What is the largest integer value less than 169?

Answer:

Step-by-step explanation:

Answer:

A=6

Step-by-step explanation:

M=3A

M+6=2(A+6)     M+6=2A+12      M=2A+6

System of equations:

M=3A            Subtract

M=2A+6

0=A-6

A=6

Let x be the speed of Santa's sleigh in still air and y be the speed of the wind. We can use the formula d = rt, where d is the distance traveled, r is the speed at which the sleigh is traveling, and t is the time elapsed, to find x and y.

For the first case, where Santa is flying with the wind, the distance traveled is 35 miles, the time elapsed is 5 minutes, and the speed of the sleigh is x + y. Since there are 60 minutes in an hour, the time elapsed in hours is 5 minutes / 60 minutes/hour = 1/12 hours. So, we can write the equation 35 miles = (x + y) * (1/12 hours). Solving for x + y, we get x + y = 35 miles / (1/12 hours) = 420 miles/hour.

For the second case, where Santa is flying against the wind, the distance traveled is 35 miles, the time elapsed is 7 minutes, and the speed of the sleigh is x - y. Since there are 60 minutes in an hour, the time elapsed in hours is 7 minutes / 60 minutes/hour = 7/60 hours. So, we can write the equation 35 miles = (x - y) * (7/60 hours). Solving for x - y, we get x - y = 35 miles / (7/60 hours) = 300 miles/hour.

We can solve for x and y by equating the expressions for x + y and x - y and then solving for x and y. Since x + y = 420 miles/hour and x - y = 300 miles/hour, we can add these equations together to get 2x = 720 miles/hour. Dividing both sides of the equation by 2, we get x = 360 miles/hour. We can then substitute this value for x into the equation x + y = 420 miles/hour to solve for y, giving us y = 420 miles/hour

For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The value of e and f is -34 and 2 respectively.

What is a system of equations?

Inconsistent System

For a system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

For the given system of equations, the value of e will be -34, while the value of f will be 2.

Hence, the value of e and f is -34 and 2 respectively.

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Answer:

he value of e and f is -34 and 2

The graph of 3x-2y≤6 is the third graph, for 3x-2y<6 is the first graph, for 3x-2y>6 is the fourth graph and for 3x-2y≥6 is the second graph. The solution has been obtained using concept of linear inequality.

What is linear inequality?

A linear inequality is one that would produce a linear equation if the equals relation were used instead of the inequality. When multiplying or dividing both sides by a negative number in order to solve the inequality, the direction of the inequality is reversed. The entire set of solutions to an inequality is known as the solution set.

We are given for graphs, of which two graphs are dotted and two are simple straight line graphs.

The dotted graphs are drawn for the inequalities having < or >

Whereas the simple straight line graphs are drawn for the inequalities having ≤ or ≥.

Now, to notice the shaded pattern, we will see whether the equations are true for (0,0) or not

1. 3x-2y≤6

⇒ 0≤6

So, the equation is true for the point.

Hence, the third graph represents this equation.

2. 3x-2y<6

⇒ 0<6

So, the equation is true for the point.

Hence, the first graph represents this equation.

3. 3x-2y>6

⇒ 0>6

So, the equation is false for the point.

Hence, the fourth graph represents this equation.

4. 3x-2y≥6

⇒ 0≥6

So, the equation is false for the point.

Hence, the second graph represents this equation.

Hence, the graphs are matched with the inequalities.

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Since, there are multiple questions so, the question answered above is attached below.

Answer:

28 km

Step-by-step explanation:

The decay rate of a certain new cell phone is 0.333

For given question,

The average lifetime of a certain new cell phone is three years.

The manufacturer will replace any cell phone failing within two years of the date of purchase.

Also, the lifetime of these cell phones is known to follow an exponential distribution.

We need to find the decay rate.

We know that an exponential decay is the process of reducing an amount by a consistent percentage rate over a period of time.

since the average lifetime of a certain new cell phone is three years, the decay rate would be 1/3 = 0.333

Therefore, the decay rate of a certain new cell phone is 0.333

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Answer:

The scale factor is 1.25 !

Step-by-step explanation:

Take the sides of one triangle and divide them by the sides of the other triangle.

45/36 = 1.25

30/24 = 1.25

35/28 = 1.25

312.5 μCi is equivalent to 0.3125 mCi.

Conversion factors refer to a relationship between the value in one unit to the value in another unit. It is used to convert a quantity expressed in one unit to another unit.

The following conversion factors are needed to convert 312.5 μCi to millicuries (mCi):1 mCi = 1000 μCiUsing the above conversion factor, we can write the given value of 312.5 μCi as:312.5 μCi = (312.5/1000) mCi= 0.3125 mCi

Therefore, the value of 312.5 μCi can be converted to millicuries (mCi) using the above conversion factor. We can rearrange the formula as shown below.312.5 μCi × 1 mCi / 1000 μCi= (312.5/1000) mCi= 0.3125 mCi

Therefore, 312.5 μCi is equivalent to 0.3125 mCi. The calculation can be summarized in a sentence as follows: To convert 312.5 μCi to millicuries (mCi), we use the conversion factor 1 mCi = 1000 μCi.

The calculation shows that 312.5 μCi is equivalent to 0.3125 mCi. The answer can be expressed as follows: 312.5 μCi = 0.3125 mCi.

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Answer:

105

Step-by-step explanation:

we can draw the line (9 cm) perpendicular to the line (11 cm)

so we get a rectangle and a right triangle

the area of the rectangle :

A = length * width

A = 15 * 6

A = 90

the base of the right triangle = 15 - 9 = 6

the height of the right triangle = 11 - 6 = 5

the area of the right triangle :

A = 1/2*base*height

A = 1/2*6*5

A = 15

the Area of the shape = area of rectangle+area of right triangle

the Area of the shape = 90+15

A = 105

a. The equator has the smallest circumference of all the circles of latitude or longitude.

The equator is an imaginary circle that is located at 0 degrees latitude and circles the Earth's surface at its widest point. Since the Earth is roughly spherical in shape, the equator represents the largest circle of latitude. However, it has the smallest circumference of all the circles of latitude or longitude because it is located at the widest point of the Earth, and its radius is equal to the Earth's radius.

In contrast, the circles of latitude and longitude located at higher latitudes have smaller radii and therefore larger circumferences than the equator. Similarly, circles of latitude and longitude located at lower latitudes have larger radii and smaller circumferences than the equator. Therefore, the equator has the smallest circumference of all the circles of latitude or longitude on the Earth's surface.

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Answer:

2.14

Step-by-step explanation:

Answer: 85%

Step-by-step explanation:

percentage increase/decrease formula: new-old/old x 100

122914-66440/66440x100=85

Answer:

No

Step-by-step explanation:

When \(x=2\), \(y=-6(2)=-12\), not \(4\).

Answer:

-5

Step-by-step explanation:

The slope of the line is found by

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

   = ( -12.5 - -2.5)/( 7.3 - 5.3)

    = ( -12.5 +2.5)/( 7.3 - 5.3)

    = -10 /2

    = -5

Answer: 5

Step-by-step explanation:

\(14-(-3)^2 =14-9=5\)

To use the integral test, we need to evaluate the following integral: ∫[infinity]1 6/5x dx Using integration by substitution with u = 6/5x, we get: ∫[infinity]1 6/5x dx = (5/6)∫[infinity]6/5 1 du.

Evaluating this integral gives us: (5/6)∫[infinity]6/5 1 du = (5/6)(1/u)|[infinity]6/5 = (5/6)(0 - 5/6) = -25/36 Since the integral evaluates to a finite value, and the series has the same general term as the function being integrated, we can conclude that the series is convergent by the integral test.

The new limits for the integral will be 5 (lower) and infinity (upper). ∫(5 to infinity) 6/u * (1/5) du. Thus, the integral is divergent. Since the integral is divergent, the original series Σ (n = 1 to infinity) 6/(5n) is also divergent.

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The equation that represents the transformation of vertical reflection and shift down by 3 of a cubic function is (a) \(g(x) = -x^{3} -3\) .

The Cubic function is represented as ; \(y=x^{3}\) ;

we have to apply the given transformations :

(i) The first transformation states that , there is a vertical reflection of the cubic function ,

So , after vertical reflection that equation becomes ⇒ \(y=-x^{3}\) ;

(ii) The second transformation is : the graph shifts down by 3 units ,

So ,after shifting down by 3 units the equation becomes ⇒ \(y = -x^{3} -3\) ;

let the function y be denoted by g(x) .

Therefore , after applying the transformation the equation becomes \(g(x) = -x^{3} -3\) .

The given question is incomplete , the complete question is

Which equation represents these transformations of a cubic function?

(i) vertical reflection

(ii) shift down 3

(a) g(x) = -x³ -3

(b) g(x) = (-x)³ +3

(c) g(x) = (x+3)³

(d) g(x) = -(x-1)³ + 3

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Answer: Fractions, decimals, and percents are all different ways of representing the same value. They are interchangeable because they represent the same proportion or part of a whole.

To convert a decimal to a percent, we multiply the decimal by 100 and add a percent sign. For example, the decimal 0.75 can be converted to a percent by multiplying it by 100, which gives 75, and adding a percent sign, which gives 75%.

When changing from a decimal to a percent, the decimal point is moved two places to the right. For example, if we have the decimal 0.75, we move the decimal point two places to the right to get 75, and then add the percent sign to get 75%.

In summary, the reason we can change between fractions, decimals, and percents is that they are different representations of the same value. When changing from a decimal to a percent, we move the decimal point two places to the right.

Step-by-step explanation: :)

Answer:

I think you need to add them.

Answer:

0.24

Step-by-step explanation:

Miles he drives: x

55.96+0.12x=49.96+0.16x

0.04x=6

x=0.24mi

To calculate the probabilities in question, you would integrate the exponential density function over the specified intervals

The exponential distribution is characterized by its density function, which is given by f(x) = λe^(-λx) for x ≥ 0, where λ is the rate parameter.

a) To calculate the probability P(X ≥ x) for each x > 0, we need to integrate the density function from x to infinity:

P(X ≥ x) = ∫[x,∞] λe^(-λt) dt

Evaluating this integral gives us the probability that the random variable X is greater than or equal to x.

b) For the conditional probability P(X ≥ x + y | X ≥ x), we use the definition of conditional probability:

P(X ≥ x + y | X ≥ x) = P(X ≥ x + y and X ≥ x) / P(X ≥ x)

Since X is a continuous distribution, the probability of X taking any specific value is zero. Therefore, the numerator simplifies to P(X ≥ x + y) and the denominator remains P(X ≥ x). Using the exponential distribution's density function, we can calculate these probabilities by integrating over the appropriate intervals.

In summary, to calculate the probabilities in question, you would integrate the exponential density function over the specified intervals.

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Answer:

1. -25

3. 15

5. -5/4

Explanation:

Considering the given functions for a(x)

1. To solve for a(8), we'll have to use the third function since we're given that x > 1 in the 3rd function and we know that 8 is greater than 1.

So we'll have;

3. To solve for a(-7), we'll use the 1st function because -7 is less than -6 and the condition is x <= -6;

5. a(-1/2)

In this case, we'll use the 2nd function is -1/2 lies between -6 and 1.

So, we'll have;

For an appropriate use the uniform distribution is to describe a continuous random variable x when relative frequencies of all possible values of x are about the same. So, option(d) is right one.

The uniform distribution is a distribution in which all values are equal. The interval [a,b] of a continuous variable X is said to be divided into one or four parts, meaning that all values in the distribution are equal or equal. If the probability density function equals f(x) = 1/(b−a), x∈[a,b] and is 0 elsewhere, we write X∼U(a,b). A curve is "uniform" when all events have the same probability. That is all occurrences of events have the same frequency. Accordingly, the correct answer is option (c).

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Answer:

52

Step-by-step explanation:

22 times 2 plus 8 is 52

Answer: 432

Step-by-step explanation:

540 x 0.8

Answer:

A single number that estimates the value of an unknown parameter is called a point estimate.

Step-by-step explanation:

Don't see the point (haha) of elaborating

Answer:

There are $\boxed{3}$ paths from $A$ to $B.$

Answer:

13x+6

Step-by-step explanation:

remove parenthesis and add like terms