Answer:
the probability that Jack draws the blue ball is 0.38539
Step-by-step explanation:
Given the data in the question;
box contains
blue balls = 5
red balls = 8
Jim and Jack start drawing balls from the box, respectively, one at a time, at random, and without replacement
Now,
on the first attempted;
⇒ ( 8/13) × ( 5/12) = 10/39
on the second attempt;
⇒ ( 8/13 ) ( 7/12) ( 6/11 ) ( 5/10 ) = 14/143
on the third attempt;
⇒ ( 8/13 ) ( 7/12) ( 6/11 ) ( 5/10 ) ( 4/9 ) ( 5/8 ) = 35/1287
on the fourth attempt;
⇒ ( 8/13 ) ( 7/12) ( 6/11 ) ( 5/10 ) ( 4/9 ) ( 3/8 ) ( 2/7 ) ( 5/6 ) = 5/1287
so we add everything;
⇒ 10/39 + 14/143 + 35/1287 + 5/1287
= 0.38539
Therefore, the probability that Jack draws the blue ball is 0.38539
Side View of a Waterslide
Select the points you need to calculate the
average rate of change from the beginning of the
slide to when the slide has covered a horizontal
distance of 15 feet.
800
O
(0, 80)
60
(5, 40)
OOO
Height (ft)
(10, 20)
(15, 10)
DONE
20
20
10
Horizontal Distance (ft)
Answer:
(0, 80)
(15, 10)
Step-by-step explanation:
The initial point the beginning of the point and the point where the horizontal distance covered is 15 ft are the two points needed to calculate the average rate of change required.
From the graph,
Initial point = (0, 80)
The point of the slide when distance covered is 15 ft = (15, 10)
These are the points needed.
A.54 pie cm^3
B.72 pie cm^3
C.126 pie cm^3
D.378 pie cm^3
==========================================================
Explanation:
The radius of each sphere is r = 3
The volume of one sphere is
V = (4/3)*pi*r^3
V = (4/3)*pi*3^3
V = 36pi
That's the volume of one sphere.
Three spheres take up 3*36pi = 108pi cm^3 of space.
---------------------------
The radius of the cylinder is also r = 3, since each tennis ball fits perfectly in the container.
The height is h = 18 because we have each ball with a diameter 6, which leads to the three of them stacking to 3*6 = 18.
The volume of the cylinder is...
V = pi*r^2*h
V = pi*3^2*18
V = 162pi
-------------------------
Subtract the volume of the cylinder and the combined volume of the spheres: 162pi - 108pi = (162-108)pi = 54pi
This is the exact volume of empty space inside the can.
This points to choice A as the final answer
One kilogram equals 2.2 pounds. If a paitent weighs 79.5kg, his weight is what in pounds?
Answer:
174.9
Step-by-step explanation:
since 1 kg is 2.2 lbs
79.5 times 2.2
they weight 174.9 lbs
Answer:
174.9 pounds
Step-by-step explanation:
Create a proportion where x is his weight in pounds:
[tex]\frac{1}{2.2}[/tex] = [tex]\frac{79.5}{x}[/tex]
Cross multiply:
x = 79.5(2.2)
x = 174.9
So, his weight in pounds is 174.9 pounds
Solve the equation ln(x - 3) + ln(x + 1) = ln(x + 7)
x = 5, or x = ???
Answer:
x = 5 or x = - 2
Step-by-step explanation:
Using the rules of logarithms
log x + log y = log (xy)
log x = log y ⇒ x = y
Given
ln(x- 3) + ln(x + 1) = ln(x + 7) , then
ln (x - 3)(x + 1) = ln (x + 7) , so
(x - 3)(x + 1) = x + 7 ← expand left side using FOIL
x² - 2x - 3 = x + 7 ( subtract x + 7 from both sides )
x² - 3x - 10 = 0 ← in standard form
(x - 5)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 2 = 0 ⇒ x = - 2
Here is some record keeping from a coffee shop about their paper cups. Cups are delivered 2,000 at a time. day change Monday +2000 Tuesday -125 Wednesday -127 Thursday +1719 Friday -356 Saturday -782 Sunday 0 1. Explain what a positive and negative number means in this situation. PLEASE HELP ME
Answer: the numbers with the plus sign are positive and the ones with the negative sign are negative
Step-by-step explanation:
z is a standard normal random variable. The P (1.41 < z < 2.85) equals a.0.4978 b.0.0771 c.0.9185 d.0.4207
Answer:
[tex]P (1.41 < z < 2.85) = 0.0771[/tex]
Step-by-step explanation:
Required
[tex]P (1.41 < z < 2.85)[/tex]
This is calculated as:
[tex]P (1.41 < z < 2.85) = P(z < 2.85) - P(z < 1.41)[/tex]
From z probabilities:
[tex]P(z < 2.85) = 0.99781[/tex]
[tex]P(z < 1.41) = 0.92073[/tex]
So, we have:
[tex]P (1.41 < z < 2.85) = 0.99781 - 0.92073[/tex]
[tex]P (1.41 < z < 2.85) = 0.07708[/tex]
Approximate
[tex]P (1.41 < z < 2.85) = 0.0771[/tex]
The angles of a quadrilateral are 2x , 3x , 7x , and 8x find x
Answer:
x = 18
Step-by-step explanation:
The sum of the angles in a quadrilateral is 360
2x + 3x + 7x + 8x = 360
Combine like terms
20x = 360
Divide both sides by 20
x = 18
Which angle is coterminal to a 185° angle?
Answer:
the answer is -175. I hope that helped
Find the slope of the line through the points (−18,−12) and (0,8).
Answer:
9/10
Step-by-step explanation:
y2-y1÷x2-x1
-18-0/-12-8
-18/-20
9/10
Answer:10/9
Step-by-step explanation:You do y2-y1 over x^2-x^1 and you get 10/9
Kin travels 440 miles by train at an average speed of 110 mph.
Ayaan flies the same distance at an average speed of 880 mph.
Find the difference between their travel times.
Give your answer in hours.
Answer:
3 1/2 hours
Step-by-step explanation:
time = distance/speed
440/110 = 4 hours
440/880 = 1/2 hours
4 minus 1/2 is 3 1/2
Answer:
hi
Step-by-step explanation:
i just need some points sorry not sorry
Represent the following rational numbers on a number line.
3 /7, -5/7, 1 1/7, -2/7
Answer:
here is your answer
Step-by-step explanation:
here is your answer
You perform an experiment in which you take 16 pots of strawberry plants and give half of them 1 gm of ammonium nitrate per liter of water and the other half receive only water. Each group is then split in half again, and exposed to either 8 or 16 hours of light each day. You monitor the height of the plants for 4 weeks. You observe that plants grown in ammonium nitrate and 16 hours of light grow taller than no ammonium nitrate and 8 hours of light. Which of the following are dependent variables in this experiment?
A. An independent variable.
B. A dependent variable.
C. A controlled variable.
D. Either an independent or dependent variable.
E. Either a dependent or standardized variable.
It is influenced by the independent variables, such as the presence or absence of ammonium nitrate and the duration of light exposure.
Therefore, the correct answer is B. A dependent variable.
Here, we have,
In this experiment, the dependent variable is the variable being measured or observed as the outcome.
It is what we are interested in studying and can be influenced by the independent variables.
In the given scenario, the height of the plants is being monitored over the four weeks.
This height measurement is the outcome of the experiment and is the dependent variable.
It is influenced by the independent variables, such as the presence or absence of ammonium nitrate and the duration of light exposure.
Therefore, the correct answer is B. A dependent variable.
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picture down below please help
Answer: please add the picture
Step-by-step explanation:
help me pleaseeeee it’s timedddddd
Answer:
10feet
Step-by-step explanation:
Given the following
Horizontal distance adjacent )= 15feet
Angle of elevation = 33.69°
Required
Height (opposite)
Using the SOH CAHTOA identity
tan theta = opposite/adjacent
tan 33.69 = H/15
H = 15tan33.69
H = 15(0.6667)
H = 9.999
H = 10feet to the nearesst foot
What means the same as 6 x 5?
What means the same as 3 + 3 + 3 + 3?
65
35
5 + 5 + 5 + 5 + 5
3 X 3
6 + 6 + 6 + 6 + 6
3 X 4
COMPLETE
COMPLETE
What means the same as 657
What means the same as 2.2.2.2. 2?
5.5.5.5.5
25
6.6.6.6.6
2 x 5
6 + 6 + 6 + 6 + 6
52
COMPLETE
COMPLETE
Answer:
6x5 can also be 6+6+6+6+6
3+3+3+3 can also be 3x4
5+5+5+5+5 can also be 25
3x3 can be 3+3+3
Step-by-step explanation:
Answer:
Here were your Answers
Step-by-step explanation:
Good Job you got it right you must be new to this app because your suppose to ask a question then someone will come and see your question and answer it for you maybe look around at other people's question's and how to use this app. Have a Nice day :) happy face This is for
omar2566 and for everyone!
Determine the equation of the circle graphed below.
10
8
10
-10
-8
-6
2
-2
-4
-6
-8
-10
Answer:
Equation = (x - 6 )² + ( y + 3 )² = 9
Step-by-step explanation:
The circle passes through ( 6, 0) and ( 6 , -6)
They are the coordinates of the diameter.
Using this we can find the centre of the circle.
Find the centre of the circle.
Centre of the circle is the mid- point of (6, 0) and ( 6, -6)
[tex]Centre = (\frac{x_1+x_2}{2} , \frac{y_1 + y_2}{2})[/tex]
[tex]=(\frac{6 + 6}{2}, \frac{0 + (-6)}{2})\\\\=(6, -3)[/tex]
Find the radius of the circle.
[tex]Radius = \frac{Diameter }{2}[/tex]
Diameter is the distance between the points (6 , 0) and ( 6, - 6)
[tex]Diameter = \sqrt{(x_2 - x_1)^2+ (y_2 - y_1)^2\\}[/tex]
[tex]=\sqrt{(6-6)^2 + (-6 -0)^2}\\\\=\sqrt{0 + 36} \\\\= 6[/tex]
Therefore,
[tex]Radius ,r = \frac{6}{2} = 3[/tex]
Standard equation of a circle:
[tex](x - a)^2 + (y - b)^2 = r^2 \ where \ (a , b) \ is \ the\ centre \ coordinates.[/tex]
Therefore , equation of the circle ;
[tex](x - 6)^2 + (y + 3)^2 = 3^2\\\\(x -6)^2 + (y + 3)^2 = 9[/tex]
PLEASE HELP QUICK!! WILL GIVE BRAINLIEST ANSWER!!!!!!!
Answer:
X = 32
Step-by-step explanation:
Angle BEC = 43 degrees
You find X by setting up the equation 137 = 3x+41
Solve for x
You find angle BEC by subtracting 137 from 180, finding the acute angle that brings the obtuse angle up to 180 degrees (a flat line)
Answer:
x = 32 degree and angle BEC = 43 degree
Step-by-step explanation:
3x + 41 = 137 degree (being vertically opposite angles)
3x = 137 - 41
x = 96/3
x = 32
angle BEC be y
137 + y =180 degree (being linear pair)
y = 180 - 137
y = 43 degree
therefore angle BEC = 43 degree
Which statements are true of the given function?
Check all that apply.
9514 1404 393
Answer:
B, E
Step-by-step explanation:
The table tells you that f(0) = 3/2. (0 is found in the x-column; 3/2 is found in the f(x) column.)
__
You can find f(4) by evaluating the formula.
f(4) = 1/2·4 +3/2 = 4/2 +3/2
f(4) = 7/2 . . . . agrees with last answer choice
Answer:
A ,B and E ;)
Step-by-step explanation:
A local grocery store charges for oranges
based on weight as shown in the graph below.
Find the price (dollars per kilogram) of
oranges at the grocery store.
dollars per kilogram
Answer:
3 dollars
Step-by-step explanation:
Khan academy said so
Write in standard form 4.91E-2
Answer:
4.91e-2 in decimal form is 0.0491
How can you help this student make sense of her method?
ONLY ANSWER IF YOU KNOW THE ANSWER
Answer: Read it to him again, and explain all the steps to him nice and slowly.
what are the first five terms of the recursive sequence
Answer: Choice D
9, 30, 93, 282, 849
============================================================
Explanation:
The notation [tex]a_1 = 9[/tex] tells us that the first term is 9
The notation [tex]a_n = 3*(a_{n-1})+3[/tex] says that we multiply the (n-1)st term by 3, then add on 3 to get the nth term [tex]a_n[/tex]
So if we wanted the second term for instance, then we'd say
[tex]a_n = 3*(a_{n-1})+3\\\\a_2 = 3*(a_{2-1})+3\\\\a_2 = 3*(a_{1})+3\\\\a_2 = 3*(9)+3\\\\a_2 = 27+3\\\\a_2 = 30\\\\[/tex]
If we want the third term, then,
[tex]a_n = 3*(a_{n-1})+3\\\\a_3 = 3*(a_{3-1})+3\\\\a_3 = 3*(a_{2})+3\\\\a_3 = 3*(30)+3\\\\a_3 = 90+3\\\\a_3 = 93\\\\[/tex]
and so on.
The terms so far are: 9, 30, 93
You should find the fourth and fifth terms are 282 and 849 respectively if you keep this pattern going.
Therefore, the answer is choice D
A rectangle is 6 centimetres longer than its width
If the perimeter of the rectangle is 28 centimetres, form an equation
involving x and solving it to find the width
of the rectangle
do u mean rectangle is longer or rectangles lenght is longer
Q3a) How many lengths of string, each 53 cm
long can be cut from a ball containing 25
meters? (2 mks)
b) What length of string, in millimeters
remains? (2 mks)
Part (a)
1 meter = 100 cm
25 meters = 2500 cm .... multiply both sides by 25
Divide the 2500 cm over the 53 cm to get 2500/53 = 47.1698
Ignore the stuff after the decimal point. This means we can cut exactly 47 smaller bits of string, each 53 cm long
Answer: 47====================================================
Part (b)
We found that we can cut exactly 47 smaller bits of string, each 53 cm long. That takes up 47*53 = 2491 cm overall
The leftovers would be 2500 - 2491 = 9 cm which isn't longer than 53 cm
Convert 9 cm to mm by multiplying by 10 (because 1 cm = 10 mm).
9 cm = 90 mm
Answer: 90 mmConsider function g.
6,
-8 < x <-2 2
g(x) =
0,
-2
-4, 4 < x < 10
What are the values of the function when x = -2 and when r = 4?
gl-2)
=
3
g(4)
=
N
[tex]x = - 2 \: then \: g( - 2) = 0 \\ x = 4 \: then \: g(4) = - 4.[/tex]
Hence, The values of the function when x = -2 is g(x) = 0 and x = 4 is
g(x) = - 4.
What is composite function?A composite function is created when one function is substituted into another function.
Given
Composite Function g
g(x) = 6, -8 ≤ x ≤ -2
g(x) = 0, -2 ≤ x ≤ 4
g(x) = -4, 4 ≤ x ≤ 10
The values of the function when x = -2
x is between -2 and 4
g(x) = 0, -2 ≤ x ≤ 4
Thus, The values of the function when x = -2 is g(x) = 0
The values of the function when x = 4
x is between 4 and 10
g(x) = -4, 4 ≤ x ≤ 10
Thus, The values of the function when x = 4 is g(x) = - 4
Hence, The values of the function when x = -2 is g(x) = 0 and x = 4 is
g(x) = - 4.
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Find csc0
Please Help!!!!!
=======================================================
Explanation:
The terminal point is at (x,y) = (3,-4)
Apply the pythagorean theorem to find that x^2+y^2 = r^2 solves to r = 5. This is the length of the hypotenuse.
Then we can determine the cosecant of the angle theta using the formula below
csc(theta) = hypotenuse/opposite
csc(theta) = r/y
csc(theta) = 5/(-4)
csc(theta) = -5/4
Side note: csc = 1/sin
How do you solve x[tex]x^{2} +4x+3=0[/tex]?
Answer:
[tex]{ \tt{ {x}^{2} + 4x + 3 = 0}} \\ { \tt{(x + 1)(x + 3) = 0}} \\ \\ { \tt{x = - 1 \: \: and \: \: - 3}}[/tex]
The sequence is defined recursively. Write the first four terms.
a 1 = -10; a n = n - a n - 1
Answer:
-10, 12, -9 and 13
Step-by-step explanation:
Given the recursive sequence
a1 = -10
an = n - an-1
a2 = 2 - a1
a2 = 2 - (-10)
a2 = 2+10
a2 = 12
a3 = 3 - a2
a3 = 3 - (12)
a3 = -9
a4 = 4 - a3
a4 = 4 - (-9)
a4 = 4+9
a4 = 13
Hence the first 4 terms are -10, 12, -9 and 13
need help asap plz!!!!!
Answer:
Step-by-step explanation:
In the simplest way, the domain of a function is basically all of the possible values of the input variable or x-axis in a graph. While the range of a function would be all of the real possible outputs that the function can create. In a graph this would be all of the possible values for the y-axis. For example, in the following function...
y = 4x + 3
The domain of this function would be any and all values for x, while the range of the function would be any and all values that the function can output for y.
The Boffo Product Company sells a waffle iron on which they have done product testing. They have determined that the amount of time the product will last can be described by a normal distribution. In particular, the average waffle iron lasts for 12 years and one standard deviation is 8 months. How long should they warranty the product for if they want no more than 6.7% of the waffle irons to fail within that time
Answer:
They should warranty the product for 7 years if they want no more than 6.7% of the waffle irons to fail within that time.
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.
The average waffle iron lasts for 12 years and one standard deviation is 8 months.
Measuring the time in months, we have that [tex]\mu = 12*8 = 96[/tex] and [tex]\sigma = 8[/tex]
How long should they warranty the product for if they want no more than 6.7% of the waffle irons to fail within that time?
This is X when Z has a p-value of 0.067, so X when Z = -1.5. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.5 = \frac{X - 96}{8}[/tex]
[tex]X - 96 = -1.5*8[/tex]
[tex]X = 84[/tex]
84 months = 7 years.
They should warranty the product for 7 years if they want no more than 6.7% of the waffle irons to fail within that time.