In the following, choose k to create a perfect-square trinomial:
(a) x² - 16x+k
(b) x² + 10x + k
(c) x² - 5x + k

Answer:

Step-by-step explanation:

To find the cost of a 33-minute taxi ride, we first need to determine the cost per minute of the taxi ride. We can do this by dividing the cost of a 14-mile taxi ride ($11.20) by the time it took (16 minutes):

$11.20 ÷ 16 minutes = $0.70 per minute

Now that we know the cost per minute, we can find the cost of a 33-minute taxi ride by multiplying the cost per minute by 33:

$0.70 x 33 minutes = $23.10

So a 33-minute taxi ride at this vacation spot would cost $23.10.

Answer:

Step-by-step explanation:

if a carton of eggs is 4.30 then 1 egg is then 1 egg is 75 cents

The coordinates for point B are 7 = √(x - 5)² + (y - 4)².

What is the distance formula?

The distance formula is used to calculate the length of the line which joins the two points in an x−y plane. The distance between two points is the length of the line joining the two points. If the two points lie on the same horizontal or same vertical line.

Here, we have

Given: Segment AB Has point A located At (5, 4). If The Distance from A To B Is 7 units.

To find the distance between any two the following formula is used.

D = √(x₂ - x₁)² + (y₂ - y₁)²

7 = √(x - 5)² + (y - 4)²

Hence, the coordinates for point B are 7 = √(x - 5)² + (y - 4)².

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Step-by-step explanation:

They are corresponding angle

Hope it helps u

Refer to the image below

Answer: $ 495. 41

Step-by-step explanation:

First, multiply $32 by 3 days and get $96.

Then multiply .69 and 289 and get $ 199.41

Lastly, add those to get and get your answer.

(32 x 3) + .69 x 289 = 495. 41

By using the equation of the trend line, it can be estimated that the​ hiker's elevation after 140 minutes will be, 1919.8 feet

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

The equation of a trend line for the​ hiker's elevation is,

y = 9.27x + 622​

x represents the number of minutes

y represents the​ hiker's elevation in feet

Elevation after 140 minutes = ?

Now, putting value of x as 140 in the given equation,

y = (9.27 x 140) + 622​

  =  1297.8 + 622

  =   1919.8

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The rock that Angela found is likely a sedimentary rock, formed from the accumulation and solidification of sediment, such as shells and pebbles, in a marine environment.

The type of rock that Angela found is likely a sedimentary rock. Sedimentary rocks are formed from the accumulation and solidification of sediment, such as sand, silt, and clay. The shells and pebbles embedded in the rock suggest that it was formed from the buildup of material in a marine environment, such as the ocean or a lake. The shells and pebbles were once separate materials, but over time, they were compacted and cemented together to form the rock.

Sedimentary rocks are typically layered, which is a characteristic formed from the accumulation of sediment over time. The shells and pebbles in the rock sample could be evidence of different layers of sediment that were compacted and cemented together.

It is also possible that the rock is a conglomerate, which is a type of sedimentary rock composed of rounded pebbles and cobbles held together by a finer-grained matrix. Conglomerates form in environments where high-energy water, such as rivers or streams, carry large rocks and sediment and deposit them in areas of low energy, such as a delta or a floodplain.

Therefore, In conclusion, the rock that Angela found is likely a sedimentary rock, formed from the accumulation and solidification of sediment, such as shells and pebbles, in a marine environment.

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The rock that Angela found is likely a sedimentary rock, formed from the accumulation and solidification of sediment, such as shells and pebbles, in a marine environment.

The type of rock that Angela found is likely a sedimentary rock. Sedimentary rocks are formed from the accumulation and solidification of sediment, such as sand, silt, and clay. The shells and pebbles embedded in the rock suggest that it was formed from the buildup of material in a marine environment, such as the ocean or a lake. The shells and pebbles were once separate materials, but over time, they were compacted and cemented together to form the rock.

Sedimentary rocks are typically layered, which is a characteristic formed from the accumulation of sediment over time. The shells and pebbles in the rock sample could be evidence of different layers of sediment that were compacted and cemented together.

It is also possible that the rock is a conglomerate, which is a type of sedimentary rock composed of rounded pebbles and cobbles held together by a finer-grained matrix. Conglomerates form in environments where high-energy water, such as rivers or streams, carry large rocks and sediment and deposit them in areas of low energy, such as a delta or a floodplain.

Therefore, In conclusion, the rock that Angela found is likely a sedimentary rock, formed from the accumulation and solidification of sediment, such as shells and pebbles, in a marine environment.

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The solution is, 2 is the greatest common factor.

and,  10x^2 + 28x − 6=0 has solutions, x = -3, 0.2  a simplified version of the equation.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Simplifying :

10x^2 + 28x − 6=0

Rearrange the terms so that -6+28x+10x^2 =0

Figuring out the value of the variable "x".

Subtract out the number "2", which is the GCF.

2(-3+14x+5x^2)=0

To factor a trinomial

2(5x^2+15x-x-3)=0

(5x-1)(x+3)= 0

i.e. x= -3

or, x= 1/5

      =0.2

Hence, The solution is, 2 is the greatest common factor.

and,  10x^2 + 28x − 6=0 has solutions, x = -3, 0.2  a simplified version of the equation.

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Answer:

A. Positive Correlation

Step-by-step explanation:

The dots seem to be going upward throughout the graph, therefore making it a [positive correlation]

The value of x in the triangle is given by x = 33.7°

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of hypotenuse = AC = 18 cm

The measure of the opposite side = AB = 10 cm

From the trigonometric relations ,

sin θ = opposite / hypotenuse

Substituting the values in the equation , we get

sin x = 10 / 18

On simplifying the equation , we get

sin x = 0.555556

Taking inverse on both sides of the equation , we get

x = sin⁻¹ ( 0.555556 )

On further simplification , we get

x = 33.7°

Hence , the value of x is 33.7°

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a) The slope of the graph is of $0.75, meaning that each lemon costs $0.75.

b) The intercept of the graph is of $0, meaning that there is not an additional fixed fee.

c) The equation of the line is given as follows: y = 0.75x.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph touches the y-axis at the origin, hence the intercept b is given as follows:

b = 0.

When x increases by 8, y increases by 6, hence the slope m is given as follows:

m = 6/8

m = 0.75.

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The work required to pump all of the olive oil to the rim of the tank is equal to the weight of the olive oil multiplied by height of the tank.

Work = 41 lb/ft3 x (height of the tank)

For example, if the height of the tank is 6 ft,

Work = 41 lb/ft3 x 6 ft = 246 lb-ft

The work required to pump all of the olive oil to the rim of the tank is equal to the weight of the olive oil multiplied by the height of the tank.

The work required to pump all of the olive oil to the rim of the tank is equal to the weight of the olive oil (which is typically measured in pounds per cubic foot) multiplied by the height of the tank in feet. Thus, the work required can be expressed as: Work = (Weight of olive oil) x (Height of tank in feet). For example, if the olive oil has a weight of 41 pounds per cubic foot and the height of the tank is 6 feet, the work required to pump the olive oil to the rim of the tank would be 246 lb-ft (41 lb/ft3 x 6 ft).

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Answer:

m = (d+2)/5

Step-by-step explanation:

d=5m-2

d+2 = 5m

m = (d+2)/5

The value for the Equation x- 6 = 53 is 59.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

x- 6 = 53

Now, make as the subject of formula and solve for x

So, add 6 on both side

x- 6+ 6= 53 + 6

x = 59

Hence, the value of x is 59.

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No, the independence condition is not met. The conditions for a binomial setting have not been met in this scenario because the names were pulled and not replaced in the hat, which violates the independence condition.

In a binomial setting, the trials must be independent, meaning that the outcome of one trial does not affect the outcome of any other trial.

Since the names were not replaced in the hat, the outcome of each draw is not independent, and the conditions for a binomial setting have not been met.

Permutation refers to the arrangement of objects in a specific order. For example, if we have three objects A, B, and C, there are six possible permutations: ABC, ACB, BAC, BCA, CAB, and CBA. The number of permutations of n objects is given by n!

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by solving this equation, the value of y = (x²+1)/(1-x²)

Equation can be used to represent relationships between variables and to solve problems. They are written using an equal sign (=) and can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

To make y the subject of the equation x = √((y-1)/(y+1)),

x = √[(y-1)/(y+1)]

we can square both sides:

x² = (y-1)/(y+1)

Next, we can multiply both sides by (y+1) to get rid of the fraction:

x² × (y+1) = y-1

x²y + x² = y - 1

Rearranging the terms:

x² + 1 = y - x²y

x² + 1 = y(1 - x²)

Divide both side by (1-x²) we get

y = (x²+1)/(1-x²)

So, y is the subject of the equation is y = (x²+1)/(1-x²)

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He owed $14,983.85 at the end of 4 years.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Given:

P = $8000

R= 16%

T= 4 years

Now, The equation that models this situation is:

A(t) = P [tex](1 + r/n)^{nt[/tex]

where:

A is the amount he owes at any time (t)

P, is the initial amount borrowed (the amount owed at time t = 0)

n is the number of times the loan is compounded annually

r is the interest rate in decimal form

So,  A(4) = 8000[tex](1 + 0.16/4)^{4.4[/tex]

A(4) = 8000[tex](1 + 0.04)^{16[/tex]

A =  $14,983.85

Hence, the amount is  $14,983.85.

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Answer:

7.3

Step-by-step explanation:

a = 2

b = 7

we can use the Pythagorean Theorem

c^2 = a^2 + b^2

c^2 = 4+49

c^2 = 53

c = sqrt(53)

c = 7.3

The General Multiplication Rule in probability states that the probability of the intersection (occurrence) of two events, A and B, is equal to the product of their individual probabilities. The formula can be written as follows:

p(A and B) = p(A) * p(B | A)

where p(A) represents the probability of event A occurring, and p(B | A) represents the probability of event B occurring given that event A has already occurred.

The formula reflects the idea that the probability of both events occurring is equal to the probability of one event occurring, multiplied by the probability of the other event occurring given that the first event has already happened.

For example, let's say we have two events: "rolling a 6 on a dice" (A) and "choosing a spade from a deck of cards" (B). The probability of rolling a 6 on a dice is 1/6, and the probability of choosing a spade given that a 6 was rolled is 13/52. Using the general multiplication rule, the probability of both events occurring would be (1/6) * (13/52) = 13/312.

In summary, the general multiplication rule is a fundamental concept in probability that helps us calculate the probability of the intersection of two events.

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Miles and meters both are units of length. To change a mile's value to meters, you simply multiply it by 1609.344.

What is 1 mile?

A mile is a customary unit of measurement in the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is also referred to as the international mile or the statute mile to distinguish it from other miles. In 1959, the statute mile was formally redefined with respect to SI units as precisely 1,609.344 meters, establishing a standard between the British Commonwealth and the United States.

To convert 1 mile to meters, multiply  1609.344 by the mile.

The model equation is y = 1609.344x

Where x is in the mile and y is in meters.

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The letter represented by the star symbol is 1.

We can start by using the rules of arithmetic. Since each symbol represents a different digit, we can represent the symbols with the numbers 0 to 9. Then we can write the equation as an algebraic expression and solve for the star symbol.

Let's assign the value of the letter represented by the star symbol to x.

A + B = 10x + x = 11x

We know that the maximum value for the result of the addition (C) is 18 (9 + 9) and that the maximum value for 11x is 990 (90 * 11), so x cannot be greater than 9.

Let's try the lowest value for x, which is 0.

A + B = 10 * 0 + 0 = 0

Since 0 cannot be a digit in A or B, x cannot be 0.

Let's try the next value for x, which is 1.

A + B = 10 * 1 + 1 = 11

Since 11 is a valid result of the addition, x = 1 is a solution.

Therefore, the letter represented by the star symbol is 1.

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In the following addition problem, different letters represent different digits, and equal letters represent equal digits. Find the value of the letter represented by the star symbol. A + B = C

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The length of the other leg is 14.14 cm rounded to two decimal places.

Given data :

Given, The hypotenuse of a right triangle measures 15 cm, and one of its legs measures 5 cm.

We know,

Hypotenuse² = Base² + Adjacent².

Therefore,

15² = 5² + Adjacent².

Adjacent = √(225 - 25).

Adjacent = √200.

Adjacent = 14.14.

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The number of different uniforms that the girl's choir can choose is given as follows:

560 uniforms.

The number of uniforms for the girl's choir  is obtained using the Fundamental Counting Theorem, with the multiplication of the number of outcomes for each trial.

The options are given as follows:

As the options for the blouse, skirt and sweater are independent, the number of uniforms is obtained as follows:

10 x 8 x 7 = 80 x 7 = 560 uniforms.

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The equation for the length of the legs is:

0.5*(x + 2)*x = 24

Remember that the area of a right triangle is equal to the product between the lengths of the legs over 2.

Then, if here the area is 24ft.

And the legs measure x and (x + 2), then the area equation will be:

x*(x + 2)/2 = 24

We can rewrite the 1/2 as 0.5, so we will get.

0.5*(x + 2)*x = 24

That is the equation on the first option.

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If McKenzie pays $150 per month, she will have paid a total of $92.832 in interest when she pays off her credit card. This is $36.224 more than she would have paid if she had paid $250 per month.

APR stands for Annual Percentage Rate, which is the interest rate associated with a loan, credit card, or other type of borrowing. It is expressed as a percentage and is typically higher than the interest rate because it includes additional costs associated with the loan such as origination fees, processing fees, and other costs.

Part A:

To calculate how long it will take McKenzie to pay off her credit card, we need to use the formula:

T = (B x i) / P

Where T is the total number of payments, B is the initial balance, i is the interest rate (in decimal form) and P is the amount of the payments.

In this case, B = 936, i = 0.01396 (13.96% expressed as a decimal) and P = 250. So, substituting these values into the formula, we get:

T = (936 x 0.01396) / 250

T = 3.784

Since payments are made monthly, we can round this to 4 payments. Therefore, it will take McKenzie 4 months to pay off her credit card if she makes payments of $250 per month.

Part B:

To calculate the amount of interest McKenzie will have paid when she pays off her credit card, we can use the formula:

I = B x i x T

Where I is the total amount of interest paid, B is the initial balance, i is the interest rate (in decimal form) and T is the total number of payments.

In this case, B = 936, i = 0.01396 and T = 4 (since we calculated this in Part A). So, substituting these values into the formula, we get:

I = 936 x 0.01396 x 4

I = 56.608

Therefore, McKenzie will have paid a total of $56.608 in interest when she pays off her credit card.

Part C:

To calculate how much more interest McKenzie will pay if she only pays $150 per month, we first need to calculate how long it will take her to pay off the credit card using this lower payment amount.

Using the same formula from Part A, we get:

T = (936 x 0.01396) / 150

T = 6.576

Since payments are made monthly, we can round this to 7 payments. Therefore, it will take McKenzie 7 months to pay off her credit card if she makes payments of $150 per month.

Now, to calculate the amount of interest McKenzie will have paid if she pays $150 per month, we can use the same formula from Part B:

I = B x i x T

Where I is the total amount of interest paid, B is the initial balance, i is the interest rate (in decimal form) and T is the total number of payments.

In this case, B = 936, i = 0.01396 and T = 7. So, substituting these values into the formula, we get:

I = 936 x 0.01396 x 7

I = 92.832

Therefore, if McKenzie pays $150 per month, she will have paid a total of $92.832 in interest when she pays off her credit card. This is $36.224 more than she would have paid if she had paid $250 per month.

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It does not always take the same time to serve every customer. Option A is correct.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
From the table,
For every order, the pair compare the unit rate of serving the customer.
1
unit rate = 2 / 8
unit rate = 1 / 4
unit rate = it took 4 minutes to serve a customer.

2.
unit rate = 4 / 16
unit rate = 1 / 4
unit rate = it took 4 minutes to serve a customer.

3
unit rate = 7 / 21
unit rate = 1 / 3
unit rate = it took 3 minutes to serve a customer.

Thus, It does not always take the same time to serve every customer. Option A is correct.

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) The probability that a randomly selected

medical student who took the test had a total

score that was less than 484 = .

) The probability that a randomly selected study

participant's response was between 504 and 516

= .

) The probability that a randomly selected study

participant's response was more than 528 =

.

) Option D is

Only the event in (c) is unusual as its probability is

less than .

The and parts of the question are not

complete.

B) Find the probability that a randomly selected

study participant's response was between 504

and 516

C) Find the probability that a randomly selected

study participant's response was more than 528.

D) Identify any unusual event amongst the three

events in A, B and C. Explain the reasoning.

a) None.

b) Events A and B.

C) Event A

D) Event C

Solution

This is a normal distribution problem with

Mean = μ =

Standard deviation = o = .

A) Probability that a randomly selected medical

student who took the test had a total score that

was less than 484 = P(x < 484)

We first normalize or standardize 484

The standardized score for any value is the value

minus the mean then divided by the standard

deviation.

z = (x-μ)/o = (484 - 500)/10.4 = - 1.54

To determine the required probability

P(x < 484) = P(z < -1.54)

We'll use data from the normal distribution table

for these probabilities

P(x < 484) = P(z < -1.54) = 0.06178

B) Probability that a randomly selected study

participant's response was between 504 and 516

= P(504 ≤ x ≤ 516)

We normalize or standardize 504 and 516

For 504

z = (x -μ)/σ = (504 500)/10.4 = 0.38

For 516

z = (x - μ)/σ = (516-500)/10.4 = 1.54

To determine the required probability

P(504 ≤ x ≤ 516) = P(0.38 ≤ Z ≤ 1.54)

We'll use data from the normal distribution table

for these probabilities

P(504 ≤ x ≤ 516) = P(0.38 ≤ Z ≤1.54)

= P(z ≤ 1.54) - P(z ≤ 0.38)

= 0.93822 - 0.64803

= 0.29019

C) Probability that a randomly selected study

participant's response was more than 528 = P(x >

528)

We first normalize or standardize 528

z = (x - μ)/σ = (528 - 500)/10.4 = 2.69

To determine the required probability

P(x > 528) = P(z > 2.69)

We'll use data from the normal distribution table

for these probabilities

PP(x > 528) = P(z > 2.69) = 1 - P(z ≤ 2.69)

= 1-0.99643

= 0.00357

) Only the in () is as its probability

is less than ..

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The complete question is as follows -

In a recent year, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.4.

A) Find the probability that a randomly selected medical student who took the test had a total score that was less than 484. The probability that a randomly selected medical student who took the test had a total score that was less than 484 is:_______.

B) Find the probability that a randomly selected study participant's response was between 4 and 6 The probability that a randomly selected study participant's response was between 4 and 6 is:_______.

C) Find the probability that a randomly selected study participant's response was more than 8. The probability that a randomly selected study participant's response was more than 8 is:________.

The probability that a randomly selected medical student who took the test had a total score that was less than 480 is 0.49, which means that approximately 49% of medical students had a score lower than 480.

To calculate the probability that a randomly selected medical student who took the test had a total score that was less than 480, we need to start by looking at the data given. In this case, the data tells us that the mean score was 500 and the standard deviation was 50. This means that the scores are normally distributed, which means that the probability of finding a score lower than 480 can be calculated using the normal distribution formula. We can use this formula to calculate the area under the curve (or probability) below the score of 480. The result of this calculation is 0.49, which means that approximately 49% of medical students had a score lower than 480.

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