The measure of the third angle in Elise angle measurement is
B 50°How to find the measure of the third sideThe third angle of the triangle is solved with knowledge of sum of angles on a triangle being equal to 180 degrees and a triangle having three angles
say the third angle measure is x, so we have that
30 + 100 + x = 180
130 + x = 180
collecting like terms
x = 180 - 130
x = 50
we can therefore say that the third angle is 50 degrees
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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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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.
Today is monday if and only if yesterday was sunday
Answer:
Step-by-step explanation:
According to the weeklybdays of a Calendar, the weekdays are scheduled as:-
Sunday-Monday -Tuesday-Wednesday-Thursday-Friday-Saturday
So, this shows that Monday comes only after Sunday. du to which the present day scheduled is Monday and the day before today(yesterday) is scheduled to be Sunday.
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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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.
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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The data in the table below were obtained for the reaction:
X + Y → P
EXP # X (M) Y (M) Initial Rate (M/s)
1 0.273 0.763 2.83
2 0.273 1.526 2.83
3 0.819 0.7632 25.47
A. What is the order of the reaction in X?
B. What is the order of the reaction in Y?
C. What is the overall order of the reaction?
The overall order of the reaction is the sum of the orders of the individual reactants, a + b. Therefore, the overall order of the reaction is 2 (1 + 1 = 2).
A. The order of the reaction in X is 1.
B. The order of the reaction in Y is 1.
C. The overall order of the reaction is 2.
The orders of a reaction can be determined from the initial rates obtained from the different experiments. The reaction rate is proportional to the concentrations of the reactants raised to the powers of the order of each reactant.
In experiment 1, the initial rate (2.83 M/s) is proportional to the concentration of X raised to the power of a (2.83 = k[X]^a). Therefore, a = 1.
In experiment 2, the initial rate (2.83 M/s) is proportional to the concentration of Y raised to the power of b (2.83 = k[Y]^b). Therefore, b = 1.
In experiment 3, the initial rate (25.47 M/s) is proportional to the concentration of X raised to the power of a (25.47 = k[X]^a) and the concentration of Y raised to the power of b (25.47 = k[Y]^b). Therefore, a = 1 and b = 1.
The overall order of the reaction is the sum of the orders of the individual reactants, a + b. Therefore, the overall order of the reaction is 2 (1 + 1 = 2).
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The um of two number i 61. The larger number i 4 more than two time the maller number. What i the maller number?
A
21
B
48
C
19
D
There i not enough information to tell. (NOT THE ANSWER)
The smaller number of the given sum is 15.
What is summation (sum)?A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total.The result that is produced when we add numbers, objects, or other things is referred to in mathematics as the sum. For instance, the sum of the addends 14 and 6 is 20.Completed question :
The sum of two numbers is 80. If the larger number exceeds four times the smaller by 5, what is the smaller number?
Given data :
Given, sum of two numbers is 61.
Let the smaller number be x
Thus the larger will be 61 - x
Also given, larger number exceeds four times the smaller number by 4.
Therefore, 61 - x = 4x + 5
5x = 56
x = 15
Thus the smaller number is 15.
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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.
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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applies the linear scan strategy to counting the number of negative * values in an array.
The linear scan strategy for counting the number of negative values in an array involves sequentially going through each element of the array and checking if it is negative.
If the element is negative, the count is incremented. Once the end of the array is reached, the count is returned.
For example, consider an array A = [-2, 3, -1, 4, -7, 9]. The linear scan strategy would be as follows:
1. Initialize count to 0
2. Check if A[0] = -2 is negative, if yes, increment count. Count = 1
3. Check if A[1] = 3 is negative, if no, continue. Count = 1
4. Check if A[2] = -1 is negative, if yes, increment count. Count = 2
5. Check if A[3] = 4 is negative, if no, continue. Count = 2
6. Check if A[4] = -7 is negative, if yes, increment count. Count = 3
7. Check if A[5] = 9 is negative, if no, continue. Count = 3
8. Return count = 3.
Therefore, the linear scan strategy for counting the number of negative values in array A is 3.
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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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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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Is each pair of systems of equations equivalent?
Explain.
23. 3x - 9y = 5
6x + 2y = 18
6x - 9y = 10
6x + 2y = 18
24.4y + 2x = -7
2y - 6x = 8
4y + 2x =-7
4y - 12x = 16
25. 5x + 3y = 19
2x + 4y = 20
10x + 6y = 38
10x + 20y = 100
While equations 24 and 25 are equivalent, equation 23 is not since the two equations are not the same.
What do math equivalent equations mean?When the solution set for two equations is the same, the equations are said to be equivalent. For instance, the equations x + 2 = 6 and 2x = 8 have the same solution set when we solve them both as follows: x + 2 = 6. Take 2 away from both sides.
What might an equivalent look like?For instance, 1 + 1 is equivalent to 2, even if 2 is said to be equal to 2. When two items or amounts are exactly the same, such as when 12 is equal to 12, but 12 is equivalent to 2/4 since they symbolise.
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While equations 24 and 25 are equivalent, equation 23 is not since the two equations are not the same.
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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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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a family has six children. each child is at least one year old, and the sum of their ages is an integer that is at most 31. what is the probability of correctly guessing the ages of all six children?
There is a 0.43% chance or probability of correctly guessing the ages of all six children.
The probability of correctly guessing the ages of all six children in a family where each child is at least one year old and the sum of their ages is an integer that is at most 31 can be calculated using combinations.
The total number of possible combinations of ages that meet the criteria can be found by multiplying the number of different outcomes for each child's age, giving us 6 x 6 x 6 x 6 x 6 x 6, or 46,656.
To calculate the probability, we need to divide the number of possible combinations that meet the criteria (46,656) by the total number of possible combinations (1,073,741,824).
This gives us the probability of 0.00433, or 0.43%.
This means that there is a 0.43% chance of correctly guessing the ages of all six children.
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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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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.
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
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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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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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]
A dress costs 54 Kate buys the dress to a discount of 28%. How much does kate pay for the dress?
Answer:
38.88 is what she paid
Step-by-step explanation:
0.28x54=15.12
15.12 = 28% of 54
the remaining percentage is 72%
15.12/28=0.54
0.54=1%
1x72 to get 72 percent so,
0.54*72=38.88
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
Use the general slicing mothod to find the volume of the following solid. The solid with a semicircular base of radius 9 whose cross section is perpendicular to the base and parallel to the diameter are squares. Place the semicircle on the xy-plane so that its diameter is on the x-axis and it is centered on the y-axis. Set up the integral that gives the volume of the solid. Use increasing limits of integration.
My online home work says the right integral is
int {0}^{9} 4(81-y^{2})dy
wich I understand but I don't know where the 4 came from.
The "4" in the integral is actually the height (or thickness) of each slice that we are using to find the volume of the solid.
In this case, we are taking infinitesimal slices perpendicular to the x-axis and the height of each slice is 4.
Let's consider the cross-sectional area of each slice. The cross-section is a square with side length equal to the diameter of the semicircular base, which is 2 * 9 = 18. The area of the square is 18^2 = 324.
However, we also need to take into account the shape of the semicircle. As we move up the solid, the area of the cross-section decreases as the height of the slice decreases. This is because the cross-sectional square is inscribed inside the semicircle, and as the height decreases, so does the width of the square. To account for this, we need to find the width of the square as a function of the height of the slice.
Let y be the height of the slice, then the width of the square is equal to the diameter of the semicircle minus twice the height of the slice. The diameter of the semicircle is 18, so the width of the square is 18 - 2y.
The area of the cross-section at height y is then given by:
A(y) = (18 - 2y)^2
A(y) = 324 - 72y + 4y^2
To find the volume of the solid, we integrate the area of the cross-section with respect to the height of the slice, from 0 to 9:
V = ∫_0^9 A(y) * 4 dy
V = ∫_0^9 (324 - 72y + 4y^2) * 4 dy
V = ∫_0^9 1296 - 288y + 16y^2 dy
V = 1296 * y - 144y^2 + 8y^3 |_0^9
V = 1296 * 9 - 144 * 9^2 + 8 * 9^3
V = 11304 - 1296 + 729 = 8737 cubic units
So, the volume of the solid is 8737 cubic units.
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Let's consider the cross-sectional area of each slice. The cross-section is a square with side length equal to the diameter of the semicircular base, which is 2 * 9 = 18. The area of the square is 18^2 = 324.
A(y) = (18 - 2y)^2
A(y) = 324 - 72y + 4y^2
V = ∫_0^9 A(y) * 4 dy
V = ∫_0^9 (324 - 72y + 4y^2) * 4 dy
V = ∫_0^9 1296 - 288y + 16y^2 dy
V = 1296 * y - 144y^2 + 8y^3 |_0^9
V = 1296 * 9 - 144 * 9^2 + 8 * 9^3
V = 11304 - 1296 + 729 = 8737 cubic units
The line representing the equation part of the constraint 7x1 + 4x2 s 28 goes through the following two pointsO (4,0) and (7,0) O (0, 4) and (7,0) O (4,0) and (0,7)O (0, 4) and (0,7) O none of the above
The line representing the equation 7x1 + 4x2 [tex]\leq[/tex] 28 goes through the following two points: (0,7) and (4,0).
Hence, option (c) is the correct choice.
The constraint equation is g(x,y)=c, and we state that x and y are constrained by g(x,y)=c.
Constrained maximum and constrained minimum points are locations (x,y) that are maxima or minima of f(x,y) with the condition that they meet the constraint equation g(x,y)=c.
As per the data given,
We have,
The equation of the constraint: 7 x_1+4 x_2[tex]\leq[/tex] 28
7 x_1+4 x_2 [tex]\leq[/tex] 28
So, putting the value of x_2=0
We will get the above expression as:
7 x_1=28
=>x_1=4
So, the points will be (4,0)
Now, putting the value of x_1=0
Thus, we will get:
4 x_2=28
=>x_2=7
So, the points will be (0,7)
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Find the parametric equation of the line through a parallel to b, using t as the parameter. a= (- 3 5) b= (-5 3) X =_____ + ______
(Type an integer or a simplified fraction for each matrix element.)
The parametric equation of the line through a parallel to b is X = [-3, 5] + t[1/4, 1]
What do you mean by equation?An equation is a mathematical statement that shows the equality or balance of two expressions. It is represented by an equal sign (=) and consists of variables, numbers, and mathematical operations. Equations are used to describe relationships between different quantities and can be solved to find unknown values. For example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving 2x = 4, and then dividing both sides by 2, giving x = 2.
The equation of a line can be represented in both point-slope form and in parametric form. The point-slope form of a line is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line.
In this case, we have two points, a and b, on the line. We can use these points to find the slope of the line, which is given by:
m = (y2 - y1) / (x2 - x1) = (b[1] - a[1]) / (b[0] - a[0]) = (3 - 5) / (-5 - (-3)) = (3 - 5) / -8 = -2 / -8 = 1/4
y - a[1] = (1/4)(x - a[0])
To convert this equation to parametric form, we can use t as the parameter and express x and y in terms of t:
x = a[0] + t
y = a[1] + (1/4)t
So the parametric equation of the line through a parallel to b is given by:
X = [-3, 5] + t[1/4, 1]
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