E1, E3, and E2, E3 are independent variables.
What is meant by independent variable?In statistical modelling, experimental sciences, and mathematical modelling, there are dependent and independent variables. Dependent variables are examined under the presumption or requirement that they are constrained by some rule or law to depend on the values of other variables. What it means to be an independent variable is exactly what it is. It is a variable that is independent of the other factors you are attempting to assess. Age is just one example of an independent variable.The independent variable is the underlying cause. Its value is independent of the other study factors. The dependent variable is the effect. The value of the independent variable depends on its modifications.[tex]$& \mathrm{P}\left(\mathrm{E}_1\right)=\frac{1}{6} \\[/tex]
[tex]$& \mathrm{P}\left(\mathrm{E}_2\right)=\frac{1}{6} \\[/tex]
[tex]$& \mathrm{P}\left(\mathrm{E}_3\right)=\frac{2+4+6+4+2}{36}=\frac{1}{2} \\[/tex]
[tex]$& \mathrm{P}\left(\mathrm{E}_2 \cap \mathrm{E}_3\right)=\frac{1}{2} \times \frac{1}{6}=\mathrm{P}\left(\mathrm{E}_2\right) \times \mathrm{P}\left(\mathrm{E}_3\right) \\[/tex]
Then,
[tex]$& \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_3\right)=\frac{1}{2} \times \frac{1}{6}=\mathrm{P}\left(\mathrm{E}_1\right) \times \mathrm{P}\left(\mathrm{E}_3\right) \\[/tex]
[tex]$& \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_2 \cap \mathrm{E}_3\right)=0 \\[/tex]
[tex]$& \mathrm{P}\left(\mathrm{E}_1\right) \mathrm{P}\left(\mathrm{E}_2\right) \mathrm{P}\left(\mathrm{E}_3\right) \equiv 0 \\[/tex]
Simplify,
[tex]$& \therefore \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_2 \cap \mathrm{E}_3\right) \equiv \mathrm{P}\left(\mathrm{E}_1\right) \mathrm{P}\left(\mathrm{E}_2\right) \mathrm{P}\left(\mathrm{E}_3\right)[/tex]
E1, E3 are independent
E2, E3 are independent
The complete question is:
Let two fair six-faced dice A and B are thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?
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What is the solution set to 8(2x-3) ≤ 20-4*?
O (-00,00)
O(-00, 2]
O (0,20)
O [2,00)
The solution set to the given inequality is (−∞, 2.5].
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is 8(2x-3) ≤ 20-4.
Here, 8(2x-3) ≤ 16
Divide 8 on both the sides of an inequality, we get
2x-3≤2
Add 3 on both the sides of an inequality, we get
2x≤5
Divide 2 on both the sides of an inequality, we get
x≤2.5
Convert the inequality to interval notation.
(−∞, 2.5]
Therefore, the solution set is (−∞, 2.5].
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if 30% of a number is 7, then what is 10% of the number ?
Answer:
70.0000
Step-by-step explanation:
aka 70%
The Tasty as Pi Bakery sells circular pies with a $9$ inch diameter. The bakery offers two different sizes of pie slices: small and large.
Cutting a pie into $5$ equal pieces produces $5$ large slices. The small slices measure $27$ degrees fewer than the large slice.
How many equal pieces should they cut a whole pie into so that each piece is a small slice?
A pie has 360 degrees, so a pie cut into 5 equal pieces produces 5 slices that each measure 360 / 5 = 72 degrees.
A small slice measures 27 degrees fewer than a large slice, so it measures 72 - 27 = 45 degrees.
To find the number of pieces a pie should be cut into so that each piece is a small slice, we need to determine how many degrees each slice measures. To do this, we divide 360 by the number of pieces:
360 / n = 45
Solving for n, we get:
n = 360 / 45 = 8
So, the Tasty as Pi Bakery should cut a whole pie into 8 equal pieces so that each piece is a small slice.
The ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6. Terrence owns 36 models cars. How many model cars does Jim own?
The provided statement indicates that Jim and Terrence each possess eight model automobiles, whereas Terrence owns six, making an 8:6 ratio. Jim is the owner of the 48 model card, then.
What does a ratio mean mathematically?If b is really not equal to 0, then an arrangement of the numbers a and b expressed as a/b is a ratio. An equation known as a percent establishes two ratios with the identical value. You might, for instance, write the ration as described in the following: 1: 3 in the case of 1 male and 3 girls.
You are aware that Jim and Terrence own an 8:6 ratio in terms of the total number of model automobiles they own.
Accordingly, you can answer the task as follows: Let's say Jim owns x model automobiles.
8/6 = x/36
x = 36*8/6
x = 288/6
x = 48
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Yasmin is participating in a 5-day cross-country biking challenge. She biked for 45,60,68 and 52 kilometers on the first four days. How many kilometers does she need to bike on the last day so that her average (mean) is 58 kilometers per day?
Step-by-step explanation:
The total distance biked by Yasmin on the first four days can be calculated as follows:
45 + 60 + 68 + 52 = 225 km
To find out how many kilometers she needs to bike on the last day to achieve an average of 58 km per day over the 5 days, we can set up an equation based on the formula for the mean:
(45 + 60 + 68 + 52 + x) / 5 = 58
Where x is the number of kilometers Yasmin needs to bike on the last day. Expanding the equation:
225 + x = 5 * 58
225 + x = 290
Subtracting 225 from both sides:
x = 65
So Yasmin needs to bike 65 kilometers on the last day to achieve an average of 58 kilometers per day over the 5 days
You randomly survey middle school students and high school students about whether they prefer spring or winter. The results
are shown in the two-way table. Find the percent of middle school students that prefer each season and the percent of high school students that prefer each season
The percentage of middle school students that prefer each season and the percentage of high school students that prefer each season is 57.93% and 42.07% respectively.
What is the percentage?The percentage is the ratio of the composition of value to the overall composition of value multiplied by 100.
Here,
Total number of students = 93 + 31 + 36 + 54 = 214
The percentage of students in middle school prefer spring,
= number of students in middle school prefer spring / total student × 100%
= 93/214 × 100%
= 43.45%
Similarly,
The percentage of students in middle school prefer winter,
= number of students in middle school who prefer winter/ total students × 100%
= 31/214 × 100%
= 14.48%
Thus, the percentage of middle school students that prefer each season and the percentage of high school students that prefer each season are 43.45 + 14.48 = 57.93% and 100-57.93% = 42.07%.
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Please answer a and b I need help really bad and please explain it would help me a ton
The value of x found using the assumption, ΔABC is an isosceles triangle and the measure using the fact that ∠ABC > ∠ACB are;
a) x = 4.5
The assumption made is that the triangle is an isosceles triangle
b) {x ∈ Z| -6 ≤ x ≤ 8}
What is an isosceles triangle?An isosceles triangle is a triangle that has a pair of congruent sides.
Let ΔABC be an isosceles triangle, we get;
∠ABC is congruent to ∠ACB, (∠ABC ≅ ∠ACB), therefore, by the definition of congruence triangles, we get;
m∠ABC = m∠ACB
The question indicates that the measure of the angles are;
∠ABC = 100 - 12·x
∠ACB = 8·x + 10
Which indicates, by the substitution property, that we get;
100 - 12·x = 8·x + 10
100 - 10 = 8·x + 12·x = 20·x
100 - 10 = 90 = 20·x
20·x = 90
x = 90/20 = 4.5
x = 4.5The assumption made is that the triangle ΔABC is an isosceles triangle
b) ∠ABC > ∠ACB, therefore;
100 - 12·x > 8·x + 10
100 - 10 > 8·x + 12·x = 20·x
100 - 10 = 90 > 20·x
20·x < 90
x < 90/20 = 4.5
x < 4.5
The possible integer values of x can be found as follows;
100 - 12·x ≥ 0
100 ≥ 12·x
x ≤ 100/12 = 8.[tex]\overline{3}[/tex]
x ≤ 8.[tex]\overline{3}[/tex]
100 - 12·x ≤ 180
100 - 180 ≤ 12·x
12·x ≥ -80
x ≥ -80/12 = -6.[tex]\overline{6}[/tex]
x ≥ -6.[tex]\overline{6}[/tex]
Similarly, we get;
8·x + 10 ≥ 0
x ≥ -10/8 = -1.25x
x ≥ -1.25
8·x + 10 ≤ 180
x ≤ (180 - 10)/8 = 21.25
x ≤ 21.25
The possible integer value of x, using the interval, x ≥ -6.[tex]\overline{6}[/tex], x ≤ 8.[tex]\overline{3}[/tex] are therefore; -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, which can be expressed as; {x ∈ Z| -6 ≤ x ≤ 8}
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The nutrition information on the cereal box says that a 1/2-cup serving provides 210 calories and 9 grams of dietary fiber. At that rate, find how many calories and grams of fiber are in a 2/3-cup serving.
Answer:
280 calories and 12 grams of dietary fiber
Step-by-step explanation:
because 210(2/3) = 140
= 140 ÷ 1/2 = 280
we do the same steps with grams
9(2/3) = 6
= 6 ÷ 1/2 = 12
Solve for x, each figure is a trapezoid
By calculating , The value of x we get is 5 as a final resultant.
What is trapezoid ?
A trapezoid is a quadrilateral with two parallel sides, called the "bases," and two non-parallel sides, called the "legs." The parallel sides can have different lengths, and the trapezoid can be either right-angled or oblique. In other words, a trapezoid is a geometric shape that has two parallel sides, two non-parallel sides and four angles.
Since a Trapezoid has 360 Degrees total and since the sides are equal we can say that
180=110+17x-15
70=17x-15
85=17x
x=5
Therefore, By calculating , The value of x we get is 5 as a final resultant.
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Which of the following equations listed below are linear equations?
Only Equation I is a linear equation. A linear equation is defined as an equation where the highest power of the variable is 1, and the relationship between the variables is a straight line.
What is Straight line?
A straight line is a type of geometric shape that is defined as a line with no curvature, extending infinitely in both directions. In other words, it is a one-dimensional object that extends indefinitely without bending or curving. Straight lines are often represented mathematically as y = mx + b, where m is the slope (or gradient) of the line and b is the y-intercept.The slope determines the steepness of the line, and the y-intercept determines where the line crosses the y-axis. Straight lines play a crucial role in mathematics, especially in geometry and linear algebra.
Only Equation I is a linear equation.
A linear equation is defined as an equation where the highest power of the variable is 1, and the relationship between the variables is a straight line. In Equation I, P is equal to 4 times s, so the highest power of the variable (s) is 1, making this a linear equation.
In Equation II, the right-hand side of the equation contains a single constant ($3), not a variable, and therefore it is not a linear equation.
Equation III is not a linear equation because it is just a constant equal to 2 and does not contain a variable.
So the answer is: 1. Equation I, only.
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A. 30.28 square feet
B. 24.28 square feet
C. 36.56 square feet
D. 30.56 square feet
Answer:
B. 24.28 square feet
Step-by-step explanation:
You want the area of a figure composed of a rectangle, triangle, and semicircle.
Area formulasThe formulas for the areas of the parts of the figure are ...
A = LW . . . . rectangle of length L and width W
A = 1/2bh . . . . triangle with base b and height h
A = π/2r² . . . . . . semicircle of radius r
RectangleThe area of the rectangle is ...
A = (4 ft)(3 ft) = 12 ft²
TriangleThe area of the triangle is ...
A = 1/2(4 ft)(3 ft) = 6 ft²
SemicircleThe semicircle has a radius that is half the diameter. The diameter is shown as 4 ft so the radius is 2 ft. The area of the semicircle is ...
A = π/2(2 ft)² = 4(3.14)/2 ft² = 6.28 ft²
Composite figure areaThe area of the composite figure is the sum of the areas of its parts:
Area = 12 ft² +6 ft² +6.28 ft² = 24.28 ft²
The area of the composite figure is about 24.28 ft².
Find r. Use law of sine. Round to the nearest tenth.
Answer:
12
Step-by-step explanation:
First find the missing angle S
Three angles of a triangle add up to 180°
So m∠S + 81 + 42 = 180
m∠S + 123 = 180
m∠S = 180 - 123 = 57°
Using the law of sines which states that the ratio of each side to the opposite angle is the same for both sides we get
[tex]\dfrac{r}{\sin 42} = \dfrac{q}{\sin81} = \dfrac{15}{\sin 57}\\\\\sin 57 = 0.83867\\\\ \dfrac{15}{\sin 57}= \dfrac{15}{0.83867}\\\\= 17.88545\\\\[/tex]
Hence
[tex]\dfrac{r}{\sin 42} = 17.88545\\\\r = 17.88545 \times \sin 42\\\\r = 17.88545 \times 0.66913\\\\r = 11.9677\\\\r = 12 \textrm{ rounded to the nearest tenth}[/tex]
As part of a larger experiment, Dale (1992) looked at six samples of a wetland soil undergoing a simulated snowmelt. Three were randomly selected for treatment with a neutral pH snowmelt; the other three got a reduced pH snowmelt. The observed response was the number of Copepoda removed from each microcosm during the first 14 days of snowmelt Reduced pH Neutral pH 256 159 149 54 123 248 (a) [3 points Write two simple models: one model for the number of Copepoda in a neutral pH snowmelt and one model for the number of Copepoda in a reduced pH snowmel. Use mathematical notations. (b) 2 points We want to test whether the two treatments have equal average numbers of Copepoda. Write the n and the alternative hypotheses using the notations defined in the previous question (c) 5 points We want to perform a t-test. What assumptions are you making? Compute the corresponding test statistic. Give the critical value for a level of significance v = 0.05. What do you conclude? (d) 5 points) Using a randomization-based analysis, test the nul hypothesis that the two treatments have equal average numbers of Copepoda versus a two-sided alternative. Use a level of significance v = 0.05.
(a) The mathematical notations is (xₙ, yₙ)
(b) The alternative hypotheses using the notations defined in the previous question is t = (Xₙ - Yₙ) / SE
(c) The assumptions making is variances of the two populations are equal.
A hypothesis is a tentative explanation or prediction of a phenomenon, and it is essential in scientific research. In this study, we have two hypotheses:
Null Hypothesis: There is no significant difference in the average number of Copepod between the reduced pH and neutral pH snowmelt treatments.
Alternative Hypothesis: There is a significant difference in the average number of Copepod between the reduced pH and neutral pH snowmelt treatments.
Model:
A model is a mathematical representation of a phenomenon, and it is used to make predictions or explanations. In this experiment, we can create two simple models:
Model for Neutral pH Snowmelt:
Let Yₙ be the number of Copepod in a microcosm treated with neutral pH snowmelt. Then, Yₙ follows a normal distribution with mean µn and standard deviation σn.
Model for Reduced pH Snowmelt:
Let Yₙ be the number of Copepod in a microcosm treated with reduced pH snowmelt. Then, Yₙ follows a normal distribution with mean µr and standard deviation σr.
Assumptions:
Before conducting a t-test, we must ensure that the data satisfies the following assumptions:
The sample is a random and representative sample of the population.
The data is normally distributed.
The variances of the two populations are equal.
The test statistic for the t-test is:
t = (Xₙ - Yₙ) / SE
where Xₙ is the sample mean of neutral pH snowmelt, Yₙ is the sample mean of reduced pH snowmelt, and SE is the standard error.
Assuming a level of significance v = 0.05, we have a critical value of t = 2.306 for a two-tailed test with 4 degrees of freedom. If our calculated t-value is greater than 2.306 or less than -2.306, we reject the null hypothesis.
We can perform a randomization test as follows:
If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference in the average number of Cope pod between the reduced pH and neutral pH snowmelt treatments. If the p-value is greater than 0.05, we fail to reject the null hypothesis.
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How to show steps upon problem to get answer
The simplified form of the expression xy( x³y⁵ - x⁷ ) is x⁴y⁶ - x⁸y.
What is the simplified form of the expression?Given the expression in the question;
xy( x³y⁵ - x⁷ )
To simplify the expression, apply distributive property.
xy( x³y⁵ - x⁷ )
xy( x³y⁵ ) - xy( x⁷ )
xy( x³y⁵ ) - xy( x⁷ )
Multiply xy and ( x³y⁵ )
x⁴y⁶ - xy( x⁷ )
Multiply xy and ( x⁷ )
x⁴y⁶ - x⁸y
Therefore, the simplified form is x⁴y⁶ - x⁸y.
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A function is given.
g(t) = t4 − t3 + t2; t = −6, t = 6
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
On solving the provided question we can say that the net change will be 17 and average rate of change = 17/1 = 17.
What is function?The subject οf mathematics includes quantities and their variatiοns, equations and related structures, shapes and their locations, and places where they can be fοund.
The term "functiοn" refers to the relationship between a set of inputs, each of which has an associated output. A cοnnection between inputs and outputs in which each input leads to a single, distinct result is known as a functiοn.
Each function is given a dοmain and a codomain, or scope. Usually, f is used to denote functiοns (x). input is an x. There are fοur main types of functions accessible. based οn the following factors: οn functions, one-to-one functions, many-tο-one functions, inside functiοns, and on functions.
The functiοn will be
h(4)=2(4²)-4
=32-4
=28
h(5)=2(5²)-5
=50-5
=45
Net change is 45-28 = 17
average rate of change = 17/1 = 17
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Write the inequality shown by the shaded region in the graph with the boundary line −5x+2y=−2
Answer:
Step-by-step explanation:
The boundary line of the shaded region in the graph, which is represented by the equation -5x + 2y = -2, can be used to write the inequality that represents the shaded region. To do this, we first need to determine which side of the boundary line the shaded region is on.
If the shaded region is on the same side of the line as the open half-plane that contains the y-axis, then the inequality is given by:
-5x + 2y > -2
If the shaded region is on the same side of the line as the closed half-plane that does not contain the y-axis, then the inequality is given by:
-5x + 2y ≥ -2
So, the inequality that represents the shaded region depends on the specific context and requirements of the problem, as well as the interpretation of the graph.
3. If an angle measures 2π radians, what is the measure of the angle in degrees?
Answer:
360 degrees
2 pi radians, means you have 2 pi of something and they are radians. It is the same 360 degrees. A radius is the line from the side of the circle to the center.
Reason: pi radians is 180 degrees. Double each value to find that 2pi radians is 360 degrees. It's a full revolution of a circle. Use a unit circle if necessary.
Rewrite the equation in Ax+By=C form
y=(1/3)x+3
To rewrite the equation in Ax + By = C form, we need to rearrange it so that the x and y terms are on the same side of the equation and the constant is on the other side and the equation become x + 3y = 9.
What is Equation?
An equation is a mathematical statement that shows the equality of two expressions or values. It typically contains one or more variables and an equal sign, which indicates that the expressions on either side of the equal sign have the same value. Equations can be used to represent various relationships between different mathematical objects and are used extensively in many fields of mathematics, science, engineering, and other disciplines. Equations can be solved to find the values of the variables that make the equation true, which is often the goal of many mathematical problems.
To rewrite the equation in Ax + By = C form, we need to rearrange it so that the x and y terms are on the same side of the equation and the constant is on the other side.
Starting with:
y = (1/3)x + 3
We can multiply both sides by 3 to eliminate the fraction:
3y = x + 9
Now we can rearrange to get the x and y terms on the left side:
-x + 3y = 9
So the equation in Ax + By = C form is:
x + 3y = 9
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Find the perimeter of the triangle whose vertices are the following specified points in the plane.
(-9,-6), (-5, 0) and (10,-7)
The required perimeter of the triangle with vertices (-9,-6), (-5, 0), and (10,-7) is 42.72 units.
What is Distance?The distance between two points (x₁, y₁) and (x₂, y₂) in the plane can be found using the distance formula,
d = √((x₂- x₁² + (y₂ - y₁)²)
Here
Using the above formula, we can find the length of each side of the triangle:
Length of the first side:
d = √((-5 - (-9))² + (0 - (-6))²)
= √(4² + 6²)
= √52 = 7.2
Similarly, the length of the second and third sides:
d =√274 = 16.5
Length of the third side:
d = √362 = 19.02
Finally, the perimeter of the triangle is the sum of the lengths of its sides, P = 7.2 + 16.5 + 19.02
P = 42.72 units
So, the perimeter of the triangle is approximately 42.72 units.
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Draw the following triangle after a 90 degrees counterclockwise rotation about the origin.
A graph of the triangle after a 90 degrees counterclockwise rotation about the origin is shown in the image attached below.
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise to the vertices for D, the coordinates of the vertices of the image point D' are as follows:
(x, y) → (-y, x)
Ordered pair A = (-3, 4) → Ordered pair A' = (-4, -3)
Ordered pair B = (-5, -1) → Ordered pair B' = (1, -5).
Ordered pair C = (-1, 2) → Ordered pair C' = (-2, -1).
In this exercise, we would use an online graphing calculator to plot the vertices of triangle A'B'C' as shown in the graph attached below.
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Write an equation for a rational function with the given characteristic.
Vertical asymptotes at x = -2 and x = 3, x-intercepts at (-4,0) and (-1,0), y-intercepts at (0,4)
f(x) =
The rational function with the given characteristics is:
f(x) = -6(x + 4)*(x + 1)/[(x - 2)*(x + 3)]
How to write the rational function?We want to write a rational function with the given characteristics, first we want to have vertical asymptotes at x = -2 and x = 3, then the denominator must be:
(x - 2)*(x + 3)
We also want to have x-intercepts at (-4,0) and (-1,0), this means that the numerator must be:
a*(x + 4)*(x + 1)
Where a is a real number, then the rational function is:
f(x) = a*(x + 4)*(x + 1)/[(x - 2)*(x + 3)]
Now we want to have an y-intercept at (0, 4)
Then we must have:
f(0) = 4 = a*(0 + 4)*(0 + 1)/[(0 - 2)*(0+ 3)]
4 = a*4/-6
(-6/4)*4 = a
-6 = a
The rational function is:
f(x) = -6(x + 4)*(x + 1)/[(x - 2)*(x + 3)]
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st other people Suppose there are no implicit premises: this is the whole argument. Which of the following is true about this argument? o A The premise entails the conclusion because, if the premise is true, the conclusion has to be true B The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false (setting aside facts not supplied by the premise) O с The premise entails the conclusion because, setting aside facts not supplied by the premise, there is no way the premise could be true and the conclusion false. D The premise does not entail the conclusion because it has no suppositional strength.
The true argument is option B) The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false
The argument presented lacks logical reasoning and does not provide enough information to support the conclusion. The premise that "Bob is 13 feet tall" is a factual statement, but it is not sufficient to conclude that "Bob is taller than most other people." Without further information about the height distribution of people.
It is impossible to make such a conclusion based solely on Bob's height. Additionally, the argument does not provide any logical reasoning to connect the premise to the conclusion, so it is not a valid deductive argument.
Therefore, the correct option is (B)
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The given question is incomplete, the complete question is :
Bob is 13 feet tall So, Bob is taller than most other people Suppose there are no implicit premises: this is the whole argument. Which of the following is true about this argument?
A The premise entails the conclusion because, if the premise is true, the conclusion has to be true
B The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false (setting aside facts not supplied by the premise)
C The premise entails the conclusion because, setting aside facts not supplied by the premise, there is no way the premise could be true and the conclusion false.
D The premise does not entail the conclusion because it has no suppositional strength
What is the answer? Provide steps please.
The given expression is proved.
What is trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
here, we have.
tan∅/(1+ sec∅)
=(sin∅/cos∅)/(1+ sec∅) [tan∅=(sin∅/cos∅)]
=(sin∅/cos∅)/(1+1/cos∅)
=sin∅/1+cos∅
multiplying both numerator & denominator by 1-cos∅, we get,
=sin∅(1-cos∅)/ sin^2∅
=(1-cos∅)/sin∅
=cosec∅ - cot∅
Hence, The given expression is proved.
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A set of data has a mean of 10 and a standard deviation of 3.
(a) Each value in the data set has 6 added to it. Write down the value of
(i) the new mean;
(ii) the new standard deviation.
(b) Each value in the original data set is multiplied by 6.
(i) Write down the value of the new mean.
(ii) Find the value of the new variance.
Answer:
Step-by-step explanation:
(a) (i) The mean of the original data set is denoted as μ and the constant value being added to each data point is denoted as c.
The formula for the new mean is simply μ + c, so the new mean is μ + 6 = 10 + 6 = 16.
(a) (ii) The standard deviation of the original data set is denoted as σ. Adding a constant value to each data point does not change the spread of the data set, so the new standard deviation is still σ = 3.
(b) (i) The mean of the original data set is denoted as μ and the constant value being multiplied to each data point is denoted as k.
The formula for the new mean is μ * k, so the new mean is μ * 6 = 10 * 6 = 60.
(b) (ii) The variance of the original data set is denoted as V. To find the new variance after multiplying each data point by k, we can use the formula: k^2 * V.
So, the new variance is 6^2 * V = 36 * V.
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Here is a definition of each variable:
μ: The mean of a set of data is the sum of all the values divided by the number of values. It represents the average value of the data set.
σ: The standard deviation of a set of data is a measure of the spread of the data set about the mean. It is the square root of the variance.
V: The variance of a set of data is the sum of the squares of the deviations of each value from the mean, divided by the number of values. It is a measure of the spread of the data set about the mean, but it is measured in squared units.
c: A constant value added to each data point.
k: A constant value multiplied to each data point.
1.2. Identify and explain TWO types of goals in line with Anelisa 'story. 1.3. Discuss the benefits of goal setting on your career choice. 1.4. Discuss any THREE challenges Anelisa experienced that could have been been obstacles in achieving his goals. 1.5. Analyse how Anelisa's personal values contributed to his success. 1.6. Critically discuss how relationships can impact negatively on the achievement of goals TOTAL ACTIVITY 1: [30] Gauteng Department of Education (2+2) (4) (2x2) (4) (3x2) (6) (4x2) (8) (2x3) (6) 2023 Grade 11 Life Orientation Task
Types of Goals in line with Anelisa's story:
Personal Growth Goals: These goals are related to Anelisa's personal development and could include things like increasing her knowledge, learning new skills, and expanding her experiences.Career Goals: These goals are related to Anelisa's professional development and could include things like advancing in her career, increasing her income, or improving her job performance.Benefits of goal setting on your career choiceGoal setting helps individuals focus their efforts, prioritize their time and resources, and measure their progress towards achieving their goals. In the context of career choice, goal setting can help individuals:
Clarify their career aspirations and identify their strengths, weaknesses, opportunities, and threats.Develop a roadmap for their career journey and align their actions with their career vision.Stay motivated and engaged in their work and avoid feeling overwhelmed or discouraged by the challenges they face.Improve their performance and productivity, and increase their chances of achieving their desired outcomes.Challenges Anelisa experienced:
Lack of resources: Anelisa may have lacked the resources needed to achieve her goals, such as financial support, access to training programs, or sufficient time to complete her tasks.Resistance from others: Anelisa may have encountered resistance from others who opposed her goals, either because they disagreed with her vision or because they felt threatened by her ambition.Self-doubt and fear of failure: Anelisa may have struggled with self-doubt and fear of failure, which could have held her back from pursuing her goals and taking calculated risks to achieve them.Anelisa's personal values, such as determination, resilience, and a strong work ethic, likely played a significant role in her success. These values likely gave her the motivation and drive to pursue her goals, despite the challenges she faced. Additionally, her values may have helped her stay focused on her goals, maintain her sense of purpose, and make decisions that aligned with her vision for her life.
Relationships can impact the achievement of goals in both positive and negative ways. On the positive side, supportive relationships can provide individuals with emotional support, encouragement, and practical resources that can help them achieve their goals. On the negative side, relationships can also be a source of conflict and distraction, especially if they are not aligned with the individual's goals or values.
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Answer:
Step-by-step explanation:
lack of financial stability Nd resoouces
Sears is having a 35% off sale on all tires. Michelin tires sells for $125, find the Sales Price.
Answer:
You will pay 81.25
Step-by-step explanation:
If the cost is 35% off, you will need to pay 100% - 35% = 65%
125 * 65 %
125 *.65
81.25
You will pay 81.25
new later
A scatter plot is shown below.
10
8
6
A
N
02 4
6
8 10 12 14 16
Which statement best explains why these data can or cannot be modeled using a line of best fit?
a. A line would not be appropriate because there is a negative association.
b. A line would not be appropriate because the points follow a nonlinear pattern.
c. A line would be appropriate because there is a positive association.
d. A line would be appropriate because the points follow a nonlinear pattern.
The points are scattered in the scatterplot and thus, a line would not be appropriate because the points follow a nonlinear pattern.
Hence, option b is the correct answer.
How can scatterplot identify relationships?Numerous different kinds of associations between two variables can be found using a scatterplot.
When there is no pattern visible in the points on a scatterplot, a relationship has no correlation.
When the points on a scatterplot exhibit a pattern rather than a straight line, a relationship is non-linear.
When the points on a scatterplot exhibit a largely straight line pattern, a relationship is linear. We shall look at this relationship in detail.
From the given graph we observe that the points do not follow a linear pattern.
The points are scattered and thus, a line would not be appropriate because the points follow a nonlinear pattern.
Hence, option b is the correct answer.
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The correct question is:
A reading specialist wanted to estimate the mean word length, in number of letters, for an elementary school history textbook. The specialist took repeated random samples of size 100 words and estimated the mean and standard deviation of the sampling distribution to be 4. 9 letters and 0. 15 letter, respectively.
Based on the information given, the estimated mean word length of the book is 4.9 letters and the estimated standard deviation of the sampling distribution is 0.15 letters.
The reading specialist is trying to estimate the population mean word length of an elementary school history textbook, but it is not practical or possible to measure the word length of every single word in the book. So, instead, the specialist takes repeated random samples of 100 words from the book and calculates the mean word length of each sample. Based on these repeated samples, the specialist estimates that the mean word length of the book is 4.9 letters. This means that, on average, the words in the book are about 4.9 letters long. The specialist also calculated the standard deviation of the sampling distribution, which is a measure of the variability of the sample means. In this case, the standard deviation of the sampling distribution is estimated to be 0.15 letters. This means that the mean word length of each random sample is expected to vary by about 0.15 letters from the population mean. It is important to note that these estimates are based on a specific set of samples and are subject to sampling variability. If the specialist were to take different random samples, the estimates may be slightly different. However, based on the information given, the estimated mean word length of the book is 4.9 letters and the estimated standard deviation of the sampling distribution is 0.15 letters.
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Greta’s family drinks 3. 1/4 quarts of milk and 1 5/6 quarts of juice in one week. About how much more milk than juice does Greta’s family drink in one week?
Answer:1 5/12 or written the other way 17/12
Step-by-step explanation:
3x + 3xy + 4x +2xy combine like term
Answer:
the final answer is 7x + 5xy.
Step-by-step explanation:
3x + 4x = 7x
3xy + 2xy = 5xy
So, the final answer is 7x + 5xy.
Answer:
5xy+7x
Step-by-step explanation:
You see which ones have the same exact variables (x or xy)
Then you add the ones with the same variables together.
3x+4x=7x
3xy+2xy = 5xy
5xy+7x
(Depending on your teacher, they may not have to be in this order)
