The Nelson family drank 1/4 of a gallon of orange juice on Saturday morning and 2/5 of a gallon of orange juice on Sunday morning. How much orange juice did they drink in all?

The length of the arc of the given circle with radius 10 cm and an angle of 2.5 radians subtended by an arc of a circle is equal to 25 cm.

Let 'y' represents the length of the arc of the given circle.

Radius 'r' of the given circle is equal to 10 cm

Angle 'α'  subtended by an arc of a circle is equal to 2.5 radians.

length of the arc = Angle subtended by an arc × Radius of the circle

⇒ y = rα

⇒ y = 10 × 2.5

⇒ y = 25 cm

Therefore, the length of the arc of a circle for the given radius 10cm and subtended angle 2.5 radians is equal to 25 cm.

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The probability that two randomly generated strings of length 9 in the DNA alphabet is 729.

We have to find the probability that two randomly generated strings of length 9 in the DNA alphabet (a, c, g, t) are identical.

Probabilities are based on occurrences, and events can result from one or more observations or experiment results.

The total number of alphabet in word DNA is 3.

So, the probability that two randomly generated strings of length 9 in the DNA alphabet = 9 × 9 × 9

The probability that two randomly generated strings of length 9 in the DNA alphabet = 729

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Answer:

13

Step-by-step explanation:

Answer:

x = -1

Step-by-step explanation:
y-0.8x=0.5

5y-2.5-4x

Get y by itself.
y = 1.3

Put 1.3 into the second equation

5(1.3) - 2.5 - 4x
6.5-2.5 - 4x
4 - 4x = 0
Get x by itself
-4x = 4
x = -1

I hope this was able to help you :D

Answer:

$16.8

Step-by-step explanation:

u got to trust me

Answer: $16.8

im sure its this it has to be

The value of distance after calculating are  AB = 4 ft and BC = 16 ft.

What is ratio?

A ratio is a comparison between two numbers or quantities. It is typically expressed as a fraction, with the first number being divided by the second number. Ratios are often used to compare values or to express a portion of a whole.

It is given in the question, that Ladd is rearranging his living room furniture. He wants his couch to sit along the 20-ft wall.

To find the length of AB and BC we need to relate them using the equations.

AB + BC = 20 ft (from the diagram) ----------- (Equation 1)

∵ AB : BC = 1 : 4

⇒ 4AB = BC

Substituting,  BC = 4AB into equation 1.

AB + 4AB = 20 ft

5AB = 20 ft

AB = 4 ft

Plugging AB = 4 ft into equation 1.

4 + BC = 20

BC = 20 ft - 4 ft

BC = 16 ft

Thus, the value of sides AB = 4 ft and BC = 16 ft , and here AB and BC are in ratio 1:4.

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The angular momentum of the the ball is 4.16kgrad/sec

Angular momentum is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity. This means that the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. It is measure d in kgrad/sec

angular momentum = mass × angular velocity

mass = 0.18kg

angular velocity = 5.2 rad/s

therefore angular momentum = 0.18× 5.2

= 4.16 kg rad/s

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The change in elevation of the car is 0.66mile.

Now, According to the question:

Trigonometric functions are immensely useful when real-life examples form a right triangle. In such cases, sine, cosine, or tangent functions are used based on the given information to determine the unknown value. For example, suppose we are looking at the top of a building and we know the height of the building and our distance from the base of the building, using the tangent function, we can easily calculate the angle made by the line of sight above the ground.

d = 4 miles is the distance covered by the car on the inclined road.

θ = 9.5° is the angle made by the road above the horizontal.

Let:

h be the change in elevation of the car.

Using the sine function, we write:

[tex]sin\theta= \frac{opposite side}{hypontenuse}[/tex]

[tex]sin\theta =\frac{h}{d}[/tex]

h = dsinθ

h = (4 mile)(Sin(9.5°))

h ≈ 0.66 mile

Therefore, the change in elevation of the car is 0.66mile.

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Answer:

see below

Step-by-step explanation:

7. (4-4). K =0

d+12-8/4+5 = d+12-2+5 =d+15

The number of hours for which the cost is the same would be 5 hours.

The cost of renting a snowboard for 5 number of hours would be same as that point i.e. $5

By costs, what do you mean?

Costs are really the monetary value of purchases made for use by a company or other accounting entity of supplies, service, labor, products, equipment, and other items.

The cost of renting a snowboard from the first company is $5 per hour + $50 deposit = $5x + $50.

The cost of renting a snowboard from the second company is $10 per hour + $25 deposit = $10x + $25. To find the number of hours for which the cost is the same, we set the two costs equal to each other and solve for x:

$5x + $50 = $10x + $25

$5x - $10x = $25 - $50

$5x = $25 - $50

$5x = -$25

x = -5

As we will not take cost in negative so it would be 5

So, we can say that the cost is same at any point of time.

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Answer: This problem can be represented by the equation y = mx + b, where y is the total charges, x is the number of days, m is the charge per day, and b is the flat fee.

To find the values of m and b, we can use the given data points to solve for the equation.

For x = 2, y = 8, so 8 = m * 2 + b

For x = 4, y = 13, so 13 = m * 4 + b

For x = 6, y = 18, so 18 = m * 6 + b

We can then use a system of equations to solve for m and b:

m * 2 + b = 8

m * 4 + b = 13

m * 6 + b = 18

Using substitution or elimination methods:

m = 2

b = 2

Therefore, the equation is: y = 2x + 2

This means that the flat fee is $2 and the charge per day is $2.

Step-by-step explanation:

The rate of change for the linear function is 2.

The initial value for the linear function is 3.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The points on the coordinate plane:

(0, 3) and (2, 7)

Now,

The equation of the line.

y = mx + c

Slope = m

m = (7 - 3) / (2 - 0)

m = 4/2

m = 2

Now,

(0, 3) = (x, y)

3 = 2 x 0 + c

3 = 0 + c

c = 3

The y-intercept is 3.

Thus,

The rate of change is 2.

The initial value is 3.

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The distance of the translation resulting from the composition of the two reflections Rk and Rh is equal to |1 + 2x|

To determine the distance of the translation resulting from the composition of two reflections Rk and Rh, we can calculate the difference in x-coordinates of the pre-image and image points.

Reflection Rk reflects points over the line x = 2,

So the x-coordinate of a point and its reflection would have a difference of 2 - x, where x is the x-coordinate of the original point.

Reflection Rh reflects points over the line x = -3,

So the x-coordinate of a point and its reflection would have a difference of -3 - x

When we compose the two reflections

The x-coordinate of a point and its image will have a difference of (2 - x) - (-3 - x)

Evaluate

Distance = 5

Hence, the distance is 5 units

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The product for (2x+1) and (5-x) is -2x²+9x+5.

A fraction represents a part of a whole.

We have to find the product of (2x+1)(5-x)

We use distributive property to find the product.

2x(5-x)+1(5-x)

10x-2x²+5-x

-2x²+10x-x+5

Add the like terms

-2x²+9x+5

Hence, the product for (2x+1) and (5-x) is -2x²+9x+5.

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The number of ways to answer the questions is given as follows:

15,625.

The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For this problem, there are six questions, each with five possible options, hence the number of ways to answer the questions is calculated as follows:

5^6 = 15,625 ways.

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Approximately 95.45% of the area under the standard normal distribution lies within two standard deviations of the mean.

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. This means that 68.27% of the area under the standard normal distribution lies within 1 standard deviation of the mean, and 95.45% of the area under the standard normal distribution lies within 2 standard deviations of the mean.

This is because the standard deviation is a measure of the spread of the data; the larger the standard deviation, the more spread out the data is.

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Substitution is a method for solving systems of equations that involves solving for one variable in one equation and then substituting that value into the other equation.

Here's how we can use substitution to solve the system of equations:

5x+y=9

10x−7y=−18

Solve one equation for one variable, for example:

y = 9 - 5x

Substitute this expression of y into the other equation:

10x - 7(9 - 5x) = -18

Solve the equation resulting from the substitution

10x - 63 + 35x = -18

45x = 45

x = 1

Substitute this value of x back into one of the original equations to find the value of y.

5(1) + y = 9

y = 4

So the solution is (x,y) = (1,4)

You can check this solution by substituting it back into both original equations.

The statement that is most likely to be true in the question that we have here is that : The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology). Option 2

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability.

In the question the probability of robotics is 0.2 while the probability of zoology club is 0.2 as well.

They have equal probability

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Answer: Answer B

Step-by-step explanation:

The given relations are:

1) It is a function.

2) not a function.

3)it is a function.

4) not a function.

A function is a relation that maps inputs into outputs, such that each output needs to be mapped into a single input.

1) For example, the first relation each input (left row) is mapped into a single output, thus, it is a function.

2) Here theinput 9 is mapped into two different outputs, then it is not a function.

3) The notation used here is (input, output), so we can see that no input is repeated,so it is a functon.

4) The input 9 is mapped into 3 different outputs, then it is not a function.

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According to the graph, the system of equations x + 4y = 6 and y = 2 x -3 has one solution that is (2,1)

In math the term called graph is defined as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

Here we know that the following equation are known:

=> x + 4y = 6

=> y = 2x - 3

And here we need to find the number of solution for the equations.

Here we have to plot the equation on the graph then we get the graph like the following.

While we looking into the graph, we have identified that the intersection point in the graph is (2,1) and there is no other intersecting point.

Therefore, option (a) is correct.

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Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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Answer:

The answer in intercept form will be

[tex] - 1 \div 3 = 5 \div 3x + c \\ [/tex]

The statement using absolute value notation will be x - 78 ≤ 22.

The student will pass the test which scores 22 points for the number 78

Absolute values are any digit's value without taking the sign into an account. Therefore, all negative numbers will be regarded as positive for absolute value. The absolute value of -5, for instance, will be 5, whereas that of -7, will be 7.

In essence, the absolute value calculates the distance from zero. Putting an absolute value on something does not imply that they are the same number but that they are the same distance from 0.

Le the score of student be = x

Forming the absolute value notation -

This can be expressed as,

x - 78 ≤ 22.

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Answer:

Step-by-step explanation:

a)  A(11) > M(11)

       45 > 40

Go to x axis where t=11 then go straight up to find the y values (temp.) on each line

b)  Look for where the lines intersect.  This is where t≈47, t≈60

c)  M(t) < A(t) where t=2, t=11

Look for where the Minn. line (dashed orange) is BELOW the Aspen line (solid blue)

The value of x is 14.28 units, this is determined using the trigonometric functions.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the connection between the sides and angles of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Consider the smaller triangle:

Sin (30) = Opposite side ÷ Hypotenuse

0.5 = Opposite side ÷ 10

Opposite side = 5

Consider the bigger triangle:

Sin (22) = Opposite side ÷ Hypotenuse

0.37 = 5 ÷ x

x = 5 / 0.35

x = 14.28

Hence, the value of x is 14.28 units, this is determined using the trigonometric identities.

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As 5/10 are Girls in Class And 1/5 of the girls wear glasses So on overall girls wear glasses is 1/10 in the whole class.

The fraction 5/10 is equal to 1/2 of the total and 1/5 of the girls wear glasses so if you multiply 1/2 and 1/5 you get 1/10, To get a total fraction of girls who wear glasses overall will be by multiplying both the fraction. So,

1/5*1/2 = 1/10

Here the answer is produced by multiplying the numerator with the numerator and similarly denominator with the denominator to get the answer of total friction of girls wearing glasses in the whole class.

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The maximized value of the objective function is 3

From the question, we have the following parameters that can be used in our computation:

C = x + y

Subject to

y >= 0

x >= 0

4x + 2y <= 8

2x - y <= 0

When the graphs of these inequalities are plotted (see attachment), we have the following feasible regions

(x, y) = (0, 0) and (1, 2)

This means that

C = 0 + 0 = 0

C = 1 + 2 = 3

3 is greater than 0

Hence, the maximized value is 3

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The number of counters Rick has is equal to 12 counters.

The number of counters Tony has is equal to 1:1.5.

The value of p is 1.5.

In order to solve this word problem, we would assign variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Let R represent the number of counters Rick has.

Let S represent the number of counters Selma has.

Let O represent the number of counters Tony has.

Let T represent total number of counters.

Translating the word problem into an algebraic equation, we have;

S = 2R     .....equation 1.

O = 2R - 6    ......equation 2.

T = R + S + O   ......equation 3.

Substituting equation 1 and equation 2 into equation 3, we have:

T = R + S + O

54 = R + 2R + 2R - 6

54 = 5R - 6

5R = 54 + 6

5R = 60

R = 60/5

R = 12 counters.

For Tony, the number of counters is given by:

O = 2R - 6

O = 2(12) - 6

O = 24 - 6

O = 18 counters.

In ratio form, we have:

O = 1:P

O = 1:(18/12)

O = 1:1.5

The number of counters Rick has is equal to 12 counters.

The number of counters Tony has is equal to 1:1.5.

The value of p is 1.5.

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Answer: Because 2 places to the right of the the decimal.

Step-by-step explanation: