15. What is the length of the diagonal for the given rectangular prism to the nearest whole unit?
0 10 cm
011 cm
06 cm
O13 cm
Length = 8 cm
Width =3 cm
Height = 7 cm

The coefficient of determination (r-squared) provides an indication of how well the regression model fits the data and the value of r is  0.3574

In this example, the r-squared value is 12.78%, which means that 12.78% of the variation in verbal SAT scores can be explained by the variation in math SAT scores. The least squares regression equation is yhat = 383.3 + 0.3489x, where yhat is the predicted verbal score and x is the math score.

The coefficient of correlation (r) provides a measure of the strength of the linear relationship between two variables. In this example, the coefficient of correlation (r) can be calculated from the coefficient of determination (r-squared) as follows: r = √r-squared = √12.78% = 0.3574. This indicates that there is a weak linear relationship between verbal and math SAT scores.

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The number of bricks needed to border the circular pool is 6.28r.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

Given, Mr. Cortez is putting a brick border around his circular pool.

So, He is boarding the circumference of the circular pool which has a distance of 2πr.

Now, The bricks are 1 foot in length.

Therefore, The number of bricks needed is,

= 2πr/1.

= 2πr.

= 6.28r.

According to the radius number of bricks can be determined.

Q. Mr. Cortez is putting a brick border around his circular pool. The bricks are 1 foot in length. How many bricks does Mr. Cortez need to buy to build the border? Use 3.14 for π.

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The value of your investment at maturity at a 10% rate of return will be,

$8470.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

Given, An initial investment of $7,000 and when you choose to invest for 14 years you get a 10% rate of return.

We know, 10% = 10/100 = 0.1.

Therefore, The value of your investment at maturity will be,

y = 7000(1 + 0.1)².

y = 7000(1.1)².

y = 7000×1.21.

y = 8470.

So, The value of the maturity will be $8470.

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The slope of a velocity graph represents the acceleration of the object.

Why does slope make things go faster?

Gravity is what causes the change in speed on a slope. Objects accelerate (move faster) when traveling downhill, and decelerate (move slower) when moving uphill (slow down).

                       They will then continue moving at the same pace on a level surface, presuming there is little friction.

=  area of graph is 1/2 t₀a₀.

=  area is less than  1/2 t₀a₀.

= area is more than 1/2 t₀a₀.

So in option (d) change in velocity is greatest.

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Answer: Acute Triangles

The slope of the graph is 1 and the y-intercept is -273.15. The slope presents the ratio between Celcius and Kelvin temperature and y-intercept shows the difference between both scales.

Based on the given graph:

(273.15, 0)

(0, -273.15)

m ?

y-intercepts?

slope:

m = y₂ - y₁

      x₂ - x₁

m = -273.15 - 0

       0 -  273.15

m = 1

y-intercept --> x = 0

x = 0 is when y = -273.15

The graph represents the relationship between temperature in Celcius scale and Kelvin scale.

The slope shows that both Celcius and Kelvin have equal ratio in measuring temperature. However, the y-intercepts shows that both scales have different zero points. The same temperature will be 273.15 lower in value under Kelvin scale than Celcius.

Then:

0°C = -273.15K

0K = 273.15°C

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Answer:

The proportional relation for t in terms of d is:

t = (53 min/day)*d.

Step-by-step explanation:

The value of length g is 21.56 inches

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

Therefore to find length g

f/sinF = g/sinG

8.8/sin23 = g/sin 107

8.8 × sin107 = g× sin 23

8.8 × 0.956 = g × 0.39

g = 8.8 × 0.956/0.39

g = 8.41/0.39

g = 21.56 inches

therefore the value of the length of g is 21.56 inches

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Answer:21.5

Step-by-step explanation:

None of the following statements are false. The angle between → and → is not equal to 90°.

Given that →=→×→ and is the angle between → and → where when they are drawn with their tails at the same point, and it is known that is not equal to 90°, none of the following statements are false.

Given that → and → are two vectors drawn with their tails at the same point, and →=→×→ is the angle between them, and it is known that is not equal to 90°, none of the following statements are false:

1. The angle between → and → is not equal to 90°.

2. The angle between → and → is greater than 90°.

3. The angle between → and → is less than 90°.

4. The angle between → and → is equal to 0°.

5. The angle between → and → is not equal to 180°.

The complete question is :

Given that →=→×→ and is the angle between → and → when they are drawn with their tails at the same point, it is known that is not equal to 90°. Which of the following is false?

A. The angle between → and → is not 90°.

B. The angle between → and → is equal to 90°.

C. The angle between →=→×→ is not 90°.

D. The angle between →=→×→ is equal to 90°.

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use the definition of big o notation to find the constants c, no which show that t(n) is o(f(n)) then  5^n+25 is not = 5^n

The main purpose of the computational complexity is to categorize the algorithms about their show. And we can represent the T(n), which is the time function with the help of the big O notation, for showcasing an algorithm runtime complexity. As an example,

T(n) = O(n3)

proves that the algorithm has the cubic time complexity.

Now let's define Bio O, and from here we will get our answer. For any function which is monotonic in nature, f(n) and g(n) from the +ve integers to the +ve integers, we assume that f(n)= O(g(n)) when exist a c>0 which is the constant, and n0 greater than 0, such that

f(n) < c * g(n), for each n>=n0

i) if O (5^n)= 4^n + 25

O (f) should be = (20^n)/f + 25

Then constant

O(5^n)= (20^n)/(5^n) + 25 = (20/5)^n +25=4^n+25

ii) O (4^n)=(20^n)/(4^n) + 25 = (20/4)^n +25=5^n+25

And 5^n+25 is not = 5^n

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complete question is

Use the definition of O (f) to show that 4^n + 25 is O (5^n) (ii) show that 5^n is not O (4^n)

The third column of the matrix is:

[tex]\begin{bmatrix}1 \\5 \\7\end{bmatrix}[/tex]

The third column of a matrix can be calculated without computing the other two columns by using the formula:

A_{ij} = (A_{i1} - A_{i2}) \times \frac{j - 1}{2} + A_{i2}

Where A_{ij} is the element in the ith row and jth column of the matrix, A_{i1} is the element in the ith row and 1st column of the matrix and A_{i2} is the element in the ith row and 2nd column of the matrix.

To calculate the third column of a matrix, we will first calculate the difference between the first two columns. For example, if we have the following matrix:

[tex]\begin{bmatrix}1 & 4 & ? \\7 & 2 & ? \\3 & 8 & ?\end{bmatrix}[/tex]

The difference between the first two columns is 3 (4 - 1 = 3). Now we can use the formula to calculate the third column. For the first row, we have A_{11} = 1, A_{12} = 4, and j = 3 (the third column). Plugging these values into the formula, we get:

A_{13} = (1 - 4) \times \frac{3 - 1}{2} + 4 = 1

For the second row, we have A_{21} = 7, A_{22} = 2, and j = 3 (the third column). Plugging these values into the formula, we get:

A_{23} = (7 - 2) \times \frac{3 - 1}{2} + 2 = 5

For the third row, we have A_{31} = 3, A_{32} = 8, and j = 3 (the third column). Plugging these values into the formula, we get:

A_{33} = (3 - 8) \times \frac{3 - 1}{2} + 8 = 7

Therefore, the third column of the matrix is:

[tex]\begin{bmatrix}1 \\5 \\7\end{bmatrix}[/tex]

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Answer:

(f − g)(x) = 4x + 17

Step-by-step explanation:

find (f − g)(x) = f(x) - g(x)

f(x) = 6x + 8 and g(x) = 2x − 9

6x + 8 - (2x − 9)

multiply the -1 to 2x − 9

6x + 8 - 2x + 9

Combine like terms

4x + 17

Answer:   choice C

Step-by-step explanation:

Took exam on FLVS

Answer: quantifies the economic devastation of natural and man-made disasters

Therefore, in order for Joey to earn the same hourly wage as Blake, she will have to labor for 8 six-month periods or 4 years.

We'll refer to the quantity of six-month intervals as x. Blake's hourly wage can be represented as 16 + 0.50x, and Joey's hourly wage may be represented as 12 + 1.50x after x intervals. We may set the two expressions equal to one another and solve for x to determine when Joey's salary will match Blake's salary:

12 + 1.50x = 16 + 0.50x \s0.50x = 4 \sx = 8

Joey will therefore need to work for 8 six-month periods, or 4 years, in order to make the same hourly rate as Blake.

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The original sum of money borrowed would be $ 2246.51.

A financial concept called future value (FV) determines the worth of an asset by using projected factors like future interest rates or cashflows. An investor could find it interesting to know how much, given a projected rate of return, their investment might be in five years. Future value is the idea that an investment will be worth more in the future if its current value is multiplied by anticipated growth.

Interest = $ 96.60

Interest is compounded 6 times in a year; n = 6

time = 1 year ; Rate of interest (r) = 4.2 %

Interest = Future Value - Principal Value

Future Value = Principal [tex]$\cdot\left(1+\frac{r}{100 \times n}\right)^{n \cdot t}$[/tex]

Substituting this value in equation (1), We get

Interest = Principal [tex]$\cdot\left(1+\frac{r}{100 \times n}\right)^{n \cdot t}-$[/tex]Principal

96.60 = Principal [tex]$\left[\cdot\left(1+\frac{4.2}{100 \times 6}\right)^{6 \cdot 1}-1\right]$[/tex]

Principal = $ 2246.51

Therefore, the original sum of money borrowed would be $ 2246.51.

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the unit rate for composing a song will be 3 weeks per song.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, Wayne plays multiple instruments in a rock band. He also composes the songs. He takes 36 weeks to write the songs for an album of 12 songs.

He took 36 weeks to compose 12 songs.

Since,

Unit rate: Divide total weeks by total songs.

Thus,

Unit Rate = 36 / 12 = 3 weeks per song.

Therefore, the unit rate for composing a song will be 3 weeks per song.

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The slope of the line perpendicular to y = x is -1. The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept. Substituting m = -1 and using the point (2, 2), we have:

y = -x + b

2 = -2 + b

b = 4

So the equation of the line passing through (2, 2) and perpendicular to y = x is:

y = -x + 4

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It is true that The area of a hexagon is the area enclosed within its six sides. It is measured in square units such as m2, cm2, yard2,in2, etc. A hexagon is a two-dimensional closed shape that has six sides and six angles.

The area of a hexagon is calculated using the formula Area = (33 s2)/2, where s is the length of one of the regular hexagon's sides. The area of a hexagon can also be calculated using the apothem by using the formula Area of hexagon = (1/2) a P, where an is the apothem's length and P is the hexagon's perimeter.

There are six lines of symmetry in regular hexagons. The midpoints of its two opposite sides are joined by three lines, and the diagonals are joined by three more lines. This denotes the existence of "mirror symmetry" in a regular hexagon.

A regular hexagon is a regular polygon with six sides. determine the regular hexagon's side length, Apply the formula for the hexagon's surface area (33 s2)/2 to calculate the area, where s is the hexagon's side length.

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The population of the world after 1 year will be 6,974,400,000 + 1.2% of 6,974,400,000 = 7,058,092,800

A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

By dividing the value by the entire value and multiplying the result by 100, one may get the percentage. The percentage calculation formula is (value/total value)100%.

The word "percentage" means "out of 100." In mathematics, percentages are used, together with fractions and decimals, to denote parts of a whole. The total is split into 100 equal pieces to calculate percentages.

Total population of the world is 6,974,400,000

The population is incresing at a 1.2% rate annually

The population of the world after 1 year will be 6,974,400,000 + 1.2% of 6,974,400,000 = 6,974,400,000 + 836928000 = 7,058,092,800

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Answer:

1) 117

2) 24

Step-by-step explanation:

Corresponding sides are in the same ratio for similar triangles

1)

For triangles MUL and WUV:

UW/UM = UV/UL

?/45 = 104/40

? = 45 x 104/40 = 117

2)
For triangles RST and RKH
RS/RK = RT/RJ

?/12 = 20/10 = 2

? = 2 x 12 = 24

If statement p is true but statement q is false, then the following compound statements are true -

Option B: p ∨ q

Option D: q → p

What is compound statement?

A compound statement is a collection of two or more statements joined together using terms like "or," "and," "if then," and "only if." Each component statement of a compound statement can be determined to be true or untrue with clarity.

If the truth value of the statement p is 'True' and truth value of statement q is 'False',

p ∧ q → False [Conjunction of both the statements will be true only when both the statements are True]

p ∨ q → True [Disjunction of two statements will be false only when both the statements are false]

(p → q) → False [p is same as q]

(q → p) → True [Implication of both the statements is false only when p is true and q is false otherwise true]

(p ↔ q) → False [Bi-conditional statements are true if and only when both the statements are true]

(q ↔ p) → False [Bi-conditional statements are true if and only when both the statements are true]

Therefore, the compound statements p ∨ q and (q → p) is true.

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Answer:

(x - 7)(x + 8)

Step-by-step explanation:

x² + x - 56
Multiples of 56 whose difference is 1: 7, 8
So, splitting the equation:
x² + 8x - 7x - 56
(x - 7)(x + 8)

The factored form of a quadratic expression is a way to rewrite the expression which shows the sums of products.

general form: [tex]y= a(x-r)(x-s)[/tex]

when the a value is equal to zero:

[tex]y=x^2+x-56[/tex]

[tex]y=(x+8)(x-7)[/tex]

Therefore , the solution of the given problem of unitary method comes out to be  $261 is the difference between kate's tax and amount with held  by employer.

After establishing the size of a little slice, multiply the quantity by two to complete a task utilizing unitary technique. Simply expression, the unit technique serves to isolate a programmed thing from a certain set or sets of sets. For example, the price of 40 pens is 400 pounds ($1.01) or Rs. It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality. It can equally integrate and reciprocate (mathematics, algebra).

Here,

Given :

=> tax for last year is $973

=> employed with held is $712

the difference between Kate's tax and amount with held is:

=> 973 - 712

=> $261.

Thus , $261 is the difference between kate's tax and amount with held  by employer.

Therefore , the solution of the given problem of unitary method comes out to be  $261 is the difference between kate's tax and amount with held  by employer.

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Answer: I'm not sure if it's right but I got 12.6

Step-by-step explanation: Multiplication

The study of mathematical logic help you in your everyday life in the following way.

Mathematical logic is a branch of mathematics that deals with the principles of reasoning and makes statements based on deductive reasoning.

It is not just a subject that helps you ace your math exams but also a useful tool in your everyday life.

Understanding the basic principles of logic can help you make better decisions, solve problems more effectively, and communicate your ideas more clearly.

Logic helps you analyze information, evaluate arguments and make informed decisions.

In everyday life, you often encounter situations where you have to make choices based on information that is incomplete or ambiguous.

Furthermore, logic can also help you improve your critical thinking skills. By understanding how to reason and argue logically, you can more easily identify and evaluate flawed arguments, understand the relationships between different ideas and reach more accurate conclusions.

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Solving the provided question, we can say that the given exponent is

[tex]32 = 2^{ 3x - 1 }[/tex] => 64 = [tex]2^{3x}[/tex] => [tex]2^{3(2)} = 2^{3x}[/tex] on comparing both side, we have x = 2

Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where

the given exponent is

[tex]32 = 2^{ 3x - 1 }[/tex]

64 = [tex]2^{3x}[/tex]

[tex]2^{3(2)} = 2^{3x}[/tex]

on comparing both side, we have

x = 2

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The Pythagorean Theorem can be used to solve for the missing sides of a triangle when given two other sides

a. The missing components that can be solved using the given values are the missing sides of the triangle (side b and side c).

b. To find the missing side, we can use the Pythagorean Theorem, which states that a^2 + b^2 = c^2, where a and b are the two sides of the triangle, and c is the hypotenuse. Therefore, we can solve for c by taking the square root of (a^2 + b^2).

The Pythagorean Theorem can be used to solve for the missing sides of a triangle when given two other sides. To do this, we take the square root of the sum of the squares of the two given sides, which gives us the length of the hypotenuse.

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The distributive property to factor out the greatest factor 24+18t is 6(4+3t).

The distributive property to factor out the greatest common factor 24+18t.

The Distributive Property is an algebraic property that is used to multiply a single value and two or more values within a set of parenthesis. The distributive Property States that when a factor is multiplied by the sum/addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation. This property can be stated symbolically as:

Well, some of the common factors that 24 and 18 shares are 2, 3, and 6.

The greatest factor is 6.

⇒ [tex]\frac{24}{6}[/tex]=4

⇒ [tex]\frac{18t}{6}[/tex]=3

Because 6x4=24 and 6 x 3t= 18t

Therefore, the distributive property to factor out the greatest factor 24+18t is 6(4+3t).

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The required solution of the given trigonometric equation is given as x = 3π/2 + 2nπ.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,
sec(x) = 1 - tan(x)

1/cosx = cosx - sinx / cosx       [secx = 1 / cosx ; tanx = sinx / cosx]
cosx = 1 + sinx
1 + sinx - cosx = 0
1 + √2[sin{x - π/4}] = 0
sin{x - π/4} = -1/√2
x - π/4 = 5π/4 + 2nπ
x = 3π/2 + 2nπ

Thus, the solution of the given trigonometric equation is given as x = 3π/2 + 2nπ.

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