Part A: The given definition states that an angle is two collinear rays with a common endpoint. Part B : A point is an example of an undefined term.In relation to angles, a point is crucial as it serves as the common endpoint of the two rays that form the angle.
Part A : The given definition states that an angle is two collinear rays with a common endpoint. However, this definition is incorrect as it contradicts the correct definition of an angle. In the correct definition, an angle is formed by two non-collinear rays with a common endpoint.
An example that contradicts the given definition is when you have two rays, AB and BC, with B being the common endpoint. If they were collinear, they would lie along the same straight line, and thus, no angle would be formed between them. To make the definition accurate, you would need to change it to: "An angle is formed by two non-collinear rays with a common endpoint."
Part B: An undefined term in geometry is a term that cannot be defined using other known geometric terms, but its meaning is generally understood. One example of an undefined term is a point. A point is a basic element in geometry, and it has no size, shape, or dimensions. It is merely a location in space. For instance, when discussing angle ABC, point B is the common endpoint of rays AB and BC.
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Simplify the product using foil. (3x-4)(6x-2)
a. 18x^2 + 30x - 8
b. 18x^2 + 18x - 8
c. 18x^2 - 30x + 8
d. 18x^2 - 18x + 8
Using FOIL, the simplified expression for the product of (3x-4)(6x-2) is c. 18x² - 30x + 8.
To simplify the product (3x-4)(6x-2) using FOIL, we follow the First, Outer, Inner, Last rule. Let's break down the process:
First: Multiply the first terms of both expressions:
(3x) * (6x) = 18x²
Outer: Multiply the outer terms of both expressions:
(3x) * (-2) = -6x
Inner: Multiply the inner terms of both expressions:
(-4) * (6x) = -24x
Last: Multiply the last terms of both expressions:
(-4) * (-2) = 8
Now, combine the results:
18x² - 6x - 24x + 8
Simplify by combining the like terms (middle terms -6x and -24x):
18x² - 30x + 8
The simplified product is 18x² - 30x + 8, which corresponds to option (c).
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PLEASE HELP!!
Solve for measure of angle a.
a = [?]°
Answer:
∠ a = 125°
Step-by-step explanation:
the measure of chord- chord angle a is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is
∠ a = [tex]\frac{117+133}{2}[/tex] = [tex]\frac{250}{2}[/tex] = 125°
Use the given circumference to find the surface area of the spherical object.
a pincushion with c = 18 cm
To find the surface area of a spherical object, we need to know the radius of the sphere. However, in this case, only the circumference of the pincushion is given, which is not enough information to directly determine the radius.
The formula relating the circumference (c) and the radius (r) of a sphere is:
c = 2πr
To find the surface area (A) of the sphere, we can use the formula:
A = 4πr^2
Since we don't have the radius, we need to solve the circumference formula for the radius first:
c = 2πr
Divide both sides of the equation by 2π:
r = c / (2π)
Now we can substitute the value of c = 18 cm into the equation to find the radius:
r = 18 cm / (2π)
r ≈ 2.868 cm (approximately)
Now that we have the radius, we can calculate the surface area using the formula:
A = 4πr^2
A = 4π(2.868 cm)^2
A ≈ 103.05 cm² (approximately)
Therefore, the surface area of the pincushion is approximately 103.05 square centimeters.
jameson plans to create a larger kennel by doubling the dimensions in the blueprint. how many times the perimeter of the original kennel is the
perimeter of the larger kennel?
The perimeter of the larger kennel will be twice as large as the perimeter of the original kennel.
To find the ratio of the perimeters of the original kennel to the larger kennel, we need to know how doubling the dimensions affects the perimeter.
Since the perimeter is the sum of all four sides, doubling each side will result in a perimeter that is double the original.
Therefore, the perimeter of the larger kennel will be two times the perimeter of the original kennel.
In mathematical terms:
Perimeter of larger kennel = 2 x perimeter of original kennel
So, the perimeter of the larger kennel will be twice as large as the perimeter of the original kennel.
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Wanda's front porch is 7 feet wide and 13 feet long. Wanda wants to stain the wood on the porch next weekend. The stain costs $2. 00 per square foot. How much will it cost to buy enough stain for the whole porch?
The amount it will cost to buy enough stain for the whole porch is $182.
To determine the cost of staining Wanda's front porch, we'll first need to calculate the area of the porch, which is a rectangle in shape. The area of a rectangle can be found using the formula: Area = length × width.
In this case, the length of Wanda's porch is 13 feet, and the width is 7 feet. So, we'll multiply these two measurements to find the area:
Area = 13 ft × 7 ft = 91 square feet
Now that we know the area, we can calculate the cost of the stain. The stain costs $2.00 per square foot, so we'll multiply the area of the porch (91 square feet) by the cost per square foot:
Cost = 91 sq ft × $2.00/sq ft = $182
Therefore, it will cost Wanda $182 to buy enough stain for the whole porch.
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How much would you have to deposit in
an account with a 4.75% interest rate,
compounded continuously, to have
$20,000 in your account 20 years later?
Answer:
Pe^(.0475 × 20) = $20,000
P = $7,734.82
In each figure congruent parts are marked. Give additional congruent parts to prove that the right triangles are congruent and state the congruence theorem that justifies your answer.
please help me
To prove that the right triangles are congruent, we need to show that they have three pairs of congruent parts (sides or angles).
Let's say that the given congruent parts are the hypotenuses and one leg of each triangle. To prove congruence, we can add one more pair of congruent parts, such as the other leg.
By the Side-Angle-Side (SAS) congruence theorem, if two triangles have two pairs of congruent sides and the included angle is also congruent, then the triangles are congruent. In this case, we have two pairs of congruent sides (the hypotenuses and one leg) and the included angle (the right angle) is congruent by definition.
Therefore, we can conclude that the two right triangles are congruent by SAS.
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The heights of 14 plants, in inches, are listed.
12, 14, 15, 15, 16, 16, 16, 17, 18, 18 ,19, 20, 22, 25
If another plant with a height of 13 inches is added to the data, how would the mean be impacted?
The mean would stay the same value of about 17.1 inches.
The mean would decrease in value to about 17.1 inches.
The mean would stay the same value of about 17.4 inches.
The mean would increase in value to about 17.4 inches.
Answer:
The mean would decrease in value to about 17.1 inches.
Step-by-step explanation:
If we add a smaller data to the mean of a numerical data set, the mean will decrease.
Hope this helps.
350 divided by 80?!?!
Answer:
350/80
cancel out the zeros
35/8
4 3/8 or 4.375
350 divided by 80 is equal to 4 with a remainder of 30, or in decimal form, it is approximately 4.375.
We have,
To divide 350 by 80, we can perform the division operation as follows:
- First, we check how many times 80 can be divided into 350. We start with the largest multiple of 80 which is less than or equal to 350, which is 4.
80 x 4 = 320
- We subtract 320 from 350 to find the remainder:
350 - 320 = 30
- Since the remainder is not zero,
We can continue dividing. We bring down the next digit of 350, which is 0.
- Now, we have 300 as the new dividend.
We ask ourselves how many times 80 can be divided into 300.
80 x 3 = 240
- Subtracting 240 from 300 gives us the new remainder:
300 - 240 = 60
- Again, the remainder is not zero, so we continue.
- We bring down the last digit of 350, which is 0, and our new dividend becomes 600.
- We ask ourselves how many times 80 can be divided into 600.
80 x 7 = 560
- Subtracting 560 from 600 gives us the new remainder:
600 - 560 = 40
- The remainder is still not zero, so we continue.
- Finally, we bring down the last digit of 350, which is 0.
Our new dividend is 400.
We ask ourselves how many times 80 can be divided into 400.
80 x 5 = 400
- Subtracting 400 from 400 gives us zero as the remainder.
Since the remainder is now zero, we can stop dividing.
Therefore,
350 divided by 80 is equal to 4 with a remainder of 30, or in decimal form, it is approximately 4.375.
In summary, 350 divided by 80 equals 4 with a remainder of 30, or 4.375.
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A method for determining whether a critical point is a relative minimum or maximum using concavity.
To determine whether a critical point is a relative minimum or maximum using concavity, we need to examine the second derivative of the function at the critical point.
If the second derivative is positive, then the function is concave up, meaning it is shaped like a bowl opening upwards. At a critical point where the first derivative is zero, this indicates a relative minimum, as the function is increasing on either side of the critical point.
On the other hand, if the second derivative is negative, then the function is concave down, meaning it is shaped like a bowl opening downwards. At a critical point where the first derivative is zero, this indicates a relative maximum, as the function is decreasing on either side of the critical point.
If the second derivative is zero, then the test is inconclusive and further analysis is needed, such as examining higher order derivatives or using other methods such as the first derivative test.
Therefore, the concavity test is a useful method for determining the nature of critical points and whether they represent a relative minimum or maximum.
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Complete question is:
What we need to examine for a method for determining whether a critical point is a relative minimum or maximum using concavity.
Full Term O Question 10 9 pts 5 1 Let f(x) = 3 + 6x? - 153 +3. 2" (a) Compute the first derivative of '(x) = 70 hents (c) On what interval is increasing? interval of increasing = (-2,-5) U (1,60) (d) On what interval is f decreasing? interval of decreasing = (-5,1) **Show work, in detail, on the scrap paper to receive full credit. (b) Compute the second derivative off f''(x) = (e) On what interval is f concave downward? interval of downward concavity = (f) On what interval is f concave upward? interval of upward concavity = **Show work, in detail, on the scrap paper to receive full credit.
Since f''(x) is always 0, f(x) is not concave upward on any interval.
On what interval is f concave upward?
The first derivative of f(x) is f'(x) = 6.
The second derivative of f(x) is f''(x) = 0.
The interval on which f(x) is increasing is when f'(x) > 0, which is when x is in the interval (-2,-5) U (1,60).
The interval on which f(x) is decreasing is when f'(x) < 0, which is when x is in the interval (-5,1).
The interval on which f(x) is concave downward is when f''(x) < 0, which is all values of x.
The interval on which f(x) is concave upward is when f''(x) > 0, which is no values of x.
To find the first derivative of f(x), we need to take the derivative of each term separately. The derivative of 3 is 0, the derivative of 6x is 6, and the derivative of -153 +3.2 is 0. Adding these up gives us f'(x) = 6.
To find the second derivative of f(x), we need to take the derivative of f'(x), which is a constant function. The derivative of a constant function is always 0, so f''(x) = 0.
To determine where f(x) is increasing, we need to find the values of x where f'(x) > 0. Since f'(x) is a constant function, it is always positive, so f(x) is increasing on the interval (-2,-5) U (1,60).
To determine where f(x) is decreasing, we need to find the values of x where f'(x) < 0. Since f'(x) is a constant function, it is always positive, so f(x) is decreasing on the interval (-5,1).
To determine where f(x) is concave downward, we need to find the values of x where f''(x) < 0. Since f''(x) is always 0, f(x) is concave downward on all values of x.
To determine where f(x) is concave upward, we need to find the values of x where f''(x) > 0. Since f''(x) is always 0, f(x) is not concave upward on any interval.
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Does anyone know how to help
The volume of the cylinder after the rotation of rectangle is V = 12π units³ = 37.68 units³
Given data ,
Let the width of the rectangle be w = 2 units
Let the length of the rectangle be l = 3 units
Now , on rotating a rectangle , we get a cylinder
And , the radius of the cylinder = 2 units
And , the height of the cylinder = 3 units
Now , Volume of Cylinder = πr²h
On simplifying , we get
V = π ( 2 )² ( 3 )
V = 12π units³
V = 37.68 units³
Hence , the volume of cylinder is V = 37.68 units³
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Levi finds a skateboard that sells for 139. 99. The store charges 6% sales taxes. About how much money will he have to spend for his skateboard
$148.39 much money will he have to spend for his skateboard.
Levi will have to spend approximately $148.39 for his skateboard.
The original price can be defined as the cost price of an item or a service. The decrease in the original price of a product or service is called the discount offered to the buyer. Generally, this discount is expressed as a percentage.
Original Sale Price means the price at which the current Owner purchased the Property (not including commissions, loan origination fees, appraisals fees, title insurance premiums and other similar transaction costs).
To calculate this, we need to find 6% of the original price and add it to the original price:
6% of 139.99 = 0.06 x 139.99 = 8.3994
Adding this to the original price gives:
139.99 + 8.3994 = 148.3894
Rounding to the nearest cent gives $148.39.
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Find the number of x-intercepts of the graph of y=-3x^2-8x+4
Sara is studying for her dba. she studied for 31/2 hours before dinner, then for another
45 minutes after dinner. how long did sara study in all?
To find out how long Sara studied in all, we need to add the time she studied before dinner and after dinner.
Sara studied for 3 1/2 hours before dinner and 45 minutes after dinner.
We can convert 3 1/2 hours to minutes by multiplying it by 60:
3 1/2 hours = 3 × 60 + 30 = 180 + 30 = 210 minutes
So, Sara studied for 210 minutes before dinner and 45 minutes after dinner.
To find the total time, we add these two values:
Total time = 210 minutes + 45 minutes = 255 minutes
Therefore, Sara studied for 255 minutes in all.
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009 10.0 points Let f be a function defined on (-1, 1] such that f(-1) = f(1) = . Consider the following properties that f might have: A. f(1) = 2; x | | B. f continuous on (-1, 1]; C. Which properties ensure that there exists cin (-1, 1) at which f'(c) = 0? - f(x) = 22/3 = x2 1. B and C only 2. none of them 3. all of them 4. B only 5. C only 6. A and C only 7. A only 8. A and B only
Properties B and C together ensure that there exists a 'c' in (-1, 1) at which f'(c) = 0.
Your answer: 1. B and C only
Which properties ensure that there exists ?
a 'c' in (-1, 1) at which f'(c) = 0, given f(-1) = f(1) = and the properties A, B, and C.
First, let's define the properties:
f(1) = 2
f is continuous on (-1, 1]
f(x) = (22/3) - x^2
To ensure that there exists a 'c' in (-1, 1) at which f'(c) = 0, we will use the Mean Value Theorem (MVT). MVT states that if a function is continuous on a closed interval and differentiable on an open interval, then there exists at least one 'c' in the interval where the derivative is 0.
Looking at property B, it states that f is continuous on (-1, 1], which satisfies the first condition of the MVT. Property C provides a specific function for f(x), which is differentiable on (-1, 1) since it is a polynomial function. Therefore, properties B and C together ensure that there exists a 'c' in (-1, 1) at which f'(c) = 0.
Your answer: 1. B and C only
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Fill in the blank: Some of the most common symbols used in formulas include (addition), - (subtraction), * (multiplication), and / (division). These are called _____
The basic arithmetic operators (+,-,*,/) are commonly used in formulas to perform mathematical calculations. They are collectively known as "operators" and are an essential component of mathematical formulas, allowing us to perform complex calculations quickly and efficiently.
The symbols mentioned in the question, i.e., (+,-,*,/) are the basic arithmetic operators that are used in mathematical formulas to perform different types of calculations. These symbols are collectively referred to as "operators" or "mathematical operators."
Operators are an essential part of mathematical formulas as they allow us to perform complex mathematical calculations in a concise and efficient manner. They act as a shorthand way of representing mathematical operations and make it easier to perform calculations without having to write out the entire equation every time.
In addition to the basic arithmetic operators mentioned above, there are other types of operators that can be used in formulas depending on the specific mathematical operation being performed. For example, there are logical operators like AND, OR, and NOT that are used in Boolean algebra to perform logical calculations.
Other operators that can be used in formulas include exponentiation (^), which is used to raise a number to a certain power, and modulo (%), which is used to find the remainder when one number is divided by another.
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A cone a radio of 3 cm and volume of 94. 2 cm find. It’s height
The height of the cone is approximately 3.4 cm.
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
We are given that the radius of the cone is 3 cm and the volume is 94.2 cm^3. Substituting these values into the formula, we get:
94.2 = (1/3)π(3^2)h
Simplifying:
94.2 = 9πh
h = 94.2 / (9π)
h ≈ 3.4
Therefore, the height of the cone is approximately 3.4 cm.
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Assuming an approximately normal data set, find the 68% confidence interval for systolic blood pressure in
women given a sample size of 1000 with a mean of 123.4 and a standard deviation of 19.9.
There is not enough evidence to conclude that Devon's true proportion of good serves is greater than 72%.
Find out the 68% confidence interval for systolic blood pressure in women from the given samples?The correct conclusion for Devon to reach is: Because the P-value of 0.06 > a (where a = 0.05), Devon should fail to reject H0. There is no convincing evidence that the proportion of services that are good is more than 72%.
The null hypothesis, H0, states that the true proportion of good serves for Devon is equal to 72%. The alternative hypothesis, Ha, states that the true proportion of good serves for Devon is greater than 72%.
The P-value is the probability of obtaining a test statistic as extreme or more extreme than the observed data, assuming that the null hypothesis is true. In this case, the P-value is 0.06, which means that if the true proportion of good serves for Devon is actually 72%, there is a 6% chance of observing a sample of 50 serves with 42 or more good serves.
Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.
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The 68% confidence interval for systolic blood pressure in women, based on the given sample, is approximate: (122.77, 124.03)
How to find a confidence interval for systolic blood pressure in women?To find the 68% confidence interval for systolic blood pressure in women, we can use the standard formula:
Confidence Interval = Mean ± (Z * (Standard Deviation / √n))
Where:
Mean = 123.4 (sample mean)
Standard Deviation = 19.9 (sample standard deviation)
n = 1000 (sample size)
Z = Z-score corresponding to the desired confidence level (in this case, 68% corresponds to 1 standard deviation on each side of the mean)
To find the Z-score, we can refer to the standard normal distribution table or use a calculator. For a 68% confidence level, the Z-score is 1.
Plugging in the values, we get:
Confidence Interval = 123.4 ± (1 * (19.9 / √1000))
Calculating the square root of 1000, we have:
Confidence Interval = 123.4 ± (1 * (19.9 / 31.62))
Simplifying further, we get:
Confidence Interval = 123.4 ± (0.6301)
Therefore, the 68% confidence interval for systolic blood pressure in women, based on the given sample, is approximate: (122.77, 124.03).
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Please help solve 5 and 6 and show work please
a. The actual area of the kitchen is 128 square feet.
b. the couch measures 1.25 inches across in the scale drawing.
How do we calculate?The scale is 1/4 inch = 2 feet,
meaning that in the drawing, each inch represents 8 feet (since 2 feet/0.25 inches = 8 feet/inch).
The kitchen in the drawing has an area of 2 square inches.
we apply the scale factor to find the actual area in square feet,
1 inch in the drawing = 8 feet in real life
So, 2 square inches in the drawing = 2 x 8 x 8 = 128 square feet in real life.
Hence, the actual area of the kitchen is 128 square feet.
we also apply the scale factor to find the couch measurement in the scale drawing,
1 inch in the drawing = 8 feet in real life
10 feet in real life = 10/8 = 1.25 inches in the drawing.
In conclusion, the couch measures 1.25 inches across in the scale drawing.
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Use the order of operations to find the value of the expression. 12 ÷ 2 × 3 − ( 7 − 5 ) a. 0 b. 6 c. 16 d. 19
Answer:
Step-by-step explanation:
12 ÷ 2 × 3 − ( 7 − 5 )
= 6 × 3 - 2 (since 7 - 5 = 2)
= 18 - 2
= 16
Answer is C
The value of the expression is 16.
What is the value of the expression 12 ÷ 2 × 3 − (7 − 5) using the order of operations?The order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), is a set of rules used to determine the sequence in which calculations are performed.
In this case, we start with the parentheses first: 7 - 5 = 2. Then, we perform multiplication and division from left to right: 12 ÷ 2 = 6, 6 × 3 = 18. we subtract the result of the parentheses: 18 - 2 = 16. Therefore, the answer is c. 16.
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Find, from first principle the deriva- tive of 1/(x²+1)
Step-by-step explanation:
[tex] \frac{1}{( {x}^{2} + 1) } = \frac{u}{v} [/tex]
u = 1
u' = 0
v = x² + 1
v' = 2x
[tex] \frac{1}{ ({x}^{2} + 1)} \\ = \frac{u'v - v'u}{ {v}^{2} } \\ = \frac{0 - (2x \times 1)}{ {( {x}^{2} + 1)}^{2} } \\ = - \frac{2x}{ { ({x}^{2} + 1) }^{2} } [/tex]
#CMIIWA dessert has both fruit and yogurt inside.Altogether,the mass of the dessert is 185g.The ratio of the mass of fruit to the mass of yogurt is 2:3 What is the mass of yogurt?
The number of fish in a lake is growing exponentially. The table shows the values, in thousands, after different numbers of years since the population was first measured.
years population
0 10
1
2 40
3
4
5
6
By what factor does the population grow every two years? Use this information to fill out the table for 4 years and 6 years.
By what factor does the population grow every year? Explain how you know, and use this information to complete the table
The population grows by a factor of 2 every year.
The number of fish in a lake is growing exponentially, with given data for different numbers of years since the population was first measured as follows:
Years | Population (in thousands)
0 | 10
1 |
2 | 40
3 |
4 |
5 |
6 |
By what factor does the population grow every two years?
From year 0 to year 2, the population grows from 10,000 to 40,000. To find the growth factor, divide the population in year 2 by the population in year 0:
40,000 ÷ 10,000 = 4.
Thus, the population grows by a factor of 4 every two years.
Using this information, we can calculate the population for years 4 and 6:
Year 4: 40,000 × 4 = 160,000 (160 in thousands)
Year 6: 160,000 × 4 = 640,000 (640 in thousands)
By what factor does the population grow every year?
To find the yearly growth factor, take the square root of the growth factor every two years:
√4 = 2.
Thus, the population grows by a factor of 2 every year.
Using this information, we can complete the table:
Years | Population (in thousands)
0 | 10
1 | 20
2 | 40
3 | 80
4 | 160
5 | 320
6 | 640
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Please help!!! Simplify[tex]\frac{\sqrt 7 + \sqrt 3}{2\sqrt 3 - \sqrt 7}[/tex]
The simplified rational expression for this problem is given as follows:
[tex]\frac{3\sqrt{21} + 13}{12}[/tex]
How to simplify the rational expression?The rational expression in the context of this problem is defined as follows:
[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}}[/tex]
The first step in simplifying the expression is removing the root from the denominator, multiplying numerator and denominator by the conjugate, as follows:
[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}} \times \frac{2\sqrt{3} + \sqrt{7}}{2\sqrt{3} + \sqrt{7}}[/tex]
Applying the subtraction of perfect squares, the denominator is given as follows:
2² x 3 - 7 = 12.
The numerator is:
[tex](\sqrt{7} + \sqrt{3})(2\sqrt{3} + \sqrt{7}) = 2\sqrt{21} + 7 + 6 + \sqrt{21} = 3\sqrt{21} + 13[/tex]
Thus the simplified expression is:
[tex]\frac{3\sqrt{21} + 13}{12}[/tex]
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the line is parallel to the graph of 2x-3y=7 and contains the point (-3, -3)
The equation of the line that is parallel to the graph of 2x-3y=7 and contains the point (-3, -3) is expressed as: y = (2/3)x - 1.
What is the Equation of Parallel Lines?To find the equation of a line that is parallel to the graph of 2x - 3y = 7, we need to determine the slope of the given line. We can rewrite the equation in slope-intercept form:
2x - 3y = 7
-3y = -2x + 7
y = (2/3)x - 7/3
This implies that the slope of this line is m = 2/3.
Thus, the equation of the line we are to find will take the following form:
y = (2/3)x + b
where b is the y-intercept of the line.
To find the y-intercept (b), substitute (x, y) = (-3, -3) and m = 2/3 into y = mx + b:
-3 = (2/3)(-3) + b
-3 = -2 + b
b = -1
Substitute m = 2/3 and b = -1 into y = mx + b:
y = (2/3)x - 1
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Lines lll, mmm, and nnn are parallel to each other and ppp is a transversal.
Also, 2\angle{x}=3\angle{y}2∠x=3∠y2, angle, x, equals, 3, angle, y
The measure of angle x is: x = (3/5)(180 - z) = (3/5)(180 - 90) = 36 degrees
And the measure of angle y is:y = (2/5)(180 - z) = (2/5)(180 - 90) = 24 degrees
Since lines lll, mmm, and nnn are parallel to each other and ppp is a transversal, we can use the angle properties of parallel lines to find the relationship between angle x and angle y.
From the given information, we have: 2x = 3y
Simplifying this equation, we get: x = (3/2)y
Now, we can use this relationship to find the measures of angles x and y in terms of a common variable. Let's use z as the common variable.
x + y + z = 180 (angles on a straight line)
Substituting x = (3/2)y, we get: (3/2)y + y + z = 180
Simplifying this equation, we get: (5/2)y + z = 180
Now, we can express y in terms of z:
(5/2)y = 180 - z
y = (2/5)(180 - z)
Similarly, we can express x in terms of z:
x = (3/2)y = (3/2)(2/5)(180 - z) = (3/5)(180 - z)
Now, we can use the relationship between angle x and angle y to find the measure of angle x in terms of z: 2x = 3y
2[(3/5)(180 - z)] = 3[(2/5)(180 - z)]
Simplifying this equation, we get: (6/5)z = 108
z = (5/6)(108) = 90
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multiply the polynomials
To multiply the polynomials (1-2t)(5t+t^2), we can use the distributive property and multiply each term in the first polynomial by each term in the second polynomial:
(1-2t)(5t+t^2) = 1(5t+t^2) - 2t(5t+t^2)
Multiplying the first term by each term in the second polynomial, we get:
5t + t^2
Multiplying the second term by each term in the second polynomial, we get:
-10t^2 - 2t^3
Combining like terms, we get:
-2t^3 - 10t^2 + 5t
Therefore, the answer is D. -2t^3 - 9t^2 + 5t.
Suppose that prices of a gallon of milk at various stores in one town have a mean of $3.75 with a standard deviation of $0.09. using chebyshev's theorem, what is the minimum percentage of stores that sell a gallon of milk for between $3.57 and $3.93? round your answer to one decimal place.
68% of the stores will sell a gallon of milk for between $3.57 and $3.93 with one standard deviation of the mean.
Mean = $3.75
Standard deviation = $0.09.
Selling variations = $3.57 to $3.93.
Chebyshev's theorem states that if k is a positive number, then, in any data at least [tex](1 - 1/k^2)[/tex] of the data will fall in K standard deviations from the mean data.
For normal distributions, 68% of the values will fall within one standard deviation of the mean.
For non-normal deviations, 75% of values will fall within 2 standard deviations of the mean.
Here we need to find the Upper limit and lower limit of the data.
$3.75 - $0.09 = $3.66
$3.75 + $0.09 = $3.84
The price range will be between $3.66 and $3.84.
To calculate the minimum percentage of stores using Chebyshev's theorem
minimum percentage = [tex]1 - 1/k^2[/tex]
minimum percentage = [tex]1 - 1/(1^2)[/tex]
minimum percentage = 0
Here, 0% of stores will fall with only one standard deviation from the Mean.
Therefore, we can conclude that 68% of the stores will sell a gallon of milk for between $3.57 and $3.93.
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Select the correct answer
a mine extracts 2 metric tons of coal in an hour. the
number of hours spent mìning, which expression re
oa. the expression is at. the amount of ore
ob. the expression
The expression that represents the amount of ore sold and how much ore can the mine sell after extracting ore for 12 hours is option B: The expression is 2t−14t. The amount of ore is 21 metric tons.
The reasoning for the selection of the expression and amount of ore can the mine sell after extracting ore for 12 hours is as follows.
1: Determine the amount of coal used for electricity generation in terms of t.
The mine uses 14 tons of coal every hour, so the total amount used for electricity generation is 14t.
2: Determine the total amount of coal extracted in terms of t.
The mine extracts 2 tons of coal every hour, so the total amount extracted is 2t.
3: Calculate the amount of coal sold in terms of t.
To find the amount of coal sold, subtract the amount used for electricity generation from the total amount extracted: 2t - 14t.
4: Determine the amount of coal sold after 12 hours.
Substitute t = 12 into the expression:
2(12) - 14(12) = 24 - 168 = -144.
However, since the mine uses 14 tons of the extracted coal every hour, it cannot sell more coal than it extracts. So, the correct expression should be 2t - 14 (without the t for the amount used for electricity generation).
5: Calculate the amount of coal sold after 12 hours using the corrected expression.
Substitute t = 12 into the expression: 2(12) - 14 = 24 - 14 = 10 metric tons.
The correct expression should be 2t - 14, and the amount of coal the mine can sell after extracting coal for 12 hours is 10 metric tons. Hence, the correct answer is option B.
Note: The question is incomplete. The complete question probably is: A mine extracts 2 metric tons of coal in an hour. The mine uses 14 ton of the extracted coal every hour to generate electricity for the mine and sells the rest. If t is the number of hours spent mining, which expression represents the amount of ore sold? How much ore can the mine sell after extracting ore for 12 hours? A) The expression is 2t−1/4t. The amount of ore is 23 3/4 metric tons. B) The expression is 2t−1/4t. The amount of ore is 21 metric tons. C) The expression is 2t+1/4t. The amount of ore is 24 metric tons. D) The expression is 2t+1/4t. The amount of ore is 24 1/4 metric tons.
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