We know that
sin(-θ) = - sinθ
and that
tanθ = sinθ / cosθ
Then
sin(-θ) = - sinθ = 1/5
↓
sin(θ) = - 1/5
We want to find cosθ. Using the second formula we have that
cosθ = sinθ / tanθ
We replace sin(θ) = - 1/5 and tanθ =√6/12:
\(\begin{gathered} \cos \theta=\frac{\sin\theta}{\tan\theta} \\ \cos \theta=\frac{-\frac{1}{5}}{\frac{\sqrt[]{6}}{12}} \\ =-\frac{1}{5}\cdot\frac{12}{\sqrt[]{6}} \\ =-\frac{12}{5\sqrt[]{6}} \\ =-\frac{12\cdot\sqrt[]{6}}{5\sqrt[]{6}\cdot\sqrt[]{6}} \\ =-\frac{12\sqrt[]{6}}{5\cdot6} \\ =-\frac{2\sqrt[]{6}}{5} \end{gathered}\)Answer: CSegment CO is congruent to segment HZ. Which congruence statement is true? Responses CO≅HZ arc C O is congruent to arc H Z OZ≅CO arc O Z is congruent to arc C O CH≅COZ arc C H is congruent to arc C O Z CH≅HZO arc C H is congruent to arc H Z O A circle with center B containing radii B O, B C, B H, and B Z. segment is drawn from point c to point o and point z to point h to form chord c o and chord z h. chord c o and chord z h are equal in length.
Based on the Chord Arcs Theorem, the congruence statement that is true is: Arc CO ≅ arc HZ.
What is the Chord Arcs Theorem?The Chord Arcs Theorem states that when two chords intersect inside a circle and are equal in length, the arcs they intercept on the circumference of the circle will also be equal in length.
In the image given below, where chords CO and HZ are congruent to each other, it means that their corresponding arcs that they intercept will have the same measure that is equal to each other, based on the chord arcs theorem.
Therefore, the congruence statement that is true is: Arc CO ≅ arc HZ
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What is the answer pleaseee
Answer: 803.84cm3
Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.
To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.
4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.
Now, we have the area of the circle. 50.24cm squared!
The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,
16cm x 50.24cm squared = 803.84cm cubed.
The volume of the can of soup is 803.84cm cubed.
write a letter to a friend in another town invite him or her to spend Christmas holidays with you
Answer:
hey my friend please come over to spend the Christmas holidays with me and my family this year. If you are afraid of your dad it's ok I'll ask my mom to call him and ask him
A woman sold an article for $1400.00 and made a profit 25%. Find the cost price and the profit
Answer:
$1120 and $280.
Step-by-step explanation:
$1400 = 125%
100% = $1120
The cost of the price was $1120.
$1400 - $1120 = $280.
The profit was $280.
Hope this helps!
A submarine was twenty feet below the surface of the water and descended an additional thirty-two and a half feet. Eventually the submarine ascended forty feet toward the surface of the water. What is the location of the submarine in the water?
Answer:
-12 1/2 feet (12 1/2 feet below the surface).
Step-by-step explanation:
I hope this helps! Have a great rest of your day!
you have decided to sell candy bars to make enough money to go to summer camp. you sell the candy bars for 2.00 each. you also decided to set up a table to sell the candy bars outside of the grocery store doors because on average 135 people pass cross through those doors every hour. If you sell 45 candy bars, how much money will it take?
input:
output:
select one for input and output :
candy bars
summer camp
people
money
Prealgebra- Determine whether the lines passing through the pairs of points are parallel, perpendicular, or neither
It is important to note the following:
• If the slopes of the two lines are equal, they are parallel.
,• If the slopes of the two lines are negative reciprocal of each other, they are perpendicular.
Let's now calculate the slope of each line. Use the formula:
\(m=\frac{y_2-y_1}{x_2-x_1}\)Let's start with line 1.
\(m=\frac{1-13}{-8-1}\Rightarrow m=\frac{-12}{-9}\Rightarrow m=\frac{4}{3}\)The slope of line 1 is 4/3.
Let's move on to line 2.
\(m=\frac{\frac{5}{3}-(-1)}{5-3}\Rightarrow m=\frac{\frac{8}{3}}{2}\Rightarrow m=\frac{4}{3}\)The slope of line 2 is also 4/3.
Since the slopes of the two lines are the same, then the two lines are parallel.
How to solve that question?
Answer:
(i) (x√x)/3 -(√x)/2
(ii) f(x) = x³/27 +3x -5
Step-by-step explanation:
You want the value of the integral in each case. One integral is indefinite, the other has conditions specified.
In each case, the power rule applies:
\(\displaystyle \int{x^n}\,dx=\dfrac{x^{n+1}}{n+1}\)
(i) indefinite integralThe integral can be rewritten as the sum of two integrals involving half powers.
\(\displaystyle \int{\dfrac{2x-1}{4\sqrt{x}}}\,dx=\dfrac{1}{2}\int{x^{\frac{1}{2}}}\,dx-\dfrac{1}{4}\int{x^{-\frac{1}{2}}}\,dx=\dfrac{x^{\frac{3}{2}}}{2\left(\dfrac{3}{2}\right)}-\dfrac{x^{\frac{1}{2}}}{4\left(\dfrac{1}{2}\right)}\\\\=\boxed{\dfrac{1}{3}x\sqrt{x}-\dfrac{1}{2}\sqrt{x}}\)
(ii) f'(x)=ax²+bYou are given the derivative and three conditions:
f'(x) = ax² +bf'(3) = 4f(3) = 5f(0) = -5Together with the integral, the conditions give rise to three equations in the three unknown coefficients.
\(\displaystyle f(x) = \int{ax^2+b}\,dx=\dfrac{a}{3}x^3+bx+c\)
Then the equations we can write for a, b, c are ...
f'(3) = 4 ⇒ a(3²) +b = 4
f(3) = 5 ⇒ (a/3)(3³) +b(3) +c = 5
f(0) = -5 ⇒ a(0³) +b(0) +c = -5
The last equation gives the value of c = -5, so the remaining equations become ...
9a +b = 4
9a +3b = 10
Subtracting the first from the second, we have ...
(9a +3b) -(9a +b) = (10) -(4)
2b = 6
b = 3
Using this in the first equation, we find 'a' to be ...
9a +3 = 4
a = 1/9
Then f(x) is ...
\(\boxed{f(x)=\dfrac{1}{27}x^3+3x-5}\)
In ADEF, f= 33 inches, ZF=140° and ZD=5°. Find the length of e, to the nearest 10th
of an inch.
The length of e is 29.53 inches.
what is Sine Law?In the following, the law of sine is presented in detail: In a triangle, the sine of angle A divided by side "a" equals the sine of angle B divided by side "b" equals the sine of angle C divided by side "c".
Given:
f= 33 inches
<F= 140, <D = 5
Now,
<E= 180 - (<F+ <D) = 180 - (140 + 5) = 35
Using Sine law
sin F / f = sin E/ e
sin 140 / 33 = sin 35 / e
0.642/ 33 = 0.573 / e
0.0194 e= 0.573
e= 29.53 inches
Hence, the length of e is 29.53 inches.
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A data set contains the values 1, 2, 5, 5, and 7.
The table shows the distance between each value and the mean of 4.
Data value
Distance between
value and mean
1
3
2
2.
5
1
5
1
7
3
Sum of distances 10
What is the mean absolute deviation (MAD) of the data set?
Answer:
2, The MAD is the MEAN STANDARD DEVIATION meaning it is the average of all the numbers distances away from the MEAN. you just add up all the distances and divide by how many there are.
When you divide with negative exponents, you divide the rational numbers like normal and then you add the exponents.
Example:
TRUE or FALSE???
Answer:
the same as multiplying them, except you're doing the opposite: subtracting where you would have added and dividing where you would have multiplied. If the bases are the same, subtract the exponents. Remember to flip the exponent and make it positive, if needed.
Step-by-step explanation:
Answer:
FALSE
Step-by-step explanation:
u cant combine # w/ different exponents bc they arnt like terms
I need help with number 10 ASAP plzz
Answer:
D (7=30x)
Step-by-step explanation:
A theater has 26 rows of seats. The first row has 18 seats, the second row has 21 seats, the third row has 24 seats, and so on. How many seats are in the theater?
please help
In total, the theater seats 1442 people.
Given : The number of rows in the theater = 26
The number of chairs in first row = 18
The number of rows in the second row = 21
The number of rows in the third row = 24
The common difference in the number of chairs for the consecutive rows \(=3\)
Thus its a Arithmetic progression.
Let n be the number of rows and d be the common difference , then the total number of chairs in n rows is given by:
\(\text{S}_{\text{n}}=\dfrac{\text{n}}{2}(2\text{a}+(\text{n}-1)\text{d})\), where a is the umber of chairs in first row .
Put a = 18, d = 3 and n = 26, we get
\(\text{S}_{\text{26}}=\dfrac{\text{26}}{2}(2(18)+(26-1)\text{3})=1442\)
Hence, In total, the theater seats 1442 people.
Hakim, Edmund and Paul share a bag of guppies. There are 132 guppies in the bag. The ratio of Hakim's share to Edmund's share is 2:3. The ratio of Edmund's share to Paul's share is 1:2. How many guppies does each boy get? Hakim , Edmund and Paul share a bag of guppies . There are 132 guppies in the bag . The ratio of Hakim's share to Edmund's share is 2 : 3 . The ratio of Edmund's share to Paul's share is 1 : 2 . How many guppies does each boy get ?
Answer:
Hakim's share = 2 x 12 = 24 guppies
Edmund's share = 3 x 12 = 36 guppies
Paul's share = 6 x 12 = 72 guppies
Step-by-step explanation:
We will have Hakim's share as the base unit.
Hakim : Edmund = 2:3
Edmund : Paul = 1:2
Hakim : Edmund : Paul = 2:3:3x2 = 2:3:6
Total units = 2+3+6 = 11 units
11 units = 132 guppies
1 unit = 132/11 = 12 guppies
Hakim's share = 2 x 12 = 24 guppies
Edmund's share = 3 x 12 = 36 guppies
Paul's share = 6 x 12 = 72 guppies
Find the equation of the line parallel to the line g(x) = -0.01x + 2.01 through the point (1, 2).
Answer:
Baka renejay to HAHAHHA
15 is what percent of 90
What is the approximate value?
Answer:
slightly less than 12
Step-by-step explanation:
if you divide 36/pi, the answer would be about 11.4591559026. this is less than 12.
Determine the coordinates of the image of figure 1 when you translate it 1 unit horizontally and -8 units vertically.
Using translation concepts, the following transformation is applied to all coordinates of the figure:
\((x,y) \rightarrow (x + 1, y - 8)\)
----------------------
Translated 1 unit horizontally means that 1 is added to the x-coordinate of all coordinates in the figure.Translated -8 units vertically means that 8 is subtracted from the y-coordinate of all coordinates in the figure.Thus, the following transformation is applied to all coordinates of the image:
\((x,y) \rightarrow (x + 1, y - 8)\)
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figure below represents a floor covered with white tiles and gray tiles. KEY = 1 square unit
According to the information, we can infer that the correct expression is (10 * 7) + (2 * 7) (option D).
How to find the correct expression?To find the correct expression we must look at the graph and interpret the information it has. In this case, some tiles are white and others are gray, so they would represent different elements. In this case, the white area is 10 * 7 tiles, so this would be the first part of the expression.
On the other hand, the second part of the expression would be 7 * 2, which represents the length, length and width of the gray area. According to the above, the correct expression would be (10 * 7) + (2 * 7), the first part in parentheses represents the white area and the second part in parentheses represents the gray area.
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I really need help with this question
The length of each side of the wood is 5 centimetres.
How to use quadratic equation to find the length of each side of the wood?Doug has 8 square pieces of wood. Each piece of wood have a side length of s cm. The total area of all 8 pieces of wood is 200 cm².
Hence, using quadratic equation let's find the length of each side of the wood.
Therefore,
8s² = 200
Hence,
8s² = 200
divide both sides of the equation by 8
s² = 200 / 8
s² = 25
s = √25
s = 5 centimetres
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Brianna made 9 1/4 bags of popcorn for a movie night with some friends. Together they ate 4 bags of it. How much popcorn was left?
There were 5 1/4 bags of popcorn left after eating 4 bags.
To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.
Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:
9 1/4 = (4 * 9 + 1) / 4 = 37/4
Now, let's subtract the 4 bags eaten from the total:
37/4 - 4
To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:
37/4 - 4/1
Now, let's find a common denominator and subtract the fractions:
37/4 - 16/4 = (37 - 16) / 4 = 21/4
The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:
21/4 = 5 1/4
Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.
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What is the value of r?O r= 4 ftr= 8 ftr = 16 ftAreaO r = 32 ft77
Question:
Solution:
According to the statement of the problem, we have that:
\(r\text{ = }\sqrt[]{\frac{Area}{\pi}}\)Notice that Area = 64pi, then replacing this data into the previous equation we get:
\(r\text{ = }\sqrt[]{\frac{Area}{\pi}}\text{ = }\sqrt[]{\frac{64\pi}{\pi}}\text{ = }\sqrt[]{64}\text{ = 8}\)so that, we can conclude that the correct solution is:
\(r\text{ = 8}\)
how many hundred billions in the number 432,845,979,484
There are 4 hundred billions in the number 432,845,979,484.
To determine how many hundred billions are in the number 432,845,979,484, we need to consider the place value of the hundred billions digit.
The number 432,845,979,484 has 12 digits, and we count the digits from right to left, starting with the units place. The digit in the hundred billions place is the seventh digit from the right.
Let's break down the number:
4 hundred billions (4 x 100,000,000,000)
3 ten billions (3 x 10,000,000,000)
2 billions (2 x 1,000,000,000)
8 hundred millions (8 x 100,000,000)
4 ten millions (4 x 10,000,000)
5 millions (5 x 1,000,000)
9 hundred thousands (9 x 100,000)
7 ten thousands (7 x 10,000)
9 thousands (9 x 1,000)
4 hundreds (4 x 100)
8 tens (8 x 10)
4 units (4 x 1)
As we can see, there are 4 hundred billions in the number 432,845,979,484.
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Solve each equation by completing the square.
d² - 24d + c
Answer:
d² - 24d + c = (d - 12)² - 144 + c
Can anyone help me on this one
Hello !
Answer :
\({x}^{ - \frac{8}{3} }\)\(\sqrt[3]{ {x}^{ - 8} }\)\(\sqrt[3]{ ({x}^{ 4}) {}^{ - 2} }\)Explanation :
\( \to \boxed{ ({x}^{a}) {}^{b} = {x}^{ab} } \)
\( \to \boxed{ {x}^{ \frac{1}{n} } {}^{} = \sqrt[n]{x} } \)
\( ({x}^{4} ) {}^{ - \frac{2}{3} } = {x}^{- \frac{2}{3} \times 4} \\ \boxed{= {x}^{ - \frac{8}{3} } } \\ \boxed{= \sqrt[3]{ {x}^{ - 8} }} \\ \boxed{ = \sqrt[3]{ ({x}^{ 4}) {}^{ - 2} }}\)
Have a nice day ;)
The dot plot shows the time trials of an experiment. Each number on the dot plot represents the amount of time, in seconds, it took to complete a trial. How many time trials were recorded during the experiment? Enter the answer in the box. time trials A number line ranging from 15 to 25 with two dots over 15, three dots over 17, two dots over 19, two dots over 20, one dot over 21, four dots over 23, one dot over 24, and three dots over 25.
There were 18 time trials recorded during the experiment.
To determine the number of time trials recorded during the experiment, we count the total number of dots on the dot plot.
According to the given information, we have:
- Two dots over 15
- Three dots over 17
- Two dots over 19
- Two dots over 20
- One dot over 21
- Four dots over 23
- One dot over 24
- Three dots over 25
By adding up these counts, we get:
2 + 3 + 2 + 2 + 1 + 4 + 1 + 3 = 18
Therefore, there were 18 time trials recorded during the experiment.
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Which of the following statements is FALSE? The correlation coefficient equals the proportion of data points that lie on a straight line. The correlation coefficient will be +1.0 only if all the data lie on an upward-tilting straight line. The correlation coefficient is undefined if all the data lie on a perfectly horizontal straight line. The correlation coefficient is a unitless number and must always lie between –1.0 and +1.0, inclusive.
Answer:
The first one is False.
Step-by-step explanation:
If the correlation coefficient can also be -1 if the data lies on an upward tilting straight line.
Determine if the equation is parallel, perpendicular, or neither y = -4 and y = 7
what answer? here, can you answer that? thankyou
It should be noted that the number of sample size based on the information will be 300.
How to explain the sampleIn order to calculate the sample size, we can use the following formula:
n = z² * p * (1-p) / E²
n = 1.96² * 0.5 * (1-0.5) / 0.05²
= 300
A questionnaire is a method of gathering data that makes use of written questions to be answered by the respondents. It is a popular method of data collection because it is relatively easy to administer and can be used to collect a wide variety of information.
In the first column, the population is the entire National Capital Region (NCR). The sample is the city of Manila. In the second column, the population is all STEM students. The sample is all academic track students. In the third column, the population is all the tablespoons of sugar in the jar. The sample is one tablespoon of sugar. In the fourth column, the population is all the vowels in the word "juice". The sample is the vowel "i".
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From past experience, it is known that a telemarketer makes a sale with probability 0.2. Assuming that results from one call to the next are independent. Determine the probability that telemarketer makes:___.
a. the first sale on the third call
b. the first sale after the third call
c. the second sale on the fifth call
d. the second sale before the fifth call