9 The circumference of a circle is about 124 inches. What is the APPROXIMATE radius of the circle?
A. 20 in
B. 40in
C. 50 in
D. 60 in

Answer: y = 4x + 1, 25 inches at 6 years old

Step-by-step explanation:

   Our y-intercept will be 1 (5 inches at a year old - 4 inches per year = 1) with a slope of 4 (4 inches a year). Our equation will look like this:

            y = 4x + 1

   Next, to solve for the length of the tusk at 6 years old, we will input this value of 6 and solve.

            y = 4x + 1 = 4(6) + 1 = 25 inches

   See attached for a graph.

   We can also check our work using a different method.

6 years - 1 year = 5 years

5 years * 4 inches a year = 20 inches

20 inches + current 5 inches = 25 inches at 6 years

Answer: 1) C. 1.75

              2) C. 5.25

Step-by-step explanation:

For this first question, the answer is C. 1 3/4

First, you will need to calculate how many hours the 3/4-hour students studied versus the 1/4-hour students.

3/4 students: 3/4 · 3 = 9/4

1/4 students: 1/4 · 2 = 2/4

9/4 - 2/4 = 7/4 = 1 3/4

Therefore, your answer for the first question is C.

For the second question, the answer is C

We must calculate how many hours each group of students studied, then add them together. You can add or multiply in this situation.

1/4 students: 1/4 · 2 = 2/4 (No need for simplifying until the end.)

1/2 students: 1/2 · 5 = 5/2

3/4 students: 3/4 · 3 = 9/4

Now, let's change the 5/2 so we can add it to the other fractions.

5/2 ·2 = 10/4

Let's add.

2/4 + 10/4 + 9/4 = 21/4

Simplify.

21/4 = 5 1/4.

Therefore, answer choice C is correct.

Hope this helped!

For the probability of 90% that it will take at least 68.195 minutes long to assemble an electronic component.

As we have the time it takes to assemble an electronic component is normally distributed.

Mean time, [tex] \mu[/tex] = 17.2 minutes

Standard deviations, [tex] \sigma[/tex]

= 3.1 minutes

We have to determine probability is 90% that it will take at least how long to assemble a component. Now, from the standard normal distribution table value of Z - score for 90% is equals to the 1.645.

Using the Z- score formula in normal distribution, [tex]Z = \frac{ X - \mu}{\sigma }[/tex]

=> 1.645 = ( X - 17.2 )/3.1

=> X - 17.2 = 31 × 1.645

=> X = 17.2 + 50.995

=> X = 68.195

Hence, the required at least the long to assemble a component is equals to the 68.195.

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Answer:

[tex]81 {d}^{4} {e}^{7} [/tex]

Step-by-step explanation:

Use properties of degrees:

1. When multiplying different degrees on one term, the degree indicators must be multiplied, for example:

[tex]( { {x}^{2}) }^{3} = {x}^{2 \times 3} = {x}^{6} [/tex]

2. When dividing like terms (with the same base) with different degrees, the degree indicators must be subtracted, for example:

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

3. When squaring a negative term in parentheses, the minus is eliminated, for example:

[tex]( { - 3x})^{2} = 9 {x}^{2} [/tex]

.

[tex] \frac{ {(( { - 3d})^{2} \times {e}^{4} )}^{3} }{ {9d}^{2} \times {e}^{5} } = \frac{729 {d}^{6} \times {e}^{12} }{9 {d}^{2} \times {e}^{5} } = 81 {d}^{4} \times {e}^{7} [/tex]

Step-by-step explanation:

We can use the kinematic equations of motion to solve this problem. Let's assume the initial velocity of the snowball is 16 feet per second and its initial height is 32 feet. Also, we know that the acceleration due to gravity is -32.2 feet per second squared (assuming downward direction as negative).

To find out when the snowball hits the ground, we can use the equation:

h = 32 + 16t - 16t^2

where h is the height of the snowball at time t. We want to find the value of t when h = 0 (since the snowball hits the ground at that point). Therefore, we can rewrite the equation as:

16t^2 - 16t - 32 = 0

Dividing both sides by 16, we get:

t^2 - t - 2 = 0

Solving for t using the quadratic formula, we get:

t = (1 ± √(1 + 8))/2

t = 2 seconds or -1 second

Since time cannot be negative, the snowball hits the ground after 2 seconds.

To find the maximum height the snowball reaches, we can use the fact that the maximum height occurs at the vertex of the parabolic trajectory. The x-coordinate of the vertex is given by:

t = -b/2a

where a and b are the coefficients of the quadratic equation. In this case, a = 16 and b = -16, so:

t = -(-16)/(2*16) = 0.5 seconds

To find the corresponding height, we can substitute t = 0.5 seconds into the equation for h:

h = 32 + 16(0.5) - 16(0.5)^2

h = 36 feet

Therefore, the maximum height the snowball reaches is 36 feet.

When adding one identical room to a pair of houses, the price increase for a house with 4000 sqft compared to a house with 1000 sqft is $150,000.

What is the basis of this problem?

We have two houses, one with a 4000 square foot floor plan and another with a 1000 square foot floor plan. Both of them are identical, and each of them is expected to receive an additional identical room. We must determine how much the price of the house with the 4000 square foot floor plan will increase compared to the house with the 1000 square foot floor plan when both of these are completed.

Let's start by identifying the amount of money needed to construct each house. The amount of money needed to construct the house with the 4000 square foot floor plan is $300,000, and the amount of money required to build the house with the 1000 square foot floor plan is $150,000.The cost of building per square foot in this case is therefore $75/sqft.

As a result, the price for a 4000 sqft house is: $75/sqft × 4000 sqft = $300,000On the other hand, the cost of constructing a 1000 sqft house is:$75/sqft × 1000 sqft = $75,000When each house gets an additional identical room, the increase in the cost of the room is $50,000. As a result, the price of the house with the 4000 square foot floor plan will increase by 4 times, or $200,000, whereas the price of the house with the 1000 square foot floor plan will increase by one, or $50,000. As a result, the price of a 4000 sqft house will be $300,000 + $200,000 = $500,000, whereas the price of a 1000 sqft house will be $150,000 + $50,000 = $200,000.

When we compare these two values, we obtain the following outcome: Suppose you add 1 identical room to a pair of houses. The two houses are identical except for square footage.

When we compare the two values, we get the following result: $500,000 - $200,000 = $300,000

Therefore, the price increase for a house with 4000 sqft compared to a house with 1000 sqft is $150,000.

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The range in which x must lie in order for a triangle to exist is: 0 < x < 2.

The correct option is (D). 0 < x < 1.

A triangle has side lengths of 1 units, 1 units, and x units.

Determine the range in which x must lie in order for a triangle to exist.

Triangle is the type of polygon that is formed when three line segments join.

A triangle can be formed when and only when the sum of any two sides is greater than the third side.

Using the triangle inequality theorem we know that,1 + 1 > x1 + x > 11 + x > 1x > 0

Now combining both results:

x > 0

Therefore, the range in which x must lie in order for a triangle to exist is: 0 < x < 2.The correct option is (D). 0 < x < 1.

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Answer:

50%

Step-by-step explanation:

There are 4 cards.  4 and 6 are not odd, which is 2 cards.

P(not odd) = number of cards that are not odd/ total number of cards

                   = 2/4 = 1/2 = .5 = 50%

Step-by-step explanation:

There are SIX sides   3 pairs of equivalent sides

   2 * ( 1 1/3 x 3     + 3 * 2  2/3   +  2 2/3 * 1  1/3 )  = 31 1/9 square yards

The function is an exponential function of the form y = a * b^x, where "a" is the initial value and "b" is the common ratio.

Using the given table, we can see that:

- The initial value is y(0) = -2, so a = -2.

- To find the common ratio, we can divide any term by the previous term. For example:

 - b = y(1)/y(0) = (-10)/(-2) = 5

 - b = y(2)/y(1) = (-50)/(-10) = 5

 - and so on.

Since we get the same value of b for all the ratios, we can conclude that the common ratio is b = 5.

Therefore, the equation for the function shown in the table is: y = -2 * 5^x.

Step-by-step explanation:

F(x) = 34    so    34 = -3x + 64

                         - 30 = -3x

                            x = 10

Answer: 54°

Step-by-step explanation: As the sum of all angles in a Pentagon is 540°

so value of X is 540° - 456 = 54°

Answer:

Step-by-step explanation:

5p+10 equals big 5

Answer:

p = 0.8; q = 0,6

Step-by-step explanation:

5p + 10q = 10

2p - q = 1

5p + 10q = 10

q = 2p - 1

5p + 10 ( 2p - 1 ) = 10

5p + 20p - 10 = 10

25p = 20

p = 0,8

q = 2 x 0,8 - 1

q = 0,6

Answer:

158

Step-by-step explanation:

The old payment is $96.60, and the new payment is $110.20. The percent increase in her new monthly payment is 14.1%.

To calculate the old payment, we multiply the original loan amount by the monthly payment per thousand, which gives us $9.66 x 55 = $531.30.

To calculate the new payment, we divide the renewed loan amount by 1000 and multiply it by the monthly payment per thousand, which gives us $11.02 x 55 = $606.10.

To calculate the percent increase, we use the formula: ((new payment - old payment) / old payment) x 100. Substituting the values, we get ((606.10 - 531.30) / 531.30) x 100 = 14.1%. Therefore, the percent increase in her new monthly payment is 14.1%.

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Answer:40

Step-by-step explanation:

90= 2x-10

Answer:

40°

Step-by-step explanation:

Measure of angle LOM(aka x) is equal to:

x+x+10 = 90

2x = 80

x = 40°

The answer of the given question is the solution to the inequality h(t) > 9 is any value of t that makes h(t) greater than 9.

An inequality is a mathematical statement that shows a relationship between two values or expressions that are not equal. It uses symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to) to express the relationship between the two values. Inequalities are often used in algebra, geometry, calculus, and other areas of mathematics to represent constraints or limits on values or to compare two different sets of values. For example, an inequality might be used to determine if a certain number falls within a certain range, or to find the maximum or minimum value of a function given certain constraints.

The solution to the inequality h(t) > 9 is any value of t that makes h(t) greater than 9.

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An angle that is coterminal with -865° and has a measure between 0° and 360° is 75°. Since Angle b is coterminal with this angle, we can conclude that the measure of Angle b is 75°.

We must locate an angle that is coterminal with the -865° angle and has a measure between 0° and 360° in order to determine the size of angle b.

To do this, we can add or remove 360-degree multiples until we have an angle that is coterminal with -865° and is between 0° and 360°.

-865° + 360° = -505° (not between 0° and 360°)

-865° + 2(360°) = -145° (not between 0° and 360°)

-865° + 3(360°) = 75° (between 0° and 360°)

As a result, an angle with a measure between 0° and 360° that is coterminal with -865° is 75°. We can infer that Angle b's measure is 75° because it contaminates with this angle.

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Answer:

22

Step-by-step explanation:

f(x) = 2x² + 4                         f(3)

f(3) = 2(3)² + 4

f(3) = 2(9) + 4

f(3) = 18 + 4

f(3) = 22

By answering the presented question, we may conclude that Therefore, trigonometry the given identity is true.

The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.  

= 1/sin x

= √(1/sin²x - 1) / (1/sin²x)

= √(1 - sin²x) / sin x

= √(cos²x) / sin x

= √(1 - sin²x) / cos x

= √(csc²x - 1) / cos x

cos x = √(csc²x - 1) / cos x

cos²x = csc²x - 1

cos²x + sin²x = csc²x

1 = csc²x

Therefore, the given identity is true.

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Answer: Assuming the field is rectangular, the distance between the two corners diagonally can be calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the length and width of the field form the two sides of the right triangle, and the diagonal is the hypotenuse.

So, using the Pythagorean theorem:

Diagonal^2 = Length^2 + Width^2

Diagonal^2 = 80^2 + 60^2

Diagonal^2 = 6400 + 3600

Diagonal^2 = 10000

Diagonal = √10000

Diagonal = 100 yards

Therefore, the soccer player will have to kick the ball 100 yards to reach the opposite corner of the field.

Step-by-step explanation:

Answer:

sin(cos⁻¹(x+1)) = √(1 - (x+1)²)

Step-by-step explanation:

The capitalized costs for 2017 is $55,000.

Capitalizing means adding the cost of an asset to its book value or cost basis. Not all costs can be capitalized.

Generally, only costs that increase an asset's useful life or productive capacity should be capitalized.

In this case, the building and truck were purchased in 2015 and have been capitalized.

The following costs incurred in 2017 should be analyzed to determine whether they should be capitalized or expensed:

Painting the building for $5,000 - This cost does not increase the useful life or productive capacity of the building.

It is considered a repair and maintenance expense and should be expensed.

Installing new windows in the building for $10,000 - This cost improves the building's insulation and prevents leaking.

It is considered a capital improvement that extends the useful life of the building. Therefore, it should be capitalized.

Installing a new conveyor system for $40,000 - This cost increases the productive capacity of the company's operations. It is considered a capital expenditure and should be capitalized.

Repainting the delivery truck for $1,000 - This cost does not increase the useful life or productive capacity of the truck. It is considered a repair and maintenance expense and should be expensed.

Installing a hydraulic lift system on the truck for $5,000 - This cost allows better handling of large loads and increases the productive capacity of the truck. It is considered a capital expenditure and should be capitalized.

Overhauling the truck's engine for $4,000 - This cost is a repair and maintenance expense and should be expensed.

Therefore, the capitalized costs for 2017 are

$10,000 (new windows in the building) + $40,000 (new conveyor system) + $5,000 (hydraulic lift system on the truck) = $55,000.

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Question:  

On January 1, 2015, Jose Company purchased a building for $200,000 and a delivery truck for $20,000. The following expenditures have been incurred during 2017: • The building was painted at a cost of $5,000. To prevent leaking, new windows were installed in the building at a cost of $10,000. • To improve production, a new conveyor system was installed at a cost of $40,000. • The delivery truck was repainted with a new company logo at a cost of $1,000. • To allow better handling of large loads, a hydraulic lift system was installed on the truck at a cost of $5,000. • The truck's engine was overhauled at a cost of $4,000. Required: 1. Determine which of those costs should be capitalized. Assume that all costs were incurred on January 1, 2017.

When Gracie distributes her carrots equally among the 5 bunnies, each bunny gets 7,878 whole carrots, and 3,939 whole carrots remain without being given to a bunny. These figures are whole numbers.According to the statement, Gracie has 5 pet bunnies that love to eat whole carrots. Gracie has 3,939 carrots to feed the bunnies, and she will use as many carrots as she can and give each bunny the same number.

To calculate the number of carrots each bunny will get:Total number of whole carrots ÷ Total number of bunnies = Number of whole carrots each bunny gets Gracie distributes the 3,939 carrots equally among the 5 bunnies, with each bunny getting 7,878 carrots. This is illustrated in the calculation below:3,939 ÷ 5 = 7,878Hence, the number of whole carrots each bunny gets is 7,878.

When it comes to the number of carrots that remain without being given to a bunny, we need to calculate it using the following formula:Total number of whole carrots − (Number of whole carrots each bunny gets × Total number of bunnies) = Number of whole carrots that remain without being given to a bunnyUsing the figures from the above calculations, the computation will be as follows:3,939 − (7,878 × 5) = 3,939 − 39,390 = -35,451. Therefore, the number of whole carrots that remain without being given to a bunny is -35,451. However, since the answer must be a whole number, we can round this up to 0 carrots. This implies that all of the carrots were given to the bunnies.

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Mr. Jackson will roll a 4 between 3 and 7 times, inclusive, out of his 30 rolls of a number cube is 0.332,

P(X=k) = [tex]C(n,k)[/tex][tex]* p^k * (1-p)^{n-k}[/tex]

Where:

P(X=k) is the probability of getting k successes

n is the total number of trials

k is the number of successful trials

p is the probability of success in one trial

(1-p) is the probability of failure in one trial

here, in the question given that

n = 30 (total number of rolls)

k = 3, 4, 5, 6, or 7 (number of times rolling a 4)

p = 1/6 (probability of rolling a 4 on one roll)

Now we can calculate the probability of rolling a 4 between 3 and 7 times:

P(3<=X<=7) = P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7)

now for  each value of k, we get:

[tex]P(X=3) = C(30,3) * (1/6)^3 * (5/6)^{27} = 0.182[/tex]

[tex]P(X=4) = C(30,4) * (1/6)^4 * x)5/6)^{26} = 0.106\\P(X=5) = C(30,5) * (1/6)^5 * (5/6)^{25} = 0.035\\P(X=6) = C(30,6) * (1/6)^6 * (5/6)^{24} = 0.008\\P(X=7) = C(30,7) * (1/6)^7 * (5/6)^{23} = 0.001[/tex]

Adding these probabilities , we get:

P(3<=X<=7) = 0.182 + 0.106 + 0.035 + 0.008 + 0.001 = 0.332

Therefore, the probability that Mr. Jackson will roll a 4 between 3 and 7 times, inclusive, out of his 30 rolls of a number cube is 0.332,

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Using the Pythagorean theorem we know that the length of the given diagonal is 21.25 units respectively.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental Euclidean geometry relationship between the three sides of a right triangle.

This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

If a²+b²=c² and c is the triangle's longest side, the triangle is a right triangle.

If a triangle is not a right triangle, there are two additional types that can exist.

So, the formula is:

a² + b² = c²

Now, insert values as follows:

12.75² + 17² = c²

162.5625 + 289 = c²

451.5625 = c²

√451.5625 = c

21.25 = c

Therefore, using the Pythagorean theorem we know that the length of the given diagonal is 21.25 units respectively.

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