A company is trying to reduce the cost of
producing one of its tools. It comes up with
a much cheaper new method of production.
A large box of tools produced by both methods
is examined by testers.
1. Two tools are selected at random, one at a time.
Part A (3 points)
One tool is chosen at random from the box. It is then replaced. A tool is
selected again. What is the probability that both selections were acceptable?
Are the events dependent or independent events? Explain.
Old Method
New Method
Acceptable
1,640
328
Defective
23
9
Part B (3 points)
One tool is chosen at random from the box. It is not replaced. A tool is selected
again. What is the probability that the first one was produced by the old
method and the second one by the new method? Are the events dependent or
independent events? Explain.

Answer:

0.5

Step-by-step explanation:

We want to get an equation with only one variable for it to be able to be solved.

To do this, we will solve the first equation for y.

[tex]x+y=2\\y=2-x[/tex]

Now, we can plug this value of y into the second equation

[tex]7x-y=2\\7x-(2-x)=2\\[/tex]

Finally, we have just one variable, and we can solve for x.

[tex]7x-(2-x)=2\\7x-2+x=2\\8x=4\\x=0.5[/tex]

Answer:

To make 10 liters of 20% alcohol solution, RSM would need to use a combination of the 18% and 40% alcohol solutions. Let's call the amount of 18% solution used "x" and the amount of 40% solution used "y".

To set up the equation, we'll use the fact that the amount of pure alcohol in the final solution must be equal to 20% of the total volume.

So:

0.18x + 0.40y = 0.20(10)

Simplifying:

0.18x + 0.40y = 2

We have one equation with two unknowns, which means we need another equation. Fortunately, we know that RSM is making a total of 10 liters of solution. So:

x + y = 10

We now have two equations with two unknowns, which we can solve simultaneously. One way to do this is to solve one equation for one variable, then substitute that expression into the other equation, like so:

x = 10 - y (from the second equation)

0.18(10-y) + 0.40y = 2 (substituting into the first equation)

1.8 - 0.18y + 0.40y = 2

0.22y = 0.2

y = 0.91

So RSM would need to use approximately 0.91 liters (or 910 milliliters) of the 40% solution, and the rest (9.09 liters or 9090 milliliters) of the 18% solution, to make 10 liters of 20% alcohol solution.

Answer:

74.43 pounds

Step-by-step explanation:

To find the amount of oxygen needed in the outer tank, we need to first find the volume of the space between the two tanks. This space is a rectangular prism with length 20 feet, width 8 feet, and height 6 feet, but with a rectangular prism removed from the center. The removed prism has length 5 feet, width 4 feet, and height 3 feet.

The volume of the rectangular prism between the two tanks is:

V = (20 x 8 x 6) - (5 x 4 x 3)

V = 960 - 60

V = 900 cubic feet

To find the amount of oxygen needed to fill this space with a density of 0.0827 pounds per cubic foot, we can multiply the volume by the density:

m = V x d

m = 900 x 0.0827

m ≈ 74.43 pounds

Therefore, approximately 74.43 pounds of oxygen is required to meet the density requirement.

Answer: 74 pounds

Step-by-step explanation:

(20*8*6) - (5*4*3)

960-60

v=900 ft3

density=0.0827

mass=0.0827*900

Mass is 74 pounds

Answer:

  x = 3√2

Step-by-step explanation:

You want the length x of the hypotenuse of an isosceles right triangle with sides of length 3.

The two legs of an isosceles right triangle are congruent. The length of the hypotenuse can be found from the Pythagorean theorem:

  x² = 3² +3²

  x² = 3²·2

  x = √(3²·2) = 3√2

The length of side x is 3√2.

__

Additional comment

A isosceles right triangle is one of two "special" right triangles. The ratios of its side lengths are 1 : 1 : √2. This tells you the hypotenuse is √2 times the side length, as we found above.

The other "special" right triangle is the 30°-60°-90° triangle. Its side lengths have the ratios 1 : √3 : 2. Both of these are seen often in algebra, trig, and geometry problems.

the radius of the track is approximately 420.38 feet.

Why is it?

The circumference of the circular track is 0.5 miles or 0.5 × 5280 = 2640 feet.

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.

Therefore, 2640 = 2 × 3.14 × r

Simplifying the equation: 2640 = 6.28r

Dividing both sides by 6.28: r ≈ 420.38 feet

Therefore, the radius of the track is approximately 420.38 feet.

Circumference is the distance around the edge of a circle or any other curved, circular object. It is also the perimeter of the circle. It is calculated by multiplying the diameter of the circle by pi (π), which is a mathematical constant that is approximately equal to 3.14.

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The equation that can be used to find d, based on the options for the parts of the equation is; (4/5) × d = 260

An equation is a statement of equivalence between expressions.

The specified equation is;  _ _ d = _

The distance of the first part of Alicia's trip = 260 miles

The part of the total distance traveled of the trip represented by the first part of Alicia's trip = 4/5

The total length of Alicia's trip = d

An equation that can be used to find the total length of Alicia's trip therefore is; (4/5) × d = 260

The total distance traveled, d, can be obtained from the above equation when d is made the subject of the equation as follows;

(4/5) × d = 260

d = 260/(4/5) = 260 × 5/4 = 325

The total distance Alicia traveled, d = 325 miles

The correct equation is therefore; (4/5) × d = 260

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The scale factor of the dilation of the square is (b) 18 : 1

To find the scale factor, we need to determine how many times the length of the original square was multiplied to obtain the length of the new square.

The length of the original square is 4.5 meters, and the length of the new square is 81 meters.

Therefore, we need to divide the length of the new square by the length of the original square to find the scale factor:

81 meters ÷ 4.5 meters = 18

So the scale factor is 18:1.

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Answer:

Step-by-step explanation:

200.55ft³

12×12= 144 (area of the square)

pi×radius² = area of a circle but since it is only half a circle, divide the answer by two and add the area of the semi circle and square for the total area

The equation of circle with endpoints at  (-3, 0) and (3, 0) is x² + y² = 9

The end points (-3, 0) and (3, 0) represent the endpoints of a diameter of the circle. The center of the circle is the midpoint of this diameter. We can find the midpoint of the diameter by averaging the x-coordinates and the y-coordinates of the endpoints:

Midpoint = ((-3 + 3)/2, (0 + 0)/2) = (0, 0)

So the center of the circle is at the point (0, 0). The radius of the circle is half the length of the diameter, which is:

Radius = 1/2 * distance between (-3, 0) and (3, 0)

= 1/2 * 6

= 3

Therefore, the equation of the circle with endpoints at (-3, 0) and (3, 0) is:

(x - 0)² + (y - 0)² = 3²

Simplifying:

x² + y² = 9

So the equation of the circle is x² + y² = 9.

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Answer:

17.2 meters

Step-by-step explanation:

We can use the tangent function to solve this problem. Let's denote the height of the tree as h. Then we have the following:

tan(51°) = h / distance from the tree to the end of the shadow

We can find the distance from the tree to the end of the shadow by using the length of the shadow and the angle of elevation of the sun. Since the shadow is 21 meters long, and the angle of elevation of the sun is 51°, we can use the following trigonometric relationship:

tan(51°) = h / distance from the tree to the end of the shadow

tan(51°) = h / x (where x is the distance from the tree to the end of the shadow)

To find x, we can use the following trigonometric relationship:

tan(39°) = h / x (where 39° is the complementary angle to 51°)

We can solve for x by rearranging this equation as follows:

x = h / tan(39°)

Substituting this expression for x into the first equation, we have:

tan(51°) = h / (h / tan(39°))

Simplifying this equation, we get:

h = (21 m) * tan(51°) / tan(39°)

Using a calculator, we find h to be the following:

h = 17.2 meters

Therefore, the height of the tree is approximately 17.2 meters.

Answer:

x = 8°

Step-by-step explanation:

∠GJL = ∠WJZ = 90° - 18° = 72° (cross angles)

(9x)° = 72° / : 9

x = 8°

Answer:

x = 8

Step-by-step explanation:

Find the measure of angle WJZ.

Since angles on a straight line sum to 180°:

⇒ m∠GJH + m∠HJW + m∠WJZ = 180°

⇒ 90° + 18° + m∠WJZ = 180°

⇒ 108° + m∠WJZ = 180°

⇒ 108° + m∠WJZ - 108° = 180° - 108°

⇒ m∠WJZ = 72°

According to the Vertical Angles Theorem, when two straight lines intersect, the opposite vertical angles are congruent.

Since line GJZ and line LJW intersect, then ∠GJL and ∠WJZ are vertical angles and therefore congruent:

⇒ m∠GJL = m∠WJZ

⇒ (9x)° = 72°

⇒ 9x = 72

⇒ 9x ÷ 9 = 72 ÷ 9

⇒ x = 8

Therefore, the value of x is 8.

Problem: Imagine a person, John, facing a scheduling conflict due to overlapping appointments.

John had a dentist appointment at 2 PM, which he expected to last an hour, but he also had a meeting scheduled with his colleague at 3 PM.

Why it was difficult: The scheduling conflict made it difficult for John to manage both appointments without disappointing either party.
Math used to solve the problem: John decided to calculate the time it would take him to travel from the dentist's office to the meeting location, considering the appointment duration and travel time.
Dentist appointment: 2 PM - 3 PM

Travel time (calculated using distance and speed): 30 minutes
Meeting time: 3 PM
John realized he would be 30 minutes late for the meeting if he attended the dentist appointment.
Outcome: John decided to reschedule his dentist appointment to an earlier time or another day to avoid the conflict.
Approaching the problem differently next time:

In the future, John could consider using a calendar app to keep track of his appointments and avoid scheduling conflicts.

Additionally, he could factor in the duration of events and travel times when scheduling appointments to ensure he has enough time between engagements.

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Step-by-step explanation:

To create a rectangle with vertices located at (-5, 3), (-5, -7), and (5, -7), we need to find the fourth vertex that completes the rectangle. Since opposite sides of a rectangle are parallel and congruent, we can determine the missing vertex by finding the midpoint of either of the two given sides and then moving in the direction perpendicular to that side by the length of the other side.

The given sides are:

Side 1: (-5, 3) to (-5, -7), which has length 3 - (-7) = 10

Side 2: (-5, -7) to (5, -7), which has length 5 - (-5) = 10

Since the sides are congruent, we can find the midpoint of Side 1 as:

Midpoint of Side 1 = [(-5 + (-5))/2, (3 + (-7))/2] = [-5, -2]

To find the missing vertex, we need to move from (-5, -2) in the direction perpendicular to Side 1 by a distance of 10 units (the length of Side 2). Since Side 2 is horizontal, we need to move vertically. We can do this by adding or subtracting 10 from the y-coordinate of the midpoint of Side 1, depending on whether we want to move up or down. In this case, we want to move down, so we subtract 10:

Missing vertex = [-5, -2 - 10] = [-5, -12]

Therefore, the fourth vertex needed to create a rectangle with vertices located at (-5, 3), (-5, -7), and (5, -7) is (-5, -12).

Answer:

the value of T that satisfies the equation 644 204 = 400 000(1+10%) is approximately 6.45.

Step-by-step explanation:

We can simplify the equation 644 204 = 400 000(1+10%) by first simplifying the percentage term on the right-hand side:

10% of 400 000 is equal to 0.1 × 400 000 = 40 000.

So the equation becomes:

644 204 = 400 000(1 + 0.1 × 1)

Now, we can use logarithms to solve for T:

T = log(base 1.1)(644204/400000)

Using a calculator, we can evaluate the right-hand side to be approximately 0.2, so:

T = log(base 1.1)(1.61051)

Using the change of base formula, we can rewrite this as:

T = ln(1.61051) / ln(1.1)

Evaluating the natural logarithms using a calculator, we get:

T ≈ 6.45

The vertices οf the given inequalities are (2,0);(-6,0); (0,-1);(0,-3);(-2,-2)

In mathematics, inequality is  a statement οf an οrder relatiοnship that is a relatiοnship between twο values that are nοt equal,—greater than, greater than οr equal tο, less than, οr less than οr equal tο—between twο numbers οr algebraic expressiοns. Such as 7<9 οr 5>3 etc.

The given system οf inequalities are:

2y-x≥ -2

2y+x≥ -6

y≤0

x≤0

Tο find the vertices we must cοnvert the inequality intο an equatiοn.

Sο the equatiοns are:

2y - x= -2-----------------(1)

2y + x= -6----------------(2)

y=0-----------------(3)

x=0 -----------------(4)

Putting the value οf equatiοn (3) in equatiοn (1) and (2) we get,

x=2 and x= -6

Again putting the value οf equatiοn (4) in equatiοn (1) and (2) we get,

y=-1 and y=-3

Sο frοm these the vertices can be written as (2,0);(-6,0) and (0,-1);(0,-3)

Nοw , subtracting equatiοn (2) frοm equatiοn (1) we get,

( 2y - x )-(2y+x)= -2-(-6)

⇒ -2x= 4

⇒x= -2

Putting this value x=-2 in equatiοn (1) we get,

2y-(-2)=-2

⇒2y+2=-2

⇒2y=-4

⇒ y= -2

Hence the vertices οf the given inequalities are (2,0);(-6,0); (0,-1);(0,-3);(-2,-2)

A graph fοr the inequalities is attached belοw.

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Answer:

Yes the Triangle are similar by A.A.A Axiom

Answer:

yes, they two triangles are similar

Step-by-step explanation:

.........

Answer: To find the premium for insuring the goods, we need to determine the total amount of insurance that is needed and then calculate the cost of the insurance based on the given rate.

The total amount of insurance needed is equal to the value of the goods in transit, which is K95 480.

To determine the cost of the insurance, we can use the given rate of K682 for every K27 200 worth of goods. We can set up a proportion:

(K682 / K27 200) = (premium / K95 480)

To solve for the premium, we can cross-multiply and simplify:

K682 * K95 480 = K27 200 * premium

premium = (K682 * K95 480) / K27 200

premium = K1 897.12

Therefore, the premium for insuring the goods is K1 897.12.

Step-by-step explanation:

The solution set of the given inequality is (-4, 4.4)

Here are the steps to follow when solving absolute value inequalities:

Isolate the absolute value expression on the left side of the inequality.

If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions.

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

|5t-1| > 21

case 1)

for positive

5t-1 > 21

5t > 22

t > 4.4

for negative

-(5t-1) > 21

-5t+1 > 21

-5t > 20

t< -4

hence the solution set of the given inequality is (-4, 4.4)

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 2.7\%\to \frac{2.7}{100}\dotfill &0.027\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{semi-annually}, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]A = 4000\left(1+\frac{0.027}{2}\right)^{2\cdot 10}\implies A=4000(1.0135)^{20} \implies \boxed{A \approx 5230.40} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Annual Percent Yield Formula} \\\\ ~~~~~~~~~~~~ \left(1+\frac{r}{n}\right)^{n}-1 ~\hfill \begin{cases} r=rate\to 2.7\%\to \frac{2.7}{100}\dotfill &0.027\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{semi-annually}, thus twice} \end{array}\dotfill &2 \end{cases} \\\\\\ \left(1+\frac{0.027}{2}\right)^{2}-1\implies 1.0135^2-1\approx 0.02718 ~~ \approx ~~ \stackrel{ 0.02718\times 100 }{\boxed{2.718~\%}}[/tex]

Answer:

A disadvantage to using equations for solving problems might be that it can be difficult to remember what an equation means without a diagram, graph, or table (Option A).

Step-by-step explanation:

Answer:

  step 1

Step-by-step explanation:

You want to know which step in Marta's simplification of 4·log₅(x) +log₅(2x) -log₅(3x) contains an error in application of properties of logarithms.

  log(a^b) = b·log(a)

  log(ab) = log(a) +log(b)

  log(a/b) = log(a) -log(b)

  [tex]4\log_5(x)+\log_5(2x)-\log_5(3x)\\\\=\log_5(x^4)+\log_5(2x)-\log_5(3x)\qquad\text{Step 1. Mistake: $4x$ instead of $x^4$}\\\\\log_5(x^4\cdot2x)-\log_5(3x)=\log_5\left(\dfrac{2x^5}{3x}\right)\\\\=\boxed{\log_5\left(\dfrac{2x^4}{3}\right)}[/tex]

The steps to find surface area of pyramid using a net of square pyramid is given below.

find the surface area of a square pyramid using a net:

The slant height of a square pyramid can be found using the Pythagorean theorem, where a and b are the length of one side of the base and h is the height of the pyramid:

slant height = √(a² + (1/2×h)²)

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The two are similar because both use a percentage as a decimal to get a new price.

Answer:

272.14100

Subtract 47.96 from 320.041

320.041 - 47.96 = 272.14100

Answer:

272.081

Step-by-step explanation:

You're welcome

According to the question the expected net gain for a player on a $1 straight bet is -$0.60.

Simply multiply each value of the discrete random variable X by its probability and add the products to get the expected value, E(X), or mean. The formula is as follows: E (X) =  ∑ x P (x)

The possible outcomes for X are winning with a probability of 1/1000 and net gain of $399, and losing with a probability of 999/1000 and net gain of -$1. Therefore, we can calculate the expected value of X as follows:

E(X) = (1/1000)($399) + (999/1000)(-$1)

E(X) = $0.399 - $0.999

E(X) = -$0.60

Therefore, the expected net gain for a player on a $1 straight bet is -$0.60. This means that, on average, a player will lose $0.60 for each $1 bet they place on this game.

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Answer:

-0.60

Step-by-step explanation:

Khan Academy

It would take the giant tortoise approximately 21.43 hours to travel 3 miles at a rate of 0.14 miles per hour.

What is distance?

Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance is a scalar quantity, meaning it has only magnitude and no direction.

We can use the formula:

time = distance ÷ speed

where "distance" is the total distance to be traveled and "speed" is the rate of travel.

In this case, the distance is 3 miles and the speed is 0.14 miles per hour. So we can substitute these values into the formula and solve for "time":

time = 3 miles ÷ 0.14 miles per hour

time ≈ 21.43 hours

Therefore, it would take the giant tortoise approximately 21.43 hours to travel 3 miles at a rate of 0.14 miles per hour.

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