Answers
[tex]\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh ~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ h=8.6\\ A=38.7 \end{cases}\implies 38.7=\cfrac{1}{2}b(8.6)\implies 38.7=4.3b \\\\\\ \cfrac{38.7}{4.3}=b\implies 9=b[/tex]
let's recall the height or altitude of a triangle is the perpendicular distance to base from the top.
Related Questions
The Area of the triangle is 10, The Area of the circle is 15, and the Area of the rectangle is 60.
Find the probability of each. Get answer as a percentage and round to the nearest tenth.
Probability of landing in Triangle- %
Probability of landing in Circle- %
Probability of landing in either Triangle or Circle- %
Answers
The probability of landing in either the triangle or the circle is approximately 29.4%.
To calculate the probability of landing in either the triangle or the circle, we first need to find the total area of all shapes. Given the area of the triangle is 10, the area of the circle is 15, and the area of the rectangle is 60.
Total area = Area of triangle + Area of circle + Area of rectangle
Total area = 10 + 15 + 60
Total area = 85
Now, we calculate the combined area of the triangle and the circle:
Combined area = Area of triangle + Area of circle
Combined area = 10 + 15
Combined area = 25
To find the probability, we will divide the combined area by the total area:
Probability = Combined area / Total area
Probability = 25 / 85
Probability ≈ 0.294
To express the probability as a percentage, multiply by 100:
Probability ≈ 0.294 × 100
Probability ≈ 29.4%
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Solve for T. Type your answer in the blank without "T=".
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The measure of the angle T made by the tangent CT and the secant AT is 45°.
Here, we have,
Given figure is a circle,
we need to find the angle T made by the tangent CT and the secant AT, also given, m arc ABC : m arc CDE = 3:1,
Let m arc ABC = 3x and m arc CDE = x
So,
We see that the arc ABE is a semicircle so m arc ABE = 180°,
Also,
m arc ABE = m arc ABC + m arc CDE
180° = 3x+x
4x = 180°
x = 45°
So,
m arc ABC = 135° and m arc CDE = 45°
Now using the properties of a circle,
We have.
m ∠T = 1/2 [m arc ABC - m arc CDE]
m ∠T = 1/2 [135° - 45°]
m ∠T = 45°
Hence the measure of the angle T made by the tangent CT and the secant AT is 45°.
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A psychological experiment was conducted to compare the lengths of response time (in seconds) for two different stimuli. To remove natural person-to-person variability in the responses, both stimuli were applied to each of nine subjects, thus permitting an analysis of the difference between response times within each person. The results are given in the following table. Use the sign test to determine whether sufficient evidence exists to indicate a difference in mean response for the two stimuli. Use a rejection region for which α ≤ .05.
Answers
The number of "+" signs to the Expected value under the null hypothesis
Step 1: State the null and alternative hypotheses:
- Null hypothesis (H0): There is no difference in mean response times for the two stimuli.
- Alternative hypothesis (Ha): There is a difference in mean response times for the two stimuli.
Step 2: Determine the critical region:
Since α (the significance level) is given as ≤ 0.05, we will use a two-tailed test and split the significance level equally in both tails. This means we will consider the critical region in the upper and lower tails, each with a significance level of 0.025.
Step 3: Apply the sign test:
The sign test is used when the data are paired and the differences between pairs are analyzed. In this case, we are comparing the response times for the two stimuli within each subject.
For each subject, compare the response times for the two stimuli and record whether the first stimulus had a shorter response time (sign "-") or a longer response time (sign "+"). Then, count the number of "+" signs and the number of "-" signs.
Step 4: Determine if the test statistic falls into the critical region:
Using the sign test, we compare the observed number of "+" signs to the expected number under the null hypothesis. If the observed number falls into the critical region, we reject the null hypothesis.
Since the actual data table is not provided, I cannot determine the exact results of the sign test. You would need to perform the calculations based on the given data. you have the actual results table, please provide it so that I can assist you further in performing the sign test and drawing a conclusion based on the results.
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The results shown to the right provide the X-values, residuals, and a residual plot from a regression analysis. Is there any evidence of a pattern in the residuals? Explain. X Residuals 0510-3-2-10123XResiduals A coordinate system has a horizontal x-axis labeled from 0 to 10 in increments of 1 and a vertical axis labeled Residuals from negative 3 to 3 in increments of 0.5. The following points are plotted: (1, 0.61), (2, negative 0.73), (2, negative 0.73), (3, 1.19), (4, negative 0.36), (5, 2.42), (6, negative 0.74), (7, negative 0.25), (8, 1.76), (9, 1.61), (10, 1.61). The plotted points have no particular pattern. 1 0.61 2 −0.73 3 1.19 4 −0.36 5 2.42 6 −0.74 7 −0.25 8 1.76 9 −1.17 10 1.61 Choose the correct answer below. A. Yes, the residuals show decreasing variation. B. Yes, the residuals show a distinct curved pattern. C. Yes, the residuals show a distinct cyclical pattern. D. No, the residuals appear to be randomly spread
Answers
the correct answer is D. No, the residuals appear to be randomly distributed
What is Residual?
The residual is the deviation from the sample mean. Errors, like other population parameters (e.g. population mean), are usually theoretical. Residuals, like other sample statistics (eg, the sample mean), are measured values from the sample.
Based on the given information, the residuals are plotted against the x values in the coordinate system. Looking at the plotted points such as (1, 0.61), (2, -0.73), (3, 1.19) and so on, no clear or systematic pattern is apparent in the residuals.
To see if there is evidence of a pattern in the residuals, we would typically look for trends, cycles, or distinct patterns. In this case, no trend or consistent shape is apparent on the residual plot. The residuals appear to be randomly scattered over the x-axis range.
So the correct answer is D. No, the residuals appear to be randomly distributed. Based on the information provided, there is no clear evidence of any pattern in the residuals.
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In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 72 and a standard deviation of 9. Grades are to be assigned according to the following rule:
The top 10% receive A's. The next 20% receive B's. The middle 40% receive C's. The next 20% received D's. The bottom 10% receive F's. What is the least amount of points that a student must score, on the final exam, in order to earn a C? (Round your answer to two decimal places. )
the answer is 72?
Answers
Rounded to two decimal places, the least amount of points a student must score on the final exam to earn a C is 67.72.
No, the least amount of points that a student must score on the final exam in order to earn a C is not necessarily 72.
To determine the minimum score required for a C, we need to calculate the cutoff point for the middle 40% of the distribution.
Since the points for the final exam are normally distributed with a mean of 72 and a standard deviation of 9, we can use z-scores to find the cutoff point.
To find the cutoff for the middle 40%, we need to find the z-score that corresponds to the 30th percentile (10% below the middle 40%).
We can use a standard normal distribution table or a calculator to find this z-score.
The z-score corresponding to the 30th percentile is approximately -0.524 (rounded to three decimal places).
Using the z-score formula, we can calculate the minimum score needed for a C:
Z = (X - μ) / σ
-0.524 = (X - 72) / 9
Solving for X, we get:
X = -0.524 [tex]\times[/tex] 9 + 72 ≈ 67.72
Rounded to two decimal places, the least amount of points a student must score on the final exam to earn a C is 67.72.
It's important to note that the exact cutoff point may vary slightly depending on rounding conventions or specific instructions provided by the professor or institution.
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Given f(x), which function is the inverse?
f(x) = 3x - 5
A) g(y) = 3y + 5
B) g(y) = // +5
C) g(y) = 3+5 3
D) g(y) = 5y 3
Answers
Answer:
g(y) = 1/3y + 5/3
Step-by-step Explanation:
We know that f(x) is synonymous with y so we can rewrite f(x) as y = 3x -5
To find the inverse of the function, we can switch y with x and x with y:
x = 3y - 5
Now we can isolate y to find the inverse of f(x):
(x = 3y - 5) + 5
(x + 5 = 3y) / 3
x/3 + 5/3 = y
1/3x + 5/3 = y
Thus, the inverse of f(x) is f^-1(x) = 1/3x + 5/3. Since we want to write the inverse in terms of y, we get g(y) = 1/3y + 5/3.
If this answer doesn't match your answer choices (some of the answer choices you provided are unclear), please attach a pic and I can help you figure out which answer choice is correct)
PLEASE HELP ASAP I PROMISE WILL GET BRAINLIEST BUT IT HAS TO BE THE RIGHT ANSWER THANKS
Answers
Based on the general properties of the MAD and the characteristics of the data sets, these matches seem reasonable.
Here, we have,
We can make some general observations to match the data sets to the appropriate MAD value without actually calculating them:
The MAD measures the average distance between each data point and the median of the data set.
Therefore, the larger the MAD value, the more spread out the data set is.
Data set 1 will have the smallest MAD value, since it is the most tightly clustered around the median.
Data set 3 will have the largest MAD value, since it is the most spread out around the median.
Data set 2 will have a MAD value between those of data sets 1 and 3.
Based on these observations, we can match the data sets to the appropriate MAD value as follows:
Data set 1 has the smallest MAD value (7).
Data set 2 has a medium MAD value (9).
Data set 3 has the largest MAD value (11).
Of course, without actually calculating the MAD values, we can't say for certain whether these matches are correct.
Therefore, based on the general properties of the MAD and the characteristics of the data sets, these matches seem reasonable.
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complete question:
The three data sets have MAD value of 7,9 and 11. Match the data sets to the apporopriate MAD value with out actuly making a calculation.
the motion of the particle takes place on ---select--- centered at (x, y) = ____that has ____the particle moves _____around _____ .
Answers
The motion of the particle takes place on a plane centered at (x, y) = (a, b) that has a radius of r. The particle moves in a circular path around the center (a, b).
Describe the motion of particles?Plane: The motion of the particle occurs on a two-dimensional plane.Centered at (x, y) = (a, b): The center of the circular path is located at the coordinates (a, b) on the plane. This means that the particle's motion is focused around this point.Radius: The circular path has a radius of r. This means that the distance from the center (a, b) to any point on the circular path is equal to r.Circular Path: The particle moves in a circular path around the center (a, b). This implies that the trajectory of the particle forms a perfect circle, with the center (a, b) as its midpoint.In summary, the motion of the particle occurs on a plane, with the circular path centered at (a, b) and a radius of r. The particle moves in a circular trajectory around the center.Learn more about Radius
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Find the mass of the wire that lies along the curve r and has density δ. 30) C1:r(t)=(3cost)i+(3sint)j,0≤t≤2π. C2:r(t)=3j+tk,0≤t≤1;δ=5t2 A) 415π2 units B) 35(83π3+1) units C) 35(81π2+1) units D) 1615π2 units
Answers
The correct option is B) 35/3 (π³ + 1) units
What is MASS?
Mass (symbolized m) is a dimensionless quantity representing the amount of matter in a particle or object. The standard unit of mass in the International System (SI) is the kilogram (kg).... The mass of an object can be calculated if the forces and accelerations are known. Weight is not the same as weight. Mark me as the most intelligent.
To find the mass of the wire that lies along the curves C1 and C2 and has density δ, we can use the formula for calculating the mass of a curve with variable density.
For curve C1:
r(t) = (3cos(t))i + (3sin(t))j, 0 ≤ t ≤ 2π
The length element ds along C1 can be calculated as:
ds = |r'(t)| dt
r'(t) = (-3sin(t))i + (3cos(t))j
|r'(t)| = √((-3sin(t))² + (3cos(t))²) = 3
Therefore, the length element ds = 3 dt.
The mass element dm along C1 is given by:
dm = δ ds
Substituting δ = 5t² and ds = 3 dt, we have:
dm = 5t² * 3 dt = 15t² dt
The mass of the wire along C1 can be calculated by integrating dm over the range 0 to 2π:
m1 = ∫[0 to 2π] dm
= ∫[0 to 2π] 15t² dt
= 15 ∫[0 to 2π] t² dt
Using the formula for integrating powers of t, we get:
m1 = 15 * [t³/3] evaluated from 0 to 2π
= 15 * [(2π)³/3 - 0³/3]
= 15 * (8π³/3)
= 40π³ units
For curve C2:
r(t) = 3j + tk, 0 ≤ t ≤ 1
δ = 5t²
The length element ds along C2 can be calculated as:
ds = |r'(t)| dt
r'(t) = k
|r'(t)| = 1
Therefore, the length element ds = dt.
The mass element dm along C2 is given by:
dm = δ ds
Substituting δ = 5t² and ds = dt, we have:
dm = 5t² dt
The mass of the wire along C2 can be calculated by integrating dm over the range 0 to 1:
m2 = ∫[0 to 1] dm
= ∫[0 to 1] 5t² dt
= 5 ∫[0 to 1] t² dt
Using the formula for integrating powers of t, we get:
m2 = 5 * [t³/3] evaluated from 0 to 1
= 5 * (1³/3 - 0³/3)
= 5/3 units
The total mass of the wire along C1 and C2 is given by the sum of m1 and m2:
Total mass = m1 + m2
= 40π³ + 5/3 units
Therefore, the mass of the wire that lies along the curves C1 and C2 with the given density is:
35/3 (π³ + 1) units
Hence, the correct option is B) 35/3 (π³ + 1) units.
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Please help me please
Answers
All the values are,
a) lim x → 3 [ 2 f (x) - g (x)] = 18
b) lim x → 3 [ 2 g (x) ]² = 16
c) lim x → 3 [ ∛ f (x) / g (x) ] + lim x → 3 [ 4 h (x) / x + 7 ] = - 1
We have to given that;
Limits are,
lim x → 3 f (x) = 8
lim x → 3 g (x) = - 2
lim x → 3 h (x) = 0
Now, We can simplify all the limits as;
1) lim x → 3 [ 2 f (x) - g (x)]
⇒ lim x → 3 [ 2 f (x)] - lim x → 3 [ g (x) ]
⇒ 2 lim x → 3 [ f (x) ] - (- 2)
⇒ 2 × 8 + 2
⇒ 16 + 2
⇒ 18
2) lim x → 3 [ 2 g (x) ]²
⇒ 4 [ lim x → 3 g (x) ]²
⇒ 4 × (- 2)²
⇒ 4 × 4
⇒ 16
3) lim x → 3 [ ∛ f (x) / g (x) ] + lim x → 3 [ 4 h (x) / x + 7 ]
⇒ ∛8 / (- 2) + 4 × 0 / (3 + 7)
⇒ - 2/2 + 0
⇒ - 1
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(Question 6)
State The Slope
Answers
Answer:
-1.72
Step-by-step explanation:
slope = change in y ÷ change in x
= (5 - -5) / (-2.1 - 3.7)
= (5 + 5)/(-2.1 - 3.7)
= 10/-5.8
= -1.72
Determine which integer will make the inequality 4x + 6 < 2x + 12 false. S:{1} S:{−1} S:{4} S:{−4}
Answers
Answer:4
Step-by-step explanation:4x+6<2x+12
4x-2x+6<12
2x+6<12
2x<12-6
2x<6
2x/2<6/2
x<3
Which of the following is an example of quantitative data?A. North America is moving across Earth's surface several centimeters per yearB. the river has flooded a low-lying areaC. the volcano is releasing much steamD. volcanoes are dangerousE. when held, one rock feels heavier than another rock
Answers
The example of quantitative data among the given options is option A. North America is moving across Earth's surface several centimeters per year
Quantitative data refers to numerical or measurable information. In option A, the statement provides specific numerical measurements by stating that North America is moving across Earth's surface several centimeters per year. This information can be quantified and measured, making it an example of quantitative data.
Options B, C, D, and E do not provide numerical or measurable information. They describe qualitative characteristics or observations that cannot be easily quantified or measured.
B. The river has flooded a low-lying area describes a qualitative observation of a flood occurrence.
C. The volcano is releasing much steam describes a qualitative observation of steam release.
D. Volcanoes are dangerous makes a general statement without providing specific numerical information.
E. When held, one rock feels heavier than another rock is a subjective comparison and does not provide specific quantitative measurements.
Therefore, option A is the example of quantitative data as it provides numerical information that can be measured and quantified.
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if we multiply 2 number to get 1 digits what will be the answer?
Answers
The multiplication of two number result 1 digits can be
1 × 1 = 1
2 x 2= 4
3 x 2 = 6
4 x 2 = 8
2 × 5 = 10
If you multiply two numbers and the product is a single digit, there are several possible answers.
Here are a few examples:
1 × 1 = 1
2 x 2= 4
3 x 2 = 6
4 x 2 = 8
2 × 5 = 10
3 × 4 = 12
6 × 2 = 12
So, depending on the numbers you choose, the answer could be 1, 10, 12, or any other single-digit number that can be obtained by multiplying two numbers together.
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find the area under the standard normal curve over the interval specified below to the right of z=3
Answers
The standard normal curve, also known as the standard normal distribution or the z-distribution, is a specific probability distribution that follows a bell-shaped curve. The area under the standard normal curve to the right of z = 3 is approximately 0.0013.
For the area under the standard normal curve to the right of z = 3, we need to calculate the cumulative probability from z = 3 to positive infinity.
The standard normal distribution, also known as the z-distribution, has a mean of 0 and a standard deviation of 1. It is a symmetric bell-shaped curve that represents the distribution of standard scores or z-scores.
Using statistical tables or software, we can find the cumulative probability associated with z = 3, which represents the area under the curve to the left of z = 3.
The cumulative probability for z = 3 is approximately 0.9987.
For the area to the right of z = 3, we subtract the cumulative probability from 1.
Therefore, the area to the right of z = 3 is approximately 1 - 0.9987 = 0.0013.
In conclusion, the area under the standard normal curve to the right of z = 3 is approximately 0.0013.
This means that the probability of randomly selecting a value from the standard normal distribution that is greater than 3 is approximately 0.0013 or 0.13%.
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lim x→0 e2x − e−2x − 4x x − sin(x)
Answers
the limit of the given expression as x approaches 0 is 16.
The limit of the given expression as x approaches 0 is indeterminate. We can use L'Hôpital's rule to evaluate it.
Differentiating the numerator and denominator separately:
lim x→0 [(2e^2x + 2e^(-2x)) - 4] / (1 - cos(x))
Taking the limit again:
lim x→0 [(4e^2x - 4e^(-2x)) / sin(x)]
Applying L'Hôpital's rule one more time:
lim x→0 [(8e^2x + 8e^(-2x)) / cos(x)]
Now, substituting x = 0 into the expression, we get:
(8 + 8) / 1 = 16
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Could you please help me figure out what the slant height is? Radius=5
Height=11
Slant=?
Answers
Answer:
s = [tex]\sqrt{146[/tex]
Step-by-step explanation:
We can create a triangle cross-section with the given radius and height as its dimensions. Because this is a cone, we know that the radius and height are at a right angle to each other. Thus, this cross-section is a right triangle, and we can apply the Pythagorean Theorem to solve for the slant height.
r² + h² = s²
↓ plugging in the given values
5² + 11² = s²
↓ simplifying the exponents
25 + 121 = s²
↓ simplifying the addition
146 = s²
↓ square-rooting both sides
s = [tex]\bold{\sqrt{146}}[/tex]
Answer:
12.08
Step-by-step explanation:
Using Pythagoras Theorem
[tex]s {}^{2} = r {}^{2} + h {}^{2} [/tex]
[tex]s {}^{2} = 5 {}^{2} + 11 {}^{2} [/tex]
[tex]s {}^{2} = 121 + 25 = 146[/tex]
[tex]s = \sqrt{146} [/tex]
[tex]s = 12.08[/tex]
Solve the problem PDE: Utt = 16uxx, BC: u(0, t) = u(1, t) = 0 IC: u(x, 0) = 3 sin(2x), u(x, t) = help (formulas) 0 < x < 1, t> 0 u₁(x, 0) = 8 sin(3x)
Answers
The solution to the given partial differential equation problem is u(x, t) = 0.
To solve the given problem, we can use the method of separation of variables. Let's assume that the solution can be written as a product of two functions, one depending only on x and the other only on t:
u(x, t) = X(x)T(t)
Now, let's substitute this solution into the partial differential equation (PDE):
X''(x)T(t) = 16X(x)T''(t)
Dividing both sides of the equation by X(x)T(t), we get:
X''(x)/X(x) = 16T''(t)/T(t)
Since the left side depends only on x and the right side depends only on t, they must be equal to a constant, which we'll denote as -λ²:
X''(x)/X(x) = -λ² = 16T''(t)/T(t)
Now, we have two ordinary differential equations to solve separately:
1) X''(x)/X(x) = -λ² with boundary conditions X(0) = 0 and X(1) = 0
2) T''(t)/T(t) = -λ²/16
1) Solving the first equation:
The general solution to this equation can be written as:
X(x) = A sin(λx) + B cos(λx)
Applying the boundary conditions, we have:
X(0) = A sin(0) + B cos(0) = 0 => B = 0
X(1) = A sin(λ) = 0 => A = 0 (since sin(λ) = 0 has no non-trivial solutions)
Therefore, the solution for the spatial part is X(x) = 0.
2) Solving the second equation:
The general solution to this equation can be written as:
T(t) = C₁ cos(λt/4) + C₂ sin(λt/4)
Applying the initial condition T(0) = 8 sin(3x), we have:
T(0) = C₁ cos(0) + C₂ sin(0) = C₁ = 8 sin(3x)
Now, we have the solutions for X(x) = 0 and T(t) = C₁ cos(λt/4) + C₂ sin(λt/4).
To find the complete solution u(x, t), we multiply the solutions:
u(x, t) = X(x)T(t) = 0 * (C₁ cos(λt/4) + C₂ sin(λt/4)) = 0
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Define a relation on Z by declaring xRy if and only if x and y have the same parity (i.e., if they are both even or both odd). Is R reflexive? symmetric? transitive? For each property, either prove R has the property or give a counterexample that lacks the property
Answers
The relation R on Z is defined as xRy if and only if x and y have the same parity.
Reflexive property: A relation R is reflexive if for all a∈Z, aRa holds true. In this case, for any integer a, aRa holds true if and only if a is either odd or even. Therefore, R is reflexive. Symmetric property: A relation R is symmetric if for all a,b∈Z, aRb implies bRa. In this case, if xRy, then x and y have the same parity. But if yRx, then y and x must also have the same parity, and thus, yRx also holds true. Therefore, R is symmetric. Transitive property: A relation R is transitive if for all a,b,c∈Z, aRb and bRc implies aRc. In this case, if xRy and yRz, then x and y have the same parity, and y and z have the same parity. Therefore, x and z must also have the same parity, which implies that xRz holds true. Therefore, R is transitive. We have proved that the relation R on Z is reflexive, symmetric, and transitive. Therefore, it is an equivalence relation.
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Solve the problem. 31) The five sales people at Southwest Appliances earned commissions last year of $14,000, $21,000, $43,000, $16,000, and $26,000. Find the mean commission.
Answers
Answer:
Therefore, the mean commission earned by the five salespeople at Southwest Appliances is $24,000.
Step-by-step explanation:
To find the mean (average) commission of the five salespeople at Southwest Appliances, you need to calculate the sum of all the commissions and divide it by the total number of salespeople.
Sum of commissions = $14,000 + $21,000 + $43,000 + $16,000 + $26,000
Sum of commissions = $120,000
Total number of salespeople = 5
Mean commission = Sum of commissions / Total number of salespeople
Mean commission = $120,000 / 5
Mean commission = $24,000
Therefore, the mean commission earned by the five salespeople at Southwest Appliances is $24,000.
X =
In the diagram below, ZHDA and ZADR are supplementary.
(7x-3)°
(2r-6)°
H
D
What is the value of r?
R
Answers
The numerical value of x in the supplementary angle is 21.
What is the numerical value of x?The supplementary angles are simply angles having the summation of 180 degrees.
From the diagram:
Angle HDA = ( 7x - 3 ) degrees
Angle ADR = ( 2x - 6 ) degrees
Since, angle HDA and angle ADR are supplementary angles, their sum will equal 180 degrees.
Hence:
Angle HDA + Angle ADR = 180
Plug in the values and solve for x:
( 7x - 3 ) + ( 2x - 6 ) = 180
7x - 3 + 2x - 6 = 180
Collect and add like terms
7x + 2x - 6 - 3 = 180
9x - 9 = 180
9x = 180 + 9
9x = 189
Divide both sides by 9
x = 189/9
x = 21
Therefore, the value of x is 21.
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2. Emmy Noether, the Mother of Modern Algebra, was born in.
1882. In what year did she celebrate her 25th birthday?
Answers
Emmy Noether celebrated her 25th birthday in the year 1907.
Given that,
In 1882, Emmy Noether was born. We need to calculate the year when she was 25.
The concept of addition is a fundamental operation in mathematics that involves combining two or more quantities to find their total or sum.
It is denoted by the "+" symbol, and the numbers being added are called addends. When two or more numbers are added together, the result is called the sum.
So,
We can easily calculate the year she turned 25 by simply adding 25 years to the year she was born.
1882 + 25 = 1907
Hence Emmy Noether turned 25 in 1907, marking the year of her birthday.
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express the internal shear in terms of x for 0≤x≤4m where x is in m.
Answers
The internal shear for 0≤x≤4m in terms of x is given by the equation V(x) = -wx, where w is the distributed load in N/m.
Internal shear refers to the shear force acting within a section of a beam. In this case, we are given a beam with a distributed load w and we need to express the internal shear in terms of x for 0≤x≤4m. To do this, we can use the equation for distributed load:
w = dW/dx
where W is the total load on the beam and dW/dx is the rate of change of load with respect to distance. Integrating this equation.
The equation for distributed load is:
w = dW/dx
where W is the total load on the beam and dW/dx is the rate of change of load with respect to distance. Integrating this equation, we get:
W(x) = ∫0x w dx
Substituting the value of w from the given equation, we get:
W(x) = ∫0x (-wx) dx = -wx^2/2
The negative sign indicates that the load is acting in the opposite direction to the positive x-axis. This means that the total load on the beam decreases as we move from the left end towards the right end.
The internal shear V(x) at a distance x from the left end of the beam is given by the derivative of W(x) with respect to x:
V(x) = dW/dx = -wx
Therefore, the internal shear for 0≤x≤4m in terms of x is given by the equation V(x) = -wx, where w is the distributed load in N/m.
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Help me these two questions please
Answers
The correct form of Pythagoras theorem is: A² + B² = C²
The legs are 12 inches and 5 inches while the hypotenuse is 13 inches
How to use Pythagoras theorem?Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
Applying Pythagoras Theorem gives us the expression as:
5 = √(13² - 12²)
where:
Legs are 5 inches and 12 inches while the hypotenuse is 13 inches
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Khalil is a waiter at a restaurant. Each day he works, Khalil will make a guaranteed wage of $35, however the additional amount that Khalil earns from tips depends on the number of tables he waits on that day. From past experience, Khalil noticed that he will get about $10 in tips for each table he waits on. How much would Khalil expect to earn in a day on which he waits on 11 tables? How much would Khalil expect to make in a day when waiting on
t
t tables?
Answers
The amounts that Khalil is expected to make are given as follows:
11 tables: $145.t tables: 35 + 10t.How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:
m represents the slope of the function, which is by how much the dependent variable y increases or decreases when the independent variable x is added by one.b represents the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, the intercept is given by the value of y at which the graph crosses or touches the y-axis.The parameters for this problem are given as follows:
m = 10, as for each table, the wage increaes by $10.b = 35, which is the guaranteed wage.Hence the function for waiting on t tables is given as follows:
y = 10t + 35.
For 11 tables, the earnings are given as follows:
y = 10 x 11 + 35 = 145.
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1) According to one study, brain weights of men are normally distributed with a mean of 1.10 kg and a standard deviation of 0.14 kg. Use the data to answer questions (a) through (e).a. Determine the sampling distribution of the sample mean for samples of size 3.b. Determine the sampling distribution of the sample mean for samples of size 12.d. Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.10 kg.e. Determine the percentage of all samples of twelve men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.10 kg.
Answers
(a) To determine the sampling distribution of the sample mean for samples of size 3, we need to consider the central limit theorem.
According to the central limit theorem, as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution, as long as the sample size is sufficiently large.
In this case, since the population is normally distributed, the sampling distribution of the sample mean for samples of size 3 will also be normally distributed.
(b) Similarly, for samples of size 12, the sampling distribution of the sample mean will also be normally distributed due to the central limit theorem.
(d) To determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.10 kg, we need to calculate the z-scores for the given values.
First, we calculate the standard error of the sample mean:
Standard Error = Population Standard Deviation / sqrt(Sample Size)
Standard Error = 0.14 kg / sqrt(3)
Next, we calculate the z-score using the formula:
z = (Sample Mean - Population Mean) / Standard Error
For this case, we are interested in finding the percentage of samples within 0.1 kg of the population mean. So we need to calculate the z-scores for the upper and lower limits:
z_lower = (1.10 - 1.10 - 0.1) / (0.14 / sqrt(3))
z_upper = (1.10 - 1.10 + 0.1) / (0.14 / sqrt(3))
Using the z-table or a statistical calculator, we can find the percentage of the area under the normal distribution curve between these two z-scores. This will give us the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.10 kg.
(e) Similar to part (d), we can follow the same procedure to determine the percentage of all samples of twelve men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.10 kg. The only difference will be in the calculation of the standard error:
Standard Error = 0.14 kg / sqrt(12)
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A company offers a basic life insurance policy to its employees, as well as a supplemental life insurance policy. To purchase the supplemental policy, an employee must first purchase the basic policy. Let X denote the proportion of employees who purchase the basic policy and Y the proportion of employees who purchase the supplemental policy. Let X and Y have the joint density function 2x+) 0
Answers
The joint density function of the proportion of employees who purchase the basic policy (X) and the proportion of employees who purchase the supplemental policy (Y) is given as 2x + y.
To understand the relationship between X and Y, we will examine the joint density function 2x + y. The joint density function represents the probability distribution of X and Y, indicating the likelihood of different combinations of X and Y values occurring.
By integrating the joint density function over the specified domain [0,1] for X and Y, we can determine the probabilities associated with different events. For example, we can calculate the probability of a certain proportion of employees purchasing both the basic and supplemental policies or only one of the policies.
Additionally, we can assess the marginal densities of X and Y by integrating the joint density function with respect to the other variable. This will provide information about the individual probabilities and behaviors related to each policy.
Analyzing the joint density function allows us to understand the purchasing patterns and the relationship between the basic and supplemental policies. It provides insights into the likelihood of employees purchasing both policies, the dependence between X and Y, and the probabilities associated with different proportions of employees purchasing the insurance policies.
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a recent survey found that out of a random sample of 150 drivers, 100 of them wear seatbelts. what is the 95onfidence interval for the proportion p of drivers that do not wear seatbelts?
Answers
The 95% CI for proportion of driver that do not wear seat belt is 0.255 < p < 0.405.
What is Confidence interval?
A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.
As given,
n = 150 = drivers
x = 100 = wear seat belts.
We have to find 95% confidence interval for proportion P that do not wear seat belt.
From 150 we have 100 wear seat belts
Not wear seat belt = 150 - 100
Not wear seat belt = 50
P = 50/150
P = 0.33
95% confidence interval for P is
CI = (P - zα/2√(P(1 - P)/n), P + zα/2√(P(1 - P)/n))
For 95% CI, zα/2 = 1.96
Substitute values,
CI = (0.33 - 1.96√(0.33(1 - 0.33)/150), 0.33 + 1.96√(0.33(1 - 0.33)/150))
CI = (0.33 - 0.075, 0.33 + 0.075)
CI = (0.255, 0.405)
Therefore 95% CI for proportion of driver that do not wear seat belt is 0.255 < p < 0.405.
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What is -8(n-1)
Simplified
Answers
Answer:
-8n + 8
Step-by-step explanation:
To simplify this expression, we will use the distribution property and distribute -8 through the parenthesis :
-8(n - 1)
-8 * n - 8 * - 1
-8n + 8
Therefore, the answer is -8n + 8
Which of the following represents a population and a sample from that population? a. None of the suggested answers are correct b. Attendees at a sporting event, and those who purchased popcorn at said sporting event c. Seniors at Boston College and students in a first-semester business statistics course d. Full-time employees at a marketing firm, and temporary summer interns at the marketing firm e. Stocks available on the TSX and stocks on the NYSE
Answers
Seniors at Boston College and students in a first-semester business statistics course represent a population and a sample, respectively(C).
A population refers to the entire group of individuals or items that we are interested in studying, while a sample is a subset of the population that is selected for analysis.
In option c, the seniors at Boston College represent a population as they are the entire group of interest. On the other hand, the students in a first-semester business statistics course represent a sample because they are a subset of the population (seniors at Boston College) and are selected for analysis. So c is correct option.
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