Therefore, the polynomial p(x) that satisfies the given conditions is:
p(x) = ax^3 + bx^2 + cx + d
p(x) = x^3 - 2x^2 + 3x + 23
So, p(2) = 1(2)^3 - 2(2)^2 + 3(2) + 23 = 9.
To find a polynomial p(2) of degree three, we need four pieces of information. We can use the given values to set up a system of linear equations:
-7a + 2b - 4c + d = 3
-a - b + c - d = 3
7a + b + c + d = -9
8a + 4b + 2c + d = -33
We can solve this system using any method of linear algebra. One way is to use row reduction:
[ -7 2 -4 1 | 3 ]
[ -1 -1 1 -1 | 3 ]
[ 7 1 1 1 | -9 ]
[ 8 4 2 1 | -33 ]
R2 + R1 -> R1:
[ -8 1 -3 0 | 6 ]
[ -1 -1 1 -1 | 3 ]
[ 7 1 1 1 | -9 ]
[ 8 4 2 1 | -33 ]
R3 - 7R1 -> R1, R4 - 8R1 -> R1:
[ -8 1 -3 0 | 6 ]
[ 0 -7 8 -1 | 51 ]
[ 0 -4 4 1 |-51 ]
[ 0 4 26 1 |-81 ]
R4 + R2 -> R2:
[ -8 1 -3 0 | 6 ]
[ 0 -3 34 0 | 30 ]
[ 0 -4 4 1 |-51 ]
[ 0 4 26 1 |-81 ]
R3 + (4/3)R2 -> R2:
[ -8 1 -3 0 | 6 ]
[ 0 -3 34 0 | 30 ]
[ 0 0 50 4 |-11 ]
[ 0 4 26 1 |-81 ]
R4 - (4/3)R2 -> R2, R3 - (5/6)R2 -> R2:
[ -8 1 -3 0 | 6 ]
[ 0 -3 34 0 | 30 ]
[ 0 0 8 4 |-34 ]
[ 0 0 8 1 |-103 ]
R4 - R3 -> R3:
[ -8 1 -3 0 | 6 ]
[ 0 -3 34 0 | 30 ]
[ 0 0 8 4 |-34 ]
[ 0 0 0 -3 |-69 ]
Now we can back-substitute to find the coefficients of the polynomial:
d = -69/(-3) = 23
c = (-34 - 4d)/8 = 3
b = (30 - 34c + 3d)/(-3) = -2
a = (6 + 3b - 3c + d)/(-8) = 1
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a student aimed to get a mean mark of 80% in his mathematics test after 9 tests his mean mark is 79%. Calculate the lowest mark he requires in his last test to enable him to achieve his target.
Answer:
89
Step-by-step explanation:
construct the formula to obtain the total of marks in first 9 tests:
79 = x/9
79 * 9 = 711
x = 711
so to get 80% in the next test we construct this formula:
80 = 711 + y / 9 + 1
the value we get for y is 89
to confirm the answer, 711+89/10 gives us 80, which is the correct value we want
Lulu has 10 feet of ribbon she uses 1 1/3 feet ribbon for a project she uses the rest of the ribbon to make bows she uses 8 inches of ribbon for each bowl how many does lulu make?
The number of bows Lulu can make from the remaining ribbon is 13 bows.
To find the remaining ribbon, first, convert 1 1/3 to an improper fraction (1*3 + 1 = 4, so 1 1/3 = 4/3). Now, subtract 4/3 from 10 feet.
10 - (4/3) = (30/3) - (4/3) = 26/3 feet of ribbon remaining.
She uses 8 inches of ribbon for each bow. Since there are 12 inches in a foot, convert the remaining ribbon to inches:
(26/3) * 12 = 104 inches of ribbon remaining.
Now, divide 104 inches by the 8 inches required for each bow to find the number of bows she can make:
104 / 8 = 13 bows.
Lulu can make 13 bows with the remaining ribbon.
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Amy graphed a function that gives the height of a car on a roller coaster as a function of time. She said her graph is the graph of a step function. Is this possible? Explain your reasoning
It is not possible for the graph of a height function of a car on a roller coaster to be a step function. Hence Amy is wrong.
A sort of function called a step function is one that only varies at discrete, isolated places in its domain and is constant everywhere else. A step function is one that "steps" down to the next integer at each integer input while remaining constant in between. An example of this is the floor function, which rounds down any input to the nearest integer.
On the other hand, it is doubtful that the height of a roller coaster car as a function of time is a step function because it is anticipated to fluctuate continually as opposed to hopping from one value to another at certain moments. Instead of abrupt increases in height that would be consistent with a step function, roller coasters often entail smooth, continuous curves and elevation changes.
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Prove that U(1, 1), Q(4,4), and A(6, 2) are the vertices of a right triangle. Â Use the following as a guide. Find the slopes of sides UQ, QA, and UA. Which segments are perpendicular? How do you know the segments are perpendicular? What are the lengths of each side? Use the Pythagorean Theorem to show that it is a right triangle. â
U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.
How do we know that UQ and QA are perpendicular?To determine whether U(1,1), Q(4,4), and A(6,2) form a right triangle, we will follow the given guide:
Find the slopes of sides UQ, QA, and UA:
Slope of UQ: (4-1)/(4-1) = 1Slope of QA: (2-4)/(6-4) = -1Slope of UA: (2-1)/(6-1) = 1/5Determine which segments are perpendicular and how we know they are perpendicular:
To determine if two lines are perpendicular, we need to check if their slopes are negative reciprocals of each other.
UQ and QA: Since the slope of UQ is 1 and the slope of QA is -1, we know that UQ and QA are perpendicular.UQ and UA: The slopes of UQ and UA are both positive, so they cannot be perpendicular.QA and UA: The slope of QA is -1, and the slope of UA is 1/5. Their product is -1/5, which is not -1, so QA and UA are not perpendicular.Find the lengths of each side:
Length of UQ: √[(4-1)² + (4-1)²] = √27Length of QA: √[(6-4)² + (2-4)²] = √8Length of UA: √[(6-1)² + (2-1)²] = √26Use the Pythagorean Theorem to show that it is a right triangle:
Since we have determined that UQ and QA are perpendicular, we can use the Pythagorean Theorem to show that it is a right triangle.
(Length of UQ)² + (Length of QA)² = (√27)² + (√8)² = 27 + 8 = 35(Length of UA)² = (√26)² = 26Since (Length of UA)² + (Length of QA)² = (Length of UQ)², we know that the triangle is a right triangle.
U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.
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HELP
Tom and Kim are playing a game in which they use a spinner with 10 sectors. One of the sectors says, "$0," four
say, "S100," three say, "$200," and two say, "$500. " Use a table to show the probability distribution.
Here is the probability distribution table:
|Outcome|Probability|
|-------|-----------|
|$0 |1/10 |
|S100 |4/10 |
|$200 |3/10 |
|$500 |2/10 |
To create the table, you simply list each possible outcome (in this case, the different amounts that could be won on the spinner), and then calculate the probability of each outcome occurring. In this case, there are 10 sectors in total, so the probability of landing on each sector is 1/10. There is 1 sector that says "$0," so the probability of getting that outcome is 1/10.
There are 4 sectors that say "S100," so the probability of getting that outcome is 4/10, or 2/5. Similarly, there are 3 sectors that say "$200," so the probability of getting that outcome is 3/10, or 3/10.
And finally, there are 2 sectors that say "$500," so the probability of getting that outcome is 2/10, or 1/5.
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What percent of the customers at the book sale spent less than 20 dollars? Show or explain how you got your answer
HELP - A strip of uniform width is plowed along all four sides of a 12-km by 9-km rectangular cornfield. How wide is the plowed strip of the cornfield is half plowed?
Answer:
Let's start by drawing a diagram of the cornfield with the plowed strip around it:
markdown
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_____________________________
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| _____________________|__
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|_______|_______________________|
The plowed strip has a uniform width, which we'll call w. We want to find w such that half of the cornfield is plowed.
The total area of the cornfield is:
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12 km x 9 km = 108 km^2
If we plow a strip of width w around the cornfield, the new dimensions of the cornfield will be:
scss
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(12 + 2w) km x (9 + 2w) km
The area of the plowed strip is the difference between the area of the new cornfield and the area of the original cornfield:
scss
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(12 + 2w)(9 + 2w) - 12(9) = 108 + 42w + 4w^2
We want half of the cornfield to be plowed, so we set the area of the plowed strip equal to half the area of the original cornfield:
scss
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108 + 42w + 4w^2 = (1/2)(108)
Simplifying, we get:
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4w^2 + 42w - 54 = 0
We can solve this quadratic equation using the quadratic formula:
css
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w = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 4, b = 42, and c = -54. Substituting these values, we get:
scss
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w = (-42 ± sqrt(42^2 - 4(4)(-54))) / 8
arduino
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w = (-42 ± sqrt(1936)) / 8
makefile
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w = (-42 ± 44) / 8
So we have two possible solutions:
makefile
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w = 1/2 km (discarded since it does not satisfy the given condition)
or
makefile
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w = 11/2 km
Therefore, the width of the plowed strip is 11/2 km = 5.5 km if half of the cornfield is plowed.
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Which type of sentence error occurs when a sentence is missing a subject or predicate? No error Fragment Subject -verb agreement Run-on
When the subject or predicate is missing from a sentence, the sentence error is a sentence fragment.
What is a sentence error?Sentence Errors are errors related to grammar and mechanics within sentences in Standard Written English.
An example of a sentence error will be "The children re us"
The phrase "re" is the error word in this sentence.
The three types of sentence errors we have are run-on sentences, sentence fragments and overloaded sentence.
In this problem, the type of sentence error that occurs when a sentence is missing a subject of predicate is a sentence fragment
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Maria claims that any fraction located between 1/5 and 1/7 on a number line must have a denominator of 6.
Enter a fraction to show Maria's claim is incorrect.
To show that Maria's claim is incorrect, we need to find a fraction that is located between 1/5 and 1/7 on a number line but does not have a denominator of 6.
One way to do this is to find the least common multiple (LCM) of 5 and 7, which is 35, and then find a fraction with a denominator of 35 that falls between 1/5 and 1/7.
To do this, we can find the equivalent fractions of 1/5 and 1/7 with a denominator of 35:
1/5 = 7/35
1/7 = 5/35
Now we need to find a fraction between 7/35 and 5/35. One such fraction is:
6/35
This fraction is located between 7/35 and 5/35 on the number line, but its denominator is 35, not 6. Therefore, Maria's claim is incorrect.
Another way to show that Maria's claim is incorrect is to find a counterexample by simply listing all the fractions between 1/5 and 1/7 and showing that not all of them have a denominator of 6. For example:
1/6, 1/7, 1/8, 1/9, 1/10, ..., 1/34, 1/35
As we can see, not all of these fractions have a denominator of 6, so Maria's claim is incorrect.
Answer:
13/70
Step-by-step explanation:
In order to show that Maria's claim is incorrect, we need to find a fraction that is located between 1/5 and 1/7 on a number line, but does not have a denominator of 6.
Let's find the common multiple (CM) of 5 and 7, which is 70, or 35. But this case try 70 and then find a fraction with a denominator of 70 that falls between 1/5 and 1/7.
equivalent fractions of 1/5 and 1/7 with a denominator of 70
1/7 < x < 1/5 , will be equivalent to 1/7 ( 10/10 ) < x < 1/5 ( (14/14)
10/70 < x < 14/70..
x is the fraction between 10/70 and 14 /70. Unknown fraction is:
13/70
This fraction is located between 10/70 and 14/70 on the number line, but its denominator is 70 , not 6. Therefore, Maria's claim is incorrect.
Ben and his housemates signed a lease for an apartment for 12 months for $563 per month of which ben agreed to pay $215 per month. which of the following statements best gives the reasons that ben’s rent payment is an essential (fixed) expense? a. it cannot be eliminated in a later budget, in order to save money. b. living expenses have a higher priority than any other type of expense. c. the spender controls the amount of the rent by choice of apartment. d. he agreed to pay the same amount every month. please select the best answer from the choices provided a b c d
The statements that gives the best reasons that ben’s rent payment is an essential (fixed) expense is he agreed to pay the same amount every month. The correct answer is D.
In personal finance, an essential expense is a regular expenditure that is necessary for maintaining a basic standard of living. These expenses are typically fixed, meaning that they do not fluctuate from month to month, and are difficult or impossible to eliminate without sacrificing basic needs like food, housing, or healthcare.
Since, this is his rent, the amount of money that he is legally bound to pay every month in order to keep on living in that location.
He has an agreement with his landlord to pay $215 each month and thus he has to do it.
Essential expenses are often considered a top priority in budgeting because they are critical to maintaining health, safety, and overall well-being. In the given scenario, Ben's rent payment is an essential expense because it is a fixed expense that is necessary for maintaining his housing, which is a basic need. The correct answer is D.
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Solve for q q : 30 + q = 43 30+q=43
The solution to the equation 30 + q = 43 is q = 13.
What is the value of q?Given the equation in the question:
30 + q = 43
To determine the value of q in the equation 30 + q = 43, isolate q on one side of the equation by performing the same operation on both sides of the equation.
30 + q = 43
q + 30 = 43
Next, we can isolate q by subtracting 30 from both sides of the equation:
q + 30 - 30 = 43 - 30
q = 43 - 30
Subtract 30 from 43
q = 13
Therefore, the value of q is 13.
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Boris's backyard has cement and grass. Find the area of the part with cement.
(Sides meet at right angles. )
4 m
1 m
2 m
grass
5 m
3 m
cement
5 m
The constant of proportionality between the number of yards Jackson can mow and the number of hours is 3/4.
To find the area of the part with cement, we need to find the area of the entire rectangle and then subtract the area of the part with grass.
The area of the rectangle is: length x width = 5 m x 4 m = 20 m²
The area of the part with grass is: length x width = 3 m x 2 m = 6 m²
So the area of the part with cement is:
20 m² - 6 m² = 14 m²
Therefore, the area of the part with cement is 14 square meters.
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The figure shown is composed of two congruent triangles and a square Measurements are given in inches 6 in 5 in 4 in A 5 in What is the total area of the figure in square inches 5 in 4 in 5 in
Answer:
60 square inches
Step-by-step explanation:
Pt refers to Pythagoras Theorem. You know two sides of a right angled triangle, how do you find the 3rd side? Pythagoras Theorem. Then the rest is easy. Just do the area of all of the 4 triangles and the area of the square and add them up
A pyramid 5 meters high has congruent triangular sides and a square base that is 5 meters on each side. Each cross section of the pyramid parallel to the base is a square. What is the volume of the solid in cubic meters?
The volume of the pyramid is approximately 41.67 cubic meters.
How to find the volume?To find the volume of the pyramid, we can use the formula:
V = (1/3) x base area x height
Since the base of the pyramid is a square with side length 5 meters, its area is:
base area = side² = 5² = 25 square meters
The height of the pyramid is also given as 5 meters.
Now, we need to find the area of one of the square cross-sections. Since the pyramid has congruent triangular sides, we know that each of these triangles is similar to the original base square.
Therefore, the side length of each square cross-section is proportional to the height of the pyramid, and we can use the ratio of corresponding side lengths to find the area of one of the squares:
5 / 5 = x / 5
where x is the side length of the square cross-section.
Solving for x, we get:
x = 5
Therefore, each of the square cross-sections has an area of 5 x 5 = 25 square meters.
Now, we can substitute the values we have found into the formula for the volume:
V = (1/3) x base area x height
= (1/3) x 25 x 5
= 41.67 cubic meters
Therefore, the volume of the pyramid is approximately 41.67 cubic meters.
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ASAP PLEASE HELP!!
I’ll give brianest
Given that the length of arc DC is 9. 77 inches and the radius of the circle is 8 inches.
to the nearest degree, what is the mZDPC?
The mZDPC is approximately 15 degrees.
How we find the mZDPC?We know that the length of an arc of a circle is given by the formula:
length of arc = (central angle / 360°) × 2πr
where r is the radius of the circle.
In this case, the length of arc DC is 9.77 inches and the radius of the circle is 8 inches. Let's use the above formula to find the central angle mZDPC:
9.77 = (mZDPC / 360°) × 2π(8)
Simplifying this equation, we get:
mZDPC = (9.77 / (2π(8) / 360°))
mZDPC = (9.77 / 0.670206) degrees
mZDPC ≈ 14.58 degrees
Rounding to the nearest degree, we get:
mZDPC ≈ 15 degrees
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order: baraclude (entecavir) 0.5mg PO daily. The drug is an oral
solution with strength of 0.05 mg/mL. How many mL will you
administer?
10mL of the baraclude oral solution to the patient.
To determine the amount of the oral solution of baraclude (entecavir) to administer, we need to use the following formula:
Amount to administer (mL) = Desired dose (mg) / Strength (mg/mL)
In this case, the desired dose is 0.5mg and the strength is 0.05mg/mL. Plugging in these values, we get:
Amount to administer (mL) = 0.5mg / 0.05mg/mL = 10mL
Therefore, you will administer 10mL of the baraclude oral solution to the patient.
Hi! To calculate the number of mL to administer, you need to consider the prescribed dose and the strength of the oral solution. The order is for Baraclude (entecavir) 0.5mg PO daily, and the solution's strength is 0.05 mg/mL.
To find the required mL, divide the prescribed dose by the solution's strength:
0.5 mg (prescribed dose) ÷ 0.05 mg/mL (solution's strength) = 10 mL
You will administer 10 mL of Baraclude (entecavir) oral solution daily.
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Find the linearization of the function at the given point. f(x, y) = e-¹⁰x-⁸y - 8y at (0, 0) A) L(x, y) = -8x - 10y B) L(x, y) = -8x - 10y + 1 C) L(x, y) = -10x - 8y + 1 D) L(x, y) = -10x - 8y
The linearization of the function f(x, y) = e-¹⁰x-⁸y - 8y at (0, 0) is L(x, y) = -10x - 8y + 1. The correct option is C.
To find the linearization of the given function at the point (0, 0), we need to compute the partial derivatives with respect to x and y and then evaluate them at the given point.
The function is f(x, y) = [tex]e^{(-10x-8y)[/tex] - 8y.
First, find the partial derivative with respect to x:
∂f/∂x = [tex]-10e^{(-10x-8y).[/tex]
Now, evaluate ∂f/∂x at (0, 0):
∂f/∂x(0, 0) = [tex]-10e^{(0)[/tex] = -10.
Next, find the partial derivative with respect to y:
∂f/∂y = [tex]-8e^{(-10x-8y)[/tex] - 8.
Now, evaluate ∂f/∂y at (0, 0):
∂f/∂y(0, 0) = [tex]-8e^{(0)[/tex] - 8 = -8 - 8 = -16.
Now, we can form the linearization:
L(x, y) = f(0, 0) + ∂f/∂x(0, 0)(x - 0) + ∂f/∂y(0, 0)(y - 0).
Evaluate f(0, 0):
f(0, 0) = [tex]e^{(-10(0)-8(0))} - 8(0) = e^{(0)} - 0 = 1.[/tex]
Finally, substitute the values into the linearization formula:
L(x, y) = 1 - 10x - 16y.
Comparing to the given options, the answer is:
C) L(x, y) = -10x - 8y + 1
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How do I do number 3?
Answer:
V = 1,728 mi³
SA = 864 mi²
Step-by-step explanation:
We can find the volume of the triangular prism by multiplying the area of one of the triangle faces by the prism's depth.
First, we can solve for the area of one of the triangle sides:
A(triangle) = (1/2) · b · h
A(triangle) = (1/2) · 24 · 18
A(triangle) = 12 · 18
A(triangle) = 216 mi²
Next, we can get the volume of the prism by multiplying the area of the triangle face by the prism's depth.
V = A(triangle) · depth
V = 216 · 8
V = 1,728 mi³
__
We can find the surface area by finding the area of each side, then adding all of those areas together.
We already know that the area of each of the triangle sides is 216 mi².
Now, we can solve for the area of the base.
A(base) = length · width
A(base) = 24 · 8
A(base) = 192 cm²
Then, we can find the area of the top side.
A(top) = length · width
A(top) = 30 · 8
A(top) = 240 mi²
Finally, we can solve for the surface area of the prism by adding the areas of each of its sides.
SA = (2 · A(triangle)) + A(base) + A(top)
SA = 2(216) + 192 + 240
SA = 432 + 192 + 240
SA = 624 + 240
SA = 864 mi²
Rewrite 32 1/2 as a radical form
Therefore, 32 1/2 can be written as a radical form of 32 + √2.
What is fraction?In mathematics, a fraction is a numerical quantity that represents a part of a whole or a ratio between two numbers. Fractions are written in the form of one integer, called the numerator, written above a line, and another integer, called the denominator, written below the line. The denominator represents the total number of equal parts into which a whole is divided, while the numerator represents the number of those parts being considered.
Here,
We can write 32 1/2 as a mixed number, which is equivalent to the fraction 65/2. To express 65/2 as a radical form, we can simplify the fraction by finding a perfect square that divides evenly into both the numerator and the denominator. In this case, 4 is a perfect square that divides into 64 (the nearest perfect square to 65) and 2, so we can write:
65/2 = (64 + 1)/2
= 64/2 + 1/2
= 32 + 1/2
Now, we can express the fraction 1/2 as a radical by taking the square root of the denominator, which gives:
32 1/2 = 32 + √2
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Un hacendado compro "5" pollos y "8" conejos por $517,00 y una semana despues a los mismos precios compro "8" pollos y "11" por $761. 00 HALLAR EL COSTO DE UN POLLO Y DE UN CONEJO NOTA: Resolver por el metodo de sustitucion
Using substitution method, the cost of a chicken is $44.56 and the cost of a rabbit is $36.78.
Let's use the substitution method to solve the problem.
Let's assume that the cost of a chicken is "x" dollars and the cost of a rabbit is "y" dollars.
From the first statement, we know that:
5x + 8y = 517 --- equation (1)
And from the second statement, we know that:
8x + 11y = 761 --- equation (2)
Now we can solve for one of the variables in terms of the other from one of the equations, and then substitute that expression into the other equation to solve for the remaining variable.
Solving equation (1) for "y", we get:
y = (517 - 5x) / 8
Now we can substitute this expression for "y" into equation (2), and solve for "x":
8x + 11[(517 - 5x) / 8] = 761
Multiplying both sides by 8 to eliminate the fraction, we get:
64x + 11(517 - 5x) = 6088
Expanding the brackets, we get:
64x + 5687 - 55x = 6088
Combining like terms, we get:
9x = 401
Dividing both sides by 9, we get:
x = 44.56
So the cost of a chicken is $44.56.
Now we can substitute this value for "x" into equation (1) to solve for "y":
5(44.56) + 8y = 517
Simplifying, we get:
222.80 + 8y = 517
Subtracting 222.80 from both sides, we get:
8y = 294.20
Dividing both sides by 8, we get:
y = 36.78
So the cost of a rabbit is $36.78.
Therefore, the cost of a chicken is $44.56 and the cost of a rabbit is $36.78.
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What is the equation of a circle with center (2,3) that passes through the point (5, 3)?
The equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]
To find the equation of a circle with center (2, 3) that passes through the point (5, 3), we'll need to use the standard equation of a circle and the given information.
The standard equation of a circle is[tex](x - h)^2 + (y - k)^2 = r^2[/tex], where (h, k) is the center and r is the radius.
Step 1: Substitute the center coordinates (h, k) = (2, 3) into the equation:
[tex](x - 2)^2 + (y - 3)^2 = r^2[/tex]
Step 2: Use the point (5, 3) to find the radius. Plug the coordinates of the point into the equation and solve for [tex]r^2[/tex]:
[tex](5 - 2)^2 + (3 - 3)^2 = r^2\\3^2 + 0^2 = r^2\\9 = r^2[/tex]
Step 3: Plug[tex]r^2[/tex] back into the equation:
[tex](x - 2)^2 + (y - 3)^2 = 9[/tex]
So, the equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]
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a manufacturing machine has a 80% defect rate. if 109 items are chosen at random, answer the following. a) which is the correct wording for the random variable? select an answer b) pick the correct symbol: ?
The correct words are number of defective items from the sample of 109 items chosen at random and correct symbol is X ~ B(109, 0.8).
Percent of defective rate in manufacturing machine = 80%
Random number of items chosen = 109
The correct wording for the random variable in this situation is,
The number of defective items in a sample of 109 items chosen at random from the manufacturing machine.
Number of defective items is successes.
A common symbol for the number of successes in a binomial distribution is X.
Use X to represent the random variable in this situation.
The notation for the binomial distribution is usually written as,
X ~ B(n, p)
where X is the random variable,
n is the sample size,
and p is the probability of success on each trial.
X ~ B(109, 0.8).
Therefore, the correcting wording is number of defective items in a sample of 109 items chosen at random and the correct symbol is equal to X ~ B(109, 0.8).
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Complete the sentence.
The focus so far has been on similar triangles, but there are also theorems that deal with similar
The focus so far has been on similar triangles, but there are also theorems that deal with similar polygon
Completing the sentenceTheorems of similar triangles are important properties that hold true for any pair of similar triangles. Some of the most commonly used theorems are:
AA Similarity Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
SSS Similarity Theorem: If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar.
SAS Similarity Theorem: If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar.
These theorems are also applicable to similar polygons
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The focus so far has been on similar triangles, but there are also theorems that deal with similar polygons.
At the airport, there are three counters for checking the luggage. the employees at each counter work independently with the time for each customer modeled as an exponential distribution. the average time is one minute for one counter, two for the next, and three minutes for the third. an actuary, who is next in line, will take the next available counter, i. e. the minimum of the three. what is the variance of the actuary's wait time
The variance of the actuary's wait time is 36 / 121.
How to calculate the varianceFrom the information, at the airport, there are three counters for checking the luggage. the employees at each counter work independently with the time for each customer modeled as an exponential distribution. the average time is one minute for one counter, two for the next, and three minutes for the third. an actuary, who is next in line, will take the next available counter,
From the complete question, the variance of the actuary's wait time will be:
= 1 / (11/6)²
= (6/11)²
= 36 / 121
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Helppppppppppppppppp
Answer:
it would be at point (6,3)
Step-by-step explanation:
If you were to reflect it over the x-axis you would get (-6,3)
Find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis.
Ilull = 5, Ou = 0°
I|v|I = 2, Ov = 60°
The component form of u + v can be found using the given lengths and angles and it is (6, √3).
To find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis we will sum the u and v.
Given Ilull = 5 and Ou = 0°, we can represent vector u as (5, 0) in component form. Given |Iv|I = 2 and Ov = 60°, we can represent vector v as (2cos60°, 2sin60°) = (1, √3) in component form.
To find u + v, we add the corresponding components of u and v. This gives us:
u + v = (5, 0) + (1, √3) = (5+1, 0+√3) = (6, √3)
Therefore, the component form of u + v is (6, √3).
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Ken bought a car last year to drive back and forth to work. Last year he spent $1,098 on gas. This year, it was $1,562. What is the inflation rate?
The inflation rate for Ken's gas expenses between the two years is approximately 42.26%.
To calculate the inflation rate for Ken's gas expenses, we can use the following formula: (Current Year Expense - Previous Year Expense) / Previous Year Expense × 100%.
In this case, the previous year's gas expense was $1,098 and the current year's expense is $1,562.
To find the difference in expenses, subtract the previous year's expense from the current year's expense: $1,562 - $1,098 = $464.
Now, divide this difference by the previous year's expense: $464 / $1,098 ≈ 0.4226.
Finally, multiply the result by 100% to get the inflation rate: 0.4226 × 100% ≈ 42.26%.
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Please Help!!
Use the credit card information below and the designated method of computing interest to fill in the blanks. (See image)
Adjusted Balance Method-
Interest $______
New Balance $______
Using the Adjusted Balance Method:
Interest: $4.15
New Balance: $569.15
How to solveTo calculate the interest and new balance using the Adjusted Balance Method, we need to first find the adjusted balance.
This method takes the previous balance, adds the purchases made before the payment, and then subtracts the payment.
Here's the calculation:
Calculate the adjusted balance:
Previous balance: $500
Purchases before May 20: $25 (May 12)
Subtotal: $525
Payment: $110
Adjusted balance: $525 - $110 = $415
Calculate the interest:
Interest rate: 1% per month
Interest: $415 * 1% = $4.15
Calculate the new balance:
Adjusted balance: $415
Purchases after May 20: $100 (May 22) + $50 (May 30) = $150
Interest: $4.15
New balance: $415 + $150 + $4.15 = $569.15
So, using the Adjusted Balance Method:
Interest: $4.15
New Balance: $569.15
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For each set of data, describe the shape of the
distribution and determine which measures of
center and spread best represent the data.
15. 28, 13, 23, 34, 55, 38, 44, 65, 49, 33, 50, 59,
67, 45
The shape of the distribution in histogram is skewed left and mean=43.071429 and standard deviation= 15.886445 are used together to measure the center and spread of the data.
What is histogram?
A grouped frequency distribution with continuous classes is graphically represented by a histogram. It is an area diagram, and its size is proportional to the frequencies in the associated classes. Due to the base's coverage of the spaces between class boundaries, all of the rectangles in such representations are contiguous.
We can make a sideways histogram. (makes it easier if typing text, but if you are writing on paper then you don't have to make it sideways) Each row will represent a range of 10 (1st row is 10 to 19, 2nd row is 20 to 29, etc)
=> 13 23 28 33 34 38 44 45 49 50 55 59 65 67
The data looks like it is slightly skewed left (hump towards the right [down]). The mean and the standard deviation are used together to measure the center and spread of the data.
Mean = [tex]\frac{ 13+23+28+33+34+38+44+45+49+50+55+59+65+67}{14}=\frac{603}{14}[/tex] = 43.071429
Standard deviation = 15.886445
Hence the shape of the distribution in histogram is skewed left and mean=43.071429 and standard deviation= 15.886445 are used together to measure the center and spread of the data.
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I NEED HELP WITH THIS ONE AND ANOTHER PLEASE
The missing lengths of BE and IJ using the concept of similar quadrilaterals are:
BE = 32
IJ = 18
How to find the lengths of similar quadrilaterals?Similar quadrilaterals are defined as quadrilaterals that have the same shape, but their sizes may vary. Thus, if two quadrilaterals are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
From the image, we are told that Quadrilateral GHIJ is similar to Quadrilateral BCDE.
Thus:
GJ/BE = IJ/DE = HI/CD
Thus:
12/BE = 6/16
BE = (16 * 12)/6
BE = 32
Similarly:
IJ/48 = 6/16
IJ = (48 * 6)/16
IJ = 18
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