From the given information provided, the value of angle LMP and angle NMP is 77 and 103 degrees respectively.
Since LMN is a straight angle, it measures 180 degrees.
We are given the measures of LMP and NMP, and we are told that LMP + NMP = LMN. Therefore, we can set up an equation:
LMP + NMP = LMN
(-16x + 13) + (-20x + 23) = 180
Simplifying and solving for x, we get:
-36x + 36 = 180
-36x = 144
x = -4
Now that we have found the value of x, we can substitute it back into the expressions for LMP and NMP to find their measures:
LMP = -16x + 13 = -16(-4) + 13 = 77 degrees
NMP = -20x + 23 = -20(-4) + 23 = 103 degrees
Therefore, the measures of LMP and NMP are 77 degrees and 103 degrees, respectively, and the measure of LMN is 180 degrees.
Question - LMN is a straight angle. LMP = -16x + 13 NMP = -20x + 23 LMP + NMP = LMN What are the measures?
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Ramona is climbing a hill with a 10 incline and wants to know the height of the rock formation. She walks 100 ft up the hill and uses a clinometer to measure the angle of elevation to the top of the formation. What is the height h of the rock formation?
The height of the rock formation is approximately 17.45 feet (rounded to two decimal places).
What is trigonometry?Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is used to solve problems involving triangles, such as finding missing sides or angles, determining distances or heights, and more. Trigonometry has applications in various fields, such as engineering, physics, architecture, and astronomy, among others.
In the given question,
We can use trigonometry to solve this problem. Let h be the height of the rock formation in feet, and let x be the horizontal distance from Ramona to the base of the rock formation in feet. Then, we have:
tan(10) = h/x
Rearranging this equation, we get:
h = x * tan(10)
We need to find the value of h, so we need to find the value of x. We can use the angle of elevation and the distance that Ramona walked up the hill to find x. We have a right triangle with height h, base x, and hypotenuse 100 ft. The angle opposite the height h is 10 degrees. So, we have:
tan(10) = h/x
sin(10) = h/100
Rearranging the second equation, we get:
h = 100 * sin(10)
Substituting this into the first equation, we get:
x * tan(10) = 100 * sin(10)
Dividing both sides by tan(10), we get:
x = 100 * sin(10) / tan(10)
Plugging this value of x into the equation for h, we get:
h = x * tan(10) = (100 * sin(10) / tan(10)) * tan(10) = 100 * sin(10)
Therefore, the height of the rock formation is approximately 17.45 feet (rounded to two decimal places).
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Xavier buys a dog collar that costs $6.79. He pays for the dog collar
with a $10 bill.
How much change does Xavier receive?
Answer: Xavier will receive $3.21 in change.
Step-by-step explanation:
To find the change Xavier receives, we need to subtract the cost of the dog collar from the amount he paid with his $10 bill:
Change = $10 - $6.79 = $3.21
Therefore, Xavier will receive $3.21 in change.
Identify the type of sequence 56,49,42,35,28,21
It is Arithmetic Sequence. An ordered group of numbers with a shared difference between each succeeding term is known as an arithmetic sequence.
For the given sequence
d= 49-56 = -7
d= 42-49 = -7
Thus, there is -7 as a common difference between the terms.
The distance between succeeding terms in an arithmetic series is always the same. It is often referred to as an arithmetic series or arithmetic progression. The following statement can be used to represent an arithmetic sequence: a, (a + d), (a + 2 d), (a + 3 d),..., where a is the first term and d is the constant difference between values.
To determine the sum of an arithmetic sequence, it is generally simple to add or subtract all the terms in a short series together. An individual can quickly determine the sum of an arithmetic series for a particular number of terms by using the generic formula for the nth term of an arithmetic sequence.
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In monopolistic competition, the end result of entry and exit is that firms end up with a price that lies a. on he upward-slopning porion of he average cost curve. b. at the very bottom of the AC curve. c. at the very top of the AC curve. d. on the downward-sloping portion of the average cost curve
In monopolistic competition, the end result of entry and exit is that firms end up with a price that lies on the downward-sloping portion of the average cost curve.
Monopolistic competition is a market condition in which many small firms compete with each other by selling slightly varied, but essentially comparable goods or services at somewhat different prices. These companies enjoy some market power, but they are not monopolies because their products or services are close substitutes for each other.
The equilibrium price in a monopolistically competitive market is a long-run, but not a short-run, outcome of entry and exit. Because the market is monopolistic, entry and exit do not have an immediate impact on the price; it simply alters the number of producers operating in the market. Over time, the entry and exit of producers in the industry will increase or decrease the number of substitutes available, driving demand curves and resulting in the price of the commodity settling on the down-sloping portion of the average cost curve in the long run.
Therefore, it can be concluded that the end result of entry and exit in monopolistic competition is that companies end up with a price that lies on the downward-sloping portion of the average cost curve.
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Please help!
(x, y)→(x + 130, y + 105 )
Graph
So the transformed rectangle has vertices A'(40, 160), B'(40, 130), C'(80, 130), and D'(80, 160).
What is transformation rule?In mathematics, a transformation rule (also known as a transformation function, transformation formula, or simply a transformation) is a mathematical rule or formula that describes how to map or transform a set of points in one coordinate system to another set of points in a different coordinate system. Transformations can be applied to various mathematical objects, such as points, lines, curves, shapes, or functions, and can be used to achieve various purposes, such as to change the size, shape, position, or orientation of an object, to create a mirror image or a rotation of an object, or to change the coordinate system of an object.
Here,
There appears to be an error in the coordinates of points B and D that you provided, as they are both (-90,25). I will assume that the correct coordinates of point D are (-50,55) to form a rectangle ABCD.
To apply the given transformation rules to each of the four vertices of the rectangle, we add 130 to the x-coordinate and 105 to the y-coordinate. Therefore, the coordinates of the transformed rectangle are:
A' = (-90 + 130, 55 + 105) = (40, 160)
B' = (-90 + 130, 25 + 105) = (40, 130)
C' = (-50 + 130, 25 + 105) = (80, 130)
D' = (-50 + 130, 55 + 105) = (80, 160)
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Complete question:
Please help! The transformation rules says: (x, y)→(x + 130, y + 105 )
Given rectangle ABCD with A(-90,55) B(-90,25) C(-50,25) D(-50,25).
Find the coordinates of transformed rectangle.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Given:
The inequality is
[tex]-3(2x - 5) < 5(2 - x)[/tex]
To find:
The correct representations of the given inequality.
Solution:
We have,
[tex]-3(2x - 5) < 5(2 - x)[/tex]
Using distributive property, we get
[tex]-3(2x)-3(-5) < 5(2)+5(-x)[/tex]
[tex]-6x+15 < 10-5x[/tex]
Therefore, the correct option is C.
Isolate variable terms.
[tex]15-10 < 6x-5x[/tex]
[tex]5 < x[/tex]
It means, the value of x is greater than 5.
Since 5 is not included in the solution set, therefore, there is an open circle at 5.
So, the graphical represents of the solution is a A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Therefore, the correct option is D.
write re(e^(1/z)) in terms of x and y. why is this function harmonic in every domain that does not contain the origin?
The formula for the real portion of a complex function can be used to write re(e(1/z)) in terms of x and y: f(z) + f(z*) = re(f(z)) / 2
How is a harmonic function determined?where z* denotes z's complex conjugate.
By applying this formula to the provided function, we obtain:
re(e(1/z)) = (e(1/z) + e(1/z*)) / 2
re(e(1/z)) = (e(x-iy) + e(x+iy)) / 2
re(e(1/z)) = (ex (cos y + I sin y) + ex (cos y - I sin y)) /2
As a result, re(e(1/z)) can be represented as ex cos y in terms of x and y.
Because it fulfills Laplace's equation, which asserts that the total of a function's second-order partial derivatives is equal to zero, this function is harmonic in every domain excluding the origin.
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True or False, suppose a hypothesis test was performed with a level of significance of 0.05. then if the null hypothesis is actually true, then there is a 5% chance that the researcher will end up accepting the alternative hypothesis in error.
If the null hypothesis is actually true, then there is a 5% chance that the researcher will end up accepting the alternative hypothesis in error, the statement is true.
If a hypothesis test is performed with a level of significance of 0.05 and the null hypothesis is actually true, then there is a 5% chance (or 0.05 probability) that the researcher will reject the null hypothesis and accept the alternative hypothesis in error.
This is known as a Type I error. The Type I error rate is determined by the level of significance of the test.
In other words, if the null hypothesis is true, but the researcher concludes that it is false (i.e., accepts the alternative hypothesis), this is an incorrect decision that is made with a probability of 0.05 or 5%, assuming a significance level of 0.05.
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The system of four forces acts on the roof truss. Determine the equivalent resultant force and specify its location along AB, measured from A.
The equivalent resultant force is 1228.3 N and its location along AB, measured from A is 4.7 m.
The system of four forces acts on the roof truss. Determine the equivalent resultant force and specify its location along AB, measured from A.For the given system of forces, the components of each force should be determined first.The angle between the horizontal and the 500 N force is 60 degrees.Cos 60 = adjacent/hypotenuse Adjacent = cos 60 x 500 = 250 N This force is resolved into two components; one horizontal and the other vertical.250 N is the horizontal component.
The vertical component of this force is resolved as follows:Sin 60 = opposite/hypotenuse Opposite = sin 60 x 500 = 433 NThe system is now resolved and we get:Resolve force 700 N into components. The angle between the horizontal and the 700 N force is 30 degrees.Cos 30 = adjacent/hypotenuse Adjacent = cos 30 x 700 = 606 N
The vertical component of this force is resolved as follows:Sin 30 = opposite/hypotenuse Opposite = sin 30 x 700 = 350 N
Resolve force 600 N into components. This force acts horizontally and thus, it has no vertical component.Resolve force 800 N into components. This force acts vertically and thus, it has no horizontal component.
The components of the forces are summarized in the table below:Force components X component (N)Y component (N)5002504337006063506006000800 This information can now be used to determine the equivalent resultant force and its location.∑Fy = 250 N + 433 N + 350 N - 800 N = 233 N∑Fx = 606 N + 600 N = 1206 N Therefore;∑F = √[(∑Fx)² + (∑Fy)²]= √[(1206)² + (233)²]= 1228.3 N From the force diagram, the distance of the equivalent resultant force from A, measured along AB is given by the ratio of the moment of the force about A and the force itself:Moment of force about A = 250 x 6 + 606 x 2.5 + 600 x 1 = 5750 N.m Therefore, Distance of the force from A = Moment of force about A / ∑F= 5750 N.m / 1228.3 N= 4.7 m (to 1 decimal place)
Therefore, the equivalent resultant force is 1228.3 N and its location along AB, measured from A is 4.7 m.
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Steven made punch by mixing 2.8 liters of orange juice, 0.75 liters of pineapple juice, and 1.2 liters of sparkling water. How many liters of punch did Steven make?
Answer:
4.75 liters of punch
Step-by-step explanation:
2.8 + 0.75 = 3.55
3.55 + 1.2 = 4.75 liters of punch
A floor which measures 15m x 8m is to be laid with tiles measuring 50cm by 25cm. Find the number of tiles required.
Cοnsequently, 960 tiles οf a 50 by 25 cm size will be needed tο cοver the 15m x 8m flοοr.
What is an example οf a measure ?Cοmparing a quantitative measurement with a recοgnized standard amοunt οf sοme kind is the act οf measurement. Fοr instance, in the measurement 10 kg, kg is indeed the basic measure used tο describe mass οf a physical quantity, and 10 is the size οf the physical quantity.
Calculate the flοοr's tοtal square fοοtage in meters, then divide it intο the area οf each tile tο determine the necessary number οf tiles. The measurements must first be changed tο a cοmparable unit. By dividing by 100, we may cοnvert centimeters tο meters:
15m = 1500cm
8m = 800cm
In square meters, the flοοr space is as fοllοws:
1500cm x 800cm = 1200000cm² = 120m²
The area οf the each tiles in square meters must nοw be determined. The size οf each tile, which is 50 by 25 centimetres, is as fοllοws:
50cm x 25cm = 1250cm² = 0.125m²
Lastly, by dividing the entire flοοr area even by area οf each tile, we can determine the necessary number οf tiles:
120m² / 0.125m² = 960 tiles
The flοοr will therefοre need 960 tiles that are 50 cm by 25 cm in size tο cοver its 15 m × 8 m surface.
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Consider a system with one component that is subject to failure, and suppose that we have 120 copies of the component. Suppose further that the lifespan of each copy is an independent exponential random variable with mean 25 days, and that we replace the component with a new copy immediately when it fails.(a) Approximate the probability that the system is still working after 3625 daysProbability(b) Now, suppose that the time to replace the component is a random variable that is uniformly distributed over (0,0.5). Approximate the probability that the system is still working after 4250 days.Probability
We have that, given the system with a component that can fail, we can find the following probabilities
a) Probability that the system continues to function after 3625 days is 0.091b) Probability that the system is still working after 4250 days is 0.018How do we calculate probability using the exponential distribution?a) To approximate the probability that the system will continue to function after 3625 days, we can use the exponential distribution and its associated properties. The probability that the system is still working after 3625 days is equal to the probability that none of the 120 components have failed, which is equal to:
Probability = e(-120*(3625-25)/25) = 0.091
b) To approximate the probability that the system will continue to function after 4250 days, we must take into account the time required to replace a defective component. Since the time required to replace a defective component is a random variable that is uniformly distributed over (0,0,5), the expected time to replacement is 0.25. Therefore, the probability that the system is still working after 4250 days is equal to:
Probability = e(-120*(4250-25)/25) * e(-120*(0.25)/25) = 0.018
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Please help me I will give the person with the right answer brainiest
Answer:
3. Yes because it is the same thing. (short answer just elaborate more)
4. No, a trapezoid cannot be a parallelogram. Trapezoid has only one pair of parallel sides while in a parallelogram there are two pairs of parallel sides.
5. see last sentence in 4
6. group 1: the diamond and the square tilted, and the square.
group 2: the second one, the cup like shape, the cup shape but taller(the last one)
7. hard to see
8. hard to see
Step-by-step explanation:
PLEASEEE HELP I NEED THIS ASAPPP
Answer:
perimeter=42
Area=90
Step-by-step explanation:
find the length of DEFG:
perimeter=a=b+a+b
28=10+b+10+b
28=20+2b
8=2b
4=b
finding the scale factor:
15/10=3/2
to find the perimeter of WXYZ:
the missing side:
=4x3/2
=6
perimeter=a+b+a+b
perimeter=15+6+15+6
perimeter=42
Area of WXYZ:
Area=bh
Area=15x6
Area=90
problem 05.058 - caps removed from sphere knowing that two equal caps have been removed from a wooden sphere of diameter 11.8 in., determine the total surface area of the remaining portion.
The total surface area of the remaining portion is approximately 23.14 in.
To find the total surface area of the remaining portion of a wooden sphere after two equal caps have been removed, use the formula SA = 4πr2. A sphere is symmetrical, and thus, the diameter of the wooden sphere is equal to the diameter of the remaining portion. The radius of the remaining portion is equal to half the diameter of the sphere minus the radius of the cap.
The diameter of the wooden sphere is 11.8 in. As such, the radius of the sphere is 5.9 in. If two equal caps are removed, the diameter of the remaining portion is equal to 11.8 in - 2x R_cap, where R_cap is the radius of the cap. Since the caps are equal, we can simplify the formula to
D = 11.8 - 2R_cap. R_cap is equal to the radius of a circle with area equal to the surface area of one cap. As such, we can use the formula SA = 2πrh + πr2 to find the surface area of the cap. We know the diameter of the sphere is 11.8 in. Thus, the radius of the sphere is 5.9 in. We also know that the height of the cap is 5.9 in. Since the caps are equal, we can use the formula to find the surface area of one cap and multiply by 2 to get the total surface area of both caps.
SA_cap = 2π(5.9 in)(5.9 in) + π(5.9 in)
2SA_cap = 2π(34.84 in2) + π(34.84 in2)
SA_cap = 2π(34.84 in2) + 109.45 in2SA_cap ≈ 219.74 in
Since the surface area of the cap is equal to 219.74 in, we can use the formula to find the radius of the cap.
219.74 in = 2πrh + πr22(219.74 in2)
= 2π(5.9 in)h + π(5.9 in)22(219.74 in2)
= 37.699 in2 + 109.45 in23r2
= 72.533 in2r ≈ 4.545 in
Using the formula D = 11.8 - 2R_cap, we can find the diameter of the remaining portion of the wooden sphere.
D = 11.8 - 2(4.545 in)D ≈ 2.71 in
The radius of the remaining portion of the wooden sphere is equal to 5.9 in - 4.545 in. Thus, the radius of the remaining portion of the sphere is 1.355 in. Finally, we can find the total surface area of the remaining portion of the sphere.
SA = 4πr2SA = 4π(1.355 in)2SA ≈ 23.14 in
Therefore, the total surface area of the remaining portion is approximately 23.14 in.
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Please help me with my math!
Answer:
To rewrite the quadratic equation in the form y = a(x - p)²+q, we need to complete the square.
y = 2x^2 + 16x + 26
y = 2(x^2 + 8x) + 26
y = 2(x^2 + 8x + 16 - 16) + 26 // Adding and subtracting (8/2)^2 = 16 inside the parentheses
y = 2((x + 4)^2 - 16) + 26
y = 2(x + 4)^2 - 32 + 26
y = 2(x + 4)^2 - 6
Therefore, the quadratic equation y = 2x ^ 2 + 16x + 26 rewritten in the form y = a(x - p)²+q is y = 2 * (x + 4) ^ 2 - 6, so the answer is D
Answer:
y= 2(x+4)^2 -6
Step-by-step explanation:
y= 2x^2 + 16x + 26
It is in the form y= ax^2 + bx + c
To rewrite in the form y=a(x-p)^2 + q
We need to fin p and q. We already have a in the original equation.
In y= 2x^2 + 16x + 26, a=2.
The formula say that: p=-b/2a
p= -16/(2*2)
p=-16/4
p=-4
In the formula, we replace a and y= 2(x-(-4))^2 +q
Obtaining, y= 2 (x+4)^2 + q
Now, to find q we need to obtain a point from the original equation. Commonly the y-intercept. In the form y= ax^2 + bx + c ; C is the y-intercept.
y-intercept: (0,c)
Therefore, in y= 2x^2 + 16x + 26
y-intercept: (0,26)
In the equation we already have:
y= 2(x+4)^2 +q
26= 2(0+4)^2 + q
26=2(4)^2 +q
26= 2(16) + q
26= 32 + q
-6 = q
Joining all the results, we obtain:
y= 2(x+4)^2 -6
The Table shows different geologic time periods: Period Number of Years Ago Jurassic 2. 08 ⋅ 108 Silurian 4. 38 ⋅ 108 Tertiary 6. 64 ⋅ 107 Triassic 2. 45 ⋅ 108 Order the time periods from oldest to youngest
The oldest and youngest the
time periods are Silurian and Tertiary respectively. Order the time periods from oldest to youngest is equals to
Silurian--> Triassic --> Jurassic -->Tertiary.
We have a table which shows different geologic time periods.
Period Number of Years Ago
Jurassic 2.08 × 10⁸
Silurian 4.38× 10⁸
Tertiary 6.64× 10⁷
Triassic 2.45× 10⁸
We have to order the time periods from oldest to youngest. Time period is the length of time during which an activity occurs and geologic time period showing the geologic eons, eras, periods, epochs, and associated. Now, we check the time periods and put in order.
So, 2.08 × 10⁸ = 2,08000,000
4.38× 10⁸ = 4,38000,000
6.64× 10⁷ = 6,6400,000
2.45× 10⁸ = 2,45000,000
Here, longest or oldest time period
= 4,38000,000
Youngest time period = 6,6400,000
Therefore, the order of time periods is Silurian --> Triassic -->Jurassic -->Tertiary. Hence, required time periods are Silurian and Tertiary.
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The table shows the number of hours spent studying for a history final exam and the score on that exam. Each row represents a single student. Which value is an outlier in the table below?
Exam Scores
Number of hours spent studying, x
Exam score
(out of 100), y
1.5
65
2
68
3.5
71
4.5
98
4.5
82
6
84
6.5
88
7
85
7
80
(1.5, 65)
(3.5, 71)
(4.5, 98)
(6.5, 88)
Answer:Given : number of hours spent studying for a history final exam and the score on that exam.
To Find : Which value is an outlier
(1.5, 65)
(3.5, 71)
(4.5, 98)
(6.5, 88)
Solution:
Number of hours spent studying =x
Exam score = y
x y
1.5 65
2 68
3.5 71
4.5 98
6 82
1.5 - 2 difference = 0.5
2 - 3.5 difference = 1.5
3.5 - 4.5 difference = 1
4.5 - 6 difference = 1.5
No outlier
65 - 68 Difference 3
68 - 71 Difference 3
71 - 98 Difference 27
71 - 82 Difference 11
Hence 98 is outlier
(4.5 , 98 ) is outlier
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Step-by-step explanation:
g(a) (5pts) what is the work needed to bring the two point charges from infinity to their current positions? (b) (5pts) at the vertex, p, of the triangle what is the electric potential due to these two charges? (c) (5pts) at the vertex, p, what is the direction of the electric field due to these two charges? (d) (5pts) at the vertex, p, what is the magnitude of the electric field due to these two charges?
The work needed to bring two point charges from infinity to their current positions is equal to the Coulomb potential energy of the system, given by: U = kQ1Q2/r, where k is the Coulomb constant, Q1 and Q2 are the two point charges, and r is the distance between them.
The electric potential due to the two charges at the vertex p is given by the sum of the potentials of each charge individually. V = kQ1/r1 + kQ2/r2, where k is the Coulomb constant, Q1 and Q2 are the two point charges, and r1 and r2 are the distances between the charges and the vertex p.The direction of the electric field due to the two charges at the vertex p is given by the vector sum of the electric field of each charge individually. The direction of the electric field due to each charge can be calculated by taking the vector difference between the position of the charge and the position of the vertex p.
The magnitude of the electric field due to the two charges at the vertex p is given by the sum of the magnitudes of the electric fields of each charge individually. Etotal = √(E12 + E22), where E1 and E2 are the electric fields due to the two charges.
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The cost for a taxi ride is $3.00 for the first mile and $2.25 for each additional mile. Rewrite the expression 3.00 +2.25(m-1) for the cost of the taxi ride in dollars as a sum of two terms, where m represents the miles traveled. Show your work.
The rewritten expression 3.00 +2.25(m-1) is 2.25m + 0.75.
How to represent a situation with an expression?The cost for a taxi ride is $3.00 for the first mile and $2.25 for each additional mile.
Therefore, let's rewrite the expression 3.00 +2.25(m-1) for the cost of the taxi ride in dollars as a sum of two terms, where m represents the miles travelled.
Hence,
m = miles travelledTherefore, the cost using expression is as follows:
3 + 2.25(m - 1)
3 + 2.25m - 2.25
combine like terms
2.25m + 3 - 2.25
2.25m + 0.75
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Select the expressions that are equivalent to (2a + 6) - (-a-5). Submit (2a + 6) (-5a - 1) (6a + 2) (-a - 5) (6a + 2) (-5a - 1) (6 + 2a) - (-a - 5)
The expression (6 + 2a) - (-a - 5) is equivalent to 3a + 11. The other options given are not equivalent to (2a + 6) - (-a-5).
What is a negative sign?In mathematics, a negative sign is a symbol used to represent a negative value or operation. It is represented by the symbol "-", which is usually placed before a number to indicate that the number is negative.
According to question:To simplify (2a + 6) - (-a-5), we can distribute the negative sign:
(2a + 6) - (-a-5) = 2a + 6 + a + 5 = 3a + 11
Therefore, the expression equivalent to (2a + 6) - (-a-5) is:
3a + 11
Out of the options given, the equivalent expression is:
(6 + 2a) - (-a - 5)
We can simplify this expression in the same way as above:
(6 + 2a) - (-a - 5) = 6 + 2a + a + 5 = 3a + 11
Therefore, the expression (6 + 2a) - (-a - 5) is equivalent to 3a + 11.
The other options given are not equivalent to (2a + 6) - (-a-5).
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Does anyone know how to solve this question with a method pls.
Answer:
(a) AC = 4√2 cm
(b) AM = 2√2 cm
(c) EM = √41 cm
(d) EF = 3√5 cm
Step-by-step explanation:
You want to solve for various lengths in the right square pyramid shown with base edge 4 cm and lateral edge 7 cm.
Right trianglesEach right triangle can be solved for unknown lengths using the Pythagorean theorem: the square of the hypotenuse is the sum of the squares of the other two sides.
Right triangles of interest here are ...
ADC . . . . for finding AC and AM (isosceles right triangle)
CME . . . . for finding EM
FME . . . . for finding EF
(a) ACAC is the hypotenuse of ∆ADC, so ...
AC² = AD² +DC²
AC = √(4² +4²)
AC = 4√2 . . . . cm
(b) AMM is the midpoint of AC, so ...
AM = AC/2 = (4√2)/2
AM = 2√2 . . . . cm
(c) EMFM is half the length of one side of the base, so is 2 cm. CM = AM = 2√2.
CE² = CM² +EM²
EM = √(CE² -CM²) = √(7² -(2√2)²)
EM = √41 . . . . cm
(d) EFEF is the hypotenuse of ∆EMF.
EF² = EM² +FM²
EF = √(EM² +FM²) = √(41 +2²) = √45
EF = 3√5 . . . . cm
ax + b = 0 is the standard form of linear equation in one variable, but why is 0 given as the answer to the equation? Shouldn’t it be a constant there, one which is not 0? Please answer
Answer:
Step-by-step explanation:
In the equation ax + b = 0, the value of x is not fixed and can vary based on the values of a and b. The purpose of this equation is to find the value of x that satisfies the equation, given the values of a and b.
For example, if a = 3 and b = -6, then the equation becomes 3x - 6 = 0. Solving for x, we get x = 2. Thus, 2 is the value of x that satisfies the equation.
The reason 0 is often used as an answer to this equation is because it represents a special case where b = 0. In this case, the equation becomes ax = 0, and the only solution is x = 0. However, in general, the value of x can be any real number that satisfies the equation.
1. it is known that amounts of money spent on clothing in a year by college students follow a normal distribution with a mean of $380 and a standard deviation of $50. what is the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year?
The probability that a randomly chosen student will spend between $300 and $400 on clothing in a year is 0.6827.
Here the given data are
mean [tex]\mu = $380[/tex],
standard deviation [tex](\sigma) = $50[/tex]
Let X be the random variable which denotes the amounts of money spent on clothing in a year by college students. The distribution of X is normal distribution.
We need to find the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year. If we have the standard normal distribution, we can easily calculate the probability from the normal distribution table. Otherwise, we have to use the standard normal distribution and convert the values to standard units. This process is called standardization. We will use the z-score formula for standardization.
Let’s standardize the given values.
Lower value [tex](X_1) = $300[/tex]
Upper value [tex](X_2) = $400[/tex]
Population mean [tex](\mu) = $380[/tex]
Population standard deviation [tex](\sigma) = $50z_1 = (X_1 - \mu) / \sigma z_1 = ($300 - $380) / $50z_1 = -1.6z_2 = (X_2 - \mu) / \sigma z_2 = ($400-$380)/$50z_2 = 0.4[/tex]
Now we need to find the area between these two z-scores using the standard normal distribution table.The probability that a randomly chosen student will spend between $300 and $400 on clothing in a year is
[tex]P(-1.6 < Z < 0.4).P(-1.6 < Z < 0.4) = P(Z < 0.4) - P(Z < -1.6)\\P(Z < 0.4) = 0.6554\\P(Z < -1.6) = 0.0548\\P(-1.6 < Z < 0.4) = 0.6554 - 0.0548 = 0.6006[/tex]
Therefore, the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year is 0.6006 (approx.) or 0.6827 (approx.).
Hence, the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year is 0.6827.
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You have a large box that measures 1.5 feet wide and 2 feet long. You pour 6 ft3 of sand into the box and level the sand inside the box with your hand.
How high is the sand inside the box?
Considering the volume of the rectangular prism, the height of the sand inside the box is of 2 feet.
How to obtain the volume of the rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:
Volume = length x width x height.
The parameters for this problem are given as follows:
Width of 1.5 feet.Length of 2 feet.Height of h feet.Volume of 6 cubic feet.Hence the height of the sand inside the box is given as follows:
2 x 1.5 x h = 6
3h = 6
h = 2 ft.
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A dairy made 98.38 ounces of yogurt. Then a local market bought 86.2 ounces of the yogurt.
How much yogurt does the dairy have left?
The amount of yoghurt left is 12. 18 ounces
How to determine the numberThe algebraic expressions are defined as those expressions that are made up of variables, terms, constants, factors and coefficients.
The expressions are also composed of some arithmetic or mathematical operations, such as;
BracketParenthesesDivisionAdditionSubtractionMultiplicationFrom the information given,
Let the total number of ounces of yoghurt be x
Let the number of ounces of yoghurt sold be y
We have that;
The number left= x - y
= 98.38 - 86.2
= 12. 18 ounces of yoghurt
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The function is defined by the following rule.
f(x) = -x-1
Complete the function table.
x
-3
-2
0
2
X
0
0
5
Answer:
Step-by-step explanation:
[tex]f(-3)=-(-)3-1=2\\\\f(-2)=-(-2)-1=1\\\\f(0)=-0-1=-1\\\\f(2)=-2-1=-3\\\\f(4)=-4-1=-5\\\\f(x)=5\rightarrow 5=-x-1\rightarrow6=-x \rightarrow x=-6[/tex]
A randomly generated list of integers from 1 to 5 is being used to simulate an
event, with the numbers 1 and 2 representing a success. What is the
estimated probability of a success?
A. 40%
B. 50%
C. 20%
D. 30%
The estimated probability of a success is 40% since the numbers 1 and 2 represent a success out of the integers 1 to 5. Therefore, the success outcomes (1 and 2) make up 2 out of 5 possible outcomes, or 40%.
To find the estimated probability of a success, we need to determine the proportion of successes in the generated list.
Out of the numbers 1 to 5, two numbers represent success (1 and 2). Therefore, the probability of success for each individual number is 2/5 or 0.4.
Since we are considering a randomly generated list of integers, we can assume that each number is equally likely to be generated. So, the estimated probability of a success can be calculated by finding the proportion of 1's and 2's in the list.
Let's assume that the list has n elements. If we generate the list multiple times, we can expect that the proportion of successes will approach the true probability of success, which is 0.4.
For example, if we generate a list of 10 integers and get the following numbers: 2, 5, 1, 3, 1, 4, 2, 5, 3, 1, then we have 4 successes out of 10 numbers. So, the proportion of successes in this list is 4/10 or 0.4, which matches the true probability of success.
Therefore, the answer is A. 40%.
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A sample of size 25 is drawn from a normal population with a population standard deviation of 100. Suppose the mean of the sample is x(bar) = 35. Recall that z0.025=1.96. A 95% confidence interval for the population mean is equal to
The 95% confidence interval for the population mean is equal to (30.4,39.6).
A confidence interval is a range of values that surrounds the point estimate, such as a sample mean, and provides a sense of the precision of the estimate. The confidence interval (CI) contains the estimated parameter at a given level of confidence, usually 95% or 99%.
The 95% confidence interval for the population mean is given by:
x(bar) ± Zα/2 * σ/√n
Where,
x(bar) = 35σ = 100n = 25Zα/2 = Z0.025 = 1.96
Substituting the values, we get:
CI = 35 ± 1.96 * 100/√25
CI = (30.4,39.6)
Hence, the 95% confidence interval for the population mean is (30.4,39.6).
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what is the z-score for the 25th percentile of the standard normal distribution?A. -0.625
B. 0.50 C. 0.60 D. -0.50 E. 0.00
The z-score for the 25th percentile of a standard normal distribution is approximately -0.625. Here option A is the correct answer.
To find the z-score for the 25th percentile of a standard normal distribution, we need to use a standard normal distribution table or calculator. The 25th percentile corresponds to a cumulative area under the standard normal curve of 0.25.
Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative area of 0.25 is about -0.68. This means that approximately 25% of the area under the standard normal curve lies to the left of -0.625.
So, among the given options, the correct answer is Option A, -0.625, Option D, -0.50, which is also incorrect. Option E, 0.00, is definitely incorrect because the 25th percentile is to the left of the mean.
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