When you know the tower's height, you may calculate your distance from it.The answer is 92.54 feet .
Determine the height of the tower ?When you know the tower's height, you may calculate your distance from it.The tangent of the angle of elevation multiplied by the horizontal distance, or doing the calculation, is all that is required to manually determine the height.
30° vertical angle from A to the tower's summit
50 + x is the horizontal separation between A and the tower's base.
Call h to get the tower's height.
tan 30 = h / (50 + x) => 50 + x = h / tan 30 => x = h / tan 30 - 50 (1)
40° vertical angle from B to the tower's summit
The tower's base is x feet away from B in a horizontal direction.
ratio: x = h / tan40; tan40 = h / tan40 (2)
Consequently, (1) and (2) are equivalent.
Tan40 = Tan30 - 50 =
30 - 40 = 50 h/tan
1,7321h - 1,1918h = 50
0.5403h = 50
h = 50/0.5403 = 92.54
Response: 92.54 feet
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Find the Banzhaf power distribution of the weighted voting system
[30: 18, 16, 13, 12]
The Banzhaf power distribution of the weighted voting system will be 34, 31, and 30.
What is the Banzhaf power distribution?List all the victorious coalitions, then tally the crucial voters, to determine a voter's power using the Banzhaf index. A crucial voter is someone whose vote, if it were altered from yes to no, would result in the measure's failure. The percentage of all swing votes that a voter may cast is used to determine that person's influence.
[30: 18, 16, 13, 12]
P₁, P₂ = 18 + 16 = 34
P₁, P₃ = 18 + 13 = 31
P₁, P₄ = 18 + 12 = 30
P₂, P₃ = 16 + 13 = 29
P₂, P₄ = 16 + 12 = 28
P₃, P₄ = 13 + 12 = 25
The Banzhaf power distribution of the weighted voting system will be 34, 31, and 30.
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Given sides b, c, and angle d
state the area of the triangle.
The area of triangle with three sides a,bc is equals to
√[s × (s – a) × (s – b) × (s – c)].
What is triangle ?
Triangle can be defined as in which it consists of three sides, three angles and sum of the three angles are 180 degrees always.
Given
in the triangle with three sides a,b,c.
Let ABC be a triangle such that the length of the 3 sides of the triangle is AB = c, BC = a and CA = b.
The semi-perimeter of triangle ABC = s = (a + b + c)/2
Then, the area of triangle ABC = √[s × (s – a) × (s – b) × (s – c)].
Therefore, The area of triangle with three sides a,bc is equals to
√[s × (s – a) × (s – b) × (s – c)].
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A point is the measurement of the distance around a shape. * 1 point True False you will get brainless pls help
Answer:true
Step-by-step explanation:
1.
2.
3.
4.
7. Given: ZBAC = ZEDC, BC = EC
Prove: AABC = ADEC
Stat
EUC
3. Given: JK = LM, ZJKM = ZLMK
YO
1.
2.
3.
4.
B
Reasons
E
L
The triangles are congruent if two of one triangle's sides and its included angle are the same as the corresponding sides and angles of another triangle.
How may a triangle's congruency be demonstrated?Triangles lining up, When all three corresponding sides are the same length and all three corresponding angles are the same size, two triangles are said to be congruent. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved.The triangles are congruent if two of one triangle's sides and its included angle are the same as the corresponding sides and angles of another triangle.Triangles lining up, When all three corresponding sides are the same length and all three corresponding angles are the same size, two triangles are said to be congruent.The complete question is,
To what extent can the congruence of the triangles be demonstrated?
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What is the intersection of y=2x-2 and y= -2x^2 +4x+ 3?
The intersection of equations y=2x-2 and y= -2x^2 +4x+ 3 is y = 3
How to determine the intersection of the linesThe general formula for the equation of a line is expressed as;
y = mx + c
Where the parameters are;
c is the intercept of the line on the y - axism is the slope of the linex is a point on the x-axisy is a point on the y -axisFrom the information given, we have the equation of the lines as;
y=2x-2 y= -2x^2 +5x+ 3Now, equate the lines, we have;
2x - 2 = -2x² + 5x + 3
collect the like terms
2x -5x + 2x² - 2 - 3 = 0
add the iike terms
2x² -3x - 5 = 0
Factorize the quadratic equation
2x² - 5x + 2x - 5 = 0
Group in pairs
(2x² - 5x) + (2x-5) = 0
x(2x -5) + 1(2x - 5) = 0
The intersection for when x = 5/2
y = 2x - 2
y = 2(5/2) - 2
y = 3
Hence, the value is 3
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Help with all please
Answer:
A is ST, PR, and UV
B is rays SQ and QT
C is point Q
D is Points S, Q, and T
Car A is rated at 33 mi/gal (miles per gallon) for city driving and 28 mi/gal for highway driving. Car B is rated at 29 mi/gal city and 33 mi/gal highway. How many gallons of gas would each vehicle consume for the following amounts of driving? (a) 300 mi of city driving plus 100 mi of highway driving (b) 100 mi of city driving plus 300 mi of highway driving
The gallons consumed when car A travels 300 mi of city driving plus 100 mi of highway driving is 12.66 gallons
The gallons consumed when car B travels 300 mi of city driving plus 100 mi of highway driving is 13.37 gallons
The gallons consumed when car A travels 100 mi of city driving plus 300 mi of highway driving is 13.74 gallons
The gallons consumed when car B travels 100 mi of city driving plus 300 mi of highway driving is 12.54 gallons
How many gallons is consumed?Gallons consumed when car A travels 300 mi of city driving plus 100 mi of highway driving = (300 / 33) + (100 / 28)
= 9.09 + 3.57 = 12.66 gallons
Gallons consumed when car B travels 300 mi of city driving plus 100 mi of highway driving = (300 / 29) + (100 / 33)
= 10.34 + 3.03 = 13.37 gallons
Gallons consumed when car A travels 100 mi of city driving plus 300 mi of highway driving = (100 / 33) + (300 / 28)
= 3.03 + 10.71 =13.74 gallons
Gallons consumed when car B travels 100 mi of city driving plus 300 mi of highway driving = (100 / 29) + (300 /33)
= 3.45 + 9.09 = 12.54 gallons
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Read the following prompt and type your response in the space provided.
Create a real-life representation of the following multiplication problem. Explain what the result represents in the problem.
15 (2/5)=6
Answer: In a real-life representation of the multiplication problem "15 (2/5) = 6," we can imagine a bag of 15 items, each of which is 2/5 of a whole. To find out how many whole items are in the bag, we can multiply 15 (the number of items) by 2/5 (the fraction of each item that is a whole).
The result of 6 represents the number of whole items in the bag.
Step-by-step explanation:
Use the distributive property to write each expression as an equivalent
algebraic expression.
-2(x-4)
Answer:
the equivalent algebraic expression is -2x -8 after applying the distributive property.
Step-by-step explanation:
The distributive property states that for any real numbers a, b, and c, a(b+c) = ab + ac.
To apply the distributive property to the expression -2(x-4), we can distribute the -2 across the parenthesis, like this:
-2(x-4) = -2x + (-2)(-4)
Simplifying the last part of the expression:
-2(x-4) = -2x -8
So, the equivalent algebraic expression is -2x -8 after applying the distributive property.
Simplify using the order of operations.
25) 25 ÷ 5 + 4 × 3 – 3
Answer: 14
Step-by-step explanation:
The random variable X is normally distributed with mean 5 and standard deviation 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and the standard deviation of Y ? The mean is 20 and the standard deviation is 102.A) The mean is 20 and the standard deviation is 50.B) The mean is 22 and the standard deviation is 102.C) The mean is 22 and the standard deviation is 100.D) The mean is 22 and the standard deviation is 50.
By multiplying the mean of random variable X by two to four, the random variable Y's mean is calculated to be 20. (5). By dividing the X standard deviation (25), by 4, the standard deviation of Y is equal to 102.
The random variable X has a mean of 5 and a standard deviation of 25. A normal distribution's mean serves as its nucleus, and the standard deviation quantifies how much the values deviate from the mean. Y = 2 + 4X is the definition of the random variable Y. By adding 2 to the mean of X (5), we can determine the mean of Y, which equals 20. By dividing the standard deviation of X (25), by 4, we can determine the standard deviation of Y, which yields a standard deviation of 102 for Y. As a result, the standard deviation is 102 and the mean of Y is 20.
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State if the two triangles are congruent. If they are, state how you know.
Select the correct response:
Yes by SAS
They are not congruent.
Yes by AAS.
Yes by ASA.
The two triangles are not congruent
What does triangular congruency mean?According to the triangle congruency laws, triangles are considered congruent when their sides and angles are equal.
The rules include
Side - Side - Side = SSS
Side, Angle, and Side = SAS
Angle Side Angle = ASA
Angle, Angle, and Side. = AAS
Hypotenuse and one leg. = HL
In the problem no information is given about the sides and just one angle is given.
Even though, for the figure it can be deduced that one side is equal but the information is not enough to determine if the triangles are congruent
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Five Seconds of Summer’s tutoring service charges a base charge of $5 and $5 per hour.
Fall Out Boy’s tutoring service charges a base fee of $9 and $3 per hour. Whose service
would you rather use?
Make a table for your system of equations. Highlight the shared point in your table.
Solve your system graphically. Label your solution on the graph.
Solve the system, algebraically using substitution. Solve for both variables and box in your answers.
Choose your response to the would you rather question. Provide evidence and math to back up your choice. Could there be a scenario in which you would pick another option and tell me your other option
Answer: The cost of both services is equal when h = 2 hours.
Step-by-step explanation: The shared point on the table is when the cost of the two services is equal, i.e. when C1 = C2, where C1 is the cost of Five Seconds of Summer's service and C2 is the cost of Fall Out Boy's service.
To graphically solve the system, we can plot the two equations on the same coordinate plane. The x-axis represents the number of hours and the y-axis represents the cost. The equation for Five Seconds of Summer's service would be y = 5 + 5x and the equation for Fall Out Boy's service would be y = 9 + 3x
We can then find the point of intersection of the two lines, which represents the point at which the cost of the two services is equal. We can label this point as (x, y) and our solution.
To solve the system algebraically using substitution, we can set C1 = C2 and solve for the number of hours (h) in terms of cost.
C1 = 5 + 5h = C2 = 9 + 3h
5 + 5h = 9 + 3h
2h = 4
h = 2
So, the cost of both services is equal when h = 2 hours.
From the above result, it is clear that Fall Out Boy's service is cheaper than Five Seconds of Summer's service. For 2 hours of tutoring, the cost of Fall Out Boy's service is $9 + 3(2) = $15 and the cost of Five Seconds of Summer's service is $5 + 5(2) = $15.
However, there could be scenarios where one service is cheaper than the other depending on the number of hours of tutoring required. For example, if a student requires more than 4 hours of tutoring, Five Seconds of Summer's service would be cheaper. And if a student requires less than 2 hours of tutoring, Fall Out Boy's service would be cheaper.
In conclusion, the best option would depend on the number of hours of tutoring required, and it is best to check both options and compare the cost before making a decision
Answer:
To compare the costs of the two tutoring services, we can set up a system of equations. Let x be the number of hours of tutoring.
Five Seconds of Summer's tutoring service:
y = 5 + 5x (base charge of $5 and $5 per hour)
Fall Out Boy's tutoring service:
y = 9 + 3x (base fee of $9 and $3 per hour)
We can make a table to compare the costs of the two services at different number of hours:
Hours (x) Five Seconds of Summer (y) Fall Out Boy (y)
0 5 9
1 10 12
2 15 15
3 20 18
4 25 21
The shared point in the table is when x = 0, y = 5 for Five Seconds of Summer's tutoring service and y = 9 for Fall Out Boy's tutoring service.
We can graph the two equations to compare the costs:
[Graph would be here if I were able to create one]
From the graph we can see that for any number of hours greater than 0, Five Seconds of Summer's tutoring service is cheaper.
We can also solve the system algebraically using substitution.
y
What is the decimal expansion of the following fraction 1/3
The decimal expansion of the following fraction 1/3 would be; 0.33
What is a fraction?A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
We need to find the expression of 1 divided by 3.
A negative divided by a negative is positive, then;
1/3 = 0.33
Therefore, The value of expression 1/3 would be; 0.33
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Select the statement regarding ethical considerations in experimental designs that is not necessarily true: A. If a research team treats two consenting groups such that one group receives a dose of a drug, and the other group receives a placebo, the team must inform the test subjects after the experiment whether they received the drug or the placebo. B. It is unreasonable for a study to knowingly cause harm to an individual, even if that individual has given consent. C. A national survey, asking respondents about drinking and smoking habits, should remain confidential with regards to the identity of respondents when reporting its findings.
D. If a medical group is going to apply a treatment to a person, that person should be notified and should agree to the treatment first.
The statement regarding ethical considerations in experimental designs that is not necessarily true is that it is unreasonable for a study to knowingly cause harm to an individual, even if that individual has given consent.
Therefore the answer is option B. It is unreasonable for a study to knowingly cause harm to an individual, even if that individual has given consent.
This statement is not necessarily true because there are some situations where knowingly causing harm to a person may be ethical in the context of medical research, such as in the case of trials for life-threatening diseases where no other treatments are available. However, in such cases, strict ethical review and oversight is usually required to ensure that the risks are minimized and that the participants are fully informed of the risks involved.
In ethical considerations in experimental designs, it is generally accepted that participants should be fully informed of the risks involved in a study and should give their informed consent before participating. This means that they should be aware of what is going to happen during the experiment, what benefits and risks are associated with participating, and what their rights are as participants.
However, there are some situations where knowingly causing harm to a person may be considered ethical in the context of medical research, such as in trials for life-threatening diseases where no other treatments are available. In such cases, strict ethical review and oversight is usually required to ensure that the risks are minimized and that the participants are fully informed of the risks involved.
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Climbing Mt. Everest is not an easy task! Not only is it a difficult hike, but the Earth's atmosphere
decreases exponentially as you climb above the Earth's surface, and this makes it harder to breathe. The air
pressure at the Earth's surface (sea level) is approximately 14.7 pounds per square inch (or 14.7 psi). In
Denver, Colorado, elevation 5280 feet, the air pressure is approximately 12.15 psi.
a.) write an exponential equation
b.) what is the air press at the top of mount everest, elevation 29,000 feet?
The exponential equation that represents the relationship between the air pressure and the elevation above the Earth's surface is
y = 14.7 x 0.827^x
The air pressure at the top of Mount Everest, elevation 29,000 feet is approximately 1.931 psi
Finding exponential equation and calculating air pressureTo write an exponential equation for the relationship between the air pressure and the elevation above the Earth's surface, we can use the form y = a x b^x,
where y is the air pressure,
x is the elevation,
and a and b are constants.
We can use the data given in the problem to find the values of a and b.
Let y = air pressure (psi)
x = elevation (feet)
We know that at sea level (x = 0), y = 14.7 psi
At Denver, Colorado, elevation 5280 feet, y = 12.15 psi
We can use these two points to find the values of a and b in the equation y = a x b^x
12.15 = 14.7 x b^5280
b = (12.15/14.7)^(1/5280)
b = 0.827
a = 14.7
The exponential equation that represents the relationship between the air pressure and the elevation above the Earth's surface is
y = 14.7 x 0.827^x
b.) To find the air pressure at the top of Mount Everest, elevation 29,000 feet, we can substitute that value for x into the exponential equation.
y = 14.7 x 0.827^29000
y = 1.931 psi
The air pressure at the top of Mount Everest, elevation 29,000 feet is approximately 1.931 psi. It's worth noting that this is a very low air pressure and the human body is not able to survive with such low pressure without proper equipment.
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males in the netherlands are the tallest, on average, in the world with an average height of centimeters (cm) (bbc news website). assume that the height of men in the netherlands is normally distributed with a mean of cm and standard deviation of cm.
The probability that a Dutch male is taller than 195 cm is 0.2525
Out of a random sample of 1000 Dutch men, people taller than 190 cm are 253 in number using statistics.
Mean = 183 cm
SD = 10.5 cm
Z score = ( Value - Mean ) /SD
Dutch male is shorter than 175 cm
Z score = ( 175 - 183)/10.5 = -0.762
from z score table probability is 0.223
Dutch male is taller than 195 cm
Z score = ( 195 - 183)/10.5 = 1.143
from z score table probability is 0.8735 for shorter than 195 cm
Hence probability that a Dutch male is taller than 195 cm = 1 - 0.8735
= 0.1265
Dutch male is between 173 and 193 cm
Z score = ( 173 - 183)/10.5 = -0.952 => 0.1705Z score = ( 193 - 183)/10.5 = 0.952 => 0.8295
0.8295 - 0.1705 =0.659
taller than 190 cm
Z score = ( 190 - 183)/10.5 = 0.6667
taller than 190 cm = 1 - 0.7475 = 0.2525
Hence in 1000 = 252.5 = 253
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The complete question is :
Height of Dutch Men. Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm) (BBC News website). Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm.a.What is the probability that a Dutch male is shorter than 175 cm?b.What is the probability that a Dutch male is taller than 195 cm?c.What is the probability that a Dutch male is between 173 and 193 cm?d.Out of a random sample of 1000 Dutch men, how many would we expect to be taller than 190 cm?
Find the range and standard deviation of the set of data.
11, 8, 5, 11, 25
The range is
(Simplify your answer.)
The Range and standard deviation of the set of data 11, 8, 5, 11, 25 is 20 and 7.68 respectively.
What is mean ?
Mean can be defined as the ratio sum of the observations and total number of observations.
Given
set of data,
11, 8, 5, 11, 25
we have to find the range and standard deviation,
We know that,
range = max - min
here max = 25
min = 5
range = 25-5
range = 20
Standard deviation ,
= √( ( Σx^2 - (Σx)^2 / n ) / (n-1) )
= √( ( Σ11^2+8^2+5^2+11^2+25^2 - (Σ60)^2 / 5 ) / (5-1) )
= √( ( 956 - (3600)^2 / 5 ) / (5-1) )
= √( ( 956 - 720) / 4 )
= √( 59 )
= 7.68
Hence, The Range and standard deviation of the set of data 11, 8, 5, 11, 25 is 20 and 7.68 respectively.
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Use the information below to find the value of y. Explain your steps
Step-by-step explanation:
2y+y=180(Sum of supplementey angle)
3y=180
y=180\3
y=60find the 100th derivative of P(x)=(x^5+x+x^7)^10 (1+x^2)^11 (x^3+x^5+x^7)
The 100th derivative of P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷) will be zero.
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given:
A polynomial,
P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷).
To find the degree:
(x⁷)¹⁰(x²)¹¹(x⁷) = x⁹⁹.
The polynomial has a degree of 99.
If we think about it intuitively,
Therefore, if we were to multiply it all out,
the leading word would be x⁹⁹.
The term's first derivative is 99x⁹⁸,
followed by 99(98)x⁹⁷,
and 99(98)(97)x⁹⁶.
And finally,
the 99th derivative is 99×98×97×96×...4×3×3×2×1× (x⁰)
=99!
So, the 100th derivative will be zero.
Therefore, by the 100th derivative, all terms will cancel out.
100th derivative will be zero.
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Diego has 3 pencils, 4 pens, and 2 highlighters in his pencil case. What is the ratio of pencils and highlighters to pens in Diego's pencil case?
O 3:6
O
O
4:9
O 5:4
07:2
(CO 2) You flip a coin 3 times. The sample space is \{HHH, HHT, HTH, THH, HTT, THT, TTH. TTT\}. Which of the following is a compound event? A. You get exactly 2 tails B. You get exactly 3 tails C. This is not an event D. You get exactly 3 heads
A compound event is a combination of multiple simple events that can occur simultaneously or independently. When talking about coin flipping, the sample space is the set of all possible outcomes of the experiment, which in this case is flipping a coin 3 times. In this case, the sample space is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}.
Option A, You get exactly 2 tails, is a compound event because it consists of three simple events, THT, HTH, and TTH. These events can happen independently of one another and therefore, it is a compound event.
Option B, You get exactly 3 tails, is not a compound event because it only consists of one simple event, TTT. This event is not a combination of other simple events and is, therefore, not a compound event.
Option C, This is not an event, is not a valid option as it is not a possible outcome.
Option D, You get exactly 3 heads, is also a compound event because it consists of one simple event, HHH. This event can happen independently of other simple events and it is, therefore, a compound event.
Hence, options A and D are compound events as they are a combination of multiple simple events that can happen independently or simultaneously.
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Go Online You can complete your homework online.
2 A group of students is painting the flag of
Brunei for a geography project. Joseph is
responsible for painting only the
background colors of the flag. How many
square inches will he cover with white paint?
(Example 1)
4=bh t=72631
yellow
white
black
yellow
A=6120
81⁄2 in.
7 in.
The required area of the white part of the flag is 612 Square inches.
What is Rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
According to question:We have,
Width = 8(1/2) = 17/2 In
Length = 72 In
Area of the white part of the flag is
= 17/2 × 72
= 612 Square inches
Thus, required area is 612 Square inches.
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The white portion of the flag must have a 612 square inch area.
What is a rectangle?A rectangle is a quadrilateral with parallel sides that are equal to one another and four equal vertices. Due to this, it is also known as an equiangular quadrilateral. Due to their equal and parallel opposite sides, rectangles are also known as parallelograms.The following is what we have:width = 8 (1/2) = 17 (2 inches).72 inches longThe white portion of the flag's area is= 17/2 × 72612 Square Inches612 square inches are therefore needed.To learn more about the area of square refer:
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Explain why these triangles are congruent by AAS (Angle-Angle-Side) and not ASA (Angle-Side-Angle).
The triangles are congruent by AAS (Angle-Angle-Side) and not by ASA (Angle-Side-Angle)
Properties of congruent triangles.When the corresponding length of sides or measure of the internal angles of two or more triangles are equal, then the triangles are said to be congruent. The congruency can be expressed in terms angles, sides, or the combination of sides and angles. An example is the SAA (Side-Angle-Angle) property which implies that a side that is not an included angle and other angles are congruent.
Considering triangles ABC and CDE, it can be seen that two angles are congruent and a side of both are congruent. Since the congruent side is not an included angle, then the congruent relations is AAS (Angle-Angle-Side).
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motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. assume a production process produces items with a mean weight of 8 ounces.
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In addition, the balance of common stock at the beginning of the year was $550,000, and the balance of retained earnings was $46,000. During the year, the company issued additional shares of common stock for $32,000 and paid dividends of $24,000. Required: Prepare an income statement. Prepare a statement of stockholders’ equity.
Answer: Income Statement:
Revenue: _________
Expenses: _________
Net Income: _________
Statement of Stockholders' Equity:
Beginning Balance:
Common Stock: $550,000
Retained Earnings: $46,000
Total: $596,000
Additions:
Common Stock: $32,000
Total: $628,000
Deductions:
Dividends: $24,000
Total: $604,000
Ending Balance:
Common Stock: $550,000
Retained Earnings: $50,000
Total: $600,000
Note: I've left the Revenue, Expenses and Net Income section in the income statement blank as it is not provided in the question. It is also important to note that these are just examples and the numbers may not match with the actual financial statement.
Step-by-step explanation:
Kayden and his children went into a grocery store where they sell apples for $ 0.75 each and mangos for $2 each. Kayden has $20 to spend and must buy a minimum of 16 apples and mangos altogether . Also, he must buy no less than 16 apples. If represents the number of apples purchased and y represents the number of mangos purchased, write and solve a system of inequalities graphically and determine one possible solution .
The system of inequalities is:
x + y ≥ 16
x*0.75 + y*2 ≤ 20
And its graph can be seen below, there we can see that one possible solution is (14, 2)
How to write and solve the system of inequalities?
Let's define the variables:
x = number of apples.
y = number of mangos.
Kayden needs to buy not less than 16 items, so the first inequality is:
x + y ≥ 16
And he can spend at most $20, then:
x*0.75 + y*2 ≤ 20
The system of inequalities is then:
x + y ≥ 16
x*0.75 + y*2 ≤ 20
To graph it just graph the two lines and shade the region correspondent, for the first inequality shade the region above the line, for the second one shade the region below the line.
You should get.
The solution set is the region where both shaded areas intercept. Then a possible solution is:
x = 14
y = 2
Learn more about systems of inequalities:
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Samantha bought an equal number of $11.00,$9.00 and $8.00 tickets for a concert. she spent $196 for all of the tickets. how many of each did she
Answer: Samantha bought 7 tickets for a concert
Step-by-step explanation:
$11.00 + $9.00 + $8.00 = 28
$196 / 28 = 7
Krystal drove at an average speed of 50 mi/h from her home in Houston to visit her sister in Philadelphia.
She stayed in Philadelphia 25 hours, and on the trip back averaged 60 mi/h. She returned home 46 hours
after leaving. How many miles is Houston from Philadelphia?
a) Write an equation using the information as it is given above that can be solved to answer this question.
Use t as your variable to represent the amount of time Krystal spent driving from Houston to Philadelphia.
Equation:
b) How many miles is Houston from Philadelphia?
Answer:
miles
Give your answer to the nearest mile
Answer: a. The equation using the information as it is given above that can be solved to answer this question is:
distance = speed x time
Let t be the amount of time Krystal spent driving from Houston to Philadelphia.
distance = 50t + 60(46 - 25 - t)
b. To find the distance between Houston and Philadelphia, we can substitute the known values into the equation and solve for t.
distance = 50t + 60(46 - 25 - t)
distance = 50t + 60(21) - 60t
distance = 50t + 1260 - 60t
distance = -10t + 1260
To find the total distance, we can set t = 25
distance = -10(25) + 1260
distance = -250 + 1260
distance = 1010
Therefore, Houston is 1010 miles from Philadelphia, to the nearest mile.
Step-by-step explanation:
A door frame that appears to be rectangular has a height of 213 cm, width of 92 cm, and one diagonal that measures 231 cm. Determine if the door frame is rectangular. Explain your thinking.
The door frame is not rectangular.
Is the door frame rectangular?If the door frame is rectangular, the sum of the square of the height and the width would be equal to the square of the diagonal.
Height² + width = diagonal²
213² + 92²
45,369 + 8,463 = 53,833
231² = 53,361
53,833 ≠ 53,361
The door frame is not rectangular because the sum of the height and the width is not equal to the diagonal.
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