What is the range of this data set? {37, 38, 44, 32, 40, 33, 29, 33, 36}
15
29
33
36

The system of three equations and three unknowns to write the equation are: 5t²+80t+6990.

Given:

Elevation              Travel time

6990 feet                    0 hours

8290 feet                    10 hours

10875 feet                   21 hours

Using this formula

y(t)=at²+bt+c

Where:

At:

t=0; y=6990

6990=a(0)²+b(0)+c

c=6990 Equation 1

At:

t=10; y=8290

8290=a(10)²+b(10)+6990

1300=100a+10b Equation 2

At:
t=21; y=10,875

10875=a(21)²+b(21)+6990

3885=441a+21b Equation 3

Using equation 2 and 3 to solve for a and bc

1300=100a+10b

1300-10b/100=a

13-0.1b=a

Plug into equation 3

3885=441(13-0.1b)+21b

3885=5733-14.1b+21b

b=80

a=13-0.1(80)

a=13-8

a=5

Hence:

Write the Equation by plugging a,b and c

y(t)=5t²+80t+6990

Therefore the system of three equations and three unknowns to write the equation are: 5t²+80t+6990.

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Equation of a Circle: (x - h)^2 + (y - k)^2 = r^2

(h, k) = center of the circle

r = radius of the circle

Center = (2, 0)

Radius = 7

Equation: (x - 2)^2 + (y - 0)^2 = 49

Answer: (x - 2)^2 + y^2 = 49

Hope this helps!

Answer:

4-20(6x-5x)^2+11

(6-5x)^2=11+(-16)

6^2-10x+25=-5

6^2-10x+20

The two co-captians can be chosen in 21 different ways.

If the two co-capitans are equivalent, then we need to find combinations.

So we want to find how many combinations of 2 elements we can make out of a set of 7 elements.

This is given by:

[tex]C(7, 2) = \frac{7!}{(7 - 2)!*2!} = \frac{7*6}{2} = 21[/tex]

So the two co-captians can be chosen in 21 different ways.

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The trigonometric function gives the ratio of different sides of a right-angle triangle. The length of the side KL is 30.81 units.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

The measure of ∠J can be written as,

Cos(∠J) = JK/JL

Cos(∠J) = 7/31.6

∠J = 77.2°

Similarly the length of side KL can be written as,

Tan(∠J) = KL/JK

Tan(77.2°) = KL/7

KL = 30.81 units

Hence, the length of the side KL is 30.81 units.

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Answer:

$ 471.78

Step-by-step explanation:

This describes an 'ordinary annuity' ====>   FORMULA:

PV= C [  1-(1+i)^-n / i ]    Looking for C    i = .05/12   n =60   PV = 25000

 plug in the numbers and calculate   C = 471.78

Answer:

i think it is D but I am not for shore

Answer:

$10.64

Step-by-step explanation:

20% out of $53.18 is $10.636 rounded to $10.64

The solution to the function [tex]f(x) = 2\sqrt{x - 2}[/tex] when x = 2 is 0

The equation of the function is given as:

[tex]f(x) = 2\sqrt{x - 2}[/tex]

When x = 2, we have:

[tex]f(x) = 2\sqrt{2 - 2}[/tex]

Evaluate the difference

[tex]f(x) = 2\sqrt{0}[/tex]

Evaluate the exponent of 0

f(x) = 2 * 0

Evaluate the product

f(x) = 0

Hence, the solution to the function when x = 2 is 0

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The probability of drawing a head card of diamonds and then a head card of hearts is:

P = 0.003

Here we assume that we have a deck of 52 cards, and we want to find:

P(Head, Diamond AND Head, Heart)

This is the probability of drawing a head of diamonds and then a head of hearts.

Remember that for each suit has 3 head cards, J, Q, and K.

Then for the first card, the probability of getting a head of diamonds is equal to the quotient between the number of cards with these properties (3) and the total number of cards (52).

P = 3/52

Then we need to draw a head of hearts, the probability is computed in the same way, but before we drew a card, so now the total number of cards is 51, so we get:

Q = 3/51

Then the joint probability is:

p = (3/52)*(3/51) = 0.003

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Answer:

Jenny has worked out the area of the whole circle using the formula π × r² where r is the radius length. She has assumed π is 3.14 which leads to her working of 3.14 × 10² = 314 units². She has to divide the total area by 4 to calculate the sector area.

Let's check

Area of sector

Answer:

88km

Step-by-step explanation:

If a car travels 40 km in 1 hour, then that same car would travel 40*2.2 km in 2.2 hours.

So, the car travelled 88km in 2.2 hours

Remember that speed is a rate!

Answer:

speed=distance/travel time

distance=2*40+60*3=80+180=260 km

travel time=2+3=5 hrs

Average speed during entire journey=260/5=52 km/h

Answer:

16

Step-by-step explanation:

The measure of angle DAB in the circle shown with the given arc length is: 2.23 radians.

Arc length = θ × r, where r is the radius of the circle, and θ is the central angle in radians.

Given the following:

Length of arc = 6.47 cm

Radius (r) = 2.9 cm

θ = m∠DAB

Plug in the values into the arc length formula:

6.47 = θ × 2.9

6.47/2.9 = θ

θ = 2.23 radians

m∠DAB = 2.23 radians

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Answer:

DAB = 2.23 radians

Hope this helps!

Step-by-step explanation:

y=3x+3

Step-by-step explanation:

The m is 3 because it is rise over run. For every 3 up it goes one over (3/1) or just 3. The b is 3 because b is where x equals 0 and it is at 3.

Take two points

Slope

Parallel lines so slopes are equal

Only y intercept will vary

So both lines have y intercept at -3 and -1 respectively

The equations

Put (0,0) on first one

On second one

So as lines are dashed symbols remain >

The inequalities are

Answer:

0.7 miles

1.4 miles

Step-by-step explanation:

Distance of the first bench from the path = 1/3 x 2.1 miles = 0.7 miles

Distance of the second bench from the path = 2/3 x 2.1 miles = 1.4 miles

Step-by-step explanation:

if you could solve 3a and 3b, you can also solve 3c. it is the same principle.

x-intercepts means y = 0.

remember, a square root has always 2 results : a positive and a negative one.

3c

0 = -(x - 3)² + 25

(x - 3)² = 25

x - 3 = ±5

x1 = +5 + 3 = 8

x2 = -5 + 3 = -2

3a

0 = (x + 1)² - 4

4 = (x + 1)²

±2 = x + 1

x1 = +2 - 1 = 1

x2 = -2 - 1 = -3

3b

0 = (x + 2)² - 9

9 = (x + 2)²

±3 = x + 2

x1 = +3 - 2 = 1

x2 = -3 - 2 = -5

Answer:

A. $115; $72/hour

B. c = 72h + 115

C. $8

Step-by-step explanation:

Part A.

1 hour: $187

2 hours: $259

2 hours - 1 hour = 1 hour

$259 - $187 = $72

$72/hour

The hourly rate is $72/hour.

Since for the first hour he charges $187, and only $72 comes from the hourly rate, then the initial cost is $187 - $72 = $115.

The initial cost is $115.

Part B.

c = 72h + 115

Part C.

Carpenter L for 6 hours:

c = 72(6) + 115 = 547

$547

Carpenter N for 6 hours:

60(6) + 195 = 555

$555

Difference: $555 - $547 = $8

The quotient of 874 and 23 determined using an area model is 38.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have:

= 874 ÷ 23

= (800 + 74 + 4) ÷ 23

We can get the answer by using the area model:

If divide 874 with 23 we get 184 as a remainder and 030 as a quotient

Further, if  we divide 184 with 23 we get 0 as a remainder and 008

874 ÷ 23 = 030 + 008 = 38

Thus, the quotient of 874 and 23 determined using an area model is 38.

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Answer:

Answer In this Picture.

Answer:

$977.20

Step-by-step explanation:

We will use the compound interest formula to solve this: A = P(1 + R) ^ T

Using this formula we plug-in the values that we already have:

A = 880(1 + .0525) ^ 2

Now if we solve this, we end up with 977.20. That is your answer.

Answer:

D is not true.

Step-by-step explanation:

[tex] |4.5| = 4.5[/tex]

[tex] | - 45| = 45[/tex]

[tex]4.5 \leqslant 45[/tex]

Answer:

the answer is 12

Step-by-step explanation:

[tex] \frac{756}{63} \\ = 12[/tex]

Answer:

3

Step-by-step explanation:

Answer:

302cm³

Step-by-step explanation:

The formula for the volume of a hemisphere is [tex]\frac{\frac{4}{3} \pi r^{3}} {2}[/tex] (volume of a sphere over 2)

Plugging in 4 for r we get the answer of [tex]\frac{256}{6}\pi[/tex]

Next we have to find the height of cone. We can get this by subtracting the radius of the hemisphere from the height of the solid. (14-4=10)

We can now find the volume of the cone using the formula [tex]\frac{1}{3} \pi r^{2} h[/tex]

Plugging in 4 for r and 10 for h we get the answer [tex]53 \frac{1}{3} \pi[/tex]

Now we can add our 2 volumes to get the volume of the solid which is 302 in decimal form (3 significant figures)

That is the answer

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