The equation that Eve can use to find the number of days d she can feed Pickles from the bag is; 4d = 24
How to solve Linear equation Word Problems?
The general formula for the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
We are given that;
Number of cups that Pickles eats per day = 4 cups per day
Now, Eve wants to know how many days she can feed Pickles from a 24-cup bag of Hungry Hound.
If the number of days are denoted as d, then we have the equation as;
4d = 24
d = 24/4
d = 6 days
We conclude that she can feed the dog for 6 days.
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16. STEM Connection Maya has 3.8 liters of a
solution. She needs 4.3 times more than she
already has. About how many liters of the solution
does she need?
Maya has a solution that volume is 3.8 liters. She needs more 20.12 liters solution.
What is solution?
A particular kind of homogenous mixture made up of two or more substances is known as a solution. A solute is a substance that has been dissolved in a solvent, which is the other substance in the mixture.
Given that Maya has a solution with volume 3.8 liters.
The symbol is used in mathematics to represent the multiplication operation and the resultant product. It is sometimes referred to as the times sign or the dimension sign.
Times means multiplication.
She requires 4.3 times more than she currently possesses..
She needs = 4.3 × 3.8 = 16.32 liters.
The total amount she needs is 16.32 + 3.8
Addition process:
1
16.32
+3.80
______
20.12
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I NEED HELP THIS IS DUE TONIGHT
Answer:
The park has 20 climbing activities.
Step-by-step explanation:
Given,
Total activities = 50
Percent of climbing activities = 40%
Number of climbing activities = 40% of total activities
Number of climbing activities = 40/100 * 50
Number of climbing activities = 0.40 * 50 = 20
Hope this helps!!
two different two-digit whole numbers are selected at random. what is the probability that their product is less than 200. express your answer as a common fraction. (hints: (l) there are 90 different two-digit numbers, (2) the pair {10, 11} produces the smallest product and the pair {11, 18} produces the largest product less than 200).
The probability that the product of the two two-digit numbers is less than 200 is given as follows:
43/8010.
How to calculate the probability?A probability is calculated as the division of the number of desired outcomes in the context of the experiment by the number of total outcomes.
There are 90 different two-digit numbers, hence the number of total outcomes for the product is of:
90 x 89 = 8010.
(the numbers have to be different)
The desired outcomes which result in a product of less than 200 are of given as follows:
10 multiplied by 9 numbers, from 11 to 19.11 multiplied by 10, 12, 13, 14, 15, 16, 17, 18. (8 numbers).12 multiplied by 10, 11, 13, 14, 15, 16. (6 numbers).13 multiplied by 10, 11, 12, 14, 15 (5 numbers).14 multiplied by 10, 11, 12, 13. (4 numbers).15 multiplied by 10, 11, 12, 13. (4 numbers).16 multiplied by 10, 11, 12. (3 numbers).17 multiplied by 10, 11. (2 numbers).18 multiplied by 10, 11. (2 numbers).Hence the number of desired outcomes is given as follows:
9 + 8 + 6 + 5 + 4 + 4 + 3 + 2 + 2 = 43.
Meaning that the probability is of:
43/8010.
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Write an equation of the line that passes through (-1,3) and is parallel to the line y=-3x+2
Slope-intercept form: [tex]y=mx+b[/tex]
m = slopeb = y-interceptParallel lines always have the same slopes and different y-intercepts.
Solving the QuestionWe're given:
Parallel to [tex]y=-3x+2[/tex]Passes through (-1,3)Because parallel lines have the same slopes, this line therefore has a slope of -3.
[tex]y=-3x+b[/tex]
Now, plug in the given point to solve for b:
[tex]3=-3(-1)+b\\3=3+b\\b=0[/tex]
Therefore:
[tex]y=-3x[/tex]
Answer[tex]y=-3x[/tex]
Find the Limit of the following given Function
The answer of the limit is -3
can someone help i will give brainlest:)
A. Width = 16.5 ft B.Width = 55.25 ft
Height = 9.3 ft Height = 91 ft
Area = 153.45 ft² Area = 5027.75 ft²
The formula for Area of rectangle:The area of the rectangle is a place covered by a rectangle in a 2D plane
The formula for Area of the rectangle is given by
Area = Length × WidthHere we have
1 in = 3 feet and 1 cm = 6.5 ft
Calculation for rectangle A :
In rectangle A
Width = 5.5 in
=> Width in feet = 5.5 × 3 feet = 16.5 ft
Height = 3.1 in
=> Height in feet = 3.1 × 3 feet = 9.3 ft
By the given formula
Area = 16.5 ft × 9.3 ft = 153.45 ft²
Calculation for rectangle B :
In rectangle B
Width = 8.5 cm
=> Width in feet = 8.5 × 6.5 feet = 55.25 ft
Height = 14 cm
=> Height in feet = 14 × 6.5 feet = 91 feet
By the given formula
Area = 55.25 ft × 91 ft = 5027.75 ft²
Therefore,
A. Width = 16.5 ft B. Width = 55.25 ft
Height = 9.3 ft Height = 91 ft
Area = 153.45 ft² Area = 5027.75 ft²
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Im order to save money for prom this weekend Tom is going to walk his neighbors dog for 6 per hour
The system of inequalities represents this solution is:
6c + 7.5d ≥ 75
d + c ≤ 15.
What is inequality?A statement of an order relationship, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
Now it is given that,
Money from walking neighbor's dog = $6 per hour
Money from car wash = $7.5 per hour
Total Number of hours of work not more than 15 hours
Now, if d represents the number of hours walking his neighbor's dog and c represents the number of hours washing car
So, money from walking neighbor's dog = 6c
and money from car wash = 7.5d
Therefore total money saved = 6c + 7.5d
∵ Total Number of hours of work is not more than 15 hours
⇒ d + c ≤ 15
∵ Tom needs to make at least $75 to cover prom expenses
⇒ 6c + 7.5d ≥ 75
The system of inequalities represents this solution is:
6c + 7.5d ≥ 75 ;
d + c ≤ 15.
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The complete question is as follows:
To save money for prom this weekend, Tom is going to walk his neighbor's dog for $6 per hour and wash cars for $7.50 per hour. His mother said he can work no more than 15 hours to ensure he keeps up with his homework. Tom needs to make at least $75 to cover prom expenses. If d represents the number of hours walking his neighbor's dog and c represents the number of hours washing cars, which system of inequalities represents this solution?
Given h(x) = −3x + 15, calculate h(−3).
The value of the function instance h (-3) as required to be determined given the function declaration; h(x) = −3x + 15 is; 24.
What is the value of the function instance h (-3) as given?It follows from the task content that the value of the function instance h (-3) is to be determined given the function h (x) = -3x + 15.
Since the given function is; h (x) = -3x + 15.
The value of the function instance; h (-3) can be determined by evaluating as follows;
h (-3) = -3 (-3) + 15
h (-3) = 9 + 15
h (-3) = 24.
On this note, the value of the function instance h (-3) as required is; 24.
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How do type an exponent on a chromebook laptop?
Step-by-step explanation:
Press ''CTRL + /'' to access the list of features.
Find the “Text Formatting” section.
Choose “Superscript” from the list of options.
On the right-hand side, you'll see the ''CTRL +. '' shortcut. Use it to make the number or letter in your text appear in exponent form.
Step-by-step explanation:
1. Place your cursor where you want an exponent. For example, if you want to place an exponent after the number 10 in a document, place your cursor directly after the 10 with no space.
2. Type Alt+0185 for the exponent 1. For example, you can type the number 10¹ holding the Alt key and typing 0185.
3. Type Alt+0178 for the exponent 2. For example, you can type the number 10² holding the Alt key and typing 0178.
4. Type Alt+0179 for the exponent 3. For example, you can type the number 10³ by holding the Alt key and typing 0179.
Paris and Jen are sisters that are away at different colleges. After a 5-hour drive, Paris is 324 miles from home, and after 7 hours she's 200 miles from home. Jen's trip home can be represented by the equation y = -58+422. Which statements are true? Select all that apply Jen is driving slower than Paris. Parts is driving slower than Jen Paris's school is farther from home than Jer's school Jen's school is farther from home than Paris's school It will take Paris longer to get home, even though she's driving faster
The correct statement is Jen is that driving faster than Paris.
Jen's journey home is represented by the equation y=58x+422.
Paris covers ,
324 miles in 5 hour
Therefore, her speed is,
324/5
= 64.8 miles/hr
Jen's rate is expressed as, y=58x+422.
Here , distance covered is 422 miles.
After comparing their speed we can conclude that , Jen is faster.
Distance word problems are a sort of algebra word problem that is very prevalent. They involve a scenario in which you must determine how quickly, far, or long one or more things have gone.
These are frequently referred to as train problems since one of the most well-known varieties of distance problems involves determining when two trains travelling in opposite directions cross paths.
Distance, pace, and time are the three fundamental components of movement and travel.
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if i have 5 fishes and 25 fisherman what would be the sqaure root
The square root representing in the statement is 25.
What is square root?In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4²= 16.
A square root of a number is a value that, when multiplied by itself, gives the number or a factor of a number that, when multiplied by itself, gives the original number.
Given that, if I have 5 fishes and 25 fishermen what would be the square root
We need to identify the squared number in the statement, in between 5 and 25 we know 25 = 5²
Which means, 25 is the square of 5
Or, 5x5 = 25
Hence, the answer square root number is 25
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what is a constant in math
A constant term in mathematics is a term in an algebraic equation whose meaning is constant or cannot change because it has no modifiable variables. For example, in the quadratic polynomial x² + 2x + 3 = 0, the term 3 is a constant.
Quadrilateral ABCD is translated to get quadrilateral A′B′C′D′. Vertex A is at (-5, 2), and vertex A′ is at (2, -2).
Quadrilateral ABCD is translated
. If vertex B is at (-6, 5), then vertex B′ is at
The vertex B' is at (1, 1)
How to find the calculation?Let's update the guidelines for translating a point.
The image of the point (x, y) is (x + h, y) T (x, y) (x + h, y) if the point (x, y) is translated horizontally to the right by h units.The image of the point (x, y) is (x - h, y) T (x, y) if the point (x, y) is translated horizontally to the left by h units (x - h, y)The image of the point (x, y) is (x, y + k) (x + h, y) T (x, y) (x, y + k) if the point (x, y) is translated vertically up by k units.The image of the point (x, y) is (x, y - k) T (x, y) if the point (x, y) is translated down vertically by k units (x, y - k)Let's apply the guidelines to resolve our issue.
Vertex A equals (-5, 2)
Vertex A' equals (2, -2)
The two points' coordinates changed, indicating that the
horizontal and vertical translations of a quadrilateral
A's x-coordinate is equal to -5.
A' has an x-coordinate of 2
Which indicates it goes to the right, therefore adhere to the first guideline presented above.
The translation formula is T (x, y) (x + h, y).
∴ x → x + h
x = -5, and x + h = 2.
∴ -5 + h = 2
Increase both sides by 5.
∴ -5 + 5 + h = 2 + 5
∴ h = 7
∴ The quadrilateral is moved seven units to the right.
A has a y-coordinate of 2
A"s y-coordinate is equal to -2.
Which means it descends, therefore apply the fourth rule listed above.
T (x, y) is the translational rule (x, y - k)
∴ y → y - k
Because y = 2 and y - k = -2,
∴ 2 - k = -2
Increase K on both sides.
∴ 2 - k + k = -2 + k
∴ 2 = -2 + k
Increase both sides by 2.
∴ 2 + 2 = -2 + 2 + k
∴ 4 = k
The quadrilateral is down four units.
Let's locate B.
T (x, y) (x + h, y - k) is the translational rule.
∵ B = (-6, 5) (-6, 5)
∵ h = 7 and k = 4
∴ B' = (-6 + 7, 5 - 4)
∴ B' = (1, 1) (1, 1)
Vertex B is located at (1, 1).
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Rather than being irrelevant or unhelpful, residuals in a simple linear regression model can be quite informative. Which of the following, in your opinion, residuals might indicate about the underlying population and the model?
Regression analysis will indicate about the underlying population and the model.
It is one of the most used and most powerful multivariate statistical techniques for it infers the existence and form of a functional relationship in a population. Once you learn how to use regression, you will be able to estimate the parameters { the slope and intercept } of the function that links two or more variables. With that estimated function, we will be able to infer or forecast things like unit costs, interest rates, or sales over a wide range of conditions.
Though the simplest regression techniques seem limited in their applications, statisticians have developed a number of variations on regression that greatly expand the usefulness of the technique. And again, the t-distribution and F-distribution will be used to test hypotheses.
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y varies inversely with the square root of x. When x=64, then y=12. Find y
when x=36
The value of y is 16.
Inverse proportionality:When one quantity's value increases compared to another's decrease or vice versa, it is said that the two are inversely proportionate.
It implies that the two quantities exhibit opposing behaviors in nature. For instance, the relationship between time and speed is inverse.
Inverse proportionality will be represented by the symbol '∝'. When two values x and y are Inverse proportional to each other then
x ∝ 1/y
Here we have
y varies inversely with the square root of x
=> [tex]y\propto\frac{1}{\sqrt{x} }[/tex]
=> [tex]y\ = \frac{k}{\sqrt{x} }[/tex]
=> [tex]\sqrt{x} y = k[/tex] ----- (1)
At x = 64, and y = 12
=> √64 × 12 = k
=> k = (8) × 12
=> k = 96
Thus the proportionality constant k = 96
Now Take x = 36 and k = 96 in equation (1)
=> √36 × y = 96
=> 6 × y = 96
=> y = 16
Therefore,
The value of y is 16.
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What is the monthly payment for a $11,000 loan for 6 years with an annual interest rate of 3.1%
The monthly payment for the $11,000 loan for 6 years with an annual interest rate of 3.1% is $181.20.
How to calculate the monthly payment?From the information, we have a $11,000 loan for 6 years with an annual interest rate of 3.1%. The interest will be:
= Principal × Rate × Time.
= $11000 × 3.1% × 6.
= $2046
The monthly payment will be:
= ($11000 + $2046) / (6 × 12)
= $13046 / 72
= $181.20
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The numbers below to put them in order from least to greatest: -19 13 -15 -8 -11 -13
The arrangement of the given numbers in ascending order is -19, -15, -13, -11, -8, 13
What is Ascending Order?
Ascending order refers to the arrangement of numbers in ascending order, from least to greatest. We must first compare numbers before we may arrange them in any order. Compare first, then order. Putting the numerals in ascending order: Count how many digits are in each number.
Solution:
Given the order is -19, 13, -15, -8, -11, -13
Arranging them in the Ascending Order
-19, -15, -13, -11, -8, 13
In the above arrangement the given numbers are arranged into ascending order
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Assuming the two clocks start synchronized, how much do sidereal and solar clocks differ after one day?
a. about 4 minutes
b. about an hour
c. about two hours
d. 24 hours
e. none of the above
If we assume the two clocks start synchronized , then the sidereal and solar clocks differ after one day , (a) about 4 minute .
What is Solar Day ?
The rotation period of the Earth with respect to the Sun, is called the solar day .
What is Sidereal Day ?
The sidereal day can be defined in terms of the rotation period of the Earth with respect to stars.
To complete a solar day, the Earth needs to rotate an additional amount, that is equal to 1/365 of a full turn.
So , the time required for this extra rotation will be 1/365 of a day, or about 4 minutes.
Hence , the solar day is about 4 minutes longer than the sidereal day.
Therefore , the correct option is (a) about 4 minutes .
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for the range c6:c41, create a new conditional format that changes the font color to red for values that are greater than or equal to 50.
The following steps would apply conditional formatting to the range:
Select the range of cells C6 : C41Click Conditional Formatting on the Home tabSet the conditionPoint to Color Scales, and then select the font color as red colorHow to apply the conditional formatting?The given parameters in the question are:
Range = C6 : C41Condition = cell that are greater than or equal to 50.Action = font color as red colorThe Conditional Formatting is located on the home tab
So, the first step to select the range and locate the Conditional Formatting option
Then set the necessary conditions and formats
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URGENT PLEASE ANSWER
Answer:
y = 371.17×1.15^x1135 in month 8Step-by-step explanation:
You want an exponential regression function for the data in the table.
a. Exponential regressionA regression function of most any kind can be found using a graphing calculator or spreadsheet. The attachment shows the function is approximately ...
y = 371.17 × 1.15^x
where y is the number sold, and x is the month.
b. Number soldUsing x=8, the predicted number sold for month 8 is ...
y = 371.17 × 1.15^8 ≈ 1135.4175 ≈ 1135
Sales for month 8 will be about 1135.
Cylinders A and B are similar solids. The base of cylinder A has a circumference of 47 units. The base of cylinder B
has an area of 97 units.
The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?
+/a N/mm/~ alt
The factor that produces the corresponding dimensions of cylinder B is: 3/2.
What are Similar Solids?Similar solids have the same shape but different sizes, and which means the ratio of their corresponding linear measurements are the same.
How to Find the Scale Factor of Similar Solids?To find the scale factor of similar solids, you can use the formula:
scale factor = (size of the similar solid) / (size of the original solid)
For example, if you have two similar solids, one with a volume of 64 cubic units and the other with a volume of 16 cubic units, the scale factor would be:
scale factor = (16 cubic units) / (64 cubic units) = 1/4
This means that the smaller solid is 1/4 the size of the larger solid.
Given the following:
Circumference of the base of cylinder A = 4π units [the radius = 2 units]
Area of the base of cylinder B = 9π units² [the radius = 3 units]
Scale factor = radius of the base of cylinder B / radius of the base of cylinder A
Scale factor = 3/2
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Complete Question:
Cylinders A and B are similar solids. The base of cylinder A has a circumference of 4π units. The base of cylinder B has an area of 9π units. The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?
how to interpret the slope? and what is the slope?
Answer:
100
Step-by-step explanation:
0 20 40 60 100
5. l
10. l
15. l
20. l
Mark all of the transformations that will result in the image changing size from the pre-image.
A Dilation of a scale factor of 0.25
B Rotation of 180 degrees.
c Reflection over the x-axis.
D Dilation of a scale factor of 3.
E Translation of 5 to the right and 3 up.
Answer:
Step-by-step explanation:
c
If the slant height of a triangular face of a square based pyramid of side
16cm is 17cm, find the volume of the pyramid.
Answer must be 1280 cube cm
Answer:
1280 cm³
I presume you are looking for the solution steps and these are below
Step-by-step explanation:
If the each side of the square pyramid is 16 and the slant height is 17, then the height of the pyramid, half the side and the slant edge form a right triangle.
The height of the pyramid can be computed using the Pythagorean theorem
Let a be each side, h the height and s the slant height
[tex]s^2 = h^2 + (a/2)^2\\\\\\s^2 = h^2 + \dfrac{a^2}{4}\\\\\textrm{Plugging in known values,}\\17^2 = h^2 + \dfrac{16^2}{4}\\\\289= h^2 + 64\\\\h^2 = 289 - 64\\\\h^2 = 225\\\\h = \sqrt{225} = 15\\\\[/tex]
The volume, V of a square pyramid of side a and height h is given by the formula:
[tex]V = \dfrac{1}{3}a^2h\\\\\\\textrm{Plugging in values,}\\\\V = \dfrac{1}{3}\cdot 16^2 \cdot 15\\\\[/tex]
[tex]V = \dfrac{1}{3} \cdot 256 \cdot 15\\\\V = 256 \cdot 5\\\\V = 1280[/tex]
The volume of the pyramid is 1280 cubic cm.
Given the slant height of the pyramid is 17 cm and the length of square base of the pyramid is 16 cm.
Now we know the volume of the pyramid with a square base = [tex]\frac{1}{3}[/tex]×area of the base×height.
So we need the values for area of the base and height of the pyramid.
Area of the square base=16×16 sq. cm.= 256 sq. cm.
Again we can apply the relation to find the value of height,
(Slant height)² = (Height)² + ([tex]\frac{1}{2}[/tex]×Length of the base)²
So, putting the values we get,
[tex](17)^2 = (height)^2 +(\frac{16}{2})^2[/tex]
⇒ [tex]289 = (height)^2+64[/tex]
⇒ [tex](height)^2= 225[/tex]
⇒ [tex]height = 15cm[/tex]
Now by appyling the volume of the pyramid we get,
Volume = [tex]\frac{1}{3} \times 256 \times 15[/tex] cubic cm. = 1280 cubic cm.
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Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠B1 is larger than ∠B2.)
a = 36, c = 44, ∠A = 31°
Possible triangles that satisfy the given conditions are:
Triangle 1: a = 36, b = 43.5, c = 44, A = 31, B = 63.5, C = 85.5
Triangle 2: a = 36, b = 27.5, c = 44, A = 31, B = 116.5, C = 33.5
What are the possible triangles that satisfy the given conditions?Generally, To use the Law of Sines to solve for the possible triangles that satisfy the given conditions, we need to know at least one additional angle or side length of the triangle. The Law of Sines states that:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the side lengths of the triangle and A, B, and C are the corresponding angles opposite those sides. Therefore, we need to know at least one additional angle or side length in order to use the Law of Sines to solve for the remaining sides and angles of the triangle.
If we let B1 and B2 be the two possible values of angle B, then we can use the Law of Sines to find the corresponding values of angles A1 and A2 and sides a1 and a2 as follows:
a1/sin(A) = c/sin(B1) a2/sin(A) = c/sin(B2)
Solving these equations for a1 and a2, we get:
a1 = c * sin(A) / sin(B1) a2 = c * sin(A) / sin(B2)
Since we are given that a = 36 and c = 44, we can substitute these values into the above equations to find the values of a1 and a2.
a1 = 44 * sin(31) / sin(B1) a2 = 44 * sin(31) / sin(B2)
Now, we can use the Law of Sines to find the corresponding values of angles A1 and A2.
A1 = arcsin(a1 * sin(B1) / c) A2 = arcsin(a2 * sin(B2) / c)
Substituting the values of a1 and a2 that we found earlier and the given value of c, we get:
A1 = arcsin(36 * sin(B1) / 44) A2 = arcsin(36 * sin(B2) / 44)
To find the possible values of angles B1 and B2, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Therefore, we have:
B1 + A1 + C1 = 180 degrees B2 + A2 + C2 = 180 degrees
Substituting the values of A1 and A2 that we found earlier, we get:
B1 + arcsin(36 * sin(B1) / 44) + (180 - 31 - B1) = 180 degrees B2 + arcsin(36 * sin(B2) / 44) + (180 - 31 - B2) = 180 degrees
Solving these equations for B1 and B2, we find that the possible values of B1 and B2 are:
B1 = 63.5 degrees B2 = 116.5 degrees
Therefore, the possible triangles that satisfy the given conditions are:
Triangle 1: a = 36, b = 43.5, c = 44, A = 31, B = 63.5, C = 85.5
Triangle 2: a = 36, b = 27.5, c = 44, A = 31, B = 116.5, C = 33.5
Note that these values should be rounded to one decimal place as requested.
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study smarter a scatterplot of versus shows a positive, nonlinear association. two different transformations are attempted to try to linearize the association: using the logarithm of the -values and using the square root of the -values. two least-squares regression lines are calculated, one that uses to predict and the other that uses to predict which of the following would be the best reason to prefer the least-squares regression line that uses to predict
The best reason to prefer the least-squares regression line that uses to predict is the Standard Deviation of the residuals is smaller.
Least Squares Regression:
Least squares is a mathematical technique that allows analysts to determine the best way to fit a curve to a graph of data points. It is commonly used to make scatterplots easier to interpret and is associated with regression analysis. Least squares is now available as part of most statistical software programs.
There are two least-squares regression lines, one to predict log(y) using x and the other to use for prediction.
a. A small value of means that the variance is explained poorly compared to the model that predicts instead, and thus the model is a poorer model. Therefore, there is no compelling reason to choose a model that predicts logic in.
b. If the standard deviation of the residuals is not too high, there will be less variability between the actual and predicted values, and thus the model will be more accurate. Therefore, there are compelling reasons to favor a model that predicts.
C. The magnitude of the slope has no effect on whether a model is good or bad, so it's not the best reason to favor a model that expects log y and x.
d. The presence of more random variation in the number of residuals does not necessarily indicate a superior model. The reason for this is that the variation between the expected and actual values is large, which can lead to large variability. This means that there is no compelling reason to prefer a model that uses to predict log y. It is normal that the distribution of residuals of residuals does not affect model quality. As a result, this is not the best reason.
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14. Which of these statements correctly describes the function y = 4x + 9?
A. It is not a linear function, and its graph is not a straight line.
B. It is a linear function, but its graph is not a straight line.
C. It is not a linear function, but its graph is a straight line.
D. It is a linear function, and its graph is a straight line.
Answer:
Step-by-step explanation:
because there is no change in slope. The graph will always be strait in this
Problem 3: Integration via the Substitution Method ( 16 points) Evaluate each of the following. Explain and show your work. You do not need to simplify your final answer. a)
(8
points
)∫ 0
3
ㅌㅣ
(2e 5t
+3) 2
3e 5t
dt
VALUE: b) (8 points)
∫( sin 2
(t 2
)+1
tcos(t 2
)
)dt
The value of the given integral [tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] is 2/75.
The given integral is [tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex].
We have to evaluate the given integral.
The given integral is definite integral. To evaluate the given integral we firstly solve the integral then we put the value in the solved integral to find the value.
We solving the integral [tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex]
Let u = 2e^{5t}+3
Now differentiating
du/dt = 10e^{5t}
e^{5t}dt = du/10
[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=\frac{3}{10}\int\frac{1}{u^2}dt[/tex]
[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=\frac{3}{10}\int{u^{-2}}dt[/tex]
[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = 3/10 [u^{-2+1}/(-2+1)]+C
[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = 3/10 [u^{-1}/(-1)]+C
[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10(1/u)+C
[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10(1/2e^{5t}+3)+C
Now;
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2e^{5t}+3}\right]^{\text{In}3/5}_{0}[/tex]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2e^{5({\text{In}3/5})}+3}-\frac{1}{2e^{5(0)}+3}\right][/tex]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2e^{({\text{In}3})}+3}-\frac{1}{2e^{0}+3}\right][/tex]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2\cdot3+3}-\frac{1}{2+3}\right][/tex]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{6+3}-\frac{1}{2+3}\right][/tex]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10[1/9 - 1/5]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10[5-9/45]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10[-4/45]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = 2/75
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The right question is:
Problem 3: Integration via the Substitution Method ( 16 points) Evaluate each of the following. Explain and show your work. You do not need to simplify your final answer.
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex]
A side of the equilateral triangle 'A' is twice the length of a side of
another equilateral triangle 'B'. How many triangles of 'B' will fit
into triangle 'A'?​
Total four triangles of B fit into triangle A as length of the equilateral triangle A is twice the length of triangle B.
As given in the question,
Types of triangles : Equilateral triangle
Number of triangle = 2
Triangle A and Triangle B
Let 'x' be the length of the triangle A
And 'y' be the length of the triangle B
As per given condition:
x = 2y
Area of equilateral triangle A = (√3/4)x²
Area of equilateral triangle B = (√3/4)y²
Now x = 2y
⇒Area of equilateral triangle A = (√3/4)(2y)²
⇒Area of equilateral triangle A = (√3/4)4y²
⇒Area of equilateral triangle A = 4 [(√3/4)y²]
⇒Area of equilateral triangle A = 4 ( area of equilateral triangle B)
Therefore, total number of four equilateral triangle of B fit into equilateral triangle A.
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Decide if the given value of x is a critical number for f, and if so, decide whether the point for x on f is a relative minimum, relative maximum, or neither.
f(x) = ( x + 5)^4; x = - 5
A. Critical number; maximum at (-5 , 0)
B. Critical number; minimum at (-5 , 0)
C. Not a critical number.
D. Critical number but not an extreme point.
The value of the function after evaluation is , f(x)=0 . Hence it is neither a minima nor a maxima.
f(x) =(x + 5)^4; x = - 5
=(-5+5)^4
=(0)^4
=0
The critical value is crucial for accurately portraying a range of properties in statistics. The critical value can be helpful for proving or disproving ideas when they are tested, in addition to validity and accuracy.
If you're taking a statistics course or are just interested in how these concepts work, it is essential to comprehend critical value and how to compute it before analyzing other statistical functions, such as margin of error and significance.
When calculating the margin of error for a set of data, statisticians utilize a measurement known as the critical value.
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