Answer:
The probability that a study participant has a height that is less than 65 inches is 0.1103.
Step-by-step explanation:
We are given that the heights in the 20-29 age group were normally distributed, with a mean of 69.9 inches and a standard deviation of 4.0 inches.
A study participant is randomly selected.
Let X = heights in the 20-29 age group.
So, X ~ Normal([tex](\mu=69.9,\sigma^{2} =4.0^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean height = 69.9 inches
[tex]\sigma[/tex] = standard deviation = 4.0 inches
Now, the probability that a study participant has a height that is less than 65 inches is given by = P(X < 65 inches)
P(X < 65 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{65-69.9}{4}[/tex] ) = P(Z < -1.225) = P(Z [tex]\leq[/tex] 1.225)
= 1 - 0.8897 = 0.1103
The above probability is calculated by looking at the value of x = 1.225 in the z table which lies between x = 1.22 and x = 1.23 which has an area of 0.88877 and 0.89065 respectively.
There are nine saxophone players in the band. The number of saxophone players is one less than twice the number of tuba players. Find the number of tuba players.
Answer:
[tex]5[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the number of tuba players.
We are given that the number of saxophone players is one less than twice the number of tuba players.
There are 9 saxophone players.
[tex]9 = 2 x-1[/tex]
[tex]9+1=2x[/tex]
[tex]10=2x[/tex]
[tex]10 \div 2=x[/tex]
[tex]5=x[/tex]
Rewrite y = square root 25X - 75 + 3 to make it easy to graph using a translation. Describe the graph
Answer:
D
Step-by-step explanation:
y = sqrt(25x-75)+3
y = sqrt(25(x-3))+3
y = sqrt 5(x-3)+3
transformations:
vertically stretched by a factor of 5
right 3 units
up 3 units
D is the best answer
The following data values represent a population. What is the variance of the
values?
8, 10, 14,4
A. 14
B. 10
C. 9
D. 13
Answer:
D: 13
So first you write down your equation ( its on the picture I posted) Then you need to find the mean which is the sum of all the values over the number of values you have (n) After finding your mean, you subtract it from every value you have. To check if what you have done is correct you add all the values you got after subtracting, if you get 0 your answer is correct. Then you square each of those answers you get after you subtract. You get the total which you then divide by the number of values you have (n)
I hope you understand, I am not that good at explaining. And I am not completely sure with my answer, but I think it's correct.
Chrissy currently has a credit card that charges 15% interest. She usually carries a balance of about $500. What will her total annual interest be with her current card?
Answer:
$900
Step-by-step explanation:
If she holds $500 and she is charged 15%; it means
The interest she pays per month is ;
$500 × 15/100 = $75
Then annually meaning for 12 months, she pays;
$75 × 12 = $900
Her annual interest on her current card is $900.
How to calculate annual interest?The annual percentage rate (APR) is the interest generated by a sum charged to borrowers or paid to investors each year. The annual percentage rate (APR) is a percentage that represents the actual annual cost of funds over the life of a loan or the income earned on an investment.Your daily periodic interest is calculated by dividing your annual percentage rate (APR) by the number of days in the year, which is typically 360 or 365 days depending on your credit card issuer. The annual interest rate is the rate that is applied over a one-year period.Therefore,
She will be taxed 15% if she holds $500, which means
The monthly interest she pays is;
$500 × 15/100 = $75
She then pays annually, which is for a full year;
$75 × 12 = $900
Hence, Her annual interest on her current card is $900.
To learn more about annual interest refer to:
brainly.com/question/20690803
#SPJ2
What is the value of -(3/4) to the power of -4
The answer would be -3 13/81 (simplified)
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than negative 1.15−1.15 and draw a sketch of the region.
Answer:
Step-by-step explanation:
Let x be the random variable representing the test scores from the bone density test. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 0
σ = 1
the probability that a given score is less than negative 1.15 is expressed as
P(x < - 1.15)
z = (- 1.15 - 0)/1 = - 1.15
Looking at the normal distribution table, the probability corresponding to the z score is 0.13
P(x < - 1.15) = 0.13
The sketch of the region is shown in the attached photo
Given that (- 2, 7) is on the graph of f(x) , find the corresponding point for the function f(x + 4).
Answer:
[tex]\boxed{\ the \ corresponding\ point\ is \ (-6,7)\ }[/tex]
Step-by-step explanation:
We know that f(-2)=7
x+4 = -2 <=> x = -6
so f(-6+4) = f(-2)=7
then the corresponding point is (-6,7)
The math department faculty at a large university wanted to know what portion of the student body believes students should be able to enroll in any math class without meeting a prerequisite. The statistics department offered to cooperate in conducting a survey, and a simple random sample of 500 students was selected from all the students enrolled in statistics classes. A survey form was sent by email to these 500 students and 236 responded. What is the population of interest for this study?
Answer:
The population of interest for this student is the students whom are enrolled in statistics classes.
Step-by-step explanation:
Sampling
This is a common statistics practice, when we want to study something from a population, we find a sample of this population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.
The population of interest are all residents of New York State.
A simple random sample of 500 students was selected from all the students enrolled in statistics classes.
This means that the population of interest for this student is the students whom are enrolled in statistics classes.
A box lunch costs b. A bag of chips is $2 extra. Choose the expression to show the cost of 12 lunches with chips and 10 lunches without?
Answer:
22b+24
Step-by-step explanation:
If a box lunch costs b and a bag of chips is $2 extra then we would have:
box lunch = b dollars
box lunch with bag of chips = b + 2 dollars
Now, we need to find the expression for the cost of 12 lunches with chips and 10 lunches without chips, this would be:
12 lunches with chips = 12 (b + 2)
10 lunches without chips = 10b
Let's sum up and simplify these two expressions:
[tex]12(b+2)+10b\\12b+24+10b\\22b+24[/tex]
Thus, the cost of 12 lunches with chips and 10 lunches without chips is 22b+24
Whats the answer?
A) 35
B)55
C)70
D)110
Answer:
D
Step-by-step explanation:
If <CAD=35, <KNL=55 because the remaining angle is 90 since it's a right angle. Therefore <KNM=110 because 55+55=110
Please answer this correctly
Answer:
Band: 30%
Chorus: 18%
Painting: 21%
Robotics: 14%
Coding: 17%
Please answer this correctly as soon as possible.I have to finish this today. A triangular prism is 19 yards long and has a triangular face with a base of 12 yards and a height of 8 yards. The other two sides of the triangle are each 10 yards. What is the surface area of the triangular prism?
total SA = 764 yd²
A triangular prism is 13 yards long and has a triangular face with a base of 12 yards and a height of 8 yards. The other two sides of the triangle are each 10 yards. What is the surface area of the triangular prism?
See attachment.
if length = 13 yards then total SA = 512 yd²
if length = 19 yards then total SA = 764 yd²
6500 rounded to the nearest thousand is __. Enter your answer without commas
Answer:
7000
Step-by-step explanation:
If the hundreds place is higher than 5, then add 1 to the thousands place.
Once a bill leaves the Congress, how can a bill become a law? (Select all that anny
Answer:
Once both the House and Senate have approved the bill in identical form, it becomes "Enrolled" and sent to the President of the United States. The President may sign the bill into law. The President can also take no action on the bill for ten days while Congress is in session and the bill will automatically become law.
Erythropoietin (EPO) is a banned drug used by athletes to increase the oxygen-carrying capacity of their blood. New tests for EPO were first introduced prior to the 2000 Olympic Games held in Sydney, Australia. Chance (Spring 2004) reported that of a sample of 830 world-class athletes, 159 did not compete in the 1999 World Championships (a year prior to the new EPO test). Similarly, 133 of 82:5 potential athletes did not compete in the 2000 Olympic Games. Was the new test effective in deterring an athlete's participation in the 2000 Olympics? If so, then the proportion of nonparticipating athletes in 2000 will be greater than the proportion of nonparticipating athletes in 1999, Use a 98% confidence interval to compare the two proportions and make the proper conclusion.
Answer:
Step-by-step
The null and the alternative hypothesis can be define as follows,
Null Hypothesis; There is no significance difference between the proportions of non participating athletes in 1999 and 2000
[tex]H_0:(p_1-p_2)\neq 0[/tex]
Alternative Hypothesis: The proportion of non participating athletes in 2000 will be more than the proportion of non participating athletes in 1999
[tex]H_1:(p_1-p_2)<0[/tex]
The proportion of nonparticipating athletes in 1999 is given by
[tex]\hat p_1 = \frac{x_1}{n_1} \\\\=\frac{159}{830} =0.1916[/tex]
The proportion of nonparticipating athletes in 2000 is given by
[tex]\hat p_2 =\frac{x_2}{n_1} \\\\=\frac{133}{825} =0.1612[/tex]
The pooled proportion can be calculated using the following formula
[tex]\hat p = \frac{x_1+x_2}{n_1+n_2} \\\\=\frac{159+133}{830+825} =0.1764[/tex]
under the null hypothesis, the test statistics can be calculated as follows
[tex]Z=\frac{\hat p_1 - \hat p_2}{\sqrt{\hat p \hat q(\frac{1}{n_1}+\frac{1}{n_2} ) } }[/tex]
[tex]=\frac{0.1916-0.1612}{\sqrt{(0.1764)(0.8236)(\frac{1}{830} +\frac{1}{825} )} } \\\\=1.6257[/tex]
Determine the P-value using the following formula
P-value = Normdist(1.6257)
=0.947993
Here, it can be observed that the P-value is greater than the level of the significance,
Hence, the null hypothesis fails to be rejected
Therefore it can be concluded that there is insufficient evidence to support that the proportions of non participating athletes in 2000 will be more than the proportions of non participating athletes in 1999
A tank contains 180 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.
Answer:
[tex]\mathbf{A(t) = 180 - 130e ^{-\dfrac{t}{30}}}[/tex]
Step-by-step explanation:
Given that:
A tank contains 180 liters of fluid in which 50 grams dissolved inside.
Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min
The salt pumped out[tex]= \dfrac{6 L}{180 L} = \dfrac{1}{30}[/tex] of initial amount added salt
At (t = 0) = 50
To determine the number A (t)
[tex]\dfrac{dA}{dt}=Rate_{in} - Rate _{out}[/tex]
[tex]A' = 6 - \dfrac{1}{30}A[/tex]
[tex]A' + \dfrac{1}{30}A = 6[/tex]
Integrating factor [tex]y = e^{\int\limits pdt[/tex]
[tex]y = e^{\int\limits \dfrac{1}{30}dt}[/tex]
[tex]y = e^{\dfrac{t}{30}}[/tex]
[tex](e^{ \frac{t}{30}}A)' =4 e ^{\dfrac{t}{30}}+c[/tex]
Taking integral on the both sides;
[tex]Ae ^{\dfrac{t}{30}}= 6 * 30 e^{\dfrac{t}{30}} + c[/tex]
[tex]A = 180+ ce^ {-\dfrac{t}{30}}[/tex]
At A(t = 0) = 50
50 = 180 + C (assuming C = [tex]ce ^{-\dfrac{t}{30}}[/tex])
C = 50 - 180
C = 130
[tex]\mathbf{A(t) = 180 - 130e ^{-\dfrac{t}{30}}}[/tex]
Pernyataan berikut yang benar adalah ....
A. Garis bagi membagi sisi menjadi dua sama panjang
B. Garis bagi membagi sudut menjadi dua sama besar
C. Garis berat membagi sudut menjadi dua sama besar
D. Garis tinggi membagi sudut menjadi dua sama besar
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
-3/4
Step-by-step explanation:
Find two points on the line
(0,1) and (-4,4)
We can use the slope formula
m = (y2-y1)/(x2-x1)
= (4 -1)/(-4 -0)
= 3/-4
= -3/4
Simplify 4^3•4^5.
help asap !
Answer:
D
Step-by-step explanation:
when there are exponents with same bases multiplied by each other, keep the base and add the exponents
4^(3)+4^(5)=4^8
4^8 is D in this question
The vertex of this parabola is at (-2,-3). When the x-value is -1, the y-value is -5. What is the coefficient of the squared expression in the parabola’s equation? A. 8 B. -8 C. -2 D. 2
Answer:
Option C is correct
Step-by-step explanation:
Given: vertex of this parabola is at (-2,-3)
To find: coefficient of the squared expression in the parabola’s equation if the x-value is -1, the y-value is -5
Solution:
The equation of parabola is of the form [tex]y=a(x-h)^2+k[/tex]
Here, a is the coefficient of the squared expression in the parabola’s equation.
Put [tex](h,k)=(-2,-3)\,,\,(x,y)=(-1,-5)[/tex]
[tex]-5=a(-1+2)^2-3\\-5+3=a(1)^2\\-2=a\\a=-2[/tex]
So, the coefficient of the squared expression in the parabola’s equation is [tex]-2[/tex]
find the LCM
of
75, 5,3
Answer:
LCM = 75
Step-by-step explanation:
1: Multiply the factor by the greatest number
Description:
The least common multiple for 75,5,3 is 75.
LCM= Least common Multiple
Please mark brainliest
Hope this helps.
Answer:
75
Step-by-step explanation:
Break each number into prime factors
75 = 25*3 = 5*5*3
5 = 5*1
3 = 3*1
Multiply by the greatest number of each factor
3 = 1 time
5 = =2 times
The least common multiple = 3 * 5*5 = 75
What’s the correct answer for this?
Answer:
D: <K = 35°
Step-by-step explanation:
<E = 55
<L = 90°
Now
<LKE = 180-90-55
<K = 35°
Answer:
[tex]\fbox{\begin{minipage}{8.8em}Option D is correct\end{minipage}}[/tex]
Explanation:
Here, we state again the definition of inscribed angle in circle:
(1) An inscribed angle has the vertex on the circle and the sides are chords.
=> In the picture shown, angle ELK is inscribed angle with vertex L and LE and LK are chords.
(2)An inscribed angle also creates an intercepted arc whose endpoints are on the angle.
=> Inscribed angle ELK creates intercepted arc EK.
(3) According to the Inscribed Angle Theorem, the measure of intercepted arc is twice as the measure of its inscribed angle.
=> Angle ELK = (1/2) arc EK
Arc EK, whose EK is diameter, is equal to measure of half of circle, or 180 degree, in other words.
=> Angle ELK = (1/2) x 180 = 90 deg
(4) As the property of sum of 3 angles inside a triangle, this sum is equal to 180 degree.
=> Considering triangle ELK:
ELK + LEK + LKE = 180 deg
or
90 + 55 + LKE = 180 deg
or
LKE = 180 - 90 - 55 = 35 deg
Hope this helps!
:)
A pyramid shaped building is 836 ft tall with a square base that is 156 ft on each side. What is the volume of the pyramid?
Answer:
6781632 ft ^ 3
Step-by-step explanation:
The first thing is to know the formula for the volume of a pyramid:
V = 1/3 * Ab * h
That is, it is one third of the product between the area of the base and the height.
The base area would be:
Ab = l ^ 2
the side equals 156 ft, replacing:
Ab = 156 ^ 2
Ab = 24336 ft ^ 2
now, replacing in the volume formula:
V = 1/3 * 24336 * 836
V = 6781632
Which means that the volume of the pyramid is 6781632 ft ^ 3
The table below represents the total cost of leasing a car at the end each month.
Month 1 -------- 3 -------- 8 -------- 12
Cost $1,859 --- $2,577 --- $4,372 --- $5,808
Write an equation in slope-intercept form to represent the total cost, y, of leasing a car for x months.
Answer:
y= 359 x+1500
Step-by-step explanation:
find the slope m= (2577-1859)÷(3-1) = 359
y=mx+b
find b : substitute x ,y, and m
get b = 1857 - 359*1 = 1500
Answer:
y= 359 x+1500
Step-by-step explanation:
Which undefined term is used to define an angle
Answer:
The undefined term which is used to define an angle is line i.e., . Further explanation: In geometry the three terms which are considered to be undefined are line, point and plane.
Answer:
Line
Step-by-step explanation:
A line is a undefined term used to define a angle. An angle is the corner that is created where two non-parallel lines meet/ intersect
Zelie planned for a square pool to have a side length of 28 ft but found that it needs to be 14 ft long to fit in her backyard. She found the change of scale below. Which is Zelie’s error? Zelie should have divided both numbers by 14. Zelie should have written the ratio as 28/7. Zelie should have written the ratio as 14/8. Zelie should have subtracted 14 from both numbers.
Answer:
Zelie should have divided both numbers by 14 to find the scale (2)
Step-by-step explanation:
Answer:
the answers A.
Step-by-step explanation:
I TOOK THE QUIZ edg 2020
Based on the measures shown, could the figure be a
parallelogram?
Answer:
its A
Step-by-step explanation:
ed 2020
Electricity usage data consists of 45 months has a mean number of units consumed is 390.47 per month with a standard deviation of 170.5 units per month. Assume that the number of units consumed are approximately normally distributed. Estimate 95% confidence interval for the average monthly electricity consumed units.
Answer:
The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 45 - 1 = 44
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 44 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0141
The margin of error is:
M = T*s = 2.0141*170.5 = 343.4
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 390.47 - 343.40 = 47.07 units per month
The upper end of the interval is the sample mean added to M. So it is 390.47 + 343.40 = 733.87 units per month
The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87
If x=10 what is (7x -5)
[tex]solution \\ x = 10 \\ now \\ (7x - 5) \\ = (7 \times 10 - 5) \\ = (70 - 5) \\ = 65[/tex]
Hope it helps....
Good luck on your assignment
Answer:
65
Step-by-step explanation:
= 7x-5
Putting x = 10
= 7(10)-5
= 70-5
= 65
Based on your understanding of the ideas of external consistency and fruitfulness, which of the following statements best describes the relevance of these ideas to the acceptance of hypotheses?a. A fruitful hypothesis is considered stronger because fruitful hypotheses are always externally consistent with previously held theories. b. A fruitful hypothesis is considered stronger because fruitful hypotheses promote scientific progress by revealing new avenues of research and analysis.c. An adequate theory is always a fruitful theory. d. All internally coherent theories are fruitful.
Answer:
b
Step-by-step explanation:
externally consistent ideas are the ideas that are consistent with other well-confirmed hypothesis.
Fruitfulness of a hypothesis can be measured from the fact it it suggests something other than what it was originally suppose to explain.
