A group of 493 people is going on a boat tour. If each boat holds 7 people, how many people will be on the last boat?

Answer:

h(x) = ½x + 5

Step-by-step explanation:

From the question given above, the following data were obtained:

Function, f(x) = 2x – 10

Inverse, h(x) =?

The inverse of the function, h(x) can be obtained as follow:

f(x) = 2x – 10

Let f(x) = y

y = 2x – 10

Interchange x and y

x = 2y – 10

Make y the subject by rearranging

x + 10 = 2y

Divide both side by 2

y = (x + 10) / 2

y = ½x + 5

Replace y with h(x)

h(x) = ½x + 5

Thus, the inverse of the function is

h(x) = ½x + 5

p = 6/11.

So we have a bag that contains 6 red marbles and 6 green marbles.

Then the total number of marbles that are in that bag is:

6 + 6  = 12

There are 12 marbles in the bag, and we assume that all marbles have the same probability of being randomly drawn.

Now we draw two marbles, we want to find the probability that one is red and the other is green.

The first marble that we draw does not matter, as we just want the second marble to be of the other color.

So, suppose we draw a green one in the first attempt.

Then in the second draw, we need to get a red one.

The probability of drawing a red one will be equal to the quotient between the red marbles in the bag (6) and the total number of marbles in the bag (12 - 1 = 11, because one green marble was drawn already)

Then the probability is:

p = 6/11.

Notice that would be the exact same case if the first marble was red.

Then we can conclude that the probability of getting two marbles of different colors is:

p = 6/11.

Start by removing 1 and the primes from the set {1, 2, 3, …, 25}. The LCM among these numbers will be their product.

{1, 2, 3, 5, 7, 11, 13, 17, 19, 23}   ==>   product = 223,092,870

Factorize the remaining numbers in the set:

{4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25}   ==>

{2², 2×3, 2³, 3², 2×5, 2²×3, 2×7, 3×5, 2⁴, 2×3², 2²×5, 3×7, 2×11, 2³×3, 5²}

From each number above, remove any factor already accounted for in the product of primes:

{2, 1, 2², 3, 1, 2, 1, 1, 2³, 3, 2, 1, 1, 2², 5}

The LCM among these factors is 2³×3×5 = 120.

Then the LCM of the numbers in {1, 2, 3, …, 25} is

223,092,870 × 120 = 26,771,144,400

so that A = 7, B = 4, and C = 0. Then

100A + 10B + C = 740

Answer:

y - intercept = 2.25

Step-by-step explanation:

y = mx + c

Where,

y = Total cost

x = additional cost

m = slope

c = y - intercept

y = 0.25x + 2.25

Relating with the above equation,

y - intercept = 2.25

Slope, m = 0.25

Step-by-step explanation:

It Jun glt tm my tb my tu meri of ft me rh my

Answer:

[tex](x^2+y^2)^3 = 16x^2y^2[/tex]

Step-by-step explanation:

We want to convert the polar equation:

[tex]\displaystyle r = 2 \sin 2\theta[/tex]

To rectangular form.

Recall the double-angle identity for sine:

[tex]\displaystyle \sin 2\theta = 2\sin\theta\cos\theta[/tex]

Hence:

[tex]\displaystyle r = 4\sin\theta\cos\theta[/tex]

Since x = rcosθ and y = rsinθ:

[tex]\displaystyle r = 4\left(\frac{x}{r}\right)\left(\frac{y}{r}\right)[/tex]

Multiply:

[tex]\displaystyle r = \frac{4xy}{r^2}[/tex]

Recall that x² + y² = r². Hence:

[tex]\displaystyle r = \frac{4xy}{x^2 + y^2}[/tex]

By squaring both sides:

[tex]\displaystyle r^2 = \frac{16x^2y^2}{(x^2+y^2)^2}[/tex]

Substitute:

[tex]\displaystyle x^2+y^2 = \frac{16x^2y^2}{(x^2+y^2)^2}[/tex]

And multiply. Therefore:

[tex](x^2+y^2)^3 = 16x^2y^2[/tex]

Answer:

Step-by-step explanation:

17x²y+8y³-4x²

it has no greatest common monomial factor.

Answer:

17x²y+8y³-4x²

Step-by-step explanation:

Answer:

List from least to greatest:-16,-10,-3,5

List from closest to zero to the very far:-3,5,-10,16

Step-by-step explanation:

In order to know if the answer is accurate,draw a number line of directed numbers...the very far negative numbers,are said to be the least than the numbers almost close to zero...

Answer:

Step-by-step explanation:

The answer is D. Use the Stat and then Edit button on your TI calculator to edit the values in L1 and L2 tables. In L1 enter 0, 1, 2, 3, 4, 5 and then arrow over and enter the y values into L2 the same way. Enter the number 12, then hit enter; enter the number 14, hit enter; enter the number 15 and then hit enter, etc. Do the same for the values that are going into L1.

When that is done, hit the Stat button again and arrow down to QuadReg and hit enter. Depending upon your calculator, you may have to arrow down to "calculate" or the calculator may display the equation immediately after hitting QuadReg. Again, it all depends upon your calculator.

The required correct quadratic regression equation that fits the given data is y = -0.89x² + 3.24x+11.93. Option D is correct.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
To find the quadratic regression equation, we need to use a calculator or software that can perform a quadratic regression analysis. Using such a tool, we obtain the following equation:

y = -0.89x² + 3.24x+11.93

This equation fits the data points (0, 12), (1, 14), (2, 15), (3, 14), (4, 10), and (5, 6) with a high degree of accuracy.

The equation is in the form of a quadratic function, which has a parabolic shape when graphed. The coefficient of the x² term (-0.89) indicates that the parabola is downward-facing, while the other coefficients determine the exact shape and position of the parabola.

Option A is incorrect because its equation does not fit the data points accurately. Option B is also incorrect because it is not a quadratic equation, and option C is incorrect because its equation also does not fit the data points accurately.

Learn more about equations here:

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Answer:

X1=6

X2=7

y1= -1

y2= 3

now,

slope = y2-y1/x2-x1

= 3+1/7-6

=4/1

=1

hence slope= 1

Answer:

Step-by-step explanation:

a) x=6 (x= 8-2)

b) x=4 ( 4x=21-5=16 -> x=4

c) x=7 (3x=34-13=21 -> x=7)

Let the perimeter be 100cm

Then value of x = 100/4

x = 25cm

Answered by Gauthmath must click thanks and mark brainliest

Answer:

b i think

Step-by-step explanation:

Answer:

Its not nonlinear

Step-by-step explanation:

Answer:

no, it is a linear function as y has a degree of 1

Answer:

4. E=4x-15(vertically opposite)

F=E(corresponding angles)

E=4x-15

5.3x+6x+O=180(angles on a straight line)

9x+0=180

9x=180-0

9x/9=180/9

x=20

Answer: Choice C. 110ft

Step-by-step explanation:

Near a 30,60,90 triangle, multiply by [tex]\sqrt{3}[/tex] to approximate the distance from point B to the tree.

Answer:

82

Step-by-step explanation:

I want to say 82 but i am not positive

Answer: [tex]\dfrac{11}{12}[/tex]

Step-by-step explanation:

Given

The odds against winning in a chess tournament are 1 to 11.

Odds is defined as the ratio of the probability of occurrence to the non-occurrence of event.

[tex]\therefore \text{Probability that event will occur is P'=}\dfrac{1}{1+11}\\\\\Rightarrow P'=\dfrac{1}{12}[/tex]

Probability of non-occurrence i.e. she wins the first prize is

[tex]\Rightarrow P=1-\dfrac{1}{12}\\\\\Rightarrow P=\dfrac{11}{12}[/tex]

Answer: 2, acute equilateral

Step-by-step explanation:

the image shows a triangle with all 3 sides congruent and 3 acute angles

Answer:

B. SAS

[tex] \frac{sm}{dl} = \frac{27}{9} = 3 \\ \frac{am}{el} = \frac{15}{5} = 3 \\ angle \: m= angle \: l[/tex]

Brainliest please~

By SAS similarity, ΔASM is similar to ΔDLE. Thus, option C is correct.

The SAS theorem is also known as the side-angle-side theorem, also known as a statement in Euclidean geometry that states two triangles are congruent if their corresponding sides are both the same length and their included angles are both of the same measures.

According to the given figure,

SM=27

DL=9

MA=15

LE=5,

∠M=∠L=31°

It is required to determine the similarity postulate that applies. Therefore,

From the ΔASM and ΔDLE, we have

[tex]\frac{SM}{DL}=\frac{27}{9} \\=3\\\frac{ML}{LE}=\frac{15}{5}\\ =3\\ Hence, \frac{SM}{DL}= \frac{ML}{LE}[/tex]

∠M=∠L=31°

Hence, by SAS similarity, ΔASM is similar to ΔDLE.

Therefore, it can be concluded that option C is correct.

Learn more about the SAS theorem here:

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Answer:

[tex]7^{7}[/tex]  =  823543

the unit position (the first) is equal to "3"

Step-by-step explanation:

Answer:

b and c

Step-by-step explanation:

Given

x² - 4x = - 5

Solve by using the method of completing the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(- 2)x + 4 = - 5 + 4

(x - 2)² = - 1 ( take the square root of both sides )

x - 2 = ± [tex]\sqrt{-1}[/tex] = ± i ( add 2 to both sides )

x = 2 ± i

Then solutions are

x = 2 - i → b

x = 2 + i → c

value of x should be 3.2 units

Answered by Gauthmath must click thanks and mark brainliest

Answer:

3 a + 4 b

Step-by-step explanation:

Biểu thức đại số biểu thị bạn Cúc mua  3  ly trà sữa và  4  ly kem là:

3 a + 4 b

Answer:

0.0735 got it right

Step-by-step explanation:

got it right

Answer:

The answer is 97!

Step-by-step explanation:

The formula for Pythagorean Theorem is a^2+b^2=c^2. (65)^2 + (72)^2 is 9409, which has a square root of 97. Hope this helped! :)

Answer:

13x^2 - xy

Step-by-step explanation:

4x^2-3xy+2xy+9x^2

=13x^2-xy

Answer:

(3,2)

Step-by-step explanation:

y = 4x – 10

y = 2

Substitute the second equation into the first

2 = 4x-10

Add 10 to each side

2+10 = 4x-10+10

12 = 4x

Divide each side by 4

12/4 =4x/4

3 = x

The solution is

(3,2)

Answer:

(3,2)

Step-by-step explanation:

y = 4x – 10...(1) y = 2...(2) You have y=2 here, substitute it in equation (1),

y = 4x – 10 2 = 4x – 10

Add both sides by 10 12=4x

Divide both sides by 4 x=3

We have x=3, and y=2. ==> (x,y) = (3,2) 

Answer:

You need to use sohcahtoa to find your answer.

first you gotta identify what sides of the triangle you have.

You're missing the hypotenuse, and you have the value of the adjacent.

since you have the adjacent and need the hypotenuse, you're going to use cosine to find x

cos(65) = 16/x

x = 37.859

Answer:

x = 37.85

this is a standard "trig" question

it requires two pieces  of insight.

First that a triangle has 180° interior angles.

from that you can determine that the third angle is 25° because

90 + 65 + β = 180

the red symbol lets you know that it is 90°

the second think that will help is SOHCAHTOA

that is if you have a "right triangle" (one with a 90° angle)

in this problem (in your mind rotate the triangle so the 65° is at the bottom left and the two long sides are pointing up

in this case you have the 16 on the bottom (adjacent to the angle) and

the x is on the hypotenuse...

you have the A& H that is COS

thus you have cos(65) = [tex]\frac{16}{x}[/tex]

x = 37.85

Step-by-step explanation: