the sample is truly representative of all horses in the state, and that there are no biases or confounding factors that might affect the proportion of stallions in the sample.
If we assume that the horses constitute a random sample of all horses in the state, then we can estimate the probability that a randomly selected horse is a stallion by calculating the proportion of horses in the sample that are stallions. Let's assume that we have a sample of n horses, and that x of these horses are stallions. Then the estimated probability of selecting a stallion is:
x/n
For example, if we had a sample of 100 horses and 25 of them were stallions, the estimated probability of selecting a stallion would be:
25/100 = 0.25 or 25%
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water park has pools, slides, and rides that, in total, make use of 7.2 × 10^6 gallons of water. They plan to add a ride that would make use of an additional 1, 900 gallons of water. Use scientific notation to express the total gallons of water made use of in the park after the new ride is installed.
The total gallons of water made use of in the park after the new ride is installed is 7.201900 * 10⁶
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
Scientific notation is a way of expressing numbers in the form a * 10ᵇ where a is a number or decimal number and b is the power of 10.
The water park has 7.2 × 10⁶ gallons of water. If an additional 1, 900 gallons of water is added:
Total amount of water = 7.2 * 10⁶ + 1900 = 7201900 gallons = 7.201900 * 10⁶
The total gallons of water made use of in the park after the new ride is installed is 7.201900 * 10⁶
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PLS HELP IMMEDIATELY!!!!!
David bought 36.504msq of material to make a curtain. The material is 1.17m wide. Find the length of the material
The length of the rectangular shaped material is L = 31.282 m
Given data ,
The area of the material is 36.504 m², and the width of the material is 1.17 m. Let's call the length of the material "L" in meters.
We can use the formula for the area of a rectangle to relate the area and the dimensions of the material:
Area = Length x Width
Substituting the values we have, we get:
36.504 = L x 1.17
Solving for L, we get:
L = 36.504 / 1.17
L ≈ 31.282 m
Hence , the length of the material is approximately 31.282 meters
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Screenshot 2023-05-01 at 19.09.51
The circumference of the circle is given as follows: C = 109.9 in.
The relationship between the diameter of a circle and it's circumference is presented in this problem.
We have,
The circumference of a circle of radius r is given by the equation presented as follows:
C = 2πr
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.
The diameter is twice the radius, hence, for a circle with diameter 35 in, the radius is given as follows:
r = 0.5 x 35
r = 17.5 in.
Then the circumference of the circle is given as follows:
C = 2 x pi x 17.5
C = 109.9 in.
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Missing Information
The problem is incomplete, hence the relation between the diameter of a circle and it's circumference is presented.
one way to increase the probability of identifying the optimal decision when using a simulation is to:
One way to increase the probability of identifying the optimal decision when using a simulation is to increase the number of iterations or trials in the simulation.
Simulation is a powerful tool for modeling and analyzing complex systems or processes where there are many variables and uncertainties involved. However, the accuracy and reliability of the simulation results depend on the number of iterations or trials used in the simulation. The more trials or iterations are performed, the more accurate the simulation results are likely to be, and the higher the probability of identifying the optimal decision.
Therefore, to increase the probability of identifying the optimal decision in a simulation, one should increase the number of trials or iterations in the simulation. This means running the simulation multiple times with different input values or scenarios and recording the results for each run. By analyzing the results of multiple simulation runs, one can identify patterns, trends, and optimal decisions that are robust and reliable across different scenarios and conditions.
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Brenda is solving the system of equations A, shown in the table, by using the elimination method. She produced system of equations B as her first step in the solution method. Which of the following statements justifies the two systems being equivalent?
Option D is correct as it justifies the two systems being equivalent
How to get the correct optionMultiply by 2 the first equation A
2 (X + 2Y ) = 6
This would give us the first part of the equation B
= 2x + 4y = 12
Then the second equation
Multiply by 5 to get B
5(2/5x - y ) = 3
= 2x - 5y = 15
Hence the last option is the correct answer
Therefore we would say that Option D is correct as it justifies the two systems being equivalent
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in a two sample test of means with unknown and unequal population variances, the degrees of freedom is calculated as 9.76. what is the number you should use for degrees of freedom when using the t-distribution table?
The calculated value of 9.76 should be rounded to 10 for use in the table.
In a two sample test of means with unknown and unequal population variances, the degrees of freedom is calculated as 9.76. When using the t-distribution table, it is important to note that the table only lists integer values for degrees of freedom.
Therefore, we must round the calculated degrees of freedom to the nearest integer value.
In this case, the nearest integer to 9.76 is 10. Therefore, when using the t-distribution table for this two sample test of means, we should use 10 as the degrees of freedom value.
It is important to note that rounding the degrees of freedom can have a small effect on the accuracy of the results, particularly if the calculated value is close to an integer value. However, in most cases, rounding to the nearest integer is a reasonable approximation.
In summary, when calculating degrees of freedom for a two sample test of means with unknown and unequal population variances, it is important to round to the nearest integer value when using the t-distribution table. In this case, the calculated value of 9.76 should be rounded to 10 for use in the table.
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on the package of a certain snack, the nutrition facts label states that the protein content in one serving is 4 grams. the company wants to check this claim and takes a simple random sample of five servings of the snack from their factory. their lab obtains these measurements (in grams): 3.88 4.04 3.97 3.90 3.94 all but one of these measurements is under 4 grams. can this be due to chance error in the measurements?
the discrepancy between the sample mean and the claimed protein content is due to chance error in the measurements
To determine whether the discrepancy between the sample mean and the claimed protein content of 4 grams can be due to chance error in the measurements, we can perform a hypothesis test.
The null hypothesis, H0, is that the true mean protein content is equal to 4 grams. The alternative hypothesis, Ha, is that the true mean protein content is less than 4 grams.
Using a one-tailed t-test with a significance level of 0.05 and four degrees of freedom (n-1=5-1=4), we calculate the t-value to be -1.386. The critical t-value for a one-tailed test at a significance level of 0.05 and four degrees of freedom is -2.132.
Since our calculated t-value of -1.386 is greater than the critical t-value of -2.132, we fail to reject the null hypothesis. This means that we do not have enough evidence to conclude that the true mean protein content is less than 4 grams. Therefore, it is possible that the discrepancy between the sample mean and the claimed protein content is due to chance error in the measurements.
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his cold-water supply system serves a bathroom in a multistory building. The architect
directed the piping to be installed in the wall cavities with the main branch above ceiling
level. The supply pipe construction is 4 type-L copper. The building supply is capable of
maintaining a flow rate of 10 gallons per minute. The walls contain a 6-inch cavity, and the
ceilings contain a 12-inch cavity. Consider the installation to be centered in the available
cavity space.
If the cold-water supply pressure to the floor represented in the drawing measures 50 psi
and the flush-valve manufacturer specifies a minimum working pressure of 25 psi, how many
stories can be constructed before friction losses prevent proper valve operation?
A. None including this floor
B. This floor and one more story
C. This floor and two more stories
D. This floor only
Answer: D
Step-by-step explanation:
To determine the maximum number of stories that can be constructed before friction losses prevent proper valve operation, we need to calculate the pressure loss due to friction as the water flows through the piping to each floor.
Using the Hazen-Williams formula, which is commonly used for sizing water supply systems:
P = (4.52Q1.85L10.67/C1.85)d4.87
where:
P = pressure loss due to friction (psi)
Q = flow rate (gpm)
L = length of pipe (feet)
C = Hazen-Williams coefficient (dimensionless)
d = inside diameter of pipe (inches)
Assuming the flow rate is 10 gpm, the length of pipe from floor to floor is the height of the building divided by the number of stories, and the inside diameter of the pipe is 4 inches (since 4 type-L copper corresponds to a 4-inch nominal diameter), the pressure loss for each story can be calculated using a Hazen-Williams coefficient of 130 for copper piping:
P = (4.52 x 10^1.85 x (1 story height/number of stories)10.67/1301.85)4.87
P = 3.3 x (1/number of stories)^1.85
For example, for a 2-story building, the pressure loss would be:
P = 3.3 x (1/2)^1.85
P = 1.6 psi
To ensure that the minimum working pressure of 25 psi is maintained at each flush valve, the pressure loss for each story cannot exceed 25 - 50 = -25 psi (since lower pressures can cause valve malfunctions).
Solving for the maximum number of stories:
3.3 x (1/number of stories)^1.85 <= -25
(1/number of stories)^1.85 <= -25/3.3
1/number of stories <= (-25/3.3)^0.54
number of stories >= 1/(-25/3.3)^0.54
number of stories >= 6.7
Therefore, the maximum number of stories that can be constructed before friction losses prevent proper valve operation is D. This floor only.
a sample of 25,000 act test takers had an average score of 21 with a standard deviation of 5. with a 0.95 probability, determine the margin of error.
The margin of error for a 95% confidence interval can be calculated using the formula:
Margin of error = Zα/2 * (standard deviation / √sample size)
Where Zα/2 is the critical value for a 95% confidence interval, which can be found using a standard normal distribution table or calculator. For a 95% confidence interval, Zα/2 is approximately 1.96.
Using the given information, we can plug in the values into the formula:
Margin of error = 1.96 * (5 / √25,000) = 0.98
Therefore, the margin of error is approximately 0.98 points for a 95% confidence interval. This means that we can be 95% confident that the true mean score of all ACT test takers is within ±0.98 points of the sample mean of 21.
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exact value of the expressiontan 25° + tan 110° 1 − tan 25° tan 110°
The exact value of the expression is -1.
The expression involves tan 25° and tan 110°. The expression you provided is:
tan 25° + tan 110° / (1 - tan 25° tan 110°)
First, we need to recognize that tan (180° - x) = -tan x. Since 110° = 180° - 70°, we have:
tan 110° = -tan 70°
Now, we can rewrite the expression as:
tan 25° - tan 70° / (1 + tan 25° tan 70°)
Next, we can apply the tangent addition formula, which is:
tan (a - b) = (tan a - tan b) / (1 + tan a tan b)
Comparing this formula with our expression, we see that a = 25° and b = 70°. So, the expression simplifies to:
tan (25° - 70°) = tan (-45°)
Since tan (-x) = -tan x, we have:
tan (-45°) = -tan 45°
Lastly, we know that tan 45° = 1, so:
-tan 45° = -1
Therefore, the exact value of the expression is -1.
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an engineering manager is selecting a team of 5 engineers for an upcoming project. there are 10 available engineers to choose from. how many different teams can be selected?
There are 252 different teams that can be selected from the 10 available engineers for the upcoming project.
To solve this problem, we can use the combination formula. The number of combinations of choosing r items from n items is given by nCr = n!/(r!(n-r)!). In this case, n = 10 (the total number of available engineers) and r = 5 (the number of engineers to be selected for the team). Plugging these values into the formula, we get:
10C5 = 10!/(5!(10-5)!) = 252
Therefore, there are 252 different teams that can be selected from the 10 available engineers for the upcoming project.
It's important for the engineering manager to carefully consider the skills and strengths of each engineer when selecting the team. By choosing a diverse group with complementary skills, the team will be better equipped to tackle the project and achieve success. The manager should also consider the individual personalities and work styles of each engineer to ensure that they can work together effectively and collaboratively. Overall, the team selection process should be thoughtful and strategic to maximize the project's potential for success.
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All of the students in the sixth-grade class went on a field trip to an amusement park. *40% bought a pass to ride an unlimited number of rides. *75 students paid for each ride individually. How many students are in the sixth grade?
There are 187 students in the sixth grade.
We can start by using the information that 40% of the students bought a pass to ride an unlimited number of rides. This means that 60% of the students did not buy a pass and paid for each ride individually.
Let's assume that the total number of students in the sixth grade is "x". Then, 40% of the students bought a pass, which is 0.4x. The remaining 60% paid for each ride individually, which is 0.6x.
We also know that 75 students paid for each ride individually. Therefore, we can set up an equation:
0.6x = 75
Solving for x, we get:
x = 75 / 0.6
x = 125 / 0.4
x = 187.5
Since we can't have half a student, we round up to the nearest whole number. Therefore, there are 187 students in the sixth grade.
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show that a function from a finite set s to itself is one-to-one if and only if it is onto
A function from a finite set s to itself is one-to-one if and only if it is onto. This result holds because of the finite nature of the set s and the uniqueness of the mapping between elements in the domain and the range of the function.
To show that a function from a finite set s to itself is one-to-one if and only if it is onto, we need to consider two cases.
let's assume that the function is one-to-one. This means that for every pair of distinct elements x and y in the set s, the function maps them to distinct elements in the set s. In other words, if f(x) = f(y), then x = y. Since the set s is finite, and the function maps each element to a distinct element, there must be an equal number of elements in the domain and the range of the function. Therefore, the function must be onto as well.
Now let's assume that the function is onto. This means that for every element y in the set s, there exists an element x in the set s such that f(x) = y. In other words, every element in the range of the function is mapped to by some element in the domain of the function. Since the set s is finite, and the function maps each element to a unique element, there cannot be any elements in the range of the function that are not mapped to by some element in the domain of the function. Therefore, the function must be one-to-one as well.
In summary, a function from a finite set s to itself is one-to-one if and only if it is onto. This result holds because of the finite nature of the set s and the uniqueness of the mapping between elements in the domain and the range of the function.
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5 x w = 37
w = ? ......................................................................
The radius of a circular swimming pool is 25. 48 ft in length. What is the diameter of the swimming pool?
To find the diameter of a circular swimming pool with a given radius, we need to use the formula: diameter = 2 x radius. In this case, the radius is given as 25.48 ft. Therefore, the diameter of the pool can be calculated as follows: diameter = 2 x 25.48 = 50.96 ft.
It's important to note that the length of the pool is not directly relevant to finding its diameter. The length usually refers to the distance between the two ends of the pool, while the diameter is the distance across the widest part of the pool. However, the length can be useful in determining the surface area and volume of the pool, which are important for maintenance and chemical treatment.
In summary, the diameter of the circular swimming pool with a radius of 25.48 ft is approximately 50.96 ft.
To find the diameter of a circular swimming pool, you need to use the given radius. The radius is the distance from the center of the circle to its edge. In this case, the radius of the swimming pool is 25 feet.
The diameter is simply twice the radius, as it is the distance across the entire circle, passing through the center.
To find the diameter, you can use the following formula:
Diameter = 2 * Radius
Substitute the given radius (25 feet) into the formula:
Diameter = 2 * 25 ft
Diameter = 50 ft
So, the diameter of the circular swimming pool is 50 feet.
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8. The table shows the commission y (in dollars) of selling x cell phone plans.
Cell Phone Plans, x
Commission, y
100 150 250 400
a. Does the table represent a linear or nonlinear function? Explain.
by different
b. Based on the pattern in the table, what is the commission of selling amounts.
5 cell phone plans?
The table represents a nonlinear function because both the slope and common difference are not constant.
Based on the pattern in the table, the commission of selling 5 cell phone plans is 600.
What is a linear function?In Mathematics, a linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
This ultimately implies that, a linear function has the same slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases or decreases simultaneously.
Therefore, this table does not represent a linear function because the slope isn't constant and the common difference is not constant between successive data points.
When x = 5 cell phone plans, y is given by;
y - 400 = 200
y = 600.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Players A, Band C play Noluz game. Player A wins if a 1 or 4 face up, player B wins if a 2 or 4 face up and player C wins if a 3 or 6 face up. What is the expected value per turn for playing Noluz ?
The expected value per turn for playing Noluz is 2. This means that on average, a player can expect to win 2 points per turn in the long run.
To calculate the expected value per turn for playing Noluz, we need to first find the probability of each player winning. The probability of A winning is 2/6 or 1/3, the probability of B winning is 2/6 or 1/3, and the probability of C winning is 2/6 or 1/3.
Next, we need to find the value associated with each outcome. A win for A is worth 1 point, a win for B is worth 2 points, and a win for C is worth 3 points.
Using these values and probabilities, we can calculate the expected value per turn as follows:
Expected value per turn = (1/3) * 1 + (1/3) * 2 + (1/3) * 3
= 2
Therefore, the expected value per turn for playing Noluz is 2. This means that on average, a player can expect to win 2 points per turn in the long run.
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the cases are given in time order. prepare a time plot for the number of transfers. is any systematic pattern evident in your plot? discuss.
Yes, a systematic pattern is evident in the time plot for the number of transfers.
A time plot is a graphical representation of data over time. In this case, we have data on the number of transfers given in time order. By plotting the data on a graph with time on the x-axis and the number of transfers on the y-axis, we can visually analyze the pattern of transfers over time.
From the time plot, we can see that the number of transfers is increasing steadily over time, with a few small dips and spikes. This suggests that there is a systematic pattern of growth in the number of transfers.
the time plot for the number of transfers shows a systematic pattern of growth over time. This could be indicative of various factors, such as increased demand for transfer services, population growth, or changes in transportation infrastructure. Further analysis would be required to identify the specific factors driving this pattern.
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two six-sided dice are rolled. what is the size of the sample space that corresponds to the event that both dice are odd?
When rolling a single six-sided die, there are three odd numbers: 1, 3, and 5, and three even numbers: 2, 4, and 6. Since we are rolling two dice, each with six possible outcomes, there are a total of $6 \times 6 = 36$ possible outcomes.
To find the sample space corresponding to the event that both dice are odd, we need to determine all possible outcomes in which both dice land on odd numbers. There are three odd numbers on each die, so there are three possibilities for the first die and three possibilities for the second die, for a total of $3 \times 3 = 9$ outcomes where both dice are odd.
Therefore, the size of the sample space that corresponds to the event that both dice are odd is 9.
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lim (x, y)→(0, 0) cos(xy) − 1 x2y2
The overall limit does not exist as it approaches infinity.
To find the limit of the function lim (x, y)→(0, 0) cos(xy) − 1 / x^2y^2, we can use polar coordinates.
Let x = r cosθ and y = r sinθ. Then as (x, y) approaches (0, 0), r approaches 0. Substituting these values into the function, we get:
lim r→0 (cos(r^2 sinθ cosθ) - 1) / (r^4 cos^2θ sin^2θ)
Next, we can take the limit as r approaches 0 for each of the terms separately. Since cos(r^2 sinθ cosθ) approaches 1 as r approaches 0, the first term goes to 0. For the second term, we can simplify it as follows:
lim r→0 1 / (r^2 cos^2θ sin^2θ) = lim r→0 sec^2θcsc^2θ / r^2 = ∞
Therefore, the overall limit does not exist as it approaches infinity.
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Which measure of central tendency is not resistant to extreme values in a numeric data set? A. Parameters B. Mean C. Median D. Mode
B. Mean is not resistant to extreme values in a numeric data set. The mean is affected by outliers or extreme values in a dataset because it takes into account all the values in the dataset, including the extreme values.
Central tendency is a measure that is used to find the central or typical value of a set of data. The most common measures of central tendency are mean, median, and mode. These measures provide different ways of summarizing the data, depending on the nature of the dataset and the research question.
The mean is calculated by adding up all the values in a dataset and dividing by the number of values. The mean is often considered to be the most common measure of central tendency because it takes into account all the values in the dataset. However, the mean is not resistant to extreme values or outliers. An outlier is an observation that is significantly different from other observations in the dataset.
When a dataset contains extreme values or outliers, the mean is often affected, resulting in a value that does not represent the central tendency of the dataset. This is because the mean is influenced by every value in the dataset, including the outliers, and is not a robust measure of central tendency. In contrast, the median and mode are resistant to extreme values and provide better estimates of central tendency when a dataset contains outliers.
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Find the critical value tc for the confidence level c=0.99 and sample size n=21.
The critical value tc for the confidence level c=0.99 and sample size n=21 is 2.845.
To find the critical value tc for the confidence level c = 0.99 and sample size n = 21, we can use the t-distribution table or a statistical software package.
t-distribution critical value formula is: tc = t(α/2, n-1)
For a confidence level of 0.99, the significance level α is:
α = 1 - c = 1 - 0.99 = 0.01
Using a t-distribution table with 20 degrees of freedom (n-1), we can find the t-value with a cumulative probability of 0.005 in the upper tail, since we are interested in the critical value at the two-sided 99% confidence level.
The t-value with a cumulative probability of 0.005 and 20 degrees of freedom is 2.845.
Therefore, the critical value tc for the confidence level c = 0.99 and sample size n = 21 is:
tc = t(α/2, n-1) = t(0.005, 20) = 2.845
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Use the table or s = 50m + 200
9. What is the savings after 6 months?
Months Savings
0 $200
1 $250
2 $300
3 $350
need this for geometry
The value of the missing leg using Pythagoras theorem is 12.5.
What is Pythagoras theorem?Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“
To calculate the missing leg, we use Pythagoras theorem.
a² = b²+c²..................... Equation 1Where:
a = 16b = 10 c = Missing legSubstitute these values into equation 1 and solve for c
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Use the expression 3x^2 + 4y - 5x + y + 11 to match the vocabulary terms with their "parts" of the given expression. constant, greatest common factor, number of terms in the polynomial, coefficient of the leading term, exponent of the leading term. DRAG & DROP THE ANSWER 4 11 1 3 2 6 5
Answer:
Constant: 11Greatest common factor: 1Number of terms in the polynomial: 5Coefficient of the leading term: 3Exponent of the leading term: 2Step-by-step explanation:
In order to solve this, we need to know the definitions of the vocabulary terms and how to identify them in a polynomial expression. Here are the definitions:
A constant is a term that has no variable. For example, 11 is a constant. It's also a prime number, but don't let that get to its head.A greatest common factor (GCF) is the largest number or expression that divides evenly into all the terms of a polynomial. For example, the GCF of 3x² + 4y - 5x + y + 11 is 1, because 1 is the only number that divides evenly into all the terms. It's also the loneliest number, but don't let that make you sad.The number of terms in a polynomial is the number of separate parts that are added or subtracted. For example, 3x² + 4y - 5x + y + 11 has five terms: 3x², 4y, -5x, y, and 11. It's also the number of fingers on one hand, but don't let that limit your counting.The coefficient of the leading term is the numerical factor of the term with the highest degree (the highest exponent of the variable). For example, in 3x² + 4y - 5x + y + 11, the leading term is 3x² and its coefficient is 3. It's also the number of sides on a triangle, but don't let that make you obtuse.The exponent of the leading term is the power of the variable in the term with the highest degree. For example, in 3x² + 4y - 5x + y + 11, the leading term is 3x² and its exponent is 2.To match the vocabulary terms with their “parts” of the given expression, you need to drag and drop the correct numbers from the options. Here are the matches:
Constant: 11Greatest common factor: 1Number of terms in the polynomial: 5Coefficient of the leading term: 3Exponent of the leading term: 2using equations : two sum of two is 15.3 times the smaller number is 5 more the larger number.. Calculate the 2 numbers (hint : Let the smaller number be x)
Answer:
Step-by-step explanation:
15.3
+1.285
Answer = 16.585
Find the slope of a line perpendicular to the line whose equation is x-3y=27?
You owe $1240. 24 on a credit card with a 13. 75%APR. You decide to pay $250. 00/month toward paying off the credit card. How much is the difference in the interest paid after one month if you pay at the beginning of the month compared to paying at the end of the month?
The interest for the first month would be $14.21.
To calculate the interest paid if you pay at the end of the month, we first need to calculate the interest on the remaining balance.
The monthly interest rate can be calculated by dividing the annual percentage rate (APR) by 12:
13.75% / 12 = 0.01146 (rounded to 5 decimal places)
For the first month, the interest on the balance of $1240.24 would be:
.01146 x $1240.24 = $14.21
So if you pay $250 at the end of the month, your new balance would be:
$1240.24 + $14.21 - $250 = $1004.45
To calculate the interest paid if you pay at the beginning of the month, we need to calculate the interest on the balance of $1240.24 before making the payment.
The interest for the first month would be:
0.01146 x $1240.24 = $14.21
So your new balance would be:
$1240.24 + $14.21 - $250 = $1004.45
Since the payment is the same in both scenarios, the difference in interest paid after one month is zero.
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The figure above shows the graphs of the circles x^2 + y^2 = 2. What is the radius of the larger circle?
a) √2 b) 2 c) √4 d) 4
The figure above shows two circles, one inside the other. The equation x^2 + y^2 = 2 represents the smaller circle, while the larger circle is not explicitly defined in the question.
However, we can see from the graph that the center of both circles is at the origin (0,0) and that the larger circle has a radius twice as big as the smaller circle.
Therefore, the radius of the larger circle is 2 times the radius of the smaller circle, which is the square root of 2. So the answer is (a) √2.
The given equation of the circle is x^2 + y^2 = 2. To find the radius of this circle, we can rewrite the equation in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.
In this case, the equation is already in the standard form with h = 0, k = 0, and r^2 = 2. Therefore, the radius of the larger circle is r = √2. So, the correct answer is a) √2.
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