If the numbers denoting the perimeter and area of the square are equal, the length of the diagonal will be 4√2 units.
What are Area and Perimeter?
An object's shape defines a region as its area. The area of a figure or any other two-dimensional geometric shape is how much space it takes up in a plane.
The whole length encircling a shape is referred to as its perimeter. Simply put, if a shape is stretched into a linear form, its perimeter is its length. In a two-dimensional plane, a shape's perimeter is the sum of its total dimensions.
Let the side of the square to be 'a'.
If Area and Perimeter of a square are equal then,
So, Area = Perimeter
a^2 = 4a
we get, a = 4 units.
Now, we can find the diagonal by using Pythagoras theorem,
We know that, Hypotenuse^2 = Base^2 + Perpendicular^2
Here, the hypotenuse will be the diagonal of the square.
So, We have,
Diagonal^2 = 4^2 + 4^2
= 16 + 16
= 32
∴ Diagonal = √32 = 4√2 units.
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Statistics can promote limitations in perception in all of the following ways except by __________. A. Defining the relationship between variables in a subjective manner b. Providing information about participants that leads to a biased point of view c. Considering alternative perspectives when defining variable relationships d. Creating personal labels for individuals that relate to participants within a study please select the best answer from the choices provided a b c d.
Statistics can promote limitations in perception in all the following ways, except by Option C. Considering alternative perspectives when defining variable relationships.
However, option C does not promote limitations in perception, as it encourages a more open-minded approach to interpreting the data. Statistics can promote limitations in perception in all the following ways, except by Option C. Considering alternative perspectives when defining variable relationshipsOption C encourages a holistic approach to analyzing statistics, rather than promoting limitations in perception. It encourages the analyst to consider different perspectives when interpreting the data, thus allowing a more comprehensive understanding.
This open-minded approach is essential in order to form valid conclusions. When taking into account multiple perspectives, the analyst is able to come to a more informed conclusion, rather than relying on a single-perspective interpretation. Option C does not promote limitations in perception, as it encourages a more open-minded approach to interpreting the data.
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Use the law of sines to solve for the variable
Answer:
y ≈ 60.6 units
Step-by-step explanation:
Given a triangle with angles 18° and 117°, and sides 21 opposite 18° and y opposite 117°, you want to know the value of y.
Law of sinesThe law of sines tells you the ratios of side length to the sine of the opposite angle are the same for all side/angle pairs in the triangle.
y/sin(117°) = 21/sin(18°)
y = 21·sin(117°)/sin(18°) ≈ 60.55
The value of y is about 60.6 units.
Andy rapidly pedaled his bike to reach a certain speed, then continued at that speed. He rapidly pedaled again, then quickly pressed on his brakes to come to a stop.
Which graph best represents Andy’s bike ride?
We can conclude that the given situation of Andy is perfectly represented by a graph (A).
What are graphs?
The set of ordered pairs is the graph of a function f in mathematics, where These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
To develop a graph is to make a diagram that depicts the relationship between two or more objects.
Make a sequence of bars on graph paper as an example of a graph.
So, we know that:
Andy pedals rapidly.
Then maintain the speed for some time.
Then again, he rapidly pedals the bike he has.
Then suddenly, he put breaks.
All these details are shown in graph (A).
(Refer to the attached (A) graph below)
Therefore, we can conclude that the given situation of Andy is perfectly represented by a graph (A).
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Diane gave 6 people candy. She split 7/8 pounds among them. What is the unit rate in pounds per person? Write your answer in simplest form.
Seawater has density 1025 kg/m^3 and flows in a velocity field v = yi + xj, where x, y, and z are measured in meters and the components of V in meters per second. Find the rate of flow outward through the hemisphere x^2 + y^2 + z^2 = 9, z >= 0.
The rate of flow outward through the hemisphere x² + y² + z² = 9, z >= 0 is zero.
Given that,
Seawater has a density of 1025 kg/m³ and moves at a constant velocity field defined by the equations v = yi + xj, where x, y, and z are measured in meters and the components of V are expressed in meters per second.
We have to find the rate of flow outward through the hemisphere x² + y² + z² = 9, z >= 0.
We know that,
v= yi + xj, and density = 1025 kg/m³
F=1025(yi + xj)
After solving the R(u,v) we get zero.
Therefore, the rate of flow outward through the hemisphere x² + y² + z² = 9, z >= 0 is zero.
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suppose that all license plates in a state have three letters and then four digits. if a plate is chosen at random, what is the probability that all three letters and all four numbers on the plate will be different? (round your answer to three decimal places.)
The probability that a randomly chosen plate contains the number 2222 is 0.000028 approximately.
The probability that a randomly chosen plate contains the sub-string HI is 0.002548 approximately.
Given that:
The license plate was in the form of 3 letters followed by 3 digits or 2 letters followed by 4 digits.
Part (A)
Let A be the way the symbol is three letters followed by three numbers, and B be the way two letters followed by four numbers.
Repetition is allowed here. There are 26 alphabetic characters and 10 unique digits.
If 3 letters followed by 3 numbers, the selection method is:
26 × 26 × 26 × 10 × 10 × 10
⇒ (26)² ×(10)⁴ = 6760000
The number of possibilities is 17576000 + 6760000 = 24336000
contains the digits 2222.
That is, the first two letters can be any alphabet, but the remaining digits he must be 2222. Disk contains number 2222:
(26) ² = 676
Probability that randomly selected disk contains number 2222:
676/24336000 ≈ 0.000028
Part (B):
Selected disk contains substring HI Number of possibilities:
3 letters followed by 3 digits, the disc has Un
26 × 1 ×10³ × 1 × 26 ×10³
2 letters followed by 4 digits, the number of possible ways is as follows.
1 × 10⁴
So the total number of ways a randomly chosen plate contains the substring HI is:
620000/24336000 ≈ 0.002548
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Is it true that f (0) = 0
May someone please help me out with this
Answer:
S=7
t=1
Step-by-step explanation:
Since we need to make these triangles congruent, s+36=43, and t+39=40. Solve for s by subtracting 36 from both sides of the equation (s+36-36=43-36 s=7), then solve for t by subtracting 39 from both sides (t+39-39=40-39 t=1)
-Hope this helped & Happy Holidays!
what is 1/4 x 1/6 = please do explanation bc i need to know the correct answer.
Answer:
To find the product of 1/4 and 1/6, we need to first find a common denominator. In this case, we can use the least common multiple of 4 and 6, which is 12. We can then rewrite 1/4 and 1/6 as 6/12 and 2/12, respectively. The product of these two fractions is then 6/12 * 2/12 = (6 * 2)/(12 * 12) = 1/12. Therefore, 1/4 x 1/6 = 1/12.
Alternatively, we can simply cancel out common factors in the numerator and denominator of the two fractions before multiplying them. In this case, we can cancel out the common factor of 1 in the numerator and the common factor of 4 in the denominator to get 1/4 * 1/6 = 1/(4 * 6) = 1/24.
Both methods give us the same answer, so we can use either one to solve this problem.
Step-by-step explanation:
Answer:
1/24
Step-by-step explanation:
We want to multiply fractions
1 1
--- * ----
4 6
Multiply the numerators
1 * 1 = 1
Multiply the denominators
4 * 6 = 24
The result is
1 1 1
--- * ---- = -----
4 6 24
For every 2 girls taking Drivers Ed classes at the high school there are 5 boys taking classes, if there are 245 boys taking classes predict the number of girls taking classes
Answer:
24 girls
Step-by-step explanation:
245÷5= 49
49÷2=24.5 so you can estimate that it is 24
what is 3.944 rounded to the nearest hundreth?
the answer is 4
Step-by-step explanation:
A number cube was rolled as part of an experiment. The results are displayed in the table below.
Number
1
2
3
4
5
6
Frequency
4
6
5
7
3
5
What is the best explanation of how to find the experimental probability of rolling a 3?
Group of answer choices
A. To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. Simplify if necessary.
B. To find the experimental probability of rolling a three, write a ratio of the number three to the total number of trials. Simplify if necessary.
C. To find the experimental probability of rolling a three, write a ratio of the total number of trials to the number three. Simplify if necessary.
D. To find the experimental probability of rolling a three, write a ratio of the total number of trials to the frequency of the number three. Simplify if necessary.
The option that has the best insight of how to find the experimental probability of rolling a 3 is option A
A. To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. Simplify if necessary.
What is an experimental probability?An experimental probability is a probability based on real or actual experiment, such that the result depends on the accuracy of the record of the occurrences during the experiment.
The result from the experiment is presented as follows;
Number [tex]{}[/tex] Frequency
1 [tex]{}[/tex] 4
2 [tex]{}[/tex] 6
3 [tex]{}[/tex] 5
4 [tex]{}[/tex] 7
5 [tex]{}[/tex] 3
6 [tex]{}[/tex] 5
The probability of an event is the ratio of the number of possible outcome to the number of required outcome.
Therefore: The probability of rolling a three is the ratio of the frequency of an outcome of threes to the sum of the frequency of all the events.
The correct option from which the best details of finding an experimental probability can be obtained is the option that states that the experimental probability of rolling a three is the ratio of the count of the number of times three occurs to the total number of trials, which is the frequency of rolling a three to the sum of all the frequencies in the experiment.
Mathematically, we get;
The probability of an event E, P(E) = [tex]\frac{Number\, of \, outcomes \, three}{Total \, number \, of \, outcomes}[/tex]
Therefore
[tex]P(3) = \dfrac{Number\, of \, times \, three\, occurs }{Total\, number \, of \, trials} = \dfrac{Freqiuency\ of \ 3s }{Sum\ of \ ther \ frequencies}[/tex]
[tex]P(3) = \dfrac{5}{4+6+5+7+3+5} =\dfrac{1}{6}[/tex]
The correct option is option A
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The drone rises 16 feet every 4 seconds. After 5 seconds, the drone is at a height of 26 feet.
Answer:the answer is 16 feet
Step-by-step explanation:
What value of n makes the equation true?
2/3n = -12
n=
Answer:
-18
Step-by-step explanation:
[tex]\frac{2}{3}n=-12 \\ \\ \frac{3}{2} \cdot \frac{2}{3}n=\frac{3}{2}(-12) \\ \\ n=-18[/tex]
5. Mr. Lee had a coupon
for $4 off his pizza order. If
he paid $48 for 4 pizzas.
What was the regular price
for 1 pizza?
Answer:
Step-by-step explanation: first we need to add 4 to 48 with will give us 52, then if we divide 52 by 4 we will get the answer for the price per pizza, 52 divided by 4 is 13 with means that Mr. Lee paid 13 dollars per pizza.
a number of eggs,e ,divided 12
Answer: the answer is 1
Step-by-step explanation: if you divide 12 by 12
how many interior diagonals does an icosahedron have? (an icosahedron is a 3-dimensional figure with 20 triangular faces and 12 vertices, with 5 faces meeting at each vertex. an interior diagonal is a segment connecting two vertices which do not lie on a common face.)
An icosahedron have 36 interior diagonals.
Given that:
Icosahedron :
Faces = 20 =F
Vertices = 12 = V
Edges = ? = E
For convex 3-dimensional polyhedral Euler's formula: or
E = V + F -2
⇒ E = 12 + 20 - 2
⇒ 30
Interior diagonals :
[tex]\left[\begin{array}{ccc} Vertices\\2\end{array}\right] - Edge[/tex]
= [tex]\left[\begin{array}{ccc} 12\\2\end{array}\right][/tex] - 30
= 12/2 × 11/1 - 30
= 66 - 30
= 36
An icosahedron has 36 interior diagonals.
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a factory has two assembly lines, A and B that make the same bottles. on monday only assembly line A was functioning and it made 600 bottles. on tuesday both assembly lines were functioning fit the same amount of time. line a made 270 bottles per hour and line b made 330 bottles per hour. line b made as many bottles on tuesday as line A did over both days. write and equation that can be used to find the numbers of hours,h,that the assembly lines were functioning in both days
A manufacturing plant has two assembly lines for producing glass bottles. The manager
was concerned about whether the proportion of defective bottles differs between the two
assembly lines. She gathered two independent samples and found the following data:
n 1 =100, ^p 1 =.1,n 2 =100, ^p 2 =.13.
(a) Set up the appropriate null and alternative hypotheses.
(b) Compute the value of the test statistic.
(c) Draw a conclusion as to whether there is a difference between the two assembly lines
Evaluate the expression for the given values.
12x+5y
------------
3z, where x=12, y = 6, and z = 3
Enter your answer in the box.
(12x+5y)/3z
substitute in values
(12(12) + 5(6)) / 3(3)
simplify
(144 + 30) / 9
add
174 / 9
factor out a 3
58 / 3
Hope this helps :)
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- Jeron
What is the equation of line passing through 3 4 and having slope 3 2?
The equation of the line passing through (3,4) and having slope m = 3/2 is y = 3/2x + 4.
Given points : (3,4)
The equation of a line with slope 3/2 and passing through point (3,4) is y = 3/2x + 4. This equation can be used to calculate the y-coordinate of any point on the line, given its x-coordinate. For example, if the x-coordinate of a point is 6, then its corresponding y-coordinate is 11. In general, for any x-coordinate, the corresponding y-coordinate is given by 3/2 times the x-coordinate plus 4.
Given slope : m = 3/2
We know that the equation of a line with slope m and passing through point (x1, y1)is given by :
y - y1 = m(x - x1)
Substituting the given values, we get
y - 4 = 3/2(x - 3)
Simplifying equation, we get
y = 3/2x + 4
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What is a variable called that can only be 1 or 0?
Answer:Binary Variable
Step-by-step explanation:Binary variable: a variable that can only take on two values, usually 0/1.
Jesse estimates that it will cost $300,000 to send his newborn son to a private college in 18 years. He currently has $65,000 to deposit in an account. What simple interest rate would he need so that $65,000 grows into $300,000 in 18 years? round to the nearest percent.
The simple interest rate would be 20%. The result is obtained by using the simple interest formula.
How to count the interest?The interest of an amount of money can be counted by the following formula.
I = P₁ - P
I = P × r × t
Where
I = interestP = principal amount (initial balance)P = final balancer = simple interest ratet = time periodJesse now has $65,000 and he deposit it in an account. After 18 years, he wishes the balance will grow into $300,000. Determine the simple interest rate!
First, let's find the interest.
I = P₁ - P
I = $300,000 - $65,000
I = $235,000
The simple interest rate is
I = P × r × t
235,000 = 65,000 × r × 18
r = 235,000 / 1,170,000
r = 0.201
r ≈ 20%
Hence, the simple interest rate he would need to deposit his money is 20%.
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David has a hose that is 27 ft long. He wants to cut it into two pieces so that the longer piece is 3 ft more than 2 times the length of the shorter piece. How long will each piece of hose be? enter your answers in the boxes.
The length of the longer and shorter pieces of hose is equal to 19ft and 8ft respectively.
As given in the question,
length of the hose = 27ft
Let 'x' be the length of the longer piece
and 'y' be the length of shorter piece
As per given condition:
System of equations are:
x = 2y + 3 __(1)
x + y = 27 __(2)
Substitute the value x from (1) in (2) we get,
2y + 3 + y = 27
⇒3y + 3 = 27
⇒ 3y = 27 - 3
⇒3y = 24
⇒y = 24/3
⇒y = 8ft.
Now,
x = 2(8) + 3
⇒ x = 19ft
Therefore, the length of the longer and shorter piece cut from a 27ft long hose is equal to 19ft and 8ft respectively.
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restaurant bills. data were collected on the amount spent by 64 customers for lunch at a major houston restaurant. these data are contained in the file houston. based upon past studies the population standard deviation is known with s 5 $6. a. at 99% confidence, what is the margin of error? b. develop a 99% confidence interval estimate of the mean amount spent for lunch.
Therefore, the solution to the given problem is a) ME= 1.93 and b) confidence interval= (19.59,23.45)
Test statistics: what are they?Using test statistics to judge statistical hypotheses is a widespread technique. A test statistic, which is a count of a data set that can be used to run the test and simplifies the data to a single number, is a common approach to express a hypothesis test.
Here,
a) Sample of customers is 64, population standard deviation is 6 and confidence level is 99%
Sample mean= 21.52
Sample size= 64
Confidence level= 99%
Population standard deviation= 6
Standard error of the mean= 0.75
Z-value= -2.5758 (From Z table)
Interval half width= 1.9319
Margin of error at 99% confidence interval is 1.93 from the output.
b) Confidence interval
Interval upper limit= 19.59
Interval lower limit= 23.45
99% confidence interval is (19.59, 23.45) from the output.
ME= (23.45- 19.59)/2 = 1.93
Therefore a) ME= 1.93 b) confidence interval= (19.59,23.45)
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QR has endpoints at Q(9, 3) and R(1, 1). Find the midpoint M of QR.
Answer = (5), (2)
The midpoint of points Q(9.3) and R(1,1) will be M(5,2).
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that the two endpoints of QR are Q(9.3) and R(1,1). The midpoint will be calculated as,
Midpoint = [x₁ + x₂]/2 , [y₁ + y₂] / 2
Midpoint = [(9 + 1 ) /2 , ( 3 + 1 ) / 2
Midpoint = 5, 2
M is the midpoint of points Q(9.3) and R(1,1) (5,2).
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Please help meeee !!!?!
Answer:
21
Step-by-step explanation:
For this problem, we basically want to find 2016/96.
2016=1920+96. So, 2016/96 = (1920+96)/96=20+1=21.
So, the hot air balloon travels 21 miles each hour.
''21'' because 2016 divided by 96 is 21
What is the equation of a line passing through x1 y1 with slope?
The equation of a line passing through (x1, y1) is y - y1 = m(x - x1).
The equation of a line:
The equation of a line means an equation in x and y whose solution set is a line in the (x,y) plane. The most popular form in algebra is the "slope-intercept" form. y = mx + b. This in effect uses x as a parameter and writes y as a function of x: y = f(x) = mx+b.
Here we have to find the equation of a line passing through (x1, y1) and the slope.
Data given:
Point on the line = (x1, y1)
Slope = m
By this we get the equation of a line as:
y - y1 = m(x - x1)
Therefore the equation of a line is y - y1 = m(x-x1).
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an educational researcher wishes to know if there is a difference in academic performance for college freshmen that live on campus and those that commute. data was collected from 273 students. can we conclude that freshman housing location and academic performance are related? location average below average above average total on campus 98 53 42 193 off campus 42 18 20 80 total 140 71 62 273 step 4 of 8 : find the value of the test statistic. round your answer to three decimal places.
Therefore , the test statistic comes out to be t = 8.645.
What is test statistic ?A test statistic is a statistic used in statistical hypothesis testing .A hypothesis test is typically expressed as a test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to perform the hypothesis test.
Here,
Parameter = u1 - u2
where
[tex]{X^{'}_{1}[/tex] = 3.27
[tex]{X^{'}_{2}[/tex] = 2.95
S1=0.23 and S2=0.29
So using formula
=> t = [tex]\frac{X^{'}_{1} - X^{'}_{2} }{Sp\sqrt{\frac{1}{n1} +\frac{1}{n2} } }[/tex]
=> t = [tex]\frac{3.27 - 2.95 }{0.23\sqrt{\frac{1}{100} +\frac{1}{100} } }[/tex]
=> t = 9.838
and
=> t = [tex]\frac{3.27 - 2.95 }{0.29\sqrt{\frac{1}{100} +\frac{1}{100} } }[/tex]
=> t = 7.802
thus,
=> t = (9.838 + 7.802) / 5 =8.645
thus t = 8.645
Therefore , the test statistic comes out to be t = 8.645.
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What is the value of. (3/4)2
Answer:its 14
Step-by-step explanation:
Answer: 1 1/2 / 1.5
Step-by-step explanation: So, if you divide 3 by 4, you should get 0.75, then you would multiply that to get 1.5 or 1 1/2 (as a fraction) I think this is the question you asked, but if so, I hoped this helped!
how does omega change over time?how does omega change over time?it increases proportionally with a.it decreases proportionally with a.it increases quadratically with time.it decreases as a increases.
As the time increases, the angular velocity i.e. omega also increases quadratically with time.
Given,
From the figure,
Radius of wheel = 0.2 m
Acceleration, a = 4t m/s^2
then the angular acceleration of wheel can be determined by formula,
[tex]a=\alpha * r[/tex]
Where, r=radius of wheel =0.2 m
[tex]4t=\alpha * 0.2\\20t=\alpha[/tex]
We know that the angular acceleration is the change in angular velocity over time.
[tex]\alpha=\frac{d\omega}{dt}\\\\20t=\frac{d\omega}{dt}\\\\d\omega=20tdt\\\\\omega=\int\limits^t_0 {20t} \, dt \\\\\omega=\frac{20t^2}{2}-0\\\\\omega=10t^2[/tex]
From the above equation it is clear that omega i.e. angular velocity is dependent of time
omega is directly proportional to square of time
For
t=1 then ω=10
t=2 then ω=10(4)=40
t=3 then ω=10(9)=90.....and so on.
It means as time increases, then angular velocity also increases quadratically with time.
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Your question is incomplete, here is the complete question.
When a body rotates about fixed axis , any point located in the body travels along the circular path. the angular acceleration α measures the rate of change of angular velocity. A cord is wrapped around a wheel, which is initially at rest when θ=0. The force F gives the cord an acceleration [tex]a= 4t\ m/s^2.[/tex]
How does omega change over time?
It increases proportionally with a. It decreases proportionally with a. It increases quadratically with time. It decreases as a increases.