Help me solve this!!!

Answer:

The percentile that corresponds to an IQ score of 115 is 34.13 %

Step-by-step explanation:

Here, we want to find the percentile that corresponds to an IQ score of 115.

To calculate this percentile, we start with making observations. From the question, we are told that the mean score is 100 while the standard deviation is 15.

Now we want to find the percentile for a score if 115. For a score of 115, we can see that the difference between this score and the mean is 15 which is exactly equal to the standard deviation.

What this means is that the score is within +1 SD of the mean.

For a score of within +1 SD of the mean, the percentile is 34.13%

A score at the mean is the 50th percentile, a score which is 1 SD above or below the mean has a percentile value of 34.13%

Please, I will like you to check the attachment to see how percentiles are valued given the number of standard deviations a particular value is from the mean.

Answer:

x = 21.2 ft

Step-by-step explanation:

x = tanФ h

h = 50

Ф = 23°

x = tan(23°) * 50

x = 21.2 ft

Answer:

Step-by-step explanation:

Let the equation of a polynomial is,

[tex]y=(x-a)^2(x-b)^1(x-c)^3[/tex]

Zeroes of this polynomial are x = a, b and c.

For the root x = a, multiplicity of the root 'a' is 2 [given as the power of (x - a)]

Similarly, multiplicity of the roots b and c are 1 and 3.

Effect of multiplicity on the graph,

If the multiplicity of a root is even then the graph will touch the x-axis and if it is odd, graph will cross the x-axis.

Therefore, graph will cross x -axis at x = b and c while it will touch the x-axis for x = a.

In this question,

The given polynomial is,

[tex]y=(x-1)^3(x-2)^1(x-4)^1(x-6)^4[/tex]

Degree of the polynomial = 3 + 1 + 1 + 4 = 9

The graph of the function will cross through the x-axis at x = 1, 2, 4 only, The graph will touch to the x-axis at 6 only.

At the zero of 2 , the graph of the function will CROSS the x-axis.

The sequence is arithmetic, since the forward difference between consecutive terms is -9.

7 - 16 = -9

-2 - 7 = -9

etc.

This means the sequence has the formula

[tex]a_n=16-9(n-1)=25-9n[/tex]

The sum of the first 30 terms is

[tex]\displaystyle\sum_{n=1}^{30}a_n=25\sum_{n=1}^{30}1-9\sum_{n=1}^{30}n[/tex]

Recall the formulas,

[tex]\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n[/tex]

[tex]\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2[/tex]

Then the sum we want is

[tex]\displaystyle\sum_{n=1}^{30}a_n=25\cdot30-\frac{9\cdot30\cdot31}2=\boxed{-3435}[/tex]

Answer:

The 95% confidence interval for the proportion opposing health care changes is (0.6082, 0.6918).

Step-by-step explanation:

The (1 - α)% confidence interval for the population proportion is:

[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

The information provided is:

[tex]\hat p=0.65\\n=500\\\text{Confidence level}=95\%[/tex]

The critical value of z for 95% confidence level is:

[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]

*Use a z-table.

Compute the 95% confidence interval for the proportion opposing health care changes as follows:

[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

     [tex]=0.65\pm 1.96\sqrt{\frac{0.65(1-0.65)}{500}}\\\\=0.65\pm 0.04181\\\\=(0.60819, 0.69181)\\\\\approx (0.6082, 0.6918)[/tex]

Thus, the 95% confidence interval for the proportion opposing health care changes is (0.6082, 0.6918).

Answer:

Step-by-step explanation:

f(x) = (x+1)³ + 4

To find f-¹(x) equate f(x) to y

That's

y = (x+1)³ + 4

Next interchange the terms x becomes y and y becomes x

That's

x = ( y+1)³ + 4

Make y the subject

(y+1)³ = x - 4

Find the cube root of both sides

That's

[tex]y + 1 = \sqrt[3]{x - 4} [/tex]

Send 1 to the right side of the equation

That's

[tex]y = \sqrt[3]{x - 4} - 1[/tex]

So we have the final answer as

[tex]f ^{ - 1} (x) = \sqrt[3]{x - 4} - 1[/tex]

Hope this helps you

Answer:

option 1

Step-by-step explanation:

f(x)=(x+1)³+4

to find the inverse interchange the variable and solve for y

inverse f(x)=(y+1)³+4

x=(y+1)³+4

x-4=(y+1)³

y+1=∛x-4

y=∛x-4 -1

Answer:

X+9=24

Or,x=24-9

:.x=15

Step-by-step explanation:

Answer:

B. x=15

Step-by-step explanation:

To find the solution to the equation, we must get x by itself on one side of the equation.

[tex]x+9=24[/tex]

9 is being added to x. The inverse of addition is subtraction. Subtract 9 from both sides of the equation.

[tex]x+9-9=24-9[/tex]

[tex]x=24-9[/tex]

[tex]x=15[/tex]

Let's check our solution. Plug 15 in for x.

[tex]x+9=24 (x=15)[/tex]

[tex]15+9=24[/tex]

[tex]24=24[/tex]

This checks out, so we know our solution is correct. The answer is B. x=15

Answer: 36 shingles can be placed on the north part of the house.

Step-by-step explanation:

Given: Length of each shingle = [tex]1\dfrac23[/tex] feet = [tex]\dfrac53[/tex] feet.

The north part of the house has a roof line that is 60 feet across.

Then, the number of  shingles can be placed  on the north part of the house = (Length of roof line in north part) ÷ (Length of each shingle)

[tex]=60\div \dfrac{5}{3}\\\\=60\times\dfrac{3}{5}\\\\=12\times3=36[/tex]

Hence, 36 shingles can be placed on the north part of the house.

Hey there! I'm happy to help!

To find the volume of a cube, you simply cube the side length (multiply it by itself three times). This is because all of the sides of a cube are the same and if you multiply the length by the width by the height it is the same number multiplied by itself three times.

We already know that the volume is 91.125 cubic inches. To find the side length, we simply do the cube root on our calculator, which tells us what number we cube to get 91.125.

∛91.125=4.5

Therefore, the side length of the sandbox is 4.5 inches.

I hope that this helps! Have a wonderful day! :D

Answer:

  28) -1

  29) 9

  30) x^2+4x+7

  31) x-2

Step-by-step explanation:

Given:

  f(x) = x + 2

  g(x) = x^2 +3

Find:

  28) f(-3)

  29) f(g(2))

  30) g(f(x))

  31) f-1(x)

Solution:

Put the function argument values into the expression and do the arithmetic.

28) f(-3) = (-3) +2 = -1

__

29) f(g(2)) = f((2)^2 +3) = f(7) = (7) +2 = 9

__

30) g(f(x)) = g(x+2) = (x+2)^2 +3 = x^2 +4x +7

__

31) The meaning of y = f^-1(x) is x = f(y).

  x = f(y) = y+2

  y = x -2

  f^-1(x) = x -2

Answer:

1.5 hours

Step-by-step explanation:

Set up a proportion:

[tex]\frac{40 miles}{1 hour}[/tex] = [tex]\frac{60 miles}{x}[/tex]

Cross multiply:

40x = 60

x = 1.5

= 1.5 hours

Answer:

248.26 cm²

Step-by-step explanation:

Surface area of the composite figure = (surface area of cuboid + surface area of hemisphere) - 2(base area of hemisphere)

Surface area of cuboid = [tex] 2(lw + lh + hw) [/tex]

Where,

l = 10 cm

w = 5 cm

h = 4 cm

Plug in the values into the formula:

[tex] SA = 2(10*5 + 10*4 + 4*5) [/tex]

[tex] SA = 2(50 + 40 + 20) [/tex]

[tex] SA = 2(110) = 220 cm^2 [/tex]

Surface area of hemisphere = 3πr²

Where,

π = 3.14

r = 3 cm

SA of hemisphere = 3*3.14*3² = 3*3.14*9 = 84.78 cm²

Base area of hemisphere = πr²

BA = 3.14*3² = 3.14*9 = 28.26 cm²

Surface area of the composite shape = (220 + 84.78) - 2(28.26)

= 304.78 - 56.52

SA = 248.26 cm²

x=2.86

Step-by-step explanation:

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

[tex] {24}^{2} + {32}^{2} = 40[/tex]

[tex]c = 40[/tex]

[tex]6x + 6 + 9x - 9 = 40[/tex]

[tex](6x + 9x) + (6 - 9) = 40[/tex]

[tex]15x - 3 = 40[/tex]

[tex]15x = 43[/tex]

[tex]x = 2.866[/tex]

[tex]23.16 + 16.74 = 39.9[/tex]

the

[tex]6(2.86) + 6 = 23.16[/tex]

[tex]9(2.86) - 9 = 16.74[/tex]

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

Explanation:

When we reflect any point (x,y) over the line y = x, the x and y coordinates swap. So for instance, we have K = (5, -9) turn into K ' = (-9, 5).

Consider a point like (1,2). We can move it down 1 unit to have it land on the line y = x, then we can move it one unit to the right to move it to (2,1). These two translations effectively move the original point to its reflected location. The distance from (1,2) to y = x, is the same as the distance from (2,1) to y = x. Furthermore, the line connecting (1,2) to (2,1) is perpendicular to y = x.

Answer and Step-by-step explanation:

The computation of points on the ellipse is shown below:-

Distance between any point on the ellipse

[tex](3 cos t, sin t) and (\frac{4}{3},0) is\\\\ d = \sqrt{(3 cos\ t - \frac{4}{3}^2) } + (sin\ t - 0)^2\\\\ d^2 = (3 cos\ t - \frac{4}{3})^2 + sin^2 t[/tex]

To minimize

[tex]d^2, set\ f' (t) = 0\\\\2(3cos\ t - \frac{x=4}{3} ).3(-sin\ t) + 2sin\ t\ cos\ t = 0\\\\ 8 sin\ t - 16 sin\ t\ cos\ t = 0\\\\ 8 sin\ t (1 - 2 cos\ t) = 0\\\\ sin\ t = 0, cos\ t = \frac{1}{2} \\\\ t= 0, \ 0, \pi,2\pi,\frac{\pi}{3} , \frac{5\pi}{3}[/tex]

Now we create a table by applying the critical points which are shown below:

t            [tex]d^{2} = (3\ cos t - \frac{4}{3})^{2} + sin^{2}t[/tex]

0           [tex]\frac{25}{9}[/tex]

[tex]\pi[/tex]           [tex]\frac{169}{9}[/tex]

[tex]2\pi[/tex]         [tex]\frac{25}{9}[/tex]

[tex]\frac{\pi}{3}[/tex]          [tex]\frac{7}{9}[/tex]

[tex]\frac{5\pi}{3}[/tex]         [tex]\frac{7}{9}[/tex]

When t = [tex]\frac{\pi}{3}[/tex], x is [tex]\frac{3}{2}[/tex] and y is [tex]\frac{\sqrt{3} }{2}[/tex]. So, the required points are [tex](\frac{3}{2},\frac{\sqrt{3} }{2})[/tex]

When t = [tex]\frac{5\pi}{3}[/tex], x is [tex]\frac{3}{2}[/tex] and y is [tex]\frac{-\sqrt{3} }{2}[/tex]. So, the required points are [tex](\frac{3}{2},\frac{-\sqrt{3} }{2})[/tex]

Answer:

340 feet

Step-by-step explanation:

we use Pythagora

d² = l² + w²

d = √300ft)² + 160ft)²

= √90000ft² + 25600ft²

= √115600ft²

= √(2⁴ₓ5²ₓ17²)ft²

= √(2²ₓ5ₓ17)ftₓ(2²ₓ5ₓ17)ft

= √340ftₓ340ft

= 340 feet

Answer:

x³ - 5x² - x + 5

Step-by-step explanation:

(x+1)(x-1)(x-5) = 0

fisrt step:

(x+1)(x-1) = x*x + x*-1 + 1*x + 1*-1 = x² - x + x - 1 = x² - 1

then:

(x+1)(x-1)(x-5) = (x²-1)(x-5)

(x²-1)(x-5) = x²*x + x²*-5 -1*x -1*-5 = x³ - 5x² - x + 5

Answer:

2hrs 24mins

Step-by-step explanation:

Very simple the time they will meet again at the point will be the LCM of their various time taken to complete a cycle.

Ans LCM(24, 36, 48) = 144 mins

= 2hrs 24mins

Answer:

The answer is 2 hours and 24 minutes

Step-by-step explanation:

Hope you get this right:)

Answer:

16x^2 - 64

Step-by-step explanation:

(4x − 8)(4x + 8)

We recognize that this is the difference of squares

(a-b) (a+b) = a^2 - b^2

                 =(4x)^2 - 8^2

                 =16x^2 - 64

Answer:

(3,-1)

Step-by-step explanation:

Graph boths functions (picture below)

Answer:

It rotated 180 degrees

Step-by-step explanation:

If you use this image and paste in on to google docs you will be able to rotate the image. Use this tool so that your can identify the amount of degrees.

If the Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin, (0,0) then the angle of rotation is option (c) 180 degrees

In geometry a quadrilateral is a four-sided polygon, having four edges and four corners

The angle of rotation is a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle.

Given,

Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin, (0,0)

Consider the coordinates of D and D'

D(2,3) and D'(-2,-3)

Connect D and D'

∠D0D' = 180 Degrees

Hence, If the Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin, (0,0) then the angle of rotation is option (c) 180 degrees

Learn more about Quadrilateral and Angle of rotation here

https://brainly.com/question/17106452

#SPJ2

Answer:

432 mm³

Step-by-step explanation:

Volume of a Rectangular Prism: V = lwh

Step 1: Define variables

l = 8

w = 6

h = 9

Step 2: Plug into formula

V = 8(6)(9)

Step 3: Evaluate

V = 48(9)

V = 432

And we have our answer!

Answer:

B. ∠A, ∠B, ∠C

Step-by-step explanation:

1. Draw a model with AB as the shortest line and BC as the longest line.

∠A connects the two shortest lines, making it the largest angle.

∠B connects the shortest and the longest lines, making it the second largest angle.

∠C connects the two longest lines, making it the smallest angle.

Answer:

A > B > C

Step-by-step explanation:

Ypu probably wouldn't think about it unless someone pointed it out, but if you look at a triangle of any type you can see that the sizes of the sides are directly related to the sizes of the angles opposed to them.

By this I mean, the largest side will have the largest angle across from it and the smallest side will have the smallest angle.

Based off of my drawing, it looks like the order is angle A, then B, then, and then C.

Answer:

The side opposite <Q is RS

The hypothenuse is QR

The side adjacent to <Q is QS

Step-by-step explanation:

Side RS is directly opposite <Q. The first statement provided in the options is correct.

The side that is opposite to <R is QS. The second statement in the options is not correct.

The longer leg of a right triangle is always the hypotenuse. Side QR in ∆QRS is the hypotenuse. The third statement given in the options is correct.

The side adjacent to <R is not SQ. RS is the side adjacent to <R. The fourth statement in the given options is not correct.

Side QS is adjacent to <Q. The fifth option is correct.

Answer:

A, C, E

Step-by-step explanation:

on edge! hope this helps!!~ （‐＾▽＾‐）

Answer:

9 + 18 = 27

27 + n + 1

= n = 27 - 1 = 26.

n = 26

9 + 18 + 26 + n + 7 =

53 + n + 7

53 + 7 + n

60 + n = 360

n = 360 - 60 = 300

so, n 300

so = 9, 18, 300, 26

Answer:

[tex]\boxed{\sf \bf \ \ -2i(6-7i)=-14-12i \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

[tex]-2i(6-7i)=-12i+14i^2=-14-12i[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

A

Step-by-step explanation:

Answer = A

Answer:

The survey result doesn't indicate the change

Step-by-step explanation:

Previous study result is 50%

Survey result:

Comparing with previous result:

Since this result is within 5% level of significance, it can be concluded that the survey result doesn't indicate the change

Answer:

federal loans = $29,000

private loans = $14,000

Step-by-step explanation:

x + y = 43000

.045x + .02y = 1585

x = 29,000

y = 14,000

Answer:

Amount of loan from federal : $ 29,000

Amount of loan from private bank : $ 14,000

Step-by-step explanation:

We know that Linda owes $43,000 in student loans. It is also given that the interest rate on the federal loans is 4.5%, while the interest rate on private loans is 2%, the total interest for a year being $1,585.

If Linda were to say own x dollars in federal loans, and y dollars in private loans, we know that she owns a total of $43,000, so -

x + y = 43,000

At the same time the loan interest amount is $1,585, while the interest rate on the federal loans is 4.5%, and the interest rate on private loans is 2%. The loans from each account will add to $1,585 -

0.045x + 0.02y = 1585

Let's solve the following system for x and y, the amount of each loan,

[tex]\begin{bmatrix}x+y=43000\\ 0.045x+0.02y=1585\end{bmatrix}[/tex] ( Substitute x = 43000 - y )

[tex]0.045\left(43000-y\right)+0.02y=1585[/tex] ( Simplify )

[tex]1935-0.025y=1585[/tex],

[tex]1935000-25y=1585000[/tex],

[tex]-25y=-350000[/tex],

[tex]y=14000[/tex],

[tex]x=29000[/tex]

Thus, the amount of loan from federal is $ 29,000 and the amount of loan from private bank is $ 14,000.

Answer:

the process of combining things in a particular order, or discovering the order in which they are combined: A common sign of dyslexia is that the sequencing of letters when spelling words may be incorrect. biology specialized.

Step-by-step explanation: