Assignment #1 (22PS) 1.9 Practice - Age Problems 1.
A boy is 10 years older than his brother. In 4 years he will be twice as old an his brother. Find the present age of each. 2. A father is 4 times as old as his son. In 20 years the father will be twice as as his son. Find the present age of each.​

A trapezoid has been divided into two right triangles and a rectangle, see the above figure. Area of the triangle on left is 9 in². The area of the triangle on the right is 9 in², and the area of the rectangle is 108 in². The area of the trapezoid is the sum of these areas, which is 126 in².

We have a trapezoid, ABCD see in above figure has been divided into two right triangles, i.e., ∆BEC, ∆DAF and a rectangle, ABEF. We have to determine the area of trapezoid. Now, as we know area of a figure divides into pieces is equals to the sum of areas of each piece of figure. So, the area of trapezoid, ABCD is sum of area of two right triangles, i.e., ∆BEC, ∆DAF and a rectangle, ABEF. From above figure, In case of right triangles,

The base length of the triangle BEC= 2 in

height of triangle BEC = 9 in

Area of triangle BEC = (1/2)× base× height

=> Area of ∆BEC = (1/2)× 9× 2

= 9 in² Similarly, Area of triangle DAF = 9 in²

Therefore, the required area is 2×( Area of the triangle), A₁ = 2× 9 sq. in

= 18 in²

Now, length of rectangle ABEF, l = 12 in

width of rectangle, w = 9 in

Area of rectangle ABEF, A₂ = l×w

= 12× 9 = 108 in²

Thus, the required area = A₁ + A₂

= 18 in² + 108 in² = 126 in²

Hence required area is 126 in².

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Complete question:

This trapezoid has been divided into two right triangles and a rectangle, see the above figure. how can the area of the trapezoid be determined using the area of each shape? enter your answers in the boxes. the area of the triangle on left is ___ in², the area of the triangle on the right is___ in², and the area of the rectangle is__ in². the area of the trapezoid is the sum of these areas, which is___ in².

The probability that the small business owner's annual profit will not exceed $100,000 is about 0.0571

We can use the central limit theorem to approximate the distribution of the annual profit. The central limit theorem states that the sum of a large number of independent and identically distributed random variables will be approximately normally distributed.

Let X be the daily profit, then the annual profit, Y, is given by Y = 105X. The mean of Y is:

μY = 105μX = 105(975) = 102375

The variance of Y is:

σY^2 = 105σX^2 = 105(129)^2 = 2244385

The standard deviation of Y is:

σY = sqrt(2244385) ≈ 1498.12

We want to find the probability that the annual profit will not exceed $100,000, which is equivalent to finding the probability that Y ≤ 100000. We can standardize Y using the formula:

Z = (Y - μY) / σY

Substituting the values, we get:

Z = (100000 - 102375) / 1498.12 ≈ -1.58

We can use a standard normal distribution table or calculator to find the probability that Z ≤ -1.58. This probability is approximately 0.0571.

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The given question is incomplete, the complete question is:

A small business owner estimates his mean daily profit as $975 with a standard deviation of $129. His shop is open 105 days a year. What is the probability that his annual profit will not exceed $100,000?

Step-by-step explanation:

The proportion of similar triangles are

[tex] \frac{3}{4} = \frac{9}{r} [/tex]

Solving for r

[tex] \frac{4}{3} = \frac{r}{9} [/tex]

[tex] \frac{9 \times 4}{3} = r[/tex]

[tex]12 = r[/tex]

Answer:

19

Step-by-step explanation:

Product of 5 and a number is 5a

5a - 26 = 69

Add 26 to both sides

5a = 69+26

5a = 95

Divide both sides by 5

A = 19

Check

(5× 19) - 26 = 65

Answer:

(1,5)?

Step-by-step explanation:

Max needs 54 horizontal rails to build a fence with 27 vertical posts.

The problem states that each section of the fence uses 3 vertical fence posts and 6 horizontal rails. This means that for every section of fence, there are 3 vertical posts and 6 horizontal rails.

To find out how many horizontal rails Max needs for a fence with 27 vertical posts, we need to figure out how many sections of fence Max needs to build.

Since each section of fence has 3 vertical posts, apply unitary method, we can divide the total number of vertical posts by 3 to find out how many sections of fence Max needs to build:

27 / 3 = 9

So Max needs to build 9 sections of fence.

Since each section of fence has 6 horizontal rails, we can multiply the number of sections by 6 to find out how many horizontal rails Max needs in total:

9 x 6 = 54

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To determine the zeros of f(x) and state the multiplicity of each zero, the following steps should be followed:

Step 1: Determine the roots of the polynomial

To solve for the roots of f(x), use the quadratic formula. f(x) = x⁴ + 12x² - 64

a = 1, b = 12, c = -64

Using the quadratic formula, we have:

x = (-b ± √(b² - 4ac)) / 2a

x = (-12 ± √(12² - 4(1)(-64))) / 2(1)

x = (-12 ± √400) / 2

x = (-12 ± 20) / 2

x₁ = -16

x₂ = 4

x₃ = x₄ = 0

Step 2: State the multiplicity of each zero

After determining the roots of f(x), determine the multiplicity of each root by using the concept of multiplicity. A root has a multiplicity of p if and only if f(x) has a factor of (x - r)ᵖ.

From the quadratic equation above, we have:

x₁ = -16 (multiplicity 1)

x₂ = 4 (multiplicity 1)

x₃ = x₄ = 0 (multiplicity 2)

Therefore, the zeros of f(x) and their multiplicities are: x = -16 (multiplicity 1), x = 4 (multiplicity 1), and x = 0 (multiplicity 2).

The final answer is as follows:

x = -16 with multiplicity 1

x = 0 with multiplicity 2

x = 4 with multiplicity 1.

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Using an equation, the amount Eric spent at the bookstore was $45.50.

An equation is a mathematical statement of the equality or equivalence of two or more algebraic expressions.

Equations are depicted using the equal symbol (=).

Let the amount that Todd spent in the bookstore = 3x

Let the amount that Eric spent in the bookstore = x - 15

The total amount spent by the two shoppers = $197

197 = 3x + x - 15

182 = 4x

45.5 = x

Check:

Amount spent by Eric = $45.50

The amount spent by Todd = 45.50(3) + 15 = $151.50

The total amount spent by the two shoppers = $197 ($45.50 + $151.50)

Thus, the equation shows that Eric spent $45.50 which is $15 less than three times the amount that Todd spent or $151.50.

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In response to the given question, we can state that We may infer that there is no common ratio for this sequence because the ratios change for each computation. As a result, it is not a geometric sequence.

A sequence is a collection of numbers (or "terms"). Examples of words are 2, 5, and 8. Certain sequences may be made infinitely long by takes advantage of a specific pattern they follow. To continue the sequence, use the case of 2,5,8 or add 3. There are formulae that show where to seek for words in a sequence. A sequencing in mathematics is a collection of items that are in some order (or events). It is similar to a set in that it has components (also called elements or terms). The length of a sequence is defined as the total, possibly unlimited number of ordered items. the act of arranging two or more elements in a logical sequence.

To get the common ratio of a geometric series, divide any phrase by the term before it.

Let us divide the second term by the first term:

4 ÷ (-1) = -4

Let us now divide the third term by the second term:

(-7) ÷ 4 = -1.75

Lastly, let us divide the fourth term by the third term:

10 ÷ (-7) = -1.42857142857 (rounded to 11 decimal places) (rounded to 11 decimal places)

We may infer that there is no common ratio for this sequence because the ratios change for each computation. As a result, it is not a geometric sequence.

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Therefore , the solution of the given problem of circle comes out to be 110°

is the angle 1.

Each area of a plane with a specific distance from this additional spot forms a circle (center). Thus, it comprises of curved spots that are separated from one another and separated by the surface. Additionally, it rotates evenly around the centre from all sides. Every set of endpoints in a circular, constrained double sphere is uniformly spaced apart from the "centre."

Here,

Given :

To find: the angle of 1

So,

From  the diagram , we can see it is showing 110 degree

So ,

Angle 1 comes out to be 110°

So, rest of circle angle is = 360° - 110° = 250°

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Answer:

x = y = 2[tex]\sqrt{3}[/tex]

Step-by-step explanation:

the triangle is a 90- 45- 45 isosceles triangle with congruent legs, that is

x = y

using Pythagoras' identity in the right triangle

x² + y² = (2[tex]\sqrt{6}[/tex] )² , that is

x² + x² = 24

2x² = 24 ( divide both sides by 2 )

x² = 12 ( take square root of both sides )

x = [tex]\sqrt{12}[/tex] = [tex]\sqrt{4(3)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex] = 2[tex]\sqrt{3}[/tex]

then

x = y = 2[tex]\sqrt{3}[/tex]

The volume of the rectangular prism is 36 cubic centimeters.

For a rectangular prism of height H, length L and width W, the volume is given by the product between these 3 quantities, here we will get:

V = H*L*W

On the image we can see a rectangular prism with the dimensions:

Height = 6cm

Length = 3cm

Width = 2cm

Then we can replace these values in the volume formula so we will get:

V=  6cm*3cm*2cm

V = 36 cm³

The volume of the prism is 36 cm³

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Complete question.

"The volume of a prism is the product between the dimensions, find the volume of the rectangular prism below".

There is a 0.0838 or 8.38% chance that a sampling of 12 eggs has a weighted mean greater than 68 grammes.

The Central Limit Theorem, which asserts that group means of a large sample size from every population, irrespective of its distribution, will be roughly distributed normally with an average equal to the inhabitants imply and a variance equal to the standard deviation of the population multiplied by the square root of the random sample, must be used to solve this problem.

As a result, there is a 0.0838 or 8.38% chance that a sampling of 12 eggs has a weighted mean greater than 68 grammes. When n is the sample size, x is the sample mean, is the population mean, and seems to be the population standard deviation.

In this instance, n = 12 eggs, x = 68 grammes, = 65 grammes, = 5 grammes. When these values are added to the formula, you obtain:[tex]z = (68 - 65) / (5 / √12) = 1.385[/tex]

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The equatiοn οf the line οf best fit is ŷ= 0.96x+3.79

The slοpe is 0.96

The y-intercept is 3.79

The heights οf peοple that have arm spans οf 66 inches is 67.15 inches and the heights οf peοple that have arm spans οf 74 inches is 74.83 inches.

When the line tοuches the y-axis, it fοrms a y-intercept. Find the y when x = 0 tο find these. The y-intercept pοint will have the shape οf (0,y) When the line tοuches the x-axis, it fοrms an x-intercept.

We have the fοllοwing cοmputatiοn summary frοm the graphing calculatοr:

Sum οf X = 486

Sum οf Y = 506

Mean X = 44.1818

Mean Y = 46

Sum οf squares (SSX) = 1225.636

Sum οf prοducts (SP) = 1171

Hence, the fοrmula fοr the line οf best fit is ŷ= 0.96x+3.79

A linear regressiοn equatiοn is mentiοned

ŷ=mx+b

Where m is the slοpe, and b is the y-intercept

Sο, the slοpe is 0.96 and the y-intercept is 3.79

The heights οf peοple that have arm spans οf 66 inches and 74 inches

This means that:

x = 66 and x = 74

When x = 66,

y=0.96*66+3.79=67.15

When x = 74,

y=0.96*74+3.79= 74.83

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Answer:

k=32

Step-by-step explanation:

One root of x^2 + 12x + k = 0 is twice the other root. Find k

k will be the product of the two roots

12 will be the sum of the two roots

12/3=4

4*2=8

The two roots are 4,8

Multiply 4 and 8, you get 32.

k=32

f(t) = t3 − 8t2 + 25t + 10. When all the parts are put together, the equation represents a combination of the 3 components, representing a law of motion for a particle.

This equation represents a law of motion, where t is measured in seconds and s in feet. This equation can be broken down into 3 parts; t3, -8t2 and 25t + 10. The t3 part of the equation represents a cubic function, which is usually associated with acceleration. The -8t2 part is a quadratic function, which is typically associated with velocity. Finally, the 25t + 10 is a linear function, which is usually associated with displacement. When all the parts are put together, the equation represents a combination of the 3 components, representing a law of motion for a particle.

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It is important to carefully select the survey population and explain why the survey is necessary. It is also important to limit the number of questions and ask them in a clear and concise manner.

Select the survey population carefully: This means selecting a group of people who are representative of the target population and have the relevant knowledge or experience to answer the survey questions. For example, if the survey is about customer satisfaction with a product, the survey population should be customers who have used the product.

Limit the number of questions: It's important to keep the survey short and focused to reduce the risk of respondent fatigue and increase the response rate. A shorter survey also makes it easier to analyze the data.

Explain why the survey is necessary: This helps to increase the response rate by providing a clear explanation of why the survey is being conducted, what the data will be used for, and how it will benefit the target population.

Select the survey population randomly: Random selection helps to ensure that the survey results are representative of the target population and minimize the risk of bias in the sample.

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what tips can you share with the group? check all that apply.

Answer:

A. 2(4a^3 - 49a)

In this case, you would simply multiply the numbers and leave the a value and exponents alone.

B. 2a(4a^2 - 49)

First, you would distribute(multiply) 2 with the numbers inside the parentheses just like you did for answer A. Then, you would distribute a with the other a values inside the parentheses, you would add this values instead of multiplying it.

F. 2a(2a - 7)(2a + 7)

You would distribute 2a inside the FIRST set of parentheses just like you did before. Then multiply that set of parentheses with the other set of parentheses.

Step-by-step explanation:

The price per unit is equal to R2.29 per unit.

Generally speaking, a unit price is sometimes referred to as price per unit or unit rate and it can be defined as the price that is being charged by a seller for the sale of a single unit of product.

In this scenario, we would determine the unit price for number of unit of electricity by using the following mathematical expression;

Unit price = Cost of electricity/Number of units

Substituting the given parameters into the unit price formula, we have the following;

Unit price = R350/152.84

Unit price = R2.29 per unit.

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The relationship between distance traveled, in miles, d, and driving time, in hours, t. The Equation is 60 miles × 10 hours = 1023 miles

Distance:

Distance is a numerical or sometimes qualitative measurement of the distance between objects or points. In physics or common usage, distance can refer to a physical length or an estimate based on other criteria. Since spatial cognition is a rich source of conceptual metaphors in human thought,  the term is also often used metaphorically to refer to a measure of the amount of difference between two similar objects or some degree of separation.

Most of these concepts of distance, whether physical or metaphorical, are formalized in mathematics using the concept of metric spaces.

According to the Question:

total distance (one way): 1,023 miles

average driving speed: 60 miles per hour

driving time on first day: 10 hours.

Now,

Average driving speed = 60 miles per hour

Driving time on first day = 10 hours.

Total distance on first day = 60 miles × 10 hours

                                           = 600 miles/ Hour.

and,

The relationship obtained from the Given equation is:

60 miles + 10 hours = 1023 miles

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Answer:

E =53.1

Step-by-step explanation:

sin=opposite ÷ hypotenuse

opposite side of E = 4

hypotenuse = 5

4÷5=0.8

sin^-1 (0.8) = 53.1

E=53.1

Answer:

the answers are 1. 12:45 pm 2. 1:30 pm

The expression which is equivalent to [tex](\frac{3}{2})^8[/tex] is [tex]$\frac{3^6}{2^8}$[/tex] . So, correct option is C.

An exponential expression is a mathematical expression that involves a base raised to an exponent. The base is usually a fixed number, and the exponent represents the number of times the base is multiplied by itself. For example, in the expression [tex]2^3[/tex] the base is 2 and the exponent is 3. This means that 2 is multiplied by itself three times, resulting in the value of 8.

Exponential expressions are commonly used in many areas of mathematics and science, as well as in everyday life. For example, they can be used to represent growth rates, decay rates, population growth, radioactive decay, and compound interest.

Exponential expressions can be simplified using the laws of exponents, which allow us to combine or simplify expressions with the same base. Some common laws of exponents include:

Product law: [tex]a^m x a^n = a^(m+n)[/tex]

Quotient law: [tex]a^m / a^n = a^(m-n)[/tex]

Power law: ([tex]a^m)^n = a^(mn)[/tex]

Negative exponent law: [tex]a^(-m) = 1 / a^m[/tex]

Zero exponent law: [tex]a^0 = 1[/tex]

Exponential expressions can also be graphed on a coordinate plane, producing a curve called an exponential function. The shape of the curve depends on the value of the base and the sign of the exponent, and can be used to model a wide range of real-world phenomena.

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An equation that represents the relationship is y = 0.01x.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios. Also, it passes through the origin (0, 0) and it can be modeled by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 1/90

Constant of proportionality, k = 0.01.

Therefore, the required equation is given by:

y = kx

y = 0.01x

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Answer:

a. i dk how to do this qn

b. cot (cos^-1(a))

let cos^-1(a) = θ

implies, cosθ = a

from the figure, cotθ = [tex]\frac{x}{\sqrt{1 -x^{2} } }[/tex]

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G is 215° North from H in bearing terms. This means that to get from point H to point G, one must travel in a northerly direction at an angle of 215°.

The bearing of G from H is 215° North. This means that to get from point H to point G, one must travel in a northerly direction at an angle of 215°. Bearings are typically measured in degrees, where north is 0° and east is 90°. To calculate the bearing of G from H, you must first draw a line from H to G. After that, calculate the angle between the line you drew and north.. This angle is the bearing of G from H. Bearings can also be expressed as a three-letter compass direction (such as NNE or SW). To calculate the three-letter compass direction, divide the bearing into four quadrants (0-90° = N, 90-180° = E, 180-270° = S, 270-360° = W) and then divide each quadrant further into three sections. For example, if the bearing of G from H is 215°, it would be expressed as SW, since it falls within the 270-360° quadrant. Bearings are useful for navigation, determining the direction of a destination from a starting point, and for plotting points on a map.

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6x + 5 + ( -2 )/( x + 7 ), The expression can be written as the quotient of 6x + 5 divided by x + 7, plus the remainder of -2, all divided by the divisor of x + 7.

To calculate (6x+5)/(x+7), first we must add x to both the numerator and the denominator to get (6x+x+5)/(x+7+x), which simplifies to (7x+5)/(2x+7). Then, divide the numerator by the denominator to get (7x+5)/(2x+7) = 3.5x + 2.5. To find the remainder, subtract 3.5x and 2.5 from both the numerator and denominator, which gives us (7x+5)-(3.5x+2.5) = 3.5x + 2.5 - (3.5x + 2.5) = 3.5x - 2.5. Lastly, divide the remainder by the divisor (2x+7) to get (3.5x-2.5)/(2x+7). Therefore, the answer is 3.5x + 2.5 + (3.5x - 2.5)/(2x+7).

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