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The inequality tha calculates the possible values of x is x < 2

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

The figure

Where, we have

3x + 2 < 10

And, we have

2x + 6 < 10

Evaluate the expressions

So, we have

3x < 8 and 2x < 4

Evaluate

x < 8/3 and x < 2

Hence, the inequality tha calculates x is x < 2

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Answer:

A

Step-by-step explanation:

fog(x) = f(g(x) = f(1/2x) = 4x/(1+6x)

Answer:

A. down

Step-by-step explanation:

The parent graph is

f(x)=x

If this graph is transformed to obtain

g(x)=f(x)−4

The subtracttion means the graph will shift downward vertically

The graph of g(x) is obtained by shifting f(x) down by 4 unit.

Therefore the direction is down.

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The volume of cylinder is denoted as πr²h

The density of a cylinder is determined by its volume, which indicates how much material it can hold or how much can be submerged inside it. The volume of a cylinder can be calculated using the formula r2h, where r denotes the radius of the circular base and h denotes the height of the cylinder. Any substance that can be evenly put into the cylinder, including liquid, may be used as the material. Shape volumes can be seen here.

This article contains a basic explanation of cylinder volume as well as examples with solutions for your convenience. The study of shapes and their characteristics is a key component of geometry in mathematics. Any three-dimensional shape must have both volume and surface area.

Hence, the volume of cylinder is denoted as πr²h

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The measure of the angle ABE = 27°.

For the given values in question;

∠ABE = 2x+7 and ∠EBF = 2x+7

The figure below shows that ABE and EBF are congruent.

Thus,

∠ABE = ∠EBF

Equating both values;

2x+7  =  4x - 13

On one side, isolate variable terms.

4x - 2x = 7 + 13

Further simplifying;

2x = 20

x = 10

Put the value of x = 10 in angle ABE

∠ABE = 2x+7

∠ABE = 2×10 + 7

∠ABE = 27

Thus, the value of the ∠ABE is found as 27°.

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The correct question is;

If angle ABE = 2x+7 and angle EBF = 4x-13 find angle ABE.

≈ 10.7 %

Hi there !

70 ............ 100%

7.5 ................x%

x = 7.5×100/70

= 750/70

≈ 10.7 %

Good luck !

Find the amount of the markup by subtracting:

76-39 = $37

Divide the amount of the mark up by the purchase price:

37/39 = 0.948 x 100 = 94.8%

Answer: 94.8 %. Round the answer as needed.

Expression 4 is not a polynomial because it contains a square root, and expression 5 is not a polynomial because it only contains a single variable term (it is a monomial).

A polynomial is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, multiplication, and non-negative integer exponents. The variables in a polynomial are typically represented by letters, such as x or y, and the coefficients are constants that multiply the variables.

by the question.

The expressions that are polynomials are:

5x³ + 2x + 10

04 + 3x³ - 2x + 1

x⁴

3x³ + 4x² + 1

-x⁵ + 3x³ - 2x + 1

Polynomials are expressions that consist of variables and coefficients, and only involve addition, subtraction, and multiplication (but not division) of these terms. All of the above expressions fit this definition.

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There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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Answer:  

y= 8(5 * 0.7) ^ 5

Step-by-step explanation:

Answer as a fraction =  4/3

Answer in decimal form = 1.33 approximately

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

Explanation:

x = number of days

y = number of inches

For instance, on day x = 3, we have y = 4 inches of flood water. This is shown by the point (x,y) = (3,4) on the diagonal line.

Divide y over x to get the value of k, which is the constant of proportionality.

k = y/x

k = 4/3

k = 1.33 which is approximate

You could also pick a point like (x,y)  = (6,8) to find that

k = y/x

k = 8/6

k = 4/3

k = 1.33

Which is the same as earlier.

We can pick any point on the diagonal line as long as it's not the origin point (0,0).

The equation of this direct variation line is y = (4/3)x. It has a slope of 4/3 and a y intercept of 0. The slope of 4/3 means that each time we move up 4 on the y axis, we move to the right 3 units on the x axis.

In short, slope = rise/run = 4/3. So rise = 4 and run = 3.

For any direct variation linear equation, the slope and constant of proportionality are the same thing.

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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Answer:

parallel: m= -1/5

parpendicular: m= 5

Step-by-step explanation:

parallel lines have the same slope

- 1      stays the same so      - 1  

 5                                            5

parpendicular lines have the opposite reciprocal slope

- 1      flipped is     - 5      turn the negative into a positive   5      or    5

 5                             1                                                                  1

(A) Let A(t) denote the amount (in grams, g) of the chemical present in the pond at time t (in hours, h). The starting amount is unknown; call it a, measured in g, so that A(0) = a.

Water containing 0.01 g/gal of the chemical flows in at a rate of 300 gal/h, which increases the amount of the chemical in the pond at a rate of

(0.01 g/gal) • (300 gal/h) = 3 g/h

and flows out at the same rate, so the amount decreases by

(A(t)/1,000,000 g/gal) • (300 gal/h) = 3A(t)/10,000 g/h

Then the net rate of change of the amount of chemical in the pond is given by the ODE,

dA(t)/dt = 3 - 3/10,000 A(t)

(B) Solve the ODE for A(t). There are several ways to do that. For instance, itt's separable, so we have

dA(t) / (3 - 3/10,000 A(t)) = dt

Integrate both sides to get

-10,000/3 ln|3 - 3/10,000 A(t)| = t + C

Solve for A(t) :

ln|3 - 3/10,000 A(t)| = -3/10,000 t + C

3 - 3/10,000 A(t) = exp(-3/10,000 t + C )

3 - 3/10,000 A(t) = exp(-3/10,000 t ) • exp(C )

3 - 3/10,000 A(t) = C exp(-3/10,000 t )

3/10,000 A(t) = 3 - C exp(-3/10,000 t )

A(t) = 10,000 - C exp(-3/10,000 t )

Since A(0) = a, we have

a = 10,000 - C exp(-3/10,000•0)   →   C = 10,000 - a

→   A(t) = 10,000 - (10,000 - a) exp(-3/10,000 t )

As t grows to infinity, the exponential term will vanish, leaving a limiting amount of 10,000 g of the undesirable chemical in the pond, which does not depend on the original amount.

Step-by-step explanation:

To determine whether a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let's denote the three sides of the given triangle as a = 23, b = 30, and c = 19. We can check if these side lengths satisfy the Pythagorean theorem as follows:

c^2 = a^2 + b^2

19^2 = 23^2 + 30^2

361 = 529 + 900

Since 361 is not equal to 529 + 900, we can see that the given triangle is not a right triangle.

Given:

Area of wood floor required = 320 sq ft

Cost of hardwood per sq ft = $4.59

Cost of lamination per sq ft = $2.79

Solution

Cost of hardwood :

When we substitute the required parameters, we have:

Cost of lamination:

When we substitute the required parameters, we have:

The difference in cost between the two types of flooring:

Answer: $ 576

Answer:

x = 24/5

Step-by-step explanation:

Answer:

D, E, and A

Step-by-step explanation:

Because 4 is also equivelent to square root of 16 and square root of 16 times square root of 3 is equal to square root of 48 which is D, and E is also correct because square root 24 x square root 2 is also square root 48 and same concept with A.

Answer:

326

Step-by-step explanation:

The value of the given expression is 326.

Given:

The given expression 2 hundreds + 12 tens + 6 ones.

To find:

The value of the given expression.

Explanation:

The numeric form of given expression is:

2 hundreds + 12 tens + 6 ones

2 hundreds + 12 tens + 6 ones

2 hundreds + 12 tens + 6 ones

Therefore, the value of the given expression is 326.

Answer:

(a)$8.75

(b)$7.5

(c)$60

Explanation:

Part A

From the table, for 3 hours, Josie earned a wage of $26.25.

Therefore:

Part B

From the graph:

When Salvadorhours worked = 2

Wages = $15

Therefore:

Part C

Each week, they worked for 8-hours daily for six days.

The total number of hours they worked in a week

Next, we calculate their earnings after one week.

The difference in Josie's and Salvador's earning after one week is $60.

According to the equation the given all necessary math work are:

\(A: (x -f)^2 +(y -g)^2 = h^2\)

B:  domain: [-5, 11]; range: [-9, 7]

C:  yes, inside

The hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides if a triangle has a straight angle (90 degrees), accοrding tο the Pythagοras theοrem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypοtenuse BC are all used in this equatiοn. The lοngest side οf a right-angled triangle is its hypοtenuse, it shοuld be emphasized.

Part A:

Use οf the Pythagοrean theοrem gets yοu tο the equatiοn fοr a circle in essentially οne step:

sum οf squares οf sides = square οf hypοtenuse

\((x -f)^2 +(y -g)^2 = h^2\) . . . . . . circle cantered οn (f, g) with radius h

Part B:

The circle will be defined fοr values οf x in the dοmain f ± h, and fοr values οf y in the range g ± h.

dοmain: 3 ± 8 = [-5, 11]

range: -1 ±8 = [-9, 7]

Part C:

The distance frοm pοint (10, -4) tο (f, g) is ...

\(h^2 = (10 -3)^2 +(-4 -(-1))^2\)

\(h^2 = 7^2 +(-3)^2 = 49 +9 = 58\)

h = √58 < 8 . . . . the distance tο the pοint is less than h=8.

The pοint is inside the circle.

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Answer:

the answer is option A population standard deviation

Answer:

Slope, \(m=\dfrac{1}{5}\)

Step-by-step explanation:

It is given that,

A road rises 20 feet for every 100 feet in horizontal distance.

Rise (vertical distance) = 20 feet

Run (horizontal distance) = 100 feet

Slope of the road is given by the ratio of rise to the run. It can be calculated as :

\(m=\dfrac{20}{100}\\\\=\dfrac{1}{5}\)

So, the slope is \(\dfrac{1}{5}\).

Answer:

\((f-g)(2)=14\)

Step-by-step explanation:

We are given the two functions:

\(f(x)=3x^2+1\text{ and } g(x)=1-x\)

And we want to find the value of:

\((f-g)(2)\)

This is equivalent to:

\((f-g)(2)=f(2)-g(2)\)

Substitute:

\(=(3(2)^2+1)-(1-(2))\)

Evaluate:

\(=(3(4)+1)-(1-2)=(12+1)-(-1)=13+1=14\)

Therefore:

\((f-g)(2)=14\)

Answer:7                                 7

Step-by-step explanation:7   7

Answer:

the area is 130

Step-by-step explanation:

The area of the rectangle for the given case is obtained as 0.7x².

A linear equation is a equation that has degree as one.To find the solution of n unknown quantities n number of equations with n number of variables are required. A linear equation can be solved by doing operations with the same number on both sides of the equation.

Suppose the length of the rectangle be x.

Then, its width is given as 70% × x = 0.7x.

Since, the area of the rectangle is the product of length and width, the following equation can be written as,

x × 0.7x = 0.7x².

Hence, the required expression for the area of the rectangle is given as 0.7x².

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Given a rectangle of which its length is nine more than triple the width. The width is _10_inches. The length is 39 inches.

Let:

l = length of the rectangle

w = width of the rectangle

"The length of a rectangle is nine more than triple the width" can be translated as:

l = 9 + 3w

perimeter = 2 l + 2w

Substitute perimeter = 98 and  l =  9 + 3w into the perimeter equation:

98 = 2 x (9 + 3w) + 2w

98 = 18 + 8w

8w = 98 - 18

8w = 80

w = 80/8 = 10 inch.

Substitute w = 10 into the length equation:

l = 9 + 3w

l = 9 + 3 x 10

l = 9 + 30 = 39

Therefore the correct answer is:

The width is _10_inches. The length is 39 inches.

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Answer:

$54.87

Step-by-step explanation:

The area of the triangular garden is (1/2) x base x height = (1/2) x 6 x 5 = 15 square feet.

The area of the rectangular mulch area is base x height = 12 x 9 = 108 square feet.

The total area to be covered with mulch is 108 - 15 = 93 square feet.

The cost of the mulch is $0.59 per square foot, so the total cost is 93 x $0.59 = $54.87.

Therefore, the total cost of the mulch will be $54.87.