Suppose 140 geology students measure the mass of an ore sample. Due to human error and limitations in the reliability of theâ balance, not all the readings are equal. The results are found to closely approximate a normalâ curve, with mean 82 g and standard deviation 3 g. Use the symmetry of the normal curve and the empirical rule as needed to estimate the number of students reporting readings between 79 g and 85 g

Answer:

Step-by-step explanation:

Use tigonometry to find the value of d

Answer:

497 m (nearest whole number)

Step-by-step explanation:

As the problem has been modeled as a right triangle, we can use the sine trigonometric ratio to find the distance d.

Sine trigonometric ratio

   [tex]\sf \sin(\theta)=\dfrac{O}{H}[/tex]

where:

From inspection of the given diagram:

Substitute the values into the formula and solve for d:

[tex]\implies \sf \sin(38^{\circ})=\dfrac{306}{H}[/tex]

[tex]\implies \sf H=\dfrac{306}{\sin(38^{\circ})}[/tex]

[tex]\implies \sf H=497.0263891...[/tex]

Therefore, the distance d between the helicopter and the landing pad is 497 m (nearest whole number).

I have no idea thank me for my help

Answer:

5.291 x 10⁶

Step-by-step explanation:

Why is 5,291,000 written as 5.291 x 106 in scientific notation?

The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.

Calculating scientific notation for a positive integer is simple, as it always follows this notation:

a x 10b

Follow the steps below to see how 5,291,000 is written in scientific notation.

Step 1

To find a, take the number and move a decimal place to the right one position.

Original Number: 5,291,000

New Number: 5.291000

Step 2

Now, to find b, count how many places to the right of the decimal.

New Number: 5 . 2 9 1 0 0 0

Decimal Count: 1 2 3 4 5 6

There are 6 places to the right of the decimal place.

Step 3

Building upon what we know above, we can now reconstruct the number into scientific notation.

Remember, the notation is: a x 10b

a = 5.291 (Please notice any zeroes on the end have been removed)

b = 6

Now the whole thing:

5.291 x 10⁶

Step 4

Check your work:

10⁶ = 1,000,000 x 5.291 = 5,291,000

Answer:

b. translation; four units left and six units down

Answer:

Option D

Step-by-step explanation:

Given equation:

This equation can be solved by:

Subtracting 2 both sides of the equation (according to step 1):

Dividing -4 to both sides of the equation (according to step 2):

Therefore, Option D is correct.

Learn more about this topic: https://brainly.com/question/27460957

Answer:

d) 4

Step-by-step explanation:

Solving for the value of x,

→ -4x + 2 = -14

→ -4x = -14 - 2

→ -4x = -16

→ x = -16/-4

→ [ x = 4 ] {option d}

Verification of the value of x,

→ -4x + 2 = -14

→ -4(4) + 2 = -14

→ -16 + 2 = -14

→ -14 = -14

→ [ LHS = RHS ]

Hence, the value of x is 4.

Answer:

1

log 10

Step-by-step explanation:

In e = 1

In e = log 10

Hope it helps you in your learning process.

Answer: D. 94.25 in²

Step-by-step explanation:

To find the total area, we will break the shape up into two different parts.

[] The rounded part is 39.25 in². Let us assume the rounded part is exactly half of a circle.

      Area of a circle:

A = πr²

      Use 3.14 for pi:

A = (3.14)r²

      Find the radius:

d / 2 = r, 10 / 2 = 5 in

      Subsittue:

A = (3.14)(5)²

A = 78.5 in²

      Divide by 2 since it is only half:

78.5 in² / 2 = 39.25 in²

[] The triangle is 55 in².

      Area of a triangle:

A = b*h/2

A = 11 * 10 / 2

A = 110 / 2

A = 55 in²

[] Total area. We will add the two parts together.

55 in² + 39.25 in² = 94.25 in²

Answer:

D. 94.25

Step-by-step explanation:

Hey there! In order to answer this question: you need to take the area of the triangle and the area of half of a circle

The formula for the area of a triangle is: base x height x 1/2

11 x 10 x 1/2 = 55

To find the area of a circle, you have to take the radius, square it, and multiply it by 3.14

So the radius is 5 since 10 is the diameter of the circle

Now we have to square that which is 25

Multiply 25 by 3.14 which is 78.5

Now since we are dealing with a half circle and the area for the whole circle is 78.5, we divide 78.5 by 2 which is 39.25

Now you have to add those two areas and that will get your final answer

55+39.25 is 94.25

So the area for this figure is 94.25 square inches

Answer:

Not true.

Step-by-step explanation:

A  rational function is like P(x) / Q(x) where P and Q are polynomials.

Examples would be x^2 / (x^2 - 2)  and  x^2 / (x^2 + 2).

Now the first one will have a vertical asymptote at x = √2 because this value would make the denominator zero.

The second one will have no asymptotes because the only value that would make x^2 + 2 = zero is not real (it would be √2i). So the domain of this  is all real numbers ,  and  no asymptotes.

Part A

[tex]\sf{ change \ of \ base \sf \ : \ \ \ \log _{b} a=\dfrac{\log _{d} a}{\log _{d} b}}[/tex]

Part B

Some common choices for base:

Part C

[tex]\longrightarrow\ \sf \log _{2} 3=\dfrac{\log _{3} 3}{\log _{3} 2}}[/tex]

[tex]\longrightarrow\ \sf \log _{2} 3=\dfrac{1}{0.631}}[/tex]

[tex]\longrightarrow\ \sf \log _{2} 3=\dfrac{1}{0.630929}}[/tex]

[tex]\longrightarrow\ \sf \log _{2} 3=1.584962501[/tex]

[tex]\longrightarrow\ \sf \log _{2} 3 = 1.58[/tex]

1.58 is the value when rounded to nearest hundredth.

Answer:

it should be over 8 inches long

Step-by-step explanation:

by the instructions

a side of a triangle is 8 inches and other one is 4 inches

and the OPPOSITE of OBTUSE angle is the 3 Rd one

As the Third side which connect the 1st and 2nd side ( of the obtuse angle) it should be over 8 inches.

Answer:

Step-by-step explanation:

Givens

These are the givens for the second line. The second line also has m (same value) as the x coordinate of one of the points. I'm not sure why you are given the first line.

x1  = - 1

x2 = m

y1 = - 2

y2 = 10

Second line formula for m

m = (y2 - y1) / (x2 - x1)            Substitute values for this equation

Solution

Note that the m you seek is both the slope of the second line, and the x  coordinate of one of the points.

m = (10 -  - 2) / (m - - 1)           Change the double minus, and combine

m = 12 / (m + 1)                       Multiply both sides by (m + 1)

m(m+1) = 12                             Remove the brackets

m^2 + m = 12                          Subtract 12 from both sides.

m^2 + m - 12 = 0                    Factor

(m + 4)(m - 3) = 0

We are told that m >0

So m- 3 = 0

m = 3

Answer

The value for m = 3. The first line also has a slope of 3

35% are in display cases which means 65% are on the wall.

this means 195 cars is 65% of the collection.

to get total number of cars in the collection divide 195 by 65%

195/0.65 = 300

answer: 300 total cars

Answer:

C

Step-by-step explanation:

Find area of all trinagles and subtract that by total area of square.

Answer:

24 days

Step-by-step explanation:

lowest common multiple of 12 and 8 is

24

For them to exercise together again, the day must be a common multiplier of 12 and 8

12 = [tex]2^{2} . 3[/tex]
8 = [tex]2^{3}[/tex]

So, their LCM is [tex]2^{3} .3 = 24[/tex]

=> After 24 days, they will exercise together again.

Answer:

219.8 yd

Step-by-step explanation:

Circumference Formula= πd or 2πr

Plug in the values. The diameter of this circle is 70 yds.

70(3.14) (replace 3.14 for π)

70*3.14=219.8 yds

Hope this helps ^^

find the sum of all the values and divide the sum by the number of values.

[tex] \frac{(61 + 98 + 60 + 60 + 57 + 81 + 93)}{7} = \frac{510}{7} [/tex]

[tex] = 72.86[/tex]

arrange the values in either ascending or descending, and find the number in the middle.

[tex]57 \: 60 \: 60 \: 61 \: 81 \: 93 \: 98[/tex]

[tex] = 61[/tex]

the most frequently occurred number.

[tex] = 60[/tex]

arrange the values in ascending order and subtract the lowest value from the highest one.

[tex]98 - 57[/tex]

[tex] = 41[/tex]

Answer:

x = 7

Step-by-step explanation:

the given angles are vertically opposite and are congruent , then

4x - 5 = x + 16 ( subtract x from both sides )

3x - 5 = 16 ( add 5 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Answer:

(2, 4)

Step-by-step explanation:

A reflection across the y-axis, will simply change the sign of your x-coordinate to positive rather than negative, this gives you a new point (2,4).

Answer:

c. X^2 - 4

Step-by-step explanation:

Replace X with Y

X = Sqrt(Y+4)

square both sides to solve for Y

X^2 = Y+4

subtract 4 from both sides

X^2 - 4 = Y

answer option C is correct

Answer:

49(1) - 2 =

49x1=49

49 - 2 = 47 is your answer

Answer:

47

__________________________________________________________

If the variable, x has an assigned value, you must multiply the number behind x by the assigned value.

[tex]49 * 1 = 49[/tex]

Lastly, subtract by 2

[tex]49 - 2 = 47[/tex]

________________________________________________________

Ask me in the comments box.

Answer:

Trapezoid

Explanation:

A trapezoid does not have two pairs of parallel sides.

Answer: D. Trapezoid

Step-by-step explanation:

Answer:

(-5, - 10 )

Step-by-step explanation:

y = - 6 is a horizontal line parallel to the x- axis passing through all points with a y- coordinate of - 6

under a reflection in this line the x- coordinate of the point V is the same

V (- 5, - 2 ) with y- coordinate - 2 is 4 units above y = - 6

the reflected point will therefore be 4 units below y = - 6, that is - 10 , then

V (- 5, - 2 ) → V' (- 5, - 10 )

Answer:

l = 6[tex]a^{4}[/tex] + 2a - 1

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = lw ( l is the length and w the width )

given A = 18[tex]a^{5}[/tex] + 6a² - 3a and w = 3a , then

3aw = 18[tex]a^{5}[/tex] + 6a² - 3a ( divide each term by 3a )

w = [tex]\frac{18a^{5} }{3a}[/tex] + [tex]\frac{6a^2}{3a}[/tex] - [tex]\frac{3a}{3a}[/tex] = 6[tex]a^{4}[/tex] + 2a - 1

Answer:

heya! ^^

here , we've been given a right angled triangle along with the measure of two of its sides.

and , we've to find the measure of its third side.

so , we'll be using Pythagoras Theorem to find the measure of the third side.

but first , let's take a look at what Pythagoras Theorem is-

Pythagoras theorem states that the square of the hypotenuse of the triangle is equal to the sum of squares of the remaining two sides.

according to the figure ,

side AB = hypotenuse = 60 cm

side AC = perpendicular = 48 cm

side BC = base = a

now by using Pythagoras Theorem ,

[tex]H {}^{2} = P {}^{2} + B {}^{2} \\ \\ (60) {}^{2} = (48) {}^{2} + a {}^{2} \\ \\ 3600 = 2304 + a {}^{2} \\ \\ a {}^{2} = 1296 \\ \\ a = \sqrt{1296} \\ \\ a = 36[/tex]

therefore ,

option ( 4 ) 36 is correct.

hope helpful :D

Answer:

[tex] \\ [/tex]

Step-by-step explanation:

Here, A right angled triangle is given with the measure of two sides and we are to find the measure of the third side.

We'll find the measure of third side with the help of the Pythagorean theorem,

[tex] \\ {\longrightarrow \pmb{\sf {\qquad (Base) {}^{2} + (Perpendicular {)}^{2} = (Hypotenuse {)}^{2} }}} \\ \\[/tex]

Here,

[tex] \\ [/tex]

So, substituting the values in the formula we get :

[tex]\\ {\longrightarrow \pmb{\sf {\qquad (a) {}^{2} + (48 {)}^{2} = ( 60{)}^{2} }}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad (a) {}^{2} = ( 60{)}^{2} - (48 {)}^{2}}}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad (a) {}^{2} =3600 - 2304}}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad (a) {}^{2} =1296}}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad a = \sqrt{1296}}}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\frak {\qquad a = 36 }}} \\ \\[/tex]

Therefore,

4 hours

T= d/s

= 2720/680

= 4

Hope this helps!

Answer:

the top one on the right

Step-by-step explanation:

i used desmos graphing calculator