22/7 * 13 * 7 = 440 cm^2
Circle B is shown, with GHJK inscribed in the circle. The mGHJ = (3x+50)°, and mzHJK = (4x)° and mLGK] = (4x-10)°.
Find HGK and JHG
Answers
The value of
m∠GHJ = (3(20°)+50)° = 110°.
m∠GkJ = (4(20°)-10)° = 70°
m∠HJK = (4(20°))° = 80°
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Here, we have
Given: Circle B is shown, with GHJK inscribed in the circle. The m∠GHJ = (3x+50)°, and m∠HJK = (4x)° and mLGK] = (4x-10)°.
we have to find the value of HJK and JHG.
We know that
m∠GHJ + m∠GkJ = 180°
(3x+50)° + (4x-10)° = 180°
7x + 40 = 180°
7x = 140°
x = 20°
Hence, the value of
m∠GHJ = (3(20°)+50)° = 110°.
m∠GkJ = (4(20°)-10)° = 70°
m∠HJK = (4(20°))° = 80°
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When is M equals to T
Answers
Basically M will be equal to T if the value of M is assigned to T or vice-versa.
Understanding equality of two variablesThe equality of numbers refers to a mathematical concept that indicates that two numbers are the same. When two numbers are equal, they represent the same quantity, and we can use the symbol "=" to indicate this relationship. For example, "2 + 3 = 5" indicates that the sum of 2 and 3 is equal to 5. Similarly, "7 = 7" indicates that the number 7 is equal to itself.
The concept of equality is a fundamental concept in mathematics and is used extensively in various mathematical operations and equations. We can use the concept of equality to compare two or more numbers, variables, expressions, and equations.
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In which
situation can the Expression
on 8×2 be used to find the total number of head wraps on the shelf
Answers
The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.
What is expression?Expression in mathematics is a combination of symbols and numbers, often using an operation, such as addition, subtraction, multiplication, or division. It can represent a number, a variable, a function, or a mathematical statement. It can also represent a combination of these things. Expressions are used to describe relationships between numbers, variables, and mathematical concepts.
The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and there are 2 shelves in total. This expression can be used to calculate the total number of head wraps on the shelves by multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves). As such, the expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.
In conclusion, the expression 8x2 can be used to calculate the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total. By multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves), the total number of head wraps on the shelf can be found, resulting in a total of 16 head wraps.
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Complete questions as follows-
In which situation can the Expression
on 8×2 be used to find the total number of head wraps on the shelf?
What is the degree of -4x to the power of 3 + 6x to the power of 4 -1
Answers
4
Leading Term:
6x4
Leading Coefficient:
6
Find the probability for each problem. Then, drag the problem to the correct column.
Answers
1.) The probability of rolling two even numbers would be = 1/4
2.) The probability of rolling one even and one odd number = 1/2
3.) The probability of flipping tails on a coin and by rolling a factor of 6 on a six sided die would be = 1/3
How to calculate the probability of the various given events?To calculate the probability the formula that should be used is given as follows;
probability = possible outcome/sample space
For question 1.):
Sample space when two dice are thrown = 36
possible outcome = (2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)= 9
Probability = 9/36 = 1/4
For question 2.)
Sample space when two dice are thrown = 36
possible outcome = 18
probability = 18/36 = 1/2
for question 3.)
Sample space when two dice are thrown = 12
possible outcome = 4
probability = 4/12 = 1/3
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Question 1 (10 marks)
Tom is preparing for a 100 meters race competition. During his practice last week, a sample of seven 100
meters races is reviewed, and the finishing times (in seconds) were as below:
13.4
15.6
13.1
14.5
14.2
13.3
15.3
It is reasonable to assume his finishing times are normally distributed.
(a) Construct a 99% confidence interval estimate of his population mean finishing time of 100 meters race.
(b) If the confidence interval estimate of his population mean finishing time of 100 meters is constructed at
95% instead of 99%, would the new confidence interval be (I) wider, (II) narrower, or (III) the same as
the interval constructed at part (a)? (Just state your answer, no calculation is needed in part (b))
Question 2 (20 marks)
A survey was conducted one month ago to review the calories of lunch boxes provided by the supplier "Better
Lunch". In a sample with 300 lunch boxes, there were 273 lunch boxes with calories below 650 and the other
27 lunch boxes with calories above 650. Besides, the mean calories was 550 and standard deviation was 40.
(a) Find the point estimate of the population proportion of lunch boxes provided by "Better Lunch" had
calories above 650.
(b) Calculate the sampling error at 98% confidence level for the estimate of the population proportion of
lunch boxes provided by "Better Lunch" had calories above 650.
(c) Construct a 98% confidence interval estimate of the population proportion of lunch boxes provided by
"Better Lunch" had calories above 650.
(d) "Better Lunch" follows government's suggestions to change the menu in order to reduce the lunch boxes'
calories. Suppose after the menu update, each lunch box's calories can be reduced by 4%. Find the
sample mean and sample standard deviation of calories of the above sample after the change. Hence,
construct a 90% confidence interval estimate of the population mean calories in a lunch box after the
change.
Answers
Question A) A 99% confidence interval estimate of his population mean finishing time of 100 meters race is (12.8081,15.5919)
Question B) Option II) narrower is the correct Option.
How to solveLet X be the time required to finish 100 meters race competition with Tom ( in seconds.)
A) A 99% confidence interval estimate of his population mean finishing time of 100 meters race is (12.8081,15.5919)
x = 14.2
s^2= 0.9867
s= 0.9933
t \aplha/2, n-1 = 3.7074
Margin of error= 1.3919
lower bound= 12.8081
upper bound= 15.5919
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What’s the length of side AB?
Answers
tan = 1/√3= perpendicular/ base
1/√3 = AB / AC
AB / 6 = 1/√3
AB = 6/√3
A ball on a spring is pulled 2 inches above its rest position and then released. After t seconds, the ball's distance, d, in inches from its rest position is given by the equation below.
d=2cos π/3t
Find all values of t for which the ball is 1 inches above its rest position.
Give a general formula for all the solutions by adding multiples of some positive integer n
t=
Answers
The general formula for all solutions of t, by adding multiples of some positive integer n, is:
t = 1 + 6k - 6n
What is the Trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships and properties of angles and triangles.
To find the values of t for which the ball is 1 inch above its rest position, we can set the value of d in the equation d = 2cos(π/3t) to 1, and then solve for t.
2cos(π/3t) = 1
Divide both sides by 2 to isolate the cosine term:
cos(π/3t) = 1/2
To find the general formula for all solutions by adding multiples of some positive integer n, we can use the periodicity of the cosine function. The cosine function has a period of 2π, which means that its values repeat every 2π units.
Therefore, we can add multiples of 2π to the angle π/3t and still obtain the same value for cosine.
cos(π/3t + 2πn) = 1/2
where n is any positive integer.
Now we can solve for t by taking the inverse cosine of both sides:
π/3t + 2πn = arccos(1/2)
π/3t + 2πn = π/3 + 2πk (using the fact that arccos(1/2) = π/3 and k is any integer)
π/3t = π/3 + 2πk - 2πn
t = 1 + 6k - 6n
Hence, the general formula for all solutions of t, by adding multiples of some positive integer n, is:
t = 1 + 6k - 6n
where k and n are any integers.
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The graph shows the cumulative frequency of points earned for a game.
A student claims that the graph shows the player earned more points from Level 2 to Level 4 than from Level 3 to Level 5. Is the student correct?
A) No, the player earned 67 points from Level 2 to Level 4 and 69 points from Level 3 to Level 5.
B) No, the player earned 42 points from Level 2 to Level 4 and 44 points from Level 3 to Level 5
C) Yes, the player earned 67 points from Level 2 to Level 4 and 69 points from Level 3 to Level 5.
D) Yes, the player earned 42 points from Level 2 to Level 4 and 44 points from Level 3 to Level 5.
Answers
Yes, the player earned 67 points from Level 2 to Level 4 and 69 points from Level 3 to Level 5.
How to determine if the student's claim is correct or not?Given that: A student claims that the graph shows the player earned more points from Level 2 to Level 3 than from Level 4 to Level 5.
Let's examine the line graph:
At level 2 the point is 45 and at level 4 the point is 112. Thus, the points earned moving from Level 2 to Level 4 will be:
= 112 - 45
= 67
At level 3 the point is 112 and at level 5 the point is 156. Thus, the points earned moving from Level 4 to Level 5 will be:
= 156 - 87
= 69
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A ski club charges $70 for a lift ticket and $20 per hour to ski. Jim paid at least $130 last week to ski. How many hours would he have skied.
Answers
Answer:
Step-by-step explanation: $130-$70 lift = $60/$20 per hour= 3 hours ski time
70+20=90
90+20=110
110+20=130
A certain college had 3,000 students enrolled in
2015. The college predicts that after 2015, the
number of students enrolled each year will be 2%
less than the number of students enrolled the year
before. Which of the following functions models the
relationship between the number of students
enrolled, f (x), and the number of years after 2015,
x?
A. f(x) = 0.02x(3000)*
B. f(x) = 0.98x(3000)*
C. f(x) = 3000(0.02)*
D. f(x) = 3000(0.98)*
Answers
The function that models the relationship between the number of students enrolled, f(x) and the number of years after 2015, x, is D. f(x) = 3000(0.98)*.
What is a function?Mathematically, a function defines a mathematical relationship or an algebraic expression involving one variable (the independent variable) and another variable (the dependent variable).
There are four main types of mathematical functions, including:
Constant Function, example, the polynomial function of degree zero.Linear Function, for example, the polynomial function of degree one.Quadratic Function, for example, the polynomial function of degree two.Cubic Function, the polynomial function of degree three.The number of students enrolled in 2015 = 3,000
The annual decrease in students enrollment = 2%
Let f(x) the model modeling the relationship between the number of students enrolled and the number of years after 2015.
Let the number of years after 2015 = x.
Thus, the correction function is D. f(x) = 3000(0.98)*.
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Write the quadratic equation whose roots are 6 and -5, and whose leading coefficient is 2.
(Use the letter .x to represent the variable.)
=0
Answers
Step-by-step explanation:
x = 6 x = -5
x - 6 = 0 x + 5 = 0
f(x) = 2(x-6)(x+5)
f(x) = 2(x² +5x - 6x - 30)
f(x) = 2(x² - x - 30)
f(x) = 2x² - 2x - 60
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Convert the following dimensions into feet using the provided scale. Fraction or
decimal answers are fine.
Measurement: 3 1/4 in. x 4 1/16 in.
Scale: 1/8 in. = 1 ft
Answers
Thus, the value of measurement in the unit of feet converted from inch are - Measurement: 26 ft. x 32.5 ft.
Explain about the scale factor:The ratio of equivalent sides on two comparable figures is known as the scale factor. Scale factor in mathematics is used to quantify how much larger or smaller one object or figure is in comparison to another. On a map, scales are frequently present. The scale factor in geography typically refers to how accurately the scale depicted on the map reflects actual distance.
Given:
Measurement: 3 1/4 in. x 4 1/16 in.
Scale: 1/8 in. = 1 ft
Convert the mixed fraction of measurement into proper fraction:
Measurement: (3*4 + 1)/4 in. x (4*16 + 1)/16 in.
Measurement: 13/4 in. x 65/16 in.
Now,
Scale: 1/8 in. = 1 ft
1 in. = 1*8 ft
1 in. = 8 ft
Thus, multiply each measurement by 8 to get the values in ft.
Measurement: 13*8/4 ft. x 65*8/16 ft.
Measurement: 13*2 ft. x 65/2 ft.
Measurement: 26 ft. x 32.5 ft.
Thus, the value of measurement in the unit of feet converted from inch are - Measurement: 26 ft. x 32.5 ft.
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Tina pet sits to earn extra money. She charges a flat service fee of $20, plus $15 per day. If one of her customers spent less than $125, which of the following inequalities could be used to solve for x, the number of days the customer paid for pet sitting?
Answers
Therefore, **x < 7** is the inequality that may be utilized to find x
What is inequality?A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).
For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".
Let x represent how many days the client paid for pet sitting.
$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.
We are aware that the customer's purchase was under $125. Consequently, we can write:
20 + 15x < 125
Putting this disparity simply:
15x < 105
x < 7
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Claim: Fewer than 97% of adults have a cell phone. In a reputable poll of 1146 adults, 90% said that they have a cell phone. Find the value of the test statistic.
The value of the test statistic is
(Round to two decimal places as needed.)
Answers
The value of test statistic is -5.83.
Define statistics?statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In other words, it is a mathematical discipline to collect, summarize data. Also, we can say that statistics is a branch of applied mathematics. statistic = (sample proportion - hypothesized proportion)/ standard error.
What is decimal system?The decimal system is a number system that uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent all possible numbers. It is also known as the base-10 system because each digit represents a power of 10. For example, in the number 123, the digit 3 represents 10^0 (which is 1), the digit 2 represents 10^1 (which is 10), and the digit 1 represents 10^2 (which is 100). The decimal system is widely used in everyday life and is the most common number system used around the world.
Here, the sample proportion is 0.9 (90% of 1146 adults said they have a cell phone), and the hypothesized proportion is 0.97 (the claim that fewer than 97% of adults have a cell phone).
The standard error can be calculated as:
standard error = sqrt[(hypothesized proportion * (1 - hypothesized proportion)) / sample size]
Substituting the values, we get:
standard error = [tex]\sqrt{(0.97*0.03)/1146}[/tex] = 0.012
Now, substituting all the values in the formula for the test statistic, we get:
test statistic = (0.9 - 0.97) / 0.012 = -5.83
Rounding to two decimal places, the value of the test statistic is -5.83.
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[tex]What is the logarithmic form of the exponential equation 4^{3} =(5x+4)[/tex]
Answers
The logarithmic form of the given exponential equation in the question, 4³ = (5x + 4) is Log₄ (5x + 4) = 3.
How to convert exponential equation to logarithmic form.The exponential-to-logarithmic format is useful because it makes it easy to compute large numeric expressions. Expressions involving exponential multiplication and division can be converted to addition and subtraction by applying logarithms. Logarithmic exponential form is a common means of converting mathematical expressions in one form to another form.
The exponential form aˣ = N is transformed and written logarithmically as LogₐN = x.
The exponential form of a for the exponent of x equal to N is converted to the logarithm of the number N in base a, equal to x.
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Carlita surveyed all the students in her grade and reported the fraction of students who liked each type of pet.
Three-sevenths liked hamsters.
Five-sixths liked dogs.
One-half liked cats.
liked snakes.
Which list has the animals in order from least liked to most liked?
A. dogs, cats, snakes, hamsters
B. snakes, dogs, cats, hamsters
C. dogs, cats, hamsters, snakes
D. snakes, hamsters, cats, dogs
Answers
On the basis of data reported by Carlita in form of fractions , on comparing the given fractions order of animals from least liked to most liked is option-D:Snakes, hamsters, cats, dogs.
What are fractions?
A fraction represents a portion of a total. This entire may refer to a place or a group of places. The Latin word "fractio," which meaning "to break," is the source of the English term "fraction." It is simpler to identify the greater or smaller fraction when comparing fractions with the same or similar denominators. We must change fractions with dislike or different denominators to fractions with like or the same denominators in order to compare them. To do this, we must determine the denominators' Least Common Multiple (LCM). We can compare fractions simply when the denominators are made the same or similar.
Given data collected by Carlita:
Fraction of students who like hamsters= [tex]\frac{3}{7}[/tex]
Fraction of students who like dogs = [tex]\frac{5}{6}[/tex]
Fraction of students who like cats= [tex]\frac{1}{2}[/tex]
Fraction of students who like hamsters= [tex]\frac{1}{9}[/tex]
To compare all four fractions [tex]\frac{3}{7}[/tex] , [tex]\frac{5}{6}[/tex] , [tex]\frac{1}{2}[/tex] & [tex]\frac{1}{9}[/tex]
We find LCM of denominators 2,6,7 & 9
prime factors:
2=2
6=2 x 3
7=7
9= 3 x 3
LCM=2 x 3 x 3 x 7
=126
Equivalent fractions with denominator 126:
[tex]\frac{3}{7}[/tex] = [tex]\frac{3}{7}[/tex] × [tex]\frac{18}{18}[/tex] = [tex]\frac{54}{126}[/tex]
[tex]\frac{5}{6}[/tex] = [tex]\frac{5}{6}[/tex] × [tex]\frac{21}{21}[/tex] = [tex]\frac{105}{126}[/tex]
[tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex] × [tex]\frac{63}{63}[/tex] = [tex]\frac{63}{126}[/tex]
[tex]\frac{1}{9}[/tex] = [tex]\frac{1}{9}[/tex] × [tex]\frac{14}{14}[/tex] = [tex]\frac{14}{126}[/tex]
On arranging least to most [tex]\frac{54}{126}[/tex], [tex]\frac{105}{126}[/tex], [tex]\frac{63}{126}[/tex] & [tex]\frac{14}{126}[/tex] we get
[tex]\frac{14}{126}[/tex] < [tex]\frac{54}{126}[/tex] < [tex]\frac{63}{126}[/tex] < [tex]\frac{105}{126}[/tex]
snakes<hamsters<cats<dogs
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Refer to the attachment for the complete question.
PLEASE HELP ON QUESTION!!!
A rectangular field has a perimeter of 150cm
Field is 15 m longer than it is wide . The width of field is a meters.
A) write down equation for this information.
If answers correct I'll rate 5 stars , a thanks and maybe brainliest.
Answers
Perimeter = 2 × (Length + Width) = 150 cm
Length = Width + 1500 cm
Let's substitute the second equation into the first equation and solve for the width:
2 × (Length + Width) = 150
2 × (Width + 1500 + Width) = 150
4 × Width + 3000 = 150
4 × Width = 150 - 3000
4 × Width = -2850
Width = -2850 / 4
Since a negative width does not make sense for a field, we can conclude that there must be an error in the problem statement or our calculations.
We should check the problem statement again to ensure that we have not misinterpreted any information.
I need help with this please
Answers
Answer:
Step-by-step explanation:
just add the two numbers up 576x1 1/2= 864
A diamond merchant received a shipment of 7/10 of a pound of diamonds. He divided the diamonds into 7 equal lots and sold them to jewelers for making rings and necklaces. What was the weight of the diamonds in each lot? Write your answer as a fraction or as a whole or mixed number.
Answers
The weight of the diamonds in each lot is 4.9 pounds.
What is the fractional idea?Here, the fractional idea can be used. A fraction represents a portion of a total. A fraction is a numerical figure that designates a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain value, or an object.
A cargo of half a pound's worth of diamonds was received by a diamond trader. He separated the stones into 4 equal lots and sold them to jewelers so they could be used to make necklaces and rings.
Total shipment = 7/10 pound
number of equal lots = 7
then, 7 x weight = 7/10
weight = 4.9
Therefore, the weight of each lot is 4.9 pounds.
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Michelle is a dentist. One-third of her patients are under the age of 12. Five-twelfths of her patients are over the age of 65. What fraction of Michelle’s patients are 12 to 65 years old?
A: 1/6
B: 3/4
C: 3/5
D: 1/4
Answers
Simplifying this fraction gives us 1/4. The answer is (D) 1/4.
What is arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.
Let's start by finding the fraction of Michelle's patients who are under 12 or over 65. We know that one-third of her patients are under 12, so two-thirds must be 12 or older. Similarly, five-twelfths of her patients are over 65, so seven-twelfths must be 65 or younger.
Now, we want to find the fraction of Michelle's patients who are between 12 and 65. To do this, we need to subtract the fraction of patients who are under 12 or over 65 from 1 (since these are the only two age groups we're considering).
Fraction of patients under 12: 1/3
Fraction of patients over 65: 5/12
Fraction of patients 12 to 65: 1 - 1/3 - 5/12
We can simplify this expression by finding a common denominator:
Fraction of patients 12 to 65: 12/12 - 4/12 - 5/12
Fraction of patients 12 to 65: 3/12
Simplifying this fraction gives us 1/4. Therefore, the answer is (D) 1/4.
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What is the height, h, of the rectangular prism shown below?
Round your answer to the nearest tenth.
h
The height is
4
√34
units.
3
Answers
The height is 3 units.
We have,
l = 4 and b= 3
Using Pythagoras theorem
d² = l² + b²
d² = 4² + 3²
d² = 16 + 9
d² = 25
d= 5 unit
let h be the height.
Again, using Pythagoras theorem
34 = 25 + h²
h² = 9
h= 3 unit
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On the Y axis, we have the profit from the trucking company and on the X axis, we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?
A. Y intercept will be less and X will be less
B. Y intercept will be less and X intercept will be greater
C. Y intercept will be greater and X will be greater
D. Y intercept will be greater and X will be less
Answers
The correct answer is: A. Y intercept will be less and X will be less.
What is slope?A linear function's slope is a gauge of how steep the line is. Between any two points on the line, it is the ratio of the change in the y-coordinate to the change in the x-coordinate. The formula is used to compute it:
slope equals (y2 - y1)/. (x2 - x1)
where any two points on the line (x1, y1) and (x2, y2) are.
The company's expenses will rise once it begins paying a driver at a rate of 0.25 cents per mile, which means its profit will decline. The profit curve on the y-axis will go vertically downward as a result of this. But, because the cost of paying the driver is fixed per mile and has no impact on the profit per mile, the slope of the line—which reflects the profit per mile—will stay the same.
Hence, A. Y intercept will be less and X will be less is correct.
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A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. A random sample of 36
stores this year shows mean sales of 52
units of a small appliance with a standard deviation of 5
units. During the same point in time last year, a random sample of 49
stores had mean sales of 46
units with standard deviation 14
units.
It is of interest to construct a 95 percent confidence interval for the difference in population means 1−2
, where 1
is the mean of this year's sales and 2
is the mean of last year's sales.
Enter values below rounded to three decimal places.
(a) The estimate is:
.
(b) The standard error is:
.
Answers
Answer:
Step-by-step explanation:
(a) The estimate for the difference in population means is 6.000.
(b) The standard error for the difference in population means is 3.208.
Conclusion:
Based on the given data, the 95% confidence interval for the difference in population means between this year's sales and last year's sales is between -0.608 and 12.608. This suggests that the population mean for this year's sales is likely to be higher than the population mean for last year's sales. This is supported by the fact that the estimate for the difference in population means is 6.000, which is greater than 0.
A stainless steel patio heater is a square pyramid. The length of one side of the base is 22.6 in. The slant height of the pyramid is 88.9 in. What is the height of the pyramid?
NEED AN ANSWER ASAP! IT'S DUE TOMORROW
Answers
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the slant height is the hypotenuse, and the height and half of the base are the other two sides.
We can set up the equation as follows:
height^2 + (base/2)^2 = slant height^2
height^2 + (22.6/2)^2 = 88.9^2
height^2 + 256.03 = 7921
height^2 = 7664.97
height = 87.6 in (rounded to the nearest tenth)
Therefore, the height of the pyramid is approximately 87.6 inches.
A car travels at an average speed of 64 mph. how long does it take to travel 304 miles 
Answers
Assuming the time begins after the car is fully accelerated to 64 mph, 4 hours 45 minutes
IG:whis.sama_ent
Verify that segments with lengths of 21 inches, 72 inches, and 75 inches form a triangle. If so, determine whether they form a right triangle.
A. triangle, right triangle
B. triangle, isosceles triangle
C. triangle, obtuse triangle
D. triangle, acute triangle
Answers
Answer:
it would be C
Step-by-step explanation:
You own 23 CDs. You want to randomly arrange 5 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?
The probability that the CDs are in alphabetical order is
Answers
The probability of choosing 5 CDs in alphabetical order out of a collection of 23 CDs is approximately 0.00003 or 0.003%.
What is combination?
In mathematics, a combination is a way of selecting objects from a larger group of objects, where the order of selection is not important. A combination is a subset of objects that are chosen from a larger set without regard to the order in which they are selected.
The formula is given by:
C(n, r) = [tex]\frac{n!}{r!* (n - r)!}[/tex]
The total number of ways to choose 5 CDs from a collection of 23 CDs is given by the combination formula:
C(23, 5) = [tex]\frac{23!}{5!* (23 - 5)!}[/tex]
= 33649
This means there are 33649 different ways to arrange 5 CDs out of the 23 CDs.
Out of these 33649 ways, only one arrangement is alphabetical. For this to happen, the first CD chosen must be the first one alphabetically, the second CD chosen must be the second one alphabetically, and so on.
The first CD can be any of the 23 CDs. However, once the first CD is chosen, there is only one CD that can be the second one alphabetically, two CDs that can be the third one alphabetically, and so on. Therefore, the probability of choosing 5 CDs in alphabetical order is:
P = 1 / C(23, 5)
P = 1 / 33649
P ≈ 0.00003
So the probability of choosing 5 CDs in alphabetical order out of a collection of 23 CDs is approximately 0.00003 or 0.003%.
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