Five students came for after-school tutoring. Lin’s teacher assigned each of them the same number of problems to complete. Then he assigned each student 2 more problems to one of the students. 27 problems were assigned in all. write an equationfor the story the find the number of problems originally assigned by the teacher.

The distance between the points A and B is 209.4 feet

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.

A boat is heading towards a lighthouse, whose beacon-light is 107 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 12°. Let a represent distance from point A to light house:

tan(12) = 107/a

a = 503.4 feet

They measure the angle of elevation a second time from point B at some later time to be 20°. Hence, if b represent distance from point A to light house:

tan(20) = 107/b

b = 294 feet

Distance from point A to B = 503.4 feet - 294 feet = 209.4

The distance between the points is 209.4 feet

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Answer:

Step-by-step explanation:

7+m>5

Answer:

m = -2

Step-by-step explanation:

yes.

The experimental probability of getting an odd number on the next toss is 51.3%.

Probability is a measure of the likelihood of an event occurring. In the case of the six-sided number cube, the theoretical probability of getting an odd number on any one roll is 3 out of 6, or 1/2, or 50%. However, this is a theoretical value and may not match the actual results obtained from a set of experiments.

The experimental probability of an event is calculated by observing the actual results of a series of trials and comparing it to the number of possible outcomes. In this case, the number cube was tossed 150 times and the results were recorded in the table. The frequency of the odd numbers (1, 3, and 5) was found to be 77.

The experimental probability of getting an odd number on the next toss can be calculated by dividing the frequency of the odd numbers by the total number of tosses, which is 150. 77/150 = 0.513 or 51.3%.

Therefore, the experimental probability of getting an odd number on the next toss of the six-sided number cube is 51.3%.

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Answer: x=3

Step-by-step explanation:

divide by the common factor 3

3x ÷ 3 = x

9÷3 = 3

hence the reason we get x=3

Answer: 3

Step-by-step explanation:

To solve for x, you need to divide 9 by 3 which equals 3.

Since 3x = (3 ⋅ 3), x = 3.

The approximate area that Poseidon is searching is given as follows:

64.13 square units.

The area of a triangle is given by half the multiplication of the base length by the height.

The coordinates of the vertices of the triangle in this problem are given as follows:

(-6,1), (4,-5) and (-1,9).

Any of the three sides can be chosen as the base, and we use the equation for the distance between two points to obtain it's length.

Choosing vertices (-6,1) and (4,-5) as the base, it's length is given as follows:

b = sqrt((4 - (-6))² + (-5 - 1)²)

b = 11.66.

The midpoint of the base has the coordinates given as follows:

The height is the distance between the vertices (-1,-2) and (-1,9), hence, as they have the same x-coordinate, the height is given as follows:

h = 9 - (-2)

h = 11.

Then the area is given as follows:

A = 0.5 x 11.66 x 11

A = 64.13 square units.

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Answer:

x = -30

Step-by-step explanation:

25 = -7 (x+5) +5x            expand brackets

25 = -7x -35 +5x             simplify

25 = -2x -35                    add 35 to both sides

60 = -2x                          multiply by sides by -1

-60 =2x                           divide by 2

x =-30

Answer:

-30

Step-by-step explanation:

25= -7x-35+5x

25+35= -2x

60= -2x both side by -2

-30=x

The answers for the asked probabilities are a) 1/6, b) 5/36, c) 1/36 and d) A and B events are not independent.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, Antonia rolls a pair of fair six-sided dice. A is the event that the first die lands on 5 and B is the event that the sum of the two dice is 6.

Probability = possible outcomes / favorable outcomes

Suppose that Antonia rolls a pair of fair six-sided dice.

All possible outcomes are:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

(36 outcomes in total)

a) A = the first die lands on 5

Favorable outcomes:

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6 outcomes)

Therefore, the probability that the first die lands on 5 = P(A) = 6/36 = 1/6

b) B = the sum of the two dice is 6

Favorable outcomes:

(1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = (5 outcomes)

Therefore, the probability that the sum of the two dice is P(B) = 6 = 5/36

c) A∩B = the first die lands on 5 and the two dice add up to 6

Favorable outcomes:

(5, 1) = 1 outcome

Therefore, the probability that the first die lands on 5 and the two dice add up to6 = P(A∩B) = 1/36

d) Two events are independent when;

P(A∩B) = P(A) · P(B)

Since,

1/36 ≠ 5/36 · 1/36

Therefore, A and B events are not independent.

Hence, the answers for the asked probabilities are a) 1/6, b) 5/36, c) 1/36 and d) A and B events are not independent.

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The value of the expression 2/3 x -4/5 is -8/15.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:
An expression,

2/3 x -4/5.

Here, we have to multiply the fraction.

So,

2/3 x -4/5,

= -8/15

Therefore, -8/15 is the value.

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Step-by-step explanation:

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The original price of the pair of jeans is equals to the $120.

We Jodi wants to buy a pair of jeans.

The purchase price of pair of jeans = $90

Discount on price of jeans = 75%

Let the original price of pair of jeans be equal to "$x". Percent is an important concept of mathematics. It is a number or ratio of fraction of hundred. It is denoted by symbol %. The formula is

% = ( part /whole )×100

Here, it is said that the price of pair of jeans, $90, is only 75% of the original price. So, we can write it as the following way 75% of x = 90

=> (75/100) of x = 90

=> (75/100) × x = 90

=> x = 90× 100/75

=> x = 9000/75

=> x = 120

Hence, required value of x is 120.

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Answer: 1/3

Step-by-step explanation: The only option would be two and that has a 1/3 chance of occuring.

155 degrees

Straight line equals 180 degrees.

180 - 25 = 155 degrees

Answer:

155 degrees

Step-by-step explanation:

A straight angle is 180 degrees. The equation to solve this would be 25+x=180; to solve this, subtract 180-25=x; x=155

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Step-by-step explanation:

the area of a triangle is

baseline × height / 2

in our case

9.3 × 3.5 / 2 = 16.275 ft²

as you can see, yes, really easy.

what was the problem ? do you need any further explanation ?

Answer:

They are not equal

  one is  -1 times  the other   answer C

Step-by-step explanation:

for t =2     15.8t - 3.8t = 24

                    3.8t - 15.8t =  - 24

Answer:

C, 24, and -24

Step-by-step explanation:

Step 1a) No, so C

Step 1b) 15.8(2)- 3.8(2)

Step 2b) 31.6 -7.6

Step 3b) 24

Step 1c) 3.8(2)- 15.8(2)

Step 2c) 7.6 -31.6

Step 3c) -24

This graph above portraiture the linear equation

The given exponential function represents decay since the base (0.13) is less than 1. And the percentage decrease of 91.68%.

The percentage rate of the decrease can be determined by taking the base and subtracting it from 1 and then multiplying the result by 100. Mathematically, this can be expressed as (1 - 0.13)*100 = 87%. To illustrate this mathematically, let's assume that the initial value of y is 100. We can then calculate the value of y after one time period (t) as follows: y = 64(0.13)t.

Plugging in t = 1, we get y = 64(0.13) = 8.32. This means that the value of y has decreased by (100 - 8.32) = 91.68, or a decrease of 91.68%. Dividing this by the initial value of 100 gives us a percentage decrease of 91.68%/100 = 0.9168 or 91.68%.

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Answer:Second option ( $8.04)

Step-by-step explanation:

Answer:

A cup

Step-by-step explanation:

Because a pint is smaller than a cup look it up it's true

It is important to use a device like a random number table in a simulation because Option A Chance plays a part in the process being simulated.

In simulations, a random number table is used to incorporate the element of chance into the process being modeled. The reason this is important is that many real-world processes involve uncertainty and randomness, and to accurately simulate these processes, it is necessary to include these elements.

For example, in simulating the stock market, stock prices can be modeled as random variables, because they are influenced by a variety of unpredictable factors such as changes in interest rates, company earnings, geopolitical events, and investor sentiment. To simulate this process, a random number table can be used to generate random numbers that represent these unpredictable factors.

By using a random number table, the simulation can model the uncertainty and randomness inherent in the real-world process, which makes the simulation more accurate and realistic. This is why it is important to use a device like a random number table in a simulation when chance plays a part in the process being simulated.

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The side lengths x and y are √( 50² - y²) and √50² - x² respectively.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

In a right angle triangle, the length of one side can be determined using the Pythagorean theorem:

x² + y² = hypotenuse²

In the given triangle the length of hypotenuse is 50 cm

x² = 50² - y²

x=√( 50² - y²)

y = √50² - x²

Hence, the side lengths x and y are √( 50² - y²) and √50² - x² respectively.

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The volume of larger solid represented by b is 3125.

The scale factor of two solids will be equal to the following formula -

volume of solid a/volume of solid b = solid a³/solid b³

Keep the values in formula to find the volume of solid b

200/ volume of solid b = 2³/5³

Rewriting the equation according to volume of solid b

Volume of solid b = 5³ × 200/2³

Performing multiplication with cube of 5

Volume of solid b = 125 × 200/8

Volume of solid b = 25000/8

Performing division on Right Hand Side of the equation

Volume of solid b = 3125

Hence, the volume of solid b is 3125.

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With the value tanθ = 4/3 on the interval (π, 3π/2), using trigonometric identities sin 2θ = 24/25 , cos 2θ = -7/25 , tan 2θ = -8/7.

First, we'll find sin 2θ:

sin 2θ = 2sinθcosθ

We can use the identity tanθ = sinθ/cosθ to find sinθ and cosθ:

sinθ = 4/5 and cosθ = 3/5

So,

sin 2θ = 2(4/5)(3/5) = 24/25

Next, we'll find cos 2θ:

cos 2θ = cos^2θ - sin^2θ = 1 - 2sin^2θ

Using the values of sinθ and cosθ that we found earlier:

cos 2θ = 1 - 2(4/5)^2 = 1 - 32/25 = -7/25

Finally, we'll find tan 2θ:

tan 2θ = (2tanθ)/(1 - tan^2θ)

Using the value of tanθ that we were given:

tan 2θ = (2(4/3))/(1 - (4/3)^2) = (8/3)/(-7/9) = -8/7

So, the values of sin 2θ, cos 2θ, and tan 2θ are:

sin 2θ = 24/25

cos 2θ = -7/25

tan 2θ = -8/7

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Answer:

[tex]y=4(x-7)^2-196[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]y=4x^2-56x[/tex]

Factor out the coefficient of the term x²:

[tex]y=4(x^2-14x)[/tex]

Add and subtract the square of half the coefficient of the term in x inside the brackets:

[tex]y=4\left(x^2-14x+\left(-\dfrac{14}{2}\right)^2-\left(-\dfrac{14}{2}\right)^2\right)[/tex]

Simplify:

[tex]y=4\left(x^2-14x+\left(-7\right)^2-\left(-7\right)^2\right)[/tex]

[tex]y=4\left(x^2-14x+49-49\right)[/tex]

Factor the perfect square trinomial created by the first three terms inside the brackets:

[tex]y=4\left((x-7)^2-49\right)[/tex]

Distribute:

[tex]y=4(x-7)^2-196[/tex]

The equation is now in vertex form y = a(x - h)² + k, where (h, k) is the vertex of the parabola (turning point).

Compare the equation with the vertex formula to identify the values of h and k:

Therefore, the coordinates of the turning point (vertex) are (7, -196).

42 feet is the length of the guy wire.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that a pole 10 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground.

After placing the pole, Liam measures the distance from the pole to the stake and from the pole to the tower.

We have to find the length of the guy wire

Let the required distance is x and the height of the tower is t.  

Use similar triangle ratios to find the value of t:  

t / 10 = (9 + 3) / 3

t / 10 = 4

t = 40 feet

Use Pythagorean to find the value of x:  

x² = 40² + (9 + 3)²

x² = 1600 + 144

x² = 1744

x = √1744

x = 42 feet

Hence, 42 feet is the length of the guy wire.

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Answer:

d

Step-by-step explanation:

d

Answer:

I think it's c sorry if im wrong

Answer: 1

Step-by-step explanation: The Distributive Property is nothing to get confused about. It is simply just a multiplication rule. Follow out the steps in this problem in order. 1/3 * 6 = 2. 2 * 1/2 = 1, and there you go! If this helped, please consider giving this a brainiest as I am one away from the next rank!

Answer: 2

Step-by-step explanation:

Answer: 23

Step-by-step explanation:

This is another parallel line theorem that is important. Over here, we will need to use the concept of corresponding angles (refer to images below). In corresponding angles, they are equal. So we know the corresponding angle to [tex]x + 1[/tex] will be equal to [tex]x + 1[/tex] since corresponding angles are equal.

Now we have to use the fact that angles on a line add up to 180°. Keeping this in mind, we can now solve it like this:

[tex](x + 1) + (7x-5) = 180\\x + 1 + 7x - 5 = 180\\8x - 4 = 180\\8x = 184\\x = 23\\\\[/tex]

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