What is the interquartile range of the following data set? 78,90,456,676,111,381,21

Answer:

[tex]{ \tt{ = \frac{ {p}^{2} + 8p + 16 }{ {p}^{2} - 16 } }} \\ \\ = { \tt{ \frac{ {(x + 4)}^{2} }{(x - 4)(x + 4)} }} \\ \\ = { \tt{ \frac{(x + 4)}{(x - 4)} }}[/tex]

[tex]\sf Your \: question \: is \: incomplete. \: [/tex]

______________________

[tex]\sf \: I \: believe \: this \: is \: the \: answer \: you \: wanted[/tex] ⟹

[tex]\sf If \: the \: discriminant \: of \: an \: equation \: is \: zero, \: then \\ \sf \: the \: equation \: will \: have \:\underline{ 1 \: real \: solution \: with \: real \: and \: equal \: roots}.[/tex]

[tex]\boxed{ \sf{Explanation}} [/tex]

[tex]\sf If \: discriminant \: of \: quadratic \: equation \: ax^{2} + bx + c \: \\ \sf is \: b^{2} - 4ac = 0 \: then \: it \: will \: have \\ \sf↦\underline{1 \: real \: solution \: with \: real \: and \: equal \: roots.} [/tex]

Answer:

see explanation

Step-by-step explanation:

If b² - 4ac = 0

Then the roots are real and equal

Answer:

Step-by-step explanation:

C = 16 * 3 = 48

Answer:

0.50 or about half a year longer.

Step-by-step explanation:

We can write an equation to model bot investments.

Oliver invested $970 in an account paying an interest rate of 7.5% compounded continuously.

Recall that continuous compound is given by the equation:

[tex]A = Pe^{rt}[/tex]

Where A is the amount afterwards, P is the principal amount, r is the rate, and t is the time in years.

Since the initial investment is $970 at a rate of 7.5%:

[tex]A = 970e^{0.075t}[/tex]

Carson invested $970 in an account paying an interest rate of 7.375% compounded annually.

Recall that compound interest is given by the equation:

[tex]\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}[/tex]

Where A is the amount afterwards, P is the principal amount, r is the rate, n is the number of times compounded per year, and t is the time in years.

Since the initial investment is $970 at a rate of 7.375% compounded annually:

[tex]\displaystyle A = 970\left(1+\frac{0.07375}{1}\right)^{(1)t}=970(1.07375)^t[/tex]

When Oliver's money doubles, he will have $1,940 afterwards. Hence:

[tex]1940= 970e^{0.075t}[/tex]

Solve for t:

[tex]\displaystyle 2 = e^{0.075t}[/tex]

Take the natural log of both sides:

[tex]\ln\left (2\right) = \ln\left(e^{0.075t}\right)[/tex]

Simplify:

[tex]\ln(2) = 0.075t\Rightarrow \displaystyle t = \frac{\ln(2)}{0.075}\text{ years}[/tex]

When Carson's money doubles, he will have $1,940 afterwards. Hence:

[tex]\displaystyle 1940=970(1.07375)^t[/tex]

Solve for t:

[tex]2=(1.07375)^t[/tex]

Take the natural log of both sides:

[tex]\ln(2)=\ln\left((1.07375)^t\right)[/tex]

Simplify:

[tex]\ln(2)=t\ln\left((1.07375)\right)[/tex]

Hence:

[tex]\displaystyle t = \frac{\ln(2)}{\ln(1.07375)}[/tex]

Then it will take Carson's money:

[tex]\displaystyle \Delta t = \frac{\ln(2)}{\ln(1.07375)}-\frac{\ln(2)}{0.075}=0.4991\approx 0.50[/tex]

About 0.50 or half a year longer to double than Oliver's money.

Answer:

(4,4)

y = 4

x = 4

Step-by-step explanation:

First we need to input y = 1/2x + 2 into 4x - 2y = 8.

4x - 2 (1/2x + 2) = 8 <-- Then solve

4x - 1x + -4 = 8

3x - 4 = 8

    +4   +4

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

3x    =    12

3             3

x = 4

Now we need to use x and apply it to find y.

y = 1/2x + 2

y = 1/2(4) + 2

y = 2 + 2

y = 4

Now to graph go on the x axis (horizontal axis) and go to 4, then up 4 on the y axis.

You need to graph the point (4,4).

I hope this helps!

Answer:

see graph  (4,4)

to manually graph just pick any two values for X in the first equation and calculate the corresponding Y value ... put a "dot" (a point on the graph)

do for both points , and draw al LINE between them...

repeat fore the second equation... the "solution" is where the two lines cross

Step-by-step explanation:

Answer:

D=8

Step-by-step explanation:

normal division rules

33 goes into 47 1 time

then it leaves 17D

if we divide 170 by 33, we get 5 and if we divide 179 by 33, we still get 5. So we have 17D-165. That leaves us with something that you multiply 33 with to have a 2 in the ones place so that you get a remainder of 2. (In order to get 2 in the remainder, we need a 2 in the ones place because 4-2=2. In order to get that we need to see which number multiplied with 33 would get us a number smaller than 179 but also has a 2 in the ones place. Theres only one number and thats 4. 33*4=132. So in order to get only 2 in the remainder, we need the rest to be subtracted. This means that 17D-165=134. This way we can see that D=8

Answer:

answer is A

hope it helps please mark as brainliest answer and give me thanks

Answer:

8 units

Step-by-step explanation:

Area of a rectangle = Width multiplied by Length

Substitute in all the known numbers into this formula to get

72 = (9) × [tex](2x+4)[/tex]

Solve the equation for x, to find out the length

[tex]9(2x+4)=72[/tex]

[tex]2x+4=72/9[/tex]

[tex]2x+4=8[/tex]

[tex]2x=8-4[/tex]

[tex]2x=4[/tex]

[tex]x=4/2[/tex]

[tex]x=2[/tex]

Length of the rectangle = [tex](2x+4)[/tex]

[tex]2(2)+4[/tex]

[tex]4+4=8[/tex]

Answer:

(g ∘ f)(2) =5

Step-by-step explanation:

f(x) = 3x − 2

g(x) = x + 1

(g ∘ f)(2).

Find f(2) = 3(2) -2 = 6-2 = 4

Then find g(4) = 4+1 = 5

Answer:

BC ≈ 14.5 cm

Step-by-step explanation:

Using the sine ratio in the right triangle

sin65° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{BC}{16}[/tex] ( multiply both sides by 16 )

16 × sin65° = BC , then

BC ≈ 14.5 cm ( to the nearest tenth )

Answer:

45

Step-by-step explanation:

9x5

Answer:

y = -3x+4

Step-by-step explanation:

The slope intercept form of an equation is

y = mx+b where m is the slope and b is the y intercept

y = -3x+4

Answer:

Step-by-step explanation:

Hey GurpTheDestoyer! Find the volume of the sphere. Round to the nearest whole number. Radius= 8 what is the volume? The Volume = 2,144.660585 cm3. Hope this helped! <3

Answer:

3 each

Step-by-step explanation:

36 / 12 = 3

.................................................

Answer:

The "zero" is where it crosses the x axis which is -2 in this graph

Step-by-step explanation:

[tex]n = \frac{6}{m + 1} [/tex]

Hope it helps you...

The value of n is n= 6/( m+1).

An expression is a set of terms combined using the operations +, – , x or , /.

Given:

mn - 3 = 3 - n

mn + n = 6

n(m+ 1) =6

n= 6/( m+1)

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ2

Angle CBD= 81°

I hope it helps you...

Answer:

81

Step-by-step explanation:

∠CBD is the exterior angle of  the ΔABC.

Exterior angle property:

Exterior angle equals the sum of opposite interior angles.

∠CBD = ∠ABC + ∠ACB

           = 53 + 28

           = 81°

Answer:

a)

(i) 5.8 hours

(ii)  6.5 hours

(iii) 6 hours

(iv) 6 hours

b) 180 hours

Answer:

-10 = x

Step-by-step explanation:

5=7+x/5

Subtract 7 from each side

5-7=7-7+x/5

-2 = x/5

Multiply each side by 5

-2 *5 = x/5 *5

-10 = x

Answer:

0.18

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Answer:

36 feet

Step-by-step explanation:

I can confirm that 36 feet is the correct answer. as seen below, I was able to get 100%

Let S be the sum. So you have

S = 1 + 2 + 3 + … + 2004 + 2005 + 2006

as well as

S = 2006 + 2005 + 2004 + … + 3 + 2 + 1

Then

2S = (1 + 2006) + (2 + 2005) + … + (2005 + 2) + (2006 + 1)

2S = 2007 + 2007 + … + 2007 + 2007

2S = 2006 × 2007

S = (2006 × 2007)/2

S = 2,013,021

which makes the last two digits 21.

Answer:

A spurious correlation wrongly implies a cause and effect between two variables. For example, the number of astronauts dying in spacecraft is directly correlated to seatbelt use in cars: Use your seatbelt and save an astronaut life!

Interesting correlations are easy to find, but many will turn out to be spurious. Three examples are the skirt length theory, the Super Bowl indicator, and a suggested correlation between race and college completion rates.

Step-by-step explanation:

Answer:

x = 11√3

y = 11

Step-by-step explanation:

Let 60 be the reference angle

sin 60 = p/h

√3/2 = x/22

or, 22√3 = 2x

or, x = (22√3)/2

so, x = 11√3

now

[tex]h^2 = p^2 + b^2\\or, 22^2 = (11\sqrt{3} )^2+y^2\\or, 484 = 363 + y^2\\or, 484-363 = y^2\\or, 121 = y^2\\or, \sqrt{121} = y\\so, y = 11[/tex]

Answer:

[tex]D. \\x>\frac{3}{2}[/tex]

Step-by-step explanation:

12(1/2x - 1/3) > 8 - 2x

6x - 4 > 8 - 2x

6x + 2x - 4 > 8 - 2x + 2x

8x - 4 > 8

8x - 4 + 4 > 8 + 4

8x > 12

8x ÷ 8 > 12 ÷ 8

x  > 1.5

Answer:

A

Step-by-step explanation:

Answer:

The answer is <ead

please mark me brainliest

Answer:  D) reflection across y = -x

Explanation:

When we reflect over y = x, we basically swap x and y. So for instance, the point (3,1) becomes (1,3).

When reflecting over y = -x, we will do the same thing but we'll make each coordinate swap in sign from positive to negative (or vice versa). The rule for reflecting over y = -x is [tex](x,y) \to (-y,-x)[/tex]

So if we apply that rule to point A(3,1) then it becomes A ' (-1, -3).

Similarly, B(1,5) moves to B ' (-5, -1)

Finally, C(6,9) becomes C ' (-9, -6)

Answer:

Step-by-step explanation:

5(a-1) -15 = 3(a+2) +4, distribute multiplication over subtraction and addition

5a -5 -15 = 3a +6 + 4, isolate the variable on one side

5a -3a = 6 +4 +5 +15, combine like terms

2a = 30, divide both sides by 2

a= 15

Answer:

[tex]5.06 x 10^{-3}[/tex]

Step-by-step explanation:

Move decimal 3 place to right.

Because the decimal was moved to right, the exponent is negative.