simplify the expression
16-4[3+2÷(9-7)]
​

The two vectors are indeed considered linearly dependent if they are collinear. So the given statement is true about two linear dependent vectors.

The set \(\{v_1, v_2,.....,v_k\}\) is considered as linearly dependent if numbers \(\{x_1, x_2, ....,x_k\}\)are not equal to zero. Then, \(x_1v_1+x_2v_2+.....+x_kv_k=0\). This equation is referred to as the equation of linear dependence or linear dependence relation.

When two vectors are collinear, or when one is a scalar multiple of the other, they are said to be linearly dependent. These collinear vectors are also referred to as parallel vectors and these vectors will lie along the same line or parallel line. The given statement is therefore true.

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Answer:

The answer is 49.

Step-by-step explanation:

\sin K = \frac{\text{opposite}}{\text{hypotenuse}}=\frac{4.4}{5.8}

sinK=

hypotenuse

opposite

​

=

5.8

4.4

​

\sin K = \frac{4.4}{5.8}

sinK=

5.8

4.4

​

K=\sin^{-1}(\frac{4.4}{5.8})

K=sin

−1

(

5.8

4.4

​

)

K=49.343\approx 49^{\circ}

K=49.343≈49

Answer:

36

Step-by-step explanation:

6 divided by 2 = 3

12 times 3  = 36

Answer:

8.5 miles per day

Step-by-step explanation:

divide 425 by 50 and boom u got the answer

Answer:

It doesnt let me see the picture. Help

Answer:

the last one

all coplanar points equidistant from a given point.

Answer:

Step-by-step explanation:

Natural Numbers :

These are numbers used for counting, they are the numbers on a number line. From -12 to 49, the natural numbers are 1, 2, 3, ..., 49.

Whole Numbers:

These are numbers that can be written without havin to write in fractions. They are 0, 1, 2, ..., 49.

Rational Numbers:

These are numbers that can be expressed as fractions.

Irrational numbers :

These are numbers that cannot be expressed as fractions.

Real Numbers:

These are numbers that can be used to measure quantities, they include negative, positive numbers and zero. From -12 to 49, all the numbers are real.

Prime Numbers:

These are numbers that are divisible only by one and themselves.

From 7 to 49, the numbers divisible by 7 are 7, 14, 21, 28, 35, 42, and 49.

Only 7 is prime.

The probability of mission success if at least 11 of the 16 patrol boats must operate for the duration of the mission is:P(X ≥ 11) = 0.174 + 0.097 + 0.039 + 0.011 + 0.002 + 0.00003≈ 0.323 or about 32.3%

To find the probability of mission success if at least 11 of the 16 patrol boats must operate for the duration of the mission, we need to use the binomial probability formula which is given by: P(X = x) = nCx * p^x * q^(n-x)where, n is the total number of trials x is the number of successful trials p is the probability of success

q = 1 - p is the probability of failure n Cx = n! / x!(n-x)! is the binomial coefficient In this case, since we want to know the probability of at least 11 boats operating for the mission, we can find the probability of 11 boats, 12 boats, 13 boats, 14 boats, 15 boats and 16 boats operating, and then add them up.

So, we have: P(X ≥ 11) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)where, n = 16 (since there are 16 patrol boats)p = 0.9 (since the probability of a patrol boat operating is 0.9)q = 0.1 (since the probability of a patrol boat not operating is 0.1)

Using the formula above, we get:P(X = 11) = 4368 * 0.9^11 * 0.1^5 = 0.174P(X = 12) = 1365 * 0.9^12 * 0.1^4 = 0.097P(X = 13) = 455 * 0.9^13 * 0.1^3 = 0.039P(X = 14) = 136 * 0.9^14 * 0.1^2 = 0.011P(X = 15) = 35 * 0.9^15 * 0.1^1 = 0.002P(X = 16) = 1 * 0.9^16 * 0.1^0 = 0.00003

Thus, if at least 11 of the 16 patrol boats are required to operate throughout the mission, the chance of mission success is P(X 11) = 0.174 + 0.097 + 0.039 + 0.011 + 0.002 + 0.00003 0.323 or roughly 32.3%.

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If A is placed in the upper left corner,there are 4 possible arrangements.

To solve the given problem, we must follow a few steps:There are three letters, A, B and C, that must be placed in a 3x3 grid, so that each row and column contain one of each letter.

Let us assume that A is placed in the upper left corner. So, there are two possible choices for the letter in the top middle box and then only one letter remaining for the top right box. That is:

After placing the letters A in the top row, the possible arrangements for the middle row will depend on the letter placed in the leftmost column, which will have 2 choices. Then the last letter can only be placed in one position.

So the number of arrangements for placing the 9 letters in the grid with the given constraints is:

2 × 1 × 2 × 1 × 1 × 1 × 1 × 1 = 4

So, there are 4 possible arrangements.

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Answer:

3) 45°

4) 135°

5) <WAX and <XAZ

6) <WAX and <WAU

7) <WAX and <YAU

8) <WAX and <XAZ

Step-by-step explanation:

3) 45°

4) 135°

5) <WAX and <XAZ

6) <WAX and <WAU

7) <WAX and <YAU

8) <WAX and <XAZ

The solution to the system of equation is as follows:

System of equation can be solved with different methods such as elimination method, substitution method and graphical method.

The system of equation can be solved with elimination as follows:

Hence,

-3y + 5x = 26

-2y - 5x  = -16

add the equation to eliminate x

Hence,

-5y = 10

divide both sides of the equation by -5

y = 10 / -5

y = -2

Hence,

- 3(-2) + 5x = 26

6 + 5x  = 26

5x = 26 - 6

5x = 20

x  = 20 / 5

x = 4

Therefore,

x = 4

y = -2

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A quadratic equation that has a GCF and none of the solutions is zero is 3x^2 + 6x + 9 = 0. The GCF is 3, and the solutions are complex numbers (-1 ± √2i), where i is the imaginary unit.

An example of a quadratic equation that has a greatest common factor (GCF) and none of the solutions is zero is:

4x^2 + 8x + 4 = 0

In this equation, the GCF is 4, which can be factored out:

4(x^2 + 2x + 1) = 0

Now, let's find the solutions of the equation by factoring:

4(x + 1)^2 = 0

Setting the factor equal to zero, we have:

x + 1 = 0

Solving for x, we find that the solution is:

x = -1

As we can see, the solution to the equation is not zero.

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Answer:a party of fishermen rented a boat for $240. two of the fishermen had to withdraw from the party and, as a result, the share of each of the others was increased by $10. how many were in the original party? provide a numerical answer.

Step-by-step explanation:

Now ,Let original number in party be "x"::

Average cost per person = 240/x

New number in the party:: x-2

New Average cost per person:: 240/(x-2)

Equation::

10 dollars =New average - old average

240/(x-2) - 240/x = 10

240x - 240(x-2) = 10x(x-2)

480 = 10x^2-20x

x^2 - 2x - 48 = 0

X = 8 (ORIGINAL)

The value of the chi-square test statistic is χ2 = 2.87, and the P-value is between 0.025 and 0.05.

Let's assume the observed counts are as follows:

Erica: 75

Jen: 5

Heather: 12

Tonya: 8

Now, we can calculate the chi-square test statistic:

χ2 = Σ((O - E)^2 / E)

where O is the observed count and E is the expected count for each category.

Calculating the chi-square test statistic:

χ2 = ((75 - 70)^2 / 70) + ((5 - 10)^2 / 10) + ((12 - 10)^2 / 10) + ((8 - 10)^2 / 10)

= 1.07 + 1 + 0.4 + 0.4

≈ 2.87

Referring to the chi-square distribution table, the P-value for a chi-square test statistic of 2.87 and 3 degrees of freedom is approximately between 0.025 and 0.05.

Therefore, the value of the chi-square test statistic is χ2 = 2.87, and the P-value is between 0.025 and 0.05.

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Answer:

theres no picture that comes with it?

Answer: 145

Step-by-step explanation:

check

Answer:

(3, - 2 )

Step-by-step explanation:

The solution is at the point of intersection of the 2 lines

The lines intersect at (3, - 2 ) ← solution

Check by substituting  x = 3 into the left side of the given equation

- 2(3) + 4 = - 6 + 4 = - 2 ← True

Step-by-step explanation:

sorry if this isn't right it's late and I'm tired so again I'm sorry if it's not right have a great day or night

The given logarithmic equation is 5 ln(x) = 20 the exponential function and the natural logarithm are inverse functions, e^(ln(x)) simplifies to x:

x = e^4 This represents a single solution. So, the correct choice is A

To solve this equation, we need to isolate the variable x.

First, divide both sides of the equation by 5:

ln(x) = 4

To eliminate the natural logarithm, we can rewrite the equation in exponential form:

e^(ln(x)) = e^4

Since the exponential function and the natural logarithm are inverse functions, e^(ln(x)) simplifies to x:

x = e^4

Therefore, the solution to the equation is x = e^4. This represents a single solution.

In exact form, the solution set is {e^4}. So, the correct choice is A. The solution set is not empty, and it consists of a single value, which is e^4.

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9514 1404 393

Answer:

  x = 40

  ∠6 = 120

Step-by-step explanation:

This question has nothing to do with parallel lines.

Angles 5 and 6 form a linear pair, so are supplementary.

  ∠6 + ∠5 = 180°

  3x +60 = 180

  3x = 120 . . . . . . . . . subtract 60

  x = 40 . . . . . . . . . . . divide by 3

Angle 6 is the supplement of angle 5 as shown above.

  ∠6 = 3x = 120

a. The system of equations is

b. For the hexagon

A hexagon is a regular polygon with six sides.

Let x be the acute angles of the hexagon and y be the obtuse angles of the hexagon.

Since he measures of the obtuse angles in the hexagon are 30 more than twice the measures of the acute angles, we have that

y = 2x + 30

Also, we know that the sum of  interior angles of a polygon is (n - 2)180.

Since x  is the interior angle and n = 6, we have that

6x = (n - 2)180.

x = (n - 2)180/6

x = 30(n - 2)

So, the system of equations is

y = 2x + 30 (1) and

x = 30(n - 2)  (2)

Since

y = 2x + 30 (1) and

x = 30(n - 2)  (2)

Substituting n = 6 into (2), we have

x = 30(6 - 2)

x = 30(4)

x = 120

Substituting x = 120 into (1), we have

y = 2x + 30

y = 2(120) + 30

y = 240 + 30

y = 270

So,

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Answer:

9) Keep the denominators the same, and subtract the numerators. Then simplify if necessary.

\( \frac{3x + 2}{x + 5} - \frac{2x - 3}{x + 5} \)

\( = \frac{3x + 2 - (2x - 3)}{x + 5} \)

\( = \frac{3x + 2 - 2x + 3}{x + 5} \)

\( \frac{x + 5}{x + 5} = 1\)

10) Find the LCD. Rewrite each rational expression as an equivalent expression with the LCD as the denominator. Add the numerators and write the sum over the LCD. Then simplify if necessary.

\( \frac{4x}{x - 2} + \frac{x - 4}{x - 5} \)

\( = \frac{4x(x - 5) + (x - 4)(x - 2)}{(x - 2)(x - 5)} \)

\( = \frac{4 {x}^{2} - 20x + {x}^{2} - 6x + 8 }{(x - 2)(x - 5)} \)

\( = \frac{5 {x}^{2} - 26x + 8}{(x - 2)(x - 5)} \)

\( = \frac{5 {x}^{2} - 26x + 8 }{ {x}^{2} - 7x + 10} \)

Answer:

3:5

Step-by-step explanation:

The correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A correlation coefficient measures the strength and direction of the relationship between two variables. In this case, the correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A positive correlation means that as one variable (in this case, happiness) increases, the other variable (GPA) also tends to increase. The magnitude of the correlation coefficient, which ranges from -1 to 1, represents the strength of the relationship. A value of 0.90 indicates a very strong positive linear correlation, suggesting that there is a consistent and significant relationship between happiness and GPA.

This means that as the level of happiness increases among high school students, their GPA tends to be higher as well. The correlation coefficient of 0.90 suggests a high degree of predictability in the relationship between these two variables.

It is important to note that correlation does not imply causation. While a strong positive correlation indicates a relationship between happiness and GPA, it does not necessarily mean that one variable causes the other. Other factors or variables may also influence the relationship between happiness and GPA.

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The correct expression that shows the number of dollars Ellen earned last month is:

c. 12w

In the given scenario, Ellen earns $12 for each time she walks the neighbor's dog. The variable "w" represents the number of times Ellen walked the dog last month.

To calculate the total amount Ellen earned, we need to multiply the number of times (w) by the amount earned per time (12 dollars). This is why the expression is 12w. By multiplying the number of walks (w) by the earnings per walk (12 dollars), we obtain the total amount Ellen earned last month.

a. 12 + w: This expression represents adding the number of walks (w) to the fixed amount of $12. However, this does not reflect the correct calculation of Ellen's earnings since she earns $12 per walk, not for each walk plus a fixed amount.

b. 12 - w: This expression represents subtracting the number of walks (w) from the fixed amount of $12. Similar to option (a), this does not accurately represent Ellen's earnings. She earns a fixed amount per walk, and subtracting the number of walks from that amount does not provide the correct calculation.

d. 12/w: This expression represents dividing the fixed amount of $12 by the number of walks (w). This also does not reflect the correct calculation of Ellen's earnings. Ellen earns a fixed amount per walk, not a variable amount that depends on the number of walks.

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To find the estimated project completion time for the given project activities, we need to first calculate the earliest start and earliest finish times and then the latest start and latest finish times.

Using the activity times given, we can calculate the earliest start and earliest finish times for each activity as follows: Activity A: Earliest start time = 0

Earliest finish time = 1

Activity B: Earliest start time = 2

Earliest finish time = 5

Activity C: Earliest start time = 5

Earliest finish time = 11

Activity D: Earliest start time = 11

Earliest finish time = 17

Activity E: Earliest start time = 5

Earliest finish time = 8 Activity F:

Earliest start time = 8

Earliest finish time = 17

Now we can calculate the latest start and latest finish times for each activity using the backward pass.

Latest finish time = 5

Latest start time = 2

Activity A: Latest finish time = 1

Latest start time = 0

Now we can calculate the slack time for each activity as follows:Activity A:

Slack time = 0

Activity B: Slack time = 0

Activity C: Slack time = 0

Activity D: Slack time = 0

Activity E: Slack time = 3

Activity F: Slack time = 0

The critical path for this project is A -> C -> D, since these activities have zero slack time. Therefore, the estimated project completion time is 17 units of time.

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Step-by-step explanation:

Volume of sphere = 4/3 * π * r³

Since 36π = 4/3 * π * r³, r³ = 27 and r = 3.

Answer:

Volume of a sphere = 4/3 pi r^3

36 pi = 4/3 pi r^3

36 = 4/3 r^3

27 = r^3

r = 3 inches

The difference quotient for the function is 8.

The function is given by:

f ( x ) = 8 x − 9, where h ≠ 0

To find f(a), substitute a for x in the function. So we have:

f ( a ) = 8 a − 9

To find f(a + h), substitute a + h for x in the function. So we have:

f ( a + h ) = 8 ( a + h ) − 9

The difference quotient can be found using the formula:

(f(a + h) - f(a))/h

Substituting the values found above, we have:

(8 ( a + h ) − 9 - (8 a − 9))/h

Expanding the brackets and simplifying, we have:

((8a + 8h) - 9 - 8a + 9)/h

= 8h/h

= 8

Therefore, the difference quotient for the function is 8.

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