Step-by-step explanation:
let's create the corresponding equation.
it is linear, because the cost per hour is constant, no matter how many hours the car parks.
t is the variable indicating the amount of hours parking.
every hour costs $2.
and $8 is the starting value (we have to pay that, even if we have 0 hours parking time).
cost(t) = 2t + 8
so, the cost after 3 hours is
cost(3) = 2×3 + 8 = 6 + 8 = $14
What is needed to get accurate measurement of distance/length? Explain
Andrew and Kate have $30 to spend on dinner, tax, and gratuity at Mo’s Restaurant. Tax is 6%, and they will give a 15% tip on the total bill after taxes. Their dinner costs $21.00. Which statement correctly explains whether Andrew and Kate have enough money to pay their bill?
Yes. They have enough to pay their bill: 30 dollars times 1.06 = 31 dollars and 80 cents and 31 dollars and 80 cents times 1.15 = 36 dollars and 57 cents.
Yes. They have enough to pay their bill: 21 dollars times 1.06 = 22 dollars and 26 cents and 22 dollars and 26 cents times 1.15 = 25 dollars and 60 cents.
No. They do not have enough to pay their bill: 30 dollars times 1.06 = 31 dollars and 80 cents and 31 dollars and 80 cents times 1.15 = 36 dollars and 57 cents.
No. They do not have enough to pay their bill: 21 dollars times 1.06 = 22 dollars and 26 cents and 22 dollars and 26 cents times 1.15 = 25 dollars and 60 cents.
Answer:
ANSWER: Yes. They have enough to pay their bill: 21 dollars times 1.06 = 22 dollars and 26 cents and 22 dollars and 26 cents times 1.15 = 25 dollars and 60 cents.
Step-by-step explanation:
convert all % to decimals
0.06 x 21 = $1.26 tax
0.15 x 21 = $3.15 tip
1.26 + 3.15 = $4.41 added payment
4.41 + 21 = = $25.41 total bill
(yes i am aware i did the method differently since i learned it another way but the answer should till be correct.)
Answer:
Yes. They have enough to pay their bill: 21 dollars times 1.06 = 22 dollars and 26 cents and 22 dollars and 26 cents times 1.15 = 25 dollars and 60 cents. Otherwise B.
Let S1= 1, S2=2+3, S3= 4+5+6
Find S7
Find S17
Find Sn
Answer:
S7 = 175S17 = 2465Sn = 1/2(n³ +n)Step-by-step explanation:
The progression of sums is ...
1, 5, 15, 34, 65, ...
So, first differences are ...
4, 10, 19, 31
Second differences are ...
6, 9, 12, ...
Third differences are constant:
3, 3, ...
This means the expression for Sn will be a cubic expression. If dn is the first of the n-th differences, then the equation can be written as ...
Sn = S1 +(n -1)(d1 +(n -2)/2(d2 +(n -3)/3(d3)))
And this simplifies a little bit to ...
Sn = 1 +(n -1)(4 +(n -2)(n +3)/2)
In simpler form, we have ...
Sn = 1/2(n³ +n)
Then the two terms we're interested in are ...
S7 = (1/2)(7³ +7) = 175
S17 = (1/2)(17³ +17) = 2465
Each term Sₙ consists of the sum of a triangular number of terms, which are given by
[tex]T_n = \displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]
The triangular numbers are given recursively for n ≥ 1 by
[tex]T_n = T_{n-1} + n[/tex]
starting with T₀ = 0.
For example,
• S₁ = 1 and
[tex]\displaystyle S_1 = \sum_{k=T_0+1}^{T_1} k = \sum_{k=1}^1 k = 1[/tex]
• S₂ = 2 + 3 and
[tex]\displaystyle S_2 = \sum_{k=T_1+1}^{T_2} k = \sum_{k=2}^3 k = 2 + 3[/tex]
• S₃ = 4 + 5 + 6 and
[tex]\displaystyle S_3 = \sum_{k=T_2+1}^{T_3} k = \sum_{k=4}^6 k = 4 + 5 + 6[/tex]
Then the n-th term of the sequence we're considering is
[tex]S_n = \displaystyle \sum_{k=T_{n-1}+1}^{T_n} k = \sum_{k=T_{n-1}+1}^{T_{n-1}+n} k[/tex]
Expanding this sum, we have
[tex]S_n = \left(T_{n-1}+1\right) + \left(T_{n-1}+2\right) + \left(T_{n-1}+3\right) + \cdots + \left(T_{n-1}+n\right)[/tex]
There are n terms on the right side, and hence n copies of [tex]T_{n-1}[/tex], and the rest of the terms make up the next triangular number [tex]T_n[/tex] :
[tex]S_n = nT_{n-1} + 1 + 2 + 3 + \cdots + n[/tex]
[tex]S_n = nT_{n-1} + \displaystyle \sum_{k=1}^n k[/tex]
[tex]S_n = nT_{n-1} + T_n[/tex]
We have a closed form for [tex]T_n[/tex], so we end up with
[tex]S_n = n \cdot \dfrac{(n-1)n}2 + \dfrac{n(n+1)}2 \implies \boxed{S_n=\dfrac{n^3+n}2}[/tex]
From here it's easy to find S₇ and S₁₇.
[tex]S_7 = \dfrac{7^3+7}2 \implies \boxed{S_7 = 175}[/tex]
[tex]S_{17} = \dfrac{17^3+17}2 \implies \boxed{S_{17} = 2465}[/tex]
Need help with a math problem If doing 5 stars and a good rating
Answer:
16:1
Step-by-step explanation:
Since there are 85 total people and 80 are students that means 5 are chaperones.(85-5) Therefore the ratio of students to chaperones is 80:5 or simplified 16:1.
I want to know my grade if I have an 86 and I get a 0 and it’s worth 20% of my grade what will my grade be?
Answer:
your grade will be an 76
Step-by-step explanation:
what is the value of the 4 in the number 27.43? write your answer as a fraction
Answer:
4 tenths or 4/10
Step-by-step explanation:
rotate segment AE about point F 144 degrees
Answer:
DC
Step-by-step explanation:
If we rotate a segment around a point 360 degrees, we have rotated it around to its original point. Similarly, if we rotate it 180 degrees, we have rotated it to the side opposite of where it once was relative to the point.
What we can do is see how much 144 degrees is of 360 and use that to determine how far around we rotate AE around F.
144/360
divide by 12 because that is a common factor of both the numerator and denominator
12 / 30
divide by 2 because that is a common factor
6/15
divide by 3 because that is a common factor
2/5
Therefore, 144/360 = 2/5. This means that we rotate segment AE 2/5 of the way around point F. We have 5 sides in the polygon ABCDE, and each represents 1/5 of the way around. Going counterclockwise, ED represents 1/5, DC represents 2/5, and so on. We are looking for 2/5, so DC is our answer
) f(x) = 4x + 5, g(x) = 2/x;
Find (g • f)(3).
[tex]\text{Given that,}\\\\f(x) = 4x+5,~~~g(x) = \dfrac 2x\\\\\\f(3) = 4(3) +5 = 12 +5 = 17\\\\\\(g\circ f)(3)=g(f(3))=g(17)=\dfrac 2{17}[/tex]
Answer:
The answer is 2/17
Step-by-step explanation: Can I get brainliest again my answer was deletedee
The sales tax rate is 8% how much money is 8% of $14
If a triangle has a base of 6' and a height of 4' its area would be what?
A= bxh 2
A= 6x4 2
A= 12 sq. ft.
Answer:
Hello There!
According to the question,
Base=6
And
Height =4
Let's know the formula
[tex] \frac{1}{2} \times base \times height \\ so \\ \frac{1}{2} \times 6 \times 4 \\ [/tex]
simplify 2 with 6 then it will look like this
[tex] \frac{1}{1} \times3 \times 4 \\ \\ [/tex]
1 has no value so
[tex]3 \times 4 = 12 {ft}^{2} \\ [/tex]
So third option
[tex]a = 12 {ft}^{2} [/tex]
is correct.
[tex]\Large\textsf{Hope \: It \: Helped}[/tex]
Answer:
Area = 12 sq ft
Step-by-step explanation:
The formula to find the area of a triangle is
1/2 bh so we will replace the letters with their number value
1/2 (6x4)
1/2 x 24 = 12
So, 12 is your answer!
Find the next two terms in the sequence -3, 0, 3, 6
Answer:
9, 12
Step-by-step explanation:
the rule is +3 for each step in the sequence
A box contains 2 red marbles, 3 white marbles, 4 green marbles, and 1 blue marble. Two marbles are drawn at random without replacement. Find the probability of selecting a white marble, then a red marble.
what is the exact value of cos(11 π/12)
Answer:
[tex]-\frac{1}{4}(\sqrt{2}+\sqrt{6})[/tex]
Step-by-step explanation:
[tex]cos(\frac{11\pi}{12})[/tex]
[tex]cos(\frac{2\pi}{3}+\frac{\pi}{4})[/tex]
[tex]cos(\frac{2\pi}{3})cos(\frac{\pi}{4})-sin(\frac{2\pi}{3})sin(\frac{\pi}{4})[/tex]
[tex](-\frac{1}{2})(\frac{\sqrt{2}}{2})-(\frac{\sqrt{3}}{2})(\frac{\sqrt{2}}{2})[/tex]
[tex]-\frac{\sqrt{2}}{4}- \frac{\sqrt{6}}{4}[/tex]
[tex]-\frac{1}{4}(\sqrt{2}+\sqrt{6})[/tex]
Helpful Tips:
Sum Identity: [tex]cos(\alpha+\beta)=cos(\alpha)cos(\beta)-sin(\alpha)sin(\beta)[/tex]
LAST ATTEMPT IM MARKING AS BRAINLIEST!! ( Pythagorean theorem )
Answer:
x=sqrt(7)
Step-by-step explanation:
Since this is a right triangle, we can use the pythagorean theorem
a^2 + b^2 =c^2 where a and b are the legs and c is the hypotenuse
x^2 + ( sqrt(7))^2 = (sqrt(14))^2
x^2+7 = 14
x^2 = 14-7
x^2 = 7
Take the square root of each side
sqrt(x^2) = sqrt(7)
x=sqrt(7)
HELP ASAP PLEASE!!!!
Answers:
c = 7d = 5=========================================================
Explanation:
For equation A, I'll transform the right hand side into a similar form as the left side. Throughout the steps below, the left hand side stays the same.
[tex]\sqrt{448x^c} = 8x^3\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{(8x^3)^2}\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{64x^{3*2}}\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{64x^{6}}\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{64x^{6}*7x}\\\\\sqrt{448x^c} = \sqrt{64*7x^{6+1}}\\\\\sqrt{448x^c} = \sqrt{448x^{7}}\\\\[/tex]
Therefore, c = 7
Notice that 7/2 = 3 remainder 1. The quotient 3 is the exponent for the term outside the root for [tex]8x^3\sqrt{7x}[/tex] while the remainder 1 is the exponent for the x term inside the root.
---------------------------------------
We do the same idea for equation B.
[tex]\sqrt[3]{576x^{d}} = 4x\sqrt[3]{9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{(4x)^3}\sqrt[3]{9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{64x^3}\sqrt[3]{9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{64x^3*9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{64*9x^{3+2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{576x^{5}}\\\\[/tex]
This must mean d = 5
Note: 5/3 = 1 remainder 2, which means [tex]\sqrt[3]{x^5} = x^1\sqrt[3]{x^2} = x\sqrt[3]{x^2}[/tex]
5x+6 ?? please help 8th grade math work
Answer:
5x + 6 = 0
5x = - 6
x = - 6/5
-6/5 is the answer
f(x)=x^2. what is g(x)?
pls help me in this question
a . If 3x,2x and (x+12) are supplymentary angles find the sizes of unknown angles
Answer:
x=28°
Step-by-step explanation:
supplementary angles equal 180°
So:
3x+2x+x+12=180°
6x+12=180
6x=168
x=28°
Therefore:
3x:
3(28)=84°
2x:
2(28)=26°
x+12:
28+12=40°
[tex]\displaystyle \text{Find the summation given that } f(x) = x^3 \text{ and } \triangle x_i = 2 + \frac{i}{4}. \\ \\\[ \sum_{i = 1}^{4} x^3 \times \triangle x[/tex]
Answer:
Click the picture and u will see the answer.
#CarryOnLearning
The summation of the given function from 1 to 4 is 10.5x³.
The given parameters:
[tex]\Sigma \ x^3 \times \Delta x, \ \ \ \Delta x = 2 + \frac{i}{4} \\\\[/tex]
The summation of the given function from i = 1, to i = 4, is calculated as follows;
[tex]\Sigma \ x^3 \times \Delta x = x ^3 (2 + \frac{1}{4} ) + x ^3 (2 + \frac{2}{4} ) + x ^3 (2 + \frac{3}{4} ) + x ^3 (2 + \frac{4}{4} )\\\\= x^3(10\frac{1}{2} )\\\\=\frac{21}{2} x^3\\\\= 10.5x^3[/tex]
Thus, the summation of the given function from 1 to 4 is 10.5x³.
Learn more about summation of functions here: https://brainly.com/question/16599038
A line has a slope of and passes through the point (4, 7). What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
7=4m +c( y intercept)
Step-by-step explanation:
use the formula y= mx +c
plz help me to answer
22/3 sorry I accidentally deleted steps
In the number 777.77 how does the value of 7 in the tenths place compare to the value of 7 in the hundredths place
Answer:
630
Step-by-step explanation:
the value of 7 in the tenths place is 70
the value of 7 in the hundredths place is 700
compare 700 and 70
So 700-70 = 630
Translate the sentence into an inequality.
The sum of a number times 2 and 21 is at least 22.
Use the variable b for the unknown number.
2b + 21 < 22
b is the unknown number so multiply it by 2 to get 2b then add 21, bring the less than sign and write the 22 after the less than sign
If the sales tax in your town was 7%, and you paid $1,400 in sales tax on your new car, then what was the original
price of the car? And what is the total price including sales tax?
Please be accurate of your answer and explain.
Answer:
$20,000
Step-by-step explanation:
20,000 / 0.07 = 1400
Simplify the expression
-4 + 3 + 5 =
Answer:
4
Step-by-step explanation:
-4+3=-1
-1+5=4
help me plzzzzzzzzzzzzz (NO LINKS)
Answer:
5^4Step-by-step explanation:
The rule when you divide two values with the same base is to subtract the exponents.
a recipe calls for 2 cups of flour for every 3 cups of sugar. If you are planning to use 5 cups of flour, how many cups of sugar should you use
Answer:
7½ cups of sugar
Step-by-step explanation:
2 cups of flour needs 3 cups of sugar
1 cups of flour needs 3/2=1.5 cups of sugar
1×5 cups of flour needs 1.5×5=7.5 cups of sugar=7½ cups of sugar ANS
Which list of angle measures could be the angle measures of a triangle?
a pupil who scored 60 in her maths exam was absent and missed English exam use the line of best fit to predict what her English mark could be
Answer:
It's 48.
Hope that helped? Also, if you need anymore answers feel free to ask me as I had that assignment on Mathswatch.
Step-by-step explanation:
Answer:
i think it's 48 if i'm wrong i'm sorry
When f(x)=4, what is the value of x?
This mapping shows a functional relationship.
Domain
Range
оо
O 2
2
4
3
-3
0
4
-1
→-1
→ 3
Check the picture below.
The value of f(x) at x=4 is 2.
What is Function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.
We have to find the value of function for x=4.
This means that from the figure we have to find the value of y when x= 4.
Now, looking into the figure we have
f(4)= 2
f(0)= -2
f(-1)= -1
f(3)= 4
So, the required value is 2.
Learn more about Function here:
https://brainly.com/question/12431044
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