Solve using the elimination method. 2x + 7y = 36
6x - 7y = - 60 ​

Answer:

See Explanation

Step-by-step explanation:

According to the Question,

Given that, A retired couple has up to $50,000 to invest. As their financial adviser, you recommend that they place at least $35,000 in Treasury bills yielding 1% and at most $10,000 in corporate bonds yielding 3%.

Therefore,

Let, x be the amount of money invested in Treasury bills

y be the amount invested in corporate bonds

Thus, the system of equations of linear inequalities is

x + y ≤ 50000

x ≥ 35000

0 ≤ y ≤ 10000

For, the graph of the system of equations of linear inequalities describes the possible amounts of each investment.

(Please find in the attachment)

Answer:

.3

Step-by-step explanation:

let x= P(f)

.65= .55+x-.2

P(F)=.3

The answer is They left a 20% tip, so the service was probably above average.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

First step is to the amount of the sales tax.

If 100% is $73.89,

5.8% will be x (tax):

100% : $73.89 = 5.8% : x.

x = $73.89 * 5.8% : 100%.

x = $4.28.

Now, we have the price for meals, sales tax, and the total amount of money left, so we can calculate how much the tip is:

$93.00 - $73.89 - $4.28 = $14.83.

So, the tip is $14.83.

Let represent it as percent.

If $73.89 is 100%, $14.83 will be x.

$73.89 : 100% = $14.83 : x.

x = $14.83 * 100% : $73.89.

x = 20%.

So, they left a 20% tip, so the service was probably above average.

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Answer:

[tex]\sigma_1 = 0.08[/tex] --- Location 1

[tex]\sigma_2 = 0.34[/tex] --- Location 2

Step-by-step explanation:

Given

See attachment for the given data

Required

The standard deviation of each location

For location 1

First, calculate the mean

[tex]\bar x_1 =\frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x_1 =\frac{30.40+30.20+30.30+30.40+30.30}{5}[/tex]

[tex]\bar x_1 =\frac{151.60}{5}[/tex]

[tex]\bar x_1 =30.32[/tex]

The standard deviation is calculated as:

[tex]\sigma_1 = \sqrt{\frac{\sum(x - \bar x_1)^2}{n-1}}[/tex]

[tex]\sigma_1 = \sqrt{\frac{(30.40 - 30.32)^2+(30.20 - 30.32)^2+(30.30 - 30.32)^2+(30.40 - 30.32)^2+(30.30 - 30.32)^2}{5-1}}[/tex]

[tex]\sigma_1 = \sqrt{\frac{0.028}{4}}[/tex]

[tex]\sigma_1 = \sqrt{0.007}[/tex]

[tex]\sigma_1 = 0.08[/tex]

For location 2

First, calculate the mean

[tex]\bar x_2 =\frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x_2 =\frac{30.10+30.90+30.20+30.70+30.30}{5}[/tex]

[tex]\bar x_2 =\frac{152.2}{5}[/tex]

[tex]\bar x_2 =30.44[/tex]

The standard deviation is calculated as:

[tex]\sigma_2 = \sqrt{\frac{\sum(x - \bar x_2)^2}{n-1}}[/tex]

[tex]\sigma_2 = \sqrt{\frac{(30.10-30.44)^2+(30.90-30.44)^2+(30.20-30.44)^2+(30.70-30.44)^2+(30.30-30.44)^2}{5-1}}[/tex]

[tex]\sigma_2 = \sqrt{\frac{0.472}{4}}[/tex]

[tex]\sigma_2 = \sqrt{0.118}[/tex]

[tex]\sigma_2 = 0.34[/tex]

Answer:

x + y = 30

y = 2x

Step-by-step explanation:

x = number of ounces of lemon juice

y = number of ounces of linseed oil

How much of each ingredient is needed to make 30 oz of floor wax?

x + y = 30

The amount of oil should be twice the amount of lemon juice.

y = 2x

Answer:

x + y = 30

y = 2x

Answer:

[tex]\bar x = 107.11[/tex]

[tex]\sigma_x = 31.07[/tex]

Step-by-step explanation:

See comment for complete question

Given

[tex]x: 97\ 178\ 129\ 90\ 75\ 94\ 116\ 100\ 85[/tex]

Solving (a): The sample mean

This is calculated using:

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x = \frac{97+ 178+ 129+ 90+ 75+ 94+ 116+ 100+ 85}{9}[/tex]

[tex]\bar x = \frac{964}{9}[/tex]

[tex]\bar x = 107.11[/tex]

Solving (b): The sample standard deviation

This is calculated as:

[tex]\sigma_x = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]

So, we have:

[tex]\sigma_x = \sqrt{\frac{(97 - 107.11)^2 +.............+ (85- 107.11)^2 }{9-1}}[/tex]

[tex]\sigma_x = \sqrt{\frac{7720.8889}{8}}[/tex]

[tex]\sigma_x = \sqrt{965.1111125}[/tex]

[tex]\sigma_x = 31.07[/tex]

Answer:

-3,-1

Step-by-step explanation:

x²+4x+3=0

x²+4x=-3

x²+4x+(2)²=-3+(2)²

(x+2)²=-3+4

(x+2)²=1

Take square root of both sides

x+2=±1

x=-2±1

x=-1 or-3

Answer:

The left side of the histogram has a cluster.

Step-by-step explanation:

The others don't make since.

It's not evenly distributed,

it's not symmetrical, and

it is definitely not a mirror image of the right side.

Answer:

A

Step-by-step explanation:

Answer:

-x-3y

Step-by-step explanation:

-5x+6y-9y+4x

-5x+4x+6y-9y

-x-3y

9514 1404 393

Answer:

  maybe

Step-by-step explanation:

It can be. It depends on the problem.

__

The rules of exponents are ...

  (a^b)/(a^c) = a^(b-c)

  a^-b = 1/a^b

Clearly, for division problems if the denominator exponent is larger, the difference 'b-c' will be negative.

__

You recall that an exponent is the way we show repeated multiplication.

 x·x·x = x³

In division, like factors cancel, so ...

  [tex]\dfrac{x\cdot x\cdot x}{x\cdot x}=\dfrac{x^3}{x^2}=\dfrac{x}{1}\cdot\dfrac{x\cdot x}{x\cdot x}=x^{3-2}=x^1=x[/tex]

Now, consider the same problem "upside down."

 [tex]\dfrac{x\cdot x}{x\cdot x\cdot x}=\dfrac{x^2}{x^3}=\dfrac{1}{x}\cdot\dfrac{x\cdot x}{x\cdot x}=x^{2-3}=x^{-1}=\dfrac{1}{x}[/tex]

Answer:

0.015

Step-by-step explanation:

1.5% = means 1.5 per 100 or simply 1.5/100.if you divide 1.5 by 100 you will get 0.015

Answer:

(2,3) (4,2) (5,2) (1,4) (0,2)

Step-by-step explanation:

because all these points have something common to each other. Now pay attention in your class and stop cheating!!

Answer:

Step-by-step explanation:

eq. of circle is (x-2)²+(y-3)²=10²

now substitute the values of x and y

which satisfies the above eq.that point lies on the circle.

Answer:

I'm going to help you figure this out because I am actually on the same assignment. If you do not understand what it is asking, it is not asking you to break down the function notation, it is simply asking you to substitute (X) with 2,3,4,5,and 6 and then to solve it on each line

Answer:

ok so its is 5 dollars for a pencil and 420 dollars for a pen(dang)

a40+2100=2140

now

b6 pencil 462 pen

60+3696=3756

Hope This Helps!!!

(a) Afua paid ¢44,500.00 for 8 pencils and 5 pens.

(b) Afua will pay ¢71,400.00 for 10 pencils and 8 pens after the price increase.

(a) To find how much Afua paid altogether for 8 pencils and 5 pens, we need to calculate the total cost for each item and then add them together.

Given:

Cost of a pencil, [tex]Pencil_{cost}[/tex] = ¢500.00

Cost of a pen, [tex]Pen_{cost}[/tex] = ¢42,000.00

Number of pencils bought, [tex]n_{pencils}[/tex] = 8

Number of pens bought, [tex]n_{pens}[/tex] = 5

Total cost of pencils,

[tex]Total_{pencil}_{cost} = Pencil_{cost} * n_{pencils}[/tex]

                      = ¢500.00 × 8

                      = ¢4,000.00

Total cost of pens,

[tex]Total_{pen}_{cost} = Pen_{cost} * n_{pens}[/tex]

                   = ¢42,000.00 × 5

                   = ¢210,000.00

Altogether, [tex]Total_{cost} = Total_{pencil}_{cost} + Total_{pen}_{cost}[/tex]                                      

                                  = ¢4,000.00 + ¢210,000.00

                                  = ¢214,000.00.

Therefore, Afua paid ¢214,000.00 for 8 pencils and 5 pens.

(b) Now, let's calculate the new total cost after the price increase.

The price of a pencil increased by 20%, which means the new pencil cost is:

[tex]New_{pencil}_{cost}[/tex] = [tex]Pencil_{cost}[/tex]+ (20% × [tex]Pencil_{cost}[/tex])

                                  = ¢500.00 + (0.20 × ¢500.00)

                                  = ¢500.00 + ¢100.00

                                  = ¢600.00

Similarly, the price of a pen increased by 10%, which means the new pen cost is:

[tex]New_{pen}_{cost}[/tex] = [tex]Pen_{cost}[/tex] + (10% × [tex]Pen_{cost}[/tex])

                          = ¢42,000.00 + (0.10 × ¢42,000.00)

                          = ¢42,000.00 + ¢4,200.00

                          = ¢46,200.00

Now, we can find the total cost for 10 pencils and 8 pens with the increased prices:

Number of pencils to be bought, [tex]n_{pencils}_{new}[/tex] = 10

Number of pens to be bought, [tex]n_{pens}_{new}[/tex] = 8

Total cost of pencils with new prices,

[tex]Total_{pencil}_{cost}_{new}[/tex] =[tex]New_{pencil}_{cost}[/tex] × [tex]n_{pencils}_{new}[/tex]

                                        = ¢600.00 × 10

                                        = ¢6,000.00

Total cost of pens with new prices,

[tex]Total_{pen}_{cost}_{new}[/tex] = [tex]New_{pen}_{cost}[/tex] × [tex]n_{pens}_{new}[/tex]

                                    = ¢46,200.00 × 8

                                    = ¢369,600.00

Altogether, [tex]New_{total}_{cost}[/tex] = [tex]Total_{pencil}_{cost}_{new}[/tex] + [tex]Total_{pen}_{cost}_{new}[/tex]

                                               = ¢6,000.00 + ¢369,600.00

                                               = ¢375,600.00

Therefore, Afua will pay ¢375,600.00 for 10 pencils and 8 pens with the increased prices.

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This is one single number that's slightly smaller than 400 thousand.

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

Explanation:

There are 26 letters in the english alphabet. We don't use letters i or o, so we have 26-2 = 24 choices for that first slot.

Then we have 10 choices for the second slot because there are 10 single digits 0 (zero) through 9.

After making the selection for the second slot, we have 10-1 = 9 choices left for the third slot. The fourth slot has 10-2 = 8 digits to pick from. The subtraction occurs because we cannot reuse the digits.

Finally, the last slot will be a letter. We have 24-1 = 23 letters left to pick from.

Overall, we have 24*10*9*8*23 = 397,440 different license plates possible.

--------------------

Extra info (optional section)

You may be wondering "why do we multiply those values?". Well consider a simple example of having only 2 slots instead of 5.

Let's say the first slot is a letter A to Z, excluding letters i and o. The second slot will be the digit from 0 through 9.

If you make a table with 24 rows and 10 columns, then you'll have 24*10 = 240 cells overall. Notice the multiplication here. The 24 rows represent each letter, and the 10 columns are the digit numeric digits.

Each inner cell is a different two character license plate. For example A5 is one such plate. This idea can be extended to have 5 characters.

Answer:

x = 5.5

Step-by-step explanation:

Based on the Mid-segment theorem of a triangle, we would have the following:

EF = 2(AB)

AB = 7

EF = 2x + 3

Plug in the values

2x + 3 = 2(7)

Solve for x

2x + 3 = 14

Subtract 3 from each side

2x + 3 - 3 = 14 - 3

2x = 11

2x/2 = 11/2

x = 5.5

3 maybe is a correct ans thxxxxxx

Answer:

i think possible the last one...

I'm not sure but i hope you get it correct!

Answer:

0.2209 = 22.09% probability that in a randomly selected office hour, the number of student arrivals is 3.

Step-by-step explanation:

We have the mean during an interval, so the Poisson distribution is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

A statistics professor finds that when she schedules an office hour for student help, an average of 3.3 students arrive.

This means that [tex]\mu = 3.3[/tex]

Find the probability that in a randomly selected office hour, the number of student arrivals is 3.

This is P(X = 3). So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 3) = \frac{e^{-3.3}*3.3^{3}}{(3)!} = 0.2209[/tex]

0.2209 = 22.09% probability that in a randomly selected office hour, the number of student arrivals is 3.

Answer:

10/7 or 1.428571429

Step-by-step explanation:

We know that x-y=0.7

So, now we have the equation 1÷0.7 or 1÷7/10

Meaning, we can multiply by the reciprocal,

And make this equation into 1×10/7= 10/7

Answer:

A and D are the answer.

Step-by-step explanation:

We can factor this by grouping

[tex]2 {x}^{2} + 5x - 3[/tex]

[tex]2 {x}^{2} + 6x - x - 3[/tex]

[tex]2x(x + 3) -1 (x + 3)[/tex]

The roots are

[tex](x + 3) = 0[/tex]

and

[tex]2x - 1 = 0[/tex]

Let solve for zero in each roots.

[tex]x = - 3[/tex]

[tex]2x = 1[/tex]

[tex]x = \frac{1}{2} [/tex]

9514 1404 393

Answer:

Step-by-step explanation:

a) The starting height is h(0) = 7.5 feet, the constant in the quadratic function.

The irrigation system is positioned 7.5 feet above the ground

__

b) The axis of symmetry for quadratic ax^2 +bx +c is x = -b/(2a). For this quadratic, that is x=-10/(2(-1)) = 5. This is the horizontal distance to the point of maximum height. The maximum height is ...

  h(5) = (-5 +10)(5) +7.5 = 32.5 . . . feet

The spray reaches a maximum height of 32.5 feet at a horizontal distance of 5 feet from the sprinkler head.

__

c) The maximum distance will be √32.5 + 5 ≈ 10.7 ft.

The spray reaches the ground at about 10.7 feet away.

Answer:

7.5

32.5

5

maximum

10.7

Step-by-step explanation:

Answer:

a) The reorder point necessary to provide a 95 percent service probability is 1557 units.

b) The Z value of 0.74 corresponds to 77% service probability.

Step-by-step explanation:  

Average weekly demand (d) = 315 units  

The standard deviation of weekly demand (\sigmad) = 90 units  

Lead time (L) = 4 weeks  

At 95% service level value of Z = 1.65  

Reorder point = d x L + safety stock  

[tex]= d \times L + (Z \times \sigma d \times \sqrt L)\\\\= 315 x 4 + (1.65 x 90 x \sqrt 4)\\\\= 1260 +(1.65 x 90 x 2)\\\\= 1260 + 297\\\\= 1557 units[/tex]

b) Earlier the safety stock was 297 units(calculated in part a)

Now the safety stock is reduced to 55%.so,55% of 297 = 163.35 units  

So the new safety stock = 297 - 163.35 = 133.65  

[tex]Safety stock = Z \times \sigma d \times \sqrt L\\133.65 = Z x 90 x 2\\133.65 = 180Z\\ Z = 133.65/180\\Z = 0.74[/tex]  

The Z value of 0.74 corresponds to 77% service probability.

Answer:

C

Step-by-step explanation:

tracing paper is your friend

Answer:

udirkkdjdjdjehdhebhgwdxddrergghg

Answer:

see below

Step-by-step explanation:

[tex] \displaystyle AB = DE[/tex]

[given]

[tex] \displaystyle \boxed{BC = EF}[/tex]

[given]

[tex] \displaystyle AB + BC = AC[/tex]

[segment addition Postulate]

[tex] \displaystyle \boxed{DE+ EF=DF}[/tex]

[segment addition Postulate]

[tex] \rm\displaystyle DE+ BC = AC \: \: \text{and} \: \: DE+ BC = DF[/tex]

[Substitution Property of Equality]

[tex] \displaystyle \boxed{AE= DE}[/tex]

[Proven]