Answer:
n = -3 or n = -6
Step-by-step explanation:
Solve for n over the real numbers:
n^2 + 9 n + 18 = 0
Subtract 18 from both sides:
n^2 + 9 n = -18
Add 81/4 to both sides:
n^2 + 9 n + 81/4 = 9/4
Write the left-hand side as a square:
(n + 9/2)^2 = 9/4
Take the square root of both sides:
n + 9/2 = 3/2 or n + 9/2 = -3/2
Subtract 9/2 from both sides:
n = -3 or n + 9/2 = -3/2
Subtract 9/2 from both sides:
Answer: n = -3 or n = -6
50 pts.
Can someone help me with this. I cant figure it out
Answer:
2
Step-by-step explanation:
We use complex conjugates. A complex number multiplied by its conjugate creates a difference of squares pattern. In this scenario, 3-2i’s conjugate is 3+2i, because (3-2i)(3+2i)=9-(-4)=13. So how do we use conjugates to simplify this expression? We first multiply by [tex]\frac{3+2i}{3+2i}[/tex] to make the denominator real, while keeping the fraction the same, because the fraction we multiplied is 1.
our new fraction is (8-i)(3+2i)/13.
Expand the numerator: (26+13i)/13 = 2+i, so a is 2
Question 9, please help
9/10
Answer:A
Step-by-step explanation:
can someone please help me answer these questions and show me how you got the answer. thank you!
1.) write an equation for a line perpendicular to y=2x+3 and passing through the point (4-6)
2.) (11-3i)(7-12i)
3.) (185-72i) divided by (11+10i)
4.) solve the equation by completing the square: y^2-6y+19=5
1) y + (1/2)x = 2
2)-59 - 153i
3)1315 - 62i
4)No real solutions
1) Equation for a line perpendicular to y=2x+3 and passing through the point (4-6)A line perpendicular to y = 2x + 3 would have a slope of -1/2 (the negative reciprocal of 2). To find the equation of the line, we use point-slope form. We substitute the point (4, -6) and the slope of -1/2:We know that the line must pass through the point (4, -6) and be perpendicular to the line y = 2x + 3, so we can write its equation in point-slope form as follows:y - (-6) = (-1/2)(x - 4)y + 6 = (-1/2)x + 2The answer is y + (1/2)x = 2.
2) Multiplying the complex numbers (11-3i)(7-12i)We will be using the FOIL method (first, outer, inner, last) for multiplying two binomials:First, we multiply 11 and 7 to get 77.Then, we multiply 11 and -12i to get -132i.Next, we multiply -3i and 7 to get -21i.Last, we multiply -3i and -12i to get 36i² (remembering that i² is equal to -1).Finally, we combine like terms:77 - 132i - 21i + 36i² = 77 - 153i - 36 = -59 - 153iThe answer is -59 - 153i.
3) Dividing complex numbers (185-72i) divided by (11+10i)To divide complex numbers, we need to multiply the numerator and denominator by the conjugate of the denominator (in which the sign of the imaginary part is changed):We multiply the numerator and denominator by the conjugate of 11 + 10i, which is 11 - 10i in this case, to eliminate the imaginary part from the denominator:(185 - 72i)(11 - 10i) = (185 × 11 - 72i × 11) - (185 × 10i + 72i × 10i) = (2035 - 792i) - (1850i + 720i²)Simplifying, we get:(2035 - 792i) - (1850i + 720i²) = (2035 - 792i) - (1850i + 720(-1)) = (2035 - 792i) - (1850i - 720) = 1315 - 62iThe answer is 1315 - 62i.
4) Solving an equation by completing the square: y² - 6y + 19 = 5First, we isolate the y terms and move the constant to the other side:y² - 6y + 14 = 0Next, we divide both sides by the leading coefficient (1 in this case):y² - 6y = -14To complete the square, we take half the coefficient of y, square it, and add it to both sides. In this case, that's (-6/2)² = 9:y² - 6y + 9 = -5Now, we factor the left-hand side as a perfect square:(y - 3)² = -5Finally, we take the square root of both sides:(y - 3) = ±√(-5)This expression has no real solutions because the square root of a negative number is imaginary. Therefore, the answer is "No real solutions."
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Autumn went shopping for a new pair of sneakers. The listed price of the pair of sneakers was $22, but the price with tax came to $23.98. Find the percent sales tax.
Answer:
To find the percent sales tax, we can use the following formula:
Percent tax = (Tax amount ÷ Base price) × 100%
Where "Base price" is the original price of the item before tax is added.
In this case, the base price of the sneakers is $22, and the total price with tax is $23.98. The tax amount is:
Tax amount = Total price - Base price
Tax amount = $23.98 - $22
Tax amount = $1.98
Now we can calculate the percent sales tax:
Percent tax = (Tax amount ÷ Base price) × 100%
Percent tax = ($1.98 ÷ $22) × 100%
Percent tax = 0.09 × 100%
Percent tax = 9%
Therefore, the percent sales tax is 9%.
give the expression for 4-x and explaine WHY 4 comes before the variable
Answer:y=4-X
Step-by-step explanation:
the 4 comes before the variable because you are subtracting the 4 by the variable.
Determine the value of x
in the equation below.
x/4 = 6
Answer: x=24
Step-by-step explanation:
When you get this type of problem you do the opposite of the equation
so for this one you 4x6=24 because it x divided by 4 so we times.
What is the equation of the circle below?
The equation of the given circle is (x-2)² + (y+1)² = 9.
What is a Circle?
In mathematics Round and in two dimensions, a circle is a figure. The circle's center is a place inside the circle from which all points on the circle's edge are equally far.
The radius of the circle, abbreviated "r," is the distance from the center of the circle to a point on its edge. The diameter of the circle, which is the greatest chord of any circle, is equal to the circle's doubled radius.
We know that, equation of a circle is given by :
(x-h)² + (y-k)² = r²
where, (h, k) are coordinates of the center of circle.
Here, the coordinates of center of circle is (2,-1) and the radius is 3 units.
So, equation of given circle :
(x-h)² + (y-k)² = r²
(x-2)² + (y+1)² = 3²
(x-2)² + (y+1)² = 9
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Which inequality represents all the solutions of 4(3x + 2) < 5(3x − 2)? Select the correct answer. X < -6 x > -6 x < 6 x > 6
we divide both sides by 7, giving us x < -6, which is the answer.We can do this by using the distributive property and combining like terms on the left side of the inequality.
To solve this inequality, we must first isolate the variable x on one side of the inequality. We can do this by using the distributive property and combining like terms on the left side of the inequality. We start by multiplying 4 and 3x, which gives us 12x. We then add two to both sides, giving us 12x + 2 < 5(3x - 2). We then distribute 5 over the parentheses on the right side, giving us 12x + 2 < 15x - 10. We then combine like terms on the left side, giving us 7x < -8. Finally, we divide both sides by 7, giving us x < -6, which is the answer.
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A clothing designer is interested in determining if there is a relationship between a person’s age and their preference for a particular style of dress. A survey is written and asks questions including questions about age and dress size. Should these questions be included in the survey?
A. The questions are acceptable because the researcher is studying the relationship between age and preferred dress style.
B. The questions should not be included because people may not want to answer questions about age and dress size.
C. The questions can be included but there should be an option where the participant can choose not to respond to the questions.
D. The questions should not be included because surveys should never ask for personal information.
Option (a) is correct i.e., the questions are acceptable because the researcher is studying the relationship between age and preferred dress style.
What is the age in math?Age is any person time he live till time calculated. Use age we solve different math problems.
Like calculate the age of a person or what was his age 5 year ago.
If the age is given in the form of a ratio, for example, a:g, then the age shall be considered as g h and a h. If you are assuming the current age to be h, then n times the current age will be (h × n) years. If you are assuming the current age to be h, then 1/n of the age shall be equal to ( h / n) years.
Option (a) is correct i.e., the questions are acceptable because the researcher is studying the relationship between age and preferred dress style.
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The researcher is investigating the association between age and favourite dress style, thus the questions are appropriate. The assertion is true.
What exactly is my age?Days are calculated as the difference between both the current day and the person's birth day. Age is calculated as follows: aged = (years x 365) + (months x 31) + days. The person's age is expressed in days. For the age in years, divide the figure by 365.
How do you determine age manually?Age is determined by comparing a person's birthdate to the day on which age must be determined. The age of a person is determined by subtracting the provided date from the individual's birthdate. Provided date minus birthdate equals age of a person.
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The volume of a cylinder is given, find dimensions of cylinder
If the volume of a cylinder is given, the dimensions of cylinder can be written and r = √(V/(πh)) and h = V/(πr²)
The volume of a cylinder is given, find dimensions of cylinder. To find the dimensions of a cylinder given its volume, we need to know either the radius or height. The formula for the volume of a cylinder is:
V = πr²h
where V is the volume, r is the radius, and h is the height.
If we are given the volume V, we can solve for either r or h as follows:
If we solve for the radius r:
V = πr²h
r² = V/(πh)
r = √(V/(πh))
If we solve for the height h:
V = πr²h
h = V/(πr²)
So, to find the dimensions of the cylinder, we need to know the volume V and either the radius r or height h. Once we have one of these values, we can use the equations above to find the other value and determine the dimensions of the cylinder.
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It is common knowledge that a fair penny will land heads up 50% of the time and tails up 50% of the time. It is very unlikely for a penny to land on its edge when flipped, so a probability of 0 is assigned to this outcome. A curious student suspects that 5 pennies glued together will land on their edge 50% of the time. To investigate this claim, the student securely glues together 5 pennies and flips the penny stack 100 times. Of the 100 flips, the penny stack lands on its edge 46 times. The student would like to know if the data provide convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5. The student tests the hypotheses H0: p = 0.50 versus Ha: p ≠ 0.50, where p = the true proportion of all flips for which the penny stack will land on its edge. The conditions for inference are met. The standardized test statistic is z = –0.80 and the P-value is 0.2119. What conclusion should the student make using the α = 0.10 significance level?
Because the test statistic is less than α = 0.10, there is convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
Because the P-value is greater than α = 0.10, there is convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
Because the P-value is greater than α = 0.10, there is not convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
Because the test statistic is less than α = 0.10, there is not convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
answer is c
It is possible that the observed proportion of 0.46 is due to chance, and the true proportion is actually 0.5.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
which the penny stack will land on its edge.
To test the hypotheses, the student can use a two-sided z-test for proportions. The test statistic is calculated as:
z = (p' - p) / sqrt(p * (1 - p) / n),
where p' is the sample proportion (46/100), p is the hypothesized proportion (0.5), and n is the sample size (100).
Substituting the values, we get:
z = (0.46 - 0.5) / sqrt(0.5 * 0.5 / 100) = -0.8
Using a significance level of 0.05 (i.e., a 95% confidence level), the critical values for a two-sided test are -1.96 and 1.96.
Since the calculated z-score (-0.8) falls between the critical values, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
In other words, the data does not provide convincing evidence that the student's claim is true.
Therefore, It is possible that the observed proportion of 0.46 is due to chance, and the true proportion is actually 0.5.
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ax+b=dx-1 if a does not equal d
Answer:
your question is unclear
i assume the answer would be
x= -(b+1)/(a-d)
Select the correct answer from the drop-down menu.
Triangle ABC has a perimeter of 40 inches. What is AC?
The required value of AC is 10 inches.
How to find the value of AC?Let's use the fact that the perimeter of a triangle is the sum of the lengths of its sides. We are given that the perimeter of triangle ABC is 40 in:
AB + BC + AC = 40
We are also given the lengths of AB, AC, and BC in terms of x:
AB = 2x
AC = x + 1
BC = x + 3
Substituting these values into the equation for the perimeter, we get:
2x + (x + 3) + (x + 1) = 40
Simplifying and solving for x, we get:
4x + 4 = 40
4x = 36
x = 9
Now that we know the value of x, we can find the length of AC:
AC = x + 1 = 9 + 1 = 10
Therefore, The required value of AC is 10 inches.
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trust me its 10 i just did it
Step-by-step explanation:
working together, shayna and huong can clean an attic in 6.16 hours. had she done it alone it would have taken huong 11 hours. find how long it would take shayna to do it alone
Working together, Shayna and Huong can clean an attic in 6.16 hours. Had she done it alone, it would have taken Huong 11 hours. Therefore, Shayna can clean the attic alone in 80 hours.
Let's denote the amount of work to be done by x units. The work done by Shayna in one hour is y.
Shayna and Huong work together for 6.16 hours, so in one hour they do 1/6.
16 of the work together.According to the problem:
x/6.16 = 1/6.16 units per hour
Therefore, the amount of work done by Huong in one hour is (x/11).
Now, we can express the amount of work done by Shayna and Huong in one hour as:
(x/11) + y = 1/6.16
To determine the value of y, we can solve the above equation. Solving the equation:
(x/11) + y = 1/6.16y = (1/6.16) - (x/11)y = (11-6.16x)/(11 × 6.16)
So the amount of work done by Shayna in one hour is y = (11-6.16x)/(11 × 6.16).
To find how long it would take Shayna to do it alone, we have to express the amount of work done by Shayna alone in one hour as x/h.
Using the unitary method we have:
x/h = yx/h = (11-6.16x)/(11 × 6.16)
hx = 11 × 6.16 - 6.16x
hx + 6.16x = 11 × 6.16
hx = (11 × 6.16)/0.84 = 80 hours
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Give 5 reasons why someone would believe in God.
pls answer this
The numinous
Answered Prayers
They are taught about the faith
Through their own experience
The teachings from the Bible
Answer:
Nobody ever said having faith would be easy, but it will be worth it and here is why.
He knows better than we do. God knows everything we are going through at this very moment and everything we will go through in the future. ...
All Things Are Possible With God.
He Is Worthy Of Our Trust.
He Knows What He Is Doing.
He is the creator of the universe
he exited before the heavens and earth
He is our father and the father of our ancestors
He has performed many miracles
He is the God who answers all prayers if you believe.
He is the one who stands by you in any situation, in good times and bad
He is a merciful, understandable and dependable God
What he says he'll do, that is what he'll do
Bea earned $11,700 commission for selling a house, calculated as 6100 of the selling price. What was the selling price of the house?
The selling price of the house was approximately $1.918 or rounded to the nearest dollar, $19,180.
How to find the selling price?We can start by setting up an equation to represent the problem. We know that the commission Bea earned is equal to 6100 of the selling price, which can be expressed as:
commission = 6100 × selling price
We also know that the commission Bea earned was $11,700, so we can substitute that into the equation:
11,700 = 6100 × selling price
Now we can solve for the selling price by dividing both sides by 6100:
selling price = 11,700 ÷ 6100
simplifying:
selling price = 1.918
Therefore, the selling price of the house was approximately $1.918 or rounded to the nearest dollar, $19,180.
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A tank contains 2860 l of pure water. A solution that contains 0. 04 kg of sugar per liter enters a tank at the rate 3 l/min the solution is mixed and drains from the tank at the same rate. (a) how much sugar is in the tank initially?
The tank contains only pure water, so the amount of sugar in the tank is zero: S(0) = 0 kg. Therefore, the amount of sugar in the tank initially is 0 kg.
The concentration of sugar in the incoming solution is 0.04 kg/l. Therefore, the amount of sugar entering the tank per minute is:
0.04 kg/l × 3 l/min = 0.12 kg/min
Since the solution is mixed thoroughly with the water in the tank, the concentration of sugar in the tank is uniform at all times. Let's assume that after t minutes, the amount of sugar in the tank is S(t) kg.
During each minute, 0.12 kg of sugar enters the tank and 3 l of solution (which contains 0.04 kg of sugar per liter) leaves the tank. Therefore, the rate of change of the amount of sugar in the tank is:
dS/dt = 0.12 kg/min - (0.04 kg/l × 3 l/min) = 0.00 kg/min
This differential equation has a constant solution: S(t) = S(0). That is, the amount of sugar in the tank is constant over time, as long as the rate of inflow and outflow of solution remains constant.
Initially, the tank contains only pure water, so the amount of sugar in the tank is zero:
S(0) = 0 kg
Therefore, the amount of sugar in the tank initially is 0 kg.
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A 15-foot ladder leaning against a wall is used to reach a window that is 12 feet above the ground. How far from the wall is the bottom of the ladder? (round to the nearest tenth)
Answer:
the answer is in the image above
a tiger eats about 15 pounds of food per day. a large dog eats about 18 ounces of food per day.how many more pounds of food does a tiger eat per day
Answer: The tiger eats 13.875 pounds more food per day than the large dog.
Step-by-step explanation: A tiger eats approximately 15 pounds of food per day, while a large dog eats about 18 ounces of food per day. To determine how many more pounds of food a tiger eats per day than a large dog, we need to convert the weight of the dog's food into pounds. Since there are 16 ounces in a pound, 18 ounces is equivalent to 18/16 = 1.125 pounds. Therefore, the tiger eats 15 - 1.125 = 13.875 pounds more food per day than the large dog.
3. True or False: The percentage distribution cannot be constructed from the frequency distribution directly. 7. True or False: The coefficient of variation is a measure of relative variation. 9. True or False: The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a hypergeometric distribution.
the sample is drawn without replacement from a class of 9 females and 18 males, so the number of males selected follows a hypergeometric distribution.
3. False: The percentage distribution can be constructed from the frequency distribution directly. A frequency distribution is a summary of the number of times each score occurs in a set of data. It shows the distribution of scores into classes or groups of equal size. It is useful in understanding the pattern of data. A percentage distribution is a distribution of data as a percentage of the total data. This distribution is constructed by dividing the frequency of each class by the total frequency and multiplying by 100.7. True: The coefficient of variation is a measure of relative variation. The coefficient of variation is a ratio of the standard deviation to the mean of the distribution expressed as a percentage. It is used to compare the variability of two or more sets of data with different means. The formula for coefficient of variation is given as CV= (standard deviation/mean) *100.9. True: The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a hypergeometric distribution. A hypergeometric distribution is a probability distribution used to calculate the probability of obtaining a specific number of successes in a fixed number of draws from a finite population. It is used to find the probability of obtaining a certain number of successes in a sample without replacement from a finite population with a specified number of successes and failures. In this case, the sample is drawn without replacement from a class of 9 females and 18 males, so the number of males selected follows a hypergeometric distribution.
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The graph of a rational function is shown below. Write the equation that represents this function.
Practice
The equation that represents the given graph is
f(x) = 1/(x - 1) - 2
The graph of a rational function
A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational
function if, it can be represented as f (x) = p (x)/q (x), where p (x) and q (x) are polynomials such that q (x) ≠ 0.
To write the equation that represents this function, we need to identify the key features of the graph.
The graph is a hyperbola with the vertical asymptote x = 1 and the horizontal asymptote y = -2.
The graph passes through the point (0, -1).
Therefore, the general form of the equation that represents the given graph isf(x) = A/(x - 1) - 2
Since the horizontal asymptote is y = -2, A = -2.
Therefore, the equation that represents the given graph is f(x) = 1/(x - 1) - 2.
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12.
Find the nth term of the following sequence
the nth term of the sequence is (16n²2 - 29n + 15)/(90n).
How to find?
To find the nth term of this sequence, we can use the formula:
an = a1 + (n-1)d
where a1 is the first term, d is the common difference, and n is the term number.
In this sequence, we can see that the common difference is not constant. However, we can still find a pattern:
a1 = 1/3
a2 - a1 = 2/5 - 1/3 = 1/15
a3 - a2 = 3/7 - 2/5 = 1/35
a4 - a3 = 4/9 - 3/7 = 1/63
We can see that the common difference is decreasing by a factor of 5 with each term. So the next difference would be 1/63× 1/5 = 1/315.
Using this pattern, we can find the nth term as:
an = 1/3 + (n-1)(1/15 - (n-2)(1/315))
Simplifying this expression, we get:
an = (16n²2 - 29n + 15)/(90n)
So the nth term of the sequence is (16n²2 - 29n + 15)/(90n).
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2b+8-5b+3=-13+8b-5 solve the equation
Answer:
b ≈ 2.636.
Step-by-step explanation:
First, we can simplify both sides of the equation by combining like terms:
2b + 8 - 5b + 3 = -13 + 8b - 5
-3b + 11 = 8b - 18
Next, we can isolate the variable term on one side of the equation by adding 3b to both sides:
-3b + 3b + 11 = 8b - 18 + 3b
11 = 11b - 18
Then, we can isolate the variable term again by adding 18 to both sides:
11 + 18 = 11b - 18 + 18
29 = 11b
Finally, we can solve for b by dividing both sides by 11:
29/11 = b
b ≈ 2.636
Therefore, the solution to the equation is b ≈ 2.636.
Answer:
b = 29/11
Step-by-step explanation:
2b + 8 - 5b + 3 = -13 + 8b - 5
-3b + 11 = -18 + 8b
-11b + 11 = -18
-11b = -29
b = 29/11
An accounting firm agrees to purchase a computer for $120,000 (cash on delivery) and the delivery date is in 270 days. How much do the owners need to deposit in an account paying 0. 65% compounded quarterly so that they will have $120,000 in 270 days?
The owners need to deposit in an account paying 0. 65% compounded quarterly so that they will have $120,000 in 270 days is $119,262.94
To calculate the amount the owners need to deposit today, we can use the formula for compound interest:
A = [tex]P(1 + r/n)^{(nt)}[/tex]
where:
A is the future value of the investment
P is the principal amount (the amount to be deposited)
r is the annual interest rate (0.65%)
n is the number of times the interest is compounded per year (4 for quarterly)
t is the time in years (270 days/365 = 0.7397 years)
Substituting the values given into the formula, we get:
$120,000 = [tex]P(1 + 0.0065/4)^{4\times0.7397}[/tex]
$120,000 = [tex]P(1.001625)^{2.9588}[/tex]
$120,000 = P(1.004845)
P = $120,000/1.004845
P = $119,262.94
Therefore, the owners need to deposit $119,262.94 in an account paying 0.65% compounded quarterly so that they will have $120,000 in 270 days.
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cot^2(135-b) if sin2b=-1/5
Therefοre, the sοlutiοn οf the given prοblem οf trigοnοmetry cοmes οut tο be cοt²(135-b) = 3.
A Trigοnοmetry is what?Relatiοnships between cubic splines and maths variable astrοphysics is believed tο have been created when the variοus fields came tοgether. Many metric prοblems can be sοlved triangle οr the results οf their calculatiοn can indeed be determined with the help οf precise mathematical methοds. Trigοnοmetry is the study οf six basic trigοnοmetric calculatiοns. They gο by a variety οf titles and acrοnyms, including sine, deviatiοn, angle, and sο fοrth (csc).
Here,
First, we need tο find the value οf cοs(b) using the given infοrmatiοn that sin(2b) = -1/5:
=> sin(2b) = 2sin(b)cοs(b)
=> -1/5 = 2sin(b)cοs(b)
We knοw that sin^2(b) + cοs^2(b) = 1, sο we can rearrange this equatiοn tο sοlve fοr cοs(b):
=> cοs²(b) = (1 - sin²(b))
Substituting this intο the equatiοn we fοund abοve:
=> -1/5 = 2sin(b)cοs(b)
=> -1/5 = 2sin(b)√(1 - sin²(b))
Squaring bοth sides and simplifying:
=> 1/25 = 4sin²(b)(1 - sin²(b))
=> 1/25 = 4sin²(b) - 4sin²(b)
=> 4sin²(b) - 4sin²(b) + 1/25 = 0
We can sοlve fοr sin^2(b) using the quadratic fοrmula:
sin²(b) = [4 ± √(16 - 4(4)(1/25))] / (2(4))
sin²(b) = [4 ± 2/5] / 8
sin²(b) = 3/10 οr 1/20
Since sin(2b) is negative, we knοw that sin(b) is negative as well, sο sin²(b) = 3/10. Therefοre:
cοs²(b) = 1 - sin²(b) = 1 - 3/10 = 7/10
Nοw we can use the identity
=> cοt²(θ) = 1 / [tan²(θ)] tο find cοt²(135-b):
1 / [tan(135-b)] = cοt(135-b)
By applying the fοrmula tan(x) = sin(x) / cοs(x):
=> tan(135-b) Equals cοs(135-b) / sin(135-b) (135-b)
The identities sin( + 90) = cοs() and cοs( + 90) = -sin() are used tο illustrate:
=> Cοs(90-b) = sin(135-b) = sin(45 + (90-b)) = sin (b)
=> Sin(90-b) = cοs(135-b) = cοs(45 + (90-b)) = cοs (b)
Using these numbers in place οf:
=> 1/tan(135-b) = sin(b) / cοs(b) (3)
=> 1 / [tan(135-b)] = cοt(135-b) = 1 / [(-1/√(3))²] = 3
Cοnsequently, cοt2(135-b) = 3.
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Complete question:
Solve for b in cot²(135-b) if sin²b = -1/5
Colette is using homegrown cucumbers to make pickles. The number of pickles she can make is determined by how many cucumbers she has on hand. p = the number of pickles Colette can make c = the number of cucumbers Colette has Which of the variables is independent and which is dependent?
The number of pickles (p) is the dependent variable, while the number of cucumbers (c) is the independent variable.
What is the dependent variable?The dependent variable is the variable that is being measured or observed and is affected by the independent variable. The independent variable is the variable that is being manipulated or changed by the researcher to determine its effect on the dependent variable.
In this scenario, the number of pickles Colette can make depends on the number of cucumbers she has. Therefore, the number of pickles (p) is the dependent variable, while the number of cucumbers (c) is the independent variable.
The independent variable is the one that can be freely chosen or manipulated, and which affects the dependent variable. In this case, Colette has control over how many cucumbers she grows, and the number of pickles she can make is affected by the number of cucumbers she has. Therefore, the number of cucumbers is the independent variable, and the number of pickles is the dependent variable.
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5. Claude is wrapping cylindrical bug spray containers in tissue paper to put them inside a box.
Each container has a height of 12. 7 centimeters and a radius of 3 centimeters.
If he is wrapping a total of 5 bug spray containers, how many square
centimeters of tissue paper will he need?
Claude will need approximately 1202.3 square centimeters of tissue paper for wrapping a total of 5 bug spray containers.
To calculate the amount of tissue paper needed, we need to find the lateral surface area of one cylinder and then multiply it by the number of cylinders being wrapped.
The lateral surface area of a cylinder can be found using the formula 2πrh, where r is the radius and h is the height of the cylinder. In this case, r = 3 cm and h = 12.7 cm.
Lateral surface area of one cylinder = 2π(3 cm)(12.7 cm) = 239.38 cm² (rounded to two decimal places)
Since Claude is wrapping 5 bug spray containers, we need to multiply the lateral surface area of one cylinder by 5:
Total tissue paper needed = 5 × 239.38 cm² = 1196.9 cm²Therefore, Claude will need approximately 1202.3 square centimeters of tissue paper.
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5x - 6 <4 + 6x Which is a graph of the solution set of the inequality?
The solution to the inequality 5x - 6 <4 + 6x is x > -10
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
5x - 6 <4 + 6x
Subtract -6 from both sides of the inequality expression
So, we have the following representation
5x < 10 + 6x
Subtract 6x from both sides of the inequality expression
So, we have the following representation
-x < 10
Divide by -1
x > -10
So, the solution is x > -10
The graph of the inequality is added as an attachment
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true or false: a pooled model will produce biased coefficient estimates when factors in the error term are not correlated with the independent variable.
The given statement is false. A pooled model will produce biased coefficient estimates when factors in the error term are not correlated with the independent variable.
What is a pooled model?A pooled model is a method that entails the estimation of regression coefficients over different groups or periods by pooling the data from those groups or periods. When a pooled model is used, the dataset is combined from different groups and treated as one group, making it a more significant dataset. It is a statistical approach that includes data from two or more groups to examine variables in a wider context.
A pooled model is used when all groups have the same coefficient estimates and the same variance. It is a helpful technique for identifying variables that influence an outcome over time, as it examines changes that occur over different periods.
The assumptions of a pooled model are:
The data has to be homogeneous.There should be no significant differences in the populations from which the samples were taken.Assuming that the data is homogenous, we can say that if factors in the error term are not correlated with the independent variable, a pooled model will produce biased coefficient estimates.Hence, the given statement is false.
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Ramona determined that her answer was incorrect because a man who is –17. 52 inches tall does not make any sense. What was Ramona’s mistake?
She substituted the 8. 5 for the wrong variable. She should have added. 444 and 8. 5. The value for y should be positive. The solution of –17. 52 should be the shoe size
Ramona's mistake was in substituting the value of 8.5 for the wrong variable, which led her to obtain a nonsensical answer of -17.52 inches for the man's height.
Based on the given information, Ramona made a mistake in substituting the wrong variable. It is unclear what the original equation was, but it seems that Ramona was trying to solve for the height of a man based on some given variables.
Ramona's mistake was in substituting the value of 8.5 for the wrong variable, which led her to obtain a nonsensical answer of -17.52 inches for the man's height. Additionally, the solution of -17.52 should not represent the man's height, but rather some other variable in the equation.
The correct approach would have been to carefully substitute the given values for the correct variables and then solve for the unknown variable. In this case, it appears that Ramona should have added 0.444 and 8.5, rather than substituting 8.5 for the wrong variable. It is also worth noting that the resulting value for y should be positive, since negative shoe sizes do not make sense.
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