Which function depicts f (x)

The prime factor trees of the numbers 90 and 135 will be 2 × 3² × 5 and 3³ × 5.

The corresponding value integer that can be divided by both is known as the lowest relevant multiple, commonly referred to as the lowest common multiple of pair (or more) numerals a and b.

The numbers are given below.

90 and 135

The prime factors of the number 90 will be given as,

90 = 2 × 3 × 3 × 5

90 = 2 × 3² × 5

The prime factors of the number 135 will be given as,

135 = 3 × 3 × 3 × 5

135 = 3³ × 5

The prime factor trees of the numbers 90 and 135 will be 2 × 3² × 5 and 3³ × 5.

More about the least common factor link is given below.

https://brainly.com/question/14875184

#SPJ1

The value of [tex]${ }^5 \mathrm{C}_2$[/tex] is 10.

The Combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In smaller cases, it is possible to count the number of combinations. Combination refers to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection or k-combination with repetition are often used.

A combination is the choice of r things from a set of n things without replacement and where order does not matter.

Here We have to find. [tex]${ }^5 \mathrm{C}_2$[/tex]

[tex]${ }^5 \mathrm{C}_2$[/tex][tex]=\frac{5 !}{2 ! \times(5-2) !}[/tex]

[tex]${ }^5 \mathrm{C}_2$[/tex][tex]& =\frac{5 !}{3 ! \times 2 !}[/tex]

[tex]${ }^5 \mathrm{C}_2$[/tex][tex]& =\frac{5 \times 4 \times 3 !}{2 \times 1 \times 3 !}[/tex]

[tex]${ }^5 \mathrm{C}_2$[/tex][tex]& =5 \times 2[/tex]

[tex]${ }^5 \mathrm{C}_2$[/tex][tex]=10\end{aligned}[/tex]

Therefore, the exact number of [tex]${ }^5 \mathrm{C}_2$[/tex] is 10.

For more such questions on Combinations:

https://brainly.com/question/13387529

#SPJ4

Answer:

many, many answers

Step-by-step explanation:

as we know an avarage is the number in between all given values. so it can be 6.5 and 7.5, 6 and 8 5 and 9, 4 and 10 and so on

If Eugene calculates how long it will take to earn his first million dollars if he earns an average gross pay of $975.00 per week.: D. Yes, Eugene needs to round the years up to the nearest whole number to show the time required to earn the full million dollars.

To determine if Eugene's answer is viable, we need to find how long it will take him to earn his first million dollars at an average gross pay of $975.00 per week.

$1,000,000 / $975.00 per week

= 1025.64 weeks

So, it will take Eugene approximately 1025.64 weeks or approximately 19.71 years (rounded to the nearest year) to earn his first million dollars.

Therefore the correct option is D.

Learn more about  Eugene's answer is viable here:https://brainly.com/question/24481961

#SPJ1

The total cost of boarding their dog including the registration fee is $237.50.

Unit rate is the amount of one quantity for a unit amount of the other quantity.

We have to find the cost of boarding dog for 1 day.

Cost for three days = $97.50

Cost for 1 day = $97.50 / 3 = $32.50

Given that, the Kittle family boarded their dog at the kennel for 7 days.

Cost for 7 days = $32.50 × 7 = $227.50

Also given, owners are also charged a $10 registration fee.

Total cost = $227.50 + $10

                 = $237.50

Hence the total cost is $237.50.

Learn more about Unit Rate here :

https://brainly.com/question/29781084

#SPJ1

The complete question is as follows :

The table show the cost of boarding a dog at a dog kennel. Owners are also charged a $10 registration fee. The Kittle family boarded their dog at the dog kennel for 7 days what was the total, with registration fee, of boarding their dog?

Days    Cost($)

3          97.50

4          130.00

5          162.50

6          195.00

Answer:

138

Step-by-step explanation:

Divide the shaded area to a rectangle and a triangle

Shaded rectangle area = 10 * 12 = 120

Shaded triangle area = (6 * 12)/2 = 72/2 = 36

Area of unshaded rectangle

Shaded area= 120 + 36 - 18 = 156 - 18 = 138

Hope this helps :)

Have a great day!

Examining the figure properly shows that chord AB in the circle has its length to be equal to 16

Information given from the question is interpreted as

let the center of the circle be O

BE = opposite = ?

OE = adjacent = 6

OB = OA = hypotenuse = radius = 10

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

10² = BE² + 6²

100 = BE² + 36

BE² =  100 - 36

BE = √64

BE = 8

Since line OE is the perpendicular bisector, BE = AE

and from the figure AB = BE + AE

= 8 + 8

= 16

Learn more on Pythagoras theorem here:

https://brainly.com/question/29363020

#SPJ1

The product of 1.3 and 0.7 based on the grid is option D 0.91.

Decimals are a form of number in algebra that have an integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number.

According to the grid 1.3 is represented using 13 squares in a row, while 0.7 is represented using 7 squares in column.

The product of 1.3 and 0.7 can thus be calculated by counting all the number of squares in the 13 rows and 7 columns.

The total number of squares in the grid id 91. Since, there are two decimal places we divide 91 by 100.

Thus, the product is 0.91.

The product can be calculated as follows:

(1.3) (0.7) = 0.91

Hence, the product of 1.3 and 0.7 is 0.91.

Learn more about decimals here:

https://brainly.com/question/548650

#SPJ1

The number of 3s that will be rolled when dice is rolled 360 times will have a standard deviation of 7.1.

The standard deviation (or ) is a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

The average degree of variability in your data set is represented by the standard deviation. It reveals the average deviation of each score from the mean.

Let X = the total number of 3s produced by rolling the die 360 times. As a result, the number of 3s that will be rolled will have a standard deviation of 7.1.

To learn more about standard deviation visit the link:

https://brainly.com/question/475676

#SPJ1

The general solution of the differential equation is y(x) = (c1 + c2x)e^(-x) + (1/5)e^(-x)(sin(ex) - (cos(ex)/e^x))

To solve the differential equation y'' + 3y' + 2y = cos(ex) using variation of parameters, we first need to find a particular solution of the form yp = u(x)e^(rx), where u(x) is a function of x and r is a constant.

The characteristic equation of the homogeneous equation is r^2 + 3r + 2 = 0, which has roots r1 = -1, r2 = -2. Thus, the general solution of the homogeneous equation is yh = c1e^(-x) + c2e^(-2x).

To find a particular solution, we use the method of variation of parameters. Let yp = u(x)e^(-x), where u(x) is a function of x. Then, y'p = u'(x)e^(-x) - u(x)e^(-x) and y''p = u''(x)e^(-x) - 2u'(x)e^(-x) + u(x)e^(-x).

Substituting yp, y'p, and y''p into the original equation and simplifying, we get:

u''(x)e^(-x) - 2u'(x)e^(-x) + u(x)e^(-x) = cos(ex)

We can solve for u(x) by dividing both sides of the equation by e^(-x)

u''(x) - 2u'(x) + u(x) = cos(ex)e^x

Now we need to find W(x) = W(y1,y2) = e^(-x)e^(-2x) = e^(-3x)

Integrating W'(x) cos(ex)e^x dx = -(1/5)e^(-x)(sin(ex) - (cos(ex)/e^x))

Hence we get the  general solution of the differential equation is

y(x) = (c1 + c2x)e^(-x) + (1/5)e^(-x)(sin(ex) - (cos(ex)/e^x))

Learn more about differential equation

brainly.com/question/17651356

#SPJ4

Using percentage profit formula, the selling price must be $24.8

Profit percentage is calculated by dividing the net profit by the total revenue and multiplying it by 100. For example, if a business has a net profit of $50,000 and total revenue of $500,000, its profit percentage is 10%.

The initial cost of the desert can be calculated using the formula of percentage profit.

percentage profit = [(selling price - cost price) / cost price] * 100

87.5 / 100 = 24 - x / x

0.875 = 24 - x / x

0.875x = 24 - x

24 = 1.875x

x = 12.8

The cost price is 12.8

The profit will be = 24 - 12.8 = 11.2

In order to keep making same percentage profit with the new cost of production.

Selling price = 11.2 + 13.60

Selling price = 24.8

The selling price is $24.8

Learn more percentage profit here;

https://brainly.com/question/19104371

#SPJ1

Answer:

is 9

Step-by-step explanation:

If a research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The minimum sample size required for the estimate is: 374.54.

n=((z⍺/2×sigma)/E)^2

Confidence interval ,c =90%

Maximum error, E =0.17

Variance, sigma^2=4

Z-score for 90% confidence interval=1.645

sigma=√4

sigma =2

Sample size = ((1.645×2)/0.17)^2

Sample size = 374.54

Therefore the sample size is 374.54.

Learn more about sample size here:https://brainly.com/question/28583871

#SPJ1

The height of the object after 3 seconds is 73.5 meters

A model function is a way of describing a real-life system or situation using mathematical concepts and language

Since the equation for the height of the object is given by:

s(t) = -4.9t² + 19.6t + 58.8 and t is the t in seconds

Thus, in order to find the height of the object after 3 seconds, you need to substitute  t = 3 into the equation. That is:

s(t) = -4.9t² + 19.6t + 58.8

s(t) = -4.9×(3)² + 19.6(3) + 58.8

s(t) = 73.5 meters

Learn more about model function on:

brainly.com/question/1415456

#SPJ1

A line segment is a straight line of points that start at one point and end at another point. A Line segment AB is written down as AB'.

In geometry, the line segment is edged by two definite points on a line. In another word, we can a segment of a line is part of the line that joins two points.

A line has no terminal points and expands limitlessly in both directions but a line segment has two definite endpoints. The dissimilarity between a line segment and a ray is that a ray has only one endpoint and its other end extends infinitely.

Read more about line segment:

https://brainly.com/question/17374569

#SPJ4

The easiest way to learn about angles depends on the individual learner, methods like Visualization, Practice Problems, and Hands-on activities can be utilized.

Learn more about the easiest way to learn an angle here: https://brainly.com/question/29211013

#SPJ4

The value of k could be 2 by using the given expression  B  = kG.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables, constants.

Given ,

the number of boys in each class varies directly with the number of girls. in one class there are 14 boys and 7 girls.

using b=kG

So here we have to find the value of k.

From the given expression

that is ,

B = kG

where by substituting the given values ,

we get,

14 = k * 7

k = 14/7

k = 2

Hence, The value of k could be 2 by using the given expression B  = kG.

To learn more about Algebraic expression from the given link.

brainly.com/question/953809

#SPJ1

Answer:

1/3

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

1 1/3 = 4/3        4 = 4/1

4/3  /  4/1     = 4/3  X 1/4  =  4/12 = 1/3

The amount of water and sugar he needs respectively to make 5% syrup are; 4.75 lbs and 0.25 lbs

Algebraic word problems are defined as questions that require translating sentences to equations, and then solving those equations. and a single variable.

Now, we are told that Anton wants to make 5 lb of sugar syrup. To get the amount of sugar that he needs to make 5% syrup. Thus;

Let x represent the number of pounds of sugar he needs to make 5% syrup

Thus;

x/5 = 5%

x/5 = 0.05

Multiply both sides by 5 to get;

x = 0.25

Thus, he needs 0.25 lbs of sugar and amount of water required = 5 - 0.25 = 4.75 lbs of water

Read more about Algebra Word Problems at; https://brainly.com/question/13818690

#SPJ1

Answer:

∠HKJ = 180 (STRAIGHT ANGLE)

∠HKI = 180-106 = 74

After the dilation, the coordinates will become (- 9, 12).

Given is the coordinate of point (- 3, 4).

The given coordinate is -

(-3, 4)

After the dilation, the coordinates will become -

(x, y) → (Kx, Ky)

The coordinates after the dilation will be -

(3 x - 3, 3 x 4)

(- 9, 12)

Therefore, after the dilation, the coordinates will become (- 9, 12).

To solve more questions on dilation, visit the link below -

https://brainly.com/question/2859427

#SPJ1

Total possible ways that they can sit around a circular table if all the members of each party all sit next to each other are equals to 14,400.

We have , A Senate committee,

Total Democrats = 5

Republicans = 5

We have to calculate the number of ways

can they sit around a circular table if each member sits next to two members of the other party.

We can use counting principle, which helps to count all the possible outcomes and the total possible ways different events can be occur. For this ,choose any 5 consecutive seats to place the Democrats, it doesn't matter which 5 consecutive seats that we choose, since we can rotate the table. Then there are 5 ways to place first member out of 5 democrats. The places available for 2nd member is 4 i.e 4 ways , similarly total ways to place the democrats in their seats. Thus, the Democrats occupy the other 5 seats and they can be arranged in the same muber of ways = 5! = 120 ways. Similarly, total ways to arrange the 5 republicans are 5! = 120 ways. So, the total arrangemets ways are (i.e Ways to arrange the Republicans) x ( Ways to arrange the Democrats) equals to 120 x 120 = 14,400.

To learn more about counting principle, refer:

https://brainly.com/question/29774420

#SPJ4

Complete question:

A Senate committee has $5$ Democrats, $5$ Republicans, and $1$ Independent. In how many ways can they sit around a circular table if all the members of each party all sit next to each other? (Two seatings are considered equivalent if one is a rotation of the other.)

Answer:

Square root of 85

Step-by-step explanation:

Answer:

Step-by-step explanation: (Don't read this if you are taking a test, please! I don't want you to get in trouble!)

The formula to find a hypotenuse is a^2 + b^2 = c^2 (a squared plus b squared = c squared).

The hypotenuse is the diagonal leg (line WH).

The line WJ = 7, and the line JH = 6.  Let's make line WJ a, and line JH b.

7^2 + 6^2 = c^2.  When you square a number, you multiply that number by itself.  7x7 + 6x6 = c^2.  7x7 = 49 and 6x6 = 36.  Now you have 49 + 36 = c^2

49 + 36 = 85.  85 = c^2.  Square root both sides.  The square root of 85 = the square root of c^2 (c). c = 9.21954446.  If you have to round the hypotenuse to the nearest hundredth, then your answer is 9.22.  The answer for the length of the hypotenuse is 9.22

I hope this helps, but please don't use this on a test!

Midpoints are A(a, b), B(a+c, b+d), C(2c, d), D(c, 0)

slope AB = slope DC = d/c

slope AD = slope BC = b/(a-c)

Given that Quadrilateral R S T V is in a coordinate plane with vertex and R(0, 0), S(2a, 2b), T(2c, 2d), V(2c, 0).

A is the midpoint of RS, B is the midpoint of ST

C is the midpoint of TV, and D is the midpoint of RV

The midpoint M of segment PQ:

M = (P +Q)/2

A = (R +S)/2 = ((0, 0) +(2a, 2B))/2 = (a, b)

B = (S +T)/2 = ((2a, 2b) +(2c, 2d))/2 = (a+c, b+d)

C = (T +V)/2 = ((2c, 2d) +(2c, 0))/2 = (2c, d)

D = (R +V)/2 = ((0, 0) +(2c, 0))/2 = (c, 0)

The slope of various segments can be found using the slope formula:

m = (y2 -y1)/(x2 -x1)

So, the slopes of the various segments are ...

slope of AB = (b +d -b)/(a +c -a) = d/c

slope of DC = (0 -d)/(c -2c) = -d/-c = d/c . . . . same as slope AB

slope of AD = (0 -b)/(c -a) = -b/(c -a) = b/(a-c)

slope of BC = (d -(b+d))/(2c -(a+c)) = -b/(c -a) = b/(a-c) same as slope AD

Pairs of opposite sides of ABCD are parallel, so quadrilateral ABCD is a parallelogram.

To know more about Midpoint and slopes:

https://brainly.com/question/14370013

#SPJ4

It would take Jay 21 minutes to clear the driveway of the snow working alone.

What is factorization ?

In math, factorization is when you break a number down into smaller numbers that, multiplied together, give you that original number. When you split a number into its factors or divisors, that's factorization. For example, factorization of the number 12 might look like 3 times 4.

Have given the equation ,

[tex]\frac{1}{j} +\frac{1}{j+21} = \frac{1}{14} \\\frac{j+21+j}{j(j+21)} = \frac{1}{14} \\\\\frac{2j+21}{j^{2}+21j } = \frac{1}{14} \\\\28j+391 = j^{2}+21j\\ j^{2}-7j-391=0\\ j^{2}-21j+14j-391=0\\[/tex]

j(j - 21) +14(j - 21) = 0

(j - 21) (j + 14) = 0

j - 21 = 0                  ,   j + 14 = 0

j = 21                         ,   j = -14

The value of j cannot be negative, because of the context.

So, it would take Jay 21 minutes to clear the driveway of the snow working alone

To learn more about factorization visit : brainly.com/question/14209188

#SPJ4

Answer:

Step-by-step explanation:

21 min PLATO

The outer perimeter of the figure is calculated as 62.84m

Perimeter is the distance around the edge of a shape. It is the sum of all the sides of a shape.

Perimeter is the total length of the outside boundary of a shape. It is calculated by adding up all of the sides of the shape.

In this problem, we already have the values given to us and we simply need to compute them.

a) P = 18.84m

b) 12m + 12m = 24m

c) 10m + 10m = 20m

The total outer perimeter of the figure is calculated as

P = 18.84 + 24 + 20 = 62.84m

Learn more on perimeter here;

https://brainly.com/question/19819849

#SPJ1

The last option is equivalent to the slope of the linear function and this is given by

2/5

A linear function consists of functions 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.

y = mx + c

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

the slope, m is calculated using the formula

m = (y₀ - y₁) / (x₀ - x₁)

The value of the slope is constant for a linear function

Learn more about slope of linear functions at:

https://brainly.com/question/29323505

#SPJ1

A frequency table is a form of data presentation that shows the number of occurrences of each value of the variable being studied. It can be used to show the average value of the variable, the intensity of the variable, and the number of times a certain value appears.

A frequency table is a data presentation tool that is used to show the number of occurrences of each value of a variable being studied. It is often used to show the average value of a variable, the intensity of a variable, and the number of times a certain value appears. To construct a frequency table, you first need to list all the possible values of the variable that you are studying. Next, count the number of occurrences of each value, and then list this count for each value. You can then use this data to calculate the average value of the variable, the intensity of the variable, and the number of times a certain value appears. Additionally, frequency tables can be used to show the times per second variations occur in various wave bands.

Learn more about variable here

brainly.com/question/29583350

#SPJ4

By solving an equation for general taxes, we will find that the percent sales tax on the pair of sneakers is 5%.

We know that for an object with a price P, and a tax of X (where X is in a percentage) the price after the tax is:

P' = P*(1 + X/100%)

Here we know that the initial price is $48 and the price after tax is $50.40, so we will get:

$50.40 = $48*(1 + X/100%)

Now we can solve this for X.

($50.40/$48) = 1 + X/100%

(($50.40/$48) - 1)*100% = X

5% = X

So the percent sales tax is 5%.

Learn more about taxes by reading:

https://brainly.com/question/26316390

#SPJ1

Answer:

Step-by-step explanation:

t