For Carolina's birthday, her mom took her and 4 friends to a water park. Carolina's mom paid $40 for 5 student tickets. What was the price for one student ticket?

Answer:

62.8

Step-by-step explanation:

The volume of the cylinder is = base * height

base=Pi*radius*radius, where

base=3.1416*2*2 , height=5

Volume=3.1416*2*2*5

Volume =62.8 cubic units.

Answer:

Option B.

Step-by-step explanation:

It is given that right cylinder has a radius of 2 units and a height of 5 units. It means

r = 2

h = 5

The volume of a right cylinder is

[tex]V=\pi r^2h[/tex]

where, r is radius and h is height of the cylinder.

Substitute r=2 and h=5 in the above formula.

[tex]V=\pi (2)^2(5)[/tex]

[tex]V=\pi (4)(5)[/tex]

[tex]V=20\pi[/tex]

On further simplification we get

[tex]V=62.831853[/tex]

[tex]V\approx 62.8[/tex]

The volume of right cylinder is 62.8 cubic units.

Therefore, the correct option is B.

Answer:

A = 44.2cm²

Step-by-step explanation:

The surface area of a square pyramid that has the sides of the base of 4 cm and a height of 10 cm is 44.2cm².

Formula: A=AB(4h2+AB)+AB

A=AB(4h2+AB)+AB=4·(4·102+4)+4≈44.1995cm²

Answer:

[tex]\large\boxed{x=-1\pm\sqrt5}[/tex]

Step-by-step explanation:

[tex]x^2+2x-4=0\qquad\text{add 4 to both sides}\\\\x^2+2x=4\\\\x^2+2(x)(1)=4\qquad\text{add}\ 1^2=1\ \text{to both sides}\\\\\underbrace{x^2+2(x)(1)+1^2}=4+1^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1)^2=5\to x+1=\pm\sqrt5\qquad\text{subtract 1 from both sides}\\\\x=-1\pm\sqrt5[/tex]

The two values of x for the given equation are ( -1  + √5 ) and ( - 1 - √5 ).

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

The solution of the given equation is:-

=  x²  + 2x - 4

x²  +  2x  =  4

x²  +  2x ( 1 )  +  1²  =  4  +  1²

(  x  +  1  )²  =  5

x  +  1   =  ± √5

x  =  -1  ± √5

Therefore the two values of x for the given equation are ( -1  + √5 ) and ( - 1 - √5 ).

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Answer:

153938040.0259 ft2

Step-by-step explanation:

R= Square root of A/π

Answer:

153,860,000 ft^2.

Step-by-step explanation:

The area = 3.14 * r^2

= π * 7,000^2

= 153,860,000 ft^2.

Answer:

AB=20

Step-by-step explanation:

Given:

r= 14.5

AB cuts r=14.5 in two parts one parts length=4

remaining length, x = 14.5 - 4 =10.5

draw a line from center of circle to point A making right angled triangle

Now hypotenuse=r=14.5

and one side of triangle=10.5

Using pythagoras theorem to find the third side:

c^2=a^2+b^2

14.5^2=10.5^2+b^2

14.5^2-10.5^2=b^2

b^2=100

b=10

AB=2b

     =2(10)

     =20

Hence length of cord AB=20!

Answer:

x² + y² = 36

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ← r is the radius

here r = 6, so

x² + y² = 6², that is

x² + y² = 36

The circle's equation is x² + y² = 36.

Given:

length of its radius is 6.

To find:

the circle's equation

The equation for a circle in center, radius form is

(x - h)² + (y - k)² = r²  

The equation of a circle centered at the origin is

x² + y² = r²  

Where, r is the radius of the circle

Here radius of the circle = 6

If the center is (0,0) then h = 0 and k = 0

x² + y² = 6²,

x² + y² = 36

Therefore, the circle's equation x² + y² = 36.

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Answer:

(1/7)(-9n + 7)

Step-by-step explanation:

1/7-3(3/7n-2/7)  can be factored:  factor out 1/7.

We get:  (1/7)[1 - 3(3n - 2)], or

              (1/7)[1 - 9n + 6], or

              (1/7)(-9n + 7)

Answer:

○C. x + 2

Step-by-step explanation:

x^4 + 2x^3 -x-2

-------------------------

x^3 -1

Factor the numerator by grouping.  Take an x^3 from the first 2 terms and -1 from the last 2 terms

x^3( x + 2) -1(x+2)

-------------------------

x^3 -1

now lets factor out the x+2

( x + 2)(x^3 -1)

-------------------------

x^3 -1

Canceling out the x^3-1, we are left with

x+2

Answer:

C. x+2

Step-by-step explanation:

The given expressions are two polynomials which have to be divided in order to find the quotient. The long division method will be used to find the quotient of the two terms.

The long division is done and the picture is attached for detail.

From the picture, we can see that the correct answer is:

C. x+2 ..

Answer:

4i sqrt(2)

Step-by-step explanation:

sqrt(-2) + sqrt(-18)

We know sqrt(ab)= sqrt(a) sqrt(b)

sqrt(-1)sqrt(2) + sqrt(9) sqrt(-2)

sqrt(-1)sqrt(2) + sqrt(9) sqrt(2)sqrt(1)

We know the sqrt(-1) is equal to i

i sqrt(2) +3 sqrt(2) i

i sqrt(2) +3i sqrt(2)

4i sqrt(2)

Answer:

a) P(z>1.16) = 0.8770

b) P(z>-0.75) = 0.2266

Step-by-step explanation:

Mean = 205 cm

Standard Deviation = 8.6 cm

a) Find the probability that an individual distance is greater than 215.00

We need to find P(X>215)

x = 215

z = x - mean /standard deviation

z = 215 - 205 / 8.6

z = 1.16

P(X>215)=P(z>1.16)

Finding value of z =1.16 from the table

P(z>1.16) = 0.8770

b) Find the probability that the mean for 25 randomly selected distances is greater than 203.70 cm

Sample size n= 25

x = 203.70

mean = x- mean / standard deviation / √sample size

mean = 203.70 - 205 / 8.6 / √25

mean = -1.3/8.6/5

mean = -0.75

Finding value from z-score table

P(mean >-0.75) = 0.2266

c) Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

If the original problem is normally distributed, then for any sample size n, the sample means are normally distributed.

[tex]\displaystyle\\\text{We will use numbers from 1 to 9.}\\\\1+2+3+4+5+6+7+8+9=\frac{9(9+1)}{2}=\frac{9\times10}{2}=\frac{90}{2}=\boxed{\bf45}\\\\\text{the sums of the numbers in each row, in each column are }=\frac{45}{3}=\boxed{\bf15}\\\\\text{Solution:}\\\\\boxed{\,2\,}\boxed{\,7\,}\boxed{\,6\,}\\\boxed{\,9\,}\boxed{\,5\,}\boxed{\,1\,}\\ \boxed{\,4\,}\boxed{\,3\,}\boxed{\,8\,}\\\\\text{Convenient rotation of the square gives 8 solutions.}[/tex]

Answer:

The slope of XZ is 3/4 , the slope of XY is -4/3 , and XZ = XY = 5 ⇒ 3rd answer

Step-by-step explanation:

* Lets look to the attached figure to solve the problem

- To prove that the Δ XYZ is an isosceles right triangle, you must

  find two sides the product of their slopes is -1 and they are equal

  in lengths

- From the figure the vertices of the triangle are;

  X = (1 , 3) , Y = (4 , -1) , Z = (5 , 6)

- The slope of the line whose endpoints are (x1 , y1) and (x2 , y2)

  is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

∵ The slope of [tex]XY=\frac{-1-3}{4-1}=\frac{-4}{3}[/tex]

∵ The slope of [tex]XZ=\frac{6-3}{5-1}=\frac{3}{4}[/tex]

∴ The slope of XY = -4/3 , the slope of XZ = 3/4

∵ -4/3 × 3/4 = -1

∴ XY ⊥ XZ

∴ ∠ X is a right angle

∴ Δ XYZ is a right triangle

- The distance between the two points (x1 , y1) and (x2 , y2) is

  [tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

∵ [tex]XY=\sqrt{(4-1)^{2}+(-1-3)^{2}}=\sqrt{9+16}=\sqrt{25}=5[/tex]

∵ [tex]XZ=\sqrt{(5-1)^{2}+(6-3)^{2}}=\sqrt{16+9}=\sqrt{25}=5[/tex]

∴ XY = XZ = 5

∴ Δ XYZ is an isosceles right triangle

* The statement which prove that is:

 The slope of XZ is 3/4 , the slope of XY is -4/3 , and XZ = XY = 5  

Answer:

its C

Step-by-step explanation:

yw :)

[tex]x^2-x[/tex] is nothing interesting you can just factor out x and result with [tex]x(x-1)[/tex].

However the difference of squares is defined as,

[tex]a^2-b^2=(a+b)(a-b)[/tex]

Hope this helps.

r3t40

Answer:

First we need to set a proportion

Currently the negative measures 15 inches by 2 inches. And the longer dimension of the printed version is 4 inches. Therefore:

[tex]\frac{2}{y} = \frac{15}{4}[/tex]

[tex]15y = 8[/tex]

[tex]y = 0.5333[/tex]

Therefore, the dimension of the shorter dimension is 0.5333.

None of the options matches this response, so maybe you forgot to add some information?

Answer:

[tex]\frac{x-1}{x+3}[/tex]

Step-by-step explanation:

Let's factor the numerator and denominator first.

x^2+5x-6 is a quadratic in the form of x^2+bx+c.

If you have a quadratic in the form of x^2+bx+c, all you have to do to factor is think of two numbers that multiply to be c and add to be b.

In this case multiplies to be -6 and adds to be 5.

Those numbers are 6 and -1 since -1(6)=-6 and -1+6=5.

So the factored form of x^2+5x-6 is (x-1)(x+6).

x^2+9x+18 is a quadratic in the form of x^2+bx+c as well.

So we need to find two numbers that multiply to be 18 and add to be 9.

These numbers are 6 and 3 since 6(3)=18 and 6+3=9.

So the factored form of x^2+9x+18 is (x+3)(x+6).

So we have that:

[tex]\frac{x^2+5x+-6}{x^2+9x+18}=\frac{(x-1)(x+6)}{(x+3)(x+6)}[/tex]

We can simplify this as long as x is not -6 as

[tex]\frac{x-1}{x+3}[/tex]

I obtained the last line there by canceling out the common factor on top and bottom.

Answer:

We can simplify this as long as x is not -6 as

\frac{x-1}{x+3}

Step-by-step explanation:

Answer:

Option B AC≅XZ

Step-by-step explanation:

we know that

ASA (angle, side, angle) means that we have two congruent triangles where we know two angles and the included side are equal

In this problem we have

∠X≅∠A

∠Z≅∠C

In the triangle ABC the included side between the angles ∠A and ∠C is the side AC

and

In the triangle XYZ the included side between the angles ∠X and ∠Z is the side XZ

therefore

AC≅XZ

Answer:

Hi there!

The answer to this question is: D

Step-by-step explanation:

The pattern is; up (red), down (blue), up (red)

so therefore the next pattern is down (blue) which is D

To find the next figure in the geometric pattern, analyze the given information and identify the pattern in the dot placements. Based on the description, each figure is obtained by adding dots in specific positions. The next figure can be determined by continuing this pattern.

The next figure in the geometric pattern can be determined by analyzing the given information. Based on the description, we can infer that each figure is obtained by adding dots in a specific pattern. The third dot is located one and two-thirds perpendicular hash marks to the right of the center top perpendicular hash mark, while the fourth dot is in the same position as the Car X figure (one perpendicular hash mark above the center right perpendicular hash mark). To find the next figure, we need to continue this pattern by adding dots in the specified positions.

Answer:

B

Step-by-step explanation:

(74+72+76+80+73+(AnswerB)75)÷6(total number of quizzes include the one she needed to take)=75(minimum average because she needs to get average of 75)

Answer:

y=x-4

Step-by-step explanation:

What you are looking for is also known as the slant asymptote.  The slant asymptote occurs when the degree of the numerator is one degree more than the denominator which is what you have.

So to find the slant asymptote we can use polynomial division.

We have a choice to use synthetic division here because the denominator is linear.

-1 goes on the outside because we are dividing by (x+1).

-1  |    1     -3      -4

   |           -1        4

   |----------------------

        1      -4        0

The asymptote is the quotient part which is y=x-4.

So answer is y=x-4.

Option D is correct, y=x-4​ is the equation of the oblique asymptote h(x)= x²-3x-4/x+1

Two or more expressions with an Equal sign is called as Equation.

To find the equation of the oblique asymptote, we need to perform polynomial division of the numerator (x² - 3x - 4) by the denominator (x + 1):

       x - 4

    ------------

x + 1 | x² - 3x - 4

        x² + x

      -------

          -4x - 4

          -4x - 4

             -------

               0

The quotient is x - 4, which represents the equation of the slant asymptote.

Hence, y=x-4​ is the equation of the oblique asymptote h(x)= x²-3x-4/x+1

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[tex]\huge{\boxed{553}}\ \ \huge{\boxed{554}}[/tex]

The numbers can be represented as [tex]x[/tex] and [tex]x+1[/tex].

We know that [tex]x+x+1=1107[/tex].

Combine like terms. [tex]2x+1=1107[/tex]

Subtract 1 on both sides. [tex]2x=1106[/tex]

Divide both sides by 2. [tex]x=553[/tex]

The first number is [tex]x[/tex], which equals [tex]\boxed{553}[/tex].

The second number is [tex]x+1[/tex], which equals [tex]553+1[/tex], which is [tex]\boxed{554}[/tex].

These numbers can be presented as n and n + 1 = 1107

2n = 1106 because we combine the n terms and subtract 1 from each side.

2n ÷ 2 = n

1106 ÷ 2 = 553

We now know that n = 553.

Our second consecutive integer must be 554. This is because our second

consecutive integer represents n + 1 so 553 + 1 =554.

Therefore, are two consecutive integers are 553 and 554.  

Answer:

2.95

Step-by-step explanation:

The radius of a circle is half of the diameter.

r = (1/2)d

r = (1/2)(5.9)

r = 2.95

Answer:

radius = 2.95

Step-by-step explanation:

The radius is the distance from the centre O to the circumference and is one half the diameter,

radius = 0.5 × 5.9 = 2.95

Answer:

d = 6.67s

Step-by-step explanation:

This is the answer because if you take 100 and divide it by 15, then you get d as 6.6666, which rounds up to 6.67s.

Check the picture below.

bearing in mind that in essence, a reference angle is the angle made with the x-axis from any terminal point.

Answer:

B if m=2

(Just to make sure that isn't m=-2, right?)

Step-by-step explanation:

7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)  

Let's plug in 2 for m.

7.8+2(0.75*2+0.4)  = -6.4*2+4(0.5*2-0.8)

If 2 is a solution, then both sides will be the same.

If 2 is not a solution, then both sides will be different.

If both sides are the same, it is a true equation.

If both sides are different, it is a false equation.

Let's simplify 7.8+2(0.75*2+0.4)

According to PEMDAS, we must perform the operations in the parenthesis.

We have multiplication and addition in ( ).  We will do the multiplication because the MD comes before the AS.

0.75*2=1.5

So now our expression 7.8+2(0.75*2+0.4) becomes 7.8+2(1.5+0.4)

Now to do the addition in the ( ).

1.5+0.4=1.9.

So now our expression 7.8+2(0.75*2+0.4) becomes 7.8+2(1.9).

We have multiplication to be perform now because again MD becomes before AS.

7.8+2(0.75*2+0.4) becomes 7.8+3.8

Last step perform the addition (the only operation left here on the left hand side)

7.8+2(0.75*2+0.4) becomes 11.6 .

Let's focus on the right now.

-6.4*2+4(0.5*2-0.8)

-6.4*2+4(1       -0.8)  I did the multiplication in the ( ) first.

-6.4*2+4(.2)              I did the subtracting in the ( ).

-12.8+.8                    I did the multiplication by -6.4*2 and 4*.2 simultaneously

-12

I'm going to put all of this together because I think it might be easier to read:

7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)  

Plug in 2 for m

7.8 + 2(0.75*2  + 0.4)=-6.4*2 + 4(0.5*2 - 0.8)

7.8 + 2(1.5        + 0.4)= -6.4*2 + 4(1       -0.8)

7.8 + 2(1.9)                = -6.4*2 + 4(.2)

7.8 +  3.8                 =   -12.8  +.8

11.6                          =-12

This is false because 11.6 is not the same as -12.

m=2 leads to a false equation

B.

The value of m for the expression 7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8) is -2. Hence, Mia's statement is false.

Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.

The given equation is,

7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)

Also, Mia solved the equation and determine that the value of m is 2.

To find the value of m, simplify the expression,

7.8 + 1.5m + 0.8 = -6.4m + 2m - 3.2

1.5m + 8.6 = -4.4m - 3.2

1.5m + 4.4m = -3.2 - 8.6

5.9m = -11.8

m = -2

Mia is incorrect because the value of m is -2,  

Therefore the statement is false.

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[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=4\\ a_1=2\\ r=\frac{1}{3} \end{cases}[/tex]

[tex]\bf S_4=2\left( \cfrac{1-\left( \frac{1}{3} \right)^4}{1-\frac{1}{3}} \right)\implies S_4 = 2\left( \cfrac{1-\frac{1}{81}}{\frac{2}{3}} \right)\implies S_4 = 2\left( \cfrac{\frac{80}{81}}{~~\frac{2}{3}~~} \right) \\\\\\ S_4=2\left( \cfrac{40}{27} \right)\implies S_4=\cfrac{80}{27}\implies S_4=2\frac{26}{27}[/tex]

Answer:

80/27.

Step-by-step explanation:

Sum of n terms = a1 * (1 - r^n) / (1 - r)

Sum of 4 terms = 2 * (1 -(1/3)^4) / ( 1 - 1/3)

= 2 * 80/81 / 2/3

= 160 / 81  *  3/2

= 480/ 162

= 80/27  (answer

Answer:

This is a right triangle

Step-by-step explanation:

Pythagoras theorem is used to determine if a triangle is right, acute or obtuse

If the sum of squares of two shorter lengths is greater than the square of third side then the triangle is an acute triangle.

If the sum of squares of two shorter lengths is less than the square of third side then the triangle is an obtuse triangle.

If the sum of squares of two shorter lengths is equal the square of third side then the triangle is a right triangle.

so,

[tex](17)^2 = (15)^2+(8)^2\\289 = 225+64\\289=289[/tex]

Therefore, the given triangle is a right triangle ..

Answer:

x= [tex]\frac{-1}{6}y+\frac{-11}{6}[/tex]

y=6x+11

Step-by-step explanation:

4x + 3y = –5 -2x + 2y = 6

- 4x - 3y  –5 -2x + 2y = 6

- 4x - 3y -2x + 2y = 6+5

-4x - 3y -2x +2y =11

-6x-y= 11

Answer:

A

Step-by-step explanation:

if he had multiplied the 2nd equation by 9 throughout successfully, he would have gotten :

6x - y = 16  (multiply by 9)

54x - 9y = 144

Answer:

(a) The error is in step 1.

See below.

Step-by-step explanation:

They did not multiply the 16 by 9.

The boy bought 9 pencils and 9 pens, with a total cost of 90 soles. This calculation is based on the cost of 3 soles per pencil and 7 soles per pen, resulting in a total expenditure that aligns with the given information.

1: Define the costs.

We know the cost of each pencil and pen:

Pencils: 3 soles each

Pens: 7 soles each

2: Let x be the number of items.

Since the boy buys the same number of pencils and pens, let x represent the number of each item he buys.

3: Set up the total cost equation.

The total cost he spends is 90 soles. We can express this as an equation:

Total cost = Pencils cost + Pens cost

90 soles = (x pencils * 3 soles/pencil) + (x pens * 7 soles/pen)

4: Simplify and solve for x.

Combine like terms:

90 soles = 3x soles + 7x soles

90 soles = 10x soles

x = 90 soles / 10 soles/item

x = 9 items

5: Find the number of pencils and pens.

Since x represents both the number of pencils and pens, he bought 9 pencils and 9 pens.

Therefore, the boy bought 9 pencils and 9 pens.

Complete question:

A boy buys the same number of pencils as pencils for 90 soles. Each pencil costs 3 soles and each pencil 7 soles. How many pencils and pens has he bought?

Answer:

The other two vertices are (4 , -2) and (4 , 2) ⇒ 2nd answer

Step-by-step explanation:

* Lets explain how to solve the problem

- All the points on a vertical line have thee same x-coordinates

- In the vertical segment whose endpoints are (x , y1) and (x , y2)

 its length = y2 - y1

- All the points on a horizontal line have thee same y-coordinates

- In the horizontal segment whose endpoints are (x1 , y) and (x2 , y)

 its length = x2 - x1

* Lets solve the problem

- The two vertices of the garden are (-1 , 2) , (-1 , -2)

- The side joining the two vertices is vertical because the points have

  the same x-coordinate

∴ The length of the height = 2 - -2 = 2 + 2 = 4

∴ The length of the height of the garden is 4 feet

∵ The garden shaped a rectangle

∵ The area of the garden is 20 feet²

- The area of the rectangle = base × height

∵ The height = 4 feet

∴ 20 = base × 4 ⇒ divide both sides by 4

∴ Base = 5 feet

∴ The length of the base of the garden is 5 feet

- The adjacent side to the height of the rectangle is horizontal line

∵ The points on the horizontal line have the same y-coordinates

∴ The adjacent vertex to vertex (-1 , 2) has the same y-coordinates 2

∵ The length of the horizontal segment is x2 - x1

∴ 5 = x - (-1)

∴ 5 = x + 1 ⇒ subtract 1 from both sides

∴ x = 4

∴ The adjacent vertex to (-1 , 2) is (4 , 2)

- Lets find the other vertex by the same way

∵ The adjacent vertex to vertex (-1 , -2) has the same y-coordinates -2

∵ x-coordinate of this vertex is the same with x- coordinate of point

 (4 , 2) because these two points formed vertical side

∴ The other vertex is (4 , -2)

∴ The adjacent vertex to (-1 , -2) is (4 , -2)

* The other two vertices are (4 , -2) and (4 , 2)

Answer: Option B

(B) (4,-2) and (4,2) <======+ 100%

Step-by-step explanation: