The number of columns is in the title floor before the change in layout is 10
Given that A rectangular tiled floor is composed of 70 square tiles. The rectangular floor is rearranged so that 2 tiles are removed from each columns and 4 tiles are added to each row. After the change in layout, the floor will still have 70 tiles, and still be rectangular asked to find the number of columns in the tile floor before the change in layout.
Let's assume the number of rows is x
The number of columns will be [tex]\frac{70}{x}[/tex]
After the changing, the rows can be x+4
The number of columns will be [tex]\frac{70}{x}[/tex]-2
The equation will be (x+4)([tex]\frac{70}{x}[/tex]-2)=70
⇒[tex]x^{2} +4x-140=0[/tex]
⇒x=10
Therefore,The number of columns is in the title floor before the change in layout is 10
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What is the reciprocal of the divisor 5 1/5 divided by 1/10
The reciprocal of the divisor 5 1/5 divided by 1/10 is 10.
The reciprocal of the divisor: Reciprocal and division of fractions are two different methods. When the numerator and denominator of a fraction are interchanged, then it is said to be its reciprocal. Suppose a fraction is a/b, then its reciprocal will be b/a. A fraction is a numerical quantity that is not a whole number.
The reciprocal of the divisor 5 1/5 divided by 1/10
To the reciprocal of the divisor.
Equation: 5 1/5 divided by 1/10
1st: Flip the 1/10 to become 10/1
2nd: Change division to multiplication
New equation: 5.1/5.10/1
⇒ 50/5
⇒ 10.
The reciprocal of the divisor 5 1/5 divided by 1/10 is 10.
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PLEASE HELP URGENT
If m<4=37°, find m<1,m<2,m<3
i would need a photo of the lines to find the values of other angles
Brianna practices the piano for 30 minutes per day. Write an expression for the number of hours she practices after n days.
Find the number of hours Brianna practices in 2, 4, and 10 days.
(Thank you in advance for helping me)
Answer: 1/2 * n
1 hour of practice in 2 days
2 hours of practice in 4 days
5 hours of practice in 10 days
Step-by-step explanation:
60 minutes=1 hour
30 minutes * 1 hour/60 minutes=
30*1/60=
30/60=1/2 hour.
1/2 * n
1/2 * 2 = 1 hour of practice in 2 days
1/2 * 4 =
4/2 = 2 hours of practice in 4 days
1/2 * 10=
10/2 = 5 hours of practice in 10 days
Can you help solve this problem?
Answer:
22 and 23
Step-by-step explanation:
The first step is to make an equation that models this problem. Since the two numbers are consecutive, make them [tex]x[/tex] and [tex]x+1[/tex].
Since it says three times the larger number is 47 more than the smaller number, that means
[tex]3 (x+1) = x+47[/tex]
[tex]3x+3 = x+47[/tex]
[tex]2x+3=47[/tex]
[tex]2x=44[/tex]
[tex]x=22[/tex]
The smaller number is 22, and the larger number is 23.
Triangle ABC lies on the coordinate plane with vertices located at A(7,6), B(-3,5), and C(-4,9). The triangle is transformed using the rule (x,y) -> (2x,y-3) to create triangle A'B'C'. Select all possible answers for the vertices of triangle A'B'C'.
Question 1 options:
(14,3)
(9,3)
(-6,10)
(-8,6)
(-6,2)
The correct options are (a) , (14,3) , (d), (-8,6) and (e) , (-6,2)
By concept of translation, the coordinates of new triangle A'B'C' are given as follows:
A' (14, 3), B' (-6,2), C (-8, 6).
What is a translation?A translation can be define or represented by a change in the graph of a function, which are done by the means of operations such as multiplication, addition or subtraction either in it’s range(i.e. the values of y) or in it’s domain(i.e. the values of x). Examples are compression of points or shifting left right or bottom up, stretching and reflections over the axis that is the x-axis or the y-axis, or rotations around the origin.
For the given question, the translation rule is given as follows:
(x , y) -> (2x, y-3).
Applying the rule to each point of triangle, we have that:
A': (2(7), 6-3) = (14, 3).
B': (2(-3), 5-3) = (-6, 2).
C': (2(-4), 9-3) = (-8, 6).
Thus, the coordinates of triangle formed i.e. A'B'C' are given as follows:
A' (14, 3), B' (-6,2), C' (-8, 6).
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The complete question is:
Triangle ABC lies on the coordinate plane with vertices located at A(7,6), B(-3,5), and C(-4,9). The triangle is transformed using the rule (x,y) -> (2x,y-3) to create triangle A'B'C'. Select all possible answers for the vertices of triangle A'B'C'.
Question 1 options:
a. (14,3)
b. (9,3)
c. (-6,10)
d. (-8,6)
e. (-6,2)
1/2 of the candles on Claire's birthday cake are pink. 2/10 of the candles are green. The rest are red. What fraction of the candles is red?
Answer:
Step-by-step explanation:
10 would be the total, since 2/10 are green. 1/2 of 10 is 5, so 5 candles are pink. 5+2=7. 10-7=red candles (3), there is ultimately 3 candles that are red.
Jim and Henry have played 41 tennis matches.
Jim has won 23 times.
Henry won the rest.
a) Estimate the probability that Jim wins.
b) Estimate the probability that Henry wins.
Answer:
a) The probability that Jim wins is 0.56.
b) The probability that Henry wins is 0.44.
Step-by-step explanation:
Hope this helps!
When Arjun makes strawberry milk, he adds 90\,\text{mL}90mL90, start text, m, L, end text of milk for every 20\text{ mL}20 mL20, start text, space, m, L, end text of strawberry syrup. Arjun's brother, Eli, adds 180\,\text{mL}180mL180, start text, m, L, end text of milk for every 45\text{ mL}45 mL45, start text, space, m, L, end text of strawberry syrup.
Which strawberry milk has a stronger strawberry taste?
Eli's strawberry milk has a stronger strawberry taste than Arjun.
According to the question we have been given that
Arjun , adds milk = 90ml
in strawberry syrup = 20ml
Eli, adds milk = 180ml
in strawberry syrup = 45ml
We need to find whose strawberry milk has stronger strawberry taste that is we have to find the concentration of the solution.
The formula for the concentration is given as :
Concentration of the solution = [tex]\frac{volume of solute}{volume of solution}[/tex] * 100%
For Arjun,
Volume of solvent = 90ml
Volume of solute = 20ml
Volume of solution = 20+90 ml = 110 ml
Concentration = (20/110)*100%
= 18.18%
For Eli,
Volume of solvent = 180ml
Volume of solute = 45ml
Volume of solution = 180+45 ml = 225 ml
Concentration = (45/225)*100%
= 20%
As we can see that the Eli's concentration of the solution is greater than Arjun's. Hence Eli's strawberry milk has a stronger strawberry taste.
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I’m confused! About this whole thing can someone help me
Answer:
Step-by-step explanation:try using quizlet
51 is a multiple of 2,3,5,6,9,10 or none
Based on the numbers given, we can say that 51 is a multiple of 3.
What is 51 a multiple of?51 is not a prime number which means that it has factors and it is a multiple of several numbers.
The factors of 51 include:
1, 3, 17, and 51
Out of the numbers given of 2,3,5,6,9,10, it therefore means that 51 is a multiple of only one number which is 3. When 3 is multiplied by 17, it gives 51.
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Calculate the coordinates of the points where the line y = 1 - 2x cuts the curve x^2+ y^2 = 2
Answer:
[tex](1, -1)[/tex] and [tex](-\frac{1}{5}, \frac{7}{5})[/tex]
In decimal form this would be (1, -1) and (-0.2, 1.4)
Step-by-step explanation:
Basically here we are trying to solve a system of 2 equations. The first one is a straight line and the second is a circle. This can be done graphically and graph is attached. There will be two points where the line cuts the circle so two solution sets
The equations are
Line Equation [tex]y = 1 - 2x[/tex] (1) and
Circle Equation [tex]x^2+ y^2 = 2[/tex] (2)
[tex]y=1-2x[/tex]
Plug this value of y into the second equation for the circle
[tex]x^2 + (1-2x)^2= 2[/tex]
Apply the perfect squares formula [tex]\left(a-b\right)^2=a^2-2ab+b^2[/tex]
[tex](1-2x)^2 = 1^2-2\cdot \:1\cdot \:2x+\left(2x\right)^2\\= 1-4x+4x^2\\\\[/tex]
So equation (2) becomes
[tex]1-4x+4x^2 +x^2 = 2 \\\\\\5x^2 -4x - 1 = 0[/tex]
Solve using the quadratic formula
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here a is the coefficient of x ², b is the coefficient of x and c is the constant
So
[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:5\left(-1\right)}}{2\cdot \:5}[/tex]
Now,
[tex]\sqrt{\left(-4\right)^2-4\cdot \:5\left(-1\right)} = \sqrt{\left(-4\right)^2+4\cdot \:5\cdot \:1}[/tex]
= [tex]\sqrt{16+20} = \sqrt{36} = 6[/tex]
Therefore
[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \:6}{2\cdot \:5}[/tex]
[tex]x_1=\frac{-\left(-4\right)+6}{2\cdot \:5}[/tex] = [tex]\frac{-\left(-4\right)+6}{2\cdot \:5} =[/tex] [tex]\frac{10}{2\cdot \:5}[/tex] [tex]= 1[/tex]
[tex]x_2 = \frac{-\left(-4\right)-6}{2\cdot \:5}[/tex] [tex]= \frac{4-6}{2\cdot \:5}[/tex] = [tex]-\frac{1}{5}[/tex]
To find corresponding values for [tex]y_1 y_2[/tex] plug these values of [tex]x_1, x_2[/tex] into the line equation
[tex]y_1 = 1- 2(1) = -1[/tex]
[tex]y_2 = 1 - 2(-\frac{1}{5}) = 1 + \frac{2}{5} = \frac{7}{5}[/tex]
So the two points of intersection are
[tex](1, -1)[/tex] and ([tex](-\frac{1}{5}, \frac{7}{5})[/tex].
In decimal form this would be (1, -1) and (-0.2, 1.4)
See attached graph
An online store sells two types of speaker docks for smartphones. The higher-priced speaker dock sells for $190 and the lower-priced speaker dock sells for $80. Last week the store sold three times as many lower-priced speaker docks as higher-priced speaker docks. Combined sales totaled $3,870. How many lower-priced speaker docks did it sell?
Using a system of equations, it is found that it sold 27 lower-priced speaker docks.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: Amount of the lower-priced speaker sold.Variable y: Amount of the higher-priced speaker sold.Last week the store sold three times as many lower-priced speaker docks as higher-priced speaker docks, hence:
x = 3y -> y = x/3.
Combined sales totaled $3,870, hence, considering the price of each speaker:
80x + 190y = 3870.
Since x = 3y:
240y + 190y = 3870.
430y = 3870
y = 3870/430
y = 9.
Hence:
x = 3y = 3 x 9 = 27.
It sold 27 lower-priced speaker docks.
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Find an expression which represents the sum of (3x+9y) and (5x+7y) in simplest forms
The sum of the expression in simplest form is 8( x + 2y)
What are algebraic expressions?Algebraic expressions are expressions made up of variables, terms, factors, constants and coefficients.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc
Given the expressions;
(3x+9y) and (5x+7y)
Let's find the sum
3x + 9y + 5x + 7y
collect like terms
3x + 5x + 9y + 7y
8x + 16y
Find common factor
8( x + 2y)
Thus, the sum of the expression in simplest form is 8( x + 2y)
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The cost of 4 boxes of pens and 3 boxes of pencils is $22.55. The cost of 3 boxes of pens and 2 boxes of pencils is $16.45. Find the cost of each.
Answer:
One pen is $4.25 and one pencil is $1.85.
Step-by-step explanation:
Let cost of pens be x and cost of pencils be y.
1. 4x+3y=22.55
2. 3x+2y=16.45
Sub. 1.-2.,
x+y=22.55-16.45
x=6.1-y
Sub. x=6.1-y into 1.,
y=1.85
x=4.25
Answer:
Cost of a box of pens = $4.25
Cost of a box of pencils = $1.85
Step-by-step explanation:
Given information:
Cost of 4 boxes of pens and 3 boxes of pencils = $22.55Cost of 3 boxes of pens and 2 boxes of pencils = $16.45Define the variables:
Let x = the cost of a box of pens.Let y = the cost of a box of pencils.Create two equations from the given information:
[tex]\textsf{Equation 1}: \quad 4x + 3y = 22.55[/tex]
[tex]\textsf{Equation 2}: \quad 3x + 2y = 16.45[/tex]
Multiply Equation 1 by 3:
[tex]\implies 3 \cdot 4x + 3 \cdot 3y = 3 \cdot 22.55[/tex]
[tex]\implies 12x + 9y = 67.65[/tex]
Multiply Equation 2 by 4:
[tex]\implies 4 \cdot 3x + 4 \cdot 2y = 4 \cdot 16.45[/tex]
[tex]\implies 12x + 8y = 65.80[/tex]
Subtract the equations to eliminate the term in x:
[tex]\begin{array}{r rr}& 12x+9y = &67.65\\- & 12x+8y = &65.80\\\cline{2-3} & y = & 1.85\end{array}[/tex]
Substitute the found value of y into one of the equations and solve for x:
[tex]\implies 3x + 2y = 16.45[/tex]
[tex]\implies 3x + 2(1.85) = 16.45[/tex]
[tex]\implies 3x + 3.7 = 16.45[/tex]
[tex]\implies 3x =12.75[/tex]
[tex]\implies x=4.25[/tex]
Solution
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Antonio is making bread. He has 9/2 cups of flour. Each loaf uses 2/3 cup of flour
How many whole loaves of bread can Antonio make? Will he have flour left over
?
Antonio can make 6 whole loaves of bread, and he will be left with 1/2 cup of flour, which is used to make 3/4th of a loaf.
In the question, we are given that Antonio is making bread. He has 9/2 cups of flour. We are also informed that each loaf uses 2/3 cup of flour.
We are asked for the number of whole loaves of bread that Antonio can make, and also, we are asked whether he will be left with some flour or not. If yes, then how much?
To find the number of loaves Antonio will make, we will divide the quantity he has by the quantity required for one loaf.
Thus, the number of loaves = (9/2) ÷ (2/3) = 9/2 × 3/2 = 27/4 = 6 3/4.
We will ignore the fractional part as we are asked for whole loaves. Thus, we can say that Antonio will make 6 whole loaves.
Also, he will be left with 3/4th of a loaf, that is, 3/4 of 2/3 cup of flour = 1/2 cup of four.
Thus, Antonio can make 6 whole loaves, and he will be left with 1/2 cup of flour, which is used to make 3/4th of a loaf.
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The volume of a rectangular pyramid is 1020 units. If the length of the rectangular
base measures 10 units and the width of the rectangular base measures 18 units, find
the height of the pyramid.
The volume of a rectangular pyramid is 1020 units is 5.67 units
The volume of a rectangular pyramid is 1020 units.
volume of rectangular pyramid = LBH
L= length of the rectangular base
B= width of the rectangular base
H= height of the pyramid
here L= 10units B= 18 units
V= LBH
H=V/(LB)
= 1020/(10)(18)
= 5.67 units
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units or by various imperial units. The definition of length is interrelated with volume
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I need help with this question
The direction of the resultant vector is 58 degrees east-north if the mouse walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m.
What is a vector?It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.
It is given that:
A mouse is trapped in a maze.
He walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m.
Based on the data given:
tanA = 8/(-10+15) = 8/5
A = tan⁻(8/5)
A = 58 degrees
The direction will be 58 degrees east-north
Thus, the direction of the resultant vector is 58 degrees east-north if the mouse walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m.
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Is the following relation linear, quadratic, or cubic? If it is linear, find the equation. Explain your reasoning and include all of your work in your final answer.
p = {( x, y ) : (1, 0), (2, 4), (3, 8), (4, 12), . . . }
Since the rate of change is constant, the relation is linear, and is modeled by:
y = 4x - 4.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that when x changes by 1, y always changes by 4, hence we have a linear relation with a slope of 4, given as follows:
y = 4x + b
When x = 1, y = 0, hence we use it to find b as follows:
0 = 4 + b
b = -4.
Hence the relation is:
y = 4x - 4.
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The triangle has side lengths l,m, and n. Find the length of each side and the perimeter of the triangle. (PLEASE SHOW WORK)
The measure of the sides is 27, 23 and 16 and the perimeter is 56 respectively
The perimeter of a triangleThe triangle is a 2 dimensional shape that has 2 sides.
Given the following sides
l = m + n - 12
n = m - 7
m = l - 1/4n
l = m + 1/4n
Substitute
m + 1/4n = m + m - 7 - 12
m + 1/4(m-7) = 2m - 19
m + 1/4m - 7/4 = 2m - 19
-m + 1/4m = -19 + 7/4
-3/4m = -19(4)+7/4
-3/4m = -69/4
-3m = -69
m = 23
Hence the value of m from the given expression is 23
n = 23 - 7
n = 16
l = 23 + 16 -12
l = 39 - 12
l = 27
n = 23 - 7
n = 16
Hence the measure of the sides is 27, 23 and 16 respectively
Perimeter = 27+23+16
Perimeter = 56
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Carlos read 150 words in one minute. He
read 5 times as many words as his younger
brother. How many words did his younger brother
read in one minute?
Answer:
30
Step-by-step explanation:
150/5 = 30
Answer: 30
Step-by-step explanation:
Please show work, and brainliest will be yours.
the other statements are.
Converse: If it has a perimeter of 10 cm, then the figure is a rectangle with sides of 2 cm and 3 cm (false)Inverse: If the figure is not a rectangle with sides of 2 cm and 3 cm, then it has a perimeter different than 10cm (false)Contrapositive: "If it has a perimeter different than 10cm, then it is not a rectangle with sides of 2cm and 3cm" (true)How to get the converse, inverse, and contrapositive statements?
For a conditional statement of the form:
If P, then Q
The other statements are:
Converse: if Q then PInverse: not P, then not Q.Contrapositive: not Q, then not P.Here the conditional is:
"if a figure is a rectangle with sides 2 cm and 3cm, then it has a perimeter of 10cm"
We can identify:
P = a figure is a rectangle with sides 2 cm and 3cm
Q = it has a perimeter of 10cm
Then the other statements are.
Converse: If it has a perimeter of 10 cm, then the figure is a rectangle with sides of 2 cm and 3 cmThis clearly is false, as we can have a circle with a perimeter of 10 cm.
Inverse: If the figure is not a rectangle with sides of 2 cm and 3 cm, then it has a perimeter different than 10cmThis is also false, the figure can be a rectangle with sides of 1cm and 4 cm for example.
Contrapositive: "If it has a perimeter different than 10cm, then it is not a rectangle with sides of 2cm and 3cm"This is true. if the figure does not have a perimeter of 10cm, then it can't be a rectangle with sides of 2cm and 3cm
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PLEASE HELP !! 51 POINTS !!
Students were asked to simplify the expression the quantity cosecant theta minus sine theta end quantity over cosecant period Two students' work is given.
Student A
Step 1: cosecant theta over cosecant theta minus sine theta over cosecant theta
Step 2: 1 minus sine theta over the quantity 1 over sine theta end quantity
Step 3: 1 − sin2 θ
Step 4: cos2 θ
Student B
Step 1: the quantity 1 over sine theta end quantity minus sine theta over the quantity cosecant theta
Step 2: the quantity 1 minus sine squared theta end quantity over sine theta all over cosecant theta
Step 3: cosine squared theta over sine squared theta
Step 4: cot2 θ
Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)
Part B: Complete the student's solution correctly, beginning with the location of the error. (5 points)
Answer:
Student B
Step 1: the quantity 1 over sine theta end quantity minus sine theta over the quantity cosecant theta
Step 2: the quantity 1 minus sine squared theta end quantity over sine theta all over cosecant theta
Step 3: cosine squared theta over sine squared theta
Step 4: cot2 θ
Step-by-step explanation:
A change in temperature of 6°C is equivalent to a change in temperature of
°F.
The length of a race is 9/10 mile. Andrew wants to place a flag every 1/3 mile. He has
3 flags. Does he have enough flags?
Answer:
Yes, he will have more than enough flags, 1/3*3 flags is 1 mile, the race is only 9/10 miles.
Step-by-step explanation:
10. A chemist needs to mix an 18% acid solution with a 45% acid solution to obtain 12 liters of
36% solution. How many liters of each of the acid solutions must be used?
Answers:
4 liters of the 18% acid
8 liters of the 45% acid
========================================================
Explanation:
Let's call the bottles A and B
Bottle A has 18% acidBottle B has 45% acidx = amount, in liters, of bottle A used
12-x = amount, in liters, of bottle B used
Bottle A has 0.18x liters of pure acid
Bottle B has 0.45(12-x) liters of pure acid
These amounts must add to 0.36*12 = 4.32 liters of pure acid since we want 12 liters of a 36% solution.
So,
0.18x + 0.45(12-x) = 4.32
0.18x + 0.45(12)+0.45(-x) = 4.32
0.18x + 5.4-0.45x = 4.32
-0.27x + 5.4 = 4.32
-0.27x = 4.32 - 5.4
-0.27x = -1.08
x = (-1.08)/(-0.27)
x = 4 liters which is the amount of bottle A needed
12-x = 12-4 = 8 liters is the amount of bottle B needed
--------------------
Check:
Using 4 liters of bottle A means we contribute 4*0.18 = 0.72 liters of pure acid from this bottle alone.
Using 8 liters from bottle B adds another 8*0.45 = 3.6 liters of pure acid
Then, 0.72+3.6 = 4.32 which matches with the 4.32 mentioned earlier. Therefore, the answer is fully confirmed.
Lynn wants to multiply
44
×
305
. She says that all she has to do is find
4
×
305
and then double that number.
Which explains whether or not Lynn's method will give her the correct answer?
Statement (C) "Lynn's method will not give her the correct answer. Multiplying by 4 and then doubling the product is the same as multiplying by 8, not by 44" is the correct explanation of the above-given situation.
What are mathematical operations?An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value. The operation's arity is determined by the number of operands.So, 4 × 305 = 1220
Double of 1220: 1220 + 1220 = 2440Which is equal to: 8 × 305 = 2440and not equal to 44 × 305 = 13420Therefore, statement (C) "Lynn's method will not yield the correct result. Multiplying by 4 and then doubling the result is equivalent to multiplying by 8, not 44 "is the correct explanation for the situation described above.
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The complete question is given below:
Lynn wants to multiply 44 × 305 44×305. She says that all she has to do is find 4 × 305 4×305 and then double that number. Which explains whether or not Lynn's method will give her the correct answer?
A. Lynn's method will give her the correct answer. Multiplying by 4 and then doubling the product is the same as multiplying by 44.
B. Lynn's method will not give her the correct answer. Multiplying by 4 and then doubling the product is the same as multiplying by 6, not by 44.
C. Lynn's method will not give her the correct answer. Multiplying by 4 and then doubling the product is the same as multiplying by 8, not by 44.
D. Lynn's method will not give her the correct answer. Multiplying by 4 and then doubling the product is the same as multiplying by 16, not by 44.
1.Elisa drew a triangle with coordinates (2, 4), (5, 3), and (7, 2). She drew an image of the triangle with coordinates (−1, 4), (2, 3), and (4, 2). Which rule best describes the transformation?
The rule that best describes the transformation is (x, y) = (x - 3, y)
How to determine the rule that best describes the transformation?The points of the triangle have the coordinates
(2, 4), (5, 3), and (7, 2).
The image of the triangle have the coordinates
(−1, 4), (2, 3), and (4, 2)
When the above points and the image are compared, we can see that the y-coordinates remain unchanged
This means that the triangle is translated horizontally
Using points (2, 4) and (-1, 4);
We have
(x, y) = (-1 - 2, 4 - 4)
Evaluate
(x, y) = (-3, 0)
Rewrite as
(x, y) = (x - 3, y)
Hence, the rule that best describes the transformation is (x, y) = (x - 3, y)
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Are test scores a good predictor of the overall grade for a course? A random sample of student grades in an
introductory statistics class was taken. The data are shown.
Test 54 56 36 87 71 69 61 38 72 40
Final 60 60 29 94 76 80 54 26 77 52
The two variables have summary statistics -58.4, -60.8, s. 16.87 and s, -21.89. The formula for the
contribution tor for the first data point is (frac{x (1)-\bar(x)}{s_{x}}) (\frac{y_{1)-\bar(y)s (yl) The value for
y, is
X
The contribution of the first data point, (54, 60) to correlation is given by the option with the equation equation;
[tex] \displaystyle{\left( \frac{54 - 58.4 }{16.87}\right)\cdot \left( \frac{60 - 60.8}{21.89 }\right)}[/tex]What is the formula the correlation coefficient?The correlation coefficient is given by the formula;
[tex]r = \frac{1}{n - 1} \times \sum( \frac{x - \bar{x}}{s_{x} })( \frac{y - \bar{y}}{s_{y} })[/tex]
Where;
(x, y) are the coordinates of a data point.
[tex] \bar{x}[/tex] = The mean for the x-values
[tex]S_{x}[/tex] = The standard deviation of the x-values
[tex] \bar{y}[/tex] = The mean of the y-values
[tex]S_{y}[/tex] = The standard deviation of the y-values
The given parameters are;
[tex] \bar{x}[/tex] = 58.4
[tex]S_{x}[/tex] = 16.87
[tex] \bar{y}[/tex] = 60.8
[tex]S_{y}[/tex] = 21.89
The formula for the contribution of the first data point, (54, 60) to correlation, r, is therefore;
[tex] \displaystyle{\left( \frac{54 - 58.4 }{16.87}\right)\cdot \left( \frac{60 - 60.8}{21.89 }\right)}[/tex]
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Pa answer please, need lang for grade 11 students
Juan is paid 1575 pesos, 1800 pesos, 2137.5 pesos
It is given that Juan Dela Cruz is paid 45 peso for every hour he works for up to 40 hours and 1.5 times i.e. 67.5 pesos for every hour after 40 hours.
The first part asks for Juan's earning if he works 35 hours
Therefore , according to the function,
Juan's pay = 35 x 45 = 1575 pesos
The second part asks for Juan's earning for 40 hours
Therefore, according to the function,
Juan's pay for 40 hours = 40 x 45 =1800 pesos
The third part asks for Juan's earning for 45 hours
Juan's pay for 45 hours according to the function=
67.5h-900 = 67.5 x 45 -900 = 2137.5 pesos
Hence, Juan is paid 1575 pesos, 1800 pesos, 2137.5 pesos
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Challenge Yossi used to have a square garage with 230 ft2 of floor space. He recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side?
with the original length as 15.17 feet and the new length as 18.57 feet, there is an increase of 22.41 % in the length of the garage.
We are given that Yossi has a garage of area = 230 feet²
We know that area of square is:
A = side²
230 = s²
s = √ 230
s = 15.17 feet
Now area is increased by 50 %
New area = 230 + 50% of 230
A' = 230 + 115
A' = 345 feet²
s² = 345
s = √ 345
s = 18.57 feet
Percent increase in length = 18.57 - 15.17 / 15.17 × 100
Percent increase in length = 22.41 %
Therefore, with the original length as 15.17 feet and the new length as 18.57 feet, there is an increase of 22.41 % in the length of the garage.
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