Step-by-step explanation:
x<16-7x<11.....................
What is the value of aaa when we rewrite 6^{x}6 x 6, start superscript, x, end superscript as ax4 ?
The equation can be rewritten as: [tex]ax^4 = (log(6))(2^4)[/tex]
Therefore, [tex]a = log(6) \ and\ x=2[/tex]
What is logarithm?A logarithm is a mathematical function that describes the relationship between a number and its exponent. It is the inverse operation of exponentiation. Logarithms are typically written as log base b, where b is the base of the logarithm and is a positive number.
The logarithm of a number x to base b is denoted as [tex]logb(x)[/tex] and it is the exponent to which we need to raise the base b in order to get the number x.
For example, if we are given [tex]log10(100) = 2[/tex], this means that [tex]10^2 = 100[/tex].
The equation [tex]6^x * 6 * 6[/tex] can be rewritten as [tex]6^x * 6^2[/tex].
To convert 6^x to ax form, we need to take the logarithm of both sides of the equation:
[tex]log(6^x) = log(6^2)[/tex]
And we can simplify the equation as:
[tex]xlog(6) = 2log(6)[/tex]
So, the value of a is log(6) and the value of x is 2.
Therefore, the equation can be rewritten as:
[tex]ax^4 = (log(6))(2^4)[/tex]
Therefore, [tex]a = log(6)\ and\ x=2[/tex]
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The scatter plot shows a hikers elevation above sea level overtime. The equation of the trend line is shown y equals 8.77x plus 686. To the nearest whole number predicted hikers elevation will be at 145 minutes
The predicted elevation of hikers at 145 minutes, based on the trend line equation, y = 8.77x + 686 is 1,958.
What is a trend line equation?A trend line equation is the equation of a linear relationship, represented as y = mx + b.
In this linear equation, y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.
Equation:y = 8.77x + 686, where x = 145 minutes
Therefore,
y = 8.77(145) + 686
y = 1,271.65 + 686
y = 1,957.65
y = 1,958
Thus, after 145 minutes of hiking, hikers' elevation will be 1,958 units.
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One angle of a triangle measures 45°. The other two angles are in a ratio of 7:20. What are the measures of those two angles?
Answer:
35° and 100°
Step-by-step explanation:
The total angle of a triangle = 180°
The total angle of two angles = 180° - 45° = 135°
One part of the ratio = 135° : (20 + 7) = 5°
The smaller angle = 5° x 7 = 35°
The bigger angle = 5° x 20 = 100°
Answer:
35° and 100°
Step-by-step explanation:
the sum of the 3 angles in a triangle is 180°
the ratio of 2 angles is 7 : 20 = 7x : 20x ( x is a multiplier )
equate the sum to the 3 angles to 180 and solve for x
45 + 7x + 20x = 180
45 + 27x = 180 ( subtract 45 from both sides )
27x = 135 ( divide both sides by 27 )
x = 5
Then
7x = 7 × 5 = 35
20x = 20 × 5 = 100
the measure of the 2 angles is 35° and 100°
Explain if the ordered pairs represent a function or not.
(1,2)(1,3)(2,4)(3,6)(0,0)(-1,4)
Which is 536,900 in scientific notation
Answer:
5.369 x 105
Step-by-step explanation:
Answer:
5.369 x 105
Cause in scientific notation, the decimal point is always after the first number from the left.
1/4 gallon of paint costs $8. 99. What is the unit price of one gallon of paint?
The unit price of one gallon of paint is going to be $35.96.
We can use the unitary method to solve this problem. The unitary method is a technique used for solving a problem by first finding the value of a single unit, and finding the necessary value by multiplying the single unit value.
In this question, it is given that 1/4 gallon of paint costs $8.99 so for 1 gallon we will have to multiply both the paint amount and the money which buys it to 4 which will conclude that 1 gallon costs $8.99 × 4 is equal to $35.96. So, 1 gallon of paint will cost $35.96.
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Name the property that i hown by each equation. A. 6a 4 = 4 6a
B. 30 60 = 15(2 4)
C. 3(8x 4) = 3(4 8x)
D. 4(6a) = (4 · 6)a
A. Commutative property of addition
B. Distributive property
C. Commutative property of addition
D. Associative property of multiplication
Commutative property of addition: The commutative property of addition says that a change in the order of the numbers being added does not affect the sum. We define a commutative property of addition as adding the numbers in any order that will give the same answer.a + b =b + a
Here, a and b is whole numbers, integers or decimals, or even fractions.
Distributive property: According to this property, multiplying the summation of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. In other words, according to the distributive property, an expression of form A (B + C) can be solved as A (B+ C) = AB + AC.Associative property of multiplication: The associative property of multiplication is defined as that while multiplying three numbers, regardless of the way the numbers are grouped, the end result will always be the same.Read more about the distributive property:
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The complete question is:
Name the property that is shown by each equation.
A. 6a + 4 = 4 + 6a
B. 30 + 60 = 15(2 + 4)
C. 3(8x + 4) = 3(4 + 8x)
D. 4(6a) = (4 · 6)a
Match each power of a power expression with its simplified expression.
(4-3)-3
(46)-3
(49)-9
(-49)²
↑
↑
1
418
49
(-4)18
40
need to know which one goes to which
Answer:
(4^6)^-3 = 1/4^18(4^0)^-9 = 4^0(4^-3)^-3 = 4^9(-4^9)^2= (-4)^18Step-by-step explanation:(4^6)^-3 = 1/4^18(4^6)^-3= 4^(6*-3)(4^6)^-3= 1/4^18(4^0)^-9 = 4^0(4^0)^-9 = 4^(0*-9)(4^0)^-9= 4^0(4^-3)^-3 = 4^9(4^-3)^-3= 4 ^ (-3*-3)(4^-3)^-3 = 4^(9)(-4^9)^2= (-4)^18(-4^9)^2= -4^(9*2)(-4^9)^2=(-4)^18
Step-by-step explanation:
Answer:
[tex](4^{-3})^{-3}=4^9[/tex]
[tex](4^6)^{-3}=\dfrac{1}{4^{18}}[/tex]
[tex](4^0)^{-9}=4^0[/tex]
[tex](-4^9)^2=(-4)^{18}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{3 cm}\underline{Exponent Rules}\\\\$(a^b)^c=a^{bc}$\\\\$a^{-n}=\dfrac{1}{a^n}$\\\end{minipage}}[/tex]
Apply the above exponent rules to simplify each expression.
[tex]\begin{aligned}\implies (4^{-3})^{-3}&=4^{-3 \times -3}\\&=4^9\end{aligned}[/tex]
[tex]\begin{aligned}\implies (4^6)^{-3}&=4^{6 \times -3}\\&=4^{-18}\\&=\dfrac{1}{4^{18}}\end{aligned}[/tex]
[tex]\begin{aligned}\implies (4^0)^{-9}&=4^{0 \times -9}\\&=4^0\end{aligned}[/tex]
[tex]\begin{aligned}\implies (-4^9)^2&=(-4)^{9 \times 2}\\&=(-4)^{18}\end{aligned}[/tex]
How do I solve for the fourth line
Answer:
y = -8/3x + 73/4
Step-by-step explanation:
A line perpendicular to the 3rd equation has a slope that is the negative inverse of the other line. It also has the same y-intercept (b) because it is forming a square.
Therefore, the equation of the 4th line is:
y = -8/3x + 73/4
Jason made a model stop sign for his model train
set. An actual stop sign measures 12 inches on
each side. Jason's model stop sign measures
1 inch on each side.
actual measures : model measures = 12 : 1 .
What is Ratio?In mathematics, a ratio shows how many times one number contains another. The comparison or simplified form of two quantities of the same kind is referred to as a ratio. This relation gives us how many times one quantity is equal to the other quantity. In simple words, the ratio is the number that can be used to express one quantity as a fraction of the other ones.
The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things. The sign used to denote a ratio is ‘:’.
A ratio can be written as a fraction, say 2/5. We happen to see various comparisons or say ratios in our daily life.
Given,
Actual sign measures 12 inches on each side
Jason's model sign measures 1 inch on each side.
Ration between actual to model sign measurement=
Measurement of actual sign / Measurement of model sign
= 12/1
Ratio = 12:1
Hence, the ratio between actual to model sign measurement is 12:1.
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Mason worked at the water park over the summer. He made $425 in June and $680 in July if he made twice as much money in august as he did june. What is the ratio of money earned in august to July
The ratio of money earned in August to July is 5/4.
Now, According to the question:
Let's know
What is Ratio?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
Mason worked at the water park over the summer. He made $425 in June and $680 in July.
And if he made twice as much money In August as he did in June.
That means, he made $850 in August.
Then, The ratio will be :
= August / June
= 850/680
= 5/4
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What is an unsolvable problem?
As a result, it may be shown that the answer to the algorithm problem at hand is a halting problem, which is indecidable and thus impossible to solve.
Algorithm : what is it ?No matter the circumstance, algorithms are fundamentally problem solvers of expression ; they exist to identify, resolve, and frequently automate of solution to a specific problem. Algorithms are frequently introduced in area introductory textbooks by characterizing them as "a series of steps to complete a problem."
Here,
one of the most common problems that hasn't been solved is the stopping problem. It asks the following question:
Does M come to a standstill when given the input w for any Turing machine with the parameters alphabet = a, b, and any string w over
It can be shown that the halting problem cannot be resolved since it is indecisive.
As a result, it may be shown that the answer to the algorithmic problem at hand is a halting problem, which is indecidable and thus impossible to solve.
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What is the y-intercept of 6x 3y =- 12?
The y-intercept of the equation 6x + 3y = -12 is -4.
Therefore the answer is -4.
The y-intercept of a linear equation is the point at which the line crosses the y-axis. In other words, it's the point at which x = 0.
To find the y-intercept of the equation 6x + 3y = -12, we can set x = 0 and solve for y.
Substituting x = 0 into the equation:
6(0) + 3y = -12
3y = -12
To find the y-intercept, we divide both sides by 3:
y = -4
So the y-intercept of the equation 6x + 3y = -12 is (0, -4). This means that when x = 0, y = -4 and the graph of this equation will cross the y-axis at the point (0, -4).
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What are the factors of the expression x² 4x 3?
The factors of the expression x² 4x 3 are (x + 3)(x − 3).
What is factor?Factor is a number that can be multiplied to produce another number. Factors are used to find the greatest common factor (GCF) and least common multiple (LCM) of two or more numbers. Factors are also used in equations to find solutions and in algebra to solve polynomials. Factors are also important in computing, since they are used to identify prime numbers and prime factorisation.
This is determined by using the factoring technique called factoring by grouping.
First, the expression is written in two groups: x2 and 4x 3. Then, each group must be factored. For the first group, the factors are x and x, since any number multiplied by itself results in the number itself. For the second group, the factors are 4 and 3, since 4 multiplied by 3 equals 12.
Next, the two factors of each group must be multiplied together. The product of x and 4 is 4x, and the product of x and 3 is 3x. The product of 4 and 3 is 12.
Finally, the two groups of factors are combined to form the final expression: (x + 3)(x − 3).
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The line of best fit for a data set is y=1. 1x+3. 4. Find the residual for each of the coordinate pairs, (x,y).
D. (1. 5,5. 05)
The residual values are -0.1, 3.8, 0.32, and 0 respectively for the given coordinate pairs.
A residual is a difference between the observed value (y) and the predicted value (y-hat) for a given x value. To find the residual for each coordinate pair (x,y), we need to substitute the x value into the equation for the line of best fit and calculate the difference between that value and the observed y value.
The equation for the line of best fit is y = 1.1x + 3.4
The residual for each coordinate pair (x,y) is given by -
Residual = Yactual - y
A. (5, 8.8) ; Yactual = 8.8
Residual = 8.8 - (1.1(5) + 3.4) = - 0.1
B. (2.5, 9.95) Yactual = 9.95
Residual = 9.95 - (1.1(2.5) + 3.4) = 3.8
C. (0, 3.72) Yactual = 3.72
Residual = 3.72 - (1.1(0) + 3.4) = 0.32
D. (1.5,5.05) Yactual =
Residual = 5.05 - (1.1(1.5) + 3.4) = 0
It's worth noting that residuals are used to measure how well the line of best fit represents the data set. The residuals should be as close to zero as possible, indicating that the line of best fit is a good representation of the data set.
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The complete question is -
The line of best fit for a data set is y=1.1x+3.4. Find the residual for each of the coordinate pairs, (x,y).
A. (5, 8.8)
B. (2.5, 9.95)
C. (0, 3.72)
D. (1.5,5.05)
7{-7+8[5-3(4+6)]-9(9-4)}
Answer:
-1764
Step-by-step explanation:
use BODMAS rule
⇒7{-7+8[5-3(4+6)]-9(9-4)}
solve round brackets
⇒7{-7+8[5-3(10)]-9()}
multiply 3 by 10 within the square bracket
⇒7{-7+8[5-30]-9(5)}
solve square bracket
⇒7{-7+8[-25]-9(5)}
move to curly brackets and multiply first
⇒{-7-200-45}
subtract
⇒7{-252}
multiply
⇒-1764 Answer
hope that helps...
Which equation has 3 as a solution set *?
The equation 3x - 9 = 0 has 3 as a solution out of all the given equations in the options.
Check the solution of equation 3x - 9 = 0
3x - 9 = 0
3x = 9
x = 3
Check the solution of equation 4x - 3 = 0
4x - 3 = 0
4x = 3
x = 3/4
Check the solution of equation 5x - 10 = 0
5x - 10 = 0
5x = 10
x = 10/5
x = 2
Check the solution of equation 7x - 49 = 0
7x - 49 = 0
7x = 49
x = 49/7
x = 7
Thus, only 3x - 9 = 0 satisfy the solution x = 3.
Hence, the correct option is A.
--The given question is incomplete, the complete question is
''Which equation has 3 as a solution set?
A. 3x - 9 = 0
B. 4x - 3 = 0
C. 5x - 10 = 0
D. 7x - 49 = 0''--
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Determine the prices for which quantity demanded is greater than quantity supplied.
The prices where the quantity demanded is greater than quantity supplied are :
$ 2$ 1$ 0When is quantity demanded greater than quantity supplied ?Quantity demanded refers to the amount of goods and services that people and businesses in an economy demand.
This amount of goods and services demanded will be more than the quantity supplied when the price of the good or service is less than the equilibrium price.
The equilibrium price here is $ 3 and so the prices less than $ 3 are $2, $1, and $ 0.
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A falcon was recorded travelling 100 metres in 0. 93 seconds.
What was its average speed
a in m/s to 3 significant figures
The average speed of the falcon to 3 significant figures will be 107.526 m/s
Distance travelled by falcon = 100 meters
Time taken by falcon to travel the distance = 0.93 seconds
As we have the formula for finding the average speed:
Average speed is a pace defined as a quantity divided by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t is used to compute average speed, where S is the average speed, d is total distance, and t is total time.
Average speed can be find by simply dividing the total distance covered by falcon by the total time taken by him to cover the distance.
So, the value of the average speed will be = (100 m/0.93 sec) =107.526 m/s
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The Measures of two sides of a triangle are 12 and 13. Use an inequality to express the range of the measure of the third side, m.
A. 1 < m < 15
B. 1 < m < 25
C. 12 < m < 25
D. 0 < m < 11
The required inequality expression for the third side is 1 < m < 25. The correct option is (B).
What is linear inequality?Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.
Unlike a linear equation it can have a range of values inside an interval.
The sides of the triangle are given as 12 and 13 units respectively.
As per the rule for sides of a triangle, the third side is always less than the sum and greater than the difference of two sides.
Then, the inequality can be written as,
13 - 12 < m < 13 + 12
⇒ 1 < m < 25
Hence, the measure of third side can be written in inequality as 1 < m < 25.
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Jack spends a total of $16.50 on one bag of popcorn and three drinks.
Jill spends a total of $29.75 for two bags of popcorn and five drinks.
Write a system of equations. Determine and state the price of a bag of popcorn and the price of a drink, to the nearest cent.
Answer:
Sure! Here's a system of equations we can set up to represent this situation:
Let x be the price of a bag of popcorn and y be the price of a drink.
Then we can set up the following system of equations:
x + 3y = 16.50 (equation for Jack's purchases)
2x + 5y = 29.75 (equation for Jill's purchases)
To solve this system of equations, we can use the substitution method.
First, we can solve for x in equation 1:
x = 16.50 - 3y
Then, we can substitute this expression for x into equation 2:
2(16.50 - 3y) + 5y = 29.75
Simplifying this equation, we get:
33 - 6y + 5y = 29.75
Combining like terms, we get:
33 - y = 29.75
Subtracting 29.75 from both sides, we get:
33 - 29.75 - y = -y
Simplifying, we get:
3.25 - y = 0
Subtracting 3.25 from both sides, we get:
-y = -3.25
Dividing both sides by -1, we get:
y = 3.25
So, the price of a drink is $3.25.
Now we can substitute this value for y back into equation 1 to solve for x:
x + 3(3.25) = 16.50
Simplifying, we get:
x + 9.75 = 16.50
Subtracting 9.75 from both sides, we get:
x = 6.75
So, the price of a bag of popcorn is $6.75.
To the nearest cent, the price of a bag of popcorn is $6.75 and the price of a drink is $3.25.
Step-by-step explanation:
what value of x would prove that the following triangle is a right angle? Answers x=7 x=2 x= 14 x= 10
Step-by-step explanation:
Pythagoras' TheoremFor Pythagoras' Theorem to be valid, the triangle must be a right-angled one.
The formula is:
c^2 = a^2 + b^2
Where c is the longest side. While a,b are the side lengths.
SolutionUsing the above formula and the measurements given in the question, we can find the value of x.
By Pythagoras' Theorem,
26^2 = (5x)^2 + (12x)^2
676 = 25x^2 + 144x^2
169x^2 = 676
x^2 = 676 ÷ 169
x^2 = 4
x = 2
The degrees of freedom for a contingency table with 10 rows and 11 columns is
O 100 O 110 O 21 O 90
Essentially, a contingency table with 10 rows and 11 columns has (D) 90 degrees of freedom.
What is a contingency table?A contingency table is a matrix-form table that shows how often different combinations of variables appear.
It's really popular in survey research, business intelligence, engineering, and scientific research. Basically, a contingency table with 10 rows and 11 columns has 90 degrees of freedom.
They are also sometimes known as two-way frequency tables and are used to show how often different combinations of variables occur.
A contingency table gives you an idea of how two variables relate to each other.
It displays one categorical variable along the rows and another categorical variable along the columns. It can help point out any interactions between them.
Therefore, essentially, a table with 10 rows and 11 columns has (D) 90 degrees of freedom.
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Complete question:
The degrees of freedom for a contingency table with 10 rows and 11 columns are:
A. 100
B. 110
C. 21
D. 90
The casino game of chuck-a-luck seems quite simple and that it would be a pretty good bet. In this game, three dice are rolled (usually inside a wire cage). You can bet a set amount, let's say $5, on a specific number 1-6. You win the amount of your bet for each appearance of your number on the dice. If the number does not appear, you lose your bet. For example, let's say you bet $5 on the number 3. If it appears on exactly one die, you win $5 (and keep your bet) with probability 75/216. If it appears on exactly two dice, you win $10 (and keep your bet) with probability 15/216. If it appears on all three dice, you win $15 (and keep your bet) with probability 1/216. If it appears on none of the dice, you lose your original $5 bet. Construct the probability distribution for chuck-a-luck and determine your expected winnings on a $5 bet.
The expected winnings on a $5 bet are -0.1157 dollars. This means that on average, you will lose about 11.57 cents for each $5 bet you make.
Therefore, the game is not a good bet, as you are expected to lose money in the long run.
What is the probability distribution?
A probability distribution is a mathematical function that describes the probability of different possible values of a variable.
The probability of winning on a $5 bet on a specific number in chuck-a-luck is determined by the number of ways that the number can appear on the three dice and the total number of possible outcomes.
If the number appears on exactly one die, there are 3 ways that this can happen out of a total of 6^3 = 216 possible outcomes, giving a probability of 3/216 or 1/72.
If the number appears on exactly two dice, there are 3 ways to choose the two dice on which it appears, and 3 ways to choose the third die, giving a total of 33 = 9 ways out of 216 possible outcomes, giving a probability of 9/216 or 1/24.
If the number appears on all three dice, there is only 1 way this can happen out of 216 possible outcomes, giving a probability of 1/216.
If it appears on none of the dice, there are (543) ways this can happen, giving a probability of (54*3)/216 = 20/216.
We can use this information to construct the probability distribution for chuck-a-luck:
x P(x)
-5 (losing the bet) 20/216
5 (winning the bet for one appearance) 1/72
10 (winning the bet for two appearances) 1/24
15 (winning the bet for three appearances) 1/216
To find the expected winnings on a $5 bet, we can multiply the value of each outcome by its corresponding probability, and sum the results:
E(X) = (-5)(20/216) + (5)(1/72) + (10)(1/24) + (15)(1/216)
E(X) = -5/43.2 + 5/72 + 5/12 + 15/216
E(X) = -0.1157
Hence, the expected winnings on a $5 bet are -0.1157 dollars. This means that on average, you will lose about 11.57 cents for each $5 bet you make.
Therefore, the game is not a good bet, as you are expected to lose money in the long run.
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A football team consists of 20 each freshmen and sophomores, 15 juniors, and 10 seniors. Four players are selected at random to serve as captains. Find the probability that
On solving the provided question, we can say that Probability ( At least one of the students is a senior) = 0.4632 approx
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
P(All four players are senior) = 0.00033 approx
P(There is one each: freshman, sophomore, junior and senior) = 0.0944 approx.
P(There are 2 sophomores and 2 freshman) = 0.0568 approx
P( At least one of the students is a senior) = 0.4632 approx
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carman has saved 80% of the money she needs to buy a new video game. if she saved$36 how much does the video game cost
Carman buy the video game in the cost of $45.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
Carman has saved 80% of the money she needs to buy a new video game.
And, she saved the cost $36.
Let total cost of the video game = x
So, We can formulate;
⇒ 80% of x = $36
⇒ 80/100 × x = 36
⇒ 8x = 360
⇒ x = $45
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A dumpster is shaped like a rectangular prism. It has a width of 8 feet, a height of 5 feet, and a volume of 880 cubic feet. What is the length of the dumpster
What is .15 written as a rational number
Answer:
it is a rational number already
Step-by-step explanation:
Graph the system on equation . Y-2x+5=0 and y+ 4x-1=0
The graph of the system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0 intersect at (0.667, - 3.667)
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, A system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0.
Let's write the terms in the order x, y therefore,
y - 2x + 5 = 0
- 2x + y = - 5.
2x - y = 5.
And
y + 4x + 1 = 0.
4x + y = - 1.
The graph of the system of equations is attached in the image.
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Makea is making smoothies. For every 4 cups of orange juice, she uses 3 tablespoons of yogurt. Which ratio of orange juice to yogurt is NOT equivalent to the ratio she wants to use in the recipe?
A-40:30
B-19:9
C-15:20
D-8:6
Answer: A ratio is a comparison of two or more values. To compare the ratios of orange juice to yogurt, we want to ensure that the proportion of orange juice to yogurt is the same in each ratio.
Option A is 40:30. To compare this ratio to the original ratio, we can convert the amounts in cups to tablespoons. 40 cups is equal to 320 tablespoons and 30 tablespoons of yogurt. The proportion of orange juice to yogurt is not the same as the original ratio since 320 is not equivalent to 3.
Option B is 19:9. To compare this ratio, we convert the amount in cups to tablespoons. 19 cups is equal to 152 tablespoons of orange juice and 9 tablespoons of yogurt. The proportion of orange juice to yogurt is not the same as the original ratio since 4 cups of orange juice is not equal to 19 cups.
Option C is 15:20. To compare this ratio, we convert the amount in cups to tablespoons. 15 cups is equal to 120 tablespoons of orange juice and 20 tablespoons of yogurt. The proportion of orange juice to yogurt is not the same as the original ratio since 4 cups of orange juice is not equal to 15 cups.
Option D is 8:6. To compare this ratio, we convert the amount in cups to tablespoons. 8 cups is equal to 64
Step-by-step explanation: