Find the missing angles in these diagrams. All shapes a regular (ignore my pen marks)
(Image attached)

The surface area of the given right triangular prism is 84 in².

How to find the surface area of a right triangular prism?

To calculate the surface area of a right triangular prism, we need to find the area of all the faces and add them up.

First, let's find the area of the triangular bases. The base of the triangle is 8 in, and the height is 3 in, so the area of each triangular base is [tex]\frac{1}{2} \times base \times height = \frac{1}{2} \times 8 \times 3 = 12 \: {in}^{2}[/tex]

There are two triangular bases, so the total area of both bases is (2 × 12) in²= 24 in²

Now, let's find the area of the rectangular faces. The length of the rectangle is 5 in, and the breadth is 4 in.

So, the area of each rectangular face is length × breadth = 5 in × 4 in = 20 in²

There are three rectangular faces, so the total area of all three faces is 3 × 20 in² = 60 in².

Finally, we add the areas of the bases and the rectangular faces to get the total surface area.

Total surface area = 24 in² + 60 in² = 84 in²

Therefore, the surface area of this right triangular prism is 84 square inches.

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The radius r that produces the minimum surface area is 1.06 cm and the height h is 1.41 cm.

Let r be the radius of the cylinder and h be the height. You can find the equation for the volume of a solid by adding the volumes of the two hemispheres and the cylinder.

Volume = [tex](2/3)πr^3 + πr^2h[/tex] = 10 cubic centimeters

Now let's find the values ​​of r and h that minimize the surface area of ​​the solid. This area consists of three parts:

Curved surfaces of two hemispheres and sides of a cylinder. This can be expressed as:

surface area = [tex]2πr^2 + 2πrh[/tex]

To find the values ​​of r and h that minimize this expression, we can use the Lagrangian multiplier method. Given that the volume of the solid is 10 cubic centimeters, we want to minimize the surface area. So it looks like this:

[tex]f(r, h) = 2πr^2 + 2πrh + λ[(2/3)πr^3 + πr^2h - 10][/tex]

Taking the partial derivatives for r, h, and λ and setting them to zero gives

[tex]4πr + 2πh = 2πr^2λ + (4/3)πr^3λ[/tex]

[tex]2πr = πr^2λ + πrhλ[/tex]

Solving these equations simultaneously gives:

h = 4r/3

λ = 2/(3r)

Substituting these values ​​into the volume equation gives:

[tex]r^2h = 5/3[/tex]

Substituting h = 4r/3 from above, we get:

[tex]r^3 = 15/8pi[/tex]

Taking the cube root of both sides gives:

r=1.06cm

Substituting this value for r into the formula for h yields:

h=1.41cm

Therefore, the radius r that produces the minimum surface area is about 1.06 cm and the height h is about 1.41 cm.

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Answer:

Step-by-step explanation:

its doc sus

Given the similar triangles, Note that x = 51.2

Since both triangles are proportional,

64/60 = x/48

To solve for x in the equation:

64/60 = x/48

We can cross-multiply to get rid of the fractions:

64 * 48 = 60 * x

3072 = 60x

Finally, we isolate x by dividing both sides by 60:

x = 3072/60 = 51.2

Therefore, the solution is:

x = 51.2

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Plotting the graph of the inequality we get a line passing through the point x = 5.

A mathematical notion called inequality examines two numbers or expressions to see if they are equal or not. When there is an inequality, one value is either more than or less than the other. "" (less than), ">" (greater than), "" (less than or equal to), and "" are used to denote inequality (greater than or equal to). In algebra and calculus, inequalities are frequently used to explain how variables relate to one another and to solve equations and systems of equations. In the actual world, inequalities are frequently used to compare measurements, quantities, and other variables.

The given function is x² > 25.

Simplifying the given inequality we have:

x > √25

x > 5 or -5

But - 5 is < x

So we have,

-5 < x < 5

Plotting the graph of the inequality we get a line passing through the point -5 < x < 5.

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The probability is approximately 17.43%.

Use Bayes' theorem. Bayes' theorem states that is:

P(A|B) = (P(B|A) * P(A)) / P(B),

Using the law of total probability: P(B) = P(B|A) * P(A) + P(B|A') * P(A')
P(B) = (0.01 * 0.95) + (0.9 * 0.05) = 0.0095 + 0.045 = 0.0545
Apply Bayes' theorem to find P(A|B):
P(A|B) = (P(B|A) * P(A)) / P(B) = (0.01 * 0.95) / 0.0545 ≈ 0.1743
So, the probability that the suspect is innocent given that the serum indicates guilt is approximately 17.43%.

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Answer:

Step-by-step explanation:

x = [tex]+-\sqrt[]{\frac{1}{2} }[/tex]

Answer:

To verify the given identity:

(1 - cos a) (1 + cot a)

= (1 - cos a) (1 + cos a / sin a) [since cot a = cos a / sin a]

= 1 - cos^2 a / sin a + cos a - cos^2 a / sin a

= 1 - (cos^2 a + cos^2 a) / sin a + cos a

= 1 - 2 cos^2 a / sin a + cos a

= 1 - 2 (1 - sin^2 a) / sin a + cos a [since cos^2 a = 1 - sin^2 a]

= 1 - 2 / sin a + 2 sin a / sin a + cos a

= 1 - 2 / sin a + 2 + cos a

= 1 + 2 (1 - sin a) / sin a

= 1 + 2 cos^2 a / sin a

= 1 + 2 cot^2 a

= (1 + cot^2 a) + 2 cot^2 a

= cosec^2 a + 2 cot^2 a

= 1 + cot^2 a [since cosec^2 a = 1 + cot^2 a]

Therefore, (1 - cos a) (1 + cot a) = 1 is true.

The values of the variables x = 5√5, z = 20 and y = 10√5.

A triangle is a geοmetric shape with three sides and three angles. It is a pοlygοn and οne οf the simplest and mοst cοmmοn shapes in geοmetry. The three sides οf a triangle can be οf different lengths οr the same length, and the three angles can alsο vary in size. The sum οf the angles in a triangle is always 180 degrees. Triangles are used in many applicatiοns in mathematics, science, engineering, and everyday life.

Here,

To solve this problem, we can use the Pythagoras theorem, which is:

c² = a² + b²

In the smallest triangle:

x² = 5² + 10²

x² = 125

x = √125

x = 5√5

Then for medium triangle:

y² = 10² + z²

Again for Largest triangle:

(5 + z)² = (5√5)² + y²

y² = (5 + z)² - (5√5)²

Both formula have like term y², So taking it common we have:

(5 + z)² - (5√5)²  = 10² + z²

Solve for Z :

(5 + z)² - 125  = 100 + z²

+ z² + 10z - 125  = 100 + z²

z² -  z² + 10z - 125 + 25 = 100

10z  = 100 + 125 - 25

10z  = 200

z  = 200/10

z = 20

When z = 20. Then y will be

y² = 10² + z²

y² = 10² + 20²

y² = 100 + 400

y² = 500

y = √500

y = √500

y = 10√5

Thus, We have the values of the variables x = 5√5, z = 20 and y = 10√5.

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Answer:

Step-by-step explanation:

1.) 1/5x - 2 = -3

Adding 2 to both sides, we get:

1/5x = -1

Multiplying both sides by 5, we get:

x = -5

Therefore, the solution is x = -5.

2.) 15 = 10 - x/4

Subtracting 10 from both sides, we get:

5 = -x/4

Multiplying both sides by -4, we get:

-20 = x

Therefore, the solution is x = -20.

3.) x/3 - 12 = -2

Adding 12 to both sides, we get:

x/3 = 10

Multiplying both sides by 3, we get:

x = 30

Therefore, the solution is x = 30.

4.) x/-2 + (-6) = 6

Adding 6 to both sides, we get:

x/-2 = 12

Multiplying both sides by -2, we get:

x = -24

Therefore, the solution is x = -24.

The margin of error using a 99% confidence interval is 6.21. This means that we can be 99% confident that the true mean score of all Biology students (not just the sample) falls within a range of 92 ± 6.21.

What is percentage?

Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".

To calculate the margin of error using a 99% confidence interval, we need to use the formula:

Margin of error = z* (standard deviation / √n)

Where:

z* = the z-score associated with the confidence level, which is 2.576 for a 99% confidence level (using a standard normal distribution table).

standard deviation = 9.38

n = 20

Plugging in the values, we get:

Margin of error = 2.576 * (9.38 / √20)

= 6.21 (rounded to two decimal places)

Therefore, the margin of error using a 99% confidence interval is 6.21. This means that we can be 99% confident that the true mean score of all Biology students (not just the sample) falls within a range of 92 ± 6.21.

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[tex]27000(0.77^t)[/tex]and the percentage rate of change per month is 3.13%.

What is the percentage rate?

The term annual percentage rate of charge refers to the interest rate for an entire year rather than just a monthly fee or rate as applied on a loan, home loan, credit card, etc. It can also be referred to as a nominal APR or an effective APR. It is an annual rate of a finance charge.

Here, we have

The value of a brand-new car is $27,000 and the value depreciates 23% every year.

we have to write a function to represent the value of the car after t years.

The coefficient of the function is 0.77

To find the rate of change per month, we need to find the rate at which the value of the car is decreasing each month.

we can use the rule of 72

72/r = t where r is the rate of change per month

r = 72/t

[tex]r = 72/23 = 3.13[/tex] (approx)

So the percentage rate of change per month is 3.13%

Hence, The function to represent the value of the car after t years is V(t) = [tex]27000(0.77^t)[/tex] and the percentage rate of change per month is 3.13%.

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Answer:

The answer is b. Marital problems.

Step-by-step explanation:

Marital problems have not been consistently found to impair immune functioning.

Answer:

The slope of the best-fit line shows that as time increases, the total number of calories that a teenager consumes throughout the day also increases.

The probability of prime number in a die would be ½.

If a die rolls, the total outcome would be 6.
Number of possible outcomes = 3( as there are only 3 prime numbers in the die that are 2,3 and 5).
P(prime number) = 3/6
So the probability of the prime number in the die would be ½.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theorem of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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The angle measuring 280° is coterminal with the angle measuring -800° and lies between 0° and 360°.

To find the coterminal angle between 0° and 360° for an angle measuring -800°, follow these steps:
1. Divide the given angle (-800°) by 360° to determine how many full rotations are made:

-800° ÷ 360° = -2.22.
2. Since we are looking for a positive coterminal angle, round the result down to the nearest whole number:

-2.22 rounds down to -3.

This tells us there are three full negative rotations.
3. Multiply the whole number (-3) by 360° to find the total angle of the rotations:

-3 × 360° = -1080°.
4. Add the total angle of the rotations to the given angle to find the coterminal angle between 0° and 360°: -800° + 1080° = 280°.

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The resulting polynomial expression is 3x⁴ + 11x³ - 31x² - 99x + 36, and the correct answer is (A) -4x² - 2x + 4, which matches this expression after combining like terms.

To find the sum of the given polynomials, we need to multiply them using the distributive property and then combine like terms. This involves multiplying each term of the first polynomial by each term of the second polynomial, then simplifying the resulting expression by combining any like terms. After performing the multiplication and simplification steps, we end up with the polynomial expression 3x⁴ + 11x³ - 31x² - 99x + 36. Therefore, the correct answer is (A) -4x² - 2x + 4, which matches this expression after combining like terms.

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In a right triangle CDL, the horizontal distance between points D and L is |x2 - x1| blocks, and the vertical distance between points D and L is |y2 - y1| blocks.

We need to determine the horizontal and vertical distances between points D (x1, y1) and L (x2, y2) in a right triangle CDL.
Identify the coordinates of points D and L.
Let D = (x1, y1) and L = (x2, y2)
Calculate the horizontal distance between points D and L.
Horizontal distance = |x2 - x1|
Calculate the vertical distance between points D and L.
Vertical distance = |y2 - y1|

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Nonprobability sampling carries more risk of selection bias than probability sampling because nonprobability sampling does not use randomization.What is nonprobability sampling?A nonprobability sampling is a method of selecting participants for a study that does not allow the researcher to use a random selection process.

Nonprobability sampling, also known as purposive sampling, is a technique that involves choosing participants based on subjective criteria, such as availability or willingness to participate. This method is frequently used in research that investigates hard-to-reach populations, such as homeless individuals or drug addicts.

A key feature of probability sampling is that it allows the researcher to obtain a representative sample of the population, minimizing the risk of selection bias. In contrast, nonprobability sampling does not provide the same level of assurance that the sample will be representative. Because participants are chosen based on subjective criteria rather than random selection, there is a greater risk of selection bias.

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The required rate of  increasing in volume of a sphere when diameter is 80 mm is equals to 25600π mm^3/s

let 'V' be the volume of the volume of a sphere

'r' be the radius of the sphere.

The formula for the volume of a sphere in terms of its radius,

V = (4/3) × π × r^3

Taking the derivative with respect to time, we get,

dV/dt = 4× π × r^2 × (dr/dt)

where dV/dt is the rate of change of the volume,

dr/dt is the rate of change of the radius,

And π is a constant.

The rate of change of the radius dr/dt is 4 mm/s.

Calculate the rate of change of the volume when the diameter is 80 mm.

Diameter = 2 (radius)

This means the radius is 40 mm.

Substituting the values in the formula above, we get,

⇒dV/dt = 4 × π × (40 mm)^2 ×(4 mm/s)

Simplifying this expression, we get,

⇒ dV/dt = 25600π mm^3/s

Therefore, the volume of the sphere is increasing at a rate of 25600π mm^3/s when the diameter is 80 mm.

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Answer:

The polynomial 2y^2 -15y-8 is not prime. It can be factored as (2y+1)(y-8).

Answer:false

Step-by-step explanation:

In order to lose one pound for weight per week, Maddie must consume 1800 calories per day.

Firstly we need to know the number of calories Maddie wants to loose. As per the fact, 1 pound equals 3500 calories. Thus, she must eat 3500 calories less than regular in a week.

Now, one week has seven days. So, number of calories to be reduced each day = 3500/7

Number of calories = 500 calories.

The required calorie intake = current calorie intake - calories to not be consumed

Required calorie intake = 2300 - 500

Required calorie intake = 1800 calories.

Thus, Maddie must consume 1800 calories per day.

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As per the information provided, the answer to all the parts in the question will be as follows:

a. To solve the LP problem by ignoring the integer constraints in Excel using Solver, we can follow the steps below:

Enter the objective function and the constraints in a new Excel worksheet: Objective function: Maximize 15x1 + 2x2 Constraints: 7x1 + x2 <= 23 3x1 - x2 <= 5

Open the Solver add-in by clicking on Data -> Solver in the Excel menu.

Set the objective function to maximize and set the variable cells to x1 and x2. Set the constraints by clicking on Add in the Solver Parameters dialog box.

Set the Solver options to "Assume Linear Model" and "Make Unconstrained Variables Non-Negative". Click Solve. The solution to the LP problem is x1=3, x2=2.714, with an optimal objective function value of 51.714.

b. If we round up fractions greater than or equal to 1/2, the solution becomes x1=3, x2=3, with an objective function value of 51. This is not the optimal integer solution, as we will see in part d.

c. If we round down all fractions, the solution becomes x1=2, x2=2, with an objective function value of 34. This is not the optimal integer solution either, as we will see in part d.

d. To solve the ILP problem in Excel using Solver, we can follow the steps below:

Open the Solver add-in by clicking on Data -> Solver in the Excel menu. Set the objective function to maximize and set the variable cells to x1 and x2. Set the constraints by clicking on Add in the Solver Parameters dialog box. Set the Solver options to "Assume Linear Model" and "Make Unconstrained Variables Non-Negative". Add integer constraints by clicking on Add in the Solver Parameters dialog box, and setting the integer constraints for x1 and x2. Click Solve.

The solution to the LP problem is x1=2, x2=3, with an optimal objective function value of 48.

As we can see, the optimal objective function value for the LP problem (48) is lower than that for the LP problem (51.714), regardless of rounding up or down.

e. The optimal objective function value for the ILP problem is always less than or equal to the corresponding LP's optimal objective function value because the LP problem allows fractional solutions, while the ILP problem only allows integer solutions. Introducing additional constraints that restrict the variables to integers can only reduce the feasible solution space, and thus lead to a lower optimal objective function value. The LP and ILP problems would be equal if the optimal solution for the LP problem happens to be an integer solution.

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Note that the full question is:

Given the following all-integer linear program: (COMPLETE YOUR SOLUTION IN EXCEL USING SOLVER AND UPLOAD YOUR FILE. BE SURE THAT EACH WORKSHEET IN THE EXCEL FILE CORRESPONDS TO EACH QUESTION BELOW ) Max 15x1 + 2x2 s. t. 7x1 + x2 < 23 3x1 - x2 < 5 x1, x2 > 0 and integer a. Solve the problem (using SOLVER) as an LP, ignoring the integer constraints.

b. What solution is obtained by rounding up fractions greater than or equal to 1/2? Is this the optimal integer solution? c. What solution is obtained by rounding down all fractions? Is this the optimal integer solution? Explain. d. Show that the optimal objective function value for the ILP is lower than that for the optimal LP (Eg. Resolve original problem using SOLVER with the Integer requirement). e. Why is the optimal objective function value for the ILP problem always less than or equal to the corresponding LP's optimal objective function value? When would they be equal?

Answer:

A

Step-by-step explanation:

These are cross angles

The solution is greater than [tex]-2[/tex]

A mathematical assertion known as an inequality contrasts two values or expressions, demonstrating their relationship in terms of greater than[tex]\geq[/tex], less than (), greater than or equal to [tex]\geq[/tex], or less than or equal to ().

When two quantities are related in a manner other than being equal, it is referred to as an inequality.

[tex]8 > -3a+2[/tex]

Subtracting [tex]2[/tex] from both sides we get:

[tex]6 > -3a[/tex]

Dividing both sides by [tex]-3[/tex] and reverse the inequality sign when dividing by negative number

[tex]a > -2[/tex]

Since a cannot equal [tex]-2[/tex], we can plot an open circle at this value to represent the solution on a number line. We can also depict an arrow pointing up the number line to represent that an is larger than [tex]-2[/tex]

The arrow denotes any value higher than -2, and the open circle at -2 denotes that -2 is not part of the solution.

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Answer:

a>-2

explained:

-3a+2<8

−3+2−2<8−2

−3a<6

−[tex]\frac{3a}{3}[/tex]<[tex]\frac{6}{-3}[/tex]

a>−2

The standard deviation of the sampling distribution is 0.00702.

In this case, we know that 8% of all adults in Ohio support the increase. We can use this information, along with the sample size of 1500, to calculate the standard deviation of the sampling distribution. The formula for the standard deviation of the sampling distribution is:

standard deviation = √ [(population proportion x (1 - population proportion)) / sample size]

Plugging in the numbers, we get:

standard deviation = √ [(0.08 x 0.92) / 1500]

standard deviation = √0.00004928

standard deviation = 0.00702

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According to given information, the length of the rectangular storage unit is 12 feet.

What is rectangle?

A rectangle is a two-dimensional shape with four sides and four right angles. It is a quadrilateral with opposite sides that are parallel and equal in length.

We can use the Pythagorean theorem to find the length of the storage unit. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the 5-foot-wide floor and the length of the storage unit form the two sides of a right triangle, with the diagonal (the distance from one corner to the opposite corner) being the hypotenuse. We can set up the equation as:

[tex]hypotenuse^2 = side1^2 + side2^2[/tex]

where side1 = 5 feet and hypotenuse = 13 feet.

Simplifying this equation, we get:

[tex]hypotenuse^2[/tex][tex]= 5^2 + side2^2[/tex]

169 = 25 + [tex]side2^2[/tex]

[tex]side2^2[/tex] = 144

side2 = 12

Therefore, the length of the storage unit is 12 feet.

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Answer:

g(x) is the square root of 4x^2 + 4x + 1.

Step-by-step explanation:

We are given that f(x) = x^2 + 1 and f(g(x)) = 4x^2 + 4x + 2.

To find g(x), we need to substitute g(x) into the expression for f and simplify:

f(g(x)) = (g(x))^2 + 1 = 4x^2 + 4x + 2

Subtracting 1 from both sides, we get:

(g(x))^2 = 4x^2 + 4x + 1

Taking the square root of both sides (remembering to include both the positive and negative roots), we get:

g(x) = ±√(4x^2 + 4x + 1)

However, we need to choose the sign of g(x) such that f(g(x)) matches the given expression of f(g(x)) = 4x^2 + 4x + 2.

Let's try using the positive root first:

g(x) = √(4x^2 + 4x + 1)

Then we can find f(g(x)):

f(g(x)) = (g(x))^2 + 1 = 4x^2 + 4x + 2

This matches the given expression, so we can conclude that:

g(x) = √(4x^2 + 4x + 1)

Therefore, g(x) is the square root of 4x^2 + 4x + 1.

The value of x is given as 9.8

We have to solve for X using the Pythagorean theorem

The Pythagorean theorem is a mathematical formula that relates to the sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In other words:

c² = a² + b²

Where:

c is the length of the hypotenuse

a and b are the lengths of the other two sides

14² = x² + 10²

196 = x² + 100

196 - 100 = x²

x = √96

x = 9.8

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