Rewrite the following equation in exponential form. log2 (16) = 4 /5​

Answer:

Impossible

Step-by-step explanation: if a cube is number from 1-6 theirs no chance of getting a number less than 1.

To determine the optimal number of matted and unmatted pictures to maximize the company's profit, we can set up a linear programming problem.

Let's denote:

- x: the number of matted pictures

- y: the number of unmatted pictures

The objective is to maximize the profit, which can be expressed as:

Profit = 40x + 35y

We need to consider the following constraints:

1) The number of pictures completed each day cannot exceed 36:

x + y ≤ 36

2) The total man-hours of labor cannot exceed 80:

4x + 2y ≤ 80

3) The number of pictures cannot be negative:

x, y ≥ 0

Now we can solve this linear programming problem to find the optimal values for x and y.

First, let's graph the feasible region defined by the constraints:

```

x + y ≤ 36

4x + 2y ≤ 80

x, y ≥ 0

```

The feasible region is the area of the graph that satisfies all the constraints.

Next, we need to evaluate the objective function (Profit = 40x + 35y) at the vertices of the feasible region to find the maximum profit.

We can use different methods such as the corner-point method or the simplex method to determine the vertices and evaluate the profit at each vertex.

Thus, once we find the vertex that yields the maximum profit, we will have the optimal values for x and y.

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The circumference of the circle with the measure of diameter as 28 cm is 87.92 cm.

Given a circle.

Also given that,

Diameter of the circle = 28 cm

We know that, radius of a circle is half the measure of the diameter of the circle.

Radius of the circle = 28 / 2 = 14 cm

The formula to find the circumference of the circle is,

Circumference = 2 πr

Here r is the radius of the circle.

Substituting the given,

Circumference = 2 π (14)

                         = 28π

                         = 28 × 3.14

                         = 87.92 cm

Hence the circumference is 87.92 cm.

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Answer:

5/12

Step-by-step explanation:

Since Julia has 12 different flowers and we know she has 5 roses

we can turn it into a fraction which will be 5/12.'

The value of y is 4.4.

Let's go through the steps to solve for y:

Distributive property:

[tex]1/5y + 2 - 4/5 = 1/2y - 1 + 1/10y[/tex]

Combine like terms:

[tex]1/5y + 2 - 4/5 = 1/2y - 1 + 1/10y[/tex]

Simplify the equation by getting rid of fractions. To do this, we can multiply every term by the least common denominator (LCD) of 10:

[tex]10 * (1/5y + 6/5) = 10 * (3/5y - 1 + 1/10y)[/tex]

Simplifying further:

[tex]2y + 12 = 6y - 10 + y[/tex]

Now, let's combine like terms again:

[tex]2y + 12 = 7y - 10[/tex]

Next, let's isolate the variable y. Subtract 2y from both sides and add 10 to both sides:

[tex]12 + 10 = 7y - 2y[/tex]

Simplifying:

22 = 5y

Finally, divide both sides by 5 to solve for y:

y = 22/5

Note: It's important to check our solution by substituting y = 4.4 back into the original equation to ensure it satisfies the equation.

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Answer:

11/2

Step-by-step explanation:

11/5 = 2/5y

11 = 2y

y = 11/2

The three statements about the measures of center that are true include the following:

A. The mean for Group A is less than the mean for Group B.

B. The median for Group A is less than the median for Group B.

C. The mode for Group A is less than the mode for Group B.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

Group A

Mean for Group A = [(1 × 5) + (2 × 4) + (3 × 1)]/(5 + 4 + 1)

Mean for Group A = (5 + 8 + 3)/10

Mean for Group A = 16/10

Mean for Group A = 1.6

Mode for Group A = 1

Median for Group A = (1 + 2)/2

Median for Group A = 3/2

Median for Group A = 1.5

Group B

Mean for Group A = [(1 × 3) + (2 × 2) + (3 × 4) + (5 × 1)]/(3 + 2 + 4 + 1)

Mean for Group A = (3 + 4 + 12 + 5)/10

Mean for Group A = 24/10

Mean for Group A = 2.4

Mode for Group B = 3

Median for Group B = (2 + 3)/2

Median for Group B = 5/2

Median for Group B = 2.5

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: A,B,C

Step-by-step explanation:

Answer:

hello

the answer is:

Sin B = CA/AB ----> Sin 65° = 5/AB ----> 0.906 = 5/AB

----> AB = 5.51

The amplitude and the period of the function f(x) = cos(5θ) are 1 and 2π/5

From the question, we have the following parameters that can be used in our computation:

f(x) = cos(5θ)

A sinusoidal function is represented as

f(x) = Acos(B(x + C)) + D

Where

So, we have

A = 1

Period = 2π/5

Evaluate

A = 1

Period = 2π/5

Hence, the amplitude is 1 and the period is 2π/5

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Answer:

$2.25

Step-by-step explanation:

Red: $2

Blue: $6

Green: $6 + $5 (original cost of game) = $11

Yellow: $20

The total number of slots on the spinner is 4, with one slot for each color. Since the spinner can land on any color with equal probability, the probability of it landing on each color is 1/4 or 0.25.

Therefore, the expected value of the game is:

(0.25 x $2) + (0.25 x $6) + (0.25 x $11) + (0.25 x $20) - $5 = $2.25

The maximum error of the midpoint approximation is 0.55.

To estimate the maximum error, we can consider the worst-case scenario by assuming that the second derivative is at its maximum value throughout the interval [11, 31]. In this case, we can use the largest possible value for M.

To find the maximum error of the midpoint approximation, we need to determine the width of the interval and divide it by 2.

Width of the interval = upper bound - lower bound = 10.5 - 9.4 = 1.1

Maximum error (E) = (Width of the interval) / 2 = 1.1 / 2 = 0.55

Therefore, the maximum error of the midpoint approximation is 0.55.

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The volume of the oblique rectangular prism that is given above would be = 212.4

To calculate the volume of the oblique rectangular prism, the formula for the volume of a prism should be used which is given below. That is;

Volume of prism= L×w×h

where;

Length = 9

width = 4

height = ?

But the height of the oblique rectangular prism can be calculated using the sine formula;

That is;

height = 8× 0.7314

= 5.9

Therefore volume = 9×4×5.9 = 212.4

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The time that the ball traveled is given as follows:

t = 2.5 seconds.

The quadratic function modeling the ball's height after t seconds is given as follows:

H(t) = -16t² + 40t.

To obtain the time traveled by the height, we must obtain the roots of the quadratic function, as follows:

-16t² + 40t = 0.

16t² - 40t = 0

t(16t - 40) = 0.

Hence the roots are:

Which means that the time traveled by the ball is given as follows:

2.5 - 0 = 2.5 seconds.

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Answer: 126 feet

Step-by-step explanation: Convert yards into feet. IF we are given different units then you must convert it.

To convert yards into feet, MULTIPLY by 3

29 yards * 3= 87 feet

13 yards * 3= 39 feet

Now, key word= THROWS IN ALL= addition

87 + 39 is 126

The test statistic is given as follows:

t = 2.52.

We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 0.3, \mu = 0, s = 0.8, n = 45[/tex]

Hence the test statistic is given as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{0.3 - 0}{\frac{0.8}{\sqrt{45}}}[/tex]

t = 2.52.

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There are 125 stickers did Sally have to start.

We have to given that,

Sally had 52 more stickers than Joe after Joe gave 1/5 of his stickers to her.

Let us assume that,

Joe had x stickers to start with.

Since, After Joe gave 1/5 of his stickers to her.

He have 4/5 of his original amount left.

That is, 4/5x

Since, Sally had 52 more stickers than Joe

Hence, We get;

4/5x + 52 = 1/5x + y  .. (i)

where y is the number of stickers Sally had to start with.

Here, they both had a total of 260 stickers,

Hence,

x + y =260  .. (ii)

From (i) and (ii);

y = 125

Thus, There are 125 stickers did Sally have to start.

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The functions have the following

Domain: (-∞, -1) ∪ (-1, ∞)

Range: (-∞, -∞) excluding -5

Vertical Asymptote: x = -1

Horizontal Asymptote: y = -5

We have,

Domain:

The domain of a function refers to the set of all possible input values (x) for which the function is defined.

In this case, the function f(x) is defined for all real numbers except when the denominator (x + 1) is equal to zero.

The domain is all real numbers except x = -1.

So, the domain is (-∞, -1) ∪ (-1, ∞).

Range:

The range of a function refers to the set of all possible output values (y) that the function can produce.

In this case, we can observe that as x approaches -1 from either side, the function approaches negative infinity.

The range is (-∞, -∞) excluding -5.

Vertical Asymptote:

A vertical asymptote occurs when the function approaches infinity or negative infinity as x approaches a certain value.

In this case, the vertical asymptote occurs when the denominator (x + 1) is equal to zero, which is x = -1.

Horizontal Asymptote:

To determine the horizontal asymptote, we need to examine the behavior of the function as x approaches positive or negative infinity.

As x approaches positive or negative infinity, the term 1/(x + 1) becomes negligible compared to -5.

The horizontal asymptote is y = -5.

Thus,

The functions have the following

Domain: (-∞, -1) ∪ (-1, ∞)

Range: (-∞, -∞) excluding -5

Vertical Asymptote: x = -1

Horizontal Asymptote: y = -5

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The surface area of the cylinder is 133 square meters.

The formula for the surface area of a cylinder is given by:

Surface Area =  2πrh + 2πr²

Given that the radius (r) is 2.3 meters and the height (h) is 6.9 meters, we can substitute these values into the formula:

Surface Area =2 x 3.14 x 2.3 x 6.9 + 2 x 3.14 x 5.29

= 2 x 3.14 x 15.87 + 33.925

= 132.8848 square meter.

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Answer: B 133

Step-by-step explanation:

Answer:

4/15 square unit (0.2667 rounded)

Step-by-step explanation:

The whole square is one square as

((1/10) x 10 (columns)) multiplied by ((1/3) x 3 (rows)) = 1 multiplied by 1 = 1.

So, with that, the area of the striped rectangles should be:

(1/10) x 4 (columns in the striped area of rects) multiplied by (1/3) x 2 (rows in the striped area of rects) = 0.4 multiplied by 2/3 = 4/15 square unit.

The probability that exactly four out of 19 adults say cashews are their favorite nut is approximately 0.251.

The probability that 12 or more stolen bikes will be returned is approximately 0.026 (rounded to the nearest thousandth).

To solve both of these probability problems, we can use the binomial probability formula:

P(X = k) = (n C k) × p^k × (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes

n is the total number of trials

k is the number of desired successes

p is the probability of success in a single trial

(1 - p) is the probability of failure in a single trial

(n C k) represents the binomial coefficient, calculated as n! / (k! x (n - k)!)

Let's solve each problem separately:

The probability that exactly four out of 19 adults say cashews are their favorite nut can be calculated as:

P(X = 4) = (19 C 4) ⁴(0.49⁴) (0.51¹⁵)

Using the binomial probability formula, we can calculate:

P(X = 4) ≈ 0.251

Therefore, the probability that exactly four out of 19 adults say cashews are their favorite nut is approximately 0.251.

To find the probability that 12 or more stolen bikes will be returned out of 335 stolen bikes, we can use the binomial probability formula. Let's denote the probability of a stolen bike being returned as p = 0.03, the number of trials as n = 335, and the number of desired successes as k = 12 or more.

Using the complement rule, we can calculate the probability of not getting 11 or fewer successes:

P(X ≥ 12) = 1 - [P(X = 0) + P(X = 1) + ... + P(X = 11)]

To perform the calculation, summing up individual probabilities can be time-consuming. However, using statistical software or a binomial probability calculator can provide a convenient solution.

Using such a calculator, we find that the probability of 11 or fewer stolen bikes being returned is approximately 0.974. Therefore, the probability of 12 or more stolen bikes being returned is:

P(X ≥ 12) = 1 - 0.974 ≈ 0.026

Thus, the probability that 12 or more stolen bikes will be returned is approximately 0.026 (rounded to the nearest thousandth).

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The rule for (f - g)(x) is (f - g)(x) = 2x² - 11x - 3 and the value of (f - g)(-2) is 27

From the question, we have the following parameters that can be used in our computation:

f(x) = 2x² - 3x + 4

g(x) = 8x + 7

The rule for (f - g)(x) is calculated as

(f - g)(x) = f(x) - g(x)

Substitute the known values in the above equation, so, we have the following representation

(f - g)(x) = 2x² - 3x + 4 - 8x - 7

So, we have

(f - g)(x) = 2x² - 11x - 3

Here, we have

x = -2

Substitute the known values in the (f - g)(x) = 2x² - 11x - 3, so, we have the following representation

(f - g)(-2) = 2(-2)² - 11(-2) - 3

Evaluate

(f - g)(-2) = 27

Hence, the value of (f - g)(-2) is 27

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The required surface area of the larger solid is approximately 147 mm². Option A is correct.

We know that,

The surface area of any form is the area of the shape that is fronted.

The surface area of a 3D object is the amount of area covering the outside.

Let's say the surface area of the bigger solid S.

Since the two solids are similar, their volumes have a ratio of (side length)³.

Let's say the ratio of the side lengths of the larger to the smaller solid as k. Then,

⇒ k³ (540 mm³) = 857.5 mm³

Simplifying the above equation, we get:

⇒ k = 7/6

So, the larger solid is about 7/6=1.183 times bigger than the smaller solid in terms of side length.

Since the surface area has a ratio of (side length)²,

we can find the surface area of the larger solid by:

⇒ (1.83²)(108 mm³)

≈ 174 mm³

Therefore, the surface area of the larger solid is approximately 147 mm².

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Answer:

  see attached

Step-by-step explanation:

You want the areas of the four triangles in the figure.

The area of a triangle is given by the formula ...

  A = 1/2bh

where b is the base of the triangle, and h is its height perpendicular to the base.

Triangles A, B, C are right triangles, so their areas are easy to figure. Triangle D will be the difference between the area of the square and the areas of the other triangles.

The calculations are shown in the first attachment. Confirmation is provided by a geometry program in the second attachment.

__

Additional comment

If all you have are the coordinates of the vertices of triangle D, this method of finding its area is as good as any. There are other methods that can also be used, but they can be more trouble.

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You will need to pay $261.76 more each month if you want to pay off the balance in one year instead of three. However, you will save a total of $953.24 - $576 = $377.24 in interest by paying off the balance in one year instead of three.

If you decide to pay off the balance over one year instead of three, the payment amount will be higher, but the total interest paid will be lower due to the shorter repayment period.

First, let's calculate the total interest paid over three years. The total payment made over three years will be the monthly payment of $126.59 times 36 months, which is $4,553.24. The total interest paid is the difference between the total payment made and the initial balance of $3600, which is $953.24.

Now, let's consider paying off the balance over one year. The total payment made over one year will be the monthly payment of $126.59 times 12 months, which is $1,519.08. To calculate the interest paid, we can use the formula:

Total interest paid = Balance × Annual interest rate × Time

where the time is expressed in years. Plugging in the values, we get:

Total interest paid = $3600 × 0.16 × 1 = $576

Therefore, if you decide to pay off the balance over one year instead of three, you will pay an additional amount each month equal to the difference between the monthly payment for one year and the monthly payment for three years, which is:

Additional monthly payment = ($4,553.24/12) - ($1,519.08/12) = $261.76

This means that you will need to pay $261.76 more each month if you want to pay off the balance in one year instead of three. However, you will save a total of $953.24 - $576 = $377.24 in interest by paying off the balance in one year instead of three.

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The bisector of angle RQP is angle PQT and angle RQT, both angles are equal and their sum is equal to angle RQP.

Angle bisector or a bisector angle is a type of angle obtained after dividing the initial angle into two equal parts.

The bisected angle can be obtained using a pair of compass and a pencil attached to it.

To bisect the given angle RQP; we will take the following steps;

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Answer:

Step-by-step explanation:

I'm sorry, but I cannot answer your question without a visual representation or description of the rectangular prism. Please provide more information or a picture so that I can assist you accurately.

Answer:

72 cm 2?? THERE Isn't anything bellow I am sorry?

Step-by-step explanation:

The width of the rectangle is 13 cm and the dimension is 26 cm x 13 cm

Given data ,

Let the length be L and width be W

Now , the width is 1/2 of the length, so we can write:

W = (1/2)L

The area of a rectangle is given by the formula:

Area = Length x Width

Given that the area is 338 square centimeters, we can write:

338 = L × W

Substituting W with (1/2)L, we have:

338 = L × (1/2)L

To solve this equation, we can multiply both sides by 2 to eliminate the fraction:

676 = L²

Taking the square root of both sides, we find:

L = √676

L = 26

So the length of the rectangle is 26 centimeters.

Substituting this value back into the equation for the width, we have:

W = (1/2)L

W = (1/2)(26)

W = 13

Hence , the dimensions of the rectangle are length = 26 centimeters and width = 13 centimeters

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The phase shift of the trigonometric function is given as follows:

D) 90º to the left.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For the cosine function, we have the same definition, we only use cos() instead of sin().

For which the parameters are given as follows:

For this problem, we have that the phase shift is of C = 90. As we are adding inside of the domain of the function, the phase shift is to the left.

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Sorry for bad handwriting

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