Answer:
Option B.
Step-by-step explanation:
Let the radius of the snare drum = r
and radius of the model = R
Ratio of the dimensions of the snare drum and the model = 1 : 4
So, [tex]\frac{r}{R}=\frac{1}{4}[/tex]
Now as per question, dimensions of the snare drum is multiplied by a scale factor of [tex]\frac{1}{2}[/tex]
Radius of the snare drum = [tex]\frac{r}{2}[/tex]
Ratio of the radius of the snare drum and cylindrical model ,
[tex]\frac{\frac{r}{2}}{R} =\frac{1}{4}[/tex]
[tex]\frac{r}{2R}=\frac{1}{4}[/tex]
[tex]\frac{r}{R}=\frac{1}{2}[/tex]
Therefore, the cylinder with Sara's dimensions will be geometrically similar but the scale factor will be 1 : 2
Option B is the answer.
What is the value of "h"?
2 + h - 48 = 30
Please answer and I will brainliest to the person who gives me the link to the profile name UsernameCorrupted.
Please I really need to find this person.
Answer:
h = 76
Step-by-step explanation:
2 + h - 48 = 30
h + 2 - 48 = 30
h - 46 = 30
h - 46 + 46 = 30 + 46
h = 76
Answer:
2+h-48=30
2-48+h=30
-46+h=30
h=30+46
∴h=76
What is the value of x in the solution to this system of linear equations?
Use substitution.
y = -3x + 3
- 2x + 2y = 6
Answer:
Step-by-step explanation:
y = -3x + 3
-2x + 2y = 6
-2x + 2(-3x + 3) = 6
-2x - 6x + 6 = 6
-8x + 6 = 6
-8x = 0
x = 0
y = -3(0) + 3
y = 0+ 3
y = 3
(0, 3)
The number of students, S, serviced by the school system in the town of Emor, t years from 2000 can be modeled by the function S(t) = 10,000(1.1). The number ...
The question is incomplete. Here is the complete question.
The number of students, S, serviced by the school system in the town of Emor, t years from 2000 can be modeled by the function S(t) = 10000.[tex](1.1)^{t}[/tex]. The number of classrooms, C, in the town of Emor, t years from 2000 can be modeled by the function C(t) = 450 + 40t. Let D be the average number of students per classroom in Emor's school system t years from 2000.
Write a formula for D(t) in terms of S(t) and C(t).
Write a formula in terms of t.
Answer: D(t) = S(t) / C(t)
D(t) = [tex]\frac{10000.(1.1^{t} )}{450+40t}[/tex]
Step-by-step explanation: First, it is asked to write D(t), which is the average number of students per classroom in terms of students, S(t) and classroom, C(t).
Average is the total number of students divided by the total number of classrooms. Therefore:
D(t) = [tex]\frac{S(t)}{C(t)}[/tex]
Second, to write in term of t, which is time in years, for the average number of students per classroom:
D(t) = [tex]\frac{10000.(1.1)^{t} }{450+40t}[/tex]
In this formula it is clear that the average number of students per classroom is dependent of the growth factor of students each year represented by [tex]1.1^{t}[/tex] and the "growth factor" of classroom each year, represented by 40t.
Evaluate 3|-5| -2|-2|
Answer:
11
Step-by-step explanation:
absolute value is always a positive number so
3|-5| -2|-2| =
3 * 5 -2*2
follow PEMDAS
15 -4 = 11
Keep getting this wrong please help!!!
Answer:
85 + 35=120
Step-by-step explanation:
85 + 35= 120
85 - 35= 50
the difference is fifty
Health issues are a concern of managers, especially as they evaluate the cost of medical insurance. A recent study of 150 executives at Elvers Industries, a large insurance and financial firm located in the Southwest, reported the number of pounds by which the executives were overweight. a. Compute the mean and the standard deviation.
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
Health issues are a concern of managers, especially as they evaluate the cost of medical insurance. A recent survey of 150 executives at Elvers Industries, a large insurance and financial firm located in the Southwest, reported the number of pounds by which the executives were overweight. Compute the mean and the standard deviation.
Pounds Overweight Frequency
0 up to 6 14
6 up to 12 42
12 up to 18 58
18 up to 24. 28
24 up to 30. 8
Solution:
This is grouped data. We would determine the midpoint or class mark, x of each class by taking their averages.
The table would become
Class. x f fx
0 up to 6 (0+6)/2 = 3 14 42
6 up to 12 (6+12)/2 = 9 42 378
12 up to 18 (12+18)/2 = 15 58 870
18 up to 24 (18+24)/2= 21 28 588
24 up to 30 (24+30)/2 = 27 8 216
Summation f = 14 + 42 + 58 + 28 + 8 = 150
Summation fx = 42 + 378 + 870 + 588 + 216 = 2094
Mean = Summation fx/Summation f
Mean, m = 2094/150 = 13.96
Standard deviation = √summation of f(x - m)²)/(n - 1)
We would create another column on the table
f x x - m f(x - m)²
14 3 - 10.96 1681.7024
42 9 - 4.96 1033.2672
58 15 1.04 62.7328
28 21 7.04 1387.7248
8 27 12.04 1159.6928
Total = 5325.12
Standard deviation = √5325.12/150 - 1)
Standard deviation = 5.98
Let x stand for the number of minutes spent waiting in line for a rollercoaster at an amusement park. 81 people are sampled at a time. The sample mean is 18 minutes and the sample standard deviation is 0.5 minutes. What is the standard deviation of the population?
Answer:
The standard deviation of the population is 4.5 minutes.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation of the population [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this question:
[tex]s = 0.5, n = 81[/tex]
So
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.5 = \frac{\sigma}{\sqrt{81}}[/tex]
[tex]\sigma = 9*0.5 = 4.5[/tex]
The standard deviation of the population is 4.5 minutes.
A 170-lb man carries a 20-lb can of paint up a helical staircase that encircles a silo with radius 30 ft. The silo is 90 ft high and the man makes exactly three complete revolutions. Suppose there is a hole in the can of paint and 8 lb of paint leaks steadily out of the can during the man's ascent. How much work is done by the man against gravity in climbing to the top
The work done by the man against gravity in climbing to the top is 16740 lb-ft
What is work done against gravity?The work done against gravity relies on the height of the object and the weight at which the object is changing.
From the given information:
Taking the vertical y-axis when y = 0, then:
The weight of the paint w(y) becomes;w(0) = 20 lb
w(90) = 20 - 8 = 12 lb
Provided that the paint leaks steadily, the function of y i.e. w(y) can be expressed as a linear function in the form:
w(y) = a + by ---- (1)
Thus;
w(0) = a = 20w(90) = 20 + 90b = 12b = (12 - 20)/90b = -4/45From equation (1)
w(y) = 20 - 4y/45
The total weight becomes;
w = w(y) + the man's weight
w = 20 - 4y/45 + 170
w = 190 - 4y/45
Therefore, the work done against gravity is computed as:
W = ∫ w dy
where;
y varies from 0 to 90[tex]\mathbf{W = \int ^{90}_{0}( 190 - \dfrac{4y}{45} )\ dy }[/tex]
W = 16740 lb-ft
Learn more about work done against gravity here:
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A _ _ _ _ _ of a circle is a segment that begins and ends on the circle; a segment whose endpoints are on the circle. It does not have to pass through the center.
Answer:
Chord
Step-by-step explanation:
I believe the word you are looking for is a chord.
PLEASE HELP ASAP (20 points) Basic Inverse Function Question
*see attachment*
Answer:
D
Step-by-step explanation:
f(x ) = [tex]x^{2} - 1\\[/tex]
inverse ----> f(x) = y = x
x = [tex]y^{2}[/tex] - 1
[tex]y^{2} = x + 1[/tex]
y = ± [tex]\sqrt{x + 1}[/tex]
Which of the following is an advantage to using equations?
Answer:
The correct option is
(A). When given two names for the same quantity, you can use algebra to solve the equations.
Step-by-step explanation:
I had thesame quiz, lucky you...next time put the options :)
What’s the correct answer for this question?
Answer:
x = 40
Step-by-step explanation:
Given 2 secants to a circle from an external point, then
The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is
8(8 + x) = 12(12 + 20) ← distribute parenthesis on both sides
64 + 8x = 12 × 32 = 384 ( subtract 64 from both sides )
8x = 320 ( divide both sides by 8 )
x = 40
pls help me to understand TwT ive been struggling oof.
what is surface area of a square pyramid that has a base of 100 ft a base of 40 ft a height of 50 ft and slant height of 60 ft?
Step-by-step explanation:
The surface area of a square pyramid is the area of the square base plus the area of the 4 lateral faces:
A = b² + 4 (½ bl)
A = b² + 2 bl
where b is the width of the base,
and l is the slant height.
Answe The surface area of a square pyramid is the area of the square base plus the area of the 4 lateral faces:
A = b² + 4 (½ bl)
A = b² + 2 bl
where b is the width of the base,
and l is the slant height.:
Step-by-step explanation:
A book store is having a sale. The book Bart wants was originally priced at $14.99. The book is now $10.04. By what percentage was the price reduced?
Answer:
33.0220147 % reduction
Step-by-step explanation:
Take the original price and subtract the new price
14.99-10.04 = 4.95
Divide by the original price
4.95/14.99 =.330220147
Change to percent form
33.0220147 %
Researchers conduct a study of obesity in children. They measure body mass index (BMI), which is a measure of weight relative to height. High BMI is an indication of obesity. Data from a study published in the Journal of the American Dietetic Association shows a fairly strong positive linear association between mother’s BMI and daughter’s BMI (r = 0.506). This means that obese mothers tend to have obese daughters. A. Identify explanatory, response, and potential lurking variables in this study. B. Can we conclude from this study that maternal obesity causes obesity in daughters?
Answer:
Step-by-step explanation:
a. The explanatory variables in this case is the mothers BMI on which the child's BMI is determined.
The response variable is the child's BMI which is also the outcome variable that exists if a child has an obese parent.
Other lurking variables may include the diets and exercise plan of either of these two variables.
b. No, this study cannot be used to conclude that maternal obesity causes obesity in daughters if the lurking variables are not dealt with.
What is the value of (3-5)4(2) – 16+ 2?
-40
-16
24
56
Answer:
-30
Step-by-step explanation:
(3-5)4(2) – 16+ 2= -2*8-14= -16-14= -30
What is the value of x in the equation 3x - y = 18, when y= 27?
O 5
O 7
O45
O 63
Answer:
Step-by-step explanation:3x-y=18
y=27
Therefore 3x-(27)=18
3x=18+27..Nb when the 27 is now being added instead of subtracted.
3x=45
3x/3=45/3 Nb the 3 is now being divided instead of being multiplied.
Therefore X=15
F(x)=3x2 +12x +5 what is the discriminant
Answer:
84
Step-by-step explanation:
This is in the form
ax^2 + bx +c
3x^2 +12x +5
a =3 b = 12 c =5
The discriminant is
b^2 - 4ac
12^2 - 4 * 3 *5
144 - 60
84
FACTORISE THIS EXPRESSTION AS FULLY AS POSSIBLE 4x2+x3
Step-by-step explanation:
4x2 + x3
Rearrange
x3 + 4x2
x2 (x + 4)
What is the value of x?
Answer:
The answer is B.
Step-by-step explanation:
Given that the total angle in a triangle is 180°. So in order to find x, you have to subatract 95° and 57° from 180°
[tex]x + 95 + 57 = 180[/tex]
[tex]x = 180 - 95 - 57[/tex]
[tex]x = 28[/tex]
The following ple chart shows the number of students in a certain school. There
are 2000 students in the school. Answer questions 21, 22 and 23 from the pie
chart.
Grade 1
30%
Grade 3
20%
Grade 4
15%
21. The number of students in grade 1 is
22. The number of students in grade 3 is
23. The number of students in grade 4 is
Answer:
G1 : 0.3(2000) = 600
G2: 0.2(2000) = 400
G3: 0.15(2000) = 300
G4: 2000/15=150
It's in the pic plz help
Answer:
It is 4 because length PO is also 4 and TR is across from it.
Step-by-step explanation:
The composite figure is made up of a rectangular prism and a___a0___.a1
Answer:
The composite figure is made up of a rectangular prism and square pyramid
Step-by-step explanation:
The figure on top is square pyramid since the base is a square and the 4 sides are triangles. The bottom is a rectangular prism since the figure is made up of side rectangular faces
Answer:
square pyramid
also the figure has 896 cm2
Determine the equation of the inverse of y=2^3x-1
Answer:
f^-1(y) =[ In(x-2) + 1] /3
Step-by-step explanation:
The inverse of this expression is to find x
Now taking In of both sides we have
y=2^3x-1
In y = In2^3x-1
In y = (3x- 1)In 2
(Iny / In2) + 1= 3x
x =[ (Iny / In2) + 1] /3
Therefore the inverse of y is
f^-1(y) =[ (Inx / In2) + 1] /3
f^-1(y) =[ In(x-2) + 1] /3
The equation of the inverse of the provided equation, which is equal to the reverse of the original equation, is y=(ln(x-2)+1)/3.
What is the inverse of an equation?The inverse of an equation is the reverse of the original equation. The equation and the inverse of it has symmetry in each other.
To find the inverse of equation, we have to interchange the variable of equation to each other.
The given equation is,
[tex]y=2^{3x-1}[/tex]
Taking log both side of the equation,
[tex]\ln y = \ln 2^{3x-1}[/tex]
Use the log of power and simplify the equation further, as,
[tex]\ln y = \ln 2^{3x-1}\\\ln y = (3x-1)\ln 2\\\dfrac{\ln y}{\ln 2} = (3x-1)\\\ln (y-2)= (3x-1)\\\ln (y-2)+1= 3x\\x=\dfrac{\ln (y-2)+1}{3}[/tex]
Interchange the place of x and y,
[tex]y=\dfrac{\ln (x-2)+1}{3}[/tex]
This is the required inverse equation.
Thus, the equation of the inverse of the provided equation which is equal to the reverse of the original equation, is y=(ln(x-2)+1)/3.
Learn more about the inverse of an equation here;
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7) ¿De cuántas maneras pueden sentarse diez personas alrededor de una mesa circular?
Answer: Around a circular table, ten people can be seated 362880 ways.
Explanation:We establish the conditions of the exercise:
Yes, all elements fit. 10 people have to sit.Being a circular arrangement we must eliminate the circular repetitionsItems are not repeated. A person cannot be repeated.It is a Combination so we use the formula:
[tex]\boldsymbol{\sf{_{n}C_{r}=\cfrac{n!}{n\cdot (n-r)!} }}[/tex]
[tex]\boldsymbol{\sf{n=10\; \; \; \; \; r=10}}[/tex]
We substitute and solve:
[tex]\boldsymbol{\sf{_{10}C_{10}=\cfrac{10!}{10\cdot (10-10)!}=9!=9\cdot8\cdot7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1=362880}}[/tex]
Determine whether the integral is convergent or divergent. 1 59 1 − x2 dx 0 convergent divergent Correct: Your answer is correct. If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES
Complete Question
The complete question is shown on the first uploaded image
Answer:
it is convergent and the solution is [tex]= \frac{33 \pi }{2}[/tex]
Step-by-step explanation:
From the question we are given
[tex]\int\limits^1_0 {\frac{33}{\sqrt{1-x^2} } } \, dx[/tex]
When integrated
[tex]= 33 sin^{-1} x \left | \ 1} \atop {0}} \right.[/tex]
[tex]= 33[ \frac{\pi }{2} - 0][/tex]
[tex]= \frac{33 \pi }{2}[/tex]
This implies that the integral converges
Función inversa f(x) = 7/x -9
Answer:
F-1(x)=7/(x+9)
Step-by-step explanation:
Change F(x) to y so y=7/x -9
Swap variables x=7/y -9
Solve x+9=7/y
7/(x+9)=y
Then change y to F inverse
F-1(x)=7/(x+9)
Thats ur inverse!!!
Answer:
(x+9)/7
Step-by-step explanation:
Let f(x) = y;
y =7/x - 9
y + 9 = 7x
x = (y + 9)/7
Substitute x for y and X = f^{-1}(x)
f^{-1}(x) =(x+9)/7 this is the inverse of f(x)
The total number of pupils in 6 classes is 192.
Find the average number of pupils in a class.
Somebody help please, I'm stuck with this question..
Answer:
32 pupils in a class
Step-by-step explanation:
You are going to divide 192 by 6 to figure out the average amount per class.
The function
R(x) = 80 + 7.440 √ x 0 ≤ x ≤ 15000
indicates that the monthly revenue R (in thousands of dollars) depends on the amount of dollars x spent on advertising each month.
a. By how much would the monthly revenue be expected to change if the monthly expenditure on advertising were to be raised from its current level of $ 6000 to $ 6001 ? (Use the marginal revenue R '(x) and round to the nearest dollar.) $ Incorrect
b. What is the revenue when the amount spent on advertising is $6000 . Round to the nearest dollar. $ Incorrect
Corrected Question
The function is: [tex]R(x)=80+7.440\sqrt{x} , 0\leq x\leq 15000[/tex]
Answer:
(a)$48.02
(b)$656,299.92
Step-by-step explanation:
(a) We are to determine the change in monthly revenue if the monthly expenditure, x is raised from its current level of 6000 to 6001.
[tex]R(x)=80+7.440\sqrt{x}\\R'(x)=\dfrac{d}{dx} (80+7.440\cdot x^{1/2})\\=7.440 \times \frac{1}{2} \times x^{\frac{1}{2}-1}\\=3.72\times x^{-\frac{1}{2}}\\\\R'(x)=\dfrac{3.72}{\sqrt{x} }[/tex]
Therefore, the expected change in monthly revenue
[tex]R'(6000)=\dfrac{3.72}{\sqrt{6000} }=$0.04802 (thousands)[/tex]
=$48.02
(b)When the amount spent on advertising is $6000
[tex]Revenue, R(6000)=80+7.440\sqrt{6000}\\=\$656.29992$ (in thousands)\\=\$656,299.92[/tex]
Ifx-10 is a factor of x2 - 8x - 20, what is the other
factor?
x +
Answer:
[tex] f(x) = x^2 -8x -20[/tex]
We know that one factor is (x-10). We know that we need to find two values that added we got -8 and multiplied we got -20. So then we can set the following options:
[tex] a(10) = -20[/tex]
[tex] a-10= -8[/tex]
And solving for a we got:
[tex] a = -8+10=-2[/tex]
And we got:
[tex] a = -2[/tex]
So then the other factor would [tex] x +2[/tex]
Step-by-step explanation:
For this case we have the following expression:
[tex] f(x) = x^2 -8x -20[/tex]
We know that one factor is (x-10). We know that we need to find two values that added we got -8 and multiplied we got -20. So then we can set the following options:
[tex] a(10) = -20[/tex]
[tex] a-10= -8[/tex]
And solving for a we got:
[tex] a = -8+10=-2[/tex]
And we got:
[tex] a = -2[/tex]
So then the other factor would [tex] x +2[/tex]
Answer:
Step-by-step explanation:
