The question asks if the data contradict the assertion of the physical model, which suggests that the mean temperature increase should not be more than 5 Celsius.
To answer the question, we need to calculate the mean temperature increase from the data given: 6.4, 4.3, 5.7, 4.9, 6.5, 5.9, 6.4, 5.1. We can do this by adding all the values and dividing them by the number of runs (8): (6.4 + 4.3 + 5.7 + 4.9 + 6.5 + 5.9 + 6.4 + 5.1)/8 = 5.4. The mean temperature increase of 5.4 does not exceed the maximum of 5 Celsius, which means that the data does not contradict the physical model.
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Grant was making banners from cardboard as a picture to celebrate Parker‘s high school graduation. How many square inches of cardboard will Grant need for each banner that he makes?
5in
4in
8in
10in
For the standard size banner with a 1-inch margin, Grant would need approximately 1596 square inches of cardboard to make one banner.
Define the term area?The amount of cardboard needed to make a banner depends on the size of the banner. If we know the dimensions of the banner, we can calculate the area of cardboard needed.
Assuming that the banner is a rectangle, let's say its width is w inches and its height is h inches.
Then, the area of the banner can be calculated as:
Area = width x height
Area = w x h
To find out how many square inches of cardboard are needed, we need to add a margin to the dimensions of the banner to account for the thickness of the cardboard. Let's say the margin is m inches.
Then, the width of the cardboard needed is (w + 2m) inches, and the height of the cardboard needed is (h + 2m) inches.
The area of the cardboard needed can be calculated as:
Area of cardboard = (width of cardboard) x (height of cardboard)
Area of cardboard = (w + 2m) x (h + 2m)
So, the total area of cardboard needed for one banner is:
Total area of cardboard = Area of cardboard + Area of margin
Total area of cardboard = (w + 2m) x (h + 2m) + 4m(w + h + 2m)
if we assume that the banner is 2 feet wide (24 inches) and 4 feet long (48 inches), and we add a margin of 1 inch on each side, then we can calculate the total area of cardboard needed as follows:
Total area of cardboard = (24 + 2) x (48 + 2) + 4(1)(24 + 48 + 2)
Total area of cardboard = 26 x 50 + 4(74)
Total area of cardboard = 1300 + 296
Total area of cardboard = 1596 square inches
So, for this standard size banner with a 1-inch margin, Grant would need approximately 1596 square inches of cardboard to make one banner.
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Landon invested $110 in an account paying an interest rate of 4. 1% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 5 years?
The amount in the account after 5 years would be $137.
Continuous compound interest is a method of calculating the interest earned on a principal amount that is continuously reinvested
We can use the formula for continuous compound interest:
A = Pe^(rt)
where:
A = final amount
P = principal amount
e = Euler's number (approximately 2.71828)
r = annual interest rate (as a decimal)
t = time in years
In this case, we have:
P = $110
r = 0.041 (4.1% expressed as a decimal)
t = 5 years
Substituting these values into the formula, we get:
A = 110e^(0.0415)
A ≈ $136.69
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What single decimal multiplier would you use to increase by 5% followed by a 15% increase?
Answer:
(1.2075)
Step-by-step explanation:
Lets assume we are increasing a price on a $100 item to help visualize the steps.
The two steps of 5% and then 15% can each be expressed as:
5%: (1+0.05) [The 1 represents the fact that the final cost is full price (1) plus 5%(0.05)]
15% (1+0.15) [Same explanation, but now with 0.15 for 15%]
We can apply these factors individually:
Assume a base of $100:
5% increase would make it $105 [$100*(1.05)=$105]
15% increase: On top of the 5%, we would go to: $105*(1.15) = $120.75
Or we can use a single multiplier.
If we look at the steps from above, we see that the algebra consisted of taking the origianl price ($100) and multiplying it twice: once with (1+0.05) and once with (1+1.15). Write this in the form of an equation:
($100)*(1+0.05)*(1+0.15) = $120.75
Let's multiply (1+0.05)*(1+0.15)
= (1.2075)
We can use this single factor (multiplier) to find the correct/same value as before:
(1.2075)($100) = $120.75
Real estate agent has 11 properties that she shows. She feels that there is a 40% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling at least 1 property in one week. Round your answer to four decimal places
The probability of selling at least one property in one week is 0.9718
We can approach this problem by finding the probability of not selling any property in a week and then subtracting it from 1 to get the probability of selling at least one property.
The probability of not selling any property in a week is the probability of not selling any one property in a week, raised to the power of the number of properties:
P(not selling any property) = (1 - 0.4)^11 = 0.0282
Therefore, the probability of selling at least one property in a week is:
P(selling at least one property) = 1 - P(not selling any property) = 1 - 0.0282 = 0.9718
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During the data preparation activities, you have identified small amount of missing numerical data. What would you do? A. I would exclude all observations with missing data. B. I would replace the missing values with the average value of that specific variable. C. Without hesitation I would exclude all variables with missing data. D. None of the above is true.
Option B is the correct answer.
The correct answer to the given question is Option B, which is "I would replace the missing values with the average value of that specific variable."What are Data Preparation activities?Data preparation activities consist of operations that change the quality, consistency, or completeness of data. These are performed to improve the data's accuracy and, as a result, the resulting insights.When it comes to numerical data, there are certain techniques you can use to deal with missing data. There are many ways to deal with missing numerical data, but one of the simplest is to use the mean or median value of the dataset to replace the missing values. This method is also known as mean imputation.Therefore, if during the data preparation activities, you have identified a small amount of missing numerical data, you should replace the missing values with the average value of that specific variable. Therefore, Option B is the correct answer. The other options such as excluding all observations with missing data, excluding all variables with missing data, and none of the above is true are not accurate.
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decrease 72 in the ratio 4:3
Answer:
4+3=7
4/7*72/1=288/7=41.1
3/7*72/1=216/7=30.9
41.1:30.9=4:3
Olivia ate at the same restaurant three times. Each visit, she ordered a sandwich and left a $2. 25 tip. She spent a total of $39. What is an equation that represents this situation, if c represents the cost of a salad?
Each visit, Olivia ordered a sandwich and left a $2. 25 tip. She spent a total of $39. Therefore, an equation that represents this situation, if c represents the cost of a salad is 4(x+2.25) = 39.
Equation:
An equation is a formula that expresses that two expressions are equal by joining them with the equal sign =.The word comparison and its cognates in other languages may have subtly different meanings; for example, in French, an equation is defined to contain one or more variables, and in English any well-formed formula composed of two expressions linked by equal signs is an equation.
According to the Question:
Let the cost of each salad = c
Therefore we can write
4(x+2.25) = 39
or, x+ 2.5 = 39
or, x = 39 − 2.5
or, x = 39 − 2.5
or, x = 26.5
Therefore, The equation that represents this situation, if c represents the cost of a salad is 4(x+2.25) = 39.
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What is the side length of a square with the area 49 sq cm
The side length of a square with an area of 49 square centimeters is 7 centimeters.
Area is a measurement of the amount of space inside a 2-dimensional shape, such as a rectangle, square, triangle, circle, or any other polygon
The area of a square is calculated by multiplying its length by its width. For a square, however, its length and width are equal.
So, if we let "x" be the side length of the square, we can express the area as,
x^2 = 49
To solve for x, we can take the square root of both sides of the equation:
sqrt(x^2) = sqrt(49)
x = 7 centimeter
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El perímetro del triangulo es 42 dm. Al determinar la medida de sus lados, obtiene que el valor de x es:
The perimeter of the triangle present in above figure is 42 dm. Then the value of x is equals to the 9 dm and all three sides of triangle are 9 dm, 11 dm and 22 dm.
We have a triangle present in above figure. The perimeter is the length of the boundaries of a shape. A triangle is a type of polygon with three sides. In other words, it is a closed two dimensional shape having three straight sides. So, perimeter of a triangle = sum of all three sides. Here, perimeter of triangle = 42 dm
Now, first side length of triangle= (3x - 5 ) dm
Second side length = (x + 2) dm
Third side length = x dm
Now, using perimeter formula for triangle,
=> 3x - 5 + x + x + 2 = 42
=> 5x = 42 + 5 - 2 = 45
=> x = 45/5 = 9
3x - 5 = 22 dm
x + 2 = 11 dm
So, sides of triangle are 9 dm, 11 dm and 22 dm.
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Complete question :
The perimeter of the triangle is 42 dm. By determining the measure of its sides, he obtains that the value of x is _? see the above figure
Write the correct answers.
1) I am an integer in Quadrant
My a-coordinate is less than-1.
My coordinate is more than 2.
My r-coordinate is greater than-3.
• The sum of the absolute values of my coordinates is 5.
Who am 17
) Plot me on the coordinate graph.
The point (-3, 4) satisfies all the given conditions, and hence, it is the point we are looking for. The integer in Quadrant II.
How do you find a point's coordinates on the Cartesian plane?An ordered pair of integers (x, y), where x is the horizontal coordinate or the abscissa and y is the vertical coordinate or the ordinate, is used to represent a point in the Cartesian plane. With regard to the x-axis and y-axis, a point on the plane may be located using these coordinates.
Let's assume that the point has coordinates (-x, y), where x > 1 and y > 2.
Then, using the distance formula, we have:
r = √(x² + y²)
Since r > -3, we have:
√(x² + y²) > -3
x² + y² > 9
Now, absolute values of the coordinates is 5, we have:
|x| + |y| = 5
Since x < -1, we have -x > 1, which means that:
|x| = -x -1
Substituting this into the equation above, we get:
(-x - 1) + |y| = 5
|x| + |y| = 5
Subtracting -x - 1 from both sides, we get:
|y| = x + 6
Substituting this into the equation x² + y² > 9, we get:
x² + (x + 6)² > 9
2x² + 12x + 27 > 0
This inequality holds for all x.
Therefore, the point (-3, 4) satisfies all the given conditions, and hence, it is the point we are looking for. The integer in Quadrant II.
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Answer:17
Step-by-step explanation:
De 150ha se quiere construir un acuario que tenga una pileta de rectangular de 9m de largo 4 de ancho y 2. 5m de profundidad. En esta se colocara una guarda de azulejos. Que cuesta 90 pesos el metro y 50 pesos por metro a la colocacion en el borde superior de la pileta
cuantos metros de azulejos se necesitan comprar?
podrías calcular el volumen dem agua de dicha pileta para que puedan vivir alli dos focas?
calcula ma densidad de la poblacion de focas
The population density of seals is 0.0111 seals/m³.
To calculate the number of meters of tiles needed to purchase, we must first calculate the area of the pool. This can be done by multiplying the length by the width:
9m x 4m = 36m²
We then multiply this area by the depth of the pool to get the total volume:
36m² x 2.5m = 90m³
Now, to calculate the number of meters of tiles needed, we must divide the total cost of the tiles, including installation, by the cost of the tiles per meter:
90 pesos + 50 pesos = 140 pesos
140 pesos ÷ 90 pesos = 1.55 meters
Therefore, 1.55 meters of tiles must be purchased to cover the pool.
To calculate the volume of water for two seals, we must first calculate the volume of the pool, which can be done by multiplying the length by the width and then by the depth:
9m x 4m x 2.5m = 90m³
We then multiply this volume by the number of seals to get the total volume of water needed:
90m³ x 2 seals = 180m³
Therefore, 180m³ of water is needed for two seals to live in the pool.
To calculate the population density of seals, we must divide the total population of seals by the total volume of water needed:
2 seals ÷ 180m³ = 0.0111 seals/m³
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Farkle flange has 2 manufacturing departments, K and Q. Otals facory overhead is $850,000. Department K is allocated $200,000 and the remainder to Department Q. Department K will use 3,800 direct labor hours and department Q will use 6,200 direct labor hours for a total of 10,000 direct labor hours at a total cost of $500,000 ($50/hr). What is the department overhead allocation rate for departments k and q, respectively?
The overhead allocation rate for Department K is $52.63 and the overhead allocation rate for Department Q is $82.26.
The overhead allocation rate for departments K and Q is calculated by dividing the overhead allocated to each department by the direct labor hours used by each department. For Department K, the overhead allocation rate is calculated by dividing $200,000 by 3,800 direct labor hours, which equals $52.63 per hour. For Department Q, the overhead allocation rate is calculated by dividing the remaining overhead of $650,000 by the 6,200 direct labor hours used by the department, which equals $104.84 costs per hour. To calculate the total factory overhead, the following formula is used:Total Factory Overhead = (Department K Overhead + Department Q Overhead) / (Total Direct Labor Hours Used) Total Factory Overhead = ($200,000 + $650,000) / (3,800 + 6,200) Total Factory Overhead = $850,000 / 10,000 .Total Factory Overhead = $85.00 per hour
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Properties of trapezoids UC^(9) Quadrilateral HIJK is an isosceles trapezoid, HJ=7z-94, and IK=2z+76. What is the value of z ?
The value of z can be determined by solving the equation 7z-94 = 2z+76, which yields z=35.
To determine the value of z in the given equation, it is necessary to solve the equation 7z-94 = 2z+76. Begin by subtracting 2z from both sides of the equation, which yields 7z-2z-94 = 76. Simplifying this yields 5z-94 = 76. To solve for z, add 94 to both sides of the equation, which yields 5z = 170. Dividing both sides by 5 yields z = 34. Since the equation is not asking for an exact value, it can be rounded to the nearest whole number, which is 35. Therefore, the value of z is 35.
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i am not sure how to do this, and i really need to get this class over with
Answer:2
Step-by-step explanation:
we know that the side are the same
[tex]\sqrt{2} ^{2} +\sqrt{2} ^{2} =y^{2}[/tex]
[tex]2+2=y^{2}[/tex]
[tex]\sqrt{4} =y[/tex]
[tex]2=y[/tex]
– x+ – 3x+5x+10x+ – 4x+4x
The expression - x - 3x + 5x + 10x - 4x + 4x simplifies to x.
If we group the like terms, we have:
(-1-3+5+10-4+4)x
What is expression ?An expressiοn in math is a sentence with a minimum οf twο numbers οr variables and at least οne math οperatiοn. This math οperatiοn can be additiοn, subtractiοn, multiplicatiοn, οr divisiοn.
Simplifying the terms inside the parentheses, we have:
1x
And simplifying further, we have the:
x
Therefore, the expression - x - 3x + 5x + 10x - 4x + 4x simplifies to x.
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3. Han and Tyler are following a polenta recipe that uses 5 cups of water for every 2
cups of cornmeal.
• Han says, "I am using 3 cups of water. I will need 1 1
- cups of cornmeal."
o Tyler says,"I am using 3 cups of cornmeal. I will need 7> cups of water."
Do you agree with either of them? Explain your reasoning.
Given logbA=2.817 and logbB=0.106, evaluate logb A/BA. 2.817B. 0.299C. 2.711D. 2.923
logbA = 2.817 and logbB = 0.106 need to be used to find logb A/BA. We know that logarithms are important in mathematics and help us to solve complex problems involving exponents or roots.
They are expressed in terms of the logarithm base, which is the number or expression that is being raised to a power. It can be solved using the quotient rule of logarithms which states that logb (x / y) = logb x - logb y.
Explanation:
The given values are: logbA = 2.817 and logbB = 0.106Let us first use the quotient rule of logarithms to simplify the expression logb A/BA = logb A - logb BA. Using this rule, we get:
logb A/BA = logb A - logb B
Now we can substitute the given values in the above expression:
logb A/BA = 2.817 - 0.106
= 2.711
Therefore, the value of logb A/BA is 2.711. Hence, option (D) 2.711D is the correct answer.
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determine whether the given first-order differential equation is linear in the indicated dependent variable by matching it with the differential equation given in (7) in section 1.1, a1(x) dy dx a0(x)y
The given first-order differential equation is linear in the indicated dependent variable because it matches the standard form of a linear first-order differential equation, a1(x) dy/dx + a0(x)y = f(x).
First, let us review what a linear first-order differential equation is. Ais a differential equation that can be written in the form:
a1(x) dy/dx + a0(x)y = f(x)
Now, let us compare the given differential equation to the standard form of a linear first-order differential equation. The given differential equation is:
a1(x) dy/dx + a0(x)y
As we can see, the given differential equation matches the standard form of a linear first-order differential equation. Therefore, we can conclude that the given differential equation is linear in the indicated dependent variable.
In conclusion, the given first-order differential equation is linear in the indicated dependent variable because it matches the standard form of a linear first-order differential equation, a1(x) dy/dx + a0(x)y = f(x).
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I need help with this
Answer:
Step-by-step explanation:
1: Quadratic
2: Exponential
3. None
6x + 5 = 5x + 8 + 2x
Is x = 3 a solution? Explain.
What is the value of x?
Answer: 5
Step-by-step explanation:
Using the law of similar triangles,
x/x-2 = x+(x+5)/x+1+x-2
x/x-2 = 2x+5/2x-1
x(2x-1) = x-2(2x+5)
2x²-x = 2x²+x-10
2x²-2x² + x +x -10 = 0
2x-10 = 0
2x = 10
x = 5
Hope this helps! :)
Solve the system of equations graphed on the coordinate axes below.
�
=
y=
−
2
3
�
+
4
−
3
2
x+4
�
=
y=
1
2
�
+
4
2
1
x+4
The solution to the system of equations y = -2x + 4 and y = 1/2x + 4 is the point (0, 4)
Calculating the solution to the systemA system of equations is a set of two or more equations that are to be solved simultaneously.
The solution of a system of equations is a set of values that satisfy all the equations in the system.
Given the equations:
y = -2x + 4
y = 1/2x + 4
The question implies that we solve graphically
So, we create a plot of the equations y = -2x + 4 and y = 1/2x + 4
And we write out the coordinate of the point of intersection between the two equations
From the graph of the system of equations (see attachment), we have the point of intersection to be (0, 4)
This means that the solution to the system of equations is (0, 4)
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Complete question
Solve the system of equations graphed on the coordinate axes below.
y = -2x + 4
y = 1/2x + 4
Evaluate the expression 2p - (p + 3) +3. For p = 6
Use the CER strategy to show your work.
Answer: 9
Step-by-step explanation: sorry if it is wrong
Answer:
0
Step-by-step explanation:
2p - (p + 3) + 3
2(6) - (6 + 3) + 3
12 - (9) + 3
12 - 12 = 0
8) Decide whether \( X \) and \( Y \) are good candidates for linear regression in the scatterplot given.
It is not possible to determine the relationship between the two variables based on this scatterplot.
The scatterplot below does not show a good candidate for linear regression because the points do not follow a clear pattern. There is no consistent trend that shows a correlation between the X and Y variables. Therefore, it is not possible to determine the relationship between the two variables based on this scatterplot.The linear regression is a statistical technique that enables the analysis of relationships between two or more continuous variables. The method attempts to find the line of best fit, which represents the overall relationship between the two variables. A scatterplot, which is a graphical display of a dataset, can be used to determine whether two variables are good candidates for linear regression.In order for two variables to be a good candidate for linear regression, they must have a strong positive or negative correlation. In other words, the points on the scatterplot must follow a clear pattern that shows a linear relationship between the X and Y variables. If there is no clear pattern or the points are randomly scattered, then it is not possible to determine the relationship between the two variables based on a linear regression model.
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Given: y = 4x² - 7x-2
If the solutions of this equation are a and b, where a < b.
What is the value of a?
the value of a is -7/4.
Simply change x in the original equation to -1/4 to determine the value of a:
y = 4x² - 7x - 2
y = 4(-1/4)² - 7(-1/4) - 2
y = 1 - (-7/4) - 2
y = 1/4 - 2
y = -7/4
What is the equation?
Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
from the question:
We must discover a solution for x before we can find the solutions to the equation y = 4x2 - 7x - 2. By calculating the quadratic equation while putting y equal to zero, we can achieve this:
4x² - 7x - 2 = 0
(4x + 1)(x - 2) = 0
This quadratic equation has two solutions:
4x + 1 = 0 or x - 2 = 0
4x = -1 or x = 2
x = -1/4 or x = 2
As a result, the equation has solutions a = -1/4 and b = 2, where a b.
Simply change x in the original equation to -1/4 to determine the value of a:
y = 4x² - 7x - 2
y = 4(-1/4)² - 7(-1/4) - 2
y = 1 - (-7/4) - 2
y = 1/4 - 2
y = -7/4
Therefore, the value of a is -7/4.
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Suppose that there are three types of apples, indicated by Z=1,Z=2,Z=3. Let the weight of an apple be denoted by the random variable Y. Let E[Y∣Z=j]=1/(2j),E[Y2∣Z=j]=1/j,j=1,2,3. If we know that inside a mystery box of apples there are equal numbers of each cultivar, what is a) the expected value for the weight of a randomly chosen apple from the box? b) the variance of the weight of a randomly chosen apple from the box?
a) The expected value for the weight of a randomly chosen apple from the box is 11/24.
b) The variance of the weight of a randomly chosen apple from the box is 19/72.
a) The expected value of the weight of a randomly chosen apple from the box can be calculated as:
E[Y] = E[E[Y|Z]] = E[1/(2Z)] = 1/2 * (1/2 + 1/4 + 1/6) = 11/24
Therefore, the expected value for the weight of a randomly chosen apple from the box is 11/24.
b) The variance of the weight of a randomly chosen apple from the box can be calculated as:
Var(Y) = E[Var(Y|Z)] + Var(E[Y|Z])
Since E[Y|Z=j] = 1/(2j) and E[Y²|Z=j] = 1/j, we have:
Var(Y|Z=j) = E[Y²|Z=j] - [E[Y|Z=j]]² = 1/j - (1/(2j))² = (3/4) * (1/j²)
Therefore, we can calculate the variance of Y as:
Var(Y) = E[Var(Y|Z)] + Var(E[Y|Z])
= 1/3 * (3/4 * (1/1²) + 3/4 * (1/2²) + 3/4 * (1/3²)) + Var(11/24)
= 1/4 * (1 + 1/4 + 1/9) + 0
= 19/72
So, the variance of the weight of a randomly chosen apple from the box is 19/72.
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Write and solve an equation: In the 2000 Summer Olympics, the United
States won 9 more medals than Russia. Together, they won 185 medals.
How many medals did the United States win?
The number of medals did the United States win is 97 using the equation x + (x + 9) = 185.
Let x be the number of medals Russia won in the 2000 Summer Olympics. Then, since the United States won 9 more medals than Russia, the number of medals the United States won is x + 9.
Together, they won 185 medals, so we can write the equation:
x + (x + 9) = 185
Simplifying the left side, we get:
2x + 9 = 185
Subtracting 9 from both sides:
2x = 176
Dividing both sides by 2:
x = 88
So Russia won 88 medals, and the United States won 88 + 9 = 97 medals.
Therefore, the United States won 97 medals in the 2000 Summer Olympics.
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A store is having a sale where all shoes are discounted by 20%.
Martin has a coupon for $3 off of the regular price for one pair of shoes.
The store first applies the coupon and then takes 20% off of the reduced price. If Martin pays $18.40 for a pair of shoes, what was their original price before the sale and without the coupon?
The original price of the shoes was $26.
What is coupon ?
A coupon is a voucher or a code that can be used to get a discount or a special offer when making a purchase.
Let the original price of the shoes be x.
According to the problem, Martin gets a discount of $3 on the original price, so he pays (x - 3) dollars.
Then, the store takes 20% off the reduced price, which means Martin pays 80% of (x - 3) dollars.
We can write this information as an equation:
0.8(x - 3) = 18.4
Simplifying:
0.8x - 2.4 = 18.4
0.8x = 20.8
x = 26
Therefore, the original price of the shoes was $26.
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Please, I just need some help. I will pick brainiest! Thanks :)
The resistance of an electric stove burner element is 11 ohms. What current flows through this
element when it runs off a 220 volt line?
The current flows through the element with resistance of an electric stove burner element is 11 ohms when it runs off a 220 volt line is equals to the 20 Ampere.
The resistance of an electric stove burner element is, R = 11 ohms.
The magnitude or amount of potential
difference in a line that is voltage V
= 220 V.
We have to determine the value current flows through this element.
According to ohm's law : If all physical conditions and temperature remain constant, the voltage across a conductor is proportional to the current flowing through it. The expression is, V = I x R
here, I-> the amount of current
V--> potential difference
R--> resistance
The current value flowing through the element is written by I = V/R
=> I = 220 V/11 ohms
=> I = 20 A
Hence, the required current value is 20 A.
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Find sin(cos^-1(1/2)) and tan (sec^-1(x/3))
√3/2 and √3x / x.
The value of sin (cos-1 (1/2)) and tan (sec-1 (x/3)) are:Sin (cos-1 (1/2)):In the trigonometry section, the cosine inverse (or arccosine) is used to find the angle whose cosine value is equal to a given number.The cosine inverse (or arccosine) of a number is the angle whose cosine is equal to that number (cos-1). Therefore, cos-1 (1/2) represents the angle that has a cosine of 1/2.The sine is the ratio of the length of the opposite side to the length of the hypotenuse of a right triangle.Sin (cos-1 (1/2)) = sqrt (1 - cos2 (cos-1 (1/2)))Since cos (cos-1 (1/2)) = 1/2, we can substitute it.Sin (cos-1 (1/2)) = sqrt (1 - (1/2)2) = sqrt (3/4) = √3/2Tan (sec-1 (x/3)):The secant inverse (or arcsecant) is used to find the angle whose secant value is equal to a given number.The secant inverse (or arcsecant) of a number is the angle whose secant is equal to that number (sec-1). Therefore, sec-1 (x/3) represents the angle that has a secant of x/3.The tangent is the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.Tan (sec-1 (x/3)) = sqrt (sec2 (sec-1 (x/3)))Since sec (sec-1 (x/3)) = 3/x, we can substitute it.Tan (sec-1 (x/3)) = sqrt (3/x) = √3 /√x = (√3 /√x) × (√x /√x) = √3x / xTherefore, sin (cos-1 (1/2)) = √3/2 and tan (sec-1 (x/3)) = √3x / x.
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