what is the surface area of a 24ft by 16 ft cylinder 288ft2 , 384ft2 , 19ft2 , 672ft2

1) Given the altitude BD, let's find its measure using some trigonometric relations on the Right Triangle:

1.2) Pythagorean Theorem to find the other leg

b²=a²+c² The hypotenuse, in this case, is labeled as "b"

32²=16²+a²

1024=256+a²

1024-256=a²

768=a²

√768=√c²

a=16√3

2) Now, let's use one trigonometric relation on the Right Triangle, based on the similarity of the triangles:

ah=bc Adjusting it:

bh=ac

32h=16√3*16

32h=256√3

h=256√3/32

h=8√3 ≈ 13.85 ≈13.9

3) So the altitude BC of that triangle is approximately 13.9

Answer:

7x = 28

Step-by-step explanation:

Divide the 28 by the 7 to isolate the x

28 / 7 = 4

x = 4

Answer:

q ^ p

Step-by-step explanation:

The symbolic form of the statement would be:

q ∧ p

Where q represents "m angle A + m angle B = 180°" and p represents "angle A and Angle B are supplementary".

The ∧ symbol represents "and" in logic, so the statement can be read as "q and p".

Answer:

2.3

Step-by-step explanation:

did the math

Answer:

- 1

Step-by-step explanation:

The average rate of change of g(x) in the close interval [ a, b ] is

\(\frac{g(b)-g(a)}{b-a}\)

Here [ a, b ] = [ 3, 6 ] , then

g(b) = g(6) = 6² - 10(6) + 19 = 36 - 60 + 19 = - 5

g(a) = g(3) = 3² - 10(3) + 19 = 9 - 30 + 19 = - 2

average rate of change = \(\frac{-5-(-2)}{6-3}\) = \(\frac{-5+2}{3}\) = \(\frac{-3}{3}\) = - 1

Answer:

5 cups

Step-by-step explanation:

To get 1 cup of sugar, u must add 1/8 by 8. now you have one cup of sugar. But to find out how much flour u need, u also need to multiply 1 3/4 by 8, which gives u 5 cups

Answer:

14 cups of flour are needed for 1 cup of sugar.

Step-by-step explanation:

Use a ratio.

cups of flour : cups of sugar

               1 3/4 : 1/8

                     ? : 1

We know that you must multiply by 8 to get from 1/8 to 1. Now we have to do the same to the other side. So, multiply 1 3/4 by 8.

1 3/4 * 8 = 14

Therefore, 14 cups of flour are needed for 1 cup of sugar.

Tell me if this was helpful:)

Answer:

Step-by-step explanation:

a = -5 and b = -6

x² - (a +b)x + ab = 0

x² - (-5 - 6)x + (-5)*(-6) = 0

x² - (-11)x + 30 = 0

x² + 11x + 30 = 0

9 cubed = 729

6 cubed = 216

729 - 216 = 513

Answer:

yes but no a statistical question is determined by requiring multiple data

Step-by-step explanation:

Answer:

well A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer. For example, "How many minutes do 6th grade students typically spend on homework each week?" is a statistical question.

Step-by-step explanation:

mark braniliest pls

Answer:

f(a)=3(a+2)-2

f(4)=3(4+2)-2

f(4)=3(6)-2

f(4)=18-2

f(4)=16

Hope  this helps!

Answer:

f(4)= 16

Step-by-step explanation:

f(4)= 3(a + 2) -2

f(4)= 3(4 + 2) -2

f(4) = 3(4) + 3(2) -2

f(4)= 12 + 6 -2

f(4)= 18-2

f(4)= 16

Answer:

Hardness your cork energy and let it rip

Step-by-step explanation:

First: You must have banger cork 7s and dub 10s on trampoline.

Second: Find a large jump

Third: Hardness your cork energy

Finally: let it rip

The area of the various shapes are:

1) Area of a circle (with radius 8in) 200.96

2) Area of Rectangle (45 *14) = 630in

3) Area of rectangle (24 *9) = 216in

4) Area of pentagon with side 10in = 172.05

5) Area of circle with diameter 20in = 314

6) Area of rectangle 5 x 8 = 40ft.

Lets take the circles first where the radius is 8in.

1) The area of a circle is

A = πr²

A =  π x r²

A = 3.14 x 8²

A = 200.96

2) Area of circle with diameter of 20 inches

Where diameter is 20inches, radius is 10inches

So
A =  3.14 x 10²

A = 3.14 x 100

A =  314

Now to the rectangles

1) Area of rectangle is L x B

Where L = Length

B = Breath

So,

A = 45 * 14 = 630in

2) A = 24 x 9 = 216 in

3) A = 5 x 8 = 40 inches

Next the pentagon.

Formula for Area of Pentagon is

Area = (1/4) * √(5 * (5 + 2 * √(5))) * s²

Where s = Side.

Since s = 10in

Area = (1/4) * √(5 * (5 + 2 * √(5))) * (10)²

A = 172.05

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Height =9.7ft

Radius=7.6 feet

Answer:

15

Step-by-step explanation:

OPTION 1:

We can use the distance formula to find the distance between these two points.

\(\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

X2 is -9, X1 is 0, Y2 is -10, and Y1 is 2, so we can substitute inside the equation.

\(\sqrt{(-9-0)^2 + (-10-2)^2}\\\\\sqrt{9^2 + -12^2}\\\\\sqrt{81 + 144}\\\\\sqrt{225}\\\\15\)

OPTION 2:

We can look at the change in x and the change in y and use the Pythagorean Theorem to find the missing length of the hypotenuse.

The x changes by 9, and the Y changes by 12.

\(a^2+b^2=c^2\) is the Pythagorean Theorem. We know a and b, so we can substitute inside the equation.

\(9^2 + 12^2 = c^2\\\\81+144=c^2\\\\225=c^2\\\\c=15\)

Hope this helped!

Answer: The distance is 15 units.

Step-by-step explanation:

Find the difference in the x and y coordinates and square them and add them together.

(0,2) and (-9,-10)  The x coordinates are 0 and -9  and the y coordinates are 2 and -10.

0-(-9) = 9

2-(-10) = 12

9^2 + 12^2 = d^2

  81 + 144 = d^2

   225 = d^2

d = \(\sqrt{225}\)  

  d= 15

The amount that the pirate has gone in debt due to his encounter with Captain Rusczyk.

The pirate has gone in debt of $38879_{5}$ dollars due to his encounter with Captain Rusczyk. This can be calculated by subtracting the amount of money he was ordered to return to the captain from the amount of money he had stolen in the first place. This is represented by the equation $41324_{5} - 2345_{6} = 38879_{5}$.

To solve this equation, the two amounts must first be converted to the same base, which in this case is base 5. The amount stolen is converted by multiplying $2345_{6}$ by $5^1 = 5_{5}$. The amount ordered to be returned is already in base 5. The final equation is then $41324_{5} - 5_{5} = 38879_{5}$.

Subtracting the two amounts gives the solution of $38879_{5}$. This is the amount that the pirate has gone in debt due to his encounter with Captain Rusczyk.

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The probability that Natalie gets all three questions correct by random guessing is (1/4) * (1/4) * (1/4) = 1/64.

Since each question has four possible options (A, B, C, or D), the probability of guessing the correct answer for each question is 1/4.

To find the probability of getting all three questions correct, we multiply the individual probabilities together:

Probability = (1/4) * (1/4) * (1/4) = 1/64.

Therefore, the probability that Natalie gets all three questions correct by random guessing is 1/64. This means that for each set of three questions, there is only a 1 in 64 chance that Natalie will guess all three correctly by pure chance.

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Answer:

D(-3, -1)

Step-by-step explanation:

The given coordinates are;

A(-1, -5), B(5, -2) and (1, 1)

The coordinates and the coordinates of the point D form a trapezium

The parallel sides of the trapezium ABCD = AB and DC

The angle ∠BAD = 90°

The coordinates of the point D = Required

Let (x, y) represent the x and y-coordinates of the point D, by the given information, we get;

The slope of the line DC = The slope of the line AB

The slope of AB = (-2 - (-5))/(5 - (-1)) = 3/6 = 1/2

∴ The slope of CD, m = 1/2

From the point C(1, 1),the equation of the line CD is therefore;

y - 1 = (1/2)·(x - 1)

∴ y = x/2 - (1/2) + 1 = x/2 + 1/2

y = x/2 + 1/2

Given that ∠BAD is 90°, therefore, AD is perpendicular to DC and we have;

The slope of AD = -1/m

∴ The slope of AD = -1/(1/2) = -2

From the point A(-1, -5), the equation of the line AD is therefore;

y - (-5) = -2·(x - (-1))

y = -2·x - 2 - 5 = -2·x - 7

y = -2·x - 7

Equating both (simultaneous) values of y to find the value of x gives;

y = y, therefore;

x/2 + 1/2 = -2·x - 7

x/2 + 2·x = 5·x/2 = -7 - (1/2) = -15/2

∴ 5·x/2 = -15/2

x = (-15/2) × (2/5) = -3

x = -3

From y = -2·x - 7, and x = -3, we get;

y = -2 × (-3) - 7 = 6 - 7 = -1

The coordinates of the point D(x, y) = (-3, -1).

Given:

The inequality is:

\(-4x-7y<15\)

To find:

The whether (-6,3) is a solution of given inequality of not.

Solution:

We have,

\(-4x-7y<15\)

We need to check the inequality for point (-6,3).

Substitute \(x=-6, y=3\) in the given inequality.

\(-4(-6)-7(3)<15\)

\(24-21<15\)

\(3<15\)

This statement is true. It means the point (-6,3) satisfies the given inequality.

Therefore, the correct option is A. Yes, the ordered pair is a solution.

Answer:

1.654

Step-by-step explanation:

Plugged in the calculator

Q6: Approximately 68.3% of the cherry tomatoes sold by Berkeley Bowl fall within the specified diameter limits of 20 mm to 32 mm.

Q7: To achieve half of the Six Sigma Quality, the standard deviation of the process should be approximately 0.22 mm for Berkeley Bowl's cherry tomatoes.

In Q6, we can use the concept of the normal distribution to determine the percentage of tomatoes within the specification limits. Since the average diameter is 26 mm and the standard deviation is 3 mm, we can assume a normal distribution and calculate the percentage of tomatoes within one standard deviation of the mean. This corresponds to approximately 68.3% of the tomatoes falling within the specified limits.

In Q7, achieving Six Sigma Quality means that the process has a very low defect rate. In this case, half of the Six Sigma Quality means reducing the variability in diameter to half the acceptable range.

The acceptable range is 32 mm - 20 mm = 12 mm. To achieve half the range, the standard deviation should be approximately half of 12 mm, which is 6 mm. Since the standard deviation is given as 3 mm, the process would need to be improved to reduce the standard deviation to approximately 0.22 mm for it to meet half of the Six Sigma Quality.

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Answer:

5/2

Step-by-step

Formula for slope is y2-y1/x2-x1

so it would be 13-3/5-1

which results to 10/4

simplify 5/2

The required slope for the line is m = 5/2.

Two pairs of coordinates are given the slope of the line that passes through points to determine.

The slope of the line is the tangent angle made by the line with horizontal. i.e. m =tanx where x in degrees.

The slope of a line (m) =\(y_2-y_1/x_2-x_1\)
   \((x_1, y_1), (x_2,y_2) = (1,3),(5,13)\)
m = 13-3/5-1
m = 10/4
m =5/2

Thus, the required slope for the line is m = 5/2.

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The sum of 488 in scientific notations is 4.88 × 10^1.

We are given that;

The number = 488

Now,

488 in scientific notation

Step 1: Move the decimal point so that there is only one non-zero digit to the left of it.

488.0

The decimal point is moved one place to the left.

4.88

Step 2: Write the number as a product of the decimal and a power of 10.

The decimal point was moved one place to the left, so the exponent is 1.

4.88 × 10^1

Therefore, by the algebra the answer will be 4.88 × 10^1.

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The truth values of the given statements in terms of q(x) are: q(0) is true, q(1) is false, q(-2) is false, and q(2) is true.

The statement q(x) is x² = 2x. Now, we will check the truth value of each statement in terms of q(x):

(i) q(0): \(0^2=2\times 0\)

   q(0): 0 = 0; so, the statement q(0) is true.

(ii) q(1): \(1^2=2\times 1\)

    q(1): 1 = 2; so, the statement q(1) is false.

(iii) q(-2): \((-2)^2=2\times (-2)\)

     q(-2): 4 = -4; so, the statement q(-2) is false.

(iv) q(2): \(2^2=2\times 2\)

     q(2): 4 = 4; so, the statement q(2) is true.

So, the truth values of the given statements in terms of q(x) are: q(0) is true, q(1) is false, q(-2) is false, and q(2) is true.

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According to the Hypothenus Leg (HL) theorem, it is to be noted that there is nothing else required to prove the congruency of the above triangles.

According to the hypotenuse-leg (HL) theorem, if the hypotenuse and a leg of a right triangle are both congruent with the corresponding hypotenuse and leg of another right triangle, the triangles are congruent. According to the HL theorem, these triangles are congruent.

In other words, the triangles are congruent if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle. Triangle ABC is congruent to triangle DEF if angle A = angle D = right angle, AB = DE (leg), and BC = EF (hypotenuse) in triangles ABC and DEF.

In the above case, the hypotenuse of both triangles have been proven to be congruent as well as the various legs AC and CD.

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To write the equation in standard form for the circle passing through (–2, 4) centered at the origin, we need to find the radius and the center of the circle.

Since the circle passes through (–2, 4), we can use the distance formula to find the radius, which is the distance from the origin to (–2, 4).

The distance formula is given by:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, x1 = 0, y1 = 0, x2 = –2, and y2 = 4. So, the radius is:

radius = sqrt((-2 - 0)^2 + (4 - 0)^2) = sqrt(20) = 2sqrt(5)

The center of the circle is the origin, since the circle is centered at the origin. Therefore, the equation of the circle in standard form is:

x^2 + y^2 = (2sqrt(5))^2 = 20

So, the equation of the circle passing through (–2, 4) centered at the origin is x^2 + y^2 = 20.

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To solve this equation, we can use substitution and algebraic manipulation. θ = 36.86°, 138.19°, 221.81°, 323.14°

Let's start by substituting secθ = 1/cosθ into the equation:

tan²θ + 4secθ – 5 = tan²θ + 4/cosθ – 5

Then, multiply both sides by cos²θ to eliminate the denominator:

tan²θ cos²θ + 4 cosθ - 5 cos²θ = 0

Now, we can use the trigonometric identity tan²θ = sec²θ - 1 to simplify the equation:

(sec²θ - 1) cos²θ + 4 cosθ - 5 cos²θ = 0

Expanding and simplifying, we get:

cos⁴θ - 5cos²θ + 4cosθ - 1 = 0

Let's substitute x = cosθ to simplify the equation:

x⁴ - 5x² + 4x - 1 = 0

We can factor this equation:

(x² - x - 1)(x² + 4x - 1) = 0

Now we solve for x:

x² - x - 1 = 0

Using the quadratic formula, we get:

x = [1 ± √5]/2

We reject the negative root because cosθ is positive in the interval [0, 360]. Therefore, we have:

cosθ = [1 + √5]/2 or cosθ = [-1 - √17]/2

To find the solutions in the interval [0, 360], we take the inverse cosine of each root and convert to degrees:

cos⁻¹([1 + √5]/2) = 36.86°, 323.14°

cos⁻¹([-1 - √17]/2) = 138.19°, 221.81°

Therefore, the solutions of the original equation over the interval [0, 360] are approximately:

θ ≈ 36.86°, 138.19°, 221.81°, 323.14°

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a. To find the 30th percentile for the standard normal distribution, we first need to locate the z-score that corresponds to this percentile. We can use a standard normal distribution table or a calculator to find this value. From the table, we can see that the z-score that corresponds to the 30th percentile is approximately -0.524. Therefore, the 30th percentile for the standard normal distribution is z = -0.524.

b. To find the 30th percentile for a normal distribution with mean 10 and standard deviation 1.5, we can use the formula for transforming a standard normal distribution to a normal distribution with a given mean and standard deviation. This formula is:
z = (x - μ) / σ
where z is the standard normal score, x is the raw score, μ is the mean, and σ is the standard deviation.
To find the 30th percentile for this distribution, we first need to find the corresponding z-score using the formula above:
-0.524 = (x - 10) / 1.5
Multiplying both sides by 1.5, we get:
-0.786 = x - 10
Adding 10 to both sides, we get:
x = 9.214
Therefore, the 30th percentile for a normal distribution with mean 10 and standard deviation 1.5 is x = 9.214. This means that 30% of the observations in this distribution are below 9.214.

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