The number of ways that a nine question true false quiz can be answered is; 512 ways
What is the number of ways of answering?
We are given;
Number of questions = 9
Options for each answer = 2 (True of false)
The power set is defined as the number of subsets of a set of n elements which is expressed as 2ⁿ
There are 2 ways to answer question 1 and as such it means that there are 2 ways to answer question 2.
For question 2; 2² = 4 ways
For question 3; 2³ = 8 ways
For question 4; 2⁴ = 16 ways
For question 5; 2⁵ = 32 ways
For question 6; 2⁶ = 64 ways
For question 7; 2⁷ = 128 ways
For question 8; 2⁸ = 256 ways
For question 9; 2⁹ = 512 ways
Thus we we conclude that, there are 512 ways to answer 9 true-false tests.
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The scatter plot shows the number of strawberries that have been picked on the farm during the month of February
1001
Number of Strawberries
116ITTIS ITT2TTAS
Days in February
Part A: Using computer software, a correlation coefficient of r= 0. 01 was calculated. Based on the scatter plot, is that an accurate value for this data? Why
or why not? (5 points)
Part B. Instead of comparing the number of strawberries picked and the day in February, write a scenario that would be a causal relationship for
strawberries picked on the farm. (5 points)
Part A:because the data points are far away from each other.
Part B: A casual relationship would be: the number of strawberries picked and the amount of fertilizers used.
What is Correlation Coefficient?
Correlation coefficient, r, is quantitative measure that measures the extent to which two variables are associated.
The closer the data points are on a scatter plot, the closer the value of r is to 1 or -1.
Part A:
The data points in the scatter plot are farther apart and the trend slopes upwards to the right, this means that the correlation coefficient, r, would be positive but very low.
Thus, based on the scatter plot given, the correlation coefficient of r = 0.01 is most likely accurate because the data points are far away from each other.
Part B:
A casual relationship would be: the number of strawberries picked and the amount of fertilizers used.
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what is the factored form 8g^2+6g-9
Answer:
A.
Step-by-step explanation:
you want to determine whether a new medication affects children's test scores. you have 10 sets of identical twins as your sample. one twin in each set takes the medication, while the other doesn't. you will compare the test scores of the medicated twins to the test scores of the unmedicated twins. the null hypothesis is that there will be no difference in test scores between the medicated and unmedicated twins. which tool within data analysis will you use?
T-test paired two samples for means should be used .
What does test score mean?
A test score is a numeric piece of information that describes how well a test-taker performed. It is described in one formal definition as "a summary of the evidence contained in an examinee's responses to the items of a test that are related to the construct or constructs being measured."here the samples are dependent, the score of one twins is compared with the score of any another from the same pair .
Hence, T-test paired two samples for means should be used
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for an ordered pair (x comma y )in a relation, the x element represents the .
for an ordered pair (x comma y )in a relation, the x element represents the horizontal axis.
Against the Wind a small plane flew 858 miles in 2 hours and 10 minutes the return trip only took 1 hour and 50 minutes what was the speed of the wind?what was the speed of the plane in still air?
Let the speed of the small plane be 'R'.
Let the speed of the wind be 'S'.
Plane's time against wind = 2 hours and 10 minutes = 13/6 hours.
Plane's time with wind = 1 hour and 50 minutes = 11/6 hours
Use formula;
Distance = speed x time
Against the wind:
858 = (13/6) (R-S) = (13/6) R - (13/6)S
With wind:
858 = (11/6)(R + S) = (11/6)R + (11/6)S
Multiplies each by 6.
5148 = 13R - 13S
5148 = 11R + 11S
Use elimination method
56628 = 143R - 143S (multiplies by 11)
66924 = 143R + 143S (multiplies by 13)
Further solving;
123552 = 276R
R = 432 miles/ hr. (speed of small plane )
And, S = 36 miles/ hr. (speed of wind)
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Tyshawn has $600 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
• He buys a new bicycle for $237.49.
He buys 3 bicycle reflectors for $14.57 each and a pair of bike gloves for $34.52.
He plans to spend some or all of the money he has left to buy new biking outfits
for $71.07 each.
●
●
Use the drop-down menu below to write an inequality representing o, the number of
outfits he can buy while staying within his budget.
Answer: The answer would be 4 biking outfits o=4
Step-by-step explanation:
First add all the money he spent excluding the outfits. The answer would be 315.72. Then subtract 600 and 315.72 = 284.28. Last multiply 71.07 by 4 which gets you 284.28. The EXACT amount he has left. Answer is he can be 4 new biking outfits within his budget. Hope I could help!
The function h is defined by h (x) = 2(x − 7).
What is the value of h (8) ?
2
23
30
9
Answer:
h(8) = 2
Step-by-step explanation:
substitute x = 8 into h(x) , that is
h(8) = 2(8 - 7) = 2(1) = 2
two cars start moving from the same point. one travels south at 60 mi/h and the other travels west at 25 mi/h. at what rate is the distance between the cars increasing three hours later? 3 hours
The distance between the two cars varies at a speed of 65 m/h after two hours.
Let y represent the car's southward travel distance.
Let x be the distance traveled by the westbound automobile.
Allow a to be the distance between the two vehicles.
A right-angled triangle can be used to symbolize these three distances. So, we can state:
a^2 = x^2 + y ^2
Given that the distances vary with respect to time, let's make a distinction.:__________(1)
2a da/dt = 2x dx/dt +2y dy/dt
Rate of distance change between two cars, da/dt
The car is traveling west (dx/dt) at 25 m/h, while the car traveling south (dy/dt) is traveling at 60 m/h.
Therefore:
dy/dt = 60 m/h and dx/dt = 25 m/h
The separation between the two cars will be after two hours:
y = 3* 60 = 180 miles
x = 3 * 25 = 75 miles
Therefore:
a^2 = x^2 + y ^2
a^2 = 75 ^2+ 180 ^2
a= [tex]\sqrt{5625 + 32400}[/tex]
a= 195
From (1):
195(da/dt) = 75(25) + 180(60)
195(da/dt) = 1875 + 10800 = 12675
da/dt = 12675 / 195 = 65 m/h
As a result, after two hours, the two automobiles' separation is varying at a speed of 65 m/h.
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a data analyst creates a scatterplot with a lot of data points. the analyst wants to make some points on the plot more transparent than others. what aesthetic should the analyst use?
Analyzers should use the Alpha aesthetic.
Using the Alpha aesthetic, specific points on a scatterplot are more transparent than others to highlight specific data points.
What is a scatterplot?
A scatter plot is a set of points plotted along a horizontal and vertical axis. In statistics (also known as variables), scatter plots are crucial to demonstrating whether a correlation exists between observational quantities or phenomena.
A scatter plot plots data points on a horizontal and vertical axis to demonstrate one variable's influence on another. Each row in the data table is represented by a marker whose position is determined by the values of the columns on the X and Y axes.
Using a scatter plot, this line indicates the prevailing direction of a phenomenon. In a scatter plot, a trend line can be used to highlight the direction and speed of price changes.
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in a certain year, 13,839 professional train pushers are diagnosed with carpal tunnel. the top cities for such diagnoses are tokyo with 2,551, osaka with 3,049, and kyoto with 1,436. if a professional train pusher recently diagnosed with carpal tunnel is randomly selected, what is the probability that they are from somewhere other than tokyo, kyoto or osaka?
Probability that the professional other than Tokyo, Kyoto or Osaka is 6803/13839.
Total number of professional train pushers who are diagnosed with carpal tunnel is 13839
Number such professional from Tokyo = 2551
Number such professional from Osaka = 3049
Number such professional from Kyoto = 1436
So, number such professional from other than these three cities = 13839 - (2551+3049+1436) = 6803
Hence the probability that the professional other than Tokyo, Kyoto or Osaka is = 6803/13839
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Gabriel Harris earns an annual salary of $156,000 as CFO of
TechMedia, Inc. He is married and claims three dependents. TechMedia
recently converted from a weekly pay plan to a monthly pay plan.
How much more will Gabriel have deducted from his monthly pay
than from his weekly pay for state income tax?
Answer:
Step-by-step explanation:
Gabriel Harris earns an annual salary of $156,000 as CFO ofTechMedia, Inc. He is married and claims three dependents. TechMediarecently converted from a weekly pay plan to a monthly pay plan.How much more will Gabriel have deducted from his monthly paythan from his weekly pay for state income tax?
Given: ΔABC Prove: The sum of the interior angle measures of ΔABC is 180°. Statement Reason 1. Let points A, B, and C form a triangle. Given 2. Let be a line passing through B, parallel to , with angles as labeled. Defining a parallel line and labeling angles 3. 4. M∠1 = m∠4, and m∠3 = m∠5. Congruent angles have equal measures. 5. M∠4 + m∠2 + m∠5 = 180° angle addition and definition of a straight angle 6. M∠1 + m∠2 + m∠3 = 180° substitution What is the missing step in this proof? A. Statement: ∠4 ≅ ∠5, and ∠1 ≅ ∠3. Reason: Alternate Interior Angles Theorem B. Statement: is parallel to. Reason: is a transversal cutting and. C. Statement: ∠1 ≅ ∠4, and ∠3 ≅ ∠5. Reason: Alternate Interior Angles Theorem D. Statement: ∠1 ≅ ∠4, and ∠3 ≅ ∠5. Reason: ∠1 and ∠4, and ∠3 and ∠5 are pairs of supplementary angles
From the given statements regarding angle the point b) DE is parallel to AC with its reason - AB is a transversal cutting DE and AC will be the correct statement.
DE and AC are parallel for this to work angle 1 is at A, angle 2 is at B and angle 3 is at C. In addition, angle 4 is the alternate interior angle to angle 1 once DE is constructed, as is angle 5 to angle 3. Then the missing reasons are alternate interior angles theorem and definition of congruent angles.
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The sides of a triangle are in the form of consecutive even integers. If its perimeter is 48cm, find the
measure of each side.
Answer:
The sides of the triangle would be 14, 16, and 18.
Step-by-step explanation:
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May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 28.45°. What is the measure of ∠P?
28.45°
75.775°
121.55°
151.55°
Step-by-step explanation:
the sum of all angles in a triangle is ALWAYS 180°.
and by using the word "congruent" : for angles that only means they are equally large.
we know the third angle.
so,
180 = P + Q + R = 2×P + 28.45
(because P = Q)
2×P = 151.55
P = Q = 151.55 / 2 = 75.775°
Which of the following is equivalent to 60 Superscript one-half?
Answer
[tex]60\sqrt{x} 2[/tex]
Step-by-step explanation:
Answer:
StartRoot 60 EndRoot
Step-by-step explanation:
Edge
HELP MEEE PLEASEEEEEE
Answer:
Length YZ is about 16.2 cm (to the first decimal place)
Step-by-step explanation:
In order to find the lenth YZ we need to know the the Pythagorean theorem which is a²+b²=c² (or leg² + leg² = hypothnose)
For this problem let a = line segment XY, let b = YZ and let your hypothnose (c) to be ZX
Substitute your known values in the equation so we know a = 5 cm and c = 17 cm so we can apply it in our equation 5²+ b² = 17² Square your known values in this case 5² and 17² which is 25 and 289 respectively. The equation is now 25+b²=289 Do the inverse operation to Isolate you unknown variable which is b. We do this by subtracting 25 on both sides after doing so the equation is now b²= 264 Square root both sides of the equation the point is to get rid of the squared part of b². After doing so your answer is b = 16.2480768093Round to the first decimal place the two remains the same so the final answer is 16.2 cmAurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling a linear function or an exponential function . (2 points)
Part B: Write a function to represent the data. Show your work. (4 points)
Part C : Determine the average rate of change between day 2 and day 4. Show your work (4 points )
Step-by-step explanation:
A
it is an exponential function.
for a linear function the charge rate would have to be constant between any pair of data points.
the change rate is
( f ( interval end ) - f ( interval begin ) ) /
( interval end - interval begin )
between (1, 2) and (2, 4) we have a charge rate of
(4 - 2) / (2 - 1) = 2
between e.g. (3, 8) and (4, 16) we have a charge rate of
(16 - 8) / (4 - 3) = 8
the change rate is therefore not constant, and it is not a linear function.
B
we see
x1 = 1, y1 = 2
x2 = x1 + 1, y2 = y1×2
x3 = x2 + 1, y3 = y2×2
we get the impression that
xn = xn-1 + 1 = x1 + (n - 1)
yn = yn-1 × 2 = y1 × 2^n
so, while going linearly along the x-axis, y increases by the powers of 2.
the function is then
f(x) = 2^x
C
the change rate between station 2 and 4 (NOT day 2 and 4) is
(16 - 4) / (4 - 2) = 12/2 = 6
A polygon has 7 sides. The interior angle measures are 131°, 119°, 125°, 133°, 125°, 138°, and x°. Find the value of x.
HELPPPP PLEASEEE ASAPP
A history teacher asked her students how many hours of sleep they had the night before a test. The data below shows the number of hours the student slept and their score on the exam. What is the best linear regression model rounded to the nearest hundredth? image A. y = 6.38 x + 35.63 B. y = 6.37 x + 0.78 C. y = 35.60 x + 6.378 D. y = 35.63 x + 6.38
The best linear regression model for the grade according to the number of hours slept is of:
A. y = 6.38 x + 35.63.
How to obtain the equation of linear regression for a data-set?To obtain the linear regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in a linear regression calculator. These points are given on a table or in a scatter plot in the problem.
For this problem, the points are given in the table given by the image at the end of the answer, and are given as follows:
(8, 83), (7, 86), (7, 74), (8, 88), (6,76), (5, 63), (7, 90), (4, 60), (9,89), (7,81).
Inserting these points into the linear regression equation, the equation is given as follows:
y = 6.38 x + 35.63.
Hence the correct option is given by option A.
Missing Information
The problem is given by the image shown at the end of the answer.
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at a university, the probability that a student takes statistics and is a business major is 0.036. the probability that a student takes statistics is 0.9. the probability that a student is a business major is 0.12. find the probability that the student takes statistics given that he or she is a business major
The probability that the student takes statistics given that he or she is a business major is 0.04.
Define probability.The probability that an event will occur is determined by the probability formula. The ratio of positive outcomes to all possible outcomes is used as the formula to determine an event's probability. Probabilities are always in the 0 to 1 range. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.
Given,
The probability that a student takes statistics and is a business major is 0.036. the probability that a student takes statistics is 0.9. the probability that a student is a business major is 0.12
Students who have taken both:
P( statistics ∩ business) = 0.036
Only a statistics major:
P( statistics/ business) = 0.9
P( student is business major)
P ( statistics / business) ÷ P( statistics/ business)
0.036/0.9
0.04
The probability that the student takes statistics given that he or she is a business major is 0.04.
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what is the area of the figure?
The area of the figure is 1875 sq.in.
In this question, we need to find the area of the given figure.
the area of the figure = area of rectangle + area of two triangles.
For rectangle,
length = 50 inch and width = 30 in.
Using the formula for the area of rectangle,
A1 = length * width
A1 = 50 * 30
A1 = 1500 sq.in.
For triangle,
base = 1/2 * length of rectangle
so, base = 25 in and height = 15 inch
Using the formula for the area of triangle,
A2 = 1/2 * base * height
A2 = 1/2 * 25 * 15
A2 = 187.5 sq.in.
so, the area of the figure would be,
A = A1 + (2 * A2)
A = 1500 + (2 * 187.5)
A = 1875 sq.in.
Therefore, the area of the figure is 1875 sq.in.
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Determine the period.
Answer:
shopkeeper sells a book at INR 960 for a profit of 20% and another book at INR 720 for a loss of 10%. Find the total profit/loss of the shopkeeper
Algebra 2 please help!
Which table of values would produce the graph shown above?
The table (D) values would produce the same graph as shown.
What is a Graph?Mathematical structures known as graphs are used to describe pairwise relationships between things. Graph theory is the study of these mathematical structures. Vertices (also known as nodes or points) and edges are what make up a graph in this sense (also called links or lines). It is possible to distinguish between directed and undirected graphs, where edges connect two vertices asymmetrically and symmetrically, respectively. One of the primary topics in discrete mathematics is graphs.
From the graph, find the intercepts,
At x = 0, the value of y is -1.
At, y = 0, the value of x is 4
So, from the given options, we can see that the values are given in table (D).
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a fair coin is tossed 28 times. what is the probability that at most 25 tails occur? a) 0.99998628 b) 0.00000152 c) 0.99999848 d) 0.00001220 e) 0.01001372 f) none of the above.
The probability that at most 25 tails occur is 0.99999848.
We know that,
P(x = x) = ⁿCₓ × pˣ × [tex]q^{n-x}[/tex]
p = probability of success = 0.5
n = number of trials = 28
q = 1 - p = 0.5
The probability of the tail occurring at most 25 times can be written as
P(X ≤ 25) = P (X = 0) + P(X = 1) + ..... + P(X = 25)
Using a binomial probability calculator,
P(X ≤ 25) = 0.99999848
Therefore the probability that at most 25 tails occur is 0.99999848
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help me on this math please!
The function rule for each are:
f(x) = -2x - 6
g(x) = 5x - 4
f(x) is less than g(x), in terms of slope, while in terms of y-intercept, f(x) is greater than g(x).
How to Write the Rule of a Function?The rule of a function can be written in slope intercept form as, f(x) = mx + b, where the slope is m and the y-intercept is the value of b.
To write the function rule for f(x), substitute m = -2 and b = -6 into f(x) = mx + b:
f(x) = -2x - 6
Find the slope of the function g(x) whose graph is given:
Slope of g(x) = rise/run = 5/1 = 5
m = 5
The y-intercept is at y = -4, therefore b = -4.
To write the function rule for g(x), substitute m = 5 and b = -4 into g(x) = mx + b:
g(x) = 5x - 4
In terms of slope, f(x) is less than g(x)
In terms of y-intercept, f(x) is greater than g(x).
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Murphy and Nikita can fill their swimming pool with one hose in 10 hours. If they use another hose to help fill the pool, the pool
can be filled in 4 hours. How long would it take the other hose to fill the pool working alone? Round to the nearest tenth.
Answer:
Step-by-step explanation:
so you just have to round where it came from
(2sin(x) - 1)(tan(x) - 1) = 0 for 0 ≤ x ≤ 2 pi
Answer: x1=π/6 ,x2 = π/4, x3 = 5π/6, x4 5π/4
Step-by-step explanation:
2sin(x)-1=0
tan(x)-1=0
sin(x)=1/2
tan(x)=1
x=π/6
x=5π/6
x=π/4
x=5π/4
x1=π/6 ,x2 = π/4, x3 = 5π/6, x4 5π/4
A jewel case contains 7 white gems, 5 green gems, and 3 blue gems. Gems are selected at random. Explain why
the events picking a green gem and then another green gem without replacement are dependent. Then, identify
the probability.
A.) P(green) is the same when it is known that a green gem has been picked already.
P(green and green) = 4/45
B.) Pgreen) is different when it is known that a green gem has been picked already.
P(green and green) = 2/21
C.) P(green) is different when it is known that a green gem has been picked already.
P(green and green) = 5/42
D.) Pgreen) is the same when it is known that a green gem has been picked already.
P(green and green) = 1/9
The second probability is affected by the first probability. So, we can say that this is a dependent probability.
Probability of choosing the first gem green = 1/3Probability of choosing the second gem green = 2/7Given,
Number of white gems = 7
Number of green gems = 5
Number of blue gems = 3
Total number of gems = 7 + 5 + 3 = 15
We have to find the probability when picking a green gem and then another green with out replacement are dependent.
Here,
Probability of choosing the first gem green = Number of green gems / total number of gems
Probability = 5/15 = 1/3
Now,
Number of green gems = 4
Total number of gems = 14
Probability of choosing the second gem green = Number of green gems / Total number of gems
Probability = 4/14 = 2/7
Here,
The second probability is affected by the first probability. So, we can say that this is a dependent probability.
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Solve the following
2( x + 3 ) = x - 4
2x + 6 = x - 4
x ≈ -0,67
or
x = -2^3
A restaurant has a 33,500 gallon aquarium and a 500 gallon aquarium. About how many times is the capacity of the smaller aquarium?
Answer:
67 times
Step-by-step explanation:
33,500 divided by 500 is equivalent to 67
