Answer:
K
Step-by-step explanation:
We can factor the given expression as:
p(p + 1)(p - 1) = p^3 - p
Notice that p^3 - p is the difference of two consecutive cubes. This can be factored further using the identity a^3 - b^3 = (a - b)(a^2 + ab + b^2):
p^3 - p = p(p^2 - 1) = p(p + 1)(p - 1)
So, we have shown that p(p + 1)(p - 1) is equal to p^3 - p, which is the product of three consecutive integers. By definition, this product is always divisible by 3.
However, we cannot conclude that p(p + 1)(p - 1) is divisible by 4, 5, or 7 for all positive integers p. Therefore, the answer is K) None of these.
is 2x^2+4=9x real rational and equal
Answer:
76(/783/)-468
Step-by-step explanation:
A school has 1800 pupils. 55% of the pupils are girls. 30% of the girls
and 70% of the boys travel by bus.
a) How may girls travel by bus?
b) How many boys travel by bus?
c) What percentage of the pupils travel by bus?
In linear equation, 65.625% of the pupils travel by bus.
What is linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
A) 1800 * 0.55 * 0.3 = 297 Girls.
B) 1800 * 0.45 * 0.7 = 567 boys
C) Girl
297/864 * 100% = 34.375%
boy -
567 ÷ (297 + 567 ) * 100% = 65.625%
864 = 297 + 567
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4 x 1 1/5= multiply. Write the product as a mixed number.
A scale drawing of a building needs to be made using the scale 1 in = 170 ft How tall will the building in the scale drawing be if the building is 850 ft tall?
The height of the building in the scale drawing will be 5 inches.
The scale ratio must be used to determine the height of the building in the scale drawing.
The scale ratio is:
1 inch = 170 feet
We can devise a ratio:
1 inch / 170 feet = x inches / 850 feet
In the scale drawing, x represents the height of the building in inches.
To find x, we can cross-multiply and simplify:
1 inch * 850 feet = 170 feet * x inches
850 inches = 170 feet * x
Dividing both sides by 170 yields:
x = 850 inches / 170 = 5 inches
As a result, the building's height will be 5 inches in the scale drawing.
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Write the equation of the circle centered at (4,-1) that passes through (13,8).
Answer:
[tex](x-4)^2+(y+1)^2=162[/tex]
Step-by-step explanation:
Determine r² by using the equation of a circle and plugging in the center (h,k)->(4,-1) as well as (x,y)->(13,8):
[tex](x-h)^2+(y-k)^2=r^2\\(x-4)^2+(y-(-1))^2=r^2\\(13-4)^2+(8+1)^2=r^2\\9^2+9^2=r^2\\81+81=r^2\\162=r^2\\[/tex]
Hence, the equation of the circle that meets these criteria is[tex](x-4)^2+(y+1)^2=162[/tex]
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table.
In response to the stated question, we may state that As a result, the overall probability of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.
What is probability?Probability theory is an area of mathematics that calculates the likelihood of an occurrence or a proposition being true. A risk is a number in the range of 0 and 1, whereas 1 implies certainty and a probability of roughly 0 indicates how likely an event seems to be to occur. Probability is a mathematical expression of the chance or chances that a given event will occur. Probabilities can alternatively be stated as integers between 0 and 1 or as % from 0% to 100%. the ratio of occurrences among equally likely choices that result in a certain event in comparison to all other outcomes.
Using the data in the table, we can compute the likelihood of a correct drive-thru order for each fast food chain, as well as the overall chance of an accurate order across all chains.
Divide the number of accurate orders by the total number of orders to find the chance of a randomly picked order being accurate at each chain:
P(accurate order) = 1246 / 1300 = 0.958 for McDonald's
P(accurate order) = 1020 / 1100 = 0.927 Taco Bell
P(accurate order) = 708 / 800 = 0.885 for Burger King
P(accurate order) = 940 / 1000 = 0.94 for Wendy's
P(adequate overall order) = 0.3 * 0.958 + 0.25 * 0.927 + 0.2 * 0.885 + 0.25 * 0.94 = 0.929
As a result, the overall likelihood of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.
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Mrs Devi bought banana cakes and marble cakes for a party. She spent $112 on the cakes. Each
piece of banana cakes cost $2.50 and the cost of each piece of marble cake was 7/5 the cost of
each piece of banana cake. 30% of what she bought were marble cakes. How many pieces of
cake did Mrs Devi buy?
In linear equation, 28 pieces of cake did Mrs Devi buy.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
Cost of M cake = $3.5
For every 3 M cakes she bought 7 B cakes.
Let 1 unit be 3 M cakes and 7 B cakes. 1 unit costs= 3(3.5) + 7(2.5)= $28
She bought $112 / $28 = 4 units of cakes.
Which means 12 M cakes and 28 B cakes.
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can you help me to solve this question?
By finding the derivative and evaluating it in x = -2, we will see that the slope is 12.
How to find the slope of the function at the given point?To find the slope of the tangent line at a given point, we need to take the derivative and evaluate it in the x-value of the given point.
Here we have the function:
f(x) = 3x² + 7
If we differentiate it with respect to x, we will get:
f'(x) = 2·3x
f'(x) = 6x
That is the derivative, now we want to find the slope at (-2, 19), to find the slope at that point we need to get:
f'(-2) = 6·-2
f'(-2) = -12
That is the slope of the graph.
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PLEASE HELP !
Use the figure below to answer the questions
From the figure 1. Two line segments are LA and EP. 2. Two rays are EC and AH. 3. Two lines are b and AP.
What are rays, line segment and line?A line segment having a single endpoint and an infinite length in one direction is known as a ray. A ray's length cannot be determined.
There are two endpoints to a line segment. Every point on the line connecting these endpoints to one another is also included. The length of a line cannot be measured, but the length of a segment can.
An eternally long and thin line is a group of points that stretches in two opposite directions.
From the given figure we observe that,
1. Two line segments are LA and EP.
2. Two rays are EC and AH.
3. Two lines are b and AP.
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Question about equations, please help!
Answer:
(a) y = 0.80x + 50
(b) Plugging x = 5 into the equation from part (a), we get y = 0.80(5) + 50 = 54, so the ordered pair associated with x = 5 is (5, 54). This means that if the car is driven for 5 miles, the total charge to the renter is $54.
(c) Let y be the total charge and solve for x:
y = 0.80x + 50
187.60 = 0.80x + 50
137.60 = 0.80x
x ≈ 172
Therefore, the car must have been driven approximately 172 miles
Answer:
(a) y = 0.8x + 50
(b) D. The ordered pair associated with the equation x = 5 is (5, 54) and it means that the charge for driving the car for 5 miles is $54.
(c) If the renter paid $187.60, the car must have been driven for 172 miles.
Step-by-step explanation:
Part (a)In the given problem, we are told that the rental car costs a flat fee of $50 plus an additional charge of $0.80 per mile driven.
Let x be the number of miles driven.
Let y be the total charge to the renter (in dollars).
We know that the total charge y will depend on the number of miles driven x, and we can express this relationship using a linear equation in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the value of y when x = 0).
In this case, we know that the cost per mile is $0.80 so the slope of the line is m = 0.8, and the flat fee is $50 so the y-intercept is b = 50.
Substitute these values into the equation to get:
[tex]y = 0.8x + 50[/tex]
[tex]\hrulefill[/tex]
Part (b)To find the ordered pair associated with x = 5, substitute x = 5 into the equation:
[tex]\begin{aligned}x=5\implies y &= 0.8(5) + 50\\&=4+54\\&=54\end{aligned}[/tex]
The ordered pair associated with the equation x = 5 is (5, 54) and it means that the charge for driving the car for 5 miles is $54.
[tex]\hrulefill[/tex]
Part (c)To find how many miles the car was driven if the renter paid $187.60, set y = 187.60 and solve for x:
[tex]\begin{aligned}\implies 0.8x + 50&=187.60\\0.8x + 50-50&=187.60-50\\0.8x&=137.60\\\dfrac{0.8x}{0.8}&=\dfrac{137.60}{0.8}\\x &= 172\end{aligned}[/tex]
Therefore, if the renter paid $187.60, the car must have been driven for 172 miles.
If h> 3 and h - 2g= 0, which of
the following must be true?
A. g> 2.5
B. g> 1.5
C. g <0.5
D. g <1.5
E. g>2
In response to the stated question, we may state that According to the inequality facts provided, the only choice that must be true is B, because g must be bigger than 1.5. As a result, the solution is: B. g > 1.5
What is inequality?In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many basic inequalities may be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are split or added on both sides. Exchange left and right.
We know that h > 3 and h - 2g = 0.
When we plug h = 2g into the first inequality, we get:
2g > 3
g > 1.5
As a result, we know that g must be bigger than 1.5, ruling out alternatives C and D.
Option A is not certainly true since we don't know if the value of g is bigger than 2.5.
Option E is also not certainly true, because we only know that g is more than 1.5, but not if it is bigger than 2.
According to the facts provided, the only choice that must be true is B, because g must be bigger than 1.5. As a result, the solution is:
B. g > 1.5
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Which of the following shows the correct evaluation for the exponential expression 6 over 7 to the power of 2 ? (2 points) a 6 over 7 plus 2 equals 2 and 6 over 7 b 6 over 7 times 2 equals 12 over 7 which equals 1 and 5 over 7 c 6 over 7 times 6 over 7 equals 36 over 49 d 6 over 7 divided by 2 equals 6 over 14
The correct answer is (c) 6/7 times 6/7 equals 36/49.
The correct evaluation for the exponential expression 6/7 to the power of 2 is (c) 6/7 times 6/7 equals 36/49.
To evaluate this expression, you need to multiply 6/7 by itself 2 times (since the exponent is 2). This gives you:
(6/7) to the power of 2 = (6/7) x (6/7) = 36/49
Therefore, the correct answer is (c) 6/7 times 6/7 equals 36/49.
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The pulse rate of the male population is known to be normal, with a mean of 73 BPM and a standard deviation of 11.3. Find the sample size necessary to be within 2 BPM of the population mean with 95% confidence.
2.5 Hence determine the total area of all the faces in mm²
2.6 Hence, determine the volume of the container in m³
Hint: The volume of the is container is determined by multiplying the area of
the base of the container by the height of the container.
Answer:
Step-by-step explanation:
gfds5u4wsr5wj6wrs
who is the first 6 millionth person to die
Answer: Beth Blauer
Step-by-step explanation:
I cannot figure out these angles. help please
The angles for the given parallel lines are estimated.
m(∠DGF ) = 92; m(∠HGF ) = 88; m(∠AGD ) = 88; m(∠BDG ) = 92; m(∠BDC ) = 88; m(∠CDE ) = 92 ; m(∠EDG ) = 88.
Explain about the transversal?A line that cuts over two parallel lines is referred to as a transversal line.
Each pair of internal angles located on the exact side of a transversal that meets two parallel lines is supplementary, or they add up to 180°.
The opposing angles created by the junction of two lines are known as vertical angles but rather vertically opposite angles.
m(∠AGH ) = m(∠BDG ) (corresponding angles)
3x + 2 = 2x + 32
x = 30
m(∠AGH ) = 3(30) + 2 = 92
m(∠BDG ) = 2(30) + 32 = 92
m(∠DGF ) = m(∠AGH ) = 92 (vertically opposite angles)
m(∠HGF ) = 180 - m(∠AGH ) = 180 - 92 = 88 (linear pair).
m(∠AGD ) = m(∠HGF ) = 88 (vertically opposite angles)
m(∠BDG ) = 92 (calculated earlier)
m(∠BDC ) = m(∠AGD ) = 88 (corresponding angles)
m(∠CDE ) = m(∠BDG ) = 92 (vertically opposite angles)
m(∠EDG ) = m(∠BDC ) = 88 (vertically opposite angles).
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For each of the (a) The mean # (b) The median The (c) The mode (d) The range (e) The variance (f) The standard deviation (g) The coefficient of variation different between the higherave -- . 215, 205, 313, 207, 227, 245, 173, 258, 103, 181. 105. 301. 19
(a) Mean: 207.7
(b) Median: 207
(c) Mode: None
(d) Range: 198
(e) Variance: 3705.5
(f) Standard deviation: 60.72
(g) Coefficient of variation: 29.34
If F1 = 4y - 6, F2 = 9y + 3 and F3 = -y - 8, simplify F1 × F2 - F3 in terms of y.
Answer:
To simplify F1 × F2 - F3 in terms of y, we need to first find the product of F1 and F2, and then subtract F3.
F1 × F2 can be expanded using the distributive property:
F1 × F2 = (4y - 6) × (9y + 3) = 4y × 9y + 4y × 3 - 6 × 9y - 6 × 3
= 36y^2 + 12y - 54y - 18
= 36y^2 - 42y - 18
Now we can subtract F3 from the result:
F1 × F2 - F3 = (36y^2 - 42y - 18) - (-y - 8)
= 36y^2 - 42y - 18 + y + 8
= 36y^2 - 41y - 10
Therefore, F1 × F2 - F3 in terms of y is 36y^2 - 41y - 10.
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A manufacturer knows that their items have a normally distributed length, with a mean of 5 inches, and standard deviation of 0.5 inches.
If one item is chosen at random, what is the probability that it is less than 4.6 inches long?
Answer:
Step-by-step explanation:
To solve this problem, we will use the properties of the normal distribution and standardize the given value using the formula:
z = (x - μ) / σ
where:
x = 4.6 inches (the given value)
μ = 5 inches (the mean)
σ = 0.5 inches (the standard deviation)
So we have:
z = (4.6 - 5) / 0.5
z = -0.8
Now we need to find the probability that the standardized value is less than -0.8. We can use a standard normal distribution table or a calculator to find this probability.
Using a standard normal distribution table, we can look up the probability for z = -0.8, which is 0.2119.
Therefore, the probability that a randomly chosen item is less than 4.6 inches long is 0.2119 or approximately 21.19%.
Need help answering all 3 of these please anyone
a. The slope of AB is [tex]m = 1[/tex] and slope of BC is [tex]m = -4/7.[/tex]
b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.
c. The mid-point of Diagonal AC is [tex](0, -1/2)[/tex]
What are the Quadrilaterals?A clοsed shape nοted fοr having sides with variοus widths and lengths is a quadrilateral. It is a clοsed, two-dimensional pοlygοn with fοur sides, fοur angles, and fοur vertices. Quadrilaterals include the trapezium, parallelοgram, rectangle, square, rhοmbus, and kite, amοng οthers.
a.
Slope is given by
[tex]A = (-2, 3) and B = (-5, 0)[/tex]
[tex]m = 1[/tex]
[tex]B = (-5, 0) and C = (2, -4)[/tex]
[tex]m = -4/7[/tex]
Thus, The slope of AB is m = 1 and slope of BC is [tex]m = -4/7[/tex] .
b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.
c. Midpoint of a segment is given by the 2 divided by of sum x and and sum of y
Thus, Diagonal [tex]A = (-2, 3)[/tex] and [tex]C = (2, -4)[/tex]
Midpoint [tex]= ((-2 + 2), (3 + -4))[/tex]
[tex]= ((0), (-1))[/tex]
Now divide them by 2
[tex]= ((0/2), (-1/2))[/tex]
[tex]= (0, -1/2)[/tex]
Therefore, the mid-point of Diagonal [tex]AC is (0, -1/2)[/tex]
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given f(x) and g(x) find the value of (gof)(5)
Answer:
Assuming that (gof)(5) means (g(f(5))):
(gof)(5) = g(f(5)) = g(3x + 7) = 5x + 2
Therefore, (gof)(5) = 5(3x + 7) + 2 = 15x + 17.
Z decreased by 15%
Express as algebra
Answer:
Z-0.15Z
Step-by-step explanation:
multiply z by the decimal form of 15, but since it's decreased by z you need to include a way of subtracting the z
The algebraic expression for the given statement is 0.85Z
What is an algebraic expression?An algebraic expression is a mathematical expression that consists of variables, numbers and operations.
Given that, Z decreased by 15%, we need to convert it into an algebraic expression
Multiply z by the decimal form of 15, but since it's decreased by z we will subtract z from that,
So,
= Z - 15% of Z
= Z - 0.15Z
= Z(1-0.15)
= 0.85Z
Hence, the algebraic expression for the given statement is 0.85Z
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PLEASE HELP ! I NEED THIS ANSWER! DUE TODAY!!
Use the figure below to answer the questions
From the figure 1. Two line segments are LA and EP. 2. Two rays are EC and AH. 3. Two lines are b and AP.
What are rays, line segment and line?A ray is a segment of a line with a single endpoint and unlimited length in a single direction. A ray cannot be measured in terms of length.
The ends of a line segment are two. These endpoints are included, along with every point on the line that connects them. A segment's length can be measured, while a line's length cannot.
A line is a collection of points that extends in two opposing directions and is endlessly long and thin.
From the given figure we observe that,
1. Two line segments are LA and EP.
2. Two rays are EC and AH.
3. Two lines are b and AP.
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$58.65 meal with a 15% tip what would be the tip and total
The Tip cost for the meal is found as: $8.7975. The total cost of the meal is $67.4475.
Explain percentage?'Percent' refers to a number that is 'out of 100. Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the whole. A percentage can be shown by the symbol % or, less frequently, by the abbreviation 'pct'.
At stores, online, in commercials, and in the media, you can see percentages practically anywhere. Understanding what percentages signify is a crucial skill that could help you save time as well as money and raise your employability.
Original cost of meal = $58.65
Tip cost = 15% of $58.65
Tip cost = 15*58.65 / 100
Tip cost = $8.7975
Total cost = Original cost of meal + Tip cost
Total cost = $58.65 + $8.7975
Total cost = $67.4475
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Determine the equation of the ellipse with foci (-8,14) and (-8,-16), and co-vertices (0,-1) and (-16,-1).
According to the given information, the equation of the ellipse is [tex](x+8)^2/256 + (y+1)^2/784 = 1.[/tex]
What is co-ordinate geometry ?Coordinate geometry, also known as analytic geometry, is a branch of mathematics that deals with the study of geometric shapes using algebraic principles. It involves the use of coordinates to represent points, lines, curves, and other geometric figures on a plane or in space.
According to the given information:we need to know the coordinates of its foci, co-vertices, and the center. We can start by finding the center of the ellipse, which is the midpoint of the line segment joining the foci:
Center = ( (-8 + (-8))/2 , (14 + (-16))/2 ) = (-8,-1)
Next, we can find the distance between the foci, which is given by:
[tex]distance between foci = 2c = sqrt[(14 - (-16))^2 + (-8 - (-8))^2] = 30[/tex]
where c is the distance from the center to either focus.
We also know that the distance between the co-vertices is given by:
distance between co-vertices = 2a = |-16 - 0| = 16
where a is the distance from the center to either co-vertex.
Finally, we can use the standard form equation for an ellipse centered at the origin:
[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]
where b is the distance from the center to either vertex.
To find b, we can use the Pythagorean theorem:
[tex]b^2 = c^2 - a^2 \\b^2 = 30^2 - 16^2\\b^2 = 784\\b = 28[/tex]
Now we have all the information we need to write the equation of the ellipse:
[tex](x+8)^2/16^2 + (y+1)^2/28^2 = 1[/tex]
Therefore, according to the given information, the equation of the ellipse is [tex](x+8)^2/256 + (y+1)^2/784 = 1.[/tex]
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What is the slope of the line passing through the points (-1, -7) and (-9, -2)?
Answer:
m = -5/8
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (-1, -7) (-9, -2)
We see the y increase by 5 and the x decrease by 8, so the slope is
m = -5/8
what percentage of the area under the normal curve lies (a) to the left of m? (b) between m s and m 1 s? (c) between m 3s and m 1 3s
The percentages of the area under curve are 50%, 68%, and 99.7%.
Assuming a standard normal distribution with mean m = 0 and standard deviation s = 1, the percentage of the area under the curve can be determined as follows
To the left of m: This is equivalent to finding the area to the left of the z-score corresponding to m = 0. This is 50%, as the normal distribution is symmetric around the mean.
Between m s and m 1 s: This is equivalent to finding the area between the z-scores corresponding to z = -1 and z = 1. Using a standard normal distribution table or calculator, this is approximately 68% (which is also known as the 68-95-99.7 rule).
Between m 3s and m 1 3s: This is equivalent to finding the area between the z-scores corresponding to z = -3 and z = 3. Using a standard normal distribution table or calculator, this is approximately 99.7% (which is also known as the 68-95-99.7 rule).
Therefore, the percentages of the area under the normal curve are: (a) 50%, (b) 68%, and (c) 99.7%.
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how do you solve this? (-3a+56)+(5a+40)
Answer:To simplify the expression, you need to combine the like terms, which are the terms that have the same variable and power. In this case, the like terms are -3a and 5a:
(-3a + 56) + (5a + 40)
= (-3a + 5a) + (56 + 40)
= 2a + 96
Therefore, the simplified expression is 2a + 96.
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Step-by-step explanation:
triangle $abc$ is an isosceles triangle with side lengths of 25, 25 and 48 centimeters. what is the area of triangle $abc$, in square centimeters?
If triangle abc is an isosceles triangle with side lengths of 25, 25 and 48 centimeters, the area of triangle ABC is 600√(3) square centimeters.
To find the area of an isosceles triangle, we need to first determine the length of the altitude or height that is perpendicular to the base of the triangle.
In an isosceles triangle, the altitude divides the base into two equal parts, creating two right triangles. Using the Pythagorean theorem, we can find the length of the altitude.
Let x be the length of the altitude. Then, we have:
(25/2)^2 + x^2 = 25^2
625/4 + x^2 = 625
x^2 = 625 - 625/4
x^2 = 468.75
x = √(468.75)
x = 5√(75)
Now that we know the length of the altitude, we can find the area of the triangle using the formula:
Area = (1/2) x base x height
In this case, the base of the triangle is 48 cm and the height is 5sqrt(75) cm. Therefore, we have:
Area = (1/2) x 48 x 5√(75)
Area = 120√(75)
Area = 120 x 5√(3)
Area = 600√(3) cm^2
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FILL IN THE BLANK the probability of one event given the known outcome of a (possibly) related event is known as __probability.
The probability of one event given the known outcome of a (possibly) related event is known as conditional probability.
Conditional probability is the measure of the probability of an event occurring given that the another event will already occurred. It is denoted by P(A | B), which represents the probability of event A given that event B has occurred. The conditional probability of A given B can be calculated using the formula:
P(A | B)=P(A and B)/P(B)
where P(A and B) represents the probability of both events A and B occurring, and P(B) represents the probability of event B occurring.
For example, consider a deck of 52 playing cards. The probability of drawing a king from the deck is 4/52, or 1/13. If one card is drawn from the deck and it is revealed to be a heart, then the probability of drawing a king from the remaining cards in the deck that are not hearts is:
P(king | heart) = P(king and heart) / P(heart)
P(king and heart) = 1/52 (there is only one king of hearts in the deck)
P(heart) = 13/52 (there are 13 hearts in the deck)
P(king | heart) = (1/52) / (13/52) = 1/13
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