Answer:
If the question is single answer correct then the answer is [tex]\frac{1}{3}[/tex] and if it's multiple options correct than the answer is [tex]\frac{1}{7}[/tex]
Step-by-step explanation:
There is a little ambiguity in the question, that whether one answer is correct or multiple options are correct, but let;s deal with both the cases.
Probability = [tex]\frac{TotalNo.OfFavourableOutcomes}{TotalOfNoOfOutcomes}[/tex]
Probability when one option is right=[tex]\frac{1}{3}[/tex]
If this is a question , where multiple options are right then the total no. of cases for it will be = TTT, TFF, FTF, FFT, TTF, TFT, FTT (FFF is not a valid case, because the question has to have at least one valid answer.)
Probability when more than one option can be right=[tex]\frac{1}{7}[/tex]
The ratio that relates how much debt a company has in proportion to its equity is?
Answer: The debt-to-equity ratio
Step-by-step explanation:
The debt-to-equity ratio is a company's debt as a percentage of its total market value. If your company has a debt-to-equity ratio of 50% or 70%, it means that you have $0.5 or $0.7 of debt for every $1 of equity
When rolling two fair, standard dice, what is the probability that the sum of the numbers rolled is a multiple of 3 or 4?
Answer:
The probability that sum of numbers rolled is a multiple of 3 or 4 is: [tex]\frac{7}{12}[/tex].
Step-by-step explanation:
The sample space for two fair die (dice) is given below:
[tex]\left[\begin{array}{ccccccc}&1&2&3&4&5&6\\1&2&3&4&5&6&7\\2&3&4&5&6&7&8\\3&4&5&6&7&8&9\\4&5&6&7&8&9&10\\5&6&7&8&9&10&11\\6&7&8&9&10&11&12\end{array}\right][/tex]
From the above table:
Number of occurrence where sum is multiple of 3 = 12
Number of occurrence where sum is multiple of 4 = 9
Total number in the sample space = 36
probability(sum is 3) = 12/36
probability(sum is 4) = 9/36
probability(sum is 3 or 4) [tex]=\frac{12}{36} +\frac{9}{36} \\=\frac{12 + 9}{36} \\=\frac{21}{36}\\=\frac{7}{12}[/tex]
Jasmine weigh 150ib he is loading a freight elevator with identical 72-pound boxes. The elevator can carry no more than 2000ib. If Jasmine rides with the boxes,how many boxes can be loaded on the elevator?
Answer:
Jasmine can load maximum of 25 boxes with herself on the elevator.
Step-by-step explanation:
Given:
Weight of Jasmine = 150 lb
Weight of each boxes = 72 lb
Load elevator can carry = 2000 lb
we need to find the number of boxes that can be loaded
Let number of boxes be 'x'
Now we know that Maximum load the elevator can carry is 2000 lb.
So We can say Weight of jasmine plus Number of boxes multiplied by Weight of each boxes should be less than or equal to Load elevator can carry.
Framing in equation form we get;
[tex]150+72x\leq 2000[/tex]
Solving the equation we get:
We will first Subtract 150 on both side;
[tex]150+72x-150\leq 2000-150\\\\72x\leq 1850[/tex]
Now Dividing both side by 72 by using Division property we get;
[tex]\frac{72x}{72}\leq \frac{1850}{72}\\\\x\leq 25.69[/tex]
Hence Jasmine can load maximum of 25 boxes with herself on the elevator.
Find the perimeter of an equilateral triangle of which one side consists of point P(1, 5) and Q(3, 10). Reminder, perimeter means add all three sides.
Answer:
3√29 ≈ 16.155
Step-by-step explanation:
The distance formula can be used to find the length of the given side.
d = √((x2-x1)^2 +(y2-y1)^2)
PQ = √((3-1)^2 +(10-5)^2) = √(4 +25) = √29
The equilateral triangle has three same-length sides (the literal meaning of "equilateral"), so the perimeter is ...
Perimeter = 3×PQ = 3√29
Which association best describes the data in the table?
x y
3 2
3 3
4 4
5 5
5 6
6 7
8 8
A. no association
B. negative association
C. positive association
Answer:
'x' and 'y' have a positive association between them.
Step-by-step explanation:
We can see in the given data that as 'x' remains constant or increases by 1 unit, or two units in it's two consecutive values, in each of the cases 'y' increases by 1 unit.
Hence, 'x' and 'y' have a positive association between them.
Answer:
C. positive associationStep-by-step explanation:
Positive and negative association describe a relation between variables about a scatter plot.
A positive association happens when one variable increases while the other one also increases.
A negative association happens when one variable decreases while the other variable increases.
It's important to know that the variable that always increases is the independent variable, it increases no matter what.
In this case, we could say that we have a positive association, because while x increases, y also increases.
You could notice that there's some repetitive number. That's normal because a scatter plot doesn't describe a perfect linear relation at the beginning, actually, it's a bit messy, however, from such data we construct a linear relationship which is called "linear regression".
Therefore, the right answer is C.
Nancy performs a full backup of her server every Sunday at 1 A.M. and differential backups on Mondays through Fridays at 1 A.M. Her server fails at 9 A.M. Wednesday. How many backups does Nancy need to restore?
Answer:
4
Step-by-step explanation:
To restore her server after a failure on Wednesday morning, Nancy would need to restore the full backup from Sunday, and then restore the differential backup from Tuesday.
Explanation:In Nancy's case, she would need two backups to fully restore her server. These would be the full backup from Sunday and the differential backup from Tuesday. Here's why:
A full backup involves copying all of the data in a system. It's the most comprehensive type of backup but also requires the most storage space and time. A differential backup, on the other hand, only backs up the data that has changed or been added since the last full backup.
Because Nancy performs full backups every Sunday, the full backup will have all the data up until Sunday at 1 A.M. The differential backup from Tuesday will contain all the changes that occurred on Monday and Tuesday until 1 A.M.
Learn more about Data Backup here:https://brainly.com/question/32115051
#SPJ12
The average score of 100 teenage boys playing a computer game was 80,000 with a population standard deviation of 20,000. What is the 95% confidence interval for the true mean score of all teenage boys?
The 95% confidence interval for the true mean score of all teenage boys is approximately 76,080 to 83,920.
To calculate the 95% confidence interval for the true mean score of all teenage boys, we'll use the formula for the confidence interval:
[tex]\[ \text{Confidence Interval} = \bar{x} \pm Z \left( \frac{\sigma}{\sqrt{n}} \right) \][/tex]
where:
- [tex]\(\bar{x}\)[/tex] is the sample mean,
- Z is the Z-score corresponding to the desired confidence level,
- [tex]\(\sigma\)[/tex] is the population standard deviation, and
- n is the sample size.
For a 95% confidence interval, the Z-score is approximately 1.96.
Given:
- Sample mean [tex](\(\bar{x}\))[/tex] = 80,000
- Population standard deviation (\(\sigma\)) = 20,000
- Sample size (n) = 100
[tex]\[ \text{Confidence Interval} = 80,000 \pm 1.96 \left( \frac{20,000}{\sqrt{100}} \right) \][/tex]
Calculate the standard error (SE):
[tex]\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{20,000}{\sqrt{100}} = 2,000 \][/tex]
Now substitute the values into the formula:
[tex]\[ \text{Confidence Interval} = 80,000 \pm 1.96 \times 2,000 \][/tex]
[tex]\[ \text{Confidence Interval} = 80,000 \pm 3,920 \][/tex]
The 95% confidence interval is from 80,000 - 3,920 to 80,000 + 3,920.
A two week old puppy weighs 11 ounces. Two weeks later, it weighs 15 ounces. Right in equation to represent the weight y of the puppy X weeks after birth.
Answer:
y = 2x +7
Step-by-step explanation:
We are given two points on the growth curve: (weeks, ounces) = (2, 11) or (4, 15).
These can be used to write the equation of a line using the 2-point form:
y = (y2 -y1)/(x2 -1x)(x -x1) +y1
y = (15 -11)/(4 -2)(x -2) +11
y = 4/2(x -2) +11
y = 2x +7 . . . . . y = weight in ounces x weeks after birth
_____
Comment on the problem
There are an infinite number of equations that can be written to go through the two given points. A linear equation is only one of them.
The greatest common divisor of two positive integers less than $100$ is equal to $3$. Their least common multiple is twelve times one of the integers. What is the largest possible sum of the two integers?
Answer:
129
Step-by-step explanation:
Let a and b be two numbers.
We have been given that the greatest common divisor of two positive integers less than 100 is equal to 3. We can represent this information as [tex]GCD(a,b)=3[/tex].
Their least common multiple is twelve times one of the integers. We can represent this information as [tex]LCM(a,b)=12a[/tex].
Now, we will use property [tex]GCD(x,y)*LCM(x,y)=xy[/tex].
Upon substituting our given values, we will get:
[tex]3*12a=ab[/tex]
[tex]36a=ab[/tex]
Switch sides:
[tex]ab=36a[/tex]
[tex]\frac{ab}{a}=\frac{36a}{a}[/tex]
[tex]b=36[/tex]
Now, we need to find a number less than 100, which is co-prime with 12 after dividing by 3.
The greatest multiple of 3 less than 100 is 99, but it is not co-prime with 12 after dividing by 3.
Similarly 96 is also not co-prime with 12 after dividing by 3.
We know that greatest multiple of 3 (less than 100), which is co-prime with 12, is 93.
Let us add 36 and 93 to find the largest possible sum of the required two integers as:
[tex]36+93=129[/tex]
Therefore, the required largest possible sum of the two integers is 129.
A couple needs $55,000 as a down payment for a home. If they invest the $40,000 they have at 4% compounded quarterly, how long will it take for the money to grow to $55,000? (Round your answer to the nearest whole number.)
Answer:
8 years
Step-by-step explanation:
Compound interest formula
[tex]A(t)= A_0(1+\frac{r}{n})^{nt}[/tex]
A(t) is the final amount 55000
A_0= 40000, r= 4% = 0.04, for quarterly n=4
[tex]55000=40000(1+\frac{0.04}{4})^{4t}[/tex]
divide both sides by 40000
[tex]1375=(1+\frac{0.04}{4})^{4t}[/tex]
[tex]1375=(1.01)^{4t}[/tex]
Take ln on both sides
[tex]ln(1375)=4tln(1.01)[/tex]
divide both sides by ln(1.01)
[tex]\frac{ln 1375}{ln 1.01}=4t[/tex]
Divide both sides by 4
t=8.00108
So it takes 8 years
The couple will need to invest their $40,000 at an interest rate of 4% compounded quarterly for about 7 years in order to reach their target of $55,000.
Explanation:The subject of this question is compound interest. Compound interest is the interest computed on the initial principal as well as the accumulated interest from previous periods. Since the couple's money is being compounded quarterly, we will need to use this information in our calculations.
First, we must understand the compound interest formula which is:
A = P (1 + r/n)^(nt)
where,
A is the final amount of money after n years. P is the principal amount (initial amount of money). r is the annual interest rate in decimal form (so 4% would be 0.04). n is the number of times the interest is compounded per year. t is the time the money is invested for in years. In this case, we are trying to find 't' when A = $55,000, P = $40,000, r = 0.04 and n = 4 (since the interest is compounded quarterly). Doing the math, we get the answer as approximately 7 years.
Find all x that satisfy the inequality (2x 10)(x 3)<(3x 9)(x 8). Express your answer in interval notation.
To find all x that satisfy the inequality (2x + 10)(x + 3) < (3x + 9)(x + 8), we expand and simplify the inequality, solve for x by considering the sign of each factor, and express the answer in interval notation. The solution is (-7, -6).
Explanation:To find all x that satisfy the inequality (2x + 10)(x + 3) < (3x + 9)(x + 8), we will first expand and simplify the inequality. Then, we will solve for x by considering the sign of each factor.
Start by expanding both sides of the inequality:The interval notation for the solution is (-7, -6). This means that all values of x between -7 and -6 (exclusive) satisfy the inequality.
Learn more about Inequality here:https://brainly.com/question/40505701
#SPJ12
Stacey owns a lot that has 180 feet of front footage and contains 36,000 square feet. She purchases two lots adjacent to each side of his lot. These side lots are each 200 feet deep and contain 19,000 square feet. What is the total front footage of all three lots?
Step-by-step explanation:
Front footage of first lot = 180 ft
Area of each side lot = 19000 ft²
Depth of each side lot = 200 ft
We have
Area = Depth x Front footage
19000 = 200 x Front footage
Front footage = 95 ft
Total front footage = Front footage of first lot + 2 x Front footage of each side lot
Total front footage = 180 + 2 x 95
Total front footage = 180 + 190
Total front footage = 370 ft
The total front footage of all three lots is 370 ft
A boat sails 20 miles wast of the port and then 15 miles south to an island how far is the boat from the port if you measure thr distance in a straight line ?
Answer:
25 miles
Step-by-step explanation:
Given: A boat sail 20 miles west of the port and then 15 miles south to an island.
Picture attached.
The distance from port to island could be measured in a straight line. It will form a hypotenous.
∴ we can use Pythogorean theorem to find the distance.
[tex]h^{2} = a^{2} +b^{2}[/tex]
Where, "a" is adjacent= 20 miles and "b" is opposite= 15 miles.
[tex]h^{2} = 20^{2} +15^{2}[/tex]
⇒ [tex]h^{2} = 400+225= 625[/tex]
⇒[tex]h^{2} = 625[/tex]
⇒[tex]h= \sqrt{625}= \sqrt{25^{2} }[/tex]
We know [tex]\sqrt{x^{2} } = x[/tex].
∴[tex]h= 25\ miles[/tex]
∴ Distance of Port from the Island is 25 miles.
Final answer:
Using the Pythagorean theorem, the straight-line distance from the port to the boat, after traveling 20 miles west and 15 miles south, is found to be 25 miles.
Explanation:
The problem presented involves calculating the straight-line distance, or 'hypotenuse', of a right-angled triangle formed by the boat's journey from the port, 20 miles west and then 15 miles south. We will use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is c² = a² + b².
Let's apply this formula to find the distance:
The distance travelled west (a) is 20 miles.
The distance travelled south (b) is 15 miles.
We can calculate the straight-line distance using the formula:
c² = 20² + 15²
c² = 400 + 225
c² = 625
c = √625
c = 25 miles
Therefore, the boat is 25 miles away from the port if measured in a straight line.
A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and then a member can buy CDs at a reduced price. If a member buys 17 CDs in one year, the cost is $111.25. Determine the cost of each CD for a member.
Answer:the cost of each CD for a member is $5.25
Step-by-step explanation:
The membership costs $22 per year, and then a member can buy CDs at a reduced price.
Let x represent the cost of each CD for a member.
Let n represent the number of CDs that each member buys. This means that the total cost of buying n CDs for a member for a year would be
22 + nx
If a member buys 17 CDs in one year, the cost is $111.25. This means that
17x + 22 = 111.25
17x = 111.25 - 22 = 89.25
x = 89.25/175 = 5.25
A vegetable garden and its surrounding that are shaped like a square that together are 11 feet wide. The path is 2 feet wide. Find the total area of the vegetable garden and path.
Area of path and garden = 11 x 11 = 121 square feet.
Area of garden only = 7 x 7 = 49 square feet.
Area of just the path = 121 - 49 = 72 square feet.
if a negative number has to be added to another negative number, does it stay negative?
Yes because the number say on one side
yes because the numbers stay on one side of the number line
A man buys 3 burgers and 2 jumbo deluxe fries for $7.40. A woman buys one burger and 4 jumbo deluxe fries for $7.80. How much is the burger and how much are the fries?Select one:a. Burger = $1.40, Fries = $1.60b. Burger = $1.50, Fries = $1.80c. Burger = $2.80, Fries = $2.00d. Burger = $2.00, Fries = $2.80
Answer: A. See photo for work.
Step-by-step explanation:
Answer:the cost of one burger is $1.4 and the cost of one fry is $1.6
Step-by-step explanation:
Let x represent the cost of one burger.
Let y represent the cost of one fry.
A man buys 3 burgers and 2 jumbo deluxe fries for $7.40. This means that
3x + 2y = 7.4 - - - - - - - - - 1
A woman buys one burger and 4 jumbo deluxe fries for $7.80. It means that
x + 4y = 7.8 - - - - - - - - -2
Multiplying equation 1 by 1 and equation 2 by 3, it becomes
3x + 2y = 7.4
3x + 12y = 23.4
Subtracting
- 10y = - 16
y = - 16/- 10 = 1.6
Substituting y = 1.6 into equation 2, it becomes
x + 4 × 1.6 = 7.8
x = 7.8 - 6.4 = 1.4
Pete wants to make turkey sandwiches for tow friends and himself.He wants each sandwich to contain 3.5 ounces of turkey.How many ounces of turkey does he need
Pete needs 10.5 ounces of turkey.
Step-by-step explanation:
Given,
Number of friends = 2
One for Pete.
Total sandwiches to be made = 2+1 = 3
Quantity of turkey in one sandwiches = 3.5 ounces
For finding the quantity of turkey for three sandwiches, we will multiply.
Turkey for 3 sandwiches = 3*3.5 = 10.5 ounces
Pete needs 10.5 ounces of turkey.
Keywords: multiplication, addition
Learn more about addition at:
brainly.com/question/10629017brainly.com/question/106300#LearnwithBrainly
A rectangle has a length that is one foot less than twice its width. it the area of the rectangle is 91 square feet then which of the following equations could be used to solve for its the width of the rectangle?
To solve for the width of the rectangle, use the equation width = (2L - 1) / 2. Set up the equation L * width = 91 and simplify it to 2L² - L - 182 = 0. Solve the quadratic equation to find the possible values for L, which will give us the width of the rectangle.
Explanation:To solve for the width of the rectangle, we can use the equation width = (2L - 1) / 2, where L is the length of the rectangle. Given that the area of the rectangle is 91 square feet, we can set up the equation as L * width = 91. Substituting the first equation into the second equation, we get:
L * ((2L - 1) / 2) = 91
Simplifying the equation, we have:
2L² - L - 182 = 0
We can then solve this quadratic equation to find the possible values for L, which will give us the width of the rectangle.
Learn more about Solving for the width of a rectangle here:https://brainly.com/question/29004072
#SPJ12
The correct equation to solve for the width of the rectangle with an area of 91 square feet and a length that is one foot less than twice its width is 2x^2 - x - 91 = 0. Therefore, the correct answer is option C.
The student's question involves finding the width of a rectangle, given that the length is one foot less than twice its width and that the area of the rectangle is 91 square feet.
We can represent the width of the rectangle with x and the length as 2x - 1. The area of a rectangle is found by multiplying its length by its width, which gives us the equation x(2x - 1) = 91.
Expanding this equation, we get 2x^2 - x - 91 = 0. Therefore, the correct equation to solve for the width of the rectangle is 2x^2 - x - 91 = 0.
The probable question may be:
A rectangle has a length that is one foot less than twice its width. it the area of the rectangle is 91 square feet then which of the following equations could be used to solve for its the width of the rectangle?
O x² + 2x + 91 = 0
O 2x² + x + 91 = 0
O 2x² - x - 91 = 0
O x² - 2x - 91 = 0
To determine whether there is a relationship between the type of school attended and verbal reasoning scores for Irish students, three samples with 25 students, in each group, were randomly selected from data used by Raferty and Hout (1985). One group of students attended secondary school, the second group of students attended vocational school, and the third group consisted of students who attended only primary school.
Here are the three sample standard deviations for the verbal reasoning scores for the three groups (secondary school, vocational school, and primary school only):
Based on this information, do the data meet the condition of equal population standard deviations for the use of the ANOVA?
A. Yes, because 14.18 − 11.71 < 2.
B. Yes, because 14.18/11.71 < 2.
C. No, because the standard deviations are not equal.
Answer:
B. Yes, because 14.18/11.71 < 2.
Step-by-step explanation:
When the ratio of the largest sample standard deviation to the smallest sample standard deviation is less than 2, the condition is said to be met.
Which inequality does the given graph represent?
A) y > 3x + 4
B) y > 1/3x − 4
C) y > 1/3x + 4
D) y ≥ 1/3x + 4
Answer:
The answer to your question is letter C
Step-by-step explanation:
Process
1.- Find two points of the dotted line
A (0, 4)
B (3, 5)
2.- Find the slope of the line
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
Substitution
[tex]m = \frac{5 - 4}{3 - 0}[/tex]
[tex]m = \frac{1}{3}[/tex]
3.- Write the equation of the line
y - y1 = m(x - x1)
y - 4 = 1/3(x - 0)
y - 4 = 1/3x
y = 1/3x + 4
4.- Write the inequality
We are interested on the upper area so
y > 1/3x + 4
Answer: C) y > 1/3x + 4
Step-by-step explanation: The line is dashed hence >. The slope is 1/3 and the y- intercept is 4. This makes the inequality y > 1/3x + 4.
Hope this helps! :)
Ricky is on the track team. Below are four of his times running 200 meters. 23.37 sec, 23.45 sec, 23.44 sec, 23.34 sec What is the difference between his best time and his worst time?
Final answer:
Ricky's best time running 200 meters is 23.34 seconds, and his worst time is 23.45 seconds. The difference between his best and worst times is 0.11 seconds.
Explanation:
The question asks what the difference is between Ricky's best and worst times running 200 meters. To find this, we need to identify the fastest (lowest) time and the slowest (highest) time from the provided times: 23.37 sec, 23.45 sec, 23.44 sec, and 23.34 sec. Ricky's best time is 23.34 seconds, and his worst time is 23.45 seconds. The difference between these times is calculated by subtracting the best time from the worst time.
Worst time (slowest): 23.45 sec
Best time (fastest): 23.34 sec
Difference: 23.45 sec - 23.34 sec = 0.11 sec
Therefore, the difference between Ricky's best and worst time is 0.11 seconds.
Solve for x. The triangles in each pair are similar.
Answer:
Step-by-step explanation:
You need to pay very close attention to the triangle similarity statement. This says that triangle NML is similar to triangle NVU. But if you look at the way that triangle NVU is oriented in its appearance, it's laying on its side. We need to set it upright so that angle N is the vertex angle, angle V is the base angle on the left, and angle U is the base angle on the right. When we do that we see that sides NV and NM are corresponding and exist in a ratio to one another; likewise with sides VU and ML. Setting up the proportion:
[tex]\frac{NV}{NM}=\frac{VU}{ML}[/tex]
Filling in:
[tex]\frac{12}{36} =\frac{9}{9x}[/tex]
Cross multiply to get
324 = 108x
and x = 3
Lucia flips a coin three times. What is the probability she gets (Head, tail, Head) in that order?
Answer: [tex]\dfrac{1}{8}[/tex]
Step-by-step explanation:
The total outcomes of tossing a coin = 2
The total number of possible outcomes of flipping coin three times =2 x 2 x 2 = 8
Favorable outcome= (Head, tail, Head) in order
i.e. Number of Favorable outcomes = 1
We know that , Probability = [tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
Therefore , The required probability [tex]=\dfrac{1}{8}[/tex]
Hence , the probability she gets (Head, tail, Head) in that order[tex]=\dfrac{1}{8}[/tex]
Find all solutions to the equation in the interval [0, 2π).
cos x = sin 2x
pi divided by two., three pi divided by two.
pi divided by six., pi divided by two., five pi divided by six., three pi divided by two.
0, π
0, pi divided by six, five pi divided by six., π
Answer:
x = π/6, π/2, 5π/6, 3π/2
Step-by-step explanation:
cos x = sin(2x)
Use double angle formula.
cos x = 2 sin x cos x
Move everything to one side and factor.
cos x − 2 sin x cos x = 0
cos x (1 − 2 sin x) = 0
Set each factor to 0 and solve.
cos x = 0
x = π/2, 3π/2
1 − 2 sin x = 0
sin x = 1/2
x = π/6, 5π/6
The total solution is:
x = π/6, π/2, 5π/6, 3π/2
Final answer:
The solutions to the equation cos x = sin 2x in the interval [0, 2π) are π/6, π/2, 5π/6, and 3π/2, derived by using the identity sin 2x = 2 sin x cos x and considering cases for cos x = 0.
Explanation:
To find all solutions to the equation cos x = sin 2x in the interval [0, 2π), we first need to use a trigonometric identity to express both sides of the equation with either sine or cosine. The identity sin 2x = 2 sin x cos x can be used here. Substituting it into our original equation, we get:
cos x = 2 sin x cos x
To solve this equation, we can divide both sides by cos x, given that cos x ≠ 0:
1 = 2 sin x
sin x = 1/2
Using the unit circle or trigonometric tables, we know that sin x takes the value of 1/2 at x = π/6 and x = 5π/6 in the interval [0, 2π). Additionally, we must consider the case when cos x = 0 to avoid division by zero. This occurs at x = π/2 and x = 3π/2, which are also solutions to the original equation given that sin(2(π/2)) = sin(π) = 0 and sin(2(3π/2)) = sin(3π) = 0, which are equal to cos(π/2) and cos(3π/2) respectively. Thus, the complete set of solutions in the interval [0, 2π) is π/6, 5π/6, π/2, and 3π/2.
An airplane flew 4 hours with a 25 mph tail wind. The return trip against the same wind took 5 hours. Find the speed of the airplane in still air. This similar to the current problem as you have to consider the 25 mph tailwind and headwind. Plane on outbound trip of 4 hours with 25 mph tailwind and return trip of 5 hours with 25 mph headwind Let r = the rate or speed of the airplane in still air. Let d = the distance
a. Write a system of equations for the airplane. One equation will be for the outbound trip with tailwind of 25 mph. The second equation will be for the return trip with headwind of 25 mph.
b. Solve the system of equations for the speed of the airplane in still air.
Answer:
r = 225 Mil/h speed of the airplane in still air
Step-by-step explanation:
Then:
d is traveled distance and r the speed of the airplane in still air
so the first equation is for a 4 hours trip
as d = v*t
d = 4 * ( r + 25) (1) the speed of tail wind (25 mil/h)
Second equation the trip back in 5 hours
d = 5 * ( r - 25 ) (2)
So we got a system of two equation and two unknown variables d and
r
We solve it by subtitution
from equation (1) d = 4r + 100
plugging in equation 2
4r + 100 = 5r - 125 ⇒ -r = -225 ⇒ r = 225 Mil/h
And distance is :
d = 4*r + 100 ⇒ d = 4 * ( 225) + 100
d = 900 + 100
d = 1000 miles
NEED HELP PLEASE I HAVE 6 DAYS TO COMPLETE EVERYTHING
Answer:
C. 4
Step-by-step explanation:
f(c) = 28 = 2x² - 4
28 = 2x² - 4
32 = 2x²
16 = x²
±4 = x
x = 4
c = 4
Answer:
Option c) is correct
ie., c=4 represents the value of c suchthat function [tex]f(c)=28[/tex]
Step-by-step explanation:
Given function f is defined by [tex]f(x)=2x^{2}-4[/tex]
To find the value of "c" such that [tex]f(c)=28[/tex]
Therefore put x=c in the given function as
[tex]f(x)=2x^{2}-4[/tex]
[tex]f(c)=2c^{2}-4[/tex]
and we have [tex]f(c)=28[/tex]
Now equating the two functions
[tex]f(c)=2c^{2}-4=28[/tex]
[tex]2c^{2}-4=28[/tex]
[tex]2c^{2}=28+4[/tex]
[tex]c^{2}=\frac{32}{2}[/tex]
[tex]c^{2}=16[/tex]
[tex]c=4[/tex]
Therefore [tex]c=4[/tex]
Option c) is correct
ie., c=4 represents the value of c suchthat function [tex]f(c)=28[/tex]
Working alone at its constant rate, pump X pumped out \small \frac{1}{3} of the water in a pool in 4 hours. Then pump Y started working and the two pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 6 hours. How many hours would it have taken pump Y, working alone at its constant rate, to pump out all of the water that was pumped out of the pool?
Answer:
P(y) take 36 h to do the job alone
Step-by-step explanation:
P(x) quantity of water pump by Pump X and
P(y) quantity of water pump by Pump Y
Then if P(x) pumped 1/3 of the water in a pool in 4 hours
Then in 1 hour P(x) will pump
1/3 ⇒ 4 h
? x ⇒ 1 h x = 1/3/4 ⇒ x = 1/12
Then in 1 hour P(x) will pump 1/12 of the water of the pool
Now both pumps P(x) and P(y) finished 2/3 of the water in the pool (left after the P(x) worked alone ) in 6 hours. Then
P(x) + P(y) in 6 h ⇒ 2/3
in 1 h ⇒ x ?? x = (2/3)/6 x = 2/18 x = 1/9
Then P(x) + P(y) pump 1/9 of the water of the pool in 1 h. We find out how long will take the two pumps to empty the pool
water in a pool is 9/9 ( the unit) then
1 h ⇒ 1/9
x ?? ⇒ 9/9 x = ( 9/9)/( 1/9) ⇒ x = 9 h
The two pumps would take 9 hours working together from the beggining
And in 1 hour of work, both pump 1/9 of the water, and P(x) pump 1/12 in 1 hour
Then in 1 hour P(y)
P(y) = 1/9 - 1/12 ⇒ P(y) = 3/108 P(y) = 1/36
And to pump all the water (36/36) P(y) will take
1 h 1/36
x ?? 36/36 x = (36/36)/1/36
x = 36 h
P(y) take 36 h to do the job alone
Is the binomial a factor of the polynomial function?
f(x)=x^3+4x^2−25x−100
(I'm not sure if the highlighted answers are correct, help!!!)
Answer:
YES
NO
NO
Step-by-step explanation:
The given polynomial is: [tex]$ f(x) = x^3 + 4x^2 - 25x - 100 $[/tex]
(x - a) is a factor of a polynomial iff x = a is a solution to the polynomial.
To check if (x - 5) is a factor of the polynomial f(x), we substitute x = 5 and check if it satisfies the equation.
∴ f(5) = 5³ + 4(5)² - 25(5) - 100
= 125 + 100 - 125 - 100
= 225 - 225
= 0
We see, x = 5 satisfies f(x). So, (x - 5) is a factor to the polynomial.
Now, to check (x + 2) is a factor.
i.e., to check x = - 2 satisfies f(x) or not.
f(-2) = (-2)³ + 4(-2)² - 25(-2) - 100
= -8 + 16 + 50 - 100
= -108 + 66
≠ 0
Therefore, (x + 2) is not a factor of f(x).
To check (x - 4) is a factor.
∴ f(4) = 4³ + 4(4)² - 25(4) - 100
= 64 + 64 - 100 - 100
= 128 - 200
≠ 0
Therefore, (x - 4) is not a factor of f(x).
Answer:
The answers are (x-5) YES (x+2) NO (x-4) NO
Step-by-step explanation:
I took the test :)
Abc is an isosceles triangle with ba=bc d lies on ac.Abd is an isosceles triangle with ab=ad angle abd=72 show that triangle bcd is isosceles.You must give a reason for each working out.
Answer:
ADB=72˚. base angles in an isosceles triangle are equal
72+72=144 180-144=36 BAD=36 ˚Angles in a triangle =180˚
180-72=108˚ BDC=108˚ angles on a straight line=180˚
Step-by-step explanation:
only three marks for this one
By exploiting the properties of isosceles triangles and the sum of angles in a triangle, we deduce that triangle BCD is isosceles with BC = BD.
Explanation:The student is asking how to prove that triangle BCD is isosceles given that triangles ABC and ABD are also isosceles with AB = BC and AB = AD, respectively, and angle ABD = 72 degrees. We can begin by noting that the sum of the angles in any triangle is 180 degrees. Because triangle ABD is isosceles with AB = AD, the angles ABD and ADB are equal, and since angle ABD is 72 degrees, angle ADB is also 72 degrees. Therefore, angle BAD, the remaining angle in triangle ABD, must be 180 - 72 - 72 = 36 degrees.
Since triangle ABC is also isosceles with AB = BC, angles ABC and BAC are equal. Angle BAD is part of angle BAC, which means angle BAC is also 36 degrees (since they both include angle BAD). Consequently, angle ABC is 36 degrees. The base angles of an isosceles triangle are equal, so angle BCA must also be 36 degrees. Because ABC is isosceles with AB = BC, and we have determined that angles ABC and BCA are equal, we conclude that angles BCD and CBD must also be equal, making triangle BCD isosceles, with BC = BD.
Learn more about Isosceles Triangles here:https://brainly.com/question/2456591
#SPJ3