a store gathers some demographic information from their customers. the following chart summarizes the age-related information they collected:agenumber of customers7220-305230-4010040-507150-606960one customer is chosen at random for a prize giveaway.what is the probability that the customer is at least 20 but no older than 60? what is the probability that the customer is either older than 40 or younger than 20?

The final price is 97.714% of the original price. To the nearest whole number, that's 98%.

Let's call the final price of the bed "x".

       $350 * 0.15 = $52.50$ discount

       $297.50 * 0.15 = $44.63 markup

       $342.13 / $350 = 0.97714

So, the final price is 97.714% of the original price.

To the nearest whole number, that's 98%.

The method used to solve this problem is applicable to a wide range of similar problems in pricing and discounting, as well as in finance and economics. This method can be used to calculate the final price of an item after applying a discount followed by a markup, or to find the original price of an item given the final price and the discount and markup amounts. The method can also be extended to problems with multiple discounts or markups, as well as problems involving different discount or markup percentages.

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The value of y0 for which the solution of the initial value problem y' − y = 1 + 3 sin t, y(0) = y0 is:

y(0) = 3√2 - 1 = 3.24

Now, According t o the question:

A linear equation or polynomial, with one or more terms, consisting of the derivatives of the dependent variable with respect to one or more independent variables is known as a linear differential equation.

The general solution y of this equation is y = y0 + y1

where y0  = A[tex]e^t[/tex] is the solution for the equation y' - y = 0 (homogeneous equation), an

  y1 = (3/2)(sint + cost) - 1 = 3√2 sin(t + (π/4)) - 1 -

particular solution of the inhomogeneous equation. Thus, we have

  y(t) =A[tex]e^t[/tex] + 3√2 sin (t + (π/4))  - 1

To have the function y(t) finite for t → ∞ ,

We have to put  A = 0. Then, it follows

y(0) = 3√2 - 1 = 3.24

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If the dot indicates the center of the circle, the equation that must be true is

The diameter of the semicircle is shown by line segment bearing the dot at the center.

By drawing a line from each end of the diameter to any location on the semicircle, the inscribed angle is created anywhere you perform this is a 90-degree angle will result.

This mean that angle B = angle A = 90 degrees

hence there addition is 180 degrees

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Answer:

Step-by-step explanation:

Alice starts with 11 cards and buys 1 per day. Benito starts with 1 card and buys 3 per day. You want equations for Alice and Benito that describe the number of cards they have (y) in terms of the number of days (x) that have passed. you also want graphs of these equations and when and where the numbers of cards are the same.

It really should be no mystery that the number of cards will be the sum of the initial number and the product of the number of days and the number of cards acquired each day:

Alice: y = 11 +1x

Benito: y = 1 +3x

See the attachment for a graph and the point where the graphs intersect:

  x = 5, y = 16 . . . . . both have 16 cards after 5 days.

__

Additional comment

The equations are defined for negative x- and y-values, but in the context of this problem the only values that make sense are ones where x ≥ 0 and y > 0.

The answer will that the point 0.22 is located in between 0 and 1 in the number line.

A number line is a representation of numerical data that has been plotted along a straight line, either horizontally or vertically. Writing the numbers down on a number line makes it straightforward to compare the numbers and perform basic arithmetic operations on them. Zero is frequently used to denote the beginning of a number line (0).

While the numbers directly to the right of zero are all positive, those directly to the left of zero are all negative. We can therefore claim that on a number line, the value of numbers increases as we move to the right. According to this assertion, the numbers on the right are consequently larger than the ones on the left.

Before we begin, keep in mind that a number line is a line with a zero in the middle, increasing positive numbers to the right of the zero, and decreasing negative numbers to the left of the zero. Since the line is infinitely long, it is impossible to display the entire line; however, we will show where the value 0.22 is situated on the line.

Hence the answer will that point 0.22 is located between 0 and 1.

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Answer:

Below

Step-by-step explanation:

See image

There were 128 children and 155 adults.

Let us first set up our system by assigning x and y to mean something. Let x = the number of children and y = the number of adults.

First equation: Children cost $1.50 and Adults cost $4.00. In order to find the amount of money a group of children will cost, we multiply the number of children, x, by 1.5.

This is represented by 1.5x. For adults, who cost 4 dollars to enter, we will use 4y. The total amount of money made on the given day was $632. To get this amount, we must add 1.5x and 4y.

1.5x+4y=632 --------(1)

Second equation: Total amount of people on the given day is 238. To get this number, we must add together x and y, or the number of children and adults.

x + y = 238-----(2)

System of equations:

1.5x+4y=632

x+y = 238

Let's use the substitution of the x variable to solve the system.

x+y=238.

y=238-x

Substitute y = 238 - x into the first equation.

1.5x + 4 (238 - x) =632

1.5x + 952 - 4x = 632  

952- 2.5x = 632

-2.5x = -320

x = 128

Substitute x =128 back into y = 238 - x

y = 283-128

y=155

There were 128 children and 155 adults.

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1. Factor out the greatest common factor (GCF) from the coefficients.

2. Split the middle coefficient into two factors that add to the middle coefficient and multiply to the last coefficient.

1. First, identify the GCF of the coefficients, which is 1. Since there is no GCF, this step can be skipped.

2. Next, split the middle coefficient (17) into two factors that add to the middle coefficient and multiply to the last coefficient.

Since 17 = 8 + 9, we can use 8 and 9 as our two factors.

3. Group the terms by the common factors.

We can group the first and last term together (6x2 + 5) and the middle term separately (17x).

4. Factor out the common factor, which is x, from the first and last group. This gives us x(6x + 5).

5. Lastly, factor the remaining quadratic expression (6x + 5).

Since 8 and 9 are the two numbers that add to the middle coefficient and multiply to the last coefficient, we can use them as our two factors. This gives us (6x + 8)(x + 9).

Therefore, the factored form of 6x2 + 17x + 5 is x(6x + 8)(x + 9).

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Notice that points ( i ), ., (vi) are approaching x=1 from the right and points

(vii), ., (xi) are approaching from the left.

The closer is a point Q to x=1, the closer is the slope of the line PQ to the slope of the tangent at x=1.

For this articular function you can treat a pair like (xi),(vi) as an upper and lower

bound on the slope of the tangent.

If you can find a pair (something like Q1=0.999, Q2=1.001) so close to x=1 that the two secant lines PQ1 and PQ2 have identical slopes within two decimal places, then you have your estimate.

The exact value of the slope at x=1 is -14π.

The thing about this function is that it alternates between up and down extremely quickly.

If I could attach a graph I would; I would recommend that you look at it in some graphing tool.

Just imagine what is happening around x=1:

The argument of sin is 14π, making the value of the function 0.

If you keep increasing x beyond 1, the argument of sin gets smaller;

when the argument of sin gets to 13.5π the value of the function reaches -1

and the direction of the slope reverses.

That means that to get any meaningful estimate of the slope you need x

such that 14π/x is in the interval (13.5π, 14.5π).

That means x must be in the interval (0.97, 1.03).

And you probably need to try values even closer to 1 to get accuracy to 2 decimal digits.

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You will see what the calculator thinks you entered (which may be a little different to what you typed), and then a step-by-step solution. There can be more than one way to find a solution.

What is meant by solution?

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The correct option for the given question of the vector is none of these.

Physical values may be represented mathematically using vectors, which have both magnitude and direction. They are helpful for resolving issues in physics, engineering, and many other disciplines. They are frequently depicted as directed line segments or arrows. The addition, subtraction, and scaling of vectors make it simple and flexible to express physical quantities and carry out mathematical operations. They are crucial for characterizing geometric objects and carrying out spatial transformations.

According to the question

The vector projection of a vector u onto a vector v is given by:

proj_v u = (u . v) / ||v||^2 * v

where (u . v) is the dot product of vectors u and v, and ||v|| is the magnitude of vector v.

For the vectors u = i + 2j + 3k and v = 3i - j + 2k, the projection of u onto v is:

proj_v u = (u . v) / ||v||^2 * v = ((i + 2j + 3k) . (3i - j + 2k)) / ||3i - j + 2k||^2 * (3i - j + 2k) = (15 + 4 - 3) / 14 * (3i - j + 2k) = 16 / 14 * (3i - j + 2k) = (8/7) * (3i - j + 2k) = 8/7 * 3i - 8/7 * j + 8/7 * 2k = 8/7 * i + 2/7 * j + 16/7 * k

Therefore, the vector projection proj_v u of u onto v is:

proj_v u = 8/7 i + 2/7 j + 16/7 k

The "None of the above", option is correct.

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Using interquartile ranges.

Interquartile range (IQR) indicates the middle half range of the data set. You can use IQR to create "fences" around your data and define outliers as values outside those fences.

This method is useful when you have some values on either end of your dataset, but you are not sure whether any of them should be considered outliers.

Outliers are data that deviate too far from other data in a data set (outlier). The existence of these data outliers will make the analysis of a series of data biased, or not reflect the actual phenomenon. The term outliers is also often associated with extreme values, both large extremes and small extremes.

As an illustration, if there are four students, the first student has a monthly allowance of Rp. 500 thousand, second students Rp. 600 thousand, third student Rp. 700 thousand, and the fourth student because he is the son of a rich man (sultan), has a monthly allowance of up to Rp. 5 million. At a glance it appears that the value of 5 million is relatively far compared to the pocket money of the other three students.

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Therefore, when CD is divided by XX, Is standard form 20

The fixed positive integers are represented by alphabets in roman numerals. I, II, III, IV, V, VI, VII, VIII, IX, and X are roman numerals that stand for the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 respectively

We know that

CD = (D – C)

CD = (500 – 100)

CD = 400

XX = (X + X)

XX = (10 + 10)

XX = 20

CD = 400 and XX = 20 in numbers.

On dividing 400 by 20

Now, 20

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The hypotenuse is 5 of a right triangle with legs of length3 and4

The Pythagoras theorem goes as follows:

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

a²+b²=c²

'A' and 'B' are the other two legs, and '=' is the hypotenuse of the right triangle. As a result, the Pythagoras equation can be used for any triangle that has one angle that is exactly 90 degrees to create a Pythagoras triangle.

Here: a=3,b=4

32+42=c²

9+16=c²

25=c²

=√25=5

So, the hypotenuse is 5

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Answer:

9 hours

Step-by-step explanation:

The time taken is inversely proportional to the number of men; if M = number of men and D = number of days this can be expressed as
[tex]D \displaystyle \propto } \dfrac{1}{M}\\\\\text{which can be expressed as an equation: }\\\\D = k \cdot \dfrac{1}{M}\\\\or\\\\D = \dfrac{k}{M}\\\\[/tex]

k is known as the constant of proportionality which can be expressed as

[tex]k = D\cdot M[/tex]

Inversely proportional means:
As the number of men increases, the time taken decreases

As the number of men decreases, the time taken  increases

We can find k from the given information with M = 3 and D = 6 hours

[tex]k = 6 \cdot 3 = 18[/tex]

[tex]\textrm{Therefore, given M= 2, D = $\dfrac{18}{2} = 9$ \;hours}[/tex]

For 2 men it will take 9 hours to repair the road

If Term I Week 1 5. A fruit shop bought 500 kg of apples for R900 and sold them for R2,80 per kg.

a)  The profit per kilogram is R1 per kilogram

b) The profit as a percentage of the cost price is 55.56%

c)  The profit as a percentage of the selling price is 35.71%

a) Selling price

Selling price for 500 kg of apples = 500 * 2.80

Selling price for 500 kg of apples = R1400

Profit per kilogram = R1400 - R900 = R500 / 500 kg

Profit per kilogram = R1 per kilogram

b) The profit as a percentage of the cost price:

= R500 / R900 * 100

= 55.56%

c) The profit as a percentage of the selling price:

= R500 / R1400 * 100

= 35.71%

Therefore the profit per kilogram is R1 per kilogram.

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The probability that all five of the children get the disease is 0.012.

The probability of a single child getting the disease from the mother is 0.41. The probability that all five children will get the disease from their mother can be found by multiplying the probability of each child getting the disease. So, the probability that all five of the children get the disease is

= 0.41 * 5

= 0.41 * 0.41 * 0.41 * 0.41 * 0.41

= 0.012.

= 1.2%

This means that there is a 0.012, or 1.2%, chance that all five of the children will get the disease from their mother.

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The volume of the pyramid is V = [tex]\frac{h}{3}(5.2) cm^{3}[/tex]  or  V = 1.73h [tex]cm^{3}[/tex] .

In mathematics, 'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc.

we know that,

The volume of the pyramid is equal to

V = [tex]\frac{1}{3} BH[/tex]

where,

B is the area of the base and

H is the height of pyramid

In this problem we have,

B = 5.2 [tex]cm^{2}[/tex]

H = h cm

substitute in the formula in V = [tex]\frac{1}{3} BH[/tex] ,

V = [tex]\frac{1}{3}[/tex]  × 5.2 × h

V = [tex]\frac{h}{3}(5.2) cm^{3}[/tex]

or

V = 1.73h [tex]cm^{3}[/tex]

Therefore, the volume of the pyramid is V = [tex]\frac{h}{3}(5.2) cm^{3}[/tex]  or  V = 1.73h [tex]cm^{3}[/tex] .

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The volume of the solid right pyramid is given as V=  1/3(b*h) and hence volume(V) is equals to h/3(5.2) cm^3 or 1.73h cm^3

In solid right pyramid volume is given by the product of base of the area and the height of the solid pyramid  and it is divided by 3 and volume is defined as the 3-dimensional  area covered by the solid right pyramid . so volume is the product of the base of the area and the height and it is divided by 3

So , here "b" is the base of the area

"h" is the height of the solid right pyramid

We have ,base B=5.2 cm^2

height H= h cm

As , Volume is given by the product of the base and height of the right pyramid and it is divided by 3 , we used to solve the volume as

V=1/3 (5.2 * h) cm^3=(h/3)(5.2) cm^3

V=1.73 h cm^3

So, the volume of the solid right pyramid is given by V=h/3 (5.2) cm^3 or V=1.73 h cm^3

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They need to ride "x = 20 - (hours a first day + hours second day)" on the third day to make their goal of biking a total of 20 hours in the park.

Let's call the number of hours Rebecca and Dan rode on the third day "x".

Then, the total number of hours they rode in the park is given by:

total hours = hours first day + hours second day + x

And, we know that their goal is to bike a total of 20 hours in the park, so we can set the equation equal to 20:

total hours = hours first day + hours second day + x = 20

We can substitute in the values for hours first day and hours second day:

20 = hours first day + hours second day + x

So, to find the number of hours they need to ride on the third day to reach their goal, we just need to solve for x:

x = 20 - (hours first day + hours second day)

We would need to know the values for hours first day and hours second day to find the exact value of x.

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volume= 127.31

if base side is 7 and height is 6

Answer: 14

Step-by-step explanation:

Volume = 1/3 x 7 x 6

Volume = 1/3 x 42

Volume = 14

The value of x is15

The value of y is 20

The value of z is 58.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

ΔWXY ≈ ΔQRS

This means,

Consecutive sides and angles are equal.

15 + x = 30

x = 30 - 15

x = 15

y = 20

40 = z - 18

z = 40 + 18

z = 58

Thus,

x = 15

y = 20

z = 58

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The probability that the proportion of students who plan on majoring in a branch of STEM is greater for Ms. Keating than for Ms. Lewis can be found by looking up the z-table. This can be done by finding the standard deviation for the difference between the two proportions, which is calculated by (55-49)/sqrt(25+23). This gives a standard deviation of 0.6.

The probability of the proportion being greater for Ms. Keating can be found by taking the difference between the two proportions (0.06) and subtracting it from 1 (1-0.06). This gives a probability of 0.94, which can be found on the z table as 0.841. This means that the probability of the proportion of students who plan on majoring in a branch of STEM being greater for Ms. Keating than for Ms. Lewis is 0.841.

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The value of (16^x)/(2^y) if 4x-y=12 is 4096.

Therefore the answer is 4096.

We are given the equation 4x - y = 12. To find the value of (16^x)/(2^y), we need to find the values of x and y. To do this, we can isolate either x or y and solve for it:

4x - y = 12

y = 4x - 12

We can substitute the expression for y into the expression for (16^x)/(2^y) to find the value:

(16^x)/(2^y) = (16^x)/(2^(4x - 12)) = (16^x)/(2^(4x)) * (2^12)

Note that 2^4 = 16, so (16^x)/(2^4x) = 1, which means that (16^x)/(2^y) =2^12.

Therefore, the value of (16^x)/(2^y) is 4096.

--The question is incomplete, answering to the question below--

"If 4x-y=12, then what is the value of (16^x)/(2^y) "

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The effect of changing from a 90% confidence interval estimate for a population proportion to a 99% confidence interval for a population proportion is an increase in the interval size by 57%.

A confidence interval is a range of values that is likely to contain the true population parameter with a certain degree of confidence.

When you increase the level of confidence, for example from 90% to 99%, you increase the width of the confidence interval.

The reason for this is that a higher level of confidence requires a wider range of values to ensure that the true population proportion is included within the interval with the specified level of confidence.

This increase in interval size allows us to be more certain that the true population proportion is included within the interval, but also makes the interval less precise in terms of estimating the population proportion.

Answer choice (C) is correct. An increase in the confidence level from 90% to 99% results in an increase in the interval size by approximately 57%.

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The solution is Option B.

The system of equations is solved and the value of x and y is ( 3 , 7 )

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 first equation be represented as A

Now , the value of A is

-2x + 3y = 15   be equation (1)

Let the first equation be represented as B

Now , the value of B is

x + y = 10   be equation (2)

On simplifying the equation , we get

Subtracting y on both sides of the equation , we get

x = 10 - y   be equation (3)

Substituting the value of x from equation (3) in equation (2) , we get

-2 ( 10 - y ) + 3y = 15

On simplifying the equation , we get

-20 + 2y + 3y = 15

Adding 20 on both sides of the equation , we get

5y = 35

Divide by 5 on both sides of the equation , we get

y = 7

Substitute the value of y in equation (3) , we get

x = 10 - 7

x = 3

Hence , the value of x and y is 3 and 7 respectively

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Answer:

Option B: (3, 7)

Step-by-step explanation:

i took the test xx

a) The pattern we noticed in the sequence is; A geometric sequence

b) The value of 3⁻¹ which is the fourth term is; 1/3

c) The value of 3⁻² which is the fifth term is; 1/9

The general formula for the nth term of a geometric progression is;

aₙ = arⁿ⁻¹

where;

a is first term

r is common ratio

We are given the sequence as;

3², 3¹, 3⁰,____

Thus;

First term a = 9

Common ratio; r = 3/9

r = 1/3

b) Thus; 3⁻¹ will be the 4th term and as such will be;

3⁰ * 1/3 = 1/3

c) Similarly, The fifth term is 3⁻² expressed as;

1/3 * 1/3 = 1/9

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The starting value of the expression is, y = 3.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The expression is,

⇒ y = 3 × q⁵

Now, For starting value substitute q = 1 in above equation,

⇒ y = 3 × q⁵

⇒ y = 3 × 1⁵

⇒ y = 3 × 1

⇒ y = 3

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No, the mean of 13.513.5 does not make sense because it is not a whole number.

The mean of a set of numbers is calculated by adding up all of the numbers in the set and then dividing by the total number of items in the set. The mean is a representation of the average of the data set. It is important to note that the mean should always be a whole number, since it is an average of the values in the set. Therefore, the mean of 13.513.5 does not make sense because it is not a whole number. A whole number mean indicates that the values in the set are all the same, or at least very close, while non-whole number means indicate that there is a greater difference between the values in the set. This is why it is important to make sure the mean of a data set is a whole number.

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The complete question is

Does the value of the mean of x make sense? the mean of 13.513.5 does not make sense because it is not a whole number

The pair (3, 36) means 3 dozens required 36 cookies

And the unit rate is 12

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have

x = dozen

y = cookies

This means that

(3, 36) means 3 dozens required 36 cookies

Using the ordered pair in (a):

The unit rate of the pair (3, 36) is 36/3 = 12.

This means that for every 1 dozen change, there is a corresponding 12 cookies change

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Steel: σs = p/A_s; Brass: σb = p/A_b; Copper: σc = p/A_c , where A_s, A_b, A_c are the areas of the steel, brass, and copper, respectively.

To calculate the tensile stresses in the steel, brass, and copper due to the force p, we use the formula: σ = p/A, where σ is the tensile stress and A is the area of the material. For the steel, the area is A_s, so the tensile stress σs is equal to p divided by A_s. For the brass, the area is A_b, so the tensile stress σb is equal to p divided by A_b. Finally, for the copper, the area is A_c, so the tensile stress σc is equal to p divided by A_c. Therefore, the tensile stresses in the steel, brass, and copper due to the force p can be calculated using the formula σ = p/A, where A is the area of the material.

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Answer:

6(2g+1) (2g-1)

Answer:

6(2g - 1)(2g + 1)

Step-by-step explanation:

24g² - 6 ← factor out the common factor of 6 from both terms

= 6(4g² - 1) ← 4g² - 1 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

4g² - 1

= (2g)² - 1²

= (2g - 1)(2g + 1)

then

24g² - 6 = 6(2g - 1)(2g + 1) ← in factored form