Jordan reads a comic book at a rate of 21 pages in 6 minutes. At this rate, how many pages does he read each minute?

Answer:

53b - 7b - 6b + 1 with b = 25 simplifies to 1001.

Step-by-step explanation:

To simplify 53b - 7b - 6b + 1 with b = 25, we substitute 25 for b and simplify the expression as follows:

53b - 7b - 6b + 1 = 53(25) - 7(25) - 6(25) + 1

= 1325 - 175 - 150 + 1

= 1001

Therefore, 53b - 7b - 6b + 1 with b = 25 simplifies to 1001.

The angle of depression is always measured from the horizontal.

A triangle is formed by the lighthouse, the ground and the boat. The angle of depression is not in the triangle, but it is equal to the angle of elevation at the boat. (Alternate angles on parallel lines)

The angle at the top of the lighthouse, inside the triangle is:

[tex]90^\circ-27^\circ=63^\circ[/tex]

The distance to the boat is the side opposite the angle of 63° while the height of the lighthouse is the adjacent side.

[tex]\dfrac{\text{opposite}}{\text{adjacent}} =\text{tan 63}^\circ[/tex]

[tex]\dfrac{\text{distance}}{245} =\text{tan 63}^\circ[/tex]

[tex]\text{distance}=245\times \text{tan 63}^\circ[/tex]

[tex]=480.83=480.84\thickapprox\boxed{\bold{480.8}}[/tex]

The solution to the initial value problem is [tex]y = (3 - e^x)/(e^x - 1)[/tex]. The domain of this solution is all values of x except x = ln(3).

A method for resolving specific kinds of first-order ordinary differential equations is called variable separation. It entails moving the equation's terms so that those involving the independent variable x are on the other side and those involving the dependent variable y are on the one side. In order to arrive at a general solution, we can then integrate both sides with respect to their respective variables. The name of the method comes from the fact that the variables on either side of the equation are separated.

The given differentiation is given as:

[tex]dy/dx = 9e^{x - y}[/tex]

Separating the variables we have:

[tex]dy/(9e^{x - y}) = dx[/tex]

Now, integrating on both sides we have:

[tex]\int dy/(9e^{x - y}) = \int dx[/tex]

Using partial fraction decomposition we have:

[tex]\int [1/(3-y) - 1/(3e^{x-y})] dy = x + C[/tex]

Integrating each term we have:

[tex]ln|3-y| - ln|3e^{x-y}| = x + C\\ln|3-y| - ln (\|y-3e^x\| = x + C\\ln|(3-y)/(y-3e^x)| = x + C\\(3-y)/(y-3e^x) = ke^x[/tex]

, where k is a constant of integration

We can solve for y:

[tex]y = (3ke^x + 3)/(ke^x + 1)[/tex]

Now, for the initial condition y = 4 and x = 0 we have:

[tex]4 = (3k + 3)/(k + 1)\\4k + 4 = 3k + 3\\k = -1[/tex]

Hence, the solution to the initial value problem is [tex]y = (3 - e^x)/(e^x - 1)[/tex].

Now, the domain of this solution is all values of x except x = ln(3)

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To find the area of the resulting surface when the given curve y = 1/4x^2 - 1/2 ln(x) is rotated about the y-axis, we can use the Surface of Revolution formula:

Surface Area = 2 * pi * ∫[x * sqrt(1 + (dy/dx)^2)] dx from a to b

Here, a = 3 and b = 5.

First, we need to find the derivative of y with respect to x (dy/dx):

y = 1/4x^2 - 1/2 ln(x)
dy/dx = (1/4 * 2x) - (1/2 * 1/x) = x/2 - 1/(2x)

Now, let's plug this into the Surface of Revolution formula:

Surface Area = 2 * pi * ∫[x * sqrt(1 + (x/2 - 1/(2x))^2)] dx from 3 to 5

We will now integrate the expression within the brackets with respect to x from 3 to 5. This might be challenging to solve analytically, so we may need to use a numerical integration method or a calculator to find the exact value.

Once the integration is completed, you will obtain the surface area of the curve when rotated about the y-axis.

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Answer:

6(15) + 25x = w

Step-by-step explanation:

6h would be the babysitting money, and since we know the hours, h, we replace the variable with the constant, 15, to get 6 * 15, or 6(15).

25x represents that each week, x, you earn $25.

Put this all together to get the answer above.

You will have $5,333.85 in your CD at the end of the 5 years.

The formulation for the future value of an investment with monthly compounding is:

[tex]CD = P(1 + \frac{r}{n} )^{(nt)}[/tex]

Wherein:

Plugging in the given values:

[tex]CD= 5000(1 + \frac{0.0125}{12} )^{(12*5)}[/tex]

[tex]CD = 5000(1.00104)^{60}[/tex]

CD = 5000(1.06677)

CD = $5,333.85

Consequently, you will have $5,333.85 in your CD at the end of the 5 years.

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Answer:

the required answer is 1 and -5

Answer:in your mouth

Step-by-step explanation:

The surface area of the right rectangular prism 280 yd².

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The surface area of a rectangular prism is expressed as;

S.A = 2( wl + hl + hw )

Where w is the width, h is height and l is length.

From the diagram:

Length l = 6 yd

Width w = 5 yd

Height = 10 yd

Plug the values into the above formula:

S.A = 2( wl + hl + hw )

S.A = 2( 5×6 + 10×6 + 10×5 )

S.A = 2( 30 + 60 + 50 )

S.A = 2( 90 + 50 )

S.A = 2( 140 )

S.A = 280 yd²

Therefore, the surface area is 280 square yards.

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The graph of the exponential function across the interval is attached below

To graph the function y = 3ˣ over the interval 1 ≤ x ≤ 2, you can follow these steps:

Choose a suitable scale for the x-axis and y-axis. Since the function grows rapidly, you may need to use a logarithmic scale on the y-axis to show the entire graph.

Plot some key points of the function. To do this, you can choose some values of x within the given interval and calculate the corresponding values of y. For example:

When x = 1, y = 3^1 = 3

When x = 1.5, y = 3^1.5 = 5.2

When x = 2, y = 3^2 = 9

Connect the plotted points with a smooth curve. Since the function is exponential, the curve will be a smooth upward curve that gets steeper and steeper as x increases.

Label the axes and add any necessary annotations or markings. For example, you may want to label the plotted points with their coordinates or add gridlines to help read off values from the graph.

Kindly find the attached graph below

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Answer:

a) a square number:64

b) a multiple of 13:65

c) a factor of 186:62

d)the prime number:61,67

Answer: The probability that a millet seed will fall next can be found by dividing the number of millet seeds by the total number of remaining seeds.

Total number of remaining seeds = 40 + 65 + 60 + 35 = 200

Probability that a millet seed will fall next = Number of millet seeds / Total number of remaining seeds

= 65 / 200

= 0.325 or 32.5% (rounded to one decimal place)

Therefore, the probability that a millet seed will fall next is 0.325 or 32.5%.

Step-by-step explanation:

Based on the information we can infer that the area of the figure is 464 ² units.

To calculate the area of this figure we must assume that it is a complete square and find its area as shown below:

Now we must find the area of the non-grid regions and subtract them from the area we found previously:

576 - 112 = 464 units ²

According to the above, the area of the figure is 464 units ²

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No, 3 is not greater than 5. This is because 5 is larger than 3.

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

3 and 5

No, 3 is not greater than 5. This is because 5 is larger than 3.

In other words, 5 is further to the right on the number line than 3.

We can also say that 5 is the greater number and 3 is the lesser number.

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Answer: If the daffodil start at 1 inch on day one, and only 1 day has passed, it will grow half of what it would in 2 days because half of 2 is 1. So the current height 1 inch + how much it will grow in one day (1.5 inches) = the final height (2.5 inches) Hope this helps :D

Step-by-step explanation:

The height of the cone is approximately 1.5 cm.

Both a cone and a cylinder have circular bottoms and are three-dimensional shapes. The lateral surfaces of the two shapes differ most noticeably from one another. A cone has a lateral surface that tapers from a point at the apex to a circular base, whereas a cylinder has a curved lateral surface that is parallel to its base. The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius of the base and h is the height, whereas the volume of a cone is calculated using V = (1/3)πr²h.

The volume of the cone is given as:

V = (1/3)πr²h

Rearranging the equation to isolate h we get:

3V = πr²h

h = (3V)/(πr²)

Now, for  volume

of 48 cm³ and a base with a radius of 4 cm we have:

h = (3(48))/(π(4)²)

h ≈ 1.5 cm

Hence, the height of the cone is approximately 1.5 cm.

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Going from top left to right then bottom left to right

Answers:

1st. answer: 94

2nd. answer: 82

3rd. answer: 142

4th answer: 88.2

5th. answer: 130

6th. answer: 178

(also I relearned how to do triangles)

(I'm going to follow you so if you have any more questions I can help)

Answer: 5 3/4 feet

Step-by-step explanation:

The original perimeter of the room is:

2(length + width) = 2(13 ft + 8 ft) = 42 ft

After the length and width are increased by "x" feet, the new perimeter becomes 53 1/2 ft.

So, we can write the equation:

2(length + x + width + x) = 53 1/2 ft

Simplifying the equation, we get:

2(length + width + 2x) = 53 1/2 ft

But we know that the original perimeter of the room was 42 ft, so:

2(length + width) = 42 ft

Substituting this into the above equation, we get:

42 ft + 2x = 53 1/2 ft

Subtracting 42 ft from both sides, we get:

2x = 11 1/2 ft

Dividing both sides by 2, we get:

x = 5 3/4 ft

Therefore, the length and width of the room were both increased by 5 3/4 feet

The acceleration acquired by the object of mass 12 Kg and is pushed with a force of 12 N, is given by 5/3 m/s².

We know that from the first law of Newton's Law that,

F = m*a

where 'F' is applied force; 'm' is mass of object and 'a' is acceleration.

Let the acceleration acquired by the object be 'A'.

Mass of the object is (m) = 12 Kg

The force applied (F) = 20 N

So from Newton's First Law of Motion we get,

F = m*a

20 = 12*A

A = 20/12

A = 5/3

Hence the acceleration will be 5/3 m/s².

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The question is in another language. The question is in English will be -

''What is the acceleration acquired by an object that has a mass of 12 Kg and is pushed with a force of 20N?''

Area of rectangle = 50 [tex]unit^2[/tex].

Perimeter of rectangle =30 unit.

Area of dilated rectangle = 1250  [tex]unit^2[/tex].

Perimeter of dilated rectangle = 150 unit.

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size.

Here the given rectangle length l = 10 unit and width = 5 unit.

Now using formulas,

Area of rectangle = lw square unit.

=> A = 10*5 = 50 [tex]unit^2[/tex].

Perimeter of rectangle = 2(l+w) unit

=> P =2(10+5) = 2(15) = 30 unit.

Here scale factor= 5

The dilated rectangle length [tex]l_1[/tex]= 10*5 = 50 unit and

width [tex]w_1 = 5\times5 = 25[/tex] unit

Now area of dilated rectangle [tex]A_1[/tex]= [tex]l_1w_1[/tex] square unit.

=>  [tex]A_1[/tex]= 50*25 = 1250  [tex]unit^2[/tex].

Perimeter of dilated rectangle [tex]P__1[/tex] = 2([tex]l_1+w_1)[/tex] unit.

=>  [tex]P__1[/tex] = = 2(50+25) = 2(75) = 150 unit.

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Answer:

  h = 10 13/14 units

Step-by-step explanation:

You want the height from the side of length 14 of a parallelogram with side length 17 and height 9.

The area of a parallelogram is the same, no matter which side is used as the "base". This means ...

  A = bh = 17(9) = 14(h)

  h = 17·9/14 = 10 13/14 . . . . units

This prompt is about rounding figures up. We can conclud t that where the above are given, both lists are not in the same order.

  To round up the first order to the second decimal place we have:

Rounding the second batch of cheese and ordering them from the least to greatst, we have:

Hence, we can submit that they are both not in the same eorder.

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As per the given Equation Each sister received 1 piece of jewelry.

Let's the number of pieces of jewelry that each sister received "x". Since there are 5 sisters, the total number of pieces of jewelry that the sisters received is 5x.

We can then set up an equation to represent the total number of pieces of jewelry that the sisters received from both grandmothers:

13 + y = 5x

This equation says that the total number of pieces of jewelry the sisters received is equal to the sum of 13 pieces from Grandma Gertrude and y pieces from Grandma Fien, and this total is also equal to the number of sisters (5) times the number of pieces each sister received (x).

To solve for x, we can first simplify the equation:

y = 5x - 13

Now we can substitute this expression for "y" into the original equation:

13 + (5x - 13) = 5x

5x = 5x

This equation is true for any value of x, which means that x can be any number. However, we are looking for the number of pieces of jewelry that each sister received, so we need to find a specific value of x.

Dividing both sides of the equation by 5, we get:

x = 1

This means that each sister received 1 piece of jewelry.

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Answer: tan 47/1 = x/.5 = x = .53618

Step-by-step explanation:

The probability of picking blue ball by Liz and Mike are equal =1/3

Probability is a branch of mathematics that deals with the study of random events or experiments. It is concerned with quantifying the likelihood or chance of a particular event occurring, given certain assumptions or conditions.

The probability of an event is typically represented as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain. For example, if you flip a fair coin, the probability of getting heads is 0.5, and the probability of getting tails is also 0.5.

There are different methods for calculating probabilities, depending on the nature of the event or experiment being considered. Some of the most commonly used methods include the classical probability method, the empirical probability method, and the subjective probability method.

Probability has many applications in various fields, including statistics, finance, engineering, and science. It is used to model and analyze complex systems and to make predictions and decisions based on uncertain information.

Given : X contains 9 blue balls and 18 red balls.

Y contains 7 blue balls and 14 red balls.

Probability of picking blue ball is 9/9+18

=9/27=1/3

Now Mike pick ball from bag Y one ball not affect these pick ball

so, 7/7+14=7/21=1/3

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Thus, with 99% confidence, we can say that the proportion of smeared ink in the 200 sheets of paper inspected falls between 1.3% and 15.7%.

To calculate the confidence interval of the proportion smeared in 200 sheets of paper inspected for smeared ink, we can use the formula:

Confidence Interval = sample proportion ± (critical value) x (standard error)

The sample proportion is the number of sheets containing smeared ink divided by the total number of sheets inspected, which is 17/200 = 0.085.

The critical value for a 99% two-sided confidence interval with 200 observations can be found using a t-distribution table or calculator, and is approximately 2.576.

The standard error can be calculated as the square root of [(sample proportion) x (1 - sample proportion) / sample size], which is the square root of [(0.085) x (1 - 0.085) / 200] = 0.028.

Plugging in these values, we get:

Confidence Interval = 0.085 ± (2.576) x (0.028)
Confidence Interval = 0.085 ± 0.072
Confidence Interval = (0.013, 0.157)

Therefore, with 99% confidence, we can say that the proportion of smeared ink in the 200 sheets of paper inspected falls between 1.3% and 15.7%. This means that we are 99% confident that the true proportion of smeared ink in the population of printed sheets falls within this range.

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A dot plot is a simple type of graph that represents data using dots. It is a one-dimensional display of data where each dot represents a single data point. Dot plots are useful for showing the distribution of a set of values, particularly when the data set is small.

To create a dot plot, you simply draw a horizontal or vertical line and plot a dot above or beside the line for each data point. The dots are usually stacked vertically or horizontally if there are multiple data points with the same value.

    |         x

 8  |     x  

 7  | x x x  

 6  | x x x x

 5  | x x x x

 4  | x x x x x

 3  | x x x x x

 2  | x x x x x x

 1  | x x x x x x x

     ---------------

        1 2 3 4 5 6 7

In this example, the dot plot shows the number of times a dice roll resulted in a particular value. The x's represent the data points, and the numbers on the left indicate the frequency of each value.

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