The diameter of a softball is 3.8 inches. Estimate the volume within the softball. Round answers to the nearest
whole number and leave in the answer.
a. Volume: 73
b. Volume: 14
c. Volume: 9
d. Volume: 58
Answers
The volume of the ball is 9π (optionC)
What is volume of a sphere?A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center.
The ball takes the shape of the sphere. The volume of a sphere is therefore calculated as ;
V = 4/3 πr³
r = d/2 = 3.8/2 = 1.9
V = 4/3 × π × 1.9³
V = 27.44 π/3
V = 9π ( nearest whole number)
therefore the volume of the ball is 9π (nearest whole number)
learn more about volume of a sphere from
https://brainly.com/question/10171109
#SPJ1
Related Questions
A stock investment was worth $1569 in the year 2000, and the stock grew steadily by 4.6% every year. Write a function to model the value of the stock t years since 2000.
V = __
Answers
Therefore , the solution of the given problem of function comes out to be growth factor resulting from the 4.6% yearly growth rate is represented by the constant factor e(0.046t).
What does the term function actually mean?On the midterm exam, there will be inquiries on design, arithmetic numbers, every class, and both actual and hypothetical places. a description of the connections between various components that come together to produce the same outcome. A service is built from a variety of unique parts that work together to deliver unique outcomes for each input. Each post also has a location, which might be the enclave, a municipality, or even something else altogether.
Here,
The value of the stock t years since 2000 can be represented by the function by assuming that the stock's value increases constantly at a rate of 4.6% per year:
=> V(t) = 1569 * e^(0.046t)
where t is the number of years since the year 2000 and e is the algebraic constant
=>e = 2.71828.
With this function, exponential growth is represented by multiplying the stock's starting value in the year 2000 (1569) by the constant factor e(0.046t) to get the value of the stock t years later.
The growth factor resulting from the 4.6% yearly growth rate is represented by the constant factor e(0.046t).
To know more about function visit:
https://brainly.com/question/28193995
#SPJ1
simple smoothing time period actual series forecast series forecast error 1 100 100 0 2 110 3 115 if a smoothing constant of .3 is used, what is the exponentially smoothed forecast for period 4? multiple choice 106.6. 103.0. 115.0. 104.4. 112.6.
Answers
The exponentially smoothed forecast for period 4 is 106.6.
As per given information,
Time period Actual series Forecast series Forecast error 1 100 100 0 2 110 3 115
Smoothing constant α=0.3
For calculating exponentially smoothed forecast for period 4,
First, we need to calculate exponentially smoothed forecast for period 2.
Smoothed forecast for period 2 = α (Actual demand for period 1) + (1-α) (Smoothed forecast for period 1)
= 0.3 (100) + (0.7) (100)= 30 + 70= 100
Next, we can calculate exponentially smoothed forecast for period 3.
Smoothed forecast for period 3 = α (Actual demand for period 2) + (1-α) (Smoothed forecast for period 2)
= 0.3 (110) + (0.7) (100)
= 33 + 70
= 103
Now, we can calculate exponentially smoothed forecast for period 4.
Smoothed forecast for period 4 = α (Actual demand for period 3) + (1-α) (Smoothed forecast for period 3)
= 0.3 (115) + (0.7) (103)= 34.5 + 72.1
= 106.6
For similar question on exponentially smoothed
https://brainly.com/question/16914603
#SPJ11
Xavier receives a paycheck of $2250. First, he spends 20% of his paycheck to buy a new mattress. Then, he spends 29 of the remaining amount to fix a leak in his kitchen. After Xavier pays these two expenses, how much will be left over from his paycheck?
Answers
Answer:
Step-by-step explanation:
he's rich
Xavier will have $1278 left over from his paycheck after spending 20% on a new mattress and 29% on fixing a leak.
Explanation:To find out how much will be left over from Xavier's paycheck after he spends 20% on a new mattress and 29% on fixing a leak, we can follow these steps:
Calculate 20% of $2250, which is $450.Subtract $450 from $2250 to find the remaining amount after buying the mattress, which is $1800.Calculate 29% of $1800, which is $522.Subtract $522 from $1800 to find the amount left over after fixing the leak, which is $1278.Therefore, Xavier will have $1278 left over from his paycheck.
Learn more about Calculating remaining amount after expenses here:https://brainly.com/question/33576466
#SPJ2
calculate the amount of heat produced, in kj, when 52.40 g of methane, ch4, burns in an excess of air, according to the following equation.
Answers
Therefore, the amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air is -39568.2 kJ
The amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air can be calculated using the following equation:
[tex]Q = mcΔT[/tex]
Where Q is the amount of heat produced (in kJ), m is the mass of the methane (in g), and ΔT is the change in temperature (in K).
Using the equation, the amount of heat produced can be calculated as follows:
Q = [tex](52.40 g)(-753.15 K) = -39568.2 kJ[/tex]
for such more questions on temperature
https://brainly.com/question/25677592
#SPJ11
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle B?
Answers
Since 4x=192, x=48
So angle B equals 3(48)-12=132°
ten chairs are arranged in a circle. find the number of subsets of this set of chairs that contain at least three adjacent chairs.
Answers
Ten chairs are arranged in a circle. The number of subsets of this set of chairs that contain at least three adjacent chairs is 310.
The given that 10 chairs arranged in a circle.
Now we have to find the number of subsets of this set of chairs that contain at least three adjacent chairs.
To solve this, we can use the concept of permutations and combinations. The first step is to consider the number of ways in which three chairs can be selected and arranged in a subset that is adjacent to each other.
This can be done in 10 different ways, as there are 10 chairs in total and we can select any one of them as the starting point.
The next step is to consider the number of ways in which we can add additional chairs to this subset. For example, we can add a fourth chair to the subset in two different ways: either to the left of the first chair or to the right of the third chair.
Similarly, we can add a fifth chair to the subset in four different ways, a sixth chair in six different ways, and so on. Using this logic, we can create the following table:
Length of subset number of ways to select the subset number of ways to add chairs
Total number of subsets31 (adjacent)
= 10 ---43 (adjacent) 10*2
=20---55 (adjacent)10*4
=40---67 (adjacent)10*6
=60---79 (adjacent)10*8
=80---810 (adjacent)10*10
=100---
As we can see from the table, the total number of subsets that contain at least three adjacent chairs is given by:
Total number of subsets = 10 + 20 + 40 + 60 + 80 + 100
= 310
Therefore, the number of subsets of this set of chairs that contain at least three adjacent chairs is 310.
Learn more about the number of subsets of chairs at: https://brainly.com/question/17514113
#SPJ11
Implementing multiple types of technology and thereby precluding that the failure of one system will compromise the security of information is referred to as ____. (p. 205)
Answers
Implementing multiple types of technology and thereby precluding that the failure of one system will compromise the security of information is referred to as redundancy.
Explanation:
What is redundancy?Redundancy is the term used to describe the use of multiple components in a system to ensure that the failure of one component does not lead to system failure. Redundancy is a method of protecting computer systems against damage and disruption caused by component failure.The use of redundancy in computer systems is usually targeted at increasing system availability and lowering the likelihood of data loss.
Multiple types of technology may be employed to achieve redundancy in a computer system, such as mirroring data across multiple disks, deploying standby servers, using a hot backup server, and so on. Redundancy can be implemented in numerous ways to provide reliable service and protect against system failure.
To know more about redundancy:
https://brainly.com/question/13266841
#SPJ11
Pls help. Questions 7-10
Answers
The key features of both equations are:
Equation 1 has a vertex at (1, -16) and opens upwards. Its axis of symmetry is x = 1
Equation 2 has a vertex at (2, 2) and opens upwards. Its axis of symmetry is x = 2.
How do we solve?To rewrite each equation in vertex form, we need to complete the square by adding and subtracting a constant from each equation.
y = x² - 2x - 15
y = (x - 1)² - 16
The vertex form of the equation is y = a(x - h)² + k, where (h, k) is the vertex. In this case, the vertex is (1, -16).
y = 2x² - 8x + 6
y = 2(x - 2)² + 2
The vertex form of the equation is y = a(x - h)² + k, where (h, k) is the vertex. In this case, the vertex is (2, 2).
Learn more about the vertex form of an equation at: https://brainly.com/question/29170049
#SPJ1
PLSSSS HELP IF YOU TURLY KNOW THISSS
Answers
Given:-
[tex] \tt \: 3x = 12[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: 3x = 12[/tex][tex] \: [/tex]
[tex] \tt \: \: x = \cancel{ \frac{12}{3} }[/tex][tex] \: [/tex]
[tex] \boxed{ \tt{ \green{ \: x = 4 \: }}}[/tex][tex] \: [/tex]
__________________
hope it helps ⸙
what is the cop of a carnot refrigerator, when t(cold) is 275 k and t(hot) is 158 c?(write as a fraction, not a percent)
Answers
In the following question, among the conditions given, the cop of a Carnot refrigerator, when t(cold) is 275 k and t(hot) is 158 c. Then the COP of the Carnot refrigerator is 1.76 (written as a fraction "88/50").
The COP of a Carnot refrigerator is calculated as: COP = T(Cold) / (T(Hot) - T(Cold))The COP of a Carnot refrigerator is given by the formula:
COP = T(Cold) / (T(Hot) - T(Cold))Where T(Cold) is the temperature of the cold reservoir and T(Hot) is the temperature of the hot reservoir.
T(Cold) = 275 K and T(Hot) = 158 °C = 431 K By substituting these values into the formula: COP = 275 / (431 - 275)COP = 275 / 156COP = 1.76 The COP of the Carnot refrigerator is 1.76 (written as a fraction 88/50).
For more such questions on Carnot refrigerator
https://brainly.com/question/13441103
#SPJ11
PLEASE HELP WITH ENTIRE WORK SHEET I AM STRUGGLING SO BAD I WILL GIVE ALL POINTS AND MARK YOU BRAINLIEST FOR EVERYTHING PLEASE HELP! :( LOTS OF LOVE <3
Answers
Answer:
1-
a. 19
b. -8
2-
a. -31
b. 0
c. -10.7
d. -3/7
e. 4
3-
a. -5
b. -60
c. 0
d. -1/4
4. -13/2
5. -85/18
6. -5/12
7. -11
8. 16/11
9. -20/27
10. 26/11
11. -55/9
Step-by-step explanation:
why did i do this
A movie theater wanted to determine the average rate that their diet soda is purchased. An employee gathered data on the amount of diet soda remaining in the machine, y, for several hours after the machine is filled, x. The following scatter plot and line of fit was created to display the data. scatter plot titled soda machine with the x axis labeled time in hours and the y axis labeled amount of diet soda in fluid ounces, with points at 1 comma 35, 1 comma 39, 2 comma 32, 3 comma 24, 3 comma 30, 4 comma 20, 5 comma 18, 5 comma 22, 6 comma 4, 6 comma 14, 7 comma 8, and 8 comma 0, with a line passing through the coordinates 3 comma 25.2 and 7 comma 4.84 Find the y-intercept of the line of fit and explain its meaning in the context of the data. The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda. The y-intercept is 40.5. The machine starts with 40.5 ounces of diet soda. The y-intercept is −5.1. The machine loses about 5.1 fluid ounces of diet soda each hour. The y-intercept is 40.5. The machine loses about 40.5 fluid ounces of diet soda each hour.
Answers
The correct answer is: The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda.
What is the equation of the line?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
The y-intercept of a line of fit is the value of y when x equals 0. In the context of this problem, the y-intercept represents the amount of diet soda that the machine starts with when it is filled.
Since the y-intercept of the line of fit is −5.1, this means that the machine starts with 5.1 ounces of diet soda.
This is a reasonable value, as it is unlikely that the machine would be completely empty when it is filled.
It's important to note that the slope of the line of fit is also relevant in this context.
The slope represents the rate at which the amount of diet soda in the machine decreases over time. However, the question only asked for the y-intercept.
Hence, the correct answer is: The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda.
To learn more about the equation of the line visit:
https://brainly.com/question/18831322
#SPJ1
6. Martin has a business washing cars. Last year he washed 20 cars a week. This year, he wants to increase his business to 1.200 cars a year. How many cars will he have to wash each month on average?
Answers
Martin will have to wash 96 cars each month on average to meet his goal of washing 1,200 cars this year.
What is average ?
Average, also known as mean, is a statistical measure that represents the central value of a dataset. It is calculated by adding up all the values in the dataset and dividing by the total number of values. The average can be used to provide a general idea of the value of the dataset and to compare different datasets. There are different types of averages, including arithmetic mean, geometric mean, and median.
According to the question:
To find out how many cars Martin will have to wash each month on average, we need to first find out how many weeks there are in a year:
52 weeks/year
Then we can use this information to calculate how many cars Martin will have to wash each week:
1,200 cars/year ÷ 52 weeks/year = 23.08 cars/week
Since Martin cannot wash a fraction of a car, he will have to round up to 24 cars/week.
Finally, we can calculate how many cars Martin will have to wash each month on average:
24 cars/week x 4 weeks/month = 96 cars/month
Therefore, Martin will have to wash 96 cars each month on average to meet his goal of washing 1,200 cars this year.
To know more about average visit:
https://brainly.com/question/25005020
#SPJ1
draw marbles from a bag which contains 5 red marbles, 6 blue marbles and 4 green marbles with replacement until you get a blue marble. a) binomial b) poisson c) hypergeometric d) none of these
Answers
the correct answer is: none of these, as only binomial distribution is applicable to this scenario.
a) This scenario follows the binomial distribution, as we are drawing marbles with replacement and interested in the number of successes (getting a blue marble) in a fixed number of trials.
b) The Poisson distribution is used to model the number of events occurring in a fixed time interval, given a certain rate of occurrence. It is not applicable in this scenario.
c) The hypergeometric distribution is used to model the probability of obtaining a certain number of successes in a sample without replacement, given a finite population of items that can be classified into successes and failures. In this scenario, we are drawing with replacement, so the hypergeometric distribution is not applicable.
d) Therefore, the correct answer is: none of these, as only binomial distribution is applicable to this scenario.
Learn more about distributive here
https://brainly.com/question/5637942
#SPJ4
I am a triangle
My base is 32
My second base is two times for the first base
My hight is 21.6
What is my area?
Answers
Answer: The area of a triangle is 1036.8 square units.
To find the area of a triangle, we can use the formula
Area = (1/2) * base * height
In this case, we are given that the first base is 32 and the second base is twice the first base, or 2*32 = 64. The height is given as 21.6. Therefore, we can plug these values into the formula and solve for the area:
Area = (1/2) * (32 + 64) * 21.6
Area = (1/2) * 96 * 21.6
Area = 1036.8
Therefore, the area of the triangle is 1036.8 square units.
Know more about Triangle at.
https://brainly.in/question/33028759
Sketch the qraphs. 2x+3y=1
Answers
Answer:
y = -2/3x + 1/3
Step-by-step explanation:
2x + 3y = 1
3y = -2x + 1
y = -2/3x + 1/3
To sketch:
Pretend x is 3. y would be -1 2/3.
Now that you have this point, draw through the point (0, 1/3).
There ya go
Do anybody know this?
Answers
The coordinate of the point U that divides the line ST in the ratio 2:5 is: (12:6)
What are the coordinates of the division of the line segment?The formula for the division of line segments in the ratio m:n is
P = {[(mx2 + nx1)/(m + n)], [(my2 + ny1)/(m + n)]}
We are given the coordinates of line Segment ST as: S(10, 2) and T(17, 16)
Thus, if the ratio is 2:5, we have:
U(x, y) = {[(2*17 + 5*10)/(2 + 5)], [(2*16 + 5*2)/(2 + 5)]}
U(x, y) = (84/7), (42/7)
U(x, y) = (12, 6)
Thus, that is the coordinate of the point U that divides the line ST in the ratio 2:5.
Read more about Division of Line segment at: https://brainly.com/question/7784483
#SPJ1
Factor completely 16x2 − 25. (4x − 5)(4x − 5)
(4x + 5)(4x − 5)
(16x + 5)(x − 5)
(16x − 5)(x + 5)
Answers
Answer:
Step-by-step explanation:
(4x - 5)(4x + 5) Option 1
16x^2 + 20x - 20x - 25
Help me with these please!!
Answers
The properties of a parallelogram indicates that the variables in the segments and angles are;
b = 1, a = 3x = 15, y = 50x = 18, y = 9x = 2, y = 4.5What is a parallelogram?A parallelogram is a four sided figure with two pairs of sides that are parallel.
Whereby the figures are parallelogram, we get;
The length of the opposite sides are the same, therefore;
1. b + 1 = 2·b
1 = 2·b - b = b
1 = b
b = 1 (symmetric property)
3·a - 4 = a + 2
3·a - a = 4 + 2
2·a = 6
a = 6/2 = 3
a = 3
2. The opposite angles of a parallelogram are congruent, therefore;
(y + 10)° = (2·y - 40)°
10 + 40 = 2·y - y = y
50 = y
y = 50
The adjacent interior angles of a parallelogram are supplementary, therefore;
(4·x)° + (2·y - 40)° = 180°
(4·x)° + (2 × 50 - 40)° = 180°
(4·x)° = 180° - (2 × 50 - 40)° = 60°
x = 60°/4 = 15°
x = 15
3. The diagonals of a parallelogram bisect each other, therefore;
y + 3 = 12
y = 12 - 3 = 9
y = 9
x - 3 = 15
x = 15 + 3 = 18
x = 18
4. The diagonals of a parallelogram bisect each other therefore;
x + 6 = 4·x
4·x = x + 6
4·x - x = 6
3·x = 6
x = 6/3 = 2
x = 2
5·y - 8 = 3·y + 1
5·y - 3·y = 1 + 8 = 9
2·y = 9
y = 9/2 = 4.5
y = 4.5
Learn more on the properties of a parallelogram here: https://brainly.com/question/4218263
#SPJ1
Jessie is painting a cardboard box for a school project and needs to know much paint she needs to cover the box.
A prism has a length of 10 inches, height of 6 inches, and width of 4 inches.
Which statement is correct about the amount of paint Jessie needs to cover the whole box?
A. Jessie should use surface area to find out she needs to cover 240 in.2 of the cardboard box with paint.
B. Jessie should use surface area to find out she needs to cover 248 in.2 of the cardboard box with paint.
C. Jessie should use volume to find out she needs to cover 240 in.3 of the cardboard box with paint.
D. Jessie should use volume to find out she needs to cover 248 in.3 of the cardboard box with paint.
help 100pts + brlnst
Answers
Option (C) is correct which is "Jessie should use volume to determine that the cardboard box requires 240 in3 of paint."
What is volume?The measurement of three-dimensional space is volume.
It is typically quantified using a variety of imperial or US-standard units as well as SI-derived units.
The concept of length and volume are related.
Volume is the three-dimensional space inhabited by matter or encompassed by a surface, and it is measured in cubic units.
The SI unit of volume is the cubic meter (m³), which is a derived unit.
So, the volume would be:
length x breadth x height
Step 1 : substitute the values given
Step 2 : 10 x 4 x 6
Then, we got: 240 inches
Therefore, option (C) is correct which is "Jessie should use volume to determine that the cardboard box requires 240 in3 of paint."
Know more about volumes here:
https://brainly.com/question/463363
#SPJ1
Answer:
c
Step-by-step explanation: I was correct
in a batch of 100 cell phones, there are, on average, 6 defective ones. if a random sample of 25 is selected, find the probability of 4 defective ones
Answers
The probability of 4 defective cell phones in a sample of 25 can be found using the binomial probability formula and is equal to 0.0263.
What is probability?Probability is a branch of mathematics that deals with calculating the likelihood of a given event occurring. In probability, we calculate the number of ways an event can happen and divide it by the total number of possible outcomes.
Probability ranges from 0 to 1, with 0 indicating no chance of occurrence and 1 indicating that the event will definitely occur.
What is the binomial probability formula?If there are only two possible outcomes in a given event, the binomial probability formula is used to calculate the probability of the event happening.
The binomial probability formula is given by: P(X = x) = (nCx)px(1 - p)n - x
Where, P(X = x) is the probability of x successes in n trials
nCx is the number of ways x successes can occur in n trials
px is the probability of a single success in a given trial(1 - p)n - x is the probability of the remaining trials being failures.
How to solve the problem?The probability of 4 defective cell phones in a sample of 25 can be calculated using the binomial probability formula.
P(X = 4) = (25C4)(0.06)4(0.94)21 = 0.0263.
Therefore, the probability of 4 defective cell phones in a sample of 25 is 0.0263.
To know more about probability refer here:
https://brainly.com/question/29110744#
#SPJ11
The geometric mean between 16 and 20 is
Answers
Answer: 17.888543819998
Step-by-step explanation:
Answer:
17.8885
Step-by-step explanation:
find the geometric mean between 16 and 20, we need to multiply the numbers and take the square root of the result. That is:
Geometric Mean = √(16 × 20)
Geometric Mean = √320
Geometric Mean ≈ 17.8885
Therefore, the geometric mean between 16 and 20 is approximately 17.8885.
of six dvd players, two are defective and four are not. if cecil randomly chooses two of these dvd players, without replacement, the probability that the two he chooses are not defective is , what is the value of ??
Answers
The probability of selecting two non-defective DVD players from a group of six is 2/5. This is based on the assumption that the selection is done without replacement.
We can use the formula for calculating probabilities of combinations:
P(not defective) = number of ways to choose 2 non-defective DVD players / total number of ways to choose 2 DVD players
Total number of ways to choose 2 DVD players out of 6 is:
C(6,2) = 6! / ([2!] [4!]) = 15
Number of ways to choose 2 non-defective DVD players out of 4 is:
C(4,2) = 4! / ([2!] [2!]) = 6
Therefore, the probability that Cecil chooses 2 non-defective DVD players is:
P(not defective) = 6/15 = 2/5
So the value of P(not defective) is 2/5.
Learn more about probability here: brainly.com/question/30034780
#SPJ4
what are the 4 uppercase letters of the alphabet in block style with rotational symmetry?
Answers
The four uppercase letters of the alphabet in block style with rotational symmetry are H, I, O, and X. Rotational symmetry refers to the property of a figure or object that appears identical after being rotated around a central point by a certain angle.
In block style writing, letters are written with straight lines and sharp corners, creating a uniform and geometric appearance. H, I, O, and X are the only uppercase letters that have rotational symmetry and can be written in block style.
H has a rotational symmetry of 180 degrees, meaning it looks the same when rotated 180 degrees around its center point.
I has a rotational symmetry of 180 degrees as well, with the dot above the letter acting as its center point.
O has a rotational symmetry of 360 degrees, meaning it looks the same when rotated any number of degrees around its center point.
Lastly, X has a rotational symmetry of 180 degrees, with the intersection of the two lines acting as its center point.
For more such questions on Rotational symmetry.
https://brainly.com/question/1531736#
#SPJ11
Determine the intercept of the line
4x-3y=17
Answers
Answer:
x = 17/4, or 4.25
The x-intercept is (4.25, 0)
Step-by-step explanation:
We can get the intercepts by isolating x and y.
4x - 3y = 17
Subtract 4x from both sides.
-3y = -4x + 17
Divide both sides by -3.
y = 4/3x - 17/3
Input 0 for x.
y = -17/3
The y-intercept is (0, -17/3)
4x - 3y = 17
Add 3y to both sides.
4x = 3y + 17
Divide both sides by 4.
x = 3/4y + 17/4
Input 0 for y.
Find all the solutions in the equation 2 cos(x)- sqrt30 =0 in the interval [0,2pi)
Answers
Answer:
For me it's C.
Step-by-step explanation:
the third one if you would like me to explain tell me.
The solutions to the trigonometric equations [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex] are x ≈ [tex]0.5514 + 2n\pi[/tex], where n is an integer.
Given that the equation [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex]
To find all the solutions to the equation [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex] , solve for x by isolating the cosine term and then applying the inverse cosine function.
Here are the steps to solve the equation:
Add [tex]\sqrt{30}[/tex] to both sides:
[tex]2cos(x) = \sqrt{30}[/tex]
Divide both sides by 2:
[tex]cos(x) = \sqrt{30} / 2[/tex]
Find the inverse cosine ([tex]cos^{-1}[/tex]) of both sides:
[tex]x = cos^{-1}(\sqrt{30} / 2)[/tex]
To determine the values of x in the interval [tex][0, 2\pi)[/tex] that satisfy the equation.
Evaluate [tex]cos^{-1}(\sqrt{30} / 2)[/tex] to find its approximate value.
[tex]cos^{-1}(\sqrt{30} / 2) = 0.5514[/tex] radians
Since the cosine function has a periodicity of [tex]2\pi[/tex], we can find other solutions by adding multiples of [tex]2\pi[/tex] to the initial solution.
So, the solutions in the interval [tex][0, 2\pi)[/tex] are:
x ≈ 0.5514 radians
x ≈ [tex]0.5514 + 2\pi[/tex]
x ≈ [tex]0.5514 + 4\pi[/tex]
...
To simplify, express the solutions as:
x ≈ [tex]0.5514 + 2n\pi[/tex]
where n is an integer.
Therefore, the solutions to the trigonometric equations [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex] are x ≈ [tex]0.5514 + 2n\pi[/tex], where n is an integer.
Learn more about solving trigonometric equations and inverse trigonometric functions here:
https://brainly.com/question/1143565
#SPJ6
What is the value of
∠FDE given the following image?
Answers
The value of ∠FDE is 36°
Define the term angles?An angle is a geometric figure formed by two rays, or lines that extend infinitely in opposite directions, that share a common endpoint called the vertex. The measure of an angle is determined by the amount of rotation between the two rays.
Here given a right angle ∠CDE = 90°
So, we can say that,
∠CDF + ∠FDE = ∠CDE
(2x)° + (x+9)° = 90°
(3x + 9)° = 90°
Simplify it, x = 27°
So, the value of ∠FDE = (x+9)° = (27+9)° = 36°
Therefore, the value of ∠FDE is 36°
To know more about types of angle, visit:
https://brainly.com/question/27962469
#SPJ1
The angle FDE is 36°. The required answer for the given question is option (A). 36°.
What is the value of <FDE?Trigonometry angles are the angles provided by the trigonometric function ratios. Trigonometry is the study of the connection between angles and triangle sides. Angle values vary from 0 to 360 degrees.
An angle is a shape in geometry made by two rays or lines that stretch indefinitely in opposite directions and have a common endpoint known as the vertex. The quantity of rotation among the two rays determines the size of an angle.
From the given figure,
∠CDF + ∠FDE = 90
Thus,
(2x)+(x+9) = 90
3x + 9 = 90
3x = 81
x = 27
Then we will have that the angle FDE is:
∠FDE = (27) + 9
∠FDE = 36
The angle of FDE is 36°
To know more about Trigonometry, visit:
https://brainly.com/question/13729598
#SPJ1
In GeoGebra, display the measure of the circumscribed angle, ∠ECD. To explore the relationship between the central angle and the circumscribed angle, move point B to different locations on the coordinate plane anywhere between A and C. Find m∠ECD + m∠EAD for five different data sets, and fill in the table.
Answers
The sum of the circumscribed angle m∠ECD and central angle m∠EAD for five different data sets are 90°, 90°,120°,150°,180°.
What is central angle?A central angle is an angle in a circle that has its vertex at the center of the circle. Its arms, which are the two rays that make up the angle, both pass through points on the circumference of the circle.
m∠ECD m∠EAD m∠ECD + m∠EAD
45° 45° 90°
60° 30° 90°
100° 20° 120°
140° 10° 150°
180° 0° 180°
The measure of the circumscribed angle, ∠ECD, is the angle formed by the intersection of two lines, AB and CD.
The measure of the central angle, ∠EAD, is the angle formed by the intersection of the lines AB and ED.
The relationship between the circumscribed angle and the central angle can be explored by moving point B to various different locations on the coordinate plane between A and C.
By doing so, both the circumscribed angle and the central angle can be measured.
From the table above, it can be seen that the sum of the measures of the circumscribed angle and the central angle is always equal to 90°.
This is because the circumscribed angle and the central angle are supplementary angles, meaning that the sum of their measures always equal to 180°.
In this case, since the sum of the measures of the circumscribed angle and the central angle is always equal to 90°, the measures of the circumscribed angle and the central angle themselves must always add up to 90°.
Since the sum of the measures of the circumscribed angle and the central angle is always equal to 90°, the measures of the circumscribed angle and the central angle themselves must always add up to 90°.
For more questions related to supplementary angles
https://brainly.com/question/2046046
#SPJ1
the procedure used to obtain your sample (i.e., random or nonrandom sampling) is not the same as the procedure for assigning participants to conditions; distinguish between random sampling and random assignment.
Answers
Random sampling is used to ensure that the sample is representative of the population, while random assignment is used to control for extraneous variables and increase the internal validity of the study.
Random sampling and random assignment are two distinct procedures that are often used in research studies, and it's important to understand the difference between them.
Random sampling refers to the process of selecting individuals or units from a larger population in such a way that every member of the population has an equal chance of being included in the sample. Random sampling is used to ensure that the sample is representative of the population and that the results can be generalized to the larger population.
Random assignment, on the other hand, refers to the process of assigning participants to different experimental conditions in a way that is completely random. This means that every participant has an equal chance of being assigned to any condition. Random assignment is used to control for extraneous variables that could influence the results of the study. By randomly assigning participants to conditions, researchers can be more confident that any differences observed between the groups are due to the manipulation of the independent variable, rather than pre-existing differences between the participants.
In summary, random sampling is used to ensure that the sample is representative of the population, while random assignment is used to control for extraneous variables and increase the internal validity of the study.
To learn more about random sampling visit: https://brainly.com/question/29852583
#SPJ11
4x = 28 I need help with this.
Answers
Answer:
x=7
Step-by-step explanation:
28/4 = 7
Answer:x=7
Step-by-step explanation: