Answer:
The t-statistic that Jacob calculates is [tex]t = -2.71[/tex]
Step-by-step explanation:
Jacob knows that the adult population gets, on average, eight hours of sleep each night. A hypothesis test can help him see if college students are different from the adult population.
At the null hypothesis, we test if the mean is of 8 hours, that is:
[tex]H_0: \mu = 8[/tex]
At the alternative hypothesis, we test if the mean is different of 8 hours, that is:
[tex]H_1: \mu \neq 8[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
8 is tested at the null hypothesis:
This means that [tex]\mu = 8[/tex]
From a sample of 101 students, Jacob tabulated that his sample of students got an average of 7.3 hours of sleep each night, with a standard deviation of 2.6.
This means that [tex]n = 101, X = 7.3, s = 2.6[/tex]
What is the t-statistic that Jacob calculates?
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{7.3 - 8}{\frac{2.6}{\sqrt{101}}}[/tex]
[tex]t = -2.71[/tex]
The t-statistic that Jacob calculates is [tex]t = -2.71[/tex]
. A population of rabbits oscillates 25 above and below an average of 129 during the year, hitting the lowest value in January (t = 0). a. Find an equation for the population, P, in terms of the months since January, t. b. What if the lowest value of the rabbit population occurred in April instead?
Answer:
Because we know that here we have an oscillation, we can model this with a sine or cosine function.
P = A*cos(k*t) + M
where:
k is the frequency
A is the amplitude
M is the midline
We know that at t = 0, we have the lowest population.
We know that the mean is 129, so this is the midline.
We know that the population oscillates 25 above and below this midline,
And we know that for t = 0 we have the lowest population, so:
P = A*cos(k*0) + 129 = 129 - 25
P = A + 129 = 129 - 25
A = -25
So, for now, our equation is
P = -25*cos(k*t) + 129
Because this is a yearly period, we should expect to see the same thing for t = 12 (because there are 12 months in one year).
And remember that the period of a cosine function is 2*pi
Then:
k*12 = 2*pi
k = (2*pi)/12 = pi/6
Finally, the equation is:
P = -25*cos(t*pi/6) + 129
Now we want to find the lowest population was in April instead:
if January is t = 0, then:
February is t = 2
March is t = 3
April is t = 4
Then we would have that the minimum is at t = 4
If we want to still use a cosine equation, we need to use a phase p, such that now our equation is:
P = -25*cos(k*t + p) + 129
Such that:
cos(k*4 + p) = 1
Then:
k*4 + p = 0
p = -k*4
So our equation now is:
P = -25*cos(k*t - 4*k) + 129
And for the periodicity, after 12 months, in t = 4 + 12 = 16, we should have the same population.
Then, also remembering that the period of the cosine function is 2*pi:
k*12 - 4*k = 2*pi
k*8 = 2*pi
k = 2*pi/8 = pi/4
And remember that we got:
p = -4*k = -4*(pi/4) = -pi
Then the equation for the population in this case is:
P = -25*cos( t*pi/4 - pi) + 129
f(x) = 4x² + 3x - 2 g(x) = 6x³ - 3x²-4 Find (f +g) (x)
Answer:
6x^3+x^2+3x-6
Step-by-step explanation:
f(x) = 4x² + 3x - 2
g(x) = 6x³ - 3x²-4
(f +g) (x) =4x² + 3x - 2+6x³ - 3x²-4
Combine like terms
=6x^3+4x^2-3x^2+3x-2-4
=6x^3+x^2+3x-6
HELPPPPPPPPPPPPPPPP!!!
Which of the following is the product of the complex numbers below?
(6+ i)(2+91)
A. 3+56i
B. 3+52i
C. 21+56i
D. 21+52i
Answer:
It's answer is 93i +558....
PLEASE HELP ME PLEASE DUE IN 30 MINUTES
Answer:
x = 82.1º
Step-by-step explanation:
tan = opp/adj
tan75 = x/22
multiply both sides by 22
22 * tan75 = x
use calculator
82.1051177665153 = x
Rounded
x = 82.1º
The manufacturer claims the mean bursting pressure for a certain type and size of PVC irrigation pipe to be at least 350 psi. A sample of 10 such pipes were experimentally determined to have the following bursting pressures: 401 359 383 427 414 415 389 463 394 428 State the null and alternative hypotheses:
Answer:
H0 : μ ≥ 350
H1 : μ < 350
Step-by-step explanation:
It is claimed that the mean is atleast 350 psi ;
10 such pipes were experimentally sampled ;
Here, the null hypothesis is the claim ; this means that the alternative hypothesis will be the opposite of the claim.
The hypothesis
H0 : μ ≥ 350
H1 : μ < 350
What is the vertex of the quadratic function below?
(-4, 0)
There is no y-intercept
(0, -1)
(-2, 3)
Answer:
(-2, 3)
Step-by-step explanation:
Jim and his dad are building a rectangular flower bed. They have a total of 35 feet of landscaping timber to use, and they want to use all of it. However, they are not sure what width and length they want the flower bed to be. In this activity, you will write a function in which the width of the flower bed, w, is the input, and the length, l, is the output. The perimeter of a rectangle is given by the equation 2l + 2w = p.If the width of the flower bed is 15 feet, what is its length? Write your answer as an evaluation of a function.
Step-by-step explanation:
the answer is in the image above
Polygon ABCD is a rectangle. What is its area? Round your answer to the
nearest tenth.
(2,4)
(4,1)
(-4,0)
4
(-2, -3)
9514 1404 393
Answer:
26 square units
Step-by-step explanation:
Counting grid squares on the graph, we see that segment AB is the hypotenuse of a right triangle with legs 2 and 3. Its length is ...
AB = √(2²+3²) = √13
We can also see that the adjacent longer sides are twice this length, each being the hypotenuse of a triangle that is 6 wide and 4 high.
AC = √(6² +4²) = √52 = 2√13
Then the area is ...
A = LW
A = (2√13)(√13) = 2·13 = 26 . . . square units
Flying against the wind a jet travels 1590 miles in 3 hours flying with the wind the same jet travels 8240 miles in 8 hours. What is the rate of the j et in still air and what is the rate of the wind?
Answer: See explanation
Step-by-step explanation:
From the information given, the following can be deduced:
Let rate of jet in still air be J
Let rate of wind be W
The formula for distance:
d = rt
Therefore, r = d/t
When, flying against the wind, then the Jet flies at a rate of J - W which will be:
= 1590mi/3hrs
= 530mph
When flying with the wind the jet will fly at a rate of J+W which will be:
= 8240mi/8hrs
= 1030 mph
Their average rate will be:
J = (530+1030)/2
= 1560/2
J = 780 mph
Since J - W = 530
Therefore, so
780 - W = 530
W = 780 - 530
W = 250 mph
The Jet in still air flies at a rate of 780 mph and the wind speed is 250 mph
Use the Law of Sines to write an expression that represents the angle measure x.
Answer:
Step-by-step explanation:
Law of sines says that the length of sides are proportional to the sine of the opposing angle.
Using the sine rule,
sin(x)/2.5 = sin(28)/3
therefore
sin(x) = 2.5 * sin(28) / 3
or
here we have
x = asin (2.5*sin(28) / 3)
so
box 1 = 2.5
box 2 = 28°
box 3 = 3
Simplify the expression.
33 · 32 + 12 ÷ 4
Answer:
1059
Step-by-step explanation:
33 · 32 + 12 ÷ 4
PEMDAS
Multiply and divide first from left to right
1056 + 3
Then add
1059
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{33\times32+12\div4}\\\\\mathsf{33\times32= \boxed{\bf 1,056}}\\\\\mathsf{\bold{1,056}+12\div4}\\\\\mathsf{12\div4=\boxed{\bf 3}}\\\\\mathsf{1,056+\bf 3}\\\mathsf{= \boxed{\bf 1,059}}\\\\\\\boxed{\boxed{\large\textsf{Answer: \huge \bf 1,059}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite40:)}[/tex]
The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Weights of Dogs in Shelter A
2 box plots. The number line goes from 6 to 30. For the weights of dogs in shelter A, the whiskers range from 8 to 30, and the box ranges from 17 to 28. A line divides the box at 21. For shelter B, the whiskers range from 10 to 28, and the box ranges from 16 to 20. A line divides the box at 18.
Weights of Dogs in Shelter B
Which is true of the data in the box plots? Select three choices.
The median weight for shelter A is greater than that for shelter B.
The median weight for shelter B is greater than that for shelter A.
The data for shelter A are a symmetric data set.
The data for shelter B are a symmetric data set.
The interquartile range of shelter A is greater than the interquartile range of shelter B.
Answer:
The median weight for shelter A is greater than that for shelter B.
The data for shelter B are a symmetric data set.
The interquartile range of shelter A is greater than the interquartile range of shelter B.
Step-by-step explanation:
The median weight for shelter A is greater than that for shelter B.
The median of A = 21 and the median of B = 18 true
The median weight for shelter B is greater than that for shelter A.
The median of A = 21 and the median of B = 18 false
The data for shelter A are a symmetric data set.
False, looking at the box it is not symmetric
The data for shelter B are a symmetric data set.
true, looking at the box it is symmetric
The interquartile range of shelter A is greater than the interquartile range of shelter B.
IQR = 28 - 17 = 11 for A
IQR for B = 20 -16 = 4 True
The run scored in a cricket match by 11 players is as follows: 7, 16, 121, 51,101, 81, 1, 16, 9, 11, and 16. Find the mean of this data
HW HELP ASAP PLZZZZZ
Answer:
last step is (2x + 5)(2x + 1)
Step-by-step explanation:
4x^2 + 12x + 5
4x^2 + (10 + 2)x + 5
4x^2 + 10x + 2x + 5
2x(2x + 5) +1(2x + 5)
(2x + 5)(2x + 1)
calculate the surface area and show work :) please help me no links!!
Answer:
294 in.²
Step-by-step explanation:
I believe this figure is a rectangular prism.
------------------------------------------------------------------------------------
Explain:
To find the surface area of a rectangular prism, use this formula:
[tex]SA=2lw+2lh+2wh[/tex]
or
[tex]SA=2(lw+lh+wh)[/tex]
[tex]l-length[/tex]
[tex]w-width[/tex]
[tex]h-height[/tex]
A phrase I use to help remember this formula is:
LISA WILSON LOST HER WITCH HAT TWICE (2)
------------------------------------------------------------------------------------
Solve:
The length of this rectangular prism is 9 in.
This width is 10 in.
The height is 3 in.
Now, I will plug the numbers into the first formula.
[tex]SA=(2*9*10)+(2*9*3)+(2*10*3)=294 in.^2[/tex]
------------------------------------------------------------------------------------
Conclude:
I, therefore, believe the area of this rectangular prism is 294 in.²
In the triangle below, which is equivalent to sinA?
Right triangle A B C is shown. B is the right angle and side A C is the hypotenuse.
sinC
sinB
cosA
cosC
Answer:
CosC
Step-by-step explanation:
EDG
Solve this asap for me
Answer:
by using middle term break method
Step-by-step explanation:
9x^2 + 12x + 4
9x^2+ (6 + 6)x + 4
9x^2 + 6x + 6x + 4
3x(3x + 2) + 2(3x + 2)
(3x + 2)(3x + 2)
(3x + 2)^2
Which graph represents the solution set of the compound inequality -4 s 3x-1 and 2x+4 518?
-10
-5
0
10
O
+
-10
-5
0
5
10
5
-10
0
5
10
+
-10
-5
0
10
Answer:
it's the first one where X is greater or equals to -1 and X is less or equals to positive 7
The compound inequality in x : -1 ≤ x ≤ 7
The correct graph is A .
Given, inequality: -4 ≤ 3x -1 and 2x + 4 ≤ 18 .
First inequality:
-4 ≤ 3x -1
Take -2 from RHS to LHS .
-4 + 1 ≤ 3x
-3 ≤ 3x
x ≥ -1
X will have values greater than equal to -1 .
Second inequality:
2x + 4 ≤ 18
take 4 from LHS to RHS.
2x ≤ 18 - 4
2x ≤ 14
x ≤ 7
x will have values less than equals to 7.
Combined result of both inequalities: -1 ≤ x ≤ 7 .Thus graph A is correct.
Know more about inequality,
https://brainly.com/question/28823603
#SPJ3
5 > Chapter 2: Modeling with Quadratic Functions > Secti
Write an equation of the parabola in intercept form.
IN AY
х
-2.
(-1,0)
(2,0)
(1, -2)
-4
4
An equation of the parabola is y=0
Answer:
the awnser is 2,0
Step-by-step explanation:
Answer:
(1,-2) is the correct answer
Mrs. Brown, Mrs. White, and Mrs. Gray are a teacher, a doctor, and a lawyer, not necessarily in that order. Each has a horse. One horse is white, one is brown, and one is gray. From the following clues, determine the occupation of each woman and the color of her horse. No one’s name is the same as the color of her horse. The teacher owns a brown horse. Mrs. Gray is a doctor.
Answers:
Mrs. Brown ( lawyer ) owns the gray horse.Mrs. White ( teacher ) owns the brown horseMrs Gray ( doctor ) owns the white horse===========================================================
Explanation:
We're given these three clues
Clue 1: No one's name is the same as the color of her horseClue 2: The teacher owns a brown horseClue 3: Mrs. Gray is a doctor.Clue 3 is what we'll start with. Since Mrs. Gray is a doctor, this means that the doctor owns either a white horse or a brown horse. The doctor can't own a gray horse because the names can't match up (eg: the last name Gray with gray horse), due to clue 1.
If Mrs. Gray owned a brown horse, then she'd be a teacher (clue 2). But clue 3 says she's a doctor. We have a contradiction if Mrs. Gray owns the brown horse. Therefore, Mrs. Gray owns the white horse.
----------------
After we concluded the last section, we now know the following:
The horses that are left are the brown and gray horse.The professions left are the teacher and lawyer.The people left are Mrs. Brown and Mrs. White.In short, we've just crossed "Mrs. Gray", "doctor", and "white horse" from the list.
Based on clue 1, we know that Mrs. Brown cannot possibly own the brown horse. Therefore, she must own the gray horse. So Mrs. White must own the brown horse.
Since Mrs. White owns the brown horse, she must be the teacher (clue 2). That leaves "lawyer" as the last profession, and that's assigned to Mrs. Brown.
----------------
Side note: I apologize for being a bit wordy, but I wanted to be very careful in the logical sense as to approach this problem. There's probably a much quicker efficient way to do this.
Find the whole using the percent proportion. 70% of what number of hay bales is
63 hay bales?
Answer:
90
Step-by-step explanation:
Let the whole number be x.
100% is to x as 70% is to 63
100/x = 70/63
10/x = 10/9
10x = 90 * 10
x = 90
Answer: 90
Step-by-step explanation:
0.7x = 63, x = 63/0.7 = 90
What is the nearest quarter hour to 10:40
[tex]\Huge \bf \over \rightarrow\mid\mathcal {\underline{ \orange{12 \: : \: 00}}} \mid[/tex]
Answer:
I think 10:45 is the nearest quarter hour.
Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 8.1 minutes and a standard deviation of 2.0 minutes. For a randomly received emergency call, find the following probabilities.
a. between 5 and 10 min
b. less than 5 min
c. more than 10 min
Answer:
a) 0.7683 = 76.83% probability that a randomly selected emergency call is between 5 and 10 minutes.
b) 0.0606 = 6.06% probability that a randomly received emergency call is of less than 5 min.
c) 0.1711 = 17.11% probability that a randomly received emergency call is of more than 10 min.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 8.1 minutes and a standard deviation of 2.0 minutes.
This means that [tex]\mu = 8.1, \sigma = 2[/tex]
a. between 5 and 10 min
This is the p-value of Z when X = 10 subtracted by the p-value of Z when X = 5.
X = 10
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10 - 8.1}{2}[/tex]
[tex]Z = 0.95[/tex]
[tex]Z = 0.95[/tex] has a p-value of 0.8289
X = 5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 8.1}{2}[/tex]
[tex]Z = -1.55[/tex]
[tex]Z = -1.55[/tex] has a p-value of 0.0606
0.8289 - 0.0606 = 0.7683
0.7683 = 76.83% probability that a randomly selected emergency call is between 5 and 10 minutes.
b. less than 5 min
p-value of Z when X = 5, which, found from item a, is of 0.0606
0.0606 = 6.06% probability that a randomly received emergency call is of less than 5 min.
c. more than 10 min
1 subtracted by the p-value of Z when X = 10, which, from item a, is of 0.8289
1 - 0.8289 = 0.1711
0.1711 = 17.11% probability that a randomly received emergency call is of more than 10 min.
sum of 15,-2 and 7 is
Answer:
20
Step-by-step explanation:
15+(-2)+7=13+7=20
[tex]\longrightarrow{\blue{20}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]\:15 + ( - 2) + 7[/tex]
➺ [tex] \: 15 - 2 + 7[/tex]
➺ [tex] \: 22 - 2[/tex]
➺ [tex] \: 20[/tex]
Note:-[tex]\sf\pink{PEMDAS\: rule.}[/tex]
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
The sum of 5 times a number and -2, added to 8 times the number.
The algebraic expression (simplify your answer)
Step-by-step explanation:
sum of 5 times a number and -2, + 8n
becomes:
5n + (-2) + 8n, or
5n -2 +8n, or. 13n - 2
√25 + √ 81 = ? Heheeh
Answer:
14
Step-by-step explanation:
sqrt(25) = 5
sqrt(81) = 9
5 + 9 = 14
Answer:
5.83095189485
Step-by-step explanation:
Its so long
Find the degree measures of the next two positive and the previous two negative angles that are coterminal with the angle 75°.
The angles are:
9514 1404 393
Answer:
435°, 795°-285°, -645°Step-by-step explanation:
Add or subtract multiples of 360° to find coterminal angles.
Positive
75° +360° = 435°
75° +2×360° = 795°
Negative
75° -360° = -285°
75° -2×360° = -645°
VIVIAN: My friend Sharon told me today that she will be driving back to Victorville, her hometown, this weekend for the first time in almost two years. NATALIE: You must not have been listening very carefully to what Sharon was saying, because I know for sure that Sharon's hometown is Vacaville, not Victorville.
Is dispute C a verbal dispute or a factual dispute?
a. Factual
b. Verbal
Answer:
The answer is "Option a".
Step-by-step explanation:
Dispute C comes under factual dispute because the words Vacaville or Victorville are two different places and they are arguing about the fact that's why option a is correct.
► What is the mean of the following data set? 98, 208, 189, 94, 117
Answer:
mean of data is 141.2
Step-by-step explanation:
mean of data = sum of data / no of data
=98 + 208 + 189 + 94 + 117 / 5
=706 / 5
=141.2
Answer:
141.2Step-by-step explanation:
98 + 208 +189 +94 +1117 =709
706/5 = 141.2
Hope this helps!
The equation of the line passing through (2, 3) with a slope of 5 is y = [] x - []
what are the answers to []
Answer:
y = 5x - 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 5, then
y = 5x + c ← is the partial equation
To find c substitute (2, 3) into the partial equation
3 = 10 + c ⇒ c = 3 - 10 = - 7
y = 5x - 7 ← equation of line