Let's start with the given expressions: Expression 1: 25(h + 36)Expression 2: 2(-10h + 1,300) + 10Now, we need to find the maximum number of hours the amusement park thinks the crew will need to complete this job represented by the variable h.
The amount that the park has budgeted to complete this job is represented by the expression 2(-10h + 1,300) + 10. To get the budgeted amount, we can simplify the above expression as follows:2(-10h + 1,300) + 10= -20h + 2,620The budgeted amount is represented by -20h + 2,620We need to compare this budgeted amount to the cost of the painting supplies and the labor to repaint the railings which is represented by 25(h + 36).
Therefore, the inequality that represents how many hours, at most, the amusement park has allotted to repaint the safety railings is given by:-20h + 2,620 ≤ 25(h + 36)Simplifying the above expression: -20h + 2,620 ≤ 25h + 900Hence, the solution is: -20h - 25h ≤ 900 - 2,620 => -45h ≤ -1720Divide by -45 on both sides: h ≥ 38.22Hence, the maximum number of hours the amusement park has allotted to repaint the safety railings is 38.22 hours.
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A real estate agent earns a 6% commission for the sale of a home. A home sold for $350,000. What was the commission earned by the agent?.
The line y = 3x - 6 is dilated by the scale factor k=3 and centered at the origin. What is the equation of the new
line
I’ll give brainliest
The equation of the new line, after dilation by a scale factor of 3 and centering at the origin, is y' = 9x - 18.
To dilate a line by a scale factor of k and center it at the origin, you multiply the coordinates of each point on the original line by the scale factor. Since the given line is y = 3x - 6, we can perform the dilation as follows:
The original line: y = 3x - 6
To dilate it by a scale factor of 3, we multiply both the x-coordinate and the y-coordinate of each point by 3:
New line: y' = 3 * y and x' = 3 * x
Substituting these values into the original equation, we have:
y' = 3(3x - 6)
Simplifying, we get:
y' = 9x - 18
Therefore, the equation of the new line, after dilation by a scale factor of 3 and centering at the origin, is y' = 9x - 18.
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-1 2/3 - -5/6 adding and subtracting rational numbers
By converting -1 2/3 to an improper fraction, we get -5/3. To add these fractions, we need to find a common denominator, which is 6. Adding the fractions gives us 5/6. Therefore, -1 2/3 - (-5/6) is equal to 5/6.
To perform the addition and subtraction of rational numbers, we start by converting -1 2/3 to an improper fraction. We multiply the whole number (-1) by the denominator of the fraction (3), which gives us -3. Adding the result to the numerator (2) gives us -3 + 2 = -1. So, -1 2/3 can be represented as -5/3.
Next, we rewrite the expression as -5/3 - (-5/6). When we subtract a negative number, it is equivalent to adding the positive value. So, -(-5/6) becomes +5/6.
To add fractions, we need a common denominator. In this case, the common denominator is 6. We multiply the numerator and denominator of -5/3 by 2 to get -10/6. Therefore, the expression becomes -10/6 + 5/6.Now that the fractions have the same denominator, we can add the numerators. -10/6 + 5/6 equals -5/6.
Hence, the final result of -1 2/3 - (-5/6) is 5/6.
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the table shows the cost, y of buying boxes, x, of cookies write an equation that models this situation
y = 5x
This equation implies that each box of cookies costs $5.
To write an equation that models the relationship between the cost, y, of buying boxes of cookies, x, we need the values from the table. Since you haven't provided the specific values in the table, I'll give you an example equation based on a general scenario.
Let's assume that the cost of buying boxes of cookies follows a linear relationship with the number of boxes purchased. In this case, the equation can be written in the form:
y = mx + b
Where:
y represents the cost of buying boxes of cookies.
x represents the number of boxes purchased.
m represents the slope of the line, which indicates the rate of change in the cost per box.
b represents the y-intercept, which is the initial cost when no boxes are purchased.
You would need to substitute the actual values from your table into this equation to create a specific model for your situation. For instance, if the table shows the following data:
Boxes (x) Cost (y)
1 5
2 10
3 15
4 20
We can use these values to find the slope (m) and y-intercept (b) using linear regression techniques. Then, the equation that models this situation would be:
y = 5x
This equation implies that each box of cookies costs $5.
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How many 6cm cubical boxes can be cut out from a cube of side 24cm
216 . Therefore, we can cut out 64 cubes with a side of 6cm from a cube with a side of 24cm, hence the total number of 6cm cubical boxes that can be cut out from a cube of side 24cm is:64 x 3 = 192.
To find out how many 6cm cubical boxes can be cut out from a cube of side 24cm, we need to divide the volume of the large cube by the volume of the small cube (6cm x 6cm x 6cm).
Given that the side of the large cube is 24cm.To calculate the number of 6 cm cubes that can be made from this, we need to find out how many 6 cm cubes are there in one side of the large cube.Dividing the side of the large cube by the side of the small cube gives:24/6 = 4Since the cube is a 3D figure, we need to multiply this by itself two more times, since there are three dimensions:4 x 4 x 4 = 64Therefore, we can cut out 64 cubes with a side of 6cm from a cube with a side of 24cm, hence the total number of 6cm cubical boxes that can be cut out from a cube of side 24cm is:64 x 3 = 192.
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PLEASE HELP!!!!For Trapezoid QRST, M and P are midpoints of the legs.
If PM=2x, QR=3x, and TS=10, find PM.
In Trapezoid QRST, with midpoints M and P on the legs, if PM is equal to 2x, QR is equal to 3x, and TS is equal to 10, we need to find the value of PM.
In a trapezoid, the midpoints of the legs divide the bases into two equal segments. Let's consider the given information:
PM = 2x (length of segment PM)
QR = 3x (length of segment QR)
TS = 10 (length of segment TS)
Since M and P are midpoints, we can conclude that PM is equal to half of QR:
PM = 1/2 * QR
Substituting the given value of QR:
2x = 1/2 * 3x
To solve for x, we can multiply both sides of the equation by 2:
4x = 3x
Subtracting 3x from both sides:
4x - 3x = 3x - 3x
x = 0
Since x is equal to 0, we can substitute it back into the expression for PM:
PM = 2x
PM = 2(0)
PM = 0
Therefore, PM is equal to 0.
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A parrallelogram with a base four times the height and an area less than 200 square feet
The height is less than 5√2 feet and the base is less than 20√2 feet.
A parallelogram is a two-dimensional shape with two pairs of parallel sides. It has four sides and four angles. It is similar to a rectangle, except that its opposite sides are parallel and not necessarily of equal length.
A parallelogram with a base four times the height has the formula A=bh, where b is the length of the base and h is the height. Therefore, if the base is four times the height, then we can write b=4h. We can substitute this value of b into the formula A=bh to obtain A=4h×h=4h². Thus, the area of the parallelogram is 4h².
Therefore, the height is less than 5√2 feet. We can find the corresponding value of the base by using the equation b=4h. Thus, the base is less than 4(5√2)=20√2 feet.Since we know the height and the base of the parallelogram, we can calculate its area. The formula for the area of a parallelogram is A=bh, so we can write:A=(20√2)(5√2)=200 square feet.Since the area of the parallelogram is less than 200 square feet, it must be less than this value.
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What is the equivalent factored form of 12x4 – 42x3 – 90x2? 6x(x – 5)(2x 3) 6x2(x – 5)(2x 3) 6x(x 5)(2x – 3) 6x2(x 5)(2x – 3).
The factored form of the expression 12x^4 - 42x^3 - 90x^2 is 6x^2(x - 5)(2x + 3).
The equivalent factored form of the expression 12x^4 - 42x^3 - 90x^2 is 6x^2(x - 5)(2x + 3).
To find the factored form, we need to factor out the greatest common factor (GCF) from the given expression. The GCF of the coefficients 12, 42, and 90 is 6, and the GCF of the variables x^4, x^3, and x^2 is x^2.
Factoring out the GCF, we have:
6x^2(2x^2 - 7x - 15)
Next, we need to factor the quadratic expression within the parentheses. We are looking for two binomials that, when multiplied together, result in 2x^2 - 7x - 15.
The factors can be found by considering two numbers whose product is -30 (the product of the coefficient of x^2, 2, and the constant term, -15) and whose sum is -7 (the coefficient of x, -7).
By trial and error, we can determine that the factors are (2x + 3) and (x - 5).
Thus, the factored form of the expression 12x^4 - 42x^3 - 90x^2 is 6x^2(x - 5)(2x + 3).
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Chase is making bookmarks. He wants to make no more than 12 bookmarks and needs 4.25 inches of fabric for each bookmark. Write an inequality to determine the amount of fabric he needs to buy.
the inequality 4.25x ≤ 12 represents the amount of fabric Chase needs to buy, ensuring that he stays within his limit of 12 bookmarks.
To determine the amount of fabric Chase needs to buy, we multiply the number of bookmarks (x) by the fabric required per bookmark (4.25 inches). This gives us the total amount of fabric needed for x bookmarks.
Since Chase wants to make no more than 12 bookmarks, we set up the inequality 4.25x ≤ 12. This means that the product of 4.25 and x should be less than or equal to 12. By doing so, we ensure that the total amount of fabric required does not exceed the limit of 12 bookmarks.
Solving this inequality, we can find the maximum value for x, which represents the number of bookmarks Chase can make within the given fabric constraint. Dividing both sides of the inequality by 4.25, we have x ≤ 12/4.25.
Therefore, the inequality 4.25x ≤ 12 represents the amount of fabric Chase needs to buy, ensuring that he stays within his limit of 12 bookmarks.
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Examine the reasons why so many artists were seeking a different world
During the late 19th and early 20th centuries, many artists were seeking a different world due to several reasons.
1. Social and Political Changes During the late 19th and early 20th centuries, social and political changes were occurring at a rapid pace. The industrial revolution led to the growth of cities, which, in turn, caused a breakdown in traditional society. As a result, many artists were seeking a different world that was more in line with their ideals.2. Technological Advancements Inventions such as the telegraph and the telephone enabled artists to communicate with one another and share their ideas. Artists were inspired by new technologies and used them to create new forms of art.3. World War I World War I was a traumatic event that had a significant impact on the artistic community. Many artists were disillusioned by the horrors of war and sought to create a new world that was free from conflict and violence.4. Industrialization and Urbanization .The growth of industry and the shift from rural to urban life had a profound effect on the artistic communit.5. Romanticism .Romanticism was a cultural movement that emphasized emotion, imagination, and individualism. Many artists were inspired by the romantic ideal and sought to create works that expressed their innermost feelings and thoughts. The movement emphasized the importance of nature, beauty, and the sublime, which were seen as antidotes to the dehumanizing effects of industrialization and urbanization.
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Noah and Gabriel have taken 6 quizzes in English class so far. There are no outliers in their quiz scores. Find the measure of variability for Noah’s scores. Noah’s scores: 84, 85, 85, 86, 90, 92 Mean: 87 Range: 92 – 84 = 8 Gabriel’s scores: 82, 85, 86, 86, 90, 94 Mean: 87. 17 Range: 94 – 82 = 12 MAD: 3. 22 What is Noah’s mean absolute deviation? StartFraction StartAbsoluteValue 87 minus 84 EndAbsoluteValue (2) StartFraction StartAbsoluteValue 87 minus 85 EndAbsoluteValue StartFraction StartAbsoluteValue 87 minus 86 EndAbsoluteValue StartFraction StartAbsoluteValue 87 minus 90 EndAbsoluteValue StartFraction StartAbsoluteValue 87 minus 92 EndAbsoluteValue over 6 EndFraction = StartFraction 3 4 1 3 5 over 6 EndFraction 1. 33 2 2. 67 3. 5.
Noah's mean absolute deviation is 2.67 when the mean score is 87.
Thus, option (3) is correct.
To calculate Noah's mean absolute deviation (MAD) based on his quiz scores, we need to find the average of the absolute differences between each score and the mean.
The formula to calculate mean absolute deviation (MAD) is
[tex]{\text} MAD[/tex] =
Given:
Noah's scores: 84, 85, 85, 86, 90, 92
Mean of Noah's scores: 87
Now, the absolute differences between each score and the mean, as
|87 - 84| = 3
|87 - 85| = 2
|87 - 85| = 2
|87 - 86| = 1
|87 - 90| = 3
|87 - 92| = 5
Now, the mean of these absolute differences are:
MAD = (3 + 2 + 2 + 1 + 3 + 5) / 6
= 16 / 6
= 2.67
Therefore, Noah's mean absolute deviation is 2.67.
Thus, option (3) is correct.
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The question attached here seems to be inappropriate form, the appropriate form is:
Noah and Gabriel have taken 6 quizzes in English class so far. There are no outliers in their quiz scores.
Find the measure of variability for Noah’s scores.
Noah’s scores: 84, 85, 85, 86, 90, 92
Mean: 87
Range: 92 – 84 = 8
Gabriel’s scores: 82, 85, 86, 86, 90, 94
Mean: 87. 17
Range: 94 – 82 = 12
MAD: 3. 22
What is Noah’s mean absolute deviation?
|87 -84| + {97 - 85| + |87-90| + |87-90| + |97-92| / 6
1. 1.33
2. 2
3. 2.67
4. 3.5
A football team carried out a report to see the impact of stretching on preventing injury. Of the 45 footballers in the squad 36 stretch regularly. Of those who stretch, 6 got injured last year. There was a total of 10 injured players last year. The results are presented in the frequency tree
Among the 45 footballers, stretching regularly is associated with a lower injury rate. Out of the 36 footballers who stretch, 6 got injured, while among the 9 footballers who do not stretch, 4 got injured.
The frequency tree represents the data from the report on the impact of stretching on preventing injury in a football team. The tree shows that out of the 45 footballers in the squad, 36 of them stretch regularly. Among the footballers who stretch, 6 got injured last year. The total number of injured players last year was 10.
From the given information, we can analyze the relationships between the different categories. Out of the 45 footballers, 36 stretch regularly, which means that 9 footballers do not stretch. Since the total number of injured players is 10 and 6 of them are from the stretching group, the remaining 4 injured players must come from the non-stretching group.
To summarize, the report suggests that among the 45 footballers, stretching regularly is associated with a lower injury rate. Out of the 36 footballers who stretch, 6 got injured, while among the 9 footballers who do not stretch, 4 got injured. These findings highlight the potential benefits of incorporating stretching exercises into the team's routine to help prevent injuries. However, it is important to consider other factors and conduct further analysis to establish a more comprehensive understanding of injury prevention in the football team.
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Explain the process of solving a system of equations using substitution
One variable, from either of the equations, the subject of that equation and substitute it in the other equation.
We have,
To describe the process of solving a system of equations using substitution.
Now,
For any given system of linear equations, we use a method called substitution method for solving the equations.
We can make one variable, from either of the equations, the subject of equation and substitute it in the other equation.
This way, we get to find the value of the remaining variable and next we substitute this value in one of the equations to get the value of the variable left.
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step by step explanation for expressions d and e Thank you loads!!!
Answer:
Step-by-step explanation:
D)
[tex]\frac{4\sqrt{b} }{\sqrt{3}-b }[/tex] > in order to get rid of root on bottom like this, you
need to multiply top and bottom by conjugate
√3 +b
[tex]=\frac{4\sqrt{b} }{\sqrt{3}-b }\frac{\sqrt{3}+b}{\sqrt{3}+b}[/tex] > Distribute on top and FOIL bottom
[tex]=\frac{4\sqrt{3b}+4b\sqrt{b} }{3 -b^{2} }[/tex] >This is simplified, you cannot combine anything else
E)
[tex]\frac{3\sqrt{a^{2} } } {\sqrt{3} } / 2a^{\frac{3}{2} }[/tex] >√a² = a
[tex]=\frac{3a } {\sqrt{3} } / 2a^{\frac{3}{2} }[/tex] >Division of fraction keep change flip
[tex]=\frac{3a } {\sqrt{3} } * \frac{1}{2a^{\frac{3}{2}} }[/tex] >Because 2a is not in parenthesis 3/2 exp.
is only for a
[tex]=\frac{3a } {\sqrt{3} } * \frac{1}{2\sqrt{a^{3} } }[/tex] > You can make 1 set of a² so 1 comes out but 1 stays
[tex]=\frac{3a } {\sqrt{3} } * \frac{1}{2a\sqrt{a } }[/tex] >put like items under root
[tex]=\frac{3a } {2a\sqrt{3a} }[/tex] >multiply top and bottom by root
[tex]=\frac{3a } {2a\sqrt{3a} }*\frac{\sqrt{3a}}{\sqrt{3a}}[/tex] >multiply
[tex]=\frac{3a\sqrt{3a} } {2a(3a)} }[/tex] >3a cancels
[tex]=\frac{\sqrt{3a} } {2a} }[/tex] >This is simplified
En la siguiente tabla se muestra la cantidad de masa muscular que incrementaron en el último mes 4 amigos que van a entrenar a un gimnasio.
¿Para cuáles personas el incremento de masa muscular se representa por un número decimal periódico mixto?
A.
Daniel y Fabio.
B.
John y Fabio.
C.
Pedro y Daniel
D.
Pedro y John
De acuerdo con lo anterior podemos inferir que para los amigos Pedro y John, el incremento de masa muscular se representa por un número decimal periódico mixto.
¿Para cuáles personas el incremento de masa muscular se representa por un número decimal periódico mixto?El número decimal periódico mixto se refiere a un número decimal que tiene una parte entera, una parte decimal y una parte periódica, que se repite de forma continua.
Al observar los incrementos de masa muscular de los amigos, encontramos que Pedro tiene un incremento de masa muscular de 5/6 kg, lo cual se representa como 0.8(3) kg, donde el "3" se repite de forma continua.
Por otro lado, John tiene un incremento de masa muscular de 16/45 kg, que se representa como 0.3(5) kg, donde el "5" se repite de forma continua.
Entonces, la respuesta correcta es la opción D: Pedro y John.
Nota: Esta pregunta está incompleta. Aquí esta la información completa:
Imagen anexada.
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Brad's dinner bill, including a 16% tip, is $10. 44. What was the amount of the bill before the tip?
Given, Brad's dinner bill, including a 16% tip, is $10.44. We need to find the amount of the bill before the tip.Let the amount of the bill before the tip be x.So, the bill amount including the tip of 16% will be x + (16/100)x or (116/100)x.
This is because, if x is the bill amount, the tip is 16% of x, which is (16/100)x, then the total bill amount will be x + (16/100)x or (116/100)x.
We know that the bill amount including the tip is $10.44. So,(116/100)x = 10.44=> x = (10.44 × 100)/116= $9 (approx) Therefore, the amount of the bill before the tip is $9. Answer: $9.
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Where will the hour hand of a clock stop if it starts at 12 and make 3/4 of a revolution clockwise?
The hour hand will stop at the 9 o'clock position.A clock typically has 12 hours marked on its face, and a complete revolution of the hour hand corresponds to 12 hours or 360 degrees.
To determine where the hour hand will stop after making 3/4 of a revolution clockwise, we need to calculate the angle it will cover in a equation.
A full revolution is 360 degrees, so 3/4 of a revolution is (3/4) * 360 = 270 degrees.
Starting at the 12 o'clock position, the hour hand will move clockwise, and after covering 270 degrees, it will stop at a new position.
To find the location on the clock where the hour hand stops, we divide 270 degrees by the angle covered by each hour mark on the clock face. Since the hour hand moves 30 degrees for each hour (360 degrees divided by 12 hours), we divide 270 by 30:
270 degrees / 30 degrees per hour = 9 hours.
Therefore, the hour hand will stop at the 9 o'clock position.
To summarize, if the hour hand starts at 12 and makes 3/4 of a revolution clockwise, it will stop at the 9 o'clock position.
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Find the solution set of the system of linear equations represented by the augmented matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set
x2 = t and solve for x1 in terms of t.)
| 1 0 0 |
| 0 1 6 | (2x3 matrix)
System of linear equations represented by the augmented matrix . It means that we can take any real value for x1 and x2, while x3 will always be -t/6. Here, the system of linear equations has an infinite number of solutions.
The augmented matrix | 1 0 0 || 0 1 6 | is representing the following system of linear equations;`x1 = 0``x2 + 6x3 = 0`Using x2 = t and
solving for x1 in terms of t;x2 = tx1 = 0 (when x2 = t)Then, the solution set of the system of linear equations represented by the augmented matrix | 1 0 0 || 0 1 6 | is {x1=0, x2=t, x3=-t/6}
where t is an arbitrary constant.
We can see that x1 and x2 are arbitrary constants, but x3 = -t/6. It means that we can take any real value for x1 and x2, while x3 will always be -t/6.
Here, the system of linear equations has an infinite number of solutions.
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A scale measured a 4. 5-pound brick as weighing 5. 3 pounds. Which measurement is more accurate but less precise than 5. 3 pounds? 4. 98 pounds 5 pounds 5. 52 pounds 6 pounds.
The measurement that is more accurate but less precise than 5.3 pounds is 5 pounds.
Accuracy refers to how close a measurement is to the true value, while precision refers to the level of consistency or reproducibility of a measurement.
In this scenario, the scale measured a 4.5-pound brick as weighing 5.3 pounds. Comparing this measurement to the true value, we can say that it is not accurate because it overestimates the weight of the brick. However, it is relatively precise because it provides a specific value (5.3 pounds) rather than a range of values.
To find a measurement that is more accurate but less precise than 5.3 pounds, we look for a value that is closer to the true weight of the brick (4.5 pounds) but still lacks precision. Among the given options, 5 pounds is the closest value to the true weight of the brick, making it more accurate. However, it is less precise because it represents a rounded value without indicating any decimals.
Therefore, among the options provided, 5 pounds is the measurement that is more accurate but less precise than 5.3 pounds.
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Write the following ratios in their lowest terms: Mixing pink paint uses 3 litres of white paint and 1 litre of red. What is the ratio of white to red?
The simplified ratio is: 3 : 1. This means that for every 3 liters of white paint, 1 liter of red paint is used in the mixture.
To find the ratio of white paint to red paint, we need to compare the amounts of white paint and red paint used. The given information states that mixing pink paint requires 3 liters of white paint and 1 liter of red paint.
The ratio of white paint to red paint can be expressed as:
White : Red
To simplify this ratio to its lowest terms, we need to find the greatest common divisor (GCD) of the two numbers (3 and 1) and divide both numbers by it.
The GCD of 3 and 1 is 1, as there are no common factors other than 1. Therefore, we divide both numbers by 1:
3 ÷ 1 = 3
1 ÷ 1 = 1
The ratio 3 : 1 represents the proportional relationship between white paint and red paint in terms of liters. It indicates that for every 3 liters of white paint, only 1 liter of red paint is needed to achieve the desired mixture.
This ratio is already in its simplest form since the GCD of 3 and 1 is 1, and there are no further common factors to divide both numbers by.
In conclusion, the ratio of white paint to red paint in the mixture is 3 : 1.
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The plates on a vacuum capacitor have a radius of 2. 5
mm and are separated by a distance of 0. 75 mm.
What is the capacitance of this capacitor?
a. 2. 3 x 10^-13 F
b. 9. 3 x 10^-11 F
c. 3. 0 x 10^-11 F
d. 2. 3 x 10^-10 F
The capacitance of a parallel plate capacitor can be calculated using the formula:
C = (ε₀ * A) / d
Therefore, the correct option is:
d. 2.3 x 10^-10 F
Where:
C is the capacitance
ε₀ is the permittivity of free space (approximately 8.854 x 10^-12 F/m)
A is the area of one of the plates
d is the separation distance between the plates
Given that the radius of each plate is 2.5 mm, the area (A) can be calculated as follows:
A = π * r^2
A = π * (2.5 mm)^2
The separation distance between the plates is 0.75 mm.
Now we can substitute the values into the capacitance formula:
C = (ε₀ * A) / d
C = (8.854 x 10^-12 F/m) * (π * (2.5 mm)^2) / (0.75 mm)
Let's calculate the value:
C ≈ 2.3228 x 10^-10 F
Rounding to the nearest significant figure, the capacitance is approximately 2.3 x 10^-10 F.
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Select all the expressions that represent a 20% discount off the price of an item that originally costs d dollars
The expressions that represent a 20% discount off the price of an item that originally costs d dollars are A. 0.8d and C. d-0.2d.
How to find the expressions ?A 20% discount off the original price means that the discounted price is equal to 80% (100% - 20%) of the original price. Therefore, we can calculate the discounted price by multiplying the original price (d) by 0.8 (representing 80%).
Expression A (0.8d) represents the discounted price as 80% of the original price (d), so it is correct. Expression C, d-0.2d" represents a 20% discount off the price of an item that originally costs d dollars.
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Full question is:
Select all the expressions below which represent a 20% discount off the price of an item that originally costs d dollars.
A. 0.8d
B. d-0.2
C. d-0.2d
D. 1-0.2d
What happens to the value of f(x) = log4x as x approaches [infinity]?.
As x approaches infinity, the value of the function f(x) = log4x approaches infinity as well. The logarithm function with a base greater than 1 increases without bound as its input increases, so the value of log4x becomes arbitrarily large as x becomes larger.
The logarithm function log4x represents the exponent to which the base 4 must be raised to obtain x. As x approaches infinity, the function evaluates the behavior of the logarithm for extremely large values.
In this case, as x becomes larger and larger, log4x increases without bound. This means that there is no finite limit or specific value that f(x) approaches as x approaches infinity. Instead, f(x) grows infinitely, indicating that the function's value becomes arbitrarily large as x becomes larger. Therefore, the value of f(x) = log4x approaches infinity as x approaches infinity.
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Catherine's pool is in the shape of a rectangle. Its dimensions are 95 feet by 55 feet. Find the length in feet of the diagonal of the pool
To find the length of the diagonal of a rectangular pool whose dimensions are given, you can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. So, if we consider the length and width of Catherine's pool as the two shorter sides of a right-angled triangle, we can use the Pythagorean Theorem to find the length of the diagonal (the hypotenuse).
The formula to find the length of the diagonal is given by: diagonal=\sqrt{length^2+width^2} where length and width are the dimensions of the rectangle. So, for Catherine's pool, we have:length = 95 feet width = 55 feet Using the formula, we get: diagonal=\sqrt{length^2+width^2}= \sqrt{(95)^2 + (55)^2}= \sqrt{9025 + 3025}= \sqrt{12050}= 109.59\ \text{feet} Therefore, the length of the diagonal of Catherine's pool is approximately 109.59 feet.
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Two vertical posts stand side by side. One post is 8 feet tall and the other is
17 feet tall, if a 24 foot post is stretched between the tops of the posts,
how far apart are the posts?
22. 6
25. 3
22. 2.
26. 7
Will mark brainliest
The answer is 25. 3. Hence, option B is the correct answer.
Given that the two vertical posts stand side by side. One post is 8 feet tall and the other is 17 feet tall, and a 24-foot post is stretched between the tops of the posts, we need to find how far apart are the posts?We have to use the Pythagorean Theorem to find the distance. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides of the triangle.The figure can be drawn as below:
Here, AB is the 24 foot post, and A and B are the tops of the shorter and the taller post, respectively.
From the figure, we can observe that:
In triangle ABC,
AB² = AC² + BC² (According to Pythagoras theorem)
AC = 8 feet
BC = 17 feet
AB = 24 feet
Substituting the values in the above formula we get,
24² = 8² + 17²
576 = 64 + 289
576 = 353 + BC²
BC² = 576 - 353
BC² = 223
BC = sqrt(223)
The distance between the two posts is the length of the line segment CD, which is BC minus the length of the line segment AD.
Therefore,
Distance between the posts = BC - AD= sqrt(223) - 24= 3.17 ft (approx)
Therefore, the answer is 25. 3. Hence, option B is the correct answer.
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Maggie is working at a store that pays by the hour and by commission (pay for how much you sell). Maggie wants to go this weekend to the lake with her friends but she needs to make at least $225 today. She gets paid $15 per hour plus $25 for every sale she makes. What are all the possible values of the number of sales that Maggie can make to go to the lake if she is scheduled to work from 8am until 4pm?
Maggie can make anywhere from 5 to 4 sales to earn at least $225 and go to the lake with her friends.
Maggie gets paid $15 per hour plus $25 for every sale she makes. The number of sales she makes can be represented by x.
In order to calculate Maggie's earnings in terms of commission, we can use the equation 25x.
To calculate Maggie's earnings in terms of hourly pay, we can use the equation 15(8), since she works from 8am until 4pm, which is 8 hours. This simplifies to 120.The total amount Maggie earns can be represented by the equation:
Total earnings = 25x + 120
To find the minimum number of sales Maggie needs to make to earn at least $225, lets set up the inequality:
25x + 120 ≥ 225
Subtracting 120 from both sides, we get:
25x ≥ 105
Dividing both sides by 25, we get:
x ≥ 4.2
Maggie cannot make a fraction of a sale, so we can round up to find the minimum number of sales she needs to make, which is 5 sales.
To find the maximum number of sales Maggie can make, lets consider the fact that she is scheduled to work from 8am until 4pm, which is 8 hours. If she makes 0 sales, she will earn $120 (her hourly pay for 8 hours of work).
To find the maximum number of sales, we can set up the equation:25x + 120 ≤ 225
Subtracting 120 from both sides, we get:
25x ≤ 105
Dividing both sides by 25, we get:
x ≤ 4.2
Maggie cannot make a negative number of sales, so we can round down to find the maximum number of sales she can make, which is 4 sales.
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The possible values of the number of sales that Maggie can make to go to the lake are 5 and 4.
Given:
Maggie gets paid $15 per hour plus $25 for every sale she makes.
She needs to make at least $225 today.
She is scheduled to work from 8 am until 4 pm.
To find:
All the possible values of the number of sales that Maggie can make to go to the lake.
Solution:
Let's consider x to be the number of sales that Maggie makes.
To determine the minimum amount she needs to earn:
Her hourly wage for 8 hours of work = $15 × 8 = $120
Total earnings that she needs = $225 - $120 = $105
If y is the number of sales she needs to make to earn $105, then:
$25y = $105
Dividing both sides by $25, we get:
y = 4.2
This means she needs to make at least 5 sales.
Let's calculate the maximum number of sales that she can make. If she has to earn $240 for 8 hours of work:
Total earnings required = $240 - $120 = $120
$25y = $120
Dividing both sides by $25, we get:
y = 4.8
This means the maximum number of sales she can make is 4.
As such, the possible values of the number of sales that Maggie can make to go to the lake are 5 and 4.
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If water flows from a pipe at 300m/min, the rate of the flow in km/h is ______.
180
18
1.8
2. Find the ratio 1 liter to 350ml
20:7
7:20
100:35
3. The monthly rent of a stall in the ratio is 5:6. As result, the stall holder has to pay $45 more per months. Find the new rent.
$225
$255
$270
4. If A:B = 3:5 and B:C = 3:7, find A:B:C
3:15:35
9:15:7
9:15:35
To convert the rate of water flow from meters per minute to kilometers per hour, we need to multiply by a conversion factor. Since there are 60 minutes in an hour and 1000 meters in a kilometer, the conversion factor is (60/1000).
So, the rate of flow in km/h is (300 * 60/1000) = 18 km/h.
Therefore, the correct answer is option b) 18.
To find the ratio of 1 liter to 350 ml, we need to convert both measurements to the same unit. Since 1 liter is equal to 1000 ml, the ratio becomes:
1 liter : 1000 ml
To simplify the ratio, we divide both sides by 50:
(1 liter / 50) : (1000 ml / 50)
Therefore, the correct ratio is option a) 20:7.
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Find the value of k, if x=2 is a zero of the polynomial
p(x) = x2
- 2k + 2
To find the value of k, we need to determine the value of k for which x = 2 is a zero of the polynomial p(x).
Given the polynomial p(x) = x^2 - 2k + 2, we know that x = 2 is a zero of the polynomial. This means that when x = 2, the polynomial evaluates to zero.
Substituting x = 2 into the polynomial, we have:
p(2) = (2)^2 - 2k + 2 = 0
Simplifying the equation, we get:
4 - 2k + 2 = 0
Combining like terms:
6 - 2k = 0
To find the value of k, we isolate the term with k by subtracting 6 from both sides:
-2k = -6
Dividing both sides by -2:
k = 3
Therefore, the value of k that makes x = 2 a zero of the polynomial is k = 3.
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733 ÷ 4
This model describes the division calculation. Start with the greatest multiple of 100 that can be multiplied by the divisor with going over the dividend.
Enter a number in each box to correctly complete the model and quotient.
The division calculation of 733 divided by 4 can be solved by finding the greatest multiple of 100 that can be multiplied by 4 without exceeding 733. The quotient is obtained by dividing this multiple by 4.
To solve 733 ÷ 4, we begin by finding the greatest multiple of 100 that can be multiplied by 4 without exceeding 733. In this case, the multiple is 700 (100 multiplied by 7). Next, we divide this multiple by 4 to obtain the quotient. The division can be performed as follows:
175
4 | 733
We start by dividing 7 (the tens digit of 700) by 4, which equals 1. We place this quotient of 1 on top. Then, we multiply 1 by 4, which equals 4, and subtract it from 7 to get the remainder of 3. We bring down the ones digit of 33, and the process is repeated. We divide 33 by 4, which gives us 8 with no remainder. Therefore, the quotient of 733 ÷ 4 is 183, with no remainder.
In summary, when dividing 733 by 4, we find the greatest multiple of 100 that can be multiplied by 4 without exceeding 733, which is 700. Dividing 700 by 4 gives us a quotient of 175. Therefore, the answer to 733 ÷ 4 is 183.
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Sean bought a laptop and a printer. He sold both items for £1,300 getting £1,150 just for the laptop. Sean made a 32% profit on the cost of the printer. What was the cost of the printer? Give your answer to 2 decimal places.
The cost of the printer was £468.75. Sean made a 32% profit on its cost price. He sold both the laptop and the printer for a total of £1,300, with the laptop alone fetching £1,150.
To find out the cost of the printer, you need to first calculate the cost of the laptop. Then, you can use that information along with the total selling price to determine the cost of the printer.
Let the cost of the laptop be L and the cost of the printer be P. Total selling price of both items = £1,300Amount Sean got just for the laptop = £1,150.Cost of printer = Total - Amount Sean got just for laptop= £1,300 - £1,150 = £150Sean made a 32% profit on the cost of the printer.
Profit percentage is calculated using the following formula:
Profit percentage = (Profit / Cost price) x 10032% = (Profit / Cost price) x 10032 / 100 = Profit / Cost price0.32 = Profit / P Profit = 0.32PNow, we know that the total selling price of both items is £1,300 and that the cost of the laptop is L. So, we can write:L + P = £1,300We also know that Sean made a profit of 32% on the cost of the printer. So, the selling price of the printer is 132% of its cost price. We can write this as: .Selling price of printer = 1.32PAdding the selling prices of bot h items, we get:L + 1.32P = £1,300Now we can substitute L + P = £1,300 into this equation:L + 1.32P = £1,300L + 1.32P = L + P + 0.32PL + 0.32P = £1,3000.32P = £150P = £150 / 0.32P = £468.75.Therefore, the cost of the printer was £468.75.
The cost of the printer was £468.75. Sean made a 32% profit on its cost price. He sold both the laptop and the printer for a total of £1,300, with the laptop alone fetching £1,150.
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