Find the distance between points M(6,16) and z (-1,14) to the nearest tenth

Answer: Answer: A dilation factor of 1 over 2

Step-by-step explanation:

The smaller polygon is half the size of the original polygon

Answer:

Dilation by a scale factor of fraction 1 over 2 followed by reflection about the y-axis

Step-by-step explanation:

x²/21 + y²/25 = 1 is the equation of the ellipse

Given: the length of the major axis = 10 and foci = (0, ± 2)

Since the foci are on the y-axis, the major axis will be along the y-axis. Thus, the equation of the ellipse is:

x²/b² + y²/a² = 1

Since the length of the major axis = 2a. Thus:

2a = 10

a = 10/2 = 5

a² = 5² = 25

c = 2

c² = a² - b²

2² = 5² - b²

4 = 25 - b²

b² = 25 - 4 = 21

Substitute a² = 25 and b² = 21 into the equation:

x²/b² + y²/a² = 1

x²/21 + y²/25 = 1

Therefore,  the equation of the ellipse is x²/21 + y²/25 = 1

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Answer:

No, a triangle cannot be created with these measurement.

Step-by-step explanation:

It must follow these rules:

a + b > c

b + c > a

a + c > b

Answer:

0.6

Explanation:

There are four forces on the box:

Weight force mg pulling down,

Normal force N pushing up,

Tension force T pulling 30° above the horizontal,

and friction force Nμ pushing to the left.

Sum of the forces in the y direction:

∑F = ma

N + T sin 30° − mg = 0

N = mg − T sin 30°

Sum of forces in the x direction:

∑F = ma

T cos 30° − Nμ = 0

Nμ = T cos 30°

μ = T cos 30° / N

μ = T cos 30° / (mg − T sin 30°)

Plug in values:

μ = (250 N) cos 30° / ((50 kg) (9.8 m/s²) − (250 N) sin 30°)

μ = 0.59

Rounded to one significant figure, the coefficient of friction is 0.6.

This value represents the present worth below which the probability is 0.5, indicating a negative present worth.

To estimate the probability that the present worth is negative using the NORM.INV function in Excel,

we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.

The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).

Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),

where t is the year. We then sum up these present values for each year.

We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.

Since we have a mean and standard deviation for the present worth,

we can calculate the corresponding probability of a negative present worth using NORM.INV.

This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,

we can estimate the probability that the present worth is negative based on the given data and assumptions.

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Answer:

D

Step-by-step explanation:

8 divided by 3 = 8/3

Answer: \(84\ mm^2\)

Step-by-step explanation:

Given

The long side of a triangle is 27 mm

The length of the base is 14 mm

height of the triangle is 12 mm

The area of a triangle is given by

\(\Rightarrow \dfrac{1}{2}\times \text{base}\times \text{height}\)

Insert the values

\(\Rightarrow \dfrac{1}{2}\times 14\times 12\\\\\Rightarrow 84\ mm^2\)

Thus, the area of the triangle is \(84\ mm^2\)

the given expression is'

y = 13x - 5

compare this equation with the standard equation

y = mx + c

here m is slope

so m = 13

thus, the slope of the equation is m = 13

Using Stokes’ Theorem to evaluate ∫ ⃑∙⃑ ,The value of ∫ ⃑∙⃑ is π.

Let S be the part of the surface z=y² that lies within the cylinder x²+y²=2, with upward orientation. Use Stoke 's theorem to evaluate ∫(C) F·dr, where F(x,y,z)=⟨-2yz,y,3x⟩ and C is the boundary curve of S.

Stoke's theorem states that the line integral of a vector field around a closed curve is equal to the surface integral of the curl of the vector field over the surface bounded by the curve.

∫(C) F·dr=∬(S) curl(F)·dS.For F(x,y,z)=⟨-2yz,y,3x⟩, curl(F)=⟨0,-3,-2y⟩.∬(S) curl(F)·dS=∬(D) curl(F)(r(u,v))·N(r(u,v)) dAwhere D is the projection of S onto the xy plane and N(r(u,v)) is the unit normal vector to S. First, we need to determine the boundary curve of S.

The cylinder x²+y²=2 can be parameterized by x=√2 cos(t) and y=√2 sin(t), 0≤t≤2π. The surface z=y² can be parameterized by r(x,y)=⟨x,y,y²⟩. Then the boundary curve of S is C: r(t)=⟨√2 cos(t), √2 sin(t), 2⟩, 0≤t≤2π. r_x=<-√2 sin(t), √2 cos(t), 0>, r_y=<0,0,1>.So, N(r(u,v))=r_x x r_y=⟨-√2 cos(t), -√2 sin(t), -√2⟩.

Since curl(F) = ⟨0,-3,-2y⟩,curl(F)(r(t)) = ⟨0,-3,-2(2 sin(t))⟩ = ⟨0,-3,-4sin(t)⟩.Now we have ∬(S) curl(F)·dS=∬(D) curl(F)(r(u,v))·N(r(u,v)) dA=∫₀²π ∫₀√2 ⟨0,-3,-4sin(t)⟩ · ⟨-√2 cos(t), -√2 sin(t), -√2⟩ dA=12π∫₀²π(3cos(t)+4sin²(t))dt=12π(3(0)+2)=π.The value of ∫ ⃑∙⃑ is π.

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Answer:

f(x)=1.5cos(16πx)+1.5

(Question on a Quiz was correct)

The trigonometric equation is f ( x ) = 1.5cos ( 16πx ) + 1.5 , when x = 3 feet , the height of the nail from the ground is 3 feet

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the trigonometric equation be represented as A

Now , the value of A is

f ( x ) = 1.5cos ( 16πx ) + 1.5

Let the diameter of the tire be x

Let the height of the nail from ground be f ( x )

On simplifying , we get

when x = 3 feet

f ( 3 ) = 1.5 cos ( 16π ( 3 ) ) + 1.5

f ( 3 ) = 1.5 cos ( 48π ) + 1.5

From the trigonometric relation cos ( nπ ) = 1

f ( 3 ) = 1.5 + 1.5 = 3 feet

Hence , the height of the nail from the ground is given by the equation with f ( x ) = 1.5cos ( 16πx ) + 1.5

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Answer:

A=12

B=2

C=11

Step-by-step explanation:

use M4th W4y to use it

The dimensions of the vegetable patch are 8 meters by 12 meters or 12 meters by 8 meters.

Let's assume the length of the vegetable patch is L and the width is W.

Given, the perimeter of the rectangular vegetable patch = 40 meters.

Perimeter = 2(L+W) = 40

Simplifying the above equation, we get

L+W = 20 (Equation 1)

Also, given that the area of the vegetable patch = 64 square meters.

Area = L*W = 64

From Equation 1, we can write W = 20-L

Substituting W in terms of L in the area equation, we get

L*(20-L) = 64

Expanding the above equation, we get

-L^2 + 20L - 64 = 0

Solving the quadratic equation, we get two possible values for L.

L = 8 or L = 12

If L = 8, then W = 20 - L = 12

If L = 12, then W = 20 - L = 8

Therefore, the dimensions of the vegetable patch are 8 meters by 12 meters or 12 meters by 8 meters.

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The equation that can be used to find x, the lesser number, is

(y - 8) * y = 240. And the two numbers can be 12 and 20 or

-12 and -20.

Let's assume the first number is x and the second number is y. According to the given information, the product of the two numbers is 240, so we have the equation xy = 240.

Additionally, it is stated that the first number is 8 less than the second number. This can be expressed as x = y - 8.

To find the equation that can be used to solve for x, we substitute the value of x from the second equation into the first equation:

(y - 8) * y = 240

This equation represents the relationship between the two numbers, where y is the greater number and y - 8 is the lesser number. By solving this equation, we can find the value of y and then calculate x as y - 8.

Now, let's solve the equation:

y² - 8y = 240

Rearranging the equation:

y² - 8y - 240 = 0

To solve this quadratic equation, we can factorize or use the quadratic formula. Factoring the equation, we have:

(y - 20)(y + 12) = 0

Setting each factor equal to zero, we have:

y - 20 = 0 or y + 12 = 0

Solving for y, we get:

y = 20 or y = -12

Since the first number (x) is 8 less than the second number (y), we have:

x = y - 8

Substituting the values of y, we get:

x = 20 - 8 or x = -12 - 8

Simplifying, we have:

x = 12 or x = -20

Therefore, the lesser number (x) can be either 12 or -20, depending on the context of the problem.

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The required  numbers is x=12 and y=24−x=24−12=12 i.e.(12,12).

What is differentiation ?

In math, isolation is one of the two important generalities piecemeal from integration. Isolation is a system of chancing the outgrowth of a function. Isolation is a process, in Maths, where we find the immediate rate of change in function grounded on one of its variables. The most common illustration is the rate change of relegation with respect to time, called haste. The contrary of chancing a outgrowth isanti-differentiation.

still, also the rate of change of x with respect to y is given by dy/ dx, If x is a variable and y is another variable. This is the general expression of outgrowth of a function and is represented as f'( x) = dy/ dx, where y = f( x) is any function.

Let the two number is x and y

According to given question.

Sum of two number =24

x+y=24

Then, y=24−x.......(1)

Again, product

 P=maximum=x × y

P=x(24−x 2)

P=24x−24x^2  .......(2)

We know that,

For maximum value

dP/dx =0

Now differentiating equation (2) with respect to x and we get,

dP/dx  =24−2x

⇒ 24−2x=0

⇒ 2x=24

⇒x=12

Again, differentiating equation (2) with respect to x and we get,

\(\frac{d^2p}{dx^2} = -2 < 0\)

Then,P is minimum at point x=12

Hence, the required  numbers is x=12 and y=24−x=24−12=12 i.e.(12,12)

This is the solution.

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Answer:

8 of 24 students are boys

the remaining 16 students are girls

the ratio of girls to boys is 16:8 or 2:1, meaning that there are 2 girls for every one boy

Answer:

g=118°

h=62°

k=98°

m=82°

Step-by-step explanation:

g is vertically opposite to 118° so they are equal

h and 118 are on a straight line

Same for k and m

The experimental probability of an odd number other than 9 being generated is 38%.

For the stated question-

Other odd numbers outside nine are as follows: 72 - 15 = 57

Probability =  (number of odd numbers except nine)]/(total number)

Probability = 57/150

Probability = 0.38.

Thus, the experimental probability of an odd number other than 9 being generated is 38%.

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the test statistic z is 1.7

What is test statistic?

A test statistic may be a datum employed in applied math hypothesis testing. A hypothesis take a look at is often laid out in terms of a test statistic, thought of as a numerical outline of a data-set that reduces the info to at least one worth that may be wont to perform the hypothesis test.

Main body:

Calculate the test statistic using the formula:

z= \(p-p'\)/\(\frac{p'(p-p')}{n}\)

where:

p = sample proportion,

n = sample size, and

Po =  population proportion under the null hypothesis

Sample size = 34 websites = n

Sample proportion = 0.20 = p'

z = (0.3 - 0.2)/ (0.2*0.1)/34

z = 0.1 *34/0.02

z = 1.7

Hence value of test statistic z is 1.7

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The required result of the sliding filament model given below.

The mechanism by which muscles contract is described by the sliding filament model. Actin and myosin myofilaments move over one another as a result of a cycle of repeated occurrences, constricting the sarcomere and creating tension in the muscle.

The A band is the middle, darkly pigmented area of the sarcomere that runs the entire length of the thick filaments. The portion of the thin filaments that cross over the thick filaments is also included. The I band is formed by the remaining thin filaments within the sarcomere but not by any thick filaments. Each A band has a narrow region in the middle called the H zone, which is made up entirely of dense filaments.

Myosin heads pull the thin filaments in the direction of the M line during muscle contraction. Because of this, the thin filaments glide inward, allowing their ends to overlap and connect at the sarcomere's core. The I band and H zone become smaller as a result.

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The triangle ABC and XZY are proved to be congruent by SAS.

Congruence of triangles: Two triangles are supposed to be harmonious assuming each of the three comparing sides are equivalent and every one of the three relating angle are equivalent in measure. These triangles can be slides, pivoted, flipped and went to be seemed to be indistinguishable.

By the rule of SAS which means, Two sides are equal thhen the angle between the two sides is also equal (SAS: side, angle, side)

BC=YZ

AC=XZ

∠ACB=∠XZY

By SAS ΔABC≅ΔXYZ

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Answer:

c

Step-by-step explanation:

Answer: median

I say this as the mean would be too off due to the one outlier (it's best used when there are multiple outliers), and the range wouldn't make sense as a mid-measurement.

Answer: A

Step-by-step explanation:

Square root of 35 is 5.9161

The median of the list of numbers is 4

The numbers are given as:

3, 5, 2, 10, 6, 3, 7, 3

Sort the numbers in ascending order

2, 3, 3, 3, 5, 6, 7, 10

The median is the middle number.

The middle numbers in the above data are 3 and 5

So, the median is:

Median =(3 + 5)/2

Evaluate

Median =4

Hence, the median of the list of numbers is 4

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At a 5% level of significance, we reject the null hypothesis and conclude that there is evidence to support the claim that less than 40% of the houses built in the city this year have certified energy-efficient windows.

1. Given data:

 Null hypothesis (H0): p >= 0.4 (proportion of houses with energy-efficient windows)

  Alternative hypothesis (H1): p < 0.4

  P-value of the test (P) = 0.037

  Level of significance (α) = 0.05

2. Since the P-value is less than the significance level, we reject the null hypothesis.

3. Interpretation:

  At a 5% level of significance, there is sufficient evidence to suggest that the real estate agent's claim, that less than 40% of the houses built this year have certified energy-efficient windows, is supported by the sample data.

Bonus:

1. Type I or Type II error:

  In this context, a Type I error is possible. It occurs when we reject the null hypothesis (H0) when it is actually true. It means that we conclude there is evidence for the claim that less than 40% of the houses have energy-efficient windows, but in reality, the true proportion is greater than or equal to 40%.

2. Consequence of Type I error:

  If a Type I error is made, it could lead to incorrect decisions or conclusions, such as implementing costly measures to increase the energy efficiency of houses unnecessarily. It is important to control the probability of Type I errors by choosing an appropriate level of significance and interpreting the results cautiously.

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Step-by-step explanation:

Use z-score table to find the z-score that corresponds to .7000   ( 70%)

approx   .525   s.d.  above the mean

  .525  * 10 =  5.25  points above 100   = 105.25

Step-by-step explanation:

I think it will be right 17.3

Answer:

\(8.7m^2 + 2m + 3.6\)

Step-by-step explanation:

I am assuming that you mean:

\(7.7m^2 + 5.5 + 7m -1.9 - 5m + m^2\)

==================================

We will simplify the expression by combining like terms.

\(7.7m^2 + 5.5 + 7m -1.9 - 5m + m^2\\\rule{160}{0.5}\\\\7.7m^2 + m^2 + 7m - 5m + 5.5 -1.9 \leftarrow \text{Rearrange the terms so all like terms are grouped together.} \\\\\boxed{8.7m^2 + 2m + 3.6}\leftarrow \text{Simplify}\)

==================================

Hope this helps!

The answer to the system of equations is (-7/11, 23/11), which stands for the intersection of the two lines.

It has one or more variables, and based on the values of the variables, it can either be true or false. Equations are frequently employed in a wide range of mathematical applications, from straightforward algebraic equations to more intricate differential equations used in calculus and physics. Equations are used to depict relationships between various mathematical objects or values. An essential part of addressing algebraic problems is to solve equations to determine the values of the variables that make the equation true.

given

We can solve one equation for one variable and then insert the expression into the second equation to apply the substitution method. For instance, we can resolve the first equation for y as follows:

y = 2x + 6

After that, we may enter the following expression in place of y in the second equation:

2x + 6 = -9x - 1

Then, we may find x:

11x = -7

x = -7/11

We may use one of the original equations to obtain the value of y once we have determined the value of x:

y = 2(-7/11) + 6 = 23/11

The answer to the system of equations is (-7/11, 23/11), which stands for the intersection of the two lines.

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Answer: Prime Numbers

Using partial derivatives the value of ∂z/∂x and ∂z/∂y at the points (3, 46, 2) and (3, 46, −2), where z is defined as the implicit equation \(z^4\) + z², x² − y − 6 = 0 is -1/5 and 1 respectively.

To calculate the partial derivatives ∂z/∂x and ∂z/∂y, we first need to differentiate the equation \(z^4\) + z², x² - y - 6 = 0 implicitly with respect to x and y, holding z constant.

Differentiating with respect to x, we get:

4z³ × ∂z/∂x + 2zx² + 2z²x × ∂z/∂x = 0

Simplifying, we get:

∂z/∂x = (-2zx²) / (4z³ + 2z²x)

Similarly, differentiating with respect to y, we get:

-1 + ∂z/∂y = 0

Simplifying, we get:

∂z/∂y = 1

Now, we can substitute the given points (3, 46, 2) and (3, 46, -2) into these formulas to get the partial derivatives at those points.

At (3, 46, 2):

z = \((6 - 81)^{(1/4)}\) = -3

∂z/∂x = (-2 × 3 × 3²) / (4 × (-3)³ + 2 × (-3)² × 3) = -18/54 = -1/3

∂z/∂y = 1

At (3, 46, -2):

z = \((6 + 81)^{(1/4)}\) = 3

∂z/∂x = (-2 × 3 × 3²) / (4 × 3³ + 2 × 3² × 3) = -18/90 = -1/5

∂z/∂y = 1

Therefore, at point (3, 46, 2), ∂z/∂x = -1/3 and ∂z/∂y = 1, and at point (3, 46, -2), ∂z/∂x = -1/5 and ∂z/∂y = 1.

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A positive y-intercept means that the line crosses the y-axis above the origin, and a negative y-intercept means that the line crosses below the origin. Arbitrary lines can be defined simply by changing the values ​​of m and b.

Slope Intercept:

The slope intercept of the straight line is used to find the equation of the straight line. The slope intercept formula requires knowing the slope of the line and the intersection of the line with the y-axis. Consider a line with slope 'm' and y-intercept 'b'. The slope-intercept shape formula for a straight line with slopes 'm' and 'b' as y-intercept is given as y = mx + b.

Positive Intercept:

A positive slope refers to a line that is slanted and slopes upward when viewed from left to right. The positive slope of a straight line can be calculated using the formula m = (y2 - y1)/(x2 - x1) = Tanθ = f'(x) = dy/dx. A positive slope means that the two quantities represented along the two axes of the coordinate system increase or decrease simultaneously. A line with a positive slope is a positive value for the ratio of climb to run. A straight line with a positive slope makes an acute angle with the positive x-axis.

                    Positive slope (m) = +slope/run = +Δy/Δx

Negative Intercept:

Negative slope means that the coordinates of the two given points are negatively related. A line with a negative slope has m < 0, and the angle θ it makes with the positive x-axis is obtuse θ, such that 90° < θ < 180°. The slope-to-run ratio of the negative slope line is negative. where slope is the change in y value, denoted by Δy, and run is the change in x value, denoted by Δx.

                          Negative slope = -rise/run = -Δy/Δx

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