The answer is t ≤ 11.
Subtract 10 from each side.21 - 10 ≥ t + 10 - 10t ≤ 119. Raju sells a watch at 5% profit. Had he sold it for 24 more he would have gained 11%. Find the cost price of the watch.
Answer:
400$
Step-by-step explanation:
Let C.P. of the watch = Rs. 100
When profit =5%; S.P. = Rs. (100+5)
= Rs. 105
and when profit = 11%;
S.P. = Rs. (100+11)
=Rs.111
Difference of two selling prices
= Rs. 111-Rs.105 = Rs.6
When watch sold for Rs. 6 more; then C.P. of the watch = Rs.
100
6
When watch sold for Rs. 24 more; then C.P. of the watch = Rs.
100
6
×
24
= Rs.
100
×
24
6
=400
Solve the system of equations below using a matrix equation.
2x + y = - 7
x − y = 4
Select one:
a.
( 1, 5 )
b.
( - 1, - 5 )
c.
( - 1, -2 )
d.
( 0, - 7 )
Answer: B. (-1, -5)
Step-by-step explanation:
Given equations
2x + y = -7
x - y = 4
Concept
[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]
[tex]A*A^{-1}=A^{-1}*A=I~(Which~is~basically~1)[/tex]
Convert into matrix
[tex]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]
Calculate the inverse of the matrix
[tex]A=\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right][/tex]
[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]
[tex]A^{-1}=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right][/tex]
Solve by multiplying the inverse of the matrix
[tex]A*A^{-1}=A^{-1}*A=I[/tex]
[tex]-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]
[tex]1*\left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3}\left[\begin{array}{ccc}3\\15\\\end{array}\right][/tex]
Simplify by multiplication
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-1\\-5\\\end{array}\right][/tex]
Therefore, the answer is [tex]\Large\boxed{(-1,~-5)}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The test scores of 15 students are listed below. Find the third decile, D3.
41, 45, 51, 57,59, 62,66,69, 75,78, 85,87,90,94,95
The third decile is 58.
What is the third decile?Decile is a statistical term that divides the data into groups of ten. The third decile is the third group of the data set.
Third decile = 3/10 x (n + 1 )
3/10 x 16 = 4.8th term = 58
Combine like terms to create an equivalent expression.
Enter any coefficients as simplified proper or improper fractions or integers.
-2/3p+ 1/5 -1+ 5/6p
Answer:
1/6 p - 4/5 or -4/5 + 1/6p They both mean the same thing.
Step-by-step explanation:
You have two sets of like terms. You have 2 terms that have the variable p as part of the term and you have 2 terms with no variable that are called constants.
-2/3p + 5/6p Are two terms that you want to combine. We need common denominators to add. The common denominator would be 6, so we will make an equivalent fraction with -2/3 with 6 as the denominator.
-2/3 = -4/6 We just multiple the top (numerator) and the bottom (denominator of the first fraction (-2/3) by 2 to the get the second faction (-4/6). Now we can add the 2 terms with p together.
-4/6p + 5/6p The denominators stays the same (6) and we add the numerators -4 + 5 = 1, So our p term is 1/6p
Now we have to combine the constant terms of 1/5 and - 1. Another name for -1 is 5/5. We are going to use this form so that our denominators are the same.
1/5 - 5/5 = -4/5
A company's sales increased 20% this year, to $6740. What were their sales last year?
The sales last year of the company is 5617
How to determine the sales last year?The given parameters are:
Company sales = 6740
Percentage increase = 20%
The sales of the company last year (x) to date is calculated as:
Company sales = (1 + Proportion) * Last year sales
Substitute the known values in the above equation
6740 = (1 + 20%) * x
Evaluate the sum
6740 = 1.2 * x
Divide both sides by 1.2
x = 5617
Hence, the sales last year is 5617
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Agri-Small Business limited expenses on petrol for their fleet is R 4 850.00 at the end of September and they have a balance of R106 360.00 remaining in their account. The company has used 25% of its September income on salaries, 11% on electricity, rates and taxes, and 42% of the remaining on insurance and investments. The total income and expenditure in September are
a. Income is R 299 596.00 and expenditure is R 193 236.00.
b. Income is R 193 236.00 and expenditure is R 4 850.00.
c. Income is R 106 360.00 and expenditure is R 4 850.00.
d. Income is R 106 360.00 and expenditure is R 299 596.00
The total income and expenditure in September are "Income is R 106 360.00 and expenditure is R 4 850.00." Option C. This is further explained below.
What are the total income and expenditure in September?Generally, the equation for Insurance and investment is mathematically given as
II= 42% of the balance
II = 0.42*0.64A
II= 0.2688A
Generally, the equation for Total After All other exp is mathematically given as
Texp = 0.64A – 0.2688A
Texp= 0.3712A
Total After All other exp = 111210
subbing ahead and equating we have
111210 = 0.3712 A
Therefore
A = 299596
The total income is 299596
Therefore, the calculation for the expense is given as
Expense = 0.25A + 0.11A + 0.2688A + 4850
Expense= 0.6288A + 4850 = (0.6288*299596) + 4850
Expense= 193236
The Expense is 299596
In conclusion, At the end of September, Agri-Small Business's minimal spending on gasoline for their fleet amounted to R 4 850.00, and they still had a balance of R106 360.00 in their account. The majority of the remaining revenue was allocated to insurance and investments by the business, which accounted for 42% of the total. Wages and salaries accounted for 25% of the company's income in September. The overall revenue and expenses for the month of September were as follows: the income was R 106 360.00, and the expenses were R 4 850.00. Option C.
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Combined, Tanya and Sanjay have 40 pens. If Tanya has four times as many pens as Sanjay, how many pens does Sanjay have?
Answer:Sanjay has 8
Step-by-step explanation: Because 8x4 equals 32 so thats how much tanya has a 32+8 equals 40. This is what I did I knew 10x4 is 40 so that couldn't be it so then I tried 8 because nine x four is 36 which would be to high so I tried 8 and it was perfect hope this helps.
If Combined, Tanya and Sanjay have 40 pens. If Tanya has four times as many pens as Sanjay, then Sanjay have 8 pens.
What is Equation?Two or more expressions with an equal signs is called as Equation.
Given that Tanya and Sanjay have 40 pens. If Tanya has four times as many pens as Sanjay, We need to find how many pens sanjay has.
Let sanjay has x number of pens.
Tanya has four times as many pens as Sanjay
So 4 times means four multiple of sanjay pens.
Tanya has four times as many pens as Sanjay can be write as 4x.
Combined of tanya and sanjay has 40 pens.
Combined means adding.
x+4x=40
Add the like terms
5x=40
Divide both sides by 5.
x=8
So Sanjay has eight pens and Tanya has 4(8)=32 pens.
Hence Sanjay have eight pens.
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Review the graph of function j(x).
On a coordinate plane, a line starts at open circle (2, 6) and goes down through (negative 2, 2). A solid circle is at (3, 6). A curve goes from solid circle (2, 3) to open circle (3, 4). A line goes from the open circle to closed circle (6, 5).
What is Limit of j (x) as x approaches 3?
3
4
5
6
The limit of j (x) as x approaches 3 is 4.
According to the question, A line begins at an open circle (2, 6) on a coordinate plane and descends through ( -2, 2). At, a complete circle is (3, 6). From a solid circle (2, 3), a curve leads to an open circle (3, 4). From the open circle to the closed circle, a line runs (6, 5).
From the graph, it can be seen that the limit of the function j(x) as the value of x approaches 3 is 4.
A diagram or pictorial representation that organizes the depiction of data or values is known as a graph.
The relationships between two or more items are frequently represented by the points on a graph.
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Answer:
4
Step-by-step explanation:
egg 2023
A new outlet is being planned with an allocated budget of $50,000 per month for advertising and planned average price of $10.00 per pizza. Estimate the monthly sales (number of pizzas) of this outlet.
Answer:
5,000
[tex]50000 \div 10 = 5000[/tex]
To maintain essential electricity, a gasoline generator at a Puerto Rico hospital uses 3 gallons of gasoline per hour. a) How many gallons of gas are needed to fuel the generator for 1 full day? 72 2 points b) How much co2 will be produced by running the generator for 1 full day? 2 points
The mass of the CO2 produced IS 630 Kg
What is gasoline?Gasoline is a kind of fuel that is composed mostly of isooctane. In most engines, gasoline is widely used hence the demand for the product is high. We know that the combustion of an alkane (of which gasoline is one) would produce carbon dioxide and water according to a balanced reaction equation.
The balanced reaction equation for the combustion of gasoline is shown in the image attached to this answer.
Since a Puerto Rico hospital uses 3 gallons of gasoline per hour, and there are 24 hours in a day, it the follows that 72 gallons of gasoline are used per day. This 72 gallons is the equivalent of 272.88 L
Now;
Given that the density of gasoline = 748.9 g/L
Mass of gasoline = 748.9 g/L * 272.88 L = 204 Kg
Number of moles of gasoline = 204 * 10^3/114 g/mol = 1789.5 moles
If 2 moles of gasoline produces 16 moles of CO2
1789.5 moles produces 1789.5 moles * 16 moles/2 moles = 14316 moles
Mass of CO2 = 14316 moles * 44 g/mol = 630 Kg
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need heeeelp please
Answer:
(x, y) = (-√3/2, 1/2)
Step-by-step explanation:
The terminal point for that angle can be read from a unit circle chart.
On the attached chart, the point of interest is the first one above the -x axis on the left side. The chart tells you the coordinates are ...
(x, y) = (-√3/2, 1/2)
100 POINTS Consider this piecewise function.
Plot f (x) on the graph.
NO LINKS
Answer:
The intervals represent the domain, or the values on the horizontal axis.
When x ≤ -3, the graph should form a straight line at y = 3. Because the interval includes x = -3, the rightmost part of the line should be capped with a closed dot. The line should continue for infinity to the left.
When -3 < x < 4, the graph should form a line with the equation (2x + 1). Because the interval does not include the endpoints, the endpoints should have open dots.
When x ≥ 4, the graph should form a straight line at y = -4. Because the interval includes x = 4, the leftmost endpoint should be a closed dot. The right of the line should continue for infinity.
**The included graph does not take the endpoints into account
Answer:
See attached for graph.
Step-by-step explanation:
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
Given piecewise function:
[tex]f(x)=\begin{cases}3 & \textsf{if }x\leq -3\\2x+1 & \textsf{if }-3 < x < 4 \\ -2 & \textsf{if } x\geq 4 \end{cases}[/tex]
Therefore, the function has three definitions:
[tex]f(x)=3 \quad \textsf{when x is less than or equal to 3}[/tex]
[tex]f(x)=2x+1 \quad \textsf{when x is more than -3 and less than 4}[/tex]
[tex]f(x)=-2 \quad \textsf{when x is more than or equal to 4}[/tex]
When graphing piecewise functions:
Use an open circle where the value of x is not included in the interval.Use a closed circle where the value of x is included in the interval.Use an arrow to show that the function continues indefinitely.First piece of function
Substitute the endpoint of the interval into the corresponding function:
[tex]\implies f(-3)=3 \implies (-3,3)[/tex]
Place a closed circle at (-3, 3).
As this piece of the function is f(x) = 3 for any value of x that is less than or equal to -3, draw a horizontal straight line to the left from the closed circle. Add an arrow at the end.
Second piece of function
Substitute the endpoints of the interval into the corresponding function:
[tex]\implies f(-3)=2(-3)+1=-5 \implies (-3,-5)[/tex]
[tex]\implies f(4)=2(4)+1=9 \implies (4,9)[/tex]
Place an open circle at (-3, -5) and (4, 9).
Join the points with a straight line.
Third piece of function
Substitute the endpoint of the interval into the corresponding function:
[tex]\implies f(4)=-2 \implies (4,-2)[/tex]
Place a closed circle at (4, -2).
As this piece of the function is f(x) = -2 for any value of x that is more than or equal to 4, draw a horizontal straight line to the right from the closed circle. Add an arrow at the end.
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PLEASE HELP ALOT OF POINTSThe Pythagorean Theorem states "The square on the hypotenuse of a
right triangle is equal to the sum of the squares on the two legs". Jaylene
produces this image in her notebook and claims that it proves the
Pythagorean Theorem is true. Is this a fair claim? Why or why not?
Answer:
choice C. Yes, this image proves the pythagorean theorem is true because 9 + 16 = 25
Step-by-step explanation:
How to find exponential function?
[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
Given:[tex]\bold{y=Ce^{kt}}[/tex][tex]\bold{(5,5)}[/tex][tex]\bold{(0, \dfrac{6}{7} )}[/tex][tex]\small\leadsto\bold{Substitute:}[/tex]
[tex]\longrightarrow\sf{ \dfrac{6}{7}= Ce^{k*0}}[/tex]
[tex]\longrightarrow\sf{\dfrac{6}{7}= C*e^0}[/tex]
[tex]\longrightarrow\sf{e^0=1}[/tex]
[tex]\therefore\sf{C= \dfrac{6}{7} }[/tex]
[tex]\therefore\sf{5=Ce^{k*5}}[/tex]
[tex]\\[/tex]
[tex] \bold{Solve \: to \: find \: k:}[/tex]
[tex]\longrightarrow\sf{5 = \dfrac{6}{7} *e^{k5}}[/tex]
[tex]\longrightarrow\sf{ \dfrac{7*5}{6} *e^{5k}}[/tex]
[tex]\longrightarrow\sf{In=( \dfrac{35}{6} ) = 5k}[/tex]
[tex]\longrightarrow\sf{1.76=5k}[/tex]
[tex]\longrightarrow\sf{k=\dfrac{1.76}{5} = 0.352}[/tex]
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
[tex]\large\sf{\boxed{\sf \dfrac{6}{7}= e^{0.352*t}}}[/tex]
Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weekly salary is $900. The following table shows the number of sales each salesman had during the first three weeks of this month.
Based on the amount that both Salesmen A and B earn per sale, the number of sales they both had was 12 sales.
How many sales did Salesmen A and B have?Sales commission is a key aspect of sales compensation. It's the amount of money a salesperson earns based on the number of sales they have been able to make.
We are told that;
Salesman A gets $65 per sale.
Salesman B gets $300 and $40 per sale.
Assuming the number of sales to take them both to the same amount is x, the relevant formulas would be:
65x = 300 + 40x
Rearranging gives;
65x - 40x = 300
25x = 300
x = 300/25
x = 12 sales
The amount that salesman A earned is = 65 * 12 = $780
The amount that salesman B earned is = 300 + (40 * 12) = $780
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You are volunteering to help with the soccer team's Valentine's Day fundraiser. Each 16-ounce bag of nuts the team sold must include at least 60% chocolate-covered nuts inside.
However, instead of receiving a shipment of separated plain nuts and chocolate nuts, they delivered two large containers of mixed nuts. The first says it is 50/50 plain and chocolate covered. The second contains 80% chocolate-covered nuts.
The team is dismayed, but you come up with a solution. You suggest combining
ounces* of the 50/50 nuts with
ounces* of the 80% chocolate-covered nuts, to create the 60% mixture required for each bag.
*estimate
Then Bob, another student on the team says, "Wait, we promised at least 60%. So if we just do half and half, won't we be giving them at least 60%?"
Bob
correct.
Proportionately, if they do half and half of 50% and 80% of the two bags, Bob is correct.
What is a proportion?A proportion is a mathematical measure that compares two variables or numbers.
Proportions can be stated in percentages or ratios, as decimals or fractions.
Data and Calculations:Content of 16-ounce bag of nuts = 60% chocolate-covered nuts
Content of first bag = 50/50 plain and chocolate-covered nuts
Content of second bag = 80% chocolate-covered nuts
A mixture of half of 50% bag with half of 80% bag will result in 65% (50% + 80%)/2.
Thus, since the promise for each 16-ounce bag is for at least 60% chocolate-covered nuts, Bob is correct.
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Question Completion:Is Bob correct?
PLEASE HELP!!
Select all the correct answers.
Consider the graph of the function f (x) = 2³.
y
-5 -4
Fm.
-~
-5
4
3-
2
-1-
-2-
-3-
-4-
-5-
O
N.
2
Which statements describe key features of function gif g (z) = f(x + 2)?
horizontal asymptote of y = 2
3 4 5
Oy-intercept at (0,4)
O y-intercept at (0, 1)
O horizontal asymptote of y = 0
O domain of (-∞0 < x < ∞0}
[tex]f(x) = 2 {}^{x} \\ g(x) = f(x + 2) = 2 {}^{x + 2} \\ g(x) = 2 {}^{x + 2} =2 {}^{x} .2 {}^{2} = 4.2 {}^{x} [/tex]
[tex]a.b {}^{x} = > horizontal \: asymp \: y = 0[/tex]
[tex]4.2 {}^{0} = 4 = > vertical \: int \: (0,4)[/tex]
[tex]a.b {}^{x} = > x ∈ \: ] -∞ , ∞ [[/tex]
Answer: Options:2 4 5The horizontal asymptote of the function f ( x ) = 2ˣ is y = 0 and the y-intercept is ( 0 , 4 )
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 denoted as f ( x )
Now , the value of f ( x ) is
f ( x ) = 2ˣ be equation (1)
The y-intercept of the function is when x = 0
So , when x = 0
f ( 0 ) = 2⁰
f ( 0 ) = 1
So , the y-intercept of the function is at ( 0 , 4 )
And , when the function f ( x ) is tending to zero , the horizontal asymptote is y = 0
Therefore , the horizontal asymptote is y = 0
The domain of the exponential function is { -∞ < x < ∞ }
Hence , the horizontal asymptote of the function f ( x ) = 2ˣ is y = 0
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The total cost to rent 5 chairs and 3 tables is $27. The total cost to rent 2 chairs and 12 tables is $81. What is the cost to rent each chair and each table
The cost to rent each chair is $1.5 and cost to rent each table is $6.5
Applications of systems of linear equationsFrom the question, we are to determine the cost to rent each chair and each table
Let c represent chair
and
t represent table
From the given information,
The total cost to rent 5 chairs and 3 tables is $27
That is,
5c + 3t = 27 ------------ (1)
Also,
The total cost to rent 2 chairs and 12 tables is $81
That is,
2c + 12t = 81 ---------- (2)
Now, solve the equations simultaneously
5c + 3t = 27 ------------ (1)
2c + 12t = 81 ---------- (2)
Multiply equation (1) by 2 and multiply equation (2) by 5
2 × [5c + 3t = 27 ]
5 × [2c + 12t = 81 ]
10c + 6t = 54 ------------- (3)
10c + 60t = 405 ------------- (4)
Subtract equation (4) from equation (3)
10c + 6t = 54
10c + 60t = 405
---------------------------
-54t = -351
t = -351/-54
t = 6.5
Substitute the value of t into equation (2)
2c + 12t = 81
2c + 12(6.5) = 81
2c + 78 = 81
2c = 81 - 78
2c = 3
c = 3/2
c = 1.5
∴ The cost of chair is $1.5 and cost of table is $6.5
Hence, the cost to rent each chair is $1.5 and cost to rent each table is $6.5
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Find all values of x in the interval [0, 2π] that satisfy the equation. 7 sin(2x) = 7 cos(x)
Answer:
x = {π/6, π/2, 5π/6, 3π/2}
Step-by-step explanation:
The equation can be solved using a double-angle trig identity and factoring.
SimplifyDividing the equation by 7 and substituting for sin(2x), we have ...
7sin(2x) = 7cos(x)
sin(2x) = cos(x)
2sin(x)cos(x) = cos(x)
2sin(x)cos(x) -cos(x) = 0
cos(x)(2sin(x) -1) = 0
Zero product ruleThe product of factors is zero when one or more of the factors is zero.
cos(x) = 0 ⇒ x = {π/2, 3π/2}
2sin(x) -1 = 0 ⇒ x = arcsin(1/2) = {π/6, 5π/6}
Solutions in the given interval are ...
x = {π/6, π/2, 5π/6, 3π/2}
__
Additional comment
When the equation is of the form f(x) = 0, then the x-intercepts of f(x) are its solutions. We can rearrange this one to ...
sin(2x) -cos(x) = 0
The solutions identified above match those shown in the graph.
Use cos a cos b=1/2 [cos (a + b) + cos (a-b)]to derive cos x + cos y= cos 2 (x+y/2) cos (x-y/2) .
The trigonometric identity cos x + cos y = 2 cos (x + y/2) cos (x - y/2), is derived using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].
In the question, we are asked to derive the trigonometric identity, cos x + cos y = 2 cos (x + y/2) cos (x - y/2), using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].
We are given the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].
Substituting a = x + y/2 and b = x - y/2 in this, we get:
cos (x + y/2) cos (x - y/2) = 1/2[cos (x + y/2 + x - y/2) + cos (x + y/2 - x - y/2)],
or, cos (x + y/2) cos (x - y/2) = 1/2[ cos (2x/2) + cos (2y/2) ],
or, 2 cos (x + y/2) cos (x - y/2) = cos x + cos y, which on inter-changing the sides, gives us:
cos x + cos y = 2 cos (x + y/2) cos (x - y/2), which is the required trigonometric identity.
Thus, the trigonometric identity cos x + cos y = 2 cos (x + y/2) cos (x - y/2), is derived using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].
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The provided question is incorrect. The correct question is:
"Use cos a cos b=1/2 [cos (a + b) + cos (a-b)]to derive cos x + cos y = 2 cos (x + y/2) cos (x - y/2) ."
Find the area of this kite
Answer:
26 units^2
Step-by-step explanation:
the area of a kite is (d1 * d2)/2
d1 = 2 + 2 = 4
d2 = 6 + 7 = 13
4 * 13 = 52
52 / 6 = 26
26 units^2 is your answer
Answer: 26
Step-by-step explanation:

I need help with the solution
The answer is Pedro.
19. At a boardroom meeting, the sales manager is happy to announce that sales have risen from $850,000 to $1,750,000 at a
rate of 4.931998% per year. How many years did it take for the sales to reach $1,750,000?
The number of years it would take sales to reach $1,750,000 is 14.65 years.
What is the number of years?The formula that can be used to determine the number of years it would take for the sales to reach $1,750,000 is:
Number of years : In (FV / PV) / r
Where:
FV = future level of sales - $1,750,000PV = present level of sales = 850,000r = rate of growth - 4.931998%Number of years : In ($1,750,000 / 850,000) / 0.04931998
Number of years : In (2.06) / 0.04931998
Number of years : 14.65 years
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QUESTION 9
Find f(g(2)) for the following:
Given: ƒ (x) = 2x² − 1, g(x)=x+2
-
Find:f(g(2))
Answer:
x = 31
Step-by-step explanation:
Given:
f(x) =
[tex]2 {x}^{2} - 1[/tex]
g(x) = x + 2
We will first find g(2).
g(2) = 2 + 2 = 4
Next we will find f(g(2)).
f(g(2))= f(4) =
[tex]2( {4}^{2} ) - 1 \\ = 2(16) - 1 \\ = 32 - 1 \\ = 31[/tex]
Suppose 45% of the population has a college degree.
If a random sample of size 437 is selected, what is the probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%? Round your answer to four decimal places.
Using the normal distribution, there is a 0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The proportion estimate and the sample size are given as follows:
p = 0.45, n = 437.
Hence the mean and the standard error are:
[tex]\mu = p = 0.45[/tex][tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.45(0.55)}{437}} = 0.0238[/tex]The probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3% is 2 multiplied by the p-value of Z when X = 0.45 - 0.03 = 0.42.
Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (0.42 - 0.45)/0.0238
Z = -1.26
Z = -1.26 has a p-value of 0.1038.
2 x 0.1038 = 0.2076.
0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.
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(05.03 LC)
The equation shows the relationship between x and y:
y = −4x + 9
What is the slope of the equation? (5 points)
Group of answer choices
−9
−4
4
9
Find the value of y.
answer choices
A. 118
B. 32.5
C. 65
D. 130
The value of 'y' is 32. 5 degrees . Option B
How to determine the valueIt is important to note that If two chords intersect inside a circle,
The measure of the angle formed is half the sum of the measure of the arcs intercepted by the angle and its vertical angle
From the diagram, it is shown that the both the chords at 'y' and the angle '65' intersect in the circle
We then have that;
[tex]y = 65[/tex] × [tex]\frac{1}{2}[/tex]
[tex]y = 65[/tex] × [tex]0. 5[/tex]
y = 32. 5 degrees
We can see that the value of 'y' in the given figure is 32. 5 degrees which is half the angle at the vertex of the intersecting chords.
Thus, the value of 'y' is 32. 5 degrees . Option B
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A private jet flies the same distance in 8 hours that a commercial jet flies in 7 hours. If the speed of the commercial jet was 144mph less than 2 times the speed of the private jet, find the speed of each jet.
Solving a system of equations, we can see that:
Speed of the private jet: 168 mi/hSpeed of the commercial jet: 192mi/hHow to find the speeds of each jet?Let's define the variables:
P = speed of the private jet.C = speed of the commercial jet.With the given information, we can write:
P*8h = D
C*7h = D
C = 2*P - 144mi/h
So we have a system of 3 equations, where D is the distance in the problem.
With the first and second equations we can write:
P*8h = D = C*7h
Isolating P, we get:
P = C*(7/8)
Now we can replace that in the last equation:
C = 2*P - 144mi/h
C = 2*C*(7/8) - 144mi/h
And now we can solve that for C.
C - 2*(7/8)*C = - 144mi/h
C*(1 - 14/8) = -144mi/h
C*(8/8 - 14/8) = - 144mi/h
C*(6/8) = 144mi/h
C = (8/6)*144mi/h = 192mi/h
Now that we know the speed of the commercial jet, we can find the speed of the private jet.
P = C*(7/8) = 192mi/h*(7/8) = 168 mi/h
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Is 3 1/4 a rational or irrational number?
Answer:
It is a rational number.
Step-by-step explanation:
A number is only irrational if it has a decimal that never ends and doesn't have a pattern. So a number like Pi (3.141592653589...) is irrational while a number like 1/3 (0.33333333...) is rational.
Hi :)
Below is the difference between rational & irrational numbers
______________RATIONALA number that can be expressed in [tex]\sf{\dfrac{p}{q}}[/tex] form, where [tex]\large\boldsymbol{q\ne0}[/tex]Evidently,
An irrational number is a number that cannot be expressed in [tex]\sf{\dfrac{p}{q}}[/tex] formLet's test the given number, [tex]\boldsymbol{3\dfrac{1}{4}}[/tex]
Well isn't it already in [tex]\sf{\dfrac{p}{q}}[/tex] form? It is.
Thus
[tex]\longrightarrow\darkblue\boldsymbol{3\dfrac{1}{4}\:is\:rational}[/tex]
[tex]\tt{Learn\:More;Work\:Harder}[/tex]
:)
In the diagram, angle ADE ≈ angle ABC the ratios blank and blank are equal.
Based on the angle-angle similarity theorem (AA), the pair of ratios that are equal is: AE/EC = AD/DB.
What is the Angle-angle Similarity Theorem (AA)?The angle-angle similarity theorem (AA) states that two triangles are similar to each other if they have two corresponding congruent angles, and therefore, the ratios of their corresponding side lengths are equal. This means their corresponding side lengths are proportional in measure.
Given that angle ADE ≅ angle ABC, we also know that:
Angle EAD ≅ CAB.
Thus, this implies that triangle EAD is similar to triangle CAB based on the angle-angle similarity theorem (AA). Therefore, the ratios of their corresponding side lengths are equal.
Thus, the ratios that are equal to each other would be:
AE/EC = AD/DB.
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