calculate the expressions 17-6×2+4÷2

Answer:

Distance is 8.49 units

Step-by-step explanation:

Answer:

d= √  72

Step-by-step explanation:

d=√  (1−7)2+(8−2)2

d=√  (−6)2+(6)2

d=√  36+36

d=√  72

d=8.485281

The value of x in parallelogram ABCD is 16/3.

To find the value of x in parallelogram ABCD, we can use the property that opposite sides of a parallelogram are equal in length.

Given that AE = 9 and BE = 3x - 7, we can set up the equation AE = BE:

9 = 3x - 7

To isolate x, we can add 7 to both sides of the equation:

9 + 7 = 3x

16 = 3x

Divide both sides of the equation by 3:

16/3 = x

Therefore, x = 16/3.

In order to find the value of x, we need to know the exact value of x.

So, the value of x in parallelogram ABCD is 16/3.

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The equation of an ellipse with x-intercepts at (4, 0) and (-4, 0), y-intercepts at (0, 9) and (0, -9), and center at (0, 0) is \($\frac{x^2}{16}+\frac{y^2}{81}=1$$\).

As per the given data the ellipse with x-intercepts at (4, 0) and (-4, 0), y-intercepts at (0, 9) and (0, -9), and center at (0, 0).

If the ellipse has its x-intercepts at points (4, 0) and (-4, 0) and y-intercepts at points (0, 9) and (0, -9), then it's symmetric across the y- axis and the x-axis.

The equation of an ellipse where the major axis 2a is greater than the minor 2b.

When 2b > 2a , then the equation becomes \($\frac{(y-h)^{2} }{b^{2} } + \frac{ (x-k)^{2} }{a^{2} } =1\)

Moreover h = 0 and k = 0 because the center is on the origin, so the equation becomes:

\($\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

Moreover,

a = 4

b = 9

The equation of the such ellipse is

\($\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

Hence, the equation of the ellipse is

\($\frac{x^2}{4^2}+\frac{y^2}{9^2}=1\)

\($\frac{x^2}{16}+\frac{y^2}{81}=1$$\)

Therefore the equation of an ellipse is  \($\frac{x^2}{16}+\frac{y^2}{81}=1$$\).

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Find the equation of the ellipse with the following properties. The ellipse with x-intercepts at (4, 0) and (-4, 0), y-intercepts at (0, 9) and (0, -9), and center at (0, 0).

The function is y = csc x. We need to write y = csc x as a ratio of sin x and/or cos x:y = 1/sin x (Since csc x = 1/sin x).

Domain of y = csc x: The domain of y = csc x is all real numbers except where sin x = 0 (i.e. x = nπ, where n is an integer).

Range of y = csc x: The range of y = csc x is (-∞, -1] U [1, ∞).

Y-intercept of y = csc x: The y-intercept of y = csc x is at point (0, undefined),

since csc 0 is undefined.All x-intercepts of y = csc x: The x-intercepts of y = csc x occur when csc x = 0. This happens when sin x = 1/0. There are no real values of x that satisfy sin x = 1/0.Vertical asymptotes of y = csc x: The vertical asymptotes of y = csc x occur when sin x = 0. This happens when x = nπ, where n is an integer.

All vertical asymptotes of y = csc x are at x = nπ, where n is an integer.

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Answer:

3

Step-by-step explanation:

Answer:

$1.25

Step-by-step explanation:

Let \(f\) equal the flat rate.

Let \(p\) equal the one-time membership processing fee.

Start with a system of equations:

\(16.50=8f+p\)

\(14=6f+p\)

Use the elimination method and multiply your second equation by \(-1\) to cancel out the \(p\)s:

\(-1(14=6f+p)\)

Now combine the equations:

\(16.50=8f+p\)

\(-14=-6f-p\)

Subtract:

\(2.5=2f\)

Divide by the coefficient of \(f\), which is \(2\) (I rearranged the equation):

\(f=1.25\)

~

Even though we're not solving for the one-time processing fee, to check our work, we'll need to solve for \(p\), so start with the initial system of equations:

\(16.50=8f+p\)

\(14=6f+p\)

Use the elimination method and multiply the first equation by \(3\), and the second equation by \(-4\):

\(3(16.50=8f+p)\)

\(-4(14=6f+p)\)

Multiply:

\(49.50=24f+3p\)

\(-56=-24f-4p\)

Subtract:

\(-6.5=-p\)

Divide by the coefficient of \(p\), which is \(-1\) (Rearranged equation):

\(p=6.5\)

~

Check your work:

\(16.50=8(1.25)+6.5\)

\(14=6(1.25)+6.5\)

Solve:

\(16.50=16.50\)

\(14=14\)

It's correct!

The value of p is 0.18.

The value of \(\bar{p}\) (p with a hat on top) is 0.21.

The standard deviation of the sampling distribution of \(\bar{p}\) is approximately 0.024.

No, this school does not have an unusually high proportion of students that are vegetarian.

In this scenario, p represents the true population proportion of undergraduates in California colleges and universities who are vegetarians. The given information states that 18% (or 0.18) of all undergraduates are vegetarians.

\(\bar{p}\) (p with a hat on top) represents the sample proportion of vegetarians in the random sample drawn by the cafeteria management. They selected 300 students, and out of those, 63 identified as vegetarians. To calculate \(\bar{p}\) , we divide the number of vegetarians in the sample (63) by the sample size (300).

Therefore, \(\bar{p}\) = 63/300 ≈ 0.21.

The standard deviation of the sampling distribution of \(\bar{p}\), denoted as σ(\(\bar{p}\)), is calculated using the formula: σ(\(\bar{p}\)) = √[(p * (1 - p)) / n], where p is the true population proportion, and n is the sample size.

In this case, σ(\(\bar{p}\)) ≈ √[(0.18 * (1 - 0.18)) / 300] ≈ 0.024.

To determine if the school has an unusually high proportion of vegetarian students, we compare the sample proportion (\(\bar{p}\)) with the population proportion (p). Since \(\bar{p}\) (0.21) is greater than p (0.18), we can conclude that the observed proportion of vegetarians in the sample is higher than the expected population proportion.

However, without further context or a specific criterion for what constitutes "unusually high," we cannot definitively state whether the school's proportion of vegetarian students is considered unusually high.

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An equation for the fish population, after years is P(t) ≈ 8000e-0.664t ± 0.00005

The equation for the fish population in a stocked lake can be determined using exponential growth.

The formula for exponential growth is

P(t) = \(P_0\)ert

where P(t) is the population after time t,

\(P_0\) is the initial population,

r is the rate of growth, and

e is the mathematical constant approximately equal to 2.71828.

The carrying capacity, K, is the maximum population that can be supported by the environment, and it is a limiting factor for population growth. When the population reaches K, the growth rate slows down until it reaches a point of equilibrium.

The carrying capacity can be estimated using a variety of methods, including the logistic model, which incorporates the carrying capacity into the equation for population growth.

However, for this problem, we are given an estimate of the carrying capacity, which we will use in the exponential growth equation.

We are also given the initial population,

\(P_0\) = 1100, and we are asked to find an equation for the fish population, P(t), after t years.

The rate of growth, r, can be determined using the following formula:

r = ln(P/K) / t

where ln is the natural logarithm, and t is the time it takes to reach the carrying capacity, K.

Since we don't have an exact value for K, we will use the estimated value of 8000.

Thus,

r = ln(1100/8000) / 1

r ≈ -0.664

The negative sign indicates that the population is decreasing, since the growth rate is negative.

Therefore, the equation for the fish population after t years is:

P(t) = 8000e-0.664t

To round to 4 decimal places, we can use the formula:

P(t) ≈ 8000e-0.664t ± 0.00005

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Answer:

the aswer is 620(d)

Step-by-step explanation:

what i did was subtract 180 from 1060 and got 880

then i divides that by 2 and got 440

once i did that i then added the 18o to the 440 and got 620

Answer:

$1537.13

Step-by-step explanation:

I have attached an image of how I solved it!

Answer:

Step-by-step explanation:

Alright so we are going to be simplifying here

-6 + x = 4x Flip sides

x-6=4x

After that,

x-6=4x  Subtract 4x from both sides

-3x-6=0

Step 3

-3x-6=0  Add 6 to the sides

-3x=6

Step 4

-3x=6  Divide the sides by 3

-2

So therefore,

Your answer would be x=-2

The solution to the equation (1 - tan² x)/(1 + tan² x) = cos x is all values of x in the domain 0 < x ≤ π.

Given equation: (1 - tan²x)/(1 + tan²x) = cos x

Using the Pythagorean Identity: 1 + tan²x= sec²x

Substituting sec²x into the equation:

(1 - tan²x)/(sec²x) = cos x

Simplifying the equation:

sec²x - tan²x = cos x

Substituting sin² x with 1 - cos² x (from the Pythagorean Identity: sin² x + cos² x = 1):

cos² x + 4 = 4 + cos² x

The equation simplifies to 4 = 4, which is always true.

Therefore, the solution to the equation (1 - tan² x)/(1 + tan² x) = cos x on the domain 0 < x ≤ 2πis all values of x in the domain 0 < x ≤ 2π.

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Given that the resistance remains constant, if the voltage decreases to one-third of its original amount, the resulting current in the circuit is 0.4A

Ohm’s law states that the potential difference between two points is directly proportional to the current flowing through the resistance.

It is expressed as;

V = IR

Where V is the voltage or potential difference, potential difference, I is the current and R is the resistance.

Given that;

Initially, A circuit has a current I = 1.2A

V = IR

R = V/I

R = V/1.2A ...... let this be equation 1

Next, voltage decreases to one-third of its original amount while the resistance remains constant.

Meaning Voltage = 1/3 of V = V/3

Hence;

V = IR

V/3 = IR

From equation 1 ( R = V/1.2A )

V/3 = I × V/1.2A

V/3 = IV/1.2A

We cross multiply

V1.2A = 3IV

I = V1.2A / 3V

I = 1.2A / 3

I = 0.4A

Therefore, given that the resistance remains constant, if the voltage decreases to one-third of its original amount, the resulting current in the circuit is 0.4A

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Answer:

0.4 A

Step-by-step explanation:

When resistance is constant, current is proportional to voltage. When 1/3 the voltage is applied, 1/3 the current will result. (1/3)* (1.2 A) = 0.4 A The resulting current will be 0.4 A.

Answer:

2

Step-by-step explanation:

The average rate of change of h(x) in the closed interval [ a, b ] is

\(\frac{f(b) - f(a)}{b-a}\)

Here [ a, b ] = [ - 2, 4 ] , then

f(b) = f(4) = - (4)² + 4(4) + 12 = - 16 + 16 + 12 = 12

f(a) = f(- 2) = - (- 2)² + 4(- 2) + 12 = - 4 - 8 + 12 = 0

Then

average rate of change = \(\frac{12-0}{4-(-2)}\) = \(\frac{12}{6}\) = 2

Answer:

a or c Im not sure

Step-by-step explanation:

I think b though

The line which represents the speed as 10 feet per second is line B thus none of the given options are correct.

A graph is a diametrical representation of any function between the dependent and independent variables.

For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.

As per the given,

Loren is running at speed of 10 feet per second.

Speed = distance covered/time taken

10 = distance covered/time taken

In line B, the ratio of distance covered/time taken is 10.

Thus, line B will be correct.

Hence "The line which represents the speed as 10 feet per second is line B thus none of the given options are correct".

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For Scott

For Spock

So The difference between them is just algebraic subtraction of their positions

The Interquartile Range (IQR) rule is a commonly used quantitative rule to determine univariate outliers and deleting a case may be justified if it is a result of a measurement error, data entry error, or if it significantly skews the results.

The Interquartile Range (IQR) rule is a commonly used method for identifying outliers in a univariate data set. It is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1). Outliers are considered to be any values that fall outside of the range Q1 - 1.5 * IQR to Q3 + 1.5 * IQR. This range encompasses approximately 75% of the data, with outliers being any values that fall outside of this range.

In some cases, deleting a case or participant may be justified if it is a result of a measurement error, data entry error, or if it significantly skews the results.

This decision should be made carefully and only after careful consideration of the implications, as removing data can affect the validity of the results and the conclusions that can be drawn from the analysis. In some cases, it may be better to keep the outlier and consider it a potential error or to conduct further analysis to determine if there is a valid reason for the outlier.

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Given:

Height of the Statue of Liberty = 305 feet

Angle of elevation = 9 degrees

To find:

The between the tourist and the Statue of Liberty.

Solution:

Using the given information, draw a figure as shown below.

In a right triangle,

\(\tan \theta=\dfrac{Perpendicular}{Base}\)

In the triangle ABC,

\(\tan 9^\circ=\dfrac{305}{x}\)

\(x=\dfrac{305}{\tan 9^\circ}\)

\(x=1925.6942\)

\(x\approx 1926\)

Therefore, the tourist is standing 1926 feet from the Statue of Liberty.

Answer:its 5

Step-by-step explanation: cuz

To fill the rectangular prism we need 1 cube.

To find the number of cubes needed to fill the rectangular prism, we can calculate the volume of the prism and divide it by the volume of a single cube.

The volume of the rectangular prism is given by the formula:

Volume = Length × Width × Height

Substituting the given values:

Volume = 8 in. × 4 in. × 21 in.

Volume = 672 in³

The volume of a cube is given by the formula:

Volume = Edge Length³

Substituting the given edge length:

Volume of a cube = (14 in.)³

Volume of a cube = 2744 in³

Now, we can divide the volume of the prism by the volume of a single cube to find the number of cubes needed:

Number of cubes = Volume of prism / Volume of a single cube

Number of cubes = 672 in³ / 2744 in³

Calculating this division gives:

Number of cubes ≈ 0.245

Since we cannot have a fraction of a cube, we need to round up to the nearest whole number. Therefore, we would need 1 cube to fill the rectangular prism.

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\(Factor out  {b}^{4} \)

\( \sqrt{30( {b}^{4} b)} \)

\(Rewrite \: {b}^{4} as  {b}^{2} {)}^{2} \)

\( \sqrt{30(( {b}^{2} {)}^{2} b)} \)

\(Reorder 30 and  {b}^{2} {)}^{2} \)

Add parentheses

\( \sqrt{( {b}^{2} {)}^{2}.(30b) } \)

Pull terms out from under the radical.

\( {b}^{2} \sqrt{30b} \)

Answer:

80 pages

Step-by-step explanation:

We can think of this as 80% of the book is 64 pages

.8x = 64

x=80

The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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Answer:

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

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

The validity of measurement or data refers to the accuracy of the measurement instrument or data-acquisition tool. The answer is option(e).

The constructive nature of perception is best described as the influence of expectations on sense-perception. The answer is option(a).

1) The validity of measurement or data refers to the accuracy of the measurement instrument or data-acquisition tool. It is a basic assessment of the instrument's accuracy, including whether it can properly and appropriately evaluate what it was intended to evaluate.

2) Our experiences can affect how we interpret sensory data, causing us to see things that aren't there or failing to see things that are. As a result, perception is a two-way street in which sensory input is combined with prior experiences to create our understanding of the world around us.

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The results obtained using the algebraic approach and the matrix approach should be the same. Both methods are mathematically equivalent and provide the most probable values of A and B that minimize the sum of squared weighted residuals.

To solve the system of equations using the weighted least squares method, we need to minimize the sum of the squared weighted residuals. Let's solve the problem using both the algebraic approach and matrices.

Algebraic Approach:

We have the following equations:

A + 2B = 10.50 + V1 ... (1)

2A - 3B = 5.55 + V2 ... (2)

2A - B = -10.50 + V3 ... (3)

To minimize the sum of squared weighted residuals, we square each equation and multiply them by their respective weights:

\(2^2 * (A + 2B - 10.50 - V1)^2\)

\(3^2 * (2A - 3B - 5.55 - V2)^2\\1^2 * (2A - B + 10.50 + V3)^2\)

Expanding and simplifying these equations, we get:

\(4(A^2 + 4B^2 + 10.50^2 + V1^2 + 2AB - 21A - 42B + 21V1)\\9(4A^2 + 9B^2 + 5.55^2 + V2^2 + 12AB - 33A + 16.65B - 11.1V2)\\(A^2 + B^2 + 10.50^2 + V3^2 + 2AB + 21A - 21B + 21V3)\\\)

Now, let's sum up these equations:

\(4(A^2 + 4B^2 + 10.50^2 + V1^2 + 2AB - 21A - 42B + 21V1) +\\9(4A^2 + 9B^2 + 5.55^2 + V2^2 + 12AB - 33A + 16.65B - 11.1V2) +\\(A^2 + B^2 + 10.50^2 + V3^2 + 2AB + 21A - 21B + 21V3)\int\limits^a_b {x} \, dx\)

Simplifying further, we obtain:

\(14A^2 + 31B^2 + 1113 + 14V1^2 + 33V2^2 + 14V3^2 + 14AB - 231A - 246B + 21V1 - 11.1V2 + 21V3 = 0\)

Now, we have a single equation with two unknowns, A and B. We can use various methods, such as substitution or elimination, to solve for A and B. Once the values of A and B are determined, we can substitute them back into the original equations to find the most probable values of A and B.

Matrix Approach:

We can rewrite the system of equations in matrix form as follows:

| 1 2 | | A | | 10.50 + V1 |

| 2 -3 | | B | = | 5.55 + V2 |

| 2 -1 | | -10.50 + V3 |

Let's denote the coefficient matrix as X, the variable matrix as Y, and the constant matrix as Z. Then the equation becomes:

X * Y = Z

To solve for Y, we can multiply both sides of the equation by the inverse of X:

X^(-1) * (X * Y) = X^(-1) * Z

Y = X^(-1) * Z

By calculating the inverse of X and multiplying it by Z, we can find the values of A and B.

Comparing Results:

The results obtained using the algebraic approach and the matrix approach should be the same. Both methods are mathematically equivalent and provide the most probable values of A and B that minimize the sum of squared weighted residuals.

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Answer: So each ounce of specialty oil cost about 0.95

Step-by-step explanation:

Answer:

The second answer is correct.

Step-by-step explanation:

1 quart = 0.95 litres

15 quarts = 15 quarts * 0.95 litres/quart, which is the second answer.

Let x = 0.263263263…

Then 1000x = 263.263263263…

Subtracting x gives

1000x - x = 263.263263263… - 0.263263263…

999x = 263

x = 263/999