The exact value for cos (α+β) is √21/25- 4√2/15, for the given quadrants II and IV
we know that cos (α+β)) = cos α cos β - sin α sin β, we are given the values of sin α=2/5 and cos β= 1/3 ( both are positive for quadrant 2 and 3). Since we know cos² a + sin² a = 1
for α, cos² α + sin² α = 1
=> cos² α = 1 - sin² α
=> cos² α = 1 - 4/25
=> cos α = √21/25
same for β, cos² β + sin² β = 1
=> sin² β = 1 -cos² β
=> sin² β = 1 -1/9
= 8/9
=2√2/3
substituting the known values in the above formula for cos (α+β)
=>cos α cos β - sin α sin β
=√21/25 *1/3- 2/5*2√2/3
=√21/25- 4√2/15
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Answer:
d. [tex]\frac{4\sqrt{2}-\sqrt{21} }{15}[/tex]
Step-by-step explanation:
The lovely person in the comments was correct on Edge so i decided to put it as an answer in case anyone was looking for it!
Have a lovely day!
Solve the inequality for x and identify the graph of its solution.
4|x + 2| < 8
Solution of the inequality 4|x + 2| < 8 is given by x > -4 and x<0.
Solution from the given graph is option B where open interval x<0 and open interval x > -4 is shown.
As given in the question,
Given inequality is :
4|x + 2| < 8
Divide by 4 both the side of inequality we get,
⇒(4|x + 2|)/ 4 < 8/4
⇒|x+2| < 2
⇒ (x+2) < 2 or (x+2) >-2
⇒ x< 2-2 or x > -2 -2
⇒ x < 0 or x > -4
Solution of its graph is shown by option B number line where open interval -4 is greater than and less than open interval 0.
Therefore, solution of the inequality 4|x + 2| < 8 is given by x > -4 and x<0.
Solution from the given graph is option B where open interval x<0 and open interval x > -4 is shown.
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in 1950, the world population was 2560 million people. in 1960, the population was 3040 million people. assume that world population grows in constant relative proportion. (a) what is the relative growth rate, k? [3p] (b) use the model to predict the population in 2020.
(i) Relative growth rate, k = 48 million people/ year
(ii) Population in 2020 is given by 5920 million people.
Given that in 1950, the population of world was 2560 million.
In 1960, the population of world was 3040 million people.
Also it is mentioned that, world population grows in constant relative proportion.
So, the difference between time = 1960 – 1950 = 10 years
The growth in population = 3040 mil – 2560 mil = 480 million
So the relative growth rate of population is = 480/10 = 48 million/year
Now N be the new population, k be the relative population growth rate, all figures in millions. And t be the time in years passes since 1950.
Then the mathematical model is,
N = 2560 + kt
So for 2020, t = 2020-1950 = 70
k = 48
So, N = 2560+48*70 = 5920
So the population in 2020 is 5920 million people.
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Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
I think it is y = -3x + 2
Step-by-step explanation:
Seventh grade > M.6 Percent of a number: tax, discount, and more SPN
A store pays $871 for a gold ring. The store marks up the price by 26%. What is the
amount of the mark-up?
Round your answer to the nearest dollar: $
Submit
Answer:
$1097.46
Step-by-step explanation:
Assume P is the finall price. The markup of 26% can be written in decimal form as 0.26. This is in additon to the full price paid for the gold ring, so we can add 1.00 to 0.26 to arrive at the factor 1.26. Multiply 1.26 times the store cost of $871 to find the amount after 26% markup:
($871)*(1.26) = $1097.46
What is the equation of the line that passes through the point (-4, 2) and has a
slope of 1/4?
Answer:
y=1/4x+3
Step-by-step explanation:
To write an equation, let's infer we need to write it in slope-intercept form. We need the y-intercept. We can plug 1/4 and (-4,2) into y=mx+b, to solve for b. We have:
2=1/4*-4+b
2=-1+b
3=b
Since we have the slope, 1/4, we can create our equation:
y=1/4x+3
Solve for b in (y=mx+b):
b=y-mx
b=2-(1/4)(-4)
b=2+1
b=3
So the equation is y= (1/4)x + 3
Which function represents the i shown in the graph below
A. G(x)=-x+2
B. G(x)=2^x-1
C. G(x)=(x+2)^2
D. -2x
One day in 2014, 1 euro was worth x rand.
One year later, 1 euro was worth (x+1) rand.
Winston changed 1000 rand into euros in both years.
In 2014 he received 4.50 euros more than in 2015.
Write an equation in terms of x and show that it simplifies to 9x²+9x-2000=0.
1000/x - 1000/(x + 1) = 4.5 is an equation in terms of x that simplifies to this quadratic equation 9x² + 9x - 2000 = 0 as shown below.
What is a quadratic equation?In Mathematics, the standard form of a quadratic equation is given by this mathematical expression:
ax² + bx + c = 0.
Since Winston changed 1000 rand into euros in both 2014 and 2015, this can be represented by this mathematical expression:
1000/x - 1000/(x + 1) = 4.5
Taking the lowest common multiple (lcm), we have:
1000/x(x + 1) = 4.5
1000/(x² + x) = 4.5
Cross-multiplying, we have the following:
1000 = 4.5(x² + x)
1000 = 4.5x² + 4.5x
Multiplying both sides of the equation by 2, we have:
2 × (1000 = 4.5x² + 4.5x)
2000 = 9x² + 9x
Rearranging the terms and equating to zero, we have:
9x² + 9x - 2000 = 0.
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write ax +by =c in terms of a? solve for a
Answer:
a = (c - by) / x
Step-by-step explanation:
ax + by = c
ax = c - by
a = (c - by) / x
Please help me I need this I'm behind
Answer:
25.5 feet because of some
Step-by-step explanation:
.,........
Answer:
Step-by-step explanation:
divide 14 7/8 by 6 because you want to find out how much 6 inches is their in 14 7/8 because that the giving inchwhen you do 6 ÷ 14 7/8 you get 2.47916666667now you multiply by 3 1/2 with is the same as 3.5 and you get 8.67708333333 and that rounds to 8.68.Answer: 8.68 feetaccording to a wired magazine article, of e-mails that are received are tracked using software that can tell the e-mail sender when, where, and on what type of device the e-mail was opened (wired magazine website). suppose we randomly select received e-mails. a. what is the expected number of these e-mails that are tracked?
There should be 12 emails total.
7.200 and 2.683 are the variance and standard deviation, respectively.
What is varience?The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other. This symbol is frequently used to represent variation: 2. Both analysts and traders use it to assess market volatility and security.The standard deviation (SD or ), which aids in determining the consistency of an investment's returns over time, is the square root of variance.Calculation of expected number of emails, variance and standard deviation:
Given thatP = 0.40 and n = 30a)The expected value of received e-mails is= n × p= 30 × 0.4= 12 b)The variance of emails received is= n × p × (1 - p)= 30 × 0.4 × 0.6= 7.200NowThe standard deviation of emails received is= sqrt(variance)= 2.683Learn more about variance here:
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please help needed very soon thanks
Answer:
2 3/5
Step-by-step explanation:
First, change all terms to improper fraction
We have;
13/2÷5/2
13/2 ×2/5
13/5
Change to mixed fraction, we have;
2 3/5
Hope it helps.. Please mark brainliest
The simplest simplified form of the given expression is 3 9/10.
First, let us understand the mixed number;
A mixed number is made up of three components: a whole number, a numerator, and a denominator. The numerator and denominator are both components of the appropriate fraction that results in the mixed number.
Change all the given terms to improper fractions, we will get;
6 1/2 = (6 * 2 + 1) / 2 = 13 / 2
1 2/3 = (1 * 3 + 2) / 3 = 5 / 3
We are given;
13/2 ÷ 5/3
= 13/2 × 3/5
= 39/10
Change to mixed fraction, we will get;
39/10 = 3 9/10
Thus, the simplest simplified form of the given expression is 3 9/10.
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Anson estimated he would need 17 hours to complete is science project. He actually needed 19 1/2 hours. What was his percent error?
Answer: 14.7%
Step-by-step explanation:
% error = (estimated - actual) / (actual) x 100
% error = (17 - 19.5) / 17 x 100 = - 14.7%
The negative sign means that he underestimated the time needed
Simplify these pls I’ll brainlist.
1) 3b (b+4) - 4 (b-5)
2) 12(3y + 6)
Final answer: 3[tex]b^{2}[/tex] + 8b + 2
12(3y + 6) = 12 x 3(y + 2) // Factor out 12 = 36(y + 2) // Simplify the multiplication Final answer: 36(y + 2)
What is equation?An equation is a statement that two mathematical expressions are equal. It consists of two expressions separated by an equal sign (=), where one expression is on the left side and the other expression is on the right side of the equal sign. An equation represents a balance or equivalence between the two expressions, and it can be solved for the unknown variable(s) by applying mathematical operations to both sides of the equation.
Given by the question.
3b (b+4) - 4 (b-5)
= 3[tex]b^{2}[/tex] + 12b - 4b + 20 // Distribute the terms.
= 3[tex]b^{2}[/tex] + 8b + 20 // Simplify the like terms.
Final answer: 3[tex]b^{2}[/tex]+ 8b + 20
12(3y + 6)
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19. Spotify revealed that about 47% of its users are aged 13-24, 25% are aged 25-34, and 28%
are 35 or older. Suppose that for the 13- to 24-year-olds, 85% identified pop as their favorite
music genre, 59% of the 25- to 34-year-olds identified pop as their favorite music genre, and
23% of the users 35 or older identified pop as their favorite music genre. Suppose we select
one Spotify user at random and record his or her age and whether his or her favorite music
genre is pop.
The probability is 0.061 to record his or her age for her favorite music genre is pop.
What is meant by probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event or statement is to occur. An event's probability is a number between 0 and 1, where 0 indicates impossibility and 1 represents certainty. The more likely an occurrence is, the more likely it will occur. A simple example is tossing a fair (unbiased) coin. Because the coin is fair, all outcomes are equally likely; the probability of "heads" equals the probability of "tails," and because no other outcomes are possible, the probability of "heads" or "tails" is 1/2.
Given,
Age Users Pop-music
13-24 47% 85%
25-34 25% 59%
35-more 28% 23%
Let the total population be 100 then
Age Users Pop-music
13-24 47% 85% of 47=39.95
25-34 25% 59% of 25=14.75
35-more 28% 23% of 28=6.44
Persons having favorite music game as pop=34.95+14.75+6.44
=61.14
Probability=61.14/100c₁
=0.061
Therefore, the probability is 0.061.
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how would you change the exponential growth model if the per capita death rate increased?group of answer choicesi would not change anything about the exponential growth model.i would decrease the initial population size.i would increase r.i would decrease r.
Using the concepts of statistics, we got that if the per capita death rate increased, then the exponential growth model would decrease the initial population size.
We know very well, the set up of a differential equation relating instantaneous population growth with respect to the time to the per capita population growth rate and the current population size at an arbitrary time is as follows:
dN / dt = rN
Now, we are told that the constant, r, is per capita population growth rate. N is current size of the population at some time. "r" is the "organisms added per reproductive period" divided by total population at that time. For instance, if the 10 rabbits are born per month and the current population is 100 rabbits, then r value = 0.1.
Hence, the exponential growth model would decrease the initial population size if the per capita death rate increased.
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What is the value of the product 2/3 x 9/5?
Answer:
[tex]\frac{6}{5}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} *\frac{9}{5} =\frac{18}{15} =\frac{6}{5}[/tex]
The value of the product of 2/3 × 9/5 is 6/5.
In the given question, we have to attempt fraction multiplication.
For fraction multiplication, we simply multiply the respective numerators and denominators with each other.
Here, in 2/3 × 9/5 ⇒ 18/15 (since 2×9=18) (since 3×5=15)
Now, since we can see that both the numerator and denominator in the solution can get divided by 3, we can simplify the fraction by dividing both the numerator and denominator by 3.
On dividing by 3, we get ⇒ 6/5
So, on multiplying 2/3 and 9/5, we get 18/15 which we later simplify into 6/5.
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Simplify the expression:
(–5.5 + 2p)(–2) =
The expression, (–5.5 + 2p)(–2), after simplification is 11-4p.
According to the question,
We have the following expression:
(–5.5 + 2p)(–2)
Now, in order to simplify this expression, we will multiply -2 into the bracket:
(Note that when a number or a variable is multiplied into the bracket then it is multiplied into every number or term within the bracket.)
-5.5*-2+2p*(-2)
We know that when two negative integers are multiplied then the result is positive and when one negative and one positive integer is multiplied then the result is negative.
11-4p
Hence, the expression, (–5.5 + 2p)(–2), after simplification is 11-4p.
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Isabel works 180 hours in one month.what is her average hourly wage,in dollars,to meet the budget?round to the nearest cent
One method is to determine the average hourly rate for all employees, regardless of where they work in your company, what they do, or how many hours they work.
How to Calculate the Average Hourly Rate for Employees ?To begin, calculate the total number of hours worked by multiplying the number of weeks in a year by the number of hours worked per week. Divide this figure by the annual salary. For example, if an employee earns $50,000 per year and works 40 hours per week, his or her hourly rate is $50,000/2,080 (40 x 52) = $24.04.
When budgeting for future projects, keep in mind that if you pay Bill $18 per hour, Lisa $16, and Hank and Jake $14, your labor costs will vary depending on who you send to the job site.
However, if you can use Bill less frequently each week and Hank or Jake more frequently, you might be able to budget for next month using the $15.82 per hour figure.
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a person's blood glucose level and diabetes are closely related, let x be a measurement in milligrams of glucose per deciliter of blood, after 12-hour fast, the variable x will have a Distribution that is approximately normal with a mean of 85 and standard deviation of 25. this is only true for adults under 50. Use this information to answer the question that follow:
what percentage of people have a blood glucose level between 100 and 125?
The percentage of people that have a blood glucose level between 100 and 125 is 21.945%
How to determine the percentage between 100 and 125?From the question, the given parameters about the distribution are
Mean value of the set of data = 85
Standard deviation value of the set of data = 25
The actual data values = 100 and 125
The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
For x = 100, we have:
Substitute the given parameters in the above equation
z = (100 - 85)/25 = 0.6
For x = 125, we have:
Substitute the given parameters in the above equation
z = (125 - 85)/25 = 1.6
The percentage between 100 and 125 is then calculated as:
P(100 < x < 125) = P(z < 1.6) - P(z < 0.6)
From the z table of probabilities, we have;
P(100 < x < 125) = 0.9452 - 0.72575
This gives
P(100 < x < 125) = 0.21945
Express as percentage
P(100 < x < 125) = 21.945%
Hence, the percentage is 21.945%
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we get statistics of 2017-2018 average starting teacher salaries by state measured by nea. given that the salary of arkansas is 33323, the sample size is 3,600 and the standard deviation is 399.876. a. what is the margin of error for a 80% confidence interval in arkansas? symbolic expression b. if we want to get a 80% confidence interval with a small margin of error, say only 7%. how many people do you need to sample?
a) The margin of error for an 80% confidence interval in Arkansas is 0.1041
b) if we want to get an 80% confidence interval with a small margin of error, say only 7%. then the sample size must be 53,599,359
The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.
n = 3600
standard deviation = 399.876
Confidence Interval = 80%
a) α = 0.20
The margin of error = Zα/2 (σ / √n)
Zα/2 = 1.4395 --- (From the tabular value)
The margin of Error = 1.4395 + 399.876 / √3600
Therefore, the Margin of Error = 8.1041
b) Margin of Error = 0.07 = 7%
α = 0.20
Critical Value = 1.2816
Sample Size = (Zc²σ² / ME²) = (Zcσ / ME)²
n = [(1.2816 * 399.876) / 0.07]²
n = 53599358.98
Therefore, Sample size, n = 53599359
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Anthony's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=57+7.4x, where y represents the expected quiz score and x represents hours spent on homework that week. What is the meaning of the x-value when y=90
The meaning of the x-value when y=90 means that Anthony will use 3.1 hours.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The relationship that can be represented by the equation y=57+7.4x,
where
y represents the expected quiz score
x represents hours spent on homework that week.
When y = 90, the value of x will be:
y=57+7.4x
57 + 7.4x = 90
Collect like terms
7.4x = 90 - 57
7.4x = 23
Divide
x = 23/7.4
x = 3.1
He'll use 3.1 hours.
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1. [-/1 Points]
DETAILS
Find the x- and y-intercepts.
7x - 6y = 1
x-intercept (x, y) = (
y-intercept (x, y) = (
(x, y) = (
multiply x times y divide by 6 on both sides and you got your answer
how do you simplify the distributive property ?
Answer:
for example 2(3+1)
to solve with the distributive property you multiply the number outside the parentheses(2) with each inside number(3 and 1) individually.
2(3)+2(1)
now solve
6+2=8
now to check it by solving the regular way
2(3+1), 3+1=4 so
2(4)
8
we can see that the answers are the same.
to use the distributive property with x in it
for example, -3(x-6)
multiply the outside number(-3) with each inside number(x and -6)
-3(x)+(-3)(-6)
simplify
-3x-(-18)
-3x+18
hope this helps!
f(-3) evaluate the function of the graph
The composition f(-3) has a value of 1
How to evaluate the function on the graph?The definition of the function is represented by the graph
So, we call the graph function f(x)
To find the function f(-3), we set the value of x in the function of the graph f(x) to -3
This is represented by
Calculate f(x), when x = -3
So, we look for the corresponsing points on the graph where x = -3
In this case;
The value of the function is 1 when the value of x is -3
This means that
f(-3) = 1
Hence, the value of the function is 1
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Diego's solar car traveled 3.16 meters farther than Justine's solar car. The equation d=j+3.16 represents this situation. What is the value of j if d=158?
The value of j based on the equation d = j + 3.16 if d = 158 is 154.84 meters.
How to find the missing parameters of an equation?Distance Diego's car traveled farther than Justine's solar car = 3.16 metersd = 158d = j + 3.16
substitute the value of d into the equation
d = j + 3.16
158 = j + 3.16
substract 3.16 from both sides
158 - 3.16 = j
j = 154.84
So therefore, based on the given equation d = j + 3.16, j = 154.84
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The value of j in the equation = 154.84
Distance
Distance is the length of space covered by the car when it moves from one location to another
Given;
Equation d=j+3.16 represent the situation
distance travelled by the car= 3.16meters
d=158
Step 1: Substituting the value of d into the equation d=j+3.16
158= j +3.16
Step 2: Subtract 3.16 from both sides
158-3.16 = j + 3.16 -3.16
Step 3: Add the equation
j= 154.84
Therefore, the value of j in the equation = 154.84
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What is the distance between (-5,-6),(-9,-4)
Answer:
The distance between [tex](-5,-6),(-9,-4)[/tex] is [tex]6 units[/tex].
Step-by-step explanation:
Distance Formula :
[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]
Given,
The two points are
[tex](-5,-6),(-9,-4)[/tex]
To calculate the distance between two points, use the distance formula.
[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]
Substitute the actual values of the points into the distance formula.
Distance[tex]=\sqrt{((-9)^{2} -(-5)^{2}) +( (-4)^{2} -(-6)^{2})}[/tex]
[tex]=\sqrt{(81-25)+(16-36)}[/tex]
[tex]=\sqrt{36}[/tex]
[tex]=6[/tex]
graph y = 1/4 x I dont know how to do
(Excuse me if this doesn't make sense).
Your formula would be (4,1)
Your zero is (0,0)
To graph it:
If your y is 1, your x is 4
If your y is 2, your x is 8.
There's a video for this if my explanation and photo doesn't help
(a) Annie and Dermot share $600 in the ratio 11:9.
(i) Show that Annie receives $330.
Ratio of amount $600 share by Annie and Dermot is 11 : 9, then amount received by Annie is $330 and Dermot is $270.
As given in the question,
Total amount share by Annie and Dermot is $600.
Ratio of amount share by Annie and Dermot is 11 : 9
Let x be the amount of money.
11x + 9x = $600
⇒ 20x = $600
⇒20x/20 = $600/20
⇒x= $30
Amount received by Annie is equal to
= 11 × 30
= $330
Amount received by Dermot is equal to
= 9 × 30
= $270
Therefore, ratio of amount $600 share by Annie and Dermot is 11 : 9, then amount received by Annie is $330 and Dermot is $270.
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To train for a triathlon, Mr Greg swims, bikes, and runs everyday. Each day he bikes 10 times the distance he swims, and run 1. 5 miles more than half the distance he bikes. If Mr. Greg covers a total of 25. 5 miles on each day of training, how many miles does he swim? Bike? Run?
He covers 15 miles on the bike, 9 miles by running and 1.5 miles while swimming which sum up to 25.5 miles which is his total training distance.
What is distance?Distance is defined as an object's entire movement without regard for direction. Distance may be defined as how much ground an item has traversed regardless of its starting or finishing place. Distance is a scalar number that indicates "how much ground an item has covered" while moving. Displacement is a vector variable that describes "how far out of place an item is"; it represents the total change in position of the object. Distance is the length along a line or line segment between two locations on the line or line segment.
Here,
He rides 15 miles, which is ten times as far as he swims.
He runs 9 miles, which is half the distance he rides (15/2=7.5). Plus the additional 1.5 miles, totaling 9.
He swims.10 of what he bikes, for a total of 15x.10 = 1.5. As a result, he swims 1.5 miles.
15 miles = bike
9 miles= run
1.5 mile =swim
Add them all together and you get 25.5 miles.
He rides his bike for 15 miles, runs for 9 miles, and swims for 1.5 miles, for a total training distance of 25.5 miles.
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Divide £72 into.
Ratio 4:5
Thus, 72 is divided into 32 and 40 in a 4:5 ratio. A ratio expresses the number of times one number contains another.
What is meant by Ratio?A ratio is the number of times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six.Similarly, the lemon to orange ratio is 6:8, and the orange to total fruit ratio is 8:14. A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero.A proportion exists as a equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls)Given:
The given ratio is 4:5.
To find: We have to divide 72 in this ratio.
To divide 72 in the 4:5 ratio, we must perform the following steps:
The ratio is 4:5.
We can write the number of the ratio as 4x and 5x by multiplying a constant x.
The total ratio is 4x+5x=9x.
So, 9x is equal to 72.
We can write-
9x=72
x=8.
So, putting the value of x we get-
4×8 and 5×8
So, the numbers are 32 and 40.
Thus 72 divides itself as 32 and 40 in 4:5 ratio.
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#SPJ1
