Answer:
Step-by-step explanation:
s = rθ, where r is the radius, θ is the radian measure of the central angle, and s is the arc length.
4.5 = 2.5θ
4.5 / 2.5 = θ
1.8 = θ
The Sanchez family had dinner at their favorite restaurant. A 9% sales tax was added to their bill. Amy paid the bill with a $10 gift certificate plus $30.60. How much did the family's dinner cost before tax? Round your answer to the nearest penny.
Answer:
The bill was $36.95 without tax.
The price before tax was the amount of $37.25 which is before a 9% sales tax was added to their bill.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Their bill was charged a 9% sales tax.
Amy paid the bill with a $10 gift certificate plus $30.60
Use the equation P + rP =T,
where P is the price before tax, r is the sales tax rate, and T is the total price, including tax.
The price before tax (P) is unknown.
The total price(T) = 30.60 + 10 = 40.60
The sales tax rate (r) = 9% = 9/100 = 0.09
⇒ P + rP = T
Substitute the values in the above equation, and we get
⇒ P + (0.09)P = 40.60
⇒ P(1 + 0.09) = 40.60
⇒ P(1.09) = 40.60
⇒ P = 30.60/(1.09)
Apply the Division operation, and we get
⇒ P = 37.247706
Rounded to the nearest hundredth
⇒ P = 37.25
Therefore, the price before tax was the amount of $37.25.
Learn more about Arithmetic operations here:
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Tyler invested $350 in an account paying an interest rate of 4.5% compounded
continuously. Assuming no deposits or withdrawals are made, how long would it
take, to the nearest tenth of a year, for the value of the account to reach $700?
Answer:
15.4 I did this on delta math
It would take approximately 15.4 years, to the nearest tenth of a year, for the value of the account to reach $700 with continuous compounding.
How to calculate compounding time?The formula for calculating the future value (FV) of an investment with continuous compounding is:
[tex]FV = Pe^{rt}[/tex]
Where P is the initial principal, r is the annual interest rate (expressed as a decimal), t is the time period (in years), and e is the mathematical constant e (approximately 2.71828).
In this case, we have P = $350, r = 4.5% = 0.045, and we want to find the time t when the FV is $700. Substituting these values into the formula, we get:
[tex]700 = 350e^{0.045t}[/tex]
Dividing both sides by $350, we get:
[tex]2 = e^{0.045t}[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(2) = ln\times e^{0.045t}[/tex]
Using the properties of logarithms, we can simplify this to:
ln(2) = 0.045t ln(e)
Since ln(e) = 1, we can simplify further to:
ln(2) = 0.045t
Finally, solving for t, we get:
t = ln(2) / 0.045 ≈ 15.4
Therefore, it would take approximately 15.4 years, to the nearest tenth of a year, for the value of the account to reach $700 with continuous compounding.
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What's the y intercept and slope?
Answer:
The slope is 4
The y-intercept is 3 OR (0, 3)
Step-by-step explanation:
Points on the graph: ( -1, -1) and (0,3)
Slope:
m=(y2-y1)/(x2-x1)
m=(3+1)/(0+1)
m=4/1
m = 4
Point slope-intercept:
y - y1 = m(x - x1)
y + 1 = 4(x + 1)
y + 1 = 4x + 4
y = 4x + 3
A person in an apartment
building sights the top and bottom of an office
building 500 ft. away. The angle of elevation
for the top of the office building is 23° and the
angle of depression for the base of the building
is 50º. How tall is the office building?
Answer:
Step-by-step explanation:
tan23=h1/500
h1=500tan23
tan50=h2/500
h2=500tan50
The height of the building is h1+h2 so
H=500(tan23+tan50)ft (exact)
H=808.1 ft (rounded to nearest tenth of a foot)
Show that (16 1/4)3 and (16 3)1/4 are equivalent
Answer:
They are both 12
Change 16 1/4 into 4.
4 • 3
12
16 • 3 is 48
1/4 of 48 is 12
Hope this helps
Dilate Point B by a scale factor of 1/2
a (1.5,-4)
b (-1.5,1)
c (-1,-1.5)
d (-2,-2)
PLEASE HELP
Answer:
B
Step-by-step explanation:
Divide each coordinate by 2
3/2=1.5
2/2=1
A train leaves at 08:36 and arrives at 10:57. It travelled at an average speed of 85 km/h.
How far did it travel? Give your answer in km to 1DP.
Answer:
199.8 km to the 1 decimal point
Step-by-step explanation:
8:36 to 9:00 is 24 min
9:00 to 10:00 is 60 min
10:00 to 10:57 is 57 min
That's a total of 24 + 60 + 57 = 141 min = 141/60 hr.
d = rt = 141/60(85) = 199.8 km to the 1 decimal point
A and b are positive integers and a-b=2 ... Evaluate the following:
27^1/3 b / 9^1/2 a
There is an image attached of the problem
Answer:
Step-by-step explanation:
a-b=2
[tex]\frac{27^{\frac{1}{3} b} }{9^{\frac{1}{2}a } } \\=\frac{(3^{3}) ^{\frac{1}{3} b} }{(3^{2} )^{\frac{1}{2} a} } \\=\frac{3^b}{3^a} \\=3^{b-a} \\=3^{-(-b+a)} \\=3^{-2}\\=\frac{1}{3^2} \\=\frac{1}{9}[/tex]
x
−
3
4
=
8
Which value of
x
satisfies this equation?
Find the value of x. Explain your reasoning. (5x − 12) + (x + 6) = because the consecutive angles of a parallelogram are . Solving for x gives x =
Answer:
x=1
Step-by-step explanation: Snap Add?
I don't know what this means:
"because the consecutive angles of a parallelogram are . Solving for x gives x ="
I know that (5x-12) + (x+6)
1. 5x-12+x+6=0
2.6x-6=0
3.6x=6
4.x=1
Alejandra plans to sew fringe on a scarf. The scarf is shaped like a rectangle. The length of the scarf is 44 inches. The width is one half the length.
Answer:
Total fringe needed = 132 inches
Step-by-step explanation:
P.S - The exact question is -
Given - Alejandra plans to sew fringe on a scarf. The scarf is shaped like a rectangle. The length of the scarf is 44 inches. The width is one half the length.
To find - How much fringe does Alejandra need?
Proof -
Total fringe needed = Perimeter of the rectangle.
Now,
We know that,
Perimeter of the Rectangle = 2(Length + Width)
Now,
Given that,
Length = 44 inches
Width = one half the length
= [tex]\frac{1}{2}[/tex] × 44 = 22 inches
⇒Width = 22 inches
∴ we get
Perimeter of the Rectangle = 2(44 + 22)
= 2(66) = 132 inches
⇒Perimeter of Rectangle = 132 inches
∴ we get
Total fringe needed = Perimeter of the rectangle = 132 inches
⇒Total fringe needed = 132 inches
HELP ASAP PLAESE HELPP
Answer:
Ur right it's C.448
Step-by-step explanation:
I did it on goo.gle lol
hope this helps luv
Please help ASAP !!!!
Answer:
AB(12, -8)?
Step-by-step explanation:
I think that's it but I haven't done something like this in a hot minute. If it's wrong I'm sorry
wich mathematical expression represent this statement?the sqaure of a number times 3
1. 7n
2. 3n^2
3.2n + 8
4. n^3/ 2
Answer:
2
Step-by-step explanation:
( n^2)×3 can be written as 3(n^2)
PLEASE HELP ASAP WILL GIVE BRAINLIEST
The scatter plot shows the number of hats and scarves each knitter sold at a knitting show.
How many hats did the knitter who sold 8 scarves sell?
A. 6
B. 5
C. 3
D. 1
Answer:
C- 3
Step-by-step explanation:
I really need help with these, if you know any it would help so much
1 - 53 is 45% of what number?
2 - if you got scored 20 out of 24 what percentage would that be?
3 - 80 is 55% of what number?
Answer:
1: 23.85
2: 83%
3: 44
Step-by-step explanation:
1 - do 53x0.45 (23.85)
2 - Divide 20 by 24, which you get 0.833333333 and move the decimal 2x to the right. You get 83.3333333, but round. So 83%
3 - do 80x0.55 (44)
Keith bought 5 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 40 cards left. How many cards did Keith
start with?
Answer:
85 cards
Step-by-step explanation:
1A) Quad ABCD is inscribed in the circle. Find x. *
1B) Using your answer from above, what is angle A? *
103
77
90
25
Answer:
∠A = 77°
Step-by-step explanation:
Given:
Inscribe quadrilateral
Opposite angles
∠A = (2x + 9)°
∠B = (3x + 1)°
Find:
Value of ∠A
Computation:
We know that in Inscribe quadrilateral sum of Opposite angles are 180
So,
(2x + 9)° + (3x + 1)° = 180°
5x + 10 = 180
x = 34°
So,
∠A = (2x + 9)°
∠A = 2(34) + 9°
∠A = 77°
Find the future amount at the end of two years for a $7000 investment that earns 7% at the end of each year
Answer:
$8,014.30
Step-by-step explanation:
Find the slope and this line.
2 ways the akkadian and assyria empire are the same
Answer:
The Akkadian and Assyrian empires were two of the world’s first empires. Their conquests reshaped Mesopotamia. The many empires that would follow, worldwide,
Step-by-step explanation:
Taylor climbed a tree and is sitting on one of the branches deciding if she wants to jump. She weighs 45 kilogram and is sitting 10 meters from the ground. What is her potential energy?
Answer:
Her potential energy is approximately 4481 J.
Step-by-step explanation:
Because the formula for potential energy is PEg = 9.81 * mass * height, just plug in the knowns. After you plug those in, you will get the potential energy as 9.81 * 450, which is approximately 4481 J.
Practice
w
MULTIPLE CHOICE
John is 4 years older than Ben. If John is 12, what is Ben's age?
determine if the following is a function or not
-4,8
-2,8
0,24
4,24
2,16
Answer:
I think that is a function
Step-by-step explanation:
Please help me I don’t understand
Answer:
C
Step-by-step explanation:
tan α=opposite side /adjacent side
tan P=16/12=4/3
tanQ=12/16=3/4
* This is the correct answer, I have taken the test and am posting the answers in hopes of helping other people :] *
What is the value of y?
Triangle A B C has right angle C with side A C labeled 5. Angle A is 60 degrees and its opposite side B C is labeled y.
Enter your answer, as an exact value, in the box.
y =
Answer:
OMG THANK YOU-
what is the distance between -3,500 and 2,000 feet
Answer: if you take 2,000- (-3,500) you get 5,500 ft, making this the distance. Also, think about it this way 2,000 is 2,000 ft from 0, and then there is another 3,500 past zero, putting these together makes the amount of space they are away from each other in total.
Note that when subtracting a negative it becomes positive, using the keep change change rule 2,000 - (-3,500) becomes 2,000 + 3,500
You are a packer for Acme Bottling Company.
You fill cartons with bottles,
seal the cartons, and stack them on pallets.
Monday through Friday you are paid $0.78 for each carton you fill.
On Saturday you are paid an additional$0.38 for each carton you fill.
What is your total pay for a week in which you
filled the following number of cartons?
Mon-210
Tues-175
Wed-224
Thurs-160
Fri-216
Sat-90
Answer:
$872.70
Step-by-step explanation:
Add all numbers from Mon-Fri.
So 985.
Multiply it by 0.78
So $768.30
Add 0.78 and 0.38
So 1.16
Then multiply 90 by 1.16
So $104.40
Then add the two numbers.
768.30+104.40
So $872.70
Hope this helps
Please can someone help I don’t understand the question if it’s right I’ll give more plsssssesssssssssssddsd
Answer:
x = 33°
Step-by-step explanation:
From the figure attached,
FB and FC are two secants intersecting each other at point F outside the circle.
Measure of angles between the secants measures half of the difference between the intercepted arcs.
x° = [tex]\frac{1}{2}(\text{arc BC}-\text{arc DE})[/tex]
x° = [tex]\frac{1}{2}(108-42)[/tex]
x = 33°
Factor Completely
5xz + 2xy - 3yz
Answer:
Your answer is 5xz + 2xy - 3yz
Step-by-step explanation:
The expression is not factorable with rational numbers.
Therefore, You cannot factor the equation.
~Hoped this helped!~
~Brainiliest, please~