Mathematics High School
Answers
Answer 1
Answer:
The number of ways a customer could choose a pizza that contains 3 different toppings is 455
Stepbystep explanation:
A customer could choose a pizza that contains 3 different toppings in C(15,3) ways, which is the number of combinations of 15 items taken 3 at a time.
The formula for combinations is given by:
C(n,k) = n! / (k! (nk)!)
where n! means n factorial, which is the product of all positive integers from 1 to n.
Plugging in n = 15 and k = 3:
C(15,3) = 15! / (3! (153)!) = 15! / (3! 12!)
Using a calculator, we find that:
C(15,3) = 455
So, the number of ways a customer could choose a pizza that contains 3 different toppings is 455. The answer is 455.
Answer 2
Answer:
The answer is 455 ways
Stepbystep explanation:
If adding only twelve, you must leave out three of the fifteen, and the number of ways is: = 15! / (3! * 12!).1∗2∗3∗4∗5∗6∗6∗8∗9∗10∗11∗12∗13∗14∗15 over(1∗2∗3)∗(1∗2∗3∗4∗5∗6∗6∗8∗9∗10∗11∗12) =13∗14∗15 over(1∗2∗3)27306 = 455
Or:15! / (3! * 12!) = 455.
Best of Luck to you! I hope this helps you.
Related Questions
anemia for the study of jordanian children in exercise 4, the sample mean hemoglobin level was 11.3 g/dl and the sample standard deviation was 1.6 g/dl. a significance test yields a pvalue of 0.0016. (a) interpret the pvalue in context. (b) what conclusion would you make if a 0.05? a 0.01? justify your answer.
Answers
(a) The interpret the pvalue in context of 0.0016 indicates that the probability of obtaining a sample mean hemoglobin level of 11.3 g/dl or lower.
(b) The conclusion would make if a 0.05 is rejected because the pvalue (0.0016) is less than the significance level.
If using a significance level of 0.01, the null hypothesis would still be rejected because the pvalue is less than 0.01.
Anemia Study Results
(a) The pvalue of 0.0016 indicates that the probability of obtaining a sample mean hemoglobin level of 11.3 g/dl or lower, assuming that the true population mean is 12 g/dl (or higher), is only 0.0016. This suggests that the observed difference between the sample mean and the hypothesized population mean is statistically significant and unlikely to be due to chance alone.
(b) If using a significance level of 0.05, the null hypothesis (that the true population mean is 12 g/dl or higher) would be rejected because the pvalue (0.0016) is less than the significance level. Therefore, it can be concluded that the sample provides evidence that the true population mean hemoglobin level is lower than 12 g/dl.
If using a significance level of 0.01, the null hypothesis would still be rejected because the pvalue is less than 0.01. In this case, the evidence is even stronger, and the conclusion that the true population mean is lower than 12 g/dl would be even more robust.
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Karabo and John are at the same rest stop alongside a highway. Karabo started driving along the highway at a constant speed of 80 km/h. An hour later, John started driving along the same highway in the same direction as Karabo at the constant speed of 100 km/h. How long will it take John to catch up with Karabo?
Answers
It will take John about 48 minutes of driving with a speed of 100km/h to catch Karabo on the Highway.
Karabo and John are at the same stop alongside the highway.
Karabo started driving along the highway with a constant speed of 80 km/h. After an hour, John also started driving in the same direction of the highway and at a constant speed of 100km/h.
Here, the distance covered by Karabo in one hour will be 80 km because his speed is 80km/h.
So, the distance D between John and Karabo is now 80 km.
John will have to cover this distance of 80 km to reach Karabo, so,
Time = Distance/Speed
Distance = 80 km,
Speed = 100km/h
Putting values,
Time = 80/100
Time = 0.8 hour.
This time will be 48 minutes, so, the time required by John is 48 minutes.
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need quick help on this math problem
Answers
The length QN on the triangle is 54 units
How to determine the length QN
From the question, we have the following parameters that can be used in our computation:
Point P = Centroid
Also, we have
QP = 18
The centroid divides each median into the ratio 2:1.
Using the above as a guide, we have the following:
QN = 3 * QP
Substitute the known values in the above equation, so, we have the following representation
QN = 3 * 18
Evaluate
QN = 54
Hence, the length is 54 units
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Which shapes from your tree construction in the Clade Race are synapomorphic?
a. Arrow
b. Circle
c. Moon
d. Triangle
e. Square
f. Cross
g. Star
h. Heart
i. Hexagon
Answers
c. Moon, d. Triangle, e. Square, h. Heart morphologies are synapomorphic from building your tree in the clade race.
In order to help businesses conduct sales transactions, employ marketing techniques, and manage their finances, inventory, and personnel, Square offers a variety of products and services. The Square app can currently be used to accept card payments in the US, Canada, Australia, Japan, the UK, Republic of Ireland, France, and Spain. With Square Payments, you can easily and safely accept all forms of payment. You can collaborate with customers rather than competing with them when it comes to how they want to pay for goods and services when you use Square Payments. Through Square, you can accept credit cards, Apple Pay, Android Pay, and a lot of other payment options.
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There are 45 people in the marching band the band has five members in each roll which equation shows the number of rows and the bear a 455 = 40 B 45÷5 = 9 C 5 times10 equals 50 D 5 times nine = 4
Answers
To determine the number of rows, we need to divide the total number of people by the number of people in each row. Using the information given, we have:
Number of people in the marching band = 45
Number of people in each row = 5
So the equation that shows the number of rows, denoted by "r", is:
r = 45/5
Simplifying the equation, we get:
r = 9
Therefore, there are 9 rows in the marching band.
The answer is (B) 45 ÷ 5 = 9.
the total number of students in a class are 90 out of which 45 are boys. if 50% of the total students secured grade 'a' out of which 20 are boys, then write a program to calculate the total number of girls getting grade 'a'.
Answers
As per the provided information, we can calculate and find that there are in total25girls present in the classroom.
We know that the total number ofstudentsis 90 and 45 of them are boys. So, the number of girls in the class is:
girls = total students boys
= 90  45
= 45
Total no. of students=90Out of which 45 are boys which means 45 are girls.
We also know that 50% of the total studentssecuredgrade 'a'. So, the totalnumberof students who secured grade 'a' is:
total grade a = total students / 2
= 90 / 2
= 45
Now, Students who gotAgrade = 90×50/100
= 45
Now, Students who gotAgrade = 90×50/100
= 45
So, 45 students got Agrademarks.
Out of which 20 are boys which means girls who got A grade = 4520=25
Hence, 25 Girls got A grade.
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brandon has a cell phone. the value of a phone decreases by 25% each year. brandon purchased the phone for $500. how many years will it take before the value of the phone is $100? answer as a decimal number rounded to two decimal places.
Answers
Brandon purchased the phone for $500 , if the value of a phone decreases by 25% each year, it will take approximately 2.77 years for the value of the phone to decrease to $100.
To find the number of years it will take for the value of the phone to decrease to $100, we can use the formula:
years = log(initial value / final value) / log(1  rate of decrease)
where log is the natural logarithm function, and rate of decrease is the percentage decrease in value each year as a decimal. In this case, the rate of decrease is 25%, or 0.25 as a decimal.
Plugging in the values, we get:
years = log(500 / 100) / log(1  0.25)
Taking the natural logarithm of both sides and simplifying, we get:
years = 2.7725887222
Rounding to two decimal places, the answer is 2.77 years.
It will take approximately 2.77 years for the value of the phone to decrease to $100.
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Triangle GHI is similar to triangle JKL. Find the measure of side LJ. Round your
answer to the nearest tenth.
11
1
H
L
41
K
8
G

Answer:
Submit Answer
attempt 1 out of 2
Answers
The measure of side LJ would be 88 + 11 = 99. Round to the nearest tenth, LJ is 99.0.
To find the measure of side LJ, we need to use the concept of similarity between triangles.
If two triangles are similar, then the ratio of their corresponding side lengths is equal.
In this case, triangle GHI is similar to triangle JKL.
Let's assume the measure of side GH is x.
Then, the measure of side GI would be 8x and the measure of side HI would be 41x.
The measure of side JK would be x and the measure of side KL would be 8x.
By using the ratios of the side lengths,
we can set up an equation:
x/8x = JK/KL
Solving for x, we get x = 11. So, the measure of side KL is
8x = 8 * 11 = 88
The measure of side LJ would be 88 + 11 = 99. Round to the nearest tenth, LJ is 99.0.
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What are the statistics related to the use of social media?
Answers
The statistics related to the use of social media is as of 2023, there are approximately 8 billion individuals on the planet, and 4.9 billion of them use social media.
Social media analytics is the process of gathering information about a specific brand, good, or service from social media websites and then evaluating that information to make smarter, more knowledgeable business decisions. These analysis' insights are frequently utilized to assess consumer sentiment about a particular brand or item. In all areas of operation, statistical data is crucial for any organization. Without the knowledge, businesses risk missing out on prospective marketing opportunities or fresh trends that are altering how consumers see a specific brand. Utilizing social media has a significant impact on a company's ability to expand. Adolescents who use social media for more than three hours a day are more likely to experience mental health issues. 32% of 12 to 17yearold children express anxiety, and 13% report depression. 25% of those aged 18 to 25 report having a mental illness.
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If (x) =
5x−2/
6
and g(x) =
6x+2/
5
, Prove that fog(x) = gof(x).
Answers
Answer:
Stepbystep explanation:
question must be f(x)=5x2/6
fog(x)= [5(6x+2/5)2]/6 = [6x+22] /6 = x
gof(x)= [6(5x2/6) +2]/5 = [ 5x2+2]/5 = x
hence fog(x)=gof(x)
Abigail wants to make 50 necklaces to sell at a craft fair. Each necklace has 11 beads. Abigail buys 18 bags of beads. Each bag has 30 beads
Answers
Abigail needs 550 beads to make 50 necklaces with 11 beads each. She needs 18 bags of beads, since each bag has 30 beads. This can be verified by multiplying 18 bags x 30 beads per bag = 540 beads. She may need to buy an extra bag to ensure she has enough beads.
The total number of beads Abigail needs is 550 (50 necklaces x 11 beads per necklace = 550 beads). Since each bag has 30 beads, Abigail needs 18 bags (550 beads/30 beads per bag = 18 bags of beads). To verify this calculation, Abigail can multiply 18 bags x 30 beads per bag = 540 beads, which is close enough to the total number of beads needed (550 beads). The remaining 10 beads can be taken from another bag, or Abigail can buy an extra bag to make sure she has enough beads.
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smartphones come with an app that keeps track of the time that the phone is being used. For teenagers, of amount of time they use their phone
Answers
Using the normal distribution, it is found that:
a) 1.39% of teenagers use their phone less than 5 hours per day.
b) 3.59% of teenagers use their phone more than 10 hours per day.
c) 49.85% of teenagers use their phone between 6 to 8 hours per day.
d) The 75th percentile of the distribution is of 8.59 hours.
What is Normal Probability Distribution?
The Zscore of a measure X of a variable that has mean represented by μ and standard deviation represented by σ is given by the fraction presented as follows:
Z = (X  μ) / σ
The mean and the standard deviation of the daily amounts they use their phone are given as follows:
μ = 7.75 and σ = 1.25
a)
The proportion that use their phone for less than 5 hours a day is given by the pvalue of Z when X = 5, hence:
Z = (X  μ) / σ
Z = (5  7.75) / 1.25
Z = 2.2
Z = 2.2 has a pvalue of 0.0139.
Thus the percentage is of 1.39%.
b)
The proportion that use their phone for more than 10 hours a day is one subtracted by the pvalue of Z when X = 10, hence:
Z = (X  μ) / σ
Z = (10  7.75)/1.25
Z = 1.8
Z = 1.8 has a pvalue of 0.9641.
1  0.9641 = 0.0359 = 3.59% (percentage).
c)
The proportion between 6 and 8 hours a day is the pvalue of Z when X = 8 subtracted by the pvalue of Z when X = 6, hence:
X = 8:
Z = (X  μ) / σ
Z = (8  7.75)/1.25
Z = 0.2
Z = 0.2 has a pvalue of 0.5793.
X = 6:
Z = (X  μ) / σ
Z = (6  7.75)/1.25
Z = 1.4
Z = 1.4 has a pvalue of 0.0808.
0.5793  0.0808 = 0.4985 = 49.85% (percentage).
d)
The 75th percentile is X when Z = 0.675, hence:
Z = (X  μ) / σ
0.675 = (X  7.75)/1.25
X  7.75 = 0.675 x 1.25
X = 8.59 hours.
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The complete question is as follows:
Smartphones come with an app that keeps track of the amount of time that the phone is being used. For teenagers, the distribution of amount of time they use their phone is approximately normal with mean = 7.75 hours per day and standard deviation = 1.25 hours per day.
(a) What percent of teenagers use their phone less than 5 hours per day?
(b) What percent of teenagers use their phone more than 10 hours per day?
(c) What proportion of teenagers use their phone between 6 to 8 hours per day?
(d) What is the 75th percentile of this distribution?
Which value is NOT equivalent to the others?
A:2to the fifth power
B:2 to the second power X 2 to the 3rd power
C:2+2+2+2+2
D:2x2x2x2x2
Answers
Answer: C
Stepbystep explanation: Because c is just 2*5, not 2^5
Gabriel is designing a rectangular planter box for their garden. It needs to cover an area of 15 1 2 m 2 15 2 1 m 2 15, start fraction, 1, divided by, 2, end fraction, start text, m, end text, squared. Gabriel wants it to be 7 3 4 m 7 4 3 m7, start fraction, 3, divided by, 4, end fraction, start text, m, end text long. How wide does the planter box need to be?
Answers
The width of the planter box needs to be 2 meters, calculated by dividing the area of 15 1/2 [tex]m^{2}[/tex] by the length of 7 3/4 m.
To find the width of the planter box, we need to use the formula for the area of a rectangle:
A = lw
where A is the area, w is the width, l is the length.
We know the area is 15 1 2 m 2 15 2 1 m 2 15, start fraction, 1, divided by, 2, end fraction, start text, m, end text, squared, and the length is 7 3 4 m 7 4 3 m7, start fraction, 3, divided by, 4, end fraction, start text, m, end text long. Here is the equation to follow:
15 1 2 m 2 = 7 3 4 m × w
To solve for w, we'll isolate it on one side of the equation by dividing both sides by 7 3 4 m 7 4 3 m7, start fraction, 3, 4 divided by start text, m, end text long, end fraction:
w = 15 1 2 m 2 ÷ 7 3 4 m = 2 m
So the width of the planter box needs to be 2 meters.
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You can use digit twice make the largest 3 digit number 825
Answers
Answer:
852
Stepbystep explanation:
If it has to be the largest 3 digit number, this would be it
How did you find the net income?
Answers
Answer:
What is net income?
Net income is the total amount of money your business earned in a period of time, minus all of its business expenses, taxes, and interest. It measures your company’s profitability. You can learn more in our guide on net income meaning. For now, we’ll get right into how to calculate net income using the net income formula.
Net income formula
Net income is your company’s total profits after deducting all business expenses. Some people refer to net income as net earnings, net profit, or simply your “bottom line” (nicknamed from its location at the bottom of the income statement). It’s the amount of money you have left to pay shareholders, invest in new projects or equipment, pay off debts, or save for future use.
The formula for calculating net income is:
Revenue – Cost of Goods Sold – Expenses = Net Income
The first part of the formula, revenue minus cost of goods sold, is also the formula for gross income. (Check out our simple guide for how to calculate cost of goods sold).
So put another way, the net income formula is:
Gross Income – Expenses = Net Income
Or, if you really want to simplify things, you can express the net income formula as:
Total Revenues – Total Expenses = Net Income
Net income can be positive or negative. When your company has more revenues than expenses, you have a positive net income. If your total expenses are more than your revenues, you have a negative net income, also known as a net loss.
Using the formula above, you can find your company’s net income for any given period: annual, quarterly, or monthly—whichever timeframe works for your business.
Answer: take the total amount of money you have earned, and subtract taxes, insurance, and retirement
Stepbystep explanation:
The bill for a meal was $33.75. The customer left $40.00 what percentage of the bill was the tip?
Answers
The bill for a meal was $33.75. The customer left $40.00, the percentage of the bill the tip was, 18.51%
What is the percentage?
Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
To calculate the tip, we need to subtract the cost of the meal from the amount left by the customer. In this case, the tip would be
⇒ $40.00  $33.75
⇒ $6.25.
To calculate the tip as a percentage of the bill, we need to divide the tip amount by the cost of the meal and multiply by 100:
⇒ ($6.25 / $33.75) x 100
⇒ 18.51%
So the tip was 18.51% of the bill.
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PLEASE HELP!
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 60° is added to the data, how does the median change?
Answers
The median without 60 is 79.5.
With 60 it’s 77 so the median decreases by 2.5.
The median would change from “79.5” to “77”, having a difference of “2.5”. The median will decrease.
heights of statistics students were obtained by the author as part of an experiment conducted for class. the last digits of those heights are listed below. construct a frequency distribution with 10 classes. based on the distribution, do the heights appear to be reported or actually measured? what do you know about the accuracy of the results?
Answers
The heights of statistics students were obtained by the author as part of an experiment conducted for class.
Last Digits of Heights: 0, 8, 4, 6, 8, 0, 3, 1, 7, 5
Frequency Distribution:
Class Frequency
09 4
1019 3
2029 1
3039 1
4049 0
5059 0
6069 0
7079 1
8089 2
9099 0
Based on the frequency distribution, the heights appear to be reported rather than actually measured. This suggests that the accuracy of the results may be questionable, as it is possible that the heights were rounded or estimated.
The heights of statistics students were obtained by the author as part of an experiment conducted for class. From the frequency distribution, it appears that the heights were reported rather than actually measured, suggesting that the accuracy of the results may be questionable.
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Suppose a is nn and the equation ax0 has only the trivial solution. Explain why a has n pivot columns and a is row equivalent to.
Answers
Suppose A is n*n and the equation Ax=0 has only the trivial solution. Then there are no free variables in this equation, thus A has in pivot columns.
If the equation Ax = 0 has only the trivial solution, there is a pivot in every column.
If the system Ax=0 has only the trivial solution that's mean that the echelon form of A hasn't free variables, therefore each column of the matrix has a pivot.
Since each column has a pivot then we can form the reduced echelon form of the A, and leave each pivot as 1 and the others components of the column will be zero. This means that the reduced echelon form of A is the identity matrix and so on A is row equivalent to identity matrix.
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This question is incomplete. Following question is complete.
Suppose A is n*n and the equation Ax=0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to In
Choose the correct answer below.
A. Suppose A is n*n and the equation Ax=0 has only the trivial solution. Then there are no free variables in this equation, thus A has in pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the n × n identity matrix, In
B. Suppose A is n × n and the equation Ax=0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in A must be on the main diagonal. Hence A is the n × n identity matrix. In
C. Suppose A is n*n and the equation Ax=0 has only the trivial solution. Then there are n free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the n × n identity matrix. In
Express each as a trigonometric function of a single angle measure.
Sin 3Ꮎ cos 2Ꮎ + cos 3Ꮎ sin 2Ꮎ
Answers
Using your angle sum formula, you can see that this is sin(A+B).
3 theta is your A, 2 theta is your B.
To combine these, plug them into the simple sin(A+B) formula.
sin(3theta + 2theta)
sin(5theta) is your answer.
factor 2x2 + 5x  7.
Answers
The factor of 2x² + 5x  7 is (2x + 7)(x + 1).
What is a factor of a polynomial?
We know that if x = a is one of the roots of a given polynomial x  a = 0 is a factor of the given polynomial.
To confirm if x  a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x  a = 0 is a factor.
Given, A quadratic expression 2x² + 5x  7.
Now, Two numbers multiply to  14 and add to + 5 is + 7 and  2.
Therefore, The factor of 2x² + 5x  7 is,
2x² + 7x  2x  7.
= x(2x + 7) + 1(2x + 7).
= (2x + 7)(x + 1).
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Determine the domain of the function . (–1, 5) (5, 5) (–[infinity], –1) u (–1, 5) u (5, [infinity]) (–[infinity], –5) u (–5, 5) u (5, [infinity])
Answers
The domain of a function is the set of all possible input values (xvalues) for which the function is defined and produces a valid output (yvalue).
In this case, the function has a fraction with a square root in the denominator, so the domain is all real numbers except for those values of x that would make the denominator equal to zero.
The denominator of the fraction is √(x^2  4x + 5), which is equal to zero when x^2  4x + 5 = 0. This is a quadratic equation that can be solved using the quadratic formula, which gives us two solutions: x = (4 ± √(4^2  4(1)(5))) / (2 * 1) = (4 ± √(16)) / 2 = (4 ± 4i) / 2
Since the square root of a negative number is not a real number, the solutions are not real numbers. This means that the denominator is not equal to zero when x = 4 ± 4i. Therefore, the domain of the function is all real numbers except x = 4, which is the only excluded value. So, the domain of the function is (∞, 4) U (4, ∞).
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Tiana is touring New York City with her family. They want to visit the Empire State Building, Central Park, and Times Square before their dinner reservations at 6:15 P. M. They want to spend 1 hour and 5 minutes at the Empire State Building, 2 hours and 30 minutes in Central Park, and 55 minutes in Times Square. What is the latest time Tiana's family can start their tour in order to make it to dinner on time?
Answers
At Times Square, they plan to spend 55 minutes, which is equivalent to 0.92 hours. To calculate the latest time Tiana's family can start their tour, we need to add the time they plan to spend at each location.
Tiana is on a tour of New York City with her family. They want to visit the Empire State Building, Central Park, and Times Square before their dinner reservations at 6:15 P.M.
They have planned to spend specific amount of time at each place.
At the Empire State Building, they plan to spend 1 hour and 5 minutes, which is equivalent to 1.0833 hours.
At Central Park, they plan to spend 2 hours and 30 minutes, which is equivalent to 2.5 hours.
At Times Square, they plan to spend 55 minutes, which is equivalent to 0.92 hours. Therefore, the total time they plan to spend on the tour is 1.0833 + 2.5 + 0.92 = 4.5133 hours.
To arrive at the dinner reservation on time, they need to start the tour by 6:15 P.M  4.5133 hours = 1:34 P.M. This is the latest time they can start their tour and still make it to dinner on time.
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1/tanx+tanx=secx*cscx
Answers
Answer and Stepbystep explanation:
To prove the identity:
1/tan(x) + tan(x) = sec(x)csc(x)
We will use the following trigonometric identities:
tan(x) = sin(x)/cos(x)sec(x) = 1/cos(x)csc(x) = 1/sin(x)
Substituting (1) into the lefthand side of the given identity, we get:
1/tan(x) + tan(x) = 1/(sin(x)/cos(x)) + sin(x)/cos(x)
Simplifying the expression on the lefthand side, we get:
1/tan(x) + tan(x) = cos(x)/sin(x) + sin(x)/cos(x)
Now, we will obtain a common denominator of cos(x)sin(x) on the righthand side:
1/tan(x) + tan(x) = (cos^2(x) + sin^2(x))/(cos(x)sin(x))
Using the identity cos^2(x) + sin^2(x) = 1, we can simplify this expression to:
1/tan(x) + tan(x) = 1/(cos(x)sin(x))
Substituting (2) and (3) into the righthand side of the identity, we get:
1/tan(x) + tan(x) = sec(x)csc(x)
Therefore, we have shown that the given identity is true.
Answer:
The given identity is valid. Please see the steps below.
Stepbystep explanation:
Given
[tex]\frac{1}{\tan x}+\tan x=\sec x \csc x[/tex]
Lets prove the identity.
Write [tex]\tan x[/tex] as a fraction with a denominator of 1 .
[tex]\frac{1}{\tan x}+\frac{\tan x}{1}=\sec x \csc x[/tex]
To write [tex]\frac{\tan x}{1}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{\tan x}{\tan x}[/tex].
[tex]\frac{1}{\tan x}+\frac{\tan x}{1}*\frac{\tan x}{\tan x}=\sec x \csc x[/tex]
Multiply [tex]\frac{\tan x}{1}*\frac{\tan x}{\tan x}[/tex].
[tex]\frac{1}{\tan x}+\frac{\tan x\tan x}{\tan x}=\sec x \csc x[/tex]
Combine the numerators over the common denominator.
[tex]\frac{1+\tan x\tan x}{\tan x}=\sec x \csc x[/tex]
Multiply [tex]\tan x \tan x[/tex].
[tex]\frac{1+\tan^2 x}{\tan x}=\sec x \csc x[/tex]
Apply the Pythagorean identity to
[tex]\frac{\sec^2 x}{\tan x}=\sec x \csc x[/tex]
Convert everything to sines and cosines.
Apply the reciprocal identity to [tex]\sec x[/tex].
[tex]\frac{\left(\frac{1}{\cos x}\right)^2 }{\tan x}=\sec x \csc x[/tex]
Apply the quotient identity to [tex]\tan x[/tex].
[tex]\frac{\left(\frac{1}{\cos x}\right)^2 }{\frac{\sin x}{\cos x} }=\sec x \csc x[/tex]
Apply the product rule to [tex]\left(\frac{1}{\cos x}\right)^2[/tex].
[tex]\frac{\frac{1^2}{\cos^2 x}}{\frac{\sin x}{\cos x} }=\sec x \csc x[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]{\frac{1^2}{\cos^2 x}*\frac{\cos x}{\sin x} }=\sec x \csc x[/tex]
Combine the fractions.
[tex]{\frac{1^2 \cos x}{\cos^2 x \sin x}=\sec x \csc x[/tex]
Factor [tex]\cos x[/tex] out of [tex]\cos^2 x \sin x[/tex].
[tex]{\frac{1^2 \cos x}{\cos x\cos x \sin x}=\sec x \csc x[/tex]
Cancel the common factor of [tex]\cos x[/tex].
[tex]{\frac{1^2}{\cos x \sin x}=\sec x \csc x[/tex]
One to any power is one.
[tex]{\frac{1}{\cos x \sin x}=\sec x \csc x[/tex]
Rewrite [tex]{\frac{1}{\cos x \sin x}[/tex] as a product.
[tex]{\frac{1}{\cos x}*{\frac{1}{\sin x}=\sec x \csc x[/tex]
Apply the reciprocal identity to [tex]{\frac{1}{\cos x}[/tex].
[tex]\sec x*{\frac{1}{\sin x}=\sec x \csc x[/tex]
Apply the reciprocal identity to [tex]{\frac{1}{\sin x}[/tex].
[tex]\sec x*\csc x=\sec x \csc x[/tex]
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A swimming pool in Hotel West Bay fits 40 people only. Another nearby swimming pool in Hotel East Bay fits 80 people. A group of 170 people decide to split into two groups; a group of 70 people to go to Hotel West Bay and a group of 100 persons to go to Hotel East Bay. Those who arrive late to the Hotel West Bay swimming pool won’t get the chance to swim and will go play badminton instead. Those arriving late to Hotel East Bay will only get the chance to play golf. What is the ratio of the number of people playing Badminton in Hotel West Bay to the number of people swimming in Hotel East Bay pool?
Answers
The ratio of the number of people playing badminton in Hotel West Bay to the number of people swimming in Hotel East Bay pool is 30/40, or 3/4.
What is Ratio?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
let's find the number of people who arrive late to Hotel West Bay and have to play badminton:
70 people in total  40 people capacity = 30 people playing badminton
let's find the number of people who arrive late to Hotel East Bay and have to play golf:
100 people in total  80 people capacity = 20 people playing golf
The ratio of the number of people playing badminton in Hotel West Bay to the number of people swimming in Hotel East Bay pool:
30 people playing badminton / (70 people in total  30 people playing badminton)
3/4
Hence, the ratio of the number of people playing badminton in Hotel West Bay to the number of people swimming in Hotel East Bay pool is 30/40, or 3/4.
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Answer: 30:80 which can reduced to 3:8
Stepbystep explanation: The number of people arriving late at Hotel West Bay and playing Badminton instead of swimming is equal to 7040= 30 people
Write a system of two linear equations showing the distance each animal can
travel to model the fair race. Be sure to define all variables
Please, someone, explain this to me.
Answers
our system of equations correctly models the fair race.Our answer was correctly verified by substituting the values of x and y into the equations.
Let x represent the distance the rabbit can travel and let y represent the distance the turtle can travel. The system of two linear equations can be expressed as:
x + y = 2000 (the total distance of the race)
x = 7y (the rabbit can travel 7 times as fast as the turtle)
Solving the system, we get x = 1400 and y = 600. This means that the rabbit can travel 1400 meters and the turtle can travel 600 meters in the race.
To check our answer, we can substitute the values of x and y into the equations:
x + y = 1400 + 600 = 2000 (the total distance of the race)
x = 7y = 7(600) = 4200 (the rabbit can travel 7 times as fast as the turtle)
Therefore, our system of equations correctly models the fair race.
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There are 20 students in your class 3/5 of them pack a lunch which method will help you find the number of students in your class who pack a lunch a multiply 20 and 5 and then multiply that product by 3 b divide 20 by 5 and then multiply that quotation by 3 c multiply 1/20 and 3/5 d multiply 20 and 5/3
Answers
To find the number of students in your class who pack a lunch, divide 20 by 5 and then multiply that quotation by 3. Option B
What are fractions?
Fractions are simply defined as part of a whole variable, number or element.
There are different types of fractions. They include;
Mixed fractionsSimple fractionsProper fractionsImproper fractionsComplex fractions
From the information given, we have that;
Total number of students in the class is 20Those that packed their lunch are 3/5
Then, we have;
20 × 3/5
60/5
Divide the values
12 students
Hence, the value is 12
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Challenge: A store is giving out cards labeled 1 through 10 when customers enter the store. If the card is an even number, you get a 10% discount on your purchase
that day. If the card is an odd number greater than 6, you get a 40% discount. Otherwise, you get a 25% discount. The table shows the results of 500 customers.
What is the relative frequency for each discount? Use pencil and paper. If the manager of the store wants approximately half of the customers to receive the 25%
discount, does this seem like an appropriate method? Explain.
Discounts
Card Number 1 2 3
5 6
8 9 10
Frequency 47 45 52 58 50 58 51 46 49 44
IL
4
7
The relative frequency for a 10% discount is
(Simplify your answer.)
Answers
Based on these calculations, approximately 51% of the customers received a 25% discount, which is close to the manager's goal of having half of the customers receive this discount.
The relative frequency for each discount can be calculated by dividing the number of customers who received each discount by the total number of customers (500).
For a 10% discount:
Number of customers who received the discount = 47 + 45 + 44 = 136
Relative frequency = 136 / 500 = 0.272
For a 25% discount:
Number of customers who received the discount = 52 + 58 + 50 + 46 + 49 = 255
Relative frequency = 255 / 500 = 0.51
For a 40% discount:
Number of customers who received the discount = 58 + 51 = 109
Relative frequency = 109 / 500 = 0.218
Based on these calculations, approximately 51% of the customers received a 25% discount, which is close to the manager's goal of having half of the customers receive this discount. However, it is unclear if this method is appropriate or not without further information about the manager's goals and the target population.
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Emmanuel and Mauricio are solving the equation 7(x+20. Finish solving each equation.
Answers
Solution of the given equation 7 ( x + 20 ) = 210 by solving different way for each Emmanuel and Mauricio is equal to x = 10.
Completion of the solution of the equation :
7 ( x + 20 ) = 210
Solving by Emmanuel way is:
7(x+20) = 210
Open the parenthesis to simplify the equation we get,
⇒ 7x + 140 = 210
⇒ 7x = 210 140
⇒ 7x = 70
⇒ x = 10
Solving by Mauricio way is:
7(x+20) = 210
Divide both the side by 7 we get,
⇒ x + 20 = 210 /7
⇒ x + 20 = 30
⇒ x = 30  20
⇒ x = 10
Therefore, the solving the given equation by Emmanuel and Mauricio way gives the solution x = 10.
The above question is incomplete , the complete question is:
Emmanuel and Mauricio are solving the equation 7(x+20) = 210 by different way of writing steps.
Emmanuel Mauricio
7(x+20) = 210 7(x+20) = 210
7x + 140 = 210 x + 20 = 30
Finish solving each equation.
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