Mr. Evans is giving a 28-question test that is made up of 2-point questions and 4-point questions. The entire test is worth 100 points. Let t represent the number of 2-point questions, and let f represent the number of 4-point questions.

Answer: 6 minutes or 600 seconds. Thats how long it takes for him to ride his bike home

Step-by-step explanation: 7200 divided by 12 is 600

Answer: To calculate the amount of simple interest, we use the formula: I = P * r * t, where P is the principal amount (7500), r is the annual interest rate (5%) and t is the time in years (5).

So, the simple interest is: I = 7500 * 5 * 0.05 = 187.5

The total amount Susan will have to pay back to the bank is the principal amount plus the interest:

7500 + 187.5 = $76 87.5

Therefore, Susan will pay the bank back $76 87.5 after 5 years.

Step-by-step explanation:

Answer:

Let's call the initial fee "x". The equation for the total cost of using a computer for t minutes at the internet cafe can be expressed as:

C = x + 0.60t

Knowing that the total charge to use a computer for 5 minutes would be $6, we can use this information to find the value of x:

C = x + 0.60 * 5

6 = x + 3

x = 6 - 3

x = 3

So, the equation representing the total cost of using a computer for t minutes at the internet cafe is:

C = 3 + 0.60t

Answer & Step-by-step explanation:

To simplify the expression 3a + 6b - 8a + 9b, we can combine the like terms (terms with the same variable).

First, we can combine the 3a and -8a terms since they have the same variable 'a'. When we subtract 8a from 3a, we get -5a.

Then, we can combine the 6b and 9b terms since they have the same variable 'b'. When we add 6b and 9b, we get 15b.

Putting it all together, we get:

3a + 6b - 8a + 9b = -5a + 15b

Therefore, the simplified expression is -5a + 15b.

3a+6b-8a+9b

9b+6b-8a+3a

15b-5a

5(3b-a)

The conditional probability that the previous state was state 2 given that the chain is currently in state 1 is equal to the probability of transitioning from state 2 to state 1.

The conditional probability of transitioning from one state to another in a Markov Chain is dependent on the transition probabilities between the states. In this case, the conditional probability of transitioning from state 2 to state 1 is equal to the probability of transitioning from state 2 to state 1. This probability can be determined by looking at the transition matrix of the Markov Chain. The transition matrix specifies the probability of transitioning from one state to another. Therefore, the conditional probability of transitioning from state 2 to state 1 given that the chain is currently in state 1, is equal to the probability of transitioning from state 2 to state 1 as specified in the transition matrix.

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The value of the given expression is 1440

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

(x²yz^4)/z

Substitute the values for x,y and z

 ((-6)²*5*2^4)/2

= (36*5*16)/2

use 16/2 = 8

= 36*5*8

= 1440

The value of the given expression is 1440

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Answer:

Step-by-step explanation:How do you find the gradient and y-intercept?The equation y = mx + c is the general equation of any straight line where m is the 

Answer:

29.13

Step-by-step explanation:

5÷34+3÷64+5÷5

= 6.8+ 21.33+ 1

=29.13

Answer:

the person above me is right just did the math for u

Step-by-step explanation:

yea cuz we smart :))

The quadratic equation has the following three features:

B. 7 is the coefficient of one term of the expression.

C. x is a variable in the expression.

D. The expression has three terms.

In this question we have the case of a quadratic equation in standard form, whose features must be understood by direct inspection. At first sight we get the following conclusions:

Lastly, we get the following roots from the quadratic equation:

x² + 7 · x + 6 = 0

(x + 1) · (x + 6) = 0

x = - 1 or x = - 6

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As per arithmetic progression the value of 15th term is 0.

An arithmetic progression, or A.P., is a sequence of numbers in which the difference between consecutive terms is constant.

To start, let's call the common difference "d" and the first term "a". We can use the formula for the nth term of an A.P., which is Tn = a + (n-1)d, where Tn is the nth term and n is the position of the term in the A.P.

Using this formula, we can find the 6th term and 9th term. For the 6th term, T6 = a + (6-1)d = a + 5d. For the 9th term, T9 = a + (9-1)d = a + 8d.

Now, using the information given, we can create an equation: 6(a + 5d) = 9(a + 8d). Expanding both sides and simplifying, we get:

6a + 30d = 9a + 72d

Subtracting 9a from both sides, we get:

-3a + 30d = 72d

Subtracting 30d from both sides, we get:

-3a = 42d

Dividing both sides by -3, we get:

a = -14d

Now that we have found the value of "a", we can use the formula for the nth term again to find the 15th term. T15 = a + (15-1)d = -14d + 14d = 0.

So, the 15th term of the A.P. is 0.

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In linear equation, 24.9  tall is the tree .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

We can set up a proportion comparing the height of each object to the length of the shadow.

     h/15 = 21.1/12.7

     h = 1.66 * 15  

   h   = 24.9

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To do trigonometry, you need to have a clear understanding of triangles and the relationships between their sides and angles. To do trigonometry without images or diagram, let's go straight to the explanation below.

When solving trigonometry word problems without a drawing/image, the following steps can be helpful:

It is important to note that in order to use trigonometry, you need to have a clear understanding of triangles and the relationships between their sides and angles.

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The height Sikdar calculated for Peak XV is approximately 29105.77 feet.

Let's first find the height of point A above the ground. We can use the tangent function:

tan(45) = height of A / d

height of A = d * tan(45)

height of A = 17409.7 * tan(45) = 17409.7 feet

h / (d - 17409.7) = height of A / d

h = (height of A * (d - 17409.7)) / d

h = (17409.7 * (17409.7 / tan(32) - 17409.7)) / (17409.7 / tan(32))

 = 29105.77 feet

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Answer:

D. [tex]56.25 mm^{2}[/tex]

Step-by-step explanation:

A = [tex]\frac{A + 2}{2}[/tex]h =

[tex]\frac{16 + 9}{2}[/tex]x4.5

Thus,

=56.25

Option D.

Answer: Pretty much correct except one thing is wrong.

Step-by-step explanation:

In place of CB you should write AB because the sides doesn't match when you flip the triangle CED.

Hope it helps!

The amount of tax owed by a head-of-household taxpayer with a taxable income of $27,811 is given as follows:

$3,062.

The amount of tax is obtained identifying the correct position in the table in this problem.

The person in this problem is the head of the household, meaning that we should observe the last column of the table.

As income of $27,811 is between $27,800 and $27,850, hence, looking at the fourth-to-last row, the amount of tax owed by a head-of-household taxpayer with a taxable income of $27,811 is given as follows:

$3,062.

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Answer:

Step-by-step explanation:

You want two integers with a product of 36 such that one is 3 less than 5 times the other.

Let x be "the other" integer. Then one is (5x-3), and the product is ...

  x(5x -3) = 36

  5x² -3x = 36 . . . . . . eliminate parentheses

  x² -0.6x = 7.2 . . . . . . . divide by 5

  x -0.6x +0.09 = 7.29 . . . . . add (0.6/2)² to complete the square

  (x -0.3)² = 7.29

  x = 0.3 +√7.29 = 0.3 +2.7 = 3

  5x -3 = 5·3 -3 = 12

The two integers are 12 and 3.

The water level in the tank will take x = 30 minutes to decrease from 15 inches to 9 inches deep. It will take 6 minutes for the water level to decrease by 0.5 inches.

The water level in the tank is currently 15 inches deep and is decreasing by 0.5 inches every minute. In order to determine how many minutes, x, it will take for the water level to measure 9 inches deep, we will need to calculate the difference between the current water level and the desired water level. To do this, we need to subtract 9 inches from 15 inches, and this will give us a difference of 6 inches. Now, since the water level is decreasing by 0.5 inches per minute, we need to divide 6 inches by 0.5 inches, which will give us 12 minutes. Since 12 minutes is equal to 2 intervals of 6 minutes, the water level will take x = 30 minutes to decrease from 15 inches to 9 inches deep.

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The new basic feasible solution will have x\ as a non-basic variable and a new basic variable with a value not equal to zero.

When a problem is in canonical form and the associated basic feasible solution is degenerate, this means that one of the basic variables has a value of zero. If the pivot operation is then performed with the basic variable with a value of zero extracted from the basis, the new basic feasible solution will have x\ as a non-basic variable and a new basic variable with a value not equal to zero. This is because the pivot operation involves exchanging the extracted basic variable with one of the non-basic variables. Therefore, the new basic feasible solution will not be degenerate, as the new basic variable will have a value not equal to zero.

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Answer: 0.73

Step-by-step explanation: Because finding the absolute value only means finding how far away a number is from 0 on a number line, the answer is 0.73.

Step-by-step explanation:

Assuming it is a constant speed of 50km/h

So you travel 50km in one hour

So if you want to go 100km traveling at the constant speed of 50km it will take two hours as you are going 50km for one hour it will take two hours to go 100km.

From the given triangle, the lengths of AB and PB becomes: 9 cm and 4 cm respectively.

Tri-, which means "three," and angulus, which means "angle or corner," are the origins of the Latin word triangulus, which means "three-cornered" or "having three angles." A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. 180 degrees is the summation of the triangle's three angles.

In ΔAPC and ΔABC

∠ABC = ∠ACP and ∠BAC = ∠CAP

∴ ΔABC ≅ ΔACP

Because ∠ABC = ∠ACP, thus ∠A = ∠A, so, ∠ABC = ∠ACP

As, ΔABC ≅ ΔACP

∴ AB = BC = AC = CP  (the corresponding sides of a similar triangle are proportional)

∵ BC = 12, AC = 6, CP = 8

∴ AB = (6/8) × 12

or, AB = 9 cm

as, ΔABC ≅ ΔACP

∴ AP : AC = AC : AB

or, AP = (6/9) × 6

or, AP = 4 cm

next, PB = AB - AP

PB = 9 - 4 cm

PB = 5 cm

Thus, the lengths of AB and PB becomes: 9 cm and 4 cm respectively.

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The complete question is as follows:

The slope of the ocean floor is: slope = (y2 - y1) / x

What is slope?

The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.

The slope of the ocean floor can be found by using the formula for the slope of a line:

slope = (change in y) / (change in x)

where the change in y is the difference in depth between the edge of the continental shelf and the beginning of the oceanic crust, and the change in x is the distance along the ocean floor between these two points.

Let's call the depth of the water at the edge of the continental shelf "y1" and the depth of the water at the beginning of the oceanic crust "y2". Then, the change in y is:

change in y = y2 - y1

Similarly, let's call the distance along the ocean floor between these two points "x". Then, the change in x is:

change in x = x

So, the slope of the ocean floor is:

slope = (y2 - y1) / x

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Answer:

To calculate the angle, you would need to use the tangent of an angle formula: tan(θ) = 107/260. Solving for θ yields an angle of 29.4 degrees. You would have to look up at an angle of 29.4 degrees to see the tip of the lighthouse.

Answer:

⁵/₄ or 1.25

Step-by-step explanation:

Firstly, represent the number as a fraction:

0.8 = ⁸/₁₀ = ⁴/₅

Then, simply flip the top and bottom:

The reciprocal of ⁴/₅ is ⁵/₄

⁵/₄ = 1.25

According to the random survey, the majors chosen by the freshmen of our university were:

To get a better understanding of the proportions of students choosing certain majors, universities can survey a sample of their entering freshmen. This survey should be representative of the population, so it should be conducted using a randomized sampling technique.

The survey should ask questions about the major the student is planning on pursuing and other relevant information, such as the student's interests and motivations.

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Answer:

i).7/18

ii).0/18

iii).0/18.

Step-by-step explanation:

Total bag of sweet = 18

Blue sweet = 5

Red sweet = 7

Green sweet = 6

i). Probability that Sue takes a red sweet = 7/18

ii). Does not take a Green sweet = 0/18

iii). takes a yellow sweet = 0/18.

As the acute angles of a right triangle are complementary, the measures of angle C and angle DAC add up to 90 degrees.

Given that it has three sections and three corners, a triangle qualifies as a polygon. It corresponds to the fundamental geometric shapes. Triangle ABC is the term used to refer to a triangle only with vertices A, B, and C. Once the points are not collinear, a unique plane and triangular in Geometric forms are discovered. Triangles are polygon because they have three parts and three corners. The points where its three sides of the triangle converge are referred to as the triangle's corners. Three pyramid angles are multiplied ta yield 180 °.

given

Provided that segment AD is an altitude, AD in triangle ABC is perpendicular to hypotenuse BC.

Triangle DAC is a right triangle, as it should be. As the acute angles of a right triangle are complementary, the measures of angle C and angle DAC add up to 90 degrees.

The same holds true for angles C and CBA's measurements.

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Answer:

2.44π cm²

or

7.68 cm²

Since the choices are not shown, I do not know whether the choices are in terms of π or totally numeric Choose one of the two above. They are both the same value

Step-by-step explanation:

Area of a circle of radius r is  A = πr²

An entire circle encompasses 360°

If a sector of the circle has an angle of Фat the center, the area of the sector is Ф/360 x πr²

Given r = 4 and Ф = 55°

Area of this sector = 55/360 x π (4)² = 55/360 x 16 x π = 2.44π

2.44π = 7.68 cm²

The steps to conduct a statistical survey are given below.

A statistical survey is any structured inquiry designed to obtain aggregated data, which may be qualitative or quantitative where the individual or corporate identities of the respondents are in themselves of little significance.

Given is to conduct a statistical survey.

The steps to conduct a statistical survey are given below -

Therefore, the steps to conduct a statistical survey are given above.

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{Question in english -

How to conduct a statistical survey}