Martina read that the average graduate student is 33 years old. She wanted to estimate the mean age of graduate students at her large university, so she took a random sample of 30 graduate students. What is Martina's margin of error?

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Explanation:

Every point on the line y = 7 has a y coordinate of 7. Two such points are (0,7) and (1,7). The x coordinate can be anything you want. This line is completely horizontal and parallel to the x axis.

We can think of y = 7 as y = 0x+7. It's of the form y = mx+b with m = 0 as the slope and b = 7 as the y intercept.

-pi/4 is the same thing as 7pi/4.

The sine function will get us the y-value we need.

Keep in mind that our y-value will be negative (based on the position of the line), and pi/4 and 3pi/4 will both have positive y-values.

Therefore, the correct expression is sin(7pi/4).

Hope this helps!! :)

Answer:

2.24

Step-by-step explanation:

the total surface area=

(3+10+5+10+6)×(20) + (2×3×24) + (2×½×(14+10)×3)

= 680 + 144 + 72

= 896 ft²

the paint will be needed at least :

896/400 × 1 gallon = 2.24 gallons

Answer:

x+8

Step-by-step explanation:

Simplify the numerator

list the factors of 16

16: 1, 2, 4, 8, 16

look for two factors that add up to the b value

in this case it is 18

by looking at the factors 2 and 8 add up 10

so you can rewrite the numerator as [tex]x^{2}+2x+8x+16[/tex]

Split the trinomial into two separate binomials each having one of the factors that add up to 10

So it should be [tex]x^{2} +2x and 8x+16[/tex]

Factor both binomials

you can factor an x from the first one

Then it is x(x+2)

Factor an 8 from the second one

8(x+2)

So it should be [tex]x(x+2) 8(x+2)[/tex]

This can rewritten as (x+8)(x+2)

So now you have [tex]\frac{(x+2)(x+8)}{x+2)}[/tex]

simplify it by canceling out the two (x+2)'s

this is because (x+2)/(x+2) is 1

Finally you get x+8

Step-by-step explanation:

-6y + y=-30

-5y = -30

y=6

x=-6 ×6= -36

Answer:

line n

Step-by-step explanation:

Line n goes through points A and G on the diagram.

Answer:

C. 64, 32, 16

Step-by-step explanation:

This geometric sequence is made by dividing the numbers by 2:

512 ÷ 2 = 256

256 ÷ 2 = 128

Hence, the next term will be

128 ÷ 2 = 64

64 ÷ 2 = 32

32 ÷ 2 = 16

Therefore, the correct answer is C.

The next 3 terms in the given geometric sequence are 64, 32, and 16, respectively. The correct option is C.

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.

The given series is a geometric sequence, therefore, the common ratio between any two terms will be the same. Therefore, we can write, the ratio as,

Common ratio, r = a₂ / a₁ = 256 / 512 = 1/2

Now, the nth term of the given sequence can be defined as,

aₙ = a₁ × r⁽ⁿ⁻¹⁾

   = 512 × (1/2)⁽ⁿ⁻¹⁾

Therefore, the next term of the given geometric progression will be,

a₄ = 512 × (1/2)³ = 64

a₅ = 512 × (1/2)⁴ = 32

a⁶ = 512 × (1/2)⁵ = 16

Hence, the next 3 terms in the given geometric sequence are 64, 32, and 16, respectively.

Learn more about Geometrical Series here:

https://brainly.com/question/4617980

#SPJ2

Answer:  A, 4^4

Step-by-step explanation:

4^7/4^3 = 4^4

Answer:

[tex]4^{4}[/tex]

Step-by-step explanation:

Rewrite the division as a fraction.

[tex]\frac{4^{7} }{4^{3} }[/tex]

Cancel the common factors.

[tex]\frac{4^{3}*4^{4} }{4^{3}*1 }[/tex]

[tex]4^{4}[/tex]

Hope this helps!

Reach out to me if you need more help with these types of problems.

Answer:

q = 55

Step-by-step explanation:

      [tex]p\ \alpha\ \frac{1}q} \\\\p = k \times \frac{1}{q}\\\\22 = k \times \frac{1}{5}\\\\22 \times 5 = k\\\\k = 110\\\\[/tex]

Find q when p = 2

   [tex]p = k \times \frac{1}{q}\\\\2 = 110 \times \frac{1}{q}\\\\2 \times q = 110\\\\q = \frac{110}{2}\\\\q = 55[/tex]

Answer:

x = + 5/4 or x = - 5/4

Step-by-step explanation:

[tex]4 x^2 = 6\frac{1}{4}\\\\4 x^2 = \frac{25}{4}\\\\x^2 =\frac{25}{16}\\\\x = \pm \frac{5}{4}[/tex]

Answer:

C: tan 60 = √3

Step-by-step explanation:

Let the adjacent part of the triangle be x and let the opposite side be y.

Thus, from trigonometric ratios;

x/10 = cos 60

We are given cos 60 = ½

Thus;

x/10 = ½

x = ½ × 10

x = 5

Similarly;

y/10 = sin 60

Now,from trigonometric relationship we know that; sin 60 = cos 30. Thus;

y/10 = cos 30

We are given cos 30 = (√3)/2

Thus;

y/10 = (√3)/2

y = 10 × (√3)/2

y = 5√3

Since it is a right angle triangle with one angle being 60°, it means the other one is 30° since sum of angles in a triangle is 180°.

Thus;

5/(5√3) = tan 30°

1/√3 = tan 30

Similarly;

5/10 = sin 60°

sin 60° = ½

Also;

tan 60 = (5√3)/5

tan 60 = √3

Also;

sin 30 = 5/10

sin 30 = ½

Looking at the options, the only correct one is Option C

Answer:

D

Step-by-step explanation:

We are given:

[tex]\displaystyle \sqrt{\sqrt[3]{2}}[/tex]

Recall the property:

[tex]\displaystyle \sqrt[b]{x}=x^{1/b}[/tex]

Hence:

[tex]\displaystyle \sqrt{\sqrt[3]{2}}=\sqrt{2^{1/3}}[/tex]

Using the same property:

[tex]\sqrt{2^{1/3}}=(2^{1/3})^{1/2}[/tex]

Recall the property:

[tex](x^a)^b=x^{ab}[/tex]

Hence, multiply:

[tex](2^{1/3})^{1/2}=2^{1/6}[/tex]

Therefore:

[tex]\displaystyle \sqrt{\sqrt[3]{2}}=2^{1/6}[/tex]

Our answer is D.

Answer:

The answer is [tex]2^{\frac{1}{6} }[/tex].

Step-by-step explanation:

To find which answer is equal to [tex]\sqrt{} \sqrt[3]{2}[/tex], start by simplifying [tex]\sqrt{} \sqrt[3]{2}[/tex]. The radical will simplify to [tex]\sqrt[6]{2}[/tex].

An easy way to determine which answer is correct, convert each of the numbers to decimal form.

For [tex]\sqrt[6]{2}[/tex], it will look like 1.122 in decimal form.

For [tex]2^{\frac{2}{3} }[/tex], it will look like 1.587 in decimal form.

For [tex]2^{\frac{3}{2} }[/tex], it will look like 2.828 in decimal form.

For [tex]2^{\frac{1}{3} }[/tex], it will look like 1.260 in decimal form.

For [tex]2^{\frac{1}{6} }[/tex], it will look like 1.122 in decimal form.

Then, by seeing which two decimal forms are the same, it causes the answer to be [tex]2^{\frac{1}{6} }[/tex].

Answer:

I think its c

Step-by-step explanation:

Answer:

x = 32 and BEC = 43

Step-by-step explanation:

3X + 41 = 137

3X = 96

X = 32

FOR BEC:

137 + 137 = 274

360-274=86 ( ANGLES AROUND A POINT ADD UP TO 360)

86/2 = 43

BEC/AED = 43 ( VERTICALLY OPPOSITE ANGLES ARE EQUAL)

hope this helps good luck!

Answer and Step-by-step explanation:

All triangles have a sum of their angles to be 180 degrees. So, to find x, we need to subtract the two given sides from 180 degrees.

180 - 38 - 83 = 59

x = 59 degrees.

#teamtrees #PAW (Plant And Water)

Answer:

Giá một cuốn sách là $ 1000

Step-by-step explanation:

Được

Tổng chi phí sách = 60000

Tổng số bạn bè = 10

Sách do mỗi người bạn mua = 2

Như vậy, tổng số sách mua của cả 10 bạn = 10 * 2 = 20

Giá của một cuốn sách = Tổng giá / tổng số sách đã mua

Giá một cuốn sách = 20000/20 = 1000

Giá một cuốn sách là $ 1000

Answer:

[tex]y=1[/tex]

Step-by-step explanation:

Given:

[tex]6=2(y+2)[/tex]

Distribute the parenthesis

[tex]6=2y+4[/tex]

Subtract both sides by 4

[tex]2=2y[/tex]

Divide both sides by 2 to get [tex]y[/tex] alone

[tex]1=y[/tex]

Hope this is helpful

Answer: 20 nickels to make $2.00

Step-by-step explanation:

Answer:

5x = 200

x=40

Step-by-step explanation:

53,38

Step-by-step explanation:

x = √15² + 8²

x = √225 + 64

x = √289

x = 17

circle's circumference = π × d

3,14 × 17 = 53,38

Answer:

[tex]{ \tt{slope = \frac{7 - 1}{0 - ( - 2)} = 3 }} \\ \\ { \tt{y = mx + c}} \\ { \boxed{ \bf{y = 3x + 7}}}[/tex]

--Answer--

negative integer

--Explanation--

28 - 45 = -17; the number subtracting is greater than the original number.

Answer:

what are the choices?? if you don't mind me asking

Answer:

42 in binary number is 101010.

Step-by-step explanation:

Answer:

my answer is 660

Step-by-step explanation:

300+250+110=660

√9 is rational and √3 irrational number

Answer: if its decimal and it wants you to round to next place to the tenths place

Step-by-step explanation: if it means to look at the hundredth's place to find your answer  if its bigger than five your second number will add up if its lower than five it stays the same

the value of y is equal negative

Answer:

the second option

yes, because they are similar triangles

Step-by-step explanation:

the scaling factor is 3

3×3 = 9

3×7 = 21

so, the ratios of the sides remain the same, and the 90 degree angle remains the same. therefore, just one triangle is larger than the other, but the relative attributes and even the orientation are the same, so yes, since we don't know the absolute coordinates of the corners, indeed, the Hypotenuse of both triangles could be on the same line.

Answer:

0

9

-2

-23

Step-by-step explanation:

a function f(x) defines a y-value for any valid x-value.

that's why it is often written as y = f(x).

the inverse function of an original function just turns the question upside down.

now we want to see for a given y-value of the original function, what was the original x-value to get this y.

therefore we try to transform the original equation that calculates y out of x into one that calculates x out of y.

so, in our example

f(x) = y = -4x - 3

4x + y = -3

4x = -y - 3

x = (-y - 3) / 4

in order to keep the usual terminology with functions also for inverse functions, which are in the end nothing else than functions again, we then name the input variable "x" again, and the result "y".

so, the inverse function is therefore as a function of x

y = (-x - 3) / 4

for x = -3, y = (--3 - 3) / 4 = (3-3) / 4 = 0

when we have y for the inverse function looking for its corresponding x value, then we are investing the inverse function and come back to the original function.

so, for y=-3 of the inverse function that means x=-3 for the inverse inverse (or original) function looking for the y, which is then the x of the inverse function.

f(-3) = -4×-3 - 3 = 12 - 3 = 9 = x of the inverse function.

for x=5 of the inverse function, y = (-5-3)/4 = -8/4 = -2

for y=5 of the inverse function that means x=5 for the inverse inverse (or original) function looking for the y, which is then the x of the inverse function.

f(5) = -4×5 - 3 = -20 - 3 = -23 = x of the inverse function.

Answer:

11

Step-by-step explanation:

mode is the number that is most frequent

11

Answer:

11

Step-by-step explanation:

Mode means the highest repeated observation in the data set,

Therefore Mode = 11, as 11 has repeated 3 times, the most in the data set