Find the area between the graph of y=x^2-2 and the x-axis, between x=0 and x=7.
Round your answer to 3 decimal places.

The jobs Deepak will accept must require at least 3 hours of work in order for him to earn at least $90 per job: 30x + 15(x) ≥ 90.

30x + 15x ≥ 90

45x ≥ 90

x ≥ 90/45

x ≥ 2

To determine the restrictions on the jobs Deepak will accept, we must first write an inequality that shows the minimum number of hours he must work in order to make at least $90 per job. This inequality is

30x + 15x ≥ 90,

which can be simplified to

45x ≥ 90

Dividing both sides of the inequality by 45 gives us

x ≥ 90/45,

which can be further simplified to x ≥ 2. This means that Deepak will only accept jobs that require at least 2 hours of work in order to make at least $90 per job.

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Amortization makes up $120.15 of colinda's first monthly mortgage payment.

We must first determine the total amount of Colinda's mortgage in order to determine the amount of her first monthly mortgage payment, which is amortization. Her 20% down payment of $25,000 reduced the mortgage balance to $100,000 ($125,000 – $25,000).

The 30-year term and 5% interest rate on the mortgage result in a $536.82 monthly payment. The portion of the mortgage payment designated for amortization is the sum that is used to pay off the loan's principle; the remainder is used to cover interest.

We can use the following formula to determine the amortization part of the mortgage payment:

Amortization = (Mortgage Payment) - (Interest Payment)

Where:

The mortgage payment ($536.72) is made each month.

Monthly interest payments are computed using the following formula: (Amount of Mortgage) (12%) Interest Rate

When we enter the values, we obtain:

Amortization is calculated as ($536.72) - ($100,000) * (0.05/12)

$536.82 - $416.67 is the amortization.  

Amount amortized : $120.15

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The system of inequalities of the scenario is x + y ≤ 24 and 6x + 5y ≥ 550

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Number of containers = x + y

Where

x = Yoghurt

y = Kefir

This means that

x + y = At most 24

Express as an inequality

x + y ≤ 24

For the earnings, we have:

6x + 5y = Total earnings

Express as an inequality

6x + 5y ≥ 550

Hence, the inequalities are x + y ≤ 24 and 6x + 5y ≥ 550

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Complete question

Nathaniel has enough goat's milk to make at most 24 containers of fermented milk product (either yogurt or kefir). Each container of yogurt sells for $6.00​​, while each container of kefir sells for $5.00 Nathaniel needs to make at least $550.

What is the system of inequalities of the scenario?

Answer:

-97290

Step-by-step explanation:

The height of Billy's drawing, obtained by using the scale factor of 0.5 inches is equivalent to 2 feet, and Billy's height of 5'6'' is 1.375 inches.

A scale factor is a number by which the dimensions of the sides (the side lengths) of an original figure is multiplied in other to obtain the dimensions (lengths of the sides) of the image.

The height of Billy's drawing can be obtained by multiplying Billy's height by the scale factor used for the drawing.

The scale of the drawing is 0.5 inches ≡ 2 feet

Billy's height = 5'6'' (5 feet 6 inches)

Dividing both sides of the scale factor by 2, we get;

0.5 inches ÷ 2 ≡ 2 feet ÷ 2

0.25 of an inch ≡ 1 ft

5'6'' (5 feet 6 inches) = 5 feet 6 inches = 5.5 feet

The scale factor equation is; 0.25 of an inch = 1 ft

Multiplying both sides of the scale factor equation by 5.5, we get;

5.5 × 0.25 of an inch ≡ 5.5 × 1 ft

1.375 inches ≡ 5.5 ft

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The solution to the differential equation is y = 2x/(y + 2x), which can be interpreted as y is equal to twice x divided by y plus twice x.

du/dx = 2(y + x)

Integrating both sides, we get

∫du/2(y + x) = ∫dx

1/2 ∫u du = x + C

(1/2)u^2 = x + C

(1/2)(y + x)^2 = x + C

y^2 + 2xy + x^2 = 2x + C

y^2 + 2xy = 2x + C - x^2

y^2 + 2xy = 2x + C - x^2

y^2 + 2xy + C = 2x + C

y^2 + 2xy + C = 2x + C

y^2 + 2xy = 2x

y(y + 2x) = 2x

y = 2x/(y + 2x)

y = 2x/(y + 2x) y = 2x/(y + 2x), which can be interpreted as y is equal to twice x divided by y plus twice x.

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p<4 is the solution of the given inequality.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is -16>-4p

Minus sixteen greater than minus four p

Divide both siders by -4

4>p

p<4

Now we have to draw this on number line.

a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

The attached figure has the graph of p<4.

Hence,  p<4 is the solution of the given inequality.

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Answer:

[tex]x^2-8x+15=0[/tex]

Step-by-step explanation:

If the roots are [tex]3[/tex] and [tex]5[/tex], the factors are [tex](x-3)[/tex] and [tex](x-5)[/tex].

Taking the leading coefficient as 1, the equation is [tex](x-3)(x-5)=0 \implies x^2-8x+15=0[/tex].

By solving an inequality we will see that for 7 movies (or more) the first store is a better deal.

We know that the first store charges $12.50 as a fixed cost plus $1.50 per movie rented, so if you rent x movies, the total cost is:

c(x) = $12.50 + $1.50*x

While the second store charges $3.50 per movie, then the cost for renting x movies here is:

h(x) = $3.50*x

We want to find the minimum value x such that c(x) < h(x), then we need to solve the inequality:

$12.50 + $1.50*x <  $3.50*x

$12.50 < $3.50*x - $1.50*x

$12.50 < $2.00*x

$12.50/$2.00 < x

6.25 < x

So, for x = 7 the first store is a better deal.

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Gary would need 15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.

Option D is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Bottles   Glue   Glitter

1              3.8       1.9

This means,

1 bottle = 3.8 oz of glue and 1.9 oz of glitter

Now,

1 bottle = 3.8 oz of glue

Multiply 4 on both sides.

4 bottle = 4 x 3.8 oz

4 bottle = 15.2 oz

1 bottle = 1.9 oz of glitter

Multiply 4 on both sides.

4 bottle = 7.6 oz

Thus,

15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.

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79 rounded to the nearest 10 is 80.

79 lies between 70 and 80. 75 is exactly half-way between 70 and 80, and 79 is between 75 and 80. So 79 is closer to 80 than 70 on the number line and it rounds up to 80.

  70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80

We round the number up to the nearest ten if the last digit in the number is 5, 6, 7, 8, or 9.

We round the number down to the nearest ten if the last digit in the number is 1, 2, 3, or 4.

If the last digit is 0, then we do not have to do any rounding, because it is already rounded to the ten.

Therefore, 79 rounded to the nearest ten = 80.

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Answer:

Step-by-step explanation:

Answer:

47.70

Step-by-step explanation:

6%= 2.7

2.7 +45

=47.7

An alias cannot be used when a table is required to be joined to itself in a recursive query is false.

The majority of relational database management systems, if not all of them, include the SQL feature known as an alias (RDBMSs). Database administrators and other database users can use aliases to cut down on the amount of coding necessary for a query and to make it easier to understand. Additionally, the real names of database fields can be protected using aliasing as an obfuscation approach.

You can alias tables and columns in SQL. A correlation name is another term for a table alias. [1] For the duration of a SELECT query, a programmer can temporarily give a table or column a different name by using an alias. The column or table are not truly renamed when an alias is assigned.

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If a rhombus has an angle measure of 120 and it’s longer diagonal has a length of 10 inches. The area of the rhombus is 28.85.

Obtuse angle = 120 so, the other two angles must add up to 60 and each would be half of 60 or 30.

Hence,

Sin 30°  = 0.5  

Sin 60° = 0.86602540378

Now let find the length of breadth

Length of breadth  = 0.5 / 0.86602540378

Length of breadth = 0.577

Now let find the area using this formula

A =b × h

Where:

b=0.577

h=0.5

A = 0.577 x 0.5

A = 0.2885

A  = 28.85

Therefore the area is 28.85.

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Answer:

2684 [tex]units^{2}[/tex]

Step-by-step explanation:

We find the area of the 4 triangles

area = 1/2 base x height  All the bases area the same measurement

a = 1/2(22)(61)

a = 671

There are 4 sides

671 x 4 = 2684

The standard deviation is 5.94 and rounded to the nearest tenth, the standard deviation is 5.9.

The standard deviation from the mean is a measure of how spread out the data is in a set of numbers. It is calculated by finding the square root of the variance of the data set, which is the average of the squared differences between each data point and the mean.

To calculate the standard deviation from the mean for the set of numbers 4, 5, 6, 14, 15, and 5, you would first need to find the mean of the set by adding all of the numbers together and dividing by the number of numbers in the set. The mean of this set is 8.17.

Next, we will need to calculate the squared differences between each number and the mean, and then average those squared differences. The variance of this set is 35.15.

Finally, we will take the square root of the variance to find the standard deviation, which is approximately 5.94. Rounded to the nearest tenth, the standard deviation is 5.9.

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Answer: Ace

Step-by-step explanation: Since the line rests on y = 100, the range is indeed y= 100.

(note that domain is x while range is y)

The equation of the line is y = 0.5x + 1 having a slope of 0.5 and y intercept of 1

The equation of a line is:

y = mx + b

Where m is the slope and b is the y intercept

From the table shown, the points are:

(-6, -2), (-4, -1), (-2, 0), (0, 1) and (2, 2)

Using any two points to get the equation. Let us use (-2, 0) and (0, 1):

y - 0 = [(1 - 0)/(0-(-2))](x - (-2))

y = 0.5x + 1

The equation of the line is y = 0.5x + 1

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The number that represents the system in this problem is given as follows:

x = 4.

The number is unknown, hence the variable that represents the number is given as follows:

x.

Then an equality is built from the sentence in the problem, which is then solved to obtain the number.

The addition of 3 to a number is given as follows:

x + 3.

The triple the sum is given as follows:

3(x + 3).

The result is 17 more than the number, hence the equality is given as follows:

3(x + 3) = 17 + x.

Then the solution for the equality, which gives the number, is obtained as follows:

3x + 9 = 17 + x

3x - x = 17 - 9

2x = 8

x = 8/2

x = 4.

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For the coordinates and their weights, the weight average is 5

From the question, we have the following parameters that can be used in our computation:

Coordinates and weights

The coordinates and weights are then given as:

The weight average is then calculated as:

Weight average = Sum of (Weight * Coordinate)/Sum of Weights

Substitute the known values in the above equation

So, we have the following equation

Weight average = (3 * 2 + 9 * 1)/(2 + 1)

Evaluate the product in the above equation

So, we have the following equation

Weight average = (6 + 9)/(2 + 1)

Evaluate the sum in the above equation

So, we have the following representation

Weight average = (15)/(3)

Evaluate the quotient in the above equation

So, we have the following equation

Weight average = 5

Hence, the weight average of the coordinates is 5

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After 40 hours the population of bacteria will be equals to 318 hours.

We can calculate the total population growth using the following equation:

A(t)= A₀× 2ᵗ/¹⁵

Where, A(t) --> the total population

A₀ --> the initial population

t --> the time in hours

From the statement we know that the population of bacterias doubles every 15 hours, so, using the formula we have: A(15) = A₀ × 2ᵗ/¹⁵

The initial population is = 50 , then

A(15) = 50×2¹⁵/¹⁵ = 100

It shows that every 15 hours, the population of bacterias doubles it size. We are asked to calculate the popualation after 40 hours, so:

A(40) = 50 × 2⁴⁰/¹⁵

= 6.35 × 50 = 317.5 ~ 318

So, after 40hours the population of bacteria will be 318.

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The graph of the equation y = -4 is a straight line perpendicular to y-axis and parallel to x-axis passing through point (0,-4)

A straight line is an infinitely wide one-dimensional figure. It is made up of an infinite number of points connected at both ends by another point. A straight line is devoid of all curves. It can be angled, vertical, or in any direction. A 180-degree angle will always result from drawing an angle between any two points on a straight line. we will learn how to read straight line equations in various formats and how to use them to answer questions about straight lines.

So that, The graph of the equation y = -4 is a straight line perpendicular to y-axis and parallel to x-axis passing through point (0,-4) as shown in attached diagram.

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[tex]8 < x+2 < 20[/tex]

a) Add -2 to all sides.

[tex]8+-2 < x+2-2 < 20+-2[/tex]

[tex]6 < x < 18[/tex]

Your answer would be [tex]6 < x < 18[/tex]

Your answer should be: (6,18)

The required measure of angle x is given as 60°, for the given quadrilateral.

A quadrilateral is a four-sided enclosed shape, whose sum of the internal angle is equal to 360°,
Examples of the quadrilateral, square, rectangle, etc.

Here,
The sum of the angle of the quadrilateral is equal to 360,
So,
x + 100 + 130 + 66 = 360
x = 360 - 296
x = 64°

Thus, the required measure of angle x is given as 60°, for the given quadrilateral.

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Answer:

The first image is right. The line on X = -1

Step-by-step explanation:

x + 2 ≥ 1

x ≥ 1 -2

x ≥ -1

The combined mass of the pebbles that are 4 1/2 grams more is 66 grams.

In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.

Given:

The mass of the pebbles is shown in the image attached below,

Calculate the combined mass as shown below,

The combined mass = 4.5 × 5 + 5 × 4 + 5.5 × 3 + 1 × 7

The combined mass = 22.5 + 20 + 16.5 + 7

The combined mass = 39 + 20 + 7

The combined mass = 66

Thus, the combined mass is 66 grams.

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