Are the two shapes are congruent?​

Answer:

Yes, Jean is correct

Step-by-step explanation:

Given

\(73 * \frac{3}{4}\)

Required

Determine the value of the result

When a positive integer is multiplied by a fraction, the result is always less than the integer

Solving further

\(Expression = 73 * \frac{3}{4}\)

\(Expression = \frac{73 * 3}{4}\)

\(Expression = \frac{219}{4}\)

\(Expression = 54.75\)

The result of the expression shows that the resulting value is less than 73.

Hence, Jean is correct

Answer:

A.

Step-by-step explanation:

This is a geometric sequence with common ratio -12/-3 = 4  ( -48/-12  = 4 and  -192 / -48 = 4).

nth term = a1 r^(n - 1) so the 8th term

= -3 * (4)^(8 - 1)

= -49,152.

The 8th term of the geometric sequence is -768

A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Formula for the n th term of a geometric sequence in the form

aₙ=a₁ rⁿ

Given sequence is   -3, -12, -48, -192, . . .

It is a geometric sequence with the ratio between consecutive terms is 4

i.e. r = 4

a₁ = -3

a₈ = -3 ×4⁸

   =-768

Thus the 8th term of this sequence is -768

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Answer:

I think it is D.

Step-by-step explanation:

152-43=109

Answer:

C

Step-by-step explanation:

angle DEC=180-152=28

AB//DEF --> angle A=angle DEC = 28 (alternate angle)

angle B=angle D=43

angle DCE=180-43-28=109

angle ACB= angle DCE = 109 (vertical angle)

angle ACD=180-109 = 71

angle BCE-angle ACD = 71 (vertical angle)

An explicit formula for aₙ, the nth term of the arithmetic sequence is aₙ = 27 - 4(n - 1).

Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:

aₙ = a₁ + (n - 1)d

Where:

From the information provided, we have the following parameters:

First term, a₁ = 27

Second term, a₂ = 31

Next, we would determine the common difference as follows:

Common difference, d = a₂ - a₁

Common difference, d = 31 - 27

Common difference, d = 4.

Substituting the parameters into the mathematical expression, we have;

aₙ = 27 + (n - 1)(4)

aₙ = 27 - 4(n - 1).

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Answer:

The least degree of the polynomial that assures an error smaller than 0.001 is 4.

The Lagrange error bound for the Taylor polynomial of degree n centered at x=2 for e^x is given by:

```

|e^x - T_n(x)| < \frac{e^2}{(n+1)!}|x-2|^{n+1}

```

where T_n(x) is the Taylor polynomial of degree n centered at x=2.

We want the error to be less than 0.001, so we have:

```

\frac{e^2}{(n+1)!}|x-2|^{n+1} < 0.001

```

We can solve for n to get:

```

n+1 > \frac{e^2 \cdot 1000}{|x-2|}

```

We know that |x-2| = 0.45, so we have:

```

n+1 > \frac{e^2 \cdot 1000}{0.45} \approx 6900

```

Therefore, n > 6899.

The least integer greater than 6899 is 6900, so the least degree of the polynomial that assures an error smaller than 0.001 is 4.

The fourth-degree Taylor polynomial centered at x=2 for e^x is given by:

```

T_4(x) = 1 + 2x + \frac{x^2}{2} + \frac{x^3}{6} + \frac{x^4}{24}

```

We can use this polynomial to estimate e^1.45 as follows:

```

e^1.45 \approx T_4(1.45) = 4.38201

```

The actual value of e^1.45 is 4.38202, so the error in this approximation is less than 0.001.

Step-by-step explanation:

Based on the average annual rainfall, we can collect 150,000 gallons of rainfall from a rooftop with a surface area of 100 feet by 200 feet.

To calculate the amount of rainfall that can be collected from a rooftop with an area of 100 feet by 200 feet, we need to use the given average annual rainfall and the given conversion factor. Given that the average annual rainfall is 7.5 gallons, we need to convert the area of the rooftop into square feet before we can use it in the calculation.

The area of the rooftop is the product of its length and width, which gives:                                                                                           Area of rooftop = 100 ft × 200 ft = 20,000 sq. ft                                                                                                                           Now, we can use this area and the given average annual rainfall as follows:                                                                    Amount of rainfall collected = Area of rooftop × Average annual rainfall = 20,000 sq. ft × 7.5 gallons= 150,000 gallons.

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Answer:

The absolute value of a number is its distance from 0. We know that distance is always a non-negative quantity. Since the absolute value is a distance, the absolute value is always non-negative.

Step-by-step explanation:

Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.

The expected value is given by the sum of each outcome multiplied by it's respective probability.

In this problem:

Hence, his expected profit for a single game is:

\(E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583\)

For 216 games, the expected value is:

\(E = 216(0.2583) = 55.8\)

Ayo can be expected to make a profit of £55.8.

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These steps are often referred to as the principle of mathematical induction or PMI.

The steps for mathematical induction are:

Base Case: Show that the statement holds for some particular value of n, usually n = 1 or n = 0.

Inductive Hypothesis: Assume that the statement holds for some arbitrary value of n = k, where k is a positive integer.

Inductive Step: Using the inductive hypothesis, show that the statement also holds for n = k + 1.

Conclusion: By the principle of mathematical induction, the statement is true for all positive integers n.

These steps are often referred to as the principle of mathematical induction or PMI. They are used to prove statements that involve an infinite set of integers by showing that the statement holds for a base case, assuming that it holds for an arbitrary value, and then showing that it holds for the next integer in the set.

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Answer:

2.92

Step-by-step explanation:

Answer:

2.92

Step-by-step explanation:

12×.59=7.08 10-7.08=2.92

To target a specific gene or region of DNA in a PCR (Polymerase Chain Reaction) reaction, scientists use specific primers that are designed to bind to the DNA sequence flanking the target region.

Primers are short, single-stranded DNA sequences that act as starting points for DNA replication during PCR. By designing primers that are complementary to the target gene or region, scientists can selectively amplify and target that specific sequence. The process involves selecting the target DNA sequence and designing two primers: one that anneals to the forward strand (5' to 3' direction) and another that anneals to the reverse strand (3' to 5' direction). These primers define the region of DNA that will be amplified. When added to the PCR reaction mixture, the primers specifically bind to their complementary sequences on the DNA template strands, allowing DNA polymerase to extend and synthesize new DNA strands from the primers.

A thermal cycler is a crucial instrument in the PCR process. It helps automate and control the temperature changes required for the different steps of PCR. The thermal cycler allows precise temperature cycling, which is essential for denaturation of the DNA template (separation of the double-stranded DNA into single strands), annealing of primers to the template DNA, and extension (synthesis of new DNA strands). The thermal cycler ensures that the reactions occur at specific temperatures and for specific durations, optimizing the efficiency and specificity of DNA amplification. To run a PCR reaction, you would need the following components and steps: DNA template: The DNA sample containing the target gene or region you want to amplify. Primers: Design and obtain forward and reverse primers that are complementary to the target DNA sequence.

PCR reaction mixture: Prepare a reaction mixture containing DNA template, primers, nucleotides (dNTPs), DNA polymerase, and buffer solution. The buffer solution provides the necessary pH and ionic conditions for optimal enzymatic activity. Thermal cycling: Load the reaction mixture into the thermal cycler. The thermal cycler will then undergo a series of temperature changes, including: Denaturation: Heating the reaction mixture to around 95°C to denature the DNA, separating the double-stranded DNA into single strands. Annealing: Cooling the reaction mixture to a temperature (typically 50-65°C) suitable for the primers to bind (anneal) to their complementary sequences on the DNA template.

Extension: Raising the temperature to the optimal range (usually around 72°C) for DNA polymerase to extend and synthesize new DNA strands from the primers. This allows replication of the target DNA sequence. Repeat cycles: The thermal cycler will repeat the denaturation, annealing, and extension steps for a predetermined number of cycles, typically 20-40 cycles. Each cycle exponentially amplifies the target DNA sequence, resulting in a significant increase in DNA quantity. Final extension: After the desired number of cycles, a final extension step is performed at 72°C for a few minutes to ensure the completion of DNA synthesis and finalize the PCR process. By following these steps and using a thermal cycler, scientists can successfully amplify and target specific genes or regions of DNA through the PCR technique.

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Based on the given information, we have the mean concentration of sodium in the drinking water of a water system in Connecticut as 26.4 mg/l and the standard deviation as 6 mg/l.

The water department selects a simple random sample of 32 water specimens over the course of a year. To answer the question using the distributions tool, we need to set the mean and standard deviation parameters on the tool to the expected mean and standard error for the distribution of sample mean concentrations.

The expected mean for the distribution of sample mean concentrations is the same as the mean concentration of sodium in the drinking water, which is 26.4 mg/l.

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The water department in Connecticut is monitoring the concentration of sodium in their drinking water. By calculating the mean and standard error for the distribution of sample means, they can determine the probability of the mean concentration exceeding the notification level of 28 mg/l. If this probability is low, the water department will notify the public and recommend necessary actions.

In this scenario, the water department in Connecticut wants to monitor the concentration of sodium in their drinking water. They have set a notification level of 28 mg/l, meaning that if the mean concentration of sodium across a sample of 32 water specimens exceeds this level, they will notify the public.

To analyze this situation, we can use the distribution of sample means. The mean concentration of sodium in the drinking water of the water system is given as 26.4 mg/l, with a standard deviation of 6 mg/l.

To find the expected mean and standard error for the distribution of sample means, we can use the following formulas:

Expected mean of sample means = population mean

                                                        = 26.4 mg/l
Standard error of sample means = population standard deviation / square root of sample size

Using the given values, the standard error of sample means can be calculated as follows:
Standard error of sample means = 6 mg/l / square root of 32

                                                      ≈ 1.06 mg/l

Now, we can use a distributions tool to find the probability that the mean concentration of sodium in the sample of 32 water specimens exceeds 28 mg/l. We will set the mean parameter on the tool to 26.4 mg/l and the standard deviation parameter to 1.06 mg/l.

By entering these values into the distributions tool, we can find the probability of obtaining a mean concentration greater than 28 mg/l. If this probability is less than a certain threshold (e.g., 0.05), it indicates that the mean concentration exceeding 28 mg/l is unlikely to occur by chance alone. In such cases, the water department would notify the public and recommend that individuals on sodium-restricted diets inform their physicians of the sodium content in their drinking water.

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Therefore (b). A chi-square statistic is always positive as it is the sum of squared deviations from expected values.

However, it can contain fractions or decimal values as it is based on continuous data. The chi-square distribution is skewed to the right and its shape depends on the degrees of freedom. The possible values for a chi-square statistic depend on the sample size and the number of categories in the data. In general, larger sample sizes and more categories will result in larger chi-square values. It is important to note that a chi-square statistic cannot be negative as it is the sum of squared deviations. Therefore, options (a) and (c) are incorrect. In conclusion, the correct answer is (b) and it is important to understand the properties and interpretation of chi-square statistics in statistical analysis.

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Answer:

199000 i think

Step-by-step explanation:

1800 x 5 = 9000

9000 + 190000 = 199000

Answer:

3 1/5 = 16/5 (If 3 1/5 is a mixed number)

=> The multiplicative inverse of 3 1/5 is 5/16

Step-by-step explanation:

Answer:

I can't see the picture but the domain is the x value.

Step-by-step explanation:

Answer: $21,876

Step-by-step explanation:

There are 4 trucks being transported. Each of those trucks weigh 5,469 pounds.

The total weight of all four trucks would be:

= weight of one truck * number of trucks

= 5,469 * 4

= $21,876

Answer:

Option 1

Step-by-step explanation:

Attached Picture

Answer:

The line representing the number of miles Nick drives while performing x oil changes is steeper than the line representing the number of miles Natalie drives while performing x oil changes because he drives farther between oil changes than Natalie does.

Answer: Coordinate in units: (2,1.25)

Step-by-step explanation:

XB=AX*3

AX+XB=AB

AX+(AX*3)=AB

AX*4=AB

AX*4=9

AX=2.25

X=-1+2.25

X=1.25 units

Coordinate in units: (2,1.25)

The coordinates of the point X on the line is (2.25, 4)

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

The graph

The location of the point X on the line such that the ratio of AX to XB is 1:3 is calculated as

X = 1/4 * (B - A)

So, we have

X = 1/4 * (8 + 1)

Evaluate

X = 2.25

This means that

X = (2.25, 4)

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Answer:

if this came out of a book use slader

Step-by-step explanation:

Answer:

AnswersMathsGCSEArticle

What are the values of x and y?

a) 3x + 5y = 26

b) 2x + 2y = 12

Step One: We need to find a way to equate either the x terms of the y terms in each equation. Multiply equation a) by 2 and equation b) by 3 to form the following equations.

a) 6x + 10y = 52

b) 6x + 6y = 36

Step Two: Take equation b) from equation a) to eliminate the x component.

a) 6x + 10y = 52

- b) 6x + 6y = 36

0x + 4y = 16

y = 4

Step Three: substitute the value of y into either equation to find the value of x.

b) 2x + 2y = 12

2x + (2x4) =12

2x + 8 = 12

2x = 4

x = 2

x=2 y=4

Step-by-step explanation:

thank you sana nakatulong yang sagot ko

Answer:

7√2

Step-by-step explanation:

Answer:

Step-by-step explanation:

I know it is right trust me and if it is wrong srry but you will get it right

Answer:

-------------------------------

Let the sides of the old rectangle are l and w.

Answer: Hence the answer is 27 square feet.

Please look at the images for more details.

The area of the customer's yard is 580π.

The distance formula is given as -

d = √(x₂ - x₁)² + (y₂ - y₁)²

Given is that this grid represents the customer’s yard. The bottom left corner is the origin point  O(0, 0), and the x- and y- axes represent the two fences. The rose bush is at point P(16, 18).

We can write the area of the customer's yard -

A = πr²

Here -

r = d

r² = d²

We can write -

A = πd²

A = π {(x₂ - x₁)² + (y₂ - y₁)²}

A = π{16 x 16 + 18 x 18}

A = 580π

Therefore, the area of the customer's yard is 580π.

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Answer:

The dealer's profit percentage is 7.692%

Step-by-step explanation:

18 × 65 = 1170

He spent Rs.1170

12 × 75 = 900

60 × (18-12) = 360

900 + 360 = 1260

He got a profit of Rs.90.

1170 × (1 + x/100) = 1260

1 + x/100 = 14/13

x/100 = 1/13

x= 7.692307692

Answer:

7.7%

Step-by-step explanation:

spent= Rs. 65*18= Rs. 1170

earned= 12*Rs. 75+6*Rs. 60= Rs. 1260

profit= Rs. 1260- Rs. 1170= Rs. 90

profit %= 90/1170*100%= 7.7%

Answer:

T' (1, -1)

Step-by-step explanation:

Since it is 2 units left, we subtract 2 from the x value and since it is 3 units up, we add 3 to the y value.

The required probability is 0.4408.

The operating characteristics of the loading gate problem are:

L = λ/ (μ - λ)

W = 1/ (μ - λ)

Lq = λ^2 / μ (μ - λ)

Wq = λ / μ (μ - λ)

ρ = λ / μ

P0 = 1 - λ / μ

Where, L represents the average number of cars either being loaded or waiting.

W represents the average time a car spends either being loaded or waiting.

Lq represents the average number of cars waiting.

Wq represents the average waiting time of a car.

ρ represents the utilization factor.

ρ = λ / μ represents the ratio of time the worker spends loading cars to the total time the system is busy.

P0 represents the probability that the system is empty.

The probability that there will be more than six cars either being loaded or waiting is to be determined. That is,

P (n > 6) = 1 - P (n ≤ 6)

Now, the probability of having less than or equal to six cars in the system at a given time,

P (n ≤ 6) = Σn = 0^6 [λ^n / n! * (μ - λ)^n]

Putting the values of λ and μ, we get,

P (n ≤ 6) = Σn = 0^6 [(6/ 48)^n / n! * (8/ 48)^n]

P (n ≤ 6) = [(6/ 48)^0 / 0! * (8/ 48)^0] + [(6/ 48)^1 / 1! * (8/ 48)^1] + [(6/ 48)^2 / 2! * (8/ 48)^2] + [(6/ 48)^3 / 3! * (8/ 48)^3] + [(6/ 48)^4 / 4! * (8/ 48)^4] + [(6/ 48)^5 / 5! * (8/ 48)^5] + [(6/ 48)^6 / 6! * (8/ 48)^6]P (n ≤ 6) = 0.5592

Now, P (n > 6) = 1 - P (n ≤ 6) = 1 - 0.5592 = 0.4408

Therefore, the required probability is 0.4408.

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We can determine coordinates if point t is between points u and v by checking if u < t < v or v < t < u.

To determine if point t is between points u and v, we need to compare their coordinates. If u < v, then point t is between points u and v if and only if u < t < v. On the other hand, if v < u, then point t is between points u and v if and only if v < t < u.

Whether or not point t is between points u and v depends on the relationship between the coordinates of u and v. If u < v, t must fall between them, and if v < u, t must also fall between them.

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sin = 3/7

1 = sin²0 + cos²0

cos²0 = 1 - 9/49

cos²0 = 40/49

cos0 = √(40) / 7

since its in Quadrant 2 the sin is positive and cos is negative

cos0 = - √(40) / 7