No this is incorrect. when a triangle undergoes translation, reflection and rotation congruence of the triangle is still maintained however dilation makes the triangle not to be congruent.
What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Transformation is basically of two major divisions
Rigid transformationnon rigid transformationNon rigid transformation are the transformation where the dimension or size of the object will be different from the image, example is dilation
In rigid transformation, the dimensions of the object is maintained through out the transformation examples of rigid transformation are
rotationreflectiontranslationSince the transformation types mentioned are all rigid transformation hence all the angles will remain same
Hence we can say that a triangle's congruence is maintained when it is subjected to translation, reflection, and rotation; nevertheless, dilatation renders the triangle incongruent.
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Could somone help me with this question please
the correct answer is A because 3x1=3
875²-125² factorise the following fully
Answer:
750000
Step-by-step explanation:
Find the equation of the line passing
through the points (4, 2) and (6, 10).
Answer:
y = 4x - 14
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 2 ) and (x₂, y₂ ) = (6, 10 )
m = [tex]\frac{10-2}{6-4}[/tex] = [tex]\frac{8}{2}[/tex] = 4 , then
y = 4x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (4, 2 ) , then
2 = 16 + c ⇒ c = 2 - 16 = - 14
y = 4x - 14 ← equation of line
i don't understand, can someone explain? ¡ 20 pointsss!!!!!
The volume of cone is 324cubic inch, volume of Cuboid volume is equal to 4,080 cubic meter and cylinder Volume is 550 cubic cm
How would you define rounding?
Making a number simpler while maintaining a value that is close to what it was is known as rounding. Although less accurate, the outcome is simpler to utilize. Example: Since 73 is closer to 70 than to 80, 73, when rounded to the closest ten, equals 70. However, 76 rises to 80.
Given: A variety of solid shapes
To determine the volume and surface area of each solid
Solution:
Cone radius = 9 inch.
H height equals 12 inch
15 feet is the slant height.
Volume equals (1/3)πr²h = 324cubic inch.
Round to nearest tenth = 320 sq inch
Surface area equals πr² + πrl = π(81 + 135) sq inch = 679 sq inch
Round to nearest tenth = 680 sq inch
Cuboid volume is equal to 16 x 15 x 17 = 4,080 cubic meter.
Round to nearest tenth = 4,080 cubic meter
Surface area is equal to 2 (15 * 17 + 15 * 16 + 17 * 16) = 1,474 square meter.
Round to nearest tenth = 1,470 square meter
cylinder Volume = πr²h = π(5)² * 7 = π 175 cubic cm = 550 cubic cm
Round to nearest tenth = 550 sq cm
cylinder Surface area is equal to 2πr(r + h ) = 10π (5+7) = 377 sq cm.
Round to nearest tenth = 380 sq cm
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Find the cost to the nearest cent. $72.95 jacket; 4% tax need help what the answer pls
an article suggests the uniform distribution on the interval (8.5, 19) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. (a) what are the mean and variance of depth? (round your variance to two decimal places.)
9.1875 are the mean and variance of depth in random variable.
What is random variable in math?
Any variable whose value is uncertain or any function that values each result of an experiment is referred to as a random variable. A random variable may be continuous or discrete (have a range of values) (any value in a continuous range).The mean of the random variable X is
E(X) =b+a/2
= 19 + 8.5/2
= 13.75
The variance of the random variable X is,
V(X) = ( b - a)²/12
= ( 19 - 8.5 )²/12
= 9.1875
If the random variable X is uniformly distributed on the interval [8.5, 19], then the mean of the random variable X is 13.75 and the variance of the random variable X is 9.1875.
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If it' 50c outide and the temperature will drop 70c in next 3hour, how cold it will get?
The cold will it get if it' 50c outside and the temperature will drop 70c in next 3 hour is -20 c.
Given:
If it' 50 c outside and the temperature will drop 70 c in next 3 hour.
Temperature (cold) = present temperature - temperature in next 3 hour.
= 50 - 70
= -20 c.
Therefore the cold will it get if it' 50c outside and the temperature will drop 70c in next 3 hour is -20 c.
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Graph the points (1,
–
5), (
–
4.5,1), and (3.5,
–
2.5) on the coordinate plane.
The points (1, 5) , (4.5, 1) , (3.5, 2.5) are shown in graph plotted.
What is a Graph?In graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". In a graph the points are plotted using coordinates in the form of (x, y) or (x, y, z) or (r, Ф, z) or (r, θ, Φ) as per need on different types of coordinate graphs.
We have the following coordinates -
(1, 5) , (4.5, 1) , (3.5, 2.5)
The following points are plotted on the graph as shown in the image attached.
For any coordinate -
(x, y)
[x] is plotted along the [x] - axis
[y] is plotted along the [y] - axis
Therefore, the points (1, 5) , (4.5, 1) , (3.5, 2.5) are shown in graph plotted.
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Answer: (1, 5) , (4.5, 1) , (3.5, 2.5)
Step-by-step explanation:
When Ashley left her house in the morning, her cell phone battery was partially charged. Let B represent the charge remaining in Ashley's battery, as a percentage, t hours since Ashley left her house. A graph of B is shown below. Write an equation for B then state the y-intercept of the graph and determine its interpretation in the context of the problem.
B = _____
The y-intercept of the function is ___ which represents
(A) the number of hours until Ashley's phone dies.
(B) the charge of the battery when Ashley left her house
(C) the percentage charge that Ashley's phone loses each hour
(D) the charge of the battery when Ashley woke up.
The y-intercept of the function is 50% which represents; (B) the charge of the battery when Ashley left her house
What is the y-intercept of the Linear Graph?The general format for the equation of a line in slope intercept form is;
y = mx + b
where;
m is slope
b is y-intercept
Now, the y-intercept is defined as the point where the graph line crosses the y-axis or the point at which x is zero.
The slope is defined as the ratio of change of the vertical axis with the horizontal axis.
From the given linear graph, we can see that;
The line intersects the y-axis at y = 50. Thus;
y-intercept = 50
Now, the y-axis represent the percentage charge remaining on the phone battery while the x-axis shows that number of hours since Ashley left her house. Thus;
When the number of hours is zero, the percentage charge remaining on the phone battery is 50%
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How do I do this?? Please help!!
Answer:
Step-by-step explanation:
You need to find the slope of each line to determine if they are parallel. Beginning with AB, you do the formula for slope and get a value of -1/3. Next, you do CD and find it also has a slope of -1/3. Because both of these lines have equal slopes it makes them parallel because they will both be traveling at the same rate and will never get closer or further from each other.
*In order for lines to be perpendicular they need to have inverse slopes
Ex. a slope of 1/2 is perpendicular to a slope of -2
y=x2+6x+7 Which function has the same solutions as the given function?
y=(x+3)2−2
y=(x+6)2−7
y=(x+4)2+3
y=(x+7)2+6
urgent need answers stat!!!!!
Answer: The first one, y = (x + 3)² - 2.
Step-by-step explanation:
To solve this question, we can see that the given function and the answer options are in different equation forms. The given is in standard, but the answer options are in vertex. We will change the given function into vertex form. This is also known as completing the square.
y = x² + 6x + 7
y = (x² + 6x) + 7
y = (x² + 6x + [tex]\frac{6}{2} ^2[/tex] - [tex]\frac{6}{2} ^2[/tex]) + 7
y = (x² + 6x + 9) + 7 - 9
y = (x² + 6x + 9) - 2
y = (x + 3)² - 2
Now, we can see the correct answer option is the first one;
"y=(x+3)2−2"
Rainforests represent 6% of the land on earth, and contain half of all living things. Find the ratio of rainforests to other habitats.
The ratio of the rainforests to other habitats= 3/47
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
Rainforests = 6%Other habitats = 100% - 6% = 94%The ratio would there fore be:6%/94%In fraction:6% = 6/100 = 3/5094% = 94/100 = 47/50= 3/47hence,The ratio of the rainforests to other habitats= 3/47
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pls answer will mark brainliest
Which expression is equivalent to 9x - (x - 8)(x + 1) + 10x?
a. -x^2+19x+8
b. -x^2+26x+8
c. 8x^2+10x+8
d. 8x^2+26x+8
Answer:
x^2+12x-8
Step-by-step explanation:
(x-8)(x+1) = x^2-7x-8
x^2+9x-7x+10x-8
simplify:
x^2+12x-8
Answer: -x^2+26x-8
Step-by-step explanation:
1. Multiply
9x-(x-8)(x+1)+10x
9x-x^2-x+8x-8+10x
2. Combine Like Terms
-x^2+26x-8
Answer: -x^2+26x-8
Age of mother i 4 time the age of her daughter after 8 year the um of their age will be 66 year. Find the age of her daughter and her mother
The age of mother and daughter are 10 and 40 years old, respectively.
Given that,
Mother is 4 times her age. Her daughter's age plus her daughter's age after 8 years equals 66 years.
It can be written into equation as :
Let Mother's age be x
Let daughter's age be y
By using algebra,
x =4y --------> (1)
(x+8) + (y+8) = 66
x+ y = 66-16
x + y = 50--> (2)
Now substitute x = 4y in (2) we get
x + y = 50
4y + y = 50
5y= 50
y = 10 years which means x = 4y = 40 years
Therefore, the age of daughter and her mother is 10 and 40 years respectively.
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Which of the following is NOT an example of a linear equation?
5x + 2zk = 2
2x + 3y = 12
2x = -3
All of the equations given are linear equations
5x + 2zk = 2 Linear equation
2x + 3y = 12 Linear equation
2x = -3 Linear equation
How to determine the function classified as linear equationInformation given in the question include
5x + 2zk = 2
2x + 3y = 12
2x = -3
What is linear function ?A linear function or equation consists of equations where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
m = sw + c
Examining the given equations all of them are of exponents of 1 that is raised to the power of 1. This is how to know linear equations
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Mario's current credit card balance is $2,109.65 with a minimum payment of $68.00. Over the next month, he plans to spend $471.00. If the APR is 31.99%, what will Mario's new balance be, including interest?
$2,512.65
$2,897.25
$2,579.63
$2,784.32
Mario's new credit balance including interest is $2579.63
Given,
Mario's current credit balance = $2,109.65
Minimum payment amount = $68.00
The amount Mario plans to spend over the next month = $471.00
APR = 31.99%
We have to find the new balance including interest.
Monthly interest rate on credit card = APR/12 = (31.99%/12)
The credit balance before interest = (current balance) + (expense for next month) - (minimum payment)
= 2109.65 + 471 - 68
= $2512.65
The credit balance after interest = 2512.65 × (1 + 0.3199/12) = $2579.63
That is,
Mario's new credit balance including interest is $2579.63
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What is the solution to the system of equations y 2 3x 3 x 2?.
The solution of two equations y=(2/3)x + 3 and x=-2 is [tex](-2,5/3)[/tex]
Define an equation .
A mathematical statement that shows that two mathematical expressions are equal.
What is a Subsitution method ?
The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
The given two equations are y=[tex]\frac{2}{3}[/tex]x + 3 and x=-2
So on subsituting x=-2 in another given equation ,we get
y=[tex]\frac{2}{3}[/tex] (-2) +3
=[tex]\frac{-4}{3}[/tex] + 3
On taking LCM both sides ,we get
y=[tex]\frac{(-4+9)}{3}[/tex]
= [tex]\frac{5}{3}[/tex]
Hence ,the solution of the system of equations is (x,y) is ([tex]-2,\frac{5}{3}[/tex])
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Correct question:
What is the solution of two equations y=(2/3)x + 3 and x=-2 ?
The solution of two equations y=(2/3)x + 3 and x=-2 is [tex](-2, \frac{5}{3})[/tex]
Define an equation .A mathematical statement that shows that two mathematical expressions are equal.
What is a Subsitution method ?The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
The given two equations are y = [tex]\frac{2}{3}[/tex]x + 3 and x=-2
So on substituting x=-2 in another given equation ,we get
y = [tex]\frac{2}{3} \times (-2) + 3[/tex]
= [tex]\frac{-4}{3} + 3[/tex]
On taking LCM both sides ,we get
y = [tex]\frac{(-4 + 9)}{3}[/tex]
= 5/3
Hence ,the solution of the system of equations is (x, y) is [tex](-2, \frac{5}{3})[/tex]
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Correct question: What is the solution of two equations y=(2/3)x + 3 and x=-2 ?
What is the answer of 170%,41/25,2,168%,89/50 from least to greatest?
Explanation:
170%,41/25,2,168%,89/50 from least to greatest?
170% = 1.7
41/25 = 1.64
2 = 2
168% = 1.68
89/50 = 1.78
Least to greatest:
41/25 , 168% , 170% , 89/50 , 2
Pleaseeeee helpppppp, i've been trying to solve this for 7 days!!!!
Solution of the given expression (9/4) -2(4x +4/3) +(5/2)x is equivalent to the following one:
-(5/12) - (11/2)x -(5/12) - 8x +(5/2)x (9/4) -2(4x) -2(4/3) + (5/2)xAs given in the question,
Given expression is equal to :
(9/4) -2(4x +4/3) +(5/2)x
Solution of the given expression (9/4) -2(4x +4/3) +(5/2)x is equivalent to the following one:
(9/4) -2(4x +4/3) +(5/2)x
= (9/4) - 2(4x) - 2(4/3) + (5/2)x
Simplify the like terms of the given expression we get,
= (9/4) -(8/3) - 8x + (5/2)x
= (27-32)/12 -8x +(5/2)x
= -(5/12) -8x + (5/2)x
= -(5/12) +((-16+5)/2)x
= -(5/12) -(11/2)x
Therefore, solution of the given expression (9/4) -2(4x +4/3) +(5/2)x is equivalent to the following one:
-(5/12) - (11/2)x -(5/12) - 8x +(5/2)x (9/4) -2(4x) -2(4/3) + (5/2)xLearn more about equivalent here
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Thando divided 1572 by a certain number,and got an answer of 104,remainder 12 what number did she divide 1572
The divisor is 15
What is Dividend Divisor Quotient Remainder Formula?
The dividend divisor quotient remainder formula shows the relationship between the dividend, divisor, quotient, and remainder which is one of the main aspects in the division. The division is a process where a number is divided into equal parts leaving behind a remainder if the number cannot be divided further.
The formula is:
Dividend = Divisor × Quotient + Remainder
Here, Dividend = 1527
let divisor = x, quotient = 104, and remainder = 12
1572 = 104x+12
1560 =104x
x = 1560/104
x = 15
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what is the process for classifying or predicting the value of the target variable of a new observation for given values of predictor variables called?
The process for classifying or predicting the value of the target variable of a new observation for given values of predictor variables called is called scoring a card.
In the given question we have to explain what is the process for classifying or predicting the value of the target variable of a new observation for given values of predictor variables called.
As we know that, a score a card is a statistical model generated using information about the portfolio's past performance. The main advantage of categorizing clients using a statistical scorecard is that it gives the client an accurate numerical forecast of their future behavior.
So, the process for classifying or predicting the value of the target variable of a new observation for given values of predictor variables called is called scoring a card.
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The right question is:
What is the process for classifying or predicting the value of the target variable of a new observation for given values of predictor variables called?
Target value predictingPredicting a recordClassifying a variableScoring a recordWrite the equation of the line in fully simplified slope-intercept form.
Answer:
The equation of the line in fully simplified slope-intercept form is [tex]y=-0.4x-4[/tex]
Step-by-step explanation:
The equation of the line in fully simplified slope-intercept form can be calculated as follows ?
The first step is to calculate the slope [tex]m[/tex] of the given line using the slope formula as follows
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Take two coordinates on the given line
[tex](-5,-2)~ \text{and} ~(5,-6)[/tex]
Substitute [tex]-6[/tex] for [tex]y_{2}[/tex], [tex]-2[/tex] for [tex]y_{1}[/tex], [tex]5[/tex] for [tex]x_{2}[/tex], [tex]-5[/tex] for [tex]x_{1}[/tex] in the slope formula
[tex]m=\frac{-6-(-2)}{5-(-5)}[/tex]
Take out the brackets in the numerator and the denominator at the right side of the equation
[tex]m=\frac{-6+2}{5+5}[/tex]
Simplify the numerator and the denominator at the right side of the equation
[tex]m=\frac{-4}{10}[/tex]
Convert the value of [tex]m[/tex] into decimal
[tex]m=-0.4[/tex]
The second step is to find the slope-intercept form of the given line by the point-slope form formula as follows
[tex]y-y_{1}=m\cdot (x-x_{1})[/tex]
Take any coordinates on the given line, take [tex](-5,-2)[/tex]
Substitute [tex]-2[/tex] for [tex]y_{1}[/tex], [tex]-5[/tex] for [tex]x_{1}[/tex], [tex]-0.4[/tex] for [tex]m[/tex]
[tex]y-(-2)=-0.4\cdot (x-(-5))[/tex]
Take out the inner bracket on the right side of the equation
[tex]y-(-2)=-0.4\cdot (x+5)[/tex]
Take out the bracket on the left side of the equation
[tex]y+2=-0.4\cdot (x+5)[/tex]
Expand the right side of the equation
[tex]y+2=-0.4x -2[/tex]
Substract [tex]2[/tex] from both sides of the equation
[tex]y+2-2=-0.4x -2-2[/tex]
Simplify the equation
[tex]y=-0.4x -4[/tex]
Hence the equation of the line in fully simplified slope-intercept form is [tex]y=-0.4x-4[/tex]
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Solve the following equation:
[tex]7^2^x-4*7^x=5[/tex]
Please explain each step
Answer:
[tex] x = \dfrac{\log 5}{\log 7} [/tex]
Step-by-step explanation:
[tex] 7^{2x} - 4 \times 7^x = 5 [/tex]
[tex] 7^{2x} - 4 \times 7^x - 5 = 0 [/tex]
[tex] (7^x)^2 - 4(7^x) - 5 = 0 [/tex]
This is a quadratic equation in 7^x.
Let u = 7^x.
Substitute u for 7^x to see the quadratic equation more clearly.
[tex] u^2 - 4u - 5 = 0 [/tex]
Now we have a factorable quadratic equation in u.
[tex] (u - 5)(u + 1) = 0 [/tex]
[tex] u - 5 = 0 [/tex] or [tex] u + 1 = 0 [/tex]
[tex] u = 5 [/tex] or [tex] u = -1 [/tex]
Now substitute back 7^x for u.
[tex] 7^x = 5 [/tex] or [tex] 7^x = -1 [/tex]
[tex] 7^x = -1 [/tex] does not have a real solution.
Continue solving [tex] 7^x = 5 [/tex] for x.
Take log of both sides.
[tex] \log 7^x = \log 5 [/tex]
[tex] x \log 7 = \log 5 [/tex]
[tex] x = \dfrac{\log 5}{\log 7} [/tex]
Answer:
[tex]x=\log_75[/tex]
Step-by-step explanation:
Given equation:
[tex]7^{2x}-4 \cdot 7^x=5[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies (7^x)^2-4 \cdot 7^x=5[/tex]
Subtract 5 from both sides:
[tex]\implies (7^x)^2-4 \cdot 7^x-5=0[/tex]
[tex]\textsf{Let \; $u = 7^x$}:[/tex]
[tex]\implies u^2-4u-5=0[/tex]
Factor the quadratic:
[tex]\implies u^2+u-5u-5=0[/tex]
[tex]\implies u(u+1)-5(u+1)=0[/tex]
[tex]\implies (u-5)(u+1)=0[/tex]
Apply the zero-product property:
[tex]\implies u-5=0 \implies u=5[/tex]
[tex]\implies u+1=0 \implies u=-1[/tex]
[tex]\textsf{Substitute back in \; $u = 7^x$}:[/tex]
[tex]\implies 7^x=5[/tex]
[tex]\implies 7^x=-1 \quad \textsf{is not valid as $7^x > 0$}.[/tex]
Therefore, the only valid solution is:
[tex]\implies 7^x=5[/tex]
[tex]\textsf{Apply log law}: \quad a^c=b \iff \log_ab=c[/tex]
[tex]\implies \log_75=x[/tex]
[tex]\implies x=\log_75[/tex]
Determine the length of the line segment shown. line segment from negative 5 comma 5 to 3 comma negative 1 6 units 8 units 10 units 36 units
The line segment from minus 5 comma 5 to minus 3 comma -1 is 10 Units long.
Given,
The line segment from negative 5 comma 5 to 3 comma negative 1
How can I determine a line segment's length?
A line that is divided into two points on a line is referred to as a line segment.
The line segment from 3 comma negative 1 to negative 5 comma 5 is determined by applying the formula;
Square root of (x₂ - x₁)² +(y₂ - y₁)²
= [tex]\sqrt{(3+5)^{2} +(-1-5)^{2} }[/tex]
= [tex]\sqrt{8^{2}+6^{2} }[/tex]
= √100
= 10 units
That is,
The line segment from minus 5 comma 5 to minus 3 comma -1 is 10 Units long.
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graph the equation y=-2/3x+5
Step-by-step explanation: Graph the line using the slope and y-intercept, or two points.
Slope: 2, 3 and the y-intercept: (0,−5)
x | y
0 -5
3 -3
During a 90-minute school play, the main character was on stage 80% of the time. What amount of time in minutes was the main character on stage?
Answer:
D 72
Step-by-step explanation:
90(.8) = 72
The amount of time in minutes that the main character was on stage is D. 72 minutes
What amount of time in minutes was the main character on stage?To determine the amount of time the main character was on stage during the 90-minute school play, we need to calculate 80% of the total duration.
To find 80% of a value, we multiply that value by 0.8 (which is the decimal equivalent of 80%).
In this case, we multiply 90 (the total duration of the play) by 0.8:
90 minutes x 0.8 = 72 minutes
Therefore, the main character was on stage for 72 minutes during the 90-minute school play.
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the car that diana bought is 8 years old. she paid $6,700. this make and model depreciates exponentially at a rate of 14.15% per year. what was the original price of the car when it was new?
The car's initial purchase price when it was brand new is 22711.89 when the vehicle Diana purchased is eight years old. It cost her $6,700.
Given that,
The vehicle Diana purchased is eight years old. It cost her $6,700. The annual rate of depreciation for this brand and model is 14.15 percent.
We have to find what was the car's initial purchase price when it was brand new.
We know that,
The formula is y=A(1-r)ˣ
Here,
y is 6700
r is 0.1415
x is 8
We get,
6700=A(1-0.1415)⁸
6700=A(0.295)
A=22711.89
Therefore, The car's initial purchase price when it was brand new is 22711.89 when the vehicle Diana purchased is eight years old. It cost her $6,700.
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Answer:$22,706.62
Step-by-step explanation: This is the correct answer.
A tutor is starting a business. In the first year, they start with 5 clients and charge $10 per week for an hour of tutoring with each client. For each year following, they double the number of clients and the number of hours each week. Each new client will be charged 150% of the charges of the clients from the previous year. Organize the weekly earnings for each year in a table.
The weekly earning for each year is $135, $520, $2040, $8080
What is expression?Numbers, symbols and operators grouped together that show the value of something.
Given that, a tutor is starting a business. In the first year, they start with 5 clients and charge $10 per week for an hour of tutoring with each client. For each year following, they double the number of clients and the number of hours each week. Each new client will be charged 150% of the charges of the clients from the previous year
The weekly earnings for 1st year are,
q = $10, p = $25, x = 5, (px+q) = $135
The weekly earnings for 2nd year are,
q = $20, p = $50, x = 10, (px+q) = $520
The weekly earnings for 3rd year are,
q = $40, p = $100, x = 20, (px+q) = $2040
The weekly earnings for 4th year are,
q = $80, p = $200, x = 40, (px+q) = $8080
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in a soccer match a tie at the end of two overtime periods leads to a shootout with five kicks taken by each team from the penalty mark. each kick must be taken by a different player. how many ways can 5 players be selected from 11
The number of ways that 5 players can be selected from the 11 eligible players is; 462 ways
The number of ways that the 5 selected players can they be designated as first, second, third, fourth, and fifth is; 120 Ways
What is Permutations and Combinations ?Permutations and combinations are ways of representing groups of objects by selecting them and sub-setting them into sets. It defines different ways of arranging a particular data group. When we choose data or objects from a particular group, it is called a permutation and the order in which they are presented is called a combination. Both concepts are very important in mathematics.
CalculationWe are given that In a soccer match;
A tie at the end of two overtime periods leads to a "shootout" with five kicks taken by each team from the penalty mark.
Each kick must be taken by a different player
Now, to find the number of ways that 5 players can be selected from the 11 eligible players, we will use combination to get;
11C5 = 11!/(5! * (11 - 5)!)
= 11!/(5! * 6!)
= 462 ways
Now, if we care about order or position, we will use permutation to get the number of ways that the 5 selected players can they be designated as first, second, third, fourth, and fifth;
5P5 = 5!/(5 - 5)
= 120 Ways
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Lilianna uses \dfrac{3}{4}
4
3
start fraction, 3, divided by, 4, end fraction calories per minute just by sitting. She uses 111 more calorie per minute by walking. Lilianna uses a total of 12\dfrac{1}{4}12
4
1
12, start fraction, 1, divided by, 4, end fraction calories walking to the park.
Lilianna uses the equation, d\left(\dfrac{3}{4}+1\right)=12\dfrac{1}{4}d(
4
3
+1)=12
4
1
d, left parenthesis, start fraction, 3, divided by, 4, end fraction, plus, 1, right parenthesis, equals, 12, start fraction, 1, divided by, 4, end fraction to represent the situation.
What does the variable ddd represent in the equation?
The variable d in the given equation represents the number of minutes that Lilianna spends walking to the park.
What does the variable d represent?Calories that Lilianna uses by sitting = 3/4
Calories that Lilianna uses by walking = calories used sitting + 1 : 1 + 3/4
Calories that Lilianna uses when she walks to the park = calories used per minute when walking x number of minutes spent walking.
Calories that Lilianna uses when she walks to the park = d(1 + 3/4)
12 1/4 = d(1 + 3/4)
d - 12 1/4 ÷ 1 3/4
d = 49 / 4 x 4/7
d = 7 minutes
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