Complete the table for the function y =
X
-2
-1
0
1
y
Now, graph the function.
Plot two points to graph the function.

Let x = number of weeks

Initial cost = $85

Cost per week = $18

Final cost = $155

An inequality that represents this situation is:

Then solve for x:

Answer: he needs to save 4 weeks to buy the skis

We have proven that from ten distinct two-digit numbers, one can always choose two disjoint nonempty subsets so that their elements have the same sum.

What is a disjoint set?

Two sets are said to be disjoint when they have no common element. If a collection has two or more sets, the condition of disjointness will be the intersection of the entire collection should be empty.

To prove that from ten distinct two-digit numbers, one can always choose two disjoint nonempty subsets so that their elements have the same sum, we can consider the following two sets:

Set A: The first five two-digit numbers, in order from smallest to largest.

Set B: The last five two-digit numbers, in order from smallest to largest.

Since the ten two-digit numbers are distinct, we know that the numbers in Set A and Set B are also distinct. Therefore, Set A and Set B are disjoint nonempty subsets.

The sum of the elements in Set A is equal to the sum of the elements in Set B. This can be seen by considering the fact that the sum of the first five two-digit numbers is equal to the sum of the last five two-digit numbers.

Therefore, we have proven that from ten distinct two-digit numbers, one can always choose two disjoint nonempty subsets so that their elements have the same sum.

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Answer:

4900

Step-by-step explanation:

70^2 means 70*70

70*70=4900

Answer:

you will do 70 times 70 because 70^2 is 70 times 70 which is 4,900.

Answer:

When x = -1/4 and when x = -15/4

Step-by-step explanation:

The x intercept will be when f(x)=0, so

0 = 4|x+2| -7

7 = 4|x+2|

|x+2|=7/4 here you have to cases

case 1

x+2=7/4

x=7/4-2

x=-1/4 = -0.25

case 2

x+2 = -7/4

x = -2-7/4

x = -15/4 = -3.75

The system of equations is.

\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)

And the solutions are y = 50 and x = 10.

Let's define the two variables:

With the given information we can write two equations, then the system will be:

\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)

Now let's solve it.

We can isolate x on the first  to get:

\(\text{x} = 60 - \text{y}\)

Replace that in the other equation to get:

\(15\times(60 - \text{y}) + 10\text{y} = 800\)

\(-2\bold{y} = 900 - 800\)

\(-2\bold{y} = 100\)

\(\text{y} = \dfrac{100}{-2} = \bold{50}\)

Then \(\bold{x=10}\).

Therefore, the solutions are y = 50 and x = 10.

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Therefore, the longest length of pencil that John can hide in the pencil holder is approximately 127.32 cm (rounded to two decimal places).

Given that John has a 100 cm³ pencil holder, the longest length of pencil he can hide in the pencil holder can be found by using the formula for the volume of a cylinder which is given by: V = πr²h where r is the radius of the cylinder and h is the height of the cylinder.The volume of a cylinder can also be expressed as V = lwh where l is the length of the cylinder, w is the width of the cylinder and h is the height of the cylinder.

If we assume that the pencil is cylindrical in shape, then its volume can be given by V = πr²l where r is the radius of the pencil and l is the length of the pencil.Since the volume of the pencil holder is given to be 100 cm³, then we have:100 = πr²h (Equation 1)

Now, we need to find the value of l that can fit inside the pencil holder. We can use the formula for the volume of the pencil to do this as follows:

V = πr²lLet V = 100 cm³ and

r = 0.5 cm

(since the pencil holder is cylindrical in shape, we can assume that it has a radius of 0.5 cm)Then, we have:100 = π(0.5)²lSolving for l, we get:

l = 100 / (π(0.5)²)

l = 100 / (0.7854)l ≈ 127.32 cm

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The inequality for this problem is defined as follows:

y ≤ 2x - 6.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

The function in this problem crosses the y-axis at y = -6, hence the intercept b is given as follows:

b = -6.

When x increases by 3, y increases by 6, hence the slope m is given as follows:

m = 6/3

m = 2.

Hence the function is:

y = 2x - 6.

The inequality is composed by the values to the left of the solid line, hence it is given as follows:

y ≤ 2x - 6.

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Answer: 120 ==> scale

8.4 m==> longer side

Step-by-step explanation:

6 m=

6*100 cm=600 cm

600/5=120 ==> scale

7*120=840 cm

840 cm=

840/100 m=8.4 m ==> longer side

Answer:

Therefore, the constant of proportionality for the given proportional relationship is 5.

Step-by-step explanation:

To determine the constant of proportionality in the given proportional relationship, we can use the formula:

Constant of Proportionality = Tickets / Games

Let's plug in the values from the table:

For the first set of values (4 games and 20 tickets):

Constant of Proportionality = 20 / 4 = 5

For the second set of values (7 games and 35 tickets):

Constant of Proportionality = 35 / 7 = 5

For the third set of values (10 games and 50 tickets):

Constant of Proportionality = 50 / 10 = 5

In all three cases, the constant of proportionality is equal to 5.

Therefore, the constant of proportionality for the given proportional relationship is 5.

Answer:

(A ruler) = X  (a pen) = Y

y = x+10

Step-by-step explanation:

Answer:

A ruler cost x pence.

Pen costs 10 pence more than the ruler

Answer:

Below

Step-by-step explanation:

edited:  FOR QIII   (I didn't see that part)

Remember for a right triangle  S-O-H-C-A-H-T-O-A

   Tan is OPPOSITE LEG / ADJACENT LEG

   make the right triangle with legs 3 and 4  ( in quadrant III)

      then the hypotenuse is 5

         sin = opp/ hyp =  - 3/5

            cos = -  4/5

                csc = 1/sin = - 5/3

                   sec = 1/cos = - 5/4

                       cot = 1/tan = 3/4

Answer:

(x+y) ³

= x³+3x²y+3xy²+y³

=x³+y³+3xy(x+y)

Brainliest please~

(x+y)3= x^3+3x^2y+3xy^2+y^3

Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).

Meaning of probability :

Probability is calculation of how likely some event will happen. Whenever we are not sure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are going to happen.

The analysis of events governed by probability is called statistics.

According to the given information :

Red section = \(\frac{2}{5}\)

multiply numerator and denominator by \(2\) we get

Red section = \(\frac{4}{10}\)

 Blue section = \(\frac{1}{2}\)

 multiply numerator and denominator by \(5\) we get

 Blue section = \(\frac{5}{10}\)

 Green section = \(1\)- Red section - Blue section

 Green section =\(1-\frac{4}{10} -\frac{5}{10}\)

  Green section = \(\frac{1}{10}\)

Therefore Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).

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Answer:I believe the answer is C

Step-by-step explanation:

The y-intercept is 2

Answer:

For A

For grace the x would be the number 18

y = 1000 (18) + 7600

y= 18000 = 7600

and that would mean y = 25600

Now for Claire you have to use the method rise over run

The equation for claire is y=800x + 7600  

11600-10000/3=800

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

y= 800(18) + 7600

y= 14,400 + 7600

y= 22,000

This shows that Claire would have $22,000 when shes 18 and Grace would have $25,600 when she is 18.

Answer:

6 cups.

2 3/4 X 3 1/3

Step-by-step explanation:

The value of the expression on evaluation is 96π / 5.

Here we have to find the value of the expression.

∫∫∫x² dV

E is indeed the solid that exists inside the cylinder x² + y² = 4 above the surface z =0.

E's precession through into xy-plane is x² + y² ≤4 where r≤2 with Ф[0, 2π].

∫∫∫ x² dV = ∫\(\int\limits^2\pi _0 {} \, \int\limits^2_0{} \, \int\limits^3r_0\) r² cos² Фrd dФ

             = \(\int\limits^2\pi _0 {} \, \int\limits^2_0 \int\limits^3r_z=0 {} \,\)r³ cos²Ф dz dr dФ

            = \(\int\limits^2\pi _0 {} \, \int\limits^2_0 {} \,\) 3\(r^{4}\)cos²Ф dr dФ

           = 3 \(\int\limits^2\pi _0 {} \,\) 1/2 \(2^{5}\)/ 5 ( 1 + cos² Ф )dr dФ

           = 48 / 5 [( Ф + 1/2 sin 2Ф)\(]^{2\pi } _{0}\)

            = 96π / 5

Therefore the value of the expression is 96π/5.

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The correlation coefficient between X and Y is Corr(X, Y) = 0.

To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.

a. Marginal distribution of X:

To find the marginal distribution of X, we integrate the joint PDF over the range of Y:

∫[0, 1] J(x, y) dy

Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:

∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1

So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.

b. Expectation of X:

The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:

\(E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3\)

Therefore, the expectation of X is E(X) = 1/3.

c. Variance of X:

The variance of X can be calculated using the formula:

\(Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36\)

Therefore, the variance of X is Var(X) = 5/36.

d. Covariance of X and Y:

The covariance of X and Y can be calculated as:

Cov(X, Y) = E(XY) - E(X)E(Y)

Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:

\(E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

\(E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

Cov(X, Y) = 1/6 - (1/3)(1/6) = 0

Therefore, the covariance of X and Y is Cov(X, Y) = 0.

e. Correlation coefficient between X and Y:

The correlation coefficient can be calculated using the formula:

Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))

Since the covariance of X and Y is 0, the correlation coefficient will also be 0.

Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.

f. Conclusion based on the correlation coefficient:

The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the

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Thus, the picture frame with the side length of 5 in. 12 in. 13 in.  is right angled at the corner shown by point B.

Triangles with a single 90° angle are known as right-angled triangles.

Right angles are what this is. It is customary for the correct angle to be located in one of the bottom corners, however this is not required.

They are available in scalene and isosceles versions.

Given dimensions are-

5 in. 12 in. 13 in.

For the triangle to be right angled, it must satisfy the Pythagorean theorem.

H² = B² + P²

In which,

Put the values:

H² = B² + P²

13² = 12² + 5²

169 = 144 + 25

169 = 169

Since LHS = RHS, this proves that, the sides of the picture frame right angles.

Thus, the picture frame with the side length of 5 in. 12 in. 13 in.  is right angled at the corner shown by point B.

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Correct question:

A picture frame is shown in the diagram. Are the corners of the picture frame right angles? Three side of the frame are- 5 in. 12 in. 13 in.

Answer: I believe it’s 3 adults and 9 girls.

Step-by-step explanation:

The correct product of (6x - 2)(6 x + 2) is 36x^2 - 4

The expression is given as:

(6x - 2)(6 x + 2).

The above expression is a difference of two squares.

And this is represented as

(a - b)(a + b)= a^2 - b^2

So, we have

(6x - 2)(6 x + 2) = (6x)^2 - 2^2

Evaluate

(6x - 2)(6 x + 2) = 36x^2 - 4

Hence, the correct product of (6x - 2)(6 x + 2) is 36x^2 - 4

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Based on the scatterplot, the form of the relationshipbetween fire spread rate and wind speed   can be described as a positive correlation.

As wind speed increases,the fire spread rate also tends   to increase.

b. Direction  -

Based on the given scatterplot,the direction of the relationship between fire spread rate and wind speed appears to   be positive.

As the wind speed   increases,the fire spread rate generally tends to increase as well.

c. Strength  -

The scatterplot suggests a   moderate to strong relationship between fire spread rate and wind speed.

The data points   exhibit a somewhat linear pattern, indicating that there is a noticeable association between these variables.

The firespread rate tends to increase consistently as the wind speed increases, suggesting a relatively strong positive correlation between the two factors.

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Full Question:

Wind and Moisture: To understand how weather and landscape affect the spread of wildfires, an experiment was conducted in a low velocity wind tunnel. A fire was started in pine litter, and the researchers measured the fire spread rate for varying wind speeds and pine litter moisture contents.

Data for fires started in pine litter that had a moisture content of 4% are shown in the table below.

Wind Speed (miles/hour) Fire Spread Rate (feet/minute)

0.76                                         0

1.78                                             2

3.34                                                4

5.38                                       6

8.10                                                8

11.75                                     10

16.70                                    12

A scatterplot of these data is shown here  -

1. Based on the scatterplot, how would you describe the following with regard to the relationship between fire spread rate and wind speed?

a. Form:

b. Direction:

c. Strength:

The formula for g(x) is 2√(x-6) + 1. The solution has been obtained using the concept of translation.

What is translation?

In mathematics, a translation involves moving a shape up, down, left, or right. The translated shapes appear to be exactly the same size as the original ones; thus, the shapes are consistent with one another. Just one or more directions have been changed. There is no change to the shape because it is simply being moved from one location to another.

The object's shift in location can occur in a variety of ways, such as initially moving left, then turning right, and so on. Each point on the form will translate by the same number of units.

We are given f(x) = 2√x

Now, shifted down 1 unit, we get

2√x + 1

Also, shifted right 6 units, we get

2√(x-6)

So, g(x) = 2√(x-6) + 1

Hence, the formula for g(x) is 2√(x-6) + 1.

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An order-preserving function is a function that preserves the order of its inputs. In other words, if x is less than y, then f(x) will be less than f(y).

The statement "f is order-preserving if x < y implies f(x) < f(y)" means that if x is less than y, then f(x) must be less than f(y). This is a necessary condition for a function to be order-preserving. However, it is not a sufficient condition. For example, the function f(x) = x^2 is not order-preserving, because 2 < 3, but f(2) = 4 > f(3) = 9.

In summary, order-preserving functions are useful in situations where we need to preserve the order of a set of data.

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