Answer:
500 pa
Step-by-step explanation:
[tex]Force = 25N\\Area = 0.05m^2\\\\Pressure = \frac{Force}{Area}\\ \\Pressure = \frac{25}{0.05}\\\\ Pressure = 500 Pascals[/tex]
A political study took a sample of 1600 voters in the town and found that 42% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is more than 39%. Determine the P-value of the test statistic. Round your answer to four decimal places.
Answer:
P- value = 0.0069
Step-by-step explanation:
Given that :
sample size n = 1600
The sample proportion [tex]\hat p[/tex] = 0.42
The population proportion p = 0.39
The null hypothesis and the alternative hypothesis can be expressed as:
[tex]H_o : p =0. 39[/tex]
[tex]H_1 : p >0.39[/tex]
The test statistics can be computed as follows:
[tex]Z = \dfrac{\hat p - p }{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
[tex]Z = \dfrac{0.42 - 0.39 }{\sqrt{\dfrac{0.39(1-0.39)}{1600}}}[/tex]
[tex]Z = \dfrac{0.03 }{\sqrt{\dfrac{0.2379}{1600}}}[/tex]
[tex]Z = \dfrac{0.03 }{\sqrt{1.486875 \times 10^{-4}}}[/tex]
[tex]Z = \dfrac{0.03 }{0.0121937484}[/tex]
[tex]Z = 2.4603[/tex]
Z [tex]\simeq[/tex] 2.46
Determine the P-value of the test statistic.
The P- value = P(Z > [tex]Z_o[/tex] )
P- value = 1 - P( Z ≤ 2.46)
Using the Excel Function ( = NORMSDIST (2.46))
P- value = 1 - 0.993053
P- value = 0.006947
P- value = 0.0069 to four decimal places
Determine if 0.292992999299992999992... is rational or irrational
and give a reason for your answer.
Answer:
Irrational
Step-by-step explanation:
Can't be put into a fraction.
5. Taking a cruise is a costly discretionary expense. In a recent year, the top five
cruise lines in the world had this many passengers:
4,133,000 2,369,000 1,295,000 928,000 679,000
Round your answers to the nearest integer.
a. The computations will be easier to work if you view this problem in terms
of thousands of passengers. Represent each number in terms of thousands
of passengers.
b. What is the mean number of passengers for these five cruise lines? (Give
the full number.)
c. What is the range? (Give the full number.)
d. What is the standard deviation? (Give the full number.)
Answer:
(a) X(in '000s) = 4133, 2369, 1295, 928, 679.
(b) The mean number of passengers for these five cruise lines is 1880.8.
(c) The range of the data is 3454.
(d) The standard deviation of the data is 1414.75.
Step-by-step explanation:
We are given that in a recent year, the top five cruise lines in the world had this many passengers:
4,133,000, 2,369,000, 1,295,000, 928,000, 679,000
(a) Let X = Number of passengers in the top five cruise lines in the world
Representing each number in terms of thousands of passengers below;
X(in '000s) = 4133, 2369, 1295, 928, 679
(b) The mean of the data is given by the following formula;
Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]
Here, n = number of observations in data = 5
So, [tex]\bar X[/tex] = [tex]\frac{4133+2369+1295+928+679}{5}[/tex]
= [tex]\frac{9404}{5}[/tex] = 1880.8
Hence, the mean number of passengers for these five cruise lines is 1880.8.
(c) The range of the data is calculated by the following formula;
Range = Highest value - Lowest value
= 4133 - 679 = 3454
Hence, the range of the data is 3454.
(d) The standard deviation of the data is given by the following formula;
Standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1}[/tex]
= [tex]\frac{(4133-1880.8)^{2}+(2369-1880.8)^{2}+.......+(679-1880.8)^{2} }{5-1}[/tex]
= 1414.75
Hence, the standard deviation of the data is 1414.75.
Regular airfare to Boston is $125 one way, but as a special discount, the fare was lowered to $105 one way. How much money will four people save altogether one way using the lower rate? ill make brainest
Answer:
$80
Step-by-step explanation:
So for this we need the cost of 4 regular tickets minus the cost of 4 discount tickets.
4(125$) = 500$
4(105$) = 420$
From here, we can find out how much is saved by the four people.
500$ - 420$ = 80$
So 80 dollars are saved by the four people.
Cheers.
what OneEnginer said
Step-by-step explanation:
use PEMDAS: please excuse my dear aunt sally
PLEASE ANSWER!!! I WILL MARK YOU AS BRAINLIEST!!!! An object is launched straight up into the air with an initial velocity of 40 m/s, from a height 30 m above the ground. Assuming that gravity pulls it down, changing its position by about 4.9 m/s2, after how many seconds will the object hit the ground? Enter your answer as rounded to the nearest tenth, such as: 42.5
Answer:
6.7 seconds
Step-by-step explanation:
Let's calculate the maximum height covered by the object
Max height= U²Sin²tita/2g
Where g is acceleration due to gravity
Max height= 40²(sin90)²/(2*9.81)
Max height= 1600/19.62
Max height=81.55 m
Total max height= 30+81.55
Total max height= 111.55 m
Time t it will take to travel from the max height at acceleration of 4.9 m/s²
S= ut + ½at²
u= 0 at Mac height
S= 111.5 m
111.5 = ½(4.9)t²
223/4.9= t²
45.5= t²
6.745 seconds= t
6.7 seconds= t
Given a sample with 5 scores: 4, 6, 8, 10, and y, and the mean of this sample is 6, what is the variance of the sample
Answer:
8+10+4+6+y /5=6
find lcm which is 5
(8+10+4+6+y/5)5=(6)5
8+10+4+6+y=30
28+y=30
y=30-28
y=2
-3 yz; use y = 3, and z=2
Answer:
-18
Step-by-step explanation:
-3 (3)(2)
-9 * 2
-18
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ - 18}}}}}[/tex]
Step-by-step explanation:
Given, y = 3 , z = 2
To find : value of -3yz
plug the values of y and z
[tex] \sf{ - 3 \times 3 \times 2}[/tex]
Multiply the numbers : - 3 and 3
⇒[tex] \sf{ - 9 \times 2}[/tex]
Multiply the numbers : -9 and 2
⇒[tex] \sf{ - 18}[/tex]
Hope I helped!
Best regards!!
47. Find the perimeter of the
semicircle of radius 7 cm.
(Take pi as 22/7
A. 16 cm
B. 24 cm
C. 36 cm
D. 38 cm
E.58 cm
Answer:
thee correct answer is in number.C. 36
Answer:
D
Step-by-step explanation:
Does anyone know this? There are 25 students names in a hat. You choose 5 names. Three are boys names and two are girls names. How many of the 25 names would you expect to be boys names?
Answer:
I would expect there to be 15 boy names and 10 girl names.
Step-by-step explanation:
There is a 3 to 2 ratio between boy and girl names, and the only numbers that add up to 25 with that ratio are 15 and 10
2. What is the sum of a number and five?
Answer:
n + 5
Step-by-step explanation:
"The sum of a number and 5" can be written symbolically as n + 5.
A marketing organization claims that more than 10% of its employees are paid minimum wage. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted
Answer:
there is insufficient evidence to support the claim that more than 10% of the employees are paid minimum wage.
Step-by-step explanation:
Given that:
A marketing organization claims that more than 10% of its employees are paid minimum wage.
The null hypothesis is:
[tex]H_o : p = 10[/tex]
The alternative hypothesis is:
[tex]H_1 : p > 10[/tex]
If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted
i.e Decision Rule: fails to reject the null hypothesis
Then the interpretation of the decision is that, there is insufficient evidence to support the claim that more than 10% of the employees are paid minimum wage.
Please help <3 Paula is writing short, casual notes for how to find the inverse of a function, f. Those notes are shown below. 1. Write the equation. 2. Replace f(x) with y. 3. Switch x and y. 4. Solve the equation for y. a. If the result does not define y as a function of x, then f has an inverse. b. If the result defines y as a function of x, then f does not have an inverse. 5. Change y to f^−1(x) if f has an inverse. Are Paula's notes correct? If not, identify Paula's error. (1 point) Paula's notes are incorrect. Step 2 should be "Replace f(x) with x." Paula's notes are incorrect. Step 4a should be "If the result does not define y as a function of x, then f does not have an inverse," and step 4b should be "If the result defines y as a function of x, then f has an inverse." Paula's notes are correct. Paula's notes are incorrect. Step 4 should be "Solve the equation for x."
Answer:
(3rd listed choice) Paula's notes are incorrect. Step 4a should be "If the result does not define y as a function of x, then f does not have an inverse," and step 4b should be "If the result defines y as a function of x, then f has an inverse."
Step-by-step explanation:
If f(y) = x can be solved for a relation for y that is a function, then f(x) has an inverse. It will be the function defined by y.
A geometric progression has a third term of 20 and a sum of infinity which is 3 times the first term. Find the first term
Answer: the first term is 45
Step-by-step explanation:
Step 1: The formular for the nth term is ar^n-1 and since we're solving for the third term ar^3-1 = ar² which is equal to 20
So ar²= 20 and we make this equation i
Step 2: the formular for the sum of infinity is Sn = a/(1-r) and according the question the sum of infinity is equals to 3 *A ( A means the first term)
Further simplification gives us
3a= a/(1-r)
We simplify Futher by multiplying both sides by (1-r)
3a.(1-r) = a/(1-r).(1-r)
3a(1-r)=a
= 3a-3ar=a
Make 3ar the subject of the formula
3ar= 2a and lets make this equation (ii)
Step 3: From the first equation since ar²=20, let's make a the subject of the formula by dividing both sides by r²
Ar²/r² = 20/r²
A=20/r²lets make this equation (iii)
Step 4: subtitle a as 20/r² into equation (ii)
Since 3ar=2a
Then 3.(20/r²).r = 2. 20/r²
= (60/r²) .r = 40/r²
60/r = 40/r2
Multiplying both sides by r² gives us
60r = 40
Divide both sides by 20 gives us
= 3r= 2
Divide both sides by 3 gives us
= r = 2/3
Step 5: substitute r for 2/3 in equation i
ar²= 20
a. (2/3)2 = 20
= a.4/9 = 20
= 4a = 180
= a = 180/4
a = 45
The equation $y = -6t^2 - 10t + 56$ describes the height (in feet) of a ball thrown downward at 10 feet per second from a height of 56 feet from the surface from Mars. In how many seconds will the ball hit the ground? Express your answer as a decimal rounded to the nearest hundredth.
Answer:
2.33 Seconds
Step-by-step explanation:
The equation y = -6t^2 - 10t + 56 expresses the height of a ball at a given time, t, on the planet Mars. We are also given that the ball is thrown with a velocity of 10 feet per second with the initial height of 56 feet.
To find the amount of time to reach the ground, we can say that the time being found will be when the ball is on the ground, or when y = 0. So we simply set our equation to 0 and solve for t.
y = -6t^2 - 10t + 56
0 = -6t^2 - 10t + 56
0 = -1 (6t^2 + 10t + -56)
0 = -1 (3t - 7) (2t + 8)
(3t - 7) = 0 OR (2t + 8) = 0
3t = 7 OR 2t = -8
t = 7/3 OR t = -4
Since time will not be negative, we will want to choose the positive solution for this quadratic equation.
Hence, the amount of time for the ball to hit the ground will be 7/3 seconds or 2.33 seconds.
Cheers.
Answer:
2.33
Step-by-step explanation:
Setting $y$ to zero, we find the following:
\begin{align*}
-6t^2 - 10t + 56 &= 0 \\
\Rightarrow \quad 6t^2 + 10t - 56 &= 0 \\
\Rightarrow \quad 3t^2 + 5t - 28 &= 0 \\
\Rightarrow \quad (3t-7)(t+4) &= 0.
\end{align*}As $t$ must be positive, we can see that $t = \frac{7}{3} \approx \boxed{2.33}.$
Use the discriminant to determine the number of solutions to the quadratic equation −45d2+4d−1=0.
Answer:
no real solutions
2 different complex solutions
Step-by-step explanation:
b^2 - 4ac = 4^2 - 4(-45)(-1) = 16 - 180 = -164
If g(x) = 3/2x + 3, and g(a) = 0, what is a ?
Answer:
a = -2
Step-by-step explanation:
g(x) = 3/2x + 3
g(a) = 0
g(a) = 3/2a +3 =0
Subtract 3 from each side
3/2a +3-3=0-3
3/2a = -3
Multiply each side by 2/3
2/3 * 3/2a = -3*2/3
a = -2
Every morning there is an 70% chance that I get to the bus on times. if each morning is independent of the others, what is the probability that I get to the bus on times at least 4 times in 5 days?
a 0.04437
b. 0.3915
c. 0.05220
d 0.5282
e 0.9657
Answer:
d 0.5282
Step-by-step explanation:
Given the following :
Probability of getting to the bus on time = 70% = P = probability of success = 0.7
(1 - p) = probability of failure = 0.3
Number of trials(n) = 5 days
Number of sucesses (r) = atleast 4 days : >= 4
This is a binomial probability problem
P(r) = nCr × P^r × (1 - P)^(n - r)
P(X >=4) = P(4) + P(5)
P(4) = 5C4 × (0.7)^4 × (0.3)^1 = 0.36015
P(5) = 5C5 × (0.7)^5 × (0.3)^0 = 0.16807
P(4) + P(5) = 0.36015 + 0.16807 = 0.52822
Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. Answer the following questions. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z = ? (x − μ) σ μ = σ = The original pulse rates are
Answer:
So we need to find the P (Z< 1.0776) which is equal to 0.86 from z- tables.
Step-by-step explanation:
Given that mean = 77.5 beats per minute
Standard deviation= s= 11.6 beats per minute
We need to find the pulse rate of randomly selected women.
Suppose randomly selected women X= 90
The test statistic used here is
z = (x − μ) /σ
Putting the values we get
z= 90- 77.5/ 11.6
z= 1.0776
So we need to find the P (Z< 1.0776) which is equal to 0.86
This is a supposed values of randomly selected women. Any other value can be solved in the same way.
Find dy/dx and d2y/dx2, and find the slope and concavity (if possible) at the given value of the parameter. (If an answer does not exist, enter DNE.) Parametric Equations Point x = 6t, y = 4t − 3 t = 4
Answer:
The slope of the function is ²/₃ and since the second derivative is zero, the concavity doesn't exist.
Step-by-step explanation:
Given;
x = 6t
y = 4t - 3
point t = 4
[tex]\frac{dy}{dx} = (\frac{dy}{dt} )/(\frac{dx}{dt} )=\frac{\frac{dy}{dt} }{\frac{dx}{dt}} \\\\\frac{dy}{dt} = 4; \frac{dx}{dt} = 6\\\\\frac{dy}{dx} =\frac{4}{6} = \frac{2}{3}[/tex]
The slope of the function is ²/₃
take the second derivative of the function;
the second derivative will be zero since the first derivative is a constant value.
[tex]\frac{d^2y}{dx^2} = 0[/tex]
Since the second derivative is zero, the concavity doesn't exist.
Please help! Find the value of x and the perimeter
Answer:
For the triangle, [tex]x=14[/tex]
For the rectangle, [tex]x=\frac{5}{2}[/tex]
Step-by-step explanation:
To solve for x in these equations, we have treat each side as it's just one number - add them all up.
The perimeter of a triangle will be the sum of all 3 of its sides.
So:
[tex]x + 4 + 2x - 3 + x = 57[/tex]
We can combine like terms to get
[tex]4x + 1 = 57[/tex]
Subtract 1 from both sides:
[tex]4x = 56[/tex]
Divide both sides by 4:
[tex]x = 14[/tex]
For the rectangle, the perimeter is [tex]2l + 2w[/tex], so we can add up the sides.
[tex]5x - 4 + 5x - 4 + 3x + 2 + 3x + 2 = 36[/tex]
Combine like terms:
[tex]16x - 4 = 36[/tex]
Add 4 to both sides:
[tex]16x = 40[/tex]
Divide both sides by 18:
[tex]x = \frac{40}{16}[/tex]
Simplifying this fraction gets us
[tex]\frac{5}{2}[/tex]
Hope this helped!
cost
11. There are 6 granola bars in each box. Which
expression can be used to find the number of
granola bars in a dozen boxes?
A (6 + 10) X (6+2)
B (6 X 10) + (6 X 2)
ation
C (6 + 10) + (6 + 2)
n
D (6 X 10) X 6 X 2)
Answer:
B
Step-by-step explanation:
since there are 6 bars in one box, you would multiple 6 by 12 and the answer B is just a complicated form of doing this (12 is a dozen but Baker's dozen is 13 just saying)
The formula for the volume V of a rectangular prism is V = ℓwh, where ℓ represents the length, w represents the width, and h represents the height. Rearrange the quantities in this formula to give a new formula for the width of the rectangular prism.
Answer:
w = [tex]\frac{V}{lh}[/tex]
Step-by-step explanation:
We can find the formula for the width by isolating w:
V = lwh
Divide each side by lh to isolate w:
[tex]\frac{V}{lh}[/tex] = w
A class is using base-ten block to represent numbers. A large cube represents 1000, a flat represents 100, a rod represents 10, and a little cube represents 1. Which of these is not a correct representation for 2,347?
Answer: 23 flats, 4 rods, 7 little cubes
Step-by-step explanation: 2300 + 40 + 7 = 2347
The only correct representation for 2,347 is 2 large cubes, 3 flats, 4 rods, 7 little cubes
Option A is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To represent 2,347 using base-ten blocks, we need:
2 thousands (represented by 2 large cubes)
3 hundreds (represented by 3 flats)
4 tens (represented by 4 rods)
7 ones (represented by 7 little cubes)
So we should have:
2 large cubes + 3 flats + 4 rods + 7 little cubes
Therefore, any option that does not have 2 large cubes, 3 flats, 4 rods, and 7 little cubes is not a correct representation for 2,347.
Let's check each option:
a) 2 large cubes, 3 flats, 4 rods, 7 little cubes
This is a correct representation for 2,347.
b) 3 large cubes, 4 flats, 7 rods
This represents 3,470, which is not the same as 2,347.
c) 20 hundreds, 3 tens, 4 ones
20 hundreds would be represented by 20 flats, which is not the same as the 3 flats needed to represent 300. Therefore, this option is not a correct representation for 2,347.
d) 23 hundreds, 4 tens, 7 ones
23 hundreds would be represented by 23 flats, which is not the same as the 3 flats needed to represent 300. Therefore, this option is not a correct representation for 2,347.
Therefore,
The only correct representation for 2,347 is option a), and options b), c), and d) are not correct representations.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
order for least to greatest 1.2, 0.12, 12, 0.012
Answer:
is this helpful
Step-by-step explanation:
0.012,0.12,1.2,12
Answer:
0.012, 0.12, 1.2, 12
Step-by-step explanation:
Look at where the point is located to help figure out the order
The GED preparation class has a teacher to student ratio of 1:12. If there are 36 students in the class, how many teachers are present?
Answer:
3
Step-by-step explanation:
Step 1: Recognize you can put 1:12 into a fraction along with 36 students with 'x' as number of teachers when you have 36 students
[tex]\frac{1}{12}[/tex]
[tex]\frac{x}{36}[/tex]
Step 2: Set the 2 fraction equal to each other
[tex]\frac{1}{12} =\frac{x}{36}[/tex]
Step 3: Cross multiple and solve for 'x'
[tex]12x=36\\x=3[/tex]
Therefore there are 3 teachers present when there are 36 students in the class
six over ten >_______> one over two
Answer:
11/20
Step-by-step explanation:
six over ten =6/10=0.6
one over two =1/2=0.5
so one number that can be between them is 0.55
which is 55/100=11/20
40 points! PLEASE HELP ASAP Find the area A of △JKL with vertices J(−4,10), K(0,3), and L(−4,−2). A= ___ square units
Answer:
24
Step-by-step explanation:
I belieive it would be 24
correct me if im incorrect
Identify the following series as arithmetic, geometric, both, or neither. 3a + 3a² + 3a³ + . . . + 3an geometric arithmetic neither both
Answer:
solution
given=3a+3a^2+3a^3+....+...+...3an
first term(t1)=3a
second term(t2)=3a^2
third term(t3)=3a^3
for arithmetic mean ,d1=d2
d1=t2_t1=3a^2_3a=3a(a_1)
d2=3a^3_3a^2=3a^2(a_1)
here d1 is not equal to d2.
so it's not an arithmetic series.
Again,for geometric mean,r1=r2
r1=d2/d1=3a^2/3a=a
r2=d3/d2=3a^3/3a^2=a
here ,r1 is equal to r2.
so ,it's an geometric series.
There are three motors available to repair Ralph’s vacuum cleaner. Motor #1 has a 65% chance of breaking by the end of the week. Motor #2 has a 35% chance of breaking by the end of the week. Motor #3 has a 5% chance of breaking by the end of week. Suppose that Ralph randomly chooses one of the three motors so that each is equally likely, and then the motor does break by the end of the week. What is the conditional probability that Ralph installed motor #1?
Answer:
0.619
Step-by-step explanation:
from the question we have the following data:
probability of motor 1 breaking = 65% = 0.65
probability of motor 2 breaking = 35% = 0.35
probability of motor 3 breaking = 5% = 0.05
since we have 3 motors the probability of any of them breaking down is = [tex]\frac{1}{3}[/tex]
but what the question requires from us is the conditional probability of the first one being installed
we have to solve this questions using bayes theorem
such that:
[tex]\frac{0.65*\frac{1}{3} }{0.65*\frac{1}{3}+0.35*\frac{1}{3}+0.05*\frac{1}{3} }[/tex]
= [tex]\frac{0.2167}{0.2167+0.1167+0.0167}[/tex]
= [tex]\frac{0.2167}{0.3501}[/tex]
= 0.618966
approximately 0.619
therefore the conditional probability ralph installed the first motor is 0.619
The absolute value of 11 is 11. True False
Answer:
TRUE. Absolute value of positive numbers stay positive.
Answer:
True
Step-by-step explanation:
The absolute value of a positive number would be the number itself. Because 11 is a positive number, its absolute value would be 11.
If it were a negative number, the absolute value would be the positive versions of that number. For example, if a number is -5, the absolute value of -5 would be 5.