For numbers 6-10, how long does it take to travel:

11. A car travels 200 kilometers in 8 hours. Calculate the average speed of the car in:

a. Kilometer per hour
b. Kilometers per minute


This question have no choices specify your answers only
​

Option(A) is the correct answer is A. 1,335 birds.

To calculate the number of birds that will be left after 20 years, we need to consider the annual decline rate of 2%.

We can use the formula for exponential decay:

N = N₀ * (1 - r/100)^t

Where:

N is the final number of birds after t years

N₀ is the initial number of birds (2,000 in this case)

r is the annual decline rate (2% or 0.02)

t is the number of years (20 in this case)

Plugging in the values, we get:

N = 2,000 * (1 - 0.02)^20

N = 2,000 * (0.98)^20

N ≈ 2,000 * 0.672749

N ≈ 1,345.498

Rounded to the nearest whole number, the number of birds that will be left after 20 years is 1,345.

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Answer:

k = 10

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ ZYM is an exterior angle of the triangle, thus

4k + 5 + 6k + 10 = 115, that is

10k + 15 = 115 ( subtract 15 from both sides )

10k = 100 ( divide both sides by 10 )

k = 10

Answer:

10

Step-by-step explanation:

< = angle

Step 1:

<YZX + <ZXY + <XYZ = 180°   Sum of a triangle

Step 2:

<XYZ = 180° - 115° = 65°   Supplementry <'s

Step 3:

6k + 10° + 4k + 5° + 65° = 180°       Algebra

Step 4:

10k + 80° = 180°     Algebra

Step 5:

10k = 100°      Algebra

Answer:

k = 10      

Hope This Helps :)

Answer:

The rate at which the distance from the goose to the pond is increasing is approximately 42.875 feet per second.

Step-by-step explanation:

We assume that goose is flying at constant velocity. After reading carefully the statement of the problem, we create the following geometrical diagram, which is included at the end of this explanation and represents the following Pythagorean identity:

\(x^{2}+y^{2} = r^{2}\) (Eq. 1)

Where:

\(x\) - Horizontal distance of the goose from pond, measured in feet.

\(y\) - Vertical distance of the goose from pond, measured in feet.

\(r\) - Resultant distance of the goose from pond, measured in feet.

We find the rate of change in time at which resultant distance is increasing by differentiating on (Eq. 1):

\(2\cdot x \cdot \dot x + 2\cdot y \cdot \dot y = 2\cdot r \cdot \dot r\)

\(x\cdot \dot x + y\cdot \dot y = r\cdot \dot r\)

\(\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{\sqrt{x^{2}+y^{2}}}\) (Eq. 2)

Where:

\(\dot x\) - Rate of change of horizontal distance, measured in feet per second.

\(\dot y\) - Rate of change of vertical distance, measured in feet per second.

\(\dot r\) - Rate of change of resulting distance, measured in feet per second.

If we know that \(x = 500\,ft\), \(y = 300\,ft\), \(\dot x = 50\,\frac{ft}{s}\) and \(\dot y = 0\,\frac{ft}{s}\), the rate at which the distance from the goose to the pond is increasing is:

\(\dot r = \frac{(500\,ft)\cdot \left(50\,\frac{ft}{s}\right)+(300\,ft)\cdot \left(0\,\frac{ft}{s} \right) }{\sqrt{(500\,ft)^{2}+(300\,ft)^{2}}}\)

\(\dot r \approx 42.875\,\frac{ft}{s}\)

The rate at which the distance from the goose to the pond is increasing is approximately 42.875 feet per second.

Answer:

$75

Step-by-step explanation:

$375÷5

=$75

That is each child got $75 after the $375 were been shared between the five children equally

Answer:

x^2+2x-8

Step-by-step explanation:

x^2+2x-8 = (x+4)(x-2)

Answer: A. x^2 -2x -8

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope of line AB is

\(\frac{2-8}{3-(-3)} = \frac{-6}{6} = -1\)

The slope of line CD is

\(\frac{-1-1}{5-7} = \frac{-2}{-2} = 1\)

Since the slopes multiply to \(-1\), these lines are perpendicular to one another.

The lines AB and CD are perpendicular to one another.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.

let (x₁, y₁ ) = A(-3,8), and (x₂, y₂ ) = B(3,2)

The slope of line AB is;

m =  ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 2 - 8) / ( 3 +3 )

m = -1

let (x₁, y₁ ) =  C(7,1) and (x₂, y₂ ) = D(5,-1)

The the slope of line CD is;

m =  ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( -1 - 1) / ( 5 - 7 )

m = 1

Since slope of AB and CD are not equal the lines are not parallel therefore, these lines are perpendicular to one another.

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Answer:

Yes.

Step-by-step explanation:

They are equivalent because if you divide 19 by 8, the result is 2.375.

Answer:

yes

Step-by-step explanation:

convert 19/8 into a decimal:

\(\frac{19}{8}\)=2.375

2.375=2.375

Hope this helps!

The quantity of ribbon that Ali started with was 16/21 feet, based on the mathematical operation of addition.

The basic mathematical operations include addition, subtraction, division, and multiplication.

In the addition operation, two or more addends are added to obtain a result called the sum or total using the equation symbol (=) and the addition operand (+).

The quantity of ribbon attached to the rearview mirror = 2/7

The remaining quantity of ribbon after the attachment = 10/21

The quantity of ribbon Ali started with = 16/21 (2/7 + 10/21)

Thus, using the addition operation, we can conclude that Ali started with 16/21 feet of ribbon.

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Answer:

The answer is 1,200

Step-by-step explanation:

(^-^)

The derivative of function f(w) = \(2/(w^2 - 4)^5 ~is ~f'(w) = -40~w~(w^2 - 4)^{-6}.\)

We have,

To find the derivative of the function \(f(w) = 2/(w^2 - 4)^5\), we can use the chain rule and the power rule for differentiation.

Let's go through the steps:

First, rewrite the function as \(f(w) = 2(w^2 - 4)^{-5}.\)

Now, let's differentiate f(w) with respect to w:

\(f'(w) = d/dw~ [2(w^2 - 4)^{-5}]\)

To apply the chain rule, we need to differentiate the outer function and multiply it by the derivative of the inner function.

Using the power rule, the derivative of (w² - 4) with respect to w is 2w.

Applying the chain rule:

\(f'(w) = -10 \times 2(w^2 - 4)^{-6} \times 2w\)

Simplifying further:

\(f'(w) = -40w(w^2 - 4)^{-6}\)

Therefore,

The derivative of function f(w) = \(2/(w^2 - 4)^5 ~is ~f'(w) = -40~w~(w^2 - 4)^{-6}.\)

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Answer:

i think 125

Step-by-step explanation:

Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

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Given :

The ratio of the amount of gold to the amount of silver is 2:5.

To Find :

The weight of gold in the alloy, if there are 80 g of silver.

Solution :

Let, amount of gold is x.

So, the ratio of amount of gold and silver is :

\(\dfrac{x}{80}=\dfrac{2}{5}\\\\x=32\ g\)

Therefore, the weight of gold in the alloy is 32 g.

Hence, this is the required solution.

Answer:

32

Step-by-step explanation:

do 80÷5=16 to get unit. Then do 16*2=32

The required, general solution for x that satisfies the equation cos(x + 30) = -1 is x = (2n + 1)π - 30.

To find the general solution for the equation cos(x + 30) = -1, we can start by considering the general form of the cosine function. The cosine function has a period of 2π, meaning it repeats every 2π radians.

In this equation, we have cos(x + 30) = -1. Since the cosine function has a maximum value of 1 and a minimum value of -1, the only way for cos(x + 30) to equal -1 is if x + 30 is an odd multiple of π. We can write this as:

x + 30 = (2n + 1)π

Here, n is an integer representing the number of periods of the cosine function. To find the general solution, we can solve for x by subtracting 30 from both sides:

x = (2n + 1)π - 30

This equation gives us the general solution for x that satisfies the equation cos(x + 30) = -1. We can see that for each integer value of n, we have a different solution.

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Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

a) The radius of the sphere is given as follows: 27.13 ft.

b) The surface area can be checked as follows: S = 4 x 3.14 x 27.13² = 9244.

The surface area for a sphere of radius r is given by the equation presented as follows:

S = 4πr².

The surface area for this problem is given as follows:

9244 ft².

Hence the radius is given as follows:

\(r = \sqrt{\frac{9244}{4 \times 3.14}}\)

r = 27.13 ft.

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Answer:

2

Step-by-step explanation:

Y = 5

x = 4

Substitute

5 + 1 - 4

6 - 4

2

Answer:

Given that x = 4 and y = 5,

\(\sf 5 + 1 - 4\\(5 + 1) - 4\\5 + 1\\= 6\\= 6 - 4\\= 2\)

Therefore, the answer is 2.

Answer:

x > -5, so the correct answer is C.

hello

if i'm right, what you're trying to ask is

Step-by-step explanation:

T = 55 + 6w

after 8 week $103

Answer:

n = 19

Step-by-step explanation:

2n > 36 ( divide both sides by 2 )

n > 18

and

5n < 100 ( divide both sides by 5 )

n < 20

so n > 18 and n < 20

thus n = 19

Answer:2

Step-by-step explanation:{[(30-60) ÷ (-30)1²-15} = (-7)=2

Answer:

Hmm im not suree :l

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:D

Step-by-step explanation:

The higher he is the longer it takes to get down to the bottom

Answer: The best problem solving strategy to solve this problem with is a formula. Additionally Brandon had $12.50 before going to the store.

Step-by-step explanation: Formula and Solving it

He Spent $2.50 on pencils.

Amount left after buying a pencil = x - 2.50

Next, he spent half of the amount left in his pocket.

He spent (x - 2.50)/2 on notebook and paper.

So the total amount he spent = 2.50 + (x -2.50)/2

Amount left when he got home =$ 5.00

That means, x - Total amount spent = 5

=> x - (2.50 + (x -2.50)/2 ) = 5

=> x - 2.50 -x/2 + 2.50/2 = 5

=> x/2 - 2.50/2 = 5

=> x/2 = 5 + 2.50/2

=> x/2 = 6.25

=>x = $12.5

The unit rate of the relationship will be 10/3. The correct option is C.

The given equation is,

y = 10/3x + 8

The general form of an equation of the line is,

y = mx +  c

here, the slope will be 10/3

Slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for a given change in the independent variable.

The slope of a line is represented by the ratio of the change in the y-axis (vertical) to the change in the x-axis (horizontal) between any two points on the line. It can also be interpreted as the rate of change of the dependent variable with respect to the independent variable.

A positive slope indicates an upward trend, while a negative slope indicates a downward trend. The slope of a line is often denoted by the letter m.

The unit relationship will be 10/3.

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The expected value of the number of cups of coffee Alex drinks each day is 00.805 cups.

the mean/ average is gotten by dividing the sum of the values in the set by their number.

The concept of mean/average is used in this ques to calculate the expected value of the number of cups of coffee Alex drinks each day.

Mean/ Average=     sum of values

                              number of values

Mean/ Average= 00.200 cups +00.163 cups+ 00.976 cups+ 01.881 cups

                                                                 4

Mean/ Average= 00.805 cups

Hence, The expected value of the number of cups of coffee Alex drinks each day is 00.805 cups.

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Answer:

Step-by-step explanation:

The length of a rectangular picture frame is 3 inches longer than it's width. If the perimeter of the picture frame is 38 Inches, what is the length and width ?

Given :

Perimeter of rectangle is 38 Inches

lenght is 3 inches more than the breadth.

let, width be x, and length be x+3

So, Breadth is 8 inches and length is 8+3= 11 inches.

Let's verify ::

Thus Solved !!