The solution of the quadratic equation is obtained as -1 ± √7. Option A and B.
What is a quadratic equation?We know that a quadratic equation has to do with the kind of equation that have the general form; y = ax^2 + bx + c. This implies that we are going to have the highest power of the variable to be x.
As such, we have the equation that have been written as; x^2 + 2x – 6 = 0. We are to find the roots of the quadratic equation which are the values for x. When we solve the quadratic equation we have;
-1 ± √7
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1) The table below shows a future estimated population and the number of hospitals in
2009 in the United States and the three states - Texas, California, and Florida. Use
the data to answer each question.
Estimated Future Population and Number of Hospitals by State (2009)
Number of
hospitals in
2009
5,008
428
343
210
United States
Texas
California
Florida
Projected
Population
316 million
26.4 million
38.3 million
19.5 million
Patients Admitted in
2009 (in Thousands)
35,527
2,621
3,433
2,453
Assume Florida has the same number of hospitals per million people as Texas.
Estimate the number of hospitals in Florida. Is this estimate close to the actual
number of hospitals in Florida in 2009?
If Florida had the same number of hospitals per million people as Texas, it would have 558 hospitals in 2009. This is slightly higher than the actual number of hospitals in Florida in 2009 (343).
What is proportional reasoning?Proportional reasoning is a mathematical process used to compare the ratios of two or more similar quantities.
This question uses the theory of proportional reasoning.
In this case, we are comparing the ratio of the number of hospitals per million people in Texas to the ratio of the number of hospitals per million people in Florida.
By comparing these two ratios, we can estimate the number of hospitals in Florida given the same ratio as Texas.
1. Calculate the number of hospitals per million people in Texas: 428 hospitals / 26.4 million people = 16.2 hospitals per million people.
2. Calculate the number of hospitals per million people in Florida: 343 hospitals / 19.5 million people = 17.6 hospitals per million people.
3. Multiply the number of people in Florida (19.5 million) by the number of hospitals per million people in Texas (16.2): 19.5 million people x 16.2 hospitals per million people = 315.3 hospitals.
4. Round the result to the nearest whole number: 315.3 hospitals = 315 hospitals.
5. Compare the estimated number of hospitals in Florida (315) to the actual number of hospitals in Florida in 2009 (343).
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a population numbers 11,000 organisms initially and grows by 16.3% each year. suppose represents population, and the number of years of growth. an exponential model for the population can be written in the form where
The exponential model for the population can be written as P(t) = 11,000(1.163)t, where P(t) represents the population size in t years and 1.163 is the growth rate.
We can calculate the population size at any time t by multiplying the initial population size (11,000) by the growth rate (1.163) raised to the power of t. For example, after 10 years the population size would be P(10) = 11,000(1.163)10 = 22,906.7. We can also use the model to predict the population size in future years. For example, the population size in 20 years will be P(20) = 11,000(1.163)20 = 40,803.7. For example, if the population is measured after 10 years, the equation would be P(10) = 11,000(1.163)^10. Solving for P(10) yields a population of 21,945 organisms. Thus, the population has grown by 16.3% per year over the 10-year period and has increased by 10,945 organisms.
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Which value for x would make the ratios equivalent?
3/8 =x/32
A x=4
B x=6
C x=8
D x=12
Answer:
D. x = 12
Step-by-step explanation:
8 x 4 = 32
3 x 4 = 12
A construction company charges $15 per for hour for debris removal, plus a one time fee for the use of a trash dumpster. The total fee for 9 hours of service is $195. Write an equation of a line, in slope intercept form, to find the total fee y for any number of hours x
An equation of a line, in slope-intercept form, for the total fee y for any number of hours x is y = 15x + 60.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
x represents the number of hours.y represents the total fee.m represents the slope of a line.c represents the y-intercept of a line.Since the total fee that is being charged by this construction company is denoted by y and it charges $15 per hour for debris removal, plus a one time fee, an equation that models this situation is given by;
y = 15x + c
Next, we would determine the y-intercept as follows;
195 = 15(9) + c
y-intercept, c = 195 − 135
y-intercept, c = 60.
Therefore, the required equation is y = 15x + 60.
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a charge nurse is reviewing orthostatic hypotension with a group of newly licensed nurses. what make the statements should the charge nurse make?'
A charge nurse is reviewing orthostatic hypotension with a group of newly licensed nurses. the statements should the charge nurse make is c) a decrease of 20 mm of Hg in the diastolic pressure with a position change indicates orthostatic hypotension.
About Orthostatic hypotensionOrthostatic hypotension — also called postural hypotension — is a form of low blood pressure that happens when standing after sitting or lying down. Orthostatic hypotension can cause dizziness or lightheadedness and possibly fainting.
Orthostatic hypotension can be mild. Episodes might be brief. However, long-lasting orthostatic hypotension can signal more-serious problems. It's important to see a health care provider if you frequently feel lightheaded when standing up.
Occasional orthostatic hypotension is usually caused by something obvious, such as dehydration or lengthy bed rest. The condition is easily treated. Chronic orthostatic hypotension is usually a sign of another health problem, so treatment depends on the cause.
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Write an algebraic equation for the following.
Three times the sum of a number and seven is two less than five times the number.
Answer:
We dissect each statement from the problem above to fully understand it.
the sum of a number and 7 is (x + 7)
3 times this is 3(x + 7)
is means the equal sign here 3(x + 7) =
Two less then 5 times the number is 5x - 2.
Therefore, the answer is B, 3(x + 7) = 5x - 2
I need to calculate the percentages of how much in increased/decreased
The percent change for each year is given as follows:
1845: 0%.1846: 12.30%.1847: -4.38%.1848: 10.69%.How to obtain the percent change?The percent change is obtained applying the proportions in the context of this problem.
The equation that defines the percent change is the change in the year divided by the initial population during the year.
Hence the percent change for each year during the period is given as follows:
1846: 15/122 = 12.30%.1847: -6/137 = -4.38%.1848: 14/131 = 10.69%.More can be learned about proportions at https://brainly.com/question/24372153
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Question 2
An ecosystem has algae as the main producer.
What most likely is the location of this ecosystem?
airair
desertdesert
mountainsmountains
seasea
Question 2
Facts:
Meerkats are small carnivores. They live in Africa. Meerkats live in extended families called gangs.
Situation:
A gang of eight meerkats lives in a desert.
Based on the given facts, what ecological level describes this gang?
Responses
biomebiome
communitycommunity
habitathabitat
population
Question 3
Kaylee is studying abiotic factors in a sea ecosystem.
What factors could she include in her study?
Select all that apply.
Responses
pressurepressure
temperaturetemperature
number of fishnumber of fish
growth of algae
Question 4,
What is a common limiting factor for populations living in desert biomes?
Responses
lack of top predatorslack of top predators
lack of waterlack of water
presence of sunlightpresence of sunlight
lack of soil nutrients
question 5.
What is carrying capacity?
Responses
the highest population of a species an environment can support over a long periodthe highest population of a species an environment can support over a long period
the highest biodiversity an environment can support for a short whilethe highest biodiversity an environment can support for a short while
the highest population of a species an environment can support for a short whilethe highest population of a species an environment can support for a short while
the highest biodiversity an environment can support over a long periodthe highest biodiversity an environment can support over a long period
a) The ecosystem is in the sea. Option D
b) The ecological level is population. option D
c) The factors in the study are pressure, and temperature
d) The common limiting factor in biomes is lack of water
e) The carrying capacity is the highest population an environment can support over a long period. Option A
What is the ecosystem?We have to note that the ecosystem has to do with the part of the habitat that is composed of the living and the non living parts. The non living parts of the ecosystem are called the abiotic factors while the living parts of the ecosystem are called the biotic factors.
In the ecosystem, we have the producers, the consumers and the decomposers and these are called the trophic or the feeding levels in the system.
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What are the last three digits of 5’201?
Answer: The last three digits are 201.
Step-by-step explanation: Hope this helps
A common aspect ratio for computer screens today is width : height = 16 : 9. The advertised size of a screen is given by the measure of its diagonal. Measure the width, height, and diagonal of at least three screens (computers, tablets, phones) in your home. Are they similar? How do you know? Are any of your screens congruent? If so, what postulates prove it? List your measurements and describe your findings carefully.
Please follow these guidelines for your discussion posts:
Write at least 150–300 words.
A common aspect ratio for computer screens is 16:9, which means that for every 16 units of width, there are 9 units of height. This aspect ratio is also used on many televisions and mobile devices.
How to explain the ratio?If a screen has an aspect ratio of 16:9, the width and height will be similar on all screens with this aspect ratio. However, the diagonal measurement will vary depending on the size of the screen.
Congruent screens are two or more screens that have the same dimensions. Two screens are congruent if and only if corresponding sides are equal and corresponding angles are equal. This can be proven using the postulates of congruence, such as the SSS (Side-Side-Side) postulate or the SAS (Side-Angle-Side) postulate.
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p1 - connecting computing a certain computer game is played between a human player and a computer-controlled player. every time the computer-controlled player has a turn, the game runs slowly because the computer evaluates all potential moves and selects the best one. which of the following best describes the possibility of improving the running speed of the game?
The best way to improve the running speed of the game is to use an algorithm which can quickly evaluate potential moves and select the best one.
For example, alpha-beta pruning is an algorithm which is used for game tree search. It prunes the search tree and eliminates the branches which are not likely to contain the optimal solution. Alpha-beta pruning uses the following formula to evaluate positions:
Max(α, Min(β, v))
Where α is the best value that the maximizing player can guarantee at the current branch of the tree, β is the best value that the minimizing player can guarantee at the current branch of the tree and v is the value of the current position. The evaluation of the position helps to quickly identify the best move. This reduces the time taken to evaluate the potential moves and thus improves the running speed of the game.
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A rectangle is divided into equal parts. Which statement is true? The lines dividing the shape must be drawn from left to right. All the equal parts must be square in shape. The lines dividing the shape must be drawn from top to bottom. All the equal parts must have the same area.
Answer:
The statement that is true is:
All the equal parts must have the same area.
This is true because when a rectangle is divided into equal parts, it means that the area of each part is the same. The lines dividing the shape can be drawn in any direction (top to bottom, left to right, diagonal, etc.) and the shape of the parts can also be different( rectangles, squares or any shape).
what is the solution to the system?
A: (-3,6)
B:(6,3)
C: (3,6)
D: (-6,3)
pls help
The solution to the system of equations include the following: B. (6, 3).
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.
By critically observing the graph of the lines representing the system of equations, we can reasonably infer and logically deduce that the correct solution set lies in Quadrant I and it is denoted by the point of intersection of both the x-axis and y-axis, which is given by the ordered pair (6, 3).
In conclusion, the ordered pair (6, 3) is a solution to the system of equations represented by the given graph.
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Choose the equation for the graph.
a) y = 2|x - 3| +1
b) y = -2|x - 3| +1
c) y = 2x - 3| − 1
d) y = -2|x + 3| − 1
e) y = 2|x + 3| +1
Answer:
not e
Step-by-step explanation:
in 2015, the national highway traffic safety administration reported the number of pedestrian fatalities in san francisco county was 24 and that the number in los angeles county was 209. can we conclude that pedestrians are safer in san francisco than in los angeles? why or why not? if you answered no, what additional data would allow us to make a conclusion about which county is safer for pedestrians?
No, we cannot conclude that pedestrians are safer in San Francisco than in Los Angeles based on the data provided. The number of pedestrian fatalities in a given county is only one factor in determining the safety of pedestrians in that county.
Other factors, such as the number of pedestrians in each county, the number of vehicles in each county, the number of traffic laws in each county, and the number of traffic enforcement officers in each county, all play a role in determining the safety of pedestrians in a given county.
We would also need to consider other factors such as the number of pedestrian-friendly infrastructure in each county, the number of pedestrian-friendly policies in each county, and the number of pedestrian-friendly initiatives in each county. With this additional data, we would be able to make a more informed conclusion about which county is safer for pedestrians.
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Elena has $10.00 to spend. Which list of items shows what Elena could buy?
The list of items that shows what Elena could buy is the list for which the sum of all prices is at most 10.
How to obtain the list of items?The maximum amount that Elena can spend is given as follows:
$10.
Hence, for each list, the sum is calculated for the prices of all the items, giving the total price.
The list with a sum of at most $10 is the list that shows what Elena can buy.
Missing InformationThe problem is incomplete, hence the general procedure needed to solve it is presented.
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8. Find a when 120 ÷ a = 12.
a =
Answer:
10
Step-by-step explanation:
120/a = 12
120=12a
120/12 = a
a = 10
Answer:
1,440
Step-by-step explanation:
120 x 12 = 1,440
120 / 1,440 = 12
Randomly selecting 20 cards out of 52 card deck, the probability of each outcome will be basically the same whether it is done with or without replacement 1
TRUE OR FALSE?
Answer:
False
Step-by-step explanation:
If the card is removed after it is picked, the number of cards in the deck decreases. For example, if you pick the first card remove it. The cards available decreases to 51, so the probability becomes 1/51 for the next draw. This is dependant probability.
In a company, 85% of the workers are women. If 315 people work for the company who aren't women, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
There are 2100 workers in the company
How many workers are there in all?
Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Since 85% of the workers are women, we can say:
The percentage of worker that aren't women = 100% - 85% = 15%
Let N represent the number of all workers. If 315 people work for the company who aren't women. We can say:
15% of N = 315
15/100 × N = 315
0.15N = 315
N = 315/0.15
N = 2100 workers
Method 2:
We can write:
N - 0.85N = 315
0.15N = 315
N = 315/0.15
N = 2100 workers
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root24 solve the initial value problem with . to solve this, we should use the substitution help (formulas) help (formulas) enter derivatives using prime notation (e.g., you would enter for ). after the substitution from the previous part, we obtain the following linear differential equation in . help (equations) the solution to the original initial value problem is described by the following equation in . help (equations)
The solution equation gives us y = 5x/2 - 2, so when x = 0, we get y = -2, which matches the initial condition.
The solution to the initial value problem can be obtained by using the substitution method. We first substitute the given function into the differential equation, which gives us the linear differential equation in y:
y' + 2y = 5x
We can then solve this linear differential equation by integrating both sides and applying the initial condition. This gives us the solution in y:
y = 5x/2 + C
where C is an arbitrary constant. To calculate the value of C, we plug in the initial condition y(0) = 2 into the equation. This gives us C = -2, so the solution to the initial value problem is given by:
y = 5x/2 - 2.
To illustrate this, let's consider the initial condition y(0) = 2. Plugging this into the solution equation gives us y = 5x/2 - 2, so when x = 0, we get y = -2, which matches the initial condition.
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are births equally likely across the days of the week? a random sample of 150 births give the following sample distribution:
Expected values are = 150/7 .Ci-square distribution is Day of the week observed count Expected Chi-square = O E (O -E )2/E
testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis. Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Statistical hypothesis: A statement about the nature of a population. It is often stated in terms of a population parameter.
Null hypothesis: A statistical hypothesis that is to be tested. : The alternative to the null hypothesis.
Test statistic: A function of the sample data.
The critical value for the chi-square statistic is determined by the level of significance (typically . 05) and the degrees of freedom. The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) where r is the number of rows and c is the number of columns.
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Expected values are = 150/7 .Ci-square distribution is Day of the week observed count Expected Chi-square = O E (O -E )2/E
testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis. Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Statistical hypothesis: A statement about the nature of a population. It is often stated in terms of a population parameter.
Null hypothesis: A statistical hypothesis that is to be tested. : The alternative to the null hypothesis.
Test statistic: A function of the sample data.
The critical value for the chi-square statistic is determined by the level of significance (typically . 05) and the degrees of freedom. The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) where r is the number of rows and c is the number of columns.
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A waffle recipie uses 6 eggs to make 16 waffles. Jenny has 9 eggs. If she alters the recipe, what is the greatest amount of waffles she can make?
Answer:
24 waffles
Step-by-step explanation:
16÷6=2.66 so she can make that many waffles per egg
9x2.66= 23.94 which would round up to 24 waffles
the 10% condition when constructing a confidence interval for a population proportion, we check that the sample size is less than 10% of the population size.
The 10% condition when constructing a confidence interval for a population proportion states that the sample size should be less than 10% of the population size.
This is expressed mathematically as follows:
n/N < 0.10
Where n is the sample size and N is the population size. For example, if the population size is 500, then we must ensure that the sample size is less than 50 (500 x 0.10 = 50). This is because if the sample size is larger than 10% of the population size, then the confidence interval will not be reliable. In other words, the results of the confidence interval may be inaccurate and biased.
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Alyson deposits $500 in the bank for 12 years. The bank offers her a 4%
simple interest rate. How much money will be in her account at the end of
the 12 years? (Remember to round your answer to the nearest cent if
necessary.)
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &12 \end{cases} \\\\\\ A = 500[1+(0.04)(12)] \implies A = 740[/tex]
You are standing 143 feet away from the base of a building and your clinometer measures 17° when it’s looking at the top of the building. (This angle is the one between the ground and the top of the building). Please calculate the height of the building.
Answer:
The height of the building is 43.7 feet.
Step-by-step explanation:
Attached is a sketch of the problem.
We can use SOH CAH TOA to find our answer.
In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse. S is for the SIN function. C is for the COS function. T is for the TAN function.
We can calculate the height of the building by using the TAN function.
So we can say the tangent of angle x is the opposite side divided by the adjacent side.
[tex]tan(x)=\frac{O}{A}[/tex]
Lets solve for [tex]O[/tex].
Multiply both sides by [tex]A[/tex].
[tex]tan(x)*A=\frac{O}{A}*A[/tex]
Simplify the right side by cancelling the common factor of [tex]A[/tex].
[tex]tan(x)*A=O\\O=A*tan(x)[/tex]
Now lets evaluate the height of the building.
In this example we are given
[tex]x=17\\A=143[/tex]
[tex]O=143*tan(17)[/tex]
[tex]O=43.7195[/tex]
1. Mrs. Johnson plans to make a batch of trail mix, and she would like to add extra raisins. If she doubles the amount of raisins in the recipe, how many cups of raisins will she need?
a cylindrical sample of saturated sandy clay has a diameter of 2.8 inches and a height of 6 inches. the total mass of the sample alone is 1,192.0 g. representative portions of the sample have been used to determine the water content w (%). the mass of these portions was 182 g before oven-drying and 151.7 g after oven-drying.
The water content of the cylindrical sample of saturated sandy clay is 2.54%.
To determine the water content of the sample, we have to calculate the mass of water present in the sample before oven-drying, next divide that value by the total mass of the sample.
Firstly, we have to calculate the mass of water present in the sample before oven-drying. We already know that the mass of the sample before oven-drying is 182g and the mass after oven-drying is 151.7g.
So the mass of water present in the sample is:
mass of water = mass before oven-drying - mass after oven-drying
mass of water = 182g - 151.7g = 30.3g
Next, divide the mass of water by the total mass of the sample and multiply by 100 to get the water content as a percentage:
water content (w%) = (mass of water / total mass of sample) * 100
water content (w%) = (30.3g / 1192.0g) * 100 = 2.54%
So, the water content of the cylindrical sample of saturated sandy clay is 2.54%.
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(50 Points and BRAINLYEST)
The prism has a square base. That base is inscribed in the circular base of the cylinder. Draw an image of the base of the composite shape.
Answer:
Step-by-step explanation:
If a laborer weighing 895N and carrying bricks weighing 575N to scaffold up a ladder 3.1 m above the ground how much work has he done?
The amount of work that the laborer has done, given the weight of the bricks and the laborer is 4, 577 Joules .
How to find the work done ?To calculate the amount of work done by the laborer, we can use the formula:
work = force x distance x
where:
force is the force applied,
distance is the distance moved,
The force applied by the laborer is the combined weight of the laborer and the bricks:
= 895N + 575N
= 1, 470N
Therefore, the work done by the laborer is:
Work = 1, 470N x 3.1m
= 4577 Nm or Joules (J)
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select the two values of x that are roots of this equation x^2 + 3x - 6=0
x = -2 and x = -3 are the two values of x that are roots of the equation x^2 + 3x - 6 = 0
What is the root of the equation?
A root of an equation is a value of the variable that makes the equation true. An equation is a statement that asserts the equality of two expressions. A root of an equation is also known as a solution or a zero of the equation.
The two values of x that are roots of the equation x^2 + 3x - 6 = 0 are x = -2 and x = -3.
To find the roots of the equation, we can use the factoring method, which consists of factoring the polynomial on the left side of the equation.
x^2 + 3x - 6 = 0
(x-2)(x+3) = 0
So, x - 2 = 0, x = 2 and x + 3 = 0, x = -3
Alternatively, we can use the Quadratic formula, which states that for any quadratic equation in the form ax^2 + bx + c = 0, the roots are given by:
x = (-b ± √(b^2 - 4ac))/ 2a
So, by plugging in the values of a, b and c we have:
x = (-3 ± √(3^2 - 41-6))/ 2*1 = (-3 ± √(9+24))/2 = (-3 ± √33)/2 = (-3 ± √33)/2 = -2, -3
Hence, x = -2 and x = -3 are the two values of x that are roots of the equation x^2 + 3x - 6 = 0
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