The correct representation for the joint probability of two dependent events Y and Z is P(Y) * P(Z|Y). Option E
The joint probability of two dependent events Y and Z can be written as the probability of Y occurring multiplied by the conditional probability of Z given Y. This can be represented as P(Y) * P(Z|Y).
Here's the justification:
P(Y) represents the probability of event Y occurring independently.
P(Z|Y) represents the conditional probability of event Z occurring given that event Y has already occurred.
When Y and Z are dependent events, the occurrence of Y affects the probability of Z happening. Therefore, we need to consider the probability of Y occurring first (P(Y)) and then the probability of Z occurring given that Y has already occurred (P(Z|Y)).
Multiplying these two probabilities together gives us the joint probability of both Y and Z occurring simultaneously, which is denoted as P(Y and Z).
Hence, the correct representation for the joint probability of two dependent events Y and Z is P(Y) * P(Z|Y). Option E.
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The parallel gram shown below has an area of 72 units^2
Answer:
h = 12 units
Step-by-step explanation:
The formula for the area of a parallelogram is given by:
A = bh, where
b is the base of the parallelogram,and h is an altitude (i.e., a perpendicular line that connects the two bases of a parallelogram).Thus, the base is 6 units. We can find the height by dividing the area by 6:
A = bh
72 = 6h
72/6 = h
12 = h
Thus, the height of the parallelogram is 12 units.
Which of the following functions is graphed below?
Answer: C
Step-by-step explanation:
the x - 2 means go right 2
the +3 means go up 3
Jessica and Barry squeezed oranges for juice. Jessica squeezed 23
5
cups of juice. Barry made 1
4
cup less than Jessica. Barry estimated that Jessica squeezed about 21
2
cups of juice.
Which is the best estimate for the amount of juice Barry made?
Jessica squeezed 235 cups of juice, Barry made 221 cups of juice, and the best estimate for the amount of juice Barry made is 198 cups.
Jessica and Barry squeezed oranges for juice. Jessica squeezed 235 cups of juice. Barry made 14 cups less than Jessica. Barry estimated that Jessica squeezed about 212 cups of juice. The best estimate for the amount of juice Barry made is 198 cups.
There are different ways to approach this problem, but one possible method is to use subtraction to find out how much juice Barry actually made, and then compare it to the estimated amount. If Jessica squeezed 235 cups of juice and Barry made 14 cups less, then Barry made 235 - 14 = 221 cups of juice.
This is the exact amount of juice that Barry made, but it may not be a convenient answer if we are looking for an estimate that is close to Barry's estimate of 212 cups of juice. One way to get such an estimate is to round 221 to the nearest ten or hundred. For example, if we round to the nearest ten, we get 220, which is only 8 cups away from Barry's estimate.
Alternatively, if we round to the nearest hundred, we get 200, which is only 12 cups away from Barry's estimate. Therefore, the best estimate for the amount of juice Barry made is 198 cups, which is obtained by rounding down to the nearest ten. This estimate is only 14 cups away from Barry's estimate, and it is also easy to compute mentally.
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which equation could use the find the length of the hypotenuse
0 6² + 11² - c²
0 6²+c² - 11²
Oc²-6²-11²
0 11²-6²-c²
Answer:
A. 6² + 11² = c²
Step-by-step explanation:
The correct equation to find the length of the hypotenuse in a right triangle is the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, if we assume that the length of one side is 6 and the length of the other side is 11, the correct equation would be:
A. 6² + 11² = c²
This equation can be simplified as follows:
36 + 121 = c²
157 = c²
Therefore, the correct equation to find the length of the hypotenuse in this case is A. 6² + 11² = c².
CAPM Elements
Value
Risk-free rate (rRF
)
Market risk premium (RPM
)
Happy Corp. stock’s beta
Required rate of return on Happy Corp. stock
An analyst believes that inflation is going to increase by 2.0% over the next year, while the market risk premium will be unchanged. The analyst uses the Capital Asset Pricing Model (CAPM). The following graph plots the current SML.
Calculate Happy Corp.’s new required return. Then, on the graph, use the green points (rectangle symbols) to plot the new SML suggested by this analyst’s prediction.
Happy Corp.’s new required rate of return is .
The new required rate of return for Happy Corp. can be calculated using the Capital Asset Pricing Model (CAPM). The formula for CAPM is:
Required rate of return = Risk-free rate + Beta * Market risk premium
Since the analyst believes that the market risk premium will be unchanged, the only factor that will affect the new required return is the risk-free rate.
Given that the analyst predicts a 2.0% increase in inflation, the risk-free rate will also increase by that amount. Therefore, the new required rate of return for Happy Corp. will be the current risk-free rate plus the product of Happy Corp.'s beta and the market risk premium.
To plot the new Security Market Line (SML) on the graph, we would use the new required return calculated above and plot it against the corresponding beta values. The SML represents the relationship between risk (beta) and return (required rate of return).
By incorporating the new required return, we can determine the new expected returns for various levels of beta and create the updated SML.
It is important to note that without specific values provided for the risk-free rate, market risk premium, and Happy Corp.'s beta, it is not possible to calculate the exact new required return or plot the new SML accurately.
These values are crucial in determining the precise position of the SML on the graph.
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Determine the percentile of 6.2 using the following data set.
4.2 4.6 5.1 6.2 6.3 6.6 6.7 6.8 7.1 7.2
Your answer should be an exact numerical value.
The percentile of 6.2 is
%.
The percentile of 6.2 in the given dataset is 30%. This means that 30% of the values in the dataset are lower than or equal to 6.2.
To determine the percentile of 6.2 in the given dataset, we need to calculate the percentage of values in the dataset that are lower than or equal to 6.2.
First, we arrange the dataset in ascending order: 4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2.
Next, we count the number of values that are lower than or equal to 6.2. In this case, there are three values: 4.2, 4.6, and 5.1.
The next step is to calculate the percentage. We divide the count (3) by the total number of values in the dataset (10) and multiply by 100.
(3/10) * 100 = 0.3 * 100 = 30%
Percentiles are used to understand the relative position of a particular value within a dataset. In this case, 6.2 is higher than 30% of the values in the dataset and lower than the remaining 70%.
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Question #2
Solve for x
2
O Saved 1
4
3
Q
69x + 2
R
70°
Simplify 15a6 bc4/ 35a2 c4
The simplified value of the expression given is 3a⁴b/ 7
Given the fraction :
15a⁶bc⁴/ 35a²c⁴divide the coefficients by 5
3a⁶bc⁴/ 7a²c⁴From division rule of indices, subtract the powers of values with Equivalent coefficients.
Hence,
coefficient of of a = 6-2 = 4coefficient of c = 4-4 = 0coefficient of b = bFinally we have :
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What is the formula?
What do the V’s equal?
Answer:
60 cm³
Step-by-step explanation:
volume of a rectangular pyramid
v = ( l * w * h ) / 3
v = ( 4 * 5 * 9 ) / 3
v = 60
Solve for x leave your answer in simplest radical form
Answer:
X=11 trust me on my mom
An architect is designing a swimming pool with a base in the shape of a right triangle according to the architect the pools depth should be 6 feet less than It’s length x and it’s width should be 8 feet less than it’s length the volume of water in the pool cannot exceed 1680 cubic feet which statement
87,959 to the nearest hundred
B
A
C
Intro
y
-6
4
3
2
+
1
2 3
x
Suppose quadrilateral ABCD has been transformed by
Ty=x. What are the coordinates for the vertices of the
reflected quadrilateral A'B'C'D'?
A' =
B' =
C' =
D'=
The coordinates of the reflected quadrilateral A'B'C'D' are:
A' = (6, 4)
B' = (-3, 2)
C' = (-1, 23)
D' = (-x, 12)
To find the coordinates of the reflected quadrilateral A'B'C'D', we need to apply the transformation Ty = x to each vertex of the original quadrilateral ABCD. The transformation Ty = x reflects each point across the y-axis.
Given the coordinates of the original quadrilateral ABCD as:
A = (-6, 4)
B = (3, 2)
C = (+1, 23)
D = (x, 12)
Applying the transformation Ty = x to each vertex, we can determine the coordinates of the reflected quadrilateral A'B'C'D':
A' = (-(-6), 4) = (6, 4)
B' = (-3, 2)
C' = (-1, 23)
D' = (-x, 12)
The reflected quadrilateral A'B'C'D' thus has the following coordinates:
A' = (6, 4)
B' = (-3, 2)
C' = (-1, 23)
D' = (-x, 12)
Therefore, the x-coordinate for point D' will be represented as -x in the reflected quadrilateral.
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Solve - the mean age of a family of seven is 23 years the median is 16 years the modes are 12 years and 45 years and the range is 35 years. Find the ages of the seven family members.
The ages of the seven family members are 12, 16, 16, 45, 45, 45, and 80 years.
To solve this problem, let's break it down step by step:
1. We are given that the mean age of the family is 23 years. The mean is calculated by summing up all the ages and dividing by the number of family members. Since there are seven family members, the total sum of their ages is 7 * 23 = 161 years.
2. The median age is 16 years. This means that when the ages are arranged in ascending order, the fourth age is 16. Since there are seven family members, the fourth age is the middle age. Therefore, the ages in ascending order are: _ _ 12 16 _ 45 _.
3. The modes are 12 years and 45 years, which means these two ages occur more frequently than any other age. Since the median is 16, it can't be one of the modes. Hence, we can conclude that the family members' ages are: _ _ 12 16 16 45 _.
4. The range is 35 years, which is the difference between the highest and lowest ages. Since the ages are arranged in ascending order, the highest age must be 45 + 35 = 80 years. Therefore, the ages of the family members are: _ _ 12 16 16 45 80.
In summary, the ages of the seven family members are 12, 16, 16, 45, 45, 45, and 80 years.
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A particular type of vaccine comes in a Brand-1 and a Brand-2. Sixty-five percent
of all patients at a certain vaccination centre want the Brand-2.
i) Among ten randomly selected patients who want this type of vaccine, what
is the probability that at least six want the Brand-2?
ii) Among ten randomly selected patients, what is the probability that the
number who want the Brand-2 vaccine is within 1 standard deviation of
the mean value?
iii) The store currently has seven vaccines of each brand. What is the probability that all of the next ten patients who want this vaccine can get the brand
of vaccine they want from current stock?
i) Probability of at least six patients wanting Brand-2: P(X ≥ 6)
ii) Probability of number of patients within 1 standard deviation of mean: P(μ - σ ≤ X ≤ μ + σ)
iii) Probability that all ten patients get their desired brand from current stock: (7/14) * (6/13) * ... * (1/5)
i) The probability of at least six patients wanting Brand-2 out of ten randomly selected patients can be calculated using the binomial distribution. We need to sum the probabilities of six, seven, eight, nine, and ten patients wanting Brand-2.
The probability can be calculated as P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10), where X follows a binomial distribution with n = 10 and p = 0.65. The answer is the sum of these individual probabilities.
ii) To calculate the probability of the number of patients who want the Brand-2 vaccine being within 1 standard deviation of the mean value, we need to find the range of values that fall within one standard deviation of the mean.
We can use the normal approximation to the binomial distribution since n = 10 is reasonably large. We calculate the mean (μ) and standard deviation (σ) using μ = n * p and σ = √(n * p * (1 - p)), where p = 0.65. Then we calculate the probability of the number of patients falling within the range μ - σ to μ + σ.
iii) Since there are seven vaccines of each brand in stock, the probability that all ten patients who want the vaccine can get the brand they want from the current stock is equal to the probability of the first patient getting their desired brand (7/14) multiplied by the probability of the second patient getting their desired brand (6/13), and so on until the tenth patient (1/5). The final probability is the product of these individual probabilities.
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9
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A system of linear equations is given by the tables. One of the tables is represented by the equation y = -x + 7
y
9
8
X
0
3
6
9
y
5
6
7
8
X
-6
-3
0
3
7
6
The equation that represents the other equation is y= 1/3
The solution of the system is (
)
X+
Reset
5
Next I
What is the value of the expression (-2)(3)º(4)-2 ?
A. -3/2
B. -1/2
C. -3/4
D. 0
The value of the expression (-2)(3)º(4) - 2 is -164.
Based on the answer choices provided, none of the options matc.
To solve the expression (-2)(3)º(4)-2, we need to follow the order of operations, which is parentheses, exponents, multiplication, and subtraction.
Let's break down the expression :
(-2)(3)º(4) -2
First, we calculate the exponent:
(-2)(81) - 2
Next, we perform the multiplication:
-162 - 2
Finally, we subtract:
-164
Therefore, the value of the expression (-2)(3)º(4) - 2 is -164.
Based on the answer choices provided, none of the options match the value of -164.
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HELP PLEASE AND HURRYY
Answer:
Part A: Answer: D.
Part B:
true
false
true
Step-by-step explanation:
Part A:
Use a tree.
Round 1 Round 2 Round 3
W W W
W W L
W L W
W L L
L W W
L W L
L L W
L L L
All possibilities are:
WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL
Answer: d.
Part B:
Winning 3 games is WWW.
WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL
Out of the 8 possible outcomes shown above, only 1 of them is WWW.
p(WWW) = 1/8
Answer: true
Winning exactly 2 games happens when there are exactly 2 W's:
WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL
p(exactly 2 wins) = 3/8
Answer: false
Wining at least 2 games means winning exactly 2 or exactly 3 times.
WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL
p(winning at least 2 games) = 4/8 = 1/2
Answer: true
Evaluate. -15 +7-(-8)
The answer options are
16
0
-16
-3
Answer:
To evaluate -15 + 7 - (-8), we can simplify the expression by first removing the double negative.
-15 + 7 + 8 = 0
Therefore, the answer is 0.
Step-by-step explanation:
The answer is:
0Work/explanation:
Remember the integer rule,
[tex]\bullet\phantom{4444}\sf{a-(-b)=a+b}[/tex]
Similarly
[tex]\sf{-15+7-(-8)}[/tex]
[tex]\sf{-15+15}[/tex]
Simplify fully.
[tex]\sf{0}[/tex]
Therefore, the answer is 0.I dont understand these can someone help?
The corresponding sides and angles of the similar and congruent triangles indicates that we get the following approximate and exact values;
Page 1;
5. [tex]\overleftrightarrow{AC}[/tex] = 4.3. 6. [tex]\overline{BP}[/tex] ≈ 7.5 7. [tex]\overline{YV}[/tex] ≈ 8
Page 2
5. [tex]\overline{DF}[/tex] = [tex]11\frac{1}{4}[/tex], 6. [tex]\overline{ED}[/tex] = 5, 7. [tex]\overline{BC}[/tex] = 22, 8. [tex]\overline{EF}[/tex] = 8
Page 3;
8. m∠ABC = 30°, 9. m∠XYP = 44°, 10. [tex]\overline{AC}[/tex] = 14
What are congruent triangles?Congruent triangles are triangles that have all three corresponding sides of the same length and all three angles of the same measure.
First Page
5. The distance from the vertex B to the line segment [tex]\overleftrightarrow{AC}[/tex] in the triangle ΔABC is the altitude of the triangle, which is 4.3
6. The distance from the vertex B to [tex]\overleftrightarrow{AC}[/tex] = [tex]\overline{BP}[/tex]
Pythagorean theorem indicates that the length of the segment [tex]\overline{BP}[/tex] can be found as follows;
[tex]\overline{BP}[/tex] = √(13.5² - 11.2²) ≈ 7.5
7. The distance from Y to [tex]\overleftrightarrow{XZ}[/tex] is the altitude of the triangle ΔXYZ, which indicates;
The distance from Y to [tex]\overleftrightarrow{XZ}[/tex] = [tex]\overline{YV}[/tex]
The Pythagorean theorem indicates that we get;
[tex]\overline{YV}[/tex] = √(13.34² - 10.67²) ≈ 8
Second page;
5. The scale factor from ΔABC to ΔDEF = 3/4
Therefore, the length of [tex]\overline{DF}[/tex] = (3/4) × 15 = 45/4 = [tex]11\frac{1}{4}[/tex]
6. The scale factor of (1/3) indicates that we get;
[tex]\overline{ED}[/tex] = (1/2) × 10 = 5
7. The ratio of the corresponding sides by length which is the scale factor is; S.F. = 18/9 = 10/5 = 2
The corresponding side to [tex]\overline{BC}[/tex] is [tex]\overline{EF}[/tex]
[tex]\overline{EF}[/tex] = 11, therefore, the length of [tex]\overline{BC}[/tex] = 2 × 11 = 22
8. The ratio of the corresponding sides by length which is the scale factor is; S.F. = 4/6 = 10/15 = 2/3
The corresponding side to [tex]\overline{EF}[/tex] is [tex]\overline{BC}[/tex]
[tex]\overline{BC}[/tex] = 12, therefore [tex]\overline{EF}[/tex] = (2/3) × 12 = 8
Third page;
8. The triangles ΔABV and ΔCVB are congruent triangles by the Leg Hypotenuse congruence theorem.
The angles ∠ABV and ∠CBV are corresponding triangles, therefore;
∠ABV ≅ ∠CBV
m∠CVB = m∠ABV = 15° (Definition of congruent triangles and symmetric and substitution property)
∠ABC = ∠ABV + ∠CBV
Therefore; m∠ABC = 15° + 15° = 30°
9. The angles ∠YXP and ∠YZP are right triangles, therefore;
m∠YXP = m∠YZP = 90°
The right triangles ΔYXP and ΔYZP are congruent by the LH congruence theorem
∠XYP ≅ ∠ZYP (Corresponding Parts of Congruent Triangles are Congruent, CPCTC)
m∠XYP = m∠ZYP (Definition of congruent triangles)
m∠XYZ = m∠XYP + m∠ZYP (Angle addition property)
m∠XYZ = 2 × m∠XYP
2 × m∠XYP = m∠XYZ = 88°
m∠XYP = 88°/2 = 44°
10. The angles ∠ACP and ∠ABP are right angles, according to the indicated markings, therefore;
∠ACP ≅ ∠ABP (All right angles are congruent)
ΔACP ≅ ΔABP by SAA congruence theorem
[tex]\overline{AC}[/tex] ≅ [tex]\overline{AB}[/tex] (CPCTC)
[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] (Definition of congruent segments)
[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] = 14
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anwser it pls aaaaaaaassaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answer:
Step-by-step explanation:
Volume = Bh
Turn the shape so the trapezoid is on the bottom/base
h=18 for overall shape
B = area of base, trapezoid
B = 1/2 (b₁ + b₂) h
b₁ = 11
b₂ = 25
h = 24 for trapezoid
B = 1/2 (11 + 25)(24)
B = 432
V = Bh
V = (432)(18)
V= 7776 in³
Please answer ASAP I will brainlist
(a) The amount for total expenditures in 2015 was about $63.2 billion.
(b) The first full year in which expenditures exceeded $110 billion was 2027.
(a) To find the amount for total expenditures in 2015, we need to substitute x = 20 into the function h(x) = [tex]23.4(1.08)^{(x-5)[/tex].
h(x) = 23.4(1.0[tex]8)^{(20-5)[/tex]
= 23.4(1.0[tex]8)^{15[/tex]
≈ 23.4(2.717)
Rounding to the nearest tenth, the total expenditures in 2015 were about $63.2 billion.
(b) To determine the first full year in which expenditures exceeded $110 billion, we need to find the value of x when h(x) is greater than $110 billion.
110 = 23.4(1.0[tex]8)^{(x-5)[/tex]
Dividing both sides by 23.4:
4.7008547... = (1.0[tex]8)^{(x-5)[/tex]
Taking the logarithm base 1.08 of both sides:
log₁.₀₈(4.7008547...) = x - 5
Using a logarithm calculator or software, we find:
x - 5 ≈ 11.75
Adding 5 to both sides:
x ≈ 16.75
Rounding to the nearest whole number, the first full year in which expenditures exceeded $110 billion was 2027.
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A spinner has five sectors of equal size the sectors are labeled 1, 2, 3, 4 and five the spinner is spun twice X is the number of times three is fun drag each bar on the horizontal axis to the correct location to create a probability distribution for X
The probability distribution for X is given as follows:
P(X = 0) = 0.64.P(X = 1) = 0.32.P(X = 2) = 0.04.How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The distribution gives the probability of each possible outcome, hence it is given as follows:
P(X = 0) = 0.64.P(X = 1) = 0.32.P(X = 2) = 0.04.Learn more about the concept of probability at https://brainly.com/question/24756209
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. Initially 100 milligrams of a radioactive substance was present.
After 6 hours the mass had decreased by 3%. If the rate of
decay is proportional to the amount of the substance present at
time t, nd the amount remaining after 24 hours.
Answer:
Incomplete Question
Solve the system of equations. 8 � + 5 � = 24 � = − 4 � 8x+5y=24 y=−4x
The solution to the system of equations is x = 2 and y = -8.
To solve the system of equations, we'll use the substitution method. The given equations are:
Equation 1: 8x + 5y = 24
Equation 2: y = -4x
We'll substitute Equation 2 into Equation 1 to eliminate one variable:
8x + 5(-4x) = 24
8x - 20x = 24 [Distribute the -4]
-12x = 24 [Combine like terms]
x = 24 / -12 [Divide both sides by -12]
x = -2
Now that we have the value of x, we can substitute it back into Equation 2 to find the value of y:
y = -4(-2)
y = 8
Therefore, the solution to the system of equations is x = -2 and y = 8.
However, let's double-check the solution by substituting these values into the original equations:
Equation 1: 8(-2) + 5(8) = 24
-16 + 40 = 24
24 = 24 [LHS = RHS, equation is satisfied]
Equation 2: 8 = -4(-2)
8 = 8 [LHS = RHS, equation is satisfied]
Both equations are satisfied, confirming that x = -2 and y = 8 is indeed the solution to the given system of equations.
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how many pattern block rhombuses would 4 triangles create?
With 4 triangles, you can create a total of 3 pattern block rhombuses, depending on their arrangement.
To determine the number of pattern block rhombuses that can be created using 4 triangles, let's start by understanding the properties and arrangement of these shapes.
Pattern block rhombuses are a type of geometric shape commonly used in mathematics education. Each rhombus is made up of 2 triangles, specifically two congruent (equal) acute triangles. The triangles are placed together in a specific way to form the rhombus shape.
When 4 triangles are used, they can be arranged in different configurations to create different numbers of pattern block rhombuses. Let's explore the possibilities:
Arrangement 1:
In this arrangement, you can create 2 pattern block rhombuses. The triangles are placed side by side, with two triangles forming one rhombus, and the other two triangles forming another rhombus.
Arrangement 2:
In this arrangement, you can create 1 pattern block rhombus. The triangles are placed on top of each other, forming a larger triangle. Since a pattern block rhombus requires two acute triangles, only one rhombus can be formed in this case.
So, with 4 triangles, you can create a total of 3 pattern block rhombuses, depending on how the triangles are arranged.
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write 718000 in standard form
Answer:
718000
Step-by-step explanation:
718000 is already in standard form
Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
The coordinate of the fourth vertex is (9,11)
What is coordinate?Any of a set of numbers used in specifying the location of a point on a line, on a surface, or in space is called coordinate
For example (6,3) is a coordinate on a plane where 6 represent the value on x axis and 3 represent the value on y axis.
Since the shape is parallelogram;
√ -3-1)² + 8-0)² = √ x-5)² + y-3)²
= √4² +8² = √ x-5)² + y -3)²
therefore, relating the two values;
4 = x-5 and 8 = y -3
x = 4+5 = 9
y = 8+3 = 11
Therefore the coordinate of the fourth vertex = ( 9,11)
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Prove the following?
The given statement proposition is a that suggests that if x is an inductive element, defined in terms of the set X as described, then it follows that every non-zero natural number can be expressed as the successor of some other natural number.
The given statement is a logical proposition involving the concept of induction. Let's break it down and analyze its components.
"If x is inductive..."
This implies that x is a concept or object that possesses the property of being inductive. In mathematics, the term "inductive" typically refers to the property of being a natural number or belonging to the set of natural numbers.
"...then so is (x ∈ X : x = Ф or x = y ∪ {y} for some y)"
Here, we have a set X that consists of elements satisfying a certain condition. The condition states that an element x in X can either be equal to the empty set (Ф) or the union of a set y with itself ({y}). This construction represents a recursive definition, where each element in X is defined in terms of a base case (Ф) and a recursive step ({y}).
"...hence each n ≠ 0 is m + 1 for some m."
This conclusion states that for every natural number n that is not equal to 0, there exists another natural number m such that n can be expressed as m + 1. In other words, any non-zero natural number is the successor of some other natural number.
Overall, the given statement is a proposition that suggests that if x is an inductive element, defined in terms of the set X as described, then it follows that every non-zero natural number can be expressed as the successor of some other natural number.
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4
Number of Years
m
N
1
16
18
18°
19°
22°
30°
20
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28
22
24
26
Average Daily Temperature
30
The mean of the temperatures in the chart is 24° with a standard deviation of 4°. Which temperature is within one
standard deviation of the mean?
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The temperature of 30° is within one standard deviation of the mean.
To determine which temperature is within one standard deviation of the mean, we need to consider the range that falls within one standard deviation above and below the mean.
Given that the mean temperature is 24° with a standard deviation of 4°, one standard deviation above the mean would be 24° + 4° = 28°, and one standard deviation below the mean would be 24° - 4° = 20°.
Looking at the temperatures in the chart, we can see that the temperature of 30° is within one standard deviation of the mean. It falls within the range of 28° (one standard deviation above the mean) and 20° (one standard deviation below the mean).
Therefore, the temperature of 30° is within one standard deviation of the mean.
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