Based on the chord-arc theorem, the value of x in the circle shown is calculated as: x = 8.
What is the Chord-Arc Theorem?The theorem states that if two chords of equal circle are congruent, then the arcs they intercepted would be congruent to each other.
The image shows that both chords are equal, therefore, their intercepted arcs would be congruent. Thus, we have:
4x + 7 = 5x - 1
Combine like terms:
4x - 5x = -7 - 1
-x = -8
x = 8
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The values in the table represent a function.
f(x)
8
X
-6
7
4
3
-5
3
-5
-2
12
Use the drop-down menus to complete the
statements.
The ordered pair given in the first row of the table can
be written using function notation as
f(3) is
◊
f(x) = -5 when x is
Done
The ordered pair given in the first row of the table can be written as (8, f(8)).
f(3) is equal to 7.
f(x) = -5 when x is -6 or -2.
The table represents a function where the input values (x) correspond to the output values (f(x)). Let's analyze the given information to complete the statements:
The ordered pair given in the first row of the table can be written using function notation as (x, f(x)) = (8, f(8)). This means that when x is equal to 8, the corresponding function value is f(8).
To find f(3), we look for the row in the table where x is equal to 3. From the given table, we can see that when x is 3, the corresponding function value f(x) is 7. Therefore, f(3) is equal to 7.
Similarly, to find when f(x) is equal to -5, we look for the rows in the table where the function value is -5. From the table, we can see that when x is equal to -6 and -2, the function value f(x) is -5. Therefore, we can say that f(x) = -5 when x is -6 or -2.
In summary:
The ordered pair given in the first row of the table can be written as (8, f(8)).
f(3) is equal to 7.
f(x) = -5 when x is -6 or -2.
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Question 6 0/2 pts 10094 Details Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 2y = 5√x, y = 4, and 2y + 2x =
We need to integrate with respect to x. The area of the region enclosed by the given curves is approximately 31.52 square units.
To sketch the region enclosed by the given curves and determine the appropriate method of integration, let's analyze the equations one by one:
Equation 1: 2y = 5√x
This equation represents a curve in the xy-plane.
By squaring both sides of the equation, we get 4y^2 = 25x.
Solving for y, we have y = ±√(25x)/2. Since y can be positive or negative, we consider both possibilities.
Equation 2: y = 4
This equation represents a horizontal line in the xy-plane at y = 4.
Equation 3: 2y + 2x = 0
This equation represents a straight line in the xy-plane. By rearranging the equation, we have y = -x.
To sketch the region, we consider the points of intersection of these curves.
At y = 4, equation 1 becomes 2(4) = 5√x, which simplifies to 8 = 5√x.
Solving for x, we find x = 64/25.
At y = -x, equation 1 becomes 2(-x) = 5√x, which simplifies to -2x = 5√x.
Squaring both sides, we get 4x^2 = 25x. Solving for x, we find x = 0 and x = 25/4.
From the equations, we see that the region enclosed is bounded by the curve 2y = 5√x, the line y = 4, and the line y = -x.
The region lies between x = 0 and x = 64/25.
To find the area of this region, we need to integrate with respect to x. The integral is given by:
A = ∫[0, 64/25] [(5√x)/2 - (-x)] dx
Simplifying the expression, we have:
A = ∫[0, 64/25] [(5√x + 2x)] dx
To evaluate the integral and find the area of the region, let's proceed with the integration of this expression:
First, let's integrate each term separately:
∫(5√x) dx = (10/3)x^(3/2) + C1
∫(2x) dx = x^2 + C2
Next, we can substitute the limits of integration and evaluate the definite integral:
A = [(10/3)x^(3/2) + x^2] evaluated from 0 to 64/25
A = [(10/3)(64/25)^(3/2) + (64/25)^2] - [(10/3)(0)^(3/2) + (0)^2]
Simplifying the expression further:
A = (10/3)(64/25)^(3/2) + (64/25)^2
A = (10/3)(4096/625) + (4096/625)
A = (10/3)(4096 + 625) / 625
A = (10/3)(4721) / 625
A ≈ 31.52
Therefore, the area of the region enclosed by the given curves is approximately 31.52 square units.
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A wall is 22 feet tall. A ladder is leaned against that wall. The top of the ladder touches the top of the wall and the bottom of the ladder rests on the ground 8 feet from the base of wall. What is the length of the ladder?
Answer:
23.41 feet
Step-by-step explanation:
The ladder forms a right angle triangle with the wall
Height of the wall (opposite) = 22 feet
Bottom of the ladder from the wall (adjacent) = 8 feet
What is the length of the ladder?
Length of the ladder (hypotenuse)
Using Pythagoras theorem
Hypotenuse ² = opposite ² + adjacent ²
= 22² + 8²
= 484 + 64
= 548
Hypotenuse ² = 548
Hypotenuse = √548
= 23.41 feet
The length of the ladder is 23.41 feet
In how many different ways can we sit n people around a round table? The sits are indistinguishable but the relative position of people is not. 3. A license plate can have four one-digit numbers or two one-digit numbers and two letters. How many different license plates are there?
There are 686,000 different license plates.
To solve this problem, we can fix one person's position and arrange the remaining (n-1) people around the table.
Since the seats are indistinguishable, we divide the total number of arrangements by n to avoid counting duplicate arrangements.
The number of different ways to sit n people around a round table is (n-1)!.
A license plate can have four one-digit numbers or two one-digit numbers and two letters.
For the first case, where the license plate has four one-digit numbers, there are 10 choices for each digit (0-9).
Therefore, there are 10 choices for the first digit, 10 choices for the second digit, 10 choices for the third digit, and 10 choices for the fourth digit. In total, there are 10^4 = 10,000 different license plates.
For the second case, where the license plate has two one-digit numbers and two letters, there are 10 choices for each digit and 26 choices for each letter (assuming only uppercase letters).
Therefore, there are 10 choices for the first digit, 10 choices for the second digit, 26 choices for the first letter, and 26 choices for the second letter. In total, there are 10^2 * 26^2 = 676,000 different license plates.
Different license plate = 10,000 + 676,000
= 686,000
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−2 ≤ 8
answer quick please
Answer: True
Step-by-step explanation:
The inequality is always True
If 0<=k<(pi/2) and the areas under the curve y=cosx from x=k to x=(pi/2) is 0.1, then k=
Answer: The integral of the function y = cos(x) from x = k to x = π/2 represents the area under the curve of the function between those limits. We can evaluate this integral as follows:
∫[k, π/2] cos(x) dx = sin(k) - sin(π/2) = sin(k) - 1
We are given that this area is 0.1, so we can write:
0.1 = sin(k) - 1
Adding 1 to both sides gives:
1.1 = sin(k)
To solve for k, we take the inverse sine (or arcsine) of both sides, keeping in mind that k is between 0 and π/2:
k = arcsin(1.1)
However, arcsin(1.1) is not a real number since the sine function is only defined between -1 and 1. Therefore, there is no value of k that satisfies the given conditions.
in a survey conducted on an srs of 200 american adults, 72% of them said they believed in aliens. give a 95% confidence interval for percent of american adults who believe in aliens.
American adults believes in alien for the given 95% confidence interval and sample surveyed is in the interval range of ( 0.66 , 0.78 ).
As given in the question,
Sample of American adults surveyed 'n' = 200
Percent of people believes in aliens are success 'p'= 72%
= 0.72
Percent of people who don't believes (failure) in aliens ' 1 - p' = 1 - 0.72
= 0.28
95% Confidence interval that represents Americans adults who believes in aliens
value of z - score for 95% confidence interval = ± 1.96
Margin of error 'MOE'= (z-score)√p ( 1- p) /n
= ( 1.96)√(0.72 × ( 1 - 0.72 )/ 200
= 1.96 ( √0.2016 / 200)
= 1.96 ×√0.001008
= 0.063
Lower limit = p - MOE
= 0.72 - 0.063
= 0.66
Upper limit = p + Margin of error
= 0.72 + 0.063
= 0.78
Therefore, 95% confidence interval with sample size of the Americans adults who believes in alien are in the interval of ( 0.66 , 0.78 ).
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what is 2 to the 14 power
Answer:
16,384
Step-by-step explanation:
find the volume of the given solid. bounded by the coordinate planes and the plane 6x + 4y + z = 24
Therefore, the volume of the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is 96 cubic units.
To find the volume of the solid bounded by the coordinate planes (xy-plane, xz-plane, and yz-plane) and the plane 6x + 4y + z = 24, we need to determine the region in space enclosed by these boundaries.
First, let's consider the plane equation 6x + 4y + z = 24. To find the x-intercept, we set y = 0 and z = 0:
6x + 4(0) + 0 = 24
6x = 24
x = 4
So, the plane intersects the x-axis at (4, 0, 0).
Similarly, to find the y-intercept, we set x = 0 and z = 0:
6(0) + 4y + 0 = 24
4y = 24
y = 6
So, the plane intersects the y-axis at (0, 6, 0).
To find the z-intercept, we set x = 0 and y = 0:
6(0) + 4(0) + z = 24
z = 24
So, the plane intersects the z-axis at (0, 0, 24).
We can visualize that the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is a tetrahedron with vertices at (4, 0, 0), (0, 6, 0), (0, 0, 24), and the origin (0, 0, 0).
To find the volume of this tetrahedron, we can use the formula:
Volume = (1/3) * base area * height
The base of the tetrahedron is a right triangle with sides of length 4 and 6. The area of this triangle is (1/2) * base * height = (1/2) * 4 * 6 = 12.
The height of the tetrahedron is the z-coordinate of the vertex (0, 0, 24), which is 24.
Plugging these values into the volume formula:
Volume = (1/3) * 12 * 24
= 96 cubic units
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the listing of elements from which you'll draw the sample is called thegroup of answer choicespopulation.sampling frame.sample.census.parameter.
The listing of elements from which you'll draw the sample is called the sampling frame. The sampling frame is a list of all the individuals or objects in a population that you are interested in studying. From the sampling frame, you can select a smaller group of individuals or objects to form a sample.
A sample is a subset of the population that you study to make inferences about the population. The population is the entire group of individuals or objects that you are interested in studying, and a census is a study of the entire population. The parameter is a numerical characteristic of a population, such as the mean or standard deviation, that you are interested in estimating.
1. Population: The entire group you want to study or gather information about.
2. Sampling frame: The list of elements (individuals or items) within the population from which you'll draw the sample.
3. Sample: A subset of the population selected for study, which is meant to represent the larger population.
4. Census: The process of collecting data from every member of a population, not just a sample.
5. Parameter: A numerical characteristic of a population, such as the mean or standard deviation, which is often estimated using a sample.
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What percent of the first 20 natural numbers are one-diget numbers
Answer:
9/20 or forty five percent (45%)
Calculate the number of ways to arrange 9 books of different tittles on a book
rack.
A. 45
B. 81
C. 368280
D. 362880
Answer:
D good luck :) also have a great day
what is the Riemann hypothesis
Answer:
What is the Riemann hypothesis simply explained?
The Riemann hypothesis asks if every non-trivial root (white dot) would be on the line down the middle. If the answer is no, we say the "hypothesis is false". This would mean that there are white dots which are not on the line given.
Please vote 4 BRAINLIEST
Show work by writing out all of the ratios in simplified form
please help i need this now!
Answer:
Option D is the correct answer.
Step-by-step explanation:
\( \frac{w}{y} = \frac{z}{x} \\ \\ by \: cross \: multiplication \\ \\ wx \: = yz\)
(Scientific Notation MC)
The distance from the Earth to the moon is about 238,000 miles. Rewrite the distance in scientific notation.
2.38 x 10−5
23.8 x 10−4
23.8 x 104
2.38 x 105
Both Option C and Option D are both correct.
We have distance from the Earth to the moon.
We have to write it in scientific notation.
What is Scientific Notation ?Scientific notation is a way of writing very large or very small numbers in the powers of 10.
According to the question -
Distance = 238000 miles
In scientific notation, we can write it as -
2.38 x \(10^{5}\) and 23.8 x \(10^{4}\).
Hence, both Option C and Option D are both correct.
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Help out with this question please!
Answer:
my answer is A
Step-by-step explanation:
if you work out the equation where you know that at the x intercept y=0 you will find A to be true
Why did the inequality sign flip?
We did not flip the inequality sign
We multiplied by a negative number (-8)
We added by a negative number (-8)
We divided by a negative number (-8)
Answer:
We multiplied by a negative number (-8)
We divided by a negative number (-8)
Step-by-step explanation:
Multiplying or dividing both sides of an equation by a negative number changes the inequality of the equation, because it changes the sign of each side of the equation
find the cube root of 1728
Answer:
12
Step-by-step explanation:
simple math.
Answer:
it is 12
I don't know how to type the process
You are asked to evaluate the food at a new restaurant on 7-point scales with bipolar adjectives such as good-bad and inexpensive-expensive. These measures represent what type of scale
The type of scale used to evaluate the food at a new restaurant on 7-point scales with bipolar adjectives such as good-bad and inexpensive-expensive is known as a Likert scale.
This type of scale is commonly used in surveys to measure attitudes and opinions towards a particular topic, in this case, the food at a new restaurant. A Likert scale consists of a series of statements or adjectives that respondents are asked to rate on a scale that ranges from strongly disagree to strongly agree or, in this case, from bad to good and from inexpensive to expensive.
The bipolar adjectives used in the scale allow for a clear distinction between the positive and negative aspects of the food, which helps to ensure that the responses are more accurate and meaningful. The 7-point scale provides a wider range of options than a binary scale, which allows for more nuanced and detailed responses.
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Summary of the data on two variables to be presented simultaneously is called a. simultaneous equations b. a histogram c Pivot table
A pivot table is summary of the data on two variables to be presented simultaneously .
A pivot table, is a data summarization tool used in spreadsheet programs or database software. It allows for the transformation and restructuring of data, enabling users to extract meaningful insights by summarizing and analyzing large datasets. The intersection cells of the table contain summary statistics or aggregated values, such as counts, sums, averages, or percentages, representing the relationship between the two variables. Pivot tables provide a concise and structured way to analyze and present data from multiple perspectives, facilitating data exploration and making it easier to identify patterns, trends, and relationships between variables.
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helppp please i dont know how to do this
The solution of the pairs of lines are as follows,
(1) Line 1 and line 2 are perpendicular to each other.
(2) Line 1 and line 3 are parallel to each other.
(3) Line 2 and line 3 are perpendicular to each other.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
Calculate the slope of each line,
LIne 1
3y = 2x + 5
y = 2/3x + 5/3
Compared with the standard equation of line y = mx + c,
Slope m = 2/3
Similarly.
The slope of line 2 = -3/2
The slope of line 3 = 2/3
Now. properties of pair of lines state that the slope of parallel lines is equal and the slope of perpendicular lines are negative reciprocal of each other,
So
Slope of line 1 = slope of line 3
But,
The slope of line 2 is the negative reciprocal of the slope of lines 1 and 3.
Thus, the solution of the pair of lines has been shown above.
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Enrique predicts that he can make additional money from sales of accessories and service for computer products sold by his store. The table at the right shows predicted percent returns for such sales. For example, if the store makes x dollars selling computer products, Enrique predicts the store with make 0.05x dollars from selling accessories. Part A In January and February of this year, the store made $2,500 from sales of accesories and services. Let x represent the amount the store with make from sales of computer products from March through December. Write an equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year. If Enrique predicts sales from accessories and services for the entire year will be $5,000, about how much money must be made from computer product sales from March through December? Explain.
The equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year is (y = 0.05x + 2500).
Given that:
Enrique predicts that he can make additional money from sales of accessories and services for computer products sold by his store.
The store makes x dollars selling computer products, Enrique predicts the store will make 0.05x dollars ($0.05) from selling accessories.
The following steps can be used in order to determine the equation that represents the predicted amount y:
Step 1 - According to the given data, the store makes x dollars selling computer products.
Step 2 - It is also given that, in January and February of this year, the store made $2,500 from sales of accessories and services.
Step 3 - So, the linear equation that represents the given situation is:
y = 0.05x + 2500
Hence the answer is The equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year is (y = 0.05x + 2500).
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on a planet far far away from earth, iq of the ruling species is normally distributed with a mean of 106 and a standard deviation of 18. suppose one individual is randomly chosen. let x
The distribution of X follows the characteristics of a normal distribution with a mean of 106 and a standard deviation of 18, reflecting the IQ distribution of the ruling species on the faraway planet. This can be denoted as X ~ N(106, 18), where "N" represents the normal distribution.
The distribution of X, representing the IQ of an individual from the ruling species on the faraway planet, is a normal distribution with a mean (μ) of 106 and a standard deviation (σ) of 18. This can be denoted as X ~ N(106, 18), where "N" represents the normal distribution.
In this distribution, the majority of IQ values will cluster around the mean of 106. The standard deviation of 18 indicates the average amount of variation or dispersion from the mean. The normal distribution is symmetric, which means that the probabilities of IQ values being above or below the mean are equal.
The shape of the normal distribution is bell-shaped, with the highest point being at the mean. As we move away from the mean, the probability of observing extreme values decreases. The spread of the distribution is determined by the standard deviation, where a larger standard deviation indicates a wider spread of IQ values.
the distribution of X follows the characteristics of a normal distribution with a mean of 106 and a standard deviation of 18, reflecting the IQ distribution of the ruling species on the faraway planet.
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On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 106 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual. What is the distribution of X? X ~ N( 106 , 18 )
Which graph shows the line y - 2 = 2(x + 2)?
Answer:
Graph B
Step-by-step explanation:
I think it os Graph B but I'm not sure because when I put it in Desmos to graph it, the line interests 6 on the Y axis.
I included a picture of what Desmos gives me
an orchard owner is investigating a new formula of fertilizer to determine if it produces more apples per tree compared to a current popular brand.part a: which of the following design is most appropriate: observational study, experiment, census, or sample survey? explain your reasoning. (3 points)part b: explain how you would implement the design you selected in part a. (4 points)part c: explain one benefit your design would provide. (3 points)
The most appropriate design would be experiment. Implementation of the design would be by selection of trees, then the application of fertilizer, followed by data collection and statistical analysis.
a) Most appropriate design: Experiment
The orchard owner wants to determine if a new formula of fertilizer produces more apples per tree compared to a current popular brand. To make a causal conclusion, an experiment would be the most appropriate design. In an experiment, the orchard owner would randomly assign the trees to receive either the new fertilizer formula or the current popular brand and then compare the number of apples produced. This allows the orchard owner to control for other variables and isolate the effect of the fertilizer on the number of apples produced.
b) Implementation:
Selection of trees: The orchard owner would randomly select a sample of trees from their orchard and divide them into two groups: the experimental group (receiving the new fertilizer formula) and the control group (receiving the current popular brand).
Application of fertilizer: Both the experimental and control groups would receive the same amount of fertilizer, but the experimental group would receive the new formula while the control group would receive the current popular brand.
Data collection: The orchard owner would measure the number of apples produced by each tree in both the experimental and control groups.
Statistical analysis: The orchard owner would use appropriate statistical tests to compare the number of apples produced by each group and determine if there is a significant difference between the two.
c) Benefit:
One benefit of this experimental design is that it allows the orchard owner to determine causality. By randomly assigning the trees to receive either the new fertilizer formula or the current popular brand, the orchard owner can be confident that any difference in the number of apples produced is due to the fertilizer and not other factors. This is important for making decisions about which fertilizer to use in the future.
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Calculator
What is the surface area of this right rectangular prism?
Enter your answer as a mixed number in simplest form by filling
in the boxes.
ft²
113
4
3 ft
42
The surface area of this right rectangular prism is 79/3 ft².
From the prism we can write the dimension of prism as
length = 3 ft
width = 2 1/2 ft
height = 1 1/3 ft
Now, surface area of this right rectangular prism
= 2 (lw + wh+ lh)
= 2(3 x 2 1/2 + 2 1/2 x 1 1/3 + 1 1/3 x 3)
= 2 (3 x 5/2 + 5/2 x 4/3 + 4/3 x 3)
= 2 (15/2 + 10/3 + 4)
= 2(79/6)
= 79/3 ft²
Thus, the surface area of this right rectangular prism is 79/3 ft².
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Estimate.
36 x 92 ~ ?
Answer:
3,312
lets be real who arctually looks at the step by step just use a calculator for this one
Which of the following allows for someone to draw conclusions about a population from the information collected in a population sample? a. magnitude statistics b. central tendency c. inferential statistics d. effect size
The correct answer is c. Inferential Statistics.
Inferential statistics is the branch of statistics that allows for drawing conclusions about a population based on the information collected from a sample. When conducting research or surveys, it is often impractical or impossible to collect data from an entire population.
Instead, a representative sample is chosen, and inferential statistics are used to make inferences or predictions about the larger population. By analyzing the characteristics and patterns observed within the sample, inferential statistics enable researchers to make generalizations or draw conclusions about the population as a whole.
This process involves applying various statistical techniques, such as hypothesis testing and confidence intervals, to estimate population parameters and assess the reliability of the conclusions. Magnitude statistics, central tendency, and effect size are important concepts in statistics, but they do not specifically address the ability to draw population-level conclusions from sample data.
Magnitude statistics focuses on the size of the effect or relationship between variables, central tendency measures summarize the central values of a dataset, and effect size quantifies the strength of an effect or relationship.
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it is claimed that the mean age of bus drivers in chicago is 50.2 years. if a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
The null hypothesis is a statement which describe the claim of 'no difference'.
Let μ be the population mean.
Given claim : The mean age of bus drivers in Chicago is 50.2 years.
i.e. μ = 50.2
Since "no difference with mean" or statements with an equal sign are used as the null hypothesis.
Then, the null hypothesis for the given situation is
Ηο : μ = 50.2
If the test fails to reject the null hypothesis, it means there is evidence to support the claim that the the mean age of bus drivers in Chicago is 50.2 years.
A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided data. Using sample data, hypothesis testing is performed to evaluate a theory' veracity. It is often referred to as just "the null," and its symbol is Hο.
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4.5kg of bananas and 3.5kg of apples cost £6.75. ^kg of apples cost £5.40. Calculate the cost of 1kg of bananas.
Answer: Let's assume the cost of 1 kilogram of bananas is represented by 'x'.
According to the given information, 4.5 kg of bananas and 3.5 kg of apples together cost £6.75. We also know that the cost of 1 kg of apples is £5.40.
Using this information, we can set up the following equation:
4.5x + 3.5(£5.40) = £6.75
Now let's solve for 'x':
4.5x + 3.5(£5.40) = £6.75
4.5x + £18.90 = £6.75
4.5x = £6.75 - £18.90
4.5x = -£12.15
x = (-£12.15) / 4.5
x ≈ -£2.70
The cost of 1 kilogram of bananas, based on this calculation, is approximately -£2.70. However, it's important to note that a negative cost doesn't make sense in this context. It's possible there may be an error in the given information or the setup of the equation.