White and solve a system of inequalities to model the following situation:
A retail store manager makes comty cloth facemasks for his employees during covid.
He has enough money to buy $100 worth of fabric.
Fabric costs $4 for a single layer mask and $6 for a mask with 2 layers of fabric.
It takes him 30 minutes to make a single layer mask and 1 hour to make double layer mask.
He only has 15 hours available to work on masks.
He wants to maximise his time and resources.
How many of each type of mask should he make

The probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 60 minutes is 0.25 .

What is probability?
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.

A highway construction site's cycle time for trucks transporting concrete is evenly spread over the range of 50 to 70 minutes, thus a = 50 and
b = 70
f(x) = 1/[b - a] = 1/[70 - 50] = 1/20 = 0.05, thus a uniform distribution.
Let P(cycle time is less than 65 minutes if it is known that the cycle time exceeds 55 minutes) be:
P(60 < X < 65) = ₆₀∫⁶⁵ f(x) dx =  ₆₀∫⁶⁵ (0.05) dx = 0.05*[65 - 60] = 0.05*5
= 0.25
Thus, the probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 60 minutes is 0.25 .

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The rate of change of the area of the square when the side length is 8 inches is 224 inches per hour.

Let s be the side of the given square.

A = s²

dA/dt = d (s²)/dt

dA/dt = 2s × ds/dt

Given ds/dt= 14 inches per hour, s = 8 inches

dA/dt = 2×14×8

dA/dt = 224 inches per hour

The area of the square is s². Since we need to find the rate of change we need to differentiate the area with respect to time which will give us  2s × ds/dt. Once we replace the given values with their respective positions we will get the desired answer. Hence the rate of change in the area of the square is 224 inches per hour.

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The equation of the line that passes through the point (8, 6) and has a slope of 0 is  y = 8.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the equation of the line passes through the point (8, 6) and has a slope of 0.

Therefore,

m = 0

Hence, let's find the y-intercept using the (8, 6)

y = mx + b

6 = 0(8) + b

b = 8

Therefore, the equation is y = 8

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Radius of Earth's moon is [tex]1.737*10^{8}[/tex]

Very big or very small numbers can be presented in a simpler way using scientific notation. Although whole numbers can be stretched to infinity, humans are unable to write such enormous numbers on paper. Additionally, it was necessary to represent the numbers that appear at the millions place after the decimal in a more straightforward manner. The extended form of a few numbers is therefore difficult to represent. So, we employ scientific notations.

Given, radius of Earth's moon is 173,700,000.

As we know, in scientific notation there is only one number to the left.

So, we need to move the decimal to 8 places.

Therefore, radius of Earth's moon is [tex]1.737*10^{8}[/tex].

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Answer: i think its -18

Step-by-step explanation:

5*(4-9*2)-2*(3*2+4)+7

= 5*(4-18)-2*(3*2+4)+7

= 5*(-14)-2*(3*2+4)+7

= 5*-14-2*(3*2+4)+7

= 5*-14-2*(6+4)+7

= 5*-14-2*(10)+7

= 5*-14-2*10+7

= -70-2*10+7

= -70-20+7

= -90+7

= -83

Answer:

Step-by-step explanation:

x² + (x + 2)² = (x + 3)²

x² + x² + 4x + 4 = x² + 6x + 9

x² - 2x - 5 = 0

[tex]x_{1}[/tex] = [tex]\frac{-(-2)+\sqrt{4+20} }{2}[/tex] = 1 + √6 ≈ 1 + 2.45 = 3.45 units

[tex]x_{2}[/tex] = [tex]\frac{-(-2)-\sqrt{4+20} }{2}[/tex] = 1 - √6 < 0 can not be solution of the given problem.

x ≈ 3.4 units

x + 2 ≈ 5.4 units

x + 3 ≈ 6.4 units

Answer:

x = 1

Step-by-step explanation:

Given equation,

→ -31 - 4x = -5 - 5(1 + 5x)

Now the value of x will be,

→ -31 - 4x = -5 - 5(1 + 5x)

→ -31 - 4x = -5 - 5 - 25x

→ -4x + 25x = -10 + 31

→ 21x = 21

→ x = 21/21

→ [ x = 1 ]

Hence, the value of x is 1.

The value of the variable x in the equation -31 -4x = -5- 5(1+ 5x) will be 1.

The given algebraic expression with the variable x is,

-31 - 4x = -5 -5(1+ 5x)

By further solving it, we get,

- 31 - 4x = -5 -5 -25x

To simplify the equation, we have to first separate the constants and variables,

=> 25x - 4x = -5 -5 + 31

=> 21x = 31 - 5 -5

=> 21x = 31- 10

=> 21x = 21

=> x = 21/21

=> x= 1.

Hence, the value of the variable x in the algebraic expression, -31 - 4x = -5 -5(1+ 5x), is found to be 1.

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Answer:

4 hostel rooms

Step-by-step explanation:

okay so for this all you need to do is read the chart

The percentage of the profit gain by karen on a pack of 8 bottles  is 220%.

Karen buys a pack of bottles of water. = 8

Karen sells all 8 bottles of water for rupees =  50p each

=  50p/100 each

= 0.5 rupees

Total rupees for 8 bottles = 8 x 0.5 = 4

The pack costs  = 1.25

Profit % = (Profit / C.P.) × 100

Profit = SP - CP

=  4 - 1.25

= 2.75

then using these values in equation we get :

profit = [tex]\frac{4 - 1.25}{1.25} * 100[/tex]

profit = (2.75/1.25 )x 100

profit = 2.2 x 100 = 220

profit = 220%

The percentage of the profit gain by karen on a pack of 8 bottles  is 220%.

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The numerical value of the expression ( jk−1 )÷j when j=−4 and k=−0.9 is -0.65.

Given the expression in the question;

To determine the numerical value of the expression, plug in the values of j and k and then simplify.

( jk − 1 ) ÷ j

Plug in j = -4 and k = -0.9

( jk − 1 ) ÷ j

( (-4 × -0.9) − 1 ) ÷ (-4)

Simplify

( 3.6 − 1 ) ÷ (-4)

( 2.6 ) ÷ (-4)

-0.65

Therefore, the value of the expression is -0.65.

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Miguel drove at a speed of 60 mph in the first part of the trip and at a speed of 50 mph in the second part of the trip.

Let the speed while dropping his son to college be x mph

Therefore speed while returning is (x - 10) mph

The distance is 300 mi

Speed = Distance/Tie

or, Time = Distance/Speed

Hence the time taken during the first part of the journey = 300/x hrs

and,

Time taken for the next part of the journey

= 300/(x - 10) hrs

It is given that the total time taken was 11 hrs

Hence we get

300/x + 300/(x - 10) = 11

or, (300x - 3000 + 300x) / x(x - 10) = 11

or, (600x - 3000) / (x² - 10x) = 11

or, 600x - 3000 = 11x² - 110x

or, 11x² -710x + 3000 = 0

Applying the shreedharacharya rule gives us

x =  (710 ± √(710² -132000)/22)

x = 50/11 or x = 60

If x = 50/11 then x - 10 will be negative.

hence x = 60

Therefore Miguel drove at a speed of 60 mph in first half and 50 mph in second half.

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Answer:

  (c)  Neither

Step-by-step explanation:

You want to know the kind of sequence that as terms 2, 7, 14, 23, 34, ....

The first differences of terms of this sequence are ...

  7 -2 = 5

  14 -7 = 7

  23 -14 = 9

  34 -23 = 11

These difference are not constant, so the sequence is not arithmetic.

These differences do not have a common ratio, so the sequence is not geometric.

However, these differences do have a common difference:

  7 -5 = 2

  9 -7 = 2

  11 -9 = 2

The fact that second differences are constant means this is a polynomial sequence of second degree. It is a quadratic sequence, neither arithmetic nor geometric.

__

Additional comment

The sequence is described by the quadratic equation ...

  a(n) = n² +2n -1

1. The linear function .f(2) = 79.4, therefore, test average for maths class after 2 test is: 79.4

2. Using the function table, the test average for science class is after the second test is: 84.

3. f(4) = 79.8

4. g(4) = 80

5. Science class was higher.

The equation of a linear function is given as .f(x) = mx + b, given that m represents the slope/unit rate, and b is the y-intercept or starting value.

The linear function for average test score in maths class is given as, .f(x) = 0.2x + 79

Write the linear function for science class;

Slope (m) = change in y/change in x = (84 - 82)/(2 - 3) = 2/-1

Slope (m) = -2

Substitute m = -2 and (x, y) = (3, 82) into y = mx + b:

82 = -2(3) + b

82 = -6 + b

82 + 6 = b

88 = b

b = 88

Substitute m = -2 and b = 88 into g(x) = mx + b:

g(x) = -2x + 88

Part 1:

Substitute x = 2 into .f(x) = 0.2x + 79

.f(2) = 0.2(2) + 79

.f(2) = 79.4

Test average for maths class after 2 test is: 79.4

Part 2:

Using the function table, when x = 2, the test average for science class is: 84.

Part 3:

Substitute x = 4 into  .f(x) = 0.2x + 79

.f(4) = 0.2(4)+ 79

.f(4) = 79.8

Part 4:

Substitute x = 4 into g(x) = -2x + 88

g(4) = -2(4) + 88

g(x) = 80

Part 5:

Science class had a higher test 4 average of 80.

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Answer:

step 2 is where she made her mistake

Step-by-step explanation:

- 4x + 1 > 9 ( subtract 1 from both sides )

- 4x > 8

divide both sides by - 4 , reversing the symbol as a result of dividing by a negative quantity.

x < - 2

By using the concept of mean and standard deviation, it can be obtained that

The mean of the distribution of sample mean ([tex]\mu_x[/tex]) = 83.3

Standard deviation of distribution ([tex]\sigma_x[/tex]) = 0.714

What is mean and standard deviation?

Suppose there is a data set and an average value of the data set needs to be calculated. To find the average value of the data set, mean is used

For Standard deviation, at first, it is important to know about variance

Variance is the sum of the square of deviation from mean.

Square root of variance is the standard deviation

A population of values has an unknown distribution with

[tex]\mu = 83.3[/tex] and [tex]\sigma = 10.4[/tex], n = 212

So the mean of the distribution of sample mean ([tex]\mu_x[/tex]) = 83.3

Standard deviation of distribution ([tex]\sigma_x[/tex]) = [tex]\frac{10.4}{\sqrt{212}}[/tex] = 0.714

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The equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.

In the given question we have to find the equation of parabola in the form of f(x)=a(x-h)^2+k

The given function is f(x)=7x^2.

The given vertex = (3,5)

The equation of the parabola with the vertex of (h,k) is

y=a(x-h)^2+k

On comparing we get; a=7, h=3, k=5

Now putting the value

f(x)=7(x-3)^2+5

Hence, the equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.

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Answer:

The answer to this equation is (-1,1)

14 people can go to the amusement park. Inequality of wealth in major cities Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income.

Inequality: 33p + $12.50 ≤ $465

14 people can go to the amusement park

Inequality:

$465= Amount of money they have

$12.50= Parking Cost

$33= Cost of tickets per person

Because they only have $465, they can't spend more than that amount.

Therefore, the inequality would be the ticket cost per person, times the amount of people being payed for (aka x) plus the parking cost is less than or equal to the amount of money they have to spend. Hence the inequality:

33p+ $12.50 ≤ $465

$465- $12.50 = $452.5 (452.5 is how much is left for tickets after subtracting the parking cost)

$33 x1 4 = $462 (14 tickets can be bought for the price of $33)

$462 - $452.5 = $9.5 (9.5 isn't enough for another person)

So, the solution to the inequality is 14 people can go to the amusement park.

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Answer: 45.5p is less than or equal to 465

Answer:

Step-by-step explanation:

my answer is attached in the photo below

The area of the parallelogram shown is 6.6 square inches.

According to the question,

We have the following information:

We have a parallelogram with base 2.2 inches and height 3 inches.

We know that the following formula is used to find the area of parallelogram:

Area of parallelogram = Base*height

Area of parallelogram = 2.2*3

Area of parallelogram = 6.6 square inches

(Please note that area of any object or figure is always given in square units. For example, it may be square meters, square inches, square feet, etc.)

Hence, the area of the parallelogram shown is 6.6 square inches.

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1) The speed of a horsefly in feet per second is; 0.63 beats per minute

2) The number of times that the dragonfly's wing beats per minute is; 3 ft/s

3) The number of times that a bumble bee travels in one minute is; 0.11 miles per minute

Dimensional analysis is defined as the study of the relationship that exists between physical quantities with the help of dimensions and units of measurement.

Dimensional Analysis is also defined as a method of problem solving that takes into consideration the identity property of multiplication whereby the product of a number and 1 will always give the same number, that is 1 × n = n whereby the value "n" remains the same after the multiplication.

1) We are given from the table that the speed of a horsefly in miles per hour = 4.4 miles per hour. We want to know the speed expressed in feet per second.

From conversions, we know that;

1 mile per hour = 1/1.467 ft/s

Thus; 4.4 miles per hour = 4.4 * 1/1.467 = 3 ft/s

2) We are given from the table that the dragonfly's wing beat per second = 38 beats per second. We want to know the dragonfly's in wing beat per minute

From conversions, we know that;

1 beat per second = 1/60 beat per minute

Thus; 38 beats per second = 38 * 1/60 = 0.63 beats per minute

3) We are given from the table that the speed of a bumble bee in miles per hour = 6.4 miles per hour. We want to know the speed expressed in miles per minute

From conversions, we know that;

1 mile per hour = 1/60 miles per minute

Thus;

6.4 miles per hour = 6.4 * 1/60 = 0.11 miles per minute

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The lengths for the missing side of each case, determined by the use of trigonometric functions, are listed below:

Case D: 50.513

Case E: 46.165

Case F: 2.052

In this problem we have three cases of right triangles, each of which has an unknown side length. Each length can be found by using trigonometric functions. Now we proceed to determine it for each case:

Case D

tan 29° = 28 / x

x = 28 / tan 29°

x ≈ 50.513

The missing side length is approximately 50.513 units.

Case E

tan 18° = 15 / x

x = 15 / tan 18°

x ≈ 46.165

The missing side length is approximately 46.165 units.

Case F

cos 70° = x / 46

x = 46 · cos 70°

x ≈ 2.052

The missing side length is approximately 2.052 units.

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The values of the variables x and y in the triangle are 1.25 and 1.75

The tringle represents the given parameter

On the triangle, we have the following equivalent ratio

5 : 8 = 5 + x : 10

7 : 8 = 7 + y : 10

These are true because the horizontal lines of the triangles are parallel

So, we have

5 : 8 = 5 + x : 10

Express as fraction

5/8 = 5 + x/10

This gives

5 + x = 6.25

Solve for x

x  = 1.25

Similarly, we have

7 : 8 = 7 + y : 10

So, we have

7/8 = 7 + y/10

This gives

7 + y = 10*7/8

Evaluate

7 + y = 8.75

So, we have

y = 1.75

Hence, the values of x and y are 1.25 and 1.75

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Answer:

Step-by-step explanation:

You want the value of p(x)=5x^3+6x^2+4x for x=-5 and x=15.

Writing a polynomial in Horner form can simplify evaluation.

  p(x) = ((5x +6)x +4)x

  p(-5) = ((5(-5) +6)(-5) +4)(-5) = (-19(-5) +4)(-5) = 99(-5) = -495

  p(15) = ((5(15) +6)(15) +4)(15) = (81(15) +4)(15) = 1219(15) = 18285

The ordered pair of the values of f(x) and g(x) of (4, 3) and (4, 3) indicates that the input value that produces the same output value for f(x) and g(x) functions is x = 3

The input values of a function are the values that serve as the argument of the function. They are also known as the independent variable. The operations of a function are performed on the input values such that each input produces only one output, which is known as the dependent variable. The set of the input values is known as the domain of the function.

The output value of a function are the values of the function that gives the image of the input values, and they are known as the dependent variable. The set of the output values is the range of the function.

The points on the graph are;

Therefore, from the graph, at the point x = 3, f(x) = g(x) = 4

The input value that produces the same output value for the two functions on the graph is the x-value of 3

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The value of f(8) is 3.

What is logarithm?

The opposite of exponentiation in mathematics is the logarithm. The exponent to which b must be raised in order to obtain a number x is hence the logarithm of a number x to the base b. For instance, since 1000 = 103, log10 of 1000 is 3, or [tex]log_1_0=3[/tex].

Let, [tex]f(x) = log_2(x)[/tex]

We have to find the value of f(8).

Plug x = 8 in the above equation.

[tex]f(8) =log_2(8)[/tex]

Here 8 = 2 x 2 x 2 = 2^3

So, replace 8 with 2^3 in the above equation.

[tex]f(8) = log_2(2^3)[/tex]

Using the log rule: [tex]log_a(a^b) = b[/tex]

Here a = 2, b = 3

So, [tex]log_2(2^3) = 3[/tex]

Hence, f(8) = 3.

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The equation of the line that passes through the points (-2,-6) and (1,2) is y = 8x/3-2/3.

According to the question,

We have the following information:

Points through which line is passing =  (-2,-6) and (1,2)

Now, we have the following values:

x1 = -2, y1 = -6

x2 = 1 and y2 = 2

We know that the following formula is used to find the slope of the line:

m = (y2-y1)/(x2-x1)

m = (2+6)/(1+2)

m = 8/3

Now, the following formula is used to find the equation of the line:

y-y1 = m(x-x1)

y+6 = 8/3(x+2)

y+6 = 8x/3+16/3

Subtracting 6 from both sides:

y = 8x/3+16/3-6

y = 8x/3-2/3

Hence, the equation of the line that passes through the points (-2,-6) and (1,2) is y = 8x/3-2/3.

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