Find the quotient.
2.4)7.68

Answer:

Step-by-step explanation:

You want the measures of the named angles in the given figure, given c=30°.

A right angle is 90°.

A linear pair totals 180°.

Vertical angles are congruent.

Angles that make up a right angle total 90°.

Angle 'a' is marked as a right angle, so a = 90°.

Angle b is complementary to angle c, so is ...

  b + c = 90°

  b = 90° -c = 90° -30° = 60°

Angle c is given as 30°.

Angle d is part of a linear pair with angle c, so is ...

  d = 180° -30° = 150°

Angle e is a vertical angle with respect to angle c, so is congruent to it.

  e = 30°

By using Pythagoras Theorem, it can be verified that

The hypotenuse of a triangle with shorter sides 1 unit each is not an integer

What is Pythagoras Theorem?

Pythagoras Theorem states that in a right angled triangle, the square of the hypotenuse is equal to the square of the sum of Perpendicular and base

According to the question given,

Shorter sides are 1 unit each

Let the length of the hypotenuse be h units

By Pythagoras Theorem,

[tex]h^2 = 1^2 + 1^2\\h^2 = 2\\h = \sqrt{2} \ units[/tex]

[tex]\sqrt{2}[/tex] is not an integer

So the hypotenuse here is not an integer.

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With the help of substitution the answer to the equation is - (-9/2 , 5/2)

acc to our question -

Hence,The solution to the equation is (-9/2, 5/2) using substitution.

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The length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.

According to the question,

We have the following information:

Two sides of a rectangular garden are 3 meters long. The area of the garden is 18 square meters.

We know that the following formula is used to find the area of rectangle:

Length*width = 18

Length*3 = 18

Length = 18/3

Length of the rectangular garden = 6 meters

Now, perimeter of the rectangular garden:

2(length+width)

2(6+3)

2*9

18 meters

Hence, the length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.

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The employee's new wage per hour is $10.83. The percentage increase of the original wage to his new​ wage is 3%.

A percent increase means how much a percentage has gone up over time. To find this number, one would need to find the difference between the original value and the final value, subtracting to find the exact total of the decrease. The formula for percent increase equals to "Increase / original number (value) x 100".

Given data:

First, we find 3% of $10.51 to get new wage per hour

= 0.03$ * $10.51

= $0.32

Then, we add this increase to $10.51.

= $10.51 + $0.32

= $10.83

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The situation can be represented using the equation 3g + 7 = 40

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

Length of three sides = g

Length of the fourth side = 7

Perimeter = 40

The perimeter of a quadrilateral is the sum of the sides of the shape

This means that

P = sum of the 4 sides

So, we have

P = g + g + g + 7

Evaluate

P = 3g + 7

Rewrite as

3g + 7 = 40

Hence. the equation that represents the situation is 3g + 7 = 40

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is 4

Answer:

The slope of this line is undefined.

The two quadratic equations are; y = x² + 2·x - 3 and y = -x² - 2·x + 3

Given,

x - intercepts = (−3,0) and (1,0).

The x-intercepts are given by the point at which the y-value of the equation are zero.

Therefore;

The quadratic equation are;

(x + 3)·(x - 1) = 0

x² + 2·x - 3 = 0

Quadratic equations;-

The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).

Here,

The equation can also be written in the form;

(-x - 3)·(x - 1) = 0

-x² - 2·x + 3 = 0

The quadratic equations are;

y = x² + 2·x - 3 and y = -x² - 2·x + 3

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The percent of Americans that had central heterochromia is A. 0061%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, it's estimated that only around 200,000 Americans have central heterochromia and the population of the United States

was 327,750,000 people.

The percent of Americans that had central heterochromia will be:

= Those with the disease / Total population × 100

= 200,000 / 327,750,000 × 100

= 0.0061%

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Answer:

She should choose the second cylinder-shaped box with a diameter of 30 cm and a height of 20 cm.

Step-by-step explanation:

The volume of a cylinder with a diameter of 20 cm (radius of 10 cm) and a height of 40 cm:

[tex]V=\pi{r^2h}[/tex]

[tex]V=\pi{(10^2)(40)}[/tex]

[tex]V\approx{12566.37\text{ cm}\textsuperscript{3}}[/tex]

The volume of a cylinder with a diameter of 30 cm (radius of 15 cm) and a height of 20 cm:

[tex]V=\pi{r^2h}[/tex]

[tex]V=\pi{(15^2)(20)}[/tex]

[tex]V\approx{14137.17\text{ cm}\textsuperscript{3}}[/tex]

Therefore, if Vesa wants to buy more popcorn, she should choose the second cylinder-shaped box with a diameter of 30 cm and a height of 20 cm.

The solution to the system graphed is (2, 0).

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is plotted as a series of markers, or dots, and is then connected to one another by a straight line.

Usually, data that changes over time is represented by a line graph.

Given:

From the graph we have two line red and purple.

The intersecting point for both line is (2, 0).

Hence, the solution to the system graphed is (2, 0).

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The equation that shows a proportional relationship between x and y is y=6x

The options represent the given parameters

As a general rule

A proportional relationship is represented as y = kx

Where k represents the constant of proportionality

So, we check the options for equations that has the same form as y = kx

We have

y = 6x

The above equation is a linear equation

In fact, it is a linear equation that shows a proportional relationship

Note that all linear equations have a constant rate of change

So, the proportional relationship is given as

y = 6x

Where the constant of proportion is 6

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The value of a, and c is 1, -3, and 0;, using the factorization of factors.

What is factorization of expressions?

To factorize an algebraic statement, we first identify the terms' greatest common factors and then arrange the terms into groups in accordance with those groups. In plain English, factorization is the process through which an algebraic statement gets expanded in the opposite direction.

Not every term may share a factor in some algebraic formulas. For instance, have a look at the algebraic formula 12a + n -na - 12. There is no specific factor that unites the terms in this statement, yet the first and last terms share a factor of 12. The common factor between the second and third terms is n. Consequently, the terms can be rearranged as follows:

12a + n - na - 12= 12a - 12 + n - an

12a - 12 - a plus n = 12(a - 1) -n (a -1)

Following regrouping, each term's common component may be shown to be (a-1): 12a + n -na - 12=(a-1) (12 – n)

In the given question,

The expression is:

[tex]\frac{31x^{2}y}{x^{5}y}[/tex]

and after simplifying the expression, we get:

[tex]\frac{31}{x^{3}}[/tex]

So, Now comparing the equation, with a[tex]x^{b}[/tex]×[tex]y^{c}[/tex], we get;

b = -3;

c = 0;

a = 1;

Hence, The value of a, and c is 1, -3, and 0;

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What is Set Theory Formula?

The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.

In a set theory, there are three major types of operations performed on sets, such as: Union of sets (∪) Intersection of sets (∩) Difference of sets (–)

Set Operations include Set Union, Set Intersection, Set Difference, Complement of Set, and Cartesian Product of Set

Set Union

The union of sets A and B (denoted by A ∪ B) is the set of elements that are in A, in B, or in both A and B. Hence, A ∪ B = { x | x ∈ A OR x ∈ B }.

n(A∪B) = n(A) + n(B) − n(A∩B)

Set Intersection

The intersection of sets A and B (denoted by A ∩ B) is the set of elements which are in both A and B. Hence, A ∩ B = { x | x ∈ A AND x ∈ B }.

n(A∩B) = n(A)+n(B)−n(A∪B)

Set Difference

The set difference of sets A and B (denoted by A - B) is the set of elements that are only in A but not in B. Hence, A - B = { x | x ∈ A AND x ∉ B }.

Complement of a Set

The complement of a set A (denoted by A’) is the set of elements which are not in set A. Hence, A' = { x | x ∉ A }. More specifically, A'= (U - A) where U is a universal set that contains all objects.

The complement of a universal set is an empty set U′ = ϕ. The complement of an empty set is a universal set ϕ′ = U.

Cartesian Product / Cross Product

The Cartesian product of n number of sets A1, A2, ... An denoted as

A1 × A2 ... × An can be defined as all possible ordered pairs

De-Morgan's Law - The De Morgan's law states that for any two sets A and B, we have (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'

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The exponential function that approximates the number of fruit flies on the banana after x days is y = 7 x 1.3ˣ.

An exponential function is a mathematical function form of y = aⁿ or y = abˣ, where b is a constant or the base of the function, a is a variable, and n is the variable exponent.

Exponential functions must always contain an exponent, which is an integer raised to some power.

When the exponent is positive, it implies the function is increasing in value and vice versa.

Percentage increase per day = 30%

The number of fruit flies found = 7

The number of days = x days

Let the number of flies after x days = y

y = 7 x 1.3ˣ

Thus, an exponential representation of the function which Emma can use to model the number of fruit flies after x days is y = 7 x 1.3ˣ.

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The number of parks per capita when there is the total population of 870,000 people and there are 212 parks is 4,103.77358.

“Per capita” is a Latin term that means “per head.” This term is used to express the average per person, the term “per capita” is occasionally used in statistics instead of “per person.”

On a given case, the per capita parks for population can be calculated by dividing total population by total parks.

According to the given illustration,

Total population of city = 870,000

Total Parks= 212

Calculation of parks per capita in the city of Indianapolis:

Per capita shops = Total population/ Total shops

Per capita shops =870,000/212

Per capita shops = 4,103.77358

Therefore, the number of parks per capita is 4,103.77358.

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The null and alternative hypotheses for the research will be H0: µ ≥ 60 vs Ha: µ < 60

In statistical hypothesis testing, null and alternative hypotheses are utilized. A test's null hypothesis always predicts that there will be no effect or relationship between variables, whereas the alternative hypothesis outlines your research prediction of an effect or link.

A null hypothesis is a straightforward contradiction of an alternative hypothesis. This implies that if one of the two hypotheses is correct, the other is incorrect.

The null and alternative hypotheses are two claims about a population that are mutually exclusive. In this case, the hypothesis are illustrated above.

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The exact value of sin(θ) given that cos(θ) = -2√5/5 is √5/5

The given trigonometry ratio is

cos(θ) = -2√5/5

By the trigonometry ratio, we have

sin²(θ) + cos²(θ) = 1

Substitute cos(θ) = -2√5/5 into the above equation

So, we have the following representation

sin²(θ) + (-2√5/5)² = 1

Evaluate the exponent

sin²(θ) + 4/5 = 1

Subtract 4/5 from both sides

This gives

sin²(θ) = 1/5

Take the square root of both sides

√sin²(θ) = √1/5

Evaluate the square root

sin(θ) = ±1/√5

Sin is positive in quadrant II

So, we have

sin(θ) = 1/√5

Rationalize

sin(θ) = 1/√5 * √5/√5

This gives

sin(θ) = √5/5

This gives the value of sin(θ)

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Step-by-step explanation:

to eliminate the always positive absolute value at the end let's set y = -3x

that makes the absolute value term = 0 in all cases.

then we have

sqrt((x - 8)² + (-3x + 4)²)

the x-value that makes this a minimum result also makes

(x - 8)² + (-3x + 4)²

a minimum.

x² - 16x + 64 + 9x² - 24x + 16

10x² - 40x + 80

the x that makes this a minimum, also makes

x² - 4x + 8

a minimum.

we get the extreme value as zero of the first derivative :

0 = 2x - 4

4 = 2x

x = 2

so, we get the minimum of all these expressions for x = 2.

as y = -3x, we get y = -3×2 = -6.

the minimum value for the expression is with

x = 2

y = -6

so, the minimum value is

sqrt((2 - 8)² + (-6 + 4)²) + |-6 + 3×2| =

= sqrt((-6)² + (-2)²) + |-6 + 6| =

= sqrt(36 + 4) + 0 =

= sqrt(40) = 6.32455532...

Answer:

  see attached (red)

Step-by-step explanation:

You want the graph of the transformed triangle defined by the lines y=x, x=6, y=-1/3x+4 after rotation 270° and reflection across the y-axis.

A graph of the lines shows the vertices of the triangle are ...

  A(3, 3), B(6, 6), C(6,2)

Rotation 270° is described by the transformation ...

  (x, y) ⇒ (y, -x)

Reflection across the y-axis is described by ...

  (x, y) ⇒ (-x, y)

Then the composition of these transformations is ...

  (x, y) ⇒ (-y, -x) . . . . . . . . equivalent to reflection over y=-x

Applying this composition to the triangle vertices, we find its final location to be ...

  A(3, 3) ⇒ A''(-3, -3)

  B(6, 6) ⇒ B''(-6, -6)

  C(6,2) ⇒ C''(-2, -6)

The triangle with these vertices is shown in red in the attachment.

There can be 2184 ways in which three posts can be selected using permutation.

What is permutation?

An arrangement of things in a specific order is referred to as a permutation. In this arrangement, the components or components of sets are arranged in a linear or sequential order.

Main Body:

Total members =14

total posts =3

As one person can not hold more than 1 post ,

total ways are = ¹⁴P₃

Therefore total ways = 14!/11!  

                                   = (14*13*12*11!)/11!

                                   = 14*13*12

                                   = 2184 ways

Hence answer is 2184 ways to select 3 members out of 14.

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Answer:

b)  64 to 76 inches.

Step-by-step explanation:

In a normal distribution, 95% of the population is within 2 standard deviations of the mean.

Given values:

Given that the mean height is 70 inches and the standard deviation is 3 inches:

[tex]\implies \mu -2 \sigma = 70-2(3)=64[/tex]

[tex]\implies \mu+2 \sigma = 70+2(3)=76[/tex]

Therefore, an appropriate height range for 95% of all people in the sample would be:

Answer:

-5/7, 10/7

Step-by-step explanation:

The slope of an equation in standard form is -a/b

so -5/7

Set x to 0 to find the vertical intercept

5(0)+7y=10

7y=10

y=10/7

38 sets

474 - 246 = 228

228 ÷ 6 = 38

12 and 30 are the two numbers are greater than 6 with HCF  6 and LCM  60.

What is Highest common factor and Least Common Multiple?

Least Common Multiple is the entire name of LCM in mathematics, whereas Highest Common Factor is the full name of HCF. When two or more numbers are given, the HCF identifies the largest factor present, while the LCM defines the least number that is exactly divisible by two or more numbers.

Assume that the two numbers with HCF of 6 are 6a and 6b, where a and b are co-prime and a, b > 1.

HCF x LCM = Product of the numbers.

6 x 60 = 6a x 6b

10 = a x b

10 can be written as, 1 x 10 and 2 x 5.

But a and b > 1.

So, 10 = 2 x 5

a = 2, b = 5

Therefore, the two numbers are,

6a = 6(2) = 12 and

6b = 6(5) = 30

Hence, the two numbers with HCF  6 and LCM  60 are 12 and 30.

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Answer:

x=3

Step-by-step explanation:

Answer: x=3

Step-by-step explanation:

First, you need to subtract x and x by itself, and do the same with the 3x. Your equation should now look like 6 = 2x. Now, divide each side of the equation with 2, and now your equation should look like 3 = x!

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

So, to double check, replace the x's with 3. The equation should be 3 + 6 = 3(3). If you do the math, it equals 9 = 9!