Olivia makes and sells bracelets and necklaces. She can make up to 60 pieces per week, but she can only make up to 40 bracelets and 40 necklaces. Write and graph a system of inequalities that shows the combination of bracelets and necklaces that she can make if she wants to sell at least 30 items per week. If necklaces sell for $80 each and bracelets sell for $5 each, what is the most amount of money she can make in a week?
Answers
We wrote a system of inequalities, identified the graph and found that the maximum money made in a week as $3300.
What is meant by inequalities?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Let x be the number of bracelets and y be the number of necklaces.
Given Olivia can make up to 60 pieces per week.
So the inequality is: x + y ≤ 60
She can make less than or equal to 40 bracelets.
So the inequality is : x ≤ 40
She can make less than or equal to 40 necklaces as well in a week.
So the inequality is : y ≤ 40
She wants to sell at least 30 items per week.
x + y ≥ 30
x+y ≤60 can be written as
We can draw the inequalities as shown below.
x + y ≤ 60 as red
x ≤ 40 as green
y ≤ 40 as violet
x + y ≥ 30 as blue
The overlapping region of all inequalities is yellow.
The money made per week: 5x + 80y
We have to find the maximum money made.
The vertices of the yellow region are:
(0,30),(0,40),(30,0),(40,0),(20,40),(40,20)
The coordinates with negative values are neglected.
From this, 5*20 + 80 * 40 = $3300 is the maximum amount.
Therefore we wrote a system of inequalities, identified the graph and found that the maximum money made in a week as $3300.
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Related Questions
It cost Nevaeh $5.39 to send 77 text messages. How much does it cost to send one text
Answers
Answer:
$0.07
Step-by-step explanation:
We know
It cost Nevaeh $5.39 to send 77 text messages.
How much does it cost to send one text?
We take
5.39 / 77 = $0.07 per text
So, it costs $0.07 to send one text.
It costs Nevaeh $0.07 to send one text message.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
To find out how much it costs to send one text message, we can divide the total cost by the number of messages:
Cost per message = total cost/number of messages
In this case, the total cost is $5.39 and the number of messages is 77, so:
Cost per message = $5.39 / 77 = $0.07
Therefore, it costs Nevaeh $0.07 to send one text message.
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Compare the rate of change of the two graphs shown.
The function for graph (1 or 2) has a higher rate of change than the function of graph (1 or 2).
.
Answers
Answer: The function of graph 2 has a higher rate of change than the function of graph 2
Step-by-step explanation:
Solve: 2x2 = 98 please help me
Answers
Answer:
1=24.5
Step-by-step explanation:
2*2=98
4=98
2= 49
which means
1 is 24.5
Ms. Baynes has $70 and spends $6 on each of y books.
Answers
6y=70 well 70/6 is 11.666……. and well she only has 70$ so she can only by 11 books
Which of the following inequalities is represented on the graph?
Number line showing range from negative five to five. The left end point is a closed dot at negative two, with a ray pointing right past five.
Responses
x ≥ –2
x ≥ –2
x ≤ –2
x ≤ –2
x > –2
x > –2
x < –2
Answers
The inequalities represented on the graph is x ≥ -2.
What are graph of inequalities?In mathematics, an inequality is a mathematical expression where neither side is equal. Inequality in mathematics is defined as a comparison between two expressions or two numbers that is not equal. In mathematics, there are several varieties of inequality, including polynomial inequality, rational inequality, and absolute value inequality.
Given that,
Number line showing range from negative five to five. The left end point is a closed dot at negative two, with a ray pointing right past five.
From the above we observe that point on negative 2 is a closed dot hence the inequality would be ≥ or ≤.
Now, the ray point past five, that is it moves in positive direction.
Hence, the inequalities represented on the graph is x ≥ -2.
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if KM=52 and NL=33, find LM
Answers
The measurement of the LM will be 42.0
What is Pythagoras theorem?The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.
Here given in the question that one side of the wall 5 feet
So as it is a rectangular bedroom it can be split into 2 right-angled triangles.
So the hypotenuse of the triangle is 13 feet
Now using the Pythagoras theorem we can find out the length of the other wall
b² = h² -p²
given KM = 52, NL = 33
So the triangle MLN
LM = √(33²+26²) = 42.0
Hence The measurement of the LM will be 42.0
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If 6 notebooks cost d dollars, how much, in dollars, does each notebook cost?
Answers
Step-by-step explanation:
6 notebooks = $d
1 notebook = $?
So
1 notebook price = $d ÷ 6
Answer:
Step-by-step explanation:
n represents the number of notebooks
d represents the cost of a notebook
n = d one notebook = d dollars
9n = 9d multiply both sides by 9
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answers
Therefore, the equations that represent circles with a diameter of 12 units and a center on the y-axis are: x² + (y - 3)²=36 and x² + (y + 8)²=36.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of two expressions separated by an equals sign (=). The expression on the left side of the equals sign is called the left-hand side (LHS), and the expression on the right side of the equals sign is called the right-hand side (RHS). Solving an equation means finding the value of the variable that makes the equation true. I
Here,
A circle with diameter 12 units and center on the y-axis has its center at (0, c), where c is a constant. The radius of the circle is half the diameter, which is 6 units.
The equation of a circle with center (0, c) and radius r is given by:
x² + (y - c)² = r²
Substituting r = 6 and simplifying, we get:
x² + (y - c)² = 36
The only two equations among the options given that match this form are:
x² + (y - 3)² = 36 (center at (0,3))
x² + (y + 8)² = 36 (center at (0,-8))
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25 points. Please show working out!
Answers
Answer:
42 m
Step-by-step explanation:
Equilateral triangle means that all sides are the same thus if the perimeter is 12 m
12m/3 = 4m for each side
The length of the boom will then how many triangles make the length which looks to be about 10.5
So 10.5 x 4 = 42 m
I need help with this please
Answers
Answer:
Both have 4 points, and sides.
Squares have 4 even sides
Rectangles have 2 short sides and 2 long sides.
how to convert 0.24 as a fraction?
Answers
The value 0.24 as a fraction is 6/25. .
In mathematics, fractions are defined as part of a whole. A whole can be an object or a group of objects. In real life, if you cut a pie out of the whole pie, that piece becomes part of the pie. Fractions are words of Latin origin. "Fractus" means "broken" in Latin. In ancient times, rest was expressed in words. Later it was introduced in numerical form.
Fractions are also called parts or sections of any quantity. Represented by the symbol '/'. Bachelor/Bachelor For example, 2/4 is the numerator above and the fraction below the denominator. In this article, you will learn the definition of fractions in mathematics, types of fractions, how to convert fractions to decimals, and many solved examples and full explanations
to convert in fraction we will muliply and devide by 100.
0.24*100/100 =6/25
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Bob has a box of chocolates containing 6 chocolate covered almonds, 4 chocolate covered peanuts, and 8 plain chocolates. If the chocolates look identical, what is the probability that the first two chocolates Bob eats will have almonds?
Answers
Answer:
The probability that the first two chocolates Bob eats will have almonds is 5/51 or 9.8% (nearest tenth).
Step-by-step explanation:
Given that Bob has a box of chocolates containing 6 chocolate covered almonds, 4 chocolate covered peanuts, and 8 plain chocolates, the total number of chocolates in the box is:
[tex]\implies \sf Total=6 + 4 + 8 = 18[/tex]
Probability Formula[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
Therefore, the probability that the first chocolate Bob eats will have almonds is:
[tex]\implies \sf P(first\;almond)=\dfrac{6}{18}[/tex]
As Bob has eaten one almond chocolate there are now 5 chocolate covered almonds left and a total of 17 chocolates. Therefore, the probability that the next chocolate Bob eats will have almonds is:
[tex]\implies \sf P(second\;almond)=\dfrac{5}{17}[/tex]
To find the total probability for two or more events, multiply the probabilities. Therefore, the probability that the first two chocolates Bob eats will have almonds is:
[tex]\begin{aligned}\implies \sf P(first\;almond)\;and\;P(second\;almond) & =\dfrac{6}{18} \times \dfrac{5}{17}\\\\ &=\dfrac{30}{306}\\\\&=\dfrac{5}{51}\\\\&=0.0980392...\\\\&=9.80392...\%\end{aligned}[/tex]
Therefore, the probability that the first two chocolates Bob eats will have almonds is 5/51 or 9.8% (nearest tenth).
An electronics store sells used game consoles for $79.00 and new ones for $149. After two weeks the store made a profit of $1,456 by selling 14 to total game consoles. How many of each type of console were sold?
Answers
The number of used games consoles is 9 and the number of new game consoles is 5
Finding the numbers of each game:Here we use the Linear equation method to solve the problem. Since we don't know the number games, represent them with variables x and y.
Now for two linear equations according to the conditions as given in the problem. Solve the equations for the values of both x and y by using the substitution method.
Here we have
An electronics store sells used game consoles for $79.00 and new ones for $149.00
Let 'x' and 'y' be the number of used and new game consoles respectively
Cost of 'x' used games consoles = 79x
Cost of 'y' new game consoles = 149y
Given total profit =$ 1456
=> 79x + 149y = 1456 ----- (1)
The total number of game consoles = 14
=> x + y = 14
=> x = 14 - y ---- (2)
Substitute (2) in (1)
=> 79(14 - y) + 149y = 1456
=> 1104 - 79y + 149y = 1456
=> 70y = 350
=> y = 5
From (2) => x = 14 - 5 = 9
Therefore,
The number of used games consoles is 9 and the number of new game consoles is 5
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The average salary for first-year teachers is $27,989.
If the distribution is approximately normal with
cr = $3250, what is the probability that a randomly
selected first-year teacher makes these salaries?
A. Between $20,000 and $30,000 a year
B. Less than $20,000 a year
Answers
The probability that a randomly selected first-year teacher makes less than $20,000 a year is approximately 0.0071.
What is the probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
To solve this problem, we can use the normal distribution and the standard normal distribution table (also known as the z-table).
Let X be the salary of a first-year teacher. We are given that X is approximately normally distributed with a mean (average) of mu = $27,989 and a standard deviation of sigma = $3250. We want to find the probability that a randomly selected first-year teacher makes certain salaries.
A. Between $20,000 and $30,000 a year
To find the probability that a first-year teacher makes between $20,000 and $30,000 a year, we need to standardize the interval using the z-score formula:
z1 = (20000 - mu) / sigma = (20000 - 27989) / 3250 = -2.45
z2 = (30000 - mu) / sigma = (30000 - 27989) / 3250 = 0.63
Using a standard normal distribution table or calculator, we can find that the probability of a random variable being between z1 and z2 is approximately 0.8461.
Therefore, the probability that a randomly selected first-year teacher makes between $20,000 and $30,000 a year is approximately 0.8461.
B. Less than $20,000 a year
To find the probability that a first-year teacher makes less than $20,000 a year, we need to standardize this value using the z-score formula:
z = (20000 - mu) / sigma = (20000 - 27989) / 3250 = -2.45
Using a standard normal distribution table or calculator, we can find that the probability of a random variable being less than z is approximately 0.0071.
Therefore, the probability that a randomly selected first-year teacher makes less than $20,000 a year is approximately 0.0071.
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. Find the area of the shaded region.
Answers
find the first 4 terms of the arithmetic sequence on the graph
Answers
Answer:
-3, 1, 5, 9
Step-by-step explanation:
Read the y-coordinate of each point.
How many multiples of 10 are possible?
Answers
Answer:
Infinite (∞)
Step-by-step explanation:
What are multiples?A multiple in math are the numbers you get when you multiply a certain number by another number or integer.
Multiples of 10 are numbers that can be divided exactly by 10. The multiples of a number are infinite.
Its in the form of a picture
Answers
The slope of UN is solved to be
= -4 / 3How to find the slope of UNThe slope of UN is solved using the points denoting U and N and the points are
U (4, -2) and N (1, 2)
Formula for slope is
= change in y direction / change in x direction
= (-2 - 2) / (4 - 1)
= -4 / 3
The slope of UN is -1 1/3
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six out of every 9 households have a guest room. margaret asked x households in her neighborhood if they have a guest room, and 24 said yes. find x.
Answers
Using proportions, we determined 24 out of every 36 households have a guest room.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Given that, six out of every 9 households have a guest room.
So, the ratio is 6:9
Margaret asked x households in her neighborhood if they have a guest room, and 24 said yes
So, the ratio is 24:x
Now, the proportion is 6:9::24:x
6x=9×24
x=36
Hence, 24 out of every 36 households have a guest room.
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the probability of at least one head in two flips of a coin is
Answers
Answer:
[tex]\frac{2}{4}[/tex] or [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
When each time a coin is flipped, there are two possible outcomes.
The chance for either heads or tails being chosen is one half.
Thus, the number of times the coin can be flipped and land on heads or tails is [tex]\frac{1}{2}[/tex].
Hope it helped!
Rasheed has four and one-sixth cups of berries. He uses one and three-fourths cups of berries to make a milkshake. He then uses one and one-half cups of berries. After he makes his milkshake and muffins, how many cups of berries will Rasheed have left?
eleven-twelfths cups
one and five-twelfths cups
one and nine-eighteenths cups
one and sixteen twenty-fourths cups
Answers
Answer:
11 /16
Step-by-step explanation:
How do you find the average value of a function from a graph?
Answers
To find the average value of a function from a graph, you can follow these steps:
Determine the interval over which you want to find the average value of the function. This is usually denoted by [a, b].Use the graph of the function to determine the function values at the endpoints of the interval, f(a) and f(b).Use the formula for the average value of a function over an interval: Average value = (1 / (b - a)) * ∫(a to b) f(x) dx where ∫(a to b) f(x) dx represents the definite integral of the function over the interval [a, b].Evaluate the definite integral to find the average value of the function over the interval. Average value = (1 / (b - a)) * ∫(a to b) f(x) dxCompare the average value of the function to its values at the endpoints of the interval. If the average value is between f(a) and f(b), then the function has a horizontal line that intersects the graph at the average value.For more questions on Graphs
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what are the real solutions to y=x^2-25
Answers
Answer:
[tex]x=-5,5[/tex]
Step-by-step explanation:
[tex]y=x^2-25\\0=x^2-25\\0=(x+5)(x-5)\\x=-5,5[/tex]
1.5 Cheaters, study components: Researchers studying the relationship between honesty, age, and self-control conducted an experiment on 160 children between the ages of 5 and 15. Participants reported their age, sex, and whether they were an only child or not. The researchers asked each child to toss a fair coin in private and to record the outcome (white or black) on a paper sheet, and said they would only reward children who report white. Half the students were explicitly told not to cheat and the others were not given any explicit instructions. In the "no instruction" group the probability of cheating was found to be uniform across groups based on a child's characteristics. In the group that was explicitly told to not cheat, girls were less likely to cheat, and while rate of cheating didn't vary by age for boys, it decreased with age for girls (Ritz et al. 2000). Identify the following
a) What are the cases?
_____all children ages 5 to 15
_____the 160 children between the ages of 5 to 15
_____the coin flips
_____boys or girls
b) What are the variables and their types?
_____The variables and types are age (discrete), sex (regular categorical), whether they were an only child or not (regular categorical)
_____The variables and types are age (discrete numerical), sex (ordinal), whether they were an only child or not (regular categorical), the result of the coin flip (regular categorical), whether the children were given instructions or not (regular categorical)
_____The variables and types are age (discrete), sex (regular categorical), whether they were an only child or not (regular categorical), the result of the coin flip (regular categorical), whether the children were given instructions or not (regular categorical), and whether the child cheated (regular categorical)
_____The variables and types are age (discrete), sex (ordinal), whether they were an only child or not (regular categorical), the result of the coin flip (regular categorical), whether the children were given instructions or not (regular categorical), and whether the child cheated (regular categorical)
c) What is the main research question?
_____Do girls cheat more or less often than boys?
_____What is the effect of age, sex, only child status, and whether or not children were given instructions on the rate of cheating in a game?
_____Do children follow directions?
Answers
160 children between the ages of 5 and 15 comprise the cases.
Age and sex child cheated are the variables and types.
What impact do age, sex, being an only child, and whether or not kids received instructions have on the frequency of cheating in games?
a) What are the cases?
The cases are: the 160 children between the ages of 5 to 15.
b) What are the variables and their types?
The variables and types are: age (discrete numerical), sex (regular categorical), whether they were an only child or not (regular categorical), the result of the coin flip (regular categorical), whether the children were given instructions or not (regular categorical), and whether the child cheated (regular categorical).
c) What is the main research question?
The main research question is: What is the effect of age, sex, only child status, and whether or not children were given instructions on the rate of cheating in a game?
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a plumer charges $25 for a service call plus $50 per hour of service. write an equation in slope - intercept form for cost , c ,after h hours of service, what will be the total cost for 8 hours of work? 10 hours of work
Answers
The total cost for 10 hours of work would be 25 + 50(10) = 525.
What is cost?Cost is the monitorial associated with the purchase of production of food or service if can include the prices of material of which is over it and other expenses that are related to the production of the code of service cost is a major fraction of when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.
The marginal cost of producing 5 items can be calculated using the equation C(x)=1300+4x/10. The marginal cost is the cost associated with producing one additional item. To calculate the marginal cost, we can plug in x=5 into the equation.
The equation in slope-intercept form for cost, c, after h hours of service is c = 25 + 50h.
The total cost for 8 hours of work would be 25 + 50(8) = 425.
The total cost for 10 hours of work would be 25 + 50(10) = 525.
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Kennedi is feeding her 5 puppies. She has half a bag of dog food left. How much of the bag
will each puppy receive?
Answers
Answer:
1/10
Step-by-step explanation:
Puppy food portions.
Unish Baskota
Kennedi is feeding her 5 puppies. She has half a bag of dog food left. How much of the bag
will each puppy receive?
If Kennedi has half a bag of dog food left and she has 5 puppies to feed, then each puppy will receive 1/5th of the remaining dog food.
To calculate this, you can divide the remaining dog food (which is half a bag) by the number of puppies (which is 5):
1/2 bag of dog food ÷ 5 puppies = 1/10 bag of dog food per puppy
So each puppy will receive 1/10th of the bag of dog food.
Each puppy would receive 1/10 of food
in general, if the sample size is large, adding an extremely large outlier to a data set will not substantially affect _____ .
Answers
In general, if the sample size is large, adding an extremely large outlier to a data set will not substantially affect the mean (average) of the data set.
This is because the mean is calculated by summing all the values in the data set and dividing by the total number of values. As the sample size increases, the influence of any individual value on the mean becomes smaller. An extremely large outlier may have a significant impact on the sum of the data set, but if the sample size is large enough, the impact on the mean will be relatively small.
However, adding an extremely large outlier to a data set can substantially affect other measures of central tendency and dispersion, such as the median and standard deviation. These measures are based on the order and spread of the data, rather than the sum of the data, and may be more sensitive to extreme values.
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how many degrees is 17 celsius in fahrenheit
Answers
The temperature in Fahrenheit that is equal to 17 degree Celsius is 62.6 Fahrenheit .
The Celsius (°C) and Fahrenheit (°F) are two common temperature scales which are used to measure the temperature. Celsius is based on the metric system, and is widely used in most countries. Fahrenheit, on the other hand, is used mostly in the United States and a few other countries.
We use the the formula "°F = (°C × 1.8) + 32" , to convert the temperature from degree Celsius to degree Fahrenheit ;
In this case , we have to convert 17 Celsius to Fahrenheit,
So , we can write the formula as : °F = (°C × 1.8) + 32
⇒ °F = (17 × 1.8) + 32 ;
⇒ °F = 30.6 + 32 ;
⇒ °F = 62.6 .
Therefore, 17 Celsius is equal to 62.6 Fahrenheit .
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if 'a' is the Geometric mean of 2 and 1/4 then find 'a'
Answers
The geometric mean of two numbers is the square root of their product. Hence, the geometric mean 'a' of 2 and 1/4 is approximately equal to 0.70710678118.
Finding the Geometric Mean of Two NumbersRecall that the geometric mean of two numbers is the square root of their product. This means that we need to multiply the two numbers (2 and 1/4) and then take the square root of the result.
Multiply 2 and 1/4:
2 × 1/4 = 1/2
Take the square root of the result:
a = √(1/2)
Simplify the square root:
a = √(1/2) = √(1)/√(2) = 1/√(2)
Rationalize the denominator by multiplying the top and bottom by √(2):
a = (1/√(2)) × (√(2)/√(2)) = √(2)/2
Approximate the result to a desired level of accuracy, if necessary. In this case, rounding to 11 decimal places gives:
a ≈ 0.70710678118
Therefore, the geometric mean 'a' of 2 and 1/4 is approximately equal to 0.70710678118
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Find m∠BDC big ideas
Answers
In the triangle BCD the value of ∠BDC is 105°.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
In ΔABC and ΔBCD it is given that -
∠A ≅ ∠B
∠ADC ≅ ∠BCD
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
So, by the theorem stated above -
∠ACD ≅ ∠BDC
In ΔACD he sum of angles of a triangle is 180°.
The equation will be -
∠ACD + ∠ADC + ∠A = 180°
Substitute the values in the equation -
∠ACD + 30° + 45° = 180°
∠ACD + 75° = 180°
∠ACD = 180° - 75°
∠ACD = 105°
Now, since ∠ACD ≅ ∠BDC.
So, ∠BDC = 105°.
Therefore, the measure of ∠BDC is 105°.
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