the standard error of the regression, se, is calculated by taking the square root of divided by .

Standard deviation - The value of x is 1.96.

What is standard normal distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

As given, for a standard normal distribution, 95% of the data points are contained in the interval [ -x , x ].

The standard normal distribution, commonly known as the z-distribution, is a unique type of normal distribution in which the mean and standard deviation are both equal to 1. By transforming its values into z-scores, any normal distribution can be standardised. Z-scores indicate how far away from the mean each number is from.

Hence, from the standard normal table, the value of x = 1.96 for 95% confidence level.

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The solution of system of equations are (4, 2). Therefore, option A is the correct answer.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given equation is y=-x+6 ---------(I)

On a coordinate plane, a line goes through (0, 0) and (4, 2).

Here, slope m=(2-0)/(4-0)

= 1/2

Substitute m=1/2 and (4, 2) in y=mx+c, we get

2=1/2 (4)+c

c=0

y=1/2 x ---------(II)

Substitute equation (II) in equation (I), we get

1/2 x=-x+6

x=-2x+12

x+2x=12

3x=12

x=4

Substitute x=4 in equation (II), we get

y=2

Then, solution of system of equations is (4, 2)

Therefore, option A is the correct answer.

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Answer:

2027 and 2029

Step-by-step explanation:

am not sure if this is what you meant

the prime numbers in the decade from 2021 to 2030 are: 2023, 2027, and 2029.

To find all the prime numbers in the decade from 2021 to 2030, we need to check each number in this range and determine if it is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Let's examine each number in the range from 2021 to 2030:

2021: Not a prime number (divisible by 7 and 17)

2022: Not a prime number (divisible by 2 and 101)

2023: Prime number (divisible only by 1 and 2023)

2024: Not a prime number (divisible by 2, 4, 8, 253, 506, and 1012)

2025: Not a prime number (divisible by 5 and 405)

2026: Not a prime number (divisible by 2, 3, 11, 61, and 122)

2027: Prime number (divisible only by 1 and 2027)

2028: Not a prime number (divisible by 2, 4, 7, 14, 31, 62, 127, and 254)

2029: Prime number (divisible only by 1 and 2029)

2030: Not a prime number (divisible by 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, and 435)

In summary, the prime numbers in the decade from 2021 to 2030 are: 2023, 2027, and 2029.

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The sum of the series of three numbers, which includes the counting number, n, the number before n, and the number after n is 3•n

A series of a sequence of numbers is the sum of the numbers up to a specified term.

The given parameters;

n = A counting number

Counting numbers are the natural numbers which is the set of all positive integers.

Given that n is a counting number, we have that n is a positive whole number.

Which gives;

The whole number before n = n - 1

The whole number after n = n + 1

Which gives;

The sum of n, the whole number before n, and the whole number after n is part of a series and can be written mathematically as follows;

The sum = n + n - 1 + n + 1 = 3•n -1 + 1 = 3•n

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We can calculate it by using a long multiplication method where you multiply every digit of 12 by 12. 144 = 1 x 12 + 4 x 1 = 12 + 4 = 16. So, the value of 144 is 16

Calculating the value of 144 is a simple mathematical operation that can be done in several ways. The most straightforward method is to multiply 12 by 12, as 144 = 12 x 12. Another way to calculate the value of 144 is to find the square of 12, as 144 = 12^2. An alternative method is to use long multiplication where you multiply every digit of 12 by 12. The result of this will be 144 = 1 x 12 + 4 x 1 = 12 + 4 = 16.

In summary, the value of 144 is 16, regardless of the method you choose to calculate it. It is a well-known fact and can be easily looked up in mathematical tables as well.

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POINT - it is a location or position in space .

LINES - it is one-dimensional form that has no thickness and may be drawn in both directions.

PLANES - it is  figure that may be stretched endlessly and is flat and two dimensional

The study of all shapes and figures in the universe is known as geometry. It is present in all living things, including plants, animals, microorganisms, and common objects. Shapes are all around us, and in this article, we'll explore how mathematics may help us solve the puzzle of geometry.

PARTS OF GEOMETRY ARE :

1 . PLANES

2. POINTS

3. ANGLES

4. CURVE

5. SURFACE

POINTS -

A point is, in essence, a location or a position in space or on a plane. Points "P0" and "P1" represent two positions on the specified line, as may be seen in the image below. Each of these sites is situated in relation to its origin.

LINES -

A line is an endlessly long, completely straight, one-dimensional form that has no thickness and may be drawn in both directions.

PLANES -

A plane is a figure that may be stretched endlessly and is flat and two dimensional. The Plane therefore includes areas, perimeters, and 2D shapes like triangles and quadrilaterals.

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Answer:

The laws of exponents are:

a)  (x^n)*(x^m) = x^(n + m)

b)  (x^n)/(x^m) = x^(n - m)

c)  (x^n)^m = x^(n*m)

Now, let's see the given equations:

1) (x-²)-³ = x⁶   (true)

Here we se the third law, the "c"

(x^(-2))^(-3) = x^(-2*-3) = x^6

Then this equation is correct.

2)  (a^m)^n = a^m^n   (false)

This law does not exist, this is false.

An example of why this is false is:

Let's use the values:

a = 2, m = 1, and n = 2

then, in the left side we have:

(2^1)^2 = (2)^2 = 4

And in the right side we have:

2^(1^2) = 2^(1) = 2

We can see that we have different things in the left side than in the right side, then that relation is false.

3)  a⁰ = 0  (false)

Let's rewrite this as:

a^0 = a^(n - n)

Now we can use the second law to rewrite this as:

a^(n - n)  = (a^n)/(a^n)

And we have a number divided by the exact same number, we know that this is equal to 1, then:

(a^n)/(a^n) = 1

this means that:

a^0 = 1.

Then this is also false.

The only correct option is the first one.

Answer:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a right triangle to represent the situation:

        |\

        | \

   h    |  \   9 ft

        |   \

        |    \

        |     \

        -------

        6 ft

Here, h represents the height on the wall where the ladder touches. We want to find the angle of elevation θ.

Using the right triangle, we can write:

sin(θ) = h / 9

cos(θ) = 6 / 9 = 2 / 3

We can solve for h using the Pythagorean theorem:

h^2 + 6^2 = 9^2

h^2 = 9^2 - 6^2

h = √(9^2 - 6^2)

h = √45

h = 3√5

So, sin(θ) = 3√5 / 9 = √5 / 3. We can solve for θ by taking the inverse sine:

θ = sin^-1(√5 / 3)

θ ≈ 37.5 degrees

Therefore, to the nearest tenth of a degree, the angle of elevation the ladder makes with the ground is 37.5 degrees.

The area of an obtuse triangle can be found using the formula A = 1/2 (b*h), where b is the base length and h is the height of the triangle.

The area of an obtuse triangle can be found using the formula A = 1/2 (b*h), where b is the base length and h is the height of the triangle. This formula is derived from the fact that the area of any triangle is half of the product of its base and height. An obtuse triangle is a triangle with one obtuse angle, meaning that one of its angles is greater than 90 degrees. To determine the area of an obtuse triangle, you must first identify the base and the height. The base is the length of the side opposite the obtuse angle, while the height is the length of the line that is perpendicular to the base and passes through the vertex of the obtuse angle. After the base and height have been determined, the formula A = 1/2 (b*h) can be used to calculate the area of the triangle.

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The value of the expression is r'(t) = (4, 6t, 12t²), T(1) = (2/7, 3/7, 6/7), r''(t) = (0, 6, 24t), r'(t) ร r''(t) = 144t³.

We are given the vector-valued function r(t) = (4t, 3t², 4t³).

To find r'(t), we need to take the derivative of each component of r(t) with respect to t:

r'(t) = (d/dt)(4t), (d/dt)(3t²), (d/dt)(4t³)

r'(t) = (4, 6t, 12t²)

To find T(1), we need to evaluate r'(t) at t = 1 and then divide by the magnitude of r'(1):

r'(1) = (4, 6(1), 12(1)²) = (4, 6, 12)

| r'(1) | = sqrt(4² + 6² + 12²) = sqrt(196) = 14

T(1) = r'(1) / | r'(1) | = (4/14, 6/14, 12/14) = (2/7, 3/7, 6/7)

To find r''(t), we need to take the derivative of each component of r'(t) with respect to t:

r''(t) = (d/dt)(4), (d/dt)(6t), (d/dt)(12t²)

r''(t) = (0, 6, 24t)

Finally, to find r'(t) ร r''(t), we need to take the dot product of r'(t) and r''(t):

r'(t) ร r''(t) = (4, 6t, 12t²) ร (0, 6, 24t)

r'(t) ร r''(t) = 0 + 6t(6t) + 12t²(24t)

r'(t) ร r''(t) = 144t³

Therefore, we have:

r'(t) = (4, 6t, 12t²)

T(1) = (2/7, 3/7, 6/7)

r''(t) = (0, 6, 24t)

r'(t) ร r''(t) = 144t³

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Answer:

what is the area of a triangle with a base of 2 5/8mm and a height of 10mm

Step-by-step explanation:

C.16 3/8mm2

Answer:

13 1/8mm² is your answer

Step-by-step explanation:

the area of a triangle with a base of 2 5/8mm and a height of 10mm.

=1/2 base×height=1/2×2 5/8 ×10=1/2×21/8×10

=21/8×5=105/8=13 1/8mm²

here

2 5/8=21/8

Answer:

2^845 is greater than 5^362.

Step-by-step explanation:

To compare the two numbers, we can evaluate them using the logarithm function with base 2 and base 5 respectively.

2^845 = 2^(845 * log2(2)) = 2^(845 * 1) = 2^845

5^362 = 5^(362 * log5(5)) = 5^(362 * 1) = 5^362

The logarithm of a number is the exponent to which the base must be raised to give that number. Since logarithm function is a monotonically increasing function, if we compare log base a of x to log base a of y, logarithm of x is greater than y if x is greater than y.

So 2^845 > 5^362 if 845 > 362 * log5(2)

We can calculate log5(2) = log5(2)/log5(2) = 0.6309

so 845 > 362 * 0.6309

845 > 229.8198

so 845 is greater than 229.8198, therefore 2^845 is greater than 5^362.

Answer:

Step-by-step explanation:

2^845 = 2^5(2^7)^120 = 32(128)^120,

5^362 = 5^2(5^3)^120 = 25(125)^120,

2^845 is bigger.

Answer:

A

Step-by-step explanation:

x² - 12x + 35

consider the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (- 12)

the factors are - 5 and - 7 , since

- 5 × - 7 = + 35 and - 5 - 7 = - 12 , then

x² - 12x + 35 = (x - 5)(x - 7) ← in factored form

Answer:

y = - \(\frac{1}{5}\) x - 9

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Given

4x + 20y = - 180 ( subtract 4x from both sides )

20y = - 4x - 180 ( divide all terms by 20 )

y = \(\frac{-4}{20}\) - \(\frac{180}{20}\) , that is

y = - \(\frac{1}{5}\) x - 9 ← in slope- intercept form

Answer:

190.47 (190 47/100)

Step-by-step explanation:

First, you need to find a common denominator, which is 100. So multiply 3/10 by 10 with both the numerator and denominator. So your new equation should be 382 30/100 - 191 87/100. Even though 382 is larger than 191, 3/100 is still less than 87/100. So what you do is cross out the first/whole number and then add the denominator.

Hope this helped! <3

Answer:

190.43

Step-by-step explanation:

Convert the denominator to 100

> 382 30/100 - 191 87/100

Subtract the whole numbers and the fractions separately

> (382 -191) + (30/100 - 87/100)

> 191 + (-57/100)

> 190 43/100

= 190.43

The perimeter of the triangle will be 28.73 and the area will be 37.86.

The following information can be Illustrated:

Angle A = 60°

Angle C = 45°

Length of side AB = 8

Since the sum of angles in a triangle is equal to 180°. This will be Illustrated as:

B = 180 - (60 + 46)

B = 75°

Using the sine rule:

BC / sin60 = 8 / sin45

BC = 9.8

The length of AC will be:

AC = 8 / sin45° × sin 75°

AC = 10.93

The perimeter of the triangle will be:

= AB + BC + AC

= 8 + 9.8 + 10.93

= 28.73

The area of the triangle will be:

= 1/2 × AB × AC × Sin(A)

= 1/2 × 8 × 10.93 × sin 60

= 37.86

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Complete question

Given: △ABC, m∠A=60° , m∠C=45°, AB=8 Find: Perimeter of △ABC and the Area of △ABC

The diagram that shows the scope of the system, indicating what elements are inside and outside the system, is called a system boundary diagram or a system context diagram.

It is a graphical representation that helps to define the boundaries of the system under consideration and identify its inputs, outputs, and interfaces with other systems or elements in its environment. The system boundary diagram is an important tool in systems thinking and analysis as it allows us to focus on the essential components of the system and understand how it interacts with its surroundings.

what is diagram?

A diagram is a visual representation of information, data, or ideas. It is a graphical or symbolic representation of concepts, relationships, or processes that are often complex or difficult to understand in written or verbal form. Diagrams are used in many different fields, including science, engineering, mathematics, business, and education, to communicate ideas and simplify complex information

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Answer:

8

Step-by-step explanation:

x=25-17

x=8

don't forget to collect like terms

Answer:

27

Step-by-step explanation:

The first angle you get with 180-61 = 119

The second angle you get by the rules of the circle which is 68/2 = 32

And finally X= 180 - 119 - 32 = 27

Answer:

Median = 116

Quartiles and median can be calculated from histograms.

From the histogram, we have the following frequency table:

\(\left[\begin{array}{ccc}Score&Frequency&Cumulative\\80 - 90&2.6&2.6&90 - 100&3.4&6&100 - 110&5&11&110 - 120& 5 & 16&120 - 130&3&19&130 - 140& 3 &22 &140 - 150&1.4&23.4& 150 - 160& 1.4 &24.8 & 160 - 170 & 1.4 &26.2 & 170 - 180 & 0.6 & 26.8& 180 - 190 & 0.6 & 27.4 &190 - 200&0.6&28\end{array}\right]\)

(a) The median

Calculate the median class as follows

\(\mathbf{Q_2 = \frac{1}{2}(n)}\)

This gives

\(\mathbf{Q_2 = \frac{1}{2}(28)th}\)

\(\mathbf{Q_2 =14th}\)

The 14th element belongs to 110 - 120 class

The median value is then calculated as:

\(\mathbf{Median = L + \frac{(n/2 -cf)}{f} \times h}\)

Where:

\(\mathbf{n/2 = 14}\)

\(\mathbf{L = 110}\) --- lower limit of the median class

\(\mathbf{cf =11}\) ---- cumulative frequency of the class before the cumulative frequency

\(\mathbf{f = 5}\) ---- frequency of the median class

\(\mathbf{h = 10}\) --- the class size

So, we have:

\(\mathbf{Median = 110 + \frac{14 - 11}{5} *10}\)

\(\mathbf{Median = 110 + \frac{3}{5} *10}\)

\(\mathbf{Median = 110 + 0.6 *10}\)

\(\mathbf{Median = 110 + 6}\)

\(\mathbf{Median = 116}\)

Hence, the median is 116

(b) The lower quartile

Calculate the median class as follows

\(\mathbf{Q_1 = \frac{1}{4}(n)}\)

This gives

\(\mathbf{Q_1 = \frac{1}{4}(28)th}\)

\(\mathbf{Q_1 =7th}\)

The 7th element belongs to 100 - 110 class

The median value is then calculated as:

\(\mathbf{Q_1 = L + \frac{(n/4 -cf)}{f} \times h}\)

Where:

\(\mathbf{n/4 = 7}\)

\(\mathbf{L = 100}\) --- lower limit of the lower quartile class

\(\mathbf{cf =6}\) ---- cumulative frequency of the class before the cumulative frequency

\(\mathbf{f = 5}\) ---- frequency of the median class

\(\mathbf{h = 10}\) --- the class size

So, we have:

\(\mathbf{Q_1= 100 + \frac{7 - 6}{5} *10}\)

\(\mathbf{Q_1= 100 + \frac{1}{5} *10}\)

\(\mathbf{Q_1= 100 + 0.2 *10}\)

\(\mathbf{Q_1= 100 + 2}\)

\(\mathbf{Q_1= 102}\)

Hence, the lower quartile is 102

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Answer:C SSS

Step-by-step explanation:

I got SSS because with the given sides equal, it can be said R is the midpoint of QT therefore QR≈RT and the triangles are congruent by SSS. The theorem used was midpoint theorem

Method:

Front: 6x8 = 48/2 = 24

Back: Also 24

Base: 8x4 = 32

Left: 6x4=24

Add your answers:

24 + 24 + 24 + 32 + 40

Answer:

TSA is 144 cm²

Answer:

The length of the line segment is

d = √(x₂ - x₁)² + (y₂ - y₁)²

(1) One of the six countries sent 41 representatives to the congress --> obviously x6=41x6=41 --> x1+x2+x3+x4+A=34x1+x2+x3+x4+A=34.

Given: x1<x2<x3<x4<A<x6x1<x2<x3<x4<A<x6 and x1+x2+x3+x4+A+x6=75x1+x2+x3+x4+A+x6=75. Q: is A≥10A≥10

Can A≥10A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11 --> sum=34sum=34 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9 --> sum=34sum=34 (answer to the question NO).

(2) Country A sent fewer than 12 representatives to the congress --> A<12A<12.

The same breakdown works here as well:

Can 12>A≥1012>A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11, x6=41x6=41 --> sum=75sum=75 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9, x6=41x6=41 --> sum=75sum=75 (answer to the question NO).

(1)+(2) The given examples fit in both statements and A in one is more than 10 and in another less than 10. Not sufficient.

Answer:

misstype?

Step-by-step explanation:

Answer:

Mistype?

Step-by-step explanation:

Carry learning!

Stay safe!

Study hard!

Answer:

C. 4.83

Step-by-step explanation:

60/72 = 0.83333333

so the answer is 4.8333333

The best point estimate for the average number of classes per semester for all students at the local college is 4, based on the study that found students completed an average of 4 classes per semester and the sample of 132 students that was taken.

Based on the information provided, the best point estimate for the average number of classes per semester for all students at the local college can be calculated as follows:
1. Identify the sample average: In this case, it is given that students completed an average of 4 classes per semester.
2. Determine the sample size: Here, the sample size is 132 students.
Since the point estimate is essentially the sample average, the best point estimate for the average number of classes per semester for all students at the local college is 4.

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Answer:

360.124 in expanded and exponential form :

300+60+1/10+2/100+4/1000