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The probability that the next report will weigh less than 45g is approximately 0.1056 or 10.56%. We can use the standard normal distribution to find the probability that the next report will weigh less than 45g.

z = (x - mu) / sigma

where z is the standard score, x is the value we want to standardize (45g), mu is the mean (60g), and sigma is the standard deviation (12g).

Substituting the given values, we get:

z = (45 - 60) / 12

z = -1.25

Next, we use a standard normal distribution table (or a calculator) to find the cumulative probability of z being less than -1.25. This gives us:

P(z < -1.25) = 0.1056

Therefore, the probability that the next report will weigh less than 45g is approximately 0.1056 or 10.56%.

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The interior angle of a parallelogram is proportional to the measure of another angle with a ratio of 0.25:1.

A parallelogram is a four-sided flat shape that has opposite sides that are parallel and equal in length. The sum of the interior angles of a parallelogram is equal to 360 degrees. If the measure of one interior angle is 0.25 times the measure of another angle, this means that there is a proportionate relationship between the two angles. To find the measure of the second angle, we can use the formula:

Angle 2 = (Angle 1) / 0.25

For example, if Angle 1 is 100 degrees, then Angle 2 is 100 / 0.25 = 400 degrees. This means that if one angle measures 100 degrees, the other angle measures 400 degrees. The sum of the two angles is 500 degrees, which is still less than the total sum of interior angles in a parallelogram, which is 360 degrees.

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The area of the given figure is 12 square meters

The given figure is a parallelogram

Parallelogram is a geometric figure that has both pair of opposites parallel sides and opposite sides are equal . Number of vertices and edges are four

The height of the parallelogram = 2 meters

The base length of the parallelogram = 6 meters

The area of the parallelogram = The height of the parallelogram × The base length of the parallelogram

Substitute the values in the equation

The area of the parallelogram = 2 × 6

Multiply the numbers

= 12 square meters

Therefore, the area is 12 square meters

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I have solved the question in general , as the given question is incomplete

The complete question is :

What is the area of the figure ?

m∠1 = m∠5, because alternate exterior angles are congruent.

Angles formed by intersecting two parallel lines with a transversal are known as angles in parallel lines.

Given:

lines a and b intersect a transversal, c.

The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles.

m∠1 = m∠5 (Alternate exterior angles are congruent)

m∠1 = m∠5, because alternate exterior angles are congruent.

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The Complete Question is attached below.

now, we're assuming the deposits of $5000 are made at the beginning of the year.

[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]

[tex]\begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 5000\\ r=rate\to 3.2\%\to \frac{3.2}{100}\dotfill &0.032\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &25 \end{cases}[/tex]

[tex]A=5000\left[ \cfrac{\left( 1+\frac{0.032}{1} \right)^{1 \cdot 25}-1}{\frac{0.032}{1}} \right]\left(1+\frac{0.032}{1}\right) \\\\\\ A=5000\left[ \cfrac{\left( 1.032 \right)^{ 25}-1}{0.032} \right]\left(1.032\right) \implies A \approx 193148.73[/tex]

The highest common factor, HCF of 18, 54, and 81 is 9.

The highest common factor is the highest factor or number that can divide two or more numbers evenly without a remainder.

The common factors of 18, 54, and 81 are 1, 2, 3, 6, and 9 because each of these numbers can divide the three numbers without a remainder.

Based on the common factors of 18, 54, and 81, we can identify that the highest factor is 9.

The highest common factor, HCF, is also described as the greatest common factor, GCF.

Thus, the HCF of 18, 54, and 81 is 9.

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What is the HCF of 18, 54, and 81?

Answer:

[tex]10^{1}[/tex]

Step-by-step explanation:

13 + 9 - 1 - 11

Add 13 and 9 to get 22.

22 - 1 - 11

Subtract 1 from 22 to get 21.

21 - 11

Subtract 11 from 21 to get 10.

10

The  probability that a product will operate properly within an expected time frame is the dimension of quality known as reliability

The probability is the ratio of the number of favorable outcomes to the total number of outcomes. The value of the probability is varies from zero to one

Here, the product will operate properly within an expected time frame is the dimension of quality

Reliability is expressed as the probability that a given item will perform its intended function with no failures for a given period of time under a given set of conditions that means the reliability is the complementary to the failure of probability

Therefore, the given statement is know as the reliability

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Range of the function shown by the graph is (-∞ , ∞)

Range is a statistical measurement of dispersion, or how much a given data set is stretched out from smallest to largest.

The range is the set of possible output values, which are shown on the

y -axis.

Given,

Graph of a function,

Range represents the y-coordinate of the function.

By the graph,

Range of the function is -∞ < y < ∞.

In interval notation,

Range = (-∞ , ∞)

Hence, (-∞ , ∞) is the range of the function shown by the graph.

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The probability that the sum of the two selected numbers is even is 1/2.

The parity of the two chosen numbers must match for the sum to be even.

Given this information, we can divide the larger problem into smaller ones. First, we may determine the likelihood that the first spinner will land on an even number.

Exists a [tex]$\frac{1}{2}$[/tex] chance that this happens, and a [tex]$\frac{1}{3}[/tex] there is a chance that the second spinner will also land on an even number, hence

[tex]$\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}$[/tex]

There is a win if both the first and second spinners land on an odd number.

[tex]$\frac{1}{2} \cdot \frac{2}{3} = \frac{2}{6}$[/tex]

chance of this happening. Adding these two probabilities together, we get

[tex]\frac{1}{6} +\frac{2}{6} =\frac{3}{6} =\frac{1}{2}[/tex]

Therefore, The probability that the sum of the two selected numbers is even is 1/2.

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Answer:

y = 2x -14

Step-by-step explanation:

The point-slope form is y =  mx + b

m = 2

y-intercept is located at (0, -14)

So, the equation is

y = 2x - 14

Answer:

y-6=2(x-4)

Step-by-step explanation:

point-slope form y-y1=m(x-x1)

The double-angle identity for cosine is cos(2x) = cos²(x) - sin²(x).

To derive the reduction identities, we can use this double-angle identity and manipulate it to express cosine or sine of x in terms of cosine or sine of a smaller angle. Here are the steps for deriving the reduction identity for cosine: Start with the double-angle identity: cos(2x) = cos²(x) - sin²(x).

Divide both sides by cos²(x): cos(2x) / cos²(x) = (cos²(x) - sin²(x)) / cos²(x).

Use the identity sin²(x) + cos²(x) = 1 to replace cos²(x) in the denominator: cos(2x) / cos²(x) = (1 - sin²(x)) / cos²(x).

Rearrange the right-hand side: cos(2x) / cos²(x) = 1/cos²(x) - sin²(x) / cos²(x).

Recognize that 1/cos²(x) is equal to sec²(x), and use the identity tan²(x) + 1 = sec²(x) to replace it: cos(2x) / cos²(x) = sec²(x) - tan²(x).

Simplify using the identity cos(x)/sin(x) = cot(x): cos(2x) / cos²(x) = cosec²(x) - cot²(x).

Simplify the left-hand side using the identity cos(2x) = 2cos²(x) - 1: (2cos²(x) - 1) / cos²(x) = cosec²(x) - cot²(x).

Rearrange and simplify: 2 - (1/cos²(x)) = cosec²(x) - cot²(x).

Recognize that 1/cos²(x) is equal to sec²(x) and cosec(x) is equal to 1/sin(x): 2 - sec²(x) = 1/sin²(x) - cot²(x).

Simplify the left-hand side using the identity 1 - sin²(x) = cos²(x): cos²(x) - sec²(x) = 1/sin²(x) - cot²(x).

Recognize that sec(x) is equal to 1/cos(x) and cot(x) is equal to cos(x)/sin(x): cos²(x) - 1/cos²(x) = sin²(x)/cos²²(x) - cos²x)/sin²(x).

Simplify: cos⁴(x) - 1 = sin²(x) - cos⁴(x).

Rearrange: 2cos⁴(x) = sin²(x) + 1.

Finally, recognize that sin²(x) + cos²(x) = 1, and use it to replace sin²(x): 2cos⁴(x) = cos²(x). This is the reduction identity for cosine: cos²(x/2) = (1 + cos(x))/2.

To derive the reduction identity for sine, we can use the same double-angle identity for cosine and manipulate it to express sine of x in terms of sine or cosine of a smaller angle. The steps are similar but may require using different.

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The total number of cows is given by the equation c = 182 cows and the total number of legs of cows is n = 728 legs

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The total number of cows and goats = 452

So , c + g = 452   be equation (1)

And , ( 5/7 )c = ( 13/27 )g

On simplifying the equation , we get

c = ( 13 x 7 ) / ( 5 x 27 ) g

c = ( 91/135 )g   be equation (2)

Substituting the value of c in equation (1) , we get

( 91 / 135 ) g + g = 452

On further simplification , we get

( 91 + 135 ) / 135 g = 452

( 226 / 135 ) g = 452

Divide by 226 on both sides of the equation , we get

( 1/135 )g = 2

Multiply by 135 on both sides of the equation , we get

g = 270 goats

Now , the number of cows = 452 - 270 = 182 cows

The number of legs = 182 x 4 = 728 legs

Hence , the number of cows is 182 cows

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The factory sales of electronic goods from a certain country to dealers from 1990 to 2001 can be modeled using a mathematical equation .

Modeling factory sales of electronic goods from a certain country to dealers from 1990 to 2001 involves creating a mathematical equation to represent the data . To begin, one must collect the data from the sales of electronic goods from the given country to dealers from 1990 to 2001. This data should include the total amount sold for each year. Once the data is collected it must be organized into a visual representation, such as a line graph or a scatter plot. The visual representation should then be examined for patterns in the data which can be used to create a mathematical equation. This equation should be able to accurately describe the data and be able to predict future data points. The equation should then be tested to ensure accuracy before it is used to model the factory sales data.

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Answer:

118

Step-by-step explanation:

Let the original number be x.

After subtracting 3, the result is x - 3.

When this result is multiplied by 5, we get (x - 3) * 5 = 575.

Expanding and solving for x, we have:

5x - 15 = 575

5x = 590

x = 118

So the original number was 118.

Answer:

the equation 2 - 8 + 33 = 0 can be factored as 27 = 0, which is a verified answer

Step-by-step explanation:

To factor the equation 2 - 8 + 33 = 0, we start by collecting all the terms on one side of the equation:

2 - 8 + 33 = 0

becomes

33 - 8 + 2 = 0

Next, we can rewrite this as:

33 - 6 = 0

Finally, we factor the left-hand side of the equation to get:

33 - 6 = (33 - 3) - 3 = 30 - 3 = 27 - 0

So the factored form of the equation 2 - 8 + 33 = 0 is 27 = 0.

Verification: We can verify that the factored form of the equation is correct by substituting 0 for 27 and checking that the equation holds. So, if we replace 0 for 27 in equation 27 = 0, we get:

27 = 0, which is true.

Therefore, the equation 2 - 8 + 33 = 0 can be factored as 27 = 0, which is a verified answer.

The compound interest rate charged is given as follows:

13% per year.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

P = 12000, A(t) = 22109.22, n = 1, t = 5.

Hence the interest rate is obtained as follows:

22109.22 = 12000(1 + r)^5

(1 + r)^5 = 22109.22/12000

1 + r = (22109.22/12000)^(1/5)

1 + r = 1.13

r = 1.13 - 1

r = 0.13.

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The values that van be put in the table based on the information will be:

Buying price (dollars) 100.

Mark-up 80.

Selling price 180

Commission 20

Profit 60

Buying price (dollars) 10

Mark-up 8

Selling price 18

Commission 2

Profit 6

Buying price (dollars) 55

Mark-up 44

Selling price 99

Commission 11

Profit 33

Buying price (dollars) 125

Mark-up 100

Selling price 225

Commission 25

Profit 75

It should be noted that the markup is 80% of the buying price. For example, when the buying price is $10, the markup will be:

= 80% × $10

= $8

The selling price is that addition of buying price and markup. This will be:

= $10 + $8

= $18

The commission is 25% of markup. This will be:

= 25% × 8

= $2

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The tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

What is Circle?

A circle is a two-dimensional geometric shape that is defined as the set of all points in a plane that are a fixed distance away from a given point, called the center of the circle. This distance is known as the radius of the circle.

A circle can also be defined as the locus of a point that moves in a plane in such a way that its distance from a fixed point is constant. The constant distance is the radius of the circle.

The minute hand on a clock makes a full rotation in 60 minutes, which means it travels the circumference of a circle with a radius of 23 cm in 60 minutes. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.

Therefore, the circumference of the circle traced by the tip of the minute hand is:

C = 2πr = 2 × 3.14 × 23 cm ≈ 144.44 cm

To find out how far the minute hand travels in 11 minutes, we need to calculate what fraction of the circumference it covers in that time. Since 11 minutes is about 18.3% of an hour (60 minutes), the minute hand travels 18.3% of the circumference of the circle in that time:

Distance traveled = 0.183 × 144.44 cm ≈ 26.4 cm

Therefore, the tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

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The value of  m∠ABD is equals to  125 degrees.

Rectangle can be defined in which opposite sides are equal.

AC and BD are diagonals of the rectangle ABCD.

Angle ABD is adjacent to angle 1 and angle ABO, where O is the intersection of diagonals AC and BD.

We know that m∠1 = 55, and we can find m∠ABO using the fact that the diagonals of a rectangle bisect each other. Since angle AOB is opposite to side AB, which is congruent to side CD, we have:

m∠ABO = 180 - m∠AOB

= 180 - (180 - m∠1) / 2

= 180 - (180 - 55) / 2

= 62.5

Therefore, we can find m∠ABD by adding m∠ABO and m∠DBO, where DBO is congruent to ABO:

m∠ABD = m∠ABO + m∠DBO

= m∠ABO + m∠ABO

= 2m∠ABO

= 2(62.5)

= 125

Hence, The value of  m∠ABD is 125 degrees.

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The equation to represent the given scenario is 642=239+64x.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Ed is on a road trip. He has already traveled 239 miles and is driving at a rate of 64 miles per hour.

Let x be the number of hours.

We know that, Distance =Speed×Time

Now, total distance = 239+64×x

642=239+64x

Therefore, the equation to represent the given scenario is 642=239+64x.

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The given value 4.1 x 10^-4 can be written in standard form as 0.00041

The standard form can be done by following the format of multiplying a *10^b where b is the power and a is the digit.

A number can be expressed in a fashion that adheres to specific standards by using its standard form. Standard form refers to any number that may be expressed as a decimal number between 1.0 and 10.0 when multiplied by a power of 10.

Hence 4.1 x 10^-4 = 0.00041

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Answer:

Answer is in the attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note for this question, we will have to make x the subject and solve for x.

The vertex of the given graph is (5, 0)

A vertex is a point on a polygon where two rays or line segments meet, and the sides or edges of the object come together. Vertex is the plural form of vertices.

A straight line that can be extended endlessly is known as a ray. An angle is created when two line segments or rays cross one another. A vertex is created by definition whenever two lines come together to produce an angle.

Thus, we can state that a vertex is formed when two line segments or rays intersect.

Here we have a graph  

The equation of the graph is y = |x - 5| + 1  

As we can see that two lines are intersected at a point (5, 0)

Therefore,

The vertex of the given graph is (5, 0)

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If repetitions of colors are allowed, there are 59,049 possible selections of collars for the 5 cats.

If Dave can choose from 9 different colors for each of his 5 cats, then he has 9 choices for the first cat, 9 for the second cat, and so on. To find the total number of possible selections, we can multiply the number of choices for each cat together:

9 x 9 x 9 x 9 x 9 = 59,049

In this case, there are 9 ways to choose the collar color for the first cat. Since Dave can choose from the same 9 colors for each of the 5 cats, so he has 9 choices for each cat. Therefore, by the principle of counting, the total number of ways to choose collars for all 5 cats is:

Therefore, if repetitions of colors are allowed, there are 59,049 possible selections of collars for the 5 cats.

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Answer:

39

Step-by-step explanation:

165 and 3/4 is equal to 165.75 and 4 and 1/4 is 4.25

165.75/4.25=39

39 uniforms could be made

Answer:

Step-by-step explanation:

There are 256 people in a room. If they are divided into groups of 4, how many groups are there?

Answer: 64

We are told that the probability of drawing a red ball doubles when an extra 6 red balls are added.

Let's assume that there are initially "x" red balls in the box. This means that there are (12 - x) non-red balls in the box.

When 6 more red balls are added, the total number of red balls becomes (x + 6), and the total number of balls in the box becomes (12 + 6) = 18.

We are told that the probability of drawing a red ball doubles when an extra 6 red balls are added. This means that the probability of drawing a red ball before the extra balls were added was:

P(red) = x / 12

And the probability of drawing a red ball after the extra balls were added is:

P(red) = (x + 6) / 18

We are also told that the second probability is twice the first:

(x + 6) / 18 = 2 * (x / 12)

Simplifying this equation, we get:

(x + 6) / 9 = x / 6

Multiplying both sides by 18, we get:

2(x + 6) = 3x

Expanding the left-hand side, we get:

2x + 12 = 3x

Subtracting 2x from both sides, we get:

12 = x

Therefore, there are initially 12 red balls in the box.

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Circle A is larger.

Circle A's radius is 58 cm and circle B's radius is 57 cm.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

We have,

Area of a circle = πr²

Circumference of a circle = 2πr

Circle A:

Area of a circle = 10562.96

πr² = 10562.96

r² = 3364

r = 58 cm ____(1)

Circle B:

Circumference = 357.96

2πr = 357.96

r = 357.96/6.28

r = 57 cm ______(2)

From (1) and (2)

58 > 57

So,

Circle A is larger.

Thus,

Circle A is larger.

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