Answer:
\( y = 8 \: \: \: x = - 10\)
Step-by-step explanation:
\(4( - 6x - 9y = - 12) \\ 3(8x + 9y = - 8) \\ \: \: \: \: \: \: \\ - 24x - 36y = - 48 \\ 24x + 27y = - 24 \\ \\ - 9y = - 72 \\ y = 8 \\ \\ \\ \\ \\ - 6x - 9y= - 12 \\ - 6x - 72 = - 12 \\ - 6x = - 12 + 72 \\ - 6x = 60 \\ x = - 10\)
AK and CG intersect at point M in plane T
Select the graph of a line that is perpendicular to the line y=−3x+2 and has a y-intercept of -6.
The linear equation we want is:
y = (1/3)*x - 6
And the graph of that line can be seen at the end of the answer.
How to find the linear equation?A general linear equation between two variables x and y is written in the slope-intercept form as:
y = m*x + b
Where m is the slope and b is the y-intercept.
Here we know that the y-intercept is -6, then we can directly replace that to get:
y = m*x - 6
To find the value of m we use the fact that this line is perpendicular to:
y = -3x + 2
And two lines are perpendicular if the product between their slopes is -1, then:
m*(-3) = -1
m = 1/3
The linear equation is:
y = (1/3)*x - 6
The graph of the linear equation below.
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The figure to the right shows a square floor plan with a smaller square area that will accommodate a combination fountain and pool. The floor with the fountain-pool area removed has an area of 432 square meters and a perimeter of 90 meters. Find the dimensions of the floor and the dimensions of the square that will accommodate the fountain and pool
Considering the area and the perimeter of a square, it is found that:
Each length of the large square floor is of 21 meters, and each length of the small square floor is of 3 meters.
What are the area and the perimeter of a square?Supposing a square of side length s, the area and the perimeter are given as follows:
Area: A = s².Perimeter: P = 4s.The area of the figure is given by the subtraction of the area of the large square, of side length x, by the area of the small square, of side length y, hence:
A = x² - y²
x² - y² = 432.
The perimeter of the figure is the perimeter of the square of side length s added to two edges of the smaller square of side length s, hence:
P = 4x + 2y
4x + 2y = 90.
Then the system of equations to find the dimensions is given as follows:
x² - y² = 432.4x + 2y = 90.The solution of this system is given by:
x = 21 m (each length of the large square floor).y = 3 m (each length of the small square floor).Missing informationThe problem is completed by the image given at the end of the answer.
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Find the volume of a right circular cone that has a height of 3.9 in and a base with a radius of 14.3 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
\(volume = \frac{1}{3} \pi {r}^{2} h \\ = \frac{1}{3} \times 3.14 \times {(14.3)}^{2} \times 3.9 \\ = 834.73 \: cubic \: in\)
Answer:835.2
Step-by-step explanation:
a. Find the ratio of the number of nonfiction book to the number of fiction books give your answer in fraction form. Give your answer in fraction form
b. How many times the number of nonfiction books is the number of fiction books? Give your answer in fraction form.
c. Suppose the number fiction books is 2/7 times the number of nonfiction books what would be the ratio of the number of nonfiction books to the number of TOTAL number of books give your answer in fraction form.
The ratio of nonfiction to fiction books is 49 : 2.
What are ratio and proportion?In its most basic form, a ratio is a comparison between two comparable quantities.
There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.
If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.
Given, The number of fiction books is 2/7 times the number of nonfiction books.
So, If we have 7 nonfiction books then we have 2/7 fiction books.
Therefore, The ratio Nonfiction : Fiction = 7 : 2/7.
Nonfiction : Fiction = 49 : 2.
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Please help! How can this set be expressed using inequalities?
The set is expressed using inequalities; \(0 < x\leq 3\), option D is correct.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
A collection of inequalities for which we consider a common solution for all inequalities is called a system of inequalities.
The set be expressed using inequalities are;
\(0 < x\leq 3\).
Thus, option D is correct.
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Construct a truth table for each of these compound propositions
a) p → ⇁p
b) p ↔ ⇁p
c) p ⊕ (p V q) d) (p ∧ q) → (p V q) e) (p → ⇁p) ↔ (p ↔ q) f) (p ↔ q) ⊕ (p ↔ ⇁q)
After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.
A truth table is a overview that projects the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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By what number should you multiply the 1st equation to cancel the x's using the elimination method?
- 3x – 2y = 2
9x + 3y = 24
The answers are
6
-9
-3
3
Please help ion know wich one and I don’t want to fail the final week
Answer:
-3
Step-by-step explanation:
1) (20 pts) Let T be the Turing machine defined by the following 5-tuples: (So, 0, So, 1, R), (So, 1, $1, 0, R), (S1, 1, $2, 1, R), (S1, B, So, 0, R). For the following tape, determine the intermediate tapes, states, and head positions, and final tape, state, and head position when Thalts. Assume T begins in the initial position. state SO BB0001B0BB
When the Turing machine T halts, the final tape is S0B0000$2B0BB, the final state is SO, and the final head position is on the second $ symbol.
The Turing machine defined by the given 5-tuples is denoted as T, where T = (Q, Σ, Γ, δ, q0, qA, qR). Here, Q represents the set of states, Σ represents the set of input symbols, Γ represents the set of tape symbols, δ represents the transition function, q0 represents the start state, qA represents the accept state, and qR represents the reject state.
To determine the intermediate tapes, states, and head positions, as well as the final tape, state, and head position when T halts, we assume T starts in the initial position.
The initial tape is as follows:
SOBB0001B0BB
The initial state is q0, and the head is initially positioned at the first symbol (leftmost).
Using the transition function, we can evaluate the subsequent steps:
δ(SO, B) = (SO, 0, SO, 1, R)
Here, the current state is SO, and the current tape symbol is B. According to the transition function, we write SO in the current state, 0 in the current tape symbol, SO in the next state, 1 in the tape cell being scanned, and move the head to the right. The new tape becomes:
S0BB0001B0BB
δ(SO, 0) = (SO, 1, $1, 0, R)
The current state is SO, and the current tape symbol is 0. Applying the transition function, we write SO in the current state, 1 in the current tape symbol, $1 in the next tape cell, and move the head to the right. The new tape becomes:
S01B0001B0BB
δ(S1, 1) = (S1, $2, $1, 1, R)
The current state is S1, and the current tape symbol is 1. Applying the transition function, we write S1 in the current state, $2 in the current tape symbol, $1 in the next tape cell, and move the head to the right. The new tape becomes:
S01B000$2B0BB
δ(S1, B) = (SO, 0, SO, 0, R)
Since the current state is S1 and the current tape symbol is B, the transition function dictates that we write SO in the current state, 0 in the current tape symbol, SO in the next state, 0 in the next tape cell, and move the head to the right. The tape remains unchanged:
S01B000$2B0BB
δ(SO, 0) = (SO, 1, $1, 0, R)
The current state is SO, and the current tape symbol is 0. Applying the transition function, we write SO in the current state, 1 in the current tape symbol, $1 in the next tape cell, and move the head to the right. The new tape becomes:
S011000$2B0BB
δ(SO, 1) = (SO, 0, SO, 0, R)
The current state is SO, and the current tape symbol is 1. According to the transition function, we write SO in the current state, 0 in the current tape symbol, SO in the next state, 0 in the next tape cell, and move the head to the right. The new tape becomes:
S010000$2B0BB
δ(SO, 0) = (SO, B, SO, B, R)
Since the current state is SO and the current tape symbol is 0, the transition function specifies that we write SO in the current state, B in the current tape symbol, SO in the next state, B in the tape cell being scanned, and move the head to the right. The tape remains unchanged:
S0B0000$2B0BB
As there is no transition function defined for the current state SO and the current tape symbol B, the Turing machine T halts.
Therefore, when T halts:
The final tape is S0B0000$2B0BB.
The final state is SO.
The final head position is on the second $ symbol.
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a newsletter publisher believes that 78% of their readers own a rolls royce. is there sufficient evidence at the 0.02 level to refute the publisher's claim? state the null and alternative hypotheses for the above scenario.
There is not enough information provided to determine if there is sufficient evidence at the 0.02 level to refute the publisher's claim. The null hypothesis is that proportion of readers owning a Rolls Royce is equal to 0.78 and alternative hypothesis is that proportion of readers owning a Rolls Royce is not equal to 0.78.
To determine if there is sufficient evidence at the 0.02 level to refute the newsletter publisher's claim that 78% of their readers own a Rolls Royce, we need to conduct a hypothesis test. Here are the null and alternative hypotheses for this scenario:
Null Hypothesis (H0): The proportion of readers who own a Rolls Royce is equal to 0.78 (P = 0.78)
Alternative Hypothesis (H1): The proportion of readers who own a Rolls Royce is not equal to 0.78 (P ≠ 0.78)
To test these hypotheses, follow these steps:
1. Collect a random sample of readers and record the number of Rolls Royce owners in the sample.
2. Calculate the sample proportion (p-hat) of Rolls Royce owners.
3. Calculate the test statistic using the formula: z = (p-hat - P) / sqrt(P * (1-P) / n), where P is the claimed proportion (0.78) and n is the sample size.
4. Determine the critical value for a two-tailed test at the 0.02 significance level (α = 0.02), which is approximately ±2.576 (from a z-table or calculator).
5. Compare the test statistic (z) to the critical value. If the test statistic is greater than or equal to the critical value or less than or equal to the negative critical value, reject the null hypothesis in favor of the alternative hypothesis. If not, fail to reject the null hypothesis.
Based on the results, you can determine if there is sufficient evidence to refute the publisher's claim at the 0.02 significance level. However, just based on the given information, there is not enough information to determine if there is sufficient evidence at the 0.02 level to refute the publisher's claim. We need the sample size.
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I NEED AN ANSWER ASAP PLEASE
Step-by-step explanation:
the correct answer is option a 6a-7
one leg of a right triangle is 6 inches longer than the other leg, and the hypotenuse is 30 inches. find the lengths of the legs of the triangle.
one leg of a right triangle is 6 inches longer than the other leg, and the hypotenuse is 30 inches. Thus,
The lengths of the legs of the triangle are 18 inches,24 inches and 30 inches.
What is triangle?Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Given that,
one leg of a right triangle is 6 inches longer than the other leg.
hypotenuse is 30 inches.
Let assume, the other leg be x
It is given that, one leg of a right triangle is 6 inches longer than the other leg. So, One leg = x + 6
Since it is a right angled triangle,
h² = p² + b²
Where, h = hypotenuse
p = perpendicular
B = Base
So, (30)² = (x+6)² + x²
or, x = -24, 18
As, the length of side cannot be negative so x becomes 18.
Thus, x + 6 = 18 + 6 = 24 inches
Hypotenuse = 30 inches
Hence, the lengths of the legs of the triangle are 18 inches, 24 inches and 30 inches.
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express x^2-8x+20 in the form (x-a)^2+a where a is an integer
Answer:
(x-4)²+4
Step-by-step explanation:
Answer:
\((x-4)^2+4\)
Step-by-step explanation:
\(x^2 - 8x + 20\\**********************************\\\frac{8}{2} =( 4 )^2 = 16 \\\\20 - 16 = 4\\**********************************\\x^2 - 8x + 16 + 4\\(x-4)^2+4\)
Mario writes the equation (x+y)2=z2+4(12xy)(x+y)2=z2+4(12xy) to begin a proof of the Pythagorean theorem.
Use the drop-down menus to explain why this is a true equation.
Answer:
Step-by-step explanation:
( x + y ^)2 finds the area of the outer square by squaring its side length.
z² + 4( 1/2xy ) finds the area of the outer square by adding the area of the inner square and the four triangles.
Answer:
1) (x+y)^2
2) z^2+4(1/2xy)
Step-by-step explanation:
( x + y )^2 finds the area of the outer square by squaring its side length.
z² + 4( 1/2xy ) finds the area of the outer square by adding the area of the inner square and the four triangles.
There are 25 students in Ms. Jackson's fifth-grade class. The students want to go on a field trip to a museum. The cost of admission to the museum for the 25 students is $625. The cost of the bus is $250.
The students plan to sell raffle tickets to pay for the trip. Each raffle ticket is sold for $5. How many tickets will each student in the class have to sell?
Answer:
175 tickets
Step-by-step explanation:
The total cost is 875
y = mx
The y is the total cost. The m is the cost of a ticket and x is the number of tickets that need to be sold
875 = 5x Divide both sides by 5
175 = x
Helping in the name of Jesus.
Answer:7 tickets
because 625+250 is 875 ..875/25=35
each ticket is $5 and 35/5 is 7
19. a television set is on sale for 15% off the original price. if the sale is $340, what was the original price of the televisions set?
Using the percentage method, we know that the original price of the TV set was $400.
What is the percentage?Percentages are just fractions with a denominator of 100.
To show that a number is a percentage, we place the percent sign (%) next to it.
For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).
So, we know that the percentage is always out of 100.
Then we automatically know that:
100% - 15% = 85%
We know:
85% = $340
15% = ?
Now, calculate the reduced price as follows:
85/340 = 15/x
85x = 15(340)
85x = 5,100
x = 5100/85
x = $60
Original price of the TV set:
Sold cost + Reduced cost
$340 + $60
$400
Therefore, using the percentage method, we know that the original price of the TV set was $400.
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(1 point) a card is drawn from a standard deck of 52 cards, the value noted, and the card replaced. this is repeated 8 times. what is the probability that: a) exactly 5 of the cards are diamonds? b) at least two of the cards are diamonds? c) at most 5 of the cards are diamonds?
a) The probability of drawing exactly 5 diamonds from a standard deck of 52 cards is 0.1425
The probability of drawing exactly 5 diamonds from a standard deck of 52 cards is
P(exactly 5 diamonds) =\((13/52) * (12/51) * (11/50) * (10/49) * (9/48) * (38/47) * (37/46) * (36/45)\)
= 0.1425
b) The probability of drawing at least two diamonds from a standard deck of 52 cards is:
P(at least 2 diamonds) = 1 - P(0 diamonds) - P(1 diamond)
=\(1 - (39/52) * (38/51) - (13/52) * (39/51)\)
= 0.9133
c) The probability of drawing at most 5 diamonds from a standard deck of 52 cards is:
P(at most 5 diamonds) = P(0 diamonds) + P(1 diamond) + P(2 diamonds) + P(3 diamonds) + P(4 diamonds) + P(5 diamonds)
=\((39/52) * (38/51) + (13/52) * (39/51) + (13/52) * (12/51) * (38/50) + (13/52) * (12/51) * (11/50) * (37/49) + (13/52) * (12/51) * (11/50) * (10/49) * (36/48) + (13/52) * (12/51) * (11/50) * (10/49) * (9/48) * (35/47)\)
= 0.8692
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b) If the joint probability distribution of three discrete random variables X, Y, and Z is given by, f(x, y, z)=. (x+y)z 63 for x = 1,2; y=1,2,3; z = 1,2 find P(X=2, Y + Z ≤3).
The probability P(X=2, Y+Z ≤ 3) is 13. Random variables are variables in probability theory that represent the outcomes of a random experiment or event.
To find the probability P(X=2, Y+Z ≤ 3), we need to sum up the joint probabilities of all possible combinations of X=2, Y, and Z that satisfy the condition Y+Z ≤ 3.
Step 1: List all the possible combinations of X=2, Y, and Z that satisfy Y+Z ≤ 3:
X=2, Y=1, Z=1
X=2, Y=1, Z=2
X=2, Y=2, Z=1
Step 2: Calculate the joint probability for each combination:
For X=2, Y=1, Z=1:
f(2, 1, 1) = (2+1) * 1 = 3
For X=2, Y=1, Z=2:
f(2, 1, 2) = (2+1) * 2 = 6
For X=2, Y=2, Z=1:
f(2, 2, 1) = (2+2) * 1 = 4
Step 3: Sum up the joint probabilities:
P(X=2, Y+Z ≤ 3) = f(2, 1, 1) + f(2, 1, 2) + f(2, 2, 1) = 3 + 6 + 4 = 13
They assign numerical values to the possible outcomes of an experiment, allowing us to analyze and quantify the probabilities associated with different outcomes.
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right triangle $abc$ has one leg of length 6 cm, one leg of length 8 cm and a right angle at $a$. a square has one side on the hypotenuse of triangle $abc$ and a vertex on each of the two legs of triangle $abc$. what is the length of one side of the square, in cm? express your answer as a common fraction.right triangle $abc$ has one leg of length 6 cm, one leg of length 8 cm and a right angle at $a$. a square has one side on the hypotenuse of triangle $abc$ and a vertex on each of the two legs of triangle $abc$. what is the length of one side of the square, in cm? express your answer as a common fraction.
The length of one side of the square is 24/7 cm.
Let the side length of the square be x.
Since the square has one side on the hypotenuse of triangle ABC and a vertex on each of the two legs, we can form two smaller right triangles within the larger triangle ABC.
Label the vertices of the square touching legs AB and AC as D and E, respectively.
Triangle ADE is similar to triangle ABC by AA similarity (both have a right angle and angle A is common).
Set up a proportion using the side lengths:
AD/AB = DE/AC, or (6-x)/6 = x/8.
Cross-multiply to find 8(6-x) = 6x.
Simplify to 48 - 8x = 6x.
Add 8x to both sides to get 48 = 14x.
Divide by 14 to find x = 48/14, which simplifies to x = 24/7.
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7. Find the area of H
8. Find the radius of H
Answer:
7. 45
8. 78
Step-by-step explanation:
Quetlon 21 of 28Which of the following represents the ratio of the hypotenuse to the short legfor the triangle shown below?30°60°A. 2:1B. 1: 5C. 3:1D. 1:2
In order to determine the ratio of the hypotenuse to the short leg, use the sine of angle 30°:
sin 30° = opposite side / hypotenuse
Take intop account that sin30° is jsut the same the required ratio.
Moreover, consider that sin 30° = 1/2, which is the same that:
opposite side / hypotenuse = 1/2
or
hypotenuse / opposite
I need the answer if you know write with explination if you don't know don't answer
Answer:
ABD ≅ ACD and PQS ≅ PRS
Step-by-step explanation:
For ABD ≅ ACD;
AB = AC = 3.5
BD = CD = 2.5
AD ≅ AD by reflexive
Since all 3 sides are congruent, SSS can be used
For PQS ≅ PRS
PQ≅PR by given
QS≅RS by given
PS≅PS by reflexive property
Since all 3 sides are congruent, SSS can be used and they are congruent
Part A
The art club had an election to select a president.
75% of the 60 members of the club voted in the election,
How many members voted?
Answer:
members.
Part B.
How many members did not vote?
Answer:
no of members who voted=
75/100x60=45members
no of members who did not vote=
60-45=15 members
In a class of students, the following data table summarizes how many students have a
brother or a sister. What is the probability that a student chosen randomly from the
class does not have a sister?
Has a brother Does not have a brother
Has a sister
3
12
Does not have a sister
2.
Answer:
Step-by-step explanation:
First we need to calculate how many total students there are. Once we have the total we have to divide the number in the category that we want by the total number of students to calculate the probability of randomly getting a student in that category.
Total Students = 3 + 12 + 2 + 7 = 24 students
Probabilities:
does not have a sister = \(\frac{2 + 7}{24}\) = 0.375 or 37.5% (multiply decimal by 100 to get percentage.
Has a brother = \(\frac{3 + 2}{24}\) = 0.208 or 20.8%
Does not have a brother = \(\frac{12 + 7}{24}\) = 0.7916 or 79.2%
Has a sister = \(\frac{3 + 12}{24}\) = 0.625 or 62.5%
What is the solution to the trigonometric inequality 2-3csc(x) > 8 over the interval radians?
\(2 - 3csc(x) > 8 \\ 2 - \frac{3}{sin(x)} > 8 \\ - 6 > \frac{3}{sin(x)} \\ - 2 > \frac{1}{sin(x)} \\ \frac{ - 1}{2} < sin(x) \: \: or \: \: \: sin(x) > \frac{ - 1}{2} \\ \\ \)
\(sin( \frac{ - \pi}{6} ) = \frac{ - 1}{2} \)
\(x \: in \: \: [0, \frac{7\pi}{6}[U] \frac{11 \pi }{6} ,2\pi] + 2k\pi\)
Answer:
D. pi<x<7pi/6 and 11pi/6<x<2
Step-by-step explanation:
Took the test and this is the correct answer
0.5 recurring as a fraction
0.5 = 5/10 = 1/2
The answer is 1/2
Which is the solution to the system of equations?
4x + 2y = -1
3x + 4y = 3
A. (0, -1)
B. (8,0)
C.(1, -7/8)
D. (-1, 3/2)
Answer:
D. (-1, 3/2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Coordinates (x, y)Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define System
4x + 2y = -1
3x + 4y = 3
Step 2: Rewrite System
4x + 2y = -1
[Multiplication Property of Equality] Multiply -2 on both sides: -2(4x + 2y) = 2[Distributive Property] Distribute -2 on both sides: -8x - 4y = 2Step 3: Redefine Systems
-8x - 4y = 2
3x + 4y = 3
Step 4: Solve for x
Combine equations: -5x = 5[Division Property of Equality] Divide -5 on both sides: x = -1Step 5: Solve for y
Substitute in x [Original Equation]: 3(-1) + 4y = 3Multiply: -3 + 4y = 3[Addition Property of Equality] Add 3 on both sides: 4y = 6[Division Property of Equality] Divide 4 on both sides: y = 3/2How many people get scores from 0 to 100 on the stanford-binet and wechsler iq tests?
50% of people get scores from 0 to 100 on the Stanford-Binet and Wechsler IQ tests.
Both Stanford -Binet and Wechsler IQ tests are being used to calculate IQ of people. Stanford- Binet calculates IQ by measuring Verbal and Non Verbal skills. Wechsler calculates IQ by measuring Verbal and performance scales. The principle to measure IQ is (Mental age/ Chronicle Age)100. If IQ of a person is more than 130 then he is considered a Gifted person. If IQ of a person is less than are equals to 110 then he is considered an Average IQ person.
According to archive information On the Stanford-Binet and Wechsler IQ tests 50% of people get scores from 0 to 100.
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Kevin bought a music CD in California which had a price of $15.00. However, he paid $16.20 for the music CD. What was the percent of tax in California?
Answer:
18%
Step-by-step explanation:
15.00 divided by 100 = .15
.15 x 1.20 for the tax = .18
therefore 18%
Answer:
The tax increase is 8%
Step-by-step explanation:
16.20 - 15.00 = 1.2
1.2 / 15.00 = 0.08
0.08 x 100 = 8%
Have a wonderful day!
(Sorry if its incorrect.)
please help 30 points and brainliest
Answer:
f =5 (8/5)
Step-by-step explanation:
thats the answer