The vectors that join the center of a clock to the hours :
At 1:00: (cos(π/6), sin(π/6)) = (√3/2, 1/2)
At 2:00: (cos(π/3), sin(π/3)) = (1/2, √3/2)
At 3:00: (cos(π/2), sin(π/2)) = (0, 1)
What is Vector?
A vector is a object that has both magnitude (size) and direction. In other words, a vector is a quantity that can be represented by an arrow or line segment, where the length of the arrow corresponds to the magnitude of the vector.
To find the vectors that join the center of a clock with radius 1 unit to the hours 1:00, 2:00, and 3:00, we can use basic trigonometry.
First, we can find the angle (in radians) between the 12:00 position and each of the desired hour positions. Since there are 12 hours on a clock and the circle has a circumference of 2πr = 2π(1) = 2π, the angle between each hour mark is:
2π/12 = π/6 radians
Therefore, the angles between the center of the clock and the hour marks are:
At 1:00, the angle is π/6 radians clockwise from the 12:00 position.
At 2:00, the angle is 2π/6 = π/3 radians clockwise from the 12:00 position.
At 3:00, the angle is 3π/6 = π/2 radians clockwise from the 12:00 position.
Next, we can use the cosine and sine functions to find the x and y components of each vector. The x-component of each vector is given by the radius times the cosine of the angle, and the y-component is given by the radius times the sine of the angle.
Therefore, the vectors that join the center of the clock to the hours 1:00, 2:00, and 3:00 are:
At 1:00: (cos(π/6), sin(π/6)) = (√3/2, 1/2)
At 2:00: (cos(π/3), sin(π/3)) = (1/2, √3/2)
At 3:00: (cos(π/2), sin(π/2)) = (0, 1)
Note that these vectors are unit vectors, meaning that they have a length of 1 unit.
To learn more about Vector, visit the link:
https://brainly.com/question/27854247
#SPJ4
5. A cylinder has radius 3 inches and height 5 inches. A cone has the same radius and height. (Lesson 5-13)
b. Find the volume of the cone.
c. What fraction of the cylinder's volume is the cone's volume?
Find the value of x. If a segment looks like a tangent, it is a tangent.
We got x = 149.53 by using Pythagorean theorem.
What is the Pythagorean theorem in plain English?According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides.Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.angle of semicircle is always be 90°.
[tex]172^2=85^2+x^2[/tex]
[tex]29584=7225+x^2[/tex]
[tex]x^2=29584-7225[/tex]
[tex]=22359[/tex]
[tex]x=\sqrt{22359}[/tex]
[tex]\boxed{\bold{x=149.53}}[/tex]
Learn more about Pythagorean theorem:
brainly.com/question/14930619
What is the solution to the inequality -0.4x 1.27> 0.8
Answer:
x < 1.175
Step-by-step explanation:
-0.4x + 1.27 > 0.8
-0.4x > -0.47
x < 1.175
[tex]7\sqrt[3]{7}-\sqrt[3]{128}[/tex]
The expression 7∛7 - ∛128 is: 49∛7 - 8∛2.
What is the expression?We can simplify this expression using the fact that ∛(a * b) = ∛a * ∛b and ∛(a^3) = a.
First, let's factor ∛128 into prime factors: ∛128 = ∛(2^7) = 2 * ∛(2^5) = 2 * ∛(32).
Next, we can simplify 7∛7 as much as possible:
7∛7 = ∛(7^3) * ∛7 = 7∛(7^2) * ∛7 = 7 * 7∛7.
Now we can substitute these simplifications into the original expression:
7∛7 - ∛128 = 7 * 7∛7 - 2 * ∛32
We can simplify ∛32 as follows:
∛32 = ∛(2^5) = 2 * ∛(2^2) = 4∛2
Now, we can substitute this back into the expression:
7 * 7∛7 - 2 * ∛32 = 7 * 7∛7 - 2 * 4∛2
= 49∛7 - 8∛2
So the simplified expression is 49∛7 - 8∛2.
Learn more about expression here:https://brainly.com/question/1859113
#SPJ1
MULTIPLE CHOICE QUESTION
True or False: Involuntary deductions
from a person's gross pay go to their
employer.
False. Taxes and Social Security contributions are not deducted from a expressions person's total compensation and do not go to their employer.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
False. Taxes and Social Security contributions are not deducted from a person's total compensation and do not go to their employer. They are instead often paid to government agencies or other approved beneficiaries.
To know more about expressions visit :-
https://brainly.com/question/14083225
#SPJ1
convert 180⁰ in to grades
Answer: 9/10
Step-by-step explanation:
16^5+16^4 is divisible by 17
Chipwich Summer Camp surveyed 100 campers to determine which lake activity was their favorite. The results are given in the table.
Lake Activity Number of Campers
Kayaking 15
Wakeboarding 11
Windsurfing 7
Waterskiing 13
Paddleboarding 54
If a circle graph was constructed from the results, which lake activity has a central angle of 54°?
Kayaking
Wakeboarding
Waterskiing
Paddleboarding
Question 12
A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.
The activity with a central angle of 54° is Kayaking and there were about 557 principals in attendance based on the prediction
The activity with a central angle of 54°The formula to calculate the central angle for an activity is:
central angle = (number of campers for the activity / total number of campers) x 360°
Using this formula, we can calculate the central angle for each activity:
Kayaking: (15/100) x 360° = 54°
Wakeboarding: (11/100) x 360° = 39.6°
Windsurfing: (7/100) x 360° = 25.2°
Waterskiing: (13/100) x 360° = 46.8°
Paddleboarding: (54/100) x 360° = 194.4°
Therefore, the activity with a central angle of 54° is Kayaking.
Predicting the number of principals in attendance at the conference?To make a prediction about the number of principals in attendance at the conference, we can assume that the proportion of principals in the exhibit room is similar to the proportion of principals in the whole conference.
In the exhibit room, out of 70 people, 52 were principals.
So, the proportion of principals in the exhibit room was 52/70
We can predict the number of principals in attendance at the conference as follows:
Number of principals = proportion of principals x total number of attendees
If we plug in the values, we get:
number of principals = 52/70 x 750 = 557
So, based on this prediction, we can say that there were 557 principals in attendance at the conference.
Read more about proportion at
https://brainly.com/question/1781657
#SPJ1
Question 9(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Histogram is the ideal type of graphic to depict the data from the school's random sample of 100 students.
Explain about the Histogram:A histogram is a representation of statistical data that makes use of rectangles to illustrate the frequency of dataset in a series of equal-sized numerical intervals.
The independent variable is represented is along horizontal axis and indeed the dependent variable is plotted along of the vertical axis in the most popular type of histogram.A histogram is a type of bar graph that displays how frequently something occurs over a range of time. Histograms compare a variety of data, as opposed to bar graphs, which compare defined amounts.Given that-
The most efficient sort of graphic to show the data would be a histogram.A histogram is an illustration of a graph that shows the proportion of data points within such a range of values.It is a useful tool for showing data distribution and also can aid in the identification of trends and patterns.The best sort of graph to use is a histogram because it displays the frequency of data points.Thus, Histogram is the ideal type of graphic to depict the data from the school's random sample of 100 students.
Know more about the Histogram
https://brainly.com/question/28164315
#SPJ1
how do i solve this??
Find the value of x and y in each triangle
Answer:
x=4 y=3
Step-by-step explanation:
because y=3 and x=4
A piece of metal with a mass of 611 g is placed into a graduated cylinder that contains25.1 mL of water, raising the water level to 56.7 mL. What is the density of the metal?A) 2.70 g/cm3 B) 7.13 g/cm3 C) 8.96 g/cm3 D) 10.5 g/cm3 E) 19.3g/cm3
The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.
The given mass of the metal is 611 g and it is kept in a elevated cylinder that contains 25.1 mL of water,
Now, let us increase the water level to 56.7 mL. The metal volume can be evaluated by subtracting the initial volume from the final volume of water released by the metal.
Hence,
Metal volume = final volume - initial volume
= 56.7 mL - 25.1 mL
= 31.6 mL
Therefore,
Density = Mass / Volume
= 611 g/31.6 mL
= 19.3 g/cm³
The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.
To learn more about density,
https://brainly.com/question/1354972
#SPJ4
Surface are. Help!!!!!!!!
The surface areas of the prisms are listed below:
Case 1: 94 in²
Case 2: 72 cm²
Case 3: 40.5 m²
Case 4: 39.1 mm²
Case 5: 130 ft²
Case 6: 136 m²
How to find the surface area of a prism
In this problem we find six cases of prisms, whose surface areas have to be found. Surface area is the sum of the areas of all faces in the prism. Face have either a rectangular or a triangular form, whose area formulas are:
Rectangle
A = b · h
Triangle
A = 0.5 · b ·h
Where:
A - Areab - Widthh - HeightNow we proceed to determine the surface areas:
Case 1
A = 2 · (4 in) · (5 in) + 2 · (3 in) · (4 in) + 2 · (5 in) · (3 in)
A = 40 in² + 24 in² + 30 in²
A = 94 in²
Case 2
A = 2 · 0.5 · (3 cm) · (4 cm) + (5 cm) · (4 cm) + (5 cm) · (3 cm) + (5 cm)²
A = 12 cm² + 20 cm² + 15 cm² + 25 cm²
A = 72 cm²
Case 3
A = 2 · (3 m) · (7 m) + 2 · (6 m) · (7 m) + 2 · (6 m) · (3 m)
A = 10.5 m² + 21 m² + 9 m²
A = 40.5 m²
Case 4
A = 2 · 0.5 · (4 mm)² + 2 · (4 mm) · (3 mm) + (5.7 mm) · (3 mm)
A = 16 mm² + 6 mm² + 17.1 mm²
A = 39.1 mm²
Case 5
A = 2 · (10 ft) · (5 ft) + 2 · (5 ft) · (1 ft) + 2 · (10 ft) · (1 ft)
A = 100 ft² + 10 ft² + 20 ft²
A = 130 ft²
Case 6
A = 2 · 0.5 · (6 m) · (4 m) + 2 · (7 m) · (5 m) + (7 m) · (6 m)
A = 24 m² + 70 m² + 42 m²
A = 136 m²
To learn more on surface area of solids: https://brainly.com/question/29301011
#SPJ1
Suppose 15% of x equals 20% of y. What percentage of x is y?
A 5
B 35
C 75
D 133 1/3
E 300
If 15% of "x" is 20% of "y", then "y" is 75 percent of "x", the correct option is (c).
The "Percentage" is defined as a way to express the proportions or rates in terms of a "relative-scale" out of 100,
We know that, 15% of "x" equals 20% of "y".
Mathematically, this can be expressed as,
0.15x = 0.20y, ...because 15% = 0.15 and 20% = 0.20;
To find what percentage of x is y, we need to express "y" as a percentage of "x".
On solving further,
We get,
⇒ 0.15x = 0.20y,
⇒ y = (0.15x)/0.20,
⇒ y = 0.75x
It is read as "y" is read as 75% of "x".
Therefore, "y" is 0.75 times "x", or 75% of "x", Option(c) is correct.
Learn more about Percentage here
https://brainly.com/question/19733442
#SPJ4
Help, please, is for today.
Answer Immeditely Please
The ratio of the lengths of the corresponding sides of the similar right triangles indicates that the length of the segment [tex]\overline{BD}[/tex] = 8 units
What are similar triangles?Similar triangles are triangles that have the same shape, and therefore, the interior angles of each triangle are congruent to the three angles in the similar triangle, however, the sizes of the triangles may be different.
The similar triangles are; ΔABD, ΔBCD, ΔACB
∠ABD ≅ ∠BCD ≅ ∠ACB (Corresponding angles in similar triangles are congruent)
[tex]\overline{AD}[/tex]/[tex]\overline{BD}[/tex] = [tex]\overline{BD}[/tex]/[tex]\overline{DC}[/tex]
4/[tex]\overline{BD}[/tex] = [tex]\overline{BD}[/tex]/16
4 × 16 = 64 = [tex]\overline{BD}[/tex]²
[tex]\overline{BD}[/tex] = √(64) = 8
The length of the segment [tex]\overline{BD}[/tex] = 8 units
Learn more on similar triangles here: https://brainly.com/question/24031436
#SPJ1
you need to answer every question and you get 25pts and brainliest
Using probability, we can find the following:
a. In the figure.
b. The probability that the first set is green is = 0.8
c. Probability that the second set is green is = 0.06
d. The probability that both the sets are green is = 0.48
e. The probability that at least one set is green is = 0.86
Define probability?The likelihood that an event will occur is described by probability. There are many circumstances in real life where we may need to foresee how something will turn out. We might be able to predict the outcome of an event or we might not. At this point, we say, "There is a chance that the event will happen or not."
Here in the question,
b.
The probability that the first set is green is:
P = 1 - 0.2
= 0.8
c.
Now the first set is given as not green.
Probability that the second set is green is:
p = 0.2 × 0.3
= 0.06
d.
Now probability that both the sets are green is:
P = 0.8 × 0.6
= 0.48
e.
When both the sets are not green, probability is:
0.2 × 0.7
= 0.14
So, probability that at least one set is green is:
P = 1- 0.14
= 0.86
To know more about probability, visit:
https://brainly.com/question/16484393
#SPJ1
For Exercises 16-18, use the following information. Brian invests $200 in an
account that pays 5% annual interest compounded continuously.
16. Write a function that models the amount y in the account after x years.
17. Write the domain and range using inequalities. Explain their meaning in this context.
18. How much will Brian have in the account after 8 years?
1. The function that models the amount in the account after x years is [tex]y(x) = 200e^{0.05t}[/tex]
2. The domain is [tex]x > = 0[/tex]. The range is [tex]y > = 200[/tex]
3. After 8 years, Brian will have $298.37 in the account.
How much money will Brian have after x years?Function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The formula for continuous compounding is [tex]A = Pe^{rt}[/tex] where the A is the amount, P is the principal, e is Euler's number, r is the annual interest rate and t is the time in years.
Data:
A = ?
P = 200
t = ?
r = 5% = 0.05
Plugging in the values, we get: [tex]A = 200e^{0.05t}[/tex]which is the function.
2. The domain of the function is x >= 0 which means the number of years must be non-negative.
The range of the function is y >= 200 since the amount in the account cannot be negative and it starts with an initial investment of $200.
3. To get amount in the account after 8 years, we will plug in x = 8 into the formula:
[tex]y = 200 * e^{0.05*8}\\y = 200 * 1.49182469764\\y = 298.364939528\\ y = $298.37.[/tex]
Read more about function
brainly.com/question/11624077
#SPJ1
Find the equation of the line that is perpendicular to the line AB and passes through the point. (0,2)
The equation of a line perpendicular to line AB and passing through point (0,2) is y = -4x + 2.
The given line has a slope of 1/4, so the slope of any line perpendicular to it will be -4 (the negative reciprocal).
Using the point-slope form of a line, we can write the equation of the line passing through the point (0,2) with slope -4 as
y - 2 = -4(x - 0)
Simplifying, we get
y - 2 = -4x
Adding 2 to both sides, we get
y = -4x + 2
Therefore, the equation of the line passing through the point (0,2) which is perpendicular to the line y=1/4x+5 is y = -4x + 2.
To know more about Equation of line:
https://brainly.com/question/21511618
#SPJ1
Just look at the photo and anything you can help me with wi be much appreciated
Randy is designing a circular garden that is 18 feet in diameter. He is buying plastic edging that costs $1. 50 per foot. He can only buy edging in whole-foot amounts. How much does it cost Randy to buy edging for his garden? Use 3. 14 for pie.
If the diameter of circular-garden is 18 feet, then it will cost Randy an amount of $85.50 to buy edges for his garden.
The "Circumference" of circle is defined as the "total-length" of the boundary or the outer edge of the circle.
The circumference formula is : Circumference = π × Diameter,
The "diameter" of garden is = 18-feet,
So, Circumference = 3.14 × 18 = 56.52 feet,
Since, Randy needs to buy plastic-edging to cover the entire circumference of garden, he needs to buy 56.52 feet of edging.
We know that, Randy can only buy edging in whole-foot amounts,
So, rounding up to the nearest whole foot, we get 57 feet,
The cost of edging is = $1.50 per foot,
So, "total-cost" for Randy to buy edging for his garden is,
⇒ Total Cost = (Cost per foot) × (Number of feet),
⇒ $1.50 × 57,
⇒ $85.50
Therefore, it will cost Randy $85.50 to buy edging for his circular garden.
Learn more about Circumference here
https://brainly.com/question/16125353
#SPJ4
Can someone help me a little so I can learn this
Answer:b
Step-by-step explanation:
Answer:
b and c
Step-by-step explanation:
b 5(7+6s—9t)
35+30s—45
c 10×(3.5+3s—4.5t)
10×3.5 +10×3s—10×4.5t
35+30s—45t
the mesures of two suplementary angles are (1/2x) and (x+30) betermine te value of x
HELPPP ASAPPPPP What is the surface area of the square pyramid represented by the net?
Enter your answer in the box.
m²
Answer:
144 m²
Step-by-step explanation:
You want to know the surface area of a square base pyramid with a side length of 6 m and a slant height of 9 m.
Surface areaThe area of the given net is the sum of the areas of 4 congruent triangles and one square. The areas of these can be found using the relevant formulas.
SA = square area + 4 × triangle area
SA = 6² + 4 × 1/2(6)(9) = 36 +108
SA = 144 . . . . square meters
__
Additional comment
The area of a square of side s is A = s².
The area of a triangle with base b and height h is A = 1/2bh.
12. Jenny's water bottle holds 1.3 liters of water. How many milliliters of water does the water bottle hold? milliliters
Answer:
1300 milliliters
Step-by-step explanation:
There are 1000 milliliters in one liter. so 1.3 liters would be 1300. 1.3 x 1000 = 1300.
15PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST ALL FAKE ANSWERS WILL BE REPORTED AND PLS PLS PLS EXPLAIN THE ANSWER OR HOW U GOT IT PLEASE AND TY
Option a. The car is 115.47 feet from the building is correct for the given right triangle.
What is law of sines?A trigonometric formula known as the rule of sines connects any triangle's sides and angles. It claims that for all three sides of a triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. In other words, if a triangle has angles A, B, and C opposing its sides and sides a, b, and c, then:
If a/sin(A) = b/sin(B) = c/sin(C), then
If some of the other sides and angles of a triangle are known, this formula can be used to solve for those unknown sides or angles. However, it is restricted to triangles and calls for the measurement of at least one angle and one side's length.
The situation can be depicted as a right triangle, with building 200 feet, the angle of depression is 30 degrees.
Now,
tan(30) = opposite/adjacent = 200/distance
distance = 200/tan(30) ≈ 115.47 feet
Hence, option a. The car is 115.47 feet from the building is correct for the given right triangle.
Learn more about law of sines here:
https://brainly.com/question/17289163
#SPJ1
SARA WANTS TO SAVE $1600 IN 8 MONTHS, HOW MUCH DOES SARA NEEEDS TO SAVE MONTHLY?
Answer:
$200
Step-by-step explanation:
Just divide 1600 by 8
1600 ÷ 8 = 200
Answer:
sara needs to save 200 monthly
Step-by-step explanation:
i just divided 1600 by 8.
hope u have a great day!!
(a) Three squares have the areas of 7 cm², 17 cm² and 10 cm², (i) Will the squares exactly surround a right angled triangle? (ii) Explain your answer.
Answer:
(i) This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.
(ii) It is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.
Step-by-step explanation:
To determine whether the three squares can exactly surround a right-angled triangle, we need to use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's assume that the three squares have side lengths a, b, and c, with areas of 7 cm², 17 cm², and 10 cm², respectively. Then, we have:
a² = 7 cm²
b² = 17 cm²
c² = 10 cm²
We need to find out whether there exist values of a, b, and c that satisfy the Pythagorean theorem. If such values exist, then the three squares can surround a right-angled triangle.
We can rearrange the equations above to solve for a, b, and c:
a = √7 cm ≈ 2.65 cm
b = √17 cm ≈ 4.12 cm
c = √10 cm ≈ 3.16 cm
Now, we can check whether the Pythagorean theorem holds:
c² = a² + b²
(√10 cm)² = (√7 cm)² + (√17 cm)²
10 cm = 7 cm + 17 cm
This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.
In general, it is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.
a. ( 24 – 59 ) – ( 48:2 -60)
Answer:
Step-by-step explanation:
5. A path bounds a circular lawn at a park. If the inner edge of the path is 132 ft. Around, approximate the amount of
area of the lawn inside the circular path. Use T < 22
6. The area of a circle is 367 cm?. Find its circumference.
7. Find the ratio of the area of two circles with radii 3 cm and 4 cm.
8. If one circle has a diameter of 10 cm and a second circle has a diameter of 20 cm, what is the ratio of the area of
the larger circle to the area of the smaller circle?
9. Describe a rectangle whose perimeter is 132 ft. And whose area is less than 1 ft?. Is it possible to find a circle whose
circumference is 132 ft. And whose area is less than 1 ft?? If not, provide an example or write a sentence explaining
why no such circle exists.
10. If the diameter of a circle is double the diameter of a second circle, what is the ratio of area of the first circle to the
area of the second?
The circumference of a circle: C = 67.98 cm
Radius of the circular lawn, which is difference between outer radius of path and inner radius of path.
outer radius: [tex]r1 = (132 + 2T)/2 = (132 + 2(22))/2 = 88 ft[/tex]
inner radius: [tex]r2 = 132/2 = 66 ft[/tex]
radius of circular lawn is r = r1 - r2 = 22 ft
Now using formula for the area of a circle:
A = πr^2 = π(22^2) ≈ 1520.53 ft^2
To find the circumference of a circle with area 367 cm^2, we can use the formula for the area of a circle to find the radius:
[tex]A = \pi r^2 \\r^2 = A/\pi = 367/\pi[/tex]
r ≈ 10.80 cm
Then we can find the circumference using the formula for the circumference of a circle:
C = 2πr ≈ 2π(10.80) ≈ 67.98 cm
To know more about circumference, here
brainly.com/question/28757341
#SPJ4