the relationship between test scores and the student-teacher ratio can be modeled as a linear function: The right choice is D) lessen test scores by 4.56 for each school locale.
In view of the data in the inquiry, the relationship between test scores and the understudy educator proportion can be numerically composed as follows:
x = 698.9 - 2.28y .................... (1)
Where,
x = test scores
y = understudy educator proportion
The slant of (- 2.28) shows the sum by which x will change at whatever point there is an adjustment of y.
Hence, when there is a reduction in the understudy educator proportion by 2 (for example y = 2), we will have:
Change in x = - 2.28 * 2 = - 4.56
The negative sign thusly shows that the test scores will decrease by 4.56 for each school area. Accordingly, the right choice is D) lessen test scores by 4.56 for each school locale.
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the complete question is:
Assume that the relationship between test scores and the student-teacher ratio can be modeled as a linear function with an intercept of 698.9 and a slope of (-2.28). A decrease in the student teacher ratio by 2 will: A) reduce test scores by 2.28 on average) result in a test score of 698.9C) reduce test scores by 2.56 on average) reduce test scores by 4.56 for every school district.
Ms Kowal invests £6000 in a simple interest account.
After 5 years her investment has earned £450 interest.
What rate of interest does the account pay?
Answer:
We can use the simple interest formula I = Prt to find the rate of interest that the account pays. Here, P is the principal amount (£6000), t is the time period (5 years), and I is the interest earned (£450). Substituting these values in the formula gives us: 450 = 6000 * r * 5. Solving for r, we get r = 0.015 or 1.5%. Therefore, the account pays a simple interest rate of 1.5%
Two ships are near a buoy in the open ocean. One ship is 20 km due north of the buoy, and the other ship is 13.5 km due east of the buoy.
Enter a number in the box to correctly complete the statement. Round the answer to the nearest tenth.
In this instance, the buoy forms the right corner of a triangle made up of the two ships and the buoy. To the closest tenth, the distance between the two ships is roughly [tex]24.1[/tex] km.
What is the distance between two object?To find the distance between the two ships, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs
(the sides that form the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).
In this case, the two ships and the buoy form a right triangle, with the buoy at the right angle.
Let d be the distance between the two ships, x be the distance of the northern ship to the buoy and y be the distance of the eastern ship to the buoy. Then we have:
[tex]d^2 = x^2 + y^2[/tex]
Substituting the given values, we get:
[tex]d^2 = (20 km)^2 + (13.5 km)^2[/tex]
[tex]d^2 = 400 km^2 + 182.25 km^2[/tex]
[tex]d^2 = 582.25 km^2[/tex]
[tex]d ≈ 24.1 km[/tex]
Therefore, the distance between the two ships is approximately 24.1 km, rounded to the nearest tenth.
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assume that 50 million households in the u.s. watched a particular show at 9:00 pm, and 90 million households had their television sets turned on at 9:00 p.m. calculate the share of audience.
The share of audience for the particular show at 9:00 pm is 55.56% for 50 million households.
We need to know the number of households that watched the programme and the total number of households with televisions on at 9:00 p.m. in order to determine the proportion of audience for that programme.
In this instance, it is stated that 90 million homes had their televisions on at 9:00 p.m. in addition to 50 million households watching the programme. Consequently, the following formula can be used to determine the show's viewership share:
Share of audience is calculated as follows: (Number of households that watched the programme / Total number of households with TVs on) x 100%
= 100% x (50 million / 90 million)
= 55.56%
As a result, 55.56% of the audience watched the specific show at 9:00 p.m. This indicates that the programme was viewed by more than half of the homes with on-air televisions at the time.
The share of audience is a crucial measurement in television ratings since it aids networks and advertisers in understanding how popular a show is and how far it might be able to reach the intended audience.
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3 2/5 -1 3/5!!
Please i need help!
Answer:
Step-by-step explanation:
3 2/5 -1 3/5 = 1.8
where is the water table in a swamp? group of answer choices well below the surface. at the surface. well above the surface. generally, 2 miles below the surface.
Generally, the water table in a swamp is located 2 miles below the surface.
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Jarvis and his family are at the dine-in movies and wish to purchase some popcom. A large popcom costs $18 and a small popcom costs $12. Jarvis offered to pay for the popcom with $50 in his wallet.
Create an inequality in standard form that describes this situation.
Use the given numbers and the following variables.
• x = the number of large popcoms
• y = the number of small popcorn
Answer:
18x + 12y ≤ 50
Step-by-step explanation:
Let x be the number of large popcoms and y be the number of small popcoms.
The cost of a large popcom is $18, and the cost of a small popcom is $12. The total cost of purchasing x large popcoms and y small popcoms is given by:
Total cost = 18x + 12y
The problem states that Jarvis has $50 in his wallet to pay for the popcoms. Therefore, we can write the following inequality:
18x + 12y ≤ 50
This inequality represents the situation where Jarvis and his family want to purchase popcoms, and Jarvis has $50 to spend. The inequality ensures that the total cost of the popcoms does not exceed $50.
Annabelle works in a deli and has been tracking the daily sales of different items over several months. Annabelle found that when there was an increase in the number of cups of hot chocolate sold, the number of cups of coffee sold also increased. Similarly, when there was a decrease in the number of cups of hot chocolate sold, the number of cups of coffee also decreased.
Which of the following is a valid conclusion?
A.
There is no correlation between the sale of hot chocolate and the sale of coffee.
B.
The increase in the sale of hot chocolate caused an increase in the sale of coffee.
C.
The increase in the sale of hot chocolate is correlated to, but not caused by, the sale of coffee.
D.
No conclusion can be drawn about the correlation or causation of the sale of hot chocolate and the sale of coffee.
Option C is the correct answer. The increase in the sale of hot chocolate is correlated to, but not caused by, the sale of coffee.
What is correlation?
Correlation is a statistical measure that shows how closely two or more variables are linked to one another. It is a measurement of the strength and direction of the linear connection between two variables, in other words.
Based on the information provided, it can be concluded that there is a correlation between the sale of hot chocolate and the sale of coffee.
Option A can't be considered because it conflicts with the material provided.
Option B indicates a causal relationship that cannot be proven merely on the basis of the observed correlation between the sales of hot chocolate and coffee.
Option D is untrue as well because a correlation has been found.
Therefore, option C is the valid conclusion that can be drawn from the given information, stating that the increase in the sale of hot chocolate is correlated to, but not necessarily caused by, the sale of coffee.
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A teacher asks his students to find a fraction that is equal to the decimal 1.45. Beto says the decimal is equal to 16/11. Rayna says the decimal is equal to 131/90 Which student is correct?
===================================================
Reason:
Dividing by 11 leads to a repeating fraction, so that rules out 16/11. The decimal value 1.45 doesn't repeat and is instead a terminating decimal.
It's a bit interesting that 16/11 = 1.454545... so if we were to round it, then 16/11 is approximately 1.45; however, 16/11 is not exactly 1.45
As for 131/90, that won't work either because 9 is a factor of 90. Dividing by 9 leads to a repeating fraction.
131/90 = 1.455555...
This rounds to 1.46
-------------
Here's one way to determine what fraction is equal to 1.45
1.45 = 1.45/1
1.45 = 145/100
1.45 = (29*5)/(20*5)
1.45 = 29/20
You can use a calculator or long division to see that 29/20 converts to 1.45
Makers of generic drugs are required to show that their generic drugs do not differ significantly from the "reference" or brand name drugs that they imitate. One aspect in which the generic drugs might differ is their extent of absorption in the blood. Twelve subjects were available for the study. Six were randomly selected to receive the generic drug first and then, after a washout period, receive the "reference" drug. The remaining six received the "reference" drug first, followed by the generic drug after the washout period. Assume that all conditions are met. The mean of the differences was 1.33 and the standard deviation of those differences was 2.90. What is the test statistic for this procedure? a. 5.50 b. 2.35 c. 1.59 d. 1.90
The mean of the differences was 1.33 and the standard deviation of those differences was 2.90. The test statistic for this procedure is 1.90. The correct option is D.
Makers of generic drugs are required to show that their generic drugs do not differ significantly from the "reference" or brand name drugs that they imitate. One aspect in which the generic drugs might differ is their extent of absorption in the blood. Twelve subjects were available for the study. Six were randomly selected to receive the generic drug first and then, after a washout period, receive the "reference" drug. The remaining six received the "reference" drug first, followed by the generic drug after the washout period. Assume that all conditions are met.
The mean of the differences was 1.33 and the standard deviation of those differences was 2.90.
A t-test statistic for a paired sample is to be calculated to find out whether or not there is a statistically significant difference between the two treatments. The formula for a t-test statistic is given below:
t= x¯d/sd / √n
where x¯d is the mean difference,
sd is the standard deviation of the differences, and
n is the number of subjects.
Using the given values, we can substitute in the formula and solve for t as follows:
t=1.33/2.90 / √12t=1.90
Hence, the test statistic for this procedure is 1.90.
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you are making cookies and missing a key ingredient eggs. you have most of the other ingredients, except you only have 1.33 cups of butter. the recipe calls for two cups of butter and three eggs to make six dozen cookies. how many eggs do you need use all of the butter?
By using equation in two variable we need to use 2 eggs to make all the cookies with 1.33 cups of butter.
To make six dozen cookies, the recipe calls for two cups of butter and three eggs. We can use proportionality to solve this question: If 2 cups of butter require 3 eggs to make 6 dozen cookies, then 1.33 cups of butter require x eggs to make all of the cookies.
x eggs = (1.33 cups of butter x 3 eggs)/(2 cups of butter). x = 1.99 eggs. Since we cannot use .99 eggs to make cookies, we would need to round up to the nearest whole number of eggs.
Therefore, we need to use 2 eggs to make all the cookies with 1.33 cups of butter.
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you measure the radius of a wheel to be 4.16 cm. if you multiply by 2 to get the diameter, should you write the result as 8 cm or as 8.32 cm?
If you take a wheel's radius of 4.16 cm and divide it by 2 to get its diameter, you should write 8.32 cm instead of 8 cm.
The breadth of a circle is two times the sweep. Therefore, if the wheel has a radius of 4.16 cm, its diameter will be
2 x 4.16 = 8.32 cm.
If the measurement is going to be used for precise engineering or calculations, it is essential to write the result as 8.32 cm because this is a measurement that is more accurate than rounding it off to 8 cm. Working with the most accurate measurement is always preferable because rounding off can result in errors.
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How To Do 387 x 72 In standard algorithm.
Answer: k898
iiii
Step-by-step explanation:
k8ni7mrvnyrt
If the dartboard has a diameter of 14 inches and each number occupies 1/20 of the board, how much space does a single number occupy in square inches?
Each number occupies 7.7 inches² of the dartboard.
What is area?In geοmetry, area is the amοunt οf space a flat shape, like a pοlygοn, circle οr ellipse, takes up οn a plane. The area οf a shape is always measured in square units. Tο find the area οf simple shapes like a square οr the area οf a rectangle, yοu οnly need its width, w, and length, l (οr base, b). The area is length times width:
First we need the area of the dartboard
Area = πr²
here r = d/2 = 14/2 = 7
Area of dartboard = πr²
[tex]$ \rm = \frac{22}{7 } \times 7 \times 7[/tex]
= 22 × 7
= 154 inches²
Now, its is said that each number occupies 1/20 of the board,
Then area of each number = 154 × 1/20
= 7.7 inches²
Thus, Each number occupies 7.7 inches² of the dartboard.
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the probability of class failure is 7%. if 56 students take a class, what number of students is expected to fail the class?
The probability of class failure is 7%. If 56 students take a class, the expected number of students who will fail the class is 4.
We will use the above formula to find the expected value of class failure. Let x be the number of students expected to fail the class.
Expected value = Probability x Total number of trials
The probability of class failure is 7%, so the probability of passing the class is 100% - 7% = 93%. The total number of trials is the total number of students taking the class, which is 56. Putting these values into the formula gives us:
Expected value = 7% x 56
Expected value = 0.07 x 56
Expected value = 3.92
We cannot have a fraction of a student, so we can round this number up to get the expected number of students who will fail the class.
Therefore, the expected number of students who will fail the class is 4.
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Tell whether the angles are complementary, supplementary, or neither.
job elimination in the past year, of businesses have eliminated jobs. if businesses are selected at random, find the probability that at least have eliminated jobs during the last year. round your answer to at least three decimal places. do not round your intermediate calculations.
The probability that at least 5 have eliminated jobs during the last year is 0.002965.
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.
n = 9
p = probability of businesses have eliminated jobs = 0.13
X = Number of businesses have eliminated jobs ~
Binomial( n= 9 , p = 0.13)
[tex]P(X \geq 5)[/tex]
[tex]P(X \geq 5) = 1-P( X < 5)[/tex]
[tex]P(X \geq 5) = 1-P( X \leq 4)[/tex]
Use following Excel command:
=1-BINOM.DIST(x, n, p, cumulative)
=1-BINOM.DIST(4,9,0.13,TRUE)
=0.0029649
=0.002965
Thus
[tex]\mathbf{{P(X \geq 5) =0.002965}}[/tex].
Therefore, probability that at least 5 have eliminated jobs during the last year is 0.002965.
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Complete question';
Job Elimination in the past year, 13% of businesses have eliminated jobs. If 9 businesses are selected at random, find the probability that at least 5 have eliminated jobs during the last year. Round the answer to at least four decimal places P(at least 5 have eliminated jobs during the last year) X
assuming a constant growth factor, by what percent did the population of gotham city grow each year? give at least 3 decimal places.
Assuming a constant growth factor, the population of Gotham City grew by approximately 4.287% each year.
This can be calculated using the formula for exponential growth, which is:
y = a * (1 + r)^t
Where: y = final value of the population
a = initial value of the population
r = annual growth rate expressed as a decimal
t = number of years
For this problem, let's assume that the initial population of Gotham City was 100,000 and that the population grew for 10 years.
Using these values, we can calculate the annual growth rate as follows:
100,000 * (1 + r)^10 = final population
r = (final population / 100,000)^(1/10) - 1
Plugging in a final population of 148,644 (which is a 48.644% increase from the initial population),
r = (148,644 / 100,000)^(1/10) - 1r = 0.04287 (rounded to 5 decimal places)
Therefore, the annual growth rate (or percentage increase) is approximately 4.287% (rounded to 3 decimal places).
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Help me with this question. 10 points!!!!!
Answer:
x = 4
Step-by-step explanation:
if a line is parallel to a side of a triangle and it intersects the other 2 sides, then it divides those sides proportionally.
line EF is parallel to side CD of the triangle and intersects the other 2 sides , then
[tex]\frac{CE}{EG}[/tex] = [tex]\frac{DF}{FG}[/tex] ( substitute values )
[tex]\frac{6}{x+8}[/tex] = [tex]\frac{5}{2x+2}[/tex] ( cross- multiply )
6(2x + 2) = 5(x + 8) ← distribute parenthesis
12x + 12 = 5x + 40 ( subtract 5x from both sides )
7x + 12 = 40 ( subtract 12 from both sides )
7x = 28 ( divide both sides by 7 )
x = 4
hills vanessa is walking up a hill. after walking 40 feet, she has climbed a total of 8 feet vertically. if she walks an additional 25 feet up the hill, how many feet will she have climbed vertically in total?
Vanessa's vertical climb rate is 0.2 feet per foot of horizontal distance. When she walks 65 feet horizontally up the hill and climbs an additional 25 feet, her total vertical climb will be 21 feet.
For every 40 feet of horizontal distance Vanessa walks, she climbs 8 feet vertically. So her vertical climb rate is 8/40 = 0.2 feet per foot of horizontal distance.
If she walks an additional 25 feet up the hill, her total horizontal distance traveled will be 40 + 25 = 65 feet.
Therefore, her total vertical climb will be 0.2 times her total horizontal distance:
8 + (0.2 * 65) = 8 + 13 = 21 feet
So, Vanessa will have climbed a total of 21 feet vertically after walking 65 feet horizontally up the hill.
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fatima is 1.27m tall. charlotte is 0.89m tall lila is taller than charlotte by half the difference betweem fatimas height and charlottes height. how tall in meters is lila?
Lila's height is 0.89 + 0.19 = 1.08m.
What is height ?
Height typically refers to the measurement of an object or person from the base to the top, usually measured vertically. It is often used in reference to the physical dimension of a person or object, such as the height of a building, tree, or individual.
According to the question:
In the context of the given problem, height refers to the height of Fatima, Charlotte, and Lila.
Fatima is 1.27 meters tall, Charlotte is 0.89 meters tall, and Lila is taller than Charlotte by half the difference between Fatima's height and Charlotte's height.
The difference between Fatima's height and Charlotte's height is 1.27 - 0.89 = 0.38m.
Half of that difference is 0.38/2 = 0.19m.
So, Lila is taller than Charlotte by 0.19m.
Therefore, Lila's height is 0.89 + 0.19 = 1.08m.
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A strain of Mycobacterium tuberculosis that is deficient in nonhomologous end joining repair should be more sensitive to damage by
X raysUV radiationGlycosylaseDepurination
Explanation:
A strain of Mycobacterium tuberculosis that is deficient in nonhomologous end joining repair should be more sensitive to damage by X-rays.
Nonhomologous end joining is a DNA repair mechanism that can join two DNA fragments with little or no homology between them. X-rays, which are high-energy electromagnetic waves, can cause damage to DNA by breaking the strands of the double helix.
This damage can be repaired by mechanisms like nonhomologous end joining, so a strain of Mycobacterium tuberculosis that is deficient in this repair mechanism would be more sensitive to damage by X-rays.
UV radiation, glycosylase, and depurination are not directly related to nonhomologous end joining repair and would not have the same effect.
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Brooke played her flute for 3/4 hour each day for 5 days and for 1/2 hour each day for 2 days how many hours did she play it in all
⇒To be able to answer this question to find how many hours Brooke played his flute for 5 days we ought to first convert the 5 days to hours.
⇒There are 24 hours in a day this means that in 5 days we have =24×5
=120 hours.
⇒We have 120 hours in 5 days , it is said that Brooke played her flute [tex]\frac{3}{4}[/tex],
Meaning she played the flute [tex]\frac{3}{4}[/tex] hours of 120 hours which is equal
[tex]\frac{3}{4} *\frac{120}{1}\\=90[/tex]
For 5 days Brooke played her flute 90 hours
⇒The next step is to convert the 2 days to hours which is equivalent to 24×2
=48 hours are in 2 days, it is said Brooke played the flute [tex]\frac{1}{2}[/tex] hours of 2 days. This simply is equivalent to
[tex]\frac{1}{2} *\frac{48}{1} \\=24[/tex]
⇒For 2 days Brooke played the flute 24 hours,
The total number of hours she played it all is =Number of hours she played it in 5 days+ Number of hours she played it in 2 days.
=90+24
=114
⇒In total of these 7 days she played the flute for 114 hours
describe in words how to calculate the probability of two mece events from their odds using the ratio method.
To calculate the probability of two separate events using the ratio method, we must first understand the odds associated with each event. The odds are expressed as a ratio, with the first number representing the chances of success and the second number representing the chances of failure. For example, the odds of an event happening might be 3:2, which indicates that there is a 3/5 chance of success.
Once the odds for each event are known, we can calculate the probability of both events occurring by multiplying the odds of each event together. So, for example, if the odds of Event A are 3:2 and the odds of Event B are 4:5, the probability of both events occurring is 3/2 * 4/5 = 6/10. This means that there is a 6 in 10 chance of both events occurring.
To sum up, calculating the probability of two separate events using the ratio method is fairly simple. Just look at the odds associated with each event and multiply them together to get the probability of both events occurring.
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For the following indefinite integral, find the full power series centered at
x=0 and then give the first 5 nonzero terms of the power series. [infinity]
Σ∫(e^9x - 1) / 6x dx
n=0
From the given information provided, the first 5 nonzero terms of the power series are 1.5 + 13.5x + 60.75x² + 183.375x³ + 1018.1595x⁴.
To find the power series for the given indefinite integral, we can first find the antiderivative of the integrand using substitution. Let u = 9x, du = 9dx, then:
∫(e⁹ˣ - 1) / 6x dx = (1/6) ∫([tex]e^u[/tex] - 1) / u du
We can then expand the integrand into a power series using the Maclaurin series for [tex]e^u[/tex] and ln(1+u):
(1/6) ∫([tex]e^u[/tex] - 1) / u du = (1/6) ∫[Σ(uⁿ/n!) - Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1))] du
= (1/6) [Σ(uⁿ/n! × du) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × du)]
= (1/6) [Σ(uⁿ/n! × 9dx) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × 9dx)]
= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺⁾ xⁿ / (n+1))
We can now simplify and group terms to obtain the power series centered at x=0:
(3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺¹⁾ xⁿ / (n+1))
= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) + (1/6) Σ((-1)ⁿ × (-9)⁽ⁿ⁺¹⁾ × xⁿ / (n+1))
To find the first 5 nonzero terms, we can plug in n=0 through n=4 and evaluate each term:
n=0: (3/2) × 1 = 1.5
n=1: (3/2) × 9x = 13.5x
n=2: (3/2) × 81x² / 2 - (1/6) × 81x² / 3 = 60.75x²
n=3: (3/2) × 729x³ / 6 + (1/6) × 729x³ / 4 = 183.375x³
n=4: (3/2) * 6561x⁴ / 24 - (1/6) * 6561x⁴ / 5 = 1018.1595x⁴
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how can the idea of a sinusoidal function be used to help us model real-world things, or to help us solve real-world problems?
Sinusoidal functions can model natural phenomena and periodic patterns in data, aiding in better understanding and more accurate predictions, while also solving real-world problems.
The idea of a sinusoidal function can be used to model real-world phenomena or solve real-world problems. Many natural phenomena can be modeled using sinusoidal functions, including tides, sound waves, and electromagnetic waves.
In addition, sinusoidal functions can be used to model periodic patterns in data, such as seasonal trends or cyclical patterns in financial data. By using sinusoidal functions to model these phenomena, we can gain a better understanding of their behavior and make more accurate predictions about their future behavior.
Sinusoidal functions can also be used to solve real-world problems, such as calculating the amplitude, frequency, or period of a wave or predicting the behavior of a system that exhibits periodic patterns.
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at an airport restaurant, two sodas and four hamburgers cost $12.00. an order of four sodas and two hamburgers costs $9.00. how much does one hamburger cost?
At an airport restaurant, the cost of one hamburger is $2.50.
How to get the cost of one hamburger?Two sodas and four hamburgers cost $12.00, and an order of four sodas and two hamburgers costs $9.00.
To know the cost of each soda and hamburger, we need to use the equation (x and y)
Use x for soda, and use y for hamburger
Two sodas and four hamburgers cost $12.00
Then, (2 x x) + (4 x y) = 12
2x + 4y = 12
We need to divide the numbers by 2, as follows:
x + 2y = 6
four sodas and two hamburgers cost $9.00
(4 x x) + (2 x y) = 9
4x + 2y = 9
We have to substitute the "x", as follows:
4 (6-2y) + 2y = 9
24 - 8y + 2y = 9
24 - 6y = 9
24 - 9 = 6y
15 = 6y
y = 2.5
Therefore, the cost of one hamburger is $2.50.
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the number of students who seek assistance with their statistics assignments is poisson distributed with a mean of 0.24 per day. what is the probability that at least three students seek assistance in 10 days?
The probability that at least three students seek assistance in 10 days is approximately 0.117.
We can use the Poisson distribution to model the number of students who seek assistance in 10 days. Let X be the number of students who seek assistance in 10 days.
Then X follows a Poisson distribution with parameter λ=2.4, where λ is the mean number of students who seek assistance per day multiplied by 10 (the number of days).
Using the Poisson probability formula, we can calculate the probability of at least three students seeking assistance:
P(X ≥ 3) = 1 - P(X < 3) = 1 - [P(X=0) + P(X=1) + P(X=2)]
We can find that:
P(X ≥ 3) = 0.117
Therefore, the probability that at least three students seek assistance in 10 days is approximately 0.117.
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What are the values of x and y? *
The values of sides x and y of the triangle are 6.75 and 11.25 units respectively.
The Pythagorean TheoremThe square of the hypotenuse side of the right-angled triangle equals the sum of the squares of the other two sides, according to Pythagoras' Theorem. The three sides of this triangle are referred to as the perpendicular, base, and hypotenuse.
by using the Pythagorean theorem:
Equation1: y ² =x ² + 9²
Equation2: (12 + x) ² =1 5 ² + y ²
Putting values of equation1 in 2 we get
(12 + x) ² =1 5 ² +x ² + 9²
144 + x²+ 2×12x = 225 + x²+ 81
x=6.75
Putting value of x in equation1
y ² =6.75 ² + 9²
y=11.25
Hence, the values of x and y are
x = 6.75 unit
y =11.25 unit
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Which system of inequalities has the solution shown in the graph?
Factor:
[tex]8 {x}^{2} + 2x - 3[/tex]
Please show the steps on how you got it!
Answer:
(2x - 1) (4x + 3)
Step-by-step explanation:
8x² + 2x - 3
= 8x² - 4x + 6x - 3
= 4x (2x - 1) + 3 (2x - 1)
= (2x - 1) (4x + 3)
So, the factor is (2x - 1) (4x + 3)