Representing Ratios that describes a ratio in the table
What is Representing Ratios?The most common way to write a ratio is as a fraction, 3/6. We could also write it using the word "to," as "3 to 6." Finally, we could write this ratio using a colon between the two numbers, 3:6. 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)A ratio can be represented in the form of a fraction using the ratio formula. The ratio formula for any two quantities say a and b is given as, a:b = a/b. Since a and b are individual amounts for two quantities, the total quantity combined is given as (a + b).To learn more about Representing Ratios refers to:
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3. Zoe is attempting to balance her checkbook. She had a beginning balance of $1, 235.46 at the beginning of the month. She
made a deposit in the amount of $83.49, then wrote check 1206 for $36.86. The next day she wrote check 1207 and check
1208 for $254.34. Zoe forgot to write the amount of check 1207 into her check register. Zoe's statement shows an ending
balance of $842.98. Find the amount of check 1207.
We can start by using algebra to represent the given information. Let x be the amount of check 1207.
What does a math equation mean?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
The beginning balance: 1,235.46
The deposit: + 83.49
Check 1206: - 36.86
Check 1207: - x
Check 1208: - 254.34
Ending balance: 842.98
We can then set up an equation to represent the balance after all the transactions are made:
1,235.46 + 83.49 - 36.86 - x - 254.34 = 842.98
Simplifying the equation:
1,235.46 + 83.49 - 36.86 - x - 254.34 = 842.98
1,235.46 + 46.63 - x = 1,087.32
x = 1,235.46 + 46.63 - 1,087.32
x = 194.77
So the amount of check 1207 is $194.77
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Carrie bought a pair of jeans for $55. The jeans were 24% off.
What was the discount?
How much did she pay for the jeans?
Answer:
Discount: $13.20
Final Price: $41.80
Step-by-step explanation:
Original price: $55
Percent discount: 24%
Amount of discount: 24% of $55 = 0.24 × $55 = $13.20
Final price = original price - amount of discount = $55 - $13.20
Actual final price = $41.80
Answer:
Discount: $13.20
Final Price: $41.80
Three ordered pairs that satisfy with y=1/2x+10 and three ordered pairs that don’t satisfy
Therefore , the solution of the given problem of ordered pair comes out to be (0, 10) , (1,10.5) and (2,11).
what are ordered pairs?Two independent variables that are put in a manner that implies a particular order are known as "ordered pairs." Inside an order pair, the primary and second components, respectively, stand in for the x and y coordinates. The ordered pair is shown using close parentheses in the sample that follows.
Here,
The solution is to insert an x and observe what ever the y is. triple-check that.
So, for instance, I may enter x = 0. Check at what the y represents.
Let me just get y on its own first, though.
=> y=1/2x+10
=> 2y = x + 20
=> y = (x+20)/2
let's substitute x = 0 now.
=> y = (0 + 20)/2 = 10
Consequently, we have a single pair that was ordered: (0, 10)
order pair for x = 1
=> y = (1+ 20)/2 = 10.5
=> (1,10.5)
Ordered pair for x = 2 and
=>y = (2+20) /2 = 11
=> (2,11)
Therefore , the solution of the given problem of ordered pairs comes out to be (0, 10) , (1,10.5) and (2,11).
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A quadratic curve cuts the y -axis at - 9 and x-axis at 1 and ‘t’ where ‘t’ < 0.
Its minimum point occurs
at x = - 1.
State the value of ‘t’ and find the equation of the curve.
The value of t is -9. The equation of the curve is y = x² + 8x -9.
What is a curve?
An abstract term used in mathematics to describe the path of a continuously moving point (see continuity). An equation is typically used to generate such a path. The term can also refer to a straight line or a series of linked line segments.
The given curve cuts y-axis at -9 and x-axis at 1 and ‘t’ where t < 0.
The equation of a quadratic curve is y = (x-a)(x-b) where a, b are x-intercepts.
Putting a = 1 and b = t in y = (x-a)(x-b):
y = (x-1)(x-t)
Since the y-intercept of the curve is -9. The curve passes through the point (0,-9).
Putting x = 0, y=-9:
-9 = (0-1)(0-t)
-9 = t
Now putting t = -9, in y = (x-1)(x-t):
y = (x-1)(x-(-9))
y = (x-1)(x+9)
y = x² - x+ 9x - 9
y = x² + 8x -9
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Ryde, a new ride-sharing app, determined that the average cost, in dollars,
3. 75 + 2x
per mile, x, will be represented by the function c(x) =. -. As the trip
gets longer in miles, x, what does the end behavior of the function tell you
about the situation?
х
The end behavior of the function c(x) = 3.75 + 2x tells us that as the distance of the trip increases or decreases, the cost of the ride increases or decreases at a constant rate of 2 dollars per mile.
The function c(x) = 3.75 + 2x represents the cost, in dollars, of a ride on Ryde as a function of the distance of the trip, in miles. The end behavior of a function refers to the behavior of the function as the input (in this case, the distance of the trip) approaches positive or negative infinity.
In this case, the end behavior of the function tells us about how the cost of the ride changes as the distance of the trip increases or decreases.
The function c(x) = 3.75 + 2x is linear with a positive slope of 2. This means that as the distance of the trip increases, the cost of the ride also increases at a constant rate of 2 dollars per mile. As x approaches positive infinity, the cost of the ride goes to positive infinity as well.
Similarly, as the distance of the trip decreases, the cost of the ride decreases at a constant rate of 2 dollars per mile. As x approaches negative infinity, the cost of the ride goes to negative infinity as well.
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what fraction (x) of your actual weight would a scale at the equator read if earth days were merely 2 hours long?
If earth days merely 2 hours long, which means the rotation period of the earth is 2 hours, your weight will become 1/144 of your actual weight.
The weight or gravitational force on a mass can also be considered as centripetal force.
The formula for the centripetal force is:
F = m v²/R
In this case,
m = your mass
v = tangential velocity or earth's rotation speed
R = earth's radius
Recall that speed = distance / time. In the problem, the distance is the circumference of the earth and the travelled time is the rotation period.
v = C/t
t₁ = 24 hours
t₂ = 2 hours
Since the units are the same, we do not need to convert the unit when comparing them.
Notice that the centripetal force is directly proportional to the square of rotation speed.
F ∝ v²
Hence,
F₁ : F₂ = v₁² : v₂²
But v is inversely proportional to rotation period. Hence,
F₁ : F₂ = t₂² : t₁²
F₁ / F₂ = (t₂ /t₁)²
F₁ / F₂ = (2 /24)²
F₁ / F₂ = (1 /12)²
F₁ / F₂ = 1/144
Hence, your weight will be 1/144 of your actual weight.
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a1 is equal to 3 and the third team a3 is equal to 192
The possible sequences are:
3,24, 192, 1536, 12288......
3,-24, 192, -1536, 12288 .......
What is a sequence?
an arrangement of two or more things in successive order. the sequential arrangement of two or more things The chronological order. a list of things or ideas that are related in some way. an action or event that follows another or others.
Given that, a₁ = 3 and a₃ = 192.
The sequence is increased rapidly. Thus it is geometric progress.
Assume that the common ratio of the geometic sequence is r.
The nth term of the sequence is [tex]a_n =a(r^{n-1})[/tex]
=[tex]3r^{n-1}[/tex] since a is the first term that is a = 3.
Putting n=3 in the sequnce:
a₃ = 3(r)²
Putting a₃ = 192 in the above equation:
192 = 3(r)²
Divide both sides by 3:
192/3 = r²
r² = 64
r = ±8
When r = 8:
The first five terms of the sequence are
a₁, a₁r¹, a₁r², a₁r³, a₁r⁴
= 3, 3×8¹, 3×8², 3×8³, 3×8⁴
= 3,24, 192, 1536, 12288
When r = -8:
The first five terms of the sequence are
a₁, a₁r¹, a₁r², a₁r³, a₁r⁴
= 3, 3×(-8)¹, 3×(-8)², 3×(-8)³, 3×(-8)⁴
= 3,-24, 192, -1536, 12288
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How do you find the domain and range without a graph?
To find the domain and range of a function without a graph is to use algebraic methods.
What is domain in function ?
The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.
One way to find the domain and range of a function without a graph is to use algebraic methods. For example, if the function is defined by an equation, you can solve for the variables to determine the domain and range. You can also use inequalities or interval notation to express the domain and range.
Another way to find the domain and range is to examine the function's definition and identify any restrictions on the input or output values. For example, if a function is defined in terms of a square root, the input values must be non-negative to avoid a complex output.
To find the domain and range of a function without a graph is to use algebraic methods.
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Thé graphique below have the same shape . What is the equation of the blue graph
The equation of the graph in blue mark is
C. g(x) = (x - 4)²What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects such as graphs.
Translation refers to a type of transformation that involve a linear movement.
Movements as seen in translation includes
leftrightupdownThe up and down movements are on the vertical direction controlled by the y coordinate. While the left and right movements are on the horizontal direction controlled by the x coordinate.
The translation in the graph is a movement 4 units to the right and this is represented as equation to be g(x) = (x - 4)²
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A stock person at Wal-Mart has decided that they would like to completely fill the ball pin in the toy section with one type of ball. The ball of the rock person decided to use has a radius of 16cm. What is the volume of each ball?
The volume of a sphere with a radius of 16cm is approximately 17157.28 cm^3
The volume of a sphere can be calculated using the formula
V = 4/3 * π * r^3, where V is the volume, π is approximately 3.14, and r is the radius of the sphere. In this case, the radius of the balls used by the stock person is 16cm. Therefore, we can substitute this value into the formula to find the volume of each ball.
V = 4/3 * π * r^3
V = 4/3 * 3.14 * (16cm)^3
V = 17157.28cm^3
So, the volume of each ball is approximately 17157.28cm^3.
It is important to keep in mind that the volume of a sphere is dependent on the radius of the sphere, so if the radius of the balls were different, the volume would also be different.
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write -62 7/10 as a decimal number
Answer: -62.7
Step-by-step explanation:
7/10 = 0.7
-62 7/10 = -62.7
Answer:62.7
Step-by-step explanation:
PACE is a parallelogram and m PAC=112 find m EPA
Answer:
m∠EPA = 68°
Step-by-step explanation:
Angle EPA is adjacent to angle PAC in parallelogram PACE.
As adjacent angles in a parallelogram sum to 180°:
⇒ m∠PAC + m∠EPA = 180°
⇒ 112° + m∠EPA = 180°
⇒ 112° + m∠EPA - 112° = 180° - 112°
⇒ m∠EPA = 68°
Therefore, the measure of angle EPA is 68°.
Complete the missing parts of the paragraph proof.
The parts in the proof is completed as follows
Slope of line DE = (c - c) / (a + b - b) = 0 / a = 0
Slope of line BC = (0 - 0) / (2a - 0) = 0 / 2a = 0
Therefore because slope of line DE = slope of line BC, DE || BC
What are parallel lines in math?The term parallel lines refers to lines in a plane that never cross each other, even when we stretch them.
The parallel lines are never in contact, hence their distance is always the same.
The slope of parallel lines are always equal.
In the proof the slope of the line DE and line BC is calculated as the values of zero was gotten
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If anyone can help me that would be amazing
Prime factorization of 96 is = 2 × 2 × 2 × 2 × 2 × 3.
What is the procedure for prime factorization?The prime factorization procedure is used to determine the prime factors of a given number, such as a composite number.
The only elements of these factors are the prime numbers.
A prime number is one that only has the number itself and factor 1 in it. For instance, the prime number 2 has two components, which are 2 and 1.
Find the prime factorization of 96These are the steps in this procedure:
Starting with the number you wish to factor, in this case 96, is step one.
2. Subtract the quantity from the smallest prime number, which is 2.
Step 3: Divide the result by 2 once more if the answer is a whole number.
Step 4: Repeat this procedure up until the point when the result is not a whole number.
Step 5: Go to 3 and repeat the process once you get to a number that is not divisible by 2.
Step 6: Continue with the following prime number and repeat the process until you reach a number that is not divisible by 3.
Step 7: Keep doing this up until you reach 1.
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A student wants to make the natural frequency of a string increase.
How could the student accomplish this?
Responses
by loosening the string
by tightening the string
by cutting the string
by decreasing the tension of the string
The natural frequency of a string increases by tightening the string. The correct option is B.
What is the natural frequency?The frequency at which a system is prone to oscillate when there is no external force acting on it. The normal mode is the oscillation pattern of a system operating at its fundamental frequency.
The sound frequency of musical instruments can be controlled by changing the settings of the strings. When the string of an instrument is stretched between two points, the tightened strings produce tension. Here, tension refers to how tightly the string is being stretched.
The tightening of the string provides higher frequency. The higher frequency vibrations are carried to the ear which considers high frequency as a high pitch.
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hi i need help and the answer thanks!
Answer:0.02 then 34/100 then 0.63 then 7/10
Step-by-step explanation:no explanaitin cause i cant be bothered
can some one please help me on this question thank you
Answer: X = 15.
Step-by-step explanation: if 12x = 180, simply divide both sides by 12. Doing this will leave just X on one side, and it’s answer, 15, on the other.
A model of a building is 11 inches tall. What is the actual height of the building if the scale states that 1 inch = 1.5 feet?
The real size (actual height) of the model is equal to 16.5 feet.
How to determine the real size of a model by scales?
Scales are an useful resource to represents systems in models at affordable size, scales (r) can be found by means of following ratio:
r = d' / d
Where:
r - Scale, in inches per feet. d' - Model size, in inchesd - Real size, in feetIf we know that r = 1 / 1.5 in / ft, d' = 11 in, then the real size of the model is:
1 / 1.5 = 11 / d
d = 16.5
The model has a real size (actual height) of 16.5 feet.
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Can anyone help me with this?
Which of the following triplets cannot be the angles of a triangle?
a. 67°, 51°, 62°
b. 70°, 83°, 27°
c. 90°, 70°, 20°
d. 40°, 132°, 18°
These three angles cannot form a triangle.
The sum of angles of a triangle is always 180°, as per the triangle angle sum theorem. This means that any three angles whose sum is greater than 180° cannot form a triangle. In the given options, option b. 70°, 83°, 27° has a sum of 180°, so it can form a triangle. Option a. 67°, 51°, 62° has a sum of 180, so it can form a triangle. Option c. 90°, 70°, 20° has a sum of 180°, so it can form a triangle. Option d. 40°, 132°, 18° has a sum of 190°, so it cannot form a triangle. To calculate the sum of angles, we can use the formula: angle1 + angle2 + angle3 = 180°. Thus, in option d. 40°, 132°, 18°, 40° + 132° + 18° = 190° which is greater than 180° and thus, these three angles cannot form a triangle.
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How to determine the log function of a graph?
the known values into the equation to determine the exact function of the graph
the known values into the equation to determine the exact function of the graph
1. Identify the type of graph you are dealing with. Is it a linear graph, an exponential graph, or a logarithmic graph?
2. Graph the data points on a coordinate plane.
3. Determine the equation of the best-fit line for the graph.
4. Determine the slope of the best-fit line.
5. Calculate the logarithmic function with the equation y = log(x) + b, where b is the y-intercept of the best-fit line.
6. Substitute the known values into the equation to determine the exact function of the graph
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2x to the 2nd power + 3x+1 when x = -2
The solution to the given expression 2x²+ 3x + 1 is 3 when substituting x = -2.
What is the expression?Expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The expression is given in the question, as follows:
2x²+ 3x + 1
We have to determine the solution to the given expression when x = -2
As per the question, we have
⇒ 2x²+ 3x + 1
Substitute the value of x = -2 in the above expression,
⇒ 2(-2)²+ 3(-2) + 1
⇒ 2(4) - 6 + 1
⇒ 8 - 6 + 1
⇒ 3
Thus, the solution to the given expression is 3.
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For what value of k is the roots of the equation KX?
The required value of k root of the quadratic equation is 2.
Explain roots of the equation?Quadratic equation's roots The roots of a quadratic equation are the values of the variables that fulfil the equation. In other words, if f() = 0, then x = is a root of the quadratic equation f(x). The x-coordinates of the sites where the curve y = f(x) intersects the x-axis are the real roots of an equation f(x) = 0.
According to question:kx(x−2√5)x+10=0
kx² −2√5 kx+10=0
Compare the preceding equation to the quadratic equation's general form, which is
ax² + bx + c=0.
a=k,b=−2√5 k,c=10
Locate a discriminator
D=b² −4ac
=(−2 k)² −4×k×10 = 20k −40 k
Put D=0 because the roots are genuine and equal (given).
20k² −40k=0
k²−2k=0
k(k−2)=0
Otherwise, k=0 or k−2=0
hence, k=0 or k=2.
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Complete question:
For what values of k are the roots of the quadratic equation kx(x−2
5)+10=0 real and equal?
A machine that drills holes for wells drilled to a depth of –72 feet in one day ( 24 hours)
3.2 If the machine drilled at a constant rate, what was the depth after 15 hours?
The machine drilled at a constant rate, so the depth after 15 hours is
-45 feet.
What is the unit rate?When comparing two different kinds of numbers with distinct units, a rate is a ratio that is employed. The unit rate, on the other hand, shows how many units of one quantity are equal to one unit of another. When the rate's denominator is 1, we refer to the rate as a unit rate.
Given A machine that drills holes,
drilled in 24 hours = -72 feet
the machine drilled at a constant rate,
so drilled in 1 hour = -72/24 = -3 feet per hour
depth in 15 hours = -3 x 15
depth in 15 hours = -45 feet
Hence the depth after 15 hours is -45 feet.
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What is zero of the polynomials Class 9?
A polynomial may have some values of the variable for which it will have a zero value. These numbers are referred to as a polynomial's zeros. They are also sometimes referred to as polynomial roots. In order to obtain the solutions to the given problem, we often determine the zeros of quadratic equations.
A polynomial in x has the usual form anxn + an-1xn-1 +..... + a1x + a0, where an, an-1,....., a1, a0, and a 0 are constants, and n is a whole number. Algebraic formulas like x + x + 5, x2 + 1/x2, for instance, are not polynomials since none of the exponents of x in these expressions are whole numbers.
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1. Find the 4th term of (2x+3y)^5
2. Find the 3rd term of (4x+y)^8
Use the Binomial Expansion to Find a Specific Term. Use that step.
Answer:
1. 1080x^2y^3
2. 114688x^6y^2
Step-by-step explanation:
1. binomial expansion : 32x^5+240x^4y+720x^3y^2+1080x^2y^3+810xy^4+243y^5
fourth term is 1080x^2y^3
2. binomial expansion:
65536x^8+131072x^7y+114688x^6y^2+57344x^5y^3+17920x^4y^4+3584x^3y^5+448x^2y^6+32xy^7+y^8
third term is 114688x^6y^2
what are the two solutions to the following absolute value?
|2x-4|=6
show your work
in a study, the data you collect is the average weight of newborn babies in ounces. what is the level of measurement?
The level of scale of measurements is the ratio scale for the data of the average weight of newborn babies in ounces.
There are four scales of measurement: Nominal, Ordinal, Interval, and Ratio.
Nominal scale: In this scale, categories are nominated names (hence “nominal”). There is no inherent order between categories. Put simply, one cannot say that a particular category is superior/ better than another.
Ordinal scale: The various categories can be logically arranged in a meaningful order. However, the difference between the categories is not “meaningful”.
Interval scale: The values (not categories) can be ordered and have a meaningful difference, but doubling is not meaningful. This is because of the absence of an “absolute zero”.
Ratio scale: The values can be ordered to have a meaningful difference, and doubling is also meaningful. There is an “absolute zero”.
Therefore, the level of scale of measurements is the ratio scale for the data of average weight of newborn babies in ounces.
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dora is traveling to visit diego at an average speed of mi/h. dora realizes that if she drives at an average speed of mi/h, her travel time will be reduced by minutes. how many miles per hour would dora's travel need to average for her travel time to increase by minutes?
Dora's travel need to average for 50 miles per hour for her travel time to increase by 6 minutes.
Dora is traveling to visit diego at an average speed 60 of mi/h.
∴ Distance = Speed x Time
d = 60 x t (i)
If dora travels with an average speed of 75 mi/h then, her travel time reduce by 6 mins the,
d = 75 x (t-6) (ii)
By solving equations we get,
60 x t = 75 x (t-6)
60t = 75t - 450
15t = 450
t = 30.
In order to increase the travel time by 6 minutes ,
d = s x (t + 6)
60t = s (t + 6)
60x30 = s (36)
s = 50 mi/hr.
So Dora will travel at 50 mi/h for her to increase the time of her journey by 6 minutes.
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Sam invited ten friends to a birthday party, but seven couldn't come. If he wanted to buy enough cupcakes so each person could have exactly five, how many should he buy?
Answer: 15
Step-by-step explanation: since seven couldnt come theres 3
5x3=15