Answer:
D) x = e - 1
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra II
Natural Logarithms ln and Euler's number eSolving logarithmic equationsStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle ln(x + 1) = 1[/tex]
Step 2: Solve for x
[Equality Property] e both sides: [tex]\displaystyle e^{ln(x + 1)} = e^1[/tex]Simplify: [tex]\displaystyle x + 1 = e^1[/tex][Equality Property] Isolate x: [tex]\displaystyle x = e - 1[/tex]Assume a researcher wants to compare the mean Alanine Aminotransferase (ALT) levels in two populations, individuals who drink alcohol and individuals who do not drink alcohol. The mean ALT levels for the individuals who do not drink alcohol is 32 with a standard deviation of 14, and 37 individuals were in the sample. The mean ALT levels for individuals who drink alcohol is 69 with a standard deviation of 19, and 38 individuals were in the sample. Construct and interpret a 95% confidence interval demonstrating the difference in means for those individuals who drink alcohol when compared to those who do not drink alcohol.
a. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.22 and 39.78.
b. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.33 and 39.67
c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.
d. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.41 and 39.59.
Answer:
c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.
Step-by-step explanation:
Given :
Groups:
x1 = 69 ; s1 = 19 ; n1 = 38
x2 = 32 ; s2 = 14 ; n2 = 37
1 - α = 1 - 0.95 = 0.05
Using a confidence interval calculator to save computation time, kindly plug the values into the calculator :
The confidence interval obtained is :
(24.32 ; 39.68) ; This means that we are 95% confident that the true mean difference in ALT values between the two population lies between
(24.32 ; 39.68) .
Which confidence level would produce the widest interval when estimating the mean of a population from the mean and standard deviation of a sample of that population?
Answer:
54% ...
Step-by-step explanation:
this is the answer I guess
The confidence level that produces the widest interval is the one with the highest percentage, which is 54%.
Option B is the correct answer.
What is z-score?A z-score also called a standard score is a measure of how many standard deviations a data point is away from the given mean of a distribution.
It measures the unusual or extreme a particular data point is compared to the rest of the distribution
We have,
The width of a confidence interval is proportional to the critical value of the corresponding confidence level.
The critical value is determined by the standard normal distribution or t-distribution, depending on the sample size and whether the population standard deviation is known.
In general,
The wider the confidence interval, the less precise the estimate of the population means.
Therefore, we want to choose the confidence level that produces the widest interval, which corresponds to the largest critical value.
For a given sample size,
The critical value increases as the confidence level increases.
For example, the critical value for a 95% confidence level is larger than the critical value for a 90% confidence level.
Therefore,
The confidence level that produces the widest interval is the one with the highest percentage, which is 54%.
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1-5. Graph MU (line MU) for M(-1, 1). (Look at the bottom of the pic)
a) The slope of the line MU is [tex]\frac{4}{5}[/tex]
b) The distance between the coordinates of the line MU is √41
c) There are differences and similarities between (a) and (b).
The slope of a line is used to describe how steep the line is. This is expressed mathematically as;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where:
(x1, y1) and (x2, y2 are the coordinate points)
From the graph shown, we are given the coordinates M(-1, 1) and U(4, 5)
a) The slope of the line MU will be expressed as;
[tex]m=\frac{5-1}{4-(-1)}\\m=\frac{4}{5}[/tex]
The slope of the line MU is [tex]\frac{4}{5}[/tex]
The formula for calculating the equation of a line is expressed as y = mx + b
b is the y-intercept.
Substitute m = 4/5 and (-1, 1) into the expression y = mx + b
[tex]1 = -(4/5) + b\\1 = -4/5 + b\\b = 1 +4/5\\b = \frac{5+4}{5} \\b = \frac{9}{5}[/tex]
Get the required equation.
Substitute m = 4/5 and b = 9/5 into y = mx + b
[tex]y=\frac{4}{5}x+\frac{9}{5}\\5y=4x+9\\5y-4x=9[/tex]
The required equation of the line is 5y - 4x = 9
b) The formula for calculating the distance between two points is expressed as;
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute the given coordinates in (a) to get the distance MU
[tex]MU=\sqrt{(4-(-1))^2+(5-1)^2}\\MU=\sqrt{(4+1)^2+(5-1)^2}\\MU=\sqrt{(5)^2+(4)^2}\\MU=\sqrt{25+16}\\MU=\sqrt{41}[/tex]
Hence the distance MU is √41
c) There are similarities and differences in the calculations in (a) and (b). The similarities lie in the usage of the change in the coordinates for the calculation of the slope and the distance.
The difference is that we do not need the slope of the line to calculate the distance MU but the slope y-intercept is required to calculate the equation of the line.
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what is the absolute value of |9|?
Answer:
9
Step-by-step explanation:
it's as simple as that 9 is 9 away from 0
Give two Examples of workers targeted for by minimum waged
Answer:
Minimum wage refers the smallest wage an employee can make per hour for all hours he or she works on the job. ... For example, New York has a higher minimum wage than Maine, as the cost of living is higher in New York.
if my answer helps you than mark me as brainliest.
Im new, and i hope someone tells me the right answers!
A factor is a natural number that can be multiplied by another natural number to get a value. The greatest common factor refers to when one compares the factors of two numbers, the largest natural number that both numbers have in common is the number's greatest common factor.
In the case of ([tex]m^2[/tex]) and ([tex]m^4[/tex]), the greatest common factor is ([tex]m^2[/tex]) because there are no factors of ([tex]m^2[/tex]) that are larger than it. No number can have a factor larger than itself. Since ([tex]m^2[/tex]) is also a factor of ([tex]m^4[/tex]) it is the greatest common factor of the two numbers.
Five students sit at a circular table. Their chairs are number in order 1 through 5. Abby sits next to both Ben and Colin. Dalia sits next to both Ben and Sarah. The numbers on Abbys and Colins chairs add up to 6. Who is in chair number 3?
Write a rule to describe the transformation.
A. reflection across y=x
B. rotation 90º clockwise about the origin
C. rotation 180º about the origin
D. rotation 90º counterclockwise about the origin
Answer:
C. rotation 180º about the origin
Step-by-step explanation:
Given
Quadrilaterals GWVY and G'W'V'Y'
Required
Describe the transformation rule
Pick points Y and Y'
[tex]Y = (5,-4)[/tex]
[tex]Y' = (-5,4)[/tex]
The above obeys the following rule:
[tex](x,y) \to (-x,-y)[/tex]
When a point is rotated by 180 degrees, the rule is:
[tex](x,y) \to (-x,-y)[/tex]
Hence, (c) is correct
Find the circumference of the circle.
10.1 in
Hint: C = xxd
x= 3.14
A.15.857 in
B.31.714 in
C.63.428 in
D.13.24 in
Step-by-step explanation:
c=3.14×3.14×10.1
=99.58196
Alice, Bob, and Carol play a chess tournament. The first game is played between Alice and Bob. The player who sits out a given game plays next the winner of that game. The tournament ends when some player wins two successive games. Let a tournament history be the list of game winners, so for example ACBAA corresponds to the tournament where Alice won games 1, 4, and 5, Caroll won game 2, and Bob won game 3.
Required:
a. Provide a tree-based sequential description of a sample space where the outcomes are the possible tournament histories.
b. We are told that every possible tournament history that consists of k games has probability 1/2k, and that a tournament history consisting of an infinite number of games has zero prob- ability. Demonstrate that this assignment of probabilities defines a legitimate probability law.
c. Assuming the probability law from part (b) to be correct, find the probability that the tournament lasts no more than 5 games, and the probability for each of Alice, Bob, and Caroll winning the tournament.
Answer:
I don't know what you think about it is not going to be a great day of school and I don't know what you think about it is not going to be a great day of school
People were asked if they owned an artificial Christmas tree. Of 78 people who lived in an apartment, 38 own an artificial Christmas tree. Also it was learned that of 84 people who own their home, 46 own an artificial Christmas tree. Is there a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees
Answer:
The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Apartment:
38 out of 78, so:
[tex]p_A = \frac{38}{78} = 0.4872[/tex]
[tex]s_A = \sqrt{\frac{0.4872*0.5128}{78}} = 0.0566[/tex]
Home:
46 out of 84, so:
[tex]p_H = \frac{46}{84} = 0.5476[/tex]
[tex]s_H = \sqrt{\frac{0.5476*0.4524}{84}} = 0.0543[/tex]
Test if the there a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees:
At the null hypothesis, we test if there is no difference, that is, the subtraction of the proportions is equal to 0, so:
[tex]H_0: p_A - p_H = 0[/tex]
At the alternative hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0, so:
[tex]H_1: p_A - p_H \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = p_A - p_H = 0.4872 - 0.5476 = -0.0604[/tex]
[tex]s = \sqrt{s_A^2 + s_H^2} = \sqrt{0.0566^2 + 0.0543^2} = 0.0784[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-0.0604 - 0}{0.0784}[/tex]
[tex]z = -0.77[/tex]
P-value of the test and decision:
The p-value of the test is the probability of the difference being of at least 0.0604, to either side, plus or minus, which is P(|z| > 0.77), given by 2 multiplied by the p-value of z = -0.77.
Looking at the z-table, z = -0.77 has a p-value of 0.2207.
2*0.2207 = 0.4414
The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.
This table gives a few (x,y) pairs of a line in the coordinate plane.
Answer:
The x-intercept of the line will be (10, 0)
Step-by-step explanation:
start from -12
get to -2...
-12 + (10) = -2
-2 + (10) = 8
therefore, the x-intercept is (10, 0)
a. 312
b. 317
c. 315
d. 316
Answer:
B.) 317
Step-by-step explanation:
100/2 = 50
124/2 = 62
180/2 = 90
634/2 = 317
20 kg potatoes are sold at $12.80 each.If you have only $48, how many 20kg bags can you buy
1/10 + 3/5
ANSWER QUICK PLS FIRST ANSWER GETS BRAINLIEST
If x+y=
= 12 and x = 2y, then x =
O
2
06
08
10
Answer:
2y + y = 12
3y = 12
y = 4
now , x = 2y
x = 2 ( 4 )
x = 8
hope that helps ✌
A local grocery store receives strawberries from suppliers in Florida and California. Currently there are 18 strawberry containers on the shelf and 11 of them are from Florida. A shopper selects three containers to purchase. What is the probability that exactly one of the containers is from the Florida supplier
Using the hypergeometric distribution, it is found that there is a 0.2831 = 28.31% probability that exactly one of the containers is from the Florida supplier.
The containers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.In this problem:
There are 18 containers, hence [tex]N = 18[/tex]11 of those are in Florida, hence [tex]k = 11[/tex].A sample of 3 containers is taken, hence [tex]n = 3[/tex]The probability that exactly one of the containers is from the Florida supplier is P(X = 1), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 1) = h(1,18,3,11) = \frac{C_{11,1}C_{7,2}}{C_{18,3}} = 0.2831[/tex]
0.2831 = 28.31% probability that exactly one of the containers is from the Florida supplier.
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Solve for x
Answer choices:
4
5
8
3
2
opposite angles are equal
[tex]\\ \sf\longmapsto 13x+19=84[/tex]
[tex]\\ \sf\longmapsto 13x=84-19[/tex]
[tex]\\ \sf\longmapsto 13x=65[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{65}{13}[/tex]
[tex]\\ \sf\longmapsto x=5[/tex]
Answer:
[tex]\boxed {\boxed {\sf x=5}}[/tex]
Step-by-step explanation:
We are asked to solve for x.
We are given a pair of intersecting lines and 2 angles measuring (13x+19)° and 84°. The angles are opposite each other, so they are vertical angles. This means they are congruent or have the same angle measure.
Since the 2 angles are congruent, we can set them equal to each other.
[tex](13x+19)=84[/tex]
Solve for x by isolating the variable. This is done by performing inverse operations.
19 is being added to 13x. The inverse operation of addition is subtraction. Subtract 19 from both sides of the equation.
[tex]13x+19-19= 84 -19[/tex]
[tex]13x= 84 -19[/tex]
[tex]13x=65[/tex]
x is being multiplied by 13. The inverse operation of multiplication is division. Divide both sides by 13.
[tex]\frac {13x}{13}= \frac{65}{13}[/tex]
[tex]x= \frac{65}{13}[/tex]
[tex]x= 5[/tex]
For this pair of vertical angles, x is equal to 5.
A smartphone consumes 4 watts of power when charging. Your power company charges 12 cents per kilowatt hour (kWh). If you leave your smartphone plugged in to the wall outlet for 24 hours, how many cents does this cost
Answer:
[tex]C=1.15cents[/tex]
Step-by-step explanation:
Generally the equation for is mathematically given by
Charge Power P=4watts
Rate r=12cents/hour
Time consumed T=24
Generally
Power consumed by smartphone in 24 hours
[tex]P_t=P*T\\\\P_t=24*4[/tex]
[tex]P_t=0.096kwh[/tex]
Therefore the Cost will be
[tex]C=12*0.096kwh[/tex]
[tex]C=1.15cents[/tex]
you start at (5,3) you move down 4 units and up 6 units. where do you end?
You end up at the point (5, 5).
Please help me! Thank you!
Find the length of BC
A. 27.22
B. 11.62
C. 22.02
D. 19.78
Answer:
B
Step-by-step explanation:
Since we know the measure of ∠B and the side opposite to ∠B and we want to find BC, which is adjacent to ∠B, we can use the tangent ratio. Recall that:
[tex]\displaystyle \tan\theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]
The angle is 54°, the opposite side measures 16 units, and the adjacent side is BC. Substitute:
[tex]\displaystyle \tan 54^\circ = \frac{16}{BC}[/tex]
Solve for BC. We can take the reciprocal of both sides:
[tex]\displaystyle \frac{1}{\tan 54^\circ} = \frac{BC}{16}[/tex]
Multiply:
[tex]\displaystyle BC = \frac{16}{\tan 54^\circ}[/tex]
Use a calculator. Hence:
[tex]\displaystyle BC \approx 11 .62\text{ units}[/tex]
BC measures approximately 11.62 units.
Our answer is B.
I need help on this math problem
Answer:
for the first one, simply add g(x) and h(x) :
x+3 + 4x+1 = 5x + 4
the second one, you would multiply them :
(x+3)(4x+1) = 4x^2 + 13x + 3
the last one, you would subtract :
(x+3)-(4x+1) = -3x + 2
and then substitute 2 for 'x' :
-3*2 + 2 = -6 + 2 = -4
Answer:
1. 5x+4
2. [tex]4x^2+13x+3[/tex]
3. -4
Step-by-step explanation:
1. (x+3)+(4x+1)
Take off the parentheses and Add.
5x+4
2. (x+3)(4x+1)
Use the FOIL method to multiply.
[tex]4x^2+x+12x+3[/tex]
[tex]4x^2+13x+3[/tex]
3. First, set up the equation as (g-h)(x)
(x+3)-(4x+1)
x+3-4x-1
Solve.
-3x+2
Substitute in 2 for x.
-3(2)+2
-6+2
-4
It looks like there is an error on this statement. Please take 15% off of this $123.00 bill.
The 15 percent-off $123 or 15 percent discount for a item in which the original price is $123 is: $18.45
15 percent-off $123Using this formula
Amount = Original Price x Discount
Let plug in the formula
Amount= 123 x 15 / 100
Amount = 1845 / 100
Amount = $18.45
Inconclusion the 15 percent-off $123 is $18.45.
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A bag of 31 tulip bulbs contains 13 red tulip bulbs, 9 yellow tulip bulbs, and 9 purple tulip bulbs. Suppose two tulip bulbs are randomly selected without replacement from the bag. (a) What is the probability that the two randomly selected tulip bulbs are both red? (b) What is the probability that the first bulb selected is red and the second yellow? (c) What is the probability that the first bulb selected is yellow and the second red? (d) What is the probability that one bulb is red and the other yellow?
Answer:
36% on first
Step-by-step explanation:
The data show the traveler spend- ing in billions of dollars for a recent year for a sample of the states. Find the range, variance, and standard deviation for the data.
20.1 33.5 21.7 58.4 23.2 110.8 30.9
24.0 74.8 60.0
Solution :
Given data :
20.1 33.5 21.7 58.4 23.2 110.8 30.9
24.0 74.8 60.0
n = 10
Range : Arranging from lowest to highest.
20.1, 21.7, 23.2, 24.0, 30.9, 33.5, 58.4, 60.0, 74.8, 110.8
Range = low highest value - lowest value
= 110.8 - 20.1
= 90.7
Mean = [tex]$\frac{\sum x}{n}$[/tex]
[tex]$=\frac{20.1+21.7+23.2+24.0+30.9+33.5+58.4+60.0+74.8+110.8}{10}$[/tex]
[tex]$=\frac{457.4}{10}$[/tex]
[tex]$=45.74$[/tex]
Sample standard deviation :
[tex]$S=\sqrt{\frac{1}{n-1}\sum(x-\mu)^2}$[/tex]
[tex]$S=\sqrt{\frac{1}{10-1}(20.1-45.74)^2+(21.7-45.74)^2+(23.2-45.74)^2+(24.0-45.74)^2+(30.9-45)^2}$[/tex]
[tex]\sqrt{(33.5-45.74)^2+(58.4-45.74)^2+(60.0-45.74)^2+(74.8-45.74)^2+(110.8-45.74)^2}[/tex]
[tex]$S=\sqrt{\frac{1}{9}(657.4+577.9+508.0+472.6+220.2+149.8+160.2+203.3+844.4+4232.8)}$[/tex][tex]$S=\sqrt{\frac{1}{9}(8026.96)}$[/tex]
[tex]$S=\sqrt{891.88}$[/tex]
S = 29.8644
Variance = [tex]S^2[/tex]
[tex]=(29.8644)^2[/tex]
= 891.8823
A circular fence is being placed to surround a tree. The diameter of the
fence is 4 feet. How much fencing is used? *
Answer:
12.6 ft
Step-by-step explanation:
Can I please get some help it would mean the world if u guys helped me and also can u show ur work and how u did it thanks! <3 =) have a nice day!
I NEEDVHELP FINDING COORDINATES AGAIN 3
Answer:
M = (1,3) - 1 right, 3 up
A = (4,0) - 4 right, 0 up
T = (3,6) - 3 right, 6 up
H = (6,2) - 6 right, 2 up
Step-by-step explanation:
Remember, to write the ordered pair using the correct order (x,y) x means it moves either left or right and y moves up or down.
First identify the x-coordinate of a point on a graph. Start at (0,0) which is where the x and y axis meet. (Basically the center of the coordinate plane.)
Then move either left or right and count the number of spaces you move until you are under or over the coordinate. The number of spaces you counted it the x value.
Next, identify the y-coordinate of a point. Now move up or down and count the number of spaces until you meet the coordinate. The number of spaces you counted is the y value.
I tried my best to explain. Let me know if you are still confused.
14. What, if any, is a real solution to 5x +1 +9 - 3?
1
C
D. There is no real solution.
I believe the question is:
What is the solution to 5x + 1 +9 - 3
In this case, we solve for X.
5x + 1 + 9 - 3
5x + 10 - 3
5x + 7
5x = -7
x = -7/5
Unfortunately, It is not one of the answer choices it looks like.
Maybe you should reword your question but hopefully this is correct.
If you meant to say 5x+1 + 9 < 3 --> 5x + 10 < 3 --> 5x < -7 --> x < -7/5
The value of x in a given expression is -7/5.
We have given that,
5x + 1 + 9 - 3
We have to determine the value of x.
What is the variable?A variable is any factor, trait, or condition that can exist in differing amounts or types. Scientists try to figure out how the natural world works
In this case, we solve for X.
5x + 1 + 9 - 3
5x + 10 - 3
5x + 7
5x = -7
x = -7/5
If you meant to say 5x+1 + 9 < 3 --> 5x + 10 < 3 --> 5x < -7 --> x < -7/5.
Therefore we get the value of x is -7/5.
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Solve the following system of equations using the elimination method.
5x - 5y = 10
6x - 4y= 4
A) (-3,5)
B) (2-7)
C) (-1,-5)
D) (-2,-4)
Answer:
D. (-2,-4)
Step-by-step explanation:
When given multi-choice questions like these and you're time bound, substitute the provided answers into the question and see if you'll get the figure beside the '='.
So, using D answers as example 1.
let -2 be x and -4 be y
Substitute these answers into the question.
5(-2)-5(-4)=10
-10+20=10 (+20 because when 2 negative values multiply each other, the operator becomes positive and so is the answer)
10=10
This means the answers provided for D(-2,-4) is the right answer.
PS: Please use or adopt this strategy to solve such questions ONLY when you've been provided with multiple answers to choose from. Plus, it also helps save time.
Thanks
