Answer:
The range of the function [tex]f(x) = -|3\cdot x+3|[/tex] is every positive real numbers plus zero.
Step-by-step explanation:
According to definition of the absolute value, the range of absolute value covers positive real numbers or zero. A linear function is a continuous function, which means the existence of an image for every element from domain. The negative sign transforms the original range to all negative real numbers plus zero.
Hence, the range of the function [tex]f(x) = -|3\cdot x+3|[/tex] is every positive real numbers plus zero.
In your bid to be elected class representative, you have your election committee survey five randomly chosen students in your class and ask them to rank you on a scale of 0-10. Your rankings are 9, 6, 1, 7, 7. (a) Find the sample mean and standard deviation. (Round your answers to two decimal places.) HINT [See Example 1.] sample mean standard deviation (b) Assuming the sample mean and standard deviation are indicative of the class as a whole, in what range does the empirical rule predict that approximately 68% of the class will rank you
Answer:
Sample mean = 6
Sample standard deviation = 3
Range = 3 to 9
Step-by-step explanation:
Given data:
Rankings (x)
9
6
1
7
7
sample size = n = 5
(a)
Sample Mean: [tex]\frac{}{x}[/tex] = ∑x/n
= 9+6+1+7+7 / 5
= 30 / 5
[tex]\frac{}{x}[/tex] = 6
Sample Standard Deviation = s = √(x- [tex]\frac{}{x}[/tex] )²/n-1
= √((9-6)² + (6-6)² + (1-6)² + (7-6)² + (7-6)²) / (5-1)
= √((3)² + (0)² + (-5)² + (1)² + (1)²) / 4
= √(9+0+25+1+1)/4
= √36 / 4
= √9
= 3
s = 3
b) In what range does the empirical rule predict that approximately 68% of the class will rank you?
As per the empirical rule, 68% of data falls within first standard deviation from the mean μ ± 1σ
[tex]\frac{}{x}[/tex] = 6
s = 3
So
6 - 3 = 3
6 + 3 = 9
Hence the range is from 3 to 9
What's the length of an arc with a central angle of 100° and a radius of 2 inches?
Answer:
the answer is 4) 10π/9 inches
Step-by-step explanation:
all answers have π on the nominator but i could not insert it for some reason
[tex]Question 7 options:\\1) \frac{40}{3}inches \\2) \frac{5}{3} inches\\3) \frac{100}{3} inches \\4) \frac{10}{9} inches[/tex]
A circle is a curve sketched out by a point moving in a plane. The length of the arc with a central angle of 100° and a radius of 2 inches is 3.49 inches.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
Given that the radius of the circle is 2 inches, while the angle made by the arc at the centre of the circle is 100°. Therefore, the length of the arc can be written as,
Length of the arc = 2 × π × R × (θ/360°)
= 2 × π × 2 inches × (100°/360°)
= 10π / 9 inches
= 3.49 inches
Hence, the length of the arc with a central angle of 100° and a radius of 2 inches is 3.49 inches.
Learn more about Circle:
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part 5 please assist me with this problems
Answer: 14) 44° 15) 6.5
Step-by-step explanation:
Law of Cosines: a² = b² + c² - 2bc · cos A
Note: The letters can be swapped
14) Given: a = 7, b = 6, c = 10, A = ???
7² = 6² + 10² - 2(6)(10) · cos A
49 = 36 + 100 - 120 cos A
49 = 136 - 120 cos A
-87 = - 120 cos A
0.725 = cos A
43.5° = A
15) Given: A = 21°, b = 18, c = 16
a² = 18² + 16² - 2(18)(16) · cos 21°
= 324 + 256 - 576 cos 21°
= 580 - 576 cos 21°
= 42.26
[tex]a=\sqrt{42.26}[/tex]
= 6.5
Evaluate the expression when x=35 and y=6 x / 5 - y
Answer:Variable expressions are expressions that involve variables, which are symbols that represent changing quantities. The value of the expression will change as the value of the variable changes.
For example, let's say with have the equation
x
+
5
When
x
=
1
, then
x
+
5
=
6
When
x
=
2
then
x
+
5
=
7
Hope that was helpful.
In a multi digit number the number place that a digit is in determines its?
Answer:
Place Value
Step-by-step explanation:
To Find:in a multi-digit number, the number place that a digit is in determines it's?
Solution :
The number place that a digit is in determines it's PLACE VALUE
Definition of place value : Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.
Thus in a multi-digit number, the number place that a digit is in determines it's PLACE VALUE.
Eg . 389
Since the digit 8 is on tens place
So, it makes us to determine its place value
Place value of 8 is 80
Hence in a multi-digit number, the number place that a digit is in determines it's PLACE VALUE.
100+678+467 helpjjsjjs
Answer:
1245 is the answer of this question
Construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe any patterns. Number of classes: 8 Data set: Reaction times (in milliseconds) of 30 adult females to an auditory stimulus
Answer:
Hello The data set is missing below is the missing data set
507,389,305,291,336,310,514,442,373,428,387,454,323,441,388,426,411,382,320,450,309,416,359,388,307,337,469,351,422,413
Step-by-step explanation:
Data set:
507,389,305,291,336,310,514,442,373,428,387,454,323,441,388,426,411,382,320,450,309,416,359,388,307,337,469,351,422,413
To CONSTRUCT a Frequency Distribution do the following
Identify the Number of classes ( 8 ). Find the data range ( 514-291) = 223 Find the width 223/8 = 27.9. ≈ 28 create 8 groups each of 28 width starting from (291). count the no of data set in each interval and use that to generate the frequency table as attached belowattached is the frequency table and histogram representation
what is one fourth divided by two
Answer:
1/8
Step-by-step explanation:
1/4 ÷ 2
copy dot flip
1/4 * 1/2
1/8
Cassandra argues that (6 2/3)6 can be simplified to 6(6 2/3), but Rafael argues that the exponent 6 2/3 should be replaced with another number. Enter the number that the exponent 6 2/3 should be replaced with.
Answer:
Assuming you mean (6^2/3)^6, the exponent 6 2/3 in the simplification should be replaced with 4
Step-by-step explanation:
Apply the power rule and multiply exponents.
6 ^2 /3 * 6
Cancel the common factor of 3
6 ^2 *2
Multiply 2 by 2 .
6 ^4
Which of the following would be a good reason to place your money into a savings account? a. You can purchase stocks with a savings account b. A savings account earns interest c. You can write checks with a savings account d. You can use a debit card to make transactions Please select the best answer from the choices provided A B C D
Answer: B. a savings account earns interest
Step-by-step explanation: Money loses value over time as the rate of inflation increases. In this scenario, when you have some money to spare, the ideal is to seek some kind of investment that earns interest.
Saving is one such option. The money in savings earns interest and is highly liquid, meaning it can be used at any time. In addition, saving is a very...
Answer:
B
Step-by-step explanation:
Find the value of x.
Answer:
Hey there!
3x-9=114
3x=123
x=41
Let me know if this helps :)
What is the radius of a circle whose equation is (X +5 )2+(Y -3 )2=four squared
Answer: 4
Step-by-step explanation:
The standard equation of a circle is (x−h)^2 + (y−k)^2 = r^2, with (h,k) being the center and r being the radius. In the equation you provided, r = 4.
Answer:
Step-by-step explanation:
(x-h)²+(y-k)²=r²
radius=r
what are all the zeros of function g(x) = (x + 2)(x − 2)(x − 3),
Answer:
-2, 2 and 3.
Step-by-step explanation:
each of the brackets could be zero.
So for example x + 2 = 0 gives x = -2.
Answer:
x=-2 x=2 x=3
Step-by-step explanation:
g(x) = (x + 2)(x − 2)(x − 3)
Set the function equal to 0
(x + 2)(x − 2)(x − 3) =0
Using the zero product property
x+2 =0 x-2 =0 x-3 =0
Solve each equation
x=-2 x=2 x=3
These are the zeros
Solve 3exponent3-2=9
Answer: No solution. 27=9
Add or Subtract to Simplify:
(x5 + x3) - (6x - x3 + 6x5)
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{ - 5 {x}^{5} + 2 {x}^{3} - 6x}}}}[/tex]
Step-by-step explanation:
[tex] \sf{( {x}^{5} + {x}^{3} ) - (6x - {x}^{3} + 6 {x}^{5}) }[/tex]
When there is a ( - ) in front of an expression in parentheses , change the sign of each term.
Also, remove the parentheses
⇒[tex] \sf{ {x}^{5} + {x}^{3} - 6x + {x}^{3} - 6 {x}^{5} }[/tex]
Collect like terms
⇒[tex] \sf{ {x}^{5} - 6 {x}^{5} + {x}^{3} + {x}^{3} - 6x}[/tex]
⇒[tex] \sf{ - 5 {x}^{5} + 2 {x}^{3} - 6x}[/tex]
Hope I helped!
Best regards!!
which pairs of angles in the figure below are vertical angles? Check all that apply
Student work
TRY IT #1
Write each of the following as a rational number.
b. 3
c-4
Answer:
b. 3 = 3/1
c. -4 = -4/1
Step-by-step explanation:
An integer can be written as a rational number with a denominator of 1. The denominator can be anything else, too, in which case the numerator must be multiplied by that same value.
__
b. 3 = 3/1 = 6/2 = 27/9
__
c. -4 = -4/1 = 8/-2 = -12/3
Solve. 3(4x - 7) =27
What is the value of the expression
(
43
+
7
2
)
2
2
2
2
(43+7
2
)
?
Answer:
The question is not clear
-ثارة
=ةرة1
What is 10 to the second power times 10 to the second power?
Answer: 10,000
Step-by-step explanation: 10 to the 2nd power or 10^2 is 100 so you multiply 100x100 which is 10,000
Answer:
10,000
Step-by-step explanation:
10^2*10^2
10^4=10,000
Marginal Revenue
The demand function for a certain boat company's 34 ft Sundancer yacht is
p = 700 − 0.01x ln(x)
where x denotes the number of yachts and p is the price per yacht in hundreds of dollars.
(a) Find the revenue function R(x) and the marginal revenue function R'(x) for this model of yacht.
R(x) = 700x−0.01x2ln(x)
R'(x) = −0.01x−0.02xln(x)+700
(b) Use the result of part (a) to estimate the revenue to be realized from the sale of the 375th 34 ft Sundancer yacht. (Round your answer to the nearest dollar.)
Answer:
Step-by-step explanation:
a) Revenue function us derives by taking the product of the number of yachts and the demand function p given. Mathematically,
R(x) = xp(x)
Given p(x) = 700 − 0.01x ln(x)
R(x) = x{700 − 0.01x ln(x)}
R(x) = 700x - x(0.01x ln(x))
R(x) = 700x - 0.01x²lnx
Hence the revenue function R(x) is expressed as R(x) = 700x - 0.01x²lnx
Marginal revenue function is derived by finding the derivative of the revenue function R(x). On differentiating;
d{R(x)}/dx = 700 - 0.01{x²(1/x)+2xlnx} (note that product rule was used to differentiate the function in parenthesis).
d{R(x)}/dx = 700 - 0.01{x+2xlnx}
Open the parenthesis
d{R(x)}/dx = 700 - 0.01x-0.02xlnx
Hence the marginal revenue function R'(x) is expressed as 700 - 0.01x-0.02xlnx.
b) In order to estimate the revenue to be realized from the sale of the 375th 34 ft Sundancer yacht, we will simply substitute the variable x = 375 into the revenue function R(x)
Given R(x) = 700x - 0.01x²lnx
R(375) = 700(375) - 0.01(375)²ln(375)
R(375) = 262500-1406.25ln(375)
R(375) = 262500-8334.74
R(375) = 254,165.26
Hence the revenue realized from the sale is approximately $254,165
For the Marginal revenue Function,
R'(x) = 700−0.01x−0.02xln(x)
R'(375) = 700−0.01(375)−0.02(375)ln(375)
R'(375) = 700−3.75−0.02(375)ln(375)
R'(375) = 700-3.75-44.45
R'(375) = 651.8
The marginal revenue is approximately $652
Wyatt is going to a carnival that has games and rides. Each game costs $1.25 and each ride costs $2.75. Wyatt spent $20.25 altogether at the carnival and the number of rides he went on is twice the number of games he played. Determine the number of games Wyatt played and the number of rides Wyatt went on.
Answer:
Wyatt played 3 games and went on 6 Rides
Step-by-step explanation:
Let games be represented as x
Let ride be represented as y
Each game cost $1.25
Each ride cost $2.75
Total money spent by Wyatt= $20.25
x1.25 + y2.75 = 20.25 ..... Equation 1
the number of rides he went on is twice the number of games he played
Y= 2x ... Equation 2
Substituting the value of y into equation 1
x1.25 + y2.75 = 20.25
x1.25 + 2(x)2.75 = 20.25
x1.25 + x5.5 = 20.25
x6.75= 20.25
x= 20.25/6.75
X= 3
Y= 2x
Y= 2(3)
Y= 6
Wyatt played 3 games and went on 6 Rides
Answer:
Wyatt played 3 games and went on 6 rides.
Step-by-step explanation:
Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to approximate the sum of the series with an error of less than 0.001. [infinity] (−1)n + 1 n2 n = 1
Answer:
at N ≥ 6
Step-by-step explanation:
Error permissible = 0.001
The series = infinity
at ( N + 1 ) ! > 1000 the inequality N ≥ 6 is valid and holds
attached below is the detailed solution using alternating series remainder
If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to (r/s)(6)?
Answer:
Step-by-step explanation:
(r/s)(x) is the quotien of r(x) = 3x - 1 and s(x) = 2x + 1:
r 3x - 1
(-----)(x) = ----------
s 2x + 1
p(n,6)=3p(n,5) what is the value of n.
Answer:
n = 10
Step-by-step explanation:
3n1!/(n-4)! = (n-1)!/( n-1-5)
3n(n-1)(n-2)(n-3)(n-4) / N-4 -------- case1 ( cancel ( n-4) from top and bottom)
= (n-1)(n-2)(n-3)(n-4)(n-5)(n-6) / n-6 --------- case 2 ( Cancel n-6 from top and
bottom and also cancel n-1,
n-2, n-3 with case 1)
3n = ( n-4)(n-5)
3n = n² - 5n - 4n + 20
3n = n² - 9n + 20
0 = n² - 9n - 3n + 20
0 = n² - 12n + 20
0 = (n-2)(n-10)
n = 2 ( not valid) n = 10
Therefore n = 10
-7/2x + 3/2 + 2 =-7/2
Answer:
x=2
Step-by-step explanation:
-7/2x + 3/2 + 2 =-7/2
Add the numbers
3/2+2
2=2/1=4/2
3/2+4/2=7/2
-7/2x+7/2=-7/2
Subtract 7/2 from both sides
-7/2x=-14/2
Multiply both sides by 2
-7x=-14
Divide both sides by -7
x=2
Hannah and Zach together earn $950 for an
advertising drop. They earn equal hourly rates
of pay. If Hannah worked for 10 hours and
Zach for 9 hours, how much
did Zach earn?
Answer:
$450
Step-by-step explanation:
Let R be the hourly pay rate in dollars per hour. Hannah worked 10 hours and Zach worked 9 hours for a total of $950, so we get the equation:
10R + 9R = 950
Solve for R:
19R = 950
R = 50
Zach worked for 9 hours, so the total he earned is:
9 hours * 50 dollars/hour = $450
If you answer these two questions, that would be awesome, on my other questions i have asked the same one twice so if you want more points go on to my other questions and just put the same thing. hopefully someone see's this.
Answer:
[tex]\sqrt[3]{x^2}[/tex]
x ^( 1/8)
Step-by-step explanation:
x ^ (5/6) ÷ x ^ (1/6)
We know that a^ b ÷ a ^c = a^ ( b-c)
x^ ( 5/6 - 1/6)
x^ (4/6)
x ^ 2/3
[tex]\sqrt[3]{x^2}[/tex]
[tex]\sqrt{x}[/tex][tex]\sqrt[\\4]{x}[/tex]
x ^ 1/2 * x ^ 1/4
We know that a^ b * a ^ c = a^ (b*c)
x ^ (1/2 * 1/4)
x ^( 1/8)
Answer:
[tex]\huge \boxed{\sqrt[3]{x^{2} } } \\ \\ \huge \boxed{x^{\frac{3}{4} } }[/tex]
Step-by-step explanation:
Part 1:
x^(5/6) ÷ x^(1/6)
Applying exponent rule : a^b ÷ a^c = a^(b-c)
x^(5/6-1/6)
x^(4/6)
Simplifying the exponent.
x^(2/3)
Converting to simplest radical form.
(x^2)^(1/3)
[tex]\sqrt[3]{x^{2} }[/tex]
Part 2:
[tex]\sqrt{x} \times \sqrt[4]{x}[/tex]
Converting to exponent form.
x^(1/2) × x^(1/4)
Applying exponent rule : a^b × a^c = a^(b+c)
x^(1/2+1/4)
x^(2/4+1/4)
x^(3/4)
Find the product:
(x+9)(x-9)
a 18
b. -81
C. - 18
d. x-64
Answer:
x^2 -81
Step-by-step explanation:
(x+9)(x-9)
FOIL
first x*x = x^2
outer -9x
inner 9x
last -9*9 = -81
Add them together
x^2 -9x+9x -81
Combine like terms
x^2 -81
Answer: B
Step-by-step explanation:
Simply using (a-b)(a+b)=a^2-b^2.
Evaluate the power (9^2).
x^2 - 81
Solve for X. The triangles are similar.
A. 4
B. 9
C. 11
D. 3
Answer:
[tex] x = 11 [/tex]
Step-by-step explanation:
Given that ∆CDE ~ ∆FGH
CD = 25
DE = 35
FG = 65
GH = 8x + 3
Therefore,
[tex] \frac{CD}{FG} = \frac{DE}{GH} [/tex]
(Similarity Theorem)
[tex] \frac{25}{65} = \frac{35}{8x + 3} [/tex]
Cross multiply
[tex] 25(8x + 3) = 35*65 [/tex]
[tex] 200x + 75 = 2275 [/tex]
[tex] 200x + 75 - 75 = 2275 - 75 [/tex]
[tex] 200x = 2200 [/tex]
[tex] \frac{200x}{200} = \frac{2200}{200} [/tex]
[tex] x = 11 [/tex]
Answer:
C. 11
Step-by-step explanation:
x = 11