What is the solution to the trigonometric inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2pi radians?
From the given information provided, the solution to the given trigonometric inequality is (π/4, 5π/4).
To solve the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians, we can use the following steps:
Rewrite the inequality in terms of tangent:
Divide both sides by cos(x) to get:
tan(x) > 1
Find the solutions of the equation tan(x) = 1:
tan(x) = 1 when x = π/4 or x = 5π/4.
Check the sign of tangent in the intervals between the solutions:
We need to check the sign of tan(x) for x values in the following intervals:
(0, π/4), (π/4, 5π/4), and (5π/4, 2π).
In the interval (0, π/4), tan(x) is positive and less than 1.
In the interval (π/4, 5π/4), tan(x) is positive and greater than 1.
In the interval (5π/4, 2π), tan(x) is negative and less than -1.
Determine the solution set:
Since we are looking for x values that satisfy tan(x) > 1, the only interval that contains such values is (π/4, 5π/4). Therefore, the solution to the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians is:
π/4 < x < 5π/4
In interval notation, we can write:
(π/4, 5π/4)
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in the school cafeteria 6 people can sit together at 1 table. if 2 tables are placed together end to end in a row 10 people can sit together. if 3 tables are placed together in a row how many can be seated? if 4 tables are placed together in a row how many people can be seated? if 5 tables are placed together in a row how many people can be seated? what patterns do you notice?
write an equation that would help find the number of people seated for any number of tables. show all your mathematical thinking giving 40 points and brainliest plss helpp
Answer:
First, we can use the information given to find out how many people can be seated at one table:
One table can seat 6 peopleNext, we can use the information given to find out how many people can be seated in a row of tables:
Two tables can seat 10 peopleTherefore, one row of tables can seat 5 people per tableUsing this information, we can find out how many people can be seated in a row of any number of tables:
Let x be the number of tables placed together in a rowOne row of x tables can seat 5x peopleSo, if 3 tables are placed together in a row, 15 people can be seated. If 4 tables are placed together in a row, 20 people can be seated. If 5 tables are placed together in a row, 25 people can be seated.
The pattern we notice is that the number of people seated in a row of tables increases by 5 for each additional table added.
To summarize, the equation that would help find the number of people seated for any number of tables is:
Number of people seated = 5x, where x is the number of tables placed together in a row.
Answer:
we are given that
6 people can sit together at 1 rectangular table.
2 tables are placed together, 10 people can sit together.
14 people can sit if three tables are put together.
It mean we get a sequence
6,10,14..........
So its making an arithmetic progression, where
First term=a=6
Common difference
Number of terms=number of table
As we know the nth term is given by the formula
Hence 402 people can sit
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Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 17 couples. Complete parts (a) through (c) below.
a. Find the mean and the standard deviation for the numbers of girls in groups of 17 births.
The value of the mean is μ=_____ (Type an integer or a decimal. Do not round.)
The value of the standard deviation is σ=____(Round to one decimal place as needed.)
b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.
Values of ___ girls or fewer are significantly low. (Round to one decimal place as needed.)
Values of ___ girls or greater are significantly high. (Round to one decimal place as needed.)
c. Is the result of 15 girls a result that is significantly high? What does it suggest about the effectiveness of the method?
The result ____ is not. is. significantly high, because 15 girls is greater than. less than. equal to _______ __ girls. A result of 15 girls would suggest that the method _______ is effective. is not effect.
The suggest that the method is effective.
Assuming different groups of couples use a particular method of gender selection and each couple gives birth to one baby, the probability of a girl is 0.5, and the groups consist of 17 couples, then:
a. The mean is μ= 8.5, and the standard deviation is σ= 3.5.
b. The values separating results that are significantly low or significantly high are 8.5 girls or fewer are significantly low, and 11.5 girls or greater are significantly high.
c. The result of 15 girls is significantly high, because 15 girls is greater than 11.5 girls. This would suggest that the method is effective.
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP
Answer:
To find the perimeter of a polygon, we add up the lengths of all the sides. In this case, we have a quadrilateral with sides of length y+8, y+7, y+7, and y+8.
Perimeter = (y+8) + (y+7) + (y+7) + (y+8)
Simplifying by combining like terms, we get:
Perimeter = 4y + 30
Therefore, the perimeter of the quadrilateral is 4y + 30.
Answer:
4y + 30
Step-by-step explanation:
To find:-
The perimeter of the given figure.Answer:-
Perimeter is simply the sum of all sides of any figure. Since here it is a quadrilateral, perimeter would be the sum of all four sides of it .
The four sides given to us are , y+7 , y+8 , y+7 and y+8. We can add them to find out the perimeter as ,
Perimeter = y+7 + y+8 + y+7 + y+8
Perimeter = 4y + 30
Hence the perimeter of the given figure is 4y+30 .
Find the value of 2 - 3x when x = 7
2 - 3x is a(n)__________.
Therefore, when the equation x = 72 - 3x, the value of 2 - 3x is -52.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. It typically contains one or more variables, which are symbols that can represent any number or value. The expressions on both sides of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation. Equations are used to describe relationships between quantities or to solve problems. They can be represented in various forms, including linear equations, quadratic equations, exponential equations, and trigonometric equations. Equations can be solved by performing operations on both sides of the equation to isolate the variable or variables.
Here,
When we are given that x = 72 - 3x, we can solve for x by first adding 3x to both sides of the equation:
x + 3x = 72
Combining like terms, we get:
4x = 72
Dividing both sides by 4, we get:
x = 18
Now that we know x = 18, we can substitute this value into the expression 2 - 3x:
2 - 3x = 2 - 3(18)
2 - 3x = 2 - 54
2 - 3x = -52
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A point A lies on the circle with the equation x^2 + y^2 = 20 and has y-coordinate -4
A point B lies on the circle and has x-coordinate √10
A tangent line set at A intersects the tangent at B at point C
As per the coordinate, the equation of the tangent line is y = (-1/2)x - 3.
In this problem, we are given the equation of a circle, x² + y² = 20, which represents all the points on the plane that are equidistant from the origin (0,0) with a distance of √20 or a radius of
=> √20/2 = 2√5.
Now, let's consider point A. We know that it lies on the circle, so it must satisfy the equation x² + y² = 20. Additionally, we are told that its y-coordinate is -4. Using this information, we can substitute y=-4 into the equation of the circle to get
=> x² + (-4)² = 20,
which simplifies to x² = 4.
Thus, point A has coordinates (±2, -4), and we can determine which one is correct by looking at the circle's equation.
Next, let's consider point B. We are told that its x-coordinate is √10. Since point B lies on the circle, it must also satisfy the equation
=> x² + y² = 20.
Using this equation, we can substitute x=√10 to get
=> (√10)² + y² = 20,
which simplifies to y² = 10. Thus, point B has coordinates (√10, ±√10).
To find the y-intercept, we can use the fact that point A lies on the tangent line. Substituting the coordinates of point A into the equation of the tangent line, we get -4 = (-1/2)(±2) + b, which simplifies to b = -3. Thus, the equation of the tangent line at point A is y = (-1/2)x - 3.
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Complete Question:
A point A lies on the circle with the equation x² + y² = 20 and has y-coordinate -4
A point B lies on the circle and has x-coordinate √10
A tangent line set at A intersects the tangent at B at point C
Find the equation of the tangent line.
4-77 Is the relationship shown in the 28+
graph at right below proportional? If
241
so, find the unit rate. If not, explain
why not.
The graph is/is not proportional
because
Unit rate:
Cost ($)
20
16-
12+
8
2 3 4 5
Number of Books
Purchased
Answer:
Step-by-step explanation:
A graph is proportional if the relationship between the two variables represented on the axes is constant, meaning that if one variable increases, the other variable also increases by the same factor. In other words, the graph forms a straight line that passes through the origin.
To find the unit rate, you need to look for the constant of proportionality, which is the ratio between the two variables represented on the graph. In this case, the variables are the number of books purchased and the cost in dollars.
If the graph is proportional, then the unit rate is the constant of proportionality, which is the cost per book. You can find the unit rate by dividing the total cost by the number of books purchased. For example, if the total cost for 4 books is $16, then the unit rate would be $4 per book.
If the graph is not proportional, then there is no constant of proportionality, and the unit rate cannot be calculated. The relationship between the two variables may be nonlinear, meaning that the rate of change between the variables is not constant.
Find the area of the figure. Use 3.14 for . 8 in 9 in OA. 97.2 in² OB. 86.24 in² O C. 61.12 in² O D. 122.24 in²
The area of the figure is option (C) 61.12 in².
What is the Area of a TriangIe?The area of a triangIe is the region encIosed within the sides of the triangIe. The area of a triangIe varies from one triangIe to another depending on the Iength of the sides and the internaI angIes. The area of a triangIe is expressed in square units, Iike, m2, cm2, in2, and so on.
What is the Area of CircIe?The area of a circIe is the amount of space encIosed within the boundary of a circIe. The region within the boundary of the circIe is the area occupied by the circIe. It may aIso be referred to as the totaI number of square units inside that circIe. Area of CircIe = πr2 or πd2/4 in square units, where
(Pi) π = 22/7 or 3.14.
r = radius of the circIe
d = diameter of the circIe
Pi (π) is the ratio of circumference to diameter of any circIe. It is a speciaI mathematicaI constant.
Area of triangIe = ½ x B x H
Given Height = 8 in
Given Breath = 9 in
Area of TriangIe = ½ x 8 x 9 = 36 in²
Area of haIf circIe = ½ (pi x r²)
= ½ (3.14 x 16)
= (½ x 50.24) in²
= 25.12 in²
Area of the figure wiII be 36 in² + 25.12 in² = 61.12 in²
Option C wiII be the correct option.
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The area of the figure will be 36 in² + 25.12 in² = 61.12 in². Option C will be the correct option.
What is the Area of CircIe?
The area of a circIe is the amount of space enclosed within the boundary of a circIe. The region within the boundary of the circIe is the area occupied by the circIe. It may aIso be referred to as the total number of square units inside that circle.
Area of CircIe = πr2 or πd2/4 in square units, where
(Pi) π = 22/7 or 3.14.
r = radius of the circIe
d = diameter of the circIe
Pi (π) is the ratio of circumference to diameter of any circIe. It is a speciaI mathematicaI constant.
Area of triangle = ½ x B x H
Given Height = 8 in
Given Breath = 9 in
Area of TriangIe = ½ x 8 x 9 = 36 in²
Area of haIf circIe = ½ (pi x r²)
= ½ (3.14 x 16)
= (½ x 50.24) in²
= 25.12 in²
Therefore, Area of the figure will be 36 in² + 25.12 in² = 61.12 in²
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A population of bacteria in culture increases according to the model P=300(2.7)^0.02t, where T is the number of hours and T=0 corresponds to 9:00 AM.
a. Use this model to estimate the number of bacteria at 11 AM.
b. Graph the function and name the p-intercept. Describe what the p-intercept represents and a reasonable domain and range for this situation.
This means that when the bacteria culture is first created (at 9:00 AM), there are already 300 bacteria present.
What is a graph?
A graph is a visual representation of data or mathematical functions. Graphs are used to present data in a clear and concise manner, making it easier for people to understand and interpret the information being presented.
a. To estimate the number of bacteria at 11 AM, we need to plug in t = 2, since 11 AM is two hours after 9:00 AM. Therefore:
P = 300(2.7)^(0.02*2)
P = 300(2.7)^0.04
P ≈ 369.13
So, there are approximately 369.13 bacteria at 11 AM.
b. To graph the function, we can use a graphing calculator or software. The p-intercept is the point where the graph intersects the y-axis, which occurs when t = 0. We can find the p-intercept by setting t = 0 in the equation:
P = 300(2.7)^(0.02t)
P = 300(2.7)^(0.02*0)
P = 300
Therefore, the p-intercept is (0, 300). This means that when the bacteria culture is first created (at 9:00 AM), there are already 300 bacteria present.
The domain of this situation is all non-negative values of t, since time cannot be negative. The range is all positive values of P, since the number of bacteria is always increasing. Therefore, a reasonable domain for this situation would be [0, ∞) and a reasonable range would be (0, ∞).
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2(2x-5)=-18 solve the equation algebraically. show all work
Answer:
Step-by-step explanation:
2(2x-5) = 18 (FOIL)
4x-10=18
4x = 28
x= 7
Answer:
x = -2
Step-by-step explanation:
2(2x - 5) = -18
Divide both sides by 2.
2x - 5 = -9
Add 5 to both sides.
2x = -4
Divide both sides by 2.
x = -2
Solve the triangle PQR (find the measures of ∠P, ∠Q, and side PQ).
(I need help finding both angle measure and side measure, please and thank you!)
Therefore , the solution of the given problem of triangle comes out to be the angles P and Q have measurements of roughly 39.39° and 58.10°, respectively.
What precisely is a triangle?A polygon is a hexagon if it has over one extra segment. It's shape is a simple rectangle. Only the sides A and B can differentiate something like this arrangement from a regular triangle. Despite the exact collinearity of the borders, Euclidean geometry only produces a portion of the cube. Three edges and three angles make up a triangle.
Here,
The rule of cosines can be applied to the triangle PQR to determine the length of side PQ:
=> PQ² = PR² + QR² - 2(PR)(QR)cos(∠PQR)
=> PQ² = 9² + 12² - 2(9)(12)cos(62°)
=> PQ² ≈ 110.03
=> PQ ≈ 10.49
As a result, side PQ is roughly 10.49 units long.
The rule of sines can then be used to determine the dimensions of angles P and Q:
=> sin(∠P) / PQ = sin(62°) / PR
=> sin(∠P) / 10.49 = sin(62°) / 9
=> sin(∠P) ≈ 0.6322
=> ∠P ≈ 39.39°
=> sin(∠Q) / PQ = sin(77°) / QR
=> sin(∠Q) / 10.49 = sin(77°) / 12
=> sin(∠Q) ≈ 0.8559
=> ∠Q ≈ 58.10°
As a result, the angles P and Q have measurements of roughly 39.39° and 58.10°, respectively.
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Please helppp grid question
0.1 for the top left, 0.2 for bottom middle
Pls help!!! Asap
Possible answers
Al m=5. L0=14, NO-12
B) m=7, 10= 14, NO= 14
C m=7, LO=12, NO= 12
D) m=4, L0=13, NO = 14
E) m=5, LO= 14, NO= 15
Answer:
C
m= 7 LO= 14 MO= 14
Step-by-step explanation:
LO and NO are going to be the same length
m + 7 = 2m
to get the variable alone subtract m from both sides
7 = m)
plug 7 into both equations
7 + 7 = 14
2 x 7 = 14
I need help with this question
Answer: the answer is c I think
5. {MCC.6.RP.A.3B} How long will it take you to ski a distance of 24 miles at a speed of 6 miles per 30 minutes?
*
1 point
Answer:
Step-by-step explanation:
It will take you 8 hours to ski a distance of 24 miles at a speed of 6 miles per 30 minutes. This is because you will have to travel the 24 miles at a rate of 6 miles every 30 minutes, so you will need to travel for 4 hours at this rate to cover the full distance. Thus, it will take you 8 hours to ski the full 24 miles at a rate of 6 miles per 30 minutes.
Answer:
120 minutes / 2 hours
Step-by-step explanation:
time = distance / velocity
[tex]time = \frac{24}{(6/30)} \\time = 120 minutes[/tex]
NEED HELP PLEASE HELP
Answer: B --3/2
Step-by-step explanation:
-4,8 TO -2,5
You would go down -3 steps first
Then you would go 2 steps.
Not sure if this is right but hopefully it works :D
Lily has an inspirational board on her bedroom wall.The number of photos on lilys inspiration board is 4 more than twice the number of quotes on her board.she has a combined total of 37 quotes and photos on her board.How many quotes are on lily inspiration board? How many pho are on lily inspiration board
In response to the stated question, we may state that As a result, Lily has equation 26 images on her inspiration board.
What is equation?In mathematics, an equation is a statement that states the equivalence of two expressions. An equation consists of two sides separated by an algebraic equation (=). For instance, the argument "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.
Assume there are x quotations on Lily's board.
According to the issue, the quantity of photographs on Lily's board is four times more than the number of quotes. As a result, the number of photographs may be expressed as 2x + 4.
We also know that there are 37 quotations and photographs on Lily's board. So let us create an equation:
x + (2x + 4) = 37
3x + 4 = 37
3x = 33
x = 11
So Lily's inspiration board contains 11 quotations.
To calculate the number of images, enter x = 11 into the equation we discovered earlier:
2x + 4 = 2(11) + 4 = 26
As a result, Lily has 26 images on her inspiration board.
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The following data was collected from 40 of Mr. O'Block's AP Physics students in 2018.
Listed below are their scores (out of 100) on the second semester final exam:
58
70
63
73
71
68
85
74
66
87
88
91
Intervals Frequency
[0-10)
[10-20)
[20-30)
[30-40)
(40-50)
[50, 60)
[60-70)
[70-80)
[80-90)
[90-100)
2015 no
80
92
O
93
80
84.
61
82
98
85
83
97
88
89
91
77
80
1) Using the data above, create a well labeled histogram on the axes below.
74
62
71
80
0
93
71
99
102
90
99
100
2
HELP ME PLEASE I REALLY NEED IT!
Draw rectangles for each interval with a height equal to the frequency. The rectangles should be adjacent to each other and have equal width.
What is rectangle?
A rectangle is a two-dimensional shape with four sides, where the opposite sides are equal and parallel, and all angles are right angles (90 degrees).
To create a histogram, you need to first group the data into intervals or bins. You can use the intervals given in the table as a guide, or you can create your own intervals.
For this example, I will use the intervals [0-10), [10-20), [20-30), [30-40), [40-50), [50-60), [60-70), [70-80), [80-90), and [90-100).
Next, count the number of scores that fall into each interval. For example, there are no scores between 0 and 10, one score between 10 and 20, two scores between 20 and 30, and so on.
Therefore, plot the intervals on the x-axis and the frequency (or count) on the y-axis. Draw rectangles for each interval with a height equal to the frequency. The rectangles should be adjacent to each other and have equal width.
below is the histogram -
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Yesterday, Eve ran a mile in 15 minutes. Today, she ran a mile in 5 minutes. What is the percent decrease in the time it takes her to run a mile? Round to the nearest whole number.
Eve now completes a percent mile in about 67% less time than she did previously.
How does math define a percent?In essence, percentages are fractions with a denominator of 100. The cent symbol (%) is placed next to a number to indicate that it is a percentage. As an illustration, if you answered 75 of 100 questions correctly on an examination (75/100), then would have received a score of 75% percent drop (original value − new value) / initial value x 100%).
Let's use "t1" for yesterday's time and "t2" for today.
t1 = 15 minutes, t2 = 5 minutes.
Using the equation, we obtain:
percentage decrease equals (t1 - t2) / (t1 x 100%) percentage decrease equals (15 - 5) / (15 x 100%) percentage decrease equals 10 / (15 x 100%) percentage decrease equals 0.666... x 100% percentage decrease equals 67%
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To solve the problem using these steps, what are the dimensions of the rectangle he should draw? on a coordinate plane, parallelogram a b c d has points (1, negative 1), (3, 2), (1, 3), and (negative 1, 0). 2 units by 4 units 3 units by 2 units 4 units by 4 units 5 units by 6 units
As per the given coordinates, dimensions of the rectangle are √13 x √13.
One way to do this is to find the distance between two parallel sides of the parallelogram. In this case, we can look at sides AB and CD, which are parallel to each other.
The distance between points A and B is the
=> √((3-1)² + (2-(-1))²) = √13
which simplifies to the square root of 13. Similarly, the distance between points C and D is the
=> √((1-(-1))² + (3-0)²) = √13.
Therefore, the length of the rectangle is the distance between sides AB and CD, which is the square root of 13.
Therefore, the width of the rectangle is 2 units. So the dimensions of the rectangle are 2 units by the square root of 13 units.
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Answer:
4 units by 4 units
Step-by-step explanation:
i got it correct on edg :)
Find the sample space for the experiment. (Enter your answer in set notation) You select two marbles (without replacement) from a bag containing eight red record the color of each marble. three blue martes (denote bye), and eight yellow martie (denote by Y). You
The total number of marbles in the bag is[tex]8 + 3 + 8 = 19[/tex]. We can represent the sample space as follows:
[tex]S = {(R, R), (R, B), (R, Y), (B, R), (B, B), (B, Y), (Y, R), (Y, B), (Y, Y)}[/tex]
Note that the sample space contains 9 elements.
The experiment involves selecting two marbles (without replacement) from a bag containing eight red marbles (denoted by R), three blue marbles (denoted by B), and eight yellow marbles (denoted by Y).
The sample space of the experiment is the set of all possible outcomes.
Each outcome is represented by an ordered pair of the colors of the two marbles selected. Since we are selecting two marbles without replacement, the order in which we select the marbles matters. Hence, we use ordered pairs to represent each outcome.
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6. If x is an integer, what is the solution set of 3 < x≤ 6?
a) {3, 4, 5}
b) {4, 5, 6}
(c)(3, 4, 5, 6}
d) {4, 5}
Answer:
B
Step-by-step explanation:
4, 5, and 6 are greater than 3 and they are also less than or equal to 6.
an insurance policy is written to cover damage to a luxury sports car. the amount of damage is uniformly distributed between $0 and $46000. in order to decrease the insurance premium, the insurance company decides to charge an ordinary deductible, d, so that the expected insurance payment with the deductible is 60 % of the expected insurance payment without the deductible. determine the value of the deductible, d.
In order to decrease the insurance premium, the insurance company should charge an ordinary deductible of $18,400.
The expected insurance payment without a deductible is the full value of the damage, or $46,000.
With a deductible.
The expected insurance payment would be 60% of that, or $27,600.
To find the value of the deductible, d, subtract the expected insurance payment with a deductible from the expected insurance payment without a deductible. This gives us d = $46,000 - $27,600 = $18,400.for such more questions on Statistics
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If you run towards a faraway friend at 5 miles per hour and she bikes towards you at 15 miles per hour, how many miles closer are you to each other after 1 hour?
Using the unitary method we calculate that the friend would be 20 miles closer in an hour.
If you are running towards a faraway friend at a speed of 5 miles per hour and she is biking towards you at 15 miles per hour, According to relative motion's concept, the total speed at which you are approaching each other is:
5 miles / hour - (- 15 miles / hour) = 20 miles / hour
Also, we know that
speed= distance/time according to which, after 1 hour, you and your friend would have closed the distance by,
20 miles/hour × 1 hour = 20 miles
Therefore, you would be 20 miles closer to each other after 1 hour.
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At the start of 2014
Mikes car was worth 12000 the value of the car decreased by 30%
Answer:
If the value of Mike's car decreased by 30%, we can calculate the new value of the car as follows:
New value = Original value - (Percentage decrease × Original value)
Percentage decrease = 30%
Original value = 12000
New value = 12000 - (0.30 × 12000)
New value = 12000 - 3600
New value = 8400
Therefore, at the end of the decrease, the value of Mike's car was 8400.
PLEASE HELP ME!
i have no clue what to do
Answer:
Step-by-step explanation:
you are going to give more info ?????
Statistics question: (answer and explanation much appreciated)
a) The probability that the player is a non-pitcher not from the Dominican Republic is given as follows: 0.7578 = 75.78%.
b) The probability that a Dominican player is a pitcher is given as follows: 0.8595 = 85.95%.
c) The probability that a non-pitcher is not Dominican is given as follows: 0.4985 = 49.85%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
Of the Dominican players, the percentages are given as follows:
5.6% of 42%.x% of 58%.The total percentage of Dominican players is of 10.5%, hence the value of x is given as follows:
0.056 x 0.42 + 0.58x = 0.105
x = (0.105 - 0.056 x 0.42)/0.58
x = 0.1405.
Of the 58% of the batter, 14.05% are from the Dominican Republic, hence the probability of chosen a batter not from the Dominican Republic is of:
p = 1 - 0.1405/0.58
p = 0.7578 = 75.78%.
14.05% of the players from the Dominical Republic are batters, hence the probability of choosing a pitcher is given as follows:
1 - 0.1405 = 0.8595 = 85.95%.
Of the 58% of the batters, 14.05% are Dominican, hence the 85.95% are not Dominican, thus the probability of choosing a non-Dominican batter is given as follows:
0.58 x 0.8595 = 0.4985 = 49.85%.
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consider using a z test to test h0: p 5 .6. determine the p-value in each of the following situations. a. ha:p..6,z51.47 b. ha:p,.6,z522.70 c. ha:p?.6,z522.70 d. ha:p,.6,z5.25
a) P-value = P(z<1.47) = 0.9292.
b) P-value = P(z>2.70) = 0.0036.
c) P-value = 2 × P(z>2.70) = 0.0072.
d) P-value = P(z>2.5) = 0.0062.
Z-test is a statistical test for the null hypothesis, which refers to the population mean, where the population standard deviation is known. P-value represents the probability value for any hypothesis, where a small p-value indicates that the null hypothesis is less accurate.
P-value, for the given values of z-test is calculated as follows: a) For ha: p < .6, z=1.47The p-value for this hypothesis test is calculated as follows: P-value = P(z<1.47) = 0.9292. Therefore, the P-value is 0.9292. b) For ha: p > .6, z=2.70The p-value for this hypothesis test is calculated as follows.
P-value = P(z>2.70) = 0.0036. Therefore, the P-value is 0.0036.c) For ha: p ≠ .6, z=2.70The p-value for this hypothesis test is calculated as follows: P-value = 2 × P(z>2.70) = 0.0072.
Therefore, the P-value is 0.0072.d) For ha: p > .6, z=2.5The p-value for this hypothesis test is calculated as follows: P-value = P(z>2.5) = 0.0062. Therefore, the P-value is 0.0062.
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you're playing a game where you defend your village from an orc invasion. there are 3 33 characters (elf, hobbit, or human) and 5 55 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from. if you randomly choose your character and tool, what is the probability that you won't be a hobbit or use an umbrella?
There is an 11/15, or around 0.733, chance that you won't be a hobbit or wear an umbrella.
Since, A total of 3 x 5 = 15 outcomes are possible given the presence of 3 characters and 5 defense mechanisms.
There are three scenarios if the character is a hobbit (hobbit with magic, hobbit with sword, and hobbit with shield), three scenarios where the tool is an umbrella (any character with an umbrella), and one scenario where neither.
As a result, there are the following number of possibilities where neither the character nor the tool is a hobbit:
15 - 3 - 1 = 11
One of these 11 outcomes is likely to occur at a rate of:
= 11/15
As a result, there is an 11/15, or around 0.733, chance that you won't be a hobbit or wear an umbrella.
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Select all numbers that are solutions to the inequality w < 1
-1. 3
5
0. 9
-5
0
The numbers that are solutions to the inequality w < 1 are: -1.3, -5 and 0
Numbers 5 and 0.9 are not solutions to the inequality because they are greater than or equal to 1. An inequality is a statement that compares two quantities or expressions using a mathematical symbol indicating their relative sizes. Inequalities are used to describe a range of values or solutions, rather than a single solution, and are often represented on a number line. Inequalities are commonly used in algebra, calculus, and other areas of mathematics, as well as in science, economics, and engineering. Solving inequalities involves finding all possible values of the variable that satisfy the inequality. This can be done by applying algebraic operations and graphing techniques to isolate the variable and determine the appropriate range of values.
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