write the equation of a line through the points (2,3) and (-1,-9)

Answer:

[tex] $$\sum_{n=1}^{5} 6(2^{n-1}) $$ [/tex]

Step-by-step explanation:

6 + 12 + 24 + 48 + 96 =

= 6 + 6 * 2 + 6 * 4 + 6 * 8 + 6 * 16

= 6 + 6 * 2^2 + 6 * 2^2 + 6 * 2^3 + 6 * 2 * 4

= 6 * 2^(n - 1)

[tex] $$\sum_{n=1}^{5} 6(2^{n-1}) $$ [/tex]

The height of the Duquesne Incline in Pittsburgh, Pennsylvania, is approximately 400 feet.

To find the height of the incline, we can use trigonometry, specifically the sine function.

Let's consider the triangle formed by the incline track, where:

The angle of elevation (angle between the incline track and the ground) is 30 degrees.

The length of the incline track (base of the triangle) is about 800 feet.

We want to find the height of the incline (the side of the triangle opposite the 30-degree angle).

Using the sine function, we have:

[tex]sin(angle) = opposite\ side / hypotenuse[/tex]

In this case, the angle is 30 degrees, the opposite side is the height (h) of the incline, and the hypotenuse is the length of the incline track (800 feet).

So, the equation becomes:

[tex]sin(30^o) = h / 800[/tex]

h = 800 * 0.5

h = 400 feet

Therefore, the height of the incline is approximately 400 feet.

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Answer:

The z-score of a 65-mph speed limit is -0.75

Step-by-step explanation:

Here, we want to calculate the z-score

To calculate the z-score, we make use of the z-score formula

Mathematically;

z-score =(x-mean)/SD

from the question we identify the values as x = 65 mph, mean = 71 mph, Standard deviation(SD) = 8 mph

Plugging these values into the equation above, we have

z-score = (65-71)/8 = -6/8 = -0.75

Answer:

3:5

Step-by-step explanation:

all figures can be divided by 8, so

swimming- 40/8= 5

arts 16/8= 2

music 24/8= 3

therefore, the ratio would be 3:5

Answer:

3/5

Step-by-step explanation:

I took it but got it wrong so i did the math problem and got this 3/5

Answer:

$165

Step-by-step explanation:

Answer:

156$

Step-by-step explanation:

Answer:

speed of train A = 70 + 20 = 90 miles per hour

speed of train B = 70 miles per hour 

Step-by-step explanation:

Let

speed of train B = a

speed of train A = a + 20

Recall

speed = distance/time

The travel time is same for both train. Therefore, let us make time subject of the formula in the speed equation.

Time = distance/speed

270/a + 20 = 210/a

cross multiply

270a = 210(a + 20)

270a = 210a + 4200

270a - 210a = 4200

60a = 4200

divide both sides by 60

a = 4200/60

a = 70

speed of train A = 70 + 20 = 90 miles per hour

speed of train B = 70  miles per hour

Answer:

[tex]\dfrac{1}{6}[/tex]

Step-by-step explanation:

Let A be the event of getting an odd number.

P(A) be the probability of getting an odd number.

Total odd numbers here are 6 i.e. [tex]\{1,3,5,7,9,11\}[/tex]

Here, total numbers in the game are 12 i.e [tex]\{1,2,3,....,12\}[/tex].

Formula for probability of an event E can be observed as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

[tex]P(A) = \dfrac{6}{12}\\\Rightarrow \dfrac{1}{2}[/tex]

Let B be the event of getting 11.

P(B) be the probability of getting 11.

Total number of possible cases is 1.

[tex]P(B) = \dfrac{1}{12}[/tex]

[tex]P(A \cap B)[/tex] is the probability that we get 11 and an odd number.

Possible number of cases = 1

[tex]P(A\cap B) = \dfrac{1}{12}[/tex]

P(B/A) is the probability that we get an 11 given that it is an odd number.

[tex]P(B/A) = \dfrac{P(A \cap B)}{P(A)}\\\Rightarrow \dfrac{\dfrac{1}{12}}{\dfrac{1}{2}}\\\Rightarrow \dfrac{1}{6}[/tex]

Hence, P(B/A) = [tex]\dfrac{1}{6}[/tex]

Answer:

The probability in fraction is [tex]\frac{1}{12}[/tex].

Step-by-step explanation:

Total number of outcomes is = 12

Now we have to find the probability that spun number is 11.

That means favorable outcome is 1.

In this case, the probability can be determined by dividing the number of favorable outcomes by the total outcome. Accordingly, the total outcomes are 12 and favorable outcome is 1.  

[tex]\text{P(The spun number is 11)}= \frac{\text{Favorable outcomes}}{\text{total outcomes}} \\\text{P(The spun number is 11)}= \frac{1}{12} \ (in \ fraction)\\\text{P(The spun number is 11)} = 0.083 \ (in \ decimal)[/tex]

Answer:

Step-by-step explanation:

Emma jogs 2 miles along the beach in 1/3 of an hour. At a constant rate, the distance that she jogs on 1 hour would be

Let x represent the number of mikes that she would jog in 1 hour.

If 2 miles = 1/3 of an hour, then

x = 1 hour

Cross multiplying, it becomes

x × 1/3 = 2 × 1

x/3 = 2

x = 3 × 2 = 6 miles

The equivalent rate with a denominator of 1 is 6/1 miles

Answer:

The Answer Is 6.  

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Answer:

elon musk

Step-by-step explanation:

elon sends out random, uncalled for tweets, which mess with the stock value.

For example, when the stock was very high, he tweeted,"Tesla stock too high"

Answer:

26771.8115

Step-by-step explanation:

24500(1.03)=25235 then continue doing this 2 more times and you get 26771.8115

Answer:

A year is 12 months long. 1.5 percent each month would total 18 percent in a year. 18 percent of 1000 is 180. The final number of fish is 1180

Step-by-step explanation:

Answer:

Step-by-step explanation:

The ratio between the volume of the small cone to that of the frustum is 1:1.

Notice that the bigger cone is double than the smaller cone, which means the smaller cone is half of the volume of the bigger cone, if you wipe the small one, you would have the frustum with the same volume as the wiped part, because if you delete the smaller cone, you would be deleting half volume of the bigger cone, giving at the end a relation 1 : 1 between the frustum and the smaller cone.

Answer: the answer is in the steps.

Step-by-step explanation:

6.25h ≤ 125.00

Answer:

six

Step-by-step explanation:

3x6=18 and 3+3+6+6= 18.

Answer:

y/x = 1

Step-by-step explanation:

sin 45 = cos 45 = y /1 = x/1

so y = x

or y/x =1

Answer:

6

Step-by-step explanation:

guess and check 6(10)+((6+7)5)=125

Answer:

She earns £11 per hour

Step-by-step explanation:

You divide £440 with 5 days of the week and then you get how much she earns in a day. And then you devide with 8 and u get £11.

Caroline will earn £11 for working per hour.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that caroline works 8 hours a day 5 days a week she earns £440 each week.

The earnings for an hour will be calculated as,

Total hours = 8 x 5 = 40 hours

Earning per hour = £440 / 40

Earning per hour =  £11

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Answer:

In Euclidean geometry, a quadrilateral is a four-sided 2D figure whose sum of internal angles is 360°. The word quadrilateral is derived from two Latin words ‘quadri’ and ‘latus’ meaning four and side respectively. Therefore, identifying the properties of quadrilaterals is important when trying to distinguish them from other polygons. So, what are the properties of quadrilaterals? There are two properties of quadrilaterals:

Step-by-step explanation:

Answer:

q2- p2

4*2-2*2

8-4

B.4

Step-by-step explanation:

The value of q² - p² is 12 for the given value of p and q.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given, The value of p = 2 and q = 4

the value of q² - p² for the given value

=> q² - p² = 16 - 4

=>q² - p² = 12

therefore, For the specified values of p and q, the value of q2 - p2 is 12.

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Answer:

9*70

Step-by-step explanation:

It is not 9+70 or 9+60 because for this problem multiplication is required.

This problem seems to want you to round to the nearest ten's place.  Because the one's place in 68 is above 5, the number will round up.

This means that the answer will be 9*70

Answer:

9*70

Step-by-step explanation:

Answer:

[tex]20943.96 ft^3[/tex]

Step-by-step explanation:

The silo is shaped as a cylinder with a hemisphere on top of it.

We need to find the volume of the shape.

The volume of a cylinder is given as:

[tex]V = \pi r^2h[/tex]

where r = radius

h = height

The volume of a hemisphere is given as:

[tex]V = \frac{2}{3} \pi r^3[/tex]

where r = radius

Therefore, the joint volume of both shapes is:

[tex]V = \pi r^2h + \frac{2}{3} \pi r^3[/tex]

The height of the silo is 60 and the diameter is 20.

This means that the radius is 10.

The cylindrical part of the silo and the hemispherical part have the same radius, 10.

The volume of the silo is:

[tex]V = \pi * 10^2 * 60 + \frac{2}{3} * \pi * 10^3\\ \\V = 18849.56 + 2094.40\\\\V = 20943.96 ft^3[/tex]

The volume of the silo is [tex]20943.96 ft^3[/tex]

Answer:

55°

Step-by-step explanation:

Using cosine law

67² = 74² + 14² - 2(74)(14)cos(L)

cos(L) = 169/396

L =55.18378419

The measure of angle L to the nearest degree is 55°.

Law of cosines of triangle states that for three length of sides of the triangle, a, b and c opposite to the angles A, B and C respectively can be related as,

a² = b² + c² - 2bc cos(A)

Given, for a triangle JKL,

j = 74 inches, k = 14 inches and l = 67 inches.

We can use law of cosines to find the measure of angle L.

Using the law of cosines,

l² = j² + k² - 2jk cos(L)

67² = 74² + 14² - (2×74×14) cos(L)

4489 = 5476 + 196 - 2072 cos(L)

4489 = 5672 - 2072 cos(L)

-1183 = - 2072 cos(L)

cos (L) = 0.5709

L = 55.18° ≈ 55°

Hence the measure of angle L is 55°.

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Answer:

option 2

452.16

You would need to use this equation...

V=πr²h

3.14 * (4)² * 9

= 452.16 cm³

Answer:

12,852

Step-by-step explanation:

V= l*w*h

V=17*18*42

V= 12,852

Answer:y=2.5 x

Step-by-step explanation:

Given

Cow give 5 gallon of milk if it eats 2 pound of grass

i.e. it gives 2.5 gallon of milk if it eats 1 pound of grass

So we can say cow given 2.5 times of milk in gallon for each pound it eats

If cow eats x pounds of grass then it must yield 2.5 times of milk

Suppose milk is denoted by y  

therefore we can write

y=2.5 x

Therefore y=2.5 x represent the relation between grass and milk produced

Answer:

Infinite solutions

Step-by-step explanation:

Distribute the 2 to (n - 1), and distribute the 2 to (3n - 1), like so:

2(n - 1) + 4n = 2(3n - 1)

2n - 2 + 4n = 6n - 2

Add like terms (2n and 4n):

6n - 2 = 6n - 2

Subtract 6n from both sides:

-2 = -2

Since we ended up with the same term on both sides, we can't do anything else, meaning this equation has infinite solutions.

Answer:

The relationships, properties, and theorems will be easier to understand when ... Just like you don't want to do a geometry problem without all the given ... In case you want to get a head start… here are arguably some of the most important theorems for triangles: ... In the figure below, both congruent angles have one arch.

Step-by-step explanation:

Answer:

x = ± 2/3

Step-by-step explanation:

9x^2 = 4

Divide each side by 9

9/9x^2 = 4/9

x^2 = 4/9

Take the square root of each side

x = ±sqrt(4/9)

x = ± 2/3

9x^2=4

/9       /9

x^2=4/9

sqrt both sides

x=+/-[tex]\sqrt{4/9}[/tex]

x=+/-([tex]\frac{\sqrt{4} }{\sqrt{9} }[/tex])

x=+/-2/3

Answer:

x=2/3, x=-2/3