Answer:
2/15Step-by-step explanation:
11/6 + -2/5 +-13/10?
11/6 + (-2/5) + (-13/10)
43/30 - 13/10
2/15
What are the points if the slope is 4 and the point is (1,-1)
The points if the slope is 4 and the point is (1,-1) are (1,-1) and (2, 3)
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the points?The given parameters are:
Slope = 4
Point = (1, -1)
The slope of 4 means that as x changes by 1, the value of y changes by 4
This means that, we have:
(x + 1, y + 4)
Substitute the known values in the above equation
(1 + 1, -1 + 4)
Evaluate
(2, 3)
Hence, the points if the slope is 4 and the point is (1,-1) are (1,-1) and (2, 3)
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Quick algebra 1 question for some points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]let \: the \: number \: be \: denoted \: by \: p \\ five \: times \: a \: number = 5p \\ square\: of \: a \: number = p {}^{2} [/tex]
[tex] \gamma - p {}^{2} = 5p - p {}^{2} [/tex]
Jeri finds a pile of money with at least $\$200$. If she puts $\$80$ of the pile in her left pocket, gives away $\frac{1}{3}$ of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away $\$200$ of the original pile and kept the rest. What are the possible values of the number of dollars in the original pile of money? (Give your answer as an interval.)
Based on the amount of money that Jerl had and then the amount that she put away, the possible values of the number of dollars in the original pile of money was ( 200, 440).
What was the amount in the original pile?The amount that was above $200 that she found can be x which means that the greater side of the inequality is:
= 200 + x
She then gave away $80:
= 120 + x
She gave away 1/3 of the money so the amount left is:
= 2/3 x (120 + x)
The lesser side of the inequality:
(x + 2) - 200 = x
So then:
((120 + x) x 2) / 3 > x
240 + 2x > 3x
240 > x
x < 240
The interval that shows the possible values of the original pile of money is therefore:
( 200, 440)
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Testing: h 0 : p = 0. 74 h0:p=0. 74 h α : p < 0. 74 hα:p<0. 74 your sample consists of 43 subjects, with 33 successes. calculate the test statistic
Test statistic is 0.42.
Given
Testing:
h0 : p = 0.74
h1 : p < 0.74
Successes x = 33
Subject n = 43
A test statistic is a number calculated by a statistical test. It describes how far your observed data is from the null hypothesis of no relationship between variables or no difference among sample groups.
It measures the accuracy of the predicted data distribution relating to the null hypothesis you use when analyzing data samples.
Test statistics z = [tex]\frac{p_{hat} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]
Where [tex]p_{hat}[/tex] = Sample proportion = [tex]\frac{x}{n}[/tex]
p = population proportion
n = sample size
z = [tex]\frac{(\frac{33}{43})-0.74 }{\sqrt{\frac{0.74(1-0.74)}{43} } }[/tex]
z = 0.42
Hence,
Test statistics is 0.42..
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Assumptions of a regression model can be evaluated by plotting and analyzing the ____________
The assumptions of a regression model can be evaluated by plotting and analyzing the error terms.
Important assumptions in regression model analysis are
There should be a linear and additive relationship between dependent (response) variable and independent (predictor) variable(s). There should be no correlation between the residual (error) terms. Absence of this phenomenon is known as auto correlation.The independent variables should not be correlated. Absence of this phenomenon is known as multi col-linearity.The error terms must have constant variance. This phenomenon is known as homoskedasticity. The presence of non-constant variance is referred to heteroskedasticity. The error terms must be normally distributed.Hence we can conclude that the assumptions of a regression model can be evaluated by plotting and analyzing the error terms.
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Find the inverse of the matrix
A=(3 4) and use it to solve the equation 3x+4y=1 5x+2y=3 simultaneously
(5 2)
By applying inverse of a matrix, we find that the solution of the system of linear equations is (x, y) = (5/7, - 2/7).
How to solve a system of equation with inverse matrices
In linear algebra, systems of linear equations with a unique solution can be represented by the following expression:
[tex]\vec A \cdot \vec x = \vec B[/tex] (1)
Where:
[tex]\vec A[/tex] - Matrix of dependent constants.[tex]\vec x[/tex] - Vector column of variables.[tex]\vec B[/tex] - Vector column of independent constants.The solution of such systems is defined by:
[tex]\vec x = \vec A^{-1}\cdot \vec B[/tex]
[tex]\vec x = \frac{1}{\det(\vec A)}\cdot adj\left(\vec A\right) \cdot \vec B[/tex], where [tex]\det \left(\vec A\right) \ne 0[/tex].
Where:
[tex]\det \left(\vec A\right)[/tex] - Determinant of the matrix of dependent constants.[tex]adj \left(\vec A\right)[/tex] - Adjoint of the matrix of dependent constants.For the case of [tex]\vec A \in \mathbb{R}_{2\times 2}[/tex], the inverse of [tex]\vec A[/tex] is:
[tex]\vec A^{-1} = \frac{1}{\det \left(\vec A\right)} \cdot \left[\begin{array}{cc}a_{22}&-a_{12}\\-a_{21}&a_{11}\end{array}\right][/tex] (2)
If we know that [tex]\vec A = \left[\begin{array}{cc}3&4\\5&2\end{array}\right][/tex] and [tex]\vec B = \left[\begin{array}{cc}1\\3\end{array}\right][/tex], then the solution of the system of linear equations is:
[tex]\vec A^{-1}= \frac{1}{(3)\cdot (2) - (5) \cdot (4)}\cdot \left[\begin{array}{cc}2&-4\\-5&3\end{array}\right][/tex]
[tex]\vec A^{-1} = -\frac{1}{14}\cdot \left[\begin{array}{cc}2&-4\\-5&3\end{array}\right][/tex]
[tex]\vec A^{-1} = \left[\begin{array}{cc}-\frac{1}{7} &\frac{2}{7} \\\frac{5}{14} &-\frac{3}{14} \end{array}\right][/tex]
[tex]\vec x = \left[\begin{array}{cc}-\frac{1}{7} &\frac{2}{7} \\\frac{5}{14} &-\frac{3}{14} \end{array}\right] \cdot \left[\begin{array}{cc}1\\3\end{array}\right][/tex]
[tex]\vec x = \left[\begin{array}{cc}\frac{5}{7} \\-\frac{2}{7} \end{array}\right][/tex]
By applying inverse of a matrix, we find that the solution of the system of linear equations is (x, y) = (5/7, - 2/7).
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A farmer with 1200 meters of fencing wishes to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. What are the dimensions of the field that produce the largest area
The perimeter of a given figure is a measure of the addition of each individual length of the sides of the figure. Thus the dimensions that would produce the largest area of the field are; length = 300 m, and width = 200 meters.
The perimeter of a given figure is a measure of the addition of each length of the sides of the figure. It always has the unit as that of the given sides of the figure.
So in the given question, the perimeter of the fence required = 1200 meters.
Thus, let the length of the enclosed rectangle be represented by l and its width by w. Thus,
Perimeter = 2l + 3w
1200 = 2l + 3w
Thus, let l be equal to 300, we have;
1200 = 2(300) + 3w
1200 - 600 = 3w
w = 200
Thus the dimensions of the field that would produce the largest area are; length = 300 m and width = 200 m.
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PLSSSS HELPPPP THANK YOUU IF YOU DOOO
Answer:
B
Step-by-step explanation:
Which equations for the line of best fit do not accurately represent the data in the scatter plot? Select all that apply.
Concluding, the equations that do not accurately represent the data in the scatter plot are B, C, and D.
Which equations do not accurately represent the data in the scatter plot?By looking at the scatter plot, we can see that as we read from left to right, the number of shoes sold (y variable) decreases.
Then the linear fit must have a negative slope, from that, we can discard options B and C.
Now, we also can see that the line starts almost at y = 70.
If you look at the option D, you can see that the constant term of that line is -70, so we can also discard that option.
Concluding, the equations that do not accurately represent the data in the scatter plot are B, C, and D.
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Convert a normally distributed score of 80 with a mean of 70 and a standard deviation of 6 into a z score.
Answer:
5/3
Step-by-step explanation:
z = (Distributed score - Mean)/Standard deviation= (80-70)/6 = 5/3
Step-by-step explanation:
z = (specific score - mean) / standard deviation
in our case
z = (80 - 70)/6 = 10/6 = 5/3 = 1.666666... ≈ 1.67
as most z-tables round the z-scores to hundredths.
not to forget : the sign matters. so, don't worry, if you have e.g. a specific score of 60 :
(60 - 70)/6 = -10/6 = -5/3 = -1.666666... ≈ -1.67
you did not do anything wrong. that is all ok and valid.
Give the equation for a circle with the given center and radius. center at (-1, 3), radius = 4
Answer:
(x + 1)² + (y - 3)² = 16
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (- 1, 3 ) and r = 4 , then
(x - (- 1) )² + (y - 3)² = 4² , that is
(x + 1)² + (y - 3)² = 16
Answer:
(x+1)^2 + (y-3)^2 = 16
Step-by-step explanation:
The standard form of an equation of a circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2. Plugging in those values, we get (x-(-1))^2 + (y-3)^2= 4^2 = (x+1)^2 + (y-3)^2 = 16.
Can someone tell me what this symbol means? Ty!!!
Answer:
Angle symbol
Angle ACB
Angle ACE
Angle DCE
In the figure below, ∠t= 133° . Find the measures of all remaining angle.
t is vertical to s because they share a point and are directly across from each other. vertical angles are congruent. therefore s=113 degrees
t and p are corresponding angles, which means they are congruent. this means p is also 113 degrees.
s and o are corresponding angles, so o is also 113 degrees.
t and u are supplementary. they share a straight line, so they add up to 180. you can find u by subtracting 113 from 180. 180-113= 67, so u is 67 degrees.
u and r are vertical angles, so r is 67 degrees.
r and m are corresponding, as well as u and q. therefore m and q both equal 67 degrees.
hope this helped :)
please help with algebra 2 question! arithmetic sequence
erica is playing a card game with her friend marquis. her points are shown in the following table:
round 1: 30 pts
round 2: 42 pts
round 3: 58.8 pts
marquis’s points in each round are represented by the following sequence:
50, 75, 112.5,…
in the table below, determine whether each row applies to eeica’s points or marquis’s points. select erica, marquis, or neither option.
(answers attached in pic) pls help!
Answer:
neitherMarquisEricaMarquisStep-by-step explanation:
The matching of exponential functions to table values involves matching both initial values and rate of growth. The value of a geometric series can be calculated from its formula, or can be shown by a calculator or spreadsheet.
Function determinationThe starting values of the two sequences are different, as are all of the starting values of the answer choices. Matching starting values is sufficient to identify which sum goes with which player.
The series ...
[tex]\displaystyle S=\sum_{k=1}^n{AB^{k-1}}[/tex]
gives the sum of a geometric sequence with first term A and common ratio B.
The first term of Erica's series is A=30. The ratio is B=42/30 = 1.4.
The first term of Marquis's series is 50. The ratio is B=75/50 = 1.5.
Using these values in the series formula, the total score after n rounds will be ...
[tex]\displaystyle \text{Erica:}\quad \sum_{k=1}^n{30(1.4)^{k-1}}\qquad\text{matches Row 3}\\\\\text{Marquis:}\quad \sum_{k=1}^n{50(1.5)^{k-1}}\qquad\text{matches Row 2}[/tex]
Total scoreThe explicit expression for these sums is ...
[tex]S=A\dfrac{B^n-1}{B-1}[/tex]
Then the total scores after 6 rounds are ...
Erica: 30(1.4^6 -1)/0.4 = 489.7152
Marquis: 50(1.5^6 -1)/0.5 = 1039.0625 . . . . . matches row 4
TableThen the required table gets filled in ...
neitherMarquisEricaMarquis__
Additional comment
The values in the attached table are total scores after each round. One must subtract the previous round's total to find the points scored in a given round.
The purpose of showing totals is to permit matching the value seen in Row 4 of the table.
AB is tangent to ⊙C at point B and AD is tangent to ⊙C at point D.
Circle C is shown. Line segments C B and C D are radii. Line segments B A and D A are tangents to circle C. Angle B C D is 124 degrees.
What is m∠A?
34°
62°
56°
124°
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
As you can see in the quadrilateral ABCD, the two angles measure 90° (as they are tangents to circle c) and one of them is given 124°
we need to find the Angle BAD : let it be x ~
By angle sum property of Quadrilaterals,
[tex]\qquad \sf \dashrightarrow \: 90 + 90 + 124 + x = 360[/tex]
[tex]\qquad \sf \dashrightarrow \: x+30 4 = 360[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 360 - 304[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 56 \degree[/tex]
Hence, Angle m A = 56°
Answer: c
Step-by-step explanation:
A plot of land in the shape of a horizontal ellipse has a pole at each focus. the foci are 16 feet from the center. if the plot of land is 40 feet across one axis, how long is it across the other axis?
If a plot of land in the shape of a horizontal ellipse has a pole at each focus. the foci are 16 feet from the center. if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.
Length across the other axisUsing Pythagoreans theorem formula
a²=b²+c²
Where:
c=16 feet
a=40/2=20 feet
Hence:
20²=b²+16²
b²=20²-16²
b²=400-256
b²=√144
b=12
2b=12×2
2b=24 feet
Therefore if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.
The complete question is are:
A plot of land in the shape of a horizontal ellipse has a pole at each focus. The foci are 16 feet from the center. If the plot of land is 40 feet across one axis, how long is it across the other axis?
a. 34 feet
b. 46 feet
c. 24 feet
d. 30 feet
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Make t the subject of the formula k=mt/[t*t]+f............**by t*t I mean square of T
Answer:
T tof = 2 ( v 0 sin θ 0 ) g . T tof = 2 ( v 0 sin θ 0 ) g . This is the time of flight for a projectile both launched and impacting on a flat horizontal surface.
Determine how the strategies are similar. Picture below
Answer: Look at stwp by step
Step-by-step explanation:
Basically we can compare both equations to get that x = √7 and y = √2 so we can substitute that into 2x + 10y to get 2√7 + 10√2
A person bought a safe which can be unlocked by entering a 2-digit
secret code. After some time, he forgot the secret code of his safe.
However, he remembers some numbers that could be the secret code.
The secret code is one among the following numbers.
5 17 29 22 11 26 27 35 39 41
Let us give him some clues to find the secret code of his safe.
It is greater than 20
It is not a prime number
It is smaller than 40
It has 13 as one of its factors
It is an odd number.
It has only 4 factors
The secret code is ____________________
39 number is the secret code as the unlock code for the safe.
According to the statement
we have given that a some numbers as a code and we have to find the correct code after applying the given conditions.
So, For this purpose
The given number set is
5 17 29 22 11 26 27 35 39 41
So,
A. One condition : It is an odd number
so, the number set become
5 17 29 11 27 35 39 41
And
B. Second condition : It is greater than 20
so, the number set become
29 27 35 39 41
And
C. Third condition : It is smaller than 40
so, the number set become
29 27 35 39
And
D. Fourth condition : It is not a prime number
so, the number set become
27 35 39
And
E. Fifth condition : It has 13 as one of its factors
so, the number set become
39.
So, 39 number is the secret code as the unlock code for the safe.
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Question
What are the coordinates of the point (−4, 2) after a translation 2 units left and 2 units up?
(−6, 4)
begin ordered pair negative 6 comma 4 end ordered pair
(−6, 0)
begin ordered pair negative 6 comma 0 end ordered pair
(−2, 0)
begin ordered pair negative 2 comma 0 end ordered pair
(−2, 4)
begin ordered pair negative 2 comma 4 end ordered pair
Answer:
(-6,4)
Step-by-step explanation:
You started at (-4,2) The first number in the ordered pair moves the number left and right and the second number moved the point up and down.
We are first told to move the point 2 units to the left. -4 is my left right number. If I am at -4 and I go to unites to the left, I will be at -6. My new point is now (-6,2). Next we are told to go up 2. The 2 number in my ordered pair tells me that I am 2 above the x axis. Now I am going to go two more units up. I am now at 4, so my new ordered pair after the translation is (-6,4)
coordinates of the point (−4, 2) after a translation 2 units left and 2 units up would be (-6, 4).
What is Translation ?
"Translation" moves points the same distance along lines that are parallel to each other.
Translation involves the initial object called the pre-image and the final object called the image. As you can see in the picture above, the rust-colored item represents the pre-image, and the blue item represents the image. Because of the arrow, we can tell the direction in which the image was moved. For other images, you may receive instructions on which image is the pre-image, or you may be asked to find the pre-image from the image.
Reflection, on the other hand, moves points along a specified line in such a way that the line bisects each line segment connecting corresponding pre-image points and image points
We are asked to find the coordinates of the points (-4,2) after a translation 2 units left and 2 units up.
We know that translating a point to the left by 'a' units means we need to subtract 'a' units from x-coordinate of the point.
Translation to 2 units left:
(-4,2) → (-4-2, 2) → (-6, 2)
We know that translating a point to upwards by 'a' units means we need to add 'a' units to y-coordinate of the point.
Translation to 2 units up:
(-6, 2) → (-6, 2+2) → (-6, 4)
Therefore, coordinates of the point (−4, 2) after a translation 2 units left and 2 units up would be (-6, 4).
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Fundamentally, pressure is defined as force per unit area. what is the source of the force in a gas sample?
The source of the force in the gas sample is; The force is composed of the sum of the collisions only between the gas molecules and the container
What is the relationship between Force and Pressure?We are given that;
Pressure = Force /Area
Now, for any gas sample, force is defined as basically the force exerted by the gas molecules when they strike the surface and bounce back inside the container where they are located.
Now, from the definition above we can conclude that the source of the force in the gas sample will be The force is composed of the sum of the collisions only between the gas molecules and the container
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In the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle. A straight line is shown and is marked with three angles. The first angle measures 60 degrees. The second angle measures 60 degrees. The third angle is labeled y. The line between the 70 degree angle and angle y extends below the straight line. The angle formed is labeled angle x. Write and solve an equation to determine the measure of angle x.
The equation that solve for x is as follows;
70 + 60 + x = 180
How to find an angle?The equation that can be used to find the measure of angle x can be found as follows:
60 + 70 + y = 180
Therefore,
130 + y = 180
subtract 130 from both sides
130 - 130 + y = 180 - 130
y = 50°
70 + 60 + x = 180
130 + x = 180
x = 180 - 130
x = 50°
x and y are vertically opposite angles.
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Your friend won't get many stars like this! What changes would you make to the equation to help your friend collect all the stars? Why are those changes going to work
The required equation that represents the line of best fit is y = 2x + 4
Finding the equation of a line of best fit.A line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.
From the given scatters plot, we only need to choose two points that aligns properly and create an equation of a line using the coordinates.
Using the following points (4, 12) and (2, 8)
The equation of the line will be in the form y = mx + b
where
m is the slope
b is the y-intercept
Determine the slope
Slope = y2-y1/x2-x1
Slope = 8-12/2-4
Sope = -4/-2
Slope = 2
Determine the y-intercept
Using the coordinate point (2, 8) and m = 2
8 = 2(2) + b
b = 8 - 4
b = 4
Hence the required equation that represents the line of best fit is y = 2x + 4
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The rate of inflation in the fictional land of sardonia is such that the price of a car costing 24000 dollars in u.s. currency will double in eleven years. what is the annual rate of inflation? what will be the price of this car in five years?
The annual rate of inflation is 35560.86%.
What is inflation?Inflation is defined as an increase in the overall price of goods and services in an economy.When the general price level rises, each unit of currency purchases fewer products and services; hence, inflation equates to a loss of money's purchasing power. Deflation, or a sustained reduction in the general price level of goods and services, is the inverse of inflation. The inflation rate, which is the annualized percentage change in a general price index, is the most commonly used metric of inflation.To find the annual rate of inflation:
48,000=24,000e^k(7)24,000 24,0002=e^k(7)ln2=lne^k7ln2=k77 7k=0.099 --> k=9.9%Now, sub in 4 and 0.099
=24,000e^(0.099)(4)=35560.86Therefore, the annual rate of inflation is 35560.86%.
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The correct question is given below:
The rate of inflation in the fictional land of Sardinia is such that the price of a car costing 24,000 dollars in U.S. currency will double in seven years. What is the annual rate of inflation? what will be the price of this car in four years?
Suppose it costs $43 to roll a pair of dice. you get paid $6 times the sum of the numbers that appear on the dice. is it a fair game?
The game is not fair as 6 times the expected sum is less than the cost, $43.
In the question, we are asked if the game is fair.
For the game to be fair, 6 times the expected sum for the pair from the game has to be greater than or equal to $43, that is,
6E(X) ≥ 43.
The expected sum for the pair, E(X) can be calculated using the formula,
E(X) = ∑x.p(x),
or, E(X) = 1/18 + 1/6 + 1/3 + 5/9 + 1/6 + 7/9 + 10/9 + 1 + 5/6 + 11/18 + 1/3,
or, E(X) = 107/18.
Now, 6E(X) = 6*(107/18) = 107/3 = 35.67.
Since, the total return from the game is $35.67, which is less than the cost of $43, the game is not fair.
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Uan zhang bought a 10-year bond that pays 8. 25 percent semiannually for $911. 10. what is the yield to maturity on this bond? (roundyour percentage answer to two decimal places. )
The yield to maturity on this bond according to the trial-and-error approach is 9.66 percent.
According to the statement
we have given that the Uan zhang bought a 10-year bond that pays 8. 25 percent interest per 6 months.
And we have to find that the yield to maturity on this bond.
So, For this purpose,
The amount given is $911. 10.
Years to maturity = n = 10
Coupon rate = C = 8.25%
Semiannual coupon = $1,000 × (0.0825/2) = $41.25
Yield to maturity = i
Present value of bond = PB = $911.10
Use the trial-and-error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate.
Try YTM = 9.4%:
= $522.90 + 391.54 ≅ $914.43
The YTM is approximately 9.66 percent. Using a financial calculator provided an exact YTM of 9.656 percent (2 × 4.828%).
So, The yield to maturity on this bond according to the trial-and-error approach is 9.66 percent.
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he system of equations below has no solution.
StartLayout enlarged left-brace 1st row two-thirds x + five-halves y = 15 2nd row 4 x + 15 y = 12
Which equation could represent a linear combination of the system?
a linear combination can be:
(a + b)*(4x + 15y) = a*12 + b*15
How to solve the given system of equations:Here we have the system of equations:
(2/3)*x + (5/2)*y = 15
4x + 15y = 12
To solve the system of equations, we first need to isolate one of the variables in one of the equations, I will isolate x on the second equation.
4x = 12 - 15y
x = (12 - 15y)/4
Now we can replace that in the other equation:
(2/3)*x + (5/2)*y = 15
(2/3)* (12 - 15y)/4 + (5/2)*y = 15
Now we can solve that for y.
2 - (10/4)*y + (5/2)*y = 15
2 = 15
That is a false equation, then we conclude that the system of linear equations has no solutions.
This means that the two lines are parallel lines, then a linear combination can be:
(a + b)*(4x + 15y) = a*12 + b*15
Where a and b are two real numbers.
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Answer:Your answer is
There are no solutions.
Step-by-step explanation:Brainliest Please?
Alex has a bag of marbles. Each marble is red or blue, and the ratio of red to blue marbles is 3 : 5. After Alex adds 10 red marbles to the bag, the ratio of red to blue marbles is 2 : 3. How many blue marbles are in Alex’s bag?
Solving a system of equations we will see that there are 150 blue marbles in the bag
How many blue marbles are in Alex’s bag?We know that initially, the ratio of red to blue marbles is 3:5
This means that if there are 8*n marbles in the bag, there are:
3*n red marbles.5*n blue marbles.Now, when he adds 10 red marbles, the new ratio is 2:3, this means that if now there are 5*m marbles, we have:
2*m red marbles3*m blue marbles.Where we will have two relations, so we have a system of equations:
3*n + 10 = 2*m
8*n + 10 = 5*m
With these two we can find the value of n and m.
To do that, we isolate m in the first equation:
m = (3*n + 10)/2
Now we can replace that in the other equation to get:
8*n + 10 = 5* (3*n + 10)/2
Now we can solve this for n:
2*(8*n + 10) = 5*(3n + 10)
16n + 20 = 15n + 50
n = 50 - 20 = 30
n = 30
And the number of blue marbles is:
5*n = 5*30 = 150
There are 150 blue marbles.
If you want to learn more about systems of equations:
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Oltp systems are designed to handle ad hoc analysis and complex queries that deal with many data items.
a. true
b. false
Answer:
b) It is false
How long is the arc intersected by a central angle of startfraction pi over 2 endfraction radians in a circle with a radius of 4.5 cm? round your answer to the nearest tenth. use 3.14 for pi.
7.1 cm long is the arc intersected by a central angle .
What is length of an arc?
The arc length of a circle can be calculated with the radius and central angle using the arc length formula. Length of an Arc = θ × r, where θ is in radian. Length of an Arc = θ × (π/180) × r, where θ is in degree.Given,
Central angle = π / 2
radius = 4.5 cm
we apply formula of length of arc.
length of the arc = angle × radius
= (π/2) × (4.5 cm)
Now put value of π = 3.14
length of the arc = (3.14 / 2) × (4.5) cm
= 7.065 cm ≈ 7.1 cm
Therefore, 7.1 cm long is the arc intersected by a central angle .
Learn more about length of an arc
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