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Related Questions
Trig question -- please help if you can!
I have to write y = r cos(θ + R) and z = r sin(θ + R) in terms of y, z, and R. I'm not really sure how to do this, so would you mind showing work so I can learn the steps properly? (teacher hasn't taught this super well, haha) Thank you!!
Answers
It is very common for television series to draw a large audience for special events of for cliff-hanging story lines. suppose that on one of these occasions, the special show drew viewers from 38.2% of all us tv households. suppose that three tv households are randomly selected. what is the probability that all three households viewed this special show?
Answers
Conditions for a Binomial Experiment are:
1) The sample is simple random sample
2) The probability of success is constant
3) The trials are independent
4) There are a fixed number of trials
Probability of success on a single trial = p = 0.382
Number of trials = n = 3
Number of successful trials= x = 3
The formula of the Binomial probability is:
P( 3 out of 3 success) = [tex]3C_{3} p^{3} (1-p)^{3-3} [/tex]
Using the values, we get:
P (3 out of 3) = 0.557 = 5.57%
Thus the probability that all three households viewed this special show is 5.57%
To find the probability that all three randomly selected households watched a special TV show when 38.2% of all households watched it, you multiply the probability for one household by itself three times, resulting in approximately 0.055 or 5.5%.
The question asks about calculating the probability that all three randomly selected US TV households watched a special television show, given that 38.2% of all US TV households viewed it. To find this probability, we use the rule of independent events since the viewing status of one household is assumed to not affect another. The probability that all three households viewed this show can be calculated by multiplying the probability of one household viewing the show three times.
The calculation would look like this:
0.382 (the probability one household watched the show) x 0.382 x 0.382 = 0.055 (approximately).
This is the probability that all three households viewed the special show.
solve and express the solution set in simplest form. 8x-2/9 = 2/1
Answers
Final answer:
The solution to the equation 8x-2/9 = 2/1 is obtained by multiplying both sides by 9, adding 2 to both sides, dividing by 72, and simplifying the fraction to get x = 5/18.
Explanation:
To solve the equation 8x-2/9 = 2/1, we first want to isolate the variable x. Here are the steps to do this:
Multiply both sides of the equation by 9 to eliminate the denominator on the left side, which gives us 72x - 2 = 18.
Add 2 to both sides to get 72x = 20.
Divide both sides by 72 to solve for x, resulting in x = 20/72.
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4. The solution in simplest form is x = 5/18.
If h(x) = 3 + 2f(x) , where f(1) = 3 and f '(1) = 4, find h'(1).
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h'(1) = 2*f'(1) = 2*4
h'(1) = 8
5 -2 (4a + 1) + 3a = 13 what is (a) equal to a) - 6/5 b) - 2 c) 2 d) 6/5
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The solution of the equation 5 -2 (4a + 1) + 3a = 13 is 2/3.
What is an equation?An equation is an expression that indicates the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given the equation as follows;
5 -2 (4a + 1) + 3a = 13
Therefore, solving the equation
3(4a+1)+3a=13
12a+3+3a=13
15a+3=13
15a=10
a=2/3
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The lengths of the legs of a right angle triangle 12 cm and 35 cm. What is the length of the hypotenuse?
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Allow x to be the hypotenuse.
12^2+35^2=x^2
144+1225=x^2
1369=x^2
x=37
c^2=a^2+b^2, where c is the hypotenuse
c^2=12^2+25^2=144+625=769
c=sqrt769= aprox 27.73
Describe the image of D first reflected across line l, then across line m.
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Explanation:
1) The first reflection, accross the line l, will be the letter D turned (with the "belly" to the left instead of the right), located to the right of the line l and to the left of the line m.
2) The second reflection, accross the line m, will turn the letter again leting it equal to the original picture, now translated to the right on the line m.
Answer:
Let's approach this step by step.
First, reflect D across line l.
From there, reflect that image across line m.
Your final image should be the letter D.
Check out the image provided.
Hope this helped someone!
Step-by-step explanation:
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2/5 of house household own pets . Of the household pets 1/3 have cats. What is the fraction of the household own cats
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1/3 * 2/5 = 2/15
2/15 of the households have cats.
Fraction of household owning pets = [tex] \frac{2}{5} [/tex]
[tex] Fraction \; of \; household \; owning \; cats \; \\\\=\; \frac{1}{3} \; of\; Fraction \; of\; household\; owning \; pets \\\\=\frac{1}{3} \times\frac{2}{5} \\ \\Multiply \; numerator\; with\; numerator\; and\; denominator\; with\; denominator\\\\= \frac{1 \times 2}{3 \times 5}= \frac{2}{15} [/tex]
Conclusion:
The fraction of the household own cats is two-fifteenth
J read 147 pages in a book. He has completed 70% of the book. How many more pages does he need to read to finish the book.
Answers
(147/x)*x=(100/70)*x
147=1.4285714285714*x
147/1.4285714285714=x
x=102.9 is your answer
A survey asks 48 randomly chosen students if they plan to buy a school newspaper this week. Of the 48 surveyed,32 plant to buy a school newspaper. If 360 students bought papers,predict the number of students enrolled at the school.
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The number of students enrolled at the school is 540.
A survey asks 48 randomly chosen students if they plan to buy a school newspaper this week. Of the 48 surveyed, 32 plan to buy a school newspaper. If 360 students bought papers, predict the number of students enrolled at the school. To solve this, we use a proportion based on the survey results to predict the total enrollment. The proportion of students who plan to buy the newspaper based on the survey is 32 out of 48, which simplifies to 2 out of 3 when reduced. If 360 students actually bought the paper, and assuming the proportion holds for the entire school, we can set up the equation:
2/3 = 360 / total students
To find the total number of students, solve for 'total students':
total students = 360 × 3 / 2
total students = 540
Therefore, based on the survey results and the actual number of newspapers bought, we can predict there are 540 students enrolled at the school.
70 POINTS!
{Questions 54 & 58}
The function f is one to one. Find to inverse. State the domain & the range of f & f^-1. Graph f & f^-1, & y=x on the same coordinate axes.
Show work please.
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The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced "f inverse". Although the inverse of a function looks like you're raising the function to the -1 power, it isn't. The inverse of a function does not mean the reciprocal of a function.
InversesA function normally tells you what y is if you know what x is. The inverse of a function will tell you what x had to be to get that value of y.
A function f -1 is the inverse of f if
for every x in the domain of f, f -1[f(x)] = x, andfor every x in the domain of f -1, f[f -1(x)] = xThe domain of f is the range of f -1 and the range of f is the domain of f -1.
Graph of the Inverse FunctionThe inverse of a function differs from the function in that all the x-coordinates and y-coordinates have been switched. That is, if (4,6) is a point on the graph of the function, then (6,4) is a point on the graph of the inverse function.
Points on the identity function (y=x) will remain on the identity function when switched. All other points will have their coordinates switched and move locations.
The graph of a function and its inverse are mirror images of each other. They are reflected about the identity function y=x.
3(10+2j) please help me
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The general form of the equation of a circle is x2+y2−4x−8y−5=0.
What are the coordinates of the center of the circle?
Enter your answer in the boxes.
( , )
Answers
(x - h)² + (y - k)² = r²
where (h, k) is the coordinate for the center and r = radius
Factor into a perfect square for x and y by adding/subtracting grouping constants.
Given equation:
x² + y² - 4x - 8y - 5 = 0
going to group all x terms together and add +4 to both sides to give a perfect square of x. This number is determined by taking the square of half the middle term coefficient. [-4x is middle term. (-4/2)² = 4]
(x² - 4x + 4) - 8y + y² - 5 = 4
(x - 2)² + y² - 8y - 5 = 4
Now for y-terms, (-8/2)² = 16
add 16 to both sides.
(x - 2)² + (y² - 8y + 16) - 5 = 4 + 16
(x - 2)² + (y - 4)² - 5 = 20
now add that 5 over.
final equation for circle:
(x - 2)² + (y - 4)² = 25
center is (2,4) and radius is 5
Answer:
(2,4)
Step-by-step explanation:
Calculate the average rate of change of the function f(x) over the interval -[4,-1] using the formula. A_____ The value of f(-1) is.B._____The value of f(-4) is. C.________ the average rate of change of f(x) over the interval [-4,-1] is D.________
GRAPH WITH QUESTION: Y intercept:5 X intercept: -2.5 slope: 2
A: [f(-4)-f(-1)]/[-5]
[f(-1)-f(-4)]/[-5]
[f(-1)-f(-4)]/[3]
[f(-4)-f(-1)]/[3]
B. 3
2
-1
C. -4
-3
4
D. -2
-1.5
2
4
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y-yo = m (x-xo)
Where:
m = 2
We choose an ordered pair:
(xo, yo) = (0, 5)
Substituting the values:
y-5 = 2 (x-0)
Rewriting:
y = 2x + 5
Part A:
The average rate of change of the function f (x) over the interval [-4, -1] using the formula:
[f (-1) -f (-4)] / [3]
Part B:
The value of f (-1) is:
y = 2 (-1) +5
y = 3
Part C:
The value of f (-4) is:
y = 2 (-4) +5
y = -3
Part D:
the average rate of change of f (x) over the interval [-4, -1] is
m = [f (-1) -f (-4)] / [3]
m = (3 - (- 3)) / 3
m = (3 + 3) / (3)
m = 6/3
m = 2
what is the ratio of 12 percent
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Examples: 12 percent of 200 would be found by mult. 200 by 0.12.
12 percent of 200 could also be found by mult. 200 by 12/100.
12%=12/100 or 12:100
Simplify
12/4:100/4= 3:25
Trigonometric Identities Help!?
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he should find a common denominator (it is cosθ) using only cos-s.
answer:
[tex]cos = \frac{cos^2}{cos} [/tex]
A trail is 7/12 mile long, which trail is shorter, than 7/12
3/8,5/6,3/4,2/3
Answers
Among the given options, the trail which is shorter than 7/12 is 3/8
Determining the magnitude of a fractionFrom the question, we are to determine which trail is shorter than 7/12
To determine which of the given fractions is shorter than 7/12, we will express all the fractions in a common denominator
The given fraction are
3/8, 5/6, 3/4, 2/3
Using a common denominator of 48,
7/12 = 28/48
For the given options,
3/8 = 18/48
5/6 = 40/48
3/4 = 36/48
2/3 = 32/ 48
Now, we will compare their numerators. The fraction which has a numerator that is smaller than the numerator in 28/48 is the fraction smaller than 7/12.
Among the fraction, 18 is the smallest of the numerators and it is lesser than 28.
18/48 corresponds to 3/8
Hence, the trail which is shorter than 7/12 is 3/8
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A rabbit weighed 4,305.6 grams. What is this weight in kilograms?
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Final answer:
To convert 4,305.6 grams to kilograms, divide the gram value by 1000, resulting in 4.3056 kilograms, since there are 1000 grams in a kilogram.
Explanation:
The question asks to convert the weight of a rabbit from grams to kilograms. To perform this conversion, we need to know that 1 kilogram is equal to 1000 grams. Thus, we can convert the rabbit's weight by dividing the total grams by 1000 to get the weight in kilograms.
The rabbit weighed 4,305.6 grams. To convert this to kilograms, we divide by 1000:
Divide 4,305.6 by 1000.The result is 4.3056 kilograms.Thus, the weight of the rabbit is 4.3056 kilograms.
he temperature equivalent to 77°F is °C.
Use the formula to convert the temperature.
Answers
Hope this helps!
So, all we have to do here is plug 77° in:
(77 - 32) × 5/9
= 45 × 5/9
= 25
So, 25°C is the answer.
Hope this helps!
Another term for dual enrollment is:
Answers
Answer:
Another term for dual enrollment is: Concurrent enrollment.
Step-by-step explanation:
Concurrent enrollment or dual enrollment are those programs where students gets enrolled in two schools simultaneously.
There are many types of dual enrollment programs available for students like studying in high school students along with taking college classes etc.
A book is opened, and the PRODUCT of the two visible page numbers is found to be 306. The equation which correctly represents this situation is A) x2 = 306 B) 2x2 = 306 C) x2 + x = 306 D) 2x2 + x = 306
Answers
Answer:
Option C is correct
[tex]x^2+x = 306[/tex]
Step-by-step explanation:
Let the consecutive page number be x and x+1
As per the statement:
A book is opened, and the PRODUCT of the two visible page numbers is found to be 306.
" PRODUCT of the two visible page numbers" translated to x(x+1)
then;
[tex]x(x+1) = 306[/tex]
Using distributive property, [tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex]
then;
[tex]x^2+x = 306[/tex]
Therefore, the equation which correctly represents this situation is [tex]x^2+x = 306[/tex]
∠1 and ∠2 are a linear pair. m∠1 = x - 29, and m∠2 = x + 61. Find the measure of each angle.
Answers
m∠1 + m∠2 = 180
Substituting the values we have:
(x - 29) + (x + 61) = 180
We clear x:
2x + 32 = 180
x = (180-32) / (2)
x = 74
Therefore, each angle will be:
m∠1 = x - 29 = 74 - 29 = 45
m∠2 = x + 61 = 74 + 61 = 135
Answer:
the measure of each angle are:
m∠1 = 45
m∠2 = 135
Answer:
1= 45
2= 135
Step-by-step explanation:
(did it on usatp)
A bakery made 10 birthday cakes and 3 wedding cakes in one week. Enter the values that form the ratio of the number of birthday cakes the bakery made to the number of wedding cakes the bakery made.
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birthday cakes = BC = 10
wedding cakes = WC = 3
We now write the relationship between the variables, which can be written in different ways.
Way 1:
BC: WC
10: 3
Way 2:
BC / WC
10/3
Way 3:
BC to WC
10 to 3
Answer:
the values that the ratio of the number of birthday cakes the bakery made to the number of wedding cakes the bakery made are:
10: 3
10/3
10 to 3
roberto has 12 tiles. each tile is 1 square inch. he will arrange them into a rectangle and glue 1-inch stones around the edge. how can roberto arrange the tiles so that he uses the least number of stones?
Answers
Think of all the combinations to get 12 square inches
1x12, 2x6, and 3x4. The perimeters of these are 26 in, 16 in, and 14 in.
You should arrange your tiles using the 3 x 4 option. You would need 14 stones.
Answer:
the answer is 4 and 2
Step-by-step explanation:
what is the cosine ratio for ∠F? p.s. show how you got your answer!
Answers
Answer:
cosF = [tex]\frac{3}{5}[/tex] is the answer.
Step-by-step explanation:
In a right angle triangle cosine of any angle = [tex]\frac{Base}{Hypotenuse}[/tex]
In the given triangle base or adjacent side of the angle is = 6
Hypotenuse given as 10
So by putting the values of hypotenuse and base in the formula
∠F = [tex]\frac{6}{10}=\frac{3}{5}[/tex]
Therefore cosine of angle [tex]cosF=\frac{3}{5}[/tex] is the answer.
13/40 as a decimal and percent
Answers
Percent: 32.5%
Answer:
Step-by-step explanation:
13/40 as a decimal = 0.325
0.325
40√ _ 130
120
_100
80
_200
200
13/40 as percent
13/40 x 100% = 0.325 x 100% = 32.5%
HELP HELP HELP !!!!!!!!
A jar contained 6 red marbles, 10 green marbles, and 8 blue marbles. A marble was selected at random, the color was recorded, and the marble was placed back in the jar. The table shows the results after 60 trials.
What was the relative frequency of selecting a red marble?
Enter your answer in the box to the nearest percent.
%
Outcome Number of times outcome occurred
Red : 13
Green: 30
Blue: 17
Answers
Item 9 A company that offers tubing trips down a river rents tubes for a person to use and “cooler” tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. Use xx to represent the number of one-person tubes rented and yy to represent the number of cooler tubes rented. How many of each type of tube does the group rent?
Answers
The group rents 11 one-person tubes and 4 cooler tubes and the two system of equations are:
x + y = 15
20x + 12.5y = 270
And the solution: x = 11, y = 4.
Define Variables:
x = number of one-person tubes rented
y = number of cooler tubes rented
Translate information into equations:
Total tubes: The group rents a total of 15 tubes. Translate this into an equation:
x + y = 15
Cost: Each one-person tube costs $20 and each cooler tube costs $12.50. Use these known costs to represent the total cost:
20x + 12.5y = 270
System of Equations:
x + y = 15
20x + 12.5y = 270
Solving for x and y:
Elimination
Multiply the first equation by -12.5:
-12.5x - 12.5y = -187.5
Add the top and bottom equations:
7.5x = 82.5
Divide both sides by 7.5:
x = 11
Substitute the value of x back into the first equation to solve for y:
11 + y = 15
y = 4
The group rents 11 one-person tubes and 4 cooler tubes.
Therefore, the two system of equations are:
x + y = 15
20x + 12.5y = 270
And the solution: x = 11, y = 4.
Complete question:
A company that offers tubing trips down a river rents tubes for a person to use and “cooler” tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. Use x to represent the number of one-person tubes rented and y to represent the number of cooler tubes rented. a one person tube costs $20 and a cooler tube costs $12.50 How many of each type of tube does the group rent? what are the two system of equations?
The system of equations representing the situation is x + y = 15 and 20x + 12.50y = 270. The group rents 11 one-person tubes and 4 cooler tubes.
Let's denote:
x as the number of one-person tubes rented
y as the number of cooler tubes rented
Given:
The cost of renting one-person tube is $20
The cost of renting a cooler tube is $12.50
The total amount spent by the group is $270
We can set up the following system of linear equations to represent the situation:
The total number of tubes rented:
x (number of one-person tubes) + y (number of cooler tubes) = 15 (total tubes)
The total cost spent:
20x (cost of one-person tube) + 12.50y (cost of cooler tube) = 270
So, the system of equations is:
x + y = 15
20x + 12.50y = 270
To find the number of each type of tube rented, we can solve this system of equations.
Now, let's solve this system of equations:
From equation 1, we can express x in terms of y:
x = 15 - y
Substitute this expression for x into equation 2:
20(15 - y) + 12.50y = 270
Now, solve for y:
300 - 20y + 12.50y = 270
-7.50y = -30
y = 4
Now that we have found y, let's substitute it back into equation 1 to find x:
x = 15 - 4
x = 11
So, the group rents 11 one-person tubes and 4 cooler tubes.
Complete Question:
A company that offers tubing trips down a river rents tubes for a person to use and "cooler' tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. Usex to represent the number of one-person tubes rented and y to represent the number of cooler tubes rented. How many of each type of tube does the group rent?
1 Person Tube = $20, Cooler Tube = $12.50.
The system of equations is ___ and ___.
The group rents ___ one-person tubes and _____ cooler tubes.
Last week, maria drove 231 miles. This week, she drove k miles. Using k, write an expression for the total mumber of miles she drove in two weeks?
Answers
since you want to find the total you must add the two numbers
The expression for the total number of miles Maria drove in two weeks is 231 + k miles.
Explanation:In order to find the total number of miles Maria drove in two weeks, we first need to find the sum of the miles she drove last week and the miles she drove this week.
Last week, Maria drove 231 miles.
This week, she drove k miles.
Therefore, the expression for the total number of miles she drove in two weeks is 231 + k miles.
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Which step in the construction of copying a line segment ensures that the new line segment has the same length as the original line segment?
Answers
1. Draw a line that is longer than the segment but shorter than the width of the page.
1a. Make sure this line is at least 1/2 inch from the left hand side.
2. Use a compass to measure the length of the original segment. Never use a ruler. Rulers do not exist in pure geometry.
3. Measure out the distance on the line you just drew with the compass. One end is on the left hand edge and the other end (the pencil end) is marking the segment so it is the same length as the compass. You are done.
The key step either two or three.
Answer:
The steps to copy a line segment are given below:
1. Lets start with a line segment AB that we have to copy.
2. Now mark a point C. below or above AB, that will be one endpoint of the new line segment.
3. Now, put the compass tip on point A of the line segment AB.
4. Spread the compass up to point B, so as the compass width is equal to length of AB.
5. Without changing the compass width, now place the compass tip on the point C that you made in step 2.
6. Now, draw an arc roughly without changing the compass settings. Mark that point D. This will form the new line segment.
7. Draw a line from C to D.
Now out of these points, i guess steps 5 and 6 are the main steps that ensure that the copied line segment is exactly the same as the original segment.