Use completing the square to solve for x in the equation (x-12)(x+4)= 9,
оо
X = -1 or 15
x = 1 or 7
X=41 41
X=4+ V73

Answer:

n+12=31

n=31-12

n=19

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

6. The probability that all 5 couples will have a baby of the preferred gender is 0.2373.

7. The probability that at least 4 of the 5 couples will have a baby of the preferred gender is 1 - 0.3672 = 0.6328.

Probability is a way to gauge how likely something is to happen. Many things are difficult to predict with absolute certainty.

Answer: The probability that one couple will have a baby of the preferred gender is 0.75. Assuming the gender of each baby is independent of the others, the probability that all 5 couples will have a baby of the preferred gender is 0.75⁵ = 0.2373.

Numeric value: 0.2373

In words: The probability that all 5 couples will have a baby of the preferred gender is 0.2373.

Answer: There are two ways to approach this problem. One way is to calculate the probability of each possible outcome (0 to 5 couples having a baby of the preferred gender) and then add up the probabilities for the outcomes where at least 4 couples have a baby of the preferred gender. Another way is to use the complement rule and subtract the probability that fewer than 4 couples have a baby of the preferred gender from 1.

Using the first method, we can calculate the probabilities as follows:

- 0 couples: 0.25⁵ = 0.0009766

- 1 couple: 5 x 0.75 x 0.25⁴ = 0.01465

- 2 couples: 10 x 0.75² x 0.25³ = 0.08789

- 3 couples: 10 x 0.75³ x 0.25² = 0.2637

- 4 couples: 5 x 0.75⁴ x 0.25 = 0.3955

- 5 couples: 0.75⁵ = 0.2373

The probabilities for the outcomes where at least 4 couples have a baby of the preferred gender are 0.3955 and 0.2373, so the total probability is 0.3955 + 0.2373 = 0.6328.

Using the second method, we can calculate the probability that fewer than 4 couples have a baby of the preferred gender as follows:

- 0 couples: 0.25⁵ = 0.0009766

- 1 couple: 5 x 0.75 x 0.25⁴ = 0.01465

- 2 couples: 10 x 0.75² x 0.25³ = 0.08789

- 3 couples: 10 x 0.75³ x 0.25² = 0.2637

The probability that fewer than 4 couples have a baby of the preferred gender is the sum of these probabilities: 0.0009766 + 0.01465 + 0.08789 + 0.2637 = 0.3672.

Therefore, the probability that at least 4 of the 5 couples will have a baby of the preferred gender is 1 - 0.3672 = 0.6328.

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As n tends to infinity, limit of the above expression is 3

Hence the sequence is conclusive (divergent).

Therefore, option (d) is the correct answer.

Given sequence is `[infinity] 3 n 1 n2 n = 2`

To check whether the given sequence is convergent or divergent or inconclusive, we use the Ratio test or D'Alembert's Ratio Test.

The formula for Ratio test is lim(n→∞)|a_{n+1}/a_n|

If the value of the above limit is greater than 1, then the sequence is divergent.

If the value of the above limit is less than 1, then the sequence is convergent.

If the value of the above limit is equal to 1, then the test is inconclusive.

|a_{n+1}/a_n| = |(3(n+1) + 1)/(n+1)²| × |n²/(3n+1)|

= 3 × (1 + 1/n) × (1 + 3/n)/(1 + 1/n)²

As n tends to infinity, limit of the above expression is 3

Hence the sequence is conclusive (divergent).

Therefore, option (d) is the correct answer.

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Answer:

B

Step-by-step explanation:

The cube of twice a number =

\({2m}^{3}\)

Decreased by 11 =

\( - 11\)

Hence, the cube of twice a number decreased by 11 =

\( {2m}^{3} - 11\)

The cube of twice a number decreased by 11 =2n^3-11

We have given options

We have to determine the correct statement

Let us consider a number n.

Expressions ismathematical statements with a minimum of two terms containing numbers or variables, or both, are connected by an operator in between.

The cube of twice a number =2n^3

Decreased by 11 =2n^3-11

Hence, the cube of twice a number decreased by 11 =2n^3-11

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the approximate arc length traced out by the endpoint of the vector-valued function f(t) = tcos(t)i + tsin(t)j over the interval [0, 2π] is approximately 10.6706 units.

What is arc?

An arc is a curved segment of a circle or any curved line. It is formed by connecting two points on the curve, and the arc itself lies on the circumference of a circle or the curved line.

To find the arc length traced out by the endpoint of the vector-valued function f(t) = tcos(t)i + tsin(t)j over a specific interval, we can use the arc length formula for a vector-valued function.

The arc length formula for a vector-valued function r(t) = xi + yj + zk over an interval [a, b] is given by:

\(L = \int[a, b] \sqrt((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2) dt\)

In this case, our vector-valued function is f(t) = tcos(t)i + tsin(t)j, where x = tcos(t), y = tsin(t), and z = 0 (since there is no z-component in the function).

Therefore, we need to calculate the derivatives dx/dt, dy/dt, and dz/dt to substitute them into the arc length formula.

dx/dt = cos(t) - tsin(t)

dy/dt = sin(t) + tcos(t)

dz/dt = 0 (since z = 0)

Now, let's compute the arc length over the interval [a, b] using the arc length formula:

\(L = \int[a, b] \sqrt((cos(t) - tsin(t))^2 + (sin(t) + tcos(t))^2 + 0^2) dt\\\\= \int[a, b] \sqrt(cos^2(t) - 2tcos(t)sin(t) + t^2sin^2(t) + sin^2(t) + 2tcos(t)sin(t) + t^2cos^2(t)) dt\\\\= \int[a, b] \sqrt(1 + t^2) dt\)

Since the interval is given as [0, 2π], we will substitute a = 0 and b = 2π into the integral:

\(L = \int[0, 2\pi] \sqrt(1 + t^2) dt\)

Using numerical software or calculators, the approximate value of the integral is found to be approximately 10.6706.

Therefore, the approximate arc length traced out by the endpoint of the vector-valued function f(t) = tcos(t)i + tsin(t)j over the interval [0, 2π] is approximately 10.6706 units.

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Answer:

V = 3,367.6 cm³

Step-by-step explanation:

Diameter of sphere (D) = 18.6 cm

radius (r) = ½(18.6) = 9.3

π = 3.14

Formula for volume of a sphere = ⁴/3πr³

Plug in the values

V = ⁴/3 × 3.14 × 9.3³

V = ⁴/3 × 3.14 × 804.357

V = (4*3.14*804.357)/3

V = 3,367.57463

V = 3,367.6 cm³ (nearest tenth)

The magazine would cost $33.93 to print a 1¾ inch ad in the "Good Ole Times" magazine.

The cost of a classified ad in the "Good Ole Times" magazine is determined by its size in column inches, with a cost of $43.50 per column inch. To determine how much the magazine would charge to print a 1¾ inch ad, we need to calculate the size of ad in column inches and then multiply that by the cost per column inch.

One way to convert 1¾ inches to column inches is to convert the fractional part (¾) to a decimal by dividing it by 4, which is the number of quarters in an inch. This gives us:

1¾ inches = 1 + ¾ inches = 1 + 0.75 inches = 1.75 inches

To express this measurement in column inches, we divide by the width of a column, which is not given in the problem. Assuming a typical newspaper column width of 2.25 inches, we get:

1.75 inches ÷ 2.25 inches per column = 0.7778 column inches

Rounding this to two decimal places, we get:

0.78 column inches

Now we can calculate the cost of the ad as follows:

Cost = Size in column inches × Cost per column inch

Cost = 0.78 column inches × $43.50 per column inch

Cost = $33.93

Therefore, the magazine would charge $33.93 to print a 1¾ inch ad.

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The probability that more than 12 out of 20 randomly selected 10-year-old children have exactly two siblings is approximately 0.106 or 10.6%.

To find the probability that more than 12 out of 20 randomly selected 10-year-old children have exactly two siblings, we can use the binomial distribution.

Let's define the following:

p = probability of a child having exactly two siblings = 0.30

n = total number of trials (selected children) = 20

We want to find the probability that more than 12 children have exactly two siblings, which can be expressed as P(X > 12), where X follows a binomial distribution.

Using the binomial probability formula, we can calculate the probability for each value of X and sum them up for X > 12:

P(X > 12) = P(X = 13) + P(X = 14) + ... + P(X = 20)

\(P(X = k) = (n C k) \times p^k \times (1 - p)^{(n - k)\)

where (n C k) is the binomial coefficient, representing the number of ways to choose k successes out of n trials.

Using this formula, we can calculate the individual probabilities for each value of X and sum them up:

P(X > 12) = P(X = 13) + P(X = 14) + ... + P(X = 20)

To simplify the calculation, we can use statistical software or binomial probability tables.

Using a statistical software package or a binomial calculator, we find that:

P(X > 12) ≈ 0.106

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Answer:

a,d,e

Step-by-step explanation:

Answer: A, C, D

Step-by-step explanation:

The fit statistic that can be used across different series that are in fact measured in different units is; MAPE

There are different statistics models in this regards such as;

Mean Absolute Error (MAE)

Mean Absolute Scaled Error (MASE)

Accuracy Percent (Accuracy %)

Mean Squared Error (MSE)

Root Mean Squared Error (RMSE)

Mean Absolute Percent Error (MAPE)

Now, we are told that we need the fit statistic that can be used across different series that are in fact measured in different units.

The correct one will be Mean Absolute Percent Error (MAPE) because the average absolute percent difference between the values that are fitted by the model and the observed data values.

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Answer:

Obtuse angle

Step-by-step explanation:

S and T are complementary. So, S and T are less than 90°.

T and U are supplementary. So, sum of T and U is 180°.

Since, T is less than 90°, U must be greater than 90°. Hence angle U is an obtuse angle.

can you please explain it more clearly

Step-by-step explanation:

Answer:

8.32*10^2 or

832.08

Step-by-step explanation:

True: When a form is created based on two or more tables, a relationship must be defined between queries.

True. When a form is created based on two or more tables, a relationship must be defined between queries in order to ensure that the form displays accurate data. Queries are used to pull data from multiple tables and present it in a single view, so it is important to define the relationships between these tables to avoid inconsistencies or errors in the displayed data. This ensures that the data from the related tables can be properly displayed and managed within the form.

When you drag and search a field from an "other" (unrelated) table, a new one-to-many relationship is created from the table in the list and the table from which you dragged the field. This relationship is established by Access, which does not enforce integrity by default.

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I think the answer would be A because 5% ×100=0.05 , and in the question they have been telling us that it decreased by 5 from the last week so the equation would be g of the last week - 0.05

The value of cos⁻¹(1/2) on the unit circle is 60°.

A circle with a radius of one unit is referred to as a unit circle. In the Cartesian coordinate plane, the unit circle is typically depicted. The second-degree equation with the variables x and y is used to algebraically represent the unit circle.

Given:

cos⁻¹(1/2)

As we know that for the unit circle, the value of the radius is 1,

Calculate the value of cos x as shown below,

cos x = radius of the circle / √(r² + p²)

cos x = 1 / √(1² + 1²)

cos x = 1 / √2

x = cos⁻ (1 / √2)

x = 45°

Thus, cos⁻¹(1/2) = 60°

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To evaluate the definite integral of the given function f(x) = ln(1+2x) over the interval [a, b], where a = 4 and n = 3, we can use the midpoint rule.

Determine the width of each subinterval: Since n = 3, we divide the interval [a, b] = [4, b] into 3 subintervals of equal width. Therefore, the width of each subinterval is (b - a)/n = (b - 4)/3.

Identify the midpoints of the subintervals: The midpoints are the points in the middle of each subinterval. For n = 3, we have 3 subintervals, so the midpoints are 4 + (1/2)(b - 4)/3, 4 + (3/2)(b - 4)/3, and 4 + (5/2)(b - 4)/3.

Evaluate the function at the midpoints: Substitute each midpoint into the function f(x) = ln(1+2x) to find the corresponding function values.

Calculate the sum: Multiply the function values at the midpoints by the width of each subinterval and sum them up. This gives [(b - 4)/3] * f(midpoint 1) + [(b - 4)/3] * f(midpoint 2) + [(b - 4)/3] * f(midpoint 3).

Simplify the expression: Combine like terms and simplify the resulting expression.

Substitute the given values: Substitute a = 4, n = 3, and the given value of b into the expression.

Evaluate the definite integral: Perform the necessary calculations to obtain the numerical value of the definite integral.

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Answer:

24

Step-by-step explanation:

Perimeter of rectangle = 2 (4x + 2x)

288= 2* 6x

288 = 12x

x = 288/12

x = 24

2(2x+4x)=288

12x=288

x=24

Answer:

A parallelogram is a quadrilateral with 2 pairs of parallel sides

If a survey asked a group of adults and youths if they prefer reading books printed on paper or electronic books. The  percent of the youths surveyed prefer reading electronic books is: 54%

Given data:

Youth book preference

Print = 34

Electronic = 40

Now let determine the percentage using this formula

Total = Print + Electronic book

Total = 34 +40

Total = 74

Now let determine the percentage of youth that preferred reading electronic book which  is calculated as :

Percentage = 40 / 74

Percentage = 0.54 × 100

Percentage = 54 %

Therefore we can conclude that 54% like to read electronic book.

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Answer:

C. 2, 1

Step-by-step explanation:

it displays the computed sum and product of the diagonal elements.

Here's a MATLAB code to find the sum and product of the diagonal elements of a given matrix `A`, as well as an example execution for `A = ones(5)`:

```matlab

% Define the matrix A

A = ones(5);

% Get the size of the matrix

[n, ~] = size(A);

% Initialize variables for sum and product

diagonal_sum = 0;

diagonal_product = 1;

% Calculate the sum and product of diagonal elements

for i = 1:n

   diagonal_sum = diagonal_sum + A(i, i);

   diagonal_product = diagonal_product * A(i, i);

end

% Display the results

disp("Sum of diagonal elements: " + diagonal_sum);

disp("Product of diagonal elements: " + diagonal_product);

```

Example execution for `A = ones(5)`:

```

Sum of diagonal elements: 5

Product of diagonal elements: 1

```

In this example, `A = ones(5)` creates a 5x5 matrix filled with ones. The code then iterates over the diagonal elements (i.e., elements where the row index equals the column index) and accumulates the sum and product. Finally, it displays the computed sum and product of the diagonal elements.

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139.2 cm² is the surface area, in cm², of the figure.

The surface area of a three dimensional shape is the total area of all of the faces. The surface area of a solid object is a measure of the total area that the surface of the object occupies.

here, we have,

The surface area of given figure = 3×Area of rectangle + 2×area of triangle base.

so, we get,

Surface area = 3×6×6+2×15.6

Surface area = 139.2 cm²

Hence, 139.2 cm² is the surface area, in cm², of the figure.

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Answer:

Using the given recursive formula, we can find the value of H(3) as follows:

H(3) = H(1) x H(2)

H(3) = 9 x 3

H(3) = 27

Therefore, H(3) = 27.

Step-by-step explanation:

Answer:

The sequence you provided is a recursive sequence where each term is defined using the two previous terms. Given that H(1) = 9 and H(2) = 3, we can find H(3) by multiplying H(1) and H(2): H(3) = H(1) x H(2) = 9 x 3 = 27.

Answer:

a. f(t) = h = 10·t/(π·r²)

b. The dependent and independent variables are ;

Dependent = The height of the water in the cup over time, h

Independent = The time of measurement of the water height in the cup

c. The domain is 0 < t < 10

d. The 5 in f(5), represents 5 seconds

e. Susan was trying to find out what the height of the water in the cup will be after 5 seconds

f. The numbers mean that at 7 seconds the water in the cup is 70 units high

Step-by-step explanation:

a. The rate at which water is added to the cup in the question = 10 mL per second

The volume of water in the cup is V = π × r² × h

dV/dt = 10

dV = 10 × dt

V = ∫10 × dt = 10·t

The height of the water in the cup, h = V/(π × r²) = 10·t/(π·r²)

Therefore, we have the function that models the height of the water in the cup over time given as follows;

f(t) = h = 10·t/(π·r²)

b. The dependent and independent variables are given as follows;

Dependent variable = The height of the water in the cup over time, h

Independent variable = The time of measurement of the water height in the cup

c. The domain is 0 < t < 10

Given that the cup has a capacity of 100 mL, we have;

The maximum volume the up can hold = 100 mL

The time it will take to fill the 100 mL cup given that the rate of at which she is pouring water into the cup at 10 mL per second = 100 mL/(10 mL/s) = 10 s

Therefore, a reasonable domain for the independent variable, t is 0 < t < 10

d. We have that the function f(t) = h = 10·t/(π·r²)

Therefore, the 5 in f(5), represents the time in seconds at which the function was being evaluated, which is 5 seconds

e. Given that Susan wrote f(5), Susan was trying to find the height of the water in the cup after 5 seconds

f. Given that Susan wrote f(7) = 70, we have that at 7 seconds the height of the water in the cup is 70 units, where one unit is 1/(π·r²)

Which gives;

f(7) = h = 10 × 7/(π·r²)  70/(π·r²)

f(7) = 70/(π·r²)

When the temperature (T) is 10 K, the value of T^4 is 10,000. This indicates that T raised to the power of 4 is equal to 10,000. Among the provided answer choices, the correct one is "10,000".  

It's important to note that raising a number to the fourth power means multiplying the number by itself four times, resulting in a significant increase in value compared to the original number.

To find the value of T^4 when T is 10 K, we need to raise 10 to the power of 4. This means multiplying 10 by itself four times: 10 × 10 × 10 × 10. Performing the calculations, we get:

T^4 = 10 × 10 × 10 × 10 = 10,000

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You would like to buy 2 cupcakes out of the total of 20 cupcakes. This proportion represents your share based on the 10% you desire.

If you and your friends are collectively buying 20 cupcakes, and you would like to buy 10% of the total, it means you want to purchase a portion that corresponds to 10% of the whole.

To calculate this, you can multiply the total number of cupcakes (20) by 10% (or 0.10), which represents the fraction or decimal form of 10%.

10% of 20 can be computed as follows:

10% of 20 = 0.10 * 20 = 2

Therefore, you would like to buy 2 cupcakes out of the total of 20 cupcakes. This proportion represents your share based on the 10% you desire.

By purchasing 2 cupcakes, you ensure that you have obtained your desired portion while leaving the remaining 18 cupcakes for your friends to distribute among themselves. This way, everyone gets a fair share, and you are able to satisfy your preference for 10% of the total quantity.

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