If a local city collects 8% sales tax if the total purchase was $216 then $17.28 is collected for sales tax.
What is Percentage?A relative value indicating hundredth parts of any quantity is known as Percentage.
Given that a local city collects 8% sales tax
The total purchase was $216.
We need to find the amount collected for sales tax.
To find this we have to find 8% of 216.
Convert 8% to the decimal value.
8/100=0.08
Now multiply 0.08 with 216
0.08×216
$17.28
Hence, if a local city collects 8% sales tax if the total purchase was $216 then $17.28 is collected for sales tax.
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The amount collected for sales tax is $16.
Step 1: Understand the Problem
The total purchase amount ($216) includes the sales tax. We need to find how much of this amount is the sales tax itself.
Step 2: Convert the Percentage to a Decimal
Convert the sales tax rate from a percentage to a decimal.
[tex]\[ \text{Sales Tax Rate} = \frac{8}{100} = 0.08 \][/tex]
Step 3: Set Up the Equation
Let ( P ) be the pre-tax purchase amount and ( T ) be the total amount including tax. The relationship can be written as:
[tex]\[ T = P + \text{Sales Tax} \][/tex]
Since the sales tax is 8% of the pre-tax amount,
[tex]\[ \text{Sales Tax} = 0.08 \times P \][/tex]
Thus, the total amount is:
[tex]\[ T = P + 0.08P = 1.08P \][/tex]
Step 4: Solve for the Pre-Tax Amount
We know the total amount ( T ) is $216.
[tex]\[ 216 = 1.08P \][/tex]
To find ( P ):
[tex]\[ P = \frac{216}{1.08} \][/tex]
[tex]\[ P \approx 200 \][/tex]
Step 5: Calculate the Sales Tax
Now, find the sales tax:
[tex]\[ \text{Sales Tax} = 0.08 \times P \][/tex]
[tex]\[ \text{Sales Tax} = 0.08 \times 200 \][/tex]
[tex]\[ \text{Sales Tax} = 16 \][/tex]
Therefore the amount collected for sales tax is $16.
Line FH and line Ik are parallel lines
Which angles are corresponding angles?
Corresponding angles are the ones that occupy the same relative position where a third line intersects two other lines. If lines FH and IK are parallel, the corresponding angles are FHB and IKB; and BHJ and BKL. They are always equal in measure if the lines are parallel.
Explanation:In geometry, lines that are parallel have several corresponding angles. Corresponding angles are the angles that occupy the same relative position at each intersection where a line intersects two other lines. If lines FH and IK are parallel and intersected by another line (Let's call it line B for easier understanding), the corresponding angles would be as follows:
Angle FHB and Angle IKBAngle BHJ and Angle BKLThese pairs are known as corresponding angles. Coresponding angles are always equal in measure if the lines are parallel to each other.
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Ethan's car can drive 30 miles per gallon of gasoline. Gasoline costs $4 per gallon, including tax. Ethan drove 180 miles on a trip. What was the total cost, in dollars, of gasoline that the car used for Ethan's trip?
I NEED THE ANSWER ASAP!!!!! THANKS
24$ I believe is the answer You divide the total number of miles driven, to the number of miles per gallon . 180 divided by 30 = 6. Then multiply the answer 6 times dollars per gallon 4$ • 6 = 24 Your answer is 24 :)
Ethan's trip cost $24 in gasoline expenses, calculated by dividing the distance by the fuel economy to find the gallons used and then multiplying that by the cost per gallon.
Explanation:To calculate the total cost of gasoline for Ethan's trip, we need to know two things: the fuel economy of the car and the distance traveled. The fuel economy is given as 30 miles per gallon, and the distance traveled is 180 miles.
First, we calculate how many gallons of gas were used during the trip:
Divide the total miles driven by the car's miles per gallon to get the number of gallons needed: 180 miles ÷ 30 miles/gallon = 6 gallons. Multiply the number of gallons by the cost per gallon to find the total cost: 6 gallons × $4/gallon = $24.
Therefore, the total cost of gasoline for the trip was $24.
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The dot plot shows the number of magazines sold. Determine the range of the data set.
A) 7
B) 8
C) 10
D) 25
Answer:
B
Step-by-step explanation:
The range is the difference between the largest and smallest members of the data set.
largest = 25 and smallest = 17
range = 25 - 17 = 8 → B
PLS HELPPP 35 pt!!!!! Evaluate (simplify) each expression 27^2 / 27 ^ 4/3
Answer:
9 on ED2020
Step-by-step explanation:
The simplified value of the expression [tex]\frac{27^2}{27 ^{4/3}}[/tex] using properties of exponents is 3² or 9.
Given Expression: [tex]\frac{27^2}{27 ^{4/3}}[/tex]
To Simplify the expression, use the following Exponents properties
Quotient Rule: [tex]a^m / a^n = a^{m-n}[/tex] Power Rule: [tex](a^m)^n = a^{(m*n)[/tex]Now, let's factorize the number of prime factors
27 = 3 x 3 x 3 or 3³
So, the Expression [tex]\frac{27^2}{27 ^{4/3}}[/tex] can be written as
[tex]\frac{27^2}{27 ^{4/3}}[/tex] = [tex]\frac{(3^3)^2}{(3^3)^{4/3}}[/tex]
Using Power Rule: [tex](a^m)^n = a^{(m*n)[/tex]
[tex]\frac{27^2}{27 ^{4/3}}[/tex] = [tex]\frac{3^{(3*2)}}{3^{3*(4/3)}}[/tex]
= [tex]\frac{3^6}{3^4}[/tex]
Using Quotient Rule: [tex]a^m / a^n = a^{m-n}[/tex]
[tex]\frac{27^2}{27 ^{4/3}}[/tex] = [tex]\frac{3^6}{3^4}[/tex]
=[tex]3^ {6-4}[/tex]
= 3²
= 9
Therefore, the simplified expression is 3² or 9.
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5. What is the combined weight of the 3/4-lb bags?
The answer would be 3.175 kg
Answer:knee r
Step-by-step explaning
A recipe for ricotta cheese calls for 1/2 cup of whole milk for every 1/4 cup of heavy cream. How much whole milk should be used for every one cup of heavy cream
A. 1/8 cup
B. 1/4 cup
C. 2 cups
D. 4 cups
Answer:
C. 2 cups
Step-by-step explanation:
So since it says for every 1/2 cup of whole milk, you need 1/4 of heavy cream, that means you will need twice as much whole milk as you do heavy cream.
So for every one cup of heavy cream, that means you need 2 cups of whole milk.
This is because 1/2 is twice as much as 1/4.
To scale up the given ratio of 1/2 cup of whole milk to 1/4 cup of heavy cream to 1 cup of cream, you need to multiply the quantity of milk by 4. This gives you 2 cups of milk for 1 cup of cream.
Explanation:The question asks us to calculate the quantity of whole milk that should we used for every cup of heavy cream, based on a given ratio. The ratio given is 1/2 cup of milk for every 1/4 cup of cream. Ratios can be scaled up or down while keeping the same relationship between quantities. In this case, we want to know how much milk to use for 1 cup of cream. Since 1 cup is 4 times larger than 1/4 cup, we simply multiply the quantity of milk by 4 as well, which gives us 1/2 cup * 4 = 2 cup. Hence, the answer is C. 2 cups of milk should be used for every cup of heavy cream.
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Compare the algebraically expressed function f(x) = -8x2 + 4x + 2 to the function shown in the graph to determine which statement is true.
A) The algebraic function has a greater maximum value.
B) The algebraic function has a lower minimum value.
C) The graphed function has a greater maximum value.
D) The graphed function has a lower minimum value.
ANSWER
A) The algebraic function has a greater maximum value.
EXPLANATION
The given function is
[tex]f(x) = - 8 {x}^{2} + 4x + 2[/tex]
This can be rewritten as:
[tex]f(x) = - 8( {x - \frac{1}{4} })^{2} + \frac{5}{2} [/tex]
The maximum value of this function is 2.5
The maximum value of the graph is less that zero.
This means that that the maximum value of the algebraic function is greater than the maximum value of the graph.
Answer:
Option A.
Step-by-step explanation:
Algebraically expressed function is f(x) = -8x² + 4x + 2
As we know in a quadratic equation f(x) = ax² + bx + c, if a is negative then the vertex will be maximum.
and the maximum value will be represented by [tex]c-\frac{b^{2}}{4a}[/tex]
From the given quadratic equation
a = -8
b = 4 and c = 2
Now we place these values in the equation.
Maximum = [tex]2-\frac{4^{2}}{4(-8)}[/tex]
= 2 + 0.5
= 2.5
From the graph attached we can easily conclude that vertex of the parabola is less than 0.5
Therefore, algebraic function has the greater maximum value.
Option A. is the answer.
If George the giraffe is 18 feet tall how many inches tall is he
To convert George the giraffe's height from feet to inches, multiply 18 feet by the conversion factor of 12 inches per foot, resulting in George being 216 inches tall.
Explanation:If George the giraffe is 18 feet tall and you want to convert his height to inches, you need to know that one foot is equal to 12 inches. To find out how many inches tall George the giraffe is, you multiply his height in feet (18 feet) by the number of inches in one foot.
Here's the calculation step by step:
Identify the height in feet: 18 feetKnow the conversion factor: 1 foot = 12 inchesMultiply the height in feet by the conversion factor: 18 feet × 12 inches/foot = 216 inchesTherefore, George the giraffe is 216 inches tall.
Please help i need it the answer right now
Answer: First graph
Step-by-step explanation:The lines wont intersect
Answer:
The answer is option A.
Which equation has an a-value of –2, a b-value of 1, and a c-value of 3? 0 = –2x2 + x + 3 0 = 2x2 + x + 3 0 = –2x2 + 3 0 = 2x2 – x + 3
ax² + bx + c = 0
You know:
a = -2
b = 1
c = 3
The 1st option is your answer
-2x² + x + 3 = 0
a = -2
b = 1
c = 3
Answer:
A: 0 = –2x2 + x + 3
Step-by-step explanation:
edge
marta is solving the equation s=2πrh+2πr^2 for h. which should be the result?
s/2πr-r=h
s-r/2πr=h
s-r/2π=h
s-2π/r=h
Answer: First option.
Step-by-step explanation:
Marta needs to subtract [tex]2\pi r^2[/tex] from both sides of the equation:
[tex]s=2\pi rh+2\pi r^2[/tex]
[tex]s- 2\pi r^2=2\pi rh+2\pi r^2- 2\pi r^2[/tex]
[tex]s- 2\pi r^2=2\pi rh[/tex]
Now she needs to divide both sides of the equation by [tex]2\pi r[/tex], then:
[tex]h=\frac{s- 2\pi r^2}{2\pi r}[/tex]
Rewriting:
[tex]h=\frac{s}{2\pi r}-\frac{2\pi r^2}{2\pi r}[/tex]
Simplifying, she should get:
[tex]h=\frac{s}{2\pi r}-r[/tex]
This matches with the first option.
Answer:
[tex]\frac{s}{2\pi r}-r=h[/tex]
Step-by-step explanation:
Given equation is [tex]s=2\pi rh+2\pi r^2[/tex].
Now we need to solve this equation for "h" and match with the given choices to find the correct choice.
[tex]s=2\pi rh+2\pi r^2[/tex]
[tex]s-2\pi r^2=2\pi rh[/tex]
[tex]2\pi rh=s-2\pi r^2[/tex]
[tex]h=\frac{s-2\pi r^2}{2\pi r}[/tex]
[tex]h=\frac{s}{2\pi r}-\frac{2\pi r^2}{2\pi r}[/tex]
[tex]h=\frac{s}{2\pi r}-r[/tex]
[tex]\frac{s}{2\pi r}-r=h[/tex]
Hence first choice [tex]\frac{s}{2\pi r}-r=h[/tex] is correct choice.
Answer this pls !!!.... and thanx !
This is the order you need to use to solve this problem: PEMDAS
(Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)
So you start with P and make your way down to S
(2x + 3)(x - 6) - 2x² + 3x + 30 First multiply (2x + 3)(x - 6) (distribute)
(2x)x - (2x)6 + (3)x - (3)6 = 2x² - 12x + 3x - 18 = 2x² - 9x - 18
(2x²- 9x - 18) - 2x² + 3x + 30 Simplify by combining like terms
-6x + 12
Answer:
- 6x + 12
Step-by-step explanation:
Expand the product of factors
= 2x² - 12x + 3x - 18 - 2x² + 3x + 30 ← collect like terms
= (2x² - 2x²) + (- 12x + 3x + 3x) + (- 18 + 30) ← simplify parenthesis
= 0 + (- 6x) + (12)
= - 6x + 12
(30 POINTS)
A restaurant did a survey among 200 customers to find their food preferences. The customers were asked about their preferences for pasta or rice. Out of the total 60 people who liked pasta, 20 also liked rice. There were 80 people who liked rice.
Part A: Summarize the data by writing the values that the letters A to I in the table below represent.
Like pasta Do not like pasta Total
Like rice A B C
Do not like rice D E F
Total G H I
Part B: What percentage of the survey respondents did not like either pasta or rice?
Part C: Do the survey results reveal a greater dislike for rice or pasta? Justify your answer.
Answer:
Below
Step-by-step explanation:
Part A:
Like Pasta / Like Rice: A = 20
Like Rice / Do not like Pasta: B = 60
Total: C = 80
Do not like rice / Like Pasta: D = 40
Do not like rice & Pasta: E = 80
Total F = 120
Total G = 60
Total H = 140
Total I = 200
Part B: Using the rule of three:
If 200 represents 100%, then how much 80 represents?
(80 * 100) / 200 = 40%
40% did not like pasta nor rice.
Part C:
From the survey we know that:
30% like rice, and 20% dislike pasta. So yes, the survey reveals a greater dislike for rice.
How can you find f(2) if f(x) = 3x2 – 2?
a. Square 2. Subtract 2 from the result, and then multiply by 3.
b. Square 2. Multiply the result by 3, and then subtract 2.
c. Multiply 2 by f.
d. Multiply 2 by 3, square the result, and then subtract 2.
Answer:
b
Step-by-step explanation:
The square of 2 and the resultant is multiplied by 3 then subtract by 2. Then the correct option is B.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
f(x) = 3x² - 2
The value of the function at x = 2 will be given as,
f(2) = 3(2)² - 2
The square of 2 and the resultant is duplicated by 3 then, at that point, taken away by 2. Then, at that point, the right choice is B.
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Solve the following equation. Then place the correct number in the box provided. 8x/7 = 8
Answer:
x = 7
Step-by-step explanation:
Assuming we need to solve for x, we cross multiply and do algebra to solve it. Steps shown below:
[tex]\frac{8x}{7}=8\\8x=7*8\\8x=56\\x=\frac{56}{8}\\x=7[/tex]
The correct answer is x = 7
Answer:
x = 7Step-by-step explanation:
[tex]\dfrac{8x}{7}=8\qquad\text{multiply both sides by 7}\\\\7\!\!\!\!\diagup^1\cdot\dfrac{8x}{7\!\!\!\!\diagup_1}=7\cdot8\\\\8x=56\qquad\text{divide both sides by 8}\\\\x=7[/tex]
What’s 3.24 rounded to the nearest tenth
Answer:
3.2
Step-by-step explanation:
it is closer to 3.2 than 3.3
Answer: 3.2
Step-by-step explanation:
2 is the the tenths place and 4 is in the hundredths. .24 rounded to .2 is now the tenths therefore 3.2 is the tenths place
What is the sum of the geometric sequence 1,-6,36,... if there are 7 terms?
Answer:
39,991Step-by-step explanation:
The formula of a sum of a geometric sequence:
[tex]S_n=\dfrac{a_1(1-r^n)}{1-r}[/tex]
We have
[tex]a_1=1,\ a_2=-6,\ a_3=36,\ ....\\\\r=\dfrac{a_2}{a_1}\to r=\dfrac{-6}{1}=-6[/tex]
Substitute:
[tex]a_1=1,\ n=7,\ r=-6:\\\\S_7=\dfrac{1(1-(-6)^7)}{1-(-6)^7}=\dfrac{1-(-279936)}{1+6}=\dfrac{279937}{7}=39991[/tex]
Someone please explain (:
Answer:
a.) 1.38 seconds
b.) 17.59ft
Step-by-step explanation:
h(t) = -16t^2 + 22.08t + 6
if we were to graph this, the vertex of the function would be the point, which if we substituted into the function would give us the maximum height.
to find the vertex, since we are dealing with something called "quadratic form" ax^2+bx+c, we can use a formula to find the vertex
-b/2a
b=22.08
a=-16
-22.08/-16, we get 1.38 when the minuses cancel out. since our x is time, it will be 1.38 seconds
now since the vertex is 1.38, we can substitute 1.38 into the function to find the maximum height.
h(1.38)= -16(1.38)^2 + 22.08t + 6 -----> is maximum height.
approximately = 17.59ft -------> calculator used, and rounded to 2 significant figures.
for c the time can be equal to (69+sqrt(8511))/100, as the negative version would be incompatible since we are talking about time. or if you wanted a rounded decimal, approx 1.62 seconds.
Answer:
a) [tex]h(t)=-16(t-0.69)^2)+13.62[/tex]
b)The maximum height is 13.62 feet.
c) 1.84 seconds
Step-by-step explanation:
The function that models the height in feet of the hammer above the ground is
[tex]h(t)=-16t^2+22.08t+6[/tex]
Factor -16 as shown;
[tex]h(t)=-16(t^2-1.38t)+6[/tex]
Add and subtract the square of half the coefficient of t.
[tex]h(t)=-16(t^2-1.38t+(-0.69)^2)--16(-0.69)^2+6[/tex]
[tex]h(t)=-16(t^2-1.38t+(-0.69)^2)--16(-0.69)^2+6[/tex]
Rewrite the first three terms as a perfect square trinomial;
[tex]h(t)=-16(t-0.69)^2)+13.62[/tex]
This function is now in the form;
[tex]h(t)=a(t-h)^2)+k[/tex]
where (h,k)=(0.69,13.62)
This implies that; the hammer reached its maximum height at t=0.69 seconds.
b) The maximum height is the y-value of the vertex.
The maximum height is 13.62 feet.
c) To answer this question we need to find the difference between the x-intercepts.
[tex]h(t)=-16t^2+22.08t+6[/tex]
a=-16,b=22.08,c=6
[tex]t_2-t_1=\sqrt{(t_1+t_2)^2-4t_1t_2}[/tex]
[tex]t_2-t_1=\sqrt{(\frac{-b}{a})^2-4(\frac{c}{a})}[/tex]
[tex]t_2-t_1=\sqrt{(\frac{-22}{-16})^2-4(\frac{-6}{-16}) }=1.84[/tex]
Hence the hammer was in the air for 1.84 seconds
i sawer there only 2 more
answer:
y=5.5x
explanation:
rise over run=rise/run= x/y
for every t shirt or "y" multiply 5.5 and it will give u the total cost or"x"
How do I do number 3?
Answer:
120 in^2
Step-by-step explanation:
Split the shape into a square and a rectangle, like you did. A square has all equal sides, so you know that 9 x 9= 81. If the whole length of the square and the triangle combined is 15, then you know the triangle base is 6. Multiply the height of the triangle by the base and .5 to get that area. Add everything together for the answer
if logM/N = 4 and logP/N =7, what can you say about the relationship between M and P?
A. P= 3M
B. M= 3P
C. P= 1000M
D. P= 100M
Answer:
C. P= 1000M
Step-by-step explanation:
[tex]log(\frac{M}{N} )=4[/tex]
Using the quotient rule of logs we can write:
log(M) - log(N) = 4
or
log(M) - 4 = log(N) (Equation 1)
[tex]log(\frac{P}{N} )=4[/tex]
Using the quotient rule of logs we can write:
log(P) - log(N) = 7
or
log(P) - 7 = log(N) (Equation 2)
Comparing equation 1 and 2, we can write:
log(M) - 4 = log(P) - 7
-4 + 7 = log(P) - log(M)
log(P) - log(M) = 3
[tex]log(\frac{P}{M} )=3[/tex]
Converting the log to exponential form we get:
[tex]\frac{P}{M}=10^{3}\\\\\frac{P}{M}=1000\\\\P=1000M[/tex]
Thus, option C gives the correct answer.
Final answer:
The relationship between M and P is that P is 1000 times greater than M; hence, the correct option is P = 1000M.
Explanation:
Given the two equations log(M/N) = 4 and log(P/N) = 7, we need to find the relationship between M and P.
To understand this relationship, we use the property of logarithms that equates to a multiplication by 10 for each unity increase in logarithmic value.
From the first equation, M/N = 10⁴, and from the second equation, P/N = 10⁷. Simplifying these, M = 10⁴ N and P = 10⁷ N.
To find the relationship between M and P, we can divide the equation for P by the equation for M:
P/M = (10⁷ N) / (10⁴ N) = 10³ = 1000.
Therefore, P is 1000 times M, which means P = 1000M
Please help me with this question.. { 8th Grade Math} I don't need an explanation just the answers.
Answer:
45 degrees
2 units
Step-by-step explanation:
A rotation is an Isometry so therefore the 45-45-90 Triangle is the exact same size and shape after the rotation.
Reduce to simplest form 3/2+(-6/5)
Answer:
[tex] \frac{3}{10} [/tex]
Step-by-step explanation:
First we need to find a common denominator for the fractions.
[tex] \frac{3}{2} + \frac{ - 6}{5} \: is \: to \: \frac{15}{10} + \frac{ - 12}{10} [/tex]
Now we just need to work out the result by adding the numerators.
[tex] \frac{15}{10} + \frac{ - 12}{10} = \frac{3}{10} [/tex]
find the value of x -3x - 0.2 = 4.9
Answer:
-2 11⁄20 = -2.55
Step-by-step explanation:
Combine like-terms to get -2x - 0.2 = 4.9. So, straight off the bat, we know that -2x has to equal 5.1 [move 0.2 to the right side of the equivalence symbol]. Then you would simply divide by -2 to get the above answer.
I am joyous to assist you anytime.
Ying Ying wants to buy some petunias.
The table compares the number of petunias Ying Ying could buy and the money that would remain in her wallet (in dollars).
What is the price of one petunia?
Answer: $0.25
Step-by-step explanation:
Let x be the total money was in her wallet and m be the cost of each petunia,
From the given table , the money left in wallet after purchasing 2 petunia =$6.50
Then we have the following equation :-
[tex]6.50=x-2m-----(1)[/tex]
Also, the money left in wallet after purchasing 8 petunia =$5
Then, we have
[tex]5=x-8m---------(2)[/tex]
Subtracting (2) from (1) , we get
[tex]6.50-5=-2m-(8m)\\\\\Rightarrow\ -2m+8m=1.50\\\\\Rightarrow\ 6m=1.50\\\\\Rightarrow\ m=\dfrac{1.50}{6}=0.25[/tex]
Hence, the price of one petunia = $0.25
Answer:
$.25
Step-by-step explanation:
doris tiene en su cartera billetes de $10 y de $20 . si en total tiene 25 billetes y $330 ¿cuantos billetes tiene de cada tipo?
Answer:
17 $10s and 8 $20s
Step-by-step explanation:
Find the value of X in the quadrilateral. (Picture)
Answer:
B
Hope this Helps! Have A Nice Day!!
Answer:
b
Step-by-step explanation:
How many ways can a president and Vice President be selected from a class of 12?
A. 23
B. 72
C. 132
D.1,320
for president, we have 12 possible options
12_
Once we’ve decided on a president we only have 11 possible people to choose from for vice president
12_11
multiplying these options together gives us:
12•11= 132
So the answer is C.132
The correct answer is C 132
Use the distributive property to remove the parentheses.
-5(6y - u - 2)
Answer:
5u - 30y + 10
Step-by-step explanation:
The area of a square is 1 square foot. What is the length of each side of the square? a. 1 ft. b. 2 ft. c. 3 ft. d. 4 ft.
Answer:
A. 1ft
Step-by-step explanation:
1 x 1 = 1 squared
So 1 foot x 1 foot = 1 square foot
Answer:
a. 1 ft
Step-by-step explanation:
The area of a square is found by using the formula
A = s^2 where s is the side length of the square
We know the area is 1 ft^2
1 = s^2
Take the square root of each side
sqrt(1) = sqrt(s^2)
1 = s
The side length is 1 ft