a numerical value used as a summary measure for a sample, such as sample mean, is known as a

Answer: 112i + 85.8j

Step-by-step explanation:

Answer:

\(\vec{H}=-32.1\:\hat{i}+79.6\:\hat{j}\)

Step-by-step explanation:

To find the components of a vector given its magnitude and direction, use the following formula:

\(\large\boxed{\vec{u}=\left(||\vec{u}|| \cos(\theta),|| \vec{u}|| \sin(\theta)\right)}\)

where:

Given:

Substitute the given values into the formula:

\(\vec{H}=\left(85.8 \cos(112^{\circ}),85.8 \sin(112^{\circ})\right)\)

\(\vec{H}=\left(-32.1, 79.6\right)\)

Therefore:

\(\vec{H}=-32.1\:\hat{i}+79.6\:\hat{j}\)

Answer:

the simplified form of the expression 2/x ÷ (x+5)/2x.

Step-by-step explanation:

To divide the expression 2/x ÷ (x+5)/2x, we can simplify the process by using the reciprocal (or flip) of the second fraction and then multiplying.

Let's break it down step by step:

Step 1: Flip the second fraction:

(x+5)/2x becomes 2x/(x+5).

Step 2: Multiply the fractions:

Now we have 2/x multiplied by 2x/(x+5).

To multiply fractions, we multiply the numerators together and the denominators together:

Numerator: 2 * 2x = 4x

Denominator: x * (x+5) = x^2 + 5x

So, the expression becomes 4x / (x^2 + 5x).

This is the simplified form of the expression 2/x ÷ (x+5)/2x.

Answer:

When it increases slowly with time

The total area of the given composite figure is 24 units² respectively.

The quantity of unit squares that cover a closed figure's surface is its area.

Square units like cm² and m² are used to measure area.

A shape's area is a two-dimensional measurement.

The space inside the perimeter or limit of a closed shape is referred to as the "area."

Area of ABGH:

l*b

5*3

15 units²

Mark point V as shown in the figure below.

Area of DVFE:

l*b

4*2

8 units²

Area of BCV:
1/2 * b * h

1/2 * 2 * 1

1 * 1

1 units²

Total area of the figure: 1 + 8 + 15 = 24 units²

Therefore, the total area of the given composite figure is 24 units² respectively.

Know more about the area here:

https://brainly.com/question/25292087

#SPJ1

Let the distance between the foot of the ladder and the wall be x, and the height of the ladder on the wall be y. Then we have a right-angled triangle with hypotenuse 13.

Applying the Pythagorean theorem, we get:

x^2 + y^2 = 13^2

Differentiating both sides of the equation with respect to time, we get:

2x(dx/dt) + 2y(dy/dt) = 0

We want to find the rate of change of the area of the triangle, which is given by:

A = (1/2)xy

Differentiating both sides with respect to time, we get:

(dA/dt) = (1/2)(x(dy/dt) + y(dx/dt))

Substituting for dx/dt and simplifying, we get:

(dA/dt) = -3y

When x = 5 and y = 12 (since the ladder is 13 feet long and the foot is 5 feet away from the wall, the height on the wall is 12 feet), we get:

(dA/dt) = -36 square feet per second

Therefore, the area of the triangle is decreasing at a rate of 36 square feet per second at the instant the bottom of the ladder is 5 feet from the wall.

To learn more about  triangle click here :

brainly.com/question/13197015

#SPJ11

Answer:

5,234 cubic centimeters

Step-by-step explanation:

The volume of a sphere can be calculated using the formula:

V = (4/3)πr^3

where V is the volume, π is pi (approximately 3.14), and r is the radius of the sphere.

Since the diameter of the bowling ball is 21.6 centimeters, the radius is half of that:

r = d/2 = 21.6/2 = 10.8 centimeters

Substituting this value into the formula, we get:

V = (4/3)πr^3 = (4/3)π(10.8)^3 ≈ 5,233.8 cubic centimeters

Rounding this to the nearest whole number, we get a measurement closest to the volume of the bowling ball of 5,234 cubic centimeters.

Your welcome

180ML of 50% solution are needed.

Finding an equation's solutions, which are values (numbers, functions, sets, etc.) that satisfy the equation's condition and often consist of two expressions connected by an equals sign, is known as solving an equation in mathematics. One or more variables are identified as unknowns when looking for a solution. An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself. Particularly but not exclusively for polynomial equations, the solution of an equation is frequently referred to as the equation's root.

EXPLANATION : To solve this question, we have initial stock solution of 10% and 50% concentration. We need to make final solution of 25% concentration of volume 16oz. \((1oz \approx 30ml)\)

To find :- Volume of 50% required

Let us assume we require x oz volume of 50% stock Solution , Then volume of 10% stock added will be (16-x) oz.

Formula used here:-   C1V1 + C2V2 = C3V3

Where C1 = 50% = 0.5 , V1 = x oz    &   C2 = 10%= 0.1  , V2= 16-x oz

C3 = 25% = 0.25 ,  V3= 16oz

Putting values we have

(0.5*x) + (0.1(16-x)) = 16*0.25

0.5x + 1.6 - 0.1x = 4

x = 6

Hence Volume of 50% solution = x = 6 oz = 6*30 ml  = 180ml

To know more about Solutions, visit;

https://brainly.com/question/7932885

#SPJ4

We have proved that the set of all points (x, y) that are equidistant from the point (f, k) and the line x.

What is a parabola?

A parabola is a plane curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits several seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.

That’s a parabola in the usual orientation. y=1 is the directrix. (f, k) is the focus. Squared distance, as usual, is the fundamental quantity.

If (x,y) is a point in the set, the squared distance to y=1 is (y−1)². The squared distance to (f, k).

     (y - 1)²=(x - f)²+(y - k)²

Hence, we can say that the set of all points (x, y) is equidistant from the point (f, k) and the line x.

To learn more about parabolas, visit:

https://brainly.com/question/4061870

#SPJ4

Answer:

0.96

Step-by-step explananation

stack the two numbers ontop of each other and it will be easier to do the multiplacation

The correct coordinates for L' after the translation are (8, -8). Option C.

To find the coordinates of point L' after the translation, we need to apply the same translation vector that maps M to M' to point L. Let's calculate the translation vector first:

Translation vector = M' - M

The coordinates of M' are (-5, 1), and the coordinates of M are (-13, 8). Therefore, the translation vector is:

Translation vector = (-5, 1) - (-13, 8)

= (-5 + 13, 1 - 8)

= (8, -7)

Now that we have the translation vector, we can apply it to the coordinates of point L:

Coordinates of L' = Coordinates of L + Translation vector

The coordinates of L are (0, -1), and the translation vector is (8, -7). Therefore, the coordinates of L' are:

Coordinates of L' = (0, -1) + (8, -7)

= (0 + 8, -1 - 7)

= (8, -8)To find the coordinates of point L' after the translation, we need to apply the same translation vector that maps M to M' to point L. Let's calculate the translation vector first:

Translation vector = M' - M

The coordinates of M' are (-5, 1), and the coordinates of M are (-13, 8). Therefore, the translation vector is:

Translation vector = (-5, 1) - (-13, 8)

= (-5 + 13, 1 - 8)

= (8, -7)

Now that we have the translation vector, we can apply it to the coordinates of point L:

Coordinates of L' = Coordinates of L + Translation vector

The coordinates of L are (0, -1), and the translation vector is (8, -7). Therefore, the coordinates of L' are:

Coordinates of L' = (0, -1) + (8, -7)

= (0 + 8, -1 - 7)

= (8, -8) Option C is correct.

For more such question on coordinates. visit :

https://brainly.com/question/31293074

#SPJ8

the capture rate will be lower than what is indicated in the confidence level.

A C% confidence interval gives an interval of plausible values for a parameter. The interval is calculated from the data and has the form, point estimate ± margin of error.

When the random and large counts conditions are met, a C% confidence interval for the population proportion p is

Point estimate ±margin of error

Ƹ± √Ƹ(1 − Ƹ)/

Where z is the critical value for the standard normal curve with C% of its area between –z and +z.

Your interval will look like: ______ < p <________

Confidence Intervals in a 4 Step Process:

Statistics Problems Demand Consistency

1. State: What parameter do you want to

estimate, and at what confidence level?

2. Plan: Identify the appropriate inference

method: check conditions.

3. Do: If the conditions are met, perform

calculations.

4. Conclude: Interpret your interval in the

context of the problem.

When constructing a confidence interval for a population proportion, it is checked that sample size is less than 10% of population size.

This condition is important due to the the fact that when sample size is less than of population size, observations are closer to independent.

If this requirement is not met, it is not possible to calculate standard deviation of distribution.

If this requirement is not met, it is not possible to calculate standard deviation of distribution correctly.

If standard deviation is not correct, confidence level will be inaccurate. There are less chances to obtain population parameter in confidence interval.

Therefore, the capture rate will be lower than what is indicated in the confidence level.

To learn more about Estimating with

Confidence :

https://brainly.com/question/29392393

#SPJ4

The capture rate will be lower than what is indicated in the confidence level.

An interval of conceivable values for a parameter is provided by a C% confidence interval. The interval is formed as a point estimate with a margin of error and is calculated from the data.

A C% confidence interval for the population proportion p when the random and large counts requirements are satisfied is 

Point estimate margin of error

Ƹ± √Ƹ(1 − Ƹ)

Where z is the critical value for the standard normal curve with C% of its area between –z and +z.

Your interval will look like: ______ < p <________

Confidence Intervals in a 4-Step Process:

1. Clarify what parameter you wish to estimate and at what level of confidence.

2. Make a plan and decide which inference technique is best. Check the circumstances.

3. If the criteria are satisfied, run the calculations.

4. Summarize: Consider your interval in light of the issue.

It is ensured that the sample size is less than 10% of the population size when creating a confidence interval for a population proportion. This requirement is crucial because observations are more likely to be independent when the sample size is smaller than the population size. Calculating the distribution's standard deviation is impossible if this condition is not satisfied. The standard deviation of the distribution cannot be appropriately calculated if this condition is not satisfied. The confidence level will be incorrect if the standard deviation is incorrect. Population parameters are less likely to be found in a confidence interval. As a result, the capture rate will be lower than what the confidence level predicts.

To learn more about confidence level :

brainly.com/question/29392393

#SPJ4

5.03 × 10^7

(word format): 5 and 3 hundredths times 10 to the 7th power

Answer:5.03 x 10^9

Step-by-step explanation:

Answer:

The expression is not factorable with rational numbers.

x² − 4x + 7

To solve this question, first, we will have a pictorial representation of the given problem.

An equilateral triangle has all its' sides equal.

So we have made the length of one side x.

To get the perimeter of the triangle, we will sum up the length of the 3 sides together.

To solve for the length of the triangle, we will analyze a right-angle part from the full triangle, the image is drawn below.

To solve for x (a side of the equilateral triangle), we will use the Pythagoras theorem:

Cross multiply, we will have:

So now we have gotten the length of a side of the equilateral triangle, the perimeter will be:

Answer:

Heath

I think

Step-by-step explanation:

Answer:

is it Heath?

Hope it helps!!!

a. A scatter plot for the data is shown below.

b. There is a strong correlation between the data and the correlation coefficient (r) is 0.7.

c. A linear model for the data is y = 3.57x - 60.64.

In this exercise, we would plot the height (inches) on the x-axis (x-coordinates) of a scatter plot while the weight (pounds) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

Part b.

In this context, we can logically deduce that there is a strong correlation between the height (inches) and the weight (pounds) because the correlation coefficient (r) is less than 1;

Correlation coefficient, r = 0.6993694 ≈ 0.7

0.7＜|r| ≤ 1  (strong correlation)

Part c.

On the Microsoft Excel worksheet, right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit (trend line) on the scatter plot.

By critically observing the scatter plot which models the relationship between the height (inches) and the weight (pounds), a linear equation for the line of best fit is given by:

y = 3.57x - 60.64

Read more on positive correlation here: brainly.com/question/3753830

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Maximizing the sum or mean difference between the residuals squared, do not accurately describe the goal of the least squares regression line.

The least squares regression line minimizes the sum of the residuals squared. This means that it aims to minimize the difference between the observed values and the predicted values squared.

This is done by finding the line that has the smallest overall distance from the data points.

The other options, such as maximizing the sum or mean difference between the residuals squared, do not accurately describe the goal of the least squares regression line.

To know more about regression visit:

https://brainly.com/question/32505018

#SPJ11

The least squares regression line minimizes the sum of the residuals squared.

In regression analysis, the least squares regression line is a line that best fits a set of data points by minimizing the sum of the squared differences between the observed values and the predicted values.

The residuals are the differences between the observed values and the predicted values, and squaring them ensures that negative and positive differences are both considered.

By minimizing the sum of the squared residuals, the least squares regression line finds the line that is closest to all the data points.

For example, let's say we have a dataset of 10 data points.

The least squares regression line is determined by finding the line that minimizes the sum of the squared differences between the observed values and the predicted values for each data point.

This means that the line is positioned in a way that it is as close as possible to all the data points, minimizing the overall error.

By minimizing the sum of the residuals squared, the least squares regression line provides the best fit to the data and can be used to make predictions or analyze relationships between variables.

It is widely used in various fields, including statistics, economics, and social sciences.

Learn more about residuals squared :

https://brainly.com/question/30641534

#SPJ11

The line integral of the scalar function xy is -0.1706.

To evaluate the line integral of the scalar function f(x, y) = xy along the parabolic path y = \(x^{2}\) connecting the origin to the point (1, 1), we need to parametrize the curve and then calculate the line integral using the parametric form.

Let's parameterize the curve by expressing x and y in terms of a single parameter t that ranges from 0 to 1, corresponding to the start and end points of the curve.

For the given parabolic path y = \(x^{2}\), we can let x = t, and therefore, y = \(t^{2}\).

The parametric form of the curve is:

x = t

y = \(t^{2}\)

Now, we need to find the differentials dx and dy in terms of dt:

dx = dt

dy = 2t * dt

Substituting the parametric equations and differentials into the scalar function f(x, y) = xy, we get:

f(t) = (t)(\(t^{2}\)) = \(t^{3}\)

The line integral of f(x, y) along the parabolic path can be calculated as follows:

∫[C] f(x, y) ds = ∫[0 to 1] f(t) * ||r'(t)|| dt

where r(t) = (x(t), y(t)) is the position vector and ||r'(t)|| represents the magnitude of the derivative vector.

To find ||r'(t)||, we compute:

r'(t) = (dx/dt, dy/dt) = (dt, 2t * dt)

||r'(t)|| = \(\sqrt{(dt)^{2}+(2tdt)^{2} }\) = \(\sqrt{(dt)^{2}+4t^{2} (dt)^{2} }\) = \(\sqrt{(1+4t^{2} )^{2} dt^{2} }\) =\(\sqrt{1+4t^{2}} }\) * dt

Now, the line integral becomes:

∫[C] f(x, y) ds = ∫[0 to 1] \(t^{3}\) * \(\sqrt{1+4t^{2}} }\) * dt

To evaluate this integral, we can make a substitution u = 1 + 4\(t^{2}\), which leads to du = 8t * dt. When t = 0, u = 1, and when t = 1, u = 5.

The integral becomes:

∫[C] f(x, y) ds = (1/8) ∫[1 to 5] (u - 1) * \(\sqrt{u}\) * (1/8) du

= (1/64) ∫[1 to 5] (\(u^{3/2}\) - \(u^{1/2}\)) du

= (1/64) [(2/5)\(u^{5/2}\) - (2/3)\(u^{3/2}\)] evaluated from 1 to 5

= (1/64) [(2/5)(\(5^{5/2}\)) - (2/3)(\(5^{3/2}\)) - (2/5) - (2/3)]

Evaluating this expression, we get:

∫[C] f(x, y) ds = (1/64) [(2/5)(\(5^{5/2}\)) - (2/3)(\(5^{3/2}\)) - (2/5) - (2/3)]

≈ -0.1706

Therefore, the line integral of the scalar function xy along the parabolic path y =\(x^{2}\) connecting the origin to the point (1, 1) is approximately -0.1706.

To learn more about line integral here:

https://brainly.com/question/32292860

#SPJ4

Answer: y = 4

Step by step explanation:

−3y + 2 = −10y + 30

Step 1: Add 10y to both sides.

−3y + 2 + 10y = −10y + 30 + 10y

7y + 2 = 30

Step 2: Subtract 2 from both sides.

7y + 2 − 2 = 30 − 2

7y = 28

Step 3: Divide both sides by 7.

7y/7  =  28/7

y = 4

Answer:

I would guess the 30 degree one.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

For a set of data to have a median that is greater than the mean, it must have an odd number of values and be skewed to the right. This means that the majority of the values in the set must be smaller than the median, with a few larger values on the right side of the distribution.

Out of the given options, the only set of data that satisfies these conditions is (B) {8, 12, 14, 14, 22}. This set has an odd number of values, and the median of 14 is greater than the mean of 14.4. The other options have either an even number of values, or are not skewed to the right.

Therefore, the correct answer is (B) {8, 12, 14, 14, 22}.

A stone arch can be twice as wide as a stone lintel because an arch distributes the weight of the structure vertically down its curve to the columns (piers) on either side while a lintel distributes the weight horizontally along the length of the stone.

A stone arch can be twice as wide as a stone lintel because an arch distributes the weight of the structure vertically down its curve to the columns (piers) on either side while a lintel distributes the weight horizontally along the length of the stone.

It requires only a small fraction of the arch's width to support itself while a lintel requires the full width of the structure that it spans. Thus, a stone arch can span a larger gap than a stone lintel and be twice as wide while using the same material.

For example, the Roman Colosseum uses an arch to span the entrances and exits while the walls supporting the upper levels use a series of stone lintels to support the structure.

Moreover, the arc prevents the need for a central support structure, which would be in the way of any events taking place in the structure. The technology of arches made them fundamental to ancient Roman architecture. For example, the arches were used to construct aqueducts, which provided a steady supply of water to the city of Rome.

Learn more about stone arch here https://brainly.com/question/11371014

#SPJ11

Answer:777

Step-by-step explanation: I do not care

There are 333 pages are in my book.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are more than 200 pages but fewer than 800 in my book.

And, All the digits of my number are the same and the number is divisible by 9.

Now,

Let a number with three same digit = xxx

So, We get;

200 < xxx < 800

Since, the number is divisible by 9.

So, By the rule of the number divide by 9, we get;

x + x + x = 9k

3x = 9k

for k = 1;

x = 3

Thus, Number of pages = 333

Therefore,  

There are 333 pages are in my book.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

Answer:

126°

Step-by-step explanation:

1. We know that 54 degrees and its adjacent are a linear pair, meaning that they add up to 180 degrees. To find the measure of the adjacent angle, we subtract 54 from 180.

2. Now, we know that adjacent of 54 is 126. Also, we know that \(l\) ║ \(m\) ║ n, and x and 126 degrees are corresponding angles. Corresponding angles are congruent within angle measures, so x = 126 degrees.

The sketch of the function will exhibit a downward trend on both sides and intersect the x-axis at -5, 1, and 4. The exact values of a and b can be chosen to achieve the desired end behavior.

To construct the desired polynomial, we know that since it has downward end behavior on both sides, the leading coefficient must be negative. Moreover, since there are three x-intercepts, the polynomial must have three linear factors corresponding to those intercepts.

Let's denote the polynomial as f(x). Since it has x-intercepts at -5, 1, and 4, the factors of the polynomial can be written as (x + 5), (x - 1), and (x - 4). To ensure downward end behavior, we need to multiply these factors by two additional linear factors. We can choose (x - a) and (x - b), where a and b are large positive values.

Therefore, the equation of the 4th-degree polynomial satisfying the given conditions is:

f(x) = -(x + 5)(x - 1)(x - 4)(x - a)(x - b)

The sketch of the function will exhibit a downward trend on both sides and intersect the x-axis at -5, 1, and 4. The exact values of a and b can be chosen to achieve the desired end behavior.

Learn more about linear factors here:

https://brainly.com/question/28969245

#SPJ11

(6x-5)-(-x-4)

6x-5=x+4

6x-x=4+5

5x=9

Answer:

A is correct pls give likes and brainliest (I actually checked the work sheet for answer key)

Answer:

[B]

Step-by-step explanation:

Given:

People leaving the library were asked how many books they checked out that day The result are: 1,2, 3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20

To Find:

Which histogram correctly shows the data set?

Solution:
Since it given from the histogram:

0-5, 6-11, 12 - 17,18-23

From the result :

1,2, 3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20

Thus,

1,2,3,5 = 0-5

8,9,10,11 = 6-11

12,13,14,15,16 = 12-17

18,20 = 18-23

From this we can see that:

for

0 - 5 = 4

6 - 11 = 4

12 - 17 = 5

18 - 23 = 2

Hence, the answer is [B]

Kavinsky

Answer:

The answer is 12.

Step-by-step explanation:

If you multiply 18 by 50, you would get how long the trip is, which is 900 miles. Then, divide 900 by 75, you would then get the answer of 12. The trip would take 12 hours at 75 mph.

x = -15

Step-by-step explanation:

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

Collect like terms and simplify

\(x - \frac{2}{3} x = - 5 \\ \frac{1}{3} x = - 5\)

Cross multiply

\(x = - 5 \times 3 \\ \\ x = - 15\)