if the displacment (x) of a body at a certain time (t) is given from the relation

x= At +B [tex]\sqrt{2t\\}[/tex]

so the dimensions of A and B are = ...............

The simple interest accumulated on the principal at 12% rate for 4 years is $3,840.

Simple interest formula is expressed as;

I = P × r × t

Where I is interest, P is principal, r is interest rate and t is time.

Given the data in the question;

First, convert the interest rate from percent to decimal.

Interest rate r = 12%

Interest rate r = 12/100

Interest rate r = 0.12

Plug the given values into the above formula and solve for interest I.

I = P × r × t

I = $8000 × 0.12 × 4

I = $3,840

Therefore, the interest earned is $3,840.

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The equation that could be used to determine x, the number of seconds, when the two tanks have the same amount of water is 120 - 1/2(x) = 100 - 1/4(x) or x = 80.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let x be the number of seconds at the moment that the two tanks have the same amount of water.

If a tank has 120 gallons of water and is being drained at a rate of 1/2 gallon each second, the the amount of water left after time = x is "120 - 1/2(x)".

If another tank has 100 gallons of water and is being drained at a rate of 1/4 gallon each second, the the amount of water left after time = x is "100 - 1/4(x)".

Equate the two expressions to determine the time, x , at which the two tanks have the same amount of water left.

120 - 1/2(x) = 100 - 1/4(x)

20 = 1/4 x

x = 80

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The Constant Of Proportionality Is 3.1

A per the table,

Amount of dietary fiber in 3 servings of banana = 9.3 grams

Amount of dietary fiber in 6 servings of banana = 9.3 grams

Amount of dietary fiber in 9 servings of banana = 9.3 grams

Amount of dietary fiber in 12 servings of banana = 9.3 grams

We need to find

The constant of proportionality.

We know that the constant of proportionality is a constant number that represents the rate at which ratios of a quantity decrease or increase.

Let the constant of proportionality be, k.

So, k = x/y

Where,

x = Quantity

y = Total Number of the quantity.

Ratio 1 = 9.3/3 = 3.1

Similarly,

Ratio 2 = 18.6/6 = 3.1

Ratio 3 = 27.9/9 = 3.1

Ratio 4 = 37.2/12 = 3.1

since all the ratios are equal;

Hence, The Constant Of Proportionality Is 3.1

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The correct option is (c).

(A) We know that sum of the interior angles of a triangle is equal to 180°.

m∠a + m∠b + m∠c = 180° (all three are interior angles)

(B) If the sum of two angles is 180°, that angle is called a supplementary angle. In other words, when two angles add to form a straight line, they are called supplementary angles.

m∠d + m∠c = 180° (both are in a straight line making an angle)

(C) Transitive properties help establish a connection by stating that if a = b and b = c, then a = c.

m∠a + m∠b + m∠c = 180°

m∠d + m∠c = 180°

Therefore, this property

We can say,

m∠a + m∠b + m∠c = m∠d + m∠c    

(D) Subtraction equality properties: Subtraction equality properties indicate that subtracting or removing an equal value from two equal elements results in a new equal quantity.

The formula for this is if a = b, then a-c = b-c

In the question,

m∠a + m∠b = m∠d

Both ∠a and ∠b are two interior angles and the exterior angle is ∠d.

According to the exterior angle property of a triangle theorem, the sum of two opposite interior angles is equal to exterior angles.

Hence, this is also correct.

Therefore, the correct option is (c) which has the correct steps and reasons for the given question.

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Answer:

A) g(x) = 14x + 30

B) The last explanation

No, because her rate of change is $12 per week which is less than William's rate of change.  

Step-by-step explanation:

A:

At the beginning William as 30 dollars (0,30)  Week zero he has 30.  Then each week, his balance goes up 14 dollars

g(x) = 14x + 30  

B:

Jennifer's bank account is increasing by 12 dollars a week, but William's is increasing 14 dollars a week.

The equation for the line of best fit of the scatter plot according to the attached image is; y = 1.5x + 0.5.

It follows from the task content that the equation of the line of best fit of the scatter plot is to be determined.

By observation, it can be inferred that the y-intercept of the line of best fit is at the point; (0, 0.5).

Also, the slope of the equation can be determined by considering the points; ( 2 , 1 ) and ( 9 , 12 ).

Therefore, since the slope is given by; m = (y2 - y1) / (x2 - x1).

In this scenario, slope, m = (12 - 1) / (9 - 2)

m = 11/7.

Hence, the slope is approximately; 1.5.

Ultimately, the equation of the line of best fit is; y = 1.5x + 0.5.

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Answer:

===========================

Correct choice is C

Answer:

c) 196.2 minutes

Step-by-step explanation:

Forming the equation,

→ y = (4.5/5) × 218

Now required value of y will be,

→ y = (4.5/5) × 218

→ y = 981/5

→ [ y = 196.2 min ]

Hence, the value of y is 196.2.

The slope of the line is 10.

Given:

The graph shows the distance traveled by an Olympic-level sprinter over time during a race.

The line begins at the line begins at the origin and passes through the point (2,20).

slope between (0,0) and (2,20).

slope m = y2 - y1 / x2 - x1

= 20 - 0 / 2 - 0

= 20/2

= 10.

Therefore the slope of the line is 10.

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The side x is √2 cm when the right angle triangle is given with hypothesis 2 cm.

Given that,

In the picture we have a right angle triangle.

We have to find the side x.

The angles are 90°, 45° and 45°.

The hypothesis is 2cm.

By the trigonometric ratio.

The study of angles and the angular relationships between two-dimensional and three-dimensional shapes is known as trigonometry.

Sin45°= opposite side/ hypothesis

1/√2= x/2

x=2/√2

x=√2

Therefore, The side x is √2 cm when the right angle triangle is given with hypothesis 2 cm.

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Answer:A

Step-by-step explanation:negative fourteen and 5 over 120

Because you multiple

2 x -7  = -14

10 x 12 = 120

1 x 5 = 5

Answer:

170%

Step-by-step explanation:

increase in price = 216 - 80 = $136

x : 100 = 136 : 80

x = 100 * 136 / 80

x = 10 * 136/8

x = 1360 / 8

x = 170 %

Answer:

170%

Step-by-step explanation:

80+170%=$216

Answer:

3.5 hours

Step-by-step explanation:

74-32=42

42/12=3.5

The average speed in miles per hour is 1.67 miles/hour

What is her average speed?

Average speed is calculated by dividing distance by time (eg miles/hour).

Given that, Noreen can walk 1/3 mile in 12 minutes.

We need to find her average speed.

We know that the total distance covered divided by the total time taken is called the average speed of Noreen.

Mathematically, it is given by :

v=d/t

t = 12 minutes = 0.2 hours

v=(1/3 mile)/0.2 hours

v = 1.67   miles/hour

So, the average speed of Noreen is 1.67  miles/hour. Hence, this is the required solution.

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Dr. Kirmser's monthly gross pay = $ 29345.65

Employers and workers are both subject to the Social Security tax, which is used to pay for the country's Social Security program. Federal Insurance Contributions Act (FICA)-mandated payroll taxes or Self-Employed Contributions Act-mandated self-employment taxes are the two ways that Social Security tax is collected (SECA).

Here we have

In 2009, Dr. Kirmser's gross pay was $381,318.60.

Social Security tax = 6.2%     [ Maximum: $106,800 ]  

=> 6.2% = 6.2/100 = 0.062  

Medicare tax = 1.45%  

=> 1.45% = 1.45/100 = 0.0145  

From the above information,

Total tax on salary =0.062 + 0.0145 = 0.0765

In 2009, Dr. Kirmser's gross pay was $381,318.60.

Tax can be calculated on Gross pay = 0.0765 × $381,318.60

= 29170.827  

As we know

Net pay = gross salary - deductions

=> Monthly gross pay = $381,318.60 - $29170.827 = $ 352147.773

Therefore,

Dr. Kirmser's monthly gross pay = 352147.773 ÷ 12 = $ 29345.65

Hence,

Dr. Kirmser's monthly gross pay = $ 29345.65

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The expression 2x + 1 = y and y = 2x + 1 has no solution.

Expression:

The expression means a mathematical statements that have two terms at least that contain variables, numbers, or both connected by the arithmetic operators.

Given,

Here we have the expressions 2x + 1 = y and y = 2x + 1.

Now, we have to find the number of solution for this expression.

When we try to find the solution(s) graphically, you would plot both of the equations as straight lines. The solution(s) lies where the lines intersect.

But here we looking into the given equation both are equal.

And if we plot these on the graph then it will simply present the straight line. And there is no intersection in it.

Which also states that there is no solution for this expression.

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The rounded value of x² = 521/73 is ± 2.67 and already rounded to the nearest hundred.

A perfect square number when taken the square root of it results in an integer.

Numbers that are not perfect squares when taken the square root of it are irrational numbers.

One method of obtaining square roots for perfect squares is prime factorization.

Given, x² = 521/73.

∴ x² = 7.13.

x = ± √7.13.

x = ± 2.67.

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At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6.

x=4.25 is the GPA highest 2.5% of the students.

We have to find the GPA of the highest 2.5% of the students.

Mean = μ = 2.9

Standard deviation = σ = 0.6

Finding the z value for corresponding area 0.9750

For 95% confidence interval ,

z = 1.96

For 97.5% confidence interval,

We get z = 2.25

From

Z = ( x - μ ) / σ

For 2.5% of the students

To solve for x

x = Z*σ + μ

x = 2.25*0.6 + 2.9

x = 1.35 + 2.9

x = 4.25   GPA of highest 2.5% of students

Hence the answer is, x=4.25 is the GPA highest 2.5% of the students.

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Answer:

Step-by-step explanation:

A = 44

a = 11

______

b - ?

A = a·b

b = A / a = 44 / 11 = 4 ( inches)

The directions on a swimming pattern says to cut an extra 15 percent of fabric to account for error, Chloe needs 0.75 yard of fabric to make a skirt and she cuts 0.8625 yards,

Given that the directions on a sewing pattern say to cut an extra 15% of fabric to account for an error, and Chloe needs a 0.75 yard of fabric to make a skirt, so she cuts 0.1125 yard, to determine if Chloe cut the correct amount of fabric the following calculation must be made:

0.75 x 1.15 = X

0.8625 = X

0.8625 - 0.1125 = 0.75

Therefore, the amount of fabric that Chloe cut is correct.

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The length of the shorter side on this plan is 2.8cm.

Based on the information illustrated, let the length of the shorter side on this plan be represented by x.

In this case, the dimensions of a room are 4.2 m by 6 m and on a plan, the longer side is equal to 4cm.

This will be illustrated as:

x/4 = 4.2 / 6

Cross multiply

6x = 4 × 4.2

x = (4 × 4.2) / 6

x = 2.8cm

The length is 2.8 cm.

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When conducting an experiment with the probability of a success of 0.02 and you are interested in the probability of 2 successes in 15 trials, the correct probability function to use is the binomial probability function. (Option B)

Binomial probability function, in probability theory and statistics, refers to the discrete probability distribution of the number of successes in a sequence of repeated independent experiments. Generally, the binomial distribution represents data generated from a yes–no question, and each with its own Boolean-valued outcome: success or failure.  As the experiment where probability of success is given and you are interested in the probability of 2 successes in 15 trials, the appropriate probability function is binomial probability function.

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Answer:

44,000 shares in a blue-chip company

Step-by-step explanation:

So since Johnson had 22,000 shares in a blue-chip company and it split 2:1, we multiple the beginning number of shares by 2 because they split into 2 different shares.

22,000*2=44,000

The scale of reading that the chef needs to see for this spice when preparing the specialty for 19 people would be = 4.5 ounce.

A chef is a trained individual in various aspects of preparation of dishes, who has the knowledge of combination of food products to achieve an adequate meal.

The quantity of spice per serving= 1/20 ounce.( For an individual)

The quantity of people to prepare specialty for = 90 people

The quantity of spice that would be used to prepare specialty for 90 people would be;

= 1/20 × 90

= 90/20

= 4.5 ounce.

Therefore, the scale reading the chef needs to see for preparing of specialty for 90 people would be = 4.5 ounce.

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The coordinates of the point that represents the weekly average per run for Week 7 is (7, 3.00).

It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = aˣ

where a is a constant and a>1

It is given that:

Jason decided to begin a workout program. He wants to start running three times a week.

As we know, the exponential function can be represented as:

f(x) = abˣ

The weekly average per run is 1 mi.

He increases his weekly average per run by 17% each week,

The exponential function:

f(x) = 1(1.17)ˣ

Plug x = 7

f(7) = 1(3.0012)

f(7) = 3.00

Thus, the coordinates of the point that represents the weekly average per run for Week 7 is (7, 3.00).

The complete question is:

Jason decided to begin a workout program. He wants to start running three times a week. At the beginning of the workout program, his weekly average per run is 1 mi. He increases his weekly average per run by 17% each week, according to an exponential growth model. Jason makes a sketch of the graph for this situation. He plots the point containing the y-intercept, (0,1) . He then plots the point representing the weekly average per run for Week 7 and rounds the coordinates of the point to the nearest tenth. What are the coordinates of the point that represents the weekly average per run for Week 7?

options:

A. (7, 3.2)

B. (7, 2.7)

C. (7, 3.0)

D. (7, 4.6)

E. (7, 4.1)

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Answer:

7,3,0

Step-by-step explanation:

Answer:

  P(basketball or baseball) = 11/24

Step-by-step explanation:

You want the probability that a randomly chosen student plays either sport, given the probability that 13 of the 24 students plays neither sport.

The probability that a student plays at least one (of the two) sports is the complement of the probability they play neither sport. If 13 of 24 students play neither sport, then (24-13)/24 = 11/24 must play at least one of the two sports.

  P(basketball or baseball) = 11/24

__

Additional comment

6+7-11 = 2 students play both sports.

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Answer:

20 slices

Step-by-step explanation:

2 3/5 = 13/5

13/5 / 1/8

(13/5)(8/1) = 20.8

about 20 slices

33.2 miles per gallon is the unit rate for miles per gallon.

Given, Grace drove 41 1/2 miles.

She used 1 1/4 gallons of gasoline.

So, Grace drove 41 1/2 miles = Grace used 1 1/4 gallons of gasoline

41(1/2) miles = 1(1/4) gallons of gasoline

83/2 miles = 5/4 gallons of gasoline

as, 5/4 gallons of gasoline = 83/2 miles

1 gallon of gasoline = (4/5)×(83/2)

1 gallon of gasoline = (2/5)×83

1 gallon of gasoline = 166/5

1 gallon of gasoline = 33.2 miles

33.2 miles/gallon is the unit rate.

Hence, 33.2 miles per gallon is the unit rate for miles per gallon.

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Answer: the answer is number 6

Answer:

The property tax increases by 35

Step-by-step explanation:

The number 333 in the equation is a constant.  It is added to the total no matter how many years after 1990.  The 35 is what is increasing every year after 1990.