To determine the distance across the Grand Canyon in Arizona, a 1 mile base line, call it AB or side c, is established along the southern rim of the canyon. Sightings are then made from points A & B to a point C across the canyon. Find the distance across the canyon from A to C if ∠BAC is 118.1 degrees and ∠ABC = 58.1 degrees.

The horizontal cross section of a rectangular prism will always be a rectangle. If the base is a square, the cross-section can also be a square.

The definition of a prism is that the cross-section parallel to the base will be uniform.

Therefore, the cross section of a rectangular prism that is sliced horizontally is a rectangle.

The unit conversion of 1200 milliliters to kilograms is: 1.2 milliliters

What the question tells us is to convert 1200 milliliters to kilograms.

Now, the conversion table shows us this conversion and it is simply expressed as:

1 milliliter = 0.001 kilograms.

We are given 1200 milliliters. Thus, converting to kilograms gives us:

1200milliliters * 0.001 kilograms/1 milliliter

= 1.2 milliliters

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The total volume of the ice cream cone A is 209.34 cubic inches.

Dimensions of a ice cream cone A:

Height = 14 inches, radius = 2 inches and radius of sphere is 2 inches.

Here, volume of a cone is 1/3 πr²h

= 1/3×3.14×2²×14

= 58.6 cubic inches

Volume a sphere is 4/3 πr³

= 4/3 ×3.14×2³

= 33.5 cubic inches

Total volume = 58.6+33.5

= 92.1 cubic inches

Therefore, the total volume of the ice cream cone A is 209.34 cubic inches.

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The persons weight that had the least absolute change is: Rebecca

We are given the initial and final weights of Ophelia, Aaron, Nathan and Rebecca.

Ophelia's change in weight = 157 - 145 = 12 lbs

Aaron's change in weight = 163 - 178 = -15 lbs

Nathan's change in weight = 217 - 136 = 81 lbs

Rebecca's change in weight = 128 - 136 = -8 lbs

The absolute value of a number or integer is the actual distance of the integer from zero, in a number line. Therefore, the absolute value is always a positive .

Thus, "absolute value" means to remove any negative sign in front of a number, and to think of all numbers as positive (or zero).

Therefore, the least absolute change is |-8 lbs| = 8 lbs

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The probability that a randomly selected product will last longer than 166 days is approximately 0.1492, οr 14.92%.

The probability οf an event οccurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn οut.

We can use the standard normal distribution to answer this question.

z = (x - μ) / σ

For x = 166, μ = 146, and σ = 19.5, we have:

z = (166 - 146) / 19.5

z = 1.03

Using a standard normal distribution table, we can find that the area to the right οf z = 1.03 is approximately 0.1492.

Therefore, the probability that a randomly selected product will last longer than 166 days is approximately 0.1492, οr 14.92%.

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Answer:

900

Step-by-step explanation:

The 9 is in the hundredth-place value.

Answer:

x= √2

(or)

x = [tex]\frac{-3\sqrt{2}}{5}[/tex]

Step-by-step explanation:

If I assume your equation was like this,

5x²-2[tex]\sqrt{2x}[/tex] - 6 = 0

([tex]x - \sqrt{2}[/tex]) ([tex]5x + 3\sqrt{2}[/tex]) = 0

[tex]x - \sqrt{2}[/tex] = 0  (or)    [tex]5x + 3\sqrt{2}[/tex] =0

x = [tex]\sqrt{2}[/tex]  (or) 5x = [tex]-3\sqrt{2}[/tex]

x = [tex]\sqrt{2}[/tex]  (or)  x = [tex]\frac{-3\sqrt{2}}{5}[/tex]

The quadratic equation can be solved to give the value of x1 = √2 and x2 = -3√2 / 5.

To solve the quadratic equation 5x² - 2√2x - 6 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Now we have two solutions, one for the positive value and one for the negative value:

x1 = (2√2 + 8√2) / 10

x2 = (2√2 - 8√2) / 10

Simplify the solutions:

x1 = (10√2) / 10 = √2

x2 = (-6√2) / 10 = -3√2 / 5

So the solutions for the equation 5x² - 2√2x - 6 = 0 are x1 = √2 and x2 = -3√2 / 5.

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1. The area of the sector is 36.265 cm² and the perimeter of the sector is 26.132 cm

2. Area of shaded part = 72.09 squared cm

3. Exact area of shaded part = 3 pi - √2 squared cm

4. Area = 61.25 and Arc length = 2.5 × 7 = 17.5

To find the area and perimeter of a sector we need to use the formulas for the area and arc length of a sector.

The formula for the area of a sector is

A = (θ/2) × r²,

where

θ is the angle in radians and

r is the radius.

The formula for the arc length of a sector is

L = θ × r,

where

θ is the angle in radians and

r is the radius.

The given angle = 2π - 1.75 radians.

θ = 2π - 1.75 = 4.533 radians.

Area = (θ/2) × r²

= (4.533/2) × 4²

= 36.265 cm²

Perimeter = (arc length) + 2r = θ × r + 2r

= 4.533 × 4 + 2 * 4

= 26.132 cm

2. Using trigonometry, we solve for base and height of the triangle

height = 12 * cos 0.75 radian = 8.78

base = 12 * sin 0.75 radian = 8.18

area of triangle = 0.5 * 8.78 * 8.18 = 35.91

Area of sector = (θ/2) × r² = 0.75 * 144 = 108

area of shaded part = 108 - 35.91 = 72.09 squared cm

3. Using trigonometry, we solve for base and height of the triangle

height = 2√2 * cos 67.5 degrees

base = 2√2 * sin 67.5 degrees

area of triangle = 0.5 * 2√2 * cos 67.5 degrees* 2√2 * sin 67.5 degrees

= √2

Area of sector = (θ/360) × pi * r² = 135/360 * pi * (2√2)² =3 pi

area of shaded part = 3 pi - √2 squared cm

4. Area = (2.5/2) ×7² = 61.25

Arc length = 2.5 × 7 = 17.5

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Answer:

x = 19m

Step-by-step explanation:

to find the other two sides of the compound shape,

(2+6+6)= 14m , and (x-2)m

area of the compound shape = (2 x 14) + 2(x-2) =28 + 2x - 2 = 2x+26 m²

area of square = 8 x 8 = 64 m²

the question states that these two shapes have the same area,

2x + 26 = 64

2x = 38

x = 38/2

x= 19m

The flag have 6.09 square feet of area that make up the red and blue portion. And the flag have 1.35 square feet more of the white portions than the red and blue portions.

The tripes can be observed to have the shape of trapezoids, the middle coloured stripe can be split into two smaller trapezoids while the top and bottom coloured are of same size.

Red and blue portions:

1/2 × (3.5 + 4.5) × 0.6 = 2.4 ft² {area of trapezoid}

top

top and bottom coloured stripe = 2 × 2.4 ft² = 4.8 ft²

1/2 × (1.9 + 2.4) × 0.3 = 0.645 ft²

middle coloured stripe = 2 × 0.645 ft² = 1.29 ft²

area of red and blue portions = 4.8 ft² + 1.29 ft² = 6.09 ft²

White portions:

area of white triangle portion = 1/2 × 3 × 2.6 = 3.9ft²

1/2 ×( 2.4 + 3.5) × 0.6 = 1.77 ft² {area of one white stripe trapezoid}

area of white stripes = 2 × 1.77 ft² = 3.54 ft²

white portions = 3.9ft² + 3.54 ft² = 7.44 ft²

In conclusion, the flag have 6.09 square feet of area that make up the red and blue portions. And the flag have 1.35 square feet more of the white portions than the red and blue portions.

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Answer:262144

Step-by-step explanation:4^9

4^3=

64^3=262144

its is our required answer

hope it will help you!

The rate at which the depth is changing at 2 am is given as follows:

D'(2) = 0.4354 feet per hour.

The equation giving the depth of the water in t hours after midnight is given as follows:

D(t) = 2cos(πt/3 + 2π/5) + 3.

The derivative of the cosine is negative sine, while the inner derivative is of π/3, hence, applying the chain rule, the derivative is given as follows:

D'(t) = -2π/3sin(πt/3 + 2π/5)

2 am is 2 hours after midnight, hence the numeric value of the derivative is given as follows:

D'(2) = -2π/3sin(2π/3 + 2π/5)

D'(2) = 0.4354 feet per hour.

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If the profit desired is $24,000 and the revenue is $112,250, then the cost is $88,250.

To find the cost, we need to use the formula:

Revenue - Cost = Profit

We can rearrange this formula to solve for the cost:

Cost = Revenue - Profit

Substituting the given values, we get:

Cost = $112250 -$ 24000

Cost = $88250

Therefore, the cost is $88250.

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The perimeter of the right triangle is 41 centimetres.

The right triangle have sides 11 centimetres, and 13 centimetres. Therefore, let's find the third side before finding the perimeter of the right triangle.

Hence, let's find the third side using Pythagoras's theorem.

Therefore,

c²  = a² + b²

where

Therefore,

11² + 13² = c²

121 + 169 = c²

c = √290

c = 17.0293863659

c = 17.03 cm

Hence,

perimeter of the right triangle = 11 + 13 + 17.03

perimeter of the right triangle = 41.0293863659

perimeter of the right triangle = 41 cm

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The perimeter of the triangle is 41 cm

To calculate the perimeter of a right triangle, we must add up the lengths of all three sides.

Assuming the sides are

opposite, a = 11 cm

adjacent, b = 13 cm

hypotenuse, c = ?

we can apply the Pythagorean theorem which determines the hypotenuse's length. The hypotenuse is recognized as the third side within a right triangle.

This principle mathematical expression reads:

c^2 = a^2 + b^2

c^2 = 11^2 + 13^2

c^2 = 121 + 169

c^2 = 290

c = sqrt(290)

c = 17

Solving for perimeter

Perimeter = a + b + c

Perimeter = 11 cm + 13 cm + 17 cm

Perimeter = 41 cm

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Answer: 6

Step-by-step explanation: you would substitute the Z for 3 so it would be 5(3)-3². You would then do 3²= 9 because it’s 3*3 and 5*3 is 15. So you would do 15-9 which equals 6

The average speed at which the canoe traveled toward the lighthouse was approximately 14.1 feet per minute.

We can solve this problem using trigonometry. Let's call the distance between the canoe and the lighthouse "x", and let's call the average speed of the canoe "s".

From the first measurement, we know that:

tan(6.5°) = (115 - 1.3) / x

x = (115 - 1.3) / tan(6.5°)

x ≈ 1012.6 feet

From the second measurement, we know that:

tan(48.7°) = (115 - 1.3) / (x - 5/60 * s)

x - 5/60 * s = (115 - 1.3) / tan(48.7°)

x ≈ 166.2 feet

Now we can use these two equations to solve for "s". We can start by solving the second equation for "x" and substituting the result into the first equation:

x = 5/60 * s + (115 - 1.3) / tan(48.7°)

x ≈ 5/60 * s + 80.2 feet

(115 - 1.3) / x = tan(6.5°)

x = (115 - 1.3) / tan(6.5°)

Substituting the first equation into the second equation and simplifying, we get:

5/60 * s + 80.2 = (115 - 1.3) / tan(6.5°)

s ≈ 14.1 feet per minute

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Answer:

50% chance for each

Step-by-step explanation:

if there are two option out of 2 then that means you have a 50 50 chance each for both

PLS GIVE BRAINLIST MEAN THE WORLD

The equation we need to find will relate the amount of remaining berries to the number of batches of jam the farmer can make is 16 = 2 1/2 + 2 1/4b (option b)

To start with, we know that the farmer picks 16 quarts of berries. Out of those, 2 1/2 quarts cannot be used, which means the farmer has 16 - 2 1/2 quarts of berries that can be used to make jam.

Now, the recipe requires 2 1/4 quarts of berries to make one batch of jam. Let's represent the number of batches of jam the farmer can make with the remaining berries as "b".

Therefore, the equation we need to find will relate the amount of remaining berries to the number of batches of jam the farmer can make is written as,

=> 16 = 2 1/2 + 2 1/4b

Hence the correct option is (b).

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Answer:

The maximum amount of water that the rectangular container will hold is equal to its volume.

The volume of a rectangular container is calculated by multiplying its length, width, and height.

Therefore, the volume of the container is:

30 inches x 22 inches x 20.8 inches = 15,456 cubic inches

So the container can hold up to 15,456 cubic inches of water.

Answer 13,728

Step-by-step explanation: 30 x 22 x 20.8 = 13,728 which makes D correct because the maximum amount of water the bottle can hold is the same as the volume.

Answer:

B.2/3

Step-by-step explanation:

Let's work backwards from the information we have to determine which diagram Ronald drew.

We know that after Ronald ate on Tuesday, there was 1/2 of the pizza remaining. This means that he ate 1/2 of the pizza on Tuesday, since he had eaten 1/3 of the pizza on Monday.

So, if we add 1/2 and 1/3, we get:

1/2 + 1/3 = 5/6

This means that Ronald ate 5/6 of the pizza in total. We also know that he ate 1/2 of the pizza on Tuesday, so the fraction he ate on Monday was:

5/6 - 1/2 = 1/3

This confirms that Ronald ate 1/3 of the pizza on Monday.

Now, let's look at the answer choices. We need to find a diagram that represents Ronald eating 1/2 of the pizza, since that's what he ate on Tuesday. The only answer choice that represents 1/2 of the pizza shaded is B. 2/3.

Therefore, Ronald drew diagram B. 2/3.

Answer:

Step-by-step explanation:

Answer:

The chord length x is growing at a rate of 1 m/min after 2π minutes.

Step-by-step explanation:

The formula for chord length x in terms of radius r is:

[tex]\boxed{x &= 2r\sin\left(\dfrac{\theta}{2}\right)}[/tex]

where θ is the central angle subtended by the chord.

The formula for arc length s in terms of radius r is:

[tex]\boxed{s=r\theta}[/tex]

where θ is the central angle subtended by the chord.

Rearrange the formula for arc length to isolate θ, then substitute this into the the formula for chord length to create an equation for x in terms of s:

[tex]\begin{aligned}\theta=\dfrac{s}{r} \implies x &= 2r\sin\left(\dfrac{\frac{s}{r}}{2}\right)\\x&= 2r\sin\left(\dfrac{s}{2r}\right)\end{aligned}[/tex]

Given the radius is 6 m, substitute r = 6 into the equation for x:

[tex]\implies x &= 12\sin\left(\dfrac{s}{12}\right)[/tex]

Differentiate with respect to s:

[tex]\begin{aligned}\implies \dfrac{\text{d}x}{\text{d}s} &= \dfrac{1}{12} \cdot 12\cos\left(\dfrac{s}{12}\right)\\\\&=\cos\left(\dfrac{s}{12}\right)\end{aligned}[/tex]

Given the arc length s is growing at a rate of 2 m/min:

[tex]\implies \dfrac{\text{d}s}{\text{d}t}=2[/tex]

Use the chain rule to create an equation for the rate of change of the chord x:

[tex]\begin{aligned}\implies \dfrac{\text{d}x}{\text{d}t}&=\dfrac{\text{d}x}{\text{d}s}\times \dfrac{\text{d}s}{\text{d}t}\\\\&=\cos\left(\dfrac{s}{12}\right) \times 2\\\\&=2\cos\left(\dfrac{s}{12}\right) \end{aligned}[/tex]

Given the arc length is growing at a rate of 2 m/min:

[tex]\implies \dfrac{\text{d}s}{\text{d}t}=2[/tex]

Integrate to create an equation for s in terms of t:

[tex]\begin{aligned}\displaystyle \int 1 \; \text{d}s&=\int 2\; \text{d}t}\\\\ s&=2t+\text{C}\end{aligned}[/tex]

Given s = 0 when t = 0, this means that C = 0. Therefore:

[tex]\implies s=2t[/tex]

If t = 2π then:

[tex]\implies s=2 \cdot 2\pi = 4\pi[/tex]

Finally, substitute s = 4π into the equation to calculate the rate of change of the chord at 2π minutes:

[tex]\begin{aligned}\implies \dfrac{\text{d}x}{\text{d}t}&=2\cos\left(\dfrac{4\pi}{12}\right) \\\\&=2 \cos \left(\dfrac{\pi}{3}\right)\\\\&=2 \cdot \dfrac{1}{2}\\\\&=1\end{aligned}[/tex]

Therefore, the chord length x is growing at a rate of 1 m/min after 2π minutes.

Answer:

Θ = 1.5 radians

Step-by-step explanation:

arc length is calculated as

arc = circumference of circle × fraction of circle , then

10.5 = 2πr × [tex]\frac{0}{2\pi }[/tex] ( cancel 2π on numerator/ denominator )

10.5 = 7 × Θ ( divide both sides by 7 )

[tex]\frac{10.5}{7}[/tex] = Θ , then

Θ = 1.5 radians

Answer:

For the given question ,

The radius r= 7

and length of an arc  =10.5

Also ,we know that

length of an arc = θ/360*(2pie *r)

where,  θ is the angle and (2*pie*r) is the circumference of the circle.

therefore, 10.5=(θ/360)* 2*pie*7

on further calculations,

θ=85.9 degrees

or θ=86 degrees(approx).

Required two transformations are translated according to the rule (x, y) → (x + 8, y + 2) reflected across the x-axis.

How to find the two transformations applied to pentagon ABCDE to create A″B″C″D″E″?

To find the two transformations applied to pentagon ABCDE to create A″B″C″D″E″, we can compare the coordinates of corresponding vertices of both pentagons.

Starting with point A, we see that it has been translated 8 units to the right and 2 units up to become A″. Therefore, the first transformation is a translation according to the rule (x, y) → (x + 8, y + 2).

Next, we can compare the y-coordinates of point A and A″ to see if a reflection has been applied. We see that the y-coordinate of A has changed from 5 to -7 in A″, indicating that a reflection has been applied across the x-axis.

Therefore, the two transformations applied to pentagon ABCDE to create A″B″C″D″E″ are:

Translated according to the rule (x, y) → (x + 8, y + 2)

Reflected across the x-axis.

The other options can be ruled out as they do not correctly reflect the transformation that was applied.

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[tex]\sf \dfrac{7}{24}.[/tex]

[tex]\sf \dfrac{7}{16} *\dfrac{4}{3}*\dfrac{1}{2}[/tex]

When multiplying fractions, we can always just multiply all the numerators together and the denominators aswell, like this:

[tex]\sf \dfrac{7*4*1}{16*3*2}=\dfrac{28}{96}[/tex]

We could divide both the numerator and denominator by 4 to fully simplify this answer:

[tex]\sf \dfrac{28/4}{96/4}=\dfrac{7}{24}[/tex]

Since the numerator (7) is a prime number, this fraction cannot be further simplified.

[tex]\sf \dfrac{7}{24}.[/tex]

Answer:

Step-by-step explanation:

The expected value of the distribution is 1 and the probability that a randomly selected student completes fewer than 2 bonus assignments is 0.75

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

a. To compute the expected value of the distribution, we need to multiply each possible number of completed bonus assignments by its probability and then add up the results. That is:

Expected value = (0 x 0.55) + (1 x 0.2) + (2 x 0.15) + (3 x 0.1) = 0 + 0.2 + 0.3 + 0.3 = 1.0

Therefore, the expected value of the distribution is 1.0.

b. To find the probability that a randomly selected student completes fewer than 2 bonus assignments, we need to add up the probabilities for the cases where x is 0 or 1. That is:

P(x < 2) = P(x=0) + P(x=1) = 0.55 + 0.2 = 0.75

Therefore, the probability that a randomly selected student completes fewer than 2 bonus assignments is 0.75 or 75%.

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The triangle with the sides 8, 11 and 12 is an acute triangle

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

8, 11 and 12

Using the pythagoras theorem, we have

12² = 11² + 8²

Evaluate the exponent on the left hand side and the sum of exponents on the right hand side

144 = 185

The above equation is false

This is because 144 and 185 are not equal

However, 144 is less than 185

This means that the triangle is an acute triangle

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The scale factor of the dilation that was done for the considered triangle is given by: Option C: 4

How does dilation works?

Dilation of a figure will leave its sides get scaled (multiplied) by same number.  That number is called the scale factor of that dilation.

It's also called scaling of a figure, but due the involvement of coordinates, it involves a center of a dilation, which is like a pinned point which stays at same place after dilation.

It's like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1).

For this case, we are specified that:

Larger triangle is dilation of the smaller triangle.

The center of the dilation is (1,-1).

From graph, we see that the base of smaller triangle is of 2 units.

The base of the larger triangle is of 8 units.

Let the scale factor of dilation be 's'.

Then we have:

length of base of dilated triangle = s × length of base of original triangle

or

8 = s * 2

s = 8/2 = 4

Thus, the scale factor of the dilation that was done for the considered triangle is given by: Option C: 4

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