The area of Aliya’s garden is 32 square feet. The garden is 8 feet long. How wide is Aliya’s garden?

When a positive point charge q is placed at point P, it produces an electric field at all points surrounding it. Electric fields are defined as the forces that a charged particle experiences when placed in the vicinity of other charged particles, and they are also called the Coulomb forces.

The electric field generated by the point charge is measured by the force it exerts on a small test charge placed at a distance r from the point charge.

This force is given by Coulomb's law, which states that the magnitude of the force between two charges is proportional to the product of the charges and inversely proportional to the distance between them.

The electric field is a vector quantity and is given by the force experienced by the test charge divided by the magnitude of the test charge.

It is represented by an arrow, with the direction of the arrow indicating the direction of the electric field at that point.

The electric field generated by a positive point charge is radially outward from the charge, which means that it points away from the charge in all directions.

This is because a positive charge repels other positive charges and attracts negative charges, and therefore, a test charge would be pushed away from the positive point charge and towards negative charges, resulting in a radially outward electric field.

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Answer:

the third opinion: \(y = \frac{1}{4}x - 1\) (or as you put it, y equals one fourth times x minus 1)

This is because it's written in slope-intercept form: y = mx + b . m is the slope, which is 1/4, and b is the y-intercept, -1

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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The value of x if the line m and n are parallel is 36 degrees

Find a similar diagram attached below:

Assuming the angles given fill the position as seen in the diagram, then the sum of both angles are supplementary i.4.;

3x-10 + 3x - 26 = 180

6x - 36 = 180

6x = 180 + 36

6x = 216

x = 216/6

x = 36

Hence the value of x if the line m and n are parallel is 36 degrees

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Answer:

$72.33

Step-by-step explanation:

125 * 0.45 = 56.25

125 - 56.25 = 68.75 (marked off price)

68.75 * 1.052 = 72.33 (add sales taxes and round off)

Final price $ 72.33

Answer: CHOICE NUMBER 4: x = 3/2 or -1

Step-by-step explanation:

2(x+3)+(−3x)(x)=x*x

−3x^2+2x+6=x^2(Simplify both sides of the equation)

−3x^2+2x+6−x^2=x^2−x^2(Subtract x^2 from both sides)

−4x^2+2x+6=0

−2(2x−3)(x+1)=0(Factor left side of equation)

2x−3=0 or x+1=0(Set factors equal to 0)

x = 3/2

or x=−1

Plug them into the equation and it works!

Hope this helps! :)

On solving the provided question, we can say that Considering that the test statistic inside the lower tail the rejection zone, the null hypothesis should be rejected.

A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.

\(H0:p=0.25\) (null hypothesis)

\(H0:p \neq 0.25\) (alternative hypothesis)

Do not reject the null because the test statistic\((-1.2) is >\) \(the critical value (-1.7531)\)

Considering that the test statistic is inside the lower tail of the rejection zone, the null hypothesis should be rejected.

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To solve the equation (2 cos θ + √3) (2 cos θ + 1) = 0, we set each factor equal to zero and solve for θ.

First factor: 2 cos θ + √3 = 0

2 cos θ = -√3

cos θ = -√3/2

To find the first fundamental solution, we need to find the angle whose cosine is -√3/2 within the range 0 to 2π (or 0 to 360 degrees). In this case, θ is in the second and third quadrants since cosine is negative.

Fundamental solution #1:

θ = π + arccos(-√3/2) ≈ 2.61799 radians

To find the second fundamental solution, we can use the periodicity of the cosine function. Since the cosine function has a period of 2π, we can add 2π to the first fundamental solution to obtain the second one.

Fundamental solution #2:

θ = 2.61799 + 2π ≈ 5.75959 radians

Now let's consider the second factor: 2 cos θ + 1 = 0

2 cos θ = -1cos θ = -1/2

To find the third fundamental solution, we need to find the angle whose cosine is -1/2 within the range 0 to 2π.

Fundamental solution #3:

θ = 2π + arccos(-1/2) ≈ 2.61799 radians

To find the fourth fundamental solution, we can again add 2π to the third fundamental solution.

Fundamental solution #4:

θ = 2.61799 + 2π ≈ 5.75959 radians

Now let's express the coterminal solutions for each fundamental solution.

Solutions coterminal to fundamental solution #1:

θ = 2.61799 + 2πk, where k is an integer

Solutions coterminal to fundamental solution #2:

θ = 5.75959 + 2πk, where k is an integer

Solutions coterminal to fundamental solution #3:

θ = 2.61799 + 2πk, where k is an integer

Solutions coterminal to fundamental solution #4:

θ = 5.75959 + 2πk, where k is an integer

Remember that these solutions are written in radians and should be listed in ascending order.

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Answer:

A^2

2.3^2 = 5.29

Answer:

Step-by-step explanation:

Simply it is 2/5.

This is because overall 5/5 is the amount of people at the tennis club.

3/5 of the people in the tennis club are women meaning:

5/5 - 3/5 = 2/5

So 2/5 of the people in the tennis club are men.

It is worth noting that there are many other possible choices for a and b that satisfy ab=0. This is because there are many ways to construct matrices with a row or column of zeros, and many ways to choose the nonzero entries in the other positions.

To find nonzero 2x2 matrices a and b such that ab=0, we need to find matrices a and b whose product is the zero matrix. A matrix multiplication is a combination of dot products between rows and columns of the two matrices. In order for the product of two matrices to be zero, one or both of the matrices must have a row of zeros or a column of zeros.

One way to construct such matrices is to set one of the matrices to have a row of zeros and the other to have a column of zeros. Let a be a matrix with a row of zeros and b be a matrix with a column of zeros, but with a nonzero entry in a different position. For example, we could choose:

a = [0 0; 1 0]

b = [0 1; 0 0]

Then, the product ab is:

ab = [0 0; 1 0] * [0 1; 0 0] = [0 0; 0 0]

So, we have found two nonzero 2x2 matrices a and b such that ab=0.

It is worth noting that there are many other possible choices for a and b that satisfy ab=0. This is because there are many ways to construct matrices with a row or column of zeros, and many ways to choose the nonzero entries in the other positions.

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4) From this pattern, we can see that the last digit of \(4^n\) will cycle through the values 4, 6, 4, 6, and so on. Therefore, the possible values of the last digit of \(4^n\) are 4 and 6.

Let's address each question one by one:

1. For which natural numbers n is the number \(3^n + 1\) divisible by 10?

To be divisible by 10, a number must end with a zero, which means its units digit should be zero. The units digit of 3^n will repeat in a pattern: 3, 9, 7, 1, 3, 9, 7, 1, and so on. Adding 1 to these units digits will give us 4, 0, 8, 2, 4, 0, 8, 2, and so on. From this pattern, we can see that 3^n + 1 is divisible by 10 when n is an even number. So, the natural numbers n for which 3^n + 1 is divisible by 10 are those that are even.

2. Find the remainder of the division of 1! + 2! + ... + 50! by 7.

To find the remainder, we can calculate the sum of the factorials modulo 7. Evaluating each factorial modulo 7:

1! ≡ 1 (mod 7)

2! ≡ 2 (mod 7)

3! ≡ 6 (mod 7)

4! ≡ 3 (mod 7)

5! ≡ 1 (mod 7)

6! ≡ 6 (mod 7)

7! ≡ 6 (mod 7)

8! ≡ 4 (mod 7)

9! ≡ 1 (mod 7)

10! ≡ 6 (mod 7)

11! ≡ 6 (mod 7)

12! ≡ 5 (mod 7)

13! ≡ 6 (mod 7)

...

50! ≡ 6 (mod 7)

Summing up the factorials modulo 7:

1! + 2! + ... + 50! ≡ (1 + 2 + 6 + 3 + 1 + 6 + 6 + 4 + 1 + 6 + 6 + 5 + 6 + ... + 6) (mod 7)

The sum of the residues modulo 7 will be:

(1 + 2 + 6 + 3 + 1 + 6 + 6 + 4 + 1 + 6 + 6 + 5 + 6 + ... + 6) ≡ 2 (mod 7)

Therefore, the remainder of the division of 1! + 2! + ... + 50! by 7 is 2.

3. Is it true that 36 divides n² + n + 4 for infinitely many natural numbers n? Explain!

To determine if 36 divides n² + n + 4 for infinitely many natural numbers n, we can look for a pattern. By testing values of n, we can observe that for any n that is a multiple of 6, n² + n + 4 is divisible by 36:

For n = 6: 6² + 6 + 4 = 52, not divisible by 36

For n = 12: 12² + 12 + 4 = 160, not divisible by 36

For n = 18: 18² + 18 + 4 = 364, divisible by 36

For n = 24: 24² + 24 + 4 = 700, divisible by 36

For n = 30: 30² + 30 + 4 = 1184, divisible by 36

For

n = 36: 36² + 36 + 4 = 1764, divisible by 36

This pattern repeats for every n = 6k, where k is a positive integer. Therefore, there are infinitely many natural numbers for which n² + n + 4 is divisible by 36.

4. What are the possible values of the last digit of 4^n, where n ∈ N?

To find the possible values of the last digit of 4^n, we can observe a pattern in the last digits of powers of 4:

\(4^1\) = 4

\(4^2\) = 16

\(4^3\) = 64

\(4^4\) = 256

\(4^5\)= 1024

\(4^6\)= 4096

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For a confidence interval, decreasing the sample size will have an effect on the width of the confidence interval it will increase the width of the interval. Therefore, the correct option is A.

A confidence interval is a range of values that are associated with a certain level of probability. It represents the degree of confidence with which we can state that the population parameter lies within the interval. The relationship between sample size and confidence interval width is inversely proportional.

The larger the sample size, the narrower the confidence interval. On the other hand, decreasing the sample size will increase the width of the confidence interval. As a result, the confidence interval's precision decreases, and the probability of capturing the true population parameter decreases.

As a result, the width of the confidence interval is inversely proportional to the sample size. When we reduce the sample size, the interval width expands, resulting in a less precise estimate of the true population parameter. Hence, option A is correct.

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Answer:

7,1

Step-by-step explanation:

The common factors for 14,−7 are 1,7 . The numbers do not contain any common variable factors. The GCF (HCF) of the numerical factors 1,7 is 7 .

Answer:

16

Step-by-step explanation:

Apply PEMDAS:

Solve the exponent, multiply from left to right, and then subtract and add from left to right.

\(3-2^2+4*3+5\\\\3-4+4*3+5\\\\3-4+12+5\\\\-1+12+5\\\\11+5\\\\\boxed{16}\)

Answer: 16

Step-by-step explanation:

The important thing to remember here is the Order of Operations

The Order of Operations states that first solve Parentheses, then Exponents, then Multiplication and Division, then Addition and Subtraction.

There are no parentheses.

Exponents: 3 - 4+4*3+5

Multiplication and Division: 3 - 4 + 12 + 5

Addition and Subtraction:

-1+12+5

11+5

16

Hope it helps <3

Answer:

Divide 4,380 by 60

4,380 ÷ 60 = 73

Step-by-step explanation:

The normal approximation can be used in a two-sample test of proportions when the sample sizes are sufficiently large.

The rule of thumb is that each sample should have at least 10 successes and 10 failures. When these conditions are met, the sampling distribution of the difference in sample proportions can be approximated by a normal distribution with a mean equal to the difference in population proportions and a standard deviation calculated from the sample proportions. This approximation allows us to calculate probabilities and make inferences using the standard normal distribution. It is important to note that this approximation may not be accurate for small sample sizes, in which case exact methods such as the Fisher's exact test should be used instead. In summary, the normal approximation can be used in a two-sample test of proportions when the sample sizes are large enough and the conditions are met.

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The values of the expressions, obtained by the combination of the functions, f(x), g(x), and h(x), and found by plugging in the values of the specified function at the indicated value of x are;

17. g(9) + h(-14) = 15

19. (1/2)·g(-6) + f(-2) = -22

21. x = -12

A function defines the relationship between an input variable and an output variable, such that each input produces only one value of the output.

The functions, f(x), g(x), and h(x), are defined as follows;

f(x) = -x² + 8·x - 11

\(g(x) =14-\dfrac{2}{3} \cdot x\)

h(x) = -x - 7

17. The value of g(9) can be found by plugging x = 9, in the function for g(x) as follows;

\(g(9) =14-\dfrac{2}{3} \times 9= 8\)

g(9) = 8

Similarly, the value of h(-14), can be found by plugging in x = -14, in the function for h(x) as follows;

h(-14) = -(-14) - 7 = 7

h(-14) = 7

Therefore, g(9) + h(-14) = 8 + 7 = 15

19. The value of g(-6), can be found as follows;

\(g(-6) =14-\dfrac{2}{3} \times (-6)= 18\)

g(-6) = 18

Similarly, for f(-2), we get;

f(-2) = -(-2)² + 8 × (-2) - 11 = -31

Therefore;

\(\dfrac{1}{2}\cdot g(-6) +f(-2) = \dfrac{1}{2} \times 18 + (-31) = 9 - 31 = -22\)

21.  h(x) = -x - 14

If the value of h(x) = -2, we get;

h(x) = -2 = -x - 14

14 - 2 = -x

-x = 12 (symmetric property)

Dividing both sides by (-1), we get;

-x/(-1) = x = 12/(-1) = -12

x = -12

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The probability of drawing at least one ace when you draw from a standard deck 25 times is 0.8648

Number of Aces in deck = 4

The probability that they pick no ace in one trail

= (52 - 4) / 52

= 48 / 52

= 12 / 13

The probability that the picks no ace in 25 trials are

= (12/35)²⁵

The probability of drawing at least one ace when we draw from a standard deck 25 times

= 1 -  (12/35)²⁵ = 0.8648

Indeed, it is conceivable you could wind up drawing a king rather than a queen from those 52 cards as you might attract a queen on the first go.

Hence the probability of drawing at least one ace when you draw from a standard deck 25 times is 0.8648.

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The expression for the area under the graph of f(x) over the interval [2, 4] is given by the limit as n approaches infinity of the Riemann sum: A = lim(n→∞) Σ[f(xi)Δx].

To express the area under the graph of f(x) as a limit, we divide the interval [2, 4] into n subintervals of equal width Δx = (4 - 2)/n = 2/n.

Let xi be the right endpoint of each subinterval, with i ranging from 1 to n. The area of each rectangle is given by f(xi)Δx.

By summing the areas of all the rectangles, we obtain the Riemann sum: A = Σ[f(xi)Δx], where the summation is taken from i = 1 to n.

To find the expression for the area under the graph of f(x) as a limit, we let n approach infinity, making the width of the rectangles infinitely small.

This leads to the definite integral: A = ∫[2, 4] f(x) dx.

In this case, the expression for the area under the graph of f(x) over the interval [2, 4] is given by the limit as n approaches infinity of the Riemann sum: A = lim(n→∞) Σ[f(xi)Δx].

Evaluating this limit would yield the actual value of the area under the curve.

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Answer:

6x square +14x+4

Step-by-step explanation:

hope this helps................

Answer:

6x^2+14x+4

Step-by-step explanation:

6x^2+12x+2x+4

6x^2+14x+4

The preferred choice would be a line graph (drawn in the figure attached) for displaying the data.

Why a line graph is the preferred option here?

What is a line graph?

An individual data point is connected by a line in a line graph, sometimes referred to as a line plot or a line chart. A line graph shows numerical values over a predetermined period of time.

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Answer:

B

Step-by-step explanation:

The x term is 1 in all the pairs this would form a horizontal line (x=1)

Answer: C) ((-2,7), (0,12), (1,4), (1,5)

Step-by-step explanation: An ordered pair will usually have a pattern that'll repersent a linear function. Out of all of the options only C as a constant pattern.

I hope this helps!

Answer:

The modes are 16, 17 and 20.

This is because they appear most often in the set of numbers. They each appear 3 times.

Have a good day :)

Answer:

• Mode is the observation that occurs most number of times.

therefore in this set of ungrouped data;

16 occurs 3 times

17 occurs 3 times

18 occurs 2 times

19 occurs 1 times

20 occurs 3 times

therefore mode here are 16,17 and 20

Answer:

==>(x+3) = 16

==> x + 3 = 16

make x the subject of formula

=> x = 16 - 3

subtract 3 from 16

=> x = 13

Step-by-step explanation:

\(3 \times x\)

\(3x\)

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following expression:

When it is a quotient, and it is the same base, the exponents are subtracted, therefore