Rebecca's friend Steve is creating thefurniture for the scale model of Hogwartsusing the same scale of 2 in: 5 ft. IfProfessor McGonagall's desk is 6 feetwide and 3 feet tall, what will it's widthand height be in the model? (Hint: Createtwo proportions.)
Answers
From the statement we know that:
0. Steve is using the scale of 2in : 5ft (model dimensions : real-life dimensions).
,1. The dimensions of the desk are w = 6ft wide and t = 3ft tall.
From point 1 we compute the proportion r between the dimensions in the model and the real-life dimensions:
\(r=\frac{2in}{5ft}\text{.}\)Now, using the proportion r we compute the dimensions of the model multiplying the real-life dimensions of point 2 by the proportion r:
\(\begin{gathered} w_{\text{model}}=r\cdot w_{\text{real}-\text{life}}=\frac{2in}{5ft}\cdot6ft=\frac{12}{5}\cdot in=2.4in, \\ t_{\text{model}}=r\cdot t_{\text{real}-\text{life}}=\frac{2in}{5ft}\cdot3ft=\frac{6}{5}\cdot in=1.2in, \end{gathered}\)where we used a calculator to compute the fractions and we got:
• 12/5 = 2.4,
,• 6/5 = 1.2.
Answer
- The width of the desk in the model is 2.4in.
- The tall of the desk in the model is 1.2in.
0.
Related Questions
An economy has two industries, farming and building. For every $1 of food produced, the farmer
uses $.20 and the builder uses $.15. For every $1 worth of building, the builder uses $.25 and the
farmer uses $.20. If the external demand for food is $100,000, and for building $200,000, what
should be the total production for each industry in dollars?
Answers
The tοtal prοductiοn fοr fοοd shοuld be $1,000,000.
What is the basic arithmetic οperatiοns?The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.
Let F and B be the prοductiοn οf fοοd and building, respectively, in dοllars. Then, we have the fοllοwing system οf equatiοns:
Fοr the prοductiοn οf fοοd:
F = 0.20F + 0.25B + 100,000
0.20F + 0.15B = 100,000
Fοr the prοductiοn οf building:
B = 0.20F + 0.25B + 200,000
0.25B + 0.20F = 200,000
We can sοlve this system using substitutiοn οr eliminatiοn. Here, we will use eliminatiοn:
0.20F + 0.25B = 200,000 (multiply the secοnd equatiοn by -1)
0.20F + 0.15B = 100,000
0.10B = 100,000 - 0.10F (subtract the secοnd equatiοn frοm the first)
B = 1,000,000 - F
Substitute this expressiοn fοr B intο οne οf the equatiοns tο sοlve fοr F:
0.20F + 0.25(1,000,000 - F) = 200,000
0.20F + 250,000 - 0.25F = 200,000
-0.05F = -50,000
F = 1,000,000
Hence, the tοtal prοductiοn fοr fοοd shοuld be $1,000,000.
We can substitute this value intο either equatiοn tο sοlve fοr B:
0.20(1,000,000) + 0.15B = 100,000
0.15B = -80,000
B = -533,333.33
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i need help for this question
Answers
Answer:
4, 4, and 8
Step-by-step explanation:
2 cups * 2 marshmallows per cup = 4 marshmallows
8 marshmallows / 2 marshmallows per cup = 4 cups of hot cocoa
16 marshmallows / 2 marshmallows per cup = 8 cups of hot cocoa
3. When the line of best fit is found by hand, it is exact.
O True
O False
Answers
What does it mean to regroup to find the sum?
Answers
The meaning of the regrouping is the grouping the place values of the numbers like ones, tens and hundreds, while doing the arithmetic operation like addition
Place value chart is defined as the chart that is used to find the place value of the digit in a number according to the the position of the digit.
To find the sum of the two or numbers first we have to regroup the numbers. Regroup is the process of grouping the same place values of the numbers and do the arithmetic operation.
Consider the numbers 12 and 34. If we want to add them together first we will group the same place value digits. In 12, 1 is number of tens and 2 is number of ones, similarly in 34, 3 is the numbers of tens and 4 is the number of ones. Therefore group 2 and 4 in ones and 1 and 3 in tens and add them together
Therefore, regrouping is the grouping the tens, hundreds of the numbers while addition
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PLEASE HELP IN THE NEXT 15 MINUTES!!!!!!!!!!
The Cross Bayou Bridge in Shreveport, Louisiana has trusses that form triangles. The exterior angle of one triangle has a measure of (5 - 3)°. If the two nonadiacent interior angles of the triangle are 43° and (3x)°, what is the value of the exterior angle, in degrees?
Answers
The exterior angle of the triangle is 62°.
What is triangle?
A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.
Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.
Let us take the triangle as ABC.
Here \(m\angle C\)= 180-(5x-3)° [Because straight line angle is 180°].
We know that sum of all angles in triangle is add upto 180° Then,
=> \(m\angle A+m\angle B+m\angle C\)=180
=> 43°+3x°+180-5x+3=180°
=> -2x=180-180-43-3
=> -2x=-46
=> x=13°
Now exterior angle ,
=> 5x-3
=> 5*13-3
=> 65-3
=> 62°
Hence the exterior angle of the triangle is 62°.
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A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
Answers
Answer:
53\(x_{123}\) == 134 cf
Step-by-step explanation:
A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
The height of the building is approximately 78.63 meters.
The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.
Draw a diagram of the situation described in the problem to get a better understanding of the problem. The diagram would have a right-angled triangle with angle of elevation of 66° at the bottom left vertex and another angle of elevation of 53° at the bottom right vertex. The object on top of the building is at the vertex of the triangle. Point M and I on the diagram are points on the horizontal line of sight and on the ground respectively. We can label the diagram with the following values:Angle of elevation from point A = 66°Angle of elevation from point P = 53° Length of line segment AM = h Length of line segment MP = x Length of line segment IP = y Length of line segment MT = 50m. We'll use these values to calculate the length of h, which is the height of the building.Use the tangent ratio to find x:tan 66° = h / x => x = h / tan 66°. Use the tangent ratio to find y:tan 53° = h / y => y = h / tan 53°.We know that x + y = 50, so substituting the expressions for x and y from step 3 gives:h / tan 66° + h / tan 53° = 50h = 50 tan 66° tan 53° / (tan 53° + tan 66°) ≈ 78.63 m.Therefore, the height of the building is approximately 78.63 meters.
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Can someone help me with this please?
Answers
Answer:
1)
D) -5<x≤-2
R) 0<y≤3
2)
D) 1≤x≤5
R)2≤y≤4
Step-by-step explanation:
(Only in 7th so might be wrong)
1)
D) -5<x≤-2
R) 0<y≤3
2)
D) 1≤x≤5
R)2≤y≤4
look at the range of where the x and y is at (1-2 included = 1<x≤2)
a water snake in a well is 30 M below the ground level its lights 20 m upward and then slips down 10 M how far it is from the ground level
\( - 30 - + 20 - - 10\)
Answers
If the water snake is initially 30 meters below the ground level and then climbs 20 meters upward, it will be 30 - 20 = 10 meters below the ground level. However, if it then slips down 10 meters, it will be 10 + 10 = 20 meters below the ground level.
4. Uncle Royce is 42. What is his target heart rate range?
O 120-180 beats per minute
O 150-200 beats per minute
O116-160 beats per minute
O170-236 beats per minute
Answers
Step-by-step explanation:
70 to 85 % of his maximum
Maximum is estimated to be 220 - age = 220 - 42 = 178
70% of this is 125
85 % is 89 151
I believe I would go with the third choice 116-160 bpm
Please helppppppppp:/
Answers
Answer:
The correct answer is C: angle 6 and angle 4.
3: Find the slope:
(2, -6), (-4,-3)
Answers
Answer:
-(1/2)
Step-by-step explanation:
Slope is the Rise/Run
Going from left to right for (2, -6), (-4,-3):
Rise = (-3 - (-6)) = 3
Run = (-4, -2) = -6
Slope = Rise/Run = 3/-6 = -(1/2)
What
is an arithmetic sequence with a common difference of −2?
Answers
Answer:
An arithmetic sequence with a common difference of −2 is 20,18,16,14,12..
Step-by-step explanation:
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is same. Here, the common difference is -2, which means that each term in the sequence is obtained by subtracting 2 from the previous term.
To find the arithmetic sequence with a common difference of -2, you can start with an first term and then subtract 2 successively to find the subsequent terms.
Let the initial term is 20. Subtracting 2 from 20, we get 18. Subtracting 2 from 18, we get 16. Continuing this pattern, we subtract 2 from each subsequent term to generate the sequence. The arithmetic sequence with a common difference of -2 starting from 20 is
20,18,16,14,12
In this sequence, each term is obtained by subtracting 2 from the previous term, resulting in a common difference of -2.
help i’ll give brainliest
Answers
Answer:
c c c c c c c c c c c c c c c c c c c c
Set up and solve an equation for the value of x. Use the value of x and a relevant angle relationship in the diagram.
(please also show an step by step process of getting EAF!)
Answers
Answer:
x = 27 , ∠ EAF = 27°
Step-by-step explanation:
∠ GAF = 90° , then
∠ GAC + ∠ CAF = ∠ GAF , that is
x + 63 = 90 ( subtract 63 from both sides )
x = 27
∠ DAE = 90°
since CD is a straight angle of 180° , then
∠ CAE = 90° , so
∠ CAF + ∠ EAF = ∠ CAE , that is
63° + ∠ EAF = 90° ( subtract 63° from both sides )
∠ EAF = 27°
determine whether each relationship is proportional by graphing on a coordinate plane. explain your reasoning.
Answers
This answer states that when graphing a linear relationship (y = 2x) on a coordinate plane, the points form a straight line, indicating that the relationship is proportional. However, when graphing a non-linear relationship (y = x2) on a coordinate plane, the points form a parabolic curve, indicating that the relationship is not proportional.
A: Relationship 1:
The relationship between x and y is y = 2x.
When graphed on a coordinate plane, the points (0,0), (1,2), (2,4), (3,6), and (4,8) form a straight line, indicating that the relationship is proportional.
Relationship 2:
The relationship between x and y is y = x2.
When graphed on a coordinate plane, the points (0,0), (1,1), (2,4), (3,9), and (4,16) form a parabolic curve, indicating that the relationship is not proportional.
This answer states that when graphing a linear relationship (y = 2x) on a coordinate plane, the points form a straight line, indicating that the relationship is proportional. However, when graphing a non-linear relationship (y = x2) on a coordinate plane, the points form a parabolic curve, indicating that the relationship is not proportional.
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-4 X - 7 + 8 X-3
PLS SOMEONE HELP
Answers
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
A magazine includes a report on the energy costs per year for32-inch liquid crystal display (LCD) televisions. The article states that 14 randomly selected 32-inch LCD televisions have a sample standard deviation of $3.42 . Assume the sample is taken from a normally distributed population. Construct 98 % confidence intervals for (a) the population variance sigma squared and (b) the population standard deviation sigma .
Interpret the results. (a) The confidence interval for the population variance is (___,___ ). (Round to two decimal places as needed.)
Interpret the results. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.)
A. With 98 % confidence, you can say that the population variance is less than ___.
B. With 2 % confidence, you can say that the population variance is between nothing and ___ .
C. With 98 % confidence, you can say that the population variance is between ___ and ___ .
D. With 2 % confidence, you can say that the population variance is greater than ___
(b) The confidence interval for the population standard deviation is (n___,___). (Round to two decimal places asneeded.)
Interpret the results. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.)
A. With 98% confidence, you can say that the population standard deviation is between ___ and ___ dollars per year.
B. With 98% confidence, you can say that the population standard deviation is greater than ___ dollars per year.
C. With 2% confidence, you can say that the population standard deviation is less than ___ dollars per year.
D. With 2% confidence, you can say that the population standard deviation is between ___ and ___ dollars per year.
Answers
Answer:
a
The confidence interval for the population variance is \( 5.49 < \sigma^2 < 37.02 \)
The correct option is C
b
The confidence interval for the population standard deviation is \( 2.34 < \sigma < 6.08 \)
The correct option is A
Step-by-step explanation:
From the question we are told that
The sample size is n = 14
The standard deviation is \(s = \$3.42\)
Generally the degree of freedom is mathematically represented as
\(df = 14 -1\)
=> \(df = 13 \)
Given that the confidence level is 98% then that level of significance is
\(\alpha = (100 -98) \%\)
=> \(\alpha = 0.02\)
Generally the 98% confidence interval for the variance is mathematically represented as
\(\frac{(n- 1) s^2}{x^2 _{[\frac{\alpha }{2} , df]}} < \sigma^2 < \frac{(n- 1) s^2}{x^2 _{[1- \frac{\alpha }{2} , df]}}\)
=> \(\frac{(14- 1) (3.42)^2}{x^2 _{[\frac{0.02 }{2} , 13]}} < \sigma^2 < \frac{(14- 1) (3.42)^2}{x^2 _{[1- \frac{0.02 }{2} , 13]}}\)
From the chi -distribution table
\(x^2 _{[1- \frac{0.02 }{2} , 13]} = 4.107\)
and
\(x^2 _{[\frac{0.02 }{2} , 13]} = 27.689\)
So
=> \(\frac{(14- 1) (3.42)^2}{27.689} < \sigma^2 < \frac{(14- 1) (3.42)^2}{4.107}\)
=> \( 5.49 < \sigma^2 < 37.02 \)
Generally the 98% confidence interval for the standard deviation is mathematically represented as
\(\sqrt{\frac{(n- 1) s^2}{x^2 _{[\frac{\alpha }{2} , df]}}} < \sigma <\sqrt{ \frac{(n- 1) s^2}{x^2 _{[1- \frac{\alpha }{2} , df]}}}\)
=> \(\sqrt{5.49} < \sigma < \sqrt{37.02 }\)
=> \( 2.34 < \sigma < 6.08 \)
Which two segments are congruent?
A) RS and XP
B) CS and XP
C) RT and SP
D) CA and RY
Answers
In the given question, the segments which are congruent are:-
RS and XP
What is congruent in math?Congruent refers to things that are exactly the same size and form. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.
What is a congruent example?Congruent refers to something that is "absolutely equal" in terms of size and form. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, then stack them on top of one another.
In the gievn figure
the length and size of RS and XP segments are equal
Hence they are congruent
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If a new sweater sells for $53 find the total cost if you are charged 5% sales tax. Round your answer to the nearest cent
Answers
Answer:
$55.65
Step-by-step explanation:
you would find 5% of 53 which is $2.65 and then add that to your original price so 53 + 2.65 = 55.65
What is the probability of rolling a 4 twice with two rolls of a number cube?
Answers
Answer:
1/36
Step-by-step explanation:
(1/6)(1/6)
What is the GCF of the expression -x2y22 - xy2z?
Answers
Answer:
i dont onderstand Thais
pleasee help me i’ll give you brainliest
Answers
Answer:
Step-by-step explanation:
its 4
Answer:
4
Step-by-step explanation:
4 ³ = 64
4 to the negative 2 = 0.0625
so 64× that is 4
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,426 was collected on the sale of 1,182 tickets. How many of each type of ticket were sold?
Answers
Answer:
You have two unknowns, two variables, therefore you need to have at least two equations in this word problem in order to find a solution. Let's review the info you are given:
The price of an Adult ticket: $5
The price of a Student ticket: $1
The two variables are: the number of Adult tickets sold (you can use variable "A"), and the number of Student tickets sold (use variable "S").
The other info you are given is the total number of tickets sold: 1,215 tickets. Use this to make your first equation: the number of adult tickets plus the number of student tickets equals 1,215.
You are also told how much money was collected: $2,591. That means, $5 from every Adult ticket and $1 from every student ticket. We don't know how many of each ticket, but we assigned variables A and S to stand in for this unknown info. The money made from all the adult tickets would be the price of the adult ticket times how many adult tickets sold (5 times A), and the money made from all the student tickets would be the price of the student ticket times how many student tickets sold (1 times S). Use this to make your second equation, which says that all the money collected from all the tickets (5 times A in addition to 1 times S) is (=) 2,591.
Now you have two equations, each equation has two variables. To solve, go back to the easiest equation (the first one) and isolate one of the variables. By isolate I mean get it on one side of the equation by itself. Since in this case these variables are being added together, you have to do the opposite of addition, which is of course subtraction. To do this, you will have to subtract the other variable ON BOTH SIDES of the equation. So, say we want to isolate the variable A, we will subtract S from both sides. Well, S minus S is zero, so now A is isolated, meaning the left side of the equation is just A = ... Now you want to subtract the S on the other side. Remember that whatever you do to one side you must do to the other.
Now that you have your equation re-worked to show A = ..., you need to "plug it into" the second equation. What I mean is, you need to substitute instead of A, put in this equation. Then you will have one equation with one variable which you can solve! Remember the rules of equations, to do work in parenthesis first, the multiply or divide, then add or subtract. You will be able to solve for S.
Once you have found S (the number of student tickets sold), you can easily find A (the number of adult tickets sold) by going back to that first equation and subtracting your value of S from 1215.
Step-by-step explanation:
list
Can you please help me
Answers
Answer:
Step-by-step explanation:
The answer is B
If 1/x + 1/3х = 5, what is the value of 3x/4
Answers
Answer:
Step-by-step explanation:
\(\frac{1}{x}+\frac{1}{3x}=5\\\\\frac{1*3}{x*3}+\frac{1}{3x}=5\\\\\frac{3}{3x}+\frac{1}{3x}=5\\\\\frac{4}{3x}=5\\\\4=5*3x\\\\4=15x\\\\\frac{4}{15}=x\)
x = 4/15
\(\frac{3}{4}x=\frac{3}{4}*\frac{4}{15}\\\\=\frac{1}{5}\)
A 4-sided polygon is classified as a quadrilateral.
True
False
Answers
Answer:
TRUEEEEEEEEEEEEEEEEEE
Step-by-step explanation:
Please help! A rectangle with an area of 104 square centimeters has a length and width in a ratio of 13:2.
What are the length and width?
length =
centimeters
width
centimeters
Answers
Answer:
length = 26 cm
width = 4 cm
Step-by-step explanation:
A = 104 cm²
A = length x width
ratio of length and width = 13 : 2
total ratio of length and width is 15 = a
so ratio of length is (13/15)a and width (2/15)a
A = length x width = (13/15)a x (2/15)a = (26/225)a² = 104
a² = 104 x 225 : 26 = 900
a = 30cm
length = (13/15)a = 13/15 x 30 = 26 cm
width = (2/15)a = 2/15 x 30 = 4 cm
Find the solution to the equation.
4(x + 7) = 38 i need it ASAP plzzz
Answers
Answer:
x = 2.5
or
x = 1/4
Step-by-step explanation:
watch the following steps:
4x + 28 = 38
4x = 38 - 28
4x = 10
x = 2.5
or
x = 1/4
Pls consider marking my answer as Brainliest! It would mean a lot!
Answer:
2.5, maybe
Step-by-step explanation:
distribute 4 into x and 7
subtract 28 from both sides (28-28, 38-28)
divide 4 and 10
2.5
it seems odd...
Order cube root of eighty-eight, twenty-eight ninths, square root of nineteen from greatest to least.
cube root of eighty-eight, twenty-eight ninths, square root of nineteen
twenty-eight ninths, square root of nineteen, cube root of eighty-eight
twenty-eight ninths, cube root of eighty-eight, square root of nineteen
cube root of eighty-eight, square root of nineteen, twenty-eight ninths
Answers
Answer:
(a) twenty-eight ninths, square root of nineteen, cube root of eighty-eight
Step-by-step explanation:
When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.
OrderThe attachment shows the ordering, least to greatest, to be ...
\(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)
__
Additional comment
We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.
One way to do the comparison is to convert these to values that need to have the same root:
√19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)
∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)
The roots will have the same ordering as 19³ and 88².
Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...
19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859
88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744
Then the ordering is ...
28/9 < 19³ < 88² ⇒ 28/9 < √19 < ∛88
Answer:
the ordering is
28/9 < 19³ < 88² ⇒ 28/9 < √19 < ∛88
Step-by-step explanation:
The Earth has a volume of 2.61 x 1011 cubic miles. What is the approximate equatorial diameter of the Earth?
A) 11,985 miles
B) 3,963 miles
C) 15,852 miles
D) 7,962 miles