the length of an instant message conversation is normally distributed with a mean of 5 minutes and a standard deviation of 0.7 minutes. what is the probability that a conversation lasts longer than 6 minutes?
Answers
The probability that a conversation lasts longer than 6 minutes is approximately 0.0764 or 7.64%.
What is probability?
The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place.
We can use the standard normal distribution to solve this problem by standardizing the variable using the formula:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
In this case, we want to find the probability that a conversation lasts longer than 6 minutes, so x = 6, μ = 5, and σ = 0.7. Substituting these values into the formula, we get:
z = (6 - 5) / 0.7 = 1.43
Next, we can use a standard normal distribution table or a calculator to find the probability that a standard normal random variable is greater than 1.43. Using a standard normal distribution table, we find that this probability is approximately 0.0764.
Therefore, the probability that a conversation lasts longer than 6 minutes is approximately 0.0764 or 7.64%.
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Related Questions
Is the event independent or overlapping:
A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?
Mutually exclusive or independent:
A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5.
Mutually exclusive or overlapping:
A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that is is a milk chocolate or has no peanuts inside?
Mutually exclusive or independent:
You flip a coin and then roll a fair six sided die. What is the probability the coin lands on heads up and the die shows an even number?
Answers
1. A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?
In this case, the spinner's outcome of landing on region three is independent of landing on region six. Each spin is unrelated to the previous spin, and the outcome of one region does not affect the outcome of the other region. Therefore, the events are independent. The probability of landing on both region three and region six is the product of their individual probabilities: 1/8 * 1/8 = 1/64.
2. A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?
In this scenario, the events are overlapping. A jersey can be both purple and have a number greater than 5 at the same time. Therefore, the probability of it being purple or having a number greater than 5 is the sum of their individual probabilities, minus the probability of the overlapping event (purple jerseys with a number greater than 5). There are 4 purple jerseys out of 10 total jerseys, and there is 1 jersey with a number greater than 5 out of 10. However, there is one jersey that satisfies both conditions (purple and number greater than 5), so we need to subtract it from the sum. So the probability is (4/10 + 1/10) - (1/10) = 4/10 = 2/5.
3. A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?
In this scenario, the events are mutually exclusive. A chocolate cannot be both a milk chocolate and have no peanuts inside at the same time. Therefore, the probability of it being a milk chocolate or having no peanuts inside is the sum of their individual probabilities. There are 6 milk chocolates out of 10 total chocolates, and there are 7 chocolates without peanuts out of 10. So the probability is 6/10 + 7/10 = 13/10, which is greater than 1. However, probabilities cannot exceed 1, so we need to take the maximum value of 1. Therefore, the probability is 1.
4. You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?
In this case, the events are independent. The outcome of the coin flip does not affect the outcome of the die roll. The probability of the coin landing heads up is 1/2, and the probability of the die showing an even number is 1/2. To find the probability of both events occurring, we multiply their individual probabilities: 1/2 * 1/2 = 1/4.
I hope this clarifies the nature of each event. Let me know if you have any further questions!
The first question:
"A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?"
Since the spinner has an equal chance of landing on each of its eight regions, the probability of landing on region three is 1/8, and the probability of landing on region six is also 1/8.
To find the probability of both events occurring (landing on region three and region six), you multiply the probabilities together:
P(landing on region three and region six) = P(landing on region three) * P(landing on region six) = (1/8) * (1/8) = 1/64.
Therefore, the probability of landing on both region three and region six is 1/64.
The events are mutually exclusive because it is not possible for the spinner to land on both region three and region six simultaneously.
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The second question:
"A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?"
To find the probability of either event occurring (purple or number greater than 5), we need to calculate the probabilities separately and then add them.
The probability of picking a purple jersey is 4/10 since there are four purple jerseys out of a total of ten jerseys.
The probability of picking a jersey with a number greater than 5 is 2/10 since there are two jerseys numbered 6 and above out of a total of ten jerseys.
To find the probability of either event occurring, we add the probabilities together:
P(purple or number greater than 5) = P(purple) + P(number greater than 5) = (4/10) + (2/10) = 6/10 = 3/5.
Therefore, the probability of picking a purple jersey or a jersey with a number greater than 5 is 3/5.
The events are overlapping since it is possible for the jersey to be both purple and have a number greater than 5.
--------------------------------------------------------------------------------------------------------------------------
The third question:
"A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?"
To find the probability of either event occurring (milk chocolate or no peanuts inside), we need to calculate the probabilities separately and then add them.
The probability of selecting a milk chocolate is 6/10 since there are six milk chocolates out of a total of ten chocolates.
The probability of selecting a chocolate with no peanuts inside is 7/10 since there are seven chocolates without peanuts out of a total of ten chocolates.
To find the probability of either event occurring, we add the probabilities together:
P(milk chocolate or no peanuts inside) = P(milk chocolate) + P(no peanuts inside) = (6/10) + (7/10) = 13/10.
Therefore, the probability of selecting a milk chocolate or a chocolate with no peanuts inside is 13/10.
The events are mutually exclusive since a chocolate cannot be both a milk chocolate and have no peanuts inside simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The fourth question:
"You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?"
The probability of the coin landing heads up is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely.
The probability of rolling an even number on the die is 3
/6 or 1/2 since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.
To find the probability of both events occurring (coin lands heads up and die shows an even number), we multiply the probabilities together:
P(coin lands heads up and die shows an even number) = P(coin lands heads up) * P(die shows an even number) = (1/2) * (1/2) = 1/4.
Therefore, the probability of the coin landing heads up and the die showing an even number is 1/4.
The events are independent since the outcome of flipping the coin does not affect the outcome of rolling the die.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
For the following system, if you isolated x in the first equation to use the substitution method, what expression would you substitute into the second equation?
-x + 2y = -6
3x + y = 8
O-2y +6
Answers
Answer: x = 2y + 6
Step-by-step explanation:
We just need to see what isolating x in the first equation looks like:
-x+2y=-6
-x=-2y-6
x = 2y + 6
We can use this in the second equation. Hope this helps!
JUST THE FIRST ONE EASY PLS ASAP
Answers
Answer:
For the first triangle, x equals 22cm.Here's how:-
x is the altitude or height of the triangle. To find it, we can use the Pythagoras theorem:-
\(altitude^{2} + base^{2} = hypotenuse^{2}\)
The base is 120cm and the hypotenuse is 122cm
Putting this in the equation, we get:-
\(altitude^{2} + 120^{2} = 122^{2}\)
\(altitude^{2} = 122^{2}- 120^{2}\)
\(altitude^{2} = 14884 - 14400\)
\(altitude^{2}\) = 484
altitude = \(\sqrt{484}\)
altitude = 22cmSo, x = 22cmA boy walks 5km due north and then 4km due east. Find the bearing of his current position from the starting point, how far is the boy now from the starting point
Answers
Use the quadratic formula to find the solutions to the quadratic equation
below.
2x²-5x+ 5 = 0
O A. x=-
OB. X=
O C. x=
5±i√55
4
OD. X=-
5± √15
4
5± √55
4
5+√15
4
Answers
A quadratic equation's solutions can be found using the quadratic formula, which is option D.
What's the quadratic equation's formula?Any quadratic problem can be resolved using the quadratic formula. First, we change the equation's form to ax2+bx+c=0, where a, b, and c are the coefficients. Then, we enter these coefficients into the formula: (-b(b2-4ac))/(2a). View examples of how to apply the formula to a range of equations.If necessary, simplify the right side while writing the left side as a square. Create two linear equations by combining the positive and negative square roots of the right side with the square root of the left side. Each of the two linear equations must be resolved.Explanation:
2x^2 - 5x +5 = 0.
x = - 5 +-\(\sqrt{5\).
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A quadratic equation's solutions can be found using the quadratic formula, which is option D.
What's the quadratic equation's formula?Any quadratic problem can be resolved using the quadratic formula. First, we change the equation's form to ax2+bx+c=0, where a, b, and c are the coefficients. Then, we enter these coefficients into the formula: (-b(b2-4ac))/(2a). View examples of how to apply the formula to a range of equations.
If necessary, simplify the right side while writing the left side as a square. Create two linear equations by combining the positive and negative square roots of the right side with the square root of the left side. Each of the two linear equations must be resolved.
2x^2 - 5x +5 = 0.
x = - 5 \(\pm\) √5
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you read a news report saying that every 25 grams of white fruits and
evegtables consumed per day leads to a 9% decrease in the risk of stroke. Assume 807 persons out
of 10,000 persons in a particular population suffer a stroke sometime in their lifetime. What is the
adjusted lifetime risk of stroke if every member of the population adds 25 grams of white fruits and
vegetables to their daily diet?
Answers
Using proportions, the adjusted lifetime risk of stroke if every member of the population adds 25 grams of white fruits and vegetables to their daily diet is of 7.34%.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships.
One example of application of proportions is for percentage problems, as the decimal equivalent of the percentage is multiplied to the total amount to find the equivalent amount.
807 persons out of 10,000 persons in a particular population suffer a stroke sometime in their lifetime, hence the risk is given by:
r = 807/10000 = 0.0807.
A 9% decrease means that the adjusted risk will be of 91% of that amount, hence:
0.91 x 0.0807 = 0.0734 = 7.34%.
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Express 6 hours 28 minutes and 16 seconds in decimal form. Round your answer to two decimal places.
Answers
Answer: 6.47 hours
Step-by-step explanation:
First, you need to change your seconds into terms of minutes.
16 seconds / 60 s in a min = .266 min
Add that to your minutes:
28+.266 = 28.266 minutes
Now convert your minutes into hours
28.266 min/60 min in an hour=.47
Add that to your hours:
6+.47= 6.47 hours total
Which of the following explains why this inequality is true?
7 3/8 × 4/5 < 7 3/8
The answers I have to choose from are:
A. When 7 3/8 is multiplied by a number greater than 1, the product is more than 7 3/8
B. When 7 3/8 is multiplied by a number greater than 1, the product is less than 7 3/8
C. When 7 3/8 is multiplied by a number less than 1, the product is more than 7 3/8
D. When 7 3/8 is multiplied by a number less than 1, the product is less than 7 3/8.
Answers
The correct option is B: The result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.
Explain about the term mixed fractions:Once kids have a firm grasp on right fractions, they are exposed to mixed numbers and improper fractions.
Divide the numerator and denominator to create a mixed fractions from an incorrect fraction. The solution to this problem is the whole number portion; the leftover portion is the numerator; its denominator stays the same.
We can convert the two fractions to decimal form in order to compare them.
7.375 is equivalent to 7 3/8, and
4/5 is equivalent to 0.8.
7.375 multiplied by 0.8 results in:
7.375 × 0.8 = 5.9
Since the result is 5.9, which is less than 7.375, it follows that 7 3/8 multiplied by 4/5 is less than 7 3/8.
Thus, the result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.
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sequence three missing terms to comple 7444> →→19-
Answers
To complete the sequence "7444> →→19-", we need to find the missing terms that fit the pattern established by the given numbers. Let's analyze the sequence and identify any discernible pattern or rule.
Looking at the sequence, we can observe that each number is decreasing by a certain value. In this case, the first number is 7444, and the second number is 19, indicating a decrease of 7425. Now, we need to continue this pattern.
To find the third missing term, we subtract 7425 from 19, resulting in -7406. Therefore, the third missing term is -7406
To find the fourth missing term, we subtract 7425 from -7406, resulting in -14831. Therefore, the fourth missing term is -14831.
To find the fifth missing term, we subtract 7425 from -14831, resulting in -22256. Therefore, the fifth missing term is -22256.
Therefore, the completed sequence is:
7444> →→19- → -7406 → -14831 → -22256
Each term in the sequence is obtained by subtracting 7425 from the previous term.
It's important to note that this solution assumes a linear pattern in which the same subtraction value is applied to each term. However, without additional context or information about the sequence, there could be alternative patterns or interpretations.
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Help with my school work, I spend 80 points on this question. I will give brainiest for correct answer.
If 1 + 2 = 3, then why does 4 + 5 not = 6?
And if 2 x 2 = 4, then why does 4 x 4 not = 8?
Answers
Answer:
Because equations is not counting, and multiply is not addition.
Step-by-step explanation:
Addition is: a process of combining two or more numbers. Addends are the numbers being added, and the result or the final answer we get after the process is called the sum. It is one of the essential mathematical functions we use in our everyday activities. There are many situations in which we add numbers.
Like lets say you have 1 apple, and your friend gives 2 more, then you have 3. If you have 4 apples, and your friend gives 5 more, then you have 9 apples.
Its always better to start with the bigger number, it makes it easier, like 2 + 1 = 3, or 5 + 4 = 9.
Now multiplication is harder. Multiplication is: the basic explanation of multiplication is adding a number, with respect to another number, repeatedly. For example, if we are multiplying 2 by 3, that means 3 is added to itself two times, i.e. 3 + 3 = 6. This is a simple technique for kids to multiply numbers.
(Answer) 2 x 2 would equal 4. (Explanation) Add a 2, with respect to 2, repeatedly, would equal 4.
(Answer) 4 x 4 would equal 16. (Explanation) Add a 4, with respect to 4, repeatedly, would equal 16.
I hope it helps you out!Mark me as brainiest please. HAVE A GREAT REST OF YOUR DAY/NIGHT!!!
Answer: Step-by-step explanation:
because 1 + 2 does equal 3 but 4 + 5 does not equal to 6 because it equals to 9.
and 2 x 2 does equal to 4 but 4 x 4 does not equal to 8 because it equals to 16.
Mark me brainiest pls.Have good day.Find the area of the figure. 5in 2in 4in 5in
Answers
Answer: Your answer is 23.5in²
Hope it helped :D
Good Luck!
Evaluating Expressions I
Slumbertec is a sleep medication designed for patients with severe insomnia. The follow function is a
pretty good measure of the dosage a patient needs depending on their weight:
where w represents the patient's weight in pounds, and
d represents the dosage required in milligrams (mg).
a. Under the function equation above, label the meaning of the variables d and w.
b. Evaluate 2w-60 when w-140.
d=2w-60
C.
17
When w 175, the value of 2w-60 is 290. Explain what this means in the context of this
function. In other words, what does this tell you about the patient and this medicine?
d. Evaluate 2w-60 when w-25. Explain what this means in the context of this function.
e. Your patient was prescribed 260 mg of Slumbertec by another doctor. What would you guess was
the patient's weight at the time when the prescription was written?
Answers
a. The meaning of the variables are:
w = weightd = dosageb. Evaluating 2w-60 when w =140. d = 220 mg
c. Evaluate 2w-60 when w= 175, d = 290 mg
This means that for a weight of 175 pounds the dose is 290 mgd. Evaluate 2w-60 when w = 25. d = -10 mg
Explanation: This means the drug is not recommended for patients weighing 25e. Evaluate 2w-60 when d = 260 mg
At the time of prescription the patient was weighing 160 poundsGiven data
d=2w-60
where:
w = weight
d = dosage
How to find the the required variable in the options
a. label the meaning of the variables
w = weight
d = dosage
b. Evaluate 2w-60 when w = 140,
d=2w-60
d = 2 * 140 - 60
d = 220
c. Evaluate 2w-60 when w= 175
d=2w-60
d = 2 * 175 - 60
d = 290
This means that for a weight of 175 pounds the dosage is 290 mg
d. Evaluate 2w-60 when w = 25
d=2w-60
d = 2 * 25 - 60
d = -10
Explanation: This means the drug is not recommended for patients weighing 25
e. Evaluate 2w-60 when d = 260
260 = 2w - 60
2w = 260 + 60
2w = 320
w = 160
At the time of prescription the patient was weighing 160 pounds
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Aris and Josiah are reading a 50-page book for their ELA class. Aris wants to know what page Josiah is reading. Josiah gives her two hints: 1. The product of the two page numbers he can see is 930. 2. The page he is reading is an odd numbered page.
Answers
Answer:
31
Step-by-step explanation:
Let x and (x + 1) be the page numbers Josiah can see
Hint 1: x(x + 1) = 930
⇒ x² + x = 930
⇒ x² + x - 930 = 0
Using quadratic formula,
\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)
a = 1, b = 1 and c = -930
\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)
\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)
Sice x is a page number, it cannot be negative
⇒ x = 30 and
x + 1 = 31
The two pages Josiah can see are pg.30 and pg.31
Hint 2: The page he is reading is an odd number
Out of the pages 30 and 31, 31 is an odd number
Thereofre, Josiah is reading page 31
helpppppp pl for 5 point
Answers
Answer:
\(3^{-2} * 3^3\)
Step-by-step explanation:
Multiply 1/9 and 27 to get 27/9 which reduces to 3. When doing these equations, you add up the exponents. To get 3, you would have to have 3^1. The get this, the only equation that would work is 3^-2 x 3^3
-2+3 gets 1. So 3^1 which gets you 3. So this is the answer.
Pls help I’ll brainlest
Answers
Answer:
30.5 feet / minute
Step-by-step explanation:
Rate of descent is the same as speed (of falling). The formula for speed is distance / time = speed
First, find how much it fell.
4595 - 3131 = 1464 feet
Divide the distance by the time.
1464 feet / 48 minutes = 30.5 feet / minute
Name 2 decimals that round to 8.64.
I need help plzzzzz
Answers
Answer:
8.643, 8.639
Step-by-step explanation:
Step-by-step explanation:
What is the number 8.64 rounded to the nearest tenth? -
What is 2.098 rounded to two decimal places? ... You could also use round-to-odd, which is like round-to-even in its ability to remove bias, ...
The supermarket has 30 aisles. 60% are empty, without any shoppers. How many empty aisles are there in the supermarket?
Answers
Answer:
18
Step-by-step explanation:
to find the percentage of something you change the percent to a decimal and multiply it by the other number, so in this case you have 0.6*30 and you get 18.
hope this helped :))
A shopping center plans to buy some desks, cupboards, and
beds. They will buy a total of 300 pieces of furniture. The ratio
of the number of desks to cupboards to beds it plans to
purchase is 5:3:2.
They budget $139,500 to buy the furniture. A desk costs $250
and a bed costs $500. What is the price of a cupboard?
$
Answers
Which function has a greater maximum?
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A coordinate plane. The x- and y-axes both scale by one. The graph is the function y equals g of x which is a parabola that opens down. The function increases through negative four, negative five and negative three, negative two. It has a maximum at negative two, one, then the function decreases through negative one, negative two and zero, negative five.
Answers
The function f(x) = \(-2(x+4)^2\) + 1 has a greater maximum.
1. The given function is f(x) = \(-2(x+4)^2\) + 1.
2. To find the maximum of the function, we need to determine the vertex of the parabola.
3. The vertex form of a quadratic function is given by f(x) = \(a(x-h)^2\) + k, where (h, k) represents the vertex.
4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.
5. The x-coordinate of the vertex is given by h = -4.
6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = \(-2(-4+4)^2\) + 1 = \(-2(0)^2\) + 1 = 1.
7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.
8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = \(-2(x+4)^2\) + 1 is greater than the maximum of g(x).
9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.
10. Hence, the function f(x) =\(-2(x+4)^2\) + 1 has a greater maximum.
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Over a 14-day period, Jamal went to the store 4 times. Based on this
information, which statement best describes how many times Jamal will go
to the store in a 5-week period?
Answers
Answer:
He will go to the store 10 times in a 5-week period.
Step-by-step explanation:
We can assume that in one week, Jamal went to the store 2 times, considering he went to the store 4 times in 2 weeks. Next, we can assume that he will go to the store 10 times in 5 weeks, since 2×5=10.
help please!! m=5 and n=2. 2m-5n!
Answers
Step-by-step explanation:
so, what's the problem ?
it's all there, we only need to take the calculator (or simply our heads) and do the calculation :
2×5 - 5×2 = 10 - 10 = 0
you see ? that was all that was needed.
put the given values for the variables into the places of these variables, and then calculate !
that is what variables are for : placeholders for actual values.
Solve the following exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.What is the exact answer? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.(Simplify your answer. Type an exact answer.)What is the answer rounded to three decimal places? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.(Simplify your answer. Type an integer or decimal rounded to three decimal places as needed.)
Answers
To solve the exponential equation, we apply natural logarithm from both sides of it:
\(\begin{gathered} 4^{1-9x}=5^x \\ \ln (4^{1-9x})=\ln (5^x) \end{gathered}\)Now, we apply the power rule of the logarithms:
\(\log _b(M^p)=p\cdot\log _b(M)\Rightarrow\text{ Power rule}\)\(\begin{gathered} \ln (4^{1-9x})=\ln (5^x) \\ (1-9x)\ln (4^{})=x\ln (5^{}) \end{gathered}\)Now, we apply the distributive property on the left side of the equation:
\(\begin{gathered} 1\cdot\ln (4)-9x\cdot\ln (4^{})=x\ln (5^{}) \\ \ln (4)-9x\ln (4^{})=x\ln (5^{}) \end{gathered}\)Now, we subtract xln(5) from both sides of the equation:
\(\begin{gathered} \ln (4)-9x\ln (4^{})-x\ln (5)=x\ln (5^{})-x\ln (5) \\ \ln (4)-9x\ln (4^{})-x\ln (5)=0 \end{gathered}\)Now, we subtract ln(4) from both sides:
\(\begin{gathered} \ln (4)-9x\ln (4^{})-x\ln (5)-\ln (4)=0-\ln (4) \\ -9x\ln (4^{})-x\ln (5)=-\ln (4) \end{gathered}\)Now, we factor x on the left side:
\(\begin{gathered} x(-9\ln (4^{})-\ln (5))=-\ln (4) \\ \text{ Divide by }-9\ln (4)^{}-\ln (5)\text{ from both sides} \\ \frac{x(-9\ln(4^{})-\ln(5))}{(-9\ln(4^{})-\ln(5))}=\frac{-\ln(4)}{(-9\ln(4^{})-\ln(5))} \\ x=\frac{-\ln(4)}{(-9\ln(4^{})-\ln(5))} \\ x=\frac{-\ln(4)}{-(9\ln(4^{})+\ln(5))} \\ x=\frac{\ln(4)}{9\ln(4^{})+\ln(5)} \end{gathered}\)Thus, the exact solution is:
\($$\boldsymbol{x=\frac{\ln(4)}{9\ln(4^{})+\ln(5)}}$$\)And the solution rounded to three decimal places is:
\($$\boldsymbol{x=0.098}$$\)Explain why the following problem will have an irrational answer 4.125+3
Answers
Answer:
The answer is rational.
Step-by-step explanation:
It won' be irrational.
4.125 and 3 are rational.
Answer: The sum is a non-repeating
Step-by-step explanation:
Which of the following numbers has the least number of 1’s in their binary representation? A) BAD(16) B) FED(16) C) CAB(16) D) ACE(16)
Note: the (16) means base 16
Answers
Answer: B
Step-by-step explanation:
Analyzing the Intervals of a Function A 2-column table with 7 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries 15, 0, 3, 0, negative 3, 0, 15. Predict which statements are true about the intervals of the continuous function. Check all that apply. f(x) > 0 over the interval (−, 3). f(x) ≤ 0 over the interval [0, 2]. f(x) < 0 over the interval (−1, 1). f(x) > 0 over the interval (–2, 0). f(x) ≥ 0 over the interval [2, )
Answers
The predicted interval for the given function is, f(x) ≥ 0 over the interval [-1,1]. So Option C is correct
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Vertical line test:-
Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.
If we get more images then it will not be a function.
For example, let us take, y² = 4ax
y = ±√4ax
For single value of x we get two values of y
Hence, it will not be a function.
Given that,
The ordered pairs of the given function
(-3,15), (-2,-5), (-1,0), (0,5), and (1,0).
It can be observed from the values of f(x) with respect to x, that the function reaches zero at x = -1, then then reach up to 5 at x = 0 and then again reaches zero at x = 1
Hence, the value of f(x) remains positive within the interval of [-1,1].
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Select the two values of x that are roots of this equation 2x^2+5x-3=0
Answers
Answer:
A and D are the answer.
Step-by-step explanation:
We can factor this by grouping
\(2 {x}^{2} + 5x - 3\)
\(2 {x}^{2} + 6x - x - 3\)
\(2x(x + 3) -1 (x + 3)\)
The roots are
\((x + 3) = 0\)
and
\(2x - 1 = 0\)
Let solve for zero in each roots.
\(x = - 3\)
\(2x = 1\)
\(x = \frac{1}{2} \)
The three steps below were used to find the value of the expression [(-10 + 2) - 1] + (2 + 3). Step 1: ? Step 2: -9 + 2 + 3 Step 3: -7 + 3 Which expression is missing from Step 1? Question 3 options: [-10 + -1 + 2] + (2 + 3) [-8 - 1] + (2 + 3) [-10 + 1] + (2 + 3) [8 + 1] + (2 + 3)
Answers
Therefore, the missing expression in Step 1 is [-8 - 1] + (2 + 3).
In order to find the missing expression in Step 1, let's analyze the given steps and the final expression.
Step 1: ?
Step 2: -9 + 2 + 3
Step 3: -7 + 3
To find the missing expression in Step 1, we need to work backwards from Step 3 to Step 1.
In Step 3, the expression "-7 + 3" gives us a result of -4.
In Step 2, the expression "-9 + 2 + 3" gives us a result of -4.
So, the missing expression in Step 1 should also evaluate to -4 when performed correctly.
Let's check the available options:
[-10 + -1 + 2] + (2 + 3) = -11 + 2 + 5 = -4
[-8 - 1] + (2 + 3) = -9 + 5 = -4
[-10 + 1] + (2 + 3) = -9 + 5 = -4
[8 + 1] + (2 + 3) = 9 + 5 = 14
Out of the given options, only option 2, [-8 - 1] + (2 + 3), correctly evaluates to -4. Therefore, the missing expression in Step 1 is [-8 - 1] + (2 + 3).
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What is the distance from C to B
please help me
Answers
Anthony works as a salesperson at an electronics store and sells phones and phone accessories. Anthony earns a $8 commission for every phone he sells and a $4 commission for every accessory he sells. On a given day, Anthony made a total of $80 in commission and sold 5 more accessories than phones. Graphically solve a system of equations in order to determine the number of phones sold, x,x, and the number of accessories sold, yy.
Answers
Answer:
There were 5 phones sold and 10 accessories sold.
Step-by-step explanation:
find the value of the power.
7-⁴
The value of the power is ( )
Answers
Answer:
1/2401
Step-by-step explanation:
\(7^{-4}=\dfrac{1}{7^4}=\boxed{\dfrac{1}{2401}}\)