Layson, Jane
Mark has a key ring with 10 similar keys. There are 3 gym locker keys, 2 car keys, I door key, and 4 toolbox keys. If Mark selects one key without looking, what is the probability he
selects a car key or door key?

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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Answer:

Factor 64h^3+216k^9

Step-by-step explanation:

The given expression is a sum of two terms:

[64h^3+216k^9

Notice that each term has a common factor. For the first term, the greatest common factor (GCF) is 64h^3, and for the second term, the GCF is 216k^9. So we can factor out these GCFs to get:

64h^3+216k^9 = 64h^3(1 + 3k^6)

This expression cannot be factored any further, so the final answer is:

64h^3+216k^9 = 64h^3(1 + 3k^6)

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in approximately 22 years, the population would exceed the food supply, even if the country doubles its initial food supply and doubles the rate at which its food supply increases.

How to calculate the rate?

To answer these questions, we need to calculate the population and food supply at different points in time and compare them.

Let's first calculate the population after t years:

Population after t years = 2,000,000 * (1 + 4%) raise to the power t

And the food supply after t years:

Food supply after t years = 4,000,000 + 0.5 million * t

Now, let's answer the first question:

If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for an additional 0.5 million people per year, would shortages still occur?

If the country doubles its initial food supply, the new food supply would be 8,000,000, and it would still increase at a rate of 0.5 million people per year. Let's calculate the year when the population exceeds the food supply:

Population = Food supply

2,000,000 * (1 + 4%)^t = 8,000,000 + 0.5 million * t

Solving for t, we get t ≈ 17.77 years.

So, in approximately 18 years, the population would exceed the food supply, even if the country doubles its initial food supply and maintains a constant rate of increase in the supply adequate for an additional 0.5 million people per year.

Now, let's answer the second question:

If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur?

If the country doubles the rate at which its food supply increases, the new rate would be 1 million people per year. Let's calculate the year when the population exceeds the food supply:

Population = Food supply

2,000,000 * (1 + 4%) raise to the power t  = 16,000,000 + 1 million * t

Solving for t, we get t ≈ 21.96 years.

So, in approximately 22 years, the population would exceed the food supply, even if the country doubles its initial food supply and doubles the rate at which its food supply increases.

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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

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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An algebraic expression for representing the Nora's income in form of Tonya's income is given by  y = ( x / 4 ) .

Let us consider 'x' represents the Tonya's income.

And variable 'y' represents the Nora's income.

Tonya income is equal to four times of Nora's income.

This implies,

Nora's income is equal to one fourth times of Tonya's income.

⇒ y = ( x / 4 )

Rewrite an algebraic expression to represents Tonya's income in terms of Nora's income we have,

Simplify by multiplying both the sides of the algebraic expression by 4 we get,

⇒ x  = 4y

Therefore, an algebraic expression to represents the Nora's income in terms of Tonya's income is equal to y = ( x / 4 ).

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Answer:

432

Step-by-step explanation:

go 16x27 and that is your answer

Answer:

The area of the figureo will be 432

BECAUSE :-

You have to multiply 16 × 27 = 432

Hope Its Help You !!

Answer:

Step-by-step explanation:

To determine if Tammy's answer of 1 3/4 for the product of 5/7 and 1 1/4 is correct, we can perform the multiplication ourselves.

First, we need to convert 1 1/4 to an improper fraction:

1 1/4 = (4 x 1 + 1)/4 = 5/4

Then, we can multiply the fractions:

5/7 x 5/4 = 25/28

As we can see, 25/28 is not equal to 1 3/4. Therefore, Tammy's answer of 1 3/4 is incorrect. The correct answer is 25/28, which is an improper fraction. We can also express this as a mixed number: 0 25/28.

Answer: $ 46.50

First divided 31 by 2

Which equals...

15.50

Then add 15.50 to 31.

46.50

The answer is $46.50

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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The subtraction of the polynomials (3.1x + 2.8z) - (4.3x - 1.2z) is -1.2x + 4x

A polynomial is an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power.

(3.1x + 2.8z) - (4.3x - 1.2z)

open parenthesis

3.1x + 2.8z - 4.3x + 1.2z

combine like terms

3.1x - 4.3x + 2.8z + 1.2z

-1.2x + 4x

Ultimately, -1.2x + 4x is the results of the subtraction of the polynomial.

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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

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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Answer:

4t - 22

Step-by-step explanation:

To find:-

Answer:-

To find out the perimeter we can simply add all the side lengths of the given figure. Since the given figure here is a rectangle, we can add up all the four sides to find the perimeter.

The four sides given to us are t-6 , t-5 , t-6 and t-5 .

Hence the perimeter of the quadrilateral would be ,

Perimeter = t-5 + t-6 + t-5 + t-6

Perimeter = 4t - 10 - 12

Perimeter = 4t - 22

Hence the perimeter of the given figure us 4t - 22.

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{$\sf\large t-5$}\multiput(-1.4,1.4)(6.8,0){2}{$\sf\large t-6$}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture} [/tex]

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 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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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  

Bending moment curve equation below point A will be:

M = 15x - 3x² for 0 ≤ x ≤ b

Determination of shear and bending moment curves.

For the beam and loading shown, we can do the following:

Equation of shear curve (above point A):V = RA - w.x

For x = a,V = RA - w.a

For x = b,V = RA - w.b

Since the loading is symmetric, RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15 - 6a for a ≤ x ≤ b

Equation of shear curve (below point A):

V = RA - w.x

For x = 0,V = RA - w.0RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15k for 0 ≤ x ≤ a

The shear curve equation becomes;

V = 15k for 0 ≤ x ≤ a

V = 15 - 6a for a ≤ x ≤ b

Equation of bending moment curve (above point A):

M = RAx - ½w.x²For 0 ≤ x ≤ a,

M = 15x - ½(6x²) = 15x - 3x²For a ≤ x ≤ b,

M = 15x - 6a(x - a) - ½(6x²)= 15x - 6ax + 6a² - 3x²

The bending moment curve equation above point A becomes:

M = 15x - 3x² for 0 ≤ x ≤ a

M = 15x - 6ax + 6a² - 3x² for a ≤ x ≤ b

Equation of bending moment curve (below point A):

M = RAx - ½w.x²For 0 ≤ x ≤ b,

M = 15x - ½(6x²) = 15x - 3x²

The bending moment curve equation below point A becomes;

M = 15x - 3x² for 0 ≤ x ≤ b

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Answer: 239

Step-by-step explanation:

Darius wrote 2 integers 256 and -17. The question is asking you to solve how much larger is 256 than -17. This means you will subtract 256 by -17 which will give you 239 (256-17). The answer remains positive because 256 is larger

Hope this helps

Answer: They are exactly 273 places away.

Step-by-step explanation:

If a number is larger than another number then you need to subtract it to get the distance. In this case, you look at the subtraction to see how far away they are.

Hope this helps!

Have a blessed day!

The theoretical probability of stopping on the color blue when spinning a spinner with the colors red, yellow, blue, and green is 25% or 1/4.

A spinner is a tool that spins around an arrow or a pointer that points towards the numbers, colors, or pictures around its edge. The probability of a certain event is the likelihood of that event occurring. In this case, we need to find the theoretical probability of stopping on the color blue.

We have four colors on the spinner, so the probability of stopping on blue can be found using the formula of theoretical probability.

The formula for theoretical probability is:

number of favorable outcomes / total number of outcomes.

Since we have four colors on the spinner, the total number of outcomes is 4. The favorable outcomes are the number of times the spinner will land on blue, which is 1.

So the probability of stopping on the color blue can be calculated as follows:

1 (favorable outcome) / 4 (total number of outcomes) = 1/4

So, the theoretical probability of stopping on the color blue is 1/4. This is because there is an equal chance of landing on any of the four colors, and since there are four colors, each has a 25% chance of being selected.

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Caden's speed is 10 mph and Rahquez's speed is 16 mph faster, which is 16+6 = 32 mph

Let's use the formula: distance = rate x time

Since Caden and Rahquez are traveling towards each other, their combined distance will be 208 miles. Let's call Caden's speed "x" and Rahquez's speed "x+6", since Rahquez is traveling 6 mph faster than Caden.

Using the formula above, we can set up the equation:

208 = (x + x + 6) * 8

Simplifying, we get:

208 = (2x + 6) * 8

208 = 16x + 48

160 = 16x

x = 10

Therefore, Caden's speed is 10 mph and Rahquez's speed is 32 mph.

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Answer:

Step-by-step explanation:

One potential drawback of using a histogram is that it can be sensitive to the choice of bin width or bin size. If the bin size is too small, the histogram may appear too noisy or have too many empty bins, which can obscure patterns in the data. If the bin size is too large, important features of the distribution may be lost or smoothed out. Additionally, histograms do not always show the actual values of the data points, but rather a summary of the data. This means that some details about the data may be lost, such as the exact values of outliers or individual data points.

The fence ought to be cut into 12 pieces, every one of length 28 m, to make three squares, each with a side length of 28 m. This will limit the total area encased by the fence.

To limit the total area encased by the fence, the three squares ought to have equivalent areas. Let x be the length of each side of the squares. Then the perimeter of each square is 4x, and the total length of the fence is 3(4x) = 12x. Since the total length of the fence is given to be 336 m, we have:

12x = 336

Addressing for x, we get:

x = 28

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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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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:

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.

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 ratio of SINA and COSA = 48/50 and 14/50

This is the boundary or contour length of a 2D geometric shape.

Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement.

According to our question,

sina = perpendicular\ hypotenuse

= 48/50

cosa= base\ perpendicular

=

14/50

Hence, The ratio of SINA and COSA = 48/50 and 14/50

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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.

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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