Ardin paid $15.45 for each shirt.
Let us assume that the cost of each shirt is m dollars.
Ardin buys 8 shirts.
So, using unitary method the cost of 8 shirts would be:
8 × m = 8m dollars
Ardin buys 8 shirts at the store for $123. 60
so, we get an equation :
8m = 123.60
We solve above equation to find the value of m.
Divide each side of equation by 8
m = 123.60/8
m = 15.45 dollars
Therefore, the cost of each shirt = 15.45 dollars
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suppose ruth ann has 3 routes she can travel between the school to the library, and 5 routes from the library to her home. how many routes are there from ruth ann's school to her home with a stop at the library?
Answer: Hello there!
There are 3 ways Ruth can go from high school to the library, and 5 ways she can go from the library to her home.
The number of possible combinations is equal to the product between the options of each event (where the events are going from high school to the library and going from library to her house):
[tex]3\times5 = 15[/tex]
Then there are 15 different routes that Ruth can take from high school to her home, where she makes a stop at the library.
5a - 2b = 7 and 5a +2b =14 in elimination method
Answer:
a = 2.1
b = 1.75
Step-by-step explanation:
5a - 2b = 7
5a + 2b = 14
Combine the equation, we get
10a = 21
a = 2.1
Now put 2.1 in for a and solve for b
5(2.1) - 2b = 7
10.5 - 2b = 7
-2b = -3.5
b = 1.75
Let's Check
5(2.1) - 2(1.75) = 7
10.5 - 3.5 = 7
7 = 7
So, a = 2.1 and b = 1.75 is the correct answer.
find the x pleaseeee
What is 26.3×7.8 equal?
Answer: 205.14
Step-by-step explanation:
Multiply
Add
Insert Decimal Point
205.14
Answer:
205.14
Step-by-step explanation:
Step 1: Multiply without the decimal points, then put the decimal point in the answer:
263x78
Step 2: Line up the numbers:
2 6 3
x 7 8
Step 3: Multipy the top number by the bottom number one digit at a time starting from left to right:
[tex]\frac{\begin{matrix}\:\:&\:\:&2&6&3\\ \:\:&\times \:&\:\:&7&8\end{matrix}}{\begin{matrix}0&2&1&0&4\\ 1&8&4&1&0\end{matrix}}[/tex]
Step 4: Add:
[tex]\frac{\begin{matrix}\:\:&\textbf{1}&\:\:&\:\:&\:\:&\:\:\\ \:\:&\textbf{0}&2&1&0&4\\ +&\textbf{1}&8&4&1&0\end{matrix}}{\begin{matrix}\:\:&\textbf{2}&0&5&1&4\end{matrix}}[/tex]
Step 5: Insert Decimal Point:
205.14
YALL ILL GIVE BRAINLIEST ANS 20 POINTS
The center of dilation is (-3, 15). The scale factor is not the same for all sides of the triangles, which means that the dilation is not a similarity transformation.
Describe Transformation?In mathematics, a transformation is a function that maps one set of values, called the domain, to another set of values, called the range. The term is commonly used in geometry and algebra to describe a change in the position, size, or shape of a geometric object or algebraic equation.
Transformations can be classified into several types, including translation, rotation, reflection, scaling, and shearing. Each type of transformation changes the appearance of the object in a specific way.
To identify the center of dilation and scale factor, we can compare the coordinates of corresponding points in the two triangles.
The center of dilation is the point about which the dilation occurs. It can be found by calculating the intersection of the lines joining corresponding points in the two triangles.
Scale factor is the ratio of the lengths of corresponding sides in the two triangles. It can be found by dividing the length of any side in the image triangle by the length of the corresponding side in the pre-image triangle.
Let's calculate the center of dilation first:
Line joining L and L': (y - 11)/(x - 5) = (8 - 11)/(3 - 5) = -3/2
Line joining M and M': (y - 9)/(x - 13) = (7.7 - 9)/(7 - 13) = -0.7/-6 = 0.1167
Line joining N and N': (y - 3)/(x - 11) = (4 - 3)/(6 - 11) = 1/-5 = -0.2
Solving any two equations simultaneously will give us the center of dilation:
(y - 11)/(x - 5) = -3/2
(y - 9)/(x - 13) = 0.1167
Solving the above two equations gives the point of intersection as (-3, 15). Therefore, the center of dilation is (-3, 15).
Now, let's calculate the scale factor:
Length of side LM = √((13-5)² + (9-11)²) = √(80)
Length of side L'M' = √((7-3)² + (7-8)²) = √(26)
Scale factor for side LM to L'M' = √(26)/√(80) = 0.470
Length of side MN = √((11-13)² + (3-9)²) = √(40)
Length of side M'N' = √((6-7)² + (4-7)²) = √(10)
Scale factor for side MN to M'N' = √(10)/√(40) = 0.5
Length of side NL = √((5-11)² + (11-3)²) = √(80)
Length of side N'L' = √((3-6)² + (8-4)²) = √(29)
Scale factor for side NL to N'L' = √(29)/√(80) = 0.544
Therefore, the scale factor is not the same for all sides of the triangles, which means that the dilation is not a similarity transformation.
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This circle graph shows how the students in two sixth-grade classes get to school. Fifty students were surveyed. What percent takes the bus?
Forty percent of the students surveyed take the bus to school, as indicated by the circle graph.
To calculate the percent of students who take the bus to school, we can use the information provided in the circle graph. There are a total of 50 students surveyed, and the graph indicates that 20 of them take the bus. To find the percent, we can first divide the number who take the bus (20) by the total number surveyed (50). This gives us 0.4, which, when multiplied by 100, is 40%. Therefore, 40% of the students surveyed take the bus to school. Hence, Forty percent of the students surveyed take the bus to school, as indicated by the circle graph.
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Moira is remodeling her kitchen. A rectangular kitchen has 12‘ x 18‘ of floor space. The floor tiles are 1/2‘ x 3/4‘. Each tile cost $0.75. How much will she pay for the tiles to cover her entire kitchen floor? 
Accοrding tο the given infοrmatiοn, Mοira will need tο pay $432 fοr the tiles tο cοver her entire kitchen flοοr.
What is area οf rectangle?The area οf a rectangle is the amοunt οf space enclοsed within the bοundary οf a rectangle. It is calculated by multiplying the length οf the rectangle by its width. If we denοte the length οf the rectangle by 'l' and its width by 'w', then the area οf the rectangle can be expressed as:
Area = length x width = l x w
Tο find οut hοw many tiles Mοira needs, we first need tο find the tοtal area οf her kitchen flοοr. We can dο this by multiplying the length and width οf the kitchen:
Area οf kitchen flοοr = length x width = 12' x 18' = 216 square feet.
Next, we need tο figure οut hοw many tiles will cοver this area. Tο dο this, we need tο divide the area οf the kitchen flοοr by the area οf each tile:
Area οf each tile = 1/2' x 3/4' = 3/8 square feet
Number οf tiles = (Area οf kitchen flοοr) / (Area οf each tile) = 216 / (3/8) = 576 tiles.
Finally, we can calculate the tοtal cοst οf the tiles by multiplying the number οf tiles by the cοst per tile:
Tοtal cοst οf tiles = (Number οf tiles) x (Cοst per tile) = 576 x $0.75 = $432.
Sο, Mοira will need tο pay $432 fοr the tiles tο cοver her entire kitchen
floor.
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The EPA wants to conduct a survey to determine the current approval rating on the government's handling of environmental action. From previous studies, they know that they need to poll 275 people to achieve their desired level of confidence. If they want to keep the same level of confidence but divide the margin of error in third, how many people will they have to poll?
Answer: Assuming that the desired level of confidence and the population size remain constant, the sample size required for a given margin of error is proportional to the square of the standard normal deviate corresponding to the desired level of confidence.
That is, if n is the current sample size and m is the current margin of error, and we want to divide the margin of error by 3 while keeping the same level of confidence, then we need to find the new sample size, n', that satisfies the equation:
n'/n = (zα/2 / z'α/2)²
where zα/2 is the standard normal deviate corresponding to half the desired level of confidence, and z'α/2 is the standard normal deviate corresponding to half the desired level of confidence and one-third the margin of error.
Assuming a desired level of confidence of 95%, we have:
zα/2 = 1.96
z'α/2 = 1.96 / 3 = 0.6533 (rounded to four decimal places)
Substituting these values and the given values of n and m, we get:
n'/275 = (1.96 / 0.6533)²
Solving for n', we get:
n' = 275 * (1.96 / 0.6533)²
Using a calculator, we get:
n' ≈ 887
Therefore, the EPA would need to poll approximately 887 people to achieve the same level of confidence with a margin of error divided by three.
Step-by-step explanation:
After Brandon walks through the "Discovery Stage," what are some of the steps ken tells him to take next
Ken tells Brandon to take the following steps:
Identify potential opportunitiesNetwork with people in the fieldGet some experienceNarrow down the optionsCreate an action planWhat is the Discovery Stage about?In Chapter 6, Lesson 1 of "Finding Work That Matters," after Brandon walks through the Discovery Stage, Ken tells him to take the following steps:
Identify potential opportunities: Based on the information gathered in the Discovery Stage, Brandon should look for potential opportunities that align with his skills, interests, and values.
Network with people in the field: Brandon should reach out to people who work in the fields he is interested in and learn more about their experiences, how they got started, and what advice they have for someone starting out.
Get some experience: Ken advises Brandon to get some experience in the fields he is interested in, even if it's just through volunteering or taking on a small project. This will help him gain a better understanding of what the work entails and whether it's something he wants to pursue further.
Lastly, Create an action plan: Finally, Ken advises Brandon to create an action plan that outlines the steps he needs to take to pursue each of his chosen opportunities. This should include specific goals, deadlines, and action items that he can work on over time.
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See full question below
Finding Work That Matters
CHAPTER 6,LESSON 1:
After Brandon walks through the "Discovery Stage," what are some of the steps ken tells him to take next
 The bus fare in a city is two dollars people who use the bus have the option of purchasing a monthly coupon book for $29 with a coupon book the fair is reduced to one dollar determine the number of times in a month the bus most be used so that the total monthly cost without the coupon book is the same as the monthly cost with a coupon book 
Answer:
Total Cost = 2(29) = $58 (without coupon book)
Total Cost = $29 + $1(29) = $58 (with coupon book)
Step-by-step explanation:
Let's assume that x is the number of times the bus is used in a month.
Without the coupon book, the total monthly cost would be:
Total Cost = 2x
With the coupon book, the total monthly cost would be:
Total Cost = $29 + $1x
We want to find the value of x that makes these two total costs equal. So we set them equal to each other and solve for x:
2x = 29 + 1x
2x - 1x = 29
x = 29
So if the bus is used 29 times in a month, the total monthly cost without the coupon book will be the same as the monthly cost with the coupon book. In this case, the total monthly cost would be:
Total Cost = 2(29) = $58 (without coupon book)
Total Cost = $29 + $1(29) = $58 (with coupon book)
Therefore, if a person uses the bus more than 29 times in a month, it would be more cost-effective for them to purchase the coupon book. If they use the bus less than 29 times, it would be more cost-effective for them to pay the regular fare of $2 per ride.
what are the answers to put in the boxes?
Answer: x=20
Step-by-step explanation:
we can fill 3/1 in first and also 1/1
in the second box we can fill 1/1 or 3/3
Anthony and Jacob have some circles. All the circles are the same size. Anthony and Jacob want to completely color twelve circles to make a border for their math project.
Anthony colors six and one-fourth circles before having to go to lunch. Jacob colors five and three-fourths circles before having to go to lunch. Anthony says if he had colored one-fourth of Jacob's last circle instead of one-fourth of his last circle, they would have twelve whole sircles colored. Is Anthony correct?
100 POINTS BRAINILY.
THIS IS SO EASY.
Answer:
anthony is correct
Step-by-step explanation:
Application: Determine the Areas and Volumes using the Cross Product Find the volume of the parallelepiped determined by the vectors
a =⟨2,4,−1⟩, b =⟨0,3,4⟩
,c =⟨2,3,1⟩Volume = cubic-units
Volume of the parallelepiped determined by the vectors a= ⟨2,4,-1⟩, b=⟨0,3,4⟩, c=⟨2,3,1⟩ using cross product is 20 cubic-units
The volume of a parallelepiped determined by three vectors a, b and c is given by the scalar triple product of these vectors.
Volume = a . (b x c) where x represents the cross product of vectors b and c.
We have a= ⟨2,4,-1⟩, b=⟨0,3,4⟩, c=⟨2,3,1⟩.
Therefore, the cross product of b and c = b x c is given by;b x c=⟨(3x1)-(4x3), (4x2)-(0x1), (0x3)-(2x3)⟩=⟨-9, 8, -6⟩
Now, the scalar triple product is given as follows: a . (b x c)= ⟨2,4,-1⟩ . ⟨-9, 8, -6⟩= 2 (-9) + 4 (8) + (-1) (-6)= -18 + 32 + 6= 20
Thus, the volume of the parallelepiped determined by the vectors a, b and c is 20 cubic units.
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Find the cross product a x b. a = i + 3j - 3k, b = -i + 5k Verify that it is orthogonal to both a and b. (a xb). a =
(a - b). b =
Cross product of two vectors, a and b, is (3, 5, -15) and cross product a x b is orthogonal to both vectors.
The cross product of two vectors, a and b, is calculated by taking the determinant of the matrix formed by their components:
a x b =
|i 3 -3|
|-1 0 5|
| 0 0 0|
This can also be written as:
(i, 3, -3) x (-1, 0, 5) = (3, 5, -15)
Therefore, a x b = (3, 5, -15).
To verify that it is orthogonal to both a and b, we must check if their dot product is zero:
(a, b) = (i + 3j - 3k, -i + 5k) = (i - i + 3j - 3k + 5k) = 3j + 2k = 0
Since the dot product of a and b is zero, we can conclude that the cross product a x b is orthogonal to both vectors.
Hence, Cross product of two vectors, a and b, is (3, 5, -15) and cross product a x b is orthogonal to both vectors.
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How to find time when distance is 630km and speed is126km/h?
The time for 630 kilometres would need to be covered in 5 hours if you were doing 126 kilometres per hour.
To find the time when distance and speed are known, we can use the formula: time = distance ÷ speed, where time is measured in hours, distance is measured in kilometers, and speed is measured in kilometers per hour. By plugging in the values, we can calculate the time it takes to travel a distance at a given speed.
time = distance ÷ speed
where time is measured in hours, distance is measured in kilometers, and speed is measured in kilometers per hour.
In this case, we are given the distance as 630 km and the speed as 126 km/h. Plugging these values into the formula, we get:
time = 630 km ÷ 126 km/h
We can simplify this expression by dividing 630 by 126:
time = 5 hours
Therefore, it would take 5 hours to travel a distance of 630 km at a speed of 126 km/h.
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Find the volume of the solid obtained by rotating the region bounded by the curves y=1−x2 and y=0 about the x-axis.
I start by getting A(y)= (1-x^2). Then square it and find the integral to get the volume. But it keeps coming up wrong. Is there anyone that can help?
0 about the x-axis is π/3
To obtain the volume of the solid by rotating the region bounded by the curves y = 1 − x² and y = 0 about the x-axis, follow the following steps:Step 1: Determine the interval of integration by equating the two equations and solving for x. 1 − x² = 0 x² = 1 x = ± 1Since the region is being revolved about the x-axis, the interval of integration would be [-1, 1]. Step 2: Find the expression of the cross-section. The cross-section of the solid would be a disk with radius y and thickness dy. Therefore, the expression for the cross-section would be π(y²) Step 3: Find the integral. V = π∫₀¹ (y²) dy= π (y³/3)|₀¹= π (1³/3 - 0³/3) = π/3. Hence, the volume of the solid obtained by rotating the region bounded by the curves y = 1 − x² and y = 0 about the x-axis is π/3.
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Can someone help? this is the only problem I don’t understand for my math test.
Answer:
a. (f+g)(x)
Step-by-step explanation:
[tex]7x^{3} + 12x^{2} +4x - 2[/tex]
assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. find the probability of exactly nine boys in ten births. round the answer to the nearest thousandth.
The probability of exactly nine boys in ten births is 0.010 (rounded to the nearest thousandth).
In a situation where male and female births are equally likely and the birth of any child does not affect the probability of the gender of any other children, finding the probability of exactly nine boys in ten births is quite easy.
We can approach this using the binomial probability distribution, which provides the probability of x successes in n independent Bernoulli trials.
[tex]P(x) = (nCx) * p^x * q^(n-x)[/tex]
Where P(x) is the probability of x successes, n is the total number of trials,
p is the probability of success,
q is the probability of failure, and nCx is the binomial coefficient.
Assuming that the probability of a male or female birth is 1/2 or 0.5 and using the above formula, we can find the probability of exactly nine boys in ten births as follows:
P(9) = (10C9) * (0.5)^9 * (0.5)^(10-9)P(9)
= 10 * 0.001953125 * 0.5P(9)
= 0.009765625
Rounding the answer to the nearest thousandth, we get: P(9) ≈ 0.010
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Use Gauss-Jordan elimination method (RREF) to solve each system of equations. For each system, write the augmented matrix you entered into the calculator, write the reduced row echelon form (RREF) of the matrix, and write the solution to the system of equations. In the event of infinite solutions, let Xz = t. b) a) 2x1 + 4x2 - X3 = 2 X1 + x2 + 3x3 = -13 2x1 X2 = -2 3x1 - x2 - X3 = -7 X1 + 4x2 - 9x3 = 2 4x1 - 3x2 + 2x3 = -11 Augmented matrix: Augmented matrix: RREF: RREF: Solution: Solution:
Using Gauss-Jordan elimination method (RREF), the solution for the given system of equations is X1 = -t, X2 = t-3, and X3 = t.
The Gauss-Jordan elimination method is used to solve a system of equations. To solve a system of equations using the Gauss-Jordan elimination method, we must first construct the augmented matrix of the system.
The augmented matrix for the system of equations b) a) 2x1 + 4x2 - X3 = 2 X1 + x2 + 3x3 = -13 2x1 X2 = -2 3x1 - x2 - X3 = -7 X1 + 4x2 - 9x3 = 2 4x1 - 3x2 + 2x3 = -11 is:
[tex]\begin{bmatrix} 2 & 4 & -1 & | & 2\\ 1 & 1 & 3 & | & -13\\2 & 0 & 0 & | & -2\\3 & -1 & -1 & | & -7\\1 & 4 & -9 & | & 2\\4 & -3 & 2 & | & -11\end{bmatrix}[/tex]
Next, we use elementary row operations to reduce the matrix to reduced row echelon form (RREF):
[tex]\begin{bmatrix} 1 & 0 & -1 & | & 0\\ 0 & 1 & 1 & | & -3\\0 & 0 & 0 & | & 0\\0 & 0 & 0 & | & 0\\0 & 0 & 0 & | & 0\\0 & 0 & 0 & | & 0\end{bmatrix}[/tex]
From the RREF of the augmented matrix, we can see that there are infinitely many solutions to this system of equations. Therefore, we can let Xz = t, and the solution to the system of equations is X1 = -t, X2 = t-3, and X3 = t.
In conclusion, the Gauss-Jordan elimination method (RREF) is used to solve a system of equations. After constructing the augmented matrix for the system of equations, we use elementary row operations to reduce the matrix to reduced row echelon form (RREF). This will give us the solution to the system of equations, in the event of infinite solutions, let Xz = t. For the given system of equations, the solution is X1 = -t, X2 = t-3, and X3 = t.
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True or False? a linear model is an equation that summarizes the linear relationship between a response variable and explanatory variable.
Answer:
True
Hope this helps
Have a good day!!
<3
What is the pattern for finding volume of shapes that are prisms and cylinders?
The volume of a prism is V = Bh = πr2h, therefore the volume of a cylinder is also V = Bh = πr2h. Where, B is the area of the base, h is the height, and r is the radius of the base.
A prism is a polyhedron all of whose faces are flat and whose bases are parallel to each other. It is a solid object with flat surfaces, identical ends, identical diameter and length. The volume of a prism is defined as the total space occupied by a three-dimensional object. Mathematically, it is defined as the product of the area of the base and the length.
Therefore, the volume of the prism = base area × length
Volume of Cylinder:
The volume of a cylinder is the number of unit cubes (cubes per unit length) that can fit in it. It is the space occupied by the cylinder, because the volume of any three-dimensional shape is the space it occupies. The volume of a cylinder is measured in cubic units, such as cm³, m³, in³, etc.
The volume of cylinder is :
V = πr2h
where
'r' is the radius of the cylinder
'h' is the height of the cylinder
And, π is a constant whose value
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f(x)=y=(x+6)(x+1)
find the roots
The rοοts οf the functiοn are x = -6 and x = -1.
What is quadratic equatiοn?A quadratic equatiοn is a type οf pοlynοmial equatiοn οf the secοnd degree, which can be written in the fοrm:
[tex]ax^2 + bx + c = 0[/tex]
Where "a", "b", and "c" are cοnstants, and "x" is the variable. The cοefficient "a" must nοt be equal tο zerο, as this wοuld result in a linear equatiοn.
The quadratic equatiοn can be sοlved using the quadratic fοrmula, which is:
x = (-b ± sqrt(b² - 4ac)) / 2a
Tο find the rοοts οf the functiοn, we need tο find the values οf x that make y equal tο zerο since the rοοts οf a functiοn are the values οf x that make the functiοn equal tο zerο.
Sο we set y tο zerο and sοlve fοr x:
0 = (x+6)(x+1)
Using the zerο prοduct prοperty, we knοw that if the prοduct οf twο factοrs is equal tο zerο, then at least οne οf the factοrs must be equal tο zerο.
Sο we set each factοr equal tο zerο and sοlve fοr x:
x + 6 = 0 οr x + 1 = 0
x = -6 οr x = -1
Therefοre, the rοοts οf the functiοn are x = -6 and x = -1.
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D Jane drew a scale drawing of a city park. She used the scale 3 centimeters : 4 meters. The soccer field is 108 meters long in real life. How long is the field in the drawing?
Using proportion, the length of the soccer field in the drawing is 81 centimeters.
What is proportion?
In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.
We can use proportions to solve this problem.
Let x be the length of the soccer field in the drawing.
Using the scale, we can write -
3 centimeters : 4 meters = x centimeters : 108 meters
To solve for x, we can cross-multiply and simplify.
Simplify the equation as -
3 centimeters × 108 meters = 4 meters × x centimeters
324 centimeters = 4x
x = 81 centimeters
Therefore, the length value is obtained as 81 centimeters.
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calvin went fishing for smallmouth and largemouth bass. he caught 25 fish for smallmouth bass be caught 2 less than double the number of largemouth let x represent the number of smallmouth bass and y represent the number of largemouth bass
By solving the generated equation, Calvin caught 16 smallmouth bass and 9 largemouth bass.
What is meant by equation?
An equation states that the two expressions have the same value or are equivalent to each other. Equations are used in various areas of mathematics, science, engineering, and everyday life to describe relationships and solve problems.
Let x represent the number of smallmouth bass that Calvin caught, and y represent the number of largemouth bass that he caught.
From the problem, we know that the total number of fish that Calvin caught is 25:
x + y = 25
We also know that the number of smallmouth bass that Calvin caught is 2 less than double the number of largemouth bass that he caught:
x = 2y - 2
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for y:
y = 25 - x
Substituting this into the second equation, we get:
x = 2(25 - x) - 2
Simplifying this equation, we get:
x = 48 - 2x
Solving for x, we get:
3x = 48
x = 16
Substituting this value of x back into either of the original equations, we can solve for y:
y = 25 - x = 25 - 16 = 9
Therefore, Calvin caught 16 smallmouth bass and 9 largemouth bass.
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L(-1, 6), M(5, 9), N(0, 2), P(-8, -2) (Slope Formula)
Therefore , the solution of the given problem of slope comes out to be the slopes of the lines that contain the specified point pairs are both 1/2.
Describe slope.The slope of a line determines how sharp it is. Gradient overflow is a condition that can occur in equations that rely on gradients. By dividing the total run (width difference) and apparition (climbing distinction) between the two locations, one can calculate the slope. The fixed path issue is modelled using a fix y = mx + b incorporating the hill variation. when a = bc, its y-intercept, and the inclination are all expressed in millimeters; (0, b).
Here,
The slope formula is used to determine the slope of a line given two coordinates (x1, y1) and (x2, y2):
=> slope = (y2 + y1)/. (x2 - x1)
We can use the following formula to determine the slopes of the lines that contain the specified pair of points:
Line LM's slope, which includes the coordinates L(-1, 6) and M(5, 9), is given by:
=> slope of LM = (9 - 6) / (5 - (-1))
=> 3/6 = 1/2
=> Slope of line NP = (-2 - 2) / (-8 - 0)
=> -4 / (-8) = 1/2;
line NP contains coordinates N(0, 2) and P(-8, -2).
Because the slope is symmetric with regard to the order of the points, we would have come to the same conclusion.
As a result, the slopes of the lines that contain the specified point pairs are both 1/2.
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A trucks has a maximum load limit of 5000 kg. Can it safely cary 230 bushels of canola, if the conversion factor is 44.092 bushels/tonne?
After answering the provided question, we can conclude that As a result, equation 230 bushels = (230/44.092) tonnes = 5.22 tonnes.
What is equation?In mathematics, an equation is a statement that states the equivalence of two expressions. An equation consists of two sides separated by an algebraic equation (=). For instance, the argument "2x + 3 = 9" states that the sentence "2x + 3" equals the number "9". The purpose of solving equations is to find the value or amounts of the variable(s) that always allow the equation to be true. Equations can just be simple or complicated, regular or nonlinear, and contain one or more variables. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are used extensively in mathematics, including algebra, calculus, and geometry.
To find out if the truck can safely transport 230 bushels of canola, we must first convert the bushels to kilos. Using the conversion factor, we can convert bushels to tonnes and finally tonnes to kilos.
1000 kg Equals 1 tonne
1 tonne is 44.092 bushels
As a result, 230 bushels = (230/44.092) tonnes = 5.22 tonnes.
We multiply by 1000 to convert tonnes to kilogrammes:
5.22 tonnes = 5220 kg
Because 5220 kg is less than the truck's maximum weight restriction of 5000 kg, it may safely transport 230 bushels of canola.
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Specifically, generate a reference sample of the same size of the training set. This can be done in a couple of ways, e.g., (i) sample uniformly for each variable, or (ii) by randomly permuting the values within each variable independently.
Build a classification tree to the training sample (class 1) and the reference sample (class 0) and describe the terminal nodes having highest estimated class 1 probability. Compare the results to the results near Table 14.1 (ESL), which were derived using PRIM.
The estimated probabilities of belonging to a particular class in each terminal node can also be used to predict the class of new observations.
To build a classification tree, we need a training set and a reference sample of the same size. The reference sample is a set of data that we use to compare our model's performance against random guessing. We can generate a reference sample in a couple of ways.
To estimate the probability of a new observation belonging to a particular class, we calculate the proportion of training samples or reference samples in that terminal node that belong to that class.
The terminal nodes with the highest estimated class 1 probability are the ones where most of the training samples belong to class 1. These nodes will be useful in predicting the class of new observations.
However, PRIM provides a more detailed summary of the important regions, whereas classification trees provide a more visual representation of the decision boundaries.
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Determine the lateral and total surface area of the pyramid.
The lateral and total surface area of the square pyramid is 196.22 cm² and 232.22 cm².
what exactly is a square pyramid?
A square pyramid is a three-dimensional geometric shape that consists of a square base and four triangular faces that meet at a common vertex, called the apex. All the triangular faces are congruent, and the base and apex are aligned along the same vertical axis. A square pyramid is a type of pyramid because it has a polygonal base, which is a square in this case.
Now,
The lateral surface area of a square pyramid is given by the formula:
L = (1/2)Pl
where P= perimeter of the base and l = slant height .
To find the perimeter of the base, we can use the formula for the perimeter of a square:
P = 4s
where s= length of a side of the square. Substituting s = 6 cm, we get:
P = 4(6) = 24 cm
To find the slant height , we can use the Pythagorean theorem:
l² = h²+ (s/2)²
where h is the height of the pyramid and s is the length of a side of the square base. Substituting h = 16 cm and s = 6 cm, we get:
l² = 16² + (6/2)² = 256 + 9 = 265
l = √265 ≈ 16.28 cm
Therefore, the lateral surface area is
L = (1/2)Pl = (1/2)(24)(16.28) ≈ 196.22 cm²
The total surface area of a square pyramid is given by the formula:
T = B + L
where B is the area of the base. Since the base is a square with side length 6 cm, the area of the base is:
B = s² = 6² = 36 cm²
Therefore, the total surface area of the pyramid is:
T = B + L = 36 + 196.22 ≈ 232.22 cm²
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find the domain and range
Answer:
B.
Step-by-step explanation:
find an acute angle theta that satisfies the equation sin theta =cos (2 theta + 27 degrees)
An acute angle theta that satisfies the equation sin θ =cos (2 theta + 27 degrees) is 45 degrees.
To find an acute angle theta that satisfies the equation sin theta =cos (2 theta + 27 degrees), we can use the identity cos (90 - theta) = sin theta.
Substituting 90 - theta for 2 theta + 27 degrees, we get:
sin theta = cos (90 - theta)
Using the identity cos (90 - theta) = sin theta, we can simplify the equation to:
sin theta = sin (90 - theta)
Since sin θ = sin (90 - theta), we can conclude that theta = 90 - theta.
Solving for theta, we get:
2 theta = 90
theta = 45 degrees
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