Answers
Answer:
(a) -2.3°/min
(b) -2.9°/min
Step-by-step explanation:
The average rate of change is the ratio of the difference in R values to the difference in the corresponding t values.
(a) m = (157.6 -226.6)/(30 -0) = -69/30 = -2.3 . . . degrees per minute
__
(b) m = (61.6 -119.6)/(70 -50) = -58/20 = -2.9 . . . degrees per minute
Related Questions
. A discount brokerage selected a random sample of 64 customers and reviewed the value of their accounts. The mean was $32,000 with a population standard deviation of $8,200. What is a 90% confidence interval for the mean account value of the population of customers
Answers
Answer:
The 90% confidence interval is [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 64
The sample mean is [tex]\= x = \$ 32, 000[/tex]
The standard deviation is [tex]\sigma= \$ 8, 200[/tex]
Given that the confidence interval is 90% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10 \%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table , the value is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{ \sqrt{n} }[/tex]
=> [tex]E = 1.645 * \frac{ 8200 }{ \sqrt{64} }[/tex]
=> [tex]E = 1686.13[/tex]
The 90% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]32000 - 1689.13 < \mu < 32000 + 1689.13[/tex]
=> [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]
Consider the following binomial experiment: A study in a certain community showed that 6% of the people suffer from insomnia. If there are 10,300 people in this community, what is the standard deviation of the number of people who suffer from insomnia?
Answers
Answer:
The standard deviation is [tex]\sigma = 24.10[/tex]
Step-by-step explanation:
From the question we are told that
The proportion of those that suffer from insomnia is p = 6% = 0.06
The sample size is n = 10300
Generally the proportion of those that do not suffer from insomnia is mathematically represented as
[tex]q = 1-p[/tex]
substituting values
[tex]q = 1 -0.06[/tex]
[tex]q = 0.94[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{n * p * q }[/tex]
substituting values
[tex]\sigma = \sqrt{ 10300 * 0.06 * 0.94 }[/tex]
[tex]\sigma = 24.10[/tex]
Using the binomial probability concept, the standard deviation of the number of people who suffer from insomnia is 24.10
Recall :
[tex] standard \: deviation, σ = \sqrt{n \times \: p \: (1 - p)} [/tex] p = probability of success = 6% = 0.061 - p = 1 - 0.06 = 0.94Sample size, n = 10300Substituting the values into the equation :
[tex] standard \: deviation, σ = \sqrt{10300 \times \: 0.06 \: (1 - 0.06)} [/tex]
[tex] standard \: deviation, σ = \sqrt{10300 \times \: 0.06 \: 0.94} [/tex]
[tex] standard \: deviation, σ = \sqrt{580.92} = 24.10[/tex]
Hence, the standard deviation is 24.10.
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An online polling site posed this question: "How much stock do you put in long-range weather forecasts?" Among its Web site users, 38, 528 chose to respond Complete parts (a) through (c) below.
a. Among the responses received, 3% answered with "a lot". What is the actual number of responses consisting of "a lot"?
b. Among the responses received, 18, 566 consisted of "very little or none". What percentage of responses consisted of "very little or none"?
c. Because the sample size of 38, 528 is so large, can we conclude that about 3% of the general population puts "a lot" of stock in long-range weather forecasts? Why or why not?
A. No, because the sample is a voluntary response sample, so the sample is not likely to be representative of the population.
B. Yes, because the sample is so large, the margin of error is negligible.
C. No, because even though the sample size is so large, there is still a margin of error.
D. Yes, because the sample size is large enough so that the sample is representative of the population.
Answers
Answer:
(a) 1155.84
(b) 48.2%
(c) D
Step-by-step explanation:
The number of total responses is, N = 38,528.
(a)
It is provided that 3% answered with "a lot".
Compute the actual number of responses consisting of "a lot" as follows:
n (a lot) = N × P (a lot)
= 38528 × 0.03
= 1155.84
Thus, the actual number of responses consisting of "a lot" is 1155.84.
(b)
The number of responses consisting of "very little or none" is,
n (very little or none) = 18,566
Compute the percentage of responses consisted of "very little or none" as follows:
[tex]P(\text{very little or none})=\frac{n(\text{very little or none})}{N}[/tex]
[tex]=\frac{18566}{38528}\\\\=0.481883\\\\\approx 0.482[/tex]
The percentage is: 0.482 × 100% = 48.2%.
Thus, the percentage of responses consisted of "very little or none" is 48.2%.
(c)
As the sample size increases the sample statistic value gets closer and closer to the actual population parameter value.
Thus, making the sample statistic an unbiased estimator of the population parameter.
And proving that the sample is a true representative of the population.
Thus, the correct option is (D).
When all possible differences between pairs of population means are evaluated not with an F test, but with a series of regular t tests, the probability of at least one:
Answers
Answer:
When all possible differences between pairs of population means are evaluated not with an F test, but with a series of regular t tests, the probability of at least one:
A. type I error is larger than the specified level of significance.
B. type II error is larger than the specified level of significance.
C. type I error is smaller than the specified level of significance.
D. type II error is smaller than the specified level of significance.
Answer : Type I error is larger than the specified level of significance.( A )
Step-by-step explanation:
An F test is a test that is used to test whether the variances between pairs of populations are equal while a T test is a test used to check if a pair of population are equal not considering the fact that the variances of the population are different .
When a T test is used to evaluate all possible differences between pairs of population instead of F test there is a probability of atleast one type 1 error larger than the specified level of significance.
simplify the following expression by combining like terms 2x+7x^2-5x+8x^2
Answers
Answer:15x^2-3x
Step-by-step explanation:
I have a circle that has a radius of 8 in. What is the circumference of the circle? What is the area of the circle? ( use 3.14 for pi).Explain your steps. Please Give A clear explanation The best answer gets brainliest.
Answers
Answer:
The circumference is 50.24 in. and the area is 200.96 in².
Step-by-step explanation:
The circumference formula is C = 2πr where C = Circumference, π = pi and r = radius. We know that r = 8 and π = 3.14 and that we're solving for C, so we can substitute those values into the equation to get C = 2 * 3.14 * 8 = 50.24 in.
The area formula is A = πr² where A = Area, π = pi and r = radius. Again, we're solving for A and we know that r = 8 and π = 3.14 so A = 3.14 * 8² = 3.14 * 64 = 200.96 in².
Answer:
The circumference is 50.24 in. and the area is 200.96 in².
Step-by-step explanation:
MARK SNOG AS BRAINLIEST
a scientist used 2 gallons of liquid for every 7 hours he works. he used__of a gallon each hour he works
Answers
Answer: 2/7 of a gallon (in decimal it’s 0.286)
Step-by-step explanation: This one’s really easy.
2/7 of 1 gallon. Checking: so that if you multiply it by 7 it equals to 2
The gallon he used each hour he works is 2/7.
What is unit rate?
A rate is a ratio that is used for comparing two different kinds of quantities which have different units. On the other hand, the unit rate illustrates how many units of quantity correspond to the single unit of another quantity.
The common examples used are:
Distance per second
Kilometer per hour
Meter per second
Earning per month
Given,
he used 2 gallons liquid for every 7 hours he works.
gallons used for per hour = 2/7
Hence, He used 2/7 gallons per hour.
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What is the value of (–7 + 3i) + (2 – 6i)?
a. –9 – 3i
b. –9 + 9i
c. –5 + 9i
d. –5 – 3i
Answers
Answer:
d
Step-by-step explanation:
(-7 + 3i) + (2-6i)
=-7 + 3i + 2 -6i
=(-7+2) + (3i -6i)
=-5 -3i
Answer:
(-7+3I)+(2-6I)
= -7+3i+2-6i
= -5-3I
so answer is d ie -5-3i
For this problem, use the tables and charts shown in this section. (Use picture provided)
A United States Citizen returning to the States declares the following items at the customs office:
3 shirts at $8.50 each
2 dresses at $27.50 each
1 pair of gold cuff links at $17.50 per pair
If he has not used his duty free exemption yet, how much duty should he pay?
0 $0.00
$5.00
$10.00
$300
Answers
Answer:
0
Step-by-step explanation:
0 because there is a $100 duty free exemption.
answer:
For this problem, use the tables and charts shown in this section.
A United States Citizen returning to the States declares the following items at the customs office:
3 shirts at $8.50 each
2 dresses at $27.50 each
1 pair of gold cuff links at $17.50 per pair
If he has not used his duty free exemption yet, how much duty should he pay?
$0.00 !
$5.00
$10.00
$300
If this first answers correct what is the answer to the second question? Are they even connected?
Answers
Answer:
see below (I hope this helps!)
Step-by-step explanation:
9) We know that the perimeters of the square and triangle are equal so to find x, we can write:
4(x - 5) = x + x + 12
4x - 20 = 2x + 12
2x = 32
x = 16
10) To find the perimeter, we can substitute x = 16 into 4(x - 5) which would be 4(16 - 5) = 4 * 11 = 44.
Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Foci: (±7, 0); major axis of length 18
Answers
Answer: [tex]\dfrac{x^2}{81}+\dfrac{y^2}{32}=1[/tex]
Step-by-step explanation:
The standard form of equation of ellipse with foci (±c,0) as:
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
, where major axis = 2a and minor axis = 2b
Given: Foci: (±7, 0); major axis of length 18
i.e. c= 7 and 2a =18 ⇒a= 9
Also,
[tex]c^2=a^2-b^2\Rightarrow\ b^2= a^2-c^2\\\\\Rightarrow\ b^2={9^2-7^2}={81-49}\\\\\Rightarrow\ b^2=32[/tex]
Put value of [tex]a^2[/tex] and [tex]b^2[/tex] , we get the required equation :
[tex]\dfrac{x^2}{81}+\dfrac{y^2}{32}=1[/tex]
PLEASE HELP!!! Sarah had a balance of $155 in her bank account at the start of the week. She withdrew $65.50 on Monday, $23.25 on Wednesday, and $26.45 on Thursday. On Friday she deposited $165.30. Write an expression that represents Sarah's spending. *
Answers
Answer:
155.00-65.50-23.25-26.45+165.30
Step-by-step explanation:
Answer:
155 + 165.3 - 65.5 - 23.25 - 26.45
Step-by-step explanation:
She had $155 dollars in the starting = +155
She withdrew $65.5 = -65.5
She withdrew another $23.25 = -23.25
She withdrew another $26.45 = -26.45
She deposited $165.3 = +165.3
The expression looks like:
155 + 165.3 - 65.5 - 23.25 - 26.45
We could solve the expression:
155 + 165.3 - 65.5 - 23.25 - 26.45
=> 320.3 - 88.75 - 26.45
=> 320.3 -115.2
=> 205.1
At the end of the week, she had a total of $205.10.
Spud's mom is going to make him a round birthday cake, and has asked for your help. Spud is a bit weird, and has already
announced that when he slices the cake, your slice will have a perimeter of 16 inches, because you're his favorite friend, and
that's his favorite number. Since you're helping his mom with the baking, what diameter cake will you recommend she makes
so that you end up with the most possible cake at weird Spud's party? (Hint: you can ignore the thickness of the cake, since
this will be the same, regardless of its diameter.)
Answers
Answer:
16 x 16 = 256
Step-by-step explanation:
So 256 might be the answer? this is confusing but are you on IXL?
Brainliest for the correct answer!! A calculator was used to perform a linear regression on the values in the table. The results are shown to the right of the table.What is the line of best fit?A.y = –0.984x + 13.5B.y = –2.9x + 13.5C.–0.984 = –2.9x + 13.5D.y = 13.5x – 2.9
Answers
Answer:
B. y = –2.9x + 13.5
Step-by-step explanation:
You can try to use the calculator to determine the best line for the values given; you will se that the calculator form, for the linear function is
y = a + bx, where a is the y intercept and b is the slope.
To determine the slope, we apply a formula, to calculate the product of the two xy and, x², plus the sum of each column.
x y xy x²
1 . 11 = 11 → x² = 1² = 1
2 . 8 = 16 → x² = 2² = 4
3 . 4 = 12 → x² = 3² = 9
4 . 1 = 4 → x² = 4² = 16
5 . 0 = 0 → x² = 5² = 25
Total x = 1 + 2 + 3 + 4 + 5 = 15
Total y = 11 + 8 + 4+ 1 + 0 = 24
Sum of xy = 11 + 16 + 12 + 4 + 0 = 43
Sum of x² = 1 + 4 + 9 + 16 + 25 = 55
n = 5
So b = 5 (43) - (15) . (24) / 5 (55) - 15² = -2.9
a = y media - b . x media → a = 24/5 - (-2.9) . 15/5 = 13.5
A plane is flying at the height of 5000 meter above the sea level. at a particular point, it is excatly above a submarine floating 1200 meter below the sea level. what is the vertical distance between them ?
Answers
Answer:
3800 meters
Step-by-step explanation:
How many faces does the polyhedron have? 3 5 6 9
Answers
Answer:
there are many types of polyhedron.
Basically about which one you want to know?
Step-by-step explanation:
Pentahydron. A polyhedron with 5 faces.
Hexahyderon. A polyhedron with 6 faces.
HeptahyderonA polyhedron with 7 faces.
Octahyderon. A polyhedron with 8 faces.
Similarly there are three more...
Please tell me if it was helpful to you.
If not, then ask me again..
22. f(x) is stretched horizontally by a factor of 2 and reflected across the x-axis. Which choice shows the correct representation of f(x) after these transformations?
Options:
A. –f(1/2x)
B. f(–2x)
C. –f(2x)
D. f(–1/2x)
Answers
Answer:
A. -f(1/2 x)
Step-by-step explanation:
Reflextion about the x-axis is
f(x) -> -f(x)
and horizontal dilation is
f(x) -> f(-x/b) where b is the factor of dilation.
so the proper answwer is
A. -f(1/2 x)
|3(x–2)|=12 pls help i need assistance
Answers
Answer:
x1 = -4
x2 = 6
Step-by-step explanation:
The 2 vertical lines are "absolute values" meaning whatever they contain has to be positive
For Example
|-3| = 3
So we can ignore if the answer we get is positive or negative because it will forced to be a positive
|3 x 4| = 12
|x - 2| = 4
x1 = 6
x2 = -2
a highschool basketball game won 36 percent of the games that it played last season the team won exactly 9 games last season what is the total number of games that the team played
Answers
Answer:
Total games played = 25
Step-by-step explanation:
Percentage games won by the basketball team = 36%
Exact number of games won by the team = 9
Let the total games played by the team = x
Therefore, total number of games won = 36% of x
= [tex]\frac{36}{100}\times x[/tex]
Equation which represents the games won by the team will be,
[tex]\frac{36}{100}\times x=9[/tex]
x = [tex]\frac{9}{0.36}[/tex]
x = 25
Therefore, total games played by the basketball team are 25.
Lisa built a rectangular flower garden that is 4 meters wide and has a perimeter of 26 meters.
What is the length of Lisa's flower garden?
Answers
Answer:
9 m
Step-by-step explanation:
Given that
Width of rectangular flower garden, w = 4 m
Perimeter of rectangular flower garden, p = 26 m
To find:
Length of Lisa's flower garden = ?
Solution:
First of all, let us understand perimeter, length and width of a rectangle.
Let ABCD be a rectangle. Please refer to the attached image.
Opposite sides of a rectangle are equal to each other.
AB = CD = Length
Let the length be [tex]l[/tex] m.
BC = DA = Width = 4 m
Perimeter of a closed image is equal to the sum of all the sides of the image.
So, perimeter of ABCD:
[tex]p = AB + BC + CD + DA \\\Rightarrow \bold{ p = 2 \times (Length +Width)}[/tex]
[tex]26 = 2 \times (l +4)\\\Rightarrow 2l =26-8\\\Rightarrow \bold{l = 9 m}[/tex]
Complete the statement to describe the expression abc+def
The expression consists of ____ terms,and each term contains___ factors
Answers
Answer:
3 each
Step-by-step explanation:
The answer is already on this site
rite
8x8*8X8X8 as
power
Answers
Answer:
8×8×8×8×8
= 8^5
because there are five 8 number
I hope this helps
if u have question let me know in comments ^_^
[tex]8\cdot8\cdot8\cdot8\cdot8=8^5[/tex]
Find the missing side of the triangle. A. √321 yd B. √221 yd C. 3√38 yd D. √21 yd
Answers
Answer:
(B) [tex]\sqrt{221}[/tex] yards
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean Theorem to find the length of x.
The Pythagorean Theorem states that [tex]a^2 + b^2 = c^2[/tex], where a and b are our legs and c is the hypotenuse.
We need to find c, and we already know a and b, so let's substitute.
[tex]10^2 + 11^2 = c^2\\\\100+121=c^2\\\\221=c^2\\\\c=\sqrt{221}[/tex]
Hope this helped!
A recent survey of 1090 U.S. adults selected at random showed that 623 consider the occupation of firefighter to have very great prestige. Estimate the probability (to the nearest hundredth) that a U.S. adult selected at random thinks the occupation of firefighter has very great prestige.
Answers
Answer:
0.572
Step-by-step explanation:
From the question,
We have
n = 1090 of US adults
x = 623 selected from this population at random who consider the occupation to be one of great prestige
So we have that
The probability of X = x/n
= 623/1090
= 0.572
We conclude that 0.572 is the probability that a US adult selected at random thinks the occupation has great prestige.
if b<0 and |b| = 4b+15 what is the value of b
Answers
Answer:
|b|= 4b+15
-b=4b+15
-b-4b= 15
-5b= 15
b= 15/-5
b= -3
the ans -3
If [tex]a<0[/tex] the [tex]|a|=-a[/tex]
So
[tex]|b|=4b+15\\-b=4b+15\\5b=-15\\b=-3[/tex]
You are conducting a hypothesis where the null reads H0: μ 10 You have Just concluded that you should fail to reject the null hypothesis because Z* 1.49 and Zc 1.645 Select the best conclusion statement.
A. There is overwhelming evidence that the mean is not 10.
B. There is not overwhelming evidence that the mean is different than 10.
C. Because the calculated value of Z was larger than the Zc, I rejected the null hypothesis
D. Because the Z* was only a little bigger than the Zc, the test supports the null hypothesis and we conclude u-10
Answers
Answer:
Option D - Because the Z* was only a little bigger than the Zc, the test supports the null hypothesis and we conclude μ = 10
Step-by-step explanation:
In z-value problems, the normal practice is that If the calculated z-value is less than the critical z-value, we will reject the null hypothesis and accept the alternative hypothesis but if it's greater than the critical z-value, we will fail to reject the null hypothesis and say that the test was not statistically significant.
In this problem, the calculated z-value of -1.49 is greater than -1.645, so we will fail to reject the null hypothesis and say that the test was not statistically significant.
Thus, in this question, we fail to reject the null hypothesis because the calculated value of z was bigger the value of z_c.
what is the magnitude of the vector?
Answers
Answer:
[tex]\boxed{\sqrt{65}}[/tex]
Step-by-step explanation:
Magnitude is solved with the following equation: [tex]\sqrt{x^{2}+y^{2}}[/tex]
Therefore, just plug in your x and y-values and solve.
[tex]\sqrt{4^{2}+7{^{2}}[/tex]
[tex]\sqrt{16 + 49}[/tex]
[tex]\sqrt{65}[/tex]
Because [tex]\bold{\sqrt{65}}[/tex] cannot be simplified further, this is the magnitude of the vector.
The SAT Reasoning Test (formerly called the Scholastic Aptitude Test) is perhaps the most widely used standardized test for college admissions in the United States. Scores are based on a normal distribution with a mean of 1500 and a standard deviation of 300. Clinton College would like to offer an honors scholarship to students who score in the top 10 percent of this test. What is the minimum score that qualifies for the scholarship?
Minimum Score:
Answers
Answer:
The score is [tex]x = 1884[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 1500[/tex]
The standard deviation is [tex]\sigma = 300[/tex]
From the question we are told that the score follow a normal distribution
i.e [tex]X \~ \ N( 1500 , 300)[/tex]
The proportion of score in the top 10% is mathematically
[tex]P(X > x ) = P( \frac{X - \mu}{\sigma } > \frac{x - \mu}{\sigma } ) = 0.10[/tex]
Where x is the minimum score required to be in the top 10%
Now the [tex]\frac{X - \mu}{\sigma } = Z (The \ Standardized \ value \ of \ X)[/tex]
So
[tex]P(X > x ) = P( Z > \frac{x - \mu}{\sigma } ) = 0.10[/tex]
So
[tex]P(X > x ) = P( Z > \frac{x - 1500}{300} ) = 0.10[/tex]
So the critical value of 0.10 from the normal distribution table is [tex]Z_{0.10} = 1.28[/tex]
So
[tex]\frac{x - 1500}{300} = 1.28[/tex]
[tex]x = 1884[/tex]
The circumference of a redwood tree trunk is 16π ft, and it is 100 ft tall. What is the approximate volume of the redwood tree trunk? 2,560π ft3 640π ft3 25,600π ft3 6,400π ft3
Answers
Answer:
volume of redwood tree is 6400 π ft^3(option 4)
Step-by-step explanation:
concept =
volume of cylinder = πr^2l
where r is the radius and l is the length of cylinder
circumference of cylinder = 2πr
_____________________________________
shape of redwood tree can be taken as cylindrical
given
circumference of a redwood tree trunk is 16π ft
2πr = 16π
=> r = 16π/2π = 8
Thus, radius is 8 feet
Therefore volume of redwood tree = πr^2l = π8^2*100 = π*64*100
volume of redwood tree =6400 π ft^3
Answer:
6,400π ft3
Step-by-step explanation:
took test and got it right
Your job in a company is to fill quart-size bottles of oil from a full -gallon oil tank. Then you are to pack quarts of oil in a case to ship to a store. How many full cases of oil can you get from a full -gallon tank of oil?
Answers
Answer:
See below.
Step-by-step explanation:
1 gal = 4 qt
With a full gallon oil tank, you can fill 4 1-qt bottles.
The problem does not mention the number of quarts that go in a case, so there is not enough information to answer the question.
Also, is the full tank really only 1 gallon, or is there a number missing there too?
