The demand function is linear, so we can write it in the form of:
q = a - bp
Where a and b are constants and q is the quantity demanded and p is the price. We have two points, one at a price of $3.25 with a quantity of 2,500, and another at a price of $2.83 with a quantity of 3,900.
We can use these two points to solve for the values of a and b in the equation.
Plugging in the first point:
2500 = a - (3.25)b
Plugging in the second point:
3900 = a - (2.83)b
We can then solve this system of equation by substituting the first equation with the second one
3900 = a - (2.83)b
=2500 + 1400 = a - (3.25)b + (2.83)b
=a - (0.42)b
So the equation is:
q = 3900 - 0.42p
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Susan bought three video games at one price
and 2 videos priced $2 below the others. The
total cost was $91.50. Find the prices of the
video games.
The price of first 3 video games is $57.3 and the other 2 videos games is $34.2 in the given arithmetic problem.
What is arithmetic problem?The study and use of numbers, mathematical relationships between numbers, and mathematical observations are all covered by the branch of mathematics known as arithmetic.
The core ideas in number theory, measurement, and computation are typically referred to as "arithmetic" (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots). It hasn't always meant the same thing, though, in the mathematical community.
Susan bought total 5 games
Lets the higher price be x
and lower be y
3x + 2y = $91.50
and
x - y = $2
x = 2 + y
Putting the value of x in first formula
3(2 + y) + 2y = 91.50
6 + 3y + 2y = 91.50
3y + 2y = 91.50 - 6
5y = 85.5
y = 85.5/5
y = 17.1
2y = 34.2
Putting the value of y in x
x = 2 + (17.1)
x = 19.1
3x = 57.3
Thus, the price of first 3 video games is $57.3 and the other 2 videos games is $34.2.
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Last year, Chris opened an investment account with 5200 . At the end of the year, the amount in the account had increased by 7%
Answer:
Step-by-step explanation:
By the way you've worded this, I'm guessing that you're looking for how much money Chris made at the end of the year.
When we're dealing with annual income, we must always consider how much was already present in savings before actually performing any operation, because that will give us the final answer.
Since Chris started with $5200, we do [tex](0.07)($5200) = $364[/tex] to find that Chris made $364 by the end of the year.
Lastly, to find his total income at the end of the year, we add [tex]5200 + 364 =[/tex] $5,564 at the end of the year.
The television show Found has been successful for many years. That show recently had a share of 31, meaning that among the TV sets in use, 31% were tuned to Found. Assume that an advertiser wants to verify that 31% share value by conducting its own survey, and a pilot survey begins with 12 households have TV sets in use at the time of a Found broadcast.
Find the probability that none of the households are tuned to Found.P(none) =
Find the probability that at least one household is tuned to Found.P(at least one) =
Find the probability that at most one household is tuned to Found.P(at most one) =
if at most one household is tuned to Found, does it appear that the 31% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Found unusual?)
yes, it is wrong?
no, it is not wrong?
The probabilities are given as follows:
None: 0.0116 = 1.16%.At least one: 0.9884 = 98.84%.At most one: 0.0744 = 7.44%.The 31% share value is not wrong, as at most one household is not an unlikely outcome, as the probability is higher than 5%.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
n = 12, p = 0.31.
The probability of none is given as follows:
P(X = 0) = (0.69)^12 = 0.0116.
The probability of at least one is given as follows:
P(X >= 1) = 1 - 0.0116 = 0.9884.
The probability of at most one is given as follows:
P(X <= 1) = P(X = 0) + P(X = 1)
In which:
P(X = 1) = 12 x 0.31 x 0.69^11
P(X = 1) = 0.0628.
Hence:
P(X <= 1) = P(X = 0) + P(X = 1)
P(X <= 1) = 0.0116 + 0.0628
P(X <= 1) = 0.0744.
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22) In 1990, the average house in Emerald City cost $280,000 and in 2007 the same house cost
$365,000. Assuming a linear relationship, write an equation that will give the price of the house in
any year, and use this equation to predict the price of a similar house in the year 2020.
23) The population of Mexico in 1995 was 95.4 million and in 2010 it was 117.9 million. Assuming a
linear relationship, write an equation that will give the population of Mexico in any year, and use this
equation to predict the population of Mexico in the year 2025.
Answer:
8,00000
Step-by-step explanation:
;_!($($+#(#(#)!#;;;;vhejdnsndbsndns sjnd snsjs s ska. snsjss
In order to gain popularity among students, a new pizza place near school plans to offer a special promotion. The cost of a large pizza (in dollars) at the pizza place as a function of time (measured in days since February 10th) may be described as⎧9, 0 ≤ t ≤ 3C(t)= ⎨9+t, 3 < t ≤ 8⎩20, 8 < t < 28(Assume t only takes whole number values.) Write an expression that describes the sentence "The cost of a large pizza is at least A dollars B days into the promotion," using function notation and mathematical symbols only.
An expression that narrates this sentence using function notation and mathematical symbol: C(B) ≥ A
According to the question,
The cost of the large pizza is at least A dollars B days into the promotion.
The statement that a pizza is at least A dollars B days into the promotion means that the cost of a large pizza B days into the promotion and denoted C(B) and it is greater than or equal to A dollars. Thus, an expression that reports this sentence using function notation and mathematical symbols is simply :
C(B) ≥ A
So, the expression is C(B) ≥ A .
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Two gentlemen are taking their morning walks, beginning from opposite ends of a park. They meet 720 meters away from one of the ends, after which they continue walking. After reaching the end of the park, each turns back. On the way back, they meet at a distance of 400 meters from other end of the park. What is the length of the park? Their speeds are constant, but not identical.
The length of the park will be 598 meters.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given that two gentlemen are taking their morning walks, beginning from opposite ends of a park. They meet 720 meters away from one of the ends, after which they continue walking. After reaching the end of the park, each turns back. On the way back, they meet at a distance of 400 meters from another end of the park.
The length of the park will be calculated as,
H² = P ² + B²
B² = (720)² - ( 400 )²
B = √ ( 358400 )
B = 598 meters
The length of the park would be 598 meters.
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[Revision] Change these fractions to decimal fractions: Exercise 9a a d 2.3 (as a commo 25 31813 b e e 12 25 2 3 b 0.55 C Change these numbers to common fractions in their lowest terms: a 0.2 d 0.264 0.006 f -1820010 C f 0.312 0.875
The required decimal value of fraction 2/5 is 0.4, and a fraction of decimal value is 0.55 is 11/20.
What is the fraction?Fraction is defined as the number of compositions that constitutes the Whole.
Here,
Given expression,
Fraction = 2 / 5
decimal value = 0.4
Given expression,
decimal value = 0.55
fraction value = 0.55 = 55/100
fraction = 11/20
Thus, the required decimal value of fraction 2/5 is 0.4, and a fraction of decimal value is 0.55 is 11/20.
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A bakery makes 40 different flavors of muffins. 25% of the flavors have chocolate as one of the ingredients. draw a tape diagram to show how many flavors have chocolate and how many dont
The flavors that have chocolate as one of the ingredients will be 10 and the flavors that don't have chocolate as one of the ingredients will be 30.
How to calculate the number of chocolate?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
In this case, the bakery makes 40 different flavors of muffins. 25% of the flavors have chocolate as one of the ingredients
The flavors that have chocolate as one of the ingredients will be:
= 25% × 40
= 10
The flavors that don't have chocolate as one of the ingredients will be:
= 40 - 10
= 30
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Urgently!! You are kindly requested to describe in DETAILS the solution of the problem. Certainly, thanks.
The growth rate of the number of bacteria is given by the formula V = 10000 - 100*m*t, where t is the time expressed in hours, m = 11. Write the equation for the growth of the number of bacteria x(t) if x(0) = 10000*m.
The equation for the growth of the number of bacteria is x(t) = 10000t - 550t² + 110000
How to determine the equation for the growth function?The growth rate of the number of bacteria is given as:
V = 10000 - 100mt,
Such that
t = time in hours,
m = 11.
To find the equation for the growth of the number of bacteria x(t), we can integrate this formula with respect to t.
Using the initial condition x(0) = 10000*m, we have
x(t) = ∫V dt + C
Substitute the known values in the above equation, so, we have the following representation
x(t) = ∫(10000 - 100mt) dt + C
Integrate
x(t) = 10000t - 50mt² + C
Recall that x(0) = 10000*m.
So, we have
10000m = 10000 * 0 - 50 * m * 0² + c
Evaluate
c = 10000m
c = 10000 * 11
c = 110000
So, the equation is
x(t) = 10000t - 50mt² + 110000
Since m = 11, we have
x(t) = 10000t - 550t² + 110000
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NO BOT ANSWERS OR WE WILL REPORT YOU. Can you see triangles in this baseball player’s posture? Many players improve their swings using the properties of geometry to evaluate their positions and postures. This is true in many other sports as well including soccer, football, and golf.
Find how players improve using the properties of geometry to evaluate their positions and postures. Choose at least three examples and explain how the concepts you learned about in this Unit relate to the examples you find.
In golf, players use the concept of angles to evaluate their club head position and the angle of attack on the ball. By understanding the principles of geometric angles, golfers can adjust their swing and improve the accuracy and distance of their shots.
How can players improve using the properties of geometry?In basketball, players use the concept of spatial awareness to evaluate their positioning on the court. By understanding geometric concepts such as lines, angles and planes, they can improve their ability to move without the ball and find open spaces on the court.
In soccer, players use the concept of geometric shapes to evaluate their positioning on the field. By understanding the principles of triangles and circles, soccer players can improve their ability to move and pass the ball effectively, as well as to anticipate the movements of the opposing team.
Overall, the concepts of geometry, such as angles, spatial awareness, and geometric shapes, are essential for athletes in many sports to evaluate their positions and postures and improve their performance.
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Sketch the graph of the function with a table of values. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) f(x, y) = y² + 4
The equation for the cross section exists x = z , -z.
What is meant by equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.
When two expressions in a variable (or variables) have the same value, the condition is said to be an equation. The equation's solution, or root, is the value of the variable for which the equation holds true. Even if the RHS and LHS are switched, an equation still holds true.
In the question it is given that
Equation of curve => x² = 49y² + z²
(a) Write an equation for the cross section at z = -7
Putting z = -7 in the equation,
⇒ x² = 49y² + (-7)²
⇒ x² - 49y² = 49
(b) Write an equation for the cross section at z = 0
Putting z=0
⇒ x² - 49y² = 0
(c) Write an equation for the cross section at z = 7
Putting z = 7 ,
⇒ x² - 49y² = 49
(d) Write an equation for the cross section at y = -7
Putting y = -7 in equation this time,
⇒ x² = 49( -7)² + z²
⇒ x² - z² = 2401
(e) Write an equation for the cross section at y = 0
Putting y = 0,
⇒ x² = z²
⇒ x = z , -z
Therefore, the equation for the cross section exists x = z , -z.
The compete question is:
Use traces to sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) x2 = 49y2 + z2 = (Write an equation for the cross section at z = -7 using x and y.) (Write an equation for the cross section at z = 0 using x and y.) (Write an equation for the cross section at z = 7 using x and y.) (Write an equation for the cross section at y = -7 using x and z.) IIIIIIII (Write an equation for the cross section at y = 0 using x and z.) (Write an equation for the cross section at y = 7 using x and z.) (Write an equation for the cross section at x = -7 using y and z.) (Write an equation for the cross section at x = 7 using y and z.)
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Analia is a school district manager. Here are some details about two schools in her district for the last school year: School A School B Number of students 3000 30003000 4000 40004000 Number of teachers 190 190190 380 380380 Graduation rate 86 % 86%86, percent 90 % 90%90, percent Budget per student $ 10 , 500 $10,500dollar sign, 10, comma, 500 $ 10 , 000 $10,000dollar sign, 10, comma, 000 % of students in sports club 62 % 62%62, percent 68 % 68%68, percent Number of sports medals won 9 99 7 77 SAT average 1200 12001200 1050 10501050 SAT range (max-min) 900 900900 700 700700 Analia wants to know which school has higher academic achievements relative to the number of teachers per student. 1) Analia thought of two different ways to define this quantity. Identify these two definitions among the following options.
The two different quantities to measure which school has higher academic performance are :
• Graduation rate / Budget per student
• SAT average / Budget per student
How to calculate the performance?To specify a number that represents academic achievement. We compare the budget per pupil for each school to a related metric or parameter that measures the academic performance of the students in each school.
The following variables could be used to gauge academic achievement:
• Each school's graduation rate.
• Each school's average SAT score.
Therefore, Graduation rate / Budget per student and SAT average / Budget per student are appropriate in this case.
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HELP PLSSS URGENT
IMAGE ATTACHED
c From the graph, it appears that around 50% of seniors had used alcohol in 2015.
d.This gives us: A=-0.8(25)+63=50%. So, both the line graph and the formula estimate that around 50% of seniors had used alcohol in 2015.
What is line graph and determine it?A line graph is a type of chart that displays data as a series of points connected by linesIt is used to visualize trends over time or changes in valueLine graphs can have multiple data series represented by different colors or styles of linesThey are useful for comparing data and identifying patterns or fluctuations.Line graph is good for showing the trend of a continuous variable over time. A=-0.8n+63 can be changed to A=25 (because 2015 is 25 years after 1990) to get the proportion of seniors who had ever drank alcohol in 2015 using the formula. A=-0.8n+63 can be changed to A=25 (because 2015 is 25 years after 1990) to get the proportion of seniors who had ever drank alcohol in 2015 using the formula.To learn more about line graph refer:
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A cylindrical candle has a diameter of 3 inches and a height of 3 inches,What is surface area, in square inches of the candle?
Step-by-step explanation:
it'll be undefined and 2 for the surface area
Find the x-intercept of the function `y=3x+6`
Find the y-intercept of the function `y=3x+6`
Question 1 : find x intercept
y=0
0=3x+6
subtract 6 from both sides, after doing that, the equation would be : -6=3x
Then divide by -3 on both sides, the answer would be : x=3
Therefore the x intercept as a coordinate is (3,0)
Question 2 : find the y intercept
x=0
y=3(0)+6
y=6
Therefore the y intercept as a coordinate would be (0,6)
Hope this helped =)
-YinAhara
The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 60 A, 25 B, and 35 C responses. Show the frequency and relative frequency distributions (use 0 decimals for the frequency column and 2 decimal for the relative frequency column).
The relative frequency of A, B and C BE 0.5, 0.20 and 0.29.
What is meant by relative frequency?The proportion between a given event's frequency and all events' frequencies in a statistical experiment.
The ratio of the total number of occurrences occurring in a particular scenario to the frequency of an event can be used to determine relative frequency. Relative frequency is defined as Subgroup frequency divided by Total frequency.
Due to the possibility of interpreting the heights of relative frequency histograms as probabilities, they are significant. These probability histograms offer a graphical representation of a probability distribution that may be used to estimate the probability that specific outcomes will materialize within a given population.
The relative frequency is the ratio of the frequency to the total frequency corresponding to each entry.
The total samples be 60 + 25 + 35 = 10
Also, the frequency corresponding to A is: 60
Corresponding to B is: 25
and corresponding to C is: 35
Hence, the Frequency table is as follows:
Data Frequency
A 60
B 25
C 35
The relative frequency table is given by:
Data Relative Frequency
A 60/120 = 0.5
B 25/120 = 0.20
C 35/120 = 0.29
Therefore, the relative frequency of A, B and C BE 0.5, 0.20 and 0.29.
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Suppose the average distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls(a)Find the sample means.(b)Find the standard error.(c)) Compute P( x bar < 240).(ii) Draw a sketch to interpret your results.(iii) Is this usual? Explain.(d)Compute p(X< 240)(e)Find the 80thpercentile of the distribution of the average of the 49 fly balls.
(a) The sample mean of the 49 fly balls is 250 feet.
(b) The standard error of the 49 fly balls is 50/sqrt(49) = 7.14 feet
(c) P(x bar < 240) = P(Z < (240-250)/7.14) = P(Z < -1.40) = 0.0822
(ii) The sketch of the distribution of the average of the 49 fly balls is a normal curve with a mean of 250 feet and a standard deviation of 7.14 feet. The probability of getting a sample mean of less than 240 feet is 0.0822.
(iii) This is usual, as the probability of getting a sample mean of less than 240 feet is 0.0822, which is within the range of expected probabilities for a normal distribution.
(d) P(X< 240) = P(Z < (240-250)/50) = P(Z < -2) = 0.0228
(e) The 80th percentile of the distribution of the average of the 49 fly balls is equal to the mean plus (1.28 * standard deviation), which is equal to 250 + (1.28 * 7.14) = 266.6 feet.
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Pls help with this question, I will give brainliest, answer is not 278.63 or 375
The area of the trapezoid is 278.63 square units.
What is a trapezoid?An open, flat object with four straight sides and one set of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases.
Given:
KFLM is a trapezoid.
Side KF = 10 units
KL = 26 units
The angle measure of KFM = 48°.
So, in ΔFPK,
Sin48° = FP / KF
Sin48° = FP / 10
FP= Sin48° x 10
FP = 0.7431 x 10
FP = 7.431
Now, the area of the trapezoid,
= 1/2 x sum of the parallel sides x distance between parallel sides,
= 1/2 (26 + 49) (7.431)
= 278.63 square units
Therefore, the area is 278.63 square units.
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Please help me solve this I have a D in math!!
Therefore, the explicit formula for f(n) is: f(n) = 10 * [tex]3^{(n - 1)}[/tex]
f(1)=10
What is explicit formula?An explicit formula for f(n), the number of members the creators have a goal of getting n weeks after the website is made available, can be determined by using the information provided that the number of members is tripled every week.
So, we can start with the initial number of members (10) and multiply it by 3 for each week.
Therefore, the explicit formula for f(n) is:
f(n) = 10 * [tex]3^{(n - 1)}[/tex]
A recursive formula for f(n) can be determined by using the information that the number of members is tripled every week, and the initial number of members is 10.
So, we can start with the initial number of members (f(1)=10) and use the previous value of f(n-1) to calculate the current value of f(n).
Therefore, the recursive formula for f(n) is:
f(n) = 3f(n-1) + 10
for n>1
f(1)=10
In this way, we can calculate the number of members for any week using the explicit formula or the recursive formula.
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7 The diagram shows a water tank. The tank is a hollow cylinder joined to a hollow hemisphere at the top.
The tank has a circular base.
-46 cm
90 cm
Diagram not
accurately drawn
Both the cylinder and the hemisphere have a diameter of 46 cm. The height of the tank is 90 cm.
Work out the volume of water which the tank holds when it is full. Give your answer, in cm³,
correct to 3 significant figures.
S
[Edexcel]
The volume of water which the tank holds when it is full is 136830 cm³.
What is volume?The amount of space a three-dimensional solid shape takes up is referred to as its volume. Though difficult to visualise in any shape, it can be compared to others. In comparison to an eraser placed inside of it, a compass box has a larger volume. The area of any two-dimensional shape can be calculated by splitting it into equal squares. When calculating the volume of solid shapes, equal cubical units will also be divided.
If the both have diameter of 46 cm then the height of hemisphere is
46/2 = 23 cm = radius
Height of the cylinder = 90 - 23
= 67
Volume of hemisphere + Volume of cylinder = volume of water
volume of water = (2/3)πr³ + πr²h
volume of water = (2/3)π(23)³ + π(23)²×67
= 136830 cm³
= 136.83 l
Thus, the volume of water which the tank holds when it is full is 136830 cm³.
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5
10 points
(5x+3)2
O 25x²+30x +9
O 25x²+9
O 16x² +24x+9
O 25x²-9
Answer:
[tex]\huge\boxed{\sf 25x\² + 30x + 9}[/tex]
Step-by-step explanation:
Given expression:= (5x + 3)²
We can also write it as:= (5x + 3)(5x + 3)
= 5x(5x + 3) + 3(5x + 3)
= 25x² + 15x + 15x + 9
= 25x² + 30x + 9[tex]\rule[225]{225}{2}[/tex]
A certificate of deposit often charges a penalty for withdrawing funds before the maturity date. If the penalty involves two months of interest, what would be tbe amount for early withdrawal on a CD paying 7 percent and valued at $18,000? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Penalty time = 2 months of interest = 2 x (7/100 x 18,000) = $2520.00
This serves as a deterrent to encourage individuals to leave their money in the CD until the maturity date.
Penalty = 2 months of interest = 2 x (Interest rate/100 x Value of CD)
= 2 x (7/100 x 18,000)
= $2520.00
A certificate of deposit (CD) is a financial product offered by banks and credit unions that allows an individual to deposit a certain amount of money for a fixed period of time, usually a few months to a few years. Most CDs will pay a higher rate of interest than a traditional savings account, but they come with certain restrictions. One of these restrictions is that if you withdraw funds from the CD before it reaches maturity, you will be charged a penalty time. This penalty usually involves two months of interest. Therefore, the amount of the penalty for early withdrawal on a CD with a value of $18,000 and paying 7 percent interest would be 2 x (7/100 x 18,000) = $2520.00. This serves as a deterrent to encourage individuals to leave their money in the CD until the maturity date.
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Find the slope of a line perpendicular to the line whose equation is
15x12y = 216. Fully simplify your answer.
The slope of the line perpendicular to the line whose equation is 15x - 12y = 216 is m{p} = -0.8.
What is the general equation of a straight line?
straight line equation: The general equation of a straight line is -
y = mx + c.
where,
{m}: slope of the line.
{c} : y-intercept
To find the slope of a line perpendicular to the line whose equation is 15x - 12y = 216, we need to find the negative reciprocal of the original line's slope.
To find the original line's slope, we can use the equation of the line in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
To convert the equation of the line from standard form to slope-intercept form, we can add 12y to both sides to get 12y = -15x + 216.
Then divide both sides by 12 to get y = -(15/12)x + 18.
So the slope of the original line is -(15/12).
The slope of a line perpendicular to the original line is the negative reciprocal of the original line's slope.
So the slope of the line perpendicular to 15x - 12y = 216 is -12/15 or -0.8
The slope of the line perpendicular to the given line is -
m = -12/15 = -0.8
Therefore, the slope of the line perpendicular to the line whose equation is 15x - 12y = 216 is m{p} = -0.8.
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Given g (x)=5x − 3, find g( −2)
f(x)=5x−3f(x)=5x-3 g(x)=x2−3g(x)=x2-3
Set up the composite result function. g(f(x))g(f(x))Evaluate g(5x−3)g(5x-3) by substituting in the value of f(5x−3)=(5x−3)2−3g(5x-3)=(5x-3)2-3
Simplify each term: g(5x−3)=25x2−30x+9−3g(5x-3)=25x2-30x+9-3 Subtract 33 from g(5x−3)=25x2−30x+6
To find the value of the function g(x) = 5x - 3 at x = -2, substitute -2 for x. This gives g(-2) = -13.
Explanation:The function given is g(x) = 5x - 3. To find the value of this function when x = -2, you substitute -2 for x in the equation. This yields:
g(-2) = 5(-2) - 3
Which simplifies to:
g(-2) = -10 - 3
So, g(-2) = -13.
In summary, you substituted -2 for x in the function g(x)=5x−3 and then performed the arithmetic operations to find that g(−2) equals -13.
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Patrick purchased some supplies for his guitar students. He bought 25 guitar picks and 25 guitar strings since they only cost $1 more than the guitar picks. He spent a total of $40. If c is the cost of one guitar pick, find the cost of one guitar string.(1 point)
The cost of the guitar string is given by the equation b = $ 1.30
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the cost of one guitar pick be = c
Let the cost of one guitar string be = b
And , Patrick bought 25 guitar picks and 25 guitar strings for = $ 40
Substituting the values in the equation , we get
25c + 25b = 40 be equation (1)
Now , cost of one guitar string = 1 + c
b = 1 + c be equation (2)
Substituting the value of b in equation (1) , we get
25c + 25 ( 1 + c ) = 40
On simplifying the equation , we get
25c + 25 + 25c = 40
Subtracting 25 on both sides of the equation , we get
50c = 15
Divide by 50 on both sides of the equation , we get
c = $ 0.30
So , the cost of one guitar string = $ 1 + $ 0.30 = $ 1.30
Hence , the cost of one guitar string is $ 1.30
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How to write Y = 1/4 (x -4) + 2
Right 3 and down 4
Function notation and vertex form
Work please
The function y = 1/4(x - 4)² + 2, after a translation right 3 units and down 4 units, is given as follows:
y = 1/4(x - 7)² - 2.
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The parent function for this problem is given as follows:
y = 1/4(x - 4)² + 2
The changes with each translation are given as follows:
Right 3 units: x -> x - 3.Down 4 units -> f(x) = f(x) - 4.Hence the function is defined as follows:
y = 1/4(x - 3 - 4)² + 2 - 4
y = 1/4(x - 7)² - 2.
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Stefan sells Jin a bicycle for $116 and a helmet for $16. The total cost for Jin is 120% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answer:
see below
Step-by-step explanation:
116+16=132 =120% * x
x=110
profit =132-110 =22
He made $12 by selling the bicycle helmet to Jin!
Step-by-step explanation:Let x be the original cost of the bicycle.
The cost of the helmet is $16, so the original cost of the bicycle and helmet is x + $16 algebraically.
Jin pays a total of $116 + $16 = $132 for the bicycle and helmet, which is 120% of what Stefan spent originally, so x + $16 = 1.2 * (x + $16)
Expanding the right-hand side gives x + $16 = 1.2x + 1.2 * $16.
Solving for x, we find that x = $104.
So, Stefan originally spent $104 for the bicycle and $16 for the helmet, for a total of $104 + $16 = $120.
Stefan sells the bicycle and helmet to Jin for $116 + $16 = $132, so he makes a profit of $132 - $120 = $12.
if a coin is tossed five times: find the probability of getting at least one tail. give answer as simplified fraction.
The probability of obtaining at least one tail is equal to one minus the probability of getting all heads when a coin is tossed five times.
The probability of obtaining at least one tail is equal to one minus the probability of getting all heads when a coin is tossed five times.
3/8
The probability of obtaining at least one tail is equal to 1 minus the probability of obtaining all heads. The probability of obtaining all heads is 1/2^5 = 1/32. Therefore, the probability of obtaining at least one tail is 1 - 1/32 = 31/32. This simplifies to 3/8.
The probability of obtaining at least one tail is equal to one minus the probability of getting all heads when a coin is tossed five times. The probability of obtaining all heads is one out of two to the power of five, which is equal to one out of thirty-two. Therefore, the probability of obtaining at least one tail is one minus one out of thirty-two, which is equal to thirty-one out of thirty-two. This simplifies to three out of eight.
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the table shows th pricing for four diffrent types of gaspline which type costs least per gallon
Based on the table which shows the pricing for four different types of gasoline, a type that cost the least per gallon is: C. type C.
How to determine the gasoline that costs least per gallon?In order to determine the gasoline that costs least per gallon, we would determine the unit rate for the cost per gallon by using the following mathematical expression;
Unit rate = Cost of gasoline/number of gallons
Substituting the given parameters into the unit rate formula, we have the following;
Unit rate = $20.20/10
Unit rate = $2.02 per gallon.
For type B, we have the following unit rate:
Unit rate = $26.04/12
Unit rate = $2.17 per gallon.
For type C, we have the following unit rate:
Unit rate = $28.24 / 24
Unit rate = $2.01 per gallon.
For type D, we have the following unit rate:
Unit rate = $30.45 / 25
Unit rate = $2.03 per gallon.
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An investor bought a share of a stock at the beginning of 2015. At the beginning of 2017, the share was worth $1050From the beginning of 2015 to the beginning of 2017 the value of the share halved each year, but from the beginning of 2017 to the beginning of 2019, the value of the share increased by 1.5 times each yearThe investor sold the share at the beginning of 2019 Find and interpret the difference between what the investor paid for the share and what the investor sold the share for
$656.25 is the difference between the investor paying for the share and the investor selling the share.
What is Equation?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that At the beginning of 2017, the share was worth $1050.
From the beginning of 2015 to the beginning of 2017 the value of the share halved each year.
In 2017 it is 1050.
In 2016, it is 2100
In 2015, it is 4200
Beginning of 2017 to the beginning of 2019, the value of the share increased by 1.5 times each year.
In 2017, 1050×1.5=1575
In 2018, 1575×1.5=2362.5
In 2019, 2362.5×1.5=3543.75
The investor paid for the share 4200 and the investor sold 3543.75.
Difference =4200-3543.75
=656.25
Hence, $656.25 is the difference between the investor who paid for the share and the investor who sold the share.
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