Answers
The correct answer is: d. x → -1 Simplifying further, we get: [tex]\frac{1}{2}+7[/tex] Which equals [tex]\frac{15}{2}[/tex]. d. x → -1
To find the limit of the expression [tex](\frac{x^2}{2} ) - (\frac{7}{x} )[/tex] as x approaches a specific value, we substitute that value into the expression.
a. x → 0:
[tex]lim (\frac{x^2}{2} ) - (\frac{7}{x} ) x \rightarrow 0[/tex]
Substituting x = 0 into the expression results in an undefined expression since division by zero is not defined. Therefore, the limit in this case is undefined.
b. x → 0:
[tex]lim (\frac{x^2}{2} ) - (\frac{7}{x} ) x \rightarrow 0[/tex]
Using L'Hôpital's rule, we can differentiate the numerator and denominator and evaluate the limit again.
[tex]lim[/tex]([tex]\frac{2x}{2}[/tex]) - ([tex]\frac{7}{1}[/tex]) as x → 0
Simplifying further, we get:
lim x - 7 as x → 0
Substituting x = 0, we find that the limit is -7.
c. x → 3/14:
lim ([tex](\frac{x^2}{2} ) - (\frac{7}{x} ) x\rightarrow \frac{3}{14}[/tex]
Substituting x = 3/14 into the expression gives:
[tex]\frac{\frac{3}{14}^2 }{2}-\frac{ 7}{\frac{3}{14} }[/tex]
Simplifying this expression, we find that the limit evaluates to [tex]\frac{-77}{6}[/tex]
d. x → -1:
[tex]lim (\frac{x^2}{2} ) - (\frac{7}{x} ) x \rightarrow 0[/tex]
Substituting x = -1 into the expression gives:
[tex]\frac{-1^2}{2} - (\frac{7}{-1} )[/tex]
Simplifying further, we get:
[tex]\frac{1}{2}+7[/tex]
Which equals [tex]\frac{15}{2}[/tex]
Therefore, the correct answer is:
d. x → -1
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Related Questions
Sample Answer: The vertical line test determines if one input has exactly one output on the graph. If any vertical line passes through more than one point on the graph, then the relation is not a function.
Which did you include in your response?
Draw vertical lines to intersect on a graph.
The relation is a function if there’s only one point of intersection on a graph.
The relation is not a function if there’s more than one point of intersection on a graph.
The vertical line test is used to determine if each input has exactly one output.
Answers
Answer: All of the choices in the response would be correct.
Step-by-step explanation:
100 Points! Geometry question. Photo attached. Only looking for an answer to B. Please show as much work as possible. Thank you!
Answers
The measure of the length VT from the diagram is 5.4
Triangular geometry and similarity theoremFrom the given diagram, we can see that the triangle TSR and TUV are similar, hence the correct expressed needed to determine the value of x is given as:
6/x+2 = 14/4x-1
Cross multiply to have
6(4x - 1) = 14(x + 2)
24x - 6 = 14x + 28
24x - 14x = 28 + 6
Simplify to have:
10x = 34
x = 3.4
Determine the measure of VT
VT = x + 2
VT = 3.4 + 2
VT = 5.4
Hence the measure of VT from the diagram is 5.4
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The difference of the present ages of the two brothers is 5 years . 6 years ago , if the product of their ages was 696, find the ratio of present age of elder brother and the younger brother.
Answers
The present age of the elder brother is in a ratio of 23 to the present age of the younger brother, which can be simplified to a ratio of 5 to 4.
Let's assume the present age of the elder brother is E years, and the present age of the younger brother is Y years. According to the given information, the difference in their ages is 5 years, which can be expressed as E - Y = 5.
Six years ago, the elder brother's age was E - 6, and the younger brother's age was Y - 6. According to the second given condition, the product of their ages at that time was 696, which can be expressed as (E - 6)(Y - 6) = 696.
To find the ratio of their present ages, we need to solve the two equations simultaneously. We can start by expanding the second equation:
(E - 6)(Y - 6) = 696
EY - 6E - 6Y + 36 = 696
EY - 6E - 6Y = 660
Now we can substitute the value of E - Y from the first equation into the second equation:
(E - Y) - 6E - 6Y = 660
5 - 6E - 6Y = 660
-6E - 6Y = 655
Simplifying the equation:
6E + 6Y = -655
Now we have a system of linear equations:
E - Y = 5
6E + 6Y = -655
Solving these equations, we find that the present age of the elder brother (E) is 23 years and the present age of the younger brother (Y) is 18 years.
Therefore, the ratio of the present age of the elder brother to the younger brother is 23:18, which can be simplified to 5:4.
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Which two of the following are not characteristics of surveys?
A. The study involves one or more treatment groups and a control
group.
B. The study compares two or more treatments.
C. Statistical analysis is applied to the results of the study.
D. Data are gathered during the course of the study.
Answers
Answer: A and B are not characteristics of surveys.
Step-by-step explanation: A survey is a type of research method that involves collecting data from a sample of individuals or groups, usually by asking them questions or observing their behavior. Surveys can be used to describe, compare, or explain various aspects of a population or phenomenon of interest.
Some of the common characteristics of surveys are:
They use a predefined set of questions or items that are standardized and consistent for all respondents or participants.They use a sampling technique to select a representative subset of the population or target group that is relevant to the research question or objective.They use a mode of data collection that is suitable for the type and format of the questions or items, such as face-to-face interviews, telephone interviews, mail questionnaires, online surveys, etc.They use statistical analysis to summarize, describe, compare, or infer the results of the data collected from the sample to the population or target group.Some of the types of research methods that involve one or more treatment groups and a control group, and that compare two or more treatments, are:
Experiments: Experiments are research methods that involve manipulating one or more independent variables (the treatments) and measuring their effects on one or more dependent variables (the outcomes). Experiments aim to establish causal relationships between variables by controlling for other factors that may influence the results. Experiments usually involve random assignment of participants to different treatment groups and a control group that receives no treatment or a placebo.Quasi-experiments: Quasi-experiments are research methods that resemble experiments but lack some of the features of true experiments, such as random assignment or manipulation of variables. Quasi-experiments aim to estimate causal relationships between variables by using natural or existing variations in the independent variables (the treatments) and comparing their effects on the dependent variables (the outcomes). Quasi-experiments usually involve non-equivalent groups that differ in their exposure to the treatments or in other characteristics that may affect the results.Observational Studies: Observational studies are research methods that involve observing and measuring existing phenomena without manipulating any variables. Observational studies aim to describe, compare, or correlate variables by using natural or existing data sources. Observational studies usually involve different groups that are selected based on their exposure to the variables of interest or based on other criteria that may affect the results.Hope this helps, and have a great day! =)
Which algebraic expression is a polynomial with a degree of 2?
O4x³-2x
O 10x²-√x
O 8x³+ 5 +3
6x² - 6x + 5
Answers
6x² - 6x + 5 is the algebraic expression that is a polynomial with a degree of 2.
The algebraic expression that is a polynomial with a degree of 2 is:
6x² - 6x + 5
A polynomial expression is a sum of terms where each term consists of a coefficient multiplied by one or more variables raised to non-negative integer exponents. The degree of a polynomial is determined by the highest exponent of the variable in any term of the polynomial.
In the expression 6x² - 6x + 5, the highest exponent of the variable x is 2 in the term 6x². The other terms have lower exponents, with -6x having an exponent of 1 and 5 having an exponent of 0. Therefore, the degree of the polynomial is 2, which is the highest exponent in the expression.
Hence, 6x² - 6x + 5 is the algebraic expression that is a polynomial with a degree of 2.
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Please help with the attached math problem…
Answers
The missing values for the inverse matrix A⁻¹ are:
a = -78b = 2c = 59d = 20e = -3The solution is:
x = -9200y = 7025z = 2375.How to convert the system of equations to matrix form?In Mathematics and Geometry, a square matrix refers to a type of matrix that is composed of an equal number of both rows and columns. Generally speaking, m × m matrix is typically referred to as a square matrix of order m.
Next, we would convert the system of three linear equations in standard form to matrix form as follows;
[tex]\left[\begin{array}{ccc}1&1&1\\10&-20&98\\5&10&-10\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}200\\250\\500\end{array}\right][/tex]
By using technology, the solutions to this system of three linear equations include the following:
x = -9200
y = 7025
z = 2375.
By using technology, the inverse of this matrix is given by;
[tex]A^{-1}=\left[\begin{array}{ccc}-78&2&11.8\\59&-1.5&-8.8\\20&-0.5&-3\end{array}\right][/tex]
Therefore, the missing values are as shown in the inverse of this matrix A⁻¹ above.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
x = 42
y = 21
Step-by-step explanation:
Since its a right triangle, we have:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
[tex]sin (60) = \frac{21\sqrt{3} }{x} \\\\x= \frac{21\sqrt{3} }{sin (60)} \\\\x= \frac{21\sqrt{3} }{\frac{\sqrt{3} }{2} } \\\\x = \frac{21\sqrt{3} *2 }{\sqrt{3} } \\\\x = 21*2\\\\x = 42[/tex]
[tex]cos (60) = \frac{y}{x}\\\\cos (60) = \frac{y}{42}\\\\y = cos (60)*42 \\\\y = \frac{1}{2} * 42\\\\y = 21[/tex]
In a class of students, the following data
table summarizes how many students have a
cat or a dog. What is the probability that a
student chosen randomly from the class has
a cat?
Has a dog
Does not have a
dog
Has a cat
2
3
Does not have a
cat
12
10
Answers
The table can be summarized as follows:
| | Has a dog | Does not have a dog |
|----------|-----------|---------------------|
| Has a cat | 2 | 3 |
| Does not have a cat | 12 | 10 |
To find the probability that a student chosen randomly from the class has a cat, we need to find the total number of students who have a cat (regardless of whether or not they have a dog), and divide it by the total number of students in the class.
The number of students who have a cat is 2 (those who have a dog and a cat) + 3 (those who have a cat but do not have a dog) = 5.
The total number of students in the class is the sum of all four categories: 2 (has a cat and a dog) + 3 (has a cat, does not have a dog) + 12 (does not have a cat, has a dog) + 10 (does not have a cat, does not have a dog) = 27.
So, the probability that a student chosen randomly from the class has a cat is 5/27.
saleswoman sells a dried-fruit mixture for $ 5.90 per pound and nuts for $ 14. 75per pound. She wants to blend the two to get a -15lb mixture that she will sell for $ 9.44per pound. How much of each should she use? Solve using matrices.
To get a 15-lb mixture, she should use enter your response here( = -lb )of dried-fruit mixture and enter your response here( = lb )of nuts.
Answers
A 15-lb mixture, she should use 1.256 pounds of dried-fruit mixture and 13.744 pounds of nuts.
Based on the given information, we can set up the following system of equations:
Equation 1: x + y = 15 (since the total weight of the mixture is 15 pounds)
Equation 2: (5.90 * x) + (14.75 * y) = 9.44 * 15 (since the total cost of the mixture is the cost per pound multiplied by the weight of each component)
Now, let's convert this system of equations into matrix form:
| 1 1 | | x | | 15 |
| 5.90 14.75 | | y | = | 9.44 * 15 |
To solve for x and y, we can use matrix algebra. We can multiply the inverse of the coefficient matrix by the right-hand side matrix to get the solution matrix:
| x | | 1 1 |^-1 | 15 |
| y | = | 5.90 14.75 | | 9.44 * 15 |
Using matrix calculations, we find that the inverse of the coefficient matrix is:
| 0.0877 -0.0576 |
| -0.0059 0.0678 |
Now, multiplying the inverse matrix by the right-hand side matrix gives us:
| x | | 0.0877 -0.0576 | | 15 |
| y | = | -0.0059 0.0678 | * | 9.44 * 15 |
Simplifying the multiplication gives us:
x = 1.256
y = 13.744
Therefore, the saleswoman should use 1.256 pounds of dried-fruit mixture and 13.744 pounds of nuts to get a 15-pound mixture.
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Graph the linear equation. Find three points that solve the equation, then plot on the graph. -5x-3y=-7
Answers
Answer:
The given linear equation is -5x-3y=-7. To graph the equation, we need to find three points that satisfy the equation and then plot them on the graph.
Let's find the x and y intercepts first.
At x = 0, we have -3y = -7, which gives us y = 7/3. So the y-intercept is (0, 7/3).
At y = 0, we have -5x = -7, which gives us x = 7/5. So the x-intercept is (7/5, 0).
Now, let's choose another point. We can choose any value for x or y and solve for the other variable. Let's take x = 1.
-5(1) - 3y = -7
-3y = -2
y = 2/3
So the third point is (1, 2/3).
Now we can plot these three points on the graph and draw a line passing through them.
Here's the graph:
|
|
| . (1, 2/3)
|
| .
| (0, 7/3)
|
|_________________________
| |
7/5 -7/15
Step-by-step explanation:
Already explained
The figure is a parallelogram. One diagonal measures 28 units. A parallelogram is shown. It has side lengths 21, 20, 21, and 20. The length of a diagonal is 28. Is the figure a rectangle? Explain. No, it is not a rectangle because the diagonals are congruent. No, it is not a rectangle because the sides of the parallelogram do not meet at right angles. Yes, it is a rectangle because the diagonals are congruent. Yes, it is a rectangle because the sides of the parallelogram do meet at right angles.
Answers
No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.
A rectangle is a special type of parallelogram where all angles are right angles (90 degrees).
In the given figure, although the diagonals are congruent (one diagonal measures 28 units), this alone does not guarantee that the parallelogram is a rectangle.
The lengths of the sides in the parallelogram are given as 21, 20, 21, and 20 units, which indicates that opposite sides are congruent.
To determine if the figure is a rectangle, we need to check if the sides of the parallelogram meet at right angles.
Since the question does not provide information about the angles of the parallelogram, we cannot conclude that the sides meet at right angles. Therefore, the correct answer is that it is not a rectangle because the sides of the parallelogram do not meet at right angles.
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AnswerD):Yes, it is a rectangle because the sides of the parallelogram do meet at right angles.
Step-by-step explanation:
ege
Which pair of angles are interior angles?
Answers
Let x = 43. Rewrite the equation in the box, replacing 4
with a (substitute).
Answers
The equation in the box with x replacing [tex]4^{\frac{1}{5} }[/tex] in the equation can be presented as follows;
What is an equation?An equation is a statement that indicates that two expressions are equivalent, by joining them with an '=' sign.
The details in the diagram indicates; x = [tex]4^{\frac{1}{5} }[/tex]
Required, to rewrite the equation in the box by plugging in x to substitute [tex]4^{\frac{1}{5} }[/tex] in the equation
The equation in the box can be presented as follows;
[tex]\underline{(4^{\frac{1}{5} })^5 = 4}[/tex]
Plugging in x = [tex]4^{\frac{1}{5} }[/tex] in the above equation, we get;
[tex]\underline{(4^{\frac{1}{5} })^5 =x^5 = 4}[/tex]
Therefore, the equation in the box becomes;
x⁵ = 4
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Currently, the number of pizzas sold by a restaurant is 80. It is estimated that the number of pizzas sold will increase by 5% each hour. Find the total number of pizzas sold at the end of 5 hours.
Round your answer to the nearest whole number if necessary.
Answers
The total number of pizzas sold at the end of 5 hours would be = 520.
How to calculate the total number of pizzas sold by the restaurant?To calculate the total number of pizzas sold, the following steps needs to be taken as follows;
The current total number of pizza sold by the restaurant = 80
The percentage increase of the number sold = 5% of 80
That is ; 5/100 × 80
= 400/100 = 4
The total number of hours spent = 5 hours
The additional number of pizzas = 5×4 = 20
Therefore,the total number of pizzas = 500+20 = 520.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Triangles (C) and (D) can be solved using the Law of Cosines, while triangles (A) and (B) cannot be solved using this theorem due to missing angle measures.
To determine which triangle should be solved by beginning with the Law of Cosines, let's briefly review the Law of Cosines. The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice their product, multiplied by the cosine of the included angle.
Now, let's analyze each given triangle and determine if the Law of Cosines is applicable:
(A) Triangle mZA with mZA = 115, a = 19, b = 13:
To apply the Law of Cosines, we need to have the measures of two sides and the included angle. In this case, we have the measures of two sides (a = 19 and b = 13), but we don't have the included angle mZA. Therefore, we cannot use the Law of Cosines for this triangle.
(B) Triangle m/B with m/B = 48, a = 22, b = 5:
Similar to the previous triangle, we are missing the measure of the included angle. Therefore, we cannot use the Law of Cosines for this triangle either.
(C) Triangle m/A with m/A = 62, mLB = 15, b = 10:
In this triangle, we have the measure of one side (b = 10) and the measures of the other two sides, including the included angle mLB. Therefore, we can apply the Law of Cosines to solve for m/A.
(D) Triangle m/A with m/A = 50, b = 20, c = 18:
Again, we have the measure of one side (b = 20) and the measures of the other two sides. Therefore, we can use the Law of Cosines to solve for m/A in this triangle as well.
In summary, triangles (C) and (D) can be solved using the Law of Cosines, while triangles (A) and (B) cannot be solved using this theorem due to missing angle measures.
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Kubin Company's relevant range of production is 13,000 to 18,000 units. When it produces and sells 15,500 units, its average costs per
unit are as follows:
Direct materials
Direct labor
Variable manufacturing overhead
Fixed manufacturing overhead
Fixed selling expense
Fixed administrative expense
Sales commissions
Variable administrative expense
Average
Cost per
Unit
$7.40
$ 4.40
$ 1.90
$ 5.40
$ 3.90
$ 2.90
$ 1.40
$0.90
Required:
1 Assume the cost object is units of production:
a. What is the total direct manufacturing cost incurred to make 15,500 units?
b. What is the total indirect manufacturing cost incurred to make 15,500 units?
2. Assume the cost object is the Manufacturing Department and that its total output is 15,500 units.
a. How much total manufacturing cost is directly traceable to the Manufacturing Department?
b. How much total manufacturing cost is an indirect cost that cannot be easily traced to the Manufacturing Department?
3. Assume the cost object is the company's various sales representatives. Furthermore, assume that the company spent $44,950 of
its total fixed selling expense on advertising and the remainder of the total fixed selling expense comprised the fixed portion of the
company's sales representatives' compensation.
a. When the company sells 15,500 units, what is the total direct selling expense that can be readily traced to individual sales
representatives?
b. When the company sells 15,500 units, what is the total indirect selling expense that cannot be readily traced to individual sales
representatives?
Answers
1. a. The Total direct manufacturing cost is $212,350. b. The Total indirect manufacturing cost is -$128,650. 2. a. the total manufacturing cost directly traceable to the Manufacturing Department is $212,350. b. the total manufacturing cost that is an indirect cost is $83,700. 3. a. the total direct selling expense that can be readily traced to individual sales representatives is $21,700. b. the total indirect selling expense that cannot be readily traced to individual sales representatives is $38,750.
1. Assume the cost object is units of production:
a. The total direct manufacturing cost incurred to make 15,500 units can be calculated by multiplying the average cost per unit for each cost component by the number of units produced:
Total direct manufacturing cost = (Direct materials cost + Direct labor cost + Variable manufacturing overhead cost) × Number of units produced
Direct materials cost = $7.40/unit × 15,500 units = $114,700
Direct labor cost = $4.40/unit × 15,500 units = $68,200
Variable manufacturing overhead cost = $1.90/unit × 15,500 units = $29,450
Total direct manufacturing cost = ($114,700 + $68,200 + $29,450) = $212,350
b. The total indirect manufacturing cost incurred to make 15,500 units can be calculated by subtracting the total direct manufacturing cost from the average cost per unit for fixed manufacturing overhead:
Total indirect manufacturing cost = Fixed manufacturing overhead cost × Number of units produced
Fixed manufacturing overhead cost = $5.40/unit × 15,500 units = $83,700
Total indirect manufacturing cost = $83,700 - $212,350 = -$128,650
Note: The negative value indicates that the fixed manufacturing overhead cost is not fully utilized within the relevant range of production. It suggests that there may be unused capacity or fixed costs that are not being allocated to the production of 15,500 units.
2. Assume the cost object is the Manufacturing Department and that its total output is 15,500 units:
a. The total manufacturing cost directly traceable to the Manufacturing Department is the sum of the direct manufacturing costs:
Total manufacturing cost directly traceable to the Manufacturing Department = Total direct manufacturing cost
Using the values calculated in part 1a, the total manufacturing cost directly traceable to the Manufacturing Department is $212,350.
b. The total manufacturing cost that is an indirect cost and cannot be easily traced to the Manufacturing Department is the fixed manufacturing overhead cost:
Total manufacturing cost that is an indirect cost = Fixed manufacturing overhead cost
Using the value calculated in part 1b, the total manufacturing cost that is an indirect cost is $83,700.
3. Assume the cost object is the company's various sales representatives. Furthermore, assume that the company spent $44,950 of its total fixed selling expense on advertising, and the remainder of the total fixed selling expense comprised the fixed portion of the company's sales representatives' compensation:
a. When the company sells 15,500 units, the total direct selling expense that can be readily traced to individual sales representatives is the sales commissions:
Total direct selling expense = Sales commissions × Number of units sold
Sales commissions = $1.40/unit × 15,500 units = $21,700
Therefore, the total direct selling expense that can be readily traced to individual sales representatives is $21,700.
b. When the company sells 15,500 units, the total indirect selling expense that cannot be readily traced to individual sales representatives is the fixed portion of the company's sales representatives' compensation:
Total indirect selling expense = Total fixed selling expense - Total direct selling expense
Total fixed selling expense = $3.90/unit × 15,500 units = $60,450
Total indirect selling expense = $60,450 - $21,700 = $38,750
Therefore, the total indirect selling expense that cannot be readily traced to individual sales representatives is $38,750.
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Select the correct answer. Which function is increasing at the highest rate? A. A linear function, f, with an x-intercept of 8 and a y-intercept of -4. B. A linear function on a coordinate plane passes through (minus 1, 3), and (2, minus 3) which intercepts axis at (0.5, 0), and (0, 1) C. D. x 1 2 3 4 5 g(x) -5 -4 -3 -2 -1
Answers
The function in option C (the table) is increasing at the highest rate among the three options.
To determine which function is increasing at the highest rate, we need to analyze the rate of change of each function. The rate of change represents how much the dependent variable (y) changes for a given change in the independent variable (x).
Let's analyze the given options:
A. A linear function, f, with an x-intercept of 8 and a y-intercept of -4.
Since this function is linear, the rate of change is constant. It means that the rate of increase is the same throughout. Therefore, it does not have the highest rate of change.
B. A linear function passing through (-1, 3) and (2, -3) intercepting the axis at (0.5, 0) and (0, 1).
We can calculate the slope of the line using the two points given: (-1, 3) and (2, -3). The slope formula is (change in y) / (change in x).
Slope = (-3 - 3) / (2 - (-1)) = -6 / 3 = -2
The negative slope indicates a decreasing function, not an increasing one. Therefore, this function does not have the highest rate of change.
C. The given table:
x 1 2 3 4 5
g(x) -5 -4 -3 -2 -1
By observing the table, we can see that as x increases, g(x) also increases. The function is consistently increasing, indicating the highest rate of change among the given options.
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Identifying equivalent expressions
HELP ME PLS
Answers
The equivalent expression of - 1 / 4 x + 3 / 4 = 12 are as follows:
-1(x / 4) + 3 / 4 = 12
-x + 3/ 4 = 12
(-x / 4) + 3 / 4 = 12
How to find equivalent expression?Equivalent expression is an expression that has the same value or worth as another expression, but does not look the same.
In other words, two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Therefore, let's find the equivalent expression of - 1 / 4 x + 3 / 4 = 12.
Hence, the equivalent expression are as follows:
-1(x / 4) + 3 / 4 = 12
-x + 3/ 4 = 12
(-x / 4) + 3 / 4 = 12
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The probability that the 5 starting members of the basketball team are lined up from shortest to tallest is 1/120. Option A.
To calculate the probability that the 5 starting members of the basketball team are lined up from shortest to tallest, we need to determine the number of favorable outcomes (arrangements where the players are lined up from shortest to tallest) and divide it by the total number of possible outcomes.
Since the order matters and we want the players to be arranged from shortest to tallest, there is only one favorable outcome. The shortest player must be in the first position, followed by the second shortest, and so on, until the tallest player is in the last position.
The total number of possible outcomes is given by the number of permutations of 5 players, which is denoted as 5!.
Therefore, the probability is:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = 1 / 5!
Probability = 1 / (5 * 4 * 3 * 2 * 1)
Probability = 1 / 120 Option A is correct.
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What is the power of a lamp rated at 12 V 2 A?
Answers
Answer:
24 W
Step-by-step explanation:
. What is the value of the discriminant of 0 = -2x² + 6x+13
Answers
The discriminant of the quadratic equation -2x² + 6x + 13 is 140.
To find the discriminant of the quadratic equation 0 = -2x² + 6x + 13, we can use the formula for the discriminant, which is given by Δ = b² - 4ac. The quadratic equation is in the form ax² + bx + c = 0, with coefficients a = -2, b = 6, and c = 13.
Substituting these values into the discriminant formula, we have:
Δ = (6)² - 4(-2)(13)
Δ = 36 - (-104)
Δ = 36 + 104
Δ = 140
The discriminant provides valuable information about the nature of the solutions of a quadratic equation.
It can take on different values, and each value indicates a different scenario:
If the discriminant (Δ) is greater than zero (Δ > 0), then the quadratic equation has two distinct real solutions.
If the discriminant is equal to zero (Δ = 0), then the quadratic equation has a single real solution (a repeated root).
If the discriminant is less than zero (Δ < 0), then the quadratic equation has no real solutions, but rather two complex solutions.
The discriminant is 140 (Δ = 140), which is greater than zero, the quadratic equation -2x² + 6x + 13 has two distinct real solutions.
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For the following event, state whether you think the difference between what occurred and what you would expect by chance is statistically significant. Explain.
An airline with a 95% on-time departure rate has 16 out of 300 flights with late departures.
Answers
The difference between the observed and expected number of late departures is statistically significant, we need to perform a binomial test by calculating the probability of observing 16 or more late departures out of 300 flights assuming the null hypothesis is true. If the resulting p-value is less than 0.05, we can conclude that the difference is statistically significant.
Based on the given information, an airline with a 95% on-time departure rate has 16 out of 300 flights with late departures. The question asks whether the difference between what occurred (16 late departures) and what you would expect by chance is statistically significant.
To determine if the difference is statistically significant, we need to conduct a hypothesis test. In this case, we can use a binomial test since we are dealing with two possible outcomes: on-time departure or late departure.
The null hypothesis (H0) assumes that the observed number of late departures is equal to what would be expected by chance. The alternative hypothesis (Ha) assumes that there is a significant difference between the observed and expected values.
In this case, the expected number of late departures can be calculated by multiplying the total number of flights (300) by the expected on-time departure rate (95%). This gives us an expected value of 300 * 0.05 = 15.
To perform the binomial test, we can calculate the probability of observing 16 or more late departures out of 300 flights, assuming the null hypothesis is true. This probability can be calculated using the binomial probability formula or by using statistical software.
If the resulting probability (also known as the p-value) is less than the significance level (usually 0.05), we can reject the null hypothesis and conclude that the difference between what occurred and what would be expected by chance is statistically significant. Otherwise, if the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the difference is not statistically significant.
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use the basic concepts of probability to identify the following . show solution .
1: 1/5 rolling a die
Answers
The probability of rolling the specific outcome 1: 1/5 on a fair six-sided die is 1/6
To identify the probability of rolling a specific outcome on a fair six-sided die, we can use the concept of probability. The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.
In this case, we want to find the probability of rolling a specific outcome, which is 1 out of 5. Since there is only one specific outcome we are interested in, and the die has a total of 6 possible outcomes (numbers 1 to 6), the probability can be calculated as:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 6
Therefore, the probability of rolling the specific outcome you mentioned (1 out of 5) on a fair six-sided die is 1/6.
In conclusion, when rolling a fair die, each of the six possible outcomes has an equal chance of occurring, resulting in a probability of 1/6 for any specific outcome.
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State if the pair of triangles are similar. If so, state how you know they are similar and complete the similarity statement.
Answers
The triangles EFG and WVU are similar by SSS
Identifying the similar triangles in the figure.from the question, we have the following parameters that can be used in our computation:
Triangle EFG and WVU
The triangles in this figure are
EFG and WVU
These triangles are similar because:
The triangles do have similar corresponding sides
i.e. Ratio = 525/252 = 875/420 = 825/396
Evaluate
Ratio = 2.083 = 2.083 = 2.083
Hence, the triangles EFG and WVU are similar
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solve
3x + y = 10
5x - 2y - 2 = 0
Answers
The solution to the system of equations is x = 18/11 and y = 56/11.
To solve the system of equations:
3x + y = 10 ...(1)
5x - 2y - 2 = 0 ...(2)
We can use the method of substitution or elimination to find the values of x and y that satisfy both equations.
Let's use the method of elimination:
Multiply equation (1) by 2 to make the coefficients of y in both equations opposite:
6x + 2y = 20 ...(3)
Now, add equations (2) and (3):
(5x - 2y - 2) + (6x + 2y) = 0 + 20
11x = 18
Divide both sides by 11:
x = 18/11
Substitute the value of x into equation (1):
3(18/11) + y = 10
54/11 + y = 10
y = 110/11 - 54/11
y = 56/11
Therefore, the solution to the system of equations is x = 18/11 and y = 56/11.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Answer:
B
Step-by-step explanation:
the secant- secant angle LMN is half the difference of the measures of the intercepted arcs , that is
∠ LMN = [tex]\frac{1}{2}[/tex] ( KP - LN)
20° = [tex]\frac{1}{2}[/tex] (96 - LN) ← multiply both sides by 2 to clear the fraction
40° = 96° - LN ( subtract 96° from both sides )
- 56° = - LN ( multiply both sides by - 1 )
56° = LN
sum of two numbers is 95.if one exeeds the other by 15,find the number (find linear equation and solve)
Answers
Sum of two numbers is 95. if one exeeds the other by 15,The smaller number is 40 and the larger number is 55.
Let's assume the smaller number is x. The larger number would then be (x + 15), as it exceeds the smaller number by 15.
According to the given information, the sum of the two numbers is 95. We can write this as an equation:
x + (x + 15) = 95
Simplifying the equation:
2x + 15 = 95
Next, let's isolate the variable:
2x = 95 - 15
2x = 80
Finally, divide both sides of the equation by 2 to solve for x:
x = 80 / 2
x = 40
So, the smaller number is 40. To find the larger number, we add 15 to it:
Larger number = 40 + 15
Larger number = 55
Therefore, the smaller number is 40 and the larger number is 55.
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I
How long will it take for a $3030 investment to grow to $6450 at an annual rate of 10.2%,
compounded quarterly. Assume that no withdrawals are made. State the exact and approximate
solution. Do not round any intermediate computations, and round your answer to the nearest
hundredth of a year.
Answers
The time required to get an accrued amount of $6,450.00 with compoundeded interest on a principal of $3,030.00 at an interest rate of 10.2% per year and compounded 4 times per year is 7.5 years.
What is the time taken to have an accrued amount of $6450?The formula accrued amount in a compounded interest is expressed as;
[tex]A = P( 1 + \frac{r}{n} )^{(nt)}[/tex]
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Principal P = $3,030
Accrued amount A = $6,450
Compounded quarterly n = 4
Interest rate r = 10.2%
Time t = ?
First, convert R as a percent to r as a decimal
r = R/100
r = 10.2/100
r = 0.102
Now, plug these values into the above formula and solve for time t.
[tex]A = P( 1 + \frac{r}{n} )^{(nt)}\\\\t = \frac{In(\frac{A}{p}) }{n[In( 1 + \frac{r}{n}) ]} \\\\t = \frac{In(\frac{6450}{3030}) }{n[In( 1 + \frac{0.102}{4}) ]} \\\\t = 7.501 \ years[/tex]
t = 7.5 years.
Therefore, the time taken to get the accrued amount is approximately 7.5 years.
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The period of y = 3cot(4x - 3x) is
Answers
the period of y = 3cot(x) remains as π. the period of y = 3cot(4x - 3x) is also π.
To find the period of the function y = 3cot(4x - 3x), we need to determine the length of one complete cycle of the function.
First, let's simplify the expression inside the cotangent function: 4x - 3x = x.
Now, the cotangent function has a period of π, which means it repeats every π units.
To find the period of the given function y = 3cot(x), we need to determine how the variable x affects the period. Since the coefficient of x is 1, it means that the period is not affected by any scaling or stretching.
In summary, the period of the function y = 3cot(4x - 3x) is π, which means the function repeats every π units along the x-axis.
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Liquid A and Liquid B are stored in cans.
Density of Liquid A: Density of Liquid B=4:3
Mass of Liquid A: Mass of Liquid B=5:2
3 cans of Liquid B are mixed with I can of Liquid A to make Liquid C.
Work out
Density of Liquid A: Density of Liquid C
Give your answer in its simplest form.
Answers
The density of Liquid A is equal to the density of Liquid C when they are mixed in the specified ratio.
To determine the density of Liquid C, we need to find the mass and volume of Liquid C and then calculate the density by dividing the mass by the volume.
Given that the density of Liquid A is in a 4:3 ratio with the density of Liquid B, and the mass of Liquid A is in a 5:2 ratio with the mass of Liquid B, we can assume that the ratio of their volumes is also 5:2. This is because density is the ratio of mass to volume.
When 3 cans of Liquid B are mixed with 1 can of Liquid A to make Liquid C, the volume ratio remains the same. So, the volume of Liquid C would be 5 + 3 = 8 units.
Since the density is the mass divided by the volume, the density of Liquid A would remain the same. Therefore, the density of Liquid A is equal to the density of Liquid C.
In conclusion, the density of Liquid A is equal to the density of Liquid C.
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