Answer:
The slope is m=2.145.
The y-intercept is b=-1.33.
Step-by-step explanation:
We have this data:
- The mean and standard deviation for x are 5.43 and 1.12, respectively.
- The mean and standard deviation for y are 10.32 and 2.69, respectively.
- The correlation is 0.893.
We have to calculate the slope and the y-intercept of the least-squares line.
With the given data, we can calculate the slope m as:
[tex]m=r\;\dfrac{s_y}{s_x}=0.893\;\dfrac{2.69}{1.12}=2.145[/tex]
Then, the y-intercept is calculated as:
[tex]b=\bar y-m\cdot \bar x=10.32-2.145\cdot 5.43=10.32-11.65=-1.33[/tex]
what is the volume of a cone with a radius of 3 and a height of 17
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▹ Answer
V ≈ 160.22
▹ Step-by-Step Explanation
V = πr²[tex]\frac{h}{3}[/tex]
V = π3²[tex]\frac{17}{3}[/tex]
V ≈ 160.22
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
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When exchanging US Dollars (USD) for Philippine Peso (PHP) the number of Philippine Pesos received is directly proportional to the number of US Dollars to be exchanged. If 550 USD can be converted into 24,334.75 PHP.
Find the constant of proportionality k.
k= ______ (If needed, round answer to 3 decimal places.)
Using the k from above find the amount of PHP given that you have 900 USD to convert. You will receive ________ PHP (If needed, round answer to 2 decimal places.)
Answer:
(a)k=44.245
(b)39820.50 PHP
Step-by-step explanation:
Part A
Let the number of PHP =y
Let the number of USD =x
The number of Philippine Pesos(y) received is directly proportional to the number of US Dollars(x) to be exchanged.
The equation of proportion is: y=kx
If 550 USD can be converted into 24,334.75 PHP.
x=550y=24,334.75Substitution into y=kx gives:
[tex]24,334.75=550k\\$Divide both sides by 550$\\k=24,334.75 \div 550\\k=44.245[/tex]
The constant of proportionality k=44.245
Part B
The equation connecting y and x then becomes:
y=44.245x
If x=900 USD
Then:
y=44.245 X 900
y= 39820.50
Therefore, given that you have 900 USD to convert. You will receive 39820.50 PHP
Which best describes the circumference of a circle?
Answer: A
Step-by-step explanation: A diameter is 2 times a circumference, and so a diameter is a line crossing through the center of a circle, since we know that, a circumference is just half of that, just half the center in the middle of a circle to the edge of a point on a circle.
5. In the figure below, triangles CPW and
BHM are congruent. Which statement must be true?
Answer:
C. side CW ≅ side BM,
Step-by-step explanation:
When two triangles are said to be congruent, it means they have the same shape and size. This implies that their corresponding sides and corresponding angles are equal.
Therefore, given that triangles CPW and BHM are congruent, their corresponding sides should be equal.
Thus, the statement side CW ≅ side BM, must be true.
Other statements given are not true.
You want to be able to withdraw $4000 a month for 30 years how much would you need to have in your account with an APR of 3.4% to accomplish this goal
Answer:
$904,510.28
Step-by-step explanation:
If we assume the withdrawals are at the beginning of the month, we can use the annuity-due formula.
P = A(1 +r/n)(1 -(1 +r/n)^(-nt))/(r/n)
where r is the APR, n is the number of times interest is compounded per year (12), A is the amount withdrawn, and t is the number of years.
Filling in your values, we have ...
P = $4000(1 +.034/12)(1 -(1 +.034/12)^(-12·30))/(.034/12)
P = $904,510.28
You need to have $904,510.28 in your account when you begin withdrawals.
Answer:
You need to have $904,510.28 in your account when you begin
help please please i give bralienst don't need to explain just put the number
Answer:
487 ÷ 14
Hope that helps.
Identify the triangle that contains an acute angle for which the sine and cosine ratios are equal. Triangle A B C has angle measures 50 degrees, 40 degrees, and 90 degrees. Triangle A B C has angle measures 45 degrees, 45 degrees, 90 degrees. The lengths of sides A C and C B are congruent. Triangle A B C has angle measures 68 degrees, 22 degrees, and 90 degrees. Triangle A B C has angle measures 60 degrees, 30 degrees, and 90 degrees.
Answer:
The sine and cosine are equal for 45 degrees.
Choose the triangle that has a 45-deg angle.
Answer:
Answer is the second choice
Step-by-step explanation:
jut did it on edge
hi i will give 50 POINTS and BRAINLIEST to whoever answers this question
Answer:
[tex]Area \ of \ Triangle = 152.46 \ m^2[/tex]
Step-by-step explanation:
[tex]Area \ of \ Triangle = \frac{1}{2} (Base)(Height)\\Where \ base = 23.1 \ m\ and \ Height = 13.2 m\\Area \ of \ triangle = \frac{1}{2} (23.1)(13.2)\\Area \ of \ triangle = \frac{304.92}{2}[/tex]
[tex]Area \ of \ Triangle = 152.46 \ m^2[/tex]
P.s. Don't lie about points
Step-by-step explanation:
ea of Triangle=152.46 m2
Step-by-step explanation:
\begin{gathered}Area \ of \ Triangle = \frac{1}{2} (Base)(Height)\\Where \ base = 23.1 \ m\ and \ Height = 13.2 m\\Area \ of \ triangle = \frac{1}{2} (23.1)(13.2)\\Area \ of \ triangle = \frac{304.92}{2}\end{gathered}Area of Triangle=21(Base)(Height)Where base=23.1 m and Height=13.2mArea of triangle=21(23.1)(13.2)Area of triangle=2304.92
Area \ of \ Triangle = 152.46 \ m^2Area of Triangle=152.46 m2
P.s. Don't lie about points
Determine the logarithmic regression of the data below using either a calculator or spreadsheet program. Then, estimate the y value when the x value is 45. Round your answer to one decimal place. (5,6),(10,15),(15,25),(20,27),(25,29),(30,30) Please help right away. I am doing something wrong with my calculations that I got 76.4 and that is not the answer! Again thank you so much!
Answer:
y = - 16.1779 + 14.1087*In(x)
y = 37.5
Step-by-step explanation:
Given the data:
X:5,10,15,20,25,30
Y:6,15,25,27,29,30
General form of a logarithmic fuction:
y = A + BIn(x)
Using the logarithmic regression calculator :
The logarithmic regression model is :
y = - 16.1779 + 14.1087*In(x)
The estimated value of y when x = 45
y = - 16.1779 + 14.1087*In(45)
y = - 16.1779 + 14.1087*3.8066624
y = - 16.1779 + 53.707059
y = 37.529159
y = 37.5
What is the sqr root of x times the sqr root of x?
Answer:
Just x
Step-by-step explanation:
√x times √x equals √x²
√x² = x
A running coach wants to know if participating in weekly running clubs significantly improves the time to run a mile. The running coach collects mean mile times for 42 runners who participate in weekly running clubs with 54 runners who do not run in clubs. The running coach measures times in January and June of the same year. All times are in seconds, and the runners all started with mile times between 8 minutes (480 seconds) and 9 minutes (540 seconds). Here are the results:
January June Change
Mean (seconds) StDev (seconds) Mean (seconds) StDev (seconds) Mean (seconds) StDev (seconds)
Running Club N = 42 530 28 520 23 10 4
Not in a Club N = 54 527 25 519 22 8 3
What is the best method for the running coach to use to determine if participating in weekly running clubs significantly improves the time to run a mile?
A) Use the difference in sample means (530 – 520) in a hypothesis test for a difference in two population means.
B) Use the difference in sample means (10 and 8) in a hypothesis test for a difference in two population means.
C) Use the sample mean 10 in a hypothesis test for a population mean.
Answer:
Option B is correct.
Use the difference in sample means (10 and 8) in a hypothesis test for a difference in two population means.
Step-by-step Explanation:
The clear, complete table For this question is presented in the attached image to this solution.
It should be noted that For this question, the running coach wants to test if participating in weekly running clubs significantly improves the time to run a mile.
In the data setup, the mean time to run a mile in January for those that participate in weekly running clubs and those that do not was provided.
The mean time to run a mile in June too is provided for those that participate in weekly running clubs and those that do not.
Then the difference in the mean time to run a mile in January and June for the two classes (those that participate in weekly running clubs and those that do not) is also provided.
Since, the aim of the running coach is to test if participating in weekly running clubs significantly improves the time to run a mile, so, it is logical that it is the improvements in running times for the two groups that should be compared.
Hence, we should use the difference in sample means (10 and 8) in a hypothesis test for a difference in two population means.
Hope this Helps!!!
ga political candidate has asked you to conduct a poll to determine what percentage of people support her. if the candidate only wants a 8% margin of error at a 95% cnofidence level, what size of sample is needed
Answer: 151
Step-by-step explanation:
if prior population proportion is unknown , then the formula is used to find the sample size :
[tex]n=0.25(\frac{z_{\alpha/2}}{E})^2[/tex]
, where [tex]z_{\alpha/2}[/tex] = Two tailed critical value for significance level of [tex]\alpha.[/tex]
E = Margin of error.
Given : margin of error = 8%= .08
For 95% confidence level , two tailed critical value = 1.96
Now, the required sample size :
[tex]n=0.25(\frac{1.96}{0.08})^2\\\\=0.25(24.5)^2\\\\=150.0625\approx151[/tex]
Hence, the size of the sample needed = 151.
1
Find the distance between (-2,3) and
(4,-1). * m
(1 Point)
Answer:
so the distance between two points is (2√13)
Step-by-step explanation:
we have to find the distance between two points
d=√(x2-x1)²+(y2-y1)²
putting the values of coordinates
d=√(4--2)²+(-1-3)²
d=√(6)²+(-4)²
d=√36+16
d=√52
d=2√13
i hope this will help you :)
A daffodil grows 0.05m every day. Plot the growth of the flower if the initial length of the daffodil is 0.8m and hence give the length of the daffodil on the 8th day.
Answer:
1.2m
Step-by-step explanation:
You must first find out how much the daffodil grew over the 8 days:
0.05 x 8 = 0.4
Then you must add how much it grew to the original height:
0.4 + 0.8 = 1.2
Hope this helps you out! : )
the length of the daffodil on the 8th day is 1.2m.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
A daffodil grows 0.05m every day.
the initial length of the daffodil is 0.8m.
You must first find out how much the daffodil grew over the 8 days:
0.05 x 8 = 0.4
Then you must add how much it grew to the original height:
0.4 + 0.8 = 1.2
hence, the length of the daffodil on the 8th day is 1.2m.
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The number of hours worked per year per person in a state is normally distributed with a standard deviation of 39. A sample of 15 people is selected at random, and the number of hours worked per year per person is given below. Calculate the 98% confidence interval for the mean hours worked per year in this state. Round your answers to the nearest integer and use ascending order.Time205120612162216721692171218021832186219521962198220522102211
Answer:
[tex]2169.67-2.624\frac{48.72}{\sqrt{15}}=2136.66[/tex]
[tex]2169.67+2.624\frac{48.72}{\sqrt{15}}=2202.68[/tex]
And the confidence interval would be given by (2137, 2203)
Step-by-step explanation:
2051 ,2061 ,2162 ,2167 , 2169 ,2171 , 2180 , 2183 , 2186 , 2195 , 2196 , 2198 , 2205 , 2210 ,2211
We can calculate the mean and deviation with these formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
And we got:
[tex]\bar X=2169.67[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean
s=48.72 represent the sample standard deviation
n=15 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=15-1=14[/tex]
Since the Confidence is 0.98 or 98%, the significance is [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and using excel we calculate the critical value [tex]t_{\alpha/2}=2.624[/tex]
Now we have everything in order to replace into formula (1):
[tex]2169.67-2.624\frac{48.72}{\sqrt{15}}=2136.66[/tex]
[tex]2169.67+2.624\frac{48.72}{\sqrt{15}}=2202.68[/tex]
And the confidence interval would be given by (2137, 2203)
I need help on question 9.
Answer: C) 40 degrees
Step-by-step explanation:
if the total angle is 70 degrees and part of it is 30 degrees
then the other part is x degrees
30 + x = 70
30 - 30 + x = 70 - 30
x= 40
Hope this helped!
<!> Brainliest is appreciated! <!>
Factorize: [tex]x^2-2x-35=0[/tex]
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▹ Answer
x₁ = -5
x₂ = 7
▹ Step-by-Step Explanation
x² - 2x - 35 = 0
x² + 5x - 7x - 35 = 0
x(x + 5) - 7x - 35 = 0
x(x + 5) - 7(x + 5) = 0
(x + 5)(x - 7) = 0
x + 5 = 0 → 0 - 5 = -5
x - 7 = 0 → 0 + 7 = 7
x₁ = -5
x₂ = 7
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
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Answer:
X = -5 X = 7Step-by-step explanation:
[tex] {x}^{2} - 2x - 35 = 0[/tex]
Write -2x as a difference
[tex] {x}^{2} + 5x - 7x - 35 = 0[/tex]
Factor out X from the expression
[tex]x(x + 5) - 7x - 35 = 0[/tex]
Factor out -7 from the expression
[tex]x(x + 5) - 7(x + 5) = 0[/tex]
Factor out x+5 from the expression
[tex](x + 5)(x - 7) = 0[/tex]
When the product of factors equals to 0, at least one factor is 0
[tex]x + 5 = 0[/tex]
[tex]x - 7 = 0[/tex]
Either,
[tex]x + 5 = 0[/tex]
[tex]x = 0 - 5[/tex]
[tex]x = - 5[/tex]
Or,
[tex]x - 7 = 0[/tex]
[tex]x = 0 + 7[/tex]
[tex]x = 7[/tex]
Hope this helps...
Best regards!!
What is 2x-y=6 converted to slope intercept form
Answer:
y = 2x - 6
Explanation:
* note
the equation provided is written in standard form.
· standard form → Ax + By = C
· slope-intercept form → y = mx + b
To convert the given equation to slope-intercept form, start by subtracting '2x' from both sides of the equation. This will move 'y' to the left side of the equation.
2x - y = 6
2x - 2x - y = 6 - 2x
-y = -2x + 6
Next, multiply both sides of the equation by negative one.
-y = -2x + 6
(-y × -1) = (-2x × -1) + (6 × -1)
y = 2x - 6
Therefore, the given equation should be y = 2x - 6 when converted to slope-intercept form.
The equation is in slope-intercept form, y = 2x - 6, where the slope (m) is 2 and the y-intercept (b) is -6.
Given is an equation of a line we need to convert it into slope-intercept form,
To convert the equation 2x - y = 6 to slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept, we need to isolate the "y" variable on one side of the equation.
Starting with the given equation:
2x - y = 6
Move the 2x term to the right side by adding "y" to both sides:
2x = y + 6
Rearrange the equation by swapping the sides:
y + 6 = 2x
Move the constant term (6) to the right side by subtracting 6 from both sides:
y = 2x - 6
Hence the equation is in slope-intercept form, y = 2x - 6, where the slope (m) is 2 and the y-intercept (b) is -6.
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Which monomial is a perfect cube? I I A 1x3 B 3x3 C 6x3 D 9x3
Answer:
option D 9x³
Step-by-step explanation:
the monomial 9x³ comes from (3x)³, which gives, 3×3×3×x×x×x= 9x³
9 is 3 times 3 and x³ is 3 times x. So here, 9x³ is a perfect cube
What is the length of Line segment B C?
11
23
40
60
Answer:
40
Step-by-step explanation:
An isosceles triangle is a triangle that has 2 congruent/equal sides and 2 congruent angles.
Side AB and side BC are the same length (the red tick marks shows that the sides are congruent)
Since they are the same length, you can set them equal to each other
Side AB = Side BC
x + 17 = 2x - 6 Subtract x on both sides
17 = x - 6 Add 6 on both sides
23 = x
Now that you know "x", you can find the length of Side BC:
2x - 6 Plug in 23 for "x"
2(23) - 6
46 - 6 = 40
Answer:
Yes, the answer is C! (40)
Find the domain and range of a function defined by a graph
Question
Use the graph of the function to find its domain and range. Write the domain and range in interval notation.
Answer: domain (-2, 3] range [-2, 2)
These are the x-values left to right the paretheses ( ) indicates "not equal to" a bracket [ ]
Step-by-step explanation: Domains are the x-values left to right the parentheses ( ) indicates "not equal to" like the open circle on the graph; a bracket [ ] means "and equal to" like the solid circke on the graphed line.
Range means the y-values, bottom to top (least to greatest in math lingo)
Consider a comparison of two models. The "complete" model has both curvature and interaction. The "reduced" model has curvature, but no interaction. You compare the two models using a nested (subset) F-test and determine that you should "reject H0 ". True or False: The reduced model fits the data better than the complete model. Group of answer choicesTrueFalse
Answer:
True
Step-by-step explanation:
The reduced model and complete are the two models that can be used to determine test the hypothesis. The best way to determine which model fits the data set is to determine the F-test. The Full model is unrestricted model whereas reduced model is restricted model. F-test determines which model to choose for hypothesis testing for better and accurate results.
Hippocrates magazine states that 32 percent of all Americans take multiple vitamins regularly. Suppose a researcher surveyed 750 people to test this claim and found that 261 did regularly take a multiple vitamin. Is this sufficient evidence to conclude that the actual percentage is different from 32% at the 5% significance level?
Select the [p-value, Decision to Reject (RHo) or Failure to Reject (FRHo)1.
a) [p-value = 0.069, FRHI
b) [p-value = 0.009, RH01
c) [p-value = 0.009, FRHol
d) [p-value = 0.019, FRH)]
e) [p-value = 0.019, RHo]
Answer:
Step-by-step explanation:
We would set up the hypothesis test.
For the null hypothesis,
p = 0.32
For the alternative hypothesis,
p ≠ 0.32
This is a two tailed test
Considering the population proportion, probability of success, p = 0.32
q = probability of failure = 1 - p
q = 1 - 0.32 = 0.68
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 261
n = number of samples = 750
P = 261/750 = 0.35
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.35 - 0.32)/√(0.32 × 0.68)/750 = 1.8
Recall, population proportion, p = 0.32
The difference between sample proportion and population proportion(P - p) is 0.35 - 0.32 = 0.03
Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.32 - 0.03 = 0.29
the p for the right tail is 0.32 + 0.03 = 0.35
These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area
From the normal distribution table, the area above the z score in the right tail 1 - 0.9641 = 0.0359
We would double this area to include the area in the right tail of z = 0.44 Thus
p = 0.0359 × 2 = 0.07
Since alpha, 0.05 < the p value, 0.07 then we would fail to reject the null hypothesis. Therefore, this is not sufficient evidence to conclude that the actual percentage is different from 32% at the 5% significance level.
John had $800 Tasha has $500 Kyle had $300 Who had the most money.
Answer:
Step-by-step explanation:Josh
By comparing the given numbers, Jhon had most money.
How to compare integers?As you move to the right on the number line, integers get larger in value. As you move to the left on the number line, integers get smaller in value.
The rules of the ordering and the comparing of the integers are given below:
If we compare numbers with different signs, then the negative number is less than positive.If numbers are both positive, then this is the case when we compare whole numbers.If numbers are both negative, then we compare numbers without signs. The bigger is the positive number; the smaller is its corresponding negative number.Given that, John had $800 Tasha has $500 Kyle had $300.
Here, 300<500<800
Therefore, by comparing the given numbers, Jhon had most money.
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find the value of x...
Answer:
x = 7
Step-by-step explanation:
This problem can be solved using angular bisector theorem.
It states that if any angle of triangle is bisected by a line , then that line
divides the opposite side of that angle in same proportion as that of two other sides which contain the angle.
__________________________________
Here one angle is is divided into parts theta
Thus,
using angular bisector theorem
14/21 = 6/3x-12
=> 14(3x-12) = 21*6
=> 3x-12 = 21*6/14 = 9
=> 3x = 12+9 = 21
=> x = 21/3 = 7
Thus, x = 7
Want Brainliest? Get this correct. Which of the following is the product of the rational expressions shown below?i
Answer:
C.
Step-by-step explanation:
First, "flip" the second term and change the sign to multiplication. Thus:
[tex]\frac{2x^3}{x+5} \cdot \frac{3x-1}{x-5}[/tex].
Now, multiply straight across:
[tex]=\frac{(2x^3)(3x-1)}{(x+5)(x-5)}[/tex]
Expand:
[tex]\frac{6x^4-2x^3}{x^2-25}[/tex]
C.
The angles in a triangle are such that one angle is 30 degrees more than the smallest angle while the third angle is four times as large as the smallest angle find the measure are of all three angles
Answer:
25, 55, 100
Step-by-step explanation:
Let's call the smallest angle x, therefore the other two angles would be x + 30 and 4x. Since the sum of angles in a triangle is 180° we can write:
x + x + 30 + 4x = 180
6x + 30 = 180
6x = 150
x = 25°
x + 30 = 25 + 30 = 55°
4x = 25 * 4 = 100°
The sum of angles is 180.
[tex] \alpha + \beta + \gamma = 180 [/tex]
[tex] \alpha + ( \alpha + 30) + (4 \alpha ) = 180[/tex]
[tex]6 \alpha = 150[/tex]
[tex] \alpha = 25 \\ \beta= 25+30=55 \\ \gamma= 4.25 =100[/tex]
Rocco is trying to find the fraction that is equivalent to the decimal 0.012. His work is shown below. Step 1: 0.012 = StartFraction 12 over 100 EndFraction Step 2: StartFraction 12 over 100 EndFraction equals StartFraction 3 over 25 EndFraction Step 3: Therefore 0.012 = StartFraction 3 over 25 EndFraction. What did Rocco do wrong? Rocco should have divided 12 by 100 in Step 2. Rocco wrote the equivalent fraction in Step 1 incorrectly. Rocco forgot to reduce the numerator when he reduced the denominator in Step 2. Rocco should have divided both the numerator and denominator by 2, not
Answer:
(B)Rocco wrote the equivalent fraction in Step 1 incorrectly.
Step-by-step explanation:
In trying to find the fraction equivalent of 0.012, Rocco's work is shown below:
Step 1: 0.012 = [tex]\dfrac{12}{100}[/tex]
Step 2: [tex]\dfrac{12}{100}=\dfrac{3}{25}[/tex]
Step 3: Therefore 0.012 [tex]=\dfrac{3}{25}[/tex]
Observe that in Step 1, Rocco wrote the equivalent fraction incorrectly.
Correctly: 0.012 = [tex]\dfrac{12}{1000}[/tex]
The correct answer is B.
Answer:
The correct answer would be number B. Hope this helps!
Step-by-step explanation:
Need help withGraph a circle
Step-by-step explanation:
The equation of this circle is:
(x-3)^2 +(y+5)^2 = 16
The equatiin of a circle in general is:
(x-a)^2 +(y-b)^2 = r^2
a and b are the coordinates of the center and r is the radius
● in the given equation: (x-3)^2 + (y+5)^2 = 16
-3 and 5 are the coordinates if the center so start by ploting the center in the point (-3,5)
16 is the radius multiplied by itself
16 is 4×4 so the radius is 4
Take a four unit radius from the center and strat drawing your circle using a compass
On a temperature versus time graph, how does the temperature at the beginning of a change of state compare with the temperature at the end of the change? always lower always the same usually lower usually higher
Answer:
Always the same
Step-by-step explanation:
The temperature at the beginning of a change of state is always the same as the temperature at the end.
This is because phase change is an isothermal process. it means that all the energy absorbed during the phase change process is utilized in the breaking of the bonds in the compound as it changes from one state of matter to another.
As a result, no increase in the temperature of the material will be detected by the thermometer.