For the roots of the polynomial to be real and equal the values of K are 0 and 4.
Now according to the question,Given: - The roots of the polynomial equation [tex]x^{2}+Kx+k=0[/tex] are real and equal.
To find: - The values of K to satisfy the given condition of roots of the equation.
Solution: -
∵ Since the given equation is a quadratic equation.
∴ For the roots of the equation to be real and equal, the discriminant must be equal to zero, i.e., D = 0.
Now,
∵ D = b² - 4ac
∴ b² - 4ac = 0 ......(1)
We have,
a = 1, b = K and c = K
putting these values in equation (1) we get,
(K)² - 4*(1)*(K) = 0
⇒ (K)² - 4K = 0
⇒ K (K - 4) = 0
⇒ K = 0 or 4
∴ The values we got for K are 0 and 4.
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PLS HELP ASAP
GIVING BRAINLIEST + 30 POINTS EACH
Answer:12
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
12
WILL MARK BRAINLIEST IF ANSWERED WITHIN 10 minutes!!!
The value of P(1≤x≤3) is 0.84
What is Probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
P(1≤x≤3) defined the probability that the result is between 1 and 3, included. You can answer this question in two ways:
1. Sum the probabilities of good events:
From the graph, we have
P ( x= 1 ) = 0.32
P ( x = 2 ) = 0.24
P ( x= 3 ) = 0.28
So,
P ( 1 <= X <= 3 ) = 0.32 + 0.24 + 0.28
= 0.84
2. Use complementary probabilities
Asking that the result is 1, 2 or 3 is the same as asking that the result is not 4. The probability that the result is 4 is 0.16, so the probability that the result is not 4 will be
P ( x not equal to 4 ) = 1 - P ( x = 4 )
= 1- 0.16
= 0.84
Therefore, The value of P(1≤x≤3) is 0.84
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each of the augmented matrices above has a row in which each entry is zero. what, if anything, does the presence of such a row tell us about the consistency of the corresponding linear system?
The presence of such a row tell us about the consistency of the corresponding linear system is inconsistent
What is Linear System?
A linear system is a mathematical model of a system that is based on the usage of a linear operator in systems theory. Linear systems often have considerably simpler features and properties than nonlinear systems.
1. The pivot positions in the first augmented matrix are a11, a22, and a33. Because the last column lacks a pivot, the linear system corresponding to the first augmented matrix is consistent.
2. The pivot positions in the second augmented matrix are a11 and a22. Because the last column lacks a pivot, the linear system corresponding to the second augmented matrix is consistent.
3. The a11, a22, and a34 elements in the third augmented matrix serve as pivot points. Because the last column has a pivot, the linear system corresponding to the third augmented matrix is consistent.
b) 1. The linear system corresponding to the first augmented matrix comprises four equations and three unknowns. The presence of a zero row indicates that one of the four equations is a linear combination of the other three linearly independent equations. As a result, the linear system corresponding to the first augmented matrix is reduced to three equations in three unknowns. The linear system is stable and has a single solution.
2. The linear system that corresponds to the second augmented matrix comprises four equations and three unknowns. The presence of two zero rows indicates that two of the four equations are linear combinations of the other two linearly independent equations. As a result, the linear system corresponding to the second augmented matrix is reduced to two equations with three unknowns. The linear system is consistent and has an endless number of solutions.
3. The linear system that corresponds to the third augmented matrix comprises four equations and three unknowns. One zero row indicates that one of the four equations is a linear combination of the other three linearly independent equations. As a result, the linear system corresponding to the third augmented matrix is transformed into three equations with three unknowns. Because the augmented matrix includes a pivot in the last column, the linear system is inconsistent.
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The presence of such a row tell us about the consistency of the corresponding linear system is inconsistent
What is Linear System?
A linear system is a mathematical model of a system that is based on the usage of a linear operator in systems theory. Linear systems often have considerably simpler features and properties than nonlinear systems.
1. The pivot positions in the first augmented matrix are a11, a22, and a33. Because the last column lacks a pivot, the linear system corresponding to the first augmented matrix is consistent.
2. The pivot positions in the second augmented matrix are a11 and a22. Because the last column lacks a pivot, the linear system corresponding to the second augmented matrix is consistent.
3. The a11, a22, and a34 elements in the third augmented matrix serve as pivot points. Because the last column has a pivot, the linear system corresponding to the third augmented matrix is consistent.
b) 1. The linear system corresponding to the first augmented matrix comprises four equations and three unknowns. The presence of a zero row indicates that one of the four equations is a linear combination of the other three linearly independent equations. As a result, the linear system corresponding to the first augmented matrix is reduced to three equations in three unknowns. The linear system is stable and has a single solution.
2. The linear system that corresponds to the second augmented matrix comprises four equations and three unknowns. The presence of two zero rows indicates that two of the four equations are linear combinations of the other two linearly independent equations. As a result, the linear system corresponding to the second augmented matrix is reduced to two equations with three unknowns. The linear system is consistent and has an endless number of solutions.
3. The linear system that corresponds to the third augmented matrix comprises four equations and three unknowns. One zero row indicates that one of the four equations is a linear combination of the other three linearly independent equations. As a result, the linear system corresponding to the third augmented matrix is transformed into three equations with three unknowns. Because the augmented matrix includes a pivot in the last column, the linear system is inconsistent.
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raise 4 to the 10th power, double the result, then divide what you have by q
Do not simplify any part of the expression.
The expression is [(4^10)×2]/q.
What is division?Division is the process of splitting a number or an amount into equal parts.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
Here, we have,
given that,
raise 4 to the 10th power, double the result, then divide what you have by q
so. we get,
[(4^10)×2]/q
Hence, The expression is [(4^10)×2]/q.
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What is the general way to write factored form?
The general way to write factored form of the given quadratic equation is given by f (x) = A ( x - u ) ( x - r ).
As given in the question,
Let us consider the standard quadratic equation as :
ax² + bx + c = 0
To represent general way of factored form take example :
Example : 2x² + 14x + 24 = 0
Split the middle term :
4x + 3x = 7x
(4x)(3x) = 12x²
⇒2(x² + 7x + 12 )= 0
⇒ x² + 4x + 3x + 12 = 0
⇒x( x + 4 ) + 3 ( x+ 4 ) = 0
⇒ ( x + 3 )(x + 4 ) = 0
Factored form of the quadratic equation is : f (x) = A ( x - u ) ( x - r ).
Therefore, in standard way the factored form of the quadratic equation is equal to f (x) = A ( x - u ) ( x - r ).
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For exercise, Martin runs 60 minutes each day. His friend Jamel lifts weights for 45
minutes each day. Which teen expends more calories through these physical
activities? Explain.
The most calories are expended per hour while running. Swimming, walking, and stationary bicycling are also great possibilities. HIIT workouts are excellent for calorie burning as well.
Which activity expends the most calories?When it comes to calorie burn per hour, running comes out on top. Other great options include stationary cycling, walking, and swimming. Calorie burning is also excellent with HIIT exercises.
Circulatory endurance refers to your body's capacity to maintain itself throughout activities like running, jogging, swimming, cycling, and anything else that requires your cardiovascular system (lungs, heart, and blood vessels) to exert itself for an extended length of time.
Regular exercise can help kids and teenagers lose weight, develop strong bones and muscles, enhance cardiorespiratory fitness, lessen the symptoms of anxiety and depression, and lower their chance of contracting diseases like heart disease.
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What is the Perimeter of a House
Answer:
153 ft
Step-by-step explanation:
[tex]16 + 1 + 2 + 2 + 5 + 2 + 2 + 8 + 5 + 18 + 9 + 5 +3 + 9 + 3 + 2 + 6 + 6 + 6 + 6 + 6 + 3 + 5 + 23 = 153[/tex]
suppose that three cards are randomly selected from a standard deck of 52 cards. what is the probability that each card is a king (k) if the sampling is done without replacement?
Three cards are randomly selected from a standard deck of 52 cards. The probability that each card is a king (k) if the sampling is done without replacement is 1/5525
Probability measures the likelihood of the occurrence of an event. The probability is defined as:
p(A) = n(A) / n(S)
Where:
n(A) = number of possible ways an event A can happens
n(S) = number of possible outcomes.
In a standard deck, there are 4 kings. Hence,
1st draw, the probability it is a king = 4/52
Suppose, that the first card is a king, then the remaining kings are 3 and the remaining cards are 51.
Hence, at 2nd draw, the probability it is a king = 3/51.
Similarly, at 3rd draw, the probability it is a king = 2/50
The probability that each card is a king:
P (3 kings) = 4/52 x 3/51 x 2/50
= 24/13260
= 1/5525
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please help!
Use the quadratic formula to find both solutions to the quadratic equation
given below.
*photo provided for easy access*
The solutions to the given quadratic equation are 1/4 and -1.
The correct options are Options E and F.
What is Quadratic Formula?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. The coefficient of x² must be a non-zero term (a ≠ 0) in order for an equation to meet the definition of a quadratic equation. The easiest method for locating a quadratic equation's roots is the quadratic formula:[tex]x = \frac{-b + \sqrt{b^{2} -4ac} }{2a}[/tex] and [tex]x = \frac{-b - \sqrt{b^{2} -4ac} }{2a}[/tex]
Given equation :
4x² + 3x -1 = 0
Here,a = 4, b = 3, and c = -1.
[tex]x = \frac{-b + \sqrt{b^{2} -4ac} }{2a}[/tex]
The roots of the equation are:
[tex]x = \frac{-3 + \sqrt{3^{2} -4(4)(-1)} }{2(4)}[/tex] and [tex]x = \frac{-3 - \sqrt{3^{2} -4(4)(-1)} }{2(4)}[/tex]
[tex]x = \frac{-3 + \sqrt{25} }{2(4)}[/tex] and [tex]x = \frac{-3 - \sqrt{25} }{2(4)}[/tex]
[tex]x = \frac{2}{8} = \frac{1}{4}[/tex] and [tex]x = \frac{-8}{8} = -1[/tex]
Hence the roots of the equation are 1/4 and -1.
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Can 2 right angles form a triangle?
A triangle can't have two right angles. If a triangle has two right angles, then the sum of its three angles will be more than the two right angles i.e. more than 180∘ which is impossible.
A right-angled triangle is one that has three sides, “base” “hypotenuse” and “perpendicular” with the angle between the base and the perpendicular is 90°.
A right-angled triangle is one of the basic shapes in geometry and it forms the foundation for trigonometry.
A right triangle has one angle exactly equal to 90 degrees
The angles other than the right angle must be acute angles, i.e. less than 90 degrees
The side opposite to vertex of 90 degrees is called the hypotenuse of the right triangle and is the longest side of the triangle
A triangle can't have two right angles. If a triangle has two right angles, then the sum of its three angles will be more than the two right angles i.e. more than 180∘ which is impossible.
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A german worker takes 600 hours to produce a car and 5 hours to produce a case of wine. An italian worker takes x hours to produce a car and 4 hours to produce a case of wine. For what values of x will it be possible to achieve gains from trade?.
The possible values of x ( in hours) will be less than four to achieve gains from trade .
Opportunity cost is what we have to sacrifice to achieve something. It is a very important concept in international trade, as it forms the basic criteria for opening a trade. For trade to take place there should be atleast comparative advantage in the production of a good by each country.
Produced item Germany France
Car 600 hours x hours
Wine 3 hours 4 hours
We have to calculate the value of "x"
Opportunity cost of a car for German worker
= 600/5 = 120 cases of wine
Opportunity cost of a wine for German worker
= 1/120 cars
Similarly, Opportunity cost of a car for Italian worker = 4/x cases of wine
Opportunity cost of wine for Italian worker
= x/4 car
A country has a comparative advantage when it can produce a good with a lower opportunity cost than another. To achieve the gains from trade, when the opportunity cost of a car for Italian worker is greater than german worker
4/x > 120 => x < 4/120 = 1/30 .
or in case of wine, x/4 < 1/120
=> x < 4/120 = 1/30
So, possible value of x is less than 4.
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the list below shows wendy's bowling scores in her last 5 games. which measure of data best describes how much these bowling scores varied
The range best describes how much these bowling scores varied.
What is the median of a data set ?
The median of a data set is the value that falls in the middle, indicating that 50% of the data points have values that are lower or equal to the median and 50% of the data points have values that are higher or equal to the median. When working with a small data collection, you must first count the number of data points (n) and organize them in ascending order.
The difference between the highest and lowest values for a given data collection is the range in statistics. As an illustration, if the data set contains 2, 5, 8, 10, 3, the range will be 10 - 2 = 8. So, another way to describe range is as the difference between the highest and lowest observation.
Given data set:
112, 123, 136, 145, 159
Range = 159 - 112 = 47
The range best describes how much these bowling scores varied.
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How do you graph a quadratic equation in factored form?
The steps to convert the graph a quadratic equation in factored form is explained below.
Factored form in math is defined as the process of expressing a given number or algebraic expression as the product of its factors is called factoring.
Here we need to explain the process of graph a quadratic equation in factored form.
There are three ways are defined to convert them.
The very first way to When every term of the equation has GCD ≠ 0 then it can be factored by taking out GCD as a common factor.
the next way is to use the Identity that is a² - b² = (a + b) (a - b)
The last way is to use the Identity (x + a)(x + b)
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Use these four expressions to make a hypothesis about the closure property of integers under each operation. select yes or no for each operation. operation example expression is the set of integers closed under the operation? addition -8 5 yes no subtraction 9 − (-11) yes no multiplication 3 · (-4) yes no division -1 ÷ 6 yes no
The answer is: Yes, Yes, Yes, No.
The expression -8 + 5 shows the sum of two integers. This expression has a value of -3. Because -3 is also an integer, the set of integers appears to be closed under addition.
The expression 9 − (-11) shows the difference between two integers. This expression has a value of 20. Because 20 is also an integer, the set of integers appears to be closed under subtraction.
The expression 3 · (-4) shows the product of two integers. This expression has a value of -12. Because -12 is an integer, the set of integers appears to be closed under multiplication.
The expression, -1 ÷ 6, shows the quotient of two integers. This expression has a value of -1/6, Because -1/6 is not an integer, the set of integers is not closed under division.
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what percentage of winners driving a chevrolet won with an average speed of at least 140 miles per hour? %
The percentage of winners driving a chevrolet won with an average speed of at least 140 miles per hour is 81.25%
Percentage represent a fraction of a hundred.
To convert a fraction into percent, first, find the equivalent fraction with 100 as its denominator.
Example:
3/5 = 60/100 = 60%
We can also convert it into percent by multiplying it by 100%
3/5 = 3/5 x 100% = 60%
In the given problem, the total number of chevrolet won is 16. Three of then have average speed less than 140 miles per hour.
Therefore,
Number of chevrolet with an average speed ≥ 140 mph = 16 - 3 = 13
Its percentage = 13/16 x 100 % = 81.25%
The table in your question is missing, most likely it was like in the attached picture.
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Subtract 5/6 - 7/12 Simplify your answer.
The value on simplifying the fraction expression 5/6 - 7/12 is obtained as 1/4.
What is a fraction?
In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
The fraction expression is given as 5/6 - 7/12.
5/6 - 7/12
First take the LCM of the denominator -
LCM = 12
Now, multiply 2 by 5 in first fraction numerator, as 6 multiplied by 2 is 12 (LCM) -
10/12 - 7/12
Now, use the arithmetic operation of subtraction -
(10 - 7)/12
3/12
Divide numerator and denominator by 3 -
1/4
Therefore, the final value as a fraction is obtained as 1/4.
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the principal would like to assemble a committee of 4 students from the 14-member student council. how many different committees can be chosen?
There are 1001 different committees can be chosen.
The problem is asking how many different committees can be chosen or the number of ways to select 4 students out of a group of 14 without regard to order. This is a combinatorics problem, and it can be solved using the combination formula:
nCr = n!/(r!(n-r)!)
Where n is the total number of items to choose from (14 students in this case) and r is the number of items to choose (4 students).
Plug in the values and solve.
14C4 = 14!/(4!(14-4)!)
14C4 = 14!/(4!10!)
14C4 = 1001
Therefore, the number of different committees that can be chosen is 1001.
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The line given by y = 1/4x − 1 is dilated by a scale factor centered at the origin. The image of the line after dilation is given by y = 1/4x - 5. What is the scale factor of the
dilation?
The scale factor of the dilation is the square root of 17.
What do you mean by dilation?A dilation is a transformation in geometry that changes the size of a figure while preserving its shape. In other words, a dilation stretches or shrinks a figure proportionally, but does not change its shape. The dilation is defined by a scale factor, which is the ratio of the length of the image to the length of the original figure. The scale factor can be greater than 1, which means the dilation is an enlargement, or less than 1, which means the dilation is a reduction. The center of dilation is a fixed point, which is used to determine the scale factor and direction of the dilation. Dilations play an important role in many areas of mathematics, including coordinate geometry and metric spaces.
The scale factor of the dilation can be found by comparing the equations of the original line and the image line. The slope of the original line is 1/4, and the slope of the image line is also 1/4. Since the slope is unchanged, the dilation did not affect the slope, and therefore the scale factor is 1 in the x-direction.
To find the scale factor in the y-direction, we can compare the y-intercepts of the original and image lines. The y-intercept of the original line is -1, and the y-intercept of the image line is -5. The difference between the y-intercepts of the original and image lines is 4, which is the change in the y-coordinate of the image relative to the original.
Therefore, the scale factor in the y-direction is 4. Since the scale factor in the x-direction is 1, the overall scale factor is the square root of (1^2 + 4^2) = the square root of 17.
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What must be added to x³ 3x 8 to get 3x³ X² 6?
The polynomial 2x³ + x² -3x +14 must be added to (x³ + 3x -8) to obtain (3x³ + x² +6).
Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The general form of the quadratic equation is: ax² + bx + c = 0,
where x is an unknown variable and a, b, c are numerical coefficients.
The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics.
Let a polynomial P must be added.
Therefore, according to the question,
P+ (x³ + 3x -8) = (3x³ + x² +6)
=> P= (3x³ + x² +6) - (x³ + 3x -8)
=> P= (3-1)x³ + x² -3x +(6-(-8) )
=> P= 2x³ + x² -3x +14
Thus, the polynomial 2x³ + x² -3x +14 must be added to (x³ + 3x -8) to obtain (3x³ + x² +6).
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is ㏑ 5 + 4 ㏑ x = 2 ㏑ 5 equivalent to ㏑ 5 x ( to power 4) = ㏑ 32 ? why so?
The equation ㏑ 5 + 4 ㏑ x = 2 ㏑5 is equivalent to 4 logx=log 5
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given equation is ㏑ 5 + 4 ㏑ x = 2 ㏑5
log 5+logx⁴= 2log5
logx⁴=2 log 5 -log5
logx⁴=log5
4 logx=log 5
Hence, the equation ㏑ 5 + 4 ㏑ x = 2 ㏑5 is equivalent to 4 logx=log 5
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If PN = 115, NO = 108, and QR = 27, find the length of SQ. Round your
answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
47⁰
Answer: SQ =
Answer:
SQ=115/4 =28.75
Step-by-step explanation:
108/27 = 115/SQ
108*SQ=27*115
108*SQ=3105
SQ=3105/108
SQ=115/4 =28.75
Tyler was studying the temperatures in North Dakota and Louisiana in the morning. By the afternoon,
the temperature in Louisiana increased by 2°C. The temperature in North Dakota in the afternoon was
10°C less than that of Louisiana in the morning.
If the combined temperature of both the states was 35°C in the afternoon, what was the temperature of
Louisiana in the morning?
21.5°C was the temperature of Louisiana in the morning. This can be solved using the concept of equations.
What is an equation?The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.
Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.
Let, the temperatures in Louisiana = x
the temperatures in North Dakota = y
y = x - 10
or, x - y = 10 ....... (i)
By the afternoon, the temperature in Louisiana increased by 2°C. So, temperature of Louisiana in afternoon: (x + 2)
(x +2) + y = 35
or, x + y = 33 ........ (ii)
now, solving this two equations we get
2x = 43
or, x = 21.5°C
Thus, 21.5°C was the temperature of Louisiana in the morning.
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5. The new playground at the park will be 45 ft. by
62 ft. What is the area of the playground?
Answer:
2790 ft²
Step-by-step explanation:
Area of rectangle with length L and width W:
area = LW
area = 45 ft × 62 ft
area = 2790 ft²
machine is set to fill paint cans with a mean of 128 ounces and a standard deviation of 0.2 ounce. a random sample of 40 cans has a mean of 127.9 ounces. does the machine need to be reset? explain.
The machine is working correctly and filling cans with a mean of 128 ounces.
The Central Limit Theorem states that the distribution of the sample means will be approximately normal, regardless of the underlying distribution of the population, as long as the sample size is large enough.
With a random sample of 40 cans, we can use the Central Limit Theorem to assume that the sample mean of paint cans is approximately normally distributed with a mean of 128 ounces and a standard deviation of 0.2/[tex]\sqrt{40}[/tex].
We can then use this information to perform a hypothesis test to determine if the sample mean of 127.9 ounces is significantly different from the population mean of 128 ounces.
The null hypothesis is that the machine is working correctly and filling cans with a mean of 128 ounces, and the alternative hypothesis is that the machine is not working correctly and filling cans with a mean different from 128 ounces.
We can use a significance level of 0.05 for this test and calculate the z-score using the formula (sample mean - population mean)/(standard deviation of sample mean).
If the calculated z-score is greater than the critical value of z (from a standard normal table) at the significance level 0.05, we reject the null hypothesis and conclude that the machine is not working correctly and filling cans with a mean different from 128 ounces.
However, based on the sample mean of 127.9 and the population mean of 128, we can see that the sample mean is 0.1 ounce below the population mean which is not a significant difference. Therefore, we fail to reject the null hypothesis and conclude that the machine is working correctly and filling cans with a mean of 128 ounces.
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Demarco has some money saved, but wants to save more. He decides to save the same amount each month. The linear equation 10y-200x=500 can be used to find y, the amount of money demarco has saved after x months. Demarco makes a graph of this equation. Tell whether each statement is true of false.
We have the table as,
a. The slope is 20.-True
b. The point (0, 500) is on the line.-False
c. The line starts downward from left to right. -False
d. The slope is -200.-False
e. The y-intercept is 50.-True
What is slope intercept form of the equation?When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.
Here the given equation is 10y-200x=500
a) Now rewrite the equation into slope intercept form then,
=> 10y-200x=500
=> 10y=200x+500
=> y = 20x+50.
We know that slope intercept form of the equation is y=mx+b. Where m is slope, Then slope of the given equation is 20.
b)Now put (x,y)=(0,500) in 10y-200x=500 then
=> 10×500-200×0=500
=> 5000≠500
Then the point (0,500) is not on the line.
c)Comparing with y = mx + d, we get,
Slope, m = 20 (Positive which implies the line starts upward from left to right)
d) The equation y=20x+50 ,y-intercept, d = 50 (That means the line passes through the point (0, 50)
e) y intercept is 50.
Hence the correct answer is
a. The slope is 20.-True
b. The point (0, 500) is on the line.-False
c. The line starts downward from left to right. -False
d. The slope is -200.-False
e. The y-intercept is 50.-True
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What’s the domain and range ?
Answer: Although I am not 100% sure, I would think the domain 2<x<6 (x being the domain and the point must be on the line) although for these signs they would be "or equal" to. The range would be 6<y<18 (y being the range and once again the point must be on the line) with "or equal" to signs.
Step-by-step explanation:
This is because since there are no concrete points, other than the two ends of this (piecewise?) function, you would have to set the domain to be all x values that fall on this line, hence x being between 2 and 6. The same happens for y, in which, since there are no points plotted, the range is all the y values on the line. Once again, I am not absolutely sure about this, but it seems logical, at least to me.
Do all parallel lines equal 180?
The total of all the angles created on a transverse that are inside either of the two parallel lines is always 180 degrees.
Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.
When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairings of that transversal. Alternate interior angles are what they are termed.
When a transversal intersects two parallel lines, co-interior angles result between the lines. On the same side of the transversal, the two angles always sum to 180 degrees.
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what is the probability that a randomly chosen family with the number of children two or more has children of the same gender
The probability that a randomly chosen family with two or more children has children of the same gender is 1/2
To find the probability that a randomly chosen family with two or more children has children of the same gender, we can use the following information:
The probability of having a boy is 1/2 and the probability of having a girl is 1/2
The number of children is 2 or more
The sample space is all possible families with two or more children.
We can use the formula of conditional probability:
P(A|B) = P(A and B) / P(B)
Where A is the event of having children of the same gender, and B is the event of having two or more children.
We can use the formula of conditional probability to find the probability of having children of the same gender given that they have two or more children.
P(A and B) = P(A) * P(B|A)
Where P(A) is the probability of having children of the same gender, which is 1/2.
P(B|A) is the probability of having two or more children given that they have children of the same gender, which can be found using the formula of conditional probability as well.
P(B|A) = 1 - P(not B|A)
Where P(not B|A) is the probability of having less than two children given that they have children of the same gender.
Given that the family has children of the same gender, the probability of having less than two children is 0, because if the family has children of the same gender, it implies that the family has at least two children.
So, P(B|A) = 1- 0 = 1
Now we can substitute these values to the first equation:
P(A|B) = P(A) * P(B|A) / P(B) = (1/2) * 1 / P(B)
The only thing left to find is P(B) which is the probability of having two or more children. We don't have the exact number, but we know that the number of children is 2 or more, so P(B) is greater than 0.
We can say that P(A and B) = P(A) * P(B|A) = (1/2) * 1 = 1/2
Thus, the probability that a randomly chosen family with two or more children has children of the same gender is 1/2.
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What are the 6 trigonometric ratios include their functions?
There are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, cosecant, tangent and cotangent.
By using a right-angled triangle as a reference, the trigonometric functions and identities are derived:
sin θ = Opposite Side/Hypotenuse
cos θ = Adjacent Side/Hypotenuse
tan θ = Opposite Side/Adjacent Side
sec θ = Hypotenuse/Adjacent Side
cosec θ = Hypotenuse/Opposite Side
cot θ = Adjacent Side/Opposite Side
Trigonometric Identities are formulas that involve Trigonometric functions.
These identities are true for all values of the variables.
Trigonometric Ratio is known for the relationship between the measurement of the angles and the length of the sides of the right triangle.
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WHich statement is true about the equation below ?
3(2-k)= -3k+2
(A) The equation has no solution.
(B) The equation has one solution.
(C) The equation has two solutions
(D) The equation has infinitely solutions.
The statement is true about the given equation 3(2-k)= -3k+2 as, follows:
"The equation has no solution".
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The equation is given in the question, as follows:
3(2 - k)= -3k + 2
Apply the distributive property of multiplication,
3 × 2 - 3 × k = -3k + 2
6 - 3k = -3k + 2
6 - 2 = 3k - 3k
4 = 0
This is not true, so the equation has no solution.
Hence, the correct answer would be an option (A).
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