All of the following are examples of performance measures that should be considered when designing a queue.
There are several performance measures that should be considered when designing a queue, including:
a. Probability that the waiting time exceeds t minutes (e.g. t can be 10 minutes): This measure can be used to assess the likelihood that customers will have to wait longer than a certain amount of time before being served. A high probability of long waiting times may indicate that the queue is not functioning effectively or that there are not enough servers to handle the demand.
b. Probability that servers are busy more than t minutes (e.g. t can be 10 minutes): This measure can be used to assess the likelihood that servers will be occupied for longer than a certain amount of time. A high probability of busy servers may indicate that the queue is not functioning effectively or that there are not enough servers to handle the demand.
c. Average waiting time: This measure can be used to assess the average amount of time that customers spend waiting in the queue before being served. A high average waiting time may indicate that the queue is not functioning effectively or that there are not enough servers to handle the demand.
Other performance measures that may be considered when designing a queue include the average number of customers in the queue, the average time that servers spend serving customers, and the probability that customers will leave the queue without being served.
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The Population of New York State can be modeled by
Answer: 19.71 Million.
An Amazon package was shipped to Samantha. The height is 15cm,
the length is 100cm, and the width is 20 cm. What is the volume of the
box?
A. 300,000 sq. cm
B. 30,000 sq. cm
C. 3,000 cubic cm
D. 30,000 cubic cm
An Amazon package shipped to Samantha. with height of 15cm, length of 100cm, and width of 20 cm, the volume of the package is
D. 30,000 cubic cmHow to find the volume of the packageVolume of a box is calculated by the product of length, width and height OR area multiplied by height
The area is solve by the product of length and width
area = length * width
length = 100
width = 20
area = 100 * 20
area = 2000 square cm
volume = area * height
volume = 2000 * 15
volume = 30 000 cubic cm
The volume of the package is 30 000 square cm
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Based on Ben's work shown, how would he respond?
The point IS a solution to the system. Only one of the equations resulted in an
identity.
The point is NOT a solution to the system. Both equations resulted in identities.
The point is NOT a solution to the system. Only one of the equations resulted in
an identity.
The point IS a solution to the system. Both equations resulted in identities.
Correct option: (A) The point IS a solution to the system. Only one of the equations resulted in an identity.
What is an identity equation?An equality that is true regardless of the values selected for its variables is called an identity. They are used to rearrange or simplify algebraic formulas. The two halves of an identity are, by definition, interchangeable, and we are always free to switch one for the other.
An identity is an equation that, regardless of the values used, is always true. Since 2x + 3x will always equal 5, regardless of the value of, this statement is an identity. The example might be written as 2x+ 3x = 5x since identities can be represented with the symbol "≡"
2x + y = 4
now, putting the values in the equation (6,-8)
2(6) + (-8) = 4
or, 12 - 8 = 4
or, 4 ≡ 4
This equation, point IS a solution to the system.
x + 3y = - 20
or, 6 + 3(-8) = -20
or, 6 - 24 = -20
or, - 18 ≠ - 20
So, for this equation the result is not identity.
Thus, option A is the correct answer.
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Sally went to the grocery store and bought 3 lbs. of apples, 2 lbs. of oranges, and 7 lbs. of bananas for $21. At
the same store Kevin bought 2 lbs. of apples, 6 lbs. of oranges and 1 lb. of bananas for $29. Heather bought
1lb. of apples, 4 lbs. of oranges and 5 lbs. of bananas for $23. Write the system of equations to determine how
much a pound of apples costs, a pound of oranges costs and a pound of bananas costs?. Equation 1:
Equation 2:
Equation 3:
0
The system of equations is:
3a + 2r + 7b = 21
2a + 6r + b = 29
a + 4r + 5b = 23
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
a = price of apples
r = price of oranges (I used r instead of letter o since o can be confused with zero)
b = price of bananas
Sally went to the grocery store and bought 3 lbs. of apples, 2 lbs. of oranges, and 7 lbs. of bananas for $21.
3a + 2r + 7b = 21
Kevin bought 2 lbs. of apples, 6 lbs. of oranges and 1 lb. of bananas for $29.
2a + 6r + b = 29
Heather bought 1 lb. of apples, 4 lbs. of oranges and 5 lbs. of bananas for $23.
a + 4r + 5b = 23
The system of equations is:
3a + 2r + 7b = 21
2a + 6r + b = 29
a + 4r + 5b = 23
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Rick is a plumber, and he is ordering a part to make a repair. He refers to this table to determine the part number. The part he must order needs to have a float diameter of less than 8 inches, weigh more than 1 pound, and fit a 5/16-SAE spud connection. Which part number should he order?
pls help
Rick should order part number G371-7 So the option A is the correct Answer
What is a part number ?
Part designs or materials are identified by part numbers, which are sometimes abbreviated as PN, P/N, part no., or part #. Its goal is to make referencing to that thing simpler. A part number clearly identifies a part design both inside and occasionally outside of a single organization. For instance, it is simpler to identify a screw as "HSC0424PP" rather than "Hardware, screw, machine, 4-40, 3/4" long, pan head, Phillips." The part number in this illustration is "HSC0424PP," which may be prefixed in database fields as "PN HSC0424PP" or "P/N HSC0424PP."
A serial number is a specific identifier of a specific instantiation of a part design, much as a part number identifies a component design (regardless of its instantiations). To put it another way, a part number designates each specific (physical) item as having been manufactured to a specific, original design;
As part number G371-7 fits perfectly to the desired requirement of float diameter of less than 8 inches, weigh more than 1 pound, and fit a 5/16-SAE spud connection that's why it is the correct answer
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Priya is comparing two functions: f(x)=10⋅x2 and g(x)=3⋅2x to find out which one has greater output values as x gets very large.
She notices that f(1)=10 and f(2)=40. However, g(1)=6 and g(2)=12. She concludes that as x continues to grow, the values of f will be greater than the values of g.
Explain or show why Priya’s conclusion is incorrect.
Explanation of why Priya's conclusion is correct.
What is a function?
An association between a number of inputs and outputs is called a function. Exactly one output is connected to each input in a function, which is an association of inputs. Every function has a range, co-domain, and domain.
Given the functions;
Simplifying,
f(x)=10x² and
g(x)=6x
The coefficient of variable x :
10 and 6,
where 10> 6.
And the value of x:
x² > x, for all x.
As x continues to grow, the values of f will be greater than the values of g.
Therefore, Priya's conclusion is correct.
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the f-distribution's curve is positively skewed. group startstrue or falsetrue, unselectedfalse, unselected
The f-distribution's curve is positively skewed. Hence, the statement is true.
We have to check whether the statement is true and false.
The given statement is "The f-distribution's curve is positively skewed."
We can compare two populations using a F statistic thanks to the F distribution. The F distribution can be used to detect whether there is a significant difference in the variance between the means of two populations for ANOVA testing. Regression analysis can also make use of the F distribution to assess how well various models fit together.
The F distribution's graph is always positive and slanted to the right, while the form might vary based on the numerator and denominator degrees of freedom.
The f-distribution's curve is positively skewed. Hence, the statement is true.
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Triangle ABC is transformed to obtain triangle A′B′C′:
A coordinate grid is labeled from negative 12 to 0 to 12 on both x- and y-axes at increments of 1. Triangle ABC has A at ordered pair 4, negative 4, B at 12,negative 4, C at 8, negative 12. Triangle A prime B prime C prime has A prime at ordered pair negative1, 1, B prime at negative 3, 1 C prime at negative 2, 3.
Which statement is correct for Triangle ABC. and Triangle A prime B prime C prime.?
Triangle ABC is similar to triangle A prime B prime C prime, because Triangle A prime B prime C prime is obtained by dilating Triangle ABC. By a scale factor of 1 over 4 and then rotating it about the origin by 180 degrees. The correct answer is B.
What is dilation?Dilation is a transformation that is used while resizing an object. The structures can be made longer or shorter via dilation. This transformation produces a picture that retains the original shape. There is, however, a significant fluctuation in the form. During a dilatation, the starting shape should be elongated or compressed.
All the coordinates of A'B'C' are -1/4 times those of ABC.
The dilation factor is 1/4, and rotation by 180° is indicated.
A'(-1, -1) = (-1/4) × A(4, -4)
= A(4x-1/4, -4x-1/4)
= (-1, -1)
B'(-3, 1) = (-1/4) × B(12, -4)
= B(12x-1/4, -4x-1/4)
= (-3, 1)
C'(-2, 3) = (-1/4) × C(8, -12)
= C(8x-1/4, -12x-1/4)
= (-2, 3)
Both coordinates are invalidated by a 180° rotation. In either sequence, it is the same as reflection across the x-axis and reflection across the y-axis.
Therefore, triangle A′B′C′ is obtained by dilating Triangle ABC by a scale factor of 1 over 4 and then rotating it about the origin by 180°.
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The complete question is:
Triangle ABC is transformed to obtain triangle A′B′C′:
A coordinate grid is labeled from negative 12 to 0 to 12 on both x- and y-axes at increments of 1. Triangle ABC has A at ordered pair 4, negative 4, B at 12,negative 4, C at 8, negative 12. Triangle A prime B prime C prime has A prime at ordered pair negative1, 1, B prime at negative 3, 1 C prime at negative 2, 3.
Which statement is correct for Triangle ABC. and Triangle A prime B prime C prime.?
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 6. and then rotating it about the origin by 90 degrees
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 4. and then rotating it about the origin by 180 degrees
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 180 degrees
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 90 degrees
Over which interval does h(x) have a negative average rate of change?
A) (-6,-4)
B) (-1 ,6)
C) (4 , 6)
D) (-4, 6)
HELP with 4 and 6 please
Answer:
4.) a.) 2.01 b.) 404.01
6.) a.) 152.17 b.) 18412.17 c.) 153.14 d.) 18565.60
Step-by-step explanation:
To solve, use the exponential growth formula [tex]A_t=A_0(1+\frac{r}{p})^t[/tex] where
[tex]A_t[/tex] = Amount as a function of time
[tex]A_0[/tex] = Original amount
[tex]r[/tex] = rate
[tex]p[/tex] = period
[tex]t[/tex] = time
For question 4, let
[tex]A_0=400\\r=0.06\\p=12\\t=2[/tex]
So,
[tex]A_t=400(1+\frac{0.06}{12})^2\\A_t=400(\frac{201}{200})^2\\A_t=400(1.01)\\A_t=404.01[/tex]
So, the second-period interest would be 404.01-402=2.01
Question 6 can be solved using the same formula, but let
[tex]A_0=18260\\r=0.025\\p=\frac{12}{4}=3\\t_1=1\\t_2=2[/tex]
So,
[tex]A_t=18260(1+\frac{0.025}{3})^1\\A_t=18260(\frac{121}{120})^1\\A_t=18412.17[/tex]
The first-period interest would be 18412.17-18260=152.17
For the second-period, use [tex]t_2[/tex]:
[tex]A_t=18260(1+\frac{0.025}{3})^2\\A_t=18260(\frac{121}{120})^2\\A_t=18260(1.02)\\A_t=18565.60[/tex]
The second-period interest would be 18565.60-18412.17=153.43
x^2−9x+38=0
Solve the Quadratic formula
The roots of x² - 9x + 38 are x = (9 + i√71 )/ 2 and x = (9 - i√71 )/ 2
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
x² - 9x + 38 = 0
It is in the form of ax² + bx + c
a = 1
b = -9
c = 38
Using the determinant formula to find the roots.
x = -b ± √(b² - 4ac) / 2a
x = 9 ± √(81 - 152) / 2
x = 9 ± i√71 / 2
x = (9 + i√71 )/ 2 and x = (9 - i√71 )/ 2
Thus,
The roots are x = (9 + i√71 )/ 2 and x = (9 - i√71 )/ 2
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d) if 36 reindeer are randomly selected, what is the probability their mean weight is less than 100kg
When 36 reindeer are chosen at random, the probability that the mean weight is less than 100 kg is 0.1492.
A standard error is the standard deviation of its sampling distribution or an interpretation of that standard deviation.
Given,
Mean of the weights = 102.4 kg
Standard deviation = 13.9 kg
To determine the probability that the mean weight of 36 reindeer will be less than 100 kg, first compute the standard error using the formula,standard error, [tex]\sigma_x=\frac{\sigma}{\sqrt{n}}[/tex]
Where, [tex]\sigma[/tex]=standard deviation
n= number of reindeer
substitute the values in the formula,
[tex]\sigma_x=\frac{13.9}{\sqrt{36}}\\\\\sigma_x=2.31667[/tex]
Now,
[tex]P(x < 100)=P(x < \frac{100-102.4}{2.316})\\\\=P(z < -1.04)[/tex]
from z-score table,
=0.1492
Thus, the probability the their mean weight is less than 100 kg is 0.1492.
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Your question is incomplete, here is the complete question.
The weight of male reindeer of the R. Santa Claus subspecies is normally distributed with mean 102.4 kg and standard deviation 13.9 kg
if 36 reindeer are randomly selected, what is the probability their mean weight is less than 100kg?
solve the system if possible by using cramer's rule. if cramer's rule does not apply, solve the system by using another method. write all numbers as integers or simplified fractions.
Using the Cramer's Rule, the solution of the given system of equation is (-17/11, 48/11)
The given system of equations are
10x+4y=2
-6x+2y=18
Solving the equations by using Cramer's rule.
We know that, the solution of a system of linear equations in two unknowns
a(1)x+b(1)y = c(1)
a(2)x+b(2)y = c(2)
is given by ∆x=∆1, and ∆y=∆2.
where,
[tex]\Delta=\text{det}\left [ \begin{matrix} a(1)&b(1) \\ a(2) & b(2)\end{matrix} \right ], \Delta(1)=\text{det}\left [ \begin{matrix} c(1)&b(1) \\ c(2) & b(2)\end{matrix} \right ]\text{ and }\Delta(2)=\text{det}\left [ \begin{matrix} a(1)&c(1) \\ a(2) & c(2)\end{matrix} \right ][/tex]
Since the given equations are;
10x+4y=2
-6x+2y=18
Now,
[tex]\Delta=\text{det}\left [ \begin{matrix} 10&4 \\ -6 & 2\end{matrix} \right ][/tex]
∆ = [(10×2)-(-6×4)]
∆ = 20+24
∆ = 44
[tex]\Delta(1)=\text{det}\left [ \begin{matrix} 2&4 \\ 18 & 2\end{matrix} \right ][/tex]
∆(1) = [(2×2)-(18×4)]
∆(1) = 4-72
∆(1) = -68
[tex]\Delta(2)=\text{det}\left [ \begin{matrix} 10&2 \\ -6 & 18\end{matrix} \right ][/tex]
∆(2) = [(10×18)-(-6×2)]
∆(2) = 180+12
∆(2) = 192
By Cramer's Rule,
∆x = ∆(1)
44 × x = -68
x = -68/44
x = -17/11
Now,
∆y = ∆(2)
44 × y = 192
y = 192/44
y = 48/11
Hence, the solution of the given system of equation is (-17/11, 48/11).
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The right question is:
Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or simplified fractions.
10x+4y=2
-6x+2y=18
Which fraction has a value that's equal to ⅞? A. 2½4 B.1⅝ c. 4%4 D. 5⅝
The improper fraction 7/8 has no value in the options given
Conversion of Improper FractionTo do this, we must divide the dividend by the divisor in order to change an improper fraction to a mixed number. After division, the acquired quotient becomes the whole numerals, the remainder becomes the new numerator, and the denominator remains the same, resulting in a mixed number.
To convert 7/8 into decimal number;
7/8 = 0.875
2 1/2 = 2.5
1 5/8 = 1.625
4% = 0.04
5 5/8 = 5.625
In the given options, none of them has a value of 7/8
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32. What is the area of the rhombus in simplest radical form? The figure is not drawn to scale.
(1 point)
The area of the rhombus is 49√6. Option B
How to determine the area of the rhombusThe formula for calculating the area of a rhombus is expressed as;
Area = pq/2
Where;
p and q are the diagonals of the rhombus
From the diagram shown, let's determine the value of p
Using the trigonometric identity;
Tan θ = opposite/adjacent
Opposite side = pAdjacent side = 7Substitute the values into the formula, we have;
tan 60 = p/7
Find the value of tan 60 and then substitute
√3 = p/7
cross multiply
p = 7√3
But;
Area = 7√3 × 7√3/2
Area = 49√6
Hence, the value is 49√6
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plsss help i’ll give brainlist to right answer
Answer:All I know is that it’s not < or > but It might be ≤
Step-by-step explanation: Bye the way, you can only give brainliest when there is two questions.
[tex]\leq[/tex]
Step-by-step explanation:
Provide the missing statements and reasons for the following proof:
The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:
S1: Line m is parallel to line n.
S2: ∠1 = ∠2
R3: Corresponding angles postulate
R5: Supplement Postulate
S7: m∠1 + m∠3 = m∠2 + m∠3
What are Supplementary Angles?
Supplementary angles, when added together will give us a sum of 180°.
Linear pair angles and corresponding angles are supplementary.
Thus, to prove that ∠1 is supplementary to ∠3:
We are given that lines m and n are parallel.
∠1 and ∠3 are corresponding angles.
So therefore, ∠1 = ∠3 by the corresponding angles postulate.
∠2 and ∠3 are linear pair, their sum therefore equals 180° based on the definition of supplementary angles.
Based on the substitution property, we have the following:
m∠2 + m∠3 = m∠1 + m∠3
m∠1+m∠3=180°
Therefore, ∠1 is supplementary to ∠3 based on the definition of supplementary.
The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:
S1: Line m is parallel to line n.
S2: ∠1 = ∠2
R3: Corresponding angles postulate
R5: Supplement Postulate
S7: m∠1 + m∠3 = m∠2 + m∠3
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joe loses 6 pounds during basketball practice. how many cups of water must he consume to replenish this loss
In order to regain the amount of water Joe losed during practice he should drink 10 cups of water.
A pound is equivalent to 453.59 mg, whereas a cup is equivalent to 236.59 ml.
You may roughly calculate that 2 cups equal 1 pound of water. The density should be 1 mg/ml if the fluid is mostly water.
The number of cups will be,
6 pounds * 453.59 (mg/pounds) * (1mg/ml) / (236.59 ml/cups)
= 10 cups .
Water is a crucial component for all living things, including people and other animals. Naturally, the water must go somewhere when it ascends the plant. Water loss will result from water evaporation (transpiration in plants)
Our breath, skin, urine, and sweat all cause water loss. A person's body will typically consume 2.5 L of water every day and expend the same amount. Your body will "inform you" you are thirsty and need to drink water if you get dehydrated (Figure 5). You have undoubtedly also noticed that when you drink less water, your pee is more concentrated.
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or A parabola opening up or down has vertex (0, – 2) and passes through (4, – 1). Write its equation in vertex form. Simplify any fractions.
The vertex (0,2) of the parabola's vertex shape, which can expand upward or downward, equals (x - 0)² + 2.
What is parabola?
Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve.
What is a vertex form of an equation?
An equation's conventional vertex form is written as:
f(x) = (x-h)² + k where;
(h, k) is the vertex
Vertex (0,2) should be replaced in the equation's vertex form.
f(x) = (x - 0)² + 2
As a result, vertex (0,2) of the parabola with an opening up or down is equal to (x - 0)² + 2.
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Calculate total pressure experienced by a diver working 15m below suraface of sea(10N/kg,density of water1g/cm3 and atmospheric pressure =100000N/m3
The total pressure experienced by a diver working 15m below surface of sea is 150000 Pa.
What is Pressure?Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
We need to find the total pressure experienced by a diver working 15m below surface of sea.
P = h·ρ·g
P = pressure
h = depth = 15 m
ρ = density = 1g/cm³=1000kg/m³
g = acceleration due to gravity = 10 m/s²
Substitute the values in the formula of total pressure.
P=1000×15×10
P=150000Pa
Hence, 150000Pa is the total pressure experienced by a diver working 15m below surface of sea.
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. three football teams are taking part in a tournament. each team plays each other team once. for a win the team scores 3 points, the other team 0 points. for a draw both teams get 1 point each. which number of points is impossible, for any team to reach at the end of this tournament?
To get a number point 1 is impossible for any of the team to reach at the end of the described tournament.
As given in the question,
Total number of footballs teams = 3
Each team plays once with other team
Let three teams are Team1, Team2, and Team3
Team1 plays with Team2 and Team3
Team2 will play with Team3
Winning points = 3
Losing team points = 0
Withdraw teams points = 1
To reach in finals suppose Team1 plays with Team2 and Team3 and win
Points of team1 = 3 + 3
= 6points
As team plays once with other team , Team1 is out of the game.
Team2 and Team3 play with each other
To reach at the end of the tournament one team has to win let it be Team2
Points of Team2 = 3
Points of Team3 = 0
No withdraw game is possible to reach into finale.
Therefore, point 1 is impossible for any team to reach at the end of the tournament.
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graph the line y=3x-4
Answer:
See attached image
Step-by-step explanation:
You can graph lines on a website called desmos graphing calculator!
Answer:
Step-by-step explanation:
you replace x with anything you want I will do 0. Then the the first point is (0,-4). Now I am gonna replace x with something else like 4. The second point is (4,8), now connect the two points and you got a line.
Geometry Suppose that a pizza must fit into a box with a
base that is 12 in. long and 12 in. wide. You can use the
quadratic function A Tr² to find the area of a pizza in
terms of its radius.
a. What values of r make sense for the function?
b. What values of A make sense for the function?
c. Graph the function. Round values of A to the
nearest tenth.
Question 39
The value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²
How to determine the Radius of the circle?You should understand that the pizza is fit inside the square box making all circumference of the circle to touch all the sides of the square box
The quadratic function reads
A= πr²
Where A= Area of circle,
π = 22/7
and r= radius of the circle
A= (22/7)*6
Width of the box is 12
Therefore 12/2 = r=6
A= (22*6*6)/7
A=113.1 in²
In conclusion, he value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²
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What is the percent decrease from 100 to 82
Percent decrease from 100 to 82 is 18% decrease.
Calculating the % decrease from 100 to 82,
[tex]\frac{82-100}{100}[/tex]×100%
[tex]\frac{-18}{100}[/tex]×100%
on simplifying we get,
-18%
here, negative sign indicates that there is a decrease of percentage.
Hence, we get 18% decrease from 100 to 82.
How to calculate Percent decrease?
Do the % growth and reduction calculations. By dividing the new number by the initial value, the percentage is computed.
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What number must multiply each side of the equation 2/5x=10 to produce the equivalent equation x = 25?
Responses
15, , 1 5 ,
52, , 5 2 ,
4
4
5
The number that must be multiplied by each side of the equation 2/5x=10 to produce the equivalent equation is x = 4.
How to illustrate the equation?An equation is a statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It should be noted that equivalent equations are the same.
Algebraic equations with equivalent solutions or roots are called equivalent equations. An equivalent equation is one that is created by adding or subtracting the same quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero number. If two systems of equations have the same solution, they are equivalent.
The equation is illustrated as:
2/5 = x/10
Cross multiply
5x = 2 × 10
5x = 20
Divide
x = 20 / 5
x = 4
The value or x is 4.
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JKLM is a parallelogram.
What is the measure of ZKLJ?
Enter your answer in the box.
Theres no point 'Z', so i'm gussing you want the angle of <KLJ?
<K and <M are the same, therefore <M = 130
<J + <K + <M + <L = 360
130 + 130 = 260, 360 - 260 = 100
<J and <L are the same
<MJK = 50 and <KLM = 50
<KLM/2 = <KLJ
50/2 = 25
Number 7. There is no answer key, no need to explain , just need the answer.
64 divided by blank equals 8
Answer: 8
Step-by-step explanation:
8 times 8 is 64
During the rebuilding after World War II, we were short of tractors. The machine and tractor stations would lend each other equipment as needed. Three machine and tractor stations were neighbors. The first lent the second and third as many tractors as they each already had. A few months later, the second lent the first and third as many as they each had. Still later, the third lent the first and second as many as they each already had. Each station now had 24 tractors.
How many tractors did each station originally have?
The number of tractors lent by the first, second and third stations results in a system of three simultaneous equations which indicates;
The first originally station had 39 tractors, the second station had 21 tractors and the third station originally had 12 tractors
What are simultaneous equations?Simultaneous equations are a set of two or more equations that have common variables.
Let x represent the number of tractors at the first station, let y represent the number of tractors at the second tractor station, and let z, represent the number of tractors at the third tractor station
According to the details in the question, after the first transaction, we get
Number of tractors at the first station = x - y - z
Number of tractors at the second station = y + y = 2·y
Number of tractors at the third station = z + z = 2·z
After the second transaction, we get;
Number of tractors at the first station = 2·x - 2·y - 2·z
Number of tractors at the second station = 2·y - (x - y - z) - 2·z = 3·y - x - z
Number of tractors at the third station = 2·z + 2·z = 4·z
After the third transaction, we get;
Number of tractors at the first station = 2 × (2·x - 2·y - 2·z) = 4·x - 4·y - 4·z
Number of tractors at the second tractor station = 6·y - 2·x - 2·z
Number of tractors at the third tractor station = 4·z - (2·x - 2·y - 2·z) - (3·y - x - z) = 7·z - x - y
The three equations after the third transaction are therefore;
4·x - 4·y - 4·z = 24...(1)
6·y - 2·x - 2·z = 24...(2)
7·z - x - y = 24...(3)
Multiplying equation (2) by 2 and subtracting equation (1) from the result we get;
12·y - 4·x - 4·z - (4·x - 4·y - 4·z) = 16·y - 8·x = 48 - 24 = 24
16·y - 8·x = 24...(4)
Multiplying equation (3) by 2 and multiplying equation (2) by 7, then adding both results, we get;
14·z - 2·x - 2·y = 48
42·y - 14·x - 14·z = 168
42·y - 14·x - 14·z + (14·z - 2·x - 2·y) = 48 + 168
40·y - 16·x = 216...(5)
Multiplying equation (4) by 2 and then subtracting the result from equation (5), we get;
40·y - 16·x - (32·y - 16·x) = 216 - 48 = 168
8·y = 168
y = 168/8 = 21
The number of tractors initially at the second station, y = 21
16·y - 8·x = 24, therefore, 16 × 21 - 8·x = 24
8·x = 16 × 21 - 24 = 312
x = 312 ÷ 8 = 39
The number of tractors initially at the first station, x = 39
7·z - x - y = 24, therefore, 7·z - 39 - 21 = 24
7·z = 24 + 39 + 21 = 84
z = 84/7 = 12
The number of tractors initially at the third station, z = 12
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I NEED HELP ON THIS QUESTION!!
Answer:
B
Step-by-step explanation:
Determine the equation of the line given by the table and compare with given options.
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 9) and (x₂, y₂ ) = (7, 19) ← 2 ordered pairs from the table
m = [tex]\frac{19-9}{7-2}[/tex] = [tex]\frac{10}{5}[/tex] = 2 , then
y = 2x + c ← is the partial equation of the line
to find c substitute any ordered pair from the table into the partial equation.
using (6, 17 ), that is x = 6, y = 17 , then
17 = 12 + c ⇒ c = 17 - 12 = 5
y = 2x + 5 ← equation of line from table, with y- intercept c = 5
thus the function with a y- intercept greater than the table line is B
