Select the correct answer. Solve the following equation for x. x2 - 9x + 18 = 0 A. x = -3; x = 6 B. x = 3; x = 6 C. x = -3; x = -6 D. x = 3; x = -6

Answer:

5) 59.7 in

6) 39.0 mi

7)

8) 50.3 mi

Step-by-step explanation:

5) C = [tex]\pi (19)[/tex]

C = 59.7 in

6) C = [tex]2\pi (6.2)[/tex]

C = 39.0 mi

7) RADIUS IS CUT OFF

use C = [tex]2\pi r[/tex]

8) C = [tex]2\pi (8)[/tex]

C = 50.3 mi

The quotient of 3.013 × [tex]10^{8}[/tex] and 6.55 × [tex]10^{5}[/tex] expressed in scientific notation is equal to 0.46 × [tex]10^{3}[/tex].

In Mathematics, a quotient is a mathematical expression that is simply used to represent the division of a number (numerator) by another number (denominator).

Generally speaking, any numerical data (number) can be written in scientific notation as shown below:

a × [tex]b^n[/tex]

Where

Next, we would rewrite the given numerical data (number) in scientific notation by dividing by 6.55 × [tex]10^{5}[/tex] as follows:

Scientific notation = 3.013 × [tex]10^{8}[/tex]/(6.55 × [tex]10^{5}[/tex])

Scientific notation = 0.46 × [tex]10^{8-5}[/tex]

Scientific notation = 0.46 × [tex]10^{3}[/tex].

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The constant angular acceleration of the centrifuge is approximately [tex]-331283[/tex] rad/min² in the negative direction.

To find the constant angular acceleration of the centrifuge, we can use the following kinematic equation:

ω² = ω₀² + 2αθ

Here, ω is the final angular velocity (0 rad/min, since it comes to rest), ω₀ is the initial angular velocity (3450 rev/min), α is the constant angular acceleration we want to find, and θ is the angular displacement (45.8 revolutions).

First, we need to convert the given angular values to radians. We know that 1 revolution equals 2π radians.

Initial angular velocity, ω₀ = 3450 rev/min × 2π rad/rev = 6900π rad/min

Angular displacement, θ = 45.8 rev × 2π rad/rev = 91.6π rad

Now, substitute the values into the kinematic equation:

[tex]0 = (6900π)² + 2α(91.6π)[/tex]

[tex]α = - (6900π)² / (2 × 91.6π)[/tex]

[tex]α ≈ -331283 rad/min²[/tex]

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According to the question, "Suppose we randomly select 5 cell-phone owners. What is the probability that all 5 of them find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating?"The formula for finding the probability of an event is:P(E) = number of favorable outcomes/number of total possible outcomes.The given data in the question states that 67% of cell-phone owners find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating.

Therefore, the probability of any cell-phone owner checking their phone when it is not ringing or vibrating is:P(E) = 67/100 = 0.67To find the probability of 5 cell-phone owners checking their phones when they are not ringing or vibrating, we have to use the multiplication rule of probability. [tex]P(E₁∩E₂∩E₃∩E₄∩E₅) = P(E₁) × P(E₂) × P(E₃) × P(E₄) × P(E₅)P(E₁∩E₂∩E₃∩E₄∩E₅) = 0.67 × 0.67 × 0.67 × 0.67 × 0.67P(E₁∩E₂∩E₃∩E₄∩E₅) = 0.2197[/tex]

Therefore, the probability that all 5 of them find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating is approximately 0.2197 or 22%.

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This means that the cube will have less surface area than the rectangular prism.

Surface area is a measure of the total exposed area of an object, or the total area of its two-dimensional surface. It is a measurement of the total exposed area of a three-dimensional object and is used to calculate the amount of material needed to cover a given area. Surface area is commonly used in physics, chemistry, engineering, and mathematics.

The prism with the least surface area of the same volume is the cube. This is because a cube has equal length, width, and height, allowing for all of the sides to be equal in size. This means that the area of each side is the same and all six sides of the cube are congruent. This creates the least amount of surface area for a given volume, as compared to any other prism. To illustrate this, take a cube and a rectangular prism with the same volume. The cube will have 6 smaller sides, while the rectangular prism will have 5 larger sides and 1 smaller side. This means that the cube will have less surface area than the rectangular prism.

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Answer:

let angle GJK be x

GJK=GHK (Base angle of isosceles triangle)

Step-by-step explanation:

x=5x+8

5x-x=8

4x=8

x=8/4

x=2 ans.

Hence,

5x+8

5*2+8

10+8

18.ans

To calculate the probability that at least 1 of 5 randomly selected American children (ages 3 to 5) is read to every day by someone at home.

To find the probability that none of the 5 children are read to, we can use the fact that the probability that a single child is not read to every day is 1 - 0.58 = 0.42. We can then use the multiplication rule to find the probability that none of the 5 children are read to, which is (0.42)⁵ = 0.0075. Finally, we can use the complement rule to find the probability that at least 1 child is read to every day, which is 1 - 0.0075 = 0.9925. Therefore, the probability that at least 1 of 5 randomly selected American children (ages 3 to 5) is read to every day by someone at home is 0.9925.

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Therefore, each internal angle would be 178 degrees in a regular polygon with 360 sides.

In mathematics, an angle is a figure made up of two rays that share a shared endpoint and are referred to as the sides of the angle and the vertex of the angle, respectively. Angles are typically measured in degrees, radians, or other angle measurement units. Angles can be categorized based on how wide they are. An acute angle is one that is less than 90 degrees, an obtuse angle is one that is higher than 90 degrees but less than 180 degrees, and a right angle is one that is 90 degrees. A reflex angle is greater than 180 degrees but less than 360 degrees, and a straight angle is precisely 180 degrees.

given

Since a polygon with that many sides would have sides that are extremely tiny in relation to the radius, if a regular polygon has 360 sides, it is a circle. Since every group of points in a regular polygon has an equal exterior angle and the sum of all exterior angles in a circle is 360 degrees, each exterior angle in a regular polygon would be measured as follows:

360 edges / 360 degrees = one degree.

Each interior angle of a regular polygon with n sides can be determined using the following formula:

Inner angle is equal to (n-2) x 180 / n.

When we enter n = 360 into this algorithm, we obtain:

(360-2) x 180 degrees / 360 = 178 degrees is the interior angle.

Therefore, each internal angle would be 178 degrees in a regular polygon with 360 sides.

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The amount or fraction of work Jerry gets done in 1 hour is 1/3 when it takes him 3 hours to clean all the tank in his section and it take Hart x hours to clean all the tanks in his section.

We know that it takes jerry 3 hours to clean all the tank in his section and it take Hart x hours to clean all the tanks in his section,

when they work together, they can clean the tanks in 1 hour.

now let work be - 1

therefore,

work x Jerry = work x Hart

1×3 = 1×x

3 = 1x

3 = x

therefore in 1 hour work done by Jerry will be 1/3.

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a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.

For visualizing the percentage distribution of different course subjects, a pie chart would be the most suitable type of chart. Pie charts are ideal for displaying the relative proportions of different categories or groups as slices of a circular pie. Each slice of the pie represents a proportion of the whole, which in this case would be the total time spent on all course subjects during homework sessions. The size of each slice will correspond to the percentage of time spent on each course subject. Therefore, a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.

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Answer:

Sam made 21 shots, and Wil made 27 shots.

Answer: V≈339.29 in

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

7 rounds to 10

9 rounds to 10

19 rounds to 20

so Vicki has 40 birds

9 rounds to 10

12 rounds to 10

29 rounds to 30

so johnny has 50 birds

now subtract 50-40=10

The expression that equals ∠BEC is 3x - 27, and the answer is B.

First, we find the measure of ∠BEC using the given information and the value of x. We get

Then, we use the fact that ∠AED is vertically opposite to ∠BEC, so ∠AED = ∠BEC = 63 degrees.

Finally, we need to find the expression among the given choices that equals 63 when x = 30.

Option A is too large, option C is too large, and option D is too small. Option B gives us

which matches the measure of ∠BEC. Therefore, the answer is B.

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Complete Question:

If the measure of BEC is (2x+3) and x=30, which expression could represent the measure of AED?

Answer:

Area = [tex]415.265 m^2[/tex]

Step-by-step explanation:

Area of a circle = [tex]\pi r^2[/tex]

[tex]A = (3.14)(11.5^2)=(3.14)(132.25)=415.265[/tex]

Yes, it is possible to have a c2 strictly convex function on a compact domain that is not also strongly convex.

Let's have a look at the following details of it.

A strictly convex function is a function whose Hessian matrix is positive-definite for all arguments. As a result, if f is differentiable and convex, it is strictly convex if and only if its Hessian matrix is positive-definite for all arguments.

The Definition of Strong Convexity: A function is said to be strongly convex if it meets the following criteria:
Let C be a convex subset of a Hilbert space H, and let f:C→ℝ be a continuously differentiable function. There is a positive constant μ such that, for all x,y∈C: f(y)≥f(x)+⟨∇f(x),y−x⟩+μ/2‖y−x‖2

Thus, it is clear from the above-mentioned definitions that it is possible to have a c2 strictly convex function on a compact domain that is not also strongly convex.

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The volume of balloon A is [tex]\frac{2}{5}[/tex] gallon and the volume of balloon B is [tex]\frac{1}{5}[/tex] gallon.

What is volume?

Any three-dimensional solid's volume is simply the amount of space it takes up. A cube, cuboid, cone, cylinder, or sphere can be one of these solids.

We are given that two balloons have a total volume of [tex]\frac{3}{5}[/tex] gallon.

Let the volume of balloon A be x and the volume of balloon B be y.

So, we get

x + y = [tex]\frac{3}{5}[/tex]

Also, it is given that the difference of their volumes is [tex]\frac{1}{5}[/tex] gallon and Balloon A has a greater volume than Balloon B.

So, we get another equation as

x - y = [tex]\frac{1}{5}[/tex]

Now, on adding both the equations, we get

⇒ 2x = [tex]\frac{4}{5}[/tex]

Now, on solving we get

⇒ x = [tex]\frac{2}{5}[/tex]

Now, on substituting the value of x in the equation, we get

⇒ [tex]\frac{2}{5}[/tex] + y = [tex]\frac{3}{5}[/tex]

⇒ y = [tex]\frac{1}{5}[/tex]

Hence, the volume of balloon A is [tex]\frac{2}{5}[/tex] gallon and the volume of balloon B is [tex]\frac{1}{5}[/tex] gallon.

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The decision that most clearly reflects a lack of understanding of the concept of sunk costs is "You study eight hours for a final exam even though there is no way now that you can pass the course".

Sunk costs refer to any costs that have already been incurred and cannot be recovered. Sunk costs are irrelevant in decision-making because they are already gone and cannot be recovered. Decision-makers must only consider future costs and benefits when making decisions.

A lack of understanding of sunk costs may result in individuals making decisions based on past costs rather than future costs and benefits. Decision-making that is influenced by sunk costs may result in inefficient resource allocation and lost opportunities.

Individuals must ignore sunk costs and instead focus on future costs and benefits to make effective decisions.

In the given options, "You study eight hours for a final exam even though there is no way now that you can pass the course" is the decision that most clearly reflects a lack of understanding of the concept of sunk costs.

Even though the student has already spent 8 hours studying, the sunk costs are irrelevant because the student cannot pass the course now. The student should focus on future costs and benefits and use the remaining time to study for other courses.

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The empirical rule states that approximately 95% of the population lies within 2 standard deviations of the mean for a normal distribution, but you found that the z-scores that mark off the middle 95% of the standard normal distribution are -1.96 and 1.96. This does not represent a contradiction, and I will explain why is it so ?

The empirical rule, also known as the 68-95-99.7 rule, is a useful guideline to help us understand the proportions of data in a normal distribution. According to this rule, about 68% of the data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. However, it is essential to note that the empirical rule is a simplified approximation.

On the other hand, the z-scores that you calculated, -1.96 and 1.96, are more precise values based on the actual standard normal distribution. These values come from a more accurate calculation using the cumulative distribution function (CDF) of the normal distribution, which gives the exact probability for any given range of z-scores.

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The events that are independent are,

1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.

2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.

3) Olivia choosing an ace and the dart hitting the bull's-eye

1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.

2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.

3) Olivia choosing an ace and the dart hitting the bull's-eye.

The other events are dependent because the outcome of the first event affects the outcome of the second event. Specifically

1) Sarah picking a number less than 5 and then picking an odd number. The second event depends on the outcome of the first event.

2) A number cube being rolled and a spinner being spun. The two events are independent of each other, but the outcomes of each event are not independent.

3) Two cards being randomly chosen from a standard deck, and Eliza choosing a jack, replacing it, and then choosing a black card. The outcome of the second event depends on the outcome of the first event, and the outcome of the first event affects the composition of the deck for the second event.

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The given question is incomplete, the complete question is:

Which events are independent? Check all that apply. Each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. Sarah picks a number less than 5, keeps it, and then picks an odd number. A number cube is rolled and a spinner is spun. Henry rolls a multiple of 2 and lands on a red portion of the spinner. Two cards are randomly chosen from a standard deck. Eliza chooses a jack, replaces it, and then chooses a black card. Two pairs of socks are randomly chosen from a drawer. Hayden chooses a black pair of socks, puts them on, and then chooses another black pair. A card is randomly chosen from a standard deck and a dart is randomly thrown. Olivia chooses an ace and the dart hits the bull’s-eye.

The new perimeter is 127.2 inches if it is multiplied by 19.

What do you mean by the are and perimeter of the square ?

The area of a square is calculated by squaring the length of one of its sides. If the area of a square is multiplied by a factor, the length of the sides will be multiplied by the square root of that factor. One way to express the concept of perimeter for a square is to state that it is the total distance around the outer boundary of the shape, which is equal to the sum of the lengths of all four sides.

Determining the the value of perimeter :

The area of the square is [tex]7.3 \times 7.3 = 53.29[/tex] square inches.

If this area is multiplied by 19, the new area will be 1012.51 square inches.

To find the new side length of the square, we take the square root of the new area:

[tex]\sqrt{1012.51} = 31.8[/tex] (rounded to one decimal place)

Therefore, the new side length of the square is 31.8 inches.

To find the new perimeter, we multiply the new side length by 4:

[tex]31.8 \times 4 = 127.2[/tex]inches

So the new perimeter is 127.2 inches.

To summarize, when the area of the square with side length 7.3 inches is multiplied by 19, the perimeter is multiplied by the square root of 19, which is approximately 4.36. The new perimeter is 127.2 inches.

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Giovanna deposited $1600 into two accounts, half in First Oak and half in West United.

Interest earned in First Oak account after 5 years at 6% simple interest:

= 0.06 x $800 x 5

= $240

Interest earned in West United account after 5 years at 5% compounded annually:

= $800 x (1 + 0.05)^5 - $800

= $800 x 1.27628 - $800

= $221.02

Total interest earned in both accounts:

= $240 + $221.02

= $461.02

Therefore, Giovanna will have earned $461.02 in interest from both accounts at the end of 5 years.

The monthly percentage rate is 1.45%, and the APR is 17.4%.

To calculate the monthly percentage rate, we can divide the finance charge by the average daily balance, then multiply by 100 to convert to a percentage

Monthly percentage rate = (finance charge / average daily balance) x 100

Monthly percentage rate = ($8.12 / $560) x 100

Monthly percentage rate = 0.0145 x 100

Monthly percentage rate = 1.45%

To calculate the APR (annual percentage rate), we need to multiply the monthly percentage rate by the number of months in a year:

APR = Monthly percentage rate x 12

APR = 1.45% x 12

APR = 17.4%

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Answer:

the area ot the triangle is half the area of the rectangle, so the area of the triangle is what sqauare units

Answer: It's  much easier to form a rectangle and multiply the width and the length and then divide it by 2  

Step-by-step explanation:

Lets assume this is a right triangle.

If you use pythagorean theorem, lets assume the tower is the longest line on the triangle.

If this is true, lets say that 9^2 (distance from end of slide to base of tower) + x^2 (length of slide) = 23^2 (height of tower)

we get the length of the slide is 21.2 meters.

Step-by-step explanation:

A is not proportional

Use the graph to record the value of y axis when x is 1, 2, 3, 4, 5, 6

And record the values of x when y is 1, 2, 3, 4, 5, 6 till the end

Using the graph Value of y

(1, 0.9) (2,1.5) (3,2.2) (4,2.5) (5, 3) (6,4) (7, 5) (10,6)

Using the graph, find the value of x when y is 1 - 10)

1.2, 2.5, 5,.....

The slope of the graph also shows that it is not proportional

B is proportional

X is 0 and y is 0

When x is 5, y is 10

Ratio x: y = 5:10 = 1:2

When x is 10, y is 20

Ratio x:y is 10: 20 = 1:2 same as above

C is not proportional

When Moyra is 32, daughter is 8

When her daughter is 22, Moyra will also be 4years older, which is 36

32: 8 = 4:1

36: 12 =3:1

From the given information provided, there were 311 children who swam at the pool that day.

Let's use C to represent the number of children who swam at the pool and A to represent the number of adults who swam at the pool.

From the problem, we know that:

C + A = 402 (Equation 1) (The total number of people who used the pool was 402)

1.50C + 2.00A = 648.50 (Equation 2) (The total receipts from admission were $648.50)

To solve for C and A, we need to eliminate one of the variables. We can do this by multiplying Equation 1 by 1.50, which will give us:

1.50C + 1.50A = 603 (Equation 3)

Now we can subtract Equation 3 from Equation 2 to eliminate C:

2.00A - 1.50A = 648.50 - 603

0.50A = 45.50

A = 91

So there were 91 adults who swam at the pool that day. To find the number of children, we can substitute A = 91 into Equation 1:

C + 91 = 402

C = 311

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As a result, the circumference of the circular walkway is approximately 367.06 square feet.

A circle is a geometric shape made up of all points that are equally spaced apart from the center. It is a flat, two-dimensional object whose radius or diameter serves as its sole defining characteristic. A circle's circumference is the distance around it, while the area of the circle is the amount of space inside it.

given

We must deduct the area of the smaller circle from the size of the larger circle in order to determine the area inside the circular path. Let's use the abbreviations "r" for the smaller circle's radius and "R" for the larger circle's radius. We are aware that the circumference of the smaller circle, which is 132 feet, is equal to the distance around the circular path.

The wider circle's circumference is 132 feet.

2πR = 132

R = 21

The breadth of the circular path, which is equal to the difference between the radii of the two circles, can now be used to calculate the radius of the smaller circle:

R - r = diameter of the circle

21 - r = diameter of the circle

r = 18

The smaller circle therefore has a radius of 18 feet.

Inside the arc of the path, there is:

R2 - r2 equals (21 - 18) = (44 - 324) = (117) 367.06 square feet.

As a result, the circumference of the circular walkway is approximately 367.06 square feet.

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ARMY DISBANDED MEANS SOLDIERS WERE RELEASED FROM SERVICE

When George Washington became president in 1789, the army he had

commanded in the American Revolution had disbanded. This means that

the soldiers were released from service and the military units were

dissolved after the end of the war.He pursued two intertwined interests:

military arts and western expansion. At 16 he helped survey Shenandoah

lands for Thomas, Lord Fairfax. Commissioned a lieutenant colonel in 1754,

he fought the first skirmishes of what grew into the French and Indian War.

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Answer:

226.865 square inches.

Step-by-step explanation:

The equation for the area of a circle is [tex]\pi r^2[/tex]. Let's use 3.14 for pi. The radius can be found by dividing 17/2 = 8.5. 8.5 squared is 72.25. Finally, multiply by pi to get 226.865.