a) the constant of proportionality multiplies every actual linear dimension
b) height of a can of fruit juice is 3.85 inches high
What is Proportionality?
The term proportionality describes any relationship that is always in the same ratio.
Explanation for answer:
Since the desire is to have students look twice as tall, we expect the constant of proportionality to be [tex]\frac{1}{2}[/tex].
Instead, we're told that the stage manager is using a height of 44 inches to represent an 80-inch door.
This means their constant of proportionality is [tex]\frac{40}{80} = 0.55[/tex]
a) Any new props can be scaled by this factor (0.55) to find their height on set.
b) A 7-inch can would be scaled to [tex]7\times 0.55 = 3.85\ inches[/tex]
Question: The school's theater club is building sets that will make ordinary students look like giants. The actors need a door, a table, and a stool that will make them look almost twice as tall!
DOOR: actual height is 80 inches and Height on Set is 44 inches
TABLE: actual height is 28 inches
STOOL: actual height is 18 inches
How can the stage manager use the constant of proportionality to find the dimensions of any new props the director requires?
What should the height of a can of fruit juice used as a prop be if its actual height is 7 inches? Show your work.
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Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 220 numerical entries from the file and r = 52 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.
(i) Test the claim that p is less than 0.301. Use = 0.05.
A button hyperlink to the SALT program that reads: Use SALT.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: p < 0.301; H1: p = 0.301
H0: p = 0.301; H1: p ≠ 0.301
H0: p = 0.301; H1: p > 0.301
H0: p = 0.301; H1: p < 0.301
Correct: Your answer is correct.
(b) What sampling distribution will you use?
The Student's t, since np > 5 and nq > 5.
The standard normal, since np > 5 and nq > 5.
The Student's t, since np < 5 and nq < 5.
The standard normal, since np < 5 and nq < 5.
Correct: Your answer is correct.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)
The hypothesis are given as follows:
H0: p = 0.301; H1: p ≠ 0.301.
a) The level of significance is of 0.05.
b) The sampling distribution is given by: The standard normal, since np > 5 and nq > 5.
The test statistic is of: z = -2.09.
c) The p-value is of: 0.0366.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence to conclude that the proportion has changed, hence:
[tex]H_0: p = 0.301[/tex]
At the alternative hypothesis, it is tested if there is enough evidence to conclude that the proportion has changed, hence:
[tex]H_1: p \neq 0.301[/tex]
What is the test statistic?The test statistic is given by the equation presented as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
The parameters of the equation are listed as follows:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.The values of these parameters for this test are:
[tex]\overline{p} = \frac{52}{220} = 0.2364, p = 0.301, n = 220[/tex]
Hence the value of the test statistic is of:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.2364 - 0.301}{\sqrt{\frac{0.301(0.699)}{220}}}[/tex]
z = -2.09.
What is the p-value?We have a two-tailed test, as we are testing if the proportion is different of a value.
Hence, using a z-distribution calculator, with z = -2.09, the p-value is of 0.0366.
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what fraction of the voters polled voted for eric jackson?
F. 1/26
G. 13/50
H. 13/37
J. 50/13
The fraction of the voters polled voted for Eric Jackson is 50/13. A fraction is a portion of a whole or, more broadly, any number of equal parts.
What is meant by fraction?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. A fraction is a portion of a larger whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complex fraction has a fraction in the integrand or denominator. The numerator of a proper fraction is smaller than the denominator.Fractions are described as parts of a whole. The total can be a single object or a group of objects.Therefore,
The fraction of the voters polled voted for Eric Jackson is 50/13
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Which equations shows a proportional relationship between x and y.
y=6x
y= x - 5
The equation that shows a proportional relationship between x and y is y=6x
How to determine the equation?The options represent the given parameters
As a general rule
A proportional relationship is represented as y = kx
Where k represents the constant of proportionality
So, we check the options for equations that has the same form as y = kx
We have
y = 6x
The above equation is a linear equation
In fact, it is a linear equation that shows a proportional relationship
Note that all linear equations have a constant rate of change
So, the proportional relationship is given as
y = 6x
Where the constant of proportion is 6
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6 books weigh 1.260 kg. How many books will weigh 3.150 kg?
Answer: 15 books
Step-by-step explanation:
Given that the weight of 6 books is 1.260 kg
⟹ weight of each book is [tex]\frac{1.260}{6}[/tex] = 0.210kg
Let the number of books that will weigh 3.150 kg be x
as we know that
weight of x books is 0.210x kg
⟹0.210x=3.150
⟹x= [tex]\frac{3.150}{0.210}[/tex] = 15
The number of books is 15
15 books will weigh 3.150 kg.
Given the weight of 6 books is 1.260 kg
⟹ weight of each book is
1.260/6
=0.210 kg
Let x be the total number of books that weigh 3.150 kg.
as we are aware
weight of x books is 0.210x kg
⟹0.210x=3.150
⟹x= 3.150/0.210
=15
So, the number of books is 15.
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The time difference, t, in minutes, taken for an object to travel from point A to B and the return journey is given by the equation (t+6) (t-8)=72. By solving the equation (t+6) (t-8)=72, find the time difference t in minutes.
Answer:
t = 12
Step by step explanation:
(t + 6)(t - 8) = 72
t² - 8t + 6t - 48 = 0
t² - 2t - 120 = 0
(t + 10)(t - 12) = 0
t + 10 = 0 OR t - 12 = 0
t = -10 OR t = 12
(reject)
Valentina is trying to decide whether to join her school's swim team. During the summer, the team practices 4 days per week. Each of those days, they practice for 3 hours in the morning and practice again in the afternoon. They practice for a total of 20 hours each week.
Which equation can you use to find h, the length of each afternoon practice in hours?
The equation used to find the length of each afternoon practice is given as follows:
4(h + 3) = 20.
What is the system of equations?The variables in this problem are defined as follows:
Variable x: length of each morning practice.Variable h: length of each afternoon practice.During the summer, the team practices 4 days per week, for a total of 20 hours each week, hence the equation is of:
4(x + h) = 20.
The number of hours practiced during the morning is of:
x = 3.
Hence the equation to solve for h is given as follows:
4(3 + h) = 20
Applying the commutative property:
4(h + 3) = 20.
Hence the second option is correct.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Valentina is trying to decide whether to join her school's swim team. During the summer, the team practices 4 days per week. Each of those days, they practice for 3 hours in the morning and practice again in the afternoon. They practice for a total of 20 hours each week.
Which equation can you use to find h, the length of each afternoon practice in hours?
Summer swim practice is 4 days per week. Each day has 3 hours of morning practice and h hours of afternoon practice. So, the number of hours of practice each day is h+3. Weekly practice is a total of 20 hours. This equation represents the situation.
4 (h+3)
=
20
days of practice per week
hours of practice each day
total hours of practice each week
The equation 4(h+3)=20 can be used to find the length of each afternoon practice in hours. Solve the equation for h.
4(h+3)
= 20
h+3
= 5 Divide both sides by 4
h
= 2 Subtract 3 from both sides
Each afternoon practice is 2 hours.
Which is the best first step when solving the following system of equations?
x+y=3
4x-y=7
O Multiply the first equation by 4.
Add the first equation to the second equation.
Multiply the second equation by -1.
Subtract the second equation from the first equation.
The best first step to solve equations, x+y = 3 and 4x-y = 7, is to add the first equation to the second equation.
According to the question,
We have the following system of equations:
x+y = 3 .....(1)
4x-y = 7 ....(2)
Now, these equations can be easily solved by adding the first equation to the second equation because we will only then have one variable which is x and y when added to -y will result in zero.
We can solve these equations by adding as follows:
x-y+4x+y = 3+7
5x = 10
x = 10/5
x = 2
Now, we can put the value of x in equation 1 to find the value of y:
2+y = 3
y = 3-2
y = 1
Hence, the correct option is B.
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A scientist claims that 9% of viruses are airborne.
If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 533 viruses would differ from the population proportion by less than 3%? Round your answer to four decimal places.
The probability that the proportion of airborne viruses in a sample of 533 viruses would differ is 0.0062.
How to calculate the probability?From the information, the scientist claims that 9% of viruses are airborne and the proportion of airborne viruses in a sample is 533 viruses.
The requirement to solve the probability between z-values is to know that the probability between the z-values is the difference between the probability of the greatest z-value and the lowest z-value.
The mean is 0.09 and the standard deviation is 0.012.
The probability will be:
= 1 - P[Z < (0.12 - 0.09/0.013)]
= 1 - P(Z < 2.5)
= 1 - 0.99379
= 0.0062
This shows the concept of solving probability regarding z values.
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I need answer help please
For given function f(x) = 7/(x² - 5),
f(a + 4) = 7/(a² + 8x + 11)
In this question we have been given a function f(x) = 7/(x² - 5)
We need to evaluate f(a + 4)
Substitute x = a + 4 in given function.
f(a + 4)
= 7/((a + 4)² - 5)
= 7/(a² + 8x + 16 - 5)
= 7/(a² + 8x + 11)
Therefore, for given function f(x) = 7/(x² - 5),
f(a + 4) = 7/(a² + 8x + 11)
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PLEASE HELP!!!!! will give points
explain in detail
Can you find two numbers that can satisfy this pattern? 6, 24, 60, 120, 210, ___, ___,
Answer:
336, 504
Step-by-step explanation:
You want the next two numbers in the sequence beginning 6, 24, 60, 120, 210, ....
DifferencesWhen attempting to identify a sequence it is often useful to look at the differences between terms, then at the differences of those, and so on. If The differences at some level are constant, that level tells you the degree of the polynomial that will describe the sequence. If they have a common ratio, then the sequence will be based on an exponential function.
1st differences: 18, 36, 60, 90
2nd differences: 18, 24, 30
3rd differences: 6, 6 . . . . . . . . constant, indicating a cubic function
EquationWe can go to the trouble to write four equations in the four coefficients of the cubic describing this sequence, or we can let suitable technology find it for us. The attachment shows a graphing calculator solution for the coefficients. The 10^-14 value for the 'd' coefficient is effectively 0. This value is due to the inexact representation of numbers in the floating point arithmetic used by the calculator.
The equation of the n-th term a[n] is ...
a[n] = n³ +3n² +2n
The next two terms are ...
a[6] = 336
a[7] = 540
__
Additional comment
The equations for the coefficients of y = ax³ +bx² +cx +d will use the given sequence values and x values of 1..4. Here they are:
6 = a·1 +b·1 +c·1 +d
24 = a·8 +b·4 +c·2 +d
60 = a·27 +b·9 +c·3 +d
120 = a·64 +b·16 +c·4 +d
The second attachment shows a calculator solution for these four equations. (a, b, c, d) = (1, 3, 2, 0)
A denim shirt at a certain factory requires 2 1/5 yards of material. How many shirts can be made from 70 2/5 yards of material?
Answer: 32
Step-by-step explanation:
If you multiply 2 1/5 by 35 you would get 70.4, .4 is equivalent to 2/5, so 70.4 = 70 2/5.
Find the quadratic function whose graph is shown to the right. Write the function in the form f(x)=a(x−h)2+k.
Help
The quadratic equation f(x) = - (x + 2)² + 17 represents the graph shown.
¿What is the quadratic equation that represents a graph?
In this problem we have the definition of a quadratic equation in its vertex form, whose definition is explained below:
f(x) = a · (x - h)² + k
Where:
a - Vertex constant.(h, k) - Vertex of the parabola.We need to determine the quadratic equation related to a graph shown.
First, determine the coordinates of the vertex:
(h, k) = (- 2, 17)
Second, find the vertex constant:
a = [f(x) - k] / (x - h)²
a = (13 - 17) / (0 + 2)²
a = - 4 / 4
a = - 1
Third, write the resulting function:
f(x) = - (x + 2)² + 17
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Last week, the total weight of the members of a weight loss support group was 2,500 pounds. This week, it was 2,525 pounds. What percent heavier is the group now? %
The percent increase from 2,500 pounds this week to 2,525 pounds is 1% increase
How to find the percent increase of the weights?From the question, we have the following parameters that can be used in our computation:
Initial weight = 2500 pounds
New weight = 2525 pounds
The percentage increment is then calculated as
Percentage = (Final value - Initial value)/Initial value * 100%
Substitute the known values in the above equation
Percentage = (2525 - 2500)/2500 * 100%
Evaluate the difference
So, we have
Percentage = 25/2500 * 100%
Evaluate the quotient
So, we have
Percentage = 0.01 * 100%
Evaluate the product
So, we have
Percentage = 1%
Hence, the percent increase is 1% increase
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guys please answer all my questions are being ignored
Line x is the perpendicular bisector of segment ZY
what does x =
Answer:
x=7
Step-by-step explanation:
these 2 triangle sides are equal to each other so just set them equal to find x
X+3=3x-11
-x. -x
3=2x-11
+11. +11
14=2x
=2. =2
7=x
Hopes this helps please mark brainliest
how to find perimeter of a triangle?
Answer:
Just add the 3 sides together
Step-by-step explanation:
if a triangle has the side values of 3, 4, 6. Then you would simply add them together!
3+4+6=13
therefor that triangles perimeter is 13
hope this helps!
What is the domain and range of the graph in set notation
The required domain of the function shown is (-∞, ∞) and the range is (-3, ∞).
Range, it is the set of values that come out to an outcome for certain mathematical operations.
Here,
A graph of the function is shown,
and the graph of the function is defined from -∞ to ∞, so the domain of the function is (-∞, ∞).
Also, the function has a value of the y-axis from -3 to ∞, and the range of the function is (-3, ∞).
Thus, the required domain of the function shown is (-∞, ∞) and the range is (-3, ∞).
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which of the following is a polynomial 5x^2+3
The correct option regarding which option represents a polynomial is given as follows:
b. ii only.
What are polynomials?Polynomials are expressions that are given in the following format:
[tex]p(x) = a_nx^n + a_{n-1}x^{n - 1} + \cdots + a_1x + a_0[/tex]
In which n is the degree of the polynomial.
The exponents n have to be all whole numbers for the expression to represent a polynomial, meaning that they cannot be negative neither fractions or decimal values.
Thus the only expression that represents a polynomial is:
ii. 5x³ + 3x² + x + 2.
The reasons for the expressions that do not represent a polynomial are given as follows:
Expression i: Negative exponents.Exponent iii: Fractional exponents, due to the root.Hence the correct option is given by option b.
Missing InformationThe problem is given by the image at the end of the answer.
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Plot a point that is in the solution region of this inequality.
y>x-3+8
The point (-6,6) is in the solution region of the inequality and is plotted in given below graph.
Given,
Equation -> y > x - 3 +8
y > x + 5
Lets take a point A(-6,6)
Putting the value in equation,
6 > -6 + 5
6 > -1
which is true.
Hence, A(-6,6) lies in the region of the inequality.
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6:3(3+3)= can anyone answer this
The Gourmand Cooking School runs short cooking courses at its small campus. Management has identified two cost drivers it uses in its budgeting and performance reports—the number of courses and the total number of students. For example, the school might run two courses in a month and have a total of 62 students enrolled in those two courses. Data concerning the company’s cost formulas appear below:
Fixed Cost per Month Cost per Course Cost perStudent
Instructor wages $ 2,970
Classroom supplies $ 310
Utilities $ 1,230 $ 65
Campus rent $ 4,900
Insurance $ 2,400
Administrative expenses $ 4,000 $ 46 $ 4
For example, administrative expenses should be $4,000 per month plus $46 per course plus $4 per student. The company’s sales should average $890 per student.
The company planned to run four courses with a total of 62 students; however, it actually ran four courses with a total of only 52 students. The actual operating results for September were as follows:
Actual
Revenue $ 52,280
Instructor wages $ 11,160
Classroom supplies $ 19,070
Utilities $ 1,900
Campus rent $ 4,900
Insurance $ 2,540
Administrative
expenses $ 3,858
Answer:
whats the question
Step-by-step explanation:
The operating profit for September was $168,418.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Using the given information, we can calculate the following:
Total fixed cost per month.
= Instructor wages + Classroom supplies + Utilities + Campus rent + Insurance + Administrative expenses
= $2,970 + $310 + $1,230 + $4,900 + $2,400 + $4,000
= $15,810
Variable cost per course.
= Cost per course for utilities + Cost per student for administrative expenses
= $65 + $4 = $69
Variable cost per student
= Sales revenue per student - Total variable cost per student
= $890 - $69
= $821
Using the planned number of courses and students, we can calculate the expected revenue:
Expected revenue.
= Planned number of courses x Planned number of students x Sales revenue per student
= 4 x 62 x $890 = $221,120
Using the actual number of courses and students, we can calculate the actual revenue and costs:
Actual revenue
= Actual number of courses x Actual number of students x Sales revenue per student
= 4 x 52 x $890
= $184,640
Total variable cost
= (Variable cost per course x Actual number of courses) + (Variable cost per student x Actual number of students)
= ($69 x 4) + ($4 x 52)
= $412
Total cost
= Total fixed cost + Total variable cost
= $15,810 + $412
= $16,222
Operating profit
= Actual revenue - Total cost
= $184,640 - $16,222
= $168,418
Therefore,
The operating profit for September was $168,418.
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Graph g(x) = -2x - 3.
The graph of the function g(x) = -2x - 3 is attached below.
Graph:
Graph refers a diagram that represents the variation of a variable in comparison with that of one or more other variables.
Given,
Here we have the function g(x) = -2x - 3
Now, we need to plot the graph of the function.
In order to plot the graph for the given function,
First we have to take some sample values for the given function and then apply it on the given function to generate the table to plot the graph.
Now, we have to take -2, -1, 0, 1, 2 are the samples value for x.
Then we get the value of the function as,
x = -2 => g(-2) = -2(-2) - 3 = 4 - 3 = 1
x = -1 => g(-1) = -2(-1) - 3 = 2 - 3 = -1
x = 0 => g(0) = -2(0) - 3 = 0 - 3 = -3
x = 1 => g(-2) = -2(1) - 3 = -2 - 3 = -5
x = 2 => g(2) = -2(2) - 3 = -4 - 3 = -7
Now, we can get the table like the below
Now, we have to plot the graph through this table, then we get the graph like the following.
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Write an equation of the line that passes through (-3,1) and is perpendicular to y= 1/2x +3
Answer: y=-2x-5
Check this in desmos
12 + -3/2 z =- 14
Solve the missing variable, Z
Answer:
z=-52/3
Step-by-step explanation:
1) 12 + -3/2 z= -14
2) -3/2 z = -26
3) z=-26(-2/3)
4) z= 52/3
Help it’s due tmr…………..
Answer:
7
Step-by-step explanation:
13x - 7 + 30 = 30 + 84
13x - 7 + 30 - 30 = 30 - 30 + 84
13x - 7 = 84
13x = 84 + 7
13x = 91
x = 91 / 13
x = 7
Need help some one please y turn in tomorrow
Answer:i think the answer is 2/4 or 3/2
Step-by-step explanation:
Which inequality is represented by the graph?
5 - 3 -2 -1 0 1 2 3
-3
(1) x>-1
(3) *<-1
(2) x≤-1
D
(4) x ≥-1
4
gering
5
Answer:
answer,(2)x≥-1
Step-by-step explanation:
it was right
Identify the values of the variables. Give your answers in simplest radical form. HELP!
The value of the variables in the right triangle are as follows;
[tex]v = \frac{3\sqrt{2} }{2}[/tex][tex]w=\frac{3\sqrt{6} }{2}[/tex]How to find the side of a right tringle?A right triangle is a triangle that has one of its angles as 90 degrees.
The side of a right triangle can be found by using trigonometric ratios.
Therefore, let's find the variable length of the right triangle as follows;
sin 30 = opposite / hypotenuse
sin 30 = v / 3√2
1 / 2 = v / 3√2
cross multiply
3√2 = 2v
divide both sides by 2
v = 3√2 / 2
Let's find the variable w.
cos 30 = adjacent / hypotenuse
cos 30 = w / 3√2
√3 / 2 = w / 3√2
cross multiply
√3 × 3√2 = 2w
3√6 = 2w
divide both sides by 2
w = 3√6 / 2
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Box A has a length of 5 feet, height of 1 foot, and width of 3 feet. Box B has a length of 4 feet, height of 3 feet, and width of 2 feet. Box C has a length of 7 feet, height of 2 feet, and width of 1 foot. Box D has a length of 3 feet, height of 3 feet, and width of 3 feet.
Lucas wants to use the box with the greatest volume. Which shipping box should he use?
Box
Lucas will be using the shipping box D as it is the box with the greatest volume of 27ft³
Volume of a rectangular boxThe volume of a rectangular box is calculated by multiplying its three dimensions which are the length, width, and height . That is Length × Width × Height in the same units.
volume of box A = 5ft × 3ft × 1ft
volume of box A = 15ft³
volume of box B = 4ft × 2ft × 3ft
volume of box B = 24ft³
volume of box C = 7ft × 1ft × 2ft
volume of box C = 14ft³
volume of box D = 3ft × 3ft × 3ft
volume of box D = 27ft³
Therefore, the shipping box with the largest volume is box D with 27ft³
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Answer:
Step-by-step explanation:
FEEL ME ITS D
ITS D
THE ONE WITH THE 333
Hey so basically I'm having trouble understanding this problem so if someone can help me with the answer that'd be great thx <3
Two poles of heights 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m,
then what will be the distance between their tops?
Answer:
The distance would be 13m.
Answer:
13 m
Step-by-step explanation:
this can be looked at like a triangle sorry for the bad drawing I’m in the car lol
But we know the base is 12m and the height of this triangle is 5 since the secon pole is 5m taller hence 14-9=5
So we use the Pythagorean theorem
a^2+b^2=c^2
12^2+5^2=c^2
144+25=c^2
169=c^2
Now find the square root of 169 to get the answer
13 m is the distance between the tops
Hopes this helps please mark brainliest
HELP MIDDLE SCHOOL MATH BRAINLIEST 30 POINTS
Answer:
Step-by-step explanation:
A. -1/3x
B. -x
c.-5/4x
