At the tart of the day, a decorator reted a 3 m ladder | againt a vertical wall o that the foot of the ladder wa | 60 cm away from the bae of the wall. | During the day, the ladder lipped down the wall, cauing | the foot of the ladder to move 80 cm further away from the bae of the wall. | How far down the wall, in centimetre, did the ladder lip? | Give your anwer to the nearet 1 cm. |

Answer:

length = 32.5, Width = 25.5

Step-by-step explanation:

Let x rep the width. Let x plus 7 rep the length.

x + x + 7 = 58

2x=58-7

2x=51

2x/2 = 51/2

x= 25.5

x plus 7 =

= 25.5 + 7

=32.5

✨️Hope that helps✨️

The equation of the function that inputs the number of weeks since the beginning of the semester and outputs the money in his bank account is

Money = 5340 - 356X(weeks)

The table will be as follows:

        Weeks                                 Money

             0                                      5340

             3                                      4272

             7                                      2848

             11                                      1424

             15                                       0

Define an account.

An account in banking is an arrangement whereby a company, typically a financial institution like a bank or credit union, accepts a customer's financial assets and holds them on the customer's behalf at the discretion of the customer.

A financial account, specifically one that covers financial asset claims or liabilities to nonresidents, is a part of a country's balance of payments in macroeconomics. Direct investment, portfolio investment, and reserve assets are broken down by sector and are all parts of the financial account.

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Answer:

B

Step-by-step explanation:

D is the father of J, who is the brother to R and A happens to be his sister.

Therefore, D is the father of J,R and A

Answer:

x = 0; y = -5

x = 9; y = 13

Step-by-step explanation:

y = x² - 7x - 5

y = 2x - 5

Use substitution to set the two right sides equal.

x² - 7x - 5 = 2x - 5

x² - 9x = 0

x(x - 9) = 0

x = 0  or  x - 9 = 0

x = 0  or x = 9

Now for each x value, we find a corresponding y vlaue.

x = 0

y = 2x - 5 = 2(0) - 5 = -5

x = 9

y = 2x - 5 = 2(9) - 5 = 13

Answer:

x = 0; y = -5

x = 9; y = 13

Answer:

(0,-5) and (9,13)

Step-by-step explanation:

Step 1: Set up

Step 2: Solve

 Substitution:

 Elimination:

Answer:

  (d)  x equals the quantity negative 5 times y plus 9 end quantity over 4

Step-by-step explanation:

You want to solve for x: 4x +5y = 9.

This can be treated like any other 2-step equation. First isolate the variable term of interest. Then divide by its coefficient.

  4x = -5y +9 . . . . . . subtract 5y

  x = (-5y +9)/4 . . . . . divide by 4

Answer:

y = 4x - 9

Step-by-step explanation:

y = mx + b

m = (y_2 - y_1)/(x_2 - x_1) = (-17 - (-5))/(-2 - 1) = -12/(-3) = 4

y = 4x + b

-5 = 4(1) + b

-9 = b

y = 4x - 9

The expression 5 × 5 × 5 is expressed using the exponent [tex]5^3[/tex]

The given expression is

5 × 5 × 5

The expression is the mathematical statement that consist of different variables, numbers and mathematical operator.

The power of a number that consider of base number and the exponent.

Therefore the power of a number is the a base number raised to the exponent.

The exponent of the number is defined as the number of times a number is multiplied by itself.

Here the given expression is

5 × 5 × 5 = [tex]5^3[/tex]

Where 5 is the base number and 3 is the exponent

Hence, the expression 5 × 5 × 5 is expressed using the exponent [tex]5^3[/tex]

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you have a fair die, with six faces containing the numbers 1,2,3,4,5,6. are the two events a and b then A and B are exhaustive.

Given

A= { 1,2,4}

B= { 2,3,4,5,6}

C= { 3,4}

D= { 2,4,5}

Solving (a): The mutually exclusive events

These are events that have no common or mutual elements

Events A to D are not mutually exclusive because each of the events have at least 1 common element with one another.

Solving (b): Exhaustive events.

Two events X and Y are said to be exhaustive if:

S= P(X n Y)

i.e. if the sample space equals the intersection of X and Y

For events A to D, we have:

AnB= { 1,2,3,4,5,6}

and the sample space is:

S= {1,2,3,4,5,6}

By comparison;

A n B= S

Hence, A and B are exhaustive.

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Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Step 1: Simplify

[tex]\frac{12}{12} =1[/tex]

Step 2: Multiply by [tex]\frac{1}{3}[/tex]

[tex]1*\frac{1}{3}=\frac{1}{3}[/tex]

Hope this helps! :)

Answer:  |-2|  is greater

Step-by-step explanation:

I hope it's right(Which i'm like 99.9 percent sure it is)

Answer:

|-2| < -4

Step-by-step explanation:

Take the absolute value of -2.

Which is 2.

2 is larger than -4.

If Minstrel Manufacturing incurred total overhead costs of $167,800 during the month, the underapplied overhead was $2,800.

Underapplied overhead arises when the applied overhead is less than the actual overhead incurred.

On the other hand, overapplied overhead suggests that the applied overhead is more than the actual overhead incurred.

Overhead application is the allocation of overhead costs to units of products or jobs using a predetermined application rate.

Predetermined overhead application rate = 150% of direct labor cost

Direct labor cost = $110,000 ($150,000 - $40,000)

Applied overhead = $165,000 ($110,000 x 150%)

Actual overhead = $167,800

Underapplied overhead = $2,800 ($165,000 - $167,800)

Thus, during the month, the company underapplied overhead by $2,800.

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Ximena need to invest $2384 so that account value reach $5,100 in

6 years.

As given in the question,

We have to find Principal ' P'

Given interest rate R = 2.2%

Amount = $5100

time t  = 6 years

Formula used

Amount = P + P( 1 + R%)^t

Putting values in the formula

5100 = P + P (1 + 2.2%)^6

5100 = P ( 1 + (1 + 2.2%)^6)

5100 = P (1 + (1.022)^6)

5100 = P (1 + 1.139)

5100 = P (2.139)

P = 5100/2.139

P = 2384.291 ≈ 2384

Therefore,  Ximena need to invest $ 2384 to reach $5,100 in 6 years with interest rate 2.2%.

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Answer:

P=4470

Step-by-step explanation:

i did it

Answer:

Step-by-step explanation:

3 is 10% of 30. Therefore, the other 27 is the resulting 90% of the whole number of 30.

The ΔSVR ≅ ΔSUT by side angle side property of triangle.

The size of the sides and angles determines whether two or more triangles are congruent. The three sides and three angles of a triangle define its size and shape, accordingly. Two triangles are said to be congruent if their respective side and angle pairs are the same.

Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.

In triangle SVR and triangle SUT

SR = ST (given)

∠RSV = ∠TSU ( Common)

SV = SU (given)

So, the ΔSVR ≅ ΔSUT by SAS property.

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Answer:

66%

Hope this helps! :)

A population has a mean of 180 and a standard deviation of 36. A sample of 84 observations will be taken. The probability that the sample mean will be between 181 and 185 is

Given n(sample size) = 84

Population mean(μ) = 180

Standard Deviation(σ) = 36

Standard error of the mean = σx-bar = σ/√n = 36/√84 = 36/9.165 = 3.927

Standardizing the sample mean we have

Z = (x-bar - μ)/σx-bar = (x-bar - μ)/σ/√n

x-bar = 180

Z(x-bar=185 at point C) = (185 - 180)/3.927 = 5/3.927 = 1.273

Z(x-bar=181 at point D) = (181 - 180)/3.927 = 1/3.927 = 0.254

The area ABCD is the probability that the sample mean will lie between 181 and 185.

The shaded Area ABCD = (Area corresponding to Z = 2 or x-bar = 185) - (Area corresponding to Z = 1 or x-bar = 181)

Area corresponding to Z = 1.273 = 0.898

Area corresponding to Z = 0.254 = 0.598

The shaded Area ABCD = 0.898-0.598 = 0.300

Therefore the probability that the sample mean will lie between 181 and 185 is 0.300.

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Answer:

It will take Ernie 6 hours to do the job by himself

Step-by-step explanation:

Rate x time = job

Burt's rate x time + Ernie's rate x time = 1 job getting completed.

[tex]\frac{1}{3}[/tex](2) + x(2) = 1  To clear the fraction multiply everything by 3

2 + 6x = 3  Subtract 2 from both sides

6x = 1  Divide both sides by 6

x = [tex]\frac{1}6}[/tex]  This is Ernie's rate

The rate is the number of jobs 1 over the number of hours 6, so it will take Ernie 6 hours to do this job by himself

Breakdown of clearing the fraction:

([tex]\frac{1}{3}[/tex])(2) + x2 = 1  Multiply everything by 3 to clear the fraction.

([tex]\frac{3}{1}[/tex])([tex]\frac{1}{3}[/tex](([tex]\frac{2}{1}[/tex]) + (3)(x2) =  (3) (1)

[tex]\frac{6}{3}[/tex] + 6x = 6

2 + 6x = 6

Answer:

y = [tex]\frac{3}{2}[/tex] x - 11

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 ) = (16, 13 ) and (x₂, y₂ ) = (4, - 5 )

m = [tex]\frac{-5-13}{4-16}[/tex] = [tex]\frac{-18}{-12}[/tex] = [tex]\frac{3}{2}[/tex] , then

y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (12, 13 ) , then

13 = 24 + c ⇒ c = 13 - 24 = - 11

y = [tex]\frac{3}{2}[/tex] x - 11 ← equation of line

Volume of the frustum of right circular cone =  271.22 [tex]units^{3}[/tex]

Volume of frustum of right circular cone:

Formula for the Volume of Frustum of Cone (V)= 1/3 πH ([tex]R^{2}[/tex]+Rr+[tex]r^{2}[/tex] )

where,

          H = Height of frustum

          R = Radius of lower base

          r = Radius of top base

According to given question,

       Height of frustum(H) = 25 units

        Radius of lower base(R) = 13 units

         Radius of top base (r) =  5 units

Substituting all the given values in the formula of volume of frustum of cone we will get,

     Volume of frustum of right circular cone(V) =  1/3 πH ([tex]R^{2}[/tex] + Rr + [tex]r^{2}[/tex] )

                                                = 1/3 π ( 13x13 + 13x5 + 5x5)

                                                = 1/3 π ( 169 + 65 +25)

                                                = 1/3 π (259)

                                                = 86.33 π

                                                = 271.22 [tex]units^{3}[/tex]

Volume of the frustum of right circular cone =  271.22 [tex]units^{3}[/tex]

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48 students can fit in one bus.

Given, a group of 234 students are going to see a thanksgiving parade, traveling in 4 busses and 3 vans.

Each bus holds 6 more than 3 times a number a van can hold.

Let the van holds 'x' students

then, bus holds 6 + 3x students

Now, according to the question

4(6 + 3x) + 3x = 234

24 + 12x + 3x = 234

24 + 15x = 234

15x = 234 - 24

15x = 210

x = 210/15

x = 14

So, bus holds 6 + 3x students

= 6 + 3(14)

= 6 + 42

= 48

Hence, 48 students can fit in one bus.

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The solution of linear equation x/6-3 = 2 is given by x=30.

Given the linear equation is,

x/6 - 3 = 2

Solving the linear equation we get,

x/6-3 = 2

x/6-3+3 = 2+3, adding 3 to both sides

x/6 = 5

x = 5*6, multiplying 5 to both sides

x = 30

Hence the solution for the given linear equation is x=30.

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Answer:

$19.43

Step-by-step explanation:

when 5.5 pounds cost $14.74 then 1 pound costs $2.68
because 14.74 divided by 5.5 equals 2.68
To calculate the price of 7.25 you multiply the price for 1 pund by 7.25
7.25 * 2.68 = 19.43

Answer:

b = -3.16

Step-by-step explanation:

3b² + 5 = -25

3b² = -30

b² = -10

b = -3.1623 (5 significant figures)

= -3. 16

Answer:

534.1875

Step-by-step explanation:

7500 ⋅ (1+3.5%)²-7500

534.1875

A)  number of ways in which president is not next to the VP =3628800-725760 =2903040

B) Number of ways =9*9!=3265920

C) number of ways VP is in one end  =2*9!=725760

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.

a)

number of ways to line up 10 members =10! =3628800

number of ways so that VP and president are next to each other =N(consider president and VP as 1 member which can interchange in 2 ways , and now we need to arrange 9 members) =2*9!=725760

therefore number of ways in whcih president is not next to the VP =3628800-725760 =2903040

b)

Number of ways =N(9 choices for left most posiition except VP and arrange rest of 9 persons)

=9*9!=3265920

c)

number of ways VP is in one end =N(choose 1 place out of 2 end for VP and then arrange rest of 9 )

=2*9!=725760

therefore number of ways VP is not at one end =3628800-725760 =2903040

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Answer:

Thus, one of the numbers is 85

Step-by-step explanation:

Answer:

Step-by-step explanation:

If AB and CD are straight lines. Then x is 45 degrees.

Angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Given,

AB and CD are straight lines

The angle at O is 360 degrees which makes complete circle.

Few of the angles are given.

x+x+4x+90=360

6x+90=360

Subtract 90 from both sides

6x=270

x=45 degrees.

Hence the value of x is 45 degrees.

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Answer:

The sum of 6 times a number and 7 turned into an equation would be:

6n + 7

Step-by-step explanation:

I found this out because the term "sum" means addition, and if you are multiplying 6 by a number, you are supposed to simplify the "number" into n. So, that's what I did:

6n + 7

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The store's profit on the video game is $35.

According to the question,

We have the following information:

Elsie bought a video game for $85.00. And the store charges 170% of its cost for the game.

Now, let's take the original price of the video game to be $x.

So, we have the following expression:

170% of x = 85

170x/100 = 85

Using the cross multiplication method:

170x = 85*100

x = 8500/170

x = 50

So, we have the cost of the video game.

Now, we know that the formula to find the profit is as follows:

Profit = Selling price - cost of the product

Profit = $(85-50)

Profit = $35

Hence, the store's profit on the video game is $35.

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