If x is normally distributed with mean 140 and standard deviation 20, find P(140 < x < 150) (round off to fourth decimal place).
Answers
P(140 < x < 150) is 0.1915 when x is normally distributed with mean 140 and standard deviation 20.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value
μ = mean = 140
σ = standard deviation = 20
z-score(x = 140) = (140 - 140) / 20
z-score(x = 140) = 0
z-score(x = 150) =(150 - 140) / 20
z-score(x = 150) = 0.5
Find the probability that corresponds to the z-score in the z-table. (see attached images)
z-score = 0 probability = 0.5000
z-score = 0.5 probability = 0.6915
This means that there's a probability of 0.500 and 0.6915 that the value of x is less than 140 and 150, respectively.
P(140 < x < 150) = 0.6915 - 0.5000 = 0.1915
Therefore, the probability that the value of x is between 140 and 150 is 0.1915.
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Related Questions
if cot theta equals -root3 then what does tan theta equal
Answers
Answer:
The tangent of theta is -1/3.
Explation step-by-Step
The tangent of theta is -1/3. This is calculated as follows:
cot theta = -√3
cot theta = 1/tan theta
-√3 = 1/tan theta
-1/3 = tan theta
A town's population is currently 6,595. If the population doubles every 29 years, what will the population be 145 years from now?
Answers
Answer:
Below
Step-by-step explanation:
145 yr / 29 yr/double = 5 doubles
6595 x 2 ^5 = 211 040 ppl
Derive an exact closed form bound in terms of n on the number of times function F called in each code segment. Use floor/ceilings as needed. Clearly explain your answer and show your work. (a) 1: function COUNT1 (n) 2: for i = 1 to 2n ^ 2 do for 1 to i do 3: k = 1 4: 5: while k <= n do 6: k = k + 8 7: F(i, j) (b) 1: function COUNT2(n) 23 for i = 1 ton do for j = 1 to i do 4: 6: for k = j ton do 5: 2966 F(i, j) F(j, k) 7: F(k, i) (c) The initial call is F(n ^ 2) 1: function F(i) 2: if i < 4 then 3: return 4: while i > 1 do 5: i leftarrow i / 4 6: F(i)
Answers
In order to calculate the exact closed form bound of the number of times function F is called in each code segment, we need to consider the number of times F is called in each line of code.
For COUNT1, line 3 calls F once, line 5 calls F n times, and line 7 calls F once more, for a total of n+2 calls.For COUNT2, line 4 calls F once, line 6 calls F n(n+1)/2 times, and line 7 calls F n(n-1)/2 times, for a total of n*(2n+1)/2 calls.For the initial call of F(n^2), the number of times F is called depends on the value of n. To calculate the exact number of calls for any value of n, we can use a recursive approach, starting from the top line of code and working our way down.
For example, for n=4, the initial call of F(16) will call F(4), which will then call F(1) four times, for a total of 5 calls. For n=8, the initial call of F(64) will call F(16), which will call F(4) four times and F(1) sixteen times, for a total of 20 calls.
Thus, for any value of n, the exact closed form bound of the number of times function F is called is given by the formula [1]:
F(n^2) + 4 * F(n/4) + 16 * F(n/16) + …Where the number of terms in the summation is equal to the number of times n is divided by 4 before it reaches 1.
For example, for n=16, the summation will have four terms (n=16, n=4, n=1), and for n=32, the summation will have five terms (n=32, n=8, n=2, n=1).
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A debate team consists of 5 freshmen and 4 sophomores. (Everyone is distinguishable.) In how many ways can they stand in line, so at least two of the sophomores are standing next to each other, and at least two of the freshmen are at the ends of the line?
Answers
The number of ways that at least two of the freshmen are at the ends of the line and at least two of the sophomores are standing next to each other will be 9.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A debate team consists of 5 freshmen and 4 sophomores. (Everyone is distinguishable.)
⇒ (3 x 3)
⇒ 9
The number of ways that at least two of the freshmen are at the ends of the line and at least two of the sophomores are standing next to each other will be 9.
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The beginning steps for determining the center and radius of a circle using the completing the square method are shown in the table.
Step 1
[original equation]: x2 + 8x + y2 − 6y = 11
Step 2
[group like terms]: (x2 + 8x) + (y2 − 6y) = 11
Step 3
[complete the square]:
Which of the following is the correct equation for Step 3?
Group of answer choices
(x2 + 8x + 4) + (y2 − 6y + 3) = 11 + 4 + 3
(x2 + 8x + 16) + (y2 − 6y + 9) = 11 + 16 + 9
(x2 + 8x + 16) + (y2 − 6y − 9) = 11 + 16 − 9
(x2 + 8x + 4) + (y2 − 6y − 3) = 11 + 4 − 3
Answers
The correct equation for Step 3 for completing the square method are shown in the table is,
⇒ (x² + 8x + 16) + (y² - 6y + 9) = 11 + 16 + 9
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
The beginning steps for determining the center and radius of a circle using the completing the square method are;
Step 1 [original equation]:
⇒ x² + 8x + y² - 6y = 11
Step 2 [group like terms]:
⇒ (x² + 8x) + (y² - 6y) = 11
Now, We ca complete the squares for determining the center and radius of a circle as;
Step 1 [original equation]:
⇒ x² + 8x + y² - 6y = 11
Step 2 [group like terms]:
⇒ (x² + 8x) + (y² - 6y) = 11
Step 3;
⇒ (x² + 8x + 16) + (y² - 6y + 9) = 11 + 16 + 9
Step 4;
⇒ (x + 4)² + (y - 3)² = 36
Thus, The correct equation for Step 3 for completing the square method are shown in the table is,
⇒ (x² + 8x + 16) + (y² - 6y + 9) = 11 + 16 + 9
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Please help me with this question.
Answers
The value of the sin(2θ) is given as follows:
-24/25.
How to obtain the sine of twice the angle?We are given the cosine of the angle, hence the following identity must be considered:
sin²(θ) + cos²(θ) = 1.
Considering the value of the cosine, the value of the sine is obtained as follows:
sin²(θ) + (3/5)² = 1
sin²(θ) = 16/25
sin(θ) = -4/5 -> apply the square root, angle in the fourth quadrant is negative.
Then the sine of twice the angle is obtained as follows:
sin(2θ) = 2sin(θ)cos(θ)
Hence:
sin(2θ) = 2 x (-4/5) x (3/5) = -24/25.
Meaning that the correct option is the third option.
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1. Explain the difference between a discrete variable and a continuous variable. Choose the correct answer below.
2. Give an example of each type. Choose the correct answer below.
1. A discrete variable has possible values that are separate numbers, while a continuous variable has possible values that form an interval.
2. The number of children in a family is a discrete variable, while the time it takes to run a marathon is a continuous variable.
Answers
what is a discrete variable and example?
Discretized variables require a certain amount of time to count. Consider counting the coins in your pocket as an example. Your bank account's funds can be counted. The balances in each person's bank accounts might also be added up. Even if it may take some time to count the last thing, it is still a countable item.
what is a Continuous Variable and example?
Counting continuous variables would literally take an eternity. In actuality, you would reach "forever" and never reach the end of the list. Consider age as an example. Age cannot be measured. why not Considering that it would take an eternity? For instance,
Twenty-five years, ten months, two days, five hours, four seconds, four milliseconds, eight nanoseconds, 99, and so on.
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The full question would be just part 1.
Explain the difference between a discrete variable and a continuous variable.
I have added a screenshot.
Answers
The value for n(A ∩ [tex]B^c[/tex]) is {3}
Option D is the correct answer.
What is a Venn diagram?A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
We have,
Set A = {1, 3}
Set B = {1, 7}
U = {1, 3, 5, 7}
[tex]B^c[/tex] = U - B = {3, 5}
A ∩ [tex]B^c[/tex].
= Numbers that are common to both A and [tex]B^c[/tex].
= {3}
Thus,
n(A ∩ [tex]B^c[/tex]) = {3}
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Which of the following shows a correct method to calculate the surface area of the cylinder?
cylinder with diameter labeled 3.2 feet and height labeled 3.8 feet
SA = 2π(1.6)2 + 3.2π(3.8) square feet
SA = 2π(1.6)2 + 1.6π(3.8) square feet
SA = 2π(3.2)2 + 3.2π(3.8) square feet
SA = 2π(3.2)2 + 1.6π(3.8) square feet
Answers
Answer:
Below
Step-by-step explanation:
The TWO ends are EACH = pi r^2 = pi (1.6)^2
there are two, so 2 * pi * (1.6)^2
the side surface area is the circumference ( pi * d) times the height
= pi * 3.2 * 3.8
Add the two underlined items to find the answer that matches
Answer:
Hey i know im late to answer but the real answer is SA = 2π(1.6)2 + 3.2π(3.8) square feet
Step-by-step explanation:
ive done the flvs quiz and i got a 100 percent!
What’s the answer to 42
Answers
No, Amit's reasoning is not correct. The correct equation is
(-$5.75) *7 = -$40.25.
What is algebraic equation?An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants.
Equations are like a balance scale. If you’ve seen a balance scale, you would know that an equal amount of weight has to be placed on either side for the scale to be considered “balanced”.
Given that, Amit's bank charged $5.75 fee per month for amount below than a certain value.
After 7 month, the total amount changed from his account is
(-$5.75) *7
= -$40.25.
Here '-' sign represent the amount will deducted from his account.
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You might need: Calculator
The expression 1.08s +1.02b predicts the end-of-year value of a financial portfolio where s is
the value of stocks and b is the value of bonds in the portfolio at the beginning of the year.
What is the predicted end-of-year value of a portfolio that begins the year with $200 in stocks
and $100 in bonds?
Show Calculator
Answers
The predicted end-of-year value of the portfolio can be calculated as follows:
What is a mathematical expression?
A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression. This mathematical procedure makes it possible to multiply, divide, add, or subtract quantities. The expression structure is as follows: Expression: Math Operator, Number/Variable, Math Operator
s = $200
b = $100
1.08s = 1.08 * $200 = $216
1.02b = 1.02 * $100 = $102
Therefore, the predicted end-of-year value of the portfolio is $216 + $102 = $318.
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X°=1? How can i solve this math?
Answers
Answer:
x=90°
Step-by-step explanation:
2 Stephanie is being treated / is treating / treats by a
doctor.
3 May I help you, sir? Or are you/you're / are you
being served?
4 Almost every UK family is owning / is owned /
owns a laptop or tablet.
5 The kids give/given / are given £10 pocket money
each week.
6
Professional footballers earn/ are earned / are being
earned a lot of money these days.
I'm really nervous I interview /'m being
Answers
3. May I help you, sir? Or are you being served?
4. Almost every UK family owns a laptop or tablet.
5. The kids are given £10 pocket money each week.
6. Professional footballers earn a lot of money these days.
Answer:
2. Stephanie is being treated by a doctor.
3. May I help you, sir? Or are you being served?
4. Almost every UK family owns a laptop or tablet.
5. The kids are given 10 euros pocket money each week.
6. Professional footballers earn a lot of money these days.
Step-by-step explanation:
Question 3
A set of data include 2000 observations. How many classes would you suggest to construct a frequency
distribution?
Answers
A total of 11 classes should be suggested to construct a frequency distribution.
What is frequency?A value's frequency is the number of times it occurs or takes place. In a frequency table, a list of objects is presented together with the frequency of each item.
The quantity of observations that take place during a specific predetermined timeframe is the frequency of a class interval. Therefore, if 20 individuals between the ages of 5 and 9 are found in the data from our study, the frequency for the 5–9 age range is 20.
The frequencies of each category are represented individually in a frequency graph; the frequencies of each category are shown cumulatively.
By doing so, we are able to analyze the data's distribution in greater detail than we could have done by using a frequency polygon and performing statistics.
If k is the number of classes and n is the number of observations, then for number of classes we should select the smallest k such that
[tex]2^k > n[/tex] ( 2 to k rule)
In our case, the no. of observations is 2000
i.e.
2¹⁰ = 1024 < 2000
With this,
2¹¹ = 2048 > 2000
Thus, A total of 11 classes should be suggested to construct a frequency distribution.
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The production possibilities curve below shows all the combinations a
clothing and cars that can be produced by the country Alpha. Use the
production possibilities curve to answer questions 2A, 2B, and 2C.
Answers
The graph known as the "production possibilities curve" (PPC) depicts all the possible permutations of output that can be created with the available resources and technology.
Explain about the production possibility curve?The maximum output for two items under resource constraints is shown by the production possibilities curve.
The graph known as the Production Possibilities Frontier (PPF) illustrates all the possible output combinations of two items that can be created with the resources and technologies currently in use. The PPF effectively expresses the ideas of choice, tradeoffs, and scarcity.
A production possibilities curve (PPC) depicts the greatest quantity of one commodity that can be produced given the degree of production of another good, the total quantity of inputs available to manufacture both commodities, and the production technique.
Therefore, if the production of the commodities declines, the production possibility curve shifts inward.
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Please help me with this question.
Answers
The area of the given region that is enclosed by a cardiod r = 20+20sinθ, is 600π
What are definite integrals?A definite integral is a formal calculation of area beneath a function, using infinitesimal slivers or stripes of the region.
Given that, we need to find an area for region that is enclosed by a cardiod
r = 20+20sinθ
Using definite integral,
[tex]\frac{1}{2}\cdot \int _0^{2\pi }\left(20+20\sin \left(\theta\right)\right)^2d\theta[/tex]
= [tex]\frac{1}{2}\cdot \int _0^{2\pi }\left(400+400\sin^2 \left(\theta\right)+800sin\theta\right)d\theta[/tex]
= [tex]\frac{1}{2}\cdot \int _0^{2\pi }\left(400+400(\frac{1-cos2\theta}{2})+800sin\theta\right)d\theta[/tex]
= [tex]\frac{1}{2}\cdot \int _0^{2\pi }\left(600+200cos2\theta}+800sin\theta\right)d\theta[/tex]
= [tex]\frac{1}{2}\cdot \:1200\pi[/tex]
= [tex]600\pi[/tex]
Hence, the area of the given region that is enclosed by a cardiod
r = 20+20sinθ, is 600π
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Your sister recently landed her dream job. As part of planning for future expenses, she started to deposit Php 1,000.00 monthly in a fund that pays 6% compounded quarterly. What is the equivalent interest?
Answers
Answer:
Php 496.69.
Step-by-step explanation:
To calculate the interest earned on your sister's deposits, we need to use the formula for compound interest:
A = P (1 + r/n)^(nt)
Where:
A = the future value of the investment (the total amount of money including interest)
P = the principal amount (the initial deposit)
r = the annual interest rate (expressed as a decimal)
n = the number of times the interest is compounded per year
t = the number of years the money is invested
Given that the deposit is Php 1,000.00 monthly and the interest rate is 6% compounded quarterly, we can substitute these values into the formula:
A = 1000 * (1 + 0.06/4)^(4*t)
We don't know the number of years, but we can use the formula to find out the future value of the investment (A) after a certain number of years, and then we can calculate the interest earned by subtracting the initial deposit from the future value.
For example, assuming the investment is for 5 years, the future value of the investment would be:
A = 1000 * (1 + 0.06/4)^(4*5) = 1496.69
The interest earned after 5 years would be:
1496.69 - (1000125) = 496.69
So the equivalent interest earned after 5 years is Php 496.69.
COMPOUND INTEREST
• Compound interest is also the amount earned
for one year calculated by multiplying the
principal by the interest rate. Borrowing,
bonding and saving in financial institution
apply compound interest. compound interest
are usually used for long term transactions.,
Read the details about the meaning of
compound interest in brainly.ph/question/
448076
Read the details about how to solve compound
interest in brainly.ph/question/2398527
Here is the Formula of compound Interest
• A= P(+tj/m^mt
A=maturity value or future value of the loan or
investment ( compound amount)
j= nominal rate or the yearly interest
m= number of conversion period per year
t period or term of the loan or investment
a= 1,000(1+ 0.06/ 4) ^ 4)
a =1,000 (1+ 0.015) ^ 4
a= 1,000 (1.015^4
a= 1000(1.0613)
a= 1061.3
compound interest( lc)
lc = A-p
Ic = 1061.3 -1000
lc = 61.3 is the interest
Victoria scored a total of 9 points
Answers
The expression that represents the total number of points Victoria scored in the basketball games for the whole season is,
5x + 9.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.
Given:
Victoria scored a total of 9 points in the first basketball game of the season.
She scored 5 points per game in each of the other x basketball games she played that season.
That means, 5x is the score.
The expression that represents the total number of points Victoria scored in the basketball games for the whole season is,
5x + 9.
Therefore, the expression is 5x + 9.
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The complete question:
Victoria scored a total of 9 points in the first basketball game of the season. She scored 5 points per game in
each of the other x basketball games she played that season.
Which of the following expressions represents the total number of points Victoria scored in the basketball games for the whole season?
If algebra tiles have the dimensions shown here, what would you call this tile collection?
In other words, what is the total area of all of the pieces?
Ignore the 3rd Question
Answers
The total area of all of the pieces is;
Total Area = 4x + 4y + 3xy + 6x² + y²
What is Area?Area is the amount of space occupied by a 2-dimensional figure. It is the quantity that measures the number of unit squares that cover the surface of a closed figure. The word 'area' means a vacant surface. The area of a shape is calculated with the help of its length and width. Length is unidimensional and measured in units such as feet (ft), yards (yd), inches (in), etc.
From the diagrams, we have the following shapes;
Rectangle (x,1) = 4 x X x 1
Rectangle (y,1) = 4 x y x 1
Rectangle (x,y) = 3 x x x y
Square (x,x) = 6 x X x X
Square (y,y) = 1 x y x y
Total Area = 4x + 4y + 3xy + 6x² + y²
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a high school sells students tickets for $5 as well as general admission tickets for $7 to attend thier football games. The school needs to bring in at least $1500 per game in order to maintain the costs of the football team
Answers
The cost of students ticket is $37.5and the cost of general admission is $187.5.
What is system of equations?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.
Assume s be the students tickets cost and g be the general admission cost.
From the given information,
⇒ s + g = 225 ..(1)
5s + 7g = 1500 ..(2)
From equation (1),
s = 225 - g
Plug the value of s in equation (2)
5(225 - g) + 7g = 1500
1125 - 5g + 7g = 1500
2g = 1500 - 1125
2g = 375
g = 187.5
Plug g = 125 in equation (1),
s + 187.5= 225
s = 225 - 187.5
s = 37.5
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The following number lines are missing some numbers. Sketch each one on your paper and use the information provided to complete the number lines. a. b. c. d.
Answers
The numbers that are missing to complete the number lines are -18,-6,0,12,18 (a), -36,-18,-9, 9, 18, 27, 36(b),-700,-350,350,1050,1400,1750 (c).
What are number lines?In maths and related areas, number lines can be defined as horizontal lines that have numbers placed on them. Moreover, the numbers are placed at equal distances and follow a pattern; for example, 1,2,3,4, etc. or 5,10,15, etc.
How to complete the number lines?Understand the sequence and complete them:
A. The numbers have an interval of 6. Then -18,-12,-6,0,6,18
B. The numbers have an interval of 9. Then: -36,-27,-18,-9,0,8,18,27,36
C. The numbers have an interval of 350. Then: -700, - 350, 0, 350, 700, 1050, 1400, 1750.
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find the perimeter, in feet, of the parallelogram. a parallelogram is 17 feet wide, 27 feet long, and 24 feet high.
Answers
The perimeter of a parallelogram P=102mm.
The perimeter of a parallelogram is defined as the total length of the boundaries, surrounding it. The sum of all the sides of a parallelogram is known as the perimeter of a parallelogram.
The formula for the perimeter of a parallelogram:
P=2(a+b).
There are some properties of a parallelogram:
The pair of opposite sides and angles of a parallelogram are parallel and equal to each other.Diagonals of a parallelogram bisect each otherPairs of adjacent angles are supplementary, the sum of all interior angles is equal to 360 degreesThe given information is slant height is 17, height is 24 and breadth is 27.
substitute the given values in the above formula.
P=2*(24+27)
P=2*(51)
P=102.
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Two friends, Feng and Kylie, took summer jobs. The equation
�
=
18.9
�
y=18.9x represents Kylie's earnings in dollars and cents,
�
y, for working
�
x hours. The graph below represents Feng's earnings in dollars and cents,
�
y, for working
�
x hours.
0
Hours Worked
Earnings (Dollars)
x
y
0
Hours Worked
Earnings (Dollars)
(10,$270)
(20,$540)
Feng's Earnings
Answers
The proportional relationship that represents Feng's earnings is given as follows:
y = 27x.
Hence Feng's rate is of 27 dollars per hour.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
Considering the two graphed points, Feng's rate is calculated as follows:
k = 540/20 = 270/10 = 27 dollars per hour.
Meaning that he/she earns a higher rate than Kylie.
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what is 4+4 tell me pls :)
Answers
Answer:
8
Step-by-step explanation:
It would be best if you put in the calculator. Have a good day.
Recently many airlines have had cancel flight in a single day republic airlines had to cancel 416 flights representing 15.1% of the airlines scheduled flights. How many flights were originally scheduled?
Answers
The number 2755 flights were scheduled.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Recently many airlines have had to cancel flights in a single day.
Republic airlines had to cancel 416 flights representing 15.1% of the airlines' scheduled flights.
The number of flights scheduled,
= 416 x 100/ 15.1
= 41600/15.1
= 2754.96
≈ 2755
Therefore, 2755 flights were scheduled.
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Please help me with the following question.
Answers
The test statistic from a single sample t-distribution is used to obtain the t-statistic increase, which remains constant.
what is sample size ?The sample size represents the number of experiences used to derive estimates for a certain population. A sample size from the population was selected. The number of participants or experiences that make up a study is referred to as the "sample size." This number is frequently represented by the symbol n. Two statistical traits are influenced by the sample size: 1) The accuracy of our estimations; 2) The power of research to draw conclusions. The samples represent the findings of random tests. A specific value is selected from a set of possible values when picking a random variable. This particular value is a sample. The potential values and their probabilities are determined by the unpredictable variable's probability density function.
given
Using the test statistic of a single sample t-distribution, the t-statistic is derived.
To ascertain whether the test statistic would change when the sample size was increased, use the concept of the "test statistic."
When the standard deviation is unknown, a hypothesis test is done on the population mean based on the data. When the statistic is large, the t-statistic has a positive value and rejects the null hypothesis.
Increase in sample size is what is stated. Because the sample size (n) is inversely proportional to the t-statistic, the t-statistic would rise.
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Subtract: (9x^3-4x^2+2x) - (2x^+6x^2-3x)
Answers
Answer:
7x^3 + 2x^2 - x
Step-by-step explanation:
To subtract the two expressions (9x^3-4x^2+2x) and (2x^+6x^2-3x), we will need to line up the terms with the same exponent and subtract them.
(9x^3-4x^2+2x) - (2x^+6x^2-3x)
= (9x^3 - 2x^3) + (-4x^2 + 6x^2) + (2x - 3x)
= 7x^3 + 2x^2 - x
So the result of the subtraction is 7x^3 + 2x^2 - x
Please note that if you want to simplify the result further, you can combine like terms.
The equation P=28+2.54w models the relation between the amount of Randy’s monthly water bill payment, P, in dollars, and the number of units of water, w, used. Interpret the P-intercept of the equation.
Provide your answer below:
The P-intercept, 2.54, means that Randy's monthly water bill payment would be 2 point 5 42.54 dollars if he used 2828 units of water.
Answers
Answer:
Step-by-step explanation: The P-intercept of the equation P = 28 + 2.54w is 28. This means that when the number of units of water used is 0 (w = 0), the amount of Randy's monthly water bill payment is 28 dollars. This is the minimum payment that Randy must make for the water usage, regardless of the actual usage.
Bally Manufacturing sent Intel Corporation an invoice for machinery with a $14,000 list price. Bally dated the invoice July 23 with 2/10 EOM terms. Intel receives a 40% trade discount. Intel pays the invoice on August 5. What does Intel pay Bally?
Answers
The amount of money Intel pay Bally is given by the equation A = $ 8,232
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 amount be represented as A
Now , the equation will be
The total invoice amount = $ 14,000
The trade discount given by Intel = 40 %
So , the amount of discount = trade discount x total invoice amount
Substituting the values in the equation , we get
The amount of discount = ( 40/100 ) x 14000
The amount of discount = 0.4 x 14000
The amount of discount = $ 5600
So , the amount after 40 % discount = total invoice amount - amount of discount
Substituting the values in the equation , we get
The amount after 40 % discount = 14,000 - 5,600
The amount after 40 % discount = $ 8,400
And , 2/10 means 2%discount if the amount received within 10 days
So , the amount after 2 % discount = amount after 40 % discount - ( 2/100 ) x amount after 40 % discount
Substituting the values in the equation , we get
The amount after 2 % discount A = 8400 - 0.02 x 8400
The amount after 2 % discount A = $ 8400 - $ 168
The amount after 2 % discount A = $ 8,232
Hence , the amount is $ 8,232
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A storm system is in the Central Texas area and moving in a straight line through Austin. The Weather Service Office forecasts that t hours after 12 noon the storm will be a distance of s(t) = 5 + 14t – 3t2 miles from Austin. How fast will the storm be moving at 4:00 pm and in what direction will it be moving? storm moving 1. storm speed = 12 mph, away from Austin. storm moving 2. storm speed = 10 mph, toward Austin. 3. storm speed = -12 mph, storm moving toward Austin. storm moving 4. storm speed = 12 mph, toward Austin. storm moving 5. storm speed = 10 mph, away from Austin. 6. storm speed = –10 mph, storm moving toward Austin.
Answers
Storm moving toward austin at speed of -10 mph.
To find the speed of the storm at 4:00 PM, we need to find the rate of change of the distance of the storm from Austin at that time. To do this, we can use the derivative of the function s(t) = 5 + 14t - 3t^2, which represents the distance of the storm from Austin.
s'(t) = 14 - 6t
At t = 4 hours, or 4:00 PM, the speed of the storm is given by:
s'(4) = 14 - 6 * 4
s'(4) = 14 - 24
s'(4) = -10 mph
So, the storm will be moving at 10 mph towards Austin at 4:00 PM.
Therefore, the answer is: 6. storm speed = -10 mph, storm moving toward Austin.
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