Answer:
c. [1.771;4.245] feet
Step-by-step explanation:
Hello!
The variable of interest is
X: height of a student at UH
X~N(μ;σ²)
You have to estimate the population standard deviation using a 95% confidence interval.
The statistic to use for the interval is a student Chi-Square with n-1 degrees of freedom. First you have to calculate the CI for the population variance:
[tex][\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}} ;\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}} ][/tex]
[tex]X^2_{n-1;1-\alpha /2}= X^2_{11;0.975}= 21.920[/tex]
[tex]X^2_{n-1;\alpha /2}= X^2_{11;0.025}= 3.816[/tex]
n=12
S= 2.5
[tex][\frac{11*6.25}{21.920} ;\frac{11*6.25}{3.816}} ][/tex]
[3.136; 18.016] feet²
Then you calculate the square root of both limits to get the CI for the population standard deviation:
[√3.136; √18.016]
[1.771;4.245] feet
I hope this helps!
A tooth-whitening gel is to be tested for effectiveness. A group of 85 adults have volunteered to participate in the study. Of these, 43 are to be given a gel that contains the tooth-whitening chemicals. The remaining 42 are to be given a similar-looking package of gel that does not contain the tooth-whitening chemicals. A standard method will be used to evaluate the whiteness of teeth for all participants. Then the results for the two groups will be compared. 1. After the treatment period, compare the whiteness of the 43 treated adults. 2. A placebo is not being used. 3. After the treatment period, compare the whiteness of the two groups. 4. Randomly select 85 adults to be given the treatment gel. 5. The remaining 42 adults receive the placebo gel. 6. Randomly select 43 adults to be given the treatment gel.
Answer:
(a) 3, 5 and 6
Step-by-step explanation:
In the experiment, 43 are to be given a gel that contains the tooth-whitening chemicals while the remaining 42 are to be given a placebo. Therefore, a placebo is used.
The 43 that will receive the gel are to be selected randomly.
After the experiment, the whiteness of the two groups will be compared to see the effect of the gel.
Therefore for the experiment to be completely random, 3, 5, and 6 apply.
(b)
For the experiment to be double-blind, the researchers who will evaluate the whiteness and interact with the subjects, and the subjects would not know which subjects received either the whitening gel or the placebo.
Five times the sum of a number and 13 is 20. Find the number
Answer:
x = -9
Step-by-step explanation:
Step 1: Write out expression
5(x + 13) = 20
Step 2: Distribute
5x + 65 = 20
Step 3: Isolate x
5x = -45
x = -9
And we have our answer!
Answer:
-9
Step-by-step explanation:
Let the number be x.
5(x+13) = 20
Expand.
5x+65 = 20
Subtract 26 on both sides.
5x = 20 - 65
5x = -45
Divide 5 into both sides.
x = -45/5
x = -9
The number is -9.
Can some help me if your good at maths
Answer:
36=2×3×3×3
36=2×3³Answer
[tex]36 = 2 \times 2 \times 3 \times 3 \\ \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} [/tex]
Step-by-step explanation:
First write the prime factors of 36 that you can see here
[tex]2 \: \: \: 2 \: \: \: 3 \: \: \: 3[/tex]
Now write 36 as a product of its prime factors.
[tex]36 = 2 \times 2 \times 3 \times 3 \\ \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} [/tex]
Find the value of each variable
Answer:
To find a we use sine
sin 60° = a / 4√3
a = 4√3sin60°
a = 6
To find b we use sine
sin 45° = a / b
a = 6
b = 6 / sin 45°
b = 6√2
To find c we use cosine
cos 60° = c / 4√3
c = 4√3 cos 60°
c = 2√3
To find d we use tan
tan 45° = a / d
a = 6
d = 6 / tan 45°
d = 6
Therefore a = 6 b = 6√2 c = 2√3
d = 6
That's option A.
Hope this helps
Any help would be great
Answer:
I don't know
Step-by-step explanation:
sorry I can't help,use a calculator
Answer:
58.5 miles
Step-by-step explanation:
Let's Use unitary Method
8 hours = 52 miles
Then,
1 hour = 52/8 miles
1 hour = 6.5 miles
Multiplying both sides by 9, We'll get
9 hours = 6.5 × 9 miles
9 hours = 58.5 miles
Two contractors will jointly pave a road, each working from one end. If one of them paves 2/5 of the road and the other 81 km remaining, the length of that road is
Using the order of operations, what should be done first to evaluate 12 divided by (negative 6) (3) + (negative 2)? Divide 12 by 5. Multiply –6 and 3. Divide 12 by –6. Add 3 and –2.
Answer:
first you need to multiply -6 and 3
Answer:
-6 and 3
Step-by-step explanation:
sorry it was an late answer I'm just tryna gain points :D
Given that (-2,7) is on the graph of f(x), find the corresponding point for the function f(x + 4).
Answer:
(-6, 7)
Step-by-step explanation:
In order to make (x+4) = -2, we must have x = -6. Then the point (-6, 7) will be on the graph of f(x+4).
__
Another way to think about this is that replacing x with x-h causes the graph to be shifted right by h units. Here, we have h=-4, so the graph is shifted left 4 units. Shifting the point (-2, 7) by 4 units to the left moves it to (-2-4, 7) = (-6, 7).
Answer:
PLATO: -6,7
Step-by-step explanation:
Which function has the same range?
Answer:
I would say the second one
Step-by-step explanation:
f(x) has a range of y<0, because it is reflected over the x axis
g(x) = -5/7(3/5)^-x is also reflected over the x axis, except also in the y axis. Regardless of the reflection in the y-axis, y still cannot be equal to or greater than 0. Therefore, I believe it is the second choice.
(The third and forth choice are the same, which rules them both out. The first on reflects it over the y-axis, meaning that x can be greater than 0.)
In a recent household telephone survey of 2,550 adults in a certain country, 27% reported that they own at least one gun. The researchers want to estimate the true percentage of adults in that country that own at least one gun. Complete parts a through f below a. Identify the population of interest to the researchers. Choose the correct answer below.
a. The set of adults that responded to the survey
b. The set of guns in the country
c. The set of adults in the country that own a gun (CMD.
d. The set of all gun ownership status (yes/no) values for all adults in the country.
Answer
option D
Step-by-step explanation:
The population of interest to the research is the set of all gun ownership status (yes/no) values for all adults in the country. Or all total adults in a country including those that own a gym or not. This is the population of interest. The sample is the 2550 individuals adults surveyed in the household telephone survey.
Use the end behavior of the graph to solve 3x^3+9x^2-12x < 0
Answer:
1. x = 4
2. x = -1
3. x = 0
Answer:
Step-by-step explanation:
Assume that 1700 births are randomly selected and 4 of the births are girls. Use subjective judgment to describe the number of girls as significantly high, significantly low, or neither significantly low nor significantly high.
Answer: Significantly low.
Step-by-step explanation:
Ok, we know that out of 1700 randomly selected, only 4 of them are girls.
Then the frequency is:
p = 4/1700
Now, using the subjective judgement (meaning that it is based on the opinion only, there is no real math involved)
I can conclude that the number of girls is significantly low, meaning that out of 1700 births we have 4 girls, then the other 1694 must be boys.
Find the x-intercepts for the quadratic function y= -1/2(x+3)^2 +4
Answer:
x= -3 +√2 ≈ -0.1716, and x = - 3 -2√2 ≈ -5.8284
Step-by-step explanation:
y= -1/2(x+3)² +4
For x -intercept, y = 0.
0 = - 1/2(x+3)² + 4 /*(-2)
0 = (x+3)² - 8
(x+3)² = 8
√(x+3)² = +/-√8
x+3 = +/-√8
x = - 3+/- 2√2
x= -3 +√2 ≈ -0.1716, and x = - 3-2√2 ≈ -5.8284
The formula for the area of a parallelogram is A = bh,
where b is the base and h is the height.
(x-4) cm
(2x2 + 2x-6) cm
(Not drawn to scale)
Answer:
B) 2x³ – 6x² – 14x + 24 square centimetersStep-by-step explanation:
The question is incomplete and lacks the required diagram. Find the diagram attached. Here is also the complete question.
"The formula for the area of a parallelogram is A = bh, where b is the base and h is the height. Which simplified expression represents the area of the parallelogram? –4x3 + 14x – 24 square centimeters 2x3 – 6x2 – 14x + 24 square centimeters –4x3 – 14x + 24 square centimeters 2x3 + 6x2 + 14x + 24 square centimeters"
Area of a parallelogram = Base * Height.
Given the height of the parallelogram = (x-4)cm
Base = (2x² + 2x-6) cm
Area of the parallelogram = (x-4)cm * (2x² + 2x-6) cm
Area of the parallelogram = (x-4)(2x²+2x-6)
Area of the parallelogram = 2x³+2x²-6x-8x²-8x+24
= 2x³+2x²-8x²-6x-8x+24
= (2x³-6x²-14x+24)cm²
a particular city had a population of 24,000 in 1900 and a population of 29,000 in 1920. Assuming that its population continues to grow exponentially at a constant rate, what population will it have in 2000
Answer:
It will have a population of 61,779 in 2000.
Step-by-step explanation:
The population for the city, in t years after 1900, can be modeled by a exponential function with constant growth rate in the following format:
[tex]P(t) = P(0)(1+r)^{t}[/tex]
In which P(0) is the population in 1900 and r is the growth rate.
Population of 24,000 in 1900
This means that [tex]P(0) = 24000[/tex]
Population of 29,000 in 1920.
1920 is 1920 - 1900 = 20 years after 1900.
This means that P(20) = 29000. So
[tex]P(t) = P(0)(1+r)^{t}[/tex]
[tex]29000 = 24000(1+r)^{20}[/tex]
[tex](1+r)^{20} = \frac{29000}{24000}[/tex]
[tex]\sqrt[20]{(1+r)^{20}} = \sqrt[20]{\frac{29000}{24000}}[/tex]
[tex]1 + r = 1.0095[/tex]
So
[tex]P(t) = P(0)(1+r)^{t}[/tex]
[tex]P(t) = 24000(1.0095)^{t}[/tex]
What population will it have in 2000
2000 is 2000 - 1900 = 100 years after 1900. So this is P(100).
[tex]P(t) = 24000(1.0095)^{t}[/tex]
[tex]P(100) = 24000(1.0095)^{100} = 61779[/tex]
It will have a population of 61,779 in 2000.
Which polynomial function could be represented by the graph below? On a coordinate plane, a cubic function crosses the x-axis at (negative 3, 0), (0, 0), (2, 0). f(x) = x3 + x2 – 6x f(x) = x3 – x2 – 6x f(x) = –2x3 – 2x2 + 12x f(x) = –2x3 + 2x2 + 12x
Answer:
third one
Step-by-step explanation:
when
x=0, y=0
x=1, y=8
x=2 y=0
and so on.
Answer:
C. f(x)= -2x^3 -2x^2 +12x
Step-by-step explanation:
edge 2020
F(x)=(x+1)(x-3)(x-4)
Answer :
x1 = -1
x2= +3
x3 = +4
I hope it helps
If you are doing it by roots how ever it would be 3
The diagram shows a circle, centre O.
Work out the value of a.
BCO=41 degrees
Answer:
a = 49°
Step-by-step explanation:
OB = OC ( both radii of the circle ), thus
Δ BOC is isosceles and the base angles are congruent, that is
∠ OBC = ∠ OCB = 41° , so
∠ BOC = 180° - (2 × 41)° = 180° - 82° = 98°
The angle on the circumference BAC is half the angle at the centre for angles subtended on the same arc , thus
a = 0.5 × 98° = 49°
If the measure of the angle ∠BOC will be 98°. Then the measure of the angle ∠BAC will be 49°.
What is a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
The central angle is double the angle at the periphery that was subtended by the same chords.
The measure of the angle ∠BCO is 41°.
The angle ∠BCO and angle ∠CBO will be congruent. Because they are angles of an isosceles triangle.
We know that the sum of all the interior angles of the triangle will be 180°. Then the measure of the angle ∠BOC will be given as,
∠BOC + ∠CBO + ∠BCO = 180°
∠BOC + 41° + 41° = 180°
∠BOC = 98°
Then the measure of the angle ∠BAC will be
∠BAC = (1/2) ∠BOC
∠BAC = 1/2 x 98°
∠BAC = 49°
If the measure of the angle ∠BOC will be 98°. Then the measure of the angle ∠BAC will be 49°.
More about the circle link is given below.
https://brainly.com/question/11833983
#SPJ2
Jack works in a supermarket. He earns $186 a week. How much does he earn in a 52 week year?
Answer:
9672 per year
Step-by-step explanation:
Take the amount he earns per week times the number of weeks he works
186* 52
9672 per year
Answer:
$9672
Step-by-step explanation:
Jack earns $186 in 1 week.
In 52 weeks,
186 × 52 = 9672
He earns $9672.
Mary is selling chocolate bars to raise money. She earns $3 for each solid milk chocolate bar sold and $4 for each caramel-filled bar sold. If m represents the number of milk chocolate bars sold, and c represents the number of caramel bars sold, which of the following expressions represents the amount of money that Mary has raised? Question 6 options: A) 3m – 4c B) m∕3 + i∕4 C) 12mc D) 3m + 4c
Answer:
3m + 4c
Step-by-step explanation:
Whenever a word problem says the word earn that means the slope, also known as the rate of change, will be positive. Knowing this you can determine that both the caramel and milk chocolate slopes will be positive. After figuring all that out the only thing left to do is to make the equation. You know you have two slopes, and each slope needs a variable, so you will have to look back at the question. It is given that m represents the milk chocolate and c represents the caramel. Now all you have to do is make the slope the coefficient to the corresponding variable. The milk chocolates are 3 dollars, so the 3 goes in front of the m and the caramel chocolates are 4 dollars, so teh 4 goes in front of the 4. Since both slopes are positive no negatives or minus signs will be used in the equation. Knowing all this information you can now create the expression 3m + 4c.
Answer:
D
Step-by-step explanation:
3m + 4c
(d) A drinks machine dispenses coffee into cups. A sign on the machine indicates that each cup contains 100ml of coffee. The machine actually dispenses a mean amount of 105ml per cup and 10% of the cups contain less than the amount stated on the sign. Assuming that the amount of coffee dispenses into each cup is normally distributed, find the standard deviation of the amount of coffee dispensed per cup in ml.
Answer:
The standard deviation of the amount of coffee dispensed per cup in ml is 3.91.
Step-by-step explanation:
Let the random variable X denote the amount of coffee dispensed by the machine.
It is provided that the random variable, X is normally distributed with mean, μ = 105 ml/cup and standard deviation, σ.
It is also provided that a sign on the machine indicates that each cup contains 100 ml of coffee.
And 10% of the cups contain less than the amount stated on the sign.
To compute the probabilities of a normally distributed random variable, first convert the raw score to a z-score,
[tex]z=\frac{X-\mu}{\sigma}[/tex]
This implies that:
P (X < 100) = 0.10
⇒ P (Z < z) = 0.10
The value of z for the above probability is, z = -1.28.
*Use a z-table
Compute the value of standard deviation as follows:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
[tex]-1.28=\frac{100-105}{\sigma}[/tex]
[tex]\sigma=\frac{-5}{-1.28}[/tex]
[tex]=3.90625\\\\\approx 3.91[/tex]
Thus, the standard deviation of the amount of coffee dispensed per cup in ml is 3.91.
If AD=BD, which of the following relationships can be proved and why?
B
o
A. A ACD= A BCD, because of ASA.
B. XACD N BOD because of SAS
C. There is not enough information to prove a relationship.
(D. A ACD S ABCD, because of AS
SUBMIT
< PREVIOUS
Answer: SAS
Step-by-step explanation:
Can someone answer this
Answer:
Step-by-step explanation:
x 6 a
8 48 c
-4 b 20
Let the unknown numbers of the multiplication grid are a, b and c.
1). 6 × 8 = 48
2). (-4)×6 = b
b = -24
3). (-4) × a = 20
a = -5
4). 8 × a = c
8 × (-5) = c
c = -40
Therefore, missing in the given multiplication grid are,
x 6 -5
8 48 -40
-4 -24 20
HELP! What is the solution to the equation below? Round your answer to two decimal places. 4x = 20 A. x = 2.99 B. x = 0.46 C. x = 1.30 D. x = 2.16
Answer:
X = 5
Step-by-step explanation:
If 4x = 20
And we are asked to find the solution.
It simply means looking for the value of x
So
4x = 20
X = 20/4
X = 5
X is simply the solution
X = 5
Answer:
D 2.16
Step-by-step explanation:
a p e x just use log
Suppose the time it takes a barber to complete a haircuts is uniformly distributed between 8 and 22 minutes, inclusive. Let X = the time, in minutes, it takes a barber to complete a haircut. Then X ~ U (8, 22). Find the probability that a randomly selected barber needs at least 14 minutes to complete the haircut, P(x > 14) (round answer to 4 decimal places) Answer:
Answer:
[tex] P(X>14)= 1-P(X<14) =1- F(14)[/tex]
And replacing we got:
[tex] P(X>14)= 1- \frac{14-8}{22-8}= 0.5714[/tex]
The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714
Step-by-step explanation:
We define the random variable of interest as x " time it takes a barber to complete a haircuts" and we know that the distribution for X is given by:
[tex] X \sim Unif (a= 8, b=22)[/tex]
And for this case we want to find the following probability:
[tex] P(X>14)[/tex]
We can find this probability using the complement rule and the cumulative distribution function given by:
[tex] P(X<x) = \frac{x-a}{b-a} ,a \leq x \leq b[/tex]
Using this formula we got:
[tex] P(X>14)= 1-P(X<14) =1- F(14)[/tex]
And replacing we got:
[tex] P(X>14)= 1- \frac{14-8}{22-8}= 0.5714[/tex]
The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714
what is the volume of a cone with the given dimensions. radius=4 cm; height= 10 cm
Answer:
[tex] 167.47 \: {cm}^{3} [/tex]
Step-by-step explanation:
[tex]V_{cone} = \frac{1}{ 3} \pi {r}^{2}h \\ \\ = \frac{1}{ 3} \pi \times {4}^{2} \times 10 \\ \\ = \frac{1}{ 3} \times 3.14 \times 16 \times 10 \\ \\ = \frac{1}{ 3} \times \: 502.4 \\ \\ = 167.466667 \\ \\ = 167.47 \: {cm}^{3} [/tex]
The television show 50 Minutes has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to 50 Minutes. Assume that an advertiser wants to verify that 20% share value by conducting its own survey, and a pilot survey begins with 14 households have TV sets in use at the time of a 50 Minutes broadcast. Find the probability that none of the households are tuned to 50 Minutes.
Answer:
The probability that none of the households are tuned to 50 Minutes is 0.04398.
Step-by-step explanation:
We are given that the television show 50 Minutes has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to 50 Minutes.
A pilot survey begins with 14 households have TV sets in use at the time of a 50 Minutes broadcast.
The above situation can be represented through binomial distribution;
[tex]P(X = r)= \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ;x = 0,1,2,3,.........[/tex]
where, n = number of samples (trials) taken = 14 households
r = number of success = none of the households are tuned to 50 min
p = probability of success which in our question is probability that households were tuned to 50 Minutes, i.e. p = 20%
Let X = Number of households that are tuned to 50 Minutes
So, X ~ Binom(n = 14, p = 0.20)
Now, the probability that none of the households are tuned to 50 Minutes is given by = P(X = 0)
P(X = 0) = [tex]\binom{14}{0} \times 0.20^{0} \times (1-0.20)^{14-0}[/tex]
= [tex]1 \times 1 \times 0.80^{14}[/tex]
= 0.04398
4. The area of a rhombus with one diagonal is 8.72 cm long is the same as the area of a square of side 15.6 cm. Find the length of the other diagonal of the rhombus.
Answer:
55.82 cm
Step-by-step explanation:
d1= 8.72 cm
a= 15.6 cm
A rhombus= 1/2*d1*d2 = A square
A square= 15.6²= 243.36 cm²
d2= 2A/d1= 2*243.36/8.72 ≈55.82 cm
Two clinical trials were designed to test the effectiveness of laser treatment for acne. Seaton et al. (2003) randomly divided participants into two groups. One group received the laser treatment, whereas the other group received a sham treatment. Orringer et al. (2004) used an alternative design in which laser treatment was applied to one side of the face, randomly chosen, and the sham treatment was applied to the other side. The number of facial lesions was the response variable.
Orringer et al. used _______________ in a ___________ design.
Seaton et al. used a completely _____________design.
Answer:
Blocking in a paired design
Completed randomized design
Step-by-step explanation:
Orringer et. al used blocking in a paired design. He use the special type of randomized block design; a matched pair design wherein there is just two treatment conditions (laser treatment and the sham treatment) and the subjects are then group the subjects in pairs using the blocking variable which is a treatment applied to one side of face randomly chosen.
While Seaton et. al. used a completely randomized design. Here the subjects/participants are just merely assigned albeit randomly to either the laser or the sham treatment.
A fort had enough food for 80 soldiers for 60 days .How long would the food last if 20 more soliders join after 15 days ?
Answer:
The food would last 51 days
Step-by-step explanation:
After 15 days are over, you could say that the 16th day would be as follows -
80 soldiers, food finished in 60 - 15 = 45 days.
If 20 more soldiers arrive, there would be a total of 100 soldiers, so if 80 soldiers can finish their food in 45 days - 1 soldier can finish = 45 * 80. Respectively, 100 soldiers can consume their food in ( 45 * 80 ) / 100 = 36 days.
As 15 days are already over, adding 36 more days = 51 days
The food would last 51 days if 20 more soldiers join after 15 days
There are several possible ways to answer this question, but I hope that explanation helps!
Answer:
A total of 51 days, or 36 days after the extra soldiers join in.
Step-by-step explanation:
Let's say a soldier eats 1 portion of food in 1 days. That portion may be divided into breakfast, lunch , and dinner, but it is still accounted as 1 portion per soldier per day.
There are 80 soldiers and enough food for 60 days.
The number of portions is
60 * 80 = 4800
The fort started with 4800 portions.
80 soldiers ate their portions for 15 days.
80 * 15 = 1200
After 15 days, they have
4800 - 1200 = 3600 portions left.
After 15 days, 20 more soldiers joined in.
Now there are 80 + 20 = 100 soldiers.
There are 3600 portions left for 100 soldiers.
3600/100 = 36
The food would last 36 days after the 15 days, or a total of 51 days.