Answer:
The x is an invisible number that is always represented by 1 so you have to solve the equation.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
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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In the diagram, the measures of 23 and 27 are 45°. The measure of 25 is
135°. Are lines cand dparallel?
F
5
8
OA. Yes, because 23 and 27 are congruent.
OB. No, because 27 and 25 are not congruent.
C. Yes, because 25 and 27 are supplementary.
D. No, because 23 and 25 are not supplementary.
The correct answer is D. No because 23 and 25 are not supplementary.
In the given diagram, it is stated that the measures of angles 23 and 27 are 45°, and the measure of angle 25 is 135°. To determine if lines C and D are parallel, we need to analyze the angles formed by these lines.
If the alternate interior angles or corresponding angles are congruent, then the lines are parallel. However, in this case, we don't have enough information about the angles formed by lines C and D to make that determination.
The fact that angle 23 and angle 27 are congruent (both measuring 45°) doesn't provide any information about the relationship between lines C and D. Similarly, the measure of angle 25 being 135° doesn't give us any insight into the parallelism of lines C and D. Therefore, we cannot conclude that lines C and D are parallel based on the given information, and the correct answer is D.
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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.
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! =)
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.
Answer: All of the choices in the response would be correct.
Step-by-step explanation:
solve
3x + y = 10
5x - 2y - 2 = 0
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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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.
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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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.
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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Two different functions are shown. Function A: Function B: How do the x-intercepts of the two functions compare? The x-intercept in function B is one-third as large as the x-intercept in function A. The x-intercept in function B is three times as large as the x-intercept in function A. The distance between the x-intercepts in function A is half the distance between the x-intercepts of function B. The distance between the x-intercepts in function A is twice the distance between the x-intercepts of function B.
The x-intercept in function B is one-third as large as the x-intercept in function A.
The x-intercepts of two functions, A and B, are compared in terms of their relative sizes and distances. According to the given information, the x-intercept in function B is one-third as large as the x-intercept in function A. This means that the value of the x-coordinate at which function B intersects the x-axis is one-third of the value of the x-coordinate at which function A intersects the x-axis.
Conversely, we can say that the x-intercept in function A is three times as large as the x-intercept in function B. The x-coordinate at which function A intersects the x-axis is three times the value of the x-coordinate at which function B intersects the x-axis.
However, the information does not provide any direct comparison of the distances between the x-intercepts of the two functions. Therefore, we cannot determine whether the distance between the x-intercepts in function A is half or twice the distance between the x-intercepts of function B based on the given information.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
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
Which pair of angles are interior angles?
Bruno had a gross income of $4925 during each pay period last year. If he got
paid monthly, how much of his yearly pay was deducted for FICA?
A. $4521.15
B. $3250.50
C. $3871.05
D. $3841.50
The amount of Bruno's yearly pay deducted for FICA is approximately
A. $4,524.15. The closest option provided is A. $4521.15.
To calculate the amount of FICA deducted from Bruno's yearly pay, we need to consider the specific FICA tax rates for Social Security and Medicare.
As of 2021, the Social Security tax rate is 6.2% on income up to a certain threshold, and the Medicare tax rate is 1.45% on all income.
Given that Bruno's gross income per pay period is $4925 and he is paid monthly, we can calculate the yearly gross income as follows:
Yearly gross income = $4925 * 12 = $59,100
To calculate the FICA deduction, we need to find the sum of the Social Security and Medicare taxes. Using the respective tax rates mentioned earlier:
Social Security deduction = $59,100 * 6.2% = $3,667.20
Medicare deduction = $59,100 * 1.45% = $856.95
Adding these two deductions together:
FICA deduction = $3,667.20 + $856.95 = $4,524.15
Therefore, the amount of Bruno's yearly pay deducted for FICA is approximately $4,524.15.
The closest option provided is A. $4521.15.
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Answer? Please someone ASAP!
The measure of angle Q is 70°
What is parallelogram property?A parallelogram is a quadrilateral with two pairs of parallel sides.
Some of the properties of a parallelogram are ;
1. They have two pair of parallel lines
2. The opposite sides are equal
3. The sum of the adjascent sides is 180°
Since we have known that the sum of the adjascent sides of a parallelogram is 180°, then we can say that;
6x+4 + 10x = 180
16x = 180 -4
16x = 176
x = 11
angle Q = 6x +4
Q = 6(11)+4
Q = 70°
Therefore the value of angle Q is 70°
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16
Find X.
25
X
Pythagorean Theorem
Answer:
3√41
Step-by-step explanation:
a^2+b^2=c^2
rearrange this to make x (a or b it doesn't matter) the subject
√b=c^2-a^2
now substitute this in:
√b=25^2-16^2
=369
then simple do the square root
√369
=3√41
Hope this helps!
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.
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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What is the solution to this system of equations? 10 y = x - 2; y = - 0.5x + 7 10 (3, 2); (6, 4); (4, 6); (2, 3)
Answer:x=bx2 is the answer
Step-by-step explanation:
Which algebraic expression is a polynomial with a degree of 2?
O4x³-2x
O 10x²-√x
O 8x³+ 5 +3
6x² - 6x + 5
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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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
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.
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.
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
Let x = 43. Rewrite the equation in the box, replacing 4
with a (substitute).
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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Identifying equivalent expressions
HELP ME PLS
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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When Ibuprofen is given for fever to
children 6 months of age up to 2 years, the
usual dose is 5 milligrams (mg) per kilogram
(kg) of body weight when the fever is under
102.5 degrees Fahrenheit. How much
medicine would be usual dose for a 18
month old weighing 21 pounds?
milligrams
Round your answer to the nearest milligram.
Answer: The usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen.
Step-by-step explanation: To find the usual dose of ibuprofen for a child, we need to follow these steps:
Convert the child’s weight from pounds to kilograms. One pound is equal to 0.4536 kilograms, so we multiply 21 by 0.4536 to get 9.5256 kilograms.Multiply the child’s weight in kilograms by the dose per kilogram. The dose per kilogram is 5 mg when the fever is under 102.5 degrees Fahrenheit, so we multiply 9.5256 by 5 to get 47.628 mg.Round the result to the nearest milligram. To round a number to the nearest milligram, we look at the digit after the decimal point. If it is 5 or more, we add one to the digit before the decimal point and drop the rest. If it is less than 5, we keep the digit before the decimal point and drop the rest. In this case, the digit after the decimal point is 6, which is more than 5, so we add one to the digit before the decimal point and drop the rest. The result is 48 mg.Therefore, the usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen. Hope this helps, and have a great day! =)
100 Points! Geometry question. Photo attached. Only looking for an answer to B. Please show as much work as possible. Thank you!
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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Graph the linear equation. Find three points that solve the equation, then plot on the graph. -5x-3y=-7
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
50 Points! Multiple choice geometry question. Photo attached. Thank you!
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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The period of y = 3cot(4x - 3x) is
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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Please help with the attached math problem…
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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Pls help I need help on this question
Answer: B
Step-by-step explanation: Hope this helps:)
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.
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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sum of two numbers is 95.if one exeeds the other by 15,find the number (find linear equation and solve)
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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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.
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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