The information in a table shows that f(x) = 3(2)x exponential function. An exponential function has the formula y = abx, wherein y and x are variables.
Describe the exponential function.An exponential function is a mathematical function with the following formula: f (x) = 1 x. where an is a fixed sum that serves as the function's basis and x is a variable. The most frequent exponential-function base is the transcendent number e, or around 2.71828. Your function must be exponential if it has the equation y = a b x, or where are constant, a Zero and b > 0 and b 1. You always used functions to the power of 2 while solving quadratic equations. An exponential function's exponent is a variable.
Here,
given:
Using the table's (0, 3):
3 = ab° , a = 3
(2) and (12):
=>12 = ab²
=>12 = 3b²
=>b² = 4
=>b = 2
=>f(x) = 3(2)ˣ
The information in a table shows that the exponential function, f(x), equals 3(2)x.
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A submarine must descend at an average rate of at least 12 feet per minute for 5 minutes. The table shows how many feet the submarine descends
in the first 4 minutes. How many feet must the submarine descend in the fifth minute?
Submarine must descend 17 feet in the 5th minute.
What is the average of the data?
Only numerical variables, whether continuous or discrete, can be used to calculate the mean. It is calculated by merely dividing the total number of values in a data set by the sum of all the values in the data set. A frequency table of data or raw data can both be used for the calculation.
Let the distance descended by submarine in 5th minute = x feet
Average distance descended by the submarine
= (Total distance distended/ Duration or time)
= (6 + 8 + 14 + 15 + x) / 5
= (43 + x) / 5
Statement given in the question → "Submarine must descend at an average rate of at least 12 feet per minute"
So the inequality for the statement will be,
(43 + x) / 5 ≥ 12
43 + x ≥ 60
x ≥ 17
Therefore, submarine must descend 17 feet in the 5th minute.
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A bag contains 9 red marbles, 4 blue marbles, and 7 yellow marbles. You randomly select three marbles from the bag. a. What is the probability that all three marbles are red when you replace each marble before selecting the next marble? Round your answer to the nearest tenth. about % b. What is the probability that all three marbles are red when you do not replace each marble before selecting the next marble? Round your answer to the nearest tenth. about %
Answer:
A) 9.1%
B) 7.4%
Step-by-step explanation:
Part A
Because you are replacing each marble before selecting the next, the probability of choosing one red marble remains the same, so choosing 3 red marbles with replacement would mean the probability gets multiplied by itself 3 times:
[tex]\displaystyle P(\text{Red+Replace})=\biggr(\frac{9}{20}\biggr)^3=\frac{9}{20}*\frac{9}{20}*\frac{9}{20}=\frac{729}{8000}\approx9.1\%[/tex]
Part B
[tex]\displaystyle P(\text{Red+No Replace})=\frac{C(9,3)C(4,0)C(7,0)}{C(20,3)}=\frac{\frac{9!}{3!(9-3)!}}{\frac{20!}{3!(20-3)!}}=\frac{\frac{9*8*7}{3*2*1}}{\frac{20*19*18}{3*2*1}}=\frac{9*8*7}{20*19*18}=\frac{7}{95}\approx7.4\%[/tex]This can also be calculated with [tex]\frac{P(9,3)}{P(20,3)}[/tex] because the order does matter in which you pick the 3 red marbles with no replacement.
Answer:
9.1%
7.4%
Step-by-step explanation:
. If a population of college student ages is skewed right, then this indicates: a. there are a greater number of older students b. the modal age is greater than the median age c. as the age of a student increases, the frequency of the student ages increases. d. there are more younger students within the population e. not enough information
The correct answer is c. as the age of a student increases, the frequency of the student's ages increases.
A skewed right population means that the data is distributed in such a way that the majority of the values are on the right side of the data set. In the case of a population of college students, this would mean that there is a greater frequency of older students (those in their late twenties or older) than younger students. As the age of a student increases, the frequency of the student's ages increases.
Option a. there are a greater number of older students is also correct, but it is not complete.
Option b. the modal age is greater than the median age is not correct, as the modal age is the most common age in the population and the median age is the middle value of the population, and there is no relationship between them.
Option d. there are more younger students within the population is not correct as a skewed right population indicates the opposite.
Option e. not enough information is not correct as the question is providing enough information to make a conclusion.
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Chose the best 3 options
The beat three options are: The slope of the line is 1/5, (2) The possible equation if the line is y=1/5x, (3) The slope and the y intercept are the same
What is slope of a line?Lope is the rate of change of y with respect to x. slope is also the increase in y over increase in x vice versa
Slope is denoted by rise/run
The Possible solutions from the graph are:
The slope and y-intercept are the sameThe possible equation of the line is y=1/5xThe slope of the line is 1/5Taking any two points on the graph : (4, 1) and -4, -1,)
We can find the slope as (1--1)/4--4
Therefore, the Slope = 2/3≡1/5
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A manufactor makes integrated circuits that each have a resistance layer with a target thickness of 200 units. A circuit won't work well if this thickness varies too much from the target value. These thickness measurements are approximately normally distributed with a mean of 200 units and a standard deviation of 12 units. A random sample of 17 measurements is selected for a quality inspection. We can assume that the measurements in the sample are independent. What is the probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value?Choose 1 answer:A) 0.16B) 0.32C) 0.40D) 0.80E) We cannot calculate this probability because the sampling distribution is not normal.
The probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value is 0.15 + 0.15 = 0.30 which corresponds to the answer B) 0.32.
What is the Central Limit Theorem?
The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
We can use the Central Limit Theorem to determine that the sampling distribution of the mean thickness of a random sample of size 17 from a population with a mean of 200 units and a standard deviation of 12 units will be approximately normal with a mean of 200 units and a standard deviation of (12 units)/√17 = 2.8 units.
Given that the mean thickness in these 17 measurements x is farther than 3 units away from the target value, we can use the standard normal table to find the probability.
Let's call X = mean thickness,
if X > 203, we have P(X>203) = P(Z> (203-200)/2.8) = P(Z>1.071) = 0.15
if X < 197, we have P(X<197) = P(Z< (197-200)/2.8) = P(Z<-1.071) = 0.15
Hence, the probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value is 0.15 + 0.15 = 0.30 which corresponds to the answer B) 0.32.
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The sun of a number, x, and 1/2 is equal to 4. What set of equations correctly repaints x
The set of equations correctly representing x are as follows:
(x + 1/2) and (x = 7/2).
What exactly is a set or group of equations?A set or group of equations that you solve all at once is referred to as a "system" of equations. The simplest linear system is one that has two equations as well as two variables. Linear equations (those that graph as straight lines) are easier to understand than non-linear ones.
What is the name of an equation system?Systems of equations in mathematics are a collection of relationships between different unknown variables that can be stated in terms of algebraic expressions. They are also known as simultaneous equations. Graphing, substitution, as well as elimination by addition, are methods that can be used to find the solutions to a basic system of equations.
According to the given information:Sum means addition (+).
Given that sum of a number, x and 1/2 is 4.
This means the adding two numbers
x+1/2=4
Now make x the subject of formula,
x=4-1/2
Finding the L.C.M = 8-1/2
x=7/2
∴ x=3 1/2
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Jackson is trying to find the density, in g/cm", of a block of wood.
The block of wood is in the shape of a cuboid.
He measures
the length as 13. 2 cm, correct to the nearest mm
the width as 16. 0 cm, correct to the nearest mm
the height as 21. 7 cm, correct to the nearest mm
He measures the mass as 1970 g, correct to the nearest 5 g.
By considering bounds, work out the density of the wood.
Give your answer to a suitable degree of accuracy.
You must show all your working and give a reason for your final answer.
The density of the wood is between 0.35 g/cm^3
The density of a substance can be calculated using the formula:
density = mass / volume
To calculate the volume of the cuboid, we can use the formula:
volume = length x width x height
So, using the measurements provided:
volume = 13.2 cm x 16.0 cm x 21.7 cm = 5541.44 cm^3
To calculate the density of the wood, we divide the mass by the volume:
density = 1970 g / 5541.44 cm^3
We can convert cm^3 to g/cm^3 by converting the volume to g
1cm^3 = 1g/cm^3
density = 1970 g / 5541.44 g/cm^3
density = 0.3555 g/cm^3
However, as the measurements provided have a degree of uncertainty, we should consider bounds to find the range of possible densities.
The lower bound for the length is 13.2 cm - 0.1 cm = 13.1 cm
The upper bound for the length is 13.2 cm + 0.1 cm = 13.3 cm
The lower bound for the width is 16.0 cm - 0.1 cm = 15.9 cm
The upper bound for the width is 16.0 cm + 0.1 cm = 16.1 cm
The lower bound for the height is 21.7 cm - 0.1 cm = 21.6 cm
The upper bound for the height is 21.7 cm + 0.1 cm = 21.8 cm
The lower bound for the mass is 1970 g - 5 g = 1965 g
The upper bound for the mass is 1970 g + 5 g = 1975 g
We can now use these bounds to calculate the range of possible densities:
Density lower bound = 1965 g / (13.3 cm x 16.1 cm x 21.8 cm) = 0.350 g/cm^3
Density upper bound = 1975 g / (13.1 cm x 15.9 cm x 21.6 cm) = 0.360 g/cm^3
So the density of the wood is between 0.35 and 0.36 g/cm^3 to one decimal place.
So the density is 0.35 g/cm^3 with an uncertainty of 0.01 g/cm^3
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What is the formula for a isosceles triangle?
The formula for an isosceles triangle is A = (1/2) * b * h, where b is the base, h is the height, and A is the area.
The formula for an isosceles triangle is A = (1/2) * b * h. This formula is used to calculate the area of an isosceles triangle. To use the formula, you need to know the base, b, and the height, h, of the triangle. The base is the length of any one of the two equal sides of the isosceles triangle, and the height is the distance from the base to the opposite vertex. Once you have these measurements, you can plug them into the formula to calculate the area of the triangle. The formula multiplies the base, b, by the height, h, and then divides the product by two. This will give you the area of the triangle, A.
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PLEASE I NEED HELP ASAPPPP!!!!!
The scatter plot shows the number of pumpkins that have been picked on the farm during the month of October: A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Pumpkins and the x axis is labeled Days in October
Part A: Using computer software, a correlation coefficient of r = 0. 51 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B: Instead of comparing the number of pumpkins picked and the day in October, write a scenario that would be a causal relationship for pumpkins picked on the farm. (5 points)
A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.
What is a Scatter Plot?A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.
Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.
Part A:
The correlation coefficient of r = 0.51 is valid based on the provided scatter plot.
Part B:
The amount of fertilizer applied in connection to the kilograms of pumpkins harvested on the farm can be a scenario where a causal relationship exists.
Hence, A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.
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I need serious help !!
================================================
Explanation:
The x and y are placeholders for numbers.
Think of them as boxes so to speak, and we fill each box with a number.
In this case we will plug in x = 6 and y = 2.
The steps are shown below.
[tex]\frac{3\text{x}+4}{\text{y}}\\\\\frac{3*6+4}{2}\\\\\frac{18+4}{2}\\\\\frac{22}{2}\\\\11\\\\[/tex]
The final answer is choice B
-----------
This means,
[tex]\frac{3\text{x}+4}{\text{y}} = 11 \ \text{when} \ \text{x} = 6 \ \text{and y} = 2 \\\\[/tex]
Put another way
[tex](\text{x},\text{y}) = (6,2) \ \text{ is a solution to } \frac{3\text{x}+4}{\text{y}} = 11[/tex]
In a visual sense, the point (6,2) is on the equation of [tex]\frac{3\text{x}+4}{\text{y}} = 11[/tex]
What is a real solution example?
Solutions refers to the answer to the problem, The example of real solution can be the solution for the value of 'x' in a equation.
What do you mean by a solution?In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
example:
x+2=0
x=-2
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For the given logistic function,
21
f(x) = 1 + 2(0.94)*
The y-intercept = (0, [?])
For x ≥ 0, the horizontal asymptote is y =
Answer:
x) = 1 + 2(0.94)*
The y-intercept = (0, [?])
For x ≥ 0, the horizontal as
how do i answer this question
The constant of variation for the given data is 1/4.
What is the constant of proportionality?If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
Given that the data in the table is,
x f(x)
-8 -2
-4 -1
0 0
4 1
8 2
The constant of proportionality will be calculated as,
F(x) = kx
-2 = k x -8
k = -2 / -8
k = 1 / 4
Here, the proportionality constant will be 1/4.
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Sugar cookies make up 38% of all sales for a local baker's cookie sales. If the baker sold 133 sugar cookies, how many total cookies did the baker sell?
The total number of cookies baker sold in all are 350 cookies.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, sugar cookies make up 38% of all sales for a local baker's cookie sales.
Let the total number of cookies be x.
Now, 38% of x=133
38/100 ×x=133
x=13300/38
x=350
Therefore, the total number of cookies baker sold in all are 350 cookies.
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which postulate proves the two triangles are congruent
Answer:
SSS
Step-by-step explanation:
If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle it is known was SSS congruence
somebody help please
Answer:
Step-by-step explanation:
because HA⊥HR, HR⊥DR, so HA ║ DR, then we know ∠DHR=∠ARH,
we konw, AR=HD, They have a common segment HR, as well as the same angle，so HRA≅RHD
Is the Z or Y axis vertical?
Answer:
yes!
Step-by-step explanation:
the y axis vertical, and the x axis is horizontal!
What baseball stat does Lawrence Hinman suggest is the most important stat for determining the best player in the game in a given year
A range of fundamental, unchanging values may exist in the world, according to ethical pluralism.
What is meant by Ethical Pluralism?According to ethical pluralism, the world may contain a variety of essential and unchangeable values. There may be more, but happiness and respect for people are two possible ones.
The notion of ethical plurality holds that there are various beliefs about what is "good" and "wrong" (moral norms), some of which may be incompatible and/or out of line with your own personal moral standards. Working in foreign societies, where you could encounter varying norms, is a component of international involvement.
The conviction that there are various viewpoints on a subject, each of which has some truth, but none of which contains the complete truth the conviction that while each moral theory somewhat captures the essence of what it means to live morally, none has the whole picture.
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Lawrence Hinman does not have a clear statement on the best baseball stat for determining the best player in a given year.
What do you mean by statistics?Statistics are a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. In baseball, statistics are used to measure the performance of individual players, teams, and even entire leagues. Some common baseball statistics include batting average, home runs, runs batted in, earned run average, and wins. These statistics are used to evaluate the performance of players, compare them to other players, and even predict future performance.
What are some common baseball statistics?Baseball statistics are a set of metrics used to measure the performance of individual players and teams in baseball. Some common baseball statistics include:
Batting average (BA)Home runs (HR)Runs Batted In (RBI)Wins (W)It is likely that different analysts and experts would have different opinions on which stat is the most important for determining the best player in a given year. Some might argue that traditional stats like batting average, home runs, and RBIs are the most important, while others might argue that newer stats like on-base percentage, slugging percentage, and WAR are more informative.
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find the measure indicated in each parallelogram
Answer:
Step-by-step explanation:
WX≅VY
VY = 7
CD≅BE
BE = 13
How do you solve systems by substitution step by step?
Answer:
1.Solve one of the equations for either variable.
2.Substitute the expression from Step 1 into the other equation.
3.Solve the resulting equation.
4.Substitute the solution in Step 3 into one of the original equations to find the other variable.
5.Write the solution as an ordered pair.
6.Check that the ordered pair is a solution to both original equations.
Step-by-step explanation:
What are the coefficients of the equation 3x 6y 13 *?
In the equation [tex]3x-6y=-13[/tex] , the coefficient of equation are , coefficient of [tex]x[/tex] is [tex]3[/tex] and the coefficient of [tex]y[/tex] is [tex]-6[/tex] .
What are Coefficients ?
The Coefficients are defined as a number that is placed with a variable. It is a integer that is multiplied by the variable and written next to it.
In simpler words, we can say that ; a coefficient is a multiplicative factor in the terms of a polynomial, a series, or any expression.
The variables that do not have a number written with them are assumed to have 1 as their coefficient.
For example, in the expression [tex]3x[/tex] , the coefficient of [tex]x[/tex] is [tex]3[/tex] , but in the expression [tex]x^{2} +3[/tex], [tex]1[/tex] is the coefficient of [tex]x^{2}[/tex].
The equation to find the coefficient is given as [tex]3x-6y=-13[/tex] ,
we see that , the numerical part with [tex]x[/tex] is [tex]3[/tex] and with [tex]y[/tex] is [tex]-6[/tex] ;
Therefore , the coefficient of [tex]x[/tex] is [tex]3[/tex] and [tex]y[/tex] is [tex]-6[/tex] .
The given question is incomplete , the complete question is
What are the coefficients of the equation 3x -6y = - 13 ?
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Write in point-slope form an equation of the line that passes through the point (1, 3) with slope -2
y- ⬜= ⬜(x- ⬜)
Consequently, y-1 = 2 is the point-slope form linear equation for the line passing through (1, 3) and having a slope of 2. (x-3).
A linear equation is defined.A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
Here,
Y = mx + c in this instance.
(y- y₁) = m(x - x₁)
where,
The coordinate for the x-axis is x and x1,
The coordinate for the y-axis is y and y1.
The slope of the line is m, and
The y-intercept can be represented by the letter c.
Replace the value of the slope and the point in the general equation to obtain the equation for the line passing through (1, 3) and having a slope of 2.
y-1 = 2(x-3) (x-3)
Consequently, y-1 = 2 is the point-slope form equation for the line passing through (1, 3) and having a slope of 2. (x-3).
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In baseball, each time a player attempts to hit the ball, it is recorded. the ratio of hits compared to total attempts is their batting average. each player on the team wants to have the highest batting average to help their team the most. for the season so far, jana has hit the ball 7 times out of 10 attempts. tasha has hit the ball 10 times out of 16 attempts. which player has a ratio that means they have a better batting average? tasha, because she has the lowest ratio since 0.7 < 0.625 tasha, because she has the highest ratio since 56 over 80 is greater than 50 over 80 jana, because she has the highest ratio since 56 over 80 is greater than 50 over 80 jana, because she has the lowest ratio since 0.7 < 0.625
Answer: i need your help, XD
Step-by-step explanation:
How many solutions will the following system have? 4x+y=13 1/2}y=-2x+5
Step-by-step explanation:
I have to assume the equations are
4x + y = 13
(1/2)y = -2x + 5
let's bring both of them into a "y = ..." form :
y = -4x + 13
y = -4x + 10
now we see that both equations are lines with the same slope but different y-intersect.
so, they are parallel but not identical.
therefore, there are 0 solutions. the lines will never intersect and have no point in common.
How do you draw a logarithmic graph?
Choose the range of values for the x-axis and the y-axis , Plot the points on the graph, using the logarithmic formula , Connect the points with a smooth curve and Label the axes and add any other details you want to include.
1. Choose the range of values for the x-axis and the y-axis. Select the minimum and maximum values for both the x-axis and the y-axis.
2. Plot the points on the graph, using the logarithmic formula. Use the formula log(x) = y to calculate the points that should be plotted on the graph. For example, if the x-axis range is from 1 to 10, and the y-axis range is from 0 to 10, then the first point would be (1,0).
3. Connect the points with a smooth curve. Once all the points have been plotted, use a ruler or a graphing calculator to connect them with a smooth curve.
4. Label the axes and add any other details you want to include. Use a ruler or a graphing calculator to label the axes and add any other details you want to include, such as a title, a legend, or a grid.
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What is the length of the hypotenuse of a 45 45 90 triangle if the length of the leg is 5?
The length of the hypotenuse will be 5√2 = 7.07
The triangle specified in the question is right-angled, one angle is mentioned to be 90°. It is also an isosceles triangle since both other angles are equal. if both angles are equal, both sides will also be equal.
So the length of both equal sides = 5 cm
Pythagoras' theorem tells us about the relationship between the three sides of a right-angled triangle. It states that the square of the hypotenuse of the right-angled triangle will be equal to the sum of squares of the other two sides. If a, b, and c are the sides
c² = a²+ b²
c = √(a²+b²)
According to Pythagoras' theorem, Hypotenuse = √base²+ alt²
Hypotenuse = √5²+5²
= 5√2
= 7.07 cm
So the length of the hypotenuse is 5√2 = 7.07 cm.
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i) a butcher has some hamburger that is 80% lean and some that is 88% lean. he wishes to make 800 ponds of a burger mix that is 83% lean. how much of each type should he use?
by splanation, in be clearly what he taking about. the hamburger, usually. is 1/4 p.1/2 p. in triple hamburger on 4 by 4
The number of used hamburgers that is 80% lean is = 500
and the number of used hamburgers that is 88% lean is = 300.
Let the number of hamburger that is 80% lean be = x.
So the number of hamburger that is 88% lean is = 800 - x
According to question after the mixing all these the total percentage of lean in 800 ponds of burgers is 83%.
So, the suitable mathematical equation is,
80% of x + 88% of (800 - x) = 83% of 800
(80/100) x + (88/100) * (800 - x) = (83/100) * 800
80x + 88 (800 - x) = 83 * 800 [Multiplying 1000 with both sides]
80x + 88 * 800 - 88x = 83 * 800
88x - 80x = 88 * 800 - 83 * 800 = 800 (88 - 83) = 5 * 800
8x = 800 * 5
x = (800 * 5)/8 = 100 * 5 = 500
Hence the number of hamburger with 80% lean is 500 and the number of hamburger with 88% lean is = (800 - 500) = 300.
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Can you help me with this
Answer:
slope = 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (1, 4) ← 2 points on the line
m = [tex]\frac{4-0}{1-(-1)}[/tex] = [tex]\frac{4}{1+1}[/tex] = [tex]\frac{4}{2}[/tex] = 2
Answer: The slope is 2.
Step-by-step explanation: To find the slope of a line, we first need to pick two points on a line. To solve this, I picked points (-2, -2) and (1, 4). The slope is rise over run, so you need to find the rise and run and divide.
We need to go 6 spaces up from (-2, -2) to get to (1, 4). This is our rise. Then, we go 3 spaces to the right. That is our run. 6 / 3 is 2, so that's your slope. Notice that if you cannot divide the rise and run into a whole number, keep it as a fraction instead.
Let me know if this is right! :)
How many terms are there in the expression 2p 3 3p 2 4p 7 *?
The total number of terms which are in the polynomial expression –2p³ – 3p² + 4p + 7 is 4 terms.
A polynomial expression is made up of multiple terms joined either by addition , subtraction or multiplication or division.
The given expression is
–2p³ – 3p² + 4p + 7
If we will break them down in simpler terms we will get ,
–2p³, – 3p², + 4p, + 7
Therefore, number of terms are found to be 4
The terms of an algebraic expression are referred to as the the components of that expression . An algebraic expression can have one or more terms.
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Speedometer readings for a motorcycle at 12-second intervals are given in the table.
t (s) 0 12 24 36 48 60
v (ft/s) 30 28 25 21 25 27
(a) Estimate the distance traveled by the motorcycle during this time period using the velocities at the beginning of the time intervals.
ft
(b) Give another estimate using the velocities at the end of the time periods.
ft
(c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain.
O (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.
O (a) and (b) are neither lower nor upper estimates since v is neither an increasing nor decreasing function of t.
O (a) is a lower estimate and (b) is an upper estimate since v is an increasing function of t.
(a) The distance traveled by motorcycle is 1548 ft.
(b) The distance traveled by motorcycle is 1512 ft.
(c) (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.
What is velocity?
The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.
Given table is:
t (s) 0 12 24 36 48 60
v (ft/s) 30 28 25 21 25 27
The distance traveled by motorcycle during this time period using the velocities at the beginning of the time intervals is:
12(30 + 28 + 25 + 21 + 25)
=12 × 129
= 1548 ft
The distance traveled by motorcycle during this time period using the velocities at the end of the time intervals is:
12(28 + 25 + 21 + 25 + 27)
=12 × 126
= 1512 ft
The distance traveled by motorcycle at the end of the time intervals is greater than the distance traveled by motorcycle at the beginning of the time intervals.
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