Answer:
The answer is B
Step-by-step explanation:
The required value of the quadratic function which is determined by the using quadratic formula would be [tex]x = \dfrac{5\pm\sqrt{97}}{12}[/tex] which is the correct answer would be an option (B).
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
We have been given that quadratic function as
5x = 6x² – 3
⇒ 6x² - 5x - 3 = 0
Compare the given function to the standard quadratic function
f(x) = ax² + b x + c = 0.
We get a = 6, b = -5 and c = -3
Using the quadratic formula to solve the above quadratic function
[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Substitute the values of a = 6, b = -5 and c = -3 in the quadratic formula
[tex]x = \dfrac{-(-5)\pm\sqrt{-5^2-4\times6\times-3}}{2\times6}[/tex]
[tex]x = \dfrac{5\pm\sqrt{25+72}}{12}[/tex]
[tex]x = \dfrac{5\pm\sqrt{97}}{12}[/tex]
Therefore, the correct answer would be an option (B).
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which ordered pair describes a translation of 6 units up up and 4 units left
Answer:
The correct answer for this is [tex](-4,6)[/tex].
Step-by-step explanation:
As it can be seen from the attached graph image:
The y-axis increases in positive values when we move in up direction i.e. we have +y-axis in upward direction.The y-axis decreases and keeps on becoming more and more negative values when we move in down direction i.e. we have -y-axis in downward direction.The x-axis increases in positive values when we move in right direction i.e. we have +x-axis in right direction.The x-axis decreases and keeps on becoming more and more negative values when we move in left direction i.e. we have -x-axis in left direction.Now, according to question, the translation is performed 6 points up i.e. towards positive y-axis and 4 points towards left i.e. towards negative x-axis.
And, as per rule, the co-ordinates are represented as [tex](x,y)[/tex] where [tex]x[/tex] is the x-co-ordinate and [tex]y[/tex] is y-co-ordinate.
So, the answer here is [tex](-4,6)[/tex].
At midnight, a passenger train left the station. Two hours later, a freight train left the same station
traveling on the same track in the same direction. At 8 a.m. the passenger train was 120 miles ahead
of the freight train. Find the rate of each train if the passenger train traveled 5 mph faster than the
freight train. ENTER ONLY THE NUMBER (do not enter variables, punctuation marks, units, symbols
or equals signs).
Answer:
speed of freight train = 40 MPH
speed of passenger train = 45MPH
Step-by-step explanation:
Let the speed of freight train be X miles per hour
speed of passenger train is 5 mph more than speed of freight train
Therefore speed of passenger train is X + 5 mph
we will use the formula to calculate distance which is givn below
distance travelled by any object is = speed * time
______________________________________________
Time at which the distance between the train are calculated = 8 AM
for freight train
since it started at 2 AM morning and traveled until 8 AM
duration for which it traveled = 8 - 2 = 6 hours
distance traveled by freight train in those 6 hours = speed of freight train * duration for which it travelled = X * 6 = 6X ----equation A
______________________________________________
for passenger train
since it started at 00.00AM morning and traveled until 8 AM
duration for which it traveled = 8 - 0 = 8 hours
distance traveled by passenger train in those 8 hours = speed of passenger train * duration for which it travelled = X + 5 * 8
= 8X + 40 ------- equation B
_______________________________________________
Distance between passenger train and freight train at 8 AM = 120 miles
also distance can be calculated using distance calculated above in equation A and B
Distance between passenger train and freight train at 8 AM in terms if X = distance traveled by passenger train in 8 hours - distance travelled by freight train in 6 hours = 8X + 40 - 6X = 2X + 40
2X + 40 distance is equal to 120 miles as given in question
therefore
2X + 40 = 120
2X = 120 -40
X = 80/2 = 40
therefore speed of freight train = X = 40 MPH
speed of passenger train = X + 5 = 40 + 5 = 45MPH
Wyatt was his room and found 57 book under his bed he stacked the books on his desk each stack had the same number of books in it and no stack had fewer than 5 books how many stacks did Wyatt make and how many books were in each stack.
Answer:
There was 3 stacks of 19 books.
Which number is irrational?
-27
3
4.12
A graph shows average temperature (degrees Fahrenheit) labeled 10 to 60 on the horizontal axis and total coat sales on the vertical axis. A line decreases from 10 to 65. Which temperature values would an interpolation be limited to? less than 3 between 3 and 60 between 20 and 80 greater than 55 ................... nvm i got it its B.between 3 and 60. but still answer to get points lol
Answer:
between 3 and 60
Step-by-step explanation:
just did it on ed.
Answer: Between 3 and 60
Step-by-step explanation: Glad you figured it out! :)
Please help in finding the radians in degrees!
Answer:
225°
Step-by-step explanation:
Multiply radians by 180°/π to get degrees.
(5π/4)×(180°/π) = (5/4)(180°) = 225°
Marissa's Beauty Salon has six hair dryers that each require 500 watts when switched
on. How much would it cost to run all six dryers for 7 hours, at a cost of $0.15 per kWh?
Round to the nearest cent.
We have been given that Marissa's Beauty Salon has six hair dryers that each require 500 watts when switched on.We are asked to find the cost to run all six dryers for 7 hours, at a cost of $0.15 per kWh.
First of all, we will find watts of energy used to switch on 6 hair dryers.
[tex]\text{Watts used per hour}=\text{Wattage per hour}\times \text{Number of hair dryers}[/tex]
[tex]\text{Watts used per hour}=500\text{ Watts}\times 6[/tex]
[tex]\text{Watts used per hour}=3000\text{ Watts}[/tex]
Now we will convert watts into kilowatts. We know that 1 kW is equal to 1000 W.
[tex]3000\text{ Watts}=\frac{3000}{1000}\text{ kW}=3\text{ kW}[/tex]
So 3 kW are used for 7 dryers for 1 hour. Now we will multiply 3 kW by 7 to find kWs used in 7 hours as:
[tex]\text{kWs used in 7 hours}=3\times 7=21[/tex]
Since the cost of 1 kWh is $0.15, so to find cost for 21 kW/h, we will multiply $0.15 by 21.
[tex]\$0.15\times 21=\$3.15[/tex]
Therefore, it will cost $3.15 to run all six dryers for 7 hours.
Using the textbook data set nlschools.csv, perform a hypothesis test to determine whether the proportion of students with language test scores greater than 37 is different for students from families of social-economic status at most 25 and students from families of social-economic status greater than 25. Perform the test at the α = 0.05 significance level.
Answer:
p-value is greater than 0.05, hence we accept the null hypothesis.
Step-by-step explanation:
See attached images
What is the mean and mad of this data set?
n=7
The number of gerbils seen per day:
2,3,5,7,8,8,9
Answer:
The mean number of gerbils seen per day is 6.
The mean absolute deviation of the data is 2.29.
Step-by-step explanation:
The mean of a data set is the value that represents the entire data set. It is the average value.
The formula to compute the mean of a data set is:
[tex]\bar x=\frac{1}{n}\sum X[/tex]
The mean absolute deviation (MAD) of a data set is the average distance amid each value and the mean. The MAD provides us with an idea about the deviation in the data set.
The formula to calculate the value of MAD is:
[tex]MAD=\frac{1}{n}\sum |x-\bar x|[/tex]
The data set for the number of gerbils seen per day is:
S = {2, 3, 5, 7, 8, 8, 9}
Compute the mean of the data as follows:
[tex]\bar x=\frac{1}{n}\sum X[/tex]
[tex]=\frac{1}{7}\times [2+3+5+7+8+8+9]\\\\=\frac{1}{7}\times 42\\\\=6[/tex]
The mean number of gerbils seen per day is 6.
Compute the mean absolute deviation of the data as follows:
[tex]MAD=\frac{1}{n}\sum |x-\bar x|[/tex]
[tex]=\frac{1}{7}\times [|2-6|+|3-6|+|5-6|+|7-6|+|8-6|+|8-6|+|9-6|]\\\\=\frac{1}{7}\times 16\\\\=2.2857\\\\\approx 2.29[/tex]
Thus, the mean absolute deviation of the data is 2.29.
Final answer:
The mean of the data set (2, 3, 5, 7, 8, 8, 9) is 6, and the mean absolute deviation (MAD) is approximately 2.29.
Explanation:
Finding the Mean and MAD of a Data Set
The mean (average) of a data set is found by adding up all the numbers in the set and then dividing by the count of those numbers. In the provided data set (2, 3, 5, 7, 8, 8, 9), the mean is calculated as follows:
Sum of the numbers = 2 + 3 + 5 + 7 + 8 + 8 + 9 = 42Count of numbers (n) = 7Mean = Sum / n = 42 / 7 = 6The mean absolute deviation (MAD) is found by calculating the absolute differences between each number in the set and the mean, averaging those absolute differences:
Absolute differences from the mean: |2-6|, |3-6|, |5-6|, |7-6|, |8-6|, |8-6|, |9-6|Absolute differences are: 4, 3, 1, 1, 2, 2, 3Sum of absolute differences = 4 + 3 + 1 + 1 + 2 + 2 + 3 = 16MAD = Sum of absolute differences / n = 16 / 7 ≈ 2.29Therefore, the mean of the data set is 6, and the MAD is approximately 2.29.
Solve −5x = 30
I need help ASAP
Answer:
x = -6
Step-by-step explanation:
−5x = 30
Divide each side by -5
-5x/-5 = 30/-5
x = -6
Answer:
x=-6
Step-by-step explanation:
−5x = 30
divide both sides by -5 to isolate x
x=-6
I hope this helps! Please mark brainliest :)
Linda wants to purchase a Leisure Heights Condominium apartment. She will
borrow $100,000 from the Duchess Savings Bank. The bank is presently
offering a 30-year fixed rate mortgage with an APR of 7.1%. Her monthly
maintenance fee will be $310.
A) What is the monthly mortgage payment?
B) What will be her combined monthly payment?
Linda's monthly mortgage payment will be approximately $664.14.
Linda's combined monthly payment, including the mortgage and maintenance fee, will be $974.14.
We have
A)
Monthly Mortgage Payment:
Loan Amount: $100,000
Interest Rate: 7.1% per annum (APR)
Loan Term: 30 years (360 months)
Monthly Interest Rate = Annual Interest Rate / 12
= 7.1% / 12
= 0.0059
Number of Payments = Loan Term in years * 12
= 30 * 12
= 360
Monthly Mortgage Payment
= (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))
Plugging in the values:
[tex]= (100,000 * 0.0059) / (1 - (1 + 0.0059)^{-360})[/tex]
= $664.14
B) Combined Monthly Payment:
Combined Monthly Payment
= Monthly Mortgage Payment + Monthly Maintenance Fee
= $664.14 + $310
= $974.14
Therefore,
Linda's monthly mortgage payment will be approximately $664.14.
Linda's combined monthly payment, including the mortgage and maintenance fee, will be $974.14.
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A) Linda's monthly mortgage payment is approximately $672.03.
B) Linda's combined monthly payment is approximately $982.03.
To determine Linda's monthly mortgage payment and her combined monthly payment, we can use the following steps:
A) Calculating the Monthly Mortgage Payment:-
We use the formula for the monthly mortgage payment on a fixed-rate mortgage:
[tex]\[ M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1} \][/tex]
Where:
- ( M ) is the monthly mortgage payment.
- ( P ) is the loan principal (amount borrowed), which is $100,000.
- ( r ) is the monthly interest rate, which is the annual rate divided by 12.
- ( n ) is the total number of payments (loan term in years multiplied by 12 months per year).
Given:
- [tex]\( P = 100,000 \)[/tex]
- Annual interest rate (APR) = 7.1% or 0.071
- Monthly interest rate [tex]\( r = \frac{0.071}{12} \approx 0.0059167 \)[/tex]
- Loan term ( n = 30 ) years, which is [tex]\( 30 \times 12 = 360 \)[/tex] months.
Substitute these values into the formula:
[tex]\[ M = 100,000 \times \frac{0.0059167(1 + 0.0059167)^{360}}{(1 + 0.0059167)^{360} - 1} \][/tex] = $672.03.
B) Calculating the Combined Monthly Payment
The combined monthly payment is the sum of the monthly mortgage payment and the monthly maintenance fee.
Given:
- Monthly maintenance fee = $310
So, the combined monthly payment ( C ) will be:
[tex]\[ C = M + 310 \][/tex]
Let's compute these values.
A) Monthly Mortgage Payment
Linda's monthly mortgage payment is approximately $672.03.
B) Combined Monthly Payment
To find the combined monthly payment, we add the monthly mortgage payment and the monthly maintenance fee:
[tex]\[ \text{Combined Monthly Payment} = 672.03 + 310 = 982.03 \][/tex]
Therefore, Linda's combined monthly payment is approximately $982.03.
If a ladder leans against a house and is 25 meters long, and the base of the ladder is 7 meters from the house, how many meters is the window to the ground.
Answer:
24 meters
Step-by-step explanation:
The Pythagorean theorem can be used to find the missing leg of the right triangle.
AB² = BC² +AC²
25² = 7² +AC²
AC = √(625 -49) = √576
AC = 24
The height to the top of the ladder is 24 meters.
In 2007, a census counted 2814 of a certain animal. This was 302 fewer than the number counted in 2006. What was the population of the animal in 2006?
The population of the animal in 2006 was
nothing. (Simplify your answer.)
La compañía XX usa cuatro empresas de transporte: A1, A2 , A3 y A4 . Se sabe que 15% de los embarques se asignan a la empresa A1 , 30% a la A2 , 35% a la A3 y 20% a la A4 . Los embarques llegan retrasados a sus clientes en 7% si los entrega A1 , 8% si es A2 , 5% si es A3 y 9% si es A4 . Si sabemos que el embarque de hoy fue entregado con retraso,
¿cuál es la probabilidad de que haya sido la empresa A1 la encargada de hacerlo?
Answer:
[tex]P(E1/R)= 0.15[/tex]
Step-by-step explanation:
Hola!
La comañía en cuestión usa 4 empresas de transporte para realizar envios. Llamemos "E" al evento de que la empresa haya sido seleccionada para un envío:
E1: La empresa A1 realiza el envío ⇒ P(E1)= 0.15
E2: La empresa A2 realiza en envío ⇒ P(E2)= 0.30
E3: La empresa A3 realiza el envío ⇒ P(E3)= 0.35
E4: La empresa A4 realiza el envío ⇒ P(E4)= 0.20
Y también conoces las probabilidades de que un envío llegue con retraso, sabiendo cual es la empresa que realizó el envío. Llamemos "R" al evento que el envío llegó con retraso. Las probabilidades mencionadas son condicionales y se simbolizan de la siguiente manera:
P(R/E1)= 0.07
P(R/E2)= 0.08
P(R/E3)= 0.05
P(R/E4)= 0.09
Tienes que calcular la probabilidad de que un embarque que ha sido entregado con retraso, haya sido enviado por la empresa A1.
Esta probabilidad también es condicional, queremos saber la probabilidad de E1 sabiendo que ya ha pasado R, se simboliza de la siguiente manera:
[tex]P(E1/R)= \frac{P(E1nR)}{P(R)}[/tex]
Para poder calcularla necesitas averiguar el valor de la probabilidad de intersección entre E1 y R, P(E1∩R), y el valor de la probabilidad de R, P(R).
La probabilidad de R es una probabilidad marginal y es igual a:
P(R)= P(E1∩R)+P(E2∩R)+P(E3∩R)+P(E4∩R)
Para calcular los valores de las intersecciones debes aplicar la definición de probabilidad condicional:
[tex]P(A/B) = \frac{P(AnB)}{P(B)}[/tex] entonces P(A∩B)= P(A/B)*P(B)
Entonces:
[tex]P(R/E1)= \frac{P(RnE1}{P(E1)}[/tex] ⇒ P(E1∩R)= P(R/E1)*P(E1)= 0.07*0.15= 0.0105
P(E2∩R)= P(R/E2)*P(E2)= 0.08*0.30= 0.024
P(E3∩R)= P(R/E3)*P(E3)=0.05*0.35= 0.0175
P(E4∩R)= P(R/E4)*P(E4)= 0.09*0.20= 0.018
Ahora puedes calcular la probabilidad de que el envío llegue con retraso:
P(R)= 0.0105+0.024+0.0175+0.018= 0.07
Por último queda calcular la probabilidad solicitada:
[tex]P(E1/R)= \frac{0.0105}{0.07}= 0.15[/tex]
Espero que tengas un buen día!
Help! Best Answer = Brainiest!
Answer:
12 = 2.5h + 4
Step-by-step explanation:
The pizza shown has a radius of 14 cm. What is the approximate area of the pizza? (Use 3.14 for
.)
A. 615.44 cm?
B. 43.96 cm?
87.92 cm
1.230.88 cm?
Answer:
A. 615.44 cm²
Step-by-step explanation:
A = pi(r²)
= 3.14(14²)
= 3.14(196)
= 615.44 cm²
Final answer:
To find the approximate area of the pizza with a radius of 14 cm, use the formula for the area of a circle and substitute the given value, resulting in 615.44 cm².
Explanation:
The approximate area of the pizza can be calculated using the formula for the area of a circle:
A = πr²
Given that the radius is 14 cm, we substitute this into the formula:
A ≈ 3.14 x (14 cm)² = 615.44 cm²
Therefore, the approximate area of the pizza is 615.44 cm², which corresponds to option A.
If p is a true statement and q is false, what is the truth value of p ∨ q?
Answer: the value is true
Step-by-step explanation:
What is the first month in which Maria's amount of land exceeds Lucia's amount of land?
Answer:
7th Month
Step-by-step explanation:
The number of hectares of Lucia's land grows arithmetically by 5 hectares each month.
Whereas, the number of hectares of Maria's land grows geometrically with a common ratio of 1.4 every month.
Writing this as sequence expressions:
For Lucia,
First term, a=11 hectares
Common difference, d=5
Therefore:
[tex]T(n)=a+(n-1)d[/tex]
[tex]11+5(n-1)=11+5n-5\\=6+5n[/tex]
For Maria,
First term, a=6 hectares
Commons ratio=1.4
[tex]T(n)=ar^{n-1}\\=6*1.4^{n-1}[/tex]
Next, we compute and compare the results for values of n of these two equations:
[tex]Lucia, T(n)=6+5n[/tex]
[tex]Maria,T(n)=6*1.4^{n-1}[/tex]
[tex]Lucia, T(1)=6+5=11[/tex]
[tex]Maria,T(1)=6*1.4^{1-1}=6[/tex]
[tex]Lucia, T(2)=6+5(2)=16[/tex]
[tex]Maria,T(2)=6*1.4^{2-1}=8.4[/tex]
[tex]Lucia, T(3)=6+5(3)=21[/tex]
[tex]Maria,T(3)=6*1.4^{3-1}=11.76[/tex]
[tex]Lucia, T(4)=6+5(4)=26[/tex]
[tex]Maria,T(4)=6*1.4^{4-1}=16.56[/tex]
[tex]Lucia, T(5)=6+5(5)=31[/tex]
[tex]Maria,T(5)=6*1.4^{5-1}=23.05[/tex]
[tex]Lucia, T(6)=6+5(6)=36[/tex]
[tex]Maria,T(6)=6*1.4^{6-1}=32.27[/tex]
[tex]Lucia, T(7)=6+5(7)=41[/tex]
[tex]Maria,T(7)=6*1.4^{7-1}=45.18[/tex]
Therefore, in the seventh month, Maria's land will exceed that of Lucia.
What number is 62.5% of 195?
Answer:
121.875 if calculated so 121.875 if it shows it or less
Answer:
121.875
Step-by-step explanation:
To find the number you multiple 195 by 0.625 (0.625 is equivalent to 62.5%) which gets you 121.875
Click the prime number cards to build composite numbers to 50.
Answer:
See Explanation
Step-by-step explanation:
A prime number is a number that has only two factors, by 1 and itself.
A composite number on the other hand are numbers which have more than two factors.
To determine the number of prime cards needed to build each composite number, we first express the number as a product of its prime factors.
These are:
4=2X2
6=2X3
8=2X2X2
9=3X3
10=2X5
12=2X2X3
14=2X7
15=3X5
16=2X2X2X2
18=2X3X3
20=2X2X5
21=3X7
22=2X11
24=2X2X2X3
26=2X13
27=3X3X3
28=2X2X7
30=2X3X5
32=2X2X2X2X2
33=3X11
34=2X17
35=5X7
36=2X2X3X3
38=2X19
39=3X13
40=2X2X2X5
42=2X3X7
44=2X2X11
45=3X3X5
46=2X2X13
48=2X2X2X2X3
49=7X7
50=2X5X5
Therefore for each of the numbers, those are the prime number cards to be used.
Take for example, the number 50, the prime numbers that will be used to build 50 are the prime factors of 50.
50=2 X 5 X 5
Therefore, its prime factors are 2 and 5.
We will use the following prime number cards:
1 card with prime number 22 cards with prime number 5A project has four activities (A, B, C, and D) that must be performed sequentially. The probability distributions for the time required to complete each of the activities are as follows: Activity Activity Time (weeks) Probability A 5 0.25 6 0.35 7 0.25 8 0.15 B 3 0.20 5 0.55 7 0.25 C 10 0.10 12 0.25 14 0.40 16 0.20 18 0.05 D 8 0.60 10 0.40 (a) Construct a spreadsheet simulation model to estimate the average length of the project and the standard deviation of the project length. Round your answers to one decimal place. Average Project Length weeks Standard Deviation in Project Length weeks (b) What is the estimated probability that the project will be completed in 35 weeks or less
Answer:
(a)
The average length of the project is 33.9 weeks
The standard deviation of the project length is 2.8 weeks
(b)
The estimated probability that the project will be completed in 35 weeks or less is 0.65
Step-by-step explanation:
(a)
The average length of the project is;
E(P) = E(A+B+C+D)
= 6.3 + 5.1 + 13.7 + 8.8
= 33.9
The standard deviation of the project length;
SD(P) = √V(P)
= √V(A+B+C+D)
= √1.01 + 1.79 + 4.11 + 0.96
= √7.87
= 2.8
(b)
Normal distribution with mean 33.9 weeks and variance of 2.8² weeks.
The estimated probability that the project will be completed in 35 weeks or less is;
[tex]P(P \leq 35) = P( \frac{P-E(P)}{SD(P)} \leq \frac{35-33.9}{2.8} )[/tex]
[tex]P(P \leq 35) = P(z\leq0.3929)[/tex]
= 0.65 → Using Excel command (NORM.S.DIST(0.3929,TRUE))
To estimate the average length and standard deviation of a project, use a spreadsheet simulation model. Calculate the expected completion time and standard deviation for each activity. To find the probability of completing the project in a certain time frame, sum up the probabilities of activities that can be completed within that timeframe.
Explanation:To estimate the average length of the project and the standard deviation of the project length, you can use a spreadsheet simulation model. Here are the steps you can follow:
Create a column for each activity (A, B, C, D) and list the possible time values for each activity.Create another column for the probability for each time value.In a separate column, calculate the product of the time value and its probability for each activity.Sum up the values from step 3 for each activity to get the expected completion time.Calculate the standard deviation using the formula: sqrt(sum of (time value - expected completion time)^2 * probability) for each activity.For part (b), to find the estimated probability that the project will be completed in 35 weeks or less, you'll need to sum up the probabilities of all activities that can be completed within 35 weeks or less.
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The probability that a student guesses the correct answer to a four-choice multiple choice question is
P(correct) = 0.25. How many correct answers should a student expect to guess on a test with 68
four-choice multiple choice questions?
answer asap pls
Since we already know that there is a 25% chance to guess the correct answer to a multiple choice question, all we have to do is multiply .25 and 68 to get the expected amount of answers a student can possibly guess. We multiply .25 since it is the decimal form of 25% and 68 is our total questions.
.25 x 68 = 17
Therefore, a student can expect to guess 17 answers correct on a test with 68 multiple choice questions.
Answer:
the answer is 17
Step-by-step explanation:
Hope this helps!
Solve for X-4 1/6 = 9 1/3
Answer:
13 1/2
Step-by-step explanation:
X-4 1/6 = 9 1/3
Add 4 1/6 to each side
X-4 1/6+ 4 1/6 = 9 1/3 + 4 1/6
x = 9 1/3 + 4 1/6
= 9 2/6 + 4 1/6
13 3/6
13 1/2
multiply (x – 4)(x + 3)
Answer:
x^2-x-12
Step-by-step explanation:
I used the box method its easier than foil method if that helps in the future
Name the constant of proportionality for the equation below:
y = -2/3 x
Answer:
[tex]-\dfrac{2}{3}[/tex]
Step-by-step explanation:
When variable y is said to be proportional to another variable x, it is written as:
[tex]y \propto x[/tex]
To introduce the equality sign, we introduce what is called the constant of proportionality, say k and write the above as:
y=kx
Comparing the given equation:
[tex]y=-\frac{2}{3}x[/tex]
We can see that our constant of proportionality:
[tex]k=-\dfrac{2}{3}[/tex]
A card is selected at random from a deck of 52 playing cards, the probability that a card 2 is selected will be ______________.
a) 13/52
b) 4/52
c) 26/52
d) 20/52
Answer:
b) 4/52
Step-by-step explanation:
Since there are only 4 playing cards in a full deck that are labeled '2', and there are 52 cards in total - then there is a 4 out of 52 chance that a '2' card will be selected!
Answer:
b) 4/52
Step-by-step explanation:
There are only 4 "2" cards in a deck of 52, so you only have a 4/52 chance of pulling one, or about 8%.
hope this helps :)
In 2002, there were 972 students enrolled at Oakview High School. Since then, the number of students has increased by 1.5% each year. Write an exponential function to model the situation, then find the number of students enrolled in 2014. Is this considered growth or decay?
Answer:
[tex]N(t) = 972(1.015)^{t}[/tex]
Growth function.
The number of students enrolled in 2014 is 1162.
Step-by-step explanation:
The number of students in the school in t years after 2002 can be modeled by the following function:
[tex]N(t) = N(0)(1+r)^{t}[/tex]
In which N(0) is the number of students in 2002 and r is the rate of change.
If 1+r>1, the function is a growth function.
If 1-r<1, the function is a decay function.
In 2002, there were 972 students enrolled at Oakview High School.
This means that [tex]N(0) = 972[/tex]
Since then, the number of students has increased by 1.5% each year.
Increase, so r is positive. This means that [tex]r = 0.015[/tex]
Then
[tex]N(t) = N(0)(1+r)^{t}[/tex]
[tex]N(t) = 972(1+0.015)^{t}[/tex]
[tex]N(t) = 972(1.015)^{t}[/tex]
Growth function.
Find the number of students enrolled in 2014.
2014 is 2014-2002 = 12 years after 2002, so this is N(12).
[tex]N(t) = 972(1.015)^{t}[/tex]
[tex]N(12) = 972(1.015)^{12}[/tex]
[tex]N(12) = 1162[/tex]
The number of students enrolled in 2014 is 1162.
The exponential function that models the given situation is [tex]P(t) = 972 \times (1.015)^{t}[/tex]. By 2014, the number of students is approximately 1162, demonstrating growth.
To model the enrollment of students at Oakview High School using an exponential function, we start with the given data:
The initial number of students (P₀) in 2002: 972.
Annual growth rate: 1.5% or 0.015 as a decimal.
The exponential formula is:
[tex]P(t) = P_0 (1 + r)^t[/tex]
where:
P(t) is the population at time t.P₀ is the initial population.r is the growth rate.t is the number of years since the initial year.In our case, the exponential formula will be:
[tex]P(t) = 972 \times (1 + 0.015)^{t}\\P(t) = 972 \times (1.015)^{t}[/tex]
To find the number of students in 2014, calculate t as follows:
t = 2014 - 2002 = 12
[tex]P(12) = 972 \times (1.015)^{12}[/tex]
Compute the result:
P(12) ≈ 972 × 1.195618
P(12) ≈ 1162 students
This is an example of 'growth', as the number of students increases over time.
Why are asymptotes in parenthesis and not brackets
Answer:
Asymptotes, in mathematics, refer to a restriction at the domain set or the range set. It's drawn as a not solid line to indicate, graphically, the values that are not defined to the function.
So, when we express the domain and range sets of a function, we use parenthesis or brackets. In case of having asymptotes we use parenthesis, because that sing indicates an exclusion of the undefined value. On the other hand, the brackets indicates inclusion.
That means, if we use brackets to indicate asymptotes in an interval, that means the value is well defined for the function, which is false.
What is the absolute value of -5.5
Answer:
positive 5.5
Step-by-step explanation:
What is the GCF of 96x5 and 64,27