First let us assign the three positive integers to be x, y, and z.
From the given problem statement, we know that:
(1/x) + (1/y) + (1/z) = 1
Without loss of generality we can assume x < y
< z.
We know that:
1 = (1/3) + (1/3) + (1/3)
Where x = y = z = 3 would be a solution
However this could not be true because x, y, and z must all be different integers. And x, y, and z cannot all be 3 or bigger than 3 because the sum would then be less than 1. So let us say that x is a denominator that is less than 3. So x = 2, and we have:
(1/2) + (1/y) + (1/z) = 1
Therefore
(1/y) + (1/z) = 1/2
We also know that:
(1/4) + (1/4) = (1/2)
and y = z = 4 would be a solution, however this is also not true because y and z must also be different. And y and z cannot be larger than 4, so y=3, therefore
(1/2) + (1/3) + (1/z) = 1
Now we are left by 1 variable so we calculate for z. Multiply both sides by 6z:
3z + 2z + 6 = 6z
z = 6
Therefore:
(1/2) + (1/3) + (1/6) = 1
so {x,y,z}={2,3,6}
Final answer:
The product of Melissa's integers is 120.
Explanation:
The product of Melissa's integers is 120.
Let the integers be a, b, and c.
According to the given information, 1/a + 1/b + 1/c = 1.
By finding common denominators and simplifying, you can determine that a * b * c = 120.
Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? If it is a direct or inverse variation, write a function to model it.
Which number is the largest? 1.2 × 104, 4.5 × 10−3, 3.8 × 103, 7.5 × 103
1.2 × 104
4.5 × 10−3
3.8 × 103
7.5 × 103
Answer: 1.2 x 10^4
Step-by-step explanation:
pls hit thanks and rate!
PLZ HELP ME! NEED THE ANSWER AS SOON AS POSSIBLE! WILL REWARD THE BRAINLIEST: The table below shows the distance y, in miles, traveled by a truck in x hours: Time (x) (hours) 1 2 3 4 Distance (y) (miles) 50 100 150 200 Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and distance traveled by the truck. [Choose the value of the correlation coefficient from 1, 0.8, 0.5, 0.02.] (4 points) Part B: What is the value of the slope of the graph of distance versus time between 3 and 4 hours, and what does the slope represent? (3 points) Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)
The figure below is a square pyramid. Which of the following could not be a cross section in the figure?
Square
Rectangle that is not a square
Trapezoid
Isosceles triangle
Answer:
A rectangle that is not a square is the actual answer.
What is the simplified form of 30 times x to the sixth power over 14 times y to the fifth power times the fraction 7 times y-squared over 6 times x to the fourth power ?
Write the following fractions as decimals 2/10,3/100
Answers:
A. .2
B. .03
C. .093
D. .1456
Have a blessed day ☺️
The graphs of f(x) = 10x and its translation, g(x), are shown.
What is the equation of g(x)?
g(x) = 10x – 3
g(x) = 10x + 3
g(x) = 10x – 3
g(x) = 10x + 3
Answer:
The equation for the function g(x) is:
[tex]g(x)=(10)^{x-3}[/tex]
Step-by-step explanation:
We are given graphs of two functions f(x) and g(x).
The function f(x) is an exponential function and is given by:
[tex]f(x)=(10)^x[/tex]
Now, we are asked to find the equation for the transformed function g(x).
We could see that the graph of the function g(x) passes through (3,1),(4,10) , (5,100) and so on.
This means that the equation or the expression for the function g(x) is given by:
[tex]g(x)=(10)^{x-3}[/tex]
( Since, when x=3 we have:
[tex]g(x)=(10)^{3-3}=10^0=1[/tex]
when x=4 we have:
[tex]g(x)=(10)^{4-3}\\\\g(x)=(10)^{1}\\\\g(x)=10[/tex]
and so on)
Answer:
(x)=(10)^(x-3)
Step-by-step explanation:
Just did it on edge 2020 :) Hope i helped!!
#12 with work please
what is another name for the set of all x-values from its graph
Given: QR = 59; RT = 59 Prove: QR = RT StatementsReason 1. QR = 59; RT = 591. Given 2. 59 = RT2. Symmetric Property of Equality 3. QR = RT3. Which property listed below is the final reason in the proof.
Answer:
By using transitive property
QR=RT
Step-by-step explanation:
Given
QR=59
RT=59
To prove that QR=RT
1. Statement QR=59; RT=59
Reason : Given in the question.
2. Statement: 59=RT
Reason: By using symmetric property of equality .
Symmteric property is that property of equality
if
ab=bc
Then ,
bc=ac
3. Statement: QR=RT
Reason: By using transitive property of equality.Transitive property : If ac=bc
and bc=ca
Then , ab=ca
Hence proved.
A square is inscribed in the circle. A point in the figure is selected at random. Find the probability that the point will be in the part that is NOT shaded.
To find the probability of selecting an unshaded area within a circle where a square is inscribed, one must calculate the areas of the shaded and unshaded regions and use these areas to determine the ratio representing the probability.
The question seeks to determine the probability that a randomly selected point within a figure that includes both a circle and a square will be in the unshaded area. To solve this problem, we would typically need to calculate the area of the shaded and unshaded regions and then use these areas to determine the probability. When calculating probability in a geometric context, the ratio of the area of the desired region to the area of the entire space (in this case, the circle) gives the probability of randomly selecting a point in that region.
Similarly, if the question pertained to the probability of selecting a chord shorter than the side of an inscribed equilateral triangle, we would consider the probability distribution of chord lengths within the circle. This problem involves understanding that selecting a chord at random equates to selecting its midpoint at random. If the midpoint lies within a certain area, the chord will be shorter than the triangle's side.
When dealing with probability questions like the one about Times Square visitors, the random variable would typically represent the characteristic we're interested in, such as being a visitor versus a resident. In evaluating probabilities, graphical methods, such as shading areas on a graph, can be useful to visually represent and calculate the likelihood of a specific range of outcomes.
Larry mixed 15 grams of salt with 210 grams of a 5% salt solution in water. What is the percent of salt in his new solution?
What is the slope of the line that contains the points (-4,2) and (6,-3)
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $2510 to rent trucks plus an additional fee of $125.25 for each ton of sugar. The second company does not charge to rent trucks but charges $250.75 for each ton of sugar.
For what amount of sugar do the two companies charge the same?
What is the cost when the two companies charge the same?
The two companies charge the same when transporting 20 tons of sugar, for $5015 for transporting that amount.
To determine what amount of sugar the two companies charge the same, we should set up an equation where both companies' cost functions are equal. For the first company, the cost function is C1 = 2510 + 125.25x, where x is the number of tons of sugar. For the second company, the cost function is C2 = 250.75x. To find the point at which C1 equals C2, we solve for x:
2510 + 125.25x = 250.75x
Subtract 125.25x from both sides:
2510 = (250.75 - 125.25)x
2510 = 125.5x
Divide both sides by 125.5:
x = 2510 / 125.5
x = 20 tons
Therefore, the two companies charge the same for transporting 20 tons of sugar. To find the cost when they charge the same, substitute x into one of the cost functions:
C1 = 2510 + 125.25(20) = 2510 + 2505 = $5015
Thus, the cost when the two companies charge the same is $5015 for 20 tons of sugar.
The results of a study indicate that the mean weight of adult skunks in an area is between 4.3 kg and 4.9 kg. What is the study’s margin of error?
Since we are given the range of the area, the margin of error can be calculated by firstly calculating the difference of the range and dividing by 2. This is expressed in this formula:
Margin of error = ± (Upper range – Lower range) / 2
Margin of error = ± (4.9 kg – 4.3 kg) /2
Margin of error = ± 0.3 kg
#23 please!!! Thanks
The length of a rectangle is 9 feet longer than the width. if the perimeter is 78 feet, find the length and width of the rectangle.
The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period. What is a cosine function that models this reaction?
f(t) = −30 cos (pi/3) t + 20
f(t) = −60 cos (pi/3) t + 30
f(t) = 30 cos (6t) + 20
f(t) = 60 cos (6t) + 30
Answer:
Option 1 - [tex]f(t)=-30 sin(\frac{\pi}{3}t)+20[/tex]
Step-by-step explanation:
Given : The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period.
To find : What is a cosine function that models this reaction?
Solution :
General form of cosine function is [tex]f(x)=A cos(Bx)+C[/tex]
Where A is the amplitude
[tex]B=\frac{2\pi}{\text{Period}}[/tex]
C is the midline
Now, We have given
The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius.
A is the average of temperature,
i.e, [tex]A=\frac{-10-50}{2}=-30[/tex]
Period of 1 cycle is 6 hour
So, [tex]B=\frac{2\pi}{6}=\frac{\pi}{3}[/tex]
The temperature is at its lowest point when t = 0 and we know lowest point is -10
So, [tex]f(t)=A\cos t+C[/tex]
[tex]-10=-30\cos 0+C[/tex]
[tex]C=20[/tex]
Substituting the values we get,
The cosine function is [tex]f(t)=-30 sin(\frac{\pi}{3}t)+20[/tex]
Therefore, Option 1 is correct.
what is the slope of the line that passes through (1,4) and (1,-3)?
A. 7
B. -7
C. undefined
D. 0
Let h = (v0^2)/4.9 sin(theta)cos(theta) model the horizontal distance in meters traveled by a projectile? If the initial velocity is 52 meters/second, which equation would you use to find the angle needed to travel 200 meters?
A) 275.92sin(2Theta)=200
B) 551.84sin(2Theta)=200
C) 200sin(2 Theta)=200
D)10.61sin(2THeta)=100
Answer:
A) 275.92sin(2Theta)=200
a p e x
If the circumference of a circle is 24, and the angle measure of an arc is 120o, which is the length of the arc?
Find the volume of each figure to the nearest tenth. Show your work. please
How to draw exactly two planes intersect the third plane does not intersect the other two?
The Empire State Building is just over 1,450 feet tall. In anticipation of visiting this landmark on your vacation, you create a model of it using blocks.
a. Suppose you are making a model where one block represents 2 feet. About how many blocks tall is your model of the Empire State Building? What is the scale factor?
Answer:
725, 1 per every 2 ft.
Step-by-step explanation:
It gives the actual height for the building, 1,450, and it says one block is two feet. Divide 1,450 by 2 and you'd get 725. And we already know dat one block is two feet so it's 1:2
(why did I start singing ``You Reposted in the Wrong Hero Academia?`` UwUz)
Ariel has a plastic ice cream cone in her food playset. The ice cream cone is a half-sphere sitting on top of a cone. What is the approximate volume of the toy ice cream cone? Use 3.14 for ππ .
the approximate volume of the toy ice cream cone is around [tex]\( \frac{32}{3}π \)[/tex]cubic inches, considering the half-sphere as[tex]\( \frac{16}{3}π \)[/tex] and the cone as [tex]\( \frac{16}{3}π \).[/tex]
let's calculate the approximate volume of the toy ice cream cone step by step.
First, we need to determine the volume of the half-sphere, which is the ice cream part.
The formula for the volume of a sphere is:
[tex]\[ V_{\text{sphere}} = \frac{4}{3}πr^3 \][/tex]
But since we only have a half-sphere, we'll divide the result by 2.
Now, we need to find the radius ((r)) of the half-sphere. We can do this by measuring the radius of the ice cream cone's base.
Let's say the radius of the ice cream cone's base is (r = 2) inches.
Substituting the value of (r) into the formula:
[tex]\[ V_{\text{half-sphere}} = \frac{1}{2} \times \frac{4}{3}π(2)^3 \][/tex]
[tex]\[ V_{\text{half-sphere}} = \frac{1}{2} \times \frac{4}{3}π(8) \][/tex]
[tex]\[ V_{\text{half-sphere}} = \frac{1}{2} \times \frac{32}{3}π \][/tex]
[tex]\[ V_{\text{half-sphere}} = \frac{16}{3}π \][/tex]
Now, let's find the volume of the cone part.
The formula for the volume of a cone is:
[tex]\[ V_{\text{cone}} = \frac{1}{3}πr^2h \][/tex]
Where (h) is the height of the cone.
Let's say the height of the cone is (h = 4) inches.
Substituting the values into the formula:
[tex]\[ V_{\text{cone}} = \frac{1}{3}π(2)^2(4) \][/tex]
[tex]\[ V_{\text{cone}} = \frac{1}{3}π(16) \][/tex]
[tex]\[ V_{\text{cone}} = \frac{16}{3}π \][/tex]
Now, to find the total volume of the ice cream cone, we'll add the volumes of the half-sphere and the cone together:
[tex]\[ V_{\text{total}} = V_{\text{half-sphere}} + V_{\text{cone}} \][/tex]
[tex]\[ V_{\text{total}} = \frac{16}{3}π + \frac{16}{3}π \][/tex]
[tex]\[ V_{\text{total}} = \frac{32}{3}π \][/tex]
So, the approximate volume of the toy ice cream cone is [tex]\( \frac{32}{3}π \)[/tex]cubic inches.
What is the sign of the product (−4)(6)(9)(3)?
A) Positive, because the products (−4)(6) and (9)(3) are negative and the product of two negative numbers is positive
B) Positive, because the products (−4)(6) and (9)(3) are positive and the product of two positive numbers is positive
C) Negative, because the product (−4)(6) is negative and the product (9)(3) is positive, and the product of a negative number and a positive number is negative
D) Negative, because the product (−4)(6) is negative and the product (9)(3) is negative, and the product of two negative numbers is a negative number
Hello,
The correct answer is C) Negative, because the product (-4)(6) is negative and the product (9)(3) is positive, and the product of a negative number and a positive number is negative.
Hope this helps!!!!
A rectangle is 13 centimeters longer than it is wide. Its perimeter is 226 centimeters. What are the length and width?
Kim's softball team is playing in the championship game. they are losing by a score of 171717 to 666. there are 444 innings to go. kim wants to know how many runs her team needs per inning to win the game if the other team does not score. (each run is worth 111 point.)
The graph of F(x) can be compressrd vertically and shifted to the right to produce the graph of G(x). If F(x) = x^3, which of the following could be the equation of g(x)?
A.) G(x) = 1/2(x-6)^3
B.) G(x) = 2(x-6)^3
C.) G(x) = 2(x+6)^3
D.) G(x) = 1/2(x+6)^3
It is option A. A vertical compression means that
the function is only a "fraction" of its original height, hence the
fractional coefficient.
REMEMBER, movement along the x-axis is always the OPPOSITE of
what you think. So left = + and right = -
So (x-6) actually means a shift 6 units to the right. (NOT
left like you would naturally think)
how much money will you have if you started with $1000 and put it in an account that earned 5% every year for 15 years