Three boxes are stacked one on top of the other. One box is 6 feet 7 inches tall, one is 5 feet 6 inches tall, and one is 5 feet 2 inches tall. How high is the stack?
Write your answer in feet and inches. Use a number less than 12 for inches.

The size of angle K (m∠K) as shown in the circle is 50°.

Tangent to a circle is the line that touches the circle at only one point.

To calculate the size of angle K (m∠K), we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

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The image of point P under a 90-degree counter Clockwise rotation about the origin is (-6, -4).

To find the image of point P = (-4, 6) after a 90-degree counterclockwise rotation about the origin, we can use the following formula:

(x', y') = (xcosθ - ysinθ, xsinθ + ycosθ)

where (x, y) are the coordinates of the original point, θ is the angle of rotation, and (x', y') are the coordinates of the rotated point.

In this case, θ = 90 degrees, so we have:

(x', y') = (-4cos90 - 6sin90, -4sin90 + 6cos90)

        = (-6, -4)

Therefore, the image of point P under a 90-degree counterclockwise rotation about the origin is (-6, -4).

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The range of the function is the set of all real numbers

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

x: -2, -1, 0, 1, 2, 3

y: -11, -4, 1, 4, 5, 4

The range of a function is the set of y values of the function

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

Range = -11, -4, 1, 4, 5, 4

This can be expressed as

Range = -11 to 4

So, we can say that the range is the set of all real numbers

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Answer:

These triangles are not similar because the ratios of corresponding sides are not equal.

To solve this inequality for x, we need to isolate x on one side of the inequality sign. Let's begin by distributing the -2 on the right-hand side:

7x + 5 < -2(4x - 3)

7x + 5 < -8x + 6

Adding 8x to both sides, we get:

15x + 5 < 6

Subtracting 5 from both sides, we get:

15x < 1

So the equivalent inequality to 7x + 5 < -2(4x-3) is 15x < 1.

Therefore, the answer is: 15x < 1.

"g" is the subject of the equation in terms of "a" and "h."

To make "g" the subject of the equation "a = (g + h)/2," we can rearrange the equation to isolate "g."

Let's follow the steps:

Multiply both sides of the equation by 2 to eliminate the fraction:

2a = g + h

Subtract "h" from both sides to isolate "g":

2a - h = g

By performing these operations, we have successfully isolated "g" on one side of the equation.

The resulting equation is "g = 2a - h."

This equation shows that "g" is equal to two times "a" minus "h."

By substituting the given values of "a" and "h" into the equation, you can calculate the corresponding value of "g."

If we have "a = 5" and "h = 3," we can substitute these values into the equation to find the value of "g":

g = 2(5) - 3

g = 10 - 3

g = 7

"a" is 5 and "h" is 3, the value of "g" is 7 according to the equation "g = 2a - h."

The equation "g = 2a - h" allows you to express "g" in terms of "a" and "h" by subtracting "h" from twice the value of "a."

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(26) The length FE in the intersecting chords is 6.

(27) The length of arc AE =  64⁰.

We know that,

The length FE is computed using the intersecting chord theorem, as shown below;

The power of a point theorem, commonly known as the intersecting chord theorem, says that:

If two chords of a circle cross inside the circle, the product of the lengths of one chord's segments equals the product of the lengths of the other chord's segments.

FE ≅ AB = 6

The length of the arc AE is computed as follows:

⇒ arc of AE + arc of AB + arc of ED = 180

Since sum of angles of a semi circle

⇒ arc of  AE + 58 + 58 = 180

⇒ arc of AE + 116 = 180

⇒ arc of AE = 64

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9x=28. x=28÷9

To calculate the tax owed by a married couple filing jointly who report a taxable income of $97,025, we can use the 2021 tax brackets and rates provided by the IRS.

The first $19,900 of their income is taxed at a rate of 10%, which equals $1,990.

The next $60,050 of their income is taxed at a rate of 12%, which equals $7,206.

The remaining $17,075 of their income is taxed at a rate of 22%, which equals $3,756.50.

Adding these amounts together gives a total tax liability of $12,952.50.

Therefore, the tax owed by a married couple filing jointly who report a taxable income of $97,025 is $12,952.50.

Answer: 15,734

Step-by-step explanation:

If you look at the table itself it has the answer however it says at least 97,000 but less than 97,050 and it says and you are-- right under married filing jointly is 15,734

Answer: Reflection on the x-axis and moved 5 units upwards.

Step-by-step explanation:

     First, we will transform the transformed function into an equation form we may be more familiar with.

g(x) = 5 - x⁴ ➜ g(x) = -x⁴ + 5

     We see that this function is reflected on the x-axis (as given by the "-") and is moved 5 units upwards (as given by the "+ 5").

     We can also graph this, see attached.

Answer:

Step-by-step explanation:

You want the radius and area of a spherical ice cream scoop with a volume of 179.59 cubic inches.

The volume of a sphere is given by the formula ...

  V = (4/3)πr³

Then the radius will be ...

  r = ∛(3V/(4π))

  r = ∛(3·179.59/(4π)) ≈ 3.49997 . . . . in

The radius is about 3.50 inches.

The area of a sphere is given by ...

  A = 4πr^2

  A ≈ 4π·(3.49997 in)² ≈ 153.9355 . . . . in²

The area of that scoop is about 153.9 square inches.

__

Additional comment

A scoop 7 inches in diameter would likely be served in a bowl.

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If f(x)=3x²-2x+5 and g(x) = x³+4x²-1 then the function obtained by multiplying two functions is  3x⁵+10x⁴-3x³+17x²+2x-5

The two functions are f(x)=3x²-2x+5 and g(x) = x³+4x²-1

We have to find (f×g)(x)

(f×g)(x)= f(x)g(x)

=(3x²-2x+5)( x³+4x²-1)

=3x⁵+12x⁴-3x²-2x⁴-8x³+2x+5x³+20x²-5

Combine the like terms

=3x⁵+10x⁴-3x³+17x²+2x-5

Hence, the function obtained by (f×g)(x) is 3x⁵+10x⁴-3x³+17x²+2x-5

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The first three terms of the Sequence are -2, 1, 6 and the tenth term is 97.

Given that the nth term of a sequence is n squared - 3.

We can find the first three terms by substituting n = 1, 2, and 3 into the formula.

When n = 1, the first term is:

a1 = 1² - 3 = -1

When n = 2, the second term is:

a2 = 2² - 3 = 1

When n = 3, the third term is:

a3 = 3² - 3 = 6

Therefore, the first three terms of the sequence are: -2, 1, 6.

To find the tenth term, we substitute n = 10 into the formula.

a10 = 10² - 3 = 97

Therefore, the tenth term of the sequence is 97.

In summary, the first three terms of the sequence are -2, 1, 6 and the tenth term is 97.

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On average, you would expect to have to ask 2.5 students before finding one who has jumper cables.

The distribution is the geometric distribution with the parameter p = 0.4.

We have,

a.

The variable of interest is the number of students who need to be stopped before finding one who has jumper cables.

The range of possible values is 1, 2, 3, 4, ...

b.

The probability that the third person asked would be the one who has a jumper cable can be found using the geometric distribution with parameter p = 0.4, where p is the probability of success (i.e., finding someone with jumper cables).

The probability can be calculated as:

P(X = 3)

= (1 - p)^(3-1) x p

= (0.6)^2 * 0.4

= 0.144

c.

The probability that the first person asked will be the one who has jumper cables.

P(X = 1)

= p

= 0.4

d.

The expected value (or mean) of the number of people who need to be asked before finding the first one with jumper cables can be calculated using the geometric distribution with parameter p = 0.4.

So,

E(X)

= 1/p

= 1/0.4

= 2.5

Thus,

On average, you would expect to have to ask 2.5 students before finding one who has jumper cables.

The distribution is the geometric distribution with the parameter p = 0.4.

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Answer:

0.8475

Step-by-step explanation:

We can model the number of defective tablets in the shipment as a binomial distribution with parameters $n=26$ (the sample size) and $p=0.15$ (the probability of a defective tablet).

To calculate the probability that the whole shipment will be accepted, we need to find the probability that the number of defective tablets in the sample is at most 1, which means that the shipment meets the required specifications.

A number line with a closed circle on -9 and shading to the left. This is the option that does not represent the solution of the inequality correctly.

1. Simplify the inequality: 8x - (5x + 4) ≥ -31
2. Distribute the negative sign: 8x - 5x - 4 ≥ -31
3. Combine like terms: 3x - 4 ≥ -31
4. Add 4 to both sides: 3x ≥ -27
5. Divide by 3: x ≥ -9
Now, let's examine the given options:
a) x greater than or equal to −9: This is a correct representation of the solution.
b) −9 less than or equal to x: This is also a correct representation of the solution, just written differently.
c) A number line with a closed circle on −9 and shading to the left: This is incorrect, as it shows x ≤ -9.
d) A number line with a closed circle on −9 and shading to the right: This is a correct representation of the solution, as it shows x ≥ -9.
Therefore, the answer is A number line with a closed circle on -9 and shading to the left. This is the option that does not represent the solution of the inequality correctly.

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The terms that can be used to classify the triangle by angle measures and side lengths include the following: D. acute and isosceles.

In Mathematics and Geometry, an isosceles triangle simply refers to a type of triangle with two (2) sides that are equal in length (side lengths) and two (2) equal angles.

This ultimately implies that, an isosceles triangle comprises two (2) side lengths that are equal and two (2) angles with the same magnitude.

In conclusion, the angle measures of each of the angles represented by this triangle is equal to 90 degrees and as such, they are acute angles.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

After purchasing goods from China, the Italian trader has a number of non-Silk Road destinations to choose from, including:

Location in India

The Indian Ocean's Spot

the region rising from the Red Sea

the region above Italy

The network of commercial routes known as the "Silk Road" was used for more than 1,500 years, from the Han dynasty of China's opening of trade in 130 BCE to the Ottoman Empire's suspension of trade with the West in 1453 CE.

Over a distance of over 6,437 kilometers (4,000 miles), the Silk Road passed through some of the most challenging landscapes in the world, including the Pamir Mountains and the Gobi Desert. Because no single administration was in charge of maintenance, the roads were usually in poor condition.

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The domain of a function is all of the possible x-values.

In the case of this function, we can see that the x-values begin at negative infinity, continue/change between -1 and 1, and pick up again to continue through positive infinity.

Therefore, the domain of the function is negative infinity to infinity, option D/#4.

Hope this helps!

Answer:

lj= 18 feet

mgm=52°

Step-by-step explanation:

lj=GJ/2=36/2=18feet

mGM=mHJ=52°

The derivative of the function [tex]f(x)=(x+2)^{x}[/tex] is [tex](x + 2)^x \left( \frac{x}{x + 2} + ln(x + 2) \right)[/tex] A, using logarithmic differentiation.

To find the derivative of the function [tex]f(x)=(x+2)^{x}[/tex] using logarithmic differentiation, take the natural logarithm of both sides of the equation. This gives us the following equation:

[tex]ln(f(x)) = x ln(x + 2)[/tex]

Then differentiate both sides of this equation with respect to x. This gives us the following equation:

[tex]\frac{f'(x)}{f(x)} = \frac{x}{x + 2} + ln(x + 2)[/tex]

Multiply both sides of this equation by f(x) and solve for f′(x). This gives us the following equation:

[tex]f'(x) = f(x) \left( \frac{x}{x + 2} + ln(x + 2) \right)[/tex]

Then substitute the function [tex]f(x)=(x+2)^{x}[/tex] into this equation. This gives us the following equation:

[tex]f'(x) = (x + 2)^x \left( \frac{x}{x + 2} + ln(x + 2) \right)[/tex]

Therefore, the derivative of the function [tex]f(x)=(x+2)^{x}[/tex] is [tex](x + 2)^x \left( \frac{x}{x + 2} + ln(x + 2) \right)[/tex]

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The interest rate required to pay a simple interest of $53.96

from a principal of $500.00 is 18.50%.

Simple interest is expressed as:

[tex]\sf I = \dfrac{P\times r \times t}{100}[/tex]

Where I is interest, P is principal, r is interest rate and t is time.

Given that:

Plug the given values into the above formula and solve for interest rate.

[tex]\sf I = \dfrac{P\times r \times t}{100}[/tex]

[tex]\sf r = \dfrac{I}{P\times t}[/tex]

[tex]\sf r = \dfrac{\$53.96}{( \$500 \times \frac{7}{12} )}[/tex]

[tex]\sf r = 0.18501[/tex]

[tex]\sf r = 0.18501\times100\%[/tex]

[tex]\sf r = 18.50\%[/tex]

Therefore, the interest rate is 18.50%.

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Answer:

The answer is down below

Step-by-step explanation:

1 -6 0 3 6

9 7 + 1 4 7

5 3 2 5 8

= 1+0 -6+3 0+6

9+1 7+4 0+7

5+2 3+5 0+8

= 1 -3 6

10 11 7

7 8 8

Answer:

1.27 X 10²

Step-by-step explanation:

standard form is in format A X 10^n, where A is a number between 1 and 10

127 = 1.27 X 10²

Answer:

A' (12, 8), B'(4, 8), C'(12, -4), D'(4, -4)

Step-by-step explanation:

Since the dilation is in the center, we just need to multiply everything by our scale factor, 2.

A (6,4) → (12, 8)

B (2,4) → (4, 8)

C (6, -2)  → (12, -4)

D (2, -2) → (4, -4)

Hope this helps!

The function r(x) - 3f(x+1) transforms the parent function f(x)=x^2 by shifting it left by 1 unit, vertically stretching it by a factor of 3, and translating it downward by 3 units. The resulting graph is a parabola with vertex at (-1,-3) and a steeper shape.

The function r(x) - 3f(x+1) is a transformation of the parent function f(x)=x^2. Let's consider each transformation step by step.

First, the function f(x+1) represents a horizontal shift of the parent function f(x)=x^2 to the left by 1 unit. This means that the vertex of the parabola is shifted to the point (-1,0).

Next, the function 3f(x+1) vertically stretches the parabola by a factor of 3. This means that the distance between the vertex and the x-intercepts of the parabola is tripled, while the shape of the parabola remains the same.

Finally, the function r(x) subtracts a constant value from the transformed function. This translates the entire graph downward by 3 units.

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The distance from point A to point B is approximately 920 feet.

Let's call the distance from point A to point B as x.

From point A, the angle of elevation to the lighthouse's beacon-light is 8 degrees.

Using the tangent function to find the height of the lighthouse (h):

tan(8) = h/1083

h = 1083 tan(8) ≈ 157.6 feet

From point B, the angle of elevation to the lighthouse's beacon-light is 4 degrees.

Using the tangent function again to find the height of the lighthouse from point B (h'):

tan(4) = h'/(1083-x)

h' = (1083-x) tan(4) ≈ 78.6 - 0.07x

Since the height of the lighthouse should be the same from both points A and B, we can set h = h' and solve for x:

1083 tan(8) = (1083-x) tan(4)

x = 1083 - (157.6/tan(4)) ≈ 920 feet

Therefore, the distance from point A to point B is approximately 920 feet.

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The experimental probability that in a group of 4 students, at least one of them has brown eyes, based on the given sample, is 0.898 or 89.8%.

We know that "2", "4", and "8" represent the 30% of students with brown eyes.

Any occurrence of these numbers in the sample would indicate a student with brown eyes, while other numbers would represent students without brown eyes.

Let's examine the sample of 20 random numbers:

3, 7, 1, 6, 4, 2, 0, 9, 8, 5, 2, 7, 6, 8, 4, 3, 1, 2, 0, 4

Out of these 20 numbers, the following represent students with brown eyes: 4, 2, 8, 2, 8, 4, 2, 4.

Total possible combinations of 4 students from the sample = C(20, 4) = 4845 (using the combination formula)

Number of combinations without any student having brown eyes = C(12, 4) = 495 (choosing 4 students from the remaining 12 who don't have brown eyes)

The number of combinations where at least one student has brown eyes = 4845 - 495 = 4350

Experimental probability of at least one student having brown eyes

= 4350 / 4845

= 0.898

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Answer: 6ft

Step-by-step explanation:

180+40x+18x+4x^2=672

4x^2+58x+180x=672

4x^2+58x-492=0

2x^2+29x-246=0

(x=6)(2x+41)=0

x=6 or x=-20.5

Should be 6ft

To solve for the remaining angles and side of the triangles, we can use the Law of Sines and the Law of Cosines.

Triangle 1: (where angle A is acute)

Given:

B = 50°

b = 5

a = 6

Using the Law of Sines:

[tex]sin A / a = sin B / b[/tex]

sin A / 6 = sin 50° / 5

sin A = (6 x sin 50°) / 5

A = arcsin[(6 x sin 50°) / 5]

A ≈ 44.14°

Using the Law of Sines again:

sin C / c = sin B / b

sin C / c = sin 50° / 5

sin C = (c x sin 50°) / 5

Using the Law of Cosines:

c² = a² + b² - 2ab x cos C

c² = 6² + 5² - 2(6)(5) x cos C

c² = 36 + 25 - 60 x cos C

c² = 61 - 60 x cos C

c ≈ √(61 - 60 x cos C)

Triangle 2 (where A is obtuse):

Given:

B = 50°

b = 5

a = 6

Using the Law of Sines:

sin A / a = sin B / b

sin A / 6 = sin 50° / 5

sin A = (6 x sin 50°) / 5

A = arcsin[(6 x sin 50°) / 5]

A ≈ 44.14° (rounded to the nearest hundredth)

Using the Law of Sines again:

sin C / c = sin B / b

sin C / c = sin 50° / 5

sin C = (c x sin 50°) / 5

Since A is obtuse, C = 180° - A - B

C ≈ 85.86° (rounded to the nearest hundredth)

Using the Law of Cosines:

c² = a² + b² - 2ab x cos C

c² = 6² + 5² - 2(6)(5) x cos C

c² = 36 + 25 - 60 x cos C

c² = 61 - 60 x cos C

c ≈ √(61 - 60 x cos C)

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