Answer:
Fail to reject the null hypothesis.
Step-by-step explanation:
People who live in Florida and also have annual pass to Disney world is 221, sample size selected for group 1 is 350.
People who do not live in Florida and have annual pass to Disney world is 365, sample size selected for Group 2 is 650.
Group 1 sample proportion is : 221 / 350 = 0.6314
Group 2 sample proportion is 365 / 650 = 0.5615
Test statistics is 0.8317
Since test stats value is greater than the sample proportion significance level, we fail to reject the null hypothesis.
Solve, expressing your answer in an exact form involving a natural logarithm and showing your steps: 3*e^1/2t+4=27
Answer:
3 e^t/2 + 4 = 27
e^t/2 = 23 / 3
Taking natural log of both sides
t/2 = ln 23/3 = ln 7.667 = 2.037
t = 4.074
Check:
3 e^4.074/2 + 4 = 27
27 = 27
The radius of a circular disk is given as 26 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error in the calculated area of the disk. (Round your answer to two decimal places.) cm2 (b) What is the relative error
Answer:
(a) Hence the maximum error in the calculated area of the disk is 32.67[tex]cm^{2}[/tex].
(b) Hence the relative error is 1.54%.
Step-by-step explanation:
Here the given are,
The Radius of the circle r = 26cm.
The maximum error in measurement dr = 0.2 cm.
Answer:
(a) [tex]A =(4245.28\pm32.66) cm^2[/tex]
(b) [tex]\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077[/tex]
Step-by-step explanation:
radius, r = 26 cm
error = 0.2 cm
(a) The area of the disc is given by
[tex]A = \pi r^2\\\\dA = 2\pi r dr\\\\dA = 2 \times 3.14\times 26\times 0.2= 32.66[/tex]
Now
A = 3.14 x r x r = 3.14 x 26 x 26 = 4245.28 cm^2
So, the area with error is given by
[tex]A =(4245.28\pm32.66) cm^2[/tex]
(b) The relative error is
[tex]\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077[/tex]
The average 30- to 39-year old man is 69.5 inches tall, with a standard deviation of 2.7 inches, while the average 30- to 39-year old woman is 64.2 inches tall, with a standard deviation of 3.2 inches. Who is relatively taller based on their comparison to their gender, LeBron James at 81 inches or Candace Parker at 76 inches?
a) Candace is relatively taller because she has a larger z-score.
b) LeBron is relatively taller because he has a larger z-score.
c) LeBron is relatively taller because he has a smaller z-score.
d) Candace is relatively taller because she has a smaller z-score.
Answer:
b) LeBron is relatively taller because he has a larger z-score.
Step-by-step explanation:
Z-score:
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.
LeBron James:
Height of 81 inches, while the average 30- to 39-year old man is 69.5 inches tall, with a standard deviation of 2.7 inches, which means that we have to find Z when [tex]X = 81, \mu = 69.5, \sigma = 2.7[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{81 - 69.5}{2.7}[/tex]
[tex]Z = 4.26[/tex]
Candace Parker:
Height of 76 inches, while the average 30- to 39-year old woman is 64.2 inches tall, with a standard deviation of 3.2 inches. This means that we have to find Z when [tex]X = 76, \mu = 64.2, \sigma = 3.2[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{76 - 64.2}{3.2}[/tex]
[tex]Z = 3.69[/tex]
Who is relatively taller?
Due to the higher z-score, LeBron James, and thus, the correct answer is given by option b.
x to the power of 3 - 7x + 6 factorise please whole step by step
Answer:
[tex](x + 3)(x - 2)(x - 1)[/tex]
Step-by-step explanation:
[tex] {x}^{3} - 7x + 6[/tex]
Factor using Rational Root Theorem.
This means our possible roots are
positve or negative (1,2,3,6). If we try positve 1, it is indeed a root.
This means that
[tex](x - 1)[/tex]
is a root.
We can divide the top equation by the root (x-1). Our new equation is
[tex]( {x}^{2} + x - 6)[/tex]
Now we can factor this completely
[tex](x + 3)(x - 2)[/tex]
So this equation in factored form is
[tex](x + 3)(x - 2)(x - 1)[/tex]
Find the value of x in each case:
9514 1404 393
Answer:
x = 36
Step-by-step explanation:
The interior angle at E is (180-2x). The interior angle at F is (180-4x). The sum of the interior angles of the triangle is 180, so we have ...
(180 -2x) +x +(180 -4x) = 180
180 = 5x . . . . . . add 5x-180 to both sides
36 = x . . . . . . . divide by 5
__
Additional comment
This value of x makes the exterior angles at E and F be 72° and 144°, respectively. The internal angles at E, F, G are then 108°, 36°, 36°, making the triangle isosceles with EF = EG.
Solve 3x to the second power +17x-6=0
The solution of the equation 3x² + 17x - 6 = 0 are, x = 1/3 and x = - 6.
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The quadratic equation is,
⇒ 3x² + 17x - 6 = 0
Now, We can solve the equation as;
⇒ 3x² + 17x - 6 = 0
⇒ 3x² + (18 - 1)x - 6 = 0
⇒ 3x² + 18x - x - 6 = 0
⇒ 3x (x + 6) - 1 (x + 6) = 0
⇒ (3x - 1) (x + 6) = 0
This gives two solutions,
⇒ 3x - 1 = 0
⇒ x = 1/3
And, x + 6 = 0
⇒ x = - 6
Learn more about the quadratic equation visit:
brainly.com/question/1214333
#SPJ2
Do 8 plz find OS thanks
Answer:
OS = 10
Step-by-step explanation:
We can use a ratio to solve
QP PR
----- = ------
QO OS
14 7
----- = -------
14+6 OS
14 7
----- = -------
20 OS
Using cross products
14 * OS = 7*20
14 OS = 140
Divide by 14
OS = 140/14
OS = 10
44 and 45 are alternate interior
angles. Find the measure of 44.
t
115/65°
43/44
44 = [?]
t
45/46
47/48
274
Fnter
Answer:
115
Step-by-step explanation:
The opposite angles (115degree angle and angle 4) are equal.
Angle 3=65
Angle 4=115
Angle 5=115
Angle 6=65
Angle 7=65
Angle 8=115
Brainliest please~
Help please, thanks
Answer: B. X It passes the vertical line test :)
Step-by-step explanation:
Diane bought new headphones originally listed for $70.99. They are 25% off. Which equation can be used to find the amount Diane will save?
Step-by-step explanation:
100% = $70.99
there is a discount of 25%.
that means 75% (100 - 25) of the original price remains.
the equation to get any x% amount of a 100% total is simply
x% amount = 100% total amount × x/100
25% = 70.99 × 25/100 = $17.75
Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 2 million barrels of oil in the well; six years later 1,000,000 barrels remain.
Required:
a. At what rate was the amount of oil in the well decreasing when there were 1,200,000 barrels remaining?
b. When will there be 100,000 barrels remaining?
Answer:
A. It was decreasing by -138,629.44 barrels
B. 26 years of time
Step-by-step explanation:
Due to the length of this question solution, I was unable to type it. The answer is contained in the attachment.
A. At 1200000
Bt = 1200000
-1/6ln2 x 1200000
Solve this using a calculator
= -138,629.4361
So the amount of oil is decreasing by -138,629.44 barrels
a family has two children. what is the probability that both are girls, given that at least one is a boy
Answer: The probability would be zero
Step-by-step explanation:
There are two children and one is a boy, so the probability of both being girls is a zero
A student writes
2
pages of a report in
2
an hour. What is her unit
rate in pages per hour?
Answer:
1 page of a report per hour
Step-by-step explanation:
2/2= 1 page per hour
Lets find unit rate
[tex]\\ \sf\longmapsto \dfrac{2\dfrac{1}{2}}{2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{5}{2}\div 2[/tex]
[tex]\\ \sf\longmapsto \dfrac{5}{4}[/tex]
[tex]\\ \sf\longmapsto 1.2pages/hour[/tex]
Find two numbers that have 2, 5, and 7 as factors.
Step-by-step explanation:
One easy way to find a number that has all of these numbers as factors is to multiply them all together, so 2 * 5 * 7 = 10 * 7 = 70, which is one number.
To find the other number, we can multiply the number we already have by any integer greater than 1, e.g. 2, to get 70* 2= 140 as our other number, making our numbers 70 and 140
Two buses leave towns 1060 kilometers apart at the same time and travel toward each other. One bus travels 14 kilometers an hour faster than the other. If they meet in 5 hours, what is the rate of each bus?
Answer:
99, 113
Step-by-step explanation:
X-the first bus
X+14-the second bus
5x+5(x+14)=1060
10x+70=1060
10x=990
X=99-the first bus
99+14=113-the second bus
A camera with a price of d dollars is discounted 25%. write two expressions to represent the price of the camera with the discount.
Answer:
17d/20
Step-by-step explanation:
100-25=85
85/100×d
=17/20×d
=17d/20
Please help! Question in image below:
Answers also below:
Answer:
11, 18, 25, 32, .....
Option D
Step-by-step explanation:
The formula for the nth term of an AP is a+(n-1)d
a+(n-1)d=a+(n-1-1)d+7
a+nd-d=a+nd-2d+7
d=7
As the common difference is 7.
The only option given which is in an AP is the 4th option
Which of the following numbers is rational? Assume that the decimal patterns continue.
9514 1404 393
Answer:
(c) √49
(d) 2.544544...(3-digit repeat)
Step-by-step explanation:
Square roots of perfect squares are rational, as are repeating decimals.
A kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs of congruent sides. Prove the diagonal connecting these vertex angles is perpendicular to the diagonal connecting the non-vertex angles. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.
Describe how to transform the graph of f(x) = x2 to obtain the graph of the related function g(x).
Then draw the graph of g(x).
1. g(x) = f(x + 1)
2. g(x) = f(x) - 2
Please help i also need to graph
9514 1404 393
Answer:
left 1 unitdown 2 unitsStep-by-step explanation:
The transformation g(x) = f(x -h) +k is a translation of f(x) to the right by h units and up k units.
1. h = -1, so the graph of g(x) is the graph of f(x) shifted left 1 unit. (blue)
__
2. k = -2, so the graph of g(x) is the graph of f(x) shifted down 2 units. (green)
X^2 + bx + 49 is a perfect squad trinomial what is one possible value of b?
a perfect square trinomial, (x + y)² = x² + 2xy + y²
so, if we have the x of the bx, what is left is the b
the expression would have to be (x + 7)², since we have the 49 and the x²
so, what's left: x² + 14x + 49,
b = 14
hope it helps :)
A right prism of height 15 cm has bases that are right triangles with legs 5 cm and 12 cm. Find the total surface area of the prism. Please explain.
a) 315 cm2 squared
b) 480 cm2 squared
c) 510 cm2 squared
d) 570 cm2
Answer:
Option (C)
Step-by-step explanation:
Surface area of a right prism = 2(Area of the triangular base) + Ph
Here, P = Perimeter of the base
h = Height of the prism
Area of the triangular base = [tex]\frac{1}{2}(\text{Height})(\text{Base})[/tex]
= [tex]\frac{1}{2}(5)(12)[/tex]
= 30 cm²
Height of the prism = 15 cm
Perimeter of the base = (5 + 12 + 13)
= 30 cm
Surface area of the right prism = 2(30) + 30(15)
= 60 + 450
= 510 cm²
Therefore, Option (C) will be the correct option.
Now suppose that not every player can play in every position. The outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch. Suppose a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers.
How many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled?
Answer:
The team can assign field positions to 9 of the 19 players in 181,440 different ways.
Step-by-step explanation:
Since the outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch, supposing a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers, to determine how many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled, the following calculation must be performed:
3 x 7 x 6 x 5 x 4 x 3 x 4 x 3 x 2 = X
21 x 30 x 12 x 24 = X
630 x 12 x 24 = X
181,440 = X
Therefore, the team can assign field positions to 9 of the 19 players in 181,440 different ways.
A store sells 5 different shirts, 6 different pants, 3 different shoes, and 9 different socks. You are making an outfit with one of each article of clothing. How many outfits can you make?
Answer:
you can make 3 outfits
Step-by-step explanation:
because,if you just have 3 shoes aotomaticly you just wear 3 shirt and 3 pants.
for the socks, one people wear 2 socks so there you have 3 outfits
Answer:
[tex]810[/tex]
Step-by-step explanation:
For each shirt, there are 6 different pairs of pants to pair with it. For each of these pairs of pants, there are 3 different shoes to pair and so on.
Therefore, there are [tex]5\cdot 6\cdot 3\cdot 9=\boxed{810}[/tex] combinations you can make.
14) The height, h metres, of a ball projected directly upwards from the ground can be modelled by h = 56t - 71, where t is the time in seconds after it leaves the ground. a) Find the height of the ball 3.5 seconds after it leaves the ground. b) At what time will the ball strike the ground again? c) When will the ball be 49 m above the ground? Briefly explain why there are two possible answers.
If you were going to install a new window in your bathroom, what needs to be measured? What
else might you need to consider?
measure horizontally
measure vertically
measure depth..
10(2x-3)=10
find the value of x
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
10(2x-3)=1020x-30=1020x=10+3020x=40x=40/20X=2It is given that,
→ 10(2x-3) = 10
Then find required value of x,
→ 10(2x-3) = 10
→ 20x-30 = 10
→ 20x = 10+30
→ 20x = 40
→ x = 40/20
→ [x = 2]
Hence, the value of x is 2.
Michelin Tires would like to estimate the average tire life of its Latitude Tour tire in terms of howmany miles it lasts. Assume the standard deviation for the tire life of this particular brand is 6000miles. Determine the sample size needed to construct a 95% confidence interval with a margin oferror within 2000 miles.ShowWork:
Answer:
6 samples
Step-by-step explanation:
Given :
Sample size, = n
Standard deviation, = 6000
Margin of Error = 2000
Confidence interval, α = 95%
Zcritical at 95% = 1.96
n = (Zcritical * σ) / margin of error
n = (1.96 * 6000) /2000
n = 11760 / 2000
n = 5.88
n = 6 samples
A jar of gumballs contains 4 reds, 2 greens, and 6 blues. What is the probability of getting two blues in a row without replacement?
Select one:
a. 3/4
b. 1/2
c. 5/22
d. 5/11
Answer:
C
Step-by-step explanation:
Hypergeometric distribution
[tex]\frac{{6\choose2}}{{12\choose2}}=\frac{15}{66}= \frac{5}{22}[/tex]
I don't get this question i need some help please!!!
Answer:
2 sqrt(2) = x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 45 = x/4
4 sin 45 = x
4 ( sqrt(2)/2) =x
2 sqrt(2) = x
Answer: D
Use sine to find the x-value:
[tex]sin(45)=\frac{x}{4} \\\\4*sin(45)=x\\\\x=\frac{\sqrt{2} }{2} *4=2\sqrt{2}[/tex]