The lake is 12,250 feets deep.
The elevation is changing in the downward direction and at a rate of -11ft/s.
So it means that the downward velocity of the probe is 11ft/s.
The value of downward acceleration is 9.8?m/s² which is equal to acceleration due to gravity.
The total time taken to reach down is 50seconds.
We can use the equation of motion because the acceleration is constant,
Using,
S = ut + 1/2at²
Where,
S is the depth of the pool,
U is initial velocity,
U is zero because the probe is dropped.
S = 1/2at²
S = 1/2××9.8×50×50
S = 12250 feets.
To know more about equation of motion, visit,
https://brainly.com/question/25951773
#SPJ1
what is the answer?
If y = -3 cos (2x), then derivative d²y / dx² is 12 cos (2x)
Given,
y = -3 cos (2x)
We have to find derivative d²y / dx²
d²y / dx² = -3 (d² cos x / dx²) = -3 d/dx (d cos 2x / dx)
According to the concept:
d cos x / dx = - sin x
Here,
d cox 2x / dx = - sin 2x
So,
d²y / dx² = (- 3 × 2) d/dx (- sin 2x)
d²y / dx² = -6 (d sin 2x / dx)
d²y / dx² = 2 × 6 cos 2x
d²y / dx² = 12 cos (2x)
That is, if y = -3 cos (2x), then derivative d²y / dx² is 12 cos (2x)
Learn more about derivative here:
https://brainly.com/question/28225159
#SPJ1
there are 60 mintnutes in one hour and 60 seconds in one minute using this imformation explain how you could convert 20 miles per hour to feet per second
Unit analysis is a helpful tool we can use to convert units.
All we have to do is multiply the original value by a fraction, to cancel out the units that we don't want.
Solving the QuestionWe're given:
Change [tex]\dfrac{20\hspace{4}miles}{hour}[/tex] to [tex]\dfrac{x\hspace{4}feet}{second}[/tex]There are a couple things we need to know before we tackle this question:
5280 in 1 mile: [tex]\dfrac{5280\hspace{4}feet}{mile}[/tex]60 seconds in 1 minute: [tex]\dfrac{60\hspace{4}seconds}{minute}[/tex]60 minutes in 1 hour: [tex]\dfrac{60\hspace{4}minutes}{hour}[/tex]Step 1 ⇒ Multiply [tex]\dfrac{20\hspace{4}miles}{hour}[/tex] by [tex]\dfrac{5280\hspace{4}feet}{mile}[/tex] to change miles to feet:
[tex]\dfrac{20\hspace{4}miles}{hour}\times\dfrac{5280\hspace{4}feet}{mile}\\\\= \dfrac{20\times5280\hspace{4}feet}{hour}\\\\= \dfrac{105600\hspace{4}feet}{hour}[/tex]
Step 2 ⇒ Multiply [tex]\dfrac{105600\hspace{4}feet}{hour}[/tex] by [tex]\dfrac{hour}{60\hspace{4}minutes}[/tex] to change hours to minutes:
[tex]\dfrac{105600\hspace{4}feet}{hour}\times\dfrac{hour}{60\hspace{4}minutes}\\\\=\dfrac{105600\hspace{4}feet}{60 minutes}\\\\=\dfrac{1760\hspace{4}feet}{minute}[/tex]
Step 2 ⇒ Multiply [tex]\dfrac{1760\hspace{4}feet}{minute}[/tex] by [tex]\dfrac{minute}{60\hspace{4}seconds}[/tex] to change minutes to seconds:
[tex]\dfrac{1760\hspace{4}feet}{minute}\times\dfrac{minute}{60\hspace{4}seconds}\\\\= \dfrac{1760\hspace{4}feet}{60\hspace{4}seconds}\\\\= \dfrac{29.3\hspace{4}feet}{second}[/tex]
Answer[tex]\dfrac{29.3\hspace{4}feet}{second}[/tex]
how would you do this?
P( A and B) is [tex]\frac{1}{15}[/tex].
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is accurate. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given Data
P(A) = [tex]\frac{1}{3}[/tex]
P(B) = [tex]\frac{1}{5}[/tex]
P (A or B) = [tex]\frac{1}{2}[/tex]
1) No, events are not mutually exclusive. as P(A) + p(B) is not equal to P(A or B)
2) P( A and B) = P(A) × P (B)
P( A and B) = [tex]\frac{1}{3}[/tex] ×[tex]\frac{1}{5}[/tex]
P( A and B) = [tex]\frac{1}{15}[/tex]
To learn more about probability, visit:
https://brainly.com/question/1123492
#SPJ9
the following table lists the ages and number of players per age group that are on a volleyball team. let A = (volleyball players who are younger than 8 years old) how many players are in the complement of A?
The number of elements in the complement of a set A is the total number of elements in the universal set minus the number of elements in the set A.
It is given that A={volleyball players who are younger than 8 years old}.
From the table, volleyball players who are younger than the age of 8, are players who are 7 years old.
Hence, the number of players in A is 5.
Add the number of players for each age to get the total number of players:
[tex]5+3+7+4=19\text{ players}[/tex]It follows that the number of players in the complement of A is:
[tex]19-5=14\text{ players}[/tex]Hence, the number of players in the comp
You have a rectangular prism whose cross section is a square with side length
3 cm. You need to know its length, but you do not have a ruler. Luckily, you have a calibrated container of water nearby. The container has marks that measure cubic centimeters of liquid. It appears to have 70 cubic centimeters of water in it, but when you submerge the prism into the water, the water level rises to the 115-cubic-centimeter mark. Determine how long your prism is.
Answer:
side length = 5cm
Step-by-step explanation:
The volume of the prism is:
V = l × w × h
But we only know the width and height which are both 3cm. See image.
We put it in the calibrated container (container with markings on it) We find out the volume is 45. Because 115 - 70 is 45.
Divide to find the missing length. See image.
Vol
= 3 × 3 × sidelength
V = 9s
45 = 9s
5 = s
see image.
Help, write an equation in slope intercept form for slope -3 and y intercept -2
Hi :)
[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
Q-u-e-s-t-i-o-n:what is an equation with slope -3 and y int. of -2A-n-s-w-e-r:[tex]\sf y=-3x-2[/tex]
- we just insert the number for slope before x in the y=mx+b formula and then write the y-intercept
[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
An agency charges $100 per person for a trip to a concert if 50 people travel in a group. But for each person above the 50, the amount charged for each traveler will be reduced by $3. If x represents the number of people above the 50, write the agency's revenue R as a function of x. (Assume that x is greater than zero.)
R(x)
The revenue of the the agency is given by the function
R(x) = 5000 - 50 x - 3x² .
A function is a relationship between an independent variable and a dependent variable which defines all points on a cartesian plane which satisfies the given condition.
The set of the independent variables is called a domain and the set of the dependent variable of the function is called a range.Each data in range is related to a particular data in the domain by the function.Now in the given Agency it is given that the charge of each tourist is $100 . Now for every tourist above 50 the charge is reduced by 3 dollars.
So for x people above 50 charge will be ( 100-3 x ) for all members.
The total revenue can be measured by the function
R(x) = ( 50 + x ) ( 100 - 3x )
or , R(x) = 5000 - 150 x + 100 x - 3x²
or, R(x) = 5000 - 50 x - 3x²
Hence the revenue function is given as : R(x) = 5000 - 50 x - 3x²
To learn more about function visit:
https://brainly.com/question/12431044
#SPJ1
Which property is illustrated by the statement? K(mp) = (km)p
Solution:
[tex]\begin{gathered} An\text{ associative property of addition;} \\ a+(b+c)=(a+b)+c \\ An\text{ associative property of multiplication;} \\ a\times(b\times c)=(a\times b)\times c \end{gathered}[/tex]Thus;
Given;
[tex]k(mp)=(km)p[/tex]FINAL ANSWER: Associative Property.
5. Which of the following is a rational number that can be written as a decimal in which one or more nonzero digits repeat?
The rational number that can be written as a decimal in which one or more nonzero digits repeat is given by:
D. 5/9.
Which numbers compose the set of rational numbers?The set of rational numbers is composed by numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.
For this problem, we have a focus on numbers that have repeating decimal part. The most known case is the division by 9, as when an integer that is not a multiple of 9 is divided by 9, the result is a decimal with a repeating decimal part.
To find the equivalent decimal to 5/9, we divide the numerator of 5 by the denominator of 9, hence:
5/9 = 0.55555...
The decimal digit 5 repeats infinitely, hence option D is correct.
More can be learned about rational numbers at https://brainly.com/question/12088221
#SPJ1
uestion 15(Multiple Choice Worth 4 points)
(02.05 MC)
What is the range of f(x) = |x| − 5?
−∞ < y ≤ −5
−5 ≤ y < ∞
0 ≤ y < ∞
5 ≤ y < ∞
Answer:
B) - 5 ≤ y < ∞============================
Given function:f(x) = |x| − 5This is an absolute value function and is the translation of f(x) = |x| down by 5 units.
We know that f(x) = |x| is never negative as per definition of absolute value. So its range is zero or positive numbers:
0 ≤ y < ∞
The given function (|x| - 5) can get values 5 less than the parent function (|x|), so its range is:
- 5 ≤ y < ∞This is option B.
i need help with the question please
The number of customers surveyed is 499.
UESTION A
ehe age ranges that fall within the required one for this question are 20-29, 30-39, and 40-49.
The number of people in these groups in total will be:
[tex]\Rightarrow65+87+70=222[/tex]Therefore, the probability of this occurring is calculated to be:
[tex]\Rightarrow\frac{222}{499}=0.4449[/tex]he probability is 0.4449.
QUESTION B
he age ranges for this question are >≥60, <20, and 20-29.
The number of people in these groups in total will be:
[tex]\Rightarrow84+93+65=242[/tex][tex]\Rightarrow\frac{242}{499}=0.4850[/tex]he probability is 0.4850.
QUESTION C
is ≥60.
The number of people in this group is 84.
[tex]\Rightarrow\frac{84}{499}=0.1683[/tex]Write the sum. 54+63 as the product of a number and relatively prime addends
54 + 63 = 13 * 9 is the expression obtained as the product of a number and relatively prime addends.
A prime number is a number that can be divided only by 1 and itself.
54+63 (given)
We now have to find the sum of the given numbers as the product of relatively prime numbers.
In order to find the numbers we will find first sum and then factor
Sum=54+63=117
Factors of 117 are 13 and 9
117 = 13 * 9
13 and 9 are relatively prime because the factor of 13 and 9 is 1.
Therefore, 54 + 63 = 13 * 9 is the expression obtained as the product of a number and relatively prime addends.
To learn more about prime addends
visit; https://brainly.com/question/2696238
#SPJ1
how many 5 digit numbers can be created using the digits 2,3,4,7,8 and 9 without repeating any digits in that five digit number
Answer:
there are 720 three digit numbers that can be created from the digits provided given that no digit may be repeated.
Step-by-step explanation:
Heather, Ahmad, and Jim have a total of $68 in their wallets. Heather has $8 less than Jim. Ahmad has 2 times what Jim has. How much does each have?
Answer:
Step-by-step explanation:
1. Set x equal to the amount of money Jim has
Jim's money = x2. Create equations of the amount of money the other people have based on x
Heather's money = x - 8Ahmad's money = 2x3. Now, we set all of these equations as equal to 68
[tex](x)+(x-8)+(2x)=68[/tex]4. Combine the like terms, which means that the previous equation will simplify to:
[tex]4x-8=68[/tex]5. Add 8 to both sides
[tex]8+4x-8=68+8[/tex]This simplifies to: [tex]4x=76[/tex]6. Divide 76 by 4
[tex]\frac{4x}{4} =\frac{76}{4}[/tex]This equals: x = 197. Plug the value of x into the previous equations:
Jim's money: $19Heather's money: [tex]19-8=11[/tex] -> $11Ahmad's money: [tex]2*19=36[/tex] -> $36Final Answer:
Jim has $19Heather has $11Ahmad has $36a=3 and b=6 and c=5 what is ab+bc?
Answer:
you have the values of a, b and c
all you gotta do is just plug them in so
ab+bc is (3)(6)+(6)(5)
which equals 48.
Answer:
48
Step-by-step explanation:
since a=3, b=6 and c=5, you would replace the letters in ab+bc with their numbers, making it (3)(6)+(6)(5). then you would multiply 3 x 6 which would be 18, and 6 x 5, which would be 30, making your expression 18+30. finally you would add them together, making it 48.
Which fraction is in simplest form? A. 11 15 B. 12 18 C. 9 21 D. 14 24
Answer : 11 15
Reasoning : The fraction is in simplest form
9 21 is able to be simplified to 3 7,
12 18 is able to be simplified to 2 3
14 24 is able to be simplified to 7 12
Evaluate.(-2).(-2)·2=060-6O 80 -8
Evaluate (-2) (-2) . 2
[tex]\begin{gathered} -2\text{ }\times\text{ -2 = 4} \\ 4\text{ }\times\text{ 2 = }\text{\textcolor{#FF7968}{8}} \end{gathered}[/tex]
John has $10,000 in debt with Discover, $4,000 in debt with Chase, $9,000 in debt with Citi Bank, and $3,000 in debt with Wells Fargo, giving him a total debt of $26,000. What percentage of John's total debt is with Discover?*
John holds 26 percent of the debt from discover bank in its total debt obligation.
What is a total debt?The Total debt represents the obligations being taken by a company in the form of debt and yet to be repaid by them to the lender.
Given that the Debt hold in discover bank is $10,000
Total debt: $26,000
Computation of ratio of debt in discover bank:
Debt proportion = Debt hold in discover bank / Total debt
Debt proportion = 10,000/ 26,000
Debt proportion = 26%
Therefore, John holds 26 percent of the debt from discover bank in its total debt obligation.
Learn more about the debt obligation in the related link:
brainly.com/question/988013
#SPJ1
You have $100 in a savings accoun and save an additional $40 each week. Your friend has $80 in a savings account and saves and addtional $10 each week. Find and intepret the sum and difference of the amounts of money in each of your savings accounts?
The sum and the difference in the amount saved in the accounts will be 180 + 50w and 20 + 30w respectively.
How to calculate the value?From the information, I have have $100 in a savings accoun and save an additional $40 each week.
Let the number of weeks be represented by w. The expression to represent this will be:
= 100 + 40w
My friend has $80 in a savings account and saves and addtional $10 each week. This will be:
= 80 + 10w
The sum will be:
= 100 + 40w + 80 + 10w
= 180 + 50w
The difference in the amount will be:
= 100 + 40w - (80 + 10w)
= 20 + 30w
Learn more about savings account in:
brainly.com/question/25787382
#SPJ1
Write an equation for the graph in slope-intercept form. Do not use spaces in the equation
Answer:
I think this is correct.
Step-by-step explanation:
y=-3x+10
I’m struggling finding the frequency, can anyone help me?
when sarah planted a tree in her yard it was 24 inches tall it grew at a rate of 2.5 inches per month the tree is now 41.5 inches tall how many months has it been since sarah planted the tree
In linear equations, 103.75 inches per month tall has it been since sarah planted the tree.
What are instances of linear equations?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5.When an equation is given in this format, finding both intercepts is rather simple (x and y).When attempting to solve systems involving two linear equations, this form is also quite helpful.Sarah planted a tree in her yard = 24 inches tall
grew at a rate =2.5 inches per month
When tree is now 41.5 inches tall = 41 . 5 * 2.5
= 103.75
Learn more about linear equation
brainly.com/question/11897796
#SPJ10
Lesson 18: Use Systems of Equations to Solve Protstems A bag of popcorn and a juice box contains 518 calories. Two bags of popcorn and 6 juice boxes have a total of 1,456 calories. How many calories are in each Bag of popcorn and juice box? A. 182 calories in each bag of popcorn and each juice box B. 259 calories in each bag of popcorn and each juice box C. 364 calories in each bag of popcorn and 121 calories in each juice box D. 413 calories in each bag of popcorn and 105 calories in each juice box
According to the given information, the sum of the calories of a bag of popcorn and a juice box is 518. Taking x as the number of calories of a bag of popcorn and y as the number of calories of a juice box, we have that:
[tex]x+y=518[/tex]Then, 2 bags of popcorn (it means 2x) and 6 juice boxes (it means 6y) have a total of 1456 calories, this is:
[tex]2x+6y=1456[/tex]Use this system of equations and solve the problem, this way:
Solve the first equation for x:
[tex]x=518-y[/tex]Use this expression and replace for x in the second equation:
[tex]\begin{gathered} 2(518-y)+6y=1456 \\ 1036-2y+6y=1456 \\ 4y=1456-1036 \\ y=\frac{420}{4} \\ y=105 \end{gathered}[/tex]Use this value to find the value of x:
[tex]x=518-105=413[/tex]It means that there are 413 calories in each bag of popcorn and 105 calories in each juice box.
1: Find the equation of a polynomial with given zeros
For this problem, we are given the zeros of a polynomial, we need to determine its expression.
The zeros are:
[tex]1,1,2+\sqrt{2},2-\sqrt{2}[/tex]Therefore we can write:
[tex]\begin{gathered} f(x)=(x-1)^2(x-2+\sqrt{2})(x-2-\sqrt{2})\\ \\ f(x)=(x^2-2x+1)(x^2-4x+2)\\ \\ f(x)=x^4-4x^3+2x^2-2x^3+8x^2-4x+x^2-4x+2\\ \\ f(x)=x^4-6x^3+11x^2-8x+2 \end{gathered}[/tex]The correct answer is option A.
need help with these due tomorrow morning do 1-6
Answer:
Step-by-step explanation:
5 over 12 is 5/17
A lawnmower with a 3-gallon gas tank uses an average of 0.6 gallons per hour. A function modeling this situation, where x represents the amount of gas in the tank, has a domain described by which inequality?
A. 0 ≤ x ≤ 5
B. 0 < x < 5
C. 0 < x < 3
D. 0 ≤ x ≤ 3
x represents the amount of gas in the tank, has a domain described by which inequality
[tex]0 \leq x \leq 3[/tex]
This is further explained below.
What is inequality?Generally, A typical 3-gallon lawnmower requires 0.6 gallons of petrol per hour.
This circumstance is modeled by a function, where x is the volume of gas in the tank.
The lawnmower's gas tank has a maximum capacity of gallons and may be completely empty (having 0 gallons of gas).
In conclusion, a function's domain is
[tex]0 \leq x \leq 3[/tex]
Read more about inequality
https://brainly.com/question/20383699
#SPJ1
Given that (-6,-8) is on the graph of f(x), find
the corresponding point for the function
f(x) + 3.
Answer:
(-6, -5).
Step-by-step explanation:
f(x)+3 represents the graph of f(x) shifted up 3 units, meaning we add 3 to the y-coordinate
will give you brainliest
Answer:
[tex]\sqrt{8}[/tex]
We use the process of elimination to solve:
When we solve [tex](\sqrt{10})^{2}[/tex] we get 10 and we know that 10 is a integer and we know all integers are rational numbers, therefore, this is rational.
When we solve [tex]\sqrt{196}[/tex] we get 14 and we know its a rational number because it can be expressed as the quotient of two integers: 14 ÷ 1. Therefore this one is, rational.
0.63, The decimal 0.6 is a rational number. It is the decimal form of the fraction 6/10. A rational number is, by definition, any number that results when one integer is divided by another. Since both 6 and 10 are integers, or whole numbers, 0.6 is a rational number.
And lastly this leaves is with [tex]\sqrt{8}[/tex] and It is a non-terminating decimal with non-repeating digits. The number 2.828427125... can't be written in p/q form. Hence, the square root of 8 is a irrational number.
- 2(m - 2) = - 3(m = 5)
m = -19 is the solution to the equation -2(m - 2) = -3(m + 5).
What is the numerical value of m in the given equation?Given the data in the question;
-2(m - 2) = -3(m + 5)m = ?To determine the numerical value of m, remove the parenthesis and simplify.
-2(m - 2) = -3(m + 5)
Apply distributive property
-2(m - 2) = -3(m + 5)
m(-2) - 2(-2) = m(-3) + 5(-3)
-2m + 4 = -3m - 15
Now, collect like terms by bring all values containing variable m to the left and all constant to the right side of the equation.
-2m + 3m = -15 - 4
m = -15 - 4
m = -19
Therefore, the numerical value of m is -19.
Learn to solve more equations here: https://brainly.com/question/9236233
#SPJ1
how much interest would $1,000 earn in 1 year at an annual rate of 2% compounded annually
The Compound Interest would be $1104.895
What is Compound Interest ?
The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound and simple interest is this. If we examine our bank statements, we will typically see that our account is credited with interest on a yearly basis. Even though the principal remains the same, the interest changes annually. We can observe that interest rises over time. As a result, we can infer that the interest the bank charges is compound interest, or CI, rather than simple interest.
Number of quarters in 5years =5×4=20
Quarterly rate of compound interest
r=24=0.5%
Initial amount
P=$1000
hence the total amount after 5years
= P(1+r/100)n
=1000(1+0.5/100)^20
=1000(1.005)^20
=$1104.895
Hence, The Interest will be $1104.895
To learn more about Compound interest click on the link
https://brainly.com/question/24924853
#SPJ10