12%
Step-by-step explanation:Her discounted price was 100% - 20% = 80% of the original price. The service fee made it be 100% + 10% = 110% of that, so her final price was ...
... 110% × 80% = 88%
of the original ticket price.
This represents a discount of 100% - 88% = 12% from the original.
To the nearest whole degree, what angle measure has a tangent of 2.0874?
The total revenue for Fred's Estates LLC is given as the function R(x)=200x−0.4x2, where x is the number of rooms booked. What number of rooms booked produces the maximum revenue?
The number of rooms booked to produce maximum revenue is required.
The number of rooms booked to produce the maximum revenue is 250.
The revenue function is
[tex]R(x)=200x-0.4x^2[/tex]
Differentiating with respect to x we get
[tex]R'(x)=200-0.8x[/tex]
Equating with zero
[tex]0=200-0.8x\\\Rightarrow x=\dfrac{-200}{-0.8}\\\Rightarrow x=250[/tex]
Double derivative of the function is
[tex]R''(x)=-0.8x[/tex]
Substituting the value of [tex]x=250[/tex]
[tex]R''(250)=-0.8\times 250=-200[/tex]
Since, it is negative the maximum value of x will be 250.
The number of rooms booked to produce the maximum revenue is 250.
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The number of rooms that produces the maximum revenue for Fred's Estates LLC is 250 rooms, calculated using the formula -b/2a, where a and b are the coefficients of the quadratic revenue function.
Explanation:To calculate the maximum revenue for Fred's Estates LLC, we need to find the value of x that maximizes the function [tex]R(x)=200*-0.4x2.[/tex]
The maximum value of a quadratic function can be found using the formula -b/2a, where a and b are the coefficients of x² and x in the function. Here, a=-0.4 and b=200.
Using the formula, [tex]x=-b/2a = -200/(2*(-0.4)) = 250[/tex] rooms. Therefore, booking 250 rooms results in the maximum revenue for Fred's Estates LLC.
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Jim needs to rent a car. A rental company charges $21.00 per day to rent a car and $0.10 driven. for every mile . He will travel 250 miles. . He has $115.00 to spend. Write an inequality that can be used to determine d, the maximum number of days that Jim can re ays that Jim can rent a car
Answer:
21d +25 ≤ 115
Step-by-step explanation:
Jim's cost will be ...
... 21.00·d + 0.10·250 = 21d +25
He wants his cost not to exceed his budget, so ...
... 21d +25 ≤ 115
_____
The solution is ...
... 21d ≤ 90 . . . . subtract 25
... d ≤ 90/21 ≈ 4.3
so Jim can rent the car a maximum of 4 days.
The inequality that can be used to express this scenario is
115 ≤ 21*d+ 25
Given data
Charges = $21 per day
Cost per driven distance = $0.10
Distance he will travel = 250 miles
Amount her has to spend = $115
Let the maximum number of days Jim can rent a car with $115 be "m"
Hence
Total amount = 21*d+ 0.1*250
Substituting and Simplifying we have
115 ≤ 21*d+ 25
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what is the solution to the system of equations?
A cardboard box has a square base and an open top. the four sides are made of wood that costs 2 dollars per square foot, while the base is made of aluminum that costs 25 dollars per square foot. if the volume of the box is to be 50 cubic feet, what is its minimum possible cost?
Answer:
$300
Step-by-step explanation:
Let x represent the side length of the square base in feet. Then the height of each side is ...
... h = (50 ft³)/(x ft)² = (50/x²) ft
The cost of the sides of the box is then ...
... (4 sides) × (x ft)(50/x² ft)/side × $2/ft² = $400/x
The cost of the bottom is ...
... (x ft)² × $25/ft² = $25x²
So, the total dollar cost is
... C = 400/x + 25x²
This will be a minimum where its derivative with respect to x is zero.
... 0 = -400/x² +50x
... 400/50 = 8 = x³ . . . . . add 400/x²; multiply by x²/50
... x = ∛8 = 2
For this value of x, the minimum cost is ...
... C = 400/2 + 25·2² = 300
The minimum possible cost is $300.
_____
Comments on the problem
1) Cardboard boxes are usually made of cardboard. They are rarely made of wood and alumninum.
2) The cost of the bottom is half the cost of the sides. When the dimensions are unconstrained, you will find (as here) the cost is shared equally between the bottom and pairs of opposite sides—each being 1/3 the total cost.
what is the solution to the equation -0.2(x-20)=4-x
Answer:
x=0
Step-by-step explanation:
-0.2(x-20)=4-x
The first step is to distribute the -.2
-.2 x -.2 * -20 = 4-x
-.2x +4 = 4-x
Add x to each side
x-.2x +4 = 4-x+x
.8x +4 = 4
Subtract 4 from each side
.8x +4-4 = 4-4
.8x=0
Divide by .8
.8x/.8 = 0/.8
x =0
Mrs.Wheeler is looking to make a deposit of $2500 dollars into the savings account
that earns simple interest at a rate of 2.02% per year. How many years will it take for her account to reach $3000 if she does not deposit or withdraw any money.
9.9 years
Step-by-step explanation:A = P(1 + rt) . . . . account balance after time t at rate r starting with principal P
... 3000 = 2500(1 + 0.0202t) . . . . filling in the given numbers
... 1.2 = 1 + 0.0202t . . . . divide by 2500
... 0.2 = 0.0202t . . . . . . subtract 1
... 0.2/0.0202 = t ≈ 9.901
It will take about 9.9 years for the account balance to reach $3000.
Can someone please answer this for me i cant figure it out.
[tex]\displaystyle x^{\frac{2}{3}}[/tex]
Step-by-step explanation:The rules of exponents tell you ...
... (a^b)(a^c) = a^(b+c) . . . . . . applies inside parentheses
... (a^b)^c = a^(b·c) . . . . . . . . applies to the overall expression
The Order of Operations tells you to evaluate inside parentheses first. Doing that, you have ...
... x^(4/3)·x^(2/3) = x^((4+2)/3) = x^2
Now, you have ...
... (x^2)^(1/3)
and the rule of exponents tells you to multiply the exponents.
... = x^(2·1/3) = x^(2/3)
Answer:
x^(2/3)
Step-by-step explanation:
(x^a.x^b)^c = x^[c*(a+b)]
using the above eqn, u can simplify the given expression to
x^[1/3*(4/3+2/3)]
=x^[1/3*(6/3)]
=x^(2/3)
ans is the 2nd choice
What is the area of a section of pavement that is 20 ft wide and 70 yd long?
Answer:
A = 4200 ft^2
Step-by-step explanation:
We know the formula for area is
A = l*w
We need to have the same units
convert yd to ft
1 yd = 3ft
Multiply each by 70
70 yds = 210 ft
A = 210 *20
A = 4200 ft^2
The area of the pavement section is 4200 square feet, computed by converting the length to the same unit as the width and multiplying width by length.
Explanation:The subject of this question is the calculation of the area of a rectangle. The rectangle in question is a section of pavement with a width of 20 ft and a length of 70 yd. Before calculating, it's important to have the measurements in the same units. Converting 70 yards to feet (since 1 yard equals 3 feet) we get 210 feet. The formula to calculate the area of a rectangle is Area = Width x Length. Substituting the given values into the formula, we get: Area = 20 ft x 210 ft which equals 4200 square feet. Therefore, the pavement section's area is 4200 square feet.
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What is the point slope form of the line with slope -3/7 that passes through the point (5, 8)?
ANSWER:
Your answer is the 3rd one: y - 8 = -3/7(x - 5)
ABOUT POINT SLOPE FORM:
y - Y1 = m (x - X1)m is the slopeY1 & X1 is a point on the lineThe form allows you to identify the slope & the point on the lineABOUT PROBLEM:
-3/7 represents m in the slope intercept form5 represents X18 represents Y1y - Y1 = m (x - X1)
y - 8 = -3/7(x - 5) --- IN POINT SLOPE FORM
Hope this helps you!!! :)
The line with a slope -3/7 and passes through the point (5, 8) has an equation of y - 8 = (-3/7)(x - 5)
The equation of a straight line is given by:
y = mx + b;
where y,x are variables, m is the slope of the line and b is the y intercept.
Since the line has a slope -3/7 and passes through the point (5, 8), the equation of the line is:
[tex]y-y_1=m(x-x_1)\\\\y-8=-\frac{3}{7} (x-5)[/tex]
Hence a line with a slope -3/7 and passes through the point (5, 8) has an equation of y - 8 = (-3/7)(x - 5)
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how many tables will be needed to seat 65 people if each table seats 7 people
Answer:
10 tables are needed to seat 65 people.
Step-by-step explanation:
Given :
There are total 65 people.
7 people can be seated on each table .
To Find : No. of tables required to seat 65 people.
Solution :
Since 7 people can sit on no. of tables = 1
1 people sit on no. of tables = 1/7
65 people sit on no. of tables
= [tex]\frac{1}{7} *65[/tex]
⇒ [tex]9.28[/tex]
⇒ 9.28 ≈ 10 tables are needed to seat 65 people.
Thus 10 tables are needed to seat 65 people.
50 POINTS!! A 96-ounce container of juice costs $4.80. At what price should a 128-ounce container be sold in order for the unit rate for both items to be the same? Explain your reasoning.
Answer:
$6.40 because 32 ounces is the difference 128 and 96 hence 32 is 1/3 of 96 so divide $4.80 by 3 which is $1.60 then add $1.60 + $4.80 =$6.40
Step-by-step explanation:
If necessary, use / for the fraction bar.
The diagram shows a green to pink ratio value of
2/5
Step-by-step explanation:There are 2 units of green and 5 units of "pink," so the ratio is ...
... green/pink = 2/5
Which description best defines the line FG⎯⎯⎯⎯⎯ ? the set of all points that are the same distance from point F as point G the set of all points between point F and point G the set containing point F and point G the set of all points between point F and point G, including point F and point G
Answer:
the set of all points between point F and point G, including point F and point G
Step-by-step explanation:
The definition of a line segment is the set of points on a line between two given end points, including those end points. The best description is the one that matches the definition.
Answer:
the set of all points between point F and point G, including point F and point G
Step-by-step explanation:
I WILL MAKE YOU THE BRAINLIEST EASY QUESTION For the visual model below, draw lines dividing each individual section into two equal parts. Then write a fraction representing the revised visual model. Do not reduce or simplify the fraction.
Answer:
see attached
Step-by-step explanation:
Each of the pie slices can be cut in half different ways. An easy way to do it and to understand it is to draw another cut from the center to the middle of the edge.
The result of cutting these slices is that instead of 8 equal pieces (of which 3 are colored), there will be 16, of which 6 are colored.
The new fraction is 6/16.
Graph The function f(x) = -(x - 2)^2 +4 Make sure to label the vertex and the intercepts
See the attachment for a labeled graph.
_____
I find it convenient to use "technology" to draw the graph. A spreadsheet, graphing calculator, or on-line graphing program can do this for you.
I need help plz plz plz help me ASAP. And SHOW YOUR WORK
Answer:
The cost of the wristband for 8 rides is $35.
Step-by-step explanation:
The expression for the cost, C, for r rides is
C = 2.5r + 15
Since she wants to go on 8 rides, r is 8.
Substitute r with 8 in the cost equation and evaluate it.
C = 2.5r + 15
C = 2.5 * 8 + 15
C = 20 + 15
C = 35
The cost of the wristband for 8 rides is $35.
tomas wrote an equation 4/5x-8=. Finish the equation so that the equation will have no solution. Explain how you know.
Answer:
Right part: [tex]\dfrac{4}{5}x+a,[/tex] where [tex]a\neq -8.[/tex]
Step-by-step explanation:
Linear equation have no solution if it is impossible for the equation to be true no matter what value we assign to the variable x.
The left part of the equation Tomas wrote is
[tex]\dfrac{4}{5}x-8.[/tex]
The right part of the equation should be of the form
[tex]\dfrac{4}{5}x+a,[/tex]
where [tex]a\neq -8.[/tex]
In this case, the equation will take look
[tex]\dfrac{4}{5}x-8=\dfrac{4}{5}x+a,\\ \\-8=a.[/tex]
Since [tex]a\neq -8,[/tex] this equality is always false.
Remark: 1) If a=8, the equation [tex]\dfrac{4}{5}x-8=\dfrac{4}{5}x+a[/tex] is equivalent to the equation
[tex]\dfrac{4}{5}x-8=\dfrac{4}{5}x-8,\\ \\0=0[/tex]
and the lest equation has infinitely many solutions.
2) When coefficient at x differs from [tex]\dfrac{4}{5},[/tex] the equation has unique solution.
Find the values of x and y that satisfies the equation.
5x + 3i = 15 + yi
Answer:
So the value of x=3 and y =3
Step-by-step explanation:
5x + 3i = 15 + yi
To find out x , set the constant terms equal to each other and solve for x
5x= 15
Divide by 5 on both sides
x= 3
To find out y , set the ';i' terms equal to each other and solve for y
3= y
So the value of x=3 and y =3
Answer: The required value of x is 3 and that of y is 3.
Step-by-step explanation: We are given to find the values of x and y that satisfies the following equation :
[tex]5x+3i=15+yi~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
[tex]a+bi=c+di~~~~~~~~~\Rightarrow a=c,~b=d.[/tex]
That is, the real and parts on both sides of the equation are equal.
From equation (i), we have
[tex]5x+3i=15+yi.[/tex]
Equating the real and imaginary parts on both sides of the above equation, we get
[tex]5x=15\\\\\Rightarrow x=\dfrac{15}{5}\\\\\Rightarrow x=3[/tex]
and
[tex]3=y\\\\\Rightarrow y=3.[/tex]
Thus, the required value of x is 3 and that of y is 3.
A college survey was taken to determine where students study. Of 147 students surveyed, 92 studied in the cafeteria, 86 studied in the student lounge, 40 studied in both the cafeteria and the student lounge. Of those interviewed how many did not study in either the cafeteria or the student lounge?
9 students did not study in either the cafeteria or the student lounge.
How to find the number
To find the number of students who did not study in either the cafeteria or the student lounge, we solve as follows
Let
C = 92
L = 86
C ∩ L = 40
We find the number in either C, L or C ∩ L
= (92 - 40) + (86 - 40) + 40
= 52 + 46 + 40
= 138
The number did not study in either the cafeteria or the student lounge
= 147 - 138
= 9
Explain how to solve the equation: b-7 =12
Answer:
19
Step-by-step explanation:
b - 7 = 12
b = 7 + 12
b = 19
Hi there! :)
Answer:
b=19
*The answer must have a positive sign.*
Step-by-step explanation:
Lesson: Addition/Subtraction/Multiplication/ and Division property of equalityFirst, you add by 7 from both sides of an equation.
[tex]b-7+7=12+7[/tex]
Then, you add by the numbers from left to right.
[tex]12+7=19[/tex]
Final answer is b=19
I hope this helps you!
Have a nice day! :)
:D
-Charlie
Thank you so much! :)
The angle of elevation from a soccer ball on the ground to the top of the goal is 34. If the goal is 8 feet tall, What is the distance from he ball to the goal?
Answer:
The distance from he ball to the goal is 11.85 feet (Approx) .
Step-by-step explanation:
As given
The angle of elevation from a soccer ball on the ground to the top of the goal is 34° .
If the goal is 8 feet tall.
Now by using the trigonometric identity .
[tex]tan \theta = \frac{Perpendicular}{Base}[/tex]
As shown in the diagram given below
[tex]\theta = 34^{\circ}[/tex]
Perpendicular = AB = 8 feet
Base = BC
Put all the values in the identity .
[tex]tan\ 34^{\circ} = \frac{AB}{BC}[/tex]
[tex]tan\ 34^{\circ} = \frac{8}{BC}[/tex]
[tex]tan\ 34^{\circ} = 0.675\ (Approx)[/tex]
[tex]BC = \frac{8}{0.675}[/tex]
BC = 11.85 feet (Approx)
Therefore the distance from he ball to the goal is 11.85 feet (Approx) .
To calculate the distance from the soccer ball to the goal with an angle of elevation of 34 degrees and a goal height of 8 feet, use the tangent trigonometric ratio. The distance is found to be approximately 11.86 feet.
Given the angle of elevation is 34 degrees and the goal's height is 8 feet, we're looking to calculate the adjacent side (distance from the ball to the goal) in a right-angled triangle where the opposite side (goal's height) and the angle are known.
To calculate the distance (let's call it d), we use the tangent function:
tan(angle of elevation) = opposite/adjacenttan(34 degrees) = 8/dSo, d = 8/tan(34 degrees).
Calculating this, we find:
d ≈ 8/0.6745d ≈ 11.86 feetTherefore, the distance from the soccer ball to the goal is approximately 11.86 feet.
Find a recursive formula for the sequence:
3, -5, 11, -21
The correct option is the last:
[tex] a_n = -2a_{n-1}+1 [/tex]
In fact, every term in the sequence is one more than twice the opposite of the previous one:
We start with 3. Twice its opposite is -6. Plus one, we get -5.
We start with -5. Twice its opposite is 10. Plus one, we get 11.
We start with 11. Twice its opposite is -22. Plus one, we get -21.
The recursive formula is: [tex]a_n-a_{n-1} = (-8)(-1)^n \times (2)^{n-2}[/tex]
To find a recursive formula for the given sequence, we need to determine the relation between consecutive terms.
Let's denote the sequence as an, where:
[tex]a_1 = 3\\a_2 = -5\\a_3 = 11\\a_4 = -21\\[/tex]
First, let's calculate the differences between consecutive terms:
[tex]a_2 - a_1 = -5 - 3 = -8\\a_3 - a_2 = 11 - (-5) = 16\\a_4 - a_3 = -21 - 11 = -32[/tex]
We observe that each difference is a multiple of 8 and that each difference is twice the previous difference but with alternating signs.
The recursive formula can be defined as:
[tex]a_n-a_{n-1} = (-8)(-1)^n \times (2)^{n-2}[/tex]
Thus the recursive formula is: [tex]a_n-a_{n-1} = (-8)(-1)^n \times (2)^{n-2}[/tex]
A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters. A cylindrical hole cut out of the center has a radius of 6 millimeters.Which expressions represent the volume of metal needed, in cubic millimeters, to make the pipe? Check all that apply.
options:
21π(10)2 – 21π(6)2
π(20)2(21) – π(6)2
2,100π – 756π
7,644π
1,344
The volume of metal is the difference of the overall volume of the cylinder and the volume of the hole in it. The formula for the volume of a cylinder is ...
... V = π·r^2·h . . . . . radius r and height h
For the overall dimensions, the radius is half the diameter, so is 10 mm. The hole is said to have a radius of 6 mm. The overall "height" is 21 mm, so the volume in mm³ will be ...
... V_overall -V_hole = π(10)^2(21) -π(6)^2(21)
... = 21π·10^2 -21π·6^2 . . . . . . . matches the first selection
... = 2100π -756π . . . . . . . . . . . matches the third selection
... = 1344π . . . . . . . . . . . . . . . . doesnt' match any selection
The correct expressions for the volume of metal needed, in cubic millimeters, to make the pipe are,
⇒ 21π(10)² – 21π(6)²
⇒ 2,100π – 756π
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters.
And, A cylindrical hole cut out of the center has a radius of 6 millimeters.
Hence, The formula for the volume of a cylinder is,
V = π·r²·h
Where, radius r and height h.
Now, For the overall dimensions, the radius is half the diameter, so is 10 mm. The hole is said to have a radius of 6 mm. The overall "height" is 21 mm,
so the volume in mm³ will be;
V (overall) -V (hole) = π(10)²(21) -π(6)²(21)
= 21π·10² -21π·6²
= 2100π -756π
= 1344π
Thus, The correct expressions for the volume of metal needed, in cubic millimeters, to make the pipe are,
⇒ 21π(10)² – 21π(6)²
⇒ 2,100π – 756π
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A recipe calls for 1 /4 start fraction, 1, divided by, 4, end fraction cup of chocolate chips for each batch of cookies. Alonzo has 1/2 start fraction, 1, divided by, 2, end fraction cup of chocolate chips. How many batches of cookies can Alonzo make?
Answer:
2
Step-by-step explanation:
1/2 cup = 2/4 cups = 2 × 1/4 cup
Alonzo can make 2 batches that each require 1/4 cup.
Operations with Complex Numbers
Answer:
B. -9/4 -4i
Step-by-step explanation:
Collect terms the way you would with any algebraic expression.
= (-3 +2 -3)i + (3/4 -3)
= -4i +(3/4 -12/4)
= -9/4 -4i
The product of the complex numbers [tex]\( (3 - 2i) \)[/tex] and [tex]\( (1 + i) \)[/tex] is [tex]\( 5 - 4i \)[/tex].
To find the product of two complex numbers, we multiply them as we would with binomials, remembering that [tex]\( i^2 = -1 \)[/tex]. Let's perform the multiplication step by step:
Given complex numbers [tex]\( (3 - 2i) \)[/tex] and [tex]\( (1 + i) \)[/tex], we multiply them directly:
[tex]\[(3 - 2i) \cdot (1 + i) = 3 \cdot 1 + 3 \cdot i - 2i \cdot 1 - 2i \cdot i. \][/tex]
Now, we simplify the expression by combining like terms and using the fact that [tex]\( i^2 = -1 \)[/tex]:
[tex]\[ = 3 + 3i - 2i - 2i^2 = 3 + i - 2(-1) = 3 + i + 2. \][/tex]
Finally, we combine the real parts and the imaginary parts:
[tex]\[ = (3 + 2) + i = 5 - 4i. \][/tex]
Therefore, the product of the complex numbers [tex]\( (3 - 2i) \)[/tex] and [tex]\( (1 + i) \)[/tex] is[tex]\( 5 - 4i \)[/tex].
Write three different fractions that are less than 40%?
1/3, 1/4, 1/5
Step-by-step explanation:40% = 40/100 = 2/5
Any fraction with a numerator of 2 and a denominator larger than 5 will be less than 40%, for example.
So, we can choose 2/6 = 1/3, 2/8 = 1/4, and 2/10 = 1/5 as some such values.
_____
We could also choose something like 39.99% = 3999/10000, or 1% = 1/100.
A customer placed an order with a bakery for cupcakes. the Baker has completed 37.5% of the order after being 81 cupcakes how many cupcakes with a customer order
Answer:
216 cupcakes
Step-by-step explanation:
81 = 0.375 × order
81/0.375 = order = 216 . . . . . divide by the coefficient of the variable
_____
About percentages
% means /100
37.5% = 37.5/100 = 375/1000 = 0.375
Derek established his own retirement account 10 years ago. He has discovered that he can obtain a better rate for the next 10 years at 12 percent interest compounded semiannually. Consequently, Derek established a new ordinary annuity account (beginning amount $0.00) and he will contribute $7,000.00 semiannually into the account for the next 10 years. What will be the value of this account at the end of the 10-year period?
$83,652.59 $244,707.61 $257,502.00 $264,501.86
Answer:
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Step-by-step explanation:
a 18 ft tall statue standing next to a globe casts a 12 ft shadow. Of the globe casts a shadow that is 2 ft ling, then how tall is it?
3 ft
Step-by-step explanation:The statue's height is 1.5 times the length of its shadow, so we expect the same relationship for the globe.
... 1.5 × 2 ft = 3 ft
_____
Comment on the problem
As a practical matter, with the sun high enough in the sky to cast a shadow shorter than the object's height, it will be quite difficult to measure the length of the shadow of the point at the top of the globe. The shadow of other parts of the globe will interfere.