Convert 4.6 cm = ________mm

Answer: 7.5

Step-by-step explanation: 2 x 7.5 = 15

The values using trigonometric ratios are sinR = 15/17; cosR = 8/17, tanR = 15/8

An equation is an expression that uses mathematical operations to show how numbers and variables are related to each other.

Pythagoras ratio is an equation that shows the relationship between the sides of a right triangle.

To find TR, using Pythagoras:

TR² = TY² + YR²

TR² = 15² + 8²

TR = 17

Trigonometric ratios show the relationship between sides and angles of right triangle.

Hence:

sinR = 15/17; cosR = 8/17, tanR = 15/8

The values are sinR = 15/17; cosR = 8/17, tanR = 15/8

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4 is the correct value from the set {1, 2, 3, 4} which is the solution to the equation 3x + 3 = 15.

A solution of an equation refers to a value or values that satisfy the given equation. It is the value or values that make the equation true when substituted for the variable(s) in the equation. Equations are mathematical expressions that contain an equals sign and can have one or more variables. A solution is typically represented as a number, but it can also be a set of numbers, a range of values, or an expression. Finding the solutions of an equation is an important part of solving mathematical problems and has many practical applications in fields such as engineering, physics, and finance.

Solution of the given equation 3x + 3 = 15 means when we put a value in x we should get the result as 15, that is left hand side of the equation should be equal to the right hand side of the equation.

Solving the equation we get,

3x + 3 - 3 = 15 - 3

3x = 12

x = 4

Therefore, the value 4 is a solution to the equation.

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Answer:

3/5 = 60% = 0.6

In the bottom row, 3/5 is the wrong fraction. 2/3 is the correct fraction.

The solution of the system of equations in this problem is given as follows:

(4,0).

The equations that compose the system in this problem are given as follows:

We solve the system graphically, hence the solution is given by the point of intersection of the graphs of the two functions.

From the graph given by the image presented at the end of the answer, the solution to the system is given as follows:

(4,0).

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I hope this helps you .

Answer:

p=30 s=30 k=90 x=0

Step-by-step explanation:

000000000000

Answer: The sequence modeling the amount of money in Samuel’s savings account is a recursive sequence. Each term in the sequence is determined by adding $75 to the previous term. The first term in the sequence is $100, representing Samuel’s initial deposit. After n months, the amount of money in Samuel’s savings account can be calculated using the formula An = An-1 + 75, where An represents the amount of money in his account after n months and An-1 represents the amount of money in his account after n-1 months.

For example, after 1 month, the amount of money in Samuel’s savings account will be A1 = A0 + 75 = 100 + 75 = $175. After 2 months, the amount of money in his account will be A2 = A1 + 75 = 175 + 75 = $250. And so on.

Answer:

20/8 or 20:8

Step-by-step explanation:

Ok, so we start off with a smaller square with one side being 8.

We then have to go from one side being 8 to one side being 20.

So, the ratio has to be a number larger than 1 to go from smaller to larger, so we can use the ratio of 20/8 (or 2.5).

Check:

2.5x8=20

The surface area of the pyramid is 532m²

A pyramid is a 3D polyhedron with the base of a polygon along with three or more triangle-shaped faces that meet at a point above the base. It is made by connecting each vertex of the base to a common tip or apex giving it its typical shape.

The general formula for the lateral surface area of a regular pyramid is L.S.A.=1/2pl

where

Given that The pyramid is a rectangular,

Therefore the surface area is

L.S.A.=1/2(14*4) *19

Surface area = 28*19 = 532m²

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Based on the information provided, a test-taker who scores at the 5th stanine is scoring:
C. within the average range.

To better understand this, let's break down the terms and concepts involved:
Stanine: Stanine (short for "standard nine") is a method used to scale test scores on a nine-point scale.

The stanine scores range from 1 (lowest) to 9 (highest).

This method is typically used in educational assessments to categorize students' performance.
Average: In the context of test scores, the average score refers to the middle range of scores that is typical for the majority of test-takers.

In the case of stanine scores, the average range falls between 4 and 6.

This means that students scoring in stanines 4, 5, and 6 are considered to be within the average range.
Now, to answer your question, a test-taker who scores at the 5th stanine is considered to be within the average range of performance.

This is because their score falls between the 4th and 6th stanines, which, as mentioned earlier, encompass the average range.

It's important to note that this doesn't mean the student is performing poorly; rather, their performance is on par with the majority of other test-takers.

Option C. within the average range is correct.  

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The documentation provided with the procedure states that the procedure will display the value of (x + y) / x.

This means that the result of the calculation will be shown to the user, and it will be the value obtained by adding x and y, then dividing the result by x.

However, the documentation also includes a very important requirement for the parameter x: it must not be 0. This is because dividing by zero is not a valid mathematical operation, and will result in an error. Therefore, it is crucial to ensure that the value of x passed to the procedure is a non-zero integer.

To summarize, the "calculate" procedure takes two integer parameters, x and y, and displays the value of (x + y) / x.

It is important to note that the value of x must not be 0, as dividing by zero is not a valid mathematical operation.

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The length of curve DE is equal to 26.25 units.

In Mathematics and Geometry, Pythagorean's theorem is modeled by the following mathematical expression:

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

In order to determine the length of the hypotenuse in this right-angled triangle, we would have to apply Pythagorean's theorem as follows;

AC² + BC² = AB²

20² + 15² = AB²

AB² = 400 + 225

AB = √625

AB = 25 units.

For the length of curve DE, we have:

DE = 105% of AB

DE = 1.05 × 25

DE = 26.25 units.

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A measure of relative fit for a simple regression line is called the r² or coefficient of determination.

A regression line, or line of best fit, is a straight line used to model the relationship between two variables in a data set. It is drawn through the data points to minimize the distance between the line and the points, representing the best fit. The line's equation is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept. The slope represents the rate of change of y with respect to x, and the y-intercept represents the value of y when x is equal to 0. The line is often used to predict the dependent variable based on the independent variable, and the accuracy of the predictions depends on how well the line fits the data.

The coefficient of determination, also known as r², is a statistical measure used to determine the relative fit of a simple regression line. This measure represents the proportion of variance in the dependent variable that can be predicted by the independent variable. The calculation involves squaring the correlation coefficient (r) between the two variables. The resulting value of r² ranges from 0 to 1, where 0 indicates that the independent variable has no explanatory power over the dependent variable, while 1 implies that the independent variable explains all the variability in the dependent variable.

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For any value of x, the corresponding value of y will always be 7, and the line will be a horizontal line passing through the point (5,7).

If a straight line is parallel to the x-axis, then it means that the line will have a constant y-value for all values of x. This means that the slope of the line will be zero, because there will be no change in y for any change in x.

To find the equation of a straight line passing through the point (5,7) that is parallel to the x-axis, we need to find the equation in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.

Since the slope of the line is zero, we can write the equation as:

y = 0x + b

where b is the y-intercept.

To find the value of b, we can use the point (5,7) that the line passes through. Substituting x = 5 and y = 7 in the equation, we get:

7 = 0(5) + b

Simplifying, we get:

b = 7

Therefore, the equation of the straight line passing through the point (5,7) that is parallel to the x-axis is:

y = 7

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Answer:5

Step-by-step explanation: you divide 15 by 3 which gives you 5

Answer:

volume

Step-by-step explanation:

Victoria should use volume measurement to determine how much sand she should buy.

Answer: Parallelogram

Step-by-step explanation: A parallelogram is a quadrilateral with opposite sides parallel. If ZL, ZM, ZN, and ZO are approximately equal, it implies that the opposite sides LM and NO are parallel, and the opposite sides LO and MN are also parallel.

It may not be a rectangle: While a parallelogram is a quadrilateral with opposite sides parallel, a rectangle is a special type of parallelogram with additional properties, such as all angles being right angles. The given information does not provide any information about the angles of the quadrilateral, so we cannot conclude that it is a rectangle.

It may not be a rhombus: A rhombus is a special type of parallelogram in which all sides are equal. The given information only states that the angles ZL, ZM, ZN, and ZO are approximately equal, but it does not provide any information about the lengths of the sides LM, LO, MN, or NO. Therefore, we cannot conclude that LMNO is a rhombus based solely on the given information.

Answer:

see explanation

Step-by-step explanation:

10

length of side opposite ∠ A is BC = 20

11

length of side adjacent to ∠ A is AC = 21

12

length of hypotenuse is AB = 29

13

sin A = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{20}{29}[/tex]

14

cos A = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{21}{29}[/tex]

15

tan A = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{20}{21}[/tex]

The circumference of a circle: C = 67.98 cm

Radius of the circular lawn, which is difference between outer radius of  path and inner radius of path.

outer radius:  [tex]r1 = (132 + 2T)/2 = (132 + 2(22))/2 = 88 ft[/tex]

inner radius:  [tex]r2 = 132/2 = 66 ft[/tex]

radius of circular lawn is r = r1 - r2 = 22 ft

Now using formula for the area of a circle:

A = πr^2 = π(22^2) ≈ 1520.53 ft^2

To find the circumference of a circle with area 367 cm^2, we can use the formula for the area of a circle to find the radius:

[tex]A = \pi r^2 \\r^2 = A/\pi = 367/\pi[/tex]

r ≈ 10.80 cm

Then we can find the circumference using the formula for the circumference of a circle:

C = 2πr ≈ 2π(10.80) ≈ 67.98 cm

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Answer:

$51,500 in her savings account.

Step-by-step explanation:

If Pamela has $50,000 in a savings account with an interest rate of 3% per year and the interest is not compounded, then in 1 year she will earn an interest of $50,000 * 0.03 = $1,500.

So, after 1 year, Pamela will have a total of $50,000 + $1,500 = $51,500 in her savings account.

The remainder when p(x) = x^4 - 4x³ - 11x² + 66x - 72 is divided by x - 4 is given as follows:

16.

The Remainder Theorem is a theorem in algebra that provides a quick way to find the remainder of a polynomial division problem. The theorem states that when a polynomial f(x) is divided by (x - a), the remainder is equal to f(a).

Hence for this problem, the remainder is given by the numeric value at x = 4, which is calculated as follows:

p(4) = 4^4 - 4(4)³ - 11(4)² + 66(4) - 72

p(4) = 16.

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Answer:

∠PQT and ∠TQR.

Step-by-step explanation:

If you're still confused about which angles are supplementary, let me give you a hint. Imagine that RP←→ is a giant ruler that you can use to measure the angles. Now, if you place the ruler on ∠PQT and ∠PQS, you'll see that they are too small to fit the whole ruler. They only cover half of it, which means they add up to 90 degrees. That's not what we want, we want 180 degrees!

Similarly, if you place the ruler on ∠TQS and ∠SQR, you'll see that they are too big to fit the whole ruler. They overlap each other, which means they are equal. And if they are equal, they must be 90 degrees each, because that's the only way two angles can add up to 180 degrees. But we don't want two 90 degree angles, we want two different angles!

The only option left is ∠PQT and ∠TQR. If you place the ruler on them, you'll see that they fit perfectly on the whole ruler. They cover it from end to end, which means they add up to 180 degrees. That's exactly what we want! So the correct answer is ∠PQT and ∠TQR. Congratulations, you've just solved a tricky geometry problem with a simple tool!

Answer:

x = 8/3

Step-by-step explanation:

y = mx + b

y = -3x + 16

8 = -3x + 16

Subtract 16 from both sides

-8 = -3x

Divide both sides by -3

8/3 = x

Answer: 12

Step-by-step explanation:

Using Phytagorean theorem

[tex]r^{2} = \sqrt{} y^{2} +x^{2}[/tex]

given: r=20 and y=16

[tex]20^{2} =\sqrt16^{2} +x^{2} \\400=\sqrt{256+ x^{2} \\[/tex]

move x to the other side (when x is moving to the other side the sign change)

x²= √400-256       subtract  

x= √144      take the square root

x=  12

f'(x) = 2x - 2 is always positive on (-∞, 1) and always negative on (1, ∞), the function is increasing and decreasing, respectively, and therefore one-to-one. Therefore, f(x) is invertible in its natural domain.

What is the exponential function?

An exponential function is a mathematical function of the form f(x) = aˣ

where "a" is a constant called the base, and "x" is a variable. Exponential functions can be defined for any base "a", but the most common base is the mathematical constant "e" (approximately 2.71828), known as the natural exponential function.

To determine if the function f(x) = x² - 2x + 3 is increasing, decreasing, even, odd, and/or invertible in its natural domain, we need to analyze its derivative and second derivative:

f'(x) = 2x - 2

f''(x) = 2

Increasing/decreasing: Since f''(x) is always positive (i.e., 2 is positive), the function is always concave up and has a minimum at x = 1. Thus, f(x) is increasing on (-∞, 1) and decreasing on (1, ∞).

Even/odd: To determine if f(x) is even or odd, we need to check if it satisfies the properties of even and odd functions.

Even function: A function f(x) is even if f(-x) = f(x) for all x in the domain. Let's check if f(x) satisfies this property:

f(-x) = (-x)² - 2(-x) + 3 = x² + 2x + 3

f(x) = x² - 2x + 3

f(-x) ≠ f(x), so the function is not even.

Odd function: A function f(x) is odd if f(-x) = -f(x) for all x in the domain. Let's check if f(x) satisfies this property:

f(-x) = (-x)² - 2(-x) + 3 = x² + 2x + 3

-f(x) = -(x² - 2x + 3) = -x² + 2x - 3

f(-x) ≠ -f(x), so the function is not odd.

Invertible: To determine if f(x) is invertible, we need to check if it has an inverse function.

A function has an inverse function if it is one-to-one, which means that it passes the horizontal line test.

To check if f(x) is one-to-one, we can analyze its derivative.

Hence,  f'(x) = 2x - 2 is always positive on (-∞, 1) and always negative on (1, ∞), the function is increasing and decreasing, respectively, and therefore one-to-one. Therefore, f(x) is invertible in its natural domain.

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Complete question:

For the following, determine if the function is increasing, decreasing, even, odd, and/or invertible on its natural domain: f(x) = x² - 2x + 3.

The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made

To determine how many diners can be expected to show up at The Orchard Cafe, we can follow these steps:

1. Identify the percentage of diners who actually show up: Since 4% of diners with reservations don't show up, the percentage of diners who do show up is 100% - 4% = 96%.

2. Calculate the expected number of diners who show up: Multiply the total number of reservations (81) by the percentage of diners who show up (96%).

81 reservations x 0.96 (96% as a decimal) = 77.76

Since the number of diners must be a whole number, you can round the result to the nearest whole number.

In this case, 77.76 can be rounded down to 77.

Your answer: The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made.

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Let's the weight of Case C = "x" grams.

From the information:

Case A = 12 times heavier than Case B,

Therefore, the weight of Case B = 1/12 of Case A's weight:

Weight of Case B = (1/12) * Weight of Case A

Case B = 16 times heavier than Case C,

so, weight of Case C = 1/16 of Case B's weight:

Weight of Case C = (1/16) * Weight of Case B

The weight of Case A = 8,640g,

Let's substitute the value into the equations to find the weight of Case C:

Weight of Case B = (1/12) * 8,640 = 720g

Weight of Case C = (1/16) * 720 = 45g

Thus, the weight of Case C is 45 grams.

Using the top number line, p + q and p + (-q) can be located as shown in the attached image.

A number line is a line on which numbers are marked at intervals, used to illustrate simple numerical operations. It is also a pictorial representation of the real numbers.

Since point p has a value of 2 and point q has |q| = 5. We can say:

p + q = 2 + 5 = 7

p + (-q) = 2 + (-5) = -3

Therefore, using the top number line, we can then locate p + q and p + (-q) with their calculated values (Check the green dot in the attached image).

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Complete Question

Check the attached image