Answer:
The company is expected to make [tex]\$ 1[/tex] on every extended warranty sold.
Step-by-step explanation:
Let [tex]X[/tex] denote whether a product with the extended warranty requires replacement in that two years. ([tex]X\![/tex] would be a random variable.) Assume that [tex]X = 1[/tex] means that the product requires replacement, and [tex]X = 0[/tex] otherwise.
Assume that this product requires replacement in that two years. That is: [tex]X = 1[/tex]. The company would then bear a cost of [tex]200 \times 1 =200[/tex] for replacing this product (since [tex]X = 1\![/tex], that cost would be the same as [tex]200 = 200 \times 1 = 200\, X[/tex].)
On the other hand, assume [tex]X = 0[/tex] (that is: this product does not require replacement in that two years.) The company would not need to pay for replacing this product. Since [tex]X = 0\![/tex], the expression [tex]200\, X[/tex] would still represent the cost for the company for this warranty.
Either way, [tex]200\, X[/tex] would denote the replacement cost that the company would bear for this product. However, given that the company would charge [tex]\$ 11[/tex] for the extended warranty, the net revenue of the company on this warranty would be [tex]((-200) \, X + 11)[/tex]. (An earning of [tex]\$11 \![/tex] minus a spending of [tex]200\, X \![/tex].)
The question states that [tex]0.5\%[/tex] of the products would need replacement in this period. In other words, the expected value of [tex]X[/tex] would be [tex]\mathbb{E}(X) = 0.005[/tex].
The expected revenue of the company on this warranty would be:
[tex]\mathbb{E}(200\, X + 11)[/tex].
Apply the linearity of expected values to find the value of [tex]\mathbb{E}(200\, X + 11)[/tex]:
[tex]\begin{aligned}& \mathbb{E}((-200)\, X + 11) \\ &= (-200)\, \mathbb{E}(X) + 11 \\ &= (-200) \times 0.005 + 11 = 1\end{aligned}[/tex].
Hence, the company is expected to make [tex]\$ 1[/tex] on every extended warranty that it sold.
2x < 8 I need help with this question please
The required solution of the given inequality 2x < 8 is x < 4.
What is Inequality?A connection in mathematics that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line. A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance. Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
The given inequality is
2x < 8
According to given question we have
Write inequality
2x < 8
Divide both sides by 2 we get,
x < 4
Therefore, the required solution of the given inequality 2x < 8 is x < 4.
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Given f(x) = 2x2 - 2x - 4, find f(3).
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~[tex]\qquad \sf \dashrightarrow \: f(x) = 2 {x}^{2} - 2x - 4[/tex]
[tex]\qquad \sf \dashrightarrow \: f(3) = 2(3) {}^{2} - 2(3) - 4[/tex]
[tex]\qquad \sf \dashrightarrow \: f(3) = 2(9) {} - 6- 4[/tex]
[tex]\qquad \sf \dashrightarrow \: f(3) = 18{} - 10[/tex]
[tex]\qquad \sf \dashrightarrow \: f(3) = 8[/tex]
What is the circumference of a circle whose diameter is 15 niches
The circumference of a circle with a given diameter of 15 inches is equal to 15pi which is equal to 47.12 inches.
What is the circumference of a circle?The circumference of a circle is the distance around the edge of the circle.
What is the formula for calculating the circumference of a circle?The formula for calculating the circumference of a circle is given by,
C = 2πr = πd
Where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle and d is the diameter.
It is also known as the perimeter of the circle.
In the question above, we're given,
Diameter of the circle (d ) = 15 inches.
So, using the formula for the circumference of the circle,
Circumference (c) = π d
= π * 15
= 47.12 inches
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statistical methods that use sample data to answer general questions about a population are called
Inferential statistics is a branch or method of statistics that makes the use of various analytical tools to draw or conclude inferences about the population data from sample data. Apart from inferential statistics, another part is descriptive statistics forms another branch of statistics.
Inferential statistics help to make conclusions about the population while descriptive statistics summarizes the features of the data set.
Inferential statistics helps to develop a good grasp of the population data by analyzing the samples obtained from it.
It helps in making concept about the population by using different analytical tests and tools.
Inferential statistics can be classified into two types of hypothesis testing and regression analysis. Hypothesis testing also includes the use of belief intervals to test the parameters of a population.
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Evaluate the following expression if w= 9, x= 7, and y= 1.
11y-5
106
16
6
7
Answer:
357
Step-by-step explanation:
whats the answer for
(x+1)(x+5)=(x+3)(x-4) +3
Answer: x = -2
Step-by-step explanation: Divide each side by factors that do not contain the variable to isolate it.
Can someone please tell me how do we solve this? Thank you.
Answer:
C
Step-by-step explanation:
jason paid 12.75 for 5.5 pounds of hamburger. how many dollars per pound
Answer: ≈2.32
Step-by-step explanation: So, we can solve this in 2 ways:
1) 12.75 / 5.5 (easiest way)
= 2.3181818181818183
(Rounded to the nearest hundredth) ≈ 2.32
2) Set up a proportional relationship:
[tex]\frac{12.75}{5.5}[/tex] = [tex]\frac{?}{1}[/tex]
Now, divide 12.75 by 5.5, and get about 2.32
Now, let's check our answer:
2.32 x 5.5 = 12.76
So, he paid about 2.32 per pound.
I hope this helped!
a florist has 133 roses.she sold 5/7 of them how many roses are left with her
A. 58
B. 38
C. 57
D. 19
Which inequality represents the phrase “A number plus 5 is greater than 12?”
Answer:
the solution and explanation/work is in the images
Answer:
x+5 > 12
Step-by-step explanation:
A number plus 5 is greater than 12 represents x + 5 > 12.
Tyrell is traveling to Chicago, Illinois. He takes a cab service from the airport to his hotel. The table shows the linear relationship between the number of miles the cab travels, x, and the total fee, y.
Cab Fare
Number of Miles ---- Total Fee
2 Miles ---------------- $15.00
5 Miles ---------------- $19.50
7 Miles ---------------- $22.50
10 Miles ---------------- $27.00
15 Miles ---------------- $34.50
What does the y-intercept mean in this situation?
A) When the cab travels 0 miles, the total fee will be $1.50.
B) When the cab travels 0 miles, the total fee will be $12.00.
C) For every additional mile the cab travels, the total fee increases by $1.50.
D) For every additional mile the cab travels, the total fee increases by $12.00.
The meaning of the y-intercept in this situation is ,
''For every additional mile the cab travels, the total fee increases by $12.00.''
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
From the table, we have the following parameters:
Points (x, y) = (2, 5) and (15.00, 19.50)
So, we would calculate the slope as follows:
Slope = (19.50 - 5)/(15.00 - 2)
Slope = 14.50/13
Slope = 1.11
Hence, We get;
Fixed fee = $15 - (1.12 x 2)
= $15 - 2.24 ≈ $12.00
So, We get;
For every additional mile the cab travels, the total fee increases by $12.00.
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How much solutions does this equation have
y= 1/4x+1
y=1/4x-1
Answer: No Solution
Step-by-step explanation:
There is no solution.
A set of equations with the same slopes and different y-intercepts have no solution.
find the vertices of this hyperbola 36x^2-y^2-216x+10y+261=0
The required vertices of hyperbola is given as (3, 5±√38).
What is an hyperbola?Hyperbola is part of conic section, and its equation is given as,
[tex](x - h)^2/a^2 + (y - k)^2/b^2 = 1[/tex], where h,k is center and a and b are the lengths of the semi-major and the semi-minor axes.
Here,
Given equation of hyperbola,
36x²-y^²-216x+10y+261=0
Equation of hyperbola in vertex form is given as,
(x - 3)²/(19/18) - (y - 5)²/38 = 1
From above equation,
h = 3 k = 5 a = √38/6 and b = √38
Vertices of the hyperbola is given as,
(h, k ± b) = (3, 5±√38)
Thus, the required vertices of hyperbola is given as (3, 5±√38).
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determine whether the graphs of each pair of equations are parallel, perpendicular, or neither.
y=-2x
2x+y=3
Answer:
parallel
Step-by-step explanation:
solve for the second equation so y is by itself
y=-2x+3
their slopes are the same so they're parallel
Which statement is correct
The yard is an English unit of length in both the British imperial and US customary systems of measurement equalling 3 feet or 36 inches.
Since 1959, it has been precisely standardised to 0.9144 metres per international agreement. The word "yard" comes from the Old English word "gerd," "gyrd," etc., which was used for measuring sticks, staves, and branches.
The term first appears in the late 7th-century regulations of Ine of Wessex where "yard of land" refers to the yardland, an ancient English tax assessment unit equivalent to one-fourth of a hide.
Around the same time, it was substituted for a branch moved by the wind in the Lindisfarne Gospels description of the messengers from John the Baptist in the Gospel of Matthew. In addition to the yardland, surveying lengths of 15 feet (4.6 m) or 16.5 feet were also referred to as "yards" in Old and Middle English (5.0 m).
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Answer:The correct statement among the given options is:
StartFraction 1 inch Over 2.54 centimeters EndFraction = StartFraction 7 inches Over 17.68 centimeters EndFraction SO 1 is the answer.
below you are given a partial excel output based on a sample of 16 observations
(tables)
The estimated regression equation is
a. Ey) = Bo + B1x12x2
b. y Bo + B1x1 + B₂X2 + €
c. 94.425 +2.63 x₁ + 12.56 x2
d. 9 = 12.924-3.682 x + 45.216 x2
The estimated regression equation is :
ŷ = 12.924 - 3.682[tex]x_{1}[/tex] + 45.216[tex]x_{2}[/tex]
S0, option(d) is the correct answer.
In statistics, an estimated regression equation is an equation constructed to model the relationship between dependent and independent variables.
The least squares method is the most widely used method for developing estimates of the model parameters.
For simple linear regression, the least squares estimates of the model parameters β0 and β1 are indicated [tex]b_{0}[/tex] & [tex]b_{1}[/tex]. Using these approximates, an estimated regression equation is constructed: ŷ = [tex]b_{0} + b_{1} x[/tex] . The graph of the estimated regression equation for simple linear regression is a straight-line approximation of the relationship between y and x.
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Carlos filled up a 15 gallon bucket with water in 150 seconds. At what rate, in gallons per second, did Carlos fill the bucket?
Answer:
Every 10 seconds is 1 gallon
A circle is inscribed into a square, find the area of the circle if one side of the square is 15 m
Answer:
follow me if this helped you
Step-by-step explanation:
Area of inscribed square.
A circle is inscribed into a square, find the area of the circle if one side of the square is 15 m
The diameter of the inscribed circle is equal to the length of the square's diagonal, which is equal to the length of one side of the square multiplied by the square root of 2 (since the diagonal of a square is equal to the square root of 2 times the length of one side). Therefore, the diameter of the inscribed circle is 15m * sqrt(2) = 15m * 1.41421356237 = 21.213203435596424m
The area of a circle is given by the formula A = π * r^2, where r is the radius of the circle. Since the diameter of the circle is 21.213203435596424m, the radius is half of that, which is 10.60660171779821m.
So the area of the circle is A = π * r^2 = π * 10.60660171779821^2 = 353.09
two functions f and g are defined over the set r of real numbers as follows: f:x > x^2-2x-1 and g:x > x-1. find the value of x for which f(x)=g(x)-2
The values of x for which f(x) = g(x) - 2 are given as follows:
x = 1 and x = 2.
How to solve the equation?The functions for this problem are defined as follows:
f(x) = x² - 2x - 1.g(x) = x - 1.The equation is given as follows:
f(x) = g(x) - 2.
Replacing the values, we have that:
x² - 2x - 1 = x - 1 - 2
x² - 2x - 1 = x - 3
x² - 3x + 2 = 0.
We can factor the equation as follows:
(x - 2)(x - 1) = 0.
Hence the solutions are obtained as follows:
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Factor completely, use the formula
a³ - 6³ = (a - b)(a² + ab + b²)
3
8m³ - 1
Using the formula a³ – b³ = (a – b)(a² + ab + b²), we have factor (8m – 1)(64m² + 8m + 1).
What is factor?Factors are the positive integers that can divide a number evenly in mathematics. Say we want to create a product by multiplying two numbers. The factors of the product are the number that is multiplied. Each number has its own factor.
Examples of factors in real life include putting candies in a box, arranging numbers in a pattern, giving chocolates to kids, and many more.
Factors are the figures that can divide an amount precisely. As a result, there is no remainder after division. Factors are the sums of numbers that you multiply to produce another number. A factor is therefore the divisor of another number.
Using the formula
a³ – b³ = (a – b)(a² + ab + b²)
8m³ - 1³ = (8m – 1)(8m² + 8m + 1²)
8m³ - 1³ = (8m – 1)(8m² + 8m + 1²)
8m³ - 1³ = (8m – 1)((8m)² + 8m + 1²)
8m³ - 1³ = (8m – 1)(64m² + 8m + 1)
8m³ - 1³ = (8m – 1)(64m² + 8m + 1)
Thus, Using the formula a³ – b³ = (a – b)(a² + ab + b²), we have factor (8m – 1)(64m² + 8m + 1)
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B varies directly as m. A study shows that m= 6 when b = 5.
The value for the proportional constant, for given data, is 5/6.
What is a Linear Function?A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0. Nevertheless, calculus and linear algebra are also used to represent linear functions.
Given that b varies directly as m
so b ∝ m
it says b is directly proportional to m,
removing the proportional sign apply a constant k,
b = km
where k is the proportional constant,
and m = 6 and b = 5
5 = 6k
k = 5/6
Hence the value of the constant is 5/6.
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What’s 30/50 in simplest for?
Answer:
Step-by-step explanation:
3/5 because 10 is their GCF
Answer:
The answer is 3/5
Step-by-step explanation:
30/50 > 6/10 >3/5
Just divide 30/50 (both numbers by 5) and then divide 6/10 (both numbers by 2). Hope this helped :)
Solve the following problem using the substitution method.
y= (-3x -2)
6x - 2y = 1
Answer:
(x,y) = (-1/4, -5/4)
Step-by-step explanation:
To solve the system of equations using the substitution method, we can start by solving one equation for one variable in terms of the other. Let's start by isolating y in the first equation:
y = -3x - 2
Now we can substitute this expression for y into the second equation:
6x - 2(-3x - 2) = 1
Simplifying this, we get:
6x + 6x + 4 = 1
12x + 4 = 1
12x = -3
x = -3/12 = -1/4
Now we can substitute this value of x back into the first equation to solve for y:
y = -3(-1/4) - 2 = 3/4 - 2 = -5/4
So the solution of this system of equations is (x,y) = (-1/4, -5/4)
You can check this solution by substitute these values back into the original equation and check that both are correct.
Tell me if this helped :)
Answer:
( - [tex]\frac{1}{4}[/tex], [tex]\frac{-5}{4}[/tex] )
Step-by-step explanation:
Substitute -3x - 2 for y
6x - 2y = 1
6x -2(-3x - 2) = 1
6x + 6x + 4 = 1 Combine like terms
12x + 4 = 1 Subtract 4 from both sides
12x + 4 - 4 = 1 - 4
12x = -3 Divide both sides both sides by 12
[tex]\frac{12x}{12}[/tex] = [tex]\frac{-3}{12}[/tex]
x = - [tex]\frac{1}{4}[/tex]
Substitute - [tex]\frac{1}{4}[/tex] for x to solve for y
y = -3x - 2
y = (-3)[tex]\frac{-1}{4}[/tex] - 2
y =[tex]\frac{3}{4}[/tex] - 2
y = [tex]\frac{3}{4}[/tex] - [tex]\frac{8}{4}[/tex]
y = [tex]\frac{-5}{4}[/tex]
The following values are placed on a number line: 170%, one and two over five, and 0.3.
Which of the following images shows the correct placement of the values?
Number line starting at negative 0.4 on the left up to 2.4 on the right. Units are marked every two tenths unit. 0.3 is labeled at 0.3. One and two fifths is labeled at 1.2, and one hundred seventy percent is labeled at 1.6.
Number line starting at negative 0.4 on the left up to 2.4 on the right. Units are marked every two tenths unit. 0.3 is labeled at 0.3. One and two fifths is labeled at 1.4, and one hundred seventy percent is labeled at 1.7.
Number line starting at negative 0.4 on the left up to 2.4 on the right. Units are marked every two tenths unit. 0.3 is labeled at 0.3. One hundred seventy percent is labeled at 0.7, and one and two fifths is labeled at 1.4.
Number line starting at negative 0.4 on the left up to 2.4 on the right. Units are marked every two tenths unit. 0.3 is labeled at 0.3. One and two fifths is labeled at 1.2, and one hundred seventy percent is labeled at 1.5.
Given the number lines (attached) the correct one is Option B) because it represents the right placement of values.
What is a number line?A number line is a depiction of a graded straight line that serves as a visual representation of real numbers in primary mathematics. Every point on a number line is presumed to be a real number, and every real number is assumed to be a point.
We can tell that option B is correct because:
0.3 is placed right after 0.2 and before 0.3;1 2/5 (which is the same as 1.4) is placed right above 1.4; and 170% which is the same as 1.7 is placed right after 1.6 and just before 1.8.Thus, option B is correct in the given number line.
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which set of ordered pairs best represents the linear function f(x) = 1/2x + 2 ?
The set of ordered pairs that best represents the linear function f(x) = (1/2)x +2 is the third option.
H { (-4, 0), (-1, 1.5), (2, 3), (4, 4)}
Which set of ordered pairs best represents the linear function?We want to see which one of the given sets best represents the linear function:
f(x) = (1/2)x +2
To identify the correct option, we need to see which set of ordered pairs only includes points that are on the linear equation.
For example, the first set starts with the point (-4, -7.5)
Replacing these values in our function we will get:
-7.5 = (1/2)*-4 + 2
-7.5 = -2 + 2
-7.5 = 0
This is false, so we can discard the first equation.
(We also can see that f(-4) = 0, so we can also discard the second option).
Now let's look at the third option, the second point is (-1, 1.5)
f(-1) = 1.5 = (1/2)*-1 + 2
1.5 = -0.5 + 2
1.5 = 1.5
This point belongs to the functions graph.
(and on the other set we have the point (-1, 3), that point clearly does not belong to the graph, so we can also discard this option).
Finally, the only remaining option is the third one, H.
{ (-4, 0), (-1, 1.5), (2, 3), (4, 4)}
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Aimee is estimating 315 x 47 by first
rounding to 1 s.f.
Which of these calculations should Aimee
use?
300 × 0
300 × 50
320 × 0
315 × 50
320 × 50
315x0
300 × 47
315x47
320 × 47
For estimation, she have to make calculation as 320x50/
How do I round to the nearest significant digit?Using one significant figure as an example 3692 should be converted to one square foot (s.f.). The number 3 is the first significant digit because it is the first non-zero digit.6 exceeds 5 in number.We round up because 6 is greater than 5 One plus three equals four, and 3692 is four thousand square feet.
How are estimates calculated?each number to the nearest significant figure.Use the 'approximately equal to' symbol to build the new estimated calculation.Consider units when calculating and use the rounded numbers to provide an approximation.
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which expression is equivalent to 19÷6•3+2
19/6 * 3+2, expression is equivalent to 19÷6•3+2
What are equivalent expressions?Expressions that are equivalent do the same thing even when they have distinct appearances.
When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
We may be given equations with algebraic expressions on both sides in some situations.
The two expressions on either side of the equation must be comparable in order for the equation to hold true for all values of the variable. F
Hence, 19/6 * 3+2, expression is equivalent to 19÷6•3+2
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What is the measure
Answer:
Angle FSM = 92° OPTION B
Step-by-step explanation:
[tex]5x+32=7x+8[/tex]
[tex]5x-7x=8-32[/tex]
[tex]-2x=-24[/tex]
[tex]x=\frac{-24}{-2} =12[/tex]
Angle FSM:
[tex]FSM=7x+28=7(12)+8=84+8=92[/tex]
Hope this helps
What’s the numerator for the following rational expression?s/t +7/t =?/t
The numerator of the indicated expression is s+7.
What are the common factors that make up 7?The numbers 7, 14, 21, 28, 35, and 42 are the multiples of 7. 3 and 7 only share 21 as their smallest common number. 21 is the least common denominator as a result. The denominators can be multiplied by one another to find the common denominator for two or more fractions.
We were given the following rational expression:
where p is the numerator and q is the denominator, is the general representation of the rational expression.
So, the expression we provide is:
Assuming the LCM, the following expression can be rewritten as
Comparing (1) with the above-mentioned general rational expression
The numerator of the given expression is p=s+7.
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A toy company spends $1800 per day for factory expenses plus $9 to make each teddy bear. They sell the teddy bears for $15 a piece. Create and solve an equation that could be used to find the number of bears, b ,the company has to sell in one day to equal its daily cost.
The number of bears, b is 300 for the company has to sell in one day to equal its daily cost.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
A toy company spends $1800 per day for factory expenses plus $9 to make each teddy bear.
And, They sell the teddy bears for $15 a piece.
Let number of bears for the company has to sell in one day to equal its daily cost = b
Hence, We can formulate the inequality as;
⇒ 15b = 9b + 1800
Solve for b;
⇒ 15b - 9b = 1800
⇒ 6b = 1800
⇒ b = 300
Thus, There are 300 teddy bears has to sell in one day.
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