Stereo speakers are manufactured with a probability of 0.100.10 being defective. TwentyTwenty speakers are randomly selected. Let the random variable X be defined as the number of defective speakers. Find the expected value and the standard deviation.

Answer:

Let's start by assigning a variable to Susan's present age. Let's call it "x".

According to the problem, in seven years, Susan will be "x + 7" years old.

Three years ago, Susan was "x - 3" years old.

The problem tells us that Susan will be 2 times as old in seven years as she was 3 years ago. So we can set up the following equation:

x + 7 = 2(x - 3)

Now we can solve for x:

x + 7 = 2x - 6

x = 13

Therefore, Susan's present age is 13 years old.

Let's assume Susan's present age is "x" years. According to the information provided, "Susan will be 2 times old in seven years as she was 3 years ago."

Seven years from now, Susan's age would be x + 7, and three years ago, her age would have been x - 3. According to the given statement, her age in seven years will be two times her age three years ago:

x + 7 = 2(x - 3)

Let's solve this equation to find Susan's present age:

x + 7 = 2x - 6

Subtracting x from both sides:

7 = x - 6

Adding 6 to both sides:

13 = x

Therefore, Susan's present age is 13 years.

The method you would use to prove the two triangles are congruent include the following: B. ASA.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.

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Missing information:

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

you did not provide enough information to answer the question

Answer:

B: Yes, because 5 miles is (8800) yards and 30 times around the route is ( ) yards.

Step-by-step explanation:

Delaney plans to run at least 5 miles each week for her health. Delaney has a circular route in the neighborhood to run. Once around that route is 420 yards. If runs that route times during the​ week, will cover at least 30 ​miles?

Answer:

0.032

Step-by-step explanation:

Answer:  0.03284281007

Step-by-step explanation:

Using function concepts, we have that:

The actual percentage of smokers in 2010 was of 23%, while the estimated was of 13%, thus, the model underestimated the percentage by 10%.

-----------------------------

The function is:

\(p + \frac{x}{2} = 33\)

In which

The percentage can be written as a function of the number of years, that is:

\(p(x) = 33 - \frac{x}{2}\)

-----------------------------

2010 is 2010 - 1970 = 40 years after 1970, thus, the estimate of the percentage in 2010 is:

\(p(40) = 33 - \frac{40}{2} = 33 - 20 = 13\)

The actual percentage of smokers in 2010 was of 23%, while the estimated was of 13%, thus, the model underestimated the percentage by 10%.

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let's solve for f :

Taking reciprocal of both sides :

Answer:

The perimeter of an equilateral traingle with height 42cm is 126cm.

Step-by-step explanation:

Given that the height or edge of an equilateral traingle is 42cm. With this information, we are asked to find the perimeter of an equilateral traingle.

The perimeter of equilateral traingle is defined as the three times of the length of edge. Mathematically;

→ Perimeter = 3a

By substituting the given values in the formula, we get the following results:

→ Perimeter = 3(42)

→ Perimeter = 126

Hence, the perimeter of an equilateral traingle with height 42cm is 126cm.

Additional information:

Answer:

267,000

Step-by-step explanation:

\(2\frac{7}9}\)

\((-1\frac{2}{3})^{2}=(-\frac{5}{3})^{2}=\frac{-5^{2}}{3^{2}}=\frac{25}{9}=2\frac{7}9}\)

The longest diagonal in the box is approximately 11.5758 inches.

What is Cuboid?

A cuboid is a three-dimensional shape that has six rectangular faces. It is also known as a rectangular prism and can be defined as a solid figure with a length, width, and height, where all the faces are rectangles.

To find the longest diagonal in a box, we need to find the length of the longest line segment that can be drawn from one corner of the box to the opposite corner. This line segment is the diagonal of the box.

Using the Pythagorean theorem, we can find the length of the diagonal. Let's label the dimensions of the box as follows:

Length = 3 inches

Width = 5 inches

Height = 10 inches

We want to find the length of the longest diagonal, which we'll call "d". Using the Pythagorean theorem, we have:

d² = 3² + 5² + 10²

d² = 9 + 25 + 100

d² = 134

FTaking the square root of both sides, we get:

d = √(134) ≈ 11.5758

Therefore, the longest diagonal in the box is approximately 11.5758 inches.

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The radius of the semicircle protractor is approximately 4.693 cm.

Given,Perimeter of a semicircle protractor = 14.8 cm.

To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.

Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =\((1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693\) cm.

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Answer:9

Step-by-step explanation:

Answer:

x=3mod4

Means that when x is divided by 4 it gives an unknown integer and a remainder of 3.

x/4 = Z + 3/4

Z= (x-3)/4

Where Z is the integer

x=5 mod6

x/6 = Y + 5/6

Y = (x-5)/6

Where Y is the integer

Z-Y must be an integer on equal to zero

(x-3)/4 - (x-5)/6

3(x-3)/12 - 2(x-5)/12

(3x-9-2x+10)/12

(x+1)/12

If it is equal to 0

x=-1. But x should be positive

If it is equal to 1

x=11

Hence the smallest possible number is 11

The age of the paint is 14,290.0 years old

For any particular drug, understanding the concept of half-life is helpful in calculating steady-state concentrations and excretion rates. Although different drugs have different half-lives, they all adhere to the same principle: 50% of the initial drug dose is eliminated from the body after one half-life.

Since radiocarbon (14C) has a half-life of 5700 30 years, it is especially helpful for dating in archaeology. However, the so-called Gamow-Teller ß-decay, an exceptional hindrance to the beta decay from 14C to 14N, is what causes this half-life to be so long.

According to the given question :-

0.18 = e^(-0.00012t)

ln(0.18) = -0.00012t

t = - ln(0.18) / 0.00012 ≈ 14289.98690076605833 ≈ 14,290.0 years old

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She is standing in front of a wall which is 10 feet away when she kicks the ball and it hits the wall and comes back to her by the virtue of Newton's third Law of motion! She kicks the ball into the air vertically above her and the ball rises to 10 feet and then comes back to her by the virtue of gravity!

The rear windshield wiper of a car rotated 120 degrees, as shown in the figure. The area cleared by the wiper blade is approximately 205.875 square inches.

The problem states that a car’s rear windshield wiper rotates 120 degrees, as shown in the figure. Our aim is to find the area cleared by the wiper.

The wiper's arm is represented by a line segment and has a length of 14 inches.

The wiper's blade is perpendicular to the arm and has a length of 25 inches.

Angular degree measure indicates how far around a central point an object has traveled, relative to a complete circle. A full circle is 360 degrees, and 120 degrees is a third of that.

As a result, the area cleared by the wiper blade is the sector of a circle with radius 25 inches and central angle 120 degrees.

The formula for calculating the area of a sector of a circle is: A = (θ/360)πr², where A is the area of the sector, θ is the central angle of the sector, π is the mathematical constant pi (3.14), and r is the radius of the circle.

In this situation, the sector's central angle θ is 120 degrees, the radius r is 25 inches, and π is a constant of 3.14.A = (120/360) x 3.14 x 25²= 0.33 x 3.14 x 625= 205.875 square inches, rounded to the nearest thousandth.

Therefore, the area cleared by the wiper blade is approximately 205.875 square inches.

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If the scale of her drawing is changed  from 1:6 to 1:4, the new scale will be larger than the original scale as 1 unit is represented by 4 inches.

To find the area of the hanger H, we will need to split the H into different rectangular parts and find their area, after which we add all the numbers up together.

The total area of H = 60 in. + 18 in. + 60 in.

Total Area of H = 138 in.²

The total area of the entire rectangular figure is 720 in.² Thus;

The total area of the beige colored area is; 720 in.² - 138 in.² = 582 in.²

Total area of the beige area is 582 in.²

The percentage of 582 in.² out of 720 in.² is;

582 in.²/720 in.² = 80.83 %

Thus, 80.83% of the entire rectangular figure will be beige colored.

Now,  if the scale of her drawing is changed  from 1:6 to 1:4, the new scale will be larger than the original scale as 1 unit is represented by 4 inches.

Dimensions of the new scale drawing = 5(3/2) = 7.5 inches by 4(3/2) = 6 inches

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The ratio of the strawberries to the blueberries is 32 strawberries: 30 blueberries (option d).

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s). The sign that is used to represent ratio is :.

The ratio of strawberries to blueberries - total number of strawberries : total number of blueberries.

(8 x 4) : 30

32 : 30

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Answer: A. 8 strawberries: 30 blueberries

Step-by-step explanation:

Answer:

The area of the shaded region is 3.

Step-by-step explanation:

Since point E lies halfway between AB and BC, the area of the shaded region (As) consists of two identical triangles with base equal to AB and height equal to half the measure of BC:

\(A_s=2 * A_t\)

Where At is the area of each triangle.

\(\displaystyle A_t=\frac{AB*BC/2}{2}\)

\(\displaystyle A_t=\frac{AB*BC}{4}\)

We know AB=3 and BC=2, thus:

\(\displaystyle A_t=\frac{3*2}{4}=\frac{6}{4}\)

Simplifying:

\(\displaystyle A_t=\frac{3}{2}\)

Finally:

\(\displaystyle A_s=2 * \frac{3}{2}\)

\(A_s=3\)

The area of the shaded region is 3.

Note the area of the shaded region is half the area of the rectangle.

Answer:

-Picture attached-

Step-by-step explanation:

The gradient would be 4, with a rising graph and the y-intercept would be 1. I attached a picture of the graph, hope it helps.

-3.75 +4.35 -6.55

-3.75 + 4.35 = 0.6

0.6 - 6.55 = - 5.95

- 3.75 + 4.35 - 6.55 = - 5.95

The domain of the function → y = √√√x is -

Domain → [0, + ∞)

Domain is the set of {x} - values for which a function {y - values} exists. It is one of the important parameter while defining the characteristics of a function.

Given is the function -

y = √√√x

Domain is the set of values along the {x} - axis. The given function is -

y = √√√x

y = √√√x = \($x^{\frac{1}{8} }\)

Refer to the graph of the function attached. We can write the domain as -

Domain → [0, + ∞)

Therefore, the domain of the function is -

Domain → [0, + ∞)

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i) 4 more gallons of petrol will be needed to complete the journey.

ii) The cost of the petrol for the 420 km journey is GH¢55.00.

i) To determine the number of gallons of petrol needed to complete the journey, we can calculate the total distance that can be covered with the available petrol and then subtract it from the total distance of the journey.

Given that the car consumes 1 gallon of petrol for every 30 km, we can calculate the distance that can be covered with 10 gallons of petrol by multiplying 10 (gallons) by 30 (km/gallon):

Distance covered with 10 gallons = 10 * 30 = 300 km

To find the remaining distance that needs to be covered, we subtract the distance covered with the available petrol from the total distance of the journey:

Remaining distance = Total distance - Distance covered with available petrol

Remaining distance = 420 km - 300 km = 120 km

Since the car consumes 1 gallon of petrol for every 30 km, we can determine the additional gallons of petrol needed by dividing the remaining distance by 30:

Additional gallons needed = Remaining distance / 30 = 120 km / 30 km/gallon = 4 gallons

Therefore, the driver will need 4 more gallons of petrol to complete the journey.

ii) To calculate the cost of the petrol for the journey of 420 km, we need to multiply the total number of gallons used for the journey by the cost per gallon.

Given that a gallon of petrol costs GH¢5.50, and the total number of gallons used for the journey is 10 (given in the problem), we can calculate the cost using the formula:

Cost of petrol = Total gallons used * Cost per gallon

Cost of petrol = 10 gallons * GH¢5.50/gallon = GH¢55.00

Therefore, the cost of the petrol for the journey of 420 km is GH¢55.00.

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The formula that can be use to determine the present value of the cash inflows of both alternatives is: PV = CF1/(1+r)^1 + CF2/(1+r)^2 + ... + CFn/(1+r)^n.

Using this formula to find the present value(PV) of the cash inflow for the two alternatives;

PV = CF1/(1+r)^1 + CF2/(1+r)^2 + ... + CFn/(1+r)^n.

Where:

PV = Present value

CF =Cash flow

r = Discount rate

n= Number of periods

Therefore the formula is: PV = CF1/(1+r)^1 + CF2/(1+r)^2 + ... +CFn/(1+r)^n.

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Answer:

The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.

Step-by-step explanation:

What is probability?

Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.

To find which 2 books describe a pair of dependent events:

A pair of two dependent events are simply those in which the selection of the second item is contingent on the selection of the first item, causing the probability to change.

Because the sample size is lowered when the initial item is taken without replacement, choosing the exact same item reduces the chance.

Now, in regard to the question, this means that for two of the occurrences to be independent, they must be on the same shelf and of the same type of book, so that the second book cannot be selected until the first one is.

Option D, where both books are on the same shelf and are of the same type, is the only option that fulfills this requirement.

Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.

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The equivalent exponential equations are given as follows:

\(2^{4x} = 2^{3(x - 3)}\)

The exponential expression for this problem is defined as follows:

\(2^{4x} = 8^{x - 3}\)

The number eight is the third power of 3, that is:

8 = 2³.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:

\(8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}\)

Meaning that the correct option is given by the fourth option.

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The appropriate Taylor series for an infinite series with the first four nonzero terms equal to ln(5/3) is 0/1!, 0/2!, 0/3!, and 0/4! .......

An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics. Near this point, the function and the sum of its Taylor series are equivalent for the majority of common functions. The polynomial or function of an infinite sum of terms is the Taylor series. The exponent or degree of each succeeding term will be greater than the exponent or degree of the one before it.

The formula is:

∑​n=0​ to ∞(fⁿ(a)(x-a)ⁿ)/n!

Here,

∑​n=0​ to ∞(fⁿ(a)(x-a)ⁿ)/n!

at n=1,

=0/1!

at n=2,

=0/2!

at n=3,

=0/3!

at n=4,

=0/4!

Appropriate taylor series for first four nonzero terms of an infinite series that is equal to ln(5/3) is 0/1!, 0/2!, 0/3!, 0/4!.......

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​​

Answer:

h is the horizontal translation

k is the vertical translation

a is the stretch parallel to the y-axis

Step-by-step explanation:

Parent equation:  \(y=x^2\)

Translate \(h\) units right:  \(y=(x-h)^2\)

(if \(h < 0\), then the translation is \(h\) units left)

Stretched parallel to the y-axis by a factor of \(a\):  \(y=a(x-h)^2\)

(if \(a < 0\), the graph is also reflected in the x-axis)

Translated k units up:  \(y=a(x-h)^2+k\)

(if \(k < 0\) then the translation is k units down)

Example attached for \(y=2(x-3)^2+4\)