The experimental probability that the next customer buys a red notebook with 150 pages is 53/386 or 13.73%.
To find the experimental probability of the next customer buying a red notebook with 150 pages, we need to first identify the total number of red 150-page notebooks sold and then divide that by the total number of notebooks sold.
From the table, we can see that 53 red 150-page notebooks were sold. The total number of notebooks sold is 386.
The experimental probability is therefore the ratio of red 150-page notebooks sold to the total number of notebooks sold:
Probability = (Number of red 150-page notebooks) / (Total number of notebooks)
Probability = 53 / 386
The simplified fraction for the experimental probability is 53/386 or 13.73%.
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A buoy is floating in the water near a lighthouse. The height of the lighthouse is 18 meters, and the horizontal distance from the buoy to the base of the lighthouse is 45 meters. What is the approximate angle of elevation from the buoy to the top of the lighthouse, rounded to the nearest whole degree?
The equivalent expression is $\boxed{4^{15} \cdot 5^{10}}$.
Find out the simplified expression inside the parentheses?We can simplify the expression inside the parentheses first, using the rule that says when you raise a power to another power, you multiply the exponents:
$\left(\dfrac{4^{3}}{5^{-2}}\right)^{5} = \left(4^{3} \cdot 5^{2}\right)^{5}$
Now, we can use the rule that says when you raise a product to a power, you raise each factor to the power:
$\left(4^{3} \cdot 5^{2}\right)^{5} = 4^{3 \cdot 5} \cdot 5^{2 \cdot 5}$
Simplifying further:
$4^{3 \cdot 5} \cdot 5^{2 \cdot 5} = 4^{15} \cdot 5^{10}$
we can substitute this expression back into the original expression:
$\left(\dfrac{4^{3}}{5^{-2}}\right)^{5} = \left(4^{3} \cdot 5^{2}\right)^{5}$
To simplify this expression further, we can use the rule that says when you raise a product to a power, you raise each factor to the power:
$\left(4^{3} \cdot 5^{2}\right)^{5} = 4^{3 \cdot 5} \cdot 5^{2 \cdot 5}$
Simplifying the exponents, we get:
$4^{3 \cdot 5} \cdot 5^{2 \cdot 5} = 4^{15} \cdot 5^{10}$
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Determine the missing length in each right triangle using the Pythagorean theorem. Round the answer to the nearest tenth, if necessary
The evaluated missing length in right triangle by using the Pythagorean theorem is 9 yards under the condition given the triangle is a right triangle.
The Pythagoras theorem projects that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides,
It is given to us that in a right triangle,
Hypotenuse = 15 yd
Perpendicular = 12 yd
Therefore, applying Pythagoras theorem;
Base² = 15² - 12²
Base² = 225 - 144
Base² = 81
Base = √81
Base = 9 yards
Hence, The missing length present in the right triangle by applying the Pythagorean theorem is,
9 yards
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The complete question is
Determine the missing length in each right triangle using the Pythagorean theorem. Round the answer to the nearest tenth, if necessary
If Juan does not read any books before day 4 and he starts reading at the same
rate as Patti for the rest of the month, how many books will he have read by
day 12?
A. 5
B. 10
C. 15
D. 20
If Juan does not read any books before day 4 and he starts reading at the same rate as Patti for the rest of the month, he would have read 6 books by day 12. The correct option is A.
If Juan does not read any books before day 4, it means he has missed out on the opportunity to read for the first three days. Assuming Patti and Juan have been reading at the same rate since day 4, we can calculate the total number of books they would have read by day 12.
Patti reads one book per day, so by day 12, she would have read a total of 9 books (from day 4 to day 12). If Juan starts reading at the same rate as Patti from day 4, he would also have read 9 books by day 12.
However, we have to account for the fact that Juan did not read any books before day 4. This means that he missed out on the opportunity to read 3 books (one book per day for the first three days). Therefore, by day 12, Juan would have read a total of 6 books (3 books missed + 3 books read from day 4 to day 12).
Therefore, the answer is A. Juan would have read 5 books less than Patti by day 12, since Patti would have read a total of 9 books and Juan would have only read 6.
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Use undetermined coefficients to solve the nonhomogeneous equation
y″+11y′+28y=e^(5x)+x+4
a) write the characteristic equation of the associated homogeneous part by using the variable .
b) write the solution the associated homogeneous part, by using arbitrary constants 1 and 2 for 1 and 2. (note that: the order of the solutions are very important. you should write first 1 such that 1(−1/4)= and second 2 such that 2(−1/7)=.)
c) write the form of the any particular solution (we are using ,, etc. for undetermined coefficients for the correspoding functions in in the same order.):
and evaluate its derivatives and then found ″
d) thus evaluate the undetermined coefficients
e) finally write the general solution y=
a) The characteristic equation is r^2 + 11r + 28 = 0.
b) The associated homogeneous equation are y1(x) = c1e^(-4x) and y2(x) = c2e^(-7x).
c) The form of the particular solution is y_p(x) = Ae^(5x) + Bx + C.
d) By solving the system of equations, it gives A = 1/28, B = 1/28, and C = -211/196.
e) The general solution is y(x) = c1e^(-4x) + c2e^(-7x) + (1/28)e^(5x) + (1/28)x - 211/196.
a) The characteristic equation of the associated homogeneous equation is r^2 + 11r + 28 = 0.
b) Factoring the characteristic equation gives (r + 4)(r + 7) = 0, so the solutions to the associated homogeneous equation are y1(x) = c1e^(-4x) and y2(x) = c2e^(-7x).
c) The form of the particular solution is y_p(x) = Ae^(5x) + Bx + C. Taking the first and second derivatives of y_p(x) gives y_p'(x) = 5A + B and y_p''(x) = 0.
d) Substituting y_p(x), y_p'(x), and y_p''(x) into the original nonhomogeneous equation gives:
0 + 11(5A + B) + 28(Ae^(5x) + Bx + C) = e^(5x) + x + 4
Simplifying this equation gives:
(28A)e^(5x) + (28B)x + 11(5A) + 11B + 28C = e^(5x) + x + 4
Comparing coefficients gives the system of equations:
28A = 1
28B = 1
11(5A) + 11B + 28C = 4
Solving this system of equations gives A = 1/28, B = 1/28, and C = -211/196.
e) The general solution to the nonhomogeneous equation is y(x) = y_h(x) + y_p(x), where y_h(x) = c1e^(-4x) + c2e^(-7x) and y_p(x) = (1/28)e^(5x) + (1/28)x - 211/196. Therefore, the general solution is:
y(x) = c1e^(-4x) + c2e^(-7x) + (1/28)e^(5x) + (1/28)x - 211/196.
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Beatrice used a slingshot to launch an egg into the air. She recorded the egg’s path using a motion detector. The following data represents the height (in feet) of the egg at certain time points (in seconds): { ( 0.0 , 16 ) , ( 1.7 , 20.46 ) , ( 2.5 , 23.16 ) , ( 3.7 , 23.51 ) , ( 5.1 , 20.07 ) , ( 6.6 , 12.4 ) , ( 7.3 , 5.62 ) , ( 8.0 , 0.15 ) }
Step 4: Determine the height from which the egg was launched.
8 feet
3 feet
16 feet
0 feet
Answer:
mmm, well, not much we can do per se, you'd need to use a calculator.
I'd like to point out you'd need a calculator that has regression features, namely something like a TI83 or TI83+ or higher.
That said, you can find online calculators with "quadratic regression" features, which is what this, all you do is enter the value pairs in it, to get the equation.
Step-by-step explanation:
Let g(x.y)= 15x2 +2y2. Compute g(3,3), g(0,-2), and g(a,b). g(3,3)= _____
The function g(x, y) is defined as 15x^2 + 2y^2. To compute g(3,3), g(0,-2), and g(a,b), we substitute the given values into the function.
To find g(3,3), we substitute x = 3 and y = 3 into the function g(x, y) = 15x^2 + 2y^2:
g(3,3) = 15(3)^2 + 2(3)^2
g(3,3) = 135 + 18
g(3,3) = 153
To find g(0,-2), we substitute x = 0 and y = -2 into the function g(x, y) = 15x^2 + 2y^2:
g(0,-2) = 15(0)^2 + 2(-2)^2
g(0,-2) = 0 + 8
g(0,-2) = 8
To find g(a,b), we substitute x = a and y = b into the function g(x, y) = 15x^2 + 2y^2:
g(a,b) = 15a^2 + 2b^2
Note: The function g(a,b) cannot be simplified further without knowing the values of a and b.
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Can please write answer in box Please Thank you
Find the total differential. w = x15yz11 + sin(yz) = dw =
The total differential of w is given by dw = (∂w/∂x)dx + (∂w/∂y)dy + (∂w/∂z)dz + (∂w/∂z)(∂z/∂y)dy + (∂w/∂z)(∂z/∂z)dz.
Differentiation is a process of finding the changes in any function with a small change in By differentiation, it can be checked that how much a function changes and it also shows the way of change Differentiation is being used cost, production and other management decisions. It gives the rate of change independent variable with respect to the independent variable. First, let's get the partial derivatives of w with respect to x, y, and z: ∂w/∂x = 15x^14yz^11, ∂w/∂y = x^15z^11cos(yz), ∂w/∂z = 11x^15y^z^10 + x^15y^11cos(yz). Next, we need to find (∂w/∂z)(∂z/∂y): ∂z/∂y = cos(y)
So, (∂w/∂z)(∂z/∂y) = x^15y^11z^10cos(y). Substituting these values into the formula for the total differential, we get: dw = (15x^14yz^11)dx + (x^15z^11cos(yz))dy + (11x^15y^z^10 + x^15y^11cos(yz))dz + (x^15y^11z^10cos(y))dy
Simplifying, we get: dw = 15x^14yz^11dx + x^15z^11cos(yz)dy + (11x^15y^z^10 + x^15y^11cos(yz) + x^15y^11z^10cos(y))dz.
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If f(x) = x2 + 4x + 6, find the following values. = 1. f(a) = 2. f(a - 1) = 3. f(a + 1) =
To find the values of f(a), f(a-1), and f(a+1) when f(x) = x^2 + 4x + 6, So, the values are: f(a) = a^2 + 4a + 6, f(a-1) = a^2 + 6a + 3, f(a+1) = a^2 + 6a + 11.
we simply substitute the given values of a into the function.
1. f(a) = a^2 + 4a + 6
2. f(a-1) = (a-1)^2 + 4(a-1) + 6 = a^2 + 2a + 1 + 4a - 4 + 6 = a^2 + 6a + 3
3. f(a+1) = (a+1)^2 + 4(a+1) + 6 = a^2 + 2a + 1 + 4a + 4 + 6 = a^2 + 6a + 11
So, the values are:
1. f(a) = a^2 + 4a + 6
2. f(a-1) = a^2 + 6a + 3
3. f(a+1) = a^2 + 6a + 11
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Graph the points (–2.5,–3), (2.5,–4), and (5,0.5) on the coordinate plane.
The points are graphed on a coordinate plane and attached
What is a coordinate planeA coordinate plane, also known as a Cartesian plane, is a two-dimensional plane with two perpendicular lines that intersect at a point called the origin.
The horizontal line is called the x-axis and the vertical line is called the y-axis. The axes divide the plane into four quadrants.
Each point on the plane can be uniquely identified by a pair of coordinates (x, y), where x is the horizontal distance from the origin along the x-axis and y is the vertical distance from the origin along the y-axis.
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4 Find the value xa where the function is discontinuousFor the point of discontinuity, give (a) f) if it exists. (b) lm (0) Im . () im 16), and (ej identity which conditions for continuity are not man -O (Use a coma o separate answers as needed Select the choice below and necessary, tal in the trawer box within your choice ОА ка) OB) is undefined (b) Select the choice below and necessary, tu in the answer box within your chale ΟΑ. lim) OB lim does not exist
So, the answer is:
(a) f(x) does not exist at xa = 16.
(b) lim f(x) as x approaches 16 does not exist.
(c) None of the conditions for continuity are met at xa = 16.
To find the value of xa where the function is discontinuous, we need to look for any points where the function is undefined or where the left and right limits of the function are not equal.
(a) From the given information, we know that the function is undefined at xa = 16. So, this is the point of discontinuity.
(b) To find the left and right limits at xa = 16, we need to approach the point from both sides of the function. So,
lim f(x) as x approaches 16 from the left (denoted as lim-) = Im = 0
lim f(x) as x approaches 16 from the right (denoted as lim+) = Im = 16
Since the left and right limits are not equal, the limit as x approaches 16 does not exist. So,
lim f(x) as x approaches 16 (denoted as lim) does not exist.
(c) To determine which conditions for continuity are not met, we need to check if the function satisfies the three conditions for continuity at xa = 16.
i) The function must be defined at xa = 16. Since the function is undefined at xa = 16, this condition is not met.
ii) The left and right limits of the function must exist and be equal at xa = 16. Since the left and right limits are not equal, this condition is not met.
iii) The value of the function at xa = 16 must be equal to the limit of the function at xa = 16. Since the limit does not exist, this condition is also not met.
Therefore, none of the conditions for continuity are met at xa = 16.
So, the answer is:
(a) f(x) does not exist at xa = 16.
(b) lim f(x) as x approaches 16 does not exist.
(c) None of the conditions for continuity are met at xa = 16.
Note: The terms "discontinuous" and "continuity" are used throughout the explanation to describe the concept and the point of interest. The term "function" refers to the given function that we are analyzing.
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Please help! asap! (any accounts that give links will be reported)
⊙O and ⊙P are given with centers (−2, 7) and (12, −1) and radii of lengths 5 and 12, respectively. Using similarity transformations on ⊙O, prove that ⊙O and ⊙P are similar. Explain
We have shown that ⊙O and ⊙P are similar using similarity transformations.
To prove that ⊙O and ⊙P are similar using similarity transformations, we need to show that they have the same shape . Let's consider a dilation transformation with a scale factor of 2, centered at point A, which is the midpoint of the line segment connecting the centers of ⊙O and ⊙P:
1.Draw a line segment connecting the centers of ⊙O and ⊙P, and label the midpoint of this line segment as point A.
2.Draw two radii from the centers of ⊙O and ⊙P to a point B on the circumference of ⊙O, and label the intersection point of AB and ⊙P as point C.
3.Draw a perpendicular line from point A to BC, and label the intersection point as point D.
4.Since AD is the perpendicular bisector of BC, we have BD = DC.
5.By the properties of dilation, the length of any line segment on ⊙O is doubled when it is transformed by a dilation with a scale factor of 2 centered at A.
6.Therefore, the length of BD is doubled to become BE, and the length of DC is doubled to become CF.
7.Since ⊙O is transformed to a circle with center A and radius 10, and ⊙P is transformed to a circle with center A and radius 24, we can see that they have the same shape but different sizes.
Therefore, we have shown that ⊙O and ⊙P are similar using similarity transformations.
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Water flows into an empty reservoir at a rate of 3200+ 5t gal/hour. What is the quantity of water in the reservoir after 11 hours? Answer:_____ gallons.
To find the quantity of water in the reservoir after 11 hours, we need to integrate the rate of flow with respect to time from 0 to 11. The quantity of water in the reservoir after 11 hours is 38,225 gallons.
∫(3200 + 5t) dt from 0 to 11
= [(3200 * 11) + (5/2 * 11^2)] - [(3200 * 0) + (5/2 * 0^2)]
= 35,200 + 302.5
= 35,502.5 gallons
Therefore, the quantity of water in the reservoir after 11 hours is 35,502.5 gallons.
To find the quantity of water in the reservoir after 11 hours with the rate of 3200 + 5t gal/hour, we need to first find the total amount of water that flows into the reservoir within that time.
Step 1: Identify the given rate of flow: 3200 + 5t gal/hour.
Step 2: Integrate the flow rate function with respect to time (t) to find the total quantity of water. The integral of the function will give us the quantity of water in gallons:
∫(3200 + 5t) dt = 3200t + (5/2)t^2 + C, where C is the constant of integration.
Since the reservoir is initially empty, the constant C will be 0.
Step 3: Substitute t=11 hours into the integrated function to find the total quantity of water:
Q(11) = 3200(11) + (5/2)(11)^2
Q(11) = 35200 + 3025
Step 4: Add the values to find the total quantity of water in gallons:
Q(11) = 38225 gallons
The quantity of water in the reservoir after 11 hours is 38,225 gallons.
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how many times does five go into 6
Answer:
1 time, though your answer would be ongoing. If you the actual answer, it's 1.2
Step-by-step explanation:
Round to the nearest tenth.
Answer:
1.2
Step-by-step explanation:
Five can go into six 1.2 times because (1.2)(5)=6. Of course, if you want to know how many times five can go into 6 as a WHOLE, then the answer would obviously be 1.
Hope this helps a bit :)
true or false, Inflation occurs in an economy when there's a reduction in the total amount of money.
Answer:
False.
Inflation occurs in an economy when there is an increase in the overall price level of goods and services over time. It is usually caused by factors such as an increase in the money supply, higher demand for goods and services, or a decrease in the supply of goods and services. Therefore, a reduction in the total amount of money in an economy would generally lead to deflation, which is the opposite of inflation.
Find the error & explain why it is wrong:
megan solved the following problem. what did she do wrong?
what is (f - g)(2)?
f(x) = 3x2 – 2x + 4
g(x) = x2 – 5x + 2
The value of (f-g)(2) is 16, provided that Megan has made no mistakes in the calculation.
Find the error in the given problem solved by Megan?The problem asks us to compute the value of (f - g)(2) where f(x) = 3x^2 - 2x + 4 and g(x) = x^2 - 5x + 2.
The notation (f - g)(2) means that we need to subtract g(x) from f(x) and then evaluate the result at x = 2. We can do this as follows:
(f - g)(x) = f(x) - g(x) = (3x^2 - 2x + 4) - (x^2 - 5x + 2) = 2x^2 + 3x + 2
Substituting x = 2, we get:
(f - g)(2) = 2(2)^2 + 3(2) + 2 = 16
Therefore, the value of (f - g)(2) is 16.
It's worth noting that the problem statement mentions "what did she do wrong?" without providing any context or information about what Megan did or didn't do. So, it's not possible to identify any error in Megan's solution based on the given information. However, based on the correct computation above, we can be sure that (f - g)(2) is indeed equal to 16.
In other words, it can be described as,
The error in Megan's solution is not clear from the given statement. However, it seems that she may have made an error while computing (f-g)(2).
To compute (f-g)(2), we need to subtract g(2) from f(2) as follows:
f(2) = 3(2)^2 - 2(2) + 4 = 12
g(2) = (2)^2 - 5(2) + 2 = -4
Therefore, (f-g)(2) = f(2) - g(2) = 12 - (-4) = 16. is the final conclusion.
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A shoe store donated a percent of every sale to charity. The total sales were $7,200 so the store donated $144. What percent of $7,200 was donated to charity?
The percentage of $7,200 that was donated to charity would be = 2%
How to calculate the percentage of the total sales that was donated?To calculate the percentage of the total sales that was donated, the following should be carried out.
The total sales at the shoe store = $7,200
The amount of money that was donated = $144
Therefore to calculate the percentage the following is done ;
= 144/7200 × 100/1
= 14400/7200
= 2%
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I need help on the quesrion attached
A simplification of the expression [tex]\frac{x^3y^3 \cdot x^3 }{4x^2}[/tex] is [tex]\frac{x^4y^3 }{4}[/tex].
What is an exponent?In Mathematics, an exponent is a mathematical operation that is commonly used in conjunction with an algebraic equation or expression, in order to raise a given quantity to the power of another.
Mathematically, an exponent can be represented or modeled by this mathematical expression;
bⁿ
Where:
the variables b and n are numbers (numerical values), letters, or an algebraic expression.n is known as a superscript or power.By applying the division and multiplication law of exponents for powers of the same base to the given algebraic expression, we have the following:
[tex]\frac{x^3y^3 \cdot x^3 }{4x^2}=\frac{x^{3+3-2}y^3 }{4}\\\\\frac{x^{3+3-2}y^3 }{4}=\frac{x^4y^3 }{4}[/tex]
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Complete Question;
Simplify each of the expressions given.
Mr. Thayer wants to measure the height of the CN tower. He stands 320 m from the base of the tower. He uses an inclinometer to measure the angle from the (horizontal) ground to the top of the tower, and it is 60°. Assume Mr. Thayer's eyes are 1.6 m above the ground.
The height of the CN tower which is 320m away from the Mr.Thayer is 555.85 meters.
Please look at the attached diagram for a clear explanation,
From the diagram point A represents, the Mr.Thayer's eyes, point B represents Mr.Thayer's foot, point C represents the base of the CN tower along with point E represents the top of the tower.
From the following diagram lets find out the height of the tower,
In right-angled triangle ADE, Tan theta = opposite/adjacent
So, Tan (60°) = DE/AD
√3 = DE/320m
DE = 320m x √3
DE= 554.25m
DE represents the height of the CN tower from the eyes of Mr.Thayer.
To find out the total height of the CN tower, the height of Mr.Thayer + the height of the CN tower from Mr. Thayer's eyes = 554.25m + 1.6m = 555.85m.
From the above explanation, we can conclude that the height of the CN tower from the base = 555.85m.
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Grams of
Peanuts
Grams of
Raisins
14
4
21
6
35
10
Enter the number of grams of peanuts in a bag for every 1 gram of raisins.
For every 1 gram of raisins, there are 3.5 grams of peanuts in a bag.
To find the number of grams of peanuts for every 1 gram of raisins, you need to set up a ratio and solve for the missing value.
1. Set up the ratio: grams of peanuts / grams of raisins.
2. You are given three sets of values: (14, 4), (21, 6), and (35, 10).
For the first set (14, 4):
3. Calculate the ratio: 14 grams of peanuts / 4 grams of raisins = 3.5 grams of peanuts per 1 gram of raisin.
For the second set (21, 6):
4. Calculate the ratio: 21 grams of peanuts / 6 grams of raisins = 3.5 grams of peanuts per 1 gram of raisin.
For the third set (35, 10):
5. Calculate the ratio: 35 grams of peanuts / 10 grams of raisins = 3.5 grams of peanuts per 1 gram of raisin.
Your answer: For every 1 gram of raisins, there are 3.5 grams of peanuts in a bag.
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CAN SOMEONE HELP PLEASE!
A restaurant is serving a special lunch combo meal that includes a drink, a main dish, and a dessert. Customers can choose from 5 drinks, 6 main dishes, and 3 desserts.
How many different combo meals are possible?
Select from the drop-down menu to correctly complete the statement.
Customers can create (14, 39, 60, 120) different lunch combo meals.
Which of the data sets below have striking deviations? Select all that apply.
A) 65, 68, 61, 63, 71
B) 99, 95, 93, 97, 98
C) 22, 83, 85, 88, 91
D) 45, 47, 43, 45, 97
E) 72, 78, 71, 67, 35
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form Passing through (-9,2) and parallel to the line whose equation is y = – 3x + 3
The equation of the line in point-slope form is y - 2 = -3(x + 9), and in slope-intercept form is y = -3x - 25.
To find the equation of the line passing through(- 9,2) and parallel to the line y = – 3x 3, we need to use the fact that resemblant lines have the same pitch.
The pitch of the given line y = – 3x 3 is-3,
so the pitch of the resemblant line we want to find is also-3. Point- pitch form Using the point- pitch form, the equation of the line is given by
y- y1 = m( x- x1),
where( x1, y1) is the given point and
m is the pitch.
Substituting the given values,
we get y- 2 = -3( x-(- 9))
y- 2 = -3( x 9)
y- 2 = -3 x- 27
y = -3 x- 25
Hence in slope-intercept form is y = -3x - 25.
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Find the equation of a line that goes throught point -2,-5 and is parallel to y = x + 2
The equation of the line that goes through the point (-2, -5) and is parallel to y = x + 2 is y = x - 3.
To find the equation of a line that goes through the point (-2, -5) and is parallel to y = x + 2, we will follow these steps:
1. Identify the slope of the given line.
2. Use the slope and the given point to find the equation of the new line.
Step 1: Identify the slope of the given line.
The equation of the given line is y = x + 2. This is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, the slope (m) is 1, as it is the coefficient of x.
Step 2: Use the slope and the given point to find the equation of the new line.
Since the new line is parallel to the given line, it will have the same slope. Therefore, the slope of the new line is also 1.
Now, we will use the point-slope form of a linear equation, which is given by y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the given point.
Plugging in the values, we have:
y - (-5) = 1(x - (-2))
y + 5 = 1(x + 2)
Now, let's rewrite the equation in slope-intercept form:
y + 5 = x + 2
y = x + 2 - 5
y = x - 3
So, the equation of the line that goes through the point (-2, -5) and is parallel to y = x + 2 is y = x - 3.
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Quinn is a budding fashion designer known for incorporating geometry into her creations. Her newest design is a simple black blouse patterned with same-size right triangles in different funky colors. The longer leg of each right triangle will be twice as long as the shorter leg, and the hypotenuse of each triangle will be 6 inches long. To the nearest tenth of an inch, what will be the length of the shorter leg of each triangle?
To the nearest tenth of an inch, the length of the shorter leg of each right triangle will be 2.7 inches.
What is the triangle?A triangle is a polygon with three sides and three angles. The sum of the three angles in a triangle always adds up to 180 degrees. There are many different types of triangles, including equilateral triangles (where all three sides are equal in length and all three angles are 60 degrees), isosceles triangles (where two sides are equal in length and two angles are equal in measure), and scalene triangles (where no sides are equal in length and no angles are equal in measure).
According to the given informationLet x be the length of the shorter leg of each right triangle. Then, the longer leg will be twice as long, so its length will be 2x. Using the Pythagorean theorem, we can write:
x² + (2x)² = 6²
Simplifying and solving for x, we get:
x² + 4x² = 36
5x² = 36
x² = 7.2
x ≈ 2.7
Therefore, to the nearest tenth of an inch, the length of the shorter leg of each right triangle will be 2.7 inches.
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Which list correctwhich list correctly identifies the steps to solving a word problem?ly identifies the steps to solving a word problem?
There is no one definitive list of steps to solving a word problem, as different types of problems may require different approaches.
However, a general set of steps that can be useful in solving many word problems is:
1. Read the problem carefully to understand what it is asking.
2. Identify the relevant information and the unknown quantity you need to find.
3. Translate the problem into an equation or set of equations that relate the given information to the unknown quantity.
4. Solve the equation(s) to find the value of the unknown quantity.
5. Check your answer to make sure it makes sense in the context of the problem.
Additional steps or variations on these steps may be necessary depending on the specific problem, but this general framework can be a useful starting point.
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if a1=5 and an=an-1 -1 then find the value of a4
a4 = 2
It is given that,
[tex]a_{1} = 5[/tex], and
[tex]a_{n} = (a_{n-1}) - 1[/tex]
Therefore, it can be said,
[tex]a_{2} = a_{1} - 1\\a_{3} = a_{2} - 1\\a_{4} = a_{3} - 1\\[/tex]
That is,
[tex]a_{2} = 5-1=4\\a_{3} = 4-1=3\\a_{4} = 3-1=2[/tex]
So, a4 = 2
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What is the approximate length, in inches of the scrap wood when they are, placed end to end
Answer:
D. 53
Step-by-step explanation:
To calculate total length, just add all those lengths:
5.5 + 6 + (6.5 x 3) + (7 x 2) + 8
5.5 + 6 + 19.5 + 14 + 8
11.5 + 19.5 + 14 + 8
31 + 14 + 8
45 + 8
53
Which is a correct example of deductive reasoning?
A. Seven straight tosses of a number cube landed on 1. The next toss will land on 1.
B. Every bicyclist Lynn has seen was on a red bike. The next bicyclist Lynn sees will be on a red bike.
C. All rectangles have four sides. All squares are rectangles. Therefore, all squares have four sides.
D.
All tennis players are athletic. Erica is athletic. Therefore, Erica is a tennis player
C. All rectangles have four sides. All squares are rectangles. Therefore, all squares have four sides.
This is an example of deductive reasoning because it starts with a general statement (all rectangles have four sides) and then applies a specific example (squares are rectangles) to come to a logical conclusion (all squares have four sides).
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Each year Wenford Hospital records how long patients wait to be treated in the Accident
and Emergency department.
In 2015 patients waited 11% less time than in 2014.
In 2015 the average time patients waited was 68 minutes.
(a) Work out the average time patients waited in 2014.
Give your answer to the nearest minute.
The average time patients waited in 2014 was approximately 76 minutes, calculated by dividing the 2015 waiting time by 0.89 as patients waited 11% less time in 2015.
Let's call the average time patients waited in 2014 as per Wenford Hospital records "x" (in minutes). According to the problem statement, patients waited 11% less time in 2015 compared to 2014, so,
0.89x = 68
Solving for x,
x = 68 / 0.89
x ≈ 76.4
Therefore, the average time patients waited in 2014 was approximately 76 minutes (rounded to the nearest minute).
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Find the critical point and determine if the function is increasing or decreasing on the given intervals. y = x2 - 4x?, x>0 (Use decimal notation. Give your answer to three decimal places.) critical point c= _____
The critical point is c = 2, the function is decreasing on the interval 0 < x < 2, and increasing on the interval x > 2.
To find the critical point of the function y = x^2 - 4x, we first need to find its derivative, which represents the slope of the tangent line at any point on the curve.
The derivative of y with respect to x is:
y' = 2x - 4
Now, we need to find the critical points, which occur where the derivative is zero or undefined. In this case, the derivative is a polynomial, so it is never undefined. To find where it equals zero, we set y' equal to zero:
0 = 2x - 4
Solving for x, we get:
x = 4/2 = 2
So, the critical point is c = 2.
Now, we need to determine if the function is increasing or decreasing on the interval x > 0. To do this, we can analyze the sign of the derivative. If y' > 0, the function is increasing; if y' < 0, the function is decreasing.
For x > 2 (to the right of the critical point), the derivative y' = 2x - 4 is positive (since 2x > 4 when x > 2). Therefore, the function is increasing on the interval x > 2.
For x < 2 (to the left of the critical point), the derivative y' = 2x - 4 is negative (since 2x < 4 when x < 2). Therefore, the function is decreasing on the interval 0 < x < 2.
In summary, the critical point is c = 2, the function is decreasing on the interval 0 < x < 2, and increasing on the interval x > 2.
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