What is the lateral surface area of the triangular prism below?

Answer:

Step-by-step explanation: you are sped that is the answer black n

a. The total length of the painted white line in the javelin throwing arena is approximately 255.984 meters.

b. The total area of grass in the shaded landing area of the javelin throwing arena is approximately 1624.6 square meters.

To find the total length of the painted white line, we need to calculate the length of the two straight segments and the two circular arcs.

a) Total length of the painted white line:

Let's break it down into components:

1. The two straight segments: Each straight segment is 95 meters long, and there are two of them.

Length of straight segments = 2 * 95 = 190 meters

2. The two circular arcs:

The throwing arena is a sector of a circle with a radius of 100 meters. The angle of the sector can be calculated using trigonometry. The angle can be found by taking the inverse cosine of the ratio of the adjacent side (which is the radius minus the throwing line distance) to the hypotenuse (which is the radius).

Angle (in radians) = cos⁻¹((radius - throwing line distance) / radius)

Now, the length of each circular arc can be calculated using the formula for the length of an arc of a circle:

Length of circular arc = radius * angle

Let's calculate the angle first:

Angle (in radians) = cos⁻¹((100 - 5) / 100)

Angle = cos⁻¹(95 / 100)

Angle ≈ 0.32492 radians

Now, we can calculate the length of each circular arc:

Length of each circular arc = 100 * 0.32492 ≈ 32.492 meters

Since there are two circular arcs, the total length of the painted white line is:

Total length = 190 (straight segments) + 2 * 32.492 (circular arcs)

Total length ≈ 255.984 meters

b) Total area of grass in the shaded landing area:

The shaded landing area is the sector of the circle with a radius of 100 meters and the angle we calculated above.

The formula to calculate the area of a sector of a circle is:

Area of sector = (angle / 2π) * π * radius²

Area of the shaded landing area = (0.32492 / (2π)) * π * 100²

Area of the shaded landing area ≈ (0.32492 / 2) * 10000

Area of the shaded landing area ≈ 1624.6 square meters

So, the total area of grass in the shaded landing area is approximately 1624.6 square meters.

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Answer:

The correct answer is 2.

Answer: $127.50

Step-by-step explanation: if we pull up our handy dandy calculator and do 15% of 150 it will output 22.50, 150 - 22 = 127.50 which brings the total to $127.50

Answer:

Step-by-step explanation:

2.63 is the value or quotient of 616/265 using long division.

We have to find the value of 616/265

In the given division the numerator is a dividend and the number in the denominator is a divisor.

616 is the dividend and 265 is the divisor.

When we perform long division the quotient will be 2.63 which is the require value.

       2.63  

____________

265 | 616

-530

______

860

-795

______

650

-530

______

120

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The surface area of given triangular prism = 24 ft².

For the given triangular prism

Base = 2 ft

height = 3 ft

side = 3ft

We know that,

Surface area of triangular prism

= side x base + 3x base x height

=  3 x 2  + 3x2x3

= 6 + 18

= 24 ft²

Thus,

Surface area = 24 ft²

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The measure of angle C is 13°.

To find the measure of angle C in the given circle, we need to use the properties of angles subtended by arcs in a circle.

Given information:

m∠J = 88° (angle J)

mArc DF = 62° (arc DF)

mArc BD = 136° (arc BD)

We can start by using the fact that the measure of an angle formed by a chord and an arc is equal to half the measure of the intercepted arc.

Since mArc DF = 62°, the measure of angle DJF (angle formed by chord DF and arc DF) is 62°/2 = 31°.

Next, we can use the fact that angles subtended by the same arc are equal.

Since mArc BD = 136°, angle BJD (angle formed by chord BD and arc BD) is also 136°.

Now, let's find angle BCD (angle formed by chord BD and chord CD). The sum of angles in a triangle is 180°, so angle BCD = 180° - angle DJF - angle BJD.

Angle BCD = 180° - 31° - 136°

Angle BCD = 180° - 167°

Angle BCD = 13°

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Answer: 0.07

Step-by-step explanation:

To find the relative frequency of people in the sample whose place of residence is suburban and whose highest degree is a two-year degree, we need to calculate the ratio of the number of people with those characteristics to the total sample size.

Looking at the contingency table, we can see that the number of people in the suburban category with a two-year degree is 21.

The total sample size is given as 311.

Therefore, the relative frequency can be calculated as:

Relative frequency = (Number of people in suburban category with two-year degree) / (Total sample size)

= 21 / 311

≈ 0.0676

Rounded to two decimal places, the relative frequency is approximately 0.07.

The regression equation is: y = -0.0068824x + 36.8881

So, the correct option is:

D) None of these.

To compute the regression equation based on the given data, we can use the formulas for slope (b1) and y-intercept (bo):

b1 = (NΣXY - ΣXΣY) / [tex](N\sum X^2 - (\sum X)^2)[/tex]

bo = (ΣY - b1ΣX) / N

Where:

N = Number of data points (in this case, 11)

ΣX = Sum of all X values (prices)

ΣY = Sum of all Y values (average number of pounds sold per day)

ΣXY = Sum of the product of X and Y values

[tex]\sum X^2[/tex] = Sum of the squares of X values

Using the provided data:

Ex = 210

Xy = 450

Zcy = 10387

Zz = 7275

Xy = 42471

Let's calculate the required values:

N = 11

ΣX = Ex + Zcy + Zz = 210 + 10387 + 7275 = 17872

ΣY = Xy = 450

ΣXY = Xy = 450

[tex]\sum X^2 = (Ex)^2 + (Zcy)^2 + (Zz)^2 = (210)^2 + (10387)^2 + (7275)^2 = 239208144[/tex]

Now, substitute these values into the formulas to find b1 and bo:

[tex]b1 = (11 \times450 - 17872 \times 450) / (11 \times239208144 - (17872)^2)[/tex]

= -14112250 / 2050445128

≈ -0.0068824

bo = (450 - (-0.0068824 [tex]\times[/tex] 17872)) / 11

= (450 + 122.7790368) / 11

≈ 36.8881

Therefore, the regression equation is:

y = -0.0068824x + 36.8881

So, the correct option is:

D) None of these.

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The complete question may be like:

Over a period of one year, retailer sells widgets at 11 different prices. He Calculates the average number of oiunds sold per day at each different price. From theese data, the following are calculated. Ex = 210, Xy = 450, Zcy = 10387, Zz? 7275 Xy? 42471 Compute the regression equation , SELEC A) y 0.20261x + 0.549951 B) y = 0.549951x + 30.410021 C) y = 0.20261. + 30.410021 D) none of these =b1x + bo.

1. The function representing the population of bacteria after t minutes is P(t) = 4900× [tex]e^{(0.08(t/60)}[/tex]

2. The percentage rate of change per minute is approximately 0.13%.

The general form of an exponential growth function ⇒ P(t) = P0 ×[tex]e^{(rt)}[/tex]

P(t) is the population at time t,

P0 is the initial population,⇒4900

r is the growth rate  ⇒ 8%

t is the time.

Therefore, our function in terms of hours (t) becomes:

P(t) = 4900 × [tex]e^{(0.08t)}[/tex]

To find per minute, there are 60 minutes in an hour,

∴ t becomes  t/60

P(t) = 4900× [tex]e^{(0.08(t/60))}[/tex]

We know the rate of change per hour is 8%, so the rate of change per minute will be 8% divided by 60, which is

[tex]e^{(0.08/60)-1}[/tex] × 100 = 0.13%.

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Answer:

  y < 2x +6

Step-by-step explanation:

You want an inequality for the given graph.

Here are some steps you can follow, in no particular order.

When you have this information, you can write the inequality in slope-intercept form.

When the boundary line is dashed, the inequality symbol you use will not include the "or equal to" case. It will be one of < or >.

When the shading is below the line, the values of y that satisfy the inequality will be less than (<) those on the boundary line. If shading is above, the y-values will be greater than (>) those on the line.

The slope and intercept go into the inequality like this:

  y < mx + b . . . . . . where m is the slope, and b is the y-intercept

For a dashed line, shaded below, with m=2 and b=6, the inequality is ...

  y < 2x +6

__

Additional comment

There are two points identified on the boundary line: (-2, 2) and (0, 6). The slope formula can be used to find the slope:

  m = (y2 -y1)/(x2 -x1)

  m = (6 -2)/(0 -(-2)) = 4/2 = 2

The point (0, 6) on the y-axis is the y-intercept. The y-value there is 6.

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The summation of 5 to power of n (where n starts from 1) is determined as 625.

The sum of the expression given is calculated by using the defined expression as sated in the question to perform the summation.

The given summation expression include;

∑5ⁿ

where;

So we are going to sum the number 5ⁿ 4 times.

The expression becomes;

5ⁿ x 5ⁿ x 5ⁿ x 5ⁿ = 5⁴ⁿ

where;

n = 1

The summation becomes;

5⁴ⁿ = 5⁴ = 625

Thus, the summation of 5 to power of n (where n starts from 1) is determined as 625.

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Answer:

-7/4

Step-by-step explanation:

we can see that every time the value of x increases by 4, the value of y decreases by 7.

let's pick two sets of coordinates (first two will be fine).

that is (-4, 6) and (0, -1)

Slope = (change in y values) / (change in x values)

= (-1 - 6) / (0 - -4)

= -7 / (0 + 4)

= -7/4.

so our slope (gradient) is -7/4

The linear function equation, y = m·x + c, indicates;

6. The growth in the y-values over each unit x-value interval is a difference of m units.

Part I. Please find attached the graph of y = x + 3, created with MS Excel, which shows that the differences between the y-values is 2 units over each x-value interval of 2 units.

a) The difference between the x-values is; k

The difference between the y-values is; m·k

The difference in the y-value is; m·k

Please find attached the completed tables in the following section

The equation of a linear function is; y = m·x + c

Where;

m = The slope of the graph = (y₂ - y₁)/(x₂ - x₁)

(x₁, y₁), and (x₂, y₂), are ordered pair of data on the graph of the linear function

c = The y-intercept of the linear function

(y₂ - y₁)/(x₂ - x₁) = m

(y₂ - y₁) = m × (x₂ - x₁)

Δy = m × Δx

When Δx = 1, we get;

Δy = m

Therefore, the y-value of a linear function increases by m, the slope value, when the x-value increases by 1, which indicates that the linear function grows by equal differences over the same interval of the input value of the function

Part I; Please find a graph of the linear function, y = 1·x + 3, which shows that each equivalent interval of 2 units in the x-axis, produces a difference in the y-value or y-axis of 2 units.

a) Considering the interval p and p + k, let y₁ represent the y-value at p and let y₂ represent the y-value at p + k, we get;

Slope, m = (y₂ - y₁)/((p + k) - p) = (y₂ - y₁)/k  

Therefore;

(y₂ - y₁)/k = m

(y₂ - y₁) = m × k

Therefore, the increase in the y-value, for an increase in the x-value of k is a constant,  m·k =  (y₂ - y₁)

Therefore the difference in the y-value for the specified x-values is a constant m·k

The possible equation in the question obtained from a similar question on the website is; y = -(1/2)·x + 10

The completed tables are;

[tex]\begin{tabular}{ | c | c | c | c | }\cline{1-4}& Interval; p = 2& p+ k = 6&\\ \cline{1-4}x-value & 2 & 6 & 4 \\\cline{1-4}y-value & y = (-1/2)\cdot (2)+10 =9 & y = (-1/2)\cdot (6)+10=\underline{7} & -2 \\\cline{1-4}\end{tabular}[/tex]

[tex]\begin{tabular}{ | c | c | c | c | }\cline{1-4}& Interval; p = 10& p+ k = 14&\\ \cline{1-4}x-value & 10 & 14 & 4 \\\cline{1-4}y-value & y = (-1/2)\cdot (10)+10 =\underline{ 5 }& y = (-1/2)\cdot (14)+10=3 & -2 \\\cline{1-4}\end{tabular}[/tex]

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Answer:

∫(1 - 25x²) dx

Step-by-step explanation:

Theoretical probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes, making option A the correct answer.

The correct answer is A. Theoretical probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. It represents the likelihood of an event occurring based on mathematical calculations and assumptions.

To provide a detailed explanation, let's break down the components of the definition:

Favorable outcomes: These are the outcomes that meet the desired criteria or event you are interested in. For example, if you are rolling a fair six-sided die and you want to find the probability of rolling a 3, the favorable outcome would be a single outcome where the die shows a 3.

Total number of possible outcomes: This refers to the complete set of all possible outcomes in the given situation. In the case of the fair six-sided die, there are six possible outcomes (numbers 1 to 6) since each face of the die represents a different number.

Theoretical probability is then calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This ratio provides an estimate of the probability of the event occurring under ideal, theoretical conditions. It assumes that each outcome is equally likely to occur.

It's worth noting that theoretical probability is based on mathematical calculations and assumptions, and it may not always reflect the actual probability observed in real-world scenarios. However, it serves as a foundation for understanding and analyzing probabilities in various contexts, such as in mathematics, statistics, and decision-making processes.

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The angle ABC in the circle is 70 degrees.

The intercepted arc is the arc that is inside the inscribed angle and whose

endpoints are on the angle. The arc angle is half the the inscribed angle.

The intercepted arc that is formed is equal to the inscribed angle,

multiplied by two (intercepted arc measure = inscribed angle × 2).

Therefore, let's find the arc angle ABC as follows:

∠ ABC = 1  /2 (360 - 120 - 100)

∠ ABC = 1  /2 (360 - 220)

∠ ABC = 1  /2 (140)

Therefore,

∠ ABC = 70 degrees

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Answer: The expression can be simplified by combining the fractions with a common denominator:

(x - 9)/(x - 4) + (x^2 - x + 5)/(x - 4)

To add these fractions, we need to find a common denominator, which in this case is (x - 4). Therefore, we can rewrite each fraction with the common denominator:

[(x - 9) + (x^2 - x + 5)] / (x - 4)

Simplifying the numerator:

(x - 9 + x^2 - x + 5) / (x - 4)

Combining like terms:

(x^2 - 2x - 4) / (x - 4)

Hence, the simplified expression is (x^2 - 2x - 4) / (x - 4).

The given histogram is bimodal, which is the last option/ option E, as bimodal distribution means that the data set has two distinct peaks or modes. In a bimodal histogram, the bars are grouped in a way that shows two prominent peaks or modes in the data.

Each bar in the histogram represents a specific range of values, and the height of the bar indicates the frequency or count of data points falling within that range. In a bimodal histogram, there will be two relatively high bars that correspond to the two modes of the data. The bimodal histogram is useful for visualizing and analyzing data sets that exhibit two distinct groups or clusters. It provides a clear visual representation of the two modes and their frequencies, which can help in identifying patterns and understanding the underlying characteristics of the data.

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The probability that she selects the route of three specific capitals is 3/43

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

States = 43

Capitals = 3

The probability is then calculated as

P = Capitals/States

substitute the known values in the above equation, so, we have the following representation

P = 3/43

Hence, the probability is 3/43

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The solution after resolving into factors are,

⇒ 8 (a - 3b) (a - b)

We have to given that,

Resolve into factors the expression,

⇒ (3a - 5b)² - (a + b)²

Now, We can simplify for resolving the factors as,

⇒ (3a - 5b)² - (a + b)²

Since, WE know that,

⇒ x² - y² = (x - y) (x + y)

Hence,

⇒ (3a - 5b)² - (a + b)²

⇒ [(3a - 5b) - (a + b)] [ (3a - 5b) + (a + b)]

⇒ [3a - 5b - a - b] [4a - 4b]

⇒ (2a - 6b) (4a - 4b)

⇒ 2 (a - 3b) × 4 (a - b)

⇒ 8 (a - 3b) (a - b)

Thus, The solution after resolving into factors are,

⇒ 8 (a - 3b) (a - b)

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The distance between the side AB are 314.2 ft.

In a triangle ABC AC = 200 ft, m ∠A = 72°, and m ∠B = 37°. we need to find the measure of the side AB,

So,

Using sine law.

Sin A / CB = Sin B / AC = Sin C / AB

Using the angle sum property of a triangle we find the value of angle C,

∠C = 180° - (∠A + ∠B)

∠C = 180° - (72° + 37°)

∠C = 180° - 109°

∠C = 71°

So,

Sin 37° / 200 = Sin 71° / AB

AB = 200 / Sin 37° × Sin 71°

AB = 314.2 ft

Hence the distance between the side AB are 314.2 ft.

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Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.

In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.

Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;

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Complete Question:

The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS

We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.

NS and NS

NS and RS

MS and RS

MS and QS

The values of x and y in simplest radical form are :

5) x = 3 and y = 3√3

6) x = 5√3 and y = 10√3

7) x = 21 and y = 14√3

Given are three right angled triangles, whose angles are 30° - 60° - 90°.

The measures of sides for a 30° - 60° - 90° triangle is in the ratio 1 :√3 :2.

That is if length of the shorter leg which is the side opposite to 30° is k, then the length of the longer leg, which is the side opposite 60° will be √3k and the length of the hypotenuse, which is the side opposite to 90° will be 2k.

5) Using the above fact, here,

2k = 6

⇒ k = 6/2 = 3

So, x = 3 and y = 3√3

6) √3 k = 15

k = 15 /√3 = 5√3

So, x = 5√3 and y = 2 × 5√3 = 10√3

7) k = 7√3

So, x = √3 × 7√3 = 21

y = 2 × 7√3 = 14√3

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The correct formula for finding the break-even point is option C:

Break even point = (0.01)(#of points)(P)/monthly savings.

In this formula, the break-even point is calculated by multiplying the number of points (#of points), the price per unit (P), and a factor of 0.01, then dividing it by the monthly savings.

It's important to note that the break-even point is the level of sales or production at which total costs and total revenue are equal, resulting in neither profit nor loss. The formula above provides a way to determine the break-even point by considering the relevant variables.

Regarding your explanation of posting the answers in your questions, I understand your situation. If you encounter any issues or limitations with the platform, feel free to provide any necessary context or information in the questions. I'm here to assist you further if needed.

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The correct options regarding the inequality are:

A. 1 hat, 1 scarf

D. 4 hats, 1 scarf

F. 2 hats, 1 scarf

Based on the time constraint, Phil can spend a maximum of 12 hours knitting, so we can set up the following inequality:

2h + 3s ≤ 12,

Phil can knit at most 6 hats per week, because 6 hats * 2 hours/hat = 12 hours.

Phil can knit at most 4 scarves per week, because 4 scarves * 3 hours/scarf = 12 hours.

Phil can use at most 900 yards of yarn, because he has 900 yards of yarn.

Phil can knit 1 hat and 1 scarf, because 1 hat * 150 yards/hat + 1 scarf * 400 yards/scarf = 550 yards < 900 yards.

Phil can knit 4 hats and 1 scarf, because 4 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 900 yards.

Phil can knit 2 hats and 1 scarf, because 2 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 700 yards < 900 yards.

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The test statistic and critical value needed to test the claim that the success is independent of the type of treatment are 9.750 and critical value is 6.635.

The expected value for each cell is calculated as follows:

E = row total * column total / grand total

The grand total is 150.

The row totals are 83 and 67.

The column totals are 86 and 64.

The expected values are as follows:

Successful: 60 * 86 / 150 = 36.4

Unsuccessful: 60 * 64 / 150 = 29.6

Surgery treatment

Successful: 67 * 86 / 150 = 49.6

Unsuccessful: 67 * 64 / 150 = 27.4

The test statistic is calculated as 9.750

The critical value is calculated as follows:

α = 0.01

df = (r-1)(c-1) = (2-1)(2-1) = 1

x²(α, df) = 6.635

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The relative frequency that a randomly selected student's favorite exhibit was either dinosaurs, or planets is 0.7.

To find the relative frequency, we will divide the number of students who chose dinosaurs or planets by the total number of students surveyed.

The total number of students surveyed is 12 + 25 + 17 + 6 = 60.

The number of students who chose dinosaurs or planets is 25 + 17 = 42.

Therefore, the relative frequency will then be 42 / 60 = 0.7.

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