The constant of proportionality is 0.0133
How to determine the constant of proportionality?From the question, the given parameters are
Relationship: p = 2 over 150 q
Rewrite the expression properly
So, we have
p = 2/150q
The above parameters can be represented as the following points
(p, q) = (150, 2)
The constant of proportionality of the points is then calculated as
k = q/p
Substitute the known values in the above equation
So, we have the following equation
k = 2/150
Evaluate the quotient in the above expression
So, we have
k = 0.0133
Hence, the relationship has a constant of proportionality of 0.0133
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EASY MATH PLEASE ANSWER
Two trains leave the same station, each 40 minutes apart. Train X leaves first at 9:45 am and heads west at a speed of 144 km/h. Train Y leaves at noon and travels directly east at a speed of 165 km/h. How far apart are these trains at 1:30 pm? Show your work.
The two trains will be a distance of 1049 km apart after 1:30 pm.
Velocity, distance and time
Velocity v is given by the distance d divided by the time t, hence according to the following rule:
v = d/t.
In the context of this problem, both trains are moving in the opposite direction from the station, hence their distance will be the sum of the distances of each train from the station.
The velocity equation can be solved for the distance as follows:
d = vt.
For train X, the velocity and the time are given as follows:
Velocity of 144 km/h, as stated in the text.Time of 3.75 hours, as 1:30 pm is 3 hours 45 minutes after 9:45 am, which is the time the train left, and 45 minutes is 75% = 0.75 of 60 minutes, which is one hour.Hence the distance that the train X will be from the station at 1:30 pm is given by:
dX = 144 x 3.75 = 540 km.
For train Y, the velocity and the time are given as follows:
Velocity of 165 km/h, as stated in the text.Time of 3.0833 hours, as the train leaves 40 minutes after train X, hence 1:30 pm is 3 hours and 5 minutes after train X left, and 5 minutes is 5/60 = 0.0833 of an hour.Hence the distance that the train Y will be from the station at 1:30 pm is given by:
dY = 165 x 3.0833 = 509 km.
Then the distance between both trains is given by:
d = dX + dY = 540 km + 509 km = 1049 km.
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Consider the following quadratic equation:35x2 = 13x + 12Step 1 of 2: Using the standard form ax² + bx + c = 0 of the given quadratic equation, factor theleft hand side of the equation into two linear factors.AnswerKeypadKeyboard Shortcuts= 0
Given: The quadratic equation below
[tex]35x^2=13x+12[/tex]To Determine: The two linear factors of the given equation using standard form of a quadratic equation
The standard form of a quadratic equation is given as
[tex]ax^2+bx+c=0[/tex]Re-write the given equation in the standard form as shown below
[tex]\begin{gathered} 35x^2=13x+12 \\ 35x^2-13x-12=0 \end{gathered}[/tex]Factor the left hand side as shown below
[tex]35x^2-28x+15x-12=0[/tex][tex]\begin{gathered} 7x(5x-4)+3(5x-4)=0 \\ (5x-4)(7x+3)=0 \\ \text{Therefore} \\ 35x^2-13x-12=0,in\text{ factored form is} \\ (5x-4)(7x+3)=0 \end{gathered}[/tex]Hence, the two linear factors of the given equation is
(5x -4)(7x + 3) = 0
A group of people were asked if they had run a red light in the last year. 478 responded "yes", and 200 responded "no".Find the probability that if a person is chosen at random, they have run a red light in the last year.
ANSWER
[tex]P=0.705[/tex]EXPLANATION
The probability that if a person has run a red light in the last year can be found by dividing the number of people that have run a red light in the last year by the total number of people in the group.
The total number of people in the group is:
[tex]\begin{gathered} 478+200 \\ \Rightarrow678 \end{gathered}[/tex]Therefore, the probability is:
[tex]\begin{gathered} P=\frac{478}{678} \\ P=0.705 \end{gathered}[/tex]X is a normally distributed random variable with mean 71 and standard deviation 9.
What is the probability that X is between 60 and 82?
Write your answer as a decimal rounded to the nearest thousandth.
Since the standard deviation is 10 and the first given score is 40, the 40 is 2 standard deviations below the mean.
On the other hand, 80 is 2 standard deviations above the mean.
Thus, we subtract the probability below the z-score which is 2, 0.97725, and the probability below the z-score which is -2, 0.02275.
[tex]\begin{gathered} P(X)=0.97725-0.02275 \\ P(X)=0.9545 \end{gathered}[/tex]We may obtain the values using the z-score table.
Therefore, the approximate value of the probability is 0.955.
Which measure is the best estimate of the area of the banner in square meters?
Answer:
6 square meters.
Explanation:
The banner is made up of two congruent triangles and two congruent trapezoids.
The banner forms a triangle with base:
[tex]\begin{gathered} 1\frac{3}{4}+1+1+1\frac{3}{4} \\ =5.5\text{meters} \end{gathered}[/tex]The height of the triangle = 2 meters.
Therefore, the area of the banner:
[tex]\begin{gathered} A=\frac{1}{2}bh \\ =\frac{1}{2}\times5.5\times2 \\ =5.5m^2 \end{gathered}[/tex]The measure that is the best estimate of the area of the banner is 6 square meters.
When 91 is divided by 1 1/9 the quotient is closest to what whole number?
Justify your answer.
When 91 is divided by 1 1/9 the quotient is closest to 81.
What is a quotient?
When we divide a number by the dividend the result of the division is known as quotient.
We are given a number as 91
We have to divide 91 by 1 1/9
We get, [tex]\frac{91}{\frac{10}{9} }[/tex]
On simplifying the above equation we get,
[tex]\frac{91}{10}[/tex]·[tex]9[/tex]
[tex]=\frac{819}{10}[/tex]
=81.9
This can be rounded off as this value is close to 82.
Hence when 91 is divided by 1 1/9 the quotient is closest to 82.
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what number is part of the solution set to the inequality below?m-20> 12 _
I need this for today , thank you
The completed two-column format used to prove the congruency of the segments [tex]\overline{ST}[/tex] and [tex]\overline{NR}[/tex] is presented as follows;
Statements [tex]{}[/tex] Reasons
1. [tex]\overline{SU}[/tex] ≅ [tex]\overline{LR}[/tex], [tex]\overline{TU}[/tex] ≅ [tex]\overline{LN}[/tex] [tex]{}[/tex] 1. Given
2. [tex]\overline{SU}[/tex] = [tex]\overline{LR}[/tex], [tex]\overline{TU}[/tex] = [tex]\overline{LN}[/tex] [tex]{}[/tex] 2. Definition of congruent segments
3. SU = ST + TU [tex]{}[/tex] 3. Segment addition postulate
LR = LN + NR [tex]{}[/tex]
4. ST + TU = LN + NR [tex]{}[/tex] 4. Substitution property of equality
5. ST + LN = LN + NR [tex]{}[/tex] 5. Substitution property of equality
6. ST + LN - LN = LN + NR - LN [tex]{}[/tex] 6. Subtraction property of equality
7. ST = NR [tex]{}[/tex] 7. Substitution property of equality
8. [tex]\overline{ST}[/tex] ≅ [tex]\overline{NR}[/tex] [tex]{}[/tex] 8. Definition of congruency
What are the postulates, properties and definition used to prove the congruency of the segments?The segment addition postulate states that a third point B can only be located on a line that has two points A and C when the distances between the points satisfy the equation, AC = AB + BCThe substitution property of equality states that if a variable, a = b then the variable a can be substituted with b in any equation.The subtraction property of equality states that the expressions on both sides of an equation remains equivalent following the subtraction of the same amount from the left and right hand side of the equation.Two segments, angles, or figures, are said to be congruent if their size and shape are the same.Learn more about the two column method used to prove statements in geometry here:
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what algebra property is this equation: (4y+1)x0=0
Answer:
It would be called the algebraic property of 0.
Step-by-step explanation:
Find the variance of the given data
147, 141, 120, 124, 128
The answers that I already tried are
11.510864 and rounded
10.29563 and rounded
Answer:
......................................
Step-by-step explanation:
3. The 9 boys in Mr. Ackerman's class went
outside for recess. They wore their gloves.
Isaiah and Michael each lost a glove while
outside. How many gloves did the boys bring
back into the classroom?
Answer:
14.
Step-by-step explanation:
Multiply 9x2 = 18
do 18-4 = 14
boom answer
Answer: 16
Step-by-step explanation:
9 boys in Mr. Ackerman's class
And gloves is plural so it means each boy has 2 gloves/
9 x 2 = 18
Then, 2 boys lost one glove..... glove is singular and there are 2 boys.
This means 2 gloves are missing
18 - 2 = 16
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need a bit of help. Show work
Answer:
1) yes
2) yes
Step-by-step explanation:
I know #1 is parallel because from the slope-intercept form shown, the slopes of line a and line b are the same, meaning it is parallel.
I known #2 is perpendicular because from the slope-intercept form shown, the slopes of line a and line b are the negative reciprocal of eachother.
Please solve no.13 (i) from here only solve (i) please
The exchange rate (US$1 = S$x) means that for every S$ she will receive 1 US dollar. Therefore, one can write the equation:
[tex]\begin{gathered} y=x\begin{cases}x=S \\ y=US\end{cases} \\ y=2000\lbrack US\rbrack \end{gathered}[/tex]Graph each equation rewrite in slope-intercept form first if necessary.Y=-1/3x+4
To graph the linear equation, follow the steps below.
Step 01: Find one point of the line.
To do it, choose a x-value and find its corresponding y-value.
Let's choose x = 0.
Substituting x in the equation to find y:
[tex]\begin{gathered} y=-\frac{1}{3}x+4 \\ y=-\frac{1}{3}*0+4 \\ y=0+4 \\ y=4 \end{gathered}[/tex]First point: (0, 4).
Step 02: Find another point of the line.
Let's choose x = 3.
Substituting x in the equation to find y:
[tex]\begin{gathered} y=-\frac{1}{3}*3+4 \\ y=-\frac{1}{3}*3+4 \\ y=-\frac{3}{3}+4 \\ y=-1+4 \\ y=3 \end{gathered}[/tex]Second point: (3, 3).
Step 03: Plot the two points and connect them to draw the graph.
The graph is shown below:
Find the 11th term in this sequence. *10 poin1) -2, 4. -8, 16, ...Find a11
Given the terms
-2, 4, -8, 16
The first term = -2
The second term is 4
The third term is -8
The fourth term is 16
We can observe that this is a geometric sequence
So to get the 11th term, we will first get the formula
Step 1: Get the common ratio (r)
[tex]\text{common ratio=}\frac{\sec ond\text{ term}}{first\text{ term}}=\frac{third\text{ term}}{\sec ond\text{ term}}[/tex][tex]r=\frac{4}{-2}=\frac{-8}{4}=-2[/tex]Step 2: Get the formula for the nth term
The formula is given by
[tex]T=r^n[/tex][tex]T=(-2)^n[/tex]where T is the nth term
n is the number of terms
Step 3: Find the 11th term
[tex]T_{11}=(-2)^{11}[/tex][tex]T_{11}=-2048[/tex]The 11th term is -2048
If 49600 dollars is invested at an interest rate of 8 percent per year, find the value of the investment at the end of 5 years for the following compounding methods. a) annual: b) semiannual: c) monthly: d) daily:
a) Value of invest when compounded annually= $72878.67
b) Value of invest when compounded semi-annually is $73420.12
c) Value of invest when compounded monthly is $73896.35
EXPLANATION
a)Annually
Given:
Principal(p)= 49600
rate (r) = 8% = 0.08
time(t) =5
Since it is compounded anually, n=1
Using the formula;
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Substitute the value and evaluate.
[tex]A=49600(1+\frac{0.08}{1})^5[/tex][tex]=49600(1.08)^5[/tex][tex]=72878.67[/tex]Therefore, the value of the investment when compounded annually is $72878.67
b) Semi-annually
In this case, the we are going to substitute all our initial values except for n.
In the case of semi annually, n= 2
That is;
Principal(p)= 49600
rate (r) = 8% = 0.08
time(t) =5
n=2
Substitute into the formula and evaluate.
[tex]A=49600(1+\frac{0.08}{2})^{2\times5}[/tex][tex]=49600(1+0.04)^{10}[/tex][tex]=49600(1.04)^{10}[/tex][tex]=73420.12[/tex]Therefore, the value of the investment when compounded semi-annually is $73420.12
c)monthly
In this case n= 12 and all other values remains the same.
That is;
Principal(p)= 49600
rate (r) = 8% = 0.08
time(t) =5
n=12
Substitute the values into the formula and evaluate.
[tex]A=49600(1+\frac{0.08}{12})^{12\times5}[/tex][tex]=49600(1+0.667)^{60}[/tex][tex]=49600(1.0667)^{60}[/tex][tex]=73896.35[/tex]Therefore, the value of the investment when compounded monthly is $73896.35
Find the area of the shaded region. Round your answer to one decimal place, if necessary. Note: The figure is not drawn to scale.
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. the area of shaded region is 15.728 inches square.
What is Area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface
The diameter of circle is 5, d=5
and the length of side of the equilateral triangle is 3.
to find the area of shaded region we need to find the area of circle and then we have to remove the area of triangle.
π(d/2)²-1/2×a²×sin60⁰
3.14(5/2)²-1/2×3²×√3/2
3.14×2.5²-1/2×9×√3/2
3.14×6.25 -1/2×9×0.866
3.14×6.25-7.794/2
3.14×6.25-3.897
19.625-3.897
15.728
Hence area of shaded region is 15.728 inches square.
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What's the common difference of the sequence -5, -2, 1,4,7, ...?
To find the common diference we substract each of the number by the previous one:
[tex]\begin{gathered} -2-(-5)=3 \\ 1-(-2)=3 \\ 4-1=3 \\ 7-4=3 \end{gathered}[/tex]Therefore the common difference is 3 and the answer is B.
The table below shows the relationship between the number of water bottles at a park that are thrown away and the number of water bottles at the park that are recycled for each of five months. Which statement correctly descrīdes the relationship between the number of water bottles that are thrown away and the number of water bottles that are recycled at the park each month? Water Bottles at a Park Water Bottles Water Bottles Thrown Away Recycled 40 12 15 24 80 110 A. The relationship is proportional. For every 3 bottles that are thrown away each month, 10 bottles are recycled. B. The relationship is proportional. For every 10 bottles that are thrown away each month, 3 bottles are recycled. c. The relationship is not proportional. The number of water bottles that are thrown away increases more from month to month than the number of water bottles that are recycled. D. The relationship is not proportional. The difference between the number of bottles that are thrown away and the number of bottles that are recycled is not the same for each month.
EXPLANATION
As we can see in the picture, there is a proportional relationship between the bottles that are thrown away each month and those recycled.
Considering two ordered pairs as for instance, (x_1,y_1)= (40,12) and (x_2,y_2)= (50,15) give us the appropiate rate.
[tex]\text{rate}=\frac{y_2-y_1}{x_1-x_1}[/tex]The rate is as follows:
[tex]rate=\frac{(15-12)}{(50-40)}=\frac{3}{10}\frac{bottles\text{ recycled}}{\text{bottles thrown away}}[/tex]In conclusion, for each 10 bottles thrown away, there are 3 bottles recycled.
The answer is the option B.
The equation of a line is x + 5y = 12. What is the y-intercept of the line? D-12 0¹2 12 please answer quickly
Answer:
12/5
Step-by-step explanation:
Find the y-intercept form of the line by isolating y:
x + 5y = 12
5y = -x + 12
5 5
y = (-1/5)x + 12/5
y = mx + b
In this form, 12/5 is b, which is the line's y-intercept.
help meeee pleasee!!!
thank youu
Answer:
(-7, 3)
Step-by-step explanation:
Since the endpoints of the interval are not included, use parentheses.
A rectangle has a height of 3x and a width of 2x-3Express the area or the entire triangle
Answer
6x² - 9x
Explanation
Given:
Height = 3x
Width = 2x - 3
The area of a rectangle = Length x Width
From the figure, length = height = 3x
Area = 3x(2x - 3)
In expanded form, we shall open the parenthesis
Area = (6x² - 9x) squared unit
What is the distance between the points (3,4) and (1,5)?
Answer:
distance between the points (3,4) and (1,5) = 2.236
Step-by-step explanation:
The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 2 dimensional plane, the distance between points (X1, Y1) and (X2, Y2) is given by the Pythagorean theorem:
[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]'
For:
[tex](X1, Y1) = (3, 4)\\\\(X2, Y2) = (1, 5)[/tex]
[tex]d = \sqrt {(1 - 3)^2 + (5 - 4)^2}\\\\d = \sqrt {(-2)^2 + (1)^2}\\\\d = \sqrt {{4} + {1}}\\\\d = \sqrt {5}\\\\d = 2.236068[/tex]
Answer:
Exact distance is [tex]\sqrt{5}[/tex]
Approximate distance is 2.2361
Round the decimal value however your teacher instructs.
====================================================
Work Shown:
I used the distance formula to get the following.
[tex](x_1,y_1) = (3,4) \text{ and } (x_2, y_2) = (1,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-1)^2 + (4-5)^2}\\\\d = \sqrt{(2)^2 + (-1)^2}\\\\d = \sqrt{4 + 1}\\\\d = \sqrt{5}\\\\d \approx 2.2361\\\\[/tex]
----------------
A slight alternative is to plot the points A(3,4) and B(1,5) and C(3,5).
Points A and B are the original points we were given. Point C helps form a right triangle. The hypotenuse is AB and the legs are AC and BC.
Leg AC = 1 unit and leg BC = 2 units
Use the pythagorean theorem [tex]a^2+b^2 = c^2[/tex] to plug in a = 1 and b = 2 to find that the hypotenuse is exactly [tex]c = \sqrt{5}[/tex] units long, which is the distance from A to B.
Given that the measure of ∠x is 120°, and the measure of ∠y is 60°, find the measure of ∠z.
The measure of ∠x is 120°, and the measure of ∠y is 60°, find the measure of , ∠z = 0°
What about the triangle angle?A triangle's internal angles always add up to 180°, although its exterior angles are equal to the sum of the two interior angles that are not next to it. Another method for calculating a triangle's exterior angle is to subtract the angle of the vertex of interest from 180°.
Given that,
For triangle,
∠x is 120°
∠y is 60°
now , ∠z = [180° - (120°+60°)]
∠z = 0°
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What is the range of the function? ƒ(x) =3/x+4 +1
Enter your answer, in interval notation, by filling in the boxes. Use the drop-down menu at the upper left of keyboard options as
necessary.
Answer:
(-∝;1)∪(1;+∞).
Step-by-step explanation:
for more details see the attached graph.
#4 ALGEBRA: Find the value of x and then determine the measure of the obtuse angle.
Answer:
See below
Step-by-step explanation:
The three angles sum to 180 degrees
4x + 3x + 8x = 180
15x = 180
x = 12
So the obtuse angle would be 8x
8 * 15 = 120°
Write an expression that could represent an estimated cost for the party. Use at least one letter. State what each part of the expression represents
The expression that can be used to represent the estimated cost for the party is T =si
How to illustrate the information?It should be noted that expression show the relationship between variables. We can get an estimated cost for the party by using the following expression:
T = s×i
where:
T = total cost of the ice cream party
s = number of ninth students
i = unit cost of ice cream
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As a reward for achieving their goals, all students in the ninth grade are invited to an ice cream party.
1) Write an expression that could represent an estimated cost for the party. Use at least one letter. State what each part of the expression represents.
The function y=f(x) is graphed below. Plot a line segment connecting the points on ff where x=-4 and x=1. Use the line segment to determine the average rate of change of the function f(x) on the interval −4≤x≤1.
The line connecting the points on the graph is shown below:
From it we notice that to get to the first point of the lineto the second we need to:
• Move down 6 squares; since each square has a length of 2 units this means that we move 12 units down.
,• Move 5 units to the right.
Therefore, we have that:
[tex]\begin{gathered} \Delta y=-12 \\ \Delta x=5 \end{gathered}[/tex]and that:
[tex]\text{ average rate of change=-}\frac{12}{5}[/tex]Which value is equivalent to 62 +42 +24? o 28 O 68 o 96 0
Answer:
128
Explanation:
Given the expression
62 + 42 + 24
Adding the values up will give;
= 62 + (66)
= 128
Hence the equivalent value is 128
Which of the following are solutions to the system graphed below?
The solution to the system of inequalities is the shaded area shown in the graph. This also includes the bounding lines of the shaded area since they are all solid lines.
To find the answer, we will check the coordinates provided in the options to see which falls within the shaded portion.
On observation, we can see that the following coordinates fall within the shaded area:
[tex]\begin{gathered} (-5,5) \\ (-4,1) \end{gathered}[/tex]The correct options are OPTION 3 and OPTION 4.
