The probability that a randomly selected group of 16 individuals from the campus will be selected is 0.8023 or 80.23%
Based on the sign in the elevator of the college library, the limit of 16 persons and weight limit of 2,500 pounds need to be adhered to. To ensure compliance with both limits, we need to consider both the number of people and their weight.
Assuming that the distribution of weights of individuals on campus is approximately normal with an average weight of 155 pounds and a standard deviation of 29 pounds, we can use this information to estimate the total weight of a group of 16 randomly selected individuals.
The total weight of a group of 16 individuals can be estimated as follows:
Total weight = 16 x average weight = 16 x 155 = 2480 pounds
To determine if this total weight is within the weight limit of 2,500 pounds, we need to consider the variability in the weights of the individuals. We can do this by calculating the standard deviation of the total weight using the following formula:
Standard deviation of total weight = square root of (n x variance)
where n is the sample size (16) and variance is the square of the standard deviation (29 squared).
Standard deviation of total weight = square root of (16 x 29^2) = 232.74
Using this standard deviation, we can calculate the probability that the total weight of the group of 16 individuals is less than or equal to the weight limit of 2,500 pounds:
Z-score = (2,500 - 2,480) / 232.74 = 0.86
Using a standard normal distribution table or calculator, we can find that the probability of a Z-score less than or equal to 0.86 is approximately 0.8023.
Therefore, the probability that a randomly selected group of 16 individuals from the campus will comply with both the number and weight limits in the elevator of the college library is approximately 0.8023 or 80.23%.
To know more about probability click on below link :
https://brainly.com/question/14210034#
#SPJ11
Which histogram represents a set of data that is left-skewed?.
The histogram that represents a set of data that is left-skewed is the one where the majority of the data is on the right side of the histogram, and the tail of the histogram extends to the left.
A left-skewed histogram is also called a negatively skewed histogram. In a left-skewed distribution, the majority of the data values are on the right side of the histogram, and the tail of the histogram extends to the left. This means that the data is clustered around higher values and gradually decreases as the values become smaller.
For example, imagine a dataset that represents the ages of a group of people. If most of the people in the group are young adults, but there are a few older individuals, the histogram would be left-skewed because the tail of the histogram (representing the older individuals) would extend to the left.
To know more about histogram,
https://brainly.com/question/30354484
#SPJ11
Kylie explained that (-4x+9)2 will result in a difference of squares because (-4x+9)²-(-4x)²+(9)²-16x²+81. Which statement best describes Kylie's explanation?
The correct expansion of (-4x + 9)² is 16x² - 72x + 81.
We have,
Step 1: Start with the expression (-4x + 9)².
Step 2: To expand this expression, we use the formula for the square of a binomial: (a - b)² = a² - 2ab + b².
Step 3: In this case, a is -4x and b is 9.
Applying the formula, we have:
(-4x + 9)² = (-4x)² - 2(-4x)(9) + (9)².
Step 4: Simplify each term in the expansion:
(-4x)² = 16x² (square the first term).
-2(-4x)(9) = 72x (multiply -2, -4x, and 9 together).
(9)² = 81 (square the second term).
Step 5: Combine the simplified terms:
(-4x + 9)² = 16x² - 72x + 81.
Thus,
The correct expansion of (-4x + 9)² is 16x² - 72x + 81.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ12
9. Given rectangle DEFG below, select all the true statements.
SHOW WORK!!
Answer:
it have the property of parallelogram ,
All interior angles measure 90° Their opposite side are congrunt and parallelHELP ME PLEASE I REALLY REALLY NEED HELP!!!
We can see here that values will:
c = 6
d = 2.
What is a square?A square is a geometric shape with two dimensions that has four equal sides and four equal 90 degree angles. It is a particular kind of quadrilateral and a regular polygon, which means that all of its sides and angles are congruent (equal in length).
We can see that using Pythagoras Theorem, a² = c² + d²
Triangle existence theorem = c + d > a
From the question, we see that: 6 < a < 7
Thus, 36 < c² + d² < 49
c + d > 7
c = 6, d = 2
Whenever the conditions are met, many values can still fit in.
Learn more about square on https://brainly.com/question/11444061
#SPJ1
the ratio of the number of victor's tools to the number of ilay's tools is 5:2. victor has 42 more tools than ilay. how many tools should victor give to ilay so that the ratio of the number of victor's tools to the number of ilay's tools becomes 3:4?
The equation is true for any value of x! This means that no matter how many tools Victor gives to Ilay, the ratio of their tools will never be 3:4. Therefore, there is no solution to this problem.
Let's start by using algebra to represent the given information. Let's say that the number of tools Victor has is represented by the variable "v" and the number of tools Ilay has is represented by the variable "i".
According to the problem, we know two things:
The ratio of Victor's tools to Ilay's tools is 5:2, which can be written as:
v/i = 5/2
Victor has 42 more tools than Ilay, which can be written as:
v = i + 42
Now, we want to find how many tools Victor should give to Ilay so that the ratio becomes 3:4. Let's say that the amount of tools Victor gives to Ilay is represented by the variable "x".
After giving x tools to Ilay, Victor will have v-x tools, and Ilay will have i+x tools. We want to find the value of x that makes the ratio of v-x to i+x equal to 3:4.
So, we can set up the following equation:
(v-x)/(i+x) = 3/4
Now we can substitute the expression for v and the ratio of v/i to get an equation in terms of i and x:
(i+42-x)/(i+x) = 3/4
Next, we can cross-multiply to get rid of the denominators:
4(i+42-x) = 3(i+x)
Simplifying this equation:
4i + 168 - 4x = 3i + 3x
Combining like terms:
i = 7x - 168
Now we have an equation that relates the number of tools Ilay has to the number of tools Victor gives him. We can substitute this into the equation v=i+42 to get an equation that only involves x:
v = 7x - 126
Finally, we can use this equation to find the value of x that makes the ratio 3:4.
(v-x)/(i+x) = 3/4
(7x-126-x)/(i+x) = 3/4
6x-126 = (3/4)(i+x)
6x-126 = (3/4)(7x-168+x)
6x-126 = (3/4)(8x-168)
6x-126 = 6x - 126
To know more about ratio,
https://brainly.com/question/29467965
#SPJ11
A 400 g sample is composed of 100 g of cesium (Cs) and 300 g of iodine (1). What is the percent by mass of I in the sample? A. 50.0% B. 70.0% C. 25.0% D. 75.0%
If 400 g sample is composed of 100 g of cesium (Cs) and 300 g of iodine, the percent by mass of I in the sample is 75%. So, correct option is D.
The percent by mass of iodine in the sample can be calculated by dividing the mass of iodine by the total mass of the sample and then multiplying by 100.
Mass of iodine = 300 g
Mass of cesium = 100 g
Total mass of sample = 300 g + 100 g = 400 g
Percent by mass of iodine = (mass of iodine / total mass of sample) x 100
= (300 g / 400 g) x 100
= 0.75 x 100
= 75%
Therefore, the correct answer is D. 75%. This means that 75% of the total mass of the sample is iodine. It is important to note that the percent by mass of cesium in the sample is 25% because the sum of the percent by mass of all components in a sample must equal 100%.
So, correct option is D.
To learn more about mass click on,
https://brainly.com/question/30310140
#SPJ1
1,000 liters equals 1 ________.
Answer:
cubic meter (m³)
Step-by-step explanation:
N/A
what is the surface area of this composite solid? a rectangular prism with a length of 11 feet, width of 11 feet, and height of 2 feet. a square pyramid with triangular sides with a height of 7 feet. square feet 242 319 363 517
The surface area of the composite solid is 286 square feet.
To calculate the surface area of this composite solid,
Find the areas of each individual shape and then add them up.
The rectangular prism has a surface area of,
2(11x2 + 11x2 + 2x11)
= 2(22 + 22 + 22)
= 2(66)
= 132 square feet.
The square pyramid has a base area of,
11x11 = 121 square feet.
The area of each triangular side can be found using the formula,
1/2 x base x height.
The base of each triangle is 11 feet (since it is the same as the length of the base of the pyramid), and the height of each triangle is 7 feet.
So each triangle has an area of 1/2 x 11 x 7 = 38.5 square feet.
There are four triangular sides, so the total area of the triangular sides is 4 x 38.5 = 154 square feet.
Adding the surface area of the rectangular prism and the square pyramid, we get
132 + 154 = 286 square feet.
Therefore, the correct answer is 286 square feet.
To learn more about pyramid visit:
https://brainly.com/question/13057463
#SPJ12
A family's monthly income is $3531. The family spends 3 over 5 of this on food. How much is spent on food
If 3 over 5 of the family income is spent on food, The amount spent on food is $2118.6
How do we calculate the amount spent on food?If their total income is 3531 dollar and 3/5 is spend on food, we find the sum total of the amount of money spend on food by multiply the fraction or ratio to the total income the family gets monthly.
Therefore; Amount spent on food = monthly income x 3/5
It becomes $3531 x 3/5 or 3531 x 0.6
= $2118.6
It means that 2/5 of the income will be 2/5 x $3531 = $1 412.4
$2118.6 + $1412.4 = 3531
Find more exercises on calculating amount spent;
https://brainly.com/question/25001541
#SPJ4
Given that object 1 has four times the mass of object 3 and seven times the mass of object 2, find the distance between objects 1 and 2 for which the net force on object 2 is zero.
To find the distance between objects 1 and 2 for which the net force on object 2 is zero, we need to use the equation for gravitational force:
F = G (m1m2 / d^2)
where F is the gravitational force between two objects, G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.
Let's start by finding the mass of each object. We are given that:
mass of object 1 = 7 x mass of object 2
mass of object 1 = 4 x mass of object 3
We can use these equations to solve for the masses of the objects:
mass of object 2 = (1/7) x mass of object 1
mass of object 3 = (1/4) x mass of object 1
Now let's consider the gravitational force between objects 1 and 2. We want to find the distance at which the net force on object 2 is zero. This means that the gravitational force between the two objects must be equal and opposite to any other forces acting on object 2. Mathematically, we can express this as:
F_gravity = - F_other
where F_gravity is the gravitational force between objects 1 and 2, and F_other is the force acting on object 2 in the opposite direction.
We don't know what the other force is, but we do know that its magnitude must be equal to the gravitational force between the two objects. So we can set up an equation:
G (m1m2 / d^2) = G (m2m_other / x^2)
where x is the distance between objects 1 and 2 at which the net force on object 2 is zero.
Now we can plug in the masses we found earlier:
G (7m2 x m_other / x^2) = G (m2m_other / x^2)
Simplifying this equation, we get:
7m2 = m_other
So the other mass is equal to seven times the mass of object 2.
Now we can plug in the masses and solve for x:
G (7m2^2 / x^2) = G (m2 x 7m2 / x^2)
Simplifying this equation, we get:
x = distance between objects 1 and 2 = sqrt(7) x distance between objects 2 and 3
So the distance between objects 1 and 2 for which the net force on object 2 is zero is the square root of seven times the distance between objects 2 and 3.
To find the distance between objects 1 and 2 for which the net force on object 2 is zero, you need to consider the mass of each object and their gravitational forces.
Let's denote the mass of object 1 as M1, object 2 as M2, and object 3 as M3. According to the information given, we have:
M1 = 4M3 and M1 = 7M2.
Next, let's denote the distance between objects 1 and 2 as D12, between objects 1 and 3 as D13, and between objects 2 and 3 as D23.
For the net force on object 2 to be zero, the gravitational forces between objects 1 and 2, and objects 2 and 3 must be equal and opposite. Using the gravitational force equation:
F12 = (G * M1 * M2) / D12^2, and F23 = (G * M2 * M3) / D23^2.
Where G is the gravitational constant.
For net force on object 2 to be zero:
F12 = F23.
(G * M1 * M2) / D12^2 = (G * M2 * M3) / D23^2.
Now, substitute M1 and M3 in terms of M2:
(G * 7M2 * M2) / D12^2 = (G * M2 * (1/4) * 7M2) / D23^2.
Simplify the equation:
7 / D12^2 = (7/4) / D23^2.
Now, you would need more information such as the distance between object 1 and object 3 (D13) or other givendistances to find the exact values of D12 or D23. But with this equation, you have set up the relationship between the distances required for the net force on object 2 to be zero.
Visit here to learn more about gravitational force:
brainly.com/question/12528243
#SPJ11
an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 150 engines and the mean pressure was 4.0 pounds/square inch (psi). assume the population standard deviation is 0.7 . the engineer designed the valve such that it would produce a mean pressure of 4.1 psi. it is believed that the valve does not perform to the specifications. a level of significance of 0.05 will be used. find the value of the test statistic. round your answer to two decimal places.
The value of the test statistic is approximately -3.02. this value represents how far the sample mean is from the hypothesized population mean in terms of the standard error of the mean.
The test statistic can be calculated using the formula: t = (X - μ) / (s / √n)
where X is the sample mean (4.0 psi), μ is the hypothesized population mean (4.1 psi), s is the population standard deviation (0.7 psi), and n is the sample size (150). Plugging in the values, we get: t = (4.0 - 4.1) / (0.7 / √150) ≈ -3.02
Therefore, the value of the test statistic is approximately -3.02. This value represents how far the sample mean is from the hypothesized population mean in terms of the standard error of the mean.
A negative value indicates that the sample mean is lower than the hypothesized population mean. A value of -3.02 is quite far from zero, suggesting that the engineer's claim that the valve performs to specifications may be false.
The next step would be to determine the corresponding p-value and compare it to the level of significance to make a decision about rejecting or failing to reject the null hypothesis.
To know more about value click here
brainly.com/question/30760879
#SPJ11
It is known that the sum of the squares of the first n terms in the Fibonacci sequence is equal to Fn - Fn+1 Show that this result is true for n = 5
The sum of the squares of the first 5 terms in the Fibonacci sequence is equal to [tex]Fn - Fn+1[/tex] , but the result is not true for n[tex]= 6[/tex] .
The Fibonacci sequence is a sequence of numbers where each number is the sum of the two preceding numbers, starting from [tex]0[/tex] and [tex]1.[/tex]
To show that the sum of the squares of the first n terms in the Fibonacci sequence is equal to[tex]Fn - Fn+1[/tex], we can use mathematical induction.
Inductive step:
Assume that the result is true for some value of n, and consider the case where n [tex]= 5.[/tex]
[tex]0, 1, 1, 2, 3[/tex]
The fifth and sixth terms of the Fibonacci sequence are:
[tex]F5 = 5[/tex] and [tex]F6 = 8[/tex]
So, for n = 5 is:
[tex]Fn - Fn+1[/tex]
[tex]F5 - F6 = 5 - 8 = -3[/tex]
We can also calculate[tex]Fn - Fn+1[/tex] for n = 6 using the values of F6 and F7:
[tex]F6 - F7 = 8 - 13 = -5[/tex]
So, we have:
[tex]Fn - Fn+1 = -F(n+1)[/tex]
[tex]15 = -3[/tex]
Which is not true, so the assumption that the result [tex]Fn - Fn+1,[/tex] is true for n = 5 leads to a contradiction. Therefore, we can conclude that the result is not true for n[tex]= 6[/tex].
Therefore, we have shown that the sum of the squares of the first [tex]5[/tex] terms in the Fibonacci sequence is equal to but the result is not true for n[tex]= 6.[/tex]
To know about sequence visit:
https://brainly.com/question/30262438
#SPJ4
which of the below statement(s) is/are correct? selecting the relevant data by deciding which data sources to collect is a data reduction subtask.converting the numeric variables into discrete representations is a data consolidation subtask.for numerical variables, normalizing the observed values between 0 and 1 is a data transformation subtask.reducing number of attributes in data is a data transformation subtask.
The correct statement is: reducing the number of attributes in data is a data transformation subtask.
Explanation:
- Selecting the relevant data by deciding which data sources to collect is a data preparation task, not specifically a data reduction subtask.
- Converting numeric variables into discrete representations is a form of data discretization, which is a data reduction subtask.
- Normalizing observed values between 0 and 1 is a form of data scaling, which is a data transformation subtask.
- Reducing the number of attributes in data is a form of dimensionality reduction, which is also a data transformation subtask.
1. For numerical variables, normalizing the observed values between 0 and 1 is a data transformation subtask.
2. Reducing the number of attributes in data is a data transformation subtask.
In these statements, data transformation subtasks are mentioned, which involve normalizing numeric variables between 0 and 1 and reducing the number of attributes in the data. The other two statements do not fit the context of data reduction, numeric variables, or data transformation.
Visit here to know more about numeric variables:
brainly.com/question/17291241
#SPJ11
Which number is rational
Answer:
-√36
Step-by-step explanation:
The first (approx. 3.567) is obviously irrational, as it continues forever; the decimal values do not end.
The next (√18) is approx. 4.243 and is irrational.
The next (π/3) is irrational because it involves an irrational number, π.
The last (-√36) is -6 and is therefore rational.
80+000
Question 8
The mean age of swimmers for all of these teams is 10.
What does a large MAD tell you?
Jason's Team
000
+
7 8 9 10 11 12 13
Age (years)
MAD = 2.4
lues are
Understand Mean and MAD-Quiz-Level F
Hannah's Team
greater than
less than
close to
far from
+
2 13
<+
7
the mean.
Dion's Team
8 9 10 11 12
Age (years)
MAD = 0.8
Large MAD tells us that the average distance between each data value and the mean is large.
Given that;
The mean age of swimmers for all of these teams is 10.
Since, MAD is the mean absolute deviation (MAD) of a set, it tells the average distance between each data value and the mean.
Hence, It is a method to express the variance in the data set.
So, the large MAD tells us that the average distance between each data value and the mean is large.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
A homeowner bought a homeowner's insurance policy when they purchased a new home. The homeowner pays an annual $650 premium for property coverage, with a deductible of $1,675. A windstorm causes $35,500 in damages to the home and property. If the claim is approved, how much will the homeowner's insurance company pay for the damages?
i have no idea for answer
I’ve been asking this question for 6 hours and got no respond, pleaseeee help me!! This is Geometry.
Answer:
The line that appears to be tangent to circle S is not actually tangent.
[tex] \sqrt{ {14}^{2} + {19}^{2} } = \sqrt{196 + 361} = \sqrt{557} [/tex]
√557 is not equal to 25.
Answer:
not a tangent
Step-by-step explanation:
You want to know if a segment 19 units long from a point 25 units from the center of a circle of radius 14 units is a tangent.
Pythagorean theoremA tangent to a circle forms a right angle with the radius to the point of tangency. You can easily check to see if the triangle shown is a right triangle by using the Pythagorean theorem.
If the triangle is a right triangle the sum of the squares of the short sides is equal to the square of the hypotenuse:
14² +19² = 25²
196 +361 = 625
557 = 625 . . . . . . . . false — not a right triangle; not a tangent
__
Additional comment
The attached figure is drawn to scale. It shows line QR intersects the circle in 2 places, so is not a tangent. The angle at Q is obtuse.
Given 3 sides of a triangle, you can classify it as acute, right, or obtuse using the "form factor" computed as follows. Form the sum of the squares of the two shorter sides, and subtract the square of the longer side:
f = 14² +19² -25² = 196 +361 -625 = -68
The interpretation is ...
f < 0 — obtuse trianglef = 0 — right trianglef > 0 — acute trianglecomplete the following statements: 1. the organs of static equilibrium are located within two expanded chamberes within the vestibule called the
The organs of static equilibrium, also known as the maculae, are located within two expanded chambers within the vestibule called the utricle and saccule.
Utricle and saccule are filled with a gel-like substance containing tiny calcium carbonate crystals called otoliths. When the head moves, the otoliths shift and stimulate the hair cells within the maculae, which send signals to the brain regarding the body's position and movement. This allows us to maintain balance and stability, especially when standing still or moving in a straight line. Any disruptions or damage to the maculae can result in issues with balance, dizziness, and vertigo.
Learn more about static equilibrium here,
https://brainly.com/question/25727573
#SPJ4
Find F'(x): F(x) = Sx² 1 (t³ - 4t² + 2)dt
The derivative of F(x) is F'(x) = 2x³ - 8x² + 4x.
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.
Let's compute F'(x):
F(x) = ∫[1 to x²] (t³ - 4t² + 2) dt
To differentiate the integral with respect to x, we'll use the Leibniz integral rule:
F'(x) = d/dx ∫[1 to x²] (t³ - 4t² + 2) dt
According to the Leibniz integral rule, we have to apply the chain rule to the upper limit of the integral.
F'(x) = (x²³ - 4x²² + 2) d(x²)/dx - (1³ - 4(1)² + 2) d(1)/dx [applying the chain rule to the upper limit]
F'(x) = (x²³ - 4x²² + 2) (2x) - (1 - 4 + 2) (0) [using the power rule for differentiation]
F'(x) = 2x(x²³ - 4x²² + 2)
F'(x) = 2x³ - 8x² + 4x
Therefore, the derivative of F(x) is F'(x) = 2x³ - 8x² + 4x.
Learn more about function on:
https://brainly.com/question/7693326
#SPJ4
two polynomials p and d are given. use either synthetic or long division to divide p(x) by d(x), and express the quotient p(x)/d(x) in the form p(x) d(x)
To divide the polynomial p(x) by d(x), we can use long division or synthetic division. Let's say we choose to use long division.
First, we need to write the polynomials in descending order of degree, with any missing terms filled in with zeros. Let's say the polynomials are:
p(x) = 3x^3 - 5x^2 + 2x + 4
d(x) = x - 2
Then, we set up the long division like this:
3x^2 + x + 4
x - 2 | 3x^3 - 5x^2 + 2x + 4
We divide the first term of p(x) by the first term of d(x), which gives us 3x^2. We write this above the division bar and multiply it by d(x), which gives us 3x^3 - 6x^2. We subtract this from p(x), bringing down the next term:
3x^2 + x + 4
x - 2 | 3x^3 - 5x^2 + 2x + 4
- 3x^3 + 6x^2
----------
-11x^2 + 2x
We repeat the process with the next term, dividing -11x^2 by x to get -11x, writing this above the division bar, and multiplying it by d(x) to get -11x + 22. We subtract this from -11x^2 + 2x, bringing down the next term:
3x^2 + x + 4 - 11/(x-2)
x - 2 | 3x^3 - 5x^2 + 2x + 4
- 3x^3 + 6x^2
----------
-11x^2 + 2x
+ 11x^2 - 22
----------
-20
Since we have no more terms to bring down, our remainder is -20. Therefore, the quotient p(x)/d(x) is:
p(x)/d(x) = 3x^2 + x + 4 - 11/(x-2) - 20/(x-2)^2
We can express this in the form p(x) d(x) by multiplying both sides by d(x):
p(x) = d(x) (3x^2 + x + 4 - 11/(x-2) - 20/(x-2)^2)
To answer your question, we'll first need the specific polynomials for p(x) and d(x) that you'd like to divide. However, I can still guide you through the general steps to perform the division and express the quotient.
1. Choose either synthetic or long division, depending on your preference and the complexity of the polynomials.
2. Divide p(x) by d(x) using the chosen method. Make sure to follow the steps of the division process carefully to obtain the correct quotient and remainder.
3. Once the division is complete, express the quotient p(x)/d(x) in the form p(x) = d(x) * q(x) + r(x), where q(x) is the quotient and r(x) is the remainder.
Visit here to learn more about polynomial brainly.com/question/11536910
#SPJ11
Define the domain of the following:
{-2, -1, 0, 2, 5}
{-2, -1, 0, 1, 2, 3, 4, 5}
All Real Numbers
{3, -1, 3, 1, 2}
The domain of the relation in the graph is:
{-2, -1, 0, 2, 5}
How to define the domain for the graph?A relation maps elements from one set (the domain) into elements from another set (the range).
Such that the domain is represented in the horizontal axis.
In the graph, we can see the points:
{(-2, -3), (-1, -1), (0, 3), (2, 1), (5, 2)}
The domain is the set of the first values of these points, then the domain is:
{-2, -1, 0, 2, 5}
The correct option is the first one.
Learn more about domains at:
https://brainly.com/question/1770447
#SPJ1
A taxicab charges $1.75 for the flat fee and $0.25 for each mile. Write an inequality to determine how many miles Eddie can travel if he has $15 to spend.
$1.75 + $0.25x ≤ $15
$1.75 + $0.25x ≥ $15
$0.25 + $1.75x ≤ $15
$0.25 + $1.75x ≥ $15
The inequality that determines the number of miles that Eddie can travel is $1.75 + $0.25x ≤ $15 (first option).
What is the inequality?The first step is to determine the inequality sign that would be used.
Here are inequality signs and what they mean:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toThe sign that would be used is (≤) less than or equal to
The form of the inequality is:
[flat fee + (cost per mile x number of miles)] ≤ total amount she has
$1.75 + ($0.25 × x) ≤ $15
$1.75 + $0.25x ≤ $15
To learn more about inequality, please check: https://brainly.com/question/5031619
#SPJ1
The 5 owners of Mei's Restaurant remodeled their business. They bought 6 tables, 48 chairs, and 4 crystal light fixtures. The cost of these purchases was divided equally among the owners. Excluding tax, how much did each owner pay?
Answer:
$391.2 per owner
Step-by-step explanation:
find the total price of the items and divide it by five
Help I don't understand.
Answer:
[tex](2x - 1)(x + 3) = [/tex]
[tex]2 {x}^{2} + 5x - 3[/tex]
A = 2, B = 5, C = -3
Find an equation for the perpendicular bisector of the line segment whose endpoints are
(
−
1
,
−
8
)
(−1,−8) and
(
7
,
−
2
)
(7,−2)
The equation of the perpendicular bisector of the line segment with endpoints (-1, -8) and (7, -2) is y = (-4/3)x - 1.
The perpendicular bisector of a line segment is the line that passes through the midpoint of the segment and is perpendicular to it. To find the midpoint of the segment with endpoints (-1, -8) and (7, -2), we can use the midpoint formula: ((x₁ + x₂)/2, (y₁ + y₂)/2)
By using given the values, we get :
((-1 + 7)/2, (-8 + (-2))/2)
= (3, -5)
So the midpoint is (3, -5).
To find the slope of the line segment connecting the two endpoints. We can use the slope formula: (y₂ - y₁)/(x₂ - x₁)
By using the given values, we get:
(-2 - (-8))/(7 - (-1))
= 6/8
= 3/4
So the slope of the line segment is 3/4.
To find the slope of the perpendicular bisector, we need to find the negative reciprocal of the slope of the line segment. The negative reciprocal of 3/4 is -4/3.
To find the equation of the line in point-slope form, we can use:
y - y₁ = m(x - x₁)
y - (-5) = (-4/3)(x - 3)
y + 5 = (-4/3)x + 4
y = (-4/3)x - 1
Therefore, the equation of the perpendicular bisector of the line segment with endpoints (-1, -8) and (7, -2) is y = (-4/3)x - 1.
To know more about Equation here
https://brainly.com/question/11408912
#SPJ4
There are six companies that sell and clean work uniforms. Their comble
revenues for the year are $4, 120,500. Two of the companies have combined annual revenues of $2,940,000. What market share do the four remaining companies have, to the nearest percent?
The market share of the four remaining companies is 29% to the nearest percent.
What market share do the four remaining companies have?The market share the four remaining companies have, to the nearest percent is calculated as follows;
The revenue of the other four companies is calculated as;
R = $4,120,500 - $2,940,000
R = $1,180,500
The market share of the four remaining companies is calculated as follows;
market share = ($1,180,500 / $4,120,500) x 100
market share = 28.65% ≈ 29%.
Learn more about market share here: https://brainly.com/question/4017104
#SPJ1
Find the area of the region bounded by the parabola y = 4x^2, the tangent line to this parabola at (5, 100), and the x-axis.
The area of the region is 25/3 square units.
What is parabola?Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve.
First, let's find the equation of the tangent line to the parabola at the point (5,100). The derivative of y = 4x² is y' = 8x, so the slope of the tangent line at x = 5 is y'(5) = 8(5) = 40. Thus, the equation of the tangent line is y - 100 = 40(x - 5), or y = 40x - 100.
To find the points of intersection of the parabola and the tangent line with the x-axis, we need to solve the equations y = 4x² and y = 40x - 100 for y = 0:
4x² = 0 => x = 0
40x - 100 = 0 => x = 2.5
So the region we want to find the area of is bounded by the x-axis and the curves y = 4x² and y = 40x - 100, with x ranging from 0 to 2.5.
To find the area, we need to integrate the difference between the two functions with respect to x:
A = ∫[0, 2.5] (40x - 100 - 4x²) dx
A = [20x² - 4/3 x³]0 to 2.5
A = 20(2.5)² - 4/3 (2.5)³ - 0
A = 25/3
Therefore, the area of the region is 25/3 square units.
Learn more about parabola on:
https://brainly.com/question/12595802
#SPJ4
each full carton of grade a eggs consists of 1 randomly selected empty cardboard container and 12 randomly selected eggs. the weights of such full cartons are approximately normally distributed with a mean of 840 grams and a standard deviation of 7.9 grams. (a) what is the probability that a randomly selected full carton of grade a eggs will weigh more than 850 grams?
It is to be noted that the probability of a randomly picked whole carton of grade A eggs to weight more than 850gm is 10.2%
How is this so?Let W represent the weight of a fun carton of eggs chosen at random. W is distributed normally, with a mean of 840 grams and a standard variation of 7.9 grams.
The z-score for a weight of 850gms is:
z = 850 - 840 / 7.9 ≈ 127.
The standard normal probability table reveals that
P (W > 850) = P( Z > 1.27) ≈ 1- 0.8980 = 0.1020.
As a result, it is acceptable to assert that the likelihood of a randomly picked whole carton of grade A eggs weighing more than 850 grams is 10.2%.
Learn more about probability at:
https://brainly.com/question/29381779
#SPJ1
Write any two natural objects which have two or more than two lines of symmetry
There are many natural objects that have two or more lines of symmetry. here are two examples:
Starfish - A starfish has five arms which can be equal in shape and size, and every arm has two lines of symmetry running down the length of the arm. this means that a starfish has a total of ten strains of symmetry, with every line bisecting two fingers.
Snowflakes - Snowflakes are intricate ice crystals which can have many strains of symmetry. the precise variety of lines of symmetry depends on the form of the snowflake.
However typically, a snowflake has as a minimum six traces of symmetry that bypass via its middle factor, creating six same hands. some snowflakes could have as many as twelve strains of symmetry, making them quite symmetrical and beautiful herbal objects.
Learn more about Starfish:-
https://brainly.com/question/31440158
#SPJ4
As shown in the diagram of rectangle ABCD below, diagonals AC and BD intersect at E.
If AE = x + 2 and BD = 4x – 16, then the length of
AC is
Answer:
4) 24
Step-by-step explanation:
Diagonals of a rectangle are congruent and bisect each other.
AE = x + 2
BD = 4x - 16
2AE = BD
2(x + 2) = 4x - 16
2x + 4 = 4x - 16
20 = 2x
x = 10
AC = BD = 4x - 16 = 4(10) - 16 = 40 - 16 = 24
Answer: 4) 24