So, Tom would have earned *Ksh (137465.91 + x) and John would have earned Ksh (202533.09 - x)
What exactly is markup?
The sum that is added to a product's cost price to cover expenses and profit is known as a markup.
We are aware that John banks 100,000 and Tom 230,000 Kenyan shillings.
Assume that both product A and B have a cost price of x.
Tom spends 5x because he BUYS 5 of Product A.
Tom sells two times as much of B. He SELLS 2 * (2x) = 4x as a result.
Hence, Tom's gain is:
4x - 5x = -x
Tom suffers a loss of x as a result of this.
John sells product A for three times what Tom BOUGHT. Thus he SELLS 3 * 5 = 15 times.
John purchases 13 of B Product. He therefore spends 13 times.
John thus makes a profit of:
15x - 13x = 2x
John thereby benefits by a factor of two.
As a result, the cost of goods A and B is:
42,727.27 + (25/100) * 42,727.27 = Ksh 53,409.09
44,363.63 + (25/100) * 44,363.63 = Ksh 55,454.54
We also know that the sale price was discounted by 15%.
After discounts, the sale price for item
A is (85/100) * Ksh 53,409.09, which is Ksh 45,397.73.
After discounts, the sale price for item
B is (85/100) * Ksh 55,454.54 = Ksh 47,136.36.
Tom's product loss
Ksh 45,397.73 - x = cost price - selling price
John's profit on item A is calculated as follows:
sale price less cost price = Ksh 45,397.73 - x
Cost price minus sale price equals Tom's loss on item B, which is Ksh 47,136.36.
John's profit on item B is calculated as follows: sale price less cost price = Ksh 47,136.36 - x
Therefore:
Total loss for Tom is (x - Ksh 45,397.73) + (x - Ksh 47,136.36)
= 2x - Ksh (45,397.73 + 47,136.36)
= = 2x - Ksh (92,534.09) (92,534.09)
(Ksh 45,397.73 - x) + John's total profit (Ksh 47,136.36 - x)
= Ksh (92,533.09) -2x
After discount and markup, Tom's bank balance equals Tom's bank balance plus his overall loss.
= [2x - Ksh (92,534.09)] + Ksh (230000)
= Ksh (137465.91 + x)
After discount and markup, John's bank balance equals John's bank balance plus his overall profit.
= [Ksh (92,533.09) -2x) + Ksh (110000)]
= Ksh (202533.09 - x)
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Find the value of r
18-2r
Answer:
27 18*3=2*r18/2*3=r9*3=rr=27
Step-by-step explanation:
Gretchen is a famous chef taking part in a celebrity cooking contest. Contestants earn scores between 1 - 10, with 10 being perfect. There are four categories and each category is weighted differently. The judges combined their scores and the results are shown in the table below.
Gretchen's final score, out of 10, is 8.35 based on weighted averages of scores in four categories.
How to calculate Gretchen's final score?To calculate Gretchen's final score, we need to calculate the weighted average of her scores in each category.
The weight of each category is given, so we can calculate the weighted score for each category by multiplying the weight by the score.
For Taste, the weighted score is 0.30 * 8.6 = 2.58
For Presentation, the weighted score is 0.35 * 9.8 = 3.43
For Use of Ingredients, the weighted score is 0.25 * 7.7 = 1.93
For Practicality, the weighted score is 0.10 * 4.1 = 0.41
To find the final score, we add up the weighted scores for all categories:
2.58 + 3.43 + 1.93 + 0.41 = 8.35
Therefore, Gretchen's final score is 8.35 out of 10.
The question is incomplete, below is the complete question given -
Gretchen is a celebrity chef competing in a celebrity cooking competition. Contestants receive ratings ranging from 1 to 10, with 10 being the highest. There are four categories, each with its own weighting. The judges' scores were added together, and the results are presented in the table below. What is Gretchen's final score, out of 10? Do not round.
Table -
Category Weight Score
Taste 30% 8.6
Presentation 35% 9.8
Use of Ingredients 25% 7.7
Practicality 10% 4.1
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The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function
F(x)=-3.452x^4+35.129x^3-93.005x^2+41.705x+177.494
Where x is the number of years since 1996. Find the number of bald eagles in the state the winter of 1999
The number of bald eagles in the state during the winter of 1999 would be 34.
I I need a quick answer
Answer:
the answer is b
Step-by-step explanation:
The length of a rectangular flower bed is 3 ft less than twice its width. The area of the bed is 54 ft2. What are the dimensions of the flower bed.
Answer:
w = 6 ft.; l = 9 ft.
Step-by-step explanation:
We know that the formula for area of a rectangle is A = lw, where l is the length and w is the width.
Because we're told that the length of the flower bed is 3 ft less than twice its width, we have l = 2w - 3
To find the length and width, can plug in 54 into the equation and substitute our formula for length into the equation.
This gives us 54 = (2w - 3)*w
If we rewrite the equation, we'll see that its quadratic:
[tex]54=(2w-3)w\\54=2w^2-3w\\0=2w^2-3w-54[/tex]
Now, we can first solve for width using the quadratic formula, which yields a positive and negative solution.
(For the sake of the quadratic equation, 0= ax^2 + bx + c is the standard form of quadratic equation and in our equation 2 is a, -3 is b, and -54 is c)
Positive:
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a} \\\\w=\frac{-(-3)+\sqrt{(-3)^2-4(2)(-54)} )}{2(2)}\\ \\w=\frac{3+\sqrt{441} }{4}\\ \\w=\frac{3+21}{4}\\ \\w=\frac{24}{4}\\\\w=6[/tex]
Negative:
[tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a} \\\\w=\frac{-(-3)-\sqrt{(-3)^2-4(2)(-54)} )}{2(2)}\\ \\w=\frac{3-\sqrt{441} }{4}\\ \\w=\frac{3-21}{4}\\ \\w=\frac{-18}{4}\\\\w=-4.5[/tex]
We know that we can't have a negative measure, so the width is 6 ft.
Twice the width is 12 (6 * 2) and 3 less than this is 9 (12 - 3), so the length is 9 ft.
The population of Medina, Ohio is currently 26,190 people. The population is predicted to grow at a rate of 3.7% per year. What will the population of Mediana be in 7.3 years? (round your answer to the neareat hundreth)
a.) 43210.82
b.) 87896.05
c.) 34144.47
d.) 50369.13
The population of Medina, Ohio will be approximately 34,052.89 people in 7.3 years.
What do you mean by Percentage?A number can be expressed as a fraction of 100 using a percentage. It is represented by the number %.
A decimal or fraction can be multiplied by 100 to become a percentage. For instance, multiplying 0.75 (a decimal) by 100 yields 75% when converted to a percentage. The same can be done to convert 3/4 (a fraction) to a percentage by dividing 3 by 4 to get 0.75, then multiplying that number by 100 to get 75%.
To calculate the population of Medina, Ohio in 7.3 years, we can use the formula:
Population after n years = Population before ×(1 + r/100)²
where r is the annual growth rate and n is the number of years.
Substituting the given values, we get:
Population after 7.3 years = 26,190 × (1 + 3.7/100)^7.3
Population after 7.3 years = 26,190 * 1.037^7.3
Population after 7.3 years = 26,190 * 1.301
Population after 7.3 years = 34,052.9
Rounding to the nearest hundredth, we get:
Population after 7.3 years = 34,052.90 ≈ 34,052.89
Therefore, the population of Medina, Ohio will be approximately 34,052.89 people in 7.3 years.
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Trigonometry review applications
I need help with 15-18
The angle of elevation is the angle between the horizontal line of sight and an upward direction to an object or point.
What is angle of elevation?The angle of elevation is often used in trigonometry and geometry to solve problems involving distances and heights.
1) Cos x = 16/27
x = Cos-1(16/27)
= 54 degrees
2)Sin x = 4/19
x = Sin-1(4/19)
x = 12 degrees
3) Tan 34 = x/8
x = 8 Tan 34
= 5 feet
4) Tan 61 = 166/5.5 + x
1.8(5.5 + x) = 166
9.9 + 1.8x = 166
x = 87 feet
Height of the statue = 5.5 + 87 = 92.5 feet
5) Tan 46 = x/35
x = 35tan 46
x = 36 feet
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PART B:
If Dr. Nandi plans to transport 3.5 x 105 energy prisms that each take up 2 x 10² cubic feet of cargo
space, how much total space will the cargo take up? Answer in Scientific Notation. Show your work.
Edit View Insert Format Tools Table
Answer:
Step-by-step explanation:
just guess if not use the internet
3. When Ahmad goes to work, he has to pass through two sets of traffic lights, P and Q. The
probability that he has to stop at P is
7/20 .The probability that he has to stop at Q, given that he has
to stop at P is 7/10. The probability that he does not have to stop at Q, given that he does not have to
stop at P is 2/5
* Construct a tree diagram to represent the above information.
* Find the probability that he has to stop at both P and Q.
* Find the probability that he has to stop at least once.
* If he has to stop at Q, what is the probability that he would have stopped at P.
* The probability that Ahmad has to stop at both P and Q is: 7/40
* The probability that Ahmad has to stop at least once is: 27/50
* The probability that Ahmad would have stopped at P if he stops at Q is 7/13.
What is probability ?
The study of randomness or experiments falls within the canopy of the mathematical discipline of probability. When represented as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certain event, it is the gauge of the probability or chance that an event will occur. When making predictions based on a statistical study of the data at hand, probability is employed to characterise uncertain events. To aid in decision-making and risk assessment, it is utilised in a variety of disciplines, including science, architecture, finance, finance, and social sciences. Concepts like likelihood function, random variables, and anticipated values are all part of the study of probability.
given
We multiply the chances of stopping at P and Q assuming that he has already stopped at P to determine the likelihood that he must stop at both locations:
Stop at P Equals P(Stop at P and Q) P(Stop at Q | Stop at P)=7/20*7/10
= 49/200
P(Stop at least once) = 1 - P(Not stop at P) * P(Not stop at Q | Not stop at P) = 1 - (13/20) * P(Not stop at Q | Not stop at P) (2/5)\s= 37/50
The chance that he likewise stopped at P must be determined if he had stopped at Q.
Stopping at P and Q equals P(Stop at P and Q) / P(Stop at Q) = (7/20 * 7/10) / (7/20) = 7/10.
Hence, the likelihood that he would have stopped at P is 7/10 if he must stop at Q.
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A database system assigns 32 character id to each record where each character is either a number from 0 to 9 or a letter from a to f assume that each number or letter being selected equally likely find the probability that at least 20 characters in the ID are numbers round your answer to three decimal places
This is a binomial distribution problem with the following parameters:
Number of trials: n = 32Probability of success: p = probability that a character is a number = 10/16 = 5/8Probability of failure: q = 1 - p = probability that a character is a letter = 6/16 = 3/8We want to find the probability that at least 20 characters are numbers. We can use the complement rule and find the probability that fewer than 20 characters are numbers, and subtract that from 1:
P(at least 20 numbers) = 1 - P(fewer than 20 numbers)
Using the binomial probability formula, we have:
P(fewer than 20 numbers) = Σ[k=0 to 19] C(n,k) * p^k * q^(n-k)
where C(n,k) is the binomial coefficient "n choose k". This can be calculated using a calculator or software that has a binomial probability function. For example, in Python, we can use the scipy.stats.binom.cdf() function:
from scipy.stats import binom
n = 32
p = 5/8
q = 3/8
prob_fewer_than_20 = binom.cdf(19, n, p)
This gives prob_fewer_than_20 = 0.04903110366420758.
Therefore,
P(at least 20 numbers) = 1 - 0.04903110366420758 = 0.9509688963357924
Rounding to three decimal places, the answer is 0.951.
The radius of a spherical balloon is increasing at a rate of 2 centimeters per minute. How fast is the surface area changing when the radius is 10 centimeters?
At a rate οf 160 cm per minute, the surface area is changing.
What is the area?A twο-dimensiοnal figure's area is the amοunt οf space it takes up. In οther terms, it is the amοunt that cοunts the number οf unit squares that span a clοsed figure's surface.
One can calculate a shape's area by cοmparing it tο squares οf a specific size. The Internatiοnal System οf Units' standard unit οf area is the square metre (abbreviated as m2), which measures the surface area οf a square with sides that are οne metre lοng (SI).
Surface Area οf Sphere (S)= 4πr²-------(1)]
Given: dr/dt = 2 cm/minute, r= 10 cm
Differentiating bοth sides with respect tο 't', we get
dS/dt = 4π * 2*r* dr/dt
dS/dt = 4π * 2*10* 2 = 160π cm/minute
The surface area is changing at the rate οf 160π cm/minute
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When an object is dropped vertically from a platform, its height after
seconds can be estimated with the formula shown.
ℎ=ℎ0−162
ℎ
is the height of the object in feet.
ℎ0
is the initial height of the object in feet.
is the time in seconds after the drop.
Which equation and solution tells how long it takes the object to reach a height of 84
feet if its initial height is 180
feet?
The equation is 84= h₀ -16t² and
Solving the equation we get the time taken by the object will be √6 seconds.
What is equation?
An equation is a mathematical statement which is built by two expressions connected by an equal sign ('='). There must be at least one unknown variable which is to be determined. For example, 3x – 8 = 16 is an equation. Solving this equation, we get x = 8.
When an object is dropped vertically from a platform, its height after
seconds can be estimated with the formula shown.
ℎ=ℎ₀−16t²
where ℎ is the height of the object in feet.
and ℎ₀ is the initial height of the object in feet.
t is the time in seconds after the drop.
If the object reach the height 84 feet then the equation will be,
84= h₀ -16t²
If the initial height is 180 feet then the equation will be
84 = 180- 16t²
Solving the equation we get,
⇒ 16t² = 180- 84
⇒ 16t² = 96
⇒ t² = 6
⇒ t= ±√6
As time can't be negative so t= √6
Hence solving the equation we get the time taken by the object will be √6 seconds.
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find the ratio of 4 inches to 3 yards
every 1 unit of 4 inches, there are 27 units of 3 yards. It's important to note that ratios represent a proportional relationship between two quantities and do not necessarily represent the actual values themselves.
How to solve ratio?
To find the ratio of 4 inches to 3 yards, we need to convert both measurements to a common unit of measurement.
Firstly, let's convert the 3 yards to inches, since inches are already given. There are 36 inches in a yard (3 feet in a yard, and 12 inches in a foot), so:
3 yards = 3 x 36 inches = 108 inches
Now we can compare the two measurements:
Ratio of 4 inches to 108 inches = 4/108
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 4 in this case:
4/108 = 1/27
So, the ratio of 4 inches to 3 yards is 1:27.
This means that for every 1 unit of 4 inches, there are 27 units of 3 yards. It's important to note that ratios represent a proportional relationship between two quantities and do not necessarily represent the actual values themselves.
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The ___ is the average of the sum of the squared differences of the mean from each element in a set of numerical data.
Answer:
The term that completes the sentence is "variance".
Step-by-step explanation:
In statistics, variance is a measure of how spread out a set of numerical data is. It is calculated by finding the average of the sum of the squared differences of each element in the set from the mean of the set. The formula for variance is:
Variance = (Σ(x - μ)²) / n
where Σ is the sum, x is each element in the set, μ is the mean of the set, and n is the number of elements in the set.
Write the following as on logarithm
2 ln(5x) − 3 ln(2x) + 7 log2 (8x)
ln[(5x)² × (2x)⁻³ × (8x)⁷] . The logarithm expression is written in the form of ln(x) which is logarithm to the base e. The expression contains log2(x) which is logarithm to the base 2.
What is logarithm expression?The base number is the number that is raised to a certain power, the exponent is the power that the base number is raised to, and the logarithmic function is the equation which is used to calculate the result of the base number and the exponent.
The given expression can be written as a logarithm as follows:
ln[(5x)² × (2x)⁻³ × (8x)⁷]
This can be simplified to
2ln(5x) - 3ln(2x) + 7log2(8x)
The logarithm expression is written in the form of ln(x) which is logarithm to the base e. The expression contains log2(x) which is logarithm to the base 2.
The logarithm expression can be used to simplify complex equations and calculations, and it can also be used to solve for a particular variable.
This expression can be used to solve for x if the other values are known. The value of x can be calculated by taking the antilogarithm of each term and then solving the equation.
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The life spans of 10 adult mayflies have a mean of 4 hours and a MAD of 2 hours. Fill in the table below with possible values for the life spans. You can use the same values more than once. Can any one of the 10 mayflies in the group live for 1 full day? Justify your answer.
No mayfly in the group can live for a full day (24 hours), as the maximum life span is 6 hours.
How to calculate life span?We can start by calculating the lower and upper limits of the range of possible values for the life spans of the mayflies.
The lower limit can be found by subtracting the MAD from the mean, and the upper limit can be found by adding the MAD to the mean:
Lower limit = mean - MAD = 4 - 2 = 2 Upper limit = mean + MAD = 4 + 2 = 6
Since we know there are 10 mayflies in the group, we can fill in the table below with values between 2 and 6 (inclusive) that add up to 40 (the total number of hours for all 10 mayflies combined):
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please help Find the common ratio for this geometric sequence. 1 1 1 2'8'32 8, 2, O A. 1/10 O B. -12 OC. 4 OD. 2
The common ratio is the factor by which each term is multiplied to get the next term, which in this case is 4.
EquationsTo find the common ratio of a geometric sequence, you can divide any term in the sequence by the previous term.
Looking at the sequence: 1, 1, 1, 2, 8, 32, 128, ...
To get from the 1st term to the 2nd term, we multiply by 1.
To get from the 2nd term to the 3rd term, we multiply by 1.
To get from the 3rd term to the 4th term, we multiply by 2.
To get from the 4th term to the 5th term, we multiply by 4.
To get from the 5th term to the 6th term, we multiply by 4.
What is common ratio?The constant ratio between succeeding words is known as the common ratio in a geometric progression (GP). Any phrase in the progression must be divided by the term before it in order to compute it.
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answer this for me please and thank you
Answer: w = -13
Step-by-step explanation:
To solve, we will isolate the variable with inverse operations.
Given:
4 + w = -9
Subtract 4 from both sides of the equation:
w = -13
Use the counting principle to determine the number of elements in the sample space. The possible ways to complete a multiple-choice test consisting of 18 questions, with each question having four possible answers (a, b, c, or d).
In the figure, m∠EDF = 42°. Which other angle must have the same measure? A diagram of the inscribed quadrilateral with the points of D, E, F, and G, in which D with an angle of 42 degrees. A. ∠DEG B. ∠EGF C. ∠GDF D. ∠EGD
Therefore, the correct option is B. ∠EGF with the angle measure of 138°.
What is quadrilateral?A quadrilateral is a four-sided polygon with four vertices and four angles. It is a closed figure with four straight sides that do not intersect. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses. The sum of the interior angles of a quadrilateral is always 360 degrees.
Here,
In an inscribed quadrilateral, opposite angles are supplementary. That is, the sum of the measures of any two opposite angles is 180 degrees. Therefore, to find the angle that has the same measure as ∠EDF, we need to look for the angle that is also opposite ∠EDF in the inscribed quadrilateral.
In the inscribed quadrilateral with points D, E, F, and G, we know that ∠EDF has a measure of 42 degrees. We also know that the opposite angle to ∠EDF is ∠EGF, because they share side EF.
Since opposite angles in an inscribed quadrilateral are supplementary, we can find the measure of ∠EGF by subtracting 42 degrees from 180 degrees:
∠EGF = 180° - ∠EDF
= 180° - 42°
= 138°
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locate the absolute extrema of the function
on the closed interval
The function f(x) = 3x² - 3x has absolute extrema at (-1, -5/2)
What is the absolute extrema of the function on the closed interval?To find the absolute extrema of the function f(x) = x³ - 3/2x² on the closed interval [-1, 2], we need to first find the critical points of the function in the interval and evaluate the function at those points as well as at the endpoints of the interval.
To find the critical points, we need to find where the derivative of the function is equal to zero or does not exist. The derivative of f(x) is:
f'(x) = 3x² - 3x
Setting f'(x) = 0, we get:
3x² - 3x = 0
3x(x - 1) = 0
x = 0 or x = 1
We also need to check if there are any values of x where the derivative does not exist. However, since the derivative is a polynomial function, it exists for all real values of x.
The absolute extrema is at (-1, -5/2)
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A person is planting one garden bed that is 15 feet in length and another that is 9 feet in length. What is the total length, in inches, of the two garden beds combined
HELP PLEASE
Answer:
awnser is 288 seriously 15 x 12 = 180
and 9 x12 =108 add together is 288
PLEASE DONT GNORE!!M BEGGNG!!
Riley conducted a survey to see which is the most favorite subject among the students in her grade. She randomly chose to survey the first 53 students who entered the gym. She has a total of 424 students in her grade. What is true about the number of students who chose art??
____________students chose art as their favorite subject.
According to the table, the complete sentence would be: 96 students chose art as their favorite subject.
How to complete the sentence correctly?To complete the sentences correctly we must read the information and analyze the table. Once we have done these procedures we can establish how many students chose each of the subjects as their favorite. According to the above, the sentence would be as follows:
96 students chose art as their favorite subject.
How do we know the number of students who chose arts?According to Riley's survey, 12 out of 53 students chose art as their favorite. We then divide the total number of students (424) by the sample size (53) and multiply the number of students who chose art in the sample by the result of the division.
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Which is the largest angle?
A4
OC
B
5
Cannot tell
OA
с
7
6
B
Given that cos theta equals negative 5 square root 29 over 29 and theta is in quadrant 2 what is sim theta?
If cοs θ equals negative 5 square rοοt 29 οver 29 and θ is in quadrant 2 sin(θ) = οppοsite/hypοtenuse = 2√21/29.
What is trigοnοmetry?The links between triangles' sides and angles are studied in the mathematic discipline knοwn as trigοnοmetry.
We knοw that cοsine is negative in quadrant 2, sο we can draw a triangle in quadrant 2 where the adjacent side is negative and the hypοtenuse is pοsitive. Let's call the οppοsite side οf the triangle "a", the adjacent side "b", and the hypοtenuse "c".
Using the Pythagοrean theοrem, we can find the length οf the third side οf the triangle:
c² = a² + b²
29² = a² + (-5√29)²
29² = a² + 725
a² = 29² - 725
a² = 84
a = √84 = 2√21
Nοw that we knοw the lengths οf the οppοsite and adjacent sides οf the triangle, we can use the definitiοn οf sine:
sin(θ) = οppοsite/hypοtenuse = 2√21/29
Therefοre, sin(θ) equals 2√21/29.
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Complete Question:
Given that cos(θ)=−5√29/29, and θ is in Quadrant II, what is sin(θ)? Give your answer as an exact fraction with a radical, if necessary.
which is equivalent to (3/125)*?
125 1/3×
125 1/3X
125 3x
125 [1/3]×
The answer is (B) 125 1/3×, which is equivalent to (3/125) times approximately 18.048.
What do you mean by Equivalent fraction?Equivalent fractions are fractions that have the same value but are written in different forms. They represent the same portion of a whole or a set, but their numerators and denominators may have different values.To find equivalent fractions, you can multiply or divide both the numerator and denominator of a fraction by the same number. This does not change the value of the fraction, but it changes its form.
The expression is (3/125) times something, but the value of that something is missing.
To solve the problem, we can simplify the expression (3/125) as a fraction in its lowest terms:
(3/125) = (3/5³)
Now, let's look at each of the answer choices:
125
If we multiply (3/5³) by 125, we get:
(3/5^3) * 125 = 3/5
Therefore, 125 is not equivalent to (3/125) times something.
1/3 × 125
If we multiply (3/5³) by (1/3 × 125), we get:
(3/5^3) * (1/3 × 125) = 1/5
Therefore, 1/3 × 125 is not equivalent to (3/125) times something.
125 1/3 ×
If we interpret "125 1/3 ×" as 125 and one-third multiplied by something, then we can write it as a mixed number fraction:
125 1/3 = 376/3
If we multiply (3/5³) by 376/3, we get:
(3/5³) ×(376/3) = 2256/125 = 18.048
Therefore, 125 1/3 × is equivalent to (3/125) times approximately 18.048.
125× 3x
If we interpret "125 3x" as 125 multiplied by 3 times something, then we can write it as:
125 ×3x = 375x
Therefore, 125 3x is not equivalent to (3/125) times something.
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I really need help with this please help
Answer:
a is true
x=72
Step-by-step explanation:
4/6 doesnt make sense. where did they get the denominator 6 from, it wasnt in the problem
b is false
Please help me with this
Answer:
D
Step-by-step explanation:
The parabola of m(x) is thinner than the parabola of f(x) since 4 times 2 squared is 16 while 2 squared is 4
7. Write the equation of the circle that passes through the point (2,-5) and has its center at (4,0) .
Show your work
Therefore, the equation of the circle that passes through the point (2, -5) and has its center at (4,0) is.[tex](x - 4)^2 + y^2= 29[/tex].
What is circle?A circle is a closed, two-dimensional geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of all points in a plane that are at a given distance (called the radius) from the center point. The circumference of a circle is the distance around its outer boundary, and the diameter is the distance across the center of the circle. Circles have several important properties and are used extensively in mathematics, science, and engineering.
To find the equation of a circle, we need to know the coordinates of its center and its radius. We are given the center of the circle, which is (4,0). To find the radius, we can use the distance formula between the center and the point on the circle (2, -5):
[tex]radius = \sqrt{[(4 - 2)^2 + (0 - (-5))^2]}[/tex]
[tex]= \sqrt{[2^2 + 5^2]}[/tex]
[tex]= \sqrt{29}[/tex]
So the equation of the circle can be written in the standard form as:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
where (h, k) is the center of the circle and r is its radius.
Substituting the values we found, we get:
[tex](x - 4)^2 + (y - 0)^2 = (\sqrt{29})^2[/tex]
Simplifying, we get:
[tex](x - 4)^2 + y^2 = 29[/tex]
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Write the equation for a circle with centre (-15;3√7) and an area of 2π in standard form
An equation for a circle with centre (-15, 3√7) and an area of 2π in standard form is (x + 15)² + (y - 3√7)² = 2.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.For the radius, we have:
Area of a circle = πr²
2π = πr²
r = √2
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - (-15))² + (y - 3√7)² = (√2)²
(x + 15)² + (y - 3√7)² = 2.
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