A statistical analysis is internally valid if option B is correct, meaning that the statistical inferences about causal effects are valid for the population studied. Internal validity refers to the accuracy of conclusions drawn from a study, specifically focusing on causal relationships within the population being analyzed.
Statistical analysis is a method of examining data to identify patterns and trends, which can help researchers make informed decisions. Regression is a technique used to determine the relationship between two or more variables, where one variable (the dependent variable) is affected by one or more other variables (independent variables).
The population refers to the entire group of individuals or objects being studied. In order to have internal validity, the statistical analysis must accurately represent the population's characteristics and the causal relationships between variables.
R² (option A) is a measure of how well the regression model fits the data but doesn't necessarily imply internal validity. Option C, t-statistics, is related to hypothesis testing and helps determine if a relationship between variables is statistically significant. However, having all t-statistics greater than |1.96| doesn't guarantee internal validity.
Lastly, option D states that the population is small (less than 2,000) and can be observed. While having a smaller population might make it easier to gather data, this does not guarantee internal validity.
In summary, internal validity is achieved when the statistical inferences about causal effects are valid for the population studied (option B). It ensures that the conclusions drawn from a study are accurate and represent the true relationships within the population.
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taxes for last year, 7 had their taxes prepared by a local professional, and the remaining 3 by H&R Block.
a.What is the probability of selecting a family that prepared their own taxes?
b.What is the probability of selecting two families, both of which prepared their own taxes?
c.What is the probability of selecting three families, all of which prepared their own taxes?
d.What is the probability of selecting two families, neither of which had their taxes prepared by H&R Block?
The probability of selecting two families, neither of which had their taxes prepared by H&R Block is (7/10) * (6/9) = 42/90, which simplifies to 7/15.
a. There are a total of 10 families. 7 had taxes prepared by a local professional, and 3 by H&R Block. This means 0 families prepared their own taxes. The probability of selecting a family that prepared their own taxes is 0/10 = 0.
b. Since no families prepared their own taxes, the probability of selecting two families, both of which prepared their own taxes is 0.
c. Similarly, the probability of selecting three families, all of which prepared their own taxes is 0.
d. If we want to select two families, neither of which had their taxes prepared by H&R Block, we are looking for families that had their taxes prepared by a local professional. There are 7 such families. The probability of selecting the first family is 7/10. After selecting the first family, there are now 9 families left, 6 of which had their taxes prepared by a local professional. The probability of selecting the second family is 6/9. Therefore, the probability of selecting two families, neither of which had their taxes prepared by H&R Block is (7/10) * (6/9) = 42/90, which simplifies to 7/15.
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The sum of two positive integers, x and y, is not more than 40. The difference of the two integers is at least 20. Chaneece chooses x as the larger number and uses the inequalities y ≤ 40 – x and y ≤ x – 20 to determine the possible solutions. She determines that x must be between 0 and 10 and y must be between 20 and 40. Determine if Chaneece found the correct solution. If not, state the correct solution.
Chaneece did not find the correct solution
Determining if Chaneece found the correct solutionFrom the question, we have the following parameters that can be used in our computation:
x and y are the integers
So, we have
x + y ≤ 40
x - y ≥ 20
Add the equations
So, we have
2x = 60
Divide
x = 30
Next, we have
30 + y ≤ 40
So, we have
y ≤ 10
This means that
x = 30 or between 20 and 30
y = 10 or between 0 and 10
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5/8x + 1/2 ( 1/4x + 10)
Answer:5+3x/4
Step-by-step explanation:
Answer:2x+1
1
Step-by-step explanation:
After 4 years, $20,000 deposited in a savings account with simple interest had earned $800 in interest. What was the interest rate?
The interest rate for the savings account is 5% after 4 years, $20,000 deposited in a savings account with simple interest earned $800 in interest.
We can use the formula for simple interest to solve the problem:
Simple interest = (Principal * Rate * Time) / 100
where Principal is the initial amount deposited, Rate is the interest rate, and Time is the time period for which the interest is calculated.
We know that the Principal is $20,000 and the time period is 4 years. We are also given that the interest earned is $800. So we can plug in these values and solve for the interest rate:
$800 = (20,000 * Rate * 4) / 100
Multiplying both sides by 100 and dividing by 20,000 * 4, we get:
Rate = $800 / (20,000 * 4 / 100) = 0.05 or 5%
Therefore, the interest rate for the savings account is 5%.
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Suppose we modify the production model to obtain the following mathematical model: Max 10X s.t. ax ≤ 40 x ≥ 0 Where a is the number of hours of production time required for each unit produced. With a=5, the optimal solution is x=8. If we have a stochastic model with a=3,a=4,a=5, or a=6 as the possible values for the number of hours required per unit, what is the optimal value for x? What problems does this stochastic model cause?
The optimal value for x in the stochastic model is a range of values from x=6 to x=8. The stochastic model causes problems due to the uncertainty in the optimal solution and the assumptions.
With a=5, the optimal solution is x=8. However, with the addition of stochasticity and possible values for a of 3, 4, and 6, the optimal value for x becomes a range of values.
The expected value of a is 4.5, which means that there is a higher probability of a lower value for a, resulting in a lower optimal value for x. Therefore, the optimal value for x becomes x=6 when a=3 or a=4, x=7 when a=5, and x=8 when a=6.
The stochastic model causes problems because the optimal solution is no longer a fixed value but rather a range of values that are dependent on the probability distribution of a.
Additionally, this model assumes that the production time is the only constraint on production, which may not always be the case in real-world production scenarios. Therefore, the stochastic model may not accurately reflect the actual production process and could lead to suboptimal production decisions.
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6. Caleb wants to buy a skateboard that costs $73. 56. If sales tax is 7%, how much would his total purchase be?
Answer:
$78.7092
Step-by-step explanation:
He wants to buy a skateboard. The percentage value of the skateboard before any changes is 100%. So $73.56 = 100%. Now when you add a sales tax to it, the price will increase by 7% so it'll now be 107% right? You just have to find how much the 107% is equal to.
100% = 73.56
1% = 73.56÷100 = 0.7356
107 % = 0.7356 × 107 = 78.7092
A pizza owner asked 50 customers to taste a new type of topping and found that 40 people liked its taste Which of these is an example of descriptive statistics?
A. 80% of the people in the city where the pizza shop is located like the taste of the pizza topping
B. 80% of all the pizza shop's customers like the taste of the pizza topping,
C. 80% of all people like the taste of the pizza topping,
D. 80% of the surveyed customers like the taste of the pizza topping.
D. 80% of the surveyed customers like the taste of the pizza topping. This is an example of descriptive statistics because it describes a specific group of 50 customers who were surveyed and their response to the new topping.
Descriptive statistics are used to summarize and describe data, often by using measures such as percentages, means, and standard deviations. In this case, the percentage of customers who liked the new topping is a descriptive statistic that summarizes the data collected from the survey.
This answer represents descriptive statistics because it summarizes and describes the information collected from the specific sample of 50 customers who participated in the taste test. It does not make assumptions or predictions about the entire population or customer base, but instead focuses solely on the data collected from the sample group.
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insect Survival Most
invertebrates produce large
numbers of offspring. Most of
these offspring die before reaching
adulthood. Suppose an insect lays
80 eggs on a plant. If 70 percent
of the eggs hatch and 80 percent
of those that hatch die before
reaching adulthood, how many
insects will reach adulthood?
The required out of the 80 eggs laid, only 11 insects are expected to reach adulthood.
If an insect lays 80 eggs on a plant, and 70% of the eggs hatch, then the number of hatched eggs is:
80 x 0.7 = 56
Now, if 80% of the hatched eggs die before reaching adulthood, then the number of insects that reach adulthood is:
56 x 0.2 = 11.2
However, we cannot have a fractional number of insects, so we need to round this to the nearest whole number. Since we are asked for how many insects will reach adulthood, we round up if the decimal is 0.5 or greater and round down if the decimal is less than 0.5. In this case, since 0.2 is less than 0.5, we round down to get:
11 insects
Therefore, out of the 80 eggs laid, only 11 insects are expected to reach adulthood.
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A 35-year-old person who wants to retire at age 65 starts a yearly retirement contribution in the amount of $5,000. The retirement account is forecasted to average a 6.5% annual rate of return, yielding a total balance of $431,874.32 at retirement age.
If this person had started with the same yearly contribution at age 40, what would be the difference in the account balances?
A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
$378,325.90
$359,978.25
$173,435.93
$137,435.93
The difference in the account balances is $138,435.93.
We have,
We can solve this problem by using the formula for the future value of an annuity:
[tex]FV = PMT \times [(1 + r)^n - 1] / r[/tex]
where FV is the future value of the annuity, PMT is the yearly contribution, r is the annual interest rate, and n is the number of years.
Using the given information, we can find the future value of the annuity if the person starts at age 35:
FV1
= $5,000 x [(1 + 0.065)^30 - 1] / 0.065
= $431,874.32
Now we can find the future value of the annuity if the person starts at age 40:
FV2 = $5,000 x [(1 + 0.065)^25 - 1] / 0.065
= $293,438.39
The difference in the account balances is:
FV1 - FV2
= $431,874.32 - $293,438.39
= $138,435.93
Therefore,
The difference in the account balances is $138,435.93.
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Find The Total Surface Area Of This Triangular Prism:
The total surface area of the triangular prism is 204 square units.
To find the total surface area of a triangular prism, we need to find the areas of all its faces and add them up.
First, we need to find the area of each triangular face. We can use the formula:
Area of a triangle = 1/2 x base x height
For the triangle with base 4 and height 3, we have:
Area of triangle = 1/2 x 4 x 3 = 6
For the triangle with base 6 and height 8, we have:
Area of triangle = 1/2 x 6 x 8 = 24
Now, we need to find the area of each rectangular face. We can use the formula:
Area of a rectangle = length x width
For the rectangular face with length 6 and width 4, we have:
Area of rectangle = 6 x 4 = 24
For the rectangular face with length 8 and width 4, we have:
Area of rectangle = 8 x 4 = 32
Finally, we add up all the areas to get the total surface area:
Total surface area = 2 x (area of triangle) + 3 x (area of rectangle)
Total surface area = 2 x (6 + 24) + 3 x (24 + 32)
Total surface area = 60 + 144
Total surface area = 204
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Find The Total Surface Area Of This Triangular Prism:
Find the linearization L(x) of the function at a. F(x) = x3 - x2 + 5, a = -3 L(x) = Fl Show My Work
[tex]L(x) = 33x + 86[/tex] represents the regression of F(x) at a = -3.
We must apply the following formula to determine the regression L(x) of the equation: [tex]F(x) = x^{3} - x^{2} + 5[/tex] at a = -3: [tex]L(x) = F'(a)(x - a) + F(a)[/tex] , where a derivative of F(x) calculated at an is denoted by F'(a).
We calculate the amount of F(-3): F(-3)
[tex]= (-3)^3 - (-3)^2 + 5[/tex]
= -27 + 9 + 5 = -13
We determine F(x)'s derivative:
[tex]F'(x) = 3x^2 - 2x[/tex]
We assess F'(-3):
[tex]F'(-3) = 3(-3)^2 - 2(-3)[/tex]
= 27 + 6 = 33
Now we can change these numbers in the L(x) formula:[tex]L(x) = -13 + 33(x + 3)[/tex]. If we condense this expression, we get: L(x) = 33x + 86
We utilise the equation [tex]L(x) = F(a) + F'(a)(x - a)[/tex], to determine the linearization of an equation at a specific point, where F(a) represents the function's value at point a and F'(a) was the function's derivative calculated at point a. We can approximate the function close to point a linearly.
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How much is 4 plus 78?
Answer:
83
Step-by-step explanation:
78 + 4= 83
the shape of a colony of bacteria on a petri dish is circular. find the approximate increase in its area if its radius increases from mm to mm. a) let represent the radius and represent the area. write the formula for the area of the petri dish.
The formula for the area of a circular petri dish can be represented as A = πr², where "A" represents the area and "r" represents the radius.
To find the approximate increase in the area when the radius increases from r₁ mm to r₂ mm, we can calculate the difference between the areas by subtracting the initial area (A₁ = πr₁²) from the final area (A₂ = πr₂²). This can be expressed as ΔA = A₂ - A₁ = πr₂² - πr₁².
In the second paragraph, let's explain the formula and how to calculate the approximate increase in the area of the bacterial colony on the petri dish. The area of a circular shape is given by the formula A = πr², where "A" represents the area and "r" represents the radius. By substituting the initial radius, r₁, into the formula, we can find the initial area, A₁ = πr₁².
Similarly, by substituting the final radius, r₂, into the formula, we can find the final area, A₂ = πr₂². To calculate the approximate increase in area, we subtract the initial area from the final area: ΔA = A₂ - A₁ = πr₂² - πr₁². This formula allows us to find the difference in the areas of the bacterial colony on the petri dish when the radius increases from r₁ to r₂.
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Find the area of each shaded sector. Round to the hundredths place
The area of each shaded sector of a circle with radius 6 units and measure of central angle 36 degrees is approximately equals to the 11.31 square units.
The area of a sector is defined as the space inside a section of the circle made by two radius and an arc. The area of a circular sector is written by the following formula [tex]Area = \frac{θ}{360°}\pi \: r^2[/tex], where, r represents the radius
θ represents the measure of central angle in degreesπ is math constant and π = 3.14See the above figure, we have a circle with radius of circle, r = 6 units
Measure of central angle, θ = 36°
Area of circle = πr²
Substitute all known values, so, Area = π× 6² = 36π
Using the formula for the area of a sector, Area of sector of circle with radius 6
[tex] = \frac{36°}{360°}π(6)²[/tex]
[tex]= \frac{1}{10} \times 36 × 3.14[/tex]
= 11.304 ~ 11.31
Hence, the required area of the shaded sector is approximately 11.31 square unit.
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Complete question:
The above figure complete the question.
Find the area of each shaded sector. Round to the hundredths place
For the following observations 14,10,7,18, x , 10, 10, 14,5 and 15, if X = 11.6 , then median, mode and standard deviation respectively are: a. 11.5 , 10 and 3.923 b. 12.5 , 12.5 and 3.8356 c. 12.5 , 13 and 14.7 d. 11.5 , 10 and 15.38 e. 13 , 10 and 3.923
The correct answer is option b.
To find the median, we need to first put the observations in order:
5, 7, 10, 10, 10, 14, 14, 15, 18, x
Since there are 10 observations, the median is the average of the 5th and 6th observations, which are both 10. Therefore, the median is 10.
To find the mode, we need to find the observation that appears most frequently. Here, both 10 and 14 appear three times each, so the data has two modes: 10 and 14.
To find the standard deviation, we need to first find the mean of the data. We know that the sum of the observations is:
5 + 7 + 10 + 10 + 10 + 14 + 14 + 15 + 18 + x
= 103 + x
Since we know that X = 11.6, we can substitute to get:
Sum of observations = 103 + 11.6 = 114.6
The mean is then:
Mean = (Sum of observations) / (Number of observations)
Mean = 114.6 / 10 = 11.46
To find the standard deviation, we need to calculate the deviation of each observation from the mean, square each deviation, find the average of the squared deviations, and then take the square root.
Deviation of 5 = 11.46 - 5 = 6.46
Deviation of 7 = 11.46 - 7 = 4.46
Deviation of 10 = 11.46 - 10 = 1.46
Deviation of 10 = 11.46 - 10 = 1.46
Deviation of 10 = 11.46 - 10 = 1.46
Deviation of 14 = 11.46 - 14 = -2.54
Deviation of 14 = 11.46 - 14 = -2.54
Deviation of 15 = 11.46 - 15 = -3.54
Deviation of 18 = 11.46 - 18 = -6.54
Deviation of x = 11.46 - x
To find the standard deviation, we need to find the average of the squared deviations.
Average of squared deviations = [(6.46)^2 + (4.46)^2 + (1.46)^2 + (1.46)^2 + (1.46)^2 + (-2.54)^2 + (-2.54)^2 + (-3.54)^2 + (-6.54)^2 + (11.46 - x)^2] / 10
= (41.7316 + 19.8916 + 2.1316 + 2.1316 + 2.1316 + 6.4516 + 6.4516 + 12.5316 + 42.8916 + (11.46 - x)^2) / 10
= (136.786) / 10
= 13.6786
Finally, we take the square root of the average of the squared deviations to find the standard deviation:
Standard deviation = sqrt(13.6786) = 3.8356
Therefore, the correct answer is option b.
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Hannah has a chicken coop with 6 hens. Let X represent the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table.
A 2-column table with 7 rows. Column 1 is labeled number of eggs with entries 0, 1, 2, 3, 4, 5, 6. Column 2 is labeled probability with entries 0. 02, 0. 03, 0. 07, 0. 12, 0. 30, 0. 28, 0. 18.
What is the median of the distribution?
3
3. 5
4
4. 2
1.39 is the median of the distribution
Creating a table:
X :___0 __ 1 __ 2 ___ 3 ____ 4 ___ 5 ___ 6
P(x):0.02_0.03_0.07, 0.12, 0.30_ 0.28_0.18.
The standard deviation = √(Var(x))
Var(x) = Σx²*p(x) - E(x)²
E(x) = ΣX*p(x)
E(x) = (0*0.02) + (1*0.03) + (2*0.07) + (3*0.12) + (4*0.30) + (5*0.28) + (6*0.18) = 4.21
Var(X) :
[tex]((0^2*0.02) + (1^2*0.03) + (2^2*0.07) + (3^2*0.12) + (4^2*0.30) + (5^2*0.28) + (6^2*0.18)) - 4.21^2[/tex]
19.67 - 17.7241
= 1.9459
Standard deviation = √(Var(X))
Standard deviation = √(1.9459)
Standard deviation = 1.3949551
= 1.39
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Full Question ;
Hannah has a chicken coop with 6 hens. Let X be the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table.
A 2-column table with 7 rows. Column 1 is labeled number of eggs with entries 0, 1, 2, 3, 4, 5, 6. Column 2 is labeled probability with entries 0.02, 0.03, 0.07, 0.12, 0.30, 0.28, 0.18.
What is the standard deviation of the distribution?
1.39
1.95
2.16
4.67
the product of a number x and 9 is 45. translate this statement into an equation
Answer: 9x=45
Step-by-step explanation:
“product” means the result from multiplying two numbers, so if the product of the two numbers is 45, then the two numbers provided (9 and x) are being multiplied.
If we were to solve for x, we could divide both sides by 9 to get 5.
What is the special case for perfect square trinormial
64x^6-y^6
Answer: I think it’s (2x+y)•(4x2-2xy+y2)•(2x-y)•(4x2+2xy+y2)
12. What is the volume of a can of peanuts with a height of 5 in. and
a lid that is 4 in. wide? Use 3.14 for pie. Round the answer to the
nearest tenth of an inch.
62.8 cubic inches is the volume of a can of peanuts with a height of 5 in. and a lid that is 4 in. wide
We have to find the volume of a can of peanuts with a height of 5 in. and
a lid that is 4 in. wide
Volume of cylinder =πr²h
h is height which is 5 in
r is radius of can which is 2 in
Plug in values of h and r
Volume = 3.14×4×5
=62.8 cubic inches
Hence, 62.8 cubic inches is the volume of a can of peanuts with a height of 5 in. and a lid that is 4 in. wide
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Question 2 (10 points) When hydrogen is added to the structure of an oil, the melting points goes down, and the oil becomes thinner and easier to pour. True False
This statement is generally true.
When hydrogen is added to the structure of an oil through a process called hydrogenation, the oil becomes more saturated with hydrogen atoms, which reduces the amount of double bonds in the oil's molecules. This can cause the melting point of the oil to decrease and the oil to become more liquid and easier to pour. Additionally, hydrogenated oils tend to have a longer shelf life and are more stable at high temperatures, making them useful in many food processing applications.
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Out of people wederval for the true population proportion of people with kids Give your awer as decimals to the places
What is the correct terpretation for the confidence intervalThe correct interpretation for the confidence interval is that with 95% confidence, the true proportion of people with kids will be in the above interval.
This means that if we were to repeat the same survey or study multiple times, about 95% of the time, the true proportion of people with kids would fall within the given interval.
It is important to note that we cannot say with certainty that the true proportion falls within the interval, as there is always a chance for sampling error or variability.
However, we can say with a high degree of confidence that the true proportion is likely to fall within the interval. Option A is incorrect because we cannot say with certainty that the true proportion is within the interval, even though it is likely. Option c is also incorrect because the confidence level refers to the long-run proportion of intervals that will contain the true value, not a probability statement about a single interval.
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Let f be a permutation on the set {1,2,3,4,5,6,7,8,9}, defined as follows f = 1 2 3 4 5 6 7 8 9
4 1 3 6 2 9 7 5 8
(a) Write f as a product of transpositions (not necessarily disjoint), separated by commas (e.g. (1,2), (2,3), ... ). f = (b) Write f-l as a product of transpositions in the same way. f-1 =
Assume multiplication of permutations f,g obeys the rule (fg)(x) = f(g(x)so (1,3)(1, 2) = (1,2,3) not (1,3,2)
Which sends 1 to 2, and then apply the permutation (1,3) to the result, which sends 2 to 3. So (1,3)(1,2) = (1,2,3), not (1,3,2).
(a) To write f as a product of transpositions, we can track the movement of each number in the permutation. Starting from 1, we see that it goes to 4, which means we can write the transposition (1,4). Next, we look at where 4 goes, which is to 6, so we can write the transposition (4,6). Continuing this process, we get:
f = (1,4)(4,6)(6,9)(9,8)(8,5)(5,2)(2,1)(7,3)
So f can be written as the product of the transpositions (1,4), (4,6), (6,9), (9,8), (8,5), (5,2), (2,1), and (7,3).
(b) To find f-1, we need to reverse the order of the transpositions in f and also reverse each transposition. For example, the transposition (1,4) becomes (4,1). Applying this process to all the transpositions in f, we get:
f-1 = (3,7)(1,2)(2,5)(5,8)(8,9)(9,6)(6,4)(4,1)
So f-1 can be written as the product of the transpositions (3,7), (1,2), (2,5), (5,8), (8,9), (9,6), (6,4), and (4,1).
(c) The rule for multiplication of permutations (fg)(x) = f(g(x)) means that we apply the permutation g to x first, and then apply the permutation f to the result. For example, if we have the permutations f = (1,2,3) and g = (1,3), then (fg)(1) = f(g(1)) = f(3) = 2. To see why this is true, note that g sends 1 to 3, and then f sends 3 to 2.
Using this rule, we can see that (1,3)(1,2) means that we apply the permutation (1,2) first, which sends 1 to 2, and then apply the permutation (1,3) to the result, which sends 2 to 3. So (1,3)(1,2) = (1,2,3), not (1,3,2).
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keisha just deposited a total of 900 into savings accounts at two different banks. the 550 she deposited at bank A will earn 2.25% interest compounded anually
The total amount she earned $945.75.
We have,
P= 900
bank A deposition= 550
R= 2.25%
So, the interest from Bank A
= 550/100 x 2.25
= 12.375
and, Interest from Bank B
= (900 - 550)/100 x 3
= 350/100 x 3
= 10.5
So, total she earned
= 10.5 + 12.375 = 22.875
In 2 years she will earned
= 22.875 x 2
= 45.75
Thus, the total amount she earned
= 900 + 45.75 = 945.75
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A bag holds 13 marbles. 6 are blue, 2 are green, and 5 are red.
If you select two marbles from the bag in a row without replacing the first marble, what is the probability that the first marble is blue and the second marble is green?
Note: you are not replacing any marbles after each selection.
PLS SHOW ALL WORK!
The probability of selecting blue marble and green marble is 1/13.
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 which is equivalent to 100%.
Probability = sample space/total outcome
total outcome = 13
The probability of picking blue in the first pick = 6/13
since there is no replacement, the total outcome for the second pick = 12
The probability of picking green in the second pick = 2/12 = 1/6
Therefore the probability of selecting blue and green marble = 6/13 × 1/6
= 1/13
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find n and m using the image of the parallelogram
n= ?
m= ?
The length of the line segments m and n which are halves of the diagonals AC and BD in the parallelogram ABCD are 6 and 11 respectively.
Diagonals of a parallelogramA parallelogram is a quadrilateral, and the diagonals always bisect each other. However, diagonals only form right angles if the parallelogram is a rhombus or a square.
For the parallelogram ABCD; the lines AC and BD are its diagonals, and they both bisect each other, that is they cut each other to form two equal parts.
So AP and PC are equal halves of the line AC, while BP and PD are equal halves of the line BD
Therefore, since PC = 6 then m = 6, and for PD = 11, then n = 11 because they form diagonals of the parallelogram ABCD.
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1. An integer is chosen randomly between 1 and 1000. What is the probability that the number
picked is divisible by either 4 or 5 or both?
2. An integer is chosen randomly between 1 and 1000. What is the probability that the number
picked is divisible by 4 and not 3?
1. The probability that the number picked is divisible by either 4 or 5 or both is 0.4. 2. The probability that the number picked is divisible by 4 and not 3 is 0.167.
1. Using the principle of inclusion-exclusion. There are 250 integers between 1 and 1000 that are divisible by 4, and 200 integers that are divisible by 5.
However, some integers are divisible by both 4 and 5 (i.e., by 20), and we have counted them twice. There are 50 integers in the range [1, 1000] that are divisible by 20.
So, the number of integers between 1 and 1000 that are divisible by either 4 or 5 or both is:
250 + 200 - 50 = 400
Therefore, the probability that the integer picked is divisible by either 4 or 5 or both is:
400/1000 = 0.4
2. Using the principle of inclusion-exclusion again, there are 250 integers between 1 and 1000 that are divisible by 4, and 333 integers that are not divisible by 3.
There are 250 integers in the range [1, 1000] that are divisible by 4, and 83 integers that are divisible by 12.
So, the number of integers between 1 and 1000 that are divisible by 4 but not 3 is:
250 - 83 = 167
Therefore, the probability that the integer picked is divisible by 4 and not 3 is:
167/1000 = 0.167
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what’s the answer to this
The value of cos X is approximately given as .80000.
The correct answer choice is option C.
What is the value of cos X?Hypotenuse = 50
Adjacent = 30
Opposite = 40
cos X = adjacent / hypotenuse
= 30/50
= 0.6
Cos 0.6 = 0.825335614
Approximately,
.80000
Hence, cos X is .8000
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Solve using the zero product property. The problem has been factored for you.
Given the parabola in which the vertex is the origin and the directrix is a horizontal line passing through the point (0,-7), a student determined that the parabola opens to the right and that the equation of the parabola is y^2=28x. Evaluate the student’s answer. A. The student’s answer is correct. B. The student determined the direction of the parabola correctly but did not correctly determine the equation of the parabola. C. The student determined the equation of the parabola correctly but did not correctly determine the direction of the parabola. D. The student used the equations for a horizontal parabola instead of a vertical parabola. Both the equation and direction of the parabola are incorrect. Please select the best answer from the choices provided
The given parabola has its vertex at the origin and the directrix as a horizontal line passing through the point (0,-7), and the equation is y^2 = 28x, which opens to the right. So, the correct answer is A) The student's answer is correct.
To determine if the student's answer is correct, we need to check if the equation of the parabola and the direction of its opening match the given conditions.
The given parabola has its vertex at the origin and the directrix as a horizontal line passing through the point (0,-7). Therefore, the axis of symmetry is the y-axis, and the focus is located at (0,7).
The standard equation of a parabola with the vertex at the origin and the directrix as a horizontal line passing through the point (0,-p) is y² = 4px, where p is the distance from the vertex to the directrix. In this case, p = 7, so the equation of the parabola is y² = 28x.
The coefficient of x in the equation is positive, indicating that the parabola opens to the right. Therefore, the student correctly determined the direction of the parabola as well.
Hence, the answer is A. The student's answer is correct.
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The line 2x+3y=-19 is tangent to a circle centered at (-4,5). What is the tangent point?
Answer:
First, let's find the equation of the circle with a centre at (-4,5). the standard form of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the centre of the circle and r is the radius.
So, substituting the center point (-4,5) into the equation, we get:
(x - (-4))^2 + (y - 5)^2 = r^2
(x + 4)^2 + (y - 5)^2 = r^2
Now, let's find the slope of the line 2x + 3y = -19 by putting it into slope-intercept form:
2x + 3y = -19
3y = -2x - 19
y = (-2/3)x - (19/3)
The slope of this line is -2/3.
At a given location, the tangent to a circle is perpendicular to the radius. As a result, we must calculate the radius of the circle with centre (-4,5) that passes through the line's point of tangency (x,y).
The radius of the circle is equal to the length of the perpendicular line segment from the centre to the tangent line (-4,5). This perpendicular line segment will be denoted by the letter d.
We may use the formula for the distance between a point and a line to get d. The distance d between the point (x,y) and the line 2x + 3y = -19 is calculated as follows:
d = |2x + 3y + 19| / sqrt(2^2 + 3^2)
To be tangent to the circle, the radius should be equal to d. Let's call this radius r.
So, we have two equations:
(x + 4)^2 + (y - 5)^2 = r^2 (equation of circle)
d = |2x + 3y + 19| / sqrt(13) (equation of distance between point and line)
Substituting d = r into the second equation, we get:
r = |2x + 3y + 19| / sqrt(13)
We can now substitute this expression for r into the equation of the circle:
(x + 4)^2 + (y - 5)^2 = (|2x + 3y + 19| / sqrt(13))^2
Since the point of tangency lies on the line 2x + 3y = -19, we can substitute (-19 - 3y)/2 for x in the above equation and solve for y:
((-19 - 3y)/2 + 4)^2 + (y - 5)^2 = (|2((-19 - 3y)/2) + 3y + 19| / sqrt(13))^2
Simplifying and solving for y, we get:
y = -5 ± 2√13
Therefore, the two tangent points are (-19/2, -5 + 2√13) and (-19/2, -5 - 2√13).