Use a 10-by-10 grid to solve.

What is 12% of 150?

The factor of the expression is (3x²+ 5)(x + 3)

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

3x³ + 9x² + 5x + 15

Group the terms in two's and factor each term

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

3x²(x + 3) + 5(x + 3)

Factor out x + 3

So, we have the following representation

(3x²+ 5)(x + 3)

Hence, the solution is (3x²+ 5)(x + 3)

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If the phone is in sale of 30% off, the money April save if she buys the phone on sale is $69.

A sale is a reduction of the basic price of a good or a service. It can occur on any stage in the process of production.

It is given that a phone sells for $230. It is now on sale for 30% off.

Now, Cost price = $230

sale percentage = 30%

so, the sale price = [tex]230 \times 30\%\\[/tex]

or  [tex]230 \times \frac{30}{100}[/tex] = $69

therefore, the money April will save if she buys the phone on sale is $69.

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Answer: -8 + (-4 )(look at the image for the solution)

Step-by-step explanation:

There will be 36.6 trees per acre after 4½ years from the end of the 5-year observation period. The solution has been obtained by using unitary method.

What is the unitary method?

The value of each individual unit is first determined using the unitary method, and only then is the value of the required number of units determined.

We are given that at the beginning of their observations, there was an average of 48 trees per acre. At the end of the 5-year period, there was an average of 42 trees per acre.

So, decline in trees per acre in 5 years is 48 - 42 = 6 trees per acre

So, decline in 1 year = 6/5 = 1.2 trees per acre

Similarly, decline in 4.5 years = 1.2 * 4.5 = 5.4 trees per acre

Thus, trees left per acre = 42 - 5.4 = 36.6 trees

Hence, there will be 36.6 trees per acre after 4½ years.

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Step-by-step explanation:

45g = 0.045kg

0.045 + 26 = 26.045

Final answer is 26.045 kg

Answer:

Step-by-step explanation:

48----------------100%

x------------------75%

x=36

The equation will be solved x = 2.

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

The given equation 2/[tex]2^{(4-3x)}[/tex] = 8

[tex]2^{(4-3x)}[/tex]  = 2/8

[tex]2^{(4-3x)}[/tex] = 2⁻²

So we can take 4-3x = -2

3x = 4+2

x = 6/3 = 2

Hence, the equation will be solved x = 2.

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The number of green rugs is more than the number of purple rugs. Then the amount of blue rug will be 29/4 square units.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Nina buys a new rug that matches three colors in her bedroom. The rug is a rectangle. There are eight squares on the rug. Four-eighths of the squares are green. One-fourth of the squares are purple.

The amount of green rug is given as,

⇒ 4/8

⇒ 1/2 square units

The amount of purple rug is given as,

⇒ 1/4 square units

The number of green rugs is more than the number of purple rugs.

The amount of blue rug is given as,

⇒ 8 - 1/4 - 4/8

⇒ (64 - 2 - 4) / 8

⇒ 29/4 square units

The number of green rugs is more than the number of purple rugs. Then the amount of blue rug will be 29/4 square units.

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Answer:

8

Step-by-step explanation:

0.06/48=800 0.01x800=8

The number of total outcomes is 12.

Here is a tree diagram for the pizza options:

Copy code

     /  |  \

 Thick Thin

  /     |     \

Red White Red White

/  |  \   / |  \   / |  \

Pep Saus Veg Pep Saus Veg Pep Saus Veg

There are two (2) options for the crust, two (2) options for the sauce, and three (3) options for the topping. Therefore, the total number of outcomes is:

Total Outcomes = 2 (options for crust) x 2 (options for sauce) x 3 (options for topping)

Total Outcomes = 12

Therefore, there are 12 total outcomes.

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Answer:The error in #1 is that it should read "3x²•(-2x⁴)=3•(-2)•x²⁴=6x⁸". The error in #2 is that it should read "4a²•3a⁵=4•a²•3•a⁵=12a⁷". The error in #3 is that it should read "x⁶•x³=x⁶•x³=x⁹". The error in #4 is that it should read "3⁴•2³=3⁴•2³=24".

Step-by-step explanation:

easy

The system of the equations are:

y = 10 + 4x

y = 25 + x

The height of tree is 30 inches tall.

The graph is given below.

The solution is (5, 30).

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation

We have,

Maple tree:

The maple tree that is 10 inches tall is

growing 4 inches per month,

This can be written as,

y = 10 + 4x _____(1)

Where y is the height of the tree.

Oak tree:

The oak tree is 25 inches tall and is growing 1 inch per

month.

This can be written as,

y = 25 + x ______(2)

Where y is the height of the tree.

Now,

From (1) and (2),

In a few months, the two trees will be the same height.

So,

10 + 4x = 25 + x

4x - x = 25 - 10

3x = 15

x = 5

Now,

y = 10 + 4x = 10 + 4 x 5 = 10 + 20 = 30

y = 25 + x = 25 + 5 = 30

Thus,

The height of tree is 30 inches tall.

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Answer:

51

Step-by-step explanation:

Answer:

The value of x is 12.

Greetings!!!

Firstly, recall the Pythagoras' theorem states that for all right-angled triangles, 'The square on the hypotenuse is equal to the sum of the squares on the other two sides'. The hypotenuse is the longest side and it's always opposite the right angle. In this triangle a² = b²+ c² and angle is a right angle.

a, b, and c represent the lengths of sides of a triangle, then: a2+b2=c2 if and only if the triangle is a right triangle.

Thus, on this question

the hypotenuse is a= 20

the value of b= 16

so the required value is c

[tex]a {}^{2} = b {}^{2} + c {}^{2} [/tex]

substitute known variables into the equation

[tex](20 ){}^{2} = (16) {}^{2} +( c) {}^{2} [/tex]

evaluate both sides

[tex]400 = 256 +( c) {}^{2} [/tex]

minus 256 from both sides

[tex]400 - 256 = (c) {}^{2} [/tex]

[tex]144 = (c) \frac{2}{} [/tex]

write bothe sides under radical in order to erase the square

[tex] \sqrt{144} = \sqrt{c {}^{2} } [/tex]

solve for c

[tex]c = 12[/tex]

Hope it helps

Answer:

x = 12

Step-by-step explanation:

Pythagoras Theorem

= Hypotenuse² = adjacent² + opposite²

From the question

Hypotenuse = 20

Adjacent = x

Opposite = 16.

The value for x

= 20² = x² + 16²

= 400 = x² + 256

= 400-256 = x²

= 144 = x²

[tex] \sqrt{144} = { \sqrt{x} }^{2} \\ \sqrt{144} = x \\ 12 = x[/tex]

Therefore adjacent (X) = 12

a. 1 hour and 45 minutes for the bacteria population to double.

To find out how long it takes for the bacteria population to double, we need to solve the equation:

2p(0) = p(h)

where p(0) is the initial population and h is the time it takes for the population to double.

Since p(h) = [tex]1000e^{(0.4h)}[/tex], we can write:

2p(0) = [tex]1000e^{(0.4h)}[/tex]

Dividing both sides by 1000, we get:

2p(0)/1000 = [tex]e^{(0.4h)}[/tex]

Taking the natural logarithm of both sides, we get:

ln(2p(0)/1000) = 0.4h

Solving for h, we get:

h = ln(2p(0)/1000) / 0.4

We know that p(0) = 1, since the initial population is given as 1,000. Substituting this value, we get:

h = ln(2) / 0.4

h ≈ 1.73

So it takes approximately 1.73 hours for the bacteria population to double.

Rounding to the nearest quarter of an hour.

we get:

h ≈ 1.75 hours

h ≈ 1 hour and 45 minutes

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Exponential growth is a pattern of data that shows a rapid increase over time, while exponential decay is a pattern of data that shows a rapid decrease over time.

An rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay.

The fundamental distinction between the two is that in an exponential decay relationship, the output values rise quickly as the input value rises, whereas in an exponential growth relationship, the output rises noticeably faster as the input value rises.

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The value of  m∠ABD is equals to  125 degrees.

Rectangle can be defined in which opposite sides are equal.

AC and BD are diagonals of the rectangle ABCD.

Angle ABD is adjacent to angle 1 and angle ABO, where O is the intersection of diagonals AC and BD.

We know that m∠1 = 55, and we can find m∠ABO using the fact that the diagonals of a rectangle bisect each other. Since angle AOB is opposite to side AB, which is congruent to side CD, we have:

m∠ABO = 180 - m∠AOB

= 180 - (180 - m∠1) / 2

= 180 - (180 - 55) / 2

= 62.5

Therefore, we can find m∠ABD by adding m∠ABO and m∠DBO, where DBO is congruent to ABO:

m∠ABD = m∠ABO + m∠DBO

= m∠ABO + m∠ABO

= 2m∠ABO

= 2(62.5)

= 125

Hence, The value of  m∠ABD is 125 degrees.

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Option (D) is correct. The approximate arc length of one slice of pie is 5.24 inches.

Assuming that the pie is cut into equally sized slices, we can use the formula for the arc length of a circle sector:

Arc length = (angle/360) x 2πr

where r is the radius of the circle, and angle is the central angle of the sector in degrees.

Since the diameter of the pie is 10 inches, the radius is half of that, or 5 inches. To find the central angle of one slice of pie, we need to know how many slices the pie is cut into. Let's assume it's cut into 6 slices, which means each slice is a sector with a central angle of 60 degrees (360 degrees / 6 slices).

Now we can calculate the arc length of one slice:

Arc length = (60/360) x 2π(5) = π(5/3) ≈ 5.24 inches

Therefore, the answer is (D) 5.24 inches.

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Answer:

11 glasses

Step-by-step explanation:

There are 200 ml glasses and we have 2.21 liter of bottels. So first of all covert liter into ml so we get 2210 ml of coca cola.now divide 2210 by 200 so we get 11 glasses

Answer:

51 stamps

Step-by-step explanation:

since salman's amount is going from 5 to 45 its being multiplied by nine. to keep the ratio true, you need to multiply the other two numbers by 9 too. Nathan then has 12 stamps and Gordon has 63. 63-12=51

The linear equation for the given coordinate points is y=-2x+97.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

From the given table, the coordinate points are (3, 91) and (4, 89).

Here, slope (m)= (89-91)/(4-3)

m= -2

Substitute m=-2 and (x, y)=(3, 91) in y=mx+c, we get

91=-2(3)+c

91=-6+c

c=97

So, the equation is y=-2x+97

Therefore, the linear equation is y=-2x+97.

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Answer:

7.8

Step-by-step explanation:

a. The percentage of the department faculty have 5 or more years of service is 76%

b. Probability that a faculty member chosen at random has between 5 and 35 years of service is 0.4.

c. The probability the representative will have less than 5 years of service given that the person has less than 15 years of service is 0.7.

The histogram is used to estimate probability of a categorical variable or probability of frequency of a particular class interval, and there is no gap among the bars of the histogram.

(a) The per cent of the department faculty have 5 or more years of service is calculated as follows,

The number of department faculty have 5 or more years of service is 38 and total frequency 50, therefore the required probability is:

P(x > 5) = 38/50 = 0.76 = 76%

(b) The probability (in decimal form) of representative will have between 5 and 35 years of service is given as,

P(5 < X < 35) = 20/50 = 0.4 = 40%

(c) The probability the representative above will have less than 5 years of service given that the person has less than 15 years of service is calculated as follows,

P(X < 5 | X < 15) = 28/40 = 0.7

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For complete question, see the figure.

The value of t is 6.5. The value of the constant is 60

What varies directly?

The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a. (where k is a constant).

Given that  d varies directly as t.

The relation between d and t is

d = kt.

Given that d = 180 when t = 3.

Putting d = 180 and t = 3 in d = kt

180 = 3k

Divide both sides by 3:

k = 180/3

k = 60

Putting k = 60  in d = kt:

d = 60t

Now putting d = 390 in d = 60t:

390 = 60t

60t = 390

Divide both sides by 60

t = 6.5

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The required true statements are B). BC = AD, D). ∠CAD = ∠LACB, E). ∠BPC = ∠APD

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

The statements that must be true are:

B. BC = AD (Opposite sides of a parallelogram are equal in length)

D. ∠CAD = ∠LACB (Opposite angles of a parallelogram are equal in measure)

E. ∠BPC = ∠APD (Opposite angles of a parallelogram are equal in measure)

The statements A and C are not necessarily true for all parallelograms.

Statement A (AP = CP) is only true for parallelograms that are rectangles or rhombi, where the diagonals bisect each other.

Statement C (m∠ABC = 90) is only true for parallelograms that are rectangles or squares, where each angle is a right angle.

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The variable gets eliminated, then the equation has no solution.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equation is given below.

(10x - 4) + ( -7 + x) = (10x + 2) + (-4 + x)

Simplify the equation, then we have

(10x - 4) + ( -7 + x) = (10x + 2) + (-4 + x)

10x - 4 - 7 + x = 10x + 2 - 4 + x

11x - 11 = 11x - 2

11x - 11x = 9

The variable gets eliminated, then the equation has no solution.

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The correct equation is given below.

(10x - 4) + ( -7 + x) = (10x + 2) + (-4 + x)

There were total 4 people at table A and each of them pay €18.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Table A's bill of €72 is split equally.

and, Table B has two more people than Table A and its bill of €108 is also split equally.

let number of people at table A be x and at table B be (x+2).

So, the number of people

x/ 72 = (x+2)/108

108x = 72x + 144

108x - 72x = 144

36x= 144

x=4

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Answer:

A ladder leans against the wall of a building. The ladder measures 66 inches and forms an angle of 45 degrees with the ground. How far from the ground, in inches, is the top of the ladder? How far from the wall, in inches, is the base of the ladder?

Step-by-step explanation:

The number of seats in each raw by the given graph is 30.

Suppose the considered function whose graph is to be made is

f(x)

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values

f(x)

are plotted on the vertical axis.

They are together plotted on the point

(x,y) = (x, f(x))

This is why we usually write the functions as:

y = f(x)

Let the number of rows in the original arrangement be x. Then, the number of seats in each row in original arrangement = x

Total number of seats = x x x = x²

From the given information,

2x(x-10)= x²+ 300

2x²-20x = x²+300

x²-20x-3000

(x-30) (x+10) = 0

x = 30, -10

Since, by the function number of rows or seats cannot be negative. So, x = 30.

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