the name Joe is very common at a school in one out of every ten students go by the name. If there are 15 students in one class, what is the probability that at least one of them is named Joe

Answer:

r=15.99

Step-by-step explanation:

r=C

2π=100.48

2·π≈15.99189

Answer:

15.99 or 16

Step-by-step explanation:

Either F or J

I think it's J, but it might be F :|

The answer to each part is given above.

Given are the functions as follows -

p(x) = - 5x + 5

q(x) = - 4x - 2

We can write -

(p о q)(5) = (- 5x + 5)(- 4x - 2)

(p о q)(5) = - 5x(- 4x - 2) + 5(- 4x - 2)

(p о q)(5) = 20x² + 10 - 20x - 10

(p о q)(5) = 20x² - 20x

(p о q)(5) = 20 x 25 - 20 x 5

(p о q)(5) = 500 - 100

(p о q)(5) = 400

(p о q)(5) = - 5x(- 4x - 2) + 5(- 4x - 2) = (q о p)(5) = 400

(q о p)(5) = 400

Therefore, the answer to each part is given above.

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The csc(theta) = 1/sin(theta) = 1/(-2/√13) = -√13/2. So, the cosecant of theta is -√13/2.

To find the cosecant (csc) of theta when a point (-3, -2) lies on its terminal side, we need to determine the hypotenuse (r) of the right triangle formed by this point.

Using the Pythagorean theorem, r^2 = (-3)^2 + (-2)^2. So, r^2 = 9 + 4 = 13, and r = √13.

The csc(theta) is the reciprocal of sin(theta). Sin(theta) is calculated as the ratio of the opposite side (y-coordinate) to the hypotenuse, or sin(theta) = -2/√13.

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Answer: 30/23

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

Step 2: Subtract 4x from both sides.

Step 3: Subtract 5 from both sides.

Step 4: Multiply both sides by 6/(-23).

lolz have a nice day!!!

Answer:

Multiply the whole equation to 6 to make it simple.

So you get:

X + 30 = 24

So: X = 24 - 30 = ( - 6 )

Answer:

c∥d by the converse of the corresponding angles theorem.

Step-by-step explanation:

Answer:

The function has 4 roots.

Step-by-step explanation:

Since the degree of the polynomial has is 4, there are a total of 4 roots (both real and complex).

Answer:

4 roots, two real and two complex.

Step-by-step explanation:

The degree of the polynomial indicates the number of solutions

Hope this helps

Given that you have to verify that:

You need to follow these steps, in order to solve the exercise:

1. You need to use this Pythagorean Identify to rewrite the denominator of the second fraction:

If you solve for:

You get:

Then, you can rewrite the expression on the right side in this form:

2. By definition:

Then, you can rewrite the denominator of the second fraction in this form:

3. Now you can cancel common terms:

4. Add the fractions using this formula for adding fractions with different denominators:

Then, you get:

5. You already know that:

Then, you can rewrite the denominator as:

6. Remember this Reciprocal Identify:

Therefore, you can determine:

Hence, the answer is:

Answer:

$880

Step-by-step explanation:

Use the equation:

\(P=(1-d)x\) with d being the discount in a decimal form, and P being the price that was bought at.

220=(1-0.75)x

simplify parenthesis terms

220=0.25x

divide both sides by 0.25

880=x

So, the original price was $880.

Hope this helps! :)

Answer:

B

Step-by-step explanation:

the slope of parallel lines are equal

Answer:

  76 units

Step-by-step explanation:

You want the length of AC in the given triangular pyramid.

The Pythagorean theorem can be used to find the lengths of AD and CD.

  AD² + 40² = 41²

  AD² = 41² -40² = 81 . . . . . = 9²

and

  CD² +40² = 85²

  CD² = 85² -40² = 5625 . . . . . = 75²

It can also be used to find AC:

  AD² + CD² = AC²

  81 + 5625 = AC²

  AC = √5706 = 3√634 ≈ 76

The length of side AC is about 76 units.

__

Additional comment

The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the legs of a right triangle.

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A fifth-degree polynomial with three terms in standard form would be written as a\(x^{2}\) + b\(x^{4}\)+ c\(x^{3}\). The closure property states that a set is closed under a certain operation if performing that operation on any two elements of the set produces a result that is also an element of the set.

Part A: A fifth-degree polynomial with three terms in standard form would be written as a\(x^{2}\) + b\(x^{4}\)+ c\(x^{3}\). The coefficient of the highest degree term (x^5) must be non-zero and all the terms must be written in descending order of the degree. This is the definition of standard form for polynomials.

Part B: The closure property states that a set is closed under a certain operation if performing that operation on any two elements of the set produces a result that is also an element of the set. In this case, the set is polynomials and the operation is subtraction. An example of this property can be seen by subtracting two polynomials, such as 4\(x^{2}\) + 3x - 5 and \(x^{2}\) + 2. The result of this subtraction would be 3\(x^{2}\) + 3x - 5, which is also a polynomial and therefore an element of the set, demonstrating the closure property.

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A fifth-degree polynomial with three terms in standard form would be written as a\(x^{2}\) + b\(y^{2}\)+ c. The closure property states that a set is closed under a certain operation if performing that operation on any two elements of the set produces a result that is also an element of the set.

Part A: A fifth-degree polynomial with three terms in standard form would be written as a\(x^{2}\) + b\(y^{2}\)+ c. The coefficient of the highest degree term (\(x^{5}\)) must be non-zero and all the terms must be written in descending order of the degree. This is the definition of standard form for polynomials.

Part B: The closure property states that a set is closed under a certain operation if performing that operation on any two elements of the set produces a result that is also an element of the set. In this case, the set is polynomials and the operation is subtraction. An example of this property can be seen by subtracting two polynomials, such as 4\(x^{2}\) + 3x - 5 and  + 2. The result of this subtraction would be 3\(x^{2}\) + 3x - 5, which is also a polynomial and therefore an element of the set, demonstrating the closure property.

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Answer:

x=2

Step-by-step explanation:

4x + 2(x - 4) is equivalent to x +2

first, distribute. 4x+2x-8

next, combine like terms. 6x-8

6x-8 = x+2

we need to group all the variable terms on one side, and all the constant terms on the other side of the equation. (6x-8)+(8-x)=(x+2)+(8-x)

get rid of the parenthesis. 6x-8+8-x=x+2+8-x

combine like terms. 6x-x-8+8=x-x+2+8

solve. 5x=10

divide both by 5. 5x/5=10/5

x=2

Answer: Part 1: 1/52 Part 2: 15/26 Part 3: 1/26

Step-by-step explanation:

A ace of hearts is only 1 card

a 8 or a diamond a 8 is a 4/52 chance and a diamond is a 26 / 52 chance

26 + 4 = 30

30/52 simplifies to 15/26

A red 7 has a 4/52 chance for a 7 and half of that for a red card so 2/52 then 1/26

Answer:

Simplified: 9 2/3

Step-by-step explanation:

Convert the mixed numbers into improper fractions

To do this, multiply the denominator by the whole number and add the numerator: (denominator × whole number + numerator)/denoninator

First fraction:

5 11/12

(12 × 5 + 11)/12

(60 + 11)/12

71/12

Next fraction:

3 9/12

(12 × 3 + 9)/12

(36 + 9)/12

45/12

Substitute these fractions in the original problem now:

71/12 + 45/12

Add the numerators only. The denominators stay the same.

(71 + 45)/12

116/12

Now that the calculations are done, convert this back into a whole number

How many times does 12 fit into 116 equally? If you answered 9 times, then you are correct. This 9 will sit as the whole number in the fraction

12 × 9 = 108

This doesn't equal 116 perfectly so we must find the left over

116 - 108 = 8 left over (which is used as the numerator)

9 8/12

If your class or problem asks that you simplify your answer, then look at both the numerator and denominator to determine any common factors within them

8 and 12 both have common factors of 2 and 4

Since 4 is the bigger number, divide both 8 and 12 by 4 to simplify your answer

9 2/3

Brief The Question Please, Thank You

Answer:

hlw its jess your ans is here ↑ ↓

:- 150 rotation and the other 30 rotation about the same point is equivalent to 150+30 = 180

rotation about that point

Solution :

From the given graph the x-intercept is 2 and y-intercept is -1 .

So, equation of line in intercept form is :

\(\dfrac{x}{2} + \dfrac{y}{-1} = 1\\\\x - 2y = 2\)

\(y = \dfrac{x-2}{2}\)

Now, putting x = 4 in above equation, we get :

\(y = \dfrac{4-2}{2}\\\\y = 1\)

Therefore, the value of function at x =4 is 1 .

The measure of angle A'B'C' will be 90 degree.

What is Translation?

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

Right angle ABC is taken by dilation with center P and scale factor 1/2 to angle A’B’C’.

Now,

Since, We know that;

When a figure is dilated by a scale factor then the shape of the figure is not change.

Thus, The measure of ABC is same as the measure of A'B'C'.

Here, The measure of angle ABC = 90 degree

Hence, The measure of angle A'B'C' = 90 degree.

Therefore, The measure of angle A'B'C' will be 90 degree.

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Considering the given linear function, it is found that table B represents the situation.

A linear function is modeled by:

\(y = mx + b\)

In which:

In this problem, the function is given by:

y = 2x + 30.

Hence, the y-intercept is of b = 30, that is, when x = 0, y = 30, and the slope of m = 2 means that when x increases by 1, y increases by 2, hence table B is the answer for this question.

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The true inequality from the list of options is (c) -x - 6 > -3.5

To determine which inequality is true when x is -5, we need to substitute -5 for x in each inequality and simplify.

a) -x – 6 < -3.5

Substituting x = -5, we get:

-(-5) - 6 < -3.5

5 - 6 < -3.5

-1 < -3.5

This is false, so option a) is not true.

b) -x – 6 > 3.5

Substituting x = -5, we get:

-(-5) - 6 > 3.5

5 - 6 > 3.5

-1 > 3.5

This is false, so option b) is not true.

c) -x - 6 > -3.5

Substituting x = -5, we get:

-(-5) - 6 > -3.5

5 - 6 > -3.5

-1 > -3.5

This is true, so option c) is true.

Hence, the correct option is (c) -x - 6 > -3.5

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Complete question

Which inequality is true when the value of x is -5?

a) -x – 6 < -3.5

b) -x – 6 > 3.5

c) -x - 6 > -3.5

d) x - 6 > -3.5

Answer:

8 hours and 26 minutes

Step-by-step explanation:

To convert 506 minutes to hours and minutes, we can use the fact that there are 60 minutes in one hour.

First, we can divide 506 by 60 to find the number of hours:

506 ÷ 60 = 8 with a remainder of 26

This means that 506 minutes is equal to 8 hours and 26 minutes.

Therefore, the conversion of 506 minutes to hours and minutes is:

8 hours and 26 minutes

The domain is all real numbers.

The range is {y|y ≤ 16}.

Option B is the correct answer.

We have,

The given parabola opens downwards and has a vertex at (-1,16).

So,

The parabola has a maximum value at y = 16.

Also, the y-intercept of the parabola is (0,15), which is below the vertex, and the parabola intersects the x-axis at (-5,0) and (3,0).

We can use the factored form of the equation of a parabola to find its equation in this case.

The factored form is:

y = a(x - h)² + k

where (h,k) is the vertex and "a" determines whether the parabola opens upwards or downwards.

Since the parabola opens downwards, "a" is negative.

Also, we know that the vertex is (-1,16), so we have:

y = a(x + 1)² + 16

To find "a", we can use one of the x-intercepts, say (-5,0).

Substituting these values into the equation gives:

0 = a(-5 + 1)² + 16

0 = 16a

a = 0

This indicates that the parabola is actually a line passing through (0,15) and (3,0). Therefore, the equation of the parabola is:

y = -x² - 2x + 15

The domain of this function is all real numbers because there are no restrictions on the values of x that can be plugged into the equation.

However, the range of the function is limited by the maximum value of y, which is 16.

Since the parabola opens downwards, all y values less than or equal to 16 are attainable.

Therefore, the domain is all real numbers, and the range is {y | y ≤ 16}.

Therefore,

The domain is all real numbers.

The range is {y|y ≤ 16}.

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The length of side i in the triangle is approximately 35 cm.

To solve for the length of side i in triangle ΔHIJ, we can use the law of sines, which states:

sin A / a = sin B / b = sin C / c

wher;

First, we can use the fact that the sum of the angles in a triangle is 180° to find the measure of angle J:

m∠H + m∠I + m∠J = 180°

55° + 30° + m∠J = 180°

m∠J = 95°

Now we can use the law of sines:

sin I / i = sin J / j

where;

Substituting the known values, we get:

sin 30° / i = sin 95° / 69

Solving for i, we get:

i = sin 30° x 69 / sin 95°

i = 35 cm

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Answer:

885.2m²

Step-by-step explanation:

a is the side length of the square at the base

h is the height of the pyramid

Given

a = 18m

Get the height using the pythagoras theorem

h² =18²-9²

h² = 324 - 81

h² = 243

h = √243

h = 15.5884m

Area of the triangle = 1/2 * 18 * 15.5884

Area of the triangle = 9 * 15.5884

Area of the triangle = 140.2956m²

Area of the 4 triangles = 4(140.2956)

Area of the 4 triangles = 561.1824m²

Base area = 18 * 18

Base area = 324m²

Total surface area = Base area + Area of the 4 triangles

Total surface area = 324 + 561.1824

Total surface area = 885.1824

Total surface area = 885.2m² (to the nearest tenth)

Answer:

Step-by-step explanation:

A room has a square floor and its height is 5m. If its volume is 720 metre cube, find the dimensions of its floor.​

we find the area of ​​the square base

720 : 5 = 144m²

we find the side of the square room

√144 = 12m

Answer:

length = 12m

width = 12m

Step-by-step explanation:

720/5 = 144

144 = area of this floor

\(\sqrt{144}\) = 12m

this floor is square

then length and width are same

so length = 12m

   width = 12m

Answer:

First one: 27

Second one: 1/8

Step-by-step explanation:

Hope this helps! :)

The point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0.

To graph the equation 2x + 3y = 6, we can rewrite it in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

Starting with the given equation, we isolate y to one side:

3y = -2x + 6

y = (-2/3)x + 2

Now, we have the equation in slope-intercept form, y = (-2/3)x + 2. The slope is -2/3, and the y-intercept is (0, 2).

To find the point where the graph intersects the x-axis, we need to determine the coordinates where y is equal to zero. This occurs when the line crosses the x-axis.

Setting y = 0 in the equation, we have:

0 = (-2/3)x + 2

(-2/3)x = -2

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

Therefore, the point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0, indicating the point of intersection with the x-axis on the graph.

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Answer:

304oz

Step-by-step explanation: