The sum of two consecutive integers is 91. Find the integers.

Answer:

33 times

Step-by-step explanation:

Set up an equation:

3 evens / 6 total = 1/2 probability of rolling an even

66 times x 1/2 probability= 33

Best prediction: 33 times

Hope this helps!

Answer:

y = 9x - 49

Step-by-step explanation:

y2 - y1/ x2 - x1

14 - 5/ 7 - 6

9/1

= 9

y = 9x + b

5 = 9(6) + b

5 = 54 + b

-49 = b

To find the probability that a participant selected at random found the products favorable, we can calculate the weighted average of the favorable responses from both the industry-sponsored and non-industry-funded studies.

For the industry-sponsored studies, 65% of participants found the products favorable, and for the non-industry-funded studies, 47% found the products favorable. Since there were 65 industry-sponsored studies and 35 non-industry-funded studies, the overall probability is:

(65/100) * 0.65 + (35/100) * 0.47 = 0.4225 + 0.1645 = 0.587 or 58.7%

If a randomly selected participant found the product favorable, we can use Bayes' theorem to calculate the probability that the study was sponsored by the food industry given this favorable response. The calculation is:

P(Industry-sponsored | Favorable) = (P(Favorable | Industry-sponsored) * P(Industry-sponsored)) / P(Favorable)

P(Favorable | Industry-sponsored) = 0.65

P(Industry-sponsored) = 65/100

P(Favorable) = 0.587

P(Industry-sponsored | Favorable) = (0.65 * (65/100)) / 0.587 ≈ 0.719 or 71.9%

Similarly, if a randomly selected participant found the product unfavorable, we can use Bayes' theorem to calculate the probability that the study had no industry funding given this unfavorable response. The calculation is:

P(No industry funding | Unfavorable) = (P(Unfavorable | No industry funding) * P(No industry funding)) / P(Unfavorable)

P(Unfavorable | No industry funding) = 0.36

P(No industry funding) = 35/100

P(Unfavorable) = 1 - P(Favorable) = 1 - 0.587 = 0.413

P(No industry funding | Unfavorable) = (0.36 * (35/100)) / 0.413 ≈ 0.305 or 30.5%

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Range: All real numbers greater than or equal to 3. The Option C.

To find the range of the function, we need to determine the set of all possible y-values that the function takes.

Since the line crosses the y-axis at (0, 2), we know that the function's range includes the value 2. Also, since the line turns at (-1, 3), the function takes values greater than or equal to 3.

Therefore, the range of the function is all real numbers greater than or equal to 3.

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Answer: C and D

Step-by-step explanation:

Plug in the X and Y from the coordinates into each equation. If both sides are equivalent, that means that the line passes through.

Answer:

x ^ 9

Step-by-step explanation:

length× breadth = x ^6 * x^3

= x ^ (6+3) = x ^ 9 unit^2

Answer:

\( \frac{ {x}^{ - 2} {y}^{ \frac{1}{2} } }{ \sqrt{36x {y}^{2} } } = \frac{ \sqrt{y} }{ {x}^{2} \sqrt{36x {y}^{2} } } = \frac{ \sqrt{y} }{6 {x}^{2}y \sqrt{x} } = \frac{1}{6 {x}^{ \frac{5}{2} } {y}^{ \frac{1}{2} } } = \frac{1}{6} {x}^{ - \frac{5}{2} } {y}^{ - \frac{1}{2} } \)

\( \frac{1}{6} \times - \frac{5}{2} \times - \frac{1}{2} = \frac{5}{24} \)

Answer:

I could but can you please put down the problem.

Step-by-step explanation:

a. The relationship between time and distance is not an arithmetic sequence, as the rate of change is not constant.

b. The distance is given by: d(n) = 5n².

An arithmetic sequence happens when the change in the output is always the same when the input changes by one, that is, the rate of change is constant.

From the table, the increases when the input(time) increases by one are given as follows:

15, 15, 35, 45.

The increases are not constant, hence the relationship between time and distance is not an arithmetic sequence.

The equation for the distance is given as follows:

d(t) = 0.5gt².

The constant is:

g = 10.

Hence:

d(t) = 5t².

At a time of n seconds, the distance is found replacing the lone instance of t by n, hence:

d(n) = 5n².

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The probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hours is 0.7492.

The random variable X is defined as the time it takes her to complete one review.

The random variable X follows a Normal distribution with parameters μ = 4 hours and σ = 1.2 hours.

A random sample of n = 16 reviews are selected as a set.

Compute the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hours as follows:

P(3.5 < X < 4.25) = P(3.5-4/1.2√16 < x- μ /σ/√n < 4.25-4/1.2/√16)

=P(-1.67 < Z < 0.83)

= P(Z < 0.83) - (P(Z < -1.67)

= 0.7967 - 0.0475

= 0.7492

Thus, the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hours is 0.7492.

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Ryan makes a profit of £240.  the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.

Ryan spends £190 to buy 80 jumpers. He sells 50% of the jumpers, i.e. 40 jumpers, at £12 each. This brings the total sales to £480. Then, he puts the remaining 40 jumpers on a Buy one get one half price offer. He sells 20 of the remaining jumpers using this offer. Therefore, the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.

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Answer:

Step-by-step explanation:

When dividing, you always have to make sure that your remainder
(40) is ALWAYS less than your divisor (24)

24<40, so the students' answer is incorrect.

under the restrictions that c is negative to ensure strict concavity, the utility function u(w) = -(b - w)c displays increasing absolute risk aversion.

To ensure that u(w) is strictly increasing, we need the derivative of u(w) with respect to w to be positive for all values of w. Taking the derivative, we have du(w)/dw = -c. For u(w) to be strictly increasing, -c must be positive, which implies c must be negative.

To ensure that u(w) is strictly concave, we need the second derivative of u(w) with respect to w to be negative for all values of w. Taking the second derivative, we have d²u(w)/dw² = 0. Since the second derivative is constant and negative, u(w) is strictly concave.

Now, let's examine the concept of increasing absolute risk aversion. If a utility function u(w) exhibits increasing absolute risk aversion, it means that as wealth (w) increases, the individual becomes more risk-averse.

In the given utility function u(w) = -(b - w)c, when c is negative (as required for strict concavity), the absolute risk aversion increases as wealth (w) increases. This is because the negative sign implies that the utility function is concave, indicating that the individual becomes more risk-averse as wealth increases.

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Answer:

21 divided by 3 = 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

The area of each of the missing faces is 40 m².

The length of each of the missing faces is 10 m.

The missing dimension is 10 m by 4 m.

Area is the region bounded by a plane shape.

To calculate the area of each missing face, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

And the length of each of the missing edge can be calculated using the formula below

Formula:

Where:

From the diagram in the question,

Given:

Substitute into equation 2

Hence, the length is 10 m.

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Answer:

exponential decay because the base is less than one

Step-by-step explanation:

Using the combination formula, it is found that the number of candidates that can get a unique number sequence is given by:

b. 45.

The order of the pieces is not important, hence the combination formula is used.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this problem, 2 pieces are taken from a set of 10, hence the number of sequences is given by:

\(C_{10,2} = \frac{10!}{2!8!} = 45\)

Which means that option b is correct.

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Answer:

372

Step-by-step explanation:

Since we know the total weight which is 714 and we know the weight of one garden which is 342, all we need to do now is subtract:

714 - 342 = 372

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

The direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

To find the maximum rate of change of the function f at the given point (5, 6, -1) and the direction in which it occurs, we can calculate the gradient of f at that point.

The gradient vector represents the direction of maximum increase of the function, and its magnitude represents the rate of change in that direction.

The gradient vector (∇f) of f(x, y, z) = (8x + 5y)/z can be found by taking the partial derivatives with respect to each variable:

∂f/∂x = 8/z

∂f/∂y = 5/z

∂f/∂z = -(8x + 5y)/z^2

Evaluated at the point (5, 6, -1), we have:

∂f/∂x = 8/(-1) = -8

∂f/∂y = 5/(-1) = -5

∂f/∂z = -((8(5) + 5(6))/(-1)^2) = -46

So, the gradient vector (∇f) at the point (5, 6, -1) is (-8, -5, -46).

The maximum rate of change of f at this point is given by the magnitude of the gradient vector:

|∇f| = √((-8)^2 + (-5)^2 + (-46)^2) = √(64 + 25 + 2116) = √2205 = 47.

Therefore, the maximum rate of change of f at the point (5, 6, -1) is 47.

To determine the direction in which this maximum rate of change occurs, we normalize the gradient vector by dividing it by its magnitude:

Direction vector = (∇f) / |∇f| = (-8/47, -5/47, -46/47).

Hence, the direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

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In the linear equation -1/4(x -1) = 2/3x + 2, the value of x is -21/11

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

In the given equation -1/4(x -1) = 2/3x + 2, we can solve for the value of x

-1/4(x -1) = 2/3x + 2

collect like terms

-1/4x + 1/4 = 2/3x + 2

2/3x + 1/4x = 1/4 - 2

(11/12)x = - 7/4

x = - 21 / 11

The value of x is -21/11

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Answer:

6.3 or 6 3/10 pounds

Step-by-step explanation:

First you convert 8 3/4 into a decimal.

8 3/4 = 8.75

You then subtract 8.75 and 2.45.

8.75 - 2.45 = 6.3

6.3 as a fraction is 6 3/10

Therefore, he has 6.3 or 6 3/10 pounds of fudge left.

Hope this helps:)

Answer:

its 63

Step-by-step explanation:

Answer:

\( \frac{15.75}{0.25} = \frac{1575}{25} \\ = 63\)

...............................

Answer:

The answer is A.

Step-by-step explanation:

As can be seen in the graph, car B starts at the "20" mark on the vertical axis, signifying that it starts 20 miles east of car A.

Hope this helped!

Answer:

Here you go sweetheart!

Step-by-step explanation:

The evaluation of the composite figure comprising of a square and an equilateral triangle is as follows;

9 (a) ∠ABD = 90°

(b) ∠BCD = 60°

(c) ∠ADC = 105°

A composite figure is a figure comprising of two or more regular geometric figures.

9. The shape of the quadrilateral ABDE = A square

The kind of triangle specified for the triangle ΔBCD = Equilateral triangle

The sides of the square ABDE are congruent by the definition of a square

Therefore; AB = BD = DE = AE by the definition of congruency

(a) Angle ∠ABD is a corner of the square ABDE, therefore;

The size of angle ∠ABD = 90° (properties of the interior angle of a square)

(b) The size of angle ∠BCD = 60° (Interior angle of an equilateral triangle)

(c) The size of angle ∠ADC is found as follows;

Triangles ΔAED and triangle ΔABD formed by the diagonal AD are congruent by Side-Side-Side, SSS congruency postulate

∠DAB ≅ ∠ADB (base angles of isosceles triangle ΔABD)

∠DAB = ∠ADB (Definition of isosceles triangles)

∠ABD + ∠DAB + ∠ADB = 180° (Angle sum properties of a triangle)

90° + 2 × ∠ADB = 180° (substitution property)

∠ADB = (180° - 90°) ÷ 2 = 45°

∠BDC = 60° (Interior angle of an equilateral triangle)

∠ADC = ∠ADB + ∠BDC (Angle addition postulate)

Therefore, ∠ADC = 45° + 60° = 105°

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