Applying mathematical operations, the greatest number of necklaces Georgia can make is 26.
How the mathematical operations are applied:The total number of beads available for making bracelets and necklaces is an addition operation between the beginning inventory of beads and the additional units purchased.
A subtraction operation is performed to determine the remainder after making bracelets.
Finally, a division operation determines the greatest number of necklaces to make.
The beginning inventory of beads = 322
The units purchased = 38 beads
The total number of beads that Georgia has = 360 (322 + 38)
The number of beads required to make bracelets = 120
The remainder after making bracelets = 240 (360 - 120)
The number of beads required for each necklace = 9
The greatest number of necklaces Georgia can make = 26 (240 ÷ 9)
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If a sample of 6 keyboards is randomly selected, what is the probability that at least 5 of these will have a mechanical defect
Answer:
0.1978 is the probability that at least 5 keyboards will have mechanical defect.
Step-by-step explanation:
Solution:
Given:
A repair facility has 25 failed keyboards.
10 keyboards have electrical defect.
15 of which have mechanical defect.
Randomly selected keyboard= 6
The set of A is the set of keyboards with electrical defect.
And the set of B is set of keyboards with mechanical defect.
N(A U B) = n (A) + n(B) – n (A ∩B)
Probability of at least 5 will have mechanical defect is:
= p( 5 mechanical defect U 6 mechanical defect)
= p(5 mechanical defect ) + p(6 mechanical defect)
=(15 C 5 x 10 C1 + 15 C6 X 10C0) / 25 C6
= 3003 X 10 / 177100 + 5005 X 1 / 177100
= 30030 + 5005 / 177100
= 35035 / 177100
= 0.1978
0.1978 is the probability that at least 5 keyboards will have mechanical defect.
Animal Instinct a pet supply shop borrows $7100 a 5 1/2% for 60 days Find (a) the amount of interest due and (b) the total amount that must be paid after 60 days (a) The interest due for 60 days is s (Simplify your answer Round to the nearest cent as needed) Enter your answer the answer banner Check An 1 Type here to searc
We know that
• The principal is $7,100.
,• The interest rate is 5.5%.
,• The time is 60 days.
We have to use the simple interest formula
\(\begin{gathered} I=P\times r\times t=7,100\times0.055\times\frac{60}{365} \\ I\approx64.20 \end{gathered}\)(a) The amount of interest would be $64.20.(b) The total amount that must be paid after 60 days is $7,164.20.Because it's the sum of the principal plus the interest.
Solve, for 0 ≤ x < 360°, the equation
5 sinx - 5 cosx = 2
In response to the query, x is equal to 60°, 120°, 240°, and 300°. These four options are the answer to the equation.
What does equation mean in its entirety?A mathematical equation is a statement that two amount or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. An equation is applied when several or more factors must be considered jointly in order to understand or explain the whole situation.
This equation can be solved using the trigonometric identity:
\(sinx = \sqrt{ (1 - cos^2x)}\)
This identity can be used as a substitution in the equation:
5 sinx - 5 cosx = 2
5 \(\sqrt{(1 - cos^2x) }\) - 5 cosx = 2
5 sqrt\((1 - cos^2x)\)) = 7 + 5 cosx
Squaring both sides:
25(\(1 - cos^2x\)) = 49 + 70 cosx + 25 \(cos^2x\)
25 - 25 \(cos^2x\) = 49 + 70 cosx + 25 \(cos^2x\)
0 = 74 + 45 cosx
45 cosx = -74
cosx = -74/45 = -2/3
The inverted cosine function can be used to determine that x = cos-1(-2/3). x must be within the range of 0° to 360°, hence x must be 300°.
5 sin - 5 cos - 5(-1/2) = 5 sqrt(3)/2 + 5/2 = 2 + 2.5 = 2.5
Since the left side of the equation is not equal to 2, x = 300° is not a solution to the equation.
We can repeat this process for the other solutions to the equation:
x = 60°, x = 120°, x = 240°, and x = 300°
These are the four solutions to the equation for 0° <= x < 360°.
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BRAINLIEST!!!
YOU HAVE 5 MINUTES!!!!
Design an easy do-it-yourself compost bin that can be put (exnfe ffpao)
together at home. You can describe it, draw and label it, or both!
Include the following in your design:
• drawing or description of design
• materials used for the bin
• size of the bin
• substances used to fill it
• household items that can go in it
• how long it takes before it is ready
• how you use the compost
2)
Compost bin design: Add these household items to
your compost bin:
Compost is ready to use in this
much time:
Use your compost this way:
Designing an easy do-it-yourself compost bin:
Drawing and Description:
The compost bin can be a simple structure made of wood or wire mesh. It consists of four sides, a bottom, and a removable lid. The sides and bottom are connected securely to form a rectangular shape, while the lid allows for easy access to the contents inside.
The bin can be placed directly on the ground or on a solid surface, depending on personal preference.
Materials Used:
Wood or wire mesh (depending on preference)
Nails or screws to assemble the structure
Size of the Bin:
The size of the bin can vary based on the available space and the amount of compostable materials you generate. A suitable size for a home compost bin could be approximately 3 feet wide, 3 feet deep, and 3 feet tall.
Substances Used to Fill It:
To fill the compost bin, you would need a mix of "green" and "brown" materials. "Green" materials include fruit and vegetable scraps, coffee grounds, tea leaves, grass clippings, and plant trimmings. "Brown" materials consist of dry leaves, shredded newspaper, cardboard, and small twigs.
Household Items That Can Go in It:
You can add a variety of household items to the compost bin, such as fruit and vegetable peels, eggshells, coffee grounds, tea bags, yard waste (leaves, grass clippings, plant trimmings), shredded paper, cardboard, and natural fibers (like cotton or wool scraps).
Time for Compost to Be Ready:
The time it takes for the compost to be ready varies depending on factors like temperature, moisture, and the type of materials used. Generally, it takes about 2 to 6 months for compost to fully decompose and become ready to use.
Using the Compost:
Once the compost has broken down into a dark, crumbly, and earthy material, it is ready to use. You can spread it in your garden beds or pots as a nutrient-rich soil amendment. It improves soil structure, retains moisture, and provides essential nutrients for plants' growth.
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3. The adult men of the Dinaric Alps have the highest average height of all regions. The
distribution of height is approximately normal with a mean height of 6 ft 1 in (73 inches)
and standard deviation of 3 inches.
Find the 40th percentile of the height of Dinaric Alps distribution for men.
a.
b. What would be the minimum height of man in the Dinaric Alps that would place
him in the top 10% of all heights?
4. On a recent math test, the mean score was 75 and the standard deviation 5. Mike scored a
93.
What is the 25th percentile for the math scores (This is the same as Qi)?
a.
b. What is the 75th percentile for the math scores (This is the same as Q3)?
Using the normal distribution, it is found that:
3 - a) The 40th percentile of the height of Dinaric Alps distribution for men is of 72.2 inches.3 - b) The minimum height of man in the Dinaric Alps that would place him in the top 10% of all heights is of 76.84 inches.4 - a) The 25th percentile for the math scores was of 71.6 inches.4 - b) The 75th percentile for the math scores was of 78.4 inches.Normal Probability Distribution
In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
It 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, which is the percentile of X.Question 3:
The mean is of 73 inches, hence \(\mu = 73\).The standard deviation is of 3 inches, hence \(\sigma = 3\).Item a:
The 40th percentile is X when Z has a p-value of 0.4, so X when Z = -0.253.
\(Z = \frac{X - \mu}{\sigma}\)
\(-0.253 = \frac{X - 73}{3}\)
\(X - 73 = -0.253(3)\)
\(X = 72.2\)
The 40th percentile of the height of Dinaric Alps distribution for men is of 72.2 inches.
Item b:
The minimum height is the 100 - 10 = 90th percentile is X when Z has a p-value of 0.9, so X when Z = 1.28.
\(Z = \frac{X - \mu}{\sigma}\)
\(1.28 = \frac{X - 73}{3}\)
\(X - 73 = 1.28(3)\)
\(X = 76.84\)
The minimum height of man in the Dinaric Alps that would place him in the top 10% of all heights is of 76.84 inches.
Question 4:
The mean score is of 75, hence \(\mu = 75\).The standard deviation is of 5, hence \(\sigma = 5\).
Item a:
The 25th percentile is X when Z has a p-value of 0.25, so X when Z = -0.675.
\(Z = \frac{X - \mu}{\sigma}\)
\(-0.675 = \frac{X - 75}{5}\)
\(X - 75 = -0.675(5)\)
\(X = 71.6\)
The 25th percentile for the math scores was of 71.6 inches.
Item b:
The 75th percentile is X when Z has a p-value of 0.25, so X when Z = 0.675.
\(Z = \frac{X - \mu}{\sigma}\)
\(0.675 = \frac{X - 75}{5}\)
\(X - 75 = 0.675(5)\)
\(X = 78.4\)
The 75th percentile for the math scores was of 78.4 inches.
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In baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 12 times out of 15 attempts. Tasha has hit the ball 9 times out of 10 attempts. Which player has a ratio that means they have a better batting average? Tasha, because she has the lowest ratio since 0.9 > 0.8
B) Tasha, because she has the highest ratio since 27 over 30 is greater than 24 over 30
C) Jana, because she has the lowest ratio since 0.9 > 0.8
D) Jana, because she has the highest ratio since 27 over 30 is greater than 24 over 30
Step-by-step explanation:
as the description says, the higher the ratio the better.
9/10 = 0.9
12/15 = 4/5 = 0.8
so, Tasha has the better batting average, as she has the higher ratio.
9/10 = 27/30
12/15 = 24/30
27/30 is higher than 24/30.
I POSTED THIS QUESTION THREE TIMES IF YOU ANSWER THIS (CORRECTLY) GO ANSWER MY OTHER QUESTIONS JUST TO GET THE POINTS YOU DONT HAVE TO ACTUALLY ANSWER THEM IF YOUR ANSWERS NOT GOOD PLZ DONT BOTHER
A machine in a shoe factory produces shoelaces. The number of shoelaces it produces is proportional to the time. It can produce twelve shoelaces in three minutes. Write an equation to represent this proportional relationship. In your answer, make sure to define the variables you used.
Answer:
12/3=4
Y= Time and X=The number of shoelaces
Answer: y = 4x (y = shoelaces & x = minutes)
Step-by-step explanation: We know that 12 shoelaces are produced in 3 minutes and that the ratio of shoelaces produced to minutes spent is proportional. We can figure out, therefore, that if you multiply the number of minutes by 4, you will get the number of shoelaces. As an equation, this would be y = 4x (y = shoelaces & x = minutes).
Good Luck!
HELP ME!!!!
ZEARN!!!!!!!!!
A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.
Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.
Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.
Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of
To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).
First, let's convert the fractions 1/5 and 2/3 to fifteenths:
\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)
\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)
Now we can rewrite the expression using the common denominator:
\(3 + \frac{3}{15}+\frac{10}{15}\)
m 32 33 There are red tiles and blue tiles in a box. The ratio of red tiles to blue tiles is 3:5. There are 12 more blue tiles than red tiles in the box. How many red tiles are in the box? A 18 B C 20 30 D 48 What is the surface area, in square inches, of the rectangular prism formed by folding the net below? 8 in. 23 in. 8 in. 36 in.
The number of red tiles in the box given the chance ratio of red to blue tiles is 18. The surface area of the rectangular prism is 2600 square inches.
Number of red tiles = x
Number of blue tiles = 12 + x
Total tiles = x + 12 + x
= 12 + 2x
Ratio of red = 3
Ratio of blue = 5
Total ratio = 3 + 5 = 8
Number of red tiles = 3 / 8 × 12+2x
x = 3(12 + 2x) / 8
x = (36 + 6x) / 8
8x = 36 + 6x
8x - 6x = 36
2x = 36
x = 36/2
x = 18 tiles
Therefore, The number of red tiles in the box given the chance ratio of red to blue tiles is 18.
b) To find the surface area of the rectangular prism, we need to find the area of each of its faces and add them together. Looking at the net, we see that there are three pairs of identical rectangles: the top and bottom faces, the front and back faces, and the left and right faces. Each of these rectangles has dimensions of 23 inches by 8 inches.
Therefore, the surface area of the rectangular prism is:
=2 * (23 in. * 8 in.) (top and bottom faces)
=2 * (36 in. * 8 in.) (front and back faces)
=2 * (23 in. * 36 in.) (left and right faces)
= 368 + 576 + 1656
= 2600 square inches
Therefore, the surface area of the rectangular prism is 2600 square inches.
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What is the x-intercept of the line graphed on the grid? 0)
A) 2
B) 4
C)- 2
D) -4
Answer:
-2
Step-by-step explanation:
It intersects with x-axis at -2 which is the x-intercept of the line.
Answer:
-2
Step-by-step explanation:
The x intercept is where the line crosses the x axis.
The line crosses where x = -2
Which inequality represents the situation described below?
The distance, d, is less than 200 miles.
A. d ≥ 200
B. d > 200
C. d ≤ 200
D. d < 200
Hello!
The distance, d, is less than 200 miles.
B. d > 200
1+2*3-4. Please answer
Answer:1(2x3)-4= 3
2x3= 6 -4=2+1=3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
2x3=6
1+6=7
7-4=3
Please select the word from the list that best fits the definition
a leader of a group of people
Answer:
a sultan
Step-by-step explanation:
i looked it up on quizlet after thinking it was sultan and i was right
anyways the answer is sultan and its correct
have a good day!
Answer
the answer is sultan
Step-by-step explanation:
Help me for this question. I just want to know if it’s right or not!
Why does paying off the highest interest rate credit card first make the most mathematical sense?
This technique allows mathematical sense since it concentrates effort on repaying the loans with the highest interest rates.
What can a credit card actually do?You can use the available credit on a credit card to buy things, debt exchanges, and/or cash withdrawals, but you eventually have to pay back the loan's principal.
How can I quickly obtain a credit card?The fastest way to receive a credit card is to submit an application and then, after being accepted, ask for expedited delivery. When you apply online, you have a chance of getting a quick response. In some circumstances, you might even get your card number immediately away so you can start making purchases.
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Does anyone know the answer to this?
OMG SUPER HARD QUESTION I DONT KNOW
bob has 2 apples then he eats 1 apple how many apples does he have left
Answer:
1 apple
Step-by-step explanation:
unless you are a psycho who counts the one he ate as still in his possession,
therefore 2 - 1 = 1
hope this helps:)
Question: 18 of 19
Lesson 18
Find the component form of the following vectors. Round your answers to the tenth.
Magnitude of v = 50, direction angle 0 = 50°
Choice 'A' OV
Choice 'B'O V
Choice 'C'OV
Choice 'D' OV
(38.3, 32.1)
(33.8, 31.2)
(32.1, 38.3)
(31.2, 33.8)
4
The component form of the following vectors is Option A. V = (38.3, 32.1).
To find the component form of a vector given its magnitude and direction angle, we can use trigonometry.
The component form of a vector in two dimensions is represented as (x, y), where x is the horizontal component and y is the vertical component.
In this case, the magnitude of the vector is given as 50, and the direction angle θ is 50°. We can use this information to calculate the horizontal and vertical components.
The horizontal component (x) can be found using the formula x = magnitude * cos(θ), and the vertical component (y) can be found using y = magnitude * sin(θ).
Let's calculate the components:
x = 50 * cos(50°) ≈ 38.3
y = 50 * sin(50°) ≈ 32.1
Rounding the answers to the nearest tenth, we get the component form of the vector V as (38.3, 32.1).
Therefore, the correct answer is A. V = (38.3, 32.1).
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The question is incomplete. Find the full content below:
Find the component form of the following vectors. Round your answers to the tenth.
Magnitude of v = 50, direction angle θ = 50°
A. V = (38.3, 32.1)
B. V = (33.8, 31.2)
C. V = (32.1, 38.3)
D. V = (31.2, 33.8)
Draw a circle with radius 4cm.
What is the length of the diameter of the circle?
How many sectors of 90° will fit inside the circle?
Draw five radii inside your circle that are equally spaced out around the circumference. Join up the ends of the radii to create a shape inside your circle.
What is the name of the shape that you have created inside your circle?
How long are the chords that are joining the radii together?
How big is the angle of each sector?
If you did the same as above with sectors of 45°, what shape would you create inside your circle?
The length of the diameter of the circle of the radius 4 cm is 8 cm and other solutions are added below
A circle with radius 4cm.See attachment for the circle
The length of the diameter of the circleThis is calculated as
Diameter (d) = 2 * Radius (r)
So, we have
d = 2 * 4 cm
d = 8 cm
Number of sectors of 90°The number of 90° sectors that will fit inside the circle is
Sectors = (360°/90°)
Sectors = 4
Five radii inside the circle equally spacedSee attachment for the circle
The name of the shape in the circleThe shape created inside the circle by joining the ends of five equally spaced radii is a regular pentagon.
Length of the chords joining the radii togetherThe length (L) of one chord is
L = 2 × r × sin(c/2)
For 6 chords created by the 5 radii, we have
Total length = 6 × 2 × r × sin(c/2)
Where
c = 360/6 = 60
So, we have
Total length = 6 × 2 × 4 × sin(60/2)
Evaluate
Total length = 24 cm
How big is the angle of each sector?Each sector of 90° in a circle has an angle of
Angle = (360/6)°
Angle = 60°
What shape would you create inside your circle?If sectors of 45° were used, the shape created inside the circle by joining the ends of the radii would be a nonagon
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Use the vertical method to multiply (4a3 – 2a + 3a2 + 1) and (3 - 2a + a²).
What would be the value of A?
Answer:
.a^3-2a+3a^2+1\right)and\left(3-2a+a 2\ri
Step-by-step explanation:
pls brainliest
Answer:
the answer is 4a^2
Step-by-step explanation:
i just took the test
The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.
The statements that will be true about parallelogram ABCD are: A, B, D, and E.
Properties of a Parallelogram -
Diagonals of a parallelogram bisect each other into congruent segments.
Opposite angles and sides of a parallelogram are always congruent.
Alternate interior angles are always congruent in measure.
Thus, the following would be true of parallelogram ABCD:
AP ≅ CP (congruent segment's of a bisected diagonal)
BC ≅ AD (congruent opposite sides)
∠CAD ≅ ∠ACB (congruent angles)
∠BPC ≅ ∠APD (congruent angles)
Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.
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What is the formula forfinding the area of a circle using its radius or diameter.
Answer:
The formula for finding the area of a circle using its radius is:
The formula for finding the area of a circle using its radius is:A = πr²
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.Note that π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14
Step-by-step explanation:
Hope it Helps
The formula for finding the area of a circle using its radius is π * r².
The formula for finding the area of a circle using its diameter is (π/4) * d².
The formula for finding the area of a circle using its radius is:
A = π * r²
where:
A represents the area of the circle,
π (pi) is a mathematical constant approximately equal to 3.14159, and
r represents the radius of the circle.
If you have the diameter of the circle instead of the radius, you can use the following formula:
A = (π/4) * d²
where:
A represents the area of the circle,
π (pi) is a mathematical constant approximately equal to 3.14159, and
d is the diameter of the circle.
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Identify the perimeter of a rectangle in which h=8 ft and A=144x ft2.
Answer:
52ft
Step-by-step explanation:
perimeter of a rectangle = 2 (height+ breath)
Area of a rectangle = height× breath
144= 8×L
L= 144/8 = 18ft
perimeter= 2(8+18)
perimeter= 2(26)= 52ft
The width of the rectangle will be 18 feet (5.49 meters). Then the perimeter of the rectangle will be 52 feet (15.85 meters).
What is the perimeter of the rectangle?Let H be the height and W be the width of the rectangle.
Then the perimeter of the rectangle will be
Perimeter of the rectangle = 2(H + W) units
The area of the rectangle will be 144 square feet (13.38 square meters) and the height of the rectangle is 8 feet (2.44 meters).
Then the area of the rectangle is given as,
A = H x W
144 = 8W
W = 144 / 8
W = 18 feet (5.49 meters)
Then the perimeter of the rectangle will be
P = 2(18 + 8)
P = 2(26)
P = 52 feet (15.85 meters)
The width of the rectangle will be 18 feet (5.49 meters). Then the perimeter of the rectangle will be 52 feet (15.85 meters).
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2. If 5 mg in 2 ml of liquid medication, how many mg is in 4 ml of medication?
Answer:
10mg
Step-by-step explanation:
We have a proportional relationship.
We know that there are 5mg in 2ml of liquid medication.
Now we want to know how many mg there are in 4 ml of medication.
First, we can rewrite it as:
4ml = 2ml + 2ml
And we know that, in every 2 ml of medicine, there are 5mg.
Then if we have two times 2ml of medicine, we have two times 5mg.
This is:
2*5mg = 10mg
Which point does not lie on the graph of x + 7y = 7?
Find the probability of at least 6 failures in 7 trials of a binomial experiment in which the probability of success in any one trial is 80%.
Round to the nearest tenth of a percent
Rounding to the nearest tenth of a percent, the probability of at least 6 failures in 7 trials with a success probability of 80% is 0.336 or 33.6%.
To find the probability of at least 6 failures in 7 trials of a binomial experiment with a success probability of 80%, we can use the binomial probability formula:
P(X ≥ 6) = 1 - P(X < 6)
where X is the number of failures in 7 trials and P(X < 6) is the probability of having less than 6 failures.
The probability of exactly x failures in 7 trials is given by the formula:
P(X = x) = (7 choose x) * 0.2^x * 0.8^(7-x)
where (7 choose x) represents the number of ways to choose x failures from 7 trials.
To find P(X < 6), we need to calculate the probability of having 0, 1, 2, 3, 4, or 5 failures:
P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
Using the formula above, we can calculate each probability and then sum them up.
P(X < 6) = 0.0008 + 0.0072 + 0.032 + 0.089 + 0.209 + 0.327
P(X < 6) = 0.664
Therefore, the probability of at least 6 failures in 7 trials is:
P(X ≥ 6) = 1 - P(X < 6)
P(X ≥ 6) = 1 - 0.664
P(X ≥ 6) = 0.336
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Deymarius drank 2/3 of a quart of water. Wesley drank 1/6 of a quart of water. how many quarts of water did they drink all together?
Answer:
5/6 quarts of water
Step-by-step explanation:
2/3 same as 4/6. 4/6 + 1/6 = 5/6
Pls help ive been stuck on this for hours
Answer:
the correct choice is marked
Step-by-step explanation:
The lengths will form a right triangle if the squares of the two shortest legs total the square of the longest. The square of a root is the number under the radical, so you're looking to see if the two smallest numbers under the radicals total the largest number under the radical.
A: 22 +88 = 110 . . . . . a right triangle
B: 66 +99 = 165 ≠ 176 . . . . an obtuse triangle
C: 22 +110 = 132 ≠ 121 . . . . an acute triangle
D: 66 +77 = 143 ≠ 154 . . . . an obtuse triangle
_____
Additional comment
The largest angle is opposite the longest side. If the longest side is too long for the triangle to be a right triangle, then the opposite angle is larger than 90°, and the triangle is obtuse. If the longest side is too short for a right triangle, then the triangle is acute.
The points A, B, C and D lie in order on a straight line
such that
AB:BD = 1:2
AC:CD= 7:2
Find AB:BC:CD
Answer:
7 + 2 = 9, so AC = 7/9 and CD = 2/9
1 + 2 = 3, so AB = 1/3 = 3/9 and
BD = 2/3 = 6/9
AB + BC = AC
3/9 + BC = 7/9, so BC = 4/9
AB:BC:CD = (3/9):(4/9):(2/9) = 3:4:2
20x +1400-40x =1000