The sample mean X is an unbiased estimator for θ.
To find a suitable statistic as an unbiased estimator for θ, we need to find a function of sample Y, YS, ..., Yn whose expected value is equal to θ.
X = (Y + YS + ... + Yn) / n
To show that X is unbiased, we need to calculate its expected value and show that is equal to θ:
E[X] = E[(Y + YS + ... + Yn) / n]
= (1/n) E[Y + YS + ... + Yn]
= (1/n) [E[Y] + E[YS] + ... + E[Yn]]
= (1/n) [nθ] (by the given density function)
= θ
Therefore, sample mean X is an unbiased estimator for θ.
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your friend claims the geometric mean of 4 and 9 is 6, and then labels the triangle, as shown. is your friend correct? explain your reasoning.
The correct option is -C: No, 6 is the geometric mean of 4 and 9, however if the altitude is 6, then the hypotenuse is the geometric mean of the two segments.
Explain about the geometric mean?An average technique multiplies several values and determines the number's root is known as the geometric mean. You locate the nth root for their product for a collection of n numbers. This descriptive statistic can be used to sum up your data.
Mean Geometric The square root of the product of two numbers is the geometric mean amongst them. The geometric mean of two positive numbers an as well as b is the positive number x as in percentage Cross multiplication results in x² = ab,.
For the given question.
geometric mean of a and b :
From the drawn diagram.
a = 4
b = 9
x = √ab
x = √9*4
x = 6
geometric mean: 6
Applying the altitude rule:
h² = x.y
6² = 9*4
36 = 36
Thus, the geometric mean calculated by friend is correct but the marking on the diagram is wrong.
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spinner is divided into seven equal sections numbered 1 through 7 If the spinner is spun twice, what is the theoretical probability that it lands on 2 and then an odd number?
A) 1/49
B) 4/49
C) 1/7
D) 4/7
Answer:
B is correct
Step-by-step explanation:
If it is spun twice then the probability of it landing on 2 and then an odd number is:
Pr(2,1) or Pr(2,3) or Pr(2,5) or Pr(2,7)
1/49 * 4
4/49
Use the given acceleration function to find the velocity vector v(t), and position vector r(t). Then find the position at time t = 4.
a(t) = eti − 6k
v(0) = 2i + 9j + k, r(0) = 0
The velocity vector and position vector and position vector at t=4 is r(4) = (e₄+2)i+36j - 44k.
a(t) = eti - 6k
Since we know that v(t) = ∫ a(t) dt
= ∫ (eti - 6k) dt
= ∫6ti-6tk+c
where c is the arbitrary vector valued constant
since it is given that
v(0) = 2i + 9j + k
therefore from above
v(0) = e * 0i - 6(0) * k + c
2i + 9j + k =i+c
C= i +9j+k
therefore,
v(t) = eti - 6tk + i + 9j + k
= (et + 1) * i + 9j + (- 6t + 1) * k
Since we know that velocity vector can be found by integration of acceleration vector.
Since, v(t) = (et + 1) * i + 9j + (- 6t + 1) * k
and we know that
R(t) = ∫ v(t)dt
= ∫ of [(a + 1)i + 9j+(-6t + 1)k]dt =(a+t)i+9tj+(-3ta+t)k+C
where C is an arbitrary vector constant.
Now,
Since it given that r(0)=0 therefore
r(0) =(e0+1)+9(0)j)+(-3(0)2+0)x+C
0=2i+ C
C= -2i
therefore
r(t)= (et+t)i+9tj+(-3t+t)k-2i
r(t)=(a+t-2)1+9tj+(-3t+t)k
Since we know that position vector can be found by integration of velocity vector
r(4) = (e4+4-2)i+9(4)j + (-3(4)+4)k
r(4) = (e4+2)1+36j-44k
Now we have found the velocity vector and position vector and position vector at t=4 which are as follows:
v(t) =(et+1)i+9j+(-6t+1)k
r(t) =(et+t-2)i+9tj+(-3t2+t)k
r(4) = (e₄+2)i+36j - 44k
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f(x)
g(x)
=6x−4
=3x
2
−2x−10
Escribe (g∘f)(x) como una expresión en términos de x.
Answer:
g(x)
=6x−4
=3x
2
−2x−10
Escribe (g∘f)(x) como una expresión en términos de x.
Step-by-step explanation:
Primero necesitamos conocer la función f(x). Luego podemos sustituir f(x) en g(x) para obtener (g∘f)(x).
Como la función f(x) no se proporcionó en la pregunta, asumiré que f(x) es:
f(x) = x^2 - 2x + 1
Entonces, podemos sustituir f(x) en g(x) de la siguiente manera:
g(f(x)) = 6f(x) - 4
= 6(x^2 - 2x + 1) - 4 (sustituyendo f(x))
= 6x^2 - 12x + 2
Por lo tanto, (g∘f)(x) = 6x^2 - 12x + 2.
State if the triangles in each pair are similar
Answer:
They are similar
Step-by-step explanation:
It's because 27/18 = 12/8
27/18 = 1.5
12/8 = 1.5
locate the absolute extrema of the function
on the closed interval
Answer:
To find the integral of f(x) = 2x + 5/3 over the interval [0, 5], we can use the definite integral formula:
∫[a,b] f(x) dx = F(b) - F(a)
where F(x) is the antiderivative of f(x).
First, we find the antiderivative of f(x):
F(x) = x^2 + (5/3)x + C
where C is the constant of integration.
Next, we evaluate F(5) and F(0):
F(5) = 5^2 + (5/3)(5) + C = 25 + (25/3) + C
F(0) = 0^2 + (5/3)(0) + C = 0 + 0 + C
Subtracting F(0) from F(5), we get:
∫[0,5] f(x) dx = F(5) - F(0)
= 25 + (25/3) + C - C
= 25 + (25/3)
= 100/3
Therefore, the definite integral of f(x) = 2x + 5/3 over the interval [0, 5] is 100/3.
The graph of y = 5x2 is
Answer:
................................
find the standard form of the equation of the ellipse having foci (2,0) and (2,6) and a major axis of length 8
The standard form of the equation of the ellipse is (x - 2)^2 / 4 + (y - 3)^2 / 7 = 1
To find the standard form of the equation of the ellipse, we first need to determine some of its properties.
The foci of the ellipse are given as (2, 0) and (2, 6). This tells us that the center of the ellipse is at the point (2, 3), which is the midpoint of the line segment connecting the foci.
The major axis of the ellipse is given as a length of 8. Since the major axis is the longest dimension of the ellipse, we can assume that the length of the major axis is 2a = 8, so a = 4.
Next, we need to determine the length of the minor axis. We know that the distance between the foci is 2c = 6, so c = 3. Since c is the distance from the center of the ellipse to each focus, we can use the Pythagorean theorem to find the length of the minor axis
b^2 = a^2 - c^2
b^2 = 4^2 - 3^2
b^2 = 7
b = sqrt(7)
Now we have all the information we need to write the standard form of the equation of the ellipse. The standard form is
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
where (h, k) is the center of the ellipse. Plugging in the values we found, we get
(x - 2)^2 / 4 + (y - 3)^2 / 7 = 1
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what is the answer?
?
No, there is not enough information
Yes, because of the intermediate value theorem
Because g(x) is continuous on the interval, we can see that the correct option is the last one (counting from the top)
Does the value c exists in the given interval?Here we have the function g(x), and we know that it is continuous on the interval [1, 6], and that:
g(1) = 18
g(6) = 11
If it is continuous, then g(x) covers all the values between 18 and 11 in the given interval, this means that there must exist a value c in the given interval such that when we evaluat g(x) in that value c, we get the outcome 12, and we know this by the intermediate value theorem.
So the correct optionis the last one.
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Work out the size of angle x. 79°) 35
Answer: 66
Step-by-step explanation:
all 3 of them should equal to 180
so 79+35 is 114
180-114 will give us the answer which is 66
A company manufactures rubber balls. The mean diameter of a ball is 12 cm with a standard deviation of 0.2 cm. Define the random variable X in words. X = ______________.
A company manufactures rubber balls, random variable X in words is diameter of the rubber ball, standard deviation is -1.5 and z-score of the x = 2 is 2.123.
A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. Random variables are frequently identified by letters and fall into one of two categories: continuous variables, which can take on any value within a continuous range, or discrete variables, which have specified values.
In probability and statistics, random variables are used to measure outcomes of a random event, and hence, can take on various values. Real numbers are often used as random variables since they must be quantifiable.
1) X denotes the diameter of the rubber ball.
So the correct option was A. (option A)
Therefore, the random variable X in words is diameter of the rubber ball.
2) For 1.5 Standard deviations left to the mean , Z score will be -1.5
option(A)
So, standard deviation to the left of the mean is -1.5.
3) [tex]Z=\frac{(x-\mu)}{\sigma}[/tex]
x=2
sigma = √2
Z = 2-(-1)/ √2
Z = 3/√2
Z = 2.123
Hence, the z-score of the x = 2 is 2.123.
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Complete question:
A company manufactures rubber balls. The mean diameter of a rubber ball is 12 cm with a standard deviation of 0.2 cm. Define the random variable X in words. X
diameter of a rubber ball
rubber balls
mean diameter of a rubber ball
12 cm
Question 2 What is the z-score of x=9, if it is 1.5 standard deviations to the left of the mean? Hint: the z-score of the mean is =0 −1.5 1.5 9 Question 3 Suppose X∼N(−1,2). What is the z-score of x=2 ? Hint: z=(x−μ)/σ 1.5 −1.5 0.2222
Which construction is shown in the diagram below?
Answer:
Step-by-step explanation:
i think it B
STUDY SKILLS 7. State ONE way in which each of the examination writing skills below could effectively assist you when writing your examinations. 7.1 Read the question 7.2 Plan the response 7.3 Answer the questions (3 x 1) (3)
Examination writing skills refer to a set of abilities that are essential for effective and successful writing in an exam context.
These skills include reading the question carefully, planning your response, writing a clear and concise answer, using appropriate terminology, providing evidence to support your argument, and presenting your answer in a logical and organized manner.
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Complete question:
State one way in which each of the examination writing skills below could effectively assist you when writing your examinations:
Read the questionPlan the responseAnswer the questionsWhat is the period of f(x)=secx?
Enter your answer in the box.
period of f(x)=secx:
Therefore , the solution of the given problem of function comes out to be f(x) = sec(x) has a period of 2. 2 is the answer.
What is function?The midterm test questions will cover all of the topics, including actual as well as fictitious locations and arithmetic variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox has a particular spot that might be used as a haven.
Here,
=> F(x) = sec(x) has a 2 phase.
Because the secant function is periodic, its values recur after a predetermined amount of time.
This interval's length is equal to the secant function's duration.
The formula for the secant function is
=> sec(x) = 1/cos.(x).
The cosine function repeats its values every 2 units of x, which is known as its period.
Consequently, the secant function has a period of 2 as well.
Therefore, f(x) = sec(x) has a period of 2. 2 is the answer.
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A cylindrical aluminum can is being constructed to have a height h of 7 inches. If the can is to have a volume of 56 cubic inches, approximate its radius r. (Hint: V = 2²h)
The radius of the can is about _ inches.
(Type an integer or decimal rounded to two decimal places as needed)
When rounded to two decimal places, the radius of the can is approximately 1.6 inches.
What exactly is a cylinder?Surface fοrmed by a straight line mοving parallel tο a fixed straight line and intersecting a fixed planar clοsed curve. a sοlid οr surface defined by a cylinder and twο parallel planes that cut all οf its elements. See Vοlume Fοrmulas Table, particularly fοr the right circular cylinder.
The volume of a cylinder can be calculated using the following formula:
V = πr²h
where
V denotes volume,
r denotes radius, and
h denotes height.
The cylindrical aluminium can has a height of 7 inches and a volume of 56 cubic inches. We can calculate the radius using the volume of a cylinder formula:
V = πr²h
56 = πr²(7)
56 = (22/7)r²(7)
56 = 22r²
56/22 = r²
2.54 = r²
r = [tex]\sqrt{2.54}[/tex]
r ≈ 1.6
As a result, when rounded to two decimal places, the radius of the can is approximately 1.6 inches.
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How many proper subsets are in {2,4,6,8...100}
Answer:
159 proper subsets.
Step-by-step explanation:
Given a set {2, 4, 6, 8...100}, how many proper subsets are there?
First, find how many subsets there are in 2 - 10:
That's 16.
Then because there are 10 10s in 100, multiply by 10:
16 x 10 = 160
Finally, because it says proper subsets, subtract by 1:
160 - 1 = 159 proper subsets.
Therefore, there are 159 proper subsets in {2, 4, 6, 8...100}
PLEASE HELP FAST!!
Find the slope of a line perpendicular to the line whose equation is
4x−6y=−24. Fully simplify your answer.
Answer: -3/2
Step-by-step explanation:
FIrst rearrange the equation in y = mx + b form.
4x - 6y = -24
-6y = -4x - 24
y = 2/3x + 4
If the line is perpendicular, the slope must be the negative reciprocal of the current line.
The negative reciprocal of 2/3 is -3/2.
A candy store owner used a cylindrical wooden log as a bench in their store. The height
of that log was 2
feet. The diameter of its base was 1.25
feet. If it costs $7.20
per square foot to paint that log at every side, how much approximately will it cost the
store owner? The total surface area of the right circular cylinder is 2nrh+2rr2
, where, r
is the radius of the base of the cylinder and, h
is the height of the cylinder
Answer:
Step-by-step explanation:
its 60
TRUE/FALSE. Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" Ris a linear transformation. If Ic.B = Tç, e then B = E = C.
Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" R is a linear transformation. If Ic.B = Tç, e then B = E = C.
The above statement is True.
In mathematics, and more specifically in linear algebra, a linear map (also called a linear map, a linear transformation, a vector space homomorphism, or in some cases a linear function) is a map between two vector spaces V → W, which performs the conservation of operations on vectors. Addition and scalar multiplication. The same names and definitions are also used for the more general case of modules over rings; see the homomorphism of modules.
A linear map is called a linear isomorphism if it is a bijection. In the case V=W, the linear map is called linear automorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily that V = W, where V is the space of functions, which is a common convention in functional analysis.
Sometimes the term linear function has the same meaning as linear map, but not in analysis.
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(a)A Chinese restaurant offers 10 different lunch specials. Each weekday for one week, Fiona goes to the restaurant and selects a lunch special. How many different ways are there for her to select her lunches for the week? Note that which lunch she orders on which day matters, so the following two selections are considered different.One possible selection:Mon: Kung pao chickenTues: Beef with broccoliWed: Kung pao chickenThurs: Moo shu porkFri: Beef with broccoliA different selection:Mon: Beef with broccoliTues: Kung pao chickenWed: Kung pao chickenThurs: Moo shu porkFri: Beef with broccoli(b)Now suppose that in addition to selecting her main course, she also selects between water or tea for her drink. How many ways are there for her to select her lunches?
(a) There are 100,000 different ways for Fiona to select her lunches for the week.
(b) There are 200,000 different ways for Fiona to select her lunches and drinks for the week.
(a) Since Fiona selects one lunch special each day, there are 10 options for Monday, 10 options for Tuesday, and so on, for a total of 10 options for each of the 5 weekdays. Therefore, the total number of ways for Fiona to select her lunches for the week is:
10 × 10 × 10 × 10 × 10 = 10^5 = 100,000
(b) In addition to the 10 lunch specials, Fiona now has 2 options for her drink, either water or tea. So for each of the 100,000 possible lunch selections from part (a), there are 2 possible drink options. Therefore, the total number of ways for Fiona to select her lunches and drinks for the week is:
100,000 × 2 = 200,000
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Three dice are rolled. What is the probability of getting the sum as 13?
When three dices are rolled.
Total number of outcomes = = 216
Sum of 13 can be achieved in the following ways:
From the digits 6,4,3
So, there are 3! ways = = 6
From the digits 6,2,5
So, there are 3! ways = = 6
From the digits 5,4,4
So, there are ways = 3
From the digits 6,6,1
So, there are ways = 3
From the digits 3,5,5
So, there are ways = 3
So, total numbers whose sum is 13=
So, Probability = .
Therefore, the probability of getting sum as 21 on rolling three dice = .
What is the end behavior of the polynomial function?
Answer: D. As x → -∞, y → -∞.
Step-by-step explanation:
The graph shows the function approaching negative infinity on the x-axis (left side). When the x-axis is decreasing, the y-axis is also decreasing towards negative infinity.
simplify algebraic rational expressions, with numerators and denominators containing monomial bases with integer exponents, to equivalent forms.
Simplifying remex's works the same way we simplify fractions. In fractions, a rational number is considered to be a simplified form when its numerator and denominator have no other common factors than 1.
Regular expressions are fractions with variables. In rational expressions, the numerator and denominator are polynomials. That is, it is of the form p(x)/q(x), where q(x) ≠ 0 and p(x) and q(x) are polynomials. Because regular expressions are nothing but fractions, we treat them as if they were fractions.
It is not possible to divide a number by 0. Check what 1/0 is with your calculator, it will return an error. Therefore, no regular expression is defined for variable values with a denominator of 0 (because it is a fraction). For example, in the expression x / (x + 2), the denominator becomes zero when x = -2, so it is called the limit of the rational expression x / (x + 2). In other words, we say x / (x + 2) for all values of x but x ≠ -2.
Simplifying a regular expression means reducing the value of a regular expression to its lowest term or simplified form. Simplifying regexps works the same way we simplify fractions. In fractions, a rational number is considered a simplified form when its numerator and denominator have no other common factors than 1. The same works for simplified rational expressions, but the only difference is that there are polynomials in the fraction. Let's see the steps to follow to simplify a regular expression.
Step 1: Factor each numerator and each denominator by taking the common factor.
Step 2: Cancel the common factor.
Step 3: Write the remaining terms in the numerator and denominator.
Step 4: Indicate limits, if any. Note that a constraint is any value that makes the denominator equal 0, including terms canceled during simplification.
Complete Question:
Simplify algebraic rational expressions, with numerators and denominators containing monomial bases with integer exponents, to equivalent forms.
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When you calculate (In) 7, you would be finding the
value of which of the following expressions?
O log10 7
O log, 10
O log, e
O log 7
Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.
what is logarithm?In mathematics, the logarithm is the reciprocal of a power. As a result, the exponent by which b must be raised to achieve a number x matches its logarithm in base b. For example, because 1000 = 103, the base-10 logarithm is 3, or log10 = 3. For example, the base 10 logarithm of 10 is 2, but the square of 10 is 100. Log 100 = 2. A logarithm (or log) is the mathematical word used to answer questions such as how many times a base of 10 must be multiplied by itself to get 1,000. The answer is 3 (1,000 = 10 10 10).
When you compute (In), you are calculating the natural logarithm of 7, which is indicated as ln(7) or loge (7).
As a result, the expression you'd be looking up the value of is: ln(7) or loge (7).
Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.
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can someone help me? please
evalute the following function h(x)=3x2+ax-1 for h(3) and find the value for a.
Answer:
Step-by-step explanation:
[tex]h(3)=3\times 3^2+3a-1 \rightarrow h(3)=26+3a[/tex]
But we cannot find [tex]a[/tex] unless we are told what [tex]h(3)[/tex] equals.
2) The table shows the number of minority officers in the U.S. military in 2000.
Army
Marines
Air Force Total
9162
1341
4282
18309
2105
914
1518
7269
4075
599
3823
11150
15342
2854
9623
36728
Assume that one person will be randomly selected from the group described in the table. Find the
probability of selecting an officer who is in the Navy, given that the officer is African American. (Do
not reduce.)
3524
A)
8909
African Americans
Hispanic Americans
Other Minorities
Total
B)
Navy
3524
2732
2653
8909
8909
18,309
C).
3524
18,309
3542
14785
D).
2)
The probability of selecting an officer who is in the Navy given that the officer is African American is 0.192.
What is the probability?Probability calculates the likelihood that an event would happen. The likelihood that an event would occur has a value that lies between 0 and 1 or 0 and 100. The more likely an event would happen, the closer the probability value would be to 1 or 100.
The probability of selecting an officer who is in the Navy given that the officer is African American = number of African Americans that are in the Navy / total number of African Americans
Total number of African Americans = 9162 + 3524 + 1341 + 4282 = 18,309
The probability = 3524 / 18,309 = 0.192
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the formula for converting degrees fahrenheit (F) to degrees Kelvin is K= 5/9 (F = 459.67) Solve for F, terms of K
The formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.
What is degrees Fahrenheit and degrees Kelvin?Degrees Kelvin and Degrees Fahrenheit are two temperature measuring measures that are widely used across the globe. While Kelvin is an international standard unit of measurement, Fahrenheit is mostly used in the United States.
The fact that they measure temperature on distinct scales explains the difference between degrees Fahrenheit (F) and degrees Kelvin (K). Whereas Kelvin is based on a scale of 100 degrees between the freezing and boiling temperatures of water at normal atmospheric pressure, Fahrenheit is based on a scale of 180 degrees between these extremes.
Given that, K = 5/9 (F - 459.67).
To obtain F in term of K we isolate the value of F as follows:
K = 5/9 (F - 459.67)
Multiplying both sides by 9/5, we get:
(9/5) K = F - 459.67
Adding 459.67 to both sides, we get:
F = (9/5) K + 459.67
Hence, the formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.
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there are 24total customers seated at 4 tables in a restaurant each table is the same size and has the same number of customers tell whether each statement is truth or false
Question 13 (2 points)
Suppose you flip a coin and then roll a die. You record your result. What is the
probability you flip heads or roll a 3?
1/2
3/4
7/12
1
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
we have 2 possible cases for the coin and 6 possible cases for the die.
so, we have 2×6 = 12 combined possible cases :
heads, 1
heads, 2
heads, 3
heads, 4
heads, 5
heads, 6
tails, 1
tails, 2
tails, 3
tails, 4
tails, 5
tails, 6
out of these 12 cases, which ones (how many) are desired ?
all first 6 plus (tails, 3) = 7 cases
so, the correct probability is
7/12
formally that is calculated :
1/2 × 6/6 + 1/2 × 1/6 = 6/12 + 1/12 = 7/12
the probability to get heads combined with the probability to roll anything on the die, plus the probability to get tails combined with the probability to roll 3.
please help!!! i really need it
Step-by-step explanation:
Lisa started with $25 on her prepaid debit card. After her first purchase, she had $22.90 left. Therefore, she spent:
$25 - $22.90 = $2.10
We know that the price of the ribbon was 14 cents per yard. To find out how many yards Lisa bought, we can set up an equation:
$2.10 ÷ $0.14/yd = 15 yards
Therefore, Lisa bought 15 yards of ribbon with her prepaid debit card.