Arithmetic sequence {12, 5, -2, -9, ...} defined by first term 12 and common difference -7.
What is arithmetic sequence ?
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence.
The sequence {12, 5, -2, -9, -16 ... } can be defined by the following items:
The first term: 12
The common difference: -7
The pattern of adding the common difference to find the next term.
Therefore, all the items that define the sequence are:
The first term: 12
The common difference: -7
This sequence is an arithmetic sequence.
Arithmetic sequence {12, 5, -2, -9, ...} defined by first term 12 and common difference -7.
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5.) On February 3rd, Cardi B borrowed $17,500.00 at 6.5% exact interest to buy a new car. She had to pay back
a maturity value of $17,873.97 to pay off the loan. On what day did Cardi pay back the loan?
Cardi B paid back the loan on February 3rd + 122.72 days = May 16th.
What do you mean by interest?Interest is a fee charged by a lender to a borrower for the use of money. It represents the cost of borrowing money and is typically expressed as a percentage of the loan amount. Interest is paid over a period of time and is calculated based on the principal amount of the loan, the interest rate, and the length of the loan term.
Simple interest is calculated only on the principal amount of the loan, while compound interest is calculated on both the principal and the accumulated interest over time. Compound interest results in a faster growth of the loan balance compared to simple interest.
Let's call the number of days Cardi B had the loan "d". The exact interest can be calculated as follows:
Interest = Principal * Rate * (Number of days / 365)
From the information provided, we know that the maturity value was $17,873.97 and the principal was $17,500.00, so the interest can be calculated as follows:
Interest = $17,873.97 - $17,500.00 = $373.97
We can now use the formula for exact interest to find the number of days:
$373.97 = $17,500.00 * 0.065 * (d / 365)
Solving for d:
d = 365 * ($373.97 / ($17,500.00 * 0.065))
d = 365 * ($373.97 / $1137.50)
d = 365 * (0.3288)
d = 122.72
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the derivative of a function f is given by f′(x)=0.2x e0.15x. which of the following procedures can be used to determine the value of x at which the line tangent to the graph of f has slope 2 ?
Here, we are required to determine at what value of x for x>0 does the line tangent to the graph of f at x have slope 2 of a function
x = 2.29
A line tangent to the graph of f is given by the derivative of the function, f (i.e f')
However, this derivative has been provided in the question as function
f′(x)=0.1x+e(0.25x).
The line tangent to the graph of f will therefore have a slope of 2 at point f′(x) = 2
Therefore, since f′(x) = 2 and f′(x)=0.1x+e(0.25x)
We can then say; 2 = 0.1x + e(0.25x).
This evaluation can then be carried out by the use of a graphing calculator and the value of x (for x > 0) is gotten to be;
x = 2.29
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What numbers are between -1 and 0
construct a truth table for each of these compound propositions. [20 pts.] a. →¬ b. ↔¬ c. ( ∧ ) → ( ∨ ) d. ( →¬) ↔ ( ↔ ) e. ( ↔ ) ⊕ ( ↔¬)
The truth table for each of the given compound propositions.
a. →¬
|A|→¬|A|
|T|F|
|F|T|
The truth table for the compound proposition →¬ can be seen in the table above. It consists of two propositions, an implication and a negation. Implication is denoted by ‘→’, and negation is denoted by ‘¬’. The implication is read as ‘if A then not A’, and the negation is read as ‘not A’. The implication is true when the antecedent is false, and the consequent is true. In this case, the antecedent is A, and the consequent is not A. Therefore, the implication is true when A is false and not A is true. This can be seen in the truth table above, where A is false and not A is true, thus making the implication true.
b. ↔¬
|A|↔¬|A|
|T|F|
|F|T|
The truth table for the compound proposition ↔¬ can be seen in the table above. It consists of two propositions, a biconditional and a negation. The biconditional is denoted by ‘↔’, and the negation is denoted by ‘¬’. The biconditional is read as ‘if and only if A then not A’, and the negation is read as ‘not A’. The biconditional is true when the antecedent and consequent are both true or both false. In this case, the antecedent is A, and the consequent is not A. Therefore, the biconditional is true when A is false and not A is true. This can be seen in the truth table above, where A is false and not A is true, thus making the biconditional true.
c. (∧ ) → ( ∨ )
|A|B|(∧) → (∨)|
|T|T|T|
|T|F|F|
|F|T|T|
|F|F|T|
The truth table for the compound proposition (∧ ) → ( ∨ ) can be seen in the table above. It consists of two propositions, an implication and a conjunction. The implication is denoted by ‘→’, and the conjunction is denoted by ‘∧’. The implication is read as ‘if A and B then A or B’, and the conjunction is read as ‘A and B’. The implication is true when the antecedent is true, and the consequent is true. In this case, the antecedent is A and B, and the consequent is A or B. Therefore, the implication is true when A and B are both true or both false. This can be seen in the truth table above, where A and B are both true or both false, thus making the implication true.
d. ( →¬) ↔ ( ↔ )
|A|B|(→¬)↔ (↔)|
|T|T|T|
|T|F|F|
|F|T|F|
|F|F|T|
The truth table for the compound proposition ( →¬) ↔ ( ↔ ) can be seen in the table above. It consists of two propositions, a biconditional and an implication. The biconditional is denoted by ‘↔’, and the implication is denoted by ‘→’. The biconditional is read as ‘if and only if A then not B’, and the implication is read as ‘if A then not B’. The biconditional is true when the antecedent and consequent are both true or both false. In this case, the antecedent is A, and the consequent is not B. Therefore, the biconditional is true when A is true and not B is false, or when A is false and not B is true. This can be seen in the truth table above, where A is true and not B is false, or when A is false and not B is true, thus making the biconditional true.
e. ( ↔ ) ⊕ ( ↔¬)
|A|B|(↔)⊕ (↔¬)|
|T|T|F|
|T|F|T|
|F|T|T|
|F|F|F|
The truth table for the compound proposition ( ↔ ) ⊕ ( ↔¬) can be seen in the table above. It consists of two propositions, an exclusive-or and a biconditional. The exclusive-or is denoted by ‘⊕’, and the biconditional is denoted by ‘↔’. The exclusive-or is read as ‘A or B, but not both’, and the biconditional is read as ‘if and only if A then not B’. The exclusive-or is true when either the antecedent or the consequent is true, but not both. In this case, the antecedent is A, and the consequent is not B. Therefore, the exclusive-or is true when either A is true and not B is false, or when A is false and not B is true. This can be seen in the truth table above, where either A is true and not B is false, or when A is false and not B is true, thus making the exclusive-or true.
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the right-hand side of the gompertz equation is f (y ) = r y ln( k y ). find the first four terms of the taylor series for this f (y ) about y = k by using the formula we found in example 2, (3).
The first four terms of the Taylor series for the right-hand side of the Gompertz equation, f(y) = ry ln(ky), about y = k is: f(y) = rk ln(kk) + (y - k)(2r) + (y - k)² / 2! (r / k) + (y - k)³ / 3! (-r / k²).
To determine this :
The right-hand side of the Gompertz equation is f(y) = ry ln(ky). To find the first four terms of the Taylor series for this f(y) about y = k, we can use the formula:
f(y) = f(k) + (y - k)f'(k) + (y - k)² / 2! f''(k) + (y - k)³ / 3! f'''(k) + ...
Where f'(k), f''(k), and f'''(k) are the first, second, and third derivatives of f(y) evaluated at y = k, respectively.
First, we need to find the derivatives of f(y):
f'(y) = r ln(ky) + r
f''(y) = r / y
f'''(y) = -r / y²
Next, we evaluate these derivatives at y = k:
f'(k) = r ln(kk) + r = 2r
f''(k) = r / k
f'''(k) = -r / k²
Finally, we substitute these values into the Taylor series formula:
f(y) = f(k) + (y - k)f'(k) + (y - k)² / 2! f''(k) + (y - k)³ / 3! f'''(k)
f(y) = rk ln(kk) + (y - k)(2r) + (y - k)² / 2! (r / k) + (y - k)³ / 3! (-r / k²)
This is the first four terms of the Taylor series for f(y) about y = k.
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PLSSS HELP I WILL GIVE BRAINLIESTT
The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. If P(terriers) = 50%, interpret the likelihood of randomly selecting a terrier from the shelter.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event
Answer:
Equally likely and Unlikely, I would say.
Step-by-step explanation:
Think about it. You have a 50/50 chance of getting a terrier. 50 and 50 are equal. Likely and Unlikely. I'd say that's the answer and that's my reasoning.
Answer:
likely
the answer is ^
give three examples of irrational numbers including one irrational number greater than 5
Answer:
Step-by-step explanation:
Pi (π) is an irrational number that represents the ratio of the circumference of a circle to its diameter. Pi cannot be expressed as a simple fraction, so it's an irrational number. Pi is approximately equal to 3.14159...
The square root of 2 is another example of an irrational number. This number cannot be expressed as a simple fraction either, so it's also irrational. The square root of 2 is approximately equal to 1.41.
The number e is greater than 5 and is also an irrational number. e represents the base of the natural logarithm and is approximately equal to 2.71828...
Which of the following equations is written in the standard form of linear equations with two variables?
a. 7x + 2y = 1
b. 9x, 2, + 7 = 5
c. 5x, 3, -2 = 0
d. 4x2 + 7y = 5
7x+2y=1 is the formula used to represent linear equations in two variables.
What are the two forms of linear equations in two variables?Different forms, including standard form, intercept form, and point-slope form, are possible for a linear equation with two variables. For instance, the identical equation 2x+3y=9 can be shown in each of the following forms: 2x+3y-9=0 (standard form), y = (-2/3)x + 3, and y - 5/3 = -2/3(x + (-2)). (point-slope form).ax + by + c = 0, where a 0, and b 0, is the form of a two-variable linear equation. A x + B y = C is the conventional form of a two-variable linear equation, where A, B, and C are real numbers and x, y are variables.The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.To learn more about linear refer to:
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what variables do you think caesars should use to predict the number of check-ins on a given day?
Caesars should use variables such as weather, season, holidays, local events, and occupancy rate to predict check-ins.
1. Weather: The weather conditions on a given day can impact the number of check-ins, as people may be less likely to travel or spend time outdoors in inclement weather.
2. Season: The time of year can also play a role in the number of check-ins, as some seasons may be busier than others due to holidays or peak travel times.
3. Holidays: Holidays can have a significant impact on the number of check-ins, as people may travel more during these times for vacation or to visit family.
4. Local events: Any local events taking place near the Caesars property, such as concerts or sporting events, could also impact the number of check-ins.
5. Occupancy rate: The occupancy rate of the Caesars property on previous days can also provide insight into the expected number of check-ins for a given day, as it can indicate trends or patterns in customer behavior.
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debras rectangular vegetable garden measures 9 1/3 yard by 12 yard a bottle of fertilizer costs $14.79 if debra needs to mix 1/8 cups of fertilizer with water for each square yard of her garden how many cups of fertilizer does she need
The amount of fertilizer Debra needs is 14 cups.
What is Area?Area of a two dimensional shape is the total region which is bounded by the object's shape.
Given that,
Debra's rectangular vegetable garden measures 9 1/3 yard by 12 yard.
Area of a rectangle = Length × Width
Area of the rectangular garden = 12 × 9 1/3
= 12 × 28/3
= 112 square yard
Number of cups of fertilizer needed for 1 square yard = 1/8 cups
Number of cups of fertilizer needed for 112 square yard = (1/8) × 112
= 14 cups
Hence 14 cups of fertilizer are needed for the whole garden.
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Calculator What is the area of the trapezoid with height 10 units? Enter your answer in the box. units² 10 12 5 12
Based on the information, we can infer that the area of this trapezoid is 192 in² (option D).
How to calculate the area of this trapezoid?To calculate the area of the trapezoid it is necessary to know the length of the bases and the height. Once we know these data we can complete the following formula to find the area:
A = 1/2 (b1 + b2) h
b1 = length of the lower base
b2 = length of the upper base
h = height
So, we just have to plug in the values to find the area of this trapezoid.
A = 1/2 (18in + 14in) 12in
A = 192in²
Based on the above, the area of this trapezoid would be 192 in² (option D).
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find the equation of the sphere if one of its diameters has endpoints
The equation of the sphere with the given endpoints is: (x - x0)² + (y - y0)² + (z - z0)² = r²
where x0 = (x1 + x2) / 2, y0 = (y1 + y2) / 2, z0 = (z1 + z2) / 2, and r = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²) / 2.
The Sphere is what?All points on a sphere are at a set distance from the centre, making it a three-dimensional geometric object. It is thought to be one of the most basic three-dimensional shapes and is a perfect circle.
A sphere with centre (x, y, z) and radius r has the equation:
(x - x0)² + (y - y0)² + (z - z0)² = r²
If one of the diameters of the sphere has endpoints (x1, y1, z1) and (x2, y2, z2), then the center of the sphere can be found by finding the midpoint of the two endpoints:
x0 = (x1 + x2) / 2
y0 = (y1 + y2) / 2
z0 = (z1 + z2) / 2
The radius can be found by finding the distance between the two endpoints:
r = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²) / 2
Therefore, the equation of the sphere with the given endpoints is:
(x - x0)² + (y - y0)² + (z - z0)² = r²
where x0 = (x1 + x2) / 2, y0 = (y1 + y2) / 2, z0 = (z1 + z2) / 2, and r = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²) / 2.
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4 1/4 x 2/3 i have to solve using an area model
The area of the phrase 1 3/4 X 2 1/2 when using an area model is 4 3/8.
How does the area model work?A method of dividing an area into smaller portions is the area model.The example provided below,
Distance = 27 = 20 + 7
length = 63 = 60 + 3
Area = (20 + 7) x (60 + 3)
= 1200 + 60 + 420 +21
= 1701 unit²
You can solve using an area model.
Ours was given
It follows that the area of the expression 1 3/4 X 2 1/2 using an area model is 4 3/8.
The complete question is,
You can solve using an area model. 1 3/4 X 2 1/2
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6. A recipe calls for 2/3 cup strawberries, 1/4 cup sugar, 1/2 cup walnuts, and 3/4 cup of
flour. Order the amounts from least to greatest. Which ingredient does the recipe require the least amount of? Explain how you know.
Answer:
1. Order from least to greatest: 1/4 cup sugar, 1/2 cup walnuts, 2/3 cup strawberries, 3/4 cup of flour
2. Sugar is the ingredient the recipe requires the least amount
Step-by-step explanation:
1.
2/3 cup of strawberries, 1/4 cup sugar, 1/2 cup walnuts, and 3/4 cup of
flour.
8/12 cup of strawberries, 3/12 cup sugar, 6/12 cup walnuts, and 9/12 cup of flour
Order from least to greatest: 1/4 cup sugar, 1/2 cup walnuts, 2/3 cup strawberries, 3/4 cup of flour
2.
Sugar is the ingredient the recipe require the least amount
Question content area top
Part 1
Suppose a city with population 700,000 has been growing at a rate of 7% per year. If this rate continues, find the population of this city in 21 years.
Based on exponential growth, city with a population of 700,000 growing at an annual rate of 7% will be 2,898,394 in 21 years.
What is the exponential growth?Exponential growth refers to an increase where a constant proportional amount is added to the initial value.
Exponential growth function can be modeled as follows:
f(x)=a(1+r)ˣ
Where:
f(x) = exponential growth function
a = initial amount
r = growth rate
{x} = number of time intervals
The current population of the city, a = 700,000
The annual growth rate, r = 7% = 0.07
The number of time intervals, x = 21 years
The population in 21 years = 700,000 x (1 + 0.07)²¹
= 700,000 x (1.07)²¹
= 700,000 x 4.14056237
= 2,898,394
Thus, using an exponential growth rate, the population of the city will grow to 2,898,394 after 21 years.
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Select the correct answer.
Which equation is equivalent to the formula below?
An equation y = a(x - h)² + k is equivalent to the formula a = (y - k)/(x - h)², So Option D is correct
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
The equation,
y = a(x - h)² + k
Equivalent equation = ?
by using rules of algebra, we can transform given equation,
the rules of algebra
1. If a number is in division operation then when it goes to another side of equal to, it will be in multiplication operation or vice-versa.
2. If a number is in addition operation then when it goes to another side of equal to, it will be in subtraction operation or vice-versa.
So,
by transferring k to the left hand side,
y - k = a(x - h)²
Now, by transferring (x - h)² to the left hand side,
(y - k)/(x - h)² = a
Hence, the equivalent equation is, a = (y - k)/(x - h)²
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Learning task 1 be referring them to each pair in letter i do the following a find the sum of each pair of radical be subtract the first radical from the second radical c find the product of each pair of radicals be divided the second radical by the radical
For task 1, you need to find the sum of each pair of radicals, subtract the first radical from the second radical, and then find the product of each pair of radicals by dividing the second radical by the first. For example:
let a = 5, b = 10
let sumRadicals = a + b // 15
let differenceRadicals = b - a // 5
let productRadicals = differenceRadicals / a // 1
To further develop this topic, you can explore how to use radicals to simplify expressions, such as removing perfect squares from inside radical expressions and rationalizing denominators. You can also look into how to multiply and divide radical expressions, as well as examples of more complex equations involving radicals.
Additionally, you can look into how to use the properties of radicals, such as the first and second properties, to simplify radical equations.
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what does the following code do? const int size = 5; double x[size]; for (int i = 2; i <= size; i ) { x[i] = 0.0; }
const int size = 5; double x[size]; for (int i = 2; i <= size; i ) { x[i] = 0.0; }
An error will occor during runtime.
What is Errors in Coding ?A runtime coding mistake occurs when the computer crashes due to anything confusing it. Your instructions can be in the wrong sequence or depend on a phase that hasn't happened yet, for instance. Or perhaps you asked the machine to perform an impossible task.
Runtime errors, logic errors, and syntax errors are the three sorts of problems that might arise when writing programs.
A logic error is a programming flaw that makes a program run improperly but not abnormally. A logic mistake may not always be obvious because it creates unwanted or undesirable output or other behaviors.
A syntax error is a mistake in the order in which a group of letters or tokens should be typed while using a certain computer language. Syntax mistakes in compiled languages are found during compilation. After fixing all syntax issues, a program will compile.
While running the statement :
const int size = 5; double x[size]; for (int i = 2; i <= size; i ) { x[i] = 0.0; }
An error will occor during runtime.
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How much is a nickel,dime,penny,quarter
Answer:
0.41 cents if youre adding
Step-by-step explanation:
jan and judy are two math geniuses. jan calculates the probability that three distinct numbers chosen at random without replacement from the set below would have an even sum. judy calculates the probability that three distinct without replacement numbers chosen at random from the set below would have an even product. what is the positive difference between the two probabilities they calculate (assuming they did so correctly!)? express your answer as a common fraction. {2, 3, 5, 7, 8, 9, 10}
The positive difference between the two probabilities is 11/35.
To calculate the probability that three distinct numbers chosen at random without replacement from the set would have an even sum, Jan would consider the number of ways to choose three even numbers (4 choose 3) and divide that by the total number of combinations of three numbers (7 choose 3).
To calculate the probability that three distinct numbers chosen at random without replacement from the set would have an even product, Judy would consider the number of ways to choose three numbers such that the product is even (3 choose 2) and divide that by the total number of combinations of three numbers (7 choose 3).
The positive difference between the two probabilities would be the difference between these two calculations. In this case, 11/35 is a positive difference, meaning that the probability of having an even product is 11/35 higher than the probability of having an even sum.
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Find the value of k, for which one root of the quadratic equation kx2 -14x+8=0 is six times the other.
Answer:
The value of k for which one root of the quadratic equation kx2 -14x+8=0 is six times the other is k = 2.
Step-by-step explanation:
4.) Lady GaGa wants to borrow $2,600 for 90 days to pay her real estate tax. State Savings and Loan charges
7.25% ordinary interest while Security Bank charges 7.5% exact interest. Which bank is a better deal and how
much will she save by choosing that bank?
Interest is a fee charged by a lender to a borrower for the use of money. It is a percentage of the principal amount (the amount borrowed) that is added to the principal over a specified period of time. The interest rate is the rate at which the interest is calculated, and it is typically expressed as an annual percentage rate (APR).
For example, if you borrow $1000 at an interest rate of 5% per year, the interest charge for one year would be $50 ($1000 * 5%). The interest and the principal form the total amount that must be repaid at the end of the loan term.
Interest can be charged on loans, such as personal loans, mortgages, and car loans, as well as on savings accounts and other investments. The purpose of charging interest is to compensate the lender for the opportunity cost of not having access to the funds during the loan term.
Let's calculate the interest charge for each bank:
For State Savings and Loan:
Interest = 2600 * 7.25% * 90/365 = $121.44
For Security Bank:
Interest = 2600 * 7.5% * 90/365 = $122.62
So, Security Bank is charging higher interest and is not a better deal.
If Lady GaGa chooses State Savings and Loan, she will save:
$122.62 - $121.44 = $1.18.
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suppose you constructed a frequency table from a data set with 6 classes, class width of 6, and minimum value of 12. assuming the data set only contains whole numbers, what is the largest possible value in the data set?
Given the class width of 6 and the minimum value of 12, the maximum value in the first class would be 12 + 6 - 1 = 17. The maximum value in the 6th and last class would be 17 + (6 x 5) = 42. Hence, the largest possible value in the data set is '42'.
A frequency table is used to organize and represent the distribution of a set of data. In this case, the data set has 6 classes and a class width of 6. This means that the range of values in each class is 6 units. The minimum value in the data set is 12, so the first class starts at 12 and ends at 12 + 6 - 1 = 17. This is because the class width is 6, so the end value of the first class would be the starting value plus the class width minus 1.
For the last class, the end value would be 17 + (6 x 5) = 42. This is because the end value of the first class is 17 and each subsequent class increases by 6 units. The largest possible value in the data set would be the end value of the last class, which is 42. This means that any value greater than 42 would not be part of the data set and would not be included in the frequency table.
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The diagonals of rectangle. QRST intersect at P. Given that m<PTS = 34° and QS=10 , find QP.
If the diagonals of rectangle QRST intersect at P, given that m<PTS = 34° and QS=10, QP is:
34.9°
The diagonals of a rectangle bisect each other. Therefore, the angle at P can be split into two equal angles, each measuring (m<PTS)/2
= 34°/2
= 17°.
Since QP is the hypotenuse of a right triangle with angles 17° and 63° (the sum of the angles in a rectangle is 180°), we can use the tangent function to find QP:
tan(17°) = QP/10Solving for QP, we have:QP = 10 * tan(17°)= 34.9391564547So, QP is 34.9°.
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the last digit of the heights of statistics students were obtained as part of an experiment conducted for a class. use the following frequency distribution to construct a histogram. what can be concluded from the distribution of the digits? specifically, do the heights appear to be reported or actually measured?
The frequency distribution of the digits indicates that the heights were reported rather than actually measured. This is because the frequency of the digits is not evenly distributed, which would be expected for a set of actual measurements.
Frequency Distribution:
Digit Frequency
0 3
1 5
2 9
3 5
4 3
5 4
6 4
7 4
8 2
9 1
From the distribution of the digits, it appears that the heights were reported rather than actually measured. This is because the frequency of the digits is not evenly distributed, which would be expected for a set of actual measurements.
The frequency distribution of the digits indicates that the heights were reported rather than actually measured. This is because the frequency of the digits is not evenly distributed, which would be expected for a set of actual measurements. For example, the frequency of the digit '2' is more than twice as high as the frequency of the digits '1' and '3', which is not likely to occur in a set of actual measurements.
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The velocity v in feet per second of a freely falling object that has fallen h feet can be represented by v=8h1/2. Find the velocity of an object if it has fallen a distance of 144 ft
Therefore , the solution of the given problem of velocity comes out to be 33.94 ft/sec is the velocity.
Define velocity.Looking at something from a distance allows us to calculate its speed. An object's speed determines how far it can travel in a certain amount of time. Utilizing the equation velocity = distance/time, velocity is computed. Miles per hour (mph), kilometers an hour (km/h), and meters a second (m/s) are the three most common units of speed (mph).
Here,
Given :
=> v = (8h) ^ 1/2
=> v = √8h
We separate the variables whose values we want to be determined in the aforementioned problems.
(1) We change the variable to become
v = √8h in order to solve for v.
Using the supplied as a replacement,
v = √8 * 144 = 33.94 ft/sec
Therefore , the solution of the given problem of velocity comes out to be 33.94 ft/sec is the velocity.
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Please help with problem
21x>5y+49x>2y>2-28x>2y
A point in the solution of the system of inequalities is (2, 0.5)
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
21x>5y+49x>2y>2-28x>2y
Express properly
So, we have the following representation
21x > 5y+49
x > 2y
2 - 28x > 2y
Next, we plot the graphs of the inequality expressions on a plane
(See attachment for the graph)
The shaded region represent the solution
And a point in this region is (2, 0.5)
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Explain why −4 = [tex]\sqrt{2-x}-2[/tex] has no real solution
The square root of a negative number is not a real number, the equation has no real solution.
How true is the assertion?The equation −4 = √(2-x)−2 has no real solution because the square root of a negative number is not a real number.
If we expand the equation, we get:
-4 = √(2-x) - 2
-4 + 2 = √(2-x)
-6 = √(2-x)
Squaring both sides of the equation, we get:
36 = 2-x
x = -34
Since the square root of a negative number is not a real number, the equation has no real solution.
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A store orders a batch of 2000 flashlights. The odds that a flashlight is defective are 0.15%. Let X be the number of defective flashlights in the batch. (a) What is the distribution of X? What is/ are the value(s) of the paramter(s) of this distribution? (b) What are expected value and standard deviation of X? (c) What is the probability that the batch contains no defective flashlights? One defective flashlight? More than two defective ones?
X follows a binomial distribution with n = 2000 and p = 0.0015. The chance that the batch contains no faulty flashlights is 0.8805 percent. The likelihood of one faulty flashlight in the batch is 1.5307. X has a standard deviation of 1.0708. The likelihood of more than two faulty flashlights in the batch is 0.0388.
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Here,
(a) X has a binomial distribution with parameters n = 2000 and p = 0.0015. The binomial distribution is a discrete probability distribution that describes the number of successes in n independent Bernoulli trials, each with success probability p.
(b) The expected value (mean) of X is given by E(X) = n * p = 2000 * 0.0015 = 3. The standard deviation of X is given by sqrt(n * p * (1 - p)) = sqrt(2000 * 0.0015 * 0.9985) = 1.0708.
(c) The probability that the batch contains no defective flashlights is given by P(X = 0) = (2000 choose 0) * 0.0015^0 * (0.9985)^2000 = 0.8805. The probability that the batch contains one defective flashlight is given by P(X = 1) = (2000 choose 1) * 0.0015^1 * (0.9985)^1999 = 1.5307. The probability that the batch contains more than two defective flashlights is given by P(X > 2) = 1 - P(X <= 2) = 1 - P(X = 0) - P(X = 1) - P(X = 2) = 0.0388.
X has a binomial distribution with parameters n = 2000 and p = 0.0015. The probability that the batch contains no defective flashlights is 0.8805.The probability that the batch contains one defective flashlight is 1.5307. The standard deviation of X is 1.0708. The probability that the batch contains more than two defective flashlights is 0.0388.
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Connie says that she can use the equation 6^2+5^2=c2 to find the distance between points X and Y in the diagram at the right
Do you agree with Connie? Explain why or why not.