Answer:
Step-by-step explanation:
The equation for free fall (as opposed to parabolic motion which would occur if the child threw the rock up into the air and it followed a parabolic path. This equation would have an upwards velocity value in it. Dropping something does not have an upwards velocity value because we are not throwing it up into the air and letting gravity take over. VERY important distinction when working with these problems!):
[tex]h(t)=-16t^2+64[/tex] and we need to know how long it will take for the rock to be ON THE GROUND. The height of anything on the ground after it falls is 0, so we sub a 0 in for h(t), since h(t) is the height of the rock at a certain time in its falling. That time is what we are solving for: the time it takes for the rock to have a height of 0.
[tex]0=-16t^2+64[/tex] and
[tex]-64=-16t^2[/tex] and
[tex]4=t^2[/tex] so
t = -2 and 2. BUT since we know that time will never be negative, then the time it takes the rock to hit the ground is
t = 2 seconds.
(4-21)(1 + 71) help plz
the answer would be -1,224 because the parentheses is your multiplication and the it is a negative
Find the area of a triangle with a height of 38 and one side of 44
In triangle it is given that,
→ Height (h) = 38 cm
→ Base (b) = 44 cm
The formula we use,
→ Area of triangle = ½ × b × h
Now we have to,
find the area of the triangle,
→ ½ × b × h
→ ½ × 44 × 38
→ (44 × 38)/2
→ 1672/2 = 836 cm²
So, 836 cm² is area of triangle.
A student researcher compares the heights of American students and non-American students from the student body of a certain college in order to estimate the difference in their mean heights. A random sample of 12 American students had a mean height of 68.4 inches with a standard deviation of 1.64 inches. A random sample of 17 non-American students had a mean height of 64.9 inches with a standard deviation of 1.75 inches. Determine the 95% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students. Assume that the population variances are equal and that the two populations are normally distributed. Find the point estimate that should be used in constructing the confidence interval.
Answer:
The point estimate that should be used in constructing the confidence interval is 3.5.
The 95% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students, in inches, is (2.25, 4.75).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
American students:
Sample of 12, mean height of 68.4 inches with a standard deviation of 1.64 inches. This means that:
[tex]\mu_A = 68.4[/tex]
[tex]s_A = \frac{1.64}{\sqrt{12}} = 0.4743[/tex]
Non-American students:
Sample of 17, mean height of 64.9 inches with a standard deviation of 1.75 inches. This means that:
[tex]\mu_N = 64.9[/tex]
[tex]s_N = \frac{1.75}{\sqrt{17}} = 0.4244[/tex]
Distribution of the difference:
[tex]\mu = \mu_A - \mu_N = 68.4 - 64.9 = 3.5[/tex]
[tex]s = \sqrt{s_A^2+s_N^2} = \sqrt{0.4743^2 + 0.4244^2} = 0.6365[/tex]
The point estimate that should be used in constructing the confidence interval is 3.5.
Confidence interval:
[tex]\mu \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower bound of the interval is:
[tex]\mu - zs = 3.5 - 1.96*0.6365 = 2.25[/tex]
The upper bound of the interval is:
[tex]\mu + zs = 3.5 + 1.96*0.6365 = 4.75[/tex]
The 95% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students, in inches, is (2.25, 4.75).
If someone earns $10 every 15 minutes, how much do they earn in an hour?
Answer: 40
Step-by-step explanation:
You multiple 15X4=60
And now multiple 10x4=40
Answer:
40$
Step-by-step explanation:
There are 60 minutes in an hour so if we break it down:
$10 = 15 minutes
$10 = 15 minutes
$10 = 15 minutes
$10 = 15 minutes
-------------------------
Add them together and we get:
$40 = 60 minutes or 1 hour
Meaning they would make 40$ in 1 hour.
Solve the following system of equations by using the inverse of a matrix.
Give your answer as an ordered triple (x , y , z)
Answer:
(x, y, z) = (-8,4,-2)
Step-by-step explanation:
.......................................
If one root of the quadratic equation is 2x2 +kx -6= 0 is 2
find the value of k
This is ur answer plz mark brainliest
Based on a poll, among adults who regret getting tattoos, 24% say that they were too young when they got their tattoos. Assume that six adults who regret getting tattoos are randomly selected, and find the indicated probability.
a. Find the probability that none of the selected adults say that they were too young to get tattoos.
b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c. Find the probability that the number of selected adults saying they were too young is 0 or 1.
Answer:
a) 0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.
b) 0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c) 0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they say they were too young to get tattoos, or they do not say this. The probability of a person saying this is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
24% say that they were too young when they got their tattoos.
This means that [tex]p = 0.24[/tex]
Six adults
This means that [tex]n = 6[/tex]
a. Find the probability that none of the selected adults say that they were too young to get tattoos.
This is P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.24)^{0}.(0.76)^{6} = 0.1927[/tex]
0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.
b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.
This is P(X = 1). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{6,1}.(0.24)^{1}.(0.76)^{5} = 0.3651[/tex]
0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c. Find the probability that the number of selected adults saying they were too young is 0 or 1.
This is:
[tex]p = P(X = 0) + P(X = 1) = 0.1927 + 0.3651 = 0.5578[/tex]
0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.
Need help really bad
Do,1 of X is
(4,0)
(4,1)
(5,1)
Answer:
(4,0)
Step-by-step explanation:
the dot is on 4 and the line is 0 so answer is 4,0
Find the missing side length, and enter your answer in the box below. If
necessary, round your answer to 2 decimal places.
6
8
The missing side length is 10 unit.
What is Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
We have,
Perpendicular = 6
Base = 8
Using Pythagoras theorem
c² = P² + B²
c² = 6² + 8²
c²= 36 + 64
c² = 100
c= 10 unit.
Thus, the missing length is 10 unit.
Learn more about Pythagoras theorem here:
https://brainly.com/question/343682
#SPJ7
HELP PLEASE!!!!
I need the answer ASAP!!!!
9514 1404 393
Answer:
c. y = (x +2)² -5
Step-by-step explanation:
If you replace the squared term with zero, you are choosing the minimum of the remaining values. (A squared term cannot have a negative value.)
a) 3
b) 4
c) -5 . . . . the graph with the least possible y-value
d) 0
Write an equation of the line that passes through the pair of points (5, 8) and
(9, 16).
Answer:
D: y = 2x - 2
Step-by-step explanation:
1. [tex]\frac{16-8}{9-5}[/tex] = 2
2. y = 2x + b
3. Insert the points into the equation: 8 = 10 + b
4. b = -2
5. y = 2x - 2
=======================================================
Explanation:
Apply the slope formula
m = (y2-y1)/(x2-x1)
m = (16-8)/(9-5)
m = 8/4
m = 2
Then use this slope, along with another point such as (x,y) = (5,8) to find b
y = mx+b
8 = 2*5+b
8 = 10+b
8-10 = b
-2 = b
b = -2
Or you could use the other point (x,y) = (9,16)
y = mx+b
16 = 2*9+b
16 = 18+b
16-18 = b
-2 = b
b = -2
Either way, we get the same y intercept.
So because m = 2 is the slope and b = -2 is the y intercept, we go from y = mx+b to y = 2x-2
-------------------
To help verify the answer, note how plugging x = 5 leads us to...
y = 2x-2
y = 2*5 - 2
y = 10-2
y = 8
So x = 5 and y = 8 pair up together. This verifies (5,8) is on the line.
Through similar steps, you should find that the input x = 9 leads to the output y = 16. So that would confirm (9,16) is also on the line, and fully confirm the answer.
please help me i need the answers help me please
Answer:
scientists
Step-by-step explanation:
Which proportion correctly shows the equivalence of two fractions?
A)
19∕95 = 57∕76
B)
32∕116 = 9∕29
C)
18∕36 = 72∕144
D)
18∕36 = 144∕72
Answer:
32/166=9/29 if two ratio are equivalent to other
Which statement describes the end behavior of this function? g(x) = 1/2|x - 3| - 7
A. As x approaches positive infinity, g(x) approaches negative infinity.
B. As x approaches negative infinity, g(x) approaches negative infinity.
C. As x approaches positive infinity, g(x) approaches positive infinity.
D. As x approaches negative infinity, g(x) is no longer continuous.
Answer:
C. As x approaches positive infinity, g(x) approaches positive infinity.
Step-by-step explanation:
We are given the following function:
[tex]g(x) = \frac{|x-3|}{2} - 7[/tex]
End behavior:
Limit of g(x) as x goes to negative and positive infinity.
Negative infinity:
[tex]\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} \frac{|x-3|}{2} - 7 = \frac{|-\infty-3|}{2} - 7 = |-\infty| = \infty[/tex]
Positive infinity:
[tex]\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} \frac{|x-3|}{2} - 7 = \frac{|\infty-3|}{2} - 7 = |\infty| = \infty[/tex]
So in both cases, it approaches positive infinity, and so the correct option is c.
a) A box contains 6 red balls, 4 white balls, and 10 black balls. Two balls are drawn at random from the box (with replacement of the first before the second is drawn). What is the probability of getting a red ball on the first draw and a white ball on the second
Answer:
Red ball=3/10
White ball=1/5
Step-by-step explanation:
Red balls=6. And all the balls are equal to 20. So probability of red ball=6/20=3/10.
White balls=4. So probability of white ball=4/20=1/5.
NB: Since the first ball was replaced, there's no need to deduct a ball from the original 20 balls.
Let L be the circle in the x-y plane with center the origin and radius 38. Let S be a moveable circle with radius 8 . S is rolled along the inside of L without slipping while L remains fixed. A point P is marked on S before S is rolled and the path of P is studied. The initial position of P is (38,0). The initial position of the center of S is (14,0) . After S has moved counterclockwise about the origin through an angle t the position of P is:
x = 14cost + 24cos(7/12t)
y= 14sint - 24sin (7/12t)
Required:
How far does P move before it returns to its initial position?
Answer:
P moves = 70.73 m
Step-by-step explanation:
Given data
Radius = 38
initial position of P = ( 38,0 )
initial position of center S = ( 14,0)
position of P ( after s moved counterclockwise )
: x = 14cost + 24cos(7/12t)
y = 14sint - 24sin(7/12t)
Determine how far P moves before returning to its initial position
attached below is the solution
P moves = 70.74 m
find the missing side length in the image below
Let missing side be x
Using basic proportionality theorem
[tex]\\ \sf\longmapsto \dfrac{45}{35}=\dfrac{x}{56}[/tex]
[tex]\\ \sf\longmapsto \dfrac{9}{7}=\dfrac{x}{56}[/tex]
[tex]\\ \sf\longmapsto 7x=9(56)[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{9(56)}{7}[/tex]
[tex]\\ \sf\longmapsto x=72[/tex]
In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments. The following information is provided.
SSTR = 200 (Sum Square Between Treatments)
SST = 800 (Total Sum Square)
The mean square within treatments (MSE) is _____.
a. 10
b. 600
c. 50
d. 200
Answer:
[tex]MSE = 10[/tex]
Step-by-step explanation:
Given
[tex]SSTR = 200[/tex]
[tex]SST = 800[/tex]
Required
Determine MSE
This is calculated as:
[tex]MSE = \frac{1}{ddf} * SSE[/tex]
Where:
[tex]SSE = SST - SSTR[/tex]
[tex]ddf \to[/tex] denominator df
So, we have:
[tex]SSE = 800 - 200[/tex]
[tex]SSE = 600[/tex]
To calculate the df, we have:
[tex]r = 13[/tex] --- observations
[tex]n = 5[/tex] treatments
So:
[tex]ddf = Total\ df - Numerator\ df[/tex]
[tex]Total = n*r-1 = 5*13 -1 = 64[/tex]
[tex]Numerator =n - 1 = 5 - 1 =4[/tex]
[tex]ddf =64-4=60[/tex]
So, we have:
[tex]MSE = \frac{1}{ddf} * SSE[/tex]
[tex]MSE = \frac{1}{60} * 600[/tex]
[tex]MSE = 10[/tex]
How many gallons each of 15% alcohol and 10% alcohol should be mixed to obtain 5 gal of 13% alcohol?
9514 1404 393
Answer:
3 gallons 15%2 gallons 10%Step-by-step explanation:
Let x represent the quantity of 15% alcohol required. Then (5-x) is the amount of 10% alcohol needed. The amount of alcohol in the mix is ...
0.15x +0.10(5-x) = 0.13(5)
0.05x +0.5 = 0.65 . . . . . . . simplify
0.05x = 0.15 . . . . . . . . . subtract 0.5
x = 3 . . . . . . . . . . . . . divide by 0.05
3 gallons of 15% alcohol and 2 gallons of 10% alcohol should be mixed.
Jean and Marie decided to buy new living room furniture worth $6000. They make a down payment of $600. They decide to pay off what they owe in 30 monthly payments. Find the amount of the payments at 9% add-on interest.
Answer:
5886$ is the ans
Step-by-step explanation:
Paid amount= 6000-600
Total Amount or Interest applicable amount = 5400$
Then
Interest Rate= 9%
by using formula
=. Total amount + Interest rate × Total
=. 5400+0.09×5400
=. 5886$
Scores on the SAT are approximately normally distributed. One year, the average score on the Math SAT was 500 and the standard deviation was 120. What was the score of a person who did better than 85% of all the test-takers
Answer:
The score of a person who did better than 85% of all the test-takers was of 624.44.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
One year, the average score on the Math SAT was 500 and the standard deviation was 120.
This means that [tex]\mu = 500, \sigma = 120[/tex]
What was the score of a person who did better than 85% of all the test-takers?
The 85th percentile, which is X when Z has a p-value of 0.85, so X when Z = 1.037.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.037 = \frac{X - 500}{120}[/tex]
[tex]X - 500 = 1.037*120[/tex]
[tex]X = 624.44[/tex]
The score of a person who did better than 85% of all the test-takers was of 624.44.
does anyone know the answer
Answer:
For some reason I cannot open the photo you have provided.
Step-by-step explanation:
Please try to re-upload?
Answer:
upper left...
there are zeros at (x)(x+3) (x-2)
Step-by-step explanation:
What is the length of BD Round to one decimal place. Thanks!
Answer:
2.7
Step-by-step explanation:
ratios help
2.5 : 5.8 :: x : 6.2
2.5/5.8 = x/6.2
solve for x :
x = approx. 2.7
Which statement is true about the parts of this expression?
StartFraction 5 over 6 EndFraction + one-fourth x minus y
The constant is StartFraction 5 over 6 EndFraction.
The only coefficient is One-fourth.
The only variable is y.
The terms StartFraction 5 over 6 EndFraction and One-fourth x are like terms.
Answer:
The constant is StartFraction 5 over 6 EndFraction
Step-by-step explanation:
StartFraction 5 over 6 EndFraction + one-fourth x minus y
5/6 + 1/4x - y
A. The constant is StartFraction 5 over 6 EndFraction.
True
B. The only coefficient is One-fourth.
False
There are two coefficients: the coefficient of x which is 1/4 and the coefficient of y which is 1
C. The only variable is y
False
There are 2 variables: variable x and variable y
D. The terms StartFraction 5 over 6 EndFraction and One-fourth x are like terms.
False
5/6 and 1/4x are not like terms
The only true statement is: The constant is StartFraction 5 over 6 EndFraction
Answer:
It's A if you don't want to read. A). The constant is 5/6
Step-by-step explanation:
Henry bought a laptop for 4500 the cost of the laptop deprecate by 6% every year.If he decided to sell the laptop after 4 years at what’s price will he sell it
Answer:
give fufcy UC fugu stuff c
Step-by-step explanation:
zp staff book
Find f(2) if f(x) = (x + 1)2.
9
6
5
Simplify: x^d • x ^18
Answer:
x^(d+18)
Step-by-step explanation:
using the law of indices
you must add the powers
Answer:
[tex] {x}^{d + 18} [/tex]
Step-by-step explanation:
[tex]\sf{x^d.x^{18} }[/tex] [tex]\sf{ x^{d+18} }[/tex]Find the total surface area of this square based pyramid. 10ft 10ft (in the image)
find x
thank you thank you thank you!!
Answer:
Step-by-step explanation:
x=120°
For f(x) = x2 - x + 3, find
a, f(2)
b. f(3a)
Answer:
a.5
b.3a+3
Step-by-step explanation:
in a,u need to replace 2 with x,so it will be 4-2+3
in b,replace 3a with x and so it will be6a-3a+3
