The amount of homework received by an RSM teacher and the time that the teacher spent grading it is the case of directly proportional.
What are direct and indirect variations ?
One quantity directly changes in response to a change in another quantity, which is referred to as direct variation. This suggests that if one quantity increases, the other will follow suit and rise in proportion. In a similar manner, if one quantity declines, the other amount also declines.
When one parameter declines while the other rises or vice versa, this is known as inverse variation. This means that the magnitude or absolute value of one item decreases as the other quantity rises, resulting in a constant value for their product. This item is also referred to as the proportionality constant.
Direct proportion occurs when one value increases and the other also increases
As the amount of homework received by an RSM teacher increases, the time that the teacher spent grading it also increases.
So, this is a case of directly proportional.
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Find the equation of the linear function represented by the table below in slope-intercept form.
The linear equation for the given table is y = 10*x - 8.
How to find the linear equation?
A general linear equation in the slope-intercept form is:
y = m*x + b
where m is the slope and b is the y-intercept.
The y-intercept is the value of y when x = 0, on the table we can see the pair (0, -8), then the y-intercept is -8.
y = m*x - 8
Using another pair from the table, like (1, 2), we can replace these values in the above linear equation:
2 = m*1 - 8
2 + 8 = m
10 = m
Then the linear equation is:
y = 10*x - 8
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Factor the expression. - 35a - 30
Answer:
-5(7a+ 6)
Explanation:
Given the expression:
-35a - 30
-35a = -5 * 7 * a
-30 = -5 * 6
You can see from the factors that -5 is common to both
Hence -5 is the GCF
Factoring out -5 from the expression will give;
-5(7a+ 6)
This gives the correct factor
Somebody please help me I need to send this tomorrow
4. Mr. Wilson has two cats, named Ramses and Kilala. Kilala weighs 6 pounds. Ramses weighs 3 times as much as Kilala. How much does Ramses weigh? Show how you figured this out.
Answer:
18
Step-by-step explanation:
6lb
*3
6lb*3=18
Help please I don't understand where to get the degrees from. And what degrees are each
SOLUTION:
(i)
[tex]\begin{gathered} \sin \text{ }\theta\text{ = }\cos \text{ }\theta \\ \end{gathered}[/tex]Sine of an angle is complementary to the Cosine of an angle so for both to be the same the angle 90 degrees must be divided into.
[tex]\theta=45^0[/tex](ii)
[tex]\begin{gathered} \tan \text{ }\theta\text{ = 0} \\ \theta\text{ = }\tan ^{-1}(0) \\ \theta\text{ = 0} \end{gathered}[/tex](iii)
[tex]\csc \text{ }\theta\text{ > sec }\theta[/tex]As said earlier sine and cosine of angles are complementary so cosecant and secant of angles are also complementary.
[tex]\begin{gathered} \text{When }\theta\text{ = 30} \\ \csc \text{ }\theta\text{ > sec }\theta \\ \frac{1}{\sin30}\text{ > }\frac{1}{\cos30} \\ \\ 2\text{ > 1.15} \\ \\ \csc \text{ }\theta\text{ > sec }\theta\text{ when }\theta=30^0 \end{gathered}[/tex]I cant remember the steps on how to work this problem
Answer:
x= 3
y=0
Step-by-step explanation:
y = -x + 3
y = 2x - 6
-x + 3 = 2x -6
3 + 6 = 2x + x
9 = 3x
3 = x
y = -3 + 3
y = 0
Answer:
(3,0)
Step-by-step explanation:
a jar contains five black buttons and six brown buttons. If 8 buttons are picked at random,what is the probability that at least 4 of them are black?
First, we write out the probability formula:
[tex]Pr(E)=\frac{n(R\text{equired outcome)}}{n(Total\text{ outcome) }}[/tex]Total number of tickets = 13
Pr(both Ashley and Matt win) = Pr(Ashley wins) x Pr(Matt wins)
[tex]\begin{gathered} Pr(\text{Ashley win ) }=\text{ }\frac{1}{13} \\ Pr(\text{Matt win) = }\frac{1}{13} \end{gathered}[/tex][tex]Pr(\text{both wins ) }=\frac{1}{13}\times\frac{1}{13}=\frac{1}{169}[/tex]The final answer is 1/169
In order to express our answer as a percentage, we multiply by a 100%
= 1/169 x 100% = 0.592% ( to 3 significant figures)
What is the first step in solving the equation 2a - 4( a - 5 ) = 10
The first step in solving for a in the equation would be:
1.distribute -4 to a and -5, then:
2a-4a+20=10
Now the next steps in solving for a:
2.Add 2a and -4a :
-2a+20=10
3.Substract 20 to both sides
-2a+20-20=10-20
then:
-2a= -10
4.Finally, divide both sides by -2
[tex]\frac{-2a}{-2}=\frac{-10}{-2}=5[/tex]then, a=5
A paddleboat can move at a speed of 14 kilometers per hour in still water. The boat is paddled 10 kilometers downstream in a river in the same time it takes to go 5 kilometers upstream. What is the speed of the river? Round your answer to the nearest tenth.
The speed of the river is 7.5 kilometers per hour.
Let the speed of boat in still water = u = 14 km/h
Let the speed of river = v = x km/h
Upstream speed = u - v = 14 - x
Downstream speed = u + v = 14 +x
Distance paddled upstream = [tex]D_{1}[/tex] = 5 km
Distance paddled downstream = [tex]D_{2}[/tex] = 10 km
Time taken (upstream) = [tex]T_{1}[/tex] = [tex]\frac{D_{1} }{u-v}[/tex]
Time taken (downstream) = [tex]T_{2}[/tex] = [tex]\frac{D_{2} }{u+v}[/tex]
According to question,
[tex]T_{1}[/tex] = [tex]T_{2}[/tex]
[tex]\frac{D_{1} }{u-v}[/tex] = [tex]\frac{D_{2} }{u+v}[/tex]
[tex]\frac{5}{14-x}[/tex] = [tex]\frac{10}{14+x}[/tex]
5(14 + x) = 10(14 - x)
14 + x = 2(14 - x)
14 + x = 28 - 2x
x + 2x = 28 - 14
3x = 14
x = [tex]\frac{14}{3}[/tex]
x = 7.5
Hence, Speed of river is 7.5 km/h.
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find the perimeter of the following polygon in these sorts of junk food the correct unit in your answer
Solution
Given a trapezoid with the following dimensions
[tex]10ft,10ft,11ft,15ft[/tex]To find the perimeter, P, of the polygon, we add up all the side lengths i.e the formula to find the perimeter, P, of the trapezoid is
[tex]\begin{gathered} P=a+b+c+d \\ \text{Where a, b, c and d are the side lengths} \end{gathered}[/tex]Where
[tex]\begin{gathered} a=10ft \\ b=10ft \\ c=11ft \\ d=15ft \end{gathered}[/tex]Subsitute the values into the formula above
[tex]\begin{gathered} P=10+10+11+15=46 \\ P=46ft \end{gathered}[/tex]Hence, the perimeter is 46ft
What is the answer to: -32/40 - 35/40
Answer:
To subtract fractions, find the LCD and then combine.
Exact Form:
− 67/40
Decimal Form:
− 1.675
Mixed Number Form:
− 1 27/40
Step-by-step explanation:
Please give the brainliest.
Answer:
− 67/40 or -1 27/40
Step-by-step explanation:
Subtract:
-32/40 - 35/40 =
-67/40
Change into a mixed number (optional):
− 67/40 =
− 1 27/40
Which of the following is an equivalent expression of 18x² +14x + 7?
Answer:
The second one
Step-by-step explanation:
....is just the equation with the order of the terms re-arranged
Complete the equation so it has no solution. 9x - 7x + 5 = ___ - 7
Answer: 2x
Step-by-step explanation: The answer is 2x, because on the LHS, 9x - 7x = 2x, so the LHS is 2x + 5, if we make the RHS 2x - 7, the equation will become 2x + 5 = 2x - 7, this makes the equation unsolvable
40 PIONTS FOR ANSWERING 2 Q'S, I WILL PICK BRIANLISET
6. For the Raleigh company, create a table to represent the cost of the cab ride given the number of miles provided for miles 5, 10, 15 and 20. List the cost for the cab ride for 15 miles.
My answer (tell me if it is right or wrong)
for 15 miles your cost would be $42.45 inclueding the fee of $1.95
7. For the Raleigh company write an equation in slope-intercept form to represent the amount charged, C, for m number of miles.
Answer:
$3.86
tell me if im wrong
Answer:
6: your answer is correct
7: C=2.7m+1.95
Step-by-step explanation:
6:
5 15.25
10. 28.95
15. 42.45
20. 55.95
question 7
slope intercept form is y=mx+b
m is slope and b is y intercept
Slope is 2.70 since that is how much we go up for a mile
And 1.95 is y intercept since it is where we start no matter what and we have to add that constant fee every time
y=2.70x+1.95
We change the y to c and the x to m to fit the problem
C=2.70m+1.95
Hopes this helps please mark brainliest
two thirds of a number is negitive 20
Answer:
The number is -30.
Step-by-step explanation:
Given statement,
→ two thirds of a number is negative 20.
The equation will be,
→ (2/3)x = -20
Now the value of x will be,
→ (2/3)x = -20
→ 2x = (-20) × 3
→ x = (-60)/2
→ [ x = -30 ]
Hence, the value of x is -30.
Answer:
[tex]-30[/tex]
Step-by-step explanation:
Set up the equation where [tex]x[/tex] is the unknown number:
[tex]\frac{2}{3}x = -20[/tex]
Divide both sides by [tex]\frac{2}{3}[/tex]:
[tex]x = -20 \div \frac{2}{3}[/tex]
Rewrite division by a fraction as multiplication by its reciprocal:
[tex]x = -\frac{20}{1} \times \frac{3}{2}[/tex]
Multiply:
[tex]x = -\frac{60}{2}[/tex]
Simplify:
[tex]x = -30[/tex]
solve the equation A-X=B-A for X.
Answer:
X= -B+2A
Step-by-step explanation:
Hope this helps and sorry if I'm wrong
Tell me how I can eliminate the x-terms in this system! ASAP!
4y+3x=-6
Y-X=-5
Options: 2, 3, 4, and 5.
Answer:
3
Step-by-step explanation:
you can eliminate x with 3 if you multiply the second equation with 3
13r+ 8v = 47
22v=63-17r
Answer:
D. 5.
Step-by-step explanation:
Yes.
solve for y
show your work.
9-4x=-3y
y=9-4x/3
you need to isolate y so you divide 3 on both sides.
y=3-4/3x
I need help solving this practice problem from my trig prep book
The period of a trigonometric function is the distance between each repetition of the function.
In this case, we have:
As we can see in the graph of the function, the distance between each repetition is 2π.
Therefore, the period of f(x) = csc(x) is 2π.
Data can be displayed in many different ways: using tables, graphs, and equations. What are the benefits and drawbacks of each of these models?
Answer:
There are many different ways to portray your findings for an individual to view and understand. However, each have their pros and cons. When using a table, all of the specific numbers of your data can clearly be seen and compared with one another without having to analyze a picture. However, since there is no visual correlation that shows the growth and decline of your data, someone who best comprehends visually may not be able to understand your findings. It sis best to vary your sources of displaying information to make sure that it is all able to be understood by any viewer. When using a graph, you have a clear visual representation of the correlation of your variables in your experimentation. This allows the viewer to comprehend your data as a picture and see the change as the picture moves. However, it take further analysis and cross referencing to get specific quantitative data as you are required to read across and down the graph. And finally, when using equations you can show the direct way that the change was caused in your experiment. Each equation has a specific input and output. However, the drawback is the person viewing your data may have to solve the equations themselves to find out your data or simply be confused as equations don’t directly show data, but rather how to find it. It is important to have a varied combination of these things to allow for your data to be throughly understood by anyone viewing it. I hope this helps! :)
Step-by-step explanation:
Formulate at least three problems that you wish to have answers using statisticsI am sorry there's no additional information or pictures on this question.
In order to create three statistics problems, we can use the concepts of mean, median and mode.
The mean of a data set is the sum of all values divided by the number of values.
The median of a data set is the middle term of the set in crescent order (if the set has an even number of values, the median is the mean between the two middle values).
The mode of a data set is the value that repeats the most in the set.
So, for our three questions, let's use the following data set:
[tex]1,3,5,2,2,8,4,1,2,3,2[/tex]The three problems are:
1) Calculate the mean of the data set
2) Calculate the median and the mode of the data set
3) Which one is greater: mean, median or mode?
how can you determine a reseentative sample of a population
A representative sample is one that accurately depicts the a population> This representative sample can be determined through sampling. The examples of sampling methods used are random sampling, stratified random sampling
How do I find the slope in this problem?
to get the slope of any straight line, we simply need two points off of it, let's use the points in the picture below
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-5)}}} \implies \cfrac{-2}{0 +5} \implies \cfrac{ -2 }{ 5 } \implies {\Large \begin{array}{llll} - \cfrac{2 }{ 5 } \end{array}}[/tex]
HELP!!!!!!!!!! I NEED THIS ASAP PLEASE!!!
Graph the systems of equations.
Both the equations are plotted on the graph and they intersect each other on (2, 4).
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, graph the equation as follows:
2x + y = 8-x + 2y = 6So plot as:
(Refer to the graph attached below)The lines of both equation intersect at (2, 4).Therefore, both the equations are plotted on the graph and they intersect each other on (2, 4).
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
2.Use the diagram below. Circle the true statements based on the given diagram.
3.Use the diagram below. Circle the angle pairs that are supplementary to each other.
4.Triangle HIJ has ∠I = 17° and ∠H = 84°. Find m∠ J.
5.An isosceles triangle has a base angle of 24°. Find the measure of the apex angle.
Step-by-step explanation:
2.
angle B is congruent to angle B'.
side BC is congruent to side B'C'.
3.
angle pairs 1 and 3, 2 and 3, 5 and 7 are supplementary (together they have 180°).
4.
please burn this into your brain for all times : the sum of all angles in a triangle is always (yes, always) 180°.
so,
angle J + 17 + 84 = 180
angle J = 180 - 17 - 84 = 79°
5.
and here we use it again.
isoceles means that the triangle has 2 equally long legs. that makes also both base angles equally large.
apex angle + 24 + 24 = 180
apex angle = 180 - 24 - 24 = 132°
Create a scatterplot using the following data relating the number of cigarettes a day smoked by a parent and thenumber of days the child missed school in the last quarter of the school year. Draw your estimate of the line of best fit.Select and give the coordinates of two points on the line. Find the slope of the line you drew. Write a sentence thatsummarizes the relationship between the two variables.
The equation for the line of best fit is given by:
y = mx + b
In which m is the slope
They are given by:
[tex]m=\frac{n\sum^{}_{}xy-\sum^{}_{}x\sum^{}_{}y}{n\sum^{}_{}x^2-(\sum^{}_{}x)^2}[/tex][tex]b=\frac{\sum^{}_{}y-m\sum^{}_{}x}{n}[/tex]Sum of x:
Sum of all values of x.
[tex]\sum ^{}_{}x=3\ast0+5+10+12+15+16+2\ast24+28+30+21+36_{}[/tex][tex]\sum ^{}_{}x=221[/tex]Sum of y:
[tex]\sum ^{}_{}y=0+2\ast2+3+2\ast5+2\ast8+10+2\ast12+2\ast15+20[/tex][tex]\sum ^{}_{}y=117[/tex]Sum of squares of x:
[tex]\sum ^{}_{}x^2=3\ast0^2+5^2+10^2+12^2+15^2+16^2+2\ast24^2+28^2+30^2+21^2+36^2_{}[/tex][tex]\sum ^{}_{}x^2=5323[/tex]Sum of xy:
[tex]\sum ^{\infty}_{n\mathop=0}xy=0\ast(0+2+5)+5\ast3+10\ast5+12\ast8+15\ast10+16\ast2[/tex][tex]+24\ast(8+12)+28\ast15+30\ast15+21\ast20+36\ast12_{}[/tex][tex]\sum ^{}_{}xy=2545[/tex]
Slope:
14 students, so n = 14.
Then
[tex]m=\frac{n\sum^{}_{}xy-\sum^{}_{}x\sum^{}_{}y}{n\sum^{}_{}x^2-(\sum^{}_{}x)^2}=\frac{14\ast2545-(221\ast117)}{14\ast5323-221^2}=0.38[/tex][tex]b=\frac{\sum^{}_{}y-m\sum^{}_{}x}{n}=\frac{117-0.38\ast221}{14}=2.36[/tex]The line of best fit is y = 0.38x + 2.36. This means that for a parents that smokes x cigarettes a day, the child is expect to miss 0.38x + 2.36 days of school during the quarter.
Graphic
Solve the system of equations.2y = 42z? +y = 3
The answer is option B
(1, 2) and (-3, -6)
Sketch a polynomial function with the following characteristics:
a. 5 real zeros
b. a zero of multiplicity 2 at x=−4
c. a zero of multiplicity 1 at x=2
d. a negative leading coefficient
The polynomic function p(x) = - x⁵ - 6 · x⁴ + 32 · x² is shown in the image of the Cartesian plane attached below.
How to derive and sketch a polynomial
In this question we must write the polynomial function and sketch the resulting curve on a Cartesian plane. We are going to take advantage of the definition of the factor form of the polynomial function:
p(x) = a · Π (x - r), for i = {1, 2, 3, ..., n}
Where:
a - Lead coefficient.r - i-th root of the polynomial.First, choose the negative lead coefficient:
a = - 1
Second, choose the roots of the polynomic root:
p(x) = - (x + 4)² · (x - 2) · x²
Third, expand the polynomic function:
p(x) = - (x² + 8 · x + 16) · (x - 2) · x²
p(x) = - (x² + 8 · x + 16) · (x³ - 2 · x²)
p(x) = - (x⁵ + 8 · x⁴ + 16 · x³ - 2 · x⁴ - 16 · x³- 32 · x²)
p(x) = - (x⁵ + 6 · x⁴ - 32 · x²)
p(x) = - x⁵ - 6 · x⁴ + 32 · x²
Fourth, sketch the polynomic function with a graphing tool.
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Express the confidence interval 0.555 < p < 0.999 in the form p+E
In order to express the confidence interval in the form p ± E, first we have to determine the midpoint of the interval, like this:
[tex]\hat{p}=\frac{0.555+0.999}{2}=0.777[/tex]The value of the error, E, can be calculated by taking the difference between p and the end of the interval, like this:
[tex]E=0.999-0.777=0.222[/tex]Then, we can express 0.555 < p < 0.999 in p + E notation as 0.777 ± 0.222
The confidence interval can be written as 0.777 ± 0.222.
The confidence interval 0.555 < p < 0.999 can be expressed in the form of p ± E.
To find the margin of error (E), we can subtract the lower limit (0.555) from the upper limit (0.999) and divide it by 2:
E = (0.999 - 0.555) / 2
E = 0.222
Therefore, the confidence interval 0.555 < p < 0.999 can be expressed as:
p ± E
where p is the point estimate and E is the margin of error. In this case, the point estimate would be the midpoint of the interval, which is the average of the lower and upper limits:
p = (0.555 + 0.999) / 2
p = 0.777
Hence, the confidence interval can be written as 0.777 ± 0.222.
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