Each individual paid the sum of $23.4 including state tax at the restaurant
PercentageIn mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%".
In the problem, their total bill is $50.88 and they gave a 30% tip
We should fid 30% of 50.88
0.3 * 50.88 = $15.264
30% of $50.88 is $15.264
If we add this up and then find the state tax to it.
15.264 + 50.88 = 66.144.
Find 6% of 66.144 to determine the state tax.
0.06 * 66.144 = 3.96864
The total amount spent is 66.144 + 3.96864 = 70.11264
We can divide this equally amongst the three people to get the individual payment = 70.11264/3 = 23.37088
Rounding this to the nearest cent, we have 23.4.
We can say each person paid $23.4 at the end of the day
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a. Find the derivative function f' for the function f.
b. Determine an equation of the line tangent to the graph of f at (a,f(a)) for the given value of a.
The derivative function f' for the function f is f'(x) = -10 / (5x+3)^2 and Equation of the line tangent to the graph of f is 5x+2y+7=0.
Given function:
f(x) = 2/5x+3
a.
f'(x) = d/dx(2/5x+3)
According to power rules:
1/u = -1/u^2
= 2(1/(5x+3)^2) d/dx(5x+3)
= 2*5 / (5x+3)^2
= -10/(5x+3)^2
Hence derivative function f' for the function f is f'(x) = -10 / (5x+3)^2.
b.
(a,f(a)) and a = -1
f(-1) = 2/5(-1)+3
= 2/-5+3
= 2/-2
= -1
point (-1,-1)
slope f'(x) = -10/(5x+3)^2
f'(-1) = -10/(5(-1)+3)^2
= -10/(-2)^2
= -10/4
m = -5/2
Equation of the line is y - y1 = m(x-x1)
y - (-1) = -5/2(x-(-1)
2(y + 1) = -5x - 5
5x + 2y + 2 + 5 = 0
5x+2y+7=0.
Equation of the line tangent to the graph of f is 5x+2y+7=0.
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pls help me asap i dont know the answer
Answer:
96
Step-by-step explanation:
Area of a triangle
A = (1/2) × base × height
A = (1/2) × 12 × 16
A = (1/2) × 192
A = 96 units²
I hope this helps!
3 pounds (lbs) = how many grams (g).
The table represents a quadratic function. Write an equation of the function in standard form.
#5 i
X
-5 -4 -3 -2
g(x) 5 2 5 14
y =
An equation of the function in standard form for the given table of values is 3x² + 24x + 50 = 0.
First, let us understand the standard form of a quadratic equation:
In Mathematics, the standard form of a quadratic equation is given by;
y = g(x) = ax² + bx + c = 0
To write a quadratic function equation in standard form, we would construct the following system of equations from the data in the given table:
5 = a(-5)² + b(-5) + c ⇒ 5 = 25a - 5b + c .......equation 1.
2 = a(-4)² + b(-4) + c ⇒ 2 = 16a - 4b + c .......equation 2.
5 = a(-3)² + b(-3) + c ⇒ 5 = 9a - 3b + c .......equation 3.
14 = a(-2)² + b(-2) + c ⇒ 14 = 4a - 2b + c .......equation 4.
From equation 1 and equation 3, we derive:
25a - 5b + c = 9a - 3b + c
⇒ 25a - 9a = -3b + 5b
⇒ 16a = 2b
⇒ b = 8a
Substituting the value of b into equation 2 and 4, we derive the following equations:
2 = 16a - 4 * 8a + c ⇒ 2 = - 16a + c
14 = 4a - 2 * 8a + c ⇒ 14 = -12a + c
By using the elimination method, the value of a is given by:
2 - 14 = (-16a + 12a) + (b - c)
-12 = - 4a
a = 3
Next, we would determine the value of b as follows:
b = 8a
b = 8 * 3
b = 24
For the value of c, we have:
2 = - 16a + c
c = 16 * (3)+ 2
c = 48 + 2
c = 50.
Substituting the respective values of a, b and c into the standard form of a quadratic equation:
ax² + bx + c = 0
3x² + 24x + 50 = 0
Thus, an equation of the function in standard form for the given table of values is 3x² + 24x + 50 = 0.
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Answer to each expression
(3 + 9) x 2 dived 4
Answer: [tex]6\\[/tex]
Step-by-step explanation:
[tex]\frac{(3+9) * 2}{4}[/tex]
Add 3 and 9 to get 12.
[tex]\frac{12 * 2}{4}[/tex]
Multiply 12 and 2 to get 24.
[tex]\frac{24}{4}[/tex]
Divide 24 by 4 to get 6.
[tex]6[/tex]
Spencer, a professional golfer, had an average score of 80 points last season. This season, however, his average score has been 5% higher. What is Spencer's current average score?
please
Answer:
84
Step-by-step explanation:
80 x 0.05 = 4
80 + 4 =84
A rectangle has an area of 120 square meters and a width of 8 meters. What is the length?
Answer:
Step-by-step explanation:
Ok:
Area's formula is width* length
1. 120 square meters and width of 8 meters. Reversing the formula, divide area by width to get length!
120/8=15 meters
2. Answer: 15 meters
5. Jen and Kevin and their children: Jon
(age 14), Beth (age 8), and Joshua
(age 4) are visiting a science museum.
Admission prices are shown below.
Museum Admission
Adult (18-64)
Youth (12-17)
Child (5-11)
Under 5
$22.50
$16.25
$9.75
Free
What will be the total cost of admission
for the family?
?
Answer:
$48.5
Step-by-step explanation:
From the question, we know that Jen and Kevin are definitely adults and the fee for adults
= $22.50
Jon is 14, and any number from 12 to 17 is classified as a youth, so his fee is
= $16.25
Beth is 8, classified as a child, her fee is
= $9.25
Joshua's age which is below 5 is granted free entry without a fee
Hence, the total cost of admission for the family is
$22.50 + $16.25 + $9.75
= $48.5
121x
10
6
4
909
-6-5-4-3-2-12- 2 3 4 5 6 x
J
-8-
-10
B
h
Which statement is true regarding the functions on the
graph?
Of(6) = g(3)
Of(3) = g(3)
Of(3) = g(6)
Of(6) = g(6)
Answer:
The Question is not Correct but answer is f 3 and g 3
Round the amount of money to the nearest hundred.
Answer:2,300
Step-by-step explanation:
The function f(x) is graphed below. What is true about the graph on the interval from x = c to x = ∞?
Answer:
It is positive and increasing
Step-by-step explanation:
After the graph, it becomes positive as it passes the y-axis, the line which is where y=0. Also, the graph is headed up and to the right(after c), so as the value of x increase, the value of the function does as well. This would mean the answers is "It is positive and increasing"
Write the equation of the line that perpendicular to y=5/2x + 9/2 that passes through the point (-5,3)
Answer:
y = -2/5 x + 1
Step-by-step explanation:
slope = -2/5
y-3 = -2/5 (x -(-5)
y-3 = -2/5 (x+5)
y - 3 = -2/5 x - 2
y = -2/5 x - 2 + 3
y = -2/5 x + 1
How many tiles would it take vanessa to cover 1 square foot
The number of tiles need to cover the closet floor is 180 tiles
The length of the side of the tile = 1/3 feet
The area of the square = Side × Side
The area of the tile = (1/3) × (1/3)
= 1/9 square feet
The width of the closet = [tex]3\frac{1}{3}[/tex] feet
Convert the mixed fraction to simple fraction
[tex]3\frac{1}{3}[/tex] feet = 10/3 feet
The length of the closet = 6 feet
Total area of the closet = 10/3 × 6
= 20 square feet
Number of tiles needed = The area of the closet / The area of the tile
Substitute the values in the equation
= 20 / (1/9)
= 180 tiles
Hence, the number of tiles need to cover the closet floor is 180 tiles
The complete question is
Vanessa wants to cover her closet floor with SRB tiles that are 1/3 foot on each side. The closet is [tex]3\frac{1}{3}[/tex] feet wide and 6feet deep, How many tiles will Vanessa need to cover the closet floor?
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A store sells barrettes for $2 each and combs for $1. Shelby buys 3 barrettes and a comb. Kendra buys 2 barrettes and 4 combs. Write an expression for the amount the two girls spent all together. Find the total amount spent.
I need help!
Answer:
19
Step-by-step explanation:
add it all up its easy
Step-by-step explanation:
Shelby buys 3 barrettes...
2*3=6
and 1 comb
1*1=1
she spent $7 in total
6+1=7
Kendra buys 2 barrettes...
2*2=4
and 4 combs
1*4=4
so Kendra spent $8 in total
4+4=8
the amount spent from the to girls was...
8+7=15
how many different rectangles are there
Need help please tough question
The value of the investment at the end of 5 years be $ 15,281.012.
Given, 10400 dollars are invested at an interest rate of 8%.
We have to find the value of the investment at the end of 5 years.
Now, on using the compound interest formula, we get
Amount = P(1 + r/100)^t
Amount = 10400(1 + 8/100)^5
Amount = 10400(1.08)^5
Amount = 10400(1.469)
Amount = 15,281.012
Hence, the value of the investment at the end of 5 years be $ 15,281.012.
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Nine less than twice the difference between a number and seven
Step-by-step explanation:
9 < 2(x - 7)
hope this helpful
The speed of a river current is 2 mph. If a boat travels 30 miles downstream in the same that it takes to travel 20 miles upstream, find the speed if the boat in the still water.
Taking into consideration the upstream and downstream speed, and the equal time taken to travel upstream and downstream distance, the speed of the boat in the still water is found out to be 10mph.
It is given to us that -
The speed of the river current = 2mph
Time taken for the boat to travel 30 miles downstream = Time taken for the boat to travel 20 miles upstream --- (1)
We have to find out the speed of the boat in still water.
Let us say that the speed of the boat in still water is x mph.
We know that -
Speed = Distance/Time
=> Time = Distance/Speed ----- (2)
When travelling upstream, the boat is slower and thus, we subtract speed of the current from the speed of the boat.
When travelling downstream, the boat is faster as it goes with the current and thus, we add the speed of the current with the speed of the boat.
From equation (1), we have
Time to travel 30 miles downstream = Time to travel 20 miles upstream
[tex]= > \frac{30}{x-2} =\frac{20}{x+2} \\= > 30(x+2)=20(x-2)\\= > 30x+60=20x-40\\= > 10x=100\\= > x=10[/tex]
Thus, taking into consideration the upstream and downstream speed, the speed of the boat in the still water is 10mph.
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If angle A is (2x) and angle B is (3x+11)° and the sum of angle A and angle B is 66°, find the measure of angle B.
11
22
44
25
The angle B is 66°
Given,
In the question:
If angle A is (2x) and angle B is (3x+11)°
and, the sum of angle A and angle B is 66°
To find the angle of B.
Now, According to the question:
Based on the given condition:
Angle A = 2x
Angle B = (3x + 11)°
The sum of angle A and B is 66°
2x + (3x + 11)° = 66°
5x + 11 = 66°
Calculate the sum or difference
5x = 66 - 11
3x = 55
x = 55/3
The angle B is = 3x + 11
Plug the value of x in angle B
3 × 55/3 + 11
= 66
Hence, The angle B is 66°
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In a garden club, 90% is ladies. The number of ladies is 12 more than 3 times the number of gentlemen.
How many ladies and how many gentlemen are in the club?
(Note: set up a rational equation and solve)
The number of ladies in the club = 18
and the number of gentlemen in the club = 2
Let x be the number of gentlemen.
So, the number of ladies would be 3x + 12
Total number of people in garden = x + (3x + 12)
= 4x + 12
In a garden club, 90% is ladies.
This means, (3x + 12) is 90 percent of (4x + 12)
We get an equation,
(3x + 12) = 90/100 * (4x + 12)
We solve above equation to find the value of x.
30x + 120 = 36x + 108
6x = 12
x = 2 (number of gentlemen)
So, the number of lades would be:
3x + 12 = 3(2) + 12
= 18
Therefore, the number of ladies in the club = 18 and the number of gentlemen in the club = 2
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A dog breeder is planning to buy more dog food. He makes a table showing how
many pounds of food he will have after shopping. The table is based on how much he
spends and how much food he already has. Which equation generates the table?
Money Spent (x) $0 $20 $40 $60
Pounds of Food (v) 4 12 20 28
O
x=y-4
y=8x-4
x = 8y +4
Oy=x+4
The equation that generate the table in slope intercept form is y = 2 / 5 x + 4
How to generate equation of a table?The equation of a linear table can be represented in different form such as slope intercept form, point slope form, standard form and general form.
Therefore, let's represent the equation of the table of money spent and pounds of food.
using slope intercept form,
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope using (0, 4) and (20, 12)
m = slope = 12 - 4 / 20 - 0
slope = 8 / 20
slope = 2 / 5
Therefore, let's find the y-intercept using (0, 4)
4 = 2 / 5(0) + b
b = 4
Therefore, the equation is y = 2 /5 x + 4
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29. Write the equation of the line that passes
through the point (-6, 1) and has a slope
of ½.
Answer:
Step-by-step explanation:
M is slope
B is y intercept
X and y are given
using the equation for the y intercept
b=y1-mx1
B=1−(1/2)⋅(−6)=4
Write in y=Mx+b
=12+4
The general equation of the line is −2+8=0
Given the equation F=95C+32 where C is the temperature in degrees Celsius and F is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs:
(−25,F1), (−5,F2)
The values of F1 and F2 are 77 and -22 degrees Fahrenheit respectively.
How to use the equation to convert from degrees Celsius to degrees Fahrenheit?Given that; the equation F=9/5C+32 and ordered pairs are (25, F1), (−30, F2)
To convert the values to degrees Fahrenheit, we have to substitute the given values into the equation to get F1 and F2 respectively:
For (25, F1);
F = 9/5 C+32
Now put C= 25 in the equation;
F1 = 9/5(25) + 32
F1 = 45 +22
F1 = 77 degrees Fahrenheit
For (−30, F2);
F = 9/5 C+32
Now put C= -30 in the equation;
F2 = 9/5(-30) + 32
F2 = -54 + 32
F2 = -22 degrees Fahrenheit
Hence, the values of F1 and F2 are 77 and -22 degrees Fahrenheit respectively.
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Given the image of the two triangle, which method can you use to show △LHJ≅△KIE
Answer:
ASA
Step-by-step explanation:
As you can see in the picture it is giving us 2 angles, in between those 2 angles are aside. Therefore it is ASA.
We can also eliminate SSS because 2 angles and shown and SAS can also be eliminated because there are 2 angles, not sides.
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: −3, ordered pair: (−4,−2)
Answer:
y = - 3x - 14
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 3 , then
y = - 3x + c ← is the partial equation
to find c substitute (- 4, - 2 ) into the partial equation
- 2 = 12 + c ⇒ c = - 2 - 12 = - 14
y = - 3x - 14 ← equation of line
Find The Value Of Tan(M-P)
Given That Sinm=-(4)/(5)
Cosp=-(15)/(17)
Both Mand P Are In Quadrant III.
The value of tan(m - p), where the value of sin(m) = -(4/5), and the value of cos(p) = -(15/17) using trigonometric identities is; [tex]tan(m - p) = \dfrac{36}{77}[/tex]
What are trigonometric identities?Trigonometric identities are equations that involve trigonometric functions which are true for all values of the input variables.
The information in the question are;
[tex]sin(m) = -\dfrac{4}{5}[/tex][tex]cos(p) = -\dfrac{15}{17}[/tex]Therefore;
[tex]cos(m) = \sqrt{1- \left(-\dfrac{4}{5}\right)^2} =\pm\dfrac{3}{5}[/tex]
The location of m is in Quadrant III, therefore;
[tex]cos(m) =-\dfrac{3}{5}[/tex]
[tex]sin(p) = \sqrt{1- \left(-\dfrac{15}{17}\right)^2} =\pm\dfrac{8}{17}[/tex]
The angle p is located in Quadrant III, therefore;
[tex]sin(p) = -\dfrac{8}{17}[/tex]
180° ≤ Angle ∠m ≤ 270°; definition of angles in Quadrant III
180° ≤ Angle ∠p ≤ 270°; definition of angles in Quadrant III
Therefore;
270° - 270° ≤ |∠m - ∠p| ≤ 270° - 180°
0° ≤ |∠m - ∠p| ≤ 90°
The trigonometric identity for tan(m - p) is presented as follows;
[tex]tan(m - p) = \dfrac{tan(m) -tan(p)}{1+tan(m)\cdot tan(p)}[/tex]
[tex]tan(m - p) = \dfrac{\dfrac{sin(m) }{cos(m) } -\dfrac{sin(p) }{cos(p) } }{1+\dfrac{sin(m) }{cos(m) } \cdot \dfrac{sin(p) }{cos(p) } }[/tex]
Therefore;
[tex]tan(m - p) = \dfrac{\left(\dfrac{ -\dfrac{4}{5} }{-\dfrac{3}{5} }\right) -\left(\dfrac{ -\dfrac{8}{17} }{ -\dfrac{15}{17}}\right) }{1+\left(\dfrac{ -\dfrac{4}{5} }{-\dfrac{3}{5} }\right) \times \left(\dfrac{ -\dfrac{8}{17} }{ -\dfrac{15}{17}}\right) } }= \dfrac{36}{77}[/tex]
[tex]tan(m - p) = \dfrac{36}{77}[/tex]
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A certain element has a half-life of approximately 15 hours. How long would it take for 500 grams of the element to decay to 299 grams? Leave your answer as an integer or simplified expression.
It would take 11.1 hours to decay from 500 grams to 299 grams.
How long takes to decay?We know that for an element with an half-life T has a decay equation that can be written as:
f(t) = A*e^(-t*ln(2)/T)
Where A is the initial amount, and f(t) is the amount of the element t hours after.
Here we know that:
A = 500g
T = 15h
Then the function is:
f(t) = 500g*e^(-t*ln(2)/15h)
And we want to find the value of t such that f(t) = 299g, then:
299g = 500g*e^(-t*ln(2)/15h)
299/500 = e^(-t*ln(2)/15h)
ln(299/500) = -t*ln(2)/15h
-ln(299/500)*15h/ln(2) = t
11.1h = t
It will take 11.1 hours.
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1. Analyze When a fraction with a numerator of 30 and a denominator of 8
is converted to a mixed number and reduced, what is the result?
A man deposited $800 in his account at the bank which offers 6% simple interest per annum
a, how much interest would he receive on the $800 after 9 months
b, how long it take for $800 to increase to $992
Answer:
Step-by-step explanation:
after 9 months, the man will have received $836. It would take 4 years to get $992 with a 6% simple interest annually
Which point is located on the line represented by the equation y + 4 = –5(x – 7)?
(-4, 7)
(-7, 4)
(7, -4)
(4, -7)
Answer:
(7,-4)
Step-by-step explanation:
y + 4 = -5(x-7) Substitute in 7 for x and -4 for y
-4 + 4 = -5 (7-7)
0 = 5(0)
0 = 0 This is a true statement.