7).
2. Hot Text: For each graph, choose the correct sentence to describe the graph.
The graph represents a proportional relationship.
The graph does not represent a proportional relationship.

Answer:The reciprocal of 2/3 is 3/2. The product of 2/3 and its reciprocal 3/2 is 1.

Step-by-step explanation:

Answer: X = 15  

Explanation:

Well, If 12 equals X minus 3 then we first must flip the signs.

which is adding. So we take 12 and add 3 which would get us 15.

Double check  :  15 (X) - 3 = 12

Answer:

\(x=4\)

Step-by-step explanation:

By the Triangle Proportionality Theorem:

\(\displaystyle \frac{x}{12}=\frac{x+1}{15}\)

By cross-multiplication:

\(\displaystyle 12(x+1)=15(x)\)

Distribute:

\(12x+12=15x\)

Subtract 12x from both sides:

\(12=3x\)

Hence:

\(x=4\)

Answer:

4

Step-by-step explanation:

The first thing you should notice is that the triangles (the smaller one and the larger one) are similar due to angle-angle similarity (the top angle equals itself, and because the bases are parallel lines cut by a transversal, the base angle of the bigger triangle is equal to the corresponding base of the smaller triangle.

Similar triangles' corresponding sides have equal ratios to one another. That means we can set up an equation: side of smaller triangle ÷ corresponding side of larger triangle = other side of smaller triangle ÷ corresponding side of larger triangle. We plug the values given to us and can change this equation to:\(\frac{x}{x + 12} = \frac{x + 1}{x + 16}\) **

We now multiply both sides of the above equation by \((x + 12)(x + 16)\) to get: \(x(x + 16) = (x + 1)(x + 12)\)

\(x^{2} + 16x = x^{2} + 13x + 12\)

\(3x = 12\)

\(x = 4\)

That means our answer, for the value of x, is 4

** Make sure you don't say \(\frac{x}{12} = \frac{x + 1}{15}\), because those aren't the sides of the larger square.

The amount of the area of the home used and the total area of the second property are 26.25 acres and 20.625 acres respectively.

The amount of land to be used for a home is the difference between the total land area and the area to be used for land :

Land Area of second property = 0.78 times the land ares

Therefore, the total area of the second property is 20.625 acres.

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The most appropriate choice for average will be given by-

Shureka Washburn must get 78 or higher in her final exam to make her average 76 or higher.

What is  average?

In a data set, there are many numbers. Average is the single number which acts as a representative of all the numbers in the data set.

Average is calculated by sum of all observations divided by total number of observations.

Here,

Let the score of Shureka Washburn in her last test be x

Score of Shurek Washburn on first test = 86

Score of Shurek Washburn on second test = 84

Score of Shurek Washburn on third test = 83

Score of Shurek Washburn on fourth test = 49

Total sum of all her scores = 86 +  84 + 83 + 49 + x

                                           =  302 + x

Average = \(\frac{302 + x }{5}\)

By the problem,

                          \(\frac{302 + x}{5} \geq 76\)

                          \(302 + x \geq 76\) \(\times 5\)

                          \(302 + x \geq 380\)

                          \(x \geq 380 - 302\)

                          \(x \geq 78\)

Shureka Washburn must get 78 or higher in her final exam to make her average 76 or higher.

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Answer:

the answer is 36

Step-by-step explanation:

Answer:

Yes, because the regression equation is based on the random sample.

Step-by-step explanation:

A simple linear regression model that describes the relationship between X and Y takes the form

Yi= ∝ + βXi + εi or

Y i= U(y.x) + εi

where εi's are the random errors. The random errors εi's are assumed to be independent of Xi and normally distributed with E(εi)= 0 and Var (εi)= σ²(y.x) , a constant for all Xi. These assumptions imply that Yi also have a common variance σ²(y.x) ,  as the only random element in the is  εi.

The estimated regression line Y= a+ bX is also the predictor of Yi= ∝ + βXi+ εi

. That is Y^ can also be used to predict an individual value Y0 of Yi rather than a mean value, corresponding to the given X0. To draw the inferences about Y0 we need to know it mean and variance.

Answer:

1

Step-by-step explanation:

R=red Y=yellow B=black

2(R)+4(B)

=6

2(Y)/6(R+B)

2/6 to get 50=50 or 3/6=1/2

you need 1 more yellow

Answer:water bottle 1.61

Flashlight 3.20

Step-by-step explanation:

Answer:

Water bottle:

✔ $1.61

Flashlight:

✔ $3.20

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) Let's denote the number of coffees sold as 'x' and the number of cappuccinos sold as 'y'.

The equation that represents the given information is:

2.50x + 3.75y = 222.50

b) To solve the equation, we need to find the values of 'x' and 'y' that satisfy the equation.

Since we have two variables and only one equation, we cannot determine the exact values of 'x' and 'y' independently. However, we can find possible combinations that satisfy the equation.

Let's proceed by assuming values for one of the variables and solving for the other. For example, let's assume 'x' is 40 (number of coffees):

2.50(40) + 3.75y = 222.50

100 + 3.75y = 222.50

3.75y = 222.50 - 100

3.75y = 122.50

y = 122.50 / 3.75

y ≈ 32.67

In this case, assuming 40 coffees were sold, we get approximately 32.67 cappuccinos.

We can also assume different values for 'x' and solve for 'y' to find other possible combinations. However, keep in mind that the number of drinks sold should be a whole number since it cannot be fractional.

Therefore, one possible combination could be around 40 coffees and 33 cappuccinos sold.

The Surface area of the composite figure is calculated as approximately: 234 sq. cm

The surface area of the composite figure is the area surrounding the faces of the solid as a whole. Therefore, we have:

Surface area (SA) = Surface area of the square prism + surface area of the square pyramid - 2(area of base)

Area of base = area of square = 6 * 6 = 36 sq. cm.

Surface area of the square prism = 2a² + 4ah

a = 6 cm

h = 4 cm

Plug in the values:

Surface area of the square prism = 2(6²) + 4*6*4

= 72 + 96

= 168 sq. cm.

Surface area of the square pyramid = 2bs + b²

b = side length = 6 cm

s = slant height = √(8² + 3²) = 8.5 cm

Plug in the values:

Surface area of the square pyramid = 2 * 6 * 8.5 + 6² = 138 sq. cm.

Surface area of the composite figure = 168 + 138 - 2(36) = 234 sq. cm

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Answer: the answer is (3,-2)

Step-by-step explanation: when you rotate a point about the origin 180 degrees clockwise, (x,y) turns into (-x,-y)

therefore

(-3,2) becomes (3,-2)

I'm pretty sure

The answer choice which must be true regarding the linear function is; The set must have a constant additive rate of change.

Since a linear function typically takes the slope-intercept form; f(x) = mx +c.

It therefore follows that the equation must have a constant slope m, which is the described additive constant rate of change.

It therefore follows that, the answer choice which is true regarding the linear function is therefore; The set must have a constant additive rate of change.

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Answer:

13.9 units

Step-by-step explanation:

Consider the right-angled triangle on the right:

Hypotenuse = 16 units

With respect to the angle 30°:

Adjacent = f

Use cosФ trigonometric function to determine f:

CosФ = \(\frac{Adjacent}{Hypotenuse}\)

Cos30° = \(\frac{f}{16}\)

Cross-multiplication is applied:

f = (16)(Cos30°)

∴f = 13.9 units (Rounded to 3 significant figures)

Gender is categorical nominal, end-of-the-year stock classification is categorical and ordinal, and distance is quantitative and ratio.

Quantitative variables are measured with numbers. Some examples include:

Weight measured in kilos

The distance measured in meters or kilometers

Time measured in seconds or hours

On the other hand, a categorical variable is defined by features, categories, or concepts rather than numbers. Here is an example:

Breeds of dogs: Poodles, Boston Terriers, German shepherds, etc.

Moreover, variables can be classified as:

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Answer:

46

Step-by-step explanation:

13a+4b

Substitute

13(2)+4(5)

Multiply

26+20

Add

46

The likelihood that he or she has a pet given that a student does not have a sibling is 60%. Therefore, the correct option is option D.

Let A denote the event that a student does not have a sibling.

Let B denote the event that a student has a pet.

Then A∩B will denote the event that the student does not have a sibling but he has a pet.

Let P denote the probability of an event in this question.

Then, we have to find the conditional probability of event B which means the likelihood of event B occurring based on the occurrence of event A.

P(B|A)

We know that:

\(P(B|A) = \frac{P(A\cap B)}{P(A)}\)

Also from the table, we have:

P(A)=0.25

and P(A∩B)=0.15

Hence,

\(P(B|A) = \frac{0.15}{0.25}\)

\(P(B|A) = \frac{3}{5}\)

\(P(B|A) = 0.6\)

which in percentage is:

0.6 * 100 = 60 %

Therefore, the likelihood that he or she has a pet too is 60% and the correct option is option D.

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Four triangles can create a set of pattern blocks that includes a total of four rhombuses.

To understand why, it's essential first to understand what pattern blocks are. Pattern blocks are shapes that are commonly used in early childhood education to teach math concepts like geometry, spatial reasoning, and fractions. They come in different shapes, including triangles, squares, hexagons, trapezoids, and rhombuses.

To create a set of pattern blocks using triangles, one can use four equilateral triangles with the same side length. When these triangles are arranged together, they form a larger equilateral triangle, as each external side of each small triangle connects to a side of another triangle. This larger equilateral triangle can then be divided into four smaller rhombuses by using two diagonals (lines connecting opposite corners) to form a "X" shape. Each of these four smaller rhombuses is made up of two adjacent triangles and forms a diamond shape. Therefore, it can be said that four equilateral triangles can form a set of four rhombuses within an equilateral triangle pattern block set.

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Answer:

\(x=a \cos t \implies \dfrac{dx}{dt}=-a \sin t\)

\(y= a \sin t \implies \dfrac{dy}{dt}=a \cos t\)

Using the chain rule:

\(\begin{aligned}\implies \dfrac{dy}{dx} & =\dfrac{dy}{dt} \times \dfrac{dt}{dx}\\\\& = a \cos t \times \dfrac{1}{-a \sin t}\\\\& = \dfrac{a \cos t}{-a \sin t}\\\\& = - \dfrac{\cos t}{\sin t}\\\\& = - \cot t\end{aligned}\)

Answer::

Explanation:

By the half-angle formula:

Let θ=150°, therefore:

Now, cos 30 = √3/2, thus:

The exact value of cos 75° is:

Answer:

382^2 mod

Step-by-step explanation:

To determine the shared secret key, we need to use the formula (g^a mod p)^b mod p = (g^b mod p)^a mod p, where g is the generator, p is the prime, a is our secret number, and b is the value sent by Aisha. Plugging in the values, we get (7^227 mod 437)^308 mod 437 = (7^308 mod 437)^227 mod 437.

To solve for the shared secret key, we first need to calculate (7^308 mod 437). This can be done by raising 7 to the 308th power and then taking the remainder when divided by 437. We can do this by repeatedly squaring 7 and taking the remainder each time. This results in the following sequence:

7^2 mod 437 = 49

7^4 mod 437 = 161

7^8 mod 437 = 267

7^16 mod 437 = 9

7^32 mod 437 = 49

7^64 mod 437 = 161

7^128 mod 437 = 267

7^256 mod 437 = 9

7^512 mod 437 = 49

Since 512 is greater than 308, we can stop here and use the value 49 as the result of 7^308 mod 437. We can now plug this value into the formula to calculate the shared secret key: (49^227 mod 437)^308 mod 437 = (49^308 mod 437)^227 mod 437.

To solve for the shared secret key, we need to find the value of 49^308 mod 437. This can be done using the same method as before, by repeatedly squaring 49 and taking the remainder each time. This results in the following sequence:

49^2 mod 437 = 67

49^4 mod 437 = 382

49^8 mod 437 = 221

49^16 mod 437 = 67

49^32 mod 437 = 382

49^64 mod 437 = 221

49^128 mod 437 = 67

49^256 mod 437 = 382

Since 256 is greater than 308, we can stop here and use the value 382 as the result of 49^308 mod 437. We can now plug this value into the formula to calculate the shared secret key: 382^227 mod 437 = 382^227 mod 437.

To find the shared secret key, we need to calculate 382^227 mod 437. This can be done using the same method as before, by repeatedly squaring 382 and taking the remainder each time. This results in the following sequence:

Answer:

Circle= 4

triangle= 7

rectangular= 2

Step-by-step explanation:

if circle + circle is 8 so one circle is 4

and circle + rectangle is 6 so rectangle is 2

and if rectangle is 2 and rectangle+ triangle is 7because rectangle + triangle is 9 so if rectangle is 2 then 7 is left so 7 + 2 is 9

The probability density function for U is: f_U(u) = (4/(1+u)^3) * e^-(1+u)/2, u > 0

The joint distribution for the length of life of two different types of components operating in a system is given by f(y_1, y_2) = {(1/8)y_1 e^-(y_1 + y_2)/2, y_1 > 0, y_2 > 0, 0, elsewhere. We are asked to find the probability density function for U = Y_2/Y_1.

To find the probability density function for U, we first need to find the joint distribution of U and Y_1. We can do this by using the change of variables formula:

f_U,Y_1(u, y_1) = f_Y_1,Y_2(y_1, uy_1) * |J|

where J is the Jacobian determinant of the transformation.

The Jacobian determinant is given by:

J = |∂(y_1, uy_1)/∂(u, y_1)| = |y_1|

So, the joint distribution of U and Y_1 is:

f_U,Y_1(u, y_1) = (1/8)y_1 e^-(y_1 + uy_1)/2 * |y_1| = (1/8)y_1^2 e^-(1+u)y_1/2

Next, we need to find the marginal distribution of U by integrating out Y_1:

f_U(u) = ∫f_U,Y_1(u, y_1) dy_1 = (1/8)∫y_1^2 e^-(1+u)y_1/2 dy_1

This integral can be solved using integration by parts. The final result is:

f_U(u) = (4/(1+u)^3) * e^-(1+u)/2

So, the probability density function for U is:

f_U(u) = (4/(1+u)^3) * e^-(1+u)/2, u > 0

This is the final answer.

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Answer: (-1) x 2² x 3

Happy to help:)

The equivalent expressions to \(24^{-7}\) are given as follows:

C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)

F. \((24^3 \times 24^4)^{-1}\)

Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.

The exponent in the denominator can be moved to the numerator with the changed signal, hence:

\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)

Applying the power of power rule, we multiply the powers, hence:

\((24^7)^{-1} = 24^{-7}\)

When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:

\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)

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The tomato plant is 49 cm tall 22 days after Allie bought it.

What are Functions?

A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is termed the domain of the function and the set Y is called the codomain of the function.

The function is H(d) = 16 + 1.5d

Since, all the options talks aabout the height of the plant after 22 days

We need to put the value of d as 22 in the function for calculating the height of the function

H(22) = 16 + 1.5(22)

H(22) = 16 + 33 = 49

The tomato plant is 49 cm tall 22 days after Allie bought it.

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Answer:

pairs of numbers is 3,-3

Step-by-step explanation:

The computation is shown below:

Let us assume a and b are the pairs of the numbers whose difference is 6

i.e.

a - b = 6

a = 6 + b

So

f = ab

f = (6 + b)b is minimum

Now

d ÷ db (6+ b)b = 0

(6+ b) + b = 0

2b = -6

b = -3

Now

a  = 6 + b

= 3

So pairs of numbers is 3,-3