To find the probability that at most 75 bicycles sold are mountain bikes, use the binomial distribution formula with a success probability of 0.70, 100 trials, and a binomial calculator to find the cumulative probability of 0 to 75 mountain bike sales. Round the answer to four decimal places.
Explanation:To find the approximate probability that at most 75 bicycles sold are mountain bikes, we can use the binomial distribution formula. In this case, the success is getting a mountain bike sale and the probability of success is 0.70. The number of trials is 100, which represents the randomly selected bike purchases. We can use a binomial calculator or software to find the probability.
The probability can be calculated as follows:
Use a binomial calculator or software to find the cumulative probability of 0 to 75 mountain bike sales with 100 trials and a success probability of 0.70. The resulting probability will be the approximate probability that at most 75 bikes sold are mountain bikes. Round the answer to four decimal places. Learn more about Probability here:
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The scenario represents a binomial probability problem. To solve, we'd calculate binomial probabilities for k from 0 to 75 (for 'at most 75' mountain bikes), where k is the count of successes, and then sum up these probabilities. This calculation involves advance statistic methods
Explanation:The subject of the question falls under probability in mathematics. Specifically, this question requires the use of the binomial distribution to find the probability of a certain event occurring. A binomial distribution is relevant because we know the probability of success (a bike sold being a mountain bike) is 70%, or 0.70, and we are looking at a fixed number of events (100 bike purchases).
In order to solve the problem, we calculate the binomial probability using the formula: [tex]P(X=k) = C(n, k)*(p^k)*((1-p)^{(n-k)})[/tex] where n = number of trials (100 in this case), k = number of successes we're looking at (75 in this case), p = probability of success on any given trial (0.70 in this case), and C(n, k) = combination of n items taken k at a time.
However, the question asks for the probability that 'at most 75 are mountain bikes'. So we also have to compute and sum up the probabilities from 0 to 75 to get the answer.
This can be quite laborious to calculate by hand, so we often use statistical software or a calculator capable of such operations to find the exact value. Hence, it is often a procedure performed in a College level Statistics class.
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which of the following is equal to the rational expression when x does not equal to 5 or -1
(x-7)(x+1)/(x+1)(x-5)
a- x+1/x-5
b-x-7/x+1
c- x+1/x-7
d- x-7/x-5
The expression that is equal to the rational expression when x does not equal to 5 or -1 is; (x - 7)/(x -5)
How to simplify Algebraic Expressions?
We want to simplify the algebraic expression;
(x - 7)(x + 1)/(x + 1)(x - 5)
Now, looking at the given expression, we see that (x + 1 ) is common to both numerator and denominator and as such they will cancel out to leave us with;
(x - 7)/(x -5)
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Sunny's garden has 9 tomato plants, 5 pepper plants, 3 squash plants, and 6 pumpkin plants. For every 3 tomato plants in Sunny's garden, there is 1 ____ plant.
Answer: Squash plant is the right answer to fill the blank.
Step-by-step explanation:
Since we have given that
Number of tomato plants = 9
Number of pepper plants = 5
Number of squash plants = 3
Number of pumpkin plants = 6
Since the ratio of tomato plants to squash plants is 9 : 3 = 3 : 1.
So, for every 3 tomato plants in Sunny's garden, there is 1 squash plant.
Hence, Squash plant is the right answer to fill the blank.
write the ratio 41 to 100 as a percent
Answer:
[tex]41\%[/tex]
Step-by-step explanation:
we have the ratio
[tex]\frac{41}{100}[/tex]
To write as percent, multiply the ratio by 100
so
[tex]\frac{41}{100}*100=41*100/100=41\%[/tex]
T-Shirts R Us advertises shirts as shown below. mc002-1.jpg Which quantities in the advertisement represent a unit rate?
Answer:
C.) $10 per shirt
Step-by-step explanation:
have a nice day
The option C is more simplified answer for given condition, unit rate is $10.
What is unit rate?When comparing two different kinds of numbers with distinct units, a rate is a ratio that is employed. The unit rate, on the other hand, shows how many units of one quantity are equal to one unit of another. When the rate's denominator is 1, we refer to the rate as a unit rate.
Given
There are 5 shirts in the image given to us composed of 3 white shirts and 2 black shirts.
A rate with 1 as its denominator is known as a unit rate.
Option A: A ratio of 3:2 or a fraction of 3/2 is indicated by 3 white shirts and 2 white black shirts.
The denominator is not 1, hence this cannot be a unit rate.
Option B: 5 white shirts to 2 black shirts. This cannot be a unit rate because the fraction 2/5 will not have 1 as the denominator.
Choice C: $10 for each shirt. Because it represents a ratio of 10:1 or a fraction of 10/1, this rate is a unit rate. Therefore, the price of 5 shirts will be $50.
D: $50 for each shirt. Because option C has provided us with a more straightforward sum of $10, which we must accept as we are dealing with unit rates, this would not be a unit rate in this question.
Hence Option C is most suitable answer.
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The complete question is in image.
The scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. if the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade? give the answer that is closest to the exact number.
The lowest marks that a student can have and still be awarded a passing grade is 44.
Step-by-step explanation:
Given :
Mean, [tex]\mu = 62[/tex]
Standard Deviation, [tex]\sigma = 11[/tex]
Calculation :
z score is given by,
[tex]z = \dfrac{x-\mu }{\sigma}[/tex] ----- (1)
Value of z corresponds to 5% is,
[tex]z =-1.65[/tex]
from equation (1) we get,
[tex]-1.65=\dfrac{x-62}{11}[/tex]
[tex]x=43.85[/tex]
[tex]\rm x = 44 \;\;(Approx)[/tex]
The lowest marks that a student can have and still be awarded a passing grade is 44.
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Find the volume of the given prism round it to the nearest tenth, 6 cm, 3.9 cm, 13.2 cm
Randy worked 18 hours each week for four weeks. for each of the next four weeks, he worked 1/3 fewer hours as the previous four weeks. what was the total number of hours he worked for the eight weeks
G a family has five children. if it is just as likely to have a boy as a girl, what is the probability that 3 of the children are girls and 2 are boys?
Given a mean of 24.5 and a standard deviation of 1.7, within how many standard deviations of the mean do the values 24, 23, 28, 23, 24, and 25 fall?
Given mean = 24.5 and standard deviation = 1.7
Within 1 standard deviations, x ∈ [24.5 - 1.7 , 24.5 + 1.7] or [22.8 , 26.2].
Within 2 standard deviations, x ∈ [24.5 - 2(1.7) , 24.5 + 2(1.7)] or [21.1 , 27.9].
Within 3 standard deviations, x ∈ [24.5 - 3(1.7) , 24.5 + 3(1.7)] or [19.4 , 29.6].
Given values are 24, 23, 28, 23, 24, and 25.
So {24, 23, 23, 24, 25} fall within 1 standard deviation and {28} falls within 3 standard deviations.
Write each of the following expressions without using absolute value. |z−7|−|z−9|, if z<7
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mean median mode range on 83 75 74 40 85 64 23 68
In the given set, the mean is 64, the median is 66, there is no mode, and the range is 62.
To find the mean, median, mode, and range of the given set of numbers: 83, 75, 74, 40, 85, 64, 23, 68.
1. Mean:
[tex]\[ \text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of numbers}} \][/tex]
[tex]\[ \text{Mean} = \frac{83 + 75 + 74 + 40 + 85 + 64 + 23 + 68}{8} \][/tex]
[tex]\[ \text{Mean} = \frac{512}{8} \][/tex]
[tex]\[ \text{Mean} = 64 \][/tex]
2. Median:
The median is the middle number when the numbers are arranged in ascending order.
Arranging the numbers in ascending order: 23, 40, 64, 68, 74, 75, 83, 85
Since there are 8 numbers, the median is the average of the two middle numbers:
[tex]\[ \text{Median} = \frac{64 + 68}{2} \][/tex]
[tex]\[ \text{Median} = 66 \][/tex]
3. Mode:
The mode is the number that appears most frequently.
In this set, there is no number that appears more than once.
So, there is no mode.
4. Range:
The range is the difference between the largest and smallest numbers.
[tex]\[ \text{Range} = \text{Largest number} - \text{Smallest number} \][/tex]
[tex]\[ \text{Range} = 85 - 23 \][/tex]
[tex]\[ \text{Range} = 62 \][/tex]
So, for the given set of numbers, the mean is 64, the median is 66, there is no mode, and the range is 62.
a _____ is a list of things where each thing appears only once and Order matters
Answer: Permutation
Permutation is a way, in which a set or number of things can be ordered or arranged. It is a listing where order matters and each thing in the list of things appears only once.
In Mathematics, permutation is the action of changing the arrangement of a set of items. .It is also called an "arrangement number" or "order
A combination lock requires 4 selections of numbers, each from 1 to 20. • how many different combinations are there? • suppose that the lock is constructed in such a way that no number maybe used twice. how many different combinations are possible?
find the range for the given data in 115, 534, 122, 599, 417, 289 A) 534 B) 167 C)115 D)484
Q # 15 please solve
Nina wants to put color tiles on a square three color tiles fit across the top of the square how many rows and Columns of the squares will Nina need how many color tiles will she use in all
Arnob may want to borrow his cousin’s tent, which is shown below. He needs to determine x, the center height of the tent, to determine if it will be large enough for his camping trip. (Picture below)
What is the center height of this tent, to the nearest tenth of a foot?
4.1 feet
8.1 feet
9.8 feet
12.0 feet
In this question, we will use Pythagoras theorem in order to find the height of the tent.
The center height of tent is 8.1 feet.
What is right triangle?Right triangle is defined as a triangle which one angle is a right angle or two sides are perpendicular.
What is Pythagoras theorem?A right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
perpendicular² + base² = hypotenuse²
Given,
Side length of each triangle = 4 feet
Hypotenuse of each triangle = 9 feet
Shared side = x
Given the triangles are right angled,
According to Pythagoras theorem,
a² + b² = c²
Here, a = 4 , b = x , c= 9
Substitute the values in Pythagoras theorem,
4² + x² = 9²
16 + x² = 81
x² = 81 - 16
x² = 65
Taking square root on both sides
x = √65
x = 8.062
x = 8.1 (Rounding nearest tenth)
Hence, the center height of tent is 8.1 feet.
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John's monthly salary is 7,000. If John deposits 0.75 of his paycheck into a savings account. How much money does he put in his savings account every month?
John deposits $5,250 into his savings account every month, which is 75% of his monthly salary.
The student's question is about how much money John deposits into his savings account from his monthly salary. To solve this, we calculate 0.75 (or 75%) of John's monthly salary of 7,000.
Calculation: 0.75 imes 7,000 = 5,250
So, John deposits $5,250 into his savings account every month.
Corey drew 8 shapes. Four are squares, two are triangles, and the rest are parallelogram. Write two fractions that name the part of the shapes that are quadrilaterals
HELP
Given right triangle ABC.
In the given right triangle, find the length of the hypotenuse, AB, if BC = 6 and AC = 5.
A.5
B.√36
C.√61
D.√11
Answer:
Correct answer is option C (√61)
Step-by-step explanation:
in this question we have given a right triangle in which
∠C=[tex]90^{0}[/tex]
BC = 6 and AC = 5
we have to find the length of the hypotenuse, AB=?
To find the the hypotenuse we will apply Pythagoras theorem (According to Pythagoras theorem, "in a right angle triangle, square of hypotenuse is equal to the sum of square of other two sides")
In ΔABC by Pythagoras theorem
[tex]AB^{2}=AC^{2}+BC^{2}[/tex]...................(1)
put values of BC and AC in equation 1
[tex]AB^{2}=5^{2}+6^{2}[/tex]
[tex]AB^{2}=25+36[/tex]
[tex]AB^{2}=61[/tex]
AB=√61
list all the possible whole number length and width of rectangles that darla can cut from the 400 square inch piece of paper
what is 0.0003840 expressed in scientific notation
0.0003840
Written in scientific notation!
Move the decimal point.
.00384 x 10^1
.0384 x 10^2
.384 x 10^3
3.84 x 10^4
38.4 x 10^5
How would you solve 1/8 divided by 6
The required 1/8 divided by 6 is equal to 1/48.
To solve 1/8 divided by 6, we can rewrite it as a fraction. The reciprocal of 6 is 1/6, so the division problem becomes (1/8) * (1/6). To multiply fractions, we multiply the numerators together and the denominators together.
Step 1 is given as:
= (1/8) * (1/6)
Step 2(simplification) is given as:
= 1 * 1 / 8 * 6
= 1/48
Therefore, the required 1/8 divided by 6 is equal to 1/48.
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Two urns contain white balls and yellow balls. The first urn contains 5 white balls and 8 yellow balls and the second urn contains 9 white balls and 2 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?
Find the perimeter and the area of a rectangle measuring 8 1/4 yd long by 4 1/8 yd wide
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Which of the following statements is true? If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are proportional. If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are congruent. If two polygons are similar, then the corresponding sides are congruent and the corresponding angles are proportional. None of the choices are correct.
The correct statement is that if two polygons are similar, their corresponding sides are proportional while their corresponding angles are congruent. Similar polygons have the same shape but can have different sizes, and this applies across various geometrical figures and principles, like the Pythagorean theorem in the context of right triangles.
Explanation:The correct statement among the given options is: If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are congruent. When polygons are similar, this means their shapes are geometrically the same but they may differ in size. The ratios of the lengths of corresponding sides of similar polygons are equal, which is true for any pairs of similar polygons, not just triangles. The corresponding angles, on the other hand, are congruent, which means they have the same measure in both polygons.
To explain this concept, we use different examples in geometry. For instance, in similar triangles, not only are the three angles in one triangle congruent to the three angles in the other, but also the sides are proportional, which can be expressed as the ratio of any two corresponding sides in the two triangles being equal. This proportional relationship is a key characteristic of similarity in geometry.
Moreover, a statement like the Pythagorean theorem applies to right triangles, stating that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem is connected to similarity because one can generate a family of similar right triangles by scaling a single right triangle.
kirsten has an area of 70 square feet for a flower garden she plants 5 varieties of flowers equally in her garden which ratio shows the square feet per flower type
The Ratio of the square feet to the per flower type is 14 : 1.
What is Ratio?A Ratio shows the relative size of two or more value.
According to the question,
Area of a flower garden = 70 square feet
Number of flower plants varieties = 5
Formula for Perimeter of square = 4a where 'a' is sides of a square
4(a) = 70
a=70/4
a=15
To find the Ratio of the square feet to the per flower type
70 : 5
14 : 1.
Hence, the Ratio of the square feet to the per flower type is 14:1
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