Consider the initial value problem 5y? , y(0) = yo For what value(s) of yo will the solution have vertical asymptote at t=4 and t-interval of existence C < 4?

Answer:

(B) C(t) = 396(1.029)^t.

Step-by-step explanation:

We can use the formula for exponential growth to find the function that models the population of Charlotte:

C(t) = C0 * r^t

where C0 is the initial population (in thousands), r is the annual growth rate, and t is the number of years after the initial population was recorded.

We are given that the population in Charlotte was 396,000 in 1990 and 872,000 in 2018. This means that the population grew by (872,000 / 396,000)^(1/28) per year on average (since there are 28 years between 1990 and 2018).

So the annual growth rate is approximately 1.029.

Therefore, the function that finds the population of Charlotte in thousands t years after 1990 is:

C(t) = 396 * 1.029^t

A graph of the line with slope 3/4 passing through the point (5, 2) is shown in the image attached below.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (5, 2), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 3/4(x - 5)

y - 2 = 3x/4 - 15/4

y = 3x/4 - 1.75

In conclusion, we would use an online graphing calculator to plot the above linear equation as shown in the graph attached below.

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The statement that "The correlation coefficient (r ) is a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables" is true.

The correlation coefficient (r) is a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables. It ranges from -1 to +1, with a value of -1 indicating a perfect negative linear relationship, 0 indicating no linear relationship, and +1 indicating a perfect positive linear relationship. The sign of r indicates the direction of the relationship, with a negative sign indicating an inverse relationship and a positive sign indicating a direct relationship. Thus, the correlation coefficient provides a useful summary of the degree to which two variables are related in a linear fashion.

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The rate of change of the circle diameter with respect to the radius is a constant value of 2.

The diameter of a circle is twice the radius, so we can write:

Diameter = 2 * Radius

To find the rate of change of the diameter with respect to the radius, we can take the derivative of both sides of this equation with respect to the radius:

diameter/d(radius) = d(2 * radius)/d(radius)

The derivative of 2*radius with respect to radius is simply 2, so we can simplify the equation:

diameter/d(radius) = 2

Therefore, the rate of change of the circle diameter with respect to the radius is a constant value of 2. This means that if we increase the radius by a small amount, the diameter will increase by twice that amount. Conversely, if we decrease the radius by a small amount, the diameter will decrease by twice that amount.

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The point on the curve y = x^2 - 3x + 5 where the normal is parallel to the tangent to the curve at the point (4, 9), we need to find the slope of the tangent at the point (4, 9) and then find the point on the curve where the slope of the normal is the same. The equation of the normal is y = -1/5x + 4.52.

First, find the derivative of the function y = x^2 - 3x + 5 to get the slope of the tangent:

dy/dx = 2x - 3

Next, plug in the x-value of the point (4, 9) to find the slope of the tangent at that point:

dy/dx = 2(4) - 3 = 5

The slope of the normal at any point on the curve will be the negative reciprocal of the slope of the tangent at that point. So, the slope of the normal at the point we are looking for will be -1/5.

To find the point on the curve where the slope of the normal is -1/5, set the derivative of the function equal to -1/5 and solve for x:

2x - 3 = -1/5

10x - 15 = -1

10x = 14

x = 1.4

Plug this x-value back into the original function to find the y-value:

y = (1.4)^2 - 3(1.4) + 5 = 4.24

So, the point on the curve where the normal is parallel to the tangent at the point (4, 9) is (1.4, 4.24).

Finally, to find the equation of the normal, use the point-slope form of a line:

y - y1 = m(x - x1)

y - 4.24 = -1/5(x - 1.4)

y = -1/5x + 4.52

So, the equation of the normal is y = -1/5x + 4.52.

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The values of a , b and c in the given quadratic sequence are

a = 2, b = 5, c = -4

The ordered collections of numbers known as quadratic sequences are based on the rule n2 = 1, 4, 9, 16, 25. (the square numbers). Every quadratic sequence has a n2 term.

Now in the given question ,

For nth term we have,

an² + bn + c

n = 1:

a + b + c = 3    Eq. 1

n = 2:

4a + 2b + c = 14    Eq. 2

n = 3:

9a + 3b + c = 29    Eq. 3

Eq. 2 minus Eq. 1

3a + b = 11    Eq. 4

Eq. 3 minus Eq. 2

5a + b = 15    Eq. 5

Eq. 5 minus Eq. 4

2a = 4

a = 2

Plug in a = 2 into Eq. 4

3(2) + b = 11

b = 5

Plug in a = 2 and b = 5 into Eq. 1.

2+5 + c = 3

c = -4

The required values are ,  a = 2, b = 5, c = -4.

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-x - 10y +3 after grouping related terms and adding their respective coefficients.

A polynomial, a set, or the quadratic coefficient of a specific term in an equation are almost all examples of coefficients in algebra. Usually numeric, but any phrase is acceptable. If the correlates are variables, them can also be referred to as "specifications" by themselves. A coefficient is calculated multiplied by a component. Examples of ratios include: In the expression 14c 14c 14c, the coefficient is 14. Word g has to have a coefficient of 1, which doubles the element by this figure. example A coefficient is 6 becuase "z" is a variable and the definition of the word is 6z. The square that x's coefficient is one.

given

-x+5-7y-3y-5+3

We add the coefficients of like phrases after combing them.

-x - 7y -3y +3

= -x - 10y +3

-x - 10y +3 after grouping related terms and adding their respective coefficients.

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Therefore , the solution of the given problem of triangle comes out to be ∠ADC  = 100 and ∠DCB  = 39 Degree.

Given that they have three quadrants or more, triangles are considered polygons. It has a straightforward geometric shape. The letters ABC form a right-angled triangle when put together. Euclidean geometry creates a new rectangle of square when the borders are incompatible. Given that they have three sides and three corners, triangles are categorised as polygons. The corners of a triangle are determined by where its three sides meet. The sum of the angles inside a triangle is 180 degrees.

Here,

Given :

A triangle ADC and Triangle DCB

To find the angle :∠ADC and ∠DCB in the figure

So,

Acc to triangle angle sum property:

43 + 3y + 7 + 2x + 17 = 180

Simplifying, we get:

2x + 3y + 67 = 180

Subtracting 67 from both sides, we get:

2x + 3y = 113

and

61 + 3y - 13 + 4x - 1 = 180

4x + 3y + 47 = 180

4x + 3y = 133

2x + 3y = 113

4x + 3y = 133

-4x - 6y = -226

Adding this to the second equation, we get:

-3y = -93

Dividing both sides by -3, we get:

y = 31

Substituting this value of y into either equation, we can solve for x:

2x + 3(31) = 113

2x + 93 = 113

2x = 20

x = 10

Therefore, the solution is x = 10, y = 31.

Thus,

∠ADC  = 3(31) + 7 = 93 + 7  = 100

∠DCB = 4(10) -1 = 40 -1  =39

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In the given question, the rocket will hit the ground in 7 seconds. The width of the rectangle is 3 cm. Kirk makes the wall in 5.5 hours. The student needs 97 marks.

The relation between the height and the time of the toy rocket has been given in the question as,

h = -4.9t²+33.6t + 4.9

where,

h= height of the rocket after getting launched

t= time after which the rocket has been launched

So, if we have to calculate how much time the rocket takes to reach the ground,

we have to take h=0 (at ground).

So, the equation becomes

0 = -4.9t²+33.6t + 4.9

Now, the roots of this equation will give the time at which the rocket will hit the ground.

So, after calculating we get

t = -0.1428 sec

or

t = 7 sec

since negative time is not possible,

the time at which the rocket will hit the ground is 7 seconds.

The length of the rectangle is = 5b-7 cm

Hence, the area is = b(5b-7) = 24

Hence, the width comes out to be = 3 cm

Kirk would be able to make the wall in 5.5 hours. This is because Jeff can make it one hour earlier than him i.e., K-1 hours. So, we get -

= (K-1) + K = 10

= 2K = 11

= K = 5.5 hours

The student already has 87 + 85 + 91 = 263 marks. He needs at least -

= (263 + x) / 4 = 90

= 97 marks

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The derivative of cosx is -sinx

Derivative defines the change in the dependent variable with respect to a small change in the independent variable

This means that if we have

y = cosx

where x is the independent variable and y is the independent variable, then the derivative of cosx i.e y will be the amount of change in y due to a small change in x.

i.e, dy/dx = -sinx

we also write this as

d/dx (cosx) = -sinx

This can be proved by the first principle where

[tex]f'(x) = \lim_{h \to 0} \frac{ [f(x + h) - f(x)] }{h}[/tex]

Hence we get

d/dx (cosx)

[tex]f'(x) = \lim_{h \to 0} \frac{ [cos(x + h) - cosx] }{h}[/tex]

[tex]= \lim_{h \to 0}\frac{[-2sin\frac{x+h+x}{2} sin\frac{x+h-x}{2}]}{h}[/tex]

[tex]= \lim_{h \to 0}\frac{ [-2sin\frac{2x+h}{2} sin\frac{h}{2} ]}{h}[/tex]

[tex]= \lim_{h \to 0}\frac{ [-sin\frac{2x+h}{2} sin\frac{h}{2} ]}{h/2}[/tex]

Now we know that [tex]\lim_{x \to0} \frac{sinx}{x} = 1[/tex]

Hence we get

-sinx

Therefore derivative of cosx = -sinx

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Answer:

1/8 = 12.5%

first, you can convert your fraction into a decimal by 1 divided by 8, which is 0.125. To change a decimal to percent, I can use DP, so D meaning decimal, and P meaning percent so we are going from the decimalcto percent by moving two places to the right, starting at your point. So 0.125 is 12.5%

Answer:

Step-by-step explanation:

You can create a vector both by enclosing the elements in square brackets like v=[1 2 3 4 5] or using commas, like v=[1,2,3,4,5]. They mean the very same: a vector (matrix) of 1 row and 5 columns.

The given table is studied and the probability for each case of the question is found as given below.

What is meant by probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. It is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

1) Earning 10000 - 13000 per month and owning exactly 2 vehicles.

Number of families surveyed = 2400

Number of families earning  10000 - 13000 per month and owning exactly 2 vehicles = 29

Therefore required probability = 29/2400 = 0.0121

2)  Earning 16000 or more per month and owning exactly 1 vehicle.

Number of families surveyed = 2400

Number of families earning 16000 or more per month and owning exactly 1 vehicle  = 579

Therefore required probability = 579/2400 = 0.241

3) Earning less than 7000 per month and does not own any vehicle.

 Number of families surveyed = 2400

Number of families earning less than 7000 per month and does not own any vehicle = 10

Therefore required probability = 10/2400 = 1/240

4) Earning 13000 - 16000 per month and owning more than 2 vehicles.

   Number of families surveyed = 2400

Number of families earning 13000 - 16000 per month and owning more than 2 vehicles = 25

Therefore required probability = 25/2400

5)  Number of families surveyed = 2400

Number of families owning not more than 1 vehicle = Number of families owning 0 vehicles + Number of families owning 1 vehicle

= (10+0+1+2+1)+(160+305+535+469+579)

= 2062

Therefore required probability = 2062/2400  = 0.86

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the probability that a continuous random variable equals any of its values is Zero.

This problem, we have been asked what is the probability of a continuous random variable being equal to any of its values, so the answer will be 0. The probability that a continuous random variable equals any of its values will be 0 point now.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

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Complete Question

The probability that a continuous random variable equals any of its value is?

On converting the length 161cm to feet , we get that 161 cm is equivalent to 5.29  feet .

There are different units that are used to measure the length or distance ;

such as feet , centimeter , meter , kilometer .

We have to convert the length : 161 centimeter to feet ;

we know that ; 1 centimeter is approximately equal to 0.0328 feet ;

So , we multiply 161 centimeter with 0.0328 ,

On multiplication ,

we get ;

⇒ 161 centimeter = 161 × 0.0328 ;

⇒ 161 centimeter = 5.2822 feet .

Therefore , 161 cm is approximately equal to 5.29 feet .

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The probability that the largest pile has 4 cards, the next largest has 3, the next largest has 2, and the smallest has 1 is approximately 0.012 or 1.2%.

To solve this problem, we need to count the number of ways to choose 10 cards from a deck of 52 cards and then divide by the total number of ways to put these cards into 4 piles.

Step 1: Count the total number of ways to choose 10 cards from a deck of 52 cards using the combination formula:

C(52, 10) = 52! / (10! × 42!) = 158,200,242,880 / (3,628,800 × 99,884,160) = 1,787,671

Step 2: Count the total number of ways to put 10 cards into 4 piles. We can think of each card as having 4 choices, one for each pile. Therefore, the total number of ways to put the cards into piles is:

[tex]4^{10}[/tex] = 1,048,576

Step 3: Count the number of ways to put 10 cards into 4 piles such that the largest pile has 4 cards, the next largest has 3, the next largest has 2, and the smallest has 1.

First, we need to choose 4 cards from the 10 cards to go into the largest pile. This can be done in C(10,4) ways:

C(10,4) = 10! / (4! × 6!) = 210

Then, we need to choose 3 cards from the remaining 6 cards to go into the next largest pile. This can be done in C(6,3) ways:

C(6,3) = 6! / (3! × 3!) = 20

Next, we need to choose 2 cards from the remaining 3 cards to go into the next largest pile. This can be done in C(3,2) ways:

C(3,2) = 3! / (2! × 1!) = 3

Finally, the remaining card goes into the smallest pile. Therefore, there is only one way to put the card into the smallest pile.

Therefore, the total number of ways to put 10 cards into 4 piles such that the largest pile has 4 cards, the next largest has 3, the next largest has 2, and the smallest has 1 is:

C(10,4) × C(6,3) × C(3,2) × 1 = 210 × 20 × 3 × 1 = 12,600

Step 4: Calculate the likelihood by dividing the number of ways in Step 3 by the number of ways in Step 2:

P = 12,600 / 1,048,576 = 0.012 or 1.2%.

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The length of w is 33.8 inches.

What is Sines law?

The law of sine or the sine law states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides. It is also known as the sine rule.

What are opposite angles ?

If two lines intersect and make an angle, say X=45°, then its opposite angle is also equal to 45°. And the angle adjacent to angle X will be equal to 180 – 45 = 135°. When two lines meet at a point in a plane, they are known as intersecting lines.

This is a law of sines problem since the triangle that contains side WY has all the angle measures & one of side measures.

a/sin a = b/sin b

7.3/sin 39 = YW/sin 8

YW = 7.3sin 8/sin 39 = 33.8

Hence , the length of w is 33.8 inches.

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The amount of photos that are giraffes is 3

1.) Caleb has 18 photos from going to the zoo.

2.) One sixth of them are giraffe pictures.

So basically, what you want to do is divide 18 by 6 = 3

The answer is : There are 3 giraffe photos out of the total 18 photos.

While the median usage for both types of apps is relatively similar, the usage range for gaming apps is much narrower than that of social media apps

From these statistics, we can conclude that gaming apps have a much narrower usage range than social media apps. To understand this concept, let's look at the interquartile range for each type of app.

The interquartile range (IQR) is the range of values between the 25th percentile and the 75th percentile of a given data set.

In this case, the IQR for gaming apps is 145 minutes, while the IQR for social media apps is 190 minutes.

This indicates that gaming apps have a much narrower range of usage than social media apps.

The median usage for gaming apps is 94 minutes, while the median usage for social media apps is 117 minutes.

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Answer: less than and less than

Step-by-step explanation: got it wrong by listening to the other answer :\

Answer:

3.16666667

Step-by-step explanation:

convert in a calculator online

inches to feet

The full amount is $10.

Let x be the full amount.

We know that 40% of the amount is equal to $4, so we can set up the equation:

0.4x = 4

To solve for x, we can divide both sides by 0.4:

x = 4 ÷ 0.4

x = 10

Therefore, the full amount is $10.

In mathematics, an expression is a combination of numbers, variables, and operations that are grouped together. It can be a simple expression, like "2 + 3", or a more complex one, like "(x + 3) / (y - 2)".

Expressions can be evaluated to produce a result, but they are not necessarily equations, since they don't always include an equal sign. They can also be used as components in larger expressions or equations.

For example, the expression "2x + 3y" can be used as part of the equation "2x + 3y = 12" to represent a relationship between x and y, or it can be used as part of a larger expression, like "(2x + 3y) / 5".

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Using the addition of the given fractions we know that Jamal drank a total (D) of six and one-half bottles of water.

One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division.

The entire amount or sum of the two whole numbers is obtained by adding them.

Mathematicians utilize addition as their main arithmetic operation to determine the sum of two or more numbers.

For instance, 7 + 7 equals 14.

So, the given fractions are:

2 1/6 and 3 7/8

Now, add them as follows:

2 1/6 + 3 7/8

13/6 + 31/8

52+93/24

145/24

6 1/24

Therefore, using the addition of the given fractions we know that Jamal drank a total (D) of six and one-half bottles of water.

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Complete question:

Jamal drank two and one-sixth bottles of water in the morning and three and seven-eighths bottles in the afternoon. Estimate how much water Jamal drank in all.

A. 5 bottles

B. five and one-half bottles

C. 6 bottles

D. six and one-half bottles

The subtracting fractions calculator online is a free online calculator showing the difference between two fractions.

The fraction represents the components of the whole in mathematics. It is important to keep track of the fraction types while subtracting fractions, whether they are like or unlike fractions. Like fractions are fractions with the same denominators, and unlike fractions are fractions with distinct denominators. When a fraction is similar, the numerator value can simply be removed. The methods to subtract the fractions are listed below if the denominators are the opposite fractions.

Take the denominator's LCM.

Now multiply the numerator and denominator values by the same number to convert the denominator value to the LCM value.

Finally, subtract the values of the fractions.

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Answer:

The profit per sweater is 29 dollars.

Step-by-step explanation:

First find the total profit.

136 - 20

116 for all 4 sweaters

Now divide by 4 since there are 4 sweaters to find the profit per sweater.

116/4

29

The profit per sweater is 29 dollars.

One milligram(mg) is equal to 1000 micrograms(mcg).

One microgram is equivalent to one millionth of a gram since the word "micro" in micrograms refers to one millionth. The prefix "milli" in milligrams, on the other hand, denotes a thousandth, making 1 milligram equivalent to a thousandth of a gram.

Given that 1 milligram is equivalent to 1000 micrograms, it is simple to convert between micrograms and milligram. In several fields, notably medicine, where accurate quantities of medications and other chemicals are frequently measured in micrograms or milligram, this translation is crucial.

The conversion between various metric prefixes is a key feature of the metric system, which is often used to represent measurements of mass, length, and volume.

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The two equations that are true for x = –2 and x = 2 are:

x2 – 4 = 0 (true for x = –2) and 4x2 = 16 (true for x = –2 and x = 2)

Quadratic equation can be defined as equation in which it is in the form of[tex]ax^2+bx+c = 0[/tex]

The options are:

x2 – 4 = 0

x2 = –4

3x2 + 12 = 0

4x2 = 16

2(x – 2)2 = 0

To check which equations are true for x = –2 and x = 2, we can substitute these values into each equation and see if it results in a true statement or not.

Substituting x = –2:

(-2)2 – 4 = 0 --> True

(-2)2 = –4 --> False

3(-2)2 + 12 = 0 --> True

4(-2)2 = 16 --> True

2((-2) – 2)2 = 0 --> False

Substituting x = 2:

22 – 4 = 0 --> False

22 = –4 --> False

3(2)2 + 12 = 0 --> False

4(2)2 = 16 --> True

2((2) – 2)2 = 0 --> True

Therefore, the two equations that are true for x = –2 and x = 2 are:

x2 – 4 = 0 (true for x = –2) and 4x2 = 16 (true for x = –2 and x = 2)

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The total surface area is 46.43 square centimeter.

The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a shape with a curved base and surface is equal to the sum of the two areas.

Given that, the area of the rectangle is 34.56 cm².

Here, the diameter is 2.75 cm, so radius =2.75/2=1.375 cm

Cylinder is made up of 1 rectangle and 2 circles.

Now, area of 2 circles =2πr²

= 2×3.14×1.375²

= 11.87 cm²

So, total surface area = 34.56+11.87

= 46.43 cm²

Therefore, the total surface area is 46.43 square centimeter.

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Answer: 9. False

              10. True

              11. False

              12. False, it is called an isosceles triangle

Step-by-step explanation: