A quadratic function f(x)f(x) is hidden from view. You must find the maximum value of the function f(x)f(x). Choose the form of the quadratic function f(x)f(x) that you would like to see in order to answer the question most efficiently.
Formula f(x):
f(x) = a* (X-Xv)² + Yv
a = principal coefficient
(x,y)=peak point
To get knots quickly, squares must be written in canonical form. That means f(x) must have the form above.
Understanding Quadratic FunctionsThe quadratic function is a polynomial function that has variables/variables with the highest power being 2 (two).
In general, quadratic functions have the following general form:
f(x) = ax²+ bx + c, a ≠ 0
with f(x) = y which is the dependent variable, x is the independent variable, while a, and b are the coefficients and c is a constant.
This is of course different from what is called a quadratic equation, in which a quadratic equation has a variable with the highest power being two and is in the form of an equation.
The general form of the quadratic equation is as follows:
ax² + bx + c = 0, a ≠ 0
where x is the independent variable, a and b are the coefficients, and c is a constant.
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consider the following porgram segment where i j and k are integer variables
For the program segment where i , j and k are integer variables , then the print statement is executed 576 times .
The program is : for i : 1 to 12 do
for j [tex]:[/tex] 5 to 10 do
for k : = 15 down to 8 do
print (i - j ) × k
This is because the program has three nested loops, each of which run a specific number of times.
The innermost loop is executed 15 - 8 + 1 = 8 times, for each value of k.
The middle loop is executed 10 - 5 + 1 = 6 times, for each value of j.
And the outermost loop is executed 12 times, for each value of i.
the total number of times print statement is executed is 8×6×12 = 576.
Therefore , The print statement will be 576 times .
The given question is incomplete , the complete question is
Consider the following program segment where i , j and k are integer variables ,
for i : 1 to 12 do
for j : 5 to 10 do
for k : = 15 down to 8 do
print (i - j ) × k
How many times the print statement is executed ?
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A nontoxic furniture polish can be made by combining vinegar and olive oil. The amount of oil should be three times the amount of vinegar. How much of each ingredient is needed in order to make 46 oz of furniture polish?
Here, the 11.5 oz of vinegar ingredient is needed in order to make 46 oz of furniture polish .
So in this problem it says a furniture polish can be made containing or combining vinegar and olive oil and the amount of oil should be three times the amount of vinegar. So I'm gonna make vinegar X. And oil three X. How much of each ingredient is needed in order to make 46 oz of furniture Polish. So I'm gonna go ahead and add these together. Okay. Yes. Which means that four x. equals 46 and divide by four So X. is 11.5. So that means that for vinegar we need 11.5 oz. And then I'm going to multiply that by three to get 34.5 oz for the oil. And if you can find those together just to check you get 46. So this would be the amount of both ingredients.
To make 46 oz of furniture polish, you will need 3 times as much olive oil as vinegar.
So, you need 46 oz / 4 = 11.5 oz of vinegar.
And 11.5 oz * 3 = 34.5 oz of olive oil.
Therefore,the 11.5 oz of vinegar ingredient is needed in order to make 46 oz of furniture polish .
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a) Input this table of values into Desmos to write a quadratic regression equation that best fits the
data set. Hint: use yz-axi + bx2 + c
b) Use your regression equation and estimate the y value if x is 23. Show your work.
х
15
17
19
20
у
423
398
308
255
297
365
401
29
The equation would become y = -3.99(23)2 + 37.2(23) - 102 which can then be simplified to y = -2213.71 + 755.6 and further simplified to y = -1458.11. This rearrangement and simplification can be completed to find the estimated y value when x is 23, which is y = 227.8.
A) y = -3.99x2 + 37.2x - 102
B) y = -3.99(23)2 + 37.2(23) - 102 = 227.8
y = -3.99(23)2 + 37.2(23) - 102
y = -3.99(529) + 857.6 - 102
y = -2213.71 + 755.6
y = -1458.11
y = 227.8
Using the given data set of x and y values, a quadratic regression equation can be written in Desmos as y = -3.99x2 + 37.2x - 102. To estimate the y value if x is 23, the equation can be rearranged and all values plugged in. The equation would become y = -3.99(23)2 + 37.2(23) - 102 which can then be simplified to y = -2213.71 + 755.6 and further simplified to y = -1458.11. This rearrangement and simplification can be completed to find the estimated y value when x is 23, which is y = 227.8.
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The table shows the circumference of a tree in centimeters, y, at x years. Choose the function that represents the data. Y = y = 2. 7xy = 2. 7xy = 2. 7x2.
The function that best represents the data in the table is y = 2.7x. This is because the circumference of the tree is directly proportional to the number of years it has been alive, which can be represented by a linear equation.
The circumference of a circle is the total length of the edge of the circle. It is calculated using the formula C = 2πr, where r is the radius of the circle. This formula is based on the fact that the circumference of a circle is equal to the length of the perimeter of the circle, which is equal to the product of the circumference and the radius. The circumference is an important measure used in many areas of mathematics and geometry, including area and volume calculations.
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88 63at a certain stage of a criminal investigation, the inspector in charge is 60% convinced of the guilt of a certain suspect. suppose, however, that a new piece of evidence which shows that the criminal has a certain characteristic (such as left-handedness, baldness, or brown hair) is uncovered. if 20% of the population possesses this characteristic, how certain of the guilt of the suspect should the inspector now be if it turns out that the suspect has the characteristic? you may suppose that the probability of the suspect having the characteristic if they are, in fact, innocent is equal to 0.2, the proportion of the population possessing the characteristic.
The probability that the inspector in-charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.
P(C) = P(C∣G)P(G) + P(C∣Gc)P(Gc) = (1)(0.6)+(0.2)(0.4) = 0.68
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
This is then used to update the inspector's belief in the suspect's guilt posterior to discovering that the suspect does have that characteristic.
P(G∣C) = (P(G)P(C∣G))/P(C)
=1(0.6)/0.68
=0.882
So the probability that the inspector in-charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.
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The probability that the inspector in charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.
P(C) = P(C∣G)P(G) + P(C∣Gc)P(Gc) = (1)(0.6)+(0.2)(0.4) = 0.68
Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
This is then used to update the inspector's belief in the suspect's guilt posterior to discovering that the suspect does have that characteristic.
P(G∣C) = (P(G)P(C∣G))/P(C)
=1(0.6)/0.68
=0.882
So the probability that the inspector in charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.
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would this be an enumerative or an analytic study? explain your reasoning.
This study is enumerative since there is a small, identifiable population of things to sample from. This investigation is analytical since there is a limitless population of items from which to sample.
The administrator may select stratified random sample or basic random sampling to solve the CSU problem.
To determine the average distance between hometown and campuses using simple random sampling, all students across the 23 CSU campuses are taken into account.
This approach is flexible, and the statistical analysis would be straightforward. In the stratified random sampling, each campus is treated as a single cluster. A random sample is taken from each campus, and the distance between home and campus is calculated.
The statistical findings would be more reliable and instructive using this strategy. This study is unmistakably enumerative. Here, the administrator is looking into the typical travel time between home and university.
By moving the students from one campus to another, he can utilize this outcome as the basis for taking the necessary action to reduce the distance.
Simply said, the administrator can use the data to create an actionable item.
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The complete question is:
The California State University (CSU) system consists of 23 campuses, from San Diego State in the south to Humboldt State near the Oregon border. A CSU administrator wishes to make an inference about the average distance between the hometowns of students and their campuses. Describe and discuss several different sampling methods that might be employed. Would this be an enumerative or an analytic study? Explain your reasoning.
The measures of the angles in triangle UVW are shown in the diagram.
What is the value of x ?
The value of x in the triangle UVW is 45°.
What is a Triangle?A polygon which has three sides and three vertices is called as triangle.
The sum of all the angles of the triangle is 180°.
Given:
The measures of the angle of the triangle UVW are 24°, 30° and (3x - 9)°.
The sum of all the angles of the triangle is 180°.
24° + 30° + (3x - 9)° = 180°.
3x - 9 = 180 - 54
3x = 135
x = 45.
Therefore, the value of x is 45°.
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how could the wording of a question or the tone of voice of the interviewer affect a survey
By speaking positively and upbeatly, you show that you are really listening to what the other person is saying. Actively listen, make encouraging sounds, and repeat what your conversation partner has said. That way they know you're listening carefully.
So this will make survey participants feel more comfortable, honest and cooperative in answering survey questions and also in the subsequent survey process
About SurveyThe survey is a quantitative study using the same structured questions for everyone, then all the answers obtained by the researcher are recorded, processed and analyzed. Surveys are also a method of capturing population data for several demographic or economic events by not counting all respondents in a country, but by taking samples (regional examples) as areas that can represent the characteristics of that country. Structured questions are called questionnaires.
The questionnaire contains questions that will be given to respondents to measure variables, the relationship between existing variables, and can be in the form of experiences and opinions from respondents.
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which of the following is an example of an association claim? group of answer choices drinking alcohol increases cellular aging. 41% of people surveyed reported that they were having a good day. viewing a recent conflict as it would look one year in the future led to increased feelings of forgiveness. people who sit within two tables of the bartender have three more alcoholic drinks, on average, than those who sit three tables away.
The example of an association claim is "Drinking alcohol increases cellular aging."
Cellular ageing is the term used to describe the alterations that take place in cells throughout time, which result in a decrease in function and a higher risk of disease.
Numerous things, such as oxidative stress, inflammation, and cellular damage brought on by environmental pollutants, contribute to these alterations.
Cells lose their ability to operate as they become older, which can lead to a variety of age-related illnesses and ailments, such as cancer, cardiovascular disease, and neurodegeneration.
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Solve all by number no trolling or bots please and don’t be rude
1)Amount of food Han's Dog eats everyday = 7/3 = 2 dog food can.
2)He will run 30/7 miles per day which is not equal to 7/30 miles
3) Amount of special cider got by each person = 48/7 ≠ 8 ounces or no person will get 1 full cup of special cider.
What is Fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
Part of a full number and a means of dividing a number into equal pieces are represented by fractions. The denominator is the total number of parts in the whole, while the numerator is the number of equal portions being counted.
number of dog food cans = 7
Number of days to feed = 3
Amount of food Han's Dog eats everyday = 7/3 dog food can.
Raul ha a goal to run 30 miles in 7 days
He will run 30/7 miles per day which is not equal to 7/30 miles
Gus has 48 fluid ounces of special cider
Number of servings Gus neec to make is 7 people
Amount of special cider got by each person = 48/7 ≠ 8 ounces or no person will get 1 full cup of special cider.
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solve the initial value problem. ′=−2,(0)=−10 (express numbers in exact form. use symbolic notation and fractions where needed.) =
The solution to the initial value problem is [tex]y = -10e^{\frac{-x^2}{2}}[/tex]. This mean that for any given x value, the corresponding y value is -10 multiplied by e raised to the power of -x squared divided by 2.
The initial value problem is a differential equation of the form y' = -2 and an initial value of y(0) = -10. This means that the slope of the function we need to find is -2, and the value at x = 0 is -10. To solve this kind of problem, we need to use the general solution for a differential equation of the form y' = k, which is[tex]y = Ce^\frac{kx}{2}[/tex], where C is a constant. To find the value of C, we need to use the initial value, which is y(0) = -10, and substitute it into the general solution to get C = -10. Thus, our solution is [tex]y = -10e^\frac{-x^2}{2}[/tex], which means that for any given value of x, the corresponding value of y is -10 multiplied by e raised to the power of -x squared divided by 2.
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if the fastest car on earth can travel 380 miles in 0.5 hours, how many minutes would it take to travel 257 miles? if the fastest car on earth can travel 380 miles in 0.5 hours, how many minutes would it take to travel 257 miles?
It would take the fastest car on earth approximately 20.27 minutes to travel 257 miles.
We can calculate the time it takes for the fastest car on earth to travel 257 miles by determining its speed and then dividing the distance to be traveled by the speed.
First, let's determine the speed of the car. The car can travel 380 miles in 0.5 hours, so its speed is:
Speed = Distance / Time = 380 miles / 0.5 hours = 760 miles per hour
Next, we need to convert the speed from miles per hour to miles per minute, so we can use it to calculate the time it takes to travel 257 miles. To do this, we divide the speed by 60:
Speed in miles per minute = 760 miles per hour / 60 minutes per hour = 12.67 miles per minute
Finally, we can calculate the time it takes to travel 257 miles by dividing the distance to be traveled by the speed:
Time = Distance / Speed = 257 miles / 12.67 miles per minute = 20.27 minutes
So it would take the fastest car on earth approximately 20.27 minutes to travel 257 miles.
Therefore, It would take the fastest car on earth approximately 20.27 minutes to travel 257 miles.
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It would take the fastest car on earth approximately 20.27 minutes to travel 257 miles.
We can calculate the time it takes for the fastest car on earth to travel 257 miles by determining its speed and then dividing the distance to be traveled by the speed.
First, let's determine the speed of the car. The car can travel 380 miles in 0.5 hours, so its speed is:
Speed = Distance / Time = 380 miles / 0.5 hours = 760 miles per hour
Next, we need to convert the speed from miles per hour to miles per minute, so we can use it to calculate the time it takes to travel 257 miles. To do this, we divide the speed by 60:
Speed in miles per minute = 760 miles per hour / 60 minutes per hour = 12.67 miles per minute
Finally, we can calculate the time it takes to travel 257 miles by dividing the distance to be traveled by the speed:
Time = Distance / Speed = 257 miles / 12.67 miles per minute = 20.27 minutes
So it would take the fastest car on earth approximately 20.27 minutes to travel 257 miles.
Therefore, It would take the fastest car on earth approximately 20.27 minutes to travel 257 miles.
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100 POINTS AND BRAINLIEST!!!!!!
Find the equation of the linear function represented by the table below in slope-intercept form.
(Table below)
x y
1 0
2 5
3 10
4 15
Answer:
e
Step-by-step explanation:
e
Answer:
Step-by-step explanation:
The slope of the line can be found by finding the rise over the run between two points on the line. Using the points (1,0) and (2,5), the slope can be found as follows:
m = (5-0)/(2-1) = 5
Now that we have the slope, we can use the point-slope form of a line to find the equation of the line in slope-intercept form. Using the point (1,0) and the slope (5), we have:
y - 0 = 5(x - 1)
Simplifying and solving for y, we have:
y = 5x - 5
So the equation of the linear function represented by the table is:
y = 5x - 5.
Higher Order Thinking Tori is making muffins. The recipe calls for 25 cups of brown sugar for the muffins and 1 cups of brown sugar for the topping. Tori has 4 cups of brown sugar. Does she have enough brown sugar to make the muffins and the topping? Explain. I need an answer like ASAP
No, Tori does not have enough brown sugar to make both the muffins and the topping.
The muffins require 25 cups of brown sugar, and the topping requires 1 cup of brown sugar, so the total amount of brown sugar required is 25 + 1 = 26 cups.
Since Tori only has 4 cups of brown sugar, she will not be able to make the muffins and the topping. She will have to either adjust the recipe or purchase more brown sugar.
So it is concluded that Tori does not have enough brown sugar to prepare the muffins and the topping.
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if i get 20 dollars every 2 weeks for 3 months how much will i have
Answer:
120
Step-by-step explanation:
3 mons = 12 weeks
$20 every 2 weeks, so average $10 / week
so 12*10 = 120
It is often useful to find the ___ of a polynomial in order to find its roots.
It is often useful to find the constant term of a polynomial in order to find its roots.
Roots of polynomials are the solutions for any given polynomial for which we need to find the value of the unknown variable. If we know the roots, we can evaluate the value of polynomial to zero.
The polynomials are the expression written in the form of:
[tex]$$a_n x^n+a_{n-1} x^{n-1}+\ldots . .+a_1 x+a_0$$[/tex]
The formula for the root of linear polynomial such as ax+b is x=-b / a
The general form of a quadratic polynomial is[tex]$a x^2+b x+c$[/tex] and if we equate this expression to zero, we get a quadratic equation, i.e. [tex]$a x^2+b x+c=0$[/tex]
The roots of quadratic equation, whose degree is two, such[tex]$ a x^2+b x+c=0$[/tex] are evaluated using the formula; [tex]$x=\left[-b \pm \sqrt{ }\left(b^2-4 a c\right)\right] / 2 a$[/tex]The formulas for higher degree polynomials are a bit complicated.
Hence, it is often useful to find the constant term of a polynomial in order to find its roots.
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Which linear inequality is represented by the graph?
ys-x-1
y²x-1
y < 3x - 1
y> 3x - 1
The linear inequality represented by the graph is given as follows:
y ≤ x/2 + 3.
How to obtain the linear inequality?First we consider the slope-intercept definition of a linear function, given as follows:
y = mx + b.
In which:
m is the slope, defining by how much y increases when x increases by one.b is the intercept, representing the value of y when x = 0.From the graph, we have that it crosses the y-intercept at y = 3, hence the intercept b is given as follows:
b = 3.
When x increases by two, y increases by one, hence the slope m is given as follows:
m = 1/2
m = 0.5.
Hence:
y = x/2 + 3.
The inequality is composed by values below the line, with a solid line, hence it is given as follows:
y ≤ x/2 + 3.
Missing InformationThe problem is given by the image presented at the end of the answer.
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Find the interquartile range (IQR) of the data set. 0, 1, 1, 2, 3, 5, 6, 6, 8, 11 iqr
The Interquartile range IQR for the data set is 4.5.
What is the interquartile range(IQR)?
The interquartile range (IQR) is a measure of the dispersion of a set of numerical data. It is defined as the difference between the 75th and the 25th percentiles of the data and is a robust statistic, meaning that it is not greatly affected by outliers. The IQR is used to summarize the spread of a dataset and is often used in combination with box plots to visualize the distribution of the data.
To find the interquartile range (IQR) of a data set, you need to first find the 25th and 75th percentiles (also known as the first and third quartiles, Q1 and Q3, respectively).
The 25th percentile (Q1) is the value below which 25% of the data falls, and the 75th percentile (Q3) is the value below which 75% of the data falls.
Here's the calculation for the IQR of the data set: 0, 1, 1, 2, 3, 5, 6, 6, 8, 11:
Order the data in ascending order:
0, 1, 1, 2, 3, 5, 6, 6, 8, 11
Find the median (Q2), which is the middle value of the data:
3
Find Q1 and Q3:
Q1 = median of the first half of the data = 1.5
Q3 = median of the second half of the data = 6
Finally, calculate the IQR:
IQR = Q3 - Q1 = 6 - 1.5 = 4.5
So, the Interquartile range IQR for the data set is 4.5.
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The line representing the equation part of the constraint 7x1 + 4x2 s 28 goes through the following two points a. (4,0) and (7,0) b. (0, 4) and (7,0) c. (4,0) and (0,7) d. (0, 4) and (0,7) e. none of the above
Point (4,0) and (0,7) (C) were passed through by the line equation of 7x1 + 4x2 = 28.
From the case, we know that:
Line equation: 7x1 + 4x2 = 28
Passed through points?
To answer this question, we can try to find some conditions:
x1 = 0; x2 =?x2 = 0; x1 =?First, we will try to find the valuf f x2 if x1 = 0:
(x1 = 0)
7(0) + 4.x2 = 28
0 + 4.x2 = 28
4.x2 = 28
x2 = 7 --> (0,7)
Next, we try if x2=0, then x1 = ...
(x2 = 0)
7x1 + 4(0) = 28
7x1 = 28
x1 = 4 --> (4,0)
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Choose Yes or No to tell whether the symbol will be reversed when the variable is isolated in each inequality. –4. 5c > 9
Answer:
Step-by-step explanation:
yes
What is 145.65 divided by 21.2?
Answer: 6.87
Step-by-step explanation:
21.2 / 145.65
Move to the decimal to the right 1 time to make 21.2 to 212 and 145.65 to 1456.5.
Then you want to look for a number you can multipl 212 into the 1456.
In this case, 212 times 6 because it equals 1272.
If you multiply 212 times 7, you get 1484 (which is over the number of 1456 { we dont want that}).
Then you continue multiplying the number until you get to 0, or in other words, a remainder. In which I got, 6.870
A random sample of size 17 is taken from a normal population with meanmu. If the sample mean is 85 and the sample standard deviation is 6, then a 95% upper confidence bound formuis87.8588.0687.1982.15
The 95% upper confidence bound for the population mean μ, given a sample size of 17 and a sample mean of 85 with a sample standard deviation of 6, is 87.85.
87.85
The 95% confidence interval for the population mean is given by
CI = Sample mean ± (t-score) * (Standard Error)
where t-score can be obtained from the t-table with degrees of freedom as n-1 and confidence level as 95%.
Therefore, for a sample size of 17, the t-score is 1.711 and the standard error is 6/√17 = 1.5.
So, the 95% upper confidence bound for μ is
87.85 = 85 + (1.711)*(1.5)
The 95% upper confidence bound for the population mean μ, given a sample size of 17 and a sample mean of 85 with a sample standard deviation of 6, is 87.85.
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Nikola Bell was recently hired at a new company, The Bells need to choose between two different health plans for their family's primary insurance: Option 1: the Deluxe Plan or Option 2: the Basic Plan.
The key variables in the Bell’s situation is the location of the nearest fast food restaurant, the cost of each plan, the number of hours that Nikolai works each week and the health of the Bell family. So the option 1, 2, 3 and 4 are the key variables.
A type of insurance called health insurance pays for medical costs incurred as a result of disease. These costs might be connected to hospitalization charges, medication costs, or professional fees.
Health insurance comes in two different categories:
1. Medical Insurance Plans: The most fundamental form of health insurance is a hospitalization or Mediclaim plan. When you are checked into a hospital, they pay for your medical care. By submitting the original bills, the compensation is based on the actual costs incurred at the hospital. Up to a specific threshold, the majority of these policies offer full family coverage.
2. Critical illness insurance policies: These policies provide coverage for a number of life-threatening illnesses. These illnesses may need ongoing care or possibly a change in lifestyle. In contrast to hospitalization plans, the payout is based on the customer's selected Critical Illness coverage rather than actual hospital costs.
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Nikola Bell was recently hired at a new company, The Bells need to choose between two different health plans for their family's primary insurance: Option 1: the Deluxe Plan or Option 2: the Basic Plan.
Identify the key variables in the Bell’s situation. (Select all that apply)
1. The location of the nearest fast food restaurant.
2. The cost of each plan.
3. The number of hours that Nikolai works each week.
4. The health of the Bell family.
5. The benefits paid by each plan.
6. The Bell’s monthly income.
write a situation for algebraic expression 7-s
There are many possible answers for this.
One example is below.
S = the number of stations included when a person canceled orders basic cable, write an expression for the number of stations a person has if he at first ordered 7 basic cable.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
algebraic expression 7-s
We can represent this as = 7 - s
now,
The value that we don't know is the number of
stations included when a person canceled orders basic cable.
So we can represent that as s.
Then, since the person at first ordered 7 premium channels, that means he is adding an 7 basic channels with out s basic channels.
So we can represent this as 7-s.
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need help with this question
The piece-wise function graphed is given as follows:
y = x² + 6, x < 3.y = -x + 6, x >= 3.What is a piecewise function?A piecewise function is a function that has different definitions, based on the input x of the function.
The two definitions for the function in this problem are given as follows:
Left of x = 3.Right of x = 3.To the left of x = 3, the function graphed is the y = x² function shifted up 6 units, hence:
y = x² + 6, x < 3.
To the right of x = 3, the function graphed is a linear function with slope -1 and x-intercept at x = 6, hence:
y = -x + 6, x >= 3.
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Answer:
x^2 + 6 for x<3
-x+6 for x<=3
Step-by-step explanation:
See the attached worksheet.
Not all of the answer options are shown on the worksheet. The equations that satisfy the graph are:
1) x^2 + 6 for x<3 [The point at (3,15) is empty, so it does not include x=3, only x<3.
2) -x+6 for x<=3 [The point at (3,3) is filled, so x<=3]
Two similar figures have a side ratio of 3:4. The area of the larger figure is 100 square units. What is the area of the smaller figure?
Enter fractions as decimals.
The area of the smaller figure is 225/4 or 56.25 square units if the two similar figures have a side ratio of 3:4.
What is ratio?Ratio can be defined as the number that can be used to express one quantity as a fraction of the other ones. The two numbers in a ratio can only be compared when they have the same unit.
Let's suppose the area of the smaller figure is x
Area of larger figure = 100 square units
The ratio of the areas:
= x/100
We also have:
Two similar figures have a side ratio of 3:4
= 3/4
Square it we will get ratio of the area
= 9/16
x/100 = 9/16
x = 900/16 = 225/4 or 56.25 square units
Thus, the area of the smaller figure is 225/4 or 56.25 square units if the two similar figures have a side ratio of 3:4.
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Determine whether the study depicts an observational study or an experiment.
Fifth-grade students are randomly divided into two groups. One group is taught math using traditional techniques. The other is taught math using a reform method. After 1 year, each
group is given an achievement test to compare its proficiency with that of the other group.
The study is an Experiment because the researchers control one variable to determine the effect on the response variable.
What is an experiment ?
A process used to confirm or deny a theory, as well as assess the effectiveness or possibility of something that has never been performed before, is called an experiment. By showing what happens when a particular element is modified, experiments shed light on cause-and-effect relationships.
Since the study randomly divided the fifth-grade students into two groups, one of which received a solution or treatment in the form of instruction using a reform or modern method while the other group did not receive any treatment because it was instructed using traditional methods, the study's rationale for doing so is that. Therefore, this shows an Experiment study.
In an experiment study, there are two different sorts of groups: the experiment group and the control group. The control group often does not receive any care or assistance from the researchers or scientists. In order to assess the response variable, which in this case is the subject or explained variable (teaching using the Reform method), researchers typically change the subject or explained variable. This allows them to draw conclusions that are based on cause and effect relationships.
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i am a 2 digit number that is divisible by 3 and 6 but not 4 and 5. The sum of my digits is and odd number it is not multiple of the difference between the digits is an odd number, what number am i?
Answer: 36
Step-by-step explanation:
The number that meets all the conditions is 36. It is divisible by 3 and 6, but not by 4 and 5. The sum of the digits is 9, which is an odd number, and the difference between the digits is 3, which is also odd. an incomparable number.
state whether the following statement is true or false. the law of sines can be used to solve triangles where three sides are known.
The statement "the law of sines can be used to solve triangles where three sides are known" is false.
A triangle is a three-sided polygon, with each side representing a line segment connecting two vertices. To fully determine a triangle, we need to know at least three pieces of information about it, such as the lengths of its sides, or the measures of its angles.
The law of sines is a mathematical formula that relates the ratios of the lengths of the sides of a triangle to the angles opposite those sides. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides of the triangle.
However, the law of sines cannot be used to solve a triangle if all three sides are known. To solve a triangle, we need to have additional information, such as the angles or some side-angle pairs. The law of sines can only be used to find missing side lengths or angle measures if we have at least one side length and one angle measure, or two side lengths and an angle not contained between them.
In conclusion, the statement "the law of sines can be used to solve triangles where three sides are known" is false. To solve a triangle, we need additional information in the form of angles or side-angle pairs.
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