The amount paid with discount for the laptop is $ 660.
What is discount?Discount is the amount of money removed from the price of an object being sold.
What is amount paid?Amount paid is the total cost of an item.
How to find how much you will pay for the laptop?Since laptop computer that you want to purchase was originally priced at $750. You will receive a 20% student discount, and the sales tax rate is 8%.
First, we need to know how much discount is given.
Since there is a 20 % discount, the amount of discount removed is 20% × $750 = 0.2 × % 750 = $ 150
Also, there is a sales tax rate of 8%. So, the amount of sales tax added is 8% × $750 = 0.08 × $ 750 = $ 60
So, the total amount paid is T = price - discount + tax
= $ 750 - $ 150 + $ 60
= $ 660
So, the amount paid is $ 660.
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4.3.2 Decrease 72 in the ratio 4:3. (3)
SOLUTION
TO DETERMINE
Decrease 72 in the ratio 4 : 3
EVALUATION
We have to Decrease 72 in the ratio 4 : 3
Let the numbers are 4x and 3x
So by the given condition
Hence the required number
= 3 × 18
= 54
FINAL ANSWER
Hence the required number = 54
x-y=16
x-y=16
Solve using the substitution method
Step-by-step explanation:
x - y = 16 ---eq(1)
x - y = 16 ---eq(2)
From eq(1)
x - y = 16
x = 16 + y ---eq(3)
Substituting the value of eq(3) into eq(2)
(16 + y) - y = 16
16 = 16
We can't get a proper value for this pair of linear Equations
But, Since both the equations are the same, the lines formed by them will be coincident and therefore they will have infinitely many solutions
What is (f- g)(x)?
f(x)=x^4-x² +9
g(x) = x³ + 3x² + 12
Enter your answer in standard form in the box.
(f-g)(x)
A function is defined as the relationship between input and output, where each input has exactly one output. The inputs are the elements in the domain and the outputs are elements in the co-domain.
Step-by-step explanation:
f(x)= x¹ - x² +9
g(x) = x³ + 3x² + 12
To find (f-g)(x):
The operations on functions are as easy as the operations on numbers or polynomials.
We have to subtract the functions to find the above mentioned operation.
(f-g) (x)= f(x)-g(x)
= (x¹ - x² +9)-(x³ + 3x² + 12)
The minus will change the signs of function g.
100 POINTS PLEASE HELP When adjusting entries in accounting, an accountant will compare their analysis of the trial balance with what source?
A. the government
C. the general ledger
B. the CEO
D. GAAP
Answer: i beleive it is the CEO
Step-by-step explanation:
Answer:
the correct answer is C, the general ledger.
Step-by-step explanation:
When adjusting entries in accounting, an accountant will compare their analysis of the trial balance with the company's general ledger accounts. The general ledger is the master set of accounts that contains all the transactions of the company, including adjusting entries. Adjusting entries are made at the end of an accounting period to update the accounts and ensure that the financial statements accurately reflect the company's financial position and results of operations. These entries may involve accruals of revenue or expenses, prepayments, depreciation, or other adjustments. After making these entries, the accountant will compare the updated balances in the general ledger to the trial balance to ensure that they are accurate and balanced. Therefore, the correct answer is C, the general ledger.
Find the diameter
Find the circumference
Find the Area
Please solve
Answer:
Diameter: 17
Circumference: 53.58
Area: 226.865
Step-by-step explanation:
How to solve for diameter of a circle:
Find the radius.Multiply the radius by 2.(The radius is half of the diameter.)
How to solve for a circumference of a circle:
Find radius.Use correct formula: [tex]2[/tex]·[tex]\pi[/tex]·[tex]r[/tex]Solve.How to solve for the area of a circle:
Use correct formula: [tex]\pi r^2[/tex]Plug in radius. Solve.Hope it helped!
for a normal distribution where the mean is 50 and the standard deviation is 10, what percentage of the area is below a score of 31 and above a score of 69 g
The solution is, the required z-score is, 0.25.
What is Z-score?In statistics, the standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores.
here, we have,
Given that :
Mean score, μ = 69
Standard deviation, σ = 4
Score, x = 64
The standardized score, Zscore can be obtained using the formular :
Zscore = (x - μ) / σ
Zscore = (69 - 68) / 4
Zscore = 1 / 4
Zscore = 0.25
Hence, The solution is, the required z-score is, 0.25.
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Find the volume of the rectangular prism with square bases as pictured below
with a = 2 cm and b = 4 cm. Do not include units in your answer.
The volume of the rectangular prism is 32 square centimeters.
What is a prism?A prism is a polyhedron in three dimensions with two identical ends.
The volume of the rectangular prism
= base area of the prism x the height of the prism.
Given:
The base of the prism is squared shape.
And the side of the square is 4 centimeters.
b = 4 and the height is 2 centimeters.
The volume of the rectangular prism,
= base area x height
= (4 x 4) x 2
= 32 square centimeters.
Therefore, the volume of the prism is 32 square centimeters.
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The complete question is given in the attached image.
The diagram shows a prism placed on a horizontal floor.
The prism has height 4m
The volume of the prism is 28m³
The pressure on the floor due to the prism is 35 newtons/m²
Work out the force exerted by the prism on the floor.
The force exerted by the prism on the floor 245 N.
What is Pressure?The physical force applied to an object is referred to as pressure. Per unit area, a perpendicular force is delivered to the surface of the objects. F/A is the fundamental formula for pressure (Force per unit area). Pascals are a unit of pressure (Pa).
Given:
height = 4 m, volume = 28 m³
Pressure = 75 N/m²
Now, Volume of prism = Area of base x height
28 = Аrеа х 4
Area = 28/4 = 7 m²
Also, Pressure = force / Area
35 = force / 7
Force = 35 x 7
Force = 245 N
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Hello! I'd like some assistance with this question. For 'd', why can we only estimate the distances? Could anyone please elaborate on the whole question?
Answer:
Please Mark As Brainliest Answer
Step-by-step explanation:
In many contexts, we can estimate distances between objects or locations, but we may not always be able to measure them precisely. There are several reasons why we might only be able to estimate distances rather than measure them exactly:
Limitations of measuring instruments: The precision of a measuring instrument can limit our ability to measure distances accurately. For example, a ruler may only have markings up to a certain level of precision, so we may need to estimate distances between the markings.
The variability of the distance: In some cases, the distance we are measuring may be constantly changing, making it difficult to measure with precision. For example, if we are trying to measure the distance between two moving objects, the distance between them will constantly change, and we may need to estimate the distance at a particular moment in time.
Environmental factors: The environment can also make it difficult to measure distances precisely. For example, atmospheric conditions such as haze or fog can obscure objects and make it difficult to judge their distance accurately.
Human perception and judgment: Finally, our own perception and judgment can also limit our ability to measure distances accurately. For example, when estimating the distance to an object, our perception of the size of the object can affect our judgment of its distance.
In many cases, despite these limitations, estimates of distances can still be useful and informative. For example, in navigation, we may not need to know the exact distance between two points, but only an estimate that is accurate enough to help us navigate from one point to the other
Answered By Unish ©
Verified Answer ✅
Evaluate the integral by changing the order of integration in an appropriate way. ∫[infinity]0∫540∫9y6e−x2+zdxdydz
The value of the integral is π(540)^2.
What is the value of the integrationWe can change the order of integration as follows:
∫^(∞)(0)∫540∫9y6e−x2+zdxdydz = ∫^(540)(0)∫^∞_0∫^√(9y^6)_(−∞)e−x^2dzdxdy
The limits of z are from −∞ to ∞, but the integrand is an even function of z, so we can simplify the integral by taking the absolute value of the integrand and multiplying it by 2:
∫^(540)(0)∫^∞_0∫^√(9y^6)(−∞)e−x^2dzdxdy = 2∫^(540)_(0)∫^∞_0∫^√(9y^6)_0 e−x^2dzdxdy
We can now evaluate the integral with respect to z:
2∫^(540)_(0)∫^∞_0[√π/2 - √π/2erf(−√x^2+z)/2]|^√(9y^6)_0 dxdy
where erf is the error function.
Substituting the limits of integration and simplifying, we get:
2∫^(540)_(0)∫^∞_0[√π/2 - √π/2erf(−3y^3/√2x)/2]dxdy
Next, we can evaluate the integral with respect to x:
2∫^(540)_(0)[√π/2(x - √2/3y^3erf(−3y^3/√2x))]|^∞_0 dy
Since the limits of integration with respect to x are from 0 to ∞, the first term in the square brackets evaluates to ∞, and the second term evaluates to √π/2. Therefore, the integral reduces to:
2∫^(540)_(0)√π/2 dy = π(540)^2
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6x+3y=15 Substitution method
y=1-x
Substitute the value of y in the first equation with the second equation.
6x + 3(1-x) = 15
Simplify and solve for x:
6x + 3 - 3x = 15
3x + 3 = 15
3x = 12
x = 4
Now, substitute the value of x in the second equation to solve for y:
y = 1 - x
y = 1 - 4
y = -3
Therefore, the solution to the system of equations is (4, -3).
find the slope
x= -1 0 1 2
y = 10 18 26 34
Answer:
x = 10182634
y = - 462847/46
Step-by-step explanation:
Divide both sides of the equation by the coefficient of variable
x = -1012y
y = - 10182634/ 1012
x = -1012y( - 10182634/ 1012)
The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week?
your answer should be a decimal rounded to the fourth decimal place
The probability that a randomly selected teacher earns more than $525 a week is 0.1820. Therefore, the probability that a randomly selected teacher earns more than $525 a week is 0.2177.
This is calculated by using the standard normal distribution formula:
P(x > 525) = 1 - P(x ≤ 525) = 1 - 0.8413 = 0.1820
The probability that a randomly selected teacher earns more than $525 a week can be found by calculating the z-score for $525 and then using the standard normal table to find the probability.
The z-score is calculated as follows:
z = (x - μ)/σ
Where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
Plugging in the values from the question, we get:
z = (525 - 490)/45 = 0.78
Now, we can use the standard normal table to find the probability that a randomly selected teacher earns more than $525 a week. The table gives us the probability that a value is less than a given z-score, so we need to subtract the probability from 1 to find the probability that a value is greater than the z-score.
The probability that a value is less than 0.78 is 0.7823. So, the probability that a value is greater than 0.78 is 1 - 0.7823 = 0.2177.
Therefore, the probability that a randomly selected teacher earns more than $525 a week is 0.2177.
Answer: 0.2177
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in a bag there are 8 blue marbles and 10 red marbles the probability of selecting two blue marbles is 8/18 times 7/17
The probability of spinning a blue is is 1/4.
What is probability?Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1. Probability is applied in many areas, including finance, statistics, weather forecasting, and gambling.
The probability of spinning a blued, then blue is 1/4. The numerator of this fraction is 1.
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A fishing supply store buys fishing rods for $11 and sells them at a markup of 220%. One day, they decide to put the rods on sale and mark them down by 20%.
What is the sale price of a fishing rod?
the sale price of a fishing rod is $28.16.
How to do?
The markup of 220% means the store sells the rods for 100% + 220% = 320% of the cost price.
So, the selling price of one fishing rod before the discount is:
320% of $11 = (320/100) x $11 = $35.20
Now, the rods are marked down by 20%, which means the selling price is reduced by 20% of $35.20:
20% of $35.20 = (20/100) x $35.20 = $7.04
Therefore, the sale price of one fishing rod after the 20% discount is:
$35.20 - $7.04 = $28.16
So, the sale price of a fishing rod is $28.16.
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express the function graphed on the axes below as a piecewise function
The piecewise function graphed is defined as follows:
y = -2x - 12, x < -5.y = -x + 5, x > 3.How to define the piecewise function?A piecewise function is a function that has multiple definitions, depending on the input x of the function.
The function in this problem has definitions for two intervals, given as follows:
x < -5.x > 3.For x < -5, the function is decreasing with a slope of -2, as when x increases by 1, y decays by 2, hence:
y = -2x + b.
When x = -6, y = 0, hence the intercept b is given as follows:
0 = -2(-6) + b
b = -12.
Hence:
y = -2x - 12, x < -5.
For x > 3, the function is decreasing with a slope of -1, as when x increases by 1, y decays by 1, hence:
y = -x + b.
When x = 5, y = 0, hence the intercept b is given as follows:
0 = -5 + b
b = 5.
Hence:
y = -x + 5, x > 3.
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x^6 • x • x^3 = x^6+3 = x^9
The given expression is equivalent to [tex]x^{10}[/tex], not [tex]x^{6+3}[/tex] or [tex]x^9.[/tex]
What are the rules of exponents?
The rules of exponents are a set of mathematical rules that simplify expressions that involve powers or exponents. Some of the basic rules of exponents include:
[tex]x^m * x^n = x^{(m+n)}[/tex] (product rule)[tex](x^m)^n = x^{(m*n)}[/tex] (power of a power rule)[tex]x^0 = 1[/tex] (zero exponent rule) (negative exponent rule)The expression [tex]x^6 * x * x^3[/tex] can be simplified using the rules of exponents as follows:
[tex]x^6 * x * x^3 = x^{(6+1+3)} = x^{10}[/tex]
Therefore, the given expression is equivalent to [tex]x^{10}[/tex], not [tex]x^{6+3}[/tex] or [tex]x^9.[/tex]
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2y-8x=6 which of the following pairs satisfies the equations (1,8) (6,27) (-2,8) (-8,-27) (-1,-1)
Answer:
Step-by-step explanation:
To determine which pairs satisfy the equation 2y - 8x = 6, we need to find values of x and y that make the equation true. One way to do this is to solve for y in terms of x:
2y - 8x = 6
2y = 8x + 6
y = 4x + 3
Now we can substitute different values of x into this equation and see what values of y we get. For example:
When x = 0, y = 3
When x = 1, y = 7
When x = -1, y = -1
When x = 2, y = 11/2
When x = -2, y = -5
So the pairs that satisfy the equation 2y - 8x = 6 are:
(0, 3), (1, 7), (-1, -1), (2, 11/2), (-2, -5)
In each of these pairs, when we substitute the values of x and y into the equation, we get a true statement
The tallest lot in New York city holds one world trade center a building that is 1776 feet tall the shortest light in New York City is empty and 0 feet tall what is the range of heights for lots in New York City
A. 1,776 feet
B. 888 feet
C. 177.6 feet
D. 0 feet
The range of heights for lots in New York City is:
1776 feet - 0 feet = 1776 feet.
What is Height ?Height is a mathematical term that refers to the vertical distance between an object's top and base. On sometimes, it has the designation "altitude." The measurement of an item along the y-axis in coordinate geometry is referred to as height in geometry.
The range of heights for lots in New York City is the difference between the tallest and shortest lots.
The tallest lot is 1 World Trade Center, which is 1776 feet tall.
The shortest lot is empty and 0 feet tall.
Therefore, the range of heights for lots in New York City is:
1776 feet - 0 feet = 1776 feet
So, the answer is A. 1776 feet.
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HELPPPP WILL MARK BL!!!!!
The quadratic equation y = 4 · x² + 28 · x + 49 is an example of a perfect square trinomial.
There are two configurations for the dimensions of the rectangle:
Configuration 1: b = 6 · (x - 1 / 2), h = x + 4 / 3
Configuration 2: b = 6 · (x + 4 / 3), h = x - 1 / 2
Is a given quadratic equation a perfect square trinomial?
In this problem we find the quadratic equation y = 4 · x² + 28 · x + 49 and we need to check if the expression represent a perfect square trinomial. A quadratic equation is a perfect square trinomial if and only if the following formula is fulfilled:
a · x² + b · x + c = r₁² · x² + 2 · r₁ · r₂ · x + r₂² = (r₁ · x + r₂)²
That is,
r₁² = a
r₁² = 4
r₁ = 2
r₂² = c
r₂² = 49
r₂ = 7
2 · r₁ · r₂ = b
2 · 2 · 7
28
The quadratic equation y = 4 · x² + 28 · x + 49 is a perfect square trinomial.
Finally, we determine the dimensions of a rectangle whose area is the quadratic equation A = 6 · x² + 5 · x - 4. The area formula for a rectangle is described by the following formula:
A = b · h
Where:
b - Baseh - HeightThen, the factored form of the quadratic equation is:
A = 6 · x² + 5 · x - 4
A = 6 · [x² + (5 / 6) · x - 2 / 3]
A = 6 · (x - 1 / 2) · (x + 4 / 3)
There are two possible configurations for the rectangle:
Configuration 1: b = 6 · (x - 1 / 2), h = x + 4 / 3
Configuration 2: b = 6 · (x + 4 / 3), h = x - 1 / 2
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Compare the investment below to an investment of the same principal at the same rate compounded annually. principal: $1,000, annual interest: 3%, interest periods: 4 , number of years: 15
The investment with annual compounding yields a higher future value of $1,520.10 compared to $1,489.36 for the given investment method.
What is compounding?The process through which an investment earns returns on both the principal and the accrued interest over time is known as compounding. To put it another way, it is the reinvestment of interest income into an investment that enables the investment to increase exponentially over time.
Compounding works on the basic premise that interest earned on an investment is added to the principal amount. The interest is then calculated using the new, higher principal amount during the subsequent interest period, yielding even more interest. When the money generated is reinvested and grows over time, this cycle keeps repeating, increasing the investment's value more swiftly.
The investment given has a principal of $1,000, an annual interest rate of 3%, and interest periods of 4 per year. The investment is held for 15 years. To compare this investment to one with the same principal and annual interest rate compounded annually, we need to calculate the future value of the investment using both methods and compare the results.
Using the given investment method, we can calculate the future value as follows:
FV = P(1 + r/n)^(nt)
FV = 1000(1 + 0.03/4)^(4*15)
FV = $1,489.36
Using annual compounding, we can calculate the future value as:
FV = P(1 + r)^t
FV = 1000(1 + 0.03)^15
FV = $1,520.10
So, the investment with annual compounding yields a higher future value of $1,520.10 compared to $1,489.36 for the given investment method. This difference occurs because compounding more frequently leads to more frequent accumulation of interest, resulting in a higher final amount.
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Write an equation for the line in slope-intercept form.
When the coordinate is (-3, -3) and the slope is -1, the y-intercept is -4.
What is slope?Slope is a measure of the stainless of a line what is surface and it represent by the letter m. It is calculated by dividing the vertical change in the line or surface by the horizontal change in the line or surface. Slope is used in mathematics engineering and other science to measure the rate of change between two point.
The y-intercept is the point at which a line crosses the y-axis when plotting coordinates on a graph. To find the y-intercept, you need to use the equation y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation would be y = -1x - 4. This equation can be used to solve for the y-intercept when the coordinate is (-3, -3). By substituting -3 for x and -3 for y, the equation can be rearranged to -3 = -1(-3) - b, which simplifies to -4 = -b. Therefore, the y-intercept is -4.
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i need the answer urgent
The individual events are overlapping. The probability of the combined event is 11/26.
What is the probability of the combined eventThe individual events are overlapping because there are face cards that are also spades (i.e., the Jack, Queen, and King of Spades). To find the probability of the combined event, we need to add the probability of drawing a face card and the probability of drawing a spade, and then subtract the probability of drawing the Jack, Queen, or King of Spades (since we would be double-counting these cards otherwise).
The probability of drawing a face card is 12/52, since there are 12 face cards in the deck (4 Jacks, 4 Queens, and 4 Kings) out of a total of 52 cards.
The probability of drawing a spade is 13/52, since there are 13 spades in the deck (including the Jack, Queen, and King of Spades) out of a total of 52 cards.
The probability of drawing the Jack, Queen, or King of Spades is 3/52, since there are 3 such cards in the deck out of a total of 52 cards.
Therefore, the probability of the combined event is:
P(face card or spade) = P(face card) + P(spade) - P(Jack, Queen, or King of Spades)
P(face card or spade) = 12/52 + 13/52 - 3/52
P(face card or spade) = 22/52
P(face card or spade) = 11/26
So the probability of the combined event is 11/26 or approximately 0.42 when rounded to two decimal places.
This shows the individual events are overlapping and the probability is 11/26
The individual events are overlapping. The probability of the combined event is 11/26.
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What is the meaning or the impact if the regression data residual is not normally distributed
The meaning or impact of the regression data residual not being normally distributed is that the assumptions of the regression model are not met. This can result in biased or misleading estimates of the regression coefficients and the overall fit of the model.
When the residuals are not normally distributed, it can indicate that there are other factors influencing the relationship between the independent and dependent variables that are not accounted for in the model. This can lead to incorrect predictions and unreliable conclusions about the relationship between the variables.
To address this issue, it may be necessary to transform the data or use a different type of regression model that does not assume normality of the residuals. It is also important to check for outliers and influential points, as these can also affect the distribution of the residuals.
In conclusion, the normality of the residuals is an important assumption of the regression model, and if it is not met, it can have a significant impact on the reliability and validity of the results.
Find the measure of
Answer:
a+75+65= 180(sum of angle of triangle)
a+140=180
a=180-140
a=40
100 POINTS HELP PLEASE How would an accountant list a balance of negative $300 in a general ledger?
A. ~ $300
B. neg. $300
C. - $300
D. ($300)
Answer: i think for me its $10,300
Step-by-step explanation: Allowance account is deducted from Accounts Receivable to determine Net ... $300 credit balance + 10,000 additional credit = $10,300 credit balance.
Answer: D
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Use a definition, postulate, or theorem to find the value of x in the figure described.
Point E is between points D and F. IfDE=x-1, EF = 4x + 5, and DF = 6x - 5, find x.
The solution is x =?
Thus, the value of x in the figure is 9.
What's collinear?Collinear refers to a term used in figure to describe a set of three or further points that lie on the same straight line. In other words, if you can draw a straight line that passes through two or further points, those points are said to be collinear.
We can use the member addition hypothetical to break for x. According to the member addition hypothetical, if three points A, B, and C are collinear, also AB BC = AC.
In this case, points D, E, and F are collinear, so we can write
DE EF = DF
Substituting the given values, we get
x- 1 4x 5 = 6x- 5
Simplifying the equation, we get
x 4 = 6x- 5
Abating 5x from both sides, we get
= x- 5
Adding 5 to both sides, we get
x = 9
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Given IQ scores are approximately normally distributed with a mean of 100 and standard deviation of 20, the proportion of people with IQs above 140 is:
The proportion of people with IQs above 140 is 2.5% of a mean of 100 and standard deviation of 20.
Which proportion do you mean?Comparative magnitude or extent; ratio; the relationship between several entities or components in terms of relative size, number, or degree. the right or ideal relationship between components of a whole; symmetry or balance. If a change in one variable can be expected from a change in the other, two variables are said to be in proportion. For secondary school chemists, there are two separate sorts of proportional relationships: direct proportion and inverse proportion.
When we find the proportion , we obtain:
P(y > 140) = 1 - P(y< 140)
= 1 - P[(x - α) / β < (140 - 100) / 20]
= 1 - P(z < 2)
= 1 - 0.9772
= 0.0228
= 2.5%.
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The drama club is selling tickets to their play to raise money for the show's expenses.
Each student ticket sells for $7 and each adult ticket sells for $10. The auditorium can
hold no more than 85 people. The drama club must make no less than $690 from
ticket sales to cover the show's costs. Also, they must sell a minimum of 10 student
tickets and at least 55 adult tickets. If a represents the number of student tickets sold
and y represents the number of adult tickets sold, write and solve a system of
inequalities graphically and determine one possible solution.
On solving the inequalities a ≥ 10, y ≥ 55, 7a + 10y ≥ 690, the solution is obtained as (20,55).
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
Use the variables a and y to represent the number of student and adult tickets sold, respectively.
Then write the following system of inequalities -
a ≥ 10 (they must sell a minimum of 10 student tickets)
y ≥ 55 (they must sell at least 55 adult tickets)
7a + 10y ≥ 690 (they must make no less than $690 from ticket sales)
The first two inequalities are constraints on the number of tickets sold, and the third inequality represents the revenue constraint.
To find a possible solution, graph these inequalities on a coordinate plane and look for the feasible region that satisfies all three inequalities.
Alternatively, solve the system of inequalities using algebra.
First, simplify the third inequality by subtracting 7a from both sides -
10y ≥ 690 - 7a
Then, divide both sides by 10 -
y ≥ (690 - 7a)/10
This inequality represents the revenue constraint in terms of the number of student tickets sold.
Now combine the revenue constraint with the other two constraints -
a ≥ 10
y ≥ 55
y ≥ (690 - 7a)/10
Use substitution to solve for a in terms of y -
y ≥ (690 - 7a)/10
10y ≥ 690 - 7a
7a ≥ 690 - 10y
a ≥ (690 - 10y)/7
To find a possible solution, substitute a = (690 - 10y)/7 into the other two constraints -
(690 - 10y)/7 ≥ 10
y ≥ 55
These inequalities can be simplified -
690 - 10y ≥ 70
y ≥ 55
The first inequality can be solved for y -
-10y ≥ -620
y ≤ 62
Since it is known y ≥ 55, the feasible values for y are between 55 and 62, inclusive -
55 ≤ y ≤ 62
Now use the expression for a in terms of y to find the corresponding values of a -
a = (690 - 10y)/7
For each value of y between 55 and 62, inclusive, we can calculate a and check whether it satisfies the constraints -
a ≥ 10
y ≥ 55
7a + 10y ≥ 690
For example, when y = 55 -
a = (690 - 10(55))/7 = 20
7a + 10y = 7(20) + 10(55) = 690
Therefore, these values satisfy all three constraints, so one possible solution is a = 20 and y = 55.
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Express $8.99 for 1.24 pounds of salmon as a unit rate. Show your work.
Answer:
7.25
Step-by-step explanation:
Divide 8.99 by 1.24