A sandbox has an area of 26 square feet . The length is 6 1/2 feet. What is the width of the sandbox

Answer:

Sₙ = 6 x (1 - 2¹⁰) / (1 - p) = 6 x 1023 = 6138

S'ₙ =2.52

Step-by-step explanation:

sum of this sequence: Sₙ = A₁ x (1 - pⁿ) / (1 - p)

Sₙ: sum of n terms

A₁: initial value 6

p: common ratio 2

n: terms 10

Sₙ = 6 x (1 - 2¹⁰) / (1 - p) = 6 x 1023 = 6138

Is there any mistake in the 2nd question - about the common ratio (-1/2)?

S'ₙ =1 + (-1/2) + 1 x (1 - (1/2)¹⁸)) / (1 - (1/2)) = 1/2 + 2 x  (1 - (1/2)¹⁸)

S'ₙ = 1/2 + 2 x (1 - 1/262144) = 1/2 + 262143/130072= 0.5 +2.02 = 2.52

Answer: Karen's weight = 125 pounds

Step-by-step explanation:

Let Karen's weight be x , this means that John's weight is 3x.

Two times John’s weight = 2(3x)

Two times John’s weight plus Karen’s weight is 875 pounds implies;

2(3x) + x = 875

6x + x = 875

7x = 875

divide through by 7

x = 125

Therefore Karen's weight = 125 pounds

John's weight = 3 x 125 = 375 pounds

Answer:

John weighs 375 pounds, and Karen weighs 125 pounds.

Step-by-step explanation:

The best way to solve this question is to assign the weights to variables.

Let's give variable j to John's weight and k to Karen's.

If John weighs 3 times as much as Karen, j=3k.

If 2x John's weight plus 1x Karen's weight = 875, then 2j + k = 875,

which can also be written as 6k + k = 875 since we established that j=3k and 2*3=6.

Now all we need to do to find k is solve the equation:

6k + k = 875  combine common factors

7k = 875 divide both sides by 7

k = 875/7

k = 125

Now that we know Karen's weight, we can find John's weight by using j=3k.

Plug the now known value of k in:

j=3k

j=3(125)

j=375

Now you have your pair:

j=375, k = 125.

Answer:

there are 8 pigs because each pig has 4 legs. meanwhile, ducks technically by definition, only have 2 legs,wings do not count as legs.

Step-by-step explanation:

so 1 pig=4 legs.

8 pigs =32 legs

so 32+2x=36

To solve the problem, set up a system of equations using the number of pigs and ducks. Solve the system of equations to find the values of 'p' and 'd'. There are 8 pigs and 2 ducks in the farmhouse.

Let's assume the number of pigs is 'p' and the number of ducks is 'd'. Since each pig has 4 legs and each duck has 2 legs, we can set up the equation: 4p + 2d = 36 (since there are 36 legs in total). We also know that there are 10 animals in total, so we can set up another equation: p + d = 10. Now we have a system of equations which we can solve to find the values of 'p' and 'd'.

Multiplying the second equation by 2, we get 2p + 2d = 20. Subtracting this equation from the first equation, we get 4p + 2d - (2p + 2d) = 36 - 20, which simplifies to 2p = 16. Dividing both sides of the equation by 2, we find that p = 8. Substituting this value back into the second equation, we get 8 + d = 10, which means d = 2.

Therefore, there are 8 pigs and 2 ducks in the farmhouse.

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Answer:

B) 6 times

Step-by-step explanation:

54/9=6

Answer:

2 units

Question:

Calculate the distance between (3 + i) and (3 − i).

Step-by-step explanation:

This problem is equivalent to the problem:

"Calculate the distance between the points (3,1) and (3,-1)."

Since the [tex]x[/tex]-coordinates are the same, this is a vertical distance.

A vertical distance be be found by computing the positive difference of the [tex]y[/tex]-coordinates. In other words, we need only the find the distance between the numbers [tex]y=1[/tex] and [tex]y=-1[/tex] on a number line.

This distance is 1-(-1)=1+1=2 units.

Answer:

3/5 0r 0.6

Step-by-step explanation:

A mod B = R

3/5 mod 6, because 3/5 < 6

so (3/5) / 6 = 0 ... R 3/5

Answer:

I could do 1 and 3

1) 2x-3y=-2 ....1

-

2x+y=14......2

=-4y=-16

y=4

Substitute (y=4) into equation 1

2x-3 (4)=-2

2x-12=-2

2x=-2+12

2x=10

×=5

3) 5x+5y=20....1

-

-3x+5y=4......2

=8x=16

x=2

Substitute (x=2) into equation 1

5 (2)+5y=20

10+5y=20

5y=20-10

5y=10

y=2

Answer: (1) x = 5 , y = 4

(2) x = -3 and y = 0

(3) x = 2 and y = 2

Step-by-step explanation:

(1) 2x - 3y = -2  ................... equation 1

   2x + y = 14 ................ equation 2

solving the system of linear equation by elimination method. We need to decide the variable to eliminate first , in this case , since the coefficient of x are the same  and they have the same signs (+), we can eliminate the variable x first by subtracting equation 1 from equation 2, so we have

2x - 2x + y - (-3y ) = 14 - ( - 2)

4y = 16

divide through by 4

y = 4

substitute y = 4 into equation 1 , we have

2x - 3 (4) = -2

2x - 12 = -2

2x = -2 + 12

2x = 10

x = 5

Therefore :

x = 5 and y = 4

(2) x = -6y - 3 ....................... equation 1

    8x + 8y = -24 ....................... equation 2

Solving the system of linear equation by substitution method , substitute x = -6y - 3 into equation 2 , equation 2 becomes

8(-6y - 3 ) + 8y = -24

expanding , we have

-48y - 24 + 8y = -24

-40y - 24 = -24

Add 24 to both sides , we have

- 40y = -24 + 24

-40y = 0

divide through by -40

y = 0/-40

y = 0

substitute y = 0 into equation 1 , equation 1 then becomes

x = -6(0) - 3

x = -3

Therefore : x = -3 and y = 0

(3)  5x + 5y = 20 ........................ equation 1

    -3x + 5y = 4  ............................ equation 2

solving the system of linear equation by elimination method , we have to decide the variable to eliminate first , since the coefficient of y are the same and are both positive, we will eliminate y by subtracting equation 2 from equation 1 , we have

5x - (-3x) + 5y - 5y = 20 - 4

5x + 3x + 0 = 16

8x = 16

x = 2

substitute x = 2 into equation 1 , equation becomes

5(2) + 5y = 20

10 + 5y = 20

5y = 20 - 10

5y = 10

y = 2

Therefore : x = 2 and y = 2

Answer:

Step-by-step explanation:

A = L * W

A = 99

L = 2w + 7

now we sub

99 = (2w + 7)(w)

99 = 2w^2 + 7w

2w^2 + 7w - 99 = 0

(2w - 11)(w + 9) = 0

2w - 11 = 0

2w = 11

w = 11/2

w = 5 1/2 ft (or 5.5 ft) <==== width is 5 1/2 ft)

L = 2w + 7

L = 2(5.5) + 7

L = 11 + 7

L = 18 ft <====== length is 18 ft

Answer:

Step-by-step explanation:

39 cars every 3 hrs.......that means (39/3) = 13 cars every hr

and if its 13 cars every hr....in 7 hrs, there will be (7 * 13) = 91 cars <==

you can either do it that way....the unit rate way...OR

you can set it up as a proportion...

39 cars to 3 hrs = x cars to 7 hrs...

39 / 3 = x / 7....cross multiply

(3)(x)= (39)(7)

3x = 273

x = 273/3

x = 91 <====

either way, u get the correct answer

Answer:

1 1/9  (10/9) meter

Step-by-step explanation:

area of rectangle = width x length

2/3 m² = 3/5 m x Length

Length = (2/3) / (3/5) = 10/9 = 1 1/9

Answer:

10/9

Step-by-step explanation:

1. Let x represent the missing angle.

The sum of angles in a triangle is 180°

65° + 57° +x =180

122° +x=180°

x=180-122

x=68°

2. Let y represent the missing angle.

Then

y+90°+40°=180°

y+130°=180°

y=180°-130°

y=50°

3. Let the missing angle be t, then

t+20°+130°=180°

t+150° =180°

t=180°-150°

t=30°

4. Let the missing angle be m, then

m+85°+50°=180°

m=180°-50°-85°

m=180-135°

m=45°

5. Let the missing angle be e, then by the exterior remote angle theorem:

137°=102° +e

137-102=e

e=35°

6. Let the unknown angle p, be the missing angle.

Then by vertical angle property and exterior angle property:

p=35° +100°

p=135°

7. Let g be the missing angle, then

g+20°+30°=180°

g+50°=180°

g=180°-50°

g=130°

8)

Let v be the missing angle:

By angle on straight line, and exterior angle theorem property,

g=(180-155)+60°

g=25°+60°

g=85°

Answer:

$20,001

Step-by-step explanation:

Let $x be the amount of dollars Lincoln needs to make in sales to earn more than $1500.

His boss pays him $500 for the week, plus a 5% commission on each vehicle he sells.

5% of $x is $0.05x, the Lincoln earns

[tex]\$(500+0.05x)[/tex] in total.

Hence,

[tex]500+0.05x>1,500[/tex]

Solve this inequality:

[tex]0.05x>1,500-500\\ \\0.05x>1,000\\ \\5x>100,000\\ \\x>20,000[/tex]

Lincoln needs to make in sales more than $20,000, so the minimum amount of dollars Lincoln needs to make in sales is $20,001

Answer:

y = -2x + 3

Step-by-step explanation:

4x + 2y - 6 = 0

2y - 6 = -4x

2y = -4x + 6

y = -2x + 3

Answer:

The slope-intercept form is,

y = -2x + 3

Step-by-step explanation:

The given equation of the line is,

4x + 2y  - 6 = 0

Subtracting "(4x- 6)" from both sides of the above equation, we get

   4x + 2y - 6 - (4x - 6) = 0 - (4x - 6)

⇒ 4x + 2y - 6 - 4x + 6 = 0 - 4x + 6

⇒ 2y = -4x + 6

Now, dividing both sides by '2' of the above equation, we get

 2y ÷ 2 = (-4x + 6) ÷ 2

⇒y = -2x + 3

This is the required slope-intercept form of the given line.

The equation is [tex]b=\frac{2A}{h}[/tex]

Step-by-step explanation:

Let us revise how to make a variable subject of an equation

∵ A = [tex]\frac{1}{2}[/tex] × b × h

∵ b is the subject

∴ Multiply the two sides by 2

∴ 2A = b × h

- Divide both sides by h

∴ [tex]\frac{2A}{h}= b[/tex]

- Switch the two sides

∴ [tex]b=\frac{2A}{h}[/tex]

The equation is [tex]b=\frac{2A}{h}[/tex]

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Answer:

Step-by-step explanation:

Answer:

82q

Step-by-step explanation:

-2(-5)q+(-72)(-q)

10q+72q

82q

Hey there! :)

-2(-5)q + (-72)(-q)

Simplify!

10q + (72q)

Since both terms contain "q," we know that we can add them together.

Simply look at it this way: 10+72 , then add the q at the end of your answer.

10 + 72 = 82 --> add the q! Therefore, your final answer is 82q.

~Hope I helped! :)

Answer:

[tex] {x}^{2} + 2x - 15[/tex]

Step-by-step explanation:

[tex]x(x + 5) - 3(x + 5) \\ = \times {x}^{2} + 5x - 3x - 15 \\ = {x}^{2} + 2x - 15[/tex]

Final answer:

To expand and simplify (x - 3)(x + 5), we use the FOIL method, resulting in [tex]x^2 + 5x - 3x - 15[/tex]. Combining like terms, we get the simplified form [tex]x^2 + 2x - 15.[/tex]

Explanation:

To expand and simplify the expression (x - 3)(x + 5), we use the distributive property, also known as the FOIL method, which stands for First, Outer, Inner, and Last. This refers to the terms you multiply together in a binomial multiplication:

First: Multiply the first terms in each binomial: x* x = [tex]x^2[/tex]

Outer: Multiply the outer terms in the binomials: x *5 = 5x

Inner: Multiply the inner terms in the binomials: -3 * x = -3x

Last: Multiply the last terms in each binomial: -3 * 5 = -15

Combining these products gives us: [tex]x^2 + 5x - 3x - 15.[/tex] We then combine like terms, which in this case are 5x and -3x:

[tex]x^2 + 2x - 15.[/tex]

So, the expanded and simplified form of (x - 3)(x + 5) is [tex]x^2 + 2x - 15.[/tex]

Answer:

Measure of Angle 5 = 150 degree.

Step-by-step explanation:

Given line g and h are parallel lines.

Let angle measuring [tex]30\ degree[/tex] be a.

From figure we can see that [tex]\angle a\ and\ \angle 3[/tex] both are Linear Pair Postulate,

i.e. [tex]\angle\ a+\angle 3 =180\ degree[/tex]

So,

[tex]30\ degree +\angle 3 =180\ degree[/tex]

[tex]\angle 3 = 180-30[/tex]

[tex]\Therefore \angle 3=150\ degree[/tex]   ------------(equation 1)

Now, [tex]\angle\ a\ and\ \angle\ 4[/tex] are alternate interior angles, and alternate interior angles are equal.

i.e. [tex]\angle\ a = \angle 4[/tex]

Therefore  [tex]\angle\ 4 =30\ degree[/tex]  ------------(equation 2)

Now, [tex]\angle 4\ and\ \angle 7[/tex] both are Linear Pair Postulate,

i.e. [tex]\angle\ 4 +\angle\ 7 = 180\ degree[/tex]

[tex]30+\angle\ 7=180[/tex]    ------------------(from equation 2)

[tex]\angle\ 7 =180-30[/tex]

[tex]\therefore\ \angle\ 7 = 150\ degree[/tex] ---------(equation 3)

Now,  [tex]\angle\ 7\ and \angle\ 5[/tex] are vertically opposite angles, and vertically opposite angles are equal.

So,

[tex]\angle 7=\angle 5[/tex]

[tex]\therefore\ \angle 5=150\ \ degree[/tex] -----------------(from equation 3)

Answer:

40 min

Step-by-step explanation:

1 x 48 + .20 .48

(1.20) (48)=  40 min

The graph of f(x) is stretched vertically by scale factor 3 and translated 2 units to the right to give the graph of 3f(x - 2)²

Step-by-step explanation:

Let us revise the vertical stretch and the horizontal translation

∵ f(x) = x²

∵ f(x) is multiplied by 3

- 3 is greater than 1, then the graph of f(x) is stretched vertically

  by scale factor 3

∴ The graph of f(x) is stretched vertically by scale factor 3

∵ x² is changed to (x - 2)²

- That means the graph of f(x) translated 2 units to the right

∴ The graph of f(x) is translated 2 units to the right

The graph of f(x) is stretched vertically by scale factor 3 and translated 2 units to the right to give the graph of 3f(x - 2)²

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Answer:

The graph of y + 1 = −3/5 (x − 4) would be a straight line. The graph figure is attached below.

Step-by-step explanation:

As the linear equation y + 1 = −3/5 (x − 4) is given.

Since y-y₁ = m (x - x₁) is the Point-slope form is the general form y-y₁=m(x-x₁) for linear equations.

Hence, from the linear equation we can determine the slop which is m = -3/5

Also, when we put x = 0 in the linear equation, we determine the y-intercept as follows:

                            y + 1 = −3/5 (x − 4)

                            y + 1 = -3/5(-4)      ∵x = 0

                            y = 12/5 - 1

                            y = 7/5

y-intercept: 7/5

Hence,

Table for some points can be made for x and values as:

0           7/5

1            4/5

The graph of y + 1 = −3/5 (x − 4) would be a straight line. The graph figure is attached below.

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Answer:

a, Prospecting cover letter

Step-by-step explanation:

Given:

Dear Ms. Meyer:

Laura Yin suggested I contact you concerning the Marketing position available at Eastern Arbor. I am inspired to  pursue my marketing interests at Eastern Arbor due to its reputation as a prestigious, innovative and growing  company in liability policies.

From the given data;

We can say that it is an E-mail which has been sent to Ms. Meyer regarding the Job opening of Marketing position available at Eastern Arbor.

It was been suggested by Laura Yin to the writing person that there is a Job opening at Eastern Arbor.

The writing person has a marketing interest which he wanted to pursue at Eastern Arbor as it is a reputed company with prestigious, innovative and growing  company in liability policies.

A Prospecting cover letters are introductory in nature. Rather than focusing on your skills and experiences that are related to a job listing (since there is no job listing), a letter of interest should highlight your marketable qualifications and skills that would be easily transferable between a number of positions.

Hence we can say that it is an Prospecting Cover letter.

Answer:

Your answer is A! Prospecting cover letter

Step-by-step explanation:

did the test

Answer:

59°

Step-by-step explanation:

Since the triangle is isosceles then the base angles are congruent.

Subtract the vertex angle from 180° and divide the result by 2, that is

base angle = [tex]\frac{180-62}{2}[/tex] = 59°

13.23  miles

Step-by-step explanation:

The vector creates an inverted right-angled triangle. The westbound car will have covered 20 miles while the southbound car will ahve covered 15 miles in 30 mins;

40 miles /hr * ½ hr = 20 miles

30 miles/ hr * ½ hr = 15 miles

To find the hypotenuse (distance between the two cars), we shall use the formulae;

a² + b² = c²

20² + 15² = c²

c² = 20² – 15²

c² =  175

c = 13.23

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Answer:

Step-by-step explanation:its not a improper fraction

Answer:

1 and 2/9

Step-by-step explanation:

7 goes into 9 1 time and there are 2 left over so that 2 would be 2/9 so it's 1 whole and 2/9

Answer: Yes

Step-by-step explanation: 144 is a perfect square. In other words, it's possible to find a whole number that can be multiplied by itself that gives us 144.

In this case, we multiply 12 by 12 or 12² to get 144 which means 144 is a perfect square. Also, it's on our perfect square list which I will attach below.

Answer:

The range of people who voted for other person = 7266 to 7872

Step-by-step explanation:

A phone survey has a margin error of +/– 4%. The range of number of people who will vote for the other candidate if 87 of 114 people said they would vote for the other person.

We get the percentage from this ,

Percentage = [tex]\frac{87}{114} \times 100[/tex] = 76.3 %

Border percentages = 72.3 and 80.3% (Since error = 4%)

We have already taken vote of 114 people so remaining = 9804

Lower end = 0.723 [tex]\times[/tex] 9804 =  7266

Upper end = 0.803[tex]\times[/tex] 9804 = 7872

Hence the range = 7266 to 7872

Answer: 21

Step-by-step explanation:

9  + 10 = 21

The expression simplifies to 81 over 16 by applying the exponent rules, particularly recognizing that any number to the power of 0 is 1 and when raising a power to a power, we multiply the exponents.

The student's question is asking to simplify the expression 3 to the power of 2 multiplied by 5 to the power of 0 whole over 4, the whole squared. To simplify this expression, we should apply the exponent rules.

Let's simplify step-by-step:

First, recognize that any number raised to the power of 0 is 1.

The expression now  simplifies to square of three, since anything multiplied by 1 remains unchanged.

Now, take the entire expression over 4 and square it as indicated.

Thus, the correct answer is 3 to the power of 4 multiplied by 1 squared over 4 squared equals 81 over 16.

Answer:

x=90

Step-by-step explanation:

x/5=72/4

simplify 72/4 into 18

x/5=18

x=18*5

x=90

The reciprocal of x/5=72/4 is 5/x = 4/72.

Given,

Which of the following uses the reciprocal property to rewrite x/5 = 72/4?

A. 5/x = 4/72

B. x/4 = 5/72

C. x/5 = 72/4

We denote the reciprocal of a number M by 1/M.

Example: 1, 1/2, 2/3,

The reciprocal is:

1 = 1/1 = 1

1/2 = 1/(1/2) = 2

2/3 = 1/(2/3) = 3/2

We have,

x/5 = 72/4

If we apply reciprocal property here we get,

1/(x/5) = 1/(72/4)

5/x = 4/72

Thus the reciprocal of x/5=72/4 is 5/x = 4/72.

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