Answer: sinθ = [tex]-\frac{\sqrt{65}}{9}[/tex]
Step-by-step explanation:
cosθ = 4/9
tan < 0
This means our reference angle is either in Quadrants II or IV, (where tangent is negative). Since cosine is positive, it must be Quadrant IV.
Therefore we know that sinθ will be negative.
we also know that [tex]cos^2(\theta) + sin^2(\theta) = 1[/tex], from the Pythagorean identities
.: 16/81 + sin^2(θ) = 1,
.: sinθ = [tex]\sqrt{\frac{65}{81} }[/tex]= [tex]\frac{\sqrt{65}}{9}[/tex]
But since this angle is in Quadrant IV, sinθ will be negative.
.: sinθ = [tex]-\frac{\sqrt{65}}{9}[/tex]
given: jg/hg=kg/ig, 1=2
prove: ef || hi
The triangles ΔIGH and ΔGFE are similar triangles. So, GJ / GE = HG / FG, then the side FE is parallel to the side HI.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the corresponding sides will be constant then the triangles will be similar triangles and the third sides of the triangles will be parallel.
GJ / GH = GK / GI, then the side KJ is parallel to the side HI.
In triangles ΔIGH and ΔGFE, then we have
∠IGH = ∠FGE (Vertival angle)
∠1 = ∠2 (Given)
Then the triangles ΔIGH and ΔGFE are similar triangles. Then we have
GJ / GE = HG / FG, then the side FE is parallel to the side HI.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ9
Whitney prepared 16 kilograms of dough after working 4 hours. How much dough did
Whitney prepare if she worked for 5 hours? Assume the relationship is directly proportional.
Answer:
Step-by-step explanation:
time take for 1 dough = 16kg/4hours= 4kg/hour
Dough in 5 hours = 4 x 5 = 20
She prepared 20kilograms of dough in 5 hours
Jerome hiked three-fourths of a mile in two-thirds of an hour. What was his hiking speed in miles
per hour?
2 mile per hour
I
b. 1 miles per hour
C.
mile per hour
d. 1 miles per hour
Answer as a mixed number = 1 1/8 mph
Answer as a decimal = 1.125 mph
Work Shown:
(3/4) of a mile : (2/3) of an hour
12*(3/4) of a mile : 12*(2/3) of an hour
9 miles : 8 hours
9/8 miles : 8/8 hours
1.125 miles : 1 hour
His speed is 1.125 miles per hour. This converts to the mixed number 1 1/8
surface area of a rectangular prism with sides of 5,4,3,3.7
Surface area of a rectangular prism is 444 square unit.
A rectangular prism is a three-dimensional shape with six faces (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular. As an outcome, there really are three sets of exactly equal faces here. A rectangular prism is also recognized as a cuboid due to its shape.
The sides of a rectangular prism is 5, 4, 3, 3.7.
This can be calculated by multiplying each of the side lengths together and then multiplying that result by two.
Surface area of a rectangular prism = 2 × (5 × 4 × 3 × 3.7)
Surface area of a rectangular prism = 2 × 222
Surface area of a rectangular prism = 444 square unit
To learn more about rectangular prism link is here
brainly.com/question/21308574
#SPJ4
The Jacob family plans to attend a concert. An adult ticket (a) is $7.50 each and a child's ticket (c) is $5.00 each. Mr. Jacob purchased a total of 11 tickets for a total of $65. How many of each kind of ticket was purchased?
Explain how to do please
Answer: Therefore, we purchased 4 adult tickets and 7 child's tickets.
Step-by-step explanation:
Through the information provided, we set up a system equation:
a + c = 11
7.50a + 5.00c = 65
By the first equation, we convert it into a form, then we get a = 11 - c. Then we plug in the a = 11 - c to the second equation:
7.50(11 - c) + 5.00c = 65
82.5 - 7.50c + 5.00c = 65
82.5 - 2.50c = 65
- 2.50c = 65 - 82.5
- 2.50c = - 17.5
c = - 17.5/- 2.50
c = 7
And we plug c = 7 back into the first equation, which is a + c = 11.
a + c = 11
a + 7 = 11
a = 11 - 7
a = 4
Therefore, we purchased 4 adult tickets and 7 child's ticket.
During a 36 - year period, lightning killed 2,457 people in the United States. Assuming that rate holds true today and is constant throughout the year. Find the probability that tomorrow: (a) No one in the United States will be struck and killed by lightning.
The probability that no one in the United States will be struck and killed by lightning tomorrow is approximately 0.835, or 83.5%.
To find the probability that no one in the United States will be struck and killed by lightning tomorrow, we can use the Poisson distribution, which models the number of rare events occurring in a fixed period of time, given the average rate of occurrence.
The Poisson distribution has the following probability mass function:
P(X = k) = (e^(-λ) * λ^k) / k!
where:
X is the random variable representing the number of events (in this case, the number of people struck and killed by lightning)
λ is the average rate of events per unit of time (in this case, the average number of people struck and killed by lightning per day)
We can use the data given in the problem to estimate the value of λ:
λ = (2457 deaths) / (36 years * 365 days/year) ≈ 0.18 deaths/day
Now we can use the Poisson distribution to find the probability that no one in the United States will be struck and killed by lightning tomorrow:
P(X = 0) = (e^(-0.18) * 0.18^0) / 0! ≈ 0.835
This means that there is a high likelihood that no one will be killed by lightning tomorrow, given the historical average rate of lightning deaths.
To learn more about probability click on,
https://brainly.com/question/30666048
#SPJ4
The lines intersect at
1 point.
different. The
parallel.
Do You Understand?
1. Essential Question How are slopes and
y-intercepts related to the number of solutions
of a system of linear equations?
The slopes and y-intercepts can be used to determine the type of relationship between the lines, and therefore the number of solutions.
What is linear equation ?
Linear equation can be defined as the equation in which the highest degree is one.
The number of solutions for a system of linear equations depends on the relationship between the slopes and y-intercepts of the lines represented by the equations. If the lines are intersecting, then there is exactly one solution where the lines cross. If the lines are parallel, then there are no solutions, as the lines will never intersect.
If the lines are coincident, then there are infinitely many solutions, as the lines represent the same line.
Therefore, The slopes and y-intercepts can be used to determine the type of relationship between the lines, and therefore the number of solutions.
To learn more about Linear equation from given link.
https://brainly.com/question/29739212
#SPJ1
an art teacher hhd 2/3 gallon of paint to pour into containers. If he poured 1/8 gallon of paint into each container until he ran out of paint how many containers hhd paint in them including the one that was partially filled
Answer: 6 containers
Step-by-step explanation:
Fraction division.
2/3 divided by 1/8.
Keep-change-flip. (or a similar method for dividing fractions)
2/3 times 8/1 is 16/3.
He will fill 5 and 1/3 containers, so 6 containers will have paint in them.
(っ◔◡◔)っ ♥
Hope this helps.
MM4343
The length of a shadow of a building is 98 ft when the sun is 66° above the horizon. Find the height of the building. Round your answer to the nearest tenth.
000
000
66°
98
If the length of a shadow of a building is 98 ft when the sun is 66° above the horizon then the height of the building is, 267.7 ft.
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
We can use the tangent function to solve for the height of the building.
tan(66°) = height of building / 98 ft
Solving for the height of the building,
we get:
height of building = 98 ft x tan(66°)
Using a calculator, the value of tan(66°) is approximately 2.73.
So,
height of building = 98 ft x 2.73
height of building = 267.74 ft
Rounding to the nearest tenth, the height of the building is approximately 267.7 ft.
To know more about angle check:
https://brainly.com/question/28451077
#SPJ1
What is the answer? How do I solve this?
You solve it using your brain.
12, x, y, 324, 972, find the sum of x and y (a) 144 (b) 52 (c) 75 (d) 109
Answer: The value of the sum of x and y is (a) 144.
Step-by-step explanation:
Given, The sequence is a Geometric Sequence.
Initially,
=> 4x3 , x , y , 324, 324x3
=> 4x3, x, y, 4x3x3x3x3, 4x3x3x3x3x3
From above,
We can deduce that,
=> x = 4 x 3 x 3
=> x = 36
Also,
=> y = 4 x 3 x 3 x 3
=> y = 108
The values of x and y are 36 and 108
Now, We can evaluate the sum of x and y,
=> x + y = 36 + 108
=> x + y = 144
Therefore, The sum of x and y is 144. Hence, option (a) is correct.
To learn more about the sum of x and y,
https://brainly.in/question/8709063
can ypu please answer this question
Answer: A=71°
Step-by-step explanation:
A+B+C=180°
A+38°+C=180°
A+C=180°-38°
A+C=142°
142°/2=71°
∴A=71°
∴C=71°
The Grade 8 learners decided to start living more healthily.They will either jog or cycle.there are 125 Grade 8 learners and they jog and cycle in the ratio 3:2.calculate how many learners participate in each sport
Answer:
We can start by finding the total number of learners who participate in jogging and cycling by multiplying the ratio by the total number of learners. Let's say x is the number of learners who jog. Then, the number of learners who cycle is 2x.
The total number of learners who jog and cycle is 125, so:
x + 2x = 125
3x = 125
x = 125 / 3
x = 41.67
Since x represents the number of learners who jog, there are 41.67 learners who jog. Since the number of learners who cycle is 2x, there are 2 * 41.67 = 83.33 learners who cycle.
Since these are whole numbers of learners, we round up to the nearest whole number to get 42 joggers and 83 cyclists.
The number of students participating in each of the sports will be 75 for jogging and 50 for cycling.
Solution:
Let's assume that the number of students who participated in jogging will be 3x and those in cycling will be 2x
Given,
3x + 2x = 125
5x = 125
So, x = 25
Therefore, the number of students in jogging will be 3*25 = 75 and in cycling will be 2*25 = 50
Learn more about Ratios and Proportions here:
https://brainly.com/question/12024093
Shape ABCD is a rectangle.
C is the point with coordinates (0,-8)
The equation of the straight line through A and B is 2y + x = 4.
Find the equations of the lines
DC, AD and BC.
Answer:
c
Step-by-step explanation:
trust me
A pet toy company performed an experiment to see how
many toys dogs might play with. Each of the 60 dogs
involved was put in a room with its owner and 4 different
toys.
The researchers recorded how many toys each of the 60
dogs used.
Fill in the blanks to complete the probability
distribution.
Do not round your answers.
Toys used
Frequency
Probability .05
0
3
1 2
2
0.25
3
3 4
21 12
9
0.35 0.2 0.15
The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.
What is the probability?
Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
To fill in the blanks, we need to use the given information to complete the probability distribution table.
We can see that there were 3 dogs (out of the 60) that did not use any toys, and the probability of a dog not using any toys is 0.05 or 5%. There were 12 dogs (out of the 60) that used 1 toy, and the probability of a dog using 1 toy is 0.2 or 20%. Similarly, there were 15 dogs that used 2 toys, 21 dogs that used 3 toys, and 9 dogs that used all 4 toys. The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.
To learn more about probability, Visit
https://brainly.com/question/13604758
#SPJ1
what is the probability of drawing a black card in a standard deck of 52 cards? (enter your probability as a fraction.)
The probability of drawing a black card in a standard deck of 52 cards is 1/2.
Probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1. There are total 52 cards out of which 26 are black cards and 26 are red cards.
There are 26 black cards (13 spades and 13 clubs) in a standard deck of 52 cards.
Therefore, the probability of drawing a black card from a standard deck of 52 cards is 26/52.
Probability = 26/52 = 1/2
So, the probability of drawing a black card is 1/2.
Learn more about probability here: brainly.com/question/13604758
#SPJ4
Use a graphing calculator to find an equation of the line of best fit for the data. Round the slope to the nearest tenth and the y
-intercept to the nearest integer.
The equation of the line of the best fit for the data will be, y=2.07x-7.5.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
The equation of the line is;
y=mx+c
y=2.07x-7.5
Hence, the equation of the line of the best fit will be, y=2.07x-7.5
Learn more about the equation of a line on https://brainly.com/question/21511618
#SPJ1
please help me with my homework!!
10. The value of a book is $58 and decreases at a rate of 10% per year; 8 years.
Answer:
$24.96
Step-by-step explanation:
The question was incomplete. If you are asking how much is the book worth after 8 years, here's how to do it
Original cost = $58
Since the rate of decrease = 10%, the cost of the book after 1 year is 90% of the original price
90% = 90/100 = 0.9
Therefore after 1 year, the book cost is 58(0.9)
After another year(effectively 2 years) the above cost will drop by another 10% to 90% of the first year value: 58(0.9)(0.9) = 58(0.9)²
So the value of the book after a period of n years is modeled by the function
V = 58 (0.9)ⁿ
After 8 years the value is
58 (0.9)⁸ = 58 x 0.43046721
V = $24.96 rounded to the nearest cent
Pls help me fast fast
The sum of the measures of angles A, D, and F is:
A + D + F = 360°
How to find the sum of the 3 angles?First, we know that the sum of the interior angles of any triangle is always equal to 180°, then we can write:
B + C + E = 180°
We also can see that:
A + B = 180°
C + D = 180°
E + F = 180°
Then we can rewrite:
E = 180° - F
C = 180° - D
B = 180° - A
And replace that on the equation above:
B + C + E = 180°
( 180° - F) + (180° - D) + (180° - A) = 180°
Moving the variables to the right side we will get:
3*180° = 180° + A + D + F
3*180° - 180° = A + D + F
360° = A + D + F
That is the sum of the 3 measures.
Learn more about angles at:
https://brainly.com/question/25716982
#SPJ1
Solve for X
This was on a Geometry Honors quiz
The value of x in the triangle is 8 units.
How to find the side of similar triangle?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Therefore, the sides x of the triangle can be found using proportion as follows:
x / x + 8 = x + 8 / 32
cross multiply
32x = (x + 8)(x + 8)
32x = x² + 8x + 8x + 64
x² + 16x - 32x + 64 = 0
x² - 16x + 64 = 0
Therefore,
x² - 16x + 64 = 0
x² - 8x - 8x + 64 = 0
x(x - 8) - 8(x - 8) = 0
(x - 8)(x - 8) = 0
Therefore,
x = 8
learn more on similar triangle here: brainly.com/question/888590
#SPJ1
Ashley created 3 music playlists using a total of 48 rock and pop songs. Each playlist has 9 rock songs. Each playlist also has the same number of pop songs. Which equation could be used to determine the number of pop songs, x
, Ashley has in each playlist?
Responses
1. x(3+9)=48
2. 3(x+9)=48
3. 3x+9=48
4. 9x+3=48
Answer:
2. 3(x + 9) = 48
Step-by-step explanation:
We are given
There are a total of 3 playlistsThere are a total of 48 rock and pop songsEach playlist has 9 rock songsEach playlist has x pop songsIf each playlist has 9 rock songs and x pop songs, then each playlist has 9 + x songs.
If there are three playlists, there are three playlists which each have x + 9 songs. In other words, 3(x+9). This represents the total number of songs, which is 48. Therefore the answer is 3(x+9)=48.
Hope this helps!
2 Gallons of Juice for $4.50. How much per Gallon?
Answer: 2.25 per gallon
Step-by-step explanation:
4.50 divided by 2 = 2.25
Solve for X and Y using substitution
y=5x-7
-3x-2y=-12
Answer:
So the solution to the system of equations is (x,y) = (3,-2).
Step-by-step explanation:
To solve for x and y using substitution, we can first substitute y=-2 into the second equation to find the value of x, and then use that to find y.
Starting with the second equation:
4x - 3(-2) = 18
Expanding the -3(-2) using the distributive property:
4x + 6 = 18
Subtracting 6 from both sides:
4x = 12
Dividing both sides by 4:
x = 3
Now that we have x = 3, we can substitute that back into the first equation to find y:
y = -2
So the solution to the system of equations is (x,y) = (3,-2).
help asap pls. question in pic
the area of the rectangle is 1000m² and The expression of the area A(x) = 200x,
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.
Area of rectangle is A = a*b
One side of rectangle is 200m
When the measure of the other side is 50 m
the area will be 50*200 = 1000m².
The expression of area A(x) = 200x,
hence the area of the rectangle is 1000m² and The expression of the area A(x) = 200x,
Learn more about rectangular by following the link below.
brainly.com/question/25292087
#SPJ1
help me please i actually cant do this
Answer:
a: Angle 1 and Angle 3
b: Angle 8 and Angle 5
c: Angle 2 and Angle 9
d: Angle 5 and Angle 3
e: none of the above
Solve for n !
[tex] \large{ \gray{ \frak{3x+5= 4(n - 5) \frac{6}{3} }}}[/tex]
Thank You!
Answer:
n = (3/8)x+(45/8)
Step-by-step explanation:
3x+5 = 4(n-5)*(6/3)
Is this written correctly?
3x+5 = 4(n-5)*(6/3)
3x+5 = 8(n-5) [Simplify: {4*(6/3) = 8)]
3x+5 = 8n-40 [Expand the parentheses]
8n-40 = 3x+5 [Rearrange]
8n = 3x+5 + 40 [Rearrange]
8n = 3x+45 [Simplify]
n = (3x+45)/8 [Divide both sides by 8]
n = (3/8)x+(45/8) [Rearrange]
What if the well was 40 feet deep, the frog climbs 6 feet per hour, and it slips back only 1 foot while resting for an hour?
If the well was 40 feet deep and the frog climbs 6 feet per hour, it would take the frog 40/6 = 6.67 hours to reach the top of the well.
However, the frog slips back 1 foot while resting for an hour, so the frog would only have covered 5 feet of the well after each hour of climbing. The frog would need to climb for a total of
40/5 = 8 hours
to reach the top of the well. Additionally, the frog would need to take 8 hours of rest to make up for the slipping back.
So the total time it would take the frog to get out of the well would be 8 hours + 8 hours = 16 hours.
If the well was 40 feet deep and the frog climbs 6 feet per hour, it would take the frog 40/6 = 6.67 hours to reach the top of the well.
Learn more about feet :
https://brainly.com/question/20111809
#SPJ4
What number would correctly replace the G?
Write a real-world situation and an algebraic expression that is represented by the bar diagram:
The expression is there are 2 chocolates and 5 lollypops having a total cost of $5. The expression is 2C + 5L = $5.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Suppose the real-time situation is if there are 2 chocolates and 5 lollypops having a total cost of $5.
The mathematical form of the expression can be written as:-
2C + 5L = 5
Here, C is the cost per chocolate and L is the cost of per Lollypop.
To know more about an expression follow
https://brainly.com/question/1895436
#SPJ9
The complete question is given below.
Write the expression if there are 2 chocolates and 5 lollypops having a total cost of $5.
place the following scores in a frequency distribution table. based on the frequencies, what is the shape of the distribution? 13, 14, 12, 15, 15, 14, 15, 11, 13, 14, 11, 13, 15, 12, 14, 14, 10, 14, 13, 15
The frequency table is:-
Data Frequency
10 1
11 2
12 2
13 4
14 6
15 5
What is a frequency table?The frequency table determines the frequency of the data. In other words, it tells us how many times the same data is repeated.
The given data set is, 13, 14, 12, 15, 15, 14, 15, 11, 13, 14, 11, 13, 15, 12, 14, 14, 10, 14, 13, 15
The frequency table can be written as:-
Data Frequency
10 1
11 2
12 2
13 4
14 6
15 5
The distribution's shape for the next data set you provided is left- or negatively skewed. This is due to the fact that as a number's value increases, so does its frequency.
To know more about the frequency table follow
https://brainly.com/question/16148316
#SPJ1
