Find the 40th term of the arithmetic sequence with a = 150 and a common difference of d =-4.
1.-6
2.6
3.-2
4.2

Answer:

Area of Parallelogram Using Diagonals ; Using Base and Height, A = b × h ; Using Trigonometry, A = ab sin (x) ; Using Diagonals, A = ½ × d1 × d2 .....

Using Diagonals: A = ½ × d1 × d2 sin (y)

Using Base and Height: A = b × h

Using Trigonometry: A = ab sin (x)

Answer: 5/11

Tip:

You can solve for these repeating fractions by putting the repeating digits over 9's!

For example, 0.33 repeating:

33/99 = 1/3

And in the case of your problem:

0.454545...

45/99 = 5/11 (simplify!)

Answer:

3.53

Step-by-step explanation:

I checked it using a calculator. :)

Answer:

B

Step-by-step explanation:

Minimum: 4

Lower Quartile (Q1): 7

Median: 9

Upper Quartile (Q2): 13

Maximum: 14

Step-by-step explanation:

B.

you can see by the box plots and notice that A doesn't have the same

Answer:

4 vertices.

6 edges.

Step-by-step explanation:

Vertices are the points where the edges meet.

Edges are the lines where the faces meet.

Answer:

5) A - slope is positive, b = 0

6) D - slope is negative, b = 1, function is linear

7) D - b = 0

8) C - slope is negative, b = negative

Step-by-step explanation:

Hope this helps!

The length of the third side is 2√34 + 6.

We can use the triangle inequality theorem to solve this problem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.

Let x be the length of the third side. Then we have:

2√34 + 6 > x

Subtracting 6 from both sides, we get:

2√34 > x - 6

Adding 6 to both sides, we get:

x < 2√34 + 6

Therefore, the length of the third side must be less than 2√34 + 6.

To find the exact length of the third side, we need to check if the triangle inequality is satisfied for an equality. In other words, we need to check if:

2√34 + 6 = x

If this is true, then the given sides can form a triangle.

Simplifying the equation, we get:

x = 2√34 + 6

The exact length is 2√34 + 6 if the triangle inequality is satisfied for an equality.

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Considering the expression of a line, the slope of line that passes through points (-2,7) and (-3,3) is 4.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m can be calculated as:

m= (y₂ - y₁)÷ (x₂ - x₁)

In this case, being (x₁, y₁)= (-2, 7) and (x₂, y₂)= (-3, 3), the slope can be calculated as:

m= (3 -7)÷ (-3 -(-2))

m= (3 -7)÷ (-3 +2)

m= (-4)÷ (-1)

m= 4

Finally, the slope is 4.

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The value of x in this figure is equal to: D. 5.

In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:

Sum of interior angles = 180 × (n - 2)

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

Sum of interior angles = 180 × (5 - 2)

Sum of interior angles = 180 × 3

Sum of interior angles = 540°.

112 + 7x + 5 + 6x + 2 + 10x - 8 + 4x + 24 = 540°.

27x = 135

x = 135/27

x = 5.

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The height of the stump is 3 ft.

The given equation represents the height of the frog, h(t), as a function of time, t. To find the height of the stump, we need to determine the height when the time, t, is equal to 0.

In the equation h(t) = -16t² + 64t + 3, we substitute t = 0:

h(0) = -16(0)² + 64(0) + 3

Since any term multiplied by zero is zero, we can simplify further:

h(0) = 0 + 0 + 3

Therefore, the height of the stump, at time t = 0, is 3 ft. This means that when the frog initially leaps from the stump, the height of the stump itself is 3 ft.

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Answer:

I believe that your answer is C and Moon.

Answer:

I'm pretty sure it would be $13.50

Answer:

$15.75

Step-by-step explanation:

7 divded by 4 = 1.75

Simply take 1.75 and multply it by 9, giving you 15.75

$15.75

Answer:

111.6

Step-by-step explanation:

92.8+28.7=121.5

121.5-9.9=111.6

Answer:

Step-by-step explanation:

x = 5

Solution of 1/4 (x-3) ≤ -2 is x ≤ 5 . The value of x will be less than or equal to 5 .

Graph is attached below.

Given,

1/4 (x-3) ≤ -2

Now,

Inequality : 1/4 (x-3) ≤ -2

Solve for x,

x - 3 ≤ -8

Take -3 from LHS to RHS.

-3 will be converted to 3 in RHS .

x ≤ -8 + 3

x≤ -5

The value of x will be less than or equal to -5.

The graph of inequality is attached below and represents the the value of x is less than or equal to 5 .

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The median of the data set is 21, the upper and lower quartile is 27 and 13 respectively.

The median of a set of data is the middle value when the data is arranged in order from least to greatest or from greatest to least. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values.

To find the median, you first need to put the data in order from least to greatest or from greatest to least. Then, if the number of data points is odd, the median is the middle value. If the number of data points is even, you find the average of the two middle values.

From the data given;

10,11,13,18,19,21,22,25,27,30,32

The median is 21

The upper quartile is 27

The lower quartile is 13

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Answer: 20

Step-by-step explanation: imagine the books in 10's cuz 30/3=10 and 2 of those tens out of the group of three are nonfiction, so that makes 20 out of 30

The standard deviation of the sampling distribution of sample means will be 0.097.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

Assume that an investigation of primary school understudies reports that the mean age at which youngsters start perusing is 5.9 years with a standard deviation of 0.8 years.

The standard deviation of the sampling distribution of sample means is given as,

⇒ 0.8 / √68

⇒ 0.8 / 8.246

⇒ 0.097

The standard deviation of the sampling distribution of sample means will be 0.097.

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Answer:

? = 77°

Step-by-step explanation:

the 3 angles in a triangle sum to 180° , that is

? + 35° + 68° = 180°

? + 103° = 180° ( subtract 103° from both sides )

? = 77°

Answer:77

Step-by-step explanation:

180-103=77

The equation √(x + 1) + 4 = 6x has a solution of x = (49 ± √241) / 72

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.

Linear Equation Definition: A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.

The equation given is

√(x + 1) + 4 = 6x

Collect like terms

√(x + 1) = 6x - 4

Square both sides

x + 1 = (6x - 4)²

x + 1 = 36x² - 48x + 16

36x² - 49x - 15 = 0

Using quadratic formula;

x = -b±√b² - 4ac / 2a

x = [-(-49)±√49² - 4(36)(-15)] / 2(36)

x = 49 ± √241 / 72

x = (49 ± √241) / 72

The solution to the quadratic equation is x = (49 ± √241) / 72

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Logically reasoning out the value to the question as $3092.

What is Logical Reasoning?

Quarter 1:

Tuition amount= $736

Fees= $37

Total amount= 736+37 = $773

Quarter 4:

Remaining=4

Total = 4X 773 = $3092

Logically reasoning out the value to the question as $3092.

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The probability that at least 8 of the 9 participants will correctly identify the tap water is 0.1953

From the given information, a blind taste test will be conducted with 9 volunteers to determine whether people can taste a difference between bottled water and tap water.

The probability that at least 8 of the 9 participants will correctly identify the tap water will be

The binomial probability is ⁿCₓ⋅px⋅(1−p)n−x .

P(x = 8) + P(x = 9)

= ⁹C₈ × 0.5⁸ × 0.5^(9-8) + 9C9 × 0.5⁹ × 0.5^(9 - 9)

= 0.1953

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Answer:

Point 1: (6.4, 117)

Point 2: (6.6, 120)

Step-by-step explanation:

Answer:

Point 1: (6.4, 117)

Point 2: (6.6, 120)

Step-by-step explanation:

The area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

To find the area of a vertical cross section through the center of the base of the cone-shaped paperweight, we need to determine the radius of the base first.

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, we know the circumference is about 12.56 inches, so we can set up the equation:

12.56 = 2πr

To solve for r, we divide both sides of the equation by 2π:

r = 12.56 / (2π)

Now we can calculate the radius:

r ≈ 12.56 / (2 × 3.14)

r ≈ 12.56 / 6.28

r ≈ 2 inches

The radius of the base is approximately 2 inches.

Since the vertical cross section passes through the center of the base, the shape of the cross section is a circle. The formula for the area of a circle is A = \(πr^2\), where A is the area and r is the radius.

Now we can calculate the area of the cross section:

A = \(πr^2\)

A ≈ 3.14 × \((2^2)\)

A ≈ 3.14 × 4

A ≈ 12.56 square inches

Therefore, the area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

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Answer:

2 1/8

Step-by-step explanation:

Hope this helps!!

Answer: 2.125

Step-by-step explanation: 3.4 x 5/8 = 2.125

Answer:

A

Step-by-step explanation:

(x-4)^2 = x^2 -4x -4x + (-4)*(-4)

= x^2-8x+16 as required

Answer:

C

Step-by-step explanation: