Drag each expression to its equivalent.
4y−3
9y
2+5y

Answer:

They ate a total of 7.5 apples.

Step-by-step explanation:

The total number of apples that these 4 students ate is:

2 + 2.5 + 1.25 + 1.75 = 7.5

Therefore, they ate a total of 7.5 apples.

Answer: 7.5

Step-by-step explanation: 2 + 2.5 = 4.5

4.5 + 1.25 = 5.75

5.75 + 1.75 = 7.5

Answer:x= 3/22

Step-by-step explanation:

Distribute

Subtract the numbers

Combine multiplied terms into a single fraction

Distribute

Find common denominator

Combine fractions with common denominator

Multiply the numbers

Add the numbers

Answer:

To find the slope of the tangent to the curve y = 4e^(3x) + (1/5)x + 4 at x = 1.5, we need to take the derivative of y with respect to x and evaluate it at x = 1.5.

The derivative of y with respect to x is:

dy/dx = 12e^(3x) + (1/5)

So, the slope of the tangent to the curve at x = 1.5 is:

dy/dx | x=1.5 = 12e^(3(1.5)) + (1/5)

dy/dx | x=1.5 = 12e^(4.5) + 0.2

dy/dx | x=1.5 ≈ 197.515

Therefore, the slope of the tangent to the curve y = 4e^(3x) + (1/5)x + 4 at x = 1.5 is approximately 197.515.

The slope of the tangent to the curve y = 4e^(3x) + 1/(5x) + 4 at x = 1.5 is approximately 512.558.

To find the slope of the tangent to the curve y = 4e^(3x) + 1/(5x) + 4 at x = 1.5, we need to take the derivative of y with respect to x and evaluate it at x = 1.5.

Taking the derivative of y with respect to x using the sum and power rules of differentiation, we get:

y' = 12e^(3x) - 1/(5x^2)

Now we substitute x = 1.5 to get:

y'(1.5) = 12e^(3(1.5)) - 1/(5(1.5)^2)

Simplifying, we get:

y'(1.5) = 12e^(4.5) - 1/11.25

Using a calculator, we can evaluate this expression to get:

y'(1.5) ≈ 512.558

Therefore, the slope of the tangent to the curve y = 4e^(3x) + 1/(5x) + 4 at x = 1.5 is approximately 512.558.

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If you invest $2,000 for 3 years at an interest rate of 6%, compounded every 6 months. The value of your investment at the end of the period is $2,397.39.

The interest rate is 6% and it is compounded every 6 months, so the period is 6 months. To calculate the value of the investment at the end of the period, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount.
P = the principal amount (initial investment)
r = the annual interest rate (6%).
n = the number of times the interest is compounded per year (2, since it's compounded every 6 months).
t = the time period in years (3)

Plugging in the numbers, we get:

A = 2,000(1 + 0.06/2)^(2*3)
A = 2,000(1 + 0.03)^6
A = 2,000(1.03)^6
A = $2,397.39

Therefore, the value of your investment at the end of the period is $2,397.39.

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a)

P(X = 2) = 0.1839

b)

P(X = 7) = 0.0573

c)

P(X = 1) = 0.3033

d)

P(X = 3) = 0.1413

We have,

a. To find P(X = 2) when λ = 2.5, we can use the Poisson probability mass function:

P(X = 2) = (e^(-λ)  x λ^X) / X!

Substituting λ = 2.5 and X = 2, we get:

P(X = 2) = (e^(-2.5) x 2.5²) / 2!

P(X = 2) ≈ 0.1839 (rounded to four decimal places)

b.

To find P(X = 7) when λ = 8.0, we can again use the Poisson probability mass function:

P(X = 7) = (e^(-λ) x λ^X) / X!

Substituting λ = 8.0 and X = 7, we get:

P(X = 7) = (e^(-8.0) x 8.0^7) / 7!

P(X = 7) ≈ 0.0573 (rounded to four decimal places)

c.

To find P(X = 1) when λ = 0.5, we use the same formula:

P(X = 1) = (e^(-λ) x λ^X) / X!

Substituting λ = 0.5 and X = 1, we get:

P(X = 1) = (e^(-0.5) * 0.5^1) / 1!

P(X = 1) ≈ 0.3033 (rounded to four decimal places)

d.

To find P(X = 3) when λ = 3.7, we can use the Poisson probability mass function:

P(X = 3) = (e^(-λ) * λ^X) / X!

Substituting λ = 3.7 and X = 3, we get:

P(X = 3) = (e^(-3.7) x 3.7³) / 3!

P(X = 3) ≈ 0.1413 (rounded to four decimal places)

Thus,

P(X = 2) = 0.1839

P(X = 7) = 0.0573

P(X = 1) = 0.3033

P(X = 3) = 0.1413

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The term you are looking for is the proportion of the total variation in the dependent variable explained by the regression model (or independent variable), which is known as the A) coefficient of determination.

The coefficient of determination, also known as R-squared, is a statistical measure that indicates the proportion of the total variation in the dependent variable that is explained by the regression model or independent variable. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data. The other terms mentioned - variable, proportion, and independent - are all related to the concept of regression analysis, which is used to identify the relationship between a dependent variable and one or more independent variables, and to quantify the extent to which changes in the independent variables affect the dependent variable.

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There are 640 acres in 1 square mile. The area of a forest is increasing at a rate of 1 acre per decade. The rate at which the area of the forest is increasing, in square kilometers per decade is C) 0.0025 square kilometers per decade.

The area of the forest is increasing at a rate of 1 acre per decade. To find the rate in square kilometers per decade, we first need to convert acres to square miles, and then square miles to square kilometers.

1 acre = 1/640 square miles (since there are 640 acres in 1 square mile)

Now, we'll convert square miles to square kilometers using the given conversion factor (1 kilometer = 0.62 mile):

1/640 square miles * (1 km / 0.62 mile)^2 = 1/640 * (1 / 0.3844) square kilometers ≈ 0.00256 square kilometers

So, the closest answer to the rate at which the area of the forest is increasing is:

C) 0.0025 square kilometers per decade

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The quotient of 13,756 divided 5 is 2, 753.

We have to divide 13756 by 5.

So, the division is

                          5 | 13765 | 2 7 5 3

                                10

                              ____

                                   37

                                   35

                                 ____

                                      26

                                      25

                                     ___

                                         15

                                          15

                                         ___

                                           0

Thus, the quotient is 2,753.

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The probability that they are all of different colors when a bag contains 9 marbles is 9/28.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

Total number of marbles=9

Number of red marbles=3

Number of blue marbles=3

Number of yellow marbles=3

Three marbles are  selected from the bag at random probability that they are all different color:

[tex]\frac{^3C_1*^3C_1*^3C_1}{^9C_3} = \frac{9}{28}[/tex].

Therefore, the probability that they are all of different colors is 9/28.

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Complete question:

A bag contains 9 marbles, 3 of which are red, 3 of which are blue, and 3 of which are yellow. If three marbles are selected from the bag at random, what is probability that they are all of different colors?

The conclusion is that in a bowl containing 9 marbles, at least 3 of them are red, at least 3 are blue, or at least 5 are said to be green.

The use of Pigeonhole Principle to prove the statement will be done in this question.

The Pigeonhole Principle is one that states that if there are more pigeons than pigeonholes, then at least one pigeonhole needs to have  more than one pigeon.

So lets assume for contradiction that there are not at least 3 red marbles, 3 blue marbles, or 5 green marbles.

Case 1: There are fewer than 3 red marbles.

If less than 3 red marbles, then max 2 red marbles. 9 - 2 = 7 marbles left. 7 marbles: blue/green. With more than 3 marbles and assumed 2 red marbles, it violate the Pigeonhole Principle.

Case 2: There are fewer than 3 blue marbles.

If 3 blue marbles, then max 2 blue marbles. 9-2=7 marbles left, red or green. "More marbles than pigeonholes - against the Pigeonhole Principle."

Case 3: There are fewer than 5 green marbles.

5 green marbles, 4 green marbles. We have more marbles than pigeonholes,  so against the Pigeonhole Principle.

So, there is  contradiction in all 3 cases, our initial assumption that there are not at least 3 red marbles, 3 blue marbles, or 5 green marbles have to be  false.

So, we can say that in a bowl containing 9 marbles, at least 3 of them are red, at least 3 are blue, or at least 5 are green.

Another is:

Total number of marbles=9

Number of red marbles=3

Number of blue marbles=3

Number of yellow marbles=3

So, the probability that they are all of different colors is 9/28.

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1:. 3.0508

2:. 1.4665

3:. 0.7194

4:. 0.1166

5:. 3.3896

The shortest distance from John's Farm house to the high way is 116.6miles. This is solved using Pythagorean theorem.

When triangulated, we find three possible distances:

D - the Gas Station to the Hotel = 100miles

P -  The gas station to the farm house = 60 miles

x - shortest distance between farm ouse to the highway

In Pythagorean format:

x² = 60² + 100²

x² = 3600 +10000
x = √13600
x [tex]\approx[/tex] 116.6 Miles.

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Answer:

  y = 4 is line parallel to x-axis. In that line, each point's y-co-ordinate is 4.

The measure of the side x is 31. 509

First, we need to know the different trigonometric identities. These identities are;

From the information given, we have that;

The opposite side = x

The adjacent side = 45

The angle, theta = 35 degrees

Using the tangent identity, we have the ratio

tan 35 = x/45

cross multiply the values, we have;

x = 45tan (35)

find the value

x = 45(0. 7002)

multiply the values

x = 31. 509

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The reflectyed point Rx is given as 6 , 3

The distance would have to be solved for first

This is the distance between the point P and the vertical line x = 2.

The distance d =  |(-2) - 2|

= |-4|

= 4

Next we have to take the point P o the other side of the line x = 2 this is the point that has the same distance

We will solve for the new coordinate

2 + 4

= 6

Hence the reflectyed point Rx is given as 6 , 3

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The solution to the absolute value equation |x-3| > 4 is (-∞, -1) U (7, ∞) in interval notation

To solve the absolute value equation |x-3| > 4 and express the answer in interval notation, follow these steps:

1. Break the absolute value inequality into two separate inequalities:
  a) x - 3 > 4 (when x - 3 is positive)
  b) -(x - 3) > 4 (when x - 3 is negative)

2. Solve each inequality:
  a) x - 3 > 4 => x > 7
  b) -(x - 3) > 4 => -x + 3 > 4 => -x > 1 => x < -1

3. Write the solution in interval notation:
  (-∞, -1) U (7, ∞)

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To determine if the given subset is a subspace, verify that it satisfies the following conditions:
  a. It contains the zero vector.
  b. It is closed under vector addition.
  c. It is closed under scalar multiplication.

let's first define the terms:

1. Vector space: A collection of vectors that follow certain rules, such as closure under addition and scalar multiplication.

2. Subset: A set containing elements that are also elements of another set, called the superset.

3. Subspace: A subset of a vector space that is also a vector space by itself, following the same rules as the superset.

Now, you have not provided specific sets to analyze, but I can give you a general approach:

1. Identify the given set and check if it belongs to a known vector space (e.g., ℝ², ℝ³, or other function spaces).

2. To determine if the given subset is a subspace, verify that it satisfies the following conditions:
  a. It contains the zero vector.
  b. It is closed under vector addition.
  c. It is closed under scalar multiplication.

If a given subset satisfies all of the above conditions, then it is a subspace of the identified vector space. If you can provide specific sets, I'd be happy to help you determine whether they are subspaces of a particular vector space.

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The minimum number of dogs that have more than 27 kg is 4, and the maximum number of dogs that have more than 27 kg is 26.

We have,

To determine the minimum and maximum number of dogs that have more than 27 kg, we need to first find the cumulative frequency for the mass data.

Mass(x)     frequency   Cumulative frequency

0 ≤ x ≤10    3                 3

10 ≤ x ≤20 9                 12

20 ≤ x ≤ 30 13                25

30 ≤ x ≤ 40 4                29

Now, we can see that there are a total of 29 dogs.

To find the minimum and maximum number of dogs that have more than 27 kg, we can use the cumulative frequency table as follows:

The minimum number of dogs that have more than 27 kg is the frequency of dogs in the 30 ≤ x ≤ 40 category, which is 4.

The maximum number of dogs that have more than 27 kg is the total number of dogs minus the cumulative frequency for the 0 ≤ x ≤ 27 category, which is 3.

Now,

The maximum number of dogs that have more than 27 kg is:

29 - 3 = 26.

Thus,

The minimum number of dogs that have more than 27 kg is 4, and the maximum number of dogs that have more than 27 kg is 26.

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Answer:

-------------------------

Area of square with side of 5 mm is:

Find total area of the figure:

Find the percent value of the ratio of areas of the square and full figure, which determines the probability we are looking for:

This is matching the choice C.

Its Fourier transform is also 0.

The Fourier transform of a function f(t) is defined as:

F(w) = (1/√(2π)) ∫[from -∞ to +∞] f(t) e^(-iwt) dt

Let's find the Fourier transform of the given function f(t) = sin 3t, k≤|t|≤2k and 0, |t|>2k.

For k≤|t|≤2k, we can write:

f(t) = sin 3t

= (1/2i) (e^(i3t) - e^(-i3t))

Using the Fourier transform properties, we can write:

F(w) = (1/2i) [∫[from -2k to -k] e^(i3t) e^(-iwt) dt + ∫[from k to 2k] e^(i3t) e^(-iwt) dt]

Applying the integral formula ∫ e^(ax) dx = (1/a) e^(ax) + C, we get:

F(w) = (1/2i) [(1/i(3-w))(e^(i(3-w)2k) - e^(i(3-w)k)) + (1/i(3+w))(e^(i(3+w)k) - e^(i(3+w)2k))]

Simplifying the above expression, we get:

F(w) = (1/2) [(sin(2kw-3) - sin(kw-3))/(kw-3) + (sin(kw+3) - sin(2kw+3))/(kw+3)]

For |t|>2k, f(t) = 0. Thus, its Fourier transform is also 0.

Therefore, the correct option is d. none of the above.

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Hi! To find the level of marketing expenditure that will maximize sales and the maximum sales value, we can follow these steps:

1. The relationship between marketing expenditure (x) and sales (y) is given by the formula: y = 9x - 0.20x^2 + 8.
2. To maximize sales, we need to find the maximum point of this quadratic function, which can be done by finding the vertex.
3. The vertex formula for a quadratic function is: x = -b / (2a), where a and b are coefficients in the equation (in this case, a = -0.20 and b = 9).
4. Calculate x (marketing expenditure) for the vertex: x = -9 / (2 * -0.20) = -9 / -0.40 = 22.50.
5. Round the marketing expenditure to 2 decimal places: 22.50.
6. Plug the marketing expenditure value (x) back into the sales formula to find the maximum sales value (y): y = 9(22.50) - 0.20(22.50)^2 + 8.
7. Calculate y: y = 202.50 - 0.20(506.25) + 8 = 202.50 - 101.25 + 8 = 109.25.
8. Round the maximum sales value to 2 decimal places: 109.25.

So, the level of marketing expenditure that will maximize sales is $22.50, and the maximum sales value is $109.25.

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a rhombus is a parallelogram with a pair of opposite equal acute angles, a pair of opposite equal obtuse angles, and four equal sides.

in other words, it is a parallelogram with 4 equal sides, including a square as a special case.

the diagonal intersection point is the midpoint of both diagonals.

the diagonals intersect each other at a right angle (90°).

and they split each vertex angle in half.

so, they split the whole rhombus into 4 equal right-angled triangles.

and remember, the sum of all angles in a triangle is always 180°.

an "obtuse" angle means an angle larger than 90°.

an "acute" angle means an angle smaller than 90°.

because of all that, in the triangle PKE the angle K must be greater than 45° (90/2 = 45), so that the rhombus angle K can be "obtuse", as it must be twice the triangle angle K.

the triangle angle E is 90°.

so, the 16° must be triangle angle P.

and the triangle angle K is then

triangle angle K = 180 - 90 - 16 = 74°.

so, rhombus angle K = rhombus angle N = 2×74 = 148°

and triangle PMN angle N = 74°.

triangle PMN angle M = triangle PMN angle P = 16°.

7. The area of the triangle is 52.2 yd².

8. The area of the triangle is 17.02 ft².

9. The area of the triangle is 9.6 mi².

10. The area of the triangle is 31.96 in².

The area of each triangle is calculated by applying the following formula as shown below;

Area = ¹/₂bh

where;

7. The area of the triangle is calculated as

A = ¹/₂ x 12 yd x 8.7 yd

A = 52.2 yd²

8. The area of the triangle is calculated as

A = ¹/₂ x 8.3 ft x 4.1 ft

A = 17.02 ft²

9. The area of the triangle is calculated as

A = ¹/₂ x 6 mi x 3.2 mi

A = 9.6 mi²

10. The area of the triangle is calculated as

A = ¹/₂ x 9.4 in x 6.8 in

A = 31.96 in²

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4 multiplied by 25 using the distributive property is equal to 100.

The distributive property is a fundamental property in mathematics that states that multiplying a number by a sum is the same as multiplying the number by each addend in the sum and then adding the products.

In this case, we have 4 multiplied by the sum of 20 and 5, which can be rewritten as 4 multiplied by 20 plus 4 multiplied by 5. Thus:

4 × (20+5) = 4 × 20 + 4 × 5

= 80 + 20

= 100

Therefore, 4 multiplied by 25 using the distributive property is equal to 100.

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Answer:

32.16 degrees

Step-by-step explanation:

The angle of depression in these problems is always the same as the angle of elevation.

With that in mind, lets solve this problem.

So we are given 2 triangle lengths. The Hypotenuse is 898 ft, and the height of your triangle is 478 ft.

There are three trig functions, sine, cosine, and tangent, but we will be using sin for this triangle because he have the opposite side to the angle(see how the side labeled 478 ft is opposite to the angle of elevation?) and the hypotenuse.

Sin is defined as opposite/hypotenuse.

Now, we make our equation:

sin(478/898) = x

x is your answer, just plug it into a calculator.

You get 32.16 degrees

The integral ∫[0,6] 1/x dx is divergent, An integral is said to be divergent if it does not have a finite value.

The given integral is:

[tex]∫[0,6] 1/x dx[/tex]

We know that the integral of 1/x is ln(x), and the antiderivative of ln(x) is xln(x) - x.

So, applying the limits of integration, we get:

[tex]∫[0,6] 1/x dx = ln(x)|[0,6] = ln(6) - ln(0)[/tex]

The natural logarithm of zero is unclear, so the indispensably isn't characterized at x = 0. In this manner, the indispensability is unique.

An integral is said to be divergent in the event that it does not have limited esteem. In other words, on the off chance that the fundamentally does not meet a genuine number, it is said to be unique.

There are a few reasons why a fundamentally may be unique. A few common reasons incorporate:

The integrand gets to be unbounded at a few points inside the limits of integration.

The integrand does not approach zero as the constraint of integration approaches boundlessness.

The limits of integration are interminable, and the integrand does not merge to a limited esteem as the limits approach interminability.

When an indispensably is disparate, it implies that the zone beneath the bend is interminable or does not exist.

This could have imperative suggestions in ranges such as material science and designing, where integrands are utilized to calculate amounts such as work, energy, and a liquid stream. 

Thus, the answer is (b) Divergent. 

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The length of the inventory cycle in days for the store when using an order quantity of 1,146 units per order is approximately 34.2216 days. To answer your question about the length of the inventory cycle in days for the store using an EOQ model and an order quantity of 1,146 units per order, we'll follow these steps:

Step:1. Calculate the EOQ (Economic Order Quantity) using the given information:
EOQ = √(2DS / H), where D is the annual demand, S is the ordering cost per order, and H is the holding cost per unit per year.
D = 10,054 units per year
S = $69 per order
H = 18% of the unit purchase cost ($83.4) = 0.18 * $83.4 = $15.012 per unit per year
EOQ = √(2 * 10,054 * 69 / 15.012) ≈ 1,146 units (the provided order quantity)
Step:2. Calculate the number of orders per year:
Number of Orders = Annual Demand / Order Quantity = 10,054 / 1,146 ≈ 8.7699 orders per year
Step:3. Calculate the inventory cycle length in days:
Inventory Cycle Length (Days) = (Operating Days per Year) / (Number of Orders per Year) = 300 / 8.7699 ≈ 34.2216 days
Therefore, the length of the inventory cycle in days for the store when using an order quantity of 1,146 units per order is approximately 34.2216 days.

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The matrix A will have one real eigenvalue of algebraic multiplicity 2 when k = -7.

To find the value of k for which matrix A has one real eigenvalue of algebraic multiplicity 2, we'll need to find the characteristic polynomial and solve for k. Here are the steps:

1. Write down matrix A:
A = | 2  k |
   |-3 -8 |

2. Find the characteristic polynomial by subtracting λ from the diagonal elements and finding the determinant of the resulting matrix:
| 2-λ  k  |
|-3   -8-λ |

3. Compute the determinant:
(2-λ)((-8)-λ) - (-3)(k) = λ^2 + 6λ + k + 16

4. The matrix A will have one real eigenvalue of algebraic multiplicity 2 if the characteristic polynomial has a double root. This occurs when the discriminant of the quadratic equation is equal to 0:
Δ = b^2 - 4ac = (6)^2 - 4(1)(k+16) = 0

5. Solve for k:
36 - 4(k+16) = 0
36 - 4k - 64 = 0
-4k = 28
k = -7

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Answer:

a

Step-by-step explanation:

Answer:A."The theoretical probability, P(gold), is 25%

explanation:It's realy simple