A bus averages 60 mi/h traveling to its destination in the first half of its trip through an expressway and 72 mi/h in the second half traveling through a motorway. What is the bus's average speed for the entire trip rounded to the nearest tenth?
A) 64.2 mi/h
B) 63.0 mi/h
C) 65.5 mi/h
D) 66.0 mi/h

Using the trigonometric tangential function, the height of the tree casting a 26-meter shadow at an angle of elevation of 24° is approximately 11 meters.

The given problem can be solved by applying trigonometric principles, specifically the tangent function. In this case, we know the shadow length (26m) and the angle of elevation of the sun (24°). The height of the tree is the side opposite the angle, and the shadow is the adjacent side. Thus, we can use the tangent equation (Tan θ = Opposite/Adjacent). So, Tan 24° = Height of the tree / 26m. By cross multiplying and evaluating Tan 24°, we get the height of the tree to be approximately 11 meters.

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It would take Brian 20 hours to build the model car on his own.

To determine the time it would take Brian to build the model car on his own, we can follow these steps:

1. Let's denote the time it takes John to build the model car as J hours.

2. Since it takes Brian 15 hours longer than John, we can express the time it takes Brian as J +15 hours.

3. If they work together, they can build the model car in 4 hours. This means that in 1 hour, they complete [tex]\(\frac{1}{4}\)[/tex] of the job together.

4. In 1 hour, John completes [tex]\(\frac{1}{J}\)[/tex] of the job, and Brian completes [tex]\(\frac{1}{J + 15}\)[/tex] of the job.

5. So, the equation representing the rate at which they work together is:

[tex]\[ \frac{1}{J} + \frac{1}{J + 15} = \frac{1}{4} \][/tex]

6. Now, we solve this equation to find J, the time it takes John to build the model car on his own.

7. Once we find J, we can find J+15  which represents the time it takes Brian to build the model car on his own.

So, the equation representing the rate at which they work together is:

[tex]\[ \frac{1}{J} + \frac{1}{J + 15} = \frac{1}{4} \][/tex]

To solve this equation, we can multiply both sides by the least common denominator, which is [tex]\( 4J(J + 15) \)[/tex], to clear the fractions:

[tex]\[ 4(J + 15) + 4J = J(J + 15) \][/tex]

Expanding and simplifying:

[tex]\[ 4J + 60 + 4J = J^2 + 15J \]\[ 8J + 60 = J^2 + 15J \]\[ J^2 + 15J - 8J - 60 = 0 \]\[ J^2 + 7J - 60 = 0 \][/tex]

Now, we have a quadratic equation. We can solve this equation using factoring, completing the square, or the quadratic formula. Let's use factoring:

[tex]\[ (J - 5)(J + 12) = 0 \][/tex]

Setting each factor equal to zero:

[tex]\[ J - 5 = 0 \] or \( J + 12 = 0 \)[/tex]

Solving each equation:

[tex]For \( J - 5 = 0 \), we get \( J = 5 \).For \( J + 12 = 0 \), we get \( J = -12 \).[/tex]

Since time cannot be negative, we discard the negative solution.

Now that we have found J=5 hours, which represents the time it takes John to build the model car on his own, we can find [tex]\( J + 15 = 5 + 15 = 20 \)[/tex] hours.

(x+1)^2-x^2=23

x^2+2x+1-x^2=23

2x+1=23

2x=22

x=11

11^2 = 121

x+1 =12

12^2=144

144-121 = 23

Answer:

answer is D ;)

Step-by-step explanation:

x = ones

y = fives

x+y = 14 total bills

 rewrite as x = 14-y

1x +5y = 50

1(14-y) +5y = 50

14-1y +5y = 50

14 +4y = 50

4y = 36

 y = 36/4 = 9

 x = 14-y = 14-9 = 5

 9+5 = 14

9x5 = 45 +5x1 = 50

 he had 9 fives and 5 ones

Answer:

There were 5 bills of '1' and 9 bills of '5'.

Step-by-step explanation:

let the number of '1' bill be x

let the number of '5' bill be y.

Total number of bills = 14

x + y = 14 ..[1]

Worth of 14 bills = 50

So,[tex]x\times 1+y\times 5=\$50[/tex]

[tex]x+5y=50[/tex]..[2]

x + y = 14

x = 14 - y

Putting value of x in [2]:

[tex]14- y +5y=50[/tex]

[tex]y=\frac{50-14}{4}=9[/tex]

y = 9

x = 14-y = 14 - 9 = 5

There were 5 bills of '1' and 9 bills of  '5'.

Answer:

For f(x)=2x² graph, the answer is A.

Step-by-step explanation:

The answer is 5 units on e2020.

To find the rate of change of height with respect to time, we use the formula dh/dt = dV/dt / (πr²) and substitute the given values for the rate of volume change and the radius.

We have the rate of volume change as 23 cm³/sec and the cylinder has a radius of 12 cm. Note that the typo '2323 cm³/sec' and '1212 cm' should be read as '23 cm³/sec' and '12 cm,' respectively.

The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. To find the rate at which the height h changes over time, we can take the derivative of the volume with respect to time, which gives us dV/dt = πr² dh/dt. We can solve this equation for dh/dt (the rate of change of height with respect to time) by dividing both sides by πr² and substituting the given values. Therefore, dh/dt = dV/dt / (πr²).

Substituting the values, we get:

dh/dt = 23 cm³/sec / (π * (12 cm)²)

Upon simplifying, we will obtain the rate at which the height of the water is decreasing in cm/sec.

Answer:  A. Horizontal compression by factor 1/3, vertical stretch by factor 2, then a reflection through the x-axis

Step-by-step explanation:

Since, If there is a function, y= a cos bx

Then a shows vertical stretch while b shows horizontal compression.

Here, Given function, y= cos x

After transformation, It is giving y = -2 cos 3x

therefore here is a horizontal compression occurs with factor 1/3.

Also Negative sign shows there also did reflection through x-axis.

And, It also, stretched vertically by factor 2. ( also shown in the below graph)

Thus, Option A) is correct.      

I think it is C

BMK ><

Answer:

c)720

Step-by-step explanation:

The mean of a set of credit scores is u=690 and o=14.

mean = 690  and standard deviation SD = 14

We use z- score formula

[tex]z=\frac{x-mean}{SD}[/tex]

z= 3.3 given

Plug in the values and find out x

[tex]3.3=\frac{x-690}{14}[/tex]

Multiply 14 on both sides

46.2 = x- 690

Now add 690 on both sides

x= 736.2

Credit score is 720 that comes under 736.2

So answer is 720

Answer:

B. 0.813

Step-by-step explanation:

A sixteen-sided number cube has the numbers 1 through 16 on each face.

So, [tex]|\ S\ |=16[/tex]

Let us assume that, A be the event that the number will be an even number. So,

[tex]A=\left \{ 2,4,6,8,10,12,14,16 \right \}[/tex] and [tex]|\ A\ |=8[/tex]

Then,

[tex]P(A)=\dfrac{|\ A\ |}{|\ S\ |}=\dfrac{8}{16}[/tex]

Let us assume that, B be the event that the number will be an odd prime number.

[tex]B=\left \{3,5,7,11,13 \right \}[/tex] and [tex]|\ B\ |=5[/tex]

Then,

[tex]P(B)=\dfrac{|\ B\ |}{|\ S\ |}=\dfrac{5}{16}[/tex]

So the probability that you will roll an even number or an odd prime number will be,

[tex]P(A\cup B)=P(A)+P(B)-P(A\cup B)[/tex]

[tex]=\dfrac{8}{16}+\dfrac{5}{16}-0[/tex] ( as independent events)

[tex]=\dfrac{13}{16}[/tex]

[tex]=0.813[/tex]

Answer:

B

Step-by-step explanation:

Step 2 he wrote distributive instead of associative

Given the provided motion physics model and using the quadratic formula, it is determined that it would take approximately 3.79 seconds for the basketball to go into the hoop after it was thrown.

The subject in consideration here is a problem related to quadratic equations in motion physics. The equation given in the question signifies a model of the height of the basketball as a function of time in the format of a quadratic equation. The equation is h = -16t² + 23t + 7.

With this equation, we can apply the quadratic formula to find the amount of time it takes for the ball to reach the hoop.

Upon using the quadratic formula, two solutions come up, t = 3.79 s and t = 0.54 s. The ball is at a height of 10 m at two times during its trajectory—once on the way up (as it rises) and once on the way down (as it falls). Since the question is about the time the ball goes into the hoop after reaching its maximum height and coming down, the larger value of t (3.79s) is considered as the valid solution.

Therefore, the time it takes for the basketball to go into the hoop after it was thrown is approximately 3.79 seconds which is not an offered option.

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The first step to solve for x in the given algebra using properties of equality is; Add 5 to both sides.

We want to simplify the algebraic expression;

3.7 = x + (-5)

When dealing with algebra like this, what we have to first do is to balance both sides of the equation.

To solve this particular algebra problem, we will use additional property of equality by adding 5 to both sides to get;

3.7 + 5 = x + (-5) + 5

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The first step to solving the expression 3.7 = x + (- 5) is,

''Add 5 to both sides''

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to give that,

An algebraic expression to simplify,

⇒ 3.7 = x + (- 5)

Now, Simplify the expression by combining like terms as,

⇒ 3.7 = x + (- 5)

⇒ 3.7 = x - 5

Use the additional property of equality by adding 5 to both sides to get;

3.7 + 5 = x + (-5) + 5

8.7 = x

x = 8.7

So, the first step is, ''Add 5 to both sides''.

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