Answer: x = 3, x= - 3
Step-by-step explanation:
x^2 - 9 = 0
=> x^2 = 9
=> x = 3, x= - 3
Assume c and d function independently. for the system to function, either c or d must function.
a. if the probability that c fails is 0.08 and the probability that d fails is 0.12, find the probability that the system functions.
b. if both c and d have probability p of failing
The probability that the system functions is 1. In part b, the probability that the system functions is 2 - 2p.
Explanation:To find the probability that the system functions, we need to find the probability that either c or d functions. Since c and d function independently, we can use the addition rule of probability. The probability that c functions is 1 minus the probability that c fails, which is 0.08, so the probability that c functions is 1 - 0.08 = 0.92. Similarly, the probability that d functions is 1 - 0.12 = 0.88. Since either c or d must function, we can add the probabilities of c and d functioning: 0.92 + 0.88 = 1.80 (which exceeds 1 since it's not possible for both c and d to function simultaneously). Therefore, the probability that the system functions is 1.
In part b, if both c and d have a probability p of failing, then the probability that c functions is 1 - p, and the probability that d functions is also 1 - p. Again, using the addition rule of probability, the probability that the system functions is: (1 - p) + (1 - p) = 2 - 2p.
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Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle B?
Enter your answer in the box.
m∠B=
General Idea:
A cyclic quadrilateral has all its vertices on the circumference of the circle. The opposite angles of a cyclic quadrilateral are supplementary, that is it add up to get 180 degrees.
Applying the Concept:
Opposite angles B and D add up to give 180 degrees.
[tex] \angle B + \angle D=180\\ \\ 4x-20+x=180\\ Grouping \; like \; terms\\ \\ 4x+x-20=180\\ Combining \; like\; terms\\\\ 5x-20 =180\\ Adding \; 20 \; on\; both\; sides\\ \\ 5x-20+20=180+20\\ Combine\; like\; terms\\ \\ 5x=200\\ Divide\; 5\; on\; both\; sides\\ \\ \frac{5x}{5} =\frac{200}{5} \\ Simplify \; fraction\; on\; both\; sides\\ \\ x=40\\ \\ Substitute \; 40\; for\; x\; in\; the\; expression\; for\; \angle B \\ \angle B=4x-20=4(40)-20=160-20\\\\\angle B=140 [/tex]
Conclusion:
When Quadrilateral ABCD is inscribed in this circle, the measure of angle B for the given diagram is [tex] 140^{\circ} [/tex]
Find the scalar and vector projections of b onto
a.a = i + j + k, b = i - j + k
How many solutions does this system have?
5x - y = 3
2y = 10x + 2
a.one
b.two
c.an infinite number
b.no solution
the given system has D. no solution as slope are same.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
here, we have,
5x - y = 3
2y = 10x + 2
now, we know that,
A system of two equations can be classified as follows:
If the slopes are the same but the y-intercepts are different, the system has no solution.
If the slopes are different, the system has one solution.
If the slopes are the same and the y-intercepts are the same, the system has infinitely many solutions.
so, the given system has D. no solution as slope are same.
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1. A/an _______ triangle has all three angles measuring less than 90°. A. right B. obtuse C. scalene D. acute
Find the length of a rectangular prism having a volume of 2830.5 cubic meters , width of 18.5 meters, and height of 9 meters.
A grocery store received two shipments of watermelon. Each watermelon in a shipment was weighed, then a line plot was made of all of the weights in a shipment. What statement about the two plots’ distributions is true?
The degree of overlap between the two distributions is moderate.
The degree of overlap between the two distributions is high.
There is no overlap between the two distributions.
The degree of overlap between the two distributions is low
Answer:
The degree of overlap between the two distributions is moderate.
Step-by-step explanation:
A grocery store received two shipments of watermelon. Each watermelon in a shipment was weighed, then a line plot was made of all of the weights in a shipment. What statement about the two plots’ distributions is true?
The true statement is - option A - The degree of overlap between the two distributions is moderate.
Answer:
A/The degree of overlap between the two distributions is moderate.
Step-by-step explanation:
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evidence:
penny and her two friends each ate 1/6 of cake . how much cake did they eat
what is the value of log5 125
Tomas wrote the equation y = 3x 3/4+. When Sandra wrote her equation, they discovered that her equation had all the same solutions as Tomas’s equation. Which equation could be Sandra’s?
Answer:
–6x + 2y = 3/2 is Sandra's equation.
Step-by-step explanation:
Given Equation of Tomas is
[tex]y=3x+\frac{3}{4}[/tex]
Solution of equation of Sandra is same as solution of Tomas Equation.
This only possible when ratio of the coefficients of the variable and constant term is equal.
So,
Multiply Tomas equation with 2.
2y= 6x + 3/2
This is one of the equation possible for Sandra's equation
Therefore, –6x + 2y = 3/2 is Sandra's equation.
Find all zeros of the function and write the polynomial as a product of linear factors. f(x) = 3x4 + 4x3 + 13x2 + 16x + 4
a store is going out of business everything is marked down 40% how much do you pay for an item that cost $150
Find the m∠DEC, if m∠BAC = 50° and m∠CBA = 70°
Answer:
the m∠DEC=60°
Step-by-step explanation:
As given, information the triangle is shown in figure-1
Given:
m∠BAC = 50°
m∠CBA = 70°
we need to find m∠DEC
Since, sum of interior angles of triangle is 180°.
In triangle ABC,
m∠BAC+m∠CBA+m∠ACB=180°
50° + 70° + m∠ACB =180°
120° + m∠ACB =180°
subtract 120° from both the sides in above,
m∠ACB =180° - 120°
m∠ACB =160°
from the figure, we can see that BC║DE,
therefore
m∠DEC=m∠ACB
m∠DEC=60°
Therefore, the m∠DEC=60°
In a rhombus, an altitude from the vertex of an obtuse angle bisects the opposite side. Find the measures of the angles of the rhombus.
The angles of the rhombus determines the inclination of the sides of the
rhombus.
The correct response;The measures of the four angles of the rhombus are 60°, 60°, 120°, and 120°.Method used to arrive at the above response;Given;The altitude of the rhombus bisects the opposite side.
The angle of the rhombus at the vertex point of the altitude = An obtuse angle
Required:The measure of the angles of the rhombus
Solution:The length of the sides of a rhombus are equal.
The opposite angles of a rhombus are equal.
Let x represent the length of a side of the rhombus, we have;
The bisector from the vertex of the obtuse angle = An altitude
The angle the altitude forms with the side it bisects = 90°
Therefore;
The triangle formed by the altitude, half the bisected side and the side of the rhombus adjacent to the bisected side = A right triangle
The hypotenuse side to the right triangle = The side of the rhombus
Let θ represent the angle opposite the altitude, and between the sides of
the rhombus, in the right triangle by trigonometric ratios, we have;
[tex]\displaystyle cos(\theta) = \mathbf{\frac{Adjacent}{Hypotenuse}}[/tex][tex]\displaystyle cos(\theta) = \frac{0.5 \cdot x}{x} = 0.5[/tex]
θ = arccos(0.5) = 60°
Therefore, two acute (opposite) angles of the rhombus are 60°
The two obtuse angles of the rhombus are each = (360° - 2×60°) ÷ 2 = 120°
The angles of the rhombus are 60°, 60°, 120°, 120°.Learn more about trigonometric ratios here:
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A dozen long stem red roses cost $57 what is the unit rate of for roses
Prove that 1/2 + 1/3 + ... + 1/n is not an integer
The sequence 1/2 + 1/3 + ... + 1/n is not an integer because no fractions in this series can sum up to a whole number. This argument aligns with the behavior of the Harmonic series, of which this sequence is a subset.
Explanation:The question asks to prove that the sum 1/2 + 1/3 + ... + 1/n is not an integer. To approach this, consider the Harmonic series, which is the sum of the reciprocals of the natural numbers: 1 + 1/2 + 1/3 + … + 1/n. This series diverges, but since it never reaches an integer beyond 1, it suggests that any sum of its subset also won't be an integer.
For a more formal proof, suppose the sum 1/2 + 1/3 + ... + 1/n is an integer. It means that some fraction in that series would have to be a whole number, as fractions add up to fractions unless there is a whole number. Since none of the terms 1/2, 1/3, etc., are whole numbers, this contradicts our assumption. Therefore, 1/2 + 1/3 + ... + 1/n is not an integer.
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In matrix T, what is the value of element t13?
Apply the distributive property to create an equivalent expression.
1/2 (2a-6b+8) =?
Answer:
a - 3b + 4
Step-by-step explanation:
The distributive property indicates that two or more terms present in a sum or subtraction multiplied by another quantity, is equal to the sum or subtraction of the multiplication of each of the terms of the sum or subtraction by the number.
So,
1/2 (2a-6b + 8) = 1/2 (2a) + 1/2 (-6b) + 1/2 (8)
Now we multiply the factor (1/2) for each of the three terms,
1/2 (2a) + 1/2 (-6b) + 1/2 (8) = (2/2)a + (-6/2)b + (8/2) = a – 3b + 4
The solution is a - 3b + 4,
So we say that 1/2(2a - 6b + 8) is equivalent to a - 3b + 4.
The distributive property is solved to the equation and the expression is represented as A = a - 3b + 4
Given data:
To apply the distributive property to the expression 1/2(2a-6b+8), distribute the 1/2 to each term inside the parentheses.
1/2(2a-6b+8) can be rewritten as:
(1/2) * 2a + (1/2) * (-6b) + (1/2) * 8
Now, let's simplify each term:
(1/2) * 2a = a
(1/2) * (-6b) = -3b
(1/2) * 8 = 4
Putting it all together, the expression becomes:
A = a - 3b + 4
Hence, on applying the distributive property to 1/2(2a-6b+8) gives the equivalent expression as a - 3b + 4.
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what is C=24x+80 R=44x breakeven point
Answer:
resumably this is number of units sold. Explanation: At the break even point Cost equals Revenue: 24x+80=44x. ⇒80=20x. ⇒x=4.
Step-by-step explanation:
KJ is tangent to circle C at J, KL is tangent to circle C at L, and mMLarc = 138°. Find mMJarc.
Given that the external angle formed by the two tangent is 40° and the
part of [tex]m \widehat{LMJ}[/tex] is 138°, we get that [tex]m \widehat{MJ}[/tex] = 87°.
Which property can be used to find [tex]m \widehat{MJ}[/tex] ?Using the two tangent angle theorem, we have;
[tex]m \angle K = \mathbf{ \dfrac{1}{2} \times \left(\widehat{LMJ} - \widehat{LJ} \right)}[/tex]
m∠K = 40°
[tex]m \widehat{ML}[/tex] = 138°
[tex]m \widehat{LMJ}[/tex] = [tex]m \widehat{ML}[/tex] + [tex]m \widehat{MJ}[/tex]
[tex]m\widehat{LJ} = \mathbf{360^{\circ} - \left(m\widehat{ML} + m\widehat{MJ} \right)}[/tex]
Which gives;
[tex]m \angle K = \dfrac{1}{2} \times \left(\widehat{LMJ} - \left( 360^{\circ} - \left(m\widehat{ML} + m\widehat{MJ} \right) \right)\right)[/tex]
Therefore;
[tex]m\angle K= \dfrac{1}{2} \times \left(m \widehat{ML} + m \widehat{MJ} - \left( 360^{\circ} - \left(m\widehat{ML} + m\widehat{MJ} \right) \right)\right)[/tex]
[tex]40^{\circ}= \mathbf{ \dfrac{1}{2} \times \left(138^{\circ} + 2 \cdot m \widehat{MJ} - 232^{\circ} \right) \right)\right)}[/tex]
Which gives;
[tex]m \widehat{MJ}[/tex] = 87°Learn more about two angle tangent theorem here:
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Final answer:
The measure of MJarc in circle C, when MLarc is 138°, is calculated to be 222°, based on the property that the sum of arcs in a circle is 360°.
Explanation:
The question revolves around the properties of a circle and its tangents. We have a circle C with two tangents KJ and KL, touching the circle at points J and L respectively. In addition, we are told that the measure of the arc ML (from M to L) is 138° and we need to find the measure of the arc MJ (from M to J).
According to the properties of circles, a tangent at any point on the circle is perpendicular to the radius at that point. Also, the measure of an angle formed by a tangent and a chord through the point of tangency is half the measure of the intercepted arc. In this scenario, MJ and ML are two arcs that form a complete circle, so the sum of mMJarc and mMLarc should equal 360°. If mMLarc is 138°, then mMJarc, the arc we are trying to find, would be 360° - 138°, which equals 222°.
What is m∠KNL?
Enter your answer in the box.
There are several relationships between angles in a transversal.
The measure of KNL is 102 degrees.
From the figure,
Angles KNJ and JNM are corresponding angles
So, we have:
[tex]KNJ = JNM[/tex]
This gives
[tex]3(x + 14) = 5x + 2[/tex]
Open brackets
[tex]3x + 42 = 5x + 2[/tex]
Collect like terms
[tex]3x - 5x = 2 - 42[/tex]
[tex]-2x = -40[/tex]
Divide both sides by -2
[tex]x = 20[/tex]
Angle KNL is
[tex]\angle KNL =3(x + 14)[/tex]
Substitute 20 for x
[tex]\angle KNL =3(20 + 14)[/tex]
[tex]\angle KNL =3(34)[/tex]
[tex]\angle KNL =102[/tex]
Hence, the measure of KNL is 102 degrees.
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The game of european roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. a ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. gamblers can place bets on red or black. if the ball lands on their color, they double their money. if it lands on another color, they lose their money.
Answer:
a) Expected amount of winnings = -$0.084
Standard deviation = $3.00
b) Expected amount of winnings = -$0.084
Standard deviation = $1.73
c) The expected winnings for both cases is exactly the same, but the spread of the wins about the expected value/mean is low in the case (b) compared to case (a).
So, with the expected winnings using the method in (a) and (b) the same, the risk associated with betting $3 dollar per game is higher because it has a higher standard deviation. This points to higher spread of losses and wins betting $3 once than betting $1 three different times.
Step-by-step explanation:
(a) Suppose you play roulette and bet $3 on a single round. What is the expected value and standard deviation of your total winnings?
It's either one wins or not with a bet of $3.
We can then obtain the probability mass function.
Random variable X represents the amount of winnings.
- If one bets $3 and picks the right colour, the person wins $6.
X = amount of winnings = 6 - 3 = $3
probability of winning = (18/37) = 0.486
- If one bets $3 and picks the wrong colour, then the person wins $0.
X = amount of winnings = 0 - 3 = -$3
Probability of losing = (19/37) = 0.514
The probability mass function is then
X | P(X)
3 | 0.486
-3 | 0.514
E(X) = Σ xᵢpᵢ
xᵢ = each variable
pᵢ = probability of each variable
E(X) = (3×0.486) + (-3×0.514) = -$0.084
Standard deviation = √(variance)
Variance = Var(X) = Σx²p − μ²
μ = E(X) = -0.084
Σx²p = (3²×0.486) + [(-3)² × 0.514] = 9
Variance = 9 - (-0.084)² = 8.993
Standard deviation = √8.993 = 2.999 = $3
(b) Suppose you bet $1 in three different rounds. What is the expected value and standard deviation of your total winnings?
With a bet of $1,
It's either one wins or not with a bet of $1.
We can then obtain the probability mass function.
Random variable X represents the amount of winnings.
- If one bets $1 and picks the right colour, the person wins $2.
X = amount of winnings = 2 - 1 = $1
probability of winning = (18/37) = 0.486
- If one bets $1 and picks the wrong colour, then the person wins $0.
X = amount of winnings = 0 - 1 = -$1
Probability of losing = (19/37) = 0.514
The probability mass function is then
X | P(X)
1 | 0.486
-1 | 0.514
E(X) = Σ xᵢpᵢ
xᵢ = each variable
pᵢ = probability of each variable
E(X) = (1×0.486) + (-1×0.514) = -$0.028
For 3 rounds of $1, the expected amount of winnings = 3 × -0.028 = -$0.084
Variance = Var(X) = Σx²p − μ²
μ = E(X) = -0.028
Σx²p = (1²×0.486) + [(-1)² × 0.514] = 1
Variance = 1 - (-0.028)² = 0.999216
Variance for combining 3 independent distributions = Σ λᵢ²σᵢ²
Variance of 3 rounds of $1 bets = 3[1²× var(X)] = 3 × var(X) = 3 × 0.999216 = 2.997648
Standard deviation = √(variance) = √(2.997648) = $1.73
(c) How do your answers to parts (a) and (b) compare? What does this say about the riskiness of the two games?
The expected winnings for both cases is exactly the same, but the spread of the wins about the expected value/mean is low in the case (b) compared to case (a).
So, with the expected winnings using the method in (a) and (b) the same, the risk associated with betting $3 dollar per game is higher because it has a higher standard deviation. This points to higher spread of losses and wins betting $3 once than betting $1 three different times.
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Solve equation...
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Solve the exponential equation algebraically and use a graphing utility
400/1+e^-x= 350
a round swimming pool has a circumference of 54 ft. Carrie wants to buy a rope to put across the diameter of the pool. the rope cost $0.85 per foot, and carrie need 3 feet more then the diameter of the pool. how much will carrie pay for the rope?
555 grams of wool were needed to knit a sweater, a hat and a scarf. The hat required 5 times less wool than the sweater and 5 grams more than the scarf. How many grams of wool did each item require?
The problem is solved by setting up a system of equations. After solving, it was found that a sweater requires 375 grams of wool, a hat requires 75 grams, and a scarf requires 70 grams.
Explanation:We are given that 555 grams of wool are needed to knit a sweater, a hat and a scarf. We are also told that the hat required 5 times less wool than the sweater, and 5 grams more than the scarf. To solve this problem, we can set up a system of equations to represent these relationships.
Let's define S as the number of grams of wool required for the sweater, H as the grams for the hat, and SC as the grams for the scarf.
From the problem, we have three equations:
S + H + SC = 555 (The total weight of the wool) H = S/5 (The hat required 5 times less wool than the sweater) H = SC + 5 (The hat required 5 grams more than the scarf)By substituting H = S/5 and H = SC + 5 into the first equation, we can solve the system of equations to find the quantity of wool required for each item:
S = 375 grams, H = 75 grams, SC = 70 grams.
Therefore, a sweater requires 375 grams of wool, a hat requires 75 grams, and a scarf requires 70 grams.
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To solve this problem, we can set up equations based on the given information and represent the amount of wool needed for each item using variables. By solving these equations, we can find the amount of wool needed for each item.
Explanation:Let's define the variables:
x = amount of wool needed for the sweater
hat = amount of wool needed for the hat
scarf = amount of wool needed for the scarf
We know that hat requires 5 times less wool than the sweater, so hat = (1/5)x.
We also know that the hat requires 5 grams more than the scarf, so hat = scarf + 5.
Considering that the total amount of wool needed for the three items is 555 grams, we have:
x + (1/5)x + (scarf + 5) = 5556x/5 + scarf + 5 = 5556x/5 + scarf = 550Now we can simplify the equation and solve for x:
6x + 5(scarf) = 550 × 56x + 5scarf = 2750multiply the first equation by 5 to get 6x + 5scarf = 2750Learn more about Wool requirements for knitting here:https://brainly.com/question/13173204
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Mike saves $42 a week for 7 weeks. During his 8-day vacation, he plans to spend $8.25 each day for snacks. Which expression shows how much money he will have left?
A) (42÷7)−(8⋅8.25)
B) (42⋅7)−(8⋅8.25)
C) (42⋅7)+(8⋅8.25)
D) 42⋅7⋅8⋅8.25
Can you please help me ??
the set of points (2,3,), (9,3), (9, -2), and (2,-2) identifies the vertices of a quadrilateral. which is the most specific describtion to tell which figure the points form?