Answer: Let x be the measure of the smallest angle in the triangle. Then we have:
One angle is three times as large as another, so the second angle is 3x.
The third angle is 80° more than the smallest angle, so it is x + 80.
The sum of the angles in a triangle is always 180°, so we can write an equation:
x + 3x + (x + 80) = 180
Simplifying and solving for x, we get:
5x + 80 = 180
5x = 100
x = 20
Therefore, the smallest angle in the triangle is x = 20 degrees, the second angle is 3x = 60 degrees, and the third angle is x + 80 = 100 degrees.
Step-by-step explanation:
the surface area of a cylinder is 936pi squares meters. the radius is 13m use the formula sa=2b=ph. to find the height of cylinder.
Answer: The formula for the surface area of a cylinder is:
SA = 2πr^2 + 2πrh
where SA is the surface area, r is the radius, and h is the height.
In this case, we know that the surface area is 936π square meters and the radius is 13 meters. So we can plug those values into the formula and solve for h:
936π = 2π(13^2) + 2π(13)(h)
Simplifying:
936π = 338π + 26πh
936π - 338π = 26πh
598π = 26πh
h = 598/26 = 23
Therefore, the height of the cylinder is 23 meters.
Step-by-step explanation:
Step-by-step explanation:
you made some mistakes with the formula.
the surface area of a cylinder is
the outside mantle area
+
the 2 circle areas on top and bottom.
the outside mantle area is
2×pi×radius×height
the 2 circle areas are
2 × pi×radius²
in total that is
2×pi×radius×height + 2×pi×radius² =
2×pi×radius×(height + radius) = 936pi
2×pi×13×(height + 13) = 936pi
pi×(height + 13) = 36pi
height + 13 = 36
height = 36 - 13 = 23 m
unit 8 homework 4 numbers 11 and 13
Step-by-step explanation:
how could you solve 10., if you cannot solve 11. ? they are using the same thing : law of sine.
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c being the sides, and A, B, C being the corresponding opposite angles.
11.
x/sin(90) = 13/sin(70)
as sin(90) = 1
x = 13/sin(70) = 13.83431104...
13.
remember, the sum of all angles in a triangle is always 180°.
angle JLM = 180 - 90 - 51 = 39°
angle LJK = 180 - 90 - 72 = 18°
14/sin(39) = JL/sin(51)
JL = 14×sin(51)/sin(39)
JL/sin(90) = JL = 14×sin(51)/sin(39) = KL/sin(18)
KL = 14×sin(51)×sin(18)/sin(39) = 5.342458907...
a battery company makes 12-volt car batteries. after many years of product testing, the company knows that the average life of its battery is normally distributed, with a mean of 44 months and a standard deviation of 7 months. a button hyperlink to the salt program that reads: use salt. (a) if the company guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (round your answer to two decimal places.) % (b) if the company does not want to make refunds for more than 9% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
a) The percentage of batteries the company expects to replace is:
0.1271 * 100% = 12.71%
b) The company should guarantee the batteries for 34 months (rounded to the nearest month) to ensure that refunds are not made for more than 9% of its batteries under the full-refund guarantee policy.
Step by step explain about both part of the question?(a) Let X be the random variable representing the life of a battery. We want to find the probability that a battery fails within 36 months after purchase, which is equivalent to finding P(X ≤ 36).
Using the normal distribution formula with mean μ = 44 months and standard deviation σ = 7 months, we have:
Z = (X - μ) / σ = (36 - 44) / 7 = -1.14
Using a standard normal table or calculator, we find that the probability of a standard normal variable being less than or equal to -1.14 is 0.1271. Therefore, the percentage of batteries the company expects to replace is:
0.1271 * 100% = 12.71% (rounded to two decimal places)
(b) Let Y be the random variable representing the length of the guarantee period in months. We want to find the value of Y such that P(X ≤ Y) = 0.09, where X has the same normal distribution with mean μ = 44 months and standard deviation σ = 7 months.
Using the inverse normal distribution formula with mean μ = 44 months and standard deviation σ = 7 months, we have:
Z = invNorm(0.09) = -1.34
where invNorm is the inverse normal function. Solving for Y, we have:
(Y - μ) / σ = Z
(Y - 44) / 7 = -1.34
Y - 44 = -1.34 * 7
Y ≈ 34.42
Therefore, the company should guarantee the batteries for 34 months (rounded to the nearest month) to ensure that refunds are not made for more than 9% of its batteries under the full-refund guarantee policy.
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7. The data show the amount spent by 8 households on heating bills in January and June last year.
$80.50 $75.00 $68.90 $87.00 $81.80 $78.20 $74.60 $69.80
$50.40 $36.70 $31.00 $47.30 $52.00 $39.60 $35.60 $31.20
Which of the following best describes the data?
O
The data are dependent because the amounts changed between January and June.
The data are independent because the heating bills in January and June came from the same households.
O
The data are dependent because the heating bills in January and June came from the same households.
The data are independent because the amount changed between January and June.
3
0
The option that best describes the data is the option;
The data are independent because the heating bills in January and June came from the same households.What are dependent and independent data?Dependent and independent data refers to the relationship between two sets of data.
The specified data in the table indicates;
The data obtained from an household in January is located directly on top the data obtained from the same household in June.
The heating bill depends on the amount of energy used in an household.
The amount of energy used in each household depends on the heating requirement of the household, such that the heating bill for an household in January is related to the heating bill for the same household in June
The correct option is therefore;
The data are related because the heating bills in January and June came from the same households.
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Can someone explain to me what co sin and tan are and how i solve questions that involve them
Answer:
Cosine, sine, and tangent are trigonometric functions used in mathematics and geometry to calculate angles and sides in right triangles.
Here is a brief explanation of each:
Cosine (cos): The cosine of an angle in a right triangle is defined as the adjacent side length divided by the hypotenuse length. In other words, it represents the ratio of the length of the adjacent side to the angle to the length of the hypotenuse. It is usually abbreviated as cos.
Sine (sin): The sine of an angle in a right triangle is defined as the opposite side length divided by the hypotenuse length. In other words, it represents the ratio of the length of the opposite side to the angle to the length of the hypotenuse. It is usually abbreviated as sin.
Tangent (tan): The tangent of an angle in a right triangle is defined as the opposite side length divided by the adjacent side length. In other words, it represents the ratio of the length of the opposite side to the angle to the length of the adjacent side. It is usually abbreviated as tan.
To solve questions that involve these functions, you need to know at least two values of a right triangle, such as the lengths of two sides or one side and an angle. Then you can use the trigonometric function and the given values to calculate the missing side or angle.
For example, if you know the length of the hypotenuse and one acute angle of a right triangle, you can use the sine or cosine function to calculate the length of one of the other sides. If you know the length of one side and one acute angle, you can use the tangent function to calculate the length of the other side.
There are also trigonometric identities and equations that can be used to simplify or solve more complex problems involving these functions.
Step-by-step explanation:
Ella is cooking a turkey and a ham. It takes 14 minutes per pound to cook a turkey and 21 minutes per pound to cook a ham. Ella is able to cook the turkey and the ham in 5 hours and 43 minutes. If the turkey weighs twice as much as the ham, how much do the turkey and the ham weigh? A. The turkey weighs 7 pounds, and the ham weighs 14 pounds. B. The turkey weighs 7 pounds, and the ham weighs 7 pounds. C. The turkey weighs 14 pounds, and the ham weighs 7 pounds. D. The turkey weighs 28 pounds, and the ham weighs 14 pounds.
Answers is what I need! Thankkksss
The possible dimensions of the plot are:
Length = 9.2 meters, width = 25.6 meters
Length = 25.6 meters, width = 9.2 meters
What is quadratic equation?
It's a second-degree quadratic equation which is an algebraic equation in x.
Let the length of the rectangular plot be L meters and the width be W meters. Then the perimeter of the plot is:
P = 2L + W
Since there are only three sides to the fence, we can set the perimeter equal to the length of the fencing:
2L + W = 44
Solving for W, we get:
W = 44 - 2L
The area of the plot is given as 210 square meters:
L * W = 210
Substituting for W, we get:
L * (44 - 2L) = 210
Simplifying and rearranging, we get a quadratic equation:
2L² - 22L + 105 = 0
Using the quadratic formula, we can solve for L:
L = (22 ± √(22² - 4(2)(105))) / (2(2))
L = (22 ± 2√34) / 4
L = 11/2 ± √34/2
We discard the negative solution, so:
L = 11/2 + √34/2 ≈ 9.2 meters
Now we can use the equation W = 44 - 2L to find the corresponding width:
W = 44 - 2(9.2) = 25.6 meters
Therefore, the possible dimensions of the plot are:
Length = 9.2 meters, width = 25.6 meters
Length = 25.6 meters, width = 9.2 meters
Note that both sets of dimensions result in the same area of 210 square meters.
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Find the area of the shaded region
the area of the region is 13.01 ft².
What is area?Area is the region bounded by a plane shape.
To calculate the area of the of the shaded region, we use the formula below
Formula:
Area of the shaded region = Area of the sector-Area of the triangleA = (∅πr²/360)-(r²sin∅/2).......................... Equation 1Where:
A = Area of the shaded regionr = Radius of the circle∅ = Angle subtends at the center of the circleFrom the question,
Given:
r = 12 ft∅ = 60°π = 3.14Substitute these values into equation 1
A = (60×3.14×12²/360)-(12²sin60°/2)A = 75.36-62.35A = 13.01 ft²Hence, the area is 13.01 ft².
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Need help!! 25 points
The amount of people infected after t weeks is modeled by the function presented as follows:
[tex]f(t) = \frac{675000}{1 + 4000e^{-t}}[/tex]
When the epidemic began, we have that t = 0, hence the number of people is given as follows:
f(0) = 675,000/(1 + 4000)
f(0) = 169 people.
Six weeks after the epidemic began, we have that t = 6, hence the number of people is given as follows:
f(6) = 675,000/(1 + 4000 x e^(-6))
f(6) = 61,841 people.
The limiting size of the infected population is the numerator of the fraction, which is 675,000, as the denominator goes to zero when t goes to infinity.
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greatest common factor of 14xy2 and 28x2y
Answer:
Step-by-step explanation:
A company has to decide whether to invest money in the development of a microbiological product. The company's research director has that there is a 60% chance that a successful development could be achieved in 2 years. However, if the product had not been successfully developed at the end of this period, the company would abandon the project, which would lead to a loss in present-value terms of $ 3 million. (Present value is designed to take the company's time preference for money into account. The concept is explained in Chapter 8) In the event of a successful development, a decision would have to be made on the scale of production. The returns generated would depend on the level of sales which could be achieved over the period of the product's life. For simplicity, these have been catorized as either high or low. If the company opted for large-volume production and high sales were achieved, then net returns with a present-value of $6 million would be obtained. However, large-scale production followed by low sales would lead to net returns with a present value of only $1 million.In contrast, if the company decided to invest only small-scale production facilities then high sales would generate net returns with a present value if facilities then high sales would generate net returns with a present value of $4 million and low sales would generate net returns with a present value of $2 million. The company's marketing manager estimates that there is a 75% chance that high sales could be achieved.(a) Construct a decision tree to represent the company's decision problem. (b) Assuming that the companys objective is to maximize its expected returns, determine the policy that it should adopt. (c) There is some debate in the company about the probability that was estimated by the research diretor. Assuming that allo other elements if the problem remain the same, determine how low this probility would have ti be before the option of not developing the product should be chosen. (d) before the final decision us nade the company us taken iver by a bew owner, who has the utilities shown below for the sums of money involved in the decision. (The owner has no ointerest in other attributes which may be associated with the decision, such as developing a prestige product or maintaining employment.) What implications does this have for the policy that you iidentified in (b) and why?Present value of net returns New owner's utility-$3m, $0m, $1m, $2m, $4m, $6m 0, 0.6, 0.75, 0.85, 0.95, 1.0
The optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.
The initial node represents the decision whether to invest in the development of the microbiological product.
The two possible outcomes are a successful development or failure after 2 years.
(b) To determine the policy that the company should adopt to maximize its expected returns, we need to calculate the expected value at each decision node.
Starting from the end nodes and working backwards, we have:
For large-scale production with high sales:
Expected value = 0.75 x $6m + 0.25 x $1m = $4.25m
For large-scale production with low sales:
Expected value = 0.75 x $1m + 0.25 x $6m = $1.75m
For small-scale production with high sales:
Expected value = 0.75 x $4m + 0.25 x $2m = $3.5m
For small-scale production with low sales:
Expected value = 0.75 x $2m + 0.25 x $4m = $1.75m
At the 2-year node, the expected value for a successful development is:
For large-scale production:
Expected value = 0.75 x $4.25m + 0.25 x $1.75m = $3.5m
For small-scale production:
Expected value = 0.75 x $3.5m + 0.25 x $1.75m = $2.81m
Finally, at the initial node, the expected value for investing in the development is:
Expected value = 0.6 x $3.5m + 0.4 x (-$3m) = $0.1m
Therefore, the policy that the company should adopt to maximize its expected returns is to invest in the development of the microbiological product, choose large-scale production if the development is successful, and choose small-scale production otherwise.
(c) If the probability of a successful development is lower than a certain threshold, the option of not developing the product should be chosen. Let p be this threshold probability. Then the expected value at the initial node is:
Expected value = p x $0m + (1-p) x (-$3m) = -$3m + $3mp
Setting this equal to zero and solving for p, we get:
p = 1
Therefore, if the probability of a successful development is lower than 100%, the company should not invest in the development of the microbiological product.
(d) The new owner's utilities represent their preferences for the sums of money involved in the decision.
The utilities are increasing and concave, indicating diminishing marginal utility of money.
This means that the new owner is risk-averse.
The policy identified in (b) may not be optimal for the new owner because their utilities are different from the present-value net returns.
To determine the optimal policy for the new owner, we need to use the new owner's utility values to calculate the expected utility of each decision branch in the decision tree.
If the company invests in large-scale production and high sales are achieved, the expected utility is 0.75 * 0.95 * 1.0 * $6m = $4.285m.
If the company invests in large-scale production and low sales are achieved, the expected utility is 0.75 * 0.95 * (1 - 0.0) * $1m = $712,500.
If the company invests in small-scale production and high sales are achieved, the expected utility is 0.75 * 0.05 * 1.0 * $4m = $150,000.
If the company invests in small-scale production and low sales are achieved, the expected utility is 0.75 * 0.05 * (1 - 0.0) * $2m = $75,000.
If the company decides not to invest in the product, the expected utility is 0.25 * (1 - 0.6) * $0m + 0.25 * 0.6 * (1 - 0.0) * -$3m = -$450,000.
Therefore, the optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.
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the $5\times 5$ grid shown contains a collection of squares with sizes from $1\times 1$ to $5\times 5$. how many of these squares contain the black center square?
the total number of squares that contain the black center square is[tex]$1 + 4 + 9 + 16 + 1 = \boxed{31}$.[/tex]
To solve this problem, we need to count the number of squares of each size that contain the black center square.
There is only one square of size[tex]$5\times 5$[/tex], which is the entire grid and obviously contains the black center square.
For squares of size[tex]$4\times 4$[/tex], there are [tex]$4$[/tex]possible squares that contain the black center square (one for each corner).
For squares of size[tex]$3\times 3$,[/tex] there are 9 possible squares that contain the black center square (one for each position that the center square could occupy, and then each of those squares could be oriented in three different ways).
For squares of size $2\times 2$, there are $16$ possible squares that contain the black center square (one for each pair of adjacent squares).
For squares of size [tex]$1\times 1$[/tex], there is only one possible square that contains the black center square (the center square itself).
Therefore, the total number of squares that contain the black center square is[tex]$1 + 4 + 9 + 16 + 1 = \boxed{31}$.[/tex]
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There are 11 squares containing the black center square in the 5x5 grid.
To find the number of squares that contain the black center square, we'll consider the sizes of the squares and their positions in the 5x5 grid.
The black center square is a 1x1 square itself, so that's 1 square.
For 2 x 2 squares containing the center square, there are 4 possible positions (the center square can be in any corner). So, that's 4 squares.
For 3x3 squares containing the center square, there is only 1 possible position (the center square is exactly in the middle). So, that's 1 square.
4. For 4x4 squares containing the center square, there are 4 possible positions (the center square can be in any corner). So, that's 4 squares.
5. For 5x5 squares containing the center square, there is only 1 possible position (the center square is exactly in the middle).
So, that's 1 square.
Now, we'll add up the number of squares we found in each step:
1 + 4 + 1 + 4 + 1 = 11.
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Please answer with explanation.
Answer:
Step-by-step explanation:
Trigonometry can be used to find the value of x
15cos35=x
x=15*0.8192
x=15*.8192
x= 12.288
x≈12.29cm
In 2008, the price of a gallon of unleaded gasoline was $4. 2. In 1990, it was only $1. 37 per gallon. What is the increase expressed as a percent change? Round to the nearest percent.
A. 66%
B. 393%
C. 193%
D. 134%
please i need help'
. ?
The percent increase in the price of a gallon of unleaded gasoline from 1990 to 2008 is 206.56%
To find the percent change from 1990 to 2008, we first need to calculate the actual change in price
Actual Change = 2008 Price - 1990 Price
Actual Change = $4.20 - $1.37
Subtract the numbers
Actual Change = $2.83
Next, we need to calculate the percent change as a ratio of the actual change to the original price in 1990
Percent Change = (Actual Change / 1990 Price) x 100%
Substitute the values in the equation
Percent Change = ($2.83 / $1.37) x 100%
Do the arithmetic operations
Percent Change = 206.56%
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The given question is incomplete, the complete question is:
In 2008, the price of a gallon of unleaded gasoline was $4. 2. In 1990, it was only $1. 37 per gallon. What is the increase expressed as a percent change? Round to the nearest percent.
A bus is traveling at a speed of 15m/s2. The driver approaches the same traffic light in another traffic lane. He does not brake and continues at the same speed. Write an equation for the distance the bus travels in time (t) (Hint: At a constant speed, the acceleration is 0m/s2)
This equation tells us that the distance the bus travels is directly proportional to the time it travels at a constant speed of 15m/s.
What is speed?
Speed is the method of measuring how quickly an object moves from one place to another. It is a scalar quantity that expresses the rate of change of distance over time. In other words, it is the distance traveled per unit of time.
If the bus is traveling at a constant speed of 15m/s, then its acceleration is 0m/s². Therefore, we can use the formula for distance traveled at constant speed:
distance = speed × time
In this case, the speed of the bus is 15m/s, so the equation for the distance the bus travels in time (t) is:
distance = 15t
This equation tells us that the distance the bus travels is directly proportional to the time it travels at a constant speed of 15m/s.
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I NEED HELP ON THIS ASAP! i already filled in the table, I just need help with Question d
The proof that the table has a constant ratio is shown below
Proving that the table has a constant ratioFrom the table of values, we have the following parameters that can be used in our computation:
f(x + 1) = ab^(x + 1)
f(x + 2) = ab^(x + 2)
f(x + 3) = ab^(x + 3)
When divided, we get the ratio r
So, we have
r = f(x + 3)/f(x + 2) = f(x + 2)/f(x + 1)
This gives
ab^(x + 3)/ab^(x + 2) = ab^(x + 2)/ab^(x + 1)
Divide through by a
b^(x + 3)/b^(x + 2) = b^(x + 2)/b^(x + 1)
Using the law of indices, we have
b^(x + 3 - x - 2) = b^(x + 2 - x - 1)
Evaluate
b^0 = b^0
This gives
1 = 1
Hence, the table has a constant ratio
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when a biased coin is tossed, heads is three times as likely to come up as tails. rearrange the following procedure in the correct order to find the probability that should be assigned to the outcome of heads and tails?
The probability of heads is 3 times that of tails, so the probability of heads is 0.75 and the probability of tails is 0.25.
Assign a probability of 0.5 to heads
Assign a probability of 0.25 to tails
When a biased coin is tossed the probability of heads is three times as likely to come up as tails.
To find the probability that should be assigned to the outcome of heads and tails the first step is to calculate the probability of heads.
Once this is done,
The probability of heads can be assigned a value of 0.5 and the probability of tails can be assigned a value of 0.25.
After that,
The probability of heads and tails can be calculated accordingly.
The probability of heads and tails when a biased coin is tossed, the first step is to calculate the probability of heads.
Once this is done the probability of heads can be set to 0.5 and the probability of tails can be set to 0.25.
With these probabilities assigned the probability of heads is three times that of tails.
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A cyclist bikes a certain distance in 25 minutes.
Write an equation that shows the relationship between speed, s, and time, t, when the distance is 50 miles.
As a result, if a bicycle covers 50 miles in 25 minutes, their speed is 120 miles per hour.
What is speed?Speed is defined in physics as the distance covered in a unit of time. What determines the velocity vector's magnitude is a scalar quantity. An item is said to be travelling faster or slower depending on its speed. It has zero speed if it isn't moving at all.
Describe distance.Therefore, a bicycle travelling 50 miles in 25 minutes is moving at a speed of 120 miles per hour.
what are miles?Miles might mean two different things. As a noun, it refers to a linear measurement unit that is 1,760 yard. It also has the adverbial meanings of greatly or far.
When the distance is 50 miles, the relationship between speed, s, and time, t, can be written as follows:
s = d/t
where d is the distance traveled, and t is the time it takes.
The distance is 50 miles in this instance, and the travel time is 25 minutes, or 25/60 hours.
When we enter these values into the formula above, we obtain:
120 miles per hour is equal to s = 50/(25/60).
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_________are important to a systems analyst who must work with people at all organizational levels, balance conflicting needs of users, and communicate effectively.
Organizational skills
Organizational skills and the ability to communicate effectively are crucial for a systems analyst who needs to work with individuals at all levels of an organization, manage conflicting user needs, and ensure that information is communicated clearly and efficiently. Interpersonal skills are important to a systems analyst who must work with people at all organizational levels, balance conflicting needs of users, and communicate effectively. The knowledge and skills in leadership and strategic management are essential for the creation and achievement of an organizational vision and strategy. These skills include effective communication, decision-making, and the ability to evaluate and measure success, as well as a deep understanding of the organization and its environment. Leadership and strategic management play a crucial role in the success of any organization. A strong and effective leader with a well-developed understanding of strategic management is essential for the creation and achievement of an organizational vision and strategy.
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observe that for every value of that satisfies , the value of is constant. what does this tell you about the behavior of the graph of on this interval?
The graph remains at a constant height (y-value) for all x-values within the specified interval. This means that the function does not change in this interval and maintains a consistent output.
If the value of is constant for every value that satisfies a certain condition, it means that the graph is a horizontal line on that interval. The behavior of the graph is constant or unchanging in terms of its vertical position.
When every value of x that satisfies a given condition results in a constant value of y, this tells us that the behavior of the graph of the function on this interval is horizontal. In other words, the graph remains at a constant height (y-value) for all x-values within the specified interval. This means that the function does not change in this interval and maintains a consistent output.
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90000000000000000000000 - 5500000000000
90000000000000000000000 - 5500000000000 =
4450000000000000000000000
Answer:
this kind of problem is hard to solve with that many zeros. but if you were to do 900,000,000-550,000,000 it would be 350,000,000
Step-by-step explanation:
if a cartesian join is used to link table a which contains two rows to table b which contains eight rows, there will be sixteen rows in the results.T/F
True. A cartesian join, also known as a cross join, returns all possible combinations of rows between two tables. In this scenario, since table a contains two rows and table b contains eight rows, there will be 2 x 8 = 16 possible combinations or rows in the result set.
When a Cartesian join is used to link two tables, it creates a combination of all possible rows between the two tables. In this case, table A has 2 rows and table B has 8 rows. To calculate the number of rows in the result, you simply multiply the number of rows in each table:
2 rows (table A) x 8 rows (table B) = 16 rows
So, when a Cartesian join is used to link table A with 2 rows to table B with 8 rows, there will be 16 rows in the result.
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The statement "if a cartesian join is used to link table a which contains two rows to table b which contains eight rows, there will be sixteen rows in the results" is a true statement.
What is a Cartesian join?
A Cartesian join, also known as a cross join or a cross product, generates a result set that combines every row from the first table with every row from the second table, with no requirements or limits.
If table A has two rows and table B has eight rows, a Cartesian join between the two tables will yield a result set with 16 rows (the product of the number of rows in each table).
So the statement "if a Cartesian join is used to link table A with two rows to table B with eight rows, the results will have sixteen rows" is valid.
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Jada swims 4 laps, which is 2/5
of the number of laps she plans to swim.
How many laps does Jada plan to swim? Use x
for the number of laps Jada plans to swim.
Equation:
Solution:
Let x be the number of laps Jada plans to swim.
According to the problem, 4 laps is 2/5 of the number of laps she plans to swim, so we can write:
4 = 2/5 * x
To solve for x, we can first multiply both sides by the reciprocal of 2/5, which is 5/2:
4 * 5/2 = x
Simplifying the left side:
10 = x
Therefore, Jada plans to swim 10 laps.
pls help I’m not understanding !
The triangle ABC ≅ triangle DEC using the SSS criteria.
Given that, BA ≅ ED. Also C is midpoint of BE and AD thus,
BC = CE
AC = CD
Now, for the triangle ABC and triangle DEC we have:
BA = ED (Given)
C is the midpoint of BE and AD (given)
BC = CE (C is the midpoint)
AC = CD (C is the midpoint)
Thus, the triangle ABC ≅ triangle DEC using the SSS criteria.
BA = ED (Given). C is the midpoint of BE and AD (given). BC = CE (C is the midpoint). AC = CD (C is the midpoint), The triangle ABC ≅ triangle DEC using the SSS criteria.
What are similar triangles?Two triangles that are similar in shape but not necessarily in size are said to be similar triangles. This indicates that the respective sides and angles in the two triangles are proportional to one another. There are numerous uses for similar triangles in geometry, such as discovering missing side lengths or angles or resolving problems with indirect measurements. Other shapes besides triangles, like circles, rectangles, and polygons, are also included in the concept of resemblance.
Given that, BA ≅ ED. Also C is midpoint of BE and AD thus,
BC = CE
AC = CD
Now, for the triangle ABC and triangle DEC we have:
BA = ED (Given)
C is the midpoint of BE and AD (given)
BC = CE (C is the midpoint)
AC = CD (C is the midpoint)
Thus, the triangle ABC ≅ triangle DEC using the SSS criteria.
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the following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal. political party support democrats 100 republicans 120 independents 80 we are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed. refer to exhibit 12-6. if the opinions of the individuals of the three groups are uniformly distributed, the expected frequency for each group is . a. .333 b. .50 c. 50 d. 100
The answer is (d) 100, which is the expected frequency for each group.
How to find the expected frequency?To determine the expected frequency for each group under the assumption of a uniform distribution of opinions, we can use the formula:
Expected frequency = (total sample size) x (proportion of group in population)
The total sample size is 300, and the proportions of Democrats, Republicans, and Independents in the population are not given, so we cannot use those directly. However, if we assume that the population proportions are roughly the same as the sample proportions, we can estimate the expected frequencies as follows:
Expected frequency for Democrats = 300 x (100/300) = 100
Expected frequency for Republicans = 300 x (120/300) = 120
Expected frequency for Independents = 300 x (80/300) = 80
Therefore, the answer is (d) 100, which is the expected frequency for each group if the opinions of the individuals of the three groups are uniformly distributed.
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PLEASE HELP ASAP!!!!
Answer:
f
Step-by-step explanation:
thats the explanation
question 1: how many style a shades can be loaded into a 40-foot container? question 2: how many style b shades can be loaded into a 40-foot container?
The total number of Style B shades that can be loaded into the container is 3,840 Style B shades in total.
A 40-foot container can hold 3,840 Style B shades.
A 40-foot container typically has a volume of 67.7 cubic meters (2,390 cubic feet), but without knowing the size and packing configuration of the shades, it's impossible to determine how many of each type can fit into the container.
Once you provide the dimensions and packing requirements for Style A and Style B shades, I can help you calculate how many of each type can be loaded into a 40-foot container.
Assuming that each carton of Style B shades has the same dimensions and that there is no wasted space within the container, we can calculate the number of cartons that can be loaded into a 40-foot container as follows:
First, we need to determine the total number of cartons that can fit in the container:
8 cartons in width x 40 cartons in length x 2 cartons in height = 640 cartons in total
Next, we need to determine the number of Style B shades in each carton:
6 shades x carton
Therefore, the total number of Style B shades that can be loaded into the container is:
640 cartons x 6 shades per carton = 3,840 Style B shades in total.
So a 40-foot container can hold 3,840 Style B shades.
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Question: How many Style B shades can be loaded into a 40-foot container? There are 6 shades x carton which could be shipped nested, with the squared foot on the bottom. According to the container dimensions, it's possible to put 8 cartons in width, 40 cartons in length and 2 cartons in height.
Verify Associative property: 2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5..
Please help tomorrow is my final exam
We verified that the associative property of addition holds for the given expression below
Verifying the Associative propertyLet's verify the associative property of addition for the given expression:
2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5
We can simplify both sides of the equation by finding a common denominator for the fractions:
2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5
Multiplying 2/3 by 20/20, we get:
40/60 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5
Multiplying 3/4 by 15/15, we get:
40/60 + 45/60 + 1/5 = (2/3 + 3/4) + 1/5
Combining the first two terms on the left-hand side, we get:
85/60 + 1/5 = (2/3 + 3/4) + 1/5
Simplifying the fraction 85/60, we get:
17/12 + 1/5 = (2/3 + 3/4) + 1/5
Multiplying 2/3 by 4/4, we get:
17/12 + 1/5 = (8/12 + 9/12) + 1/5
Combining the fractions in the parentheses, we get:
17/12 + 1/5 = 17/12 + 1/5
Since both sides of the equation are equal, we have verified that the associative property of addition holds for the given expression:
2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5.
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What is the correct answer choice to #3/the first problem?Please explain if you are able to.
What does IQR tell me about the data values in the box plot?
The IQR in problem 3 is equal to 10.
The IQR tells us about the measure of the spread of the data contained in the box plot.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the given box plot, the five-number summary for the given data set include the following:
Minimum (Min) = 30.First quartile (Q₁) = 65.Median (Med) = 70.Third quartile (Q₃) = 75.Maximum (Max) = 80.How to calculate the interquartile range (IQR)?Mathematically, interquartile range (IQR) of a data set is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):
Interquartile range (IQR) of data set = Q₃ - Q₁
Interquartile range (IQR) of data set = 75 - 65
Interquartile range (IQR) of data set = 10.
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Using scientific notation, (5 x 10^6) (9 × 10^-2) = 6 x 10^n, where 1 ≤ b < 10 and
n is an integer.
What is the value of b? |
What is the value of n?
The equation (5 x 10⁶) (9 × 10⁻²) = 6 x 10⁴ when written in scientific notation. The value of b is 5 and the value of n is 4.
What is scientific notation?Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in standard decimal form. The number is written in the form of a number between 1 and 10 multiplied by a power of 10.
The value of b in this equation is 5. This is because the decimal points in both terms must be aligned in order to multiply them together.
The decimal points in each term are 6 and 2, respectively.
Since 6 is greater than 2, the decimal point for the total must be aligned with 6.
This means that the number 5 must be multiplied by 10⁶, resulting in b being 5.
The value of n in this equation is 4. This is because when the two terms are multiplied together, the exponents must be added.
The exponents of 10 in each term are 6 and -2, respectively.
When these are added together, they equal 4, resulting in the exponent of 10 in the new term to be 4.
Therefore, the equation (5 x 10⁶) (9 × 10⁻²) = 6 x 10⁴ when written in scientific notation. The value of b is 5 and the value of n is 4.
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