Answer:
The answer to 1+1 is 2.
Answer:
2
Step-by-step explanation:
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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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
The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are given in the table.
A 2-column table with 9 rows. Column 1 is labeled Weight (x) with entries 8, 12, 18, 24, 30, 32, 35, 37, 40. Column 2 is labeled Height (y) with entries 22, 23, 26, 30, 32, 33, 35, 36, 38.
Using technology, what is the correlation coefficient?
–0. 997
–0. 503
0. 503
0. 997
The correlation coefficient using technology is 0.997.
Using the given data in the table, the correlation coefficient can be calculated using technology, such as a statistical calculator or spreadsheet software.
Using python
import numpy as np
# Input the data
weight = np.array([8, 12, 18, 24, 30, 32, 35, 37, 40])
height = np.array([22, 23, 26, 30, 32, 33, 35, 36, 38])
# Calculate the correlation coefficient
correlation_coefficient = np.corrcoef(weight, height)[0, 1]
# Print the correlation coefficient
print("Correlation Coefficient:", correlation_coefficient)
The out put will be
Correlation Coefficient: 0.997088376189
The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, in this case, weight (x) and height (y) of a child.
Upon calculating, the correlation coefficient (r) is approximately 0.997. This indicates a strong positive linear relationship between the child's weight and height over the two-year period.
Corelation shows dependency of x on y variable and vice versa.
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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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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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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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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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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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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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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.
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.
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
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)
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.
Determine the location and value of the absolute extreme values off on the given interval, if they exist 8x? f(x) - +22x2 - 24x on (-7,11 G What in are the absolute maximum maxime off on the given interval? Select the correct choice below and, if necessary, to in the answer bowen to completo your choice A. Tho absolute maximum/maxima isarea- (Use a comma to separato answers as needed. Type exact answers, using radicals as rended) B. There is no absolute maximum off on the given interval What are the absolute minimum/minima off on the given interval? Select the correct choice below and. If necessary, in the wwer boxes to complete your in O A The absolute minimum/minima is/are at (Use a comma to separate answers as needed. Type exact answers, using radical as needed) B. There is no absolute minimum off on the given interval
The absolute maximum will be at (11, 10373).
The absolute minimum is at (-1.963, -25.294).
What in are the absolute maximum maxime off on the given interval?
To determine the location and value of the absolute extreme values of the function f(x) = 8x³+ 22x² - 24x on the interval (-7, 11), follow these steps:
Find the critical points by taking the derivative of the function and setting it equal to zero:
f'(x) = 24x² + 44x - 24
Solve for x:
Factor the equation: 4(6x² + 11x - 6) = 0
Using the quadratic formula, x = (-11 ± √(121 + 144))/12
x ≈ -1.963, 0.630
Check the endpoints and the critical points to find the absolute maximum and minimum:
f(-7) ≈ 461
f(-1.963) ≈ -25.294
f(0.630) ≈ -16.102
f(11) ≈ 10373
Compare the values:
The absolute maximum is at x = 11, with a value of 10373.
The absolute minimum is at x ≈ -1.963, with a value of ≈ -25.294.
Answer:
The absolute maximum is at (11, 10373).
The absolute minimum is at (-1.963, -25.294).
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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.
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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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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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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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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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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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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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
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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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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A cube is sliced perpendicular to its base what is the shape of the resulting two dimensional cross-section 1. trapezoid 2. square 3.circle
If a cube is sliced perpendicular to its base, the resulting two dimensional cross-section will be a square. This is because each face of a cube is a square, and a perpendicular slice across the base will result in a square shape. A trapezoid or a circle would not result from a perpendicular slice of a cube.
When a cube is sliced perpendicular to its base, the shape of the resulting two-dimensional cross-section is a square.
Step-by-step explanation:
1. A cube has six faces, all of which are squares.
2. When you slice the cube perpendicular to its base, you are cutting it in a direction that is at a 90-degree angle to the base.
3. Since all the faces of a cube are squares, the resulting cross-section from a perpendicular slice will also be a square.
So, the correct answer is option 2, a square.
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Lines AC and BD intersect at point O. Lines AC and BD intersect at point O. If m∠AOD = (10x − 7)° and m∠BOC = (7x + 11)°, what is m∠BOC?
A. 6°
B. 53°
C. 89°
D. 106°
Answer: the answer is B. 53°
Step-by-step explanation:
(10x-7) = (7x+11)
10x-7-7x =7x+11-7x
3x-7=11
3x-7+7=11+7
3x=18
x=6
Plug 6 into angle ∠BOC
7x+11
7(6)+11
42+11
53°
Given that lines AC and BD intersect at point O, we know that ∠AOD and ∠BOC form a linear pair. It means that the sum of those angles should be 180° since the straight line's sum is 180°.
Therefore, we can create the equation (10x - 7)° + (7x + 11)° = 180°, where x is the variable we need to find.
By combining like terms, we simplify this equation to 17x + 4 = 180.
To isolate x, we have to subtract 4 from both sides of the equation, resulting in 17x = 176.
Now, dividing both sides by 17, we find that x equals approximately 10.35.
Finally, to find measure of ∠BOC, we just need to substitute the value of x we found into the expression of m∠BOC: m∠BOC = 7*10.35 + 11, which is approximately 83.47°.
Based on the choices given, C. 89° is the closest to our calculated value. Therefore, the answer is C. 89°.
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Mario is buying a number of hamburgers from the local store that cost $2. 90 each. He is also buying one packet of hamburger rolls at a cost of $4. 75. He has $39. 55 to spend at the store. Write and solve an inequality that shows how many hamburgers, h, Mario can afford to buy.
Write the inequality.
_____________
Solve in inequality
______________
The inequality is 2.90h + 4.75 ≤ 39.55, and after solving, we find that Mario can afford to buy a maximum of 12 hamburgers (h ≤ 12).
Let's denote the number of hamburgers Mario can buy as h. We know that each hamburger costs $2.90, and the hamburger rolls cost $4.75. Mario has a total of $39.55 to spend. To write an inequality that represents this situation, we can use the following equation:
2.90h + 4.75 ≤ 39.55
Now, let's solve the inequality:
Step 1: Subtract 4.75 from both sides of the inequality to isolate the term with h.
2.90h ≤ 34.80
Step 2: Divide both sides of the inequality by 2.90 to solve for h.
h ≤ 34.80 / 2.90
Step 3: Perform the division to find the maximum number of hamburgers Mario can buy.
h ≤ 12
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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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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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