What is the surface area of the cylinder with height 7 mi and radius 8 mi?

We have the following system of equations,

[tex]\left \{ {{y=x^2-1} \atop {y=5-x}} \right.[/tex]

We are asked to solve the system of equations using substitution.

What is substitution?

Substitution is a method of solving a system of equations where you solve for one of the equations (pick either equation) for one of the variables (pick one of the variables), then using this new equation to "substitute" back in to the other.

Given this set of equations, [tex]\left \{ {{y=x^2-1} \atop {y=5-x}} \right.[/tex], notice how both of the equations are already solved for the variable, [tex]y[/tex]. Since both these equations equal [tex]y[/tex], we can set them equal to each other and solve for, [tex]x[/tex].

[tex]\left \{ {{y=x^2-1} \atop {y=5-x}} \right.[/tex]

[tex]\Longrightarrow 5-x=x^2-1[/tex], substituted "[tex]5-x[/tex]" for [tex]y[/tex] into the top equation.

[tex]\Longrightarrow -x^2-x+6=0[/tex]

[tex]-1[\Longrightarrow -x^2-x+6=0][/tex]

[tex]\Longrightarrow x^2+x-6=0[/tex]

[tex]\Longrightarrow (x-2)(x+3)=0[/tex]

[tex]\Longrightarrow x=2 \ and \ x=-3[/tex]

Now take these values of x ([tex]x=2 \ and \ x=-3[/tex]) and plug them into either of the two original equations to solve for [tex]y[/tex].

When x=2:

[tex]y=5-x;x=2[/tex]

[tex]\Longrightarrow y=5-(2)[/tex]

[tex]\Longrightarrow y=3[/tex]

When x=-3:

[tex]y=5-x;x=-3[/tex]

[tex]\Longrightarrow y=5-(-3)[/tex]

[tex]\Longrightarrow y=5+3[/tex]

[tex]\Longrightarrow y=8[/tex]

Thus, we get two solutions to the given system of equations, (-3,8) & (2,3).

The value after conversion Fahrenheit to Celsius is equal to 375 Fahrenheit to 190.556 Celsius.

The unit which represents the measurement of the temperature in Standard form is given by Fahrenheit and Celsius.

Relation between Fahrenheit and Celsius is represented by the formula as written below

(°F − 32) × 5/9 = °C

Here Substitute the value 375 Fahrenheit in the above formula to get into Celsius ,

= ( 375°F − 32) × 5/9

= 343 × 5/9

= 1715 / 9

= 190.55555 Celsius

= 190.556 Celsius

Therefore, the converted value of 375 Fahrenheit into the Celsius is given by 190.556 Celsius .

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Answer:

  120°

Step-by-step explanation:

You want to know the measure of the obtuse angle x° at B in the attached diagram.

This problem is quickly solved by using your knowledge of "special" triangles. Referring to the attached figure, triangles ACE and DGC are isosceles right triangles, so their base angles are 45°. Triangle CDE is equilateral, so all of its internal angles are 60°.

Line AB forms a "straight angle" at C. That means the sum of angles on one side of the line is 180°. This can be used to find the measure of angle DCB.

  ∠ACE +∠ECD +∠DCB = 180°

  45° +60° +∠DCB = 180°

  ∠DCB = 180° -105° = 75°

From above, you know that angle CDG is 45°.

The marked angle x° is an exterior angle to triangle BCD. As such, its measure is equal to the sum of the remote interior angles of that triangle:

  x° = ∠BCD +∠BDC = 75° +45°

  x° = 120°

__

Additional comment

As with many math problems there are other ways to work this. If you draw a perpendicular to AB at C, you find it makes a 45° angle with CE and a 15° angle with CD. That same 15° measure is the measure of angle GCB. Of course, angle G is 45°, so it takes x° = 120° to make the internal angle sum of ∆GCB equal to 180°.

If a p-series is 1 np, you can determine if it converges or not. It converges when p > 1. This is how you test a P series convergence.

The situation diverges if the terms are not close to zero. If you are able to fully control a well-known divergent series with the series, it diverges. To determine if a p p -series is converging or diverging, one can apply the p p -series test. If the denominator's power satisfies p>1 p > 1, the series converges; otherwise, it diverges.

A sequence's convergence can be checked using a variety of techniques. We only need to know the sequence's limit at n n to infinity in some cases. If a series of absolute values P |an| is convergent, the series P an is said to be absolutely convergent.The Geometric Series test is the opposite of the P-Series test in that it requires us to locate a variable raised to a number. We are trying to find a raised number that is a variable!

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Answer:

The domains are (1,4,9) Ranges are (-1,-2,-3)

Step-by-step explanation:

The domain is on the x-axis and the range is on the y-axis

Answer: Impossible to answer/ 12 chickens 8 rabbits

Step-by-step explanation: The question asks how many hens there are, or female chickens. We do not know if the chickens are female or male, so we cannot answer. If you meant how many chickens there were, then we start with 20 chickens and 0 rabbits. Doing so, we have 40 legs. When we switch a chicken for a rabbit, we have 19 chickens and 1 rabbit, and 42 legs. So, we can subtract 56-40 giving us 16 extra legs we need, so we divide 16/2 giving us 12 chickens and 8 rabbits.

A table used to find the area under the standard normal distribution to determine the probability of a z-score being less than a given value.

A negative z-score table is a tool used in statistics to find the probability of a z-score being less than a certain value. A z-score is a measure of the number of standard deviations an observation or data point is above or below the mean of a dataset.

The standard normal distribution is a bell curve with a mean of zero and a standard deviation of one. The negative z-score table lists the area under the curve to the left of a negative z-score, which can be used to calculate probabilities. The table is used by finding the corresponding row and column for the desired z-score and reading the probability from the table.

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Answer:

x > -8

Step-by-step explanation:

5 - (x + 5) > -2(x + 4) (distribute)

5 -x - 5 > -2x -8 (combine like terms)

-x > -2x - 8 (add 2x to both sides)

x > -8

The appropriate numerical measures of center and spread to describe a given distribution of a quantitative variable depend on the shape, symmetry, and presence of outliers in the data.

Measures of center include mean, median, and mode. The mean is affected by extreme values, while the median is resistant to outliers. The mode is useful when looking for the most common value or values in a distribution.

Measures of spread include range, interquartile range (IQR), variance, and standard deviation. The range is the difference between the maximum and minimum values, but it is sensitive to outliers. The IQR is the range of the middle 50% of the data and is resistant to outliers. Variance and standard deviation both measure the spread of the data around the mean, with the variance being the average squared deviation from the mean and the standard deviation being the square root of the variance.

In general, if the data is approximately symmetric and without outliers, the mean and standard deviation are appropriate measures of center and spread, respectively.

If the data is skewed or has outliers, the median and IQR are more appropriate. If the distribution has multiple modes, the mode may be useful to describe the distribution, but it should be used with caution as it may not be unique or well-defined for certain distributions.

Ultimately, the choice of measures of center and spread depends on the characteristics of the data and the research question being investigated. It is always a good practice to use multiple measures of center and spread and to visualize the distribution of the data using histograms or boxplots to gain a better understanding of the data.

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Answer:

10

Step-by-step explanation:

[tex]7.2\\+\\2.8\\--\\10[/tex]

10 is an integer, there is no way to express it in decimal form.

Answer: 10

Step-by-step explanation:

2.8+7.2=10

yup

Answer: The correct digits for the combination lock are 1, 5, and 8, in that order.

Step-by-step explanation:

Based on the given clues, we can deduce the correct digits for the combination lock as follows:

From the clue "128 One digit is right and in its place," we know that one of the digits is 1.

From the clue "157 One digit is right, but in the wrong place," we know that either 5 or 7 is a correct digit, but in the wrong position. Since we already know that one of the digits is 1, the correct digit must be 5. Therefore, the second digit is 5 and it is in the wrong place.

From the clue "841 Two digits are right but both are in the wrong place," we know that the digits 8 and 4 are correct, but they are both in the wrong position. Therefore, the last digit must be 4 or 8. However, we also know from the clue "624 One digit is right, but in the wrong place" that the last digit is not 4. Therefore, the correct third digit is 8.

So, the correct digits for the combination lock are 1, 5, and 8, in that order.

Therefore, the combination for the lock is 158.

Answer: The scale factor is 2/5 and the length of BC is 10

Given: We have to find the factor of dilatation by looking at the pre-image ABCD and the image A'B'C'D' and then we have to find the length of the segment BC.

Explanation: To calculate the dilatation factor we have to look at two given segments, the side D'C' and the side DC since the segment DC belong to the pre-image and the segment D'C' belongs to the image we know that the factor of dilation will be the same for the change relation between those two sides and any other side of the figure so:

Scale factor = 2/5

Now in order to find the measure of the side BC we have to multiply 4 by the inverse scale factor because we are going from the image to the pre-image so:

Length of BC = 4 * 5/2 = 10

The distance of 7km in miles is 4.349597 miles.

It's important to note that kilometers are the primary unit of distance measurement in most countries, while miles are used primarily in the United States and a few other countries. To convert 7km to miles, we need to know the conversion factor between the two units.

By knowing how to convert between these two units is a useful skill when traveling internationally or when working with different units of measurement. Here, One kilometer is equal to 0.621371 miles.

Therefore, to convert 7km to miles, we simply multiply 7 by the conversion factor:

7km x 0.621371 miles/km = 4.349597 miles

So, 7km is equal to approximately 4.35 miles.

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Answer: 20.8

Step-by-step explanation: .

The numbers between 20 and 30 are: 21,22,23,24,25,26,27,28,29 Even numbers, other than 2 are not prime because by definition of being even they are divisible by 2.

Prime numbers are numbers that can only be divisible by themselves or 1. Examples of prime numbers include 2, 3, 5, 7, 11, and so on. In this tutorial, you will learn how to check if a number is a prime number. We will discuss how to write a prime number program in python – this program prints numbers that are prime numbers within a given range.

There is just one perfect number between 20 and 30. The number 28 is a perfect number. Its factors are 1, 2, 4. 7, 14, and 28. Why is 2 the only prime number? Two is a prime because it is divisible by only two and one. All the other even numbers are not prime because they are all divisible by two. That leaves only the odd numbers.

Hence, The numbers between 20 and 30 are: 21,22,23,24,25,26,27,28,29 Even numbers, other than 2 are not prime because by definition of being even they are divisible by 2.

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Answer:

13

Step-by-step explanation:

943.50 + 31.50x = 1353

This is in the form y=mx+b.

To isolate for x, move 943.50 to the other side and subtract it from 1353.

31.50x = 409.50

now, divide by 31.50 to get x by itself.

x =13

The team can bring 13 players to the tournament.

The missing side length, C, is approximately 23.53 units.

To find the missing side length in a right triangle, we need to use trigonometry. Given the angle A = 27° and the side length opposite to it, B = 12C, we can follow the following steps to find the missing side length:

1. Locate the angle measured: In this case, we are given angle "A = 27°."

2. Label the sides of the right triangle: Let's label the hypotenuse as H, the side opposite to angle A as O, and the side adjacent to angle A as A. We can choose any side as the hypotenuse, so let's choose H to be the side opposite to angle B.

3. Which side do you know? Which side are you trying to find?: We know the length of side B and are trying to find the length of side C.

4. Decide which trig function (cosine, sine, or tangent) fits the sides chosen in step 3: We are given the length of the opposite side (B) and are trying to find the length of the adjacent side (C), so we will use the tangent function.

5. Write your equation. Fill in the known measurements: The tangent of angle A is defined as the ratio of the length of the opposite side to the length of the adjacent side. So we can write:    tan(A) = B/C

      Substituting the known values, we get:

      tan(27°) = 12/C

6. Create two fractions. Cross-multiply to solve: To solve for C, we can cross-multiply and simplify the equation as follows:

      tan(27°) = 12/C  

      C * tan(27°) = 12          

      C = 12/tan(27°)                                                                                

        Using a calculator, we can evaluate the value of tan(27°) to be approximately 0.5095. Therefore,                                                     

       C = 12/0.5095 ≈ 23.53

Hence, the missing side length, C, is approximately 23.53.

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The measure of ∠S is 75 degrees

The cosine rule is for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula:

cos(S) = (q² + r² - s²)/2qr  

where q, r and s are the lengths and Q, R and S are the angles

Using the formula:

cos(S) = (q² + r² - s²)/2qr

cos(S) = (99² + 17² - 96²)/(2*99*17)

cos(S) = 0.2597

S = cos⁻¹(0.2597)

S = 75 degrees

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Answer:

Below

Step-by-step explanation:

I will assume this question has messed up syntax and is supposed to be :

x^5  *   x^4   * x    =

x^5   * x^4   * x^1

x^(5 + 4+ 1) =  x^10

To  calculate unit vector online we have to divide the original value of the vector by its magnitude.

A vector with a length of one is known as a unit vector. A direction vector is a unit vector that represents a spatial direction.

It is possible to determine the unit vector along the same direction if you are given an arbitrary vector. To accomplish it, use the following formula:

û = u / |u|,

Our distance calculator can be used to determine a vector's magnitude, or you can use the straightforward equation:

|u| = √(x² + y² + z²)

Finding the midpoint of a segment can be done with the help of the vector magnitude calculation.

When defining linear transformations, the unit vector is a helpful concept to understand. The matrix norm, for instance, represents the amount by which a unit vector is stretched when multiplied by a matrix.

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The percent error for patricks estimate for the first day of school is 25%.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25

We are given that;

Time patrick took= 45min

To find the percent error, we first need to find the difference between Patrick's estimate and the actual time it took him to get ready.

Actual time - Estimated time = Error

45 minutes - 45 minutes = 0 minutes

The error is 0 minutes, which means Patrick's estimate was exactly right and there was no error.

However, if we assume that Patrick made a mistake when he estimated and that his actual time is the correct value, then we can find the percent error as follows:

Error = | Actual time - Estimated time | = | 45 minutes - 60 minutes | = 15 minutes

Percent error = (Error / Estimated time) x 100% = (15 minutes / 60 minutes) x 100% = 25%

Therefore, the percentage error will be 25%.

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At 7 a.m., the temperature was 2°.

Temperature is a measure of the average kinetic energy of particles in a system, measured in degrees on a specific scale (such as Celsius or Fahrenheit). The higher the temperature, the faster the particles move. Temperature is also related to heat, which is the transfer of energy between two systems at different temperatures. Heat always flows from a higher temperature system to a lower temperature system. In addition, temperature is related to pressure, which is the force exerted by the particles in a system. When the temperature of a system increases, so does the pressure.

At 7 a.m., the temperature was 2°. This is because temperatures dropped by 2° per hour until 2 o'clock in the morning. In the 6 hours (from 2 a.m. to 8 a.m.) there were 12° of decrease in temperature (2° per hour x 6 hours). This means that the temperature at 7 a.m. was -6° (2° - 12° = -6°).

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He also added lettuce, tomatoes, and cheese. Kenneth also made sure to put plenty of condiments like mayonnaise and mustard on each sandwich.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.


Kenneth's family was excited to get to the beach. When they arrived, they set up their umbrellas and beach chairs and found a spot to settle down. After they were all settled, Kenneth passed out the sandwiches he had made. Everyone was satisfied with the delicious sandwiches Kenneth had created.

Kenneth's family enjoyed their day at the beach. They swam in the ocean, built sandcastles, and played volleyball. They even laid out and got a nice tan. As the day got hotter, Kenneth's family got hungrier. Fortunately, they still had the sandwiches Kenneth had made. Everyone was thankful for the delicious sandwiches that Kenneth had prepared for them.

After a fun day at the beach, Kenneth's family packed up their things and headed home. Kenneth was happy that he could provide for his family and make their day even better. He was grateful for the opportunity to make the sandwiches for his family and make their day at the beach even more enjoyable.

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Answer:

It will take about 13.5 years for the money to grow to $5,500
That would be about 13 years and 6 months

Step-by-step explanation:

The formula for accrued amount(principal + interest) is given by:
[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}\quad(1)\\[/tex]

where
P = Principal amount
r = R/100 where R is the annual interest rate as a percentage
n= number of times compounded per year
t = number of years

Given

A = $5,600
P = $3,500
R = 3.35% ==> r = 3.35/100 = 0.0335
n = 12 (since there are 12 months in a year)

We have to find out t

Plugging known values into equation (1)

[tex]5500 = 3500\left(1+ \dfrac{0.0335}{12}\right)^{12t}\\\\5500 = 3500 \left(1+ 0.002791\right)^{12t}\\\\5500 = 3500 (1.002791)^{12t}[/tex]

Switch sides so unknown appears on the left side:
[tex]3500 (1.002791)^{12t} = 5500[/tex]

Divide by 3500 both sides:
[tex](1.002791)^{12t} = \dfrac{5500 }{3500}\\\\(1.002791)^{12t} = 1.5714\\\\[/tex]

Take logs on both sides:
[tex]\ln \left(1.002791^{12t}\right)=\ln \left(1.5714\right)\\\\[/tex]

We have
[tex]\ln \left(1.002791^{12t}\right) = 12t\ln \left(1.002791\right)\\\\[/tex]

Therefore we get
[tex]12t\ln \left(1.002791\right)=\ln \left(1.5714\right)\\\\t\ln \left(1.002791\right)=\ln \left(1.5714\right)\\\\\\[/tex]

Dividing both sides by [tex]12\ln \left(1.002791\right)[/tex] this works out to
[tex]t=\dfrac{\ln \left(1.5714\right)}{12\ln \left(1.002791\right)}[/tex]

[tex]t = 13.51359\; years[/tex]

Rounding to one decimal place
[tex]t = 13.51\; years\\[/tex]

This would be roughly 13 years and 6 months

answer : x(2)x(-3--6)

The area of hemisphere is given by  3πr² and the volume of the hemisphere is given by 2/3πr³.

When we divide the sphere into two equal halves, we get a hemisphere. The curved surface area of the hemisphere plus the base area will add up to the hemisphere's total surface area. Here, the foundation has a circular shape. We may discover many examples of hemispheres in daily life, such as how our planet Earth is divided into the southern and northern hemispheres.

A hemisphere's surface area is the sum of all of its faces. When a sphere is cut along a plane that runs through its centre, a three-dimensional shape known as a hemisphere is created. A hemisphere is, in other terms, one-half of a sphere.

3πr²

 A hemisphere has one flat circular base and a curving surface. The quantity of unit cubes that can fit inside a hemisphere is known as its volume.

2/3πr³.

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The complete ratio table is

Hours       Weeks

168              1

1008             6

840               5

How to complete the table?

The mathematical operation that would be used to determine the missing values are division and multiplication. In order to convert hours to weeks, divide by 168 hours. To convert weeks to hours, multiply by 168.

1008 hours to weeks = 1008 / 168 = 6 weeks

5 weeks to hours = 5 x 168 = 840 hours

Hence , The complete ratio table is

Hours       Weeks

168              1

1008             6

840               5

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51 centimetres equal to 20.08 inches.

In the International System of Units( SI), the current replication of the metric system, a centimetre (symbol cm) is a unit of length.

The symbol of inch is 'in'.

As one inch was exactly equal to 25.4 millimetres.

1 in equal to 2.54 cm

So, 1 cm equals [tex]\frac{1}{2.54}[/tex]  inch

Here we want to convert 51 cm to inches.

For the conversation of cm into the inches multiply the cm value by 0.3937 or  [tex]\frac{1}{2.54}[/tex]

We can write as:

51 cm = 51 × [tex]\frac{1}{2.54}[/tex] inches.

51 cm = 20.08  inches (rounded to two decimal places)

Therefore, 51 cm is equivalent to 20.08 inches.

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The value for the length of CD is equal to 3.9 mm using the intersecting secant theorem

The intersecting secant theorem, also known as the secant-secant theorem, states that when two secant lines intersect outside a circle, the product of the length of one secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.

DY × CY = BY × AY

{AY = 2 mm + 6 mm}

2.5 × CY = 2 mm × 8 mm

2.5 × CY = 16 mm

CY = 16mm/2.5 {divide through by 2.5}

CY = 6.4

{CD = CY - DY}

CD = 6.4 - 2.5

CD = 3.9

Therefore, the value for the length of CD is equal to 3.9 mm using the intersecting secant theorem.

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