Find the cosine ratio of angle .​

I do want the answer but please also explain to me how to do it so that I don't have keep asking

Answer:

x=10.2-2(×+5)........ given

×=20-2×-10............... avoid the bracket

x=10-2×..............collect the like terms

x+2x=10-2×+2×...... add 2x from both side

3x=10................simplify

3x/3=10/3..........divide both side by 3

x= 3.333.............x is solved

Step-by-step explanation:

i hope it is help full

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. A vector a that has the same direction as 〈−8,7,8〉 but has length 5 is〈−3.0136, 2.6439, 3.0136〉.

To find a vector with the same direction as 〈−8,7,8〉 but with a length of 5, we need to scale the vector 〈−8,7,8〉 by a factor that will result in the desired length. Since scaling a vector by a factor k results in a vector that has a length k times larger than the original vector, we can find the appropriate scaling factor by dividing the desired length by the length of the original vector.

First, we need to find the length of 〈−8,7,8〉 using the formula for the magnitude of a vector:

|〈−8,7,8〉| = \(\sqrt{(-8)^2 + 7^2 + 8^2)}\) = \(\sqrt{177}\)

Next, we divide the desired length of 5 by the length of the original vector to find the scaling factor:

\(\frac{5}{\sqrt{177} }\)  ≈ 0.3767

Finally, we multiply each component of 〈−8,7,8〉 by the scaling factor to get the vector a with the same direction as 〈−8,7,8〉 and a length of 5:

a = 0.3767 * 〈−8,7,8〉 = 〈−3.0136, 2.6439, 3.0136〉

Therefore, the vector a that has the same direction as 〈−8,7,8〉 but has length 5 is 〈−3.0136, 2.6439, 3.0136〉.

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a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Answer: .81

Step-by-step explanation: divide 9 and 11

The average number of fleas on a single Blue Jay in Akron is slightly higher than the average for the state of Ohio.

The average number of fleas on a single Eastern Blue Jay in the state of Ohio is 300, with a standard deviation of 14. In Akron, OH, a flock of 49 Blue Jays had an average of 314 fleas.

To analyze this data, we can use the concept of the z-score. The z-score measures how many standard deviations an individual data point is from the mean.

First, we need to calculate the z-score for the average number of fleas in the flock of Blue Jays in Akron. To do this, we subtract the mean (300) from the observed value (314) and then divide by the standard deviation (14).

z-score

= (314 - 300) / 14 = 14 / 14 = 1

The z-score of 1 tells us that the average number of fleas in the flock of Blue Jays in Akron is 1 standard deviation above the mean.

This means that the average number of fleas on a single Blue Jay in Akron is slightly higher than the average for the state of Ohio.

It's important to note that the z-score allows us to compare data points from different distributions. In this case, we compared the average number of fleas in the Akron flock to the average for the entire state of Ohio.

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The value of sin20. sin 30. sin 40. sin 80  is 0.6679.

Sine function in trigonometry is referred to as the ratio between the opposite leg of the angle ( for an acute angle.)

For a right-angle triangle, it is the ratio between the length opposite the angle and the length of the hypotenuse.

Sine is positive in the first and second quadrants and it is negative in the third and fourth quadrants.

0.9129 * (-0.9880) * 0.7451 * (-0.9939)

= 0.6679

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30 % of the measurements are found below the 30th percentile. 70 % of the measurements are found above the 30th percentile.

Percentile is a comparison score between a particular score and the scores of the rest of a group.  

Percentile = percentage of people who scored below you / Total percentage of  people who gave the exam.

For example, 99 percentile means 99 percentage of people are below the person who scored 99 percentile.

Hence, 30 % of the measurements are found below the 30th percentile and 70 % of the measurements are found above the 30th percentile.

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Answer:

1/18

Step-by-step explanation:

-1/2 + 5/9 =

-9/18 + 10/18 = 1/18

Answer:

1/18

Step-by-step explanation:

Answer:

£10

Step-by-step explanation:

3:4 is equal to 3/4 (three-quarters)

Paul gets 75%, and Brian gets 25%.

Paul gets £30.  30 is 3/4 of what number?

75/100 × x = 30

Multiply both sides by 100 and divide both sides by 75

x = 30 × 100/75

x = 30 x 1.33333333333

x= 40

£30 is 75% of £40

30/40 x 100 = 75%

10/40 x 100 = 25%

Brian gets £10

The surface given by the equation \(4x^2 - 16y^2 + z^2 = 16\) is a hyperboloid of two sheets. It consists of two distinct surfaces that intersect along the z-axis and open upwards and downwards.

To identify the surface defined by the equation \(4x^2 - 16y^2 + z^2 = 16,\) we can analyze the equation and determine its geometric properties.

First, let's rewrite the equation in a standard form:

\(4x^2 - 16y^2 + z^2 = 16\)

By rearranging terms, we have:

\((x^2/4) - (y^2/1) + (z^2/16) = 1\)

Comparing this equation to the standard form of a hyperboloid, we can see that the x and z terms have positive coefficients, while the y term has a negative coefficient. This indicates that the surface is a hyperboloid of two sheets.

The trace of the surface can be obtained by setting one variable constant and examining the resulting equation. Let's consider the traces in the xz-plane (setting y = 0) and the xy-plane (setting z = 0).

When y = 0, the equation becomes:

\(4x^2 + z^2 = 16\)

This represents an ellipse in the xz-plane centered at the origin, with the major axis along the x-axis and the minor axis along the z-axis.

When z = 0, the equation becomes:

\(4x^2 - 16y^2 = 16\)

This represents a hyperbola in the xy-plane centered at the origin, with the branches opening along the x-axis and the y-axis.

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identify the surface from the following equation \(4x^2-16y^2 z^2=16\)

Answer: $5000

Step-by-step explanation:

We can use the formula:

tip = rate × cost

where the rate is the percentage written as a decimal. In this case, the rate is 0.09 (9% expressed as a decimal), and the tip is $450. We want to find the cost of the manicure, which is represented by the variable b. So, the equation becomes:

450 = 0.09b

To solve for b, we can divide both sides of the equation by 0.09:

b = 450 ÷ 0.09

b = 5,000

Therefore, the cost of the manicure was $5,000.

Answer:

Use Desmos or GeoGebra.

Step-by-step explanation:

Answer: 160 bouncy balls

Step-by-step explanation:

There were a total of 4+7+9=20 packs of bouncy balls.

Since there are 8 balls in each package, there is a total of 20(8)=160 balls.

Answer:9,378,727,447,079.929‬

Step-by-step explanation:

Answer:

9.37414075 13 squared digit I don’t remember what it is called for that number so yea

Step-by-step explanation:

8011542/84 is 94257.43529 (already added 4) and 94257.43529 is about 9.37414075 13 squared digit I don’t remember what it is called for that number but that is the answer

Answer:

m∠XCY = 60°

Step-by-step explanation:

From the figure attached,

Circle has been given with the inscribed angles ∠XWY and ∠XCY formed by the same arc XY.

By the property of the inscribed angles,

"Measure of the inscribed angle formed by the same arc are equal"

m∠XWY ≅ m∠XCY

60x = 61x - 1

61x - 60x = 1

x = 1

Therefore, m∠XCY = 61x - 1

                                = 61(1) - 1

                                = 60°  

Answer: Angle C

Step-by-step explanation:

In any triangle, the side opposite the largest angle is always the longest side.

Here, angle C has the largest measurement of 70 degrees. Therefore, the longest side of triangle ABC will be opposite angle C.

The specified details of the triangle, obtained using the segments joining the midpoints of the sides of the triangle ΔADG and trapezoid ACFG indicates that we get;

4. \(\overline{CE}\) is a midsegment of ΔBDF

\(\overline{BF}\) is the midsegment of trapezoid ACFG

5. CE = 12 cm, AG = 36 cm

6. m∠2 = 116°, m∠3 = 32°, m∠4 = 58°, m∠5 = 58°, m∠6 = 64°

The midpoint of a segment or the side of a triangle is a point that divides the segment into two parts of the same length.

4. The details of the diagram indicates that the segment \(\overline{CE}\) is the midsegment of triangle ΔBDF

\(\overline{BF}\) is the midsegment of trapezoid ACFG

5. \(\overline{CD}\) is congruent to \(\overline{BC}\) by the definition of the midpoint of \(\overline{BD}\), similarly;

\(\overline{BC}\) is congruent to \(\overline{AB}\), by the definition of midpoint of \(\overline{AC}\), therefore;

\(\overline{CE}\) is the midsegment of triangle ΔBDF, therefore;

CE = (1/2) × BF

CE = (1/2) × 24 cm = 12 cm

CE = 12 cm

ΔBDF and ΔADG and ΔCDE are similar triangles, therefore;

\(\overline{BD}\) = (2/3) × \(\overline{AD}\)

Similarly, by the relationship between similar triangles we get;

\(\overline{BF}\) = (2/3) × \(\overline{AG}\)

BF = 24 cm, therefore;

24 = (2/3) × AG

AG = (3/2) × 24 = 36

AG = 36 cm

6. The length of a median of a right triangle, drawn from the right angled vertex, is half the length of the hypotenuse side.

Therefore; ΔACM and ΔABM are an isosceles triangles

m∠1 = m∠3 = 32°

m∠2 = 180° - (32° + 32°) = 116°

m∠2 = 116°

m∠3 = 32°

m∠4 = m∠5 = 90° - m∠1

m∠4 = m∠5 = 90° - 32° = 58°

m∠4 = 58°

m∠5 = 58°

m∠6 = 180° - (m∠4 + m∠5)

m∠6 = 180° - (58° + 58°) = 64°

m∠6 = 64°

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The correct answer is Option C. A researcher might choose purposive sampling over systematic sampling for several reasons. One key reason is that purposive sampling allows the researcher to study a particular type of participant.

This means that the researcher can select individuals who possess specific characteristics or traits that are relevant to their study.

By handpicking participants, the researcher can ensure that the sample represents the specific population they are interested in studying, which is particularly useful when investigating rare or hard-to-reach populations.

On the other hand, systematic sampling involves selecting participants at regular intervals from a larger population.

This method may not provide the same level of control in selecting participants based on specific characteristics.

While systematic sampling can be more efficient in terms of time and cost, it may not be suitable for certain research objectives that require a targeted approach.

It is important to note that neither method is inherently cheaper or more expensive than the other, and the choice between them depends on the research objectives and the specific population under investigation.

Therefore, option A is incorrect.

Option B is also incorrect because external validity is still important in research regardless of the sampling method chosen.

Option D is also incorrect since researchers using purposive sampling must still specify their population of interest.

Thus, the correct answer is option C.

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Angela made $350 per week 25 years ago and Walker made $200 per week 25 years ago.

Let's assign variables to represent Angela and Walker's salaries 25 years ago. Let A be Angela's salary 25 years ago and W be Walker's salary 25 years ago.

Using the information given in the problem, we can set up two equations:

A + W = 550 (their total salary 25 years ago)
4A + 3W = 2000 (their total current salary)

To solve for A and W, we can use substitution or elimination. Let's use substitution.

From the first equation, we can rearrange to solve for A:

A = 550 - W

Substitute this into the second equation:

4(550 - W) + 3W = 2000

Distribute the 4:

2200 - 4W + 3W = 2000

Simplify:

W = 800

Now that we know Walker's salary 25 years ago was $800, we can plug that into the first equation to solve for Angela's salary:

A + 800 = 550

A = -250

Uh oh, a negative salary doesn't make sense in this context. We made a mistake somewhere.

Let's go back to our original equations and try elimination instead:

A + W = 550
4A + 3W = 2000

Multiplying the first equation by 4, we get:

4A + 4W = 2200

Subtracting the second equation from this, we get:

W = 200

Now we can plug this into either equation to solve for A:

A + 200 = 550

A = 350

So Angela made $350 per week 25 years ago and Walker made $200 per week 25 years ago.

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Variables that indicate the distance a target is from the level achieved are called performance metrics or progress indicators.


Variables that indicate the distance a target is from the level achieved are called performance metrics or progress indicators. These variables help measure and track progress towards a goal by providing a quantitative or qualitative measure of how far the target is from the desired level of achievement.

Performance metrics can be represented in various forms, such as distance covered, percentage completed, points earned, or even subjective evaluations. For example, in a fitness program, a performance metric could be the number of miles run or the number of push-ups completed.

These metrics enable individuals or organizations to assess their progress and make necessary adjustments to reach their desired outcomes.

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Answer:

C I think

Step-by-step explanation:

Hehehehehehe

Answer:

its D

Step-by-step explanation:

Answer:

multiplication

Step-by-step explanation:

Answer:

Your rationalizing factor becomes : [ 9 + 25^(1/3) - 3 x 5^(1/3) ]. Therefore, Therefore, and both are rational and as such is also rational.

The least amount of money Ms. Magee can spend on the tile to cover her table is $81.20.

Area is the measure of the size of a two-dimensional surface or region in a plane. It is the amount of space inside the boundary of a flat object, such as a square, rectangle, circle, or triangle.

The area of the circular table can be found using the formula:

Area = π x (radius)²

Since the diameter of the table is 8 feet, the radius is half of that, or 4 feet.

Area = 3.14 x (4)²

Area = 3.14 x 16

Area = 50.24 square feet

To cover the table with tile, Ms. Magee will need to purchase enough tile to cover an area of 50.24 square feet. Since each tile piece measures 1.75 square feet, the number of tiles needed can be found by dividing the area of the table by the area of each tile:

Number of tiles needed = Area of table / Area of each tile

Number of tiles needed = 50.24 / 1.75

Number of tiles needed ≈ 28.68

Since Ms. Magee cannot purchase a fractional number of tiles, she will need to purchase at least 29 tiles. The cost of each tile is $2.80, so the total cost of the tiles will be:

Total cost = Number of tiles x Cost per tile

Total cost = 29 x $2.80

Total cost = $81.20

Therefore, the least amount of money Ms. Magee can spend on the tile to cover her table is $81.20.

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Answer:

40 km

Step-by-step explanation:

a) Green is 0.3, Yellow is 0.1

b) There are 12 green pins in the bag

Given,

In the question:

There are some colored pins in a bag. The pins can be green, yellow, purple, or grey. A pin is going to be taken at random from the bag.

The table shows the probabilities of picking a purple or grey pin.

The table is not given in the question :

So, The table is :

Colors:          Green         Yellow      Purple        Grey

Probability:                                         0.35           0.25

To find the :

a)Complete the table.

There are 14 purple pins in the bag.

b)Work out how many green pins are in the bag.

Now, According to the question:

The probability is the ratio between the possible outcomes over the total outcomes:

The value of the probability of possible outcomes is greater than 0 and smaller than 1 (0 < P < 1)

The sum of the probabilities of all outcomes must equal 1.

A bag contains some green, yellow, purple and grey pins

∵ The probability of picking a purple pin P(purple) = 0.35

The probability of picking a grey pin P(grey) = 0.25

→ The total of all possible outcomes is 1

The sum of the probability of green and yellow pins = 1 - 0.35 - 0.25

The sum of the probability of green and yellow pins = 0.4

P(green) + P(yellow) = 0.4 ⇒ (1)

∵ The probability of picking a green pin is 3 times the probability

of picking a yellow pin

P(green) = 3 P(yellow) ⇒ (2)

→ Substitute (2) in (1)

3 P(yellow) + P(yellow) = 0.4

4 P(yellow) = 0.4

→ Divide both sides by 4

P(yellow) = 0.1

The probability of picking a yellow pin is 0.1

→ Substitute P(yellow) in (20 by 0.1

P(green) = 3(0.1)

P(green) = 0.3

The probability of picking a green pin is 0.3

Green = 0.3, Yellow = 0.1

There are 14 purple pins in the bag

P(purple) = 0.35

0.35 of purple pins = 14

→ To find the total number of pins in the bag divide 14 by 0.35

The total number of pins = 14 ÷ 0.35

The total number of pins = 40 pins

P(green) = 0.3

The number of green pins = 0.3 × 40

The number of green pins = 12 pins

Hence, There are 12 green pins in the bag.

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The optimal solution for the given linear programming problem using the Big-M method is x₁ = 4, x₂ = 2, with a maximum value of Z = 22.

To solve the given linear programming problem using the Big-M method, we first convert it into standard form by introducing slack, surplus, and artificial variables.

The objective function is to maximize Z = 4x₁ + 3x₂. The constraints are 2x₁ + x₂ ≥ 10, -3x₁ + 2x₂ ≤ 6, x₁ + x₂ ≥ 6, and x₁, x₂ ≥ 0.

We introduce slack variables s₁, s₂, and s₃ to convert the inequalities into equalities. The initial Big-M tableau is set up with the coefficients and variables, and the artificial variables are introduced to handle the inequalities. We set a large positive value (M) for the artificial variables' coefficients.

In the first iteration, we choose the most negative coefficient in the Z-row, which is -4 corresponding to x₁. We select the s₂-row as the pivot row since it has the minimum ratio of the RHS value (6) to the coefficient in the pivot column (-3). We perform row operations to make the pivot element 1 and other elements in the pivot column 0.

After multiple iterations, we find that the optimal solution is x₁ = 4, x₂ = 2, with a maximum value of Z = 22. This means that to maximize the objective function, x₁ should be set to 4 and x₂ should be set to 2, resulting in a maximum value of Z as 22." short

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The standard deviation of the sample proportion is 10.

In math standard deviation is defined as the statistical measure of diversity or variability in a data set.

Here we have given that about 19% of young adults have high blood pressure. consider the proportion of people with high blood pressure in random samples of 45 young adults.

And we need to find the the standard deviation of this sample proportion

Let us assume the expected population standard deviation to be 10, and employing t-distribution to estimate sample size, the study would require a sample size of: 44 to estimate a mean with 67% confidence and a precision of 1.5.

Which means that, if you select a random sample of 44 from a population, and determine the mean to be say y, you would be 67% confident that the mean in the population lies somewhere between y - 1.5 and y + 1.5.

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Answer:

Step-by-step explanation: