Answer:
[tex] 25.5 -3.3= 22.2[/tex]
[tex] 25.5 +3.3= 28.8[/tex]
And the confidence interval would be given by: [tex] 22.2\leq \mu \leq 28.8[/tex]
Step-by-step explanation:
[tex]\bar X=25.5[/tex] represent the sample mean for the sample
ME= 3.3 represent the margin of error
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 margin of error is given by;
[tex] ME =t_{\alpha/2}\frac{s}{\sqrt{n}}= 3.3[/tex]
And the confidence interval would be given by:
[tex] 25.5 -3.3= 22.2[/tex]
[tex] 25.5 +3.3= 28.8[/tex]
And the confidence interval would be given by: [tex] 22.2\leq \mu \leq 28.8[/tex]
The population of Boomtown is currently 3000 and expected to grow by 2.3% over the
next year. What will its population be by then?
The population of Dullsville, on the other hand, is currently 13000 and expected to
decrease by 4.1% over the next year. What will its population be by then?
Answer:
a) The Expectation of the Population to grow in the next year
= 3069
b) The Expectation of the Population decrease in the next year
= 12,467
Step-by-step explanation:
Explanation:-
a)
The population of Boom town is currently 3000
Given expected to grow by 2.3 % over the next year
= [tex]3000 X \frac{2.3}{100} = 69[/tex]
= 69
The Expectation of the Population growth in the next year
= 3000 +69 = 3069
b)
The population of town is currently 13000
Given expected to grow by 4.1 % over the next year
= [tex]13000 X \frac{4.1}{100} = 533[/tex]
The Expectation of the Population decrease in the next year
= 13000 - 533 = 12,467
Your friend believes that he has found a route to work that would make your commute faster than what it currently is under similar conditions. Suppose that data were collected for a random set of 7 days, where each difference is calculated by subtracting the time taken on the current route from the time taken on the new route. Assume that the populations are normally distributed. Your friend uses the alternative hypothesis Ha:μd<0. Suppose the test statistic t is computed as t≈−3.201, which has 6 degrees of freedom. What range contains the p-value?
Answer:
The range of p-values
0.01 < p < 0.025
Step-by-step explanation:
Explanation:-
Given random sample size 'n' = 7
Assume that the populations are normally distributed
Null Hypothesis :H₀:μd=0.
Alternative Hypothesis:H₁:μd<0.
Degrees of freedom
ν = n-1 =7-1 =6
given the test statistic t = - 3.201
we will use single tailed test in t-distribution table
The test statistic t= 3.201 is lies between the critical values is 0.01 and 0.025
The range of p-values
0.01 < p < 0.025 (check t- distribution table single tailed test)
Final answer:-
The range of p-values
0.01 < p < 0.025
James notes the angle of elevation of the top of tower to be 30 degree if James is 100meter away horizontally from the base of the tower find the height of the tower?
Answer:
Around 57.74 feet
Step-by-step explanation:
The tower and James form a right triangle, where the other two angles are 30 degrees and 60 degrees. The tangent of an angle is equivalent to the length of the opposite side divided by the length of the adjacent side, which means:
[tex]\tan 30=\dfrac{x}{100} \\\\x=\tan 30 \cdot 100 \approx 57.74[/tex]
Hope this helps!
Could someone help me with this trigonometry question where you have find the x which is the adjacent. the reference angle is 39 degree and the opposide side is 30 cm.
Answer:
37.047
Step-by-step explanation:
Sin(39) = 30/hyp
Cos(39) = x/hyp
hyp = 30/Sin(39)
and hyp = x/Cos(39)
hyp = hyp
30/Sin(39) = x/Cos(39)
x = 30(Cos(39))/Sin(39)
x is approximately equal to 37.047
What is the area of a rectangle with a base of 23 feet and a height of 6 feet
Answer:
Step-by-step explanation:
Area of rectangle = l × b
= 23 × 6
= 138 feet
hope this helps
plz mark it as brainliest!!!!!!!
y - 15=x Solve for Y
Answer:
y = x+15
Step-by-step explanation:
y - 15=x
Add 15 to each side
y - 15+15=x+15
y = x+15
Answer:
[tex]y=x+15[/tex]
Step-by-step explanation:
[tex]y - 15=x[/tex]
Add [tex]15[/tex] on both sides of the equation.
[tex]y - 15+15=x+15[/tex]
The [tex]y[/tex] should be isolated on one side of the equation.
[tex]y=x+15[/tex]
Triangle QRS is dilated according to the rule DO,2 (x,y). On a coordinate plane, (0, 0) is the center of dilation. Triangle Q R S has points (negative 3, 3), (2, 4), and (negative 1, 1). What is true about the image ΔQ'R'S'? Select three options. Which statements are true? DO,2 (x,y) = (2x, 2y) Side Q'S' lies on a line with a slope of -1. QR is longer than Q'R'. The vertices of the image are closer to the origin than those of the pre-image. The distance from Q' to the origin is twice the distance from Q to the origin.
Answer:
Options A, B and E are correct
Step-by-step explanation:
From the information given above, we would draw a dilation that produces an image that is the same shape as the original image, but has a different size.
The scale factor is 2
QRS → Q'R'S' = (x,y) → 2(x,y)
The coordinates of ∆QRS
Q (-3, 3)
R (2, 4)
S (-1, 1)
To get the coordinates of Q'R'S', we would multiply each coordinate of the original triangle by the scale factor of 2 since the dilation is from the origin. In order words, each vertex of QRS is multiplied by 2 to get each of the vertex of Q'R'S'.
2 (x,y) = (2x, 2y)
The coordinates of ∆Q'R'S' becomes:
Q' (-6, 6)
R' (4, 8)
S' (-2, 2)
To determine the statements that are true about the image ΔQ'R'S,
we would graph the coordinates of the two triangles.
Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.
See attached the diagram for better explanation.
Let's check out each options and compare it with diagram we obtained:
a) DO, 2 (x,y) = (2x, 2y)
A dilation about the origin with a scale factor 2 is described using the above notation.
Q' = 2(-3,3) = [2(-3), 2(3)] = (-6, 6)
R' (4, 8) = 2(2,4) = [2(2), 2(4)] = (4, 8)
S' (-2, 2) = 2(-1,1) = [2(-1), 2(1)] = (-2, 2)
This option is correct
b) Side Q'S' lies on a line with a slope of -1
Q' (-6, 6)
S' (-2, 2)
coordinate (x, y)
Slope = m = (change in y)/(change in x)
m = (6-2)/[-6-(-2)]
= 4/(-6+2) = 4/-4
m = -1
This option is correct
c) QR is longer than Q'R'
Length of QR (-3 to 2) = 5
Length of Q'R' (-6 to 4) = 10
QR is not longer than Q'R'
This option is false
d) The vertices of the image are closer to the origin than those of the pre-image
The scale factor determines how much bigger or smaller the dilation image will be compared to the preimage. In a transformation, the final figure is referred to as the image. The original figure is referred to as the preimage.
From the diagram, the vertices of the preimage (original image) are closer to the origin than those of the dilation image.
This option is false
e) The distance from Q' to the origin is twice the distance from Q to the origin.
The distance from Q' to the origin (6 to 0) = 6
The distance from Q to the origin (3 to 0) = 3
The distance from Q' to the origin = 2(the distance from Q to the origin)
This option is correct
Answer:
A,B and E is correct
Step-by-step explanation:
Rewrite the expression in the form z^n
[tex] \sqrt[5]{z {}^{4}z {{}^{ \frac{ - 3}{2} } } } [/tex]
Answer:
[tex]z^{0.5}[/tex]
Step-by-step explanation:
So first simplify inside:
[tex]z^4z^{-1.5}=z^{2.5}[/tex]
Now divide that by 5:
[tex]z^{0.5}[/tex]
If P(-2, 1) is rotated 90°, its image is
The image of P(-2,1) after it is rotated 90° is (-1,-2).
A bread machine produces 159 loaves of bread per hour. The machine operates 10 hours per day. How many loaves of bread does it produce per day? _____ loaves
Answer:
It can produce 1590 loaves of bread per day.
Step-by-step explanation:
Given that the bread machine operates only 10 hours per day. So in order to calculate how many loaves can be produce a day, you have to multiply it by 10 :
[tex]1hour = 159loaves[/tex]
[tex]10hours = 159 \times 10[/tex]
[tex]10hours = 1590loaves[/tex]
Please answer this correctly
Mark all of the values that are between 61 and 80. See the diagram below. You should mark exactly 6 values.
If an arrow is shot upward on Mars with a speed of 52 m/s, its height in meters t seconds later is given by y = 52t − 1.86t2. (Round your answers to two decimal places.) (a) Find the average speed over the given time intervals.
Answer:
A. (I) v = 46.42 m/s; (ii) v = 47.35 m/s; (III) v = 48.09 m/s; (iv) v = 48.26 m/s; (v) v = 58.28 m/s
B. v = 48.28 m/s
Note: the question is missing some values. The full Question is provided below:
If an arrow is shot upward on Mars with a speed of 52 m/s, its height in meters t seconds later is given by y = 52t − 1.86t2. (Round your answers to two decimal places.)
(a) Find the average speed over the given time intervals. (i) [1, 2] m/s (ii) [1, 1.5] m/s (iii) [1, 1.1] m/s (iv) [1, 1.01] m/s (v) [1, 1.001] m/s
(b) Estimate the speed when t = 1. m/s
Step-by-step explanation:
Height, y = 52t - 1.86t²
Velocity = ∆y/∆t = 52 - 1.86 * 2t = 52- 3.72t
A. Average velocity = (v1 + v2)/2
(i) At t = 1, 2
Average velocity = (52 - 3.72*1 + 52 -3.72*2)/2 = 46.42 m/s
(ii) At t = 1,1.5
Average velocity = (52 - 3.72*1 + 52 - 3.72*1.5)/2 = 47.35 m/s
(iii) At t = 1,1.1
Average velocity = (52 - 3.72*1 + 52 -3.72*1.1)/2 = 48.09m/s
(iv) At to = 1, 1.01
Average velocity = (52 - 3.72*1 + 52 - 3.72*1.01)/2 = 48.26 m/s
(iv) At t = (1, 1.001)s
Average velocity = (52 - 3.72*1 + 52 - 3.72*1.001)/2 = 48.28 m/s
B. Speed at t = 1s
Velocity = 52 - 3.72 * 1 = 48.28 m/s
Assuming the below results were obtained in a study used to test the accuracy of the rapid diagnostic test for influenza, calculate and interpret the sensitivity of the rapid diagnostic influenza test.
Frequency of Flu Cases Frequency of Non-Fu Cases
Frequency of Individuals who 47 10
Screened Positive
Frequency of individuals who 43 100
Screened Negative
A) When the rapid diagnostic influenza test is used, 52.22% of individuals who have the flu test positive for the flu.
B) When the rapid diagnostic influenza test is used, 90.91% of individuals who have the flu test positive for the
C) When the rapid diagnostic influenza test is used, 47.78% of individuals who have the flu test positive for the flu.
D) When the rapid diagnostic influenza test is used, 9.09% of individuals who have the flu test positive for the flu.
Answer:
c
Step-by-step explanation:
At the Rowlett Holiday Parade
there were a total of 51 floats. If
7 of those floats were from
sports teams, what percent
were NOT sports teams?
Answer:
[tex] p =\frac{7}{51}= 0.1372[/tex]
And then the probability that is NOT from sport temas using the complement rule is given by:
[tex] q = 1-p =1- \frac{7}{51}= 0.8627[/tex]
And if we convert that into % we got:
[tex] 0.8627 *100= 86.27\%[/tex]
Approximately 86.27% of the floats were NOT sports teams
Step-by-step explanation:
For this case we can begin finding the % of floats that were from sport tems using the Laplace definition of probability given by:
[tex]p = \frac{Possible}{Total}[/tex]
And replacing we got:
[tex] p =\frac{7}{51}= 0.1372[/tex]
And then the probability that is NOT from sport temas using the complement rule is given by:
[tex] q = 1-p =1- \frac{7}{51}= 0.8627[/tex]
And if we convert that into % we got:
[tex] 0.8627 *100= 86.27\%[/tex]
Approximately 86.27% of the floats were NOT sports teams
I need help with all three :(
Answer:
1: Glide
2: Reflection
3: Reflection
Step-by-step explanation:
1): The first one is glide because you are just moving the triangle and not changing anything to the angle and the size.
2): The second one is a reflection because you are reflecting across an invisable line. Basicly think of it as a mirror. In the picture below, you can see the line of reflection.
3): The third one is also a reflection for the same reason as the second, (view attached image below for line of reflection.
A garden bed contains 8 tomato plants, 4 squash plants and 8 bell pepper plants. What percentage of the plants are tomato plants
Answer:
33.33%
Step-by-step explanation:
Add them together 8 plus 8 plus 8 which is 24 there are 8 tp so its 8/24 which is equal to 1/3 so the percent is
The length of the sides of a square are initially 0 cm and increase at a constant rate of 8 cm per second. Write a formula that expresses the side length of the square, s (in cm), in terms of the number of seconds, t , since the square's side lengths began growing. s
Answer:
s(t)=8t
Step-by-step explanation:
The length of the sides of a square are initially 0 cm and increase at a constant rate of 8 cm per second.
Let the length of the Square = s
[tex]\dfrac{ds}{dt}=8 $cm/seconds, s_0=0 cm[/tex]
We solve the differential equation above subject to the given initial condition.
[tex]\dfrac{ds}{dt}=8\\ds=8$ dt\\Take the integral of both sides\\\int ds=\int 8$ dt\\s(t)=8t+C, where C is the constant of integration\\When t=0, s=0cm\\s(0)=0=8(0)+C\\C=0\\Therefore, s(t)=8t[/tex]
The formula that expresses the side length of the square, s (in cm), in terms of the number of seconds, t , since the square's side lengths began growing is:
s(t)=8t (in cm)
if a-2= (2^2/3+2^1/3) find a^3-6a^2+12a-14
Answer:
Step-by-step explanation:
7. 1, for r = 0 - 1, for r = 1 Hence, determine alo. Using characteristic root ... find the solution of the recurrence relation y, + 9 y, 2 = 6y, 1, subjected to the ... Solve a, -5a, 1 + 6a, 2 = 0 , given initial conditions ao = 2 and a1 = 5. ... Solve the recurrence relation a, – 7a, 1 + 16a, 2 – 12a, 3 = 0 for n > 3 with ... 2"; 3. a = (2)” – n.
Answer:
2
Step-by-step explanation:
I solved in the picture
Hope this helps ^-^
en un parque hay una zona de columpios y una pista de patinaje que ocupa en total 5 quintos del espacio .si los columpios ocupan 2 septimos del parque . que fraccion del parque ocupa la pista de patinaje
Answer:
The rink occupies 69% of the whole park, approximately, which is equivalent to 280/408.Step-by-step explanation:
To solve this problem, we need to find the number which express the whole park.
Notice that the park is divided in two sections, one occupies 5/8 of the total, and the other occupies 2/7 of the total. So, the sum would be
[tex]\frac{5}{8}+\frac{2}{7}=\frac{35+16}{56} =\frac{51}{56}[/tex]
Now we have the total space there, we need to divide 5/8 by 51/56, so
[tex]\frac{5}{8} \div \frac{51}{56}=\frac{5}{8} \times \frac{56}{51}=\frac{280}{408} \approx 0.69[/tex]
Therefore, the rink occupies 69% of the whole park, approximately, which is equivalent to 280/408.
Solve x-6y = 11 for y
Answer:
2
Step-by-step explanation:
Answer: y = 11 - x / -6
Step-by-step explanation:
X - 6y = 11
Since we are solving for y, we need to isolate the variable.
Move x to the other side of the equation.
- 6y = 11 - x
Now divide bith sides by -6 to cancel out -6y and get the variable y
-6y/ -6 = 11 - x/ -6
y = 11 - x / -6
Im not sure if it was solving for y, or if it was solve for x if y = 11
Anyone know this at all?
Answer:
24.2
Step-by-step explanation:
You are given the hypotenuse and angle, and you want to find the length of the adjacent side.
The mnemonic SOH CAH TOA reminds you that the relation between angle and sides is ...
Cos = Adjacent/Hypotenuse
cos(41°) = x/32
x = 32·cos(41°)
x ≈ 24.2
What weighs more a pound of feathers or a pound of pennies
you and a group of friends spent at least $73.00 at a local pizzeria. Drinks for the table totaled $13 and it was $15 per pizza. how many pizzas could they order
Answer:
4 pizza's
Step-by-step explanation:
hope this helps :)
Jacob put his 731 Marbles and 37 bags if he puts the same amount in each bag how many marbles were in each bag how many marbles were left out of the backs
Answer:
19 marbles in each bag 28 left over
Step-by-step explanation:
the first step to this problem is to find out the number of marbles in each bag.
if there were 731 marbles and 37 bags, we need to divide 731 by 37.
731/37 = 19[tex]\frac{28}{37}[/tex]
therefore there are 19 marbles in each bag.
the second part of the question is to determine how many are left out or in other words how many numbers are "left over"
since the fraction is 28/37 there are 28 marbles that are left out of the bag.
feel free to ask questions, hope this helped you!
Find the area of the triangle
Answer:
Step-by-step explanation:
The formula for the area of a triangle is base*height divided by 2. Remember this because itll be important for everything you do in math relating to geometry and calculus. Assuming you go that far
[tex]\frac{base*height}{2} =\frac{14*8}{2} =\frac{112}{2} = 56 units^2[/tex]
Answer:
A =56 units^2
Step-by-step explanation:
The area of a triangle is given by
A =1/2 bh where 14 is the base and 8 is the height
A = 1/2 (14)8
A =56 units^2
An amount of money earned #24 in 4 years at a rate of 5% per year simple intrest. what was the amount of money
Answer:
4.8
Step-by-step explanation:
simple interest=Principal ×time×rate ÷100
=24×4×5÷100
=4.8
What percent of forty-eight is thirty?
Answer:
P = 62.5 %
Step-by-step explanation:
Of means multiply and is means equals
P * 48 = 30
Divide each side by 48
P = 30/48
P = .625
Change to percent form
P = 62.5 %
Answer:
62.5%
Step-by-step explanation:
30 is 62.5% of 48 since:
30÷48=0.625
0.625×100=62.5%
New York City is known for it's tourist attractions and high priced real estate. The mean hotel room rate is $202 per night. Assume that the room rates are normally distributed with a standard deviation of $70.What is the probability that a hotel room costs between $210 and $290?
Answer:
[tex]P(210<X<290)=P(\frac{210-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{290-\mu}{\sigma})=P(\frac{210-202}{70}<Z<\frac{290-202}{70})=P(0.114<z<1.26)[/tex]
And we can find this probability with this difference
[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)[/tex]
And we can find the difference with the normal standard distirbution or excel:
[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)=0.896-0.545=0.351[/tex]
Step-by-step explanation:
Let X the random variable that represent the hotel room cost of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(202,70)[/tex]
Where [tex]\mu=202[/tex] and [tex]\sigma=70[/tex]
We are interested on this probability
[tex]P(210<X<290)[/tex]
The z score formula is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using the formula we got:
[tex]P(210<X<290)=P(\frac{210-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{290-\mu}{\sigma})=P(\frac{210-202}{70}<Z<\frac{290-202}{70})=P(0.114<z<1.26)[/tex]
And we can find this probability with this difference
[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)[/tex]
And we can find the difference with the normal standard distirbution or excel:
[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)=0.896-0.545=0.351[/tex]
Shari wrote the numbers from 1 to 16 on a card.
Next, she crossed out all the numbers which are factors of 80.
Then, she crossed out all the numbers which are multiples of 3.
How many numbers were not crossed out?
What is the general form of this equation:
The line passes through the point (-2,4) with a slope -2/3
Answer: y= -2/3 + 8/3
Step-by-step explanation:
-2/3 is the slope so you just need the y-intercept to write the equation in general form or slope intercept form
4= -2/3(-2) +b
4 = 4/3 + b
-4/3 -4/3
b= 8/3
general form is y= -2/3 + 8/3
