all group of 43 people are going to a concert if 6 people fit in each car how many cars will they need to take​

The graph of y = 3 x 2^x passes through the coordinate points (2,12) and (3,24).

To write a question in the form of y=a x b^x that passes through the coordinate points (2,12) and (3,24), we need to solve for the values of a and b.

First, let's substitute the coordinates (2,12) into the equation:
12 = a x b^2

Next, let's substitute the coordinates (3,24) into the equation:
24 = a x b^3

We now have two equations with two unknowns (a and b), which we can solve using algebra.

From the first equation, we can solve for a:
a = 12 / b^2

We can then substitute this value of a into the second equation:
24 = (12 / b^2) x b^3

Simplifying this equation, we get:
2 = b

We can then substitute this value of b back into the equation for a:
a = 12 / 2^2
a = 3

Therefore, the equation of the graph that passes through the coordinate points (2,12) and (3,24) is:
y = 3 x 2^x

We can check that this equation is correct by plugging in the coordinates:
When x = 2: y = 3 x 2^2 = 12
When x = 3: y = 3 x 2^3 = 24
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The name of shape ABCDE is regular pentagon and the length of line AE is 5 cm

The complete question is added as an attachment

From the question, we can see that

The shape ABCDE has 5 equal sides

This means that ABCDE is a regular pentagon

In (a), we have

5 equal sides

Given that

BC = 5 cm

We have

AE = 5 cm

Hence, the length is 5 cm

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The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4  × 10³

From the question, we are to simplify the given expression

The given expression is

6 × 10⁻³ / 8 × 10⁻⁶

Simplifying the expression

6 × 10⁻³ / 8 × 10⁻⁶

This can be written as

6/8 × 10⁻³/10⁻⁶

Reduce the fraction

3/4  × 10⁻³/10⁻⁶

Apply the division law of indices

3/4  × 10⁻³ ⁻ ⁽⁻⁶⁾

3/4  × 10⁻³ ⁺ ⁶

3/4  × 10³

Hence, the value is 3/4  × 10³

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Answer:

  B)  15/17

Step-by-step explanation:

You want the sine of acute angle A in the right triangle shown.

The sine of the angle is the ratio ...

  Sin = Opposite/Hypotenuse

We can go to the trouble to figure the hypotenuse, or we can choose the only suitable answer from the list provided. (It is the one marked already.)

The leg lengths of the triangle shown are 8 and 15, with leg 15 being opposite angle A. This is the first clue that the ratio will have 15 in the numerator. Only answer choice B matches.

The value of the sine function is never greater than 1, eliminating answer choices A, C, and E, leaving choices B and D.

Since the side opposite angle A is the longest of the two legs, we know that angle A is more than 45°, and its sine is more than √2/2. That means choice D can be eliminated, since it is less than 1/2.

The sine of angle A is 15/17.

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Answer:

1. 61/100

2. 3 43/100

3. 9/1000

4. 4 7/10

5. 1 1/2

6. 13/100

7. 5 1/500

8. 21/1000

Answer:

Step-by-step explanation:

Given function:

As any square root function, its range is all non-negative numbers:

The domain the x values when the expression under root is non-negative:

or

Answer:

5,800 people

Step-by-step explanation:

We can find the enrollment for next semester by multiplying:

5,780(1.0035) = 5,800.23

We can round this to 5,800 people.

Answer:

500

hope this helps

Let's use v1(t) and v2(t) to represent the speed of the first and second runners, respectively, at time t. The functions v1 and v2 must both be continuous in the time variable t, hence this assumption must be made.

So, their difference, a(t), is similarly a continuous function in the variable t, with the formula a(t) = v1(t)-v2(t).  

Now, using the principle of contradiction, one may demonstrate that t1, t2, such that a(t1) is less than or equal to 0 and a(t2) is higher than or equal to 0, exist because the overall average speed of both runners is identical.

Now, we may utilize the continuous function a's Intermediate Value Property to locate a t0 between t1 and t2, where a(to)=0 and the runners are moving at the same speed at this point.

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The required probability is 3 √7 / 32.

Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.

Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7

The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is:  P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.

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System Linear equation has no solution , because it is paralell lines but no intersection.

What is system linear equation?

An equation for a line is known as a linear equation. alternatively, y + 0.5x 3.5 = 0 and others. (Note that each linear equation is the same.) When multiple linear equations interact, we get a system of linear equations.

Here the given system linear equations,

\(3y=\frac{3}{2}x+6\) -------> 1    and \(\frac{1}{2}y-\frac{1}{4}x=3\) --------> 2

Divide by 3  of equation 1 on both sides then,

\(y=\frac{1}{2}x+2\)  -----------> 3

Now put 3 into 2 then,

=> \(\frac{1}{4}x+1-\frac{1}{4}x=3\)

=> 1=3

Hence the given system equation has no solution , because it is paralell lines but no intersection.

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The unit circle is a circle with radius 1 centered at the origin of the Cartesian Plane. In a pair of coordinates (x,y) on the unit circle x2+y2=1, coordinate x is the cosine of the angle formed by the point, the origin, and the x-axis. Coordinate y is the sine of the angle.

Answer:

70%of 20 is 14 so it is 6

Step-by-step explanation:

20-14=6

Answer:

C.

Step-by-step explanation:

We have five unshaded, 1 half of unshaded, and 1 shaded, Thus, It will be showed as \(\frac{1}{6}\)  ➗ \(2\)

The median, mean, range and mode will be 6, 5.4, 9 and 7.

What is median?

The median is the middle number in the data set when the data set is written from least to greatest.

The median is the number in the middle when arranged in an ascending order. The numbers will be:

0, 3, 4, 6, 6, 7, 7, 7, 9.

The median is 6.

The range is the difference between the highest and lowest number which is: = 9 - 0 = 9

The mode is the number that appears most which is 7.

The mean will be the average which will be:

= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.

= 49/9

= 5.4

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To factor the expression 4x^2 - 25, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, we have 4x^2 - 25, which can be written as (2x)^2 - 5^2. Comparing it with the difference of squares formula, we can identify that a = 2x and b = 5. Therefore, the correct option is:

b. (2x)^2 - (5)^2

Using the difference of squares formula, we can factor it as follows:

(2x + 5)(2x - 5)

Hence, the correct factorization of 4x^2 - 25 is (2x + 5)(2x - 5), which is equivalent to option b.

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Answer:

h(x) = -x^2 - 1

Step-by-step explanation:

well y, h(x), f(x), n(x), or any other something of x is all the same thing y.

So if f(x) is -x^2 - 1,

Then h(x) is also -x^2 - 1

Answer:

  70 ft

Step-by-step explanation:

You want the actual width of a gym that is represented as 7 inches on a drawing with a scale of 1 in : 10 ft.

Each inch represents 10 feet, so 7 inches will represent ...

  7 × 10 ft = 70 ft

The gym is 70 ft wide.

__

Additional comment

You can also write and solve an equation that shows the measures are proportional:

  actual width / drawing width = (10 ft) / (1 in) = (gym width) / (7 in)

Multiplying both sides of this proportion by 7 in, we have ...

  gym width = (7 in) × (10 ft)/(1 in) = 7 × 10 ft = 70 ft

Answer:

You probably already got this answer

Step-by-step explanation:

!

Answer:

             x     +             6      ≥        15

Step-by-step explanation:

Add any number greater than equal to 9 to the number 6 and you get a result of at least 12. Any number less than 9 produces a result that is not at least 15.

Just saying the question was not that descriptive so I don't know if this is what you asked for... Sorry!

Answer:

434

Step-by-step explanation:

We can think of this problem like this:

\(\frac{percentage}{100} * number = newnumber\)

in this case, our percentage is 140, and our number is 310.

So lets plug in our values and solve!

\(\frac{140}{100} * 310 = newnumber\)

=

\(1.4*310 = newnumber\)

=

\(1.4*310 = 434\)
Hope this helps! :3

Note:

This formula can be changed depending on what your trying to find.

For instance, if you had one hundred and forty percent of what number is 310, we could rewrite this formula as:
\(\frac{100}{percentage}*number=newnumber\)

Which then would equal

\(\frac{100}{140}*310= \frac{310}{1.4}= 221.43\)

Hope this all helps! :3
if you have any other questions, feel free to let me know!

The end behavior of the graph of the polynomial function:

As x approaches ∞, y approaches -∞

As x approaches -∞, y approaches ∞

What is an end behavior?

The behavior of the function graph at the "ends" of the x-axis is known as the end behavior of a function, or f.

Here, we have

f(x) = –x⁵ + 9x⁴ – 18x³

F(x) is a fifth-degree (odd function ) with a negative leading coefficient

If the exponent is odd and the leading coefficient is negative then the end behavior is

As x approaches ∞, y approaches -∞

As you go on the right, f(x) goes down

As x approaches -∞, y approaches ∞

As you go on the left, f(x) goes up.

Hence, the end behavior of the graph of the polynomial function: As x approaches ∞, y approaches -∞

As x approaches -∞, y approaches ∞

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Check the picture below.

\(\sin( \theta )=\cfrac{\stackrel{opposite}{0.5}}{\underset{hypotenuse}{0.64}} \implies \sin^{-1}(~~\sin( \theta )~~) =\sin^{-1}\left( \cfrac{0.5}{0.64} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{0.5}{0.64} \right)\implies \theta \approx 51.4^o\)

Make sure your calculator is in Degree mode.

Answer:

A cylinder

Step-by-step explanation:

Shape A is a cone

Shape B is a cylinder

The coordinates of B after the rotation of 90 degrees about the origin is (c) (-5, 1)

The figure of the pentagon missing in the question is added at the end of this solution as an attachment

From the question, we have the following parameters that can be used in our computation:

Coordinate of point B = (1, 5)

Also, from the question, we have the transformation to be

Rotation of 90 degrees about the origin

Mathematically, the rotation of 90 degrees about the origin can be represented as

(x, y) → (-y, x)

Substitute the known values in the above equation, so, we have the following representation

Coordinate of point B after rotation = (-5, 1)

Hence, the coordinate of point B after the rotation is (c) (-5, 1)

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A library's design is scaled at  \(\frac{1}{3}\) inch = 1 feet. The library in the drawing is 12 inches height. The library's true height is 432 inches, or 36 feet.

Given that,

A library's design is scaled at  \(\frac{1}{3}\) inch = 1 feet.

The library in the drawing is 12 inches height.

We can take  \(\frac{1}{3}\) inch = 1 feet

1 inch=3 feet = 36 inches.

36 inches is the actual height .

Now actual height of the library is

Multiplication of the height of the library in the drawing is 12 inches and the new height 36 inches.

12\(\times\)36=432 inches

We can say 432 inches is equal to 36 feet.

Therefore, 432 inches or 36 feet is the actual height of the library.

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Answer:

77 Miles Per Hour

Step-by-step explanation:

Its that

Answer:

962.5 miles

Step-by-step explanation:

385 / 2 = 192.5

this is the amount per hour

192.5 times 5 = 962.5

Answer:

53 mph   and  71 mph

Step-by-step explanation:

bus 1 rate = x

bus 2 rate = x + 18

rate times time = distance

( x    +    x+18) * 6 = 744

(2x+18) * 6 = 744

2x + 18 = 124

2x = 106

x = 53       the other bus is  53 + 18 =  71  mph