The area bounded by y = in(x)/x, y = 0, and x = e¹⁹ is 361/2 square units.
To find the area bounded by the curves y = ln(x)/x, y = 0, and x = e¹⁹, we need to integrate the function ln(x)/x with respect to x over the interval [1, e¹⁹].
∫[1, e¹⁹] ln(x)/x dx
To solve this integral, we use integration by parts with u = ln(x) and dv/dx = 1/x dx.
∫ ln(x)/x dx = ∫u dv = uv - ∫v du
where v = ln(x) and du/dx = 1/x dx.
∫ ln(x)/x dx = ln(x)^2/2 |[1, e¹⁹] - ∫[1, e¹⁹] (1/x)(ln(x)/2) dx
Evaluating the definite integral at the limits gives:
ln(e¹⁹)²/2 - ln(1)²/2 = 361/2
So the area bounded by the curves y = ln(x)/x, y = 0, and x = e¹⁹ is 361/2 square units.
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The coordinates of the vertices of △ABC are A(3,0), B(2,−3), and C(0,3). The coordinates of the vertices of △XYZ are X(1,0), Y(0,3), and Z(−2,−3). Which series of transformations correctly shows that △ABC≅△XYZ?
A: a translation 2 units down and a reflection over the x-axis
B: a translation 2 units up and a reflection over the y-axis
C: a translation 2 units right and a reflection over the y-axis
D: a translation 2 units left and a reflection over the x-axis
The series of transformations correctly shows that △ABC≅△XYZ is D
a translation 2 units left and a reflection over the x-axis.
How do you solve for the transformation?if a translation happens to each point of △ABC horizontally to the left by 2 units, which means subtracting 2 from the x-coordinate of each vertex, we notice that a transformation of ABC to coordinates that are almost identical to XYZ but let it be called it A'B'C'
A(3, 0) ⇒ A'(1, 0)
B(2, -3) ⇒ B'(0, -3)
C(0, 3) ⇒ C'(-2, 3)
Secondly, if a reflection happens to A'B'C' at the x axis the transformation becomes identical to △XYZ
A'(1, 0) ⇒ X(1, 0)
B'(0, -3) ⇒ Y(0, 3)
C'(-2, 3) ⇒ Z(-2, -3)
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if the circumference is 24 inches what is the radius
Answer:
3.819inch
Step-by-step explanation:
Circumference(C)=24inch
radius(R)=?
Now,
C=2piR
24=2piR
12=piR
12/pi=R
R=3.819
What is the probability of spinning a 1 or 2? Write your answer as a fraction AND decimal
Answer:
Probability of spinning 1 or a 2
Fraction=6/8
decimal=0.75
Let me know if it helped
Will mark brainliest (to whoever explains this clearly)
lizzie came up with a divisibility test for a certain number m that doesn't equal 1:
-break a positive integer n into two-digit chunks, starting from the ones place. (for example, the number 354764 would break into the two-digit chunks 64, 47, 35.)
- find the alternating sum of these two-digit numbers, by adding the first number, subtracting the second, adding the third, and so on. (in our example, this alternating sum would be 64-47+35=52.)
- find m, and show that this is indeed a divisibility test for m (by showing that n is divisible by m if and only if the result of this process is divisible by m).
Lizzie's divisibility test works for numbers that are multiples of 11.
How does Lizzie's divisibility test work?Lizzie's divisibility test for a number m works as follows: break a positive integer n into two-digit chunks, find the alternating sum of these two-digit numbers, and if the result is divisible by m, then n is also divisible by m.
For example, if we have a number n = 354764, we would break it into the two-digit chunks 64, 47, and 35, then find the alternating sum of these numbers (64 - 47 + 35 = 52).
If we want to test if n is divisible by m = 4, we check if 52 is also divisible by 4. If 52 is divisible by 4, then we can conclude that 354764 is also divisible by 4.
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Assuming an approximately normal data set, find the 68% confidence interval for systolic blood pressure in
women given a sample size of 1000 with a mean of 123.4 and a standard deviation of 19.9.
There is not enough evidence to conclude that Devon's true proportion of good serves is greater than 72%.
Find out the 68% confidence interval for systolic blood pressure in women from the given samples?The correct conclusion for Devon to reach is: Because the P-value of 0.06 > a (where a = 0.05), Devon should fail to reject H0. There is no convincing evidence that the proportion of services that are good is more than 72%.
The null hypothesis, H0, states that the true proportion of good serves for Devon is equal to 72%. The alternative hypothesis, Ha, states that the true proportion of good serves for Devon is greater than 72%.
The P-value is the probability of obtaining a test statistic as extreme or more extreme than the observed data, assuming that the null hypothesis is true. In this case, the P-value is 0.06, which means that if the true proportion of good serves for Devon is actually 72%, there is a 6% chance of observing a sample of 50 serves with 42 or more good serves.
Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.
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The 68% confidence interval for systolic blood pressure in women, based on the given sample, is approximate: (122.77, 124.03)
How to find a confidence interval for systolic blood pressure in women?To find the 68% confidence interval for systolic blood pressure in women, we can use the standard formula:
Confidence Interval = Mean ± (Z * (Standard Deviation / √n))
Where:
Mean = 123.4 (sample mean)
Standard Deviation = 19.9 (sample standard deviation)
n = 1000 (sample size)
Z = Z-score corresponding to the desired confidence level (in this case, 68% corresponds to 1 standard deviation on each side of the mean)
To find the Z-score, we can refer to the standard normal distribution table or use a calculator. For a 68% confidence level, the Z-score is 1.
Plugging in the values, we get:
Confidence Interval = 123.4 ± (1 * (19.9 / √1000))
Calculating the square root of 1000, we have:
Confidence Interval = 123.4 ± (1 * (19.9 / 31.62))
Simplifying further, we get:
Confidence Interval = 123.4 ± (0.6301)
Therefore, the 68% confidence interval for systolic blood pressure in women, based on the given sample, is approximate: (122.77, 124.03).
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Nancy's Cupcakes recorded how many cupcakes it recently sold of each flavor. â
â
âchocolate cupcakes 2
âpistachio cupcakes â 1
âbanana cupcakes â 5
âpumpkin cupcakes â 6
ââConsidering this data, how many of the next 21 cupcakes sold would you expect to be pumpkin cupcakes?â
A
9
B
7
C
6
D
3
Part B
What is probability of a chocolate cupcakes being sold?
â Probability (chocolate cupcakes) =
%
Note: Write your answer as a percentage rounded to the nearest whole number. â
We would expect 9 pumpkin cupcakes to be sold in the next 21 cupcakes. The probability of a chocolate cupcake being sold is approximately 14%.
The question asks to determine how many of the next 21 cupcakes sold would be expected to be pumpkin cupcakes, and also to find the probability of a chocolate cupcake being sold.
First, let's analyze the given data:
- Chocolate cupcakes: 2
- Pistachio cupcakes: 1
- Banana cupcakes: 5
- Pumpkin cupcakes: 6
Total cupcakes sold: 2 + 1 + 5 + 6 = 14
To find the expected number of pumpkin cupcakes in the next 21 sold, calculate the proportion of pumpkin cupcakes in the original data, and then multiply by 21:
(6 pumpkin cupcakes / 14 total cupcakes) * 21 = 9 (rounded)
So, we would expect 9 pumpkin cupcakes to be sold in the next 21 cupcakes (Answer A).
For Part B, we need to find the probability of a chocolate cupcake being sold. To do this, divide the number of chocolate cupcakes by the total number of cupcakes:
Probability (chocolate cupcakes) = (2 chocolate cupcakes / 14 total cupcakes) = 0.142857
Now, convert this probability to a percentage and round to the nearest whole number:
0.142857 * 100 = 14.29% ≈ 14%
So, the probability of a chocolate cupcake being sold is approximately 14%.
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Jon has 8 packets of soup in his cupboard, but all the labels are missing. he knows that there are 5 packets of tomato soup and 3 packets of mushroom soup. he opens three packets at random. work out the probability that all three packets are the same variety of soup.
Answer:
37.5%
Step-by-step explanation:
If all were the same from opening 3, it would all have to be mushroom soup. This would look like: desired outcome/total quantity: 3/8 = 0.375 = 37.5%
Qn in attachment . ..
Answer:
Step-by-the answer is (a) 16
The circle has Center O. It’s radius is 4cm, and the central angle a measures 140 degrees. what is the area of the shaded region. give the exact answer in terms of n , and be sure to include the correct unit in you’re answer
The area of the shaded region in term of π is 6.22π cm²
What is area of sector?A sector is a region or space bounded by two radii and an arc. There are two types of sector, the major sector and the minor sector. The of the sector is determined by the angle formed the two radii.
Area of sector = tetha/ 360 × πr²
where r is the radius of the circle.
= 140/360 × π × 4²
= 2240π/360
Area = 6.22 πcm²
Therefore the area of the shaded part is 6.22π cm²
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This system of equations has been placed in a matrix: y = 700x + 200
y = 5,000 − 75x
Complete the matrix by filling in the missing numbers
The completed matrix represents the system of equations in a convenient format for solving using matrix operations.
How to find the matrix ?The given system of equations has been represented in a matrix form, where the coefficients of the variables x and y and the constant terms are arranged in a matrix. To solve the system of equations, we can use matrix operations to isolate the variables and find their values. The completed matrix shows that the coefficient of x is 700, the coefficient of y is -200, and the constant term is 0 for the first equation. Similarly, the coefficient of x is -75, the coefficient of y is 200, and the constant term is 5000 for the second equation.
To solve this system using matrix operations, we can perform row operations to eliminate one of the variables. For example, we can multiply the first row by 75 and the second row by 200, and then add the two rows to eliminate x. This gives us a new system of equations with only one variable, which we can solve to find the values of x and y.
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What are the features of function gif g(x) = f(x + 4) + 8?
=
vertical asymptote of r = -4
x-Intercept at (1,0)
range of (8,00)
y-intercept at (0,10)
domain of (4,00)
The features of function gif g(x) = f(x + 4) + 8 is vertical asymptote of r = -4.
What is logarithm function?Since they enable us to convert an exponential equation into a logarithmic equation and vice versa, logarithmic functions are employed to solve equations involving exponents. They are also used in a variety of disciplines, including science, finance, and engineering.
Given equation:
g(x) = f(x + 4) + 8.
f(x) → f(x + 4)
Horizontal translation less 4 unit.
(x, y) → (x - y), y
f(x, y) + 8
Vertical translation up 4 unit.
(x, y) → (x, y + d)
f(x)
Vertical Asymptote x = 0,
f(x + 4) + 8
Vertical Asymptote x+ 4 = 0
x = -4
Therefore, the features of function gif g(x) = f(x + 4) + 8 is vertical asymptote of r = -4.
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Line segment RS is shown below with coordinates R(-8, -3)
and S(3, -3). Which coordinate below would represent R' if
point R was reflected across the x-axis?
A. (-8, 3)
B. (3, 3)
C. (8, -3)
D. (-3,-3)
10 9 8 7 6 5 4 3 2 1 1
R
2
4
-5
-6
10
•S.
S
Answer:
If point R is reflected across the x-axis, its y-coordinate will change sign. Therefore, the y-coordinate of R' will be 3 (the opposite of -3). Thus, the answer is A. (-8, 3)
Step-by-step explanation:
Evaluate the triple integral ∫∫∫ (x+8y)dV where E is bounded by the parabolic cylinder
y = 7x^2 and the planes
2 = 2x, y = 35x, and
2 = 0.
The triple integral ∫∫∫ (x+8y)dV where E is bounded by the parabolic cylinder is 512,604.17.
The triple integral is ∫∫∫(x+8y)dV.
Curves from the question are:
y = 7x², z = 2x, y = 35x, z = 0
Then, 7x² = 35x
Divide by x on both side, we get
7x = 35
Divide by 7 on both side, we get
x = 5
And z = 2x or z = 0. So
2x = 0
x = 0
Now the limits are:
x = 0 to x = 5
y = 7x² to y = 35x
z = 0 to z = 2x
Now the integral is
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\int_{7x^{2}}^{35x}\int_{0}^{2x}(x+8y)dzdydx[/tex]
Now first integrate with respect to z
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\int_{7x^{2}}^{35x}(x+8y)[z]_{0}^{2x}dydx[/tex]
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\int_{7x^{2}}^{35x}(x+8y)[2x-0]dydx[/tex]
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\int_{7x^{2}}^{35x}(2x^2+16xy)dydx[/tex]
Now integrate with respect to y
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\left[2x^2(y)_{7x^{2}}^{35x}+16x(\frac{y^2}{2})_{7x^{2}}^{35x}\right]dx[/tex]
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\left[2x^2(35x - 7x^2)+16x(\frac{1225x^2}{2}-\frac{49x^4}{2})\right]dx[/tex]
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\left[2x^2(35x - 7x^2)+8x(1225x^2-49x^4)\right]dx[/tex]
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\left[70x^3 - 14x^4+9800x^3-392x^5\right]dx[/tex]
∫∫∫(x+8y)dV = [tex]\left[\frac{70x^4}{4} - \frac{14x^5}{5}+\frac{9800x^4}{4}-\frac{392x^6}{6}\right]_{0}^{5}[/tex]
∫∫∫(x+8y)dV = [tex]\left[\frac{70(5)^4}{4} - \frac{14(5)^5}{5}+\frac{9800(5)^4}{4}-\frac{392(5)^6}{6}\right]-\left[\frac{70(0)^4}{4} - \frac{14(0)^5}{5}+\frac{9800(5)^4}{4}-\frac{392(5)^6}{6}\right][/tex]
∫∫∫(x+8y)dV = [10937.5 - 8750 + 1531250 - 1020833.33]-0
∫∫∫(x+8y)dV = 512,604.17
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The complete question is:
Evaluate the triple integral ∫∫∫(x+8y)dV where E is bounded by the parabolic cylinder.
y = 7x² and the planes
z = 2x, y = 35x, and
z = 0
If a 1. 5-volt cell is to be completely recharged, each electrion must be supplied with a minimum energy of
To completely recharge a 1.5-volt cell, each electron in the cell must be
supplied with a minimum energy of 2.403 × 10^-19 joules.
To completely recharge a 1.5-volt cell, each electron in the cell must be
supplied with an energy greater than or equal to the potential difference of
the cell, which is 1.5 volts.
The minimum energy required to supply to each electron can be
calculated
using the formula:
E = qV
where E is the energy in joules (J), q is the charge of an electron (1.602 ×
10^-19 coulombs), and V is the potential difference in volts.
Substituting the given values, we get:
[tex]E = (1.602 × 10^-19 C) × (1.5 V)E = 2.403 × 10^-19 J[/tex]
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Dixon made a $2,000 down payment on an $8,000 car. The down
payment was what percent of the price?
Answer:
25%
Step-by-step explanation:
one 4th of 8,000 is 2,000 convert it to a percent and there you go!
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The sum of the measurement of angle p and angle s is 140°.
• the measurement in degrees of angle p is represented by the expression (5x + 30)°
• the measure of angle s is 80°
What is the value of x?
A)38
B)6
C)10
D)22
Answer:
x=6
Step-by-step explanation:
(5x+30)+80=140
5x+110=140
5x=30
x=6
answer: B
(Dilations MC)
Triangle ABC with vertices at A(-3, -3), B(3, 3), C(0, 3) is dilated to create triangle A'B'C' with vertices at A(-6, -6), B(6, 6), C(0, 6). Determine the scale factor used.
02
1|2
03
-in
The scale factor used is 2.
What is triangle?It is one of the simplest polygon shapes and is commonly used in mathematics and geometry. The sum of the internal angles of a triangle is always 180 degrees.
Define vertices of triangle?The vertices of a triangle are the three points in a two-dimensional (2D) or three-dimensional (3D) space that define the corners or corners of the triangle. In a 2D plane, the vertices are typically denoted as A, B, and C, and in a 3D space, they can be represented as (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) where (x, y, z) are the coordinates of each vertex along the x, y, and z axes respectively. The vertices of a triangle are connected by three line segments, known as edges, to form the sides of the triangle. The combination of the three vertices and the edges connecting them determines the shape and size of the triangle.
To find the scale factor used to dilate triangle ABC to A'B'C', we can compare the corresponding side lengths of the two triangles.
The distance between A(-3, -3) and B(3, 3) is √((3-(-3))^2 + (3-(-3))^2) = 6√2.
The distance between A'(-6, -6) and B'(6, 6) is √((6-(-6))^2 + (6-(-6))^2) = 12√2.
So the scale factor used to dilate triangle ABC to A'B'C' is:
scale factor = length of corresponding side in A'B'C' / length of corresponding side in ABC
= (12√2) / (6√2)
= 2
Therefore, the scale factor used is 2.
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The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = negative 2 sine (pi (t one-half)) 5. which of the following equations can also model this situation? h = negative 2 cosine (pi t) 5 h = negative 2 cosine (pi (t one-half)) 5 h = 2 cosine (pi t) 5 h = 2 cosine (pi (t one-half)) 5
The correct answer for the equation is [tex]h = -2cos(\pi t) + 5[/tex] . The correct option is (1)
Given:
[tex]h= -2sin(\pi\tfrac{t}{2} )[/tex]
Examine the answer choices:
[tex]h = -2cos(\pi t) + 5[/tex]
Amplitude: |-2| = 2 (same as the given equation)
Frequency: π (same as the given equation)
Phase Shift: None (different from the given equation)
[tex]h = -2cos(\pi (t/2)) + 5[/tex]
Amplitude: |-2| = 2 (same as the given equation)
Frequency: π/2 (different from the given equation)
Phase Shift: None (different from the given equation)
[tex]h = 2cos(\pi t) + 5[/tex]
Amplitude: |2| = 2 (different from the given equation)
Frequency: π (same as the given equation)
Phase Shift: None (different from the given equation)
[tex]h = 2cos(\pi(t/2)) + 5[/tex]
Amplitude: |2| = 2 (different from the given equation)
Frequency: π/2 (different from the given equation)
Phase Shift: None (different from the given equation)
The correct equation is [tex]h = -2cos(\pi t) + 5[/tex] .The correct option is (1).
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what is the x-intercept of the graph of the function f(x) = x-16x + 64
The x-intercept of the function f(x) = x² - 16x + 64 is x = 8.
How to find the x-intercept of a graph?The x-intercept of the graph can be found as follows:
f(x) = x² - 16x + 64
The x-intercept is the point at which the graph of an equation crosses the x-axis. In other words, the x-intercept is where a line crosses the x-axis on a graph.
The x-intercept is the value of x when y = 0.
Therefore,
x² - 16x + 64 = 0
Let's factorise
x² - 8x - 8x + 64 = 0
x(x - 8) -8(x - 8) = 0
Therefore,
(x - 8)(x - 8) = 0
Therefore,
x = 8
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A local flooring company is retiling your kitchen. Your kitchen is a rectangle with dimensions of 7 ft by 15 ft. You are going to use square tiles that measure 6 by 6 inches. Assuming the tiles lay completely flush with one another on the floor (no space in between) How many tiles will the flooring company need to buy?
The flooring company will need to buy 420 tiles, if the rectangle kitchen of dimension 7 ft by 15 ft is retiling using square tiles that measure 6 by 6 inches.
First, we need to convert all the measurements to the same unit. We can convert the dimensions of the kitchen from feet to inches by multiplying by 12:
Length: 7 ft x 12 in/ft = 84 in
Width: 15 ft x 12 in/ft = 180 in
Next, we need to find the area of the kitchen in square inches:
Area = length x width = 84 in x 180 in = 15,120 sq in
Now, we can find the area of one tile in square inches:
Area of one tile = 6 in x 6 in = 36 sq in
Finally, we can divide the area of the kitchen by the area of one tile to find the total number of tiles needed:
Number of tiles = Area of kitchen / Area of one tile
Number of tiles = 15,120 sq in / 36 sq in = 420
Therefore, the flooring company will need to buy 420 tiles.
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1. A tree was cut down. What 3D shape does it closely resemble?
A. Prism
B. Pyramid
C. Cylinder
D. Cone
2. A ball with radius 5. 5 cm fits tightly inside a cube. Find the volume of the
unoccupied space inside the cube. Round to the nearest cm.
A. 531
B. 166
C. 697
D. 634
The volume of the unoccupied space inside the cube is the volume of the cube minus the volume of the ball, which is approximately 166.
1. D. Cone. When a tree is cut down, its trunk typically has a roughly cylindrical shape with a tapered end, which closely resembles a cone.
2. B. 166. The diameter of the ball is 11 cm, which is also the length of the diagonal of the cube. Let's call the side length of the cube "s". Then, we can use the Pythagorean theorem to find s:
s^2 + s^2 + s^2 = 11^2
3s^2 = 121
s^2 = 121/3
The volume of the cube is s^3, which is approximately 166. The volume of the ball is (4/3)πr^3, where r is the radius of the ball. Since the ball fits tightly inside the cube, its diameter is equal to the side length of the cube, which is s√3. Thus, r = (s√3)/2 - 5.5.
The volume of the unoccupied space inside the cube is the volume of the cube minus the volume of the ball, which is approximately 166.
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Find the diameter of a circle with a circumference of 63 feet. Round your answer to the nearest thousandth.
Answer: 20.054
Step-by-step explanation:
D = 2R
R = (C/2π)
Let f(x)= 3x and g(x)= 3(x+1)^2. Find (fg)(x) and (f/g)(x).
State the domain of each.
Evaluate the following: (fg)(5) and (f/g)(5)
The value of the domains is given as:
(fg)(5) equals 1620 (f/g)(5) is equivalent to 5/36.How to solveIn order to find the results of (fg)(x) and (f/g)(x), we must begin by multiplying and dividing the two functions, respectively:
(fg)(x) = f(x) * g(x) = [tex]3x * 3(x + 1)^2 = 9x(x + 1)^2[/tex]; its domain containing all real numbers.
Similarly, (f/g)(x) = f(x) / g(x) = in a domain that does not [tex]3x / 3(x + 1)^2 = x / (x + 1)^2[/tex]include x = -1 (if g(x) ≠ 0).
Let us now evaluate (fg)(5) and (f/g)(5):
(fg)(5) =[tex]9(5)(5 + 1)^2 = 9(5)*(6)^2[/tex] = 9(5(36)) = 1620 while
(f/g)(5) = [tex]5/(5 + 1)^2 = 5/(6)^2[/tex] = 5/36.
Consequently, (fg)(5) equals 1620 and (f/g)(5) is equivalent to 5/36.
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Simplify rational ( trinomial only)
Simplify the following expression completely.
Answer: [tex]\frac{x-4}{x-7}[/tex]
Step-by-step explanation:
[tex]\frac{x^{2}-5x+4 }{x^{2} -8x+7}[/tex]
factor the top and bottom by finding numbers that multiply to the last term but add to middle
for top part:
-4 and -1 multiply to +4 and add to -5
for bottom part:
-7 and -1 multiply to to +7 and add to -8
Those are your factored numbers, put into factored form
[tex]\frac{(x-4)(x-1)}{(x-7)(x-1)}[/tex] now cross off same factors from top and bottom only
[tex]\frac{x-4}{x-7}[/tex]
HELP! WILL GIVE BRAINLEST! An angle of 1. 5 rad intercepts an arc on the unit circle. What is the length of the intercepted arc?
The length of the intercepted arc on the unit circle is equal to the radius of the circle times the angle in radians. In this case, since the unit circle has a radius of 1, the length of the intercepted arc is simply equal to the angle in radians.
So, the length of the intercepted arc for an angle of 1.5 radians is 1.5 units (since the angle is given in radians, not degrees).
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A new car is purchased for 29,000 and over time it’s value depreciates by one half every 3. 5 years what is the value of the car 20 years after it was purchased to the nearest hundred dollars
The required answer is the nearest hundred dollars: $902.09 is approximately $900.
To find the value of the car 20 years after it was purchased, we can use the formula for exponential decay:
Value = Initial value * (1 - Depreciation rate) ^ (time elapsed / time for depreciation)
1. Determine the depreciation rate: The car's value depreciates by one half every 3.5 years, so the depreciation rate is 50% or 0.5.
Depreciation is a term that refers to two aspects of the same concept: first, the actual decrease of fair value of an asset, such as the decrease in value of factory equipment each year as it is used and wears, and second, the allocation in accounting statements of the original cost of the assets to periods in which the assets are used (depreciation with the matching principle).
Depreciation is thus the decrease in the value of assets and the method used to reallocate, or "write down" the cost of a tangible asset (such as equipment) over its useful life span
2. Calculate the number of depreciation periods: Since the car's value halves every 3.5 years, we need to find out how many 3.5-year periods are in 20 years. To do this, divide 20 by 3.5: 20 / 3.5 ≈ 5.71 periods.
3. Use the exponential decay formula:
Value = 29,000 * (1 - 0.5) ^ (5.71)
Value ≈ 29,000 * (0.5) ^ (5.71)
Value ≈ 29,000 * 0.0311
Value ≈ 902.09
4. Round the value to the nearest hundred dollars: $902.09 is approximately $900.
So, the value of the car 20 years after it was purchased is approximately $900.
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Question: Nora needs to cut some equal pieces of yarn for her Science project. The piece of yarn she has is 67. 6 inches long. Each piece of yarn must be 1. 3 inches in lenght. How many pieces of yarn will Nora have.
Nora will be able to cut 52 equal pieces of yarn for her Science project.
To find out how many equal pieces of yarn Nora can cut for her Science project, we need to divide the total length of the yarn by the length of each piece.
Total length of yarn: 67.6 inches
Length of each piece: 1.3 inches
Step 1: Divide the total length by the length of each piece.
67.6 inches ÷ 1.3 inches = 52
Nora will have 52 equal pieces of yarn, each 1.3 inches long, for her Science project.
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A function is a rule that assingns each value of independent variable to exactly value of the dependent variable
A function is a rule that assingns each value of independent variable to exactly one value of the dependent variable.
A function is a mathematical concept that relates two sets of values, known as the domain and the range. The domain is the set of independent variables, while the range is the set of dependent variables. A function is a rule that assigns to each value in the domain exactly one value in the range.
For example, if we have a function f(x) = 2x + 3, the domain would be any possible value of x, and the range would be any possible value of 2x + 3. So if we put x = 2, then f(x) = 2(2) + 3 = 7. Therefore, the function assigns the value of 7 to the value of 2 in the domain.
Functions are used in various branches of mathematics, science, and engineering to model and analyze relationships between two or more variables. They are an important concept in calculus, where they are used to study rates of change and optimization problems.
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Help please!
the elevation of death valley, california is -282 feet. the elevation of tallahassee, florida is 203 feet. the elevation of westmorland, california is 157 feet.
1: compare the elevations of death valley and tallahassee using > or <.
2: compare the elevations of death valley and westmorland.
The elevation of Death Valley, California and Tallahassee, Florida can be compared by using the inequality symbol > or <. On comparing death valley and tallahassee, Tallahassee elevation > Death Valley elevation. On comparing death valley and westmorland, Westmorland elevation > Death Valley elevation.
1.
Since the elevation of Death Valley is -282 feet, which is a negative value, and the elevation of Tallahassee is 203 feet, which is a positive value, we can conclude that the elevation of Tallahassee is greater than the elevation of Death Valley.
Therefore, we can use the > symbol to compare the elevations of these two locations, and write the inequality as: Tallahassee elevation > Death Valley elevation.
2.
The elevation of Death Valley is -282 feet, while the elevation of Westmorland is 157 feet.
Since the elevation of Westmorland is a positive value and is greater than the elevation of Death Valley, we can use the > symbol to compare the elevations of these two locations, and write the inequality as:
Westmorland elevation > Death Valley elevation.
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If 2/3 of a mini pizza cost $2. 40, what would 1/2 of a mini pizza cost?
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
1/2 of a mini pizza would cost $0.60.
If 2/3 of a mini pizza cost $2.40, then 1/3 of a mini pizza would cost half of that:
1/3 of a mini pizza = 1/2 * $2.40 = $1.20
To find the cost of 1/2 of a mini pizza, we can divide the cost of 1/3 of a mini pizza by 2:
1/2 of a mini pizza = 1/2 * $1.20 = $0.60
Therefore, 1/2 of a mini pizza would cost $0.60.
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