In the gym, there are 100 feet between the opposing corners.
Given,
The length of the rectangular gymnasium = 80 feet
The width of the rectangular gymnasium = 60 feet
We have to find the distance between opposite corners of the gymnasium;
Here,
The distance between opposite corners of the gymnasium is the diagonal of the rectangle;
Diagonal of rectangle = [tex]\sqrt{width^{2} + length^{2} }[/tex]
Then,
Diagonal = [tex]\sqrt{80^{2} +60^{2} }[/tex]
Diagonal = [tex]\sqrt{6400+3600}[/tex]
Diagonal = √10000
Diagonal = 100 feet
That is,
The distance between the opposite corners if the gymnasium is 100 feet.
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5 parts!!! 100 pionts I WILL GIVE BRANLIST
part 1 Using the table provided above, list the average gas price for 2010.
part 2 Find the linear regression equation that models the data above. Round to the nearest thousandth if needed.
part 3 List the domain of the linear regression equation in interval notation. Round to the nearest thousandth if needed.
part 4 List the range of the linear regression equation in interval notation. Round to the nearest thousandth if needed.
part 5 Use the linear regression equation to predict how much you expect gas to cost in 2025?
1. The average gas price for 2010 is of: $2.22.
2. The linear regression equation is given as follows: y = 0.176x + 0.5.
3. The domain is: [0,∞).
4. The range is: [0.5,∞).
5. Gas is expected to cost $4.55 in 2025.
How to obtain the linear regression equation?The linear regression is obtained inserting the points of the table into a linear regression calculator.
The variables of the problem are given as follows:
Input x: number of years after 2002.Output y: cost of gas.Hence the points are given as follows:
(0, 0.7), (1,1.04), (2, 1.15), (3, 1.38), (4, 1.86), (5, 1.70), (6, 2.55), (7, 1.29), (8, 2.22), (9, 2.56).
Inserting these points into a calculator, the equation is given as follows:
y = 0.176x + 0.5.
The estimate for 2025 is the numeric value when x = 23, as 2025 is 23 years after 2002, hence:
y = 0.176(23) + 0.5 = $4.55.
The domain and the range are given as follows:
Domain: values of 0 and greater, representing the number of years after 2002.Range: values of 0.5 and greater, representing the costs.More can be learned about linear regression at https://brainly.com/question/29613968
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jogger runs around a circular track of radius 70 ft. let (x,y) be her coordinates, where the origin is the center of the track. when the jogger's coordinates are (42, 56), her x-coordinate is changing at a rate of 18 ft/s. find dy/dt.
The derivative dy/dt when the x coordinate's rate of change 18 feet is 13.5 feet.
Given,
The radius of the circular track in which the jogger runs = 70 feet
The coordinates of the jogger = (42, 56)
The rate of change in x coordinate = 18 feet/sec
Let (x,y) be the coordinates
We have to find dy/dt;
Then we know x,y satisfies the equation of the circle as
x² + y² = 70²
Let us differentiate this implicit function with respect to t
2x dx/dt + 2y dy/dt = 0
At this point, dx/dt 18 and x = 42. y = 56
Substitute to have
2 × 42 × 18 + 2 × 56 dy/dt = 0
1512 + 112 dy/dt = 0
dy/dt = 1512/112
dy/dt = 13.5 feet
Therefore,
The derivative dy/dt here is 13.5 feet
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Which best describes the location of A', the image of A
after a dilation by a factor of 1/2 with center at C?
c²
A' will be closer to A than to C
O A' will be half way between C and A
O A' will be closer to C than to A
C will be the midpoint of the line
connecting A and A'
'A
Answer:
1/c2
Step-by-step explanation:
On 2 May 2000, a man borrowed a sum of money from a bank at 6.5% p.a. simple interest and on 2 September 2000, the interest amounted to $137.50. Calculate the amount of money he borrowed.
The amount of money borrowed by the man from the bank on on 2 May 2000 is $6346.15.
Explain the term simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.The formula for calculating simple interest;
SI = P R T/100,
where
P stands for principal, R for rate of interest, and T for time period. Here, the rate (r%) is expressed as r/100, where r% is the percentage rate.In the case of simple interest, the principal is the amount of money that does not change over the course of a year.
Time = 4/12 year
For the given values-
137.50 = P × 6.5 × 4 /1200
P = 137.50 × 1200 / 6.5 × 4
P = $6346.15
Thus, the amount of money borrowed by the man from the bank on on 2 May 2000 is $6346.15.
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pretty please can someone answer this for me????? ty
The value of the function f(1)-f(-7) = -11
What is a function?A function from a set X to a set Y assigns to each element of X exactly one element of Y.
Given are a function,
For x = 1, take -x²-3x
f(1) = -1²-3 = -4
For x = -7, take |x+5|-9
f(-7) = |-7+5|-9 = -7
f(1)-f(-7) = -7-4 = -11
Hence, The value of the function f(1)-f(-7) = -11
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Before doing laundry, an unlucky student must recover from illness. The number of days the student is ill is determined as follows. We toss a fair coin and we roll a fair 6-sided die. If the coin is heads, the student is ill for n days, where n is the outcome of the die roll. If the coin is tails, the student is ill for 2n days, where n is the outcome of the die roll. What is Ex(u)? Example: If the die roll is 5, the student delays for U = 5 days if the coin toss is heads and U = 10 days if the coin toss is tails.
The student will be out of class for 2n days if the coin comes up tails, where n is the result of the die roll, which the probability will be 25.
An unfortunate student must recover from illness before washing laundry. The following formula is used to calculate the student's illness duration. We roll a fair 6-sided die and toss a fair coin. The student is absent from class for n days if the coin comes up heads, where n is the result of the die roll.
Ex(u) = (1/2)(1/6)*5+(1/2)(1/6)10+(1/2)(1/6)15+(1/2)(1/6)20 + (1/2)(1/6)25+(1/2)(1/6)*30
Probability = 25
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PLEASE FAST 20 POINTS
An octagon has 8 sides. One angle of a regular octagon measures (9w + 8)°. Determine the value of w. Round to the nearest whole number.
w = 19
w = 16
w = 14
w = 135
For the octagon whose measure of angle is (9w + 8)°, the value of w is 14.
What is angle?An angle is the formed when two straight lines meet at one point, it is denoted by θ.
Given that,
Angle of regular octagon = 9w + 8
Since, angle of an octagon is 135°
Equate 9w + 8 to 135,
9w + 8 = 135
9w = 127
w = 14.11
w = 14
The required value of w is 14.
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Answer:
he octagon whose measure of angle is (9w + 8)°, the value of w is 14.
Step-by-step explanation:
What is angle?
An angle is the formed when two straight lines meet at one point, it is denoted by θ.
Given that,
Angle of regular octagon = 9w + 8
Since, angle of an octagon is 135°
Equate 9w + 8 to 135,
9w + 8 = 135
9w = 127
w = 14.11
w = 14
The required value of w is 14.
i hope this helps !!!!!
1/2(x-8)+1=2(1/8x-1)
Answer:4
Step-by-step explanation:
distribute 1/2 into x-8 and distribute 2 into 1/8x-1 on other side
1/2x-4+1=1/4x-2
combine like terms
1/4x=1
multiply both sides by 4 to solve x
x=4
what is the additive inverse of -4x - 8
The additive inverse of (-4x - 8) is 4x+8.
What is Additive Inverse?
Additive inverse refers to any number that when added to the original number gives the result as zero. For instance, the additive inverse of 8 is -8 as 8 + (-8) = 0. It is possible to get the additive inverse of negative numbers too. For example, the additive inverse of -10 will be 10 as -10 + 10 = 0.
The additive inverse of any given number can be found by changing the sign of it. The additive inverse of a positive number will be a negative, whereas the additive inverse of a negative number will be positive. However, there will be no change in the numerical value except the sign. For example, the additive inverse of 8 is -8, whereas the additive inverse of -6 is 6.
The addition of a number and its additive inverse is equal to the additive identity.
we know that (-4x - 8) + (4x+8) = 0 .
Hence, The additive inverse of (-4x - 8) is 4x+8.
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(1 point) find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have distinct digits :
The number of positive integers with exactly four decimal digits that is positive integers between 1000 and 9999 is 4536.
The positive integers between 1000 and 9999 inclusive have 4 digits.
The first digit cannot be zero because otherwise, it will become a digit integer.
So, the first digit can be filled in 9 ways.
The second digit can be filled by 9 different ways.
Because the second digit cannot be the same as that of the first digit but zero can be the second digit.
The third digit can be filled by 8 different ways.
The fourth digit can be filled in 7 different ways.
Number of four decimals digits = 9 * 9 * 8 * 7
= 81 * 8 * 7
= 81 * 56
= 4536 digits.
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compare continuous functions f, g, and h, and match the statements with the function they best describe. drag each description to the correct location on the table. this function has the highest y-intercept.this function is increasing over the longest interval.this function is decreasing over the longest interval.this function has the lowest y-intercept.
From the given properties of the functions,
Function 'f' is decreasing in the longest interval [-0.8, 0.6]Lowest y-intercept → y = -1 (function g)Highest y-intercept → y = 3 (function h)Function 'h' in increasing in the longest interval → (-∞, ∞)Functions given in the picture are 'f', 'g' and 'h'.
From the graph given for function 'f',
y - intercept = 1
Increasing in the interval → (-∞, -0.8] and (0.6, ∞)
Decreasing in the interval → [-0.8, 0.6]
From the table given for the function 'g',
Decreasing in the interval → [-2, 2]
y-intercept = -1
For function 'h',
h(x) = 4x³ + 3
Table of the input-output values for function will be,
x h(x)
-2 -29
-1 -1
0 3
1 7
2 35
Therefore, function 'h' will increase in the interval → (-∞, ∞)
y-intercept → y = 3
Therefore, from these properties of the functions we conclude,
Function 'f' is decreasing in the longest interval [-0.8, 0.6]Lowest y-intercept → y = -1 (function g)Highest y-intercept → y = 3 (function h)Function 'h' in increasing in the longest interval → (-∞, ∞)To know more about Function check the below link:
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the weights of a certain dog breed are approximately normally distributed with a mean of 53 pounds, and a standard deviation of 6.2 pounds. use your graphing calculator to answer the following questions. write your answers in percent form. round your answers to the nearest tenth of a percent. a) find the percentage of dogs of this breed that weigh less than 53 pounds. % b) find the percentage of dogs of this breed that weigh less than 46 pounds. % c) find the percentage of dogs of this breed that weigh more than 46 pounds. %
(i) The percentage of dogs of this breed that weigh less than 53 pounds P(X<53) = 50.0%
(ii) The percentage of dogs of this breed that weigh less than 46 pounds P(X<46) = 15.2%
(iii) The percentage of dogs of this breed that weigh more than 46 pounds P(X>46) = 84.8%
What is Standard Deviation?
The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values. A low standard deviation implies that the values of the set tend to be near to the mean (also known as the expected value), whereas a high standard deviation shows that the values are spread out over a larger range.
Solution:
Mean weight (μ) = 53 pounds
Standard deviation (σ) = 6.2 pounds
The z-score for any given weight, 'X', is given by the following expression;
z = (X - μ)/σ
(i) P(X<53)
Since 53 pounds is exactly the mean weight, 50% of the dogs weight more than 53 pounds while 50% weight less than 53 pounds.
P(X<53) = 50.0%
(ii) P(X<46)
z = (46-53)/6.2
z = -1.12
this is equivalent to 15.2 percentile
P(X<46) = 15.2%
(iii) P(X>46)
P(X>46) = 100% - P(X<46) = 100% - 15.2%
P(X>46) = 84.8%
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Using the factor theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ?.
The polynomial (A) f(x)=x³-2x²-3x+6 has the zeros 2, radical 3, and negative radical 3 thanks to the factor theorem.
What is Factor Theorem?A factor theorem is a tool used in mathematics to thoroughly factor polynomials.
It is a theorem that connects the polynomial's zeros and factors.
The factor theorem states that (x-a) is a factor of f(x) if f(a)=0 and f(x) is a polynomial of degree n 1 and 'a' is any real number.
So, the Factor Theorem states that P(k) must equal zero if (x - k) is a factor of polynomial P(x).
A polynomial function with the zeros 2, 3, and -3 is provided to us. As a result, we can set k = 2, 3, -3.
The Factor Theorem states that P(2), P(3,) and P(-3) must all equal 0.
Tests of each option reveal that only option A is accurate:
f(x) = x³ – 2x² – 3x + 6
Testing each of the three results in:
[tex]\begin{aligned}f(2) & =(2)^3-2(2)^2-3(2)+6 \\& =(8)-(8)-(6)+(6) \\& =0 \stackrel{\checkmark}{=} 0 \\f(\sqrt{3}) & =(\sqrt{3})^3-2(\sqrt{3})^2-3(\sqrt{3})+6 \\& =(3 \sqrt{3})-(6)-(3 \sqrt{3})+6 \\& =0=0 \\f(-\sqrt{3}) & =(-\sqrt{3})^3-2(-\sqrt{3})^2-3(-\sqrt{3})+6 \\& =(-3 \sqrt{3})-(6)+(3 \sqrt{3})+6 \\& =0=0\end{aligned}[/tex]
Therefore, with the help of the factor theorem, polynomial (A) f(x)=x³-2x²-3x+6 has the zeros 2, radical 3, and negative radical 3.
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Complete question:
Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3, and negative radical 3?
a. f(x) = x3 – 2x2 – 3x + 6
b. f(x)= x3 – 2x2 + 3x + 6
c. f(x) = x3 + 2x2 – 3x + 6
d. f(x) = x3 + 2x2 – 3x – 6
f a circle has an area that is 225 pi square feet or more, what are the possible diameters d for the circle?
The diameter of the circle is 30 feet.
What is diameter?
The center of the circle is the midpoint of a line segment that connects two points on the circle's perimeter, and this line segment is indicated by the diameter of a circle.
The diameter of a circle is precisely equal to twice the radius' length.
Let us suppose the diameter of a circle is D then, the area is computed according to the formula
[tex]A = \frac{\pi D^2}{4}[/tex]
where
A is the area and D is the diameter.
Plug A = 225 pi in the above equation,
[tex]225 \pi =\frac{\pi D^2}{4} \\225 = \frac{D^2}{4} \\D^2 = 900\\D = 30[/tex]
Hence, the diameter of the circle is 30 feet.
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Pls help
, I really need an answer for this rn
Answer: 34.00 and 2.10
Step-by-step explanation:
b. suppose that the population mean waist size is 85 cm and that the population standard deviation is 15 cm. how likely is it that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm?
The average waist size of the population is 85 cm, and the standard deviation is 15 cm. then A sample mean waist size of at least 86.3 cm has a 0.931 probability of occurring.
We can use the Z-score formula to find the probability.
Z = (86.3 - 85) / (15 / sqrt(277))
Z = 0.2 / 0.106
Z = 1.89
The probability of a sample mean waist size of at least 86.3 cm is 0.931.
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(a) residents of a city have monthly incomes (in dollars) that are distributed around an unknown mean, with a standard deviation of 500 dollars. the incomes are recorded for a random sample of 36 residents. an average value of 1500 dollars is obtained. what is the 90%-confidence interval for the population mean estimate?
The 90% confidence interval for the population mean estimate is (1362.9167,1637.0833).
Given that,
n=36 residents
Standard deviation = 500 dollars
Mean u = 1500 dollars
X = 1500 dollars
(1-α)% = 90%
(1-α)= 0.9
α = 0.10
α/2 = 0.05
Z α/2 = Z 0.05
Z α/2 = 1.645
90%-confidence interval for the population mean estimate is
=X ± Z α/2 (σ/√n)
= 1500 ± (1.645)(500/√36)
=(1362.9167,1637.0833)
Therefore, the 90%-confidence interval for the population mean estimate is (1362.9167,1637.0833).
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the number 120 is increased by 50%, and the result is then decreased by 30% to give the number x. what is the value of x?
Answer:
x = 126
Step-by-step explanation:
1. 120 + 120(.50) = 180
2. 180 - 180(.30) = 126
PLEASE HELP!!!!
Suppose you are developing an Excel spreadsheet that finds the unit
price of any object. You plan to put the number of units in cell E2, and
the price of the object in cell D2.
What formula should you write in cell C2 to find the unit price?
The formula for D2 to be placed in order to find the unit price is D2 = B2/C2.
What is the unit price?
The average price of a product is calculated by dividing the total sales revenue by the total units sold. Managers must define "comparable" units when a single product is sold in variants, such as bottle sizes.
To find the unit price of an object, You divide the price by the Object. We need to find how much an object cost per unit.
Let, us consider an Example we have 50lbs of Kulfi (Object) that cost 8.00 dollars(price).
To find the Unit cost, We take the 8.00 and divide it by 50, which results in 0.16 cents per pound. We can check this by multiplying 0.16 by 50=8.00
So, Object= Number of units in cell = C2
Price of Object = B2
Unit Price Formula = D2
Therefore, by considering the above example.,
Object = C2 = 50
Price = B2 = 8.00
D2 Formula= Price of Object/ Number of Units
Therefore, The formula for D2 to be placed in order to find the unit price is D2 = B2/C2.
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8 baskets ?
16 movies = ————
?
How many movies will fit into 24
baskets?
Answer:
48 movies
Step-by-step explanation:
8/16=1/2
24/48=1/2
Help me please I’m begging and crying
Answer:
x=-12
Step-by-step explanation:
it would be -2=-x-14 then solve as normal algebraic equation
add 14 to each side 12=-x
then divide by -1 on each side so you get x=-12 for the final answer hope this helps
ANSWER PLSSSSSS
This scatter plot shows the number of magazines checked out and the number of books checked out.
Choose the statement that is best supported by the data in the scatter plot.
The data shows a negative linear association between the number of magazines checked out and the number of books checked out.
The data shows a negative linear association between the number of magazines checked out and the number of books checked out.
1The data shows a positive linear association between the number of magazines checked out and the number of books checked out.
2The data shows a positive linear association between the number of magazines checked out and the number of books checked out.
3The data shows a non-linear association between the number of magazines checked out and the number of books checked out.
4The data shows no apparent association between the number of magazines checked out and the number of books checked out.
The correct statement regarding the scatter plot is given as follows:
The data shows a negative linear association between the number of magazines checked out and the number of books checked out.
What is the scatter plot?The scatter plot, as shown by the image given at the end of the answer, is a series of points of the data-set in the following format:
(Number of books checked out, Number of magazines checked out).
From the graph, the points are given as follows:
(2,4), (3,6), (4,0), (4,2), (5,7), (6,5), (7,2), (9,1).
Inserting these points into a linear regression calculator, the line of best fit is given as follows:
y = -0.36x + 5.18
Which has a negative slope, meaning that it is a negative linear relationship and the first option is correct.
Missing InformationThe scatter plot is given by the image shown at the end of the answer.
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What is the value of x?
1/4 (6x - 2) = x - 2
Answer:
Step-by-step explanation:
0
Answer:
x = 3
Step-by-step explanation:
1/4 (6x - 2) = x - 2
1.5x - 0.5 = x - 2
1.5x = x - 1.5
0.5x = 1.5
x = 3
Could you please give me brainliest for this? Thank you!
A researcher is concerned about the level of knowledge possessed by university students regarding United States history. Students completed a high school senior level standardized U.S. history exam. Major for students was also recorded. Data in terms of percent correct is recorded below for 32 students. Compute the appropriate test for the data provided below.
Education Business/Management Behavioral/Social Science Fine Arts
62 72 42 80
81 49 52 57
75 63 31 87
58 68 80 64
67 39 22 28
48 79 71 29
26 40 68 62
36 15 76 45
Source SS df MS F
Between 63.25 3 21.0833333333 .04
Within 12298.25 28 439.2232143 Total 12361.5 31 What is your computed answer? F = .04 (3,28), not significant
What would be the null hypothesis in this study? There will be no difference in history test scores between students with different academic major.
What would be the alternate hypothesis? There will be a difference somewhere in history scores between the four groups with different academic major.
What probability level did you choose and why? p = .05 There is little risk involved if either a Type I or a Type II major is made.
What were your degrees of freedom? 3, 28
Is there a significant difference between the four testing conditions? No significant differences were found between the four groups in terms of performance on a U.S. history exam.
Interpret your answer. Students regardless of academic major performed equally (in this case poorly) on a high school senior standardized U.S. history exam.
If you have made an error, would it be a Type I or a Type II error? Explain your answer. If I have made an error, it would be a Type II error. There really is a difference in history knowledge between academic major but somehow I failed to demonstrate that with this study.
On solving the provided question, significant difference between the four testing conditions is α = 0.10
What does the term "alternative hypothesis" mean?An alternative hypothesis is one in which the researchers predict a difference (or an effect) between two or more variables, indicating that the observed pattern of the data is not the result of chance.
Null hypothesis: : μ1 ≥ μ2, There is no significant difference in history test scores between students with different academic major
Alternative Hypothesis: Ha : μ1 < μ2. Exam outcomes in history are substantially more varied among students with different academic specialties.
Determine the significance level. α = 0.10
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3) you roll a die 48 times with the following results. number 1 2 3 4 5 6 frequency 2 14 2 12 3 15 use a significance level of 0.05 to test the claim that the die is fair. use the p-value method. (a) set up the null hypothesis and alternative hypothesis and indicate the claim. (b) calculate the test statistic. be sure to set up the equation. round to three decimal places.
The claim to be indicated is that there is enough evidence to reject the null hypothesis and the test statistic would be 21.75
What do you understand by Hypothesis testing?A type of statistical inference called hypothesis testing uses data from a sample to make inferences about a population parameter or population probability distribution. The parameter or distribution is initially assumed in a preliminary manner. The null hypothesis is also known as H0, because it is the default assumption. Then, the opposite of what the null hypothesis claims is characterized as an alternative hypothesis (designated Ha). Using sample data, the hypothesis-testing technique determines whether or not H0 may be rejected. If H0 is rejected, the statistical inference is that the alternative hypothesis Ha is correct.
How to solve?
If the die is fair, the probability of getting any of the six numbers is equal (1/6).
The test statistic (TS) is given as:
TS=∑(Oi−Ei)2Ei∼χ2n−1
TS=(4−8)^2/8+(13−8)^2/8+…(2−8)^2/8
TS=21.75
In conclusion, the die is unfair.
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5. Find the value of x.
48
8x
Answer:
Step-by-step explanation:
try 6
Answer: 6
Step-by-step explanation: 6 x 8 = 48
how many ways are there to deal hands from a standard playing deck to four players if: (a) each player gets exactly 13 cards. (b) each player gets seven cards and the rest of the cards remain in the deck?
Th number of possible ways for
a) each player gets exactly 13 cards = 52! / (13! 13! 13! 13!)
b) each player gets seven cards and the rest of the cards remain in the deck = 52! / (7! 7! 7! 7! 24!)
In this question, we have been given that there are four players. the select cards from the standard deck of 52 cards.
We need to find the number of possible ways for given situations.
(a) each player gets exactly 13 cards.
Using combination, we get an expression,
^{52}C_13 * ^{39}C_13 * ^{26}C_13 * ^{13}C_13
= 52! / (13! 13! 13! 13!)
= 53644737765488792839237440000
(b) each player gets seven cards and the rest of the cards remain in the deck
Using combination, we get an expression,
^{52}C_7 * ^{45}C_7 * ^{38}C_7 * ^{31}C_7 * ^{24}C_24
= 52! / (7! 7! 7! 7! 24!)
Therefore, a) each player gets exactly 13 cards = 52! / (13! 13! 13! 13!)
b) each player gets seven cards and the rest of the cards remain in the deck = 52! / (7! 7! 7! 7! 24!)
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Y= -4 cos 5x -10 please answer this someone
The trigonometric function, Y = -4·cos 5·x - 10 is undefined at Y = 0, but the function arranged as Y = -4·cos(5·x - 10) has an x-intercept at x = π/10 + 2
What is a trigonometric function?A trigonometric function indicates the relationship between angles and the lengths of sides of angles.
The specified function can be presented as follows;
Y = -4·co(5·x) - 10
There are two unknown variables
The number of equations is one
The number of equations is less than the number of unknowns, the equation is said therefore, to be undetermined.The function, at Y = 0, can be evaluated as follows;
Y = 0 = -4·co(5·x) - 10
cos(5·x) = 10/(-4) = -2.5
5·x = arccos(-2.5) = Undefined
However, when the function is; Y = -4·cos((5·x) - 10), we get;
At Y = 0
0 = -4·cos((5·x) - 10)
cos((5·x) - 10) = 0/(-4) = 0
5·x - 10 = arccos(0) = π/2
Therefore;
x = (π/2 + 10)/5 = π/10 + 2
(-π/2 + 10)/5
An x-intercept is at x = π/10 + 2
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A company is producing picture frames as well as the glass for the front of the frames. The amount of wood required for the frame is represented by the function W(x), and the amount of glass is represented by the function G(x). The frames have lengths represented by the function f(x) and widths represented by g(x). Which statement describes the combined functions W(x) and G(x)? The amount of glass required has a constant rate of change, but the amount of wood does not. The amount of wood required has a constant rate of change, but the amount of glass does not. Both the amount of wood required and the amount of glass required have a constant rate of change. Neither the amount of wood required nor the amount of glass required has a constant rate of change.
The correct statement regarding the rate of change of the functions is given as follows:
The amount of wood required has a constant rate of change, but the amount of glass does not.
How to obtain the rate of change of the functions?The rate of change of a function is obtained as the change in the output of the function divided by the change in the input of the function.
For the wood function, we have that when x is increased by one, the output of the function W(x) is increased by 10, hence the rate of change is constant.
For the glass function, we have that:
When x increases by one from 2 to 3, the output G(x) increases by 21.When x increases by one from 3 to 4, the output G(x) increases by 33.Hence the rate of change is not constant, and then the second statement is the correct statement.
Missing InformationThe table is given by the image shown at the end of the answer.
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if you repeated the experiment with a glass of water that had 5 teaspoons of salt and another glass that had 10 teaspoons, what do you think would happen?
This procedure demonstrates that there is room between matter particles. The existence of salt ions is indicated by their accommodation in water.
1. When salt is dissolved in water, the chemical bond between the salt atoms is broken by the water molecule.
2. When a teaspoon of salt is added to water, the salt molecules fill any open places in the water. Since water is a fluid with atoms that may move around freely, when salt is dissolved in it, these open spaces are filled, making salt particles invisible.
3. The resulting solution becomes denser. The mass of the solution increases when salt is added to water. As a result, the solution's density rises.
4. This procedure demonstrates that there is room between matter particles. The existence of salt ions is indicated by their accommodation in water.
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