13. The number of elephants at the circus was two fifths of the number of horses. If there were 16 elephants, how many
horses were there?

Answer:

Quedan 3 libras de azúcar en el costal.

Step-by-step explanation:

Una kilo es aproximadamente dos libras y dos libras y media equivalen a un paquete, para determinar la cantidad remanente de libras de azúcar luego de las ventas se calcula la masa vendida por regla de tres compuesta:

\(x = 5\,p \times \frac{2,5\,kg}{1\,p}\times \frac{2\,lb}{1\,kg}\)

\(x = 25\,lb\)

Juana vendió 25 libras de azúcar. Entonces, la masa remanente de azúcar en el costal es:

\(x = 28\,lb-25\,lb\)

\(x = 3\,lb\)

Quedan 3 libras de azúcar en el costal.

The total amount of sugar left in the sack is 3 pounds.

Using the conversion:

1 kg = 2lb

2.5kg =5lb

Amount of sugar left in the sack = Total  - amount sold

Amount of sugar left in the sack = 28lb - 25lb

Amount of sugar left in the sack = 3lb

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Answer:

7.2

Step-by-step explanation:

The radius of the circle is 14.

The length of the chord is 12.

Half the length of the chord and radius form a right angled triangle as shown in the diagram below.

We need to find one of the sides of the triangle, d in the diagram.

Using Pythagoras rule:

\(14^2 = 12^2 + d^2\\\\196 = 144 + d^2\\\\d^2 = 196 - 144 = 52\\\\d = \sqrt{52} = 7.2\)

The distance between the chord and the center of the circle is 7.2

Answer: 4sqrt10

Step-by-step explanation: The Chord is 12 so half the chord is 6 so the base is 6 and the radius is the hypotenuse, which is 14. and the distance is the missing leg.

so 14^2=6^2+x^2

196=36+x^2

sqrt160=x

4sqrt10=x

Comparing this with the left-hand side expression -V cosec^2θ - 3V^2cosec^2θcotθ, we can see that both sides are equal.

To prove the given equation, we will differentiate both sides with respect to θ and simplify the expression.

Differentiating V cotθ + V^3cosecθ with respect to θ:

d/dθ(V cotθ + V^3cosecθ) = d/dθ(V cotθ) + d/dθ(V^3cosecθ)

Applying the differentiation rules:

= V (-cosec^2θ) + 3V^2cosecθ(-cosecθcotθ)

= -V cosec^2θ - 3V^2cosec^2θcotθ

Now, we need to express the right-hand side of the original equation in terms of dV/dθ:

V cotθ + V^3cosecθ = V(cotθ + V^2cosecθ)

                      = V(cotθ + cotθV^2)

                      = Vcotθ(1 + V^2)

Taking the derivative of the right-hand side with respect to θ:

d/dθ(Vcotθ(1 + V^2)) = V(−cosec^2θ)(1 + V^2) + Vcotθ(0)

                           = -Vcosec^2θ(1 + V^2)

Comparing this with the left-hand side expression -V cosec^2θ - 3V^2cosec^2θcotθ, we can see that both sides are equal. Therefore, we have proved that dV/dθ = V cotθ + V^3cosecθ.

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Answer:

Step-by-step explanation:

We observe that:

Also:

Find the value of y:

Answer:  \(\frac{19}{6} : \frac{17}{6}\)

Step-by-step explanation:

Let us first represent the ratio.

3\(\frac{1}{6} : \frac{17}{6}\)

Now we need to convert 3\(\frac{1}{6}\) into a improper fraction.

\(\frac{19}{6} : \frac{17}{6}\)

Now it is in its simplest form.

The final answer is  \(\frac{19}{6} : \frac{17}{6}\)

Answer:

\( y = - \frac{1}{2} x - 9\)

Step-by-step explanation:

\(y + 7 = - \frac{1}{2} (x + 4) \\ \\ y + 7 = - \frac{1}{2} x + (- \frac{1}{2}) \times 4 \\ \\ y = - \frac{1}{2} x - 2 - 7 \\ \\ y = - \frac{1}{2} x - 9\)

Answer: B

Step-by-step explanation:

    This equation is in y = mx + b form, also known as slope-intercept form.

   First, we will look at the y-intercept. Our y-intercept is -3, so the line will hit the y-axis at -3. This rules options A and C as incorrect.

   Next, we will look to the slope. The slope is positive, 2 4/7, so the line will be going "up the stairs" from the bottom left to the top right. This rules out option D as incorrect, leaving us with our answer: B.

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The Minimum number of lines needed to cover all zeroes is 2.

To determine the minimum number of lines needed to cover all the zeroes after row and column reductions, we must first perform the reductions on the given matrix. The matrix is not provided in a standard format, but I will assume it is a 3x3 matrix based on the 9 given numbers:
Initial matrix:
4 7 6
6 6 9
6 9 6
Row reduction - Subtract the minimum value of each row from all elements in that row.
Row 1: 4 - 4 = 0, 7 - 4 = 3, 6 - 4 = 2
Row 2: 6 - 6 = 0, 6 - 6 = 0, 9 - 6 = 3
Row 3: 6 - 6 = 0, 9 - 6 = 3, 6 - 6 = 0
Row-reduced matrix:
0 3 2
0 0 3
0 3 0
Column reduction - Subtract the minimum value of each column from all elements in that column.
Column 1: 0 - 0 = 0, 0 - 0 = 0, 0 - 0 = 0
Column 2: 3 - 0 = 3, 0 - 0 = 0, 3 - 0 = 3
Column 3: 2 - 2 = 0, 3 - 2 = 1, 0 - 0 = 0
Row- and column-reduced matrix:
0 3 0
0 0 1
0 3 0
Draw the minimum number of lines needed to cover all zeroes.
1. Draw a line through the first row, covering one zero.
2. Draw a line through the second column, covering the two remaining zeroes.
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Answer:

76

Because 11*8=88 and 4*3=12

88-12=76

Answer:x= 3/22

Step-by-step explanation:

Distribute

Subtract the numbers

Combine multiplied terms into a single fraction

Distribute

Find common denominator

Combine fractions with common denominator

Multiply the numbers

Add the numbers

Answer: 52 degrees.

Step-by-step explanation:

A triangle adds up to 180 degrees total, and we know one angle. 180 minus the known angle (76) is 104.

Because the two lines are the same, the angle at D and F are also the same. Divide 104 in half, and they are both 52 degrees.

A certain plane is described by 2x+3y+4z=16. Find the unit vector normal to the surface in the direction away from the origin.Firstly, we will obtain the coefficients of the x, y and z variables from the equation of the plane:2x + 3y + 4z = 16The coefficients are 2, 3, and 4 respectively.

Now, we will calculate the magnitude of the normal vector, ||N||, using the formula:||N|| = √(a² + b² + c²)where a, b, and c are the coefficients of the x, y, and z variables respectively.||N|| = √(2² + 3² + 4²)= √(4 + 9 + 16)= √29Therefore, the unit normal vector in the direction away from the origin is given by:N = (2/√29) i + (3/√29) j + (4/√29) k. Given the equation of a plane as 2x + 3y + 4z = 16, we have to find the unit vector normal to the surface in the direction away from the origin. Here's how we can do it:To find the unit vector normal to the surface, we first need to find the coefficients of the x, y, and z variables from the equation of the plane. In this case, the coefficients are 2, 3, and 4 respectively.Next, we can use the formula ||N|| = √(a² + b² + c²) to calculate the magnitude of the normal vector, where a, b, and c are the coefficients of the x, y, and z variables respectively. In this case, ||N|| = √(2² + 3² + 4²) = √29.Finally, we can find the unit normal vector in the direction away from the origin by dividing each coefficient by the magnitude of the normal vector, ||N||. Thus, the unit normal vector is:N = (2/√29) i + (3/√29) j + (4/√29) k

Therefore, the unit vector normal to the surface in the direction away from the origin is (2/√29) i + (3/√29) j + (4/√29) k.

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In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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The two triangles n = (75 + 3) / 5 = 18. The measure of angle q is 18 degrees.

1. First, find the value of n by using the equation 5(n - 3) = 75 + 3

2. Next, add 75 and 3 together and divide by 5. This gives us a value of 18 for n.

3. Finally, use the equation 5(n - 3) to determine the measure of angle q in triangle qrs. This equals 5(18 - 3) = 5(15) = 75 degrees.

The two triangles qrs and xyz are similar, meaning they have the same angle measures. In order to find the measure of angle q in triangle qrs, we must first find the value of n. The measure of angle x in triangle xyz is 75 degrees and the measure of angle q in triangle qrs is equal to 5(n - 3) degrees. We can use this equation to solve for the value of n. To do this, we add 75 and 3, then divide by 5. This gives us a value of 18 for n. Therefore, the measure of angle q in triangle qrs is 18 degrees.

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Answer:

600 feet

Step-by-step explanation:

Half an hour is 30 minutes.

If the snake moves 20 feet per minute, you can multiply the 20 by 30.

600.

Answer:

DC = 1332.95 feet

Step-by-step explanation:

From the figure attached,

Let the measure of DC = h ft

And measure of side BC = a ft

By applying tangent ratio in ΔBCD,

tan(56°) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

             = \(\frac{DC}{BC}\)

             = \(\frac{h}{a}\)

h = a[tan(56°)] --------(1)

By applying tangent rule in ΔACD,

tan(22°) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

tan(22°) = \(\frac{DC}{BC+AC}\)

             = \(\frac{h}{a+2400}\)

h = (a + 2400)tan(22°) ------- (2)

Equating the values of h from equations (1) and (2),

a[tan(56°)] = (a + 2400)tan(22°)

a[tan(56°) - tan(22°)] = 2400[tan(22°)]

1.0785a = 968.6629

a = 899.085 ft

From equation (1),

h = 899.085[tan(56°)]

h = 1332.948

h ≈  1332.95 ft

Answer:

1, 27, 3, 9,

Step-by-step explanation:

To find the factors of 27 you need to find which whole number times another whole number = 27

We know that 1*27 = 27

We also know that 3*9 = 27

The factors are all the numbers that are used in the multiplication.

In this example the numbers are: 1, 3, 9 and 27

Answer:

1,9,3,27

Step-by-step explanation:

if we break it down we can see:

1x27=27

9x3=27

Answer:

Wrong values are plotted in the question statement graph.

Please find correct graph.

Step-by-step explanation:

Given that:

\(y =x+3\) and \(-1<x<5\)

i.e. we can put a value of x in the equation which is greater than -1 and lesser than 5.

OR

we can say, the points where x = -1 and x = 5 will not be included in the graph (they will be shown as hollow circle).

Now, let us put the values one by one:

x = -1, y = -1 + 3 =2

x = 0, y = 0 + 3 = 3

x = 1, y = 1 + 3 = 4

x = 2, y = 2 + 3 = 5

x = 3, y = 3 + 3 = 6

x = 4, y = 4 + 3 = 7

x = 5, y = 5 + 3 = 8

Therefore, the table of values become:

\(\begin{center}\begin{tabular}{ c c } x & y\\ -1 & 2\\ 0 & 3 \\ 1 & 4 \\ 2 & 5 \\ 3 & 6 \\ 4 & 7 \\5 & 8\\\end{tabular}\end{center}\)

Points (-1, 2) and (5, 8) will not be included in the graph.

Please find attached corrected graph.

Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

To calculate the annualized rate of return, we can use the formula for compound interest. The correct answer is 11.66%.

The formula for compound interest is given by: A = P(1 + r)^t, where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the time in years.

In this case, the initial investment (P) is BD 14,000, the final amount (A) is BD 52,600, and the time (t) is 12 years. We need to solve for the annual interest rate (r).

\(BD 52,600 = BD 14,000(1 + r)^{12}\)

By rearranging the equation and solving for r, we find:

\((1 + r)^{12} = 52,600/14,000\)

Taking the twelfth root of both sides:

\(1 + r = (52,600/14,000)^{(1/12)}\\r = 0.1166 / 11.66 \%\)

Therefore, Areej has earned an annualized rate of approximately 11.66% on this investment.

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For the answer of factors of expression (12 + 54), in the form of a(b + c), where a is the GCF of 12 and 54 is equals to 6( 2 + 9).

In math, to factor a number means to express it as a product of (other) whole numbers, called its factors. For example, if 7x5 = 35, 7 and 5 are both factors. The divisors that give the remainder to be 0 are the factors of the number. We have an expression of numbers, 12 + 54. We have to write this expression in form of a( b + c), where a is GCF of 12 and 54. Now, we can write the factors of 12 and 54 are 12 = 2×2×3

54 = 2×3 ×3×3

The greatest common factor, GCF of 12 and 54 is 2×3 = 6. So, 12 + 54 = 6× 2 + 6×9

Taking out the common factor 6 from above expression, 6( 2 + 9) which is required form a( b + c). Hence, required expression is 6( 2 + 9).

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Answer:

A D and F becuase if you times 15 by them the answer is over 20

Answer:

y = −3x − 23

Step-by-step explanation:

The equation of the line in the slope-intercept form is y= x/3 + 6.

The slope of the perpendicular line is negative inverse: m = −3.

So, the equation of the perpendicular line is y = −3x + a.

To find a, we use the fact that the line should pass through the given point:

−2 = (−3) ⋅ (−7) + a.

Thus, a = −23.

Therefore, the equation of the line is y = −3x − 23.

Answer: y =−3x − 23

Answer:

25p

Step-by-step explanation:

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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The symbolic forms for the given statements are: (b) p ∨ r, (c) p ∧ q, (d) q ~ r, and (e) p ∨ q. Statement (a) cannot be expressed symbolically.

(a) x ≥ 5: This statement represents a numerical inequality, and it cannot be expressed symbolically.

(b) p ∨ r: The symbolic form for the statement "p ∨ r" is a logical disjunction, meaning it represents the logical "OR" operation between the propositions p and r.

(c) p ∧ q: The symbolic form for the statement "p ∧ q" is a logical conjunction, indicating the logical "AND" operation between the propositions p and q.

(d) q ~ r: The symbolic form for the statement "q ~ r" is a negation, where the proposition r is negated, represented by the symbol "~".

(e) p ∨ q: The symbolic form for the statement "p ∨ q" is a logical disjunction, indicating the logical "OR" operation between the propositions p and q.

In logic, different symbols are used to represent various logical operations and relationships between propositions. The statements provided have different symbolic forms based on the logical operations they represent.

The "∨" symbol represents logical disjunction (OR), "∧" symbol represents logical conjunction (AND), and "~" symbol represents negation. It is important to understand the symbolic forms to accurately represent and analyze logical statements.

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Rational numbers are defined as "a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q." This quote can be broken down to make it easier to understand. In basic terms, a rational number is a real number that is an integer, fraction, terminating decimal, or repeating decimal.

Integer

An integer is any positive or negative whole number including 0. Examples of integers include 4, -9, and 0.

Fraction

All fractions that do not have a 0 denominator (which makes the number undefined) are rational numbers. Additionally, complex fractions are not always considered rational numbers. Complex fractions are fractions where either the numerator or denominator is a decimal or fraction itself. Examples of rational fractions include \(\frac{4}5}\), \(\frac{7}{4}\), and \(\frac{2}{2}\).

Terminating Decimals

Terminating decimals are decimals that have a finite number of digits. This means that the decimal stops at some point. Examples of terminating decimals include 0.346, 0.47834, and 0.345832454525456

Repeating Decimals

Repeating decimals are any decimal that is not terminating but has some pattern that repeats for infinity. Examples of repeating decimals include \(0.\bar 9\), \(0.\bar8\bar6\), and \(0.\bar 5\bar7\bar8\bar4\). In this case, the bar notation represents numbers that repeat forever.