Tom sees an enormous thundercloud approaching
from the west. He sees a lightning flash at the top
of the cloud and hears thunder 15 seconds later. His
angle of sight to the top of the cloud is 65°. How
high is the top of the thundercloud off the ground?
Sound takes 5 seconds to travel 1 mile.

If x is the largest side :

If 4.1 is the greatest side :

Range of possible sizes for side 'x' :

Answer:

The group that is most likely able to have a lower mean age of painting students is Group A

Step-by-step explanation:

mean = sum of all terms divided by total number of terms

Looking at the graph data you have provided you can see that group A's students are a younger than students in Group B.

Which means when you calculate the mean the group which would give you the lower ratio with the same denominator of K (let there is K number of students in the class) will have lower mean age

here group A students are younger therefore their ratio will be lower

hence lower mean age

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Answer:

5

Step-by-step explanation:

median basically means the number which is in the middle so 8,8,9, 5 ,10,4,9

the median is 5 because left and right middle is 5 that's why it is median

All the solution of the equation x³ + 8x² + 100x + 800 = 0 will be 10i, -10i, and -8. Then the correct option is D.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The equation is given below.

          x³ + 8x² + 100x = -800

x³ + 8x² + 100x + 800 = 0

Then the factor of the equation will be

x³ + 8x² + 100x + 800 = 0

x² (x + 8) + 100(x + 8) = 0

        (x² + 100)(x + 8) = 0

Then all the solution of the equation will be

x = 10i, -10i, and -8.

Then the correct option is D.

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Answer:

d

Step-by-step explanation:

Answer:

2.5 gallons of the 20% solution must be replaced by the 36% solution.

Step-by-step explanation:

[tex].12(20 - x) + .36x = 20(.15)[/tex]

[tex]2.4 - .12x + .36x = 3[/tex]

[tex]2.4 - .24x = 3[/tex]

[tex] - .24x = - .6[/tex]

[tex].24x = .6[/tex]

[tex]x = 2.5[/tex]

Answer:

$15,539.67

Step-by-step explanation:

Compound Interest Formula

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

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=11000\left(1+\frac{0.058}{4}\right)^{(4 \times 6)}[/tex]

[tex]\implies \sf A=11000(1.0145)^{24}[/tex]

[tex]\implies \sf A=15539.67451...[/tex]

Therefore, the value of the investment after 6 years will be $15,539.67 to the nearest cent.

Δ DGC is right angled triangle because Line E G is perpendicular-to CC', Option D is the correct answer.

Triangle is a polygon with three sides , angles and vertices.

It is given that the there are two Triangles , ABC and A'B'C' as an image of the ABC

* Line segment AA' has a midpoint at point F

*D is the mid point of the line joining BB' .*

The figure is attached with the answer.

the line of reflection of the object is always perpendicular to the object and the image.

it is also given that CGF is a right angle.

Therefore triangle DGC is right angled triangle , (the option given in the question is incorrect ) ,  Line E G is perpendicular-to CC'.

Option D is the correct answer.

Please Refer to the image for correct coordinates.

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Answer:

it would look like this

Step-by-step explanation:

The conversion to logarithm function will be that log3 27 = 3.

From the information given, we are to convert the exponential equation to logarithm function. This will be:

log 3 27

This will be log 3 3³

= 3 × log 3^3

= 3 × 1

= 3

Therefore, x = 3.

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Placing the equations under the correct solution, we get

x = 3                                      x ≠ 3

-14x = -42                              -5 + x = -9

[tex]-\frac{3}{5} +x = \frac{12}{5}[/tex]                          [tex]\frac{x}{3} =9[/tex]

[tex]\frac{x}{4} =\frac{6}{8}[/tex]                                    

x -5 = -2            

From the question, we are to place the equations under the correct solution

To do this, we will solve the equations one after the other

x = -42/-14

x = 3

x = -9 + 5

x = -4

∴ x ≠ 3

[tex]x = \frac{12}{5} +\frac{3}{5}[/tex]

[tex]x = \frac{12+3}{5}[/tex]

[tex]x = \frac{15}{5}[/tex]

x = 3

[tex]x=\frac{6\times 4}{8}[/tex]

[tex]x=\frac{24}{8}[/tex]

x = 3

x = 3 × 9

x = 27

∴ x ≠ 3

x = -2 + 5

x = 3

Hence, placing the equations under the correct solution, we get

x = 3                                      x ≠ 3

-14x = -42                              -5 + x = -9

[tex]-\frac{3}{5} +x = \frac{12}{5}[/tex]                          [tex]\frac{x}{3} =9[/tex]

[tex]\frac{x}{4} =\frac{6}{8}[/tex]                                    

x -5 = -2            

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Answer:

1073

Step-by-step explanation:

it's simple addition

The expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)

A cubic equation in algebra is a one-variable equation of the form ax3+bx2+cx+d=0 where an is nonzero. The roots of the cubic function defined by the left side of this equation are the solutions to this equation.

Given expression 2x³-3x²-3x+2 whose one of factor is (x-2)

We have to find second factor of given equation

First we will be rational root theorem to given expression so will get following expression:

[tex]\left(x+1\right)\frac{2x^3-3x^2-3x+2}{x+1}[/tex]

So one factor is (x-1) and now simplifying [tex]\frac{2x^3-3x^2-3x+2}{x+1}[/tex]  we get              2x² - 5x +2 and the factor of 2x² - 5x +2 will be (2x-1)(x-2)

Hence the expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)

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Answer:

An obtuse triangle can not have more than one angle measured greater than 90.

Step-by-step explanation:

Obtuse triangles have 2 acute angles (less than 90 degrees) and 1 obtuse angle (greater than 90).

The statements that describe a triangular prism are:

A triangular prism is a three-dimensional object that is made up of one base that has the shape of a triangle and three lateral sides that have the shape of a rectangle. A triangular prism has 5 faces, 9 edges and 6 vertices.

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Answer:

the answer to that is B. 5 cells

The area of the square is 16 square inches and its perimeter is 16 inches.

What is Area of square ?

A square is a two-dimensional geometric shape with four equal sides and four right angles. The area of a square is the measure of the region enclosed by the square. The area is expressed in square units, such as square inches, square meters, or square feet.

The area of a square is given by the formula:

A = s²

where A is the area and s is the length of a side.

If the side length of the square is 4 inches, the area can be calculated as:

A = 4² = 16 square inches.

The perimeter of a square is given by the formula:

P = 4s

where P is the perimeter and s is the length of a side.

If the side length of the square is 4 inches, the perimeter can be calculated as:

P = 4 x 4 = 16 inches.

Therefore, the area of the square is 16 square inches and its perimeter is 16 inches.

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The formula for number of buses per person is b = p/50

This is a way of using a variable to represent other variables in a function.

Given the expression

p = kb

If k = 50, then;

p = 50b

Make b the subject of the formula

p/50 = 50b/50
b = p/50

Hence the formula for number of buses per person is b = p/50
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Compare the quantity in Column A with the quantity in Column B.

Column A Column B, The two quantities are equal.

Generally, the surface that has one end or side that is higher than the other (or vice versa); is a surface that slopes up or down.

In conclusion, Compare the number in Column A with the number in Column B.

The two amounts are identical in Columns A and B.

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The correct answer is option B which is P ( A|B) will be ( 4 / 9 ).

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Given that:-

The total sample will have 9 numbers

S = { 1,2,3,4,5,6,7,8,9} = 9

Even Number = { 2,4,6,8} = 4

Odd Number  = { 1,3,5,7,9} = 5

P ( A ) = ( 4 / 9 )

P ( B ) = ( 5 / 9 )

The probability will be calculated as:-

P( A:B ) = [tex]\dfrac{P(A)\times P(B)}{P(B)}[/tex]

P( A:B ) =[tex]\dfrac{( 5/9 ) ( 4/9 )}{5 / 9 }[/tex]

P( A:B ) = 4 / 9

Therefore the correct answer is option B which is P ( A|B) will be ( 4 / 9 ).

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We will apply the Pythagoras theorem to find the measure of the unknown leg in a triangle when one leg and the hypotenuse are provided dimensions.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometric function.

According to Pythagoras, the sum of the squares of two sides equals the square of the longest side.

[tex]\rm h^2 = p^2+ b^2[/tex]

Where,

h is the hypotenuse

p is the perpendicular

b is the base

If any of the two is given the third side will be obtained using the  Pythagoras theorem.

In a triangle with given measurements for one leg and the hypotenuse, we will determine the measure of the unknown leg by the Pythagoras theorem.

Hence we willl apply the pythogorous theorem for finding the unknown side.

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Solution: 8p+44

Detailed explanation:

First we can "expand" by multiplying 6 times the parentheses and then 2 times the other set of parentheses.

[tex]--\mapsto\boldsymbol{6(p+6)+2(p+4)}\\\\---\mapsto\boldsymbol{6p+36+2p+8}[/tex]

To make life easier let's just put the p's next to each other.

[tex]--\mapsto\boldsymbol{6p+2p+36+8}[/tex]

Now let's add the p's

[tex]---\mapsto\boldsymbol{8p+44}[/tex]

Voila! There's our answer!

__________________

Hope I helped! Best wishes.

Reach far. Aim high. Dream big.

____________________

Answer:

See below ~

Step-by-step explanation:

Linear pairs add up to 180 degrees.

⇒ 4x - 10 + 3x + 43 = 180

⇒ 7x + 33 = 180

⇒ 7x = 147

⇒ x = 21

∠A = 4(21) - 10

∠A = 84 - 10

∠A = 74°

∠B = 3(21) + 43

∠B = 63 + 43

∠B = 106°

The statement D is false that No irrational number is rational.

The set of real numbers includes integers, rational numbers, and irrational numbers.

This implies that all irrational numbers and integers are also real numbers.

Thus, statements A and B are correct.

Rational numbers are numbers that can be written as the division of two integers, which thus also include all integers.

The set of irrational numbers then contains all real numbers that are NOT rational numbers

Therefore, the set of irrational numbers does not include integers, which implies that statement D is false.

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Answer:

y = 7/6x - 62/3

Step-by-step explanation:

The equation for slope:

y = mx + b

m is the slope and b is the y-intercept

y = 7/6x + b

-9 = 7/6(10) + b

-9 = 35/3 + b

-62/3 = b

since we were given the key ( how it should be sort out or used )

then we get all the numbers out which are:

21, 23, 30, 32, 32, 35, 43, 44, 46, 48, 49, 49, 50, 52, 52, 53, 55

then we go ahead to answer the questions:

a) Range = highest number minus Lowest number

55 - 21 = 34

b) 17 (by counting all individual ages ).

c) Median = the middle age

(but before that, we must arrange the ages either a cording to their sizes either from biggest to smallest (descending order) or from smallest to biggest (ascending order)

so we arrange in ascending order but the numbers are already arranged so we don't have to stress ourselves:

Median = 46 (the number in the middle ).

Hope you ace your tests, Good luck ✅.

Answer:

y= -x-7

Step-by-step explanation:

Slope intercept form: y = mx + b

m = slope

b = y intercept

The first thing you must do is isolate y so that it is by itself on the left side of the equation:

-x = y + 7

Subtract 7 to both sides:

-x - 7 = y + 7 - 7

-x - 7 = y

Flip:

y = -x - 7

-x = y + 7 in slope intercept form is y = -x - 7

This means the slope is -1 and the y-intercept of the equation is (0, -7)

The statement about using the line of best fit for the given scatter plot is; False

When we have a scatter plot, it is always best to look for the line of best fit or curve of best fit depending on the nature of the variation of the plotted points.

Now, from the scatter plot image attached, we can see that the points are already looking like a curved plot form and so what we will need her will be a curve of best fit and not a line of best fit plot and as such the statement about using a line of best fit plot is false.

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The sum of the triangular numbers is [tex]\frac{n(n+1)(n+2)}{6}[/tex]

According to the question, the series of triangular numbers is given as in the form of the number of dots constituting the equilateral triangles i.e.
1, 3, 6, 10, 15 . . . . .n

triangular number are the sequence and series of the numbers and each number represents and constitute in visualization of  series of  equilateral triangle.

given series in the figure
1, 3, 6, 10, 15, . . . . . .  ., n
each number represents the number of dots containing in triangle
now the series can be given by
[tex]S = \frac{n(n+1)}{2}[/tex]  for n = 1, 2, 3, 4,. . . . .n
now , according to the question the sum of the series can be given as
⇒  ∑S
⇒   ∑[tex]\frac{n^2+n}{2}[/tex]
⇒  [tex]\frac{1}{2}[\sum n^2+\sum n]\\\frac{1}{2}[\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}] \\\frac{n(n+1)}{4}[\frac{(2n+1)}{3}+1] \\\frac{n(n+1)}{4}[\frac{(2n+1+3)}{3}] \\\frac{n(n+1)}{4}[\frac{(2n+4)}{3}] \\\frac{n(n+1)}{4}2[\frac{(n+2)}{3}]\\\frac{n(n+1)(n+2)}{6}[/tex]

Thus, the sum of the triangular number is given by [tex]\frac{n(n+1)(n+2)}{6}[/tex]

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Answer:

3 ÷ y

Step-by-step explanation:

Quotient refers to the division of two values, in this case 3 and y.

Answer:

3/y

Step-by-step explanation: