Solve the following:

The negative correlation coefficient of -0.73 between consumption of vitamin A and the cancer rate of a particular type of cancer suggests that as vitamin A consumption increases, the cancer rate tends to decrease.

A correlation coefficient measures the strength and direction of the linear relationship between two variables.

In this case, a correlation coefficient of -0.73 indicates a negative correlation between consumption of vitamin A and the cancer rate.

Interpreting this correlation, it can be inferred that there is an inverse relationship between the two variables. As consumption of vitamin A increases, the cancer rate tends to decrease.

However, it is important to note that correlation does not imply causation.

It would be incorrect to conclude that consuming more vitamin A causes this type of cancer. Correlation does not provide information about the direction of causality.

Other factors and confounding variables may be involved in the relationship between vitamin A consumption and cancer rate.

To establish a causal relationship, further research, such as experimental studies or controlled trials, would be necessary. These types of studies can help determine whether there is a causal link between vitamin A consumption and the occurrence of this particular cancer.

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A regular polyhedron is defined as a 3-dimensional shape whose faces are all regular polygons of equal size and shape, and whose vertices are connected by the same number of edges. A regular polyhedron is also known as a Platonic solid or Platonic solid.

The term "regular" is used to differentiate it from "irregular" polyhedra, which have faces of different shapes and sizes and which can be any combination of polygons. The five Platonic solids are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.

A regular polyhedron has a certain number of edges, faces, and vertices that are unique to it. The number of edges (E), vertices (V), and faces (F) of a regular polyhedron are related by the equation V - E + F = 2. This is known as Euler's formula for polyhedra.

For example, a cube has 6 faces, 8 vertices, and 12 edges. If we plug these values into Euler's formula, we get: V - E + F = 2 8 - 12 + 6 = 2 This confirms that a cube is a regular polyhedron.

In general, a regular polyhedron with n faces will have 2n edges, n vertices, and n/2 faces meeting at each vertex. This is because each face has n edges, and each edge is shared by 2 faces, so there are 2n edges in total.

At each vertex, n/2 faces meet, since each face shares 1/n of the vertex. This means that the angle between any two adjacent faces is 360/n degrees.

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The location of √ 7 on a number line between 2 and 3.

A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.

A number line is a long straight line with numbers marked at equal intervals. On a number line, we can argue that as we move to the right, the value of numbers increases. This signifies that the numbers on the right are more than those on the left.

A number line shows how numbers are related. It's a line with check marks next to each number. The numerals get smaller as you move left on the number line. The numbers grow larger as you move closer to the number line.

In this case, ✓7 is 2.65. This number can be found between 2 and 3. This should be the true statement since the options aren't given.

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The total number of cars both the student and the teacher made is 49

let

total cars = x

cars made by student = s

cars made by teacher = t

Total = student + teacher

x = s + t

s = 2/7x

So,

x = 2/7x + t

x - 2/7x = t

t = (7x - 2x) / 7

t = 5/7x

Similarly,

s = t - 21

s = 5/7x - 21

equate both s equation

2/7x = 5/7x - 21

2/7x - 5/7x = -21

(2x - 5x) / 7 = -21

- 3/7x = -21

x = -21 ÷ -3/7

= -21 × - 7/3

= (-21 × -7) / 3

= 147/3

x = 49

Therefore, the total number of cars both the student and the teacher made is 49

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Answer:

Megan would make five free throws and miss five.

Step-by-step explanation:

Answer:

The initial height of the candle is H = 15cm

The rate at which the candle burns is 2.5 cm per hour

Then after one hour, the height of the candle is:

h = 15cm - 2.5cm = 12.5cm

after two hours is:

h = 15cm - 2*2.5cm = 10cm

then, after t hours, the height of the candle is:

h = 15cm - (2.5cm/h)*t

now, the domain of h (or the range of the function) is:

h ∈ [0cm, 15cm]

when t = 0, h(0h) = 15cm

and the maximum value of t will be such that the candle is totally consumed:

h(t) = 0 = 15 - 2.5*t

t = 15/2.5 = 6

Then the domain of the function is:

t ∈ [0h, 6h]

The vertices of the image reflected across the line y = x are; P'(-4,-7), Q'(-8, -7), R'(-3, 3)

We are given the vertices of the triangle as;

P(-7,-4), Q(-7, -8), and R(3, -3)

Now, in transformations, there are different types such as;

Dilation

Reflection

Rotation

Translation

However, in this case we are dealing with reflection of triangle PQR.

Now, the transformation rule for reflection across the line y = x is;

(x, y) → (y, x)

Thus, applying the reflection transformation rule above to our triangle coordinates gives us;

P(-7,-4) → P'(-4, -7)

Q (-7, -8) → Q'(-8, -7)

R(3, -3) → R'(-3, 3)

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Answer:

63

Step-by-step explanation:

Set up the proportion

(6x+3)/17 = (8x - 1)/21                 Cross Multiply

21 * (6x + 3) = 17 (8x - 1)             Remove the brackets

126x + 63 = 136x - 17                 Subtract 126x from both sides

63 = 136x - 126x - 17                 Combine

63 = 10x - 17                              Add 17 to both sides

63 + 17 = 10x                             Combine the left

80        = 10 x                             Divide by 10

80/10 = x

x = 8

Now you want 8x - 1

8*8 - 1 = 63                

The measure of the differences of all observations from the mean, expressed as a single number is called the "standard deviation". It is a commonly used measure of the amount of variability or dispersion within a set of data.

The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences between each observation and the mean.

It is expressed in the same units as the data itself, and provides a way to understand how spread out the data is from the average or mean value.

A small standard deviation indicates that the data points tend to be close to the mean, while a large standard deviation indicates that the data points are more spread out.

The standard deviation can be used to compare the variability of different sets of data, and can also be used in statistical tests to determine if the difference between two sets of data is statistically significant.

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Answer: 20cm

Step-by-step explanation:

The perimeter of a rectangle can be calculated as 2(l+w)

2(6+4)

2(10)

20

Hope it helps, and if you want more info on perimeter, just ask <3

Answer:

20 cm

Step-by-step explanation:

Use folmula P=2(l+w)

Answer:

0.60922709536

Step-by-step explanation:

not sure if this is what you are looking for????

√6

im putting yall on folks

The hyperbola centered at the origin's equation that complies with the requirements is x²/9 - y²/25 = 1.

The hyperbola has a horizontal transverse axis because it has x-intercepts.

The equation for a hyperbola with a horizontal transverse axis has the following standard form:

(x - h)²/a² - (y - k)²/b² = 1.

There is a center at (h,k).

The vertices are separated by a distance of 2a.

a and b have values of;

2a = x₂ - x₁ = 3 - (-3) = 3 + 3 = 6 for "a," and a = 6/2 = 3 and b = 5.

The hyperbola's equation, with its center at the origin, that meets the requirements is;

(x - h)²/a² - (y - k)²/b² = 1,

or, (x - 0)²/3² - (y - 0)²/5² = 1,

or, x²/9 - y²/25 = 1.

As a result, the hyperbola's equation, centered at its origin, that fulfills the requirements is x²/9 - y²/25 = 1.

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The provided question is incomplete. The complete question is:

"Find the equation of the hyperbola centered at the origin that satisfies the given conditions: x-intercepts = +,-3 and asymptote at y=5/3x"

h(x) can also be expressed as f(x) - g(x) where f(x) = 3x and g(x) = x² - 3x.

What is function ?

A function is a mathematical rule or relationship between two sets of objects, often called the input and output, that assigns each input value exactly one output value. In other words, a function is a set of ordered pairs, where each input has only one output value.

For example, the function f(x) = 2x assigns to each value of x its double. If we put in x=1, the output is f(1) = 2(1) = 2. If we put in x=2, the output is f(2) = 2(2) = 4. Each input value has exactly one corresponding output value, which is the definition of a function.

Functions are often represented as graphs, with the input values on the x-axis and the output values on the y-axis. The graph of a function is a visual representation of the set of ordered pairs that define the function.

To express h(x) = 3x = x² as f - g, we need to find two functions f(x) and g(x) such that f(x) - g(x) = h(x).

One possible way to do this is to let f(x) = x² + 3x and g(x) = x². Then we have:

f(x) - g(x) = (x² + 3x) - x² = 3x = x² = h(x)

Therefore, h(x) can be expressed as f(x) - g(x) where f(x) = x² + 3x and g(x) = x².

Another possible way to do this is to let f(x) = 3x and g(x) = x² - 3x. Then we have:

f(x) - g(x) = 3x - (x² - 3x) = 6x - x² = h(x)

Therefore, h(x) can also be expressed as f(x) - g(x) where f(x) = 3x and g(x) = x² - 3x.

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The expressions that show the number of students for each activity are;

Note that this is a fraction problem.

We are given;

Total number of students in the middle school = x

A) From the given table, we can deduce that;

B: Now, the expression to show the students that like either drama or dance is;

(1/7)x + 26 + (1/7)x + 22

⇒(2/7)x + 48

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Full Question:

A middle school with x students ran a survey to determine the students' favorite activities. The table indicates the number of students who enjoy each activity. Answer parts A and B.

Table:

Activity:

Dance- 22 more than one-seventh of the students

Baseball- 24 fewer than four-sevenths of the students

Drama- 26 more than one-seventh of the students.

To find the angle of intersection between the helix and the sphere at each point, we need to find the values of t where the helix intersects the sphere and then calculate the angle between the tangent vector of the helix and the normal vector of the sphere at those points.

Let's start by finding the values of t where the helix intersects the sphere.

We have the equation of the sphere: \(x^2\)+\(y^2\) +\(z^2\) = 2.

Substituting the coordinates of the helix into the equation of the sphere, we get:

\((cos(πt/2))^2\) +\((sin(πt/2))^2\) +\(t^2\)= 2.

Simplifying the equation, we have:

\(cos^2(πt/2) + sin^2(πt/2) + t^2\) = 2.

Since\(cos^2(θ) + sin^2(θ)\)= 1 for any angle θ, we can simplify further:

1 +\(t^2\) = 2.

Solving for t, we find:

\(t^2\) = 1.

This gives us two possible values for t: t = 1 and t = -1.

Now, let's calculate the angle of intersection at each point.

At t = 1:

The point of intersection is r(1) = (cos(π/2), sin(π/2), 1) = (0, 1, 1).

To find the tangent vector of the helix at t = 1, we take the derivative:

r'(t) = (-π/2)sin(πt/2), (π/2)cos(πt/2), 1.

Plugging in t = 1, we get:

r'(1) = (-π/2)sin(π/2), (π/2)cos(π/2), 1 = (-π/2, 0, 1).

The normal vector of the sphere at the point of intersection can be found by taking the gradient of the sphere equation:

∇(\(x^2 + y^2 + z^2\)) = 2x, 2y, 2z.

Plugging in the coordinates of the point (0, 1, 1), we get:

∇(\(0^2 + 1^2 + 1^2\)) = (0, 2, 2).

To find the angle between the tangent vector and the normal vector, we can use the dot product:

θ = cos^(-1)((-π/2, 0, 1) · (0, 2, 2) / |(-π/2, 0, 1)|| (0, 2, 2)|).

Calculating the dot product and magnitudes, we have:

θ = cos^(-1)((-π/2)(0) + (0)(2) + (1)(2) / |(-π/2, 0, 1)|| (0, 2, 2)|).

θ = cos^(-1)(2 / sqrt(π^2/4 + 4)).

Using a calculator, we find:

θ ≈ 0.9 radians (rounded to one decimal place).

At t = -1:

The point of intersection is r(-1) = (cos(-π/2), sin(-π/2), -1) = (0, -1, -1).

To find the tangent vector of the helix at t = -1, we take the derivative:

r'(t) = (-π/2)sin(πt/2), (π/2)cos(π

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Answer:

For the first question, the slope is -3.

For the second question, the point is (-6,7)

Step-by-step explanation:

In point-slope form, to identify the slope, its the number that's before the parenthesis, which in this case, its -3.

In point-slope form, to identify the points, its the number that replaces y1 and x1, which in this case, its -7 and 6. However, in point-slope form, the numbers are the opposite of what they are. For an example, in this equation, -7 is negative, buts its point would actually be positive.

The number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

The number of calories that Darrell will burn in 1 minute while kayaking is obtained applying the proportions in the context of the problem.

For each input-output pair in the table, the constant of proportionality is of 4, hence the number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

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Answer:

944 cm²

Step-by-step explanation:

get the area of each side: 12*10+10*16+12*16= 472

2 sets of each side: 944

To determine the slope of a line is best to write the equation on the slope-intercept form.

The general structure of that form is

Where

m is the slope

b is the y-coordinate of the y-intercept

Then to determine the slope of the given equation you have to write it in terms of y

Pass the x-term to the other side

Divide both sides by 10

From this equation, we can determine that the slope corresponds to the coefficient that multiplies the x-term

The slope is m=-2

Given P(A/B) = .4, P(B) = .6 then P(A∩B) = .667 is False.

The formula for conditional probability is:

P(A/B) = P(A∩B) / P(B)

where,

P(A∩B) = probability of both A and B events occurring at the same time.

We have to find P(A∩B) so,

Substitute the values in the above formula

0.4 = P(A∩B) / 0.6

By moving 0.6 to the left side we get

P(A∩B) = 0.4 × 0.6 = 0.24

Thus, P(A∩B) ≠ 0.667

Hence P(A/B) = .4, P(B) = .6 then P(A∩B) = .667 is False.

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Here ya go.

Answer in picture

The correct answer is  you will get approximately £1.30 for one Australian dollar.

To find out how many British pounds you will get for one Australian dollar, we need to determine the exchange rate between the British pound and the Australian dollar.

Given that £1 = US$1.11316 and A$1 = US$0.8558, we can calculate the exchange rate between the British pound and the Australian dollar as follows:

£1 / (US$1.11316) = A$1 / (US$0.8558)

To find the value of £1 in Australian dollars, we can rearrange the equation:

£1 = (A$1 / (US$0.8558)) * (US$1.11316)

Calculating this expression, we get:

£1 ≈ (1 / 0.8558) * 1.11316 ≈ 1.2992

Therefore, you will get approximately £1.30 for one Australian dollar.

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∫dF=F(x,y)=12ax2+bxy+12ℓy2+c=0 is the exact ode.

Specifically, an exact equation is a differential equation that can be solved instantly without the aid of any specialized methods. If the result of a straightforward differentiation, a first-order differential equation (of one variable) is referred to as an exact differential or exact differential. The equation

P(x, y)dy/dx + Q(x, y) = 0,

or in the equivalent alternate notation

P(x, y)dy + Q(x, y)dx = 0,

is exact if

∂P(x, y)/∂x =  ∂Q(x, y)/∂y

In this instance, a function R(x, y) will exist whose partial x-derivative is Q and partial y-derivative is P, and whose equation R(x, y) = c (where c is constant) will implicitly establish a function y that will satisfy the initial differential equation.

An exact ODE is one where the equation can be written as  dF=0  for some  F(x,y). Expanding using chain rule, this means an equation of the form

∂1Fdx+∂2Fdy=0

Now if the second partials of  F  exist and are continuous, they must be equal due to Clairaut. So, given an equation

Mdx+Ndy=0

if we have

∂2M=∂1N

then there is an  F  such that

M=∂1F, N=∂2F

and hence that equation is exact, and the solution is simply

∫dF=0

We have

M=ax+by⇒∂2M=b

N=kx+ℓy⇒∂1N=k

so to be exact, we must have that  b=k .

Then, integrating  M  and  N , we have

F(x,y)=∫Mdx=12ax2+bxy+g(y)

F(x,y)=∫Ndy=bxy+12ℓy2+h(x)

and comparing these two, we can see that

∫dF=F(x,y)=12ax2+bxy+12ℓy2+c=0

is a solution to the equation for any  a,b,c,ℓ . You can solve for  y  by quadratic methods.

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The expected claim size is 950 and the variance is 125000/9.

The probability that a claim is no greater than 500 is 0.8, which means the probability of a claim being greater than 500 is 0.2. The claim sizes are uniformly distributed on (0; 500] and on (500; 1500].

Therefore, the probability of a claim being in the range of (0; 500] is 0.8/2 = 0.4 and the probability of a claim being in the range of (500; 1500] is 0.2/2 = 0.1.

The expected claim size is calculated as the weighted average of the claim sizes in each range, where the weight is the probability of a claim being in that range. Thus, the expected claim size is (0.4 x 250 + 0.1 x 1000) = 950.

The variance of the claim size is calculated as the weighted average of the squared deviations from the expected claim size, where the weight is the probability of a claim being in that range. Thus, the variance is (0.4 x (250 - 950)^2 + 0.1 x (1000 - 950)^2) = 125000/9.

Therefore, the expected claim size is 950 and the variance is 125000/9.

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Answer:

Blue car: 30.8 miles per galon

Red car: 27 miles per galon

Blue car can travel longer distances on one galon!

Step-by-step explanation:

Blue car:

38 1/2=77/2=38.5 miles

1 1/4=5/4=1.25 gasoline

38.5/1.25=30.8miles per galon

Red car:

21 3/5=108/5=21.6 miles

4/5=0.8 gasoline

21.6/0.8=27 miles per galon

__________

\( \: \)

Answer in the picture.

Answer:

9

Step-by-step explanation:

Answer:

5%

.35x = 2800

x = 8000

p(160,000)=8000

p=.05 = 5%

Step-by-step explanation:

Answer:

\((8+x)(8-x)\)

Step-by-step explanation:

We need to factorize \(64-x^{2}\)

We know that \(8^{2}=64\),  Hence we can replace 64  and we get

\(64-x^{2} =8^{2}-x^{2}\)

Using \(a^{2}-b^{2}=(a+b)(a-b)\) what we get is \((8+x)(8-x)\)

Hence \(64-x^{2}\) can be factorized as \((8+x)(8-x)\).

We already have an algebraic expression of this type, so using this method is time efficient.

He would travel 32.5 miles in 30 minutes. 130 split into a half is 65, split again and you get 32.5 miles.