You can spend at most $3.50 at a market. Apples cost $0.40 each, and pears cost $0.65 each. Let x be numbers of apples and y be numbers of pears. Write an inequality that represents the numbers of apples and pears you can buy. Is (3,4) a solution of the inequality?

If the total time to travel downstream and return upstream to the starting point is 6 hours. If the total distance downstream and back is 30 miles, the speed of the river (current speed) is 6.

Time = Distance/speed

Time taken to row upstream:

(30/2) /(9 - x)

15/(9-x)

Time taken to row downstream:

15/(9 + x)

Total time spent is 6 hours hence,

15/(9- x) + 15/(9 + x) = 6

Cross multiplying

15(9 + x) + 15(9 - x) = 6(9+ x)(9 - x)

= 135 + 15x + 135- 15x =6(81 -9x + 9x - x²)

=270 = 6(81 - x²)

270/6 = 81- x²

45 = 81- x²

x² = 81- 45

x²= 36

x =√36

x = 6

Therefore If the total time to travel downstream and return upstream to the starting point is 6 hours. If the total distance downstream and back is 30 miles, the speed of the river (current speed) is 6.

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To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction and then multiply it by the reciprocal of the fraction.

Step 1: Convert the mixed number to an improper fraction:

7 5/6 = (6 * 7 + 5) / 6 = 47/6

Step 2: Multiply the improper fraction by the reciprocal of the fraction:

47/6 ÷ 2/3 = 47/6 * 3/2

Step 3: Simplify the fraction if possible:

47/6 * 3/2 = (47 * 3) / (6 * 2) = 141/12

Step 4: Simplify the fraction further, if necessary:

141/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

141/12 = (141 ÷ 3) / (12 ÷ 3) = 47/4

Therefore, 7 5/6 ÷ 2/3 is equal to 47/4 or 11 3/4.

Answer:

y + 3= -7(x + 2)

Step-by-step explanation:

...........

The correct expression is  \($(150 \cdot 1.15)^7$\) (Choice A).

The problem states that the painting's value increases by a factor of 1.15 each year. This means that the value at the end of each year is 1.15 times the value at the beginning of the year. Therefore, after one year, the value of the painting is\($150 \cdot 1.15 = 172.50$\).

To find the value after 7 years, we need to multiply the value of the painting each year by 1.15 a total of 7 times. This can be represented mathematically as \($(150 \cdot 1.15)^7$\). This expression is equal to the starting value of the painting, 150, multiplied by 1.15$ raised to the 7th power, which represents the 7 years of appreciation.

If we were to choose expression B, it would give an incorrect result because it uses a value of 1.1 instead of 1.15 to represent the yearly increase in value.

Expressions C and D are also incorrect because they are not taking into account the compounding effect of the yearly increase. Expression C adds the initial value and the total years together, and expression D adds the initial value to the yearly increase multiplied by 7, neither of which correctly reflects the exponential growth of the painting's value.

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Using the principle of probability, the estimated number of times Jessica will be on time is 34.

Given the Parameters :

The best estimate for the number of times Jessica will be on time can be calculated thus :

Hence, we have ;

Mean number of times = (0.64 × 53)

Mean number of times = 33.92

Hence, the estimated number of times Jessica will be on time is 34.

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If the random variable x is normally distributed with a mean equal to 0.45 and a standard deviation equal to 0.40, then P(x ≥ .75) is 0.9227.

A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean and negative if it lies below the mean.

Given the problem above, we need to find what the z-score is when P(x ≥ .75).

The formula for calculating a z-score is given by:

\(Z=\dfrac{\text{x}-\mu}{\sigma}\)

Where:

Now,

\(Z=\dfrac{\text{x}-\mu}{\sigma}\)

\(Z=P(\text{x} \geq 0.75) = \huge \text(\dfrac{P(Z \geq (0.75 - 0.45)}{0.40}\huge \text)\)

\(Z= P\huge \text (\dfrac{Z \geq0.30}{0.40}\huge \text)\)

\(Z=P(Z \geq 0.75) = 1 - P(Z < 0.75)\)

\(Z=1 - 0.077337\)

\(Z\thickapprox 0.9227\)

Therefore, the z-score of P(x ≥ .75) is 0.9227.

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Darlene's net proceeds from the investment into shares would be $ 8, 279 .

First, find the initial broker fee:

=  Initial investment × Broker fee rate

= 20, 000 x 1. 5 %

= 20, 000 x 0. 15

= $ 300

The total fees incurred to buy and sell are:

= 300 initial broker + 21 later broker

= $ 321

The net proceeds would then be:

= Final value of stock - Initial investment - Total fees

= 28, 600 - 20, 000 - 321

= 8, 600 - 321

= $ 8, 279

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Full question is:

Darlene purchases $20,000 worth of stock on her brokers advice and pays her broker a 1.5% broker fee. She sells her stock when it increases to $ 28,600  two years later, and uses a discount broker who charges $21 per trade. Compute Darlene's net proceeds after the broker fees are taken out.

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Answer:

you can make 12 cans of them

Answer: 180 i think

Step-by-step explanation: .5*200+.2X=.3(200+X)

100+.2X=60+.3X

.2X-.3X=60-100

-.1X=-40

X=-40/-.1

X=400 OUNCES OF 20% COPPER.

PROOF

.5*200+.2*400=.3(200+400)

100+80=.3*600

100+80=180

180=180

Answer: 100 ounces of the alloy.

Step-by-step explanation: To solve, we create an equation:

First, though, let's define some variables and values -

x = amount of the alloy we are trying to find

0.3 = 30% copper

0.6 = 60% copper

50 = 50 ounces of the alloy

0.3(x) + 0.6(50) = 0.4(x+50) - original equation

0.3x + 0.6*50 = 0.4x + 0.4*50 - expanded

subtract 0.3x and 0.4*50 on both sides to get...

0.2*50 = 0.1x - simplified

calculate...

10 = 0.1x - simplified

divide both sides by 0.1 to get...

100 = x --> x = 100

Answer:

  5.925 pints

Step-by-step explanation:

The rest of the paint is 1 -1/4 = 3/4 of the total amount:

  (3/4)(7.9 pt) = 5.925 pt

Sharon used 5.925 pints of blue paint to paint her bedroom walls.

The number of square inches or area of gift wrap that the makeup artist will need is 10.8π square inches.

Given that,

A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap.

Radius of each lipstick = 0.6 inch

Height of the lipstick = 2.4 inches

Now,

Area of the each lipstick = 2πrh + 2πr², where r is the radius and h is the height.

Area = 2π (0.6) (2.4) + 2π (0.6)²

        = 2.88π + 0.72π

        = 3.6π

Area of the wrap for 3 lipsticks = 3 × 3.6π = 10.8π square inches.

Hence the area is 10.8π square inches.

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Answer:

There will be 66 bacteria in 8 hours.

Step-by-step explanation:

The number of bacteria after t hours is given by the following formula.

\(P(t) = P(0)(1-r)^{t}\)

In which P(0) is the initual number of bacteria and r is the decay rate.

Researchers recorded that a certain bacteria population declined from 750,000 to 250 in 48 hours after the administration of medication.

This means that \(P(0) = 750000, P(48) = 250\)

We use this to find r. So

\(P(t) = P(0)(1-r)^{t}\)

\(250 = 750000(1-r)^{48}\)

\((1-r)^{48} = \frac{250}{750000}\)

\(\sqrt[48]{(1-r)^{48}} = \sqrt[48]{\frac{250}{750000}}\)

\(1-r = 0.84637\)

So

\(P(t) = 750000(0.84637)^{t}\)

How many bacteria will there be in 8 hours?

8 hours from now, in this context, is 8 + 48 = 56 hours. So this is P(56).

\(P(56) = 750000(0.84637)^{56} = 65.83\)

Rounding to the nearest number

There will be 66 bacteria in 8 hours.

Answer:

197,488

Step-by-step explanation:

This problem requires two main steps. First, we must find the unknown rate, k. Then, we use that value of k to help us find the unknown number of bacteria.

Identify the variables in the formula.

AA0ktA=250=750,000=?=48hours=A0ekt

Substitute the values in the formula.

250=750,000ek⋅48

Solve for k. Divide each side by 750,000.

13,000=e48k

Take the natural log of each side.

ln13,000=lne48k

Use the power property.

ln13,000=48klne

Simplify.

ln13,000=48k

Divide each side by 48.

ln13,00048=k

Approximate the answer.

k≈−0.167

We use this rate of growth to predict the number of bacteria there will be in 8 hours.

AA0ktA=?=750,000=ln13,00048=8hours=A0ekt

Substitute in the values.

A=750,000eln13,00048⋅8

Evaluate.

A≈197,488.16

At this rate of decay, researchers can expect 197,488 bacteria.

y = 21

i might be wrong, sorry if i am!!

Answer:

Y=21

Step-by-step explanation:

Y/28=24/32

Y=24×28

--------

32

Y=21

The connection maps city to height at air terminal. The area is urban communities (Augusta, Denver, Springfield, Birmingham). The reach is heights (235, 5883, 235, 285).

The connection isn't a capability since two urban communities have a similar height.

(a) The arrangement of requested matches characterizing the connection is: (Augusta, 235), (Denver, 5883), (Springfield, 235), (Birmingham, 285)

(b) The space of the connection is the arrangement of x-values, or the names of the urban communities, which are Augusta, Denver, Springfield, and Birmingham.

(c) The scope of the connection is the arrangement of y-values, or the rises at the air terminal in feet, which are 235, 5883, 235, and 285.

(d) To decide whether the connection characterizes y as an element of x, we want to check whether every x-esteem has precisely one comparing y-esteem. For this situation, the x-esteem "Springfield" has two comparing y-upsides of 235, and that implies that the connection isn't an element of x. A connection is possibly viewed as a capability on the off chance that every x-esteem has precisely one comparing y-esteem.

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Answer:

  102 gallons of 55% antifreeze

  68 gallons of 80% antifreeze

Step-by-step explanation:

55% antifreeze:   x

80% antifreeze:   y

x + y = 170                        ===>  -.55(x + y = 170)   ===>   -.55x - .55y = -93.5

.55x + .80y = .65(170)      ===>                                          .55x + .80y = 110.5      

                                                                                         ________________

add the two equations to eliminate a variable:                        0.25y = 17

divide by 0.25 to isolate y:                                                               y = 68

substitution to find x:    

  x + y = 170

  x + 68 = 170

          x = 102

Answer:

Step-by-step explanation:

Let the quadratic function be

y=a(x+4)²-1

∵(-7,8) lies on it.

8=a(-7+4)²-1

8+1=a(-3)²

9a=9

a=9/9=1

so quadratic function  is

f(x)=1(x+4)²-1

or

f(x)=x²+8x+16-1

so quadratic function is

f(x)=x²+8x+15

Answer:

The statements that can be used to compare the characteristics of the functions are:

1. g(x) has the greatest maximum value.

2. All three functions share the same domain.

Explanation:

- The table shows the values of three functions - f(x), g(x), and h(x) - evaluated at different values of x.

- We cannot determine the domain of f(x) or h(x) from the given table but we can see that g(x) has a domain of all real numbers.

- We can see that g(x) has the highest maximum value among the three functions, which is 8.

- We cannot determine the range of f(x) or g(x) from the given table but we can see that h(x) has a range of all negative numbers.

- We cannot say anything about the domain or range of f(x) based on the given table.

- Therefore, the two statements that can be used to compare the characteristics of the functions are: g(x) has the greatest maximum value and all three functions share the same domain.

Answer:

\(\displaystyle m=1\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (-1, 0)

Point (0, 1)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

1

Step-by-step explanation:

To do this you just need to know the slope equation y2 - y1 over x2- x1 so if you plug in 2 coordinates you can do (0,1) and (-1,0) and when you plug it into the formula you get 1/1 which is 1 so the slope is 1

Answer:

Almost equals 28°

Step-by-step explanation:

cos(x)= 12/18

x= cos^-1 (12/18)

So it equals 48.1896°

Answer:

9:29pm

Step-by-step explanation:

Answer: I think its B instead of A

Answer:

2/3

Step-by-step explanation:

Answer:

A dot product is the product of the magnitude of the vectors and the cos of the angle between them. A cross product is the product of the magnitude of the vectors and the sine of the angle that they subtend on each other.

Step-by-step explanation:

Answer:

1500kg

Step-by-step explanation:

50*30=1500

Answer:

c = -11

expression value = 245

c = 0

expression value = 3

c = 15

expression value = 453

Step-by-step explanation:

Given expression = \(2c^2 + 3\)

for c = -11 , we put c in place of c in given expression

\(2(-11)^2 + 3 = 2(121) + 3 = 242 + 3 = 245\)

for c= 0

\(2(0)^2 + 3 = 2(0) + 3 = 0 + 3 = 3\)

for c = 15

\(2(15)^2 + 3 = 2(225) + 3 = 450 + 3 = 453\)

Answer:

-x^2 +4x +6

Step-by-step explanation:

f(x)=4x+1

g(x)=x^2-5

(f-g)(x) = 4x+1 - (x^2-5)

Distribute the minus sign

           = 4x+1 - x^2 +5

           = -x^2 +4x +6