A bus left freetown at 7:45 am and arrived Kenema at 1:30pm. If the distance is 2,700 km what is the average speed of the bus?​

Answer: \(x=n\pi +(-1)^n\dfrac{\pi}{6}\), \(x=n\pi +(-1)^n\left(\dfrac{-\pi}{6}\right)\)

Step-by-step explanation:

Given

\(\sin x-\sqrt{1-3\sin^2x}=0\)

Take the square root term to the right-hand side

\(\Rightarrow \sin x=\sqrt{1-3\sin^2x}\\\text{Squaring both sides}\\\Rightarrow \sin^2x=1-3\sin^2x\\\Rightarrow 4\sin^2x=1\\\\\Rightarrow \sin^2x=\dfrac{1}{4}\\\\\Rightarrow \sin x=\pm\frac{1}{2}\)

for

\(\sin x=\dfrac{1}{2}\)

\(x=n\pi +(-1)^n\dfrac{\pi}{6}\)

for

\(\sin x=\dfrac{-1}{2}\)

\(x=n\pi +(-1)^n\left(\dfrac{-\pi}{6}\right)\)

Answer:

the answer is c because decreased by means the symbol minus so y decreased by 24 will be y-24

Answer:

D.

Step-by-step explanation:

End behavior : Left up and right down

Even degree with negative leading coefficient

Answer:

A) 24310

B) 18 seasons

Step-by-step explanation:

A) We are given the team has 17 players and there are 9 different positions in the team.

This is a combination question and thus, the number of different line-ups the team can make is;

C(17, 9) = 24310

B) We are told the basketball games consists of 9 innings.

Thus,

Number of games you can fill = 24310/9 = 2701.1111

And then we are told a season consists of 147 games.

Thus;

Number of complete seasons can the team play without repeating a line-up =

2701.1111/147 ≈ 18 seasons

Answer:

a

Step-by-step explanation:

1 5/16

Your answer should be above.

Answer:

A

Step-by-step explanation:

Answer: C = 36

Step-by-step explanation: 36 divided by 4 minus 5 = 4 so 36 is C

Hope it helped :D

Provide a reason for each given statement:

Reason 1:

Given

Reason 2:

SQ bisects the angle RQT.

Reason 3:

SQ bisects the angle RST

Reason 4:

Reflexive property of the congruence

Reason 5:

ASA criterion.

Notice that since two angles form the triangles are congruent, then RQS and TQS are similar triangles. Then, it is enough to show that they have one congruent side to prove that they are in fact more than similar, but congruent.

Answer:

(7s-2)+3+(s+3) = 52, or 8s+4 = 52.

Step-by-step explanation:

Since s is the son's age, "two less than seven times" the son's age would be represented by 7s-2. To represent this in 3 years, we would add 3: (7s-2)+3. In 3 years, the son's age, s, would be represented by s+3. We are told that the sum of these ages will be 52; this gives us (7s-2)+3+(s+3) = 52.

To simplify this, combine like terms. 7s+s = 8s; -2+3+3 = 4. This gives us 8s+4=52.

(7s-2)+3+(s+3)=52, or 8s+4 = 52

The slope of the line is 7/9

It is important to note that the equation of a line is represented as;

y = mx + c

Where;

The formula for calculating the slope of a line is expressed as;

Slope, m = y₂ - y₁/x₂ - x₁

Now, let's substitute the values into the formula from the points given we have;

Slope, m =1 -(-6)/ -3 - (-6)

expand the bracket

Slope, m = 1 + 6/ 3 + 6

add the values

Slope, m = 7/9

Hence, the value is 7/9

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The expansion will be 64d^6 + 1152d^5 + 9720d^4 + 43740d^3 + 98415d^2 + 145458d + 729

We can expand (2d+3)^6 using the binomial theorem, which states that:

(a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nCn-1 * a^1 * b^(n-1) + nCn * a^0 * b^n

where nCk is the binomial coefficient, given by:

nCk = n! / (k! * (n-k)!)

Expanding (2d+3)^6 using this formula, we get:

(2d+3)^6 = 6C0 * (2d)^6 * 3^0 + 6C1 * (2d)^5 * 3^1 + 6C2 * (2d)^4 * 3^2 + 6C3 * (2d)^3 * 3^3 + 6C4 * (2d)^2 * 3^4 + 6C5 * (2d)^1 * 3^5 + 6C6 * (2d)^0 * 3^6

Simplifying each term using the binomial coefficient formula, we get:

(2d+3)^6 = 1 * 64d^6 * 1 + 6 * 32d^5 * 3 + 15 * 16d^4 * 9 + 20 * 8d^3 * 27 + 15 * 4d^2 * 81 + 6 * 2d * 243 + 1 * 1 * 729

Simplifying each term further, we get:

(2d+3)^6 = 64d^6 + 1152d^5 + 9720d^4 + 43740d^3 + 98415d^2 + 145458d + 729

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The multiplication of the expression (s - 3)³ is determined as s³ - 9s³ + 27s - 27.

The product of the expression given as (s - 3)³ is calculated  as follows;

The given expression;

(s - 3)³, this can also be written as;

(s - 3)³ =  (s - 3) (s - 3) x (s - 3)

We will simplify the expression as follows;

(s - 3)(s - 3) x (s - 3)

= (s - 3)(s - 3) x (s - 3)

= (s² - 3s -3s + 9 )(s - 3)

= ( s² - 6s + 9 ) (s - 3)

= s³ - 3s² - 6s² + 18s + 9s - 27

= s³ - 9s³ + 27s - 27

Thus, the given expression can be simplified using binomial theorem or using simple multiplication method as shown above.

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Answer:

زيتوقزي نيهقوتيمسنستثو. تيتق

Answer:

Hope this helps ;)

Step-by-step explanation:

To find the time it takes the T-shirt to reach its maximum height, we need to find the value of t when the velocity of the T-shirt is zero, because at this point the T-shirt has reached its maximum height and starts falling back down. We can find the velocity of the T-shirt by taking the derivative of the height equation with respect to time:

v(t) = h'(t) = 72

The velocity of the T-shirt is a constant 72 feet per second, so it will never reach a velocity of zero and will never reach its maximum height. The T-shirt will keep going up indefinitely.

If the problem had specified that the T-shirt was launched with an initial upward velocity of -72 feet per second (meaning it was launched downward), then we could have found the time it takes the T-shirt to reach its maximum height by setting v(t) = 0 and solving for t. In this case, we would find that t = 1, so it would take the T-shirt 1 second to reach its maximum height. The maximum height would be h(1) = -16 + 72(1) + 6 = 62 feet.

Answer

-64

just use ur calculator since my teacher let us use the calculator i just typed in 16.(-4) and got -64  

Answer:

-64 is answer

Step-by-step explanation:

16.(-4)

= -64

Answer:

0.101

Step-by-step explanation:

Given that :

Standard deviation, s = 0.2

Sample variance, s² = 0.0653

Sample size, n = 10

Population variance = σ² = 0.04

We use the Chi square distribution :

(n - 1)s² / σ²

For P(s² ≥ 0.065)

(n - 1)s² / σ² = (10 - 1)*0.0653 / 0.04

(n - 1)s² / σ² = 0.585 / 0.04 = 14.625

P(s² ≥ 14.625) = 0.101 ( chi squee calculator).

The equation for the line of best fit is given as follows:

y = 50x/3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b.

The parameters of the definition of the linear function are given as follows:

From the graph, when x = 0, y = 0, hence the intercept b is given as follows:

b = 0.

Hence:

y = mx.

When x = 3, y = 50, hence the slope m is given as follows:

3m = 50

m = 50/3.

Hence the equation is:

y = 50x/3.

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\(\bold{\huge{\underline{ Solution \: 1 }}}\)

Theorem 1 :- SSS Similarity

Theorem 2 :- AA similarity

Theorem 3 :- SAS similarity

Theorem 4 :- AAA similarity

Here, We have given statement that

From above theorem, we can conclude that

Hence, Option C is correct

\(\bold{\huge{\underline{ Solution \: 2 }}}\)

The given statement is proved by using Pythagorean theorem.

That is,

\(\sf{\red{ (Hypotenuse)^{2} = ( Perpendicular)^{2} + ( Base) ^{2}}}\)

Hence, Option D is correct that is Pythagorean theorem.

By translation, the image of the triangle X is equivalent to the triangle E.

Herein we find the representation of a triangle, whose vertices are described below:

A(x, y) = (5, 5), B(x, y) = (5, 6), C(x, y) = (7, 5)

Whose image must be determined by a rigid transformation known as translation:

P'(x, y) = P(x, y) + T(x, y)

Where:

Now we proceed to determine the images of the vertices of the triangle:

A'(x, y) = (5, 5) + (4, - 3)

A'(x, y) = (9, 2)

B'(x, y) = (5, 6) + (4, - 3)

B'(x, y) = (9, 3)

C'(x, y) = (7, 5) + (4, - 3)

C'(x, y) = (11, 2)

Therefore, the triangle E is the image of the triangle X.

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Answer: 2 1 4

Step-by-step explanation: cant say.

The capacity of a jug is 3.5 l correct to the nearest 0.1 l. This places the volume of the jug between 3.50 l and 3.59 l

The capacity of a glass is 0.25 l correct to the nearest 0.01 l. This places the volume of a glass between 0.259 and 0.250 l

The maximum number of glasses that can surely be filled is equal to the whole number that lies just below 3.50/0.259.

3.50/0.259 = 13.51

The required value of the greatest number of glasses that can be surely filled is 13.

\( = 2(3( {(9})^{2} - 5) + 5(3)) \\ = 2(3(81 - 5) + 15) \\ = 2( 3(76) + 15) \\ = 2(228 + 15) \\ = 2(243) \\ = 486\)

ATTACHED IS THE SOLUTION

YOU DID NOT PROVIDE FULL OPTIONS THEREFORE I WON'T BE ABLE TO CHOOSE.

GOODLUCK .

Answer: 90$

Step-by-step explanation:  50% of 60 is 30 so 60+30=90

Answer:

Option B

Step-by-step explanation:

The sample populations are independent of each other and hence for comparing of mean of two population it is very essential that the two populations independent of each other.

Now here one population set consist of only people who eat fast food and the other set of population consists of people who do not eat fast food.

Answer:

$154

Step-by-step explanation:

Find the rate per hour as;

if  11 hours =$242

     1 hour =?

Perform cross product as:

{$242 *1} / 11 = $22

For 7 hours the amount made will be:

7* $22 = $154

Given data:

The given time for Harry is t=4 years.

The given time for Ingred is t'=6 years.

The given rate of interest for Harry is r=4.2%.

The given rate of interest for Ingred is r'=3.9%.

The expression for the difference in the interest is,

Answer:

a) 500 m

b) 10 s

c) 320 m

d) 8.94 s (2 dp)

Step-by-step explanation:

Given equation:   \(\sf y=500-5x^2\)

where:

a)  The height of the helicopter above the water is the height of the raft when x = 0:

\(\sf \implies 500-5(0)^2=500 \ m\)

b) The raft reaches the water when y = 0:

\(\sf \implies 500-5x^2=0\)

\(\sf \implies 5x^2=500\)

\(\sf \implies x^2=100\)

\(\sf \implies x=\pm 10\)

As time is positive, \(\sf x=10 \ s\)

c) The height of the raft above the water 6 s after it is dropped
is when x = 6:

\(\sf \implies 500-5(6)^2=500 -180=320 \ m\)

d) When the raft is 100 m above the water, y = 100:

\(\sf \implies 500-5x^2=100\)

\(\sf \implies 5x^2=400\)

\(\sf \implies x^2=80\)

\(\sf \implies x=\pm \sqrt{80}\)

As time is positive, \(\sf x= \sqrt{80}=8.94 \ s \ (2 \ dp)\)

Answer:  I believe it would be C

Step-by-step explanation:

I am not 100% sure but I hope this helps :)

As given by the question

There are given that the quantity:

Now,

(1)

According to the concept, the given quantity is known as discriminant of the polynomial.

Hence, the correct option is C.

And,

(2)

According to the polynomial concept, the value of discriminant is negative, that means less than zero, then it has no real solution.

Hence, the correct option is B

Answer:

The graphs below have the same shape. What is the equation of the blue graph? A. G(x) = (x + 3)^3 B. G(x) = x^3 + 3 C. G(x) = x^3 - 3 D. G(x) = (x - 3)^3

The blue graph is a horizontal shift to the left by 3 units of F(x) = x³.

G(x) = (x + 3)³.

In mathematics, translation is the process of moving an object from one position to another without changing its shape, size, or orientation.

It involves sliding the object in a particular direction by a certain distance.

We have,

From the graph, the blue graph is G(x) = (x + 3)³.

The function f(x) = (x + 3)³ is a transformation of the function f(x) = x³.

Specifically, it is a horizontal shift to the left by 3 units.

To see why,

Let's consider the effect of replacing x with x + 3 in the original function f(x) = x³.

f(x + 3) = (x + 3)³

Notice that f(x + 3) is equal to f(x) translated horizontally to the left by 3 units.

For example, when x = 0, we have:

f(0) = 0³ = 0

f(0 + 3) = 3³ = 27

So the point (0, 0) on the graph of f(x) = x³ is transformed to the point

(-3, 27) on the graph of f(x) = (x + 3)³.

Similarly, we can see that every point on the graph of f(x) = x³ is shifted horizontally to the left by 3 units to obtain the graph of f(x) = (x + 3)³.

Therefore,

The blue graph is G(x) = (x + 3)³.

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