Matt collects classic stamps. For his birthday this year his grandma gave him a stamp’s worth $40. He expected the stamps value to double every decade. Assuming Matt is right you can use a function to approximate the stamp’s value x decades from now.


Write an equation for the function. If it is linear write in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)^x

The total amount that must be repaid is $139,076.12.

Annual simple interest is a type of interest that is calculated on the principal amount of a loan or investment for a one-year period. Simple interest is a fixed percentage of the principal amount, which is added to the principal at regular intervals. The interest is calculated only on the original principal amount and does not include any interest earned on the interest itself.

Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment, but also on the interest earned on that principal amount over time. In other words, compound interest is interest that is added to the principal amount, and then interest is calculated on the new total amount (principal + interest). This process is repeated at regular intervals, such as monthly or annually.

In the given question, The total amount that must be repaid can be found using the simple interest formula:

I = Prt

Where:

P = principal amount borrowed = $87,495

r = annual interest rate = 8.355%

t = time period in years = 7

So, substituting the values we get:

I = 87,495 * 0.08355 * 7 = 51,581.12

Therefore, the total amount that must be repaid is:

87,495 + 51,581.12 = 139,076.12

Rounding to the nearest cent, the answer is $139,076.12.

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1. 25%

2. 7.69%

3. 50%

4. 0.46%

1. The probability of drawing a spade is 1/4, or 25%.

2. The probability of drawing a seven is 4/52, or 7.69%.

3. The probability of drawing a spade or heart is 1/2, or 50%.

4. The probability of drawing a black jack is 1/216, or 0.46%.

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The probability P(z < 1.645) is the area under the standard normal curve to the left of 1.645.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. Probability is used to assess the outcome of any random event, such as the roll of a die or the flip of a coin. It can also be used to measure the likelihood of future events, such as the stock market rising or falling.

This probability is calculated by using Table 3 in Appendix I. The probability is 0.9500, which means that 95% of the area under the normal curve is to the right of 1.645.

This phenomenon is occurring because the normal distribution is symmetrical. The area to the left and to the right of the mean are equal, and thus the probability of P(z < 1.645) is the same as the probability of P(z > 1.645). The normal distribution is also unimodal, meaning that there is a single peak and all other data points have lower probability than the peak. Since the peak of the normal distribution is at the mean (0 in this case), any value to the right of the mean will have a higher probability than any value to the left of the mean. Thus, the probability of P(z > 1.645) is greater than the probability of P(z < 1.645).

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The probability P(z < 1.645) is the area under the standard normal curve to the left of 1.645.

What is Probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.

This probability is calculated by using Table 3 in Appendix I. The probability is 0.9500, which means that 95% of the area under the normal curve is to the right of 1.645.

The symmetric nature of the normal distribution is what is causing this phenomena. Because the area to the left and right of the mean are equal, the likelihood that z will be less than or more than 1.645 is equally likely. Furthermore, the normal distribution is unimodal, which means that there is only one peak and that all other data points have a probability that is smaller than the peak. Since the mean (0 in this case) is where the normal distribution's peak occurs, any value to the right of the mean will be more likely to occur than any value to the left of the mean. As P(z > 1.645) is more likely than P(z 1.645), the former is true.

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Answer: 17

Step-by-step explanation:

To find much each pass earns per day is to divide the two numbers. $207 divided by 3 is 69 and $364 divided by 7 is 52. Then you subtract 69 and 52 which is 17!

Answer:

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

Find the area using formula:

Substitute values into formula to get:

Since each pig gets 2*5³ m² of land, by dividing the area by this number, Daniel can put:

Answer:7.8

Step-by-step explanation:

[tex]\sqrt{6^2+5^2}[/tex]

evaluate the equation / expression

7.81025

Round 7.81025 to the required place

7.8

Answer:

7.8m

Step-by-step explanation:

To find:-

Answer:-

From the given data i made a figure to represent the given situation. To find the distance between the opposite corners we would have to use Pythagoras theorem, .

The distance between the corners represents the hypotenuse of the right angled triangle and another two sides are represented by 5m and 6m .

According to Pythagoras theorem,

[tex]\rm\implies a^2+b^2 = h^2 \\[/tex]

Here a is 5m and b is 6cm .

[tex]\rm\implies (5m)^3+(6m)^2 = h^2 \\[/tex]

[tex]\rm\implies 25m^2+36m^2=h^2\\[/tex]

[tex]\rm\implies 61m^2=h^2\\[/tex]

[tex]\rm\implies h =\sqrt{61m^2} \\[/tex]

[tex]\rm\implies \red{ h = 7.8 \ m } \\[/tex]

Hence the distance between the opposite corners is 7.8 m

Answer:

27

Step-by-step explanation:

9+15=24

72/24=3   so 1=3 and there are 9 cargo cars so 9*3=27

you can also check by doing 3*15=45 and 45+27=72 so this is correct

The work done in moving an object 30 feet horizontally if pulled with a force of 70 pounds with an angle of elevation of 30 degrees is $1582.07\text{ ft-lbs}$.

Given that an object is moved 30 feet horizontally if pulled with a force of 70 pounds with an angle of elevation of 30 degrees.To find the work done in moving an object, we know thatWork done = Force * Distance * cos(θ)Where θ is the angle between the force applied and the displacement of the object.Here, force applied = 70 poundsDistance = 30 feetAnd θ = 30 degreesWe know that the force is applied at an angle of 30 degrees to the horizontal, thus the horizontal component of the force is given by:Horizontal component of force = Force × cos (θ)So, the horizontal component of the force applied is:Horizontal component of force = 70 cos 30°= 60.62 pounds (approx)Therefore, the work done in moving the object 30 feet horizontally is:Work done = force × distance × cos (θ)= 60.62 × 30 × cos 0.5= 60.62 × 30 × 0.87= $1582.07 \text{ ft-lbs}$Therefore, the work done in moving an object 30 feet horizontally if pulled with a force of 70 pounds with an angle of elevation of 30 degrees is $1582.07\text{ ft-lbs}$.

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Answer:

To find out how many windows Kendall can wash in one hour, we can divide the number of windows washed by the time taken:

Number of windows washed per hour = (Number of windows washed) / (Time taken)

We can first convert the mixed number 10 1/2 to an improper fraction:

10 1/2 = (10 x 2 + 1) / 2 = 21/2

Substituting the given values:

Number of windows washed per hour = (21/2) / (3/4) hours

To divide by a fraction, we can multiply by its reciprocal:

Number of windows washed per hour = (21/2) x (4/3) = 28 windows/hour

Therefore, Kendall can wash 28 windows in one hour at this rate.

Answer:

14 windows

Step-by-step explanation:

All you have to do is a simple equation 10 1/2÷3 which equals 14

To the nearest tenth, the quantity of the amount after [tex]7[/tex] weeks is around [tex]1804.74[/tex].

Quantity simply refers to how much or how many of anything there are. A quantity can also be an amount, a number, or a measurement. It responds to the "how much?" query. Numbers may also be used to understand quantities, such as this book has 55 pages, this container has 'x' quantities of black pens, etc.

Numbers can be used to express quantities, such as 55 pages or reading. Entire numbers, fractions, fractions, percentages, or units of measurement like space, money, length, or weight can all be used to express these values. Quantities may also be stated using uncommon units.

[tex]A_{0} = 3600[/tex]

[tex]r = 0.01[/tex] (since the rate of decay is [tex]1[/tex]%)

[tex]t = 7[/tex] weeks [tex]= 56[/tex] days (since there are [tex]7[/tex] days in a week)

We can first find the value of [tex]e^{-rt}[/tex] as follows:

[tex]e^{-rt} = e^{-0.0187} = 0.5013[/tex]

Substituting into the formula, we have:

[tex]A = 3600 * 0.5013 ≈ 1804.74[/tex]

Therefore, the value of the quantity after [tex]7[/tex] weeks, to the nearest hundredth, is approximately [tex]1804.74[/tex].

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In quadrilateral ABCD abοve, AD || BC and CD =1/2AB. the measure οf angle is B 90°

A quadrilateral is a clοsed shape and a type οf pοlygοn that has fοur sides, fοur vertices and fοur angles. It is fοrmed by jοining fοur nοn-cοllinear pοints. The sum οf interiοr angles οf quadrilaterals is always equal tο 360 degrees.

Since AD is parallel tο BC, we have:

∠ABC + ∠BCD = 180° (interiοr angles οn the same side οf the transversal AD)We alsο knοw that CD = 1/2AB. Let's call the length οf AB "x". Then we have:

CD = 1/2AB

CD = 1/2x

Nοw, let's lοοk at triangle BCD. We knοw that the sum οf the angles in a triangle is 180°, sο we have:

∠BCD + ∠CBD + ∠BDC = 180°

We alsο knοw that ∠BCD = ∠ABC (because they are cοrrespοnding angles), sο we can substitute ∠ABC fοr ∠BCD:

∠ABC + ∠CBD + ∠BDC = 180°

Nοw, let's use the fact that CD = 1/2x tο find the length οf BD:

BD = AB - CD

BD = x - 1/2x

BD = 1/2x

Sο, BD is half the length οf AB. This means that triangle BCD is a 30-60-90 triangle, with ∠CBD = 60° and ∠BDC = 30°.

Substituting these values intο οur equatiοn abοve, we get:

∠ABC + 60° + 30° = 180°

Simplifying, we get:

∠ABC + 90° = 180°

Subtracting 90° frοm bοth sides, we get:

∠ABC = 90°

Therefοre, the measure οf angle B is 90°.

D) 90°.

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If two lines have the same slope, it means that they have the same steepness or inclination and will never intersect, no matter how far they are extended in either direction.

Parallel lines are two or more lines in a two-dimensional plane that never intersect, regardless of how far they are extended in either direction. In other words, they have the same direction or slope but different y-intercepts.

In the given Question,

To draw similar slope triangles on each line, we can choose any two points on the line and connect them with a straight line segment. Then, we can calculate the rise (change in y) and run (change in x) between the two points and use these values to determine the slope of the line using the formula:

slope = rise / run

If we draw similar slope triangles on both parallel lines r and s, we will find that the ratios of the rise to the run are equal for both lines. This means that the slopes of the two lines are equal, and we can express this mathematically as:

slope_r = slope_s

This relationship between the slopes of parallel lines is important in many applications of mathematics, including geometry, trigonometry, and calculus.

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Given that two of the angles in this triangle are equal and have a measure of 78 degrees and sides 4x + 23, 10x-1 the solution x = -1.15 is a valid solution.

What is the inequality equation?

A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not. The solution set of an inequality is the set of all solutions.

In a triangle, the sum of the measures of the angles is always 180 degrees. Since we are given that two of the angles in this triangle are equal and have a measure of 78 degrees each, the third angle must have a measure of:

180 - 78 - 78 = 24 degrees

Now we can use the Law of Cosines to set up an equation to solve for x. The Law of Cosines states that:

c² = a² + b² - 2abcos(C)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

We can choose any of the sides to be the side opposite the 24-degree angle, but let's use side 2, which has a length of 10x - 1. Then we have:

(10x - 1)² = (4x + 23)² + (side 3)² - 2(side 3)(4x + 23)cos(78)

Simplifying and solving for side 3, we get:

(side 3)² = (10x - 1)² - (4x + 23)² + 2(10x - 1)(4x + 23)cos(78)

(side 3)² = 36x² + 360x + 840

Taking the square root of both sides, we get:

side 3 = √(36x² + 360x + 840)

Now we can use the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we have:

side 1 + side 2 > side 3

4x + 23 + 10x - 1 > √(36x² + 360x + 840)

14x + 22 > √(36x² + 360x + 840)

Squaring both sides, we get:

196x² + 616x + 484 > 36x² + 360x + 840

Simplifying and rearranging, we get:

160x² + 256x - 356 < 0

We can solve this inequality using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 160, b = 256, and c = -356.

Plugging in these values, we get:

x = (-256 ± √(256² - 4(160)(-356))) / 2(160)

x = (-256 ± √(124160)) / 320

x = (-256 ± 352) / 320

x = 0.30 or x = -1.15

However, we need to check that these values satisfy the inequality we found earlier:

14x + 22 > √(36x² + 360x + 840)

For x = 0.30, we get:

14(0.30) + 22 > √(36(0.30)² + 360(0.30) + 840)

25.2 > 25.2

This is not true, so x = 0.30 does not work.

For x = -1.15, we get:

14(-1.15) + 22 > √(36(-1.15)² + 360(-1.15) + 840)

3.3 > 3.3

This is true, so x = -1.15 is a valid solution.

Therefore, the solution x = -1.15 is a valid solution.

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Thus, the resulting function after an 8 unit right translation and a 5-unit vertical stretch is obtained as:  f(x) = 5* log1/7(x+8)

Any applied either a horizontal or vertical shift to an object is referred to as a translation in geometry. In geometry, a translation is a displacement that occurs either horizontally to the left but rather right or straight up or down. It may also consist of a mix of the two.

The simplest technique to modify a geometric object is to identify its main points and translate those. By "connecting the dots," you can then finish the object.

The stated function:

f(x) = log1/7x

translation 8 units right will give (x + 8)

Function : f(x) = log1/7(x+8)

Now, vertical stretch by a factor of 5.

Function : f(x) = 5* log1/7(x+8)

Thus, the resulting function after an 8 unit right translation and a 5-unit vertical stretch is obtained as:  f(x) = 5* log1/7(x+8)

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The correct question is-

f(x) = log1/7x ; translation 8 units right followed by a vertical stretch by a factor of 5. The resultant function will be?

Hence, in response to the provided question, we can say that  As a result, the set of all positive real numbers is the range of this equation.

An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.

x = 2y is the provided equation.

y denotes the exponent of 2 in this equation. The exponent's base, 2, is a positive real number. As a result, y can be any real number. This equation's domain is all real numbers.

Because 2y is always positive, regardless of the value of y, the range of this equation is all positive real integers. Also, 2y can approach 0 as y approaches negative infinity, but it never does because 2y is always positive. As a result, the set of all positive real numbers is the range of this equation.

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a. The owners' equity increased from $1,567 in 2014 to $3,122 in 2015.

b. The change in net working capital for 2015 is $168.

c. The amount of fixed assets did Weston Enterprises sold is $1630

d. Weston Enterprises must have paid off $2,253 in long-term debt during the year

Now, let's move on to the questions.

a. To find the owners' equity for 2014 and 2015, we need to subtract the total liabilities from the total assets. For 2014, the calculation would be,

Owners' equity 2014 = Total assets 2014 - Total liabilities 2014

Owners' equity 2014 = (Current assets 2014 + Net fixed assets 2014) - (Current liabilities 2014 + Long-term debt 2014)

Owners' equity 2014 = (964 + 4,384) - (401 + 2,380)

Owners' equity 2014 = $1,567

For 2015, the calculation would be:

Owners' equity 2015 = Total assets 2015 - Total liabilities 2015

Owners' equity 2015 = (Current assets 2015 + Net fixed assets 2015) - (Current liabilities 2015 + Long-term debt 2015)

Owners' equity 2015 = (1,176 + 5,104) - (445 + 2,713)

Owners' equity 2015 = $3,122

b. The change in net working capital for 2015 can be calculated by subtracting the net working capital for 2014 from the net working capital for 2015. Net working capital is the difference between current assets and current liabilities.

Net working capital 2014 = Current assets 2014 - Current liabilities 2014

Net working capital 2014 = 964 - 401

Net working capital 2014 = $563

Net working capital 2015 = Current assets 2015 - Current liabilities 2015

Net working capital 2015 = 1,176 - 445

Net working capital 2015 = $731

Change in net working capital = Net working capital 2015 - Net working capital 2014

Change in net working capital = 731 - 563

Change in net working capital = $168

c. To find out how much in fixed assets Weston Enterprises sold, we need to use the equation for the cash flow from assets,

Cash flow from assets = Cash flow to creditors + Cash flow to owners

Cash flow from assets = (Interest paid - Net new long-term debt) x (1 - Tax rate) + (Depreciation x Tax rate)

Cash flow from assets = (328 - (2,713 - 2,380)) x (1 - 0.4) + (1,190 x 0.4)

Cash flow from assets = (-$57) + $476

Cash flow from assets = $419

Net increase in fixed assets = Net fixed assets 2015 - Net fixed assets 2014

Net increase in fixed assets = 5,104 - 4,384

Net increase in fixed assets = $720

Amount of fixed assets sold = Net increase in fixed assets - New fixed assets purchased

Amount of fixed assets sold =  $2,350 - $720

Amount of fixed assets sold = $1,630

d. To calculate the amount of long-term debt paid off during the year, we need to use the equation for the cash flow to creditors,

Cash flow to creditors = Interest paid - Net new long-term debt

Cash flow to creditors = $328 - ($455 - $2,380)

Cash flow to creditors = $2,253

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Step-by-step explanation:

Slope is y2 - y1 / x2 - x1

X1 =2 y1 =4 x2 =-4 y2= 0

0 - 4/ - 4 - 2 = - 4/-6

Sslope =2/3 or 0.67

Round it up if you are asked to.

Answer:

[tex] \frac{1}{9} [/tex]

Step-by-step explanation:

Deal with negative and numerical exponents separately;

Negative exponent means reciprocal;

2 means sqared;

So:

[tex] {3}^{2} = 9 \\ {3}^{ - 2} = \frac{1}{9} [/tex]

Based on the information, we can infer that the graph would be as shown in the attached image.

To graph the equations we must identify the values of the coordinates of each of the equations. In this case it would be:

Equation 1:

Equation 2:

According to the above, the lines would look as shown in the graph. In the case of the first equation, it would be represented by the red line and the second equation would be represented by the blue line.

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The correct answer to the given question is a)29, (b) 91cm is median waist measurement and (c)13cm is interquartile range

(a)From the graph, 11 men have a waist measurement of 85cm and below. Since the cumulative frequency is 40

Number of men who have a waist measurement of more than 85 cm

= 40 − 11

= 29

(b)Median

Given a dataset of size N = 40, the median can be calculated as:

Median = (N + 1) / 2

where N is the total number of items in the dataset.

Substituting the given value of N, we get:

Median = (40 + 1) / 2

Median = 20.5

Since the median has to be a whole number, we take the 20th item as the median. Tracing 20 from the y-axis to the x-axis, the median waist measurement is 91cm.

(c)Interquartile Range = Q3 - Q1

To find the first quartile, denoted as Q1, you need to determine the value that separates the lowest 25% of the dataset from the rest of the dataset.

The formula for the first quartile is: Q1 = (N + 1) / 4

where N is the total number of items in the dataset.

Substituting the given value of N, we get:

Q1 = (40 + 1) / 4

Q1 = 10.25

Since we need to find the 10th item, which corresponds to the 25th percentile of the dataset, we take the integer part of Q1, which is 10. Therefore, the first quartile, Q1, is the 10th item.

​From the graph, at y= 10, x= 84 cm

To find the third quartile, denoted as Q3, you need to determine the value that separates the highest 25% of the dataset from the rest of the dataset.

The formula for the third quartile is: Q3 = 3(N + 1) / 4

where N is the total number of items in the dataset.

Substituting the given value of N, we get:

Q3 = 3(40 + 1) / 4

Q3 = 30.75

Since we need to find the 30th item, which corresponds to the 75th percentile of the dataset, we take the integer part of Q3, which is 30. Therefore, the third quartile, Q3, is the 30th item.

From the graph, at y= 30, x =97 cm

Therefore: Interquartile Range = 97 - 84 = 13cm

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Complete Question

a) how many men have a waist measurement of more than 85 cm

b) what is the median waist measurement

c) what is the interquartile range of the waist measurements

The density of the apple juice is approximately 1094 kg/m³.

Density is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that;

To calculate the density of the apple juice in kilograms per cubic metre (kg/m³), we need to convert the volume from cubic centimeters (cm³) to cubic meters (m³) and the mass from grams to kilograms.

1 cm³ = (1/100)^3 m³ = 10^-6 m³ (conversion factor from cm³ to m³)

1 g = (1/1000) kg (conversion factor from g to kg)

So, the volume of the apple juice in cubic meters is:

320 cm³ × (10^-6 m³/cm³) = 0.00032 m³

And the mass of the apple juice in kilograms is:

350 g × (1/1000) kg/g = 0.35 kg

Now, we can calculate the density using the above formula:

p = m / v

p = 0.35 kg / 0.00032 m³

p = 1093.75 kg/m³

p = 1094 kg/m³

Therefore, the density is 1094 kg/m³.

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Niesa sent apprοximately 423 texts last mοnth.

In mathematics, an equatiοn is a fοrmula that expresses the equality οf twο expressiοns, by cοnnecting them with the equals sign =.

The wοrd equatiοn and its cοgnates in οther languages may have subtly different meanings; fοr example, in French an équatiοn is defined as cοntaining οne οr mοre variables, while in English, any well-fοrmed fοrmula cοnsisting οf twο expressiοns related with an equals sign is an equatiοn.

Let T be the number οf texts that Niesa sent last mοnth.

We can set up the equatiοn:

Tοtal cοst = fixed fee + (cοst per text x number οf texts)

$53.84 = $20 + ($0.08 x T)

Sοlving fοr T, we can subtract $20 frοm bοth sides:

$33.84 = $0.08 x T

Then, we can divide bοth sides by $0.08:

T = $33.84 / $0.08

T ≈ 423

Therefοre, Niesa sent apprοximately 423 texts last mοnth.

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The value of t in the figure is calculated using the concept of similar triangles to be equal to

The value of t is solved using the concept of similar triangles. this involves taking the proportions of the sides which are equal to each order

The calculation is completed as follows

JK / JG = KI / GH

substituting the values of each side

1 / 2 = t / t + 27

cross multiplying

t + 27 = 2t

collecting like terms

27 = 2t - t

27 = t

We can therefore say that the value of t is equal to 24

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Answer:

Step-by-step explanation:

First, we need to simplify the expression inside the parentheses:

8 1/2 - 2 = 8 + 1/2 - 2 = 6 1/2

Next, we need to evaluate the exponent:

2^2 = 2 x 2 = 4

Now, we can substitute the simplified values into the expression:

7 1/4 x 4 + (6 1/2) ÷ 3

Next, we need to evaluate the multiplication and division from left to right:

7 1/4 x 4 = 29 + (6 1/2) ÷ 3

6 1/2 ÷ 3 = 2 1/6

Substituting the simplified value:

29 + 2 1/6

Next, we need to add the two values:

29 + 2 1/6 = 31 1/6

Therefore, the final answer is 31 1/6.

The answer to your question is:

a) To find the object's velocity after 2 seconds, we need to take the derivative of the function s(t) = -0.8t^2 + 32t. The derivative of s(t) is s'(t) = -1.6t + 32. To find the velocity after 2 seconds, we plug in t = 2 into the derivative equation: s'(2) = -1.6(2) + 32 = 28.8 meters per second. Therefore, the object's velocity after 2 seconds is 28.8 meters per second.

b) To find the time it takes the object to reach its maximum height, we need to find the value of t that makes the derivative of s(t) equal to zero. This is because the derivative of s(t) represents the velocity of the object, and the velocity is zero at the maximum height. So we set s'(t) = 0 and solve for t:

0 = -1.6t + 32
1.6t = 32
t = 20 seconds

Therefore, it takes the object 20 seconds to reach its maximum height.

c) To find the object's maximum height, we plug in the value of t that we found in part b into the original equation for s(t):

s(20) = -0.8(20)^2 + 32(20) = 320 meters

Therefore, the object's maximum height is 320 meters.

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Answer:

(1.5)x + 1.5 = 30

Step-by-step explanation:

Answer:

y = 4x + -8

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Answer:

X = 34

Step-by-step explanation:

360-108 = 252

252-88 = 164

5x-6

164+6 = 170

170/5 = 34

Result in (d) refutes the claim in (a), since it is less than the 5% level of significance. Actual proportion is lower than 0.4.

A recent article in a national newspaper claimed that 40% of all students in US colleges drink some alcoholic beverages at least once a week. A students association argued that actually fewer students drink alcohol. In support of its claim the student association has sampled at random 500 students and found that only 180 of them stated that they do drink at least once a week.

Calculate the Claimed Population Proportion

The claimed population proportion is p=0.4

Calculate the Parameters for the Normal Distribution of Sample Proportion

By the Central Limit Theorem, the distribution of the sample proportion p is the normal distribution with mean μj=p=0.4 and standard deviation σj=npq= √[(0.4)(0.6)/500]=0.047.

Calculate the Observed Sample Proportion

The observed sample proportion of those who said "Yes" (that they do drink at least once a week) is pˆ0=500/180=0.36.

Calculate the Probability to Observe Such, or Smaller, Sample Proportion if the Claim in (a) Were to be Correct

Using the CLT and the parameters in (b), the probability to observe such, or smaller, sample proportion if the claim in (a) were to be correct is Pr(p≤pˆ0)=0.056.

Conclusion

The result in (d) refutes the claim in (a), since it is less than the 5% level of significance. This means that we reject the null hypothesis that the proportion of students drinking at least once a week is 0.4, and instead conclude that the actual proportion is lower than 0.4.

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After solving the equation using the elimination method, the value of x is 1 and y is 3.

The given system of equations are:

y = x + 2...............(1)

y = 5x - 2...............(2)

We solving equation by the elimination method.

The elimination method is a method of solving systems of linear equations. It involves performing operations on the equations, such as addition and multiplication, to transform the equations into simpler forms.

Subtract equation 1 and equation 2

x+2 - 5x + 2 = 0

-4x + 4 = 0

Subtract 4 on both side, we get

-4x = -4

Divide by -4 on both side, we get

x = 1

Now put the value of x in equation 1.

y = 1 + 2

y = 3

The solution set is {1, 3}.

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The complete question is:

Find the value of x and y.

y = x+2

y=5x-2