Six grapefruit cost as much as a dozen oranges. The cost of a dozen grapefruit and two dozen oranges
is $12. If Susan purchased one orange and one grapefruit, how much did she spend? Show your
thinking.
a.Write System of equations for the above problem.
b. Solve the system of equations
c.Explain the meaning of the solution in the context of the problem.
Answers
Answer:
$0.73
Step-by-step explanation:
Let's say an orange costs O dollars and a grapefuit costs G dollars.
We add G dollars for each grapefuit and O dollars for each orange, so, for example, 12 grapefuit = G added 12 times = 12 *G = 12G
a.
6G = 10O
12G + 24O = 12
6 grapefuit = 6G = 10 oranges = 10O
b.
6G = 10O
12G + 24O = 12
We can solve this using substitution. First, we can solve the first equation for G. After that, we can plug that into the second to find O and go from there.
6G = 10O
divide both sides by 6 to remove the coefficient for G
G = (10/6)O
plug that into the second equation
12*(10/6)O + 24O = 12
20O + 24O = 12
44O = 12
divide both sides by 44 to solve for O
O=12/44 = 6/22
6G = 10O
6G = 60/22
divide both sides by 6 to solve for G
10/22 = G
c.
These solutions mean that an orange (O) costs 6/22 dollars and a grapefuit (G) costs 10/22, so 1O + 1G = 16/22 dollars ≈ $0.73. Note that O and G are kept as fractions because they are not exact dollar amounts, e.g. 0.27 repreating
Related Questions
Match the equation to its solution. Shade every part of the picture
that corresponds to the color of the solution. Show your c
Answers
The matched solution to the equation is as follows;
y = -4x - 1 and (-1, 3)x - y = 5 and (7, 2)3x + y + 2 = 0 and (3, -11)How to solve equation of a line?The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.
Hence, the equation in slope intercept form is y = mx + b
where
m = slopeb = y-interceptTherefore, the equation to be matched with solution are as follows:
we will have to express it in slope intercept form for easier calculation.
Hence,
a . y = -4x - 1
b.
x - y = 5
y = x - 5
c.
3x + y + 2 = 0
y = - 3x - 2
Therefore, let's match the equation with the solution.
y = -4x - 1 and (-1, 3)
y = -4(-1) - 1
y = 4 - 1 = 3
y = x - 5 and (7, 2)
y = 7 - 5 = 2
y = - 3x - 2 and (3, - 11)
y = -3 (3) - 2
y = -9 - 2
y = - 11
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A cab company charges according to the following rate chart. Which graph correctly represents the charge, y, in dollars for a cab ride of x miles? Cab Rates by Mile Miles Charge Flag drop fee (0 miles) $5.00 g miles $1.00 per mile miles $2.00 per mile for each mile over 10
Answers
The graph is the one that correctly represents the linear piece-wise function is the first graph.
How to solve for the graphFirst we have a linear function as
Mx + b
mc= slope, this is the rate of change, how y changes as x changes by 1.
b = y-intercept, y value as x = 0
y = 5 + x
x ≤ 10
at 10 we have 5 + 10 = 15
at 2 dollars
y = 15 + 2(x - 10)
at 14
y = 15 + 2(14 - 10)
15 + 2*4
= 23
Hence we can conclude that the first graph here is the correct one.
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we want to determine the probability of obtaining at most 4 successful operations in 10 independent surgical operations where the probability of success is the same for each operation. the appropriate formula to be used is
Answers
Using (D) the binomial formula, which is used to determine probability when independent events are known, we will get the probability in the scenario.
What is the binomial formula?In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment).
The binomial probability is nCx⋅px⋅(1−p)n−x if the likelihood of success on a single trial is p.
When a process is repeated a certain number of times (for example, in a set of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of witnessing a defined number of "successes."
So, in the given situation we will find the probability with help of the binomial formula which is used to calculate the probability when independent events are given.
Therefore, using (D) the binomial formula, which is used to determine probability when independent events are known, we will get the probability in the scenario.
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Complete question:
We want to determine the probability of obtaining at most 4 successful operations in 10 independent surgical operations where the probability of success is the same for each operation. The appropriate formula to be used is
(A) the mean of the binomial distribution.
(B) the hypergeometric formula.
(C) the mean of the hypergeometric distribution.
(D) the binomial formula.
A large nationwide poll recently showed an unemployment rate of 9% in the US. The mayor of a local town wonders if this national result holds true for her town, so she plans on taking a sample of her residents to see if the unemployment rate is significantly different than 9% in her town.
Let p represent the unemployment rate in her town. Here are the hypothesis she'll use:
H0 : p=0.09
H1 : p≠0.09
Under which of the following conditions would the mayor commit a Type I error?
a. She concludes the town's unemployment rate is not 9% when it actually is.
b. She concludes the town's unemployment rate is not 9% when it actually is not.
c. She concludes the town's unemployment rate is 9% when it actually is.
d. She concludes the town's unemployment rate is 9% when it actually is not.
Answers
Type I error is formed when she concludes the town's unemployment rate is not 9% when it actually is, which is an option (a).
Given that:
A large nationwide poll recently showed an unemployment rate of 9% in the US.
The mayor of a local town wonders if this national result holds true for her town, so she plans on taking a sample of her residents to see if the unemployment rate is significantly different than 9% in her town.
Here the null hypothesis is taken as that the unemployment rate is 9%, whereas the alternative hypothesis is that it is not 9%.
Type I error is the error formed when the null hypothesis is rejected, but the hypothesis is actually true.
So, here the conclusion is that the unemployment rate is not 9%, but it actually is 9%.
Hence, the correct option is (a).
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A high school track is 9.76 meters wide. It is divided into 8 lanes of equal width for
track and field events. How wide is each lane?
Answers
Answer:
1.22
Step-by-step explanation:
9.76/8
A new car is purchased for $ 40 , 000 $40,000 and over time its value depreciates by one half every 3 years. What is the value of the car 17 years after it was purchased, to the nearest hundred dollars?
Answers
Can someone help me out? :(
Answers
Answer:
the length of AB is 5
Step-by-step explanation:
4, -3
Explanation:
From A go to the right 4, and then from B go down 3
x/7 ≥ − 6=============
Answers
The range of value of x in the inequality x/7 ≥ -6 is x≥ -42
What is inequality?Inequality, is a statement of an order relationship. Some terms used in inequality are ,greater than, greater than or equal to, less than, or less than or equal to. They are used between two numbers or algebraic expressions.
greater than has the sign >
greater than or equal to has the sign ≥
less than has the sign < and
less than or equal to has ≤
solving the range of value of x in the inequality x/7 ≥- 6
multiply both sides by 7
x ≥ -42
Therefore the range of value of x is x ≥ -42
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Problem 1 A car has an initial speed of vo= 25m/s to the east and a constant acceleration of a = 3m/s² when a water drop begins to fall from rest. After dropping a distance of h= 10m, the water drop strikes the hood of the car. Aerodynamic drag is not considered here. (1) Determine the speed of the drop and the speed of the car when the strike occurs. [16 pt.] (2) Determine the velocity and acceleration the drop appears to have with respect to a passenger in the car (direction and magnitude). [16 pt.]
Answers
The speed of the water drop when it strikes the hood is approximately 14.0 m/s downward, and the speed of the car at that moment is approximately 29.3 m/s to the east.
The drop appears to have a velocity of approximately 29.3 m/s to the west and 14.0 m/s downward with respect to the passenger in the car.
The drop appears to have an acceleration of approximately 3 m/s² to the west and 9.8 m/s² downward with respect to the passenger in the car.
Determining speed and velocity(To determine the speed of the water drop and the speed of the car when the drop strikes the hood,
use the kinematic equations of motion.
First, we can find the time it takes for the drop to fall 10m using the kinematic equation:
distance h = 10m,
\(h = 1/2 at^2\)
where
h is the vertical distance,
a is the acceleration due to gravity (9.8m/s²), and t is the time.
Substituting the values, we have;
\(10 = 1/2 (9.8) t^2 \\
t^2 = 20/9.8 \\
t ≈ 1.43 seconds\)
Next, find the final velocity of the drop using the kinematic equation:
\(v = vo + at\)
where v is the final velocity,
vo is the initial velocity (which is 0m/s for the drop),
a is the acceleration due to gravity, and
t is the time we just calculated.
Substituting the values, we have
v = 0 + (9.8)(1.43)
v ≈ 14.0 m/s downward
Finally, find the speed of the car when the drop strikes the hood using the kinematic equation:
\(v = vo + at\)
v = 25 + (3)(1.43)
v ≈ 29.3 m/s to the east
Therefore, the speed of the water drop when it strikes the hood is approximately 14.0 m/s downward, and the speed of the car at that moment is approximately 29.3 m/s to the east.
To determine the velocity and acceleration
The velocity of the water drop with respect to the passenger in the car is simply the vector difference between the velocity of the water drop and the velocity of the car:
v_drop,p = v_drop - v_car
where v_drop is the velocity of the water drop (14.0 m/s downward) and
v_car is the velocity of the car (29.3 m/s to the east).
Substituting the values, we get:
v_drop,p = (0, -14.0, 0) - (29.3, 0, 0)
v_drop,p = (-29.3, -14.0, 0) m/s
Thus, the drop appears to have a velocity of approximately 29.3 m/s to the west and 14.0 m/s downward with respect to the passenger in the car.
The acceleration of the water drop with respect to the passenger in the car is simply the vector difference between the acceleration of the water drop and the acceleration of the car:
a_drop,p = a_drop - a_car
where a_drop is the acceleration due to gravity (9.8 m/s² downward) and
a_car is the acceleration of the car (3 m/s² to the east).
Substituting the values, we have,
a_drop,p = (0, -9.8, 0) - (3, 0, 0)
a_drop,p = (-3, -9.8, 0) m/s²
Therefore, the drop appears to have an acceleration of approximately 3 m/s² to the west and 9.8 m/s² downward with respect to the passenger in the car.
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a line passes through the point (-6,6) and has a slope of 4/3. write an equation in point-slope form for this line.
Answers
Answer: m=4x+3-6
Step-by-step explanation: This is most likely wrong but it's the best I have, hope it helps!
Hello there! :)
Point-Slope Form:
y-y1=m(x-x1)
y1=6
x1=-6
m=4/3
Plug in the values:
y-6=4/3(x-(-6)
y-6=4/3(x+6)
Therefore, our final answer is: \(y-6=\frac{4}{3}(x+6)\)Hope this helps you!
~Just a felicitous girlie
#HaveAnAwesomeDay
\(SilentNature\) here to help
Are triangles adc and ebc congruent? triangle adc is overlapping triangle ebc so that they both share angle ace, point b is on segment ac, point d is on segment ec, segments ad and eb intersect at point f, segments bc and dc are each marked with one dash, and angles cad and ceb are each marked with an arc yes, by sss yes, by aas yes, by sas not enough information
Answers
The answer is "Not enough information" to determine congruence between triangles ADC and EBC.
Based on the given information, we can determine whether triangles ADC and EBC are congruent.
To establish congruence, we need to show that corresponding sides and angles are equal.
1. Sides:
- Segment AD intersects segment EB at point F.
- Segment BC and DC are marked with one dash each.
- Since we don't have any information about the lengths of these segments, we can't determine whether the sides are equal.
- Therefore, we cannot conclude congruence based on the side lengths alone.
2. Angles:
- Triangle ADC and triangle EBC share angle ACE.
- Angles CAD and CEB are each marked with an arc.
- Although we know the angles are equal, it is not sufficient to establish congruence by angles alone.
Based on the given information, we do not have enough information to determine whether triangles ADC and EBC are congruent. The side lengths and angles are not enough to establish congruence.
In conclusion, the answer is "Not enough information" to determine congruence between triangles ADC and EBC.
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the base of a ladder should be set out a distance equal to ____ the height to the point of support.
Answers
The base of a ladder should be set out a distance equal to one-fourth (1/4) the height to the point of support. This ensures stability and safety while using the ladder. It is important to pay attention to this detail when using a ladder to prevent accidents and injuries.
The base of a ladder should be set out a distance equal to 1/4 the height to the point of support.
Determine the height to the point of support (H).
Calculate the appropriate distance for the base of the ladder by using the formula: Distance = 1/4 * H.
Set the ladder's base at the calculated distance from the wall or support.
The base of a ladder should be set out a distance equal to one-fourth (1/4) the height to the point of support. This ensures stability and safety while using the ladder. It is important to pay attention to this detail when using a ladder to prevent accidents and injuries.
This guideline ensures that the ladder is placed at a safe angle to prevent it from slipping or falling.
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HELP ME ak = y +w, for a
Answers
Answer:
yea
Step-by-step explanation:
Hope this helps.
chee can paint a room in 10 hours. melique can paint the same room in 6 hours. how long does it take for both jee and melique to paint the room it they are working together?
Answers
Based on the given conditions, formula:
6 • 10/6 + 10
Calculate
6 × 10/16
Reduce
3 × 5/4
Calculate
3 × 5/4
Answer: 15/4
Alternative Forms: 3.75, 3 3/4
What are the new coordinates? Marking brainliest whoever gets it!
Answers
Answer:
a = (9,8)
b=(10,6)
c=(4,3)
Step-by-step explanation:
basically, you just take the original coordinates and add the translation to it.
so a was -1,6 so just at 10 to -1 as they are x coordinates nad add 2 to 6 because they are Y coordinates and you just do it for all of the points.
(Will give brainliest) In your own words, say what a rational number is. Give at least three different examples of rational numbers.
In your own words, say what an irrational number is. Give at least two examples.
Answers
Hey there!
A rational number is a number that CAN be turned in to a fraction, like 0.5, or 9, 0r -\(3^2\).
A rational number is a number that CANNOT be turned into a fraction, like pi, or √2.
Hope it helps and have a great dayyyyy!!!!!
Helpppp plz!!!! Bout to FINSH
Answers
if i’m not mistaken
Answer:
A
Step-by-step explanation:
An observational study found that the amount of time a child spends learning a second language is associated with standardized testing performance. The correlation coefficient was found to be r = 0.94. A conclusion was made that the more time a child spends learning a second language, the better the child performs on standardized tests. Why is such a conclusion not correct? (2 points)
The sample was not representative of the population.
The correlation value should be negative for such a conclusion.
The correlation value should equal 0 for such a conclusion.
Causation cannot be determined from an observational study.
The correlation value implies that less than 90% of the variability in standardized testing performance can be explained by learning a second language.
Answers
Answer: the answer is that causation cannot be determined from an observational study.
Step-by-step explanation:
The conclusion is not correct because Causation cannot be determined from an observational study.
When do we perform observational study, sample survey?Observational study is usually chosen when the researches the system is likely to produce different result if interfered.
Sample survey is done if the population is too big to analyze or destructible as the analysis occurs.
We are given that the correlation coefficient was found to be r = 0.94.
Also, the conclusion was made that the more time a child spends learning a second language, the better the child performs on standardized tests.
Since the correlation value implies that less than 90% of the variability in standardized testing performance can be explained by learning a second language.
The conclusion is not correct because Causation cannot be determined from an observational study.
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Use the ingredients from the food bank’s recipe for vegetable bean soup shown below.
AlternativeText
Anna makes a pot of the soup. She is using a 14-cup measuring cup.
Part A
How many times will Anna need to fill the measuring cup to measure 78 cup of turnips? Show your work.
Answers
Anna can only fill the measuring cup a whole number of times, she will need to fill it 6 times to measure 78 cups of turnips.
What is division in mathematics?
Division is the process of splitting a number or an amount into equal parts.
To find the number of times Anna will need to fill the measuring cup, divide the number of cups of turnips by the size of the measuring cup:
78 cups/14 cups:
= 78/14
=5.57 measures
Hence, Anna can only fill the measuring cup a whole number of times, she will need to fill it 6 times to measure 78 cups of turnips.
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Who drove the fastest? Select the correct answer.Immersive Reader
(0/1 Point)
Trevor drove 202 miles in 4 hours.
Maggie drove 330 miles in 6 hours.
Nev drove 412 miles in 8 hours.
Juanita drove 261 miles in 5 hours.
Answers
Aaron bought these ingredients to make the trail mix recipe. How many pounds of trails mix will he make
Answers
Answer: 48 pounds of trails mix
Step-by-step explanation:
<3
Answer:48
Step-by-step explanation:
basically do 16 divided by each and add them
I don’t know what I’m doing
A graphical device used for enumerating sample points in a multiple-step experiment is a a. bar chart b. pie chart c. histogram d. None of the other answers is correct.
Answers
None of the listed methods are used for enumerating sample points in a multiple-step experiment. So, option D is the correct answer.
Graphical methods are important mathematical tools that are very helpful when it comes to managing a vast amount of data. These also help when we need to visually represent data. These methods help quite a lot since they make it easier to keep track of data and understand it as well.
A bar chart and a histogram are similar tools that are used to represent data by plotting them as rectangular bars. These can be either vertical or horizontal. A pie chart is also a tool that uses a shape for data visualization. In its case, it represents data in the shape of a circle and all categories/data sets have their slices. So, this means that these three are not methods that can be used for enumerating sample points in a multiple-step experiment. Hence, option D is the correct option.
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Translate the following verbal expressions into
algebraic expressions:
16 increased by 4 times a number
Three times the difference of x and 8
3 less than the product of 5 and y
Answers
Answer:
16 + 4n
3(x - 8)
(5 × y) - 3
Step-by-step explanation:
16 increased by 4 times a number:
16 + 4n
Three times the difference of x and 8:
3(x - 8)
3 less than the product of 5 and y:
(5 × y) - 3
What is the length of C D on a grid, C is (-5, 5) and D is (4, -2), to the nearest tenth? Iready Help ASAP
Answers
Answer:
11.4
Step-by-step explanation:
You want the distance between C(-5, 5) and D(4, -2).
DistanceThe distance formula is ...
d = √((x2 -x1)² +(y2 -y1)²)
For the given points, the distance is computed to be ...
d = √((4 -(-5))² +(-2 -5)²) = √(81 +49) = √130
d ≈ 11.4
The length of CD is about 11.4 units.
__
Additional comment
The distance formula is an application of the Pythagorean theorem. It computes the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates.
can someone help me find the equation for this line please
Answers
Answer:
y = x + 1
Step-by-step explanation:
The line y = x goes through the origin, and forms a perfect 45 degree angle with the x axis.
This is that same line, moved upward 1 unit, so the y value comes out 1 unit more.
Also, in y = mx + b form (slope-intercept form), we see slope m = 1 and y-intercept b = 1, so
y = 1x + 1 = x + 1
y = x + 1
Part E
With two of the angles fixed on ∆DEF, what do you notice about the shape of ∆DEF when compared with ∆ABC?
Answers
If two angles of triangle ∆DEF are fixed, the third angle is determined since the sum of the interior angles of a triangle is always 180 degrees.
Therefore, the shape of ∆DEF is fixed and cannot be changed without altering the angles.
Comparing ∆DEF to ∆ABC, we can say that they may have different shapes. If the third angle of ∆DEF is different from the corresponding angle of ∆ABC, then the triangles will not be congruent and will have different shapes. However, if the third angle of ∆DEF is the same as the corresponding angle of ∆ABC, then the triangles will be similar and have the same shape, but they may be scaled or rotated versions of each other.
In summary, if two angles of ∆DEF are fixed, we cannot determine the shape of ∆DEF relative to ∆ABC without additional information such as the lengths of the sides.
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5 5xe" dx [integrate by Parts]
Answers
Final answer for the given integral is: \(5x * e^x - 5 * e^x + C\), integrating by parts involves choosing a function to differentiate and another to integrate, using the formula to solve for the integral, and then simplifying the result with the constant of integration.
Given the integral ∫5x * e^x dx, we'll use integration by parts to solve it. Integration by parts is based on the product rule for differentiation and is given by the formula: \(∫u dv = uv - ∫v du.\)
First, we need to choose u and dv. In this case, we'll choose u = 5x and \(dv = e^x dx\). Now, we need to find du and v. Differentiating u, we get du = 5 dx, and integrating dv, we obtain\(v = e^x.\)
Using the integration by parts formula, we have:
\(∫5x * e^x dx = (5x) * (e^x) - ∫(e^x) * (5 dx)\)
Simplifying the integral, we get:
\(∫5x * e^x dx = 5x * e^x - 5∫e^x dx\)
Next, we integrate e^x dx, which is simply e^x. So, the integral becomes:
\(5x * e^x - 5 * e^x + C\)
Here, C represents the constant of integration. Thus, the final answer for the given integral is: \(5x * e^x - 5 * e^x + C\)
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the following is a summary of a one-way between-subjects anova: f(2, 37) = 3.42, p < .05, η 2 = .12. how many pairwise comparisons need to be made for this anova result?
a.2
b.3
c.4
d.12
Answers
The pairwise comparisons that need to be made for this anova result will be b.3
How to calculate the valueIn order to determine the number of pairwise comparisons needed for a one-way between-subjects ANOVA with three groups, we can use the formula:
N = (k * (k-1)) / 2
Where N represents the number of pairwise comparisons and k represents the number of groups. In this case, k = 3.
Plugging in the values:
N = (3 * (3-1)) / 2
N = (3 * 2) / 2
N = 6 / 2
N = 3
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What is 121−−−√? please help
Answers
Answer:
11 × 11 = 121
\(\\---> \sqrt{121} = 11\)
Which of the following expressions is equivalent to 810 x 9?
O (800 x 9) + (10 x 9)
O (81 x 9) + (10 x 9)
O (600+ 310) x 9
O
814 x 5
Answers
Answer:
(800 x 9) + (10 x 9)
Step-by-step explanation:
Find out what 810 x 9 is:
810 x 9 = 7290
Then see which expression has the same answer. Personally I'd check all of them, but luckily the first expression is the correct one so you don't need to go through the rest (since it only asks for one correct expression):
(800 x 9) = 7200
(10 x 9) = 90
7200 + 90 = 7290