At a NASCAR race, the lead car has 7 1/2 laps to go. Suddenly there is a caution flag, so all the racers must hold position while continuing at a reduced speed for 5/6 of a lap. When racing resumes, how many laps does the lead car have to go?

Answer:

it will have one real solution

Step-by-step explanation:

Answer:

m = 3

Explanation:

the slop is 3

The conversion of the unit centimeters to feet is written as 147 centimeters = 4.82283 feet.

Centimeters and feet are the units that are used for measuring the length of the any given parameter.

Conversion of the unit centimeter into feet is written as :

Value of  one centimeter =  0.0328084 feet.

To convert the given value 147 centimeters substitute in the given relation we have,

⇒ ( 147 × 1 ) centimeters = ( 147 ×  0.0328084 ) feet

⇒ 147 centimeters = ( 4.822835 ) feet

⇒  147 centimeters = ( 4.8228 ) feet ( Round upto four decimals )

Therefore, after conversion the measurements centimeters to feet we have 147 cm is equal to  ( 4.8228 ) feet ( Round upto four decimals ) .

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The required height of domino number 7 is 11.76 cm (rounded to two decimal places).

Arithmetic progression is the series of numbers that have common differences between adjacent values.

Here,
Since each subsequent domino is 13% taller than the one before, we can find the height of each domino by multiplying the height of the previous domino by 1.13.

Starting with the height of the smallest domino, we can calculate the height of each subsequent domino using this rule:

Height of domino n = Height of domino (n-1) × 1.13

Using this formula, we can find the height of each domino:

Height of domino 1 = 5.00 cm × 1.13 = 5.65 cm

Height of domino 2 = 5.65 cm × 1.13 = 6.38 cm

Height of domino 3 = 6.38 cm × 1.13 = 7.21 cm

Height of domino 4 = 7.21 cm × 1.13 = 8.16 cm

Height of domino 5 = 8.16 cm × 1.13 = 9.22 cm

Height of domino 6 = 9.22 cm × 1.13 = 10.41 cm

Height of domino 7 = 10.41 cm × 1.13 = 11.76 cm

Therefore, the height of domino number 7 is 11.76 cm (rounded to two decimal places).

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The gradient of the surface can be described as a vector.

The gradient of a surface, which is a vector, represents the size and direction of the sharpest increase in value at a certain location. The magnitude of this vector, which denotes the direction of the greatest rate of rise of the surface, indicates how steep the rise is. The influence of this gradient is felt along a surface, which is the difference. It stands in for a unit that is level with the ground.

In mathematics, the vector grad f(x,y,z) = (df/dx, df/dy, df/dz) represents the gradient of a three-variable function with scalar values, f(x,y,z). Variables like optimization and electromagnetism employ the gradient of a surface, which is a crucial notion in vector calculus. In particular, the gradient of a surface is frequently used to compute the normal vector to a surface or to identify the direction of the steepest rise or drop in a landscape.

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The error in the solution is that, In step 2, the Distributive Property was applied incorrectly.

Equations are mathematical expressions consisting of two or more variables and constants on two sides connected by an equal to sign.

Solution of the equation is the value of the variable that the equation holds true.

Given equation is,

8 - [tex]\frac{a}{2}[/tex] = 3 (4 - 5a)

Using the multiplication property of equality, multiplying whole equation by 2,

(2 × 8) - a = 6 (4 - 5a)

16 - a = 6 (4 - 5a)

Distributive property states that, for three numbers or expressions, a, b and c,

a (b + c) = ab + ac

Applying that,

6 (4 - 5a) = (6 × 4) - (6 × 5a) = 24 - 30a

But the student didn't multiply 6 with 5a, and thus he got 24 - 5a in step 2.

Hence the incorrect step is step 2 because of incorrect use of distributive property.

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Your question is a bit confusing. The complete question with an image is given below.

A student provided the steps for solving an equation. Which statement describes the error in the solution?

Equation : 8 - [tex]\frac{a}{2}[/tex] = 3 (4 - 5a)

Answer: look at the image for the answer and explanation

Step-by-step explanation:

The indefinite integral of cos(x) is sin(x) + C, and we can find the definite integral of cos(x) between two limits by evaluating sin(x) + C at the upper and lower limits and subtracting the results.

The integral of cos(x) is sin(x) + C, where C is the constant of integration.

The notation for the integral of cos(x) is ∫cos(x) dx, where the symbol ∫ represents the integral sign, cos(x) is the function being integrated, and dx represents the variable of integration, which in this case is x.

The antiderivative of cos(x) is sin(x), meaning that if we take the derivative of sin(x), we get cos(x). The constant of integration, C, is added because the derivative of a constant is always zero.

Therefore, the indefinite integral of cos(x) is sin(x) + C, and we can find the definite integral of cos(x) between two limits by evaluating sin(x) + C at the upper and lower limits and subtracting the results.

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Answer:

Step-by-step explanation:

1 yard = 1/2in shadow

Then 8ft = 192 * 1/2in

Then the radio tower is 192 yards (1 yard = 3 feet)

The radio tower = 576 feet

Answer:

Step-by-step explanation:

576

The number of ways the adults and the kids can be served is 831600

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

Volume = 1 gallon 3 pints

By conversion

1 gallon = 8 pints

So, we have

Volume = 8 pints +  3 pints

Volume = 11 pints

Also, we have

Adult = 2 cups

Kid = 1 cup

Convert to pints

Volume = 11 pints

Adult = 4 pints

Kid = 2 pints

The number of ways is then calculated as

Ways = 11!/(4! * 2!)

Evaluate

Ways = 831600

Hence, the number of ways is 831600

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The percentage of the increase in the cost of season tickets is 8%.

A ratio or value that may be stated as a fraction of 100 is called a percentage. Moreover, it is indicated by the symbol "%."

Given:

In the last year,

$2450 was the cost of the season ticket.

This year, the cost is $2,646.

Let n be the percentage in increase amount in the season ticket.

So, applying the percentage formula,

2646 - 2450 = (2450 x n/100)

196 = 2450 x n/100

19600 = 2450 x n

Applying cross multiplication,

we get,

n = 19600/2450

n = 8

Therefore, the required value of the percentage is 8%.

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Answer:

Step-by-step explanation:

(90 +100) / 2 = 190/2 = 95

Answer: The average rate of change from (-3,5) is 4.

Step-by-step explanation: This question is incomplete there a function is needed

So, suppose f(x) = 2x²-5

Given that, x= -3 to x= -5

let a = -3 and b=5

F(a) = F(-3) = 2(-3)²-5 = 13

F(b) = F(5) = 2(5)² -5 = 45

The transformed parent cube root function's equation is,

y = ∛(x-4) - 1.

The equation of the function is satisfied by all (and only those) points that lie on the graph of the function.

Hence, if a point fits on a function's graph, it must also fit the function.

The parent cube root function is transformed in the shown graph

The Parent cube root function is

y = ∛(x -h) - k

where the value of h  and k is equal to 0

h=0, k=0 in parent function

At (0,0) in the parent function, the graph changes orientation.

We can observe from the above graph that it changes direction at (4,-1) meaning it is moved 4 units to the right and 1 unit down.

So, the value of h=4  and value of k=1

The equation of the transformed function is,

y = ∛(x-4) - 1

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Answer: The new perimeter is 2334 inches.

Step-by-step explanation:

The way to find perimeter is 2L + 2W. The original length was 799 inches and 23 inches were added. 799 in. + 23 in. = 822 in. The width is 245 in. 2(822) + 2(245) = Perimeter. 1844 in. + 490 in. = 2334 in. is the Perimeter.

The slope of a line that is parallel to the line containing the points (3, 4) and (2, 6) is -2.

To find the slope of a line that is parallel to the line containing the points (3, 4) and (2, 6), we first need to find the slope of the line containing these points. We can use the slope formula:

m = (y2 - y1) / (x2 - x1)

Where:

m = slope

(x1, y1) = coordinates of the first point (3, 4)

(x2, y2) = coordinates of the second point (2, 6)

Substituting the given values, we get:

m = (6 - 4) / (2 - 3)

m = -2

The slope of the line containing the points (3, 4) and (2, 6) is -2.

Since we are looking for a line that is parallel to this line, the slope of the parallel line will also be -2.

Therefore, the slope of the parallel line is -2.

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The total cost for 10 hours of work would be 25 + 50(10) = 525.

Cost is the monitorial associated with the purchase of production of food or service if can include the prices of material of which is over it and other expenses that are related to the production of the code of service cost is a major fraction of when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.
The marginal cost of producing 5 items can be calculated using the equation C(x)=1300+4x/10. The marginal cost is the cost associated with producing one additional item. To calculate the marginal cost, we can plug in x=5 into the equation.

The equation in slope-intercept form for cost, c, after h hours of service is c = 25 + 50h.

The total cost for 8 hours of work would be 25 + 50(8) = 425.

The total cost for 10 hours of work would be 25 + 50(10) = 525.

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Answer:

Step-by-step explanation:

256. You can make this observation because they pattern has a rule that you multiply by 2 to get the next number.

Answer:

Another observation we can make about this number pattern is that each term is obtained by doubling the previous term. This means that the pattern is an example of exponential growth, where the growth factor is 2.

We can also observe that the sequence is a power of 2, where the first term is 2^2, the second term is 2^3, the third term is 2^4, and so on. In other words, the nth term in the sequence can be represented by the formula 2^(n+1).

Additionally, we can see that the sequence is an increasing sequence, where each term is greater than the previous one. This is because we are multiplying each term by 2, which means that each subsequent term will be twice as large as the previous one.

Answer:

About 16 years

Step-by-step explanation:

The formula for compound interest is

[tex]P(t)=P_{0}(1+r/n)^n^t[/tex], where P0 is the principal, r is the interest rate, n is the number of compounding periods, and t is the time in years.

For this problem, our n = 12 because there are 12 months in a single year and we must convert our percentage to a decimal (3.60/100 = 0.0360): [tex]7000=4000(1+0.0360/12)^1^2^t\\7000=4000(1.003)^1^2^t\\1.75=1.003^1^2^t\\log(1.75)=log(1.003)^1^2^t\\log(1.75)=12t*log(1.003)\\\frac{log(1.75)}{log(1.003)} =12t\\1/12*\frac{log(1.75)}{log(1.003)}=t\\ 15.56818868=16=t[/tex]

Answer:

8x8 > 9x7 (64 > 63)

Step-by-step explanation:

The three internal angles of the triangle are α = 21.3°, β = 139.7°, and θ = 88.9°.

We can use the Law of Cosines to solve for the angles of the triangle:

cos(α) = (b² + c² - a²) / (2bc)

cos(β) = (a² + c² - b²) / (2ac)

cos(θ) = (a² + b² - c²) / (2ab)

Substituting the values given in the problem, we get:

cos(α) = (12.2² + 50.6² - 18.5²) / (2 x 12.2 x 50.6) = 0.929

α = cos⁻¹(0.929) = 21.3°

cos(β) = (18.5² + 50.6² - 12.2²) / (2 x 18.5 x 50.6) = -0.777 (note the negative value)

β = cos⁻¹(-0.777) = 139.7°

cos(θ) = (18.5² + 12.2² - 50.6²) / (2 x 18.5 x 12.2) = 0.056

θ = cos⁻¹(0.056) = 88.9°

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A for loop in MATLAB allows a user to repeatedly execute a set of instructions for a specific number of times or until a specified condition is met.

In MATLAB, a for loop is a control structure that allows users to repeatedly execute a block of code a specific number of times or until a specific condition is met. The loop variable takes on a sequence of values specified by the user, and the statements within the loop are executed for each value of the loop variable.

For loops are a powerful tool in MATLAB for automating repetitive tasks and iterating over arrays and matrices, among other uses. They can help streamline complex computations and make code more efficient and easier to read.

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The weight of th baby elephant in the month of March would be 247.5 Kg.

Weight of a body is the force exerted by the earth on the body on the surface of the earth towards its center.

Given is that in January a baby elephant weighs 180kg. By March the weight of the baby elephant had increased by ⅜.

Assume the weight of the baby elephant in March would be {x} Kg. We can write -

{x} = 180 + 3/8 of 180

{x} = 180 + 3/8 x 180

{x} = 180 + 67.5

{x} = 247.5 Kg

Therefore, the weight of th baby elephant in the month of March would be 247.5 Kg.

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Answer:

x = [tex]\frac{1}{19}[/tex]

Step-by-step explanation:

2 = 19x + 1  Subtract 1 from both sides

2 - 1 = 19x + 1 - 1

1 = 19x  Divide both sides by 19

[tex]\frac{1}{19}[/tex] = [tex]\frac{19x}{19}[/tex]

[tex]\frac{1}{19}[/tex] = x

The instantaneous rate of change calculator is the tool that displays the rate of change

The change in the rate at a certain point is referred to as the instantaneous rate of change in mathematics. It is equivalent to the rate of change in a function's derivative value at a particular location. The obtained graph is identical to the slope of the tangent line if a graph for the instantaneous rate of change at a particular point is drawn.

A free online tool known as the Instantaneous Rate of change calculator shows the rate of change, the first-order differential equation for the specified function. This tool speeds up the calculation and shows the rate of change at a particular position in a split second. With time, the tool is now widely accepted and is often used is variety of calculations.

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It is proved that x⁻¹/(x⁻¹ + y⁻¹) + x⁻¹/(x⁻¹ - y⁻¹) = 2y²/(y² - x²).

What is an equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions written on the left and right sides. We have LHS = RHS (left-hand side = right-hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it contains no "equal to" symbol. It will be regarded as a phrase.

Given that

x⁻¹/(x⁻¹ + y⁻¹) + x⁻¹/(x⁻¹ - y⁻¹) = 2y²/(y² - x²)

Now solve the left-side expression:

L.H.S =

x⁻¹/(x⁻¹ + y⁻¹) + x⁻¹/(x⁻¹ - y⁻¹)

Now apply the formula a⁻¹ = 1/a:

= (1/x)/(1/x +1/y) + (1/x)/(1/x - 1/y)

= (1/x)/((x+y)/xy) + (1/x)/((y-x)/xy)

Now taking common  (1/x)/(1/xy):

= (1/x)/(1/xy)[1/(x+y) + 1/(y-x)]

= (xy)/(x)[(y - x + x + y)/(x+y) (y-x)]

= y[2y/(x+y) (y-x)]

Applying the algebraic identity (x - y)(x + y) = x² - y²:

= 2y²/(y² - x²)

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To calculate the value of g we have to multiply the G( universal gravitational constant) and M( mass of body) divide by R square.

Earth's acceleration caused by gravity, or the magnitude of g, is 9.8 m/s2. According to this, an item falling freely on Earth would accelerate by 9.8 metres per second. The gravity of the Earth is to blame for this acceleration.

The acceleration due to gravity formula is given by

[tex]g = \frac{GM}{R^2}[/tex]

Where,

G is the universal gravitational constant, G = 6.674×10-11m3kg-1s-2.

M is the mass of the massive body measured using kg.

R is the radius of the massive body measured using m.

g is the acceleration due to gravity measured using m/s2.

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The length of side x in simplest radical form with a rational denominator is   [tex]\sqrt{3} /2[/tex].

What is the equilateral triangle?

In an equilateral triangle, all sides are equal in length.

That means that all the angles of the triangle will be congruent.

Since a triangle has 3 angles that always add up to 180 degrees, each angle is 60 degrees.

Therefore, the hypotenuse of the equilateral triangle is 1.

So,

[tex]x = 1 * sin60[/tex]°

[tex]x = 1 * \sqrt{3} /2\\x = \sqrt{3} /2[/tex]

Hence, The length of side x in simplest radical form with a rational denominator is   [tex]\sqrt{3} /2[/tex].

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Answer:

a8

Step-by-step explanation:

Here you go.

nth term is ar^n-1

Answer:

I'd say the first and third options would be correct.

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

If it is a fair spinner then

First option is true

second option is true

third option cannot be determined from info given  

4th option is true