John started his collection with 35 baseball cards and collects 4 new cards every week. Frank started the same collection with 50 baseball cards and collects 2 new cards every week. How long will it take John to collect more cards than Frank.

Answer:

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Step-by-step explanation:

a recursive formula in a geometric sequence allows a term to be found by multiplying the preceding term by the common ratio r

here r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{-2}\) = 8 , then

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

The correct option that compares both weights is; B. The weights for regular cola are greater than those for diet cola.

From the two histograms given, we see that the x-axis represents the weights in lb of regular cola and diet cola.

Now, from careful observation, it is clear that the weights spread for regular cola are wider than that for diet cola.

Secondly, we see that the weights for regular cola are largely greater than those of diet cola.

Thus, we can conclude that the correct option that compares both weights is; B. The weights for regular cola are greater than those for diet cola.

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Answer:

y=x+8

Step-by-step explanation:

The answer is y=x+8

Answer:

Step-by-step explanation:

Center is at (0, 0)  for circle  you need to find the slope from center to point so that you can find perpendicular slope.  

slope = (4-0)/(4-0) =1

the perpendicular slope needs to be flipped and opposite sign

m(tan)= -1   point for tan = (4,4)   put in point-slope form

y-4= -1(x-4)

y-4 =-1x+4

y = -x +8

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9514 1404 393

Answer:

  C.  2x -15

Step-by-step explanation:

The respective numbers of naira are ...

  laraba: x

  kunie: x-15 . . . . . 15 less than laraba

Then the total is ...

  laraba + kunie = x +(x -15) = 2x -15 . . . . matches choice C

The estimates for the number of transistors per IC, using an exponential function, are given as follows:

The format of an exponential function is presented as follows:

\(y = ab^\frac{x}{n}\)

In which the parameters of the function are listed as follows:

Moore's Law states that the number of transistors per IC doubles every two years, hence the values of parameters b and n both have values of two, hence:

b = 2, n = 2.

The number of transistors per IC in the reference year of 1972 was of 4000, hence the initial value is of:

a = 4000.

Then the exponential function is:

\(y = 4000(2)^{\frac{x}{2}}\)

2012 is 2012 - 1972 = 40 years after 1972, hence the estimate is given as follows:

\(y = 4000(2)^{\frac{40}{2}} = 4,194,304,000\)

2040 is 68 years after 1972, hence hence the estimate is given as follows:

\(y = 4000(2)^{\frac{68}{2}} = 6.87 \times 10^{13}\)

The chart is given by the image at the end of the answer.

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Answer:

8

Step-by-step explanation:

3/4 cup leaves 1/4 cup from each cup

1/4+1/4+1/4=3/4

so it would be 3/4+3/4+3/4+3/4+3/4+3/4+3/4+3/4=8 cups

The institution from the industrial revolution is the national institute of space and technology. Hence, option B is correct.

Agrarian and handcraft economies were replaced by industrialized and machine production during the Industrial Revolution in modern history. New modes of living and working were made possible by these technical advancements, which profoundly altered society.

In the 18th century, this practice started in Britain and then extended to other regions of the world. The English economics professor Arnold Toynbee (1852–83), who originally used the word to characterize Britain's economic growth from 1760 to 1840, although it had been used by French writers earlier.

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Step-by-step explanation:

Answer:

670,000

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

670,000

Step-by-step explanation:

Here's a tip to help you remeber

5 or more let it score

4 or less let it rest

That means that if the last number is 5 or if it's greater than 5 it will round up. But if it's 4 or less than 4 it will round down.

Answer:

If they each mate shouldn't you have about 120

Step-by-step explanation:

The fourth root of -81 is not a real number is 3√i.

A number that can be represented in the form a + bi is an imaginary number. In this case, a and b are real numbers, while I is the imaginary unit, which is equal to the square root of -1. In mathematics, imaginary numbers are used to expand on the real number system and to describe values that cannot be stated using real numbers.

Complex numbers, which are numbers of the type a + bi, where a and b are real numbers, are one of the principal applications for imaginary numbers. Several mathematical and scientific disciplines, such as electrical engineering, signal processing, and quantum physics, require complex numbers.

The value of -81 can be written as i²(3)⁴.

Taking the fourth root of the number we get 3√.

Hence, the fourth root of -81 is not a real number is 3√i.

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The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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The total area of the composite figure which has triangle and rectangle is  24.41 square inches

The given composite figure has two triangles and one rectangle

Area of rectangle =length × width

=4.6×3.15

=14.49 square inches

Area of left side triangle, it has base of 3.3 in and height 3.15 inches

Area of triangle = 1/2×3.3×3.15

=5.1975 square inches

Area of triangle on right side

Base = 3 in

Height = 6.3-3.15=3.15 in

Area of triangle = 1/2×3×3.15

=4.725 square inches

Total area = 14.49 + 5.1975  + 4.725

=24.41 square inches

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a numerical expression is a mathematical statement involving only numbers and one or more operation symbols. and a algebraic expession is an expressions that includes at least one variable and at least one operation. Order of operation goes (), exponent, divison, multiplication, addtion and subratcion

Answer:

Step-by-step explanation:

cos A = \(\frac{\sqrt{8} }{3}\)

Answer:

57

Step-by-step explanation:

this is the boybfiend

Answer:

Empirical Rule

Step-by-step explanation:

The Empirical Rule is also known as the Sigma rule or the 68-95-99.7% rule. The rule state that for a given data set, 68% of all data values will fall within the first standard deviation from the mean. The rule also states that 95% of all data values would fall within two standard deviations, while almost all the data which amounts to about 99.7% will fall within three standard deviations.

The empirical rule is used in forecasting based on the given datasets because it is a certainty that after obtaining the standard deviation, data values can be assigned to the categories they fall into, under the Empirical rule.

13 is the range, 17.0 is the population variance, and 4.1 is the population standard deviation.

The range of a collection of data is a measurement of its variability. It is the difference between a set of data's highest and lowest value.

Given ,

11,11,16,17,15,13,9,18,5,7

Highest value = 18

Lowest value = 5

Range = 18-5 = 13

The following formula works well for population variance:

Population Variance = Σ(x-mean)²/N

N is total element in the data = 10

x are the individual data

Calculating the mean is necessary before we can obtain the variance and standard deviation.

mean = Σfx/N

Mean = 122/10

Mean = 12.2

Variance = 170.16/10

Population variance = 17.016

Population variance ≈ 17.0 (to 1 d.p)

Population standard deviation = √Population Variance

Population standard deviation = √17.016 = 4.125

≈ 4.1 (to 1 d.p)

The complete question is:

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 11,11,16,17,15,13,9,18,5,7

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Answer:

\(\frac{2}{3}\)

Step-by-step explanation:

The equation for slope is:

\(Slope = \frac{y_2-y_1}{x_2-x_1}\)

We can plug the given coordinates into the equation:

\(Slope = \frac{0-2}{-4-(-1)}=\frac{-2}{-4+1}=\frac{-2}{-3}=\frac{2}{3}\)

Answer:

44 inches

Step-by-step explanation:

If the width of the room is 19 feet, and the width of the scale drawing of the room is 38 inches, to determine the scale of feet to inches, divide both values by 19:

⇒ 19 ft = 38 inches

⇒ 19/19 ft = 38/19 inches

⇒ 1 ft = 2 inches

Therefore, 1 foot is represented by 2 inches on the scale drawing.

To calculate the length of the scale drawing, multiply the actual length of the room by 2:

⇒ 22 × 2 = 44 inches

Therefore, the length of the scale drawing is 44 inches.

The diameter of the tin in the picture is  \(3d/5\) where 'd' is the diameter of the tin in reality.

Determining the diameter of tin:

Since there is no indication of dimensions, represent the diameter with a variable 'd' and find the diameter of the tin according to the given condition in the problem.

Here we have assumed that the diameter of the tin is 'd' in reality and the diameter of the tin picture can be calculated as given below.  

Here we have

A ricoffy tin container with no dimensions indicated

Let d and h be the diameter and height of the tin

Given that the container is 2/5 times smaller than d

then the diameter of the tin in the picture \(= d - 2/5(d)\)

\(= [5d - 2d]/5 = 3d/5\)

Therefore, The diameter of the tin in the picture is  \(3d/5\) where 'd' is the diameter of the tin in reality.

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Answer:

Point A is at (0, –4).

Point B is at (–8, –7).

Step-by-step explanation:

point A is 4 units down : y = –4

Point B is 8 units to the left : x = –8

and 7 units down: y = –7

A : (0, –4)

B : ( –8, –7)

The proportion equivalent with Two-thirds would be 6/9.

Since we know that the proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that the  proportion with Two-thirds

If you actually divide it’ll make since , so first  we want to divide the 2 , then you want to multiply the third of the two

2/3 x 3/3

6/9

thus, the answer will be 6/9.

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Each friend had originally 13 action figures before buying 11 more.

Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.

a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.

Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.

The total number of action figures will be 5(x + 11) = 5x + 55.

Now, according to the problem,5x + 55 = 120

This is our equation that models the problem.

b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.

5x + 55 = 120

5x = 120 - 55 (subtract 55 from both sides)

5x = 65x = 13

Therefore, each friend had originally 13 action figures before buying 11 more.

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Answer:  j(x) = (x-1)(x+2)

The x-1 part is because of the root x = 1

The root x = -2 leads to the factor x+2

A degree 3 polynomial with real coefficients having zeros 2 and 3 - 2i and a lead coefficient of 1 is x³- 8x² + 25x-26.

Given that, a degree 3 polynomial with real coefficients having zeros 2 and 3 - 2i and a lead coefficient of 1.

Cubic polynomial is a type of polynomial based on the degree i.e. the highest exponent of the variable. Hence, a cubic polynomial is a polynomial with the highest power of the variable or degree is 3. A polynomial is an algebraic expression with variables and constants with exponents as whole numbers.

We have P(x) = (x-x1)(x-x2)(x-x3),

x1 =2, x2 =3-2i, since the complex zeros always appear in pares, and the pare is symmetric about x-axis, so the other complex zero is x3=3+2i, therefore we have:

P(x) = (x-2) (x-(3-2i)) (x-(3+2i))

= (x-2) (x-3+2i) (x-3-2i)

= (x-2) (x(x-3-2i)-3(x-3-2i)+2i(x-3-2i))

= (x-2) (x²-3x-2xi-3x+9+6i+2xi-6i-4i²)

= (x-2) (x²- 6x + 9 - 4 (-1))

= (x-2) (x²- 6x + 13)

= (x(x²- 6x + 13)-2(x²- 6x + 13))

= x³- 6x² + 13x-2x²+12x-26

= x³- 8x² + 25x-26

Therefore, a degree 3 polynomial with real coefficients having zeros 2 and 3 - 2i and a lead coefficient of 1 is x³- 8x² + 25x-26.

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By using Percentage , Profit distributed to Charity A is £ 624 and Charity B is £ 336

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.

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

Total ticket sold = 800

Cost of each ticket is £ 2

Total fund raised (raw) = 2 * 800 = £1600

4% of the ticket won a prize of £20 each

so total number of tickets winning a prize = 4 % of 800 = 32

Total prize money distributed = 32 * 20 = £ 640

Total amount to distribute to charity = 1600 - 640 = £ 960

Total profit that goes to Charity A is = 65 % of 960 = £624

And rest to charity B is = £ 336

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