After the tax and the tip are counted, we conclude that each friend must pay $30.
How much should each person pay?We know that the meal cost is $72.50.
Now, there is a 6.75% sales tax and a 15% tip on the waiter (we assume that the tip is based on the total meal cost, after the tax is applied).
Then the total meal cost is:
C = $72.50*( 1 + 6.75%/100%) = $72.50*(1 + 0.0675) = $77.39
Now we also need to add the tip, which is a 15% of that, so the total cost with the tip included is:
C' = $77.39*(1 + 15%/100%) = $88.998 = $90
(Where we rounded up).
Then, if there are 3 friends, each one must pay:
$90/3 = $30
Each friend must pay $30.
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Which equation represents the line that is perpendicular to and passes through (-8,-2)?
x = -2
x = -8
y = -6
y = -8
The equation of the line that is perpendicular to y = 1/6 is: B. x = -8.
How to Find the Equation of Perpendicular Lines?Perpendicular lines have slope values that equals -1 when multiplied together, that is, they are negative reciprocals.
Given the equation, y = 1/6, the slope is 0. This means it is a vertical line, therefore, the line that is perpendicular to it would automatically be a vertical line with an undefined slope which passes through (,8, -2).
The line therefore, would intercept the x-axis at -8. The equation would be: x = -8.
Equation of the perpendicular line is therefore: B. x = -8.
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On Monday the change in the value of one share of a companies stock can’t be represented as -$2.85 Tuesday the value of one share of the companies that changes again which of these describes a situation that would bring the total change for the two days to zero dollars
Step-by-step explanation:
If a stock's price falls all the way to zero, shareholders end up with worthless holdings. Once a stock falls below a certain threshold, stock exchanges will delist those shares.strong earning result in the stock price moving up and vice versa.
in the question you asked,the situation that will make stock price move from -$2.85 to zero means the stock, bond, or commodity market, or an index representing them, currently trades higher than it did at some specific point in the past.
A gallon of stain is enough to cover 200 square feet of decking. Bradley has two areas of decking he would like to cover with stain. One rectangular area is 23 feet by 10.4 feet, and the other is 10.5 feet by 7.2 feet. Which expression gives the number of gallons of stain Bradley will need?
Left-bracket (23) (10.5) + (10.4) (7.2) right-bracket divided by 200
Left-bracket (23) (10.4) + (10.5) (7.2) right-bracket divided by 200
Left-bracket (23) (10.5) + (10.4) (7.2) right-bracket times 200
Left-bracket (23) (10.4) + (10.5) (7.2) right-bracket times 200
The expression that we need to get is:
[tex]N = \frac{(23)*(10.4) + (10.5)*(7.2)}{200}[/tex]
So the correct option is the second one.
Which expression gives the number of gallons of stain Bradley will need?
We know that 1 gallon is enough to cover 200 ft².
We have two rectangular areas, one of:
23 feet by 10.4 feet, and other of 10.5 feet by 7.2 feet.
Then the total area is:
A = (23 ft)*(10.4 ft) + (10.5ft)*(7.2 ft)
The number of gallons needed is given by the quotient between the area that we want to cover, and the area that covers one gallon, so the expression is:
[tex]N = \frac{(23ft)*(10.4ft) + (10.5ft)*(7.2ft)}{200ft^2} \\\\N = \frac{(23)*(10.4) + (10.5)*(7.2)}{200}[/tex]
So the corerect option is the second one.
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Which of these ordered pairs is a solution to the linear inequality y > 3x + 2?
(–1, –5)
(–2, –7)
(2, 8)
(2, 9)
The ordered pairs that is a solution to the linear inequality y > 3x + 2 is
(2, 9)
How to find solution of inequality?The inequality is as follows;
y > 3x + 2
Therefore, let's try option 1
(-1, -5)
-5 > 3(-1) + 2
-5 > -3 + 2
-5 > - 1 (This is false)
(–2, –7)
-7 > 3(-2) + 2
-7 > -6 + 2
-7 > -4 (This is false)
(2, 8)
8 > 3(2) + 2
8 > 6 + 2
8 > 8 (false)
(2, 9)
9 > 3(2) + 2
9 > 8 (This true)
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A six sided die, a 20 sided die, and a 12 sided die are rolled, what’s the probability of all three happening. Showing 3 on the first die, showing either 19 or 20 on the second die, and showing an odd number on the third die
The probability of all three events happening when the dies are rolled is; 0.0083
What is the Probability of Rolling a Die?A) On the first die, it has 6 sides and 3 must come out, that is, 1 event out of 6 possible, therefore the probability is: 1/6
B) On the second die, it has 20 sides and if 19 or 20 can come out, that is 2 events out of 20 possible, so the probability is: 2/20 = 1/10
C) On the third die, which is 12 sides, an odd number can come out. The odd numbers would be 1, 3, 5, 7, 9, 11; i.e, 6 events out of 12 possible numbers.
Thus, the probability would be: 6/12 = 1/2
The final probability would be;
(1/6) * (1/10) * (1/2) = 0.0083
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HELP ME PLEASE
LOOK AT IMAGE
Answer:
the answer is congruent making d midpoint
40°
87°
Xº
Q
Image not to scale
38°
Calculate the missing internal angle x.
Hence, the missing internal angle is [tex]15[/tex].
What is the angle?
An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays.
Angles are also formed by the intersection of two planes. These are called dihedral angles.
Here given that,
[tex]Q = 87 + 40Q = 127X + 127 + 38 = 180X = 180 - 127 - 38X = 15[/tex]
Hence, the missing internal angle is [tex]15[/tex].
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A family has two cars. The first car has a fuel efficiency of miles 15 per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. During one particular week, the two cars went a combined total of 975 miles, for a total gas consumption of 55 gallons. How many gallons were consumed by each of the two cars that week?
The first car consumed 25 gallons of fuel while the second car consumed 30 gallons of fuel.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the first car consumption and y represent the second car consumption, hence:
x + y = 55 (1)
Also:
15x + 20y = 975 (2)
From both equations:
x = 25, y = 30
The first car consumed 25 gallons of fuel while the second car consumed 30 gallons of fuel.
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Find the measure of side b.
b = _ yd
The data represent the age of world leaders on their day of inauguration. Find the five-number summary, and construct a boxplot for the data. Comment on the shape of the distribution.
The five-number summary is: 41, 56, 65, 67, 69.
The box plot that represents the data is: option B.
Correct statement for the shape of the distribution is: B. the distribution is skewed to the left.
What is the Five-number Summary?The five-number summary is a five data value that describes the distribution of a data set, which include: lower and upper quartiles, minimum and maximum values, and the median of the data.
The five-number summary is used to construct a box plot.
Given the data, 65, 56, 67, 68, 66, 66, 67, 69, 48, 57, 59, 68, 59, 41, 44, the five-number summary for the data is:
Minimum: 41Quartile Q1: 56Median: 65Quartile Q3: 67Maximum: 69This means that the box plot that will represent this data will have a box that ranges between 56 and 67, and the data at both whiskers will be 41 and 69, while the data at the point where the vertical line divides the box would be 65.
Thus, the box plot that represents the data is: option B.
The median is closer to the right of the third quartile/upper quartile, therefore: B. the distribution is skewed to the left.
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I need help with the slope
Answer:
Line A
Step-by-step explanation:
Hello!
Given that the x-values is the time in minutes, and the y-axis is the number of dishes stacked, for every minute, the line should go up by 7.
This means, that the value of y when x is 1 should be 7. The line that follows this rule is Line A. For every minute, 7 dishes are stacked.
The answer is Line A.
there was 506 tickets sold for the school play they were either student tickets or adult tickets there was 56 more student tickets sold than adult tickets sold how many adult tickets were sold
Answer:
A = 228 tickets
Step-by-step explanation:
We need to set up a system of equation to find the number of adult tickets sold, where A represents the adult tickets and S represents the student tickets.
Because the number of adult and student tickets together equals 506, we have A + S = 506.
Because there are 56 more student tickets than adult tickets we have A + 56 = S
And the way the system is already set up allows us to use substitution.
Thus, we have:
[tex]A + S=506\\A+56 = S\\\\A+A+56 =506\\2A+56=506\\2A=456\\\\A=228\\228+56=S\\278=S[/tex]
The number of student tickets was not necessary to find in this problem, but I found anyway just in case you wanted check the work or wanted to prove the validity of the values.
Factor
(a-2b) (3x-5y) + (2b-a)(x-y)
Answer:
8by + 2ax - 4bx - 4ay
Step-by-step explanation:
I assume you mean expand so:
(a - 2b)(3x - 5y) + (2b - a)(x - y)
3ax - 5ay - 6bx + 10by + 2bx - 2by - ax + ay
Now collect like terms:
2ax - 4ay - 4bx + 8by
This is your answer but in a better order:
8by + 2ax - 4bx - 4ay
Solve the differential equation
[tex]y {}^{(5)} -4y {}^{(4)} +4y'''-y''+4y'-4y=69[/tex]
The given differential equation has characteristic equation
[tex]r^5 - 4r^4 + 4r^3 - r^2 + 4r - 4 = 0[/tex]
Solve for the roots [tex]r[/tex].
[tex]r^3 (r^2 - 4r + 4) - (r^2 - 4r + 4) = 0[/tex]
[tex](r^3 - 1) (r^2 - 4r + 4) = 0[/tex]
[tex](r^3 - 1) (r - 2)^2 = 0[/tex]
[tex]r^3 - 1 = 0 \text{ or } (r-2)^2=0[/tex]
The first case has the three cubic roots of 1 as its roots,
[tex]r^3 = 1 = 1e^{i0} \implies r = 1^{1/3} e^{i(0+2\pi k)/3} \text{ for } k\in\{0,1,2\} \\\\ \implies r = 1e^{i0} = 1 \text{ or } r = 1e^{i2\pi/3} = -\dfrac{1+i\sqrt3}2 \text{ or } r = 1e^{i4\pi/3} = -\dfrac{1-i\sqrt3}2[/tex]
while the other case has a repeated root of
[tex](r-2)^2 = 0 \implies r = 2[/tex]
Hence the characteristic solution to the ODE is
[tex]y_c = C_1 e^x + C_2 e^{-(1+i\sqrt3)/2\,x} + C_3 e^{-(1-i\sqrt3)/2\,x} + C_4e^{2x} + C_5xe^{2x}[/tex]
Using Euler's identity
[tex]e^{ix} = \cos(x) + i \sin(x)[/tex]
we can reduce the complex exponential terms to
[tex]e^{-(1\pm i\sqrt3)/2\,x} = e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) \pm i \sin\left(\dfrac{\sqrt3}2x\right)\right)[/tex]
and thus simplify [tex]y_c[/tex] to
[tex]y_c = C_1 e^x + C_2 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_3 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right) \\ ~~~~~~~~ + C_3 e^{-(1-i\sqrt3)/2\,x} + C_4e^{2x} + C_5xe^{2x}[/tex]
For the non-homogeneous ODE, consider the constant particular solution
[tex]y_p = A[/tex]
whose derivatives all vanish. Substituting this into the ODE gives
[tex]-4A = 69 \implies A = -\dfrac{69}4[/tex]
and so the general solution to the ODE is
[tex]y = -\dfrac{69}4 + C_1 e^x + C_2 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_3 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right) \\ ~~~~~~~~ + C_3 e^{-(1-i\sqrt3)/2\,x} + C_4e^{2x} + C_5xe^{2x}[/tex]
what is the range if the given function?
Answer:
Second option
Step-by-step explanation:
The range is the set of output values a function can take. As shown in the table, as x is substituted in, y is the corresponding value.
You throw a ball at a height of 6 feet above the
ground. The height h (in feet) of the ball after t seconds can be modeled by the equation
h=-16t² +62t +6. After how many seconds does the ball reach a height of 27 feet?
Answer:
0.375 second and 3.5 second
Step-by-step explanation:
The position can be modeled by a quadratic function [tex]\displaystyle{h=-16t^2+62t+6}[/tex]. We are tasked to find the time when a ball reaches a height of 27 feet. Therefore, let h = 27:
[tex]\displaystyle{27=-16t^2+62t+6}[/tex]
Solve for t:
[tex]\displaystyle{27-6=-16t^2+62t}\\\\\displaystyle{21=-16t^2+62t}\\\\\displaystyle{16t^2-62t+21=0}[/tex]
Since the equation is quite complicated and more time-consuming to solve, i'll skip the factoring or quadratic part:
[tex]\displaystyle{t=0.375, 3.5}[/tex]
After done solving the equation, you'll get t = 0.375 and 3.5 seconds. These solutions are valid since both are positive values and time can only be positive.
Hence, it'll take 0.375 and 3.5 seconds for a ball to reach 27 feet.
23 1/2% as a mixed decimal (as a percent)
Answer: 23,5%
Step-by-step explanation:
[tex]23\frac{1}{2} %[/tex]% = [tex]\frac{47}{200}[/tex] = 0,235 = 23,5%
If the greatest value the variable m can be is less than 9, which of the following inequalities best shows all the possible values of m?
m < 9
m > 9
m ≤ 9
m ≥ 9
The inequality which shows all possible values of m is; m < 9.
Which inequality best shows all possible values of m?It follows from the task content that the variable in discuss, m is described as less than 9.
On this note, the most appropriate inequality to represent the set of all possible values of m is; m < 9.
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cual es la mitad de 980
Al aplicar operaciones de aritmética básica, tenemos que la mitad de 980 es igual a 490.
¿Cuál es la mitad de un número par?
En esta pregunta tenemos un número par de tres dígitos que termina en cero. De acuerdo con la teoría numérica, un número de base 10 de más de un dígito que tenga un número par relacionado con números impares como último dígito, tendrá un número impar si es dividido por 2.
Ahora bien, si tenemos un número par con más de un dígito que termina en cero, entonces tendrá un número par que termina en 0 si es dividido por 2.
Si dividimos 980 por 2, entonces tenemos 490 como resultado:
980/2 = 98/2 × 10 = 49 × 10 = 490
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explain why x squared = 16 has two solutions. What are the solutions.
Find the reminder when 3x² + 2x -7 is divided by x - 1
Answer:
-2
Step-by-step explanation:
When x = 1, 3x² + 2x - 7 = -2.
A study showed that low intenstisy vibration therapy reduce pain levels in patients with fibromyalgia. During each session in the study, vibration pads were placed on the pain site indicated by the patient. Pain reduction was measured through self-reporting after each session. Another study is being design to examine whether low intensity vibration therapy also reduces pain in patients suffering from ruptured disks at the lumbar region of the back. Three hundred male patients are subjects the new study. Part A: What is an appropriate design for the new study? Include treatments used, method of. treatment assignment, and variables that should be measure
Part b: if the study consists of 150 male and 150 female patients instead of 300 male patients would you change the study design if so, how would you modify your design? if not, why not?
Part c: could your design be double blind
Answer:
I didn't got the question well
Find the integral
∫(cos(1/x)) /x^2 dx
Answer:
Step-by-step explanation:
∫(cos(1/x)/x² dx
[tex]put~\frac{1}{x} =t\\diff.\\\frac{-1}{x^2} dx=dt\\\int(- cos~t~)dt=-sin~t+c\\=-sin (\frac{1}{x} )+c[/tex]
Which point do the graphs of f and g have in common?
The point that the graphs of f and g have in common are (1,0)
How to get the points?The given functions are:
f(x) = log₂x
and
g(x) = log₁₀x
We know that logarithm of 1 is always zero.
This means that irrespective of the base, the y-values of both functions will be equal to 0 at x=1
Therefore the point the graphs of f and g have in common is (1,0).
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Answer:
Its (1,0)
and the second one is A. F
Step-by-step explanation:
Find the vertex of the quadratic function.
ƒ(x) = 2(x−1)² +3
a. (1,3)
b. (2, -1)
c. (-1,3)
d. (2,3)
hi,
the function is given with it's canonic form.
canonic form is : f(x) = a ( x-α)² + β
α and β are the value of the coordonnates of the vertex.
so here we have : ƒ(x) = 2(x−1)² +3
with α = 1 and β = 3
so vertex is V (1;3)
So yes, answer is A.
quick question for 40 points
Given the drawing as shown below and that plla, name a pair of
alternate interior angles.
le
A
B
C
D
Lc = 4f
Zb and Ze
Zd=48
Zd= Le
d
do
8
9
Answer:
Angle D & Angle E
Step-by-step explanation:
Angle C & Angle F are ALTERNATE EXTERIOR angles.
Angle B & Angle E are CONSECUTIVE angles.
Angle D & Angle G are CORRESPONDING angles.
An international company has 21,700 employees in one country. If this represents 17.7% of the company's employees, how many employees does
it have in total?
Round your answer to the nearest whole number.
Answer:
122,599
Step-by-step explanation:
In words, what I am is asking is 17.7% of what number is 21,700. I will need to change 17.7% to a decimal. To do that, I move the decimal 2 places to the left. Then solve.
.177 x w = 21700 Divide both sides by .177
w = 122,599
What is the area of a desktop that is 2 1/2 feet by 5 feet?
The area of the desktop is 12. 5 feet square
How to determine the area
The formula for area of a rectangle;
Area = length × width
Length = 2. 5 feet
Width = 5 feet
Area = 2. 5 × 5
Area = 12. 5 feet square
Thus, the area of the desktop is 12. 5 feet square
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questions 5 and 6 please!
formula: y = ax + q
Answer:
5) y = 1x + 2
6) y = -0.5x + 6
Explanation:
5)
Given points are (-3, -1), (2, 4)
[tex]\sf slope \:formula: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Here, find slope:
[tex]\rightarrow \sf slope \ (a) = \dfrac{4-(-1)}{2-(-3)} = \dfrac{5}{5} = 1[/tex]
Find Equation:
y = ax + q
Here found that a = 1, take (x, y) = (-3, -1)
[tex]\sf -1 = 1(-3) + q[/tex]
[tex]\sf q - 3 = -1[/tex]
[tex]\sf q = -1 + 3[/tex]
[tex]\sf q = 2[/tex]
So, in total equation:
y = 1x + 2
-------------------------------------------------------------------------------------
6)
Given points are (-2, 7), (2, 5)
[tex]\sf slope \:formula: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Here, find slope:
[tex]\rightarrow \sf slope \ (a) = \dfrac{5-7}{2-(-2)} = -0.5[/tex]
Find Equation:
y = ax + q
Here found that a = -0.5, (x, y) = (-2, 7)
[tex]\sf 7 = -0.5(-2) + q[/tex]
[tex]\sf 7 = 1 + q[/tex]
[tex]\sf q = 7-1[/tex]
[tex]\sf q = 6[/tex]
So, in total equation:
y = -0.5x + 6
Answer:
Since √3√3 is equal to 1 , you simply rearranged the way it was written. The value of the simplified fraction stays the same