Answers
Answer:
[tex]\large \boxed{\boxed{\textsf{$(x+2)(x-4)$}}}[/tex]
[tex]\boxed{\boxed{\large \textsf{$x=-2, x=4$}}}[/tex]
Factorising the expression:This is a quadratic expression, in the form:
[tex]\boxed{\large \textsf{$ ax^2+bx+c$, where$\ a \neq 0$}}[/tex]
To factorise this expression, we will need to have 4 terms. Currently there are only 3. To do this, we need to find 2 integers, that add together to form the middle term, -2, and multiply together to form the constant term, -8.
[tex]\large \textsf{the 2 integers $\Rightarrow$ 2 and -4}\\ \textsf{$-4+2 = -2$\ (coefficient of middle term)}\\ \textsf{$-4 \times 2=-8$\ (constant term)}[/tex]
Now we can split the middle term into 2 terms, using the integers we just found:
[tex]\large \textsf{$x^2+2x-4x-8$}[/tex]
Now we can factorise this.
[tex]\large \textsf{Group each pair of terms together, and take out a common factor.}\\ \\ \large \textsf{$x(x+2)-4(x+2)$}\\ \\ \large \textsf{Now take out the common factor from the expression: (x+2)} \\ \\ \large \textsf{$(x+2)(x-4)$}[/tex]
This leaves us with our fully factorised expression:
[tex]\large \boxed{\boxed{\textsf{$(x+2)(x-4)$}}}[/tex]
Solving the expression:To solve the quadratic expression, we can make it equal to zero:
[tex]\large \textsf{$x^2-2x-8=0$}[/tex]
Primarily, to solve this, we can used the factorised form from above, and apply the zero-product property.
Zero-product property:The zero-product property states that:[tex]\large \textsf{If $a\times b=0$, then $a=0$ or $b=0$ (or both $a=0$ AND b=0)}[/tex]
[tex]\large \textsf{$\therefore$ if $(x+2)(x-4)=0$, then $(x+2)=0$, and/or $(x-4)=0$ }[/tex]
[tex]\large \textsf{$\implies \boxed{\boxed{x=-2, x=4}}$ }[/tex]
Similarly, we can also use the quadratic formula to solve this equation:
Quadratic Formula:[tex]\boxed{\Large \textsf{$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$} \large \textsf{, for $ax^2+bx+c=0$}}[/tex]
[tex]\large \textsf{$\Rightarrow a=1, b=-2, c=-8$}\\ \\ \Large \textsf{$x=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(-8)}}{2(1)}$}\\ \\ \boxed{\boxed{\large \textsf{$\therefore x=4, x=-2$}}}[/tex]
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Related Questions
suppose it is reported that 80% of all people subscribe to a cable television service versus others. a student believes it is different and decides to test this claim by randomly sampling people and responded that they subscribe to cable or satellite television versus others at a level of significance. student work: : : the test z-statistic is , and the p-value is . since we fail to reject . therefore, there is not sufficient evidence at level of significance to conclude the proportion of people who subscribe to a cable television service versus others is different from %. task: the student who submitted their work failed to check the conditions for the problem. let's help them out. remind the student of the conditions and how to check them. tell the student why we need to check each condition.
Answers
To perform a hypothesis test on the proportion of people who subscribe to a cable television service versus others, we need to check the following conditions:
1. Random Sampling: Ensure that the sample is randomly selected, which means each person has an equal chance of being selected. This is important to avoid biases and ensure the sample is representative of the population.
2. Independence: If sampling without replacement, the sample size (n) should be less than 10% of the population size (N) to assume independence. This is called the 10% Rule. Independence is important because the outcome of one person's choice should not affect another person's choice.
3. Normality: We need to ensure that the sampling distribution of the sample proportion (p-hat) is approximately normal. This can be checked using the success-failure condition, which states that both np and n(1-p) should be greater than or equal to 10. This ensures that the distribution is sufficiently normal to apply the z-test.
To help the student, remind them to:
1. Verify that the sample is random.
2. Check the independence condition by confirming the sample size is less than 10% of the population size.
3. Check the normality condition by calculating np and n(1-p) and making sure both values are greater than or equal to 10.
It is crucial to check these conditions because if they are not met, the hypothesis test's results may not be valid or reliable. Meeting these conditions ensures that the statistical methods applied are appropriate and provide accurate results for making conclusions.
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Police discover a body in the back seat of a car on a nice spring day. The ambient temperature is 74F . The vas has coles ro 79F . How long gas it been since the time of death?
Info to know:
Before death- body maintains a temperature of 98.6F
0-12 hours- body cools at 1.4F per hour
After 12 hours- body cools at 0.7F until it reaches the temperature of the environment.
Answers
It has been 16 hours since the time of death.
How to solveStage 1: First 12 hours
12 hours * 1.4F per hour = 16.8F
Stage 2: After 12 hours
Since the body has already cooled 16.8F in the first 12 hours, we only need to find the remaining temperature drop:
19.6F - 16.8F = 2.8F
Now, we can calculate the time taken for the remaining temperature drop using the second cooling rate:
2.8F / 0.7F per hour = 4 hours
Adding the time taken for both stages, we get:
12 hours (Stage 1) + 4 hours (Stage 2) = 16 hours
So, it has been 16 hours since the time of death.
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I NEED HELP what is 1/4 x 20 =
21
Answers
The solution of the fractions 1 / 4 × 20 / 21 is 5 / 21.
How to solve fractions?A fraction is number with numerator and denominator. Therefore, let's multiply the fractions.
1 / 4 × 20 / 21 = 20 / 84
Hence, let's reduce the fraction by dividing the numerator and denominator by 4.
20 / 84 ÷ 4 / 4
20 / 84 ÷ 4 / 4 = 5 / 21
Therefore, the fraction is 5 / 21.
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For a lottery, the probability of a winning ticket is 0. 10. What is the probability the 20th ticket purchased is the second winning ticket? O 0. 015 O 0. 090 O 0. 257 O 0. 29
Answers
The probability that the 20th ticket purchased is the second winning ticket is 0.10
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.
The probability of a winning ticket is = 0. 10
Thus,
This means there is a 10% chance of winning with each ticket purchased.
The likelihood that the 20th ticket will be the second winning ticket is the same as the chance that any other ticket will be the second winning ticket, which is 0.10. This is because each ticket purchase is autonomous and has no bearing on the results of other tickets. Therefore, the probability of the 20th ticket purchased being the second winning ticket is also 0.10 or 10%
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Make x the subject of the formula y=x(a+b)
Answers
y=x(a+b)
Divide both sides by (a+b)
x=y/(a+b)
Miriam makes a square quilt by arranging square quilt blocks into an array. The quilt has 8 rows of quilt blocks and a total area of 7,744 square inches. What is the side length, in inches, of one of the quilt blocks?
Answers
Answer:
11
Step-by-step explanation:
If quilt has 8 rows of "quilt-blocks" and has an area of 7,744 square inches, then the "side-length" of one quilt blocks is 11 inches.
Let us assume that each quilt block has a side length of "x" inches.
Since the quilt has 8 rows of quilt blocks, the total number of quilt blocks in the quilt is 8 times the number of quilt blocks in each row, which is 8x.
The shape of a quilt is a square and has a "total-area' of 7744 square inches, we equate the area equation;
We get,
⇒ (x × 8)² = 7744,
Simplifying the equation,
We get,
⇒ 64x² = 7744,
Dividing both sides by 64,
We get,
⇒ x² = 121,
⇒ x = 11,
Therefore, each quilt-block has a side length of 11 inches.
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find the newton raphson method formula for finding the square root of a real number r from the equation x^2-r=0 is
a. xi+1= xi/2
b.xi+1= 3xi/2
c.xi+1= 1/2 (xi+ r/xi)
d.xi+1=1/2(3xi - r/xi)
Answers
Option (c) is the correct formula for the Newton-Raphson method to find the square root of a real number r from the equation [tex]x^2 - r = 0[/tex]
The Newton-Raphson method is an iterative method for finding the root of a function. To use this method to find the square root of a real number r from the equation [tex]x^2 - r = 0[/tex], we first define a function [tex]f(x) = x^2 - r[/tex]. The root of this function is the square root of r.
The Newton-Raphson method starts with an initial guess x0 for the root and then iteratively improves the guess using the formula:
[tex]xi+1 = xi - f(xi)/f'(xi)[/tex]
where f'(x) is the derivative of f(x). In this case,[tex]f(x) = x^2 - r[/tex], so f'(x) = 2x.
Substituting these values, we get:
[tex]xi+1 = xi - (xi^2 - r)/(2xi)[/tex]
Simplifying, we get:
[tex]xi+1 = xi - (xi/2 - r/2xi)[/tex]
[tex]xi+1 = 1/2(xi + r/xi)[/tex]
Therefore, the formula for the Newton-Raphson method to find the square root of a real number r from the equation [tex]x^2 - r = 0[/tex] is:
[tex]xi+1 = 1/2(xi + r/xi)[/tex]
Option (c) is the correct formula for the Newton-Raphson method to find the square root of a real number r from the equation[tex]x^2 - r = 0[/tex]. This formula involves taking the average of the current guess xi and r/xi as the next guess. This method is efficient and converges quickly to the square root of r.
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A submarine is exploring the ocean floor and begins to ascend to the surface. The depth of the submarine in the water can be modeled by the function `d=500t-4,500` where t is the time (in minutes) since the submarine began to ascend
Answers
For the depth function of submarine in water is, d = 500t - 4,500, where t is the time (in minutes), the intercepts say x-intercept and y-intercept values are -4500 and 9 respectively.
The x-intercept is the point where a line cross or meet the x-axis, and the y-intercept is the point where a line cross or meet the y-axis. For y-intercept we are setting x to zero and for x-intercept we are setting y = 0 and determining their corresponding values. We have a submarine is exploring the ocean floor and begins to ascend to the surface.
The depth of submarine in the water can be modeled by equation, d = 500t - 4,500, where t is the time (in minutes). We have to determine the x and y intercept values. As we know, equation of line in slope intercept form is y = mx + b
where, b--> y-intercept
m --> slope
In this case b = - 4500, m = 500
So, y-intercept= -4500 for t = 0. Now, for x-intercept that for t value, plug d = 0, 0 = 500t - 4500
=> 500 t = 4500
=> t = 9
So, x-intercept = 9
Hence, required value is 9.
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Complete question:
A submarine is exploring the ocean floor and begins to ascend to the surface. The depth of the submarine in the water can be modeled by the function `d=500t-4,500` where t is the time (in minutes) since the submarine began to ascend. Find the intercepts of the graph of the equation:
x-intercept:
y-intercept:
In order to gain more insight on-employee’s preferences, twenty-three (23) employees from the Private Sector were asked about automobile of their preference. Five (5) of them dislike all the three brands. Eight (8) preferred both LEXUS and MERCEDES. Another eight (8) of them preferred both MERCEDES and AMAROK. Four (4) of them preferred all three brands. Four (4) prefer MERCEDES only. The remainder preferred AMAROK only.
i. How many of the twenty-three (23) employees prefer LEXUS only? ii. How many of the twenty-three (23) employees prefer AMAROK only? iii. From the total of one hundred and seventy-five (175) employees from both Public and Private Sector, how employees disliked all the three brands? iv. What is the percentage increase in the number of employees who preferred all three brands? v. Compute the percentage decrease in the proportion of employees that prefer all three brands?
Answers
Since we do not have information on a previous survey, we cannot calculate this percentage
i. To find the number of employees who prefer LEXUS only, we need to subtract the number of employees who preferred both LEXUS and MERCEDES, and the number of employees who preferred all three brands, from the total number of employees who prefer LEXUS:
LEXUS only = Total number of LEXUS preference - (Number of employees who prefer both LEXUS and MERCEDES) - (Number of employees who prefer all three brands)
LEXUS only = (8 + 4) - 8 - 4
LEXUS only = 8
Therefore, 8 employees prefer LEXUS only.
ii. To find the number of employees who prefer AMAROK only, we need to subtract the number of employees who preferred both MERCEDES and AMAROK, and the number of employees who preferred all three brands, from the total number of employees who prefer AMAROK:
AMAROK only = Total number of AMAROK preference - (Number of employees who prefer both MERCEDES and AMAROK) - (Number of employees who prefer all three brands)
AMAROK only = (8 + 4) - 4 - 4
AMAROK only = 4
Therefore, 4 employees prefer AMAROK only.
iii. We are given that 5 employees dislike all three brands. Since this information is only from the Private Sector, we cannot determine the number of employees who dislike all three brands in the total of 175 employees from both Public and Private Sectors.
iv. The percentage increase in the number of employees who preferred all three brands is the difference between the number of employees who preferred all three brands in the current survey and the number of employees who preferred all three brands in a previous survey, divided by the number of employees who preferred all three brands in the previous survey, multiplied by 100%. Since we do not have information on a previous survey, we cannot calculate this percentage.
v. The proportion of employees who preferred all three brands in the current survey is 4/23 or approximately 0.174. To compute the percentage decrease in the proportion of employees who preferred all three brands, we need to compare this proportion with the proportion of employees who preferred all three brands in a previous survey. Since we do not have information on a previous survey, we cannot calculate this percentage.
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Find the value of x in the
following parallelogram.
3x-12
4x-24
x = [ ? ]
Answers
Answer:
[tex]3x - 12 = 4x - 24[/tex]
[tex]x = 12[/tex]
To find the value of x in the given parallelogram, set up an equation using the given sides and solve for x. The value of x is 12.
Explanation:To find the value of x in the given parallelogram, we need to use the properties of a parallelogram. In a parallelogram, opposite sides are equal in length. So, we can set up an equation using the given sides:
3x - 12 = 4x - 24
Now, we can solve the equation to find the value of x:
3x - 4x = -24 + 12
-x = -12
x = 12
Therefore, the value of x is 12.
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You must study for your test in one of three periods, t = 0, 1, 2. The instantaneous utility cost of studying at t = 0 is 8, at t = 1 is 10, and at t = 2 is 12. You are a naive quasi-hyperbolic discounter with β = 0.75 and δ = 1.
a) In which period will you study? [1 mark]
b) You like to reward yourself with a chocolate cake when you finish study. Your instantaneous utility from eating this cake is equal to 6. Discuss whether binding the unpleasant task to a pleasant task overcome procrastination in this example? [1 mark]
c) After completing this unit you learn about your present bias and become a sophisticated quasi-hyperbolic discounter. Does being sophisticated change the period in which you study? (Assume that there is no cake.)
Answers
Since the utility cost is lowest at t=0, you will conduct your research during period 0 as a quasi-hyperbolic discounter. Procrastination may be beaten if the painful job was linked to an enjoyable task.
a) As a naive quasi-hyperbolic discounter, you must choose the period to study based on your discount factors (β = 0.75, δ = 1) and the utility costs. To determine this, you must compare the present value of the utility costs of studying in each period:
At t = 0: Utility cost = 8 (since you're studying now, no discounting is applied)
At t = 1: Utility cost = 10 x β = 10 x 0.75 = 7.5
At t = 2: Utility cost = 12 x β x δ = 12 x 0.75 x 1 = 9
Since the utility cost is lowest at t=0 (8), you will study during period 0.
b) By binding the unpleasant task (studying) with the pleasant task (eating chocolate cake with utility of 6), it may help overcome procrastination if the combined utility is less than the utility cost of studying in later periods. In this case:
At t = 0: Combined utility cost = 8 - 6 = 2
Since the combined utility cost at t=0 (2) is lower than the utility costs of studying in periods 1 and 2 (7.5 and 9), binding these tasks could help overcome procrastination.
c) As a sophisticated quasi-hyperbolic discounter, you're now aware of your present bias. However, since there is no cake involved, the utility costs remain the same as in part (a):
At t = 0: Utility cost = 8
At t = 1: Utility cost = 7.5
At t = 2: Utility cost = 9
Even though you're now sophisticated, the period in which you study does not change. You will still study during period 0, as it has the lowest utility cost.
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Simplify. Rewrite the expression in the form 9^n. (9^-3)(9^12)
Answers
Answer:
The given expression can be simplified using the rule for multiplying powers with the same base by adding their exponents.
(9^-3)(9^12) can be written as (1/9^3)(9^12)
Now, using the rule of adding exponents, (1/9^3)(9^12) can be simplified as 9^(12-3) = 9^9.
Therefore, the expression (9^-3)(9^12) simplified as 9^9.
Step-by-step explanation:
Find the value of x.
Answers
The value of x is 116°
Given that a circle, with two congruent chords, FG and DE we need to find the central angle x,
Here we will use the properties of circle,
Since, the chords are equal, so, the measure of the arc intercepted by them will be equal,
arc DE = arc FG = 116°
Also, we know that the central angle is equal to the measure of the arc intercepted by it,
Therefore, x = m arc DE
x = 116°
Hence, the value of x is 116°
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The theoretical probability of each letter is 0. 2. What is the experimental probability of drawing a card with the letter for which the experimental probability is closest to the theoretical probability? express your answer as a decimal
Answers
For theoretical probability of each letter is 0.2, the experimental probability of drawing a card with the letter for which the experimental probability is closest to the theoretical probability is equals the 0.5.
Theoretical Probability: The theoretical probability of an event is the probability of a particular event based on mathematical calculations, assuming ideal conditions. The theoretical probabilities do not take into account the flaws of the system.
Experimental probability: The experimental probability of an event is the actual probability of an event occurring based on the results of facts rather than mathematical calculations
The theoretical probability of each letter = 0.2 = 2/10
We have to determine the experimental probability of drawing a card with the letter for which the experimental probability is near to the theoretical probability. Now, total possible outcomes = 10 and each letter comes two times
so, the experimental probability = 10/20
= 0.5
Hence, required value is 0.5.
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Determine which formula for standard error applies, and then calculate the standard error. (Use at least 3 decimal places after the zeros end.)N = 500, n = 44, p = 0.45Group of answer choices0.02220.01130.4760.0750.06850.0717
Answers
The formula for standard error that applies to this problem is SE = sqrt[p(1-p)/n], where SE represents the standard error, p represents the probability of success, and n represents the sample size. In this case, N represents the population size, but it is not necessary for calculating the standard error.
Substituting the values given in the problem, we have:
SE = sqrt[0.45(1-0.45)/44] = 0.0717 (rounded to four decimal places)
Therefore, the standard error for this problem is 0.0717. This value represents the degree of variability or uncertainty in the sample proportion, or the degree to which the sample proportion is likely to deviate from the true population proportion. A larger sample size or a more extreme probability of success (closer to 0 or 1) would result in a smaller standard error, indicating greater precision in the estimate of the population proportion.
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Dotermine if the argument is valid or not If the ice melts or a food occurs, then the global temperature has increased the global temperature has not increased. Therefore, a food occurs. Choose the correct answer below The argument is valid The argument is not vald
Answers
The argument is not valid.
The argument assumes that a flood occurs only if the global temperature has increased, but this is not necessarily true. A flood can occur due to other reasons such as heavy rain, land use changes, or other natural disasters. Therefore, the conclusion "a flood occurs" does not necessarily follow from the premises given.
This means that if either the ice melts or a flood occurs, then the global temperature must have increased. However, the converse of this statement is not necessarily true. That is, the global temperature can increase for reasons other than the ice melting or a flood occurring. Therefore, it is not valid to conclude that a flood must occur just because the global temperature has not increased.
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In a circle, a 270º sector has area 432π What is the radius of the circle?
Answers
The radius of the circle is 24 units.
How to find the radius of the circle?We know that for an arc defined by an angle θ on a circle of radius R, the area is:
A = (θ/360°)*π*R²
Here we can see that the area of the sector is 432π and the angle is 270°, then we can replace that in the formula above so we get:
432π = (270°/360°)*π*R²
432 = (3/4)*R²
(4/3)*432 = R²
√576 = R
24 = R
The radius is 24 units.
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PLEASE HELP ITS URGENT I INCLUDED THE PROBLEM IN IMAGE I WROTE IT DOWN!!!
Answers
Answer:
The answer would be D. [tex]\frac{5\sqrt{11} }{11}[/tex]
Manatees are one creature found in coastal waterways. To study this creature, a random sample of 12 manatees were selected, the sample manatees were released before their weights (in pounds) were carefully recorded: 956, 1012, 954, 988, 973, 1048, 1075, 1064, 856, 1026, 1031, 1064. Assuming the underlying distribution of manatee weights is normal.
1(5 points). Find a 95% confidence interval for the true mean weight.
2(5 points). In a similar study 10 years ago, researchers concluded that the true mean weight of manatees was approximately 1000 pounds. Implement a hypothesis test to verify if there is any evidence to suggest the true mean weight is less than 1000 pounds now. Solve the hypothesis using PP-value method. Let α=0.05.
Answers
Confidence interval for the true mean weight is (964, 1043.8)
P-value= 0.5836≥0.5 then conclude that null hypothesis is rejected.
What is null hypothesis?
The assertion that there is no link between the two sets of data or variables under investigation is known as the null hypothesis. The word "null" refers to the idea that any empirically observed difference is entirely attributable to chance and that no underlying causal link exists.
Given,
Data= 956, 1012, 954, 988, 973, 1048, 1075, 1064, 856, 1026, 1031, 1064
n=12
Mean = sum(x)/n=sum(x)/12= 12047/12= 1003.9167
We get the standard deviation from the given data by using formula
Std. deviation= 62.7976
C=95%= 0.95
α= 1-0.95=0.05
Critical value= 2.201
The 95% confidence interval for the true mean value is=
=(1003.9167±2.201*62.7976/√12)
= (1003.9167±39.9)
= (964, 1043.8)
2)The null and alternative hypothesis,
H0:μ=1000
Hα: μ<1000
The statistic is (t)= (1003.9167-1000)/ 62.7976/√12
=0.216
The P-value from online calculator
P-value= 0.5836≥0.5
Then conclude that null hypothesis is rejected.
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Set A = 0,3,8 Set A is Not a subset of which set of numbers?
Answers
The Set A defined as A = { 0,3,8} is not a subset of which set is set rational numbers. So, option(a) is right one.
Set is defined as a well defined collection of objects. It is denoted by capital letters of alphabets. The set represented by clearly brackets. We have a set A = { 0,3,8}
Subset is a also a set. A set A is called subset of another set B iff all elements of the set A are elements of the set B. Now,
Set of whole numbers is defined as W = {0,1,...∞}Set of integers, Z = {-∞,..., -1,1,...∞}Set of rational numbers, Q = {-∞,..., 1/2, -1,1,1/2,...∞}The counting set is defined as a set with finite number of elements. It has range set {-∞, ∞}. As we see set A is consists three elements that is counted set. Also, these elements belong to whole and integers set. Hence, set A is subset of whole numbers, natural numbers and counting set.
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Complete question :
Set A = 0,3,8 Set A is Not a subset of which set of numbers?
a) Rational numbers
b) Integers
c) Whole numbers
d) Counting numbers
The graph shows the number of kilometers Gina swims. What is the slope of the line and what does it mean?
Question content area bottom
Part 1
The slope is
enter your response here.
(Type an integer or a simplified fraction.)
Part 2
What does the slope mean?
(Type an integer or a simplified fraction.)
A.
The slope is the time Gina spends while swimming. She swims_____ hours.
The slope is Gina's speed while swimming. She swims
enter your response here kilometers per hour.
C.
The slope is the number of kilometers Gina travels while swimming. She swims _kilometers
enter your response here in kilometers.
enter your response here
Answers
The slope of the line is 3 which represents that the time is rising as the distance increases.
How to calculate the slopeThe slope of the line that passes through the pair of points (3, 6) and (1, 3) is calculated as follows:
slope = (6 - 3) / (3 - 2)
slope = (3) / (1)
slope = 3
In this case, the slope of 3 means that the time is rising as the distance increases.
Therefore, the slope of the line that passes through the pair of points (3, 6) and (1, 3) is 3.
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2. [10 marks] Solve the Cauchy problem 2ux + y = cos x = U.2,0) = sina
Answers
The solution of the Cauchy problem is y = (sina - 1/(2u - 1))e^(ux)cos(sqrt(1 - u^2)x) + (1/(2u - 1))cos(x).
To solve the Cauchy problem 2ux + y = cos x, we first need to find the general solution of the corresponding homogeneous equation 2ux + y = 0.
The characteristic equation is r^2 - 2ur + 1 = 0, which has roots r = u ± sqrt(u^2 - 1).
Case 1: u^2 < 1
In this case, the roots are complex conjugates, so the general solution of the homogeneous equation is
y = c₁e^(ux)cos(sqrt(1 - u^2)x) + c₂e^(ux)sin(sqrt(1 - u^2)x).
Case 2: u^2 > 1
In this case, the roots are real and distinct, so the general solution of the homogeneous equation is
y = c₁e^(r1x) + c₂e^(r2x),
where r1 = u + sqrt(u^2 - 1) and r2 = u - sqrt(u^2 - 1).
Case 3: u^2 = 1
In this case, the root is r = u, so the general solution of the homogeneous equation is
y = c₁e^(ux) + c₂xe^(ux).
Now, we can find the particular solution of the non-homogeneous equation using the method of undetermined coefficients.
Assuming a particular solution of the form y = Asin(x) + Bcos(x), we have
2uB - Asin(x) - Bcos(x) = cos(x).
Matching coefficients, we get A = 0 and 2uB - B = 1, so B = 1/(2u - 1).
Therefore, the particular solution is y = (1/(2u - 1))cos(x).
The general solution to the Cauchy problem is then
y = c₁e^(ux)cos(sqrt(1 - u^2)x) + c₂e^(ux)sin(sqrt(1 - u^2)x) + (1/(2u - 1))cos(x).
To determine the constants c₁ and c₂, we use the initial condition y(2,0) = sina.
Substituting x = 0, we get
c₁ + (1/(2u - 1)) = sina.
Substituting x = pi/2sqrt(1 - u^2), we get
c₂sqrt(1 - u^2) = 0.
Since sqrt(1 - u^2) ≠ 0, we have c₂ = 0.
Therefore, c₁ = sina - 1/(2u - 1), and the solution of the Cauchy problem is
y = (sina - 1/(2u - 1))e^(ux)cos(sqrt(1 - u^2)x) + (1/(2u - 1))cos(x).
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14. section 7.3; problem 2: interpretation a. we are 90% certain that the difference in percentages of men and women experiencing food cravings fall within in the specified interval. b. we are 90% certain that the percentages of men and women experiencing food cravings both fall within in the specified interval. c. 90% of men and women feel that the difference report experiencing food cravings a percentage of the time, specified within the given interval. d. the specified interval represents 90% of the data for men and women having food cravings.
Answers
The correct interpretation is option (a). It states that we are 90% certain that the difference in percentages of men and women experiencing food cravings falls within the specified interval.
Your question is asking for the correct interpretation of a 90% confidence interval for the difference in percentages of men and women experiencing food cravings. Here are the interpretations of each statement:
a. We are 90% certain that the difference in percentages of men and women experiencing food cravings falls within the specified interval.
b. We are 90% certain that the percentages of men and women experiencing food cravings both fall within the specified interval.
c. 90% of men and women feel that the difference report experiencing food cravings a percentage of the time, specified within the given interval.
d. The specified interval represents 90% of the data for men and women having food cravings.
This interpretation accurately reflects the confidence interval for the difference in percentages between the two groups.
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You have
$
15.00
$15.00 and you need to make copies of a flyer at a store that charges
$
0.40
$0.40 per copy. Find the inequality that represents the number of copies you can make. Use
�
x as the variable.
What is the maximum number of copies you can afford to make?
Answers
Answer:
.40x < 15
x < 37.5 copies
The maximum number of copies is 37.
37 × $.40 = $14.80
Consider the following system of equations:
y = −x + 2
y = 3x + 1
Which description best describes the solution to the system of equations?
a
Line y = −x + 2 intersects line y = 3x + 1.
b
Lines y = −x + 2 and y = 3x + 1 intersect the x-axis.
c
Lines y = −x + 2 and y = 3x + 1 intersect the y-axis.
d
Line y = −x + 2 intersects the origin.
Answers
Answer:
Step-by-step explanation:To solve the system of equations, we can set the two expressions for y equal to each other:
−x + 2 = 3x + 1
Solving for x, we get:
4x = 1
x = 1/4
Substituting this value of x into either of the original equations, we get:
y = −(1/4) + 2
y = 7/4
Therefore, the solution to the system of equations is the point (1/4, 7/4), which is the point of intersection of the two lines.
So the correct description of the solution to the system of equations is:
a
Line y = −x + 2 intersects line y = 3x + 1.
Elizabeth has some stickers. She divide her stickers equally amiung herself and two friends. Each person get 4 stickers. Which equation repersents the total number,s,of stickers?
Answers
The correct equation representing the total number, s, of stickers is option C. s/3 = 4.
The formula or relation that can accurately indicate the total number of stickers, number of girls and number of stickers received by girl is as follows -
Total number of stickers/number of girls = number of stickers received by each girl
(We will perform division as number of stickers must be more than number of girls)
Keep the representative value of each
s/3 = 4
Solving it to know the number of stickers
s = 4 × 3
s = 12
Hence, there were 12 stickers divided four each among three girls. Thus, the correct answer is C. s/3 = 4.
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The complete question is -
Elizabeth has some stickers. She divide her stickers equally amiung herself and two friends. Each person get 4 stickers. Which equation repersents the total number,s,of stickers?
A. s + 3 = 4
B. s 3 = 4
C. s/3 = 4
D. 3s = 4
karen, who turns eighty years old this year, has just learned about blood pressure problems in the elderly and is interested in how her blood pressure comoares to those of her peers. She has uncovered an article in a scientific Journal that reports that the mean systolic blood pressure measurement for women over seventy-five is 134.1 mmHg, with a standard deviation of 5.7 mmHg. Assume that the article reported correct information. Complete the following statements about the distribution of systolic blood pressure measurements for women over seventy-five. х (a) According to Chebyshev's theorem, at least 36% of the measurements lie between___mmHg and ___ mmHg. (Round your answer to 1 decimal place.) (b) According to Chebyshev's theorem, at least (Choose one) 36% measurements lie between 122.7 mmHg an of the 56% 75% 84% 89%
Answers
(a) According to Chebyshev's theorem, at least 36% of the measurements lie between 122.7 mmHg and 145.5 mmHg. (b) According to Chebyshev's theorem, at least 56% measurements lie between 122.7 mmHg and 147.2. So, the correct option is 56%.
(a) Using Chebyshev's theorem to find how much data falls within a certain number of standard deviations from the mean.
Using k = 2, to capture at least 75% of the data (which is 1 - 1/2^2 = 0.75).
Using k = 2, we can say that at least 75% of the data falls within the range of 134.1 - 2(5.7) = 122.7 mmHg and 134.1 + 2(5.7) = 145.5 mmHg.
The percentage of data that falls outside of this range is (1 - 0.75)/2 = 0.125, or 12.5%.
Therefore, at least 12.5% of the data falls in each, below 122.7 mmHg and above 145.5 mmHg. This means that at least 36% of the data falls within the range of 122.7 mmHg and 145.5 mmHg.
(b) We can use Chebyshev's theorem again, this time with k = 2.5, since we want to capture at least 56% of the data (which is 1 - 1/2.5^2 = 0.64).
Using the same calculations as in part (a), we find that at least 64% of the data falls within the range of 121.0 mmHg and 147.2 mmHg.
Therefore, we can say that at least 56% of the data falls within this range, since 56% is less than 64%.
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PLS HELP ASAP 100 POINTS
Find the measure of ∠YOZ by answering the questions.
1. Find the measure of ∠WOV. Which angle relationship did you use? (3 points)
2. Now find the measure of ∠YOZ. Which angle relationship did you use?
3. Check your answer by using another strategy to find the measure of ∠YOZ. Describe your strategy, and show that it gives the same measure for ∠YOZ. (4 points)
Answers
The measure of ∠WOV is 60°. You would use complementary angles that are adjacent (∠WOV, and ∠XOW)
How to explain the angleThe measure of ∠YOZ is 60°. You would use the vertical angles that are non-adjacent (∠WOV, and ∠YOZ). These two angles are congruent so they would have the same measure. These angles combined also create supplementary angles
Another way to find the measure of ∠YOZ would be to make/write an equation and solve for x. For example, (3x+30)°=60°. x would equal 10 because 10x3=30+30=60°
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Help me please and thank you so much!!!
Answers
The volume of the figure is given as follows:
V = 132 ft³.
How to calculate the volume?The volume of a triangular prism is given as half the multiplication of the dimensions of the triangle, as follows:
V = 0.5 x l x w x h.
The dimensions of the triangle in this problem are given as follows:
3 ft, 8 ft and 11 ft.
Hence the volume of the prism is given as follows:
V = 0.5 x 3 x 8 x 11
V = 132 ft³.
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What is 011.4583 as a fraction?
Answers
Answer:
11.4583 = 114583 / 10000
Step-by-step explanation: