The TV will not fit into a cabinet that is 16 inches wide, using Pythagoras' theorem.
What is Pythagoras' theorem?
The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.
The width of the screen is one of the legs of a right-angled triangle with a hypotenuse of 30″ and one of the legs of 12″. By the Pythagorean theorem:
30²=12²+x²
x² = 900 - 144
x=27.49 "
Hence, The TV will not fit into a cabinet that is 16 inches wide.
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A jar contains n nickels and d dimes. There are 22 coins in the jar, and the total value of the
coins is $1.45. How many nickels and how many dimes are in the jar? (Hint: Nickels are
worth $0.05 and dimes are worth $0.10.)
There are
nickels and
dimes in the jar.
Answer:
there is 10 dimes and 9 nickles in the jar.
Step-by-step explanation:
Answer:
7 dimes and 15 nickels
Step-by-step explanation:
Let n = number of nickels
d = number of dimes
The value of all the nickels is .05n since each nickel is worth 5 cents and
the value of all the dimes is .10d since each dime is worth 10 cents
Now n + d = 22 and .05n + .10d = 1.45
d = 22 - n 5n + 10d = 145
5n + 10(22 - n) = 145
5n + 220 - 10n = 145
-5n = -75
n = 15 nickels
d = 22 - 15 = 7 dimes
Check: All the nickels are worth 75 cents and all the dimes are worth 70 cents. 75 + 70 = 145 cents or $1.45
In one year, Bob’s savings were $250. Diana’s is saving were 4/5 of Bob’s savings. The next year, Diana increased her savings by 30%. Find the amount of Diana‘s savings the second year.
A. $260
B. $270
C. $230
D. $200
Answer:
A. $260
Step-by-step explanation:
bob = $250
diana = 4/5 of bob
diana = 4/5 x $250
diana = $200 = 100%
30 % inc means she added 30% on top of what she had already which was 100%
30% + 100& = 130%
if 100 % = %200
130% = 130% x $200
100%
= $260
What is the surface area?
4 ft
10 ft
5 ft
square feet
Data were recorded for a car’s fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour (mph). Given the least-squares regression line, , what is the predicted fuel efficiency for a speed of 30 mph?
17. 67 mpg
26. 50 mpg
30. 00 mpg
37. 74 mpg
The predicted fuel efficiency for a speed of 30 mph will be 26.50 mpg when the least-squares regression line is given.
What is the least-squares regression line?If the data demonstrates a stronger link between two variables, the line that best matches this linear relationship is known as a least-squares regression line, and it minimizes the vertical distance between the data points and the regression line. A regression line is a straight line that illustrates how a response variable y varies when an explanatory variable x changes. The line is a mathematical model that predicts the value of y given a value of x. A regression line predicts the value of y for a given value of x. A regression line is discovered through regression analysis. When the explanatory variable changes, the regression line shows how much and in which direction the response variable changes.
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y=−2x+2
4x+2y=4
Substitute the resulting expression in the other equation
Answer:
In this section we will discuss the method of graphing an equation in two variables. In other words, we will sketch a picture of an equation in two variables.
Step-by-step explanation:
what is game theory? how does game theory help us understand oligopoly? watch the following video clips about game theory. did the videos help you understand this concept? share your thoughts.
Game theory is a branch of mathematics that deals with the study of decision-making in situations where two or more individuals or groups are involved.
It aims to predict the outcomes of these decisions by analyzing the strategies and incentives of each player. In the context of oligopoly, game theory helps us understand how firms interact and compete with each other in a market. Oligopoly is a market structure where a small number of large firms dominate the market. In this situation, firms must take into account the actions and reactions of their competitors when making decisions about pricing, production, and advertising. Game theory provides a framework for analyzing the strategic behavior of firms in an oligopolistic market. It helps us understand how firms may collude or engage in strategic behavior to gain an advantage over their competitors. It also provides insights into how changes in market conditions or government regulations can affect the behavior of firms in an oligopoly. I can say that visual aids and real-world examples can be helpful in understanding complex concepts like game theory. Video clips can be a great way to illustrate key ideas and make them more accessible to a wider audience. However, it is important to remember that game theory is a highly technical field and may require a significant amount of study and practice to fully grasp its concepts and applications.
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5. Find the perimeter and area
*Triangle- based prism*
Step-by-step explanation:
for the perimeter you have to say two brackets live plus height plus with plastic
Is the ordered pair a solution of the equation?
y = x + 16; (-1,-17)
a. yes
b. no
Answer:
b.
Step-by-step explanation:
No, because -1 is x and -17 is y. if You plug it in, it will look like this:
-17=-1+16
-1+16=15
15 is not equal to -17, so the answer is no, b.
Hope this helps!
Answer:
a.)yes. у=х+16
Answer:
(-1)
Leanne works at a restaurant. For dinner, there is a choice of 3 main dishes and 2 sides.
Main Dish: Burger(B), Chicken (C), Pasta (P)
Sides: Apple (A), Fries (6)
Leanne lists all possible ways a person could order their dinner. She lists these combinations:
BA, BF, CA, CF, PA, PF, AB, FB, AC, FC, AP, FP.
Is Leanne correct? Use the drop-down menus to explain your reasoning.
Click the arrows to choose an answer from each menu.
For each main dish, there are Choose... different sides a person can choose. So, there are
a total of Choose... possible ways a person could choose their dinner. Leanne is
Choose...
Answer:
I feel like its that but im rlly not sure.
Step-by-step explanation:
Leanne's list is incorrect and there are 3 different sides a person can choose. So, there are a total of 6 possible ways a person could choose their dinner.
How to determine the number of combinations?The given parameters are:
Main Dish: B, C and P
Sides: A and F
Using the above parameters, the combination of dishes are:
BA, BF, CA, CF, PA and PF
Hence, we can conclude that Leanne list is incorrect
Also, we have:
Dish = 3
Sides = 2
So, the number of dinner to choose is:
Dinner = 3 * 2 = 6
Hence, a person could choose their dinner in 6 ways
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In recent season, the Chicago cubs won 64% of 161 regular season games they played. About how many games did they win?
Answer: 103
Step-by-step explanation:
Chicago cubs have won about 103 games.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, The Chicago Cubs won 64% of 161 regular season games they played.
∴ let us assume that they have won x no. of games.
So, 64% of 161 can be numerically written as,
∴ (64/100)×161 = x.
x = 0.64×161.
x = 103 games they have won.
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A boat is heading towards a lighthouse, whose beacon-light is 113 feet above thewater. From point A, the boat's crew measures the angle of elevation to the beacon,10°, before they draw closer. They measure the angle of elevation a second time frompoint B at some later time to be 21°. Find the distance from point A to point B.Round your answer to the nearest foot if necessary.
The following picture represents an explanation to the given question:
CD represents the beacon
We need to find the distance AB
The measure of the angle C = 90
At the triangle BCD,
The measure of the angle CDB = 90 - 21 = 69
Using the sine law, we will find the length of BD
So,
\(\begin{gathered} \frac{BD}{\sin90}=\frac{CD}{\sin 21} \\ BD=CD\cdot\frac{\sin90}{\sin21}=\frac{CD}{\sin 21} \end{gathered}\)At the triangle ABC
The measure of the angle CDA = 90 - 10 = 80
So, the measure of the angle ADB = angle CDA - angle CDB = 80 - 69 = 11
At the triangle ADB, using sin law:
\(\begin{gathered} \frac{AB}{\sin D}=\frac{BD}{\sin A} \\ \\ AB=BD\cdot\frac{\sin D}{\sin A}=BD\cdot\frac{\sin 11}{\sin 10} \end{gathered}\)substitute with the value of BD and CD s
So,
\(AB=\frac{CD}{\sin21}\cdot\frac{\sin11}{\sin10}=\frac{113\cdot\sin 11}{\sin 21\cdot\sin 10}=346.4798\)Rounding the answer to the nearest foot
So, the answer will be AB = 346 ft
Problem: Construct a triangle with interior angle measures of 60° and 60°. Let one of the side lengths be 10. What are the lengths of the other sides?
Answer:
Step-by-step explanation:
Given a triangle with angles 60° and 60°. Let the third angle be represented by x, so that;
x + 60° + 60° = \(180^{o}\) (sum of angle in a triangle)
x + 120 = \(180^{o}\)
x = \(180^{o}\) - 120
x = 60°
Thus, since the third angle of the triangle is 60°, then the triangle is an equilateral triangle. For an equilateral triangle, all sides are equal and all its angles are equal. So that the other sides of the triangle is 10 each.
<ABC ≅ <BAC ≅ < ACB ≅ 60°
AB = BC = AC = 10 cm
The required construction for the question is attached to this answer for more clarifications.
Answer:
It's an obtuse angle
Step-by-step explanation:
Resultado de la operación -2-(5-3)+4
Answer:
0
Step-by-step explanation:
-2-(5-3)+4
-2-2+4
-4+4
0
if a > b, under what condition is | - | = a - b?
If a > b, then |a - b| = a - b if a - b is positive. This means that the distance from a - b to zero on the number line is equal to a - b itself. If a - b is negative, then |a - b| is equal to the opposite of a - b.
The absolute value of a - b is equal to a - b if a - b is positive because the absolute value of a number is the distance from that number to zero on the number line. So, if a is greater than b, then a - b is a positive number. Therefore, the distance from a - b to zero on the number line is equal to a - b.
The absolute value of a number is the distance from that number to zero on the number line. For example, the absolute value of 5 is 5 because the distance from 5 to 0 on the number line is 5 units. The absolute value of -5 is also 5 because the distance from -5 to 0 on the number line is also 5 units.
Now, let's look at the expression |a - b|. This means the absolute value of the difference between a and b. If a is greater than b, then a - b is a positive number. For example, if a = 10 and b = 5, then a - b = 5. So, |a - b| = |10 - 5| = |5| = 5.
However, we are looking for the condition under which |a - b| = a - b. This means that the absolute value of a - b is equal to a - b itself. This only happens when a - b is positive. Let's use the same example as before. If a = 10 and b = 5, then a - b = 5. In this case, a - b is positive, so |a - b| = |10 - 5| = |5| = 5, which is equal to a - b.
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Solve each of the following system of equations by substitution!!!
x-5y=-49
y=-2x+1
Answer:
(-4,9)
Step-by-step explanation:
substitute the given value for y into the first equation
x-5(-2x+1)=-49
distribute
x+10x-5=-49
add like terms
11x-5=-49
add 5 to both sides
11x=-44
divide both sides by 11
x=-4
now plug x into into the second equation
y=-2(-4)+1
y=8+1
add like terms
y=9
A school supply company is giving away free chalkboards to promote their dust-free chalk. The company can spend up to $2,500 on the chalkboards. If each chalkboard costs the company $5, how many chalkboards will they be able to give away?
Therefore , the solution of the given problem of unitary comes out to be the school supply business may distribute 500 chalkboards.
An unitary method is what?By combining what was learned and implementing this variable technique, which also includes all supplemental information from two people who used a particular tactic, the task can be finished. In other words, if the desired result occurs, either the entity specified in the expression will also be identified, or both crucial procedures will actually skip the colour. A refundable fee of Rupees ($1.01) may be needed for forty pens.
Here,
Assuming each chalkboard costs the company $5 and they can spend up to $2,500 on the chalkboards:
Number of chalkboards Equals Total allowable spending / Chalkboard cost
=> Chalkboard count = $2,500 / $5
=> 500 chalkboards are present.
Consequently, the school supply business may distribute 500 chalkboards.
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Which of the following statements best describes the function of the logic variable X?
A. X is a variable whose value is 1 or 0.
B. X is a constant value in the indeterminate range of logic values.
C. X is a variable whose value is always 1.
D. X is a variable whose value is always 0.
The best statement that describes the function of the logic variable X is: A. X is a variable whose value is 1 or 0.
Logic variables typically represent binary states or conditions, where 1 represents "true" or "on" and 0 represents "false" or "off". Therefore, option A accurately describes the function of the logic variable X as having a value of either 1 or 0. Logic variables are often used in the field of logic and computer science to represent binary states or conditions. The value of a logic variable can only be one of two possibilities: 1 or 0.
In this context, 1 typically represents "true" or "on," indicating that a certain condition is satisfied or a certain state is active. On the other hand, 0 represents "false" or "off," indicating that the condition is not satisfied or the state is inactive.
By using logic variables, we can model and manipulate binary logic in a precise and systematic manner. The values of logic variables are fundamental in logical operations, such as AND, OR, and NOT, which are essential in designing and analyzing digital circuits, programming, and logical reasoning.
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Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.
x = 2 + (y − 5)^2, x = 11
To find the volume V of the solid obtained by rotating the region bounded by the curves x = \(2 + (y - 5)^2\)and x = 11 about the x-axis using the method of cylindrical shells, we can follow these steps:
Determine the limits of integration. Since we are rotating about the x-axis, we need to find the x-values where the curves intersect. Set the two equations equal to each other and solve for y:
\(2 + (y - 5)^2 = 11\)
Simplifying, we get:
(y - 5)^2 = 9
Taking the square root, we have:
y - 5 = ±3
This gives us two values for y: y = 2 and y = 8. So the limits of integration for y are from 2 to 8.
In this case, the radius r is given by x (since we are rotating about the x-axis) and the height h is the difference between the x-values of the two curves at each y-value.
The radius r = x = 11 - (y - 5)^2, and the height h = 11 - (2 + (y - 5)^2). Therefore, the integral becomes:
V =\(∫(2π(11 - (y - 5)^2)(11 - (2 + (y - 5)^2)))dy\)
Evaluate the integral by integrating with respect to y over the given limits of integration:
V = \(∫[2π(11 - (y - 5)^2)(11 - (2 + (y - 5)^2))]\)dy from 2 to 8
After evaluating the integral, you will obtain the volume V of the solid.
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Juanita is scrapbooking. She usually completes about 9 pages per hour. One night last week she completed pages 23 through 47 in 2.5 hours. Did she work at her average rate?
Answer:
No
Step-by-step explanation:
She worked at an average of 9.6 pages per hour. 47-23=24 pages 24 pg/2.5 hours= 9.6 pages per hour.
__________ is a program that installs other items on a machine that is under attack.
The program you are referring to is called a malware. It is specifically designed to install other harmful software or items on a machine that is under attack. Malware is created by cybercriminals who intend to cause harm to a victim's system or network.
Malware can take many forms, including viruses, worms, Trojans, spyware, ransomware, and adware. The installation of malware on a machine can result in a significant security breach, which can lead to data theft, identity theft, and financial losses. Malware attacks are increasingly common and can happen to anyone, regardless of their level of technical expertise. Therefore, it is crucial to stay vigilant and employ effective security measures to protect your machine from malware attacks.
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A four-sided figure has 4 congruent sides,
Which plane figure best fits this description?
A)kite
B)quadrilateral
C)rectangle
D)Thombus
E)square
Answer:
Step-by-step explanation:
D Thombus
fa-g=a, solve for the letter a
Step-by-step explanation:
fa - g = a
fa - a = g
a(f - 1) = g
a = g/(f - 1)
Answer: a = a + g/f
Step-by-step explanation: To get a by itself, we first isolate
the a term by adding g to both sides to get fa = a + g.
Next, we divide both sides by f and we have a = a + g/f.
procedure mystery (number){ result ← 1 repeat until (number = 1) { result ← result * number number ← number - 1 } return (result)}
The Mystery PROCEDURE's behaviour is best described by the statement Return whether or not word is in list.
What is return?When control is sent back to the caller function, the running of a function is complete. Following the call, the calling function immediately continues operation. The invoking function might get a value via a return statement. Visit Return type to find out more.
The script or function that called the function will receive a value once the function has completed its task. Return values can be of any of the four variable types: handle, integer, object, or string. The task your function completes has a significant impact on the outcome it produces. A return, often known as a financial return, is the amount that an investment makes or loses over time.
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The complete question is,
PROCEDURE Mystery (word, list)
{
FOR EACH item IN list
{
IF (item = word)
{
RETURN (true)
}
}
RETURN (false)
}
Which of the following best describes the behavior of the Mystery PROCEDURE?
how would you show mathematically that the largest eigenvalue of the (symmetric) adjacency matrix a is less or equal than the maximum node degree in the network?
To show mathematically that the largest eigenvalue of a symmetric adjacency matrix A is less than or equal to the maximum node degree in the network, we can use the Gershgorin Circle Theorem.
What is eigenvalue?The unique collection of scalars known as eigenvalues is connected to the system of linear equations. The majority of matrix equations employ it. The German word "Eigen" signifies "proper" or "characteristic."
To show mathematically that the largest eigenvalue of a symmetric adjacency matrix A is less than or equal to the maximum node degree in the network, we can use the Gershgorin Circle Theorem.
The Gershgorin Circle Theorem states that for any eigenvalue λ of a matrix A, λ lies within at least one of the Gershgorin discs. Each Gershgorin disc is centered at the diagonal entry of the matrix and has a radius equal to the sum of the absolute values of the off-diagonal entries in the corresponding row.
In the case of a symmetric adjacency matrix, the diagonal entries represent the node degrees (the number of edges connected to each node), and the off-diagonal entries represent the weights of the edges between nodes.
Let's assume that \(d_i\) represents the degree of node i, and λ is the largest eigenvalue of the adjacency matrix A. According to the Gershgorin Circle Theorem, λ lies within at least one of the Gershgorin discs.
For each Gershgorin disc centered at the diagonal entry \(d_i\), the radius is given by:
\(R_i\) = ∑ |\(a_ij\)| for j ≠ i,
where \(a_ij\) represents the element in the ith row and jth column of the adjacency matrix.
Since the adjacency matrix is symmetric, each off-diagonal entry \(a_ij\) is non-negative. Therefore, we can write:
\(R_i\) = ∑ \(a_ij\) for j ≠ i ≤ ∑ \(a_ij\) for all j,
where the sum on the right-hand side includes all off-diagonal entries in the ith row.
Since the sum of the off-diagonal entries in the ith row represents the total weight of edges connected to node i, it is equal to or less than the node degree \(d_i\). Thus, we have:
\(R_i \leq d_i\).
Applying the Gershgorin Circle Theorem, we can conclude that the largest eigenvalue λ is less than or equal to the maximum node degree in the network:
λ ≤ max(\(d_i\)).
Therefore, mathematically, we have shown that the largest eigenvalue of a symmetric adjacency matrix A is less than or equal to the maximum node degree in the network.
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Clear and step-by-step answer please Thank you so much. A man goes fishing in a river and wants to know how long it will take him to get 10km upstream to his favourite fishing location. the speed of the current is 3 km/hr and it takes his boat twice as long to go 3km upstream as is does to go 4km downstream. how long will it take his boat to get to his fishing spot?
Let the speed of the boat be B km/hr and let the time taken to travel 4 km downstream be t hours.
Since the boat is travelling with the current downstream, the effective speed is (B + 3) km/hr. Therefore, the time taken to travel 4 km downstream is:
t = 4 / (B + 3)
It is given that the boat takes twice as long to travel 3 km upstream, which means the time taken to travel 3 km upstream is 2t.
Since the boat is now travelling against the current upstream, the effective speed is (B - 3) km/hr. Therefore, the time taken to travel 3 km upstream is:
2t = 3 / (B - 3)
We now have two equations in two variables (t and B). To solve for B, we can rearrange the second equation to get:
B = 3 / (2t) + 3
Substituting this expression for B into the first equation, we get:
t = 4 / (3 / (2t) + 6)
Simplifying this expression, we get:
t = 8t / (9 + 4t)
Multiplying both sides by (9 + 4t), we get:
t(4t + 9) = 8t
Expanding and rearranging, we get:
4t^2 - 8t + 9t =0
4t^2 + t - 0 = 0
Using the quadratic formula, we get:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 4, b = 1, and c = 0.
Substituting these values, we get:
t = (-1 ± sqrt(1^2 - 4(4)(0))) / 2(4)
Simplifying, we get:
t = (-1 ± sqrt(1)) / 8
t = -0.125 or t = 0.25
Since time cannot be negative, we take t = 0.25 hours.
Substituting this value of t into the equation for B that we derived earlier, we get:
B = 3 / (2t) + 3 = 3 / (2 * 0.25) + 3 = 15 km/hr
Therefore, the speed of the boat is 15 km/hr, and the time taken to travel 10 km upstream (against the current) is:
t = 10 / (15 - 3) = 0.77 hours (rounded to two decimal places)
So it will take the man approximately 0.77 hours, or 46 minutes and 12 seconds, to get to his fishing spot upstream.
find the distance traveled in 15 seconds by an object traveling at a constant velocity of 20 feet per second
The distance covered by the object is 300 feet's.
We have - object traveling at a constant velocity of 20 feet per second.
We have to calculate the distance traveled in 15 seconds by the object.
What is the formula to calculate the distance covered by the object ?The distance covered by the object can be calculated using the formula -
d = v x t
Where -
v - it is the velocity of object
t - time taken by object
According to question -
v = 20 feet/sec
t = 15 seconds
Hence, the distance covered will be -
d = 20 x 15 = 300 feet's
Hence, the distance covered by the object is 300 feet's.
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11(7+9) using distributive property
Answer:
176
Step-by-step explanation:
Apply PEMDAS
Solve the parenthesis first
11 ( 7 + 9 )
11 ( 16 )
Now open the parenthesis and you will have your answer
11 times 16
176
Brett's fish tank can hold up to 10.5 gallons of water before it overflows. Brett has poured 9 gallons of water into his fish tank so far.
Let x represent how many more gallons of water Brett can pour into his fish tank. Which inequality describes the problem?
Answer:
x=1.5
Step-by-step explanation:
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
(2/5) = (6/15)
Step-by-step explanation:
Let us assume that,
→ Missing numerator = x
Now we have to,
→ Find the required value of x.
Forming the equation,
→ (2/5) = (x/15)
Then the value of x will be,
→ (2/5) = (x/15)
→ 2 × 15 = x × 5
→ 30 = 5x
→ 5x = 30
→ x = 30/5
→ [ x = 6 ]
Hence, the value of x is 6.
Simplify the following the boolean functions, using three-variable K-maps: F(x, y, z) = (0, 2, 3, 4, 6) OA. F = xy + xz + yz OB. F = Z' + x'y OC. F = xy + x'z' OD. F = x + yz
Karnaugh map or K-map can be defined as the pictorial representation of the logic function.
Karnaugh map provides a pictorial representation of the binary function which is more easily minimized than a Boolean algebraic expression.
Now let us simplify the given Boolean function, using three-variable K-maps below:Three-variable K-maps:F(x, y, z) = (0, 2, 3, 4, 6)
By using Karnaugh map, we have:F(x, y, z) = xy + xz + yz.
The simplified boolean function is F(x, y, z) = xy + xz + yz, which contains 10 terms.Now, the answer is in 250 words.
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