Here, we can use the fact that ln(x) grows slower than any positive power of x. That means that as x approaches infinity, ln(x) approaches infinity slower than x. Therefore, (ln(x))/x approaches zero as x approaches infinity. Using this fact, we can see that the entire expression approaches zero as x approaches infinity. Therefore, the limit is equal to zero.
To get the limit of lim (ln(x))²/3x as x approaches infinity, we can use l'Hospital's Rule. Taking the derivative of the numerator and denominator separately, we get: lim 2ln(x) * 1/x / 3
x→[infinity]
Simplifying this expression, we get: lim 2ln(x) / (3x)
x→[infinity]
Using l'Hospital's Rule again, we take the derivative of the numerator and denominator separately: lim 2 * 1/x / 3
x→[infinity]
Simplifying further, we get: lim 2/ (3x)
x→[infinity]
Since the denominator approaches infinity as x approaches infinity, the limit is equal to zero.
Alternatively, we can use an elementary method to find the limit. We can rewrite the expression as: (ln(x))^2 = (ln(x)) * (ln(x))
Then we can use the fact that ln(x) grows slower than any positive power of x. That means that as x approaches infinity, ln(x) approaches infinity slower than x. Therefore, (ln(x))/x approaches zero as x approaches infinity. Using this fact, we can see that the entire expression approaches zero as x approaches infinity. Therefore, the limit is equal to zero.
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Why are Georgia's state agencies important to the efficient functioning of the state?
They enable the Georgia General
Assembly to pass laws and establish
the state budget.
A
со
They enable the Supreme Court of
Georgia to interpret the state's laws.
B
D
о о
They enable Georgia's local
governments to check the power of the
state government.
They enable Georgia's executive
branch to enforce the state's laws
Georgia's state agencies are important for the efficient functioning of the state because they enable the Supreme Court to interpret laws, the General Assembly to establish the state budget and pass laws, and the executive branch to enforce laws.
Georgia's state agencies are important to the efficient functioning of the state because they enable the Georgia General Assembly to pass laws and establish the state budget, enable the Supreme Court of Georgia to interpret the state's laws, enable Georgia's local governments to check the power of the state government, and enable Georgia's executive branch to enforce the state's laws.
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--The given question is incomplete, the complete question is given
" Why are Georgia's state agencies important to the efficient functioning of the state? "--
To assess the accuracy of laboratory scale, a standard weight known to weigh 10 grams is weighed repeatedly. the weight is weighed 40 times. the mean result is 10.230 grams. the standard deviation of the scale readings is 0.020 gram. construct a 98% confidence interval for the mean of repeated measurements of the weight. what is the margin of error? round your answers to three decimal places.
To construct a 98% confidence interval for the mean of repeated measurements of the weight, we can use the formula:
Confidence interval = mean ± (t-value) x (standard error)
where the standard error is the standard deviation of the sample divided by the square root of the sample size, and the t-value is based on the degrees of freedom (n-1) and the desired level of confidence. Since we are given the sample mean, standard deviation, and sample size, we can plug in the values and solve for the confidence interval and margin of error.
First, we need to calculate the standard error:
Standard error = standard deviation / √n
Standard error = 0.020 gram / √40
Standard error = 0.00316 gram
Next, we need to find the t-value for a 98% confidence interval with 39 degrees of freedom. We can use a t-distribution table or calculator to find the t-value, which is approximately 2.423.
Substituting the values into the formula, we get:
Confidence interval = 10.230 ± (2.423)(0.00316)
Confidence interval = 10.230 ± 0.00766
Rounding to three decimal places, the 98% confidence interval for the mean weight is (10.222, 10.238) grams. The margin of error is half the width of the confidence interval, which is 0.00766/2 = 0.00383 grams
how do you assure that solver will find the optimal solution (if one exists) for an optimization model with integer decision variables?
Using a branch-and-bound algorithm combined with an effective search strategy and an appropriate selection of branching rules you can find the optimal solution for an optimization model with integer decision variables.
Solving an optimization model with integer decision variables requires a branch-and-bound algorithm, which recursively partitions the feasible region into smaller sub-regions until the optimal solution is found or proven to be infeasible. An effective search strategy, such as depth-first or best-first search, is used to explore the sub-regions efficiently.
The selection of branching rules is critical to the performance of the algorithm, as it determines the order in which variables are selected for partitioning. Effective branching rules, such as the most constrained variable or the strongest branching rule, can significantly reduce the number of nodes explored and improve the chance of finding the optimal solution. Additionally, using advanced techniques, such as domain reduction and cutting planes, can further enhance the performance of the algorithm.
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the mean, as a measure of central location, would be inappropriate for which one of the following? multiple choice incomes of lawyers ages of adults at a senior citizen center marital status of college students at a particular university number of pages in textbooks on statistics
The mean would be inappropriate as a measure of central location for data in option D: number of pages in textbooks on statistics, that has extreme outliers or is skewed.
Out of the options given, the number of pages in textbooks on statistics could potentially have extreme outliers, such as a textbook with significantly more pages than the rest of the sample. Therefore, the mean may not be the most appropriate measure of central location for this type of data. A better measure might be the median, which is less affected by extreme values.
In contrast, the mean would be an appropriate measure of central location for the incomes of lawyers, ages of adults at a senior citizen center, and marital status of college students at a particular university, as these data sets are less likely to have extreme outliers or be heavily skewed.
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Complete question:
the mean, as a measure of central location, would be inappropriate for which one of the following? multiple choice
incomes of lawyers
ages of adults at a senior citizen center
marital status of college students at a particular university
number of pages in textbooks on statistics
What is the difference between n=0 4E(1+3n) and ? 0 2 5 6
The difference between the summations of these two sequence is zero.
To compute the difference between the summation of (1 + 3n) from n = 0 to 4 and the summation of (3i - 5) from i = 2 to 6, we can first evaluate each summation individually and then subtract the result of the second summation from the first.
The summation of (1 + 3n) from n = 0 to 4 can be written as:
∑(1 + 3n) = (1 + 3(0)) + (1 + 3(1)) + (1 + 3(2)) + (1 + 3(3)) + (1 + 3(4))
= 1 + 4 + 7 + 10 + 13
= 35
Similarly, the summation of (3i - 5) from i = 2 to 6 can be written as:
∑(3i - 5) = (3(2) - 5) + (3(3) - 5) + (3(4) - 5) + (3(5) - 5) + (3(6) - 5)
= 1 + 4 + 7 + 10 + 13
= 35
Therefore, the difference between the two summations is:
∑(1 + 3n) - ∑(3i - 5) = 35 - 35 = 0
This means that the sum of the first sequence is equal to the sum of the second sequence.
Correct Question :
What is difference between Σ(1+3n) from n = 0 to 4 and Σ(3i-5) from i = 2 to 6.
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What is the value of the expression, when x = 6?
X^3 + 4
help please! thanks a lot <3
The equation f(x) = -f(x) has two solutions.
How many solutions are for f(x) = -f(x)?The equation f(x) = -f(x) is only true for a number whose sign does not matter, and that number is zero.
That is because -0 = +0
Then the number of solutions that the equation f(x) = -f(x) has is equal to the number of times that the graph of f(x) crosses the x-axis (that is the number of values of x such that f(x) = 0)
We can see that the graph crosses it twice, then the equation:
f(x) = -f(x)
has two solutions.
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A person invests 7000 dollars in a bank. The bank pays 5. 5% interest compounded monthly. To the , how long must the person leave the money in the bank until it reaches 13200 dollars?
A=P(1+r/n)^nt
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 13200\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years \end{cases}[/tex]
[tex]13200 = 7000\left(1+\frac{0.055}{12}\right)^{12\cdot t} \implies \cfrac{13200}{7000}=\left(1+\frac{0.055}{12}\right)^{12t}[/tex]
[tex]\cfrac{66}{35}=\left(\frac{12+0.055}{12}\right)^{12t}\implies \cfrac{66}{35}=\left(\frac{12.055}{12}\right)^{12t}\implies \log\left( \cfrac{66}{35} \right)=\log\left[ \left(\frac{12.055}{12}\right)^{12t} \right] \\\\\\ \log\left( \cfrac{66}{35} \right)=t\log\left[ \left(\frac{12.055}{12}\right)^{12} \right]\implies \cfrac{\log\left( \frac{66}{35} \right)}{\log\left[ \left(\frac{12.055}{12}\right)^{12} \right]}=t\implies \boxed{11.56\approx t}[/tex]
1.) Identify the similar triangles in each figure. Explain why they are similar and use the given information to find x and y.
2.) The area of a rectangle is 108 cm2. The ratio of the width to the length is 3:4. Find the length and the width.
Figure (a) have similar triangles, while figure (b) do not; and the length and the width of the rectangle are 12 cm and 9 cm,
Identifying the similar triangles in each figure.Figure (a)
The similar triangles in this figure are
ABC and AED
This is because:
The triangles have similar corresponding sides and congruent angles
Also, ABC is divided by 3 to get AED
So, we have
x = 15/3 = 5
y = 10/3
Figure (b)
The triangles in this figure are not similar triangles
The length and the width of the rectangleWe have
Area = 108
Width : Length = 3 : 4
So, we have
Width = 3/4Length
The area is
Area = Length * Width
Area = Length * 3/4Length
Length * 3/4Length = 108
3/4Length² = 108
Length² = 144
Length = 12
Recall that
Width = 3/4Length
Width = 3/4 * 12
Width = 9
Hence, the length and the width of the rectangle are 12 cm and 9 cm, respectively
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if in a certain population, people are born at an average rate of 9 people every 2 seconds and people die at an average rate of 3 people every 2 seconds, by approximately how many people does the population increase in 1 day?
The population is estimated to increase by approximately 38,880 people in 1 day.
To calculate the population increase in 1 day, we first need to convert the birth and death rates to a per-day basis. Since there are 60 seconds in a minute and 60 minutes in an hour, there are 60 x 60 = 3600 seconds in an hour, and 24 x 3600 = 86,400 seconds in a day. Therefore, in a day, the population will increase by: [(9 people/2 seconds) x (86,400 seconds/day) / 2] - [(3 people/2 seconds) x (86,400 seconds/day) / 2] = 38,880 people/day.
We multiply the per-second rates by the number of seconds in a day (divided by 2 since we are counting births and deaths separately) to get the per-day rates. We subtract the death rate from the birth rate to get the net population increase per day.
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What is the circumference of
this circle?
d = 12 cm
circumference = [?] cm
Round your answer to 2 decimal places.
Answer
Enter
Answer:
Step-by-step explanation:
Circumference = π × diameter
3.14 = π
3,14 × 12 = 37.68 cm
Ben was helping the school custodian set up chairs in the gym for an assembly. They needed to seat 180 students and put the same number of chairs in each row. The custodian suggested having 18 rows of chairs. After hearing the custodian's plan and doing some quick mental math, Ben suggested a different arrangement for the same number of seats. He explained that, by putting 5 more chairs in each row, they could have fewer rows, and students in the back row would be able to see better. How many rows will Ben's plan have? How many chairs were in each row of Ben's plan?
Answer:
He would have 12 rows with 15 chairs in each row.
Step-by-step explanation:
180 divided by 18 is 10
10 plus 5 is 15
180 divided by 15 is 12.
a jar contains 5 black and 3 red buttons. if you randomly select 3 buttons, what is theprobability that exactly 2 of them are black?
So the probability that exactly 2 of the 3 selected buttons are black is 15/28 or approximately 0.5357.
To find the probability that exactly 2 out of 3 selected buttons are black, we need to consider all possible ways of selecting 2 black buttons and 1 red button, and then add up their probabilities.
The total number of ways of selecting 3 buttons out of 8 is:
(8 choose 3) = 8! / (3! * 5!) = 56
The number of ways of selecting 2 black buttons out of 5, and 1 red button out of 3 is:
(5 choose 2) * (3 choose 1) = (5! / (2! * 3!)) * (3! / (1! * 2!)) = 30
Therefore, the probability of selecting exactly 2 black buttons out of 5 and 1 red button out of 3 is:
P(2 black, 1 red) = 30 / 56 = 15 / 28
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What are the two points plotted on the graph?
Answer:
Step-by-step explanation:
the mean of a set of data is -1.82 and its standard deviation is 3.91. find the z score for a value of 4.51.
The value of z-score concerning for 4.51 is 1.62 under the given condition that the mean of a set of data is -1.82 and its standard deviation is 3.91.
The formula for evaluating a z-score is
z = (x-μ)/σ,
Here
x = raw score,
μ = population mean,
σ = population standard deviation.
For the given case,
Mean = -1.82
Standard deviation = 3.91.
To evaluate the z-score for a value of 4.51,
z = (x - μ) / σ
= (4.51 - (-1.82)) / 3.91
= 6.33 / 3.91
= 1.62
The value of z-score is 1.62
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A cone is 14cm high and it's base radius 4/2cm.calculate the volume of water that is exactly half the volume of the cone.
Step-by-step explanation:
The volume of a cone is given by the formula:
V = (1/3)πr^2h
where r is the radius of the base and h is the height of the cone.
In this case, the cone has a height of 14 cm and a base radius of 4/2 cm, which is equal to 2 cm. Therefore, the volume of the entire cone is:
V = (1/3)π(2 cm)^2(14 cm) = (4/3)π(28 cm^3) = 37.333... cm^3
To find the volume of water that is exactly half the volume of the cone, we need to divide the volume of the cone by 2:
V_water = (1/2)V = (1/2)(37.333...) cm^3 = 18.666... cm^3
To calculate the height of the water in the cone, we can use the formula:
V_water = (1/3)πr^2h
where h is the height of the water.
We know the volume of water (18.666... cm^3) and the radius of the base (2 cm), so we can rearrange the formula to solve for h:
h = 3V_water / (πr^2) = 3(18.666...) / (π(2 cm)^2) ≈ 2.366 cm
Therefore, the height of the water in the cone is approximately 2.366 cm.
PART A
Write the systems of equations represented by the graph.
PART B
What is the solution?
The solution of the system of equations y = -(4/3)x + 2 and y = x - 5 is (3, -2)
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
The first line passes through (0, 2) and (3, -2), hence:
y - 2 = [(-2-2)/(3-0)](x - 0)
y = -(4/3)x + 2
The first line has an equation of y = -(-4/3)x + 2
The second line passes through (5, 0) and (0, -5), hence:
y - 0 = [(-5-0)/(0-5)](x - 5)
y = x - 5
The second line has an equation of y = x - 5
The solution of the equation is (3, -2)
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Consider the following incomplete deposit slip: Description Amount ($) Cash, including coins 15 00 Check 1 62 44 Check 2 27 83 Check 3 45 75 Subtotal ?? ?? Less cash received ?? ?? Total 62 23 How much cash did the person who filled out this deposit slip receive? a. $381.23 b. $451.02 c. $88.79 d. $436.02 Please select the best answer from the choices provided A B C D
The person who filled out the deposit slip received $88.79 in cash. The correct answer is option c.
To find out how much cash the person who filled out the deposit slip received, we need to fill in the missing amounts on the slip.
First, we need to calculate the subtotal by adding the amounts of the checks and cash:
Subtotal = 15.00 + 62.44 + 27.83 + 45.75
Subtotal = 151.02
Next, we need to determine the amount of cash received by subtracting the subtotal from the total:
Total = Subtotal - cash received
62.23 = 151.02 - cash received
To solve for cash received, we can subtract the total from the subtotal:
Cash received = Subtotal - total
Cash received = 151.02 - 62.23
Cash received = 88.79
Therefore, correct option is C.
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What is the perimeter of the triangle?
3m³ +4m²-5m
2m³ +3m² + 4m
5m³-5m²-5
Answer:
10m³ + 2m²- 1m - 5
Step-by-step explanation:
Add like terms together. I am busy I wish I could explain but I gtg. Please ask if you have any other questions!
and
Have a great day!!
A diagonal of a cube measures 150 cm. The diagonal of a face measures 10 cm.
What is the length, in centimeters, of an edge of the cube? Round the answer to the nearest tenth.
centimeters
Let s be the length of an edge of the cube. Then, by the Pythagorean theorem, we have:
s^2 + s^2 = (10 cm)^2
2s^2 = 100 cm^2
s^2 = 50 cm^2
s = sqrt(50) cm
Also, by the Pythagorean theorem, we have:
s^2 + s^2 + s^2 = (150 cm)^2
3s^2 = 22500 cm^2
s^2 = 7500 cm^2
s = sqrt(7500) cm
Therefore, the length of an edge of the cube is:
s ≈ 86.6 cm (rounded to the nearest tenth)
Answer:
Let's use the Pythagorean theorem to solve this problem.
If the diagonal of a face measures 10 cm, then we know that the edge of the cube is given by:
edge = 10/√2
Simplifying this expression, we get:
edge = 5√2
Now, we can use the diagonal of the cube to find the length of an edge. If the diagonal of the cube measures 150 cm, then we have:
edge√3 = 150
Substituting the expression we found for the edge, we get:
5√6 = 150/√3
Simplifying this expression, we get:
edge ≈ 19.2 cm
Rounding to the nearest tenth, we get the final answer:
The length of an edge of the cube is approximately 19.2 centimeters.
mark me brilliant
Kiran drove from Tortula to Cactus, a distance of 250 mi. She increased her speed by 10 mi/h for
the 360-mi trip from Cactus to Dry Junction. If the total trip took 11 h, what was her speed from Tortula to Cactus?
Answer:
Let x be Kiran's speed from Tortula to Cactus.
The time it took her to drive from Tortula to Cactus is 250/x.
The time it took her to drive from Cactus to Dry Junction is 360/(x+10).
The total time of the trip is 250/x + 360/(x+10) = 11.
Multiplying both sides of the equation by x(x+10), we get:
250x + 360 = 11x^2 + 110x
11x^2 - 140x + 360 = 0
Factoring the equation, we get:
(x-12)(x-30) = 0
Therefore, x = 12 or x = 30.
Since x is the speed, it must be a positive number. Therefore, x = 12.
Kiran's speed from Tortula to Cactus was 12 mph.
Step-by-step explanation:
to prove that δdef ≅ δdgf by sas, what additional information is needed? ∠def ≅ ∠dgf ∠dfe ≅ ∠dfg de ≅ dg dg ≅ gf
Two corresponding sides of the triangles are congruent by congruence postulate, meaning DE ≅ AB and EF ≅ BC. The included angle between the congruent sides is also congruent, meaning ∠DEF ≅ ∠ABC.
To prove that ΔDEF and ΔABC are congruent by SAS (Side-Angle-Side), we need to have the following additional information:
1. The length of two sides of each triangle must be equal.
2. The included angle between these two sides must be equal.
3. The length of the third side of each triangle must be equal.
If we have this information, we can use the SAS congruence postulate to prove that ΔDEF and ΔABC are congruent.
To prove that ΔDEF and ΔABC are congruent by the Side-Angle-Side (SAS) Congruence Postulate, you'll need the following additional information:
Once you have this information, you can apply the SAS Congruence Postulate to conclude that ΔDEF and ΔABC are congruent.
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What is the sum of the lengths of the two diagonals of a 5 by 12 triangle
The sum of lengths of the two diagonals in a rectangle whose dimensions are 5 by 12 units is 26 units.
As, The length of the diagonal of rectangle
d = √l² + w²
d = √12² + 5²
d= √144+ 25
d= 13 unit
Thus, the sum of lengths of the two diagonals in this rectangle is
= 13 + 13
= 26 unit
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PLS HELP
What would the Volume and Surface area of a pentagonal pyramid be if the Apothem is 3 square root 2 and the height is 3
The volume and surface area of a pentagonal pyramid are 31.18 cubic units and 134.13 square units respectively.
How to determine the valueThe formula for the area of a regular pentagon with side length s and apothem is expressed as;
A = (5/2) × s × a
Also, the volume of a pyramid is given by the formula:
V= (1/3) × A × h
Given that;
A is the base area of the pyramid h is the height of the pyramid.Using the Pythagorean theorem, we have;
l = √(h^2 + a^2)
Substitute the values
l = √(3^2 + (3√2)^2)
expand the bracket
l = √(9 + 18)
Add the values
l = √27
l = 3√3
The base of the pyramid is a regular pentagon, so we can find its area using the formula:
A = (5/2) × s × a
Substitute the value of the apothem
a = s / (2√(5-2√5))
3√2 = s / (2√(5-2√5))
divide the values
s = 6√(5-2√5)
Therefore, the base area of the pyramid is:
A = (5/2) × s × a
Substitute the values
A = (5/2) × 6√(5-2√5) × 3√2
Multiply the values
A = 31.18 square units
To determine the value surface area of the pyramid, we need to find the area of the triangular faces.
Using the formula for area of a triangle given as;
A = (1/2) × b × h
Substitute the values, we get:
A = (1/2) × A × l
A = (1/2) × 31.18 × 3√3
A = 26.83 square units
The surface area of the pentagonal pyramid is:
Surface area = 5A
Surface area = 134.13 square units
To find the volume of the pyramid, we can use the formula:
V = (1/3) × A × h
V = (1/3) × 31.18 × 3
V = 31.18 cubic units
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an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 160 engines and the mean pressure was 7.1 pounds/square inch (psi). assume the population standard deviation is 1.0 . if the valve was designed to produce a mean pressure of 6.9 psi, is there sufficient evidence at the 0.01 level that the valve performs above the specifications? step 2 of 6 : find the value of the test statistic. round your answer to two decimal places
The test statistic for this hypothesis test is 2.00, which is less than the critical value of ±2.617 at the 0.01 level of significance.
To conduct a hypothesis test, we need to calculate a test statistic. In this case, we will use a t-test since the population standard deviation is unknown and we have a sample size of 160 engines. The test statistic measures how many standard deviations the sample mean is from the hypothesized population mean under the null hypothesis.
The formula for the t-test statistic is:
t = (x - μ) / (s / √n)
where x is the sample mean (7.1 psi), μ is the hypothesized population mean under the null hypothesis (6.9 psi), s is the sample standard deviation (1.0 psi), and n is the sample size (160 engines).
So, plugging in the values we have:
t = (7.1 - 6.9) / (1.0 / √160)
t = 2.00
This means that the sample mean is 2.00 standard deviations away from the hypothesized population mean under the null hypothesis.
To determine if this test statistic is statistically significant at the 0.01 level, we need to compare it to a critical value from the t-distribution with 159 degrees of freedom (df = n-1). The critical value for a two-tailed test at the 0.01 level of significance is ±2.617.
Since our test statistic (2.00) is less than the critical value (-2.617), we fail to reject the null hypothesis. This means that we do not have sufficient evidence to conclude that the valve performs above specifications at the 0.01 level of significance.
Therefore, we fail to reject the null hypothesis and cannot conclude that the valve performs above specifications.
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please help I am so stuck it keeps saying it is wrong.
The options showing the front elevation of each prism are given as follows:
a) Prism X: Option B.
b) Prism Y: Option E.
What is the front elevation of a prism?The front elevation of a prism is defined as how we can see the prism looking at the front of it's shape.
Looking at the front of prism X, on the orange section, we see it as a right triangle pointing to the right, hence it is represented by option B.
Looking at the front of prism Y, on the orange section, we see it as an isosceles triangle, which is represented by option E.
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please help me solve
Answer:
23.6 years
Step-by-step explanation:
Given that a population is described by y = 82700e^(-0.00036t), you want to know the value of t when the population is 82000.
SolutionSubstitute the given number for y and solve for t:
82000 = 82700e^(-0.00036t)
820/827 = e^-0.00036t . . . . . . . . . . divide by 82700, simplify
ln(820/827) = -0.00036t . . . . . . . . take natural logs
t = ln(820/827)/-0.00036 ≈ 23.6 . . . . . divide by the coefficient of t
It will take approximately 23.6 years.
__
Additional comment
The problem statement tells us y₀ is 82700, so we used that in the given equation.
It's a bit odd that the population is reported in thousands of thousands. It could be described as 82.7 million, declinding to 82 million.
Question 2
Suppose that you want to design a set of four congruent square pyramids whose combined volume is the same as the volume of a single
rectangular pyramid. What values of land h for the four square pyramids and what values of I, w, and h for the rectangular pyramid will produce
Identical volumes? There is more than one correct answer.
Answer: the answer is 10
Phone numbers consist of a three-digit area code followed by seven digits. If the area code must have a 0 or1 for the second digit, and neither the area code nor the seven-digit number can start with 0 or 1, how many different phone numbers are possible? How did you come up with your answer?
a.
8 times 10 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 = 6,400,000,000
b.
8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 = 1,280,000,000
c.
8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 = 128,000,000
d.
8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 times 10 = 12,800,000,000
Please select the best answer from the choices provided
Answer:
The correct answer is (b) 1,280,000,000.
Step-by-step explanation:
Explanation:
For the area code, we have two choices for the second digit (0 or 1), and 8 choices for each of the first and third digits (since they cannot be 0 or 1). Therefore, there are 8 x 2 x 8 = 128 possible area codes.
For the seven-digit number, we have 8 choices for the first digit (since it cannot be 0 or 1), and 10 choices for each of the remaining 6 digits. Therefore, there are 8 x 10 x 10 x 10 x 10 x 10 x 10 = 8 x 10^6 possible seven-digit numbers.
To get the total number of possible phone numbers, we multiply the number of possible area codes by the number of possible seven-digit numbers:
128 x 8 x 10^6 = 1,280,000,000
Therefore, there are 1,280,000,000 possible phone numbers that satisfy the given conditions.
Alan worked 32 hours last week and earned $315. 20 this week he worked 35 hours and earned $344. 75 the relatiomship between the number of hours alan worked and the money he earns is proportional what is the constant of proportionality for this situtation?
A constant of proportionality of $9.85 per hour.
To discover the consistent of proportionality between the quantity of hours Alan labored and the cash he earned, we will use the formulation:
Constant of proportionality = (money earned) / (quantity of hours worked)
We are given that Alan earned $315.20 for working 32 hours, so we can substitute these values into the formulation:
Consistent of proportionality = $315.20 / 32
Simplifying this expression, we get:
Constant of proportionality = $9.85/hour
In addition, we're for the reason that Alan earned $344.75 for working 35 hours, so we are able to use these values to check whether the connection between the range of hours labored and the cash earned is proportional:
$344.75 / 35 = $9.85/hour (approximately)
Since the ratio is about the identical for each instances,
Therefore, we can conculde that the relationship among the number of hours Alan worked and the cash he earned is proportional, with a constant of proportionality of $9.85 per hour.
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