What is the coefficient in the algebraic expression 5x + 2

The transformed function would have a value of -5 when the parent root function has a value of 4.

The function that transforms the parent root function with a horizontal compression by a factor of 2 and a downward shift of 6 units can be represented as follows:

\(f(x) = \frac{1}{2} \times \sqrt{x} - 6\)

This function takes the parent root function, which is represented as \(\sqrt{x}\), and applies a horizontal compression by a factor of 2 by dividing the function by 2. It then applies a downward shift of 6 units by subtracting 6 from the function.

For example, if we input the value x = 4 into the function, we would get the following result:

\(f(4) =\frac{1}{2} \times \sqrt{4} - 6 = \frac{1}{2} \times 2 - 6 = 1 - 6 = -5\)

This means that the transformed function would have a value of -5 when the parent root function has a value of 4.

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The equation of the circle with center (3, -4) and a radius of 6 units is (x - 3)^2 + (y + 4)^2 = 36.

The equation of a circle with center (h, k) and radius r is:

(x - h)^2 + (y - k)^2 = r^2

Substituting the values given, we get:

(x - 3)^2 + (y + 4)^2 = 6^2

Expanding and simplifying, we get the final equation of the circle:

(x - 3)^2 + (y + 4)^2 = 36

Therefore, the equation of the circle with center (3, -4) and a radius of 6 units is (x - 3)^2 + (y + 4)^2 = 36.

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Answer:

44 ft^2

Step-by-step explanation:

so first, you get the area for the outer rectangle

12*4=48

so the area is 48, but there is a 2x2 square cut out so subtract that area

2*2=4

48-4=44

Answer:

x = -32

Step-by-step explanation:

You must get the variable (x) on one side in order to solve this problem. Do this by multiplying 4 on both sides in order to get rid of the fraction. -8 times 4 is -32, so the equation should now read to be x=-32

The geometric mean of 3√5/4 and 5√5/4 is 5√3/4.

Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.

To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.

The formula for the geometric mean is given by:

GM = n√x1 x2 . . . xn

Solving for the geometric mean between 3√5/4 and 5√5/4 using the formula:

GM = n√x1 x2 . . . xn

where n = 2, x1 = 3√5/4, and x2 = 5√5/4

GM = √(3√5/4)(5√5/4)

GM = √(75/16)

GM = 5√3/4

Hence, the geometric mean of 3√5/4 and 5√5/4 is 5√3/4.

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Answer:

\( \sqrt{15 } > \pi\)

Step-by-step explanation:

The left side is greater than the right side, which means that the given statement is always true.

The equation x² + 1 = 37 can be solved by factoring. The solutions are x = 6 and x = -6. These solutions can be checked by substituting them back into the original equation and verifying that both sides are equal.

To solve the equation x² + 1 = 37 by factoring, we rearrange the equation to obtain x² = 36. We recognize that 36 can be factored as the square of 6, so we have (x - 6)(x + 6) = 0. By setting each factor equal to zero, we find two possible solutions: x - 6 = 0, which gives x = 6, and x + 6 = 0, which gives x = -6.

To check the solutions, we substitute x = 6 and x = -6 back into the original equation x² + 1 = 37. When x = 6, we have 6² + 1 = 37, which is true. Similarly, when x = -6, we have (-6)² + 1 = 37, which is also true. Hence, both solutions satisfy the original equation.

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To obtain the lateral surface area of a triangular pyramid, you need to calculate the combined area of all the triangular faces excluding the base.

Here's the step-by-step process:

1. Identify the base and the height of the triangular pyramid.

The base is a triangle, and the height is the perpendicular distance from the base to the apex of the pyramid.

2. Calculate the area of each triangular face.

For each triangular face, you need to determine the length of the base of the triangle (b) and the corresponding height (h) perpendicular to that base.

Calculate the area of each face using the formula: Area = (1/2) * base * height.

3. Sum up the areas of all the triangular faces.

Add up the areas of all the triangular faces to obtain the lateral surface area.

The formula for the lateral surface area (LSA) of a triangular pyramid can be expressed as:

LSA = Area_face1 + Area_face2 + Area_face3 + ...

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Answer:

  perimeter = 16 ft

Step-by-step explanation:

You want the perimeter of an isosceles triangle with side length 5 ft and altitude 4 ft.

The side lengths being equal mean the triangle is isosceles. That also means altitude PS bisects the peak angle and segment QR. Once we find the length QS using the Pythagorean theorem, we can double that measure to find QR.

The Pythagorean theorem tells us ...

  QS² +PS² = QP²

  QS² +(4 ft)² = (5 ft)²

  QS² = (25 ft²) -(16 ft²) = 9 ft² . . . . . evaluate squares, subtract 16 ft²

  QS = √(9 ft²) = 3 ft

Now we know the base length is ...

  QR = 2·QS = 2(3 ft) = 6 ft

The perimeter is the sum of the outside edge lengths:

  Perimeter = PQ +QR +RP

  Perimeter = (5 ft) +(6 ft) +(5 ft) = 16 ft

The perimeter of ∆PQR is 16 feet.

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Additional comment

With some practice, you can learn to recognize a 3-4-5 right triangle. That is the triangle used here for each of the right triangles that make up ∆PQR. Once you identify the long side as 4 and the hypotenuse as 5, you know immediately the short side is 3.

The set {3, 4, 5} is called a "Pythagorean triple." Other triples commonly seen in high school problems are {5, 12, 13}, {7, 24, 25}, {8, 15, 17}. Legs of these lengths form a right triangle. Knowing any two (or their ratio) tells you immediately the value of the third. Of course, these triples can be scaled by any factor. (3, 4, 5) scaled by 2 is (6, 8, 10), another commonly seen triple.

There are no isosceles right triangles that have integer values for both the legs and the hypotenuse. If the legs are both 4, the hypotenuse will be 4√2 ≈ 5.657... (an irrational number), not 5.

Tangent of a circle is a line which touches the circle at a point from outside the circle.

Given a tangent to a circle through a point outside the circle.

We have to draw a tangent to a circle from point outside the circle.

Tangent of a circle is a line which touches the circle at a point from outside the circle.. The point at which tangent touches the circle is known as point of contact.The radius of the circle and tangent are perprndicukar to each other at the point of contact. There cannot be any tangent  to the circle through a point inside the circle. There can be one tangent to a point on the circle. The steps of drawing a tangent to a circle are as under:

1) Draw a circle with the radius neede with center O.

2) Join center of the circle O and any point P on the circle OP is the radius of the circle.

3) Draw a line perpendicular to radius OP through point P which is the intersection point of tangent and circle.

This line is the tangent to the circle at P.

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Answer:

igu

you could crop out question n use pic :)

Answer: B

Step-by-step explanation:

First find the area of the rectangle:

A = lw

A = 6*12 = 72 mm^2

Find the area of the semi circle:

A = (pi*r^2)/2

A = (3.14)*(3^2)/2 = 14.13 mm^2

Total area = 72 + 14 = 86 mm^2

Answer:

\(\frac{x^{2}}{400} + \frac{y^{2}}{976} = 1\)

Step-by-step explanation:

The distance between foci with respect to origin is determined by mean of the Pythagorean Theorem:

\(2\cdot c = \sqrt{(0-0)^{2}+[24-(-24)]^{2}}\)

\(2\cdot c = 48\)

\(c = 24\)

The distance between origin and any of the horizontal co-vertices is:

\(a = \sqrt{[10-(-10)]^{2}+(0-0)^{2}}\)

\(a = 20\)

Now, the distance between origin and any of the vertical co-vertices is determined by the following Pythagorean relationship:

\(c^{2} = b^{2} - a^{2}\)

\(b^{2} = a^{2} + c^{2}\)

\(b = \sqrt{a^{2}+c^{2}}\)

\(b = \sqrt{20^{2}+ 24^{2}}\)

\(b = 4\sqrt{61}\)

Lastly, the equation of the ellipse in standard form is:

\(\frac{x^{2}}{400} + \frac{y^{2}}{976} = 1\)

Answer:

x^2/100+y^2/676=1

Step-by-step explanation:

Answer:

833.85 m²

Step-by-step explanation:

area of trapezium = 1/2 ( a + b ) * h

                              = 1/2 ( 13 + 38 ) * 32.7

                               = 833.85 m²

Answer:

Step-by-step explanation:

We know that:

Work:

Hence, the area of the trapezoid is 833.9 m².

A zip code is a sequence of 5 digits, each between 0 and 9, there are 100,000 possible five-digit zip codes.

The number of possible five-digit zip codes, the number of options for each digit position.

Since each digit  any number from 0 to 9 (10 options), there are 10 possibilities for the first digit, 10 possibilities for the second digit, 10 possibilities for the third digit, 10 possibilities for the fourth digit, and 10 possibilities for the fifth digit.

To find the total number of possible zip codes, the number of possibilities for each digit position together:

10 × 10 × 10 × 10 × 10 = 100,000

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Answer:

3rd statement is correct

Since, the average age of 33 fifth-graders is 11. the average age of 55 of their parents is 33. The average age of all of these parents and fifth graders is 24.75.

Average age of the population calculated as the arithmetic mean. Another parameter determining the average age of the population is the median age. High-level terms.

Given In the question:

Average age of 33 fifth graders is 11 years.

Average age of parents is 33 Years.

Therefore,

The sum of the ages of the fifth graders is 33 × 11,

and, the sum of the ages of the parents is 55 × 33.

Therefore, the total sum of all their ages must be 2178,

and given 33 + 55 = 88 people in total, their average age is

                                  = 2178/88

                                  = 99/4

                                  = 24.75    

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Answer:

  22. x = 0.228 or 8.772

  24. x = -0.869 or 1.535

Step-by-step explanation:

The solutions are all irrational, so it would be tedious arriving at a solution using tables. I prefer a graphing calculator for this.

The first attachment shows the problems with graphs of left-side and right-side expressions. The points of intersection are the solutions.

The second attachment shows the difference of the two sides of the equation. The x-intercepts of that difference are the solutions. The graph also shows the vertex of the quadratic, which lets you write down the exact solution. For y = a(x -h)^2 +k, the solutions are x = h ±√(-k/a) where (h, k) is the vertex and 'a' is the leading coefficient of the quadratic.

__

22. x = 0.228 or 8.772

  graphs in first attachment are red and orange

  graph in second attachment is black

  x = 4.5 ± √18.25

__

24. x = -0.869 or 1.535

  graphs in first attachment are blue and purple

  graph in second attachment is red ('a' = 3)

  x = (1 ±√13)/3

To determine which of the given quadrature formulas are of the interpolatory type, let's first understand the concept of an interpolatory quadrature formula.

An interpolatory quadrature formula is one that approximates the integral of a function using a weighted sum of the function's values at specific points, known as nodes.

Now let's analyze the given quadrature formulas:

a) Sf(dx*(2))

This formula doesn't provide any information about the nodes or weights to be used for approximation.

Therefore, we cannot determine if it is of the interpolatory type.

b) Sf(a)dx = f(-1) + f(1)

This formula approximates the integral of a function using the sum of the function's values at the nodes x = -1 and x = 1.

The weights associated with these nodes are both 1.

Since this formula uses specific nodes and weights, it can be considered an interpolatory quadrature formula. In conclusion, the second formula (Sf(a)dx = f(-1) + f(1)) is of the interpolatory type.

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Answer:

c; y = 2x

Step-by-step explanation:

if it was without the coupon the fee would be the $2 per mile (2x) with the $35 which would be

y = 2x + 35

but with the coupon the $35 reservation is removed so only 2x is left

y = 2x

The probability of the event B, which is the probability that a person prefers pie, is approximately 0.2345.

From the venn diagram, we can see that there are a total of 24 + 93 + 10 + 18 = 145 people.

The event B represents the people who prefer pie, which is 24 + 10 = 34 people, because these are the people who prefer pie or both pie and cake.

So the probability of the event B, P(B), is the proportion of people who prefer pie or both pie and cake out of the total number of people:

P(B) = (number of people who prefer pie or both pie and cake) / (total number of people)

P(B) = (24 + 10) / 145

P(B) = 34 / 145

P(B)= 0.2345

Therefore, the probability of the event B, which is the probability that a person prefers pie, is approximately 0.2345.

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Answer:

1, 2, 4, 8, 16, 32, 64

Step-by-step explanation:

There are 6 possible arrays for 64.

An array is a set of items, images, or numbers arranged in rows and columns. Arrays are practical illustrations of multiplication ideas.

The given number is,

64.

To find the array for the number 64,

Find factors of 64.

Factors

= 64, 32, 16, 8, 4, 2, 1

The number of factors = 6

Hence, total 6 possible arrays for 64.

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Receipt of May is 835

Net cash flow of April is 210

Cumulative balance of March is 240

Explanation

Net cash flow = Receipt - Expense

Receipts amount = Expenses+Net cash flow

Cumulative balance amount =Cumulative amount for April-Net cash flow for April

1,3,4 that is the answer

Answer:

Step-by-step explanation:

x³ + 6x² + 5x - 12

A factor of the polynomial is the value of x when substituted into the expression will make it zero

Choosing x + 4

x = - 4

We have

(- 4)³ + 6(- 4)² + 5(- 4) - 12

-64 + 96 - 20 - 12 = 0

Since the result is zero

x + 4 is a factor of the polynomial

Hope this helps you

Answer:

375

Step-by-step explanation:

Lily paid $750 each month for 36 months to pay off her car loan.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example: so

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To calculate the amount that Lily paid each month, we can divide the total cost of the car by the number of monthly payments:

So,

Amount paid each month

= Total cost / Number of payments

In this case,

The total cost is $13,500 and the number of payments is 36:

Amount paid each month = $13,500 / 36

We can simplify this fraction by dividing both the numerator and the denominator by the greatest common factor of 13,500 and 36, which is 18:

Amount paid each month = $750

Therefore,

Lily paid $750 each month for 36 months to pay off her car loan.

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The probability that the average number of moths in 60 traps is greater than 0.4 is approximately 0.9738 or 97.38%.

(a) To find the mean and standard deviation of the average number of moths in 60 traps, we can use the properties of the normal distribution and the central limit theorem.

The mean of the average number of moths in 60 traps is equal to the mean of the individual moth counts, which is 0.5.

The standard deviation of the average number of moths in 60 traps is equal to the standard deviation of the individual moth counts, divided by the square root of the sample size.

standard deviation = 0.7 / sqrt(60) = 0.0905

the mean and standard deviation of the average number of moths in 60 traps are 0.5 and 0.0905, respectively.

(b) To use the central limit theorem to find the probability that the average number of moths in 60 traps is greater than 0.4, we need to standardize the distribution of sample means using the Z-score formula:

Z = (sample mean - population mean) / (standard deviation / sqrt(sample size))

Substituting the given values, we have:

Z = (0.4 - 0.5) / (0.7 / sqrt(60)) = -1.94

Using a standard normal table or a calculator with a normal distribution function, we can find that the probability of getting a Z-score greater than -1.94 is approximately 0.9738.

The probability that the average number of moths in 60 traps is greater than 0.4 is approximately 0.9738 or 97.38%.

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The MMPI-2 test is used for the assessment of psychopathology and personality of patients.

It includes 567 true-false questions, resulting in 10 clinical scales, among which one is the anxiety subscale.

A score of 30 or less is usually considered very low.

The questions are answered by the patient, usually in a clinical or research setting.

A one-sample t-test is conducted in the problem, whereby a sample of 18 participants in a yoga group is tested for anxiety scores.

The following are the parameters of the one-sample t-test:Groups:

18 participants

Null hypothesis: The anxiety scores of Felipe's yoga group are statistically equal to 30." value: 30

Type of test: One-tailed test

Alternative hypothesis: The anxiety scores of Felipe's yoga group are greater than 30.

Degrees of freedom: n - 1 = 17T-observed value: (35.2 - 30) / (10.4 / sqrt(18)) = 2.41T-critical value: 1.734

Reject or retain null hypothesis: Since the t-observed value (2.41) is greater than the t-critical value (1.734), Felipe should reject the null hypothesis, which implies that his yoga group's scores are greater than 30.P-value: 0.014Cohen’s d value: (35.2 - 30) / 10.4 = 0.5

If the " value were reduced to 0.01, Felipe would still reject the null hypothesis, since the p-value (0.014) is lower than the alpha level (0.01).

For the sample mean: 35.2CI for 42%: 35.2 ± 0.58CI for 79%: 35.2 ± 1.16CI for 95%: 35.2 ± 2.13

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If "coffee-shop" is 5 blocks East of Amber's house and park is 3 blocks West of Amber's house, then the distance in blocks between "coffee-shop" to park is 8 blocks.

The distance between the "coffee-shop" and "Amber's house" is 5 blocks to the East, and the distance between the "park" and "Amber's house" is 3 blocks to the West.

To find the distance between the "coffee-shop" and the park, we can add the distances from the coffee shop to Amber's house and from Amber's house to the park:

On adding both the distance ,

We get,

⇒ 5 + 3 = 8,

Therefore, the distance between the coffee shop and the park is 8 blocks.

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Drawing 2 cm 5 times in a straight line will give us a 10 cm line segment after dilation.

Dilation is the process of increasing an object's size without altering its form. Depending on the scale factor, the object's size may rise or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's form doesn't change.

A dilation is a function f from a metric space M into itself that, for any locations x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is a positive real integer. Such a dilatation is a resemblance of the space in Euclidean space.

Meaning of Dilation in Math. Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

To dilate 2 cm to 10 cm we need to scale 2 cm 5 times

so drawing 2 cm 5 times in a straight line will give us a 10 cm line segment.

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i cant understand your question define briefly

Answer:

60 ft

Step-by-step explanation:

a² + b² = c²

20² + 15² = c²

c = √625

c = 25

total distance = 20 ft + 15 ft + 25 ft = 60 ft