Answer:
To find the diagonal length, you can use the Pythagorean theorem.
If one side is 28 inches, and the board is a square, the other side must also be 28 inches.
a = side 1
b = side 2
c = diagonal length
a^2 + b^2 = c^2
(28)^2 + (28)^2 = c^2
784 + 784 = c^2
1568 = c^2
Square root both sides.
c = about 39.6 inches diagonal length
Work out the value of x. Show your working clearly.
the random variable x is the number of occurrences of an event over an interval of 10 minutes. it can be assumed the probability of an occurrence is the same in any two time periods of an equal length. it is known that the mean number of occurrences in 10 minutes is 4.2. the probability there are 8 occurrences in 10 minutes is
The likelihood of 8 occurrences in a period of 10 minutes is around 0.091 or 9.1%.
According to the Question
A Poisson distribution issue exists here. The Poisson distribution is a discrete probability distribution that quantifies the likelihood of a certain number of events occurring at a certain average rate, regardless of the interval between occurrences, in a given amount of time or space.
The following formula determines the likelihood that x will occur in a Poisson distribution with parameter λ :
P(x; λ) is equal to x / (λx * e(-λ))!
where
λ = the average number of occurrences within the specified time period.
λ in this situation is 4.2. (the mean number of occurrences in 10 minutes).
In order to determine the likelihood of 8 occurring in 10 minutes:
P(8; 4.2) = (4.2^8 * e^(-4.2)) / 8!
⇒ P(8; 4.2) = 0.091 or 9.1%.
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a mechanical system comprises three subsystems in series with reliabilities of 0.98, 0.96, and 0.94. what is the overall reliability of the system?
The system's total dependability is 0.8813.
The reliability of the individual components determines the overall reliability of multi-component systems.
R = (0.98) (0.96) (0.94)
= 0.8813
The likelihood that a system operates well for a given period of time is known as reliability. When performing this right action:
No maintenance or repairs are necessary. The system correctly complies with the established performance requirements.
The dependability decreases when more time is taken into account for reliability calculations since it obeys the exponential failure rule.
In other words, a system's reliability will initially be high and steadily decline to its lowest level over time.
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The value of the overall reliability of the system is 0.8813.
The possibility that a system will work successfully over a certain time period is referred to as reliability. No repair is necessary or done during this right procedure. The system adheres to the performance standards as specified.
The overall reliability of multi-component systems is determined by the reliability of the individual components.
R = (0.98) (0.96) (0.94)= 0.8813
The possibility that a system will perform well over a particular length of time is referred to as dependability. There is no need for maintenance or repairs while doing this appropriate step. The system satisfies the defined performance criteria.
Because it follows the exponential failure rule, dependability falls as more time is factored into reliability assessments.
In other words, the reliability of a system will begin high and gradually drop to its lowest level over time.
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express cos V as a fraction in simplest terms
The value of cos v in simplest terms in fraction form is 17/18
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here: The triangle ΔXWV with WV=17 , XV=18,
We know cos ∅= base/hypotenuse
here hypotenuse is XV as it is opposite to the right angle. and the base of the triangle is 17
∴ Cos v=17/18
We can also find the measure of the third angle by using the pythogarean theorm as
WX=√18²-17²
=√35
Hence, The value of cos v in simplest terms in fraction form is 17/18
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Answer choices
AA
SAS
SSS
GIVEN
alternative interior angles are congruent
Vertices angles are congruent
The first statement is given, the second statement is true because they are vertically opposite angles and the third statement is true by SAS congruency of triangles.
What is congruence of triangles?
Two triangles that are congruent will have precisely the same three sides and three angles.
The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions.
The first statement is true because this is already given in the question.
The second statement is true because ∠KLJ and ∠MLN are vertically opposite angles and we know that vertically opposite angles are always equal. Therefore, the second statement is true.
The third statement is true because of the SAS congruency of triangles.
As we are given ratio of two sides equal to ratio of corresponding sides and the angle between the sides to be equal.
Hence, the two triangles are congruent.
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Solve this system of equations by graphing. First graph the equations, and then type the solution.
3x-y=-6
y=x+4
The solution is (_,_)
The solution to the system of equations in this problem is given as follows:
(5,9).
How to obtain the solution to the system of equations?The system of equations for this problem is defined as follows:
3x - y = 6.y = x + 4.We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
From the image given at the end of the answer, the solution to the system of equations is given as follows:
(5,9).
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The input is multiplied by 2, then 5 is subtracted
The function that matches the description is given as follows:
f(x) = 2x - 5.
How to define the function?The parent function for this problem is given as follows:
f(x) = x.
The first transformation is a multiplication by two, hence the function is defined as follows:
f(x) = 2x.
The final transformation is a subtraction by 5, then the function is defined as follows:
f(x) = 2x - 5.
Meaning that the last option is the correct option.
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Find the solution to the system of equations given below using elimination by addition. 4x + 3y = -20 6x +12y = −10
Answer:8
Step-by-step explanation:
dd
What is the factored form of 4x+16
Answer:
The factored form of 4x+16 is (4x + 8)(2). This can be found by using the distributive property, or by using the prime factorization method.
Tell whether each figure creates the conditions to form a unique triangle, more than one triangle, or no triangle.
_________3 in.
________6 in. ___
________10 in. _____________
From the figure we see that by the conditions , the figure does not form any Triangle .
A Triangle is defined as the three sided closed figure made up of line segments .
In the figure , the two lines forms a right angle at the base , that means both the line segments are perpendicular ,
and if the two line are perpendicular to the same base then the two line will be called as parallel lines and we know that parallel lines do not intersect .
Therefore , The triangle will form No Triangle as the lines do not meet .
The given question is incomplete , the complete question is
Tell whether the figure given below creates the conditions to form a unique triangle, more than one triangle, or no triangle.
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Exit Ticket
DQ,FP, RE are all medians of Ader, and C is the centroid. DQ = 24, FC = 10, RC = 7.
Find DC, CQ, FP, and CE.
P
E
D.
R
Using the property of median, the values of DC = 16, CQ = 8, FP = 15, and CE = 14.
As DQ = 24, FC = 10, RC = 7.
As we know that the centroid divide each median in the ratio of 2:1.
The diagram of the question is given below:
So, we divide the median DQ in the ratio 2:1
2x + x = 24
3x = 24
Divide by 3 on both side, we get
x = 8
So the length of DC = 16 and CQ = 8
Ac FC = 10 which is 2 part of the ratio 2:1.
So the value of 2x = 10
So x = 5. Now the value of CP = 5
Now the value of FP = FC + CP
FP = 10 + 5
FP = 15
As RC = 7 which is 1 part of the ratio 2:1.
So the value of CE = 2x = 2×7 = 14
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How much of a(n) 60% orange juice drink must be mixed with 5 gallons of a 30% orange juice drink to obtain a mixture that is 50% orange juice?
Answer: To obtain a mixture that is 50% orange juice, you must find the amount of 60% orange juice needed to bring the overall concentration of orange juice to 50%.
We can start by using the formula:
(amount of 60% orange juice) / (amount of 60% orange juice + amount of 30% orange juice) = desired concentration
Let's call the amount of 60% orange juice that we need to add x.
So the equation will look like this:
(x) / (x + 5 gallons) = 0.5
We can then solve for x:
x = (0.5 * x + 0.5 * 5 gallons)
x = 2.5 gallons
So, 2.5 gallons of 60% orange juice must be mixed with 5 gallons of 30% orange juice to obtain a mixture that is 50% orange juice.
Step-by-step explanation:
A survey was given to a random sample of 45 voters in the United States to ask about
their preference for a presidential candidate. Of those surveyed, 80% of the people
said they preferred Candidate A. Determine a 95% confidence interval for the
percentage of people who prefer Candidate A, rounding values to the nearest tenth.
Answer: A confidence interval is a range of values that is likely to contain the true population value with a certain level of confidence. To determine a 95% confidence interval for the percentage of people who prefer Candidate A, we can use the following formula:
(Sample proportion) +/- (Margin of error)
The margin of error can be calculated using the formula:
Margin of error = (Critical value) * (Standard deviation)
The critical value is a factor used to compute the margin of error. The critical value for a 95% confidence interval is approximately 1.96. The standard deviation is calculated as:
Standard deviation = √((Sample proportion) * (1 - Sample proportion) / (Sample size))
Plugging in the given values:
Sample proportion = 80% = 0.8
Sample size = 45
Margin of error = (1.96) * √((0.8) * (1 - 0.8) / (45))
Step-by-step explanation:
Gina Wilson All Things Algebra Unit 5: Congruent Triangles homework 1 PLEASE HELP
As per the angle sum property, the value of x is 14°
In math the term called angle sum property states that the sum of interior angles of a triangle is 180°.
Here we have the following diagram and we need to find the value of x.
While we looking into the diagram, we have identified the value of the angles are listed as follows:
=> (10x - 11)°
=> (3x - 2)°
=> (3x + 1)°
Now we have to solve this by using the angle sum property then we get,
=> (10x - 11)° + (3x - 2)° + (3x + 1)° = 180°
When we simplify this one then we get,
=> 16x - 12 = 180°
=> 16x = 168°
=> x = 14°
Complete Question
Find the value of x one the following diagram.
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The citizens of Herrington County have an existing dog
park for dogs to play, but have decided to build another
one so that one park will be for small dogs and the other
will be for large dogs. The plan is to build a rectangular
fenced in area adjacent to the existing dog park, as
shown in the sketch. The county has enough money in
the budget to buy 1000 feet of fencing.
What should the dimensions of the dog park be to maximize the area?What is the maximum area of the park?
To maximise the area it should be build as a square having side=250 feet each and having area=62500 feet.
what are squares?
A square is a two-dimensional plane figure with four equal sides and all four angles are equal to 90 degrees. The properties of the rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.
The most important properties of a square are listed below:
All four interior angles are equal to 90°.All four sides of the square are congruent or equal to each other.The opposite sides of the square are parallel to each other.The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other.The square has 4 vertices and 4 sides.The diagonal of the square divides into two similar isosceles triangles.The length of diagonals is greater than the sides of the square.Area of square=(side)²
Perimeter of square=4*side
Now,
Given
total fencing available=1000feet
perimeter=1000
4*s=1000
s=250 feet
Therefore,
Area=250^2
=62500 feet^2
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Talia travelled part of the journey by train and the rest by bus.The total fare was sh 400.On return,the fare of the bus was hiked by a half of what he paid and the total fare of the return journey hiked to sh 4800.Find the train fare.
Answer: Let x be the fare of the train, and y be the fare of the bus.
We know that:
x + y = 400 (the total fare of the journey)
And, on the return journey the fare of the bus is hiked by a half of what Talia paid initially, so the fare of the bus on the return journey is:
y * 1.5 = y + (y/2)
And the total fare of the return journey is hiked to 4800, so:
x + y + (y/2) = 4800
We can substitute the first equation into the second equation:
x + (y + (y/2)) = 4800
x + y + (y/2) = 4800
x + (y + (y/2)) = 4800
So, we can solve the system of equations by substituting the first equation into the second equation and solving for x.
x + y = 400
x = 4800 - (y + (y/2))
x = 4800 - y - (y/2)
x = 4800 - y - (1/2)y
x = (4800 - y) - (1/2)y
x = 4800 - (3/2)y
Now we have an equation for x in terms of y. To solve for x, we can use the value of y from the first equation
x = 4800 - (3/2)(400)
x = 4800 - 600
x = 4200
So the train fare is 4200 sh
Step-by-step explanation:
The cost C (in dollars) of producing x cell phone cases is C=2.2x+10.6. The revenue R (in dollars) for selling x cell phone cases R = 6.91x.
To calculate profit, subtract the cost from the revenue.
(a) Write and simplify an equation for the profit P in terms of x.
P = ?
Answer:
P =4.71x-10.6
Step-by-step explanation:
R = 6.91x
C=2.2x+10.6.
P = R - C = 6.91x-2.2x -10.6 =4.71x-10.6
if 3/4 of a certain number is equal to 4 1/2 find the number
Answer:
6
Step-by-step explanation:
4 1/2= 4.5
3/4=0.75
4.5/0.75= 6
just to check, 3/4 x 6 =4.5
2 + 7^3 + 4(9-6)^2/6
Answer:
The answer is 351
Step-by-step explanation:
Hope this helps!
how do i simplify -5x+x and 2p+5p
Answer: For your answer you would add like terms so for -5x+x you would get -4x, and for your other you would get 7p.
You brake your car from a speed of 55 mph. The table shows data that represent your car's speed versus the amount of time elapsed from the moment that you began to brake.
Elapsed Time (sec)
Speed (mph)
1
45
2
35
3
25
4
15
5
15
6
15
Evaluate the following graph based on the data in the table.
A graph has elapsed time (seconds) on the x-axis, and speed (miles per hour) on the y-axis. A line goes through points (1, 45), (2, 35), (3, 25), (4, 15), (5, 15), (6, 15).
What is the slope of the line segment that represents the period of time during which the speed decreases?
a.
The slope is 0.
c.
The slope is 10.
b.
The slope is -10.
d.
The slope is -11.
The slope of the line segment that represents the period of time during which the speed decreases is: C: The slope is -10.
How to find the Slope?The parameters given are:
Starting speed of the car = 55 km/hr
Let us suppose when t=0 , the speed of car was 55 km/hr.
Then car broke down.
The following Data are given regarding car's speed versus the amount of time elapsed from the moment that it began to brake.
Elapsed Time (sec) Speed (mph) → 1 :45 ,2 :35, 3 :25, 4 :15, 5 :15 ,6 :15
Slope of line passing through two points (a, b) and (p, q) is given by the formula:
Slope = (q - b)/(p - a)
Thus, Slope of line passing through two points (1,45) and (2,35) is:
Slope = (35 - 45)/(2 - 1)
Slope = -10
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Consider the equation. X + 5 7 = 31 7 If you use the addition property of equality, what number would you add to both sides of the equal sign to isolate the variable? What is the solution?
Regarding the addition property of equality, the number would add to both sides of the equal sign to isolate the variable x = 26/7.
What amount would you add to both sides of the equal sign if you were to isolate the variable using the addition property of equality?
The official term for the equality-related characteristic that enables one to multiply both sides of an equation by the same amount. One of the most frequently applied properties for solving equations is this one.
To solve the problem, you would take away 5/7 from both sides.
What is the remedy?
x = 3 and 5/7 or 26/7.
x + 5/7 = 31/7
Subtract 5/7 from both sides of the equation:
x + 5/7 - 5/7 = 31/7 - 5/7
x = 26/7
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Answer:
1: -5/7
2: 26/7
Step-by-step explanation:
Look at the following speeds.
4mph 8mph 16mph 32mph 64mph 128mph
By what factor did the speeds change for each consecutive speed from the first speed to the sixth speed.
A. 8
B. 32
C. 4
D. 2
The factor by which ths speed increases is 2, then the correct option is D.
By what factor did the speeds change for each consecutive speed?Here we have the sequence of numbers:
4, 8, 16, 32, 64, 128
Where these have units of miles per hour, but can be ignored, as we only care for the numbers. To get the factor by which the speed change for each consecutive speeds, we just need to take the pairs of consecutive numbers and take their quotients.
We will get:
8/4 = 2
16/8 = 2
32/16 = 2
etc.
Then the factor is 2, the correct option is D.
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4 3/4 - 6/4 = ? I need help .
The solution to the mixed fraction 4 3/4 - 6/4 is 3 1/4
What is a mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
To solve the question
Convert the mixed fractions into improper fractions
4 3/4 - 6/4
= 19/4 -6/4
we can simplify, since the denominators are the same
19-6/4
=13/4
converting to mixed fractions, we have
3 1/4
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A shipping container will be used to transport several 80-kilogram crates across the
country by rail. The greatest weight that can be loaded into the container is 27000
kilograms. Other shipments weighing 13600 kilograms have already been loaded into
the container. Which inequality can be used to determine x, the greatest number of
80-kilogram crates that can be loaded onto the shipping container?
80(13600+ x) ≤ 27000
27000 13600 - 80x
27000 13600 + 80x
80(13600+ x) ≥ 27000
Submit Answer
The inequality expression that can represent the above scenario is
80x + 13600 ≤ 27000.
In mathematics, Inequality is an expression that is used for unequal comparison of two numerical expressions or algebraic expressions.
Instead of an equal sign here, we use signs like Less than (<), Greater than (>), Less than or equal (≤), Greater than or equal (≥), and Not equal (≠), etc.
Like Linear equations here we use variables like x, y, z .. etc. to represent the unknown quantities or numbers
Here we have
A shipping container will be used to transport several 80-kilogram crates across the country by rail.
The greatest weight that can be loaded in container is 27000 kilograms.
Other shipments weight = 13600 kilograms
Let 'x' be the number of crates that can be transported
Weight of 'x' number of crates = 80kg × (x) = 80x kg
As we know the greatest weight that can be loaded is 27000 kilograms. So here is the total weight of 'x' crates and the other shipment's weight must be less than 27000 kilograms but not more.
=> 80x + 13600 ≤ 27000
Therefore,
The inequality expression that can represent the above scenario is
80x + 13600 ≤ 27000.
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What does it mean when you substitute a value into an equation and the result is a true statement?
What it means when you substitute a value into an equation and the result is a true statement is; The solution of the equation
How to find the solution of an equation?
Solving an equation is very synonymous to trying to find the answer to a puzzle. Now, an algebraic equation states that two algebraic expressions are equal.
In order for us to solve an equation, we will have to determine the values of the variable that makes the equation a true statement. Thus, any number that makes the specific equation to be true will be referred to as a solution of the equation.
A solution to an equation is defined as a value of a specific variable that makes a statement to be true when substituted into the equation. Thus, the process of finding the solution to an equation is simply called solving the equation.
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Write about a real-world situation that can
be represented by the equation y = 7x. Be sure to explain what the variables
represent in the situation.
Answer:
the equation could represent your paycheck at the end of a shift. y is equal to the total amount of money you made, 7 is equal to your hourly wage, and x is equal to the number of hours worked. For example if you worked two hours one day, the equation would be y=7(2), which could be simplified to y=14, so after a two hour shift you would make a total of $14
Step-by-step explanation:
F(-7, 12) and G(3, -8)
The coordinates of the midpoint M of the segment FG is (-2,2).
This question is incomplete, the complete question is;
What is the midpoint M of a line having two endpoints F(-7, 12) and G(3, -8),
What is the coordinates of the midpoint M of the segment FG?The midpoint formula is expressed as;
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
Given the data in the question;
Point F (-7, 12)
x₁ = -7y₁ = 12Point G (3,-8)
x₂ = 3y₂ = -8To determine the midpoint, plug the given points into the formula above and simplify.
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
M = ( (-7 + 3 )/2, ( 12 + (-8) )/2 )
M = ( ( -4 )/2, ( 12 - 8 )/2 )
M = ( ( -4 )/2, ( 4 )/2 )
M = ( -2, 2 )
Therefore, the midpoint M of the segment is (-2,2)
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An open box i to be contructed from a quare piece of heet metal by removing a quare of ide 3 feet from each corner and turning up the edge. If the box i to hold 300 cubic feet, what hould be the dimenion of the heet metal?
The sheet metal should have a total area of 12.9 x 12.9 = 166.41 square feet.
The sheet metal must be large enough to form a cube with a volume of 300 cubic feet, so the side length of the sheet must be the cube root of 300, which is approximately 6.9 feet. To find the dimensions of the sheet metal, we must take into account the four 3 foot squares that will be removed from each corner. Therefore, the sheet metal should have a length of 6.9 feet + 6 feet (4 times the 3 foot squares) = 12.9 feet and a width of 12.9 feet. This will give the box a volume of 300 cubic feet, and the sheet metal should have a total area of 12.9 x 12.9 = 166.41 square feet.
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|x-2|=|4+x| How does this make sense, HOW
The solution of the absolute value equation:
|x-2|=|4+x|
is x = -1
How to solve the equation?Here we want to solve the following equation:
|x - 2| = |4 + x|
A general absolute value function can be rewritten into two equations, in this case these are:
x - 2 = 4 + x
x - 2 = -(4 + x)
The first one has no solution, but the second one does.
x - 2 = -(4 + x)
x - 2 = -4 -x
2x = -4 + 2
2x = -2
x = -2/2 = -1
That is the solution.
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