STATSS QUESTION!
The Florida Department of Transportation plans to develop a new section of interstate highway and receives 20 bids for the project. The state plans to hire five of the bidding companies. How many different combinations of five companies can be selected from the 20 bidding companies?
A. 15540
B. 15504
C. 1860480
D. 1860840
Evaluate and write your answer correct to two significant figures: 7² +4³ =
[tex] \sqrt{60} [/tex]
Answer:
7^2+4^3= 113 √60= 2√15
Step-by-step explanation:
7^2+4^3
49+4^3
49+64
113
√60
√4*15
√2^2*15
√2^2√15
2√15
The Carson family drives to the city for an event. They pay $2.50 per hour for a parking meter. They park for 4.22 hours. Explain how to estimate the cost the Carson family will pay. Then find the actual cost.
The Carson family will pay $2.50p and the actual cost comes out to be $10.55. The solution has been obtained by using the linear equation.
What is a linear equation?
The linear equation has a degree of 1. It is evident that there are no variables in linear equations with exponents greater than one. This graph's equation yields a straight line.
We are given that the Carson family pays $2.50 per hour for a parking meter.
Let the number of hours be 'p'.
So, we get the linear equation as
Cost = $2.50p
Now, we are given that they park for 4.22 hours.
So, p = 4.22
From this, we get
Cost = $2.50 * 4.22
Cost = $10.55
Hence, the Carson family will pay $2.50p and the actual cost comes out to be $10.55.
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if 4/7 of students prefer cereal for breakfest how many pefer ceareal out of 147 students
Answer:
84
Step-by-step explanation:
ez
4/7 of 147 = 4/7 x 147/1
1. a. Derek reads at a rate of 25 words per minute. If he reads constantly until he is finished, how long would it take him to read a 225 word article?
Use the Slope-intercept form to solve. y=mx+b
y=total amt m=rate/slope x=minutes
Nine minuts.
b. If Derek’s friend Sarah reads the same 225 word article and it takes her 10 minutes to read it, who reads faster and how do you know?
PLS LIST HOW YOU GOT THE QUESTION...THANKS<3
Answer:
The answer to part (a) is 9 minutes. The answer to part (b) is that Derek reads faster than Sarah.
Step-by-step explanation:
a. To solve this problem, we can use the formula:
time = distance / rate
where "distance" is the number of words in the article and "rate" is the reading speed in words per minute. We want to find the time it takes Derek to read the article, so we can plug in the given values:
time = 225 / 25
time = 9
Therefore, it would take Derek 9 minutes to read the 225 word article if he reads constantly until he is finished.
b. To determine who reads faster, we can compare the reading rates of Derek and Sarah. Derek's reading rate is 25 words per minute, and Sarah's reading rate is:
225 words / 10 minutes = 22.5 words per minute
Since Derek's reading rate is higher than Sarah's reading rate, we can conclude that Derek reads faster than Sarah.
How I got the question:
Here are the steps I took to answer the question:
a. To solve for how long it would take Derek to read a 225 word article:
Step 1: Identify the given information
Derek's reading rate is 25 words per minute
The article has 225 words
Step 2: Identify the formula to use
We can use the formula: time = distance / rate, where "distance" is the number of words in the article and "rate" is the reading speed in words per minute.
Step 3: Plug in the values and solve
distance = 225 words
rate = 25 words per minute
time = distance / rate = 225 / 25 = 9 minutes
Therefore, it would take Derek 9 minutes to read the 225 word article if he reads constantly until he is finished.
b. To compare Derek's and Sarah's reading rates and determine who reads faster:
Step 1: Identify the given information
Derek's reading rate is 25 words per minute and it takes him 9 minutes to read the article.
Sarah took 10 minutes to read the same 225 word article.
Step 2: Calculate Sarah's reading rate
Sarah's reading rate = distance / time = 225 words / 10 minutes = 22.5 words per minute
Step 3: Compare the reading rates of Derek and Sarah
Derek's reading rate is 25 words per minute and Sarah's reading rate is 22.5 words per minute.
Step 4: Interpret the answer
Since Derek's reading rate is higher than Sarah's reading rate, we can conclude that Derek reads faster than Sarah.
I hope this helps you understand how to approach these types of problems! If it didn't help you, I'm sorry. If you need more help (or have questions) feel free to ask me! :]
G(x)= - x^2/4 +7
What is the average rate of change of g over the interval [-2,4]
The average rate of change of function G during the interval [-2,4] is fond as: -1/3.
Explain about the average rate of change?It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.The slope of the straight line connecting two places is used to compute the average rate of change here between two points.Use the formula to determine f(x) average's rate of change between x=a and x=b.
average rate change = f(b)−f(a) / (b−a)
G(x)= - x^2/4 +7
interval [-2,4]
a = -2 and b = 4
G(a) = - 2^2/4 +7
G(a) = - 1 + 7
G(a) = 6
Now,
G(b) = - 4^2/4 +7
G(b) = - 4 + 7
G(b) = 3
Put the values:
average rate change = G(b)−G(a) / (b−a)
average rate change = 3 - 6 / (4 + 2)
average rate change = -3/6
average rate change = -1/3
Thus, the average rate of change of function G during the interval [-2,4] is fond as: -1/3.
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One large box and two small boxes weigh a total of 100 pounds. One large box and four small boxes weigh a total of 140 pounds. The weight limit of a trailer is 1200 pounds.
Write an inequality that represents the numbers of large, x, and small, y, boxes that can be loaded in the trailer.
An equality that represents the numbers of large, x, and small, y, boxes that can be loaded in the trailer is 2x + y ≤ 60.
What is inequality?Inequality is the relationship between two expressions or values that are not equal to one another.
Due to that, 100 pounds are the combined weight of one large box and two small boxes. 140 pounds are the combined weight of one large box and four small boxes.
Let the weights of large and small boxes be x and y respectively.
x + 2y = 100
x = 100-2y...(i)
x + 4y = 140
x = 140 - 4y...(ii)
Solving eq(i) and eq(ii)
100 - 2y = 140 - 4y
2y = 40
y = 20
Put y = 20 in eq(i)
x = 100 - 40
x = 40
Therefore, the weights of large and small boxes are 40 and 20 pounds respectively.
Now, Since the weight limit of a trailer is 1400 pounds
Establishing the inequality,
40x + 20y ≤ 1400
or,
2x + y ≤ 60
Thus, an inequality that represents the numbers of large, x, and small, y is 2x + y ≤ 60.
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Use a calculator to find the following. Round your answer to four places past the decimal point. sec 45° 46'
Answer:
1.327
Step-by-step explanation:
To find the value of sec (45° 46'), we first need to convert the angle to decimal degrees.
(45⁰,46') = 45⁰ + (46/60)⁰ = 45.7667⁰
Now using the calculator,
sec(45.7667⁰) = 1.327
Note to Remember
sec(a) = 1/cos(a)
Which of the following is equivalent to x4−36 for all values of x?
The correct answer is option c) [tex](x^2-6)(x^2-6)[/tex] which is equivalent to [tex]x^4-36[/tex] for all values of x.
The expression [tex]x^4-36[/tex] can be factored using the difference of squares formula, which states that [tex]a^2 - b^2[/tex] = (a + b)(a - b):
[tex]x^4 - 36 = (x^2)^2 - 6^2[/tex]
[tex]= (x^2 + 6)(x^2 - 6)[/tex]
Therefore, the answer is option c) [tex](x^2 - 6)(x^2 - 6)[/tex].
we can factor x^4 - 36 using the difference of squares formula:
[tex]a^2 - b^2[/tex] = (a + b)(a - b)
If we let a = [tex]x^2[/tex] and b = 6, we get:
[tex]x^4 - 36 = (x^2)^2 - 6^2[/tex]
[tex]= (x^2 + 6)(x^2 - 6)[/tex]
Therefore, we can rewrite [tex]x^4 - 36[/tex] as the product of two factors, [tex](x^2 + 6)[/tex] and [tex](x^2 - 6)[/tex]. This means that for any value of x, [tex]x^4 - 36[/tex] can be expressed as [tex](x^2 + 6)(x^2 - 6)[/tex].
Option a) [tex](x^2 - 18)(x^2 - 18)[/tex] is not equivalent to [tex]x^4 - 36[/tex], as expanding this expression gives [tex]x^4 - 36x^2 + 324[/tex].
Option b) [tex](x^2 + 18)(x^2 + 18)[/tex] is also not equivalent to [tex]x^4 - 36[/tex], as expanding this expression gives [tex]x^4 + 36x^2 + 324[/tex].
Option d) (x^2 + 6)(x^2 + 6) is not equivalent to[tex]x^4 - 36[/tex], as expanding this expression gives [tex]x^4 + 12x^2 + 36[/tex].
Therefore, the only option that is equivalent to [tex]x^4 - 36[/tex] for all values of x is option c) [tex](x^2 - 6)(x^2 - 6)[/tex].
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The complete question is:
Which of the following, for all values of x, is equivalent to [tex]x^4-36[/tex]?
a) [tex](x^2-18)(x^2-18)[/tex]
b) [tex](x^2+18)(x^2+18)[/tex]
c) [tex](x^2-6)(x^2-6)[/tex]
d) [tex](x^2+6)(x^2+6)[/tex]
957
6
54
32
1
Y
V
U
N
0 1 2 3 4 5 6 7 8 9 10
You moved 5 units up, 2 units right, 1 unit up, and ended at ordered pair (3, 7).
Where did you begin?
A) Point 7
The coordinates of the point where you begin with is (1, 1) given that you ended at (3, 7)
Calculating the point where you begin withBy the problem statement
Starting at the point (x, y), moving 5 units up would give us the point (x, y + 5). Moving 2 units right from there would give us the point (x + 2, y + 5). Finally, moving 1 unit up would give us the point (x + 2, y + 6).We know that this point is (3, 7), so we can set the x and y values equal to their corresponding expressions in terms of the starting point:
x + 2 = 3
x = 1
y + 6 = 7
y = 1
Therefore, the starting point was (1, 1).
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help i gave a picture i will give brainiac
The relative frequency of 6 hours of sleep would be 10/45 or 0.222, the relative frequency of 7 hours of sleep would be 15/45 or 0.333, and the relative frequency of 8 hours of sleep would be 20/45 or 0.444.
The relative frequency of each survey outcome can be determined by dividing the number of responses for each outcome by the total number of responses. For example, if there were 10 responses of 6 hours of sleep, 15 responses of 7 hours of sleep, and 20 responses of 8 hours of sleep, the relative frequency of 6 hours of sleep would be 10/45 or 0.222, the relative frequency of 7 hours of sleep would be 15/45 or 0.333, and the relative frequency of 8 hours of sleep would be 20/45 or 0.444. This formula can be used to calculate the relative frequency of any survey outcome: x/n, where x is the number of responses for the outcome and n is the total number of responses. The relative frequency is a measure of how common each outcome is in the survey.
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a teacher asks a student to create a hierarchy diagram. Which could be the correct hierachy diagram?
A hierarchy diagram is a visual representation of a structure, typically showing the relationships between various components or elements.
Depending on the context and purpose of the hierarchy diagram, there could be several different correct ways to organize and present the information. For example, if the teacher is asking the student to create a hierarchy diagram to show the levels of organization in a biological system, the correct diagram might start with the most general category (e.g., Kingdom), followed by progressively more specific categories (e.g., Phylum, Class, Order, Family, Genus, Species). The diagram might look something like this:
Kingdom
Phylum
Class
Order
Family
Genus
Species
Alternatively, if the teacher is asking the student to create a hierarchy diagram to show the organizational structure of a business or organization, the correct diagram might start with the highest level of authority (e.g., CEO), followed by lower levels of management, departments, teams, and individual employees. The diagram might look something like this:
CEO
Executive Team
Senior Management
Middle Management
Department Heads
Teams
Employees
Ultimately, the correct hierarchy diagram depends on the specific context and purpose of the diagram, and the student should consider what categories or components are most important to include and how they are related to one another.
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Find the length of the third side. If necessary, round to the nearest tenth.
16
12
The third side will be οf length 10.58.
What is Pythagοras theοrem?The hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides if a triangle has a straight angle (90 degrees), accοrding tο the Pythagοras theοrem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypοtenuse BC are all used in this equatiοn. The lοngest side οf a right-angled triangle is its hypοtenuse, it shοuld be emphasized.
Nοw using the Pythagοras theοrem we can find οut the length οf the οther wall:
b² = h²- p²
b² = 16²- 12² = 112
b = 10.58
Hence the third side will be οf length 10.58
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Complete question:
I need help! Please include an explanation.
Using Combinations, the answer is (C) the number of ways to choose 2 representatives from 8 students is 28.
What are combinations ?Combination and option are synonymous terms.
A combination is a choice of objects drawn from a certain group of items. Nothing is being organised here, I assure you. We pick them.
Determine how many distinct r options or combinations there are given a given set of n objects. Combination differs from arrangement and permutation.
The number of distinct sets of r items that can be produced from each of the n given unique objects can be easily calculated using combinatorial formulas.
The order in which the students are chosen does not matter, and we want to choose 2 students from a group of 8. This is a combination problem, and we can use the formula for combinations:
n choose k = n! / (k!(n-k)!)
where n is the total number of items, k is the number of items to be chosen, and ! denotes factorial (e.g., 5! = 5 x 4 x 3 x 2 x 1 = 120).
In this case, we have:
n = 8 (the total number of students)
k = 2 (the number of representatives to be chosen)
So, the number of ways to choose 2 representatives from 8 students is:
8 choose 2 = 8! / (2!6!) = (8 x 7) / (2 x 1) = 28
Therefore, the answer is (C) 28.
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Help me please, Which equation can be used to find the value of x?
Worth 20
Answer:
168 = 18 * x + 12 * 2x
Step-by-step explanation:
It's the only one that makes sense. You can mark out the 2nd and last one. We don't add 2x + x; for the 3rd, they need to subtract 18 - 2x, so that's not right either.
john can fix 3 chairs in 12 minutes joe can fix 5 chairs in 20 minutes how many chairs can they fix together in 60 minutes
Step-by-step explanation:
In one hour john can fix 15 chairs ( 3 x 5)
in one hour joe can fix 15 chairs (5 x 3)
total = 30 chairs in one hour
Answer: 15 chairs they fix together in 60 min.
Step-by-step explanation:
jhon efficiency =3/12=4
joe efficiency = 5/20 =4
both efficiency =8
there for 2/8*60
=15
Solve the inequality for x
-x/10≤7/2
Answer:
x ≥ -35
Step-by-step explanation:
-x/10 ≤ 7/2
Multiply both sides by 10
-x ≤ 35
Divided both sides by -1
x ≥ -35
So, the answer is x ≥ -35
What is the equation of the line that is perpendicular to
the given line and has an x-intercept of 6?
O y=-3x+8
O y=-3x+6
O y=x-8
O y = x-6
The equation of the line that is perpendicular to the line passing through (-4,4) and (4,-2) and has an x-intercept of 6 is: y = (4/3)x - 8.
What is slope ?
Slope is a measure of the steepness or slant of a line. It is defined as the ratio of the vertical change between two points on a line to the horizontal change between those same two points. In other words, slope is the change in y divided by the change in x.
The slope of a line can be positive, negative, zero, or undefined. A positive slope means that the line is rising from left to right, while a negative slope means that the line is falling from left to right. A slope of zero means that the line is horizontal, while an undefined slope means that the line is vertical.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).
According to the question:
First, we need to find the slope of the line passing through (-4,4) and (4,-2) using the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-4,4) and (x2, y2) = (4,-2)
slope = (-2 - 4) / (4 - (-4)) = -6/8 = -3/4
The equation of a line perpendicular to this line will have a slope that is the negative reciprocal of the slope of the given line. That is,
slope of perpendicular line = -1 / (-3/4) = 4/3
Now we can use the slope-intercept form of a line to find the equation of the line with slope 4/3 that passes through the point (6,0), which is the x-intercept given in the question:
y = mx + b, where m is the slope and b is the y-intercept
Plugging in m = 4/3 and the point (6,0), we get:
0 = (4/3)(6) + b
b = -8
Therefore, the equation of the line that is perpendicular to the line passing through (-4,4) and (4,-2) and has an x-intercept of 6 is:
y = (4/3)x - 8
So the answer is: y = (4/3)x - 8.
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HOW IS A NUMBER LINE LIKE A MODEL?
Answer: A number line is like a model because number lines and models both graph and show data. Both models and number lines use a numerator and denominator to show value. A number line is a form of a model. So basically, number lines are models. I really don't know what else to say. ✨YOUR WELCOME✨
Step-by-step explanation:
What I said up there ⬆
What is the solution to the system of equations below?
2x - 3y = -6
x + 5y = 23
Answers
(3,4)
(6,6)
(8,3)
(4,3)
In a recent frisbee tournament, Hybrid scored 2 less points than Rival. Their combined scores were 28. Let h represent Hybrid and r represent Rival Which pair of equations can be used to determine their scores?
h + r = 28 h = r - 2
h + r = 28 h + r = 2
h + 28 = r h = 2
h - r = 28 h = r - 2
The pair of equations that can be used to determine their scores is h + r = 28 h = r - 2. The correct option is a.
What is an equation?Equations that happen simultaneously or a system of equations The simultaneous solution of two or more equations is necessary for algebra (i.e., the solution must satisfy all the equations in the system).
For a system to have a unique solution, the number of equations must equal the number of unknowns.
Variable h: number of points scored by Hybrid.
Variable r: number of points scored by Rival.
Hybrid scored 2 fewer points than Rival, hence:
h = r - 2.
Their combined scores were 28, hence:
h + r = 28.
Therefore, the correct option is a. h + r = 28 h = r - 2.
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Solve for x and y, please fast
Answer:
x = 5
y = 7.07
Step-by-step explanation:
We use the equation
A² + B² = C²
Y is the hypothenuse, so it will be the C
5² + 5² = C²
25 + 25 = C²
50 = C²
C = 7.07
Find the equation of the axis of
symmetry for this function.
f(x) = -2x² - 12x +36
Hint: To find the axis of symmetry, use the equation: x =
-b
2a
Simplify your answer completely. Enter
the number that belongs in the green box.
x = [?]
The equation of the axis of symmetry for the function f(x) = -2x² - 12x + 36 is x = 3.
What are quadratic equations?
In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0.
The equation of the axis of symmetry for a quadratic function of the form f(x) = ax² + bx + c is given by:
x = -b / 2a
Comparing with the given function, we have:
a = -2, b = -12
Substituting these values into the formula, we get:
x = -(-12) / 2(-2) = 3
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What percentage of the data values represented on a box plot falls between the lower quartile and the upper quartile? 25% 33.3% 50% 75%
Answer:50%
Step-by-step explanation:
Answer:
c 50%
Step-by-step explanation:
If f (x) = StartRoot x EndRoot + 12 and g (x) = 2 StartRoot x EndRoot, what is the value of (f – g)(144)?
The value of the difference of composite function is (f-g)(144) = 0.
What is Composite function?A composite function is one that uses the output of one function as the entry for another. The function f g (x) fg(x) fg(x) fg(x) fg(x) is also referred to as "f of g of x" or "f g fg fg of x," and it combines two functions if we have f and g.
According to question:To find the value of (f-g)(144), we first need to find f(144) and g(144).
We have:
[tex]$$f(x) = \sqrt{x} + 12$$[/tex]
So;
[tex]$$f(144) = \sqrt{144} + 12 = 12 + 12 = 24$$[/tex]
Similarly,
[tex]$$g(x) = 2\sqrt{x}$$[/tex]
So:
[tex]$$g(144) = 2\sqrt{144} = 2 \cdot 12 = 24$$[/tex]
Now we can calculate (f-g)(144):
[tex]$$(f-g)(144) = f(144) - g(144) = 24 - 24 = 0$$[/tex]
Therefore, (f-g)(144) = 0.
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Roberto has $200 in spending money. He wants to buy some video games that cost $25.50 each. Write and solve an inequality to find the number of games that Roberto can buy. Enter your answer in the box.
Roberto can buy 7 games
Equation=25.50x=200
You would divide each side of the equation by 25.50. You would then get x=7.843, but since Roberto doesn't have anymore money, he can not buy 8 games. So, you would round down to 7 games.
Writing Prompt 2
Answer the following questions. For full credit, you must show your work or explain your answer.
The floor plan of one room in a bookstore is a
square with an area of 576 square feet. Part of
this room is taken up by a café. The border of
the café runs from the midpoints of two
adjacent walls.
I
café
Find the area, in square feet, of the café. Show your work AND explain how you found your answer in
complete sentences.
The area of the café whose boarder runs through the mid-point of the adjacent walls is 288 square feet.
What is area of square?Four equal sides and four equal angles make up the closed, two-dimensional object known as the square. At the vertices, the square's four sides correspond to its four angles. The area of a square is equal to the entire area taken up by the form, and its perimeter is equal to the sum of the lengths of all of its sides. The quantity of square units required to completely fill a square is known as its area. In other terms, the territory inhabited inside a square's perimeter is its area.
Given that, area of the room is 576 square feet.
Thus, the side of the room has a length of:
√576 = 24 feet.
The café's perimeter runs from the middles of two adjacent walls, making it a square that occupies half the space in the room. As a result, the café's location is:
(1/2)(576 sq ft) = 288 sq ft
The area of the café whose boarder runs through the mid-point of the adjacent walls is 288 square feet.
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√14p^5
Degree, leading coefficient, standard form, and classification of the polynomial by number of terms?
The features of the polynomial are
Degree = 5Leading coefficient = √14Standard form = √14p⁵Classification = MonomialHow to determine the features of the polynomialThe polynomial expression is given as
√14p⁵
The given expression is a monomial (a polynomial with one term) of degree 5 and leading coefficient √14.
The standard form of a monomial is simply the term itself, so the standard form of √14p⁵ is also √14p⁵
The classification of the polynomial by number of terms is univariate, which means it has only one variable (p), and it is a monomial, which means it has only one term.
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How many solutions does the system of linear equations does it have? -8x+5y= -8 8x-5y=- 7
Answer:
No solution
Step-by-step explanation:
-8x + 5y = -8
8x - 5y = -7
0 = -15
This is not true. So, there is no solution.
. [T] A mass on a spring bounces up and down in simple harmonic motion, modeled by the function ()=−6cos s ( t ) = −6 cos t where s is measured in inches and t is measured in seconds. Find the rate at which the spring is oscillating at =5 t = 5 s.
The spring is oscillating at a rate of 5.75 in/s at time t = 5 seconds.
What is rate οf οscillating?The recurrent οr periοdic change οf a quantity arοund a central value (οften an equilibrium pοint) οr between twο οr mοre different states is knοwn as οscillatiοn.
Alternating current and a swinging pendulum are twο cοmmοn examples οf οscillatiοn.
In physics, οscillatiοns can be use tο simulate cοmplex interactiοns like thοse between atοms.
The beating οf the human heart (fοr circulatiοn), business cycles in ecοnοmics, predatοr-prey pοpulatiοn cycles in ecοlοgy, geοthermal geysers in geοlοgy, vibratiοn οf strings in guitars and οther string instruments, periοdic firing οf nerve cells in the brain, and the periοdic swelling οf Cepheid variable stars in astrοnοmy are just a few examples οf dynamic systems that οscillate οutside οf mechanical systems. the wοrd.
(a) The rate of oscillation is the speed of the mass. The velocity of the mass is the derivative of s(t):
[tex]$ \rm v(t)=s^{\prime}(t)=6\sin t$[/tex]
The rate at t = 5s is then = ∣s'(5)∣
= 5.75 in/s
Hence, The spring is oscillating at a rate of 5.75 in/s at time t = 5 seconds.
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