PLZ ANSWER ASAP!!!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

10 + 3x = 30 + 7x

collect terms that look alike on one side.

we can see that 3x & 7x have something in common which is x.

so move one of these to either of the equality's sides.

0 = 30 + 7x -10 - 3x

i changed the sign of 3x to -3x & 10 to -10 because we'll have to subtract 3x or 10 from the left side inorder for them to vanish & appear on the right hand side.

collect like terms.

0 = 30 - 10 + 7x - 3x

0 = 20 + 4x

take 20 to the left side to find x by dividing by 4.

20 = 4x

20 / 4 = x

5 = x

Answer:

\(\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}\)

Answer:

$79.08

Step-by-step explanation:

Find 20% of 65.90. 20% as a decimal is 0.20. Multiply 0.2 and 65.90.

65.90 x 0.20 = 13.18

Add 13.18 to the original price.

13.18 + 65.90 = 79.08

x     4      3     2      1

f      3      5     4      2

Total number of scores in table are ∈ f =  3 + 5 + 4 + 2 = 14

According to the question, given that

x     4      3     2      1

f      3      5     4      2

Total number of scores are ∈ f =  3 + 5 + 4 + 2 = 14

Therefore, after sum of score we get total number of scores is 14

The average or computed center value of a group of values is known as the mean, and it is used to determine the central tendency of the data. The entire collection of data or distribution is identified by a single number using the statistical metric known as central tendency.

We can use the direct technique, the assumed mean method, or the step deviation method to determine the mean of grouped data. The frequency of several observations or variables that are combined together is the subject of the mean of grouped data. Let's examine each of these approaches in turn.

Direct Method

The direct approach is the most straightforward way to determine the mean of the grouped data. The mean of the data is given by, if the values of the observations are x1, x2, x3, and x4 and their associated frequencies are f1, f2, f3, and f4, respectively.

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1. The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The Probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

1. The outcomes in the sample space of choosing a letter from the word THANKS are: T, H, A, N, K, S.

  The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. To find the number of outcomes in the sample space, we multiply the number of outcomes for each word.

  Number of outcomes in the sample space = Number of outcomes for the first word × Number of outcomes for the second word

  Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The probability of choosing the letters AA would be the number of favorable outcomes (which is 0 in this case) divided by the total number of outcomes in the sample space.

  Probability of choosing AA = Number of favorable outcomes / Total number of outcomes

  Probability of choosing AA = 0 / 30 = 0.

Therefore, the probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

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Answer:

5(9y + 4).

Step-by-step explanation:

GCF of 45y and 20 is 5

Answer is 5(9y + 4).

Answer:

132°

Step-by-step explanation:

We use the circle theorem which states that :

Opposite angles in a cyclic quadrilateral add up to 180 .

Now we know that angles ADC and ABC add up to 180. So :

We make an equation and solve for x :

x+(3x-12) = 180

4x-12 = 180

4x = 192

x = 48

Now we substitute the value of x into Angle B :

3(48) -12 =

144 - 12 = 132

Angle B = 132 °

Hope this helped and have a good day

The number of bags bought by Javier will be 2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Javier bought three more bags of Reese's than lollipops and two fewer bags of starburst than lollipops. bags of lollipops cost $3.75 each, bags of Reese's cost $5.50 each, and bags of starburst cost $4.25 each. He spends a total of $48.50.

From the equations and solve them to get the number of lollypops.

R = L+3

L = S - 2

The equation for total cost will be,

3.75L + 5.5R + 4.25S = 48.5

3.75( s - 2) + 5.5( S + 1) + 4.25S

3.75S - 7.5 + 5.50S + 5.5 + 4.25 S = 48.5

13.5S = 48.5 + 2

13.5S = 50.2

S = 4

The number of lollypops will be,

L = S - 2

L = 4 - 2

L = 2

Therefore, the number of bags bought by Javier will be 2.

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The pseudo-inverse of A is:

A+ =

⎡ cosφ/σ1 -sinφ/σ2 ⎤

⎢ sinφ/σ1 cosφ/σ2 ⎥

⎣ 0 0 ⎦

The pseudo-inverse of a 2x3 matrix A, we first need to compute the singular value decomposition (SVD) of A.

The SVD of A can be written as A = \(U\Sigma V^T\), where U and V are orthogonal matrices and Σ is a diagonal matrix with non-negative diagonal elements in decreasing order.

Since A is a 2x3 matrix, we can assume that the rank of A is either 2 or 1. If the rank of A is 2, then Σ will have two non-zero diagonal elements, and we can compute the pseudo-inverse as A+ = \(V\Sigma ^{-1}U^T\).

If the rank of A is 1, then Σ will have only one non-zero diagonal element, and we can compute the pseudo-inverse as A+ = \(V\Sigma^{-1}U^T\), where \(\Sigma^{-1\) has the reciprocal of the non-zero diagonal element.

Let's assume that the rank of A is 2, so we need to compute the SVD of A.

Since A is a 2x3 matrix, we can use the formula for SVD to write:

A = \(U\Sigma V^T\) =

⎡ cosθ sinθ ⎤

⎣-sinθ cosθ ⎦

⎡ σ1 0 0 ⎤

⎢ 0 σ2 0 ⎥

⎣ 0 0 0 ⎦

⎡ cosφ sinφ 0 ⎤

⎢-sinφ cosφ 0 ⎥

⎣ 0 0 1 ⎦

where θ and φ are angles that satisfy 0 ≤ θ, φ ≤ π, and σ1 and σ2 are the singular values of A.

The diagonal matrix Σ contains the singular values σ1 and σ2 in decreasing order, with σ1 ≥ σ2.

The pseudo-inverse of A, we first compute the inverse of Σ.

Since Σ is a diagonal matrix, its inverse is easy to compute:

\(\Sigma^{-1\)=

⎡ 1/σ1 0 0 ⎤

⎢ 0 1/σ2 0 ⎥

⎣ 0 0 0 ⎦

Next, we compute \(V\Sigma^{-1}U^T\):

A+ = VΣ^-1U^T =

⎡ cosφ -sinφ ⎤

⎣ sinφ cosφ ⎦

⎡ 1/σ1 0 ⎤

⎢ 0 1/σ2 ⎥

⎡ cosθ -sinθ ⎤

⎣ sinθ cosθ ⎦

The pseudo-inverse is not unique, and there may be different ways to compute it depending on the choice of angles θ and φ.

Any valid choice of angles will yield the same result for the pseudo-inverse.

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The pseudo-inverse A+ of a 2x3 matrix A does not exist.

The pseudo-inverse of a matrix is a generalization of the matrix inverse for non-square matrices. However, not all matrices have a pseudo-inverse.

In this case, we have a 2x3 matrix A, which means it has more columns than rows. For a matrix to have a pseudo-inverse, it needs to have full column rank, meaning the columns are linearly independent. If a matrix does not have full column rank, its pseudo-inverse does not exist.

Since the given matrix A has more columns than rows (2 < 3), it is not possible for A to have full column rank, and thus, its pseudo-inverse does not exist.

Therefore, the pseudo-inverse A+ of the 2x3 matrix A is undefined.

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Answer:

2-(3x-4) = 2x -9

-6x + 8 = 2x - 9

6x = 17

x = 2.833

3 approximately

Answer:

17/61 or  0.27

Step-by-step explanation: 17 out of 61 times Jordan will pull out strawberry so the probability of pulling out a strawberry chew is 17/61 which is 0.27 as a decimal

Answer:

0.28

Step-by-step explanation:

0.278 rounded is 0.28

The area of a rhombus can be found by multiplying the length of one of its sides by the height of a perpendicular line from the center to a side.

The height of the rhombus is the distance from the center of the rhombus to one of its sides, perpendicular to that side.

The formula for the area of a rhombus can be written as A = s*h, where A is the area, s is the length of one of the sides of the rhombus, and h is the height of the rhombus.

It's important to note that this method of finding the area of a rhombus without diagonals can only be used when the rhombus is a regular polygon, a polygon with all sides and angles congruent. When the rhombus is not a regular polygon, then you can find the area by using the diagonals.

Additionally, it's important to mention that a rhombus can be defined as a parallelogram with all sides congruent or a square with its angles not 90 degrees.

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Cindy should hire the 12th worker as it would result in a net increase in profit, with additional revenue exceeding the cost of hiring. Insufficient information is provided to determine the demand curve for labor or compare its elasticity. Events that would shift the factory's demand for capital include new, more efficient machines and rising wages due to a labor shortage.

a. To determine whether Cindy should hire a 12th worker, we need to compare the additional revenue generated with the additional cost incurred. Hiring the 12th worker would increase total revenue by $150 ($2,750 - $2,600) per day, but it would also increase costs by $100. Therefore, the net increase in total profit would be $50 ($150 - $100). Since the net increase in profit is positive, Cindy should hire the 12th worker.

b. By hiring the 12th worker, Cindy can increase her total revenue from $2,600 per day to $2,750 per day. The additional revenue generated by the 12th worker exceeds the cost of hiring that worker, resulting in a net increase in profit.

c. To determine the firm's demand curve for labor, we need information about the marginal product of labor (MPL) and the wage rates. Unfortunately, this information is not provided, so we cannot complete the labor demand table or derive the demand curve for labor.

Without specific data or information about changes in the quantity of labor demanded and wage rates, we cannot determine which demand curve (from part b or c) is more elastic. The elasticity of the demand curve depends on the responsiveness of the quantity of labor demanded to changes in the wage rate.

The events that would shift the factory's demand for capital are:

a. New shoemaking machines being twice as efficient as older machines would increase the productivity of capital. This would lead to an increase in the demand for capital as the factory would require more capital to produce the same quantity of shoes.

b. The wages that the factory has to pay its workers rising due to an economy-wide labor shortage would increase the cost of labor relative to capital. This would make capital relatively more attractive and lead to an increase in the demand for capital as the factory may substitute capital for labor to maintain production efficiency.

The event "Many consumers decide to walk barefoot all the time" would not directly impact the demand for capital as it is related to changes in consumer behavior rather than the production process of the shoemaking factory.

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The value of x  for The quadrilateral which is a trapezoid is if the top is 21 and the bottom is 27 is option 2 that is 5.

Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides.

From the given diagram, the expression below is true:

2(5x - 1) = 21 + 27

Expand

10x - 2 = 48

10x = 48 + 2

10x = 50

Divide both sides by 10

10x.10 = 50/10

x = 5

Hence the value of x is 5

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Answer:

24

Step-by-step explanation:2x+42= 90

2x=90-42

2x=48

x=24

Step-by-step explanation:

2x°+42°=90°

2x+42°-42°=90°-42°

2x/2=48°/2

x=24°

But Iam not sure I just try

The probability of drawing a yellow card or a blue card is 9/25.

The probability of drawing a yellow card or a blue card can be calculated using the principle of addition. To find the probability of an event occurring, we add the individual probabilities of each event and subtract the probability of both events occurring together.
In this case, we want to find the probability of drawing a yellow card or a blue card.
Step 1: Calculate the probability of drawing a yellow card:
There are a total of 30 cards in the deck, and 6 of them are yellow. So, the probability of drawing a yellow card is 6/30 or 1/5.
Step 2: Calculate the probability of drawing a blue card:
There are 6 blue cards in the deck. So, the probability of drawing a blue card is 6/30 or 1/5.
Step 3: Calculate the probability of drawing both a yellow card and a blue card:
Since the cards are replaced in the deck after each draw, the probability of drawing a yellow card and a blue card together is the product of their individual probabilities:
(1/5) * (1/5) = 1/25
Step 4: Calculate the probability of drawing a yellow card or a blue card:
To find the probability of drawing a yellow card or a blue card, we add the individual probabilities of each event and subtract the probability of both events occurring together:
(1/5) + (1/5) - (1/25) = 5/25 + 5/25 - 1/25 = 9/25
Therefore, the probability of drawing a yellow card or a blue card is 9/25.

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The given sequence G₁ = 3, Gn=5+Gn-1 is an example of a function that is neither linear nor exponential. It is a recursive function or a sequence that is defined by using the previous terms of the sequence to calculate the next term.

Based on the given information, the recursive formula for the sequence is:

Gn = 5 + Gn-1, with G₁ = 3

Now, let's find the first few terms:

G₂ = 5 + G₁ = 5 + 3 = 8
G₃ = 5 + G₂ = 5 + 8 = 13
G₄ = 5 + G₃ = 5 + 13 = 18

From this, we can observe that the differences between consecutive terms are constant (5), so this sequence is a linear function.

Now, let's analyze the given sequences:

F = 7.5 - 1.9 is neither a sequence nor a function, so we cannot classify it.

The sequence with terms 1, 8, 27, 64, 234 does not have a constant difference or ratio, so it is neither a linear nor an exponential function.

The sequence with terms 8, 12, 1, 2, 3, 4, 18, 27 does not have a constant difference or ratio either, so it is also neither a linear nor an exponential function.

In conclusion:
- Linear Function: Gn = 5 + Gn-1 with G₁ = 3
- Exponential Function: None of the provided sequences
- Function That Is Neither Linear Nor Exponential: Both provided sequences

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If a=4, b= 7, and B= 75°, the area of triangle ABC is approximately 13.476 square units.

To find the area of triangle ABC given the values of a, b, and B, we can use the formula:

Area = (1/2) * a * b * sin(B)

where a and b are the lengths of two sides of the triangle and B is the angle between them, measured in degrees.

Substituting the given values, we get:

Area = (1/2) * 4 * 7 * sin(75°)

Using a calculator to evaluate the sine of 75°, we get:

Area = (1/2) * 4 * 7 * 0.96593

Area ≈ 13.476 square units

The formula for the area of a triangle involves using the length of two sides and the angle between them.

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Answer:

C. 720

Step-by-step explanation:

10 - 3 is 8 so you multiply all the numbers from 10 through 8

10 * 9 * 8 = 720

That is the answer. Hope it helped!

Answer:

C: 720

Step-by-step explanation:

i got 100% on the quiz

Answer:

to answer this question i need to know what and what x together to get the area

Step-by-step explanation

Answer:

what kind of question is

Step-by-step explanation:

that

In the given scenario ladder is 6.52 feet long.

Given that,

The angle between ground and ladder = 62 degree

The distance of ladder from ground and ladder = 3 feet

We have to find the length of  ladder.

Since we know that,

The trigonometric ratio

cosθ = adjacent/ Hypotenuse

Here we have,

Adjacent =  3 feet

Hypotenuse = length of ladder

Thus to find the length of ladder we have to find the value of hypotenuse.

Therefore,

⇒ cos62 = 3/ Hypotenuse

⇒    0.46 = 3/ Hypotenuse

⇒ Hypotenuse =  3/0.46

                          = 6.52

Thus,

length of ladder  = 6.52 feet.

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Solution:

Explanation:

The position, velocity, and acceleration of mass A can be found by taking the first and second derivatives of the given equation with respect to time, t. The first derivative will give us the velocity, and the second derivative will give us the acceleration.

(a) When t = 1 s:
Position, x = 10 sin 2(1) + 15cos2(1) + 100 = 10 sin 2 + 15cos2 + 100 = 114.96 mm
Velocity, v = dx/dt = 20 cos 2t - 30 sin 2t = 20 cos 2(1) - 30 sin 2(1) = -17.32 mm/s
Acceleration, a = dv/dt = -40 sin 2t - 60 cos 2t = -40 sin 2(1) - 60 cos 2(1) = -41.23 mm/s^2

(b) The maximum velocity and acceleration can be found by finding the critical points of the first and second derivatives, respectively. This is done by setting the derivatives equal to zero and solving for t.

For maximum velocity:
0 = 20 cos 2t - 30 sin 2t
30 sin 2t = 20 cos 2t
tan 2t = 2/3
2t = tan^-1(2/3)
t = 0.2915 s

For maximum acceleration:
0 = -40 sin 2t - 60 cos 2t
60 cos 2t = -40 sin 2t
tan 2t = -3/2
2t = tan^-1(-3/2)
t = 0.6405 s

Therefore, the maximum velocity occurs at t = 0.2915 s and the maximum acceleration occurs at t = 0.6405 s.

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(a) The position, velocity and acceleration of mass A is 110 mm,  -10 mm/s,  -50 mm/s2 respectively.

(b) The maximum velocity and the maximum acceleration of A is 20.81 mm/s, -61.87 mm/s2 respectively.

The position, velocity and acceleration of mass A when t = 1 s can be determined by substituting t = 1 s into the given equation, x = 10 sin 2t + 15cos2t + 100.

Position: x = 10 sin 2(1) + 15cos2(1) + 100 = 110 mm

Velocity: x' = 20 cos 2(1) - 30 sin 2(1) = -10 mm/s

Acceleration: x'' = -40 sin 2(1) - 30 cos 2(1) = -50 mm/s2

The maximum velocity of A can be determined by finding the points of inflection in the equation. This occurs when x'' = 0. Solving for t:

-40 sin 2t - 30 cos 2t = 0

sin 2t = 0.75

2t = sin-1(0.75) ≈ 0.927 radians

t = 0.464 s

Maximum Velocity: x' = 20 cos 2(0.464) - 30 sin 2(0.464) = 20.81 mm/s

The maximum acceleration of A can be determined by finding the points of extrema in the equation. This occurs when x' = 0. Solving for t:

20 cos 2t - 30 sin 2t = 0

cos 2t = 1.5

2t = cos-1(1.5) ≈ 0.524 radians

t = 0.262 s

Maximum Acceleration: x'' = -40 sin 2(0.262) - 30 cos 2(0.262) = -61.87 mm/s2.

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Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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Answer:

I think the perimeter is 50cm the solids is 600cm³

Step-by-step explanation:

Perimeter: (5×10)=50cm

Solids: divided with 2box(A box & B box)

Abox: 5cm x 5cm x 12cm

=300cm³

Bbox: 5cm x 12cm x 5cm

=300cm³

Solids:(Abox +Bbox) 300cm³ + 300cm³

=600cm³

I think, I'm sorry if it's wrong

Answer:

in terms of pi: 112.5pi mm squared

substituting pi for 3.14: 353.25 mm squared

Step-by-step explanation:

Surface area cone equation:

Πr2 + π*r*s

4.5^2 = 20.25pi

400 + 20.25 = 420.25

sqrt(420.25) = 20.5

20.25pi + 92.25pi = 112.5pi