Suppose we are buying beans and rice to feed a large gathering of people, and we plan to spend $120 on the two ingredients. Beans cost $2 a pound and rice costs $0.50 a pound.
If x represents pounds of beans and y pounds of rice, the equation 22 + 0.50y = 120 can represent the constraints in this situation.
The line below shows the graph of this equation (ignore the points not on the line).
Please help me I would appreciate it so much
Answers
The true statements about the constraints in this situation are:
If we buy 30 pounds of beans we can buy with 120 pounds of rice.If we buy no beans we can buy 240 pounds of rice.If we buy 20 more pounds of rice, we would have to buy 5 less pounds of beans.How to determine the true statements?In order to determine the true statements, we would substitute the value of x and y into the given linear equation and then evaluate. From the information provided, the constraints in this situation are modeled or represented by this linear equation:
2x + 0.50y = 120
Where:
x represents pounds of beans.y represents pounds of rice.When x = 40 and y = 60, we have:
2x + 0.50y = 120
2(40) + 0.50(60) = 120
80 + 30 = 120
110 ≠ 120 (Not a solution).
When x = 30 and y = 120, we have:
2x + 0.50y = 120
2(30) + 0.50(120) = 120
60 + 60 = 120
120 = 120 (True solution).
Therefore, if we buy 30 pounds of beans we can buy with 120 pounds of rice.
When x = 0 and y = 240, we have:
2x + 0.50y = 120
2(0) + 0.50(240) = 120
0 + 120 = 120
120 = 120 (True solution).
Therefore, if we buy no beans we can buy 240 pounds of rice.
When x = 0 - 5 and y = 240 + 20, we have:
2x + 0.50y = 120
2(0 - 5) + 0.50(240 + 20) = 120
-10 + 130 = 120
120 = 120 (True solution).
Therefore, if we buy 20 more pounds of rice, we would have to buy 5 less pounds of beans.
When x = 0 + 10 and y = 240 - 60, we have:
2x + 0.50y = 120
2(0 + 10) + 0.50(240 - 60) = 120
20 + 90 = 120
110 = 120 (Not a solution).
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Related Questions
The radioactive substance cesium-137 has a half-life of 30 years. The amount A(t) (in grams) of a sample of cesium -137 remaining after t years is given by the following exponential function.A (t) = 523 (1/2)^t/30Find the initial amount in the sample and the amount remaining after 100 years.Round your answers to the nearest gram as necessary.Initial amount:Amount after 100 years:
Answers
After 100 years:
Replace t by 100:
A (t) = 523 (1/2)^t/30
A (100) = 523 (1/2)^100/30 = 523 (1/2) ^10/3 = 51.88 =52 grams
The initial amount of the sample is 523
A bag contains twelve balls labeled 1 through 12. One ball will be randomly picked.
What is the probability of picking an even number?
Write your answer as a fraction in simplest form
Answers
Hello there!
If a bag has 12 balls labelled 1 through 12, that means that the balls inside the bag includes:
1 2 3 4 5 6 7 8 9 10 11 12
When creating a fraction for a probability, the numerator usually consists of a specific probability you are trying to find; the denominator usually consists of the total amount of samples in the bag.
In this example: What is the probability of picking an even number?
Ask yourself: What are we trying to find?
We are trying to find the probability of even numbers.
Then ask yourself: What is the amount of possibilities that we can get an even number from the bag?
The bag consists of: 1 2 3 4 5 6 7 8 9 10 11 12
Even numbers are divisible by 2 and has a remainder of 0 ; which means in this bag, the bolded numbers are even.
Then we can conclude that in this bag, counting all of the bolded numbers, we have 6 possibilities of choosing an even number.
Finally, think about: What is the total amount of samples in this bag?
We know that there are 12 balls, so 12 would be the total amount.
To conclude, we can find 6 even numbers in a bag of 12 balls;
Therefore, the chances you can pick an even number is [tex]\frac{6}{12} ,[/tex] or [tex]\frac{1}{2}[/tex].
If you write every whole number from I to
100. how many times will you write the digit
"2"?
Answers
Answer:
20 times
Step-by-step explanation:
Digit 2 appears 20 times in first 100 natural numbers
The bar graph shows the percentage of college freshmen in a certain country with an average grade of Ain high school.The data displayed by the bar graph can be described by the mathematical model p =4x- + 25 where xis the number of years after 1980 and p is the percentage of college freshmen who had an average
Answers
Okay, here we have this:
Considering the provided formula and information, we are going to calculate the requested percent of college freshmen in 2010, so we obtain the following:
So since x corresponds to the number of years after 1980, in this case we will replace x with 30, since it is 30 years after 1980, we have:
p=4x/5+25
Replacing:
p=4(30)/5+25
p=120/5+25
p=24+25
p=49
So, as we can see, the model assumes that in 2010 the percentage was 49%, and the real one is 47%. It means that the model overestimates the real value by 2%.
14. Consider this system of equations.y = -2x2 + 9y = 4x + 3What values of x are solutions to the system of equations?A.x = -9 and x = 7B.x= -7 and x = 9C.x = -3 and x = 1D.x = -1 and x = 3
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Consider this system of equations:
[tex]\begin{gathered} y=-2x^2\text{ +9} \\ y\text{ = 4x + 3} \end{gathered}[/tex]Step 2:
The details of the solution are as follows:
CONCLUSION:
The values of x that are the solutions to the system of equations are:
[tex]x\text{ =- 3 and x = 1 -- OPTION C}[/tex]
5x^2-25=100 solve by taking square root
Answers
Answer:
x=5,−5
Step-by-step explanation:
Find the mean for n = 200 and p = 0.24 when the conditions for the binomial distribution are met.
Answers
The mean value of expected value for a binomial distribution is given by the next formula:
[tex]\mu_x=n\cdot p[/tex]Where n is the number of trials and p is the probability of success. So, using the given data:
[tex]\begin{gathered} \mu_x=200\cdot0.24 \\ \mu_x=48 \end{gathered}[/tex]So the expected value or mean is 48
the scale of topographical of map is 1:50000.what is the area of a dam which is represented on the map by an area of 3.5 centimeter square
Answers
The scale of a topographical map is 1:50000. This means that 1 cm on the map is 50 000 cm on reality.
[tex]1\operatorname{cm}\rightarrow50000\operatorname{cm}[/tex]Now, we can take the
i really need help can anyone help solve the attatched question
Answers
please help thank you
Answers
Answer:
%25 of customers ordered ice tea.
Step-by-step explanation:
To find percentage = Part/Whole x 100
35/140 x 100 = 0.25 x 100 = %25
35 of 140 can be written as:
35/140
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
Therefore, the answer is 25%
If you are using a calculator, simply enter 35÷140×100 which will give you 25 as the answer.
Divide write the answer as a fraction in simplest form 7/8 divided by 6 =
Answers
Answer:
[tex]\frac{7}{48}[/tex]Explanation: We have been given a fraction 7/8 and we need to divide it by 6 and write it in simplest terms.
Dividing and simplifying gives us following:
[tex]\frac{7}{8}\text{ Divied 6}\rightarrow\frac{7}{8}\times\frac{1}{6}=\frac{7}{48}=\frac{7}{48}[/tex]you are playing a game of hide - and - seek with two friends . while one of your friends counts , you and your other friend are given a chance to hide in one of five possible hiding spots . you are each allowed to pick a hiding spot , and are permitted to share a hiding spot . your friend finishes counting and checks one of the five hiding spots . assuming that everyone's decisions are made uniformly at random , what are the chances that your friend does not find anyone in the first spot that they check ?
Answers
The probability the friend finds no one in the first spot is 60%.
What is probability?Probability is the chance or likelihood that an expected event occurs when there are many possible outcomes or events.
For instance, the probability that when the counting friend goes to the hiding spot, they can or cannot find a friend there.
The two friends can only hide in 2 spots, leaving 3 spots with nobody.
The number of hiding spots = 5
The number of friends hiding = 2
The number of counting friends = 1
The number of spots they can hide = 2 out of 5
The probability of finding a person in a hiding spot = 2/5 or 40%
The probability of not finding a person in a hiding spot = 3/5 (1 - 2/5) or 60% (1 - 40%).
The chances that your friend finds anyone in the first spot are 60%.
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f(x)=4x+2; Find f(8)
Answers
We have:
[tex]f(x)=4x+2[/tex]And want to find f(8), for this we simply replace x with 8 and operate:
[tex]f(8)=4(8)+2\Rightarrow f(8)=34[/tex]a ball dropped from rest and falls for 8 seconds
whats the final velocity
and whats te average velocity
how far did it fall
Answers
(07.02 HC)
Barbara draws pens randomly from a box containing 5 pens of the same shape and size. There is 1 green pen, 3 red pens, and 1 blue pen. She draws 1 red pen and then
another red pen without replacing the first one. Find the probability of drawing 1 red pen followed by another red pen, and show the equation used.
Answers
Answer: She already got rid of two red pens, so there's one red pen left.
5-1=4-1=3. 1 red 1 blue 1 green. 100/3=33.3333333… so her chance of getting another red pen is 33.3333333333333333333333% and a 66.66666666666666666666% chance of not.
Step-by-step explanation
101x^2+231x-334=-2 find the A,B,C
Answers
The roots of the equation is 1 and 3.28
The given equation is a quadratic
To find the roots of a quadratic equation, the formula is
[tex]\frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]
The equation is 101x^2+231x-334=-2 we need to find the A,B,C
101x^2+231x-332 = 0
here a is 101, b is 231, and c is -332
[tex]\frac{-b + \sqrt{b^{2} - 4ac } }{2a}\\\frac{-231 + \sqrt{231^{2} - 4(101)(-332) } }{2(101)}\\\frac{-231 + \sqrt{53361 + 134128 } }{202}\\\frac{-231 + \sqrt{187489 } }{202}\\\\\frac{-231 + \sqrt{187489 } }{202}\\\\\frac{-231 + 433 }{202}\\\\=\frac{202}{202}\\\\ 1[/tex]
[tex]\frac{-b - \sqrt{b^{2} - 4ac } }{2a}\\\frac{-231 - \sqrt{231^{2} - 4(101)(-332) } }{2(101)}\\\frac{-231 - \sqrt{53361 + 134128 } }{202}\\\frac{-231 - \sqrt{187489 } }{202}\\\\\frac{-231 - \sqrt{187489 } }{202}\\\\\frac{-231 -433 }{202}\\\\=\frac{664}{202}\\\\ 3.28[/tex]
Therefore, the roots of the equation is 1 and 3.28
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the weights of items produced by a certain company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounces. the manager of the production line wants to discard any item whose weight is in the lower 2.5%. what is the maximum possible weight for the items discarded?
Answers
Using standard deviation, the maximum possible weight for the items discarded is 28004 ounces.
What is meant by standard deviation?The standard deviation is a statistic that describes the degree of volatility or dispersion in a set of numerical values. A low standard deviation means that the values tend to be close to the established mean, whereas a large standard deviation suggests that the values exist distributed throughout a greater range.A measure of a data set's variance from the mean is referred to as "standard deviation." While a high standard deviation indicates that the data are more spread, a low standard deviation suggests that the data are clustered around the mean.So,
Mean = 4.5Standard deviation = 0.3(A) P(x > 4.14)
z = (4.14 - 4.5) / 0.3= -1.20P(z > -1.20) = P(z < 1.20)= 0.8849(B) P(4.8 < x < 5.04)
= P (4.8 - 4.5/0.3 < x - μ/σ < 5.04 - 4.5/0.3)= P(1 < z < 1.80)= P(z < 1.80) - P(z < 1)= 0.9641 - 0.8413= 0.1228 or 12.28 %(C) P(x > x) = 0.05
z value will be, 1.6451.645 = (x - 4.5) / 0.3x = 4.9935(D) P(x < 5.01)
= (z = x - μ/σ)= (5.01 - 4.5) / 0.3 = 1.7P(z < 1.70) = 0.9554n = 27875/0.9954= 28004Therefore, using standard deviation, the maximum possible weight for the items discarded is 28004 ounces.
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Correct question:
The weights of items produced by a company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounces. a. What is the probability that a randomly selected item from the production will weigh at least 4.14 ounces? b. What percentage of the items weighs between 4.8 and 5.04 ounces? c. Determine the minimum weight of the heaviest 5% of all items produced. d. If 27,875 items of the entire production weigh at least 5.01 ounces, how many items have been produced?
Why are there two possible solutions to the equation, X2 = 100?
Answers
Answer:
100 is perfect square
Step-by-step explanation:
in x² =100, we have x×x=100 and x could be ±10 since both 10² and (-10)² is equal to 100
If y varies directly with x, write an equation for the direct variation. Then find each value.1. If x= -12 when y= -3 find x when y= -6
Answers
Since y varies directly with x then
[tex]\begin{gathered} \frac{y}{x}=k \\ \text{Where k }is\text{ the constant of proportionality} \end{gathered}[/tex]So,
[tex]\frac{y}{x}=\frac{-3}{-12}=\frac{3}{12}=\frac{1\cdot3}{4\cdot3}=\frac{1}{4}[/tex]Then, 1/4 is the constant of proportionality. So that,
[tex]\begin{gathered} \frac{y}{x}=\frac{1}{4} \\ \frac{-6}{x}=\frac{1}{4} \\ -\frac{6}{x}\cdot x=\frac{1}{4}\cdot x \\ -6=\frac{x}{4} \\ 4\cdot-6=\frac{x}{4}\cdot4 \\ -24=x \end{gathered}[/tex]When Madison left her house this morning, her cell phone was 80% charged and itthen started to lose 8% charge for each hour thereafter. Write an equation for B, interms of t, representing the charge remaining in Madison's battery, as a percentage, thours after Madison left her house.
Answers
Given:
Initially, the cell phone was 80% charged.
Then started to lose 8% charge for each hour thereafter.
To find:
The equation for B in terms t
WXYZ is a kite. Angle WXY has a measure of 133 degrees and angle ZYX has a measure of 34 degrees. Find the measure of angle ZWY.
Angle ZWY has a measure of what
degrees.
Answers
Angle ZWY has a measure of 13 degrees.
Define angles.An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. a geometric shape made up of two lines that meet at the same point or two planes that meet at the same line. the distance in degrees between such lines or planes.
Given,
Angle WXY has a measure of 133 degrees
Angle ZYX has a measure of 34 degrees
Angle ZWY:
= 180 - 133 -34
= 13
Angle ZWY has a measure of 13 degrees.
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in 1982, the us mint changed the composition of pennies from all copper to zinc with copper coating. pennies made prior to 1982 weigh 3.1 grams. pennies made since 1982 weight 2.5 grams. if you have a bag of 1267 pennies, and the bag weighs 3541.9 grams, how many pennies from each time period are there in the bag?
Answers
Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams. 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.
Given that,
The 1982 change in pennies composition from all copper to zinc with copper coating was made by the US Mint. Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams.
We have to find how many coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.
An issue of quantity and amount. In this context, the term "amount" refers to weight. The variables should be identified with letters that will make them easy to distinguish: Z for largely zinc and C for all copper. Create weight and quantity equations:
C + Z = 1287
3.1 C + 2.5 Z = 3601.5
By multiplying all three components of the first equation by -2.5 and placing them under the second equation, drawing a line, and then subtracting, you can eliminate the Z using this method.
3.1 C + 2.5 Z = 3601.5
-2.5 C - 2.5 Z = -3217.5
--------------------------------
0.6 C = 384
Divide both sides by .6.
C = 640
Subtract 640 from 1287.
Z = 647
Therefore, 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.
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Find the slope between these two points:
(9,3),(19,-17)
Answers
Answer:
Slope = -2
Step-by-step explanation:
(9, 3), (19, -17)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -17 - 3 -20
m = ------------ = ------------ = -------- = -2
x₂ - x₁ 19 - 9 10
y - y₁ = m(x - x₁)
y - 3 = -2(x - 9)
y - 3 = -2x + 18
+3 +3
-----------------------
y = -2x + 21
I hope this helps!
type the correct answer in each box. use numerals instead of words if neasary
Answers
This is given point in the fourth quadrant.
In this point, the adjacent is
[tex]\frac{5}{13}[/tex]The opposite is y.
Find hypotenuse h using the pythagorean theorem:
[tex]\begin{gathered} h^2=(\frac{5}{13})^2+y^2 \\ h=\sqrt[]{\frac{25}{169}+y^2} \end{gathered}[/tex][tex]\sec (\theta)[/tex]is equal to hypotenuse by adjacent.
[tex]\cot (\theta)[/tex]is equal to adjacent by opposite.
In the fourth quadrant,
[tex]\sec \theta[/tex]is positive , and
[tex]\cot \theta[/tex]is negative.
So,
[tex]\begin{gathered} \sec \theta=\frac{h}{\frac{5}{13}} \\ =\frac{13\sqrt[]{\frac{25}{169}+y^2}}{5} \\ \cot \theta=\frac{\frac{5}{13}}{-y} \\ =-\frac{5}{13y} \end{gathered}[/tex]Please answer only if you know the answer.
Answers
Step-by-step explanation:
The slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of 3/4 is y = (3/4)x - 31/4.
What is the slope-intercept form?
The slope-intercept form of a line is y=mx + c.
Where, x and y are coordinates. m = slope and c = y intercept.
Given, slope (m) = 3/4
Substituting the values of (x, y) as (5, -4) and m = 3/4, we get:
-4 = (3/4) × 5 + c
⇒ c = -4 - (3/4) × 5 = -4 - 15/4 = -31/4
Now, putting the value of c in the standard equation:
y = (3/4)x - 31/4
⇒ 4y = 3x - 31
⇒ 3x - 4y = 31
Answer is Option C
Tom surveyed 150 students at his school to find out each student's favorite color. His results are shown in the circle graph above. Candace asked 15 of her friends from the same school to choose their favorite color, and 5 people chose yellow. According to Tom's survey, how many of Candace's friends would have been expected to choose yellow?
Answers
We have that in Tom's survey he obtained that 20% of the students like the yellow color (see graph above).
Then, in Candance's (small) survey, she asked 15 friends. According to Tom's survey, Candance should have obtained that 20% of her friends like the yellow color.
Therefore, we need to find 20% of 15 (friends) to find the expected number of friends that Candance should have had using the results of Tom's survey. Then, we have:
[tex]\frac{20}{100}\cdot15=\frac{300}{100}=3[/tex]Hence, according to Tom's survey, Candance's friends would have been expected to be 3 to choose (of her 15 friends) yellow (3 is 20% of 15).
A wholesaler sells a guitar for $1,396.20. What is the percent markup based on cost if the wholesaler paid $780 for the guitar?
Answers
The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%
Given,
The cost price of the guitar = $780
The selling price of the guitar = $1396.20
We have to find the markup percent based on the cost;
Markup percentage;
The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %.
Markup percent = (Selling price - cost price) / cost price x 100
= (1396.20 - 780) / 780 x 100
= 616.20 / 780 x 100
= 0.79 x 100
= 79%
That is,
The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%
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Write the equation of the line in y=mx+b form using the following two points:
(-2,-1) and (-1,-2)
Enter you equation here: type your answer....
10 points
Answers
Answer: The slope-intercept form for a line with the coordinates of (-2,-1) and (-1,-2) is:
y= -1.00x + -3.00
(results are in decimal form, rounded to the nearest 100th)
i hope i helped it is for if it was for like slope intercept form
Step-by-step explanation:
write an equation of the line below.
Answers
Answer:
y = 2x + 3
Step-by-step explanation:
The y-intercept is where x = 0. Therefore, the y-intercept would be 3. To find the slope, you do Δy/Δx (Δ = Change In). To find that, you go up 4 times, then move to the right 2 times to reach the second dot. Now, you do 4 / 2, which equals 2. Your final equation will be y = 2x + 3.
Does anyone know why this is wrong??
Answers
[tex]=-10x^4-4x^3+6x^2[/tex]