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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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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:

The volume of the display case in cubic inches is 10,328 1/16 in.

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.

The relative frequency of a person having the flu and testing positive for the flu is 0.1053/0.901 = 0.117, or approximately 11.7%. The relative frequency table is given below.

To get the relative frequencies, we divide each cell value by the total frequency of the table.

This is how we construct relative frequency table.

To construct a relative frequency table, we need to determine the different possible outcomes and their corresponding frequencies based on the given information.

Let's define the following events:

A: a person has the flu

B: a person tests positive for the flu

Then, using the information given in the problem, we can construct the following relative frequency table:

                   A (has the flu)   not A (does not have the flu) Total

B              0.13*0.81 = 0.1053          0.08*0.87 = 0.0696              0.1749

not B       0.19*0.81 = 0.1540           0.63*0.87 = 0.5471               0.7011

To                   0.2843                                 0.6171                         0.901

In this table, the values in the cells represent the product of the probability of the row event and the probability of the column event. For example, the value 0.1053 in the top left cell represents the probability of a person having the flu (event A) and testing positive for the flu (event B), which is calculated as 0.13 x 0.81.

The total frequency for each row and column is calculated by summing the values in that row or column. The total frequency for the entire table is the sum of all the values, which is 0.901 in this case.

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The triangle which can be drawn as per the condition described is only option 2. an isosceles triangle with measure  20° and 80°.

Triangle which can be drawn as per the measurements are,

An acute triangle with sides measuring 7, 4, 2.

In an acute triangle, the square of the longest side is less than the sum of the squares of the other two sides.

According to the Pythagorean theorem.

7²< 4² + 2²

49 < 16 + 4

49 < 20

This is a contradiction, since 49 cannot be less than 20.

It is not possible to draw triangle.

An isosceles triangle with measures of angle 20° and 80°.

Sum of interior angles  of a triangle is 180°

Here, third angle = 180° - ( 20° + 80° )

⇒Third angle = 80°

Two angles are congruent ⇒ opposite sides to congruent angles are also congruent.

It forms a isosceles triangle.

An obtuse triangle with sides measuring 5, 10 and 15.

Side lengths 5, 10, and 15 do not form a triangle at all.

Since the sum of the two shorter sides is less than the longest side.

5 + 10 = 15

It is not possible to have an obtuse triangle with sides measuring 5, 10, and 15.

An scalene triangle with angle measuring 110° and 35°.

Sum of the interior angles is always 180°.

Measure of the third angle ,

180° - 110° - 35° = 35°

Three angles of the triangle measure 110°, 35°, and 35°.

It represents isosceles triangle.

Therefore, the possible triangle as per the given condition is only option 2. isosceles triangle with measure 20° and 80°.

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[tex] {( \frac{9}{4} )}^{3} [/tex]

=

[tex] \frac{729}{64} [/tex]

Answer: 11 25/64

Step-by-step explanation: 2 1/4 x 2 1/4= 5 1/16 x 2 1/4 = 11 25/64

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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Answer:

Lana has completed 22 out of 32 puzzles in her book. To find the percentage of the puzzle she has completed, divide the number of puzzles she has completed by the total number of puzzles in the book and multiply by 100.

22/32 x 100 = 68.75%

Lana has completed 68.75% of the puzzles in her book.

Answer:

Lana has completed 68.75% of the puzzles in her puzzle book.

Step-by-step explanation:

Lana has completed a total of 22 puzzles and there are 10 puzzles remaining, so the total number of puzzles in the book is:22 + 10 = 32To find the percentage of puzzles Lana has completed, we can use the following formula:percentage = (completed puzzles / total puzzles) x 100%Substituting the values, we get:percentage = (22 / 32) x 100%

percentage = 0.6875 x 100%

percentage = 68.75%Therefore, Lana has completed 68.75% of the puzzles in her puzzle book.

The figure is indeed symmetric and the number of lines of symmetry the snowflake has is C. Yes; 6 lines of symmetry.

Generally a snowflake is hexagonal and has 6-way radial symmetry. Thus, one can rotate it 60 degrees (the sixth of full rotation) and it still appears the same.

So, overall, this means that a snowflake holds 6 lines of symmetry which divide it into two identical halves reflecting each other. Consequently, it can be rotated in 60-degree increments and still holds identicality. Akin to this final property, the snowflake artifact possesses six uniquely divided

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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.

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.

Answer:

Table B is proportional since y = 1.5x:

4.5 ÷ 3 = 1.5

7.5 ÷ 5 = 1.5

10.5 ÷ 7 = 1.5

[tex] {(3x + 7)}^{2} - ((2x + 5) \times x) [/tex]

[tex] = 7 {x}^{2} - 5x + 49[/tex]

Answer:

Since (2x, x + 17, x + 21, ...) is an arithmetic sequence, we know that the common difference between consecutive terms is constant.

The common difference can be found by subtracting any two consecutive terms in the sequence. Let's subtract the second term (x + 17) from the first term (2x):

2x - (x + 17) = x - 17

Now let's subtract the third term (x + 21) from the second term (x + 17):

(x + 17) - (x + 21) = -4

Since the common difference is constant, we can set the two expressions for the common difference equal to each other:

x - 17 = -4

Solving for x, we get:

x = 13

Therefore, the value of x that makes the sequence (2x, x + 17, x + 21, ...) an arithmetic sequence is x = 13.

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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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.

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.

Answer:32mi/gal

Step-by-step explanation:

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

416/13 = 32

32mi/gal

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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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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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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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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The book value of the automobile at the end of 3 years is $13,000.

The straight-line method is method of depreciation that allocates the same depreciation expense each year.

Straight line depreciation expense = (Cost of asset - Salvage value) / useful life

($32,500 - 0) / 5 = $6,500

Total depreciation in 3 years = $6,500 x 3 = $19,500

Book value = cost of the automobile - total depreciation

$32,500 - $19,500 = $13,000

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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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Using the model to estimate f(x) when x = 5 and x = 10, the vaues are 18.33 and 17.78

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

f(x) = -0.11x + 18.88

Also, we have

x = 5 and x = 10

Substitute the known values in the above equation, so, we have the following representation

f(5) = -0.11 * 5 + 18.88 = 18.33

f(10) = -0.11 * 10 + 18.88 = 17.78

Hence, the values are 18.33 and 17.78

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Complete question

Question: A statistician calculated the following linear model to describe the data: f(x) = – 0.11x + 18.88 Use the model to estimate f(x) when x = 5

We can see here that the statements that are true are:

B. The symbol should be used because (8, 13, 22, 36) is a set and none of the elements in - 13 is a set.

C. The ∉ symbol should be used because ∉ is not an element of the set.

F. The ∈ symbol should be used because ∉ is not an element of the set.

A set in mathematics is a collection of unique objects, referred to as elements or members, that are paired off according to some shared quality.

Numbers, letters, words, forms, persons, and other mathematical things can all be included in a set.

We can see here that -13 ∉  (8, 13, 22, 36).

These statements are true because -13 is not actually an element of (8, 13, 22, 36). Thus, in the given set of data, -13 is not seen in the given set.

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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 couple needs to deposit about $554.49 each month end until they retire to reach their goal.

To find the monthly deposit needed, we'll use the future value of an ordinary annuity formula:

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

We already know the future value (FV) as $953,776.53, and we want to solve for PMT, the monthly deposit:

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

We'll use the same r (0.08/12) and a new n (35 * 12) for the 35 years until retirement:

PMT = 953776.53 / [((1 + 0.08/12)^(35*12) - 1) / (0.08/12)]

PMT ≈ 554.49

Thus, the couple needs to deposit about $554.49 each month end until they retire to reach their goal.

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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