After answering the prοvided questiοn, we can cοnclude that Sο, we can equatiοn chοοse values οf a and b such that Cοv(X¯, μ) < (1 − a)/2 σ/n and MSE(θˆ) > MSE(θ), like a = 0.9 and b = 0.5.
What is equatiοn?An equatiοn in mathematics is a prοcedure that affects the equaIity οf equatiοns. Twο sides οf an equatiοn are cοnnected by the algebraic οperatοr (=). Fοr instance, the claim "2x + 3 = 9" asserts that the cοmment "2x + 3" means the value "9" in tοtal. The gοal οf sοlving equatiοns is tο identify the factοr(s) that will cause the equatiοn tο be true.
Equatiοns may be straightfοrward οr cοmplex, cοnstant οr nοn-linear, and cοntain οne οr mοre variables. Examples include raising the variable x tο the pοwer οf 2 in the equatiοn "x² + 2x - 3 = 0," fοr example. In mathematics, particularly in algebra, equatiοns, and geοmetry, lines are frequently used.
MSE(θˆ) = E[(θˆ − θ)²]
= E[((X1 + · · · + Xn)/n − μ²)²]
= E[((X1 − μ) + · · · + (Xn − μ))/n]²
= V[(X1 − μ)/n + · · · + (Xn − μ)/n]
= V[(X1 − μ)/n] + · · · + V[(Xn − μ)/n] (since the Xi's are independent)
Thus, MSE(θˆ) = σ²/n
b. Fοr MSE(θˆ) < MSE(θ), we want:
We can see that this is satisfied fοr any value οf a such that 0 < a < 1.
c. Fοr MSE(θˆ) > MSE(θ), we want:
σ/n > V[(1 − a)X¯ + aμ] = (1 − a)²Var(X¯) + aVar(μ) + 2a(1 − a)Cοv(X¯, μ)
σ²/n > (1 − a)(σ²/n) + 2a(1 − a)Cοv(X¯, μ)
Cοv(X¯, μ) < (1 − a)/2 σ²/n
Sο, we can chοοse values οf a and b such that Cοv(X¯, μ) < (1 − a)/2 σ/n and MSE(θˆ) > MSE(θ), such as a = 0.9 and b = 0.5.
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The graph shows the velocity versus time for 4 different cars on a race track. If all four cars have the same mass, which one experiences the largest net force?
Answer:
Step-by-step explanation: 1
the diameter of a spherical balloon is 21.6 centimeters
The parameter for determining the diameter of an object depends on the specific object being measured. Here are some examples of parameters that can be used to determine diameter the answer is 5276.7 cm3. Thus, option D is correct.
What are the parameter for determining the diameter?The formula for the volume of a sphere is [tex]V = (4/3)πr^3[/tex] , where r is the radius of the sphere.
Since we are given the diameter of the sphere, we can find the radius by dividing the diameter by 2:
[tex]r = 21.6 cm / 2 = 10.8 cm[/tex]
Substituting this value into the formula, we get:
[tex]V = (4/3)\pi(10.8)^3[/tex]
[tex]= 4.18879 \times (10.8)^3[/tex]
[tex]= 5276.794 cm^3[/tex]
Rounding to the nearest tenth, we get:
[tex]V \approx 5276.8 cm^3[/tex]
Therefore, the answer is D) 5276.7 cm3.
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The given question is incomplete. the complete question is given below.
The diameter of a sphere is 21.6 cm. What is the sphere's volume? Round to the nearest tenth, if necessary. A) 693.2 cm3 B) 1453.8 cm3 C) 1868.5 cm3 D) 5276.7 cm3
Help with this problem guys
→no trolling please i really need it ←
FACE is a rhombus the following measures are 9. CY= 39.05 cm, 10. FC= 40 cm, 11. AY ≈ 39.05 cm, 12. YE = 20 cm, 13. FA ≈ 39.05 cm, 14. AC ≈ 48.99 cm, 15. Perimeter ≈ 156.20 cm.
Describe Rhombus?A rhombus is a quadrilateral with all four sides of equal length. It is also known as a diamond or a lozenge. The opposite sides of a rhombus are parallel to each other, and the diagonals of a rhombus bisect each other at a right angle. Additionally, the diagonals of a rhombus are perpendicular bisectors of each other. This means that they split the rhombus into four congruent right triangles.
Since FACE is a rhombus, all four sides are equal in length. Additionally, the diagonals bisect each other at a right angle, so we can use the Pythagorean theorem to find the lengths of various segments in the figure.
9. CY: Since FC is a diagonal of the rhombus, it bisects angle FCE. This means that triangle FCY is a right triangle with FC as the hypotenuse and FY and CY as the legs. Using the Pythagorean theorem, we can find that CY is:
CY² = FC² - FY²
CY² = 40² - 15²
CY² = 1525
CY ≈ 39.05 cm
10. FC: We already know that FC = 40 cm, since it is one of the diagonals of the rhombus.
11. AY: By symmetry, we know that AY is equal in length to CY, so AY ≈ 39.05 cm.
12. YE: Since YE is half of EA, and we know that EA = 40 cm, we can find that YE = 20 cm.
13. FA: Since all four sides of the rhombus are equal, FA has the same length as CY and AY, so FA ≈ 39.05 cm.
14. AC: Since AC is a diagonal of the rhombus, it bisects angle EAF. This means that triangle ACE is a right triangle with AC as the hypotenuse and AE and EC as the legs. We can use the Pythagorean theorem to find that:
AC² = AE² + EC²
AC² = 40² + 2*(YE)²
AC² = 40² + 2*(20²)
AC² = 1600 + 800
AC² = 2400
AC ≈ 48.99 cm
15. Perimeter of the given rhombus FACE: Since all four sides of the rhombus are equal, we can find the perimeter by multiplying the length of one side by 4. Using any of the values we found above for the length of a side, we get:
Perimeter = 4*CY
Perimeter ≈ 156.20 cm
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Answer:
9. CY = 15 cm
10. FC = 30 cm
11. AY = 20 cm
12. YE = 20 cm
13. FA = 25 cm
14. AC = 25 cm
15. Perimeter FACE = 100 cm
Step-by-step explanation:
In a rhombus:
All sides of a rhombus are congruent.The diagonals are perpendicular bisectors of each other.Given the diagonals bisect each other, Y is the point of intersection, and CY = 15 cm, then:
[tex]\begin{aligned}\overline{FY} &= \overline{CY} \\&= 15 \; \sf cm\end{aligned}[/tex]
[tex]\begin{aligned}\overline{FC} &= \overline{FY} + \overline{CY} \\&= 15 + 15 \\&= 30 \; \sf cm\end{aligned}[/tex]
Given the diagonals bisect each other, Y is the point of intersection, and EA = 40 cm, then:
[tex]\begin{aligned}\overline{AY}&=\overline{EA} \div 2\\&=40 \div 2\\&=20\; \sf cm\end{aligned}[/tex]
[tex]\begin{aligned}\overline{YE} &= \overline{AY} \\&= 20 \; \sf cm\end{aligned}[/tex]
As the diagonals bisect each other at 90°, m∠FYA = 90°. Therefore, triangle FYA is a right triangle.
As we know the lengths of legs of the triangle FYA, we can use Pythagoras Theorem to calculate the length of the hypotenuse (FA).
[tex]\begin{aligned}\overline{FY}^2+\overline{AY}^2&=\overline{FA}^2\\15^2+20^2&=\overline{FA}^2\\225+400&=\overline{FA}^2\\625&=\overline{FA}^2\\\overline{FA}&=\sqrt{625}\\\overline{FA}&=25\; \sf cm\end{aligned}[/tex]
As the sides of a rhombus are equal in length:
FA = EC = AC = FE = 25 cmThe perimeter of rhombus FACE is the sum of its side lengths:
[tex]\begin{aligned}\sf Perimeter&=\overline{FA}+\overline{EC}+\overline{AC}+\overline{FE}\\&=25+25+25+25\\&=100\; \sf cm\end{aligned}[/tex]
Note: The attached diagram is drawn to scale.
State any excluded values of a domain and identify the type of break in the graph at the value of x
f(x)=x+7/x-2
Answer:
The excluded value in the domain is x = 2 because the denominator of the rational function becomes zero at this value of x, which results in division by zero.
At x = 2, there is a vertical asymptote, which means that the graph of the function approaches positive or negative infinity as x approaches 2 from either side.
Sierra left $4.50 as a tip for a waiter. This was 18% of the bill before the tip. How much was her total bill before the tip?
$
Answer$81
Step-by-step explanation:
Question 14
Josh used the zeros of a polynomial to sketch the following graph of the function.
based on the graph above what are the zeros of the polynomial?
help me pls D:
quiz
The zeros of the polynomial are given as follows:
Option B: (3,0) and (-2,0)
What are the zeros of the polynomial?The zeros of a polynomial function are the values of the independent variable (usually denoted by x) that make the function equal to zero. In other words, they are the values of x for which the function crosses the x-axis.
The values of x for which the graph of the polynomial crosses the x-axis are given as follows:
x = -2 and x = 3.
At these points, the y-coordinate is of zero, hence the points on the graph are given as follows:
(3,0) and (-2,0).
Meaning that the correct option is given by option B.
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2 dot plots with the same number of data points.
Look at these dot plots. Which statement is true about the two data sets?
A Both have the same mode.
B Both have a gap between 28 and 31.
C Both have the same range.
D Both have the same number of data points.
Answer: is d
explain your answer
I’m thinking of three numbers: X, Y, and Z. We have X ≤ Y ≤ Z. The median of the
three numbers is 90, the mean of the three numbers is 92, and the range of the three
numbers is 6. What are the values of X, Y, and Z? Show your work
The X, Y, and Z values are 84, 90, and 90, respectively. To answer this question, we need to understand the meaning of the words "median", "mean" and "range".
What is median?Median is the middle number of a set of numbers - it is the number in the middle when the numbers are ordered from smallest to largest.
Since the median is 90, this means that Y (the mean number) is 90. Since the average is 92, this means that the sum of the three numbers is 276 (92 x 3). The interval is 6, which means that the difference between the largest number and the smallest number is 6.
To solve for X and Z, we can use the equation X Y Z = 276. We know that Y is 90, so we can plug 90 into Y:
X 90 Z = 276
Then we can subtract 90 from both sides to find the value of X and Z:
X Z = 186
Since the range of the three numbers is 6, this means that X and Z must be 6 plus. The only two numbers that differ by six and add up to 186 are 84 and 90.
Therefore the X, Y, and Z values are 84, 90, and 90, respectively.
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I need to find f(g) f(x) please
The answers f(g(x)) = x and g(f(x)) = x tell us that the two functions f(x) and g(x) are inverses of each other.
What is inverse?The inverse of a function is a second function that "undoes" the effect of the first function. More specifically, if f is a function that maps elements from a set A to a set B, then its inverse function, denoted as f^(-1), maps elements from B back to A.
According to question:(a) To find f(g(x)), we need to substitute the expression for g(x) into f(x):
f(g(x)) = g(x) / (6 + g(x))
Substituting the expression for g(x) yields:
f(g(x)) = (6x / (1 - x)) / (6 + (6x / (1 - x)))
This equation can be made simpler by first locating a common denominator:
f(g(x)) = (6x / (1 - x)) / ((6(1 - x) / (1 - x)) + (6x / (1 - x)))
f(g(x)) = (6x / (1 - x)) / ((6 - 6x + 6x) / (1 - x))
f(g(x)) = (6x / (1 - x)) / (6 / (1 - x))
f(g(x)) = 6x / 6
f(g(x)) = x
To find g(f(x)), we need to substitute the expression for f(x) into g(x):
g(f(x)) = 6f(x) / (1 - f(x))
Substituting the expression for f(x) yields:
g(f(x)) = 6(x / (6 + x)) / (1 - (x / (6 + x)))
To simplify this expression, we can first find a common denominator:
g(f(x)) = 6(x / (6 + x)) / (((6 + x) / (6 + x)) - (x / (6 + x)))
g(f(x)) = 6(x / (6 + x)) / ((6 + x - x) / (6 + x))
g(f(x)) = 6(x / (6 + x)) / (6 / (6 + x))
g(f(x)) = x
(b) The answers f(g(x)) = x and g(f(x)) = x tell us that the two functions f(x) and g(x) are inverses of each other. This means that when we apply one function and then the other, we get back to the original input value. Specifically, if we apply f(x) to x and then apply g(x) to the result, we get x back, and if we apply g(x) to x and then apply f(x) to the result, we also get x back. This is a useful property when analyzing functions and their relationships.
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Kim invested $200 and it increases by 20% each month for 1 year. How much money will she have after 1 year? Show the equation.
Answer:
(200x20%)(12)=$480
Step-by-step explanation:
1. 200x20%=$40
There are 12 months in a year
2. 40x12= $480
Can someone help me please
$4000 are invested in a bank account at an interest rate of 10 percent per year.
Find the amount in the bank after 7 years if interest is compounded annually.
--------------
Find the amount in the bank after 7 years if interest is compounded quarterly.
---------------
Find the amount in the bank after 7 years if interest is compounded monthly.
---------------
Finally, find the amount in the bank after 7 years if interest is compounded continuously.
---------------
Answer:
To find the amount in the bank after 7 years, we can use the formula:
A = P(1 + r/n)^(nt)
where:
A = the amount in the bank after 7 years
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
For the given problem:
P = $4000
r = 10% = 0.1
t = 7 years
a) Compounded Annually:
n = 1
A = 4000(1 + 0.1/1)^(1*7) = $7449.36
b) Compounded Quarterly:
n = 4
A = 4000(1 + 0.1/4)^(4*7) = $7650.13
c) Compounded Monthly:
n = 12
A = 4000(1 + 0.1/12)^(12*7) = $7727.27
d) Compounded Continuously:
n → ∞ (as n approaches infinity)
A = Pe^(rt) = 4000e^(0.1*7) = $8193.85
Therefore, the amount in the bank after 7 years increases as the compounding frequency increases. If interest is compounded continuously, the amount in the bank will be the highest.
The quadrilateral on the graph below is rotated about the point (0, 0). What are the new coordinates of Point B and Point C after a 90 degree clockwise rotation?
A 90 degree clockwise rotation about the point (0,0), the new coordinates of Point B are (3, -1) and the new coordinates of Point C are (1, -2).
How do you check if a quadrilateral is a rectangle on a graph?A quadrilateral can be proven to be a rectangle in a number different ways. Here are the three simplest methods: 1. Establish that all angles are 90 degrees; 2. Establish that two opposed angles are 90 degrees; and 3. Establish that the diagonals are equally long and intersect one another.
The following transformation matrix can be used to rotate a point (x,y) 90 degrees clockwise with respect to the origin (0,0):
|0 1|\s|-1 0|
This transformation matrix can be applied to each point to determine its new coordinates upon rotation.
Point B is the first point, and its initial coordinates are (-1, 3). The transformation matrix in use:
|0 1| |-1| |3|
|-1 0| x |3| = |-1|
After rotating Point B 90 degrees clockwise, the new coordinates are: (3, -1).
The transformation matrix is then applied to Point C, whose initial coordinates are (2, 1):
|0 1| |2| |1|
|-1 0| x |1| = |-2|
After rotating in a clockwise direction by 90 degrees, Point C's new coordinates are (1, -2).
As a result, after rotating 90 degrees in a clockwise direction around Point 0, Point B's new coordinates are (3, -1), while Point C's new coordinates are (1, -2).
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Write the next three terms of the geometric sequence where a_1 = - 8 and r = -2
a_1 = -8
a_2 =
a_3 =
a_4 =
Answer:
a_2 = 16
a_3 = -32
a_4 = 64
Step-by-step explanation:
Multiply each term by r to get the next term.
a_1 = -8
a_2 = -8 × (-2) = 16
a_3 = 16 × (-2) = -32
a_4 = -32 × (-2) = 64
In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.
Using trigonometric functions, we can find that the value of the angle N is 3°.
What are trigonometric functions?The six fundamental trigonometric operations make up trigonometry. Trigonometric ratios are useful for describing these methods. The sine, cosine, secant, co-secant, tangent, and co-tangent functions are the six fundamental trigonometric functions. On the ratio of a right-angled triangle's sides, trigonometric identities and functions are founded. Trigonometric formulas are used to determine the sine, cosine, tangent, secant, and cotangent values for the perpendicular side, hypotenuse, and base of a right triangle.
Here, using the cosine theorem:
CosM = n² + l² - m²/2nl
⇒ Cos 149° = 27² + 70² - m²/2 × 27 × 70
⇒ -0.981 = 729 + 4900 - m²/3780
⇒ 5629 - m² = -3708
⇒ m² = 9337.
Now Cos N = m² + l² - n²/2ml
= (9337 + 4900 - 729) / (2 × √9337 × 70)
= 0.9985
Cos N = 0.9985
Putting [tex]Cos^{-1}[/tex] on both sides:
[tex]Cos^{-1}[/tex] Cos N = [tex]Cos^{-1}[/tex] 0.9985
⇒ N ≈ 3°
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The complete question is:
In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.
What is What is the meaning of "bidule"?
Step-by-step explanation:
In French, "bidule" is a slang term that can be used to refer to an unspecified object or thing. It can also be used to refer to a person in a vague or non-specific way
Scientists are making an aerial study of a volcano. Their helicopter is circling at a 4 km radius around the volcano's crater, and one of the scientists notices a new vent that is 45° east of due south from the crater. What is the position of the new vent relative to the crater?
Answer:
2√2 km south and 2√2 km west of the volcano's crater.
Step-by-step explanation:
If the scientist is at the center of the circle with the volcano's crater, then the new vent is located 45° east of due south, or 135° counterclockwise from due north.
To describe the position of the new vent relative to the crater, we can use the bearing or direction angle, which is the angle between the north direction and the line connecting the crater and the new vent, measured counterclockwise.
To find the bearing, we can draw a right triangle with the hypotenuse equal to the distance from the center of the circle to the new vent, which is also the radius of the circle, or 4 km. The opposite side of the triangle is the north-south component of the line connecting the crater and the new vent, which is equal to the radius times the sine of the angle between the line and due south. The adjacent side is the east-west component of the line, which is equal to the radius times the cosine of the angle.
Using trigonometric functions, we can calculate:
Opposite side = 4 km x sin(135°) = 4 km x (-√2/2) = -2√2 km (southward direction)
Adjacent side = 4 km x cos(135°) = 4 km x (-√2/2) = -2√2 km (westward direction)
Therefore, the new vent is located 2√2 km south and 2√2 km west of the volcano's crater. Its position relative to the crater can be described as "southwest by south."
Express using algebra.
24% of z
Answer: 0.24z
Step-by-step explanation: If you make 24% a decimal you will get 0.24. Then you make your equation 0.24z or 0.24 x z .
En un canal se necesitan diariamente 36 kg de maiz para alimentar a 480 gallinas ¿Cuantos kg se necesitan ahora si se vendieron 120 gallinas?
Resolver con reglla de 3
Answer:
Step-by-step explanation: it is -2x + 430298= -9n79000.
Identify the nonlinear equation.
Responses
A y = 3x - 7y = 3 x - 7
B y = xy = x
C y = 3y = 3
D y = x2
PLS HELP
Answer:y=0.5
Step-by-step explanation:Comme tu peux le voir, y est égal à au tiers de 3, se qui équivaut à 1. Si 2x=y, cela signifie que x=y/2, soit 0,5
At Spirit Night slices of pizza cost $2 and pretzels cost $1. The school store sold 150 items and made a total of $250. Write a systems of
equations to represent the situation where x represents the number of slices of pizza sold and y represnts the number o pretzels
Answer:
[tex]x + y = 150[/tex]
[tex]2x + y = 250[/tex]
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Given circle E with diameter CD and radius EA. AB is tangent to E at A. If
EC = 3 and EA = 3, solve for AC. Round your answer to the nearest tenth if
necessary. If the answer cannot be determined, click "Cannot be determined."
C
A
B
The circle E with diameter CD and radius EA having the length of AC is approximately 4.2 units.
What is Pythagoras' Theorem?
In a right-angled triangle, the square of the hypotenuse side equals the sum of the squares of the other two sides.
Since EA is a radius of circle E, and AB is tangent to E at A, we know that AB is perpendicular to EA. Thus, triangle EAB is a right triangle.
Let x be the length of AC. Then, by the Pythagorean Theorem in triangle EAC, we have:
[tex]AC^{2} = EA^{2} +EC^{2}[/tex]
[tex]AC^{2} = 3^{2} + 3^{2}[/tex]
[tex]AC^{2} = 18[/tex]
AC ≈ 4.2 (rounded to the nearest tenth)
Therefore, the length of AC is approximately 4.2 units.
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solve equation
log 4x=2
Answer: x=25
Step-by-step explanation:
log 10 4x = 2
10^2 = 4x
100 = 4x
25 = x
m grade> Y.4 Area and perimeter: word problems JFR
A rectangular garage is 6 meters wide and 7 meters long. What is its perimeter?
Answer:
26 meters
Step-by-step explanation:
To solve the perimeter you need to know the formula which is 6 + 7 x 2 and you get 26 meters
0.83 divided by 2.1995
It’s about 0.3773.
Just a quick question, why didn’t you use a calculator?
How to get the unadjusted cost of sales in cost and management accounting
Answer:
Step-by-step explanation:
To calculate unadjusted cost of goods sold, sum the beginning inventory value and the cost of goods manufactured, then subtract the ending inventory value.
b. Rewrite 4 x 63 as the product of a unit fraction and a whole number.
Solve.
Rewriting 4 x 3/6 as the product of a unit fraction and a whole number is: 12 * 1/6
How to multiply fractions?The parameters are given as:
Number - 4
Fraction - 3/6
The following steps can be used to determine the product as the product of a whole number and a unit fraction:
Step 1 - Remember the whole number are those numbers that involve all positive integers and zero.
Step 2 - Also remember that the unit fraction is nothing but a fraction whose numerator is 1.
Step 3 - Write the given expression.
4 * 3/6
Step 4 - Convert the given fraction into a unit fraction by multiplying 4 by 3 in the above expression.
4 * 3 * 1/6
Step 5 - Simplify the above expression.
12 * 1/6
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What is the area of the composite figure?
Answer:
It is the area of combined shapes of one or more simple polygons and circles.
A rectangular box has a length that is 4 feet longer than its width, w.
Write an algebraic expression, in simpliest form, to find the perimeter of the box.
Step-by-step explanation:
The length of the rectangle is 4 feet longer than its width w, which means the length is w + 4
The perimeter of a rectangle is the sum of the lengths of all four sides which can be expressed as:
Perimeter = 2(length + width)
Substituting w + 4 for length and w for width, we get:
Permiter = 2(w + 4 + w)
Simplifying this expression, we get:
Perimeter = 2(2w + 4)
Perimeter = 4w + 8
Therefore, the algebraic expression to find the perimeter of the rectangular box is 4w + 8
You have been asked to build a scale model of your school out of toothpicks. Imagine your school is 30 feet tall. Your scale is 1 ft:1.68 cm.
If a toothpick is 6.3 cm tall, how many toothpicks tall will your model be?
The model will be
toothpicks tall.
Your mother is out of toothpicks, and suggests you use cotton swabs instead. You measure them, and they are 7.6 cm tall. How many cotton swabs tall will your model be? If necessary, round your answer to the nearest whole number.
The model will be approximately
cotton swabs tall.
Answer:
8 toothpicks
7 cotton swabs
Step-by-step explanation:
Since the school is 30 feet tall and the scale is 1 ft : 1.68 cm, 30 feet will require a scale model of 1.68 x 30 = 50.4 cm
Since each toothpick is 6.3 cm tall, the total number of toothpicks required for 50.4 cm = 50.4/6.3 = 8 toothpicks
If using cotton swabs each 7.6 cm tall, the number of cotton swabs would be 50.4/7.6 = 6.63
Rounding this to the nearest number means you will need 7 cotton swabs
Ezra works two summer jobs to save for a laptop that costs at least $1100 he charges $15/hr to mow lawns and $10 an hour to walk dogs. Recall the inequality that represents this situation: 15x + 10y >_ 110
is (60,20) a solution? How do you know? What does this power represent?
Answer:
The inequality that represents this situation is 15x + 10y ≥ 1100, since Ezra needs to earn at least $1100 to buy the laptop.
To check if (60, 20) is a solution to this inequality, we need to substitute x = 60 and y = 20 into the inequality and see if it is true:
15(60) + 10(20) ≥ 1100
900 + 200 ≥ 1100
1100 ≥ 1100
Since 1100 ≥ 1100 is true, this means that (60, 20) is a solution to the inequality. This means that if Ezra works 60 hours mowing lawns and 20 hours walking dogs, he will earn enough money to buy the laptop.
The point (60, 20) represents the combination of hours worked for mowing lawns (x) and walking dogs (y) that will result in Ezra earning enough money to buy the laptop. The x and y values are the inputs or variables, while the inequality 15x + 10y ≥ 1100 is the constraint that must be satisfied. The solution (60, 20) is the output or result of the system of inequalities, and represents the combination of hours worked that will satisfy the constraint.