the completed pairs are - √5 units, 2 units
Starting with the first pair, we have √5 units on both tiles, so we can place them in the same box.
Moving on to the second pair, we have √3 units on one tile and √5 units on the other. We need to find a pair that matches √3 units. Since there is no tile with √3 units, we cannot place this pair in the same box.
Lastly, we have two tiles left - one with √5 units and another with 1 unit. We need to find a pair that matches 1 unit. Since there is no tile with 1 unit, we cannot place this pair in the same box either.
Therefore, the completed pairs are:
- √5 units, √5 units
- √5 units, 2 units
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the hypotenuse of a right triangle is 3 times as long as its shorter leg. the longer leg is 12 centimeters long. to the nearest tenth of a centimeter, what is the length of the triangle's shorter leg?
Find the area of a sector with a central angle of 180° and a diameter of 5. 6 cm. Round to the nearest tenth
The area of the sector with a central angle of 180° and a diameter of 5.6 cm is approximately 11.8 [tex]cm^2[/tex].
To find the area of a sector, we need to know the central angle and the radius or diameter of the circle that the sector is a part of. In this case, we are given a central angle of 180° and a diameter of 5.6 cm.
Find the radius of the circle is the first step. We can do this by dividing the diameter by 2:
radius = diameter/2 = 5.6/2 = 2.8 cm
Next, we can use the formula for the area of a sector:
Area of sector = (central angle/360°) x π x [tex]radius^2[/tex]
Plugging in the given values, we get:
Area of sector = [tex](180/360) * \pi * (2.8)^2[/tex]
= [tex](1/2) * 3.14 * 2.8^2[/tex]
= [tex]11.77 cm^2[/tex]
Rounding to the nearest tenth, we get:
Area of sector ≈ 11.8 [tex]cm^2[/tex]
Therefore, the area of the sector is approximately 11.8 [tex]cm^2[/tex].
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I'm confused with this question please help.
Answer:
70
Step-by-step explanation:
Ill give it to you if you really need it its gonna take a while to explain
:)
a square with side length is inscribed in a right triangle with sides of length , , and so that one vertex of the square coincides with the right-angle vertex of the triangle. a square with side length is inscribed in another right triangle with sides of length , , and so that one side of the square lies on the hypotenuse of the triangle. what is ?
The value of x/y is 35/37. The correct answer is option B).
Let's start by the first right triangle and the inscribed square. We know that the square has side length x and is inscribed in the right triangle with sides 3, 4, and 5, where 5 is the hypotenuse. Since one vertex of the square coincides with the right-angle vertex of the triangle, we have that the side length x of the square is also the length of the altitude from the right angle to the hypotenuse of the triangle. Therefore, we can write:
x = [tex](3*4)/5 = 12/5[/tex]
Now the second right triangle and the inscribed square:
We know that the square has side length y and is inscribed in the right triangle with sides 3, 4, and 5, where 5 is the hypotenuse. Since one side of the square lies on the hypotenuse of the triangle, we have that the sum of the areas of the two smaller squares is equal to the area of the larger square. Therefore, we can write:
[tex]x^{2} + y^{2} = 5^{2} = 25[/tex]
Substituting[tex]$x = {12}/{5}[/tex] gives
[tex](12/5)^{2} + y^{2} = 25[/tex]
Simplifying this equation gives
[tex]y^{2} = 25 - (144/25) = (25^{2} - 144)/25 = 481/25[/tex]
Taking the square root of both sides gives
y = [tex]\sqrt{481}/5[/tex]
Finally, we compute x/y:
x/y = [tex]12*\sqrt{481}/ \sqrt{481}*5[/tex]
x/y = 35/37
The correct option is B)
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--The given question is incomplete, the complete question is
"A square with side length x is inscribed in a right triangle with sides of length 3, 4, and 5 so that one vertex of the square coincides with the right-angle vertex of the triangle. A square with side length y is inscribed in another right triangle with sides of length 3, 4, and 5 so that one side of the square lies on the hypotenuse of the triangle. What is x/y?
(A) 12/13
(B) 35/37
(C) 1
(D) 37/35
(E) 13/12"
List all possible rational zeros for the function. (Enter your answers as a comma-separated list.)
f(x) = 2x3 + 3x2 − 10x + 7
The rational zeros for the function, f(x) = 2·x³ + 3·x² - 10·x + 7, found using the rational roots theorem are;
-7, -7/2, -1, -1/2, 1/2, 1, 7/2, 7
What is the rational roots theorem?The rational roots theorem is a theorem in algebra that can be used to find the roots of a polynomial equation. According to the theorem, the rational roots of a polynomial that has integer coefficients have the form p/q, where, p is a factor of the constant term and q is a factor of the leading coefficient.
The rational roots theorem can be used to find the possible rational zeros of a polynomial.
The rational roots theorem states that if a polynomial function has integer coefficients, then any rational zero of the function must have the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient
The specified function, f(x) = 2·x³ + 3·x² - 10·x + 7, the constant term is 7 and the leading coefficient is 2. Therefore, the possible rational zeros of the function are of the form p/q, where p is a factor of 7 and q is a factor of 2.
The factors of 7 are 1, and 7, and the factors of 2 are 1 and 2, Therefore, the possible rational zeros of the functions are;
±1/1, ±7/1, ±1/2, ±7/2
The possible rational zeros of the function f(x) = 2·x³ + 3·x² - 10·x + 7 are;
-7, -7/2, -1, -1/2, 1/2, 7/2, 7
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please help with solving find the value of k and the two roots of x
The approximate value of K of the given quadratic equation is: 16.842
How to solve Quadratic equations?The general expression of a quadratic function is:
ax² + bx + c = 0
The quadratic formula to find the roots is expressed as:
x = [-b ± √(b² - 4ac)]/2a
The product of the 2 roots of the quadratic equation is equal to the constant term.
Let a and b be used to denote the roots of a given quadratic equation.
But according to given condition, one root is equal to the square of the other root. Thus: b = a²
Thus:
a + a² = k
a * a² = 48
a³ = 48
a = 2∛6
Thus:
2∛6 + (2∛6)² = k
k = 16.842
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1. What is the asymptotic slope of the best fit line for the equation, y = 5x^4+3, when plotted on log-log plot?
2. What is the maximum number of inversions in a list of 100 distinct elements?
3. What is the minimum number of inversions in a list of 100 distinct elements?
1. Asymptotic slope of the best line for the equation y = 5x⁴ + 3 plotted on a log-log plot is 4. To find this, first note that the dominant term in the equation is 5x⁴. On a log-log plot, the slope corresponds to the exponent of the dominant term. In this case, the exponent is 4.
2. The maximum number of inversions in a list of 100 distinct elements is 4,950. This occurs when the list is sorted in descending order.
To calculate the maximum number of inversions, use the formula n * (n - 1) / 2, where n is the number of elements. In this case, n = 100, so the maximum number of inversions is 100 * 99 / 2 = 4,950.
3. The minimum number of inversions in a list of 100 distinct elements is 0. This occurs when the list is already sorted in ascending order, meaning no inversions are present.
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Determine whether the quadratic function y=x^2+6x+10 has a maximum or minimum value.
45. a survey conducted by the american automobile association showed that a family of four spends an average of $215.60 per day while on vacation. suppose a sample of 64 families of four vacationing at niagara falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $74.50. develop a 95% confidence interval estimate
The required 95% confidence interval representing the true population mean falls within the given interval, based on the given sample mean is equals to (233.00, 271.90).
Use the t-distribution,
To construct a confidence interval for the population mean,
The sample size is relatively small (n = 64)
And the population standard deviation is unknown.
The formula for the confidence interval is,
[tex]\bar{x}[/tex] ± tα/2 × (s/√n)
where [tex]\bar{x}[/tex] is the sample mean,
s is the sample standard deviation,
n is the sample size,
And tα/2 is the critical value of the t-distribution with (n-1) degrees of freedom, corresponding to the desired confidence level.
For a 95% confidence interval, the critical value of the t-distribution with 63 degrees of freedom is approximately 1.998.
Plugging in the given values, we get,
252.45 ± 1.998 × 74.50/√64)
Simplifying we get,
252.45 ± 19.45
This implies,
The 95% confidence interval for the mean amount spent per day by a family of four visiting Niagara Falls is (233.00, 271.90)
Therefore, 95% confidence interval that the true population mean falls within this interval, based on the given sample is (233.00, 271.90).
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The above question is incomplete , the complete question is:
A survey conducted by the American automobile association showed that a family of four spends an average of $215.60 per day while on vacation. suppose a sample of 64 families of four vacationing at Niagara falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $74.50.
a. Develop a 95% confidence interval estimate of the mean amount spent per day by a family of four visiting Niagara Falls (to 2 decimals).
question in picture below
The inequality shown by the graph is 4y+3x≤8x+2y+16 (option C).
Describe Inequality?In mathematics, an inequality is a statement that compares two values, expressing that one value is greater than, less than, or equal to the other. It is represented by symbols such as <, >, ≤, ≥, and ≠. For example, 5 > 3 is an inequality that means "5 is greater than 3", while 2x + 3 ≤ 7x - 2 is an inequality that means "the sum of 2 times x and 3 is less than or equal to 7 times x minus 2". Inequalities are commonly used in algebra, geometry, and real analysis to express relationships between quantities and to find solutions to equations and systems of equations.
To determine the inequality shown by the graph with coordinates (0,8) and (0, 3.25), we need to find the slope-intercept form of the equation for the line passing through these points.
The slope of the line is:
(y2 - y1) / (x2 - x1) = (3.25 - 8) / (0 - 0) = -4.75 / 0 (which is undefined)
Since the line is vertical, its equation is x = 0.
Substituting this into the inequality options, we can see that only option C results in a true statement:
A) 4y+3x≤8x+6y+16 -> 4(8) + 3(0) ≤ 8(0) + 6(8) + 16 -> 32 ≤ 64 (not true)
C) 4y+3x≤8x+2y+16 -> 4(8) + 3(0) ≤ 8(0) + 2(8) + 16 -> 32 ≤ 32 (true)
B) 4y-3x≤5x+2y+16 -> 4(8) - 3(0) ≤ 5(0) + 2(8) + 16 -> 32 ≤ 32 (true)
D) 4y-3x≤8x+2y+16 -> 4(8) - 3(0) ≤ 8(0) + 2(8) + 16 -> 32 ≤ 32 (true)
Therefore, the inequality shown by the graph is 4y+3x≤8x+2y+16 (option C).
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at the westside zoo there are 6 gorillas and 4 orangutans. at the central zoo there are 4 gorillas and 3 orangutans. do the two zoos have the same ratio of gorillas to orangutans? explain.
2:1
Step-by-step explanation:
So first you want to lay down all the information by writing down the number of gorillas and orangutans at Westside Zoo (6,4)
Next you want to write down the number of gorillas and orangutans at Central Zoo (4,3)
Now we want to put them in a subtraction like-form of equation
6-4 4-3
Now we take the remaining values and that's our answer for the ratio to gorillas and orangutans (2:1)
-Hope this helps!
?
What is 2+2 x 2+y equaled to
Answer:
6 + y
Step-by-step explanation:
By BODMAS rule,
1st : Multiply
Then add,
2 + 2 x 2 + y
2 + (2 x 2) + y
= 2 + 4 + y
= 6 + y
Which of the following equations will produce the graph shown below?
A. X^2- y^2/4= 1
B. Y^2/9 - x^2/4=1
C. Y^2- x^2/9= 1
D. Y^2/2 - x^2/4= 1
From following equations option B will produce the hyperbola graph shown in the figure
what is hyperbola ?
A hyperbola is a type of conic section, which is a curve that is formed by the intersection of a plane and a double cone. A hyperbola can also be defined as the set of all points in a plane, the difference of whose distances from two fixed points (called the foci) is a constant.
In the given question,
Based on the shape of the hyperbola shown on the y-axis graph, we can tell that the hyperbola has a vertical transverse axis, which means that its equation must have the form:
(y - k)² / a² - (x - h)²/ b² = 1
where (h, k) is the center of the hyperbola, a is the distance from the center to the vertices, and b is the distance from the center to the co-vertices.
Option A is not correct because it produces a hyperbola with a horizontal transverse axis, whereas the given graph has a hyperbola with a vertical transverse axis.
We can eliminate option D since its equation has a transverse axis that is not vertical.
Next, we can eliminate option A since the coefficient of x² is positive, which means that the transverse axis is horizontal.
Option C has a transverse axis that is also horizontal, so we can eliminate it as well.
That leaves us with option B, which has a vertical transverse axis and its equation fits the form we determined earlier. Therefore, the equation Y²/9 - x²/4=1 will produce the hyperbola shown on the y-axis graph
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a) Complete the number machine so that z = 5w-3 Input
Output z obtained as: multiply w with 5 and then subtract 3 from the result: w --> *5 ---> -3 ---> z.
Explain about the linear equations?There are only one or two variables in a linear equation.
No variable can be multiplied by a number larger than one or can be utilized as the denominator of either a fraction in a linear equation.All of the points fall on the same line when you identify the values that together constitute a linear equation true as well as plot those values on a coordinate grid. A linear equation has a straight line as its graph.The relationship involving distance and time in this equation will be linear for any provided steady rate. However, as distance is commonly defined as a positive number, the first quadrant of this relationship's graphs will typically include the only points.The given expression is:
z = 5w-3
Here:
Input value : 5w-3
Output value : z
So,
Output z obtained as:
multiply w with 5 and then subtract 3 from the result:
w --> *5 ---> -3 ---> z
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Write the expression as a single power of 6 6^8/6^4
To simplify this expression, we can use the rule of exponents that states when dividing two powers with the same base, we can subtract their exponents. Therefore:
6^8/6^4 = 6^(8-4) = 6^4
So the expression 6^8/6^4 can be simplified as a single power of 6, which is 6^4.
Show that if AB = AC and A is nonsingular, then the cancellation law holds; is, B = C.
When AB = AC and A is nonsingular, then the cancellation law holds; is, B = C. The statement is true.
In matrix algebra, the cancellation law is a crucial property to know. It states that if AB = AC, then B = C when A is a nonsingular matrix.
The given statement is true, which means that if AB = AC and A are nonsingular, then B = C. The cancellation law in matrix algebra is a property that helps in solving linear equations involving matrices. It states that if AB = AC and A is a nonsingular matrix, then B = C.
Therefore, we can say that if AB = AC and A is nonsingular, then B = C is true.
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Patricia has a savings account with $89 in it that earns 4.7% simple interest per year. How much money, to the nearest penny, will Patricia have in 5 years?
Answer:simpler interest is 109.92. Annual compounded interest is 111.98
Step-by-step explanation:
Answer: $209.2
Step-by-step explanation:
hey! i'm gonna try to make this as simple as possible;
with simple interest, the formula to this is I = PRT (Interest = Principle x Rate x Time).
we're going to take the $89 , 4.7% simple interest and the 5 years together into the same sentence like the formula.
89 (Principle, the money) x 4.7% (Interest rate) x 5 (Time). we'll narrow down the decimal by moving the decimal forward once so we get a decimal of .47 / 0.47.
back to the equation, it is now 89 x .47 x 5. multiply all those and you'll get a sum of 209.15! by the end of the five years, patricia will have $209.15. to the nearest penny, she will have $209.2. (5 or more, it goes to the next number. 4 or less, it stays in the same place.)
hope this helped :)
Ruby wants to make 45 cupcakes.
Use your answer to b) to work out fi she has enough sugar left.
Since Ruby has 3 cups of sugar left, she has enough sugar to make the 45 cupcakes she wants
How to solveIf Ruby needs 2 cups of sugar to make 45 cupcakes, then we can calculate how much sugar she needs for one cupcake by dividing 2 cups of sugar by 45 cupcakes:
2 cups of sugar / 45 cupcakes = 0.0444 cups of sugar per cupcake (rounded to 4 decimal places)
To make 45 cupcakes, Ruby would need:
45 cupcakes x 0.0444 cups of sugar per cupcake = 1.998 cups of sugar (rounded to 3 decimal places)
Since Ruby has 3 cups of sugar left, she has enough sugar to make the 45 cupcakes she wants (3 cups of sugar > 1.998 cups of sugar needed for 45 cupcakes).
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Ruby wants to make 45 cupcakes.
Use your answer to b) to work out fi she has enough sugar left.
Ruby needs 2 cups of sugar to make 45 cupcakes, and she has 3 cups of sugar left.
Pls helpppp and explain if you canI’ll mark you brainlist
Answer:
B) a 180° rotation about the origin
Step-by-step explanation:
Anyone know how to do this?
The value of length of side of triangle AD using the angle bisector theorem is obtained as: AD = 4.68.
Explain about the angle bisector theorem?Angles are measurements created by joining two lines, also known as the vertex. Geometric forms such as triangles but also rectangles contain internal angles produced by their sides.
The sum of the internal angles of each geometric figure gives it a general size. We can do operations like bisecting an angle geometrically.Every angle that is bisected is split into two equal-sized angles. Starting at the vertex that makes up the primary angle, the bisector is drawn.Using the angle bisector theorem in the given triangles:
The ratios of the sides will be equal.
AB / BC = AD / DC
AB = 9 ; BC = 11.7 AD = 3.6
Put the values.
9/11.7 = 3.6 / AD
AD = 3.6*11.7 / 9
AD = 4.68
Thus, the value of length of side of triangle AD using the angle bisector theorem is obtained as: AD = 4.68.
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168=18×x+12×2x
What is the value of x?
Answer:
X=4
Step-by-step explanation:
First you would simplify the numbers on the right which would give you 168=18x+24x. Since the two numbers have the same variable you can add them which would then give you 168=42x. Lastly you isolate the x by dividing 42 so that x=4.
Write a statement to match this number sentence. |-5| = |5|
Statement to match the given number sentence is The absolute value of -5 is equal to the absolute value of 5.
What is absolute value?It is the distance of a number from zero on a number line, and is always positive.
The absolute value of -5 is 5 because -5 is 5 units away from zero on the number line.
Similarly, the absolute value of 5 is 5 because 5 is also 5 units away from zero on the number line.
Therefore, the absolute value of -5 is equal to the absolute value of 5, and the statement for this number sentence is "The absolute value of -5 is equal to the absolute value of 5."
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Choose ALL answers that describe the polygon ABCD if measure A is congruent to measure B, and measure C is congruent to measure D.
and segment Ab is parallel to segment CD
Parallelogram
Quadrilateral
Rectangle
Rhombus
Square
Trapezoid
The answers that describe the polygon ABCD if measure A is congruent to measure B, and measure C is congruent to measure D, and segment AB is parallel to segment CD are;
A. Parallelogram
B. Quadrilateral
C. Rectangle
D. Rhombus
E. Square
What is a parallelogram?In Mathematics, a parallelogram simply refers to a four-sided geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that is composed of two (2) equal and parallel opposite sides.
What is a rhombus?In Mathematics and Geometry, a rhombus is a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent (equal).
In conclusion, a square, parallelogram, rectangle, rhombus, and quadrilateral satisfies the given conditions.
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can you please answer this for me
Answer:
x = 8
Step-by-step explanation:
the angle between the tangent and the radius at the point of contact A is 90°
then Δ ABP is right at A
using Pythagoras' identity in the right triangle
BP² = AP² + AB² , that is
(x + 9)² = x² + 15² ← expand parenthesis on left side using FOIL
x² + 18x + 81 = x² + 225 ( subtract x² from both sides )
18x + 81 = 225 ( subtract 81 from both sides )
18x = 144 ( divide both sides by 18 )
x = 8
What is the measure of angle ABC?
I measured it with a protractor and it is around 135 degrees.
I honestly don't know if this is correct but I hope this helps. Feel free to remove my answer if you think this is wrong.
In triangle rst, m∠r > m∠s m∠t. which must be true of triangle rst? check all that apply. m∠r > 90° m∠s m∠t < 90° m∠s = m∠t m∠r > m∠t m∠r > m∠s m∠s > m∠t
Only two options are necessarily true for the triangle,
m∠r > 90°
m∠s + m∠t < 90°
In any triangle, the sum of the three angles is 180 degrees. If m∠r > m∠s + m∠t, then angle r must be the largest angle in the triangle. Additionally, the sum of the other two angles (s and t) must be less than 90 degrees.
Option m∠s = m∠t is not necessarily true because the two angles could be different and still add up to be less than m∠r. Options m∠r > m∠t, m∠r > m∠s, and m∠s > m∠t are not necessarily true and depend on the specific values of the angles in triangle RST.
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sami planned to spend the weekend camping, so on friday night he drove from his house to the nearest campsite at a speed of 60 miles per hour. after the weekend was over, he went the same way home, but he drove at a speed of 40 miles per hour because of the bad weather. if altogether he spent a total of 7 hours driving, how many hours did the trip to the campsite take?
The trip to the campsite took 2 hours for Sami.
The total time taken by Sami on his journey = 7 hours
Let the time taken by Sami while going from his house to the campsite be 'x' hours
And, the time taken by Sami while coming back from the campsite to his house be 'y' hours
Speed while going from house to campsite = 60 miles per hour
Speed while coming back from campsite to house = 40 miles per hour
Distance from house to campsite and back will be equal as Sami will take the same route.
Let the distance be 'd'.
So, according to the question,
Distance = Speed × Time
We know that,
Time taken while going from house to campsite + Time taken while coming back from campsite = 7 hours
x + y = 7 ...(1)
Distance while going from house to campsite = Distance while coming back from campsited = 2d ...(2)
Distance = Speed × Timex = d/60 ...(3)
y = d/40 ...(4)
Substituting (2), (3) and (4) in (1), we get,
d/60 + d/40 = 7
Solving the equation, we get d = 120
Therefore, Time taken while going from house to campsite, x = d/60 = 2 hours
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please help i have until saturday
Considering the Pythagorean Theorem, we have that:
The length of the rectangular plot is of 264 ft.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.For this problem, we have that:
The sides are the length and 170 ft.The hypotenuse is of 314 ft.Hence the length is obtained as follows:
l² + 170² = 314²
l = sqrt(314² - 170²)
l = 264 ft.
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A nut store normally sells cashews for $4.00 per pound and peanuts for $1.50 per pound. But at the end of the month
the peanuts had not sold well, so, in order to sell 30 pounds of peanuts, the manager decided to mix the 30 pounds of
peanuts with some cashews and sell the mixture for $3.50 per pound. How many pounds of cashews should be
mixed with the peanuts to ensure no change in the revenue?
The manager should mix
pounds of cashews with the peanuts.
Therefore, the manager should not mix any cashews with the peanuts to ensure no change in revenue.
What is revenue?Revenue is the total amount of money a business or organization earns from selling goods or services during a specific period. It is calculated by multiplying the price of each unit sold by the total number of units sold. Revenue represents the income generated by a company's normal business activities and is used to pay for expenses, invest in future growth, and distribute profits to shareholders or owners. It is an important metric for measuring the financial health and performance of a business.
by the question.
Let's assume that x pounds of cashews are mixed with the 30 pounds of peanuts.
The total weight of the mixture would then be 30 + x pounds.
To ensure no change in revenue, the amount earned by selling the peanuts and cashews separately should be equal to the amount earned by selling the mixture.
The revenue earned by selling 30 pounds of peanuts is 30 x $1.50 = $45.
If y pounds of cashews are sold separately, the revenue earned would be y x $4.00 = $4y.
The total revenue earned by selling the peanuts and cashews separately would be $45 + $4y.
When the 30 pounds of peanuts and x pounds of cashews are mixed together and sold for $3.50 per pound, the total revenue earned would be (30 + x) x $3.50 = $105 + $3.50x.
Since the revenues from selling the mixture and selling the peanuts and cashews separately are equal, we can set the equations equal to each other and solve for x:
$45 + $4y = $105 + $3.50x
$3.50x - $4y = -$60
x - 4/7y = -60/7
We still have one unknown variable y, so we need another equation to solve for both x and y.
We know that the total weight of the mixture is 30 + x pounds. If we add y pounds of cashews to the mixture, the total weight becomes:
30 + x + y
We can set this equal to the total weight of the peanuts and cashews sold separately:
30 + y
Solving for y:
30 + x + y = 30 + y
x = 0
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The table represents some points on the graph of an exponential function
Which function represents the same relationship?
The function [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex] represents the same relationship.
Here given a function f(x)
When x= 0,1,2,3,4 the value of f(x) will be 648,216,72,24,8 respectively.
The function that represents the same relationship as the table is [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex]
We can see that each successive value of f(x) is one-third of the previous value. So, we know that the function is of the form [tex]f(x) = a { (\frac{1}{3} )}^{x} [/tex] for some constant a.
To find the value of a, we can use the fact that f(0) = 648.
Substituting x = 0 into the equation gives f(0) = a(1/3)⁰ = a = 648
So, the function is [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex]
Therefore, the correct answer is [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex]
So, option D is the correct option.
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