Given
[tex]\begin{gathered} f(x)=5x \\ g(x)=5x-7 \end{gathered}[/tex]According to rules of transformation:
f(x)+c shift c units up and f(x)-c shift c units down.
For the given function g(x) = 5x-7, 7 is being subtracted from 5x.
Where 5x is represented by f function.
Therefore, we could apply the rules of transformation f(x)-c shift c units down.
Here the value of c is 7.
Answer: g(x) is translated 7 units down from f(x)
What is the median of the data set 4 7 9 10 5 12 6
The median is the value of the data set that separates the sample in halves.
To determine the median of a determined data set, you have to calculate its position.
The given sample has n=7 elements, to determine the position of the median given that the data set is odd, you have to use the following formula:
[tex]\text{PosMe}=\frac{1}{2}(n+1)[/tex]Replace it with n=7
[tex]\begin{gathered} PosMe=\frac{1}{2}(7+1) \\ \text{PosMe}=\frac{1}{2}\cdot8 \\ \text{PosMe}=4 \end{gathered}[/tex]This result indicates that the media is the fourth observation of the data set.
Next, you have to order the data set from least to greatest:
Original data set: 4, 7, 9, 10, 5, 12, 6
Ordered from least to greatest: 4, 5, 6, 7, 9, 10, 12
Once the data set is ordered, you have to count starting from the left until you reach the fourth observation:
O4, 5, 6, 7, 9, 10, 1
The fourth value of the data set is 7, which means that the median of the data set is 7.
Median=7
2
how do i solve (4x^3 + 2x - 3) divided by (x - 3) with long division??
We want to divide 4x³ + 2x - 3 by x - 3 with the long division method
First, we rewrite the polynomial as:
4x³ + 0x² + 2x - 3
Them we divide the first term of the dividend by the highest term of the divisor:
4x²
x - 3 |4x³ + 0x² + 2x - 3
Then we multiply the divisor by this result:
| 4x²
x - 3 |4x³ + 0x² + 2x - 3
4x³ - 12x²
Now we subtract this result from the dividend:
| 4x²
x - 3 |4x³ + 0x² + 2x - 3
4x³ - 12x²
|12x² + 2x - 3
Now we can repeat all the previous steps using the last result as dividend:
| 4x² + 12x
x - 3 | 12x² + 2x - 3
12x² - 36x
|38x - 3
And we repeat these steps once more:
4x² + 12x + 38
x - 3 | 38x - 3
34x - 102
|99
The final term is the remainder
Then, we have:
4x³ + 2x - 3 = (x - 3)*(4x² + 12x + 34) + 99
consider triangle 1 and triangle 2for which value of Q would the two triangles be similar - 136 -105 -75-31
Given:
If the given triangles are similar.
The corresponding angles should be congruent.
Both triangles have the same angle 105 degrees.
The second angle is 31 degrees and q.
[tex]q=31^o[/tex]If triangles are similar then the value of q is 31 degrees.
Is the following relation a function? Justify your answer.
No, because there is an input value with more than one output value
No, because there is an output value with more than one input value
Yes, because each input value has only one output value
Yes, because each output value has only one input value
Answer:
A
Step-by-step explanation:
There are two inputs for one output, which means the relation is not a function.
Answer:
A
Step-by-step explanation:
Assume that a particular professional baseball team has 12 pitchers, 5 infielders, and 8 other players. If 3 players' names are selected at random, determine the probability that 2 are pitchers and 1
is an infielder.
What is the probability of selecting 2 pitchers and 1 infielder?
(Type an integer or a simplified fraction.)
Step-by-step explanation:
Pitchers(p) = 12
Infielders(i) = 5
Others(o) = 8
Total players = 25
Probability(2p and 1i) =
[tex]( \frac{2}{25} ) \times ( \frac{1}{25} ) = ( \frac{2}{625} )[/tex]
Solve the system of linear equations by substitution:x - y = -2 and 3x - y = 2
To solve the system by substitution, isolate one variable from one equation and substitute the expression obtained for that variable into the other equation.
[tex]\begin{gathered} x-y=-2 \\ 3x-y=2 \end{gathered}[/tex]Isolate x from the first equation:
[tex]\begin{gathered} x-y=-2 \\ \Rightarrow x=y-2 \end{gathered}[/tex]Substitute x=y-2 into the second equation:
[tex]\begin{gathered} 3x-y=2 \\ \Rightarrow3(y-2)-y=2 \end{gathered}[/tex]Solve for y:
[tex]\begin{gathered} \Rightarrow3y-6-y=2 \\ \Rightarrow2y-6=2 \\ \Rightarrow2y=2+6 \\ \Rightarrow2y=8 \\ \Rightarrow y=\frac{8}{2} \\ \Rightarrow y=4 \end{gathered}[/tex]Substitute y=4 into the expression of x to find its value:
[tex]\begin{gathered} x=y-2 \\ \Rightarrow x=4-2 \\ \Rightarrow x=2 \end{gathered}[/tex]Therefore, the solution to the given system is:
[tex]\begin{gathered} x=2 \\ y=4 \end{gathered}[/tex]Is this a right triangle?Use the Pythagorean Theorem to find out!20 cm12 cm16 cmYesNo
If this is a right triangle, then the Pythagorean theorem has to be valid.
This means that the sum of the squares of the legs has to be equal to the square of the hypotenuse (NOTE: we can identify the potential hypotenuse by finding the side with the most length).
Then, we calculate:
[tex]\begin{gathered} 12^2+16^2=20^2 \\ 144+256=400 \\ 400=400\longrightarrow\text{True} \end{gathered}[/tex]As the Pythagorean theorem is valid for this side's lengths, we know that this triangle is a right triangle.
Answer: Yes.
Solve this system of linear equations. Separatethe x- and y-values with a comma.6x + 20y = -623x - 9y = -12Enter the correct answerDONE
Given the following systems of linear equations,
6x + 20y = -62 (Equation 1)
3x - 9y = -12 (Equation 2)
Step 1 : Solve 6x+20y=−62 for x:
6x + 20y + (−20y) = −62 + (−20y) (Add -20y to both sides)
6x = −20y −62
6x/6 = (−20y −62)/6 (Divide both sides by 6)
x = (-10y/3) + (-31/3)
Substitute to Equation 2:
3x−9y=−12
3[(-10y/3) + (-31/3)] - 9y = -12
−19y−31=−12 (Simplify both sides of the equation)
−19y−31+31=−12+31 (Add 31 to both sides)
−19y=19
-19y/-19 = 19/-19 (Divide both sides by -19)
y= −1
Step 2: Substitute −1 for y in x =(-10y/3) + (-31/3)
x =(-10(-1)/3) + (-31/3)
x = -7
Answer:
x=−7 and y=−1
Write a rule for the given translation.P(-3,6) to P^1(-4,8)
To turn P(-3,6) to P'(-4,8), we have to
•Move 1 unit to the left (from -3 to -4)
•Move 2 units up (from 6, to 8)
2. Angela is arranging 32 pictures in a photo album. She wants to
have the same number of pictures in each row. How can she
arrange her pictures?
Angela can arrange pictures in 6 different ways; (1 x 32), (2 x 16), (4 x 8), (8 x 4), (16 x 2), (32 x 1).
Given,
Angela have 32 pictures with her.
She wants to arrange it in an album with equal number of pictures in each row.
We have to find the possible arrangements.
Here,
32 pictures.
Lets see the possibilities.
1 row = 32 pictures in a row2 rows = 32/2 = 16 pictures in each row4 rows = 32/4 = 8 pictures in each row8 rows = 32/8 = 4 pictures in each row16 rows = 32/16 = 2 pictures in each row32 rows = 1 picture in each row.That is,
Angela can arrange pictures in 6 different ways; (1 x 32), (2 x 16), (4 x 8), (8 x 4), (16 x 2), (32 x 1).
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Use the triangle to answer the question.Find the sine of angle Y.
In a right triangle, given an angle, the ratio between the opposite side of this angle by the hypotenuse is equal to the sine of the angle. Using this relation in our triangle, we have
[tex]\sin Y=\frac{6}{10}=\frac{3}{5}[/tex]Can I get help, the last tutor didn't help me that much.
We know that
• The volume of one ball is 221 cubic centimeters.
Since the ball is spherical, we can find its radius with the following formula.
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ 221\cdot\frac{3}{4\pi}=r^3 \\ r^3=\frac{663}{4\pi} \\ r=\sqrt[3]{\frac{663}{4\pi}}\approx3.75 \end{gathered}[/tex]The diameter would be double than the radius, by definition.
[tex]d=2(3.75)=7.5[/tex]Since there are three balls in the cylinder, the height would be
[tex]h=3(7.5)=22.5[/tex]Now, we find the volume of the cylindrical package.
[tex]V=\pi r^2h=\pi(3.75)^2(22.5)\approx993.52[/tex]Therefore, the volume of the cylindrical package is 993.52, approximately.If we have a system of two linear equations in two variables that has no solution, what would we see on the graph?
Answer:
The graph will have two lines which will never intersect
Hello! I need some help with this homework question, please? The question is posted in the image below. Q5
ANSWER:
STEP-BY-STEP EXPLANATION:
We can determine the domain and range of the function, knowing that the domain is the interval of values in x and the range is the interval of values in y.
Therefore:
[tex]\begin{gathered} D=\lbrack-5,5\rbrack \\ R=\mleft[-5,\frac{25}{17}\mright] \end{gathered}[/tex]When a function is inverted, the domain and range are inverted, therefore:
[tex]\begin{gathered} D=\mleft[-5,\frac{25}{17}\mright] \\ R=\lbrack-5,5\rbrack \end{gathered}[/tex]Which means that the inverted function goes from -5 to 25/17 in x and from -5 to 5 in y.
In addition to this we must take into account that when the inverse function is done, in most cases a reflection is made in y = x.
The only graph that meets all of the above is graph A
Which of these would not produce a representative sample that determines the favoritesport of the students at the local high school?ask every tenth student from a list of names in the student directoryask every tenth student who arrives at school on Wednesdayask ten students wearing football jerseys each day for a weekask five students from each classroom chosen by picking numbersMy Progress >
Answer: ask ten students wearing football jerseys each day for a week
This sample wouldn't b representative because, the use of a footblla
Section 11 - Topic 5Probability and Independence• In your own words, describe what the word independeyou.Now describe dependent..
In probability , there are two events independent events and dependent events.
Independent Events :
Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur.
Example
. Choosing a marble from a jar AND landing on heads after tossing a coin.
Dependent Events :
If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.
Example
Buying ten lottery tickets and winning the lottery.
find the solution of this system of equations-7y=-34-2x2x+4y=10
we have the system
-7y=-34-2x ------> equation A
2x+4y=10 ------> equation B
In the equation A
Multiply by -1
-2x+7y=34------> new equation A
Adds new equation A and equation B
-2x+7y=34
2x+4y=10
------------------
7y+4y=34+10
11y=44
y=4
Find the value of x
Substitute the value of y in equation A or equation B
2x+4(4)=10
solve for x
2x+16=10
2x=10-16
2x=-6
x=-3
therefore
the solution is the point (-3,4)The table below shows distance as it relates to how many seconds have passed.1510time(seconds)distance, y =y = f(x)(meters)30150 300Write a formula to describe the distance as a linear function of time.
I need help with math. I have a big exam coming up but I do t understand this lesson at all. Can I have help answering all the questions?
Step 1
Given;
[tex]\begin{gathered} Head\text{ represent male} \\ Tail\text{ represent female} \end{gathered}[/tex]The total number of puppies is 4 represented by 4 coins.
Step 2
Find the experimental probability that exactly 3 of the puppies will be female
[tex]\begin{gathered} From\text{ table we find that THTT, TTHT, HTTT and HTTT are the only outcomes that } \\ \text{show exactly 3 females} \\ Remember\text{ tail\lparen t\rparen is for female puppies} \end{gathered}[/tex]Therefore, the total number of samples/coin tosses=20
The formula for probability is;
[tex]Pr\left(event\right)=\frac{Numberofrequiredevent}{Total\text{ number of events}}[/tex]Total number of events =the total number of samples/coin tosses=20
Number of required events= outcomes with 3 T's from the tab;e=4
Hence.
[tex]=\frac{4}{20}=0.2=0.2\times100=20\text{\%}[/tex]Answer;
[tex]\frac{4}{20}=0.20=20\text{\%}[/tex]The population of the county, which follows the exponential growth model,
increased from 491,675 in 2000 to 782,341 in 2010.Write the exponential growth function.
Step 1
Given; The population of the county, which follows the exponential growth model,
increased from 491,675 in 2000 to 782,341 in 2010.
Write the exponential growth function.
Step 2
The exponential function is given as;
[tex][/tex]use properties of operations to write an equivalent expression. will sand image
Use properties of operations to write equivalent expressions
WRITING EQUIVALENT EXPRESSIONS USING PROPERTIES
Commutative Property of Addition :
When adding, changing the order of the numbers does not change the sum. ...
Commutative Property of Multiplication : ...
Associative Property of Addition : ...
Associative Property of Multiplication : ...
Distributive Property :
2.8 w + 5.6
= 2.8 ( w + 2 ) ----------- OPTION B
am I correct? Somone please help
Answer:
≠Step-by-step explanation:
7/5 = 1.4
15/10 = 1.5
so 7/5 is not equal to 15/10
the good answer is ≠Which of the following is true of points on the line y=5/3 x + 1/2? (1) For every 3 units that increases, y will increase by 5 units. (2) For every 5 units that x increases, y will increase by 2 units. (3) For every 2 units that x increases, y will increase by 1 unit. (4) For every 1 unit that x increases, y will increase by 2 units.
4) For every 1 unit that x increases, y will increase by 2 units.
1) For the function y=5/3x +1/2
If we remember that "rise over run" mnemonics, that'll make it easier to memorize it.
2) Plotting the graph of this function. Look at point A (1,2)
Counting from bottom to up (2 units "rise" on the y-axis, point A is 1 unit to right "run". So, For every 1 unit that x increases, y will increase by 2 units.
The length of a rectangle is 5 ft less than double the width, and the area of the rectangle is 33f * t ^ 2 Find the dimensions of the rectangle. length___with____
The length of rectangle is : 6ft .
Width of rectangle is : 5.5ft .
What is an area of rectangle?The area of rectangle is :
A = l × w
Here given,
length is 5ft less than twice the width,
So the equation can be represented in terms of length as,
l = 2w - 5
Given area = 33sqft
By substituting value of length,
33 = (2w - 5) × w
By applying distributive property,
33 = 2w² - 5w
= 2w² - 5w - 33
By factoring the equation:
(2w - 11)(w + 3) = 0
To find value of zeros,
2w - 11 = 0
2w = 11
w = 5.5
Similarly,
w + 3 = 0
w = -3
Since width cannot be negative , the width will be:
the width = 5.5 ft.
Also find length by substituting value of width in equation,
33 = 5.5l
33/5.5 = l
l = 6 ft.
∴ The length = 6ft, and width = 5.5ft.
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proportional relationships, math
The answer is yes, the equation represents a proportional relationship.
The reason is that a proportional relationship is best described as that in which the value of one variable depends on what happens to the other variable. Just like having one more child every year would mean spending more money on education, etc.
In a proportiona; relationship as shown in this question, y is the total cost of a pizza and each x (each topping) would determine how much is y. So requesting for 5 more toppings would result in 1.5 multiplied by 5, and requesting 10 more would result in 1.5 multiplied by 10. So as the amount of toppings (x variable) increases, the total cost (y variable) likewise would increase.
As x increases or decreases, the value of y would likewise increase or decrease. That makes this equation a proportional relationship
Tom Blasting invested $4,500 in an investment paying 10% compounded quarterly for 3 years. Find the interest
Given that Tom invested $4500 in an investment paying 10% compounded quarterly for 3 years.
We have to find the interest for the given time period.
We know that the formula of amount on a principal P, rate r per annum, time t years where interest is compounding quarterly is:
[tex]A=P(1+\frac{r}{4})^{4t}[/tex]Here, P = 4500, r = 0.1 and t = 3. So,
[tex]\begin{gathered} A=4500(1+\frac{0.1}{4})^{4(3)} \\ =4500(1+0.025)^{12} \\ =4500(1.025)^{12} \\ =4500(1.3448) \\ =6051.6 \end{gathered}[/tex]So, the amount we get is $6051.6.
Now, it is known that the interest is the difference between the amount and the principal. So,
[tex]\begin{gathered} \text{ interest}=\text{ amount-principal} \\ =6051.6-4500 \\ =1551.6 \end{gathered}[/tex]Thus, the interest is $1551.6.
? Question
Refer to section 1.3.2, Credit scores, beginning on page 22 of the report.
Arrange the five tiers of credit scores in order, starting with the lowest tier of credit scores.
The five credit score tiers are listed in ascending order, starting with the lowest tier:
Deep Subprime < Subprime < near prime < prime < superprime
The ability of a consumer to get credit may be significantly influenced by their credit score. These interactive graphs demonstrate how lending behavior has changed for different credit score profiles of borrowers.
We concentrate on the following five commercially available credit score levels:
Subprime's credit scores is between 580 to 619.
Prime's credit score level is between 660 to 719.
The credit score level of deep subprime is below 580.
The credit score level of near prime is 620 - 659.
The credit score level of superprime is 720 or above.
Therefore, the five tires of credit scores from lowest to highest are:
Deep Subprime < Subprime < near prime < prime < superprime
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Enter an equation that represents the data in the table. 3 5 10 8 16 10 20 у 6 An equation is y = 6
Given data:
The given table is shown.
The expression for the equation passing through the points (3, 6) and (5, 10) is,
[tex]\begin{gathered} y-6=\frac{10-6}{5-3}(x-3) \\ y-6=\frac{4}{2}(x-3) \\ y-6=2(x-3) \\ y=2x \end{gathered}[/tex]Thus, the equation of the line is y=2x.
write the equation of the line with the points (0,2) and (4,10) standard form
A small college is forming a planning committee from 10 administrators, 16 faculty members, and 9 staff members. In how many ways can a planning committee be formed if there are 3 members from each group?
The number of ways that the planning committee can be formed if there are 3 members from each group is 6545 ways.
What are combinations?Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects. This can be illustrated by ⁿCr
The combination formula is illustrated thus:
ⁿCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time
The number of people will be:
= 10 + 16 + 9
= 35
The number of ways will be:
= ³⁵C₃
= 35! / (35 - 3)! 3!
= 35! / 32! 3!
= 35 × 34 × 33 / 3 × 2
= 6545 ways
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6545 ways can a planning committee be formed if there are 3 members from each group.
What is combination?Combination is a way of selecting items from a collection where the order of selection does not matter.
The formula for combination is ⁿCr = n! / ((n – r)! r!)
Where n is total number of objects and r is number of objects we have to choose.
The committee has 10 administrators, 16 faculty members, and 9 staff members.
The total number of persons
10+16+9
35
Now we need to select 3 persons from 35 persons
n=35 and r=3
³⁵C3 = 35! / ((35 – 3)! 3!)
=35! / ((32)! 3!)
=35×34×33×32! / (32! 3!)
=35×34×33 /6
=6545 ways
Hence in 6545 ways can a planning committee be formed if there are 3 members from each group.
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