Write out the algebraic expression:
5 less than the product of a number and 2

The answer is (1,400)  because its 400 jump ropes per hour.

The solution to the equations is an infinite number of solutions and it means that we cannot find a unique price for an apple and an orange

Let the price of an apple be $x and that of an orange be $y.

Condition 1:

They need $10 for 4 apples and 4 oranges.

Thus, the equation is expressed as;

4x + 4y = 10

Divide through by 2 to get;

2x + 2y = 5 .....(1)

Condition 2:

They needs $15 for 6 apples and 6 oranges.

Thus, the equation is expressed as;

6x + 6y = 15

Divide through by 3 to get;

2x + 2y = 5 .....(2)

We see that both equations are identical and this denotes that we cannot find a unique price.

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Answer:

Step-by-step explanation:

it is D i took the test

Answer:

should be, must be, gotta be it

Step-by-step explanation:

13² = 7² + x²

169 = 49 + x

x² = 169 - 49

x² = 120

x = \(\sqrt{120}\) (do this stpd calculus)

x = 2\(\sqrt{30}\)

________

\( \: \)

x² = 13² - 7²

x² = 169 - 149

x² = 120

x = √120

x ≈ 2√30m

Answer:

Correct choices

\(\csc (\theta) = - \dfrac{5}{3} \quad \quad \text{2nd option}\\\\\cot(\theta) = \dfrac{4}{3} \quad \quad \text{3rd option}\\\\\cos(\theta) = -\dfrac{4}{5} \quad \quad \text{4th option}\\\\\)

Step-by-step explanation:

\(\text{If \;$ \tan\theta = \dfrac{3}{4} $}} \\\\\text{then }\\\theta = \tan^{-1} \left(\dfrac{3}{4}\right)\\\\= 36.87^\circ \text{ in Q1}\\\)

But since tan θ is periodic it will also be 3/4 in Q3 which is 180° + 36.87 = 216.87°

Answer:

A. Not

B. IS

C. IS

Step-by-step explanation:

The value of W(4) is 10, based on the given information that W(0) = 10 and the fact that the Wronskian remains constant for all values of t.

To find the value of W(4), we need to determine the Wronskian of x1(t) and x2(t) at t = 4, given the information that W(0) = 10.

The Wronskian is defined as W(t) = x1(t)x2′(t) - x1′(t)x2(t), where x1(t) and x2(t) are solutions of the given differential equation.

Since W(0) = 10, we can substitute t = 0 into the Wronskian formula:

W(0) = x1(0)x2′(0) - x1′(0)x2(0) = 10.

Now we need to find the value of W(4). We don't have direct information about x1(t) and x2(t), so we cannot calculate the Wronskian explicitly. However, if we know that the Wronskian is a constant, then it remains the same for all values of t.

Therefore, W(4) = W(0) = 10.

In conclusion, the value of W(4) is 10, based on the given information that W(0) = 10 and the fact that the Wronskian remains constant for all values of t.

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Answer:

4.05882352941

Step-by-step explanation:

69/17 is equal to 4.05882352941

The projection matrices P1 and P2 onto the lines through vectors a1 and a2, respectively, can be computed by\(P1 = A1(A1^T A1)^(-1)A1^T\) and\(P2 = A2(A2^T A2)^(-1)A2^T\), where A1 and A2 are the matrices formed by the vectors a1 and a2 as columns. The product P1P2 represents the projection onto the subspace spanned by a1 and a2.

Given vectors a1 = (-1, 2, 2) and a2 = (2, 2, -1), we can construct the matrices A1 and A2 as A1 = (-1, 2, 2) and A2 = (2, 2, -1). To compute the projection matrix P1 onto the line through a1, we use the formula \(P1 = A1(A1^T A1)^(-1)A1^T\). Similarly, for the projection matrix P2 onto the line through a2, we use the formula\(P2 = A2(A2^T A2)^(-1)A2^T\).

To find the product P1P2, we multiply the projection matrices P1 and P2. The resulting product represents the projection onto the subspace spanned by a1 and a2. This means that any vector projected onto this subspace will be the closest approximation to the original vector within the span of a1 and a2. The product P1P2 combines the projections onto the lines through a1 and a2, effectively projecting the vector onto the plane defined by the span of a1 and a2.

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Answer:

use quadratic analysis

3x-2=4

3x=4+2

3x=6

x=2

Answer:

1. Given

2. Addition Property of Equality

3. Division Property of Equality

Step-by-step explanation:

The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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Answer:

They donated 7/10 of their profits. This cannot be simplified any further.

mark me BRAINLIEST

Tysmm!!

Answer:

Step-by-step explanation:

2/10 and 1/10 are easily addable fractions so all you have to do is add the numerator to get, 3/10. After that you need to convert 2/5 into tenths so that you can continue to add it correctly. If you multiply the numerator and the denominator of 2/5 to convert it, you will get 4/10 to add.

Answer: 7/10

Answer:

The missing length = 30.

Step-by-step explanation:

Since the polygons are similar corresponding sides are in the same proportion So:

15/18 = 25/x

15 * x = 18*25

x =  18*25/15

= 30

Answer: 30

Step-by-step explanation:

These shapes are similar, which means their corresponding sides are proportional. A proportion will do nicely for this problem. 18/x=15/25. Cross multiplying 18 and 25 will give you a value that you can divide by 15 to get your answer.

Answer:

对不起兄弟我不知道 Duìbùqǐ xiōngdì wǒ bù zhīdào

Allura, this is the solution:

As you can see we have two right triangles in the figure:

Therefore,

Step 1: Let's calculate the hypotenuse of the left triangle, as follows:

c² = a² + b²

c² = 12² + 18²

c²= 144 + 324

c² = 468

c = 21.63

Step 2: Let's calculate the sides of the right triangle on the right, this way:

Leg 1 = 21.63

Leg 2 = x

Hypotenuse = 12 + y

Height of the right triangle = 18

In consequence, to find the value of the hypotenuse and y, we have:

c = 21.63²/√21.63² - 18²

c = 468/√468 - 324

c = 468/12

c = 39

Step 3: Now, we can solve for y, this way:

39 = 12 + y

y = 39 - 12

y = 27

The correct answer is D. 27

If it is found that r​₀ (Pearson correlation coefficient) is equal to 0, it indicates that there is no linear association between the two variables (body temperature and head circumference) in the sample.

The Pearson correlation coefficient, denoted by r, measures the strength and direction of the linear relationship between two variables. It ranges between -1 and +1, where -1 indicates a perfect negative linear relationship, +1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.

In this case, if the calculated r₀ is equal to 0, it suggests that there is no linear association between body temperature and head circumference in the sample of twenty statistics students. However, it's important to note that the absence of a linear association does not necessarily imply the absence of any relationship between the variables. There might still exist a non-linear relationship or other forms of association that are not captured by the Pearson correlation coefficient.

To determine the presence or absence of any association between the variables, it is advisable to examine additional measures, such as conducting hypothesis tests or considering other types of correlation coefficients, depending on the nature of the data and the research question. Additionally, considering the sample size of twenty students, it is crucial to interpret the results with caution and avoid generalizing the findings to the entire population.

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Answer:

x = 5.85641

Step-by-step explanation:

Step 1: Find missing leg of left triangle

sin30° = x/16

16sin30° = x

x = 8

Step 2: Find missing leg of right triangle

8² + b² = 16²

b² = 192

b = 8√3

Step 3: Find x by taking the difference

8√3 - 8 = 5.85641

To orthogonally diagonalize the matrix A, we will follow these steps:
1. Find the eigenvalues of matrix A.
2. Find the eigenvectors corresponding to each eigenvalue.
3. Normalize the eigenvectors to form an orthogonal basis.
4. Construct the orthogonal matrix Q and the diagonal matrix D.

To orthogonally diagonalize the matrix A, we need to find the eigenvalues and eigenvectors of A.

A = [[3, -1], [-1, 3]]

The characteristic polynomial of A is:

det(A - λI) = det([[3-λ, -1], [-1, 3-λ]]) = (3-λ)² - 1 = λ² - 6λ + 8 = (λ-2)(λ-4)

So the eigenvalues are λ₁ = 2 and λ₂ = 4.

To find the eigenvectors, we need to solve the system of equations:

(A - λ₁I)x = 0 and (A - λ₂I)x = 0

For λ₁ = 2, we have:

(A - 2I)x = [[1, -1], [-1, 1]]x = 0

This system has two linearly independent solutions:

v₁ = [1, 1] and v₂ = [-1, 1]

For λ₂ = 4, we have:

(A - 4I)x = [[-1, -1], [-1, -1]]x = 0

This system has one linearly independent solution:

v₃ = [1, -1]

To orthogonalize the eigenvectors, we need to normalize them and put them as columns of an orthogonal matrix Q.

Q = [[1/√2, -1/√2, 0], [1/√2, 1/√2, 0], [0, 0, 1]]

The diagonal matrix D has the eigenvalues on the diagonal:

D = [[2, 0], [0, 4]]

Finally, we can check that QTAQ = D:

QTAQ = [[1/√2, -1/√2, 0], [1/√2, 1/√2, 0], [0, 0, 1]]T[[3, -1], [-1, 3]][[1/√2, -1/√2, 0], [1/√2, 1/√2, 0], [0, 0, 1]] = [[2, 0, 0], [0, 4, 0], [0, 0, 4]] = D

Therefore, matrix A is orthogonally diagonalized by Q and D.

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The product of 4 and 1 over 10 times negative three times 5 over 12 is -15/ 24

Given the information;

4 and 1 over 10 times negative three times 5 over 12, determine the product

This can be expressed as;

\(\frac{4 + 1}{10} * \frac{-3 * 5}{12}\)

First, solve for the numerators

\(\frac{5}{10} * \frac{-15}{12}\)

Multiply the numerators and denominators

\(\frac{-75}{120}\)

Find the common divisor

= - 15/ 24

Thus, the product of 4 and 1 over 10 times negative three times 5 over 12 is -15/ 24

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The expected time for activities, use the formula for expected value and multiply the time for each activity by its probability. Therefore, the expected time for these activities is 2.8 hours.

To calculate the expected time for activities, we can use the formula for expected value.

The expected value is calculated by multiplying the time for each activity by its probability of occurrence, and then summing up these values. The formula for expected value is: Expected Value = (Time1 * Probability1) + (Time2 * Probability2) + ... + (TimeN * ProbabilityN) Here's a step-by-step example:

1. List all the activities and their corresponding times and probabilities.

2. Multiply the time for each activity by its probability.

3. Sum up the values obtained in step 2.

For example, let's say we have two activities: Activity 1: Time = 2 hours, Probability = 0.6 Activity 2: Time = 4 hours, Probability = 0.4 Using the formula, we calculate the expected time as follows: Expected Time = (2 hours * 0.6) + (4 hours * 0.4) = 1.2 hours + 1.6 hours = 2.8 hours

Therefore, the expected time for these activities is 2.8 hours.

Here full question is not provided  but the full answer given above.

Remember, this is just one example, and you can use the same formula for any number of activities with their respective times and probabilities. In summary, to calculate the expected time for activities, use the formula for expected value and multiply the time for each activity by its probability. Then, sum up these values to get the expected time.

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Answer:

f(x) = 1/(x+2) + 7

Step-by-step explanation:

The graph depicts the line of 1/x shifted to the left by 2 and up by 7.

Diego can make 56 bags with each bag containing 8 brownies and 12 cookies.

To package both items, he can divide the items into groups of 8 brownies and 12 cookies. He will then make 56 of these groups, ensuring each bag contains 8 brownies and 12 cookies.

Diego has 48 brownies and 64 cookies to package. To make the same combination of items in each bag, he needs to group the items into groups of 8 brownies and 12 cookies.

This can be done by dividing the 48 brownies into 6 groups of 8, and the 64 cookies into 5 groups of 12. He then needs to combine these two groups together, making 56 total bags.

Each of these bags will contain 8 brownies and 12 cookies. This is one way of packaging both items so that each bag has the same combination.

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The value where the histogram balances when supported at that point is called the mode of the distribution.

The mode of distribution is the value that appears most frequently in the data set. It is often used as a measure of central tendency, along with the mean and median. The mode is especially useful when dealing with categorical or discrete data, where the possible values are limited and well-defined.

For example, the mode of a list of test scores might be the score that occurs most frequently, indicating the most common level of performance. In a histogram, the mode is the value where the distribution is highest, or where the histogram balances when supported at that point.

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Given:

The function is

\(g(x)=-3x+12\)

Consider the given domain of g is {-2,0,2}.

To find:

The solution set  if the domain of g for the given domain.

Solution:

Domain is the set of input values and range is the set of output value.

We have,

\(g(x)=-3x+12\)

Domain of g is {-2,0,2}.

For x=-2,

\(g(-2)=-3(-2)+12\)

\(g(-2)=6+12\)

\(g(-2)=18\)

For x=0,

\(g(0)=-3(0)+12\)

\(g(0)=0+12\)

\(g(0)=12\)

For x=2,

\(g(2)=-3(2)+12\)

\(g(2)=-6+12\)

\(g(2)=6\)

Now, the solution set  of the given domain of g is

\(\{f(-2),f(0),f(2)\}=\{18,12,6\}\)

Therefore, the solution set is {18,12,6}.

Answer:

25m

Step-by-step explanation:

A square is a parallelogram having all sides equal. Hence, if Casey walked diagonally, she should have gone 25m as the rules of square states.

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Answer:

B

Step-by-step explanation:

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

Answer:  \(\textsf{Option C, 3}\sqrt{2}\)

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

Given:  \(\sqrt{18}\)

Find: \(\textsf{Simplify the expression}\)

Solution: In order to get a number outside of the square root there must be two of them inside of the square root.  The first step that we need to take is to break down the number 18 into it's lowest factors and then take out the numbers can be taken out.

Break down the number 18

Take 3 outside of the square root

Therefore, the option that would best match the results that were solved for is option C, \(\textsf{3}\sqrt{\textsf{2}\)

Answer:

20 mph

Step-by-step explanation:

Average speed is given as total distance traveled divided by total time taken:

S = d / t

Let us find the total distance traveled.

He traveled 12 minutes (0.2 hours) at a speed of 15 mph. The distance to the grocery store is therefore:

d = s * t

d = 15 * 0.2 = 3 miles

He travels the same distance to get back home, this means that his total distance traveled is 6 miles.

Let us calculate the time taken to get home from the grocery store:

t = d /s

t = 3 / 30 = 0.1 hour

Therefore, his total time is:

t = 0.2 + 0.1 = 0.3 hours

His average speed is therefore:

s = 6 / 0.3 = 20 mph

The slope of a linear function is always the same thus the missing values are y₂ = 5 , y₃ = 8, and y₄ = 12.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

In another word, a linear function is a function that varies linearly with respect to the changing variable.

As per the given table,

Take (2,3) and (6,19)

Slope = (19 - 3)/(6 - 2) = 4

To maintain the same slope,

(y₂ - 3)/(3 - 2) = 4

y₂ = 5

(y₃ - 4)/(4 - 3) = 4

y₃ = 8

(y₄  - 8)/(5 - 4) = 4

y₄ = 12

Hence "The slope of a linear function is always the same thus the missing values are y₂ = 5, y₃ = 8, and y₄ = 12".

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Answer:

B. 6in

Step-by-step explanation:

We can use the Pythagorean theorem [ a² + b² = c² ] to find the missing side.

8² + b² = 10²

64 + b² = 100

b² = 36

b = 6

Best of Luck!