The area of a circle with a radius of 5 cm is 78.5 square centimeters.
How to find the area?Here we want to find the area of a circle whose radius is r = 5cm.
Remember that the area of circle of radius R is given by the formula below:
A = π*R²
Where π = 3.14
Replacing the values that we know, we will get the area:
A = 3.14*(5cm)²
A = 78.5 cm²
The area is 78.5 square centimeters.
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Please help with the attached math problem…
The missing values for the inverse matrix A⁻¹ are:
a = -78b = 2c = 59d = 20e = -3The solution is:
x = -9200y = 7025z = 2375.How to convert the system of equations to matrix form?In Mathematics and Geometry, a square matrix refers to a type of matrix that is composed of an equal number of both rows and columns. Generally speaking, m × m matrix is typically referred to as a square matrix of order m.
Next, we would convert the system of three linear equations in standard form to matrix form as follows;
[tex]\left[\begin{array}{ccc}1&1&1\\10&-20&98\\5&10&-10\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}200\\250\\500\end{array}\right][/tex]
By using technology, the solutions to this system of three linear equations include the following:
x = -9200
y = 7025
z = 2375.
By using technology, the inverse of this matrix is given by;
[tex]A^{-1}=\left[\begin{array}{ccc}-78&2&11.8\\59&-1.5&-8.8\\20&-0.5&-3\end{array}\right][/tex]
Therefore, the missing values are as shown in the inverse of this matrix A⁻¹ above.
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On a number line, point C is at 8, and the midpoint E of CD is at -3.
Point D is at
on the number line.
Answer: C
Step-by-step explanation:
Point D is at -14 on the number line.
How to determine the midpoint of a line segment?In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).
Since E is the midpoint of line segment CD, we can logically deduce the following relationship:
Line segment CD = Line segment C + Line segment D
Midpoint E = (point C + point D)/2
By substituting the given points into the equation above, we have the following:
-3 = (8 + D)/2
-6 = 8 + D
D = -6 - 8
D = -14
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The period of y = 3cot(4x - 3x) is
the period of y = 3cot(x) remains as π. the period of y = 3cot(4x - 3x) is also π.
To find the period of the function y = 3cot(4x - 3x), we need to determine the length of one complete cycle of the function.
First, let's simplify the expression inside the cotangent function: 4x - 3x = x.
Now, the cotangent function has a period of π, which means it repeats every π units.
To find the period of the given function y = 3cot(x), we need to determine how the variable x affects the period. Since the coefficient of x is 1, it means that the period is not affected by any scaling or stretching.
In summary, the period of the function y = 3cot(4x - 3x) is π, which means the function repeats every π units along the x-axis.
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7 3/8 as an inpropuar fracition
Mahmud Mahtab company's shareholders equity December 30.2020 are given below-
Sources of equity capital Common stock (Tk.100par 30.000 shares) = 30,00,000 TK, Additional paid up capital = 15,00,000 TK, Retained earnings = 55,00,000 TK,
Shareholders total equity = 1,00,00,000 TK.
The price of the stock on December 30 was Tk.500, On December 31,2020 Mahmud Mahtab declared:
(1) 10% stock dividend.
(2) 2 for I stock split.
(3) 1 for 5 reverse stock split.
REQUIREMENT :
What would happen to the accounts for the above decision?
1) 10% stock dividend: Increase in shares, no change in equity value.
2) 2 for 1 stock split: Doubles shares, no change in equity value.
3) 1 for 5 reverse stock split: Decreases shares, no change in equity value.
The decisions made by Mahmud Mahtab regarding stock dividend, stock split, and reverse stock split would result in the following changes to the accounts:
1) 10% Stock Dividend:
A stock dividend is a distribution of additional shares of stock to existing shareholders. In this case, a 10% stock dividend means that for every 10 shares held, shareholders will receive an additional share. As a result, the following changes would occur:
- Common stock: The number of shares would increase by 10% (3,000 additional shares).
- Additional paid-up capital: There would be no change.
- Retained earnings: There would be a reduction of the amount equal to the market value of the shares issued as dividends.
2) 2 for 1 Stock Split:
A stock split involves dividing existing shares into a larger number of shares. In a 2 for 1 stock split, each existing share would be split into two shares. The following changes would take place:
- Common stock: The number of shares would double (60,000 shares).
- Additional paid-up capital: There would be no change.
- Retained earnings: There would be no change.
3) 1 for 5 Reverse Stock Split:
A reverse stock split combines a number of existing shares into a smaller number of shares. In a 1 for 5 reverse stock split, every five shares would be consolidated into one share. The accounts would be affected as follows:
- Common stock: The number of shares would decrease by 80% (24,000 shares).
- Additional paid-up capital: There would be no change.
- Retained earnings: There would be no change.
Note: The above changes would affect the number of shares and their par value, but the total shareholders' equity (1,00,00,000 TK) would remain unchanged.
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saleswoman sells a dried-fruit mixture for $ 5.90 per pound and nuts for $ 14. 75per pound. She wants to blend the two to get a -15lb mixture that she will sell for $ 9.44per pound. How much of each should she use? Solve using matrices.
To get a 15-lb mixture, she should use enter your response here( = -lb )of dried-fruit mixture and enter your response here( = lb )of nuts.
A 15-lb mixture, she should use 1.256 pounds of dried-fruit mixture and 13.744 pounds of nuts.
Based on the given information, we can set up the following system of equations:
Equation 1: x + y = 15 (since the total weight of the mixture is 15 pounds)
Equation 2: (5.90 * x) + (14.75 * y) = 9.44 * 15 (since the total cost of the mixture is the cost per pound multiplied by the weight of each component)
Now, let's convert this system of equations into matrix form:
| 1 1 | | x | | 15 |
| 5.90 14.75 | | y | = | 9.44 * 15 |
To solve for x and y, we can use matrix algebra. We can multiply the inverse of the coefficient matrix by the right-hand side matrix to get the solution matrix:
| x | | 1 1 |^-1 | 15 |
| y | = | 5.90 14.75 | | 9.44 * 15 |
Using matrix calculations, we find that the inverse of the coefficient matrix is:
| 0.0877 -0.0576 |
| -0.0059 0.0678 |
Now, multiplying the inverse matrix by the right-hand side matrix gives us:
| x | | 0.0877 -0.0576 | | 15 |
| y | = | -0.0059 0.0678 | * | 9.44 * 15 |
Simplifying the multiplication gives us:
x = 1.256
y = 13.744
Therefore, the saleswoman should use 1.256 pounds of dried-fruit mixture and 13.744 pounds of nuts to get a 15-pound mixture.
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Assignment
Practice using function notation.
The values in the table represent a function.
f(x)
8
X
-6
7
4
3
-5
3
-5
-2
12
Use the drop-down menus to complete the
statements.
The ordered pair given in the first row of the table can
be written using function notation as
O
f(3) is
O
f(x) = -5 when x is
In the first row, the ordered pair can be expressed as f(8) = -6 in function notation.
Of(3) is 18.
Of(x) = -5 when x is -2.
The given table represents a function, and we need to express the values in function notation and determine specific inputs that correspond to certain outputs.
In the table's first row, the ordered pair are shown which can be expressed as function notation:
f(8) = -6
This means that when the input (x) is 8, the corresponding output (f(x)) is -6.
f(x) = -5 when x is -2.
This means that when the input (x) is -2, the value of the function (f(x)) is -5.
In the table, the function is defined by the equation f(x) = 8x - 6. Each input value (x) is multiplied by 8 and then subtracted by 6 to determine the corresponding output (f(x)).
By substituting different values for x into the function, we can find the corresponding values for f(x) in the table.
when x = 3, we have:
f(3) = 8(3) - 6
f(3) = 24 - 6
f(3) = 18
So, f(3) is 18.
Similarly, when x = -2, we have:
f(-2) = 8(-2) - 6
f(-2) = -16 - 6
f(-2) = -22
Thus, when x is -2, f(x) is -22.
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2+2=? ???¿??????¿????????
Answer:4
Step-by-step explanation:1+1 is 2, so if you take 2+2 it is 4, same as 2×2 is 4.
Please awnser asap I will brainlist
They can buy 140 vans, 70 small trucks, and 70 large trucks.
How to find the number of van, small trucks and large truck needed?The truck company plans to spend 14 million on 280 vehicles. Each commercial van cost 55,000 dollars. Each small truck 20,000 dollars and each large truck 70,000 dollars. They needed twice as many van as small truck
Therefore,
let
s = number of small truck
number of van = v
let
l = number of large truck
v + s + l = 280
55,000(v) + 20,000(s) + 70,000(l) = 14,000, 000
11v + 4s + 14l = 2800
Hence,
v = 2s
So,
26s+ 14l = 2800
26s + 14l = 2800
3s + l = 280
multiply equation(ii) by 14
26s + 14l = 2800
42s + 14l = 3920
subtract the equation
16s = 1120
s = 70
Therefore, they can buy the following:
number of small truck = 70
number of van = 140
number of large truck = 280 - 140 - 70 = 70
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
The probability that the 5 starting members of the basketball team are lined up from shortest to tallest is 1/120. Option A.
To calculate the probability that the 5 starting members of the basketball team are lined up from shortest to tallest, we need to determine the number of favorable outcomes (arrangements where the players are lined up from shortest to tallest) and divide it by the total number of possible outcomes.
Since the order matters and we want the players to be arranged from shortest to tallest, there is only one favorable outcome. The shortest player must be in the first position, followed by the second shortest, and so on, until the tallest player is in the last position.
The total number of possible outcomes is given by the number of permutations of 5 players, which is denoted as 5!.
Therefore, the probability is:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = 1 / 5!
Probability = 1 / (5 * 4 * 3 * 2 * 1)
Probability = 1 / 120 Option A is correct.
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The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 26.50 mpg and a standard deviation of σ = 3.25 mpg.
(a) What is the standard error of X¯¯¯
, the mean from a random sample of 25 fill-ups by one driver? (Round your answer to 4 decimal places.)
The standard error represents the average deviation of the sample means from the true population mean. Rounding this value to four decimal places, the standard error of X¯¯¯ is approximtely 0.6500 mpg.
A smaller standard error indicates that the sample means are more likely to be close to the population mean.To calculate the standard error of X¯¯¯, the mean from a random sample of 25 fill-ups by one driver, we can use the formula:
Standard Error (SE) = σ / sqrt(n),
where σ is the standard deviation and n is the sample size.
In this case, the standard deviation (σ) is given as 3.25 mpg, and the sample size (n) is 25.
Plugging in these values into the formula, we have:
SE = 3.25 / sqrt(25).
Calculating the square root of 25, we get:
SE = 3.25 / 5.
Performing the division, we find:
SE ≈ 0.65.
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w=32-0.05n what is the glass tanks volume
The equation W = 32 - 0.05n represents the volume of water used, the glass tank's volume will be equal to W plus the volume occupied by the marbles.
In the given equation W = 32 - 0.05n, W represents the volume of water (in liters) Andrei uses, and n represents the number of marbles used. We can interpret this equation as follows: as Andrei increases the number of marbles used (n), the volume of water required (W) decreases.
To determine the glass tank's volume, we need to consider the relationship between the volume of water used and the number of marbles used. We can rearrange the equation to solve for n:
W = 32 - 0.05n
0.05n = 32 - W
n = (32 - W) / 0.05
The volume of the glass tank can be inferred from the equation, as the total volume will be the sum of the volume occupied by marbles and the volume occupied by water.
If we assume that the volume occupied by the marbles is constant, then the remaining volume in the tank will be filled with water. Therefore, the glass tank's volume can be represented as:
Glass Tank Volume = Volume of Water (W) + Volume of Marbles
The given equation W = 32 - 0.05n represents the volume of water used based on the number of marbles, but it does not directly provide information about the glass tank's volume. Further information about the marbles or the tank's dimensions is required to determine the glass tank's volume accurately.
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Wanahton purified a portion of water with
900
900900 grams of contaminants. Each hour, a third of the contaminants was filtered out.
Let
�
(
�
)
g(n)g, left parenthesis, n, right parenthesis be the amount of contaminants (in grams) that remained by the beginning of the
�
th
n
th
n, start superscript, start text, t, h, end text, end superscript hour.
�
gg is a sequence. What kind of sequence is it?
the sequence g is a decreasing sequence.
Here is the step-by-step solution to the problem based on the information given in the question:
Wanahton purified a portion of water with 900 grams of contaminants. Each hour, a third of the contaminants was filtered out.Let g(n) be the amount of contaminants (in grams) that remained by the beginning of the nth hour. g is a sequence. We need to determine the kind of sequence.The amount of contaminants in the beginning
= 900 grams
Amount of contaminants filtered out
= (1/3) * 900 = 300
grams Amount of contaminants left after first
hour = 900 - 300 = 600
gramsAmount of contaminants filtered out in the second
hour = (1/3) * 600 = 200
grams Amount of contaminants left after the second
hour = 600 - 200 = 400 grams
Amount of contaminants filtered out in the third
hour = (1/3) * 400 = 133.33 grams
(rounded to two decimal places)Amount of contaminants left after the third
hour = 400 - 133.33 = 266.67 grams
(rounded to two decimal places)In this way, the sequence will continue. We can observe that the amount of contaminants in the beginning is decreasing and the sequence is decreasing as well
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onsider the following ordered pairs that represent a relation.
{(–4, –7), (0, 6), (5, –3), (5, 2)}
What can be concluded of the domain and range for this relation? Check all that apply.
The domain is the y values of the ordered pairs.
The range is the set of output values.
The given relation is a function.
Zero is included in the range of the relation.
5 is included in the domain of this relation.
the statement “Zero is included in the range of the relation” is correct and the statement “5 is included in the domain of this relation” is also correct.
if we observe the given ordered pairs we can easily determine that,The domain is the set of all x-values from the ordered pairs in the relation.
So, the domain of the given relation is {−4,0,5} because we have only three unique x-values from the given ordered pairs.
The range is the set of all y-values from the ordered pairs in the relation.
So, the range of the given relation is {−7,−3,2,6} because we have four unique y-values from the given ordered pairs.
Also, we can conclude that the given relation is not a function since we have the same x-value (5) corresponding to two different y-values (−3,2).
And it is true that the zero is included in the range of the relation since we have the ordered pair (0,6) which gives the y-value of 6.
So, the statement “The given relation is a function” is incorrect. But the statement “Zero is included in the range of the relation” is correct and the statement “5 is included in the domain of this relation” is also correct.
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The triangles shown below must be congruent.
True or false
True because corresponding sides and angles of the triangles are congrent.
A triangle has two sides of length 15 cm and 17 cm. Select all the values of its third side that would make it a right triangle. A triangle has two sides of length 15 cm and 17 cm. Select all the values of its third side that would make it a right triangle.
Based on the Pythagorean theorem, in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side. So, we can use this to find the possible values of the third side of the triangle.
The two given sides are 15 cm and 17 cm. We can label the unknown side as "x". Then, we can set up an equation:
15^2 + 17^2 = x^2
Simplifying this equation, we get:
225 + 289 = x^2
514 = x^2
x = sqrt(514)
Therefore, the possible value of the third side that would make it a right triangle is approximately 22.72 cm.
Which of the following amounts are equal to 24 pints? Select all that apply.
A.
48 cups
B.
192 fluid ounces
C.
3 gallons
D.
48 quarts
The amount that is equal to 24 pints can be determined by using the conversion factors between different units of volume. The following amounts are equal to 24 pints:
A. 48 cups: There are 2 cups in 1 pint. Therefore, 24 pints = 24 × 2 cups = 48 cups.
B. 192 fluid ounces: There are 8 fluid ounces in 1 cup, and 2 cups in 1 pint. Therefore, 24 pints = 24 × 2 cups = 48 cups = 48 × 8 fluid ounces = 384 fluid ounces. Hence, 192 fluid ounces are equal to 24 pints.
C. 3 gallons: There are 8 pints in 1 gallon. Therefore, 24 pints = 24/8 gallons = 3 gallons.
D. 48 quarts: There are 2 pints in 1 quart. Therefore, 24 pints = 24/2 quarts = 12 quarts. Hence, 48 quarts are not equal to 24 pints.
Therefore, the correct answers are A, B, and C.
A sequence of transformations map ABC to A’B’C. The sequence of transformations that maps ABC to A’B’C is a reflection across the _ followed by a translation _
The sequence of transformations that maps ABC to A’B’C is a reflection across the line y = x followed by a translation of 10 units right and 4 units up.
How to obtain the transformations?The equivalent vertices C and C' are given as follows:
C(-4, 2).C'(12,0).Considering the change in the orientation of the figure, it was reflected over the line y = x, for which the rule is given as follows:
(x,y) -> (y,x).
Hence:
(-4,2) -> (2,-4)
To go from (2,-4) to (12,0), the translation rule is given as follows:
(x,y) -> (x + 10, y + 4)
Hence the translation is defined as follows:
10 units right and 4 units up.
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Find the missing side.
+
18
12
x = [?]
Round to the nearest tenth.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{18}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{12} \end{cases} \\\\\\ x=\sqrt{ 18^2 - 12^2}\implies x=\sqrt{ 324 - 144 } \implies x=\sqrt{ 180 }\implies x\approx 13.4[/tex]
The missing side of a right-angled triangle, assuming it to be the hypotenuse with other sides as 12 and 18, can be calculated using the Pythagorean theorem. The square root of the sum of 12^2 and 18^2 gives the length of the hypotenuse, which is approximately 21.6 when rounded to the nearest tenth.
Explanation:This question relates to the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².
Assuming that the missing side in your question (x) is the hypotenuse and the other two sides are 12 and 18, you can calculate it using the aforementioned theorem. Therefore, you find x by calculating the square root of (12² + 18²), or √(144 + 324) which equals to √468. This value, rounded to the nearest tenth, is 21.6.
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Which fraction is represented by point A on the number line?
The fraction represented by point A, it is crucial to have information about the scale, intervals, and the relative position of point A on the number line.
With these details, you can calculate the fraction accurately.
Point A on the number line represents a fraction that requires additional information to determine its precise value.
I can provide you with a general approach to finding the fraction corresponding to a given point on the number line.
A number line represents a range of values, typically with a specific scale or interval.
The scale can be divided into equal parts, such as units or fractions.
To determine the fraction represented by point A, we need to know the scale and the position of point A relative to that scale.
Let's consider a number line that ranges from 0 to 1, with evenly spaced tick marks representing tenths.
If point A is located halfway between the tick marks representing 0.4 and 0.5, then it represents the fraction 0.45 (or 9/20 in simplified form).
If the number line has a different scale or is divided into different intervals, the fraction represented by point A will be different.
Without specific details about the number line and the position of point A, it is impossible to determine the fraction precisely.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
x = 42
y = 21
Step-by-step explanation:
Since its a right triangle, we have:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
[tex]sin (60) = \frac{21\sqrt{3} }{x} \\\\x= \frac{21\sqrt{3} }{sin (60)} \\\\x= \frac{21\sqrt{3} }{\frac{\sqrt{3} }{2} } \\\\x = \frac{21\sqrt{3} *2 }{\sqrt{3} } \\\\x = 21*2\\\\x = 42[/tex]
[tex]cos (60) = \frac{y}{x}\\\\cos (60) = \frac{y}{42}\\\\y = cos (60)*42 \\\\y = \frac{1}{2} * 42\\\\y = 21[/tex]
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The diagram to the right BC is parallel to DE.
Here, AD=15,
DB=12,
AE=10, and
EC=8.
We need to determine if BC||DE or not.
angle ADE = 180 - 90 = 49.106 degree.
Now, using the triangle BDC, we can find the value of sin[angle CDB] as follows.
angle CDB = angle DAB = angle ABD = 180 - angle ADE - angle EDC
To determine if BC is parallel to DE, we can use the concept of proportional sides of the triangle.
From the information given, AD = 15, DB = 12, AE = 10, and EC = 8.
If BC is parallel to DE, then by the intercept theorem (also known as Thales' theorem), the Die segments AD/DB and AE/EC must be the same.
Let's calculate these ratios:
AD/DB = 15/12 = 5/4
AE/EC = 10/8 = 5/4
AD/DB = AE/EC = 5/ 4, so we can conclude that: BC is parallel to DE.
The reason for this is that if two ratios are equal, it means that the corresponding sides of the triangle formed by the intersecting lines are proportional, which is a characteristic of parallel lines.
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I completed 2/3 of my project last month and 1/4 of it this week, what fraction of my project is not completed
Hello!
Answer:
11/12
Step-by-step explanation:
To solve this problem, we would need to find the denominator of the 2 numbers. In this case, it is 12. We will now convert the fractions to twelfths.
2/3 = 8/12
1/4 = 3/12
After we add 8/12 and 3/12, we get our answer 11/12.
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Rounded to the nearest tenth of a percent, the probability is approximately 27.8%.
To determine if the event of rolling a pair of dice and getting doubles or a sum of 6 is mutually exclusive, we need to assess whether the two outcomes can occur simultaneously or if they are mutually exclusive.
Let's analyze the two outcomes separately:
1. Getting doubles: When rolling a pair of dice, getting doubles means that the numbers on both dice are the same. The possible outcomes for getting doubles are (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). There are a total of 6 outcomes that satisfy this condition.
2. Getting a sum of 6: To get a sum of 6, the numbers on the two dice should add up to 6. The possible outcomes for this condition are (1,5), (2,4), (3,3), (4,2), and (5,1). There are a total of 5 outcomes that satisfy this condition.
Now, to determine if the two outcomes are mutually exclusive, we need to check if there are any outcomes that satisfy both conditions. In this case, the outcome (3,3) satisfies both conditions (doubles and sum of 6).
Since there is one outcome that satisfies both conditions, we can conclude that the event of rolling a pair of dice and getting doubles or a sum of 6 is not mutually exclusive.
To find the probability of this event, we need to determine the total number of possible outcomes when rolling a pair of dice. Each die has 6 sides, so there are 6 possible outcomes for each die, resulting in a total of 6 * 6 = 36 possible outcomes when rolling a pair of dice.
The probability is calculated by dividing the number of favorable outcomes (satisfying the condition) by the total number of possible outcomes.
Favorable outcomes = 6 (for doubles) + 5 (for sum of 6) - 1 (for the overlapping outcome) = 10
Probability = Favorable outcomes / Total number of outcomes = 10 / 36 ≈ 0.2778
Rounded to the nearest tenth of a percent, the probability is approximately 27.8%.
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You are given the great circle of a sphere is a length of 25 miles. What is the volume of the sphere
Answer: 268
Step-by-step explanation:
State if the pair of triangles are similar. If so, state how you know they are similar and complete the similarity statement.
The triangles EFG and WVU are similar by SSS
Identifying the similar triangles in the figure.from the question, we have the following parameters that can be used in our computation:
Triangle EFG and WVU
The triangles in this figure are
EFG and WVU
These triangles are similar because:
The triangles do have similar corresponding sides
i.e. Ratio = 525/252 = 875/420 = 825/396
Evaluate
Ratio = 2.083 = 2.083 = 2.083
Hence, the triangles EFG and WVU are similar
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For the following event, state whether you think the difference between what occurred and what you would expect by chance is statistically significant. Explain.
An airline with a 95% on-time departure rate has 16 out of 300 flights with late departures.
The difference between the observed and expected number of late departures is statistically significant, we need to perform a binomial test by calculating the probability of observing 16 or more late departures out of 300 flights assuming the null hypothesis is true. If the resulting p-value is less than 0.05, we can conclude that the difference is statistically significant.
Based on the given information, an airline with a 95% on-time departure rate has 16 out of 300 flights with late departures. The question asks whether the difference between what occurred (16 late departures) and what you would expect by chance is statistically significant.
To determine if the difference is statistically significant, we need to conduct a hypothesis test. In this case, we can use a binomial test since we are dealing with two possible outcomes: on-time departure or late departure.
The null hypothesis (H0) assumes that the observed number of late departures is equal to what would be expected by chance. The alternative hypothesis (Ha) assumes that there is a significant difference between the observed and expected values.
In this case, the expected number of late departures can be calculated by multiplying the total number of flights (300) by the expected on-time departure rate (95%). This gives us an expected value of 300 * 0.05 = 15.
To perform the binomial test, we can calculate the probability of observing 16 or more late departures out of 300 flights, assuming the null hypothesis is true. This probability can be calculated using the binomial probability formula or by using statistical software.
If the resulting probability (also known as the p-value) is less than the significance level (usually 0.05), we can reject the null hypothesis and conclude that the difference between what occurred and what would be expected by chance is statistically significant. Otherwise, if the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the difference is not statistically significant.
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Sample Answer: The vertical line test determines if one input has exactly one output on the graph. If any vertical line passes through more than one point on the graph, then the relation is not a function.
Which did you include in your response?
Draw vertical lines to intersect on a graph.
The relation is a function if there’s only one point of intersection on a graph.
The relation is not a function if there’s more than one point of intersection on a graph.
The vertical line test is used to determine if each input has exactly one output.
Answer: All of the choices in the response would be correct.
Step-by-step explanation:
A restaurant Serves 80 Costumers 20% do not Order drinks How many. People do Order drinks?
Among the 80 customers, 64 individuals choose to order drinks at the restaurant.
To find the number of people who order drinks at the restaurant, we can start by calculating the percentage of customers who do not order drinks.
Given that 20% of the customers do not order drinks, we can calculate the number of customers who do not order drinks by multiplying 80 (total customers) by 0.20 (20% expressed as a decimal):
Number of customers who do not order drinks = 80 * 0.20 = 16.
Since the total number of customers is 80, and 16 customers do not order drinks, we can subtract the number of customers who do not order drinks from the total number of customers to find the number of customers who do order drinks:
Number of customers who order drinks = 80 - 16 = 64.
Therefore, 64 people order drinks at the restaurant.
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Find the original slope of (-6,-1) and (0,3)
Answer:
slope (m) = 2/3
Step-by-step explanation:
slope = change in x /change in y
Also, slope is y2 - y1 / x2 -x1. That is what I apply for this activity, hence:
slope = 3 - (-1) / 0 - (-6)
= 3 + 1 / 0 + 6
= 4 / 6
= 2/3
∴ slope(m) = 2/3
