There are eleven divers on a swim team. If the team can only send four divers to a competition, how many ways can they send four

Answer:

second option

Step-by-step explanation:

5 newton pushing it to the right

while a mere 4 newton pushing it to the left

more force pushing towards right

Subtraction is a mathematical operation that reflects the removal of things from a collection. The temperature change from -4.2 to 9.1 is 13.3.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The temperature change from -4.2 to 9.1 is,

ΔT = 9.1 - (-4.2) = 9.1 + 4.2 = 13.3

Hence, the temperature change from -4.2 to 9.1 is 13.3.

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Answer:

A. 11"

B. 39"

25 - 15 < x < 25 + 15

10 < x < 40

*x = whole number

Answer:

Step-by-step explanation:

Given two side lengths for a triangle, the triangle inequality tells you the third side must have a length between the difference and the sum of the given sides.

__

The difference of the given sides 25 and 15 is ...

  25 -15 = 10

The smallest integer greater than 10 is 11.

The third side must be at least 11 inches long.

__

The sum of the given sides is ...

  25 +15 = 40

The largest integer smaller than 40 is 39.

The third side must be at most 39 inches long.

_____

Additional comment

Formally, the triangle inequality tells you that sides a, b, c must satisfy ...

  a +b > c  and  b +c > a  and  c +a > b

When we're considering the length of third side (c), there are 3 cases to consider. 1) c is shortest; 2) c is between the other lengths; 3) c is longest. Without loss of generality, we can assume a > b.

1) c is shortest:

conclusion: c > a-b

2) a > c > b:

conclusion: c > a-b

3) c is longest:

conclusion: a -b < c < a+b . . . . . . for a>b

Answer:

Hi! The answer is B!

I would suggest using a graphing calculator to compare all the lines. You can use this free one called Desmos, sorry i was not able to attach a link :)

Answer: 8

Step-by-step explanation:

To find the diagonal, we need to use two formulas:

Area of a square: [tex]A = s^{2}[/tex] (Area = side * side)

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

Since  every side of a square is the same:

[tex]a^2 = b^2\\a = b = \sqrt{32} \\a^{2} = 32\\b^2 = 32[/tex]

Our equation:

[tex]32 + 32 = c^2\\64 = c^2\\8 = c[/tex]

The picture below visually explains the problem

Hope this helps!

Answer:

Step-by-step explanation:

The total number of bags in the bottle = 20 + 15 = 35

Then

the probability that the first bag is blue = 20/35

If we replace the first bag :

the probability that the second (picked) bag is blue = 15/35

Conclusion:

If two bags are picked at random one after the other with replacement

Then

the probability that the first bag is blue and then red is :

(20÷35)×(15÷35)

= (4÷7)×(3÷7)

= 12÷49

= 0.244897959184

Answer:

c

Step-by-step explanation:

the -2 causes a shift 2 units right

Answer:

need more information to answer for you.

Step-by-step explanation:

Answer:

  x ≈ 8.99

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between trig functions and sides in a right triangle. Here, the geometry of the problem can be modeled by a right triangle. We are given one side and want to find the difference in lengths of the other side for two different angles.

__

The tower height is the side opposite the angle of elevation. The distance from the tower to the end of the shadow is the side adjacent to the angle of elevation, so the relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(angle of elevation) = (tower height)/(length of shadow)

Solving for the length of shadow, we have ...

  length of shadow = (tower height)/tan(angle of elevation)

The difference in shadow lengths is 2x for the two different angles, so we have ...

  2x = 24.57/tan(30°) -24.57/tan(45°)

__

Dividing by 2 and factoring out the tower height, we have ...

  x = 12.285(1/tan(30°) -1/tan(45°)) = 12.285(√3 -1)

  x ≈ 8.993244

The value of x is about 8.99.

[tex]\text{She is not correct because}\\\\20\% = \dfrac{20}{100} = \dfrac 2{10} = 0.2 \neq 0.02[/tex]

Answer:

Step-by-step explanation:

Problem 1

Any pair of equilateral triangles are always similar triangles. We can use the SSS (side side side) similarity theorem to prove this. One triangle is an enlarged copy of the other, or a shrunken reduced copy.

The rectangle is NOT similar to the square. They are different shapes. Similar figures are figures that are the same shape, but different sizes.

==========================================================

Problem 2

horizontal/vertical = horizontal/vertical

24/x = 6/5

24*5 = 6x

120 = 6x

x = 120/6

x = 20

Answer: The flagpole is 20 ft high (about 2 stories tall)

==========================================================

Problem 3

The formula to use is [tex]z = \sqrt{x*y}[/tex]

z = geometric mean of x and y

We multiply the numbers and take the square root. This only works for two values at a time. The geometric mean of three numbers will involve the cube root. Four numbers involves the 4th root, and so on.

==========================================================

Problem 4

For each figure, the y is the altitude and can be determined using the geometric mean formula.

The decimal values are approximate.

==========================================================

Problem 5

For 45-45-90 triangles, we divide the hypotenuse over sqrt(2) to find the leg length.

For the first triangle in the first row, we have y = 18/sqrt(2) = 9*sqrt(2) after rationalizing the denominator. Multiply top and bottom by sqrt(2).

Take this process in reverse to determine the hypotenuse if you know the leg length. This explains why the hypotenuse is 3.2*sqrt(2) for the second triangle in the first row.

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

For 30-60-90 triangles, we go from the short leg x to the hypotenuse 2x.

Double the short leg to get the hypotenuse.

2x = 36

x = 36/2

x = 18

This is for the first triangle in the bottom row.

For the other triangle in this bottom row, we have a long leg of 4*sqrt(3). This must mean the short leg is exactly 4 units long. Therefore, the hypotenuse is 2*4 = 8 units long.

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

Answer:

Hi,

a=b+3

Step-by-step explanation:

[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=-1&&-1&a+1&-a-b-1\\---&---&---&---&---\\&1&-a-1&a+b+1&c-a-b-1\\\end{array}[/tex]

[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=2&&2&4-2a&2b+8-4a\\---&---&---&---&---\\&1&2-a&b+4-2a&c+2b+8-4a\\\end{array}[/tex]

Thus:

c+2b+8-4a=c-a-b-1

3b-3a=-9

a=b+3

Using translation concepts, it is found that the variables h and k affect the graph of the function as follows:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we consider the parent cube root function as follows:

[tex]y = \sqrt[3]{x}[/tex]

Then, these following changes happened:

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Considering the given quadratic equation, the correct statement is given by:

The airplane reaches its maximum height of 81 feet in 12 seconds.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the equation is given by:

h(t) = -(t - 12)² - 81.

The vertex is (12,81), with a negative leading coefficient, hence it is a maximum point and the correct statement is given by:

The airplane reaches its maximum height of 81 feet in 12 seconds.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The angle sum theorem tells you the sum of angles of a triangle is 180°. Angles of a linear pair are supplementary, so total 180°. These facts can be used to write a relation that can be solved for x.

__

The interior angle at the right end of the line is the supplement of 4x:

  180° -4x

The interior angle at the left end of the line is the supplement of 2x:

  180° -2x

  86° +(180° -4x) +(180° -2x) = 180°

Then the solution to the triangle is ...

  266° = 6x . . . . . . . . . add 6x-180°

  x = 266°/6 = 44 1/3° . . . . . divide by 6

Answer:

a dash is 1/8 tsp.

Step-by-step explanation:

a dash is 1/8 tsp or called 0.13

The function on the table is decreasing on the interval [-2, 0).

A function is decreasing if, as x increases, f(x) decreases.

We can see that at x = -2, f(-2) = 12.

Then at x = 0, f(0) = 0.

And for the value after that:

x = 1, f(1) = 3

So now the function increases. Then we conclude that the function is decreasing on the interval [-2, 0), and after that the function increases.

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Answer: 8

Step-by-step explanation:

The discriminant is [tex]b^2-4ac[/tex]

in the equation:

[tex]-x^2+4x-2[/tex]

A = -1, B = 4, C = -2

plug into equation

[tex]4^2-4(-1)(-2)[/tex]

[tex]16-8[/tex]

⇒ [tex]8[/tex]

Answer:

-2.6112

Step-by-step explanation:

= 0.510 (3+0.2) x -1.6

= 0.510 x 3.2 x -1.6

= -2.6112

hence answer is -2.6112.

Answer:

C

Step-by-step explanation:

Evaluating the options :

Option A

⇒ 5/2x + 7/2 = 3/4x + 14

⇒ 2.5x - 0.75x = 14 - 3.5

⇒ 1.75x = 10.5

⇒ x = 6

⇒ No ×

===========================================================

Option B

⇒ 5/4x - 9 = 3/2x - 12

⇒ 1.5x - 1.25x = -9 + 12

⇒ 0.25x = 3

⇒ x = 12

⇒ No ×

=========================================================

Option C

⇒ 5/4x - 2 = 3/2x - 4

⇒ 1.5x - 1.25x = -2 + 4

⇒ 0.25x = 2

⇒ x = 8

⇒ Yes √

C is the right answer.

Answer:

2 % amount = 12000     7% amount = 1000 dollars

Step-by-step explanation:

x = 2% amount

 then  13 000 - x  = 7% amount

.02x   + .07 (13000-x)  = 310

-.05x + 910 = 310

.05x = 600

x = 600/.05 = 12000      then the 7% amount is 1000

Based on the sides of LMN and OPQ, the congruence postulate that applies is B. Congruent - SSS.

It is used when the two triangles given have three equal corresponding sides which also have equal angles.

All three sides of LMN and OPQ are equal sides and have equal angles and so the SSS rule applies.

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The point-slope form of the equation for the line is y - 3 =1/2(x - 2)

From the question, we are to determine the point-slope form of the equation for the line

The point-slope form of the equation of a line is given by

y - y₁ = m(x - x₁)

Where (x₁, y₁) is a point on the line

and m is the slope of the line

From the given information,

Slope, m = 1/2

and we have the point (2,3)

∴ The point-slope form of the equation for the line is

y - 3 =1/2(x - 2)

Hence, the point-slope form of the equation for the line is y - 3 =1/2(x - 2)

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Answer:

58.5 ft

Step-by-step explanation:

sin 70=55/length

length=58.5 ft

Answer:

Step-by-step explanation:

2/3 - 5/4 + 7/3

=8/12 - 15/12 + 28/12 (LCM=12)

(8 - 15 + 28)/12

=21/12

=7/4

The probability of coin landing with heads is an independent event.

The probability of winning 1st and 2nd prize is a dependent event.

Independents events are events whose occurrence do not depend on each other. They are random events. The probability of a coin landing on heads is a random event.

Dependent events are events that are not random. The outcome of one event depends on the outcome of another event.

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Answer:

1/3

Step-by-step explanation:

[tex]|\Omega|=30\\|A|=10\\\\P(A)=\dfrac{10}{30}=\dfrac{1}{3}[/tex]