a. The probability that all the marbles are red is calculated as follows:
(7 choose 3) / (18 choose 3) = (35 / (816)) = 0.0429
So, the probability that all the marbles are red is 0.0429, rounded to 4 decimal places.
b. The probability that none of the marbles are red is calculated as follows:
(12 choose 3) / (18 choose 3) = (220 / 816) = 0.2696
So, the probability that none of the marbles are red is 0.2696, rounded to 4 decimal places.
The circle below is centered at the origin and has a radius of 8. What is its
equation?
The equation of a circle centered at the origin that has a radius of 8 is: D. x² + y² = 64.
What is the equation of a circle?In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Substituting the given points into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 0)² = 8²
x² + y² = 64.
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Leah ate 9 hot dogs every 21 hours. At that rate how many would she eat in 35 hours
Answer:
15
Step-by-step explanation:
9/21 aproximatly = 0.42 then x35 = 15
when does the circle intersect the y axis
Answer:
i thinks its A im not for sure but give some money if its wrong fam bc im nice like that
Step-by-step explanation:
Need Help Asap Today
The area of the wall is 275 ft square
The number of gallon to cover the wall approximately is 3
the price of the paint is $73.5
How to solve for the area of the wall1. The area of the wall is given as l * w
this is the value that is used to solve for the area of a rectangle
the length is given as 10 ft
the width is given as 22 ft
the area would be 10 * 22
= 220 ft square
find the area of the triangle = rectangular part is given as height = 15 ft - 10 ft = 5 ft
base = 22 ft
area = 1/2 b h
= 0.5 * 22 * 5
= 55
total area = 220 + 55 = 275 ft square
2. If 1 gallon of paint covers 105 ft
the amount that would cover 275 ft would be gotten when we cross multiply
1 = 105 ft
x = 275 ft
275 ft = 105 x
x = 275 / 105
x = 2.619
x ~ 3 gallons of paint
3. If one gallon is 24.5 dollars, the total amount that you would purchase is 3 * 24.5
= $73.5
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Two angles form a linear pair. If one angle is
9 times the measure of the other angle, what are
the measures of each angle?
Answer:
18°, 162°
Step-by-step explanation:
Angles that form a linear pair are supplementary, so their measures add to 180°.
Let the measure of the smaller angle = x.
The larger angle measures 9x.
9x + x = 180
10x = 180
x = 18
9x = 9(18) = 162
Answer: 18°, 162°
Solve the inequality √x+2 > -1.
The final inequality is x > - 1.
Option D is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
√(x + 2) > -1
Squaring both sides.
x + 2 > (-1)²
x + 2 > 1
Subtracting 2 on both sides.
x > 1 - 2
x > -1
Thus,
x > - 1 is the final inequality.
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A shipping container is in the form of a right rectangular prism and it can hold 1800 cubic feet of shipped goods when it is full. Its length is 30 ft and its height is 7 ft 6 inches. Find the width of the container in feet. Round your answer to the nearest tenth if necessary.
The width of the container can be calculated by dividing the product of the length and height by the volume. The width is 28.1 ft.
[tex]30 ft x 7.5 ft = 225 ft^3[/tex]
[tex]1800 ft^3 / 225 ft^3 = 8[/tex]
[tex]225 ft^3 / 8 = 28.125 ft[/tex]
Width = 28.1 ft
To calculate the width of the shipping container, you need to divide the product of the length and height by the volume. The length of the container is given as 30 ft, and the height is given as 7 ft 6 inches or 7.5 ft. Thus, the product of the length and height is [tex]225 ft^3[/tex]. The volume of the container when it is full is given as [tex]1800 ft^3[/tex]. To find the width, divide the product of length and height by the volume. Thus,[tex]225 ft^3 / 1800 ft^3 = 8[/tex]. Then, divide the product of length and height by the result you got in the previous step, that is,[tex]225 ft^3 / 8 = 28.125 ft[/tex]. This is the width of the container. Round this value to the nearest tenth and you get 28.1 ft as the width of the container.
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PLS HELP ANSWER QUICKLY PLS
Answer:
10
Step-by-step explanation:
a² + b² = c²
8² + 6² = c²
64 + 36 = c²
100 = c²
c = 10
3) Find the sum of the first 50 terms. *
8 + 20+32 +44 + ...
15100
Step-by-step explanation :
Sum of first 50 terms for the AP:
[tex]\dashrightarrow { \boxed{\sf S = \dfrac{n}{2} (2a + (n - 1)d )}}[/tex]
where ,
Total no. of terms (n)= 50 Comman difference (d) = 20 - 8 = 12 First term (a) = 8On substituting the values , we get :
[tex]\dashrightarrow \sf S = \dfrac{50}{2}(2 \times 8 + (50 - 1) \times 12) \ \\ \\ \dashrightarrow \sf S = 25(16 + 49 \times 12 ) \\ \\ \dashrightarrow \sf S = 25(16 + 588 )\\ \\ \dashrightarrow \sf S = 25(604 )\\ \\ \dashrightarrow \sf S = 15100 \\ [/tex]
[tex] \therefore[/tex] Sum of the first 50 terms is 15100
Solve for x
.........
The solution for x in the trapezoid is x = 12
How to solve for x in the trapezoid?
The midsegment of a trapezoid is a line segment that connects the midpoints of the parallel sides of the trapezoid.
The midsegment of a trapezoid is parallel to the bases of the trapezoid and is equal in length to half the sum of the lengths of the two bases. That is:
DE = 1/2 * (KL + JM)
14 = 1/2 * (11 + 3x - 19)
14 = 1/2 * (3x - 8)
14 * 2 = 3x - 8
28 = 3x - 8
3x = 28 + 8
3x = 36
x = 36/3
x = 12
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for which values of k are the expressions 12d + 8 and 4(3d + 5) - 8 equivalent
A: No values
B. When d = 0
C: when d = 1
D.All values
Answer: A) No values of k are the expressions 12d + 8 and 4(3d + 5) - 8 equivalent.
What does "equivalent value" mean?They are the same if one amount or value has the same value as another.
We need to set the formulae 12d + 8 and 4(3d + 5) - 8 equal to one another and solve for k to get the values of k for which they are equivalent:
12d + 8 = 4(3d + 5) - 8
When we simplify this equation, we obtain:
12d + 8 = 12d + 12
When we take away 12d from both sides, we obtain:
8 = 12
There are no variables of k for which the expressions are similar because this equation is false for all values of d.
As a result, the response is A) No values.
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A cellular phone company uses the formula $16+ $0.04m to calculate each subscriber's monthly
bill, where m is the number of minutes used. If Angelo uses 142 minutes on his phone this month,
how much will his bill be?
Figure ABCD is a kite. Find the
value of x.
A
B
D
x = [?]
AB = 4x
AD = x + 15
C
Answer:
x=5
Step-by-step explanation
4x=x+15
x=5
Answer:
Since ABCD is a kite, AB=AD and BC=CD
Given:
AB = 4x
AD = x + 15
equating both sides;
4x = x + 15
4x - x = 15
3x = 15
x = 15/3
x = 5
Match the graph of the system of equations with the appropriate description of the solution.
No solution.
The solution is (0, 0).
The solution is (-1, -2).
There are infinitely many solutions.
The requried solution of the system of equations is (-1, -2). Option C is correct.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
Two intersecting lines will have exactly one solution (i.e., a unique point of intersection) if and only if they are not parallel.
In other words, if the slopes of the two lines are different, they will intersect at a single point. This is because the slopes of the lines determine how steep they are, and if they are not the same, they will eventually cross at a single point. So from the graph, both lines intersect at (-1, -2) implying that The solution is (-1, -2).
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A system is made up of two subsystems, A and B, connected in-series (i.e., the system fails if either subsystem fails). Subsystem A is made up of components 1 and 2, connected in series. Component 1 fails according to a Poisson process with rate 0.2 per month, whereas component 2 fails as a Poisson process with rate 0.08 per month. Subsystem B is made up of a single component 3, which is subject to repeated disruptions. The disruptions arrive as a Poisson. process with rate 1.2 per month but only 20% of them cause the failure of component 3.
a) Find the probability that the system will fail during a 3-month period.
b) Find the probability that there will be no more than two failures of the system during a 6-month period.
c) Find the probability that the next system failure will occur within a year.
Answer: a) The probability that the system will fail during a 3-month period can be calculated as the sum of the probabilities of subsystem A and subsystem B failing, since the system fails if either one fails. The probability of subsystem A failing in 3 months is given by P(A) = 1 - e^(-0.2 * 3) * (1 + 0.2 * 3 + (0.2 * 3)^2 / 2!) = 0.0664. The probability of subsystem B failing in 3 months is given by P(B) = 1 - e^(-1.2 * 3) * (1 + 0.2 * 3 + (0.2 * 3)^2 / 2!) = 0.36. Therefore, the probability that the system will fail in 3 months is P(system) = P(A) + P(B) = 0.0664 + 0.36 = 0.4264.
b) To find the probability that there will be no more than two failures of the system during a 6-month period, we need to use the cumulative distribution function (CDF) of the Poisson distribution. Let X be the number of failures of the system in 6 months. The CDF is given by F(x) = P(X <= x) = 1 - P(X > x), where P(X > x) is the probability that there will be more than x failures. Therefore, the probability that there will be no more than two failures of the system during a 6-month period is given by F(2) = 1 - P(X > 2). We can use the formula for the Poisson distribution to find P(X > 2), which is P(X > 2) = e^(-6 * (P(A) + P(B))) * ((6 * (P(A) + P(B)))^3 / 3! + (6 * (P(A) + P(B)))^2 / 2! + 6 * (P(A) + P(B)) / 1! + 1). Plugging in the values for P(A) and P(B) from part (a), we get F(2) = 1 - e^(-6 * 0.4264) * ((6 * 0.4264)^3 / 3! + (6 * 0.4264)^2 / 2! + 6 * 0.4264 / 1! + 1) = 1 - 0.2079 = 0.7921.
c) To find the probability that the next system failure will occur within a year, we need to find the cumulative distribution function (CDF) of the time between failures, which is the sum of the time between failures of subsystem A and subsystem B. Let X be the time between failures of subsystem A, which follows an exponential distribution with rate 0.2 per month. Let Y be the time between failures of subsystem B, which also follows an exponential distribution with rate 1.2 * 0.2 = 0.24 per month. Then the CDF of the time between failures is given by F(t) = P(X + Y <= t) = 1 - P(X + Y > t0.2 * 12) * e^(-0.24 * 12) = 1 - 0.17 = 0.83. Therefore, the probability that the next system failure will occur within a year is 0.83.
Step-by-step explanation:
Question 5
A line passes through the point (-1, -1) and has a slope of 6.
Write an equation in point-slope form for this line.
An equation in point-slope form for this line is y=6x+5.
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
Given that;
Point on a line (-1,-1)
Slope of the line 6
Now, substituting the values in the general formula of line
y+1=6(x+1)
y+1=6x+6
y=6x+5
Therefore, the equation with the given slope will be y=6x+5.
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You (or your parents) are debating about whether to buy a new car for $19,072.00 or a used car for $15,635.00. Sales tax is 4.5%. You (or your parents) plan to make a down payment of $1,200.00 and your credit rating is fair. What is the difference in interest accrued by the end of the first month?
The difference in the interest accrued by the end of the first month, given the credit rating and the cost is $ 21. 97
How to find the difference ?First, find the amount borrowed to pay for the new car or the used car.
New car :
= ( 19, 072 x ( 1 + 4. 5 % sales tax )) - 1, 200 down payment
= $ 18, 730. 24
The used car :
= 15, 635. 00 x ( 1 + 4. 5 %) - 1, 200
= $ 15, 138. 58
The difference in interest at the first month is :
= ( Amount borrowed for new car x Monthly APR for fair credit rating ) - ( Amount borrowed for old car x Monthly APR for fair credit rating )
= ( 18, 730. 24 x 7. 55 % / 12 ) - ( 15, 138. 58 x 7. 60 % / 12 )
= $ 21. 97
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Use the Pythagorean Theorem to find the length of the missing side of the right triangle. Then find the value of each of the six trigonometric functions of .
θ
A
B
C
a = 16
b = 30
c
Question content area bottom
Part 1
The length of the missing side of the right triangle is
1) The length of the missing side of the right triangle is 34.
2) The values of the six trigonometric functions of θ are:
sin θ = sin A = 8/17
cos θ = cos A = 15/17
tan θ = tan A = 8/15
csc θ = csc A = 17/8
sec θ = sec A = 17/15
cot θ = cot A = 15/8
What is Pythagorean Theorem?
Pythagoras Theorem is a method for calculating the missing length of a right-angled triangle. The triangle has three sides: the hypotenuse (which is usually the longest), the opposite (which does not touch the hypotenuse), and the adjacent (which is always the shortest) (which is between the opposite and the hypotenuse).
Part 1
To find the length of the missing side (c) of the right triangle, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, we have:
a² + b² = c²
Substituting the given values, we get:
16² + 30² = c²
Simplifying, we get:
256 + 900 = c²
1156 = c²
Taking the square root of both sides, we get:
c = sqrt(1156) = 34
Therefore, the length of the missing side of the right triangle is 34.
Part 2
To find the values of the six trigonometric functions of θ, we need to know one of the acute angles of the triangle. Let's call the acute angle opposite side a as angle A. Using the given values, we can find the sine, cosine, tangent, cosecant, secant, and cotangent of angle A as follows:
sin A = a/c = 16/34 = 8/17
cos A = b/c = 30/34 = 15/17
tan A = a/b = 16/30 = 8/15
csc A = 1/sin A = 17/8
sec A = 1/cos A = 17/15
cot A = 1/tan A = 15/8
Therefore, the values of the six trigonometric functions of θ are:
sin θ = sin A = 8/17
cos θ = cos A = 15/17
tan θ = tan A = 8/15
csc θ = csc A = 17/8
sec θ = sec A = 17/15
cot θ = cot A = 15/8
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PLEASE HELP
A piece of copy paper has a thickness of approximately 4 × 10-3 in, and a human hair has a thickness of approximately 1 × 10-3 in. Which of the following is true?
A.
A human hair is approximately forty times thicker than a piece of copy paper.
B.
A piece of copy paper is approximately four times thicker than a human hair.
C.
A piece of copy paper is approximately forty times thicker than a human hair.
D.
A human hair is approximately four times thicker than a piece of copy paper.
The statement that is true is: B. A piece of copy paper is approximately four times thicker than a human hair.
What is a scientific notation?Scientific notation is a system of expressing extremely large figures in a standard form.
Considering the figures given in the question,
Thickness of copy paper = 4 × 10^-3 in
Thickness of human hair = 1 × 10^-3 in
So that;
Thickness of copy paper/ Thickness of human hair = 4 × 10^-3/ 1 × 10^-3
= 4 × 10^-3 * 10^3
= 4
Thus it can be concluded that the copy paper is approximately four times thicker than a human hair. Thus option B.
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Help with this question?
Answer:
a.18%
b.68%
Step-by-step explanation:
for a you need to multiply 2 to get 18 out of 100 to get 18% and for b you need to multiply 4 to get 68 out of 100 to get 68%
Find all y-intercepts of the graph of
x² -10x + y² - 10y + 25 = 0.
Answer:
yjgdy
hgjg
hhjj
hggh
hhj
12) Identify the trigonometry ratio that would be used to find x.
B
11
37°
A) sine
OB) cosine
OC) tangent
The required trigonometry ratio that would be used to find x is cosine. Option B is correct.
If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
Consider the triangle ACB, in order to determine the measure of x, we can use the cosine operator of the trigonometric ratio.
So,
cosB = BC/AB
cos37 = 11/x
0.8 = 11/x
x = 11 / 0.8
x = 13.75
Thus, the required trigonometry ratio that would be used to find x is cosine. Option B is correct.
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just need a answers thank u mwa
Answer:
The answer is 112ft
Step-by-step explanation:
32+16+8+8+16+8+8+16 = 112ft
Answer:
112ft
Step-by-step explanation:
The length of the little rectangle jutting out is the only unmarked length, so once we find that we can just add up all the sides to find the perimeter.
We see the overall length of the shape is 24ft and the length of the top of the shape, minus the unmarked length, is 16ft. This means the unmarked length is 24ft-16ft=8ft
Now add up each side to get to the perimeter:
32ft + 16ft + 16ft + 8ft +8ft +8ft +8ft +16ft = 112ft
The average January temperature in your city is 45° F, but the actual temperature can vary up to 5° F warmer or colder depending on the year. Write an absolute value inequality that expresses the actual temperature in your city.
An absolute value inequality that expresses the actual temperature in your city, given that the average January temperature is 45° F and the temperature can vary up to 5° F warmer or colder, would be: | x - 45 | ≤ 5.
Where x represents the actual temperature in degrees Fahrenheit.
What is absolute value inequality?An inequality with an absolute value expression is referred to as an absolute value inequality. A quantity is enclosed in vertical bars (| |), which stand for the distance between that quantity and zero on the number line, to indicate an absolute value statement. The absolute value of an integer is always positive, hence regardless of the sign of x, |x| indicates the distance of x from zero.
Finding all feasible values of the variable that meet the inequality is the goal when resolving an absolute value inequality. To accomplish this, we first isolate the expression defining the absolute value, and then divide the inequality into two cases, one for positive and one for negative expressions defining the absolute value. Then, we resolve each case separately and combine the solutions.
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You deposit $3000 in a savings account at Yorktown Bank, which has a
rate of 5%. Find the interest at the end of the first year.
Answer:
$150
Step-by-step explanation:
Interest = Principal x Rate x Time (in years)
I = 3000(.05)(1)
I = 150
What is the measure of each angle in a regular polygon with 14 sides? If necessary, round your answer to the nearest tenth.
The measure of each angle in the regular polygon is 154.3 degrees
How to determine the measure of each angle in a regular polygonFrom the question, we have the following parameters that can be used in our computation:
Number of sides, n = 14
The measure of each angle is calculated as
Angle = ( n − 2 ) × 180/n
substitute the known values in the above equation, so, we have the following representation
Angle = (14 − 2) × 180/14
Evaluate
Angle = 154.3
Hence, the angle is 154.3
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What is the driving time for a 1800-mile trip if you drive at an average speed of 45 miles per hour? What is the driving time at 69 miles per hour?
Answer:
40 hours
26.09 hours
Step-by-step explanation:
What is the driving time for a 1800-mile trip if you drive at an average speed of 45 miles per hour?
1800 / 45 = 40 hours
What is the driving time at 69 miles per hour?
1800 / 69 = 26.09 hours
Step-by-step explanation:
The driving time for a 1800-mile trip at an average speed of 45 miles per hour can be calculated as
Driving time = Total distance / Average speed
Driving time = 1800 miles / 45 miles per hour = 40 hours
Similarly, the driving time at an average speed of 69 miles per hour can be calculated as:
Driving time = 1800 miles / 69 miles per hour = 26 hours
So if you drive at an average speed of 45 miles per hour, the driving time for a 1800-mile trip would be 40 hours, and if you drive at an average speed of 69 miles per hour, the driving time would be 26 hours.
Which equation represents a proportional relationship?
y=-x
y = 5x + 1
y = −5 (x + 1)
o y =15x
I need help on solving for "B"
The y-intercept b of the equation of the line is 30.
How to find the equation of a line?The graph represent a linear relationship between the temperature in degree farad and time in minutes.
Therefore, let's find the y-intercept b of the equation.
Hence, using slope intercept form,
y = mx + b
where
m = slopeb = y-interceptTherefore,
y = 20x + b
where
b = y-interceptUsing (6, 150) let's find b as follows:
y = 20x + b
150 = 20(6) + b
150 - 120 = b
Therefore,
b = 30
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parallelagram abcd has the angle measures shown
Answer:
Theres nothing shown
Step-by-step explanation:
