The measure in degrees of the central angle in the circle graph for the people that chose red is 72 degrees.
What is the central angle?A central angle is an angle formed by two radii (or rays) that intersect at the center of a circle. It is an angle whose vertex is at the center of the circle, and its sides are the radii that intersect the circle's circumference.
According to the given information:
To find the measure in degrees of the central angle for the people that chose red, we need to calculate the percentage of people that chose red out of the total number of people surveyed, and then convert that percentage into degrees.
Total number of people surveyed = 180 (brown) + 60 (black) + 90 (red) + 120 (blue) = 450
Percentage of people that chose red = (Number of people that chose red / Total number of people surveyed) * 100 = (90 / 450) * 100 = 20%
Now, we can convert the percentage into degrees using the formula for calculating the central angle in a circle graph:
Central angle = (Percentage / 100) * 360
Plugging in the percentage of people that chose red:
Central angle for red = (20 / 100) * 360 = 72 degrees
So, the measure in degrees of the central angle in the circle graph for the people that chose red is 72 degrees.
To know more about central angle visit:
https://brainly.com/question/17718047
#SPJ1
10. You practice playing the recorder for 2 hours. Your friend practices playing the recorder for as many hours as you. Does your friend practice for fewer hours, more hours, or the same number of hours as you? O more hours fewer hours the same number of hours
Answer: the same
Step-by-step explanation:
because it says they practice as many hours as you do
Divide using long division. Check your answer
(x3+3x2-x+2)/(x-1)
After performing long division on (x3+3x2-x+2)/(x-1) we get x² + 4x +3 leaving a remainder of 5.
Long division refers to the method of performing a division of two numbers or polynomials by hand. Furthermore, it involves several steps to evaluate in order to find a quotient and a remainder. It is considered an important and crucial form of practice in the branch of mathematics.
In the subject of dividing a polynomial, first, we divide the highest degree term of the dividend by the highest degree term of the divisor, and the remaining result is subtracted from the dividend. The calculation is as follows in the picture
To learn more about long division,
https://brainly.com/question/30059812
#SPJ4
draw the reflection of the triangle across the y axis
Answer:
Image
Step-by-step explanation:
find the general solution of the given higher-order differential equation. 16 d 4y dx4 40 d2y dx2 25y
The general solution of the given higher-order differential equation is y(x) = c1e[tex].^{x/2}[/tex]cos((1/2)√5x) + c2e[tex].^{x/2}[/tex]sin((1/2)√5x) + c3eˣ + c4e⁻ˣ.
The given higher-order differential equation is:
16(d⁴y/dx⁴) + 40(d²y/dx²) + 25y = 0
To find the general solution of this differential equation, we can assume that y(x) has the form:
y(x) = e[tex].^{rx}[/tex]
where r is a constant to be determined.
Differentiating y(x) four times with respect to x, we get:
d⁴y/dx⁴ = r⁴e[tex].^{rx}[/tex]
Differentiating y(x) two times with respect to x, we get:
d²y/dx² = r²e[tex].^{rx}[/tex]
Substituting these derivatives and y(x) into the differential equation, we get:
16(r⁴e[tex].^{rx}[/tex]) + 40(r²e[tex].^{rx}[/tex]) + 25e[tex].^{rx}[/tex] = 0
Simplifying this equation by dividing through by e[tex].^{rx}[/tex], we get:
16r⁴ + 40r² + 25 = 0
This is a quadratic equation in r². Solving for r² using the quadratic formula, we get:
r² = [-40 ± √(40² - 4(16)(25))] / 2(16)
r² = [-40 ± √(3600)] / 32
r² = [-40 ± 60] / 32
We get two possible values for r²:
r² = 5/4 or r² = 1
Taking the square root of each value, we get:
r = ±(1/2)i√5 or r = ±1
Thus, the general solution of the given higher-order differential equation is:
y(x) = c1e[tex].^{x/2}[/tex]cos((1/2)√5x) + c2e[tex].^{x/2}[/tex]sin((1/2)√5x) + c3eˣ + c4e⁻ˣ
where c1, c2, c3, and c4 are constants determined by the initial or boundary conditions of the specific problem.
Learn more about differential equation :
https://brainly.com/question/14926307
#SPJ4
The complete question is :
find the general solution of the given higher-order differential equation : 16(d⁴y/dx⁴) + 40(d²y/dx²) + 25y = 0
Which answer choice correctly identifies the missing length of the polygon if the perimeter is 137 m?
a(26
b(25
c(24
d(23
Answer:
a
Step-by-step explanation:
to find the missing side x , subtract the sum of the 5 given sides from the given perimeter.
x = 137 - (39 + 37 + 12 + 10 + 13) = 137 - 111 = 26 m
Question A scale model of a ramp is a right triangular prism as given in this figure. In the actual ramp, the triangular base has a height of 0.6 yards. What is the surface area of the actual ramp, including the underside? Enter your answer as a decimal in the box. yd² Right triangular prism. Each base is a triangle whose legs are 8 in, 5 in, and 5 in. The height of the triangles is 3 in. The prism is oriented so that the side labeled 8 in is on the bottom. The distance between the bases is labeled 4 in.
The surface area of the actual ramp, including the underside, is approximately 15.38 yd².
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
To find the surface area of the actual ramp, we need to first find the dimensions of the ramp.
We are given that the scale model of the ramp is a right triangular prism with legs of 8 in, 5 in, and 5 in, and a height of 3 in. We can use these dimensions to find the dimensions of the actual ramp.
Since the ramp is a scale model, the ratio of the dimensions of the model to the actual ramp is the same for all corresponding dimensions. The height of the triangular base in the actual ramp is given as 0.6 yards, which is equal to 21.6 inches. So, we have:
height of actual ramp / height of model = 21.6 in / 3 in = 7.2
We can use this ratio to find the dimensions of the actual ramp:
height of actual ramp = 7.2 * 3 in = 21.6 in
length of actual ramp = 7.2 * 8 in = 57.6 in
width of actual ramp = 7.2 * 5 in = 36 in
Now we can find the surface area of the actual ramp. The surface area of the top and bottom of the ramp is the area of the triangular base plus the area of the rectangle formed by the length and width of the ramp:
Area of triangular base = (1/2) * base * height = (1/2) * 5 in * 5 in = 12.5 in²
Area of rectangular top and bottom = length * width = 57.6 in * 36 in = 2073.6 in²
Total surface area of top and bottom = 2 * (Area of triangular base + Area of rectangular top and bottom) = 2 * (12.5 in² + 2073.6 in²) = 4153.2 in²
The surface area of the sides of the ramp is the area of the three rectangles formed by the height and width of the ramp:
Area of one side rectangle = height * width = 21.6 in * 36 in = 777.6 in²
Total surface area of sides = 3 * Area of one side rectangle = 3 * 777.6 in² = 2332.8 in²
Finally, we add the surface area of the top and bottom to the surface area of the sides to get the total surface area of the ramp:
Total surface area of ramp = Surface area of top and bottom + Surface area of sides = 4153.2 in² + 2332.8 in² = 6486 in²
Converting to yards and rounding to two decimal places, we get:
Total surface area of ramp = 6486 in² / (36 in/yd)² = 15.38 yd² (rounded to two decimal places)
Therefore, the surface area of the actual ramp, including the underside, is approximately 15.38 yd².
To learn more about triangle from the given link:
https://brainly.com/question/2773823
#SPJ1
11
10. Write the expression in the form
ax+b that is equivalent to
(3.6x-1.4)-(1.8x-5.5). Select the
coefficient and constant to complete
the expression.
-5.4
-1.8
1.8
5.4
x +
6.9
4.1
(-4.1)
(-6.9)
The given expression in the form ax + b will be (B) 1.8x + 4.1.
What are expressions?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.
An example is the expression x + y, which combines the terms x and y with an addition operator.
In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers.
So, we have the expression:
(3.6x-1.4) - (1.8x-5.5)
First, solve it in the form of ax + b as follows:
(3.6x-1.4) - (1.8x-5.5)
3.6x-1.4 - 1.8x+5.5
1.8x + 4.1
So, we have the expression: 1.8x + 4.1
Then, the coefficient and content will be (B) and the correct expression would be 1.8x + 4.1.
Therefore, the given expression in the form ax + b will be (B) 1.8x + 4.1.
Know more about expressions here:
https://brainly.com/question/1859113
#SPJ1
The power of a statistical test of hypotheses is
the smallest significance level at which the data will allow you to reject the null hypothesis.
equal to 1 - (P-value).
the probability that the test will reject both one-sided and two-sided hypotheses.
the probability that a significance test will reject the null hypothesis when a particular alternative value of the parameter is true.
The power of a statistical test of hypotheses is the probability that the test will reject the null hypothesis when a particular alternative value of the parameter is true.
It is the ability of the statistical test to detect a true difference between groups, or a true relationship between variables, when it exists. A high power indicates that the test has a low probability of making a type II error (failing to reject a false null hypothesis).
The power of a test is affected by various factors such as the sample size, level of significance, effect size, and variability of the data.
Learn more about statistical test
https://brainly.com/question/14128303
#SPJ4
It is not equal to 1 - (P-value), nor is it the smallest significance level at which the data will allow you to reject the null hypothesis or the probability that the test will reject both one-sided and two-sided hypotheses.
The correct answer is: The power of a statistical test of hypotheses is the probability that a significance test will reject the null hypothesis when a particular alternative value of the parameter is true. It is the ability of the test to detect a true difference or effect between two groups or conditions. The power is influenced by factors such as the sample size, effect size, and significance level, and is usually calculated before conducting a study to ensure that it has sufficient power to detect meaningful differences. It is not equal to 1 - (P-value), nor is it the smallest significance level at which the data will allow you to reject the null hypothesis or the probability that the test will reject both one-sided and two-sided hypotheses.
learn more about statistical test
https://brainly.com/question/14128303
#SPJ11
deigo has budgeted $35 from his summer job earnings to buy shorts and socks for soccer. He neefs 5 pairs of socks and a pair of shorts. The socks cost different amounts in different stories. The shorts he wants cost $19.95. list some other possible prices for the socks that would still allow diego to stay with in his budget
Some possible prices for the socks that would meet this condition are $2.99, $2.50, $3.00, $2.95, etc.
Define rateA rate is a measure of the amount of change of one quantity with respect to another quantity. It expresses how much one quantity changes in relation to another quantity over a given time or distance.
If Diego has budgeted $35 for 5 pairs of socks and a pair of shorts, we can subtract the cost of the shorts from the total budget to find the amount he has left for the socks:
$35 - $19.95 = $15.05
To find the possible prices for the socks, we can divide the amount Diego has left by the number of pairs of socks he needs:
$15.05 / 5 pairs = $3.01 per pair
Therefore, Diego would be able to stay within his budget if he finds socks that cost $3.01 or less per pair. Some possible prices for the socks that would meet this condition are $2.99, $2.50, $3.00, $2.95, etc.
To know more about pair, visit:
https://brainly.com/question/29122030
#SPJ1
the dot plot below shows the number of songs carly downloaded over 15 successive weekends. what is the greatest number of songs downloaded?
The greatest number of songs downloaded is 10."
How we find the greatest number of songs downloaded?"What is the greatest number of songs downloaded?" is:
Identify the highest point on the dot plot.Read the number of songs downloaded at that highest point.A dot plot is a graphical representation of data using dots. In this case, the dot plot shows the number of songs Carly downloaded over 15 successive weekends. Each dot represents the number of songs downloaded during a particular weekend
To find the greatest number of songs downloaded, we need to identify the highest point on the dot plot. This can be done by visually examining the dot plot and looking for the highest dot.
Once we identify the highest dot, we can see the number of songs downloaded during that particular weekend, which is the greatest number of songs downloaded over the 15 successive weekends.
if the highest dot on the dot plot represents 10 songs downloaded, then the answer to the question would be "The greatest number of songs downloaded is 10."
Learn more about Dot plot
brainly.com/question/21862696
#SPJ11
this histogram shows the number of people who volunteered for community service and the number of hours they worked. how many volunteers worked more than 15 hours?
The number of volunteers who worked more than 15 hours can be found by summing up the frequencies
of the bars in the histogram that represent the groups with more than 15 hours of community service.
To determine how many volunteers worked more than 15 hours using the given histogram.
Identify the section of the histogram that represents volunteers who worked more than 15 hours.
Read the height (frequency) of the bars representing the groups of volunteers with more than 15 hours of community
service.
Add the frequencies of these bars to get the total number of volunteers who worked more than 15 hours.
In conclusion, the number of volunteers who worked more than 15 hours can be found by summing up the frequencies
of the bars in the histogram that represent the groups with more than 15 hours of community service.
for such more question on volunteers
https://brainly.com/question/28935014
#SPJ11
If 55% of a number is 110 and 40% of the same number is 80, find 95% of that number.
Answer:
.40n = 80, so n = 200
.95 × 200 = 190
Answer:
190
Step-by-step explanation:
Please help me with this homework
Answer: 10
Step-by-step explanation:
10
mateo has drawn a line to represent the parallel cross-section of the triangular prism. is he correct? explain. riangular prism lying on a rectangular face and a line drawn along the length of a rectangular face
Based on the information provided, Mateo has drawn a line to represent the parallel cross-section of the triangular prism. Is he correct? Yes, he is correct. Here's an explanation:
A triangular prism has two triangular bases and three rectangular faces. When a triangular prism is lying on a rectangular face, it means that one of its rectangular faces is on the bottom. If Mateo draws a line along the length of this rectangular face, he is creating a parallel cross-section of the triangular prism.
This is because the line he drew is parallel to the triangular base of the prism, and the two bases are also parallel to each other. A parallel cross-section is created when a plane cuts through a solid parallel to its base, and in this case, Mateo's line fulfills this condition.
Therefore, Mateo is correct in representing the parallel cross-section of the triangular prism by drawing a line along the length of a rectangular face.
Learn more about prism at https://brainly.com/question/31315453
#SPJ11
Need help ASAP
there are 600 poetry books at the library.Of the poetry books,8.5 are for children.How many poetry books at the library are for children
The number of poetry books at the library that are for children is 510
How many poetry books at the library are for childrenfrom the question, we have the following parameters that can be used in our computation:
Books = 600
If 8.5/10 of the poetry books are for children, we can calculate the number of poetry books for children as follows:
Number of poetry books for children = (8.5/10) x 600
Number of poetry books for children = 510
Therefore, there are 510 poetry books at the library for children.
Read more about proportion at
https://brainly.com/question/870035
#SPJ1
answer asap, 12 points !!!
Answer:
Step-by-step explanation:
domain is -infinity to positive infinity range is -3 to infinity. Increasing from -3 to infinity and decreasing from - infinity to -3 and it’s minimum
Gina has a credit card balance of $5,820 and her minimum payment is $87.30. What rate is used to determine Gina’s minimum payment?
Jackie has $500 in a savings account.The interest rate is 5% per year and is not compounded. How much will she have in total in 1 year?
Answer:
$525
Step-by-step explanation:
Jackie starts with $500, and the interest rate is 5% per year.
This means that, after one year, Jackie will have accumulated 5% interest with the $500 she put into the savings account.
Now, we can find 5% of $500 by converting 5% to its fraction form, which is 5/100. 5% of a value means that you need to multiply the fraction (or decimal) by the said value. So, we have:
[tex]\frac{5}{100}[/tex] · 500 =
[tex]\frac{2500}{100}[/tex] =
25
Therefore, the amount of interest she has accumulated in one year is $25. Combined with the money in her savings account, she has $525, since $500 + $25 = $525.
Sam is stacking cans of vegetables at the Store His shelf is 10 inches tall, 10 inches deep, and 50 inches wide The cans are 4 inches tall and each has a volume of 50 24 in³ How many cans will fit on the shelf?
Answer:
48
Step-by-step explanation:
You want to know the number of cans 4 inches tall with a volume of 50.24 in³ that will fit on a shelf with a height and depth of 10 inches and a length of 50 inches.
DiameterThe diameter of the can will be found from the volume formula:
V = (π/4)d²h
d = √(4V/(πh)) = √(4·50.24/(4·3.14)) = √16 = 4 . . . inches
The cans are 4 inches in diameter.
NumberThe number of cans that will fit in each dimension will be the integer part of the dimension divided by the size of the can in that dimension.
Height: (10 in)/(4 in/can) = 2.5 cans . . . . cans will fit 2 cans high
Depth: (10 in)/(4 in/can) = 2.5 cans . . . . cans will fit 2 cans deep
Length: (50 in/4 in/can) = 12.5 cans . . . . cans will fit 12 cans long
A total of 2 × 2 × 12 = 48 cans will fit on the shelf.
__
Additional comment
There will be 2 inches of empty space in each direction.
<95141404393>
a repairable product with a constant failure rate of 0.0078 failures per hour has mean time to repair of 40 hours. find its availability
The availability of this repairable product is approximately 0.762, or 76.2%.
In order to find the availability of a repairable product, we need to consider its failure rate and mean time to repair. The formula for availability (A) is:
A = MTBF / (MTBF + MTTR)
Where MTBF is Mean Time Between Failures and MTTR is Mean Time To Repair.
Since we have a constant failure rate (λ), we can calculate the MTBF as the inverse of the failure rate:
MTBF = 1 / λ
In this case, the failure rate (λ) is 0.0078 failures per hour. Let's calculate the MTBF:
MTBF = 1 / 0.0078 = 128.205 hours
Now, we know the MTTR is 40 hours. We can use the availability formula to find the answer:
A = MTBF / (MTBF + MTTR)
A = 128.205 / (128.205 + 40)
A = 128.205 / 168.205
A ≈ 0.762
So, the availability of this repairable product is approximately 0.762, or 76.2%.
Learn more about Availability here: brainly.com/question/19907540
#SPJ11
this lesson will focus on finding the perimeter of rectangles. truefalse\
Answer:
Step-by-step explanation:
false
Find the missing measure.
The missing angles in the given pair of lines AB and CD with transversals EF & GH intersecting at O & missing sides on the basis of similarity of triangles are:
∠IKF=w°=109°
JO=z=2.7 units
∠JLO=x°=39°
∠DLO=y°=141°
What is similarity?
If two forms or figures have an equal number of comparable sides and angles, they are said to be similar. Similar figures are those when two or more figures share the same shape but have varied sizes.
Given that
∠KIO=39°
∠IKO=71°
∠IOK=70°
IO=12 units
KO=8 units
LO=4 units
a)We know that ∠KIO=∠OLJ {alternate interior angles}
∠KIO=∠OLJ=39°
∴x° = 39°
b)We know that ∠OLJ+∠OLD=180° {linear pair}
x°+y°=180°
39°+y°=180°
y°=180-39
y°=141°
c)We know that ∠IKO+∠IKF=180° {angles on straight line}
71°+w°=180°
w°=180-71
w°=109°
d)In ΔOKI and ΔOJL, we can see that
∠OIK=∠OLJ=39°
∠OKI=∠OJL=71°
∠KOI=∠JOL=70°
as the angles are congruent, we can say that ΔOKI and ΔOJL are similar.
∴Sides will be in same ratio
[tex]\frac{OI}{OL}[/tex] = [tex]\frac{OK}{OJ}[/tex] = [tex]\frac{KI}{JL}[/tex]
Taking [tex]\frac{OI}{OL}[/tex] = [tex]\frac{OK}{OJ}[/tex]
[tex]\frac{12}{4} = \frac{8}{z}[/tex]
3z = 8
z =2.667
z≈2.7 units
To know more about similarity, visit:
https://brainly.com/question/26451866
#SPJ1
1. Classify the type of linear correlation you might expect with each pair of variables. 3K
a) hours of lacrosse practice, goals scored in a lacrosse game
b) students' average marks, the numbers of siblings in their families
c) distances from students' homes to their schools, the time they spend on the school bus each day
a) Positive correlation, b) No correlation, c) Negative correlation
How to determine the type of linear correlationa) Positive correlation - as the hours of lacrosse practice increase, the number of goals scored in a lacrosse game is likely to increase as well.
b) No correlation - there is no obvious relationship between a student's average marks and the number of siblings in their family.
c) Negative correlation - as the distance from a student's home to their school increases, the time they spend on the school bus each day is likely to decrease.
Learn more about correlation at https://brainly.com/question/13879362
#SPJ1
5 cm x 3 cm X A 84 What is the surface area, in square centimeters, of the triangular prism? B 92 C 72 D 6 cm 50 ¯¯¯ 4 cm 5 cm 3 cm
In the given problem, the surface area of the triangular prism is 65 square centimeters. The answer is not listed among the options provided
To to Calculate Surface Area?We need to find the surface area of the triangular prism, which is the sum of the areas of all its faces.
The triangular faces of the prism are congruent triangles, so we can find their area by multiplying the base and height and dividing by 2. The dimensions of the triangular faces are 5 cm (base) and 4 cm (height).
Area of each triangular face = (5 cm x 4 cm)/2 = 10 cm²
The rectangular faces are congruent rectangles, so we can find their area by multiplying the length and width. The dimensions of the rectangular faces are 5 cm x 3 cm and 3 cm x 4 cm.
Area of each rectangular face = (5 cm x 3 cm) = 15 cm²
Total surface area of the prism = 2 x Area of triangular face + 3 x Area of rectangular face
= 2 x 10 cm² + 3 x 15 cm²
= 20 cm² + 45 cm²
= 65 cm²
Therefore, the surface area of the triangular prism is 65 square centimeters. The answer is not listed among the options provided, so there might be a mistake in the question or answer choices.
Learn more about prism here: https://brainly.com/question/1297098
#SPJ1
what is the average size of a customer's bill at a restaurant that earns daily $3,250 for the meals that it sells to 200 customers? $32.50 $20.00 $16.25 $15.84
The average size of a customer's bill at a restaurant that earns daily $3,250 for the meals that it sells to 200 customers is $16.25. Therefore, the right answer is option (c).
The average or mean is calculated by taking the ratio of the total sum of the outcomes of an event to the frequency or the number of times the event occurs.
It can be written as [tex]\frac{n_1+n_2+.....+n_a}{a}[/tex].
In the given question, the sum of the customer bill is given as $3,250.
And the number of customers served is given to be 200.
Therefore, the average size of a customer's bill is calculated by [tex]\frac{3250}{200}[/tex]
Which turns out to be $16.25.
Learn more about Average:
https://brainly.com/question/28798526
#SPJ4
The answer is $16.25. To find the average size of a customer's bill, you would divide the total earnings by the number of customers.
$3,250 / 200 customers = $16.25 per customer.
To find the average size of a customer's bill at the restaurant, you need to divide the total daily earnings by the number of customers. Here's a step-by-step explanation:
1. The restaurant earns $3,250 daily from the meals it sells.
2. The restaurant serves 200 customers daily.
Now, calculate the average bill size:
3. Divide the total daily earnings ($3,250) by the number of customers (200).
$3,250 ÷ 200 = $16.25
The average size of a customer's bill at the restaurant is $16.25.
To learn more about average size : brainly.com/question/773358
#SPJ11
If cosθ=-3/4 and tanθ is negative find sinθ
If cosθ=-3/4 and tanθ is negative, then sinθ= √(7)/4.
Since cosθ = -3/4 and θ is an angle in the second quadrant where cosθ is negative, we know that sinθ must be positive.
The Pythagorean identity is a trigonometric identity that relates the three basic trigonometric functions: sine, cosine, and tangent
To find sinθ, we can use the Pythagorean identity
sin^2θ + cos^2θ = 1
Substituting the value of cosθ we get
sin^2θ + (-3/4)^2 = 1
Simplifying
sin^2θ + 9/16 = 1
sin^2θ = 7/16
Taking the square root of both sides, we get
sinθ = ±√(7)/4
Since we know that sinθ is positive in the second quadrant, we take the positive value
sinθ = √(7)/4
Learn more about Pythagorean identity here
brainly.com/question/10285501
#SPJ4
Solve this proportion 12/m = 18/9
Answer:
m = 6
Step-by-step explanation:
We have the proportion:
12/m = 18/9
To solve for m, we can cross-multiply the terms in the proportion:
12 × 9 = 18 × m
Simplifying both sides of the equation, we get:
108 = 18m
Dividing both sides by 18, we get:m = 6
Therefore, the solution to the proportion 12/m = 18/9 is m = 6.
Answer: m = 6
Step-by-step explanation:
First, we will rewrite this proportion:
[tex]\displaystyle \frac{12}{m} =\frac{18}{9}[/tex]
Next, we will cross-multiply:
12 * 9 = 18 * m
108 = 18m
Lastly, we will divide both sides of the equation by 18:
m = 6
We can also solve this proportion another way.
We know that 18/9 = 2, so 12/m must equal 2 as well.
12/6 = 2, so m = 6.
A cylinder has radius R and height R√3. Point A lies on the top circle and point B lies on the bottom circle of the cylinder. The distance between the axis of the cylinder and line AB is (R√3)÷2. What is the angle between line AB and the axis?
Answer: The angle between line AB and the axis of the cylinder is 60 degrees.
Step-by-step explanation:
Let's draw a cross-sectional diagram of the cylinder to help visualize the problem.
Label the center of the top circle as O and the center of the bottom circle as O'.
Label the midpoint of line AB as M.
Draw a line from M to the center of the cylinder, which intersects the axis of the cylinder at point C.
Because line AB is perpendicular to the axis of the cylinder, line MC is also perpendicular to line AB.
Label the length of line MC as h, and the distance between point M and the axis of the cylinder as x.
By the Pythagorean theorem, we know that OM^2 + h^2 = R^2 (the radius of the cylinder)
Similarly, O'M^2 + h^2 = R^2
Subtracting these two equations, we get OM^2 - O'M^2 = 0, which means that OM = O'M = R.
Therefore, triangle MOC is an isosceles triangle with MO and O'M both equal to R.
Because x is the distance between line AB and the axis of the cylinder, we know that x = MC - (R√3)÷2.
We also know that h = R - x (because OM = R).
Using the Pythagorean theorem, we can solve for MC: (R^2 - h^2)^0.5 = MC
Substituting h = R - x, we get MC = (2Rx - x^2)^0.5
Setting MC = (R√3)÷2 (from the problem statement), we can solve for x: x = R(3 - 3^0.5)^0.5
Finally, using the tangent function, we can solve for the angle between line AB and the axis of the cylinder: tanθ = (R√3)÷2 / x, where θ is the angle we are looking for.
Substituting x from step 15, we get tanθ = 1 / (3 - 3^0.5)
Using a calculator, we can solve for θ: θ = 60 degrees.
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
The graphical representation that would be the best for this data would be a circle graph. That is option C.
What is a circle graph?A circle graph, which is also called a pie chart, is defined as a type of data representation where by the information concerning a data set is displayed in a circular form and in a way that the various information displayed is a percentage of the total data set involved.
Now, the number of students that were surveyed = 100 students.
The number of subjects that are preferred by the students would be represented as x,y,z.
Therefore to represent the number of students that preferred a particular subject on the circle graph the following is carried out;
For subject x = Number of X/100 × 360/1
Learn more about histogram here:
https://brainly.com/question/30764929
#SPJ1
The set B = {1 + t2, t + t2, 1 + 2t + t2} is a basis for P2.
Find the coordinate vector of p(t) = 1 + 4t + 7t2 relative to B
The coordinate vector of p(t) relative to the basis B is:
[ -1 ]
[ 2 ]
[ 2 ]
To find the coordinate vector of p(t) = 1 + 4t + 7t2 relative to the basis B = {1 + t2, t + t2, 1 + 2t + t2}, we need to express p(t) as a linear combination of the basis vectors and then write down the coefficients as a column vector.
We have:
p(t) = a(1 + t2) + b(t + t2) + c(1 + 2t + t2)
Expanding this out, we get:
p(t) = (a + c) + (b + 2c)t + (a + b + c)t2
Comparing coefficients with the polynomial 1 + 4t + 7t2, we get the following system of equations:
a + c = 1
b + 2c = 4
a + b + c = 7
Solving this system, we find:
a = -1
b = 2
c = 2
Therefore, the coordinate vector of p(t) relative to the basis B is:
[ -1 ]
[ 2 ]
[ 2 ]
To learn more about vector visit;
brainly.com/question/29740341
#SPJ11