Which relationship would most likely be casual? Select two options a positive correlation between the number of homework assignments completed and the grade of the exam

The distance at that point from the helicopter to the object is 7km

To determine the value, we need to know the different trigonometric identities.

These identities are listed thus;

From the information given, we have that the;

The angle at the point of the object is expressed as;

180 - (64 + 58)

add the values, we have;

180 - (122)

Now, subtract the values, we get;

58 degrees

Since, the angle measure is equal , then, we have that;

The distance = 7km

Hence, the distance is 7km

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50 to 41

this is

decrease in 18 %

answer: decrease by 18%

Answer:

\(\huge\boxed{\bf\: \frac{93}{20}=4.65}\)

Step-by-step explanation:

\(3 \frac { 1 } { 4 } + 1 \frac { 2 } { 5 }\)

Now,

\(3 \frac { 1 } { 4 } \\= \frac{4 * 3+1}{4}\\= \frac{13}{4}\)

Then,

\(1 \frac { 2 } { 5 }\\= \frac{1* 5+2}{5} \\= \frac{7}{5}\)

So,

\(3 \frac { 1 } { 4 } + 1 \frac { 2 } { 5 }\\= \frac{13}{4}+\frac{7}{5}\\ \\\mathrm{LCM = 20}\\\\= \frac{65}{20}+\frac{28}{20} \\=\boxed{\bf\: \frac{93}{20}=4.65}\)

\(\rule{150pt}{2pt}\)

The function f(x) = \(5(3)^x+3\) is continuous everywhere on its domain, which is (-∞, ∞).

The function f(x) =  \(5(3)^x+3\)   is continuous everywhere because it is an exponential function with a base of 3, which is a positive number. Exponential functions with positive bases are continuous over their entire domain.

To see why, consider the definition of continuity: a function f(x) is continuous at a point x = c if the limit of f(x) as x approaches c exists and is equal to f(c). For an exponential function with a positive base, as x approaches c, the function values either increase to infinity or decrease to 0, depending on whether the exponent is positive or negative, respectively. In either case, the limit exists and is equal to the function value at c, so the function is continuous at c. Since this holds for all points in the domain, the function is continuous everywhere it is defined.

The domain of f(x) is all real numbers, so the function is continuous on the interval (-infinity, infinity), or in interval notation, the domain is (-∞, ∞).

In summary, the function f(x) = 5(3)ˣ +3 is continuous everywhere on its domain, which is (-∞, ∞).

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Answer: No, it’s not a statistical question

Step-by-step explanation:this question only pertains to one person and it not something that can be represented as a statistic.

The square root of the decimal number is √0.0016 = 0.04

Here we can find the square root of the decimal number:

N = 0.0016

Notice that we can write this number as:

0.0016 = 16*10⁻⁴

Now we can take the square root of that, so we will get:

√(16*10⁻⁴)

We can distribute the square root to get:

√16*√10⁻⁴

These two are easy, we will get:

√16*√10⁻⁴ = 4*10⁻² = 0.04

That is the square root.

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Answer:

negative five (-5) is the answer

The population of the city will be approximately 44,968 people five years from now.

To calculate the population five years from now, we need to determine the population growth over that period. The city's population is increasing at a rate of 2.4% per year, which means the population is growing by 2.4% of its current value each year.

First, let's find the population growth for one year:

Population growth for one year = 2.4% of 40,000 = 0.024 * 40,000 = 960 people

Next, we can calculate the population after five years:

Population after five years = 40,000 + (Population growth for one year * 5)

                        = 40,000 + (960 * 5)

                        = 40,000 + 4,800

                        = 44,800

Rounding the population to the nearest person, the estimated population five years from now is approximately 44,968 people.

Note that the population growth calculation assumes a steady growth rate of 2.4% per year. In reality, population growth can be affected by various factors and may not follow a precise exponential pattern.

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The equation of the line will be given as y = -4x - (- 17/ 4).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given that:-

The equation of the line will be given as:-

y  -  y₁ = m ( x  -  x₁)

slope m will be calculated as:-

\(m =\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1+1}{\dfrac{-3}{4}+\dfrac{1}{4}}=-4\)

The equation will be:-

y  -  (1/4)  =  -4( x +  1 )

y  = -4x  -  (17/4)

Therefore the equation of the line will be given as y = -4x - (- 17/ 4).

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The Cartesian equation for the curve r^2 cos(2θ) = 16 can be determined using the relation between cartesian and polar coordinates.

The relation between  cartesian and polar coordinates is
x = r cos(θ)
y = r sin(θ)

First, note that r^2 = x^2 + y^2.

Now, we need to find cos(2θ). Using the double-angle formula, we have:

cos(2θ) = 2cos^2(θ) - 1 = 2(x^2/r^2) - 1

Now, substitute r^2 and cos(2θ) into the original equation:

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

Simplify the equation:

2x^2 - (x^2 + y^2) = 16
x^2 - y^2 = 16

Now we have the Cartesian equation for the curve:

x^2 - y^2 = 16.

This equation represents a hyperbola, as it has the general form of a hyperbola equation

(A^2 - B^2 = C^2, where A, B, and C are constants).

So, the Cartesian equation for the curve r^2 cos(2θ) = 16 is x^2 - y^2 = 16, and the curve is a hyperbola.

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Answer:

can u type out the question i cant see the photo i will help thou

Step-by-step explanation:

Answer:

29

-26

Step-by-step explanation:

the equation of f(x) is given. to find f(8) just apply 8 in the place of x in the equation

same method for f(-3) just apply -3 in place of x

Answer:

(x+9)² +(y+8)² = 73

Step-by-step explanation:

The standard form of equation of a circle is expressed as;

(x-a)² +(y-b)² = r²

(a,b) is the centre of the circle

r is the radius

Get the midpoint;

Given the coordinate (-1, -11) and (-17, -5).

a= x1+x2/2

b = y1+y2/2

a = -1-17/2

a = -18/2

a = -9

b =  -11 - 5/2

b = -16/2

b = -8

Get the diameter using the distance formula

d = √(y2-y1)² +(x2-x1)²

d = √(-5+11)² +(-17+1)²

d = √(6)² +(-16)²

d = √36+256

d = √292

r = d/2

r = √292/2

r² = 292/4

r² = 73

Get the equation

Recall rhat

(x-a)² +(y-b)² = r²

(x+9)² +(y+8)² = 73

Answer:

y=5x+10

Step-by-step explanation:

y-11=5(x+2)

y-11=5x+10

  +11      +11

y=5x+21

First, open Excel, then go for the Body Mass column. Second, In Excel, you can do this using the AVERAGE function: =AVERAGE(column_ range). Third, determine the upper limit of the interval by adding 20 to the mean. Forth, In Excel, use the COUNTIF function: =COUNTIF(column_ range, "<="&upper_ limit). Fifth, calculate the percentage of body mass.

Sixth, the percentage to 2 decimal places using Excel's ROUND function: =ROUND(percentage, 2)

To answer the question, we need to calculate the number of body masses that fall within the interval u + 20, where u is the mean body mass of the population.

First, we need to find the mean body mass. We can do this by using the AVERAGE function in Excel. Select the column with the body mass data and click on the Formulas tab. Click on the More Functions dropdown menu and select Statistical. Then, click on AVERAGE. Excel will automatically select the column with the body mass data and give you the mean value.

Next, we need to add 20 to the mean body mass to get the upper limit of the interval. We can do this by typing "=AVERAGE(B2:B152)+20" in a cell, where B2:B152 is the range of body mass data. This will give us the upper limit of the interval.

Now, we need to find the number of body masses that fall within this interval. We can do this by using the COUNTIF function in Excel. Type "=COUNTIF(B2:B152,"<="&upper limit)-COUNTIF(B2:B152,"<"&mean)" in a cell, where B2:B152 is the range of body mass data, the upper limit is the upper limit of the interval, and mean is the mean body mass. This will give us the number of body masses that fall within the interval u + 20.

To find the percentage of body masses that fall within this interval, we need to divide the number of body masses that fall within the interval by the total number of body masses and multiply by 100. We can do this by typing "= a number of body masses within interval/151*100" in a cell, where the number of body masses within the interval is the result of the COUNTIF function. This will give us the percentage of body masses that fall within the interval u + 20.

Therefore, the answer to the question is the percentage of body masses that fall within the interval u + 20, which we calculated using Excel.

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Step-by-step explanation:

Hey, there!!

Let's simply work with it,

The given coordinates are, P(-2,3) and Q(5,4).

Now, finding the P' and Q'.

Reflection on x- axis .

P(x,y)---------> P' (x,-y)

P (-2,3)----------> P'(-2,-3)

Now, let's find Q'

Reflection on y-axis.

Q(x,y)----------> Q'(-x,y)

Q(5,4)---------> Q'(-5,4)

Now, The points are P'(-2,-3) and Q'(-5,4)

By distance formulae,

\(P'Q' = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} } \)

Putting their values,

\(P'Q' = \sqrt{( { - 5 + 2)}^{2}( {4 + 3)}^{2} } \)

\(P'Q' = \sqrt{( { - 3)}^{2} + ( {7)}^{2} } \)

Simplifying them we get,

\(pq = \sqrt{58} \)

Therefore, the distance between P'and Q' is root under 58 units.

Hope it helps...

Answer:

4x+2

Step-by-step explanation:

I'm not sure what they mean by defining a variable but this question could be modeled through the following equation

4x+2 where x (the variable) is a book

a). The gradient of r/r^2 is (∇r)/r^2 = (∇r)/(x^2 + y^2 + z^2)

b). The gradient of r/r is (∇r)/r = (∇r)/|r|.

c). ∇r = ∂x/∂x i + ∂y/∂y j + ∂z/∂z k = i + j + k

d). The gradients of the given expressions are as follows: (∇r)/r^2 = (∇r)/(x^2 + y^2 + z^2), (∇r)/r = (∇r)/|r|, ∇r = i + j + k, and -∇r/r^3 = -∇r/(x^2 + y^2 + z^2)^3.

The gradient of a vector r is denoted by ∇r and is found by taking the partial derivatives of its components with respect to each coordinate. In this problem, the vector r is given as r = xi + yj + zk.

Let's calculate the gradients of the given expressions one by one:

(a) ∇r/r^2:

To find the gradient of r divided by r squared, we need to take the partial derivatives of each component of r and divide them by r squared. Thus, the gradient of r/r^2 is (∇r)/r^2 = (∇r)/(x^2 + y^2 + z^2).

(b) ∇r/r:

Similarly, to find the gradient of r divided by r, we need to take the partial derivatives of each component of r and divide them by r. Therefore, the gradient of r/r is (∇r)/r = (∇r)/|r|.

(c) ∇r:

The gradient of r itself is found by taking the partial derivatives of each component of r. Therefore, ∇r = ∂x/∂x i + ∂y/∂y j + ∂z/∂z k = i + j + k.

(d) -∇r/r^3:

To find the gradient of -r divided by r cubed, we multiply the gradient of r by -1 and divide it by r cubed. Thus, -∇r/r^3 = -∇r/(x^2 + y^2 + z^2)^3.

In summary, the gradients of the given expressions are as follows: (∇r)/r^2 = (∇r)/(x^2 + y^2 + z^2), (∇r)/r = (∇r)/|r|, ∇r = i + j + k, and -∇r/r^3 = -∇r/(x^2 + y^2 + z^2)^3.

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The child passes through 18π radians in the course of the carousel ride.

To determine the number of radians the child passes during the 6-minute ride on the carousel, we need to know the distance traveled in terms of radians.

Since there are 20 horses spaced evenly around the carousel, each horse is separated by an angle of 360/20 = 18 degrees or π/10 radians.

Therefore, during one rotation of the carousel, the child passes through 20π/10 = 2π radians. And since the carousel completes one rotation every 40 seconds, the angular velocity is 2π/40 = π/20 radians per second.

To find the total distance traveled in radians during a 6-minute ride, we need to multiply the angular velocity by the time elapsed.

6 minutes is equal to 360 seconds,

so the child passes through π/20 x 360 = 18π radians during the ride.

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Answer:

The order should be:

0.7, 0.73, 0.81, 0.9

Step-by-step explanation:

Answer:

Inequality is \(4x+3y\leq 87\)

Slope intercept form is \(y\leq 29-\frac{4}{3}x\)

Solutions are \((2,3)\,,\,(3,4)\)

Graph: attached to the question

Step-by-step explanation:

Given: Group dance numbers last 4 minutes and a solo performance lasts 3 minutes. The maximum duration for the recital is 87 minutes.

To find: inequality (in standard form) that describes the given situation, inequality in slope-intercept form, solutions for the inequality

To graph: the inequality

Solution:

x denotes the number of group dances on the program

y denotes the number of solo numbers on the program

Total duration of group dance numbers = \(4x\) minutes

Total duration of solo performance = \(3y\) minutes

According to question,

\(4x+3y\leq 87\)

Slope intercept form of equation is \(y\leq mx+c\) where m denotes slope of line and c denotes y-intercept of the line.

Slope intercept form of \(4x+3y\leq 87\) :

\(4x+3y\leq 87\\3y\leq 87-4x\\y\leq 29-\frac{4}{3}x\)

For \((x,y)=(2,3)\),

\(4(2)+3(3)\leq 87\\8+9\leq 87\\17\leq 87\,\,which\,\,is\,\,true\)

So, \((2,3)\) is a solution of the inequality.

For \((x,y)=(3,4)\),

\(4(3)+3(4)\leq 87\\12+12\leq 87\\24\leq 87\,\,which\,\,is\,\,true\)

So, \((3,4)\) is a solution of the inequality.

Graph: attached as image

Answer:

The area is 45 inches

Step-by-step explanation:

L×W=A

There are a total of 1,326 different ways to draw two cards from a standard 52-card deck, with the first card being a diamond and the second card being a king.

The formula for this type of problem is given by the combination formula, which is expressed as C(n,r). In this case, we want to determine the number of combinations of two cards from a standard 52-card deck, with the first card being a diamond and the second card being a king. Therefore, n = 52 and r = 2.

Using the combination formula, we can calculate the number of ways to draw two cards such that the first card is a diamond and the second card is a king as follows: C(52,2) = 1326. This means that there are a total of 1,326 different ways to draw two cards from a standard 52-card deck, with the first card being a diamond and the second card being a king.

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The volume of the ring-shaped solid that remains after drilling is 3961.73cm³.

The radius of the cylindrical drill is 5cm and the radius of the sphere is found to be 10cm.

After drilling,

The radius of the of the sphere will act as a hypotenuse to the triangle where the base is the radius of the cylinder and the perpendicular is the height of the cylinder.

So, we can say,

Height H of cylinder = √(10² - 5²)

Height H of cylinder = 8.66 cm.

The volume V of the ring shape remaining,

V = Volume of sphere - volume of cylinder

V = 4/3πR³ - 1/3πr²H

R is the radius of sphere and r is the radius of cylinder,

Putting values,

V = 4/3π(10)³ - 1/3π(5)²8.66

V = 3961.73 cm³.

So, the volume that remains is 3961.73cm³.

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Answer:

25/6

I don't really know how I got it, sorry I can't help with that

Answer:

The scores from Mrs. Rijo’s class are the closest to the class mean.

Step-by-step explanation:

Just took the test

Answer:

7m+8

Step-by-step explanation:

distributive prop then pemdas

Answer:

(x-6)²+(y+3)²=17²

Step-by-step explanation:

The equation of a circle with center (a,b) and radius r is given by the formula:

(x - a)² + (y - b)² = r²

In this case, the center of the circle is (6,-3), and it passes through the point (-9,5). To find the radius of the circle, we need to calculate the distance between the center and the point on the circle. Using the distance formula, we get:

r = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-9 - 6)² + (5 - (-3))²]

= √[225 + 64]

= √289

= 17

So, the radius of the circle is 17. Now we can plug in the values for the center and radius into the equation of a circle:

(x - 6)² + (y + 3)² = 17²

Answer:

32 feet

Step-by-step explanation:

The area of a rectangle is \(a = lw\), where the area equals the length times the width. Since we are given the area and the width, we can divide them to find the width, since it's the inverse operation.

⇒ 1152 ÷ 36 ≈ 32 feet