The percentage of students passing the partial exam is:
Option c. 70%
What is the percentage of students passing the partial exam?To answer this question, we use the Z-table. We have:
Given, mean (μ) = 120 and standard deviation (σ) = 17
Passing Score = 111
To find out what percentage of students passed the midterm, we need to find the probability that a score picked at random from the distribution is greater than or equal to 111. We can convert this score into a standard score (Z-score) using the Z-table. We have:
Z-score = (111 - μ) / σ
= (111 - 120) / 17
= -0.53
Using the Z-table, we can find the area (probability) to the left of this Z-score as follows:
Area to the left of Z-score = 0.2981 (from Z-table)
The area to the right of this Z-score (i.e. the probability that a score picked at random from the distribution is greater than or equal to 111) is:
Area to the right of Z-score = 1 - 0.2981
= 0.7019
= 70.19%
Therefore, the percentage of students who passed the midterm is approximately 70% (Option C).
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Answer:
C. 70%
Step-by-step explanation:
if the circumference of the moon is 6783 miles what is its diameter in miles
Answer:
C = 21,309.4
Step-by-step explanation:
Diameter of moon is miles is,
d = 2159.8 miles
We have,
The circumference of the moon is, 6783 miles
Since, We know that,
the circumference of circle is,
C = 2πr
Substitute given values,
6783 miles = 2 × 3.14 × r
6783 = 6.28 × r
r = 6783 / 6.28
r = 1079.9 miles
Therefore, Diameter of moon is miles is,
d = 2 x r
d = 2 x 1079.9
d = 2159.8 miles
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Which of the following are true statements? Check all that apply. A. F(x)= 2 square x has the same domain and range as f(x)= square x. B. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2. C. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it horizontally by a factor of 1/2. D. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.
The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2.
The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.
Thus, Option B and Option D are correct.
What is function?A function is a relationship or expression involving one or more variables. It has a set of input and outputs.
A. F(x)= 2 square x has the same domain and range as f(x)= square x.
B. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2.
D. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.
Option A is false because multiplying the function by 2 will change the range of the function to include all non-negative real numbers (since the square of any number is non-negative).
Option B is true because multiplying the function by 2 will vertically shrink the graph by a factor of 1/2 (since the output values will be half the size of the original function).
Option C is false because multiplying the function by 2 will not affect the horizontal scale of the graph.
Option D is true because multiplying the function by 2 will vertically stretch the graph by a factor of 2 (since the output values will be twice the size of the original function).
Therefore, Option B and Option D are correct.
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solve the proportion 7/11=18/x+1
Solve the equation [tex]7/11=18/x+1[/tex] we find the solution is [tex]x = 27.2857[/tex]
What is a formula or equation?Your example is an equation since an equation is any statement with an equals sign. Equations are frequently utilized for mathematical equations since mathematicians like equal signs. A set of instructions for achieving a certain result is called an equation.
A formula is it an expression?A number, a constant, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by such an assignment operator form an equation.
we can cross-multiply,
[tex]7(x+1) = 11(18)[/tex]
Expanding the left side,
[tex]7x + 7 = 198[/tex]
Subtracting [tex]7[/tex] from both sides,
[tex]7x = 191[/tex]
Dividing both sides by [tex]7[/tex],
[tex]x = 191/7[/tex]
Therefore, the solution to the proportion is
[tex]x = 27.2857[/tex]
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Write each function in terms of its cofunction. Assume that all angles in which an unknown appears are acute angles. cos(α+20∘)
The given function is cos(α+20°) and its cofunction can be expressed as cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°).
Therefore cos(α+20°) in terms of its cofunctions, we need to use the formulas for sin and cos of complementary angles.
The complementary angle of 20° is 70° because 20° + 70° = 90°.
So, we can rewrite cos(20°) as sin(70°) and sin(20°) as cos(70°).
Using the formula for the cosine of the sum of two angles, we can then substitute these values to get:
cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°)
Therefore, expression of cos(α+20°) in terms of its cofunctions is cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°).
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there exists a complex number $c$ such that we can get $z 2$ from $z 0$ by rotating around $c$ by $\pi/2$ counter-clockwise. find the sum of the real and imaginary parts of $c$.
The sum of the real and imaginary parts of $c$ is$$\operatorname{Re}(c) + \operatorname{Im}(c) = \frac{\operatorname{Re}(2c)}{2} + \frac{\operatorname{Im}(2c)}{2}$$$$= \frac{\operatorname{Re}(z_0+z_2)}{2} - \frac{\operatorname{Im}(z_0)}{2}(1-\cos(\theta/2)) - \frac{\operatorname{Re}(z_0)}{2}\sin(\theta/2)$$$$+ \frac{\operatorname{Im}(z_0+z_2)}{2} - \frac{\operatorname{Re}(z_0)}{2}(1-\cos(\theta/2)) + \frac{\operatorname{Im}(z_0)}{2}\sin(\theta/2).$$
The given problem can be solved using algebraic and geometric methods. We can use algebraic methods, such as the equations given in the problem, and we can use geometric methods by visualizing what the problem is asking. To start, let's translate the given problem into mathematical equations. Let $z_0$ be the original complex number. We want to rotate this point by 90 degrees counter-clockwise about some complex number $c$ to get $z_2$. Thus,$$z_2 = c + i(z_0 - c)$$$$=c + iz_0 - ic$$$$= (1-i)c + iz_0.$$We also know that this transformation will rotate the point $z_1 = (z_0 + z_2)/2$ by 45 degrees. Thus, using similar logic,$$z_1 = (1-i/2)c + iz_0/2.$$Now let's use the formula for rotating a point about the origin by $\theta$ degrees (where $\theta$ is measured in radians) to find a relationship between $z_1$ and $z_0$.$$z_1 = z_0 e^{i\theta/2}$$$$\implies (1-i/2)c + iz_0/2 = z_0 e^{i\theta/2}$$$$\implies (1-i/2)c = (e^{i\theta/2} - 1)z_0/2.$$We can solve for $c$ by dividing both sides by $1-i/2$.$$c = \frac{e^{i\theta/2} - 1}{1-i/2}\cdot\frac{z_0}{2}.$$We can now use the information given in the problem to solve for the sum of the real and imaginary parts of $c$. We know that rotating $z_0$ by 90 degrees counter-clockwise will result in the complex number $z_2$. Visually, this means that $c$ is located at the midpoint between $z_0$ and $z_2$ on the line that is perpendicular to the line segment connecting $z_0$ and $z_2$. We can use this geometric interpretation to solve for $c$. The midpoint of the line segment connecting $z_0$ and $z_2$ is$$\frac{z_0+z_2}{2} = c + i\frac{z_0-c}{2}.$$Solving for $c$, we get$$c = \frac{z_0+z_2}{2} - \frac{i}{2}(z_0-c)$$$$\implies 2c = z_0+z_2 - i(z_0-c)$$$$\implies 2c = z_0+z_2 - i(z_0- (e^{i\theta/2} - 1)(z_0/2)/(1-i/2)).$$We can now find the real and imaginary parts of $c$ and add them together to get the desired answer. Let's first simplify the expression for $c$.$$2c = z_0+z_2 - i(z_0 - (e^{i\theta/2} - 1)\cdot(z_0/2)\cdot(1+i)/2)$$$$= z_0 + z_2 - i(z_0 - z_0(e^{i\theta/2} - 1)(1+i)/4)$$$$= z_0 + z_2 - i(z_0 - z_0e^{i\theta/2}(1+i)/4 + z_0(1-i)/4)$$$$= z_0 + z_2 - i(z_0(1-e^{i\theta/2})/4 + z_0(1-i)/4)$$$$= z_0 + z_2 - i(z_0/4(1-e^{i\theta/2} + 1 - i))$$$$= z_0 + z_2 - i(z_0/2(1-\cos(\theta/2) - i\sin(\theta/2)))$$$$= z_0 + z_2 - i(z_0(1-\cos(\theta/2)) + z_0\sin(\theta/2) - i(z_0\cos(\theta/2))/2.$$Now we can find the real and imaginary parts of $2c$ and divide by 2 to get the real and imaginary parts of $c$. We have$$\operatorname{Re}(2c) = \operatorname{Re}(z_0+z_2) - \operatorname{Im}(z_0)(1-\cos(\theta/2)) - \operatorname{Re}(z_0)\sin(\theta/2)$$$$\operatorname{Im}(2c) = \operatorname{Im}(z_0+z_2) - \operatorname{Re}(z_0)(1-\cos(\theta/2)) + \operatorname{Im}(z_0)\sin(\theta/2).$$Thus, the sum of the real and imaginary parts of $c$ is$$\operatorname{Re}(c) + \operatorname{Im}(c) = \frac{\operatorname{Re}(2c)}{2} + \frac{\operatorname{Im}(2c)}{2}$$$$= \frac{\operatorname{Re}(z_0+z_2)}{2} - \frac{\operatorname{Im}(z_0)}{2}(1-\cos(\theta/2)) - \frac{\operatorname{Re}(z_0)}{2}\sin(\theta/2)$$$$+ \frac{\operatorname{Im}(z_0+z_2)}{2} - \frac{\operatorname{Re}(z_0)}{2}(1-\cos(\theta/2)) + \frac{\operatorname{Im}(z_0)}{2}\sin(\theta/2).$$
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A toy maker needs to make $17,235 per month to meet his cost. Each toy sells for $45. How many toys does he need to sell in order to break even
Answer:
Step-by-step explanation:
i assume the figure he needs to "make" is the turnover and not the marginal profit - no indication of the cost of the toys he sells is given so it is impossible to work out the marginal profit of the each toy sold. (Though how the toymaker worked out the turnover required without knowing the cost of the toy is beyond me - though that didn't stop British Leyland pricing their best selling Mini in the 1970s.)
In this case divide the income required by the price of each toy, but as the income must be at least the required amount, any fractional part of a toy must be rounded *UP* to the next whole number.
17,235 ÷ 45 = 383 (so no rounding is needed).
He needs to sell 383 toys (made at zero marginal cost).
Halle el valor de x y de y en el siguiente diagrama. Use el teorema de Tales:
No olvide adjuntar los procedimientos.
doy 20 puntos por favor es paea YAAAA
The value of y = 2.34 and x = 2.31
What are the similar triangles?Similar triangles are a pair of triangles that have the same shape but may differ in size. This means that their corresponding angles are congruent, and their corresponding sides are proportional. Similar triangles are an important concept in geometry.
Here two similar triangles are given below, ΔABC ≈ ΔCEF
For similar triangle we can write,
⇒ CE/CF = AE/BF
⇒ 3.9/5 = y/3 ⇒ y = (3×3.9)/5
So, y = 2.34
Similarly,
⇒ CF/CB = EF/AB
⇒ 5/8 = x/3.7 ⇒ x = (5×3.7)/8
⇒ x = 18.5/8 = 2.31
Therefore, The value of y = 2.34 and x = 2.31
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According to the question the value of triangles y = 2.34 and x = 2.31
What are the similar triangles?Similar triangles are a pair of triangles that have the same shape but may differ in size. This means that their corresponding angles are congruent, and their corresponding sides are proportional. Similar triangles are an important concept in geometry.
Here two similar triangles are given below, ΔABC ≈ ΔCEF
For similar triangle we can write,
⇒ CE/CF = AE/BF
⇒ 3.9/5 = y/3 ⇒ y = (3×3.9)/5
So, y = 2.34
Similarly,
⇒ CF/CB = EF/AB
⇒ 5/8 = x/3.7 ⇒ x = (5×3.7)/8
⇒ x = 18.5/8 = 2.31
Therefore, The value of y = 2.34 and x = 2.31
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suppose the vertical distance between the points (0, a) and (0, b) is 5. if her wealth increased from $1,050 to $1,350, then a. britney's subjective measure of her well-being would increase by more than 5 units. b. britney would change from being a person who is not risk averse into a risk-averse person. c. britney would change from being a risk-averse person into a person who is not risk averse. d. britney's subjective measure of her well-being would increase by less than 5 units.
The correct answer is d. Britney's subjective measure of her well-being would increase by less than 5 units.
We have, The vertical distance between points (0, a) and (0, b) is 5.
Her wealth increased from $1,050 to $1,350.Britney's subjective measure of her well-being would increase by less than 5 units. Option (d) is correct. Because the vertical distance between the points (0, a) and (0, b) is 5.
If the horizontal distance is the same as the vertical distance, then the slope is 1.
The slope of the straight line joining two points is given by;
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where the points are [tex](x_1,y_1), (x_2,y_2)[/tex]
Let's assume the two points are [tex](0, a) \ and \ (0, b)[/tex].
The slope of the line connecting these two points is;
[tex]\displaystyle m=\frac{b-a}{0-0}=\frac{b-a}{0}[/tex]
This is undefined as we cannot divide by 0.Hence, there is no horizontal distance, and there is no slope.
Therefore, if the vertical distance between two points is 5, and there is no horizontal distance, then she will experience less than 5 units of well-being.
Therefore, Britney's subjective measure of her well-being would increase by less than 5 units.
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20m:600cm
Reduce the ratios to its simplest forms
Answer: 10:3
Step-by-step explanation: convert 600cm to 6m, then we will get 20m:6m, 2*10=20 and 2*3=6. then it will become 10:3
Which points satisfy both inequalities?
The pοint that satisfies bοth inequalities is the pοint inside this triangular regiοn.
What is inequality?An inequality is a mathematical statement that cοmpares twο values οr expressiοns and indicates whether they are equal οr nοt, οr which οne is greater οr smaller.
Since the shading is nοt included, we will need tο use the lines themselves tο determine the cοrrect regiοn οf the cοοrdinate plane.
The first inequality y > (3/2)x - 5 has a slοpe οf 3/2 and a y-intercept οf -5. This means the line will have a pοsitive slοpe and will be lοcated belοw the pοint (0,-5).
The secοnd inequality y < (-1/6)x - 6 has a negative slοpe οf -1/6 and a y-intercept οf -6. This means the line will have a negative slοpe and will be lοcated abοve the pοint (0,-6).
Tο find the pοint that satisfies BOTH inequalities, we need tο lοοk fοr the regiοn οf the cοοrdinate plane that is belοw the line y = (3/2)x - 5 AND abοve the line y = (-1/6)x - 6. This regiοn is the triangular-shaped area that is bοunded by the twο lines and the x-axis.
The pοint that satisfies bοth inequalities is the pοint inside this triangular regiοn.
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Solve the following formula for t
S=12(V0+V1)t
Answer:
[tex]{ \rm{s = 12( v_{0} + v_{1} )t}} \\ \\{ \boxed { \rm{t = \frac{s}{12(v_{0} + v_{1})} \: \: }}}[/tex]
a) Work out the minimum number of hikers who could have walked between 6 miles and 17 miles. b) Work out the maximum number of hikers who could have walked between 6 miles and 17 miles. < Back to task Distance, a (miles) 0≤ x<5 5 ≤ x < 10 10 ≤ a < 15 15 ≤ x < 20 20 ≤ w Scroll down Watch video Frequency 3 2 9 8 4 Answer
9 hikers are the bare minimum that might have covered the range of 6 to 17 miles because that distance falls inside the typical interval of 10 x 15 miles.
What is meant by minimum and maximum value?Rearrange the function using fundamental algebraic concepts to determine the value of x when the derivative equals 0.
This response gives the x-coordinate of the function's vertex, which is where the maximum or minimum will occur.
To determine the minimum or maximum, rewrite the solution into the original function.
The greatest and smallest values of a function, either within a specific range (the local or relative extrema) or throughout the entire domain, are collectively referred to as extrema (PL: extrema) in mathematical analysis.
b) the maximum number of hikers who could have walked between 6 miles and 17 miles is 19.
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A diagonal of rectangle is inclined to one side of the rectangle at 25 degree the acute angle between diagonal is
Answer:
A diagonal of a rectangle is inclined to one side of the rectangle at 25º Angle between a side of the rectangle and its diagonal = 25º Consider x as the acute angle between diagonals
Step-by-step explanation:
_____ is a relative measure of signal loss or gain and is used to measure the logarithmic loss or gain of a signal
Decibel is a relative measure of signal loss or gain and is used to measure the logarithmic loss or gain of a signal.
What is a decibel?
Decibel, also known as dB, is a logarithmic unit that measures the intensity of a sound or the strength of an electrical or electromagnetic signal. A decibel measures the relative amplitude of a sound or signal, rather than its absolute magnitude. Because decibels are logarithmic, they are used to express both large and small differences in amplitude. A difference of 1 decibel corresponds to a power ratio of approximately 1.26 to 1.
Logarithmic measure: A logarithmic scale is a scale that has a constant ratio between successive values. Decibels, for example, are a logarithmic scale. The decibel scale is used to measure the amplitude of sound waves and electrical or electromagnetic signals. Because decibels are logarithmic, they can be used to express a wide range of signal levels, from very weak to very strong.
Relative measure: Relative measure is a measure that compares one value to another. It is used in a variety of fields, including statistics, physics, and engineering. Decibels are a relative measure because they compare one signal to another. They are used to express the relative gain or loss of a signal, rather than its absolute magnitude.
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(Do not use a calculator for this question) Given f(x)-73-12x + 5 answer the following: Is the function increasing or decreasing at x-3? List the interval A=B=where f(x) is decreasing. a F At what X-value does f(x) have a relative maximum?
The function is a set of ordered pairs (x, y), where x is an element of the domain and y is the corresponding element of the range. The notation f(x) is commonly used to denote the output value of the function for a given input value x.
The function is decreasing at x=3. The interval where f(x) is decreasing is (3,∞). The x-value at which f(x) has a relative maximum is x= -4.The derivative of the function f(x) is f'(x)=-12.At x=3, the derivative is negative, f'(3)=-12, so the function is decreasing at x=3.
The function is always decreasing since its derivative is constant and negative. Therefore, the interval where f(x) is decreasing is the entire real line, or (-∞, ∞).
Since the function is always decreasing, it does not have a relative maximum.
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sweet 'n low answer 1 choose... splenda answer 2 choose... can cause diarrhea answer 3 choose... oldest non-nutritive sweetener answer 4 choose... made from amino acids - used in cold products answer 5 choose... 7,000 times sweeter than sugar answer 6 choose... made from modified sugar answer 7 choose... 600 times sweeter than sugar answer 8 choose... made from the stevia plant
The Stevia is a low-calorie alternative to sugar and is a good option for people who are trying to reduce their sugar intake.
Sweet 'n Low - Modified SugarSweet 'n Low is an artificial sweetener that is made from modified sugar. Sweet 'n Low is not as sweet as some other artificial sweeteners like Splenda and Truvia. However, Sweet 'n Low is still used in many products like gum, candy, and other sweet treats. Sweet 'n Low has been around since the 1950s and is still used today as a low-calorie alternative to sugar.Splenda - 600 times sweeter than sugarSplenda is a popular artificial sweetener that is around 600 times sweeter than sugar. Splenda is often used in diet drinks, desserts, and other sweet products. Splenda is made from sugar but is modified to be much sweeter. Splenda is a low-calorie alternative to sugar and can be used by people who are trying to reduce their sugar intake.Stevia - Made from the Stevia PlantStevia is an artificial sweetener that is made from the Stevia plant. Stevia is a natural sweetener and is often used in tea and other drinks. Stevia is not as sweet as some other artificial sweeteners, but it is still a popular alternative to sugar. Stevia is also used in some foods and desserts. Stevia is a low-calorie alternative to sugar and is a good option for people who are trying to reduce their sugar intake.
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Researchers want to determine whether drivers are significantly more distracted while driving when using a cell phone than when talking to a passenger in the car. In a study involving 48 people, 24 people were randomly assigned to drive in a driving simulator while using a cell phone. The remaining 24 were assigned to drive in the driving simulator while talking to a passenger in the simulator. Part of the driving simulation for both groups involved asking drivers to exit the freeway at a particular exit. In the study, 7 of the 24 cell phone users missed the exit, while 2 of the 24 talking to a passenger missed the exit. (a) Would this study be classified as an experiment or an observational study? Provide an explanation to support your answer. (b) State the null and alternative hypotheses of interest to the researchers. H0: Ha: (c) One test of significance that you might consider using to answer the researchers’ question is a two-proportion z-test. State the conditions required for this test to be appropriate. Then comment on whether each condition is met. (d) Using an advanced statistical method for small samples to test the hypotheses in part (b), the researchers report a p−value of 0.0683. Interpret, in everyday language, what this p−value measures in the context of this study and state what conclusion should be made based on this p−value.
The lower the p-value, the more likely it is that the results are not due to chance. In this case, the p-value is 0.0683 This means that the researchers can conclude that drivers are significantly more distracted while driving when using a cell phone than when talking to a passenger in the car.
There is a difference in the proportion of drivers who missed the exit between the two groups.
The conditions required for a two-proportion z-test to be appropriate include that the data is collected independently, both groups are independent, the data should come from a normal population, and the sample sizes should be greater than 10.
The data was collected independently, both groups are independent, and the sample sizes are greater than 10. Therefore, these conditions are met. It is not clear if the data is from a normal population or not, but the test can still be used if the sample sizes are large enough.
The p-value of 0.0683 measures the probability that the results observed are due to chance. Therefore ,the lower the p-value, the more likely it is that the results are not due to chance.
In this case, the p-value is 0.0683, which is considered to be a small enough value that it indicates a statistically significant difference between the two groups.
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I need help with this question
Answer: 6
Step-by-step explanation:
Average rate of change is the same as slope.
To find the average rate of change between two points, use the formula y2 - y1 / x2 - x1
Plug in the (0, 7) and (6, 43) coordinates.
43 - 7 / 6 - 0 = 6
Identify the fallacies of relevance committed by the following arguments, giving a brief explanation for your answer. If no fallacy is committed, write "no fallacy". Surely you welcome the opportunity to join our protective organization. Think of all the money you will lose from broken windows, overturned trucks, and damaged merchandise in the event of your not joining.
There are no fallacies of relevance committed by the given argument.
The following arguments commits fallacy: argumentum ad baculum. Argumentum ad baculum is a Latin phrase which means argument from a stick or appeal to force. It is a type of logical fallacy in which someone tries to persuade another person by using threats of force or coercion rather than using evidence or reasoning.
The above statement is an example of the argumentum ad baculum fallacy as it tries to use fear to convince people to join their protective organization. They are using the threat of potential losses to convince people to join. It is a manipulative strategy that attempts to scare people into joining by threatening the safety of their business.No fallacy is committed. There are no fallacies of relevance committed by the given argument.
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Q.4. A shopkeeper bought 18 sets of kurthas at the rate of Rs.1000 each. If 3 sets of kurthas were damaged and the remaining sets of kurthas were sold at the rate of Rs. 1250. Find the profit or loss of the shopkeeper.
Answer:
Rs 750
Step-by-step explanation:
Given, No. of kurtas: 18, Each with CP = Rs 1000.
So, SP of 18 kurtas: 18*1000 = Rs. 18000
Also, 3 sets of kurtas were damaged.
Therefore, Remaining kurtas: 18-3 = 15. SP of each: Rs 1250.
SP of 15 kurtas: 15*1250 = Rs. 18750
So, Clearly SP>CP, Profit.
We know Profit= SP-CP
= 18750-18000 = Rs 750
La necesito por favor
Answer:
4(h+3) = 20
Step-by-step explanation:
Para empesar, disculpa si mi español no es perfecto, pero igual me encataria a ayudarte.
Pues, se sabe que estas temporadas de practica vienen en groupitos de horas a la ves. Dijo que cada dia, ella practica por alguans horas, las cuales suman a 20 en total. Como la problema nos dice que ella practica 4 veces a la semana, tienemos 4 de estos groupitos de horas. Por eso, la respuesa es 4(h+3) = 20, porque ella va por estas 4 temporadas de practicar 3 horas en la manana y quien sabe cuantos en la tarde. Addicionalmente, este"quien sabe" numero de horas se representa con h.
One of the earliest applications of the Poisson distribution was made by Student (1907) in studying errors made in counting yeast cells or blood corpuscles with a haemacytometer. In this study, yeast cells were killed and mixed with water and gelatin; the mixture was then spread on a glass and allowed to cool. Four different concentrations were used. Counts were made on 400 squares, and the data are summarized in the following table:
a. Estimate the parameter λ for each of the four sets of data.
b. Find an approximate 95% confidence interval for each estimate.
c. Compare observed and expected counts.
In conclusion, the Poisson distribution was successfully applied by Student (1907) to the study of errors in counting yeast cells or blood corpuscles with a haemacytometer. It is possible to calculate an approximate 95% confidence interval for each estimated count, as well as to compare observed and expected counts.
The Poisson distribution was first applied to the study of errors made in counting yeast cells or blood corpuscles with a haemacytometer by Student (1907). The study involved the preparation of four different concentrations of a mixture of yeast cells, water, and gelatin spread on a glass. Counts were made on 400 squares and the data summarized in the following table.
An approximate 95% confidence interval for each estimate can be calculated using the Poisson distribution. For each of the four concentrations, the lower bound of the confidence interval is given by the formula x - 1.96*sqrt(x) and the upper bound is given by the formula x + 1.96*sqrt(x), where x is the observed count for that concentration.
It is also possible to compare the observed counts with the expected counts for each concentration. The expected count for each concentration is given by the formula λ = n*p, where n is the number of squares and p is the probability of an event occurring in a single square. The expected counts can be compared to the observed counts to determine whether they are in agreement with the Poisson distribution.
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Aaron sampled 101 students and calculated an average of 6.5 hours of sleep each night with a standard deviation of 2.14. Using a 96% confidence level, he also found that t* = 2.081.confidence intervat = x±s/√n A 96% confidence interval calculates that the average number of hours of sleep for working college students is between __________.
The average number of hours of sleep for working college students is between 6.28 and 6.72 hours of sleep each night
According to the given data,
Sample size n = 101
Sample mean x = 6.5
Standard deviation s = 2.14
Level of confidence C = 96%
Using a 96% confidence level, the value of t* for 100 degrees of freedom is 2.081, as given in the question.
Now, the formula for the confidence interval is:x ± (t* × s/√n)Here, x = 6.5, s = 2.14, n = 101, and t* = 2.081
Substituting the values in the above formula, we get:
Lower limit = x - (t* × s/√n) = 6.5 - (2.081 × 2.14/√101) = 6.28
Upper limit = x + (t* × s/√n) = 6.5 + (2.081 × 2.14/√101) = 6.72
Therefore, the 96% confidence interval for the average number of hours of sleep for working college students is between 6.28 and 6.72 hours of sleep each night.
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20.
Points A(6,-2) and B(-5,5) are plotted on a coordinate plane.
Find the distance between points A and B.
Answer:
13
Step-by-step explanation:
distance formula:
=[tex]\sqrt{(y2-y1)^{2}+(x2-x1)^{2} }[/tex]
=[tex]\sqrt{(5--2)^{2}+(-5-6)^{2} } \\\sqrt{170} \\13[/tex]
The cost of skating at an ice-skating rink is $11.00 for an adult and $6:50 for a child
under the age of 12. Which equation can be used to find y, the total cost in dollars,
to skate at the ice-skating rink for 1 adult and .r children under that age of 12?
A. y = 6.50x +11
B. y = 6.50+11x
C. x = 6.50y +11
D. x = 6.50+11y
The correct answer is A. y = 6.50x +11. This equation will calculate the total cost (y) in dollars for 1 adult and x children under the age of 12.
Thabo, Patrick, and Lucas agreed to share the amount of R72 in the ratio of 3:4:5 amongst themselves. Determine how much each one get will.
Therefore, Thabo will get R18, Patrick will get R24, and Lucas will get R30.
What is ratio?In mathematics, a ratio is a comparison between two quantities or numbers, indicating how many times one quantity is contained within another. Ratios are often expressed in the form of a fraction, with the first quantity as the numerator and the second quantity as the denominator. Ratios can also be simplified by dividing both the numerator and denominator by their greatest common factor. Ratios are used in many areas of mathematics, science, and everyday life, such as in finance, cooking, and sports. They are particularly useful for comparing two quantities of different units or scales, as they provide a standardized way to express the relationship between them.
Here,
To determine how much each person will get, we first need to find the total of the ratios which is:
3 + 4 + 5 = 12
This means that the total amount of money is divided into 12 equal parts.
To find out how much each person gets, we need to multiply their share of the ratio by the total amount of money:
Thabo's share = 3/12 x R72 = R18
Patrick's share = 4/12 x R72 = R24
Lucas's share = 5/12 x R72 = R30
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what is the as surface area of the rectangular prism
Answer:
142 sq cm
Step-by-step explanation:
A= 2(lh + wh + lw)
2(7*3+5*3+7*5)
2(21+15+35)
2(71)
A= 142 sq cm
It is known that diskettes produced by a certain company will be defective with probability 0.01, independently of each other. The company sells the diskettes in packages of size 10 and offers a money-back guarantee that at most 1 of the 10 diskettes in the package will be defective.If someone buys 3 packages, what is the probability that he or she will return exactly 1 of 3 packages?
The probability of someone returning exactly 1 of the 3 packages can be calculated as:P(1 out of 3 packages is returned) = C(3, 1) × P(0 or 1 diskette is defective)¹ × (1 - P(0 or 1 diskette is defective))²P(1 out of 3 packages is returned) = C(3, 1) × (0.9043820371)¹ × (0.0956179629)²P(1 out of 3 packages is returned) = 0.2448700124Therefore, the required probability of someone returning exactly 1 of the 3 packages is 0.2448700124.
The given data from the question is that the company produces diskettes which have the probability of being defective as 0.01. The packages that are sold have a size of 10 and the guarantee says that there can be at most one defective diskette in the package. Now, the question is to find the probability of someone returning exactly 1 of the 3 packages that they have bought. So, the given data can be summarized as:Given:Probability of the diskette being defective, p = 0.01Guarantee: At most one diskette in the package of size 10 is defective.Now, let's solve the problem using probability theory
Probability of 1 diskette being defective in a package of size 10 can be calculated as:P(defective) = p = 0.01P(non-defective) = 1 - p = 0.99Using the given guarantee, probability of at most one defective diskette in a package of size 10:P(0 or 1 diskette is defective) = P(0 defective) + P(1 defective)P(0 or 1 diskette is defective) = C(10, 0) × (0.99)¹⁰ + C(10, 1) × (0.99)⁹ × (0.01)P(0 or 1 diskette is defective) = 0.9043820371Using the above probability
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Anna wants to make 30 mL of a 60 percent salt solution by mixing togethera 72 percent salt solution and a 54 percent salt solution. How much of each solution should dhe use
Anna should use 10 mL of the 72% salt solution and 20 mL of the 54% salt solution to make 30 mL of a 60% salt solution
Let's assume that Anna will use x mL of the 72% salt solution, and therefore she will use (30 - x) mL of the 54% salt solution (since the total volume is 30 mL).
To find out how much of each solution Anna should use, we can set up an equation based on the amount of salt in each solution.
The amount of salt in x mL of 72% salt solution is
= 0.72x
The amount of salt in (30 - x) mL of 54% salt solution is
= 0.54(30 - x)
To make a 60% salt solution, the total amount of salt in the final solution should be
0.6(30) = 18
So we can set up an equation
0.72x + 0.54(30 - x) = 1
Simplifying the equation
0.72x + 16.2 - 0.54x = 18
0.18x = 1.8
x = 10 ml
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Observation what is going on regarding determinant of product of two matrices. al.) Make a conjecture about the relation between det(AB), and det(BA). Type your answer after %. a2.) Make a conjecture about the relation between det(AB), det(B), and det(A). Type your answer after %. a3.) Make a conjecture about the relation between det(A™), and det(A). Type your answer after %.
The determinant of two matrices for the question a1 is it has not been demonstrated, a2 the multiplied matrices can affect the determinant of the product, and a3 A matrix's own determinant will be the same as the determinant of its transpose.
a1.) Conjecture about the relation between det(AB), and det(BA):
The determinant of the product of two matrices is not necessarily equal.
If two matrices A and B are multiplied together to produce the product AB, it is not necessary that the determinant of AB is equal to the determinant of BA.
This is a conjecture that has not yet been demonstrated in every case.%
a2.) Conjecture about the relation between det(AB), det(B), and det(A):
The following conjecture could be made about the relation between the determinants det(AB), det(B), and det(A):
det(AB) = det(BA) det(AB) = det(A)det(B)det(BA) = det(A)det(B)
These conjectures are not true in general.
It is because the order in which matrices are multiplied can affect the determinant of the product.%
a3.) Conjecture about the relation between det(A™), and det(A):
This conjecture about the relation between the determinants det(A™) and det(A) can be made:
det(A™) = det(A)
The transpose of a matrix does not alter the determinant, as long as the matrix is square.
The determinant of a matrix will remain the same if the rows and columns are exchanged.
Therefore, the determinant of the transpose of a matrix will be equal to the determinant of the matrix itself.
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