A major river flowing out of the Himalayas

Answer:

7

Step-by-step explanation:

[tex]\dfrac 13(15+6)\\\\\\=\dfrac{21}3\\\\\\=7[/tex]

Answer:

213.75

Step-by-step explanation:

95×9=855

855÷4=213.75

The approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m. -21 tickets per hour

The missing part of the question is represented by the following function:

[tex]T(h) = \frac{386 + 110h}{h}[/tex]

10:00 a.m is 3 hours after 7:00 am and 1:00 p.m is 6 hours after 7:00 am.

This means that:

h = 3 at 10:00 am

h = 6 at 1:00 pm

Next, we calculate T(3) and T(6)

[tex]T(3) = \frac{386 + 110*3}{3} =238.7[/tex]

[tex]T(6) = \frac{386 + 110*6}{6} =174.3[/tex]

The average rate of change is then calculated as:

[tex]T'(h) = \frac{T(3) - T(6)}{3 - 6}[/tex]

This gives

[tex]T'(h) = \frac{238.7 - 174.3}{-3}\\[/tex]

Evaluate

T'(h) = -21

This means that the approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m. -21 tickets per hour

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Answer:

4/5

Step-by-step explanation:

First, we know that we have 5 envelopes. So the denominator of the probability is going to be x/5. We then realize that only one envelope has the car, so the probability of that is 1/5. If we subtract 1/5 from the probability of choosing an envelope (5/5), we get 5/5-1/5=4/5.

Using the given information, the diver's score is 6.2

From the question, we are to calculate the diver's score

From the given information,

The five judges score a dive as 6.0, 6.3, 6.2, 6.8, and 6.1.

Since the highest and lowest scores are discarded

Then, we will discard 6.8 and 6.0

The remaining scores are 6.1, 6.2, and 6.3

Now, the diver's score will be the average of the remaining scores

∴ The diver's score = (6.1 + 6.2 + 6.3) /3

The  diver's score = 18.6 / 3

The diver's score = 6.2

Hence, the diver's score is 6.2

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Answer:

y = (1/3)*x + 5

Step-by-step explanation:

Step 1: determine slope or m

m = change in y-coordinates ÷ change in x-coordinates

m = (4-7)/(-3-6) = -3/-9 = 1/3

Step 2: determine y-intercept or b

y = m*x + b

y = (1/3)*x + b

4 = (1/3)*(-3) + b

4 = -1 + b

b = 5

Step 3: substitute values for m and b into the slope intercept equation

y = (1/3)*x + 5

The coordinates of the point that divides the segment into a 3:2 ratio is (-2.2, -1.2)

The points are given as:

G = (-4,3)

H = (-1,-4)

Ratio, m : n = 3 : 2

The coordinate of the point is calculated using:

[tex](x,y) = \frac{1}{m + n} * (mx_2 + nx_1, my_2 + ny_1)[/tex]

This gives

[tex](x,y) = \frac{1}{3 + 2} * (3 * -1 + 2 * -4, 3 * -4 + 2 * 3)[/tex]

Evaluate

[tex](x,y) = \frac{1}{5} * (-11, -6)[/tex]

Evaluate the product

(x,y) = (-2.2, -1.2)

Hence, the coordinate of the point is (-2.2, -1.2)

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Answer:

Polynomial

Step-by-step explanation:

⇒ It cannot be option 1 as y does not vary with an exponent

⇒ It cannot be option 2 as y does not relate to any logarithmic values of x

⇒ It cannot be a option 4 as there no irrational numbers under a root

⇒ Therefore it is a polynomial, as it is written in the form : y = ax³ + bx² + cx + d (cubic polynomial)

Answer:

Step-by-step explanation:

Comment

There was a flat fee of 10 dollars

Each 1/4 hour brought in 3,75

The total charge was 55 dollars.

Equation

Charge = 10 + 4*3.75*x                     as an hourly rate,

Solution

55 = 10 + 4*3.75x                                Combine

55 = 10 + 15x                                       Subtract 10 from both sides

55-10= 10-10 + 15x

45 = 15x                                               Divide by 15

45/15 = 15x/15

x = 3 hours

Answer 3 hours  

3 hearts

4 triangle

H:T

3:4

So, ratio of hearts to triangles in simplest form is 3:4

(we can't simplify any further - HCF of 3 & 4 is 1)

Hope this helps!

The bearing of R from P is 019 and the distance |PR| is 8.75

A cyclist set out from a town P on a bearing of 060 to a town Q, 5 km away. He then moves on a bearing of 345 to a town R, 6km from Q.

See attachment

Start by calculating the distance PR using the following cosine ratio

PR² = PQ² + QR² - 2 * PQ * PR cos(Q)

Substitute known values

PR² = 5² + 6² - 2 * 5 * 6 cos(105)

Evaluate

PR² = 76.53

Take the square root of both sides

PR = 8.75

Next, calculate angle R using the following sine ratio

PQ/sin(R) = PR/sin(Q)

Substitute known values

5/sin(R) = 8.75/sin(105)

Evaluate the quotient

5/sin(R) = 9.06

Multiply both sides by sin(R)

9.06 * sin(R) = 5

Divide both sides by 9.06

sin(R) = 0.5519

Take the arc sin of both sides

R = sin⁻¹(0.5519)

Evaluate

R = 34

Calculate angle P using:

P = 180 - 34 - 105

P = 41

The bearing of R from P is then calculated as:

Bearing = 060 - 41

Evaluate

Bearing =  019

Hence, the bearing of R from P is 019

In (b), we have:

PR = 8.75

Hence, the distance |PR| is 8.75

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The rocket's height when the distance between you and the rocket is 100 feet is 98.9 feet

The function is given as:

d = √216 +h²

At a distance of 100 feet, it means that:

d = 100

So, we have:

√216 +h² = 100

Take the square of both sides

216 +h² = 10000

Subtract 216 from both sides

h²= 9784

Take the square root of both sides

h = 98.9

Hence, the rocket's height when the distance between you and the rocket is 100 feet is 98.9 feet

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Answer:

47.5 games

Step-by-step explanation:

Finding A :

⇒ Games by A : Games by B = 3 : 1

⇒ Games by A : 10 = 3 : 1

⇒ Games by A = 30

==============================================================

Finding C :

⇒ Games by B / Games by C × Games by A / Games by B = 3 × 4/3

⇒ Games by A / Games by C = 4

⇒ Games by C = 30/4

⇒ Games by C = 7.5

==============================================================

Total games won :

⇒ Games by A + Games by B + Games by C

⇒ 30 + 10 + 7.5

⇒ 47.5 games

Answer: The awnser is linear.

I hope this helped.

Step-by-step explanation:

Answer:

[tex]\frac{\left(3x^2-6x+3\right)}{\left(x-1\right)3x-93x^2-3x^3x-33x^2-6}: -\frac{\left(x-1\right)^2}{x^4+41x^2+x+2}[/tex]
[tex]\frac{3x^2-6x+3}{\left(x-1\right)\cdot \:3x-126x^2-3x^3x-6}[/tex]
[tex]\frac{3\left(x-1\right)^2}{\left(x-1\right)\cdot \:3x-126x^2-3x^3x-6}[/tex]
[tex]\frac{3\left(x-1\right)^2}{-3\left(x^4+41x^2+x+2\right)}[/tex]
[tex]\frac{\left(x-1\right)^2}{-\left(x^4+41x^2+x+2\right)}[/tex]
[tex]-\frac{\left(x-1\right)^2}{x^4+41x^2+x+2}[/tex]

Answer:

3x-3

Step-by-step explanation:

use synthetic division

Answer:

See below

Step-by-step explanation:

Each 32 feet of depth is 1 more atmosphere of pressure on the diver  

The number of days it will take to consume the given power = 4.5 days

The amount of power consumed per day = 1440watt-hours

Therefore X days = 6480 watt-hours?

Make X the subject formula;

X = 1 × 6480/1440

X = 4.5 days

Therefore, The number of days it will take to consume the given power = 4.5 days.

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Answer:

x > 8

Step-by-step explanation:

14 - 2(x + 1) < - 4 ← distribute parenthesis and simplify left side

14 - 2x - 2 < - 4

12 - 2x < - 4 ( subtract 12 from both sides )

- 2x < - 16

divide both sides by - 2 , reversing the symbol as a result of dividing by a negative quantity.

x > 8

Parameterize S by the vector function

[tex]\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle[/tex]

with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.

Compute the outward-pointing normal vector to S :

[tex]\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle[/tex]

The integral of the field over S is then

[tex]\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv[/tex]

[tex]\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv[/tex]

[tex]\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}[/tex]

The equation for the relationship between the thickness and number of weeks is y = 3.8 - 0.2x

Ice lost at 7 weeks = 7(0.2) = 1.4 meters

Total thickness of ice before loss = Ice remaining after 7 weeks + Ice lost at 7 weeks

= 2.4 + 1.4

= 3.8 meters

The equation:

y = Total thickness of ice before loss - (Ice lost per week × Number of weeks)

= 3.8 - (0.2 × x)

y = 3.8 - 0.2x

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Answer:

2(7x-4) = 7x(2)-4(2) = 14x-8

but

(7x-4)^2 = (7x-4) (7x-4)

Answer:

(a)  128 ft

(b)  4 s

(c)  Vertex:  (1, 144)

Step-by-step explanation:

Given information:

The height of the projectile at launch is the value of h(t) when t = 0 (the y-intercept).

Therefore, from inspection of the graph, the y-intercept is (0, 128).

So the height of the projectile at launch is 128 ft.

The length of time it took for the projectile to land is the time from the beginning (when t = 0) to when the height is 0 (the x-intercept).  

From inspection of the graph, the x-intercept is (4, 0)

So the length of time it took for the projectile to land is 4 s.

The vertex is the turning point (minimum/maximum point).

Therefore, from inspection of the graph, the vertex is (1, 144).

The vertex represents the time and height at which the projectile was at its maximum.  So at the time of 1 second, the projectile was at its maximum height of 144 ft.

Answer:

[tex]\textsf{A)} \quad 5u^3-2u^2+5u+8[/tex]

Step-by-step explanation:

Given expression:

[tex](-2u^3+5u-1)+(7u^3-2u^2+9)[/tex]

Remove parentheses:

[tex]\implies -2u^3+5u-1+7u^3-2u^2+9[/tex]

Collect like terms:

[tex]\implies -2u^3+7u^3-2u^2+5u-1+9[/tex]

Combine like terms:

[tex]\implies 5u^3-2u^2+5u+8[/tex]

Option A

The range of name lengths is equal to 8.

In Mathematics and Statistics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.

In Mathematics and Statistics, the range of a data set can be calculated by using this mathematical expression;

Range = Highest number - Lowest number

From the given data set, we have:

Highest number = 10.

Lowest number = 2.

By substituting, we have:

Range = 10 - 2

Range = 8.

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Answer:

range is subtracting the highest number from the lowest number. so we want to find the difference

Step-by-step explanation:

all you do is 105-85 which is 15.

Answer:

16 square units

Step-by-step explanation:

16 square units

Answer:

a)  1 cupcake = $5.50

b)  1 Popsicle = $3.50

Step-by-step explanation:

Let s = cost of one soda

Let c = cost of one cupcake

Let p = cost of one Popsicle

From the given information we can create 3 equations:

Subtract Equation 1 from Equation 2 to eliminate the variable s:

    s + 3c + 3p = 40

-        s + c + p = 22

          2c + 2p = 18

Substitute Equation 3 into this new equation and solve for p:

⇒ 2c + 2p = 18

⇒ 2(p + 2) + 2p = 18

⇒ 2p + 4 + 2p = 18

⇒ 4p = 14

⇒ p = 3.5

Substitute the found value of p into Equation 3 and solve for c:

⇒ c = p + 2

⇒ c = 3.5 + 2

⇒ c = 5.5

To find the cost of a soda (s), substitute the found values of p and c into Equation 1:

⇒ s + c + p = 22

⇒ s + 5.5 + 3.5 = 22

⇒ s = 13

Therefore,

719ft

office area=12(20)=240ft

storage=(20-12)(40-(12+15)=8(13)=104ft

home theater=25(15)=375ft

total area= 240+104+375=719ft

Answer: See the screenshots below

I'm answering in this format because the questions aren't numbered, so its hard to reference them consistently (so we're both on the same page).

All decimal values are approximate. I decided to round to 4 decimal places, but feel free to use another level of precision.