Find the solution of the following:
a) 20t = -10

Number of ways to form four letters strings formed using a, b, c, d, e with the given conditions is equal to 150ways.

As given in the question,

Given letters are a, b, c, d, e has

Number of vowel = 2

Number of consonant= 3

Number of letter strings to be formed = 4

Condition:

First letter must be vowel

Last letter must be consonant

First place filled in 2 ways

Second and Third place filled in 5ways

Last place filled in 3 ways

Total number of ways to form four letters strings

= 2 × 5 × 5 × 3

= 150

Therefore, number of ways to form four letter string is 150 ways.

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Answer:

19

Step-by-step explanation:

Okay here , we are dealing with absolute values.

This means we shall be taking the positive values only of terms inside the double tube | |

So -7 absolute value is 7

and thus multiplied by 4 gives 28

and we are subtracting 9 from this;

This gives 28-9 = 19

y=-2x

Step-by-step explanation:

it can't be y=2x and y=-½ because it passes by the opposite side of the given graph

Answer:

both

Step-by-step explanation:

a.) The type of distribution that is represented by the histogram is a left skewed histogram.

b.) The type of sampling this will represent is a simple random sampling.

A left skewed histogram can be defined as the type of distribution where by the tails is displayed towards the left of the histogram. This is represented in the histogram given in the diagram above.

A simple random sampling is defined as the type of sampling whereby every member of a population is given an equal chance to be selected. Since the information represented is the sample of an entire league, making another bigger league from it gives them all equal chance to be selected.

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Consider the given system of equations. 3x + 2y = 16 ... (1)x + y = 4 ... (2)To solve the given system of equations by the elimination method, we need to eliminate one variable from the two given equations.

For that, we will multiply the equation (2) by 3 and then subtract the obtained equation from equation (1).3x + 2y = 16 ...

(1)x + y = 4 ... (2)Multiplying equation (2) by 3, we get:

3(x + y = 4)

⇒ 3x + 3y = 12 Now, subtracting the above equation from equation (1), we get:3x + 2y = 16

⇒ 3x + 2y - (3x + 3y) = 16 - 12

⇒ 3x - 3x + 2y - 3y = 4

⇒ -y = 4

⇒ y = -4

Substituting the value of y in equation (2), we get:x + y = 4

⇒ x + (-4) = 4

⇒ x - 4 = 4

⇒ x = 4 + 4

= 8

Hence, the solution of the given system of equations is:x = 8, y = -4.So, the answer for the given problem is, To solve the given system of equations, we use the elimination method. Multiplying equation (2) by 3, we get: 3(x + y = 4)

⇒ 3x + 3y = 12.

Now, subtracting the above equation from equation (1), we get: 3x + 2y = 16

⇒ 3x + 2y - (3x + 3y) = 16 - 12

⇒ 3x - 3x + 2y - 3y = 4

⇒ -y = 4

⇒ y = -4.

Substituting the value of y in equation (2), we get: x + y = 4

⇒ x + (-4) = 4

⇒ x - 4 = 4

⇒ x = 4 + 4 = 8. Hence, the solution of the given system of equations is x = 8, y = -4.

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The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

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Answer:

Missouri admitted as a slave state.

Maine admitted as a free state.

Slavery disallowed in future territories north of 36°30' except within Missouri itself.

Step-by-step explanation:

Answer:

(x-1)(x-2)(x-3)

Step-by-step explanation:

hy vọng nó giúp

Answer:

x3−7x2+17x−20

Step-by-step explanation

BTW the 3 and the 2 are like the tiny numbers at the top cuz i don't know how to do that on a computer

This statement is false. when constructing a congruent line segment to cd the ray needed for the construction it must be not shorter.

Because when constituting a configured line segment to CD the ray never can be shorter. The reason is when we constitute a configured it's Ray line is always increase that mean it's go up Hight and it's must be longer . That's why this statement is false.

Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments. When two lines are the same length, they are said to be congruent. Superimposable figures that entirely enclose each other when stacked one atop the other are congruent segments. The congruent segments continue to be congruent even after being turned, flipped, or rotated.

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Answer:

64

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

8^2

= 8 * 8

64

If my answer helped, kindly mark me as the brainliest!!

Thanks!!

Answer:

17hrs 45mins

Step-by-step explanation:

Timespan is 17 hour(s) and 45 minute(s).

Taking into account the least-squares regression line ln(element)=2.304-0.101(time). 1.496 grams of an unstable element will still be present after 8 years.

Given that,

Taking into account the least-squares regression line ln(element)=2.304-0.101(time).

We have to find how many grams of an unstable element will still be present after 8 years.

The equation is ln(elements)=2.304-0.101(time) with the element and time.

ln is nothing but a natural logarithm.

So,

We substitute 8 years in place of time.

ln(element)=2.304-0.101(time).

ln(element)=2.304-0.101(8)

ln(element)=2.304-0.808

ln(element)=1.496

Therefore, 1.496 grams of an unstable element will still be present after 8 years.

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The probability of the three independent events all occurring in three consecutive dice rolls is 1/216.

Assuming a fair six-sided die, the probability of any single roll resulting in a specific number is $1/6$. Since the events are independent, the probability of all three events occurring in three consecutive rolls is the product of the probabilities of each individual event.

Therefore, the probability of getting a specific number on three consecutive rolls is:

$P = (1/6) * (1/6) * (1/6) = 1/216$

So the probability of the three independent events all occurring in three consecutive dice rolls is 1/216.

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There is no minimum value for the side length x, and thus it is not possible to determine the dimensions of the most economical shed.

To find the dimensions of the most economical shed, we need to consider the cost of each component (base, roof, and sides) based on the given cost per square foot. Let's denote the side length of the square base as x.

The volume of the shed is given as 729 cubic feet, and since the base is square, the height of the shed is also x.

The cost of the base would be the area of the base (x * x) multiplied by the cost per square foot, which is 5 * x².

The cost of the roof would be the area of the base (x * x) multiplied by the cost per square foot, which is 6 * x².

The cost of the sides would be the sum of the areas of all four sides (2 * x * x) multiplied by the cost per square foot, which is 4 * 5.5 * x².

To find the most economical shed, we need to minimize the total cost, which is the sum of the costs of the base, roof, and sides.

Total Cost = Cost of Base + Cost of Roof + Cost of Sides

= 5 * x² + 6 * x² + 4 * 5.5 * x²

= 11 * x² + 22 * x²

= 33 * x²

To minimize the total cost, we need to minimize x², which means finding the minimum value of x.

Taking the derivative of the total cost function with respect to x and setting it to zero, we can find the critical points:

d(Total Cost)/dx = 66 * x = 0

From this, we can see that x = 0 is not a valid solution. Therefore, we can divide both sides by 66 to find:

x = 0

Since the side length cannot be zero, we can conclude that the minimum value of x is not achievable.

Hence, there is no minimum value for the side length x, and thus we cannot determine the dimensions of the most economical shed based on the given volume and cost information.

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Answer:

-7/-3

Step-by-step explanation:

The point (6,9) should be labeled as x1 and y1 and the point (0,-5) should be labeled as x2 and y2, so the slope equation ends up as -5-9 / 0-6, which turns out to be -14 / -6, but when you simplify it, it becomes -7 / -3. :)

The slope of line given below is 7/3.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

We have the points as (6, 9) and (0, -5)

So, the slope of line

slope = (-5 - 9)/ (0-6)

slope = -14 / (-6)

slope = 7/3

Thus, the required slope is 7/3.

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The statement ''the symbol μ ˆ p represents the proportion of a sample of size n, not the proportion of a sample of size n.'' is false because the symbol "μ ˆ p" does not represent the proportion of a sample of size n.

In statistical notation, the symbol "μ ˆ p" typically represents the sample proportion, which is an estimate of the population proportion. The sample proportion is obtained by dividing the number of occurrences of a specific event in the sample by the sample size.

On the other hand, the population proportion, denoted by "p," represents the proportion of the entire population that exhibits a certain characteristic or has a specific attribute.

The symbol "μ ˆ p" could be a typographical error or a confusion between different symbols used in statistics. The correct symbol to represent the sample proportion is usually denoted as "p ˆ" or "p-hat." The symbol "μ" typically represents the population mean.

Therefore, it is incorrect to state that "μ ˆ p" represents the proportion of a sample of size n.

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Answer:3x10^0 or 3x10 to the power of 0

Step-by-step explanation:

I did the same exact one with my teacher i hope this helps you

Answer:

0.7 is a rational number

Step-by-step explanation:

Rational numbers are defined as numbers that result when two integers are divided.

The square pyramid's volume is 108 cm². Thus, option b is correct.

Volume is the measure of space within a particular 3D object in mathematics. For instance, a fish tank measures three feet long by one foot wide by two feet high. The volume is calculated by multiplying the length, the breadth, and the height, or 3 x 1 x 2, which equals six. The fish tank, therefore, has a 6 cubic foot volume. A sound's volume also indicates how loud it is. Check the TV remote. It has a button for volume control.

The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim. The quantity of space occupied by a three-dimensional object can also be used to describe volume. By counting the number of unit cubes it contains, one can determine the volume of a solid like a cube or cuboid. The best approach to understanding volume is to conceive of it as the area encircled or occupied by any solid item or anything with three dimensions.

The following formula can be used to determine the volume of a square pyramid:

\(\mathrm{V = \frac{1}{3} B h}\)

where V is the volume, B is the base's area, and h is the pyramid's height.

The area of the pyramid in this instance, whose base is a square with sides measuring 9 cm, is:

B = side length²

= 9² cm

= 81 cm

The height of the pyramid is 4 cm.

Using the formula with these values as input, we obtain

\(\mathrm{V = \frac{1}{3} B h}\)

\(\mathrm{V = \frac{1}{3} \times 81 \times 4}\)

= 108 cm²

The square pyramid's volume is 108 cubic centimeters as a result.

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Answer:

60

Step-by-step explanation:

180 - 120 = 60

when dealing with interior and exterior angles, the highest is 180 degrees

Answers:

The respective functions f(x) obtained from the given derivatives and points are

35. f(x) = 2x² + x - 1.

36. f(x) = 3x - x² - 1.

37. f(x) = -x²/2 - x³/3 + 9/2.

38. f(x) = x³ + 3x² - 2x + 6.

39. f(x) = (1/4)x⁴ + 2/x + 2x - 19/4.

40. f(x) = 2x⁽¹/²⁾ + (1/2)x² + 1/2.

41. f(x) = -e⁽⁻ˣ⁾ + (1/2)x² + 5.

42. f(x) = 3ln|x| - 4x + 4.

To find the function f(x) based on the given derivative f'(x) and a particular point (a, b), we can integrate f'(x) with respect to x and then use the given point to determine the constant of integration.

Let's go through each exercise:

35. f'(x) = 4x + 1; (1, 2)

Integrating f'(x) gives:

f(x) = 2x² + x + C

Using the given point (1, 2), we can substitute x = 1 and y = 2 into the equation:

2 = 2(1)² + 1 + C

2 = 2 + 1 + C

C = -1

Therefore, f(x) = 2x² + x - 1.

36. f'(x) = 3 - 2x; (0, -1)

Integrating f'(x) gives:

f(x) = 3x - x² + C

Using the given point (0, -1), we can substitute x = 0 and y = -1 into the equation:

-1 = 0 + 0 + C

C = -1

Therefore, f(x) = 3x - x² - 1.

37. f'(x) = -x(x + 1); (-1, 5)

Integrating f'(x) gives:

f(x) = -x²/2 - x³/3 + C

Using the given point (-1, 5), we can substitute x = -1 and y = 5 into the equation:

5 = -(-1)²/2 - (-1)³/3 + C

5 = -1/2 + 1/3 + C

C = 27/6 = 9/2

Therefore, f(x) = -x²/2 - x³/3 + 9/2.

38. f'(x) = 3x² + 6x - 2; (0, 6)

Integrating f'(x) gives:

f(x) = x³ + 3x² - 2x + C

Using the given point (0, 6), we can substitute x = 0 and y = 6 into the equation:

6 = 0 + 0 - 0 + C

C = 6

Therefore, f(x) = x³ + 3x² - 2x + 6.

39. f'(x) = x³ - 2/x² + 2; (1, 3)

Integrating f'(x) gives:

f(x) = (1/4)x⁴ + 2/x + 2x + C

Using the given point (1, 3), we can substitute x = 1 and y = 3 into the equation:

3 = (1/4)(1)⁴ + 2/1 + 2(1) + C

3 = 1/4 + 2 + 2 + C

C = -19/4

Therefore, f(x) = (1/4)x⁴ + 2/x + 2x - 19/4.

40. f'(x) = x⁽⁻¹/²⁾ + x; (1, 2)

Integrating f'(x) gives:

f(x) = 2x⁽¹/²⁾ + (1/2)x² + C

Using the given point (1, 2), we can substitute x = 1 and

y = 2 into the equation:

2 = 2(1)⁽¹/²⁾ + (1/2)(1)² + C

2 = 2 + 1/2 + C

C = 1/2

Therefore, f(x) = 2x⁽¹/²⁾ + (1/2)x² + 1/2.

41. f'(x) = e⁽⁻ˣ⁾ + x; (0, 4)

Integrating f'(x) gives:

f(x) = -e⁽⁻ˣ⁾ + (1/2)x² + C

Using the given point (0, 4), we can substitute x = 0 and y = 4 into the equation:

4 = -e⁽⁻⁰⁾+ (1/2)(0)² + C

4 = -1 + 0 + C

C = 5

Therefore, f(x) = -e⁽⁻ˣ⁾ + (1/2)x² + 5.

42. f'(x) = 3/x - 4; (1, 0)

Integrating f'(x) gives:

f(x) = 3ln|x| - 4x + C

Using the given point (1, 0), we can substitute x = 1 and y = 0 into the equation:

0 = 3ln|1| - 4(1) + C

0 = 0 - 4 + C

C = 4

Therefore, f(x) = 3ln|x| - 4x + 4.

These are the respective functions f(x) obtained from the given derivatives and points.

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ANSWER:

1. translation: 3 units right and 1 unit down

2. 130°

Assuming the shape of the balloon remains the same, the volume of the balloon is directly proportional to the cube of its height. Therefore, we can use the following proportion:

(air volume)₁ / (height)₁³ = (air volume)₂ / (height)₂³

where:

(air volume)₁ = 108 in.³ (when the height is 4 in.)

(height)₁ = 4 in.

(height)₂ = 8 in.

We can solve for (air volume)₂ as follows:

(air volume)₂ = (air volume)₁ × (height)₂³ / (height)₁³

(air volume)₂ = 108 in.³ × (8 in.)³ / (4 in.)³

(air volume)₂ = 108 in.³ × 64 / 64

(air volume)₂ = 108 in.³

Therefore, the balloon must hold 108 in.³ of air for the clown's face to be 8 in. tall.

Answer:

x=7

Step-by-step explanation:

x-8=-1, x-8+8=-1+8,-1+8=7

Answer:

x<7

Step-by-step explanation: