You roll a 6-sided die.
What is P(less than 2)?
Write your answer as a fraction or whole number.

1. The domain of the linear regression equation is of: [0,∞).

2. The range of the linear regression equation is of: [0.5,∞).

3. The domain is composed by the input values of the function while the range is composed by the output values.

4. The estimate for the cost of gas in 2025 is of $4.55.

The linear regression equation in this problem is defined as follows:

y = 0.176x + 0.5.

In which the variables are given as follows:

2025 is 23 years after 2002, hence the estimate is given as follows:

y = 0.176(23) + 0.5 = $4.55.

The domain and the range are defined as follows:

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Answer:

7. D.58

Because 90-32=58 (that cube on the edge means 90degree)

8. A.45

Because 180-135=45

9. C. Because angles are equal

10. C. 95

180-85=95

The first term on the left-hand side represents the flux of the quantity D(pu δ) across the cell boundaries, and the second term represents the change of this flux within the cell.

To integrate the 1D steady-state convection-diffusion equation over a typical cell, we can start with the given equation:

D/dx(pu δ) = d/dx (rd δ/dx)

Here, D is the diffusion coefficient, p is the velocity, r is the reaction term, u is the concentration, and δ represents the Dirac delta function.

To integrate this equation over a typical cell, we need to define the limits of the cell. Let's assume the cell extends from x_i to x_i+1, where x_i and x_i+1 are the boundaries of the cell.

Integrating the left-hand side of the equation over the cell, we have:

∫[x_i to x_i+1] D/dx(pu δ) dx = D∫[x_i to x_i+1] d(pu δ)/dx dx

Using the integration by parts technique, the integral can be written as:

= [D(pu δ)]_[x_i to x_i+1] - ∫[x_i to x_i+1] d(D(pu δ))/dx dx

Similarly, integrating the right-hand side of the equation over the cell, we have:

∫[x_i to x_i+1] d/dx (rd δ/dx) dx = [rd δ/dx]_[x_i to x_i+1]

Combining the integrals, we get:

[D(pu δ)][x_i to x_i+1] - ∫[x_i to x_i+1] d(D(pu δ))/dx dx = [rd δ/dx][x_i to x_i+1]

This equation can be further simplified and manipulated using appropriate boundary conditions and assumptions based on the specific problem at hand.

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Complete Question:

There are 8 rows and 8 columns, or 64 squares on a chessboard.

Suppose you place 1 penny on Row 1 Column A,

2 pennies on Row 1 Column B,

4 pennies on Row 1 Column C, and so on …

Determine the number of pennies in Row 1

Determine the number of pennies on the entire chessboard?

Answer:

255 in the first row

18,446,744,073,709,551,615 in the entire board

Step-by-step explanation:

Given

\(Rows = 8\)

\(Columns = 8\)

Solving (a): Number of pennies in first row

The question is an illustration of geometric sequence which follows

\(1,2,4....\)

Where

\(a =1\) --- The first term

Calculate the common ratio, r

\(r = \frac{T_2}{T_1} = \frac{4}{2} = 2\)

The number of pennies in the first row will be calculated using sum of n terms of a GP.

\(S_n = \frac{a(r^n - 1)}{n - 1}\)

Since, the first row has 8 columns, then

\(n = 8\)

Substitute 8 for n, 2 for r and 1 for a in \(S_n = \frac{a(r^n - 1)}{r - 1}\)

\(S_8 = \frac{1 * (2^8 - 1)}{2 - 1}\)

\(S_8 = \frac{1 * (256 - 1)}{1}\)

\(S_8 = \frac{1 * 255}{1}\)

\(S_8 = 255\)

Solving (b): The entire board has 64 cells.

So:

\(n = 64\)

Substitute 64 for n, 2 for r and 1 for a in \(S_n = \frac{a(r^n - 1)}{r - 1}\)

\(S_{64} = \frac{1 * (2^{64} - 1)}{2 -1}\)

\(S_{64} = \frac{(2^{64} - 1)}{1}\)

\(S_{64} = \frac{(18,446,744,073,709,551,616 - 1)}{1}\)

\(S_{64} = \frac{18,446,744,073,709,551,615}{1}\)

\(S_{64} = 18,446,744,073,709,551,615\)

Answer:

Step-by-step explanation: its 1.45-3.10 and then its =1.35

ez

have a good day

Option D is the correct response, and it is false to say that it is always necessary to use the Pythagorean Theorem when finding the distance between two points on a coordinate plane.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in mathematics that relates to the lengths of the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The correct response is D) false; If the two points create a horizontal or vertical line segment, the Pythagorean Theorem is not needed.

When finding the distance between two points on a coordinate plane, the Pythagorean Theorem is used to calculate the distance only when the two points do not create a horizontal or vertical line segment.

If the two points create a horizontal line segment, then the distance between the two points is simply the difference between their x-coordinates. If the two points create a vertical line segment, then the distance between the two points is simply the difference between their y-coordinates. In both cases, the Pythagorean Theorem is not needed.

Therefore, option D is the correct response, and it is false to say that it is always necessary to use the Pythagorean Theorem when finding the distance between two points on a coordinate plane.

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Based on the options provided, it seems that the question is asking whether the budgeted amount is enough to cover expenses, savings, and emergencies. The answer would be either A, B, C, or D.

A) No, it's short $207.0.
B) No, it's short $227.0.
C) Yes, there's a surplus of $207.0.
D) Yes, there's a surplus of $227.0.

Unfortunately, without more information about the specific budgeted amount and the actual expenses, savings, and emergencies, it is impossible to determine the correct answer. It is important to regularly track expenses and compare them to the budgeted amount to ensure that there is enough money to cover all necessary expenses and unexpected events. If there is a shortfall, it may be necessary to adjust the budget or find ways to increase income or decrease expenses to ensure financial stability.

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Answer: 30

Step-by-step explanation:

i don’t know, but i know it’s 30

Answer: 28

Step-by-step explanation:

270 people enter the line for the escalator during" the time interval 0 < / < 300 and  80 people are at Mn Line at time 300. 414.285714 sec. is the first time that there are no people in line for the escalator and 33. 0133 time is the number of people in line minimum.

X(t) = 44 ( t/100)³ * (1-t/300)⁷

for 0≤t≤300

for t≥ 300

a) Total number of people = ∫³⁰⁰₀ r(t)*dt

∫³⁰⁰₀ 44(t/100)³ * (1-t/300)⁷ * dt

∫³⁰⁰₀ (11 (1-t/300)⁷ / 250000 * t³) * dt

∫³⁰⁰₀ -11 / 250000 * (t-300)⁷ * t³ * (1/300)⁷ dt

= -11 (1/300)⁷ / 250000 ∫³⁰⁰₀ (t-300)⁷ * t³ * dt

Now Integrate with respect to 't'

using substitution

Let  u = t-300

du = dt

∫ u⁷ * (u + 300)³ * du

∫ (u¹⁰ + 900 u⁹ +270000 u⁸ + 27000000 u⁷) * du

= u¹¹/11 + 90 u¹⁰ + 30000 u⁹ + 3375000 u⁸

Undo the substitution

u= (t-300)

= [ (t-300)¹¹ / 11 + 90 (t-300)¹⁰ + 30000(t-300)⁹ + 337500(t-300)⁸]³⁰⁰₀

Substitutes the limits

= [0- ((-300)¹¹/ 11 + 90 * (-300)¹⁰ + 30000 * (-300)⁹ + 3375000 * (-300)⁸]

= 270 people

b) Constant rate of 0.7 people per second

This is the rate of exit

at t = 0.20 people in line

People in a line at t = 300 is = 20+ ∫³⁰⁰₀ ((r(t) - 0.7 ) * dt

= 20 + ∫³⁰⁰₀ 44(t/100)³ * (1-t/300)⁷- 0.7 dt

= 20 + 270 - 0.7 * 300

= 80 people

c) t = 300 sec

people = 80

when t>300 , r(t) = 0

rate of exit remains the same

= 80 + ∫ ( 0-0.7) * dx

= 80 + [-0.7x] = 0

= 80 - [0.7x] = 0

= 80 - 0.7 t + 0.7 * 300 = 0

= 80 - 0.7t + 210 = 0

= - 0.7 t = -290

t = 414.285714 sec.

d) f(t) = 20 + ∫⁶₀ (r(x) - 0.7) * dx

f(t) = r(t) - 0.7

f(t) = 0       (for critical point)

r(x) = 44 (t/100)³ * (1-t/300)⁷

r(t) = 0

we get t= 33.0133 sec.

t = 166.575 sec.

Now check for the value

when t=0

f(t) 20

when t= 33.0133

f(t) = 3.803 ≈ 4

when t = 166.575

f(t) = 158.07 ≈ 158

when t= 300

f(t) = 80

so the minimum number of people is 4 at the time t= 33. 0133

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Answer:

Jason likely misplaced the decimal, because 3 times 1 = 3, and if the decimal was between the 2 and the 5, the number would be near 3.

Step-by-step explanation:

Jason applied 2 and 82.242 miles

Answer:

b

Step-by-step explanation:

In the regression line y = a+ bx+ e, a is the slope of the regression line.

The above statement is False.

The correct Statement is :

The linear regression line has an equation of the form Y =a + bX

where, Y is called the dependent variable or response.

X means independent or predictor or explanatory variable.

a is the y-intercept and b is the slope of the line.

Regression Line:

A regression line is a statistical tool that shows the correlation between two variables. Specifically, it is used when the variation of one (the dependent variable) depends on changes in the value of the other (the independent variable).

Simple linear regression has two cases:

The formula for the least squares regression line (LSRL) from Y to X is:

                           Y=a + bX + ɛ

where,

Y is the dependent variable.

a is the Y intersection.

b is the slope of the regression line.

X is the independent variable.

ɛ is the residual (error).

and

b = (N∑XY-(∑X)(∑Y) / (N∑X2– (∑X)2) ;

and

a = (∑Y – b ∑X) / N

where, N is the total number of observations.

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Answer:

She will give 78 students to the sixth student.

Step-by-step explanation:

The pattern is adding 6 each time.

Answer: 786 ft

Step-by-step explanation:

The Ferris wheel is circular in shape so this can be treated as a circle.

If the radius is 125 ft, the circumference can be calculated with the formula:

= 2 * π * radius

= 2 * 22/7 * 125

= 785.71 ft

= 786 ft

Answer:

83.333333333

Step-by-step explanation:

add 70+90+90=250/3= 83.3333333

To find the expected value of the game, we need to calculate the expected value of the random variable X, which represents the image value of bills.Therefore, the expected value of the game to you is $16.50.

The probability distribution of X can be filled in as follows:

x   | $1   | $5   | $10  | $50

P(X) | 1/4  | 1/4  | 1/4  | 1/4

The probabilities are equal because each bill has an equal chance of being drawn.

To calculate the expected value, we multiply each value of X by its corresponding probability and sum them up:

E(X) = (1/4 * $1) + (1/4 * $5) + (1/4 * $10) + (1/4 * $50)

    = $0.25 + $1.25 + $2.5 + $12.5

    = $16.5

Therefore, the expected value of the game to you is $16.50.

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Answer:

-6,0

Step-by-step explanation:

Answer:

inorder For Regina and joseph to each earn the same amount of money regina will have to work 6.50x10.7+16  and joseph

7.50x10.+10

Step-by-step explanation:

Solution

The graph

The vertex of a parabola is the point at the intersection of the parabola and its line of

symmetry

Any other point is a point on the graph, you can choose any desired point on the graph

The volume of the given triangular prism is 315 cm³.

The volume of a triangular prism, we need to multiply the base area of the triangular base by the height of the prism.

The triangular base has a base length of 5 cm and a height of 7 cm, and the height of the prism is 9 cm.

Calculate the area of the triangular base.

The area of a triangle can be calculated using the formula:

Area = (base length × height) / 2

Plugging in the values, we have:

Area = (5 cm × 7 cm) / 2

Area = 35 cm²

Calculate the volume of the prism.

The volume of a prism can be calculated by multiplying the base area by the height of the prism.

Volume = Base area × Height

Volume = 35 cm² × 9 cm

Volume = 315 cm³

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Answer:

You can say x to the power of 2 or you can say x squared.

Hope that answers your question!

The methods that are fair include __A, B and C__ because __D__ is flawed due to increased chances of winning based on one's skill, ___F___ is flawed due to poor randomization, and ___E___ is flawed due to unequal probabilities of winning and losing.

Probability is a value used to measure the degree of occurrence of a random event. The word probability itself is often referred to as opportunity or possibility. Probability is generally the chance that something will happen.

The concept of probability has an important role in everyday life, starting from the scientific field, the government sector, the business or industry sector, to small issues such as entering the office or not due to thick clouds which are likely to rain heavily and flood .

In studying probability, there are three keywords that must be known namely experiments, outcomes and events or events.

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The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.

The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.

Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):

275 liters / 1000 = 0.275 cubic meters

Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:

∛(0.275) ≈ 0.640

Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.

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Okay, according with the identities of parallelograms we have: AE=CE and BE=DE.

Replacing we obtain:

AE=CE

2x=x+2

2x-x=2

x=2

BE=DE

y+10=4y−8

10+8=4y-y

18=3y

y=18/3

y=6

And considering that BD=BE+DE, we got:

BD=(y+10)+(4y-8)=(6+10)+(4*6-8)=(16)+(24-8)=16+16=32

So, finally we obtain that the length of BD is 32 units.

Answer:

Step-by-step explanation:

15

Answer:

Step-by-step explanation:

Solve 20x + 5y =  for y

20x + 5y = 0

subtract 20x both sides

5y = -20x

simplify:

y = -20x

        5

finally

y = -4x

State B with the second-lowest population has the lowest population density. Then the correct option is B.

The process of making choice is by identifying the correct decision, gathering information, and assessing alternative solutions.

The second-lowest density for the states will be given as

\(\rm D_A = \dfrac{1055173}{2677} = 394.16\)

\(\rm D_B = \dfrac{1333089}{36418} = 36.61\)

\(\rm D_C = \dfrac{3596677}{5543} = 648.87\)

\(\rm D_D = \dfrac{6745408}{10555} = 639.07\)

Thus, state B with the second-lowest population has the lowest population density. Then the correct option is B.

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Answer:

The rock will take approximately 3.992 seconds to reach the canyon floor.

Step-by-step explanation:

For all \(a\cdot t^{2}+b\cdot t + c = 0\), its roots are determined by the Quadratic Formula:

\(t = \frac{-b\pm\sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}\)

In this case, it corresponds to instants when rock is either launched or hits the floor. If we know that \(a = -16\), \(b = 0\) and \(c = 255\), the time it takes the rock to reach the canyon floor is:

\(t = \frac{-0\pm\sqrt{(0)^{2}-4\cdot (-16)\cdot (255)}}{2\cdot (-16)}\)

\(t \approx 3.992\,s\)

The rock will take approximately 3.992 seconds to reach the canyon floor.

Given:

On a map, the scale shown is 1 inch : 5 miles.

Area of park = 75 square miles.

To find:

The area of the park on the map.

Solution:

Ratio of the areas of similar figures is equal to the ratio square of their corresponding sides.

\(\dfrac{\text{Area of park on the map}}{\text{Actual area of the park}}=\dfrac{\text{Side of park in map}^2}{\text{Actual side of park}^2}\)

Let A be the area of the park on the map.

\(\dfrac{A}{75}=\dfrac{1^2}{5^2}\)

\(A=\dfrac{1}{25}\times 75\)

\(A=3\)

Therefore, the area of the park on the map is 3 square inches.