Examine the equation below used for determining the balance on a bank account. Look through this chapter and your notes to help you write a problem that could be modeled by the equation.

The 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)

Given the equation that models the situation expressed as:

4x + 6y = 48

We are to find 4 possible solutions for x and y. Note that the values of x and y must be integers.

If there are no cars i.e. at when x = 0

4(0) + 6y = 48

0 + 6y = 48

6y = 48

y = 48/6

y = 8

One of the solution is (0, 8)

If there are 3 cars, i.e. at when x = 0

4(3) + 6y = 48

12 + 6y = 48

6y = 48 - 12

y = 36/6

y = 6

The second solution will be (3, 6)

If there are 6 cars, i.e. at when x = 6

4(6) + 6y = 48

24 + 6y = 48

6y = 48 - 24

y = 24/6

y = 4

The third solution will be (6, 3)

If there are 9 cars, i.e. at when x = 9

4(9) + 6y = 48

36 + 6y = 48

6y = 48 - 36

y = 12/6

y = 2

The fourth solution will be (9, 2)

Hence the 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)

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A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat  lowest cost is at (x,y) is (3,2).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given,

Function:

C = x + 1.5y

Subjected to:

30x + 20y ≥ 13/10 ×100 ≥ 130

10x + 4y ≥ 1/5 × 100 ≥ 20

50x + 75y ≥ 3 × 100 ≥ 300

Feasible region:

(0, 13/2), (3,2) (6,0)

C = x + 1.5y

(0, 13/2) ⇒ C = 0+ (1.5)(13/2)

(0.13/2) ⇒ C = 9.75

(3,2) ⇒ C = 3+ (1.5)(2)

(3,2) ⇒ C = 6

(6,0) ⇒ C = 6 + 0

(6,0)⇒ C = 6

A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat  lowest cost is at (x,y) is (3,2).

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the probability would be taking a purple one. there are only 2 red beads

3/2 or 2/3

The probability that the two beads selected from the bag at random is purple or red is 5/8.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Total number of beads = 8

2 of the beads are blue.

1 of the beads is green.

3 of the beads are purple.

Red beads = 8 - (2 + 1 + 3) = 8 - 6 = 2

Now,

The probability that the two beads selected are purple or red.

= Probability that the two beads are purple + Probability that the two beads are red.

= 3/8 + 2/8

= 5/8

Thus,

The probability that the two beads selected are purple or red is 5/8.

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Answer: 92

Step-by-step explanation:

The probability of a foot of male being between 10 and 12. 5 inches is 59%.

The z score of the distribution is found as-

z = (x - μ)/σ

In which,

μ = mean = (11)

σ = standard distribution (1.5)

The likelihood that a male's foot measures between 10 and 12. 5 inches.

P(10 < x < 12.5)

For x = 10

z = (10 - 11) / 1.5

z = -0.67

check the p-value fro z score table.

p (z = -0.67) = 0.2514

For x = 12.5

z = (1.5 - 11)/1.5

z = 1

p (z = 1) = 0.8413

P(10 < x < 12.5)  = 0.8413 - 0.2514

P(10 < x < 12.5)  = 0.5899

P(10 < x < 12.5)  = 58.99%

P(10 < x < 12.5)  = 59%.

Thus, the likelihood of a male's foot being between 10 and 12. 5 inches is 59%.

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The complete question is attached in figure.

Answer: The phone was £120 before the discount.

Answer:

0.000065 km

Step-by-step explanation:

To get from cm to km you need to divide 6.5 by 0.000001 which equals 0.000065km

Answer:

A/ 80 grams

Step-by-step explanation:

We know that 430 - 280 = 150,  so each marble weights 5 grams. Then we take 5 times 40 = 200 grams. Then we take 280 subtract 200 = 80 grams

Answer:

[tex]r = 2279.41[/tex]

The number of years to double the investment is 8.824 years.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

P = $3,900

R = 8%

n = 2

A = 2P = 2 x 3,900 = $7,800

Now,

A = P [tex](1 + r/n)^{nt}[/tex]

7,800 = 3,900 [tex](1 + 0.04)^{2t}[/tex]

78/39 = [tex](1.04)^{2t}[/tex]

2 = [tex](1.04)^{2t}[/tex]

Taking logs on both sides.

log 2 = 2t log(1.04)

0.30 = 2t x 0.017

0.30/0.017 = 2t

17.65 = 2t

Divide both sides by 2.

t = 17.65 / 2

t = 8.824 years.

Thus,

The number of years to double the investment is 8.824 years.

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The coordinates of G' after the rotation = (6, 5)

In this question we have been given a point G, located at (-5, 6) is rotated 270° counterclockwise.

We need to find the coordinates of G' after the rotation.

a point (-5, 6) is located in the second quadrant.

First 90° counterclockwise rotation gives (-6, -5)  because x & y are interchanged and in Quadrant III both coordinates will be negative.

Second 90° counterclockwise rotation yields (5,-6) because x & y are interchanged and in Quadrant IV the y coordinate will be negative.

Last 90° counterclockwise rotation yields (6, 5) because x & y are interchanged and in Quadrant I both coordinates will be positive.

Therefore, the coordinates of G' after the rotation = (6, 5)

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The probability that x < y is 1/8 or 0.25 .

What is probability of an event?
The possibility or chance of an event happening is commonly believed to be the probability of it happening. In the most basic scenarios, the probability that a specific event 'A' will occur as a result of an experiment is calculated by dividing the number of ways that 'A' can happen by the total number of possible outcomes.
P(A) = Number of events concerning 'A' / Total events in consideration.

Given, the vertices of the rectangle are (0, 0), (4, 0), (4, 1), (0, 1).
On carefully analyzing and plotting the vertices roughly, we get that the given rectangle has a width of 4 units and a height of 1 unit.
Therefore, the area of the given rectangle = Width*Height = 4*1 = 4 units²
Also, it can be assessed that the line x = y passes through the points of the rectangle at (0, 0) and (1, 1).
Thus, the area for which x < y will be an isosceles triangle with side length of 1 units and co-ordinates of vertices as (0, 0), (0, 1) and (1, 1).
The area of the isosceles triangle thus assumed = 0.5 × 1² = 0.5 units²
Probability that x < y is P(E): 0.5/4 = 1/8 = 0.25
Therefore, the probability that x < y is 1/8 or 0.25 .

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The simplest radical form of  √(11/(x + 4)) when x is 16 is; ¹/₁₀√55

Surds are actually the expressions of the number, and often use radicals. Meanwhile, the radical is just the symbol used to express the square root.

We are given the expression of the surd as;

√(11/(x + 4))

We want to solve this for when x = 16. Thus, we plug in 16 for x in the surd to get;

√(11/(16 + 4))

= √(11/20)

Now, we can rewrite the fraction in the bracket to have the denominator as a perfect square by multiplying both numerator and denominator by 5 to get;

√(55/100)

Square root of 100 is 10 and as such we now have;

√(55/100) = ¹/₁₀√55

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Step-by-step explanation:

so, after clarification from your side, we know

f(x) = 12500 × (0.82)^x

so, with every new year we are multiplying the value of the previous year by 0.82.

in other words

f(n) = f(n-1) × 0.82

with f(0) = 12500

because anything to the power of 0 equals 1.

A

so, the price is decreasing every year, because any multiplication with a positive value smaller than 1 decreases the original number.

multiplying an amount by a decimal number like 0.82 creates exactly 82% of the original amount because 1 represents 100%.

that means the value decreases every year by 100 - 82 = 18% compared to the value of the previous year.

B

1 5600

2 3136

3 1756.16

4 983.45

remember, Part A showed always an 18% decrease over the previous year.

from 5600 to 3136, this was a change of

100% = 5600

1% = 100%/100 = 5600/100 = $56

the price difference was 5600 - 3136 = 2464

how many % was that decrease ?

as many as how often 1% fits into 2464 :

2464 / 56 = 44%

that was much more than Part A.

from 3136 to 1756.16, this was a change of

100% = 3136

1% = $31.36

the price difference was 3136 - 1756.16 = $1,379.84

how many %

1,379.84 / 31.36 = 44%

again.

from 1756.16 to 983.45, this was a change of

100% = 1756.16

1% = $17.5616

the price difference was 1756.16 - 983.45 = 772.71

hire many %

772.71 / 17.5616 = 43.99997722...%

and again 44% (just a little rounding uncertainty).

so, product B recorded a much greater percentage change in value over the previous year than product A :

44% to 18%

The matrix

[tex]MN = \left[\begin{array}{ccc}-2&1&0\\17&2&-3\\11&12&-5\end{array}\right][/tex]

The given matrix is

[tex]M = \left[\begin{array}{ccc}1&0\\-4&3\\2&5\end{array}\right][/tex]

[tex]N = \left[\begin{array}{ccc}-2&1&0\\3&2&-1\\\end{array}\right][/tex]

The Order of M = (3×2)

The Order of N = (2×3)

Since the number of columns of M is equal to the number of rows, the multiplication of M and N is possible,

The order of the matrix formed is MN = ( 3 × 3 )

So,

[tex]MN = \left[\begin{array}{ccc}-2+0&1+0&0+0\\8+9&-4+6&0-3\\-4+15&2+10&0-5\end{array}\right] \\\\MN = \left[\begin{array}{ccc}-2&1&0\\17&2&-3\\11&12&-5\end{array}\right][/tex]

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The length of the X using law of cosine is 34.30yd.

What is cosine?

In a right angled triangle, the cosine of an angle is:

The length of the adjacent side divided by the length of the hypotenuse.

The abbreviation is cos

cos(θ) = adjacent / hypotenuse

Consider that;

[tex]X = \sqrt{a^2+b^2-2abcosX}[/tex] (using law of cosine)

[tex]X = \sqrt{21^2+18^2-2\times 21\times 18\times cos(123 ^\circ)}[/tex]

[tex]X = \sqrt{441+324-756\times (-0.5446)}[/tex]

X = 34.30 yd

If A, B, and C are the measures of the angles of an oblique triangle, and a, b, and c are the lengths of the sides opposite the corresponding angles, then the square of a side of the triangle is equal to the sum of the squares of the other two sides minus twice the product of the two sides and the cosine of the included angle.

[tex]c^2 = a^2+ b^2- 2abcos C[/tex]

We have to the value of X which is present on the side c,

so, from the above formula we modified for the X,

and the formula become,

[tex]X = \sqrt{a^2+b^2-2abcosX}[/tex](using law of cosine)

rest of the solutions are only calculation which is elaborated  above which provide us the value of  X = 34.30 yd.

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The domain of the graph is (d) all set of real values

The graph represents the given parameter

This graph represents a function

Say the graph represents the function f(x)

The x values represent the domain

i.e domain = Set of all x values

On the graph, we can see that the graph extends across the x-axis till infinity on both sides

This means that

Domain = All set of real values

Hence, the domain of the relation is (d) all set of real values

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Answer:

4

Step-by-step explanation:

12÷3=4

Answer:

235

Step-by-step explanation:

When estimating the product of two decimals, first round the decimals to their nearest whole numbers.

Therefore,

So an estimate of the product of the two decimals is:

[tex]\implies 4.8 \times 47.1 \approx 5 \times 47[/tex]

Partition 47 into tens and units:

[tex]\implies 5 \times 47 = 5 \times (40 + 7)[/tex]

Apply the distributive property of multiplication over addition:

[tex]\begin{aligned}\implies 5 \times (40 + 7) &= (5 \times 40) + (5 \times 7)\\&=200+35\\&=235\end{aligned}[/tex]

Therefore:

[tex]\boxed{4.8 \times 47.1 \approx 235}[/tex]

Answer: 160

Step-by-step explanation:

because you times 40 by 4 as 4 is the first term and 4x10=40 <3

hope this helped <3

The rule which describes the function graphed in the attached image as required to be identified is; Output = 8 - input.

It follows from the task content that the rule which is a representative of the function which is as graphed in the attached image is to be identified.

By observation, the relation which best describes the graph is; (7, 1), (6, 2), (5, 3).....

The inference which can therefore be drawn from the given graph is that;

The output value is the subtraction of the input value from 8 in each case.

Ultimately, the required rule which represents the function is; Output = 8 - input.

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The total cost for an order of 30 copies is $17.50.

So, calculate the total cost as follows:

We have:

Here, x implies a number of orders of copies and in question, it says the order of 30 copies.

So, Substitute x=30 in equation 1,

Hence, the total cost for an order of 30 copies is $17.50.

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Answer:

  45,000

Step-by-step explanation:

Given a 30 minute sample of a constant stream shows 2250 people entered the gate, you want an estimate of the total number of people through the gate in 10 hours.

A half-hour period is 1/20 of the 10-hour period the gate was open. The rate is assumed constant, so the 2250 people entering in that half-hour period is presumed to be 1/20 of the total attendance.

  20 · 2250 = 45000

The estimated festival attendance is 45,000 people.

The scale factor of a figure with a shape with a side length of 12 and is dilated to a shape with 4 is 1/3.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given that a figure with side length of 12 units is being dilated in a figure with side length of 4.

In this case, the scale factor = 4/12 = 1/3

Hence, The scale factor of a figure with a shape with a side length of 12 and is dilated to a shape with 4 is 1/3.

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Answer:

the correct she answer should be 5

Step-by-step explanation:

The solution set for the given inequality is  {.......-4, -3, -2, -1, 0, 1, 2, 3}, so the for x=5 the inequality is false. Therefore, the correct answer is option B.

The given inequality is 5x+6≤2x+15.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Here, the inequality can be solved as follows

5x+6≤2x+15

Subtract 6 on both the sides of the inequality, we get

5x+6-6≤2x+15-6

5x≤2x+9

Subtract 2x on both the sides of the inequality, we get

5x-2x≤2x+9-2x

3x≤9

Divide 3 on both the sides of the inequality, we get

x≤3

Here, solution set is {.......-4, -3, -2, -1, 0, 1, 2, 3}

So, the for x=5 the inequality is false.

Therefore, the correct answer is option B.

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The mean of the distribution is 24.444.

Given, that 87.3% of all homes have a large-screen tv. a sample of 28 homes is selected.

Now, we have to find the mean of the distribution

As, we know

E(x) = np

where, n is the sample and p is the probability of success

So, n = 28 and p = 87.3% = 0.873

Now, on using the formula we get,

E(x) = (28)(0.873)

E(x) = 24.444

So, the mean of the distribution is E(x) = 24.444

Hence, the mean of the distribution is 24.444.

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Answer:

Step-by-step explanation:

It will be 115$

Answer:  the answer is $21.7391304348 or round to $21.74 is the cost for 50 gallons

Step-by-step explanation: I did the calculations and it costs $2.30  a gallon

Sheri should invest $2000 in mutual fund and $13,200 in bond.

Let the amount to be invested in mutual fund be x. So, the amount to be invested in bond will be (15,200 - x). Forming the equation now -

1%×x + 4%×(15,200 - x) = 548

x/100 + 60,800/100 - 4x/100 = 548

60,800 - 3x = 54800

3x = 60800 - 54800

3x = 6000

x = 6000 ÷ 3

x = 2000

Amount to be invested in mutual fund = $2000

Amount to be invested in bond = 15,200 - 2000

Amount to be invested in bond = $13,200

Sheri should invest $2000 and $13,200 in mutual fund and bond respectively.

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In writing the equations that describe each of the colonies A ad B we have;

We know that the increase or decrease of population are exponential problems. We such, we must be able to look at the problem form the exponential perspective. This is how we would be able to know how to write the appropriate equation that would be able to be used in each of the cases that have been shown in the problem.

We are told  that; a scientist is observing two ant colonies. The colonies each have 800 ants when he begins observing them. The population of Colony A increases by 25% each week. The population of Colony B decreases by 25% each week. In each equation, y represents the ant population with respect to a number of weeks, x.

Thus;

For colony A we can write;

y = 800e^0.25x

For colony B we can write;

y = 800e^-0.25x

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The first step is to find the increase in quantity.

The percentage increase is 10%.

From the information, the original quality is 1,500 and the new quality is 1,650.

The first step is to find the increase in quality will be:

= New quantity - Old quantity

= 1650 - 1500

= 150

The percentage increase will be:

= Increase / Old Quantity × 100

= 150 / 1500 × 100

= 10%

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