Using the integers −9 to 9 at most one time each, place a digit in each box ( ___ , ____) and. ( ___ , ____) to create endpoints for the longest possible line segment both numerically and graphically whose midpoint is (1, 3)

Ali's strategy is essentially the same as Mary's strategy. Both strategies estimate the HST as 15% of the price. However, Mary's strategy involves taking half of 10% of the price.

Mary suggests estimating the HST in Ontario as finding 10% of the price, taking half of this answer and adding the two. Ali proposes finding 10% of the price, then 5% of the price and adding the two answers.

Their strategies differ in the way they approach finding the estimate, but both methods can be used to arrive at the same result.

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The HST in Ontario is 13%, which can be estimated using 15%. Mary tells Ali that it can be estimated as: find 10% of the price, take a half of this answer and add the two. Ali tells Mary that he thinks they should find 10% of the price, then 5% of the price and add the two answers. Compare their strategies.

The equation that represents the relationship between p and a is a = p - 6.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 0)/(7 - 6)

Slope (m) = 1/1

Slope (m) = 1.

At data point (6, 0) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 0 = 1(x - 6)  

y = x - 6 ≡ a = p - 6

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Answer: A.

Step-by-step explanation: we just need to distribute and see that the only plausible answer is a because when distributed it equals 3x=6

Answer:

The correct number line that shows the solutions to x+8 > 15 is option B.

Step-by-step explanation:

The correct number line that shows the solutions to x+8 > 15 is option B.

On this number line, you can see that the values of x that make the inequality true are greater than 7. Therefore, the solution set for this inequality is x > 7.

The recursive sequence that represents the sequence defined by the following explicit formula is given as follows:

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The first term and the common ratio for this problem is given as follows:

[tex]a_1 = -32, q = -\frac{1}{4}[/tex]

The common ratio means that each term is the previous term multiplied by -1/4, hence the recursive formula is given as follows:

[tex]a_{n + 1} = -\frac{1}{4}a_n[/tex]

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4) residual =actual -predicted =26708-10376.71 =16331.29

1) predicted change = -140.74

2) predicted change =317.74

3) predicted GNP =-11093.17-140.74*10+317.74*72 =10376.71

4) residual =actual -predicted =26708-10376.71 =16331.29

A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.

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The correct terms in the expression are,

⇒ 3x and 5x

We have to given that;

The quadratic equation is,

⇒ 15x² + x - 2 = (? - 1) (? + 2)

Now, We can simplify as;

⇒ 15x² + x - 2

⇒ 15x² + 6x - 5x - 2

⇒ 3x (5x + 2) - 1 (5x + 2)

⇒ (3x - 1) (5x + 2)

Thus, The correct terms in the expression are,

⇒ 3x and 5x

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I got you, buddy!

Let x be the length of the shortest side. Then, the length of the second side is 2x, and the length of the third side is x + y, where y is the additional length.

The perimeter of the triangle is the sum of the three sides, so we have:

x + 2x + (x + y) = 60

Simplifying this equation, we get:

4x + y = 60

We also know that the area of a triangle is given by:

A = (1/2)bh

where b is the length of the base, and h is the height. Since the base of the flower bed is the shortest side of length x, we can choose the height to be y. Therefore, we have:

A = (1/2)xy

Now we need to solve for x and y. We can use the equation for the perimeter to solve for y:

y = 60 - 4x

Substituting this into the equation for the area, we have:

A = (1/2)x(60 - 4x)

Simplifying and expanding, we get:

A = 30x - 2x^2

To maximize the area, we can take the derivative of A with respect to x and set it equal to 0:

dA/dx = 30 - 4x = 0

Solving for x, we get:

x = 7.5

Substituting this back into the equation for y, we get:

y = 60 - 4x = 45

Therefore, the dimensions of the flower bed are:

shortest side = x = 7.5 feet second side = 2x = 15 feet third side = x + y = 52.5 feet

A square of a binomial is a polynomial expression that results from multiplying a binomial by itself. The result is a trinomial expression with three terms.

Answer:32mi/gal

Step-by-step explanation:

106485 - 106069 = 416mi (the distance that you traveled)

416/13 = 32

32mi/gal

Answer:

Step-by-step explanation:

If the ratio of orange goldfish to yellow goldfish is 3:5, then we can write:orange goldfish : yellow goldfish = 3 : 5We know that Ben has 6f orange goldfish. We can use this information to set up a proportion and solve for the number of yellow goldfish in terms of f:3/5 = 6f/yellow goldfishTo solve for yellow goldfish, we can cross-multiply:3 * yellow goldfish = 5 * 6fSimplifying:yellow goldfish = 30f/3 = 10fTherefore, Ben has 10f yellow goldfish in terms of f, given that he has 6f orange goldfish and the ratio of orange to yellow goldfish is 3:5.

Therefore, we need 17 towels of brand C to clean a single sq ft

Brand A:

we add up all the sq ft cleaned by brand a

0.75+1.50+2.25=4.5

and we add up all paper towels used in total

6+13+20=39

now

to clean 4.5 square ft, we need 39 towels. how many we need to clean a single square foot?

4.5 sq ft ___________39 towels

1 sq ft_____________A

and A= 1 sq ft * 39 towels / 4.5 sq ft

and that gives us 8.6 towels, so we need 9 towels to clan a square foot with the brand A

now we repeat this with bran b and c

brand B:

0.75+1.75+2=4.5 sq ft

9+22+25= 56 towels

4.5 sq ft________56 towels

1 sq ft__________B

B= 1 sq ft * 56 towels / 4.5 sq ft = 12.4

so we need 13 towels of brand B

at last

brand C:

1+1.75+2.5=5.25 sq ft

17+29+41= 87 towels

5.25 sq ft________87 towels

1 sq ft__________C

C= 1 sq ft * 87 towels / 5.25 sq ft = 16.57 towels

Therefore, we need 17 towels of brand C to clean a single sq ft

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1.) The average monthly income for Brianna would be = $1,850

2.) The average monthly expenses for Brianna would be =$3,145

3.) The total monthly cash flow = =$ −1,295

The monthly pay check after tax = $1600

The annual scholarship stipend = $3000

That is 3000/12 = $250

Therefore, the average monthly income = 1600+250 = $1,850.

The average monthly expenses = 700+120+75+140+25+110+100+300+250+(12000+1000+1500+800+600/12)

= 1820 + 15900/12

= 1820 + 1325

= $3,145

The monthly cash flow = 1850-3145 =$ −1,295

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Answer:

To simplify 9 1/8 - 2 1/4, we need to first convert the mixed numbers to improper fractions.

9 1/8 = (8 x 9 + 1)/8 = 73/8

2 1/4 = (4 x 2 + 1)/4 = 9/4

Now we can subtract the two fractions:

73/8 - 9/4

Since the two fractions have different denominators, we need to find a common denominator. The least common multiple of 8 and 4 is 8, so we can convert the second fraction to have a denominator of 8:

73/8 - (9/4)x(2/2) = 73/8 - 18/8 = 55/8

Therefore, 9 1/8 - 2 1/4 = 55/8, which is an improper fraction. If we want to convert it back to a mixed number, we can divide the numerator by the denominator:

55/8 = 6 7/8

So the simplified answer is 6 7/8. Answer: 6 7/8.

Answer:

6 7/8

Step-by-step explanation:

9 1/8 - 2 1/4 =

      9 1/8

  -   2 1/4

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

The common denominator for the fractions is 8.

      9 1/8

  -   2 2/8

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

Since the bottom fraction is greater than ther upper fraction, we borrow 1 from the nine. 1 is the same as 8/8, so we take 1 from 9 and add 8/8 to 1/8.

      8 9/8

  -   2 2/8

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

      6 7/8

Answer: 6 7/8

If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′ are: D. A′(−2.4, 3.6), B′(−1.2, 1.2), C′(2.4, −1.2), D′(2.4, 2.4).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 3/5 centered at the origin as follows:

Ordered pair A (-4, 6) → Ordered pair A' (-4 × 3/5, 6 × 3/5) = Ordered pair A' (-2.4, 3.6).

Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3/5, 2 × 3/5) = Ordered pair B' (-1.2, 1.2).

Ordered pair C (4, -2) → Ordered pair C' (4 × 3/5, -2 × 3/5) = Ordered pair C' (2.4, -1.2).

Ordered pair D (4, 4) → Ordered pair D' (4 × 3/5, 4 × 3/5) = Ordered pair D' (2.4, 2.4).

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Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Answer:

We can use the information provided to estimate the number of ducks that have red marks on the bottom.

If only 3 out of 50 people have won a small prize, then we can estimate that the probability of winning a small prize is 3/50 or 0.06. Since the person wins a small prize if there’s a red mark on the bottom of the duck, we can estimate that the proportion of ducks with red marks is also 0.06.

So, we can estimate the number of ducks with red marks as follows:

Number of ducks with red marks = 0.06 x 160

Number of ducks with red marks = 9.6

We can estimate that there are about 9 or 10 ducks with red marks on the bottom.

Answer: The correct answer is (2,5π/4).

Step-by-step explanation:

The correct polar coordinates of the point (-√2, -√2) are (r, θ) = (2, 5π/4).

Explanation:

Using the formulas for converting Cartesian coordinates to polar coordinates:

r = √(x^2 + y^2)

θ = atan2(y, x)

Plugging in the given values:

r = √((-√2)^2 + (-√2)^2)

= √(2 + 2)

= √4

= 2

θ = atan2(-√2, -√2)

= 5π/4 radians

So, the correct polar coordinates of the point (-√2, -√2) are (r, θ) = (2, 5π/4).

The probability that a person has the virus given that they have tested positive find the P(A/B)=0.0045

We can use Bayes' theorem to find the probability that a person has the virus given that they have tested positive:

P(A | B) = P(B | A) * P(A) / P(B)

where P(B | A) is the probability of testing positive given that the person has the virus, P(A) is the prior probability of a person having the virus (1/300), and P(B) is the total probability of testing positive.

To find P(B), we can use the law of total probability, which states that:

P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)

where P(B | not A) is the probability of testing positive given that the person does not have the virus. This is the false positive rate, which is 5% or 0.05 in this case. P(not A) is the complement of P(A), which is 299/300.

Substituting the values, we get:

P(B) = 0.85 * 1/300 + 0.05 * 299/300

= 0.059

Now we can plug in the values into Bayes' theorem:

P(A | B) = 0.85 * 1/300 / 0.059

= 0.0045 or 0.45%

Therefore, the probability that a person has the virus given that they have tested positive is 0.45% or 0.0045 (rounded to the nearest tenth of a percent).

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Multiplicative inverse of given expression is 9/5.

The given expression,

-4/9 + (2/5 + 3/5)

Simplify it,

⇒ -4/9 + (2+3)/5

⇒ -4/9 + 5/5

⇒ -4/9 + 1

⇒ (-4 + 9)/9

⇒ 5/9

So its multiplicative inverse =  1/(5/9) = 9/5

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The equation for the rectangle is adding the interior angles:

x + x - 5 + 71 + y + 21 = 360°

Solving that for y, we will get:

2x + y + 87 = 360

Remember that the sum of the interior angles of any figure with 4 sides must be 360°.

Then we can write an equation:

x + x - 5 + 71 + y + 21 = 360°

2x + y + 87 = 360

Solving it for y:

y = 273 - 2x

Now there is a clear problem in the diagram because the angle in the bottom left is clearly larger than 90°, but it says that the angle measures 71°, so there we have a problem.

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The functions g(x) = -√x - 3 and h(x) = x + 4 meet the requirements, and f(x) = g(h(x)) is true for f(x) = -√(x+4) - 3.

We are given f(x) and we need to find functions g(x) and h(x) such that f(x) = g(h(x)). The given function is f(x) = -√(x+4) - 3.

To find g(x) and h(x), we can split the given function into two simpler functions. Let's first look at the inner function, which deals with the input of the square root. We can define h(x) as the function inside the square root, which is:

h(x) = x + 4

Now we need to find g(x) such that when h(x) is plugged into it, we get the original function f(x). Since we have the square root and a subtraction, we can define g(x) as:

g(x) = -√x - 3

Now let's verify if f(x) = g(h(x)):

g(h(x)) = g(x + 4) = -√(x + 4) - 3

As you can see, g(h(x)) = f(x), which confirms that the functions g(x) and h(x) we found satisfy the condition.

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The option that is a representation that shows y as a function of x is the graph in option 2. The answer is B.

A function is any relation or table of values which may be represented in a graph that has only one possible y value that is assigned to each x-value.

The first option is not a function because x-value 0 has two corresponding y-values, 4 and 9.

In the third option, we also have two y-values, 5 and -5, that is assigned to one x-value, 0. So, it is not a function.

The graph in option 2 represents y as a function of x, because no two y-values is assigned to the same x-value.

The answer is: B.

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Maria can estimate the total tuition for all 4 years to be $122400

How to determine the tuition fee?

Tuition payments, usually known as tuition in American English and as tuition fees in Commonwealth English, are fees charged by education institutions for instruction or other services.

The given parameters are

Period of school = a 4-year college

Tuition fee per semester = The tuition is $15,300 per semester.

Number of semester = 2=4 = 8 semesters

Total cost = $15,300 per semester. * 8 = $122400

Therefore the cost of the tuition for 4 years is $122400

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The total amount Maria can estimate for the cost of a 4-year college program at the University of Bayou is $122,400

A college program consists of courses that are taken as part of an accredited course, which leads to the award of a degree.

The tuition per semester for the University of Bayou = $15,300

The number of semester in an academic year = Usually 2 semesters

The number of years Maria intends to spend in college = 4 years

The estimate of the total tuition, found using the basic arithmetic operations is therefore;

Tuition for a 4 year program = 15,300 × 2 × 4 = 122400

The total tuition Maria can estimate for 4 year of college is $122,400

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Answer:

a. $1,240

b. $1,960

c. 9 years

d. 17 years

Step-by-step explanation:

For interest you multiply the percent with 1,000 and add the number you get for your answer. So 1,000 times 6% is 60. Each year the account earns $60 worth of interest. You multiply 60 by 4 and your result is 240. You add 240 to 1,000 and get your answer for a $1,240.

You repeat the same process for b. 16 times 60 is 960. You add 960 and 1,000 and your answer is $1,960.

So we know the account already has $1,000 so all that has to be done is to divide 500 by 60 and your result is 8.3. However you it is anual interest so you cannot but in a decimal so you round up to 9. Making it 9 years

Same process dividing 1,000 by 60 which gives you 16.6 rounding up to 17. Making it 17 years.

The value of the variable x in the equation 6 / -4.5 = 8 / 4x is - 3 / 2.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Therefore, let's solve the equation.

The variable in the equation is x . A variable is a number represented with letter in an equation.

Therefore,

6 / -4.5 = 8 / 4x

cross multiply

6(4x) = -4.5(8)

24x = - 36

divide both sides of the equation by 24

Therefore,

x = -36 / 24

x = - 3 / 2

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Answer:

56 cm

Step-by-step explanation:

have a good day God bless :)

7(x-2) - 2(x-3)

= 7x - 14 - 2x + 6   // Distribute the coefficients

= 5x - 8  // Combine like terms and simplify

Therefore, 7(x-2) - 2(x-3) simplifies to 5x - 8.

Answer:

7(x-2) - 2(x-3) simplifies to 5x - 8.

Step-by-step explanation:

To expand and simplify 7(x-2) - 2(x-3), we can use the distributive property and simplify the resulting expression.

7(x-2) - 2(x-3) = 7x - 14 - 2x + 6

Combining like terms, we get:

= (7x - 2x) + (-14 + 6)

= 5x - 8

Therefore, 7(x-2) - 2(x-3) simplifies to 5x - 8.

The missing angles measures in the diagram above when calculated is given below:

<1 = 42°

<2 = 76°

<3 = 62°

<4 = 76°

For <1:

The total angle on a straight line = 180°

That is: angles <1+62°+<4 = 180

<1 = 180-62+76

= 180-138

= 42°

For <4: 180= 62+42+<4

<4 = 180-104

= 76°

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