The height above the ground in meters of a model rocket on a particular launch can be modeled by the equation h = -4.9[tex]t^{2}[/tex] + 102t + 100, where t is the time in seconds after its engine burns out 100 m above the ground. The rocket reach a height of 600 m.
To determine whether the rocket will reach a height of 600 m, we need to solve the equation
-4.9[tex]t^{2}[/tex] + 102t + 100 = 600
We can simplify this equation by moving all the terms to one side
-4.9[tex]t^{2}[/tex] + 102t - 500 = 0
Now we can use the quadratic formula to solve for t
t = (-b ± [tex]\sqrt{(b^{2}-4ac) }[/tex]) / 2a
In this case, a = -4.9, b = 102, and c = -500. By putting these values into the formula gives
t = (-102 ±[tex]\sqrt{102^{2}-4(-4.9)(-500) }[/tex])) / 2(-4.9)
Simplifying the expression under the square root
t = (-102 ± [tex]\sqrt{10404}[/tex]) / -9.8
t = (-102 ± 102) / -9.8
t = 0 or 10.408
Since we are interested in the time after the engine burns out (100 m above the ground), we can discard the solution t = 0. Therefore, the rocket will reach a height of 600 m at t = 10.408 seconds.
To use the discriminant to explain our answer, we can look at the expression under the square root in the quadratic formula
[tex]b^{2}[/tex] - 4ac
If this expression is positive, there are two real solutions to the quadratic equation, which means the rocket will reach a height of 600 m at some point in its flight. If the expression is zero, there is one real solution, which means the rocket just reaches a height of 600 m at its highest point and then falls back down. If the expression is negative, there are no real solutions, which means the rocket never reaches a height of 600 m.
In this case, the expression [tex]b^{2}[/tex] - 4ac is equal to 10404, which is positive.
Hence, there are two real solutions to the equation, and the rocket will reach a height of 600 m.
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i need help please-
question: if you borrow $1500 for 5 years at an annual interest rate of 5%, what is the total amount of money you'll have to pay back?
Answer:
Step-by-step explanation:
first, you have to find the interest.
formula: Principal × Rate × Time ÷ 100
Principal - $1500
Rate - 5%
Time - 5 yrs
I=PRT÷100
= $1500 × 5% × 5yrs ÷ 100
= 1500 × 5 × 5÷ 100
= 37500 ÷ 100
= $ 375
That's the interest.
Amount = Principal + Interest
= $ 1500 + $375
=$ 1875
That's the total amount you'll have to pay back.
Of the three variations of linked lists (circular, with header and trailer nodes, and doubly linked), which would be most appropriate for each of the following applications and why in detail?
Do NOT use others, please use your own words.
1. You want to search a list for a key and return the keys of the two elements that come before it and the keys of the two elements that come after it.
2. A text file contains integer elements, one per line, sorted from smallest to larges. You must read the values from the file and create a sorted linked list containing the values.
3. A list is short and frequently becomes empty. You want a list that is optimal for inserting an element into the empty list and deleting the last element from the list.
Three different applications of linked list are mentioned here.
1. The most appropriate variation of a linked list for searching a list for a key and returning the keys of the two elements that come before it and the keys of the two elements that come after it would be a doubly linked list. A doubly linked list allows for bi-directional traversal, which means that it is easy to move forward and backward through the list. This makes it easy to locate the element with the key you are searching for and also retrieve the keys of the two elements that come before and after it.
2. The most appropriate variation of a linked list for creating a sorted list from a text file containing integer elements, one per line, sorted from smallest to largest would be a sorted linked list. A sorted linked list is a type of singly linked list that maintains its elements in a sorted order. As each element is added to the list, it is placed in its correct position to maintain the sorted order of the list.
3. The most appropriate variation of a linked list for a list that is short and frequently becomes empty, and is optimal for inserting an element into the empty list and deleting the last element from the list would be a circular linked list with header and trailer nodes. A circular linked list with header and trailer nodes is a type of singly linked list that has a special header node at the beginning of the list and a special trailer node at the end of the list. This type of linked list is optimal for inserting an element into an empty list because it is easy to update the header and trailer nodes to point to the new element. It is also easy to delete the last element from the list by updating the trailer node to point to the second-to-last element. Additionally, since this type of linked list is circular, it is easy to traverse the list repeatedly without having to worry about reaching the end of the list.
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Three different applications of linked list are mentioned here.
1. The most appropriate variation of a linked list for searching a list for a key and returning the keys of the two elements that come before it and the keys of the two elements that come after it would be a doubly linked list. A doubly linked list allows for bi-directional traversal, which means that it is easy to move forward and backward through the list. This makes it easy to locate the element with the key you are searching for and also retrieve the keys of the two elements that come before and after it.
2. The most appropriate variation of a linked list for creating a sorted list from a text file containing integer elements, one per line, sorted from smallest to largest would be a sorted linked list. A sorted linked list is a type of singly linked list that maintains its elements in a sorted order. As each element is added to the list, it is placed in its correct position to maintain the sorted order of the list.
3. The most appropriate variation of a linked list for a list that is short and frequently becomes empty, and is optimal for inserting an element into the empty list and deleting the last element from the list would be a circular linked list with header and trailer nodes. A circular linked list with header and trailer nodes is a type of singly linked list that has a special header node at the beginning of the list and a special trailer node at the end of the list. This type of linked list is optimal for inserting an element into an empty list because it is easy to update the header and trailer nodes to point to the new element. It is also easy to delete the last element from the list by updating the trailer node to point to the second-to-last element. Additionally, since this type of linked list is circular, it is easy to traverse the list repeatedly without having to worry about reaching the end of the list.
On January 1, 2019, Hackman Corporation issued $1 million face value 12% bonds dated January 1, 2019, for $1,023,000. The bonds pay interest semiannually on June 30 and December 31 and are due December 31, 2023. Hackman uses the straight-line amortization method
Hackman Corporation will record interest expense of $58822 on each interest payment date for the life of the bonds.
Hackman Corporation issued$ 1 million face value 12 bonds dated January 1, 2019, for$. The bonds pay interest semiannually on June 30 and December 31 and are due December 31, 2023. Hackman uses the straight- line amortization system to regard for the bond decoration. The periodic decoration amortization is$ 2,300, and the semiannual decoration amortization is$ 1,150.
Annual effective interest rate = (Face value of the bonds × Coupon rate) / Issue price of the bonds
Annual effective interest rate = ($1,000,000 × 12%) / $1,023,000 = 11.76%
Effective interest rate for the period = (1 + (11.76% / 2))^(6 / 12) - 1 = 5.75%
Interest expense = $1,023,000 × 5.75% = $58,822.50
Therefore, the amount of interest expense that Hackman Corporation should recognize on June 30, 2019, is approximately $58,822.50.
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IS UVW =XYZ ? IF SO NAME THE POSULATE THAT APPLIES
Answer:
option c
might not be congruent
Step-by-step explanation:
as the triangles that have three pairs of congruent angles i.e. AAA might not have the sides of the same length.
so, AAA is not a congruence rule or congruent postulate
HELP! Consider the quadratic equation x2+7x+8=0 . Which of the following is the correct form after substituting a, b, and c into the Quadratic Formula? Responses x=−7 ±(7)2−(1)(8)√2(1) x=−7 ±(7)2−(1)(8)√2(1) x=−7 ±(7)2−4(1)(8)√2(1) x=−7 ±(7)2−4(1)(8)√2(1) x=7 ±(7)2−4(1)(8)√2(1) x=7 ±(7)2−4(1)(8)√2(1) x=(7)2−4(1)(8)√2(1) 100 points!!
The option that is the correct form after substituting a, b, and c into the quadratic formula is; x = (-7 ± √(7² - 4·(1)·(8)))/((2)·(1))
What is the quadratic formula?The quadratic formula which can be used to solve the quadratic equation of the form f(x) = a·x² + b·x + c = 0
The quadratic formula is; x = (-b ± √(b² - 4·a·c))/(2·a)
The quadratic equation x² + 7·x + 8 = 0, evaluated using the quadratic formula can be expressed as follows;
The values of a, b, and c obtained from the specified quadratic equation are; a = 1, b = 7, and c = 8, therefore;
x = (-7 ± √(7² - 4×1×8))/(2×1)
The correct option is therefore; x = (-7 ± √(7² - 4×1×8))/(2×1)
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the average residential electrical power use (in hundreds of watts) per hour is given in the following table.
The average residential electrical power use refers to the amount of electrical energy consumed by households. It is typically measured in hundreds of watts per hour. By examining the provided table, you can identify the specific values for average power consumption in a residential setting.
According to the given table, the average residential electrical power use is measured in kilowatt-hours (kWh) per month, not hundreds of watts per hour. However, to convert it to the requested unit, we can divide the monthly average by the number of hours in a month (720 hours) and then multiply by 100 to get the average residential electrical power use in hundreds of watts per hour.
So, for example, if the monthly average is 600 kWh, the hourly average would be (600 kWh / 720 hours) x 100 = 83.33hundreds of watts per hour.
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Martin incorrectly said that the slope of this graph is 3 select the correct reasoning to find the slope
If line passes through points (0,3) and (-3,0), then the slope calculated by Martin as "3" is incorrect because the correct slope is 1.
The "Slope" of a line is defined as measure of its steepness or inclination, and it describes how much the line rises or falls over a given distance in the horizontal direction.
To find the slope of a line passing through two points (x₁, y₁) and (x₂, y₂), we use the slope formula ⇒ slope = (y₂ - y₁) / (x₂ - x₁),
In this case, the two points are (0, 3) and (-3, 0). Substituting the coordinates in formula, we get:
⇒ slope = (0 - 3)/(-3 - 0),
⇒ Slope = -3/-3,
⇒ Slope = 1,
Therefore, the correct slope of the line passing through the points (0, 3) and (-3, 0) is 1, not 3 as Martin incorrectly said.
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The given question is incomplete, the complete question is
The line in the graph passes through the points (0,3) and (-3,0), Martin incorrectly said that the slope of this line is "3" . What is the correct slope?
1.0- ! 0.8- 8 8 Chance.of.Admit 0.6- 8 : 8 0.4- 290 310 320 330 340 GRE. Score 300 Confidence Level for Slope and Intercept: Regression Analysis of Chance.of.Admit (Y) explained by GRE.Score (X) Coefficient Table: Estimate Std. Error t value Prl>[t]) Cl Lower Bound (Intercept) -2.44 0.12 -20.68 0.00 -2.67 GRE.Score 0.01 0.00 26.84 0.00 0.01 R-squared: 0.6441835 sigma: 0.08517377 CI Upper Bound -2.20 0.01 8. Is the linearity condition met? Yes, the residual plot is normal. Yes, there is no megaphone pattern found in the scatterplot Yes, the scatterplot shows a linear pattern in the data Yes, there is no megaphone pattern in the residual plot. 9. Select "Proceed to Regression Analysis". Refer to the table. If we perform at test for the slope of the regression line, what is the test statistic and p-value for this procedure? t = -20.68, p-value = -2.67 t = 26.84, p-value = 0.00 t = 26.84, p-value = 0.01 t = -20.68, p-value = 0.00 10. Calculate a 95% confidence interval for the slope on the line. Assuming that a = 0.05, can we use this interval as evidence that there is a linear relationship between GRE score and chance of admission? No. We don't know the alternative hypothesis, so we cannot make a conclusion on the relationship between GRE score and chance of admission. Yes. Because our alternative hypothesis is one-sided and O is not found in the confidence interval, we reject the null hypothesis and conclude that there is a linear relationship between GRE score and chance of admission. No. Confidence intervals cannot be used to make conclusions for hypothesis tests. Yes. Because our alternative hypothesis is two-sided and O is not found in the confidence interval, we reject the null hypothesis and conclude that there is a linear relationship between GRE score and chance of admission.
The test statistic and p-value for the slope of the regression line are t = 26 and p-value = 0.00.
Based on the given information, the analysis is focused on determining whether there is a linear relationship between GRE score and the chance of admission. The pattern observed in the scatterplot shows a linear pattern in the data, indicating a potential linear relationship between the two variables.
To test this hypothesis, a regression analysis was performed, which yielded a coefficient table with estimates for the intercept and slope of the regression line. The p-value for the slope test was found to be 0.00, which suggests strong evidence for a significant linear relationship between GRE score and the chance of admission.
Furthermore, a 95% confidence interval for the slope was calculated, which did not include the null value of zero. This means that we can reject the null hypothesis and conclude that there is a linear relationship between the GRE score and the chance of admission.
In summary, based on the analysis and statistical tests performed, there is evidence to support a linear relationship between the GRE score and the chance of admission.
The test statistic and p-value for the slope of the regression line are t = 26. ,an p-value = 0.00.
A 95% confidence interval for the slope on the line is (0.01, 0.01). Since 0 is not found in the confidence interval and our alternative hypothesis is two-sided, we reject the null hypothesis and conclude that there is a linear relationship between GRE score and the chance of admission.
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the uniform probability density function for ta business executive, transferred from chicago to atlanta, needs to sell her house in chicago quickly. the executive's employer has offered to buy the house for 212,000, but the offer expires at the end of the week. the executive does not currently have a better offer but can afford to leave the house on the market for another month. from conversations with her realtor, the executive believes the price she will get by leaving the house on the market for another month is uniformly distributed between $200,000 and 230,000. (a) if she leaves the house on the market for another month, what is the mathematical expression for the probability density function of the sales price? let x
The mathematical expression for the probability density function of the sales price is PDF(x) = 1/30,000 for 200,000 <= x <= 230,000.
Based on your question, we want to find the mathematical expression for the probability density function (PDF) of the sales price, given that the price is uniformly distributed between $200,000 and $230,000.
The function f(x) represents this probability density function, where the height of the function is 1/3000 (the width of the range of possible prices is 30,000, so the area under the function must equal 1), and it is 0 outside of that range.
For a uniform distribution, the probability density function is constant across the given range. To find the value of this constant, we can use the formula:
PDF(x) = 1 / (b - a)
where a is the lower limit of the range ($200,000), b is the upper limit of the range ($230,000), and x represents the sales price.
This is because the executive believes that the price she will get by leaving the house on the market for another month is uniformly distributed between $200,000 and $230,000, which means that the probability is equal.
Plugging in the values, we get:
PDF(x) = 1 / (230,000 - 200,000)
PDF(x) = 1 / 30,000
So the mathematical expression for the probability density function of the sales price, if she leaves the house on the market for another month, is:
PDF(x) = 1/30,000 for 200,000 <= x <= 230,000
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helppp fast plssss!!
Explain how u got answer
A. -2.5
B. 40
C. 2.5
D. -40
identify an appropriate transformed model for these data. fit this model to the data and conduct the usual tests of model adequacy.
Based on the given information, I assume that you have a dataset and you are required to identify an appropriate transformed model for it. There are different types of transformations that can be applied to data such as logarithmic, square root, power, etc. The choice of the transformation depends on the nature of the data and the research question being addressed.
To identify an appropriate transformed model, you can start by examining the distribution of the response variable. If the distribution is skewed or has heavy tails, a transformation may be necessary to normalize the data. One way to assess the distribution is by creating a histogram or a density plot of the response variable.
Once you have identified an appropriate transformation, you can fit the transformed model to the data using regression analysis. The regression model will include the transformed response variable and one or more predictor variables.
After fitting the model, it is important to conduct the usual tests of model adequacy to ensure that the model is appropriate for the data. These tests include examining the residuals for normality, checking for homoscedasticity (i.e., equal variances), and testing for outliers and influential observations.
In summary, identifying an appropriate transformed model involves examining the distribution of the response variable and choosing a transformation that normalizes the data. Once the model is fitted, the usual tests of model adequacy should be conducted to ensure that the model is appropriate for the data.
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A man finds a purse with an unknow number of ducats in it. After he spends 1/4, 1/5, and 1/6 of the amount, 9 ducats remain. It is required to find out how much money was in the purse.
The total amount of money in the purse was approximately 23 ducats. A man finds a purse with an unknown number of ducats in it. After he spends 1/4, 1/5, and 1/6 of the amount, 9 ducats remain. To find the initial amount in the purse, let's represent it as "x".
He spent (1/4)x, (1/5)x, and (1/6)x. The sum of these fractions plus the remaining 9 ducats equals the total amount:
(1/4)x + (1/5)x + (1/6)x + 9 = x
To solve this equation, first find a common denominator for the fractions, which is 60. Rewrite the equation with the common denominator:
(15/60)x + (12/60)x + (10/60)x + 9 = x
Combine the fractions:
(37/60)x + 9 = x
Now, isolate x on one side of the equation:
9 = (23/60)x
To find x, divide both sides by (23/60):
x = 9 / (23/60)
x = 9 * (60/23)
x = 540/23
Since x represents the number of ducats, it should be a whole number. So, we round it to the nearest whole number:
x ≈ 23
Therefore, there were approximately 23 ducats in the purse initially.
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Find the height of the right prism.
$S=480\text{ in.}^2$S=480 in.2
A right triangular prism. Height is labeled h. The two shorter sides on the triangluar faces are labled 8 and 15 inches.
The height is inches.
The height of the right triangular prism whose surface are is 480 square inches is equal to 9 inches.
Total surface area of the right prism = 480 square inches
Surface area of a right triangular prism is,
S = 2B + Ph
where S is the surface area,
B is the area of the triangular base,
P is the perimeter of the base,
and h is the height of the prism.
First, area of the triangular base.
Use the formula for the area of a triangle,
B = (1/2)bh
where b is the base of the triangle
and h is the height of the triangle.
⇒ B = (1/2) × 8 × 15
⇒ B = 60 in²
Since the base is a right triangle,
Use the Pythagorean theorem to find the length of the third side,
c² = 8² + 15²
⇒ c² = 64 + 225
⇒ c² = 289
⇒ c = 17
Perimeter of the base is,
⇒ P = 8 + 15 + 17
⇒ P = 40 inches
Surface area of right prism = 480
⇒ 2B +Ph = 480
⇒ 2×60 + 40h = 480
⇒40h = 480 - 120
⇒ h = 360 /40
⇒ h = 9 inches.
Therefore, the height of the right prism is equal to 9inches.
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Find the length of the missing side of the right triangle. Round to three decimal places, if necessary. 1) a -10, b 24 Solve the problem. If necessary, round to the nearest tenth.
Answer: We can use the Pythagorean theorem to solve this problem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have:
a = -10
b = 24
c = ?
Using the Pythagorean theorem, we can solve for c:
c^2 = a^2 + b^2
c^2 = (-10)^2 + 24^2
c^2 = 676
c = sqrt(676)
c = 26
Therefore, the length of the missing side of the right triangle is 26 units.
The length of the missing side of the right triangle is 26. To find the length of the missing side of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
The formula is:
[tex]c² = a² + b²[/tex]
In this problem, a = 10 and b = 24. To find the length of the missing side (the hypotenuse, c), we can plug these values into the formula:
c² = 10² + 24²
c² = 100 + 576
c² = 676
Now, we take the square root of both sides to find the length of the missing side:
c = √676
c = 26
So, the length of the missing side (the hypotenuse) of the right triangle is 26.
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What is 1/4+4/7?????
Answer:
23/28
Step-by-step explanation:
1/4 + 4/7
make them have same denominator of 28
7/28 + 16/28
=23/28
Answer:
23/28
Step-by-step explanation:
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construct your understanding questions (to do in class) 1. help max devise an equation for each of the following in terms of x and y. a. the area of their campsite : A =
b. The length of the yellow caution tape : L = 120 ft.
Answer: L = 2 * (x + y) = 120
We frame the questions using the provided information:
1a. To help Max devise an equation for the area (A) of their campsite in terms of x and y, first recall that the area of a rectangle is given by the formula A = length * width.
Let x represent the length of the campsite and y represent the width. Now, write an equation for the area (A) in terms of x and y.
Answer: A = x * y
1b. To help Max devise an equation for the length of the yellow caution tape (L) in terms of x and y, first consider that the length of the tape should be equal to the perimeter of the campsite. The perimeter of a rectangle can be found using the formula P = 2 * (length + width). In this case, the length of the yellow caution tape (L) is given as 120 ft.
Let x represent the length of the campsite and y represent the width.
Write an equation for the length of the yellow caution tape (L) in terms of x and y.
Answer: L = 2 * (x + y) = 120
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Help with what u can please!
The building is 51 feet tall
The value of x is 1.5
How to find the length of the buildingThe length of the building is solved by comparing the building's height by John's height as this forms similar triangles
The comparison is done using the proportions as below
John's shadow / John's height = building's shadow / building's height
6 / 4.5 = 68 / building's height
cross multiplying
building's height x 6 = 4.5 * 68
building's height = 4.5 x 68 / 6
building's height = 51 feet
Solving for x
Using proportions
15 / 10 = 23x / 20x - 8
cross multiplying
(20x - 8) * 15 = 22x * 10
300x - 120 = 220x
300x - 220x = 120
80x = 120
x = 1.5
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true/false. because of the periodic properties of shm, the mathematical equations that describe this motion involve sine and cosine functions. for example, if the block is released at a distance a from its equilibrium position, its displacement x varies with time t according to the equation
True. The mathematical equations that describe simple harmonic motion (SHM) involve sine and cosine functions. For example, if the block is released at a distance from its equilibrium position, its displacement x varies with time t according to the equation x = a cos(ωt), where ω is the angular frequency of the motion.
True. Due to the periodic properties of Simple Harmonic Motion (SHM), the mathematical equations that describe this motion involve sine and cosine functions. If the block is released at a distance A from its equilibrium position, its displacement x varies with time t according to the equation:
x(t) = A * cos(ωt + φ)
where A is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle. Both sine and cosine functions are used to describe the displacement, velocity, and acceleration of an object in SHM because of their periodic nature.
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Blaise proposes his own pay schedule to his boss. Blaise proposes that he is paid just $115 the first day, $125 the second day, 135 the third day and so on. Blaise will make how much money at the end but of the 2 weeks on his own pay schedule?
Blaise will make $1575 at the end of weeks on his personal pay schedule.
Step 1: determine the number of days in weeks
They're five working days in a per week, so then there are a total of 10 working days in a weeks.
Step 2: Calculate Blaise's profits for every day
using the given pay schedule, Blaise's profits for the primary 10 days would be:
Day 1: $115
Day 2: $125
Day 3: $135
Day 4: $145
Day 5: $155
Day 6: $165
Day 7: $175
Day 8: $185
Day 9: $195
Day 10: $205
Step 3: Now we will addition of Blaise's profits
adding up the profits from the first 10 days, we get:
$115 + $125 + $135 + $145 + $155 + $165 + $175 + $185 + $195 + $205 = $1575
Therefore On his own pay plan, Blaise will earn $1575 at the end of each week.
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g a simple undirected graph has 10 edges. 2 of the vertices are of degree 4, and the rest of the vertices are of degree 3. how many vertices are in this graph?
Therefore, there are 4 vertices in this graph.
Let V be the number of vertices in the graph. The sum of the degrees of all vertices in an undirected graph is twice the number of edges, so in this case, the sum of degrees is 2 * 10 = 20.
We know that two vertices have degree 4, so the degrees of the remaining vertices must add up to 20 - 2 * 4 = 12.
If there are v vertices of degree 3, then the total degree contributed by those vertices is 3v, so we have:
3v + 2 * 4 = 20
3v = 12
v = 4
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13. A town has a population of 7,500. The mayor asked two different employees to conduct a
survey to determine whether residents of the town are in favor of the construction of a new
baseball stadium.
●
Denise surveyed 150 randomly selected residents at a recent baseball game.
Tamira surveyed 150 randomly selected residents living in different sections of town.
The table below shows the results of the two surveys.
New Baseball Stadium
In Favor
125
30
Denise's Survey
Tamira's Survey
Opposed
20
105
No Opinion
5.
15
Which statement identifies the more reliable survey and provides a valid conclusion based on
that survey?
A. Denise's survey is more reliable than Tamira's survey, and approximately 6,250 residents of
the town would likely be in favor of the construction of a new baseball stadium.
B. Denise's survey is more reliable than Tamira's survey, and approximately 1,250 residents of
the town would likely be opposed to the construction of a new baseball stadium.
C. Tamira's survey is more reliable than Denise's survey, and approximately 1,500 residents of
the town would likely be in favor of the construction of a new baseball stadium.
D. Tamira's survey is more reliable than Denise's survey, and approximately 6,000 residents of
the town would likely be opposed to the construction of a new baseball stadium.
C. The more reliable survey would be: Tamira's survey is more reliable than Denise's survey, and approximately 1,500 residents of the town would likely be in favor of the construction of a new baseball stadium.
How to get the reliable surveyTаmirа's survеy is mоre reliаble bеcаusе shе survеyed rеsidеnts frоm diffеrеnt sectiоns оf thе town, whiсh is а mоre representаtive sаmple оf thе entire populаtiоn. Denise's survеy, оn thе othеr hаnd, wаs cоnducted аt а bаsebаll gаme, whiсh might hаve introduced а biаs towаrds people who аre mоre likеly to bе in fаvor оf thе new stаdium.
Bаsed оn Tаmirа's survеy, 30 out оf 150 rеsidеnts (20%) аre in fаvor оf thе cоnstructiоn.
If we extrаpolаte this percentаge to thе entire populаtiоn оf 7,500 rеsidеnts, we cаn estimаte thаt аpproximаtely 1,500 rеsidеnts (20% оf 7,500) would likеly bе in fаvor оf thе new bаsebаll stаdium.
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solving two-step Inequalities
9x-3>6
Answer:
Step-by-step explanation: x= 1/3
Answer: x>1
Step-by-step explanation:
9x-3>6
move the 3 over so: 9x>6+3, 9x>9
divide both sides by 9: (9x)/9>9/9, x>1
and bam, that's your answer x>1
Which of the following equations is graphed below?
A. x-3y=6
B. x+3y=6
C. x-3y=-6
D. x+3y=-6
The linear equation on the graph is the one in option D:
3y +x = -6
Which is the equation in the given graph?On the given graph, we can see a linear equation that passes through the the y-axis at the value y = -2
Then the line is of the form:
y = ax - 2
Where a is a negative value.
Also, notice that each 3 units moved in x, there is a decrease of 1 unit in the y-value, then the slope is -1/3, the line is:
y = (-1/3)*x - 2
We can rewrite that as:
3y = -x - 6
3y +x = -6
Then we can see that the correct option is D.
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Help solving please, I need the full process please
Answer:
g = 13/4 or 3.25
Step-by-step explanation:
Step 1: First we can distribute the 2 on the right-hand side (rhs) of the equation:
[tex]\frac{2*5-2*g}{3}\\\\ \frac{10-2g}{3}[/tex]
Step 2: We can also rewrite this fraction since we have two inverse operations, namely multiplication and division:
[tex]\frac{10}{3}+\frac{-2g}{3}\\ \\ \frac{10}{3}-\frac{2g}{3}\\ \\ \frac{10}{3}-\frac{2}{3}g[/tex]
Step 3: We can convert both sides into whole numbers by multiplying both sides by the least common denominator (lcd), which is essentially the lowest multiple shared by the denominators 6 and 3.
The lowest multiple shared by the two numbers is 6 as 6*1 = 6 and 3*2 = 6
Thus, we multiply both sides by 6:
left-hand side (lhs)
[tex]\frac{7}{6}*\frac{6}{1}\\ \\ \frac{42}{6}\\ \\ 7[/tex]
right-hand side (rhs)
[tex](\frac{10}{3}-\frac{2}{3}g)*\frac{6}{1}\\ \\ (\frac{10}{3}*\frac{6}{1})+(-\frac{2}{3}g*\frac{6}{1})\\ \\ \frac{60}{3}-\frac{12}{3}g\\ \\ 20-4g[/tex]
Since we have simplified both sides, we can now solve for g:
[tex](7=20-4g)-20\\(-13=-4g)/-4\\13/4=g\\3.25=g[/tex]
You can keep the mixed number or use the decimal answer as both are the same answer in different forms.
For such a problem, it can be helpful to check by plugging in 3.25 for g in the equation
[tex]\frac{7}{6}=\frac{2(5-3.25)}{3}\\ \\ \frac{7}{6}=\frac{2(1.75)}{3}\\ \\ \frac{7}{6}=\frac{3.5}{3}\\\\ 1.167=1.167[/tex]
Quadrilateral RSTU is reflected across the line x = 1. Determine the coordinates of R’, S’, T’, and U’.
Quadrilateral R S T U plotted in the first quadrant of a coordinate plane. The vertices are at R (5, 2), S (4, 4), T (5, 6), and U (6, 4).
R’: (
,
)
S’: (
,
)
T’: (
,
)
U’: (
,
)
If quadrilateral RSTU is reflected across the line x = 1, then the coordinates of R’, S’, T’, and U’ are (-3, 2), (-2, 4), (-3, 6) and (-4, 4) respectively.
To reflect a point across the line x = 1, we can use the formula (2a - x, y), where (a, b) is the original point and x = 1 is the line of reflection.
Using this formula, we can find the coordinates of the reflected points as follows:
The x-coordinate of the line of reflection is 1, so the new x-coordinate for each point will be 2(1) - x = 2 - x.
The y-coordinate for each point will remain the same.
Therefore, the reflected coordinates are:
R' = (2(1) - 5, 2) = (-3, 2)
S' = (2(1) - 4, 4) = (-2, 4)
T' = (2(1) - 5, 6) = (-3, 6)
U' = (2(1) - 6, 4) = (-4, 4)
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graph a right tringle with two points forming a hipothanose using the sides find the distance between the two points to the (nearest tenth if nessacery) (7,3) (5,-4)
The solution is, the distance between the two points to the (nearest tenth if nessacery) (7,3) (5,-4) is √53.
Here, we have,
We have information on the hypotenuse, now we must calculate the sides.
we have find the distance between the two points to the (nearest tenth if nessacery) (7,3) (5,-4)
we know that,
Formula: distance= √(x_2-x_1)²+(y_2-y_1)²
Using the x-coordinates of the points of the hypotenuse we obtain
7- (5) = 2
Using the y-coordinates of the points of the hypotenuse we obtain
3 - (-4) = 7
Now lets graph
Distance
d = √2² + 7²
=√53
The distance would be √53.
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how long will it take joe to turn the sheet metal into 5 pieces?
The solution is : 140 cm of the original piece is left after Joe cuts three pieces.
Given that,
Given the piece of string
3.5m
As we know that
3.5m = 350 cm
so the length of a piece of string = 350 cm
As joe cuts three pieces from it, and each 70 cm long.
so the total length of three pieces which were
cut by joe = 70cm + 70cm + 70cm = 210 cm
So, subtracting the total length of the three pieces that were cut from the total length of the string:
350 cm - 210 cm = 140 cm
Therefore, 140 cm of the original piece is left after Joe cuts three pieces from it.
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complete question:
A piece of string is 3-5 m long. Joe cuts three pieces from it,
each 70 cm long. How much of the original piece is left?
The mean age for the population of inmates in state correctional facilities is 31.84. Some researchers believe that this may not be the same for some groups of inmates. In a sample of Native American inmates (n=112), researchers find a mean age of 33.46 with a standard deviation of 9.62. Create a 95% confidence interval around the sample mean value. Interpret your confidence interval.
The confidence interval around the sample mean value is (31.66, 35.26). This means that we can be 95% confident that the true mean age of all Native American inmates in state correctional facilities falls within this range.
Based on the information provided, the mean age of Native American inmates in state correctional facilities is 33.46, which is higher than the mean age of the entire inmate population (31.84). However, because this is only a sample of Native American inmates, we need to calculate a confidence interval to estimate the true mean age of all Native American inmates in state correctional facilities.
To create a 95% confidence interval, we will use the formula:
Confidence Interval = Sample Mean +/- (Critical Value x Standard Error)
The critical value for a 95% confidence interval with 111 degrees of freedom (n-1) is 1.98. The standard error can be calculated using the formula:
Standard Error = Standard Deviation / Square Root of Sample Size
Plugging in the values, we get:
Standard Error = 9.62 / Square Root of 112 = 0.91
Confidence Interval = 33.46 +/- (1.98 x 0.91) = 33.46 +/- 1.80
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1. Explain why the product of powers rule works (ex: x^4 * x^3 = x^7)
2. Explain why we multiply exponents when raising a power to a power (ex: (x^2)^3
The Explanation for product of powers rule works and multiply exponents when raising a power to a power is shown below.
1. We know,
When the terms with the same base are multiplied, the powers are added.
So, 7² x 7³
Here the base is same (7) and multiplication applied here then the powers get added.
So, [tex]7^{2+3[/tex]
= [tex]7^5[/tex]
2. Now, According to the power to the power rule, when a base is raised to a higher power, the two powers are multiplied while the base stays the same.
So, (7²)³
= [tex]7^{2 .3}[/tex]
= [tex]7^6[/tex]
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HELPPP DUE IN A HOUR!!!!
The value of x in the similar triangle is 4.5 units.
How to find similar triangle?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Using the proportional relationship of the similar triangles,
3 / x = 9 / 9 + 4.5
3 / x = 9 / 13.5
cross multiply
13.5 × 3 = 9x
40.5 = 9x
divide both sides by 9
x = 40.5 / 9
x = 4.5
Therefore,
x = 4.5 units.
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