Audrey is planning to drive from City X to City Y. The scale drawing below shows the distance between the two cities with a scale of ¼ inch = 24 miles.
City X
City Y
3 in
Answers
The actual distance between the two cities is 288 miles.
What is the actual distance?A scale drawing is a smaller version of a larger image / city. The scale drawing is reduced by a constant ratio. This means that the scale drawing of the two cities would be smaller than the actual cities.
The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. This means that the scale drawing of the two cities would be smaller than the actual cities.
The actual distance between the two cities = (3 x 24) ÷ 1/4
= 3 x 24 x 4 = 288 miles
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Related Questions
the magnitude of a vector can be different in different coordinate systems.
Answers
Depending on the coordinate system used, a vector's magnitude can vary. A vector may be enhanced by the addition of a scalar. When one of a vector's components is nonzero, the vector can have a magnitude of zero.
What is magnitude of a vector ?
A vector's magnitude, represented by the symbol |v|, is used to determine a vector's length. The distance between the vector's beginning point and endpoint is what this amount essentially represents.
What does the vector coordinate system mean?
An ordered list of integers (a tuple) that represents a vector in terms of a specific ordered basis is known as a coordinate vector in the language of linear algebra.
The coordinates (5, 2, 1) in a three-dimensional Cartesian coordinate system with the axes as its basis serve as an accessible example.
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Working together, two pumps can drain a certain pool in 3 hours. If it takes the older pump 12 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?
Answers
if it take 12 hours for a older pump and 3 hours for 2 pumps you would multiply 3x2 witch equals 6 and 6÷12 equals 3
Liliana wants to find the area of a polygon. First, she breaks apart the polygon into two trapezoids. What is Liliana's next step?
Answers
Liliana's next step is to find the area of each of the two trapezoids.
How to determine her next stepFrom the question, we have the following parameters that can be used in our computation:
Liliana wants to find the area of a polygon. First, she breaks apart the polygon into two trapezoids.Given that she has broken the polygon into two trapezoids, the next step ti so calculate the area of each trapezoid
This is done using
Area = 1/2 * (sum of parallel sides) * height
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In the inequality 3x + 4y ≤ 5, which of the following ordered pair is the solution?
A. (7,2)
B. (2,-1)
C. (5,-1)
D. (6,1)
Answers
Answer: (2, -1)
Step-by-step explanation:
To determine if an ordered pair is a solution to an inequality, we substitute the values of x and y into the inequality and see if the resulting expression is true or false.
A. For (7,2), we have:3(7) + 4(2) = 21 + 8 = 29 29 > 5, so (7,2) is not a solution to the inequality.
B. For (2,-1), we have:3(2) + 4(-1) = 6 - 4 = 2 2 ≤ 5, so (2,-1) is a solution to the inequality.
C. For (5,-1), we have:3(5) + 4(-1) = 15 - 4 = 11 11 > 5, so (5,-1) is not a solution to the inequality.
D. For (6,1), we have:3(6) + 4(1) = 18 + 4 = 22 22 > 5, so (6,1) is not a solution to the inequality.
So, the ordered pair that is a solution to the inequality is (2,-1).
WHICH IS EQUIVALENT TO
Answers
The equivalent exponential function is ( 8 ) ^ ( 3x/4 ).
option A.
What is the equivalent of the exponential function?The equivalent of the exponential function is calculated by applying the following formula.
Generally, for an exponential function of (√a)³ = ( a ) ^ (2/3)
The given exponential function = ∛ (8) ^ (1/4)× , the equivalent function is determined as;
∛ (8) ^ (1/4)× = ( 8 ) ^ ( 1 / 4 ) ( 3x )
= ( 8 ) ^ ( 3x/4 )
Thus, the equivalent exponential function is determined by applying exponential rules.
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the unit kilowatt-hour is a measure of the unit kilowatt-hour is a measure of power. the amount of power used per second. an amount of energy. the rate at which energy is transformed.
Answers
The unit kilowatt-hour measures the amount of energy used or produced, whereas the rate at which energy is transformed is measured in kilowatts.
The unit kilowatt-hour (kWh) is a measure of energy, not power. Energy is a measure of the amount of work that can be done, and is usually measured in joules. Power, on the other hand, is a measure of the rate at which energy is transformed, and is usually measured in watts.
A kilowatt-hour is the amount of energy used or produced when a power of one kilowatt is used for one hour. For example, if a 100-watt light bulb is left on for 10 hours, it will have used
100 * 10 = 1000 watt-hours or 1 kilowatt-hour of energy.
So to summarize, the unit kilowatt-hour measures the amount of energy used or produced, whereas the rate at which energy is transformed is measured in kilowatts.
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Kayla is looking at a graph that has a parabola on it. The parabola touches the x-axis at 3 and 9. Which of the following functions could have been graphed on her paper?
Answers
The function graphed on the paper could be a quadratic function which has the two real roots equal to 3 and 9.
What is Parabola?A parabola is a two dimensional figure on a plane which is U shaped and any point on the parabola is at an equal distance from a fixed point called focus and a fixed line called directrix.
The graph of a function is parabola when the function is quadratic.
Quadratic functions are of the form f(x) = ax² + b x + c.
Given that, the parabola touches the x-axis at 3 and 9.
This indicates that roots of the quadratic equation are 3 and 9.
That is, f(x) = 0, when x = 3 and x = 9.
It may be of the form f(x) = (x - 3)(x - 9) = x² - 3x - 9x + 27 = x² - 12x + 27.
So the function representing the graph on the paper is a quadratic function whose roots are 3 and 9 and the function could be of the form f(x) = x² - 12x + 27.
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divide the sum of 11 and g by 9 in algebraic expression
Answers
The algebraic expression can be written as:
(11 + g)/9
How to write the algebraic expression?
Here we want to write:
"divide the sum of 11 and g by 9"
As an algebraic expression.
The sum of 11 and g can be written as:
(11 + g)
Where g is the variable in this problem.
And now we just divide that by the number 9, then the algebraic expression is the next one:
(11 + g)/9
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a class has 10 boys and 12 girls. 3 students are chosen at random to clean the classroom each day. how many unique cleaning teams exist?
Answers
The number of different unique cleaning teams should be 1540.
What are permutation and combination?A permutation is an arrangement of things where order matters, AB and BA are two different permutations.
The combination is a selection of things where order does not matter, AB and BA are the same combinations.
Given, A class has 10 boys and 12 girls and 3 students are chosen at random.
So, the team of 3 can be chosen as 3 boys, 3 girls, 1 boy 2 girls, and 1 girl and 2 boys and the total teams will be the sum of different combinations which is,
= [tex]^{10}C_3 + ^{12}C_3 + ^{10}C_1\times^{12}C_2 + ^{12}C_1\times^{10}C_2[/tex].
= (10×9×8)/6 + (12×11×10)/6 + 10×(12×11)/2 + 12×(10×9)/2.
= 120 + 220 + 660 + 540.
= 1540.
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if 12 bagels cost $35 how much would one cost
Answers
Answer:$2.97
Step-by-step explanation: 35 divided by 12 = 2.97
Line p intersects lines a and b. a b. By which theorem is ∠1 ≅ ∠8?
Answers
The transversal Alternate Interior Angle Theorem is the theorem for which ∠1 ≅ ∠8
What is the theorem?If line p intersects lines a and b and angles 1 and 8 are opposite angles, then they are congruent (equal) by the Transversal-Alternate Interior Angle Theorem.
The Transversal-Alternate Interior Angle Theorem states that if a transversal intersects two lines, then alternate interior angles are congruent. In other words, if a transversal line (such as line p in this case) cuts two other lines (lines a and b), then the angles on one side of the transversal will be equal to the corresponding angles on the other side. These corresponding angles are called alternate interior angles.
So, in this case, angle 1 and angle 8 are alternate interior angles and are equal to each other as per the Transversal-Alternate Interior Angle Theorem.
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A 5 kilograms bag of beans cost $18.50. At the same rate, what amount of money would 9 kilograms bag of beans cost?
Answers
Answer: $33.3
Step-by-step explanation:
1kg of beans cost $3.70 then $3.70x9= $33.3.
Hope this helps.
a children's book publisher is interested in kid's opinions of their new book. a random sample of children are shown the book and the proportion of those kids who like the book is found. if the publisher changes from a sample size of 100 to a sample size of 1000, what affect will it have on the sampling distribution
Answers
If the publisher changes from a sample size of 100 to a sample size of 1000, the precision of the estimate will be more accurate and the publisher will have more confidence in the results.
Increasing the sample size from 100 to 1000 will result in a more precise estimate of the proportion of children who like the book. The larger sample size will lead to a narrower sampling distribution, meaning that the estimates of the proportion will be more tightly clustered around the true value. This increased precision can provide the publisher with more confidence in the results and a better understanding of the opinions of children on the new book.
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plssssss help me! i don’t understand.
Answers
1. Arrange the numbers from smallest to largest value.
2. Next you find the number that is in the very middle, that is the median.
3. If there are two numbers that are in the middle you add them together and then divide by two.
In the example, for instance, 19,050 an 19,600 are the two middle numbers. So you add them together (19,050 + 19,600 = 38,650) and then divide by two to get your median (38,650/2 = 19,325).
So 19,325 is your median.
Hope this helps! :)
a ball of radius 13 has a round hole of radius 7 drilled through its center. find the volume of the resulting solid.
Answers
The volume of the resulting solid is 3,280.953 cm3.
The volume of the resulting solid is calculated by subtracting the volume of the inner sphere (the hole) from the volume of the outer sphere (the ball). The volume of a sphere is calculated by the formula V=4/3πr3. Therefore, the volume of the outer sphere is V1=4/3π(13)3=4,714.286 cm3. Similarly, the volume of the inner sphere is V2=4/3π(7)3=1,433.333 cm3. Subtracting V2 from V1 gives the volume of the resulting solid as V3=4,714.286 - 1,433.333=3,280.953 cm3. Therefore, the volume of the resulting solid is 3,280.953 cm3.
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while attending school, you work part time at a coffee shop. last year, you made $8,700. why might you still file your taxes, even though you made less than the standard deduction?
Answers
Even if we earned less than the standard deduction, we nonetheless file taxes since, regardless of their income, freelancers are always required to pay tax on their earnings.
What is a freelancer?Freelancer, freelancer, or freelance worker are phrases frequently used to describe someone who is self-employed and isn't necessarily long-term dedicated to a certain employer.
Others work independently or use websites or professional associations to find work.
Freelancers are occasionally represented by a business or a temporary agency that resells their services to clients.
Independent contractors must always pay taxes on their wages, regardless of how much they make.
The term "freelancing" is most frequently used in the culture and creative industries, and use of this term may indicate participation in these sectors, even though the term "independent contractor" would be used in a different register of English to designate the tax and employment classes of this type of worker.
Therefore, even if we earned less than the standard deduction, we nonetheless file taxes since, regardless of their income, freelancers are always required to pay tax on their earnings.
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Haley's clothing store sold 540 shirts with the ratio o f short sleeve to long sleeve being 3:9. how many short sleeve were sold
Answers
The short sleeve shirts sold by haley were 405
What is a ratio?The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"
Given here: Haley's clothing store sold 540 shirts with ratio of short sleeve to long as 3:9
let 3x and 9x long and short sleeves were sold respectively
Then we have
3x+9x=540
12x=540
x=540/12
x=45
Thus 3x=135 and 9x=405
Hence, The short sleeve shirts sold by haley were 405
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Carlos has noticed that because each of his purchases have been somewhat similar, it has been easy
figure out the cost of each item. However, his last set of receipts has him puzzled. One week he tried out
cheaper brands of cat and dog food. On Monday he purchased 3 small bags of cat food and 5 small bags of
dog food for $22.75 Because he went through the small bags quite quickly, he had to return to the store on
Thursday to buy 2 more small bags of cat food and 3 more small bags of dog food, which cost him $14.25.
Based on this information, figure out the price of each bag of the cheaper cat and dog food. Explain your
reasoning.
Answers
Price of each bag of cat food is $3 and the price of each bag of dog food is $2.75.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Let x be the cost of each small bag of cat food and y be the cost of each small bag of dog food.
Given that,
On Monday Carlos purchased 3 small bags of cat food and 5 small bags of dog food for $22.75.
3x + 5y = 22.75
On Thursday he buy 2 more small bags of cat food and 3 more small bags of dog food, which cost him $14.25.
2x + 3y = 14.25
So we have two linear equations.
3x + 5y = 22.75 and 2x + 3y = 14.25
Multiplying throughout the first equation with 2 and the second equation with 3, we get the two equations as,
6x + 10y = 45.5 and
6x + 9y = 42.75
Subtracting second from first,
y = 2.75
Substituting y = 2.75 in 2x + 3y = 14.25,
2x = 14.25 - 8.25
x = 3
Hence the the price of cat food and dog food are $3 and $2.75 respectively.
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a metric ruler contains ten equally spaced increments between each labeled centimeter. when using this ruler to record the length of an object in centimeters, how many decimal places should be recorded?
Answers
When using a metric ruler with ten equally spaced increments between each labeled centimeter, the length of an object can be recorded to one decimal place.
A metric ruler is typically divided into centimeters (cm) and millimeters (mm). The ruler has ten equally spaced increments between each labeled centimeter, which means that each centimeter can be divided into ten equal parts. Each of these parts represents a millimeter, and they can be used to measure smaller lengths with more precision.
When using a metric ruler to record the length of an object in centimeters, the smallest division on the ruler that can be used to measure the length is a millimeter. The length of the object can be estimated to the nearest millimeter by aligning it with the closest division on the ruler.
To express the length of the object in centimeters, the number of millimeters must be divided by 10. The resulting value will represent the length of the object in centimeters, rounded to the nearest tenth of a centimeter. This means that the length of the object can be recorded to one decimal place.
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3. Adam has created a fitness app that currently
has 1,250 downloads. If the number of
downloads for the app is doubling every month,
How many downloads will the app have after 10
months?
Answers
Answer:the fitness app will have 1,280,000 downloads after 10 months.
Step-by-step explanation:
To find the number of downloads after 10 months, we need to calculate the number of downloads after each month and add them up. Here's the formula to calculate the number of downloads after n months:
Number of downloads after n months = 1,250 * 2^n
Substituting n=10 in the formula, we get:
Number of downloads after 10 months = 1,250 * 2^10 = 1,250 * 1024 = 1,280,000
So, the fitness app will have 1,280,000 downloads after 10 months.
PLEASE HELP 50 POINTS
Answers
Answer:
Isosceles acute triangle
Step-by-step explanation:
angle CBD = 56 because you have to subtract 180 - 124 = 56
angle BDC = 62
add CBD = 56 and BDC = 62
56+62+c(angle c)=180
c= 62 b=56 d=62
2 angles are equal and therefore it is Isosceles
Non of the angles are obtuse and therefore it is acute triangle!
Hope I helped!
help meeeeh please with this question
Answers
a) This can't be correct because we will see that she found 6.7 animals, and that can't be.
b) in this case the fraction of plants ios 2/5, then the number of plants is 8.
Can Jill's statement be correct?a) We know that she found 20 species of animals and plants, so, if she says that a fraction of 1/3 of these are animals, then the number of animals will be:
A = (1/3)*20 = 20/3 = 6.7
That is not a whole number, so it isn't correct.
b) If 3/5 of the species were animals, then 2/5 were plants, so the number of plants is given by:
P = (2/5)*20 = 2*20/5 = 2*4 = 8
There are 8 plants in this case.
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A 20-minute TV program consists of two commercials, each 13 over 4 minutes long, and three equal-length entertainment segments. How long is each entertainment segment? Enter your answer as a decimal.
Answers
The length of each entertainment segment written as a decimal is 4.5 minutes
How long is each entertainment segment?Total time of the TV program= 20 minutes
Number of commercials= 2
Time taken for each commercial= 13/4 minutes
Total time taken for 2 commercials= 2(13/4)
= 26/4
= 13/2 minutes
Number of minutes remaining after commercials= Total time of the TV program - Total time taken for 2 commercials
= 20 - 13/2
= (40-13) / 2
= 27/2 minutes
Number of entertainment segment = 3
Time spent on each entertainment segment= Number of minutes remaining after commercials / 3
= 27/2 ÷ 3
multiply by the reciprocal of 3
= 27/2 × 1/3
= 27/6 minutes
= 4.5 minutes
Therefore, each entertainment segment will take 4.5 minutes from the 20 minutes TV program.
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What is the answer to both parts of the question
Answers
b. Yes. Write an equation of each line, then solve this system of linear equations using substitution.
the eleventh term of an arithmethic sequence is 69 while the sum of the first three terms is 45. find the third term
Answers
The third term of this arithmetic sequence is 21.
eleventh term of an arithmetic sequence is 69.
a₁₁ = a + 10 d = 69
also sum of the first three terms is 45
the first three terms are a, a + d, a + 2d
a + a + d + a + 2d = 45
3a + 3d = 45
a + d = 15
a = 15 - d
so, a + 10 d = 69
15 - d + 10d = 69
9d = 69 - 15
9d = 54
d = 6
a = 15 - 6 = 9
a₃ = a + 2d
= 9 + 2(6)
a₃ = 21
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If f(x) = 2x² + 3 and g(x)=x2-7, find (f+ g)(x).
Answers
Answer: 3x2 - 4
Step-by-step explanation:
2x2 + 3 + (x2 - 7)
2x2 + 3 + x2 - 7
3x2 - 4
(i don't know if this is right let me know)
you are given a system of 4 linear equations in 3 variables x, y, z. explain why it is impossible for the system to have exactly two solutions.
Answers
A system of 4 linear equations in 3 variables x, y, z can have at most one solution.
It is because a system with more than three equations and only three variables will not have a unique solution due to the fact that the dimension of the solution space of 3-dimensional equations is three, so adding an extra equation will result in an over-determined system.
In other words, there are not enough variables in the system to meet the requirements of all the equations, which leads to an over-determined system where there is either no solution or a unique solution. If the system has exactly two solutions, it means that the solution space of the system of equations has a dimension greater than 3, which contradicts the fact that the dimension of the solution space of a system of 3-dimensional equations is 3.
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100 is no less than 20 times a number t
Answers
Answer:
You can put this solution on YOUR website!
100 >= 20t (that's "more than or equal to")
Divide each side by 20
5 >= t [5 is more than or equal to t]
or, conversely, t <= 5 [t is less than or equalequal to 5]
A solid metal cube of side 6 cm is recast into a solid sphere. Find the radius of the sphere.
Answers
Answer:
Answer provided in image May it help you !!!
Step-by-step explanation:
a scientist randomly divided a group of 100 lab rats into two groups of 50. one group was fed regular rat chow while the other was fed the same amount of rat chow with added ddt (an insecticide). both groups were housed in the same room with the same environmental conditions. at the end of the experiment, rats were weighed and the mean difference was calculated. what is the independent variable?
Answers
the answer is DDT
your welcome and have a great rest of your day