Errors student make is the % values in the equation were wrongly written and Instead of writing x - 1 for the amount of the 7% solution, write 1 - x.
Define equation.There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value of a given data set are called equation.
Given
A student has a 2% salt water solution and a 7% salt water solution. To best imitate salt water at a local beach, he needs 1 liter of a 3.5% salt water solution. He defines x as the amount of 2% solution and writes this equation:
0.2x + 0.7(x – 1) = 0.35(1)
He requires 1 litre of a 3.5% salt water solution to accurately mimic the salt water at a nearby beach.
He constructs the following equation, where x is the volume of the 2% solution:
0.2x + 0.7(x - 1) = 0.35(1)
After resolving the equation, he ascertains that x is around 1.17 litres.
Errors student make:
A) The % values in the equation were wrongly written.
B) Instead of writing x - 1 for the amount of the 7% solution, write 1 - x.
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A school is arranging a field trip to the zoo. The school spends 546.53 dollars on passes for 40 students and 3 teachers. The school also spends 351.60 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
There are $21.5 money was spent on a pass and lunch for each student.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that:
The amount spent by school on pass of 40 students and 3 teachers = $546.53
And, the amount spent for the lunch only for students = $351.60
Now,
The money spent for pass of 43 person = $546.53
Then, The amount of pass for each person = 546.53/43
= $12.71
Since, there are 40 student then amount of lunch for each students = ⇒ 351.60/40
⇒ $8.79
Therefore, amount of pass and lunch for each student = 12.71 + 8.79
= $21.5
Thus, $21.5 is the required answer.
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For which situation does one quantity change at a constant rate per unit interval relative to another quantity?
Responses
For every day that passes, a person drives 54 miles.
.
For every month that passes, a savings account earns interest at a rate of 1.5%
For every week that passes, a vine doubles in length 2 times a week.
.
For every year that passes, a population of insects increases by 6%
Answer:
(a) For every day that passes, a person drives 54 miles
Step-by-step explanation:
You want to know the situation in which one quantity changes relative to another at a constant rate.
DrivingThe rate of change is described as 54 miles for each day. This is a constant rate of change. Miles relative to days are described by a linear function.
SavingsWe assume the description means that the balance in the savings account increases by 1.5% with each passing month. While this interest rate is a constant, the amount by which the balance changes each month is not constant. The balance relative to time is described by an exponential function.
VineIf the vine doubles in length twice a week, its length increases by 300% each week. As with savings, this growth rate is constant, but the amount of growth each week is not. The length of the vine is described by an exponential function.
PopulationAs with savings, this growth rate is constant, but the amount of increase each year is not. The population is described by an exponential function.
The situation with a constant rate of change is ...
For every day that passes, a person drives 54 miles.
__
Additional comment
When the quantity is graphed, the "rate of change" refers to the slope of the curve on the graph. The graph of an exponential growth function does not have a constant slope, but has a slope that increases exponentially.
<95141404393>
What is the distance between points m and n? meters
Answer: 9.8
Step-by-step explanation:
how to find the standard deviate and variance of a discrete random variable in ap stats organic chem tutor
Calculation the variance and standard deviation of the discrete random variable is given by σ² = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex] and standard deviation is the square root of Variance 'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].
As given in the question,
Variance is used to represent the dispersion of the values in the data from the calculated mean.[tex]( x_{i} - \bar{x})[/tex] represent the dispersion of the given data values from the mean.Variance is given by σ² = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex] Standard deviation is the square root of the variance it represents the amount of dispersion of all the given data values.Standard deviation is given by 'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].Therefore , the variance and standard deviation of the discrete random variable is calculated with the help of the following formulas:
Variance 'σ²' = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex] and standard deviation 'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].
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In a video game, a player follows a certain path that can be partially modeled by the functionf(x)=x(x−5)(x−3) . This function can be graphed on a coordinate plane.
The graph of the function f(x) = x(x - 5)(x - 3) is given by the image shown at the end of the answer.
How to draw the sketch of the graph?To draw the sketch of the graph, we need to consider these three following features:
The x-intercepts.The y-intercept.The end behavior.The function in this problem is defined as follows:
f(x) = x(x - 5)(x - 3).
From the factor theorem, the x-intercepts are taken from the linear factors, as follows:
x = 0.x - 5 = 0 -> x = 5.x - 3 = 0 -> x = 3.The y-intercept is the value of y when the graph of the function crosses the y-axis, that is, the value of y when x = 0, hence:
f(0) = 0(0 - 5)(0 -3) = 0.
In the problem, we have a cube function, hence:
At the left tail(negative infinity) it goes to negative infinity.At the right tail(positive infinity) it goes to positive infinity.More can be learned about functions at https://brainly.com/question/24808124
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What is the value of p in the equation 8p 2 = 4p - 10?
Answer:
Step-by-step explanation:
Determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number, if necessary.
Answers: 7 units
14 units
25 units
26 units
answer : 26
steps
get hypotenuse
a² + b² = c²
7² + 8² = c²
49 + 64 = c²
113 = c²
square root of c is √113 which 10.63
7 + 8 + 10.63 = 25.63
Sonny has 2x + 3 dollars. Allan has 6x + 4 dollars. How much money did Sonny have if they both had $407 all together?
Answer:
$103
Step-by-step explanation:
In order to determine how much money Sonny has, we need to write a mathematical equation to solve for x. We know how much money Sonny and Allan each have in terms of x, and we can add the two expressions together to equal a total amount of $407. This will be represented and simplified as follows:
2x + 3 + 6x + 4 = 4078x + 7 = 407Now we can solve the equation for x.
8x = 400x = 50We know that x is equal to 50, so we can plug it back into Sonny's expression to find out how much money she has.
2(50) + 3 = 100 + 3 = 103Sonny has $103.We can check our work by solving for the amount of money Allan has and then adding up the two amounts to make sure the total is $407.
6(50) + 4 = 300 + 4 = 304CHECK: $103 + $304 = $407Mrs. Boggs asked her students to create a cylinder to hold
chocolate candies using a standard piece of paper (8.5 inches by 11 inches.)
Some of the students made cylinders that were 11 inches tall, and others created cylinders that were 8.5 inches tall.
The students began discussing the amount of chocolate candies
that each person could store. Oliver said that each cylinder
would hold the same amount of chocolate candies because they used the same size paper. Anna disagreed.
Who is correct? Try it out with a piece of paper and then use the calculations on the next page to compare.
The cylinder made with a paper size of 8.5 inches by 11 inches is having more volume and thus contains more chocolate, so, the statement by Oliver is wrong.
What is cylinder?
A cylinder is a three-dimensional solid that maintains two parallel bases spaced at a set distance from one another. These bases often have a circular form (like a circle).
Given:
The size of the first paper = 8.5 inches by 11 inches,
The size of the second paper = 11 inches by 8 inches,
The width of the paper when folded becomes the circumference of the cylinder circle, so,
Circumference of the cylinder for the first case = 2 × π × r
11 = 2 × π × r,
r = 1.75 inches,
The volume of the cylinder for the first case = π × r² × h
The volume of the cylinder for the first case = π × (1.75)² × 8.5
The volume of the cylinder for the first case = 81.78 inches³
Calculate the volume for the second case,
Circumference of the cylinder for the second case = 2 × π × r,
8.5 = 2 × π × r
r = 1.35 inches
The volume of the cylinder for the second case = π × (1.35)² × 11
The volume of the cylinder for the first case = 63.24 inches³
As we know, the cylinder with a higher volume contains more chocolate.
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Matthew Westhoven deposited $925 in a new regular savings account that earns 5.5% interest compounded semiannually for 1 year. What is the compound interest?
The compound interest received by Matthew Westhoven is $51.80
What is compound interest?The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You'll have $110.25 after the second year is over.
Given, the principal amount (P) = $925
Compound interest percentage (r) = 5.5% = 0.055
Time period (t) = 1
Since, it is semiannually compounded (n) = 2*t = 2
Amount (A) = P(1 + r/n)^nt
= 925(1 + 0.055/2)^2
= 925(1.0275)^2
= 925(1.056)
= 976.80
Thus, Interest amount (CI) = A - P
= $976.80 - $925
= $51.80
The compound interest received by Matthew Westhoven is $51.80
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Find the lengths of segments AD and BD. Then check your answers using a different method.
Answer: BD = 5
Step-by-step explanation:
Using the Pythagorean theorem [tex]a^{2} + b^{2} =c^{2}[/tex] where c is the hypotenuse, we can solve for BD[tex]a^{2} +12^{2} =13^{2}[/tex]
[tex]a^{2} =13^{2}-12^{2}[/tex]
[tex]a = \sqrt{25}[/tex]
[tex]a = 5[/tex]
Therefore BD = 5
Mikaela purchased a paddleboard originally priced at $699. If all merchandise was on sale for 40% off and the state tax rate is 7. 25%, what is the total amount that mikaela spent on the paddleboard?.
The total amount that Mikaela spent on the paddleboard will be $449.80.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths.
As per the given,
Original price = $699
The selling price = $699 - 40% of $699
⇒ $699 - 0.40 x $699 = $419.4
The state tax (assuming it applied to the selling price) will be as,
7.25% of $419.4 = (7.25/100) x 419.4 = $30.4065
Final amount = $419.4 + $30.4065 = $449.80
Hence "Mikaela will have spent $449.80 in total on the paddleboard".
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14x+17.5<−66.5 can you guys help me
Answer: < -6
Step-by-step explanation:
Find the inverse of f(x) = 2(x-2) ^2 +1
Find the inverse of y = ^3√x-3
Answer:
f^-1(x) = 2(x-2)^2 + 1
f^-1(x) = (x+3)^3
Step-by-step explanation:
The inverse of a function is found by switching the roles of the dependent and independent variables. In other words, we can find the inverse of a function by interchanging the x and y values in the equation. So, the inverse of the function f(x) = 2(x-2)^2 + 1 can be written as f^-1(x) = 2(x-2)^2 + 1.
1. To find the inverse function explicitly, we can use the following steps:
2. Replace f(x) with y in the original function to obtain y = 2(x-2)^2 + 1.
3. Solve for x in terms of y to obtain x = +/- sqrt((y-1)/2) + 2.
The inverse function f^-1(x) can then be written as f^-1(x) = +/- sqrt((x-1)/2) + 2.
Note that this inverse function is not a one-to-one function, because for some values of x (namely, x < 1), the function has two possible values of y (i.e. it has two solutions). Therefore, the inverse function is not a function in the strict mathematical sense, but it is still a useful concept in certain contexts.
To find the inverse of a function, we switch the roles of the dependent and independent variables, so the inverse function can be written as x = ^3√y-3.
1. To find the inverse function explicitly, we can use the following steps:
2. Replace y with x in the original function to obtain x = ^3√y-3.
3. Solve for y in terms of x to obtain y = (x+3)^3.
The inverse function can then be written as f^-1(x) = (x+3)^3.
Note that this inverse function is a one-to-one function, meaning that for every value of x, there is only one corresponding value of y. Therefore, the inverse function is a function in the strict mathematical sense.
By identifying the vertical asymptote, one can determine the denominator of this
function is
The denominator of function is -x/2 - 1 and vertical asymptote x = -2.
What is vertical asymptote?A vertical line that is not a part of the function's graph but serves as a guide is known as a vertical asymptote. Because it occurs at an x-value outside of the function's domain, the graph cannot cross it. There may be more than one vertical asymptote for a function.
Given graph
the function of graph is F(x) = [tex]2\frac{\left(-\frac{x}{2}\ +\ 1\right)}{\left(\frac{x^{2\ }}{4}-1\right)}[/tex] = 2(1- x/2)/(x²/4 - 1)
reducing the equation
F(x) = 2/(-x/2 - 1)
denominator is -x/2 - 1
for vertical asymptote -x/2 - 1 = 0
x = -2
Therefore for function is -x/2 - 1 and vertical asymptote at x = -2.
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HELP PLEASEEEE ASAP
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $29,521. The variable costs will be $12 per book. The publisher will sell the finished product to bookstores at a price of $25.25 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
Answer:
2,228
Step-by-step explanation:
Each unit will make 13.25 in profit before incorporating the one time cost. This means that 29,521/13.25= the amount needed to break even.
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
The expressions in the table represent the number of canned goods collected by two homerooms during a charity food drive.
Homeroom Cans Collected
Mr. Juarez 8n−7
Ms. Wade 6n+3
Write an expression that shows the total number of cans collected by both homerooms.
Part B
The students in Mr. Juarez's homeroom collected more cans than students in Ms. Wade's homeroom. Write an expression that represents how many more cans were collected.
The expression that shows the total number of cans collected by both homerooms is 14n - 4
The expression for more cans collected is 8n - 7 > 6n + 3
The total number of cans collectedFrom the question, we have the following parameters that can be used in our computation:
Homeroom Cans Collected
Mr. Juarez 8n−7
Ms. Wade 6n+3
The total number of cans collected is calculated as
Cans collected = Mr. Juarez + Ms. Wade
Substitute the known values in the above equation, so, we have the following representation
Cans collected = 8n - 7 + 6n + 3
Evaluate the like terms
Cans collected = 14n - 4
How many more cans were collectedHere, we have
Mr. Juarez's homeroom collected more cans
This means that
Mr. Juarez > Ms. Wade
Substitute the known values in the above equation, so, we have the following representation
8n - 7 > 6n + 3
Hence, the expression is 8n - 7 > 6n + 3
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on the number line, the distance between x and y is greater than the distance between x and z. does z lie between x and y on the number line?
yes, z can lie between x and y but z can also lie on another side of x in Number lines.
With an example, define number line?
Number lines in mathematics are horizontal straight lines on which numbers are arranged in equal intervals.
A number line can be used to visualize all the numbers in a succession. The endpoints of this line go on forever.
What does the math number line mean?
A horizontal line with uniformly spaced numerical increments is called a number line. How the number on the line can be answered will depend on the numbers that are provided.
How a number is used—for example, to plot a point—depends on the question that goes with it.
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Please help if possible.
Answer:
$1020.00000$1020.15050$1020.18436$1020.19742$1020.20078Step-by-step explanation:
You want to find the effect of compounding 2% annual interest on $1000 at different intervals for a year. The intervals are ...
1 per year4 per year12 per year52 per year365 per yearCalculatorThe attached calculator display shows the result:
yearly: $1020.00000quarterly: $1020.15050monthly: $1020.18436weekly: $1020.19742daily: $1020.20078Given the side measures, which of the following could form a right triangle?
A. 61 m, 60 m, 11 m
B. 24 in, 34 in, 28 in
C. 55 ft, 45 ft, 35 ft
D. 48 cm, 46 cm, 15 cm
The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).
What is the right triangle is triangle?
A right triangle is a triangle in which one angle measures 90 degrees. The sides of a right triangle can be used to determine if a triangle is a right triangle using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Using this information, we can determine which of the given sets of side measures could form a right triangle:
A. 61 m, 60 m, 11 m: We can use the Pythagorean theorem to see if these sides could form a right triangle. We'll let the hypotenuse be the side with a length of 61 m, and the other two sides are the ones with lengths of 60 m and 11 m. Plugging these values into the Pythagorean theorem, we get:
(61 m)² = (60 m)² + (11 m)²
61² = 60² + 11²
61² ≠ 60² + 11²
Since the left side does not equal the right side, these sides cannot form a right triangle.
B. 24 in, 34 in, 28 in: Using the Pythagorean theorem, we can see that these sides could form a right triangle:
(34 in)² = (24 in)² + (28 in)²
34² = 24² + 28²
34² = 24² + 28²
The left side equals the right side, so these sides could form a right triangle.
C. 55 ft, 45 ft, 35 ft: Using the Pythagorean theorem, we can see that these sides could form a right triangle:
(55 ft)² = (45 ft)² + (35 ft)²
55² = 45² + 35²
55² = 45² + 35²
The left side equals the right side, so these sides could form a right triangle.
D. 48 cm, 46 cm, 15 cm: Using the Pythagorean theorem, we can see that these sides could not form a right triangle:
(48 cm)² ≠ (46 cm)² + (15 cm)²
48² ≠ 46² + 15²
Since the left side does not equal the right side, these sides cannot form a right triangle.
Hence, The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).
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A bakery used `25\%` less butter this month than last month.
The bakery used `240` kilograms of butter this month.
How much did it use last month?
In linear equation, The amount of butter used is an illustration of equivalent ratio.
The amount of butter used last month is 300kg.
What is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Because the bakery used 25% more last month, the amount they used is then calculated using
Amount = ( 1 + 25%) * last month
Substitute 240kg for Last Month
Amount = ( 1 + 0.25) * 240
Remove brackets
Amount = 1.25 * 240kg
= 300 kg
Hence, the amount of butter used last month is 300kg.
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Rufus has collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25 pounds each week. In how many weeks will Rufus have a total of 400 pounds of cans?
Answer: 12
Step-by-step explanation:
Tires A mechanic checked the tire pressures on each car that he worked on
for one week. The random variable x represents the number of tires that
were underinflated.
0
P(x) 0.30
1
2
0.25 0.25
3
0.15
4
0.05
The expected value for the given problem is E(x) = 1.4.
What is expected value?
The expected value is a generalization of the weighted average in probability theory. Informally, the expected value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.
A projected average value for an investment at some point in the future is known as the expected value (EV).
Investors use expected value to gauge an investment's merit, frequently in relation to how risky the investment is.
The formula for to find the expected value is given as,
E ( X ) = μ = ∑ x P ( x ) .
E(x) = 0*0.30 + 1*0.25 + 2*0.25 + 3*0.15 + 4*0.05
E(x) = 1.4
Hence, the expected value for the given problem is E(x) = 1.4.
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need help! can't figure it out :/
Answer:
please tell me if you get the answer. I need it too!
7. Use the Division Property of Equality to write an equation that is
equivalent to 5x = 14.
Answer: x = 14/5 or x = 2.8
Step-by-step explanation:
Step 1: Divide both sides of the equation by five: a common nonzero real number.
(5x)/5= 14/5
Step 2: Simplify
x = 14/5
Which of the following statements is correct for a triangle?
A. triangle can have two obtuse angles
B.The difference of two sides of a triangle is greater than any other side of the same triangle.
C.A triangle can have an obtuse angle and a right angle.
D.None of these
You mix 1 fourth cup of crisp wheat cereal with 1 1 half cups of crisp rice cereal. Find and interpret the value of the ratio of crisp wheat cereal to crisp rice cereal.
The amount of crisp wheat cereal is _____ the amount of crisp rice cereal
Response:
Answer:
The value of the ratio of crisp wheat cereal to crisp rice cereal is 1/4 to 1 1/2, which can be simplified to 1/4 to 3/2. This means that for every 4 parts of crisp wheat cereal, there are 3 parts of crisp rice cereal. The amount of crisp wheat cereal is therefore less than the amount of crisp rice cereal. Specifically, the amount of crisp wheat cereal is 1/4 * the amount of crisp rice cereal.
Step-by-step explanation:
A quadratic function has roots at 2 and 4 and a vertex at (3, −2). What is the equation of the function in vertex form?
Answer:
Step-by-step explanation:
member c: works 7 hours per week at $7.25 per hour member d: works 9 hours per week at $6.35 per hour a. a and b b. a and c c. b and c d. b and d
Only member B and D will reach their goal.
Given;
Amount to be saved = $285
Total time to save money = 5 weeks
Now,
For member A:
Working hours = 8 per week
per hour earnings = $6.15
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hour
= 8 × 5 × 6.15
= $246
For member B:
Working hours = 10 per week
per hour earnings = $5.85
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 10 × 5 × 5.85
= $292.5
For member C:
Working hours = 7 per week
per hour earnings = $7.25
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 7 × 5 × $7.25
= $253.75
For member D:
Working hours = 9 per week
per hour earnings = $6.35
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 9 × 5 × $6.35
= $285.75
Since, the amount earned by member B and D is greater than the goal amount and the amount earned by member A and C is less than the goal amount
therefore,
Only member B and D will reach their goal
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Your question is incomplete. Please find the missing content below:
To be able to go on the band trip, four band members each get a part-time job. Each person has 5 weeks in which to save his or her money. Analyze the four individual plans below and decide which of the four people will reach his or her goal of saving $285? Member A: Works 8 hours per week at $6.15 per hour Member B: Works 10 hours per week at $5.85 per hour Member C: Works 7 hours per week at $7.25 per hour Member D: Works 9 hours per week at $6.35 per hour
For what values of x, y, and z is this a parallelogram?
The values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.
What are the Properties of Angles of a Parallelogram?
A parallelogram is a quadrilateral with equal and parallel opposite sides. There are some special properties of a parallelogram that make it different from the other quadrilaterals.
The opposite angles of a parallelogram are congruent (equal). All the angles of a parallelogram add up to 360°. All the respective consecutive angles are supplementary.The consecutive angles are supplementary then,
5y + 7y - 24 = 180
12y = 180 + 24
12y = 204
y = 204/12
y = 17
The opposite angles of a parallelogram are congruent (equal) then,
5y = 4x + 7
5(17) = 4x + 7
85 = 4x + 7
85 -7 = 4x
4x = 78
x = 78/4 = 19.5
x = 19.5
the consecutive angles are supplementary, then
4x + 7 + 3z = 180
4(19.5) + 7 + 3z = 180
78 + 7 + 3z = 180
85 + 3z = 180
3z = 180 - 88
3z = 92
z = 92/3
z = 30.6
All the angles of a parallelogram add up to 360°, then:
4x + 7 + 3z + 5y +7y - 24 = 360
To check is this a parallelogram? put the values of x, y, and z in the above equation:
4(19.5) + 7 + 3(30.6) + 5(17) +7(17) - 24 = 360
356.8 ≠ 360
hence, the values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.
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