A tetrahedron is a triangular pyramid with 4 congruent faces. If the area of one of the faces is 21 m² and the height of the tetrahedron is 6 m, what is the volume of the figure in cubic meters?​

The intersection points of the two conics are therefore[tex](1 + √14, -1 + √14)[/tex]and [tex](1 - √14, -1 - √14).[/tex]Hence, the two conics intersect at two points.

The point or points of intersection and the number of places the following 2 conic intersect is to be determined. The system over the real numbers for [tex]x² + y² = 34 and 3x - 3y = 6[/tex] is to be solved.

To determine how many points the following 2 conic intersect at, the two equations must be solved simultaneously. The points of intersection can then be determined by substituting the value of x or y into the other equation and solving for the remaining variable.The equation 3x - 3y = 6 is the equation of a straight line. Solving the equation for y, [tex]y = x - 2[/tex].

So the line passes through the point (0, -2) and (2, 0) on the x-axis. Now, substitute the value of y into the equation x² + y² = 34 to get[tex]x² + (x - 2)² = 34[/tex], expanding this gives 2x² - 4x - 26 = 0, which simplifies to x² - 2x - 13 = 0.The solution to the quadratic equation [tex]x² - 2x - 13 = 0[/tex] is given as[tex]x = 1 + √14, 1 - √14[/tex]. The corresponding value of y for each x can be calculated by substituting the value of x into the equation y = x - 2.

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Answer:

If the ratio of the number of cats to dogs at the animal shelter is 9 to 5, this means that for every 9 cats at the shelter, there are 5 dogs.

We can express this ratio as:

number of cats : number of dogs = 9 : 5

To find the possible number of cats to dogs, we need to look for pairs of numbers that have a ratio of 9:5. Here are some possible pairs:

   9 cats : 5 dogs

   18 cats : 10 dogs

   27 cats : 15 dogs

   36 cats : 20 dogs

   45 cats : 25 dogs

   54 cats : 30 dogs

   ...

We can see that there are infinitely many possible pairs of numbers that have a ratio of 9:5. To narrow down the possibilities, we need more information such as the total number of animals at the shelter or the number of cats or dogs at the shelter.

Answer:

A= 2w^2 + 11w +12

Step-by-step explanation:

(w + 4)(2w + 3) = l x b = A

2w^2 + 3w +8w +12 = A

A= 2w^2 + 11w +12

Shaina made a container of lemonades and her brother drank 1/4 of it. Her father then drank 2/3 of the remaining 3/4, which is equivalent to drinking 1/2 of the container.

Shaina made a container of lemonades and her brother drank 1/4 of it, leaving 3/4 in the container. Her father then drank 2/3 of the remaining 3/4, which is equivalent to drinking 2/3 x 3/4 = 6/12 = 1/2 of the container. In other words, her father drank 1/2 of the container.

We can also solve this problem using algebra. Let 'x' represent the total amount of lemonade in the container. Then, her brother drank 1/4x, leaving 3/4x in the container. Her father then drank 2/3 of the remaining lemonade, which is equal to 2/3 x (3/4 x) = 6/12 x = 1/2x. Since her father drank 1/2x of the container, we can conclude that x = 1/2x, which means that x = 2/2x = 1. Therefore, the total amount of lemonade in the container was 1 and her father drank 1/2 of it.

To summarize, Shaina made a container of lemonades and her brother drank 1/4 of it. Her father then drank 2/3 of the remaining 3/4, which is equivalent to drinking 1/2 of the container. This can be expressed algebraically as 2/3 x (3/4 x) = 1/2x, where x = 1, the total amount of lemonade in the container.

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If Lucinda used a random selection method, made an effort to ensure that the sample is representative, and the sample size is large enough, then it's possible that the sample is indeed random.

what are perpendicular lines?

Perpendicular lines are two lines that intersect at a 90-degree angle, forming four right angles at the point of intersection. In other words, if you were to draw a perpendicular line from one of the lines to the other at their point of intersection, it would form a right angle with each of the original lines.

Without having access to more information about how Lucinda selected the sample of students, it's difficult to determine whether or not the sample is truly random.

However, there are a few things that we can consider when trying to determine whether or not the sample is random. For example:

Did Lucinda use a random selection method to choose the students? If she simply surveyed her friends or classmates, for example, the sample would not be random.

Did Lucinda make any effort to ensure that the sample is representative of the larger population of students? For example, did she make sure to include students from a variety of grades, genders, and ethnic backgrounds.

Therefore, if Lucinda used a random selection method, and made an effort to ensure that the sample is representative, and the sample size is large enough, then it's possible that the sample is indeed random.

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Answer:

Step-by-step explanation:

A reflection across the line y = x will not carry the square onto itself, since the vertex (0, 2) would be reflected to (2, 0) which is not a vertex of the original square.

A reflection across the line y = -x would also not carry the square onto itself, since the vertex (0, 2) would be reflected to (−2, 0) which is not a vertex of the original square.

However, a reflection across the x-axis would carry the square onto itself since all of the vertices lie in the same quadrant, and reflecting across the x-axis does not change their signs.

A 45° or 90° rotation about the origin would also carry the square onto itself since the square has rotational symmetry of order 4.

Therefore, the correct answers are C, D, and E.

Answer: 3P-3q

Step-by-step explanation:

1. Rearrange the terms so that the constants are on the left

(P-q) x 3 ( Is times 3)

3(P-q)

2. distribute

3(P-q)

3P-3q

3.Solution

3P-3q

The value of [tex]e^{In 5}[/tex] is equal to 5 which of option B. According to the property of logs and logarithm rules the given equation is done.

The natural log, or log to the base e, is denoted by ln. ln can also be written as [tex]log_{e}[/tex].

So, we can write the given expression as:

[tex]e^{log_{e}^(5) }[/tex]

The property of logs is:

[tex]a^{log_{a}^(x) } = x[/tex]

This means that if the number an is raised to a log whose base is the same as the number a, the answer will be equal to the log's argument, which is x.

The number e and the base of log are the same in the given case. As a result, the answer to the expression will be the log argument, which is 5.

Therefore, the value of [tex]e^{log_{e}^(5) }[/tex] = [tex]e^{In 5}[/tex] = 5. Correct option is option B.

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The average number of items in all the gift bags is 7.4.

Average, also known as mean, is a numerical value that represents the central or typical value in a set of numbers. It is calculated by adding up all the numbers in a set and dividing the sum by the total number of values in the set. The average is a useful tool for summarizing a large amount of data into a single value that can be easily understood and compared to other values.

In the given question,

We can use the weighted average formula to find the average number of items in all the gift bags:

Average number of items = (proportion of green bags x average items in green bags) + (proportion of yellow bags x average items in yellow bags) + (proportion of blue bags x average items in blue bags)

Proportion of green bags = 50% = 0.5

Proportion of yellow bags = 20% = 0.2

Proportion of blue bags = 30% = 0.3

Average items in green bags = 8

Average items in yellow bags = 5

Average items in blue bags = 8

Substituting the values into the formula, we get:

Average number of items = (0.5 x 8) + (0.2 x 5) + (0.3 x 8)

Average number of items = 4 + 1 + 2.4

Average number of items = 7.4

Therefore, the average number of items in all the gift bags is 7.4

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Answer:

If the larger bottle of shampoo gives 25% more for the same price, then it must contain 1.25 times the amount of shampoo in the smaller bottle. Let's represent the size of the smaller bottle as x ounces.

Thus, we can set up the following equation:

x * 1.25 = 6.7

Solving for x, we get:

x = 6.7 / 1.25

x ≈ 5.36

Therefore, the size of the original smaller bottle of shampoo is approximately 5.4 ounces (rounded to the nearest tenth).

Answer:

There were 62 people on the train to begin with.

Step-by-step explanation:

Firstly,i I subtracted 21 with 18 so i got 3.

It means that the train got 3 more people from the start.

Then i subtracted 65 with 3.

And so i got 62.

The length of side x in simplest radical form with a rational denominator is equal to 4.472 units.

An isosceles triangle is a triangle with two equal sides. Also, the angles opposite to the two equal sides are also congruent.

According to Pythagoras' theorem, the square on the hypotenuse of a right-angled triangle equals the sum of the squares on the remaining two sides.

So, the length of other side is also equal to [tex]\sqrt{10}[/tex].

Now, lets use Pythagoras theorem to find the length of x.

Length of Hypotenuse is equal to [tex]\sqrt{y^2 + y^2}[/tex]

x = [tex]\sqrt{y^2 + y^2}[/tex]

x = [tex]\sqrt{\sqrt{10}^2+\sqrt{10 ^2} }[/tex]

x = [tex]\sqrt[2]{10+10}[/tex]

x = 4.472 units

Therefore, the length of side x in simplest radical form with a rational denominator is equal to 4.472 units.

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The solution of the given problem of equation comes out to be the quadratic function's expression is  [tex]y = -2x² + 8x + 3[/tex]

Variable words are commonly used in complex algorithms to show uniformity between two incompatible claims.

Academic expressions called equations are used to show the equality of various academic numbers. Instead of a unique formula that splits 12 into two parts and can be used to analyse data received from [tex]y + 7[/tex]  , normalization in this case yields b + 7.

Here,

A quadratic function's curve is shown in the provided illustration. The quadratic function's expression is

=> [tex]y = -2x² + 8x + 3[/tex]

We can use the knowledge that a quadratic function's standard form is

=>  [tex]y = ax² + bx + c[/tex]  , where a, b, and c are constants, to see this.

When y =  [tex]-2x² + 8x + 3[/tex] is provided,

we can see that a = -2, b = 8, and c = 3 by comparing it to the standard form.

Therefore, the quadratic function's expression is [tex]y = -2x² + 8x + 3[/tex]

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If on a monte carlo roulette wheel, there are 37 slots: 18 red, 18 black, and 1 green, the probability of getting 26 straight blacks is approximately 3.143 x 10^-16.

The probability of duplicating the exact sequence of 26 straight blacks that occurred on August 18, 1913, is extremely low. Each spin of the wheel is an independent event, so the probability of getting a black on any given spin is always 18/37, regardless of what happened on previous spins.

To calculate the probability of getting 26 straight blacks, we can use the formula for the probability of a sequence of independent events, which is the product of the probabilities of each event. Therefore, the probability of getting 26 straight blacks is (18/37)^26, which is an extremely small number, approximately 3.143 x 10^-16.

Therefore, the probability of duplicating the 26 straight blacks that occurred on August 18, 1913, is so low that it's effectively impossible. It's important to note that each spin of the wheel is independent, so even if the wheel had produced 25 straight blacks, the probability of the next spin being black would still be 18/37.

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linear Equation to represent the description "8 more than 4 times number 28" is: y = 4x + 8

What is linear equation ?

A linear equation is an algebraic equation that describes a straight line relationship between two variables, typically denoted as x and y. The general form of a linear equation is:

y = mx + b

where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point at which the line crosses the y-axis).

The slope, m, represents the rate of change of y with respect to x, or how steep the line is. It is calculated as the change in y divided by the change in x between any two points on the line.

According to the question:
a. An equation to represent the description "8 more than 4 times number 28" is:

y = 4x + 8

where x represents the number 28, and y represents the result of multiplying 28 by 4 and then adding 8.

b. A real-world situation that this equation could represent is the cost of purchasing a certain number of items. For example, if the price of one item is $28, and there is a discount of 8 dollars for every four items purchased, the equation y = 4x + 8 could be used to calculate the total cost y of purchasing x items. The 4x term represents the cost of the items before the discount, and the +8 term represents the discount. For instance, if a customer wants to purchase 12 items, they would pay 4 * $28 = $112 for the first 12 items, minus $8 for the discount, resulting in a total cost of $104.

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Hence, the population proportion's 95% confidence interval is (0.210, 0.290), rounded to the thousandths place.

A mathematical concept known as proportionality describes the relationship between two quantities that have different sizes but keep the same ratio or proportion. In other words, to preserve the same ratio, if one item changes, the other quantity must also change in proportion. For instance, if an automobile's speed and distance are proportionate, doubling the distance it travels will cause the car to go twice as quickly while retaining the same speed-to-distance ratio. Equations or ratios in mathematics are frequently used to express proportionality.

given

We can use the following formula to determine the lower and upper bounds of the 95% confidence interval for the population proportion:

Lower limit: sqrt((p * q) / n) * p - z

Upper limit: sqrt((p * q) / n) = p + z

With q = 1 - p, z is the z-score corresponding to the level of confidence, and p is the sample proportion.

Here, p = 130/520 = 0.25, q = 1 - p = 0.75, n = 520, and the z-score is 1.96 at a 95% confidence level (from the standard normal distribution).

Lower limit: 0.210 (0.25" * 0.75") - 1.96 * sqrt(0.25" * 0.75")

The maximum is equal to 0.25 + 1.96 * sqrt((0.25 * 0.75) / 520) = 0.290.

Hence, the population proportion's 95% confidence interval is (0.210, 0.290), rounded to the thousandths place.

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Answer:

We can use the given equation to find the expected LSAT score (S) for a student who studies for 10 hours:

S = 130 + 2.2h

S = 130 + 2.2(10)

S = 130 + 22

S = 152

Therefore, if a student studies for 10 hours, we would expect her LSAT score to be 152.

The LCD of 2/5, 1/2, and 3/4 is equal to 20.

In Mathematics, LCD is an abbreviation for least common denominator or lowest common denominator and it can be defined as the smallest number that can act as a common denominator for a given set of fractions.

Next, we would determine the factors of the denominators for the given fraction 5, 2, and 4 as follows;

5 = 5 × 1

2 = 2 × 1

4 = 2 × 2 × 1

Therefore, the least common denominator (LCD) would be calculated as follows:

Least common denominator (LCD) = 5 × 2 × 2 × 1

Least common denominator (LCD) = 20.

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The probability of Kim getting a 2 and a head is 1/12.

A subfield of mathematics known as probability studies random occurrences and the possibility that they will occur. It is a technique of putting a number on the degree of ambiguity surrounding a situation or result. A number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event, is used to express probability. The probability of an occurrence is determined by dividing the number of possible outcomes by the number of ways the event may occur. Several disciplines, including science, engineering, economics, and statistics, employ probability.

For a fair dice, the probability of getting a 2 on the dice is 1/6.

The probability of getting a head on the coin is 1/2.

Thus,

P(getting a 2 and a head) = P(getting a 2) × P(getting a head)

= (1/6) × (1/2)

= 1/12

Hence, the probability of Kim getting a 2 and a head is 1/12.

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The expression (5/7)^-1  can be written without an exponent as 8/5.

Exponents have a number of important properties, such as the product rule (a^m × a^n = a^(m+n)) and the power rule ((a^m)^n = a^(m*n)). They are used in a wide range of mathematical contexts, including algebra, calculus, and geometry.

Given that (5/8)^-1, then we can deduced that the  negative exponent is the samething as putting it in the denominator, which can be exprtessed as;

=[1/ (5/8)]

=[1 ÷ (5/8)]

[1 * 8/5]

=8/5

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Answer: 163.36 in

Step-by-step explanation: Using the formula C=2πr you can plug in the radius and get your answer.

C=2 x pi x 26

C = 163.362817987

round as needed

Answer: 163.36

Im pretty sure all you have to do is use the formula

C=2πr

Step-by-step explanation:

C=2π(26)

163.36

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

All you have to do is subtract 6 from 14. The answer is 8. If the question is something like this one, always take the remainder and subtract it from how many you had in the beginning to get the answer.

Good luck

Peyton

The side opposite to angle Y is the longest, and angle Y is the largest angle in triangle XYZ. So, the angles can be ordered from greatest to least as follows:

angle Y > angle Z > angle X.

What is triangle ?

A triangle is a three-sided polygon, or a closed two-dimensional shape with three straight sides and three angles. The sum of the angles in a triangle always adds up to 180 degrees. The sides of a triangle can be of different lengths, and the angles can be acute (less than 90 degrees), right (equal to 90 degrees), or obtuse (greater than 90 degrees).  

To order the angles from greatest to least in triangle XYZ, we need to determine which side is the longest. By the Law of Cosines, we know that:

[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]

where c is the side opposite to angle C, and a and b are the other two sides.

So, let's calculate [tex]c^2[/tex] for each angle:

For angle X: [tex]c^2 = 25^2 + 27^2 - 2(25)(27)*cos(X)[/tex] ≈ 173.65

For angle Y: [tex]c^2 = 24^2 + 27^2 - 2(24)(27)*cos(Y)[/tex] ≈ 267.43

For angle Z: [tex]c^2 = 24^2 + 25^2 - 2(24)(25)*cos(Z)[/tex] ≈ 121.97

Therefore, the side opposite to angle Y is the longest, and angle Y is the largest angle in triangle XYZ. So, the angles can be ordered from greatest to least as follows:

angle Y > angle Z > angle X

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To find the two consecutive odd integers, let's set up an equation using the given information. Let x be the smaller odd integer, then the next consecutive odd integer is x+2.

The problem states that the product of these two integers is 77 more than twice the larger integer. In equation form, this can be written as:

x * (x + 2) = 2(x + 2) + 77

Now, let's solve for x:

x * (x + 2) = 2x + 4 + 77
x^2 + 2x = 2x + 81
x^2 = 81

To find the value of x, take the square root of both sides:

√(x^2) = √81
x = 9

So, the smaller odd integer is 9. The next consecutive odd integer is 9 + 2 = 11.

Therefore, the two consecutive odd integers are 9 and 11.

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The two consecutive odd integers are 9 and 11.

To find the two consecutive odd integers whose product is 77 more than twice the larger, we can set up the following equation:
x * (x + 2) = 2(x + 2) + 77
Here, x represents the first odd integer, and x + 2 represents the second consecutive odd integer. Now, let's solve the equation step by step:
1. Expand the equation: x^2 + 2x = 2x + 4 + 77
2. Simplify the equation: x^2 + 2x = 2x + 81
3. Subtract 2x from both sides: x^2 = 81
4. Take the square root of both sides: x = ±9
Since we're looking for positive integers, x = 9. Therefore, the two consecutive odd integers are 9 and 11.

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Answer:

  13/32

Step-by-step explanation:

You want the area of the shaded portion of the unit square shown.

Points B, C, E are shown as equidistant from point F, so will lie on a circle centered at F. The center of that circle is at the point of coincidence of the perpendicular bisectors of BE, BC, and CE.

Without loss of generality, we can let line EF lie on the x-axis such that E is at the origin. Chord EB of the circle has a rise of 1/2 for a run of 1, so a slope of 1/2. Its midpoint is (1, 1/2)/2 = (1/2, 1/4). The perpendicular line through this point will have slope -2, so its equation can be written ...

  y -1/4 = -2(x -1/2)

  y = -2x +5/4

Then the x-intercept (point F) will have coordinates (0, 5/8):

  0 = -2x +5/4 . . . . . y=0 on the x-axis

  2x = 5/4

  x = 5/8

Trapezoid EFCD will have upper base 5/8, lower base 1, and height 1/2. Its area is ...

  A = 1/2(b1 +b2)h

  A = (1/2)(5/8 +1)(1/2) = (1/4)(13/8) = 13/32

The shaded area is 13/32.

__

Additional comment

The point-slope equation of a line through (h, k) with slope m is ...

  y -k = m(x -h)

Around 0.13% or 0.0013 of children find relief for less than four hours.

The percentage of children who experience relief for less than four hours if the relief time follows a lognormal distribution is determined as follows:

Step 1: Define the parameters of the problem. Assume that relief times are normally distributed with a mean of μ = 5.5 hours and a standard deviation of σ = 0.5 hours. We want to find the percentage of children who experience relief for less than four hours.

Step 2: Convert the normal distribution to the standard normal distribution using the formula: z = (x - μ) / σwhere x is the relief time in hours.

Step 3: Find the z-score corresponding to the value of x = 4:z = (4 - 5.5) / 0.5 = -3

Step 4: Use a standard normal distribution table to find the percentage of the area under the curve to the left of z = -3. This is equivalent to the percentage of children who experience relief for less than four hours.

Using the standard normal distribution table or calculator, we get that the percentage of children who experience relief for less than four hours is approximately 0.13% or 0.0013.


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The height of the image after being scaled down by 80% three times is 76.8mm, which is not within the required range for a U.S. passport photo.

Scaling is the process of increasing or decreasing the size of a picture by dividing or multiplying its dimensions. An picture is expanded when it is scaled up, and its size is decreased when it is scaled down. An picture is affected by scaling when its size and, consequently, appearance, are altered. An picture may become pixelated or fuzzy if it is scaled up or down excessively, and information may be lost if it is scaled down too much. The aspect ratio of an image—the proportion of its width to its height—can also be impacted by scaling. The picture could look stretched or squished if the aspect ratio is modified.

Given that the image is 150 mm in height.

Thus, 80% of the image is:

150mm x 0.8 = 120mm

The scaling is performed 3 times, thus:

120mm x 0.8 = 96mm

96mm x 0.8 = 76.8mm

Hence, the height of the image after being scaled down by 80% three times is 76.8mm, which is within the required range for a U.S. passport photo.

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The complete question is: