Answer:
1/4
Step-by-step explanation:
The probability of tossing tails on a fair coin is 1/2. The probability of rolling a multiple of 2 on a fair six-sided number cube is 1/2 (since there are three multiples of 2: 2, 4 and 6). Since these two events are independent, the probability of both events happening is the product of their individual probabilities: (1/2) * (1/2) = 1/4.
3
Rewrite the following equation as a function of x.
21x+3y-45=0
A. f(x)= 7x-15
B. f(x)=-7x-6
C. f(x)=3x+6
D. f(x) = -7x + 15
Answer:
D. -7x + 15
Step-by-step explanation:
In order to rewrite the equation as a function of x, we have to isolate y on the left-hand side of the equation:
[tex](21x+3y-45=0)+45\\(21x+3y=45)-21x\\(3y=-21x+45)/3\\y=-7x+15[/tex]
The line segment AB has coordinates A(2, -3) and B(5, 9). What is the slope of its perpendicular bisector?
The answer of the given question based on the line segment is , the slope of the perpendicular bisector of the line segment AB is -1/4.
What is Slope?Slope is a measure of the steepness of a line on a graph. It describes the rate at which the line rises or falls as it moves from left to right, and it is defined as ratio of vertical change (rise) to horizontal change (run) between any two points on line.
To find the slope of the perpendicular bisector of the line segment AB, we first need to find the midpoint of AB:
Midpoint of AB = [(x-coordinate of A + x-coordinate of B)/2, (y-coordinate of A + y-coordinate of B)/2]
= [(2 + 5)/2, (-3 + 9)/2]
= [3.5, 3]
So the midpoint of AB is (3.5, 3).
The slope of line segment AB is:
slope of AB = (y-coordinate of B - y-coordinate of A)/(x-coordinate of B - x-coordinate of A)
= (9 - (-3))/(5 - 2)
= 4
The slope of a line perpendicular to AB is the negative reciprocal of the slope of AB. So the slope of the perpendicular bisector of AB is:
slope of the perpendicular bisector=-1/slope of AB
= -1/4
Therefore, the slope of the perpendicular bisector of the line segment AB is -1/4.
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I’m stuck on this 3 questions help
Answer:Umm... what grade am I gonna learn that in?
Step-by-step explanation:
Sorry, I tried but I have no idea what that is...
Find 3 times the quantity 7.25 minus 4.5
Answer:
17.25
Step-by-step explanation:
3*7.25= 3*7+ 3*0.25=21+0.75=21.75. 21.75-4.5=17.25.
Answer:
376.58 or 20.570824
Step-by-step explanation:
combined event. Randomly drawing and immediately eating two red pieces of candy in a row from a bag that contains red pieces of candy out of 52 pieces of candy to
The probability of randomly drawing and immediately eating two red pieces of candy in a row from a bag that contains 6 red pieces of candy out of 37 pieces of candy total is 5/222, or approximately 0.0225 or 2.25%.
Let's calculate the probability of the first draw being red. Since there are 6 red pieces of candy out of a total of 37 pieces of candy, the probability of drawing a red candy on the first try is 6/37.
Now, let's calculate the probability of the second draw being red given that the first draw was red. Since we did not replace the first candy before drawing the second one, there are only 5 red candies left out of a total of 36 candies. Therefore, the probability of drawing a second red candy is 5/36.
To find the probability of the combined event of drawing and immediately eating two red candies in a row, we need to multiply the probability of the first event by the probability of the second event, given that the first event occurred. So the probability of both events occurring is:
(6/37) x (5/36) = 5/222 or approximately 0.0225 or 2.25%.
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Complete Question:
Determine whether the following individual events are independent or dependent. Then find the probability of the combined event.
Randomly drawing and immediately eating two red pieces of candy in a row from a bag that contains 6 red pieces of candy out of 37 pieces of candy total.
Let us say, there are 2 positive numbers,both are more than 20, and .
They are connected to eachother such that when summed up,they become 100.
Also, where .
Find of and in:-
2.n=2,
3.n=3,
4.n=4 &
5.n=5
Hint:Answer can also be in decimals,for example if X=24.5 and Y=77.5,then,
Yn/X=(77.5x1)/24.5=3.16(Approximately 3).
The valid solutions are:
n = 2: X ≈ 33.33, Y ≈ 66.67
n = 3: X = 25, Y = 75
How to solve for the positive numbersLet X and Y be two positive numbers, both greater than 20, such that X + Y = 100 and Y = nX. We are asked to find the values of X and Y for different values of n.
n = 2
Y = 2X
X + Y = 100
X + 2X = 100
3X = 100
X = 100/3 ≈ 33.33
Y = 2 * 33.33 ≈ 66.67
n = 3
Y = 3X
X + Y = 100
X + 3X = 100
4X = 100
X = 100/4 = 25
Y = 3 * 25 = 75
n = 4
Y = 4X
X + Y = 100
X + 4X = 100
5X = 100
X = 100/5 = 20
Y = 4 * 20 = 80
However, the condition states that both numbers must be greater than 20. In this case, X = 20, so this solution does not satisfy the condition. We cannot find the values of X and Y for n = 4, as they do not satisfy the given conditions.
n = 5
Similar to the case with n = 4, for any higher values of n, the value of X will be equal to or smaller than 20, which does not satisfy the given conditions. Therefore, we cannot find the values of X and Y for n = 5, as they do not satisfy the given conditions.
In summary, the valid solutions are:
n = 2: X ≈ 33.33, Y ≈ 66.67
n = 3: X = 25, Y = 75
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The midpoint of a line segment is (8,5),and one of the endpoints is (13,6).what are the coordinates of the other endpoint?
The coordinates of the other endpoint of the line segment are (13-8, 6-5), which simplifies to (5,1).
What is coordinates?Coordinates are a set of two or more numbers that represent a location on a map, chart, graph, or in a geographic coordinate system. Coordinates can be in a two-dimensional format, such as latitude and longitude, or in a three-dimensional format, such as X, Y, and Z. Coordinates are often used to pinpoint exact locations on a map, such as a house, city, or country. Coordinates can also be used to define an area, such as a region or district.
The midpoint of a line segment is the point which lies in the middle of two other points along the line. The coordinates of the midpoint of a line segment are (8,5). This means that the line segment in question has one endpoint at (13,6) and the other endpoint is located at the midpoint's opposite. The coordinates of the other endpoint of the line segment can be determined by subtracting the midpoint's coordinates from the known endpoint's coordinates.
Therefore, the coordinates of the other endpoint of the line segment are (13-8, 6-5), which simplifies to (5,1). Thus, the coordinates of the other endpoint of the line segment are (5,1).
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The coordinates of the other endpoint are (3, 4).
To find the coordinates of the other endpoint of the line segment, given the midpoint (8,5) and one endpoint (13,6), you can use the midpoint formula.
The midpoint formula is: Midpoint = ((a + b) / 2, (c + d) / 2)
You are given the midpoint (8,5) and one endpoint (13,6), so you can set up the following equations using the midpoint formula:
8 = (13 + b) / 2
5 = (6 + d) / 2
Now, solve for b and d, which represent the coordinates of the other endpoint:
8 * 2 = 13 + b
16 - 13 = b
b = 3
and
5 * 2 = 6 + d
10 - 6 = d
d = 4
So, the coordinates of the other endpoint are (3, 4).
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Find the average rate of change of f(x) = 3x² - 5 on the interval [4, t]. Your answer will be an expression
involving t
Answer: [tex]\frac{3t^{2}-48 }{t-4}[/tex]
Step-by-step explanation:
Rate of change is still rise/run or your y's/x's
When x=4, y=3(4)²-5=43
When x=t, y=3t²-5
rate of change = [tex]\frac{3t^{2}-5-43 }{t-4}[/tex] = [tex]\frac{3t^{2}-48 }{t-4}[/tex]
Which of the following best describes a consumer
A consumer is best described as the end user of a product
Solve the following equations using any method. Show your work. Eind the exact solution. Write
the solutions in simplest form.
5. x² + 4x = 3
The equation is solved to a simplified form as x = -4 ±√14
How to solve the expression
From the information given, we have that the quadratic equation is given as;
x² + 4x = 3
collect the like terms
x² + 4x - 3 = 0
Using the quadratic formula, we have
x = -b±√b² - 4ac/2a
From the equation;
ax + bx + c = 0
a = 1
b = 4
c = -3
Substitute the values
x = -4 ± √(4)² - 4(1)(-3)/2(1)
expand the bracket, we get;
x = -4 ± √16 + 12/2
Add the values
x = -4 ± √28/2
Divide the values
x = -4 ±√14
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PLEASE HURRY AND ANSWER
The figure shows a 300 foot tower on the side of a hill that forms a * 7 deg angle with the horizontal. Find the length of each of the two guy wires that are anchored 120 feet uphill and downhill from the tower's base and extend to the top of the tower.
Part A=
Part B=
The length of each of the two guy wires that are anchored are 328.85 ft and 323.45 ft
Finding the length of each of the two guy wiresStart by calculatng the height h from the horizontal to the base of the hill
So, we have
tan(7) = h/120
This gives
h = 14.7
The length of the first guy is
Length² = (14.7 + 120)² + (300)²
Evaluate
Length = 328.85
Next, we calculate the base length b as
b² = (120)² + (14.7)²
b = 120.9
The length of the second guy is
Length² = (120.9)² + (300)²
Length = 323.45
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Thaddeus models the number of hours of daylight in his town as
D(t) = 2.5sin(t) + 12, where D is the number of daylight hours and tis
the time in months since January 1.
What are the least and greatest numbers of daylight hours over the course of
a year?
A. Least: 9.5 hours; greatest: 14.5 hours
B. Least: 7.25 hours; greatest: 14.5 hours
C. Least: 2.5 hours; greatest: 12 hours
D. Least: 6 hours; greatest: 12 hours
The correct answer is option A:
Least: 9.5 hours; greatest: 14.5 hours.
Since, We have;
The function D(t) has a maximum value of 2.5 + 12 = 14.5 hours when sin(t) = 1, which occurs twice per year when,
t = π/2 + 2πn
or t = 3π/2 + 2πn for integers n.
The function has a minimum value of -2.5 + 12 = 9.5 hours
when sin(t) = -1,
which occurs twice per year when t = -π/2 + 2πn or t = 5π/2 + 2πn for integers n.
Therefore, the least number of daylight hours over the course of a year is 9.5 hours, and the greatest number of daylight hours over the course of a year is 14.5 hours.
So, the correct answer is option A:
Least: 9.5 hours; greatest: 14.5 hours.
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a tv network claimed about 4,50,00,000 people ( rounded to the nearest ten lakhs ) watched the coverage of a special event. What could be the greatest possible and least possible number of people who could have watched the program so as to make the claim of TV network correct?
The claim of the TV network that 4,50,00,000 people watched the coverage of the special event could be correct if the actual number of people who watched the program was anywhere between 4,49,95,000 and 4,50,05,000.
Rounding to the nearest ten lakhs means rounding to the nearest a million.
So, 4,50,00,000 rounded to the nearest ten lakhs is either 4,40,00,000 or 4,60,00,000.
To find the greatest possible and least possible number of people who could have watched the program, we need to consider the range of values that would round to 4,50,00,000.
For the least possible value, we need to subtract 5 lakhs from 4,50,00,000:
4,50,00,000 - 5,00,000 = 4,49,95,000
So, the least possible number of people who could have watched the program is 4,49,95,000.
For the greatest possible value, we need to add 5 lakhs to 4,50,00,000:
4,50,00,000 + 5,00,000 = 4,50,05,000
So, the greatest possible number of people who could have watched the program is 4,50,05,000.
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Do the following side lengths form a unique triangle? 5,7,13
In order for three sides to make a triangle, if any two sides are added together, their sum should be greater than the third side:
→ 5 + 7 = 12 < 13 (DOES NOT check off the rule)
→ 7 + 13 = 20 > 5 (Checks off the rule)
→ 5 + 13 = 18 > 7 (Checks off the rule)
As shown, even though 2 of the statements check off the rule the third one does not, this means that the sides don't make a triangle.
7. Find the total distance from the
waterfalls to the canoes and then
to the fishing area.
The total distance from the waterfalls to the canoes and then to the fishing area is 12.
How to calculate the distanceFrom 9 and 10 we already know their coordinates. The distance from waterfax: to canoes: 2-(-4) = 6.
The distance from canoes to fishing is also 6. Understand that the total distance = 6+6 = 12
In conclusion, the total distance from the waterfalls to the canoes and then to the fishing area is 12.
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Given -13.84(4.7), find the product.
Answer: -65.048
Step-by-step explanation:
-13.84(4.7) = -65.048
(you could also use a calculator)
The vertices of the parallelogram are A(-1, -2), B(3, -2), C(4, 3) and D(0, 3). Find the area of the parallelogram.
PLEASE HURRY
Answer:
19.6 units
Step-by-step explanation:
A = base x height
Pythagoras to get the height
height must be vertical in the base
In circle O, OP=3 and m∠POQ=80°. Find the area of shaded sector. Express your answer as a fraction times π.
Answer:
[tex]2\pi[/tex]
Step-by-step explanation:
First, let's find the area of circle O.
The formula is [tex]\pi r^2[/tex].
Plugging in the radius 3, we get the area is [tex]9\pi[/tex].
To get the area of the sector, we have to find out what fraction of 360 degrees the POQ is.
[tex]\frac{80}{360} = \frac{2}{9}[/tex].
We now multiply [tex]\frac{2}{9}[/tex] by 9, getting 2.
The answer is [tex]2\pi[/tex]
pleaseee hurrrrrryyy
Angle C is 25 degrees (Vertically opposite angles)
What are vertically opposite angles?
An angle pair created by the intersection of two straight lines or rays is said to be vertically opposite. Four angles are formed at the intersection point of two lines. Angles created by the junction of two lines that are opposite to one another vertically are known as vertically opposing angles. They are sometimes referred to as pairs of angles that are vertically opposed.
Since we have angles on a straight line;
B + 25 = 180
B = 155 degrees
Since B and D are vertically opposite, D = 155 degrees
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GIVING BRNLIEZT Use the net to compute the surface area of the three-dimensional figure.
Responses
A 130 units2
130 units 2
B 182 units2
182 units 2
C 166 units2
166 units 2
D 152 units2
The net to compute the surface area of the three-dimensional figure is 166 square units.
We have,
the surface area of the three-dimension figure:
The surface area is the area calculated for the three-dimensional object. As the three-dimensional object is made up of 2D faces, the surface area is the sum of the areas of all the faces of the figure.
A cuboid is a three-dimensional figure having length, width, and height. The surface area of a cuboid can be calculated by adding together the areas of the six faces.
For the given cuboid, length l = 8 , width w = 5 and height h = 5.
The surface area of the figure is given by;
SA = 2 (lw+lh+wh)
=70 + 56 + 40
= 166
Hence, the net to compute the surface area of the three-dimensional figure is 166 square units.
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compare the function with the parent function without graphing y=sqrt(x-3)
With comparison to parent function, the transformation is 3 units to right.
The given function is y=√x.
The parent function is the simplest form of the type of function given y=√(x-3).
The transformation from the first equation to the second one can be found by finding a, h, and k for each equation.
y=a√(x-h)+k
Factor a 1 out of the absolute value to make the coefficient of x equal to 1.
y=√x
Factor a 1 out of the absolute value to make the coefficient of x equal to 1.
y=√(x-3).
Here, a=1, h=3 and k=0
To find the transformation, compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis, and if there is a vertical stretch.
Parent Function: y=√x
Horizontal Shift: Right 3 Units
Vertical Shift: None
Reflection about the x-axis: None
Vertical Compression or Stretch: None
Therefore, with comparison to parent function, the transformation is 3 units to right.
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A multiple-choice test consists of 30 questions with possible answers of a, b, c, d, e. Estimate the probability that with random guessing the number of correct answers is at least 14. Use Excel to obtain more accuracy.
Note that in tis case, the estimated probability of getting at least 14 correct answers is 0.038, or about 3.8%.
How is this so?The binomial distribution may be used to solve this problem, where the number of trials (n) is 30, the chance of success (p) is 1/5 (since there are 5 alternative responses and only one is accurate), and we wish to know the likelihood of receiving at least 14 correct answers.
We may calculate the cumulative chance of receiving 13 or fewer right answers using a calculator or statistical software. As a result, the likelihood of receiving at least 14 accurate answers is:
1 - 0.962 = 0.038
With random guessing, the estimated probability of getting at least 14 correct answers is 0.038, or about 3.8%.
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Choose all that are true. A rhombus is a :
A. Trapezoid
B. Quadrilateral
C. Rectangle
D. Parallelogram
E. Square
I thought square since a square is a rhombus and a quadrilateral since it is one I think.
Answer:
B and D are correct. A rhombus is a quadrilateral and a parallelogram.
Tar Heel Corporation had current and accumulated E&P of $530,000 at December 31 20X3. On December 31, the company made a distribution of land to its sole shareholder, William Roy. The land's fair market value was $130,000 and its tax and E&P basis to Tar Heel was $28,000. William assumed a mortgage attached to the land of $11,500. The tax consequences of the distribution to William in 20X3 would be:
The tax consequences of the distribution to William in 20X3 would be Dividend of $118,500 and a tax basis in the land of $130,000.
How to find the tax consequences ?The tax consequences would include the dividend that the William Roy, the shareholder, gets from owning the land. This dividend is:
= Market value of land - Mortgage attached
= 130, 000 - 11, 500
= $ 118, 500
Then, William Roy would have to recognize a tax basis on the land for the fair market value. This means that the tax basis would therefore be $ 130, 000.
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What is the answer to this question
Answer:
4th option
Step-by-step explanation:
observing the graph we can say that the racing game is approximately 25% of the total
so
if 1 hour is ----------------------> 100%
X-----------------------------25%
x=25/100------> 1/4=0.25 hours
convert to minutes
0.25*60---------> 15 minutes
the answer is 15 minutes
Milan and Nicole are standing on a riverbank, 100 meters apart, at points A and B respectively. (See the figure below.) Nicole is 130 meters from a house located across the river at point C. Suppose that angle A (angle BAC) is 55°. What is the measure of angle B (angle ABC)? Round your answer to the nearest tenth of a degree.
The angle that has been marked as B can be obtained as 86 degrees.
Solving a triangleTo solve a triangle, you need to find the measures of its angles and sides. There are different methods to solve a triangle, depending on the information given.
If you are given the measures of all three angles, you can use the fact that the sum of the angles in a triangle is always 180 degrees to find the missing side lengths.
Using the sine rule;
100/Sin C = 130/Sin 55
Sin C = 100 Sin 55/130
C = Sin-1( 100 Sin 55/130)
C = 39 degrees
Now;
B = 180 - (55 + 39)
B = 86 degrees
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1) What is the set of solutions for each problem? :
Find all x ∈ (All Real Numbers) such that
x^{2} - x + 6=0
2) What is the set of solutions for each problem?
Find all x∈ (All Real Numbers) such that
(x-3)²(2x+(√3))(x+5)=0
3) What is the set of solutions for each problem?
Find all even integers that are divisible by 5.
In format of : "The set of elements is {__ : n∈ ___}
A clinical psychologist noticed that the siblings of his obese patients are often not overweight. He hypothesized that the normal-weight siblings consume fewer daily calories than the obese patients. To test this using a matched pairs design, he compared the daily calorie intake of obese patients to that of a “matched” normal-weight sibling. The calories consumed for each sibling pair are given in the table on page 304.
Test whether or not obese patients consume significantly more calories than the normal-weight at a .05 level of significance.
The calculated t-value (4.14) is greater than the critical t-value (2.447), we can reject the null hypothesis and conclude that obese patients consume significantly more calories than their normal-weight siblings at a .05 level of significance.
To test whether obese patients consume significantly more calories than their normal-weight siblings, we can perform a paired t-test at a significance level of .05.
First, we need to calculate the differences in calorie intake between each sibling pair:
Sibling Pair Obese Patient Calorie Intake (cal) Normal-Weight Sibling Calorie Intake (cal) Difference
1 2,450 1,500 950
2 3,500 1,800 1,700
3 3,000 2,100 900
4 2,700 2,000 700
5 2,800 1,900 900
6 3,400 2,000 1,400
7 3,000 2,000 1,000
Next, we need to calculate the mean difference and standard deviation of the differences:
Mean difference = (950 + 1,700 + 900 + 700 + 900 + 1,400 + 1,000) / 7 = 1,014.29
Standard deviation of differences = 382.46
Using these values, we can calculate the t-value:
t = (mean difference - 0) / (standard deviation of differences / [tex]\sqrt{n}[/tex])
where n is the number of sibling pairs (in this case, n = 7).
t = (1,014.29 - 0) / (382.46 / [tex]\sqrt{7}[/tex]) = 4.14
Finally, we can compare the t-value to the critical t-value at a .05 level of significance with 6 degrees of freedom (n-1):
t_critical = 2.447
We may rule out the null hypothesis and reach the conclusion that obese individuals consume considerably more calories than their normal-weight siblings at a.05 level of significance because the estimated t-value (4.14) is higher than the critical t-value (2.447).
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After 1 year, $500 deposited in a savings account with simple interest had earned $75 in interest. What was the interest rate?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 75\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 75 = (500)(\frac{r}{100})(1) \implies 75=5r\implies \cfrac{75}{5}=r\implies \stackrel{ \% }{15}=r[/tex]
Solve for θ if−10sinθ−8=5√3−8 and 0≤θ<2π.
The solutions are θ = 5π/3 and θ = 4π/3 for equation -10sinθ - 8 = 5√3 - 8, option D is correct.
The given equation is -10sinθ - 8 = 5√3 - 8
Adding 8 to both sides, we get:
-10sinθ = 5√3 - 8 + 8
Simplifying, we get:
-10sinθ = 5√3
Dividing both sides by -10, we get:
sinθ = -5√3/10
Simplifying the fraction, we get:
sinθ = -√3/2
We know that sinθ = -√3/2 when θ = 4π/3 and θ = 5π/3 (among other angles).
However, since 0 ≤ θ < 2π, only the angles in the second and third quadrants are valid solutions for sinθ = -√3/2.
Therefore, the solutions are θ = 5π/3 and θ = 4π/3, option D is correct.
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