The linear functions for each case are given as follows:
1. C(n) = 5n + 150.
2. C(m) = 0.05m + 20.
3. L(t) = 30t - 300.
What is a linear function?A linear function, in slope-intercept format, is given by:
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).For each item in this problem, we have that the meaning of the coefficients is explained as follows:
The rate per class/mile/rise represents the slope.The initial fees or the initial position represents the intercept.Hence the functions are given as follows, considering the stated variables:
1. C(n) = 5n + 150.
2. C(m) = 0.05m + 20. (5 cents = $0.05).
3. L(t) = 30t - 300. (300 feet below the surface is represented by a negative value, while a rise is represented by a positive value).
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
The equations that have the same solutions as 2.3p – 10.1 = 6.5p – 4 – 0.01p are as follows:
2.3p – 10.1 = 6.49p - 4230p - 1010 = 650p - 400 - pHow to find same solution equation?Systems of equations that have the same solution are called equivalent systems.
Therefore, the equation that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p can be calculated as follows:
Hence, let's find the solution of this :
2.3p – 10.1 = 6.5p – 4 – 0.01p
Simplifying the above equation by collecting like terms gives;
2.3p – 10.1 = 6.5p – 4 – 0.01p
2.3p – 10.1 = 6.5p – 0.01p - 4
Therefore, one of the equivalent solution is as follows:
2.3p – 10.1 = 6.49p - 4
Both sides of an equation will remain equal, when both sides are
multiplied by the same value.
Therefore, let's multiply both sides by 100,
2.3p – 10.1 = 6.5p – 4 – 0.01p
100(2.3p – 10.1) = 100(6.5p – 4 – 0.01p)
230p - 1010 = 650p - 400 - p
Therefore, another equivalent solution is 230p - 1010 = 650p - 400 - p
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#4 Write an equation, in slope-intercept form, for a line that passes through (3, 4) and has a y-intercept of -8.
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ - 8 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- 8}(x-\stackrel{x_1}{3}) \\\\\\ y-4=-8x+24\implies {\Large \begin{array}{llll} y=-8x+28 \end{array}}[/tex]
Which law is used to come to the stated conclusion? If no conclusion can be drawn, answer "no conclusion". If Rae is the driver today then Maria is the driver tomorrow. Annis the driver today.
DEFINITIONS:
1) Law of Contrapositive: This law reverses the conclusion and the hypothesis of the inverse of the conditional statement. This is expressed as:
[tex]\begin{gathered} \text{Original Statement: If p, then q} \\ \text{Contrapositive Statement: If not q, then not p} \end{gathered}[/tex]2) Law of Detachment: This law states that if the conditional statement is true, and the hypothesis is true, then the conclusion is true as well. This is expressed as:
[tex]\begin{gathered} 1)\text{ If p, then q} \\ 2)\text{ p} \\ \text{Then},\text{ statement q is true} \end{gathered}[/tex]3) Law of Syllogism: This law is explained as:
[tex]\begin{gathered} 1)\text{ If p, then q} \\ 2)\text{ If q, then r} \\ \text{Then,} \\ 3)\text{ If p, then r is true} \end{gathered}[/tex]QUESTION:
The statements provided can be separated as shown below:
[tex]\begin{gathered} 1)\text{ p = Ray is the driver today} \\ 2)\text{ q = Maria is the driver tomorrow} \\ 3)\text{ r = Ann is the driver today} \end{gathered}[/tex]The question states that
[tex]\text{If p, then q}[/tex]and
[tex]r\text{ is true}[/tex]This conclusion cannot be proved using any of the rules above.
Therefore, no conclusion can be drawn on the truth of the statement.
5. Jenny has $65 in her checking account. She bought 9 equally priced DVDs and paid with acheck. Her new account balance is $32. How much was each DVD?
This implies that, the money spent on the 9 equally priced DVDs is:
[tex]\text{Money Spent on the 9 equally priced DVDs= 65 -32 =\$3}3[/tex]Therefore, the amount spent on each DVD is:
[tex]\frac{33}{9}=\text{ \$3.67}[/tex]Hence, each DVD costs $3.67
The value of an industrial embroidery machine is decreasing according to the function defined byV(t) = 10,890(3)–0.21where tis the number of years since the machine was purchased. What does the y-intercept represent?OA. the value of the machine after 3 yearsB.the amount of time it takes for the value of the machine to reach zeroOC.the original value of the machineODthe rate at which the value of the machine depreciates21 Edimentum All rights reserved
Solution
We have the following expression:
[tex]V(t)=10890(3)^{-0.2t}[/tex]for this case the y intercept is given when t=0 so we have:
[tex]V(0)=10890(3)^{-0.2\cdot0}=10890[/tex]And this value represent the following:
C. the original value of the machine
Since thats the starting value without depreciation
Please help us with this math problem so we can sleep to night
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
Jupiter's mass = 1.89 x 10^27 kg
Moon's mass = 7 x 10^22 kg
Step 02:
We must analyze the problem to find the solution.
[tex]\frac{j\text{ mass}}{m\text{ mass}}=\frac{1.89\cdot10^{27}}{7\cdot10^{22}}=0.27\cdot10^5[/tex]0.27x10^5 = 27000
The answer is:
The mass of Jupiter is 27,000 times the mass of the moon.
how many zeros does the product of 25^5 ×150^4 ×2008 ^3 end with?
Answer:
13 trailing zeros
Explanation:
Our goal is to rewrite the expression such that we have 10 as a factor. Then the power of 10 will give us the number of trailing zeros.
The product can be rewritten as
[tex](5^2)^5\cdot(2\cdot3\cdot25)^4\cdot(2^3\cdot251)^3[/tex]which can further be rewritten as
[tex]5^{10}\cdot(2^4)(3^4)(5^8)\cdot2^9\cdot251^3[/tex][tex]\Rightarrow2^{13}\cdot3^4\cdot5^{18}\cdot251^3[/tex][tex]10^{13}\cdot3^4\cdot5^6\cdot251^3[/tex]We see that by rewriting our expression 10 appears with a power of 13; therefore, the expression has 13 trailing zeros.
If line q has a slope of -3, what is the slope of any line perpendicular to q?
The slope of the perpendicular line is equal to -3.
What is the slope of a line?
A line's slope provides information on the steepness and direction of the line. By determining the difference seen between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of either a straight line through them. The letter "m" is frequently used to denote slope.Two lines must have a slope product of -1 in order to be perpendicular to one another.Given that,
the slope of line q, m= -3
the slope of any line perpendicular to given line q=1/m
1/-3
=-3
The slope of the perpendicular line is equal to -3.
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A 99% confidence interval for the mean of a population is such that:A. There is a 99% chance that it contains the standard deviation of the populationB. There is a 99% chance that it contains the mean of the populationC. There is a 99% chance that it contains all the values in the population.D. It contains 99% of the values in the population
Step 1
It means that there is a 99% chance that the interval you have calculated from your data (a random sample of some kind) covers the true value of what you are using that data to learn about.
This means that there is a 99% chance it contains all the values in the population
Answer;
[tex]Option\text{ C}[/tex]BRAINLIEST (statistics) (please help fast)
As an introduction to probability, a student is asked to roll a fair, six-sided number cube seven times. The results of those seven rolls are shown below.
1, 4, 4, 4, 4, 6, 5
What is the IQR of the data?
1
1.53
2
5
Step-by-step explanation:
first find the median (middle value) of the lower and upper half of the data. these values are quartile 1 (Q1) and quartile 3 (Q3). the IQR is the difference between Q3 and Q1.
first sort the data low to high.
the median of the whole data set is 4.
1, 4, 4, 4, 4, 5, 6
the lower half is
1, 4, 4
the upper half is
4, 5, 6
the median of the lower half is 4
1, 4, 4
the median of the upper half is 5
4, 5, 6
the IQR is then
5 - 4 = 1
Answer:
A) 1Step-by-step explanation:
Given data:
1, 4, 4, 4, 4, 6, 5We need to find the IQR of data.
What is the IQR:
IQR is the difference of medians of upper and lower halves of the data.or
IQR = Q3 - Q1Find Q3 and Q1:
Q3 = 5, since upper half consists of 4, 5, 6.Q1 = 4, since lower half consists of 1, 4, 4.Find the IQR:
IGR = 5 - 4 = 1Correct choice is A
An isosceles triangle has an angle that measures 102 degrees. What measures are possible for the other two angles ? Choose all that apply 75, 39, 18, 8
Answer:
39 °
Step-by-step explanation:
Isosceles means two angles , x, are =
x + x + 102 = 180 ( the sum of triangle angles always = 180)
2x = 78
x = 39 °
Jakia is a member of the Usaah club at rshs for the 2020-2021 school year she works at a local fast food restaurant after school and on weekends. She saving for the college tour schedule for December 2021 . Jakia saved 20 in June ,25 in july,30 in August, and plans to continue this pattern each mouth how much money will jakia save in November 2021
November savings = 45
Explanation:
Amount saved in June = 20
Amount saved in July = 25
Amount saved in August = 30
From the above, there is an increament of 5 as the month increases:
30-25 = 25-20 = 5
September = August savings + increament
September saving = 30 + 5 = 35
October = September savings + increament
October = 35 + 5 = 40
November = October savings + increament
November savings = 40 + 5
November savings = 45
Use the four-step procedure for solving the following variation problem.The height that a ball bounces varies directly as the height from which it was dropped. A tennis ball dropped from 17 inches bounces 11.9 inches. From what height was the tennis ball dropped if it bounces 42 inches?The tennis ball needs to be dropped from the height of ?that it bounces 42 inches.(Type an integer or a decimal.)
If we drop a ball from 60 inches height it bounces 42 iches.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
The height that a ball bounces varies directly as the height from which it was dropped.
A tennis ball dropped from 17 inches bounces 11.9 inches.
We need to find from which height if we drop a ball bounces 42 iches.
Let us consider x as the unknown height
Let us form a equation by the given data
17/11.9=x/42
Apply cross multiplication
17×42=11.9x
714=11.9x
Divide both sides by 11.9
60=x
Hence if we drop a ball from 60 inches height it bounces 42 inches.
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I need help with this question! I worked it out however my answer is not an answer choice.
The given expression is:
[tex]undefined[/tex]Evaluate 9yl – yº if y = – 8.-71-73- 2- 64
First of all, we need to rules to solve this:
[tex]\begin{gathered} a^0=1,a\ne0 \\ a^1=a,a\text{ any number} \end{gathered}[/tex]So, the equation to be evaluated can be reduced to:
[tex]\begin{gathered} y=-8\Rightarrow9y^1-y^0=9y-1 \\ \Rightarrow9y^1-y^0=9\cdot(-8)-1=-72-1=-73 \\ \Rightarrow9y^1-y^0=-73 \end{gathered}[/tex]Then, the answer is -73, the second option
Helen has a 4 kilometer-head start on París how long will it take París to catch Helen if helen travels at 6 kilometers per hour and París traveled at 8 km per hour
Assume "h" = number of hours traveled
Helen's speed = 6km per hour and is 4km advanced than Paris
Paris' speed = 8km per hour
Therefore, we can form the following equations:
a. Helen's distance traveled = 4km + 6km (h) = 4 + 6h
b. Paris' distance traveled = 8km (h) = 8h
For us to determine how long will Paris be able to catch Helen, we'll have to assume they have traveled the same distance. In this case:
Helen's distance traveled = Paris' distance traveled
[tex]\begin{gathered} 4+6h=8h \\ \text{Subtrach 6h on both sides of the equation.} \\ 4+6h-6h=8h-6h \\ 4=2h \\ \text{Divide two on both sides.} \\ \frac{4}{2}=\frac{2h}{2} \\ 2=h \end{gathered}[/tex]Therefore, it will take 2 hours for Paris to catch up with Helen which is at 16km.
Which degree polynomials have ends that head off in opposite directions?Even degree polynomialsOdd degree polynomialsEven and odd degree polynomialsNone of the choices
Answer:
Odd degree polynomials
Explanation:
In order to determine what degree polynomials have ends that head off in opposite directions, recall the rules of the leading coefficient test.
When using the Leading coefficient test, the following rule applies:
• When the ,degree is odd, and the leading coefficient is positive, the graph ,falls to the left and rises to the right.
,• When the ,degree is odd, and the leading coefficient is negative, ,the graph rises to the left and falls to the right.
,• When the degree is even and the leading coefficient is positive, the graph rises to the left and right.
,• When the degree is even and the leading coefficient is negative, the graph falls to the left and right.
Thus, we see that when the degree of the polynomial is odd, the ends head off in opposite directions.
The second option is correct.
Raj worked 51 hours last week. He earns $ 14.02 per hour plus overtime, at theusual rate, for hours exceeding 40 hours. What is his gross pay? Round answer totwo decimal places. If answer does not have two decimal places then include zeroso that it does. For the units use a word not a symbol. Be sure to attach your workto this question in order to receive credit for your answer.Your Answer:units:
Given:
Raj worked 51 hours last week.
He earns $ 14.02 per hour
[tex]\begin{gathered} \text{Gross salary=14.02}\times51 \\ =\text{ \$715 .02} \end{gathered}[/tex]Gross salary is 715.02 dollar per week
The outdoor temperature was 8° at midnight the temperature declined 5° during each of the next three hours. What was the temperature at 3 AM?
After performing mathematical operations, we can conclude that the temperature at 3:00 am would be 3°.
What do we mean by mathematical operations?Any mathematical operation that converts zero or more discrete input values into discrete output values is known as a discrete operation.The number of operands affects how complicated the operation is.Functions that convert numerical inputs into numerical outputs are the four mathematical operations (i.e., another number).These are addition, subtraction, multiplication, and division.So, the temperature at 3:00 am:
The temperature at midnight is 8°.Temperature falls by 5° in the next 3 hours.Then, the temperature at 3:00 am can be calculated as:
8 - 5 = 3°Therefore, after performing mathematical operations, we can conclude that the temperature at 3:00 am would be 3°.
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- 10> - 11 1/5 means that - 11.33 is located to the left of- 7.40 on the number line.
On the number line, the numbers increase from left to right like that
-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
Then -10.33 will come before -7.40 like that
-11, -10, -9, -8, -7, -6
since -11 is left -7, then -11.33 will be left -7.40
It is YES
How do you write 4,260 in scientific notation?x 10Submit
4.26 × 10³
Explanation:To write 4260 in scientific notation, we would move the point from right to left starting at 0 to the place in between 4 and 2
The number of movement = 3
[tex]4260\text{ = 4.260}\times10^{n\text{ umber of movement}}[/tex][tex]\begin{gathered} 4260\text{ = 4.260}\times10^3 \\ =\text{ 4.26}\times10^3 \end{gathered}[/tex]1) Drag and drop the numbers to place them in increasing order.
-1.6
0.6
- 1/6
3/7
2) Drag and drop the numbers to place them in increasing order.
-1.3
1.4
-0.6
0.7
The most appropriate choice for ascending order and descending order will be given by -
1) Numbers in increasing order are -1.6, [tex]-\frac{1}{6}[/tex], [tex]\frac{3}{7}[/tex], 0.6
2) Numbers in increasing order = -1.3, -0.6, 0,7, 1.4
What is ascending order and descending order?
Ascending order is the method of arranging of set of numbers from their lowest value to their highest value.
Descending order is the method of arranging of set of numbers from their highest value to their lowest value.
Here,
1)
[tex]-\frac{1}{6} = -0.167[/tex]
[tex]\frac{3}{7} = 0.429[/tex]
Numbers in increasing order are -1.6, -0.167, 0.429, 0.6
Numbers in increasing order are -1.6, [tex]-\frac{1}{6}[/tex], [tex]\frac{3}{7}[/tex], 0.6
2)
Numbers in increasing order = -1.3, -0.6, 0,7, 1.4
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The function f(x) = 2 * (2) ^ x was replaced with f(x) + k resulting in the function graphed below
PLEASE HELP WILL MARK BEAINLY
Example:
f(x) = (x - 1)2, f(x) = 8x , f(x) = x2 - x , f(x) = 7. Summary: From the given functions, f(x) = 7 is the even function.
Find the rational function which represents the graph. If you could help with both sections that would be amazing
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given points on the graph
[tex]\begin{gathered} \text{ Points are given in the form of }(x,y) \\ \therefore\text{ points are:} \\ (x_1,y_1)=(2,0) \\ (x_2,y_2)=(0,-2) \end{gathered}[/tex]STEP 2: Write the slope-intercept form of the equation of a line
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is the y-intercept} \end{gathered}[/tex]STEP 3: Write the formula to get the equation of a line using two given points
[tex](y-y_1)=m(x-x_1)[/tex]STEP 4: We use the given points to get the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]STEP 5: Substitute the given points into the formula in step 4 to get the slope
[tex]m=\frac{-2-0}{0-2}=\frac{-2}{-2}=1[/tex]STEP 6: Since we have a slope and two points, we use the formula in step 3 to get the function that represents the line
[tex]\begin{gathered} (y-y_1)=m(x-x_1) \\ U\sin g\text{ point }(2,0) \\ (y-0)=1(x-2) \\ y=1(x-2) \\ y=x-2 \end{gathered}[/tex]STEP 7: We get the rational function of the line using the given hole
[tex]\begin{gathered} \text{hole}=(5,3) \\ \text{equation of line }\Rightarrow y=x-2 \\ \\ To\text{ get the rational function, we write the function of each coordinate that makes it undefined} \\ (5,3)\Rightarrow x=5\Rightarrow x-5 \\ (5,3)\Rightarrow y=3\Rightarrow y-3 \\ We\text{ divide the equation of the line in step 6 by the expressions above} \\ \text{Hence, the rational function is given as:} \\ \frac{y}{y-3}=\frac{x-2}{x-5} \end{gathered}[/tex]Hence, the rational function representing the line with the given hole is:
[tex]\frac{y}{y-3}=\frac{x-2}{x-5}[/tex]Line A has a slope of −3 . Line B has a slope of 4. Line C has a slope of 2.
Which line is closest to being horizontal?
Line A
Line B
Line C
I don't know.
Line C is closest to being horizontal.
Given,
Line A has a slope of −3.
Line B has a slope of 4.
Line C has a slope of 2.
To find the which line is closest to being horizontal?
Now, According to the question:
Slope of line A (m1) = -3
Slope of line B (m2) = 4
Slope of line C (m3) = 2
Slope of horizontal line = 0
Closest to being horizontal is given by l m l
For line A = l-3 l = 3
For line B = l4l = 4
For line C = l2l = 2
As 2 is smaller it is closest to horizontal
Hence, Line C is closest to being horizontal.
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Jimmy ran 20 meters west from home and then turned north to jog 25 meters. Jimmy ran 45 meters, but could have arrived at the same point by jogging in a straight line. How many meters could he have jogged using a straight line distance?
Responses
3.5 meters
3.5 meters
45meters
7 meters
The distance he would've covered is 32.02m if he ran through a straight line.
What is Pythagoras's Theorem?In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
We can proceed to use this to find the distance from point a to point b assuming he ran through a straight line.
Mathematically, the theorem can be expressed as
[tex]x^2 = y^2 + z^2\\[/tex]
Let's substitute the values into the equation and solve.
[tex]x^2 = 20^2 + 25^2\\x = 32.02m[/tex]
Jimmy would've jogged 32.02m if he ran through a straight line.
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Find the area and the circumference of a circle with diameter 8cmUse 3.14 for n , and do not round your answer
ANSWER:
Circumference of the circle is 25.12 centimeters
Area of the circle is 50.24 square centimeters
STEP-BY-STEP EXPLANATION:
We have that the formula for the circumference and the area are the following:
[tex]\begin{gathered} c=2\cdot\pi\cdot r \\ A=\pi\cdot r^2 \end{gathered}[/tex]The radius is equivalent to half the diameter, therefore, we replace:
[tex]\begin{gathered} r=\frac{d}{2}=\frac{8}{2}=4 \\ \text{ replacing} \\ c=2\cdot3.14\cdot4=25.12\text{ cm} \\ A=3.14\cdot4^2=50.24cm^2 \end{gathered}[/tex]the circumference of the circle is 25.12 cm and the area is equal to 50.24 square centimeters
The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 259.1 and a standard deviation of 68.2. (All units are 1000 cells/µl.) Using the empirical
rule, find each approximate percentage below.
a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 54.5 and 463.77
b. What is the approximate percentage of women with platelet counts between 122.7 and 395.5?
a. Approximately % of women in this group have platelet counts within 3 standard deviations of the mean, or between 54.5 and 463.7
(Type an integer or a decimal. Do not round.)
PLEASE HELP ASAP
Using the Empirical Rule, it is found that:
a. Approximately 99.7% of women in this group have platelet counts within 3 standard deviations of the mean, or between 54.5 and 463.7.
b. Approximately 95% of women in this group have platelet counts between 122.7 and 395.5.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is given as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of 68%.The percentage of scores within two standard deviations of the mean of the distribution is of 95%.The percentage of scores within three standard deviations of the mean off the distribution is of 99.7%.Hence for item a the percentage is of 99.7%, as the measures are within 3 standard deviations of the mean.
In item b, the measures are within two standard deviations of the mean, as:
259.1 - 2 x 68.2 = 122.7.259.1 + 2 x 68.2 = 395.5.Hence the percentage is of 95.5%.
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What is the equation of the line that passes through the point ( − 8 , − 3 ) that is parallel to the line 5 x − 8 y = − 40 ? Write the equation in slope-intercept form.
Robbie wants to plot the .four, five on a coordinate plane which statement describes how to plot this point starting from the origin
We were told in the question that Robbie wants to plot the point (4, 5) on a coordinate plane. we are to determine from the option the statement that describes how to plot it.
Plotting on a coordinate plane already gives us the idea of x and y axis which is the vertical and the horizontal.
We were given positive values for both points which implies that:
Since 4 is the x-axis and positive and 5 is y-axis and also positive. We can draw a statement that:
We move 4 units to the right and then 5 units up.
With this, the correct option is C.
