Mom's car is 180 inches long. Dad's truck is 75% longer than mom's car. How long is the truck?

We can show that N+1/N - N = N+1/(N+1). Using this result, we can explain why 101 is close to, but slightly less than, 10.05. Additionally, without using a calculator, we can find the roots of the quadratic equation \(x^2 + 7x - 13 = 0.\).

1. Proof of N+1/N - N = N+1/(N+1):

To show that N+1/N - N = N+1/(N+1), we can simplify the left side as follows:

N+1/N - N = (N+1 - N)/N = 1/N = N+1/(N+1). Therefore, the equation N+1/N - N = N+1/(N+1) holds.

2. Explanation of why 101 is close to, but slightly less than, 10.05:

Using the result from the previous step, we can substitute N = 10 into the equation N+1/N - N = N+1/(N+1):

10+1/10 - 10 = 10+1/(10+1) = 10.1 - 10.1/11 = 10.1 - 0.91 = 9.19.

Therefore, 101 = 10.1 is close to, but slightly less than, 10.05.

3. Finding the roots of x^2 + 7x - 13 = 0:

To find the roots of the quadratic equation x^2 + 7x - 13 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac))/(2a),

where a = 1, b = 7, and c = -13.

Substituting these values into the quadratic formula, we get:

x = (-7 ± √(7^2 - 4(1)(-13)))/(2(1)),

x = (-7 ± √(49 + 52))/(2),

x = (-7 ± √(101))/(2).

Without using a calculator, we can approximate the square root of 101 as slightly greater than 10.05. Therefore, the roots of the quadratic equation x^2 + 7x - 13 = 0 are approximately:

x ≈ (-7 + √(101))/2 and x ≈ (-7 - √(101))/2, correct to 2 decimal places.

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Answer:

£57.6

Step-by-step explanation:

On the arranged survey, the statistical margin of error is supposed to be 14.73 SEK.

In a large consumer survey, 610 randomly selected customers are interviewed in a large grocery store. They are asked, among other things, how much they have shopped for. On average, they have shopped for 412 SEK with a standard deviation of 181 SEK .

Estimate with a 95% confidence interval the average purchase amount in the entire population. The formula for finding the margin of error is given as;

Margin of Error = z * (σ/√n)

Where:

σ is the standard deviation

n is the sample size

z is the Z-score for the desired confidence level, which is 95%.

Z-score corresponding to 95% confidence level is 1.96

Margin of Error = 1.96 * (181/√610) = 14.73

The statistical margin of error is 14.73 SEK.

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Answer:

-1

Step-by-step explanation:

To find the slope given two points use the formula

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

   = ( 8-2)/(4-10)

    = 6/-6

   = -1

The probability of the entire sample space group of answer choices is always equal to 1. This means that the sum of the probabilities of all possible outcomes in an experiment is equal to 1.

The reason for this is that the sample space represents all possible outcomes of an experiment, and one of these outcomes must occur. Therefore, the sum of the probabilities of all possible outcomes must be equal to 1. This allows us to calculate the probability of an event by dividing the number of outcomes that satisfy the event by the total number of possible outcomes.

It is important to note that probabilities are always between 0 and 1, inclusive. This means that the probability of an event can never be negative or greater than 1. If the probability of an event is 0, it means that the event is impossible, while a probability of 1 indicates that the event is certain to occur. Probabilities between 0 and 1 represent events that are possible but not certain to occur, and the closer the probability is to 1, the more likely the event is to occur.

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Answer:

Step-by-step explanation:

i cant give you an exact answer but look up the formula for trapezoid and look up the formula for triangle and you will get your answer.

Answer:  Area 89m^2

Step-by-step explanation:

To find the area of the rectangle we multiply

Base * Height = Area

8 * 13 = 104

Now we find the area that isn't shaded

I inference that the base of the triangle is 5m  

5 * 6 = 30

Now divide that by 2

30/2 = 15

Subtract 15 from 104

104 - 15 = 89m^2

Answer:

-8,-4,6

Step-by-step explanation:

Just answered it

the option that represents a socket is c.) "192.168.1.1:80".

A socket is typically represented by a combination of an IP address and a port number.

In the given options:

a.) "01-23-45-67-89-AB" does not represent a valid socket as it is in a MAC address format, not an IP address and port number format.

b.) "21" alone does not represent a valid socket as it is only a single number without an IP address or port number.

c.) "192.168.1.1:80" represents a valid socket as it consists of an IP address ("192.168.1.1") and a port number (":80").

d.) "10.1.1.15" alone does not represent a complete socket as it only contains an IP address without a port number.

Therefore, the option that represents a socket is c.) "192.168.1.1:80".

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Identity properties of addition are known to commutative in nature.

Given A and B, A and B are commutative or possess identity property of addition if;

A+B = B+A

For identity property, the two integers you are summing must include zero. For exmaple, a+0 = 0+a = a

The answer must always give the non-zero integer. Let us use 8 and 0 for example. This two possess the identity property of addition because;

8+0 = 0+8 = 8 (identity property of addition)

Answer:

y=6. &. x = -10

Step-by-step explanation:

if 4x + 5y = -10

then 4x = -10 -5y. ---------->(1)

if 4x + 3y = -22

then 4x = -22 -3y. ------------>(2)

from equation (1) & (2) :

then -10 -5y = -22 -3y

then 22 -10 = 5y -3y

12 = 2y

then y=6

substituting in (1) or (2):

then. x= -10

Madison figures out the average and range of chloride readings from wells close to the ocean. Other than a query, she has carried out an operation. The answer id option (d).

The standard deviation is a measure of variance from the mean that takes spread, dispersion, and dispersion into account. The standard deviation displays a "typical" divergence from the mean. It is a well-liked measure of variability since it retains the primary units of measurement from the data set.  A minor variation occurs when the numbers are close to the mean, while a high variation occurs when they are far from the mean.

The standard deviation describes the degree to which the results deviate from the mean. The average deviation, which depends on all values, is the most often used metric for measuring dispersion. Consequently, the standard deviation's value can be altered even by a slight change in one value.

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The formula for calculating the effective annual rate of interest with quarterly compounding is:

(1 + r/4)^4 - 1 = A/P

where r is the quarterly interest rate, A is the final amount, and P is the principal.

In this case, P = $2,000, A = $3,000, and the time period is 7 years or 28 quarters.

So we have:

(1 + r/4)^4 - 1 = 3000/2000

(1 + r/4)^4 = 1.5

1 + r/4 = (1.5)^(1/4)

r/4 = (1.5)^(1/4) - 1

r = 4[(1.5)^(1/4) - 1]

To get the effective annual rate, we need to convert the quarterly rate to an annual rate by multiplying by 4:

effective annual rate = 4[(1.5)^(1/4) - 1] ≈ 8.84%

Therefore, the effective annual rate of interest at which $2,000 will grow to $3,000 in seven years if compounded quarterly is approximately 8.84%, rounded to 2 decimal places.

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Answer:

The points lie on a vertical line.

Step-by-step explanation:

The x-values in the given two points are the same. If they were graphed and then connected, it would form a vertical line.

[see graph]

So, the points would lie on a vertical line.

7.1 cm  long is the arc intersected by a central angle .

What is length of an arc?

Given,

Central angle = π / 2

radius = 4.5 cm

we apply formula of length of arc.

length of the arc = angle ×  radius

                              = (π/2) × (4.5 cm)

Now put value of π = 3.14

length of the arc = (3.14 / 2) × (4.5) cm

                            = 7.065 cm ≈ 7.1 cm

Therefore, 7.1 cm  long is the arc intersected by a central angle .

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Answer:

There are 3nplus1 square tiles in the nth figure.

Answer:

A. Distributive Property

Step-by-step explanation:

The 2 is being distributed to the 5 and the 9.

Answer:

Distributive Property

Step-by-step explanation:

You are distributing 2➡️(5+9)

Answer: x=pi/8+npi    and x=5pi/8+npi

Step-by-step explanation:

Answer:

71+what ever is inside the triangle is 180

180-71=109

so we know the angles of a triangle add up to 180

109+20+x=180

129+x=180

x=51

Hope This Helps!!!

Answer:

The final solution is all the values that make (x-6)(x+5)=0 true.

x=6, -5

Answer:

False

Step-by-step explanation:

The sequential search algorithm is very simple to implement. It scans all the elements in the array starting at the first element, examining each element in turn and stopping when it finds a match

However, it is very inefficient since you are comparing  all the elements prior to the given element

This could be very time consuming for large data arrays

False The sequential search algorithm is simple and most efficient to use with a large data array.

False. While the sequential search algorithm is simple to implement and understand, it is not the most efficient method for searching large data arrays. The sequential search algorithm checks each element in the array one by one until it finds the desired value, resulting in an average case-time complexity of O(n). In comparison, other search algorithms, such as the binary search algorithm, offer better efficiency, particularly when dealing with large datasets. The binary search algorithm, for instance, has a time complexity of O(log n), making it significantly faster for large data arrays.

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Answer:

Step-by-step explanation:

Unit price = 9.60/8 = $1.2

Answer:

The unit price is $1.20

Step-by-step explanation:

All you have to do is divide 9.60 into 8

9.60 divided by 8=1.2

Answer:

2 only

Step-by-step explanation:

the slope is 2 in function 1 and function 2 is the only other slope that is 2 as well

Answer:

\(X=12.125\%\)

Step-by-step explanation:

From the question we are told that:

Cost Price \(CP=734\)

Sale Price \(SP=823\)

Generally the equation for Profit  P is mathematically given by

 \(Profit=SP-CP\)

 \(P=823-734\)

 \(P=89\)

Therefore as a percentage

Percentage Profit X is given as

 \(X=\frac{89}{734}*100\)

\(X=12.125\%\)

Answer:

x= -2, -1, 0, 1, 2

y= -7, -6, -5, -4, -3

The equivalent expression using the property is 10x + 16 = 8

This a property where a value is distributed over the values in parenthesis.

Given the following expression

2(5x+8) = 8

Using the Distributive property;

2(5x + 8) = 8

2(5x) + 2(8) = 8

10x + 16 = 8

Subtract 16 from both sides

10x = 8 - 16
10x = -8

x = -8/10

Hence the equivalent expression using the property is 10x + 16 = 8

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Lin should aim the ball at 7.8 feet away from point  B

From the question (see attachment), we have the following equivalent ratios:

\(AB : BE = DC :CE\)

This is so because triangles ABE and DCE are similar triangles.

Such that:

\(BE + CE = 20\)

\(AB = 16\)

\(DC = 16 + 9 = 25\)

So, we have:

\(AB : BE = DC :CE\)

\(16 : BE = 25: CE\)

Make CE the subject in \(BE + CE = 20\)

\(CE=20 - BE\)

Substitute 20 - BE for CE in \(16 : BE = 25: CE\)

\(16 : BE = 25: 20 - BE\)

Express as ratio

\(\frac{16 }{ BE} = \frac{25}{ 20 - BE}\)

Cross multiply

\(16(20 - BE) = 25BE\)

Open bracket

\(320 - 16BE = 25BE\)

Collect like terms

\(25BE + 16BE = 320\)

\(41BE = 320\)

Divide both sides by 41

\(BE = 7.8\)

Hence, she should aim at 7.8 feet away from point  B

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Answer:You want to make a bank shot. Sketch the path of the cue ball so it will bounce off of the bottom side and knock the yellow stripe 9 ball into the top middle pocket.

Step-by-step explanation:

The 33rd term of the given Arithmetic progression will be -132.

What is an Arithmetic progression?

A series of numbers is called a "arithmetic progression" (AP) when any two subsequent numbers have a constant difference. Arithmetic Sequence is another name for it.

Given, first term= a1= 28

and, a93 = -432

we know that, a93 = -432

                   a + 92d = -432 (where d is the common difference)

                  28 + 92d = -432

                     92d = -432-28

                             = -460

                       d = -460/92 = -5.

Now, we can find the a33,

               a33 = a + 32d

                       = 28 + (32× -5)

                       = 28-160

                       = -132.

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The probability that there are 5 remaining balls is 1/10.

Let's assume that there are initially w white balls and b black balls in the urn. Without loss of generality, let's assume that the first ball drawn is white.

Case 1: All remaining balls are white.

If there are w white balls initially, then the probability of drawing a white ball on the first draw is w / (w + b).

The probability of drawing another white ball on the second draw is (w - 1) / (w + b - 1), and so on.

We need to continue drawing balls until all remaining balls are white. The probability of this happening is:

P1 = w / (w + b) (w - 1) / (w + b - 1) ...  1 / (w + b - w + 1)

Simplifying this expression, we get:

P1 = w! x b! / (w + b)!

Case 2: All remaining balls are black.

If there are b black balls initially, then the probability of drawing a white ball on the first draw is b / (w + b).

The probability of drawing another black ball on the second draw is (b - 1) / (w + b - 1), and so on.

We need to continue drawing balls until all remaining balls are black. The probability of this happening is:

P2 = b / (w + b) (b - 1) / (w + b - 1) ...  1 / (w + b - b + 1)

Simplifying this expression, we get:

P2 = w! x b! / (w + b)!

The probability that there are 5 remaining balls is the sum of P1 and P2, when w + b = 6:

P = P1 + P2 = 3! 3! / 6! + 3! 3! / 6!

  = 2 3! 3! / 6!

  = 1/10

Therefore, The probability that there are 5 remaining balls is 1/10.

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