Clinic offers maria 15% discount off her total cost.

Answer:

  [15-√226, 1] ∪ [29, 15+√226]

Step-by-step explanation:

You want all solutions to |x^2 - 30x - 1| + |x^2 - 30x + 29| = 30.

The equation resolves to a piecewise equation whose domains are delimited by the points where the absolute value arguments are zero.

The argument of the left absolute value function will be zero where ...

  x^2 - 30x - 1 = 0

  x = (-(-30) ±√((-30)² -4(1)(-1)))/(2(1) = 15 ± √226 ≈ {-0.0332964, 30.0332964}

The argument of the right absolute value function will be zero where ...

  x^2 -30x +29 = 0

  (x -29)(x -1) = 0

  x = {1, 29}

In this domain, both absolute value arguments are positive, so the equation is ...

  x^2 -30x -1 +x^2 -30x +29 = 30

  2x^2 -60x +28 = 30 . . . . . collect terms

  x^2 -30x -1 = 0 . . . . . . . . . write in standard form

  x = {15 -√226, 15 +√226} . . . . solutions to the equation

These solutions are not in the domain we have defined for this equation.

In this domain, the left absolute value argument is negative, and the right argument is positive, so the equation is ...

  -(x^2 -30x -1) +(x^2 -30x +29) = 30

  30 = 30

All values of x in this domain (15-√226 ≤ x ≤ 1) are in the solution set.

In this domain, both absolute value arguments are negative, so the equation is ...

  -(x^2 -30x -1) -(x^2 -30x +29) = 30

  -2x^2 +60x -58 = 0 . . . . . . write in standard form

  x^2 -30x +29 = 0 . . . . . . . divide by -2

The solutions to this are x={1, 29}, neither of which is in the domain we have defined for this equation.

In this domain, the left absolute value argument is negative and the right argument is positive. The equation resolves to the same one as for the domain 15-√226 ≤ x ≤ 1: 30 = 30. Hence, all x-values in this domain (29 ≤ x ≤ 15+√226) are part of the solution set.

In this domain, both absolute value arguments are positive, so the equation is ...

  x^2 -30x -1 = 0 . . . . . . . . . write in standard form

  x = {15 -√226, 15 +√226} . . . . solutions to the equation

These solutions are not in the domain we have defined for this equation.

In interval notation, the solution set for the equation is ...

  [15-√226, 1] ∪ [29, 15+√226]

Answer:

1

Step-by-step explanation:

6=2y+4

2=2y

y=1

Answer:(22.5/3)-1.75=e

Step-by-step explanation:

3x/3=22.5/3

x=7.5 per book

7.5-1.75=5.75 per book after coupon

Trigonometry is the application of certain functions to determine the value of a quantity. The tree stands 10.77 meters tall.

Some trigonometric functions can be used to solve the given problem. Let s represent the distance from the tip of the tree's shadow to where Aria stands, so that;

s = 27.75 - 23.5

= 4.25 m

s = 4.25 m

Also, let the angle formed by the line connecting the tree's tip and the shadow's tip be, so that;

Tan θ = opposite / adjacent

Here given,

Opposite side = 1.65

Adjacent side = 4.25

          = 1.65 / 4.25

          = 0.3882

θ = Tan⁻¹ 0.3882

  = 21.216

θ = 21.216°

We get θ = 21.216°

The tree's height, h, can be calculated as follows:

Tan 21.216° = h/27.75

h = Tan 21.216° x 27.75

  = 0.3882 x 27.75

h = 10.77m

As a result, the tree's height is 10.77m.

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Given expression 60% of 25 is equivalent to 0.6 × 25.

What do you mean by percentage?

a % is a quantity or ratio that can be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Given expression:

60% of 25

⇒ [tex]\frac{60}{100} \times[/tex] 25

⇒ 0.6 × 25

⇒ 15

Therefore, given expression 60% of 25 is equivalent to 0.6 × 25.

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The equation of the exponential function represented in this table is;

y = 6(1.8)ˣ

We are given the table of values of the exponential function and we can write the coordinates as;

(3, 34.99)

(4, 62.99)

(5, 113.37)

(6, 204.07)

(7, 367.33)

The general formula for an exponential function is;

y = a(b)ˣ

where;

a is the initial value

b is the constant multiplier

For the third coordinate, we have;

a(b)³ = 34.99    ------(1)

For the fourth coordinate, we have;

a(b)⁴ = 62.99    ------(2)

Divide eq 1 by eq 2 to get;

b = 1.8

Put 1.8 for b in eq 1 to get;

a(1.8)³ = 34.99

a = 6

This gives the exponential equation as; y = 6(1.8)ˣ

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Answer:

It sounds like you want to use the equation h = "-5" - 2 t + 36 to calculate how many seconds it will take for a coin to fall from a balcony to a fountain below. The only problem is that the equation you provided is not correct. The correct equation for the height of an object in free fall is h = -16t^2 + vt + h0, where t is the time in seconds, h0 is the initial height of the object, and v is the initial velocity of the object.

To solve for the time it will take for the coin to fall to a height of 12 feet, you need to know the initial height of the balcony and the initial velocity of the coin. Assuming the initial height of the balcony is 36 feet and the initial velocity of the coin is 0 (since it is not moving when it is released), you can plug these values into the equation to solve for t:

h = -16t^2 + 0 + 36

12 = -16t^2 + 36

-24 = -16t^2

t^2 = 1.5

t = sqrt(1.5)

t = approximately 1.22 seconds

So it will take approximately 1.22 seconds for the coin to fall from the balcony to a height of 12 feet.

Answer:

To factor out the GCF from the given expression, we can use the distributive property. This property states that we can distribute a common factor to all of the terms in an expression by multiplying the common factor by each term separately. In this case, the common factor is n, so we can distribute it to each term by multiplying it by -26, 7, and 13:

(-26n * n) + (7n * n) + (13n * n)

This gives us:

-26n^2 + 7n^2 + 13n^2

We can then combine like terms by adding the coefficients of n^2:

(-26 + 7 + 13) * n^2

This gives us the final result:

-6 * n^2

Therefore, we can factor out the GCF of -6n^2 from the given expression.

Step-by-step explanation:

Answer:

1/82.

Step-by-step explanation:

In a cross country race with 40 athletes, 10 of them are on the same team. The probability that the top four finishers are all from that same team is given by the expression 10P4/40P4.

The expression 10P4 represents the number of ways that the top four finishers can be chosen from the team of 10 athletes. Since the order in which the athletes finish does not matter, this is equivalent to choosing 4 athletes from a group of 10 without regard for order, which can be done in 10!/(4!6!) = 210 ways.

The expression 40P4 represents the number of ways that the top four finishers can be chosen from the entire group of 40 athletes. Since the order in which the athletes finish does not matter, this is equivalent to choosing 4 athletes from a group of 40 without regard for order, which can be done in 40!/(4!36!) = 34,650 ways.

Therefore, the probability that the top four finishers are all from the same team is given by the expression 10P4/40P4 = 210/34,650 = 1/164. This can be simplified to 1/82 by dividing the numerator and denominator by 2, so the final answer is 1/82.

The slope of the function is which describes the direction and steepness and the slope for the equation will be m = (-30)

This is the process of finding the rate of change of the value y (dependent variable) of the function changes with respect to that of the variable x (independent variable). The slope itself describes the direction and steepness of the line.

slope = m = rise / run = [tex]\frac{y2 - y1}{x2 - x1}[/tex],

To find the slope , In the case of a straight line y=mx+b, the slope m=Δy/Δx measures the change in y per unit change in x. This can be interpreted as a measure of "sensitivity''; for example, if y=100x+5, a small change in x corresponds to a change one hundred times as large in y, so y is quite sensitive to changes in x.

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Answer: it is 8 and if you need me to explain tell me.

a) The range of values that the game operator can use to represent a winner getting a basketball is of: 50 to 100.

b) The percentage of the 10 simulated winners who got a basketball is of: 40%.

The range of values is the set that contains all possible values that can result in a person getting a basketball.

There is a 51% probability of the winner getting a basketball, hence supposing that the last 51 values represent the winner getting a basketball, the range of values is given as follows:

50 to 100.

From the 10 simulated winners, 4 had numbers ranging from 50 to 100, hence the percentage of them who won a basketball is calculated as follows:

p = 4/10 x 100% = 40%.

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We only need to multiply by 10 to determine the length because we know the length is 10 meters longer than our width is 38.75 meters for L.

The formula for a rectangle's perimeter is

2w + 2L = P where w stands for width and l for length.

The length is 10 meters longer than the breadth, according to this dilemma. So:

L = 10 + w

In our perimeter equation, we may replace L with 10 + w and also 80 in place of P, our perimeter, to solve:

2W + 2(10 + W) = 100

2W + 20 + 2W = 100

4W + 20 = 100

-25. -20

4W = 75

75 /4 =

18.75 meters in W

We only need to multiply by 10 to determine the length because we know the length is 10 meters longer than our width:

18.75 + 10 = 38.75 meters for L.

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The direction of the point (-3, 2) is 3 units to the left and 2 units up from the origin (0, 0). Obtained by applying the translation rules.

The translation rules are:

(x, y) → (x + a, y); translated by 'a' units to the right

(x, y) → (x - a, y); translated by 'a' units to the left

(x, y) → (x, y + a); translated by 'a' unit up

(x, y) → (x, y - a); translated by 'a' units down

The given points are (-3, 2) and (0, 0).

The point (-3, 2) is 3 units to the left and 2 units up from the origin (0, 0).

This is obtained by the rules:

(x, y) → (x - a, y); translated by 'a' units to the left

(x, y) → (x, y + a); translated by 'a' unit up

Thus, option C is correct.

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Yes, the system of inequalities in the graph may be solved using the point (2,4).

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics.  To indicate various types of inequalities, a variety of notations are used:

A > B indicates that an is greater than b.

A and b are not equivalent in either scenario. an is strictly less than or strictly greater than b in certain relations, which are referred to as strict inequalities. Equivalence is disregarded.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way, per definition.

The points (4,2) are among the parameters provided.

y<2x+3

y≥-4x+1

By solving these inequalities:

y<2x+3

Let y<0

0<2x+3

-3<2x

x<-3/2

(-3/2,0)

when x<0

y<2(0)+3

y<3

(0,3)

y≥-4x+1

x≥0

y≥0+1

y≥1

(0,1)

y≥0

0≥-4x+1

x≥-1/4

(-1/4,0)

The graphs are drawn using coordinates, and the lines intersect at specific locations (4,2)

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The amount that Tom’s most recent book earn is 10^7.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

Since Tom’s most recent book earned 10*4 times as much money as his first book which was 10³.

The total amount of the recent book will be:

= 10⁴ × 10³

= 10^(4 + 3)

= 10^7

The amount is 10^7.

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Answer:

4(x-2 +y) = 4x-8+4y

Step-by-step explanation:

You have to apply the distributive law

4(x-2+y) = 4x + 4 (-2) + 4y

Then solve it which equals

4 x +4 (-2) + 4y

Then multiply the numbers

4 (-2) = -8

Which gets you 4x-8+4y

Answer:

E

Step-by-step explanation:

The adjusting journal entries for the following unrelated transactions are as follows:

a) Dec. 31, 2020: Debit Interest Expense Php. 6,667

Credit Interest Payable Php. 6,667

(To record the adjusting entry.)

b) Dec. 31, 2020: Debit Insurance Expense Php. 12,500

Credit Prepaid Insurance Php. 12,500

(To record the adjusting entry under the asset method.)

Debit Prepaid Insurance Php. 17,500

Credit Insurance Expense Php. 17,500

(To record the adjusting entry under the expense method.)

c) Dec. 31, 2020: Debit Interest Revenue Php. 12,000

Credit Interest Receivable Php. 12,000

(To record the adjusting entry.)

d) Dec. 31, 2020: Debit Unearned Rent Revenue Php. 133,333

Credit Rent Revenue Php. 133,333

(To record the adjusting entry under the Liability method.)

Debit Rent Revenue Php. 66,667

Credit Unearned Rent Revenue Php. 66,667

(To record the adjusting entry under the income or revenue method.)

One of the methods is the asset method (similar to the liability method) that records the asset when cash is received.

Another is the expense method (similar to the revenue or income method) that records the amount as expense until adjusted.

a) Dec. 31, 2020: Interest Expense Php. 6,667 Interest Payable Php. 6,667

b) Dec. 31, 2020: Insurance Expense Php. 12,500 Prepaid Insurance Php. 12,500

Prepaid Insurance Php. 17,500 Insurance Expense Php. 17,500

c) Dec. 31, 2020: Interest Revenue Php. 12,000 Interest Receivable Php. 12,000

d) Dec. 31, 2020: Unearned Rent Revenue Php. 133,333 Rent Revenue Php. 133,333

Rent Revenue Php. 66,667 Unearned Rent Revenue Php. 66,667

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The required equations can be used to model the situation is x = 1/2y - 3 and y = 10(x-1)

What is equation ?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

Equations can be classified as either conditional equations or identities. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth. When two expressions are joined together by the equals sign ("="), the result is an equation.

If the smaller number is 3 less than half a larger number, this is expressed as:

x = 1/2y - 3 ⇒(1)

If the larger number is 10 times 1 less than the smaller number, this is expressed as;

y = 10(x-1) ⇒ (2)

Substitute equation 2 into 1 as shown;

x = 1/2y - 3

x = 1/2(10x-10)- 3

x = 5x - 5 - 3

-4x = -8

x = 2

The required equations can be used to model the situation is x = 1/2y - 3 and y = 10(x-1)

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Answer:

a d

Step-by-step explanation:

Answer:

45 pounds of meat.

Step-by-step explanation:

= 120 ( 3/8)

= 360 / 8

= 45

Answer:

p(x) = (x+7)(x+5)(-x+1)(x-35).

Step-by-step explanation:

To factor p(x), we can use the following steps:

Find the factors of 35 that add up to 4, which is the coefficient of the quadratic term (x^2). In this case, the factors of 35 that add up to 4 are 7 and 5.

Use these factors to rewrite the quadratic term as the product of two binomials. In this case, we can write the quadratic term as (x+7)(x+5).

Substitute this expression into the original polynomial to get p(x) = (x+7)(x+5) + 2x + 35.

To complete the factorization, we need to find two numbers that multiply to 35 and add up to 2. These numbers are -1 and -35.

Use these numbers to rewrite the remaining linear term as the product of two binomials. In this case, we can write the linear term as (-x+1)(x-35).

Substitute this expression into the polynomial to get p(x) = (x+7)(x+5) + (-x+1)(x-35).

Finally, we can factor p(x) as the product of two quadratics: p(x) = (x+7)(x+5)(-x+1)(x-35).

Answer:

  $11,127.75

Step-by-step explanation:

You want to use the compound interest formula A=Pe^rt to find the value of an $8000 investment compounded continuously at 11% for 3 years.

Put the values of the variables into the formula and do the arithmetic.

  A = $8000·e^(0.11·3) ≈ $11127.75

The accumulated value after 3 years will be $11,127.75.

The least amount possible is $25 and the number of miles is 25 miles

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

Yellow Taxi service charges a $15 flat fee plus $2.50

This means that

Yellow Taxi: y = 15 + 2.5x

For the graph, we have

y-intercept = 10

(x, y) = (0, 10) and (2, 16)

So, the slope is

slope = (y₂ - y₁)/(x₂ - x₁) = (16 - 10)/(2 - 0) = 3

So, we have

Black and White Taxi service: y = 10 + 3x

Yellow Taxi: y = 15 + 2.5x

When he travels for 5 miles, we have

Black and White Taxi service: y = 10 + 3 * 5 = 25

Yellow Taxi: y = 15 + 2.5 * 5 = 27.5

Hence, the least amount possible is $25

This means that we equate the above equations

So, we have

15 + 2.5x = 10 + 3x

Evaluate the like terms

0.5x = 5

Divide

x = 25

Hence, the distance is 25 miles

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The range of Sanders support among millennials in within 90% confidence interval is between 53% and 57%.

Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are being used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the entire.

In order to answer this question, a statistical power (90% CI) must be calculated for the percentage of millennials who had a favorable impression of Sanders.

The sample size is n=1,754.

The p-hat, taken from the poll, is

[tex]$\hat{p}=0.55$[/tex]

The estimated standard deviation is equal to:

[tex]$$\sigma_p=\sqrt{\frac{p(1-p)}{N}}=\sqrt{\frac{0.55 * 0.45}{1754}}=0.012$$[/tex]

For a 90% CI, the z-value is z = 1.645.

Then, the confidence interval is

[tex]$$\begin{aligned}& \hat{p}-z * \sigma_p \leq p \leq \hat{p}-z * \sigma_p \\& 0.55-1.645 * 0.012 \leq p \leq 0.55-1.645 * 0.012 \\& 0.55-0.02 \leq p \leq 0.55+0.02 \\& 0.53 \leq p \leq 0.57\end{aligned}$$[/tex]

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The complete question is-

Throughout the 2016 Presidential election primaries, Millennials (those aged 20 t 36 years) consistently supported Senator Bernie Sanders over Secretary Hillary Clinton. According to the 2016 Gallup poll of 1,754 Millenials, 55% had a favorable opinion of Sanders than Hillary Clinton (38%). Calculate the 90% confidence interval for Bernie Sanders. *round to two decimals (Please read the rules for rounding in the preface page xvi. If the number you are rounding is followed by 5, 6, 7, 8, 9 round the number up. If the number is followed by 0,1,2,3,4, you are rounding down, meaning you do not change the number). The 90% confidence interval for Bernie Sanders is to

Answer:

The latus rectum of an ellipse is a line segment that is perpendicular to the major axis of the ellipse and passes through one of its foci. If the ellipse has a major axis of length 2a, then the latus rectum will have a length of a. Therefore, if the latus rectum is equal to half of the major axis, then the major axis must have a length of 2a, and the latus rectum will have a length of a.

The point (√6, 1) can be the end point of the latus rectum if it lies on the ellipse. To determine if this is the case, you can substitute the coordinates of the point into the standard equation of an ellipse. If the point satisfies the equation, then it lies on the ellipse and can be the end point of the latus rectum.

The standard equation of an ellipse with major axis of length 2a and minor axis of length 2b is:

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

Where (h, k) is the center of the ellipse. In this case, we don't know the values of a, b, h, and k, so we can't determine if the point (√6, 1) lies on the ellipse. However, we can use the fact that the latus rectum has a length of a to find the center of the ellipse.

Since the latus rectum is perpendicular to the major axis and passes through the focus, it must also pass through the center of the ellipse. Therefore, the midpoint of the line segment defined by the coordinates (√6, 1) and the center of the ellipse must be the center of the ellipse. The coordinates of the center can be found by taking the average of the x-coordinates and the average of the y-coordinates. In this case, the center of the ellipse will have coordinates:

(x, y) = ((√6 + h) / 2, (1 + k) / 2)

Once you know the center of the ellipse, you can use the standard equation of an ellipse to find the values of a, b, h, and k. Once you have those values, you can determine if the point (√6, 1) lies on the ellipse and can be the end point of the latus rectum.

I hope this helps. Let me know if you have any other questions.

There are 7 packs of candy, but only two people can share it equally. 7/2= 3.5. If each person gets 3.5 bags, they both have an equal amount.

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The area of the right triangle is 27,000 square units. The result is obtained by using the determinant method.

The area of a triangle in coordinate geometry can be found by using the determinant formula.

[tex]Area \: of \Delta ABC = \frac{1}{2} \left[\begin{array}{ccc}x_{1} &y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right][/tex]

The vertices of a right triangle are:

Using the determinant formula, the area of the triangle is

[tex]Area \: of \Delta ABC = \frac{1}{2} \left[\begin{array}{ccc}525 &260&1\\725&260&1\\525&-10&1\end{array}\right][/tex]

Area of ΔABC = 1/2 |525(260-(-10)) - 725(260-(-10)) + 525(260-260)|

Area of ΔABC = 1/2 |525(270) - 725(270) + 0|

Area of ΔABC = 1/2 |141,700 - 195,750|

Area of ΔABC = 1/2 |-54,000|

Area of ΔABC = 27,000 unit square

Hence, the area of ΔABC is 27.000 square units.

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