Answer:
PART A:
The equations must be changed to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, in order to be graphed in the coordinate plane.
Here is Matt's equation:
y = 40x + 50
The y-intercept of this equation is 50, while the slope is 40.
Here is Kylie's equation:
y = 50x
The slope of this equation is 50, and the y-intercept is 0. | /
| /
| /
| /
| /
-----|------------------
| / \
|/ \
/-------------\
0 1 2 3 4 5 6 x-axis
The red line shows Kylie's distance from the beginning point, while the blue line shows Matt's distance from it.
PART B:
When Matt begins driving later than Kylie, there is one circumstance in which they are never both at the same distance from the starting location at the same time. Let's imagine, for illustration, that Matt begins driving 20 minutes after Kylie. Thus, the set of equations that best describes this circumstance is:
(Matt's distance) y=40x+50
Kylie's distance is given by y = 50(x – 20).
Under this system, we deduct 20 from Kylie's x-value to reflect Matt's advantage of a 20-minute head start.
We can set the two equations equal to one another to determine how many solutions this system has:
40x + 50 = 50(x - 20) (x - 20)
40x + 50 = 50x - 1000\s100 = 10x
x = 10
This tells us that the two drivers will never be at the same distance from the starting point at the same time. There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.
There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.
PART A:
The equations must be changed to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, in order to be graphed in the coordinate plane.
Here is Matt's equation:
y = 40x + 50
The y-intercept of this equation is 50, while the slope is 40.
Here is Kylie's equation:
y = 50x
The slope of this equation is 50, and the y-intercept is 0. | /
| /
| /
| /
| /
-----|------------------
| / \
|/ \
/-------------\
0 1 2 3 4 5 6 x-axis
The red line shows Kylie's distance from the beginning point, while the blue line shows Matt's distance from it.
PART B:
When Matt begins driving later than Kylie, there is one circumstance in which they are never both at the same distance from the starting location at the same time. Let's imagine, for illustration, that Matt begins driving 20 minutes after Kylie. Thus, the set of equations that best describes this circumstance is:
(Matt's distance) y=40x+50
Kylie's distance is given by y = 50(x – 20).
Under this system, we deduct 20 from Kylie's x-value to reflect Matt's advantage of a 20-minute head start.
We can set the two equations equal to one another to determine how many solutions this system has:
40x + 50 = 50(x - 20) (x - 20)
40x + 50 = 50x - 1000\s100 = 10x
x = 10
This tells us that the two drivers will never be at the same distance from the starting point at the same time. There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.
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Consider the parabola given by the equation:
f
(
x
)
=
4
x
2
+
8
x
−
1
Find the following for this parabola:
A) The vertex:
B) The vertical intercept is the point
C) Find the coordinates of the two
x
intercepts of the parabola and write them as a list, separated by commas:
It is OK to round your value(s) to to two decimal places.
The value following are
vertex: (6, -9)
y-intercept: (0, 27)
X = 3, 9
Finding Vertex (Part A)
Consider the formula -b/2a. This formula gives you the x-coordinate of the vertex.
[tex]y = 1x^2 - 12x + 27[/tex]
a = 1
b= -12
c =27
-b/2a = - (-12)/2(1) = 12/2 = 6 (x-coordinate of vertex)
When solving for the y-coordinate of the vertex you will need to substitute your 'x" back into the equation.
[tex]y = 1(6)^2 - 12(6) + 27[/tex]
y = 36 - 72 + 27 = -9 (y-coordinate of vertex)
--------------------------------------------------------------------------
Y- Intercept (Part B)
When looking for the y-intercept your "x" must always be 0.
Substitute 0 in every "x" in the equation.
y =[tex]1(0)^2 - 12(0) + 27[/tex]
y = 27
y-intercept: (0, 27)
-----------------------------------------------------------------------------
X- Intercepts (Part C)
To find the values of the "x" factor.
[tex]y = 1x^2[/tex] - 12x + 27
[tex]0 = 1x^2[/tex] - 12x + 27
0 = (x - 3 )(x - 9 )
(x-3) = 0 (x-9) = 0
x = 3 x = 9
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The rim of the volcanic crater shown below is a circle. The diameter is 620 m. What is the circumference of the rim of the crater in kilometres (km)?
Find the missing dimension of the triangle. A=13.5 b=6.75 h = __ in.
The height of the given triangle having an area of 13.5in.² and a base length of 6.75 in. is 4 in.
What is a triangle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. Any three points in Euclidean geometry, when they are not collinear, produce a distinct triangle.
In a two-dimensional plane, a triangle's area is the area that it completely encloses. A triangle is a closed shape with three sides and three vertices, as is common knowledge. The entire area occupied by a triangle's three sides is referred to as its area. Half of the product of the triangle's base and height provides the general formula for calculating the area of the triangle.
In this question, we are given,
Area of triangle A = 13.5 in.²
Base of triangle b = 6.75 in.
We are asked to find the height h of the triangle.
Now formula of the area is:
A = 1/2 * b * h
13.5 = 1/2 * 6.75 * h
h = 13.5 *2 / 6.75 = 4 in.
Therefore the height of the given triangle is 4 in.
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n environmental agency frequently samples the water in a region to ensure that the levels of a certain contaminant do not exceed 30 parts per billion (ppb). From 12 randomly selected samples of the water, the agency constructed the 99 percent confidence interval (22.5, 28.7).
We are 99 percent confident that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb
The correct interpretation of the interval is " We are 99 percent confident that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb "
What is confidence interval?
In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as the confidence interval. Analysts frequently employ confidence ranges that include 95% or 99% of anticipated observations.
We need to find correct interpretation of the interval.
Among all answer choices given, the correct option is :
We are 99 percent confident that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb
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7. According to new research in 2021, Puerto Rican Reggaeton star Bad Bunny again took the title of
most-streamed artist in the world on Spotify. He received over 9.1 billion streams (9, 100, 000, 000)
without releasing a new album last year.
Use this number of streams with your equation to calculate how much money Bad Bunny may have
made via Spotify. (Worlds Most Streamed Songs (Spotify), 2021)
The requried, Bad Bunny may have made around $34.6 million from his 9.1 billion streams on Spotify in 2021.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
As of 2021, Spotify's average payout per stream is about $0.0038, which means that an artist earns approximately 0.38 cents per stream.
So, to calculate Bad Bunny's potential earnings from 9.1 billion streams on Spotify, we can use the following equation:
Earnings = Number of Streams x Payout per Stream
Earnings = 9,100,000,000 x $0.0038
Earnings = $34,580,000
Therefore, based on this rough estimate, Bad Bunny may have made around $34.6 million from his 9.1 billion streams on Spotify in 2021. It's important to note that this is just an estimate and that the actual amount he earned could be higher or lower depending on the factors mentioned earlier.
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When testing for current in a cable with 10 color-coded wires, the author used a meter to test 2 wires at a time. How many different tests are required for every possible pairing of 2 wires?
what is combination ?
In mathematics, a combination is a way of selecting items from a collection, such that the order of selection does not matter. The combination formula gives the total number of ways to choose k items from a set of n distinct items without regard to the order in which they are chosen.
The combination formula is given by:
n choose k = n! / (k! * (n-k)!)
Explanation:
If we have 10 color-coded wires, we can choose 2 wires out of them in (10 choose 2) ways.
(10 choose 2) is a combination formula given by:
(10 choose 2) = 10! / (2! * (10-2)!)
= (10 * 9) / 2
= 45
This means that we need to perform 45 tests to cover all possible pairings of 2 wires from 10 color-coded wires.
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which of the following is an example of conditional probability?
Answer:
the answer is (a) the probability that a person will order pie
Write a PYTHON program that:
1) Asks the user to input a sequence of comma separated numbers, e.g., 4,6,7,454,78 (no space in between)
2) Transforms the input string into a list using the function split(). For example, userstr.split(',') will split the string userstr at each ',' and return a list of separated items.
3) Checks whether the user input is all-digit (use .isdigit() function). If yes, go to next step; if not, let the user try until they get it right.
4) Converts all items in the list into integer
5) Adds all numbers together and return the sum.
Answer:
while True:
user_input = input("Please enter a sequence of comma-separated numbers: ")
if user_input.replace(",", "").isdigit():
break
print("Invalid input! Please try again.")
num_list = user_input.split(",")
num_list = [int(num) for num in num_list]
total_sum = sum(num_list)
print("The sum of the numbers is:", total_sum)
Step-by-step explanation:
This program uses a while loop to repeatedly ask the user for input until they provide a valid sequence of comma-separated numbers (all-digit input). The .isdigit() function is used to check if the input is all-digit. If the input is valid, the program splits the input string at each ',' using the .split() function, converts each item in the resulting list into an integer using list comprehension, then adds all numbers together using the sum() function. Finally, the program outputs the total sum.
Find the number of years necessary for an investment to double at each of these rates of simple interest. Round to the nearest tenth if necessary.
Interest Rate: 11%
It would take approximately 6.5 years for an investment to double at a simple interest rate of 11%.
According to given information :To find the number of years necessary for an investment to double at a simple interest rate of 11%, we can use the following formula:
n = 72 / r
where n is the number of years required for the investment to double, and r is the interest rate.
Plugging in the values, we get:
n = 72 / 11
n ≈ 6.5 years (rounded to the nearest tenth)
Therefore, it would take approximately 6.5 years for an investment to double at a simple interest rate of 11%.
What is simple interest ?Simple interest is a type of interest that is calculated on the principal amount of a loan or investment. It is a fixed percentage of the original amount borrowed or invested, and it is not compounded over time.
The formula for calculating simple interest is:
I = P * r * t
where I is the interest, P is the principal amount, r is the interest rate, and t is the time period.
For example, if you borrow $1,000 for two years at a simple interest rate of 5%, the interest you would pay is calculated as follows:
I = 1,000 * 0.05 * 2
I = $100
So, you would have to pay back the $1,000 principal plus $100 in interest, for a total of $1,100.
Simple interest is commonly used in short-term loans or investments, and it is usually easier to calculate and understand than compound interest, which takes into account the effect of earning interest on previously earned interest.
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Property damage liability pays for injuries to a driver or their passengers caused by an uninsured or underinsured driver. True or false
The statement that the Property damage liability pays for injuries to a driver or their passengers caused by an uninsured or underinsured driver is false.
What is Auto Insurance Policy?Auto insurance policy is a contract between the insurance company and the person being insured which protects the person under any financial loss caused by accident or theft.
There are mainly six types of auto insurance coverage that the company basically provide.
They are Property damage liability, Bodily injury liability, PIP, Uninsured and underinsured motorist coverage, collision and comprehensive.
Property damage liability pays for the damage that the person insured causes to someone else's property, which include someone else's car, buildings or so.
The given coverage in the statement is the Uninsured and underinsured motorist coverage.
Hence the given statement is false.
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Arrange the following fractions in descending order; 2/3, 3/4, 1/6, 5/12
A factory selling cell phones has a marginal cost function C(x)=0.01x2−3x+229, where x represents the number of cellphones, and a marginal revenue function given by R(x)=429−2x. Find the area between the graphs of these curves and x =0. What does this area represent?
The area between -
C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 is 492097.4 square
units.
What is function?A function is a relation between a dependent and a independent variable. Mathematically we can write the function as -
y = f(x)
Given is that a factory selling cell phones has a marginal cost function C(x) = 0.01x² - 3x + 229, where {x} represents the number of cellphones, and a marginal revenue function given by R(x) = 429 - 2x.
We can write the area between -
C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 as -
Area = ∫C(x) dx + ∫{C(x) - R(x)} dx
We can write the area with limits as -
Area =
∫(0.01x² - 3x + 229) dx {limits from 229 to 429}
+
∫(0.01x² - 3x + 229 - 429 + 2x) dx {limits from 429 to 629}
Area = 71548.7 + 420548.7
Area = 492097.4 square units
Therefore, the area between -
C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 is 492097.4 square
units.
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Please help find the radius, circumference, and area
Pippin went to a game room that charged $4 admission, plus $0. 25 per token. The equation which represents his total cost is y = 0. 25x + 4. What are the ordered pairs for the equation when you use these x-values: 5, 10, 20?.
Answer:
5 = $ 5.25. 10= $ 6.50. 20= $9.00
Step-by-step explanation:
if this is wrong you can completely write me a really rude email or message or something
What is the solution to this question?
Answer:
Step-by-step explanation:
To solve the equation (-1)/(x-5) = 2/(x+4), we can start by cross-multiplying:
(-1)(x+4) = 2(x-5)
Expanding both sides and simplifying, we get:
-x - 4 = 2x - 10
Bringing all the x terms to one side and all the constant terms to the other, we get:
3x = 6
Dividing both sides by 3, we get:
x = 2
So the solution to the equation is x = 2. However, we need to check if this value of x makes the denominators of the original equation non-zero. Plugging x = 2 into the original equation, we get:
(-1)/(2-5) = 2/(2+4)
Simplifying, we get:
1/3 = 1/3
Since both sides are equal, the solution x = 2 satisfies the original equation. Therefore, the only solution to the equation is x = 2.
Answer: x = 2
Step-by-step explanation:
[tex]\boldsymbol{\sf{The\:exercise\:is \longmapsto \ \dfrac{-1}{x-5}=\dfrac{2}{x+4} }}[/tex]
We cross multiply.
-(x + 4) = 2(x - 5)
We apply the multiplicative law of distribution.
-x -4 = 2(x - 5)
-x - 4 = 2x - 10
We rearrange the unknown terms to the left side of the equation.
-x - 2x = -10 + 4 <===Combine as terms===> -3x = -10 + 4
We calculate -10 + 4 = -6.
-3x = -6
We divide both sides of the equation by the coefficient of the variable.
[tex]\boldsymbol{\sf{x=\dfrac{-6}{-3} \iff \ x=\dfrac{6}{3} }}[/tex]
x = 2
A regular pentagon has an area of 118.25 square meters, and each side of the pentagon measures 4.3 meters.
What is the length of an apothem of the pentagon?
Enter your answer in the box.
m
The length of the apothem of the pentagon is approximately 11 meters.
What is a polygon?Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,
Examples of polygons, equilateral triangles, squares, pentagons etc.
Here, we have,
To solve this problem, we can use the formula for the area of a regular pentagon:
A = (5/2) × s × a
Where A is the area of the pentagon, s is the length of one side, and a is the apothem (the distance from the center of the pentagon to the midpoint of a side).
We know that the area of the pentagon is 118.25 square meters and the length of one side is 4.3 meters. We can substitute these values into the formula and solve for the apothem:
118.25 = (5/2) × 4.3 × a
Divide both sides by (5/2) x 4.3:
a = 118.25 / ((5/2) × 4.3)
= 118.25 / 10.75 ≈ 11 meters
Therefore, the length of the apothem of the pentagon is approximately 11 meters.
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is 5 yards and 2 feet greater than 200 in
The stem and leaf plot shows the number of laps around a track
that several teams walked as part of a fund-raiser for the library.
The teams that walked more than 50 laps raised an extra $100 for
the library.
What fraction of the teams raised this extra money?
The fraction of the teams that raised the extra money, given the number of teams laps needed to be walked, is D. 1 / 3
How to find the fraction ?To find the fraction of teams that raised the extra money, you need to count the number of teams who were able to walk more than 50 laps. The number of teams who walked more than 50 laps walked:
53, 63, 63, and 65 miles so 4 teams did so.
The total number of teams is the number of leafs which is 12 teams.
The fraction of teams who raised the extra money is :
= 4 teams / 12 total teams
= ( 4 ÷ 4 ) / ( 12 ÷ 4 )
= 1 / 3
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On a cutting operation 2 sq ft of sheet steel is wasted for every 32 sq ft used. What is the percent waste?
(Type a whole number or an exact decimal. If the decimal does not terminate. Round to the one decimal place)
Answer: To find the percent of waste, we need to first determine the fraction of waste.
For every 32 square feet used, 2 square feet are wasted. This can be expressed as:
2/32 = 1/16
So, the fraction of waste is 1/16.
To find the percentage, we need to multiply this fraction by 100:
1/16 * 100 = 6.25
Therefore, the percent of waste is 6.25%.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Here are the steps to calculate the percent waste of sheet steel:
Determine the amount of steel wasted per unit of steel used. The problem tells us that 2 sq ft of steel is wasted for every 32 sq ft used. Therefore, the waste-to-use ratio is 2/32.
Simplify the waste-to-use ratio, if necessary. In this case, the ratio can be simplified by dividing both the numerator and denominator by 2:
2/32 = 1/16
Convert the waste-to-use ratio to a percentage. To do this, we multiply the simplified ratio by 100:
1/16 * 100 = 6.25
Round the result, if necessary. The problem asks for a whole number or an exact decimal, so we round the result to one decimal place:
6.25 rounded to one decimal place is 6.3.
Therefore, the percent waste of sheet steel is 6.3%.
A study was conducted showing the relationship between the average maintenance cost and the age of a car in years.
Number of observations: 13
Least Squares | Standard | T
Parameter | Estimate | Error | Statistic| P-Value
Intercept | 54.7757 | 54.87 | 0.998282 | 0.3396
Slope | 120.689 | 11.8442 | 10.1898 | 0.0000
a) What is the formula for the regression function based on the output above (Write your equation in the context of question)?
b) Interpret the slope of the regression equation (In the context of question)?
c) Construct an 95% interval to predict the maintenance cost for a car that is 7 years old?
d) Based on this analysis, can we conclude that a relationship exists between the maintenance cost and the age of the car in years? What is the null and alternative hypothesis? Justify your answer using three steps process.
Answer:
Step-by-step explanation:
a) The formula for the regression function is:
Maintenance Cost = 54.7757 + 120.689 x Age of Car
b) The slope of the regression equation is 120.689. This means that on average, for every one year increase in the age of a car, the maintenance cost is expected to increase by $120.689.
c) To construct a 95% interval to predict the maintenance cost for a car that is 7 years old, we can use the formula:
Y = a + bX ± tα/2 * SE
where Y is the predicted maintenance cost, a is the intercept, b is the slope, X is the age of the car, tα/2 is the t-value for the 95% confidence level with n-2 degrees of freedom (11 in this case), and SE is the standard error of the estimate.
Plugging in the values, we get:
Y = 54.7757 + 120.689 * 7 ± 2.201 * 11.8442
Y = 923.167 ± 26.010
Therefore, we can be 95% confident that the maintenance cost for a car that is 7 years old will be between $897.16 and $949.17.
d) The null hypothesis is that there is no significant linear relationship between the average maintenance cost and the age of a car in years. The alternative hypothesis is that there is a significant linear relationship between the average maintenance cost and the age of a car in years.
To test the hypothesis, we can perform a t-test on the slope coefficient using the t-statistic and the p-value provided in the output. The t-statistic is 10.1898, which is much greater than the critical t-value at the 0.05 level of significance for a two-tailed test with 11 degrees of freedom (2.201). The p-value is 0.0000, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant linear relationship between the maintenance cost and the age of the car in years.
g(-9)=
Evaluate the function
From the graph, the value of the function g(-9) is 1
Evaluating a function from the graphFrom the question, we are to evaluate the function using the given information from the graph.
The given function is g(-9)
To evaluate the function, g(-9), from the graph, we will locate the point where x = -9 on the cartesian plane and then we will trace the point straight to the function graph. From the point on the function graph, we will read the value on the y-coordinate of the point by tracing a straight line to the y-axis.
From the graph,
The value of g(-9) is 1
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Assume that military aircraft use ejection seats designed for men weighing between 132. 4132. 4 lb and 217217 lb. If women's weights are normally distributed with a mean of 168. 7168. 7 lb and a standard deviation of 48. 848. 8 lb, what percentage of women have weights that are within those limits
The percentage of women with weights that are within the limits is:
60.93%
What percentage of women have weights that are within those limits?Can be calculated using the normal distribution formula. First, we need to find the z-scores for both the lower and upper limits:
z-score for lower limit = (132.4 - 168.7) / 48.8 = -0.74
z-score for upper limit = (217 - 168.7) / 48.8 = 0.99
Next, we can use a z-table to find the corresponding probabilities for these z-scores:
Probability for lower limit = 0.2296
Probability for upper limit = 0.8389
Finally, we can subtract the lower probability from the upper probability to find the percentage of women with weights that are within those limits:
Percentage = 0.8389 - 0.2296 = 0.6093
Therefore, approximately 60.93% of women have weights that are within the limits of 132.4 lb and 217 lb.
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if a student is randomly chosen, find the probability that the student is male or earned grade a. leave your answer as a reduced fraction.
The expression to obtain the final probability as a reduced fraction.
What is fraction?A fraction is a mathematical representation of a part of a whole or a part of a group. It consists of two numbers separated by a horizontal line, where the number on the top is called the numerator, and the number at the bottom is called the denominator. The numerator represents how many parts are being considered, and the denominator represents the total number of equal parts that make up the whole or group. Fractions can be written in various forms, such as proper fractions, improper fractions, and mixed numbers, and can be added, subtracted, multiplied, and divided using specific rules and techniques.
We cannot provide a specific numerical answer without more information on the gender and grade distribution of the students. However, we can use the following formula to calculate the probability that a student is either male or earned grade A:
P (male or grade A) = P(male) + P (grade A) - P (male and grade A)
The probability of selecting a male student and the probability of selecting a student who earned a grade A are two independent events, so we can add their probabilities. However, we need to subtract the probability of selecting a male student who also earned a grade A, since we don't want to count that student twice.
If we have the probabilities of each event, we can plug them into the formula and simplify the expression to obtain the final probability as a reduced fraction.
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The population of a city increases by 0.5% per year. If this year's population is 201,000, what will next year's population be, to the nearest individual?
Next year's population is 202,005
How to calculate the quantity of next year's population?
The population of a city increases by 0.5% per year
This year's population is 201,000
Next year's population can be calculated as follows
201,000 × 0.5/100
= 201,000 × 0.005+1
= 201,000 × 1.005
= 202,005
Hence next year's population is 202,005
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Write an equation for the word problem below
Sarah is renting a water filtration system from her water company. It has a startup fee of $36 plus $6 per month. If Sarah has a budget of $300, how many months can she rent the system?
Answer:
The Equation is (300-36)÷6.
Step-by-step explanation:
$300-$36=$264 (The budget after paying the set up fee)
$264/6=44 months. That's how many months she can rent.
So the equation would be (300-36)÷6.
(Sorry if this is wrong!)Fill in the blanks:
1) if tan x=0, then tan(-x)= ___
2) If sin x= 0.3, then sin(-x)= ____
3) If cos x= 0.3, then cos(-x)= ____
4) If tan x= -2, the tan (pi+x)= ____
The values are :
tan(-x) = 0sin(-x) = -0.3cos(-x) =0.3tan(pie + x) = 2What is trigonometry ?
Trigonometry is a branch of mathematics that deals with the relationships and properties of angles and the trigonometric functions such as sine, cosine, and tangent. It is based on the study of the geometric properties of triangles and is used extensively in fields such as physics, engineering, architecture, and astronomy.
In trigonometry, the relationships between the sides and angles of a triangle are expressed using the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios between the sides of a right triangle, where one angle is 90 degrees. Trigonometric functions can also be defined for any angle, not just those in a right triangle, using the unit circle or other methods.
Trigonometry has many practical applications, such as in navigation, surveying, and the design of structures such as bridges and buildings. It is also used extensively in science and engineering, particularly in fields such as physics, mechanics, and electromagnetics.
If tan x = 0, then tan(-x) = 0.
The tangent function is an odd function, which means that tan(-x) = -tan(x). However, since tan x = 0, this means that -tan(x) = 0 as well. Therefore, tan(-x) = 0.
If sin x = 0.3, then sin(-x) = -0.3.
The sine function is an odd function, which means that sin(-x) = -sin(x). Since sin x = 0.3, this means that -sin(x) = -0.3. Therefore, sin(-x) = -0.3.
If cos x = 0.3, then cos(-x) = 0.3.
The cosine function is an even function, which means that cos(-x) = cos(x). Since cos x = 0.3, this means that cos(-x) = 0.3 as well.
If tan x = -2, then tan(pi+x) = tan(pi + atan(-2)) = tan(2.0344 + pi) = -2.
To find tan(pi + x), we need to use the identity tan(a + pi) = -tan(a). In this case, a = atan(-2), which is the inverse tangent of -2. Using a calculator or a table, we can find that a is approximately 2.0344 radians. Therefore, tan(pi + x) = -tan(2.0344) = -(-2) = 2.
Hence, values are
tan(-x) = 0sin(-x) = -0.3cos(-x) =0.3tan(pie + x) = 2To know more about trigonometry visit :
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A circular device has a diameter of 4.5 inches. What is the radius of the device?
Answer:
Hello there! If the circular device has a diameter of 4.5 inches, the radius of the device would be 2.25 inches.
Step-by-step explanation:
The diameter of the circle is a line segment that not only passes through the center of the circle, but also has endpoints that are on the circle and opposite sides to each other. The radius, on the other hand, is half the distance of the diameter, or the distance from any point on the circle to the center of the circle. I've attached a picture below to show you what that would look like, if you're a visual learner.
Since we know the diameter of the circular device is 4.5 inches, and we know that the radius of a circle is half the length of the diameter of that same circle, that means the radius of the circular device would be [tex]\frac{4.5}{2}[/tex] or 2.25 inches long.
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what is the solution to the equation
The requried solution of the two linear equations is given as x = (b - d)/a-c and y = a (d - c)/(a-c).
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
The question seems to be incomplete so the solution is a standard solution by assuming a standard linear equation.
The given equation,
ax + y = b - - - - - (1)
cx + y = d - - - - -(2)
Subtract equation 2 from 1
ax - cx + y - y = b - d
x(a - c) = b - d
x = b - d / a - c
Now,
Put x in equation 1
a (b - d) / (a - c) + y = b
y = b - a(b - d)/(a - c)
y = ab - ac -ab + ad/(a - c)
y = a (d - c)/(a - c)
Thus, the requried solution of the two linear equation are given as x = (b - d)/a-c and y = a (d - c)/(a - c).
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The question seems to be incomplete,
The solution given is standard solution for the simultaneous equations.
A 3 in thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 64 in3
When a cube's top is chopped off to create a rectangular box, the original cube's side length is 5.43 feet as a result.
what is rectangle ?A rectangular is a square with four right angles in Euclidean geometry and trigonometry. You may also speak to it as an equiangular tetra, meaning that all of its edges are equal. A straight angle could also be found in the parallelogram. Rectangles with four evenly sized sides are called squares. Four 90 ° vertices and equal equal sides make up a quadrant with the look of a rectangle. As a basis, it's also known as a raster images rectangle. A rectangle is also referred to as a trapezoidal since its opposite angles are equal but parallel.
given
Let x represent the cube's edge in feet.
Cube volume equals side 3
Hence, the given cube's volume,
The top of a cube is now chopped off in a 4 foot thick chunk.
The slice's volume is equal to x x x 4 = 4x2 ft2.
The volume of the final figure is therefore equal to the sum of the volumes of the cut and cube figures.
= ( x³ - 4x² ) ft²
The answer to the query is
Finding the zeros of the function will lead to the discovery of the solution to the aforementioned equation ( by graphing ),
We discovered that
The equation's graph crosses x at (5.426,0)
Hence, 5.426 is the equation's zero.
⇒ x = 5.426 ≈ 5.43
When a cube's top is chopped off to create a rectangular box, the original cube's side length is 5.43 feet as a result.
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a study was conducted that resulted in the following relative frequency histogram. determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.
If the bars of a histogram roughly follow a symmetrical bell or hill shape, then the distribution is approximately normally distributed.
What is Histogram?Histogram a diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.
Given is relative frequency histogram.
The histogram is not given, so will discussion the property that tells whether the histogram indicates a normal distribution or not.If the bars roughly follow a symmetrical bell or hill shape, then the distribution is approximately normally distributed.Therefore, if the bars of a histogram roughly follow a symmetrical bell or hill shape, then the distribution is approximately normally distributed.
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