Answer:
[tex]P(B \cup b) =\frac{4}{7}[/tex]
Step-by-step explanation:
Total Number of students, the Universal Set [tex]n(\mathcal{E})[/tex]=28
Let the number of those who play basketball =B
Let the number of those who play baseball =n
Number who play neither sport, [tex]n(B\cup b)'[/tex]=12
From Set Theory,
Since we want to determine the probability that a student chosen randomly from the class plays basketball or baseball, we only simply exclude those who play neither sports.
Mathematically,From Set Theory,
[tex]\mathcal{E}=n(B \cup b)+n(B \cup b)'\\28=n(B \cup b)+12\\n(B \cup b)=28-12\\n(B \cup b)=16[/tex]
The Probability that a student chosen randomly from the class plays basketball or baseball
[tex]P(B \cup b)=\frac{n(B \cup b)}{n(\mathcal{E})}\\=\dfrac{16}{28}\\ =\dfrac{4}{7}[/tex]
Answer:
4/7
Step-by-step explanation:
4/7
Given that 10% of the nails made using a certain manufacturing process have a length less than 2.48 inches, while 5% have a length greater than 2.54 inches, what are the mean and standard deviation of the lengths of the nails? Assume that the lengths have a normal distribution.
Answer:
The mean, μ is 2.5063 and
The standard deviation, σ = 2.0499 × 10⁻²
Step-by-step explanation:
Here we have
[tex]z = \frac{x- \mu}{\sigma}[/tex]
[tex]z \sigma ={x- \mu}{}[/tex] and
10% have length < 2.48 in while
5% have length > 2.54 in
and
From the z score table
Critical z at 10% to the left = -1.282
Critical z at 5% to the right = 1.645
Therefore, the equations become
-1.282σ = 2.48 - μ → μ -1.282σ = 2.48
1.645σ = 2.54 - μ → μ + 1.645σ = 2.54
Solving the above equations gives
The mean, μ = 2.5063 and
The standard deviation, σ = 2.0499 × 10⁻².
Final answer:
Using the Z-score method and the percentages provided, two equations are set up and solved simultaneously to determine the mean and standard deviation of the lengths of the nails.
Explanation:
Given the information that 10% of the nails produced are shorter than 2.48 inches and that 5% are longer than 2.54 inches, and assuming the lengths are normally distributed, we can determine the mean (μ) and standard deviation (σ) of the lengths of the nails. We can use the Z-score formula which is (X - μ) / σ, where X is the value of the length, μ is the mean, and σ is the standard deviation.
Here, we have two Z-scores corresponding to the given percentages. For 10%, the Z-score is approximately -1.28, and for 5%, the Z-score is approximately 1.645. Now, setting up two equations,
(2.48 - μ) / σ = -1.28
(2.54 - μ) / σ = 1.645
we have a system of equations with two unknowns. Solving these equations simultaneously gives us the values for the mean and standard deviation of nail lengths.
To solve the system, multiply the first equation by σ to get μ = σ * -1.28 + 2.48 and the second equation by σ to get μ = σ * 1.645 + 2.54. By setting these two equations for μ equal to each other, you can solve for σ and afterwards find μ.
To solve the given system of equations:
1. (2.48 - μ) / σ = -1.28
2. (2.54 - μ) / σ = 1.645
We can use the method of substitution or elimination. Let's use the substitution method.
From equation 1, we can isolate μ :
(2.48 - μ) / σ = -1.28
2.48 - μ = -1.28σ
μ = 2.48 + 1.28σ
Now, we substitute this expression for μ into equation 2:
(2.54 - (2.48 + 1.28σ)) / σ = 1.645
(2.54 - 2.48 - 1.28σ) / σ = 1.645
(0.06 - 1.28σ) / σ = 1.645
0.06 - 1.28σ = 1.645σ
0.06 = 1.645σ + 1.28σ
0.06 = 2.925σ
Now, we solve for σ :
σ = [tex]\frac{0.06}{2.925}[/tex]
σ ≈ 0.0205
Now that we have found the value of \( σ \), we can substitute it back into the expression we found for \( μ \) to find its value:
μ = 2.48 + 1.28σ
μ = 2.48 + 1.28(0.0205)
μ ≈ 2.48 + 0.02628
μ ≈ 2.50628
So, the solution is approximately μ ≈ 2.50628 and σ ≈ 0.0205 .
Humans usually have 20 baby teeth, which are replaced by 32 adult teeth. Raul said he has lost 6 of his baby teeth. Write two fractions equivalent to this number. Explain your answer.
The question is not very clear, since the most logical thing is to think that the fraction is with respect to the number of baby teeth, if so:
6/20 and 3/10, these would be the two fractions.
But the literal question is to express the number 6, as a fraction.
We can do it by multiplying and dividing by the same number, for example:
6 * 2/2 = 12/2
6 * 10/10 = 60/10
This would be the two fractions.
Help ASAP
https://brainly.com/question/15912533?answeringSource=feedPersonal%2FhomePage%2F18
Answer:
Last one: 5x - 3√y + 1
Step-by-step explanation:
8x + √1 - √9y - √9x^2
8x + 1 - 3√y - 3x
5x + 1 - 3√y
5x - 3√y + 1
CAN YOU PLEASE MARK MY ANSWER BRANLIEST
Which pair show equivalent expressions
4. A circular aluminum sign has a radius of 28 centimeters. If a sheet of aluminum
costs $0.33 per square centimeter, how much will it cost to make the sign? Use
3.14 to approximate a.
The cost for making the sign is $812.38
Step-by-step explanation:
Radius = 28 cm
Cost of aluminum per square cm = $0.33
Area of the sign = π(r x r)
= (3.14) (28 x 28)
= (3.14) (784)
= 2461.76 square cm
Total cost to make the sign = 2461.76 x 0.33
= 812.38
The cost for making the sign is $812.38
To find the cost of making the circular aluminum sign, first calculate the area of the circle, then multiply the area by the cost per square centimeter. The total cost is $812.65.
To determine the cost to make a circular aluminum sign with a radius of 28 centimeters, we first need to find the area of the circle. The formula for the area of a circle is:
→ A = πr²
Given:
→ Radius, r = 28 cm
→ π ≈ 3.14
We can now calculate the area:
→ A = 3.14 × (28 cm)²
→ A = 3.14 × 784 cm²
→ A = 2,462.56 cm²
Next, we calculate the cost of the aluminum sheet:
→ Cost = Area × Price per cm²
→ Cost = 2,462.56 cm² × $0.33/cm²
→ Cost = $812.65
Therefore, it will cost $812.65 to make the circular aluminum sign.
Solve this equation for x. 2x² + 122 – 7= 0
2rº + 12z - 7 = 0
Step 1: What is the first step to solve this equation?
O Combine like terms.
O Factor the trinomial.
Isolate the constant term by adding 7 to both sides
of the equation.
Check
Intro
Answer:
Combine like terms is the first step.
Step-by-step explanation:
Subtract '122-7' on both sides and that gives you [tex]2x^2=-115[/tex]
Anyone know the answer to these?
Step-by-step explanation:
Speakers =£ 31.5
Headphones =£ 4.8
Book =£ 3.85
Mobile phone =£ 36
mouse = £12.75
DVD =£ 10.2
Hope it will help you :)
Help pls I need this
Write a function rule for “The output is 6 greater than three times the input.” Use x for the independent variable and y for the dependent variable.
Answer:
y = 6+3x
Step-by-step explanation:
If y = f(x), it means y is depending on x. This shows that y is the independent variable and x is the dependent variable.
y variable will be the output depending on the input variable x.
According to the function rule, “The output is 6 greater than three times the input." This can be expressed mathematically as 3x+6 (x being the input)
Three times the input = 3x
6 greater than three times the input = 6+3x
Since y is output then;
y = 6+3x
The function rule is [tex]\boldsymbol{y=6+3x}[/tex].
Function RuleA function rule is an equation that represents the relationship of the dependent and independent variables.
[tex]\boldsymbol{x}[/tex] is the independent variable.
[tex]\boldsymbol{y}[/tex] is the dependent variable.
The output is [tex]6[/tex] greater than three times the input.
[tex]y=6+3x[/tex].
So, the function rule is [tex]\boldsymbol{y=6+3x}[/tex].
Find out more information about function here:
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To use the two sample t procedure to perform a significance test on the difference of two means, we assume: a) The populations' standard deviation are known. b) The samples from each population are independent. c) The sample sizes are large. d) The distributions are exactly normal in each population.
Answer:
The option which is an exception is;
c) The sample sizes are large
Step-by-step explanation:
Here the requirement to perform a two sample t procedure are as follows;
1. The two samples have equal variance, hence the variance should be known
2. The samples for which the two sample t procedure is performed must be independent
3. The data are in alignment with the normal distribution probability
4. The samples are random samples taken from the different respective population
Since the sample size is known, we do not assume that the sample size are large.
Therefore options a), b) and d) are all correct except option c).
Which answer shows 0.05 written in scientific notation?
0.5 times 10 Superscript negative 1
5 times 10 Superscript negative 2
5 times 10 Superscript negative 1
5 times 10 Superscript 2
Answer:
B
Step-by-step explanation:
Answer: B
Step-by-step explanation:
If you have a negative exponent its like you divide it
10^-2 = 0.01 then multiply it by 5 = 0.01 x 5 = 0.05
What is the area of the following circle?
Answer:
A=153.938 or 154
Step-by-step explanation:
A= pi r^2
A=pi(7)^2
A=pi(49)
A=153.938 or 154
Answer:
49π or 153.86
Step-by-step explanation:
Hi there,
The formula for area of a cirlcle is A = [tex]\pi[/tex][tex]r^{2}[/tex]
So, to find the area, simply plug in the radius into the equation.
A = π * [tex]7^{2}[/tex]
A = 49π
The area is either 49π or if you use 3.14 for pi, it's 153.86.
Hope this helps!
- Emily
During her lunch hour, Shawna asked 40 students how many after-school clubs they joneu. THICH WIVE
of clubs that the students joined.
2,2,3,0, 3, 2, 4, 2, 1, 4, 3, 2, 4, 1, 0, 2, 1, 3, 2, 0,
1, 1, 2, 1,0,3,0, 1, 4, 1, 1, 0, 2, 3, 2, 0, 3, 2, 0, 1
If this sample is representative of the student population of 360 students, about how many students in the school joi
clubs?
15 students
63 students
109 students
189 students
O
Answer:
maybe 15 students or 63 students and if not I am sorry of that's wrong
max and some friends shared the cost of a meal. The meal cost $51 and each person contributes $17. How many people share the cost meal?
Answer:
3 people
Step-by-step explanation:
$51/$17 = 3 people
- We know to start with $51 dollars because that is the total price of the meal.
- We also know each meal costs $17.
- Next, ask youself what we are trying to find? We are trying to find how many people are eating.
- Therefore to find that we need to take our starting amount $51 divided by $17 because that is the cost of 1 meal.
- $51/$17 = 3 people (whole cost/individual cost = # of people)
- To check this take 3 x 17 = 51 (Now we know it is correct)
- If you would like a further explanation please let me know.
The probability of none will have high blood pressure if twenty percent of Americans age 25 to 74 have blood pressure .If 16 randomly selected Americans age 25 to 74 are selected
Answer:
The probability that none will have high blood pressure is 0.0281
Step-by-step explanation:
The correct question is as follows;
Twenty percent of Americans ages 25 to 74 have high blood pressure. If 16 randomly selected Americans ages 25 to 74 are selected, find each probablility. a. None will have high blood pressure
This is a binomial problem. We shall solve in that line
The probability of success is 20% or 0.2 [(Americans ages 25 to 74 have high blood pressure)] p = 0.2
The probability of failure q is thus 1-p = 1-0.2 = 0.8
The probability of none is thus;
P(X= 0) = 16C0 p^0 q^16
= 16C0 * 0.2^0 * 0.8^16 = 0.0281
which graph represents a line with a slope of -2/3 and a y-intercept equal to that of the line y=2/3x-2
Answer: the first one
Step-by-step explanation:
Answer:
A or the first one on the left
rolls
Which reaction shows that the enthalpy of formation of C2H4 IS A Hp = 52.5
kJ/mol?
A. 2C(s) + 2H₂(g) + 52.5 kJ → C₂H₄ shows that the enthalpy of formation of C₂H₄ is 52.5 kJ/mol.
Step-by-step explanation:
Enthalpy of formation of C₂H₄ is given as 52.5 kJ/mol.
There are 4 options given and they are:
A. 2C(s) + 2H₂(g) + 52.5 kJ → C₂H₄
B. 2C(s) + 4H(g) + 52.5 kJ → C₂H₄
C. 2C(s) + 2H₂(g) → C₂H₄ + 52.5 kJ
D. 2C(s) + 4H(g) → C₂H₄ + 52.5 kJ
Here the reactants absorb some energy from the surroundings and gives the product and it is an endothermic reaction.
So A and B is taken into account, but in B there are 4 H atoms involved in the reaction. So in the reaction A hydrogen molecules are involved and also energy is absorbed by the reactants.
So option A is the answer.
Answer: 2C(s) + 2H₂(g) + 52.5 kJ → C₂H₄
In the early 1900's, the deer population of the Kaibab Plateau in Arizona increased rapidly because hunters had reduced the number of predators. However, the food supply was not great enough to support the increased population and the population eventually began to decline. The deer population for the years 1905 to 1930 can be approximated by the polynomial where x is the number of years from 1900. Evaluate the polynomial to find the deer population in 1920.
Answer:
The deer population in 1920 is 104000
Step-by-step explanation:
Here we have the deer population is given approximately by the following equation;
Population of deer = -0.125·x⁵ + 3.125·x⁴ + 4000
Where x = number of years from 1900
Therefore, in 1920, we have x = 20
Hence, the deer population in 1920 is then
-0.125·20⁵ + 3.125·20⁴ + 4000
Which gives
-400000 + 500000 + 4000 = 104000
The deer population in 1920 is therefore, 104000.
Stephen spent $4 on milk, $6 on eggs, and $11 on cereal. He wrote the ratio 6
11
to describe some of his purchases. Explain why the ratio is not a fraction.
Answer:
Mass is a measure of the amount of matter in an object. Mass is usually measured in grams (g) or kilograms (kg). ... An object's mass is constant in all circumstances; contrast this with its weight, a force that depends on gravity. Your mass on the earth and the moon are identical.
Answer:
Step-by-step explanation:
The ratio of 6
11
compares money spent on eggs to money spent on cereal. This is a part-to-part comparison, not a part-to-whole comparison.
A deli prepares sandwiches with one type of bread (white or wheat), one type of meat (ham, turkey, or chicken), and one type of cheese (cheddar or Swiss). Each combination is equally likely. Find the probability of choosing a sandwich at random and getting turkey and Swiss on wheat bread.
The probability of choosing a sandwich at random with turkey and Swiss on wheat bread is calculated by multiplying the independent probabilities of selecting each component. With 2 bread choices, 3 meat choices, and 2 cheese choices, the calculated probability is 1/12.
To find the probability of choosing a sandwich at random with turkey and Swiss on wheat bread, we consider the possible options for each category that can be selected independently. We have 2 bread options (white or wheat), 3 meat options (ham, turkey, or chicken), and 2 cheese options (cheddar or Swiss). To find the probability of one specific combination, we multiply the probabilities of each choice.
The probability of selecting wheat bread is 1/2 because there are 2 options for bread. The probability of selecting turkey as the meat is 1/3 since there are 3 meat options. Finally, the probability of selecting Swiss cheese is 1/2, as there are 2 cheese options.
The combined probability is the product of these probabilities:
(1/2) * (1/3) * (1/2) = 1/12
So, the probability of randomly choosing a sandwich with turkey and Swiss on wheat bread is 1/12.
The probability of randomly selecting a sandwich with turkey and Swiss on wheat bread is 1 out of 12 possible combinations.
To find the probability of choosing a sandwich at random that is turkey and Swiss on wheat, we need to calculate the total number of possible different sandwich combinations and then find the probability of the one specific combination. There are 2 types of bread (white, wheat), 3 types of meat (ham, turkey, chicken), and 2 types of cheese (cheddar, Swiss). The total number of sandwich combinations is the product of the number of choices for each component: 2 * 3 * 2 = 12.
Only one of these combinations is turkey and Swiss on wheat. Therefore, the probability of randomly selecting a turkey and Swiss on wheat sandwich is 1 out of the total number of combinations. Mathematically speaking, the probability (P) is P = 1/12.
The deli sandwich scenario is related to a fundamental concept in statistics and probability, where you assess the outcomes of a certain event given a set of choices.
I need to know what 2+2 is
Answer:
The answer for this question is 4.
Step-by-step explanation:
2+2=4
If Jacob owns 12 books, how many different ways can he arrange 3 of these books on a single bookshelf
Final answer:
To find the number of different ways Jacob can arrange 3 books on a single bookshelf out of 12 books, we use the concept of permutations. The number of arrangements is 1320.
Explanation:
To find the number of different ways Jacob can arrange 3 books on a single bookshelf out of 12 books, we use the concept of permutations. Permutations calculate the number of ways to arrange objects in a specific order. In this case, we need to find the number of permutations of 3 books out of 12, which can be calculated using the formula:
P(n, r) = n! / (n - r)!
Where n is the total number of books (12) and r is the number of books to be arranged (3).
Substituting the values into the formula, we get:
P(12, 3) = 12! / (12 - 3)! = 12! / 9!
Calculating the factorial, we have:
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 479,001,600
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880
Now, dividing the factorial values, we can calculate the number of arrangements:
P(12, 3) = 479,001,600 / 362,880 = 1320
Therefore, Jacob can arrange 3 books on a single bookshelf in 1320 different ways.
A balloon is 23 feet below a tree limb. The balloon floats up 19 feet. What is it’s position relative to the tree limb
Answer:
It is 4 feet below the tree limb now
step by step
it starts at -23 or 23 below and rises 19 or adds 19 to the -23
so -23+19=-4. or 4 feet below the tree limb
Final answer:
After floating up 19 feet from its initial position of 23 feet below the tree limb, the balloon is 4 feet below the limb.
Explanation:
The student's question pertains to finding out the position of a balloon relative to a tree limb if the balloon starts 23 feet below the tree limb and then floats up 19 feet. We begin by acknowledging that the balloon's initial position is -23 feet (since it is below the limb, we consider this as negative). Upon floating up 19 feet, we perform the arithmetic operation of adding +19 feet to the initial position.
The calculation is as follows: -23 feet + 19 feet = -4 feet.
Therefore, the balloon's final position relative to the tree limb is 4 feet below it, since the result is still negative, indicating that the balloon did not reach or surpass the height of the limb.
The cost of buying a small piece of land in a remote village since the year 1990 is represented by the following table . Which model c(t) the cost of the piece of land t years since 1990, best fits the data?
Answer:
C(t)=30+3.5t
Step-by-step explanation:
Yeah this is the answer
Answer:
C(t)=30+3.5t
Step-by-step explanation:
Time increases by 2, the average difference in the cost is approximately 7.
So if d is the common difference of the function modeling this relationship, then 2d≈72.
Therefore, d≈ 7/2 = 3.5
Since the initial cost of the land is 30 thousand dollars, the function that best models its cost t years since 1990 is C(t)=30+3.5t
A tent originally sold for $260 and has been marked down to $208. What
is the percent of discount?
The percent discount of the tent is 20%.
A discount reduces the price of an item. After a discount, the price of an item is reduced.
In order to determine the percent discount, the difference in price of the tents have to determined.
$260 - $208 = $52
The percent discount = ($52 / $260) x 100 = 20%
To learn more about how to calculate discounts, please check: https://brainly.com/question/26061308
work out the missing numbers:
a)(-4)x =320
Answer:
x=-80
Step-by-step explanation:
Answer:
[tex]x=-80[/tex]
Step-by-step explanation:
[tex]a) (-4)x=320\\\\x=\frac{320}{-4} \\\\x=-80[/tex]
If the area of a right triangle is 6.22 square inches and its base is 3.11 inches, write an equation that relates the area to the height, h, and the base. Solve the equation to determine the height.
Answer: (a) 12.44 - 3.11h = 0
(b) 4in²
Step-by-step explanation:
Area of a triangle = (1/2)bh, where b is the base and h is the height.
Now from the question, Area = 6.22in² and the base is 3.11inches.
Therefore, the equation that relates the area to the height and the base wiil be
Area = (3.11)h/2
6.22 x 2 = 3.11 x h
12.44 = 3.11h
12.44 - 3.11h = 0
(b) to find the value of h from the equation, make h the subject of the formula by solving for h
12.44 = 3.11h
h = 12.44/3.11
= 4in²
Casey wants to buy a gym membership. Gym A has a $50 joining fee & costs $40 per month. Gym B has no joining fee & cost $65 per month. When would Casey pay the same amount to be a member of either gym? How much would he pay?
Answer:
1; after 2 months
2; $130
Step-by-step explanation:
In this question, we are trying to compare the fees to be paid in two different gyms, to determine when the amount paid would be equal and also what this amount would be.
Now since we do not know the exact number of months, we can represent this unknown by x
so mathematically, at the end of m months, at the first gym , Casey would have paid a total of 50 + 40m
For the second gym, at the end of the second month, casey would have paid a total of 65m only
now we need to know when these fees would be the same. we simply equate what we have on both ends
mathematically, that is 50 + 40m = 65m
65m-40m = 50
25m = 50
m = 50/25
m = 2 months
The fees to be paid is
50 + 40(2) = 65(2) = $130
Two consecutive whole numbers total 17. Find the larger.
Answer:
9
Step-by-step explanation:
Consecutive means in a row
x = 1st number
x+1 = 2nd number
x+x+1 = 17
Combine like terms
2x+1 = 17
Subtract 1 from each side
2x+1-1=17-1
2x = 16
Divide each side by 2
2x/2 =16/2
x=8
x+1 = 9
The larger number is 9
if Lydia buys 1/2 pound of the Breakfast Tea and 2 pounds of the Dark Roast coffee, how many 1- pound bags of Pumpkin Spice coffee can she buy?
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Lydia is at a coffee shop and knows she can spend no more than $65
before tax. She sees this price list in the coffee shop.
Dark Roast Coffee $7.50
Pumpkin Spice Coffee $10.50
Breakfast Tea $23.50
if Lydia buys 1/2 pound of the Breakfast Tea and 2 pounds of the Dark Roast coffee, how many 1- pound bags of Pumpkin Spice coffee can she buy?
Given Information:
Shopping Budge = $65
Price of Dark Roast Coffee = $7.50
Price of Pumpkin Spice Coffee = $10.50
Price of Breakfast Tea = $23.50
Amount of Breakfast Tea required = 1/2 pound
Amount of Dark Roast coffee required = 2 pounds
Required Information:
How many 1-pound Pumpkin Spice Coffee can she buy = ?
Answer:
n = 3 bags of 1-pound Pumpkin Spice Coffee
Step-by-step explanation:
We are given that the amount of Breakfast Tea required is 1/2 pound so the cost of Breakfast Tea is
Cost of Breakfast Tea = 1/2*23.50 = $11.75
We are also given that the amount of Dark Roast coffee required is 2 pounds so the cost of Dark Roast coffee is
Cost of Dark Roast coffee = 2*7.50
Cost of Dark Roast coffee = $15
We know that total Lydia's total budget is $65
11.75 + 15 + 10.50x = 65
Where x represents the amount of Pumpkin Spice coffee required
10.50x = 65 - 11.75 - 15
10.50x = 38.75
x = 3.64 pounds
That means Lydia can buy 3.64 pounds of Pumpkin Spice coffee.
Now assuming that the Pumpkin Spice coffee is sold only in 1-pound bags then the required number of bags that Lydia can buy is
n = 3.64 pound/1-pound
n = 3.64
Since bags cannot be in fraction so
n = 3 bags
Note: we can not round off to 4 bags since that would surpass the given budged.
Two of the angles in a triangle measure 90° and 16°. What is the measure of the third angle?
Answer:
74°
Step-by-step explanation:
All interior angles of a triangle add up to 180°, so to find the measure of the third angle here, we can use this:
180 - (90+16)
180 - 106
= 74°
Hope this helps!