As the town gets smaller, the population of high school students decreases by 6% each year. The senior class has 160 students now. 7 years will it have about 100 students.
The formula for calculating exponential decay is given by:
P(t) = [tex]P_0 e^{rt}[/tex]
Where,
P(t) = population after t years
[tex]P_0[/tex] = initial populationr = annual decay ratet = time in years
A decay rate refers to the amount of decrease in a population over a given period of time. A negative value indicates that the population is decreasing.
The problem gives that the senior class has 160 students now. In the next year, the population will decrease by 6%. So, the new population will be (1-6%) of the original population.
That is,P(1) = P(0) (1-6%)= P(0) 0.94
Where,
P(0) = 160 is the initial population of the senior class.
P(1) = 160 × 0.94 = 150.4 students in the next year
Similarly, the population after two years is
P(2) = P(1) × 0.94 = 141.4 students
P(3) = P(2) × 0.94 = 133.0 students
P(4) = P(3) × 0.94 = 125.0 students
P(5) = P(4) × 0.94 = 117.5 students
P(6) = P(5) × 0.94 = 110.2 students
P(7) = P(6) × 0.94 = 103.3 students
Since we are interested in the population when it is about 100, it is clear that it will be after 7 years (since it will be less than 100 for the 6th year and more than 100 for the 7th year).
Therefore, the senior class will have about 100 students after 7 years.
For similar question on exponential
https://brainly.com/question/2456547
#SPJ11
Trisha is running a marathon race. She runs the race at a steady pace. She makes a graph to show how far from the finish line she will be as she runs the race.
Answer:
Step-by-step explanation:trisha is running a marathon race she runs th erace at a steady pace she makes a graph to show how far from the finsh line she will be as she runs the race
=2
The alphabet of jumbo jumbo tribe consists of 4 letters a word in their language is any sequence of five or fewer letters, how many words are there in the language of mumbo jumbo tribe
The total number of words with 5 or les sletters is 1,364
How many words are there in the language of mumbo jumbo tribe?We want to see how many words of 5 or less letters can be done with 4 different characters.
There are 4 words with one letter.
Now words with two letters, suppose that the word is represented by:
_,_
Each blank represents a letter, so we have 4 options per blank, then the number of words with two letters is 4*4 = 16
And with 3 is 4*4*4 = 64
And with 4 is 4*4*4*4 = 256
And finally,with 5 is: 4*4*4*4*4 = 1,024
The total sum gives:
4 + 16 + 64 + 256 + 1,024 = 1,364
These is the number of words.
Learn more about counting at:
https://brainly.com/question/31175912
#SPJ1
Jerry had 35 rabbit stickers. he split the stickers evenly among 7 pieces of paper. how many stickers did jerry put on each piece of paper?
Answer:
5
Step-by-step explanation:
You have to divide 35 by 7.
35/7 is 5.
So, he puts 5 stickers on each paper.
How do I solve: [tex](\frac{1}{216})^{3v-1} =(\frac{1}{6})^{2v-2}[/tex]
(Please work it out step-by-step, if you can)
Answer:
Step 1: Simplify the exponents on both sides of the equation. Recall that (a^b)^c = a^(b*c), so we can write:
(1/216)^(3v-1) = (1/6)^(2v-2)
= (6^-1)^(2v-2) (since 1/6 = 6^-1)
= 6^(-(2v-2)) (since (a^-b) = 1/(a^b))
= 6^(2-2v) (since -(2v-2) = -2v + 2)
Step 2: Rewrite 1/216 as a power of 6. We have:
1/216 = 6^(-3)
Substituting this into our equation gives:
6^(-3(3v-1)) = 6^(2-2v)
Step 3: Use the property that if a^x = a^y, then x = y. Since both sides of the equation have the same base (6), we can equate the exponents:
-3(3v-1) = 2-2v
Step 4: Solve for v. First, simplify the left-hand side of the equation:
-3(3v-1) = -9v + 3
Now we can rewrite the equation as:
-9v + 3 = 2 - 2v
Step 5: Solve for v. Add 9v to both sides and subtract 2 from both sides:
-7v = -1
Finally, divide both sides by -7 to obtain:
v = 1/7
Therefore, the solution to the equation is v = 1/7.
VerificationTo verify that v = 1/7 is the solution to the equation:
(1/216)^(3v-1) = (1/6)^(2v-2)
We can substitute v = 1/7 into the equation and simplify both sides to see if they are equal:
Left-hand side:
(1/216)^(3v-1) = (1/216)^(3(1/7)-1) = (1/216)^(2/7)
Right-hand side:
(1/6)^(2v-2) = (1/6)^(2(1/7)-2) = (1/6)^(-10/7) = (6/1)^10/7
Simplifying:
(1/216)^(2/7) = (6/1)^(10/7)
Taking the seventh root of both sides:
1/6 = 1/6
Since both sides of the equation are equal, we have verified that v = 1/7 is the solution to the equation.
The simple intrest owed on a loan of 5,600after 4 years is 1,008 what percent reprsents the annual in intrest rate on the loan
The annual interest rate on the loan is 4.5% using simple interest formula and concepts.
To calculate the annual interest rate on the loan, we need to use the simple interest formula:
Simple Interest = (P × r × t) / 100
P stands for principal, r stands for annual interest rate, and t stands for time in years.
Given principal amount is $5,600, the simple interest earned after 4 years is $1,008. Therefore, we can plug in values into formula and solve for r:
$1,008 = (5,600 × r × 4) / 100
Multiply LHS and RHS by 100 and divide by 5,600 × 4, we will obtain:
r = $1,008 / $22400 = 0.045 or 4.5%
Hence, the annual interest rate on the loan is 4.5%.
It is significant to remember that simple interest does not compound and has a linear relationship to time. This indicates that the interest charged on the loan is the same each year and does not compound. Short-term loans and personal loans frequently employ simple interest. However, compound interest, which takes into account the cumulative interest over time, is utilised for long-term loans such as mortgages. To make wise financial decisions, it is crucial to comprehend the distinction between simple and compound interest.
Learn more about simple interest here:
https://brainly.com/question/8100492
#SPJ4
The value of a book is $258 and decreases at a
rate of 8% per year. Find the value of the book
after 11 years.
Answer:
The value of the book after 11 years is $103.11
The equation should be 258*0.92, 11 times repeating.
The answer should be 103.106443494, but if you round it the answer is 103.11
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &258\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &11\\ \end{cases} \\\\\\ A = 258(1 - 0.08)^{11} \implies A=258(0.92)^{11}\implies A \approx 103.11[/tex]
2.5 * 10^5 ____ 4.2 * 10^-7
i need to compare these
Answer: 250,000 > .00000042
Step-by-step explanation:
2.5 times 10^5 means move the decimal to the right 5 times.
2.5
1. 25.
2. 250.
3. 2,500.
4. 25,000.
5. 250,000.
250000 __ 4.2 times 10^-7
10^-7 would mean move the decimal to the left that many times.
4.2
1. .42
2. .042
3. .0042
4. .00042
5. .000042
6. .0000042
7. 00000042
250,000 > .00000042
What are the solutions to the system of conics?
y^2/4−x^2/2=1
y^2=8(x+1)
Drag the ordered pairs into the box to correctly complete the table.
The cοmplete table with the οrdered pairs is:
(2-√6,2√(6-2√6)) (2+√6,2√(6-2√6)) (2+√6,-2√(6-2√6))
(2-√6,2√(6+2√6)) (2+√6,-2√(6+2√6)) (2+√6,2√(6+2√6))
What is quadratic equatiοn?A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn in οne variable οf the fοrm: [tex]ax^2 + bx + c = 0.[/tex]
Tο find the sοlutiοns tο the system οf cοnics, we can use substitutiοn tο eliminate οne variable and οbtain a quadratic equatiοn in the οther variable. Then, we can sοlve this quadratic equatiοn tο find the pοssible values οf the remaining variable.
Frοm the given system οf cοnics:
[tex]y^2/4 - x^2/2 = 1 ...(1)[/tex]
[tex]y^2 = 8(x + 1) ...(2)[/tex]
We can eliminate [tex]y^2[/tex] frοm equatiοn (1) by multiplying bοth sides by 4:
[tex]y^2 - 2x^2 = 4[/tex]
Substituting the value οf [tex]y^2[/tex] frοm equatiοn (2), we get:
[tex]8(x + 1) - 2x^2 = 4[/tex]
Simplifying and rearranging, we get:
[tex]x^2 + 2x - 2 = 0[/tex]
We can sοlve this quadratic equatiοn using the quadratic fοrmula:
[tex]x = (-2 \± \sqrt{(2^2 - 4(1)(-2))}) / (2(1))[/tex]
x = (-2 ± √12) / 2
x = -1 ± √3
Substituting these values οf x in equatiοn (2), we can find the cοrrespοnding values οf y:
When x = -1 + √3, we get:
[tex]y^2[/tex] = 8((-1 + √3) + 1) = 8√3
y = ±2√(2√3)
Therefοre, the sοlutiοns are:
(-1 + √3, 2√(2√3)) and (-1 + √3, -2√(2√3))
When x = -1 - √3, we get:
[tex]y^2[/tex] = 8((-1 - √3) + 1) = -8√3
This equatiοn has nο real sοlutiοns fοr y.
Therefοre, the cοmplete table with the οrdered pairs is:
(2-√6,2√(6-2√6)) (2+√6,2√(6-2√6)) (2+√6,-2√(6-2√6))
(2-√6,2√(6+2√6)) (2+√6,-2√(6+2√6)) (2+√6,2√(6+2√6))
To learn more about quadratic equation from the given link:
https://brainly.com/question/17177510
#SPJ1
Write a story problem to go with the multiplication problem 3 x 7/8. Then, solve the problem.
Answer:
Step-by-step explanation:
Story Problem:
Samantha is baking cookies and her recipe calls for 3 cups of flour. She only has a bag of flour that is 7/8 full. If each cup of flour weighs the same, how much flour does Samantha have left after taking out the 3 cups needed for the recipe?
Solution:
To solve the problem, we need to multiply the amount of flour in the bag by 3/1 (which is the same as multiplying by 3).
3 x 7/8 = (3 x 7)/8 = 21/8
So, Samantha has 21/8 cups of flour in the bag.
To find out how much flour she has left after taking out the 3 cups needed for the recipe, we need to subtract 3 from 21/8:
21/8 - 3 = 21/8 - 24/8 = -3/8
Samantha has -3/8 cups of flour left in the bag, which means she doesn't have enough flour to make the recipe. She needs to get more flour before she can continue baking.
Answer:
Look below
Step-by-step explanation:
Ken drinks 7/8 of a carton of milk each day. How much milk does
he drink in 3 days?
7/8*3
21/8
2 5/8 cartons of milk a day
Rachael has a life insurance
policy that will pay her family
$45,000 per year if she dies.
Rachael's insurance company
expects that it would have to pu
$2,500,000 into a bank account
so that it could make the
payments. What does Rachael's
insurance company expect the
interest rate to be?
The insurance company expects the interest rate to be around 4.16%.
How to find determine Rachael's insurance company expect the interest rate to be?To find the expected interest rate, we can use the formula for present value of an annuity:
PV = PMT x (1 - (1 + r)^(-n)) / r
Where:
PV = present value of the annuity, which is the amount the insurance company needs to deposit
PMT = payment per period, which is $45,000
r = interest rate per period, which is what we need to find
n = total number of periods, which is unknown
We know that the insurance company needs to deposit $2,500,000 to make the payments, so we can set:
PV = $2,500,000:
$2,500,000 = $45,000 x (1 - (1 + r)^(-n)) / r
To solve for r, we can use trial and error or an iterative method. Here, we'll use trial and error.
Let's assume n = 20, which is a reasonable number of years for an insurance policy. Then we can solve for r:
$2,500,000 = $45,000 x (1 - (1 + r)^(-20)) / r
$2,500,000r = $45,000 x (1 - (1 + r)^(-20))
(1 + r)^(-20) = 1 - ($45,000 / $2,500,000) x r
1 + r = (1 - ($45,000 / $2,500,000) x r)^(-1/20)
r ≈ 0.0416 or 4.16%
Therefore, the insurance company expects the interest rate to be around 4.16%.
Learn more about interest rate at https://brainly.com/question/25793394
#SPJ1
z varies directly as x^2. If z= 8 when x= 2, find z when x= 6.
Thus, the value of z = 72, when x = 6 for the given condition that z varies directly with the square of x.
Define about the direct proportion:The connection among two variables is known as a direct proportion when their ratios are comparable to a fixed value.
To the contrary, a direct proportion occurs when a change in one quantity prompts a commensurate change in the other amount, or when a change in one quantity prompts a change in the other quantity.The proportional sign (∝) is used to represent a direct proportion. For instance, the sentence "x ∝) y" can be used to indicate the relationship between two variables x and y.Given data:
z varies directly as x².
z= 8 when x= 2.
So,
z ∝ x²
z = k x²
k = z/ x² (k is the constant of proportionality)
z= 8 when x= 2.
k = 8/(2)²
k = 2
Now, when x = 6
z = k x²
z = 2 * (6)²
z = 72
Thus, the value of z = 72, when x = 6 for the given condition that z varies directly with the square of x.
Know more about the direct proportion
https://brainly.com/question/29864115
#SPJ1
1. Use the following information and the map of downtown Seattle to answer questions one and two. Harrison St, Thomas St, and Denny Way are parallel. On Broad St, the distance between Mercer St and Denny Way is 0.7 miles. The distance between those same streets on Aurora Ave is 0.45 miles.
a) On Aurora Ave the distance between Thomas St to Denny Way is 0.2 miles. What is the distance
between these two streets on Broad St? Round your answer to the nearest tenth of a mile.
The distance between these two streets on Broad St is 0.3 miles.
We can use proportions to solve the problem.
Let's assume x is the distance between Thomas St and Denny Way on Broad St.
We know that on Aurora Ave, the distance between Thomas St and Denny Way is 0.2 miles, and on Broad St, the distance between Mercer St and Denny Way is 0.7 miles.
So, we can set up the following proportion:
0.2/0.45 = x/0.7
Simplifying, we get:
x = (0.2/0.45) * 0.7
x = 0.3111 miles
Rounded to the nearest tenth, the distance between Thomas St and Denny Way on Broad St is 0.3 miles.
For such more question on distance:
https://brainly.com/question/28551043
#SPJ11
the Midpoint for the coordinates (3, -8) and (-9, -11)
three points on the graph of the function f(x) are {(0,4), (1,10) (2,25)}. Which equation represents f(x)?
The equation that represents f(x) is f(x) = [tex]3x^2[/tex] + 3x + 4. To determine the equation that represents the function f(x) based on the given points, we can use the general form of a quadratic function:
f(x) =[tex]ax^2[/tex]+ bx + c
where a, b, and c are constants that we need to determine. We can use the given points to form a system of equations:
[tex]a(0)^2[/tex] + b(0) + c = 4 -- Equation 1
[tex]a(1)^2[/tex] + b(1) + c = 10 -- Equation 2
[tex]a(2)^2[/tex] + b(2) + c = 25 -- Equation 3
Simplifying each equation, we get:
c = 4 -- Equation 1a
a + b + c = 10 -- Equation 2a
4a + 2b + c = 25 -- Equation 3a
Substituting Equation 1a into Equation 2a and Equation 3a, we get:
a + b = 6 -- Equation 2b
4a + 2b = 21 -- Equation 3b
Solving for b in terms of a in Equation 2b, we get:
b = 6 - a
Substituting b = 6 - a into Equation 3b, we get:
4a + 2(6 - a) = 21
Simplifying and solving for a, we get:
a = 3
Substituting a = 3 into b = 6 - a, we get:
b = 3
Substituting a = 3 and b = 3 into Equation 1a, we get:
c = 4
Therefore, the equation that represents f(x) is:
f(x) = [tex]3x^2[/tex] + 3x + 4
This quadratic function passes through the given points {(0,4), (1,10), (2,25)}, as can be verified by plugging in the x-values of each point into the equation and checking that the y-values match.
Learn more about quadratic function here:
https://brainly.com/question/18958913
#SPJ1
The value of x is__?
The measure of is angle 1 is__?
The measure of angle 2 is __?
The measure of angle 3 is __?
The measure of angle 4 is __?
The measure of angle 5 is __?
The measure of angle 6 is __?
The measure of angle 7 is __?
The measure of angle 8 angles 2 and 3 are____ angles.
The value of x is 24
The measure of is angle 1 is 101°
The measure of angle 2 is 79°
The measure of angle 3 is 101°
The measure of angle 4 is 101°
The measure of angle 5 is 79°
The measure of angle 6 is 79°
The measure of angle 7 is 101°
The measure of angle 8 is 79°
What are angles on a parallel line?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
3x +19 = 5x-29 ( opposite angle)
collect like terms
5x-3x = 29+19
2x = 48
x = 24
angle 1 = 180-(3×24+7)
= 180- 79
= 101°
angle 2 = 3x+7 = 79°( opposite angles)
angle 3 = 101° ( opposite angles)
angle 4 = angle 1 = 101° ( corresponding angles)
angle 5 = 79° ( corresponding angles)
angle 6 = angle 5 = 79°( opposite angle)
angle 7 = angle 4 = 101 ( corresponding angles)
angle 8 = angle 7 = 79 ( opposite angle )
learn more about angle on parallel lines from
https://brainly.com/question/24607467
#SPJ1
Rewrite each equation without absolute value for the given conditions y=|x-3|+|x+2|-|x-5| if 3
Two families go to a movie on Saturday night. The Jefferson family purchases 2 adult tickets and 2 youth tickets for $42. 50. The Mendoza family purchases 4 adult tickets and 3 youth tickets for 76. 25 dollars
The cost of one adult tickets would be $12.5 and the cost of one youth tickets would be $8.75 .Therefore the cost of six adult tickets and eight youth tickets would be 6(12.5) + 8(8.75) = $145.
Let the cost of adult tickets be x.
Let the cost of youth tickets be y.
So, from the given condition given in question the equations are :-
For The Jefferson family,
2x + 2y = 42.50
x + y = 21.25 —---------- equation(1)
and for The Mendoza family,
4x + 3y = 76.25 —------ equation(2)
To solve above equation 4 × equation(1) - equation(2).
y = 8.75
and x = 12.5
Hence the cost of one adult tickets would be $12.5 and the cost of one youth tickets would be $8.75 .
Therefore the cost of six adult tickets and eight youth tickets would be 6(12.5) + 8(8.75) = $145.
Visit here to learn more about the equations: https://brainly.com/question/10413253
#SPJ4
—-------- Correct question format is given below —--------
(Q). Two families go to a movie on Saturday night. The Jefferson family purchases 2 adult tickets and 2 youth tickets for $42.50. The Mendoza family purchases 4 adult tickets and 3 youth tickets for $76.25. How much would it cost to purchase six adult tickets and eight youth tickets?
whats 1 4/6 as a improper fraction
Answer:
1 4/6 as an improper fraction is 5/3
Step-by-step explanation:
What is an improper fraction?
An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
How do you convert a mixed number to an improper fraction?
To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and add the numerator. Then, you put that sum over the denominator.
For example, 1 4/6 can be converted to an improper fraction as follows:
1 x 6 + 4 = 10
10/6 = 5/3
So, 1 4/6 as an improper fraction is 5/3.
a manufacturer knows that their items have a normally distributed length, with a mean of 14.7 inches, and standard deviation of 4.8 inches. if 25 items are chosen at random, what is the probability that their mean length is less than 12.4 inches?
The probability that the mean length of the 25 items is less than 12.4 inches is approximately 0.0009
We can solve this problem by using the Central Limit Theorem (CLT), which states that the sample mean of a large enough sample size from any distribution with a finite mean and variance will follow a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, the population mean is 14.7 inches, the population standard deviation is 4.8 inches, and the sample size is 25. Thus, the mean of the sample means is also 14.7 inches, and the standard deviation of the sample means is 4.8 inches / sqrt(25) = 0.96 inches.
To find the probability that the mean length of the 25 items is less than 12.4 inches, we can standardize the sample mean using the z-score formula
z = (x - mu) / (sigma / sqrt(n))
where x is the sample mean we want to find the probability of (in this case, 12.4 inches), mu is the population mean (14.7 inches), sigma is the population standard deviation (4.8 inches), and n is the sample size (25).
Substituting these values, we get
z = (12.4 - 14.7) / (4.8 / sqrt(25)) = -3.13
We can then use a standard normal distribution table or calculator to find the probability that a standard normal variable is less than -3.13, which is approximately 0.0009.
Learn more about probability here
brainly.com/question/29677848
#SPJ4
expedia would like to test if the average round-trip airfare between philadelphia and dublin is less than $1,200. the correct hypothesis statement would be
The correct hypothesis statement in this case would be "The average round-trip airfare between Philadelphia and Dublin is less than $1,200".
The hypothesis statement for the test of the average round-trip airfare between Philadelphia and Dublin being less than $1,200 would be “The average round-trip airfare between Philadelphia and Dublin is less than $1,200”.What is hypothesis?A hypothesis is a suggested explanation for a phenomenon or a theory that is tested using various experiments.
It is the first step in research that aids in forming a research question and establishes a framework for the study.The hypothesis statement:In hypothesis testing, the hypothesis statement is a declarative statement or an assertion that specifies the existence or non-existence of a phenomenon. In hypothesis testing, there are two hypothesis statements: null hypothesis and alternative hypothesis.
The null hypothesis would be that the average round-trip airfare between Philadelphia and Dublin is equal to or greater than $1,200. The alternative hypothesis would be that the average round-trip airfare between Philadelphia and Dublin is less than $1,200.
Learn more about Hypothesis
brainly.com/question/29519577
#SPJ11
Solve For X Question 1
Answer:
x=52
Step-by-step explanation:
Set equal to 180
x-30+3x+2=180
solve for x
4x-28=180
4x=208
x=52
plug in to check
The gas tank in Karla’s car holds 12 gallons of gas. Can Karla drive 360 miles without having to stop and buy more gas?
Answer:
she would have to go 30 miles per hour or less to make this possible
Step-by-step explanation:
if it went over 35 31 miles per hour they would run out of gas before they got there
Find the frequency with the largest amplitude Find the frequency w for which the particular solution to the differential equation dạy dy 2- + dt2 + 2y = eiwt dt has the largest amplitude. You can assume a positive frequency w > 0. Probably the easiest way to do this is to find the particular solution in the form Aeiwt and then minimize the modulus of the denominator of A over all frequencies w. W= number (rtol=0.01, atol=1e-08) ?
The frequency with the largest amplitude is `w ≈ 2.303` (rtol=0.01, atol=1e-08).
The question asks us to find the frequency w for which the particular solution to the differential equation [tex]dạy dy 2- + dt2 + 2y = eiwt dt[/tex]has the largest amplitude.
We can assume a positive frequency w > 0.
Let's find out how to solve this problem:
We need to find the particular solution in the form Aeiwt, and then minimize the modulus of the denominator of A over all frequencies w. It means the denominator of A will have a maximum amplitude if we minimize the modulus. The amplitude of the solution is given by the value of |A|.
Let us assume the particular solution to be `[tex]y = Aeiwt`.[/tex]
Substitute the above solution in the given differential equation.
Then, we get:[tex]`d^2(A e^(iwt))/dt^2 + 2(A e^(iwt)) = e^(iwt)`[/tex]Applying the differential operator on the above equation,
we get: [tex]`(iwt)^2 A e^(iwt) + 2A e^(iwt) = e^(iwt)`Therefore, `A = 1 / (1 - (w^2) + 2i)`.[/tex]
Thus, the amplitude of the particular solution is:
[tex]`|A| = 1 / sqrt((1 - w^2)^2 + 4w^2)`[/tex]
Now, we need to minimize the above expression to get the frequency w at which the amplitude of the particular solution is maximum. This can be done by minimizing the modulus of the denominator of A over all frequencies w.To minimize the above expression, we take the derivative of the expression with respect to w and equate it to zero, which gives us: [tex]`(8w^2) / ((w^2 - 1)^2 + 4w^2)^(3/2) - (2(w^2 - 1)) / ((w^2 - 1)^2 + 4w^2)^(3/2) = 0`[/tex]
Simplifying the above expression, we get: `
[tex]2w^2 = w^4 - 3w^2 + 1`[/tex]
Therefore, [tex]`w^4 - 5w^2 + 1 = 0`.[/tex]
Solving the above equation gives us:
`[tex]w^2 = (5 ± sqrt(21)) / 2`[/tex].Since we know that w > 0, we choose the positive value of w.
Thus, the value of w is: [tex]`w = sqrt((5 + sqrt(21)) / 2)` or `w ≈ 2.303[/tex]`.
for such more question on frequency
https://brainly.com/question/26146342
#SPJ11
So, the bounce heights form a geometric sequence: 27, 18, 12. Two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet.
In this case, the bounce heights form a geometric sequence with a common ratio of 2/3. , the ball reaches a height of [tex]8[/tex] feet on the third bounce,
What is the geometric sequence?The definition of a geometric sequence is a set of numbers where each term is created by multiplying the preceding term by a fixed factor.
If the bounce heights form a geometric sequence with common ratio "r", we can write:
27 = initial height
[tex]18 = 27r[/tex]
[tex]12 = 18r = 27 \times r^2[/tex]
Solving for "r", we get:
[tex]r = 2/3[/tex]
So, the fourth bounce height would be:
[tex](12) \times (2/3) = 8[/tex]
Therefore, the ball reaches a height of 8 feet on the third bounce, not the fourth bounce as stated in the original statement.
Learn more about geometric here:
https://brainly.com/question/13008517
#SPJ9
How do you do this step by step please thank uu
The value for the given expression is 60.
What is a Quadratic Function?The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
The exercise asks the value of the given expression a²-4a, for a=10. Thus, you should replace the variable a with the number 10. See below.
a²-4a
10²-4*10
100-40=60
Read more about the quadratic function here:
brainly.com/question/1497716
#SPJ1
A(-6,3), B(2,5) and C(0,-5) form a triangle. D is the midpoint of BC.
(a)Find the values of AC², AB², AD² and DC².
(b)Hence show that AC² + AB²= 2(AD² + DC²).
After answering the provided question, we can conclude that triangle 2(AD² + DC²) = 2(58 + 26) = 168
What precisely is a triangle?A triangle is a locked, double-symmetrical target made up of 3 line segments known as sides that interlock at three points known as vertices. Triangles are distinguished by their sides and angles. Triangles can be rectangular prism (all factions equal), ellipse, or scalene based on their sides. Triangles are classified as acute (all angles are under 90 degrees), okay (one angle is equal to 90 degrees), or orbicular (all angles are greater than 90 ° c) (all angles greater than 90 degrees). The continent of a triangle can be calculated using the formula A = (1/2)bh, where an is the suburb, b is the triangle's base, and h is the triangle's height.
(a) The distance formula is:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Length of AB:
AB = √[(2 - (-6))² + (5 - 3)²] = √64 = 8
Length of AC:
AC = √[(0 - (-6))² + (-5 - 3)²] = √100 = 10
Length of BC:
BC = √[(2 - 0)² + (5 - (-5))²] = √144 = 12
Midpoint of BC:
D = [(0 + 2)/2, (-5 + 5)/2] = (1, 0)
Length of AD:
AD = √[(1 - (-6))² + (0 - 3)²] = √58
Length of DC:
DC = √[(1 - 0)² + (0 - (-5))²] = √26
Now we can find the values of AC², AB², AD², and DC²:
AC² = AC² = 100
AB² = AB² = 64
AD² = AD² = 58
DC² = DC² = 26
(b) AC² + AB² = 2(AD² + DC²).
AC² + AB² = 100 + 64 = 164
2(AD² + DC²) = 2(58 + 26) = 168
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
Heidi swims 50 meters at an average speed of 1.25 meters per second
How many seconds did it take her?
Answer: 62.5 would be the answer.
Step-by-step explanation: You have to multiply how many meters per second by the whole total meters.
50x1.25=62.5.
*********************************************************************************************
Hope this helps! ^^
Select all that apply. help
NR = QR: This statement is true. In a rhombus, the diagonals bisect each other, so NR is equal in length to QR.
What is Rhombus ?
A rhombus is a quadrilateral with four equal-length sides. The opposite angles of a rhombus are equal to each other, and the diagonals bisect each other at right angles. This means that the diagonals of a rhombus are perpendicular to each other and divide the rhombus into four congruent right triangles.
From the given information, we know that MNPQ is a rhombus, and that NQ and PM are diagonals that intersect at point R.
NQ is perpendicular to MP: This statement is false. In a rhombus, the diagonals are perpendicular bisectors of each other, so we know that NQ is perpendicular to PM at point R, but not necessarily to the entire diagonal MP.
NP is perpendicular to QP: This statement is also false. In a rhombus, opposite sides are parallel and congruent, but not necessarily perpendicular to each other.
NR = QR: This statement is true. In a rhombus, the diagonals bisect each other, so NR is equal in length to QR.
Angle MNQ is congruent to angle PNQ: This statement is false. While we know that NQ is perpendicular to PM at point R, we cannot conclude that angle MNQ is congruent to angle PNQ. In fact, there is not enough information given to determine the measure of either angle.
Learn more about Rhombus here
https://brainly.com/question/8900765
#SPJ1
a sample of 1200 computer chips revealed that 53% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature claimed that more than 50% do not fail in the first 1000 hours of their use. is there sufficient evidence at the 0.10 level to support the company's claim? state the null and alternative hypotheses for the above scenario.
The null hypothesis is that the proportion of computer chips that do not fail in the first 1000 hours of use is equal to 50%. The alternative hypothesis is that the proportion is greater than 50%.
At the 0.10 level of significance, we will reject the null hypothesis if the test statistic is greater than 1.28. The test statistic can be calculated using the formula:
[tex]z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$[/tex]
where [tex]\hat{p}$[/tex] is the sample proportion, [tex]p_0$[/tex] is the hypothesized proportion under the null hypothesis, and $n$ is the sample size.
In this case, we have [tex]\hat{p} = 0.53$, $p_0 = 0.50$, and $n = 1200$.[/tex] Substituting these values into the formula, we get:
[tex]z = \frac{0.53 - 0.50}{\sqrt{\frac{0.50(1-0.50)}{1200}}} = 2.77$[/tex]
Since the test statistic is greater than 1.28, we reject the null hypothesis and conclude that there is sufficient evidence at the 0.10 level to support the company's claim that more than 50% of computer chips do not fail in the first 1000 hours of their use.
Therefore, the null hypothesis is equal to 50%, and the alternative hypothesis is 50%. The test statistic is 2.77, which is greater than the critical value of 1.28 at the 0.10 level of significance, so we reject the null hypothesis and conclude that there is sufficient evidence to support the company's claim.
To know more about null hypothesis, refer here:
https://brainly.com/question/30535681#
#SPJ11
Answer the question below in the screenshot, thanks! (please answer quickly, I'm on edge so I can't move on!)
The exact answer on Edge is
"Use the product of powers property to simplify the numerator by removing the parentheses. Follow the order of operations by removing the innermost parentheses first. Cube the quantity to get the product of 2 to the third power, r to the 6th power, and t to the third power, or 2^3r^6t^3 in the numerator. "