Answer:
Dependent Variable = tips left by male customers
Independent Variable = T-Shirt color worn by waitresses
Step-by-step explanation:
Dependent variable is the variable that changes when the independent variable changes.
In other words, when the independent variable is varied, the dependent variable changes. The dependent variable is the effect or outcome of the manipulation of the independent variable.
In the study referred to in the question above, the amount of tips given to waitresses is dependent on the color of the T-shirt the waitresses wear.
Therefore, the dependent variable is T-Shirt color, while the independent variable is the amount of tips given.
The rate of change of the number of squirrels S(t) that live on the Lehman College campus is directly proportional to 30 − S(t), where t is the time in years. When t = 0, the population was 15, and when t = 2, the population increased to 20. Find the population when t = 3.
Answer:
S(3)=22
Step-by-step explanation:
The rate of change of the number of squirrels S(t) that live on the Lehman College campus is directly proportional to 30 − S(t).
[tex]\dfrac{dS}{dt}=k(30-S(t))\\ \dfrac{dS}{dt}+kS(t)=30k\\$The integrating factor: e^{\int k dt}=e^{kt}\\$Multiply all through by the integrating factor\\ \dfrac{dS}{dt}e^{kt}+kS(t)e^{kt}=30ke^{kt}[/tex]
[tex](Se^{kt})'=30ke^{kt} dt\\$Integrate both sides\\ Se^{kt}=\dfrac{30ke^{kt}}{k}+C$ (C a constant of integration)\\Se^{kt}=30e^{kt}+C\\$Divide both sides by e^{kt}\\S(t)=30+Ce^{-kt}[/tex]
When t=0, S(t)=15
[tex]15=30+Ce^{-k*0}\\C=15-30\\C=-15[/tex]
When t = 2, S(t)=20
[tex]20=30-15e^{-2k}\\20-30=-15e^{-2k}\\-10=-15e^{-2k}\\e^{-2k}=\dfrac23\\$Take the natural log of both sides$\\-2k=\ln \dfrac23\\k=-\dfrac{\ln(2/3)}{2}[/tex]
Therefore:
[tex]S(t)=30-15e^{\frac{\ln(2/3)}{2}t}\\$When t=3$\\S(t)=30-15e^{\frac{\ln(2/3)}{2} \times 3}\\S(3)=21.8 \approx 22[/tex]
Suppose that x has a binomial distribution with n = 201 and p = 0.45. (Round np and n(1-p) answers to 2 decimal places. Round your answers to 4 decimal places. Round z values to 2 decimal places. Round the intermediate value (σ) to 4 decimal places.) (a) Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x.
Answer:
a) It can be used because np and n(1-p) are both greater than 5.
Step-by-step explanation:
Binomial distribution and approximation to the normal:
The binomial distribution has two parameters:
n, which is the number of trials.
p, which is the probability of a success on a single trial.
If np and n(1-p) are both greater than 5, the normal approximation to the binomial can appropriately be used.
In this question:
[tex]n = 201, p = 0.45[/tex]
So, lets verify the conditions:
np = 201*0.45 = 90.45 > 5
n(1-p) = 201*(1-0.45) = 201*0.55 = 110.55 > 5
Since both np and n(1-p) are greater than 5, the approximation can be used.
Which of the following are true? If false, explain briefly.
​a. A very high​ P-value is strong evidence that the null hypothesis is false. ​
b. A very low​ P-value proves that the null hypothesis is false. ​
c. A high​ P-value shows that the null hypothesis is true.
d. A​ P-value below 0.05 is always considered sufficient evidence to reject a null hypothesis.
Answer:
The correct options are;
a. False
b. True
c. True
d. False
Step-by-step explanation:
We look at each of the options as follows
a. A very high p-value is strong evidence that the null hypothesis is false;
The above statement is false because the p-value indicates the likelihood of the null hypothesis being correct, therefore, a high p-value is indicative of the correctness (truth) of the null hypothesis
b. A very low p-value shows that the null hypothesis is false
The above statement is true
c. A high p-value shows that the null hypothesis is true
The above statement is true
d. A P-value below 0.05 is always considered sufficient evidence to reject a null hypothesis.
The above statement is false as the p-value below which we reject the null hypothesis is dependent on the value of the significance level, α.
The U.S. Commission on Crime randomly selects 600 files of recently committed crimes in an area and finds 380 in which a firearm was reportedly used. Find a 95% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used.
Answer:
95% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used.
(0.59445 , 0.67155)
Step-by-step explanation:
Explanation:-
Given random sample size 'n' = 600
sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{380}{600} = 0.633[/tex]
95% of confidence interval for Population proportion is determined by
[tex](p^{-} - Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^{-} )}{n} } , p^{-} +Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^{-} )}{n} })[/tex]
Level of significance : α = 0.05
[tex]z_{\frac{0.05}{2} } = Z_{0.025} =1.96[/tex]
[tex](0.633 - 1.96 \sqrt{\frac{0.633 (1-0.633 )}{600 }}, (0.633 + 1.96 \sqrt{\frac{0.633 (1-0.633 )}{600 }[/tex]
On calculation , we get
(0.633 - 0.03855 , (0.633 + 0.03855)
(0.59445 , 0.67155)
Conclusion:-
95% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used.
(0.59445 , 0.67155)
Please HELP
2^8-10-15\div3=2
8
−10−15÷3=
Answer:
241
Step-by-step explanation:
We want to evaluate the expression:
[tex]2^8-10-15\div3[/tex]
We follow the order of operations: PEMDAS
Since there are no parenthesis(P), we evaluate the exponents(E)
[tex]2^8-10-15\div3=256-10-15\div3[/tex]
Next is Division (D)
[tex]256-10-15\div3=256-10-5[/tex]
We can then simplify since we have only subtraction.(S)
[tex]256-10-5=241[/tex]
Therefore:
[tex]2^8-10-15\div3=241[/tex]
Budget
8.) If Peter Gower paid $650 for rent
monthly for an entirely year, how
much should he budget for rent
each month?
Answer:
I
(a) $108.33
(b) $54.17
(c) $7.800
(d) $650
a =
2
4
b =
(3
-2
Work out 3a + b as a column vector.
Answer:
As a column vector 3a +b = (9,10)
Step-by-step explanation:
A =
(2
4)
b =
(3
-2)
3a = 3*2 = 6
3*4= 12
3a + b = 6. + 3
12. +(-2)
3a +b = 9
10
As a column vector 3a +b = (9,10)
which interval describes the range of this function?
Answer:
Range. The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. In plain English, the definition means: The range is the resulting y-values we get after substituting all the possible x-values
Step-by-step explanation:
A researcher wishes to estimate the proportion of left-handed people among a certain population. In a random sample of 820820 people from the population, 22.722.7% are left-handed. Find the margin of error for the 95% confidence interval for the population proportion. Round to four decimal places.
Answer:
The margin of error for the 95% confidence interval for the population proportion is of 0.0287.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Find the margin of error for the 95% confidence interval for the population proportion.
We have that [tex]n = 820, p = 0.227[/tex]
So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.227*0.773}{820}} = 0.0287[/tex]
The margin of error for the 95% confidence interval for the population proportion is of 0.0287.
The coordinates of the points below represent the vertices of a rectangle.
P (2, 2) Q (6, 2) R (6, 5) S (2, 5)
What is the perimeter, in units of rectangle PQRS?
Answer:
18 units
Step-by-step explanation:
5+5=10
4+4=8
8+10=18 units
Answer:
14
Step-by-step explanation:
The perimeter of a rectangle is the sum of the lengths of the 4 sides of a rectangle. Since in a rectangle opposite sides are congruent, you just need to find the lengths of any two adjacent sides because adjacent sides cannot be opposite. Then add them and multiply the sum be 2 to account for the opposites sides.
Two find the distance between any two points, you can use the distance formula. If the two points lie on the same vertical line (both points have the same x-coordinate), or if the two points lie on the same horizontal line (both points have the same y-coordinate), then just subtract the different coordinates and take the absolute value.
PQ = |2 - 6| = |-4| = 4
QR = |2 - 5| = |-3| = 3
perimeter = 2(length + width)
perimeter = 2(4 + 3)
perimeter = 2(7)
perimeter = 14
One t-shirt is sold for every 5 people who attend a concert.what is one way to write the unit rate in words?
1 T-Shirt for every 5 people
First of all, B & C are wrong, because they say 5 T-shirts for one person.
Next, we will look at A & D. A is more grammatically correct, and so you should use A.
OR
Answer:
The last one
I can’t figure this out it’s difficult for can anyone help me Plz
Answer:
the correct option is D
Step-by-step explanation:
JK IS longer than JL
The “line of best fit” for a scatterplot is the line that __________.
Answer:
Scatter plots are used to plot data points on a horizontal and a vertical axis in the attempt to show how much one variable is affected by another. Each row in the data table is represented by a marker whose position depends on its values in the columns set on the X and Y axes
Step-by-step explanation:
I need the answer here is the question:
Write the fraction in simplest form . And the picture ☝
Answer:
i need points sorry
Step-by-step explanation:
nfefgrn
what two decimals are equivalent to 4.400
Answer:
4.4
4.40
Step-by-step explanation:
These two decimals above are equivalent to 4.400 because no matter the amount of zeroes, the numbers are the same. For example, 4.400 is also equivalent to 4.400000000000000000000000000000000. As long as the "4's" maintain the same place (ones place and tens place), the decimals will be congruent to one another.
I Really Need Help with this not good with graphs
Answer:
D
Step-by-step explanation:
The one dot that is a lot farther away from the rest of the points is an outlier so the answer is D.
Figure 2 was constructed using figure 1. For the transformation to be defined as a rotation, which statements must be true? Select three options. The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2). The transformation is rigid. Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2. Segment CP is parallel to segment CP'. If figure 1 is rotated 180° about point C, it will be mapped onto itself.
Answer:
all but the last two
Step-by-step explanation:
Rotation is a rigid transformation that moves every point of a figure through the same rotation angle about the center of rotation. Each point has the same distance from the center it had before the rotation. Hence the following are true:
The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2). The transformation is rigid. Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.__
Statements that do not apply are ...
- Segment CP is parallel to segment CP'. (A segment to the center of rotation will only be parallel to the corresponding segment on the image if the rotation is a multiple of 180°.)
- If the figure is rotated 180° about C, it will be mapped to itself. (This will be true in general only if C is a center of rotational symmetry of even order.)
Answer:
A,B,C
Step-by-step explanation:
I'm sure cause I got it right depends what your Edgenu is, mine is 2020
~Help me with this please! I will mark as BRANLIEST and if you answer correctly there would be a 55 point question for you!!!
Answer:
Simply here we use system of 2 equations.
Step-by-step explanation:
Let x be the cost of one small shirt and let y be that of one large shirt.
(4x +14y =210) (-3)
12x +11y =110
-12x - 42y= -630 note:cross 12x and - 12x
12x +11y =110
__________
-42y +11y = - 630 +110
-31y = -520
Y=520/31
Replace y in second equation:
12x +11y =110
12x +11(520/31) =110
12x +5720 =110
12x =110 - 5720/31
X= - 385/62
So one small shirt costs - 385/62 $
And a large one costs 520/31 $
Though I think there's something wrong in this problem since i verified my answer using calculator the same prices are obtained and as u see the cost of a small shirt is negative which is unbelievable.. So plz make sure from anyone else. I tried my best to help.
A box contains 2 red marbles, 3 white marbles, 4 green marbles, and 1
blue marble. Two marbles, one after the other, are drawn at random
WITHOUT replacement. Find the probability of: selecting a green marble
on the second draw if the first marble is blue *
1/6
2/13
4/9
1/9
Answer:
Solution is 4/9
Explanation:
A box contains:
2 red marbles,
3 white marbles,
4 green marbles,
1 blue marble.
=> Total: 2 + 3 + 4 + 1 = 10
After selected a blue one without replacement, the remaining number: 10 - 1 = 9
=> Probability of drawing a green one: P = 4/9.
Hope this helps!
:)
In ΔGHI, the measure of ∠I=90°, IG = 6.8 feet, and HI = 2.6 feet. Find the measure of ∠G to the nearest degree.
Answer:
[tex]\angle G=20.8\approx 21^{\circ}[/tex]
Step-by-step explanation:
Given: In ΔGHI, [tex]\angle I[/tex]=90°, IG = 6.8 feet, and HI = 2.6 feet
To find: [tex]\angle G[/tex]
Solution:
Trigonometry defines relationship between the sides and angles of the triangle.
For any angle [tex]\theta[/tex],
[tex]tan\theta[/tex] = side opposite to [tex]\theta[/tex]/side adjacent to [tex]\theta[/tex]
In ΔGHI,
[tex]tan G=\frac{HI}{GI}[/tex]
Put [tex]HI=2.6 \,\,feet\,,\,GI=6.8\,\,feet[/tex]
So,
[tex]tan G=\frac{2.6}{6.8}=0.38[/tex]
Therefore, [tex]\angle G=20.8\approx 21^{\circ}[/tex]
Answer:
G=24.6236≈24.6
If a person is randomly selected, find the probability that his or her birthday is not on New Year's Day. Ignore leap years.
Answer:
Ignoring leap years, May has 31 days, a year has 365 days. 334 days of the year are NOT in May so the probability of a birthday not being in May = 334/365 = approximately 91.5%
Step-by-step explanation:
The probability of event A which represents that the man's birthday is not on New Year's Day is 0.99.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -
P(A) = n(A)/n(S)
Given is a person who is randomly selected.
Assume that Event A represents that the man's birthday is not on New Year's Day.
Total number of days in a year = n(S) = 365
Total number of days not on New Year's Day = n(A) = 364
Therefore, the probability that the man's birthday is in May will be -
P(A) = n(A)/n(S)
P(A) = 364/365
P(A) = 0.99
Therefore, the probability of event A which represents that the man's birthday is not on New Year's Day is 0.99.
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simplify 4x/7-x/21 find
The answer is 11x/21
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer:
[tex] \frac{11x}{21} [/tex]
Step-by-step explanation:
[tex] \frac{4x}{7} - \frac{x}{21} \\ = \frac{12x - x}{21} \\ = \frac{11x}{21} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
rudo is making pizzas he needs 3/4 cup of cheese to make one whole pizza. he has 2/8 cup of cheese
Answer: He can make 1/3 of pizza.
Step-by-step explanation: Divide 2/8 by 3/4. When you divide fractions you need to keep the first number exactly as it is and change the sign to multiplication and flip the second number. It is going to be 2/8 times 4/3. Which is 8/24 and if you simplify it, divide 8 and 24 by 8, and the answer is 1/3.
The required solution is 1/3.
It is required to find the remaining part to make one whole pizza.
What is fraction?A fraction having whole numbers for the numerator and denominator. A fraction is a number of the form: ab where a and b are integers and b≠0. It represents the division of two numbers.
Given:
He has 2/8 cup of cheese.
Divide 2/8 by 3/4.
When you divide fractions you need to keep the first number exactly as it is and change the sign to multiplication and flip the second number. It is going to be 2/8 times 4/3. Which is 8/24 and if you simplify it, divide 8 and 24 by 8, and the answer is 1/3.
Therefore, the required solution is 1/3.
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simplify the equation below and find the value of x
4/2x-5)= 20
Answer:
x=13/5
Step-by-step explanation:
Kyla makes a triangular school pennant. The area of the triangle is 180 square inches. The base of the pennant is z inches long. The height is 6 inches longer than twice the base length.
What is the height of the pennant? Recall the formula
A = bh.
Answer:
Height of the pennant is 30 inches.
Step-by-step explanation:
Given that:
Area of pennant = 180 sq inches
Base of pennant = z inches
Height of pennant = (2z + 6) inches
Also, it is a triangular pennant and area of a triangle can be given as:
[tex]A = \dfrac{1}{2} \times Base\times Height[/tex]
Putting the values in above formula:
[tex]180 = \dfrac{1}{2} \times z \times (2z+6)\\\Rightarrow 360 = 2z^{2} + 6z\\\Rightarrow 180 = z^{2} + 3z\\\Rightarrow z^{2} + 3z -180 = 0\\\Rightarrow z^{2} + 15z -12z -180 = 0\\\Rightarrow z(z + 15) -12(z+15) = 0\\\Rightarrow (z + 15) (z-12) = 0\\\Rightarrow z = 12\ or\ z=-15[/tex]
Value of z can not be negative, so value of Base, z = 12 inches.
Height is given as 2z + 6 so, height = 2[tex]\times[/tex]12 +6 = 30 inches
Answer:
C.30 inches
Step-by-step explanation:
In a science class, 40% of the students received a grade of A, 30% received a grade of B, and 20% received a grade of C on a project. The others fell short of a passing grade. a. If 12 students received an A, how many students were in the science class? b. How many students received a failing grade?
Answer:
30 students are in the science class and 3 students recieved a failing grade.
Answer:
30, 3
Step-by-step explanation:
a. Let's call the total students x. If 40% x = 12, 0.4x = 12, x = 12/0.4 = 30 students.
b. We know that 100 - 40 - 30 - 20 = 10% of all students failed. This is 10% * 30 = 0.1 * 30 = 3 students.
A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 64 months and a standard deviation of 7 months. Using the empirical (68-95-99.7) rule, what is the approximate percentage of cars that remain in service between 43 and 50 months?
Answer:
[tex] z =\frac{50-64}{7}= -2[/tex]
[tex] z =\frac{43-64}{7}= -3[/tex]
We know that within two deviations from the mean we have 95% of the data from the empirical rule so then below 2 deviation from the mean we have (100-95)/2 % =2.5%. And within 3 deviations from the mean we have 99.7% of the data so then below 3 deviations from the mean we have (100-99.7)/2% =0.15%
And then the final answer for this case would be:
[tex] 2.5 -0.15 = 2.35\%[/tex]
Step-by-step explanation:
For this case we have the following parameters from the variable number of motnhs in service for the fleet of cars
[tex] \mu = 64, \sigma =7[/tex]
For this case we want to find the percentage of values between :
[tex] P(43< X< 50)[/tex]
And we can use the z score formula given by:
[tex] z = \frac{X-\mu}{\sigma}[/tex]
In order to calculate how many deviation we are within from the mean. Using this formula for the limits we got:
[tex] z =\frac{50-64}{7}= -2[/tex]
[tex] z =\frac{43-64}{7}= -3[/tex]
We know that within two deviations from the mean we have 95% of the data from the empirical rule so then below 2 deviation from the mean we have (100-95)/2 % =2.5%. And within 3 deviations from the mean we have 99.7% of the data so then below 3 deviations from the mean we have (100-99.7)/2% =0.15%
And then the final answer for this case would be:
[tex] 2.5 -0.15 = 2.35\%[/tex]
What is 0.03% written as a decimal?
O A. 0.3
O B. 0.0003
O C. 0.003
O D. 0.03
The percentage 0.03% when it is written as a decimal is equivalent to 0.0003.
What are decimals?
A decimal is a number that is made up of integers and non-integers. The whole numbers are separated from numbers that are not whole number by a decimal point.
0.03% is equal to 0.03/100.
0.03/100 is equal to 0.0003
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g(-2) for
g(x)=2x^3 3x^2 =4
PLEASE ANSWER THIS YOU WILL GET 20 POINTS I NEED HELP ASAP THANK YOU SO MUCH
Answer:
g(-2)
g(x)=2x^3 3x^2 =4
i'm not exactly sure what you are asking for but if its something like
g(x)=2x^3+3x^2-4 and then g(-2)
then you just have to multiply
2(-2)^3=-16
+3(-2)^2-4=8
=-8
2(-2)^3=-16
2(-2)^3-+3(-2)^2-4
=-32
What is 3 1/2 miles - 3,520 yards? (And put your answer in miles)
Answer:
3 1/2 miles is 6160 yards and 3,520 yards is 2 miles
Step-by-step explanation:
