The temperature dropped 5°C every hour for 6 hours. What was the total number of degrees the
temperature changed in the 6 hours?
The total change in the temperature was

Answer:

1. List (in order) the five phases a single 2 solar mass will go through in its life.

2. List (in order) the five phases a single 25 solar mass will go through in its life.

3. List (in order) the five phases a single 60 solar mass will go through in its life.

Phase options (can be used more than once, some may not be used at all):

Type II Supernova

Protostar

White Dwarf

Giant Phase

Main sequence

Neutron Star

Brown Dwarf

Black Hole

Type 1a Supernova

Planetary Nebula

Step-by-step explanation:

Answer:

carly=25 camden=5

Step-by-step explanation:

carly:camden= 5:1

5+1=6

30/6=5

carly= 5x5=25

camden=5x1=5

Answer:

Infinite solutions or the solution is all real numbers

Step-by-step explanation:

5(r+9) = 5r + 45 when simplified

This is identical to the RHS with the exception that there is an x instead of r.

What it means that if you were to graph those 2 lines in the coordinate plane they would be right on top of each other. 2 identical straight lines intersecting forever with infinite solutions.

Answer:

I'm so sorry I don't know the answer but I thought you should know that your pfp is pogchamp :))

Dream Team is life :p

Statisticians calculate the Consumer Price Index (CPI) by combining the 80,000 prices of individual products using a weighted average based on their relative importance or expenditure weights.

The Consumer Price Index is a measure of the average change over time in the prices paid by urban consumers for a basket of goods and services. To calculate the CPI, statisticians collect price data for a representative sample of approximately 80,000 individual products that are commonly purchased by urban consumers. These products cover a wide range of categories, including food, housing, transportation, healthcare, and more.

Each product's price is then multiplied by its respective expenditure weight, which represents the proportion of total consumer spending allocated to that product. These weights are determined through surveys and data analysis to reflect the typical spending patterns of urban consumers. The resulting values are then summed up to obtain a total expenditure amount.

To calculate the CPI, statisticians divide the total expenditure by a base period expenditure and multiply the result by 100. The base period is typically a reference point or benchmark year against which the price changes are measured. This process allows for tracking and comparing price changes in the basket of goods and services over time, providing insight into inflation and changes in the cost of living.

In summary, statisticians calculate the Consumer Price Index by combining the prices of 80,000 individual products using a weighted average based on their expenditure weights, representing the relative importance of each product in urban consumers' spending patterns. This method allows for measuring and monitoring changes in the overall price level and cost of living.

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(a) Matrix for relation R {(a, b) | a > b} has 4950 nonzero entries.

(b) Matrix for relation R {(a, b) | b - a = 51} has 49 nonzero entries.

(c) Matrix for relation R {(a, b) | ab is a multiple of 3} has 5644 nonzero entries.

Let's analyze each relation separately to determine the number of nonzero entries in the corresponding matrix.

(a) Relation R: {(a, b) | a > b}

In this case, for every pair (a, b) in the relation, a must be greater than b. We need to count the number of such pairs.

Since the set A consists of the first positive 100 integers, we have 100 choices for a. For each a, there are (a - 1) choices for b (all the integers less than a). Thus, the number of pairs (a, b) satisfying a > b is:

Number of pairs = 99 + 98 + ... + 1 = (99 × 100) / 2 = 4950

Therefore, the matrix representing relation R has 4950 nonzero entries

(b) Relation R: {(a, b) | b - a = 51}

In this case, for every pair (a, b) in the relation, the difference between b and a is 51. We need to count the number of such pairs.

Since the set A consists of the first positive 100 integers, we can choose a from 1 to 49 (inclusive), as for any greater than 49, b would exceed 100.

Thus, the number of pairs (a, b) satisfying b - a = 51 is:

Number of pairs = 49

Therefore, the matrix representing relation R has 49 nonzero entries.

(c) Relation R: {(a, b) | ab is a multiple of 3}

In this case, for every pair (a, b) in the relation, the product of a and b must be a multiple of 3. We need to count the number of such pairs.

Since the set A consists of the first positive 100 integers, we have 100 choices for both a and b.

To calculate the number of pairs (a, b) satisfying ab is a multiple of 3, we need to exclude the pairs where both a and b are not multiples of 3.

Number of pairs = (100 × 100) - (66 × 66) = 10000 - 4356 = 5644

Therefore, the matrix representing relation R has 5644 nonzero entries.

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The cost of 7 bags of bananas will be $52.78.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition,substraction, multiplication, and division.

Given that at the produce store, you can buy 4 bags of bananas for $30.16. The cost of 7 bags will be calculated as:-

4 bags = $30.16

1 bag = $30.16 / 4

7 bags = ( 7 x $30.16) / 4

7 bags = $52.78

Therefore, the cost of 7 bags of bananas will be $52.78.

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Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

HOPE THIS HELPSSSS

The only point where the tangent line is vertical is (0, 0)..

To find the points on the curve where the tangent line is horizontal or vertical, we need to find where the slope of the tangent line is zero (for a horizontal tangent line) or undefined (for a vertical tangent line). The slope of the tangent line is given by the derivative of y with respect to x, dy/dx:

dy/dx = (dy/dt)/(dx/dt) = (3t^2 - 6t)/(3t^2 - 3)

Setting the numerator equal to zero, we get:

3t^2 - 6t = 0

Factorizing, we get:

3t(t - 2) = 0

So the critical points are t = 0 and t = 2.

At t = 0, we have x = 0 and y = 0, so the point is (0, 0).

At t = 2, we have x = 2 and y = -8, so the point is (2, -8).

To determine if the tangent line is vertical or horizontal at each point, we need to look at the derivative dx/dt:

dx/dt = 3t^2 - 3

At t = 0, dx/dt = -3, which means the tangent line is vertical.

At t = 2, dx/dt = 9, which means the tangent line is not vertical.

To find out if the tangent line is horizontal at t = 2, we can look at the derivative of dy/dt:

dy/dt = 9t^2 - 6t

At t = 2, dy/dt = 24, which means the tangent line is not horizontal.

Therefore, the only point where the tangent line is vertical is (0, 0).

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Answer:

-1

Step-by-step explanation:

Simplify both sides: 3x + (2(x) + 2(-9)) = 8x + x -14

Add/Combine like terms: 3x+2x= (5x-18) = (9x-14)

New Equation: 5x-18 = 9x-14

add 14 to both sides: 5x-4 = 9x

Subtract 5x from both sides: -4 = 4x

Divide both sides by 4 to get: -1 = x

Answer: x = -1

The tank contains 150 liters of fluid, in which 40 grams of salt is dissolved. The number of grams of salt in the tank remains constant at 40 grams regardless of the time t.

At a rate of 5 liters per minute, brine containing 1 gram of salt per liter is pumped into the tank. Simultaneously, the well-mixed solution is pumped out at the same rate.

To find the number A(t) of grams of salt in the tank at time t, we can use the following equation:

A(t) = initial amount of salt + (rate of salt in - rate of salt out) * time

Let's break down the equation:

- The initial amount of salt in the tank is 40 grams.
- The rate of salt in is 1 gram per liter, and since the rate of flow is 5 liters per minute, the rate of salt in is 5 grams per minute.
- The rate of salt out is also 5 grams per minute, as the well-mixed solution is pumped out at the same rate as it is pumped in.

Now we can plug these values into the equation:

A(t) = 40 + (5 - 5) * t

The rate of salt in and the rate of salt out cancel each other out, so the equation simplifies to:

A(t) = 40

Therefore, the number of grams of salt in the tank remains constant at 40 grams, regardless of the time t.

In conclusion, the number of grams of salt in the tank remains constant at 40 grams regardless of the time t.

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Answer:

\(Y= -3x+2\)

Step-by-step explanation:

Slope : \( - 3\)

y-intercept = 2

Answer:

899 ft

Step-by-step explanation:

if point a is 400 feet from the base and 499 feet away from the top you would need to add 400+499 together to get 899

The values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

√15/(y + 2) = y/√15 {opposite/adjacent}

y(y + 2) = (√15)² {cross multiplication}

y² + 2y = 15

y² + 2y - 15 = 0

by factorization;

(y - 3)(y + 5) = 0

y = 3 or y = -5

by Pythagoras rule:

(√15)² = x² + y²

15 = x² + 3²

x = √(15 - 9)

x = √6

z² = (√6)² + 2²

z = √(6 + 4)

z = √10

Therefore, the values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

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Answer:

11 x 2

Step-by-step explanation:

By BODMAS rule,

B - Brackets

O - Orders

D - Division

M - Multiplication

A - Addition

S - Substraction

Consider DMAS alone.

Here, there is no division.

So,

Multiplication ( x ) should be the first step.

Therefore, the figure's volume is 32 times Prism A's length less 40 cubic feet.

In three dimensions, each object takes up some space. What is being assessed is the size of this region. The volume of an item is the region that fills its three-dimensional boundaries. It is additionally known as an object's potential.

To determine the volume of the figure, we need to find the dimensions of both prisms and then add their volumes together.

Let's start by finding the width of Prism A. Since Prism A and Prism B are attached to each other, they must share a common width. We know the width of Prism B is 4 feet, so the width of Prism A must also be 4 feet.

Now we can calculate the volume of Prism A:

Volume of Prism A = length x width x height

Volume of Prism A = unknown x 4 feet x 8 feet (since we don't know the length of Prism A)

We don't know the length of Prism A, but we do know that it is connected to Prism B, which has a length of 2 feet. Therefore, the length of Prism A must be the remaining distance between the two prisms, which is:

Length of Prism A = total length - length of Prism B

Length of Prism A = unknown - 2 feet

Now we can substitute this value into the volume equation for Prism A:

Volume of Prism A = (unknown - 2 feet) x 4 feet x 8 feet

Next, we can calculate the volume of Prism B:

Volume of Prism B = length x width x height

Volume of Prism B = 2 feet x 4 feet x 3 feet

Volume of Prism B = 24 cubic feet

Finally, we can add the volumes of the two prisms together to get the total volume of the figure:

Total volume = Volume of Prism A + Volume of Prism B

Total volume = (unknown - 2 feet) x 4 feet x 8 feet + 24 cubic feet

Without knowing the value of "unknown", we cannot calculate the exact volume of the figure. However, we can simplify the equation by multiplying out the terms:

Total volume = (32 x unknown - 64) cubic feet + 24 cubic feet

Total volume = 32 x unknown - 40 cubic feet

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Answer:

28x

Step-by-step explanation:

7×3x=21x+x×7=7x

21x+7x×28x

1) the displacement of the particle over the interval [0, 2] is 2 meters.

2) the total distance traveled by the particle over the interval [0, 2] is 4 meters.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

Question 1: To compute the displacement of the particle over [0, 2], we need to find the net change in position. The displacement can be calculated by integrating the velocity function over the given interval.

Given velocity function v(t) = 3t² - 2t - 1, we integrate it with respect to t over the interval [0, 2]:

Displacement = ∫[0 to 2] v(t) dt

Let's calculate the integral:

Displacement = ∫[0 to 2] (3t² - 2t - 1) dt

To find the antiderivative, we integrate each term separately:

Displacement = ∫[0 to 2] (3t²) dt - ∫[0 to 2] (2t) dt - ∫[0 to 2] (1) dt

Simplifying further:

Displacement = [t³] evaluated from 0 to 2 - [t²] evaluated from 0 to 2 - [t] evaluated from 0 to 2

Displacement = (2³) - (2²) - (2) - ((0³) - (0²) - (0))

Displacement = 8 - 4 - 2 - (0 - 0 - 0)

Displacement = 8 - 4 - 2

Displacement = 2 meters

Therefore, the displacement of the particle over the interval [0, 2] is 2 meters.

Question 2: To compute the total distance traveled by the particle over [0, 2], we need to find the sum of the absolute values of the velocity function integrated over the given interval.

Given velocity function v(t) = 3t² - 2t - 1, we integrate the absolute value of the velocity function over the interval [0, 2]:

Total Distance = ∫[0 to 2] |v(t)| dt

Let's calculate the integral:

Total Distance = ∫[0 to 2] |3t² - 2t - 1| dt

To find the integral, we consider different cases based on the sign of the velocity function within the interval [0, 2].

Case 1: When v(t) ≥ 0

Within the interval [0, 2], the velocity function 3t² - 2t - 1 is positive or zero. So we can directly integrate it:

∫[0 to 2] (3t² - 2t - 1) dt

Using the same steps as in Question 1, we find the integral to be (2 meters).

Case 2: When v(t) < 0

Within the interval [0, 2], the velocity function 3t² - 2t - 1 is negative. To consider the absolute value, we negate the velocity function:

∫[0 to 2] -(3t² - 2t - 1) dt

Using the same steps as in Question 1, we find the integral to be (-2 meters).

Total Distance = |2 meters| + |-2 meters| = 2 meters + 2 meters = 4 meters

Therefore, the total distance traveled by the particle over the interval [0, 2] is 4 meters.

Hence, 1) the displacement of the particle over the interval [0, 2] is 2 meters.

2) the total distance traveled by the particle over the interval [0, 2] is 4 meters.

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The correct expression  and diagram represent "three times a number" is shown in option 2.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

"three times a number"

Now,

Let a number = x

Hence, We get;

⇒  "three times a number"

⇒ 3 × x

⇒ 3x

Thus, The correct expression  and diagram represent "three times a number" is shown in option 2.

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The correct statement is: provided that the sample size is reasonably large (for any population).

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

These conditions include a random sample from the population and a sufficiently large sample size (typically, n > 30 is considered large enough).

Therefore, the Central Limit Theorem is important because it allows us to make inferences about the population mean using the normal distribution, even if we do not know the population distribution.

This is useful in many applications of statistics, including hypothesis testing, confidence intervals, and estimating population parameters

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Given,

The given conditional statement is :If John is on a vacation, then he is in London.

Converse: If John is in London, then he is on vacation.

Inverse: If John is not on vacation, then he is not in London.

Contrapositive: If John is not in London, he is not on vacation.

From the properties of conditional statement we know that:

if p→q then

Inverse is : ∼p→∼q

Contrapositive: ∼q→∼p

Converse: q→p

Let us elaborate on the above conditions. Let us take two statement p and q  such that If p happens then q also happens.

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Answer:

Step-by-step explanation:

1)100,000 2)16,807 3)160,000 4)7,776

KotikWithU avatar

5)13,824=128 (It is not correct because 2x4x4x4 = does not equal 24^3 which is 13,824

KotikWithU avatar

6) 5x5x5x5 = 5^4 7) 2x2x2 = 2^3 8) 12x12x12x12x12 = 12^5

KotikWithU avatar

If I was you I would not risk my safety and wouldn't follow any links

KotikWithU avatar

Actually, that is more like it 1) 10^5 = 10x10x10x10x10 2) 7^5 = 7x7x7x7x7 3) 20^4 = 20x20x20x20 4) 6^5 = 6x6x6x6x6

KotikWithU avatar

9) 2^3 = 2x2x2 (8) 10)10^4 = 10x10x10x10 (10,000) 11)2^0 (2)

KotikWithU avatar

Reply if it helped you, thank you.

KotikWithU avatar

I am not sure about last one, sorry

Dee.

Step 1

Rearrange the equation

Step 2

Test all options by rearrangement

Option A

Option B

Option C

Option D

Hence, the equivalent options to the equation are options B and C

Answer:

The correct unit price is $1.22 per pair.

Step-by-step explanation:

The contractor accidentally labeled each dozen as a pair rather than each individual pair.

Answer:

E

Step-by-step explanation:

E

Suppose that the joint probability density of two random variables X1 and X2 is given by F(x1,X2) = {6e^-2x1-3x2 for x1 > 0 and x2 > 0, otherwise.

Find the probability P(I2).

Solution: The joint probability density of two random variables X1 and X2 is given by F(x1, x2) = {6e^(−2x1 − 3x2) for x1 > 0 and x2 > 0, otherwise. Find the probability P(I2).It is known that, for any joint probability density function f(x, y) and any real number a,b,c, and d such that a ≤ b and c ≤ d, we have: P(a ≤ X ≤ b, c ≤ Y ≤ d) = ∫(c to d) ∫(a to b) f(x,y)dxdy.

We use this formula to calculate the required probability. We have:I2 = {X2 > 2X1}. Hence, we want to find the probability that X2 > 2X1. This probability can be written as: P(I2) = P(X2 > 2X1) = ∫(0 to ∞) ∫(2x1 to ∞) f(x1,x2)dx2dx1= ∫(0 to ∞) ∫(2x1 to ∞) 6e^(−2x1 − 3x2) dx2dx1= 6 ∫(0 to ∞) e^(−2x1) ∫(2x1 to ∞) e^(−3x2) dx2dx1Now, let's solve the inner integral first. We get:∫(2x1 to ∞) e^(−3x2) dx2= (-1/3) e^(−3x2)|2x1 to ∞= (-1/3) e^(−6x1)Now we substitute this value of the integral back into the outer integral. We get: P(I2) = 6 ∫(0 to ∞) e^(−2x1) (-1/3) e^(−6x1) dx1= (-2) ∫(0 to ∞) e^(−8x1) dx1= (-2) (1/8)= -1/4. Hence, the required probability P(I2) is equal to -1/4.

Therefore, the correct option is (D) -1/4.

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The required rate for water being poured into the cup when the water level is 9 cm = 40.5π cm³/sec

For given question,

We have been given the height of a conical paper cup i.e., h = 10 cm

and the radius of a conical paper cup r = 10 cm

The cup is being filled with water so that the water level rises at a rate of 2 cm/sec

We need to find the rate at which water being poured into the cup when the water level is 9 cm

We know that the volume of the cone is \(V=\frac{\pi r^2 h}{3}\)

We can relate h and r as we know that the slope = h/r

                                                                                  = 10/5

                                                                                  = 2

Now, we make the volume a formula in a single variable

\(\Rightarrow V=\frac{\pi (\frac{h}{2} )^2 h}{3}\\\\\Rightarrow V=\frac{\pi h^3}{12}\)

Differentiating above equation with respect to time,

\(\Rightarrow V'=\frac{3\pi h^2 h'}{12} \\\\\Rightarrow V'=\frac{\pi h^2 h'}{4}\)

Substituting values,

\(\Rightarrow V'=\frac{\pi \times 9^2\times 2}{4}\\\\\Rightarrow V'=40.5\pi~~cm^3/sec\)

Therefore, the required rate for water being poured into the cup when the water level is 9 cm = 40.5π cm³/sec

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