Answer:c
Step-by-step explanation:
When an accountant records on hand, they are noting a company’s
A. human resources; total liquid assets
B. cash; total of amount dollars, money orders, checks, and other forms of
money
W
C. supplies; materials that need to be purchased soon
D. inventory; number of employees on payroll
Answer:
The correct answer is D. inventory; number of employees on payroll. An accountant records on hand to note a company's inventory, which is the stock of goods available for sale or use in the production process. The number of employees on payroll refers to the human resources aspect of a company, which is separate from the inventory.
6. Linden shared 237 litres of milk in 3 smaller litre containers. How many 3 litre containers would he get from his supply of milk?
Using division operation, the number of containers that Linden would get from his supply of milk is 79 containers.
What is division operation?Division operation involves the dividend divided by the divisor to obtain a result called the quotient.
Division operation is one of the four basic mathematical operations, including multiplication, addition, and subtraction.
Total liters of milk = 237
The content of the liter containers = 3 liters
The number of containers = 79 (237 ÷ 3)
Thus, based on division operation, Linden, who is sharing 237 liters of milk in containers will need 79 3-liter containers.
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identify all the linear functions with a rate of change greater than or equal to 1.5
A certain species of bacteria in a laboratory culture begins with 50 cells and doubles in number every 30 minutes. Write a function
fix) to model the situation where x is the number of 30-minute time periods.
since we know the number is doubling, so if say it was "x" right now so 30 minutes later will be "x" + 100 of "x", namely 2x, so that simply means the rate of growth is 100%.
[tex]\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1.00\\ t=minutes\\ c=period \dotfill &30 \end{cases} \\\\\\ A=P(1 + 1.00)^{\frac{t}{30}}\implies A=P(2)^{\frac{t}{30}}\hspace{5em}f(x)=P(2)^{\frac{x}{30}}[/tex]
If the number x² y is a negative integer, then -y is a positive number
Answer: Yes, this statement is true. If the number x² y is a negative integer, it means that x² is a positive integer and y is a negative integer. Therefore, -y would be a positive number.
Step-by-step explanation:
Question 1 of 10
How many zeros does the polynomial function, y = (x-2)(x+3)² have?
OA. 1
OB. 3
OC. 2
OD. 4
SUBMIT
Answer:
C. 2
Step-by-step explanation:
A polynomial function has one or more real numbers as roots or zeros. These roots correspond to the values of x for which the function takes on the value of zero.
In this case, y = (x-2)(x+3)², we can factor the equation to find its zeros. The expression (x-2)(x+3)² can be factored into two terms: (x-2) and (x+3)².
The first term, (x-2), is equal to zero when x = 2, meaning that x = 2 is a root of the function.
The second term, (x+3)², is equal to zero when x = -3, meaning that x = -3 is another root of the function.
So, the function y = (x-2)(x+3)² has two roots, or zeros, at x = 2 and x = -3.
Marianna finds an annuity that pays 8% annual interest, compounded quarterly. She invests in this annuity and contributes $10,000 each quarter for 6 years. How much money will be in her annuity after 6 years? Enter your answer rounded to the nearest hundred dollars.
Answer:
Marianna will have $19,700 in her annuity after 6 years.
Step-by-step explanation:
To find the amount of money in the annuity after 6 years, we need to calculate the compound interest earned over that time period.
First, let's find the interest rate per quarter: 8% annual interest divided by 4 quarters per year = 2% interest per quarter.
Next, we'll calculate the number of quarters that the money is invested: 6 years x 4 quarters per year = 24 quarters.
Now we can use the formula for compound interest to find the total amount of money in the annuity after 6 years:
A = P * (1 + r/n)^(nt)
Where:
A = final amount
P = initial investment ($10,000 in this case)
r = interest rate per quarter (2% or 0.02)
n = number of times the interest is compounded in a year (4)
t = number of years invested (6)
Plugging in the values:
A = $10,000 * (1 + 0.02)^(24)
A = $10,000 * 1.96634438
A = $19,663.44
Rounding to the nearest hundred dollars: $19,700
So, Marianna will have $19,700 in her annuity after 6 years.
Linear Functions Question! Please Help Asap!
The value the function given by (A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18} and (A ∩ B) = {7}.
What is union of sets?We carry out specific operations in mathematics, such as addition, subtraction, multiplication, etc. Generally speaking, these operators accept two or more operands and output a result dependent on the operation carried out. Similar to this, in set theory, several operations are typically done on two or more sets to obtain a new set of elements depending on the operation. The number of elements supplied by the operation and processing the result of a collective set is represented by the union and overlap of sets. All of the components are taken into account in the outcome when there is a union, but only the ones that are shared when there is an intersection.
The union of the two sets depict all the terms present in both the sets.
Thus, the value of (A ∪ B) is:
(A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18}
The intersection of the sets depict all the common terms present in the two sets thus the value of (A ∩ B) is:
(A ∩ B) = {7}
Hence, the value the function given by (A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18} and (A ∩ B) = {7}.
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-ax^(2)+2x+2a if a=7 and x=-5
Answer: -151
Step-by-step explanation:
First Plug everything in
-7(5)^(2)+2(5)+2(7)
Then use order of operations and first deal with the exponent
-7(25)+2(5)+2(7)
then multiply left to right
-175+10+14
combine
so the answer is -151
G(x)=-4x^2+36/x+3
What key features does f(x), shown in the graph, share
with g(x), shown in the equation? Select three options.
at least one x-intercept
at least one y-intercept
Dan oblique asymptote
O a vertical asymptote
the domain of x
The function g ( x ) in the graph has one x-intercept , y intercept and an oblique asymptote , a vertical asymptote
What are Asymptotes?An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required
There are 3 types of asymptotes
Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero
Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero
Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b
Given data ,
Let the function be represented as g ( x )
Now , the value of g ( x ) is
g ( x ) = ( -4x² + 36 ) / ( x + 3 )
On simplifying , we get
g ( x ) = -4 ( x² - 9 ) / ( x + 3 )
On further simplification , we get
g ( x ) = -4 ( x + 3 ) ( x - 3 ) / ( x + 3 )
g ( x ) = -4 ( x - 3 )
g ( x ) = -4x + 12
Now , the function has a vertical asymptote at ( 0 , 12 )
The function has a horizontal asymptote at ( 3 , 0 )
Hence , the function is solved
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Answer:
at least one x-intercept
at least one y-intercept
domain of x
Step-by-step explanation:
took ed2023
What is the value of x? enter your answer, as a decimal, in the box. Do not round your answer. X= a right triangle with vertices labeled as a, b, and c. Side c b is the base and the top vertex is a. Side a b contains a midpoint d. A line segment drawn from c to d bisects angle a c b into two parts labeled as a c d and b c d. Angles a c d and b c d are marked with single arc. Side a c is labeled as 4. Base c b is labeled as 7. 5. Segment a d is labeled as 3. Segment b d is labeled as x.
In right triangle ACB with CD bisects angle ACB and intersects at midpoint of AB at point D the value of x is equal to 5.625.
In right triangle ABC,
BC is the base.
Midpoint of AB is D.
CD bisects ACB.
Measure of ∠ACD = Measure of ∠BCD
AC = 4
BC = 7.5
AD = 3
BD = x
CD bisects angle ACB and intersect at midpoint of AB at point D.
This implies
BD / AD = BC / AC
⇒x / 3 = 7.5 / 4
⇒ x = ( 7.5 × 3 ) / 4
⇒ x = 22.5 / 4
⇒ x = 5.625
Therefore, the value of x in the right triangle ACB with given dimensions is equal to 5.625.
The above question is incomplete , the complete question is :
What is the value of x? Enter your answer, as a decimal, in the box. x= A right triangle with vertices labeled as A, B, and C. Side C B is the base and the top vertex is A. Side A B contains a midpoint D. A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D. Angles A C D and B C D are marked with single arc. Side A C is labeled as 4. Base C B is labeled as 7.5. Segment A D is labeled as 3. Segment B D is labeled as x.
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Question 5b
A trailer truck carries 11, 430 bottles, each weighing 14 ounces. To the nearest ton,
how much weight does the truck carry?
The truck carries
tons.
The total weight of the bottles the truck carries is 6020 ounces.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
Example:
2 + 1x + 4y = 7 is an expression.
3 + 3x + 3 = 7 is an expression.
We have,
Number of bottles the truck carries = 430
One bottle weight = 14 ounces
Now,
The total weight of the bottles.
= Number of bottles x Weight of one bottle
= 430 x 14
= 6020 ounces
Thus,
The total weight of the bottles the truck carries is 6020 ounces.
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Here is a triangle.
4x + 20
x +32
4x + 20
Does the triangle contain an obtuse angle?.
Explain your reasoning.
Please help me urgent need
Answer:
No
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
x + 32 + 4x + 20 + 4x + 20 = 180
9x + 72 = 180 ( subtract 72 from both sides )
9x = 108 ( divide both sides by 9 )
x = 12
then the 3 angles are
x + 32 = 12 + 32 = 44°
4x + 20 = 4(12) + 20 = 48 + 20 = 68°
4x + 20 = 68°
an obtuse angle is greater than 90°
none of the 3 angles in the triangle are obtuse
Answer:
No
Step-by-step explanation:
All angles of a triangle add up to 180°.
4x + 20 + 4x + 20 + x + 32 = 180
1. Simplify
9x + 72 = 180
2. Subtract 72 from both sides.
9x = 108
3. Divide both sides by 9.
x = 12
Replace x by 12 in each angle.
- 12 + 32 = 44°
- 4(12) + 20 = 68°
- 4(12) + 20 = 68°
All of the angles are less than 90°, so they aren't obtuse.
The temperatures, in °C , at midnight on 10 consecutive days were 4, 1, 0, –2, –1, –3, 1, –2, 3, –1. (a) Find the difference between the highest and the lowest temperature
Answer:
7 degrees C
Step-by-step explanation:
To solve this question, we can start by ordering the temperatures from least to greatest:
4, 1, 0, -2, -1, -3, 1, -2, 3, -1 --> -3, -2, -2, -1, -1, 0, 1, 1, 3, 4
the lowest temperature would be -3 in this list, and the highest temperature in this list would be 4. We can find the difference in temperature using subtraction:
4-(-3) = 4+3=7
The difference is 7 degrees C.
23 inches of wire cost 92 cents at the same rate, how much (in cents) will 34 inches of wire cost?
Answer:
Step-by-step explanation:
Let's use the formula rate = cost/length to find the cost of one inch of wire. We know that 23 inches of wire cost 92 cents, so the rate of one inch of wire can be found by dividing 92 cents by 23 inches:
rate = cost/length = 92 cents/23 inches = 4 cents/inch
Now that we have found the rate of one inch of wire, we can use it to find the cost of 34 inches of wire. We simply multiply the rate by the length:
cost = rate * length = 4 cents/inch * 34 inches = 136 cents
So, 34 inches of wire will cost 136 cents.
Step-by-step explanation:
the trick is to find the "norm" rate, which is the rate for one unit.
from there we can get the rate for any number of units just by multiplying.
so,
23 in for 92 cents.
that means the rate is
23/92 = 23/(23×4) = 1/4
so, by dividing numerator and denominator by 23 (in this case it has an integer result also for the denominator) we get the price for 1 inch of wire : 4 cents.
so, 34 inches then have the length/price ratio (we multiply numerator and denominator by 34)
1/4 × 34/34 = 34/136
that means 34 inches cost 136 cents (= $1.36).
DUE TODAY PLS I JUST NEED HELP
Answer:
(a)
smaller value = 125 ft
larger value = 250 ft
(b)
31250 ft²
Step-by-step explanation:
(a)
In total, the farmer used 875ft worth of fencing.
In terms of x, the total fencing used is: 2x + x + x + x + 2x = 7x
This means 7x=875ft. Dividing both sides by 7, we find x=125ft
The dimensions of the rectangular enclosure in terms of x are "x and 2x". Subbing in 125ft for x, these dimensions become "125ft and 2(125ft)" or "125ft and 250ft".
(b)
Since we know the enclosure is 125ft long and 250ft wide, and since the area of a rectangle is its length times its width, the are of the enclosure is:
125ft * 250ft = 31250 ft²
Answer:
(a)
smaller value =125 ft
larger value = 250 ft
(b)
31250 ft?
Demonstrating the properties of rotations, if a line segment with endpoints (0,−3) and (0,−7) is rotated 90° clockwise, what is an endpoint of this rotated segment?
Answer: -3, 0
Step-by-step explanation:
If a line segment with endpoints (0,−3) and (0,−7) is rotated 90° clockwise, an endpoint of this rotated segment is (-3, 0) and (-7, 0).
What is a rotation?In Mathematics and Geometry, a rotation is a type of transformation that moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
By applying either a rotation of 90° clockwise or a rotation of 270° counterclockwise to the coordinate of this line segment with endpoints (0,−3) and (0,−7), the coordinate of its image;
(x, y) → (y, -x)
Point (0,−3) → Point (-3, 0)
Point (0, -7) → Point (-7, 0)
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Answers for this photo?
The slope for:
1 = 1/2 (Option E)
2 = 2 (Option C)
3 = -1/2 (Option H)
4 = -2 (Option A)
What is slope in Maths?The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.
The formula for slope (m) is given as:
m = Rise/Run = y2-y1/x2-x1
(x1,y1) = Coordinates of the first point in the line
(x2,y2) = Coordinates of the second point in the line.
1) The points are:
x1= -2
y1 = 2
x2 =2
y2 = 4
m = (4 - 2) / (2 - (-2))
m = 2 / 4
m = 1/2
Thus, Δy/Δx = 1/2
2) The points are:
x1= -1
y1 = -12
x2 =5
yx = 0
m = (y2 - y1) / (x2 - x1)
Substituting the given values, we get:
m = (0 - (-12)) / (5 - (-1))
m = 12 / 6
m = 2
Thus, Δy/Δx = 2
3) Where the points are:
x1= 2
y1 = -6
x2 = - 4
y2 = -3
Substituting the given values, we get:
m = (-3 - (-6)) / (-4 - 2)
m = 3 / (-6)
m = -1/2
Thus, Δy/Δx = -1/2
4) Where the points are:
x1= 0
y1 = 3
x2 = 1.5
y2 = 0
Substituting the given values, we get:
m = (0 - 3) / (1.5 - 0)
m = -3 / 1.5
m = -2
Thus, Δy/Δx = -2
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What would you need to invest to produce $23711 if your interest rate is 3.6% compounded monthly for 15 years? Round your answer to the nearest dollar.
Answer:
$10576.38
Step-by-step explanation:
To calculate the investment amount required to produce $23711 at an interest rate of 3.6% compounded monthly for 15 years, you can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A is the amount of money you have after "t" years,
P is the initial investment amount (what you want to find),
r is the interest rate as a decimal,
n is the number of times the interest is compounded per year,
t is the number of years the investment will be compounded for.
In this case,
r = 0.036
n = 12 (because the interest is compounded monthly)
t = 15
So, we can plug in the values into the formula and solve for P:
A = P * (1 + 0.036/12)^(12 * 15)
$23711 = P * (1.003)^(180)
$23711 = P * 2.2375
Dividing both sides by 2.2375:
P = $23711 / 2.2375
P = $10576.38
So, to produce $23711 at an interest rate of 3.6% compounded monthly for 15 years, you would need to invest $10576.38. Rounded to the nearest dollar, this amount is $10576.
graph the inequality p < -8.
Answer:
I have graphed it and attached an image in the explanation part.
Step-by-step explanation:
Given the following observation for ortime serie X
t=1,2,3,4,5,6,7,8,9,10
Xt=47,64,23,71,38,64,55,41,59,48
Find
r(2)
Answer:t he autocorrelation of the time series X at lag 2 is approximately -0.018.
Step-by-step explanation:
To find the autocorrelation of the time series X at lag 2, we need to calculate the covariance between X(t) and X(t-2). This can be done using the following formula:
r(2) = cov(X(t), X(t-2)) / var(X(t))
where cov(X(t), X(t-2)) is the covariance between X(t) and X(t-2), and var(X(t)) is the variance of X(t).
To calculate the covariance, we'll use the following formula:
cov(X(t), X(t-2)) = sum((X(t) - mean(X(t))) * (X(t-2) - mean(X(t-2)))) / (n - 1)
where n is the number of observations in the time series. To calculate the variance, we'll use the following formula:
var(X(t)) = sum((X(t) - mean(X(t)))^2) / (n - 1)
First, let's calculate the mean of X(t):
mean(X(t)) = (47 + 64 + 23 + 71 + 38 + 64 + 55 + 41 + 59 + 48) / 10 = 51
Next, let's calculate the covariance between X(t) and X(t-2):
cov(X(t), X(t-2)) = sum((X(t) - 51) * (X(t-2) - 49)) / (10 - 1) = -10.3
Finally, let's calculate the variance of X(t):
var(X(t)) = sum((X(t) - 51)^2) / (10 - 1) = 563.7
Plugging in these values, we can find the autocorrelation at lag 2:
r(2) = cov(X(t), X(t-2)) / var(X(t)) = -10.3 / 563.7 = -0.018
So the autocorrelation of the time series X at lag 2 is approximately -0.018.
Of the 125 persons applying for a certain job at data processing center,79 had previous work experience and 62 had college degree, while 38 has both work experience and college degree.
i)How many applicants did not have college degree
ii)how many applicants did not have experience
iii) how many applicants had college degree but no experience
iv)how many applicants had either college degree or experience but not both
1. the number ( of people without college degree ) = 125 - (24 +38)= 63
2. number of people without experience ) = 125- ( 41+38) = 46
3. number ( of applicants with college degree but no experience) = 24
4. n( of applicants with either college degree or experience) = 24+41 + 38 = 103
What is set?A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
number of people that have previous work experience only) = 79-38 = 41
number ( of persons that have college degree only) = 62- 38 = 24
1. the n( of people without college degree ) = 125 - (24 +38)= 63
2. n( of people without experience ) = 125- ( 41+38) = 46
3. n( of applicants with college degree but no experience) = 24
4. n( of applicants with either college degree or experience) = 24+41 + 38 = 103
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the table shows the rate at which justin can make widgets. how many widgets can justin make in 36 minutes?
The number of widgets that Justin can make in 36 minutes is given as follows:
y = 36k.
In which the constant k is the number of widgets that can be made per minute, and is obtained dividing a value of y by it's respective value of x from the table.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
The variables for this problem are given as follows:
Input x: number of minutes.Output y: number of widgets.The constant is obtained as follows:
k = y/x.
For a time of 36 minutes, we have that x = 36, hence the number of widgets is given as follows:
y = 36k.
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Suppose you deposit $1,000 into a
savings account that earns simple
interest. After 4 years, the savings
account balance is $1,200. Determine
the annual interest rate.
100
1000
The annual interest rate on the saving account is 5%.
What does an annual interest rate refers to?Also known as annual percentage rate (APR) is the interest generated by a sum charged to borrowers or paid to investors each year. Its represents the actual yearly cost of funds over the life of a loan or the income earned on an investment.
To determine our annual interest rate, we can use the formula for simple interest: I = Prt. We need to find "r" which is our interest rate.
Now, we know the interest earned (I = $200) and the principal (P = $1,000), we can substitute those values into the formula:
$200 = $1,000 * r * 4
r = $200 / ($1,000 * 4)
r = 0.05. Therefore, the annual interest rate is 0.05 or 5%.
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EDAT: COMBINATION
An engineering faculty is going to form a committee for accreditation. The faculty is currently made up of 20 engineers. Exactly seven (7) engineers are needed to form the committee. In how many ways can they form the committee if:
1. Engr. Marzo and Engr. William refuses to work in the committee together. (10 pts)
2. Engr. Cara wants to be part of the committee with Engr. Danny but Engr. Danny will refuse to be part of the committee if Engr. Hillary is part of the committee. (10pts)
3. Engineers Gillian, Fernando and Ophelia will work in the committee if all three of them is part of the committee. (10 pts)
The number of combinations of different engineers is found to form a 7 member committee according to the given conditions.
What is meant by combination?
Combinations are ways to choose things from a collection where the order of the choices is irrelevant. It is described as an arrangement of items where the order in which they are chosen is irrelevant.
Given,
Number of engineers in the faculty = 20
Number of engineers required to form a committee = 20
1) Number of ways when either engr. Marzo or engr. William is only present.
Excluding Marzo and William, we have 18 engineers.
So we can select 6 engineers from these 18 = 18C6 = [tex]\frac{18!}{6!12!}[/tex] = 18564
Number of ways we can select only one from Marzo and William = 2C1 = 2
So the total number of combinations for forming a committee = 18564 + 2 = 18566
2) Engr. Cara and Eng. Danny are present.
Engr. Hillary is not considered.
So we have to select 5 members from the rest of the 15 people
Number of combinations are = 15C5 = 3003
3) Engineers Gilliam, Fernando and Ophelia are selected.
Now we have to select the rest of the 4 members from the remaining 15 people
Number of combinations = 15C4 = 1365
Therefore the number of combinations of different engineers are found to form a 7 member committee.
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please help me with intersections i’ll give you brainlist
Answer:
(-3,-1)
Step-by-step explanation:
The two lines intersect at that point. -3 is in the x axis and -1 is in the y axis.
A company is making T shirts. They know that the probability of a shirt being defective is (.02).
The company makes a profit of $20 for every shirt they sell. However, each defective shirt costs
the company $35 in replacement costs. How much money does the company really make per
Shirt?
The amount of money the company makes per shirt $18.90
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The chances that event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes
= X/n
To calculate the expected profit per shirt, we need to consider the two possible outcomes:
the shirt is defective or not defective.
If the shirt is not defective, the company makes a profit of $20.
If the shirt is defective, the company incurs a cost of $35 and no profit.
The probability of a shirt being defective is 0.02, so the probability of a shirt not being defective is:
= 1 - 0.02
= 0.98.
Therefore, the expected profit per shirt can be calculated as:
Expected profit = (probability of not defective) x (profit per non-defective shirt)
+ (probability of defective) x (cost per defective shirt)
Expected profit = 0.98 x $20 + 0.02 x (-$35)
Expected profit = $19.60 - $0.70
Expected profit = $18.90
So the company really makes $18.90 per shirt, taking into account the cost of defective shirts.
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Triangle adb, point c lies on segment ab and forms segment cd, angle acd measures 90 degrees. Point a is labeled jungle gym and point b is labeled monkey bars. Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If beth places the swings at point d, how could she prove that point d is equidistant from the jungle gym and monkey bars?.
To prove that point d is equidistant from the jungle gym and monkey bars, we need to show that the distances from d to both points are equal.
Let's call the distance from d to the jungle gym "x" and the distance from d to the monkey bars "y". We need to show that x = y.
Since angle acd is a right angle, we can use the Pythagorean theorem to relate the distances:
ad^2 + cd^2 = ac^2
We know that ad = bd (since the jungle gym and monkey bars are the same distance from d), so we can write:
bd^2 + cd^2 = ac^2
We also know that c lies on ab, so we can write:
ac = ab - bc
Substituting this into our equation, we get:
bd^2 + cd^2 = ab^2 - 2abbc + bc^2
Since d is on cd, we can write cd = y, and since c is on ab, we can write ab = x + y. Substituting these into our equation, we get:
bd^2 + y^2 = (x + y)^2 - 2xy + x^2
Simplifying, we get:
bd^2 - x^2 = 2xy - y^2
Now, if we can show that bd = x, then we will have proven that y = x and therefore that point d is equidistant from the jungle gym and monkey bars.
To do this, we can use the fact that triangle adb is isosceles (since ad = bd). This means that angle adb is equal to angle bad. We also know that angle acd is a right angle. Therefore, angle adb + angle acd = 90 degrees.
Since angle adb = angle bad, we can write:
2 angle adb + angle acd = 180 degrees
Substituting in the values of our angles, we get:
2 angle adb + 90 degrees = 180 degrees
Solving for angle adb, we get:
angle adb = 45 degrees
Now, we can use the fact that triangle adb is isosceles to write:
angle bad = (180 - 45)/2 = 67.5 degrees
Finally, we can use the law of sines to relate bd and x:
bd/sin(67.5) = x/sin(45)
Simplifying, we get:
bd = x
Therefore, we have shown that point d is equidistant from the jungle gym and monkey bars.
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Answer:
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The table shows the total numbers of visitors to a website t days after it is online.
a. Determine wether the table represents an exponential growth function, an exponential decay function, or neither.
b. How many people will have visited the website after it is online 47 days? Round to the nearest whole number.
a) The table represents an exponential growth function.
b) The number of people that will have visited the website after 47 days online is given as follows: 17,716 people.
How to model the exponential function?An exponential function is modeled as follows:
y = a(b)^x.
In which:
a is the initial value.b is the rate of change.The parameters for this problem are given as follows:
a = 11000.b = 12100/11000 = 1.1. > 1 -> exponential growth.Considering that the reference day is the day 42, the function is defined as follows:
y = 11000(1.1)^(x - 42).
Hence, after day 47, the number of visitors is given as follows:
y = 11000 x (1.1)^5.
y = 17,716.
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