Answer:
a)
H₀ : µd = 0
H₁ : µd < 0
b)
The test statistic is
tₙ₋₁ = α / s√n
c)
at 0.10 level of significance,
tₙ₋₁ , ₐ
t₃₀₋₁ , ₀.₁₀ = t₂₉, ₀.₁₀ = 1.311
d)
given that T(critical) = 1.62
∴ T(critical) = 1.62 > t₂₉, ₀.₁₀ = 1.311
at 10% level of significance,
REJECT H₀
Since 1.62 > 1.311, we can reject the null hypothesis.
1
1
A baseball weighs approximately
3
pound. A golf ball weighs about pound.
10
What expression can be used to find the combined weight of a baseball and a golf ball?
Answer:
6 pounds 10 ounces
Step-by-step explanation:
I take this to mean "a baseball weighs approximately 3 pounds and a golf ball three pounds ten ounces."
Adding these two weights together, we get 6 pounds 10 ounces.
Simplify i12
A.-1
B.-i
C.i
D.1
Answer:
D 1
Step-by-step explanation:
i^12
We know i^4 = 1
Rewriting
i^4^3
1^3
1
Answer:
part 1- D. 1
part 2- Square root of -144 =12i
Step-by-step explanation:
Got them correct
1 Dorji
ran 2km in 20 minutes. A that rake how far would he
run in an hour?
-->
Answer:
8km
Step-by-step explanation:
if he took 20km in 20min how about 1h
do cross multiplication( use 60min instead of 1h)1h = 60min
The arc length apothem shown below is 15 feet. Part 1) State the equation that relates arc length to central angle. Part 2) Find the angle apothem in radians. Part 3) Convert your answer from Part 2 to degrees and write it to the nearest hundredth of a degree
Answer:
ans right down there
Step-by-step explanation:
Here,Part 1
if the circle has a radius r so,
15 = r theta
here, theta is in radian.
Part 2
[tex]theta = \frac{15}{6} = 2.5[/tex]
part 3
[tex]theta = \frac{2.5 \times 180}{\pi} [/tex]
or theta =
143.2394487827058021919953870352629258310136811664108038729006
Find an equation of the circle whose diameter has endpoints , (−6,−1) and (2,3).
Answer:
first... You think and Conceptualize
A diameter divides a circle into equal halves
We're given the end points of the Diameter.
With this we can fine the Center of the circle.
The End Points are
(-6, -1) and ( 2, 3)
Half-way through the diameter gives the center of the circle
So We'd apply the Mid-Point formula to get the co-ordinate of the center.
X= x₁ + x₂/2 , Y = y₁ + y₂/2
X = -6 + 2/2, Y = -1 + 3/2
X= -2. Y = 1
The Midpoint is (-2, 1)
The Radius would be the distance between the center and a point on the circumference.
We already have 2 points of the circumference (Which are the endpoints of the diameter).
So we can pick any of them arbitrarily.
I'd go with (2,3)
So We'd apply the distance between Points formula to get the magnitude of the radius
(-2,1) (2,3)
D = √(x₁ - x₂)² + (y₁ - y₂)²
D = √(-2-2)² + (1-3)²
D=√(-4)² + (-2)²
D=√20.
Our Radius is √20.
Equation of Circle =
(x-h)² + (y-k)² = r²
Where h and k are the center of the circle(-2,1)
(x-(-2))² + ( y - 1 )²= (√20)²
(x + 2)² + ( y - 1)² = 20
Our Answer
(x + 2)² + (y - 1)² = 20.
This should be it.
Have a great day!
Hello again. if someone gives me a hand with this book thickness excercise please thanks
Answer:
Known:
• a book have front, back and 200 pages
• front= 0.7 mm
• back= 0.7 mm
• each page= 0,14 mm
ask:
calculate the minimum thickness...?
answer:
a. 200 p × 0,14 = 28 mm
b. front + back = 0.7+0.7= 1.4 mm
Thickness= 28+1,4 = 29,4 mm
I hope this helps
if u have question let me know in comments^_^
When a number is tripled, its value increases by 10. What is the original value?
[tex]3x=x+10[/tex]
We tripple something and get 10 more than something.
Put the x-es on the left and non x-es to the right,
[tex]2x=10[/tex]
Divide both sides by 2,
[tex]x=5[/tex]
Et Viòla.
Hope this helps :)
When a number is tripled, its value increases by 10 then the original number is 5.
Let's call the original number "x". According to the problem, when this number is tripled, its value increases by 10. Mathematically, we can represent this as an equation:
3x = x + 10
Now, we can solve for "x" step by step:
1. Subtract "x" from both sides of the equation:
3x - x = 10
2. Simplify the left side:
2x = 10
3. Divide both sides by 2 to solve for "x":
x = 10 / 2
x = 5
So, the original number "x" is 5.
In other words, if you take a number, triple it (multiply by 3), and then increase the result by 10, you would end up with the value 5. This can be verified by checking:
3 * 5 = 15
15 + 10 = 25
The equation 3x = x + 10 represents the relationship between the original number and its tripled value with an increase of 10. Solving this equation helps us find the original value that satisfies the given condition.
To know more about Equation here
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The chart shows a certain city's population by age. Assume that the selections are independent events. If 8 residents of this city are selected at random, find the probability that the first 2 are 65 or older, the next 3 are 25-44 years old, the next 2 are 24 or younger, and the last is 45-64 years old.
Answer:
0.000014
Step-by-step explanation:
The chart is not provided so i will use an example chart to explain the answer. Here is a sample chart:
City X's Population by Age
0-24 years old 33%
25-44 years old 22%
45-64 years old 21%
65 or older 24%
In order to find probability of independent events we find the probability of each event occurring separately and then multiply the calculated probabilities together in the following way:
P(A and B) = P(A) * P(B)
probability that the first 2 are 65 or older
Let A be the event that the first 2 are 65 or older
The probability of 65 or older 24% i.e. 0.24
So the probability that first 2 are 65 or older is:
0.24(select resident 1) * 0.24(select resident 2)
P(A) = 0.24 * 0.24
= 0.0576
P(A) = 0.0576
probability that the next 3 are 25-44 years old
Let B be the event that the next 3 are 25-44 years old
25-44 years old 22% i.e. 0.22
So the probability that the next 3 are 25-44 years old is:
0.22 * 0.22* 0.22
P(B) = 0.22 * 0.22 * 0.22
= 0.010648
P(B) = 0.010648
probability that next 2 are 24 or younger
Let C be the event that the next 2 are 24 or younger
0-24 years old 33% i.e. 0.33
So the probability that the next 2 are 24 or younger is:
0.33 * 0.33
P(C) = 0.33 * 0.33
= 0.1089
P(C) = 0.1089
probability that last is 45-64 years old
Let D be the event that last is 45-64 years old
45-64 years old 21% i.e. 0.21
So the probability that last is 45-64 years old is:
0.21
P(D) = 0.21
So probability of these independent events is computed as:
P(A and B and C and D) = P(A) * P(B) * P(C) * P(C)
= 0.0576 * 0.010648 * 0.1089 * 0.21
= 0.000014
What is the equation of the line that passes through the point (8,3) and has a slope
of
1/4
Answer:
y = 1/4x+1
Step-by-step explanation:
Using slope intercept form
y = mx+b
where m is the slope and b is the y intercept
y =1/4 x+b
Substituting in the point
3 = 1/4(8)+b
3 = 2+b
Subtract 2 from each side
3-2 = b
1 =b
y = 1/4x+1
Answer:
y=1/4x+1
Step-by-step explanation:
the equation for a line is y=mx+b
where m is the slope and b is the y-intercept. since we have our slope given and and x,y given we can use that to solve for b. we get:
3=1/4(8)+b
3=2+b
1=b
therefore the y-intercept is b
so the equation is y=1/4x+1
Find the missing probability.
P(A) = 23,P(An B)= P(B|A) =?
Answer:
the formular is
p(B/A)=P(AnB)/P(A)
so the missing probability is:-
P(AnB)=P(B/A)×23
And the other missing probablility is:-
p(B/A)=P(AnB)/23
1) Find the volume and surface area of the composite figure below
2) Find the surface area of the composite figure below
1.
[tex]volume = 64(21 + 4\pi) = 2148.5714 \: cubic \: feets[/tex]
[tex]surface \: area = 752 + 64\pi = 953.143 \: square \: feets[/tex]
2.
[tex]surface \: area = 220 + 9\pi = 248.257 \: square \: feets[/tex]
What does it mean when the resulting temperature is above 0 on the number line? What does it mean when a temperature is below 0?
Answer:
It means that above 0 degrees Celsius the water does not freeze, whereas 0 degrees are freezing teperatures of water.
Step-by-step explanation:
Water freezes at 0 degrees Celsius, but the freezing temperature can be lowered by adding salt to the water. A student discovered that adding half a cup of salt to a gallon of water lowers its freezing temperature by 7 degrees Celsius. What is the freezing temperature of the gallon of salt water?
0° - 7° = -7°
A box of chocolates contains five milk chocolates, three dark chocolates, and four white chocolates. You randomly select and eat three chocolates. The first piece is milk
chocolate, the second is white chocolate, and the third is milk chocolate. Find the probability of this occuring.
Answer:
60/220
Step-by-step explanation:
we use combination,
[tex] (\frac{5}{1} ) \times ( \frac{4}{1} ) \times ( \frac{3}{1} )[/tex]
[tex]5 \times 4 \times 3 = 60[/tex]
then, all divided by,
[tex] (\frac{12}{3}) = 220 [/tex]
[tex]60 \div 220[/tex]
The probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The sample contains five milk chocolates, three dark chocolates, and four white chocolates. Therefore, the probability that the first piece is milk chocolate is
[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]
[tex]\rm Probability=\dfrac{5}{12}[/tex]
Now, since the chocolate is been eaten the sample size will reduce from 12 chocolates in total to 11 chocolates in total (four milk chocolates, three dark chocolates, and four white chocolates). Therefore, the probability of the second piece being white chocolate is
[tex]\rm Probability=\dfrac{\text{Number of White choclates}}{\text{Total number of choclates}}[/tex]
[tex]\rm Probability=\dfrac{4}{11}[/tex]
Now, as the chocolate is been eaten the sample size will reduce from 11 chocolates in total to 10 chocolates in total (four milk chocolates, three dark chocolates, and three white chocolates). Therefore, the probability of the third piece being milk chocolate is
[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]
[tex]\rm Probability=\dfrac{4}{10}[/tex]
Thus, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is
[tex]\rm Probability=\dfrac{5}{12}\times \dfrac{4}{11} \times \dfrac{4}{10} = \dfrac{80}{1320} = 0.06[/tex]
Hence, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.
Learn more about Probability:
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All human blood can be "ABO-typed" as O, A, B, or AB, but the distribution of the types varies a bit among groups of people. Here are the distributions of blood types for a randomly chosen person in China and in the United States:The probability O A B ABChinese 0.35 0.27 0.26 0.12American 0.45 0.4 0.11 0.04Suppose we randomly select an American and a Chinese, independently of each other, apply multiplication and addition probability rules, compute:a. Pr(They both have type O)b. Pr( they both have the same blood type)c. Pr( at least one person has type O)
Answer:
a. Pr(They both have type O)
= Pr(They both have type O)
= 0.35 x 0.45
= 0.1575 = 15.75%
b. Pr( they both have the same blood type)
= Pr( they both have the same blood type)
= 2/8
= 0.25 = 25%
c. Pr( at least one person has type O)
= Pr (at least one person has type O)
= 1 - 0.3575
= 0.6425 = 64.25%
Step-by-step explanation:
a) Data:
O A B AB
Chinese 0.35 0.27 0.26 0.12
American 0.45 0.4 0.11 0.04
b) Calculations:
i. Pr(They both have type O)
= Probability of Chinese with O multiplied by Probability of American with O
= 0.35 * 0.45
= 0.1575 = 15.75%
ii. Pr( they both have the same blood type)
= Probability of two out of 8 outcomes
= 2/8
= 0.25 = 25%
iii. Pr( at least one person has type O)
= Probability of (1 – p(none) )
The probability of none = p(none O blood type)
= p(none)
for Chinese = (0.27 + 0.26 + 0.12) * for American ( 0.4 + 0.11 + 0.04)
= 0.65 * 0.55 = 0.3575
Pr (at least one person has type O) = 1 - 0.3575
= 0.6425
Please Help I will give you a lot of points if you do!
Recall that a ⇒ b ⇔ ¬a ∨ b. So we can write
q ⇒ (p ∧ r ) ⇔ ¬q ∨ (p ∧ r )
Then the negation of this would be, for instance,
¬(¬q ∨ (p ∧ r )) ⇔ ¬(¬q) ∧ ¬(p ∧ r )
… ⇔ q ∧ (¬p ∨ ¬r )
… ⇔ (¬p ∧ q) ∨ (q ∧ ¬r )
… ⇔ ¬(p ∨ ¬q) ∨ (q ∧ ¬r )
… ⇔ (p ∨ ¬q) ⇒ (q ∧ ¬r )
It's impossible to tell what kind of statement your program is expecting, but since there are 5 slots available, my money would be on q ∧ (¬p ∨ ¬r ), so long as ¬p and ¬r are options.
Solve the equation for x by graphing.-4x-1 5x=4
Answer: Undefined
Step-by-step explanation:
slope is undefined
no y intercept
This line is vertical
Can the sides of a triangle be in the given ratio? 3:4:5
Answer:
Yes
Step-by-step explanation:
Yes, and it’s a right triangle.
3²+4²=5²
9+16=25
25=25
Answer:
Yes
Step-by-step explanation:
In order to determine if a triple of values will form a triangle, we must apply the Triangle Inequality Theorem, which states that for a triangle with lengths a, b, and c:
a + b > c
a + c > b
b + c > a
Here, let's suppose that since the ratio of the sides is 3 : 4 : 5, then let the actual side lengths be 3x, 4x, and 5x, where x is simply a real value.
With loss of generality, set a = 3x, b = 4x, and c = 5x. Plug these into the Triangle Inequality to check:
a + b > c ⇒ 3x + 4x >? 5x ⇒ 7x > 5x ⇒ This is true
a + c > b ⇒ 3x + 5x >? 4x ⇒ 8x > 4x ⇒ This is also true
b + c > a ⇒ 4x + 5x >? 3x ⇒ 9x > 3x ⇒ This is true
Since all three conditions are satisfied, we know that a true triangle can be formed given that the ratio of their sides is 3 : 4 : 5.
~ an aesthetics lover
3 1/2 ft into inches
Answer:
42 inches
Step-by-step explanation:
1 ft = 12 inch
Answer:
42 inches.
Step-by-step explanation:
Unit of measurement:
1 foot = 12 inches.
3 ft x 12 inches = 36 inches.
1/2 foot x 12 inches = 12/2 = 6 inches.
36 inches + 6 inches = 42 inches
42 inches is your answer.
~
look at the image below forr the question plz
Answer:
[tex]308 \ m^3\\[/tex]
Step-by-step explanation:
The volume of a three-dimensional shape is the amount of space the figure takes up. This can be found by multiplying all of the dimensions of a figure together. In essence, the following formula can be used to find the volume.
[tex]A=l*w*h[/tex]
Where (l) represents the figure's length; (w) is the width: and (h) the height. Substitute the given values into the formula and solve for the volume.
[tex]A=l*w*h[/tex]
[tex]A=7*4*11[/tex]
Simplify,
[tex]A=7*4*11[/tex]
[tex]A=28*11[/tex]
[tex]A=308[/tex]
HELP ME ILL GIV ROBUX Identify the property shown by the equation. 14 × 6 = 6 × 14 A. Commutative Property B. Associative Property C. Identity Property D. Distributive Property PLEASE HELP ME
Answer:
A. Commutative Property
Step-by-step explanation:
Hello!
This is the Commutative property which is when you can change the order of the numbers and the result does not change.
Hope this helps!
plz help me on this question best and right answer gets brainliest
Answer:
| - 5| 5
| 6 | 6
| - 9 | 9
the numbers will be positive when they come out from the absolute value
Answer and Step-by-step explanation:
The absolute value of a value is the positive version of that value.
| | <- Brackets are used to show that a value is being absolute.
|-5| = 5 The negative 5 with absolute brackets becomes a positive 5.
|6| = 6 A positive 6 with absolute brackets stays a positive 6.
|-9| = 9 A negative 9 with absolute brackets becomes a positive 9.
#teamtrees #PAW (Plant And Water)
Solve the equation for solutions in the interval [0, 2 π). Use algebraic methods and give exact values. Support your solution graphically. cos2x = 0
Answer:
45° or 135°
Step-by-step explanation:
Cos 2x = 0
2x = cos^-1 0
2x = 90° or 270°
x= 45° or 135°
Answer:
Step-by-step explanation:
● cos 2x = 0
We khow that Pi/2 equals 0.
So
● 2x = Pi/2 or 2x= -Pi/2
Then:
● x = Pi/4 or x = -Pi/2
So the solutions are:
● x = Pi/4 + 2×k×Pi
● or x = -Pi/4 + 2×k×Pi
Where k is an integer
The picture below has a graphical solution
● Pi/4 is approximatively 0.785 and -Pi/4 is approximatively -0.785
● the output of both Pi/4 and -Pi/4 is 0
So our answer was righr
Please answer this correctly without making mistakes
Answer:
10 9/20
Step-by-step explanation:
Hey there!
If Hillsboro to Campbell is 16 2/20 and Hillsboro to Oxford is 5 13/20,
we’ll do
16 2/20 - 5 13/20
Imrpoper form
322/20 - 113/20
322 - 113
209/20
10 9/20 miles from Oxford to Campbell.
Hope this helps :)
James stand at the centre of a regular field. he first take 50 steps North then 25 step West and finally 50 steps on the bearing of 315°.
i. sketch James movement
ii. how far west is James final point from the centre?
iii. how far north is James final point from the centre?
iv. describe how you would guide a jhs student to find the bearing and distance of James final point from the centre.
Answer:
Step-by-step explanation:
i. For navigation purposes, bearing is measured clockwise from north. In (x, y) coordinates, a distance D at a bearing B will have coordinates ...
(x, y) = (Dsin(B), Dcos(B))
Then 50 steps north (bearing 0°) will put James at coordinates ...
(x, y) = (50sin(0), 50cos(0)) = (0, 50)
The movement 25 steps west (bearing 270°) will add a displacement of ...
(x, y) = (25sin(270°), 25cos(270°)) = (-25, 0)
Finally, the movement of 50 steps on bearing 315° will add a displacement of ...
(x, y) = (50sin(315°), 50cos(315°)) = (-25√2, 25√2)
These movements are shown by the arrows to N, W, and F in the attached diagram.
__
ii. James's final displacement is the sum of the individual displacements:
(0, 50) +(-25, 0) +(-25√2, 25√2) = (-25(1+√2), 25(2+√2))
James is 25(1+√2) ≈ 60.4 steps west of center.
__
iii. James is 25(2+√2) ≈ 85.4 steps north of center.
__
iv. The distance can be found using the Pythagorean theorem (or distance formula). The distance from the origin to the final position (OF in the diagram) will be the root of the sum of the squares of the north and west displacements:
distance = √(85.355² +60.355²)
distance ≈ 104.5 steps
The bearing can be found using the arctangent function. The diagram shows you the reference angle (relative to the +y direction) has an opposite side equal to the west displacement, and an adjacent side equal to the north displacement. Then the bearing angle (β) will be ...
tan(β) = opposite/adjacent = -60.355/85.355
β ≈ arctan(-0.707106) ≈ -35.3°
The positive bearing angle is 360° added to this, or
bearing = 324.7°
Which of the following is the graph of the quadratic parent function
This is the graph of y = x^2. It is a parabola that opens upward and has its vertex at the origin. Applying various transformations to the parent function will allow us to produce any parabolic graph we want. In effect, the parent function is like the most basic building block.
SOVE, REDUCE TO LOWEST TEERMS SIMPLIFY IMPROPER FRACTIONSAS MIXED FRACTIONS
Which best describes the relationship between the line that passes through the points (8, 2) and (3,
5) and the line that passes through the points (-3,-7) and (0, -12)?
Answer:
C
Step-by-step explanation:
They are neither perpendicular nor parallel since line 1 has slope=-3/5 and line 2 has slope=-5/3. They are neither equal nor have a product equal to - 1.
You are considering the services of three different employment agencies, all of which can get you a job that starts at $2,000 a month. Agency A charges 50 percent of the first month's gross salary. Agency B charges 10 percent of your monthly salary for the first six months. Agency C charges a $100 up-front fee and a flat fee of $500 when you are placed. Compare the three choices. Which of these offers the least expensive overall fee?
Answer:
Agency C offers the least expensive overall fee
Step-by-step explanation:
Alone from gross salary, you would make 24000 a year.
Agency A
24000 - ( 2000 x 0.5)
= 23,000
$1000 fee
Agency B
24000 - ( 2000 x 0.1 ) x 6
= 24000 - 200 x 6
= 24000 - 1200
= 22,800
$1200 fee
Agency C
24000 - (500 + 100)
= 24000 - 600
= 23,400
$600 fee
Kathleen ordered a box of different colored light bulbs to use for stage lighting at the concert. Of the 60 bulbs in the box, 20% were red, 30% were orange, 30% were green, and 20% were blue. Of the blue ones, approximately 10% were damaged. What is the closest estimate for the number of blue bulbs that were damaged?
Answer:
1 bulb
Step-by-step explanation:
First find the number of blue bulbs
60 * 20 %
60 * .2
12 blue bulbs
10 % of the blue were damaged
12 * 10%
12 * .10
1.2
Rounding to the nearest whole number
1 bulb
(5.5 * 10^-6 + 6.3 * 10^-6)^2
9514 1404 393
Answer:
exact: 1.3924×10^-10rounded to 2 sf: 1.4×10^-10Step-by-step explanation:
The factor 10^-6 can be brought out:
((5.5 +6.3)×10^-6)^2 = (11.8^2)×10^-12 = 1.3924×10^-10
Often, a problem like this wants you to round to a precision appropriate to the given values. Here, that is 2 significant figures:
≈ 1.4×10^-10
_____
Additional comment
Your scientific or graphing calculator can do this nicely, even showing you the result in scientific notation. A spreadsheet can do the same.
The usual rules of exponents apply.
(a^b)(a^c) = a^(b+c)
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)