[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{-4}~,~\stackrel{y_1}{2})\qquad Q(\stackrel{x_2}{2}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{(~~2 - (-4)~~)^2 + (~~4 - 2~~)^2} \implies PQ=\sqrt{(2 +4)^2 + (4 -2)^2} \\\\\\ PQ=\sqrt{( 6 )^2 + ( 2 )^2} \implies PQ=\sqrt{ 36 + 4 } \implies PQ=\sqrt{ 40 }[/tex]
what are the common factors of 6 12 and 30
Answer:
HCF = 6.
Step-by-step explanation:
The Highest Common factor is 6.
Other common factors are 1, 2 and 3.
dr. huang required half of a group of healthy volunteers to study a reading passage for 1 hour. the other half of the participants studied for 15 minutes. dr. huang then administered a test of participants' memory of details from the passage. what was the dependent variable?
The correct answer is results of the memory test.
Given that,
Dr. Huang asked the healthy volunteers in a group to read a chapter for an hour. The other half of the attendees spent 15 minutes studying. Dr. Huang next asked participants to recall specifics from the paragraph in a test.
To find :what was the dependent variable ?
It is something on which other elements depend. The test score for a instance, may be the dependent variable because it could vary based on a number of variables, including how much you studied, how much sleep you got the night before the test, and even how hungry you were.
Therefore, the correct answer is results of the memory test.
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I need help with this question for Geometry.
The measure of side FD is given as follows:
FD = 81.5.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.Hence the proportional relationship measuring the side lengths is given as follows:
FD/23 = 39/11.
Applying cross multiplication, the measure of side FD is obtained as follows:
11FD = 39 x 23
FD = 39 x 23/11
FD = 81.5. (rounded to the nearest tenth).
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Finding the Area of a Circle continued Find the missing measurements. Use 3.14 for T. Show your work.
Radius: 6 mm
Diameter: 12 mm
Area:.
Radius:
Diameter: 24 cm
Area:
Radius:
Diameter: 16 ft
Area:
Radius:
Diameter: 2 km
Area:
Answer:
Step-by-step explanation:
1. Area=113.1 mm^2
2. Radius=12mm
Area=452.4 mm^2
3. Radius=8 mm
Area=201.06 mm^2
4. Radius=1 km
Area=3.1416 km^2
Find the gradient of the straight line joining A(2,-5) and B(-7,-3).
1. -9/2
2. -2/9
3. -9
4. 1/9
Answer:
Step-by-step explanation: I do know bro is, sorry
what is the value of x
Answer:
The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown".
Answer:
30
Step-by-step explanation:
triangle interior angles sum = 180
so x+2x-15+105 = 180
so 3x = 180-90 = 90
x =30
After you multiply everything out in the box, then write your final answer below after you combine your like terms! (x+1)(x+5)
Answer:
x^2 + 6x + 5
see attached image for sol
Answer:
[x^2 + 6x + 5]
Step-by-step explanation:
(x + 1)(x + 5)
Utilize FOIL
First
Outer
Inner
Last
x * x = x^2
x * 5 = 5x
1 * x = x
1 * 5 = 5
x^2 + 5x + x + 5
Combine like terms:
[x^2 + 6x + 5]
if a process is best situated close to the information corner of the om triangle, then this must mean:
Capacity is very expensive, so it is run at high utilization. There is a lot of variability in arrivals and processing times. Waiting or throughput times are long for this process.
Gaining understanding of the trade-offs operations managers must make is a major contribution of OR/MS models. One such trade-off concerns capacity, inventory, and variability: while the firm would want to function at 100% capacity utilization with very no inventory and tolerate high levels of unpredictability, this is not realistic.
The trade-off between these three competing goals is demonstrated and clarified using the conventional G/G/1 queueing paradigm. This insight can be described as a relationship between capacity, inventory, and the third parameter of information in situations where greater information can be used to lessen the variability in services or in arrivals (rather than variability).
Adopting the terminology of Lovejoy (1998), this inter- relationship is referred to as the OM triangle. Finding her company's ideal location in relation to the OM triangle is the manager's responsibility, as was mentioned in this article.
With variable arrival and processing times, there is a long wait period. It should have high utilization because of expensive capacity.
Therefore, the correct option is All the other answers are correct (A).
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complete question: If a process is best situated close to the inventory corner of the OM triangle, then this must mean:
a. All the other answers are correct.
b. Capacity is very expensive, so it is run at high utilization.
c. There is a lot of variability in arrivals and processing times.
d. Waiting or throughput times are long for this process.
Please help simplify the algebraic fraction
[tex] \frac{x {}^{2} - 4xy + 4y {}^{2} }{2x - 4} \div \frac{x - 2y}{x - 2} \times \frac{x { }^{2}- 4 }{4} [/tex]
After simplification, value of expression is (x - 2y) (x² - 4) / 8.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The algebraic fraction is,
⇒ (x² - 4xy + 4y²) / (2x - 4) ÷ (x - 2y) / (x - 2) × (x² - 4) / 4
Now, Simplify the expression as;
⇒ (x² - 4xy + 4y²) / (2x - 4) ÷ (x - 2y) / (x - 2) × (x² - 4) / 4
⇒ (x² - 4xy + 4y²) / (2x - 4) × (x - 2) / (x - 2y) × (x² - 4) / 4
⇒ (x² - 4xy + 4y²) / (2x - 4) × (x - 2) / (x - 2y) × (x - 2) (x + 2)/ 4
⇒ (x - 2y)² / 2(x - 2) × (x - 2) / (x - 2y) × (x - 2)(x + 2) / 4
⇒ (x - 2y) / 2 × (x² - 4) / 4
⇒ (x - 2y) (x² - 4) / 8
Thus, After simplification, value of expression is (x - 2y) (x² - 4) / 8.
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problems 10,11,12,13 on homework 3 right triangles and trigonometry
The missing sides are of the given triangle are of 26.69 units and 11.33 units.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
Given that:
One angle of a right angled triangle measures 67 degrees.
Hypotenuse of that right angled triangle measures 29 units.
To find:
Missing sides of the triangle.
Calculations:
The sine trigonometric ratio gives us ratio of perpendicular to hypotenuse from perspective of the considered angle.
Referring to the figure attached below,
sin∠ACB = AB/AC
sin 67° = AB/29
0.9025 = AB/29
i.e. AB = 26.69
Similarly,
cos∠ACB = AB/AC
cos 67° = AB/29
0.3907= AB/29
i.e. AB = 11.33
Thus, the missing sides are of the given triangle are of 26.69 units and 11.33 units.
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n a large school, it was found that 76% of students are taking a math class, 75% of student are taking an english class, and 72% of students are taking both. find the probability that a randomly selected student is taking a math class or an english class. write your answer as a decimal, and round to 2 decimal places if necessary.
The probability that a randomly selected student is taking a math class or an English class is 0.79.
Using the formula for the union of two events, P(A or B) = P(A) + P(B) - P(A and B), where A is the event "taking a math class" and B is the event "taking an English class", we can find the desired probability:
P(A or B) = 0.76 + 0.75 - 0.72 = 0.79
So, "0.79" (which is given in upto two decimal places) is the probability that a randomly selected student is taking a math class or an English class.
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simplify in order -2/4 (12 - 8y + 20m)
The simplified solution is -6+4y-10m.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
-2/4 (12 - 8y + 20m)
now, dividing & multiplying we get,
⇒ -2(3-2y+5m)
⇒-6+4y-10m
Hence, The simplified solution is -6+4y-10m.
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Answer:
did this for points
oci hcduibghvfv
Step-by-step explanation:
:)
an outlier in a data set can significantly affect the value of the mean but not the median. True or False
The required statement "outlier in a data set can significantly affect the value of the mean but not the median" is true.
What is mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
According to question:The average of a group of variables is referred to as the mean in mathematics and statistics.
There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Thus, given statement is true.
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according to rank size rule, what is the population of the 5th largest city within a region in which the largest city has 5,5 million people?
According to the Rank-Size Rule, the population of the 5th largest city in this region is estimated to be 1.1 million people.
The Rank-Size Rule states that the population of a city (n) in a region is proportional to the population of the largest city (P1) in that region, with a power of -1.
So, the population of the nth city in a region can be calculated using the formula:
Pn = P1 / n^1
So, for the 5th largest city in a region where the largest city has 5.5 million people, the population can be calculated as follows:
P5 = 5.5 million / 5^1 = 1.1 million
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If it beats 75 times per minute, how many times does your heart beat in 5 hours?
Answer:
22500
Step-by-step explanation:
This is because 75 x 60 = 4500 (that gives us the beats per hour)
4500 x 5 = 22500 (that gives us the beats per 5 hour)
Answer:
5×60=300mins
1min=75heartbeat
300min=300×75=22500heartbeat
approximately how long will it take for $250 to grow to $1,000 at an annual rate of 8%?
Answer: 18 years.
Step-by-step explanation:
Turn into an equation:
y=250(1.08)^x
see what number you plug in for x makes y 1000,
and that number is 18.
An experiment is conducted where weights are added to a spring which is then measured. • When 4 grams are added to the spring, the spring stretches 12 centimeters. • When 6 grams are added to the spring, the spring stretches 18 centimeters. • Let w represent the amount of weight added to the spring. • Let s represent the distance the spring is stretched. Which of the following is true about the relationship between w and s?
The relationship between w and s can be represented as s = 3w.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side
When 4 grams are added to the spring, the spring stretches 4 × 3 = 12 centimeters.
When 6 grams are added to the spring, the spring stretches 6 × 3 = 18 centimeters.
In this way, if w grams are added to the spring, the spring stretches w × 3 centimeters.
Let s represent the distance the spring is stretched.
s = 3w
Hence the required relationship is s = 3w.
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Solve this, please will give points
The coordinate point of C is (4.5, 6).
What is the section formula?When a point on a line segment divides it into two segments, the formula used to determine the coordinates of that point is known as the section formula. Let us say, we have a point P(x,y) that divides the line segment with marked points as A (x1,y1) and B(x2,y2). To find the coordinates, we use the section formula, which is mathematically expressed as:
P(x, y) = P(x, y) = [(mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)]
Given that, Philip travels from town A, with coordinates (1, 6) to town B, with coordinates (7, 6).
The ratio of Philip's Bruces rates is 7:5.
Substitute (x₁, y₁)= (1, 6), (x₂, y₂)= (7, 6) and m:n=7:5 in the section formula, we get
C(x, y) = [(7×7+5×1)/(7+5), (7×6+5×6)/(7+5)]
C(x, y) = (54/12, 72/12)
C(x, y) = (4.5, 6)
Therefore, the point is (4.5, 6).
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Answer:
Step-by-step explanation:
What error did Kellyanne make?
The error kelly made was that sin f is h/e and g = EF
What is area of a triangle ?The area of a triangle is given by 1/2 base × height. In the triangle base is g and height is h
In trigonometry, sin(tetha) =[opp/ hypotenuse)
cos (tetha) = adj/hypotenuse
tan(tetha) = opp/ hypotenuse
sinF = e/h
sinE = h/f
this two does not have g at all. so we either use tan or cos.
g is divided into two, let's name it g1 and g2
cos F = g1/e
cos E = g2/f
g1 = e(cos F)
g2 = f(cos E)
g = g1+g2
g = e(cos F) + f(cos E)
A = 1/2bh
A = 1/2 ×( e( cos F) + f(cos E) ) h
Therefore the actual value of the area is /2 ×( e( cos F) + f(cos E) ) h
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Both equations in a system of linear equations have y-intercepts at (0,2)
a. Is it possible for this system to have only one solution? Explain your
reasoning.
b. Is it possible for this system to have no solution? Explain your
reasoning.
c. Is it possible for this system to have infinitely many solutions? Explain
your reasoning.
is 2 more than 5 times the
Both equations in a system of linear equations have y-intercepts at (0,2) but it is not possible for this system to have only one solution because it depends on another point as well. Option C
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
Given :Both equations in a system of linear equations have y-intercepts at (0,2).
The following steps can be used in order to determine the system have only one solution or not:
According to the given data, both equations in a system of linear equations have y-intercepts at (0,2).
The equation of a line is given by: [tex]\frac{y-y_{1} }{x-x_{1} } = \frac{y_{2} - y_{1} }{x_{2} -x_{1} }[/tex]
From the above steps, it can be concluded that it does not say that the system to have only one solution because it depends on another point as well.
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What is the lateral surface area of the rectangular prism below? QUICK
The lateral surface area of the rectangular prism is 36 squared centimeters.
What is lateral surface area of a shape?Lateral surface of any given shape is all its surface excluding its base and top. Such that the lateral surface area of a given shape is the area of all its surface apart from that of its base and top.
In the given rectangular prism, its lateral surface area can be determined as:
i. area of a rectangle 1 = length x width
= 6 * 2
= 12
area of its rectangular sides = 2 * 12
= 24 squared centimeters
ii. area of a rectangular surface 2 = 3 * 2
= 6
area of its rectangular sides 2 = 2 * 6
= 12 squared centimeters
Therefore,
its lateral surface area = 24 + 12
= 36 squared centimeters
The lateral surface area of the prism is 36 squared centimeters.
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a 21-ft ladder is leaning against a building. if the base of the ladder is 9 ft from the base of the building, what is the angle of elevation of the ladder?
A 21-ft ladder is leaning against a building. if the base of the ladder is 9 ft from the base of the building, then the angle of elevation of the ladder will be: α = 71° .
From trigonometry we have:
cos α = 7/21
7 = 21 cos(α)
and:
α = arc cos(7/21) = 70.5 ≈ 71∘
The angle of elevation is the angle between the horizontal line of sight and the article.
Considering that, A 21-ft stepping stool is resting up against a structure. Assuming the foundation of the stepping stool is 9 ft from the foundation of the structure,
Subsequently, Angle of Elevation is x = 71° and the Level of stepping stool arriving at the wall = 21 ft .
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Joel wants to buy a new tablet from a store having a 20% off sale. The tablet he wants has an original cost of $190.
Which expressions would represent the sale price?
A. 0.80p
B. p + 0.20p
C. 1.20p
D. p - 0.20p
Answer:
D. p - 0.20p
Step-by-step explanation:
we are to seat five boys, five girls, and one parent in a circular arrangement around a table. in how many ways can this be done if no boy is to sit next to a boy and no girl is to sit next to a girl? what if there are two parents?
As per the permutation concept the number of ways to seat 5 boys, 5 girls, and 1 (or 2) parent in a circular arrangement around a table such that no boy is to sit next to a boy and no girl is to sit next to a girl is 72,000.
The concept of permutation comes into play when we need to find the number of ways to arrange a set of elements.
We can use the formula for circular permutation, which is (n-1)! where n is the number of elements. In this case,
=> n = 11 (5 boys + 5 girls + 1 parent).
Therefore, the total number of permutations possible is
=> (11-1)! = 10!.
Next, we need to find the number of permutations possible for arranging the boys and girls.
Since each boy or girl can be placed in 5! ways (5 possible positions), the number of permutations for arranging the boys and girls becomes
=> 5! * 5! = 120 * 120 = 144,000.
Therefore, we need to divide the above result by 2. The final answer is
=> 144,000 / 2 = 72,000.
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PLEASE HELP ASAP!!!!
WILL MARK BRAINLIEST
A and B and C are three villages on a highway. The distance between A and B is 18km. A motorbiker moved from A at speed of 10km/hr. At the same time , another man at village B started moving at 4km/hr. How long does it take the motorbiker to catch up to the man ? If they both reach C at the same time then what is the distance between C and B.
Answer:
Let A B = x miles = 18
B C = y miles
t1 = (18 + y) / 10 time for biker 1 to reach C
t2 = y / 4 = y / 4
t1 = t2 both bikers reach C at same time
(18 + y) / 10 = y / 4
72 + 4 y = 10 y
y = 12 distance from B to C
Check:
A C = 12 + 18 = 30 km
t1 = (18 + 12) / 10 = 3 hr
t2 = 12 / 4 = 3 hrs
So both meet at C in 3 hrs
) Express 8x-x² in the form a- (x + b)²
Pls bro help
Answer: To express the expression 8x - x² in the form a - (x + b)², we can complete the square method.
First, we'll add (1/2)^2 = 1/4 to both sides of the expression:
8x - x² + 1/4 = 1/4
Next, we'll rearrange the left-hand side to the desired form:
(2x - 1/2)² - 1/4 = 1/4
Now, we can identify a = -1/4, b = 1/2, so the expression is:
a - (x + b)² = -1/4 - (x + 1/2)²
Step-by-step explanation:
a vending machine contains $3.00 in nickels and dimes. if the number of dimes is 5 more than twice the number of nickels, how many coins of each type
Answer:
tmr afternoon on a thursday bc im getting a hamburger with no honey mustard.
Step-by-step explanation:
im doing it rn.
To solve this problem, we can set up an equation by considering the value of nickels and dimes. By solving the equation, we can find the number of nickels and the number of dimes.
Explanation:Let's assume the number of nickels as x.
The value of nickels is 0.05x dollars.
The number of dimes is stated as '5 more than twice the number of nickels,' which can be expressed as (2x + 5) dimes.
The value of dimes is 0.10(2x + 5) dollars.
Since the total value of the coins is $3.00, we can set up the equation:
0.05x + 0.10(2x + 5) = 3.00
Solving the equation will give us the number of nickels and dimes.
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find the HCF and LCM of: 35
Answer: [tex]5*7[/tex]
Work: 25 = 5 × 5 35 = 5 × 7
Hope it helps!
in a large school, it was found that 66% of students are taking a math class, 74% of student are taking an english class, and 45% of students are taking both. find the probability that a randomly selected student is taking a math class or an english class. write your answer as a decimal, and round to 2 decimal places if necessary.
The answer is 1.95 or 1.95 = 1.95. The probability that a randomly selected student is taking a math class or an English class can be found using the formula for the union of two events:
P(A or B) = P(A) + P(B) - P(A and B)
where A is the event of taking a math class and B is the event of taking an English class.
Given that 66% of students are taking a math class, P(A) = 0.66. Given that 74% of students are taking an English class, P(B) = 0.74. Given that 45% of students are taking both, P(A and B) = 0.45.
Therefore, the probability that a randomly selected student is taking a math class or an English class can be calculated as follows:
P(A or B) = 0.66 + 0.74 - 0.45 = 1.95
Rounding to 2 decimal places, the answer is 1.95 or 1.95 = 1.95.
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