The ratio of time that the red ball reaches the ground when compared with the green ball is 2:1
By using the equations of motion we first find the acceleration and time of both the balls using [tex]v^{2} -u^{2} =2as[/tex] and [tex]v=u+at[/tex]
where,
v=final velocity,
u=intial velocity,
a=acceleration,
s=height,
t=time
For the red ball,[tex]v^{2} -u^{2} =2as[/tex], v=4m/s, u=0m/s, s=3m by substitiuting in the equation we get ,
[tex]4^{2} -0^{2} =2*a*3[/tex],
acceleration=a=16/6=8/3,
[tex]v=u+at[/tex] by substituting we get,
4=0+8/3*t,
time taken by the red ball to reach ground t=3/2
For the green ball,[tex]v^{2} -u^{2} =2as[/tex], v=8m/s, u=0m/s, s=3m by substituting in the equation we get ,
[tex]8^{2} -0^{2} =2*a*3[/tex],
acceleration=a=64/6=32/3,
[tex]v=u+at[/tex] by substituting we get,
8=0+32/3*t,
time is taken by the green ball to reach ground t=3/4
and their ratio of time red ball/green ball=(3/2)/(3/4)=2/1,
hence time to reach the ground is independent of their mass
therefore, the ratio of time that the red ball reaches the ground when compared with the green ball is 2:1
To know more about equations of motion:
https://brainly.com/question/25951773
#SPJ4
Suppose that you use a pair of chopsticks
and apply a force of 1 are
N over a distance of 0.01 m. How much
work do you do? If the output force of the
chopsticks is only 0.5 N, how far do the tips
of the chopsticks move?
0.01 N of work is to be done to move the chopsticks to a distance of 0.01 m
0.02m far the tips of the chopsticks move.
What is work done?
Every time a force pushes something over a distance, work is done. By multiplying the force by the distance moved in the force's direction, you may determine the energy transferred, or work done. Energy transmitted equals work done, which is force times the distance travelled in the force's direction.
1. WD = F×d
= 1×0.01
= 0.01 N
2. d = WD/F
= 0.01/(0⋅5)
= 0.02m
0.02m far the tips of the chopsticks move.
Learn more about Work done from the link below
https://brainly.com/question/22015026
#SPJ1
in a test for particular illness, a false-positive result is obtained about 1 in 125 times the test is administered. if the test is administered to 15000 people, obtain the approximate probability of there being more than 135 false-positive results?
The probability of being more than 135 false-positive result is equal to 0.0853.
As given in the question,
Probability of false positive 'p' = 1/125
= 0.008
Number of people tested 'sample size n' = 15,000
Mean 'μ' = np
= 15000 × 0.008
= 120
Standard deviation 'σ' = √n × p × ( 1 - p )
= √15000 × 0.008 × ( 1 - 0.008)
=√ 15000 × 0.008 × 0.992
= √119.04
= 10.9
z = (X - μ) /σ
Approximate probability of being more than 135 false-positive results
= P( X > 135)
= P[( X - μ )/σ > ( 135 - μ)/σ
= P ( z > (135 - 120)/ 10.9)
= P ( z > 1.37)
= 1 - P ( z ≤ 1.37)
= 1 - 0.9147
= 0.0853 ( from z table)
Therefore, probability of being more than 135 false-positive results is equal to 0.0853.
Learn more about probability here
brainly.com/question/11234923
#SPJ4
Can the equation x² = 10 be solved by factoring?
Solve it x = +/-
The required simplified solution of the given expression is given as ±√10.
Given that,
To determine the simplified solution of x² = 10, by factorization.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
x² = 10
Taking square root on both sides,
x = ±√10
Thus, the required simplified solution of the given expression is given as ±√10.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ1
sorry for the bad picture but help needed asap! points!!!
Please help I need help with both questions fast
zoom in
5. Does the graph represent a function?
ОО
Yes
No
*REQUIRED
*REQUIRED
6. Explain why the graph is or is not a
function below.
Type response
Answer:
Below
Step-by-step explanation:
YES function because there is only ONE value of Y for each value of X
Cassie volunteers at an animal shelter. She needs a totsl of 40 hours of volunteers time for a class. So far, she has volunteered for 18.5 hours. How many more hours does she need to volunteer.
Answer: 21.5 hrs
Step-by-step explanation:
40 - 18.5 = 21.5 hours left
Answer:
21.5
Step-by-step explanation:
hope it helps
determine the smallest integer value of x in the solution of the following inequality
4x-9>=17
Step-by-step explanation:
4x - 9 ≥ 17
4x ≥ 17 + 9
4x ≥ 26
4x/4 ≥ 26/4
x ≥ 13/2
x ≥ 6.5
G is the centroid of triangle abc. what is the value of x? what is the length of segment dg? units what is the length of segment ag? units what is the length of segment ad? units
According to the Centroid Ratio Theorem , we have:
x = 37 , DG = 22,
AG = 44 and AD = 66
Centroid Ratio Theorem:
The Centroid ratio theorem states that the centroid of the triangle is at 2/3 of the distance from the vertex to the mid point of the side.
according to the centroid ratio theorem, we have,
AG = 2/3 (AD) ----------------------------- (1)
AG = x + 7
DG = x - 15
AD = x + 7 + x- 15 = 2x - 8
Putting the values in equation (1)
x + 7 = 2/3 (2x - 8)
⇒ 3(x + 7) = 2( 2x - 8)
⇒3x + 21 = 4x - 16
⇒ -x = -37
⇒ x = 37
Putting the value of x= 37
DG = 37 - 15 = 22
AG = 37 +7 = 44
AD= 2×37 - 8 = 66
Learn more about Centroid ratio of theorem :
https://brainly.com/question/20627009
#SPJ4
pls send the correct answer and show work!
Answer: x = 140°
Step-by-step explanation:
The sum of all interior angles in a pentagon is 540°.
Since you have every other angle except for one, you can subtract them from the total:
540°-120°-118°-89°-73° = 140°
Therefore the x angle is equal to 140°.
when sample size increases, everything else remaining the same, the width of a confidence interval for a population parameter will:
when sample size increases, everything else remaining the same, the width of a confidence interval decreases.
The sample size is defined as the the number of observations or participants included in a study.
The confidence interval is defined as the mean of the estimate plus and minus the variation in that estimate. That means when you do the test multiple times, then the value may be vary from the estimated value. The confidence interval is the range of those values.
So when the sample size increases the width of the confidence interval decreases
Hence, when sample size increases, everything else remaining the same, the width of a confidence interval decreases.
Learn more about confidence interval here
brainly.com/question/24131141
#SPJ4
A sine wave is offset 1/6 cycle with respect to time 0. What is its phase in degrees and radians?.
Its phase is 60 degrees and π/3 radian
From the question, we have
Each complete cycle measures 360 degrees.
So, 1/6 cycle = 1/6 × 360° = 60°
Each complete cycle measures 2π radian.
So, 1/6 cycle = 1/6 × 2π = π/3 radian
Multiplication:
In mathematics, multiplying two or more numbers yields the product of the numbers. One of the basic mathematical operations is one that we commonly perform. The most obvious example is using multiplication tables. Mathematicians multiply two integers to illustrate the process of repeatedly adding one number to another. The types of numbers that can be included include natural numbers, fractions, integers, whole numbers, and others. When M is multiplied by n, it either adds or subtracts from itself 'n' times.
To learn more about multiplication visit: https://brainly.com/question/5992872
#SPJ1
three letters are written to three different people and three envelopes are appropriately addressed. if each letter is placed into a randomly selected envelope so that each envelope contains exactly one letter, what is the probability that at least one person will receive the correct letter?
The probability that at least one person will receive the correct letter is 2/3.
Given data,
Let's say that the letter matching to the envelope is A, B, and C.
Each envelope has exactly one letter inside it once the letters are randomly placed inside.
Aa, Bb, Cc, Aa, Bc, Cb, Ab, Ba, Cc, Ab, Bc, Ca, Ac, Bb, Ca, Ac, Ba, Cb, are all possible combinations.
Thus, the total number of scenarios is 6 (n(S)).
A=(Aa, Bb, Cc), (Aa, Bc, Cb), (Ac, Bb, Ca), (Ab, Ba, Cc), n(A)=4
let A be an event that at least one letter is in its right envelope.
So,
The probability that at least one letter is in the right envelope P(A) = n(S) / n(A) = 4 / 6
= 2 / 3
To learn more about probability click here:
brainly.com/question/11234923
#SPJ4
hi help me pls help help
Step-by-step explanation:
many greetings to your teacher, there are some definitions missing.
this can only be done if JM and LH are true diameters of the circle.
1. if LH is a diameter, then angles KAH + LAK = 180°.
KAH = 90° (right angle).
so,
angle LAK = 180 - 90 = 90°.
2.
with JM and LH being diameters, JAH = LAM = 42°.
JAH + JAK = 90°.
angle JAK = 90 - 42 = 48°.
3. angle LAJ = LAK + JAK = 90 + 48 = 138°.
4. see also 2.
these are angles of intersecting lines (diameters). they must be the same on both sides of such an intersected line (just left-right mirrored).
JAH = LAM = 42°.
5. angle KAM = LAK + LAM = 90 + 42 = 132°.
6. arc angle LK = angle LAK = 90°.
7. arc angle JK = angle JAK = 48°.
8. arc angle LMG = angle LAG = 180 - HAG =
= 180 - 30 = 150°.
9. arc angle JH = angle JAH = 42°.
10. arc angle KLM = angle KAM = 132°.
4
The ratio of words
missed to correct B
on Marcy's spelling
test was 1:4. If she
got 4 words wrong,
how many were
correct?
A
6.RP.1: Ratio Concepts
C
D
4
8
16
20
Marcy got only 1 correct answer.
What is ratio?The relationship in quantity, amount, or size between two or more things in proportion.
Given that, the ratio of words corrects to wrong is 1:4
She got 4 wrong answers so, her correct answers count = 1
Hence, the Marcy answered only one correct answer.
For more references on ratio, click;
https://brainly.com/question/13419413
#SPJ1
A rental car company charge $37. 93 per day to rent a car and $0. 11 for every mile driven. Taylor want to rent a car, knowing that:
She plan to drive 50 mile. She ha at mot $300 to pend. Which inequality can be ued to determine
d
d, the maximum number of day Taylor can afford to rent for while taying within her budget?
The inequality that can be used to determine the maximum number of days, d, Taylor can afford to rent for while staying within her budget is $37. 93(d) + $0. 11(50) < $300 or d < 7.76.
Inequality is defined as the relationship between non-equal numbers or expressions separated by <, >, ≤, or ≥.
Let d be the maximum number of days Taylor can afford to rent for while staying within her budget.
If a rental car company charges $37. 93 per day to rent a car and $0. 11 for every mile driven, and Taylor plans to drive 50 miles, then it will cost her $37. 93(d) + $0. 11(50).
If she has $300 at most to spend, then the inequality should be d < 7.76
$37. 93(d) + $0. 11(50) < $300
37. 93d + 5.5 < 300
37. 93d < 294.5
d < 7.76
Learn more about inequality here: brainly.com/question/13912022
#SPJ4
Jessica bought 5 yards of fabric, plus 20% extra fabric. Derek bought 3 yards of fabric, plus 25% extra. Who bought more fabric? How much more? SHOW WORK PLEASE AND THANK U !!! <3
A. Jessica bought 1/4 yard more than derek.
B. Jessica bought 2 and 1/4 yards more than derek.
C. Derek bought 1/4 yards more than jessica.
D. Derek bought 2 and 1/4 more than jessica.
Jessica bought [tex]2\frac{1}{4}[/tex] yards of fabric more than Derek.
According to the question,
We have the following information:
Jessica bought 5 yards of fabric, plus 20% extra fabric. Derek bought 3 yards of fabric, plus 25% extra.
Now, we will find first the extra fabric they both bought:
For Jessica, we have:
20% of 5
20*5/100
1 yard
Now, the total fabric Jessica has:
5+1
6 yards
For Derek, we have:
25% of 3
25*3/100
3/4 yards
Now, the total fabric Derek has:
3 + 3/4
Taking 4 as the least common factor and adding the fractions:
15/4 yards
Now, we will subtract the fabric Derek has from the fabric Jessica has:
6 - 15/4
(24-15)/4
9/4
Converting this into mixed fraction:
[tex]2\frac{1}{4}[/tex] yards
Hence, the correct option is B.
To know more about Jessica bought here
https://brainly.com/question/2551588
#SPJ1
line has a slope of –1/9 and includes the points (10,6) and (s,7). What is the value of s?
Answer:
s=1
Step-by-step explanation:
Slope formula is
Δy/Δx
Substitute in:
7-6/s-10=-1/9
cross multiply
7-6=-1/9s+10(1/9)
7-6=-1/9s+10/9
1-10/9=-1/9s
-1/9=-1/9s
divide both sides by -1/9
thus:
1=s
s=1
(check by plugging back in)
7-6/1-10=-1/9
The side lengths of triangle ABC are written in terms of the variable p, where p≥ 3. p+4 4p-1 3p B
Which is correct regarding the angles of the triangle? mm mzB O m/B>m/A> mZC Omze>m/A> m/B Omzc>m/B> m/A
The correct statement that regarding the angles of triangle is option (C) m∠C > m∠A > m∠B
The value of p ≥ 3
Consider the value p = 3
The length of the side AB = 4p - 1
= 4×3 - 1
= 12 - 1
= 11 units
The length of side BC = 3p
= 3×3
= 9 units
The length of the side AC = p + 4
= 3 + 4
= 7 units
Then length of AB > length of BC > length of AC
The angles opposite to the side AB, BC and AC are m∠C , m∠A and m∠B
Then m∠C > m∠A > m∠B
Hence, the correct statement that regarding the angles of triangle is option (C) m∠C > m∠A > m∠B
Learn more about triangle here
brainly.com/question/17738167
#SPJ1
If you put aside $25 each month for 12 months in a CD, how much will you have saved?
The height of a triangle is 5 m longer than the base. If the area is 150 m2 , how long is the base?.
The base of the triangle is 15 meters.
Here, we are given that the height of a triangle is 5 m longer than the base.
Let the height of the triangle be h
Then, the base of the triangle will be = h - 5
Further, we are given that area of the triangle = 150 meter square
We know that area of a triangle = 1/2 × base × height
⇒ 150 = 1/2 × h × (h-5)
150 × 2 = h(h-5)
300 = [tex]h^{2}[/tex] - 5h
[tex]h^{2}[/tex] - 5h - 300 = 0
Now, we solve the above quadratic equation by splitting the middle term.
[tex]h^{2}[/tex] + 15h - 20h - 300 = 0
h( h + 15) - 20( h + 15) = 0
(h - 20) (h + 15) = 0
Thus, h = 20 or -15
But since height cannot be negative, h = 20
⇒ base = h - 5
= 20 - 5
= 15 meters
Thus, the base of the triangle is 15 meters.
Learn more about triangles here-
https://brainly.com/question/1058720
#SPJ4
I need help. 10 point for whoever can help.
Answer:
B=4
Hope that helps! :)
The jenkins family drinks 3/4 of a gallon of orange juice every 3 days. How many orange juice do they drink per day?
Answer:
1/4
Step-by-step explanation:
3/4 divided by 3=1/4
There are 15 girls in your class this year. That is a 15% increase from last year. Write a proportion to solve for the number of girls in the class last year.
First, we have to recognize that if the current number of girls in the class is a 15% increase from last year, then this year's number is 115% of last year's number.
With that, we can set up a proportion comparing last year to this year, in both percentages and numbers:
[tex]\dfrac{100}{115} = \dfrac{x}{15}[/tex]
Note that both numerators are last year's values and the denominators are this year's values.
If we multiply both sides by 15, we have that x ≈ 13.043478260869565. Since we're dealing with whole people, we'd say that there were 13 girls in the class last year.
In a positive correlation, __________.
A.
the independent variable is always negative
B.
an increase in the independent variable has a corresponding increase in the dependent variable
C.
the dependent variable is always positive
D.
a decrease in the independent variable has a corresponding increase in the dependent variable.
Answer:
B
Step-by-step explanation:
In a positive correlation, an increase in the independent variable has a corresponding increase in the dependent variable.
What is correlation?
Correlation is a statistical measure that expresses the extent to which two variables are linearly related. We know a positive correlation—when the correlation coefficient is greater than 0 signifies that both variables move in the same direction. Also, A positive correlation exists when one variable decreases as the other variable decreases or one variable increases while the other increases.
I would appreciate it if you mark my answer as brainliest.
can someone help find the volume
Answer:
the first one 792 ft²
Step-by-step explanation:
you do length times width times height = lxwxh
Please help, for the second variable I couldnt read my own hand writting so im no sure if its f or r, someone please help soon
Answer:
k = [tex]\frac{fr^2}{90}[/tex]
Step-by-step explanation:
f = k [tex]\frac{90}{r^2}[/tex] ( multiply both sides by r² to clear the fraction )
fr² = 90k ( divide both sides by 90 )
[tex]\frac{fr^2}{90}[/tex] = k
solve for x
3(-7x-3)+4x= -(x-3)
it doesnt accept 3/4 as an answer
thanks in advance
Answer:
[tex]3( - 7x - 3) + 4x = - (x - 3)[/tex]
[tex] - 21x - 9 + 4x = - x + 3[/tex]
[tex] - 21x + 4x + x = 9 + 3[/tex]
[tex] - 16x = 12[/tex]
[tex] - 16 \div ( - 16x = 12)[/tex]
[tex]x = - \frac{3}{4} [/tex]
Step-by-step explanation:
it is negative 3/4 not positive 3/4
Find the simplified product where x20: √5x (√8x²-2√x)
√10x
2x √40x-2x
O 2x10x-2√5x
O2x10x-2x√√5
DONE
The solution of the expression is 2√5x(√2-1).
From the question, we have
√5x ( √8x² - 2√x)
= √5x ( 2√2x - 2√x)
= √5x(√2-1)(2√x)
= 2√5x(√2-1).
The solution of the expression is 2√5x(√2-1).
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
To learn more about multiplication visit: https://brainly.com/question/5992872
#SPJ1
Answer: ITS D
Step-by-step explanation:
2x sqrt 10x - 2x sqrt 5
Lydia buy 5 pound of apple and 3 pound of banana for a total cot of $8. 50. Ari buy 3 pound of apple and 2 pound of banana for a total cot of $5. 25. Thi ytem of equation repreent the ituation, where x i the cot per pound of apple, and y i the cot per pound of banana
We need to multiply equation 2 with 3 and result is x = 1.25. The cost of one apple and one banana is $1.25 and $0.75 respectively.
Forming the equation using given variables x and y. Firstly writing the equation based on Lydia's items.
5x + 3y = 8.50 : Equation 1
Now writing the equation based on Ari's items.
3x + 2y = 5.25 : Equation 2
Now we need to equate one variable to find the other variable. So, multiplying equation 1 with 2 and equation 2 with 3.
10x + 6y = 17 : Equation 3
9x + 6y = 15.75 : Equation 4
Subtracting equation 4 from equation 3. We get the result -
x = 1.25
Keep the value of x in equation 1 to find the value of y
5×1.25 + 3y = 8.50
6.25 + 3y = 8.50
3y = 8.50 - 6.25
3y = 2.25
y = 2.25/3
y = 0.75
Thus, the cost of one apple is $1.25 and cost of one banana is $0.75.
Learn more about equation -
https://brainly.com/question/21405634
#SPJ4
The complete question is -
lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. this system of equations represents the situation, where x is the cost per pound of apples, and y is the cost per pound of bananas. 5x 3y = 8.5 3x 2y = 5.25 if you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate the y terms when making a linear combination? complete the multiplication and add the equations. what is the result? what is the price per pound of apples? what is the price per pound of bananas?
the united company had 15 applications for funding this year. if 8 of these applications can be funded, how many different lists of successful applications are there
A company received 15 funding applications and want to select 8 of them to be funded. The number of different lists of successful applications is 6,435
Suppose we have n objects in total and we want to select r objects among total objects, the number of ways they can be selected is given by the combination formula:
ⁿCr = n! / [r! (n-r)!]
Data from the problem:
n = total applications = 15
r = number of selected applications = 8
Hence, the number of different lists of successful applications is:
¹⁵C₈ = 15! / [8! (15-8)!]
= 15! / [8! 7!]
= 6,435
Thus, the number of different lists can be selected is 6,435
Learn more about combination here:
https://brainly.com/question/17139330
#SPJ4
