Then the equation that represents the total rent will be y = 5x + 7. Then the correct option is C.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The table is given below.
Number of Days Rented Rental Cost ($)
1 12
2 17
3 22
4 27
At x = 1, the value of y is 12.
12 = m + c ...1
At x = 2, the value of y is 17.
17 = 2m + c ...2
Subtraction equation 1 from equation 1, then we have
2m - m = 17 - 12
m = 5
Then the value of 'c' is given as,
17 = 2 x 5 + c
17 = 10 + c
c = 7
Then the equation that represents the total rent will be y = 5x + 7. Then the correct option is C.
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What is the side length of the smaller square in the diagram?
The side length of the smaller square is 3 cm.
Given that:-
Length of the larger square = [tex]3\sqrt{2}[/tex] cm.
We have to find the length of the smaller square.
As the length of the larger square is equal to the diameter of the circle
Hence,
Diameter of the circle = [tex]3\sqrt{2}[/tex] cm
Now,
The diameter of the circle is equal to the diagonal of the square.
Hence, diagonal of the square = [tex]3\sqrt{2}[/tex] cm
Let the length of the square be x cm.
Hence, by pythagoras theorem, we can write,
[tex]x^2+x^2=(3\sqrt{2} )^2\\x^2+x^2=18\\2x^2=18\\x^2=9\\[/tex]
x = 3 cm
Hence, the length of the smaller square is 3 cm.
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According to this rate shown in this graph, after 12 minutes the coffee is about 110 degrees. After one hour (60 minutes), what do you think the temperature would be?
After one hour (60 minutes, the value of the temperature is 550 degrees.
What is temperature?Temperature is the degree of hotness and coldness that a body contains.
In this case, after graph, after 12 minutes the coffee is about 110 degrees. The temperature per minute will be:
= 110 / 12
= 9.167° per minute.
Therefore, the temperature after 1 hour which is 60 minutes will be:
= Time × Rate
= 60 × 9.167°
= 550°
The temperature is 550°.
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suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. we find the heights of 60 people. (you may need to use the standard normal distribution table. round your answers to the nearest whole number.) (a) how many would you expect to be between 165 and 175 cm tall? people (b) how many would you expect to be taller than 167 cm?
The expected number of people between 165 and 175 is 41.
The expected number of people taller than 168 is 39.
Given that the mean and standard deviation of people's heights (measured in centimeters) are 170 and 5 respectively. The heights of 60 people are revealed.
μ = 170
σ = 5
n = 60
(a) The probability would you expect to be between 165 and 175 cm tall;
P( 165 < x < 175 ) = P( (165 - 170)/5 < z < (175 - 170)/5 )
= P( -1 < z < 1 )
= P( z < 1) - P( z < -1 )
= 0.8413 - 0.1587
= 0.6826
Expected number of people between 165 and 175 = n * p
= 60 * 0.6826
= 40.956
≅ 41
(b) The probability would you expect to be taller than 167 cm;
P( x > 167 ) = P( z > (167 - 170)/5 )
= P( z > -0.6 )
= 0.7257
Expected number of people taller than 168 = n * p
= 60 * 0.7257
= 43.542
≅ 39
Hence,
The expected number of people between 165 and 175 is 41.
The expected number of people taller than 168 is 39.
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Find DE, please help me
Step-by-step explanation:
ABC and CDE are similar triangles.
similar shapes means that both shapes have the same angles. and : that there is one scaling factor for all lines of one of the shapes to calculate the lengths of the lines of the other shape.
we see that all the other sides of ABC are scaled 2:1 to the corresponding sides of CDE. that means the sides of ABC are twice a long as the sides of CDE.
the same scaling factor has to apply to AB vs. DE.
therefore,
11x - 25 = 2(4x + 1) = 8x + 2
3x = 27
x = 9
DE = 4x + 1 = 4×9 + 1 = 36 + 1 = 37
Why are most streets designed in a way that they are perpendicular or parallel to each other? ...
The simple reason why streets are usually designed parallel or perpendicular to each other is because that pattern makes it easy for users to connect people easily.
What is meant by perpendicular and parallel streets?A perpendicular street can simply be defined as a street which intersect another streets. However, on the other end, two streets are said to be parallel to each other when they are in the same distance apart. The same is applicable in mathematics as a perpendicular line intercept another line and parallel lines don't meet.
That being said, when streets are parallel or perpendicularly designed, residents of the environment find it easy to communicate with each other. Business owners use this easy accessibility to easily describe their addresses to customers.
So therefore, it can be deduced from the given explanation above that when streets are designed with good planning, it makes people access it easily.
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Carlos is a receptionist at a law firm. he spends 2 minutes routing each phone call as it comes in. write an equation that shows how the total number of minutes carlos spends routing calls, y, depends on the number of calls, x.
The equation to show the total no. of minutes Carlos spends routing calls is y = 2x
To find the required equation, use the following given data:
Time taken by Carols for routing each call = 2 minutes
Total number of calls = x
Total number of minutes Carol spends routing calls = y
The one-dimensional function takes up a single input value (x) and outputs a single evaluation of the given input (y).
So, by practical application of one-dimensional function,
Total number of minutes Carols spends routing calls (y) = Time taken by Carols for routing each call * Total number of calls (x)
∴ The equation will be y = 2*x
Thus, y = 2x shows the total number of minutes Carlos spends routing the calls.
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Parallelogram PQRS is shown. m/S=(3x), m/R=120, and m/Q=(2y). Find the value of y.A.
20
B.
30
C.
40
D.
60
Option B. From the parallelogram PQRS the value of y is given to be 30
How to solve for the value of y from the parallelogramIn order to get the value of y we have to use the formula
2y + 120 = 80
where the value 120 is the angle that is stated as 120 from the question
2y = 180 - 120
2y = 60
y = 60 / 2
y = 30
Hence the value of y = 30
We can go ahead to get the value of x as well
3x + 120 = 180
take the like terms
3x = 180 - 120
3x = 60
divide through by 3 to get x
60 / 3 = x
20 = x
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Divide [tex]4\frac{2}{15}[/tex] by 3.1.
[tex]\fbox{1.333333}[/tex]
[tex]4\frac{2}{15} \div3.1[/tex]
Simplify:
[tex]4\frac{2}{15} \div3.1[/tex]
[tex]=1.333333[/tex]
let's firstly convert the mixed fraction to improper fraction and the decimal one to a fraction.
[tex]\stackrel{mixed}{4\frac{2}{15}}\implies \cfrac{4\cdot 15+2}{15}\implies \stackrel{improper}{\cfrac{62}{15}}\hspace{10em} 3.\underline{1}\implies \cfrac{31}{1\underline{0}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{62}{15}\div \cfrac{31}{10}\implies \cfrac{62}{15}\cdot \cfrac{10}{31}\implies \cfrac{62}{31}\cdot \cfrac{10}{15}\implies \cfrac{2}{1}\cdot \cfrac{2}{3}\implies \cfrac{4}{3}\implies 1\frac{1}{3}[/tex]
Theo mows a lawn. After working for 1 3/5 hours, he has mowed 7/9 of the lawn. Can Theo mow the lawn in 2 hours if he continue to mow at the same rate?
Yes, he can mow the lawn in 2 hours.
What is work done?We can define the work done as, a work done in a given period of time.
Given that, Theo mows a lawn. After working for 1 3/5 hours, he has mowed 7/9 of the lawn
In [tex]1\frac{3}{5}[/tex] hours he mows 7/9 part of lawn
Therefore, in 8/5 hours he is mowing 7/9 part of lawn
In 1 hour = 7/9*5/8 = 35/72
In 2 hours = 35/72*2 = 35/36 ≈ 1
Hence, Yes, he can mow the lawn in 2 hours.
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under what circumstances would a score that is 10 points below the mean be considered to be an extreme value? select one: a. when the mean is much greater than 10 b. when the mean is much less than 10 c. when the standard deviation is much greater than 10 d. when the standard deviation is much less than 10
The correct option d. when the standard deviation is much less than 10.
Describe the term standard deviation?The term "standard deviation" (or "σ") applies to a measurement of the data's dispersion from the mean. A low standard deviation indicate that the data are grouped around the mean, although a large standard deviation indicates that the data are more dispersed.When a value is 10 points beyond the norm, it is said to be an extreme value or an outlier.
When a point deviates significantly from the mean in comparison to other points, it is referred to as an outlier. Z-scores can be used to establish this. Remember the z-score formula:
z = (x - μ) / σ
μ = mean σ = standard deviationx = point of interestThe outlier should have a very big magnitude z-score. We are aware that the score in this issue is 10 points just below mean, we can say:
A lesser value of would raise the magnitude of a z-score, increasing it to the maximum extent achievable.
Therefore, this point would be an outlier whether its standard deviation was drastically lower than 10.
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Some doctors recommend that men drink 3 liters of water every day. there are approximately 29.6 milliliters in 1 fluid ounce. which measurement is closest to the number of fluid ounces in 3 liters? responses 89 fl oz 89 fl oz 10 fl oz 10 fl oz 101 fl oz 101 fl oz 33 fl oz 33 fl oz
The measurement closest to the number of fluid ounces there are in 3 liters is 101 fl oz.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
If there are approximately 29.6 milliliters in 1 fluid ounce, then divide 3 liters by 29.6 milliliters to get the amount of fluid ounces it has.
29.6 milliliters = 1 fluid ounce
3 liters = 3000 milliliters
3000 milliliters / 29.6 milliliters = 101 fluid ounce
Hence, 3 liters ≈ 101 fluid ounces.
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A skydiver fell toward Earth at a steady speed for 10.0 seconds. He fell 593 meters in that
time. What was his speed?
Answer:
59.3 meters/second
Step-by-step explanation:
593 / 10 = 59.3
A marathon is 26.2 miles long. There is a water station every 1 31/100 miles along the race route. Which expression represents the total number of water stations?
The expression that represents the total number of water stations is 26.2 ÷ 1.31
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
It's important to note as an illustration, the expression x + y has the terms x and y with an addition operator between them.
In this case, the marathon is 26.2 miles long and there is a water station every 1 31/100 miles along the race route. The expression will be:
= 26.2 ÷ 1 31/100
= 26.2 ÷ 1.31
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Whose limeade has a weaker like flavor?
well, your proportion setup is good, let's simply use that then
[tex]\stackrel{Jaylan}{\cfrac{~~ \frac{ 3}{4 } ~~}{\frac{1}{5}}}\implies \cfrac{3}{4}\cdot \cfrac{5}{1}\implies \cfrac{15}{4}\implies \cfrac{3\frac{3}{4}}{1}~\frac{water}{lime} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Wanchen}{\cfrac{~~ \frac{ 2}{3 } ~~}{\frac{1}{6}}}\implies \cfrac{2}{3}\cdot \cfrac{6}{1}\implies \cfrac{12}{3}\implies \cfrac{4}{1}~\frac{water}{lime}[/tex]
well, the one with the lesser lime flavor will be the one that put too much water in the drink, the more water the less the fruit mix, the more waterdowned the drink is, well hell who put more water per lime? well Wanchen, shame on you.
If the taxi company only has $10.50 to spend, what value does this represent?
The statement "If the taxi company only has $10.50 to spend" represents that the maximum amount to spend is $10.50.
Amount to spend by the taxi driver ≤ 10.50.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
The taxi company only has $10.50 to spend.
This means that,
The maximum amount to spend is $10.50.
We can also represent as:
Amount to spend by the taxi driver ≤ 10.50.
Thus,
The statement "If the taxi company only has $10.50 to spend" represents that the maximum amount to spend is $10.50.
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Calculate the area of the square!
Answer:
The answer is 169
Step-by-step explanation:
a random variable is normally distributed with a mean of 25 and a standard deviation of 5. if an observation is randomly selected from the distribution, what value will 15% of the observations be below?
the 2 values X(19.8,30.2) is value will 15% of the observations be below .
by hypothesis .
What is hypothesis ?
A hypothesis is an assertion, a notion put up for the purpose of debating and then examined to discover if it might be true. Prior to conducting any relevant research, other than a brief background review, the hypothesis is developed using the scientific method.Here, Mean(\mu) and Standard Deviation (\sigma)= 5. You need to find the 2 values of which the smallest has 15% of the values below it i.e (Z<x)= 0.15 and the largest has 15% of the values above it i.e(Z>y)= 0.15.
Now we need to refer to the Z tables and see which value of x corresponds to 0.15, and we see that -1.04 is = 0.149 \sim 0.15
Now we know that the Z value is given by Z = X - μ/σ
Substituting we get
-1.04= (X-25)/5
therefore -5.2= X-25 or X= 19.8
Now let us get the value of X for (Z>y)=0.15`. Since Z tables give values for Z<a only, hence we can write that
Z>y=0.15 is the same as Z<y= 1-0.15= 0.85. We now check the Z tables and see which value of Z corresponds to 0.85, and we get 0.850 = +1.04
Again, substituting Z in the equation Z = X - μ/σ
we get
+1.04= (X-25)/5
Therefore 5.2= X-25, therefore X= 30.2
From the 2 values X(19.8,30.2)
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the binominal distribution: a. is symmetric irrespective of the value of the probability of success. b. models n independent replications of a bernoulli experiment, each with a probability p of success. c. assumes that the average number of occurrences per unit is a constant and that occurrences are independent. d. is a discrete distribution used to model the number of occurrences in some unit of measure
The correct option is B "Models n independent replications of a Bernoulli experiment each with a probability p of success".
What is binomial distribution?It is a frequency distribution of the number of successful outcomes that could occur in a set number of trials with an equal chance of success. In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p. When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution. The probability of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.
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(DUE IN 2 HOURS PLEASE HELP) Find an equation for the line that passes through the points (5, 2) and (-4, 5).
Answer:
Y= -1/3x+11/3
Step-by-step explanation:
pls hurry and thanks 40 pts
The angle of x in the triangle is 75 degrees.
How to find the angles of triangle?The sum of angles in a triangle is 180 degrees. The triangle is a an isosceles triangle.
An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.
Therefore, the base angles are equal.
The third angle of the triangle is 30 degrees(vertically opposite angles)
Hence,
x + x + 30 = 180
2x + 30 = 180
2x = 180 - 30
2x = 150
x = 150 / 2
x = 75 degrees
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The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (4,160) and (6,240) to find the number of soda bottles the machine can make each minute.
The number of soda bottles the machine can make each minute = 40
In this question, we have been given the graph shows the relationship between time and the number of soda bottles a machine can make.
Also, we have been given two points (4,160) and (6,240)
We need to find the number of soda bottles the machine can make each minute.
i.e., we need to find the slope of line passing through points (4,160) and (6,240)
Using the formula of slope,
m = (240 - 160) / (6 - 4)
m = 80/2
m = 40
Therefore, the number of soda bottles the machine can make each minute = 40
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3y - x - (4x - 5y)/10 - 7y+2x/4
what is the smallest odd number you can make with 3 4 6 and 8
Answer: You cannot.
Step-by-step explanation:
3 can be multiplied into an odd number
4 cannot be multiplied into an odd number
6 cannot be multiplied into an odd number
8 cannot be multiplied into an odd number
Overall, you will not be able to get an odd number with the numbers provided.
Answer: 4683
Step-by-step explanation:
To have an odd number, and since the only odd number you have in your list is 3, that would be in the one's place. Then, you have to put the smallest number (except for 3) in the front. Now, you have two more places to fill in (4 _ _ 3). Like the 4, put the 6 after the 4 to have the smallest possible hundreds place. Now place the eight. Your final number should be... 4683.
The graph of a quadratic function with vertex (-3,1) is shown in the figure below. Find the range and the domain
The domain of the given quadratic function is { -3 }
and range is { 1 }
What is a domain and range ?A function's domain is the set of values that can be plugged into it. This set symbolizes the x values in a function like f. (x). Additionally, we can deduce that a function's range refers to the set of values it can accept. There are values in this set that the function returns when we enter an x value.
The domain of the given quadratic function is { -3 }
and range is { 1 }
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Rachel bought three and fifty-two hundred pounds of apples at the store. How is this written in number form?
3.0052
3.052
3.502
3.52
Answer: 3.52
Step-by-step explanation: fifty-two hundredths as a number would be 0.52, so 3.00 + 0.52 would be 3.52
assume the state of arkansas placed a tax on playing cards of 6 cents per pack. if the state generated $48600 in revenue, how many packs of cards were sold?
The number of pack of cards sold at the state of Arkansas is 8100.
Describe the term division?Multiplication is the complete reverse of division. If participants of 4 add up to 12, then 12 divided into three classes of equally sized results in 4 in each group.For the values given in question.
The tax on playing card in state of Arkansas = 6 cents per pack.
Total revenue generated = $48600.
Divide total revenue by one pack price to get the number of packs.
Number of pack = Total revenue/price of each pack
Number of pack = $48600/6
$48600.Number of pack = 8100
Thus, the number of pack of cards sold at the state of Arkansas is 8100.
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A triangle has sided with lengths of 20 miles, 25 miles, and 30 miles. Is it a right triangle ?
Answer:
No
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
For a Triangle to be a Right-Angled Triangle, should follow the Pythagoras Theorem which states that
If a is the larger side and b , c are the lengths of the other two sides
Then [tex]a^{2} =b^{2} +c^{2}[/tex]
Here a=30 , Then [tex]a^{2}=30^{2} =900[/tex]
and b=20 , c=25 , Then [tex]b^{2} +c^{2} =20^{2} +25^{2} =1025[/tex]
Since [tex]a^{2} \neq b^{2} +c^{2}[/tex]
Then the Triangle is not Right Triangle
n a recent survey in a statistics class, it was determined that only 60% of the students attend class on fridays. from past data it was noted that 98% of those who went to class on fridays pass the course, while only 20% of those who did not go to class on fridays passed the course. a. what percentage of students is expected to pass the course?
The percentage of students expected to pass the course is 66.8%
The given data represents;
In a recent survey in a statistics class, it was determined that only 60% of the students attend class on Fridays. from past data, it was noted that 98% of those who went to class on Fridays passed the course, while only 20% of those who did not go to class on Fridays passed the course.
We need to find the percentage of students who are expected to pass the course.
Let 'A' be the event of passing,
'B' be the event of attending on Fridays.
P (A I B) = 0.98 * P (A I B') = 0.2
P (B) = 0.6
Then, P (B') = 1 - 0.6
= 0.4
→ P (A ∩ B) = P (A I B) * P (B)
= 0.98 * 0.6
= 0.588
→ P (A ∩ B') = P (A I B') * P (B)
= 0.2 * 0.4
= 0.08
∴ P(A) = P (A ∩ B) + P (A ∩ B')
= 0.588 + 0.08
= 0.668
Hence, the percentage of students expected to pass the course is 66.8%
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The state board of education has $5,647 to buy new calculators. each calculator costs $2. after buying as many calculators as it can with its budget, how much money will the state board of education have left over?
By basic arithmetic, the state board of education will have $1 left .
What is meant by basic arithmetic?The area of mathematics known as arithmetic deals with the study of numbers and the numerous operations that can be performed on them. The four fundamental arithmetic operations in mathematics are addition (finding the sum), subtraction (finding the difference), multiplication (finding the product), and division (finding the quotient). These operations can be applied to all real numbers. The usage of fundamental arithmetic operations is the focus of the field of mathematics known as arithmetic.
Addition, subtraction, multiplication, and division are the four operations employed in arithmetic.
The total amount the state board has = $5647
The cost of calculator = $ 2
The total number of calculators bought = 5647/2
= 2323.5
≈ 2823
So, the cost of 2323 calculators
= 2823 × 2
= 5646
So, the money the state board of education left = $5647 - $5646
= $1
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I need to know the answer
Step-by-step explanation:
The graph of [tex]p(x)=2x^3[/tex] is less steep than [tex]f(x)=2.5x^3[/tex] because the coefficient 2 is less than the coefficient 2.5. That makes points on the graph of p(x) lie closer to the x-axis than points on the graph of f. For example, if x = 2, the point (2, 20) is on the graph of f but the point (2, 16) is on the graph of p (so it lies under the point (2, 20).
The graph of [tex]p(x)=-x^3[/tex] is less steep than the graph of f and it is reflected over the x-axis. The negative coefficient -1 is doing that. The values of the function p(x) are opposite sign to values of f(x).
The graph of [tex]p(x)=3x^3[/tex] is steeper than the graph of f(x) because the coefficient 3 is larger than the coefficient 2.5, making the points on the graph of p lie farther away from the x-axis than points on the graph of f(x).
