Transform the quadratic equation into a perfect square equation by completing the square.x² + 4x + 2 = 0Enter your answer in the boxes.
Given: A quadratic equation,
\(x^2+4x+2=0\)Required: To transform the equation by completing the square.
Explanation: The general quadratic equation of the form,
\(ax^2+bx+c=0\)can be transformed into a complete square by adding and subtracting the following term,
\((\frac{1}{2}b)^2\)Hence, adding 4 and subtracting 4 from the given equation,
\(x^2+4x+4-4+2=0\)\(x^2+2\times2\times x+\text{ }2^2-2=0\)Now the equation can be transformed as follows,
\((x+2)^2-2=0\)or,
\((x+2)^2=2\)Final Answer: The
The next model of a sports car will cost 13.6% more than the current model. The current model costs $58,000 . How much will the price increase in dollars? What will be the price of the next model?
Increase price:
Price of next model:
Answer:
increase price: $7,888
price of next model:65,888
An isoline that connects all points of highest mean temperature on a world map is called Group of answer choices the thermal equator. the temperature range line. the highest mean temperature isoline. an isobar.
An isoline that connects all points of highest mean temperature on a world map is called the highest mean temperature isoline.
An isoline is a line on a map that connects points of equal value for a particular variable. In this case, the isoline connects all points of the highest mean temperature, indicating regions with the highest average temperatures.
Therefore, it is referred to as the "highest mean temperature isoline." The other options mentioned are not specifically related to the concept described.
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Suppose IQ scores were obtained for 20 randomly selected sets of twins. The 20 pairs of measurements yield x = 96.62, y= 94.75, r=0.879, P-value = 0.000, and ŷ = -2.59 + 1.01x, where x represents the IQ score of the twin born first. Find the best predicted value of ý given that the twin born first has an IQ of 109?
Answer:the best predicted value of ý when the twin born first has an IQ of 109 is 107.50
Step-by-step explanation:
Given the regression equation:
ŷ = -2.59 + 1.01x
We need to predict the value of ý when x (IQ score of the twin born first) is 109.
So we substitute x = 109 into the regression equation:
ŷ = -2.59 + 1.01(109)
ŷ = -2.59 + 110.09
ŷ = 107.50
Therefore, the best predicted value of ý when the twin born first has an IQ of 109 is 107.50.
3) Which choice shows the values from least
to greatest?
A. -88.-75.-71,-53
B. -53,-88-71, -75
C. -75. -88 -71.53
D. 75 -88-53-71
given FH with coordinates F(4,-5) and H(-8,19), if G lies on FH such that that the ratio of FG to FH is 1:6, find the coordinates of G
Answer:
G = (2, -1)
Step-by-step explanation:
You want ...
FG/FH = 1/6 = (G -F)/(H -F)
H -F = 6(G -F)
H +5F = 6G . . . . . . add 6F, simplify
G = (H +5F)/6 . . . . .divide by 6
Substituting the given coordinates, we get ...
G = ((-8, 19) +5(4, -5))/6 = (-8+20, 19 -25)/6 = (12, -6)/6
G = (2, -1)
you have a set of points with a y:x constant ratio of 3:7. what is the equation of the line passing through these points?
The equation of the line passing through these points i.e (7,3 ) and (14,6) is
y = (3/7) x or 3x - 7y = 0 ,
Which is linear equation of two variables.
A linear equation is an algebraic equation of the form y = mx + b , with only one constant and one first-order (linear) term, m is the slope and b is the y-intercept.
We have given that,
the ratio of y and x is y : x = 3 : 7
So the ratio of x and y can be expressed as ,
x : y = 7 : 3 ( reverse order)
So let's consider two points as
(x₁, y₁)=(7 , 3) and (x₂, y₂) = (14 , 6)
The equation of the line passing through these points will be,
( y - y₁ )/ (y₂ - y₁) = (x - x₁)/(x₂ - x₁)
=> (y - 3)/(6-3) = (x - 7)/(14 - 7)
=> (y - 3)/3 = (x - 7)/7
=> 7(y - 3) = 3( x - 7)
=> 7y - 21 = 3x - 21
=> 7y = 3x
=> y = (3/7) x
Hence, y = (3/7) x is required equation of line.
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9. Determine where the graph represents a function explain your answer.
The vertical line test is a visual test to determine if a graph represents a function; since a function can only have one output for every input if a vertical line intersects a curve in more that one point the it is not the graph of a function.
In this case we any vertical line will only intersect one point then we conclude that:
The graph represents a function. Using the vertical line test, the graph intersects any vertical line at only one point.
Leo drew a line that is perpendicular to the line shown on the grid and passes through the point (f, g).
a. True
b. False
Any line perpendicular to it would have an undefined slope and would not pass through point (f, g) where f and g could be any values. In this case, the statement is false.
The statement "Leo drew a line that is perpendicular to the line shown on the grid and passes through the point (f, g)" can be true or false.
It depends on the line shown on the grid and the coordinates of point (f, g).
Two lines are perpendicular if their slopes are opposite reciprocals of each other.
To find the slope of the line perpendicular to the line shown on the grid,
we can use the negative reciprocal of the slope of the given line.
If the line drawn by Leo has this slope and passes through point (f, g), then the statement is true.
If not, then the statement is false.
For example, if the line shown on the grid has a slope of 2/3 and passes through the point (0,0),
then the perpendicular line drawn by Leo would have a slope of -3/2 and pass through point (f, g) where f and g could be any values.
In this case, the statement is true.
However, if the line shown on the grid has a slope of 0 and passes through point (1,1), then any line perpendicular to it would have an undefined slope and would not pass through point (f, g) where f and g could be any values. In this case, the statement is false.
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Find the volume of the rectangular prism.
5 m
8 m
8 m
Answer:
The answer is: Volume = 320
Step-by-step explanation:
5 × 8 × 8 = 320
Answer:
320
Step-by-step explanation:
Volume of a rectangular prism = Length*Width*Height = 5*8*8 = 320
Hope this helps!!!
Justin is taking an anti-inflammatory drug and the instructions say that the patient must receive 11 mg for each 20 kg of body weight. If Justin weighs 253 lb, what dosage should he receive?
First, we need to convert 253 lb to kilograms. Given that 1 kg is equivalent to 2.205 lb, then:
\(253\text{ lb = }253\text{ lb}\cdot\frac{1\text{ kg}}{2.205\text{ lb}}\approx114.74\operatorname{kg}\)The dosage Justin should receive is directly proportional to his weight. Given that a dosage of 11 mg corresponds to a weight of 20 kg, then to find the dosage that corresponds to 114.74 kg we can use the next proportion:
\(\frac{11\text{ mg}}{x\text{ mg}}=\frac{20\operatorname{kg}}{114.74\operatorname{kg}}\)Solving for x:
\(\begin{gathered} 11\cdot114.74=20\cdot x \\ \frac{1262.14}{20}=x \\ 63.1\approx x \end{gathered}\)He should receive a dosage of 63.1 mg
Complete the statement to show an equivalent ratio,
4) 7:6 is equivalent to 21 :
Answer:
18
Step-by-step explanation:
to get from 7 to 21 you must multiply by 3
you have to do the same then to the denominator
6x3 = 18
To check:
see if 7/6 = 21/18
by seeing it their cross-products are equal
does 7(18) = 6(21)?
126=126
$2,300 at 7% interest for 9 years. What would the interest be?
We want to find the simple interest accrued on $2,300 at 7% interest for 9 years.
The formula for simple interest is given as;
\(I=\frac{P\times R\times T}{100}\)Inserting the values, we have;
\(I=\frac{2300\times7\times9}{100}=\text{ \$1449}\)Therefore, the interest is $1449
1. According to the podcast, why and how is chicken the reason American trucks dominate the truck market in the United States? Briefly explain. 2. Name two reasons a party (e.g., a politician or an industry association) may want to impose a tariff? 3. Who are they usually trying to protect? Who would be hurt by a tariff on automobiles? Explain. 4. Describe how competition encourages innovation? In your answer to this question, include a discussion on why American trucks "basically stayed the same over the years. 5. Describe ways foreign companies tried to get around American-imposed tariffs on automobiles. 6. Do you think the methods you described in your previous answer are efficient for an economy? Why or why not? 7. Lastly, how can a tariff be used as a bargaining chip? In your opinion, is that a good reason to impose tariffs - why or why not?
1. Chicken became the key product that drove the creation of the Interstate Highway System, which led to the dominance of American trucks in the US truck market.
2. A party may want to impose a tariff to protect domestic industries from foreign competition or to generate revenue for the government.
3. A party is usually trying to protect domestic industries, but a tariff on automobiles would hurt both domestic consumers who would pay higher prices and foreign producers who would face reduced demand.
4. Competition encourages innovation by providing incentives for companies to improve their products and services to stay ahead of their rivals; American trucks stayed the same because they faced little competition due to protectionist policies.
5. Foreign companies tried to get around American-imposed tariffs on automobiles by establishing factories in the US, forming joint ventures with American companies, or exporting through third countries.
6. The methods used to get around tariffs can be efficient in the short term, but they may not be sustainable or desirable in the long term as they can lead to trade imbalances and undermine the competitiveness of domestic industries.
7. Tariffs can be used as a bargaining chip to negotiate better trade deals, but they should be imposed judiciously and only as a last resort to avoid damaging the economy and harming consumers.
1. In the podcast, chicken is cited as the reason why American trucks dominate the truck market in the United States.
This is because in the 1960s, the government imposed regulations on the trucking industry that limited the amount of weight a truck could carry.
To get around these regulations, the industry started using smaller trucks to transport goods, which were often not strong enough to handle the weight.
However, they found that if they put chicken on the back of the trucks, the weight of the cargo would distribute more evenly and the smaller trucks could handle the load.
This led to the development of the modern pickup truck, which is now a staple of the American automobile market.
2. Parties may want to impose tariffs for various reasons, such as to protect domestic industries and jobs from foreign competition, to raise revenue for the government, or to level the playing field in international trade.
Two specific reasons for imposing tariffs could be to protect national security interests or to address unfair trade practices by other countries.
3. Tariffs are usually imposed to protect domestic industries and jobs, and the parties that are being protected are typically the producers of the goods or services in question.
However, tariffs can also harm consumers who may have to pay higher prices for imported goods or may have fewer choices in the marketplace. For example, if a tariff is imposed on automobiles, domestic car manufacturers may benefit, but consumers may have to pay more for cars, and foreign automakers may lose market share.
4. Competition encourages innovation by creating incentives for companies to improve their products or services to gain a competitive advantage.
In the case of American trucks, the lack of competition may have contributed to their lack of innovation over the years. Since they dominated the market, there was little pressure to improve or innovate, and as a result, they have largely stayed the same.
However, the rise of foreign competition in recent years has led American truck manufacturers to invest more in innovation to stay competitive.
5. Foreign companies have tried to get around American-imposed tariffs on automobiles in various ways, such as by moving production to countries not subject to the tariffs, by exporting parts and assembling them in the United States, or by lobbying the government for exemptions or tariff reductions.
6. The methods used by foreign companies to get around tariffs may not be efficient for the economy as a whole because they can lead to higher costs and inefficiencies in the supply chain.
However, they may be necessary for individual companies to remain competitive in the short term.
Ultimately, a more efficient solution would be to address the root causes of the trade imbalances that lead to tariffs in the first place.
7. A tariff can be used as a bargaining chip by threatening to impose tariffs on imports from a country unless they make concessions in trade negotiations.
While this can be an effective strategy in certain situations, it can also lead to a trade war and harm both economies.
In general, tariffs should be used sparingly and as a last resort, and efforts should be made to address underlying trade issues through diplomacy and negotiation.
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Which of these lists correctly orders the binary numbers from smallest to largest? Choose 1 answer: Choose 1 answer: (Choice A) A 001100110011, 011001100110, 010101010101, 101010101010 (Choice B) B 001100110011, 010101010101, 011001100110, 101010101010 (Choice C) C 101010101010, 010101010101, 011001100110, 001100110011 (Choice D) D 101010101010, 011001100110, 010101010101, 00110011
The correctly arranged binary numbers from smallest to largest is; B) 001100110011, 010101010101, 011001100110, 101010101010
How to work with Binary Numbers?Binary numbers are numbers that are made of only 1 and 0. Now, let us look at the options;
A) 001100110011, 011001100110, 010101010101, 101010101010; This is not well arranged from smallest to biggest because the 2nd and 3rd numbers both have 12 terms but the 2nd term is larger because it starts with 011 while the 3rd term starts with 010 which is not meant to be.
B) 001100110011, 010101010101, 011001100110, 101010101010; Thus is well arranged because unlike the option A above, this one has the second and third term correctly positioned and also the 4th term is the biggest.
Options C & D are not properly arranged for the resaons given in options A and B.
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What are the key features of g(x), including the end behavior, y-intercept, and zeros in the equation g(x) = (x + 5)(x + 2)(x − 5) .
The key features of the functions are
The y-intercept is -50The end behaviour is: as x ⇒ +∝, y ⇒ +∝ and As x ⇒ -∝, y ⇒ -∝How to determine the key featuresThe y-intercepts
This is the point where the graph crosses the y-axis i.e. when x = 0
Given that the function is g(x) = (x + 5)(x + 2)(x - 5)
So, we have
y-intercept = (0 + 5)(0 + 2)(0 - 5)
Evaluate
y-intercept = -50
How the graph behaves (end behaviour)
To do this, we check the values of x in relation to the values of y
So, we have
g(x) = (x + 5)(x + 2)(x - 5)
Calculate g(∝) and g(-∝)
g(∝) = (∝ + 5)(∝ + 2)(∝ - 5) = ∝
g(-∝) = (-∝ + 5)(-∝ + 2)(-∝ - 5) = -∝
This means that the end behaviour is
As x ⇒ +∝, y ⇒ +∝ and As x ⇒ -∝, y ⇒ -∝
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find the radian measure of an angle at the center of a circle with radius 77.0 cm that intercepts an arc length of 128 cm
The radian measure of the angle at the center of the circle is approximately 1.6623 radians.
We are given that the radius of the circle is 77.0 cm and the length of the intercepted arc is 128 cm. We need to find the radian measure of the angle at the center of the circle.
To solve this problem, we use the formula relating the angle at the center of a circle, the radius of the circle, and the arc length intercepted by the angle.
The formula is given byθ = s/rwhereθ = angle at the center of the circle in radians s = arc length intercepted by the angle r = radius of the circle Substituting the given values, we getθ = 128/77.0 = 1.6623 radians (rounded to four decimal places)
Therefore, the radian measure of the angle at the center of the circle is approximately 1.6623 radians.
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.2. Determine whether the feasible set for each of the following systems of constraints is convex, and if not, indicate points x^1 and x² that violate definition. a) (x1)² + (x2)² > 9
x1 + x2 ,10
x1, x2 > 0
The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.
To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.
a) (x1)² + (x2)² > 9
This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.
b) x1 + x2 ≤ 10
This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.
c) x1, x2 > 0
This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.
Now, let's analyze the intersection of these constraints:
Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).
To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.
If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).
Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.
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If w = -4, which inequality is true?
Answer: -5 - 4w > 10
give lil pump brainliest now
Answer:
Variable
constant
Step-by-step explanation:
to the people who looked up the one question and it didn't come up here's the answer
Samuel used 1 3/4 cups of dry oatmeal to make 4 servings. Which proportion could be used to calculate the amount of dry oatmeal needed to make 3 servings?
Answer:
1 3/4 / 4
x / 3
Step-by-step explanation:
The answer is about 1.31 cups.
hope this helps
Find cot x if cos x =1/7 and sin x < 0.
By answering the presented question, we may conclude that the value of the trigonometry is cot x = -√3 / 4
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
cot x = cos x / sin x.
we have cos x = 1/7 and sin x < 0.
\(sin^2 x + cos^2 x = 1\\sin^2 x + (1/7)^2 = 1\\sin^2 x = 1 - (1/7)^2 = 48/49\\\)
sin x = -√(48/49) = -(4/7)√3
cot x = cos x / sin x = (1/7) / (-(4/7)√3)
cot x = -√3 / 4
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Write the system of linear equations represented by the augmented matrix to the right use WXY and Z for the variables Write the equation for all the rows
Question: Write the system of linear equations represented by the augmented matrix to the right use W, X, Y and Z for the variables :
Solution:
An augmented matrix is equivalent to a system of linear equations. In this case, the given matrix is represented by the following system of linear equations:
-1 w - 3x +5y +2z = 13
0w + 1x + 3y + 0z = 10
0w + 0x +y - 1z = 3
1w - 3x + 0y + 0z = -2
this is equivalent to:
w - 3x +5y +2z = 13
x + 3y = 10
y - z = 3
1w - 3x = -2
So that, the correct answer is:
w - 3x +5y +2z = 13
x + 3y = 10
y - z = 3
1w - 3x = -2
3x-5=4x+2can i get help anyone
Answer:
3(x+5) = 4x
Step-by-step explanation:
What is the equation for the line with a slope of -3 that passes through the
point (0,5)?
A. Y = 5x - 3
B. Y = -3x – 5
C. Y = -3x + 5
The equation for the line which passes through the slope -3 and point ( 0, 5) is given by option c. y = -3x + 5.
Slope of the equation 'm' = -3
Line passes through the point = (0,5).
let us consider the coordinates of the point ( 0,5) be ( x₁ , y₁ )
Formula used to get equation of the line passing through ( x₁ , y₁ ) and slope 'm'.
y - y₁ = m ( x - x₁ )
Substitute the value we have,
⇒y - 5 = -3 ( x - 0)
⇒ y - 5 = -3x
⇒ y = -3x + 5
Therefore, the equation for the line passing through given slope and point is equal to option c. y = -3x + 5.
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Which of the following is NOT true for conducting a hypothesis test for independence between the row variable and column variable in a contingency table?
Choose the correct answer below.
A.
Tests of independence with a contingency table are always right-tailed.
B.Small values of the
chi squaredχ2
test statistic reflect significant differences between observed and expected frequencies.
C.The number of degrees of freedom is
(rminus−1)(cminus−1),
where r is the number of rows and c is the number of columns.
D.
The null hypothesis is that the row and column variables are independent of each other
The statement that is NOT true for conducting a hypothesis test for independence between the row variable and column variable in a contingency table is:
C. The number of degrees of freedom is minus (rminus−1)(cminus−1), where r is the number of rows and c is the number of columns.
The correct answer is C. The number of degrees of freedom for a hypothesis test of independence in a contingency table is calculated as (r-1)(c-1), where r is the number of rows and c is the number of columns. The degrees of freedom reflect the number of independent pieces of information available for estimating the expected frequencies in the table.
A. Tests of independence with a contingency table can be one-tailed or two-tailed, depending on the research question and the alternative hypothesis. The choice of the tail direction determines the critical region for rejecting the null hypothesis.
B. Small values of the chi-squared test statistic indicate a lack of significant differences between observed and expected frequencies, while large values indicate significant differences. This is because the chi-squared test measures the discrepancy between observed and expected frequencies.
C. This statement is incorrect. The correct formula for calculating the degrees of freedom is (r-1)(c-1), where r is the number of rows and c is the number of columns. The degrees of freedom reflect the number of independent pieces of information available for estimating the expected frequencies in the contingency table.
D. The null hypothesis in a hypothesis test for independence is that the row and column variables are independent of each other. The alternative hypothesis, on the other hand, suggests that there is a relationship or association between the variables. The goal of the hypothesis test is to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
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Naser solved (7)/(8)a=14 for a. The steps Naser used are shown. (7)/(8)a=14 (7)/(8)a*(8)/(7)=14*(7)/(8) a=12(1)/(4) Which statement best describes Naser's worked -out solution?
The statement that best describes Naser's worked out solution is "Nasers solution is correct because he multiplied the right side of the equation by the fraction 7/8. (Option A)
How is this so?By multiplying the right sides by the fraction 7/8, Naser was able to eliminate the fraction on the left side thus making a the subject of the formula.
This gives us
a = 14 x 7/8
a = 98/8
a = 12 1/4
Which is the correct answer.
Thus, it is right to state that Nasers solution is correct because he multiplied the right side of the equation by the fraction 7/8.
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Full Question:
See attached image.
the distribution of the diameters of a particular variety of oranges is approximately normal with a standard deviation of 0.3 inch. how does the diameter of an orange at the 67th percentile compare with the mean diameter? 0.132 inches above the mean 0.201 inches below the mean 0.132 inches below the mean 0.440 inches above the mean 0.201 inches above the mean question 4 corr
The diameter of an orange at the 67th percentile will be 0.132 inches above the mean diameter. Thus, the correct option is A) 0.132 inches above the mean.
Given data:
The distribution of the diameters of a particular variety of oranges is approximately normal with a standard deviation of 0.3 inch.
The degree of data dispersion from the mean is indicated by the standard deviation. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Formula used:
z-score = (x-μ) / σ
At the 67th percentile, the z-score will be 0.44.
To find the diameter of an orange at the 67th percentile, we will use the formula of the z-score.
z-score = (x-μ) / σ
0.44 = (x-μ) / 0.3
0.132 = x - μ
x = 0.132 + μ
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I need to find the area of this parallelogram
Answer:
Step-by-step explanation:
2. Which inequality represents all solutions of -3b-52-6b - 13.
Ob26
Ob>-8/3
O b s8/3
Obs6
Answer:
b≥ - 8/3
Step-by-step explanation:
-3b-5≥-6b - 13.
Add 6b to each side
-3b+6b-5≥-6b+6b - 13
3b-5≥ - 13
Add 5 to each side
3b-5+5≥ - 13+5
3b≥ - 8
Divide by 3
3b/3≥ - 8/3
b≥ - 8/3
Karen has a bag containing 423 rubber ducks.
If Karen gives 30 rubber ducks to every person she meets, then she will have enough for _____ people and she will have _____ extra ducks left over.
Answer:
karen will have enough for 14 people, and she will have 3 extra ducks left over
Step-by-step explanation:
divide 423 by 30
423/30 = 14
14 times 30 is 420, so subtract 420 from the total number of rubber ducks
423 - 420 = 3
so, karen will have enough for 14 people and 3 ducks will be left over !!
Answer:
Karen we'll have enough for 14 people and have 3 ducks left over.