a container is shaped like a triangular prism. each base of the container is an equilateral triangle with the dimensions shown. image the container has a height of 15 centimeters. what is the lateral surface area of the container in square centimeters?

For the given triangle when G is the incenter of ABC the value of DG = 12, FC = 35, BG = 13.41, BF = 6.

The intersection of all three of the triangle's interior angle bisectors is where a triangle's incenter is located. It may be thought of as the intersection of the triangle's internal angle bisectors. Due to the junction point of the central axis being the centre of the triangle's inscribed circle, this point will be equally spaced from each of the triangle's sides.

The centre of a triangle's inscribed circle, which is the biggest circle that can fit within the triangle, is known as the incenter.

Given that, G is the incenter of the triangle.

Thus, EG = GF = DG.

Now, the value of DG is determined using the Pythagoras Theorem:

(37)² = DG² + (35)²

1369 = DG² + 1225

DG = 12

Now, FC = 35.

For, BG we have:

BG² = 6² + 12²

BG² = 36 + 144

BG = 13.41

BF = 6

Hence, for the given triangle when G is the incenter of ABC the value of DG = 12, FC = 35, BG = 13.41, BF = 6.

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Answer:

Sure, I can help you with that! First, we know that the vertex form of a quadratic function is: f(x) = a(x - h)^2 + k where (h, k) is the vertex of the parabola. So we can plug in the values we have: f(x) = a(x - 2)^2 + 1 Now we just need to find the value of "a". To do that, we can use the fact that the function goes through the point (4, 5). So we can plug in those values: 5 = a(4 - 2)^2 + 1 Simplifying, we get: 5 = 4a + 1 4a = 4 a = 1 So now we know that the quadratic function is: f(x) = (

In the given situation with the help of the given mass and volume, the density is 9.45 g/cm³ respectively.

Mass per unit volume is the definition of a material's density.

In essence, density is a measurement of how closely stuff is packed.

It is a particular physical characteristic of a specific thing.

The Greek scientist Archimedes made the discovery of the density principle.

We can travel through low-density materials like air, which has a density significantly lower than that of human tissue.

Granite is a different material altogether.

Never attempt to traverse stone.

So, we have:

Volume: 38 cm

Mass: 359.1 g

Now, the density:

D = m/v

Insert values as follows:

D = m/v

D = 359.1/38

D = 9.45 g/cm³

Therefore, in the given situation with the help of the given mass and volume, the density is 9.45 g/cm³ respectively.

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Answer:

(x-4) (x+4)

Step-by-step explanation:

(a-b)(a+b) results a^2 - b^2

So, x is our "a" and 4 is our "b"

Answer:

19.124

Step-by-step explanation:

sin 21=16/x

do the reciprocal and u will find

x/16=1/sin 21

multiply both sides by 16

x=1/sin21×16

the answer will be 19.124

Answer:

Yes, the triangle with side lengths 6, 8, and 10 is a right triangle.

Explaination:

We can use the Pythagorean theorem to check if a triangle is a right triangle or not. According to the Pythagorean theorem, in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse). In other words:

a^2 + b^2 = c^2

where a and b are the lengths of the two shorter sides, and c is the length of the longest side (the hypotenuse).

In this case, the two shorter sides are 6 and 8, and the longest side (the hypotenuse) is 10. So we can plug these values into the equation above:

6^2 + 8^2 = 10^2

Simplifying:

36 + 64 = 100

100 = 100

Since the equation is true, this means that the triangle satisfies the Pythagorean theorem, and therefore it is a right triangle.

We can estimate that about 74 people voted in the election, which is the same as the actual number of voters.

What are the voters?

To estimate the number of people who voted in the election, we can use the proportion of registered voters who actually voted.

If we know that there are 8,246 registered voters in the town of Mayfield and 74 voters cast their vote, we can calculate the proportion of registered voters who voted as follows:

Proportion of voters = Number of voters / Number of registered voters

Proportion of voters = 74 / 8,246

Proportion of voters = 0.00897

We can then use this proportion to estimate the number of people who voted by multiplying it by the total number of registered voters:

Estimated number of voters = Proportion of voters x Number of registered voters

Estimated number of voters = 0.00897 x 8,246

Estimated number of voters = 73.9 (rounded to the nearest whole number)

Therefore, we can estimate that about 74 people voted in the election, which is the same as the actual number of voters.

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Complete question is: There are 8,246 registered to vote in the town of mayfield, about 74 people voted in the election, which is the same as the actual number of voters.

This means that the only restricted value of [tex]x[/tex] is [tex]x=6[/tex], since using this value in the original equation would lead to both denominators being equal to [tex]0[/tex].

In mathematics, an equation is a claim that two expressions are equivalent. Two sides that are separated by the algebraic symbol (=) make up an equation.

For instance, the claim "[tex]2x+3=9[/tex]" contends that the number "[tex]9[/tex]" is equal to the statement  Finding the value or values of the variable(s) necessary for the equation to be true is the goal of equation solving.

Equations can include one or more parts and be straightforward or complex, regular or nonlinear. The formula "[tex]x^{2} +2x-3=0[/tex]" raises the variable x to the second power.

In many different branches of mathematics, including algebra, calculus, and geometry, lines are used.

[tex]4+2/(x-6)= 6/(x-6)\\4(x-6) +2 =6\\4x -22 = 0\\4x = 22\\x = 11/2\\[/tex]

Therefore the only restricted value of [tex]x[/tex] is [tex]x=6[/tex], since using this value in the original equation would lead to both denominators being equal to [tex]0[/tex].

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The calculated radius of the cylidner when approximated is 8.0 meters

The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, h is the height, and π is a constant approximately equal to 3.14.

To find the radius of a cylinder with volume 1607 m³ and height 8 m, we can rearrange the formula as:

r^2 = V / (πh)

Substituting the given values, we get:

r^2 = 1607 / (3.14 x 8)

r^2 ≈ 63.973

Taking the square root of both sides, we get:

r ≈ 8.0

Therefore, the radius of the cylinder is approximately 8.0meters.

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By the property of the mid point theorem of triangle:

(1) MN = 1/2 QR and (ii) MN || QR

A point that divides a line segment into two equal halves is the midway of the segment. The line segment's midpoint is located precisely in the middle.

(1) MN = 1/2 QR

By the property of the mid point theorem of triangle:

MN = 1/2 QR , As M and Na are the mid points sides QP and PR of triangle .

(ii) MN || QR

And thus, both the lines MN and QR will be parallel.

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complete question:

In the figure M and N are mid point at QP and PR prove that: respectively

(1) MN = 1/2 QR

(ii) MN || QR

The figure is attached.

Answer:

give up on math this just too hard

Step-by-step explanation:

no

a. 90 degree clockwise rotation about the origin (x, y) → (y , -x). b. 180 degree clockwise rotation about the origin (x, y) → (-x, - y). c. 270 degree clockwise rotation about the origin (x, y) → (-y, x).

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

The mapping statement for each rotation in the is given as:

a. 90 degree clockwise rotation about the origin (x, y) → (y , -x)

b. 180 degree clockwise rotation about the origin (x, y) → (-x, - y)

c. 270 degree clockwise rotation about the origin (x, y) → (-y, x).

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Here is your answer hope this helps:

m=8

8x8=64

64+9= 73

Burger Quick is able to estimate their wait time more consistently because it has a smaller IQR (Interquartile Range).

What is an IQR?

The IQR represents the range of the middle 50% of the data, and is a measure of the spread of the data. A smaller IQR indicates that the data is less spread out and more consistent. Therefore, since Burger Quick has a smaller IQR than Super Fast Food, it is able to estimate their wait time more consistently.

It is calculated by finding the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset. The quartiles are values that split the data into four equal parts: Q1 represents the 25th percentile, Q2 (also known as the median) represents the 50th percentile, and Q3 represents the 75th percentile. The IQR therefore represents the range of the middle 50% of the data.

The IQR is a useful measure of variability because it is less sensitive to outliers than the range or standard deviation, which can be skewed by extreme values in the data. The IQR is often used in box plots to show the spread of the data and identify potential outliers.

What is Burger Quick?

Burger Quick is likely a hypothetical or fictional drive-thru restaurant used in a statistical analysis or problem. It was mentioned in a question about box plots and wait times at drive-thru restaurants, and may not actually exist as a real establishment.

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To find the minimum value of a quadratic function most efficiently, we would like to see the quadratic function in its vertex form.

The vertex form of a quadratic function is given by:

f(x) = a(x - h)^2 + k

where (h, k) is the vertex of the parabola, and "a" determines the direction and the "stretch" of the parabola.

If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards.

The minimum value of the function occurs at the vertex if the parabola opens upwards (a > 0), and the maximum value occurs at the vertex if the parabola opens downwards (a < 0).

In this case, since we're looking for the minimum value, we would want a quadratic function where a > 0. Once we have the vertex form, we can easily identify the vertex (h, k), and the minimum value of the function will be k.

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Using the inverse variation formula, p × q = k, where k is a constant, we can solve for q when p is equal to 2, given that p and q vary inversely and p is 24 when q is 23 when p is equal to 2, q is equal to 276.

When two variables vary inversely, as one variable increases, the other variable decreases proportionally, and vice versa. In this problem, p and q vary inversely, which means that if we multiply p by some constant, we need to divide q by the same constant to maintain the inverse variation.

First, we need to find the value of k using the given information:

p × q = k

24 × 23 = k

k = 552

Now that we have the value of k, we can use it to solve for q when p is equal to 2:

p × q = k

2 × q = 552

q = 276

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The area of the triangular base of the prism is 9.5 unit².

What is an area?

To find the area of the triangular base, we need to use the formula for the volume of a triangular prism:

V = (1/2)×b×h×H

Where b is the length of the base of the triangle, h is the height of the triangle, and H is the height of the prism.

We know that the volume of the prism is 27.36 unit³ and the height of the prism is 2.88 units. So we can plug these values into the formula:

27.36 = 1/2×b×h×2.88

Simplifying this equation, we get:

b×h = 19

We don't know the values of b and h separately, but we can use the fact that the area of a triangle is equal to (1/2)×b×h. So we can rewrite the equation as:

2 × (Area of triangular base) = 19

Dividing both sides by 2, we get:

Area of triangular base = 9.5 units²

Therefore, the area of the triangular base of the prism is 9.5 unit².

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Yes 10 people would be unusual as it falls outside of 2 standard deviation of mean.

Here, the mean number of  the famous brand name is 4.80000019, and the standard deviation is 0.73

so, μ = 4.80000019 and σ = 0.73

the number of people = 10

⇒ n = 10

Consider μ ± 2σ

= 4.80000019 ± 2(0.73)

= 4.80000019 ± 1.46

= [4.80000019 - 1.46, 4.80000019 + 1.46]

= [3.34000019, 6.26000019]

As we know 6.26000019 <  8

This means that, it falls outside of 2 standard deviation of mean.

Therefore, it would be unusual to randomly select 10 people and find that greater than 8 recognize the famous brand name.

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Solving the equation 2^x + 124 = 5^y for x and, we get x = 0 and y = 5

From the question, we have the following parameters that can be used in our computation:

2^x + 124 = 5^y

Set x = 0

So, that we calculate the of y

Using the above as a guide, we have the following:

2^0 + 124 = 5^y

This gives

1 + 124 = 5^y

Evaluate the like terms

So, we have

5^y = 125

Express 125 as 5^3

So, we have

5^y = 5^3

Evaluate

y = 3

Hence, the solution is x = 0 and y= 3

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Option D : The statement that is true about the quadratic function f(x)=-x²+8x-7, which states that the zeros are 1 and 7, because f(x) = -(x - 1)(x - 7).

To find the zeros of the quadratic function f(x) = [tex]-x^2 + 8x - 7[/tex], we need to set f(x) equal to zero and solve for x:

[tex]-x^2 + 8x - 7 = 0[/tex]

We can solve this quadratic equation using the quadratic formula or by factoring. Let's use factoring.

We can rewrite the quadratic expression as:

[tex]-(x^2 - 8x + 7)[/tex]

To factor the expression, we need to find two numbers whose product is 7 and whose sum is -8. These numbers are -1 and -7. Therefore, we can rewrite the expression as:

-(x - 1)(x - 7)

So the zeros of the function are x = 1 and x = 7.

Therefore, the statement that is true is option D: The zeros are 1 and 7, because f(x) = -(x - 1)(x - 7).

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Which statement about f(x)=-x²+8x-7 is true?

A. The zeros are 1 and -7, because f(x)=-(x-1)(x+7)

B. The zeros are -1 and -7, because f(x)=-(x+1)(x+7)

C. The zeros are -1 and 7, because f(x)=-(x+1)(x-7)

D. The zeros are 1 and 7, because f(x)=-(x-1)(x-7)

Answer:

6

Step-by-step explanation:

The percent of those interviewed said they like orange juice for breakfast is 58%.

A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent.

The percent of those interviewed said they like orange juice for breakfast will be:

= Orange juice taker /  Total respondent

= 29/50

= 0.58

= 58%

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According to the 2020 report to Congress on the prevention and reduction of underage drinking, approximately 16.8% of individuals in the United States, between the ages of 12 and 20, reported consuming alcohol in the past month when being surveyed.

The report is based on data from the 2019 National Survey on Drug Use and Health (NSDUH), which is an annual survey conducted by the Substance Abuse and Mental Health Services Administration (SAMHSA). There are approximately 16.8% of individuals in the United States consume alcohol in the past month when being surveyed, between the ages of 12 and 20.

It is important to note that consuming alcohol before the age of 21 is illegal in the United States, and underage drinking can lead to a variety of negative consequences, including impaired driving, risky sexual behavior, and increased risk of alcohol use disorder later in life.

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The required value of the 30th percentile of the given data set 7 12 3 14 17 20 5 3 17 4 13 2 15 9 15 18 16 9 1 6 is equal to 5.

To find the value of the 30th percentile,

We need to sort the data set in ascending order first,

1, 2, 3, 3, 4, 5, 6, 7, 9, 9, 12, 13, 14, 15, 15, 16, 17, 17, 18, 20

The 30th percentile is the value below which 30% of the data falls.

To find this value, we can use the formula,

P = (n / 100) × x

where P is the desired percentile (30th percentile in this case),

n is the total number of data points,

And x is the rank of the value corresponding to the desired percentile.

Here,

The total number of data points n = 20

x = (30 / 100) × 20

  = 6.

This means that the value corresponding to the 30th percentile is the 6th value in the sorted data set, which is 5.

Therefore, the value of the 30th percentile for the given data set is 5.

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The expression equivalent to 4(15 - 7) is 32.

What is an expression?

An expression is a combination of values, variables, operators, and function calls that are evaluated to produce a result. An expression can be as simple as a single value or as complex as a multi-level nested set of calculations.

We can simplify the expression 4(15 - 7) by performing the operation inside the parentheses first (since parentheses take precedence over multiplication). We get:

15 - 7 = 8

Substituting this value back into the expression, we get:

4(8)

Multiplying 4 by 8, we get:

32

Therefore, the expression equivalent to 4(15 - 7) is 32.

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Complete question is: The expression equivalent to 4(15 - 7) is 32.

Answer:

-4x +6y - 8

Step-by-step explanation:

See the attachment below:

The -10 + 6 = -4 not 4

Answer:

Step-by-step explanation:

-10x - 9y + 6x + 15y - 8 =​

-4x+6y -8

If you paid $16 in sales tax on a new phone. The phone costs $320. the percent of sales tax is 5%.

To find the percent of sales tax, we need to divide the amount of sales tax by the cost of the phone, and then multiply by 100 to convert to a percentage:

Percent of sales tax = (Sales tax / Cost of phone) x 100%

Percent of sales tax = (16 / 320) x 100%

Simplifying the expression inside the parentheses:

Percent of sales tax = 0.05 x 100%

Multiplying:

Percent of sales tax = 5%

Therefore, the percent of sales tax is 5%.

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