Mr. Cole packed 20 pounds into a suitcase, and Mrs. Cole packed 23 pounds into the same suitcase. They then had to remove 8 pounds because it was too heavy. How many pounds was their suitcase after making it lighter?

Answer:

77.5

Step-by-step explanation:

Its rising at a constant rate between +10-15 each hour, so we if we were to add 25 or so to the 50, it would be close to 77.5, so I would assume the answer was B

Answer:

(-4,-1)

Step-by-step explanation:

We are given T(1,2)=(-1,1) and T(1,-1)=(2,3) and T is a linear transformation.

This implies for scalars a and b that

T(a(1,2)+b(-1,1))=aT(1,2)+bT(-1,1)

T((a,2a)+(-b,b))=a(-1,1)+b(2,3)

T((a-b,2a+b))=(-a,a)+(2b,3b)

T((a-b,2a+b))=(-a+2b,a+3b)

This means we should be able to solve the system below to find a and b for T(3,3):

a-b=3 and 2a+b=3

Add equations to eliminate b and solve for a:

3a=6

Divide 3 on both sides:

a=2

If a-b=3 and a=2, then b=-1.

Plug in a=2, b=-1:

T((a-b,2a+b))=(-a+2b,a+3b)

T((2--1,2×2+-1)=(-2+2×-1,2+3×-1)

T(3,3)=(-4,-1).

Answers:

a = 2

b = 3

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Explanation:

Plug in x = 0 and y = 2 to find that

y = a*b^x

2 = a*b^0

2 = a*1

2 = a

a = 2

Then plug in x = 3 and y = 54 to determine the value of b

y = a*b^x

y = 2*b^x

54 = 2*b^3

2b^3 = 54

b^3 = 54/2

b^3 = 27

b = (27)^(1/3)

b = 3

So we have y = a*b^x update to y = 2*3^x

Answer:

Since, mean of 200 items was 50 and number of items =200

So, mean =50

Also, we know mean = number of itemssum of items

∴50=200sum of items

Sum of items = 200×50=10000

Later on, it was discovered that the two items were misread as 92 and 8 instead of 192 and 88 respectively

Then  misread         instead         Correct item

             92                   192              192-92=100

              8                     88               88-8=80

∴ Correct sum of items =10000+180=10180

∴ Correct mean = number of items/sum of items

=10180/200 =50.9

Answer:

Hello,

203.6

Step-by-step explanation:

Sum of the item first= 50*200=10000

new sum is 10000+(192-92)+(88-8)=10180

New mean=10180/200=50.9

Answer:

-7 degrees

Step-by-step explanation:

the temperature was 16 degrees then was the decrease by 23 degrees so subtract 23 from 16 and the answer is -7

Answer:

-1.25

Step-by-step explanation:

you first have to cross multiply

12(b-1)=4(7b+2)

12b-12=28b+8

group the like terms

12b-28b=8+12

-16b/-16=20/-16

b= -1.25

I hope it helps

Step-by-step explanation:

Answer is in the picture..

hope it helps

Answer:

7 and 4

Step-by-step explanation:

when you multiply 7×4 the answer is 28 and when you add them the answer is 11.

I hope this helps

Answer:

4 and 7

Step-by-step explanation:

xy = 28 ..........1

x + y = 11........2

x = 11 - y.........3

substitute 3 in 1:

(11 - y)*y = 28

-y² + 11y - 28 = 0

y² - 11y + 28 = 0

( y - 7)( y - 4) = 0

y = 7 or y = 4

subs in 2:

x = 4 or x = 7

pairs: (4 ; 7) and (7 ; 4)

Answer:

To maximize the monthly rental profit, 90 units should be rented out.

The maximum monthly profit realizable is $38,200.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, y_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

[tex]y_{v} = -\frac{\Delta}{4a}[/tex]

Where

[tex]\Delta = b^2-4ac[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].

In this question:

Quadratic equation with [tex]a = -12, b = 2160, c = -59000[/tex]

To maximize the monthly rental profit, how many units should be rented out?

This is the x-value of the vertex, so:

[tex]x_{v} = -\frac{b}{2a} = -\frac{2160}{2(-12)} = \frac{2160}{24} = 90[/tex]

To maximize the monthly rental profit, 90 units should be rented out.

What is the maximum monthly profit realizable?

This is p(90). So

[tex]p(90) = -12(90)^2 + 2160(90) - 59000 = 38200[/tex]

The maximum monthly profit realizable is $38,200.

Answer:

A

Step-by-step explanation:

It just makes the most sense

Answer:

Each kids weight in a chart

Step-by-step explanation:

I chose this because its the most organized way of doing that

Answer:

x = -5/2 y +25/2

Step-by-step explanation:

5y + 2x = 25

Subtract 5y from each side

5y + 2x -5y= -5y+25

2x = -5y +25

Divide by 2

2x/2 = -5y/2 +25/2

x = -5/2 y +25/2

Answer:

6

Step-by-step explanation:

200. Move decimal twice to the left. 1% of 200 is 2. 2*3 is 6.

Answer:

18

Step-by-step explanation:

7-5=2

2x9=18

36 different value meal packages are possible

Step-by-step explanation:

To answer this question, multiply all given numbers together.

4*3*3

12*3

36

Answer: 18.75 lb.ft

Step-by-step explanation:

Given

Force required to stretch spring 8 in. is 18 lb

it can be written

[tex]\Rightarrow F=kx\\\Rightarrow 18=k(8)\\\\\Rightarrow k=\dfrac{18}{8}=\dfrac{9}{2}\ lb/in.[/tex]

Work done in stretching from its natural length to 10 in.

[tex]\Rightarrow W=\dfrac{1}{2}kx^2\\\\\Rightarrow W=0.5\times \dfrac{9}{2}\times (10)^2\\\\\Rightarrow W=225\ lb.in.\ or\\\Rightarrow W=18.75\ lb.ft[/tex]

Ans; 7× [2-6 { 1+66}] —> 7× [2 - 6 { 67} ] —> 7× [2-402] —> 7×[- 400] —> = – 2800

I hope I helped you ^_^

9514 1404 393

Answer:

  (2x -11)(x -1)

Step-by-step explanation:

The middle term can be rewritten as a sum using the coefficients of the first and last terms. Then the expression can be factored by pairs of terms.

  2x^2 -13x +11 = 2x^2 -2x -11x +11 = 2x(x -1) -11(x -1)

  = (2x -11)(x -1)

Note: you may need to delete the comma

============================================================

Explanation:

The info "5 months" is never used to compute the mean. We could easily replace it with "6 months" or "7 months" or any stretch of time, and still get the same answer. So we'll ignore this value.

What we'll do is add up the 21 items given to us, and then divide by 21.

Because there are so many values, and it's easy to get lost, I'm going to add up across the rows

Those subtotals then add up to this

1,499,116+1,586,126+1,591,076+842,147 = 5,518,465

This is the same as adding up all 21 values.

Finally, we divide that sum over 21 as there are 21 values in this list

(5,518,465)/21 = 262,784.047619048

That value then rounds up to 262,785

If your teacher just wanted things to the nearest whole number (without rounding up), then the answer would be 262,784

Side note: using a spreadsheet program would probably be the most efficient/fastest method for this type of problem.

It’s already in ascending order.

3/5= .6

5/8= .625

5/6= .833

7/4= 1.75

Quadratic Formula: (-b +/- sqrt(b^2 - 4ac)) / 2a

2x^2 - 3x = 12

2x^2 - 3x - 12 = 0

a = 2

b = -3

c = -12

(--3 +/- sqrt( (-3)^2 - 4(2)(-12) )) / 2(2)

3 +/- sqrt( 9 + 96 ) / 4

3 +/- sqrt(105) / 4

Answers: [tex]\frac{3 + \sqrt{105} }{4}[/tex], [tex]\frac{3 - \sqrt{105} }{4}[/tex]

Hope this helps!

Answer:

x = 20

y = 10

Answered by Gauthmat

Answer:

+∞.

Step-by-step explanation:

That would be positive infinity.

The extreme value of the given polynomial [tex]f(x) = x^{2} -4[/tex] is ∞.

Extreme values of a polynomial are the peaks and valleys of the polynomial—the points where direction changes.

The following steps which are required to find the extreme value of polynomial are:

According to the given question.

We have a polynomial

[tex]f(x) = x^{2} -4[/tex]

Since, in the given polynomial the coefficient of [tex]x^{2}[/tex] is positive . Therefore, the extreme value of the given polynomial is infinity because the value will continue to grow as x increases.

Hence, the extreme value of the given polynomial [tex]f(x) = x^{2} -4[/tex] is ∞.

Find out more information about extreme value of a polynomial here:

https://brainly.com/question/16597253

#SPJ2

Answer:slope 2/3

Y-int 6

Step-by-step explanation:

9514 1404 393

Answer:

  $8414

Step-by-step explanation:

The compound interest formula is useful for this.

  A = P(1 +r/n)^(nt)

where P is the principal invested at annual rate r compounded n times per year for t years. A is the ending balance.

  A = $5000(1 +0.035/2)^(2·15) = $5000·1.0175^30 ≈ $8414.00

Ivan will have $8414 in his account after 15 years.

Answer:

y = 2x - 5

Step-by-step explanation:

[tex]y+3=2(x-1)\\y+3=2x-2\\y+3-3=2x-2-3\\y=2x-5[/tex]

Answer:

The right solution is "68%".

Step-by-step explanation:

The empirical rule is:

[tex]X\sim N(8.43, 1.5)[/tex]

According to the question,

= [tex]P(6.93< \mu < 9.93)[/tex]

= [tex]P(\frac{6.93-8.43}{1.5} < \frac{\mu -8.43}{1.5} < \frac{9.93-8.43}{1.5} )[/tex]

= [tex]P(z(1)-P(z(-1))[/tex]

= [tex]68[/tex] (%)

Thus the above is the right solution.

Answer:

170.7

Step-by-step explanation:

We are aware that the base is a square, with side lengths 8cm, and we are given that the height is 8 cm. Since the volume of a square based pyramid is 1/3 x base area x height, we receive 1.3 x 64 x 8 which is 512/3 which is in turn 170.666 recurring. However, since this question asks you to round the the nearest tenth, you get 170.7

Answer: 1360 ways.

Step-by-step explanation:

Number of men = 11

Number of women = 8

Total members = 8 + 11 = 19

Firstly, the number of ways of selecting 1 woman for female president out of 8 will be:

= 8C1

= 8

Since Pete can not be a treasurer, then the treasurer will then be selected from the remaining 10(11 - 1). The number of ways of selecting 1 treasurer out of 10 will be:

= 10C1

= 10

Thirdly, since none can hold more then one office, in this case, the selection will be done by selecting 1 person out of 7 women and 10 men. Therefore, the number of ways of selecting 1 person out of 17 will be:

= 17C1

= 17

Therefore, the total number of ways will then be:

= 8 × 10 × 17

= 1360

Answer:

25827165

Step-by-step explanation:

from the question that we have here

the total population = 54 students

the sample size = 6 students

So given this information carol has to pick the total samples from the 54 students that we have here

the total ways that she has to do this

= 54 combination 6

= 54C6

= [tex]\frac{54!}{(54-6)!6!}[/tex]

= 25827165

this is the total number of possible samples that could occur given the total population of 54 students.

Answer: (3a + 1) (a + 3)

Step-by-step explanation:

Concept:

Here, we need to know the idea of factorization.

It is like "splitting" an expression into a multiplication of simpler expressions. Factoring is also the opposite of Expanding.

Solve:

Given = 3a² + 10a + 3

STEP ONE: separate 3a² into two terms

3a

a

STEP TWO: separate 3 into two terms

3

1

STEP THREE: match the four terms in ways that when doing cross-multiplication, the result will give us 10a.

3a     1

a       3

When cross multiply, 3a × 3 + 1 × a = 10a

STEP FOUR: combine the expression horizontally to get the final factorized expression.

3a  ⇒   1

a   ⇒    3

(3a + 1) (a + 3)

Hope this helps!! :)

Please let me know if you have any questions