For simple linear regression, the explanatory variable is numeric.
What is simple linear regression?Simple linear regression is a statistical method that allows researchers to understand the relationship between two continuous variables. A simple linear regression model is used to represent the relationship between a dependent variable (Y) and an independent variable (X) by making a linear equation of the form
Y = a + bX, where a is the constant, and b is the regression coefficient.
In simple linear regression, the explanatory variable is of numeric type. This statistical method involves the use of two numeric variables, namely the explanatory (independent) variable and the response (dependent) variable, which are analyzed to establish a linear relationship between them.
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What is the simplest form of 8(5k+7)−10(6k−7)
The simplest form of the given expression is -20k + 126.
To find the simplest form of the expression 8(5k+7)−10(6k−7), follow these steps:
1. Distribute the numbers outside the parentheses to the terms inside the parentheses:
8 × 5k + 8 × 7 - 10 × 6k + 10 × 7
2. Perform the multiplication:
40k + 56 - 60k + 70
3. Combine like terms (terms with the same variable and exponent):
(40k - 60k) + (56 + 70)
4. Simplify the expression by performing the subtraction and addition:
-20k + 126
The simplest form of the given expression is -20k + 126.
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a rectangular container 12 cm long, 8 cm wide, and 36 cm high was one - third full. when some syrup from a bottle was poured into the container, it got half full. find the volume of the syrup poured from the bottle into the container in millimeters
when some syrup from a bottle was poured into the container, it got half full. The volume of the syrup poured from the bottle into the container in millimeters is 576,000 cubic millimeters.
Since for solving the problem we need to find the volume of the container in millimeters. We are given the length, breadth, and height which are 12 cm,8 cm, and 36 cm.Now the volume of the container is:
V = l x w x h = 12 cm x 8 cm x 36 cm = 3,456 cubic cm. Now we convert the above result into millimeters by multiplying by 1,000, so we get V= 3456 x 1000= 34560000 cubic mm
Now to find the volume of the syrup that was poured into the container, we know that the container was one-third full before the syrup was added and half full after the syrup was added.onsidering x to be the volume of the syrup poured from the bottle into a container and n to be the volume of the syrup in the container after it was added:
1/3(V) + x = 1/2(V), where v is the volume of the container in millimeters, so we substitute the calculated value of the volume we get :
=>1/3(V) + x = 1/2(V)
=>x = 1/2(V) - 1/3(V)
=> x = 1/6(V) = 1/6(3,456,000) = 576,000 cubic mm
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Question 7(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The table shows the number of goals made by two hockey players.
Player A Player B
1, 4, 5, 1, 2, 4, 5, 5, 11 1, 2, 1, 3, 2, 3, 4, 1, 8
Find the best measure of variability for the data and determine which player was more consistent.
Player A is the most consistent, with a range of 10.
Player B is the most consistent, with a range of 7.
Player A is the most consistent, with an IQR of 3.5.
Player B is the most consistent, with an IQR of 2.5.
Player B is the most consistent, with a range of 7.
The best measure of variability for this data would be the range, which is the difference between the maximum and minimum values.
For Player A: Range = 11 - 1 = 10
For Player B: Range = 8 - 1 = 7
Therefore, Player A has a higher range and thus more variability in their data. So, the correct answer is:
Player B is the most consistent, with a range of 7.
What is variability?
Variability refers to the degree of variation or diversity in a set of data or observations. It is a measure of how spread out the data points are from the central tendency, such as the mean or median.
What is range?
Range is a statistical measure that describes the difference between the maximum and minimum values in a dataset. It is calculated by subtracting the smallest value from the largest value.
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Answer:
(d) Player B is the most consistent, with an IQR of 2.5.
Step-by-step explanation:
Given these numbers of goals, you want to know which player is most consistent, and the best measure of that.
A: {1, 1, 2, 4, 4, 5, 5, 5, 11}B: {1, 1, 1, 2, 2, 3, 3, 4, 8}Variability measuresThe variability measures we're to consider here are range and IQR.
The range is the difference between the maximum and the minimum:
A: 11 -1 = 10B: 8 -1 = 7The smaller range indicates player B is more consistent.
The IQR is the difference between the upper and lower quartiles. In each of these 9-element data sets, those quartiles will be the average of elements 2 and 3, and the average of elements 7 and 8 when the data is in order.
A: ((5+5) -(1+2))/2 = 3.5B: ((3+4) -(1+1))/2 = 2.5The smaller IQR indicates player B is more consistent.
OutliersIn each case, the maximum data value is more than 1.5 times the IQR above the upper quartile value, so can be considered an outlier. The outlier has a direct effect on range, so range is not a good measure of variability.
Player B is the most consistent, with an IQR of 2.5, choice D.
__
Additional comment
If the outlier is excluded from each data set, the IQR for player A remains the same at 3.5. The IQR for player B drops to 2.0.
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the standard error tells multiple choice how often the examiner made an error. how often the experimental variable was tested. the relationship between the control and test groups. whether or not the research has been published in a scientific journal. how uncertain a particular value is.
Answer:the jimboluis
Step-by-step explanation:
that’s it
A triangle has angle measures 122° and 32°. What is the measure of the third angle?
Answer:
26°
Step-by-step explanation:
We know
A triangle is 180°
A triangle has Angle measures 122° and 32°
What is the measure of the third angle?
We take
180 - (122 + 32) = 26°
So, the measure of the third angle is 26°
Determine the magnitude of the force P for which the resultant of the four forces acts on the rim of the plate. Given: F= 320 N. 30° 120 N 80 N P x 250 mm F 7 The magnitude of the force P is N.
The magnitude of the force P is 464.77 N.
STEP BY STEP EXPLANATION:
Step 1: Break down each force into components.
F = 320 N at 30°
Fx = F * cos(30°) = 320 * cos(30°) = 277.13 N (horizontal)
Fy = F * sin(30°) = 320 * sin(30°) = 160 N (vertical)
120 N is in the horizontal direction (assume positive x-direction):
Fx2 = 120 N
80 N is in the vertical direction (assume positive y-direction):
Fy2 = 80 N
Step 2: Sum up the components.
Total horizontal force (Fxtotal) = Fx + Fx2
= 277.13 + 120 = 397.13 N
Total vertical force (Fytotal) = Fy + Fy2
= 160 + 80 = 240 N
Step 3: Find the magnitude of the resultant force.
Resultant force (R) = sqrt(Fxtotal^2 + Fytotal^2)
= sqrt(397.13^2 + 240^2) = 464.77 N
Step 4: Determine the magnitude of the force P.
Since the resultant of the four forces should act on the rim of the plate, it means that the force P should be equal in magnitude and opposite in direction to the resultant force R.
The magnitude of the force P is 464.77 N.
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Laura has a strip of ribbon 1 m long. How many one thirds strips can be cut from it
From the given information provided, Laura can cut 3 one-thirds strips from the 1 meter long ribbon.
If Laura has a strip of ribbon 1 meter long, we need to find out how many one-thirds strips can be cut from it.
To do this, we need to divide the length of the ribbon by the length of each one-third strip:
Number of one-thirds strips = Length of ribbon / Length of one-third strip
The length of each one-third strip is 1/3 meters, since one-third of a meter is required to make each strip.
So we can substitute these values into the formula:
Number of one-thirds strips = 1 meter / (1/3 meter)
Number of one-thirds strips = 1 meter x (3/1)
Number of one-thirds strips = 3
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planets x, y and z take $360$, $450$ and $540$ days, respectively, to rotate around the same sun. if the three planets are lined up in a ray having the sun as its endpoint, what is the minimum positive number of days before they are all in the exact same locations again?
By using LCM, we find that the three planets x, y and z will be in the exact same locations again after $5400$ days.
To find the minimum positive number of days before the planets are all in the exact same locations again, we need to find the least common multiple (LCM) of the three given periods of rotation.
The prime factorization of each of the given periods of rotation is as follows
$360 =[tex]2^3 \cdot 3^2 \cdot 5$[/tex]
$450 =[tex]2 \cdot 3^2 \cdot 5^2$[/tex]
$540 =[tex]2^2 \cdot 3^3 \cdot 5$[/tex]
To find the LCM, we need to take the highest power of each prime factor that appears in any of the three factorizations. So the LCM is:
[tex]$LCM = 2^3 \cdot 3^3 \cdot 5^2 = 2^3 \cdot 27 \cdot 25 = 5400$[/tex]
Therefore, the three planets will be in the exact same locations again after $5400$ days.
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how many ways are there to put beads of different colors on the vertices of a cube, if rotations of the cube (but not reflections) are considered the same?
There are 70 ways to put 8 beads of different colors on the vertices of a cube, if rotations of the cube (but not reflections) are considered the same.
Let us start by determining the number of ways to put 8 beads of different colors on the vertices of a cube without any restrictions.
We can choose the first color in 8 ways, the second color in 7 ways, the third color in 6 ways, and so on. Therefore, the total number of ways is 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320.
However, rotations of the cube (but not reflections) are considered the same. There are 24 such rotations. Specifically, there are 4 rotations that preserve the orientation of the cube (i.e., rotations by 0°, 90°, 180°, and 270° around an axis passing through the centers of opposite faces), and there are 6 pairs of rotations that exchange the two sets of 4 vertices that are symmetrically positioned with respect to the centers of opposite faces.
Each of these 24 rotations maps one arrangement of the beads to another.
Thus, we must count the number of arrangements of the beads that are mapped to each other by each rotation. If we do this for each rotation, we get a total of (40,320/24) = 1680 distinct arrangements of the beads.
If we now take any of these 1680 arrangements and apply any of the 24 rotations, we will get an arrangement that we have already counted. Therefore, there are (1680/24) = 70 arrangements of the beads that are distinct when rotations (but not reflections) are considered the same.
In other words, there are 70 ways to put 8 beads of different colors on the vertices of a cube, if reflections are not considered distinct.
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What whole number makes the equation true? x 1/2=8/2
x = 8 is the whole number that solves the equation, making it true. A whole number is a number that does not have any fractions or decimals.
It is a positive integer or zero, such as 0, 1, 2, 3, 4, 5, and so on. Whole numbers are used to count objects or things that can be represented as a whole, such as people, cars, apples, and so on.
Whole numbers are closed under addition, subtraction, and multiplication operations, which means that if you add, subtract or multiply two whole numbers, the result will always be another whole number. However, whole numbers are not closed under division operation, which means that when dividing two whole numbers, the result may not be a whole number.
To solve for x in the equation:
x 1/2=8/2
We can isolate x by multiplying both sides by the reciprocal of 1/2, which is 2/1:
x 1/2 * 2/1 = 8/2 * 2/1
Simplifying the left side, we get:
x = 16/2
x = 8
Therefore, the whole number that makes the equation true is x = 8.
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What is the exact value of sin(cos^-1 (√2/2)) + tan^-1 (sin(π/2))
[tex]\qquad \qquad \textit{Inverse Trigonometric Identities} \\\\ \begin{array}{cccl} Function&Domain&Range\\[-0.5em] \hrulefill&\hrulefill&\hrulefill\\ y=cos^{-1}(\theta)&-1 ~\le~ \theta ~\le~ 1& 0 ~\le~ y ~\le~ \pi \\\\ y=tan^{-1}(\theta)&-\infty ~\le~ \theta ~\le~ +\infty &-\frac{\pi}{2} ~\le~ y ~\le~ \frac{\pi}{2} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies \theta \hspace{5em}\stackrel{\textit{so we can say}}{cos(\theta )=-\cfrac{\sqrt{2}}{2}} \\\\\\ \theta =cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies \stackrel{ \textit{on the II Quadrant} }{\theta =\cfrac{3\pi }{4}} \\\\[-0.35em] ~\dotfill\\\\ sin\left[ cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right) \right]\implies sin\left( \cfrac{3\pi }{4} \right)\implies \boxed{\cfrac{\sqrt{2}}{2}}[/tex]
now let's find the angle for the inverse tangent
[tex]sin\left( \cfrac{\pi }{2} \right)\implies 1\hspace{5em}\stackrel{\textit{so we can say}}{tan^{-1}\left[ sin\left( \frac{\pi }{2} \right) \right]}\implies tan^{-1}(1) \stackrel{ \textit{on the I Quadrant} }{\implies\boxed{\cfrac{\pi }{4}}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin\left[ cos^{-1}\left( -\frac{\sqrt{2}}{2} \right) \right]~~ + ~~tan^{-1}\left[ sin\left( \frac{\pi }{2} \right) \right]\implies \cfrac{\sqrt{2}}{2}~~ + ~~\cfrac{\pi }{4} \implies \boxed{\cfrac{2\sqrt{2}+\pi }{4}}[/tex]
for the sine function we end up in the II Quadrant because the inverse cosine function range is constrained to the I and II Quadrants only, so our angle comes from that range.
Likewise, our angle from the inverse tangent comes from the I Quadrant, because inverse tangent range is only I and IV Quadrants.
Graph the solution set of the inequality 1/2y < -3
The circle at -6 is closed because the inequality does not include the possibility of y being equal to -6.
What is inequality?Inequality refers to a situation in which there is a difference or disparity between two or more things, usually in terms of value, opportunity, or outcome. Inequality can take many forms, including social, economic, and political inequality.
by the question.
the solution set of the inequality 1/2y < -3
Graph the solution set of the inequality 1/2y < -3 - 1
To solve the inequality 1/2y < -3, we can begin by isolating the variable y on one side of the inequality:
1/2y < -3
Multiplying both sides by 2 yields:
y < -6
So, the solution set of the inequality is all real numbers y that are less than -6.
To graph the solution set on a number line, we can draw a closed circle at -6 and shade to the left of it, indicating that all values to the left of -6 are solutions to the inequality. The graph would look like this:
<=======o----------------------
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Diego used unit cubes to make a rectangular prism what is the volume of the prism
can we see a picture or equation
HELP ME!!! Find the unknown (labled in the figure)
Therefore, the value of a for triangle 2 is 44 degrees.
What is triangle?A triangle is a closed geometric shape that has three sides and three angles. It is one of the basic shapes in geometry and is used in many different areas of mathematics and science. The sum of the angles in a triangle is always 180 degrees, and there are many different types of triangles, including equilateral, isosceles, and scalene triangles, depending on the lengths of their sides and the sizes of their angles. Triangles are also commonly used in trigonometry, which is the branch of mathematics that deals with the relationships between the sides and angles of triangles.
Here,
The sum of the interior angles of a triangle is always 180 degrees. Therefore, for triangle 1, we have:
95 + 39 + x = 180
Simplifying the equation, we get:
134 + x = 180
x = 46
For triangle 2, we have:
90 + a + x = 180
Substituting the value of x from above, we get:
90 + a + 46 = 180
Simplifying the equation, we get:
a = 44
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DUE TOMORROW WELL WRITTEN ANSWERS ONLY!!!!!!!!
Sketch a graph of g given by g(Θ) = sin (Θ) + 3.
Step-by-step explanation:
2 pictures are attached
sin waves are used in many medical devices like to measure heart beats
In this polygon, all angles are right angles. What is the area of this polygon? Enter your answer in the box. ___ft² 23 ft 9 ft 26 ft 13 ft
The area of this polygon is equal to 428 ft².
How to calculate the area of this polygon?In order to calculate the area of this polygon, we would have to determine the total area of the two different parts of the given composite figure.
Therefore, the total area of this polygon is the sum of the area of the each geometric figure (rectangle):
Area of rectangle A = Length × Width
Area of rectangle A = 13 × 26
Area of rectangle A = 338 ft²
Area of rectangle B = 9 × (23 - 13)
Area of rectangle B = 9 × 10
Area of rectangle B = 90 ft²
Therefore, total area is given by:
Total area = 90 + 338
Total area = 428 ft²
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What is the value of the expression 16 + 4 − (5 x 2) + 2? (2 points) a 10 b 12 c 14 d 18
Answer: b. 12
Step-by-step explanation:
16 + 4 − (5 x 2) + 2
= 16 + 4 - 10 + 2
= 20 - 12
= 12
Answer:
Step-by-step explanation:
8
The cost of 5 skirts and 3 blouses is sh. , 750. Mueni bought three of the the skirts and one of the blouses for sh. 850. Find the cost of each item solve with formula
As per the unitary method, the cost of one skirt is sh 20 and the cost of one blouse is sh 550.
Let us assume that the cost of one skirt is x and the cost of one blouse is y. We can now form two equations based on the given information.
Equation 1: 5x + 3y = 1750
This equation represents the cost of 5 skirts and 3 blouses together, which is given as sh 1750.
Equation 2: 3x + y = 850
This equation represents the cost of 3 skirts and 1 blouse, which is given as sh 850.
To apply the unitary method here, we can first find the value of one skirt by dividing equation 1 by 5, and then find the value of one blouse by subtracting 3 times the value of one skirt from equation 2.
Dividing equation 1 by 5, we get:
x + (3/5)y = 350
Subtracting 3 times the value of one skirt from equation 2, we get:
y = 850 - 3x
y = 850 - 3(350/5)
y = 550
So, we have found the value of y, which is the cost of one blouse. Now, we can substitute this value of y in equation 1 to find the value of x, which is the cost of one skirt.
5x + 3(550) = 1750
5x + 1650 = 1750
5x = 100
x = 20
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A football is kicked into the air. The height of the football can be modeled by the equation , where h is the height reached by the ball after x seconds. Find the values of x when h = 0.
ℎ=−16x^2+48x
As a result, during its flight, the football will strike the ground twice: once when it is kicked off and once more 3 seconds later.
What are equations used for?A mathematical equation, including such 6 x 4 = 12 x 2, states that two quantities and values are equivalent. a meaningful noun. Equations are employed when two or more variables need to be added up and the results need to be computed in order to comprehend or explain the entire issue. As a result, the football will hit the ground twice during its flight: once after the game has kicked off and again three seconds later.
h =
0 = -16x² + 48x
0 = 16x(3 - x)
Either 16x or (3 - x) equals 0, which makes this equation equal to zero.
Hence, the answers to x are:
x = 0, when 16x = 0
when 3 - x = 0, x equals 3.
The football will therefore strike the ground twice during its flight—once when it is kicked off and once more 3 seconds later.
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Debra’s rectangular vegetable garden measures 9 1/3 yards by 12 yards. A bottle of garden fertilizer costs $14.79. If Debra needs to mix 1/8 cup of fertilizer with water for each square yard of her garden, how many cups of fertilizer does she need?
She needs 14 cups of fertiliser.
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.
Area = length * width
Find the area of the garden:
Area = 9 1/3 * 12
= 28/3 * 12
= 112 yards²
Find the amount of the fertiliser needed:
1 yards² = 1/8 cup
112 yards² = 1/8 * 112 = 14 cups
She needs 14 cups of fertiliser.
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The student enrollement of a high school was 1350 in 2012 and increases 9% each year. What is the estimated enrollment in 2022
The estimated enrollment of a high school in 2022 is approximately 2775 students.
To calculate the estimated enrollment in 2022, we need to use the formula for compound interest:
A =[tex]P(1 + r)^t[/tex]
where:
A = final amount (enrollment in 2022)
P = initial amount (enrollment in 2012)
r = annual interest rate (increase rate)
t = number of years (10)
We know that P = 1350 and r = 0.09 (9%). We can plug these values into the formula:
A = [tex]1350(1 + 0.09)^{10[/tex]
A = [tex]1350(1.09)^{10[/tex]
A = 2774.92
Therefore, the estimated enrollment in 2022 is approximately 2775 students.
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3g^2h^4 - 5g^2h^4 + 6g - 7h + g - h
Answer: -2g^7h^8
Step-by-step explanation:
suppose that you have a collection of n spins, each of which points up or down with equal probability. what is the probability that exactly n of them will point up? give both an exact expression and an approximation valid for large n. are there any additional conditions on n for your large n approximations to be valid?
The probability that exactly n of the collection of n spins will point up is given by the Binomial distribution. The Binomial distribution is a discrete probability distribution that models the number of successes (x) in a given number of trials (n) with a fixed probability of success (p) on each trial.
In this case, we have n trials, with a fixed probability of success of 0.5 (since each spin can point up or down with equal probability). The number of successes we're interested in is n. Thus, the probability of n successes is given by:P(X = n) = (nCn)(0.5)^n = 0.5^nwhere nCn is the number of ways to choose n items from n items, which is 1.Approximation for large n:When n is large, we can use the normal approximation to the Binomial distribution.
Specifically, we use the Normal distribution with mean np and variance np(1-p). In this case, p = 0.5, so the mean and variance are both (0.5)n. Therefore, the probability of n successes is approximately:P(X = n) ≈ φ(x) = (1/σ√2π)exp[-(x-μ)^2/2σ^2]where μ = np = (0.5)n and σ^2 = np(1-p) = (0.5)n(0.5) = (0.25)n.
Plugging these values in, we get:P(X = n) ≈ φ(x) = (1/σ√2π)exp[-(n/2n)^2/2(0.25)n] = (1/σ√2π)exp[-(1/8n)] = (1/√2πn)exp[-(1/8n)]Note that for the large n approximation to be valid, we require np and n(1-p) to be at least 10. In this case, np = (0.5)n and n(1-p) = (0.5)n, so this condition is satisfied for any n.
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the original triangle and its projection are similar. what is the missing length n on the projection?
The missing length n on the projection is y.
The original triangle and its projection are similar if the three angles are the same. In this case, the missing length n on the projection can be determined by applying the concept of similarity. First, we need to find out the ratio between the lengths of the original triangle and its projection. For example, if the length of the side of the original triangle is x, and the length of its projection is y, the ratio between them is x/y.
Then, using the similar triangles theorem, we can state that the ratio between the other lengths of the original triangle and its projection is the same. This means that if we know one of the lengths, we can calculate the other one. Therefore, if the length of the side of the original triangle is x, and the ratio is x/y, then the length of the projection must be y.
Finally, we can calculate the missing length n on the projection. We know that the length of the projection is y, and we can use the ratio x/y to calculate n. Therefore, n = x*y/x, which is equal to y.
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Which expression is equivalent to 8x − 4x + 3?
Answer:
4x+3
Step-by-step explanation:
Answer:
A. 4x+3
Step-by-step explanation:
Combining like terms 8x and −4x
Will give you the asnwer to 4x
which will give you 4x + 3
Answer this question. I will give brainlist.
The given diagram represents a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.
The given diagram represents a right circular cylinder with a height of 10 meters and a radius of 7 meters, which means the base of the cylinder is a circle with a radius of 7 meters. The equation of the circle is (x - 0)² + (y - 0)² = 7², where (0, 0) is the center of the circle.
The cylinder has been sliced by a plane that is parallel to the base and 4 meters from the center of the cylinder. This means the distance between the center of the cylinder and the plane is 4 meters.
Mathematically, the equation of the ellipse can be written as (x - 0)²/4² + (y - 0)²/5² = 1, where the center of the ellipse is (0, 0), and the semi-major axis is 5 meters and the semi-minor axis is 4 meters.
So, the given diagram described as a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², sliced by a plane parallel to the base and 4 meters from the center of the cylinder, resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.
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A pharmacist has an 18% alcohol solution and a 40% alcohol solution. How much of each should he mix together to make 10L of a 20% alcohol solution? Pls help
0.18x + 4 - 0.40x = 2
-0.22x = -2
x = 9.09
Therefore, the pharmacist should mix 9.09 liters of 18% alcohol solution and 0.91 liters of 40% alcohol solution to make 10 liters of 20% alcohol solution.
[tex]x=\textit{Liters of solution at 18\%}\\\\ ~~~~~~ 18\%~of~x\implies \cfrac{18}{100}(x)\implies 0.18 (x) \\\\\\ y=\textit{Liters of solution at 40\%}\\\\ ~~~~~~ 40\%~of~y\implies \cfrac{40}{100}(y)\implies 0.4 (y) \\\\\\ \textit{10 Liters of solution at 20\%}\\\\ ~~~~~~ 20\%~of~10\implies \cfrac{20}{100}(10)\implies 2 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{lcccl} &\stackrel{Liters}{quantity}&\stackrel{\textit{\% of Liters that is}}{\textit{alcohol only}}&\stackrel{\textit{Liters of}}{\textit{alcohol only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&x&0.18&0.18x\\ \textit{2nd Sol'n}&y&0.4&0.4y\\ \cline{2-4}&\\ mixture&10&0.2&2 \end{array}~\hfill \begin{cases} x + y = 10\\\\ 0.18x+0.4y=2 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=10\implies y=10-x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation from above}}{0.18x+0.4(10-x)=2}\implies 0.18x+4-0.40x=2 \\\\\\ -0.22x+4=2\implies -0.22x=-2\implies x=\cfrac{-2}{-0.22}\implies \boxed{x\approx 9.09} \\\\\\ \stackrel{\textit{since we know that}}{y=10-x}\implies y\approx 10-9.09\implies \boxed{y\approx 0.91}[/tex]
what is the probability that the person selected will be someone whose response is never and who is a woman?
The probability that the person selected will be someone whose response is never and who is a woman is 3/7.
The probability that the person selected will be someone whose response is never and who is a woman can be found by using conditional probability.What is conditional probability?Conditional probability is the likelihood of an event occurring given that another event has already occurred. The probability of event A happening given that event B has already occurred is known as conditional probability.Mathematically, the formula for conditional probability is:P(A|B) = P(A ∩ B) / P(B)Where,P(A|B) represents the probability of event A given that event B has already occurred.P(A ∩ B) represents the probability of both A and B occurring.P(B) represents the probability of event B occurring.The given scenario states that the person selected should have two attributes: the response never and the gender woman. Let A be the event that the person selected has a response never and B be the event that the person selected is a woman. Therefore, we need to find the probability of event A given event B.P(A|B) = P(A ∩ B) / P(B)Therefore, we need to find the probability of both A and B occurring and the probability of event B occurring.P(B) = 70/120P(B) = 7/12There are 50 women in the group. The number of women who have never responded is 30. Therefore,P(A ∩ B) = 30/120P(A ∩ B) = 1/4Therefore,P(A|B) = P(A ∩ B) / P(B)P(A|B) = 1/4 / 7/12P(A|B) = 3/7The probability that the person selected will be someone whose response is never and who is a woman is 3/7.
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a square has a side length of 3 1/2 inches. the scale factor of 2/3 was used to create a new square. what is the side length of the new square
Answer:
Step-by-step explanation:
The side length of the original square is 3 1/2 inches.
To find the side length of the new square, we need to apply the scale factor of 2/3 to the original side length.
To do this, we multiply the original side length by the scale factor:
(2/3) x 3 1/2
To multiply a fraction by a whole number, we can first convert the whole number to a fraction with a denominator of 1:
(2/3) x (7/2)
To multiply two fractions, we can multiply their numerators together and their denominators together:
(2/3) x (7/2) = (2 x 7) / (3 x 2) = 14/6
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:
14/6 = (2 x 7) / (2 x 3) = 7/3
Therefore, the side length of the new square is 7/3 inches.
Find the area of the shaded area of the figure.
The dimly lit area is 58 square units in size. The area of a two - dimensional figure is the area that its perimeter encloses.
Area – what is it?The area is the space occupied by any two-dimensional figure on a plane. A rectangle's area is how much space it occupies in a the double plane.
The shaded area's size will be determined using the formula
10 units multiplied by 7 units gives a total area of 70 units.
Gap size equals 2 units multiplied by 6 units, or 12 units.
The shaded figure's area is 70 units divided by 12 units, or 58 units.
As a result, 58 square units make up the area of shaded zone.
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