In a pyramid, the area of the base, A, is measured by the formula A=3v/h, where V= volume and h=height. Solve the formula for h

To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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Answer:

B

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

-4x + 136 + 52 = 180             {supplementary  angles}

        -4x + 188 = 180

Subtract 188 from both sides

                -4x = 180 - 188

                -4x = -8

Divide both sides by (-4)

          x = -8/-4

x = 2

89.09% of books will weigh 11 pounds or more, then the number of books will be 129.

The z-score is a numerical measurement used in statistics to refer to how much a given value differs from the standard deviation.

The weights of books in a bookcase are normally distributed with a mean of 11.6 pounds and a standard deviation of 1.3 pounds. There are 136 books on the bookshelf.

Then the z-score when the books will weigh 11 pounds or more will be

\(z= \frac{11-13.5}{2.3} \\\\z= -1.0869\)

Then the probability will be

\(P(x > 11) = 1-P(x < 11 ) = 0.8909\)

89.09% of books will weigh 11 pounds or more, then the number of the books will be

=145 × 0.8909

=129.1805 ≈ 129

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The relationship between man and nature is portrayed as one of harmony, where nature offers solace and inspiration to individuals.

The poem emphasizes the transformative power of nature and the benefits it brings to individuals. By immersing oneself in nature, individuals can experience a sense of renewal and rejuvenation. The imagery of blossoming flowers suggests growth, beauty, and vitality that can be mirrored in human experiences. Spending time in nature offers a respite from the hectic pace of life, providing tranquility and a source of inspiration.

The relationship between man and nature in the poem is portrayed as one of harmony and mutual appreciation. Nature is depicted as a nurturing force that offers solace and a sanctuary for individuals seeking peace and reflection. By immersing themselves in the natural world, individuals can cultivate a deeper connection with nature and tap into its inherent wisdom and healing qualities.

The poem highlights the notion that by embracing nature, individuals can find solace, inspiration, and a sense of belonging in the larger natural order.

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Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

a. The equation that represents the given data is y = 700x + 2,000.

b. The average daily attendance at Disneyland on its 80th anniversary is 58,000.

We are given the data about average daily attendance at Disneyland's anniversary celebrations. At Disneyland's 40th anniversary, the average daily attendance was 30,000 people. On the 60th anniversary, the average daily attendance was 44,000 people. We need to create an equation that would represent y, the average daily attendance, based on x, the number of years after Disneyland opened.

We can write the data in the form of points on the coordinate axes. The coordinates of the points are (40, 30,000) and (60, 44,000). We can use the two-point form to write an equation.

(y - y1) = [(y2 - y1)/(x2 - x1)]*(x - x1)

(y - 30,000) = [(44,000 - 30,000)/(60 - 40)]*(x - 40)

(y - 30,000) = [(14,000)/(20)]*(x - 40)

(y - 30,000) = (700)*(x - 40)

y = 700x - 28,000 + 30,000

y = 700x + 2,000

Now, we need to find out the average daily attendance at Disneyland on its 80th anniversary.

y = 700*80 + 2,000

y = 56,000 + 2,000

y = 58,000

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Using the Factor Theorem, the inequality that represents the given region is:

\(y < \frac{(x + 40)(x - 50)}{21}\)

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient.

The roots are given as follows:

\(x_1 = -40, x_2 = 50\)

Hence:

y = a(x + 40)(x - 50)

It includes the point (-55,-75), hence:

-75 = a(-55 + 40)(-55 - 50)

a = 75/(15 x 105)

a = 1/21

Hence the region less than the equation is:

\(y < \frac{(x + 40)(x - 50)}{21}\)

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Answer:

D

Step-by-step explanation:

Answer:

I would say B

Step-by-step explanation:

Answer: the first option is correct a  

A. 30 paintings and 42 bracelets

B. 20 paintings and 42 bracelets

C. 15 paintings and 50 bracelets

D. 10 paintings and 44 bracelets

Step-by-step explanation:

just trust me lol

Answer:

51

Step-by-step explanation:

Answer:

51

Step-by-step explanation:

3(5+12) (taking the common between the two numbers)

3(17)

51

brainliest please

Answer:

1: 1/4 dollars or .25 dollars or 25%

2: 150 cents

3: 100 cents

4: 1/100 dollars, or 0.01 dollars, or 1%

Step-by-step explanation:

The answers to the given problems are found by converting the units as $0.25, 150 cents, 100 cents and $0.01.

A measurement unit is a unit to measure certain quantities. For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.

The given problem can be solved as follows,

(1) The cost of sticker in cents is 25.

Since 1 dollar = 100 cents

⇒ 1 cent = 1/100 dollars

⇒ 25 cent = 25/100 = 0.25 dollars.

Thus, the cost of sticker is $0.25.

(2) The cost of the pen is 1.50 dollars.

Since 1 dollar = 100 cents

⇒ 1.50 dollar = 1.50 × 100 = 150 cents

(3) There are 100 cents in one dollar.

(4) There are 1/100 = 0.01 dollars in one cent.

Hence, the answers to all the problems are obtained as $0.25, 150 cents, 100 cents and $0.01.

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Answer:

x lies between 0 and 1 on the number line

Step-by-step explanation:

As we move to the left from 0.99, the first integer we reach is 0; as we move to the right from 0.99, the first integer we reach is 1.

Thus, 0 < x > 1:  x lies between 0 and 1 on the number line.

Step-by-step explanation:

x - 8 > -3

x > -3 + 8 (add 8 to both sides)

x > 5

Hence 3.{x|x€R,x>5} is correct.

Answer:

B.

Step-by-step explanation:

I think B is the answer.......

Answer: y = -3/4x + 7

Step-by-step explanation:

first find slope:

y2-y1 / x2 - x1

1-4 / 8-4

-3/4

now just plug the slope (m) into the equation of a line using one of the points to find the y intercept

ill use (8,1)

1 = (-3/4)(8) + b

now solve :)

1 = -6 + b

7 = b

so now plug in the slope and the y intercept into the slope intercept form to find the equation of the line

y = -3/4x + 7

The general solution to the equation +rtan 0 = 6 sec 0 tan 0 de is r = 6/cos 0.

This means that r can take any value that satisfies this condition, as long as there are no lost solutions.

To obtain the general solution, we start by simplifying the equation using trigonometric identities. We know that sec 0 = 1/cos 0, and we can substitute this into the equation to get:

r tan 0 = 6/cos 0 tan 0

Dividing both sides by tan 0, we get:

r = 6/cos 0

This is the general solution to the equation, as r can take any value that satisfies this condition. However, it is important to note that there may be lost solutions, which occur when the simplification process involves dividing by a variable that may be equal to zero for certain values of 0. Therefore, it is important to check for such values of 0 that may result in lost solutions.

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The equation of the circle in standard form is (x-6)² + (y-11)² = 121.

The equation of a circle can be defined in the standard form :

(x-a)² + (y-b)² = r²,

Here (a,b) is the center of the circle, and r is the radius of the circle.

We know that circle is said to be tangent to the x-axis if its center lies on the x-axis.

Thus , Let the center is given to be (6,11) and is tangent to the x-axis. Hence, the equation of the circle can be written as follows;

(x-6)² + (y-11)² = r².

The radius of the circle can be determined by nothing that it is tangent to the x-axis, which means the distance from the center (6,11) to the x-axis is equal to the radius of the circle.

Thus the x-axis is perpendicular to the y-axis, the distance between the center (6,11) and the x-axis is the distance between (6,11) and (6,0). Therefore, r = 11 - 0 = 11

Thus, the equation of the circle is; (x-6)² + (y-11)² = 121.

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The complete question is;

Consider the circle with a center  (6,11) and which is a tangent to the x-axis. The objective is to find the equation of the circle is in standard form and to graph the circle.

The probability density function for a normal distribution N(68, 5) reaches its maximum height at x = 68, which is the mean of the distribution. The function does not touch the x-axis at μ±30.

The probability density function (PDF) for a normal distribution is bell-shaped and symmetrical around its mean. In this case, the mean (μ) is 68, and the standard deviation (σ) is 5.

(a) To find the x value at which the PDF reaches a maximum, we look at the mean of the distribution, which is 68. The PDF is highest at the mean, and as we move away from the mean in either direction, the height of the PDF decreases. Therefore, the x value at which f(x) reaches a maximum is x = 68.

(b) The PDF of a normal distribution does not touch the x-axis at μ±30. The x-axis represents the values of x, and the PDF represents the likelihood of those values occurring. In a normal distribution, the PDF is continuous and never touches the x-axis. However, the PDF becomes close to zero as the values move further away from the mean. Therefore, the probability of obtaining values μ±30, which are 38 and 98 in this case, is very low but not zero. So, the PDF does not touch the x-axis at μ±30, but the probability of obtaining values in that range is extremely small.

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Answer:

the first one

Step-by-step explanation: it worked for me i passed it

a) The 95% confidence interval is (0.712, 0.868).

b) The 99% confidence interval is (0.686, 0.894).

c) The sample size needed for a 95% confidence interval is 381.

d) The sample size needed for a 99% confidence interval is 644.

The confidence intervals and sample sizes, we can use the formula for the confidence interval of a proportion:

Confidence Interval:

Confidence level = 1 - α

Sample proportion (P(cap)) = 79/100 = 0.79

a) 95% Confidence Interval: For a 95% confidence level, α = 1 - 0.95 = 0.05 Using the formula, the margin of error (E) can be calculated as:

E = z × √((P(cap) × (1 - P(cap))) / n)

For a 95% confidence level, z = 1.96 (z-value for 95% confidence)

Substituting the values:

0.04 = 1.96 × √((0.79 × (1 - 0.79)) / n)

Solving for n:

n = ((1.96)² × 0.79 × (1 - 0.79)) / (0.04)²

n ≈ 380.2

Rounding up to the nearest integer, the sample size needed is 381.

b) 99% Confidence Interval: For a 99% confidence level, α = 1 - 0.99 = 0.01 Using the same formula as above, with z = 2.576 (z-value for 99% confidence):

0.04 = 2.576 × √((0.79 × (1 - 0.79)) / n)

Solving for n:

n = ((2.576)² × 0.79 × (1 - 0.79)) / (0.04)²

n ≈ 643.94

Rounding up to the nearest integer, the sample size needed is 644.

c) Sample Size for 95% Confidence Interval: To find the sample size needed for a 95% confidence interval with a margin of error of ±0.04, we can rearrange the formula:

n = ((z)² × P(cap) × (1 - P(cap))) / (E)²

Substituting the given values:

n = ((1.96)² × 0.79 × (1 - 0.79)) / (0.04)²

n ≈ 380.25

Rounding up to the nearest integer, the sample size needed is 381.

d) Sample Size for 99% Confidence Interval: To find the sample size needed for a 99% confidence interval with a margin of error of ±0.04:

n = ((z)² × P(cap) × (1 - P(cap))) / (E)²

Substituting the values:

n = ((2.576)² × 0.79 × (1 - 0.79)) / (0.04)²

n ≈ 643.94

Rounding up to the nearest integer, the sample size needed is 644.

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Local minima and maxima of f correspond to points where f'(x) changes sign from positive to negative or vice versa.

1. The function f(x) = et - ex represents the difference between the exponential functions et and ex. It describes the growth or decay of a quantity over time.

2. To determine the intervals where f is increasing or decreasing, we analyze the sign of the derivative f'(x). If f'(x) > 0, f is increasing; if f'(x) < 0, f is decreasing. In this case, f'(x) = et - ex.

3. Local minima and maxima occur when f'(x) changes sign from positive to negative or vice versa. In other words, they occur at points where f'(x) = 0 or where f' is undefined.

4. The concavity of f is determined by the sign of the second derivative f''(x). If f''(x) > 0, f is concave up; if f''(x) < 0, f is concave down. In this case, f''(x) = et - ex.

5. Inflection points of f occur where the concavity changes, i.e., where f''(x) changes sign. At these points, the curve changes from being concave up to concave down or vice versa.

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Answer:

(23)(39)

Step-by-step explanation:

When you have to look for the "product" of two numbers, it implies multiplication.

With this, get rid of 23 + 39 = 62 as an answer.

Now simply enough, multiply 23 by 39,

23 * 39 = 897

Meaning that A. (23)(39) = 897 is the answer.

Answer:

The length of one of the legs is a 18

Step-by-step explanation:

Here, we want to find the length of one of the legs

Since it’s an isosceles triangle, the length of two sides are equal.

what this mean is that;

x + 10 = 4x - 14

4x -x = 14 + 10

3x = 24

x = 24/3

x = 8

The length of the leg will be x + 10 = 8 + 10 = 18

Therefore, the volume of the solid bounded by the paraboloids z=x^2 y^2 and z=8-x^2-y^2 is 8π cubic units by double integral.

To find the volume of the solid bounded by the paraboloids z=x^2 y^2 and z=8-x^2-y^2, we can use a double integral over the region of intersection of the two surfaces.

Since both surfaces are symmetric about the xy-plane, we can integrate over the circular region in the xy-plane where the two surfaces intersect. This region is given by the equation:

x^2 + y^2 = 4

Therefore, we can use polar coordinates to integrate over this region. The limits of integration for r are from 0 to 2, and the limits of integration for θ are from 0 to 2π.

The integral to find the volume is:

V = ∬R (8 - x^2 - y^2 - x^2 y^2) dA

Converting to polar coordinates, we have:

V = ∫(0 to 2π) ∫(0 to 2) (8 - r^2 - r^4 cos^2 θ) r dr dθ

Evaluating the inner integral first, we have:

V = ∫(0 to 2π) [-r^4/4 - r^2/2 + 8r]∣(0 to 2) dθ

V = ∫(0 to 2π) [16 - 8 - 0] dθ

V = 8π

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According to Baddeley and Hitch's research, the most important factor in determining whether rugby players will remember a particular game is the amount of time that has elapsed since the game was played.

Specifically, players were more likely to remember games that occurred early in the season and those that were particularly important or emotionally charged, while they were less likely to remember games that occurred later in the season or those that were less meaningful or emotionally significant.

This phenomenon is known as the "serial position effect" and has been observed in other contexts as well.

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Answer:

a)4/10

b)5/100000000000೦

c)6

Answer:

4.5

Step-by-step explanation:

The mean number of miles the hiker walked for the 6 days was 6.5 miles.

To calculate the mean or average of a set of numbers, we add up all the numbers and then divide the sum by the number of items in the set. In this case, we have the number of miles the hiker walked on each of the six days. To find the total number of miles the hiker walked, we simply add up all the numbers

8 + 5 + 7 + 2 + 9 + 8 = 39

Next, we divide the total number of miles by the number of days (which is 6) to get the average or mean number of miles the hiker walked per day:

Mean number of miles = Total number of miles / Number of days

= 39 / 6

= 6.5

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