wants to join a gym. The cost of a gym membership is a one time $100 fee plus $30 per month. Write an expression that describes the cost of gym membership after M months.

Answer:

24

Step-by-step explanation:

area = wl (6×4 = 24)

w width l length

The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

To solve the inequality y + 7 ≤ -1, we need to isolate the variable y on one side of the inequality sign.

Starting with the given inequality:

y + 7 ≤ -1

We can begin by subtracting 7 from both sides of the inequality:

y + 7 - 7 ≤ -1 - 7

y ≤ -8

The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

In the context of a number line, all values to the left of -8, including -8 itself, will make the inequality true. For example, -10, -9, -8, -8.5, and any other value less than -8 will satisfy the inequality. However, any value greater than -8 will not satisfy the inequality.

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The following question may be like this:

What is a solution of the inequality shown below? y+7≤-1

option : c. 2x + 15 = 145

cuz, the angles are vertical opposite angles

Answer:

2x + 15 = 145

Step-by-step explanation:

vertical angles are congruent

=> (2x + 15)° = 145°

To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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Answer: 35

Step-by-step explanation:

Answer:

(x-1990)×25

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

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HAVE A GREAT DAY

The Equation is 25x-47500 as a function of the number of years since 1990.

To find equation for the number of students .

Statement that the values of two mathematical expressions are equal.

Given that:

The number of students in high school has been increasing linearly since 1990.

In 1997, 1125 students and in 2000, there were 1200 students.

Increase the number of students in 1997-2000

=1200-1125=75

In 3 years 75 student increased

In 1st years 25 student increased

number of students that will  increasing  in 1990=25

Equation=(x-1900)*25

Equation=25x-47500

where x is date/year

So, the Equation is 25x-47500 as a function of the number of years since 1990.

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Answer:

y + 2.4 ≤ 35

Step-by-step explanation:

Less than or equal to sign is ≤

The sentence can be represented by the inequality:

y + 2.4 ≤ 35

Subtract 2.4 from both sides

y + 2.4 - 2.4 ≤ 35 -2.4

y ≤ 35 - 2.4

y ≤ 32.6

Therefore, y is less than or equal to 32.6

Answer

Sum of the first 13 terms = 8191

Explanation

The sum of terms in a geometric term is given as

where

a = first term = 1

r = common ratio = ratio of consecutive terms = (Second term)/(First term) = (2/1) = 2

n = number of terms = 13

Hope this Helps!!!

When A is 14 and C is 18, the value of B is 7.74.

Value is a term that can be used in many different contexts to describe the importance of something. It can be used to describe the value of a good or service in terms of its office utility, its capacity to satisfy a need or desire, or its extreme usefulness. Value can also refer to a person or a group in terms of their value or contribution to society.

The Pythagorean Theorem is the equation

A² + B² = C²

It says that the square of the longest side of a right triangle is equal to the sum of the squares of the two shorter sides (the hypotenuse).

In the example given, A is 14 and C is 18.

To find B, we must solve the equation.

We can do this by substituting

A = 14 and C = 18

This gives us:

A² + B² = C²

14² + B² = 18²

We can now subtract 14² From both sides of the equation,

giving us B² = 18² - 14²

or B² = 256 - 196,

or B² = 60.

Finally, we take the square root of both sides of the equation to find B: B = √60, or B = 7.74.

Therefore, when A is 14 and C is 18, the value of B is 7.74.

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tan ? = 22/48

tan ? = 11/24

tan ? = 0.4583

? = 24.62 degrees ( approximately )

\(\tan(?)=\dfrac{22}{48} \\\\ ?=\arctan\dfrac{22}{48} \approx24^{\circ}\)

Answer:

1025

Step-by-step explanation:

 1 0 0 0

+      2 5

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

 1  0 2 5

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

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A statistic can never be larger than a parameter is not a correct statement. The correct statement among the following is as follows: IV Only. The statement "A statistic can be calculated whereas a parameter can never be established" is the correct statement.

Statistics and parameters are two fundamental concepts in statistical analysis. Both of these concepts are widely used in various researches and surveys.

A statistic is a numerical value that represents a particular characteristic of the sample and is used to estimate an unknown parameter. A parameter is a numerical value that represents a particular characteristic of a population.Statistics can be larger, smaller, or equal to parameters. A statistic is a value that is calculated from a sample, whereas a parameter is a value that represents a population characteristic and is estimated from the sample.A parameter can be established, but it is only possible if the entire population is considered for analysis. In contrast, a statistic is calculated from a sample of the population and represents only the characteristics of the sample.

:A statistic can never be larger than a parameter is not a correct statement. The correct statement is IV Only. The statement "A statistic can be calculated whereas a parameter can never be established" is the correct statement.

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Hello

To solve this question, we would solve for the area of the semi-circle and area of the rectangle.

The dimensions of the rectangle is

Area of a rectangle is given as

The area of the rectangle is 6600m^2

The formula of area of a semi-circle is

But the radius would be half the value of the width of the training field

Area of the semi-circle is

The area of the semi-circle is 1709.73m^2

The area of the training field is area of the rectangle + 2(area of the semi-circle)

NB: We are multiplying the area of the semi-circle by 2 because we have two semi-circle attached to the rectangle

The area of the training pitch is

From the calculations above, the area of the training pitch is 10019.46m^2

The difference between the length and width of the garden is 2.55 yards.

Two or more expressions with an Equal sign is called as Equation.

Given that jan created a garden that was 8.5 yards long and 5.95 yards wide.

Length=8.5 yards

Width=5.95 yards.

We need to find the difference between the length and width of the garden.

8.5-5.95

Eight point five minus five point nine five

2.55

Hence,  the difference between the length and width of the garden is 2.55 yards.

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The proof of the congruent sides RU and TS is given below.

What is congruent triangles?

In any orientation, two triangles are said to be congruent if their three sides and three angles are equal.

Therefore, if two triangles have the same number of sides on each side, they are said to be congruent. Additionally, we can determine that they are congruent if we have a side, an angle between the sides, and then another side that is congruent, in that order: side, angle, side.

Let the given figure is a rectangle RSTU.

Since the all four angles of rectangle are of 90 degree.

So, each angle of rectangle RSTU is 90 degree.

Let, US divides the angle RUT and angle RST and form two new triangles, ΔSRU and ΔSTU.

Both the triangles having same measure of angles and sides.

⇒  ΔSRU ≅ ΔSTU

As the triangles are congruent so their sides are congruent.

Hence, RU is congruent to TS.

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An equation of the plane containing the point (1,2,1) and perpendicular to the planes L_1 :x+y=2 L_2 :2x+y−z=1 is  -x + y - z + 2 = 0.

First, let's find the normal vectors of L1 and L2:

Normal vector of L1: (1, 1, 0)

Normal vector of L2: (2, 1, -1)

Next, we'll find the cross product of these two normal vectors:

(1, 1, 0) x (2, 1, -1) = (-1, 1, -1)

The cross product (-1, 1, -1) gives us a vector perpendicular to both planes L1 and L2. Now, we can use this vector and the point (1, 2, 1) to form the equation of the desired plane.

Using the point-normal form of a plane equation, the equation of the plane containing the point (1, 2, 1) and perpendicular to planes L1 and L2 is:

-1(x - 1) + 1(y - 2) - 1(z - 1) = 0

Simplifying the equation, we get:

-x + y - z + 2 = 0

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The equation of the line passing through the points (0,-2) and (2,0) is y = x - 2.

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, and can be represented using symbols and/or words. Equations are used to solve problems in mathematics, science, engineering, and other fields.

In the given question,

We can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

First, we need to find the slope of the line passing through the points (0,-2) and (2,0):

slope = (change in y)/(change in x)

slope = (0 - (-2))/(2 - 0)

slope = 2/2

slope = 1

Now that we have the slope, we can use one of the given equations and substitute the coordinates of one of the points to find the y-intercept:

y = mx + b

-2 = 1(0) + b

b = -2

So the equation of the line passing through the points (0,-2) and (2,0) is y = x - 2.

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To determine the distance between the buildings, we can use trigonometry and the given information. Let's consider the triangle formed by Sari, building A, and building B. The side opposite the 40° angle is the distance between the buildings that we want to find.

Using the tangent function, we can set up the following equation: tan(40°) = opposite/adjacent. tan(40°) = distance between the buildings/20 meters. To find the distance between the buildings, we rearrange the equation: distance between the buildings = 20 meters * tan(40°). Using a calculator, we can evaluate the expression: distance between the buildings ≈ 20 meters * 0.8391 ≈ 16.782 meters. Therefore, the buildings are approximately 16.782 meters apart. To determine the distance between the buildings, we can use trigonometry and the given information. Let's consider the triangle formed by Sari, building A, and building B. The side opposite the 40° angle is the distance between the buildings that we want to find.

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The probability of selecting two socks of same color is 0.96.

According to the given question.

Total number of green socks = 4

Total number of yellow socks = 6

So, the total number of socks in a drawer = 4 + 6 = 10

Since as we know that, the probability of an event is computed as: P(E) = Number of favourable outcome /Total number of outcomes. Hence, the probability is the possibility of the occurrence of a random event.

So, the probability of selecting a green scoks = 4/10 = 2/5

And the probability of selecting a yellow socks = 6/10 = 3/5

Therefore, the probability of selecting two socks of same color

= probability of selecting both the green socks or probability of selecting both the yellow socks

= [( 2/5) + (2/5)] × [(3/5)+(3/5)]

= (4/5) × (6/5)

= 24/25

= 0.96

Hence, the probability of selecting two socks of same color is 0.96.

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Answer:

57

Step-by-step explanation:

Straight line value=180

Given Value=123

Value of ∆TKL

=180-123

=57(Ans)

Answer:

57

Step-by-step explanation:

The required area of the circle is 50.24cm².

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

So, we have the circumference:

8π

Now, calculate for π as follows using the circumference formula (2πr):

8π = 2πr

8π/2π = r

4 = r

Now, calculate the area when r = 4cm (πr²) as follows:

πr²

π(4)²

16π

50.24

Therefore, the required area of the circle is 50.24cm².

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Complete question:
The circumference of a circle is 8π cm. what is the area in square centimeters?

Explanation:

The flat horizontal portion S is where the distance (y) does not increase or decrease. So Ted is stationary during this time frame.

In terms of speed, we would say speed = distance/time = (change in y)/(change in x). Note how this is the slope.

Rise = 0 because the horizontal line does not go up or down. The run is any positive number, though convention usually has Run = 1. Therefore, slope = rise/run = 0/1 = 0. All flat horizontal lines have a slope of 0 to indicate no upward or downward movement.

The ratio of the time taken to compute LU factorization vs. back/forward substitution depends on several factors such as the size and sparsity of the matrix, the specific implementation of the algorithms, and the hardware used to perform the computations.

However, in general, LU factorization takes more time than back/forward substitution. This is because LU factorization involves decomposing the original matrix into two matrices, L and U, which requires more computations than simply solving the system of equations using back/forward substitution once the L and U matrices are available.

As a rough estimate, the time taken for LU factorization can be several times larger than the time taken for back/forward substitution, especially for large and dense matrices.

However, the exact ratio can vary widely depending on the specific factors mentioned above.

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Answer:

200 cm³ is the volume of the pyramid

Answer:

200 cubic centimeters

Step-by-step explanation:

l = length = 10 cm

w = width = 10 cm

h = height = 6cm

V = lwh / 3

= 10 * 10 * 6 / 3

= 100 * 6 / 3

= 600 /3

= 200 cubic cm

Hope this helps! Tell me if I am incorrect!

Answer:

the answer is 9

Step-by-step explanation: