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Which answer best describes how to solve this story problem?

There are 4 fewer blue pens in a box than black pens. There are 15 black pens in each box.

How many blue pens are in 3 boxes?

Add 15 and 4. Then multiply the sum by 3.

Subtract 4 from 15. Then multiply the difference by 3.

Subtract 4 from 15. Then divide the difference by 3.

Answer:

For the first question it would be New Haven and it would be 4.7 degrees warmer. As for the second question it would be 3 hours after midnight the temperature is -2.5°C. Hope this helps!

Step-by-step explanation:

The largest possible value of the incident angle to undergo the total internal reflection is 61.04 degrees.

The angle between the top surface and bottom surface of the diamond is α=45∘.

The given problem will utilize Snell's law for the solution. As per Snell's law, the ratio of the sine of the angle of incidence and sine of the angle of refraction is equal to the ratio of refracted index and incident index.

As per Snell's law,

sin i / sin r = n' / n

n' is the refractive index of a diamond. (n' =2.45)

n is the refractive index of air. (n = 1)

Thus, the required largest possible value of the incident angle to undergo the total internal reflection is 61.04 degrees.

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Answer:

Step-by-step explanation:

The amount of Chemical  B needed is 1.6 g.

This refers to a diagram that shows a series of one or more points, lines, line segments, curves, or areas that represents the variation of a variable when compared with that of one or more other variables.

The quantity of Chemical B is plotted against the quantity of  Chemical A.

Chemical B  is plotted on the vertical axis using the scale of 1 cm to represent 2 units. Chemical A is plotted on the horizontal axis using the scale of 1 cm to represent 1 unit.

Therefore, on the graph, the line passing through the origin of the graph shows that when  1.4 g of Chemical A is used  1.6 g of Chemical B is needed.

Chemical B  is plotted on the vertical axis using the scale of 1  cm to represent 2 units.

To get the amount of Chemical B is  on vertical axis =  2 grams

                                                                                             5 boxes

                                                                                       =0.4 g

Tracing the mass of Chemical A used 1.4 g it meets the line passing through the center at 4th line (4th box).

To get the amount of Chemical B is  on vertical axis = amount of Chemical B per box * the number of line (boxes).

To get the amount of Chemical B is  on vertical axis = 0.4 g * 4 lines (boxes)

                                                                                        = 1.6 g

Hence The amount of Chemical  B needed is 1.6 g.

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Answer:

D. Precipitation

Step-by-step explanation : Gravity causes precipitation to fall from clouds and water to flow downward on the land through watersheds. Energy from the sun and the force of gravity drive the continual cycling of water among these reservoirs. As the water is heated, it changes state from a liquid to a gas.

Answer:

4/5

Step-by-step explanation:

the numerator of fraction is 1 less than its denominator. If the numerator is increased by 4 and the denominator is increased by 5, the new fraction becomes equivalent to 4/5. what is the original fraction?

Let n = numerator

d = denominator

n = d - 1

\(\frac{d - 1}{d}\)

\(\frac{d - 1 + 4}{d + 5}\) = \(\frac{4}{5}\)

\(\frac{d + 3}{d+ 5}\) = \(\frac{4}{5}\)

cross multiply

5(d + 3) = 4(d + 5)

5d + 15 = 4d + 20

d = 5

n = d - 1

5 - 1 = 4

original fraction 4/5

Answer: 9.7 seconds

Step-by-step explanation:

\(16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7\)

Answer:

always true

Step-by-step explanation:

Original inequality:

\(-6(2x-10)+12x\le180\)

Distribute the -6

\(-12x+60+12x\le180\)

Combine like terms:

\(60\le180\)

As you can see the expression on the left side is constant, so it is always true, since the constant (60) is less than 180

Answer:

35 miles

Step-by-step explanation:

Total Miles driven at full tank = 230 miles

Miles drive at full tank from Austin to Dallas = 195 miles

How many miles will be left once he arrives in Dallas?

Number of miles remaining at full tank = Total Miles driven at full tank - Miles drive at full tank from Austin to Dallas

= 230 miles - 195 miles

= 35 miles

To calculate the energy stored in a spherical cell, we can use the equation for the energy of a charged capacitor:

E = (1/2) * C * V^2

Where:

E is the energy stored

C is the capacitance of the cell

V is the membrane potential

(a) The diameter of the spherical cell is given as 16 μm. To find the capacitance, we need to determine the radius of the cell, which is half the diameter. Therefore, the radius is 8 μm.

(b) The capacitance of a spherical capacitor can be calculated using the formula:

C = (4πε₀r) / (1 - (r/R))

Where:

ε₀ is the vacuum permittivity (approximately 8.854 x 10^-12 F/m)

r is the radius of the spherical cell

R is the radius of the outer conducting shell (assumed to be infinity for a cell)

Substituting the values into the equation, we have:

C = (4πε₀ * 8 μm) / (1 - (8 μm/∞))

Since the term (8 μm/∞) approaches zero, we can simplify the equation to:

C = 4πε₀ * 8 μm

(c) Now we can calculate the energy stored in the cell using the given membrane potential of -90 mV. Substituting the values into the energy equation:

E = (1/2) * (4πε₀ * 8 μm) * (-90 mV)^2

Simplifying and converting the units:

E = (1/2) * (4πε₀ * 8 μm) * (0.090 V)^2

Finally, we calculate the numerical value:

E ≈ 9.05 x 10^-18 J

Therefore, the energy stored in the 16-μm-diameter spherical cell with a membrane potential of -90 mV is approximately 9.05 x 10^-18 joules.

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The volume of the solid is (3π/5) units^3.  To find the volume of the solid formed by rotating the region in the 1st quadrant enclosed by the curves y=x^1/4 and y=x/64 about the y-axis, we can use the method of cylindrical shells.

First, we need to determine the limits of integration. Since the region is in the 1st quadrant, we can integrate from y=0 to y=1. To find the corresponding x-values for these limits, we can set y=x^1/4 and y=x/64 equal to 1 and solve for x:

x^1/4 = 1 => x = 1

x/64 = 1 => x = 64

So, our limits of integration are x=1 to x=64.

Next, we need to find an expression for the radius of each cylindrical shell. The radius is simply the distance from the y-axis to the curve at a given y-value. So, for a given y, the radius is:

r = x - x^1/4

Finally, we need to find an expression for the height of each cylindrical shell. The height is the infinitesimal change in y, which is simply dy. So, the volume of each cylindrical shell is:

dV = 2πr dy

Putting it all together, we have:

V = ∫(2πr) dy from y=0 to y=1

= ∫2π(x - x^1/4) dy from y=0 to y=1

= 2π ∫(x - x^1/4) dy from y=0 to y=1

= 2π ∫(y^4 - y) dy from y=0 to y=1

= 2π [y^5/5 - y^2/2] from y=0 to y=1

= 2π [(1/5) - (1/2)]

= (3π/5) units^3

Therefore, the volume of the solid is (3π/5) units^3.

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Answer:

Step-by-step explanation:

-x² + 70x - 600

If we multiply all by -1, we have

x² - 70x + 600

If we factorise this, we have

x² - 10x - 60x + 600

x(x - 10) - 60(x - 10)

(x - 10) (x - 60)

x = 10

x = 60

If the company sells 10, or 60 items, their profit is 0

The difference between the areas of the posters is 56 in².

There are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example,  in a square, all angles are 90° and all sides present the same value.

The area of a square is given by: A= a², where  a=the length of the side.

         A=(13 in)²

         A= 169 in²

         A=(15 in)²

         A= 225 in²

Therefore, the difference in square inches between the area of Latrice's poster and the area of Nura's poster is 225 - 169=56 in²

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Answer:

6^11/3

Step-by-step explanation:

6⁴/6⅓

6⁴-⅓

6^11/3

Answer:

3/5

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

Experimental probability is based on the result of an experiment that has been carried out multiples times

experimental probability that she will see birds in her garden on July 1 = number of days she saw a bird in June / total number of days in June

= 18/30

To transform to the simplest form. divide both the numerator and the denominator by 6

Researchers try to gain insight into the characteristics of a sample population by examining a sample of the population.

A sample is a subset of individuals or units taken from a larger population. Researchers use sampling methods to select a representative group of individuals from the population they are interested in studying. By studying the sample, researchers can make inferences and draw conclusions about the characteristics, behaviors, or trends that may exist within the entire population.

The goal of sampling is to obtain a sample that accurately represents the population in terms of its relevant characteristics. Researchers carefully select their samples to ensure that they are representative and minimize bias. This allows them to generalize the findings from the sample to the larger population with a certain level of confidence.

By examining a sample, researchers can collect data, analyze patterns, and draw conclusions about the population as a whole. This approach is more feasible and practical than attempting to study the entire population, especially when the population is large or geographically dispersed.

Therefore, researchers use samples to gain insight into the characteristics of a population, making option d. "Sample" the correct answer.

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Answer:

a= 126 degrees

b= 54 degrees

r= 54 degrees

s= 126 degrees

Step-by-step explanation:

Opposite Q is length PR

Adjacent is 7

Hypotenuse is 19

We got AH - which is CAH or cos

Cos-1( 7/19) = 68.38....

It's 68.4 degrees

The closest answer to this is B. So, choose that because it maybe due to a typing error.

Hope this helps!

Answer: \((-3,18),\ (3,6)\)

Step-by-step explanation:

Given

Functions are \(x^2-2x+3\ \text{and}\ -2x+12\)

Equate them to solve

\(x^2-2x+3=-2x+12\\\Rightarrow x^2=9\\\Rightarrow x=\pm 3\\\therefore y=6,18\\\text{Ordered pairs are}\\(-3,18),\quad (3,6)\)

Answer:

a.

Step-by-step explanation:

x=4

3(2)=6

6(4)=24

24 is your answer!

Answer:

b

Step-by-step explanation:

Answer:

The 1st Picture

Step-by-step explanation:

An exponential function is a base with an exponent of x. The parent graph f(x) will always have an asymptote at x= 0 and curve steeply.

Answer:

A

Step-by-step explanation:

took it a minute ago on edg

The name of every month ends in the letter y is the given statement. February is a counterexample to this statement. This is because February does not end with the letter 'y'. So the right  option is (c) February.

What is a counterexample?

In mathematics, a counterexample is an example that opposes or disproves a statement, proposition, or theorem. It is a scenario, an instance, or an example that goes against the given statement.

Therefore, a counterexample demonstrates that the given statement is false or invalid.In this case, the statement is: "The name of every month ends in the letter y." We have to find which of the months listed does not end in "y."February is the only month in the options listed that does not end in the letter "y."

Thus, it is a counterexample to the given statement. Therefore, the correct option is C, February.

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Answer:

Here we do not have the options, so I will answer in a general way.

We have two statements:

p = A number is greater than 25

q = A number is less than 35

We want to have:

p ^ q is true

This means:

p and q are true.

So, we need to find a number such that both conditions are meet, so we need to find a number N such that

The number N is greater than 25  (from p)

The number N is less than 35 (from q)

So N can be any number between 25 and 35

So, some of the possible values of N are:

N = 26

N = 27

N = 28.6

N = 33

N = 34

Concluding, any number N ∈ (25, 35) can be a solution.

(Note that N = 25 and N = 35 are not solutions)

Answer:

-6, 6

Step-by-step explanation:

I hope this helps :)

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Two integer variables x and y, prompts the user to enter values for them using the Scanner class, and performs addition, subtraction, multiplication, and division operations on those variables:

import java.util.Scanner;

public class VariableOperations {

   public static void main(String[] args) {

       Scanner scanner = new Scanner(System.in);

       System.out.print("Enter the value for x: ");

       int x = scanner.nextInt();

      System.out.print("Enter the value for y: ");

       int y = scanner.nextInt();

       // Addition

       int addition = x + y;

       System.out.println("Addition: " + addition);

       // Subtraction

       int subtraction = x - y;

       System.out.println("Subtraction: " + subtraction);

       // Multiplication

       int multiplication = x * y;

       System.out.println("Multiplication: " + multiplication);

       // Division

       if (y != 0) {

           double division = (double) x / y;

           System.out.println("Division: " + division);

       } else {

           System.out.println("Cannot divide by zero.");

       }

   }

}

This code prompts the user to enter values for x and y, performs the four basic arithmetic operations, and displays the results on the screen.

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Answer:

y = 4x + 24

Step-by-step explanation:

The slope is the number in front of the x-value.

Slope intercept form is in the form of

y = mx + b  (or as how I learned it)

m is the slope, and b is the y-intercept (the number that is left on the side.)

You can rearrange this by moving the x to the right side by subtracting it from both sides.

You now have 1/8y = 3 - 1/2x

which can be rearranged to

1/8y = -1/2x + 3.

You need to change the y to 1 whole instead of 1/8, so you multiply it by 8 since 8 divided by 8 is 1.

y = -4x + 24

Given :-

To find:-

Answer:-

As we know that the diagonals of a rhombus bisects each other at right angles, so in the given figure ∆WOX is a right angled triangle, right angled at O .

Also , we know that all sides of the rhombus are equal.

So that;

\(\implies WX = WY = YZ = ZX \dots (i) \\\)

Again, in ∆WOX , by Pythagoras theorem , we have;

\(\implies WX^2 = WO^2 + OX^2 \\\)

And here ,

So on substituting the respective values, we have;

\(\implies WX^2 = 8^2 + 6^2 \\\)

\(\implies WX^2 = 64 + 36 \\\)

\(\implies WX^2 = 100 \\\)

\(\implies WX = \sqrt{100}=\boxed{10} \\\)

Hence the measure of WX is 10 .

Now again from equation (i) , we have;

\(\implies WX = WY \\\)

Therefore,

\(\implies \underline{\underline{ WY = 10}} \\\)

Hence the measure of WY is 10 .

and we are done!

Answer:

WY is 5 units.

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

Properties of a rhombus:

Given diagonals of 6 and 8 units.

According to the properties we mentioned above, WY is a hypotenuse of a triangle with legs equal to the half of the diagonals.

Use Pythagorean theorem to find the length of WY:

From the given choices, only P[{clubs}) = 0.7, P{{diamonds}) = 0.3 satisfies the requirements of the definition of probability.

The choice that fulfills the requirements of the definition of probability is:

P[{clubs}) = 0.7, P{{diamonds}) = 0.3.

For an event A in a sample space S, the probability of A, denoted by P(A), must satisfy the following conditions:

P(A) is a non-negative real number: This means that the probability of an event cannot be negative.

P(S) = 1: The probability of the sample space is always equal to 1. This implies that at least one of the events in the sample space must occur.

If A and B are two mutually exclusive events, then P(A or B) = P(A) + P(B): This means that the probability of either event occurring is equal to the sum of their individual probabilities.

In the given sample space S = {clubs, diamonds}, the probabilities of the two events must add up to 1, since there are only two possible outcomes.

Therefore, the probabilities of the events cannot be negative or greater than 1.

From the given choices, only P[{clubs}) = 0.7, P{{diamonds}) = 0.3 satisfies the requirements of the definition of probability.

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