a distribution has the five number summary, 12,21,43,62,71. what is the interquartile range (IQR) of this distribution

Answer:

6^ -24

Step-by-step explanation:

We know that a^b^c = a^ (b*c)

(6^-4)^6  = 6^ (-4*6) = 6^ -24

Answer:

b

Step-by-step explanation:

I would use b.

Why?

[tex]2 \csc(2x)[/tex]

[tex]2 \frac{1}{\sin(2x)}[/tex]

[tex]\frac{2}{\sin(2x)}[/tex]

[tex]\frac{2}{2\sin(x)\cos(x)}[/tex]

[tex]\frac{1}{\sin(x)\cos(x)}{/tex]

[tex]\frac{1}{\sin(x)\frac{1}{\cos(x)}[/tex]

[tex]\csc(x) \sec(x)[/tex]

I applied the identity sin(2x)=2sin(x)cos(x) in line 3 to 4.

Answer: OPTION B.

Step-by-step explanation:

It is important to remember these identities:

[tex]csc(x)=\frac{1}{sin(x)}\\\\sec(x)=\frac{1}{cos(x)}[/tex]

Knowing this, we can say that:

[tex]csc(x) sec(x)=\frac{1}{sin(x)}*\frac{1}{cos(x)}=\frac{1}{sin(x)*cos(x)}[/tex]

Now we need to use the following Double angle identity :

[tex]sin(2x)=2sin(x)cos(x)[/tex]

And solve for [tex]sin(x)cos(x)[/tex]:

[tex]\frac{sin(2x)}{2}=sin(x)cos(x)[/tex]

The next step is to make the substitution into [tex]\frac{1}{sin(x)*cos(x)}[/tex] and finally simplify:

[tex]\frac{1}{\frac{sin(2x)}{2}}=\frac{\frac{1}{1}}{\frac{sin(2x)}{2}}=\frac{2}{sin(2x)}=2csc(2x)[/tex]

Answer:

Option A

Step-by-step explanation:

Given:

Center of circle = (h,k)= (3,8)

Radius = r = 5

The standard form of equation of circle with center and radius is:

[tex](x-h)^2+(y-k)^2=r^2\\Putting\ the\ values\\(x-3)^2+(y-8)^2=(5)^2\\Simplifying\\x^2+9-6x+y^2+64-16y=25\\x^2+y^2-6x-16y+9+64=25\\x^2+y^2-6x-16y+73=25\\x^2+y^2-6x-16y+73-25=0\\x^2+y^2-6x-16y+48=0[/tex]

Therefore, the general form of the equation of circle given is:

[tex]x^2+y^2-6x-16y+48=0[/tex]

Hence, option A is correct ..

Answer:

D

Step-by-step explanation:

Given

9 - 7x = (4x - 3)² + 5 ← expand the squared factor

9 - 7x = 16x² - 24x + 9 + 5, that is

9 - 7x = 16x² - 24x + 14 ( subtract 9 - 7x from both sides )

0 = 16x² - 17x + 5, that is

16x² - 17x + 5 = 0 ← in standard form → D

Answer:

6

Step-by-step explanation:

60% of 40 = 24

25% of 24 = 6

Therefore, 6 girls in  the class wear glasses.

[tex]\large\boxed{\text{C}).\,15\,\text{cm}}[/tex]

In this question, we're trying to find what the radius of the circular pie is.

In this question, we know that the area of the pie is 706.5 cm²

We can use the area to find our radius.

We would use the formula [tex]r=\sqrt\frac{A}{\pi}[/tex] to find the radius.

R= radius

A = Area

Your equation should look like this:

[tex]r=\sqrt\frac{706.5}{\pi}[/tex]

Now, you will solve.

[tex]r=\sqrt\frac{706.5}{\pi}\\\\\text{You can make it simpler by turning}\, \pi\,\text{into} 3.14\\\\r=\sqrt\frac{706.5}{3.14}\\\\\text{Divide 706.5 by 3.14}\\\\r=\sqrt225\\\\\text{Now, get the square root of 225}\\\\r=15[/tex]

When you're done solving, you should get 15.

This means that the radius of the pie is 15 cm.

Final answer:

To find the radius of the pie given its area of 706.5 cm², we use the formula A = πr² and solve for r, yielding an approximate radius of 15 cm. This corresponds to option C) on the given list.

Explanation:

To find the radius of the pie given its area, we can use the area formula for a circle: A = πr². Since the area of the pie is given as 706.5 cm², we can rearrange the formula to solve for the radius (r).

The rearranged formula to solve for the radius is: r = √(A/π).

Substituting the given area, we have:
r = √(706.5 cm²/π)
r = √(706.5/3.14159265359)
r ≈ √(225)
r ≈ 15 cm

Therefore, the radius of the pie is approximately 15 cm, making option C) the correct answer.

Answer:

The slope is 745 and the y-intercept is 500

The slope means The amount of money increases by $745 per month

The y-intercept means the business opened with initial amount $500

Step-by-step explanation:

* Lets explain how to solve the question

- The graph represents the relation between the number of months

  since the business opened and the total amount of money the

  business has earned

- The x-axis represents the number of month

- The y-axis represents the amount of money

- In the line the slopes from any two points on the line are equal

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

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

- The equation of the line is y = mx + c ,where m is the slope of the line

 and c is the y-intercept

* Lets check is the relation between x and y is linear by calculating the

 slopes between each to points

∵ (2 , 1990) , (5 , 4225) , (9 , 7205) are points from the graph

- m1 is the slope of the points (2 , 1990) and (5 , 4225) , m2 is the slope

 of the points (5 , 42250) and (9 , 7205) , m3 is the slope of the points

 (2 , 1990) and (9 , 7205)

∵ [tex]m_{1}=\frac{4225-1990}{5-2}=745[/tex]

∵ [tex]m_{2}=\frac{7205-4225}{9-5}=745[/tex]

∵ [tex]m_{3=\frac{7205-1990}{9-2}}=745[/tex]

∴ m1 = m2 = m3 = 745

∴ The relation between the number of months and the amount of

   money is linear

* The slope is 745

∵ The form of the linear equation is y = mx + c

∵ m = 745

∴ y = 745 x + c

- The y-intercept means the line intersect the y-axis at point (0 , c),

  then to find c substitute x and y of the equation by the coordinates

  of any point on the line

∵ x = 2 , y = 1990

∴ 1990 = 745(2) + c

∴ 1990 = 1490 + c ⇒ subtract 1490 from both sides

∴ c = 500

∵ c is the y-intercept

* The y-intercept is 500

* The slope represents the rate of increasing of money per month

∴ The amount of money increases by $745 per month

* The y-intercept represents the initial amount of money when the

  business opened

∴ The business opened with initial amount $500

Answer:

The slope is 745 and the y-intercept is 500

The slope means The amount of money increases by $745 per month

The y-intercept means the business opened with initial amount $500

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/5 + 1/5^-2

1/5 + 1/25

1/5 = 5*1 / 5*5

5/25 + 1/25

6/25 which cannot be reduced or changed.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=5x+2&(1)\\3x=-y+10&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\3x=-(5x+2)+10\\3x=-5x-2+10\qquad\text{add 5x to both sides}\\8x=8\qquad\text{divide both sides by 8}\\x=1\\\\\text{put the value of x to (1):}\\\\y=5(1)+2\\y=5+2\\y=7[/tex]

Answer:

y-int:3

slope:-3

Step-by-step explanation:

6x-2y=-6

change to y=mx+b: -2y=-6x-6

divide by -2

y=3x+3

Answer:

1/12 of a gallon of water in each container

Step-by-step explanation:

Answer = [tex]\frac{Water}{Containers}[/tex] = 1/12

Answer:

Oliver poured [tex]\frac{1}{12}[/tex] gallons of water in each container.

Step-by-step explanation:

Oliver has the amount of water = 0.5 gallons.

He pours all of the water into 6 containers.

So amount of water in each container will be = [tex]\frac{\text{Total amount of water}}{\text{Number of containers}}[/tex]

= [tex]\frac{0.5}{6}[/tex]

= [tex]\frac{\frac{1}{2} }{6}[/tex]

= [tex]\frac{1}{12}[/tex] gallons of water.

Therefore, in each container amount of water poured will be [tex]\frac{1}{12}[/tex] gallons.

This is a linear equation in standard form [tex]\( Ax + By = C \).[/tex] None of the options provided in the multiple-choice question exactly match this equation in standard form

To find the equation of a line perpendicular to the given line and passing through a specific point, follow these steps:

1. Identify the slope of the original line.

  The line given is [tex]\( y = -10x + 1 \)[/tex]. The slope (m) of this line is -10.

2. Find the perpendicular slope:

  The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. Therefore, the perpendicular slope [tex]\( m_{\perp} \) is \( \frac{1}{10} \)[/tex]  because [tex]\( m_{\perp} = -\frac{1}{m} \).[/tex]

3. Use the point-slope form to find the equation:

  The point-slope form is [tex]\( y - y_1 = m_{\perp}(x - x_1) \)[/tex], where [tex]\( (x_1, y_1) \)[/tex] is the point the line passes through, which is (5,7) in this case.

4. Plug in the point and the perpendicular slope:

  [tex]\( y - 7 = \frac{1}{10}(x - 5) \)[/tex].

5. Simplify the equation to get it into slope-intercept form  [tex](\( y = mx + b \))[/tex]:

  [tex]\( y = \frac{1}{10}x - \frac{1}{10}(5) + 7 \)[/tex].

  [tex]\( y = \frac{1}{10}x - \frac{1}{2} + 7 \)[/tex].

  [tex]\( y = \frac{1}{10}x + \frac{13}{2} \)[/tex] after combining like terms.

The equation in slope-intercept form is [tex]\( y = \frac{1}{10}x + \frac{13}{2} \),[/tex]which corresponds to one of the choices given in the multiple-choice question. Let's identify which one it is.

The equation that represents a line which is perpendicular to the line [tex]\( y = -10x + 1 \)[/tex] , passing through the point (5,7), is:

[tex]\[ y = \frac{1}{10}x + \frac{13}{2} \][/tex]

This can be simplified to:

[tex]\[ 10y = x + 65 \][/tex]

Or:

[tex]\[ x - 10y = -65 \][/tex]

This is a linear equation in standard form \( Ax + By = C \). None of the options provided in the multiple-choice question exactly match this equation in standard form

7v(4v2-8v+1)+8(4v2-8v+1)

28v3-56v2+7v+32v2-64v+8

Answer= 28v3 -24v2 -57v +8

ANSWER

alternate interior angles theorem

EXPLANATION

According to the alternate interior angles theorem, when two parallel lines are are intercepted by a straight line (transversal) the angles in the interior corners of a Z-shape pattern are congruent.

From the above diagram line r is parallel to line s, therefore

[tex] \angle \: 3 \cong \angle6[/tex]

and

[tex] \angle \: 4\cong \angle5[/tex]

because they are alternate interior angles.

See attachment for how to spot alternate interior angles.

Question:

Given that r||s and q is a transversal, we know that  by the [________].

Answer:

alternate interior angles theorem

Answer:

3                     sqrt(3)

-----------    or  -----------

2 sqrt(3)            2

Step-by-step explanation:

3 sqrt(8)

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

4 sqrt(6)

3 sqrt(4*2)

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

4 sqrt(3*2)

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

3 sqrt(4) sqrt(2)

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

4 sqrt(3) sqrt(2)

Canceling the sqrt(2) and sqrt(4) is 2

3*2

----------

4 sqrt(3)

3

-----------

2 sqrt(3)

We can simplify the answer be multiplying by sqrt(3)/sqrt(3)

3                 sqrt(3)

----------- * ----------

2 sqrt(3)     sqrt(3)

3 sqrt(3)

-----------

2 *3

sqrt(3)

-----------

2

Answer:

False.

Step-by-step explanation:

To see if these sides can form a right triangle, all we need to do is see if the following equation holds [tex]a^2+b^2=c^2[/tex] where [tex]c[/tex] is the larger measurement.  [tex]a \text{ and } b[/tex] it doesn't really matter which you assign as 5 or 8.

So I'm choosing the following [tex]a=5,b=8,c=12[/tex].

[tex]c[/tex] has to be 12 because 12 is the largest.

Now we got to see if [tex]a^2+b^2=c^2[/tex] holds.

That is, we need to see if [tex]5^2+8^2=12^2[/tex] holds.

[tex]5^2+8^2=12^2[/tex]

[tex]25+64=144[/tex]

[tex]89=144[/tex]

That's totally false.  89 is definitely not 144 so 5,8, and 12 cannot be put together to form a right triangle.

Answer:

√135

Step-by-step explanation:

3^2+b^2=12^2

9+b^2=144

9-9+b^2=144-9

b^2=135

√135=b

[tex]3\sqrt5-2\sqrt7+\sqrt{45}-\sqrt{28}=\\3\sqrt5-2\sqrt7+\sqrt{9\cdot5}-\sqrt{4\cdot7}=\\3\sqrt5-2\sqrt7+3\sqrt{5}-2\sqrt{7}=\\6\sqrt5-4\sqrt7[/tex]

Answer:

nope its not. You should  count it like this  (8 / 2) * (2 + 2)

Step-by-step explanation:

(8 / 2) * (2 + 2)

4 * 4

16

[tex]\text{Hey there!}[/tex]

[tex]\text{PEMDAS means: Parentheses, Exponents, Multiplication, Division, Addition}\\\text{, \& Subtraction}[/tex]

[tex]\text{\underline{No}, it is \underline{NOT} correct because you had to work with the parentheses first}[/tex]

[tex]\dfrac{8}{2}(2 + 2) = \ ? \\ \\ (2 + 2) = 4 \\ \\ \dfrac{8}{2}(4) = \ ? \\ \\ \dfrac{8}{2}= 4 \\ \\ \text{4(4)\ = 16} \\ \\ \boxed{\boxed{\huge\text{Answer should be: 16 }}}[/tex]

[tex]\text{You had to do what was inside the parentheses first, then}\text{ divsion}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

The sum of three positive integers given their product is 7, analyze the factors of the product and sum them up.

The sum of three positive integers whose product is 8 can be found by analyzing the factors of 8.

Given that the product of three different positive integers is 8, the three integers are 1, 2, and 4. Therefore, the sum of these integers is 1 + 2 + 4 = 7.

Answer:

x-intercept (-8,0)

y-intercept (0,2)

Step-by-step explanation:

To find the x-intercept, you set y equal to 0.

Like this:

-2(0)+x=2(0)-8

  0  +x=0    -8

        x=   -8

So the x-intercept is (-8,0).

To find the y-intercept, you set x equal to 0.

Like this:

-2y+0=2y-8

  -2y =2y-8

Subtract 2y on both sides

 -4y=-8

Divide both sides by -4

   y=2

So the y-intercept is (0,2)

[tex]\large\boxed{12\,\text{apples}}[/tex]

In this question, we're trying to find how many apples Jenson picked from the basket.

Lets gather information that can help us.

Important information:

With the information above, we can solve the question.

We know that he picked up a fruit 40 times, but we need to find how many apples he picked up during the 40 times.

The probability of picking an apple is 0.3, which is equivalent to 30%

This means that 30% of the 40 times he picked an apple.

We would multiply 40 by 0.3 to get our answer.

[tex]40*0.3=12[/tex]

This means that Jenson picked 12 apples.

Answer:    B.12

Step-by-step explanation:

Answer:

[tex]\large\boxed{\dfrac{4}{x}+6}[/tex]

Step-by-step explanation:

Six more than the quotient of four and a number x:

[tex]\dfrac{4}{x}+6[/tex]

Answer:

[tex]\frac{4}{x}+6[/tex]

Step-by-step explanation:

We have been given a  word phrase. We are supposed to represent our given word phrase into an algebraic expression.

The quotient of four and a number x will be 4 divided by x. We can represent this information in an expression as:

[tex]\text{Quotient of four and a number }x=\frac{4}{x}[/tex]

Six more than the quotient of four and a number x would be [tex]\frac{4}{x}+6[/tex]

Therefore, our required expression would be [tex]\frac{4}{x}+6[/tex].

Answer:

a is the only true one if you meant 6 times 5!

Step-by-step explanation:

Before we being

n!=n*(n-1)*(n-2)*...(3)(2)(1)

Example: 5!=5(4)(3)(2)(1) and 10!=10(9)(8)(7)(6)(5)(4)(3)(2)(1)

Yes that operation is multiplication.

a) Does 6!=6*5!

Let's see

6!=6*5*4*3*2*1

5!=5*4*3*2*1

So 6*5!=6(5*4*3*2*1)=6*5*4*3*2*1=6!

So true!

b) Does 4!+2!=6! ?

4!=4(3)(2)(1)

2!=2(1)

6!=6(5)(4)(3)(2)(1)

Does

4(3)(2)(1)+2(1)=6(5)(4)(3)(2)(1)

24          +2  =720

26=720 (this is not true)

So 4!+2! is not 6!

c) Does 6!/3!=2! ?

6!=6(5)(4)(3)(2)(1)

3!=3(2)(1)

If you divide 6! by 3!, then the factors 3 and 2 and 1 cancel and you are left with 6(5)(4).

So the question becomes is 6(5)(4)=2!

2!=2(1)=2

6(5)(4)=2?

No way! That is saying 120=2 which is not true.

The evaluations of the statements are: (a) false because non-integer factorials are not defined, (b) false because the sum of 4! and 2! does not equal 6!, and (c) false because 6! divided by 3! is 120, not 2!.

Let's evaluate each statement one by one.

This statement is false. The factorial function is defined for non-negative integers. Since there is no definition for non-integer factorial such as 6.5!, this comparison is invalid. A correct statement may involve only integer factorials.

This statement is also false. To show this, let's calculate each factorial:

Adding 4! and 2! gives 24 + 2 = 26, which is not equal to 6! (720). This statement could be corrected by finding two factorials that add up to another factorial, if such a pair exists.

This statement is false. By calculating the factorials, we have:

Therefore, 6!/3! is equal to 720/6, which simplifies to 120, not 2 (which is the value of 2!). The correct statement is 6!/3! = 120.

https://brainly.com/question/15689921

#SPJ6

Answer:

278.9 units^3 to the nearest tenth.

Step-by-step explanation:

This is a cylinder on the bottom . resting on the cylinder is a prism.

Volume of the cylinder = π r^2 h  where r = 1/2 * 7 = 3.5 and h = 6.

V = π * 3.5^2 * 6 = 230.907 units^3.

Volume of the prism = l*w*h

= 4*4*3 = 48 units^3.

Volume of the composite figure = 230.907 + 48

= 278.9.

Answer:

2/7

Step-by-step explanation:

If two events A and B are independent, then P(A and B)=P(A)P(B).

So since Q and R are independent, then P(Q and R)=P(Q)P(R).

Let's substitute and evaluate:

[tex]P(Q\text{ and }R)=P(Q)\cdot P(R)=\frac{4}{7} \cdot \frac{1}{2}=\frac{4}{14}[/tex].

Both 2 and 14 are divisible by 2, so to reduce 4/14 we could divide top and bottom by 2:

4/14=(4/2)/(14/2)=2/7

Answer:

[tex]y=3x+8[/tex]

Step-by-step explanation:

Slope-intercept form is as follows:

[tex]y=mx+b[/tex]

In this equation, "m" represents your slope and "b" represents your y-intercept.

To convert your equation into slope-intercept form, distribute your 3 across your parentheses and then add 5 to both sides to isolate for y.

[tex]y-5=3(x+1)\\y-5=3x+3\\y=3x+8[/tex]

Answer:

=3501 yards.

Step-by-step explanation:

The three ships form a triangle.  From the Voyager the angle between the Norman and the Gladstone=180-(55+48)=77°

Let the position of the Voyager be V that of Norman be N and that of the Gladstone be G

Then, the distance between Norman and voyager is g

g/sin G=v/ Sin V

4590/Sin 77=g/Sin 48

g=(4590 Sin 48)/Sin 77

=3500.8 yards

The distance between the Norman and the voyager= 3501 yards.

1st one

Step-by-step explanation:

I have answered ur question

Answer:

A

Step-by-step explanation:

Given

x² - 8x = 3

To complete the square

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

x² + 2(- 4)x + 16 = 3 + 16

(x - 4)² = 19 ( take the square root of both sides )

x - 4 = ± [tex]\sqrt{19}[/tex] ( add 4 to both sides )

x = 4 ± [tex]\sqrt{19}[/tex]

Solution set is (4 - [tex]\sqrt{19}[/tex], 4 + [tex]\sqrt{19}[/tex] )

Answer:

the answer is D

Step-by-step explanation:

if you look on the graph and compare the statements you'll see none of them correlate except for the last one. 7 erasers cost 3.50, since the point on the graph is (7, 3.50)

Answer:

The correct option is D) Seven eraser cost $3.50

Step-by-step explanation:

Consider the provided graph.

The graph shows the relationship between the total cost and the number of erasers bought at the student store.

Here the x-axis represents the number of erasers bought and the y-axis represents the total cost.

Now consider the provided options.

Options (A) Each eraser cost $1.00

This option is incorrect because when x = 1 the value of y = 0.5, that means the cost of each eraser is $0.5

Options (B) Each eraser cost $1.50

This option is incorrect as the cost of each eraser is $0.5

Options (C) Three eraser cost $6

This option is incorrect because when x = 3 the value of y = 1.5, that means the cost of 3 eraser is $1.5

Options (D) Seven eraser cost $3.50

This option is correct because when x = 7 the value of y = 3.5, that means the cost of 7 eraser is $3.5