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The equivalent expression to -4x² + 2x - 5(1 + x) is given as follows:

-4x² - 3x - 5.

The expression for this problem is defined as follows:

-4x² + 2x - 5(1 + x)

To obtain the equivalent expression, we apply the distributive property to -5(1 + x) as follows:

-5(1 + x) = -5 - 5x.

Then the expression is given as follows:

-4x² + 2x - 5 - 5x.

Combining the like terms, we have that the expression is given as follows:

-4x² - 3x - 5.

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The perimeter of the given rectangle is option (b) 2x + 2y + 14.

Perimeter is a mathematical term used to describe the distance around the boundary of a two-dimensional shape.

In this case, we are given a rectangle with a length of x+8 and a width of y-1, and we are asked to find its perimeter, p.

To find the perimeter of a rectangle, we need to add up the lengths of all four sides. In a rectangle, opposite sides are equal in length, so we can simplify the calculation by multiplying the sum of the length and width by two. This gives us the formula:

perimeter = 2(length + width)

Substituting the given values for the length and width of our rectangle, we get:

p = 2(x+8 + y-1)

p = 2(x+y+7)

Simplifying further, we get the answer:

p = 2x + 2y + 14

Therefore, the correct option is (b).

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Complete Question:

What is the perimeter, p, of a rectangle that has a length of x + 8 and a width of y − 1?

a) p = 2x + 2y + 18

b) p = 2x + 2y + 14

c) p = x + y − 9

d) p = x + y + 7

Answer:

Equation: 4(x + 1.5) = 38

Ticket Cost: $8, or x = 8

Step-by-step explanation:

The processing fee for each ticket is $1.50, or 1.5. This applies to each ticket, meaning that the price of one ticket (or x) should be added to 1.5. x + 1.5 represents the sum of a ticket and the processing fee. Since there were 4 tickets purchased, x + 1.5 is multiplied 4 times. That results in 4(x + 1.5). Finally, the total amount of money spent was $38, so 4(x + 1.5) = 38.

4(x + 1.5) = 38

4x + 6 = 38

4x = 32

x = 8

Check:

4 * 8 = 32 (cost of 4 tickets)

4 * 1.5 = 6 (cost of 4 processing fees)

32 + 6 = 38 (4 tickets + 4 processing fees = total)

Answer: no exact answer

Step-by-step explanation:

Robin ride her bike this week 35 miles.

Robin rides her bike 3 miles to school.

She rides home a different way that is 4 miles long.

This week, Robin rode to school and back 5 times.

For one time ride to school from house = Rode to School + Rode To home

For one time ride to school from house = 3 + 4

For one time ride to school from house = 7

Robin rides total of 5 times.

So, For five time ride to school from house = 5 × For one time ride to school from house

For five time ride to school from house = 5 × 7

For five time ride to school from house = 35 miles

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The complete question is:

Robin rides her bike 3 miles to school. She rides home a different way that is 4 miles long. This week, Robin rode to school and back 5 times. How many miles did Robin ride her bike this week?

The maximum number of points on the circles that a line passing through all three circles can touch is 36.

Two circles may cross in two points, one point, or no points on a aeroplane, digression circles are coplanar circles that cross at a single point.Concentric circles are coplanar circles that share a common centre.

You can select any two circles in (₂³) ways and each pair will intersect at 2 points. Therefore total 3*2=6 points.

Similarly, 4 lines will intersect at (₂⁴)=6

points.

Now each line will intersect at 2 points with a circle. And since we can select a circle in (³₁) ways and a line in (₁⁴) ways, therefore total (₁³)∗(₁⁴)∗2=24 points they will intersect.

Therefore, total number of intersection points = 6 + 6 + 24 = 36 points.

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The probability of being assigned a general practitioner or a doctor under the age of 50 is 11/19 or approximately 0.5789 (rounded to four decimal places).

We are given that there are 5 general practitioners (GPs) out of 19 doctors in the hospital, which means that the probability of being assigned a GP is 5/19.

We are also given that there are 9 doctors under the age of 50 out of the 19 doctors in the hospital, which means that the probability of being assigned a doctor under the age of 50 is 9/19.

However, we need to subtract the probability of being assigned a doctor who is both a GP and under the age of 50 because this group is counted twice in the above probabilities.

We are given that there are 3 doctors who are both GPs and under the age of 50. Therefore, the probability of being assigned a doctor who is both a GP and under the age of 50 is 3/19.

To use the inclusion-exclusion principle, we add the probabilities of being assigned a GP and being assigned a doctor under the age of 50, and then subtract the probability of being assigned a doctor who is both a GP and under the age of 50.

P(GP or Under 50) = P(GP) + P(Under 50) - P(GP and Under 50)

= 5/19 + 9/19 - 3/19

= 11/19

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There are quadratic equations as many as lead coefficients are. The functions that represent each parabola are:

Case A: y = (1 / 3) · (x + 4) · (x - 2)

Case B: y = (x + 4) · (x - 2)

Case C: y = 2 · (x + 4) · (x - 2)

Case D: y = - (1 / 3) · (x + 4) · (x - 2)

Case E: y = - 2 · (x + 4) · (x - 2)

In this problem we find five case of quadratic equations whose roots are x = - 4 and x = 2, but whose vertices are different. Quadratic equations can be described as a factor product of the form:

y = a · (x + 4) · (x - 2)

Where a is the lead coefficient.

The following parameters are for each parabola:

Case A: (x, y) = (- 1, - 3)

Case B: (x, y) = (- 1, - 9)

Case C: (x, y) = (- 1, - 18)

Case D: (x, y) = (- 1, 3)

Case E: (x, y) = (- 1, 18)

Now we determine the lead coefficient for each case:

Case A

- 3 = a · (- 1 + 4) · (- 1 - 2)

- 3 = - 9 · a

a = 1 / 3

Case B

- 9 = a · (- 1 + 4) · (- 1 - 2)

- 9 = - 9 · a

a = 1

Case C

- 18 = a · (- 1 + 4) · (- 1 - 2)

- 18 = - 9 · a

a = 2

Case D

3 = a · (- 1 + 4) · (- 1 - 2)

3 = - 9 · a

a = - 1 / 3

Case E

18 = a · (- 1 + 4) · (- 1 - 2)

18 = - 9 · a

a = - 2

All differences between all quadratic equations are due to different lead coefficients.

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it would be 5 pennies and two dimes

if 3 are quarters, that is 75 cents. if you add two dimes, it's now 95, and making the total number of coins 5. then you add 5 pennies, you get a total of 100 cents, one dollar, and now have 10 coins. hope its right

The number of pet-owners that are in the union of cat owners and other pet owners is given as follows:

20 pet-owners.

The set representing the union of two sets is composed by all the elements that belong to at least one of the sets.

Hence the union of pet-owners that are in the union of cat owners and other owners is composed as follows:

Hence the total number is given as follows:

11 + 9 = 20.

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Explanation:

The domain is the set of allowed x inputs.

In this case, we can plug in anything but x = 2 because of the vertical asymptote here.

This means the domain is the interval notation [tex](-\infty,2) \cup (2,\infty)[/tex] that notation basically says "start with the entire real number line. Then poke a hole, or remove, 2 from the number line".

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

The range is the set of possible y outputs. In this case, the domain and range lead to the same interval notation since we're kicking out "2" each time. This time we focus on the horizontal asymptote. The curve gets closer and closer to these dashed lines but never actually reaches them.

Since [tex](-\infty,2) \cup (2,\infty)[/tex] is one of the possible ways to represent the range, one of the answers is choice A.

The interval notation [tex](-\infty,2) \cup (2,\infty)[/tex] is too vague because it's not clear if we're talking about the domain or range. The notation [tex]\left\{\text{y}|\text{y} \in \text{R}, \ \text{y} \ne 2\right\}[/tex] is more specific. It says "y is a real number such that it cannot equal 2". In other words "y can be anything but 2". This tells us that choice D is another answer.

So either y < 2 or y > 2 which represents us being below the horizontal asymptote or above it respectively.

The third and final answer is choice E.

To compare the two investment options, we must compute the future value (FV) of each account after 30 years of compounding at a 2.5% rate.As an outcome, the IRA will have a future value that is $107,116.33 greater than the Roth IRA.

We have monthly payments of $416.66 for 30 years, or 360 months, on the IRA. Using the following formula to calculate the future value of an annuity:

[tex]FV = PMT * [(1 + r)^n - 1] / r[/tex]

We can calculate the future value of the IRA using the following formula: where PMT is the monthly payment, r is the monthly interest rate (2.5% / 12), and n is the number of payments (360):

[tex]FV IRA = 416.66 * [(1 + 0.025/12)^360 - 1] / (0.025/12) = $358,888.91[/tex]

We have annual payments of $5000 for 30 years on the Roth IRA. Using the following formula to calculate the future value of a lump sum:

[tex]PV * (1 + r)n = FV[/tex]

where PV is the present value (the lump sum), r is the annual interest rate (2.5%), and n is the number of years (30), we can calculate the Roth IRA's future value:

5000 * (1 + 0.025)30 = $251,772.58 FV Roth

As a result, the IRA will outperform the Roth IRA in terms of future value by:

$358,888.91 - $251,772.58 = $107,116.33 FV IRA - FV Roth

As a result, the IRA will have a future value that is $107,116.33 greater than the Roth IRA.

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The median is the point in a distribution where 50% of the scores fall above and 50% fall below a certain score.

In a distribution, the median is the number that separates the top 50% of scores from the bottom 50% of scores. When the data is organised from lowest to highest, it is the midway value.

The mode is the most common value in a distribution, and it is not always the same as the median. The mean is the total of all scores divided by the number of scores, and it is impacted by outliers or extreme values in the data. Depending on the context, the term "average" can refer to either the mean or the median. When individuals say "average" without any qualification, they typically mean the mean.

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Answer:

55

Step-by-step explanation:

Since 1 rectangle is 10 and there are 5, that means the whole length is 50.

Which means with can set the equation equal to 50

[tex]x - 5 = 50[/tex]

Adding 5 gets us

[tex]x = 55[/tex]

Option A: The probability of rejecting H_o, whether it's true or not, best describes the notion of the P-value of a hypothesis test.

The level of marginal significance within the hypothesis test that represents the probability of occurrence of a given event is referred to as its P-value. In order to provide the least significance at which the null hypothesis would be rejected, it is utilized as a choice for the rejection point. This signifies that the option A is correct.

The P-value is known as the probability value. It can be defined as the probability of getting a result that is either the same or more advanced than the actual observations. There is more support for the alternative hypothesis when the P-value is low.

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Correct way to ask the question is:

Which one of the following best defines the notion of the P-value of a hypothesis test?

The probability of rejecting H_o, whether it's true or not

The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true.

The probability of the type I error

The probability of the type II error

The quadratic trinomial of the given expressions are z² + 4 + 4z, 16 + n² - 8n, m² + 100 + 20m respectively.

A trinomial is an algebraic expression that has three terms. An algebraic expression consists of variables and constants of one or more terms.

A polynomial is an algebraic expression that has one or more terms and is written as [tex]a_0x^n + a_1x^{ n - 1} + a_2x^{n-2} + ...+ a_n x^0[/tex] in the standard form. Where [tex]a_0, a_1, a_2, ....,a_n[/tex] are constants and n is a natural number.

A quadratic trinomial is a type of algebraic expression with variables and constants. It is expressed in the form ax² + bx + c, where x is the variable and a, b and c are non-zero real numbers. A quadratic trinomial also describes the discriminant D where it defines the quantity of an expression and it is written as D = b² - 4ac.

Given:

(-z - 2)²

⇒ [-(z + 2)]²

⇒ (z)² + (2)² + 2(z)(2)

⇒ z² + 4 + 4z

(4 - n)²

⇒ (4)² + (n)² - 2(4)(n)

⇒ 16 + n² - 8n

(-m - 10)²

[-(m + 10)]²

⇒ (m)² + (10)² + 2(m)(10)

⇒ m² + 100 + 20m

So, the expressions are converted into quadratic trinomial.

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Answer:

110°

Step-by-step explanation:

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Answer: 110˚

Step-by-step explanation:

Complementary angles have a sum of 90˚

With this knowledge, we can say <B = 90 - <A = 90 - 20 = 70˚

Supplementary angles have a sum of 180˚

With this knowledge we can say <C = 180 - <B = 180 - 70 = 110˚

∴ Measure of angle C = 110˚

Significant figures with representation of x are a) 14.8 m = 14.x m. b) $10.25 = 10.2x. c) 0.05 L = 0.0x L. d) 1.000 g/mL = 1.00x g/mL. e)  6200cm = 6200x cm. f)  403 kg = 40x kg.

a) 14.8m has 3 significant figures. Representation with x in place of estimated digit: 14.x m. b) $10.25 has 4 significant figures. Representation with x in place of estimated digit: 10.2x. c) 0.05 L has 1 significant figure. Representation with x in place of estimated digit: 0.0x L. d) 1.000 g/mL has 4 significant figures. Representation with x in place of estimated digit: 1.00x g/mL. e) 6200cm has 2 significant figures. Representation with x in place of estimated digit: 6200x cm. f) 403 kg has 3 significant figures. Representation with x in place of estimated digit: 40x kg. Significant figures are the digits in a measurement that are reliable and accurate. They provide an indication of the precision of a measurement, and allow us to communicate the level of certainty we have in a particular value. When determining the number of significant figures in a measurement, we typically follow a set of rules. Non-zero digits are always significant, zeros between non-zero digits are significant, and trailing zeros to the right of the decimal point are significant. Zeros at the beginning of a number or to the left of a non-zero digit are not significant. The use of significant figures is important in science and engineering to ensure accurate and reliable measurements. When performing calculations with measurements, the result should be reported with the same number of significant figures as the least precise measurement used in the calculation. In addition, when rounding a number, the last digit should be rounded to the nearest value consistent with the number of significant figures being used. Understanding significant figures is an important part of scientific and mathematical communication, and can help to ensure accuracy and consistency in the reporting of data and calculations.

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Answer: The equation of the tangent to a parabolic curve y = ax^2 + bx + c at the point (h, k) can be expressed as:

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

So, we know the equation of the tangent at vertex of the parabolic curve is 3x - 4y = 5, so the vertex of the parabolic curve is (h, k) = (2, -3/2).

The equation of a parabolic curve with vertex (h, k) and focus (h, k + p) is given by:

y = a(x - h)^2 + k, where a = -1/4p.

So, substituting the values of the vertex (2, -3/2) and the focus (1, 2) into the above equation, we have:

-3/2 = a(2 - 2)^2 - 3/2, so a = -1/4p.

And, substituting the values of the focus (1, 2) into the equation y = a(x - h)^2 + k, we have:

2 = -1/4p(1 - 2)^2 - 3/2, so p = 1/2.

So, the equation of the parabolic curve with focus (1, 2) and vertex (2, -3/2) is:

y = -1/4 * 1/2 * (x - 2)^2 - 3/2.

This is the equation of the parabola that has the equation of the tangent at vertex 3x - 4y = 5 and focus at the point (1, 2).

Step-by-step explanation:

Answer: The slope of a line in the form y = mx + b can be found by taking the coefficient of x, which is m. In this equation, the slope is not in that form, so we need to isolate y and put it in that form.

Starting with the equation:

3x - 1/2y = 5x + 4

We'll isolate y by subtracting 3x from both sides:

-1/2y = 2x + 4

And then multiply both sides by -2 to solve for y:

y = -4x - 8

So the slope of the line is -4.

Step-by-step explanation:

In 25 ways we can select 2-digit number from the given digits.

Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.

Given that, a two-digit number whose 1st digit it 0,1,2,3, or 4, and whose 2nd digit is 5,6,7,8, or 9.

Number of ways selecting 1st digit is

P(5, 1) = 5!/(5-1)!

= 5

Number of ways selecting 2nd digit is

P(5, 1) = 5!/(5-1)!

= 5

Now, 5×5=25

Therefore, in 25 ways we can select 2-digit number.

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Answer:

$82.21

Step-by-step explanation:

cost of meal: $78.30

15% discount: 15% of $78.30 = 0.15 × $78.30 = $11.75

tip: 20% of $78.30 = 0.20 × $78.30 = $15.66

total cost = $78.30 - $11.75 + 15.66 = $82.21

Answer: $82.21

First, we need to convert the volume of the juice in the jar from liters to milliliters, since the volume of the glasses is given in milliliters.

1 liter = 1000 milliliters

So, 70 liters = 70 * 1000 = 70,000 milliliters

Next, we'll divide the volume of the juice in the jar by the volume of each glass to find out how many glasses can be filled with the juice.

70,000 milliliters ÷ 150 milliliters/glass = 466.67 glasses (rounded to the nearest whole number)

Therefore, 466 glasses can be filled completely with the juice.

Finally, we can find out how much juice is left in the jar by subtracting the total volume of the juice used to fill the glasses from the volume of the juice in the jar.

70,000 milliliters - (466 glasses x 150 milliliters/glass) = 70,000 milliliters - 69900 milliliters = 800 milliliters

So, 800 milliliters of juice is left in the jar.

Let's call the average speed for the last three hours "S".

First, we need to find the total distance that Mr. Jackson traveled in the last three hours. He traveled 300 miles in total, and he covered 64 miles in the first 90 minutes, so he had 300 - 64 = 236 miles left to travel.

Next, we need to find the time he spent traveling in the last three hours. If he traveled for three hours, and the first hour he traveled at 66 miles per hour, then he covered 66 miles in the first hour. So, he had 236 - 66 = 170 miles left to travel in the last two hours.

Finally, we can use the formula for average speed: distance divided by time. The total distance he traveled in the last three hours was 170 miles, and the time he spent traveling was 2 hours, so his average speed for the last three hours was:

S = 170 miles / 2 hours = 85 miles per hour

So, Mr. Jackson's average speed for the last three hours was 85 miles per hour.

Answer:

68 mph

Step-by-step explanation:

Let's call the average speed for the last three hours "S".

The total distance traveled for the last three hours is 300 - 64 * 1.5 = 300 - 96 = 204 miles.

So, over the last three hours, Mr. Jackson covered a distance of 204 miles at a speed of S.

The time it took him to cover that distance is 3 hours.

We can use the formula distance = speed * time to find S:

204 = S * 3

Solving for S:

S = 68 mph

So the average speed for the last three hours was 68 mph.

The area of the semi circle is 14.13 units²

a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180°. It has only one line of symmetry.

The area of a semicircle is the half of the area of a full circle.

The area of a full circle is πr², therefore the area of a semicircle is ½πr²

r = d/2 = 6/2 = 3

A = ½πr²

= 1/2 × 3.14 × 3²

A = 28.26/2

A = 14.13 units²

therefore the area of the semi circle is 14.13 units²

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4214.7 is the balance in the account after 2 months .

What does compound and simple interest mean?

A fixed proportion of the principal amount borrowed or lent is what is known as simple interest and is paid or received over a given period of time.

                                Borrowers are required to pay interest on interest in addition to principal because compound interest accrues and is added to the total amount of interest from earlier periods.

P = $4200

R = 2.1% = 2.1/100 = 0.021  =

     T = 2 month = 2/12 = 1/6

    I = PRT

     = 4200 * 0.021 * 1/6 = 14.7

 Amount = P + I = 4200 + 14.7  = 4214.7

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Answer: 2

Step-by-step explanation:

Answer:

x=15°

∡Q= 75°

Step-by-step explanation:

supplementary angles means the sum of the angles =180°

so, 5x+105°=180°

5x=75°

x=15°

∡Q= 75°

Answer: The two lines never intersect

Step-by-step explanation:

An algebraic solution for a system of equations means that the graphs of the two equations intersect at some point. If no such point can be found, it means the graphs never intersect.