Tomika and Mark had $3,800 in medical expenses and paid an additional $8,009 for medical insurance. The insurance covered 60% of the medical expenses. The IRS allows medical and dental expense deductions for the amount that exceeds 7.5% of a taxpayer's adjusted gross income. If their adjusted gross income is $101,598, how much can they claim as a medical deduction?

The value of x is 15.

What is an angle?

When two lines come together at a common point, an angle is created. They are expressed as a number of degrees, denoted by the symbol °. Acute, right, obtuse, and reflex angles are the other three significant types of angles.

Given that ∠ADB and ∠BDC are supplementary angle.

∠ADB = (2x - 15)° and ∠BDC = 11x°.

Two angles are supplementary angle, if their sum is equal to 180°.

Therefore,

∠ADB + ∠BDC = 180°

Putting the value of ∠ADB and ∠BDC:

(2x - 15)° + 11x° = 180°

2x - 15 + 11x = 180

Combine like terms:

(2x + 11x) -15 =180

13x - 15 =180

Add 15 with both sides:

13x = 180 +15

13x = 195

Divide both sides by 13:

x = 15

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The location of B under the Line Segment Partition is 6.8

What is Line Segment Partition?

A line segment is partitioned when it is divided into equal parts according to a specified ratio. The total number of partitions of the line segment must be equal to the sum of the two values in the ratio.

Given in the question that on a number line AC;

Location of Point A = 4

Location of point C = 11

point B lies between points A and C

So, B divides line AC in the ratio AB: BC = 2:3.

Thus;

BC = 3/5 of the total length of the AC

AB = 2/5 the total length of the AC

Then, total length of AC = 11-4 = 7

BC = 3/5 * 7 = 4.2

AB = 2/5 * 7 = 2.8

Thus, the location of point B is; 4 + 2.8 = 6.8

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a) car A is ahead of car B after 3 minutes.

b) Velocity is the shaded region.

c) the area under curve b is greater than the area under curve a.

a) The total distance  represented by the shaded region A, the area under the graph of v(t).

(c) A is a triangle, so its area is

A =1/2(base)(height)

   = 1/2(5 sec)(80 ft/s) = 200 ft

b) The meaning of area of the shaded region in this problem is: Velocity

Velocity is the directional velocity of a moving object as an indicator of the rate of change of position, observed from a certain frame of reference and measured at a certain time reference (eg 60 km/h northward).

c) The distance travelled will be represented by the area

under the velocity graph.

However,  first convert everything to meters and seconds:

320 km/h = 1000

Now,

60·60 320 m/s ≈ 88.89 m/s.

A =1/2(base)(height)

= 1/2(30 sec)(88.89 m/s) ≈ 1333.3m

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Answer: for the graphs if it crosses the same line twice if you draw a line down the top to bottom it is not a function and if the x repeats for the table and equals something different it is not a function

Step-by-step explanation

for tables (5,8) (6,9) (5,2) (1,5) this would not be a function because 5 equals two different things

After solving for angles, the value of p in the given angles is 44°.

An angle is formed when two straight lines or rays meet at a single terminal.

The place where two points converge is known as an angle's vertex.

The name "angel" comes from the Latin word "angulus," which means "corner."

Angles are also produced when two planes intersect.

These are what are known as dihedral angles.

So, we know that ∠CAD = 90°.

And since ∠CAB is s straight angle. Then,

∠CAD + ∠DAB = 180

90 + p + 46 = 180

p + 136 = 180

p = 180 - 136

p = 44°

Therefore, after solving for angles, the value of p in the given angles is 44°.

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A. The relative frequency of the people that had mechanical issues is 30%.

B. The relative frequency of the people that did not have mechanical issues is 70%.

C. The relative frequencies in (a) and (b) suggest that the new car has been relatively unreliable, as 30% of buyers experienced mechanical issues within the first two years. This suggests that the car has not been built to a high standard of quality, and that buyers should be prepared for potential issues with the car.

There are total 1680 ways to arrange 4 magazines in a row of 8 choices

What is Permutation?

The term permutation refers to a mathematical computation of the number of possible arrangements of a given collection. Simply said, a permutation is a term that defines the amount of different ways something may be organised or arranged. The order of the arrangement is important in permutations.

Solution:

Since, order of the arrangement matter too

we will use Permutation

Total Ways of Arrangement = 8P4

Total Ways of Arrangement = 8!/4!

Total Ways of Arrangement = 8*7*6*5*4!/4!

Total Ways of Arrangement = 1680 ways

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Answer:

Each pen is 2.20

Step-by-step explanation:

We first need to find the total cost of the pens

20.50 - 2.90 = 17.60

Now we can divide by the number of pens purchased.

17.60 / 8

2.20

Each pen is 2.20

Answer:

$ 2.20

Step-by-step explanation:

First, let us find the total cost of pens.

$ 20.50 - $ 2.90 = $ 17.6

And now let us find the cost per pen.

For that, let the cost of a pen be x.

Number of pens Cost

8 $ 17.6

1 x

Use cross multiplication and find the value of x.

8x = 1 × 17.6

8x = 17.6

Divide both sides by 8.

x = $ 2.2

Therefore,

Cost of a pen is $ 2.20

P-value = 0.0384

As P-value < 0.05, reject the null hypothesis.

A statistic (a number obtained from the sample) used in statistical hypothesis testing is known as a test statistic. Usually, a hypothesis test is described in words.

A test statistic is a figure obtained from a statistical analysis. It explains how distant your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.

The alternative and null hypotheses are listed below.

Lack of hypothesis H0: μ = 13

Ha: 13 Alternative Hypothesis

Statistical test, z = (xbar - mu)/(sigma/sqrt(n))

z = (11 - 13)/(8/sqrt(50))

z = -1.77

Region of Rejection

For α= 0.05, this is a left-tailed test.

Z has a critical value of -1.645.

Therefore, if z -1.645, reject H0 and accept the null hypothesis.

P-value Approach

P-value = 0.0384

As P-value < 0.05, reject the null hypothesis

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The 15 percent tip on a dinner bill of 48.71 dollars is 7.3 dollars

The dinner bill is 48.71 dollars. Let's estimate a 15 percent tip on the dinner bill as follows:

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.

In other words, Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Therefore, let's estimate the 15% tip on the dinner bill of 48.71 dollars.

dinner tip = 15% of 48.71

dinner tip =  15 / 100 × 48.71

Hence, the estimated 15% tips of the dinner bill is as follows:

dinner tip = 7.3065 dollars

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Use / for the fraction bar if necessary. if p − 1 is a factor of p^4 + p^2 + p - k , the value of k is 1 + p^2 + p^4.

A fraction bar is a graphic representation of fractions that is useful for fraction comparison and fraction operations. Part-to-whole representational models like fraction bars or fraction strips are used. One unit out of a whole is represented by each segment of a fraction bar.

To comprehend the value of a fraction, utilize fraction bars. They can also be utilized for comparing fractions and, subsequently, adding and removing fractions. The ability to visualize a fraction bar for just any fraction is crucial.

p - 1 = p^4 + p^2 + p - k

k = 1 + p^2 + p^4

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Answer:

7

Step-by-step explanation:

hope it helps!

Answer:

7

Step-by-step explanation:

7 over one is a whole number

that there is no smallest positive rational number is proven below.

What is Rational Number?

Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.

So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that numerator or denominator doesn't have commonly divisible.

Let r be any reasonable number.

We can infer that r/2 is rational because r is a rational number.

There is no smallest rational number so we can assume that r/2 r because r/2 is rational.

Hence, proved that here is no smallest positive rational number.

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Assuming simple interest rate, to reach the account value of 28500 dollars, it needs 27.2 years.

Assuming simple interest rate, the formula for the future value is:

FV = PV (1 + r x n)

Where:

PV = present value

r = interest rate per period

n = number of periods

Parameters given in the problem,

r = 8.5% = 0.085

PV = 8600

FV = 28500

Plug these parameters into the formula:

28500 = 8600 (1 + 0.085 x n)

1 + 0.085 x n = 3.313

0.085 x n = 2.313

n = 27.2

Hence, it needs 27.2 years to reach 28500 dollars.

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The average speed of a bus that travels 150 km in 3 hours is 50 kilometres per hour.

The average speed is directly proportional to the total distance covered and inversely proportional to the total time taken. Using the mentioned information to write the formula of average speed -

Average speed = total distance covered ÷ total time taken

Keep the values in formula to find the average speed of the bus

Average speed of the bus = 150/3

Performing division on Right Hand Side of the equation to find the average speed of the bus

Average speed of the bus = 50 kilometres per hour

Hence, the average speed is 50 kilometres per hour.

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The equation x² + y² = a² in form of a differential form is; dy/dx = -x/y

A differential equation is defined as one that contains the derivative of a function. For example, f(x) + 3 = 4f'(x) - 2.

We are given the equation;

x² + y² = a²

Thus, differentiating to be in differential form is;

2x(dx) + 2y(dy) = 0

-2x(dx) = 2y(dy)

dy/dx = -x/y

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To find the range of numbers we subtract the largest number by the lowest numbers.

In the given question,

We have to explain, the range of a numbers.

The range refers to all the entities (output) that result from a relation or function. The Range set is made up of all used output values (dependent values).

The difference between both the highest and lowest numbers in a collection or set is known as the range.

To find the range of numbers we subtract the largest number by the lowest numbers.

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A: he percent of respondents who do not like hamburgers and burritos both = 16.09 %

B: Marginal relative frequency of all customers that like hamburgers= 0.65

C: Those who like Hamburgers but not burritos.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

                         Like Hamburgers ↓  Does Not Like Hamburgers↓    Total↓

Likes burritos →                 39                           38                                   77

Does not like burritos →    95                           33                                 128

Total →                                134                           71                                 205

So, according to the above table, a total of 77 customers like burritos, out of which 38 do not like hamburgers, hence, the remaining 77-38= 39 like Hamburgers.

A total of 128 customers do not like burritos, out of which 95 do like hamburgers, hence, the remaining  128 - 95 = 33 do not like Hamburgers.

A total of 134 customers like hamburgers, but 71 do not like it, hence, the total respondents are 205.

Part A: The percent of respondents who do not like hamburgers and burritos both

There are 33 such respondents.  

Hence, percentage = (033/205) *100 = 16.09 %

Part B: Marginal relative frequency of all customers that like hamburgers

It will be the ratio of the sum of the customers that like hamburgers to the total number of respondents

Hence, ratio  134/205 = 0.65

Part C: The data point that has the strongest association of its two factors.

For this, we need to find the ratio of all the four data with the total.

Those who like Hamburgers and burritos = 39/134 = 0.29

Those who like Hamburgers but not burritos = 95/134 = 0.71

Those who like burritos but not Hamburgers = 38/71 = 0.53

Those who do not like burritos or Hamburgers = 33/71 = 0.47

So, the answer is those who like Hamburgers but not burritos.

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Answer:

Step-by-step explanation:

The formula distance = rate x time also indicates a linear relationship.

Given,

Linear relationship;

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.

We have to determine the calculations for a linear relationship;

Here,

Distance = rate x time is another equation that results in a linear relationship. This linear relationship would be represented in the top right quadrant of a graph with an X and Y axis because distance is often a positive quantity.

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The dimensions of the rectangular field is 15 meters long and 14 meters wide.

A rectangle is a two-dimensional figure that has 2 pair of parallel sides that are of the same length. The corners made by these sides are right triangles.

Let x = length of the rectangular field

y = width of the rectangular field

If the area of the land is 210 square meters, then the product of its length and width is equal to 210 square meters.

A = l x w

210 = xy

x = 210/y

Serenity has 58 m of fencing for the perimeter of the rectangular field.. Hence,

P = 2l + 2w

58 = 2x + 2y

Substitute the expression of x and solve for y.

58 = 2x + 2y

58 = 2(210/y) + 2y

58 = 420/y + 2y

Multiply both sides by y and divide by 2.

29y = 210 + y²

y² - 29y + 210 = 0

(y - 14)(y - 15) = 0

y = 14 ; y = 15

Hence, y = 14.

Substitute the value of y and solve for x.

x = 210/y

x = 210/14

x = 15

Hence, the length and width of the field is 15 meters and 14 meters, respectively.

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There is sufficient proof to presume that under 77% of messages are spam.

A statistical hypothesis test  is a technique for measurable induction used to conclude whether the information within reach adequately support a specific theory. Speculation testing permits us to offer probabilistic expressions about populace boundaries.

Given the information in the inquiry;

Test size n = 500

x = 361

p₀ = 77% = 0.77

q₀ = 1 - p₀ = 1 - 0.77 = 0.23

p = x/n = 361/500 = 0.722

Speculation;

Null hypothesis H₀ : p ≥ 77% or 0.77

Alternative hypothesis  Hₐ : p ≥ 77% or 0.77

Test Measurement

z = ( p - p₀ )/√( ( p₀ × q₀ )/n )

so we substitute

z = ( 0.722 - 0.77 )/√( ( 0.77 × 0.23 )/500 )

z = - 0.048/√( 0.1771/500 )

z = - 0.048/√0.0003542

z = - 0.048/0.01882

z = - 2.55

so our p-worth will be;

p-value = p( z < - 2.55 ) {from table }

p-value = 0.0054

at 0.05 degree of importance ∝

p-value ( 0.0054 ) is not as much as importance level ∝ ( 0.05 )

Accordingly we Reject Null hypothesis H₀

Thus, there is sufficient proof to presume that under 77% of messages are spam.

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After 400 miles is the total charge for each vehicle the​ same ie $340

What is equation ?

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

An equals sign is a part of a mathematical expression referred to as an equation. A lot of equations include algebra. In math, algebra is employed when you don't know the precise amount to calculate.

x= number of miles

car cost is  240+0.25x

van cost is 180+0.40x

When the equations are equal

240 + 0.25x = 180 +0.40x

60 = 0.15x

15x = 6000

x=400

400 miles.  

They will each cost $340

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Answer: 7.7%

Step-by-step explanation:

So the answer is 7.7

To find the percent error, start by listing the key information from the problem.

Greta's scale shows the package weighing 3 pounds.

The scale at the post office shows the package weighing 3.25 pounds.

First, find the amount of error. It is the difference between 3.25 and 3, which is 0.25.

Now, use the formula to find the percent error.

percent error =

amount of error

correct amount = 0.25

3.25

= 0.0769…

You can rewrite this as a percent rounded to the tenths place, 7.7%. So, the percent error for Greta's scale measurement is about 7.7

The function f, in the slope-intercept form is f= -3x+6.

The slope or gradient of the line is a numerical value used to describe a line's steepness and direction in mathematics. It was first used to describe slope in O'Brien's (1844) and Todhunter's (1888) versions of the equation for a straight line, which are both written as "y = mx + b" and "y = mx + c," respectively. The choice of the letter m for slope has no apparent justification.

Calculating slope involves comparing the "vertical change" to the "horizontal change" between any two points on a line, or any two points. The ratio, which provides the same number for each, is occasionally given as a quotient ("rise over run").

Here given,

For a linear function f,

f(2)=0 and f(4)=-6

So, from the given hint the points are (2, 0) and (4, -6)

Here slope m=(-6-0)/(4-2)

m=-6/2

m= -3

We know that the equation of the function in slope-intercept form is:

f=mx +c

By substituting the point (2, 0) and m= -3 in the function we get,

0= -3(2)+c

c=6

Now, by substituting m= -3 and c=6 in the function, we get

f= -3x+6

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The answer is true. The curve of t-distribution has thicker tails than the curve of the standard normal distribution.

The t-distribution is also called as Student's t-distribution which is a type of probability distribution with a bell shape which is similar to  normal distribution but has thicker tails. It is used to estimate population parameters when sample sizes are small or variances are unknown. T-distributions have a higher probability of extreme values more than normal distributions which results in thicker tails.

Tail thickness is determined by a t-distribution parameter called degrees of freedom, with lower values resulting in heavier tails and higher values resulting in the t-distribution resembles standard normal distribution with a  standard deviation of 1and mean of 0.

Thus, t-distribution has thicker tails than the normal distribution.

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Answer:

he will score 10 goals in 5 games

The terms 4t and 120 represents the cost of 4 cups of tea and total cost respectively.

A system of equation is defined as the group of equations having the same degree and same number of variables.

The given system can have one or more than one or no solutions at all.

The system having no solutions are called inconsistent while the ones having them are called consistent.

The given problem can be solved as follows,

Suppose the number of cups of tea and lemonade be t and l respectively.

Then, the following equations can be formed for the given case,

The equation for total cost is given as,

4t + 2l = 120                 (1)

And, the equation for the number of cups is given as,

l = 5t                             (2)

Now, the term 4t in equation (1) represents the cost for 4 cups of tea and 120 represents the total cost.

Hence, the given terms represent the cost of 4 cups of tea and the total cost of tea and lemonade.

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