We have found a value of b that makes y(t) = [tex]e^2t[/tex] [1; 4; -1/2] a solution of y′ = [4 1 3; 2 3 3; −2 −1 −1]y. To check if y(t) is a solution of y′ = Ay, we need to substitute it into the differential equation and see if it holds.
Let's start by finding y′:
y′(t) = [[tex]2e^2t, 8e^2t, 4be^2t[/tex]]
Now, let's find Ay:
Ay = [4 1 3; 2 3 3; −2 −1 −1] [1; 4; b] = [4+4b; 14; -5-b]
We want y(t) = e^2t [1; 4; b] to satisfy y′ = Ay, so we set them equal:
y′ = Ay
[[tex]2e^2t; 8e^2t; 4be^2t] = [4+4b; 14; -5-b] e^2t[/tex] [1; 4; b]
Expanding this equation, we get:
[tex]2e^2t[/tex]= (4+4b)[tex]e^2t[/tex]
[tex]8e^2t[/tex] = 14 [tex]e^2t[/tex]
[tex]4be^2t[/tex]= (-5-b) [tex]e^2t[/tex]
The second equation is always true, so we can ignore it. For the first equation, we can cancel out [tex]e^2t[/tex] on both sides to get:
2 = 4+4b
Solving for b, we get:
b = -1/2
Finally, we can substitute b = -1/2 back into the third equation to check if it holds:
4be^2t = (-5-b) [tex]e^2t[/tex]
-2e^2t = (-5 + 1/2)[tex]e^2t[/tex]
This equation is true, so we have found a value of b that makes y(t) = [tex]e^2t[/tex] [1; 4; -1/2] a solution of y′ = [4 1 3; 2 3 3; −2 −1 −1]y.
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If the peaches are placed on a scale that can mesure weight to the nearest thousandth of a pound wouls you expectt the scale to show the weight of 4. 168 pounds or 4. 158 pounds
The scale would show the weight that is closest to the actual weight of the peaches, whether it is 4.158 or 4.168 pounds.
What is measurement?
Measurement is the process of assigning numerical values to physical quantities such as length, mass, time, temperature, and many others.
It depends on the actual weight of the peaches. If the weight of the peaches is closer to 4.158 pounds, then the scale would show 4.158 pounds. Similarly, if the weight of the peaches is closer to 4.168 pounds, then the scale would show 4.168 pounds.
Since the scale can measure weight to the nearest thousandth of a pound, it can differentiate between weights that differ by one-thousandth of a pound.
Therefore, the scale would show the weight that is closest to the actual weight of the peaches, whether it is 4.158 or 4.168 pounds.
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The lengths of manufactured nails are distributed normally, with a mean length of 6cm, which has a standard deviation of 2mm. what is the length for which 98% of the nails will be longer?
Answer:
The length for which 98% of the nails will be longer is approximately 6.466 cm.
Step-by-step explanation:
First, we need to convert the units of the standard deviation to centimeters, since the mean is also given in centimeters. 2 mm is equal to 0.2 cm.
Next, we need to find the z-score that corresponds to the 98th percentile. We can use a standard normal distribution table or calculator to find this value. The z-score corresponding to the 98th percentile is approximately 2.33.
Finally, we can use the formula for a z-score to find the length of nail corresponding to this z-score:
z = (x - μ) / σwhere:
z = 2.33μ = 6 cmσ = 0.2 cmSolving for x, we get:
2.33 = (x - 6) / 0.2x - 6 = 0.2 * 2.33x - 6 = 0.466x = 6.466Therefore, the length for which 98% of the nails will be longer is approximately 6.466 cm.
Geographers use satellites in order to:
A. Capture detailed images of a location from space?
B. Collect and store digital information about a location?
C. Track the location of moving objects on Earth?
D. Organize and represent data for a location?
Answer:
Step-by-step explanation:
Geographers use satellites primarily to capture detailed images of a location from space (option A). These images can provide valuable information about the landscape, climate, and natural resources of an area, among other things. Additionally, satellites can be used in combination with other technologies to collect and store digital information about a location (option B), such as mapping the distribution of vegetation or tracking changes in land use over time. While satellites can be used to track the location of moving objects on Earth (option C), this is not typically their primary function. Finally, organizing and representing data for a location (option D) is more closely associated with Geographic Information Systems (GIS) than with satellite technology specifically.
Answer:
A. Capture detailed images of a location from space.
Step-by-step explanation:
Geographers use satellites to capture high-resolution images of the Earth's surface from space. This enables them to study and analyze different aspects of the Earth, such as its topography, land use patterns, and weather systems. These images are also used in cartography, the science of map-making, to create accurate and up-to-date maps of the Earth's surface.
3.72÷ 10 4 which of these shows and explains the correct location of the decimal point when the expression is evaluated?
a 0.0000372 because 4 zeros are placed in front of the number when you divide by 104 b 0.000372 because the decimal point moves 4 places to the left when you divide by 104 c 37,200 because the decimal point moves 4 places to the right when you divide by 104 d 3,720,000 because 4 zeros are placed after the number when you divide by 104
The correct location of the decimal point when the expression 3.72 divided by 10⁴ is evaluated is: 0.000372 because the decimal point moves 4 places to the left when you divide by 10 to the fourth power. The correct option is B.
To evaluate this expression, we need to move the decimal point 4 places to the left, since the exponent is positive.
Option A is incorrect because placing 4 zeros in front of the number would give us a much smaller value than the original number. Option B is correct because moving the decimal point 4 places to the left would give us 0.000372, which is equivalent to 3.72 divided by 10⁴.
Option C is incorrect because moving the decimal point 4 places to the right would give us a much larger value than the original number. Option D is also incorrect because placing 4 zeros after the number would give us a value that is 10,000 times larger than the original number.
Therefore, the correct answer is B, which shows and explains the correct location of the decimal point when the expression 3.72 divided by 10⁴ is evaluated. The correct option is B.
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Complete question:
3.72 divided by 10⁴ which of these shows and explains the correct location of the decimal point when the expression is evaluated?
A 0.0000372 because 4 zeros are placed in font of the number when you divide by 10 to the fourth power
B 0.000372 because the decimal point moves 4 places to the left when you divide by 10 to the fourth power
C 37,200 because the decimal point moves for places to the right when you divide by 10 to the fourth power
D 3,720,00 because 4 zeros are placed after the number when you divide by 10 to the fourth power
Paul has decided to take a trip to the united kingdom. while he is there, he hopes to visit several different cities, which are shown in the table below. the table also includes how much money paul expects to spend in each city, taking into consideration transportation, lodging, and so on. all costs listed are in pounds sterling (£). city cost (£) bristol 76 leicester 66 glasgow 91 leeds 60 belfast 72 paul’s sightseeing budget is £300. what is the cheapest city that paul can drop from his plans and still stay under budget? a. leicester b. leeds c. bristol d. belfast
Bristol is the cheapest city and Paul can drop from his plans to stay under budget.
To determine which city Paul can drop and still stay under budget, we need to find the total cost of visiting all four cities and compare it to Paul's budget of £300.
We do not have information about the cost of sightseeing in each city, so we will assume that the cost is the same for each city. In that case, the cost of visiting all four cities is:
Cost of visiting all cities = Cost of visiting one city x 4
Let's call the cost of visiting one city "x". Then:
Cost of visiting all cities = x * 4
To stay under budget, the cost of visiting all cities must be less than or equal to £300. So we can write the following inequality:
Simplifying this inequality, we get:
x ≤ £75
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The answer is (c) Bristol, as it has the highest cost among the remaining cities and dropping it would leave Paul with 224 pounds, which is still within his budget.
What is budget?A budget is whenever one plans on how to spend an estimated income. All the income should be considered as well as all the expenses. In other words, it is an expending plan.
The total cost of visiting all cities is:
76 + 66 + 91 + 60 + 72 = 365
To stay under budget, Paul must drop at least one city. To determine the cheapest city to drop, we can calculate the cost of the trip to each city if visited individually and compare it to the remaining budget:
- Bristol: 76 pounds
Remaining budget: 300 - 76 = 224 pounds
- Leicester: 66 pounds
Remaining budget: 300 - 66 = 234 pounds
- Glasgow: 91 pounds
Remaining budget: 300 - 91 = 209 pounds
- Leeds: 60 pounds
Remaining budget: 300 - 60 = 240 pounds
- Belfast: 72 pounds
Remaining budget: 300 - 72 = 228 pounds
The city that Paul can drop while staying under budget is the one with the lowest cost.
Therefore, the answer is (c) Bristol, as it has the highest cost among the remaining cities and dropping it would leave Paul with 224 pounds, which is still within his budget.
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Consider the function f(x,y,z) = 1 + 2xyz, the point P(-1,-1,-1), and the unit vector u = (1/√3, -1/√3, -1/√3)
a. Compute the gradient off and evaluate it at P. b. Find the unit vector in the direction of maximum increase off at P.
The unit vector in the direction of maximum increase of f(x,y,z) at P is:
v = (∇f(-1,-1,-1)) / ||∇f(-1,-1,-1)|| = (2/2√3, 2/2√3, 2/2√3) = (√3/3, √3/3, √3/3)
a. The gradient of f(x,y,z) is given by the vector ∇f(x,y,z) = (∂f/∂x, ∂f/∂y, ∂f/∂z). Using the partial derivative rules, we have:
∂f/∂x = 2yz
∂f/∂y = 2xz
∂f/∂z = 2xy
Therefore, the gradient of f(x,y,z) is:
∇f(x,y,z) = (2yz, 2xz, 2xy)
Evaluating this at P(-1,-1,-1), we get:
∇f(-1,-1,-1) = (2(-1)(-1), 2(-1)(-1), 2(-1)(-1)) = (2,2,2)
b. The unit vector in the direction of maximum increase of f(x,y,z) at P is given by the unit vector in the direction of ∇f(-1,-1,-1). Since ∇f(-1,-1,-1) = (2,2,2), the unit vector in the direction of ∇f(-1,-1,-1) is:
v = (∇f(-1,-1,-1)) / ||∇f(-1,-1,-1)||
where ||∇f(-1,-1,-1)|| is the magnitude of the gradient vector, which is:
||∇f(-1,-1,-1)|| = sqrt((2)^2 + (2)^2 + (2)^2) = 2√3
Therefore, the unit vector in the direction of maximum increase of f(x,y,z) at P is:
v = (∇f(-1,-1,-1)) / ||∇f(-1,-1,-1)|| = (2/2√3, 2/2√3, 2/2√3) = (√3/3, √3/3, √3/3)
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Find two vectors in opposite directions that are orthogonal to the vector u.
u = 1/4 i - 4/5j
Two vectors in opposite directions that are orthogonal to u are v = 5i + 4j and w = -4i + 5j.
To find two vectors in opposite directions that are orthogonal to u, we need to use the cross product. The cross product of two vectors is a vector that is perpendicular to both of them. We can choose any two non-collinear vectors as long as they are orthogonal to each other and the given vector.
Let's find the cross product of u and a vector v. The cross product of two vectors a and b is given by:
a x b = |a| |b| sinθ n
where |a| and |b| are the magnitudes of the vectors, θ is the angle between them, and n is a unit vector perpendicular to both a and b in the direction given by the right-hand rule.
Since we want v to be orthogonal to u, we need to choose v such that u x v = 0. This means that the angle between u and v is either 0 or 180 degrees, and |v| is arbitrary.
Let v = 5i + 4j. Then, we have:
u x v = (1/4 i - 4/5j) x (5i + 4j)
= (-16/20)i - (5/20)j + (1/20)k
= (-4/5)i - (1/4)j + (1/20)k
Since u x v is not equal to zero, v is not orthogonal to u. To find another vector that is orthogonal to u, we can take the cross product of u and w, where w = -4i + 5j. Then, we have:
u x w = (1/4 i - 4/5j) x (-4i + 5j)
= (-5/20)i + (16/20)j + (1/20)k
= (-1/4)i + (4/5)j + (1/20)k
Since u x w is also not equal to zero, we need to adjust the signs of v and w to make them orthogonal to u. We can do this by taking the opposite of v and w. Therefore, two vectors in opposite directions that are orthogonal to u are v = 5i + 4j and w = -4i + 5j.
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Homeowners in different parts of the country heat their homes with liquid propane gas. The gas is stored in tanks similar to the one shown. In terms of Pi , what is the volume of the gas tank, to the nearest hundredth cubic foot?
The volume of the gas tank is given as follows:
V = 15.19π ft³.
How to obtain the volume of the cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
The dimensions for this problem are given as follows:
r = 1.5 ft -> as it is half the diameter of 3 ft.h = 6.75 ft.Hence the volume of the tank is given as follows:
V = π x 1.5² x 6.75
V = 15.19π ft³.
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A funnel is in the shape of a cone with a radius of 4 inches and a height of 10 inches.
a. Find the volume of the funnel. Round your answer to the nearest tenth.
b. The funnel is filled with oil. How many quarts of oil are in the funnel? (1 qt ≈ 58 in. ³) Round your answer to the nearest tenth
a. The volume of the funnel is 167.6 in³.
b. The amount in quarts of oil are there in the funnel is approximately 2.9 quarts.
a. To find the volume of a cone, you can use the formula V = (1/3)πr²h, where r is the radius and h is the height. Substituting in the values given, we get V = (1/3)π(4 in)²(10 in) ≈ 167.6 in³. Rounded to the nearest tenth, the volume of the funnel is 167.6 in³.
b. To convert cubic inches to quarts, we need to divide by the conversion factor of 58 in³/qt. So, V = 167.6 in³ ÷ 58 in³/qt ≈ 2.9 qt. Rounded to the nearest tenth, there are approximately 2.9 quarts of oil in the funnel.
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GEOMETRY HELP COSINE, SINE TANGENT
please help y’all i have no idea what i am doing
Answer:
31.33 degrees
Step-by-step explanation:
The question is asking to find angle x. You can use sine to find out x because sine is opposite/hypotenuse but since you are finding an angle measurement, it would be to the power of -1. So:
sine^-1=13/25
31.33
Find the general solution to y"’+ 4y" + 40y' = 0. In your answer, use C1, C2 and C3 to denote arbitrary constants and x the independent variable.
The general solution to y"’+ 4y" + 40y' = 0 is y(x) = C1[tex]e^{(-2x)}[/tex]cos(6x) + C2[tex]e^{(-2x)}[/tex]sin(6x), where C1 and C2 are arbitrary constants.
To find the general solution, we first assume that y(x) has the form [tex]y(x) = e^{(rx)}.[/tex]
Substituting this into the differential equation, we get the characteristic equation r³ + 4r² + 40r = 0.
Factoring out r, we get r(r² + 4r + 40) = 0. The quadratic factor has no real roots, so we can write r = 0, -2 ± 6i.
This gives us three linearly independent solutions e^(0x) = 1, [tex]e^{(-2x)[/tex]cos(6x), and [tex]e^{(-2x)[/tex]sin(6x). Therefore, the general solution is y(x) = C1[tex]e^{(-2x)[/tex]cos(6x) + C2[tex]e^{(-2x)[/tex]sin(6x) + C3.
Since the differential equation is homogeneous, the constant C3 is the arbitrary constant of integration.
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WILL GIVE BRAINLIEST
Given the parent function g(x) = log2 x
What is the equation of the function shown
in the graph?
Answer:
To determine the equation of the function shown on the graph, we need to analyze its characteristics. From the graph, we can see that the function passes through the point (2, 0) and has a vertical asymptote at x = 1. This information allows us to conclude that the function is a transformation of the parent function g(x) = log2 x. Specifically, it appears to be a horizontal compression and a vertical translation.
To find the equation of the function, we can start by applying the horizontal compression. Let k be the compression factor, then the function can be written as f(x) = log2(kx). Next, we can apply the vertical translation by adding or subtracting a constant, let h be the vertical shift, then the equation becomes f(x) = log2(kx) + h.
To determine the values of k and h, we can use the point (2, 0) and the fact that the vertical asymptote is at x = 1. Setting k = 1/2 since 2k = 1 (corresponding to a horizontal compression by a factor of 1/2), we can find h by substituting the point (2,0) into the equation and solving for h:
0 = log2(1) + h
h = 0
Therefore, the equation of the function shown on the graph is f(x) = log2(1/2 x), which can also be written as f(x) = log2(x) - 1.
Answer:
log2 (x - 3) - 2
Step-by-step explanation:
When x = 4
log2 of (4 - 3) - 2
= log2 1 - 2
= 0 - 2
So we have the point
(4, -2)
and when x = 7
we have y = log2(7-3) - 2
= log2 4 - 2
= 2-2
= 0
- so we have the poin7 (7,0)
Where c= ___ r=___ and d=____
Pls help quick it’s timed
The values of the sequence defined by the formula aₙ = crⁿ⁻¹ - d are c = 7, r = 2, and d = 7.
What is a sequenceA sequence is defined as an arrangement of numbers in a particular order.
Given aₙ = crⁿ⁻¹ - d, then;
c - d = 0...(1)
cr - d = 7...(2)
cr² - d = 21...(3)
from equal (1), c = d so that equation (2) becomes;
cr - c = 7 and;
c = 7/(r - 1)...(4)
put 7/(r - 1) for c and d in equation (3);
7/(r - 1)(r²) - 7/(r - 1) = 21
7r² - 7 = 21(r - 1)
7r² - 21r + 14 = 0
r² - 3r + 2 = 0
by factorization;
r = 1 or r = 2
denominator in equation (4) will be zero if r = 1, so we put 2 for r in equation (4) to get c;
c = 7/(2- 1)
c = 7.
Therefore, values of the sequence defined by the formula aₙ = crⁿ⁻¹ - d are c = 7, r = 2, and d = 7.
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help me with pythagorean therom pleaseeeeeeeeeeeee i will legit do anything if someone can help i will give brainliest just help me pleaseeeeeeeeeeee
6.6,your answer is correct.
As the theorem is a^2+b^2=c^2 you first must assign the proper components to each variable. Since 12 is the longest since it is the hypotenuse that means it is c so in this case 144. And since 10 is the leg it is a.
To solve you must take
10^2+b^2=12^2
100+b=144
144-100=44
Since b^2 is 44 you must find the square root [tex]\sqrt{44}[/tex]=6.6
Ð
B
1) This shape is a Regular Hexagon. Line
BE is a line of symmetry.
F
Ñ
a) Calculate the size of Angle ABE
b) Work out the size of Angle DCE
c) Calculate the size of Angle BEC
E
D
2) A regular polygon has an exterior angle which is 20°.
a) Calculate the size of its interior angle
b) How many sides must the polygon have? Explain why!
All interior angles are equal, so Angle ABE = 120°.
the exterior angle is equal to 60 degrees.
Angle BCE is equal to 180 degrees.
The polygon must have 18 sides because its exterior angles sum to 360°, and each exterior angle is 20°.
1) In a regular hexagon:
a) Angle ABE is an interior angle. To calculate the size of Angle ABE, we first find the sum of interior angles of a hexagon, which is (n-2)×180°, where n is the number of sides.
For a hexagon, n = 6, so the sum of interior angles is (6-2)×180° = 720°. Since it's a regular hexagon, all interior angles are equal, so Angle ABE = 720°/6 = 120°.
b) Angle DCE is an exterior angle. In a regular hexagon, the exterior angles are equal. To find the size of an exterior angle, we can use the formula: exterior angle = 360°/n, where n is the number of sides. For a hexagon, n = 6, so Angle DCE = 360°/6 = 60°.
c) Angle BEC is the sum of Angle ABE and Angle DCE. Therefore, Angle BEC = 120° + 60° = 180°.
2) For a regular polygon with an exterior angle of 20°:
a) The sum of the interior angle and exterior angle for any polygon is 180°. So, the size of its interior angle = 180° - 20° = 160°.
b) To find the number of sides in the polygon, we can use the formula for the exterior angle: exterior angle = 360°/n, where n is the number of sides. We know that the exterior angle is 20°, so 20° = 360°/n.
Solving for n, we get n = 360°/20° = 18 sides. The polygon must have 18 sides because its exterior angles sum to 360°, and each exterior angle is 20°.
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Pls help due very soon
3. consider the following box plot.
(a) find the interquartile range.
(b) what percent of values is included in the interquartile range?
Considering the following box plot, The interquartile range is a measure of the spread of the middle 50% of the data.
The interquartile range (IQR) is a measure of statistical dispersion that represents the range between the first quartile (Q1) and the third quartile (Q3) in a dataset. It provides a measure of the spread or variability of the middle 50% of the data.
However, explain how to calculate the interquartile range and the percentage of values included in the interquartile range based on a box plot:
(a) To find the interquartile range, you need to calculate the difference between the upper quartile (Q3) and the lower quartile (Q1). In other words, IQR = Q3 - Q1. The interquartile range is a measure of the spread of the middle 50% of the data.
(b) The interquartile range includes 50% of the values in the data set. This means that the other 50% of values lie outside the interquartile range.
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what is the surface area of a cube whith edges that are 4 1/2 inches long
The surface area of the cube is 60.75 in²
What is surface area of cube?Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. The sides and surfaces of a cube are equal. A cube can also be called square prism.
The surface area of a cube is expressed as;
SA = 6l²
where l is the edge length.
l = 4 1/2 = 9/2
SA = 6(9/2)²
SA = 6 × 81/4
SA = 243/4
= 60.75 in²
Therefore the surface area of the cube with edge length 4 1/2 in is 60.75 in²
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The S&P stock Index fell by an average of 8% each day. Write an equation or function that models the data
If the S&P stock index fell by an average of 8% each day, we can model the
data using exponential decay. Let P represent the initial value of the S&P
stock index and t represent the number of days. Then, the equation for the
S&P stock index after t days is:
[tex]P(t) = P * (0.92)^t[/tex]
Here, 0.92 represents the daily decay factor, which is derived from
subtracting 8% from 100% (100% - 8% = 92%). As each day passes, the
value of P(t) decreases exponentially by a factor of 0.92.
It's important to note that this equation assumes that the S&P stock index
falls by exactly 8% each day, which may not be a realistic scenario in real
life. Additionally, this equation only models the decay of the S&P stock
index value and does not take into account any external factors that may
affect its value.
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The chamber of commerce for a beach town asked a random sample of city dwellers, "Would you like to live at the beach?" Based on this survey, the 95% confidence interval for the population proportion of city dwellers who would like to live at the beach is (0. 56, 0. 62)
The 95% confidence interval for the population proportion of city dwellers who would like to live at the beach is estimated to be between 0.56 and 0.62.
How to find the sample size of the random survey?A statistical inference is a range of values within which the true value of a population parameter, such as the proportion of city dwellers who would like to live at the beach, is likely to fall with a certain level of confidence. In this case, the chamber of commerce for a beach town asked a random sample of city dwellers whether they would like to live at the beach, and based on the survey results, they constructed a 95% confidence interval for the population proportion.
The 95% confidence interval they obtained was (0.56, 0.62). This means that if they were to repeat their survey many times and construct a confidence interval each time, approximately 95% of those intervals would contain the true value of the population proportion.
In practical terms, this means that the chamber of commerce can be reasonably confident that the true proportion of city dwellers who would like to live at the beach falls somewhere between 0.56 and 0.62. It also suggests that the proportion of city dwellers who would like to live at the beach is relatively high, with more than half of the sample expressing a desire to do so. However, it is important to keep in mind that this confidence interval is based on a sample of city dwellers, and the true population proportion could differ from this estimate.
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At the team banquet, guests were served a box meal that contains one side (mac and cheese, biscuit or fries), one sandwich (burger or chicken sandwich) and on dessert (chocolate cupcake or vanilla cupcake). What is the probability of someone getting the mac and cheese or fries, with a burger and chocolate cupcakw? (simplify fraction)â
The probability of someone getting the mac and cheese or fries, with a burger and a chocolate cupcake is 1/6.
To determine the probability of someone getting the mac and cheese or fries, with a burger and a chocolate cupcake, we need to look at the possible combinations and find the ones that meet these criteria.
There are 3 side options, 2 sandwich options, and 2 dessert options, making a total of 3 x 2 x 2 = 12 possible combinations.
Now let's find the combinations that fit the desired meal:
1. Mac and cheese, burger, chocolate cupcake
2. Fries, burger, chocolate cupcake
There are 2 favorable combinations. Therefore, the probability is:
2 (favorable combinations) / 12 (total combinations) = 1/6
So, the probability of someone getting the mac and cheese or fries, with a burger and a chocolate cupcake is 1/6.
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SOMEONE HELP!! giving brainlist to anyone who answers
Answer:
We can use the Pythagorean theorem to find the length of the third side of the triangle ABC:
AB^2 = AC^2 + BC^2
(29)½^2 = 5^2 + 2^2
29 = 25 + 4
29 = 29
So the triangle is a right triangle with angle A being the angle opposite the side AC. Therefore, we can use the tangent function to find tan A:
tan A = opposite/adjacent = AC/BC = 5/2
So the exact value of tan A is 5/2.
Tres amigos compran un pan Francés. Antoni comió 7/9 y Miguel
Eduardo comió 5/9. ¿Qué parte del pan Francés quedó para Fabian?
Answer:
Si Antoni comió 7/9 del pan francés y Miguel Eduardo comió 5/9, entonces la cantidad total de pan que comieron juntos es 7/9 + 5/9 = 12/9.
Esto significa que los tres amigos comieron 12/9 del pan, lo cual es equivalente a 4/3 del pan francés.
Para encontrar la cantidad de pan que quedó para Fabian, podemos restar 4/3 del pan francés de la cantidad total del pan francés, que es 1. Entonces:
1 - 4/3 = 3/3 - 4/3 = (3 - 4)/3 = -1/3
Esto significa que Antoni y Miguel Eduardo comieron más del pan francés de lo que había disponible, lo que no es posible. Por lo tanto, no hay una cantidad del pan francés que quedó para Fabian.
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Noah edits the school newspaper. He is planning to print a photograph of a flyer for the upcoming school play. The original flyer has an area of 576 square inches. The picture Noah prints will be a dilation of the flyer using a scale factor of . What will be the area of the picture of the flyer in the newspaper?
The area of the picture of the flyer in the newspaper is 36 square inches.
The area of a figure is squared when the dimensions are multiplied by the scale factor k. Thus, if the scale factor of dilation is k, then the area of the new figure will be k² times the area of the original figure. In this case, the scale factor is 0.25, since the picture is a dilation with a scale factor of 1/4. Therefore, the area of the picture will be:
Area of picture = scale factor² x Area of original flyer
Area of picture = (0.25)² x Area of original flyer
= 0.0625 x 576 square inches
= 36 square inches
Therefore, the area of the picture of the flyer in the newspaper will be 36 square inches.
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Hi! I'm in desperate need of your assistance, please!!
Answer: x = 47
Step-by-step explanation:
45 + x = (2x - 2)
add 2 to both sides
47 + x = 2x
subtract x on both sides
47 = x
PLEASEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
Step-by-step explanation:
AngleSideSide because it's bad
but also, if you had an angle, a side and a side
For your example: let's say CD≅AS
You could change the angle of S or D and the parameters of the triangle would still be true. Because you can change something and still have AngleSideSide be true, would make them not congruent any more.
Which axis is point 5 located on?
Point 5 is located on the x-axis (horizontal one)
In which axis is the point 5 located on?On a general coordinate axis we have two axes.
The vertical one is called the y-axis, and here we put the outputs.
The horizontal one is called the x-axis, here we put the inputs.
Here we can see that point 5 (P5) is located on the horizontal axis, then the correct option is the first one, x-axis.
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a cylinder and a cone have the same diameter: 8 inches. the height of the cylinder is 6 inch what is the volume of each
The volume of the cylinder with a height of 6 inches and a diameter of 8 inches is 904.78 cubic inches.
The volume of the cone with a height of 6 inches and a diameter of 8 inches is 201.06 cubic inches.
What are the volumes of a cylinder and a cone with same diameter of 8 inches, if the height of the cylinder is 6 inches?The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. Since the diameter is 8 inches, the radius is half of that, which is 4 inches. So, the volume of the cylinder is:
V = π(4)²(6)
V = π(16)(6)
V = 96π
V ≈ 301.59 cubic inches (rounded to two decimal places)
The formula for the volume of a cone is V = (1/3)πr²h. Again, since the diameter is 8 inches, the radius is 4 inches. So, the volume of the cone is:
V = (1/3)π(4)²(6)
V = (1/3)π(16)(6)
V = (1/3)(96π)
V ≈ 100.53 cubic inches (rounded to two decimal places)
However, since the problem only asked for the diameter and not the radius, we can simplify the calculations by using the formula for the volume of a cylinder with diameter D directly, which is:
V = π(D/2)²h
V = π(8/2)²(6)
V = π(4)²(6)
V = 16π(6)
V ≈ 301.59 cubic inches (rounded to two decimal places)
Similarly, we can use the formula for the volume of a cone with diameter D directly, which is:
V = (1/3)π(D/2)²h
V = (1/3)π(8/2)²(6)
V = (1/3)π(4)²(6)
V = (1/3)(16π)(6)
V ≈ 100.53 cubic inches (rounded to two decimal places)
Thus, the main answer is the volume of the cylinder is 904.78 cubic inches and the volume of the cone is 201.06 cubic inches, both rounded to two decimal places.
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Emily has 6 pages of homework to do. If she can finish 38 of a page in one hour, how many hours will her homework take?
Emily's homework will take approximately 9 hours to complete.
Emily has 6 pages of homework and she can finish 3/8 of a page in one hour, we can calculate the total number of hours required to complete her homework.
To find the number of hours, we divide the total number of pages by the number of pages she can finish in one hour:
Number of hours = Total number of pages / Pages finished in one hour
Number of hours = 6 pages / (3/8) pages per hour
To divide by a fraction, we can multiply by its reciprocal:
Number of hours = 6 pages * (8/3) pages per hour
Simplifying the multiplication:
Number of hours = 48/3
Number of hours = 16
Therefore, Emily's homework will take approximately 16 hours to complete.
Hence, the answer is that Emily's homework will take approximately 9 hours to complete.
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3⋅50. 2w=720
What is the solution of the equation?
Round your answer, if necessary, to the nearest thousandth
The solution to the equation is w = 285.
How to solve a mathematical equation involving multiplication and variables?To solve the equation 3⋅50 + 2w = 720, we first simplify the left side by multiplying 3 and 50, which gives us 150.
Therefore, the equation becomes 150 + 2w = 720. Next, we isolate the variable term by subtracting 150 from both sides of the equation, resulting in 2w = 570.
To solve for w, we divide both sides of the equation by 2, giving us w = 285.
Therefore, the solution to the equation is w = 285.
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expanded form 6.27x10 4
Answer:62700
Step-by-step explanation:
You take your original value and move the decimal point 4 times to the right as it is a positive power.