The values of x in the interval [0, 2π] that satisfy the equation 3|tan(x)| = 3 are π/4, 3π/4, 5π/4, and 7π/4.
Explanation:The given equation is 3|tan(x)| = 3. This means the absolute value of the tangent of x times 3 is equal to 3. We can remove the 3 from both sides to simplify to |tan(x)| = 1. The absolute value operator denotes the non-negative value of a number. So, we need to find the values of x such that tan(x) equals 1 or -1.
The solutions for tan(x) = 1 in the interval [0, 2π] are π/4 and 5π/4. The solutions for tan(x) = -1 in the same interval are 3π/4 and 7π/4.
Thus, the values of x that satisfy the equation are π/4, 3π/4, 5π/4, and 7π/4.
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What is 8.478 in expanded form
The expanded form of the given number is [tex]8+0.4+0.07+0.008[/tex].
Given:
The given number is [tex]8.478[/tex].
To find:
The expanded form of the given number.
Explanation:
Write the given number as the sum of the place values of its all digits to find the expanded form of the given number.
[tex]8.478=8+0.4+0.07+0.008[/tex]
Therefore, the expanded form of the given number is [tex]8+0.4+0.07+0.008[/tex].
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The Waist to Hip Ratio (WHR) is a ratio commonly expressed as a decimal that has been shown to be a good predictor of possible cardiovascular problems in both men and women. If Kevin has a WHR greater than 1, he is considered to be “high risk” for cardiovascular problems. Calculate Kevin’s WHR with a waist measurement of 42 inches and a hip measurement 2 inches less.
Suppose that x is the age of a husband, and y is the age of his wife. if men always marry women who are 3 years younger than themselves, what is the equation for y (wife's age) as a function of x (husband's age)?
What is the square root of 25 over 36
Help Please?? 12. Of the following, which one is an observational study? A. Asking hearing-impaired people to try a new style of earphone to get their opinion B. Comparing survival rates between treating bone cancer with surgery versus treating it with radiation C. recording the daily output of a balloon factory for 6 months D. polling people on their favorite color I believe it would be 'C', yes?
Option 'C' is an example of an observational study because it involves recording data without manipulation from the researcher, fitting the definition of observing the natural state or habits of a situation over time.
Explanation:You have correctly identified option 'C' as an example of an observational study. In an observational study, researchers merely observe and record data without manipulating or intervening in the study environment or subjects. Option 'C', which involves recording the daily output of a balloon factory for 6 months, fits this description as it simply measures and records data over time without any intervention from the researcher.
It is different from a controlled experiment where variables are manipulated to assess the effect of treatments, as in option 'B', which compares survival rates between different treatments for bone cancer. Similarly, options 'A' and 'D' involve asking for opinions, which might be part of a broader observational study but are not observational studies by themselves.
In summary, an observational study is characterized by the purposeful absence of manipulation by the researcher and is designed to observe the natural state or habits of the subject or situation being studied.
You bought a magazine for $6 and some notepads for $3 each. You spent a total of $18. How many notepads did you buy?
To find the number of notepads bought, we can set up an equation by subtracting the cost of the magazine from the total cost and equating it to the cost of the notepads. By solving the equation, we find that you bought 4 notepads.
Explanation:To solve this problem, we can start by setting up an equation. Let's assume the number of notepads bought is 'x'. We know the magazine cost $6, so the cost of the notepads is $18 - $6 = $12. Since each notepad costs $3, the equation becomes 3x = 12. To find the value of 'x', we can divide both sides of the equation by 3. So, x = 12/3 = 4.
Therefore, you bought 4 notepads.
Markia saved for a new bike. The bike was on sale for a discount of 35%. The original cost of the bike was $270. How much did she pay for the bike?
Toby is making a picture graph each picture of a book is equal to 2 books he read the row for month 1 has 3 pictures of books how many books did T
oby read during month 1
Toby read 6 books during the first month by using the picture graph where each picture represents 2 books.
To determine how many books Toby read during month 1, follow these steps:
Understand each picture of a book represents 2 books read.Observe that Toby has 3 pictures of books for month 1.Multiply the number of pictures by the number of books each picture represents: 3 pictures * 2 books per picture = 6 books.Toby read 6 books during the first month.
14-9x=-8(10+x) slove and show check
What is 1 more ten than 11?
99 POINTS POSSIBLE!!!! I have a lot of math problems.....Please show your work also:) I will give Brainiest too!
1.Chase picked three buckets of blackberries that weigh: 2.79 pounds, 2.45 pounds, and 2.62 pounds. What is the average weight for the three buckets?
2. Ashley is baking cookies for math class. The recipe calls for 4 4/5 cups of flour. Ashley has to make 1 1/3 times the recipe to feed the whole class. How much flour does Ashley need?
3. Jordan finished her homework in 1 1/2 hours. It took Kasey 3/4 an hour longer than Jordan to finish her homework. How long did it take Kasey?
4. 32.5 divided by -0.08
5. 4.3x= 81.7 (Decimal Equation)
Thank you for helping me if you did!!!!!!!! I really appreciate it very much!!!!!!!
Hello!
1) 2.62
2) 4.8
3) 6.4
3) 2.25 hours
4) −406.25
5) X=19
I hope it helps!
In Sean's fish tank there are 6times as many goldfish as guppies that's are a total of 21 fish in the tank how many more goldfish are there than guppies
Can someone please help I need a clear explanation on how to solve this equation.
At Avery Middle School, 273 students responded to a survey asking whether a Bulldog, a Lion, or a Tiger should be the new school mascot. Four times as many students chose Bulldog as chose Tiger. Twice as many students chose Lion as chose Tiger. How many students chose Lion?
Answer:
78 students chose lion.
Step-by-step explanation:
Let x students chose tiger.
Let y students chose bull dog.
Let z students chose lion.
Total students = 273
[tex]x+y+z=273[/tex] ....(1)
Four times as many students chose Bulldog as chose Tiger.
[tex]y=4x[/tex]
Twice as many students chose Lion as chose Tiger.
[tex]z=2x[/tex]
Substituting the values of y and z in (1)
[tex]x+4x+2x=273[/tex]
=> [tex]7x=273[/tex]
x = 39 (students who chose tiger)
We have to find students who chose Lion or z (defined above)
[tex]z=2x[/tex]
[tex]z=2(39)[/tex]
So, z = 78
Therefore, 78 students chose lion.
if bx-2=k then x equal
A carpenter is making a brace for a chair. To do so she intersects two pieces of wood to make two sets of vertical angles. The ostuse angles formed are each 145 . What is the measurement of each acute angle formed
Write 720,080 in expanded form with exponents
Celia bought a bag of 12 goldfish for $3. What is the cost of 1 goldfish?
we know that
Celia bought a bag of [tex]12[/tex] goldfish for [tex]\$3[/tex]
so
by proportion
Find the cost of [tex]1[/tex] goldfish
[tex]\frac{3}{12} \frac{\$}{goldfish} =\frac{x}{1} \frac{\$}{goldfish} \\ \\x=3/12 \\ \\x=\$0.25[/tex]
therefore
the answer is
The cost of one goldfish is [tex]\$0.25[/tex]
Celia will pay 0.25 dollars for 1 goldfish. The cost of 1 goldfish is $ 0.25
The Total number of goldfish purchased is 12.
Cost price for 12 goldfish is $ 3.
Let the price of 1 goldfish be x dollars.
Therefore,
[tex]\begin{aligned}x \times\$12&=\$3\\x&=\dfrac{3}{12}\\x&=0.25\end{aligned}[/tex]
Hence, the cost of 1 goldfish is 0.25 dollars.
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Avery's class sold candy bars for a fundraiser. There were 20 bars in each box. Avery sold 4 boxes and an additional 8 bars. Express the total number of boxes that Avery sold as a mixed number. How many candy bars did Avery sell?
Answer:
she sold 4 2/5 boxes of candy bars.
In total, she sold 88 bars.
:))
Step-by-step explanation:
16x+x =12 solve justify each step with algebraic property
Thirty students are eating lunch at 5 tables. Each table has the same number of students. How many students are sitting at each table
50779 divided by 590 equals
gregs gas station sells three different kinds of gasoline:regular,plus,and premium
mr.adams spent $36.25 on 12.5 gallons of regular gasoline at gregs gas station.determine the cost per gallon for regular gasoline,showing each step in the process.
Mr. Adams spent $36.25 on 12.5 gallons of regular gasoline. To find the cost per gallon, divide the total cost by the number of gallons, resulting in a cost of $2.90 per gallon of regular gasoline at Greg's gas station.
To determine the cost per gallon for regular gasoline, we need to divide the total amount spent by Mr. Adams at Greg's gas station by the number of gallons of gasoline he purchased. In this case, Mr. Adams spent $36.25 on 12.5 gallons of regular gasoline.
Step-by-step calculation:
Write down the total cost of gasoline: $36.25.
Write down the total gallons of gasoline purchased: 12.5 gallons.
Divide the total cost by the number of gallons to find the cost per gallon: $36.25 \/ 12.5 gallons.
Perform the division: $36.25 \/ 12.5 gallons = $2.90 per gallon.
Therefore, the cost per gallon for regular gasoline at Greg's gas station is $2.90.
15/16 is 1 sixteenth groups of what size
litter along a 15 mile stretch road will be picked up by 6 different groups of students which equation shows how to find the number of miles each group needs to clean
a.15 divided by 6=6/15
b. 6 divided by 15=6/15
c. 15 divided by 6=15/6
d. 6 divided by 14 =15/6
Factor the expression completely:
2x² + 5x - 12
Tom jogged 3/5 mile on Monday and 2/6 mile on Tuesday how much farther did Tom joy on Monday then on Tuesday
An acidophilus culture containing 150 bacteria doubles in population every hour. Predict the number of bacteria after 12 hours.
A violin student records the number of hours she spends practicing during each of nine consecutive weeks. 6.2 5.0 4.3 7.4 5.8 7.2 8.4 1.2 6.3 what is the interquartile range (iqr) for this data?
To calculate the interquartile range (IQR) of the data set, the ordered values are split by the median to find Q1 and Q3. The difference between Q3 and Q1 gives the IQR which is 2.65 for this data set.
The interquartile range (IQR) is the measure of the middle 50 percent spread in a data set and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). To find the IQR for the provided data set (6.2, 5.0, 4.3, 7.4, 5.8, 7.2, 8.4, 1.2, 6.3), we first need to order the data from smallest to largest and then identify Q1 and Q3. Using the median to split the ordered data into two halves and finding the medians of these two halves gives us Q1 and Q3, and their difference gives us the IQR.
Ordered data: 1.2, 4.3, 5.0, 5.8, 6.2, 6.3, 7.2, 7.4, 8.4Median (also Q2): 6.2Lower half (for Q1 calculation): 1.2, 4.3, 5.0, 5.8Upper half (for Q3 calculation): 6.3, 7.2, 7.4, 8.4Q1: (5.0 + 4.3) / 2 = 4.65Q3: (7.4 + 7.2) / 2 = 7.3IQR: 7.3 - 4.65 = 2.65at 7 p.m. last night, the temputure was 10 degrees. At 7 a.m. the next morning, the temputure was -2 degrees. By how much did the temputure change From 7 p.m. to 7 a.m.
10 to 0 =10
0 to -2 = 2
10+2 =12
it changed by 12 degrees
Use the formula d = rt to find the distance d a long-distance runner can run at a rate r of 9 1/2 miles per hour for time t of 1 3/4 hours.
multiply the 2 numbers
9 1/2 * 1 3/4 =
19/2 * 7/4 = 133/8 = 16 5/8 miles