A building is 210 m tall. A scale model is built using a scale factor of 0. 5.
a) Determine the height of the model to the nearest centimeter, if necessary.
b) What are the actual dimensions of the bed, couch, and desk?
Answers
a) The height of the scale model is 105 m. b) The actual dimensions of the bed, couch, and desk are twice as large as their corresponding dimensions in the scale model.
a) To determine the height of the scale model, we multiply the height of the actual building by the scale factor of 0.5:
Height of scale model = 0.5 x 210 m = 105 m.
b) Since the scale factor is 0.5, the actual dimensions of the bed, couch, and desk are twice as large as their corresponding dimensions in the scale model.
For example, if the length of the couch in the scale model is 10 cm, then the actual length of the couch is 2 x 10 cm = 20 cm. Similarly, if the width of the desk in the scale model is 8 cm, then the actual width of the desk is 2 x 8 cm = 16 cm.
Therefore, to find the actual dimensions of the bed, couch, and desk, we simply multiply the corresponding dimensions in the scale model by 2.
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Related Questions
can yall help me with this
Answers
Answer:
B
Step-by-step explanation:
If you see two negatives next to each other, just think of them as adding. So add 8 and 7, you get 15.
Find the missing side of each triangle
Answers
Pythagorean Theorem:
a²+b²=c², where a=leg 1, b=leg 2, and c=hypotenuse.
Define variables:
Leg 1=√10km, leg 2=x, and hypotenuse=√15. So, a=√10, b=x, c=√15.
Substitute variables in and solve for undefined variable:
(√10)²+(x)²=(√15)²
Simplify:
10+x²=15
Squares are inverse operations of square roots, so they cancel each other out, or “undo” each other. For example: 10•10=100 and √100=10, so √10²=10. Or, 6•6=36, so √36=6, thus √6²=6.
Solve for x:
Subtract 10 from both side:
x²=15-10
x²=5
Take the square root of x² to both sides so we are left with just x. Again, this works because x•x=x², so √x²=x, thus √x²=x. And, whatever we do to one side, we must do to the other to keep the equation balanced.
√x²=√5
x=√5km
Answer:
Choice A.): x=√5km
The vertices of AABC have coordinates A(-2, -1), B (10,-1), C (4,4). State the
area of AABC.
HELP ASAP
Answers
Answer:30
Step-by-step explanation:
State the equation of the graphed function.
Answers
The equation of the graphed function is given as follows:
f(x) = x³ + 2x² - 5x - 6.
How to obtain the equation of the function?
The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.
From the graph, the zeros of the function are:
x = -3.x = -1.x = 2.Hence the function is:
f(x) = a(x + 3)(x + 1)(x - 2).
In which a is the leading coefficient.
Expanding the product, we have that:
f(x) = a(x² + 4x + 3)(x - 2)
f(x) = a(x³ + 2x² - 5x - 6).
When x = 0, y = -6, hence the leading coefficient a is obtained as follows:
-6a = -6
a = 1.
Hence the function is:
f(x) = x³ + 2x² - 5x - 6.
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John predicted that his project would require, in effort, 25 person-days (d/p) for plan development, 75 d/p for software development, 20 d/p for reviews, 30 d/p for tests, 20 d/p for training and 5 d/p for methodology. His project cost 250 days/p, because he had to redo several modules following the test results.
a) Calculate the costs of non-compliance, enforcement, prevention and evaluation.
Show your calculations below.
b) Calculate the percentage of effort, out of the total cost, devoted to each component:
Answers
a. the costs of non-compliance, enforcement, prevention and evaluation are -75 d/p, -$7500, $17500 and $5000 respectively
b. The percentage of effort devoted to each component is:
Plan development: 10%Software development: 30%Reviews: 8%Tests: 12%Training: 8%Methodology: 2%a) To calculate the costs of non-compliance, enforcement, prevention, and evaluation, we need to determine the deviations in effort for each component and multiply them by the corresponding cost per person-day.
Non-compliance cost:
Non-compliance cost = Actual effort - Predicted effort
To calculate the actual effort, we need to sum up the effort for each component mentioned:
Actual effort = Plan development + Software development + Reviews + Tests + Training + Methodology
Actual effort = 25 + 75 + 20 + 30 + 20 + 5 = 175 d/p
Non-compliance cost = Actual effort - Predicted effort = 175 - 250 = -75 d/p
Enforcement cost:
Enforcement cost = Non-compliance cost * Cost per person-day
Assuming a cost of $100 per person-day, we can calculate the enforcement cost:
Enforcement cost = -75 * $100 = -$7500 (negative value indicates a cost reduction due to underestimation)
Prevention cost:
Prevention cost = Predicted effort * Cost per person-day
Assuming a cost of $100 per person-day, we can calculate the prevention cost for each component:
Plan development prevention cost = 25 * $100 = $2500
Software development prevention cost = 75 * $100 = $7500
Reviews prevention cost = 20 * $100 = $2000
Tests prevention cost = 30 * $100 = $3000
Training prevention cost = 20 * $100 = $2000
Methodology prevention cost = 5 * $100 = $500
Total prevention cost = Sum of prevention costs = $2500 + $7500 + $2000 + $3000 + $2000 + $500 = $17500
Evaluation cost:
Evaluation cost = Total project cost - Prevention cost - Enforcement cost
Evaluation cost = $25000 - $17500 - (-$7500) = $5000
b) To calculate the percentage of effort devoted to each component out of the total cost, we can use the following formula:
Percentage of effort = (Effort for a component / Total project cost) * 100
Percentage of effort for each component:
Plan development = (25 / 250) * 100 = 10%
Software development = (75 / 250) * 100 = 30%
Reviews = (20 / 250) * 100 = 8%
Tests = (30 / 250) * 100 = 12%
Training = (20 / 250) * 100 = 8%
Methodology = (5 / 250) * 100 = 2%
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the expected cell frequency is based on the researcher's opinion.
True or false
Answers
False. The expected cell frequency in statistical analysis, specifically in the context of contingency tables and chi-square tests, is not based on the researcher's opinion. Instead, it is determined through mathematical calculations and statistical assumptions.
In contingency tables, the expected cell frequency refers to the expected number of observations that would fall into a particular cell if the null hypothesis of independence is true (i.e., if there is no relationship between the variables being studied). The expected cell frequency is calculated based on the marginal totals (row totals and column totals) and the overall sample size.
The expected cell frequency is computed using statistical formulas and is not influenced by the researcher's opinion or subjective judgment. It is a crucial component in determining whether the observed frequencies in the cells significantly deviate from what would be expected under the null hypothesis.
By comparing the observed cell frequencies with the expected cell frequencies, statistical tests like the chi-square test can assess the association or independence between categorical variables in a data set.
Thus, the statement "the expected cell frequency is based on the researcher's opinion" is false. The expected cell frequency is derived through statistical calculations and is not subject to the researcher's subjective input.
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Translate each of these quantifications into English and determine its truth value.
a) ∀x∈R (x2 = −1)
b) ∃x∈Z (x2 = 2)
c) ∀x∈Z (x2 > 0)
d) ∃x∈R (x2 = x)
Answers
Truth values (a) False (b) False (c) False (d) True
Here is the translation of these quantifications into English and determine its truth value. a) ∀x∈R (x^2 = -1)
Translation: For all x belonging to the set of real numbers, x squared equals -1.
Truth value: False. No real number squared can equal a negative value.
b) ∃x∈Z (x^2 = 2)
Translation: There exists an x belonging to the set of integers such that x squared equals 2.
Truth value: False. No integer squared can equal 2.
c) ∀x∈Z (x^2 > 0)
Translation: For all x belonging to the set of integers, x squared is greater than 0.
Truth value: False. When x equals 0 (x=0), x squared equals 0, which is not greater than 0.
d) ∃x∈R (x^2 = x)
Translation: There exists an x belonging to the set of real numbers such that x squared equals x.
Truth value: True. There are two real numbers that satisfy this condition: x=0 and x=1.
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The maximum rate of return that can be earned for a given rate of interest occurs when interest is compounded
A) annually.
B) daily.
C) monthly.
D) continuously.
Answers
The maximum rate of return that can be earned for a given rate of interest occurs when interest is compounded continuously.
What is compounded continuously?In theory, continuously compounded interest means that an account balance is constantly earning interest, as well as refeeding that interest back into the balance so that it, too, earns interest.
Continuous compounding calculates interest under the assumption that interest will be compounding over an infinite number of periods.
The formula in order to calculate continuous compounding is given by:
\(A=pe^{rt\)
Thus, the maximum rate of return that can be earned for a given rate of interest occurs when interest is compounded continuously.
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in a particular statistics exam, the 35th percentile of final exam score is 42, and the 70th percentile of final exam score is 76. a histogram of the scores approximately follows the normal curve. what is the approximate standard deviation of the final exam scores? hints: what is the z value in the normal table that gives you closest to 35% of the area between -z and z? now what does that tell you about the number of sds in between 42 inches and 76 inches? you might find it helpful to draw a picture of the normal curve with original units and standard units. group of answer choices A. 7.5 B. 37.8 C. 13.1 D. 20.7
Answers
The approximate standard deviation is B) 37.8.
What is the relationship between percentiles and standard deviations in a normal distribution?To find the approximate standard deviation of the final exam scores, we can use the properties of the normal distribution and percentiles.
First, let's find the z-value that corresponds to the closest area to 35% in the normal table. From the table, we find that the z-value is approximately -0.385.
Since the percentile corresponds to the area under the normal curve, we know that the score 42 is located at approximately -0.385 standard deviations from the mean.
Similarly, the z-value corresponding to the 70th percentile is approximately 0.525. The score 76 is located at approximately 0.525 standard deviations from the mean.
By subtracting the z-values corresponding to the percentiles, we can find the approximate number of standard deviations between 42 and 76.
0.525 - (-0.385) = 0.91
This means that the distance between 42 and 76 is approximately 0.91 standard deviations.
To find the approximate standard deviation, we divide this distance by the number of standard deviations.
Since we know that 0.91 standard deviations correspond to a range of 34 (76 - 42), we can set up the proportion:
0.91 / x = 34 / x
Solving for x, we find:
x = 34 / 0.91 ≈ 37.36
Therefore, the approximate standard deviation of the final exam scores is approximately 37.36.
Among the given answer choices, the closest option is B. 37.8.
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Two functions are ________ equivalent if they produce the same output for a specific input value.
Always
Sometimes
Never
Answers
Answer:
always
Step-by-step explanation:
i hope this helps you!
Answer:
Always
Explanation:
I hope this helped and good luck!
help please fractions
Answers
Answer:
48 pipes
Step-by-step explanation:
3/4 of 1 foot = 0.75 foot
36/0.75=48
An underwater canyon begins at 40 feet below sea level and is 105 feet deep. What is the elevation of the bottom of the canyon?
Answers
Answer:
145 ft below sea level
Step-by-step explanation:
40 + 105 = 145
Answer:
145 feet
Step-by-step explanation:
HELP ME PLS
GRADES ARE DUE TODAY
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Most of this exercise is looking at different ways to identify the slope of the line. The first attachment shows the corresponding "run" (horizontal change) and "rise" (vertical change) between the marked points.
In your diagram, these values (run=1, rise=-3) are filled in 3 places. At the top, the changes are described in words. On the left, they are described as "rise" and "run" with numbers. At the bottom left, these same numbers are described by ∆y and ∆x.
The calculation at the right shows the differences between y (numerator) and x (denominator) coordinates. This is how you compute the slope from the coordinates of two points.
If you draw a line through the two points, you find it intersects the y-axis at y=4. This is the y-intercept that gets filled in at the bottom. (The y-intercept here is 1 left and 3 up from the point (1, 1).)
The formula to find the volume of a sphere is = 4 3, where is the radius of the 3
sphere. What is the formula in terms of ?
Answers
Answer:
d.
took the test
Step-by-step explanation:
A company sells confetti in boxes in the shape of a triangular pyramid. Each box contains 240 cubic centimeters of confetti. If the height of the box is 15 centimeters, which of the following could be the dimensions of the base of the box?
Answers
Answer:
Base, 8 cm; height, 4 cm i think
Step-by-step explanation:
PLEASE HELP NOW --- >N is a 2-digit even number. If the last two digits of N^2 is the same as N, what is the sum of digits of N?
Answers
Answer:
76.
Step-by-step explanation:
It is given that N is a 2-digit number.
Last two digits of N^2 is the same as N.
We know that, a number is even if it ends with 0,2,4,6,8.
\(2^2=4,4^2=16,6^2=36,8^2=64\)
If 0 is in end then we get two zeros in the square of that number.
It is clear that, number should ends with 6 to get the same number at the end.
\(16^2=256\)
\(26^2=676\)
\(36^2=1296\)
\(46^2=2116\)
\(56^2=3136\)
\(66^2=4356\)
\(76^2=5776\)
\(86^2=7396\)
\(96^2=9216\)
It is clear that last two digits of (76)^2 is the same as 76.
Therefore, the required number is 76.
Divide.
Write your answer in simplest form.
6/5 divided by 5/8
Answers
6/5x8/5
6x8 5x5
48/5x5
48/25
Decimal (1.92)
Answer:
The simplest form would be 1 23/28.
Step-by-step explanation:
Khan academy : >
solve for a
•A=125
•A=37
•A=55
Answers
Answer:
37 degrees
Step-by-step explanation:
Answer:
A=37
Step-by-step explanation:
PLS SOMEONE HELP ME ASAP
Answers
Answer:
A. (2i)(8) = d. 16i
B. 16i³ = b. -16i
C. (2i)⁴ = a. 16
D. (2i)(8i) = c. -16
Step-by-step explanation:
A. Multiply 2i by 8 to get 16i, which corresponds to d.
B. The exponent is 3 more than a mulitple of 4 in 16i³, so the answer is negative. -16i corresponds to b.
C. (2i)⁴ has an exponent that is a multiple of 4, so the i isn't needed. 16 corresponds to a.
D. (2i)(8i) simplifies to 2(8) * i². The exponent is 2 more than a multiple of 4, so the answer is negative, without an i. -16 corresponds to c.
Problem 2: Prove that the square of any integer a is either of the form 3k or of the form 3k + 1, for some integer k. Hint: By the Euclidean algorithm, a must be of the form 3q or 3q + 1 or 3q + 2, fo
Answers
The square of any integer a can be expressed in one of two forms: 3k or 3k + 1, where k is an integer.
We will consider three cases based on the possible forms of the integer a: 3q, 3q + 1, and 3q + 2, where q is an integer.
Case 1: If a is of the form 3q, then a = 3n, where n = q. In this case, a^2 = (3n)^2 = 9n^2 = 3(3n^2). Therefore, the square of a is of the form 3k, where k = 3n^2.
Case 2: If a is of the form 3q + 1, then a = 3n + 1, where n = q. Squaring a gives a^2 = (3n + 1)^2 = 9n^2 + 6n + 1 = 3(3n^2 + 2n) + 1. Thus, the square of a is of the form 3k + 1, where k = 3n^2 + 2n.
Case 3: If a is of the form 3q + 2, then a = 3n + 2, where n = q. In this case, a^2 = (3n + 2)^2 = 9n^2 + 12n + 4 = 3(3n^2 + 4n + 1) + 1. Hence, the square of a is also of the form 3k + 1, where k = 3n^2 + 4n + 1.
In all three cases, we see that the square of any integer a can be expressed either as 3k or 3k + 1, where k is an integer. Therefore, we have proved that the square of any integer a falls into one of these two forms.
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Solve the proportion 2/7=x/42
A. 1/2
B. 12
C. 2/7
D. 6
Because algebra is going to help me raise a family, buy a house, and pay taxes.
Answers
84/7= 12
X= 12
Math will help you get a degree and you will raise a family with more money- afford a house— and pay your taxes.
pls help 6x+15=6(x-3) pls help with answer and explaining
Answers
Answer:
-33
Step-by-step explanation:
distribute;
6x + 15 = 6x - 18
subtract;
-15
simplify;
- 33
subtract from both sides;
-6
total;
-33
Answer:Answer is 0=-33
Step-by-step explanation:What you need to do is bring x by itself on one side and the other numbers on the other side The steps are
6x+15=6x-18
6x-6x=-18-15
0=-33
Please help! I think I know the answer but I don't trust myself xD (Theres a screenshot attached)
Answers
Answer:
the second one
Step-by-step explanation:
The last one
Explanation:
-7 times 2 will be -14 and -7 times 5d would be -35d which is exactly what they ask for
Anh's math book costs $26.62 less than her art book cost. Her math book costs $83.38. How much did her art book cost
PLEASE HELP MEEEEEEE FAST PLEASEEE IM REALLY DESPERATE SORRY BUT PLEASE
Answers
Answer:
$110
Step-by-step explanation:
If her art book costs $26.62 less than her math book, and her math book costs $83.38, then all you have to do is add 26.62 to 83.28. Then the answer would be 110.
solve 12=-r-11 i really need help
Answers
that’s the answer
What is the domain of the step function f(x) = [2x]- 1?
O {x|x2-1}
O {x|x ≥ 1}
O x x is an integer}
O {x|x is a real number}
Answers
Domain: {x | x is a real number}
Option D, "{x | x is a real number}" accurately represents the domain of the function.
The domain of the step function f(x) = [2x] - 1, where [2x] represents the greatest integer less than or equal to 2x, can be determined by considering the restrictions on the input values.
In this case, the step function is defined for all real numbers. However, the greatest integer function imposes a restriction. Since the greatest integer function only outputs integers, the input values (2x) must be such that they produce integer outputs.
For any real number x, the greatest integer less than or equal to 2x will always be an integer. Therefore, the domain of the function f(x) = [2x] - 1 is:
Domain: {x | x is a real number}
Option D, "{x | x is a real number}" accurately represents the domain of the function.
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please help me I'm running out of time!!
Answers
Answer:
The answer is hotdog you can cook the hotdog and eat it
Not negative because
-13X-13X-13X-13
If even than it’s always going to be positive if odd always going to be negitive
Hope this helps
In the figure, a∥b and m∠3 = 34°.
What is the m∠7?
Enter your answer in the box. |__|
Answers
Therefore, In the figure, a∥b angle m∠7 = 34° .
What is angle ?An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common terminus, and are referred to as the sides of the angle. Angles of two rays lie in the plane containing the rays. Angles can also result from the intersection of two planes. Dihedral angles are the name given to them.
Here,
Given that a and b are parallel lines,
∠3 and ∠7 are corresponding angles and congruent
m∠3 = 34°
thus ,m∠7 =m∠3 = 34°
so, m∠7 = 34°
Therefore, In the figure, a∥b m∠7 = 34° .
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(Histograms and Line Plots LC)
The following is a list of movie tickets sold each day for 10 days.
14, 35, 20, 23, 42, 87, 131, 125, 64, 92
Which of the following intervals are appropriate to use when creating a histogram of the data?
0 – 29, 30 – 59, 60 – 89, 90 – 119, 120 – 149
0 – 30, 30 – 55, 55 – 80, 80 – 105, 105 – 130
0 – 24, 25 – 49, 50 – 74, 75 – 99, 100 – 125
0 – 35, 35 – 70, 70 – 105, 105 – 140
Answers
The class intervals appropriate to use in creating a histogram of the data are 0 – 30, 30 – 55, 55 – 80, 80 – 105, and 105 – 130. The correct option is B.
What are the class intervals?A histogram is used to represent data graphically. the histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.
The width of the intervals must be equal. This means that the difference between the lower bound and the upper bound must be equal. Also, the upper bound of the preceding interval must be the same as the lower bound of the next interval.
This means that the intervals must be overlapping. Of all the options, it is 0 – 30, 30 – 55, 55 – 80, 80 – 105, and 105 – 130 that satisfy both conditions.
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Answer:first option
Step-by-step explanation:
Reba needs to simplify the expression below.
6 and one-half + 3.5 times 2 minus 7 divided by 3
Which operation should she perform first?
Answers
Answer:
she should preform division
Step-by-step explanation:
Answer:
Actually, it's C multiplication Cutty you can't be giving Wrong answers.
Step-by-step explanation:
It's C Multiplication because Were using the PEMDAS technique and this stands for
P- Parenthesis
E- Exponents
M- Multiplication
D- Division
A- Addition
S- Subtraction
So if you see in the Pemdas technique It will be C Multiplication.