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Answer:

x = 15

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

3x - 5 is an exterior angle of the triangle, then

3x - 5 = x + 25 ( subtract x from both sides )

2x - 5 = 25 ( add 5 to both sides )

2x = 30 ( divide both sides by 2 )

x = 15

Answer:

40° and 115°

Step-by-step explanation:

x+3x-5+25°=180°(angle on a straight line)

4x+20=180°

4x=180°-20

4x=160°

x=160/4

x=40°

The other angle

3x-5=3(40)-5

120-5=115°

total

40°+25°+115°=180°

Options A and B are functions as either if of the inputs is relating to a different output or different inputs relating to a single output.

A function can be thought of as a set of inputs that produces some output.

We know a relation is a function if every input relates to a different output sometimes many input relates to one output but one input relates to different outputs is not a function.

Option A is a function as every input relates to a different output.

Option B is not a function as the input - 4 relates to two different outputs 12 and 15.

Option C is also a function as every preimage has a different image.

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The depth of the personal submarine is -14.9 meter.

An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.

Given that,

The submarine descends 20.6 meters and then ascends 5.7 meters. it means 20.6 is a negative number and 5.7 is a positive number.

Now,

To find the depth adding the -20.6+5.7

-20.6+5.7

-14.9

Hence, The depth of the personal submarine is -14.9 meter

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The 95% confidence interval for the mean of the population lies between

(17.61, 62.39)

Construct a 95% confidence interval for the mean:

To construct a 95% confidence interval for the mean of the population, we must start with finding the following:

Mean

n=4

Mean=(25+47+32+56)/n

         =(160)/4

         =40

Mean is 40

Standard deviation σ

                             = [tex]\frac{1}{n-1}( \sum x^{2} -n(mean)^{2} )[/tex]

                             = [tex]\frac{1}{3} (6994-4(40)^{2} )[/tex]

                            σ= 14.07

Now, we construct 95% confidence interval CI:

Confidence interval=mean± t-table value*(standard deviation/√n)

Given a t-table value of 3.1824 from z-distribution table, mean=40, n=4, and standard deviation=14.07, we have:

Confidence interval=(40±3.1824(14.07/√4)

                               =(40±22.39)

                               =(40-22.39, 40+22.39)

Confidence interval=(17.61, 62.39)

The question was incomplete, below is the complete question:

You are given the following information obtained from a random sample of four observations taken from a large, normally distributed population.

25 47 32 56

Construct a 95% confidence interval for the mean of the population

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Answer:

The opposite of an integer and negative number is a positive integer number. In this case, the opposite of -4 is +4.

Answer:

slope = (3/10)

Step-by-step explanation:

(-3, 3) and (7, 6)

(x₁, y₁)        (x₂, y₂)

        y₂ - y₁         6 - 3             3              3

m = ------------ = ------------ = ------------ = ----------

        x₂ - x₁         7 - (-3)        7 + 3           10

I hope this helps!

The sets of lengths that are Pythagorean triples are:

A. 10, 24, 26

D. 9, 40, 41

E. 15, 20, 25

A Pythagorean triple can be described as a set of three numbers of the side lengths of a right triangle whereby the square of the longest side is equal to the sum of the squares of the two other sides.

For 10, 24, 26, we have:

10² + 24² = 26²

676 = 676 [true]

The set, 10, 24, 26 is a Pythagorean triple.

For 14, 48, 49, we have:

14² + 48² = 49²

2,500 = 2,401 [not true]

The set, 14, 48, 49, is NOT a Pythagorean triple.

For  9, 12, 16, we have:

9² + 12² = 16²

225 = 256 [not true]

The set, 9, 12, 16, is NOT a Pythagorean triple.

For  9, 40, 41, we have:

9² + 40² = 41²

1,681 = 1,681 [true]

The set, 9, 40, 41, is a Pythagorean triple.

For  15, 20, 25, we have:

15² + 20² = 25²

625 = 625 [true]

The set, 15, 20, 25, is a Pythagorean triple.

The correct set of options are, A, D, and E.

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y = 3x - 1 is the equation in slope-intercept form.

What exactly does slope intercept mean?

y = 3x +b  passes through the point (2,5)

5 = 3 * 2 + b

5 = 6 + b

b = 5 -6

b = -1

y = 3x +b

y = 3x - 1 is the equation in slope-intercept form.

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Answer:

x = 115°

Step-by-step explanation:

Line a and line b are parallel lines

x° and the angle with measure 115° are alternate exterior angles so they have same measurement and each is 115°

[tex] - {k}^{2} + 3k = 28 - 2 {k}^{2} \\ - {k}^{2} + 2 {k}^{2} + 3k - 28 = 0 \\ {k}^{2} + 3k - 28 = 0 \\ (k + 7)(k - 4) = 0 \\ \\ k + 7 = 0 \\ \\ ork - 4 = 0 \\ \\ k = - 7 \\ \\ or \\ \\ k = 4[/tex]

ATTACHED IS THE SOLUTION

I GROUPED THE LIKE TERMS TOGETHER FIRST AFTER THAT THEN FACTORISED.

Answer:

324 square inches

Step-by-step explanation:

A = S squared

A = 18 x 18

A = 324square inches

The solutions to the equation are x = 5 and x = 3

The equation is given as

|x - 4|= 1

The above equation is an absolute value equation

When the absolute value sign is removed from the equation, we have

x - 4 = 1 or x - 4 = -1

Add 4 to all sides of the equation

So, we have the following equations

x = 1 + 4 or x = 4 - 1

Evaluate

x = 5 or x = 3

This means that the value of the equation is x = 5 or x = 3

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The graph represents the cosine graph, the coordinates of B is (-180, -1 )

This is a type of graph used to depict cosine values of angles. The maximum and minimum points in these type of graph is 1 and -1.

The zero points gives the maximum point on the graph, hence the graph starts at ( 0, 1 )

Point B is found by analyzing the graph.

The point is located at the minimum which is -1. this is for the output value.

The input value which is the x direction we look at the cycles covered. one full cycle is 360 degrees or -360 degrees.

Point B is in the negative and coves half cycle which is -180

Hence B ( -180, -1)

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well, the change was 8 bucks.

if we take 20 to be the 100%, what is 8 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 20 & 100\\ 8& x \end{array} \implies \cfrac{20}{8}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{5}{2}=\cfrac{100}{x}\implies 5x=200\implies x=\cfrac{200}{5}\implies x=40[/tex]

Adam's account balance at the end of the month is 19.13 dollars.

The amount present in Adam's bank account at the beginning of the month is $174.85.

The transactions he wrote are,

58.00

-316.35

102.96

The Transactions which have positive sign are credit amount and the transaction with negative sign are debit amount.

We can write,

The balance at the end of the month = Initial balance present + Credit amount + debit amount

So, balance in Adam's account can be found by simple addition and subtraction,

Balance = 174.85 + 58.00 + 102.96 - 316.38

Balance = 335.81 - 316.68

Balance = 19.13

The amount in Adam's bank account at the end of the month is 19.13 dollars.

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Given the function:

The given function is a linear function

The rate of change of the linear function = the slope of the function

The slope = the coefficient of x = -1/4

So, from the given options, you will select the function that has a slope that is greater than (-1/4)

The cost of renting the meeting room by the manager for the hours 1,2,3 and 4 defined by the function of (t) = function of (t-1) + 20, given that function of (1) = 100 is 520.

A function can be defined as a mapping whose co-domain is the set of real numbers.

Given the mapping defined as function of (t) = function of (t-1) + 20, for function of (1) = 100

Hence,

.f (2) = function of (2-1) + 20

.f (1) + 20

100 + 20 = 120

.f (3) = function of (3-1) + 20

.f (2) + 20

120 + 20 = 140

f (4) = f (4-1) + 20

.f (3) + 20

140 + 20 = 160

This can be seen in a table as shown above!

We can conclude with the proper mapping of the defined function of (t) = function of (t-1) + 20 for function of (1) = 100 that the total cost for the hours 1,2,3 and 4 for renting the meeting room is 520.

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Answer:

The percent of change is about a 16.95% increase.

The predicted population in 2019 is 158,000 people.

sry if im wrong

Step-by-step explanation:

The total of animals is a prime number and hence the ratio can only be expressed as fraction.

To find the ratio in the given question, we must first of all add the total sum of the animals given and then find the ratio to each one.

Total number of items given

[tex]12 + 5 + 6 = 23[/tex]

The ratio of spiders to mosquitoes to rats are

[tex]\frac{12}{23}:\frac{5}{23}:\frac{6}{23}[/tex]

The total sum of animals is a prime number and can't be divided, however, the ratio is expressed as simple as possible.

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Answer:

(4 , 1)

Step-by-step explanation:

This is because to find the coordinate on a graph, it is written as ( x , y) and x is on 4 and y is on 1.

that's my opinion.

Nice question

In the given groups of Relative Frequencies the best represented by a pie chart would be Option D. 25%; 24%; 26%; 25%.

Relative frequencies are more commonly used because they allow you to compare how frequently values occur relative to the overall sample size. They are calculated by dividing the total number of responses by the number of responses for each category. Pie charts depict relative frequencies by showing how much of the total pie each category represents. Raw frequencies and relative frequencies can be displayed in frequency tables and bar charts.

According to the question we can get,

25% = [tex]\frac{1}{4}[/tex]

[tex]\frac{1}{4}[/tex] × 360° = 90°

24% approach 25%

26% approach 25%

So Option D would be the group of relative frequency best represented by a pie chart.

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Option A, Pie chart best used for displaying frequency distributions when one or two categories make up a large proportion of the total.

A piechart is best which is used for displaying frequency distribution when one or two categories make up a large proportion.

Hence, the Pie chart is best.

Pie chart - A pie chart is a statistical visualization in the shape of a split region that displays numerical information. The arc length of each slice in a pie chart is proportionate to the quantity represented.

Explanation of incorrect options,

Bar graph - A bar chart is a form of chart or graph that depicts categorical data using rectangular bars whose height or length is proportionate to the value they represent. face. Bars can be drawn vertically or horizontally. A histogram is another name for a vertical bar chart.

Comparative pie chart - Pie graphs have pie graphic areas comparing ratios by frequency. The greater the radius of the pie chart, the greater the number of individuals it depicts. This allows you to compare the two data sets visually.

Comparative bar graph - Chart displaying continuous comparisons of columns indicating different portions of the same category. This facilitates the comparison of visual data.

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Raising 4,929 to the place value of the underlined digit will give a value of 4930.

It should be noted that rounding up of numbers simply means raising the number to the nearest ten, hundred, or thousand.

In this case let's assume that the underlined number is 2. Therefore, raising 4929 will give 4940. It should be noted that the number beside it is more than 5. Therefore, 1 will be added to 2 making 3. The new number is 4930.

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Any transformation that leaves the sides and angles of flat figures unaltered is referred to as rigid transformation or isometry. Congruent pictures are produced by reflection in the plane, translations, rotations, or a combination of them.

A transformation that maintains the size and shape of a geometric figure is known as a rigid transformation (or isometry). is a unique kind of transformation that doesn't alter a figure's size or shape.

The complete question is:

Make a conjecture. How are rigid transformations and congruent figures related? Check all that apply

a) rigid transformations preserve segment lengths and angle measures.

b) Rigid transformations produce congruent figures.

c) If two figures are congruent, then there is a rigid transformation or a combination of rigid transformations that will map one onto the other.

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The degrees to radians conversion is given as 1° = π/180 radian thus the conversion of 310° is (31/18)π.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

It is known that π radian = 180°.

1° = (π/180) radian.

Multiply both sides by 310

310° = (π/180)310

310° = (31/18)π

Hence "The degrees to radians conversion is given as 1° = π/180 radian thus the conversion of 310° is (31/18)π".

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The given question is incomplete complete question is ;

Convert the angle \theta=310^\circθ=310∘

theta, equals 310, degrees to radians.

The law which makes this argument true is referred to as the Law of Syllogism.

The Law of Syllogism is also referred to as reasoning by transitivity and it states that if two (2) statements are true, then a third true statement can be logically derived.

Mathematically, the Law of Syllogism follows a specific pattern and can be represented by the following conditional statements:

In this context, we can reasonably infer and logically deduce that the Law of Syllogism makes the conclusion based on the two premises.

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The remainder of the polynomial 4x³-20x-50 / (x - 3) would be the expression 4x²+20x+52.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

We have to determine the remainder of the quantity 4 x cubed minus 20 x minus 50 end quantity divided by the quantity x minus 3 end quantity.

4x³-20x-50 = (4x³-4x²-16x-50) + (4x²+16x)

Divide both sides by (x - 3) to get

4x³-20x-50 = (4x³-4x²-16x-50)/(x-3)+(4x²+16x)/(x-3)

⇒ 4(x²+4x+12)+(4x²+16x)/(x-3)

⇒ 4x²+16x+48+(4x²+16x)/(x-3)

⇒ 4x²+16x+48+4(x+4)

⇒ 4x²+20x+52

Therefore, the remainder of the polynomial 4x³-20x-50 / (x - 3) would be the expression 4x²+20x+52.

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