At 12.30 p.m, a car overtook a van along an expressway. The car and the van were travelling at
average speeds of 90Km/h and 70 Km/h respectively. After 1/2 hour the speed of the car
was reduced by 10 km/h. How far apart were the two vehicles at 2 .00 p.m?

Answer:

-4x+19

Step-by-step explanation:

Otherwise known as option B :D

The solution to the system of equations y=-3x+5 and 2x+y=6 is (x,y) = (-1,8).

To solve the system of equations using substitution, we can substitute the expression for y in the second equation with the expression for y in the first equation:

2x + y = 6

2x + (-3x + 5) = 6 (substitute y = -3x + 5)

2x - 3x + 5 = 6

-x + 5 = 6

-x = 1

x = -1

Now that we have found the value of x, we can substitute it back into either of the original equations to find the value of y:

y = -3x + 5

y = -3(-1) + 5

y = 8

We can check our solution by verifying that it satisfies both equations:

y = -3x + 5 => 8 = -3(-1) + 5 => 8 = 8 (true)

2x + y = 6 => 2(-1) + 8 = 6 => 6 = 6 (true)

Thus, our solution is correct.

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[tex]f(2) = g(2) = 4[/tex], which means that the graphs of the two functions intersect at x = 2.

To show that the graphs of the functions   [tex]f(x) = 2^x[/tex] and [tex]g(x) = \sqrt(4x + 1) + 1[/tex]  intersect at the abscissa point x = 2, we need to show that both functions have the same value at  [tex]x = 2.[/tex]

First, we evaluate f(2):

[tex]f(2) = 2^2 = 4[/tex]

Next, we evaluate g(2):

[tex]g(2) = \sqrt(4(2) + 1) + 1 = \sqrt9 + 1 = 4[/tex]

Therefore,  [tex]f(2) = g(2) = 4[/tex] , which means that the graphs of the two functions intersect at [tex]x = 2[/tex] .

To visualize this, we can plot the two functions on the same set of axes:

As we can see from the graph, the two curves intersect at the point (2, 4).

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The complete question is: How can you show that the graphs of the functions f(x) = [tex]2^x[/tex] and g(x) = √(4x + 1) + 1 intersect?

The probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes is only 0.02%.

P(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X = k) = (100 choose k) * 0.078^k * (1 - 0.078)^(100-k)

P(X <= 4) = (100 choose 0) * 0.078^0 * (1 - 0.078)^(100-0) + (100 choose 1) * 0.078^1 * (1 - 0.078)^(100-1) + (100 choose 2) * 0.078^2 * (1 - 0.078)^(100-2) + (100 choose 3) * 0.078^3 * (1 - 0.078)^(100-3) + (100 choose 4) * 0.078^4 * (1 - 0.078)^(100-4)

Using a calculator or software, we can find that:

P(X <= 4) = 0.000203

This means that the probability is 0.02%.

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Charges for TV advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is the percentage of population of 110 million TV households.The CBS television show 60 minutes recently had a rating of 7.8, indicating that 7.8% of the household were tuned to that show.An advertiser conducts an independent survey of 100 households and finds that only 4 were tuned to 60 minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes.Does the result suggest that the rating of 7.8 is too high?

Answer:

30%

Step-by-step explanation:

The areas of the trapezoids is,

A = 48 sq units.

Since, The formula to find the area of a trapezoid of a trapezoid is,

⇒ A = 1/2(b₁ + b₂ )h.

Hence, it is stated that the height of each unit is 2.

Now let's substitute the variables in the formula with the actual bases and heights as;

A = 1/2(8 + 4)8,

A = 6 × 8,

A = 48 sq units.

Thus, the areas of the trapezoids is,

A = 48 sq units.

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Answer: I believe the only option would be Length.

The length determines the distance between the two endpoints.

I can't think of a reason why you'd need to use height or width when measuring a line on a graph. Besides if it were height, it'll just be the length of the line when vertical. And all generated graphed lines have the same width. You wouldn't need to measure it.

Hopefully it's correct.

Answer:

Triangle P has been rotated clockwise by 90° about the point (0,0).

PLEASE MARK IT THE BRAINLIEST!!!!

The perimeter of the composite figure is 46 metres.

The perimeter of a figure is the sum of the whole sides of the 2 dimensional figure. Therefore, the perimeter of the composite figure is the sum of the whole sides.

Therefore, the perimeter of the figure can be found as follows:

perimeter of the shape = 5 + 6 + 9 + 11 + 3 + 12

perimeter of the shape = 11 + 9 + 11 + 15

perimeter of the shape =20 + 11 + 15

perimeter of the shape = 31 + 15

perimeter of the shape = 46 metres

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The rule used to obtain the transformed function is given as follows:

g(x) = -0.5f(x).

Examples of transformations are given as follows:

The parent function in this problem is given as follows:

f(x).

The parent function is reflected across the x-axis, hence:

g(x) = -f(x).

The parent function is also compressed by a factor 0.5, hence:

g(x) = -0.5f(x).

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The graph of the function g(x) has an equation of g(x) = 6√(x - 3)

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

f(x) = 3√x

The transformed function g(x) is given as

g(x) = 2f (x − 3)

In f(x) = 3√x , we have

f(x - 3) = 3√(x - 3)

Multiply both sides by 2

So, we have

2f(x - 3) = 2 * 3√(x - 3)

Evaluate the products

2f(x - 3) = 6√(x - 3)

Recall that

g(x) = 2f (x − 3)

So, we have

g(x) = 6√(x - 3)

This means that the graph of the function g(x) has an equation of g(x) = 6√(x - 3)

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An equation for L, in terms of t, representing the amount Kadeesha owes her friend after t weeks is L = 8t + 120.

The table of values is as follows;

Number of Weeks               Amount of Money Owed

0                                                    $120

1                                                    $128

2                                                    $136

3                                                    $144

In order to write a linear equation to describe this situation, we would assign variables to the amount of money that Kadeesha borrowed originally and the number of weeks respectively, and then translate the word problem into a linear equation as follows:

Since Kadeesha originally borrowed $120 and agreed to pay back her friend $8 per week, a linear equation which can be used to model the total amount of money that Kadeesha owed is given by;

L = 8t + 120

When t = 0, the value of L is given by;

L = 8(0) + 120

L = $120.

When t = 1, the value of L is given by;

L = 8(1) + 120

L = $128.

When t = 2, the value of L is given by;

L = 8(2) + 120

L = $136.

When t = 3, the value of L is given by;

L = 8(3) + 120

L = $144.

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The measure of angle JKM is 26°

The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the opposite angles in the triangle.

Also the sum of angle in a triangle is 180°

Therefore ;

3x+64 = 5x+4

collecting like terms

5x -3x = 64-4

2x = 60

x = 60/2

x = 30

since x = 30

value of the exterior angle = 5x+4

= 5×30+4

= 150+4 = 154

therefore angle JKM = 180-( 154)

= 26°

Therefore the measure of angle JKM is 26°

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Answer:   is d

Step-by-step explanation:

well it is just     3 times 3 times 3 times 3

We need to use equations C and D:

C. 4 ÷ 12 = 1/3

D. 16 ÷ 12 = 4/3

We need to divide the total amount of pasta by 12. Therefore, we need to use equations C and D:

C. 4 ÷ 12 = 1/3

D. 16 ÷ 12 = 4/3

Equation C shows that each serving is 1/3 of a pound

Equation D shows that Mariana can make 4/3 servings

Therefore, Mariana can make 4/3, or approximately 1.33, servings of 12 pounds each.

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Answer: w(t) = 60 * 4^(t-1).

Step-by-step explanation:

The given ordered pairs model an exponential function of the form w(t) = ab^t, where w is the function name, t is the input variable, a is the initial value, and b is the growth factor.

From the first ordered pair (1, 60), we can see that the initial value a is 60. From the second and third ordered pairs (2, 240) and (3, 960), we can see that the output value is multiplied by 4 when the input value increases by 1. This means that the growth factor b is 4.

So, the function equation in sequence notation is w(t) = 60 * 4^(t-1).

a) over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.

b) the average temperature of the water in the system is 1527.

c) over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.

a) g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt

g'(-3) = -2

b) The absolute maximum value of g on the closed interval [-5, 5]=

10 + 2√7.

c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.

What is right Riemann sum formula?

The right Riemann sum formula uses the right-most value of each interval as the value of the function over that interval.

a) g(5) = 2(5) + [tex]\int\limits^5_0[/tex] ƒ(t) dt

= 10 + 2√7

g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt

g'(-3) = 2 + [tex]\int\limits^3_0[/tex]ƒ'(t) dt

= 2 - (4 + 0)

= -2

b) The absolute maximum value of g on the closed interval [-5, 5]=

10 + 2√7.

This is because the highest value of ƒ(t) dt on the interval= 4√7, which occurs at x = 2.

The highest value of g is thus given by 10 + 2√7.

c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.

This is because ƒ'(t) dt is undefined at these points, so the second derivative of g is also undefined.

a) To evaluate the  S'(t) dt, we need to calculate the area under the curve of the temperature data given in the table. To do this, we use the trapezoidal rule. This gives us the following:

[tex]\int\limits^10_0[/tex] S'(t) dt = [(142 + 210 + 254 + 280 + 274 + 268)/2] × 8

= 17,088

This means that over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.

This can be interpreted in the context of the problem as the average rate at which the temperature of the water in the solar steam power system is changing over the given time interval.

b) To approximate the average temperature of the water in the system using a right Riemann approximation, we need to calculate the area under the curve of the temperature data given in the table. We can do this using the right Riemann sum formula, which gives us the following:

Right Riemann Approximation = [(210 + 254 + 280 + 274)/4] × 6 = 1527

In this case, the right-most value of each interval is lower than the true average over that interval, so the approximation will be lower than the true average.

c) To determine the total change in the temperature of the system for the interval 10≤t≤20, we need to calculate the area under the curve of the equation S'(t)=-√2xe (√x²-100)/x.

This can be done using the definite integral of the equation, which gives us the following:

Total Change = ∫1020-√2xe (√x²-100)/x dx

= -14,351

This means that over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.

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Answer:

(A.)

Step-by-step explanation:

you just have to follow the order that there going in so when they say less than you use the less than sign

Note that adding one pair does not make the table a function. This is why it is trickly. For the table to be a function, each value of x must be related to only one unique value of y and vice versa.

For the table to become a function, we must eliminate any repeated ordered pairs such as (3, 8) and (7, 8)

For example, we can say (3, 6) and (7, 8) then pick the last to be (5, 10)

So the table becomes a function when you have:

X    Y

6     0

3     6

9     12

7     8
5     10

The word linear function in mathematics refers to two separate but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.

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Answer:

Slope = 14.000/2.000 = 7.000 x-intercept = 3/7 = 0.42857 y-intercept = -3/1 = -3.00000

y intercept = -3

slope = 7/1

The probability that a customer who visited any of the three website designs made a purchase is 4.5%.

To find the probability that a customer who visited any of the three website designs made a purchase, we need to find the average probability of purchase across all three designs.

We can do this by taking the mean of the three probabilities:

Mean probability = (4.5% + 5.2% + 3.8%) / 3

= 13.5% / 3

= 4.5%

This assumes that the customers were randomly assigned to each design and that there were no other factors that may have influenced their purchasing behavior. Additionally, the sample size and duration of the experiment may also affect the accuracy of the results.

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Answer:Therefore, f(-x) = -x^3 - 3x^2 - 2x + 2.

Step-by-step explanation:o find f(-x), we replace every instance of x in the function f(x) with -x:

f(-x) = (-x)^3 - 3(-x)^2 + 2(-x) + 2

Simplifying, we get:

f(-x) = -x^3 - 3x^2 - 2x + 2

The recursive formula for the geometric sequence is given as follows:

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The first term of the sequence is given as follows:

[tex]a_1 = -\frac{1}{8}[/tex]

Each term is the previous term multiplied by two, hence the common ratio is given as follows:

q = 2.

Then each term is the previous term multiplied by two, and the recursive rule is given as follows:

[tex]a_n = 2a_{n - 1}[/tex]

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Answer:

Step-by-step explanation:

V = πr²h

h = V/(πr²)

V = 42 gal

42 gal x 3.7854 l/gal = 158.987 l

158.987 l = 158,987 ml = 158,987 cm³

r = 18/2 = 9 in

9 in x 2.54 cm/in = 22.86 cm

h = (158987 cm³) / π(22.86 cm)² ≈ 96.82 cm

depending on how you round, the more precise answer is 96.8285 ≈ 96.83

Answer: 6s + 10n less than or equal to 90

To the nearest mile, the distance that Marcus ran is 6 miles.

To calculate the total distance that Marcus ran in the morning, we will sum up the distance for all the routes that he ran.

From the map, the distances that Marcus ran are as follows:

1 inches + 3 inches + 2 inches + 3 inches

= 8.3 inches

The scale then shows that 4 inches equal 3 miles. Now, we convert 8.3 inches to miles and this gives us:

8.3 inches × 3 miles/4 inches

= 6.225

To the nearest miles, this is 6 miles.

Complete Question:

Marcus looked up the path that he had taken on his run this morning on the map shown below.

To the nearest mile, what is the total distance that he ran?

6 miles

8 miles

11 miles

25 miles

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The value of the container's contents is approximately $983.25

To find value of the contents, we must calculate its volume first.

Volume = length x width x height

Volume = 4.5 ft x 11.5 ft x 10.5 ft

Volume = 534.375 cubic feet

The container is full and its contents have a volume of 534.375 cubic feet. If its contents weigh 0.4 pounds per cubic, then, total weight of the contents is:

= Volume x Weight per cubic foot

= 534.375 cubic feet x 0.4 pounds per cubic foot

= 213.75 pounds

If the contents are worth $4.60 per pound on average, then the total value of the contents is:

= Weight x Value per pound

= 213.75 pounds x $4.60 per pound

= $983.25.

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