If matric learners do not obtain the marks they need to enter their chosen study programmes, there are several strategies they can implement to still achieve their academic and career goals:
1. Consider alternative study programmes: Matric learners who did not obtain the marks they need for their first choice of study programme should consider other programmes that may be similar or related to their original choice. They can also look at bridging courses, diploma programmes or short courses that will enable them to develop the skills and knowledge they need for their chosen career.
2. Upgrade matric results: Some learners may choose to re-write some of their matric subjects to improve their results. This can be done through night school, part-time courses or through online platforms. This will require dedication, hard work and perseverance, but it can be an effective way to meet the entry requirements for their desired study programmes.
3. Attend a tertiary institution with lower entry requirements: Matric learners who do not meet the requirements for their desired study programme at their first choice institution can consider attending another institution with lower entry requirements. This will enable them to obtain a qualification in their chosen field, which they can use to pursue further studies or career advancement.
4. Take a gap year: Taking a gap year to gain work experience or travel can provide learners with valuable skills and experiences that can enhance their application for their chosen study programme in the future. This time can also be used to upgrade their matric results or to explore other interests and career options.
In conclusion, while not obtaining the marks required to enter a chosen study programme can be disappointing, it is important for matric learners to remain positive and proactive. By considering alternative study programmes, upgrading matric results, attending institutions with lower entry requirements, or taking a gap year, learners can still achieve their academic and career goals.
PLEASE HELPP!!!! DUE IN 2 HOURSSSS!!!!!!
5) Solve.
The altitude leg of a right triangle has a length of √32 cm. Its hypotenuse measures 9 cm.
How long is its base leg?
(A). b = 5cm
(B). b = 9cm
(C). b = 6cm
(D). b = 7cm
Answer:B
Step-by-step explanation:
Answer: D : 7cm
Step-by-step explanation:
find x, show proofs
The side x of the similar triangle is 12.7 units.
How to find the side of a triangle?The triangles are similar triangle.
Two triangles are said to be similar when they have two corresponding angles congruent and the sides proportional.
Therefore, using the proportion
37- 5 / x = x / 5
Evaluate the difference of 37 and 5
32 / x = x / 5
Cross multiply the equation
x × x = 32 × 5
So, we have
x² = 160
Take the square root of both sides
x = √160
Evaluate the square roots
x = 12.6491106407
Hence, the value of x is x = 12.7 units (when approximated)
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the quotient of 7 and the sum of 8 and m
Answer: :)
n
_
8
I used n as the unknown number
Step-by-step explanation:
The quotient is the result of division between two numbers.
The quotient of a number (I used n) and 8 would be n 8
The question is present in the image
The value of variables are,
a = 0
c = 7
d = 2
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ [tex]\frac{32x^{4} y^{3} z^{- 6} }{(4x^{2} y^{-2} z^{-2})^2 } = \frac{Ax^ay^c}{z^d}[/tex]
Now, We can simplify as;
⇒ [tex]\frac{32x^{4} y^{3} z^{- 6} }{(4x^{2} y^{-2} z^{-2})^2 } = \frac{Ax^ay^c}{z^d}[/tex]
⇒ [tex]\frac{32x^{4} y^{3} z^{- 6} }{(16x^{4} y^{-4} z^{-4}) } = \frac{Ax^ay^c}{z^d}[/tex]
⇒ [tex]\frac{2x^0y^7}{z^2} = \frac{Ax^ay^c}{z^d}[/tex]
By comparing, we get;
a = 0
c = 7
d = 2
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Pls Help! Will give brainliest!
Write the following linear equation in function notation. y = 2x + 5
(A.) f = 2x + 5
(B.) f(x) = 2x + 5
(C.) It is already written in function notation.
(D.) f(y) = 2x+ 5
The given expression is already written in function notation.
Solving linear equationFunction notation is a way of representing a mathematical relationship between two variables, where one variable (usually denoted as x) is the input and the other variable (usually denoted as y) is the output. In this case, y is a function of x, which means that the value of y depends on the value of x.
To write the linear equation y = 2x + 5 in function notation, we replace y with f(x) to get:
f(x) = 2x + 5
This means that f(x) is a function of x, where the output f(x) is equal to 2 times the input x plus 5. The variable f(x) represents the value of y for a given value of x.
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7. A pot of water is heated to 200°F. The table shows typical temperature readings for the pot. The room temperature is 70°F.
After 5 minutes the pot of water is 164°F. How long will it take the water to cool to 150°F? Round to the nearest minute.
A. About 4 min
B. About 3 min
C. About 8 min
D. About 6 min
The amount of time it would take the water to cool to 150°F is: C. About 8 min.
How to find an equation of the line of best fit for the data?In this scenario, the time would be plotted on the x-axis of the scatter plot while the temperature would be plotted on the y-axis of the scatter plot.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the time and temperature, an exponential equation for the line of best fit is given by:
[tex]y = 192e^{-0.028x}[/tex]
When temperature y = 150°F, the value of x (in minutes) can be calculated as follows:
[tex]150 = 192e^{-0.028x}[/tex]
ln(150/192) = -0.028x
x = -0.24686007793/0.028
x = 8 mins.
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To help pay for culinary school, Keiko borrowed money from her credit union.
She took out a personal, amortized loan for $50,000, at an interest rate of 5.5%, with monthly payments for a term of 10 years.
For each part, do not round any intermediate computations and round your final answers to the nearest cent.
If necessary, refer to the list of financial formulas.
(a) Find Keiko's monthly payment.
$0
(b) If Keiko pays the monthly payment each month for the full term,
find her total amount to repay the loan.
$0
(c) If Keiko pays the monthly payment each month for the full term,
find the total amount of interest she will pay.
$0
X
If to help pay for culinary school, Keiko borrowed money from her credit union:
a. Keiko's monthly payment is $542.63.
b. The total amount to repay the loan is $65,115.60
c. The total amount of interest she will pay is $15,115.60
What is the monthly payment?(a) To find Keiko's monthly payment, we can use the formula for calculating the monthly payment for an amortized loan:
P = (r * A) / (1 - (1 + r)^(-n))
Where:
P =Monthly payment
A= loan amount
r = Monthly interest rate
n = Total number of payment
Plugging in the values for Keiko's loan, we get:
P = $50,000
r = 0.055 / 12 = 0.00458
n = 10 * 12 = 120
P = (0.055/12 * $50,000) / (1 - (1 + 0.055/12)^(-120)) = $542.63
(b) If Keiko pays the monthly payment each month for the full term, the total amount she will repay the loan will be:
Total amount = Monthly payment * Total number of payments
= $542.63* 120 = $65,115.60
(c) If Keiko pays the monthly payment each month for the full term, the total amount of interest she will pay will be:
Total interest = Total amount - Loan amount
=$65,115.60 - $50,000 = $15,115.60
So, Keiko will pay a total of $15,115.60 in interest over the 10-year term of the loan.
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PLSS ANSWER QUICKLY ASAP
Answer:
the answer is A
hope it helps u
mark brainlist
Answer: D
As x Values-Decrease, the function increases toward positive infinity.
As the x values decreases, the function decreases towards y=-2
Step-by-step explanation:
It's a basic function that follows within the 2^x format. Where x-> infinity would mean that y-> infinity as well. However, since there was a translation within the y unit (hence the -2) the asymptote decreased by two.
So as the x unit increases, so does the y.
However, as the x unit decreases, the y decreases to -2.
ANWSER QUICK
After a couple of years, you’ve decided to sell your house. You originally bought it for $250,000 and spent an additional $10,000 in renovations, Your realtor thinks you can sell it for $290,000.
The profit to be made by selling the house for $290000 is $30000
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
You originally bought it for $250,000 and spent an additional $10,000 in renovations, Hence:
Total money spent = $250000 + $10000 = $260000
The realtor thinks you can sell it for $290,000. Therefore:
Profit = $290000 - $260000 = $30000
The profit to be made by selling the house is $30000
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2.- Encuentra los valores correspondientes en el rango para las siguientes funciones.
a) Si f(x) = x³ + 3x² - 4x, calcular f(0); f(-1); f(3)
HACER LAS OPERACIONES CORRESPONDIENTES. Encuentra la función resultante para
la operación con funciones que se te pide y calcula el valor correspondiente en el rango
3.- (fx g)(x), si f(x) = (x + 1)² y g(x)=2x-3,
4.- (f-g)(x), si f(x) = 5x² + 3x - 1 y g(x)=x²- 2x + 6,
Quiero explicación tengo una duda y no le entiendo al cuadrado que hay que hacer x³ + 3x². 5x² 1)²
Answer:
Step-by-step explanation:
sorry I don’t know
Evaluate the given expression:
In answering the question above, the solution is The answer is s 4 = 632 expressions as a result.
what is expression ?In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
Let's start by condensing the expression included within the summation:
[tex]2(3^n - 1) = 2*3^n - 2[/tex]
We may now enter the following expression in the original equation:
[tex]s_4[/tex] = 4 * ∑[tex](k=1[/tex]to [tex]4) 2(3^k - 1)[/tex]
[tex]s_4 = 4 * [2(3^1 - 1) + 2(3^2 - 1) + 2(3^3 - 1) + 2(3^4 - 1)]\\s_4 = 4 * [2(3^1 + 3^2 + 3^3 + 3^4) - 8]\\s_4 = 4 * [2(3^1 + 3^2 + 3^3 + 3^4) - 2^3]\\s_4 = 4 * [2(80) - 8]\\s_4 = 632[/tex]
The answer is s 4 = 632 as a result.
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Which expression represents the distance between Q and R
Answer:
Translation
Step-by-step explanation:
Translation
Mica is going to buy a computer for $2,000. He
can finance it at the store for 14% interest for
2 years, or he can use his credit card at 21%
interest for 1 year.
1. Find the monthly payment for each option.
Answer in the box.
2. Find the total repayment for each option.
Answer in the box.
Answer: To find the monthly payment for each option, we can use the following formula:
Monthly Payment = Total Cost * (Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))
For the option to finance at the store for 2 years at 14% interest:
Total Cost = $2,000
Monthly Interest Rate = 14% / 12 = 0.011667
Number of Months = 2 years x 12 months/year = 24 months
Substituting these values into the formula, we get:
Monthly Payment = $2,000 * 0.011667 / (1 - (1 + 0.011667)^(-24)) = $95.13
Therefore, the monthly payment for financing at the store for 2 years at 14% interest is $95.13.
For the option to use his credit card at 21% interest for 1 year:
Total Cost = $2,000
Monthly Interest Rate = 21% / 12 = 0.0175
Number of Months = 1 year x 12 months/year = 12 months
Substituting these values into the formula, we get:
Monthly Payment = $2,000 * 0.0175 / (1 - (1 + 0.0175)^(-12)) = $185.44
Therefore, the monthly payment for using his credit card at 21% interest for 1 year is $185.44.
To find the total repayment for each option, we can multiply the monthly payment by the number of months:
For the option to finance at the store for 2 years at 14% interest:
Total Repayment = $95.13/month x 24 months = $2,283.12
Therefore, the total repayment for financing at the store for 2 years at 14% interest is $2,283.12.
For the option to use his credit card at 21% interest for 1 year:
Total Repayment = $185.44/month x 12 months = $2,225.28
Therefore, the total repayment for using his credit card at 21% interest for 1 year is $2,225.28.
Step-by-step explanation:
The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year.
P = $370, r = 2%, t = 2 years
Step-by-step explanation:
Using the formula for simple interest:
Simple Interest = P * r * t
where P is the principal, r is the rate of interest, and t is the time in years.
Substituting the given values:
Simple Interest = $370 * 0.02 * 2 = $14.80
Therefore, the simple interest owed for the use of the money is $14.80.
The sum of two numbers is 37. If one of the numbers is greater by 1 than the two times the other, find the numbers.
Five students came for after-school tutoring. Lin’s teacher assigned each of them the same number of problems to complete. Then he assigned each student 2 more problems. 30 problems were assigned in all.
The number of problems assigned initially to each student by Lin’s teacher is 4.
What is an Equations?Equations are mathematical statements that have two algebraic expressions on either side of equals (=) sign. The phrases written on the left and right sides are equal, as shown by this example.
Equations can be resolved in order to ascertain the value of a variable that represents an unknowable quantity. In the absence of the "equal to" symbol, a statement is not an equation. That will be taken into consideration as a phrase.
Lin’s teacher assigned each of them the same number of problems to complete.
Total number of problems assigned by Lin's teacher to students = 30
Let the total number of problems assigned to each student initially be x
So, the number of problems assigned to all the students initially = 5x
Also it is given that Lin's teacher assigns 2 more problems to each student
which means he gives 10 more problems to solve
5x+10 = 30
5x = 20
x = 4
Hence, The number of problems assigned initially to each student by Lin’s teacher is 4.
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Solve for the following....
[tex]\boxed{\tt 4x-(9-3x)=8x-1}[/tex]
Answer:
-8
Step-by-step explanation:
4x - 9 + 3x = 8x - 1
7x - 9 = 8x - 1
7x = 8x + 8
x = -8
Therefore, the solution to the equation 4x - (9 - 3x) = 8x - 1 is x = -8.
Given:-
[tex] \sf \: 4x - ( 9 - 3x ) = 8x - 1[/tex][tex] \: [/tex]
Solution:-
[tex] \sf \: 4x - ( 9 - 3x ) = 8x - 1[/tex][tex] \: [/tex]
[tex] \sf \: 4x - 9 + 3x = 8x - 1[/tex][tex] \: [/tex]
[tex] \sf \: 4x + 3x - 9 = 8x - 1[/tex][tex] \: [/tex]
[tex] \sf \: 7x - 9 = 8x - 1[/tex][tex] \: [/tex]
[tex] \sf \: 7x - 8x = -1 + 9[/tex][tex] \: [/tex]
[tex] \sf \: -1x = 8[/tex][tex] \: [/tex]
[tex] \sf \: x = \cancel \frac{8}{ - 1} [/tex][tex] \: [/tex]
[tex] \underline{ \sf \color{lightgreen} \: x = -8 \: }[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps! :)
For problems 7-12, consider the sets below, and indicate if each statement is true or false.
A = {1, 2, 3, 4, 5} B = {1, 3, 5} C = {4, 6} U = {numbers from 0 to 10}
7. 3 ∊ B 8. 5 ∊ C 9. B ⊂ A 10. C ⊂ A 11. C ⊂ B 12. C ⊂ U
Using the sets from above, and treating U as the Universal set, find each of the following:
13. A ⋃ B 14. A ⋃ C 15. A ⋂ C 16. B ⋂ C 17. A c 18. B c
The correct statements are 7. 3 ∈ B, 9. B ⊂ A, 12. C ⊂ U
13. A ⋃ B = {1, 2, 3, 4, 5, } 14. A ⋃ C = { 1, 2, 3, 4, 5, 6}
15. A ⋂ C = { 4 } 16. B ⋂ C = { }
17. [tex]A^{c}[/tex] = {6, 7, 8, 9, 10} 18. [tex]B^{c}[/tex] = {0, 2, 4, 6, 7, 8, 9, 10}
What are sets:
In mathematics, a set is a collection of distinct objects, which are called its elements or members. These objects can be anything - numbers, letters, people, animals, or other sets.
Sets are typically denoted using curly braces, and the elements of the set are listed inside the braces, separated by commas.
Here we have
A = {1, 2, 3, 4, 5} B = {1, 3, 5} C = {4, 6} and U = {numbers from 0 to 10}
=> U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
i. Indicate if each statement is true or false.
7. 3 ∈ B which means 3 belongs to set B
Since, set B = {1, 3, 5}
=> ∴ 3 ∈ B is true
8. 5 ∈ C which means 5 belongs to set C
The set C = {4, 6}
=> 5 ∈ C is false
9. B ⊂ A which means B is a subset of A and elements of B are belongs to set A.
Since elements of B are lies in set A
=> B ⊂ A is true
10. C ⊂ A which means C is a subset of A
Since all the elements of C are not lie in set A
=> C ⊂ A is false
11. C ⊂ B which means C is a subset of B
Since all the elements of C are not lie in set B
=> C ⊂ B is false
12. C ⊂ U which means C is a subset of U
Since all the elements of C are lies in U
=> C ⊂ U is true
13. A ⋃ B = {1, 2, 3, 4, 5} ∪ {1, 3, 5} = {1, 2, 3, 4, 5, }
14. A ⋃ C = {1, 2, 3, 4, 5} ∪ {4, 6} = { 1, 2, 3, 4, 5, 6}
15. A ⋂ C = {1, 2, 3, 4, 5} ⋂ {4, 6} = { 4 }
16. B ⋂ C = {1, 3, 5} ⋂ {4, 6} = { }
17. [tex]A^{c}[/tex] = The elements in the universal set but not in A = {6, 7, 8, 9, 10}
18. [tex]B^{c}[/tex] = The elements in universal set but not in B = {0, 2, 4, 6, 7, 8, 9, 10}
Therefore,
The correct statements are 7. 3 ∈ B, 9. B ⊂ A, 12. C ⊂ U
13. A ⋃ B = {1, 2, 3, 4, 5, } 14. A ⋃ C = { 1, 2, 3, 4, 5, 6}
15. A ⋂ C = { 4 } 16. B ⋂ C = { }
17. [tex]A^{c}[/tex] = {6, 7, 8, 9, 10} 18. [tex]B^{c}[/tex] = {0, 2, 4, 6, 7, 8, 9, 10}
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-3 + ___= -1.9
What is in the missing blank
Answer:
1.1
Step-by-step explanation:
-3+1.9 =-1.1
-3+1.1=-1.9
Answer:
-3 + 1.1 = -1.9
Step-by-step explanation:
Let us assume that,
→ Missing number = m
Now we have to,
→ Find the required value of m.
Forming the equation,
→ -3 + m = -1.9
Then the value of m will be,
→ -3 + m = -1.9
→ m - 3 = -1.9
→ m = -1.9 + 3
→ [ m = 1.1 ]
Hence, the value of m is 1.1.
On jeopardy during the month of September the champions Won a total of $694563 assuming that there were 22 jeopardy shows in September what was the average amount won each day by the champions
Answer:
To find the average amount won each day by the champions, we need to divide the total amount won by the number of days:
Average amount won each day = Total amount won / Number of days
Total amount won = $694,563
Number of days = 22
Average amount won each day = $694,563 / 22 = $31,611.95 (rounded to the nearest cent)
Therefore, the average amount won each day by the champions on Jeopardy in September was approximately $31,611.95.
Step-by-step explanation:
b) Which is the better price—17% off $35 or 12% off $32? Explain.
Answer:
35$ - 17% gives you 29.05$
while 32$ - 12% gives you 28.16$
so 35$ - 17% would be your answer
Kira works mowing lawns and babysitting. She earns $9.20 an hour for mowing and $7.50 an hour for babysitting. How much will she earn for 6 hours of mowing and 1 hour of babysitting?
Answer:
$62.70
Step-by-step explanation:
of means "x"
and means "+"
6 hours of mowing and 1 hour of babysitting
(6 hours of mowing) + ( 1 hour of babysitting)
6 hours of mowing
6 hours x mowing
6x9.20 = answer 1
1 hour of babysitting
1 hour x babysitting
1 x 7.50 = answer 2
add both answers together to get final answer
5x ^ 2 y^ prime prime +23xy^ prime +16.2y=0
Answer:
Step-by-step explanation:
5
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.
The graph's function g(x) has a single x-intercept, a y intercept, a vertical asymptote, an oblique asymptote, and both.
Describe Asymptotes?Asymptotes are points along a line that a curve approaches but never touches. The term "asymptote" refers to the point at which a function's graph converges. Asymptotes are often not necessary when graphing functions.
There are three distinct asymptotes.
Asymptote horizontal (HA) - Given that it is horizontal, its equation has the form y = k. The horizontal asymptote is the point at which the function f(x) tends to zero.
As it is a vertical line, the vertical asymptote's equation has the form x = k. When the denominator of a rational function approaches towards 0, vertical asymptotes are defined.
The equation for the slanting asymptote (also known as the oblique asymptote) is y = mx + b since the line is inclined.
given the information,
Let's write the function as g. (x)
The value of g (x) is right now.
g (x) = ( -4x² + 36) / (x + 3)
We gain by simple.
g (x) = -4x² - 4×9) / (x + 3)
We gain more after additional simplification.
g (x) = -4 (x + 3) (x - 3) / (x + 3)
g (x) = -4x + 12
There is now a vertical asymptote for the function at (0, 12)
There is a horizontal asymptote for the function at (3, 0)
The function is so resolved.
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The complete question is:
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
Answer:
Step-by-step explanation:
What is the future value of a 10-year investment of $1200 at an APR of 7% compounded monthly?
Round to nearest cent
The future value of a 10-year investment of $1200 at an APR of 7% compounded monthly is $2366.84
what is compound interest ?
Compound interest is the interest earned on an initial deposit or investment, plus all the interest that has accumulated on it over time. It is interest calculated on both the principal amount and any interest earned from previous periods, which is added to the principal amount at the end of each compounding period.
[tex]FV = P * (1 + r/n)^{n*t}[/tex]
Where:
FV = Future Value
P = Principal or initial investment
r = Annual interest rate
n = Number of times interest is compounded per year
t = Time in years
According to the question:
In this case:
P = $1200
r = 7% = 0.07
n = 12 (compounded monthly)
t = 10
Plugging these values into the formula, we get:
[tex]FV = P * (1 + r/n)^{n*t}[/tex]
[tex]FV = 1200 * (1 + 0.07/12)^{12*10}[/tex]
[tex]FV = 1200 * (1.00583333)^{120}[/tex]
[tex]FV = 1200 * 1.97236812[/tex]
[tex]FV = 2366.84[/tex]
Therefore, the future value of a 10-year investment of $1200 at an APR of 7% compounded monthly is $2366.84 (rounded to the nearest cent).
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You write 6 3/10 pages of a report in 2 1/3 hours. What is the average number of pages you write per hour?
the answer is 2 5/14
Answer:
Step-by-step explanation:
To find the average number of pages written per hour, we need to divide the total number of pages written by the total time taken:
Total pages written = 6 3/10 = 63/10
Total time taken = 2 1/3 = 7/3
Average pages written per hour = Total pages written / Total time taken
= (63/10) / (7/3)
= (63/10) x (3/7)
= 9/2
Therefore, the average number of pages written per hour is 9/2, which is equal to 4.5 pages per hour.
Select which option is most appropriate for describing the number line below.
Answer:
Answer D is correct
Step-by-step explanation:
The function y = 8.5(1.1)^x models the population in thousands of a town where x is the number of years after 2000. What will be the town's population in 2007? Give the answer to two decimal places. Answers to choose from: A. 16.56 thousand B. 12 thousand C. 8.52 thousand D. 5 thousand
Pls help I rly appreciate it! :)
The population in thousands of a town in the year 2007 is 16.56 thousand.
What use does the base value serve in an exponential function?In an exponential function, the base value controls how quickly the function increases or decreases. The function expands exponentially if the base value is more than 1, whereas it degrades exponentially if the base value is between 0 and 1. Faster growth or decay is indicated by a bigger base value.
Given that,
y = 8.5(1.1)ˣ
The value of x is calculated as:
x = 2007 - 2000 = 7 years.
Substitute the value of x in the given function:
y = 8.5(1.1)⁷
y = 16.56
Hence, the population in thousands of a town in the year 2007 is 16.56 thousand.
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A race official needs to know how long it takes an average contestant to run an obstacle course. There are a total of 200 contestants. How can he find a reasonable estimate for the amount of time it takes to run the obstacle course?
A. Time any contestant on the course and use that time
B. Time himself on the course and use that time
C. Time 2 contestants and average their times
D. Time 20 contestants and average their times
The best option to find a reasonable estimate for the amount of time it takes to run the obstacle course among 200 contestants is to option D: Time 20 contestants and average their times.
Define reasonable estimate?A reasonable estimate is an approximation that is based on logical reasoning and information available, and it is within a reasonable margin of error. It is not expected to be precise, but it is expected to provide a fair idea of the value being estimated.
For example, estimating the cost of a renovation project within 5% of the actual cost would be considered a reasonable estimate.
By timing only one contestant, the time might not be representative of the entire group since individual performances can vary significantly. Timing the race official himself also won't give an accurate estimate since the official might not be a typical contestant in terms of speed and agility.
On the other hand, timing 2 contestants and averaging their times might not provide a big enough sample size to get a good estimate.By timing 20 contestants, there is a higher chance that the sample size will be representative of the entire group, and the average time will provide a more accurate estimate of the typical performance on the obstacle course.
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(100 POINTS) Use the function f(x) to answer the questions.
f(x) = −16x2 + 60x + 16
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
a. The x-intercepts are 1/4 and 4. b. The vertex of the graph of f(x) is (1.875, 56), and it represents a maximum point on the graph.
What is axis of symmetry?The object's form is symmetrical because of the axis of symmetry, which is a straight line. On each of its sides, the axis of symmetry produces a perfect reflection. It could be lateral, vertical, or horizontal. The two sides of an object are the same if we fold and unfold it along the axis of symmetry. Various forms have various symmetry lines. There are four lines of symmetry in a square, two lines in a rectangle, infinite lines in a circle, and no lines of symmetry in a parallelogram. There are n axes of symmetry in a regular polygon with n sides.
We know that,
To find the x-intercepts, we set f(x) equal to 0 and solve for x:
-16x² + 60x + 16 = 0
4x² - 15x - 4 = 0
4x² - 16x + x - 4 = 0
4x (x - 4) - 1(x - 4) = 0
(4x - 1) (x - 4) = 0
x = 1/4
x = 4
The x-intercepts are 1/4 and 4.
The vertex of the graph of f(x) can be found using the formula x = -b/2a
x = -60 / (2(-16)) = 1.875
To establish whether the vertex is a maximum or minimum, we examine the shape of the coefficient of the x square term, which is negative (-16). This signifies that the graph expands down and the vertex is a maximum.
Hence, the vertex of the graph of f(x) is (1.875, 56), and it represents a maximum point on the graph.
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