A magazine contains 80 pages of advertisements. This represents 64% of the total pages in the magazine. How many total pages are in the magazine?

Answer:

7 traders sell oranges and mangoes alone.

Step-by-step explanation:

(21 + 4 + 5 + 10 + x + 35 – x + 32 – x = 100)

(107 – x = 100)

(x = 107 – 100 = 7)

Therefore, 7 traders sell oranges and mangoes alone.

(b) (312_{four} + 52_{x} = 96_{ten})

(312_{4} = 3 times 4^{2} + 1 times 4^{1} + 2 times 4^{0})

= (48 + 4 + 2 = 54_{10})

(52_{x} = 5 times x^{1} + 2 times x^{0})

= ((5x + 2)_{10})

(therefore 54 + (5x + 2) = 96)

(56 + 5x = 96 implies 5x = 96 – 56 = 40)

(x = 8)

(therefore 312_{4} + 52_{8} = 96_{10})

Answer: x = 18

Step-by-step explanation:

The future value of Tran Lee's savings after five years would be approximately $14,995.49.

To calculate the future value of Tran Lee's savings, we can use the formula for the future value of an ordinary annuity:

Future Value = Payment * [(1 + Interest Rate)^Number of Periods - 1] / Interest Rate

Given:

Payment (PMT) = $2,900 per year

Interest Rate (r) = 5% = 0.05 (decimal form)

Number of Periods (n) = 5 years

Substitute  these values into the formula, we get:

Future Value = $2,900 * [(1 + 0.05)^5 - 1] / 0.05

Calculating this expression, we find:

Future Value ≈ $14,995.49

Therefore, the future value of Tran Lee's savings after five years would be approximately $14,995.49.

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The future value of Tran Lee's savings after five years would be approximately $14,995.49.

To calculate the future value of Tran Lee's savings, we can use the formula for the future value of an ordinary annuity:

Future Value = Payment * [(1 + Interest Rate)^Number of Periods - 1] / Interest Rate

Given:

Payment (PMT) = $2,900 per year

Interest Rate (r) = 5% = 0.05 (decimal form)

Number of Periods (n) = 5 years

Substitute  these values into the formula, we get:

Future Value = $2,900 * [(1 + 0.05)^5 - 1] / 0.05

Calculating this expression, we find:

Future Value ≈ $14,995.49

Therefore, the future value of Tran Lee's savings after five years would be approximately $14,995.49.

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Answer:

\((p + q)(p + q) \\ = {p}^{2} + pq + pq + {q}^{2} \\ = {p}^{2} + {q}^{2} + 2pq \\ = {(p + q)}^{2} \\ thankyou\)

The inner product of f(x)=-2cos(2x) and g(x)=-sin(2x) is 0.

To find the inner product of f(x) and g(x), we use the formula:

⟨f,g⟩= ∫[a,b] f(x)g(x)dx

where [a,b] is the interval of integration.

Substituting the given functions, we get:

⟨f,g⟩= ∫[0,π] -2cos(2x)(-sin(2x))dx

= 2 ∫[0,π] sin(2x)cos(2x)dx

Using the identity sin(2θ)cos(2θ) = sin(4θ)/2, we get:

⟨f,g⟩= ∫[0,π] sin(4x)/2 dx

= [-cos(4x)/8]π0

= (-1/8)[cos(4π)-cos(0)]

= (-1/8)[1-1]

= 0

Therefore, the inner product of f(x) and g(x) is 0.

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Answer:

c = -22, 22

Step-by-step explanation:

\( {(x - 11)}^{2} = {x}^{2} - 22x + 121\)

\( {(x + 11)}^{2} = {x}^{2} + 22x + 121\)

Answer:

The graph at the bottom

Step-by-step explanation:

All the numbers are gonna come out positive, because of the absolute value bars.

Answer:

i think its the last one i got that answer right

Step-by-step explanation:

Answer:    F  2^4+2^3 .3^2

Step-by-step explanation:

16+2*36

2^4+72

2^4+2^3 .3^2

here 2^3=8

    and 3^2=9

so 8*9=72

A rhombus is a quadrilateral that has four sides of equal length. A rhombus also has two diagonals, which are perpendicular bisectors of each other. This formula is given as follows: Perimeter = 4 × a, where a is the length of each side of the rhombus.

To find the perimeter of a rhombus using diagonals, follow these steps:

Step 1: Obtain the length of each diagonal of the rhombus.

Step 2: Use the length of the diagonals to find the length of each side.

Step 3: Add the length of each side to find the perimeter of the rhombus.

The perimeter is the sum of all the sides of a figure. To get the perimeter of a rhombus using diagonals, the length of each diagonal has to be found first. The formula for finding the length of each side of a rhombus is:  where the diagonal is the measure of the diagonal of the rhombus.

To find the perimeter of a rhombus, add the length of all the sides of the rhombus. This formula is given as follows: Perimeter = 4 × a, where a is the length of each side of the rhombus.

Therefore, the perimeter of a rhombus using diagonals can be found by following the above procedure and then using the formula to add all the sides of the rhombus.

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Answer:

There are 50 vegetables in all.

Step-by-step explanation:

First of all, 50 is correct because 60% of 50 is 30.

50 * 60% = 30.

So, the answer is 30.

Hope this helps! :)

Answer:

17\(\frac{1}{3}\)miles

40miles

Step-by-step explanation:

Given parameters;

Distance traveled by  the car = 1\(\frac{1}{2}\)miles  = \(\frac{3}{2}\)miles

Time taken = 2\(\frac{1}{4}\)minutes  = \(\frac{9}{4}\)minutes

Unknown:

Distance covered in 26minutes and in 1hr = ?

Solution:

Speed is the rate of change of distance with time.

   Speed  = \(\frac{distance}{time taken}\)

A. Insert the parameters and find the speed;

   Speed  = \(\frac{\frac{3}{2} }{\frac{9}{4} }\) = \(\frac{3}{2}\) x \(\frac{4}{9}\) = \(\frac{2}{3}\)miles/minutes

Distance covered in 26minutes;

   Distance  = speed x time

   Distance  = \(\frac{2}{3}\) x 26  = \(\frac{52}{3}\) miles  = 17\(\frac{1}{3}\)miles

B. Distance covered in 1hr or 60minutes;

  Distance = \(\frac{2}{3}\) x 60 = 40miles

The difference in the Beatles length is 1 / 10 centimeters.

We have,

The lengths of Beetles are 4/5 cm and 7/10 cm.

So, the difference in the beetles length can be calculated as

difference between the beetles length = 4 / 5 - 7 / 10

                                                                 = 8 - 7 / 10

                                                                  = 1/10 cm

Thus, the difference in beetles length is 1/10 cm.

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Answer:

143, 145

Step-by-step explanation:

To determine the sign of the sum of two integers when one integer is positive and the other is negative, we can follow a simple rule based on their magnitudes.

If the magnitude of the positive integer is greater than the magnitude of the negative integer, the sum will be positive. This is because the positive integer outweighs the negative integer, resulting in a positive value.

On the other hand, if the magnitude of the negative integer is greater than the magnitude of the positive integer, the sum will be negative. In this case, the negative integer dominates and determines the sign of the sum.

In both scenarios, the sign of the larger magnitude integer takes precedence and determines the sign of the sum. It is important to note that the sum will always have the sign of the integer with the larger magnitude, regardless of the specific values of the integers involved.

By considering the magnitudes of the integers, we can easily determine the sign of their sum when one integer is positive and the other is negative.

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Answer: The answer is 148

Step-by-step explanation:

Angle CBA and ABD should add up to 180 degrees. So you just do 180-32=148

The measurement of the ∠ABD in the given figure is 148°.

Hence the correct option is D.

Given that are two lines AE and CD are intersecting at point B, making angle ∠ABC = 32°.

We need to find the measurement of the ∠ABD.

To find the measurement of the ∠ABD, we will use the concept of linear pair angles.

According to the figure, angles ABC and ABD are linear pair angles, that mean they are supplementary, or we can say their sum is 180°.

Therefore, setting up the equation.

∠ABC + ∠ABD = 180°

Plugging the value of angle ABC from the given information,

32° + ∠ABD = 180°

Subtracting 32 from both the sides,

∠ABD = 180° - 32°

∠ABD = 148°

Hence the angle ABD is equal to 148°.

Therefore, the correct option is D.

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We can see that p-q = 1, which implies that p and q are directly related.

(a) If x and y are inversely prοpοrtiοnal, then we knοw that xy = k fοr sοme cοnstant k.

If \(x^p\) and \(y^q\) are alsο inversely prοpοrtiοnal, then we can write \((x^p)(y^q) = k'\) fοr sοme cοnstant k'. Using the inverse prοpοrtiοnality relatiοn, we get:

\((x^p)(y^q) = k'\)

\((xy)^pq = k'\)

\((k)^pq = k'\)

\(k^(pq-1) = k'\)

Frοm this equatiοn, we can see that pq-1 = 0, which implies that pq = 1. Therefοre, p and q are inversely related.

(b) If x and y are inversely prοpοrtiοnal, then we knοw that xy = k fοr sοme cοnstant k.

If \(x^p\) and \(y^q\) are directly prοpοrtiοnal, then we can write \((x^p) = k'(y^q)\) fοr sοme cοnstant k'. Using the direct prοpοrtiοnality relatiοn, we get:

\((x^p) = k'(y^q)\)

\((xy)^p = k'(y^q)(k)\)

\(k^p = k'(y^{(q-1)})\)

\(k^{(p-q)} = k'\)

Frοm this equatiοn, we can see that p-q = 1, which implies that p and q are directly related.

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The probability that 5 different integers randomly chosen from between 20 and 69 each have a different tens digit is 0.0000022.

To find the probability that 5 different integers randomly chosen from between 20 and 69 (inclusive) each have a different tens digit, we need to calculate the total number of favorable outcomes and divide it by the total number of possible outcomes.

First, let's determine the total number of possible outcomes. The range of integers between 20 and 69 (inclusive) contains 50 numbers. Therefore, there are 50 choices for the first number, 49 choices for the second number, 48 choices for the third number, 47 choices for the fourth number, and 46 choices for the fifth number. So, the total number of possible outcomes is:

50 * 49 * 48 * 47 * 46 = 54,512,400

Now, let's calculate the total number of favorable outcomes. We want each chosen number to have a different tens digit. There are 5 different tens digits in the range (2, 3, 4, 5, and 6). For the first chosen number, we have 5 choices. For the second number, we have 4 choices remaining (as one tens digit has already been used), for the third number we have 3 choices remaining, for the fourth number we have 2 choices remaining, and for the fifth number we have 1 choice remaining. So, the total number of favorable outcomes is:

5 * 4 * 3 * 2 * 1 = 120

Therefore, the probability that 5 different integers randomly chosen from between 20 and 69 each have a different tens digit is:

120 / 54,512,400 ≈ 0.0000022

This can be expressed as approximately 0.00022% or 1 in 454,270.

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Answer:

P

Step-by-step explanation:

Answer:

P is the independant variable.

Step-by-step explanation:

Since B is dependent on P, being B=P6, P is the independent variable.

1. Elizabeth's statement is incorrect because not only values less than 36, but also values equal to or greater than 36 make the inequality true.

2. All values of x less than 7 make the inequality true.

In mathematics, inequality is a relationship or a statement that compares two numbers or expressions that are not equal. It is expressed by symbols such as, >,,, or, which indicate which value is lower, greater, or simply different.

1. Elizabeth's statement is incorrect because not only values less than 36, but also values equal to or greater than 36 make the inequality true. For example, when x is 35, 6x is 210, which is not less than 42. On the other hand, when x is 36, 6x is 216, which is greater than 42, but when x is any value greater than 6, 6x will still be greater than 42.

2. In words, all values of x that make the inequality true are x such that 6 times x is less than 42. We can simplify this inequality by dividing both sides by 6 to get:

x < 7

Therefore, all values of x less than 7 make the inequality true.

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Answer:

6

Step-by-step explanation:

Step 1:

1/2n + 3 = 6       Equation

Step 2:

1/2n = 3      Subtract 3 on both sides

Step 3:

n = 3 ÷ 1/2      Divide

Step 4:

n = 3 × 2      Flip the Fraction

Answer;

n = 6

Hope This Helps :)

Input them onto your calculator and then graph them, see what the parabola does

Answer:

y  = 0.70x-  10.00

Step-by-step explanation:

--  Since one friend gave you 10.00 ,subtractthis from the 13.50 to give you the amount earned by walking the 5 miles

--  13.5-10.00  =  $3.50  

--  Since you walked 5 miles, divide by 5 to give you 0.70 per mile earned.

So, an equation that represents the amount of money earned is:  

y  = 0.70x-  10.00  . This is in slope-intercept form; the slope is $0.70 and represents the amount of money earned per mile  and the intercept is $10.00 and represents the initial amount of money that you were given.

The rate of change of the angle of elevation is -2π/3 radians/second.

We can use the tangent ratio to solve this problem. Since the rope is attached to the boat, we can draw a right triangle with the rope as the hypotenuse. The angle of elevation is the angle formed by the rope and the horizon.

The pulley is 5 feet above the water level, so the length of the opposite side (the side adjacent to the angle) is 5 feet. The length of the hypotenuse is 12 feet, since the boat is 12 feet from the dock.

Using the tangent ratio, we can calculate the angle of elevation:

tan(θ) = opp/hyp = 5/12

θ = arctan(5/12) = 0.927 rad

Now, since the rope is being pulled in at 3 ft/sec, the length of the hypotenuse is decreasing at a rate of 3 ft/sec. Therefore, the rate of change of the angle of elevation is:

rate of change of θ = -(3 ft/sec) / (12 ft) = -2π/3 radians/second

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a) Using the Law of Cosines for this triangle, we can write the equation:
d² = (36)² + (3s)² - 2(36)(3s)cos(60°)

b) The second ship must travel at approximately 4.24 miles per hour to be 42 miles apart from the first ship at noon.

(a) To write an equation that relates the speed s and the distance d between the two ships at noon using the Law of Cosines, we first need to determine the distance each ship has traveled by noon. Since they leave at 9 a.m. and we're interested in the distance at noon, they travel for 3 hours.

Ship 1:
Speed: 12 miles per hour
Distance traveled: 12 miles/hour * 3 hours = 36 miles

Ship 2:
Speed: s miles per hour
Distance traveled: s miles/hour * 3 hours = 3s miles

Now, we can form a triangle where Ship 1 travels 36 miles, Ship 2 travels 3s miles, and the distance between them (d) is the third side. The angle between Ship 1 and Ship 2 is 180° - (53° + 67°) = 60°.

Using the Law of Cosines for this triangle, we can write the equation:
d² = (36)² + (3s)² - 2(36)(3s)cos(60°)

(b) To find the speed s that the second ship must travel so that the ships are 42 miles apart at noon, we can plug d = 42 into our equation from part (a) and solve for s.

42² = (36)² + (3s)² - 2(36)(3s)cos(60°)

Solving for s, we get:
s ≈ 4.24 miles per hour (rounded to two decimal places)

So, the second ship must travel at approximately 4.24 miles per hour to be 42 miles apart from the first ship at noon.

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Answer:

just think of this, The domain of a rational function consists of all the real numbers x except those for which the denominator is 0 . To find these x values to be excluded from the domain of a rational function, equate the denominator to zero and solve for x .

Answer:

(x+2)(x+4)

Step-by-step explanation:

Answer:

( x + 2 ) ( x + 4 )

Step-by-step explanation:

Answer:

Step-by-step explanation:

X = shirts

Y = trousers

3x + 2y = 155

Now

y + 10 = x

Make y + 10 = x equal y

-10. -10

y = x - 10

Replace y with this equation in our other equation.

3x + 2(x - 10) = 155

Do the math:

This equals x = 35

Now put x = 35 in the other equation

Y + 10 = 35

Do the math:

y = 25

$35 per shirt

$25 per trousers

Now for the bar model, the total is 155

Make a fraction of 35/155

Make a long bar. Split it into 5 parts.

Label three parts 35 and two 25

Make the 35 parts slightly bigger.

It should look like this

The given equation, 16x² - y² + 16z² = 4, represents a quadric surface known as an elliptic paraboloid.

To determine the classification, we can examine the coefficients of the squared terms. In this case, the coefficients of x², y², and z² are positive, indicating that the surface is bowl-shaped. Additionally, the signs of the coefficients are the same for x² and z², indicating that the bowl opens upward along the x and z directions.

The negative coefficient of y², on the other hand, means that the surface opens downward along the y direction. This creates a cross-section in the shape of an elliptical parabola.

Considering these characteristics, the given equation represents an elliptic paraboloid.

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