Answer:
[tex]\Delta s \approx 754.579\,m[/tex] (See explanation below).
Step-by-step explanation:
Each floor has a height of 3 meters. Then, the number of floors of the cylinder is:
[tex]n = \frac{30\,m}{3\,m}[/tex]
[tex]n = 10\,floors[/tex]
Let consider that spiral makes a revolution per floor. Then, the parametric equations of the spiral are:
[tex]x = r\cdot \cos \theta[/tex]
[tex]y = r\cdot \sin \theta[/tex]
[tex]z = \Delta h \cdot \frac{\theta}{2\pi}[/tex]
Length of the staircase can be modelled by using the formula for arc length:
[tex]\Delta s = \int\limits^{20\pi}_{0} {\sqrt{\left(\frac{dx}{d\theta} \right) ^{2}+\left(\frac{dy}{d\theta} \right)^{2}+\left(\frac{dz}{d\theta}\right)^{2}}} \, d\theta[/tex]
[tex]\Delta s = \int\limits^{20\pi}_{0} {\sqrt{\left(-r\cdot \sin \theta\right)^{2}+\left(r\cdot \cos \theta\right)^{2}+\left(\frac{\Delta h}{2\pi} \right)^{2}} } \, d\theta[/tex]
[tex]\Delta s = \int\limits^{20\pi}_{0} {\sqrt{r^{2}+\frac{(\Delta h)^{2}}{4\pi^{2}} }} \, d\theta[/tex]
[tex]\Delta s = \sqrt{(12\,m)^{2}+\frac{(3\,m)^{2}}{4\pi^{2}} } \cdot (20\pi-0)[/tex]
[tex]\Delta s \approx 754.579\,m[/tex]
A major home improvement store conducted its biggest brand recognition campaign in the company's history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot". A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad (i.e.. if there is evidence that the population proportion of "like the ads a lot" for the company's ads is less than 0.22) at a 0.01 level of significance. Referring to the above, the null hypothesis will be rejected if the test statistic is:
The null hypothesis will be rejected if the test statistic is: greater than -2.33
The null hypothesis will be rejected if the test statistic falls within the critical region, which is determined by the significance level (0.01 in this case).
To determine the test statistic, calculate the z-score for the sample proportion and compare it to the critical value.
The formula to calculate the z-score for the sample proportion is:
[tex]z = (\hat{p} - p) / \sqrt(p * (1 - p) / n)[/tex]
Where:
[tex]\hat{p}[/tex] is the sample proportion (230/1189 = 0.193)
p is the population proportion (0.22)
n is the sample size (1189)
Calculating the z-score:
z = (0.193 - 0.22) / [tex]\sqrt[/tex](0.22 * (1 - 0.22) / 1189)
z = -2.25
To determine if the null hypothesis is rejected or not, compare the absolute value of the z-score to the critical value for a one-tailed test at a 0.01 significance level.
The critical value for a one-tailed test at a 0.01 significance level is approximately -2.33.
If the absolute value of the calculated z-score is greater than 2.33, we reject the null hypothesis.
Since absolute value of the calculated z-score is not greater than 2.33, null hypothesis is not rejected.
here are the ingredients needed to make 8 pancakes
250ml milk
1 egg
140 g flour
5 g butter
a) simon makes 4 pancakes
workout how much milk he needs
b) craig makes 12 pancakes
workout how much butter he needs
To calculate milk needed for a different number of pancakes and determine the amount of butter for a varied pancake quantity.
To calculate the amount of milk needed for 4 pancakes that Simon is making:
Divide the amount of milk needed for 8 pancakes (250ml) by 2 since 4 is half of 8. 250ml ÷ 2 = 125ml.
To determine the amount of butter for the 12 pancakes that Craig is making:
Since the recipe calls for 5g of butter for 8 pancakes, we can calculate the amount needed for 12 pancakes by setting up a proportion: (5g/8 pancakes) = (x/12 pancakes). Solving for x gives x = 7.5g.
Mass of Weight(C)
eight
A restaurant buys 9 pounds of truffles. Suppose truffles cost $168 per ounce.
How much would the restaurant pay for the truffles?
a $1,512
b $2,688
c $12,096
d $24,192
I need the answer now plz
The restaurant pay $24,192 for 9 pounds of truffles.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
A restaurant buys 9 pounds of truffles.
as, 1 pound = 16 ounce
So, the restaurant buys
= 16 x 9
= 144 ounce of truffles.
If truffles cost $168 per ounce.
So, the cost for 9 pounds ruffles is
= 144 x 168
= $ 24,192
Learn more about Unitary Method here:
https://brainly.com/question/22056199
#SPJ6
solve this system using a systems of equations. Discount Rental Cars charges a daily fee plus a mileage fee for renting its cars. Barney was charge 145.00 for 3 days and 310 miles, while Mary was charge 250.00 for 5 days and 600 miles. What does discount Rental Cars charge per day and mile?
Answer:
Barney 145 3 Days 310 Miles
Mary 250 5 Days 600 Miles
A) 3 D + 310 M = 145
B) 5 D + 600 M = 250
Multiplying A) by -5/3
A) -5 D - 516.6666M = -241.66666666
B) 5D + 600M = 250
Adding A) and B)
83.3333 M = 8.3333333333
M = .10 per mile
3 D = 114
Daily Rate = 38 dollars per day
Step-by-step explanation:
Find the midpoint of A and B where A has coordinates (2, 4)
and B has coordinates (-3, -9).
Answer:
(-0.5,-2.5)
Step-by-step explanation:
(x1 + x2) / 2 = x midpoint
(y1 + y2) / 2 = y midpoint
x)
2 + -3 = 5
5 / 2 = -0.5
y)
4 + -9 = -5
-5 / 2 = -2.5
= (-0.5, -2.5)
The midpoint of A and B where A has coordinates (2, 4) and B has coordinates (-3, -9) is (-1/2, -5/2)
What is Coordinate Geometry?A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.
We have to find the midpoint of A and B where A has coordinates (2, 4)
and B has coordinates (-3, -9).
Midpoint = (2-3/2, 4-9/2)
=(-1/2, -5/2)
Hence, the midpoint of A and B where A has coordinates (2, 4) and B has coordinates (-3, -9) is (-1/2, -5/2)
To learn more on Coordinate Geometry click:
brainly.com/question/27326241
#SPJ2
The Highway Safety Department wants to study the driving habits of individuals. A sample of 37 cars traveling on a particular stretch of highway revealed an average speed of 70.7 miles per hour with a standard deviation of 6.3 miles per hour. Round to 4 decimal places. 1.Calculate a 90% confidence interval for the true mean speed of all cars on this particular stretch of highway
Answer:
90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].
Step-by-step explanation:
We are given that a sample of 37 cars traveling on a particular stretch of highway revealed an average speed of 70.7 miles per hour with a standard deviation of 6.3 miles per hour.
Firstly, the pivotal quantity for 90% confidence interval for the true mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average speed of cars = 70.7 miles per hour
s = sample standard deviation = 6.3 miles per hour
n = sample of cars = 37
[tex]\mu[/tex] = true mean speed
Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.
So, 90% confidence interval for the true mean, [tex]\mu[/tex] is ;
P(-1.688 < [tex]t_3_6[/tex] < 1.688) = 0.90 {As the critical value of t at 36 degree of
freedom are -1.688 & 1.688 with P = 5%}
P(-1.688 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.688) = 0.90
P( [tex]-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90
P( [tex]\bar X-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90
90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]70.7-1.688 \times {\frac{6.3}{\sqrt{37} } }[/tex] , [tex]70.7+1.688 \times {\frac{6.3}{\sqrt{37} } }[/tex] ]
= [68.9517 miles per hour , 72.4483 miles per hour]
Therefore, 90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].
The interpretation of the above interval is that we are 90% confident that the true mean speed of all cars will lie between 68.9517 miles per hour and 72.4483 miles per hour.
A recreation center is offering special prices on its pool passes and gym memberships for the summer. On the first day of the offering, a family paid $96 for 4 pool passes and 2 gym memberships. Later that day, an individualbought apool pass for herself, a pool pass for a friend,and 1
This mathematics question from middle school algebra asks to solve a system of equations to find the price of pool passes and gym memberships at a recreation center. The problem is partially incomplete due to a cutoff in the additional information needed to set up the second equation. Consequently, we cannot provide a final answer without this information.
Explanation:The question involves a linear system of equations, which is a topic in algebra within the field of mathematics. The problem presents a scenario where a family purchases a combination of pool passes and gym memberships for a total cost, and another individual purchases a different combination of the same items for a different total cost. To solve, we set up two equations based on the given information.
Step-by-step solution:
Let the price of one pool pass be p dollars and the price of one gym membership be g dollars.According to the given information, 4p + 2g = $96.Unfortunately, the rest of the question seems to be cutoff. To proceed further, we would need the additional information about the second combination of purchases that the individual makes.If complete information were provided, we would use the additional information to set up a second equation and solve the system of equations either by substitution or elimination method to find the values of p and g.Without the full information, this question is incomplete, and thus we cannot provide a final answer.
If 8(x) is the inverse of f(x) and f(x) = 4x + 12 what is g(x) ?
g(x) = 12x + 4
g(x) = x-12
g(x) = x-3
g(x) - x-3
Answer:
(y-12)/4
Step-by-step explanation:
If g(x) is the inverse of f(x)
and f(x) = 4x + 12
f⁻¹(x) = g(x)
let f(x) be represented as y
f(x) = y
y = 4x + 12
subtract 12 from both sides
y-12= 4x
divide both sides by 4
(y-12)/4 = x
so f ⁻¹ (y)= (y-12)/4 so g(x) = (x-12)/4
The table shows the results of a poll of 200 randomly selected juniors and seniors who were asked if they attended prom. Find the probability of each of the events.
juniors seniors
yes 28 97
no 56 19
Express your answer as a fraction, using the backslash. Example: 17 would be written as 1/7.
a) P (a junior who did not attend prom)
b) P (did not attend prom | senior)
c) P (junior | attended prom)
Answer:
(a)[tex]\frac{7}{25}[/tex]
(b)[tex]\frac{19}{116}[/tex]
(c)[tex]\frac{28}{125}[/tex]
Step-by-step explanation:
Number of juniors who attended prom,n(J)=28
Number of seniors who attended prom,n(S)=97
Total of those who attended prom=125Number of juniors who did not attend prom,n(J')=56
Number of seniors who did not attend prom,n(S')=19
Total of those who attended prom=75Total Number of students=200(a) P (a junior who did not attend prom)
[tex]P(J')=\frac{56}{200}= \frac{7}{25}[/tex]
(b)
[tex]P(Senior)=\frac{116}{200}[/tex]
[tex]P ($did not attend prom$ | senior)=\frac{\text{P(seniors who did not attend prom)}}{P(Senior)} \\=\frac{19/200}{116/200} \\=\frac{19}{116}[/tex]
(c)P (junior | attended prom)
[tex]P(Senior)=\frac{84}{200}[/tex]
[tex]P (Junior|$ attended prom$)=\frac{\text{P(juniors who attended prom)}}{P(\text{those who attended prom)}} \\=\frac{28/200}{125/200} \\=\frac{28}{125}[/tex]
Answer:
A. P = 7/25
B. P = 19/116
C. P = 28/125
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly this way:
Juniors Seniors Totals
Yes 28 97 125
No 56 19 75
Totals 84 116 200
2. Find the probability of each of the events.
Let's recall that the formula of probability is:
P = Number of favorable outcomes/Total number of possible outcomes
A. P (a junior who did not attend prom)
P = Juniors who did not attend prom/Total number of students surveyed
P = 56/200
P = 7/25 (Diving by 8 numerator and denominator)
B. P (did not attend prom | senior)
P = Seniors who did not attend prom/Total number of seniors surveyed
P = 19/116
C. P (junior | attended prom)
P = Juniors who attend prom/Total number of students attended prom
P = 28/125
The minimum length L of a highway sag curve can be computed by where θ 1 is the downhill grade in degrees (θ 1 < 0°), θ 2 is the uphill grade in degrees (θ 2 > 0°), S is the safe stopping distance for a given speed limit, h is the height of the headlights, and α is the alignment of the headlights in degrees. Compute L for a 55-mph speed limit, where and Round your answer to the nearest foot.
Answer:
The answer to the nearest foot is = 15 feet
Step-by-step explanation:
Solution
The first set taken is to Compute L for a 55-mph speed limit
Given that
L =(θ2 -θ1)/200 (h +S Tan ∝) =
= ( u + 5) 336²/200 (1.9 +336 tan 0.7°)
= 9° (336)²/200 (1.9 +336 tan 0.7°) = 14.7652094
= 15 feet { 9° = 9*π/180 = π/20}
Note: Kindly find an attached image for the complete question given and answered
There are 3 paper clips and 5 erasers in a paper stack. If 2 items are drawn at random without replacement what is the probability that one draw a paper clip and then an eraser?
Answer:
15/56
Step-by-step explanation:
Total = 8
3/8 × 5/7
15/56
Uni made a model of a 1970 Ford Mustang using a scale of .5 inches = 9 in. If the actual car is 15 ft long, how long is the model car?
Answer:
The model car is 10 inches long
Step-by-step explanation:
To solve this question, we use conversion of units
Feet to inches.
Each feet has 12 inches.
The car is 15ft long.
So the car has 15*12 = 180 inches.
.5 inches = 9 in.
Rule of three
.5 inches - 9 inches
x inches - 180 inches
[tex]9x = 180*0.5[/tex]
[tex]9x = 90[/tex]
[tex]x = \frac{90}{9}[/tex]
[tex]x = 10[/tex]
The model car is 10 inches long
To find the length of Uni's model car, we convert the actual car's length to inches, set up a proportion with the given scale, and cross-multiply to solve for the model car's length, resulting in a model that is 10 inches long.
The subject matter of the question is related to scale models, which falls under the field of Mathematics. To solve this problem, we need to find the length of the model car based on the given scale and the actual length of the car.
The scale given is 0.5 inches = 9 inches. Firstly, we need to convert the actual length of the car from feet to inches, so we can work in the same units. There are 12 inches in a foot, so a 15 feet long car is 15 x 12 inches long, which is 180 inches. Now, we need to set up a proportion to find the length of the model car:
Actual car length (inch) : Model car length (inch) = Actual scale (inch) : Model scale (inch) 180 inches (actual car length) : x inches (model car length) = 9 inches (actual scale) : 0.5 inches (model scale)
By cross-multiplying, we get:
(180 inches x 0.5 inches) = (x inches x 9 inches)
Dividing both sides by 9 inches, we get:
x inches = (180 inches x 0.5 inches) / 9 inches
So, the length of the model car is:
x inches = 10 inches.
Therefore, Uni's model car is 10 inches long.
True or False: The megaspore that develops into the megagametophyte leaves the flower when it
reaches maturity
Answer: gang in la
Step-by-step explanation:
The equation can be used to determine the number of centimeters, y, in a given number of inches, x. The equation was used to fill in the table below. Inches in Centimeters Number of Inches Number of Centimeters 2 5.08 10 25.4 63.5 40 101.6 What value is missing from the table?
Answer:
25 Inches
Step-by-step explanation:
Given the table:
[tex]\left|\begin{array}{c|c|c|c|c}\text{Number of Inches}&2&10&&40\\\text{Number of Centimeters}&5.08&25.04&63.5&101.6\end{array}\right|[/tex]
We want to determine the missing value on the table.
Let the missing value be x.
1 inch = 2.54 cm
x inch = 63.5
Expressing the above as a ratio
[tex]\dfrac{1}{x}=\dfrac{2.54}{63.5} \\$Cross Multiply$\\2.54x=63.5\\$Divide both sides by 2.54$\\x=25 \:Inches[/tex]
Therefore, the missing value is 25.
Answer:
25 Inches
Step-by-step explanation:
hope this helps :))
A woman is emptying her aquarium at a steady rate with a small pump. The water pumped to a 12-in.-diameter cylindrical bucket, and its depth is increasing at the rate of 4.0 in. per minute. Find the rate at which the aquarium water level is dropping if the aquarium measures 24 in. (wide) × 36 in. (long) × 18 in. (high).
Answer:
Therefore the rate at which water level is dropping is [tex]\frac{11}{21}[/tex] in per minute.
Step-by-step explanation:
Given that,
The diameter of cylindrical bucket = 12 in.
Depth is increasing at the rate of = 4.0 in per minutes.
i.e [tex]\frac{dh_1}{dt}=4[/tex]
[tex]h_1[/tex] is depth of the bucket.
The volume of the bucket is V = [tex]\pi r^2 h[/tex]
[tex]=\pi \times 6^2\itimes h_1[/tex]
[tex]\therefore V=36\pi h_1[/tex]
Differentiating with respect yo t,
[tex]\frac{dV}{dt}=36\pi \frac{dh_1}{dt}[/tex]
Putting [tex]\frac{dh_1}{dt}=4[/tex]
[tex]\therefore\frac{dV}{dt}=36\pi\times 4[/tex]
The rate of volume change of the bucket = The rate of volume change of the aquarium .
Given that,The aquarium measures 24 in × 36 in × 18 in.
When the water pumped out from the aquarium, the depth of the aquarium only changed.
Consider h be height of the aquarium.
The volume of the aquarium is V= ( 24× 36 ×h)
V= 24× 36 ×h
Differentiating with respect to t
[tex]\frac{dV}{dt}=24\times 36 \times \frac{dh}{dt}[/tex]
Putting [tex]\frac{dV}{dt}=36\pi\times 4[/tex]
[tex]36\pi\times 4= 24\times 36\times \frac{dh}{dt}[/tex]
[tex]\Rightarrow \frac{dh}{dt}=\frac{36\pi \times 4}{24\times 36}[/tex]
[tex]\Rightarrow \frac{dh}{dt}=\frac{11}{21}[/tex]
Therefore the rate at which water level is dropping is [tex]\frac{11}{21}[/tex] in per minute.
To find the rate at which the aquarium water level is dropping, calculate the volume of water being pumped into the bucket per minute and the volume of the aquarium. Then, divide the volume of water by the volume of the aquarium to find the rate.
Explanation:To find the rate at which the aquarium water level is dropping, we first need to determine the flow rate of water being pumped into the cylindrical bucket.
Now, let's find the rate at which the aquarium water level is dropping:
By calculating the above expression, you can find the rate at which the aquarium water level is dropping.
Learn more about Rate at which aquarium water level is dropping here:https://brainly.com/question/32037009
#SPJ11
The water level in the aquarium is dropping at an average rate of π/6 inches per minute. This is obtained by relating the volumes and their rates of change in both the bucket and the aquarium.
Explanation:The subject of this question is calculus, specifically, related rates. The situation describes two rates: one at which the depth of water in the bucket is increasing, and one at which the water level in the aquarium is dropping - a classic related rates problem.
To comprehend this, let us calculate the volume rates of each one: the bucket and the aquarium. The bucket is referred as cylindrical with a radius of 6 inches (half of 12 inches). The volume of a cylinder is V = πr²h. The depth or height, h, is increasing at the rate of 4 inches per minute, so dh/dt = 4 in/min. The rate at which the volume has been changing, dV/dt = πr²dh/dt = π * (6 in)² * 4 in/min = 144π in³/min.
The aquarium is a rectangular prism, thus its volume can be calculated by V = l*w*h. Therefore, the rate at which the water level is dropping is dV/dt / (l*w) which equals 144π in³/min divided by the area of the aquarium (24in*36in = 864 in²), which gives dh/dt = 144π / 864, which reduces to dh/dt = π/6 in/min downwards. Hence, the water level in the aquarium is dropping at π/6 in/min on an average.
Learn more about related rates here:https://brainly.com/question/33509029
#SPJ3
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 428428 gram setting. It is believed that the machine is underfilling or overfilling the bags. A 7171 bag sample had a mean of 433433 grams with a variance of 441441. Assume the population is normally distributed. A level of significance of 0.010.01 will be used. Specify the type of hypothesis test.
Answer:
z-test
Step-by-step explanation:
-A z-test is a test used to determine the difference in two population means of known variances.
-The sample size has to be large enough, [tex]n\geq 30[/tex](n=71).
-And, the population must follow a normal distribution.
-Since our sample meets all the above conditions, the hypothesis test used is a z-test
Question 3
4 pts
(03.05)
What does 7 >-2 indicate about the positions of 7 and -2 on the number line? (4 points)
0
7 is located on the right of -2, and -2 is located on the right of o
0
7 is located on the left of -2, and -2 is located on the right of o
04
7 is located to the right of -2
7 is located on the left of -2
Question 4
4 pts
Answer:
7 is located to the right of -2
Step-by-step explanation:
Larger numbers are to the right on a number line, so the statement that 7 is larger than -2 means ...
7 is located to the right of -2
What is the common difference in the following arithmetic sequence?
7,3,-1,-5
Answer:
-4
Step-by-step explanation:
Each term is 4 less than the term before it, so the common difference is -4.
Answer:
B. -4 on edge !!
Step-by-step explanation:
Got it right :)
The design of a concrete mix requires 2,314 lb/yd3 of gravel having a moisture content of 3.5% and absorption of 4.2%, and 899 lb/yd3 of sand having a moisture content of 5.7% and absorption of 1.4%, and 244 lb/yd3 of free water. What is the weight of the mixing water per cubic yard that should be used at the job site?
Answer:
Weight of mixing water=224.541 lb
Step-by-step explanation:
Taking 1 cubic yard of concrete
Mass of gravel = 2314 lb
Moisture content = 3.5% Absorption 4.2%
Extra water needed = (4.2-3.5)*2314/100= 16.198 lb
Mass of sand= 899 lb
Moisture content = 5.7% Absorption =1.4%
Water released = (5.7-1.4)*899/100= 38.657 lb
Free water = 244 lb
Weight of mixing water = free water + extra water needed-water released = 244+16.198-38.657=224.541 lb
Weight of mixing water=224.541 lb
A bag contains 3 white balls, 4 green balls, and 5 red balls. A ball is drawn at random. How many total number of outcomes are there?
Answer:
12.
Step-by-step explanation:
Given that,
Number of while balls are 3
Number of green balls are 4
Number of red balls are 5
We need to find the total number of outcomes. We know the total number of outcomes in is number of choices.
In this case, total number of outcomes are the sum of all color balls i.e. 3 + 4 + 5 = 12 balls.
Hence, the total number of outcomes are 12.
Final answer:
The total number of outcomes when one ball is drawn at random from a bag containing 3 white, 4 green, and 5 red balls is 12.
Explanation:
A bag contains 3 white balls, 4 green balls, and 5 red balls. The total number of possible outcomes when a ball is drawn at random is simply the sum of all the balls in the bag. Since each ball can be selected in one distinct way, we calculate the total number of outcomes by adding the number of white balls, the number of green balls, and the number of red balls.
So, the total number of outcomes is:
3 (white) + 4 (green) + 5 (red) = 12 (total outcomes)
Therefore, there are 12 different possible outcomes when one ball is drawn at random from this bag.
Ten years ago, college students spent an average of 120 hours per semester on extra-curricular activities. A researcher believes that now college students spend less time on extra-curricular activities than they did ten years ago. A simple random sample of 100 college students found that in the past year the average number of hours spent per semester in extracurricular activities was 107 hours with a standard deviation of 45 hours. If we are testing at a significance level of 0.05, based on the p-value, what is your conclusion?
Answer:
We conclude that the college students spend less time on extra-curricular activities than they did ten years ago.
Step-by-step explanation:
We are given that Ten years ago, college students spent an average of 120 hours per semester on extra-curricular activities.
A simple random sample of 100 college students found that in the past year the average number of hours spent per semester in extracurricular activities was 107 hours with a standard deviation of 45 hours.
Let [tex]\mu[/tex] = average time spent on extra-curricular activities.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 120 hours {means that the college students spend more or equal time on extra-curricular activities than they did ten years ago}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 120 hours {means that the college students spend less time on extra-curricular activities than they did ten years ago}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average number of hours spent per semester = 107 hrs
s = sample standard deviation = 45 hours
n = sample of college students = 100
So, test statistics = [tex]\frac{107-120}{\frac{45}{\sqrt{100} } }[/tex] ~ [tex]t_9_9[/tex]
= -2.889
The value of t test statistics is -2.889.
Now, the P-value of the test statistics is given by following formula;
P-value = P( [tex]t_9_9[/tex] < -2.889) = 0.00314
Since, the P-value is less than the level of significance as 0.05 > 0.00314, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the college students spend less time on extra-curricular activities than they did ten years ago.
what is the equation of the horizontal line that passes through ( 2 -2 )
Answer:
y = -2
Step-by-step explanation:
The equation of a horizontal line is ...
y = constant
In order to make it go through a point with a y-coordinate of -2, the value of the constant must be -2.
Your line is y = -2.
n a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2472 subjects randomly selected from an online group involved with ears. 1022 surveys were returned. Construct a 99% confidence interval for the proportion of returned surveys.
Answer:
0.3876<p<0.4389
Step-by-step explanation:
-Given [tex]n=2472, \ x=1022 , \ CI=0.99[/tex]
-We calculate the proportion of surveys returned:
[tex]\hat p=\frac{1022}{2472}\\\\=0.4134[/tex]
For a 99% confidence interval:
[tex]z_{\alpha/2}=2.576[/tex]
#The margin of error is calculated as;
[tex]ME=z_{0.005}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=2.576\times \sqrt{\frac{0.4134(1-0.4134)}{2472}}\\\\=0.0255[/tex]
The confidence interval are then:
[tex]CI=\hat p\pm ME\\\\=0.4134\pm 0.0255\\\\=[0.3876,0.4389][/tex]
Hence, the confidence interval is 0.3876<p<0.4389
Reina is buying a house either with brick or with siding, with 1 floor or with 2 floors, and in the city, the suburbs, or the
country. On top of that she can choose from 6 different interior paints and 9 different exterior paints.
Using the fundamental counting principle, simplify the expression
combinations
to determine the number of possible
There are possible combinations.
Reina decides she definitely wants a brick house with one floor. Now the number of possible combinations is
Answer:
1. There are 648 total combinations that can be chosen.
2. After she choses two possiblilities the total number changes to 108 total posibilities to chose from
Step-by-step explanation:
possibility: 1/2 x 1/3 x 1/2 x 1/6 x 1/9 = 648
then you remove the first two because she chose those ones
1/2 x 1/6 x 1/9 = 108 possibilities left
Answer:
Step-by-step explanation:
1. C
2. C
3. B
Fluoxetine, a generic anti-depressant, claims to have, on average, at least 20 milligrams of active ingredient. An independent lab tests a random sample of 80 tablets and finds the mean content of active ingredient in this sample is 18.7 milligrams with a standard deviation of 5 milligrams. If the lab doesn't believe the manufacturer's claim, what is the approximate p-value for the suitable test
Answer:
[tex]t=\frac{18.7-20}{\frac{5}{\sqrt{80}}}=-2.326[/tex]
[tex]df=n-1=80-1=79[/tex]
[tex]p_v =P(t_{(79)}<-2.326)=0.0113[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=18.7[/tex] represent the sample mean for the content of active ingredient
[tex]s=5[/tex] represent the sample standard deviation for the sample
[tex]n=80[/tex] sample size
[tex]\mu_o =20[/tex] represent the value that we want to test
t would represent the statistic
[tex]p_v[/tex] represent the p value for the test
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean for the active agent is at least 20 mg, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 20[/tex]
Alternative hypothesis:[tex]\mu < 20[/tex]
The statistic would be:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Now we can calculate the statistic:
[tex]t=\frac{18.7-20}{\frac{5}{\sqrt{80}}}=-2.326[/tex]
P value
The degrees of freedom are calculated like this:
[tex]df=n-1=80-1=79[/tex]
Since is a one left tailed test the p value would be:
[tex]p_v =P(t_{(79)}<-2.326)=0.0113[/tex]
Option (e) 0.0113 is correct. The approximate p-value for the lab's one-sample t-test on fluoxetine is 0.0113.
To determine the approximate p-value for the lab's test on fluoxetine, we can use a one-sample t-test. Here's a step-by-step explanation:
Null Hypothesis (H₀): The mean content of the active ingredient is at least 20 milligrams (μ ≥ 20 mg).Alternative Hypothesis (Hₐ): The mean content of the active ingredient is less than 20 milligrams (μ < 20 mg).Calculate the test statistic using the formula:(bar{x} - μ) / (s/√n)
where bar{x} is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
Substituting the values:bar{x} = 18.7, μ = 20, s = 5, n = 80
t = (18.7 - 20) / (5/√80)
t = -1.3 / (5/8.944)
t = -1.3 / 0.559
t = -2.325
Using a t-distribution table or calculator, we find the p-value for t = -2.325 with (n - 1) = 79 degrees of freedom. The approximate p-value is 0.0113.Therefore, the correct answer is e. 0.0113.
Complete question:
Fluoxetine, a generic anti-depressant, claims to have, on average, at least 20 milligrams of active ingredient. An independent lab tests a random sample of 80 tablets and finds the mean content of active ingredient in this sample is 18.7 milligrams with a standard deviation of 5 milligrams. If the lab doesn't believe the manufacturer's claim, what is the approximate p-value for the suitable test?
a. 0.0226
b. 0.4885
c. 0.5115
d. 0.15
e. 0.0113
What is 1/3x1/3x1/3[/tex]?
Answer:
i believe the answer is 1/27
Step-by-step explanation:
you take the fractions and multiply them all together.
1x1x1 equals 1
and 3x3x3 equals 27
meaning the answer is 1/27 :)
To calculate 1/3 x 1/3 x 1/3, you're effectively cubing 1/3, which results in (1/3)^3 or 1^3/3^3, simplifying to 1/27.
Explanation:The student is asking about the multiplication of fractions and exponentiation rules in algebra. To solve 1/3 x 1/3 x 1/3, you multiply the fractions normally. When multiplying identical fractions, we simply raise the fraction to the power of the number of times it is being multiplied by itself. So 1/3 x 1/3 x 1/3 is equivalent to (1/3)^3. When you raise a fraction to an exponent, you raise both the numerator and the denominator to that power. Therefore, (1/3)^3 equals 1^3/3^3, which simplifies to 1/27.
The example given with 3².35 relates to the rules of exponents, which state that when multiplying exponential terms with the same base, you can add the exponents (x^p x x^q = x^(p+q)). For the concept of cubing of exponentials, you would cube the base and multiply the existing exponent by 3 to execute the operation effectively.
Which shapes can the shaded area be divided into to find the area?
O
a rectangle and a triangle
a rectangle and a square
a trapezoid and a rectangle
a trapezoid and two triangles
Answer:
A rectangle and a triangle
Step-by-step explanation:
An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 270 cars, they found a mean MPG of 27.8. Assume the variance is known to be 6.25. A level of significance of 0.02 will be used. Make a decision to reject or fail to reject the null hypothesis. Make a decision.
Answer:
The calculated value z = 1.3145 < 2.326 at 0.02 level of significance
The null hypothesis is accepted
Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.
Step-by-step explanation:
Step(i):-
An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.
The mean of the Population 'μ' = 28.0miles/gallon
Given data after testing 270 cars, they found a mean MPG of 27.8. Assume the variance is known to be 6.25.
The sample size 'n' = 270
Mean of the sample 'x⁻' = 27.8
Given Population variance 'σ² = 6.25
The standard deviation of Population 'σ' = √6.25 = 2.5
Step(ii):-
Null hypothesis :H₀: 'μ' = 28.
Alternative hypothesis :H₁: 'μ' ≠28.
The test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{27.8-28 }{\frac{2.5}{\sqrt{270} } } = \frac{-0.2}{0.15214}[/tex]
Z = -1.3145
|Z| = |-1.3145|= 1.3145
Step(iii):-
The tabulated value of z-score at 0.02 level of significance = 2.326
The calculated value z = 1.3145 < 2.326 at a t 0.02 level of significance
The null hypothesis is accepted
Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.
Consider the exponential function
g(x)=190,000•1.03x, which models the value of Evie’s house, where x represents the number of years since she purchased the house.
What is the value of Evie’s house after 5 years rounded to the nearest dollar?
Answer:
$220262
Step-by-step explanation:
We are given that an exponential function
[tex]g(x)=190000\cdot(1.03)^x[/tex]
Where x=Number of years
We have to find the value of Evie's house after 5 years .
Substitute the values in the given function
[tex]g(5)=190000\cdot(1.03)^5[/tex]
[tex]g(5)=220262.07[/tex]
[tex]g(5)\approx 220262[/tex]
Hence, the value of Evie's house after 5 years=$220262
The Movie Haven is planning to order new medium-size popcorn containers. It has a choice of four different containers. It costs the company $0.02 per cubic inch of popcorn to fill a container. The company does not want the new container to cost more than $3.00 to fill. Which container should the company use? Use 3.14 for Pi.
Answer:
the answer is container c
b=11.14in2
12in
Step-by-step explanation:
Answer:
Answer is C
Step-by-step explanation: