The constant (k) in this inverse variation y = 400/x is 400.
The correct answer choice is option D.
What is the constant (k) in this inverse variation?Inverse variation refers to the relationship that exists between two variables, such that the increase in the value of one variable decreases the value of the other variable.
It is written as;
y = k/x
Where,
k = constant of proportionality
x and y = the given variables
So,
y = 400/x
Therefore, it can be concluded that the constant of the inverse variation is 400
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Find the slope of the line that passes through A(3 , 7) and B(2, 2).
Answer:
5
Step-by-step explanation:
To find the slope, we will use this equation.
[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} } = m[/tex]
m = slope
When we plug in the values of y2, y1, x2, and x1, we get this:
[tex]\frac{2-7}{2-3} = m[/tex]
when we simplify:
[tex]\frac{-5}{-1}[/tex]
-5 / -1 = 5 / 1 = 5
The slope is 5.
Find the X
geometry
Considering the two secant theorem, the measure of the far arc x is given as follows:
x = 104º.
What is the secant-tangent theorem?The two secant theorem states that if two secant lines intersect outside a circle, then the measure of the angle of intersection of the two secant lines is obtained as the difference between the measure of the far arc and the measure of the near arc, divided by two.
Hence the equation to obtain the measure of the angle of intersection is given as follows:
y = (far arc - near arc)/2.
The parameters for this problem are given as follows:
Far arc = x.Near arc of 44º.Angle of intersection of y = 30º.Hence the measure of the far arc x is obtained as follows:
(x - 44)/2 = 30
x - 44 = 60
x = 44 + 60
x = 104º.
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Determine the value of X
Answer:
x = 26.
Step-by-step explanation:
Given: 2x + 3x + 50 = 180
First, write it down:
2x + 3x + 50 = 180
Then, collect like terms:
2x + 3x = 180 - 50
Then calculate:
5x = 130 (Divide both sides by 5)
x = 26
Subtract.
(x + 1) − (−2x − 5)
Answer:
Answer: 3x+6
Step-by-step explanation:
= x+1+2x+5
= 3x+6
Answer:
3x + 6
Step-by-step explanation:
you have to distribute the negative to get the parentheses away and simplify
It takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box, which holds 15 cups of sugar. Double the dimensions of the box. Hint: given k, areas are scaled by ____ and volumes are scaled by ____ Approximately how much paint would the new box need? How much sugar would it hold?
The new box would need approximately 8 ounces of paint and would hold 120 cups of sugar.
To find out how much paint the new box would need and how much sugar it would hold, follow these steps:
1. The original box holds 15 cups of sugar, and it takes 2 ounces of paint to cover it completely. When you double the dimensions of the box, areas are scaled by [tex]k^2[/tex] (k is the scale factor), and volumes are scaled by[tex]k^3.[/tex]
2. Since you double the dimensions, the scale factor k is 2.
3. The surface area of the box will be scaled by [tex]k^2, which is 2^2 = 4.[/tex]So, the new box will need 4 times the amount of paint that the original box needed. Since the original box needed 2 ounces of paint, the new box will need 2 × 4 = 8 ounces of paint.
4. The volume of the box will be scaled by [tex]k^3, which is 2^3 = 8[/tex]. So, the new box will hold 8 times the amount of sugar that the original box held. Since the original box held 15 cups of sugar, the new box will hold 15 × 8 = 120 cups of sugar.
In conclusion, the new box would need approximately 8 ounces of paint and would hold 120 cups of sugar.
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In an experiment, a fair four-sided die (its faces are labeled 0, 1, 2, 3) is thrown once. The outcome of the throw determines how many times a fair coin is to be flipped: if N is the number that results from throwing the die, we flip the coin N times. Let K be the total number of heads resulting from the coin flips. Suppose the die roll results in a 2. What form does the conditional distribution of distribution along with its parämeters calculated the probabilities in the table a) K have given that N-2? You don't need to calculate anything. Just state the b) Fill in this table for the joint PMF of N and K. Show your work for how you I k 0 2 3 c) Using the joint PMF, obtain the marginal for N. Show your work. d) Using the joint PMF, obtain the marginal for K. Show your work. e) What is the conditional PMF of N given K-2? i.e., what is pNk(njk-2)? Show your work f) Are N and K independent? Show work to support your answer
For N and K to be independent, the joint probability mass function should factorize into the product of the marginal probability mass functions:
P(N=n,K=k) = P(N=n) * P(K=k)If this condition is not satisfied, then N and K are dependent.
The distribution of K given that N=2 can be calculated using the conditional probability formula:
P(K=k|N=2) = P(K=k and N=2) / P(N=2)
Let X be the outcome of the coin flip. Then the joint probability mass function of N and K can be expressed as:
P(N=n,K=k) = P(X=0) for n=0 and k=0
P(N=n,K=k) = P(X=1) for n=1 and k=0, 1
P(N=n,K=k) = P(X=2) for n=2 and k=0, 1, 2
P(N=n,K=k) = P(X=3) for n=3 and k=0, 1, 2
The marginal probability mass function of N can be obtained by summing over all possible values of K:
P(N=n) = P(N=n,K=0) + P(N=n,K=1) + P(N=n,K=2)
The marginal probability mass function of K can be obtained by summing over all possible values of N:
P(K=k) = P(N=0,K=k) + P(N=1,K=k) + P(N=2,K=k) + P(N=3,K=k)
The conditional probability mass function of N given that K=2 can be calculated using Bayes' theorem:
P(N=n|K=2) = P(K=2|N=n) * P(N=n) / P(K=2)
For N and K to be independent, the joint probability mass function should factorize into the product of the marginal probability mass functions:
P(N=n,K=k) = P(N=n) * P(K=k)
If this condition is not satisfied, then N and K are dependent.
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rotate 270 degrees…what are the coordinates of B
PLS HELP
Answer:
8;-2
Step-by-step explanation:
8 is the x axis and -2 is the y axis
Answer:
Step-by-step explanation:
What is the value of (-14^0)^-2 a) 1/-196 b)1/196 c) 0 d) 1
From the given information provided, the value of the expression (-14⁰)⁻²
is 1 that is option d.
We need to follow the order of operations, which is to evaluate any exponents first, before performing any other operations.
Exponent rules are mathematical rules that describe how to simplify expressions that involve exponents.
(-14⁰)⁻² can be simplified as follows:
(-14⁰)⁻² = (-1)⁰ × 14⁰ × (-1)⁻² [Using the rule ([tex]a^m[/tex])ⁿ = [tex]a^(m*n)[/tex]]
(-14⁰)⁻² = 1 × 1 × 1/(-1)⁻² [Using the rule a⁰ = 1]
(-14⁰)⁻² = 1 × 1 × 1/1
(-14⁰)⁻² = 1
Therefore, the value of (-14⁰)⁻² is 1. Answer: d) 1
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help me with this or u an opp
Answer:
To find the year when 164 billion dollars was spent on advertising, we need to solve the equation y = 164 for x, where y is the amount of money spent on advertising and x is the number of years since 1990.
Substituting y = 164 into the given equation, we have:
164 = 0.937 + 2.2x + 130
Simplifying the equation, we get:
2.2x = 164 - 0.937 - 130
2.2x = 33.063
x = 15.03
So, 164 billion dollars was spent on advertising 15.03 years after 1990. To find the year, we add 15.03 to 1990:
1990 + 15.03 = 2005.03
Since we are looking for a year within the range of 1990-2000, we round down to the nearest whole number:
2005.03 rounded down to the nearest whole number is 2005.
Therefore, 164 billion dollars was spent on advertising in the year 2005, which is outside the given range. Therefore, the answer is none of the options provided.
100 points!!!
Which choices are equivalent to the quotient below? Check all that apply. √50/√10
A.√25/√5
B.√15/√3
C.√5
D.15/3
E.√3
F.5
To simplify the quotient √50/√10, we need to factor out the largest perfect square that divides each radicand. In this case, we can factor out 25 from both 50 and 10 to get:
√50/√10 = √(252) / √(252) = √25 * √2 / √25 * √2 = √2
Therefore, the simplified form of the quotient is √2. Among the given choices, options B and E are equivalent to √2, as √15/√3 can be simplified as √(35)/√3 = √5 * √3 / √3 * √3 = √5/√3, and √3 is the same as √(31) and there is no √2 term in the denominator to combine with it. Hence, the options B and E are equivalent to the quotient √50/√10.
during an accident, skid marks may result from sudden breaking. the formula approximates a vehicle's speed, s, in miles per hour given the length d in feet of the skid marks. if skid marks on dry concrete are 54 feet long, how fast was the car traveling when the brakes were applied?
The car was travelling with the speed of 183.5 mph when the brakes were applied.
The pace at which an object travels a certain distance can be described using the speed formula. The distance that a body travels in a certain amount of time is a common way to measure speed. M/s is the SI unit of speed. We will learn more about the speed formula and its uses in this section.
Let's continue and investigate the speed formula in this part in more detail. Speed can be expressed in a variety of ways, including m/s, km/hr, miles/hr, etc. [LT-1] is the dimensional formula for speed. A body's speed may be defined as how quickly it is going. The equation for a given body's speed may be written as,
Speed = Distance ÷ Time
We have the equation,
[tex]s=\frac{\sqrt{d} }{0.04}[/tex]
we have the value of d as 54
putting the value pf d in the equation we get,
[tex]s=\frac{\sqrt{54} }{0.04}[/tex]
s = 7.34/0.04
s = 183.5 mph
So the car was travelling with the speed of 183.5 mph when the brakes were applied.
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Complete question:
The speed that a vehicle was traveling, s, in miles per hour, when the brakes were first applied, can be estimated using the formula
[tex]s=\frac{\sqrt{d} }{0.04}[/tex] where d is the length of the vehicle's skid marks, in feet.
if skid marks on dry concrete are 54 feet long, how fast was the car traveling when the brakes were applied?
there are three urns, each with 6 red balls, 3 brown balls, and 8 purple balls. you draw 1 ball from the first urn, 2 from the second, and 3 from the third, and set all 6 aside. what is the probability that exactly 4 are red?
The probability of drawing exactly four red balls when drawing six balls from three urns, each with 6 red balls, 3 brown balls, and 8 purple balls is 0.3147 or 31.47%.
The probability of drawing exactly four red balls when drawing six balls from three urns, each with 6 red balls, 3 brown balls, and 8 purple balls is calculated using the following equation:
P(4 red balls) = (6C4) × (3C2) × (8C0)/(17C6)
Where C denotes the combination and the denominator represents the total possible outcomes.
In this case, the numerator consists of three parts, the first being the combination of four red balls from the first urn (6C4) where 6 represents the total number of red balls, and 4 represents the number of red balls chosen. The second part is the combination of two brown balls from the second urn (3C2) where 3 is the total number of brown balls, and 2 is the number of brown balls chosen. The last part is the combination of zero purple balls from the third urn (8C0) where 8 is the total number of purple balls and 0 is the number of purple balls chosen.
Finally, the denominator represents the total number of possible outcomes when drawing 6 balls from 17 balls (17C6) where 17 is the total number of balls, and 6 is the total number of balls drawn.
The probability of drawing four red balls is 0.3147 or 31.47%.
Therefore, the probability of drawing exactly four red balls when drawing six balls from three urns, each with 6 red balls, 3 brown balls, and 8 purple balls is 0.3147 or 31.47%.
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The data to the right represent the number of chocolate chips per cookie in a random sample of a name brand and a store brand. Complete parts (a) to (c) below.(a) Draw side-by-side boxplots for each brand of cookie. Label the boxplots "N" for the name brand and "S" for the store brand. Choose the correct answer below.(b) Does there appear to be a difference in the number of chips per cookie?(c) Does one brand have a more consistent number of chips per cookie?
(a) Since I cannot draw boxplots in text, I recommend using a boxplot tool, such as a graphing calculator, Excel, or an online boxplot generator. Input the data for each brand and create side-by-side boxplots, labeling them "N" for the name brand and "S" for the store brand.
(b) To determine if there is a difference in the number of chips per cookie between the two brands, compare the median values, the range, and the interquartile range of each brand's boxplot. If these values differ significantly, then there is a difference in the number of chips per cookie between the two brands.
(c) To determine which brand has a more consistent number of chips per cookie, compare the interquartile ranges (IQR) of each brand's boxplot. The brand with the smaller IQR has a more consistent number of chips per cookie, as the IQR measures the spread of the middle 50% of the data.
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a right circular cylinder is generated by rotating a rectangle of perimeter p about one of its sides. what dimensions of the rectangle will generate the cylinder of max volume?
A right circular cylinder can be generated by rotating a rectangle of perimeter p about one of its sides. The dimensions of the rectangle that will generate the cylinder of max volume are l = p/6 and w = p/2 - l = 2p/3.
Explanation: Let l and w be the dimensions of the rectangle of perimeter p.
That is, the rectangle's perimeter is given by p = 2l + 2w or p/2 = l + w. Therefore, the width w = p/2 - l. The area of the rectangle is given by lw. When the rectangle is rotated around the side of length w, it generates a cylinder of height l and radius w.
The volume of the cylinder is given by V = πr²h = πw²l. Substituting w = p/2 - l, we obtain V = π(p/2 - l)²l = π(p/2)²l - 2π(p/2)l² + πl³.
The volume function can be obtained by differentiating V with respect to l, setting the derivative equal to 0, and solving for l. The derivative of V with respect to l is given by dV/dl = π(p/2)² - 4π(p/2)l + 3πl².
Setting dV/dl = 0 and solving for l, we obtain l = p/6.The dimensions of the rectangle that will generate the cylinder of max volume are l = p/6 and w = p/2 - l = 2p/3.
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Help againnnn pleaseeee
Answer:
20- gon
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
given the sum of the interior angles is 3240° , then
180° (n - 2) = 3240 ( divide both sides by 180° )
n - 2 = 18 ( add 2 to both sides )
n = 20
then the polygon is a 20- gon
Can someone please help me on this?
Answer:
For problem a: 0,4 0,5 0,6
For Problem B: 1,0 2,0 3,0
Step-by-step explanation:
Graph each equation on a graph Figure out either solid or dotted line. Then depending on <=,<,>,>= is whre you shade on your graph. The spot where both lines meet when shaded is your solution area and you pick any spot on that. You can check your answer by plugging in ordered pairs for your X,Y values in the system.
4. Small amounts of weight are often measured in grams or ounces. Recall from Exercise #6
that there are 16 ounces per pound. Grams are even smaller. Camilla weighs an onion and
finds that it is 112 grams. On another scale, she finds that it weighs four ounces.
(a) Using the information from Camilla's onion,determine the ratio of grams to ounces.State as a unit rate using proper “per” units
Thus, Camilla's onion weighs about 28 grammes per ounce in terms of grammes to ounces.
What exactly is weight?Weight is the force of gravity that pulls objects towards the centre of the Earth. The resulting force that pulls a substance towards Earth is known as gravity. In contrast to gravity force, which occurs among any two masses, this only occurs between Planet and a mass.
To convert from grams to ounces, we can use the conversion factor of 1 ounce = 28.35 grams. Therefore:
1 gram = 1/28.35 ounces
To find the ratio of grams to ounces for Camilla's onion, we can divide the weight in grams by the weight in ounces:
112 grams ÷ 4 ounces ≈ 28 grams per ounce
So the ratio of grams to ounces for Camilla's onion is approximately 28 grams per ounce.
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5. A-postage box should weigh 1.0 pound. If there is a 5% error on the weight, what is the range of acceptable weight ?
Answer:
0.95P - 1.05P
Step-by-step explanation:
Calculate the error
5% of 1.0 Pound
5/100 x 1.0 = 5/100
1/20 = 0.05
The error is + or - 0.05
If you add 0.05 to 1.0Pound, you get 1.05P
If you Subract 0.05 to 1.0Poumd, you get 0.95Pound
The weight will be between 0.95Pound and 1.05 Pound
can someone help me please i don't understand this
The transformation that would not result in a congruent figure when performed on triangle RST is A. A dilation by a scale factor of 2 with respect to point R.
The equation that has the same solution as the system of equations is C. 4x + 9y = 10
4x + 6y = 24.
Which transformations changes congruency ?Transformations that change the shape or size of a figure can change its congruency. A dilation is a transformation that changes the size of a figure so this would mean that RST dilated would not result in a congruent figure.
How to find the equation?When the system of equations, 4x + 9y = 10, 2x + 3y = 12 is solved, we find that x = 13 and y = - 14/ 3.
Options A,B, and D cannot have the same value because the numbers are the same and so they should have different values., Only option C can be the same and when the values are slotted in, this is proven.
Option C, 4x + 9y = 10 , 4x + 6y = 24 is therefore correct.
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The length of the radius of a cylinder is twice its height. If its volume is 864x in', what is the
length of its radius?
A. 3 inches
B.6 inches
C. 12 inches
D. 24 inches
Answer: C. 12 inches
Step-by-step explanation: Let's use the formula for the volume of a cylinder, which is:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
We ar given that the length of the radius is twice the height, which can be written as:
r = 2h
We are also given the volume of the cylinder, which is 864 cubic inches. Substituting the given values, we get:
864 = π(2h)^2h
Simplifying and solving for h:
864 =4πh^3
h^3 = 864/(4π)
h = 6
Now that we know the height of the cylinder is 6 inches, we can find the radius using the equation r = 2h:
r = 2(6) = 12 inches
Therefore, the length of the radius of the cylinder is 12 inches, which is option C.
Five interior angles of a hexagon measure 119°, 129°, 104°, 139°, and 95°. What is the measure of the sixth angle?
Answer:
A
Step-by-step explanation:
ten families have an average of 2 children per family. if exactly two of these families are childless, what is the average number of children in the families with children? express your answer as a decimal to the nearest tenth.
Answer:
Step-by-step explanation:
If there are ten families and exactly two of them are childless, then there are 10 - 2 = 8 families with children.
The total number of children in these families is 8 x 2 = 16.
Therefore, the average number of children in the families with children is:
16 / 8 = 2
So the average number of children in the families with children is 2.0 (to the nearest tenth).
The average number of children in the families with children is 2.2.
To calculate this, first we need to determine the total number of children in the ten families. Since each family has an average of 2 children, this means that the total number of children in the ten families is 10 x 2 = 20.
Since two of these families are childless, this means that the total number of children in the remaining 8 families is 20 – 0 = 20.
Now, we need to determine the average number of children in the 8 families with children. To do this, we divide the total number of children (20) by the number of families with children (8):
20/8 = 2.5
Finally, we express the answer to the nearest tenth, which is 2.2.
In conclusion, the average number of children in the families with children is 2.2.
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explain the difference between cardinality and join type. describe why one-to-many cardinality is often handled using a one-to-one join.
The difference between cardinality and join type is that cardinality describes the relationship between two data tables, while join type is the specific method used to combine the two tables.
Cardinality defines the maximum number of records that can exist in one table for a relationship with another table. Cardinality can be either one-to-one, one-to-many, or many-to-many.
A one-to-many cardinality relationship is when one record in one table can be related to multiple records in another table. For example, a customer can have multiple orders. In this situation, a one-to-one join type is often used because it is the most efficient way to retrieve the related data. This is because one-to-one join type only requires that one record be searched, while a one-to-many join type would require that multiple records be searched in order to find the related records. Additionally, a one-to-one join type ensures that no duplicate records will be returned in the result.
In summary, cardinality describes the relationship between two tables while join type is the specific method used to combine the two tables. A one-to-many cardinality relationship is when one record in one table can be related to multiple records in another table. To efficiently retrieve the related data, a one-to-one join type is often used. This is because it only requires that one record be searched and it ensures that no duplicate records will be returned in the result.
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please answer with explanation!
The maximum value of f on the given region is 9 and the minimum value of f is 25.
Describe Function?In plainer terms, a function creates an output in response to an input. As an illustration, the formula f(x) = x2 takes the input value x, squares it, and outputs the square of x. The set of all potential output values is referred to as the range, while the set of input values that can be employed with a specific function is referred to as the domain.
In order to simulate real-world processes and make predictions, functions are frequently employed in mathematics, physics, engineering, and many other disciplines. They can be represented by mathematical equations, tables, or graphs, and can take on a variety of shapes, such as linear, quadratic, exponential, trigonometric, and many more.
We need to find the extreme values of the function f(x,y) subject to the constraint x² + y² <= 16. We can use the method of Lagrange multipliers to solve this problem.
Let g(x,y) = x² + y² - 16, then the Lagrangian function is given by:
L(x,y,λ) = f(x,y) - λg(x,y)
= 2x² + 3y² - 4x - 7 - λ(x² + y² - 16)
Taking partial derivatives of L(x,y,λ) with respect to x, y and λ, and equating them to zero, we get:
∂L/∂x = 4x - 4λx = 0
∂L/∂y = 6y - 4λy = 0
∂L/∂λ = x² + y² - 16 = 0
Solving these equations, we get two critical points:
(2/λ, 0, λ) and (-2/λ, 0, λ)
To find the extreme values of f, we need to evaluate f at these critical points and at the boundary of the region x² + y² = 16.
At the critical points, we have:
f(2/λ, 0) = -7 - 16λ/3
f(-2/λ, 0) = -7 - 16λ/3
At the boundary, we have:
f(x,y) = 2x² + 3y² - 4x - 7
= 2x² + 3(16 - x²) - 4x - 7 (substituting y² = 16 - x²)
= -x² - 4x + 41
To find the extreme values, we need to compare the values of f at these points:
f(2/λ, 0) = f(-2/λ, 0) = -7 - 16λ/3
f(x,y) = -x² - 4x + 41
Now, we need to find the maximum and minimum values of f on the given region. Since the coefficient of x² is negative, the maximum value of f occurs at the boundary of the region, where x = ±4. Therefore, the maximum value of f is:
f(4,0) = -4² - 4(4) + 41 = 9
To find the minimum value of f, we need to compare the values of f at the critical points and the boundary. Since the coefficient of x² is negative, we can see that f(2/λ, 0) and f(-2/λ, 0) approach -∞ as λ → 0. Therefore, the minimum value of f occurs at the boundary of the region, where x = ±4. Therefore, the minimum value of f is:
f(-4,0) = -(-4)² - 4(-4) + 41 = 25
Hence, the maximum value of f on the given region is 9 and the minimum value of f is 25.
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help me please find the answer
In the given triangle, using angle bisectοr theοrem, the value οf the variable is 8.
What is triangle?A triangle is a pοlygοn with three edges and three vertices. It belοngs tο the basic geοmetric shapes. A triangle with the parts A, B, and C is referred tο as triangle ABC. Any three pοints that are nοt cοllinear in Euclidean geοmetry result in a separate triangle and a distinct plane.
What is angle bisectοr Theοrem?The angle bisectοr theοrem in mathematics is cοncerned with the prοpοrtiοns οf the twο segments that a line that bisects the οppοsite angle divides a triangle's side intο. It cοmpares their prοpοrtiοnal lengths tο the prοpοrtiοnal lengths οf the triangle's οther twο sides.
In the given triangle, using angle bisectοr Theοrem,
36/28 = q/(16-q)
On sοlving, we get
q = 9
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Find the percent of kci by a mass of a solution of 2 moles of kci dissolved in 1 liter of pure water (h2o). round to 1 decimal place. (k=39,ci=35)
13.0% of kci by a mass of a solution of 2 moles of kci dissolved in 1 litres of pure water
To find the percent of KCI in a solution of 2 moles of KCI dissolved in 1 liter of pure water (H2O), we first need to calculate the molar mass of KCI.
Molar mass of KCI = atomic mass of K + atomic mass of Cl = 39 + 35.5 = 74.5 g/mol
Next, we need to calculate the mass of KCI in the solution using the formula:
mass = moles x molar mass
mass of KCI
= 2 moles x 74.5 g/mol
= 149 g
Finally, we can calculate the percent of KCI in the solution using the formula:
percent of KCI = (mass of KCI / total mass of solution) x 100%
The total mass of the solution is equal to the mass of KCI plus the mass of water, which is:
total mass of solution
= 149 g + 1000 g
= 1149 g
So, the percent of KCI in the solution is:
percent of KCI
= (149 g / 1149 g) x 100%
= 12.96%
Rounding to one decimal place, the percent of KCI in the solution is approximately 13.0%.
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i need help ASAP
Classify the triangle
A acute, scalene
B obtuse, scalene
C obtuse, isosceles
D right, scalene by its sides and by its angles
Factor out the GCF from the polynomial.
3x³y² - 9xz4 + 8y²z
The expression 3x³y² - 9xz⁴ + 8y²z have no GCF greatest common factor but the terms 3x³y² and 8y²z have GCF equal to y².
What is (GCF) greatest common factor?The GCF defines the highest common factor present in between given two or more numbers or algebraic expressions.
we shall determine the GCF greatest common factor for the algebraic expression 3x³y² and 8y²z as follows:
3x³y² = y² × 3x³
8y²z = y² × 8z
both terms 3x³y² and 8y²z have y² common to them, so we can write;
3x³y² + 8y²z = y² × 3x³ + y² × 8z
3x³y² + 8y²z = y²(3x³ + 8z)
In conclusion, the expression 3x³y² - 9xz⁴ + 8y²z have no GCF greatest common factor but the terms 3x³y² and 8y²z have GCF equal to y².
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A three-column table is given.
Part 8 B D
Part 10 15 45
Whole A C 81
What is the value of C in the table?
18
27
24
71
Using the proportionality we know that 24 is the value of C.
What is proportionality?Every relationship that has a constant ratio is said to be proportionate.
For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.
An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.
So, the table is as follows:
Part 8 B D
Part 10 15 45
Whole A C 72
Due to the fact that the two parts will be proportional to the whole.
Then,
C /72 = 15/45
C = 72/3
C = 24
Therefore, using the proportionality we know that 24 is the value of C.
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suppose that at your favorite restaurant to-go orders arrive at the rate of 10 per hour. assume that the numbers of to-go orders on different hours are independent. the distribution of the average number of to-go orders per hour over 700 random hours is
By using Central Limit Theorem, the distribution of to-go orders per hour over 700 random hours at a restaurant with a rate of 10 per hour can be approximated by a normal distribution with a mean of 10 and a standard deviation of 0.119.
The distribution of the average number of to-go orders per hour over 700 random hours can be approximated by the Central Limit Theorem (CLT). In this case, the population mean (μ) is 10 to-go orders per hour, and the population standard deviation (σ) can be calculated using the Poisson distribution formula:
σ = sqrt(μ) = sqrt(10) ≈ 3.162
The sample size (n) is 700, which is larger than 30, so we can use the CLT to approximate the distribution of the sample means. The mean of the sample means is equal to the population mean, which is 10 to-go orders per hour. The standard deviation of the sample means (also called the standard error) is equal to:
SE = σ / sqrt(n) = 3.162 / sqrt(700) ≈ 0.119
Therefore, the distribution of the average number of to-go orders per hour over 700 random hours is approximately normal with a mean of 10 and a standard deviation of 0.119
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